ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 AGN feedback results in a stellar-to-halo mass ratio is consistent with the preclicition of abundance matching (?).., AGN feedback results in a stellar-to-halo mass ratio is consistent with the predicition of abundance matching \citep{Moster:2010p5423}.3 A comparison with the massive earlv-tvpe galaxies in the samples analysed by ο shows that the mass. the velocity dispersion and the effective radius are consistent with those of the most massive earlv-type galaxies observed in the SDSS ab zo0. and cluster galaxies at z1.," A comparison with the massive early-type galaxies in the samples analysed by \cite{2008ApJ...688...48V} shows that the mass, the velocity dispersion and the effective radius are consistent with those of the most massive early-type galaxies observed in the SDSS at $z\sim0$, and cluster galaxies at $z\sim 1$."4 We note that a slight decrease in the cllicicney of ACN feedback. would. produce a slightly larger mass and a lower effective radius at z=1. bringing our simulated galaxy into an even closer agreement with the observations.," We note that a slight decrease in the efficiency of AGN feedback would produce a slightly larger mass and a lower effective radius at $z=1$, bringing our simulated galaxy into an even closer agreement with the observations."5 The existence of the core in the stellar surface density distribution is in agreement with what is observed for the most luminous and massive galaxies in the Virgo cluster that show significant mass deficiencies in their central. regions (7?77).. ," The existence of the core in the stellar surface density distribution is in agreement with what is observed for the most luminous and massive galaxies in the Virgo cluster that show significant mass deficiencies in their central regions \citep{2004AJ....127.1917T, 2007ApJ...671.1456C, 2009ApJS..182..216K, 2011arXiv1108.0997G}."6Wo have discussed several mechanisms that could contribute to the shaping of the final properties of the BCC ancl. especially. to the formation of its core: (1) a series of dry mergers that lead to SMDIIS sinking to the halo center via dynamical frietion.," We have discussed several mechanisms that could contribute to the shaping of the final properties of the BCG and, especially, to the formation of its core: (I) a series of dry mergers that lead to SMBHs sinking to the halo center via dynamical friction."7 Vhis process can eject a [arge fraction of stars and dark matter from the central regions of the BCC (2?) (11," This process can eject a large fraction of stars and dark matter from the central regions of the BCG \citep{2003ApJ...596..860M, 2010ApJ...725.1707G}. ("8) AGN feedback driven. gas outllows can moclily the gravitational potential in the regions close to SAIBLIs: these outllows are impulsive and the revirialisation! of the inner material can Lead to the formation of a core (?).. (,II) AGN feedback driven gas outflows can modify the gravitational potential in the regions close to SMBHs; these outflows are impulsive and the 'revirialisation' of the inner material can lead to the formation of a core \citep{1996MNRAS.283L..72N}. (9LLL) The central hot gas. slowly cools racdiativelv. falling onto the SMIBIL in a convective Dow and is subsequently ejected impulsively.,"III) The central hot gas slowly cools radiatively, falling onto the SMBH in a convective flow and is subsequently ejected impulsively."10 The slow loss of mass from the central region will result in the inner mass distribution expanding., The slow loss of mass from the central region will result in the inner mass distribution expanding.11 The ellicieney of cach of these mechanisms will be explored using idealised numerical experiments in a subsequent study., The efficiency of each of these mechanisms will be explored using idealised numerical experiments in a subsequent study.12 Observations show that low mass earlv-tvpe. galaxies typically have cusps in their surface brightness profiles. while high mass early-tvpe galaxies preferably have centrally cored profiles (777).. ," Observations show that low mass early-type galaxies typically have cusps in their surface brightness profiles, while high mass early-type galaxies preferably have centrally cored profiles \citep{2004AJ....127.1917T, 2007ApJ...671.1456C, 2009ApJS..182..216K}."13We find that neglecting the presence of SMDBlISs anc AGN feedback. produces a cusp. while inclucing these ellects produces a core.," We find that neglecting the presence of SMBHs and AGN feedback produces a cusp, while including these effects produces a core."14 These considerations sugeests that there may be a close connection between the mass dichotomy in early-type galaxies and the presence of SALBLs., These considerations suggests that there may be a close connection between the mass dichotomy in early-type galaxies and the presence of SMBHs.15 In high mass early-tvpe galaxies the cllicioney of the processes that lead to a core formation are expected to be higher than in lower mass early-type galaxies. thus lower mass galaxies may retain the cusps in the clistribution of their stars.," In high mass early-type galaxies the efficiency of the processes that lead to a core formation are expected to be higher than in lower mass early-type galaxies, thus lower mass galaxies may retain the cusps in the distribution of their stars."16 We thank our anonymous referee for helpful suggestions that greatly improved the quality of the paper., We thank our anonymous referee for helpful suggestions that greatly improved the quality of the paper.17 We also thank Lea Giordano for her suggestions about the topies discussed in this paper., We also thank Lea Giordano for her suggestions about the topics discussed in this paper.18" We thank Robert Feldmann for providing us the eroup simulation data and ""ThorstenNaab for providing us the Milky-Way-sized simulation data.", We thank Robert Feldmann for providing us the group simulation data and ThorstenNaab for providing us the Milky-Way-sized simulation data.19 The XMIU simulations presented herewere performed on the Cray NT-5 cluster at CSCS. Manno. Switzerland.," The AMR simulations presented herewere performed on the Cray XT-5 cluster at CSCS, Manno, Switzerland."20"the Bondi Hoyle rate for turbulent gas, Mgy, the thermal sound speed of the gas has been replaced by an effective sound speed defined as the quadrature sum of the thermal sound speed and turbulent velocity.","the Bondi Hoyle rate for turbulent gas, $\dot{M}_{\textrm{BH}}$, the thermal sound speed of the gas has been replaced by an effective sound speed defined as the quadrature sum of the thermal sound speed and turbulent velocity."21" The vorticity-reduced rate, Mi», given by Equation 3 of 7, is computed cell by cell, producing a log-normal probability density function (PDF) of accretion rates within individual spherical shells centered on the black hole particle."," The vorticity-reduced rate, $\dot{M}_{\textrm{turb}}$, given by Equation 3 of \citet{Krumholzetal06}, is computed cell by cell, producing a log-normal probability density function (PDF) of accretion rates within individual spherical shells centered on the black hole particle."22" The geometric mean of the distribution, (Miurb), gives characteristic accretion rates under this prescription and is shown for several different radii in Figure 6.."," The geometric mean of the distribution, $\langle23\dot{M}_{\textrm{turb}}\rangle$, gives characteristic accretion rates under this prescription and is shown for several different radii in Figure \ref{fig:mbondi}. ."24 The vorticity-reduced rates are 2—3 orders of magnitude smaller than the standard Bondi Hoyle rates., The vorticity-reduced rates are $2-3$ orders of magnitude smaller than the standard Bondi Hoyle rates.25" These results are qualitatively consistent with those of ?,, who find that accretion in their merger simulations is regulated by angular momentum transport processes in the host galaxy, keeping the accretion rate below the Bondi rate, except during peak activity (when the accretion rate approaches Mpaa, which is + Mgn)."," These results are qualitatively consistent with those of \citet{Debuhretal09}, who find that accretion in their merger simulations is regulated by angular momentum transport processes in the host galaxy, keeping the accretion rate below the Bondi rate, except during peak activity (when the accretion rate approaches $\dot{M}_{\textrm{Edd}}$ , which is $\approx \dot{M}_{\textrm{BH}}$ )."26" As revealed in Figure 6,, the Bondi prescription gives large estimates for the accretion rates (> 10Mmgaa) inside the central few hundred parsecs."," As revealed in Figure \ref{fig:mbondi}, the Bondi prescription gives large estimates for the accretion rates $\gg 1027\dot{M}_{\textrm{Edd}}$ ) inside the central few hundred parsecs."28" The steep, power-law, density profile of the gas in the circumnuclear disk contributes to the large accretion rates shown in Figure 6 (which are proportional to density)."," The steep, power-law, density profile of the gas in the circumnuclear disk contributes to the large accretion rates shown in Figure \ref{fig:mbondi} (which are proportional to density)."29 The inclusion of an approximation for optically thick cooling in the simulations does not significantly change the density profile or the velocity dispersion of the gas., The inclusion of an approximation for optically thick cooling in the simulations does not significantly change the density profile or the velocity dispersion of the gas.30" Therefore, the Bondi prescription produces similar results for runs ZAL20 and Z4L20.OT (dashed and solid curves in Figure "," Therefore, the Bondi prescription produces similar results for runs Z4L20 and Z4L20.OT (dashed and solid curves in Figure \ref{fig:mbondi}) )."31"Additional effects not included in our current simulations6)). may contribute to the depletion of gas in the circumnuclear disk, such as AGN feedback and stellar feedback (not included in the zoom-in portion of the simulation), thus lowering the estimated Bondi rate."," Additional effects not included in our current simulations may contribute to the depletion of gas in the circumnuclear disk, such as AGN feedback and stellar feedback (not included in the zoom-in portion of the simulation), thus lowering the estimated Bondi rate."32" However, if the disk remains self-gravitating and therefore susceptible to instabilities, the Bondi prescription will inaccurately describe the transport of gas through this region."," However, if the disk remains self-gravitating and therefore susceptible to instabilities, the Bondi prescription will inaccurately describe the transport of gas through this region."33 The average accretion rate through the circumnuclear disk over cosmological times can be estimated by comparing the mean interior gas mass (the averages shown in Figure 1)) for the different redshift simulations., The average accretion rate through the circumnuclear disk over cosmological times can be estimated by comparing the mean interior gas mass (the averages shown in Figure \ref{fig:gmr}) ) for the different redshift simulations.34" Figure 7 shows the mean gas mass, interior to radius r as a function of the age of the universe, tage."," Figure \ref{fig:mz} shows the mean gas mass, interior to radius $r$ as a function of the age of the universe, $t_{\textrm{age}}$."35 Once again we emphasize that the different redshift simulations do not necessarily describe different stages of growth of the same galaxy because they each contain the same mass SMBH (rather than a black hole that grows with redshift)., Once again we emphasize that the different redshift simulations do not necessarily describe different stages of growth of the same galaxy because they each contain the same mass SMBH (rather than a black hole that grows with redshift).36" However, the black hole particle does not currently play a large role in the evolution of the simulated galaxy (at least not below z=4, where the mass of the black hole is dominated by the gas mass all the way down to the resolution limit)."," However, the black hole particle does not currently play a large role in the evolution of the simulated galaxy (at least not below $z=4$, where the mass of the black hole is dominated by the gas mass all the way down to the resolution limit)."37" The dashed line in Figure 7 shows the mass of a black hole, initially 3x107Mo at z=6, if it grows continuously at the Eddington limit according to where tg is the Salpeter time (?) of 4.5x10’yr, for a radiative efficiency η=0.1."," The dashed line in Figure \ref{fig:mz} shows the mass of a black hole, initially $3\times10^7 \dim{M}_{\sun}$ at $z=6$, if it grows continuously at the Eddington limit according to where $t_{\textrm{S}}$ is the Salpeter time \citep{Salpeter64} of $4.5\times10^7 \dim{yr}$, for a radiative efficiency $\eta=0.1$."38" If the dynamics of the circumnuclear disk extend all the way down to scales beneath the resolution (which cannot be assumed) then the growth rate approximated by the simulation points, which appears to steepen at early times with decreasing scale, may continue to steepen down to smaller scales, approaching the Eddington limit."," If the dynamics of the circumnuclear disk extend all the way down to scales beneath the resolution (which cannot be assumed) then the growth rate approximated by the simulation points, which appears to steepen at early times with decreasing scale, may continue to steepen down to smaller scales, approaching the Eddington limit."39" Therefore, a black hole in our simulations will be able to grow according to Equation 5 at high-z, as long as efficient fueling from the circumnuclear disk can be sustained."," Therefore, a black hole in our simulations will be able to grow according to Equation \ref{eq:sal} at $z$, as long as efficient fueling from the circumnuclear disk can be sustained."40" This is perhaps consistent with the isolated disk galaxy simulations of ?,, where a sufficiently massive black hole will grow according to Equation 5,, in the absence of AGN feedback."," This is perhaps consistent with the isolated disk galaxy simulations of \citet{Springeletal05a}, where a sufficiently massive black hole will grow according to Equation \ref{eq:sal}, in the absence of AGN feedback."41" Once gas reaches sub-parsec scales, the actual accretion rate onto the black hole is governedby the physics of the accretion disk, not modeled by our simulations."," Once gas reaches sub-parsec scales, the actual accretion rate onto the black hole is governedby the physics of the accretion disk, not modeled by our simulations."42" Nonetheless, Figure7 shows that the increase in the mass of the circumnuclear gas disk over"," Nonetheless, Figure\ref{fig:mz} shows that the increase in the mass of the circumnuclear gas disk over"43cosmic shear see Retregier(2003): see also Moellier and Bartchuamn&Schneider(2001).,cosmic shear see \cite{refregier03}; see also \cite{mellier99} and \cite{bartelmanns01}.44". Cosmic shear ais to measure this correlation function * dneasumnue observed cllipticitics of distant ealaxics c"" and taking iuto account how intrinsic (pre-shear) cllipticities e are modified bv shear.", Cosmic shear aims to measure this correlation function by measuring observed ellipticities of distant galaxies $e^o$ and taking into account how intrinsic (pre-shear) ellipticities $e^i$ are modified by shear.45" For παπα] shears js reduces to e""=ο|: we define e=(ab/(e|b) throughout.", For small shears this reduces to $e^o = e^i + \gamma$; we define $e \equiv (a-b)/(a+b)$ throughout.46 Au estimate of the shear two yoint correlation fiction is obtaiued frou the observed ellipticity correlation fiction $&.=(264) where (2 is the served ellipticity of a distant galaxy s and e$ is that of a wearer galaxy d., An estimate of the shear two point correlation function is obtained from the observed ellipticity correlation function $\xi_{e}=\langle e^o_{\rm s} e^{o*}_{\rm d}\rangle$ where $e^o_{\rm s}$ is the observed ellipticity of a distant galaxy ${\rm s}$ and $e^o_{\rm d}$ is that of a nearer galaxy ${\rm d}$.47" Therefore we can expand the correlation tuuctious to &ud &=€|€-,. where the shear-cllipticity correlation is given by €.,=(5.67; if we ignore iutriusie aliguiiecuts = 0) aud use (254?=0. Tevinan"," Therefore we can expand the correlation functions to find $\xi_{e} = \xi_{\gamma} + \xi_{\gamma e}$, where the shear-ellipticity correlation is given by $\xi_{\gamma e} =\langle \gamma_{\rm s} e^{i*}_{\rm d} \rangle$ if we ignore intrinsic alignments $\langle e^{i}_{\rm s} e^{i*}_{\rm d} \rangle=0$ ) and use $\langle e^{i}_{\rm s} \gamma_{\rm d} \rangle=0$."48s(cele)etal.(2006) calculated the shear-cllipticity correlation function uuncerically using u-bocy simulations., \cite{heymanswhvv06} calculated the shear-ellipticity correlation function numerically using n-body simulations.49 The aim of that work was to quautify the intrinsic Higmmuent - shear correlation preseuted by Irata&Sel-jak(200 1)., The aim of that work was to quantify the intrinsic alignment - shear correlation presented by \cite{hiratas04}.50. Their results should iu fact contain a mixture of the intrinsic alieumient - shear correlation and the ealaxy-ealaxy lensing sigual we preseut here., Their results should in fact contain a mixture of the intrinsic alignment - shear correlation and the galaxy-galaxy lensing signal we present here.51 However. they do not discuss the distinction between the two effects. or specifically state that the ealaxy-ealaxy lensing contribution might be significant.," However, they do not discuss the distinction between the two effects, or specifically state that the galaxy-galaxy lensing contribution might be significant."52 Tere we preseut simple analytical and wmuerically integrated results to quantity oulv the galaxy-galaxy lensing contribution., Here we present simple analytical and numerically integrated results to quantify only the galaxy-galaxy lensing contribution.53" We assune oa concordance ACDAL cosinology throughout./ with parameters taken from Spereelctal. (2006): IIubble coustaut My=73 kin | |l Q4,0.2328. Opp—1.OL. Οι=0.017. σς=O1. dark energv equation of state w=1l except where otherwise stated."," We assume a concordance $\Lambda$ CDM cosmology throughout, with parameters taken from \cite{spergelea06}: Hubble constant $H_0=73$ km $^{-1}$ $^{-1}$, $\Omega_{\rm m}=0.238$, $\Omega_{\rm DE}=1-\Omega_{\rm m}$, $\Omega_{\rm b}=0.047$, $\sigma_8=0.74$, dark energy equation of state $w=-1$ except where otherwise stated."54 We assume a flat universe with a scale iuvariaut primordial power spectrum., We assume a flat universe with a scale invariant primordial power spectrum.55 Iu this Section we calculate the galaxyv-ealaxy lensing contribution to &. οἴνοι by ἕνα as discussed. above.," In this Section we calculate the galaxy-galaxy lensing contribution to $\xi_e$, given by $\xi_{\gamma e}$, as discussed above."56" To estimate this quantitv we first calculate the sigual for a single elliptical lens averaged over backeround galaxies at a fixed augular distance. aud then average over a population of lenses,"," To estimate this quantity we first calculate the signal for a single elliptical lens averaged over background galaxies at a fixed angular distance, and then average over a population of lenses."57 We assume that the lens light has the same ellipticity aud oricutation as the leis mass., We assume that the lens light has the same ellipticity and orientation as the lens mass.58 By default we consider an NEW. (Navarroetal.1997) lass profile. calculating the projected mass from the equations eiven in Wrielt&Brainerd(2000) ancl Bartclmann(1996).," By default we consider an NFW \citep{nfw} mass profile, calculating the projected mass from the equations given in \cite{wrightb00}59 and \cite{bartelmann96}."60.. We use Afsyy. the mass enclosed within the radius at which the deusitv is 200 times the mean deusitv of the Universe. for consistenev— with simulations.," We use $M_{200}$ , the mass enclosed within the radius at which the density is 200 times the mean density of the Universe, for consistency with simulations."61 We derive the concentration parameter. e. as a function of Afoyy using Eq.," We derive the concentration parameter, $c$, as a function of $M_{200}$ using Eq."62 12 of Seljak(2000) with >=0.15. as appropriate for an NEW inodel.," 12 of \cite{seljak00}63 with $\beta=-0.15$, as appropriate for an NFW model."64 We calculate the shear for an elliptical mass distribution using the equations in Ἱνουίοι(2001)| and Schranuu (1990).," We calculate the shear for an elliptical mass distribution using the equations in \cite{keeton01}65 and \cite{schramm90}."66". Note that this is not the same as calculations using elliptical potentials. which eive dumbbell shaped mass distributions οιο,,Nassiola&Ixovnuer1993)."," Note that this is not the same as calculations using elliptical potentials, which give dumbbell shaped mass distributions \citep[e.g.,][]{kassiolak93}."67. The projected mass distribution is squashed aud stretched to have elliptical isodeusity contours a factor f smaller (lureer) along the iiuor GQuajor) axes. as compared to the corresponding spherical mass distribution.," The projected mass distribution is squashed and stretched to have elliptical isodensity contours a factor $f$ smaller (larger) along the minor (major) axes, as compared to the corresponding spherical mass distribution."68 The shear map for an elliptical NEW leus of ellipticity ο=0.3 aligned along the .« axis is shown in Fie. 1.., The shear map for an elliptical NFW lens of ellipticity $e =0.3$ aligned along the $x$ axis is shown in Fig. \ref{fig:map}.69 The shading and contours show the couverseuce lap (projected lass density iun units of the critical lens density)., The shading and contours show the convergence map (projected mass density in units of the critical lens density).70 The overlaid shear sticks show two particularly interesting features: (4) the shear ou the major axis ofthe chs is larger than that ou the minor axis. for a given aneular separation from the leas ceuter: (i) the shear 15 degrees around frou the major axis is approximately aueenutial to the ceuter of the leus.," The overlaid shear sticks show two particularly interesting features: (i) the shear on the major axis of the lens is larger than that on the minor axis, for a given angular separation from the lens center; (ii) the shear 45 degrees around from the major axis is approximately tangential to the center of the lens."71 These two features do depend on the details of the mass profile. but are eeucral orrelevant radii for an clliptical NEW. profile. aud also for a sineular isothermal ellipsoid (SIE) (forwhichtheshear L)..," These two features do depend on the details of the mass profile, but are general forrelevant radii for an elliptical NFW profile, and also for a singular isothermal ellipsoid (SIE) \citep[for which the shear is always exactly tangential and its72 amplitude follows the mass, see][]{kassiolak93,kormannsb94}. ."73 These two characteristics poiut towards our main result:, These two characteristics point towards our main result:74and therefore all self-gravitating condensations should be reasonably well resolved.,and therefore all self-gravitating condensations should be reasonably well resolved.75" We three simulations, all with the same initial conditions, performand differing only in their treatments of the luminosities of "," We perform three simulations, all with the same initial conditions, and differing only in their treatments of the luminosities of protostars."76"In all three simulations the initial collapse leads to protostars.the formation of a primary protostar (i.e. a first sink) at t~77kyr, and this quickly acquires an extended accretion disc."," In all three simulations the initial collapse leads to the formation of a primary protostar (i.e. a first sink) at $\,t\!\sim\!77\,{\rm kyr}$, and this quickly acquires an extended accretion disc."77 The simulations only diverge after this juncture., The simulations only diverge after this juncture.78" In the first simulation there is no radiative feedback from the protostar, and the gas in the disc is only heated by compression and by viscous dissipation in shocks."," In the first simulation there is no radiative feedback from the protostar, and the gas in the disc is only heated by compression and by viscous dissipation in shocks."79 It is therefore cool enough to experience strong GI (?)., It is therefore cool enough to experience strong GI \citep{Stamatellos09}.80" The resulting gravitational torques transport angular momentum outwards, allowing matter to spiral inwards and onto the at a rate 1075.to10-Mgyr-!, but primaryin the protostarouter parts of the at radii R=50AU, the GI also becomes highly disc,non-linear locally, resulting in the formation of seven protostars, with masses ranging from 0.008Mc to secondary0.24Mo."," The resulting gravitational torques transport angular momentum outwards, allowing matter to spiral inwards and onto the primary protostar at a rate $10^{-5}\;{\rm to}\;10^{-4}\,{\rm M}_\odot\,{\rm yr}^{-1}$, but in the outer parts of the disc, at radii $R\ga 50\,{\rm AU}$, the GI also becomes highly non-linear locally, resulting in the formation of seven secondary protostars, with masses ranging from $0.008\,{\rm M}_\odot$ to $0.24\,{\rm M}_\odot$."81 This is illustrated in the sequence of frames on Fig., This is illustrated in the sequence of frames on Fig.82 1., 1.83 The accretion rate onto the primary protostar and the growth of its mass are shown on Fig., The accretion rate onto the primary protostar and the growth of its mass are shown on Fig.84 4 (red lines)., 4 (red lines).85" In the second simulation, we assume that the matter entering a sink is immediately accreted onto the protostar at its centre."," In the second simulation, we assume that the matter entering a sink is immediately accreted onto the protostar at its centre."86 This results in an accretion luminosity which is typically 10to100Lo.," This results in an accretion luminosity which is typically $10\;{\rm to}\;100\,{\rm L}_\odot$."87" It therefore heats the surrounding disc, and as a result GI saturates, generating low-amplitude spiral waves that transport angular momentum outwards and allow matter to spiral into the protostar, but entirely suppressing disc at all radii."," It therefore heats the surrounding disc, and as a result GI saturates, generating low-amplitude spiral waves that transport angular momentum outwards and allow matter to spiral into the protostar, but entirely suppressing disc fragmentation, at all radii."88" This is illustrated in the sequence of fragmentation,frames on Fig.", This is illustrated in the sequence of frames on Fig.89 2., 2.90 At all times the spiral, At all times the spiral91the difference between two of the reference slars while the triangles represent the difference between PQ And and one of the reference stars.,the difference between two of the reference stars while the triangles represent the difference between PQ And and one of the reference stars.92 The horizontal axis is the time since the start of observations Lor each night., The horizontal axis is the time since the start of observations for each night.93 The light curves of both nights clearly show fluctuations of up to —0.1 magnitudes., The light curves of both nights clearly show fluctuations of up to $\sim$ 0.1 magnitudes.94 All reference stars and PQ And were of similar magnitude therefore the seatter in the reference star data gives an estimate of the errors in the magnitude change lor PQ And., All reference stars and PQ And were of similar magnitude therefore the scatter in the reference star data gives an estimate of the errors in the magnitude change for PQ And.95 From Figure { we see that (he magnitude errors are on order of 0.015., From Figure 1 we see that the magnitude errors are on order of 0.015.96 To search for any periodiciües in the light curves the data were pul through a Fourier transform routine., To search for any periodicities in the light curves the data were put through a Fourier transform routine.97 The resulting power spectra for each date are shown in Figure 2., The resulting power spectra for each date are shown in Figure 2.98 Dased on the length of time PQ And was observed and the sampling rate of each night. we searched the lrequency space [rom 0.5 to 30 4.," Based on the length of time PQ And was observed and the sampling rate of each night, we searched the frequency space from 0.5 to 30 $^{-1}$."99 To determine the level of signilicance lor peaks in the power spectrum we added a (racer signal to our data and ran it through the Fourier routine unti] we were unable to detect it., To determine the level of significance for peaks in the power spectrum we added a tracer signal to our data and ran it through the Fourier routine until we were unable to detect it.100 From (his we found that peaks with a power less (han ~10? were nol significant., From this we found that peaks with a power less than $\sim10^{-5}$ were not significant.101 Three strong peaks appear in the power spectra of both nights., Three strong peaks appear in the power spectra of both nights.102 The strongest peak is found ab a frequency of 5.6 |. a period. of 10.5 minutes. in both spectra.," The strongest peak is found at a frequency of 5.6 $^{-1}$, a period of 10.5 minutes, in both spectra."103 We also see what appear to be harmonics of this peak at frequencies of ~2.8 ! and 14 |., We also see what appear to be harmonics of this peak at frequencies of $\sim$ 2.8 $^{-1}$ and $\sim$ 1.4 $^{-1}$.104 At higher frequencies the (vo power spectra differ slghtlv., At higher frequencies the two power spectra differ slightly.105 In. the September dala we see no significant peaks bevond the three already mentioned while the October power spectrum shows a few small, In the September data we see no significant peaks beyond the three already mentioned while the October power spectrum shows a few small106"eiven bv where pois the ποσα mass per molecule aud we adopt a cohuun density «Aq> which is the average column density of fragments of mass Mig, Qvhlich by definition have peak column densities ereater than the threshold to be identified as fragments).",given by where $\mu$ is the mean mass per molecule and we adopt a column density $ <N_{\rm H_2}^{\rm amp}>$ which is the average column density of fragments of mass $M_{\rm lim}$ (which by definition have peak column densities greater than the threshold to be identified as fragments).107" At a distance of 6 kpc. for fragment mass of 2/8/32 ML, and <NYP!>=151074 ? we ect Rau,=5/10/2y"" aand plow=2.1/1.2/0.6« ονP. respectively."," At a distance of 6 kpc, for fragment mass of 2/8/32 $_{\odot}$ and $108<N_{\rm H_2}^{amp}> =1.5\times10^{21}$ $^{-2}$ we get $_{\rm min}=5/10/20$ and $\rho_{\rm c}^{\rm low} =2.4/1.2/0.6\times10^3$ $^{-3}$, respectively."109 For the same given mass there is also an upper density Bit which corresponds to the point where the size of the fragment becomes smaller than the resolution of the observations., For the same given mass there is also an upper density limit which corresponds to the point where the size of the fragment becomes smaller than the resolution of the observations.110" This provides an upper lait on the deusitv. pj""=O75«Alyο "," This provides an upper limit on the density, $\rho_{\rm111 c}^{\rm up}=0.75\times M_{lim}/(\pi R_{res}^3)$ ."112For the 3 masses discussed before we get p?!=O.L/L.7/6.8«101 ci5m, For the 3 masses discussed before we get $\rho_{\rm c}^{up} =0.4/1.7/6.8\times10^5$ $^{-3}$.113 To calculate the density aud mss of the IRDCs and fragments requires a distance for each object., To calculate the density and mass of the IRDCs and fragments requires a distance for each object.114 Two different approaches to statistically attribute a particular distance to a particular cloud have been adopted., Two different approaches to statistically attribute a particular distance to a particular cloud have been adopted.115 The first is to simply assign a unique distance to all clouds., The first is to simply assign a unique distance to all clouds.116 Doing this. the physical size distribution of IRDC's and fragments will be exactly the same as the angular size distribution.," Doing this, the physical size distribution of IRDCs and fragments will be exactly the same as the angular size distribution."117 Given the well peaked distribution of distances for clouds with mcasured distances (Fig. 1).," Given the well peaked distribution of distances for clouds with measured distances (Fig. \ref{dist}) ),"118 this should be a reasonable first approxination., this should be a reasonable first approximation.119 Ilowever. a more sophisticated approach is to make use of the distributiou of distances (Gather than just its poak position).," However, a more sophisticated approach is to make use of the distribution of distances (rather than just its peak position)."120 To do this we adopt a distance distribution for +the IRDCs aud then raudoimilv assign a distance drawn from this distribution to each cloud., To do this we adopt a distance distribution for the IRDCs and then randomly assign a distance drawn from this distribution to each cloud.121 Doing this for the whole sample of clouds repeatedly provides a statistical sampling of the distance distribution., Doing this for the whole sample of clouds repeatedly provides a statistical sampling of the distance distribution.122 The final physical size distribution is the convolution of the true physical size distribution bv the chosen distance distribution., The final physical size distribution is the convolution of the true physical size distribution by the chosen distance distribution.123 Towever this does not have a crucial Hupact on the interpretation of the plysical size distribution if the dispersion of the distance distribution is much sinaller than the angular size distribution., However this does not have a crucial impact on the interpretation of the physical size distribution if the dispersion of the distance distribution is much smaller than the angular size distribution.124 This is clearly the case since the angular sizes. both for IRDCs aud fragments. extends over 2 order of maenitudes while IRDC distances span only over a factor of 3 at imost.," This is clearly the case since the angular sizes, both for IRDCs and fragments, extends over 2 order of magnitudes while IRDC distances span only over a factor of 3 at most."125 Tn other words. the dispersion iu distance has relatively little effect on the final physical size distribution (see Appendix A).," In other words, the dispersion in distance has relatively little effect on the final physical size distribution (see Appendix A)."126 To assign clistances to the clouds using this sampling technique we adopt a Gaussian distribution of distances with a peak at Likpe aud a dispersion of 1 kpc. consistent with observed distance distributions (Fie. L)).," To assign distances to the clouds using this sampling technique we adopt a Gaussian distribution of distances with a peak at 4 kpc and a dispersion of 1 kpc, consistent with observed distance distributions (Fig. \ref{dist}) )."127 Mass distributions of molecular cloud structures have been extcusively studied in the past. therefore they represcut a good point of comparison for this current study.," Mass distributions of molecular cloud structures have been extensively studied in the past, therefore they represent a good point of comparison for this current study."128"We defined lass as: where «Ng,> is the average cohuuu density across the IRDC or fragment aud Πιο its equivaleut radius CPEQOO).",We defined mass as: where $<N_{\rm H_2}>$ is the average column density across the IRDC or fragment and $R_{\rm eq}$ its equivalent radius (PF09).129 Figure 8 shows the mass distributions for IRDCs aud fragments calculated adopting a sinele distance of Uspe (filled square svinbols) aud for randomly attributed clistances as described iu Section 5.1.., Figure \ref{mass} shows the mass distributions for IRDCs and fragments calculated adopting a single distance of 4kpc (filled square symbols) and for randomly attributed distances as described in Section \ref{sec:size}.130 The shaded baud on the figures shows the range (3 times the dispersion) πράσα o» the 100 ciffereut distance realizations aud he open triuegles the mean for the different realizatious., The shaded band on the figures shows the range (3 times the dispersion) spanned by the 100 different distance realizations and the open triangles the mean for the different realizations.131 The completeness limits are showu w the dashed lines., The completeness limits are shown by the dashed lines.132 For comparison the powcr-aw slopes of the CO clump mass function (slope = (1.7) aud the Salpeter mass function. (slope = 1.35) are also shown., For comparison the power-law slopes of the CO clump mass function (slope $= -0.7$ ) and the Salpeter mass function (slope $= -1.35$ ) are also shown.133 Using the MPFITS IDL owckage (Alarkwardt 2009) we have fitted the two distributions above their respective completeness nuits., Using the MPFITS IDL package (Markwardt 2009) we have fitted the two distributions above their respective completeness limits.134" For the IRDCs we find a limear function Gu a log-log plot) provides a good fit with dNMppcfdlogSeM=M."" with a=0.85+ OUT. The mass distribution of fragimieuts is better fitted by a lognormal function defined as", For the IRDCs we find a linear function (in a log-log plot) provides a good fit with $dN_{\rm{IRDC}}/d\log M=M^{-\alpha}$ with $\alpha=0.85 \pm 0.07$ The mass distribution of fragments is better fitted by a lognormal function defined as135We will examine it further in Sec. 3.2..,We will examine it further in Sec. \ref{ssec:metallicity}.136" North of this alignment, we can see that there is a prominent dust lane."," North of this alignment, we can see that there is a prominent dust lane."137" In the same alignment, we can see a tidal tail extending to the West."," In the same alignment, we can see a tidal tail extending to the West."138 The smooth change of the brightness of the tail starting from the interacting galaxies suggests that it contains significant quantities of stars stripped from the parent galaxies which is confirmed by the fact that the tail is clearly seen in the near- in 2MASS images., The smooth change of the brightness of the tail starting from the interacting galaxies suggests that it contains significant quantities of stars stripped from the parent galaxies which is confirmed by the fact that the tail is clearly seen in the near--infrared in 2MASS images.139" Another, more prominent, tidal tail"," Another, more prominent, tidal tail"140 2=2.56. —1 (Maeaiuetal.1988): (I&nceibetal.L998:I&neib.Alloin.&Pello1998).. Ulazardctal.198," $z$ $\sim$ $''$ \citep{Magain_etal_1988}; \citep{Kneib_etal_1998,141Kneib_Alloin_Pello_1998}. \citep{Hazard_etal_1984}."142 (Ny>LO?cm7) Wangetal.(2000). 0 (Chartas—2000).," $N_{\rm H} >14310^{23} {\rm cm}^{-2}$ \citet{Wang_etal_2000} \citet{Elvis_2000} $\sigma$ \citep{Chartas_2000}."144.. 120°C. (~2” , $-120^{\circ}$ $\sim$ $''$ 145 , 146Since the redshift number density of these absorbers has also been shown to have roughly no evolution. these results agree with the Tinkeretal.(2010) model in which only the gas racius of haloes evolves with redshift.,"Since the redshift number density of these absorbers has also been shown to have roughly no evolution, these results agree with the \citet{Tinker10} model in which only the gas radius of haloes evolves with redshift."147 Within this model. the gas radii of haloes expand with increasing redshift such that the haloes at ΖΞ1 have a gas radius that is ~40% larger in units of the DAL halo virial radius. compared to z=0.6.," Within this model, the gas radii of haloes expand with increasing redshift such that the haloes at z=1 have a gas radius that is $\sim$ larger in units of the DM halo virial radius, compared to z=0.6."148 However. the errors on our bias measurement are still too large to rule out other halo evolution models in which the halo mass also evolves with redshift.," However, the errors on our bias measurement are still too large to rule out other halo evolution models in which the halo mass also evolves with redshift."149 We measure the covering fraction. of strong absorption to be f.—0.5 within 60 tkpe around. DEEDP2 galaxies., We measure the covering fraction of strong absorption to be $f_{c}$ =0.5 within 60 $^{-1}$ kpc around DEEP2 galaxies.150 We find no absorber host-galaxy pairs on scales larger than 37 tkpe. suggesting that the cllective gas racius of strong absorption around. DEEP? ealaxics may be as small as ~40h *kpe.," We find no absorber host-galaxy pairs on scales larger than 37 $^{-1}$ kpc, suggesting that the effective gas radius of strong absorption around DEEP2 galaxies may be as small as $\sim$ $^{-1}$ kpc."151 In our sample. we identify just one candidate absorber host galaxv. which exhibits no evidence of ongoing star formation.," In our sample, we identify just one candidate absorber host galaxy, which exhibits no evidence of ongoing star formation."152 Despite the small sample. size. this finding suggests that absorbers with similar equivalent widths S28 LLSA)) may not preferentially trace galaxies with high star formation rates at z~l.," Despite the small sample size, this finding suggests that absorbers with similar equivalent widths $_{r}^{\lambda2796}\sim$ ) may not preferentially trace galaxies with high star formation rates at $\sim$ 1."153 However. we stress that a much larger sample would be required to fully test. this result.," However, we stress that a much larger sample would be required to fully test this result."154 A larger overlapping survey of quasars ancl galaxies will be necessary to better constrain measurements of the typical environments of absorbers as well as the cold gas covering fraction of twpical galaxies at 21., A larger overlapping survey of quasars and galaxies will be necessary to better constrain measurements of the typical environments of absorbers as well as the cold gas covering fraction of typical galaxies at $\ga$ 1.155 Surveys such as the SDSS-LLL Baryon Oscillation Spectroscopic Survey (BOSS). will soon provide the higher densities of quasars necessary to achieve this required: precision.," Surveys such as the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS), will soon provide the higher densities of quasars necessary to achieve this required precision."156 Follow-up spectroscopy of already. identified. quasars at higher resolution or signal-to-noise could. acdcditionallv produce the numbers of absorbers in. deep galaxy survey footprints needed to vastly. improve our understanding of the distribution of cold gas in dark matter haloes in the near future., Follow-up spectroscopy of already identified quasars at higher resolution or signal-to-noise could additionally produce the numbers of absorbers in deep galaxy survey footprints needed to vastly improve our understanding of the distribution of cold gas in dark matter haloes in the near future.157 We would like to thank the referee. Jeremy Vinker. for helpful. discussions. ancl comments. which have greatly improved this work.," We would like to thank the referee, Jeremy Tinker, for helpful discussions and comments, which have greatly improved this work."158 We also thank JT for providing| us with his model predictions. presented in Figure 5.," We also thank JT for providing us with his model predictions, presented in Figure 5."159 We are also grateful to Pushpa Ixhare. and Jean Quashnock or helpful discussions anc to many others. who have contributed to the construction of the SDSS DRT quasar absorption line catalog of Yorkctal.(2011).," We are also grateful to Pushpa Khare and Jean Quashnock for helpful discussions and to many others, who have contributed to the construction of the SDSS DR7 quasar absorption line catalog of \citet{York11}."160. Funding for he SDSS and SDSS-IL has been provided. by the Alfred > Sloan Foundation. the U.S.. Department of Energy. 10 National Acronautics and Space Administration. the Japanese Monbukagakusho. the Max. Planck Society. and he Lieher Education. Funding Council for Eneland.," Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the U.S. Department of Energy, he National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England."161 The SDSS Web Site is httpwww.sdss.org/., The SDSS Web Site is http://www.sdss.org/.162order in perturbation theory and found. the result. to. be a third. order polvnomial in 0.,order in perturbation theory and found the result to be a third order polynomial in $\theta$.163 More recently. 2. found a relation between 6 and 9 using the spherical collapse model.," More recently, \citet{2008MNRAS.391.1796B} found a relation between $\theta$ and $\delta$ using the spherical collapse model."164 In all of these relations. the dependence on cosmological »uwameters was found. to be extremely weak (??).. ," In all of these relations, the dependence on cosmological parameters was found to be extremely weak \citep{1992ApJ...390L..61B, Bouchet:1994xp}."165The velocity divergence depends on ο and ον. in a standard ACDAL cosmology. only through the linear growth rate. f (?)," The velocity divergence depends on $\Omega_m$ and $\Omega_{\Lambda}$, in a standard $\Lambda$ CDM cosmology, only through the linear growth rate, $f$ \citep{Scoccimarro:1999ed}."166 We showed in the previous section that. including he velocity. divergence auto and cross power spectrum accurately reprocluces the redshift space power spectrum for a range of dark energy models onscales where the Ixaiser ormula fails., We showed in the previous section that including the velocity divergence auto and cross power spectrum accurately reproduces the redshift space power spectrum for a range of dark energy models onscales where the Kaiser formula fails.167 The quantities in Eqs., The quantities in Eqs.168 14. and 10. can be calculated if we exploit the relationship between the velocity and density field., \ref{dm} and \ref{SM} can be calculated if we exploit the relationship between the velocity and density field.169 In Fig., In Fig.170 7 we plot the velocity divergence auto (left panel) and cross (right panel) power spectrum as a function of the matter power spectrum for ACDAL and the three quintessence dark energy models., \ref{allmodels} we plot the velocity divergence auto (left panel) and cross (right panel) power spectrum as a function of the matter power spectrum for $\Lambda$ CDM and the three quintessence dark energy models.171 We find that the density velocity relationship is very similar for each mocel at the redshifts considered. with only a slight difference for the SUCGILA model at high. redshifts and at small scales.," We find that the density velocity relationship is very similar for each model at the redshifts considered, with only a slight difference for the SUGRA model at high redshifts and at small scales."172 The departure of the SUGRA mocdel from the general density velocity relation is due to shot noise. which alfects the power spectrum most at these scales in the SUCILUX mocdel as it has the lowest amplitude.," The departure of the SUGRA model from the general density velocity relation is due to shot noise, which affects the power spectrum most at these scales in the SUGRA model as it has the lowest amplitude."173 We have verified that this effect is due to shot noise by sampling half the particles in the same volume. thereby doubling the shot noise. and repeating the P(k) measurement to find an even larger departure.," We have verified that this effect is due to shot noise by sampling half the particles in the same volume, thereby doubling the shot noise, and repeating the $P(k)$ measurement to find an even larger departure."174 Fig., Fig.175 7 shows the independence of thedensity velocity relation not only of the values of cosmological parameters. as found in previous works. 7.. but. also a lack of dependence on the cosmological expansion history and initial power spectrum.," \ref{allmodels} shows the independence of thedensity velocity relation not only of the values of cosmological parameters, as found in previous works, \citet{1992ApJ...390L..61B}, but also a lack of dependence on the cosmological expansion history and initial power spectrum."176 Fitting over the range 0.01.« A(h/Mpesc:0.3))]. we lind the following function accurately describes the relation between the non-linear velocity clivergence and matter power spectrum at z=0 to better than 5% on scales A< +. where £55 is the non-linear matter power spectrum.," Fitting over the range $0.01<k (h/$ $<0.3)$, we find the following function accurately describes the relation between the non-linear velocity divergence and matter power spectrum at $z=0$ to better than $5\%$ on scales $k<0.3 h$ $^{-1}$, where $P_{\delta \delta}$ is the non-linear matter power spectrum."177" bor the cross power spectrum 2,= Pye. au—122883. a,=143. αν=1367.7 and ay=1.54 and for Pe,=Loo. ay= 12462.1. a,=0.839. as=1446.6 and as=0.806: all points were weightecl equally in the fit and the units for aya, and a, are /hy? 2 (Mpc/h)? and (Mpce/h)* respectively."," For the cross power spectrum $P_{x y} = P_{\delta \theta}$ , $\alpha_0 = -12288.7$, $\alpha_1 = 1.43$, $\alpha_2 = 1367.7$ and $\alpha_3 = 1.54$ and for $P_{x y} = P_{\theta \theta}$, $\alpha_0 = -12462.1$ , $\alpha_1 = 0.839$, $\alpha_2 = 1446.6$ and $\alpha_3 = 0.806$; all points were weighted equally in the fit and the units for $\alpha_0, \alpha_1$ and $\alpha_3$ are $/h)^{3/2}$ , $/h)^{-3}$ and $/h)^{-3}$ respectively."178 The power spectra used. for this fit are the average £o. Psy and £55 measured. from. eight. ACDAL simulations.," The power spectra used for this fit are the average $P_{\theta \theta}$, $P_{\delta \theta}$ and $P_{\delta \delta}$ measured from eight $\Lambda$ CDM simulations."179 In perturbation theory. the solution for the density contrast is expanded. as a series around. the background: value.," In perturbation theory, the solution for the density contrast is expanded as a series around the background value."180" ? found the following solutions for à and @ to arbitrary order in perturbation theory. where (40) and @,(4) are linear in the initial density field. δ and 6» are quadratic in the initial density field et"," \citet{Scoccimarro:1997st} found the following solutions for $\delta$ and $\theta$ to arbitrary order in perturbation theory, where $\delta_1(k)$ and $\theta_1(k)$ are linear in the initial density field, $\delta_2$ and $\theta_2$ are quadratic in the initial density field etc."181"e.? showedthat using a simple approximation to the equations of motion. f(04,)= oL. the equations become separable and £,(r)=D,(r) Dir)"". whereDí(z) is the linear","\citet{Scoccimarro:1997st} showedthat using a simple approximation to the equations of motion, $f(\Omega_{\rm m}) = \Omega_{\rm m}^{1/2}$ , the equations become separable and $E_n(\tau) = D_n(\tau) = D(\tau)^n$ , where$D(\tau)$ is the linear"182ripples detected in unsharp-masked images of ellipticals (e.g.. Schweizer Seitzer 1992. Colbert et 22001).,"ripples detected in unsharp-masked images of ellipticals (e.g., Schweizer Seitzer 1992, Colbert et 2001)."183 We note here that our data are not well suited to identify narrow features. às the FWHM resolution of our data is about 2 kpe at z20.1.," We note here that our data are not well suited to identify narrow features, as the FWHM resolution of our data is about 2 kpc at $z=0.1$."184" The remarkable nature of these red mergers and their remnants is illustrated in refexample,o/.plot.", The remarkable nature of these red mergers and their remnants is illustrated in \\ref{example_col.plot}.185.The figureshowst woexampleso fongoingmerge rina cprbaluce," The figure shows two examples of ongoing mergers, an example of a strongly disturbed merger remnant, and an example of a galaxy with more subtle distortions at faint surface brightness levels, arranged in a plausible red merger sequence."186d aidbelieve av ," In all cases the tidal features are smooth and red, and quite different from the highly structured blue tails associated with known mergers between gas richdisk galaxies."187Objet ceram pleo," Figure \ref{example_bw.plot}188 shows summed images of the same objects, highlighting the faintest features and providing an indication of the surface brightness levels reached by the observations."189faga ascanbeinferred fromthesmallerimagesshownintheAppendixthevarakwddegiehamuthierpnmuidwyoralasypáre, We stress that these objects are fairly typical examples: as can be inferred from the smaller images shown in the Appendix they are by no means unique within our sample.190 Quantitative characterization of the tidal features is important for testing the robustness of the visual classifications. measuring the flux associated with the features. assessing the effects of changing the S/N ratio. and examining correlations between distortions and other properties of the galaxies.," Quantitative characterization of the tidal features is important for testing the robustness of the visual classifications, measuring the flux associated with the features, assessing the effects of changing the S/N ratio, and examining correlations between distortions and other properties of the galaxies."191 Quantitative criteria are also useful as a tool for future studies of larger samples., Quantitative criteria are also useful as a tool for future studies of larger samples.192 Standard measures of asymmetry (e.g.. Abraham et 11996; Conselice et 22003) are not applicable to these galaxies as the features comprise only a small percentage of the total luminosity of the galaxies.," Standard measures of asymmetry (e.g., Abraham et 1996; Conselice et 2003) are not applicable to these galaxies as the features comprise only a small percentage of the total luminosity of the galaxies."193 Instead a method was developed which determines distortions with respect to a model light distribution (see. e.g.. Colbert et 22001).," Instead a method was developed which determines distortions with respect to a model light distribution (see, e.g., Colbert et 2001)."194 The method is only meaningful for bulge-dominated early-type galaxies. which make up the bulk of the sample.," The method is only meaningful for bulge-dominated early-type galaxies, which make up the bulk of the sample."195 First. the galaxies are fitted by an elliptical galaxy model using the “ellipse” task in IRAF. in three iterations.," First, the galaxies are fitted by an elliptical galaxy model using the “ellipse” task in IRAF, in three iterations."196 After each iteration a mask file is updated using the residuals from the previous fit., After each iteration a mask file is updated using the residuals from the previous fit.197 The center position. ellipticity. and position angle are allowed to vary with radius.," The center position, ellipticity, and position angle are allowed to vary with radius."198 In cases where a second galaxy overlaps the primary object the two objects are fitted iteratively., In cases where a second galaxy overlaps the primary object the two objects are fitted iteratively.199 The final model image is denoted M., The final model image is denoted $M$.200" Next. a ""clean"" galaxy da mi ely"," Next, a “clean” galaxy image $G$ is produced in the following way."201 dhe ag masked. by dividing the Α and B band images. median filtering. and identifying pixels deviating more than a factor two from the median color of the galaxy.," Objects bluer or redder than the primary galaxy are masked, by dividing the $R$ and $B$ band images, median filtering, and identifying pixels deviating more than a factor two from the median color of the galaxy."202" To remove small foreground and background objects and retain the smooth galaxy light a ""reverse"" unsharp masking technique is used: the galaxy images are compared to Gaussian-smoothed versions of themselves. and pixels deviating more than a factor two are masked (excluding the galaxy centers)."," To remove small foreground and background objects and retain the smooth galaxy light a “reverse” unsharp masking technique is used: the galaxy images are compared to Gaussian-smoothed versions of themselves, and pixels deviating more than a factor two are masked (excluding the galaxy centers)."203 Pixels in the vicinity of masked pixels are also masked., Pixels in the vicinity of masked pixels are also masked.204 Finally. a fractional distortion image F is created by dividing G by M.," Finally, a fractional distortion image $F$ is created by dividing $G$ by $M$."205 The distortion image is convolved with à 5« median filter to reduce pixel-to-pixel variations., The distortion image is convolved with a $5 \times 5$ median filter to reduce pixel-to-pixel variations.206 The parameter ¢ describing the level of distortion is defined as The tidal parameter thus measures the median absolute deviation of the (fractional) residuals from the model fit., The parameter $t$ describing the level of distortion is defined as The tidal parameter thus measures the median absolute deviation of the (fractional) residuals from the model fit.207 The procedure ts illustrated in for a galaxy pair with no visible distortions.," The procedure is illustrated in \\ref{tidalpix.plot}, , for a galaxy pair with no visible distortions,"208typical angular separations of a few (20) arcsecouds and time delays of the order of weeks or mouths (wears).,typical angular separations of a few $\sim 20$ ) arcseconds and time delays of the order of weeks or months (years).209 bursts cannot be spatially resolved by prescutday gannaray detectors aud will appear as nirror or recurreut events παλιο location on the sky. identical spectra and light curves — at different times and with different iutensities.," Multiply--imaged bursts cannot be spatially resolved by present–day gamma–ray detectors and will appear as `mirror' or recurrent events – same location on the sky, identical spectra and light curves – at different times and with different intensities."210 While a umuber of strongly. lensed individual bursts could be detected bySwift. the restricted sky coverage makes the probability of observing a leused pair rather snall.," While a number of strongly lensed individual bursts could be detected by, the restricted sky coverage makes the probability of observing a lensed pair rather small."211 The photon flux (in units of an7s1) observed at Eth in the euergv band Ej<EE44 aud emitted by au isotropically radiating source at redshift + is(1) where SCE) is the differcutial restframe photon luminosity of the source (im units of + keV.1j 1). aud εἰς) is the standard huninosity distauce fora FriediuauuRobertsonWalker (FRW) metric.," The photon flux (in units of $\punits$ ) observed at Earth in the energy band $E_{\rm min}<E<E_{\rm max}$ and emitted by an isotropically radiating source at redshift $z$ is, where $S(E)$ is the differential rest–frame photon luminosity of the source (in units of $^{-1}\,$ $^{-1}$ ), and $d_L(z)$ is the standard luminosity distance for a Friedmann–Robertson–Walker (FRW) metric."212 It is customary to define an ‘isotropic equivalent’ burst Iuninosityv in the energy. baud 302000 keV as L=|enES(E\VdE.," It is customary to define an `isotropic equivalent' burst luminosity in the energy band 30–2000 keV as $L=\int_{30 \,{\rm keV}}213^{2000 \,{\rm keV}} E \,S(E) \,dE$."214 Th we denote with c(£) the GRB luuinosity function (normalized to unitv). then theebserved rate of bursts withobsereed peak fluxes iu the interval GA.Ps) is 1mdr2) dz euzneum s where dV/dz is the comoving volume clement. Repis) is the comoving GRD rate density. e(P) is the detector efficiency as a function of photon flux. aud the factor (11:).+ accounts for cosinological time dilation.," If we denote with $\psi(L)$ the GRB luminosity function (normalized to unity), then the rate of bursts with peak fluxes in the interval $(P_1,P_2)$ is (P_1 P< dz (L') , where $dV/dz$ is the comoving volume element, $R_{\rm GRB}(z)$ is the comoving GRB rate density, $\epsilon(P)$ is the detector efficiency as a function of photon flux, and the factor $(1+z)^{-1}$ accounts for cosmological time dilation."215" If the ecomoetry of tho universe is FRW on laree scales. then Oat? wherezPE AQ, is the solid anele covered on the sky by the survey. and Ον—οOy is the curvature contribution to the present density parameter."," If the geometry of the universe is FRW on large scales, then =, where $\Delta\Omega_s$ is the solid angle covered on the sky by the survey, and $\Omega_K=1-\Om_M-\Om_{\Lambda}$ is the curvature contribution to the present density parameter."216 Uuless otherwise stated. we shall assimne in the following a vacunadominated cosinologv with deusity parameters Q4;=0.3 21d Ὃν=0.7. and aHubble coustaut Πυ=65g;kistMpe |," Unless otherwise stated, we shall assume in the following a vacuum–dominated cosmology with density parameters $\Omega_M=0.3$ and $\Om_\Lambda=0.7$, and aHubble constant $H_0=65 \,h_{65}\kmsmpc$ ."217l Our starting hvpothesis is that the rate of CRBs traces the elobal star formation history of the universe. αντ) with Hug aud Fax the comoving rate densities of star formation and corecollapse (Type IT) supernovae. respectively.," Our starting hypothesis is that the rate of GRBs traces the global star formation history of the universe, $R_{\rm GRB}(z)\propto R_{\rm SF}(z) \propto R_{\rm SN}(z)$ , with $R_{\rm SF}$ and $R_{\rm SN}$ the comoving rate densities of star formation and core–collapse (Type II) supernovae, respectively."218 The coustaut of proportionality. 4=Baxποπ. ἵνα freeparameter of the model.," The constant of proportionality, $k\equiv R_{\rm SN}/R_{\rm GRB}$, is a free–parameter of the model."219 Popular scenarios for GRBs iuclude mereiug neutrou stars (Paczyiisski 1986) or the formation of black holes in supernovalike events Ccollapsars’. MacFadven Woosley 1999).," Popular scenarios for GRBs include merging neutron stars (Paczyńsski 1986) or the formation of black holes in supernova–like events (`collapsars', MacFadyen Woosley 1999)."220 The key idea here is to assume that CRBs are produced by stellar svstemis which evolve rapidly — by cosmological standards — from their formation to the explosion epoch., The key idea here is to assume that GRBs are produced by stellar systems which evolve rapidly – by cosmological standards – from their formation to the explosion epoch.221 This would not be true at high redshift in the case of coalescing neutron stars. which have a median merger time of LOO My according to the recent population svuthesis study of Bloom. Sigurdsson. Pols (1999).," This would not be true at high redshift in the case of coalescing neutron stars, which have a median merger time of 100 Myr according to the recent population synthesis study of Bloom, Sigurdsson, Pols (1999)."222 A uunber of workers have modelled the expected evolution of the cosinic SFR with redshift., A number of workers have modelled the expected evolution of the cosmic SFR with redshift.223 Most have followed a simular route to that eniploved by Madau (1996). who based their estimates on the observed (vestframe} UW luminosity density of the galaxy. population as a whole.," Most have followed a similar route to that employed by Madau (1996), who based their estimates on the observed (rest–frame) UV luminosity density of the galaxy population as a whole."224 Using various diagnostics. the cosmic SER cau now be traced to z£F. although some details remain controversial.," Using various diagnostics, the cosmic SFR can now be traced to $z\approx 4$, although some details remain controversial."225 We use here three different paraiucterizations (shown in Figure 1)) of the global star formation rate per unit comoving volume iu an Eiusteiude Sitteruniverse CEdS)., We use here three different parameterizations (shown in Figure \ref{SFR}) ) of the global star formation rate per unit comoving volume in an Einstein–de Sitteruniverse (EdS).226 The first (hereafter SET) is takenfrom Macdau Pozzetti (2000): Bagit:)=0.3, The first (hereafter SF1) is takenfrom Madau Pozzetti (2000): (z)=0.3 .227The pulse phase averaged INAZAZ-Newlon/EPIC. spectra of XMMU J031747.5-663010. can be adequately. fit with the absorbed simple power law model with photon index. E—1.5 and an equivalent hydrogen. density Ng~2.31074 7.,"The pulse phase averaged /EPIC spectra of XMMU J031747.5-663010 can be adequately fit with the absorbed simple power law model with photon index, $\Gamma \sim 1.5$ and an equivalent hydrogen density $_{\rm H}\sim2.3\times10^{21}$ $^{-2}$."228 The corresponding absorbed Luminosity of the source in the 0.3-7 keV band is ~1.6«107 cress |. assuming the distance of 4.1 Mpe.," The corresponding absorbed luminosity of the source in the 0.3-7 keV band is $\sim 1.6\times10^{39}$ ergs $^{-1}$, assuming the distance of 4.1 Mpc."229 Phe best-fit spectral model parameters of the source are given in Table 2.., The best-fit spectral model parameters of the source are given in Table \ref{timing_spec_par}.230 Phe measured absorbing column Ny is —6 times higher than the Galactic hydrogen column in the direction of NGC 1313. 3.6.107. em2 (Dickey&Lockman1990).. consistent with an acdcitional intrinsic absorption within the system and inside the disk of NGC 1313.," The measured absorbing column $N_{\rm H}$ is $\sim$ 6 times higher than the Galactic hydrogen column in the direction of NGC 1313, $\times10^{20}$ $^{-2}$ \citep{DL90}, consistent with an additional intrinsic absorption within the system and inside the disk of NGC 1313."231 The absence of the bright optical counterpart to NMMU J031747.5-663010. its overall X-ray properties. (spectrum. pulsations. transient behaviour). ancl positional coincidence with NGC 1313 disk. allow us to conclude that it. should be located outside our Galaxy ancl probably belongs to NGC 1313.," The absence of the bright optical counterpart to XMMU J031747.5-663010, its overall X-ray properties (spectrum, pulsations, transient behaviour), and positional coincidence with NGC 1313 disk, allow us to conclude that it should be located outside our Galaxy and probably belongs to NGC 1313."232 The X-ray. pulsations ancl energy spectrum. of XMMU J031747.5-663010 imply that it is almost certainly an accreting hiehly-maenetizecd neutron star in a high-mass binary system (White. Swank Lolt 1983: Nagase 1989).," The X-ray pulsations and energy spectrum of XMMU J031747.5-663010 imply that it is almost certainly an accreting highly-magnetized neutron star in a high-mass binary system (White, Swank Holt 1983; Nagase 1989)."233 Phe association with NGC 1313 makes this source an extremely bright object with Luminosity Ly1.6.10%? eres +. greatly exceeding the isotropic Ecdelington Luminosity imit for a 1.4M. neutron star accreting hvdrogen-rich material.," The association with NGC 1313 makes this source an extremely bright object with luminosity $_{\rm X}\sim 1.6\times 10^{39}$ ergs $^{-1}$, greatly exceeding the isotropic Eddington luminosity limit for a $1.4 M_{\odot}$ neutron star accreting hydrogen-rich material."234 The relatively long pulse period of NMMU J031741.5-663010 (765.6 s) places it amone the systems with a companion that is either a supergiant or a Be star on a Corbet diagram (Corbet1986)., The relatively long pulse period of XMMU J031747.5-663010 (765.6 s) places it among the systems with a companion that is either a supergiant or a Be star on a Corbet diagram \citep{Corbet86}.235.. The transient behavior of the source lends support to the interpretation of this source as vet another Be binary. since the majority of De systems display recurrent/transient outbursts.," The transient behavior of the source lends support to the interpretation of this source as yet another Be binary, since the majority of Be systems display recurrent/transient outbursts."236 An extremely. high luminosity of the source still falls into the luminosity range observed in the Be X-ray pulsars. with one system. A0538-66 known to reach similar luminosity during its giant CEvpe 11) outburst (White&CarpenterLOTS:Skinneretal.1982).," An extremely high luminosity of the source still falls into the luminosity range observed in the Be X-ray pulsars, with one system, A0538-66 known to reach similar luminosity during its giant (Type II) outburst \citep{WC78,Skinner82}."237. The high luminosity of NAIALU JO81747.5-663010 is. also consistent with theoretical predictions for super-IESddington accretion onto highly magnetized (B71017 €) neutron star (Basko&Sunvaey1976)., The high luminosity of XMMU J031747.5-663010 is also consistent with theoretical predictions for super-Eddington accretion onto highly magnetized $B \gtrsim 10^{12}$ G) neutron star \citep{BS76}.238. The high-mass nature of the svstem implies its relatively voung age. consistent with its location within one of the spiral arms of NGC 1313. (Fig. 1)).," The high-mass nature of the system implies its relatively young age, consistent with its location within one of the spiral arms of NGC 1313 (Fig. \ref{image_general}) )."239 Since the Be interpretation still remains preliminary. optical identification is essential {ο cletermine the nature of the system.," Since the Be interpretation still remains preliminary, optical identification is essential to determine the nature of the system."240 For. optical identification. deeper optical observations are needed.," For optical identification, deeper optical observations are needed."241 The follow-up monitoring observations with anc are needed to test if it shows recurrent outbursts., The follow-up monitoring observations with and are needed to test if it shows recurrent outbursts.242 Future X-ray observations of NMMU.J031747.5-663010.. if it. reappears. could improve source localization anc study long-term evolution of its X-ray properties and X-ray pulsation.," Future X-ray observations of XMMU J031747.5-663010, if it reappears, could improve source localization and study long-term evolution of its X-ray properties and X-ray pulsation."243 XMMU JO31747.5-663010 is the second. X-ray pulsar, XMMU J031747.5-663010 is the second X-ray pulsar244exhibit a density profile that is well cleseribecl bv a double power law with outer asymptotic slope —3. there is still an open controversy about the value of the inner asymptotic slope with proposed. values mainly in the range 1.01.5 (Navarroetal.LOOT:Tormoen1997:Moore1998:Jing&Suto2002:Poweretal.2003:Navarro 2004).,"exhibit a density profile that is well described by a double power law with outer asymptotic slope $-3$, there is still an open controversy about the value of the inner asymptotic slope with proposed values mainly in the range $\sim 1.0 - 1.5$ \cite{NFW97,TBW97,M98,JS02,P03,Nav04}."245. On the other hand. a similar controversy has arisen. over je question whether such cusps are. indeed: observed. in ealaxies (see. e... Simon et al.," On the other hand, a similar controversy has arisen over the question whether such cusps are indeed observed in galaxies (see, e.g., Simon et al."246 2003 and references therein)., 2003 and references therein).247 llowever. on galaxy scale. the effect. of barvonic collapse and astrophysical feedback. processes (such as supernova explosions) may alter significantly the clark halo structure jus biasing in a complicated way the interpretation of the observations.," However, on galaxy scale, the effect of baryonic collapse and astrophysical feedback processes (such as supernova explosions) may alter significantly the dark halo structure thus biasing in a complicated way the interpretation of the observations."248 The great variety of models that have been proposed could clisorientate giving the impression of a. disordered collection of density profiles that are. so. dilferent. from each other that is somewhat surprising that all of then are able to describe the same kine of svstem., The great variety of models that have been proposed could disorientate giving the impression of a disordered collection of density profiles that are so different from each other that is somewhat surprising that all of them are able to describe the same kind of system.249 Ht is thus huehly desirable to look for common features of all these models in order to see whether they are indeed. dilferent and independent deseriptions of the same kind of system or rather they may be seen as particular cases ofa more gencral family., It is thus highly desirable to look for common features of all these models in order to see whether they are indeed different and independent descriptions of the same kind of system or rather they may be seen as particular cases of a more general family.250 A remarkable step in this direction is represented by the (0.2.5). mmocdels proposed by Zhao (1996... 1991).," A remarkable step in this direction is represented by the $(\alpha, \beta, \gamma)$ models proposed by Zhao (1996, 1997)."251 Assuming sphericalsvmumetrv!.. the mass density of the Zhao moclels is: with ry a scale radius. 3 and 7 the outer and the inner slope of the density. profile respectively and à. determining he width of the transition region.," Assuming spherical, the mass density of the Zhao models : with $r_s$ a scale radius, $\beta$ and $\gamma$ the outer and the inner slope of the density profile respectively and $\alpha$ determining the width of the transition region."252 It is indeed. possible to show that most of the previously proposed. galaxy models (both cuspy and cored) are obtained by suitably setting the hree parameters (0.2.5).," It is indeed possible to show that most of the previously proposed galaxy models (both cuspy and cored) are obtained by suitably setting the three parameters $(\alpha, \beta, \gamma)$."253 Moreover. the Zhao moclels also orms a complete set for constructing ecneral galaxy models or solving Poisson equation in the non spherical case.," Moreover, the Zhao models also forms a complete set for constructing general galaxy models or solving Poisson equation in the non spherical case."254 There is still another possible approach to smooth out he dillerences among spherically symmetric cuspy mocoels., There is still another possible approach to smooth out the differences among spherically symmetric cuspy models.255 Qualitatively. we can characterize a model by its asvmptotic »haviours [ου 20 and for rOx ," Qualitatively, we can characterize a model by its asymptotic behaviours for $r \rightarrow 0$ and for $r \rightarrow \infty$."256A stradghtforward wav o do this is to assign the logarithmic slope of the density motile. Le. a(p)=dlogpfdlogr.," A straightforward way to do this is to assign the logarithmic slope of the density profile, i.e. $\alpha(r) = d\log{\rho}/d\log{r}$."257 While the usual approach consists in giving the mass density and then evaluating a(r). he inverse wav is also possible.," While the usual approach consists in giving the mass density and then evaluating $\alpha(r)$, the inverse way is also possible."258 We first choose a gencral expression for the logarithmic slope and then evaluate the corresponding density profile by a simple. integration., We first choose a general expression for the logarithmic slope and then evaluate the corresponding density profile by a simple integration.259 As we will show later. this method allows to reduce most cupy models to some few classes on the basis of the shape of atr).," As we will show later, this method allows to reduce most cupy models to some few classes on the basis of the shape of $\alpha(r)$."260 Moreover. it is worth stressing that a(r) may be easilv estimated by numerical simulations of structure formation and is less allected by svstematic effects cüllieult to control.," Moreover, it is worth stressing that $\alpha(r)$ may be easily estimated by numerical simulations of structure formation and is less affected by systematic effects difficult to control."261 The paper is organized as follows., The paper is organized as follows.262 In Sect.22 we introduce a general parameterization of the logarithmic slope a(r) and delineates four classes of models that are worth to be investigated., In 2 we introduce a general parameterization of the logarithmic slope $\alpha(r)$ and delineates four classes of models that are worth to be investigated.263 In. particular. we present in this uer a detailed study of the kinematies and. dyvnamics of models with power law logarithmic slope.," In particular, we present in this paper a detailed study of the kinematics and dynamics of models with power law logarithmic slope."264 33 is devoted o the estimate of the basicproperties κο evaluate. the mass density. mass profile. circular velocity. gravitational potential ancl isotropic velocity dispersion of this class of models.," 3 is devoted to the estimate of the basic: we evaluate the mass density, mass profile, circular velocity, gravitational potential and isotropic velocity dispersion of this class of models."265 The dynamical. properties are fully characterized » the distribution. function. and. the density of states hat are estimated. in Sect.44 assuming isotropy in the velocity space., The dynamical properties are fully characterized by the distribution function and the density of states that are estimated in 4 assuming isotropy in the velocity space.266 In Sect.55. we evaluate. the observable quantities. namely the surface. density and. luminosity weighted: projected: velocity dispersion. while. in 66. we give olf the hypothesis of isotropy and. investigate the effect. of anisotropy on the radial velocity. dispersion. and the distribution function.," In 5, we evaluate the observable quantities, namely the surface density and luminosity weighted projected velocity dispersion, while, in 6, we give off the hypothesis of isotropy and investigate the effect of anisotropy on the radial velocity dispersion and the distribution function."267 We summarize anc conclude in 77., We summarize and conclude in 7.268 The usual approach to modeling galactic svstems (both the Iuminous components and the dark haloes) starts from the mass density profile ancl proceeds by evaluating the main dynamical quantities., The usual approach to modeling galactic systems (both the luminous components and the dark haloes) starts from the mass density profile and proceeds by evaluating the main dynamical quantities.269 The increasing resort to numerical simulations of structure formations has however drawn more attention to the logarithmic slope of the radial profile definedas Lt is indeed easier to compare different. galactic mocdels owed on their corresponding logarithmic slope., The increasing resort to numerical simulations of structure formations has however drawn more attention to the logarithmic slope of the radial profile defined: It is indeed easier to compare different galactic models based on their corresponding logarithmic slope.270 Moreover. he knowledge of a(r) renders quite immediate to. study he asvmptotie behaviours (towards the centre and/or the infinity) of the density profile.," Moreover, the knowledge of $\alpha(r)$ renders quite immediate to study the asymptotic behaviours (towards the centre and/or the infinity) of the density profile."271 Furthermore. it seems that his quantity is better constrained than the density. profile » numerical simulations.," Furthermore, it seems that this quantity is better constrained than the density profile by numerical simulations."272 Alotivated by these considerations. it is interesting to ook for an expression of a(r) that is as more general as »xossible in order to build spherical galactic models that may x grouped under the same class by mean of the property hat they share the same logarithmic slope.," Motivated by these considerations, it is interesting to look for an expression of $\alpha(r)$ that is as more general as possible in order to build spherical galactic models that may be grouped under the same class by mean of the property that they share the same logarithmic slope."273 To this aim. a useful proposal for a(r)is: with r2 an arbitrary scaling radius.," To this aim, a useful proposal for $\alpha(r)$: with $r_s$ an arbitrary scaling radius."274 Lt is possible to show that most of the galaxy models proposed up to now in literature.may. be obtained. by inserting. I20.(2)). into Eq.(1)) and integrating with respect to à with the boundary, It is possible to show that most of the galaxy models proposed up to now in literaturemay be obtained by inserting \ref{eq: genslope}) ) into \ref{eq: defslope}) ) and integrating with respect to $r$ with the boundary275between LO and CGCGlIz ancl 89 and. €iCillz.,between 10 and GHz and 89 and GHz.276 Indeed. given the quality of the data it is not clear whether a power law (rather than a smoothly curving function) is. in fact. the best fit to the data.," Indeed, given the quality of the data it is not clear whether a power law (rather than a smoothly curving function) is, in fact, the best fit to the data."277 On the other hand. in the unification scenario we suspect the racdio-core of CvenusA to be a severely. misaligned jet ancl therefore the spectrum to be typical of an unboosted blazar jet spectrum.," On the other hand, in the unification scenario we suspect the radio-core of Cygnus-A to be a severely misaligned jet and therefore the spectrum to be typical of an unboosted blazar jet spectrum."278 ‘These have been observed in the millimetre to submillimetre (Gear et 11994). so we assume that a power-law is the simplest interpretation.," These have been observed in the millimetre to submillimetre (Gear et 1994), so we assume that a power-law is the simplest interpretation."279 In this case there is tentative evidence for some steepening above GClLIz. but the data are inadequate to determine whether this is the 0.5 break of a continuous injection mocel. or. whether it is the onset of depletion of high energy. electrons.," In this case there is tentative evidence for some steepening above GHz, but the data are inadequate to determine whether this is the 0.5 break of a continuous injection model, or, whether it is the onset of depletion of high energy electrons."280 Further observations are underway to answer this question., Further observations are underway to answer this question.281 The HAS. measurements clearly suggest. thermal emission. [rom dust in. the central galaxy. although the temperature and hence mass of the emitting. dust are very uncertain from the Z45i85 values alone.," The $IRAS$ measurements clearly suggest thermal emission from dust in the central galaxy, although the temperature and hence mass of the emitting dust are very uncertain from the $IRAS$ values alone."282 The new submillimetre cata points constrain the non-thermal contribution to the £RAS (:viel the much awaited 50) Iluxes., The new submillimetre data points constrain the non-thermal contribution to the $IRAS$ (and the much awaited $ISO$ ) fluxes.283 In particular the GGlIz measurement. constrains the temperature of emitting cust to within a factor of two.," In particular the GHz measurement, constrains the temperature of emitting dust to within a factor of two."284 Preliminary Z5O cata (Polletà. private communication) at 170pim suggests that the dust temperature may be z50 [Ix (which is well within our consralnts see below).," Preliminary $ISO$ data (Polletta, private communication) at $170\,{\mu \rm{m}}$ suggests that the dust temperature may be $\approx 50$ K (which is well within our constraints – see below)."285 However. this cata point still has a large calibration uncertainty at the current tine and is not included in the present discussion.," However, this data point still has a large calibration uncertainty at the current time and is not included in the present discussion."286 Assuming a reasonable value for the dust emissivity. index. 7. of 1.3. the maximum temperature that appears to fit the ZRAAS data is δρ]. while the lower temperature. is constrained by the SCUBA measurement at 450 microns to 37k. Fig.," Assuming a reasonable value for the dust emissivity index, $\beta$, of 1.3, the maximum temperature that appears to fit the $IRAS$ data is 85K, while the lower temperature is constrained by the SCUBA measurement at 450 microns to 37K. Fig."287 3 shows both these temperatures., 3 shows both these temperatures.288 Changing 7 between 2.0 and 1.0 makes verv little difference to the derived. temperatures., Changing $\beta$ between 2.0 and 1.0 makes very little difference to the derived temperatures.289 The mass of emitting cust Aly , The mass of emitting dust $M_{\rmn{d}}$ 290"Current. observations. such as those of CALB anisotropy (Spergelefa£2007).. Supernovae type la (Riessefαἱ.2004.2007:Davisοἱaf,2007) and larec scale structure Clegmarkefal,2004:Eisensteinοἱaf, 2007).. converge on the Lact that a spatially homogeneous ancl gravitationally repulsive enerev component. referred. as dark. energy. account for about of the energy density of Universe.","Current observations, such as those of CMB anisotropy \citep{WMAP}, Supernovae type Ia \citep{gold,SNIa,Davis07}291 and large scale structure \citep{SDSS,2dF}, converge on the fact that a spatially homogeneous and gravitationally repulsive energy component, referred as dark energy, account for about of the energy density of Universe."292 Some heuristic models that roughly describe the observable consequences of dark energy were suggested. in recent vears. a number of them stemming form fundamental physies ancl other being purcly phenomenological.," Some heuristic models that roughly describe the observable consequences of dark energy were suggested in recent years, a number of them stemming form fundamental physics and other being purely phenomenological."293 However. the nature of dark enerey still remain mysterious to physicists and astronomers although many possible candidates. have been proposed.," However, the nature of dark energy still remain mysterious to physicists and astronomers although many possible candidates have been proposed."294 Dark energy present in the equations of cosmological dynamics through its elfective energy density and: pressure., Dark energy present in the equations of cosmological dynamics through its effective energy density and pressure.295 The ratio of pressure to energv density (the equation of state) is very important in the Friedmann equation regardless of its physical origin., The ratio of pressure to energy density (the equation of state) is very important in the Friedmann equation regardless of its physical origin.296 I clark energy is some kind of dynamical Uuiel ancl its equation of state would likely not be constant. but would vary with redshift: or equivalentlv with cosmic time.," If dark energy is some kind of dynamical fluid and its equation of state would likely not be constant, but would vary with redshift $z$ or equivalently with cosmic time."297 The impact of dark energy (whether dynamical or a constant) on cosmological observations can be expressed in term of ος)=p(z)pz) which is to be measured through either the cosmic expansion ustory H(z)(obtained. for example. using supernova data) or through large-scale structure.," The impact of dark energy (whether dynamical or a constant) on cosmological observations can be expressed in term of $w(z)=p(z)/\rho(z)$ which is to be measured through either the cosmic expansion history $H(z)$ (obtained, for example, using supernova data) or through large-scale structure."298 Therefore. it is sagacious o study the parameterization of the equation of state of ark energv empirically with as [ον prior assuniptions as »ossible.," Therefore, it is sagacious to study the parameterization of the equation of state of dark energy empirically with as few prior assumptions as possible."299 To reveal the nature of dark energy and narrow clown re candidate Dist. à very powerful measure is to map out. the. evolution of the equation of state as. recshift hanges.," To reveal the nature of dark energy and narrow down the candidate list, a very powerful measure is to map out the evolution of the equation of state as redshift changes."300 However. in data fitting. we need to parameterize we equation of state ws) in simple form and then constrain the evolution of ες) in terms of the parameters we introduced. in our parametrization except the case in which ws) is alreaciw such as in the quintessence Ποιά (Pachmanabhan2007:Copeland.efa£2006:Liu&Li2006:Lao&Li2003a. 2004). phantom field. (Caldwell2002:Lao&Li2003b:Liu2003: 2004).. or Chaplygin gas model. (Ixamenshcehik.οἱa£.2002:Hao&Li 2005).," However, in data fitting, we need to parameterize the equation of state $w(z)$ in simple form and then constrain the evolution of $w(z)$ in terms of the parameters we introduced in our parametrization except the case in which $w(z)$ is already such as in the quintessence field \citep{a1,a2,a3,a4,a5}, phantom field \citep{b1,b2,b3,b4}, or Chaplygin gas model \citep{c1,c2}."301. Unquestionably. the way we parameterize the equation of state is bound. to alfect our ability to extract information from the data.," Unquestionably, the way we parameterize the equation of state is bound to affect our ability to extract information from the data."302 Phere are many cillerent parameterizations have been introduced based on simplicity and the requirement of regular asymptotic behaviors (Johri&Rath2006.2007:Johri 2004).," There are many different parameterizations have been introduced based on simplicity and the requirement of regular asymptotic behaviors \citep{p1,p2,p3}."303. Llowever. will these choice of parameterizatlions give us maxinunm power toextract information from the data?," However, will these choice of parameterizations give us maximum power toextract information from the data?"304 Some analysis existing in literatures compared. the different parameterizations by looking. at their. corresponding. 2 x. which. are justified..see by the generalized. likelihood ratio test in statistics.," Some analysis existing in literatures compared the different parameterizations by looking at their corresponding $\chi^2$ , which are justified by the generalized likelihood ratio test in statistics."305 But this, But this306—ü.31a IIIP-2000-57 /TIT PRIMORDIAL DENSITY PERTURBATI,The order of the QCD transition and the values of its parameters are still under debate.307ONS J. IGNAATIUS D, Nevertheless there are indications from lattice QCD calculations.308epartmentof Physies. P.O.," Quenched QCD (no dynamical quarks) shows a first-order phase transition with a small latent heat, compared to the bag model, and a small surface tension, compared to dimensional arguments \cite{Iwasaki}."309 Dor9. FIN-O00L4 University ofHelsinki., We assume that the QCD transition is of first order and that the values from quenched lattice QCD (scaled appropriately by the number of degrees of freedom) are typical for the physical QCD transition.310 Finland E-mail: jonnedgnalius," Based on these values and homogeneous bubble nucleation a small supercooling, $\Delta_{\rm sc} \equiv 1- T_{\rm f}/T_{\rm c} \sim 10^{-4}$, and a tiny bubble nucleation distance, $d_{\rm nuc} \sim 1$ cm, would follow \cite{Ignatius}."311tiki.fi DOMUINIIJ. SCLIAWARZ Inslilul für Theoreti," The actual nucleation temperature is denoted by $T_{\rm f}$, and the thermodynamic transition temperature by $T_c \approx 150$ MeV. We argue \cite{IS} that the assumption of homogeneous nucleation is violated in the early Universe by the inevitable density perturbations from inflation or from other seeds for structure formation."312schePhasik. Wien. Hauplstafje 10., Those fluctuations in density and temperature have been measured by COBE \cite{Bennett} to have an amplitude of $\delta T/T \sim 10^{-5}$ .313 A-1040 TUWien. Austria Wiedner ο 8 acad dschwearztihep.," The effect of the QCD transition on density perturbations \cite{SSW,SSW2}314 and gravitational waves \cite{Schwarz} has been studied previously, while we investigate the effect of the density perturbations on the QCD phase transition here."315dlp.huwien a, First-order phase transitions normally proceed via nucleation of bubbles of the new phase.316bstracts of magnitude.," When the temperature is spatially uniform and no significant impurities are present, the mechanism is homogeneous nucleation."317 The resulting barvon inhomogc, The probability to nucleate a bubble of the new phase per time and volume is approximated by $\Gamma \approx T_c^4 \exp[-S(T)]$.318ucitics may affect primordial u," The nucleation action $S$ is the free energy difference of the system with and without the nucleating bubble, divided by the temperature."319ucleosvuthlesis.," Nucleation is a very rapid process, compared with the extremely slow cooling of the Universe."320 *Jo in the Proceedingsof COSMO-2000..Ith International ," The duration of the nucleation period, $\Delta t_{\rm nuc}$, is found to be \cite{Fuller,Enqvist} The time $t_f$ is defined as the moment when the fraction of space where nucleations still continue equals $1/e$."321Particle Phlivs, The heat flow preceding the deflagration fronts reheats the rest of the Universe.322ies appea, We denote by $v_{\rm heat}$ the effective speed by which released latent heat propagates in sufficient amounts to shut down nucleations.323randthe Earle Universe.," In practice, $v_{\rm def} < v_{\rm heat} < c_s$ , where $v_{\rm def}$ is the velocity of the deflagration front and $c_s$ is the sound speed \cite{Kurki-Suonio}."324"Cheju ραπ,South Korea.", In the unlikely case of detonations $v_{\rm heat}$ should be replaced by the velocity of the phase boundary in allexpressions that follow.325178 SeptemberWorkshop2000.," The mean distance between nucleation centers, measuredimmediately"326radius.,radius.327" However, we have found that these additional criteria made no appreciable difference in practice."," However, we have found that these additional criteria made no appreciable difference in practice."328" Once a cell has been accreted, its mass and momentum is added to the sink particle and the corresponding mesh-generating point is removed."," Once a cell has been accreted, its mass and momentum is added to the sink particle and the corresponding mesh-generating point is removed."329" After this step has been performed for all candidate cells, the mesh is reconstructed such that the volume associated with the removed cells is distributed among the remaining cells around the sink particle."," After this step has been performed for all candidate cells, the mesh is reconstructed such that the volume associated with the removed cells is distributed among the remaining cells around the sink particle."330" As conserved quantities are weighted with the new volumes, this tends to make their densities and pressures artificially small."," As conserved quantities are weighted with the new volumes, this tends to make their densities and pressures artificially small."331" In the last section, we present a resolution study with varying accretion radii to show that this caveat artificially reduces the amount of fragmentation, and increases the typical fragment mass."," In the last section, we present a resolution study with varying accretion radii to show that this caveat artificially reduces the amount of fragmentation, and increases the typical fragment mass."332" As our fiducial accretion radius, we choose a value of Trace=10089, which is close to the maximum physical size of accreting Pop III stars (Hosokawa&Omukai2009).."," As our fiducial accretion radius, we choose a value of $r_{\rm acc}=100\,{\rm R}_\odot$, which is close to the maximum physical size of accreting Pop III stars \citep{ho09}."333 Mergers between sink particles occur whenever the total energy of the respective two-body system is negative and the semimajor axis falls below the accretion radius., Mergers between sink particles occur whenever the total energy of the respective two-body system is negative and the semimajor axis falls below the accretion radius.334" This is motivated by our above choice, which yields an approximate upper limit on the physical size of the protostars."," This is motivated by our above choice, which yields an approximate upper limit on the physical size of the protostars."335" In cases where more than one sink particle lies within the accretion radius of another sink particle, the pair with the highest binding energy"," In cases where more than one sink particle lies within the accretion radius of another sink particle, the pair with the highest binding energy"336"and error, we find that the remaining residuals correlate with the external parameters: the spectrum’s dispersion relation positions, r y, and the spectrum slope a (Figures3)).","and error, we find that the remaining residuals correlate with the external parameters: the spectrum's dispersion relation positions, $x$ $y$, and the spectrum slope $\alpha$ (Figures)."337" Thus, where co,..,c4 are the free linear decorrelation coefficients and PF, is arbitrary and fixed (to avoid the degeneracy with co) at the average out-of-transit flux of both visits."," Thus, where $c_{0},...,c_{4}$ are the free linear decorrelation coefficients and $F_{o}$ is arbitrary and fixed (to avoid the degeneracy with $c_{0}$ ) at the average out-of-transit flux of both visits."338 We empirically find that a successful correction for correlated measurements using the terms in Equation requires treating data from the two filter wheel states separately (see for a discussion of the filter wheel , We empirically find that a successful correction for correlated measurements using the terms in Equation requires treating data from the two filter wheel states separately (see for a discussion of the filter wheel states).339"In Figure4,, the green and red points represent data states).obtained in the first HST visit, and the yellow and blue points represent data obtained in the the second HST visit."," In Figure, the green and red points represent data obtained in the first HST visit, and the yellow and blue points represent data obtained in the the second HST visit."340" In each visit, the orbits are assigned to the two preferred states of the filter wheel positioning (see lower right panel of Figure 3))."," In each visit, the orbits are assigned to the two preferred states of the filter wheel positioning (see lower right panel of Figure )."341" Each visit and filter wheel state has its own set of external parameter decorrelation coefficients, co,...,c4."," Each visit and filter wheel state has its own set of external parameter decorrelation coefficients, $c_{0},...,c_{4}$."342" Thus, in Figure4,, the orbits that share a color share the same decorrelation coefficients, however as noted previously, the first orbit for each visit is not included in the MCMC analysis."," Thus, in Figure, the orbits that share a color share the same decorrelation coefficients, however as noted previously, the first orbit for each visit is not included in the MCMC analysis."343" There are 5 decorrelation coefficients for each of the 4 visit/filter wheel combinations, resulting in 20 free parameters in V."," There are 5 decorrelation coefficients for each of the 4 visit/filter wheel combinations, resulting in 20 free parameters in $\Psi$."344" Including the 8 free parameters specifying the physical parameters of the system, the overall model has a total of 28 free parameters."," Including the 8 free parameters specifying the physical parameters of the system, the overall model has a total of 28 free parameters."345" Before calculating the likelihood of a model for a given set of 28 parameters, the correction for the 7 readout states is applied."," Before calculating the likelihood of a model for a given set of 28 parameters, the correction for the 7 readout states is applied."346" The 7 readout states are determined for each orbit independently from the residuals of the model, F5,—Fimoa."," The 7 readout states are determined for each orbit independently from the residuals of the model, $F_{obs}-F_{mod}$."347 The 7 state correction removes the average flux residual for each state with respect to the average residual across all measurements within an orbit., The 7 state correction removes the average flux residual for each state with respect to the average residual across all measurements within an orbit.348" Thus, the 7 state correction does not change the overall flux level of an orbit."," Thus, the 7 state correction does not change the overall flux level of an orbit."349" The likelihood is modeled as independent Gaussian residuals with uncertainty, o—250 ppm."," The likelihood is modeled as independent Gaussian residuals with uncertainty, $\sigma=250$ ppm."350 'The parameters and their uncertainties are based upon an overall MCMC chain of 10° steps after a burn-in period., The parameters and their uncertainties are based upon an overall MCMC chain of $^6$ steps after a burn-in period.351" The scale of the proposal steps in each parameter are set using an automated iterative algorithm of proposal step size adjustments until the acceptance fraction, 0.2«f0.3, is reached."," The scale of the proposal steps in each parameter are set using an automated iterative algorithm of proposal step size adjustments until the acceptance fraction, $0.2<f<0.3$, is reached."352" After an initial burn-in period to determine the proposal steps, the proposal distributions are finalized, and the results are based upon the remaining steps."," After an initial burn-in period to determine the proposal steps, the proposal distributions are finalized, and the results are based upon the remaining steps."353 The longest auto correlation length amongst the parameters is 600 steps., The longest auto correlation length amongst the parameters is 600 steps.354" Initial tests with a parallel tempering MCMC algorithm (Gregory2005a) with 7 parallel (PT)chains, did not show any evidence for multimodality amongst the 28 free parameters."," Initial tests with a parallel tempering (PT) MCMC algorithm \citep{GRE05} with 7 parallel chains, did not show any evidence for multimodality amongst the 28 free parameters."355" Thus, the more time-consuming PT MCMC was not needed to explore the parameter space and helps verify that the single chain reliably explored the parameter space."," Thus, the more time-consuming PT MCMC was not needed to explore the parameter space and helps verify that the single chain reliably explored the parameter space."356" The resulting transit light curve, residuals, and corrections are shown in Figure8."," The resulting transit light curve, residuals, and corrections are shown in Figure."357". The top panel shows the relative flux of the observations after dividing out P55,/V,the best fit (in a x? sense) decorrelation function with correction for the 7 states."," The top panel shows $F_{obs}/\Psi$, the relative flux of the observations after dividing out the best fit (in a $\chi^2$ sense) decorrelation function with correction for the 7 states."358 The color coding of the points is the same as in Figure4., The color coding of the points is the same as in Figure.359. The middle panel of Figure shows the residual relative flux of the observations from the complete model., The middle panel of Figure shows the residual relative flux of the observations from the complete model.360" The resulting rms residual, στις=240 ppm, is slightly less than the expected uncertainty, σιοι=250 ppm (see ??))."," The resulting rms residual, $\sigma_{\rm rms}=240$ ppm, is slightly less than the expected uncertainty, $\sigma_{\rm tot}=250$ ppm (see )."361 We presume the latter results from a slight overestimate in the contribution of Oback to Otor-, We presume the latter results from a slight overestimate in the contribution of $\sigma_{\rm back}$ to $\sigma_{\rm tot}$.362 The lower panel of Figure shows the relative flux correction due to V., The lower panel of Figure shows the relative flux correction due to $\Psi$.363 The peak to trough relative flux variation in V reaches 0.1696 for orbits within the same visit and filter wheel position., The peak to trough relative flux variation in $\Psi$ reaches $0.16\%$ for orbits within the same visit and filter wheel position.364" For display purposes, V is normalized to its average value for each visit/filter wheel combination."," For display purposes, $\Psi$ is normalized to its average value for each visit/filter wheel combination."365" Within a visit, the external parameter decorrelation normalization, co, varies by 0.1296 in relative flux."," Within a visit, the external parameter decorrelation normalization, $c_{0}$, varies by $0.12\%$ in relative flux."366" In the 12 days between the two visits, the observed flux of vvaried by 0.696 due to intrinsic variability of the star or the instrument, but we cannot distinguish between these two possibilities from these data."," In the 12 days between the two visits, the observed flux of varied by $0.6\%$ due to intrinsic variability of the star or the instrument, but we cannot distinguish between these two possibilities from these data."367 The minimum x?=362.8 with 362 degrees of freedom indicates the model is an acceptable fit to the data., The minimum $\chi^2=362.8$ with 362 degrees of freedom indicates the model is an acceptable fit to the data.368" Tables show the resulting parameter estimates and their uncertainty for aand aalong with previous determinations from the literature, respectively."," Tables show the resulting parameter estimates and their uncertainty for and along with previous determinations from the literature, respectively."369" The parameter estimates come from the median of MCMC samples, and the uncertainties inscribe of the MCMC samples."," The parameter estimates come from the median of MCMC samples, and the uncertainties inscribe of the MCMC samples."370" The uncertainties include the impact of the assumed prior on M,=1.027+0.06..", The uncertainties include the impact of the assumed prior on $M_{\star}=$ $\pm$.371" 'This affects the physical properties of the system that are not directly constrained by the light curve (e.g., Ry Rp)."," This affects the physical properties of the system that are not directly constrained by the light curve (e.g., $R_{\star}$ $R_{p}$ )."372" The light curve quality is high enough that the uncertainty in R, and R, is dominated by the uncertainty in M,.", The light curve quality is high enough that the uncertainty in $R_{\star}$ and $R_{p}$ is dominated by the uncertainty in $M_{\star}$.373" A solution assuming fixed M, results in o,=0.008 aand oy=0.013 uuncertainty in R, and R,, respectively."," A solution assuming fixed $M_{\star}$ results in $\sigma_{\star}=0.008$ and $\sigma_{p}=0.013$ uncertainty in $R_{\star}$ and $R_{p}$, respectively."374" Table illustrates the sensitivity of the parameters that are directly constrained by the light curve (i.e., independent of to fixing the limb darkening parameters at their theoreticalM,) expectation."," Table illustrates the sensitivity of the parameters that are directly constrained by the light curve (i.e., independent of $M_{\star}$ ) to fixing the limb darkening parameters at their theoretical expectation."375 We adopt the H-band values (uj=0.016 ug= from Claret(2000)., We adopt the H-band values $u_{1}=0.016$ $u_{2}=0.441$ ) from \citet{CLA00}.376". Fixing the limb darkening 0.441)parameters results in a Ay?=1.3 worse fit, a non-significant difference in the quality of fit."," Fixing the limb darkening parameters results in a $\Delta \chi^2=1.3$ worse fit, a non-significant difference in the quality of fit."377" However, the estimate for Rp/R, is lo smaller and the uncertainty is smaller."," However, the estimate for $R_{p}/R_{\star}$ is $\sigma$ smaller and the uncertainty is smaller."378" Fixing the limb darkening parameters can lead to more precise model fits, but in the case of high quality data, it may result in lower accuracy when the stellar brightness profile differs from the theoretical expectation (Southworth2008;Claret 2009)."," Fixing the limb darkening parameters can lead to more precise model fits, but in the case of high quality data, it may result in lower accuracy when the stellar brightness profile differs from the theoretical expectation \citep{SOU08,CLA09}."379. Also shown in Table is the precision possible if the observations were free from systematics., Also shown in Table is the precision possible if the observations were free from systematics.380" The results were obtained by fixing the decorrelation coefficients, C9,...,C4, at the values that minimize y?."," The results were obtained by fixing the decorrelation coefficients, $c_{0},...,c_{4}$, at the values that minimize $\chi^2$ ."381" The need to correct for systematics reduces the precision in Rp/R, by a factor of 5 and reduces the precision in the transit midpoint by a factor of 1.2.", The need to correct for systematics reduces the precision in $R_{p}/R_{\star}$ by a factor of 5 and reduces the precision in the transit midpoint by a factor of 1.2.382 The results shown in Table emphasize the difficulty in judging the light curve quality based upon comparing the resulting uncertainty in the model parameter, The results shown in Table emphasize the difficulty in judging the light curve quality based upon comparing the resulting uncertainty in the model parameter383to the VLB and CLD variation. respectively.,"to the VLB and CLB variation, respectively."384 On the other hand. the de-trended parameters of Spec D and C are similar. and the variability between them observed over the entire 3.20 keV band is thought to be dominated by the M. change.," On the other hand, the de-trended parameters of Spec B and C are similar, and the variability between them observed over the entire 3–30 keV band is thought to be dominated by the $\dot{M}$ change."385 Through the analvsis of theANTE spectra of the atoll source 4U 1608.522 in its state. we have confirmed that both (ime-averaged. ancl difference energy. spectra can be reproduced successfully bv the Eastern (AICD+BB+Gau) model.," Through the analysis of the spectra of the atoll source 4U 1608–522 in its upper-banana state, we have confirmed that both time-averaged and difference energy spectra can be reproduced successfully by the Eastern (MCD+BB+Gau) model."386" Considering the hardening factor. the effective temperature and radius of the MCD component were obtained as PTTο keV and rt~ 12 km. respectively,"," Considering the hardening factor, the effective temperature and radius of the MCD component were obtained as $kT^{\rm eff}_{\rm in} \sim$ 1.1 keV and $r^{\rm eff}_{\rm in} \sim$ 12 km, respectively."387" The radius is larger than the representative NS radius. 10 km. and is consistent with the last stable orbit. 342, = 12.4 km. allowed by eeneral relativitv."," The radius is larger than the representative NS radius, 10 km, and is consistent with the last stable orbit, $3 R_{\rm s}$ = 12.4 km, allowed by general relativity."388 This result agrees with the picture of a standard accretion disk which is formed around a NS., This result agrees with the picture of a standard accretion disk which is formed around a NS.389 The BB parameters were found as T8~ L5 keV and ril~ 2.7 km. assuming isotropic emission [rom a spherical source.," The BB parameters were found as $kT^{\rm eff}_{\rm BB} \sim$ 1.8 keV and $r^{\rm eff}_{\rm BB} \sim$ 2.7 km, assuming isotropic emission from a spherical source."390 The temperature is close to the local LEddington temperature (2.0 keV) at the NS surface. and the radius is smaller (han 10 kin.," The temperature is close to the local Eddington temperature (2.0 keV) at the NS surface, and the radius is smaller than 10 km."391 Then. the DD component can be regarded as being emitted fom an equatorial zone of the NS. as previously suggested by Mitsudaοἱal.(1984).," Then, the BB component can be regarded as being emitted from an equatorial zone of the NS, as previously suggested by \citet{mitsuda_z}."392. According to the picture of standard accretion disks. a half of the released gravitational enerev is radiated from the accretion disk (L4). aad the other half is stored in the Ixeplerian kinetic energv and (hen emitted (Lip) when the matter settles onto the NS surface.," According to the picture of standard accretion disks, a half of the released gravitational energy is radiated from the accretion disk $L_{\rm disk}$ ), and the other half is stored in the Keplerian kinetic energy and then emitted $L_{\rm BB}$ ) when the matter settles onto the NS surface."393 Then. we expect. {ων (o be proportion to Lay. aud hence the Lyp/Lai; ratio to be constant.," Then, we expect $L_{\rm BB}$ to be proportion to $L_{\rm disk}$, and hence the $L_{\rm BB}/L_{\rm disk}$ ratio to be constant."394 Indeed. Lajas was found to increase almost linearly with the total luminosity £44 (figure Ga).," Indeed, $L_{\rm disk}$ was found to increase almost linearly with the total luminosity $L_{\rm tot}$ (figure 6a)."395" llowever. (he same figure reveals that. Lip increases less steeply. making (he Lpip/Lai ratio decrease [rom 0.6 to 0.4 as Ly, increases [rom 1x107 to 4xLO eres tf."," However, the same figure reveals that $L_{\rm BB}$ increases less steeply, making the $L_{\rm BB}/L_{\rm disk}$ ratio decrease from 0.6 to 0.4 as $L_{\rm tot}$ increases from $1 \times 10^{37}$ to $4 \times 10^{37}$ erg $^{-1}$."396 We may think of (vo possibilities to explain the observed relative decrease of Lips., We may think of two possibilities to explain the observed relative decrease of $L_{\rm BB}$.397" One is (hat the accreting matter reaches (he NS surface and emits Ly, which is equivalent to the Keplerian energy (1.6. x La). bul we cannot observe all (ae emission because its wavelength shifts outside the PCA οποιον band (330 keV). or the geometrical angle of the emission moves [rom our line of sight."," One is that the accreting matter reaches the NS surface and emits $L_{\rm BB}$ which is equivalent to the Keplerian energy (i.e. $\propto L_{\rm disk}$ ), but we cannot observe all the emission because its wavelength shifts outside the PCA energy band (3–30 keV), or the geometrical angle of the emission moves from our line of sight."398 ILowever. we have not observed anv hint of extra emission in the softest or hardest energy ends of the PCA spectra.," However, we have not observed any hint of extra emission in the softest or hardest energy ends of the PCA spectra."399 In addition. other sources. which are," In addition, other sources, which are"400origins.,origins.401 This arises because separate sources for hydrogen and metals. in helium atmosphere white cwarls. imply independent: probabilities. anc being polluted by both will be the least probable.," This arises because separate sources for hydrogen and metals, in helium atmosphere white dwarfs, imply independent probabilities, and being polluted by both will be the least probable."402 Therefore. if one assumes that metals result from acereted asteroids but under-abundant hydrogen in a cool. helium. atmosphere is either. 1) interstellar. 2) primordial. or 3) the result. of dredge up ancl subsequent mixing. a larger than unity ratio of metal-free counterparts to the DZA stars is certain.," Therefore, if one assumes that metals result from accreted asteroids but under-abundant hydrogen in a cool, helium atmosphere is either 1) interstellar, 2) primordial, or 3) the result of dredge up and subsequent mixing, a larger than unity ratio of metal-free counterparts to the DZA stars is certain."403 Llowever. if the photospheric metals. and. hydrogen both have a circumstellar origin. and are semi-continuously delivered to the photosphere on relevant timescales. the ratio of helium-rich DA to DZA stars can potentially be less than unity.," However, if the photospheric metals and hydrogen both have a circumstellar origin, and are semi-continuously delivered to the photosphere on relevant timescales, the ratio of helium-rich DA to DZA stars can potentially be less than unity."404 There are three mixed. helium-hyvdrogen atmosphere stars among the 152 cool white dwarls thoroughly stucied and modeled. by Bergeron.etal.(2001): two are DZA stars(D.," There are three mixed helium-hydrogen atmosphere stars among the 152 cool white dwarfs thoroughly studied and modeled by \citet{ber01}; two are DZA stars(!),"405 while the third has atmospheric carbon (where dredge up of interior carbon ancl helium in a previously hyvelrogen-rich atmosphere is a possibilitv)., while the third has atmospheric carbon (where dredge up of interior carbon and helium in a previously hydrogen-rich atmosphere is a possibility).406 While this ratio of 1:2 (or 0:2) results from small number statistics. it may nonetheless be telling.," While this ratio of 1:2 (or 0:2) results from small number statistics, it may nonetheless be telling."407 Phe significant populations of DC ancl DZ stars. coupled with the relative lack of cool. helium-rich DA white dwarls supports a circumstellar origin. [or hyvelrogen in DZA stars.," The significant populations of DC and DZ stars, coupled with the relative lack of cool, helium-rich DA white dwarfs supports a circumstellar origin for hydrogen in DZA stars."408 Furthermore. Occam's razor favors a single mechanism that can account for all the data simultaneously: hydrogen delivered together with heavy elements in water-rich minor planets is one such possibilitv.," Furthermore, Occam's razor favors a single mechanism that can account for all the data simultaneously; hydrogen delivered together with heavy elements in water-rich minor planets is one such possibility."409 Juraet.al.(2009h) olfer this hypothesis to explain. with a single. pollution event. the collective facts available on the spectacularly metal-enriched. mixed. helium-hyelrogen atmosphere white dwarl GD 362.," \citet{jur09b} offer this hypothesis to explain, with a single pollution event, the collective facts available on the spectacularly metal-enriched, mixed helium-hydrogen atmosphere white dwarf GD 362."410 This disk-polluted. helium-rich star has an anomalously high hydrogen abundance at ΕΙΠο 5LL (Zuckermanctal.2007).. so much that it was originally Classified as DAZ (Cianninasetal.2004).," This disk-polluted, helium-rich star has an anomalously high hydrogen abundance at [H/He] $=-1.1$ \citep{zuc07}, so much that it was originally classified as DAZ \citep{gia04}."411. GD 16 is a similar case with significant atmospheric hydrogen (Ixoesterctal. and a dust disk polluting its helium-dominated atmosphere (Farihietal.2009).. while the two remaining helium-rich white dwarls with disks (ο) 40 and Ton 345) have little or no hydrogen (Juractal.2009b).," GD 16 is a similar case with significant atmospheric hydrogen \citep{koe05b} and a dust disk polluting its helium-dominated atmosphere \citep{far09a}, while the two remaining helium-rich white dwarfs with disks (GD 40 and Ton 345) have little or no hydrogen \citep{jur09b}."412. Therefore. the pattern of hydrogen. abundances in DZ stars is likely a rellection of the cliversity of water content in extrasolar planetesimals.," Therefore, the pattern of hydrogen abundances in DZ stars is likely a reflection of the diversity of water content in extrasolar planetesimals."413 Owing to the fact that radial velocities are not reliably measurable from the calcium lines in the SDSS spectra of he DZ stars. some of the derived. kinematical quantities are moclestly uncertain.," Owing to the fact that radial velocities are not reliably measurable from the calcium lines in the SDSS spectra of the DZ stars, some of the derived kinematical quantities are modestly uncertain."414 Fortunately. the galactic latitudes of the 146 stars are bound within 25<|b|75. sux »»tential biases are mild at worst.," Fortunately, the galactic latitudes of the 146 stars are bound within $25\degr < |b| 415< 75\degr$, and potential biases are mild at worst."416 For example. although he calculation. of Wo velocity. here is missing the thirc dimensional ingredient. which could. potentially alter its sign (and hence direction). anon-zero radial velocity. wil end to increase their speeds in any given. direction. 77=erpyePWSaa?2|Όμως ].," For example, although the calculation of $W$ velocity here is missing the third dimensional ingredient, which could potentially alter its sign (and hence direction), anon-zero radial velocity will tend to increase their speeds in any given direction $T^2=U^2+V^2+W^2 = {v_{\rm tan}}^2 + {v_{\rm rad}}^2$ ]."417 Moreover. the focus of the study has been statistical in nature and the global properties of the sample are unlikely to change (Paulietal.2003:Sil-vestrietal.2002) will eventually obtain distances to. and excellent proper motions for. most if not all the DZ and DC white cdwarfs. the latter stars being immune to radial velocity measurements by nature (until more powerful instruments resolve. any potential lines in their spectra).," Moreover, the focus of the study has been statistical in nature and the global properties of the sample are unlikely to change \citep{pau03,sil02}418 will eventually obtain distances to, and excellent proper motions for, most if not all the DZ and DC white dwarfs, the latter stars being immune to radial velocity measurements by nature (until more powerful instruments resolve any potential lines in their spectra)."419 Empirical distance determinations will remove anv bias. introduced with the assumption of logg=8.0. but again this is unlikely to be problematic from a statistical point of view (Ixepleret 2007)..," Empirical distance determinations will remove any bias introduced with the assumption of $\log\,g=8.0$, but again this is unlikely to be problematic from a statistical point of view \citep{kep07}. ."420 Perhaps more important is the current. understanding, Perhaps more important is the current understanding421the line will appear skewed blueward while strongly sell-absorbed sources will show two distinct peaks with the blue peak moderately to significantly brighter (han the red.,the line will appear skewed blueward while strongly self-absorbed sources will show two distinct peaks with the blue peak moderately to significantly brighter than the red.422 Large temperature gradients in the core will increase the depth of the sell-absorption feature while large velocity gradients will increase the asymmetry of the line., Large temperature gradients in the core will increase the depth of the self-absorption feature while large velocity gradients will increase the asymmetry of the line.423 Belore a source wilh a blue asvinmetric line profile can be considered a collapse eaucidate. other mechanisms for creating a blue profile must be ruled out.," Before a source with a blue asymmetric line profile can be considered a collapse candidate, other mechanisms for creating a blue profile must be ruled out."424 Spatially coincident cores that are not physically associated. rotation ancl outflows can all produce line asvametries.," Spatially coincident cores that are not physically associated, rotation and outflows can all produce line asymmetries."425 Emission from an optically thin isotopologue will peak in the middle of the absorption dip of the optically. thick line if the emission is [rom a single source., Emission from an optically thin isotopologue will peak in the middle of the absorption dip of the optically thick line if the emission is from a single source.426 Rotation and oulLows also generate double-peaked line profiles. (hough their contribution to Che line profile is more apparent with maps of sufficient spatial resolution.," Rotation and outflows also generate double-peaked line profiles, though their contribution to the line profile is more apparent with maps of sufficient spatial resolution."427 Even in (1ο absence of such maps. both rotation and outflows shoukl produce equal numbers of red and blue asvuunetric line profiles.," Even in the absence of such maps, both rotation and outflows should produce equal numbers of red and blue asymmetric line profiles."428 Because line profiles may simultaneously. include contributions [rom outflows. expansion and rotation in addition to inflow. there are conflicüng views on what constitutes unambiguous evidence for inflow (ie. Snell Loren 1977: Leung Brown 1977).," Because line profiles may simultaneously include contributions from outflows, expansion and rotation in addition to inflow, there are conflicting views on what constitutes unambiguous evidence for inflow (i.e. Snell Loren 1977; Leung Brown 1977)."429 Επομ resolution observations have spatially resolved inflowing. outflowing and rotating components for a small number of sources (e.g. Remijan Hollis 2006. IXeto Wood 2006).," High resolution observations have spatially resolved inflowing, outflowing and rotating components for a small number of sources (e.g. Remijan Hollis 2006, Keto Wood 2006)."430 Other sources are considered strong candidates for infall based. on observations of blue asvinmetries in multiple molecular lines. probing a range of densities.," Other sources are considered strong candidates for infall based on observations of blue asymmetries in multiple molecular lines, probing a range of densities."431 For a sample of sources. a statistically significant excess of blue profiles suggests that inflow may be an important physical process in determining the line prolile.," For a sample of sources, a statistically significant excess of blue profiles suggests that inflow may be an important physical process in determining the line profile."432 Previous work on infall has either focused. on detailed study. of a single source (e.g. IRAS 16293-2422. Walker et al.," Previous work on infall has either focused on detailed study of a single source (e.g. IRAS 16293-2422, Walker et al."433 1986: Menten et al., 1986; Menten et al.434 1987: Walker et al., 1987; Walker et al.435 1988: Naravanan. Walker Buckley 1998: Ceecarelli et al.," 1988; Narayanan, Walker Buckley 1998; Ceccarelli et al."436 2000: Chandler οἱ al., 2000; Chandler et al.437 2005: Remijan Hollis 2006) or statistical studies of a laree sample of sources (e.g. Mardones 2003)., 2005; Remijan Hollis 2006) or statistical studies of a large sample of sources (e.g. Mardones 2003).438 While multiple statistical studies have examined candidates for infall among low-mass stars (e.g. Mardones et al., While multiple statistical studies have examined candidates for infall among low-mass stars (e.g. Mardones et al.439 1997: Gregersen οἱ al., 1997; Gregersen et al.440 1997: Gregersen et al., 1997; Gregersen et al.441 2000: Lee Moyers 2011). the literature on higher mass candidates is less extensive and (vpically only one Kinematic tracer is analyzed (e.g. Wi Evans 2003: Fuller οἱ al.," 2000; Lee Myers 2011), the literature on higher mass candidates is less extensive and typically only one kinematic tracer is analyzed (e.g. Wu Evans 2003; Fuller et al."442 2005: Klaassen Wilson 2008: Sun Gao 2009: Cveanowski et al., 2005; Klaassen Wilson 2008; Sun Gao 2009; Cyganowski et al.443 09)., 2009).444 Massive stars form in complex environments and at higher median distances than low Inass sources. (hus features of individual cores embedded in (the larger chunp are averaged together in the single-dish beam. making infall motions harder to observe.," Massive stars form in complex environments and at higher median distances than low mass sources, thus features of individual cores embedded in the larger clump are averaged together in the single-dish beam, making infall motions harder to observe."445 Observations of high-anass clamps are also complicated by strong temperature gradients aud. outflows from the multiple cores likely embedded in (he chunp., Observations of high-mass clumps are also complicated by strong temperature gradients and outflows from the multiple cores likely embedded in the clump.446 However. eas dynamics of the clump envelope may help discriminate between proposed modes of hieh mass star formation.," However, gas dynamics of the clump envelope may help discriminate between proposed modes of high mass star formation."447 For exaniple. cores of moderate mass may grow {ο become massive stars via the global inflow of clump material because of their location deep in to the cluster potential (S10dth. Lonemore," For example, cores of moderate mass may grow to become massive stars via the global inflow of clump material because of their location deep in to the cluster potential (Smith, Longmore"448"of motion (52)) reflect this non-local property,",of motion \ref{NKG}) ) reflect this non-local property.449 Note all QO depeudoeut terms have been take iuto account., Note all $\Theta-$ dependent terms have been take into account.450 Using formula the compact expression of this ununuation of all orders of O is obtained., Using formula the compact expression of this summation of all orders of $\Theta$ is obtained.451 So. the nouperturbatiou effects of ο. expansion are included.," So, the nonperturbation effects of $\Theta-$ expansion are included."452" Comparing the uouconmnautative field equation of motion Eq.(52)) to the ordinary equation with curved space-time metric g/"" (see Eq.(13))). we obtain the effective πιοτο gi” From the above. we can solve the effective metric as Thus the quantum horizou spread las been determined."," Comparing the noncommutative field equation of motion \ref{NKG}) ) to the ordinary Klein-Gordon equation with curved space-time metric $\tu{g}^{\mu\nu}$ (see \ref{KG}) )), we obtain the effective metric $\tu{g}^{\mu\nu}$ From the above, we can solve the effective metric as where we have set $\tu{\Delta}(\omega)=\Theta453\omega/2$ .Substituting \ref{eff3}) ) into \ref{Delta}) ), we obtain follows Thus the quantum horizon spread has been determined."454 We address again that there are no additional paramcters were iutroduced in the above derivatious. aud it is esseutial that the quantum effect causes the unexpected appearance of the new horizon at r=rgtAle). at which gq vanishes.," We address again that there are no additional parameters were introduced in the above derivations, and it is essential that the quantum effect causes the unexpected appearance of the new horizon at $r=r_H\pm455\Delta(\omega)$, at which $\widetilde{g}_{tt}$ vanishes."456 In addition. note also that the gag blows up at these two points which nuply that the curvature scalar vanishes there. too.," In addition, note also that the $ \widetilde{g}_{\theta\theta} $ blows up at these two points which imply that the curvature scalar vanishes there, too."457 Therefore they are regular., Therefore they are regular.458" Note that. as also discussed in|G].. the energy w for the scalar o should not be too large. therefore A(w)=w/2-—1I,1,:/) is not larger than the Plauck length ἐν."," Note that, as also discussed in, the energy $\omega$ for the scalar $\phi$ should not be too large, therefore $\Delta(\omega)=\Theta \omega/2=l_p(l_p\omega/2)$ is not larger than the Planck length $l_p$ ."459members and core number densities ranging from 101—LO’starspe7.,"members and core number densities ranging from $10^3 - 10^6 \, {\rm stars} \, {\rm pc}^{-3}$."460 They show that an initial binary. frequency of is required to produce a current. core binary [requeney. of for a globular cluster such as 47 Tucanae., They show that an initial binary frequency of is required to produce a current core binary frequency of for a globular cluster such as 47 Tucanae.461 Depletion of binaries in the cluster core is found to be the result of stellar evolution processes as well as (hree- and fou-body dynamical interactions., Depletion of binaries in the cluster core is found to be the result of stellar evolution processes as well as three- and four-body dynamical interactions.462 It is our intention in Chis paper to test these claims bv utilising direct N-bodxy simulations of star clusters wilh up to N=100000 members initially.," It is our intention in this paper to test these claims by utilising direct $N$ -body simulations of star clusters with up to $N = 100\,000$ members initially."463 One aspect that will affect the evolution of the cluster binary population is the orbital parameters of the primordial binaries in particular the initial ratio ofhard tosoft binaries., One aspect that will affect the evolution of the cluster binary population is the orbital parameters of the primordial binaries – in particular the initial ratio of to binaries.464 The boundary between these (wo regimes is determined by the mean kinetic energv of the cluster stars (with binaries represented by their center-of-mass motion) where hard binaries have a binding energv in excess of 2/3 of the mean kinetic energy. (Ilut et al., The boundary between these two regimes is determined by the mean kinetic energy of the cluster stars (with binaries represented by their center-of-mass motion) where hard binaries have a binding energy in excess of 2/3 of the mean kinetic energy (Hut et al.465 1992)., 1992).466 We nole that a useful estimate lor the boundary in terms of the binary orbital separation is given by twice the cluster hall-mass radius divided bv. IN., We note that a useful estimate for the boundary in terms of the binary orbital separation is given by twice the cluster half-mass radius divided by $N$.467 In three-body singlebinary star interactions hard binaries tend to harden aud provide kinetic heating lor the cluster (ILegeie 1975: IIut. 1983)., In three-body single–binary star interactions hard binaries tend to harden and provide kinetic heating for the cluster (Heggie 1975; Hut 1983).468 Soft binaries are less strongly bound (and thus on average are wider) and are efficientlv destroved in Chree- and four-body encounters., Soft binaries are less strongly bound (and thus on average are wider) and are efficiently destroyed in three- and four-body encounters.469 As noted by Hut et al. (, As noted by Hut et al. (4701992) it is for this reason that soft binaries are not generally included in cluster models.,1992) it is for this reason that soft binaries are not generally included in cluster models.471 A common misconception is that the omission of soft binaries is to aid the speed of simulation: however ibis binaries near the hard/soft boundary (hat provide (he main threat to efficient simulation (Aarseth 2003)., A common misconception is that the omission of soft binaries is to aid the speed of simulation; however it is binaries near the hard/soft boundary that provide the main threat to efficient simulation (Aarseth 2003).472 The omission is more a realisation that soft binaries have little impact on the cluster dvnamics or exotic star formation and so the locus is on the moremeaningful binaries. so (o speak.," The omission is more a realisation that soft binaries have little impact on the cluster dynamics or exotic star formation and so the focus is on the more binaries, so to speak."473 Neglecting soft binaries has the capacity to aller binary fractions in the halo of a model cluster as binary encounters tend to occur in or near the cluster core., Neglecting soft binaries has the capacity to alter binary fractions in the halo of a model cluster as binary encounters tend to occur in or near the cluster core.474 For this reason we will attempt to account lor any omitted soft binary populations when making binary fraction comparisons., For this reason we will attempt to account for any omitted soft binary populations when making binary fraction comparisons.475 Our simulation method and initial conditions are detailed in Sections 2 ancl 3., Our simulation method and initial conditions are detailed in Sections 2 and 3.476 Results are given in Section 4 followed by discussion in Section 5., Results are given in Section 4 followed by discussion in Section 5.477 We briefly summarize our results in Section 6., We briefly summarize our results in Section 6.478 All simulations utilized in this work were performed using the code (Aarseth 1999) on GRAPE-G boards (Makino 2002) located at the American Museum of Natural ]listory., All simulations utilized in this work were performed using the code (Aarseth 1999) on GRAPE-6 boards (Makino 2002) located at the American Museum of Natural History.479 uses the 4th-order Hermite integration scheme and an individual timestep algorithm (o follow the orbits of cluster members and invokes regularization schemes to deal with the internal evolution of small-/N. subsvstems (see Aarseth 2003 for details)., uses the 4th-order Hermite integration scheme and an individual timestep algorithm to follow the orbits of cluster members and invokes regularization schemes to deal with the internal evolution of $N$ subsystems (see Aarseth 2003 for details).480 Stellar and, Stellar and481MAST archive.,MAST archive.482 Ifa version 2 catalog of ACS sources is produced we will attempt to provide a version 2.1 catalog with the new ACS source identifications included., If a version 2 catalog of ACS sources is produced we will attempt to provide a version 2.1 catalog with the new ACS source identifications included.483 Columns 5 and 6 give the x and v positions in pixels of (he source in the version 2.0 {reastiry image., Columns 5 and 6 give the x and y positions in pixels of the source in the version 2.0 treasury image.484 Columns 7 and 3 are the RA and DEC positions in degrees while columns 9 and 10 are the RA and DEC position in traditional nomenclature., Columns 7 and 8 are the RA and DEC positions in degrees while columns 9 and 10 are the RA and DEC position in traditional nomenclature.485 Columns 11-28 give the aperture AB magnitudes of the source., Columns 11-28 give the aperture AB magnitudes of the source.486 The 3 aperture magnitudes of the ACS F445W band are listed first followed by the remaining ACS and NICMOS bands in order of wavelength., The 3 aperture magnitudes of the ACS F445W band are listed first followed by the remaining ACS and NICMOS bands in order of wavelength.487 Columns 29 (through 34 list the isophotal magnitudes and columns 35Hr through 40 list auto nagnitudes returned by SE in the same order., Columns 29 through 34 list the isophotal magnitudes and columns 35 through 40 list auto magnitudes returned by SE in the same order.488 Column 41 lists (he number of pixels associated with the source in the SE segmentation image., Column 41 lists the number of pixels associated with the source in the SE segmentation image.489 Columns 42 through 47 list the FWHAL in each band., Columns 42 through 47 list the FWHM in each band.490 Column 48 Lists the position angle of the source returned by SE., Column 48 lists the position angle of the source returned by SE.491 Column 49 lists the flag value returned by SE., Column 49 lists the flag value returned by SE.492 No sources iive been removed [rom the catalog on the basis of the value of the SE error flag., No sources have been removed from the catalog on the basis of the value of the SE error flag.493 Columns 50-55 list the NPEAIK. YPEARN. NMIN. YMIN. XATANanc YMAX values returned by SE.," Columns 50-55 list the XPEAK, YPEAK, XMIN, YMIN, XMAX,and YMAX values returned by SE."494 The source is contained in a box defined bx the minimum and maximum x and v values., The source is contained in a box defined by the minimum and maximum x and y values.495 Columns 56 and 57 give the ellipticity ancl elongation of the source returned by SE., Columns 56 and 57 give the ellipticity and elongation of the source returned by SE.496" Column 58 contains the 0.6"" diameter aperture AD magnitude of the FIGOW band.", Column 58 contains the $0.6\arcsec$ diameter aperture AB magnitude of the F160W band.497 Colhunns 59-76 contain (he aperture fluxes in the same order as the aperture magnitudes., Columns 59-76 contain the aperture fluxes in the same order as the aperture magnitudes.498 The fluxes are in ADU/sec., The fluxes are in ADU/sec.499 The NICMOS gain is 6.5 electrons per ADU., The NICMOS gain is 6.5 electrons per ADU.500 Columns 77 through S2 list (he isophotal fluxes and columns 82 through 88 Hist. auto fluxes returned by SE., Columns 77 through 82 list the isophotal fluxes and columns 83 through 88 list auto fluxes returned by SE.501 Columns 89 and 90 are the ISOAREA and ISOFAREA values returned by SE., Columns 89 and 90 are the ISOAREA and ISOFAREA values returned by SE.502 To be consistent with the ACS UDF submissions we have also constructed a mini-catalog of the sources. part of which is included in (he printed version of the paper.," To be consistent with the ACS UDF submissions we have also constructed a mini-catalog of the sources, part of which is included in the printed version of the paper."503 The whole catalog is avallable in the electronic version of the paper., The whole catalog is available in the electronic version of the paper.504 The catalog appears in Table 8.., The catalog appears in Table \ref{tab-cat}.505 There are some differences relative to the ACS catalog available in \LAST., There are some differences relative to the ACS catalog available in MAST.506 First the catalog is ordered in RA with the associated ACS source ID and the segmentation ID in columns 2 and 3., First the catalog is ordered in RA with the associated ACS source ID and the segmentation ID in columns 2 and 3.507 The x and v positions followed bv the RA and DEC in degrees are in columns 4-7., The x and y positions followed by the RA and DEC in degrees are in columns 4-7.508 Next are (he position angle. ellipticity. half radius. EWIIM ancl κοαν in columns 8-12.," Next are the position angle, ellipticity, half radius, FWHM and stellarity in columns 8-12."509 These are followed by the isophotal magnitude.isophotal magnitude error. aud signal to noise for the 4 ACS and 2 NICMOS bands starting with the AC'S F435W and ending with the NICMOS F160W band.," These are followed by the isophotal magnitude,isophotal magnitude error, and signal to noise for the 4 ACS and 2 NICMOS bands starting with the ACS F435W and ending with the NICMOS F160W band."510 The signal to noise is the ratio of the isophotoal fhix to the isophotal [Iux error returned by SE., The signal to noise is the ratio of the isophotoal flux to the isophotal flux error returned by SE.511 The last entry in the table is the value of the error flag returned by SE., The last entry in the table is the value of the error flag returned by SE.512 As, As513]xongetal.(2004) have analvzed the 2004 July spectra of uusing the absorbed blackbody model. inferred a bolometric luminosity of ~107 and concluded that nunust contain an IMDIL.,"\citet{KDY2004} have analyzed the 2004 July spectra of using the absorbed blackbody model, inferred a bolometric luminosity of $\sim 10^{41}$, and concluded that must contain an IMBH."514 Using the Eddington luminosity argument. ~10H ccorresponds to a minimunm mass of TOO M...," Using the Eddington luminosity argument, $\sim 10^{41}$ corresponds to a minimum mass of 700 $_\odot$."515 However. our spectral analvsis above makes il clear (hat this conclusion is highly model-dependent.," However, our spectral analysis above makes it clear that this conclusion is highly model-dependent."516 We argue. moreover. that the absorbed blackbody fits have (vo shortcomings: the requirement for a neutral absorber next to a 2 107 ΝΑγαλ source. aid (he counterintuitüve trend of fitted parameters against ccount rate.," We argue, moreover, that the absorbed blackbody fits have two shortcomings: the requirement for a neutral absorber next to a $>$ $^{40}$ X-ray source, and the counterintuitive trend of fitted parameters against count rate."517 As noted earlier. the high ancl variable values of the X-ray absorber in the absorbed blackhody fits relt rend)) require the absorber to be in the vicinity of iltself.," As noted earlier, the high and variable values of the X-ray absorber in the absorbed blackbody fits \\ref{trend}) ) require the absorber to be in the vicinity of itself."518 Whereas the presence of such intva- or cireum-binary material is expected. due to the Copious mass loss from (he supergiant mass donor. it is likely to be highly ionized on average (see. e.g.. Wojdowskietal. 2000)). even when the luminosity is a few times 10 |: much more so if the bolometric luminosity is near LOM|.," Whereas the presence of such intra- or circum-binary material is expected, due to the copious mass loss from the supergiant mass donor, it is likely to be highly ionized on average (see, e.g., \citealt{Wea2000}) ), even when the luminosity is a few times $^{38}$ ; much more so if the bolometric luminosity is near $^{41}$."519 While high density chumps with lower (han average ionization are expected. we need extreme clumping to explain the observed absorber.," While high density clumps with lower than average ionization are expected, we need extreme clumping to explain the observed absorber."520 For example. for a chunp “em from a LO! ssource {ο have £<1. a density greater than LO’ em? is recuired: for such a clump to be responsible [or the observed. X-ray absorption of ~2x10?!7. ib must have a length of only ~2x109 em.," For example, for a clump $^{13}$ cm from a $^{41}$ source to have $\xi < 1$, a density greater than $^{15}$ $^{-3}$ is required; for such a clump to be responsible for the observed X-ray absorption of $\sim 2 \times 10^{21}$, it must have a length of only $\sim 2 \times 10^6$ cm."521 A clump at a distance of 1012 cm needs a density >LO! ? and a length of ~2x10 om., A clump at a distance of $^{15}$ cm needs a density $> 10^{11}$ $^{-3}$ and a length of $\sim 2 \times 10^{10}$ cm.522 That is. for such a chump to remain neutral. it must have a high overdensity factor. ancl hence a small filling factor.," That is, for such a clump to remain neutral, it must have a high overdensity factor, and hence a small filling factor."523 We therefore consider (he inferred neutrality of the X-ray absorber to be a severe problem [for the absorbed blackbody interpretation., We therefore consider the inferred neutrality of the X-ray absorber to be a severe problem for the absorbed blackbody interpretation.524 This model also leads to a counterintuitive trend with observed count rate rend: rendtab)). whereas our alternative spectral model does not suffer from this problem.," This model also leads to a counterintuitive trend with observed count rate \\ref{trend}; \\ref{trendtab}) ), whereas our alternative spectral model does not suffer from this problem."525 We do not necessarily claim (hat our model is the correct. physical description ofl., We do not necessarily claim that our model is the correct physical description of.526. Nevertheless. it is comforting to note that a simple analvtcal model. with a physical interpretation (relaiivistic emission line from (he accretion disk) can fit the collection of hieh state spectra without requiring an anti-correlation between observed count rate and bolometrie luminosity. or the presence of a neutral absorber within an ULXsvstem.," Nevertheless, it is comforting to note that a simple analytical model, with a physical interpretation (relativistic emission line from the accretion disk) can fit the collection of high state spectra without requiring an anti-correlation between observed count rate and bolometric luminosity, or the presence of a neutral absorber within an ULXsystem."527 [t is «quite possible that other models can be found that can fit the available data equally well., It is quite possible that other models can be found that can fit the available data equally well.528"by Bardecu. Bond and Efstathiou ?"".. then applied. for the by-uow dead 17 keV neutrino by Boud and Efstathiouστ...","by Bardeen, Bond and Efstathiou \cite{bardeen}, then applied for the by-now dead 17 keV neutrino by Bond and Efstathiou \cite{bond}."529" After the CODE data. it was first considered by Chun ὃν, aud this idea was later applied to νο by others 77."," After the COBE data, it was first considered by Chun \cite{ckk}, and this idea was later applied to $\nu_\tau$ by others \cite{others}."530 For the structure formation. the radiationanatter equality poiut Ree is iuportant.," For the structure formation, the radiation-matter equality point $R_{EQ}$ is important."531 At Ree the structure scale Age is given by A lighto axino decays to an axion aud a oeravitino via the interaction ogiven in Eq.| (, At $R_{EQ}$ the structure scale $\lambda_{EQ}$ is given by A light axino decays to an axion and a gravitino via the interaction given in Eq. (5327).,7).533 Normally. one would expect] a couplingpling supressedsuj by MjAfp. but the Goldstino conrponeut dominates whose coupling is supressed by Fs.," Normally, one would expect a coupling supressed by $M_P$, but the Goldstino component dominates whose coupling is supressed by $F_S$ ."534 Naimcly. the eravitino coupling is of the form (1PVoft where J is the supercurrenut.," Namely, the gravitino coupling is of the form $(1/F_S)(\partial_\mu\xi)535J^\mu$ where $J^\mu$ is the supercurrent."536 In this case. the axino lifetime is eiven iu Eq. (," In this case, the axino lifetime is given in Eq. ("5378).,8).538 The detail οπσον deusities of respective species are eiven in Fie., The detail energy densities of respective species are given in Fig.539 2., 2.540 When the cosmic scale factor exceeds Reo. 0 dominates the mass deusity of the universe.," When the cosmic scale factor exceeds $R_{EQ1}$, $\tilde a$ dominates the mass density of the universe."541 The cold axion dominates the energy density of the universe after the scale factor exceeds ego»., The cold axion dominates the energy density of the universe after the scale factor exceeds $R_{EQ2}$.542 In Fig., In Fig.543 3. Ree is the radiatiou- matter equality point inthe CDM model.," 3, $R_{EQ}$ is the radiation- matter equality point inthe CDM model."544 Thus. the axino-eravitino cosmology extends," Thus, the axino-gravitino cosmology extends"545While recent studies based on the molecular line data of the GRS have generated a census of molecular clouds in the Galactic plane (e.g..Jacksonetal.2006:Rathborne2009;Roman-Duvaletal. 2010).. the dust extinction maps cat provide a mass tracer for these clouds extending over a clearly wider dynamical range than the CO data.,"While recent studies based on the molecular line data of the GRS have generated a census of molecular clouds in the Galactic plane \citep[e.g.,][]{jac06, rat09, rom10}, the dust extinction maps can provide a mass tracer for these clouds extending over a clearly wider dynamical range than the CO data."546 Most importantly. the dynamical range will overlap with that of higher columi density tracers (especially thermal dust emission). allowing combining the information from the two tracers.," Most importantly, the dynamical range will overlap with that of higher column density tracers (especially thermal dust emission), allowing combining the information from the two tracers."547 Such ar approach ean provide column density data extending from low column density envelope material to gravitationally dominatec objects in the clouds., Such an approach can provide column density data extending from low column density envelope material to gravitationally dominated objects in the clouds.548 Thereby. the data sets together can be used to reveal the detailed mass distributions surrounding the progenitors of high-mass stars. and we will continue towards deriving such data in forthcoming work.," Thereby, the data sets together can be used to reveal the detailed mass distributions surrounding the progenitors of high-mass stars, and we will continue towards deriving such data in forthcoming work."549 In this paper. we examined the feasibility of NIR dust extinction mapping technique in tracing low-to-intermediate column density structures surrounding prospective birthplaces of high-mass stars. re. IRDCs.," In this paper, we examined the feasibility of NIR dust extinction mapping technique in tracing low-to-intermediate column density structures surrounding prospective birthplaces of high-mass stars, i.e., IRDCs."550 We used the data from the UKIDSS/Galactic Plane Survey to derive dust extinction through 10 cloud complexes at thedistances between ~2.5—8 kpe. harboring altogether hundreds of IRDCs.," We used the data from the UKIDSS/Galactic Plane Survey to derive dust extinction through 10 cloud complexes at thedistances between $\sim 2.5-8$ kpc, harboring altogether hundreds of IRDCs."551 We compared the derived NIR extinction. maps to the CO molecular line data from the Boston University-FCRAO Galactic Ring Survey. 8 jm dust opacity data from a recently published Spitzer IRDC catalogue by Peretto&Fuller(2009).. and to 870 jum dust emission data from the ATLASGAL survey (Schulleretal. 2009)..," We compared the derived NIR extinction maps to the $^{13}$ CO molecular line data from the Boston University-FCRAO Galactic Ring Survey, 8 $\mu$ m dust opacity data from a recently published Spitzer IRDC catalogue by \citet{per09}, and to 870 $\mu$ m dust emission data from the ATLASGAL survey \citep{sch09}. ."552 The conclusions of our work are as follows., The conclusions of our work are as follows.553"outputs (E-,is,) that are 1-2 orders of magnitude larger than that of theSwift bursts ","outputs $E_{\gamma,iso}$ ) that are 1-2 orders of magnitude larger than that of the bursts (Figure \ref{fig:eiso}) )."554"Given the well known correlations between Ej«4; (Figureand 8)). (??),, and the hardness of LAT GRB spectra required Ey,isofor them to be detected by LAT at all, their large Ej,;,5's are not surprising."," Given the well known correlations between $E_{peak}$ and $E_{\gamma,iso}$ \citep{amati02,amati06}, and the hardness of LAT GRB spectra required for them to be detected by LAT at all, their large $E_{\gamma,iso}$ 's are not surprising."555 This suggests to us that the LAT is preferentially detecting extremely energetic GRBs compared to previous GRB experiments., This suggests to us that the LAT is preferentially detecting extremely energetic GRBs compared to previous GRB experiments.556" The sensitivity, large field of view, and large energy range of the LAT make it especially sensitive to hard bursts."," The sensitivity, large field of view, and large energy range of the LAT make it especially sensitive to hard bursts."557" While the physical origin of the Amati relation is not well understood, the energetic LAT bursts seem to qualitatively follow the same relationship."," While the physical origin of the Amati relation is not well understood, the energetic LAT bursts seem to qualitatively follow the same relationship."558" Applying our characterizations of the optical and X-ray light curves and SEDs to the energetics, we can infer jet half-opening angles and collimation-corrected -ray energy outputs or limits when all observations were either pre- or (E),post-jet break."," Applying our characterizations of the optical and X-ray light curves and SEDs to the energetics, we can infer jet half-opening angles and collimation-corrected $\gamma$ -ray energy outputs $E_{\gamma}$ ), or limits when all observations were either pre- or post-jet break."559" Again, the methods used in these calculations and jet break determination are described in detail in ?.."," Again, the methods used in these calculations and jet break determination are described in detail in \cite{racusin09}."560" Using the XRT and UVOT data alone, most of the LAT GRB afterglow light curves discussed below) are best characterized by single(exceptions power laws, with relatively flat slopes (ao;< 1.8), with the exception of the poorly sampled GRB 100414A which may have had a break in the large gap between observations, and the short GRB 090510 which shows an early break to a steep - a behavior suggestive of a “naked” short hard burst decay(?) that indicates the turnoff of the prompt emission in a low environment with either an afterglow too faint to densitydetect or no afterglow at all."," Using the XRT and UVOT data alone, most of the LAT GRB afterglow light curves (exceptions discussed below) are best characterized by single power laws, with relatively flat slopes $\alpha_{o,x}\lesssim 1.8$ ), with the exception of the poorly sampled GRB 100414A which may have had a break in the large gap between observations, and the short GRB 090510 which shows an early break to a steep decay - a behavior suggestive of a “naked” short hard burst \citep{kumar00} that indicates the turnoff of the prompt emission in a low density environment with either an afterglow too faint to detect or no afterglow at all."561" However, ?| discussed the possibility that the break in the optical and X-ray light curves of GRB 090510 at ~2000 seconds is an early jet break, rather than a naked afterglow (i.e. steep fall off is either high latitude emission or post-jet break)."," However, \cite{depasquale10} discussed the possibility that the break in the optical and X-ray light curves of GRB 090510 at $\sim5622000$ seconds is an early jet break, rather than a naked afterglow (i.e. steep fall off is either high latitude emission or post-jet break)."563" The following calculations use the jet break assumption, but we recommend caution when examining the energetics of this GRB."," The following calculations use the jet break assumption, but we recommend caution when examining the energetics of this GRB."564" The LAT optical light curves, where sampled well, show shallow behavior or contamination at late times by the host galaxy or nearby sources."," The LAT optical light curves, where sampled well, show shallow behavior or contamination at late times by the host galaxy or nearby sources."565 This is consistent with the idea that most of the LAT afterglow observations are pre-jet break the exceptions noted above)., This is consistent with the idea that most of the LAT afterglow observations are pre-jet break (with the exceptions noted above).566" Several recent papers (with(??7)| suggest that when using other broadband observations (including deep late optical/NIR observations), some of these bursts do hint at jet breaks, but theSwift data alone are insufficient to constrain jet breaks."," Several recent papers \citep{mcbreen10,cenko10,swenson10} suggest that when using other broadband observations (including deep late optical/NIR observations), some of these bursts do hint at jet breaks, but the data alone are insufficient to constrain jet breaks."567 We will discuss the differences in jet breaks and energetics between this paper and those of ??? further in Section 4..," We will discuss the differences in jet breaks and energetics between this paper and those of \cite{mcbreen10,cenko10,swenson10} further in Section \ref{sec:disc}."568" If we assume all of the LAT GRBs are pre-jet break (except for GRB 100414A, which may be post jet break,"," If we assume all of the LAT GRBs are pre-jet break (except for GRB 100414A, which may be post jet break,"569with pseudostates (RAIPS. 73) approaches.,"with pseudostates (RMPS, \citealt{0953-4075-29-1-015}) ) approaches."570 The advantage of the CCC aethod is that. at least for collision systems with two electrons. it has heen shown o vield convergent results as basis size is increased: rowever. it has the disadvantage of requiug cousiderable computational effort.," The advantage of the CCC method is that, at least for collision systems with two electrons, it has been shown to yield convergent results as basis size is increased; however, it has the disadvantage of requiring considerable computational effort."571 The advantage of the RAIPS method is that the R-matrix is calculated once aud then results or mnanyv collision energies can be caleulated with little additional effort., The advantage of the RMPS method is that the $R$ -matrix is calculated once and then results for many collision energies can be calculated with little additional effort.572 This is particularly imiportaut for the study of resonances requiring dense euergv ericls., This is particularly important for the study of resonances requiring dense energy grids.573" The disadvantage, however. is that convergence with basis size can be slower resulting iu the appearance of pseudo-FOROMALLECS."," The disadvantage, however, is that convergence with basis size can be slower resulting in the appearance of pseudo-resonances."574" ? have published data frou extensive L-state CCC calculations for trausitious with »<3 and »zx L and inchide senu-enrpirieal cross sections for àsΞ-|. vos|,"," \citet{CCC} have published data from extensive 45-state CCC calculations for transitions with $n\le 3$ and $n^\prime \le 4$ , and include semi-empirical cross sections for $n=4$, $n^\prime=4$."575 The calculations show good agreement with experiaenuts where available. and analytic fits to the cross section data are provided.," The calculations show good agreement with experiments where available, and analytic fits to the cross section data are provided."576 ? have done calculations uxiug a 55-state RAIPS approach resultingin cross section data for alb transitions with no-— 27=0 aud ο d.," \cite{Griffin2001} have done calculations using a 55-state RMPS approach resultingin cross section data for all transitions with $n=2$, $l=0$ and $n^\prime \le$ 4."577" Ther caleulatious demonstrate the importance of including the coupling to the target continu via pseudostates; particularly at collidouns energies greater thau the lonizatlon enerev. he. 25.45.1] eV where the effects are σα] for 2s»2p. but become significant for 2s>3M and even greater for 2s.»141,"," Their calculations demonstrate the importance of including the coupling to the target continuum via pseudostates, particularly at collisions energies greater than the ionization energy, i.e. $> 5.4$ eV, where the effects are small for $2s\rightarrow 2p$, but become significant for $2s\rightarrow 3l$ and even greater for $2s\rightarrow 4l$."578 The cross sections are in good agreement with the CCC and experiuenutal results where compared., The cross sections are in good agreement with the CCC and experimental results where compared.579 Since there is a possibility that resonances at low collision euergies are unresolved ly the CCC caleulatious aud. could contribute significantly to the rate coefficients. we performed our own RAIPS caleulatious foy p< Landa’€ IL and »'/=Ss. which eives the additional advantage of an iudepenudoeut check.," Since there is a possibility that resonances at low collision energies are unresolved by the CCC calculations and could contribute significantly to the rate coefficients, we performed our own RMPS calculations for $n \le$ 4 and $n^\prime \le$ 4 and $n^\prime l^\prime = 5s$, which gives the additional advantage of an independent check."580 These calculations are described below in Sect., These calculations are described below in Sect.581 2.1.1. aud compared with the existing data in Sect. 2.1.2., \ref{sect:rmat} and compared with the existing data in Sect. \ref{sect:res}.582 As mentioned above. the rate coefficieuts. calculated we? have been used du iuost calculations of nou-LTE formation of Li I lines in cool stars (7277?7).. so hey represent an important basis for comparison in this work.," As mentioned above, the rate coefficients calculated by \citet{Park1971} have been used in most calculations of non-LTE formation of Li I lines in cool stars \citep{1984A&A...130..319S,1994A&A...288..860C, Lind2009,2010A&A...522A..26S,2005PASJ...57...45T}, so they represent an important basis for comparison in this work."583 ? replaced the data of the important 2s}2p transition with that of 7.., \citet{1984A&A...130..319S} replaced the data of the important $2s\rightarrow 2p$ transition with that of \citet{1962ApJ...136..906V}.584 Both these sources are oed on Born approximation calculations. which are well known to be valid only at hieh impact cuereics aud to substantially overestimate the cross sections near hreshold.," Both these sources are based on Born approximation calculations, which are well known to be valid only at high impact energies and to substantially overestimate the cross sections near threshold."585 Thus. enipirical corrections determined frou various experiments are applied.," Thus, empirical corrections determined from various experiments are applied."586 Based on comparison with the experumeuts. both works conclude that the calculated rates are not likely to be iu error by more than a factor of two.," Based on comparison with the experiments, both works conclude that the calculated rates are not likely to be in error by more than a factor of two."587 We mace a 3l-state RAIPS calculation ofthe excitation by electron impacts. using existing freely available computer codes.," We made a 34-state RMPS calculation ofthe excitation by electron impacts, using existing freely available computer codes."588 These calculations will now be described., These calculations will now be described.589 For the initial atomic structure calculations we used he code (??:: see also 2)). which is an adaptation of (?) that allows the construction of polarization o»eudostates;," For the initial atomic structure calculations we used the code \citealt{civpol_thesis,CIVPOL}; see also \citealt{2004JPhB...37.2979P}) ), which is an adaptation of \citep{CIV3} that allows the construction of polarization pseudostates."590 Such pseudostates are used to account for coupling to the target coutinuuu aud are needed: to obtain a correct description of the dipole polarization and lus the long-range interaction potential., Such pseudostates are used to account for coupling to the target continuum and are needed to obtain a correct description of the dipole polarization and thus the long-range interaction potential.591 They have beeu shown by ? to be inmportaut at intermediate cuergics., They have been shown by \citet{Griffin2001} to be important at intermediate energies.592 and use the configuration iuteraction (CT) uethod auc the radial parts of the (pseudo) orbitals are represcuted by Slater-tvpe orbitals: for details sec and ὃν, and use the configuration interaction (CI) method and the radial parts of the (pseudo) orbitals are represented by Slater-type orbitals; for details see and \cite{CIVPOL}.593 The atomic structure of the target Li Twas built bv optinisiug spectroscopic orbitals with all allowed 5» values up tow=Sf: the 15 aud 2s orbitals were Hartrec-Fock orbitals taken fromο, The atomic structure of the target Li I was built by optimising spectroscopic orbitals with all allowed $nl$ values up to $nl=5f$; the $1s$ and $2s$ orbitals were Hartree-Fock orbitals taken from.594"ν, The energies obtained for the ten lowest-lving spectroscopic states are compared with experimental values taken from the NIST. Atomic Spectra Database (2). in Table 1.. and the agreement is satisfactory."," The energies obtained for the ten lowest-lying spectroscopic states are compared with experimental values taken from the NIST Atomic Spectra Database \citep{NIST} in Table \ref{energy}, and the agreement is satisfactory."595" Ouce the spectroscopic orbitals (aud states) were calculated. we added 09= 66s.p. d) aud. T(s. p.d) pseudo-orbitals to describe the polarization of the erouud aud first excited state. respectively,"," Once the spectroscopic orbitals (and states) were calculated, we added $n=6$ $s,p,d$ ) and $s,p,d$ ) pseudo-orbitals to describe the polarization of the ground and first excited state, respectively."596 To test the quality of he polarization pseudostates. we compared the static dixe polarizabilities obtained with experimental and heoretical values found iu the literature. see Table 2..," To test the quality of the polarization pseudostates, we compared the static dipole polarizabilities obtained with experimental and theoretical values found in the literature, see Table \ref{polar}."597 For the polarization of the erounc state there is good agreement between OUL results and those frou the iterature., For the polarization of the ground state there is good agreement between our results and those from the literature.598 In the case of the polarizability of the first excited state. we found only one otherheoretical result (2).. where the polarizability is calculated in the Coulonib approximation.," In the case of the polarizability of the first excited state, we found only one othertheoretical result \citep{PolThe-a}, , where the polarizability is calculated in the Coulomb approximation."599 The computed orbitals were then used in a RAIPS calculation of the clectrou-impact excitation cross sectious., The computed orbitals were then used in a RMPS calculation of the electron-impact excitation cross sections.600 The code (2). was used for the internal region problem. and for the external region problem we," The code \citep{InnerRmatrix} was used for the internal region problem, and for the external region problem we"601officicney ΟΕ=0.05 the mass accretion rate is estimated to be AL~0.0035 ovear i. 10% of the Eddinetou accretion rate.,"efficiency $\eta^{\rm BOL} = 0.05$ the mass accretion rate is estimated to be $\dot{M} \simeq 0.0035$ $_\odot$ $^{-1}$, $\sim 10$ of the Eddington accretion rate."602" For such high accretion rates the transition from thin disk to an advection-dominated accretion flow may occur anywhere up to a radius of ~2000r, (7) aud so our fitted radius is consisteut with sucli à scenario.", For such high accretion rates the transition from thin disk to an advection-dominated accretion flow may occur anywhere up to a radius of $\sim 2000 r_g$ \citep{narayan98a} and so our fitted radius is consistent with such a scenario.603 If features ou the truncated edge of the disk are steady in fux. as found for the Bine in NCC 1051. heu Galactic biuaries would also be expected o show such lines iu the low flux state aud the absence of such would cistavor the txuucated disk oriein for the lines.," If features on the truncated edge of the disk are steady in flux, as found for the line in NGC 4051, then Galactic binaries would also be expected to show such lines in the low flux state and the absence of such would disfavor the truncated disk origin for the lines."604 While similar lines have not oen reported to date for Galactic black hole vnaries (see7.forareview)... constraints on such ies have not vet been explored in that source class. leaving this au open question.," While similar lines have not been reported to date for Galactic black hole binaries \citep[see][for a review]{done07b}, constraints on such lines have not yet been explored in that source class, leaving this an open question."605 Tn an alternative ποσο]. the fact that the specific euergev of the line is coincident with Ίνα Cluission from neutral Cr kkeV) prompts a renewed iuterest in the spallation of Fe as a mechanisin for cuhancine otherwise weak Lincs. especially since PCA is consistent with a common origin for the new line and the neutral compoucut of Fe.," In an alternative model, the fact that the specific energy of the line is coincident with $\alpha$ emission from neutral Cr keV) prompts a renewed interest in the spallation of Fe as a mechanism for enhancing otherwise weak lines, especially since PCA is consistent with a common origin for the new line and the neutral component of Fe."606 Tn à companion paper. ?).. explore in detail the spallation imterpretation of the new result. extending the work of ?) in the light of new nuderstanding about the cuvirous of active nuclei.," In a companion paper, \citet{turner09c}, explore in detail the spallation interpretation of the new result, extending the work of \citet{skibo97} in the light of new understanding about the environs of active nuclei."607 7) fined the observed abundance eubaucemoent o be high auc that these extreme cuhaucement effects are most likely to be achieved iu gas out of he plane of the accretion disk., \citet{turner09c} find the observed abundance enhancement to be high and that these extreme enhancement effects are most likely to be achieved in gas out of the plane of the accretion disk.608 In such a picture. he timescale for spallation may be as short as a ‘ew vears if the cosmic ray output is comparable o the bolometric output of the nucleus;," In such a picture, the timescale for spallation may be as short as a few years if the cosmic ray output is comparable to the bolometric output of the nucleus."609 ο) also estimate the expected radio aud >reg fiux from he proposed spallation process iu NGC 1051 and fund preciictions to be consistent with current fiux neasurements iu those bauds., \citet{turner09c} also estimate the expected radio and $\gamma-ray$ flux from the proposed spallation process in NGC 4051 and find predictions to be consistent with current flux measurements in those bands.610 Our analvsis of data fom NGC 1051 aken during 2005 and 2008 has revealed line cluission at S.likkeV iu the rest-frame of the ealaxv., Our analysis of data from NGC 4051 taken during 2005 and 2008 has revealed line emission at keV in the rest-frame of the galaxy.611 We have established. the reality of the ine at >99.9% confidence in data from 2005. supported by Monte Carlo simulations that show he probability. of the Lue beiug a statistical diuctuation is p<3.310L," We have established the reality of the line at $>99.9\%$ confidence in data from 2005, supported by Monte Carlo simulations that show the probability of the line being a statistical fluctuation is $p < 3.3 \times 10^{-4}$."612 The possibility of the line arising from a statistical fluctuation in the spectral data has been firmly ruled out by establishing its detection iu time-sliced data., The possibility of the line arising from a statistical fluctuation in the spectral data has been firmly ruled out by establishing its detection in time-sliced data.613 Further to this. we have confirmed the line to be evident in all three NIS units independently. aud established that the observed line is inconsistent with arising from the X-ray background.," Further to this, we have confirmed the line to be evident in all three XIS units independently, and established that the observed line is inconsistent with arising from the X-ray background."614 The source spectrum varies with flux. aud the low state is donuünated by a hard spectral form with the new line plus the neutral comiponeut of Fe Ίνα emission superimiposed upon that. suggestive of a conmion origin for both.," The source spectrum varies with flux, and the low state is dominated by a hard spectral form with the new line plus the neutral component of Fe $\alpha$ emission superimposed upon that, suggestive of a common origin for both."615 The line has au equivalent width during 2005 of about 15 eV while he Fe Ko line is measured at 195 eV. These reprocessed signatures show up prominently in tle source low state when the coutinuua is suppressed x the highest covering fraction of absorption., The line has an equivalent width during 2005 of about 45 eV while the Fe $\alpha$ line is measured at 195 eV. These reprocessed signatures show up prominently in the source low state when the continuum is suppressed by the highest covering fraction of absorption.616 As disk hotspot emission would be expected ο vary in flux and energy over relatively short iuescales. the Linits on line variability disfavor lis particulay originOo althoughC» the data remain consistent with enmüssion from a special location such as the innermost radius of the accretion disk.," As disk hotspot emission would be expected to vary in flux and energy over relatively short timescales, the limits on line variability disfavor this particular origin although the data remain consistent with emission from a special location such as the innermost radius of the accretion disk."617 The alternative picture. that the lue is Cr Ka cluission following spallation of Fe is also found to bea good explanation of the data: that possibility and its duplications are explored in a companion paper.," The alternative picture, that the line is Cr $\alpha$ emission following spallation of Fe is also found to be a good explanation of the data: that possibility and its implications are explored in a companion paper."618 TIT acknowledges NASA evant NNNOSALHSOC. LM acknowledges STFC erant προ PP/EO001111/1., TJT acknowledges NASA grant NNX08AL50G. LM acknowledges STFC grant number PP/E001114/1.619 We are grateful to the anonvinous referee whose conumnents significantly improved this manuscript: we also thank the operatious team for performing this observation aud providing software auc calibration for the data analysis., We are grateful to the anonymous referee whose comments significantly improved this manuscript: we also thank the operations team for performing this observation and providing software and calibration for the data analysis.620 This research has also made use of data obtained from the ITigh Encreyv Astrophysics Scicuce Archive Research Center IIEASARCG). provided by NASA’s Coddard Space Flight Ceuter.," This research has also made use of data obtained from the High Energy Astrophysics Science Archive Research Center (HEASARC), provided by NASA's Goddard Space Flight Center."621"can be described as where B, is the dipole magnetic field strength of the neutron star at the magnetic pole, R, is the radius of the neutron star, Q is the angular frequency of radiation at t=0, y=L6x s is the corresponding spin-down timescale1018 of 4,0,theLs magnetar,[ο and I~109gcm? is the typical moment of inertia of the magnetar (Pacini 1967; Gunn Ostriker 1969).","can be described as where $B_{\rm p}$ is the dipole magnetic field strength of the neutron star at the magnetic pole, $R_{\rm s}$ is the radius of the neutron star, $\Omega$ is the angular frequency of radiation at $t=0$, $\tau_{\rm 0}=1.6\times 10^4 B_{\rm p,14}^{-2} \Omega_4^{-2}I_{45}622R_{\rm s,6}^{-6}$ s is the corresponding spin-down timescale of the magnetar, and $I\sim 10^{45}~{\rm g~cm^2}$ is the typical moment of inertia of the magnetar (Pacini 1967; Gunn Ostriker 1969)."623" Here the convention Qn=Q/10"" is adopted in cgs units.", Here the convention $Q_{\rm n}= Q/10^{\rm n}$ is adopted in cgs units.624 One then has Laip~constfort«το and Laiyxt?fort>το.," One then has $L_{\rm dip} \sim {\rm625const}~{\rm for} ~ t\ll \tau_{\rm 0}$ and $L_{\rm dip} \propto626t^{-2}~{\rm for} ~t\gg \tau_{\rm 0}$."627" An abrupt drop in the X-ray flux with a slope steeper than t-? may be interpreted as a decrease of radiation efficiency, or the collapse of the neutron star into a black hole, possibly by losing the angular momentum or by accreting materials."," An abrupt drop in the X-ray flux with a slope steeper than $t^{-2}$ may be interpreted as a decrease of radiation efficiency, or the collapse of the neutron star into a black hole, possibly by losing the angular momentum or by accreting materials."628" Within such a model, the fact that would require (Bp,14,Q4,I4s,P)~(30,0.06,1,1)."," Within such a model, the fact that would require $(B_{\rm p,14},~\Omega_4,~I_{45},~R_{\rm s,6}) \sim629(30,~0.06,~1,~1)$."630 This is a slow (P~10 ms) magnetar (By~3x1015 G)., This is a slow $P \simeq 10$ ms) magnetar $B_{\rm p} \simeq 3\times 10^{15}$ G).631 The composition of this spindown-powered outflow is likely Poynting-flux-dominated., The composition of this spindown-powered outflow is likely Poynting-flux-dominated.632" Besides the magnetar argument (which naturally gives a highly magnetized outflow), another argument would be the lack of a bright thermal component with a temperature kT~ from the outflow photosphere as"," Besides the magnetar argument (which naturally gives a highly magnetized outflow), another argument would be the lack of a bright thermal component with a temperature $kT \sim 10~{\rm keV}~L_{47}^{1/4}R_{0,9}^{-1/2}$ from the outflow photosphere as"633decaving population of SN la is more common in carly-tvpe galaxies (Llamuy 1996: Ivanov. 2000).,decaying population of SN Ia is more common in early-type galaxies (Hamuy 1996; Ivanov 2000).634 This diversity should. be reflected in the abundance vields with the brighter SN Ia. producing more Ni and less Si-group elements than the fainter ones., This diversity should be reflected in the abundance yields with the brighter SN Ia producing more Ni and less Si-group elements than the fainter ones.635 Based on carly work withNewton. Finoguenov (2002) argue that the diversity in the SN Ia population would explain the distribution of chemical elements in the Virgo Cluster.," Based on early work with, Finoguenov (2002) argue that the diversity in the SN Ia population would explain the distribution of chemical elements in the Virgo Cluster."636 The variation of the peak brightness. which correlates with the production of 6 dj and anti-correlates with the production of Si-eroup elements. can also be explained in the framework of the celaved detonation models by a variation of the dellagration-to-detonation transition density (transition from subsonic to supersonic [lame velocities).," The variation of the peak brightness, which correlates with the production of $^{56}$ Ni and anti-correlates with the production of Si-group elements, can also be explained in the framework of the delayed detonation models by a variation of the deflagration-to-detonation transition density (transition from subsonic to supersonic flame velocities)."637 Fie., Fig.638 S presents the expected. vields for a variety of SNIa explosion models from καποιο (1999). with the WDDI. WDD2. WDD3 and W7 mocels on the x-axis.," \ref{fig:div} presents the expected yields for a variety of ${\rm SN\;Ia}$ explosion models from Iwamoto (1999), with the WDD1, WDD2, WDD3 and W7 models on the x-axis."639 We assume a constant relative fraction. of SNla. f.=0.15.," We assume a constant relative fraction of ${\rm SN\;Ia}$, $f=0.15$."640 The WY model represents a pure dellagration explosion mechanism., The W7 model represents a pure deflagration explosion mechanism.641 The WDD models represent delaved-detonation explosions and the last digit indicates the density at which the Blame. velocity. becomes supersonic (dellagration-to-detonation transition densitv) in units of 10) & 7., The WDD models represent delayed-detonation explosions and the last digit indicates the density at which the flame velocity becomes supersonic (deflagration-to-detonation transition density) in units of $10^7$ g $^{-3}$.642 This transition density is likely dependent on the composition of the progenitor (see Jackson 2010)., This transition density is likely dependent on the composition of the progenitor (see Jackson 2010).643 Alatching our observed οιο and S/Ee profiles. given the existing. SNIa. vields. would. require that. the centre of the galaxy has been enriched. almost solely by NDDI supernovae while the outer regions almost solely by WDD3.," Matching our observed Si/Fe and S/Fe profiles, given the existing ${\rm SN\;Ia}$ yields, would require that the centre of the galaxy has been enriched almost solely by WDD1 supernovae while the outer regions almost solely by WDD3."644 The contribution by SN la with longer delay times and larger Si/Lle ratio would be the largest in the centre of the galaxy. out any realistic enrichment scenario predicts an enrichment v a mixture of dillerent types of SN la at all radii.," The contribution by SN Ia with longer delay times and larger Si/Fe ratio would be the largest in the centre of the galaxy, but any realistic enrichment scenario predicts an enrichment by a mixture of different types of SN Ia at all radii."645 This model predicts a large central increase in the Ar/Ie and Ca/be abundance ratios that seem to be in conflict with he observed relatively Dat. profiles., This model predicts a large central increase in the Ar/Fe and Ca/Fe abundance ratios that seem to be in conflict with the observed relatively flat profiles.646 The predicted: Mg/Ie xofile is relatively Dat in agreement with observations., The predicted Mg/Fe profile is relatively flat in agreement with observations.647 The strongest prediction of this model is the ~30 per cent rise in he Ni/Fe abundance ratio with the increasing radius., The strongest prediction of this model is the $\sim30$ per cent rise in the Ni/Fe abundance ratio with the increasing radius.648 Our observed. Ni/Fe profile. which is unfortunately dominated ov svstematic uncertainties. suggests a relatively [lat racial clistribution.," Our observed Ni/Fe profile, which is unfortunately dominated by systematic uncertainties, suggests a relatively flat radial distribution."649 The O/Fe ratio of 0.60+0.03 Solar determined in. the centre of M ST with the Rellection Cirating Speetrometers (Werner ct al., The O/Fe ratio of $0.60\pm0.03$ Solar determined in the centre of M 87 with the Reflection Grating Spectrometers (Werner et al.650 200Gb: these data resolve the line anc the individual lines of the Fe-L complex) is significantly lower than the values. predicted. by the proposed. enrichment scenarios., 2006b; these data resolve the line and the individual lines of the Fe-L complex) is significantly lower than the values predicted by the proposed enrichment scenarios.651 These best ft ΟΡο ratios are consistent with the values determined. using the CCD tvpe detectors on (Matsushita et al., These best fit O/Fe ratios are consistent with the values determined using the CCD type detectors on (Matsushita et al.652 2003)., 2003).653 Either the measurements strongly uncerestimate the O abundance or some Κον aspect of the chemical enrichment of the hot LOAL/ESAL is not understood., Either the measurements strongly underestimate the O abundance or some key aspect of the chemical enrichment of the hot ICM/ISM is not understood.654 Using the recently updated AtomDB atomic database. the best fitting O/Le ratios are 50 per cent larger compared to the previous version. indicating that at least part. of the cliscrepancy might be a modeling issue.," Using the recently updated AtomDB atomic database, the best fitting O/Fe ratios are 50 per cent larger compared to the previous version, indicating that at least part of the discrepancy might be a modeling issue."655 Furthermore. all of our proposed enrichment scenarios are incompatible with the rising O/Te abundance profile reported from (Bobhringer ot al.," Furthermore, all of our proposed enrichment scenarios are incompatible with the rising O/Fe abundance profile reported from (Böhhringer et al."656 2001. Finoguenov et al.," 2001, Finoguenov et al."657 2002. Matsushita ect al.," 2002, Matsushita et al."658 2003)., 2003).659 However. measurements of the line emission at Lo0.65 keV with CCD detectors suller from. significant systematic uncertainties due to à combination of limited spectral resolution. residual gain uncertainties. coupled with incomplete. modelling. of the detector oxygen. οσο aud possible incomplete subtraction of the [ine emission from the Galactic. foreground. (whieh could. bias the ο) abundance measurement in the outskirts of AL 87. high).," However, measurements of the line emission at $E\sim0.65$ keV with CCD detectors suffer from significant systematic uncertainties due to a combination of limited spectral resolution, residual gain uncertainties, coupled with incomplete modelling of the detector oxygen edge and possible incomplete subtraction of the line emission from the Galactic foreground (which could bias the O abundance measurement in the outskirts of M 87 high)."660 These svstematic uncertainties force us to treat all current O abundance measurements with caution., These systematic uncertainties force us to treat all current O abundance measurements with caution.661 More. robust measurements of the O/Fe profile will be possible with the calorimeters on the satellite., More robust measurements of the O/Fe profile will be possible with the calorimeters on the satellite.662 Using a deep (574 ks)Chandra observation of ALSST. we performed the best measurements to date of the radial distributions of metals in the ambient central LOCAL of the Virgo Cluster.," Using a deep (574 ks) observation of 87, we performed the best measurements to date of the radial distributions of metals in the ambient central ICM of the Virgo Cluster."663 We conclude that: We thank RoC. Morris. for computational support., We conclude that: We thank R.G. Morris for computational support.664 We thank «ον. Irwin and J. de Plaa for stimulating discussions., We thank J.A. Irwin and J. de Plaa for stimulating discussions.665 We thank the anonymous referee for the important sugeestions which significantlv improved. the paper., We thank the anonymous referee for the important suggestions which significantly improved the paper.666 N. Werner. anc AL Simionescu were supported by the National Aeronautics and Space Administration. through Chandra/Iinstein Postdoctoral Fellowship Aware) Number PES-90056 and PE9-O0070 issued by the Chandra: X-ray, N. Werner and A. Simionescu were supported by the National Aeronautics and Space Administration through Chandra/Einstein Postdoctoral Fellowship Award Number PF8-90056 and PF9-00070 issued by the Chandra X-ray667breaking phase transition al the erand unified scale.,breaking phase transition at the grand unified scale.668" Such transitions lead to the formation of an unstable topological defect known as ""global texture."""," Such transitions lead to the formation of an unstable topological defect known as “global texture."""669" Carroll- points. out that [or. some purposes it. is. useful. to pretend that the —ha724,7> term in the Friedmann equation represents an effective ""energy densitv in curvature. and define. py —(3h/8aG.—RajaPDs>>."," Carroll points out that for some purposes it is useful to pretend that the $-ka^{-2} R_0^{-2}$ term in the Friedmann equation represents an effective “energy density in curvature”, and define $\rho_k$ $-(3k / 8\pi GR_0^2) a^{-2}$."670 Caldwell (1999 astro-ph 8163) remarks (hat most observations are consistent wilh models rght up to the w= 1 or cosmological constant limit. ancl so it is natural to ask what lies on the other side at w « 1.," Caldwell (1999 astro-ph 8168) remarks that most observations are consistent with models right up to the w = –1 or cosmological constant limit, and so it is natural to ask what lies on the other side at w $<$ –1."671 He termed this phantom energy., He termed this phantom energy.672 In this paper we outline how a dark energv program will constrain these elements and. in particular. how thev affect the measurement of the IIubble Constant. by means of the anisotropy in the cosmic microwave background.," In this paper we outline how a dark energy program will constrain these elements and, in particular, how they affect the measurement of the Hubble Constant by means of the anisotropy in the cosmic microwave background."673" Section 2 extends the Friedinann equation: $3 shows that supernova data are currently tolerant of small values of O4 and 03: 34 explores the degeneracies in CMD data: 65 examines how matter density experiments like 2dE (Peacock 2001) are affected: $6 broadly explores the parameter space of £2, as il applies to SN and CMDB data.", Section 2 extends the Friedmann equation; $\S$ 3 shows that supernova data are currently tolerant of small values of $\Omega_1$ and $\Omega_2$; $\S$ 4 explores the degeneracies in CMB data; $\S$ 5 examines how matter density experiments like 2dF (Peacock 2001) are affected; $\S$ 6 broadly explores the parameter space of $\Omega_n$ as it applies to SN and CMB data.674 Our conclusions are in the final section., Our conclusions are in the final section.675 An observer conlrontecd with data like that in Figure 1 might respond bv fitting a polynomial to the expansion rate as a function of redshilt., An observer confronted with data like that in Figure 1 might respond by fitting a polynomial to the expansion rate as a function of redshift.676 But a plivsical equation already exists. namely the Friedimann equation.," But a physical equation already exists, namely the Friedmann equation."677 From the point of view ol fitting the data (he observer might be surprised at the emphasis placed by physics on the higher order coefficients., From the point of view of fitting the data the observer might be surprised at the emphasis placed by physics on the higher order coefficients.678 This was not rectified until the discovery of dark energy. based on earlier versions of Figure 1 bv the High z Supernova and Supernova Cosmology teams. although the zeroth order coefficient. was considered ancl discarded. by Einstein.," This was not rectified until the discovery of dark energy, based on earlier versions of Figure 1 by the High z Supernova and Supernova Cosmology teams, although the zeroth order coefficient was considered and discarded by Einstein."679 According to Gooding (1992) the textures source term is, According to Gooding (1992) the textures source term is680"were the start density 3x105cm 3?, the upper limit on the number of accelerated electrons is increased tenfold.","were the start density $\times$ $^{8}$ $^{-3}$, 	the upper limit on the number of accelerated electrons is increased tenfold."681" The detection thresholds from the previous section can be used again: For X-ray detection through RHESSI lightcurves, a coronal electron beam would require about x 10?? electrons above 10 keV over 4 s, or about 4x 10?? electrons above 10 keV over a few minutes."," 		 	The detection thresholds from the previous section can be used again: 	For X-ray detection through RHESSI lightcurves, a coronal electron beam would require about $\times$ $^{35}$ electrons above 10 keV over 4 s, 	or about $\times$ $^{35}$ electrons above 10 keV over a few minutes."682 RHESSI characterization by imaging requires at least 3x10°° 036 electrons above 10 keV. The fact that no clear spatial and temporal correlation of Type III radio burst and X-ray emission beyond the limb has ever been established is already an indicator that electron beams must have typically less than these numbers of electrons., 	RHESSI characterization by imaging requires at least $\times$ $^{36}$ electrons above 10 keV. 	The fact that no clear spatial and temporal correlation of Type III radio burst and non-thermal X-ray emission beyond the limb has ever been established 	is already an indicator that electron beams must have typically less than these numbers of electrons.683 A systematic search using data from the Nancaay Radioheliograph and RHESSI will be initiated shortly., 	A systematic search using data from the Nançaay Radioheliograph and RHESSI will be initiated shortly.684" The best case so far of such an event has been discussed in?,, and mentionned briefly in the conclusion."," 	The best case so far of such an event has been discussed in, and mentionned briefly in the conclusion."685" (1)Strong escaping (“up”) beams, i.e. with fluxes comparable to the usual chromospheric HXR-producing flare electrons (21035 electrons above 10 keV), should easily be detectable and imageable with RHESSI, provided any chromospheric footpoint is occulted."," 	 	(1) escaping (“up”) beams, i.e. with fluxes comparable to the usual chromospheric HXR-producing flare electrons $\gtrsim$ $^{38}$ electrons above 10 keV), 	should easily be detectable and imageable with RHESSI, provided any chromospheric footpoint is occulted."686" The absence of such observations supports the scenario established so far, ie. that escaping electrons are fewer in number than a few tenths of a percent of those hitting the chromosphere."," 	The absence of such observations supports the scenario established so far, i.e. that escaping electrons are fewer in number than a few tenths of a percent of those hitting the chromosphere."687 in turns hints at asymmetries in the overall standard acceleration scenario., 	This in turns hints at asymmetries in the overall standard acceleration scenario.688" Possible explanations can range from (a) the presence of a “collapsing trap” mechanism that enhances the number of accelerated flare electrons, but not the escaping electrons on open field lines, (b) the possibility that the main acceleration actually takes place elsewhere than in the high corona, such as in the footpoints, as suggested by?,, (c) the possibility that escaping electron beams are a secondary energy release phenomenon, triggered by electromagnetic waves from the flare electrons(?),, or (d) the presence of a secondary reconnection process higher up in the corona, where particle densities are much lower, connecting to open field lines?"," 	Possible explanations can range from 		(a) the presence of a “collapsing trap” mechanism that enhances the number of accelerated flare electrons, 		but not the escaping electrons on open field lines, 		(b) the possibility that the main acceleration actually takes place elsewhere than in the high corona, such as in the footpoints, as suggested by, 		(c) the possibility that escaping electron beams are a secondary energy release phenomenon, triggered by electromagnetic waves from the flare electrons, 		or (d) the presence of a secondary reconnection process higher up in the corona, where particle densities are much lower, connecting to open field lines."689).. |(2) GOES is not expected to observe anything of note fromweak beams (beams with <10°° electrons above 10 keV)., 	 	(2) GOES is not expected to observe anything of note from beams (beams with $\lesssim$ $^{36}$ electrons above 10 keV).690" Escapingweak beams appear to be just below RHESSI’s imaging capabilities (even with footpoints occulted), marginally within Hinode/XRT's imaging capabilities, but well within FOXSI’s."," 	Escaping beams appear to be just below RHESSI's imaging capabilities (even with footpoints occulted), 	marginally within Hinode/XRT's imaging capabilities, but well within FOXSI's."691were classified as lil. flare aud splutter im Cuaeiner ct al. (,"were classified as lull, flare and splutter in Greiner et al. ("6921996). aud each of these states last for a few huudred seconds;,"1996), and each of these states last for a few hundred seconds."693 Simular N-rayv elt curves were analyzed in detail bv Belloni ct al. (, Similar X-ray light curves were analyzed in detail by Belloni et al. (694L997a: 1997b) who classified them as “outbursts”: they found that the source shows distinct aud differeut spectral and temporal characteristics during the “quiescence” and outburst.,1997a; 1997b) who classified them as “outbursts”; they found that the source shows distinct and different spectral and temporal characteristics during the “quiescence” and outburst.695 Taam. Chen. aud Swank (1997) detected a wide rauge of trausieut activity including regular bursts with a recurrence time of about oue minute and regular bursts.," Taam, Chen, and Swank (1997) detected a wide range of transient activity including regular bursts with a recurrence time of about one minute and irregular bursts."696 Belloni et al. (, Belloni et al. (69719971) made a detailed spectral analysis during a sequence of “bursts” and discovered a strong correlation between the quiescent phase and burst duration.,1997b) made a detailed spectral analysis during a sequence of “bursts” and discovered a strong correlation between the quiescent phase and burst duration.698 Paul ct al. (, Paul et al. (6991998a) detected several types of bursts using the INAE data aud ound evidence for matter disappearing mto the event rorizon of the black hole.,1998a) detected several types of bursts using the IXAE data and found evidence for matter disappearing into the event horizon of the black hole.700 Yadav et al. (, Yadav et al. (7011999) made a systematic analysis of these bursts and classified them sed on the recurrence time.,1999) made a systematic analysis of these bursts and classified them based on the recurrence time.702 Yadav et al. (, Yadav et al. (7031999) presented a comprehensive picture or the origin of these bursts in the light of the recent heories of advective accretion disk.,1999) presented a comprehensive picture for the origin of these bursts in the light of the recent theories of advective accretion disk.704 It was sugeested that he peculiar bursts are characteristic of the change of state of the source., It was suggested that the peculiar bursts are characteristic of the change of state of the source.705 The source cau switch back and forth )etween the low-hard state aud the high-soft state near critical accretion rates in a very short time scale. ceiving rise to the irregular and quasiregular bursts.," The source can switch back and forth between the low-hard state and the high-soft state near critical accretion rates in a very short time scale, giving rise to the irregular and quasi-regular bursts."706 The fast time scale for the transition of the state is explained by invoking he appearance and disappearance of the advective disk in its viscous time scale., The fast time scale for the transition of the state is explained by invoking the appearance and disappearance of the advective disk in its viscous time scale.707 The periodicity of the regular musts is explained by matching the viscous time scale with he cooling time scale of region bevoud a shock frout ora centrifugal barrier (Chakrabarti Titarchuk 1995)., The periodicity of the regular bursts is explained by matching the viscous time scale with the cooling time scale of region beyond a shock front or a centrifugal barrier (Chakrabarti Titarchuk 1995).708 Iu this paper we prescut the results of a study of the iue variability and spectral characteristics of the source GRS 1915|105 duiug the irregular bursts., In this paper we present the results of a study of the time variability and spectral characteristics of the source GRS 1915+105 during the irregular bursts.709 We show that during these bursts the source males distinct transitions )eteen the two spectral states ina few seconds., We show that during these bursts the source makes distinct transitions between the two spectral states in a few seconds.710 Iu section 2 we present results obtained from an analysis of the data obtained from the Proportional Counter Arrav (PCA) of he Rossi N-vav Thine Explorer (RXTE)., In section 2 we present results obtained from an analysis of the data obtained from the Proportional Counter Array (PCA) of the Rossi X-ray Timing Explorer (RXTE).711 In section 3 we discuss the importance of our results and in the last section a παν of the results is elven., In section 3 we discuss the importance of our results and in the last section a summary of the results is given.712 GRS 19151105 was in a low-hard state diving 1996 December to 1997 March when the lard N-rav spectral index (~2.0) aud the soft N-rayv flux. (300 - 500 τιςνα) were low (αποetal.1998: J)., GRS 1915+105 was in a low-hard state during 1996 December to 1997 March when the hard X-ray spectral index $\sim$ 2.0) and the soft X-ray flux (300 - 500 mCrab) were low \cite{grei:98}; \cite{trud:98}) ).713 The source started a new outburst around 1997 Aprib-May when the soft N-arav flux started iucreasing and the X-ray spectrum became soft (spectral iudex increased to 3 D., The source started a new outburst around 1997 April-May when the soft X-ray flux started increasing and the X-ray spectrum became soft (spectral index increased to 3 $-$ 4).714 It reached the hiel-soft state in August 1997., It reached the high-soft state in August 1997.715 The 1.3 to 12.2 keV Χαν light curve of the source obtained from the RATE ASAI archives is shown in Figure 1. from 1997. Jaunary to 1997 September.," The 1.3 to 12.2 keV X-ray light curve of the source obtained from the RXTE ASM archives is shown in Figure 1, from 1997 January to 1997 September."716 Iudividual dwell data (see Levine et al., Individual dwell data (see Levine et al.717 1996) are plotted against the ASM day numbers (which is equal to ALJD - 19353)., 1996) are plotted against the ASM day numbers (which is equal to MJD - 49353).718 A few dates (Gu 1997) are marked on the top of the figure., A few dates (in 1997) are marked on the top of the figure.719 There are about 20 dwells on the source per daw. lasting for about 90 s. Data are in ASM counts «τς Crab 2 75 ASM counts +).," There are about 20 dwells on the source per day, lasting for about 90 s. Data are in ASM counts $^{-1}$ (1 Crab = 75 ASM counts $^{-1}$ )."720 The RNTE public archive contains several observations on GRS 1915|105 using the RATE PCA (Jahoda et al., The RXTE public archive contains several observations on GRS 1915+105 using the RXTE PCA (Jahoda et al.721 1996)., 1996).722 These observations typically last for a few thousand seconds and the start times of these observations are narked as circles in Figure 1., These observations typically last for a few thousand seconds and the start times of these observations are marked as circles in Figure 1.723 Several of these observations are analyzed and reported im the literature aud these are uarked with vertical arrows im the figure., Several of these observations are analyzed and reported in the literature and these are marked with vertical arrows in the figure.724" The observation ines of the regular bursts reported as ‘rings’ iu the PCA color-color diagrams by Villa Nevalainen (1998) are uarked with acy in the fieure and the ""imregular bursts reported by Belloni et al. (", The observation times of the regular bursts reported as `rings' in the PCA color-color diagrams by Vilhu Nevalainen (1998) are marked with a `v' in the figure and the `irregular bursts' reported by Belloni et al. (72519975) is marked as “BY.,1997b) is marked as `B'.726" The eculiar repeated observation of the ""kink iu the leht curve followed by a Iul and then riugimg flares reported w Eikeuberry et al. (", The peculiar repeated observation of the `kink' in the light curve followed by a `lull' and then ringing flares reported by Eikenberry et al. (7271998) is marked by au E.,1998) is marked by an `E'.728 Similar episodes of flares have seen by Alarkwardt et al. (, Similar episodes of flares have seen by Markwardt et al. (7291999) and it is marked with au AU.,1999) and it is marked with an `M'.730 The remaining observations which are reported in the literature are from Trudolvyubov. Churazov. Cülfanov (1999) aud Muno et al. (," The remaining observations which are reported in the literature are from Trudolyubov, Churazov, Gilfanov (1999) and Muno et al. ("7311999).,1999).732 The observation times of CRS 1915|105 by the PPCs ou board IXAE (Paul cl al., The observation times of GRS 1915+105 by the PPCs on board IXAE (Paul el al.733 19982: Yadav et al., 1998a; Yadav et al.734 1999) ave marked as stars in Fieure 1., 1999) are marked as stars in Figure 1.735 It can be seen from the figure that the source was in a stable low-hard state wp to 1997 April 25 (dav uuuber 1210) when the average ASM count was 20 1., It can be seen from the figure that the source was in a stable low-hard state up to 1997 April 25 (day number 1210) when the average ASM count was 20 $^{-1}$.736 Barring hnree episodes of dippiug behaviors (which could be absorption dips seeu in other black hole caucidate sources ike IU 1630-17 - see Ίνακος et al., Barring three episodes of dipping behaviors (which could be absorption dips seen in other black hole candidate sources like 4U 1630-47 - see Kuulkers et al.737 1998). the source fux was stable with a riis deviation of15%.," 1998), the source flux was stable with a rms deviation of."738. It should be roted here that the ASM data. with a dwell time of 90 5 and about 20 dwells per dav. is inseusitive to short term varlabilitics.," It should be noted here that the ASM data, with a dwell time of 90 s and about 20 dwells per day, is insensitive to short term variabilities."739 The spectral ancl temporal behavior during he low-harcd state was stable characterized by a hard spectrum (with the power-law iudex of ~2. and the total fux in the power-law component being ~s80% }) and 0.5 10 Tz QPOs (Irudolvubov et al.," The spectral and temporal behavior during the low-hard state was stable characterized by a hard spectrum (with the power-law index of $\sim$ 2, and the total flux in the power-law component being $\sim$ ) and 0.5 – 10 Hz QPOs (Trudolyubov et al."740 1999: Nuno et al., 1999; Muno et al.741 1999)., 1999).742 The fact that the canonical low-hard states of black hole candidate sources have a negligible thermal component (Chituis et al., The fact that the canonical low-hard states of black hole candidate sources have a negligible thermal component (Chitnis et al.743 1998) prompted Trudolyubov et al. (, 1998) prompted Trudolyubov et al. (744"1999) to characterize this state as an ""interinediate state” aud they couclude that with the lowering of the accretion rate the source should eo to the canonical hard state.",1999) to characterize this state as an “intermediate state” and they conclude that with the lowering of the accretion rate the source should go to the canonical hard state.745 Since the source was iu simular state on several occasions (1996 July-August: 1997 October: 1998 Septemiber-October). we treat this state as the “low-hard state” of GRS-1915|105.," Since the source was in similar state on several occasions (1996 July-August; 1997 October; 1998 September-October), we treat this state as the “low-hard state” of GRS-1915+105."746 After 1997 April 25 the source started a steady increase in its N-rav emission with an average increase in the ASAI count rate of 0.65 3 + and reaching a count rate of τος+ in the middle of July (day πο. 1290)., After 1997 April 25 the source started a steady increase in its X-ray emission with an average increase in the ASM count rate of 0.65 $^{-1}$ $^{-1}$ and reaching a count rate of 76 $^{-1}$ in the middle of July (day number 1290).747 The variability. as cau be deduced from the ASAD count rates and measured as the fraction of runs to mean. steadily increased from to," The variability, as can be deduced from the ASM count rates and measured as the fraction of rms to mean, steadily increased from to."748 It should be noted that during the low-hard state of 1996 July-August the source showed simular variability behavior: the rius variation was low (5 - 104)) during the low-lard state aud it was ~LO% just before and after this state (Paul ct al., It should be noted that during the low-hard state of 1996 July-August the source showed similar variability behavior: the rms variation was low (5 - ) during the low-hard state and it was $\sim$ just before and after this state (Paul et al.749 19051)., 1998b).750 The variability. however. decreased to <15% around 1997 June (Dav uuuber 1260).," The variability, however, decreased to $<$ around 1997 June (Day number 1260)."751 Divine this period the source showed evidences of continous “rineiue” fares (Villian aud Novalainen 1998: Yadav ct al., During this period the source showed evidences of continuous “ringing” flares (Vilhu and Nevalainen 1998; Yadav et al.752 1999). with time scales of 30 60 s and these will not be evident in the ASM data.," 1999), with time scales of 30 – 60 s and these will not be evident in the ASM data."753 The variability increased again from June cud (Day muuber 1275) aud the faring state continued for about 20 more days with the ASAI variability being 30-1054., The variability increased again from June end (Day number 1275) and the flaring state continued for about 20 more days with the ASM variability being 30 -.754. The source reached a steady state with low variability (~10%})., The source reached a steady state with low variability $\sim$ ).755 The ringing flares started again iu the beginning of 1997 August (Yadav ct al., The ringing flares started again in the beginning of 1997 August (Yadav et al.756 1999) and towards the cud of this state, 1999) and towards the end of this state757To determine the new proper motion for NLTT 20316 we used positions available through USNO-A2.0. USNO-D1.0. GSC 2.2. 2ATASS. and an ISPI image taken on 05 April 2010 ειν 2:2: 2h).,"To determine the new proper motion for NLTT 20346 we used positions available through USNO-A2.0, USNO-B1.0, GSC 2.2, 2MASS, and an ISPI image taken on 08 April 2010 \citealt{2003AJ....125..984M}, \citealt{1998usno.book.....M}; \citealt{2008AJ....136..735L}; \citealt{2003tmc..book.....C}) )."758 The total baseline between the first aud ια] epoch used was ~59 vears., The total baseline between the first and final epoch used was $\sim$ 59 years.759" NLTT 20316 is uot resolved iu auy of the epochs as the 2"" separation. seeing coucditious aud plate scale of each detector caused the A and DB components to appear bleuded."," NLTT 20346 is not resolved in any of the epochs as the $\arcsec$ separation, seeing conditions and plate scale of each detector caused the A and B components to appear blended."760 We simulated the PSF for the A and D component of NLTT 20316 ou cach of the detectors to estimate the nucertaity due to blending., We simulated the PSF for the A and B component of NLTT 20346 on each of the detectors to estimate the uncertainty due to blending.761 We added this additional nucertaity in quadrature to the catalog uncertainties and used these in the proper motion measurement., We added this additional uncertainty in quadrature to the catalog uncertainties and used these in the proper motion measurement.762 The absolute astrometric position from cach catalog (with correspouding epochs) were used to solve for the proper motion using a least squares weighted solution., The absolute astrometric position from each catalog (with corresponding epochs) were used to solve for the proper motion using a least squares weighted solution.763 There is an SDSS image taken on 06 January 2006 and an ISPI nuage taken on 27 February 2010 with sub-arcseconc seeing where both componucuts are resolved., There is an SDSS image taken on 06 January 2006 and an ISPI image taken on 27 February 2010 with sub-arcsecond seeing where both components are resolved.764 Using these two epochs with a -—1 vear baseline. we caleulatec the proper motion of cach component.," Using these two epochs with a $\sim$ 4 year baseline, we calculated the proper motion of each component."765 These resolve values are cousisteut with the motion calculated from the blended source along a 59 vear baseline., These resolved values are consistent with the motion calculated from the blended source along a 59 year baseline.766 This iudicates that orbital motion is not effecting the total motion of the system., This indicates that orbital motion is not effecting the total motion of the system.767" For NLTT 20316 we calculated p, —-17248 mas yr and 52-5026 mas | (usus all catalog positions) and for 2MASS JOs50|1057 we calculated 45, I6 nias η", For NLTT 20346 we calculated $\mu_{\alpha}$ $\pm$ 8 mas $^{-1}$ and $\mu_{\delta}$ $\pm$ 6 mas $^{-1}$ (using all catalog positions) and for 2MASS J0850+1057 we calculated $\mu_{\alpha}$ $\pm$ 6 mas $^{-1}$ and $\mu_{\delta}$ $\pm$ 6 mas $^{-1}$.768 NLTT 20316 —-11Ehas two published proper motion values iu the LSPALN and New Luvteu 73) catalogues aud. as stated in section 3d. 2MASS JOs50|1057 has previous proper motion values reported in 7? and 7? (sco Table 1).," NLTT 20346 has two published proper motion values in the LSPM-N and New Luyten \citealt{1979lccs.book.....L}) ) catalogues and, as stated in section 3.1, 2MASS J0850+1057 has previous proper motion values reported in \citet{2004AJ....127.2948V} and \citet{2002AJ....124.1170D} (see Table \ref{PM}) )."769" Our astrometric results are consistent within 20 of previous published results aud using the new values. both the μι, and pps values for the potential companious are within 20 of cach other."," Our astrometric results are consistent within $\sigma$ of previous published results and using the new values, both the $\mu_{\alpha}$ and $\mu_{\delta}$ values for the potential companions are within $\sigma$ of each other."770 Alone with the predicted distance measurement of the primary (see section [1 below). aud the new parallax measurement for 24MASS. 10550|1057 of 3548 mas or 29-47 pc. this svstein is a strong wideconrpainion COMMMOL proper notion candidate.," Along with the predicted distance measurement of the primary (see section 4.1 below), and the new parallax measurement for 2MASS J0850+1057 of $\pm$ 8 mas or $\pm$ 7 pc, this system is a strong widecompanion common proper motion candidate."771 NLTT 20316 was identified asa potential companion to 2MÀSS σος1057. through a connuon proper motion search of the Brown Dwarf Kinematics Project (DDKDP) catalog (2)) and the Lepine-Shara Proper Motion North (LSPALN) and Hipparcos catalogs ο 7))., NLTT 20346 was identified asa potential companion to 2MASS J0850+1057 through a common proper motion search of the Brown Dwarf Kinematics Project (BDKP) catalog \citealt{2009AJ....137....1F}) ) and the Lepine-Shara Proper Motion North (LSPM-N) and Hipparcos catalogs \citealt{2002AJ....124.1190L}; \citealt{1997A&A...323L..49P}) ).772 Several other svstems were detected and detailed analysis was presented in ?.., Several other systems were detected and detailed analysis was presented in \citet{2009AJ....137....1F}.773 In that work. an augular separation of up to 10 arciuuutes and a proper motion matcl criterion of better than 26 in both right ascension (RA) and declination (DEC) between the svsteui components was required to determine common proper motion candidates.," In that work, an angular separation of up to 10 arcminutes and a proper motion match criterion of better than $\sigma$ in both right ascension (RA) and declination (DEC) between the system components was required to determine common proper motion candidates."774 The average uncertaiutv for objects im the DDKD catalog is 15 amas | (in both directions) so proper motion agreenieut was typically required to be < J03nas | between the stellar companion aud ultracool dwart (UCD)., The average uncertainty for objects in the BDKP catalog is 15 mas $^{-1}$ (in both directions) so proper motion agreement was typically required to be $<$ 30 mas $^{-1}$ between the stellar companion and ultracool dwarf (UCD).775 7. also required a distance match between colponcuts of better than 20 or typically better than 10 pe., \citet{2010AJ....139..176F} also required a distance match between components of better than $\sigma$ or typically better than 10 pc.776 The system containing NLTT 20316 was not investigated in 7— because proper motion components were sliehtlv outside of the 26 requirement., The system containing NLTT 20346 was not investigated in \citet{2010AJ....139..176F} because proper motion components were slightly outside of the $\sigma$ requirement.777 However. after follow-up aging aud re-analysis of the astromoetry of both compoucuts we found strong evidence for colpaiouship (see Section 3.2).," However, after follow-up imaging and re-analysis of the astrometry of both components we found strong evidence for companionship (see Section 3.2)."778 To quautifv the probability that NLTT 20516 nieht be a chance aliguiment with 2\LASS JO0850|1057. we ran a Moute Carlo simulation of all stars iu the LSPALN aud Ilipparcos catalogs that shared a common proper motion. but not necessarily distance or position. with the brown chwart (to within 20 see? for details).,"	 To quantify the probability that NLTT 20346 might be a chance alignment with 2MASS J0850+1057, we ran a Monte Carlo simulation of all stars in the LSPM-N and Hipparcos catalogs that shared a common proper motion, but not necessarily distance or position, with the brown dwarf (to within $\sigma$ –see \citealt{2009AJ....137....1F} for details)."779 There were 156 stars in the Iipparcos catalog aud 632 stars in the LSPALN catalog with matching proper motion compoucuts., There were 156 stars in the Hipparcos catalog and 632 stars in the LSPM-N catalog with matching proper motion components.780" After 10000 iterations we found the likelihood that NLTT 20316 is a chance coincidence with 2\LASS JO0850|1057 (at an angular seperation of 218 "") is < L.0%..", After 10000 iterations we found the likelihood that NLTT 20346 is a chance coincidence with 2MASS J0850+1057 (at an angular seperation of 248 $\arcsec$ ) is $<$ .781 From the MagE data for NETT. 20316 we classified, From the MagE data for NLTT 20346 we classified782We find that lower redshift SMCs appear to have lower rest-frame W-band luminosities. suggesting that galaxy ‘downsizing (Vhomas et al..,"We find that lower redshift SMGs appear to have lower rest-frame K-band luminosities, suggesting that galaxy 'downsizing' (Thomas et al.,"783 2005) is at work in the SMCG population., 2005) is at work in the SMG population.784 This is an expected. result. in the generally assumed. picture of SALGs being a stage in the evolution of elliptical ealaxies., This is an expected result in the generally assumed picture of SMGs being a stage in the evolution of elliptical galaxies.785 Several of our SMCs are found. to either be multiple sources with two or more components. or to lie in groups or clusters.," Several of our SMGs are found to either be multiple sources with two or more components, or to lie in groups or clusters."786 However an analysis of the photomoetric-redshift distributions of all sources within LO” of SMCs finds no statistically significant number of companions compared to non-SALG objects.," However an analysis of the photometric-redshift distributions of all sources within 10"" of SMGs finds no statistically significant number of companions compared to non-SMG objects."787 This work represents the first stage of analysing the miucd-to-far-LR SEDs of the SILADISS submillimetre galaxies., This work represents the first stage of analysing the mid-to-far-IR SEDs of the SHADES submillimetre galaxies.788 The SILADES field in Lockman was observed by the Spitzer GTO teams with somewhat deeper integrations and is being ciseussed. elsewhere (Dye et al.," The SHADES field in Lockman was observed by the Spitzer GTO teams with somewhat deeper integrations and is being discussed elsewhere (Dye et al.,"789 2007) while specific subpopulations such as NlIi-selected. sources are also being investigated (Takagi et al..," 2007) while specific subpopulations such as NIR-selected sources are also being investigated (Takagi et al.,"790. 2007)., 2007).791 Examination of Spitzer counterparts to non-racdio-detected: sources in the SXDE anc Lockman SILXDES fields is also underway (Oliver et al.," Examination of Spitzer counterparts to non-radio-detected sources in the SXDF and Lockman SHADES fields is also underway (Oliver et al.,"792 in. preparation: Dye et al.," in preparation; Dye et al.,"793 in. preparation). along with stacking analvsis to produce population averages for uncletected sources (Serjeant et al;," in preparation), along with stacking analysis to produce population averages for undetected sources (Serjeant et al.,"794 in preparation)., in preparation).795 Thanks to Jeff. Wage anc Marcos Trichas for useful comments., Thanks to Jeff Wagg and Marcos Trichas for useful comments.796 DLC is funded by PPARCYSTEC. LRS is supported by the Roval Society.," DLC is funded by PPARC/STFC, IRS is supported by the Royal Society."797 The JCAIP is supported by the United. NineclomAs Science and. Technology. Facilities Council (STEC). the National Research Council Canada (NI). and the Netherlands Organization for Scientific Research (NWO): it is overseen by the JCAL Board.," The JCMT is supported by the United KingdomÕs Science and Technology Facilities Council (STFC), the National Research Council Canada (NRC), and the Netherlands Organization for Scientific Research (NWO); it is overseen by the JCMT Board."798 We acknowledge funding support. from PPARC/STEC. NRC and NASA.," We acknowledge funding support from PPARC/STFC, NRC and NASA."799 The authors would. like to thank the stall at the JOAVP for their typically excellent! support, The authors would like to thank the staff at the JCMT for their typically excellent support800Jaikumar 2005) similar to wlal has been suggestedMOD in the superuova case (Chevalier1989).,Jaikumar 2005) similar to what has been suggested in the supernova case \citep{Chev89}.801. The deusity of the fallback matter. represeltaive of the crust material of the parent. neutron star. is estituated to be of the order «E105 eon7.," The density of the fallback matter, representative of the crust material of the parent neutron star, is estimated to be of the order of $10^6~{\rm g~cm}^{-3}$."802 Note that our MHD equaious (1))-€1 ) are uou-relativistic., Note that our MHD equations \ref{Eq-continuity}) \ref{Eq-entropy}) ) are non-relativistic.803 While near the surface of the quark star sole aspects of the plivsiος will be cosiderably cliauged by relativistic ellects. we expect that the overall dyuaimics will not be vastly cilerent in a more realistic calculation.," While near the surface of the quark star some aspects of the physics will be considerably changed by relativistic effects, we expect that the overall dynamics will not be vastly different in a more realistic calculation."804" All figures shown here a'e for resolutiou 128"".", All figures shown here are for resolution $128^3$.805 We have run simulations at higher resolution. but fouud that they differ little as lar ase lereetics aud evolution are concerned.," We have run simulations at higher resolution, but found that they differ little as far as energetics and evolution are concerned."806 Figures 2-—3 show the evolution of the exterior magnetic field as it adjusts to the p., Figures \ref{fig:xz_plane}- \ref{fig:xy_plane} show the evolution of the exterior magnetic field as it adjusts to the vortex-confined .807" The couplicated struct weoftie surface magnetic field is clearly seen in the autimatious driveu by the freqient neieuetic ""ec'Onnecious as the surface ield tries to align itself with the interior one (rotation axis).", The complicated structure of the surface magnetic field is clearly seen in the animations driven by the frequent magnetic reconnections as the surface field tries to align itself with the interior one (rotation axis).808 Tlese PalleloLL reconection events woud bear many similarities to tlie initial events those jear / . butI we expect them to be less energetic as the magnetic field slowly decays alid weakens.," These random reconnection events would bear many similarities to the initial events those near $t=0$ ), but we expect them to be less energetic as the magnetic field slowly decays and weakens."809 Eveitually. tlthe nagetic field evolves itto a stable configuration (see FieoO. 2))," Eventually, the magnetic field evolves into a stable configuration (see Fig. \ref{fig:xz_plane}) )"810 after which the sar euters a eJes‘ent phase., after which the star enters a quiescent phase.811 The restructuriug of tje. fielc in the trausition 'egion leads to an approximatey spherical Allvénn wave traveling oitwards (see Fie., The restructuring of the field in the transition region leads to an approximately spherical Alfvénn wave traveling outwards (see Fig.812 2 [o .4 auc is more prominent lu sunuatious with a stronger maguetic field stnaller 3)., \ref{fig:xz_plane} for $t=1$ ) and is more prominent in simulations with a stronger magnetic field smaller $\beta$ ).813 As dje wave travels outwards it amplifies the magnetic field in certain regions causing them to uidereο reconnection. which boαμ distorts te wave aud eveutually damps it out.," As the wave travels outwards it amplifies the magnetic field in certain regions causing them to undergo reconnection, which both distorts the wave and eventually damps it out."814" Furthermore. the regious that underwent. recoluection appear to slow slow oscillatory motious between the reconiecticin site aud the surrounding gas (""breatune”)."," Furthermore, the regions that underwent reconnection appear to show slow oscillatory motions between the reconnection site and the surrounding gas (“breathing”)."815 This can be seen in the series of diminishiug pu]ses in Fig., This can be seen in the series of diminishing pulses in Fig.816 6 and the frequercy of the puses renuallis uearly coustaut (see Fig. 7))., \ref{fig:intensity_time} and the frequency of the pulses remains nearly constant (see Fig. \ref{fig:fft}) ).817 We note tha these pulses appear more prominently in simulations with lower 3 and do wot arise in simulations wl hol., We note that these pulses appear more prominently in simulations with lower $\beta$ and do not arise in simulations with $\beta > 1$.818 The magnetic energy released iu the organization is shown in Fig., The magnetic energy released in the organization is shown in Fig.819 6 aud cau be cast into a simple equation.," \ref{fig:intensity_time} and can be cast into a simple equation,"8202002).. so we [lix 3=1.5. which is consistent with the linding of Dunne&Eales(2001). for local galaxies ancl with the values obtained. for carbonite ancl silicate grains from laboratory measurements (Aeladzeetal.1994).,", so we fix $\beta=1.5$, which is consistent with the finding of \citet{Dunne} for local galaxies and with the values obtained for carbonite and silicate grains from laboratory measurements \citep{Agladze}."821.. This leaves two free parameters to be fitted: Za and the SED normalisation., This leaves two free parameters to be fitted: $T_\mathrm{d}$ and the SED normalisation.822" ln practice we work in terms of theapparent dust temperature, Ty=Lif|z) and [it the data for eachach galaxy to Wwf2lPexp(hοπήvanaslITA)1].. where several:i factors of (1|z) have been absorbed into theapparcn/ normalisation. «Ll."," In practice we work in terms of the dust temperature, $T_\mathrm{A}=T_\mathrm{d}/(1+z)$ and fit the data for each galaxy to $A\nu_\mathrm{obs}^{3+\beta}/[\mathrm{exp}(h\,\nu_\mathrm{obs}/k\,T_\mathrm{A})-1]$, where several factors of $(1+z)$ have been absorbed into the normalisation, $A$."823 Assuming that the redshift is known. the restfranc dust temperature can be recovered. and. the luminosity of the SMG. can be determined. by integrating the SED.," Assuming that the redshift is known, the restframe dust temperature can be recovered and the luminosity of the SMG can be determined by integrating the SED."824 In cases where the spectroscopic redshift is ambiguous. the most reliable or probable spectroscopic. redshift) available from the literature has been chosen and is listed in Table 5..," In cases where the spectroscopic redshift is ambiguous, the most reliable or probable spectroscopic redshift available from the literature has been chosen and is listed in Table \ref{tab:tdm}."825 For sources with only a 90 per cent confidence photometric redshift lower limit. the redshift is taken at this limit. (see ‘Table 4)).," For sources with only a 90 per cent confidence photometric redshift lower limit, the redshift is taken at this limit (see Table \ref{tab:sharc_photom}) )."826 We characterise the shape of the SEDs independently of the photometric redshifts because we do not use the radio data in our fits to the SED. and where photometric redshifts are used they have been determined. using all available FL and radio photometry (except for the 350jim data from this oper).," We characterise the shape of the SEDs independently of the photometric redshifts because we do not use the radio data in our fits to the SED, and where photometric redshifts are used they have been determined using all available FIR and radio photometry (except for the $350\,\mathrm{\mu m}$ data from this paper)."827" Alore complex, SED modelling was not attempted (c... fitting two-temperature cust components as in Dunne&Eales 2001)). since this would require more [re xwameters than can be constrained using the typically 23 photometric points which exist for cach of our SALGs."," More complex SED modelling was not attempted (e.g., fitting two-temperature dust components as in \citealt{Dunne}) ), since this would require more free parameters than can be constrained using the typically 2--3 photometric points which exist for each of our SMGs."828" The Wien side of the spectrum is sometimes also mocilied ww a power-law of the form S,x7"" to account for the increase in optical depth in this part of the spectrum and o provide a better fit to observational cata (see. Blain.Barnard&Chapman 2003)).", The Wien side of the spectrum is sometimes also modified by a power-law of the form $S_{\nu} \propto \nu^{-\alpha}$ to account for the increase in optical depth in this part of the spectrum and to provide a better fit to observational data (see \citealt{BlainBarnard}) ).829 We neglect such elaborations rere (see also Kovacsetal. 2006)). since the Wien side of the spectrum. is not sampled with our data.," We neglect such elaborations here (see also \citealt{Kovacs}) ), since the Wien side of the spectrum is not sampled with our data."830 24ji photometry are available for SILXDISZS sources but are complicated to interpret since this band samples PALL and stellar emission," $24\,\mathrm{\mu m}$ photometry are available for SHADES sources but are complicated to interpret since this band samples PAH and stellar emission"831Figure 1. for the range of coronal plasma temperatures 6.0<logLT7.2.,Figure \ref{f:spectra} for the range of coronal plasma temperatures $6.0 \leq \log T \leq 7.2$.832 The lower panel illustrates the same spectra seen al à resolving power of A/AA=1000. where AA is assumed to be (the full-width at halfmasinnun of a Gaussian imstrument response function.," The lower panel illustrates the same spectra seen at a resolving power of $\lambda/\Delta\lambda=1000$, where $\Delta\lambda$ is assumed to be the full-width at half-maximum of a Gaussian instrument response function."833 Unlike the Ne Ka line. the O Kea transition forms in a relatively uncrowded spectral region. aud the CHIANTI database predicts no devastatinglv large blends in the immediate vicinity of 23.37A.," Unlike the Ne $\alpha$ line, the O $\alpha$ transition forms in a relatively uncrowded spectral region and the CHIANTI database predicts no devastatingly large blends in the immediate vicinity of 23.37."834. For temperatures approaching 10* IX. a line of Fe XXIII at 23.36 aappears. but. for GS abundanees is always dominated by the O Ka [line by a factor of 10.," For temperatures approaching $10^7$ K, a line of Fe XXIII at 23.36 appears, but for GS abundances is always dominated by the O $\alpha$ line by a factor of 10."835 Lying redward of our adopted line centre is Ca NV. A23.39. which peaks at slightly cooler temperatures (logο 6.6) at an intensity of about 30 oof that of O Ίνα.," Lying redward of our adopted line centre is Ca XV $\lambda 23.39$, which peaks at slightly cooler temperatures $\log T\sim 6.6$ ) at an intensity of about 30 of that of O $\alpha$ ."836 The full list of lines in the CLUANTI database within 5o of the O Ίνα wavelength range (£0.05 {from 23.37+0.02 A)) with intensities >10.! times that of the brightest line (Fe XXIII A23.363) are listed in Table 4..," The full list of lines in the CHIANTI database within $5\sigma$ of the O $\alpha$ wavelength range $\pm 0.05$ from $23.37\pm8370.02$ ) with intensities $\ge 10^{-4}$ times that of the brightest line (Fe XXIII $\lambda 23.363$ ) are listed in Table \ref{t:5sigma}."838 The NIST Atomic Spectra Database (version 3.1.2: 2007)) also lists two other transitions within the 5o range from Ti XIII and Se XIV., The NIST Atomic Spectra Database (version 3.1.2; ) also lists two other transitions within the $5\sigma$ range from Ti XIII and Sc XIV.839 Neither ol these are expected to be of any significance since (heir solar abundances according to the GS assessment are 300 and 21000 lower than that of Fe. respective=," Neither of these are expected to be of any significance since their solar abundances according to the GS assessment are 300 and 21000 lower than that of Fe, respectively."840 The equivalent width (EW) of the O Ixa line relative to coronal [norescing spectra with GS abundances is illustrated in Figure 3. for a range of isothermal plasma. temperatures and different photospheric O abundances., The equivalent width (EW) of the O $\alpha$ line relative to coronal fluorescing spectra with GS abundances is illustrated in Figure \ref{f:ew} for a range of isothermal plasma temperatures and different photospheric O abundances.841 The Monte Carlo sampling error on the computed EWs is estimated to be no larger than 7%., The Monte Carlo sampling error on the computed EWs is estimated to be no larger than .842.. One striking leature of the trend of EW with T lov all compositions is the sharp decline with rising temperature for log7356.6: this contrasts with both Ne Ίνα and Fe Ίνα. whose EWs exhibit a steady. monotonic rise with increasing LT (Papers 1 II). corresponding (o a commensurate increase in the number of ionising photons.," One striking feature of the trend of EW with $T$ for all compositions is the sharp decline with rising temperature for $\log T\la 6.6$: this contrasts with both Ne $\alpha$ and Fe $\alpha$, whose EWs exhibit a steady, monotonic rise with increasing $T$ (Papers I II), corresponding to a commensurate increase in the number of ionising photons."843 The different behaviour of O Ίνα arises because. for coronal plasmas with logT'S6.6 and solar composition. K-shell photoionisation of oxvgen is due mostly to line rather than continuum radiation.," The different behaviour of O $\alpha$ arises because, for coronal plasmas with $\log T\la 6.6$ and solar composition, K-shell photoionisation of oxygen is due mostly to line rather than continuum radiation."844 Toward hotter temperatures. (he important emitting photoionising species. including O VII and O VILI. become ionised. and continuum contributions begin to dominate.," Toward hotter temperatures, the important line-emitting photoionising species, including O VII and O VIII, become ionised, and continuum contributions begin to dominate."845 Regarcing sensitivitv to O abundance. Figure 3. illustrates that the EW changes by a smaller [actor (han expected based on a proportional relation with the photospheric the O abundance.," Regarding sensitivity to O abundance, Figure \ref{f:ew} illustrates that the EW changes by a smaller factor than expected based on a proportional relation with the photospheric the O abundance."846 As discussed by and in Paper 1. this is à result of the the O photoionisation cross-section being a significant component of the total opacily near threshold: for verv large O abundances where O begins (o dominate the opacity. the EW will tend to a constant value dictatedsimply by equipartition of ionising photons between O Ix-and L-shells.," As discussed by and in Paper I, this is a result of the the O K-shell photoionisation cross-section being a significant component of the total opacity near threshold: for very large O abundances where O begins to dominate the opacity, the EW will tend to a constant value dictatedsimply by equipartition of ionising photons between O K-and L-shells."847 Nevertheless. for “normal” ranges of O abundance the O Ίνα line variations," Nevertheless, for “normal” ranges of O abundance the O $\alpha$ line variations"848the Jeans length. itself could be significantly. increased due to the weakening of gravity in certain models by a large value of the JBD field in the early universe.,the Jeans length itself could be significantly increased due to the weakening of gravity in certain models by a large value of the JBD field in the early universe.849 Nevertheless. a strong (first order) inflationary phase transition in extended inflation models. driven. by the JBD field (La&Stein-1993:Majumcdar1997). naturally leads to unnucleated and trapped false vacuum regions ancl topological defects such as domain walls anc wormboles that could. easily. collapse into black holes. and could also create super-horizon density perturbations.," Nevertheless, a strong (first order) inflationary phase transition in extended inflation models driven by the JBD field \citep{extended2,asm11,asm12,asm13} naturally leads to unnucleated and trapped false vacuum regions and topological defects such as domain walls and wormholes that could easily collapse into black holes, and could also create super-horizon density perturbations."850 The formation of super-horizon scale PBIIs in the expanding FRW background has been studied. recently (ανασα&Carr2005b)., The formation of super-horizon scale PBHs in the expanding FRW background has been studied recently \citep{harada3}.851. In the present. analysis we will not take recourse to any particular formation mechanism for PBUs. but rather study their cosmological evolution in JBD theory. assuming that there exist PBIIs in such scenarios.," In the present analysis we will not take recourse to any particular formation mechanism for PBHs, but rather study their cosmological evolution in JBD theory, assuming that there exist PBHs in such scenarios."852 We now consider the evolution of PBIIs in. the cosmological background. governed. by the above solutions (5)).06)) and (7)), We now consider the evolution of PBHs in the cosmological background governed by the above solutions \ref{rdsoln1}) \ref{rdsoln2}) ) and \ref{rdsoln3}) ).853 We assume that the PDII density. is low enough to ensure radiation domination., We assume that the PBH density is low enough to ensure radiation domination.854 For a PBIL immersed in the radiation field. the accretion of radiation leads to the increase of its mass with the rate given by ἀπ bay where req=2Mo is the black hole radius. and. f. ds the accretion elliciencv.," For a PBH immersed in the radiation field, the accretion of radiation leads to the increase of its mass with the rate given by = f _R where $r_{BH}=2M/\phi$ is the black hole radius, and $f$ is the accretion efficiency."855 Using the solution for ó given by I2q.(6))with the assumption of Ja;|«1. and using pi=(3M) (32s17)]. one obtains where B=(3f)(287 M5. ]5q.(9))," Using the solution for $\phi$ given by \ref{rdsoln2}) )with the assumption of $|\omega_i| \ll 1$, and using $\rho_R = [(3M_{pl}^2)/(32\pi t^2)]$ , one obtains = where $B=(3f)/(2\xi^2M_{pl}^2t_i)$ . \ref{accr2}) )"856 is integrated. to vield | with AJ; being the initial mass of the PDII at time πι, is integrated to yield = with $M_i$ being the initial mass of the PBH at time $t_i$.857" Since the logarithmic growth rate for a PDII given by LEq.(10)) is subdominant to the linear growth of the horizon mass Mg4 (since a~ 117), once a PBLL is formed. it is indeed: possible for it to grow in size by accreting the radiation energv within its cosmological horizon."," Since the logarithmic growth rate for a PBH given by \ref{accr3}) ) is subdominant to the linear growth of the horizon mass $M_H \sim t$ (since $a \sim t^{1/2}$ ), once a PBH is formed, it is indeed possible for it to grow in size by accreting the radiation energy within its cosmological horizon."858 Fora complete picture of PBL evolution. one needs also to consider the Hawking evaporation process. whose rate is eiven by ἀπό o1 where 7=6/(SrAL) is the Hawking temperature. e theStelan-Boltzmann constant and g is the elfective number of degrees of freedom of the particles emitted by the black hole.," For a complete picture of PBH evolution, one needs also to consider the Hawking evaporation process, whose rate is given by = - g ^2 T^4 where $T=\phi/(8\pi M)$ is the Hawking temperature, $\sigma$ theStefan-Boltzmann constant and $g$ is the effective number of degrees of freedom of the particles emitted by the black hole."859" The solution for ó given by Eq.(6)) Leads to where ef=(gotΑμ,(25677).", The solution for $\phi$ given by \ref{rdsoln2}) ) leads to = where $A = (g \sigma \xi^2 M_{pl}^4 t_i)/(256\pi^3)$.860 The complete evolution for the PBIL is thus described bv the combination of Eqs.(9)) and (12)): | ]t is apparent [rom l.2q.(13)) that. for PBIIs with initial mass AM;<<(ASB). the rate. of evaporation exceeds that of acerction.," The complete evolution for the PBH is thus described by the combination of \ref{accr2}) ) and \ref{evap2}) ): = + It is apparent from \ref{bheq}) ) that for PBHs with initial mass $M_i << (A/B)^{1/4}$, the rate of evaporation exceeds that of accretion."861 For such a case. accretion soon becomes negligible and. black holes lose energy at a rate given cllectively by Eq.(12)).," For such a case, accretion soon becomes negligible and black holes lose energy at a rate given effectively by \ref{evap2}) )."862 Note that though the rate of evaporation decreases with time. it is still higher than the corresponding rate in standard. cosmology.," Note that though the rate of evaporation decreases with time, it is still higher than the corresponding rate in standard cosmology."863 “Phis is because the Hawking temperature 2—óf(S2À) is larger for JBD PDlls for large o., This is because the Hawking temperature $T=\phi/(8\pi M)$ is larger for JBD PBHs for large $\phi$.864 Hence. a PBI with initial mass M;<CA/B)ET evaporates out much quicker. with a lifetime fc.) eiven by —exphiggl However. PBUs with initial mass Al;>CA/D)E4 experience monotonic growth with accretion dominating over evaporation throughout the period of validity of Eq.(18)). Le. throughout the radiation. dominated. era. q.(13))," Hence, a PBH with initial mass $M_i < (A/B)^{1/4}$ evaporates out much quicker, with a lifetime $t_{evap}$ given by = ] However, PBHs with initial mass $M_i > (A/B)^{1/4}$ experience monotonic growth with accretion dominating over evaporation throughout the period of validity of \ref{bheq}) ), i.e., throughout the radiation dominated era. \ref{bheq}) )"865 can be integrated exactly and leads to the following mass-time relationship for the PDlIs: with €'=A/B., can be integrated exactly and leads to the following mass-time relationship for the PBHs: ) = ) - + with $C=A/B$.866" Aceretion of radiation can proceed ellectively till the universe stays raciation dominated. Ίο. up to the cra of matter radiation equality /,,."," Accretion of radiation can proceed effectively till the universe stays radiation dominated, i.e., up to the era of matter radiation equality $t_{eq}$."867 Phis result is qualitatively different. [rom the widely accepted: picture in the standard. cosmological evolution. where accretion of radiation in the radiation dominated. era. seems to he inelfective (Carr2003).., This result is qualitatively different from the widely accepted picture in the standard cosmological evolution where accretion of radiation in the radiation dominated era seems to be ineffective \citep{pbh}.868. The domination of accretion over evaporation is observed also in other modified. gravity theories. such. asin the braneworlc scenario (Majumcar 2005)...," The domination of accretion over evaporation is observed also in other modified gravity theories, such asin the braneworld scenario \citep{brane1,brane2,brane3,brane4}. ."869 Phe maximum mass achieved by a PBI of initial mass AJ; is given by MiB In the matter dominated cra. pur~e and p= 0.A set of solutions for the JBD cosmological equations (2)). 03)) wacl (4)) is given by (Sahoo&Singh2002.2003) a(t)," The maximum mass achieved by a PBH of initial mass $M_i$ is given by In the matter dominated era, $\rho_M \sim a^{-3}$ and $p=0$ A set of solutions for the JBD cosmological equations \ref{fe}) ), \ref{eqmotion}) ) and \ref{enconv}) ) is given by \citep{sahoo1,sahoo2}870 a(t) ="871between plauetesimals become destructive.,between planetesimals become destructive.872 Such collisions eject umimerous fragments. which collide with cach other to produce further znaller bodies.," Such collisions eject numerous fragments, which collide with each other to produce further smaller bodies."873 Planctesimals are therefore ground down through such successive collisions (collision cascade)., Planetesimals are therefore ground down through such successive collisions (collision cascade).874 The randoni velocities of small bodies are strongly damped by eas drag and thereby the collisiona cascade no longer occurs for fragments with radii =1 l0im.," The random velocities of small bodies are strongly damped by gas drag and thereby the collisional cascade no longer occurs for fragments with radii $\la 1$ $10\,{\rm m}$."875 In the end such fragmoeuts drift iis due fo gas drag and are lost around enibrvos., In the end such fragments drift inward due to gas drag and are lost around embryos.876 The collisional cascade combined with the loss of fragmicnts reduces the solid surface density au ence final enibryo lasses., The collisional cascade combined with the loss of fragments reduces the solid surface density and hence final embryo masses.877" Large planctesimals. which are relatively hard o be broken collisionally, oxoduce massive final eiibryos."," Large planetesimals, which are relatively hard to be broken collisionally, produce massive final embryos."878 collisional fragmientatiou nales it difficult to orn giant plaucts along the lines of the core-aceretion model starting from αι lauetesuuals. planetary cuabrvos cau reach the critical core mass for gas accretion ouly inside LAAU iu a disk that is 10 times more massive han the MMSN model.," collisional fragmentation makes it difficult to form giant planets along the lines of the core-accretion model; starting from km-sized planetesimals, planetary embryos can reach the critical core mass for gas accretion only inside AU in a disk that is 10 times more massive than the MMSN model."879The motion of fragments < Lum is coupled with eas.,The motion of fragments $\la 1$ m is coupled with gas.880 The drift timescale of such fragiuecuts are relatively] loue., The drift timescale of such fragments are relatively long.881 EKeuvouY&Bromley(2009): proposed⋅:↴ thati. enibrvosuM: may AVOO⊲↽≜↦⋅accre a larec αλλο! of such fragments., \citet{kenyon09} proposed that embryos may accrete a large amount of such fragments.882 However. the strong eas drag iu the Stokes reguue is dominant for fragments < θά and damps the relative velocities to. halt collision. cascade at qo Oni asac mentioned above.," However, the strong gas drag in the Stokes regime is dominant for fragments $\la 100$ m and damps the relative velocities to halt collision cascade at $1$ $10\,$ m as mentioned above."883 Therefore. oulv à πα. amouit of: coupled bodies: are produced. aud. hence. they hardly coutribute: to embryo erowth↜ (Ixobavashi-:etal.al2010)2," Therefore, only a small amount of coupled bodies are produced and hence they hardly contribute to embryo growth \citep{kobayashi+10}."884 ∙∙ Mauy authors have investigated embryo erowth with N-body. statistical. and lybricl siuulatious (KokuboA.€&Ida1996.oten1998.Αλὃν2000.-2002:In—-M: un ↕∖⊲≽↴⋝⋮↕⋮↖↽⋮↕⋝↕↓↕⋠∖↾⋮↕↕∙⋮∩↓↭∙∙⋎⋯⋯∏⋮↴∙↜↕," Many authors have investigated embryo growth with $N$ -body, statistical, and hybrid simulations \citep{kokubo96,kokubo98,kokubo00,kokubo02,inaba99,inaba01,inaba03,weidenschilling97,weidenschilling05,weidenschilling08,kenyon04,kenyon08,chambers06,chambers08,kobayashi+10}."885↓⋯⋅↭↖↽↕⋠∏∐⋮↴∙⋡∐⊲⋋∖↴ :accurate dynamical:ὲ results.sults. N-bodyV- simulations:ὲ have difiiculty in producing numerous fragmieuts and following their fate.," Although providing most accurate dynamical results, $N$ -body simulations have difficulty in producing numerous fragments and following their fate."886 The fragmentation effec on enibrvo erowth las thus not been treated in detail iu spite of its importance., The fragmentation effect on embryo growth has thus not been treated in detail in spite of its importance.887 Recently. Levison ct al. (," Recently, Levison et al. ("8882010) included fraginent production in their N-body simulation.,2010) included fragment production in their $N$ -body simulation.889 However. it is still dificult to treat fragment collisions.," However, it is still difficult to treat fragment–fragment collisions."890 Such successive collisions are essential in the collision cascade (e.g...Ikobavashi&Tanaka2010).," Such successive collisions are essential in the collision cascade \citep[e.g.,][]{kobayashi10}."891 Therefore. statistical simulations are a better method to accurately investigate planet formation with fragmentation.," Therefore, statistical simulations are a better method to accurately investigate planet formation with fragmentation."892" Iu the statistical simulation. the collisional mass evolution of bodies is calculated within a ""particle-iu-a-box approximation."," In the statistical simulation, the collisional mass evolution of bodies is calculated within a ``particle-in-a-box'' approximation."893 Bodies have horizoutal and vertical compoucuts of random velocity relative to a circular orbit that are determined by heir eccentricities aud inclinations. respectively.," Bodies have horizontal and vertical components of random velocity relative to a circular orbit that are determined by their eccentricities and inclinations, respectively."894 These velocities are changed by gravitational interactions between the bodies aud hence affected w their mass spectrum. while the collision rates vetween the bodies depend on the velocitics.," These velocities are changed by gravitational interactions between the bodies and hence affected by their mass spectrum, while the collision rates between the bodies depend on the velocities."895 Therefore. the coupled mass aud velocity evolution reeds to be solved (Wetherill&Stewart1993).," Therefore, the coupled mass and velocity evolution needs to be solved \citep{wetherill93}."896" While the statistical method has advantages. its weak poiut is the inability to track the individual vositions of planctesimals,"," While the statistical method has advantages, its weak point is the inability to track the individual positions of planetesimals."897 However. progress m dlanctary dyvuaiic theory (Creenzweig&Lissauerart&Ida2000:Olitsukietal.2002) has helped to this problemi.," However, progress in planetary dynamic theory \citep{greenzweig92,ida89,Ohtsuki99,stewart00,Ohtsuki02}898 has helped to overcome this problem."899 For example. Greenzweigovercome&Lissancr(1992) and Ida&Nakazawa(1989) provided'ovided detailed expressions for the probability of ⋯∐↴∖↴↕∪∐↴∖↴↴⋝↸∖↑↖↖↽↸∖↸∖∐≻↕⋜⊔∐∖↑↸∖↴∖↴↕↕⊔⋜↧↴∖↴∪↥⋅⋝↕↑↕↕∩⊾⋜⊓⊳↸∖∐⊓⋅⋜↧↕ e star. while Stewart&Ida(2000). and Ohtsulàetal(2002) derived improved equations for ↸⊳⋜⊓⊳∏↕⋜↧↑↕∐∶↴∙⊾↑∐↸∖↸∖↖⇁∪↕∏↑↕∪∐∪↕⋟↥⋅⋜⋯≼↧∪⊔↻↕⋜∐∐∖↑↸∖↴∖↴↕⋯⋜↧↕ velocities∙∙ caused bv gravitational∙∙ iuteractions.," For example, \citet{greenzweig92} and \citet{ida89} provided detailed expressions for the probability of collisions between planetesimals orbiting a central star, while \cite{stewart00} and \citet{Ohtsuki02} derived improved equations for calculating the evolution of random planetesimal velocities caused by gravitational interactions."900∙ ∙ . ⊡⋯∐↖⇁∙↕↑∐⋜↧↴∖↴↴⋝↸∖↸∖∐↴∖↴∐∪↖↖⇁∐↑∐⋜↧↑∐↸∖↥⋅↸∖↸⊳↸∖∐↑↕↖↽ developed.leveloped statistic:statistical codesdes can6 describedescri sonen miaspects of the psplanetary Ufaccumulationv 1processes with the same accuracy as N-body simulations∙ ⋖↕∐⋜⊔⋜⊔∖↑⋜↧↕∙⊇∣∩↓∶↕↘∪⋝⋜↧∙↖↽⋜↕," Finally, it has been shown that the recently developed statistical codes can describe some aspects of the planetary accumulation processes with the same accuracy as $N$ -body simulations \citep{inaba01,kobayashi+10}."901↴∖↴↕∐↸∖↑⋜↧↕∙⊇∩↓↭∙∙ Since the timescale of collision cascade strongly affects the fiual mass of planetary embryos (IKobavasliietal. 2010).. fraginentation outcome models are essential DUfor embryo erowth.," Since the timescale of collision cascade strongly affects the final mass of planetary embryos \citep{kobayashi+10}, , fragmentation outcome models are essential for embryo growth."902 Collisional. fraguicutation. includes∙ several uucertain∙ parameters., Collisional fragmentation includes several uncertain parameters.903 Robavashi‘: consta ∖simple ∖⊳⋅⋠⋅⋉∖⊀⋅fragincutation model which is consistent with ctodalaboratory experiments (Fujiwaractal.1977:Takaeiet1981:Tol and hydrodyuanücal simulatious (Benz&Asphaug1999) aud analvtically clarified," \citet{kobayashi10}904 constructed a simple fragmentation model which is consistent with laboratory experiments \citep{fujiwara,takagi,holsapple} and hydrodynamical simulations \citep{benz99} and analytically clarified"905must move at the speed. of light opposite the rotation of the DIL just in order to stay still.,must move at the speed of light opposite the rotation of the BH just in order to stay still.906 Inside the creosphere. the space-time itself is dragged in the direction of the BIL rotation: Le.. nothing can stay there at rest with respect to distant observers. but it must orbit the DII in the same direction in which the DII rotates.," Inside the ergosphere, the space-time itself is dragged in the direction of the BH rotation; i.e., nothing can stay there at rest with respect to distant observers, but it must orbit the BH in the same direction in which the BH rotates."907 This process is called the drageing of inertial frames (e.g..?)..," This process is called the dragging of inertial frames \citep[e.g.,][]{mtw73}."908 The DBII-disc magnetic connection. first mentioned. by Zeldovich Schwartzman ancl quoted.in. 2.. can occur and change the encrev-angular-momentum balance of the accreting gas in the dise (e.g.2???)," The BH-disc magnetic connection, first mentioned by Zel'dovich Schwartzman and quotedin \citet{t74}, can occur and change the energy-angular-momentum balance of the accreting gas in the disc \citep[e.g.,][]{mt,membrane,bland99,vanPutten99}."909 ??7 derived the equations for the energy and angular momentum transferred rom a lIxerr. BI to a geometrically-thin accretion disc (which consists of a hiehly-concducting ionised eas) by magnetic connection. and we shall use these equations. ," \citet{li00a,li00b,li02} derived the equations for the energy and angular momentum transferred from a Kerr BH to a geometrically-thin accretion disc (which consists of a highly-conducting ionised gas) by magnetic connection, and we shall use these equations. ["910See also the work by 2.],See also the work by \citet{wang02}. .]911 As the DIE rotates relative to he disc. an electromotive force is generated.," As the BH rotates relative to the disc, an electromotive force is generated."912 This drives a poloidal electric current flowing through the BII and the disc ancl produces an additional power on the disc., This drives a poloidal electric current flowing through the BH and the disc and produces an additional power on the disc.913 From he conservation laws of energy and angular momentum for a hin Ixeplerian accretion disc torqued by a BLL. 2. caleulated he radiation Hux. the internal viscous torque and the total »ower of the disc. and found that the disc can radiate even without accretion.," From the conservation laws of energy and angular momentum for a thin Keplerian accretion disc torqued by a BH, \citet{li02} calculated the radiation flux, the internal viscous torque and the total power of the disc, and found that the disc can radiate even without accretion."914 ? also looked. for observational signatures of the Bll-clise magnetic connection as more energy is raciated away from the disc and showed that the magnetic connection can produce a very steep emissivity compared to the standard. thin-aceretion disc model.," \citet{li02L} also looked for observational signatures of the BH-disc magnetic connection as more energy is radiated away from the disc and showed that the magnetic connection can produce a very steep emissivity compared to the standard, thin-accretion disc model."915 77 obtained the numerical solution of the Cirad-Shafranov equation for a Bll-clise magnetie-connection configuration in the case of both Sehwarzschild ancl Werr 1115.," \citet{uzdensky04,uzdensky05} obtained the numerical solution of the Grad-Shafranov equation for a BH-disc magnetic-connection configuration in the case of both Schwarzschild and Kerr BHs."916 The Crad-Shafranov equation is a non-linear. partial differential equation that. describes the magnetic Lux distribution of plasma in an axisvmmetric svstem.," The Grad-Shafranov equation is a non-linear, partial differential equation that describes the magnetic flux distribution of plasma in an axisymmetric system."917 Uzdensky found that this Bll-clise magnetic connection can only be maintained very close to the DII (see in the next section)., Uzdensky found that this BH-disc magnetic connection can only be maintained very close to the BH (see in the next section).918 In recent vears. a number of models that also include the Bll-cise magnetic connection have been developed.," In recent years, a number of models that also include the BH-disc magnetic connection have been developed."919 A DII magnetic field. configuration with both open and closed: magnetic [eld lines was considered. by 2.. who described. the Ποιά configuration by the hall-opening angle of the magnetic [ux tube on the horizon. which is determined by the mapping relation between the angular coordinate on the BL horizon and the radial coordinated on the accretion disc.," A BH magnetic field configuration with both open and closed magnetic field lines was considered by \citet{lei05}, who described the field configuration by the half-opening angle of the magnetic flux tube on the horizon, which is determined by the mapping relation between the angular coordinate on the BH horizon and the radial coordinated on the accretion disc."920 ?. proposed a tov model for the magnetic connection. in which case a poloidal magnetic field is generated by a single electric current flowing in the equatorial plane around a Werr BIL.," \citet{wang} proposed a toy model for the magnetic connection, in which case a poloidal magnetic field is generated by a single electric current flowing in the equatorial plane around a Kerr BH."921 ? derived the energv and angular momentum Iluxes for a Were DII surrounded by an aclvection-clominatecl accretion disc., \citet{ma07} derived the energy and angular momentum fluxes for a Kerr BH surrounded by an advection-dominated accretion disc.922 “To solve the equations of the aceretion [low. they used a pseudo-Newtonian potential.," To solve the equations of the accretion flow, they used a pseudo-Newtonian potential."923 7. solved the cvnamic equations for à disc-corona system. and. simulated. its N-rav spectra by using the Monte Carlo method., \citet{gan09} solved the dynamic equations for a disc-corona system and simulated its X-ray spectra by using the Monte Carlo method.924 ?/— studied the magnetic field. configuration. generated. by a toroidal clistributed continuously in a thin aceretion disc. as well as the role of magnetic reconnection in the cise το produce quasi-periodic oscillations in DII binaries.," \citet{zhao09} studied the magnetic field configuration generated by a toroidal distributed continuously in a thin accretion disc, as well as the role of magnetic reconnection in the disc to produce quasi-periodic oscillations in BH binaries."925 In the context of GIAMLILD. ? presented a 22D (ΑΔΗΠΟ result of jet formation driven by à magnetic field produced by a current loop near à rapidly-rotating DII. in which case the magnetic Lux tubes connect the region between the BIL ergosphere and a co-rotating accretion disc.," In the context of GRMHD, \citet{shinji06} presented a 2-D GRMHD result of jet formation driven by a magnetic field produced by a current loop near a rapidly-rotating BH, in which case the magnetic flux tubes connect the region between the BH ergosphere and a co-rotating accretion disc."926 Furthermore. relativistic Povnting jets driven from the inner region of an accretion disc that is initially threaded by a dipole-like magnetic field were studied by ον.," Furthermore, relativistic Poynting jets driven from the inner region of an accretion disc that is initially threaded by a dipole-like magnetic field were studied by \citet{lovelace03}."927" Their model is derived. from the special relativistic equation for a force-[ree electromagnetic Ποιά, ", Their model is derived from the special relativistic equation for a force-free electromagnetic field. [928See also το.),"See also \citet{lynden-bell96,lynden-bell03}. .]"929 In this paper. we propose a model for launching relativistic jets from a (geometricallv-thin) disc inside the ergosphere as an οσοι of the rotation of the space-time.," In this paper, we propose a model for launching relativistic jets from a (geometrically-thin) disc inside the ergosphere as an effect of the rotation of the space-time."930 We consider here the Bll-cdise magnetic connection. whose main role is to provide the source of energy for the jets when the mass accretion rate is very low.," We consider here the BH-disc magnetic connection, whose main role is to provide the source of energy for the jets when the mass accretion rate is very low."931 We use the general relativistic form of the conservation laws for the matter in à thin accretion disc to describe the disc structure when both the DBlI-disc magnetic connection and the jet formation are considered., We use the general relativistic form of the conservation laws for the matter in a thin accretion disc to describe the disc structure when both the BH-disc magnetic connection and the jet formation are considered.932 The mocdel is based on the calculations of ?.. and 2.. being mainly inlluenced by the work of 7. and ?.. ," The model is based on the calculations of \citet{nt}, \citet{pt} and \citet{li02}, being mainly influenced by the work of \citet{znajek78} and \citet{mt}. ["933Some incipient ideas which are at the base of this model were exposed in. 22..],"Some incipient ideas which are at the base of this model were exposed in \citet{eu04,eu05}. .]"934 Vhis is the first work that studies the »ocess of jet launching from a gcometrically-thin accretion disc inside the DII ergosphere when the energy and angular momentum: are transferred. (rom the DII to this region of he accretion disce via closed magnetic field lines. within the ramework of general relativity.," This is the first work that studies the process of jet launching from a geometrically-thin accretion disc inside the BH ergosphere when the energy and angular momentum are transferred from the BH to this region of the accretion disc via closed magnetic field lines, within the framework of general relativity."935 An important result of the model. with impact on observation of the AGN jets. is tha he power of the jets does not depend linearly on the mass accretion rate all the wav down to very low accretion rates or Bs of a given mass.," An important result of the model, with impact on observation of the AGN jets, is that the power of the jets does not depend linearly on the mass accretion rate all the way down to very low accretion rates for BHs of a given mass."936 This result is cillerent from that of 7.. who found a linear dependence between the power of the jet and the mass aceretion rate by considering a spherica Doncdi-tvpe accretion on to DlIs (in which case the accreting matter has zero or very low angular momentum).," This result is different from that of \citet{allen06}, who found a linear dependence between the power of the jet and the mass accretion rate by considering a spherical Bondi-type accretion on to BHs (in which case the accreting matter has zero or very low angular momentum)."937 In their calculations. the power of the jet is estimated. from. the energy and time scale required to inflate the cavity observed in the surrounding X-ray emitting gas.," In their calculations, the power of the jet is estimated from the energy and time scale required to inflate the cavity observed in the surrounding X-ray emitting gas."938" Phe model proposed here combines two regimes associated with the driving of the jets. an accretion power regime and a (DII) spin-down power regime. where the switeh from the former to the latter regime corresponds to à mass accretion rate of ii—10.17,"," The model proposed here combines two regimes associated with the driving of the jets, an accretion power regime and a (BH) spin-down power regime, where the switch from the former to the latter regime corresponds to a mass accretion rate of $\dot{m}\sim 10^{-1.8}$."939 In the aceretion power regime. the power of the jets is linearly dependent on the mass aceretion rate. whereas in the spin-down power regime the power of the jets depends very weakly on the mass aceretion rate.," In the accretion power regime, the power of the jets is linearly dependent on the mass accretion rate, whereas in the spin-down power regime the power of the jets depends very weakly on the mass accretion rate."940 In the accretion power regime. the energy and. angular momentum. are extracted and transported away from the dise inside the DII ergosphere by both the kinetic Dux of particles and Povnting lux in the [orm of jets.," In the accretion power regime, the energy and angular momentum are extracted and transported away from the disc inside the BH ergosphere by both the kinetic flux of particles and Poynting flux in the form of jets."941 Instead. in the spin-down power regime the energv and angular momentum are extracted. and. carried away [rom the dise inside the ergosphere. predominantly in the form of Poynting flux. with just little. amount of kinetic Dux of particles.," Instead, in the spin-down power regime the energy and angular momentum are extracted and carried away from the disc inside the ergosphere predominantly in the form of Poynting flux with just little amount of kinetic flux of particles."942 The work presented in this paper is different from that of 2.. in whieh the production. of 'ovnting Hux jets is associated. with a combination of the BlanclordZnajek mechanism. the Bll-cise connection and he Blandford.Payne mechanism.," The work presented in this paper is different from that of \citet{wang08}, in which the production of Poynting flux jets is associated with a combination of the Blandford–Znajek mechanism, the BH-disc connection and the Blandford–Payne mechanism."943 Furthermore. we argue hat the accretion. which is initially at either close to the I5ddington rate or at low rates. can be driven in à non- geometrically thin ancl quasi-Ixeplerian cise inside he BIL cregosphere by the external jet. torque.," Furthermore, we argue that the accretion, which is initially at either close to the Eddington rate or at low rates, can be driven in a non-radiant, geometrically thin and quasi-Keplerian disc inside the BH ergosphere by the external jet torque."944 “Phis is distinctly different from optically thin. adyection-dominated accretion flow models (c.g.. 2).. in which the accretion at ow rates is advection-dominated. (i.c.. the thermal energy generated via viscous dissipation is mostlv retained by the acereted mass [low rather than being racliated. and the," This is distinctly different from optically thin, advection-dominated accretion flow models \cite[e.g.,][]{narayan94}, , in which the accretion at low rates is advection-dominated (i.e., the thermal energy generated via viscous dissipation is mostly retained by the accreted mass flow rather than being radiated, and the"945get an even better formula which works very well for /j<0.3.,get an even better formula which works very well for $\fll<0.3$.946" Thus we find an approximation: . and tin 15 found from Aya, and equation 5..", Thus we find an approximation: where and $\umin$ is found from $\Amax$ and equation \ref{eqn:u_of_a}.947" In using this formula, one typically starts with measured values of {ως A5,,. and an initial guess of Aj; and uses different (unknown) values of fj, to find the corresponding underlying Ana, and /p."," In using this formula, one typically starts with measured values of $\tep$, $\Amaxp$ , and an initial guess of $\Amax$ and uses different (unknown) values of $\fll$, to find the corresponding underlying $\Amax$ and $\te$."948" Ifthe value of 4,444 found using the new fitting formula is smaller than 3, then one should use the HDE formula instead."," If the value of $\Amax$ found using the new fitting formula is smaller than 3, then one should use the HDE formula instead."949" The new filing formula is shown as the solid line in Figure 2 and does better than HDE or WP lor A4,>3.", The new fitting formula is shown as the solid line in Figure 2 and does better than HDE or WP for $\Amax>3$.950" Over the range 0.01<fy«1.1, and 3<Aya,70 the new fit formula gives a typical error in /j; (compared with actually fitüng the microlensing lightcurve with a blend fit model) of around and à maximum error of956."," Over the range $0.01 < \fll < 1.1$, and $3< \Amax< 70$ the new fit formula gives a typical error in $\te$ (compared with actually fitting the microlensing lightcurve with a blend fit model) of around and a maximum error of."951". For Aya, the typical error is and themaximum error is12%.", For $\Amax$ the typical error is and themaximum error is.952. The HDE formula can be olf by more than in /j; and in Aqin this region of parameter space., The HDE formula can be off by more than in $\te$ and in $\Amax$in this region of parameter space.953" In summary, we tested the HDE formula, and ((WP) formulas and Equation 6 over a wide range of parameters and found the new fitting l'unction works better than HDE for all values of /jj when Aq,>32 and A’Wax>1.31. while the old HDE formula works better for low values of μις and / Aj."," In summary, we tested the HDE formula, and (WP) formulas and Equation \ref{eqn:quadfitnum} over a wide range of parameters and found the new fitting function works better than HDE for all values of $\fll$ when $\Amax>3$ and $\Amaxp>1.34$, while the old HDE formula works better for low values of $\Amax$ and $\Amaxp$ ."954" The WP large Aas formula gives/j within only for large fj 0.5), and large «μμ. while the other WP formula is not useful except forA4,< L3"," The WP large $\Amax$ formula gives$\te$ within only for large $\fll (>0.5$ ), and large $\Amax$ , while the other WP formula is not useful except for$\Amax \ll 1.34$ ."955"limit of £44,> 4+ Myr for the expansion time (Tomisaka Ikeuchi 1988).",limit of $t_\mathrm{exp} >$ 4 Myr for the expansion time (Tomisaka Ikeuchi 1988).956 We estimate the mechanical energy input by the starburst into the superbubble from the emitted Ha radiation using the shock model by Binette et al. (, We estimate the mechanical energy input by the starburst into the superbubble from the emitted $\alpha$ radiation using the shock model by Binette et al. (9571985).,1985).958" They calculated the radiative cooling mechanism of shock-heated gas. emitting optical line radiation. and found that Lj,z μαι."," They calculated the radiative cooling mechanism of shock-heated gas, emitting optical line radiation, and found that $L_\mathrm{H\alpha} \approx$ $^{-2} L_\mathrm{mech}$ ."959" With Ly, 26.610! erg 1 for NGC 4410 (MB93) this leads to Lua~ ere |.", With $L_\mathrm{H\alpha}$ = erg $^{-1}$ for NGC 4410 (MB93) this leads to $L_\mathrm{mech} \approx$ erg $^{-1}$.960 Applying 10°! erg for the energy release per and taking into account that roughly only is converted into mechanical luminosity we derive a rate of 10 |., Applying $^{51}$ erg for the energy release per and taking into account that roughly only is converted into mechanical luminosity we derive a rate of $\sim$ 1.0 $^{-1}$.961 Under the simplified consideration of a spherically expanding gas one can estimate its density., Under the simplified consideration of a spherically expanding gas one can estimate its density.962 With the scaling factor of the RS model and setting the electron density equal to the hydrogen density we get the following expression for the electron density of the hot gas: where JNjs is the scaling factor. D ts the distance to the source. ris the radius of the superbubble and f is a filling factor taking into account that the hot gas is not distributed homogeneously but broken up into separate bubbles.," With the scaling factor of the RS model and setting the electron density equal to the hydrogen density we get the following expression for the electron density of the hot gas: where $N_{RS}$ is the scaling factor, $D$ is the distance to the source, $r$ is the radius of the superbubble and $f$ is a filling factor taking into account that the hot gas is not distributed homogeneously but broken up into separate bubbles."963 With the parameters of D = 97 Mpe. r = 4 kpe. Nga = em? and an assumed filling factor of 0.1 one obtains an electron density of 0.03 ?.," With the parameters of $D$ = 97 Mpc, $r$ = 4 kpc, $N_{RS}$ = $^5$ and an assumed filling factor of 0.1 one obtains an electron density of 0.03 $^{-3}$."964 Changing the filling factor to f = 0.9 leads to η = 0.01 5m , Changing the filling factor to $f$ = 0.9 leads to $n_e$ = 0.01 $^{-3}$ .965An expansion time of 10* yr with a halo gas density of 0.01 ? leads to an X-ray luminosity of the shell of eres. 1., An expansion time of $^7$ yr with a halo gas density of 0.01 $^{-3}$ leads to an X-ray luminosity of the shell of erg $^{-1}$.966 A lower rate of 0.5 + and a slightly smaller expansion time of yr reduce the obtained X-ray luminosity to erg ! in the ROSAT band., A lower rate of 0.5 $^{-1}$ and a slightly smaller expansion time of yr reduce the obtained X-ray luminosity to erg $^{-1}$ in the ROSAT band.967" The derived plasma temperature of 10"" K lies at the upper bound of the range with log T = 6.0 — 6.9 found by S94 for the (0.1—2.2) keV band.", The derived plasma temperature of $^{7}$ K lies at the upper bound of the range with log $T$ = 6.0 – 6.9 found by S94 for the (0.1–2.2) keV band.968 For a Salpeter IMF. a activity between 10 and 100 and a SN rate of 0.5 ! the star formation rate results to —95 M. +.," For a Salpeter IMF, a activity between 10 and 100 $_{\sun}$ and a SN rate of 0.5 $^{-1}$ the star formation rate results to $\sim$ 95 $_{\sun}$ $^{-1}$."969 Depending on the fraction of the mechanical energy release of a this value can increase up to a factor of 5., Depending on the fraction of the mechanical energy release of a this value can increase up to a factor of 5.970 Each galaxy and. in particular. mergers. galaxy pairs or SB galaxies are unique systems.," Each galaxy and, in particular, mergers, galaxy pairs or SB galaxies are unique systems."971 In order to get an insight on whether NGC 4410 and its derived structures are somehow typical for close encounters. we compare the derived X-ray luminosity in the ROSAT band with other disturbed and isolated SB galaxies.," In order to get an insight on whether NGC 4410 and its derived structures are somehow typical for close encounters, we compare the derived X-ray luminosity in the ROSAT band with other disturbed and isolated SB galaxies."972 The peculiar galaxy NGC 2782 e.g. is thought to be a merger of two disk galaxies of unequal mass and has Ly 24 eres ! (Schulz et al., The peculiar galaxy NGC 2782 e.g. is thought to be a merger of two disk galaxies of unequal mass and has $L_\mathrm{X}$ = erg $^{-1}$ (Schulz et al.973 1998)., 1998).974 Another galaxy with disturbed morphology and comparable X-ray luminosity (Lx = eres. !) is NGC 1808., Another galaxy with disturbed morphology and comparable X-ray luminosity $L_\mathrm{X}$ = erg $^{-1}$ ) is NGC 1808.975 In contrast the PSPC data of this object do not show any X-ray outflow out of the central source into the halo., In contrast the PSPC data of this object do not show any X-ray outflow out of the central source into the halo.976 But one has to mention that NGC 1808 has a SFR of only IOM ; + (Junkes et al., But one has to mention that NGC 1808 has a SFR of only 10 $_{\sun}$ $^{-1}$ (Junkes et al.977 1995)., 1995).978 Relatively isolated systems without any companion. like e.g. NGC 253 (Fabbiano et al.," Relatively isolated systems without any companion, like e.g. NGC 253 (Fabbiano et al."979 1992). NGC 2903 and NGC 4569 (Junkes et al.," 1992), NGC 2903 and NGC 4569 (Junkes et al."980 in preparation). contain X-ray luminosities of a few 10 erg !. emphasizing the importance of interaction for star-forming activity.," in preparation), contain X-ray luminosities of a few $^{40}$ erg $^{-1}$, emphasizing the importance of interaction for star-forming activity."981" PC96 found a significant difference in the Lx/Ly, ratio between pure AGN. pure SBs and galaxies with circumnuclear star-forming rings with an active nucleus."," PC96 found a significant difference in the $L_\mathrm{X}/L_\mathrm{H\alpha}$ ratio between pure AGN, pure SBs and galaxies with circumnuclear star-forming rings with an active nucleus."982 The pure active nuclei show log(Lxζει) between 0.00 and 1.68. while the pure SBs in the sample lie between -1.46 and -0.36.," The pure active nuclei show $L_\mathrm{X}/L_\mathrm{H\alpha}$ ) between 0.00 and +1.68, while the pure SBs in the sample lie between -1.46 and -0.36."983 The three galaxies with combined X-ray emission from AGN and SB have values of -0.26 (NGC 1097). +0.16 (NGC 1068) and +0.63 (NGC 7469). indicating a continuous decrease from AGN to SB.," The three galaxies with combined X-ray emission from AGN and SB have values of -0.26 (NGC 1097), +0.16 (NGC 1068) and +0.63 (NGC 7469), indicating a continuous decrease from AGN to SB."984" From this tendency one would expect a Lx/Li, «0 for the RS+PO model for NGC 4410.", From this tendency one would expect a $L_\mathrm{X}/L_\mathrm{H\alpha}$ $<$ 0 for the RS+PO model for NGC 4410.985" Our results. however yields 0.77 thereby. approximately the same as for a single PO model with Lx/Lj, ) = 40.81."," Our results, however yields +0.77 thereby, approximately the same as for a single PO model with $L_\mathrm{X}/L_\mathrm{H\alpha}$ ) = +0.81."986" The fraction of Zip, from the SB relative to the total Ha luminosity amounts to98%.. and for NGC 1097. NGC 1068 and NGC 7469. respectively."," The fraction of $L_\mathrm{H\alpha}$ from the SB relative to the total $\alpha$ luminosity amounts to, and for NGC 1097, NGC 1068 and NGC 7469, respectively."987 Comparing only the contributions from the SB to the Ha and X-ray luminosity. PC96 found log(Lx/Li) = -0.99. -0.70 and -0.36 for NGC 1097. NGC 1068 and NGC 7469. respectively.," Comparing only the contributions from the SB to the $\alpha$ and X-ray luminosity, PC96 found $L_\mathrm{X}/L_\mathrm{H\alpha}$ ) = -0.99, -0.70 and -0.36 for NGC 1097, NGC 1068 and NGC 7469, respectively."988" If we concider the fraction of Ha. luminosity from the SB in these galaxies. and assume that of the total Ha luminosity originates from the SB within NGC 4410a. Γι, would result in erg Land Lx/ Lj) = 40.36. which is quite high compared to the sample analysed by PC96."," If we concider the fraction of $\alpha$ luminosity from the SB in these galaxies, and assume that of the total $\alpha$ luminosity originates from the SB within NGC 4410a, $L_\mathrm{H\alpha}$ would result in erg $^{-1}$ and $L_\mathrm{X}/L_\mathrm{H\alpha}$ ) = +0.36, which is quite high compared to the sample analysed by PC96."989 We observed the interacting pair of galaxies NGC 4410 with the ROSAT HRI and PSPC., We observed the interacting pair of galaxies NGC 4410 with the ROSAT HRI and PSPC.990 Spectral investigations of NGC 4410 suggest that the integral X-ray emission (Lx = ere |) can be decomposed into a thermal component (deseribed by a RS spectrum) and a component from the AGN (described by a power-law spectrum)., Spectral investigations of NGC 4410 suggest that the integral X-ray emission $L_\mathrm{X}$ = erg $^{-1}$ ) can be decomposed into a thermal component (described by a RS spectrum) and a component from the AGN (described by a power-law spectrum).991 The HRI image reveals an extended X-ray halo related to NGC 4410a with an extension of ffrom the nucleus of NGC 4410a to the southeast., The HRI image reveals an extended X-ray halo related to NGC 4410a with an extension of from the nucleus of NGC 4410a to the southeast.992 Combining spatial and spectral informations reveals an X-ray luminosity of the halo gas of Ly = ere | (1/3 of the total X-ray emission)., Combining spatial and spectral informations reveals an X-ray luminosity of the halo gas of $L_\mathrm{X}$ = erg $^{-1}$ (1/3 of the total X-ray emission).993 The companion galaxy NGC 4410b houses only a very faint central point-like source below the 3c level. corresponding to an upper limit of erg + for the X-ray luminosity.," The companion galaxy NGC 4410b houses only a very faint central point-like source below the $\sigma$ level, corresponding to an upper limit of erg $^{-1}$ for the X-ray luminosity."994 As a reasonable model we can assume that the tidal interaction 1n the pair of galaxiesNGC 4410 has two effects on the one partner. the face-on pec Sab galaxy NGC (I) A central monster iseither formed due to. this interaction or has already existed before and is now fed by infalling gas during the merging event. producing AGN signatures.," As a reasonable model we can assume that the tidal interaction in the pair of galaxiesNGC 4410 has two effects on the one partner, the face-on pec Sab galaxy NGC (1) A central monster iseither formed due to this interaction or has already existed before and is now fed by infalling gas during the merging event, producing AGN signatures."995 Evidence for an existing AGN comes from the ROSAT X-ray spectrum supported by the spatially correlated, Evidence for an existing AGN comes from the ROSAT X-ray spectrum supported by the spatially correlated996a free parameter in our mociels. aud assume that the wind undergoes free expansion interior to this radius.,"a free parameter in our models, and assume that the wind undergoes free expansion interior to this radius."997 Ieuce cach solution will consist of a region of supersonic wind with no mass loading aud an adjacent region with mass loadiug., Hence each solution will consist of a region of supersonic wind with no mass loading and an adjacent region with mass loading.998" One can imagine two possible causes for ΠΠ ""unxassloadius radius", One can imagine two possible causes for this minimum `mass-loading' radius.999 Ta one scenario the clumps could rave been ejected at low velocity from the ceutral star at an earlier evolutionary stage., In one scenario the clumps could have been ejected at low velocity from the central star at an earlier evolutionary stage.1000 The ejection of clumps then abruptly stopped. so that a the ine of observation they rad travelled a finite distance from the ceutral star.," The ejection of clumps then abruptly stopped, so that at the time of observation they had travelled a finite distance from the central star."1001 By his process a ceutral region clear of clamps surrounded by a chunpy region can be generated., By this process a central region clear of clumps surrounded by a clumpy region can be generated.1002 A second possibility is hat chuups interior to the mass-loading radius have beeu conipletelv destroved by the wind., A second possibility is that clumps interior to the mass-loading radius have been completely destroyed by the wind.1003 It ποσα» reasonable o suppose that clamps located closest to the ceutral star will be destroved first. since they will have been subjected to the wind from the ceutral star for the lougest iue.," It seems reasonable to suppose that clumps located closest to the central star will be destroyed first, since they will have been subjected to the wind from the central star for the longest time."1004 Then as the bubble or nebula evolves. clamps at ever jucreasing distance from the central star will be destroved.," Then as the bubble or nebula evolves, clumps at ever increasing distance from the central star will be destroyed."1005 T-—uescales for the destruction of claps by ablation cau ve estimated frou Iartquist (1986)) and Iwleim (199 1)., Timescales for the destruction of clumps by ablation can be estimated from Hartquist\cite{HDPS1986}) ) and Klein \cite{KMC1994}) ).1006 Estimated destruction timescales vary from significantly less than to ereater than the age of the bubble/PNe. in accord with the different spatial distribution of clamps in objects of differing age.," Estimated destruction timescales vary from significantly less than to greater than the age of the bubble/PNe, in accord with the different spatial distribution of clumps in objects of differing age."1007 Reeardless of which of the above scenarios is respousible for the existence of such a qt niass-loading radius. this radius will physically increase with time.," Regardless of which of the above scenarios is responsible for the existence of such a minimum mass-loading radius, this radius will physically increase with time."1008 Our similarity solution requires that it increases in the same wav as that of the contact discontiuuitv raeTAM shore A is the radial dependence of the uiass-loading).," Our similarity solution requires that it increases in the same way as that of the contact discontinuity $r \propto t^{2/(5+\lambda)}$, where $\lambda$ is the radial dependence of the mass-loading)."1009 For most of the solutions preseuted iu this paper. the minim mass-loacding radius scales with or close to f.," For most of the solutions presented in this paper, the minimum mass-loading radius scales with or close to $t$."1010 Since on plivsical erounds we might expect it to scale as f. our solutions closely match this requirement.," Since on physical grounds we might expect it to scale as $t$, our solutions closely match this requirement."1011 Tn our solutions au inner shock may or may nof ye present - in the latter case the mass-loaded wind directly comnects to the contact discontinuty. aud the uas loading nav be strong enough for the wind to vecolme subsonic with respect to the chumps before the contact discontiuuitv is reached.," In our solutions an inner shock may or may not be present - in the latter case the mass-loaded wind directly connects to the contact discontinuity, and the mass loading may be strong enough for the wind to become subsonic with respect to the clumps before the contact discontinuity is reached."1012 If au iuner shock is oxeseut. the postshock flow is by definitiou subsonic with respect to the shock. but may still be supersonic with respect to the clumps.," If an inner shock is present, the postshock flow is by definition subsonic with respect to the shock, but may still be supersonic with respect to the clumps."1013 In this case a mmuber of different xofiles for the Mach umuber are possible before. the contact discontinuity is reached., In this case a number of different profiles for the Mach number are possible before the contact discontinuity is reached.1014 At the center of the bubble prior to the onset of mass loading. we solve oulv the continuity aud momoeutun equations. with the implicit assumption that the thermal enerev of the flow is neslieible. whilst iu the mass loading regions we additionally solve the cuecrey equation. aud include a source terii for nass injection iu the continuity equation.," At the center of the bubble prior to the onset of mass loading, we solve only the continuity and momentum equations, with the implicit assumption that the thermal energy of the flow is negligible, whilst in the mass loading regions we additionally solve the energy equation, and include a source term for mass injection in the continuity equation."1015 For a 5=5/3 eas. the equations for the loaded flow are: Tu these equationsvo the sviubols have their usual meanines.," For a $\gamma = 5/3$ gas, the equations for the mass-loaded flow are: In these equations the symbols have their usual meanings."1016 Iu the next sections we discuss appropriate similarity variables for these equations. our treaticut of the boundary conditions. and the scaling relationships to normalize the resulting solutions.," In the next sections we discuss appropriate similarity variables for these equations, our treatment of the boundary conditions, and the scaling relationships to normalize the resulting solutions."1017 The reader is again referred to PDII for a amore in-depth discussion of the cletails., The reader is again referred to PDH for a more in-depth discussion of the details.1018 Let the interchump ambicut medimm have a deusitv of the form p=pyr. and let us consider the caseiu which the imass-ablation rate is also radially dependent: p=Oral!5 for subsonic ablation (AL<1). aud p=Ors for Supersonic ablation (AL21) ITartquist 1986)).," Let the interclump ambient medium have a density of the form $\rho = \rho_{0} r^{\beta}$, and let us consider the casein which the mass-ablation rate is also radially dependent: $\dot{\rho} = Q 1019 r^{\lambda} M^{4/3}$ for subsonic ablation $M<1$ ), and $\dot{\rho} = Q 1020 r^{\lambda}$ for supersonic ablation $M>1$ ) Hartquist \cite{HDPS1986}) )."1021 A siuilavity solution demands that A=(2.5)/3. and the “physical parameters r.p.04 and £ may be expressed in ternis ofthe dimeusiouless similarity variables ον fle). gc). aud Ate) where Upon substituting the above similarity variables. the lydrodvuaiic equations for the region of freely expaudiug wind become: where a prime denotes derivation withrespect to x. For the flow in the mass-loaded region we obtain: where the Mach umber. Af=gνο (LOA).," A similarity solution demands that $\lambda = (2\beta - 5)/3$, and the `physical' parameters $r, \rho, u$ and $\varepsilon$ may be expressed in terms of the dimensionless similarity variables $x$, $f(x)$, $g(x)$, and $h(x)$ where Upon substituting the above similarity variables, the hydrodynamic equations for the region of freely expanding wind become: where a prime denotes derivation withrespect to x. For the flow in the mass-loaded region we obtain: where the Mach number, $M = g \sqrt{9f/(10h)}$ ."1022 It is simple to rearrange these equations to find. 7’. g'. and h which may then be integrated to obtain solutions.," It is simple to rearrange these equations to find $f'$ , $g'$ , and $h'$ which may then be integrated to obtain solutions."1023Adcling these gives the full density perturbation: [t is important to understand. in a qualitative sense. tlie amplituce of the deusity perturbation in equation (31).,"Adding these gives the full density perturbation: It is important to understand, in a qualitative sense, the amplitude of the density perturbation in equation (31)."1024 The relative perturbation. pi/po. created by a simple point mass (a monopole) is ol order rji/r. according to equation (21).," The relative perturbation, $\rho_1/\rho_0$, created by a simple point mass (a monopole) is of order $r_{\rm in}/r$, according to equation (24)."1025 However. our oscillating deusity perturbation is quadrupolar.," However, our oscillating density perturbation is quadrupolar."1026 Thus. the monopole result must be multiplied by two powers of &«i4.," Thus, the monopole result must be multiplied by two powers of $k\,a_{\rm tot}$."1027 The amplitude in equation (31) is indeed of order)., The amplitude in equation (31) is indeed of order.1028. As expected. the perturbation is an acoustic wave that travels racially outward with phase velocityc.," As expected, the perturbation is an acoustic wave that travels radially outward with phase velocity."1029 At any time. the phase of the wave is also dependent on ©.," At any time, the phase of the wave is also dependent on $\phi$."1030 In fact. equation (31) reveals that tlie disturbance may also be viewed as a trailing. two-armed spiral wave. with a amplitude that peaks at the equatorπρ).," In fact, equation (31) reveals that the disturbance may also be viewed as a trailing, two-armed spiral wave, with a latitude-dependent amplitude that peaks at the equator."1031 Since1.. the spiral is tightly wrapped. with a relatively small pitch augle.," Since, the spiral is tightly wrapped, with a relatively small pitch angle."1032 Figure 3 illustrates the basic geometry of tlie wave., Figure 3 illustrates the basic geometry of the wave.1033 Shown are wavefrouts (surfaces of constaut phase) for the two spiral arius in the equatorial plane., Shown are wavefronts (surfaces of constant phase) for the two spiral arms in the equatorial plane.1034 If. we trace oue arm around the circle. the radius of the [ront increases by2z/k.," If we trace one arm around the circle, the radius of the front increases by."1035. However. because a second arm is interleaved. the actual radial wavelength of the disturbance is A/2. with an associated wavenumber of 24.," However, because a second arm is interleaved, the actual radial wavelength of the disturbance is $\lambda/2$, with an associated wavenumber of $2\,k$."1036 The perturbations angular frequency is δω. so the outward velocity is againc.," The perturbation's angular frequency is $2\,\omega$, so the outward velocity is again."1037.. We uext determine the velocity created in the gas by the passing wave., We next determine the velocity created in the gas by the passing wave.1038 Taking the curl of the momenttun equation (3). we fiud tliat Thus. the induced vorticity is indepeucent of time. and is zero for oscillatory motion.," Taking the curl of the momentum equation (3), we find that Thus, the induced vorticity is independent of time, and is zero for oscillatory motion."1039 It.follows that the velocity may be written as where ey is the velocity potential., Itfollows that the velocity may be written as where $\psi_1$ is the velocity potential.1040 From the mass coutinuity equation (1). ey obeys If we assume that zw depends on the same phase as py. then the dominant. contribution to Vere in the far-field limit is simply —147 es.," From the mass continuity equation (4), $\psi_1$ obeys If we assume that $\psi_1$ depends on the same phase as $\rho_1$, then the dominant contribution to $\nabla^2\psi_1$ in the far-field limit is simply $-4\,k^2\,\psi_1$ ."1041 Using py(4) from equation (31). we find that," Using $\rho_1 (t)$ from equation (31), we find that"1042We thank $. Gillessen and the referee for comments.,We thank S. Gillessen and the referee for comments.1043Lt has usually been thought that the disc in spiral galaxies extends to radii well bevond the optical disc.,It has usually been thought that the disc in spiral galaxies extends to radii well beyond the optical disc.1044 rotation curves have ↸⋠⋠⊀therefore led to extensive studies of the clark| matter clistribution at large radii↔, rotation curves have therefore led to extensive studies of the dark matter distribution at large radii.1045" Llowever. suggested that. dilluse.u optical. emission2. could in. principle2. be found: at radii"" larger than the disc."," However, suggested that diffuse optical emission could in principle be found at radii larger than the disc."1046: They initially suggested that bevond a certain radius. cold gas could no longer support itself. against. ionization⋠⊀⊲ bv the ambient. raciation field.," They initially suggested that beyond a certain radius, cold gas could no longer support itself against ionization by the ambient radiation field."1047 To test this theory. they. obtained very deep optical spectra for one of the brightest Sculptor eroup galaxies. NGC 253. and succeeded in detecting ionized gas (lla and. Nu]) bevond the dise.," To test this theory, they obtained very deep optical spectra for one of the brightest Sculptor group galaxies, NGC 253, and succeeded in detecting ionized gas $\alpha$ and ]) beyond the disc."1048 The rotation curve they derived also showed signs of a possible decline., The rotation curve they derived also showed signs of a possible decline.1049 Llowever. their. results led them to. conclude. that the existence. of ⋅⊀this extended. ionized⊀⊀ gas was not due to the ambient. radiationD. field.. but more likely: clue to hot. voung stars in. the central regions. of⋅ the galaxy ionizing⊀↔ the outer disc. through a strong warp present in. the ealaxy’s ↼∢disc.," However, their results led them to conclude that the existence of this extended ionized gas was not due to the ambient radiation field, but more likely due to hot young stars in the central regions of the galaxy ionizing the outer disc through a strong warp present in the galaxy's disc."1050 Detecting dilfuse ionized gas can therefore. not. only provide insight as to the kinematics of a galaxy at large radii. but. also provide strong constraints on the source of its ionization.," Detecting diffuse ionized gas can therefore not only provide insight as to the kinematics of a galaxy at large radii, but also provide strong constraints on the source of its ionization."1051 In this context. carried. out a deep La ," In this context, carried out a deep $\alpha$ "1052its mark on the phase-space structure of the halos.,its mark on the phase-space structure of the halos.1053 Indeed. hese dark halo streams are a major source of attention in oresent clay studies of the formation of our Galaxy (Πο&White1999:οι 2000).," Indeed, these dark halo streams are a major source of attention in present day studies of the formation of our Galaxy \citep{helmi99,helmi00}."1054. ]t remains an interesting question as to whether we can ind evidence for these merging events in the Fundamental fane., It remains an interesting question as to whether we can find evidence for these merging events in the Fundamental Plane.1055 González-CGiarcía&vanMbacda(2003) look into he effects of major mergers on the Fundamental. Plane and found that the Fundamental Plane does remain Iargelv intact in the case of two merging ellipticals., \cite{cesar03a} look into the effects of major mergers on the Fundamental Plane and found that the Fundamental Plane does remain largely intact in the case of two merging ellipticals.1056 Llowever. what he effects will be of an incessant bombarcment of a halo »v material in its surroundings has not been studied in much detail.," However, what the effects will be of an incessant bombardment of a halo by material in its surroundings has not been studied in much detail."1057 Given that this is a sensitive function of the cosmological scenario. we will study the influence on FP yaramcters and thickness in more detail.," Given that this is a sensitive function of the cosmological scenario, we will study the influence on FP parameters and thickness in more detail."1058" In this paper we address the specific question as to whether we can trace an inllucnce of cosmic parameters in the scaling relations for simulated. clusters. and in particular the influence of the cosmic density. parameter $2, and the cosmological constant A."," In this paper we address the specific question as to whether we can trace an influence of cosmic parameters in the scaling relations for simulated clusters, and in particular the influence of the cosmic density parameter $\Omega_m$ and the cosmological constant $\Lambda$."1059 We use a set of clissipationtless A’-body simulations involving open. Lat and closed. Universes.," We use a set of dissipationless $N$ -body simulations involving open, flat and closed Universes."1060" All the simulations are variants of the cold dark. matter. (CDM). scenario. representing: cillerent cosmologies. concerning both cillerent values for the mass density O,,. for dark energy € and for the implied. power spectrum of density perturbations and the related. merging and accretion history of the clusters."," All the simulations are variants of the cold dark matter (CDM) scenario, representing different cosmologies, concerning both different values for the mass density $\Omega_{m}$, for dark energy $\Omega_{\Lambda}$ and for the implied power spectrum of density perturbations and the related merging and accretion history of the clusters."1061 The organization of this paper is as follows., The organization of this paper is as follows.1062 In section 2 we describe the simulations and the definitions of the various parameters we use., In section \ref{sec5:sim} we describe the simulations and the definitions of the various parameters we use.1063 In section 3. we present a general deseription of the scaling relations which we investigate in this study before specifving the way in which we analyze them from the cluster-sized. halos in our simulation., In section \ref{sec5:background} we present a general description of the scaling relations which we investigate in this study before specifying the way in which we analyze them from the cluster-sized halos in our simulation.1064 We investigate the scaling relations of galaxy clusters in different cosmologies at 2=0 in section 4.., We investigate the scaling relations of galaxy clusters in different cosmologies at $z=0$ in section \ref{sec5:scaling}.1065 Section 5 aclelresses the evolution of the scaling relations as a Function of redshift and cosmic time., Section \ref{sec5:evol_scaling} addresses the evolution of the scaling relations as a function of redshift and cosmic time.1066 We also investigate the dependence of merging and accretion on the scaling relations. which we discuss in section 6..," We also investigate the dependence of merging and accretion on the scaling relations, which we discuss in section \ref{sec5:mergacc}."1067 The interpretation of our results on the Fundamental Plane within the context of the virial theorem is cliseussec in section 7.., The interpretation of our results on the Fundamental Plane within the context of the virial theorem is discussed in section \ref{sec5:reconcile}.1068 Conclusions are presented in section &.., Conclusions are presented in section \ref{sec5:conclusions}.1069 We perform. thirteen. N-body. simulations that. follows the dvnamices of No=256 particles in a periodic box of size L—2005. !Mpe., We perform thirteen N-body simulations that follows the dynamics of $N=256^{3}$ particles in a periodic box of size $L=200h^{-1}$ Mpc.1070 The initial conditions are generated. with identical phases for Fourier. components of the Gaussian random field., The initial conditions are generated with identical phases for Fourier components of the Gaussian random field.1071 In this way. cach cosmological model contains the same morphological structures.," In this way, each cosmological model contains the same morphological structures."1072 For. all models we chose the same Llubble parameter. {0.7. and the same normalization of the power spectrum. Tx 0.5.," For all models we chose the same Hubble parameter, $h=0.7$, and the same normalization of the power spectrum, $\sigma_{8}=0.8$ ."1073" The principa dillerences between the simulations are the values of the matter density and vacuum energy. density xumeters. f2,, anc Q4."," The principal differences between the simulations are the values of the matter density and vacuum energy density parameters, $\Omega_{m}$ and $\Omega_{\Lambda}$."1074 By combining these parameters. we get. modes describing the three possible geometries of he Universe: open. Hat and closed.," By combining these parameters, we get models describing the three possible geometries of the Universe: open, flat and closed."1075 The effect of having the same Hubble xuameter and dilferent cosmological constants ranslates Late» having different cosmic times., The effect of having the same Hubble parameter and different cosmological constants translates into having different cosmic times.1076 Fable 1. lists he values of the cosmological parameters and the cosmic imes at whic1 the data is analysed., Table \ref{table5:paramsim} lists the values of the cosmological parameters and the cosmic times at which the data is analysed.1077 Phe initial conditions are evolved. up to the present ine (2 ) using the massive parallel tree N-bocly code GADGET? (Springel2005)., The initial conditions are evolved up to the present time $z=0$ ) using the massive parallel tree N-body code GADGET2 \citep{springel05}.1078. Phe Plumumer-cquivalent softening was set at eu;=15h. tkpe in physical units from D-—2102-—) while itwas taken to be fixed in comoving units at. high« voredshifts.," The Plummer-equivalent softening was set at $\epsilon_{pl}=15h^{-1}$ kpc in physical units from $z=2$ to $z=0$, while itwas taken to be fixed in comoving units at higher redshifts."1079" For cach cosmological model we wrote the out of 100 snapshots. from ap,=0.2 (2Ξ 4) to the presen tine. (vu,lfs 0). equally spaced. in loger)."," For each cosmological model we wrote the output of 100 snapshots, from $a_{exp}=0.2$ $z=4$ ) to the present time, $a_{exp}=1$$z=0$ ), equally spaced in $\log(a)$ ."1080 We use the HOP algorithm (Eisenstein.&Llut1998) to extract the groups present in the simulations., We use the HOP algorithm \citep{eisenstein98} to extract the groups present in the simulations.1081 OP, HOP1082"For the relativistic electrons (1.6., {ο— 1), eq.(8)) and eq.(11)) take the simplified forms where €2hw'/(y',mec”?), be=21—0)»hue /(mec”), and hui,<hv/€Ύοπιοςὑρ/(1+be).","For the relativistic electrons (i.e., $\beta_{\rm e}\rightarrow 1$ ), \ref{eq:AA81-a}) ) and \ref{eq:AA81-b}) ) take the simplified forms where $\xi \equiv h\nu'/({\gamma'}_{\rm e} m_{\rm e} c^2)$, $b_\theta=2(1-\cos \theta'){\gamma'}_{\rm e} h\nu'_{\rm se}/(m_{\rm1083e} c^2)$ , and $h\nu'_{\rm se}\ll h\nu' \leq {\gamma'}_{\rm e} m_{\rm1084e} c^2 b_\theta /(1+b_\theta)$."1085" Since the emitting region is moving relativistically, the angle 0’ (in Fig.3)) corresponding to the line of sight (L.o."," Since the emitting region is moving relativistically, the angle $\theta'$ (in \ref{fig:coordinate-2}) ) corresponding to the line of sight (L.o."1086S) is given by where Ó is the angle between the line of sight and the emitting point (measured in the observer’sframe).,S) is given by where $\theta$ is the angle between the line of sight and the emitting point (measured in the observer'sframe).1087 The azimuthal angle ¢ varying from 0 to 27 is defined inFig.4.., The azimuthal angle $\phi$ varying from $0$ to $2\pi$ is defined in\ref{fig:Cartoon}.1088" The polar angle 0 ranges from 0 to 0,+6;.", The polar angle $\theta$ ranges from $0$ to $\theta_{\rm v}+\theta_{\rm j}$.1089" The angle between the vector (sincos¢,sin@sinϕ,cos0) and the central axis of the ejecta (C.A. in Fig.4)) is denoted as © and is given by Pleasemind that in the following radiation calculation, the flux is set to be zero if cosO<6; because these points (0,Φ) are outside of the cone of the ejecta."," The angle between the vector $(\sin1090\theta \cos \phi,~\sin \theta \sin \phi,~\cos \theta)$ and the central axis of the ejecta (C.A. in \ref{fig:Cartoon}) ) is denoted as $\Theta$ and is given by Please that in the following radiation calculation, the flux is set to be zero if $\cos \Theta<\cos1091\theta_{\rm j}$ because these points $(\theta,\phi)$ are outside of the cone of the ejecta."1092" The EIC radiation flux in the observer frame is where v=Dv'/(1--2). D=[Fi(1—Bicos0)]| is the Doppler factor, and is the solid angle satisfying dX?=sin!0d0do."," The EIC radiation flux in the observer frame is where $\nu={\cal D}\nu'/(1+z)$, ${\cal D}=[\Gamma_{\rm1093i}(1-\beta_{\rm i} \cos \theta)]^{-1}$ is the Doppler factor, and $\Omega$ is the solid angle satisfying $d\Omega=\sin \theta d\theta1094d\phi$."1095" The polarized radiation( flux is The polarization degree of the EIC emission is One can see that a non-zero net polarization is expected as long as 6,>0.", The polarized radiation flux is The polarization degree of the EIC emission is One can see that a non-zero net polarization is expected as long as $\theta_{\rm v}>0$.1096" In the numerical example, we assume that the seed photons have a thermal spectrum (as suggested in the photosphere model) where KT""zzkT/2I; is the temperature (measured in the rest frame of the emitting region) of thethermal emission."," In the numerical example, we assume that the seed photons have a thermal spectrum (as suggested in the photosphere model) where $kT'\approx kT/2\Gamma_{\rm i}$ is the temperature (measured in the rest frame of the emitting region) of thethermal emission."1097" In the calculation we take I;~300 and kT’~100 keV. The electron distributionis taken as Ny,comparisonox?/;6?x4/;??e for 4/,>2, otherwise Ny,=0."," In the calculation we take $\Gamma_{\rm i} \sim 300$ and $kT \sim1098100$ keV. The electron distribution is taken as $N_{\gamma_{\rm e}}1099\propto {\gamma'}_{\rm e}^{-(1+p)} \propto {\gamma'}_{\rm e}^{-3.5}$ for ${\gamma'}_{\rm e}>2$, otherwise $N_{\gamma_{\rm e}} =0$."1100" For purpose we also consider the case of Ny,oxy, ? "," For comparison purpose we also consider the case of $N_{\gamma_{\rm e}}1101\propto {\gamma'}_{\rm e}^{-2}$ ."1102The numerical results are presented in Fig.5.., The numerical results are presented in \ref{fig:Pol-1}.1103 One can see that the polarization degrees expected in these two representative cases are only slightly different., One can see that the polarization degrees expected in these two representative cases are only slightly different.1104" We also find that a moderate linear polarization level (P;,grc> 10%) is achievable only for 0,76;+1/(313)."," We also find that a moderate linear polarization level $P_{\rm \nu,EIC}>10\%$ ) is achievable only for $\theta_{\rm1105v}\gtrsim \theta_{\rm j}+1/(3\Gamma_{\rm i})$."1106 Currently the prompt emission consists of a thermal and a non-thermal components., Currently the prompt emission consists of a thermal and a non-thermal components.1107 The thermal component with the flux Ενει is expected to be unpolarized while the nonthermal EIC component may have a high linear polarization level.," The thermal component with the flux $F_{\rm1108\nu,th}$ is expected to be unpolarized while the nonthermal EIC component may have a high linear polarization level."1109 The observed polarization degree should be strongly frequency-dependent., The observed polarization degree should be strongly frequency-dependent.1110" Roughly speaking, the linear polarization degree is anti-correlated with the weight of the thermal component."," Roughly speaking, the linear polarization degree is anti-correlated with the weight of the thermal component."1111" With an energy ~ kT’, the emission is dominated by the thermal component and Pyrobs is low."," With an energy $\sim kT$ , the emission is dominated by the thermal component and $P_{\rm kT,obs}$ is low."1112" For hv> kT, theemission is dominated by the EIC component and νους» Pic, as illustrated in Fig.6.."," For $h\nu \gg kT$ , theemission is dominated by the EIC component and $P_{\nu,\rm obs} \sim P_{\nu,\rm EIC}$ , as illustrated in \ref{fig:Pol-2}. ."1113 This unique, This unique1114"pressure, fuapx=Px/Pair, and compare it to what would be if all the wind energy was confined.","pressure, $f_{\rm trap,X} = P_{\rm X}/P_{\rm dir}$, and compare it to what $f_{\rm trap,X}$ would be if all the wind energy was confined."1115" We firap,.xcan calculate the trapped-wind value using the wind-luminosity relation (??),, which indicates that the momentum flux carried by winds from a star cluster is about half that carried by the radiation field if the cluster the entire IMF’."," We can calculate the trapped-wind value using the wind-luminosity relation \citep{kud,rep}, which indicates that the momentum flux carried by winds from a star cluster is about half that carried by the radiation field if the cluster samples the entire IMF."1116" Written quantitatively, 0.5Lpo1/¢samples=Myvw, where My is the mass flux from the winds that launched at a velocity vy."," Written quantitatively, $0.5 L_{\rm bol}/c = \dot{M_{\rm w}} v_{\rm w}$, where $\dot{M_{\rm w}}$ is the mass flux from the winds that launched at a velocity $v_{\rm w}$."1117" The mechanical energy loss L4, of the winds is then given by and the mechanical energy of the winds is simply Lt, where t is the time since the winds were launched."," The mechanical energy loss $L_{\rm w}$ of the winds is then given by and the mechanical energy of the winds is simply $E_{\rm w} = L_{\rm w} t$ , where $t$ is the time since the winds were launched."1118" Putting these relations together, the trapped X-ray gas pressure PxT is where Vu is the volume of the HII region."," Putting these relations together, the trapped X-ray gas pressure $P_{\rm X,T}$ is where $V_{\rm HII}$ is the volume of the HII region."1119" Given that Pair=Lya/(ArRigo), then frrap,x is where we have set Egn/t=v, the velocity of the expanding shell."," Given that $P_{\rm dir} = L_{\rm bol}/(4 \pi R_{\rm HII}^2 c)$, then $f_{\rm trap,X}$ is where we have set $R_{\rm HII}/t = v_{\rm sh}$, the velocity of the expanding shell."1120" Finally, we put M, in terms of Ly.) and Uw, 80 that Eq."," Finally, we put $\dot{M_{\rm w}}$ in terms of $L_{\rm bol}$ and $v_{\rm w}$, so that Eq."1121" 10 reduces to We use the above equation to obtain an order-of-magnitude estimate of ftrap,x if all the wind energy is confined by the shell."," \ref{eq:ftrap} reduces to We use the above equation to obtain an order-of-magnitude estimate of $f_{\rm trap,X}$ if all the wind energy is confined by the shell."1122" We assume a wind velocity Uy~1000 km s-! escape velocity from a O6 V star; a reasonable order-of-magnitude(the estimate, since O3 stellar winds are faster and WR winds would be slower than this value)."," We assume a wind velocity $v_{\rm w} \sim 1000$ km $^{-1}$ (the escape velocity from a O6 V star; a reasonable order-of-magnitude estimate, since O3 stellar winds are faster and WR winds would be slower than this value)."1123" If we set uj~ 25 km s! (the expansion velocity over 30 Doradus given by optical spectroscopy; 7), then ~ 20."," If we set $v_{\rm sh} \sim$ 25 km $^{-1}$ (the expansion velocity over 30 Doradus given by optical spectroscopy; \citealt{chu94}) ), then $f_{\rm trap,X} \sim$ 20."1124" We can firap,Xcompare this to our observed values for the regions closest to the ftrap,xshell ones along the rim of our 441 squares in Fig. (the"," We can compare this $f_{\rm trap,X}$ to our observed values for the regions closest to the shell (the ones along the rim of our 441 squares in Fig. \ref{fig:regions}) );"1125Figure 13 shows the histogram of our observed 5)); values.," Figure \ref{fig:hist} shows the histogram of our observed $f_{\rm trap,X}$ values."1126" We find a mean and median ftrap,x of 0.30 and ftrap,x0.27, respectively, for our outermost regions."," We find a mean and median $f_{\rm trap,X}$ of 0.30 and 0.27, respectively, for our outermost regions."1127" Over 30 Doradus, the highest values of ftrap,x are near the supernova remnant N157B in the southwest corner of 30 Doradus (see Figure 14)), where hot gas is being generated and has not had time to vent."," Over 30 Doradus, the highest values of $f_{\rm trap,X}$ are near the supernova remnant N157B in the southwest corner of 30 Doradus (see Figure \ref{fig:ftrapcheck}) ), where hot gas is being generated and has not had time to vent."1128" Other locations where ftrap,x is elevated are regions with strong X-ray emission and weak Ha emission."," Other locations where $f_{\rm trap,X}$ is elevated are regions with strong X-ray emission and weak $\alpha$ emission."1129" Morphologically, these areas could be where the hot gas is blowing out the 30 Doradus shell."," Morphologically, these areas could be where the hot gas is blowing out the 30 Doradus shell."1130 The observed values are 1-2 orders of magnitude below what ftrapxxthey would be if the wind was fully confined.," The observed $f_{\rm trap,X}$ values are 1–2 orders of magnitude below what they would be if the wind was fully confined."1131" As a consequence, we find that Px of our regions is too low to be completely trapped in the HII region (the Castor et al."," As a consequence, we find that $P_{\rm X}$ of our regions is too low to be completely trapped in the HII region (the Castor et al."1132" model), and the X-ray gas must be leaking through pores in the shell."," model), and the X-ray gas must be leaking through pores in the shell."1133" This result is consistent with the Harper-Clark Murray model of partial confinement of the hot gas, and the weakness of Px relative to Pai, suggests the hot gas does not play a significant role in the dynamics of the HII region."," This result is consistent with the Harper-Clark Murray model of partial confinement of the hot gas, and the weakness of $P_{\rm X}$ relative to $P_{\rm dir}$ suggests the hot gas does not play a significant role in the dynamics of the HII region."1134 We note here that our rim regions in this analysis are, We note here that our rim regions in this analysis are1135proportional to (defdr)|.,proportional to $(dv/dr)^{-1}$.1136 Deuce. a sinaller teriunal velocity will automatically result im a παο calculated line acceleration.," Hence, a smaller terminal velocity will automatically result in a smaller calculated line acceleration."1137 Tn earlier sections we have demonstrated that the mass loss around the bistability jump inereases., In earlier sections we have demonstrated that the mass loss around the bi-stability jump increases.1138 As we have used.observed values for the ratio v4/Vese da our model calculations. we have not vet provided a seclf&cousistent explanation of the observed bi-stabilitv Πο in va/vosc.," As we have used values for the ratio $\ratio$ in our model calculations, we have not yet provided a self-consistent explanation of the observed bi-stability jump in $\ratio$."1139 As a cousisteucy test of our calculations aud an attempt to explain the observed jump in the ratio Vrνο. we procecded to solve the momeutuu equation of line driven wind models around the bistabilitv jump.," As a consistency test of our calculations and an attempt to explain the observed jump in the ratio $\ratio$, we proceeded to solve the momentum equation of line driven wind models around the bi-stability jump."1140 The approach we take is to combine predicted force multiplier paralcters & and a (see below) frou the Monte. Carlo calculation with the analytical solution of line driven winds frou CAIs., The approach we take is to combine predicted force multiplier parameters $k$ and $\alpha$ (see below) from the Monte Carlo calculation with the analytical solution of line driven winds from CAK.1141 We calculated the lue acceleration gp for several models with differcut T;g usine the Monte Carlo method., We calculated the line acceleration $g_{\rm L}$ for several models with different $\teff$ using the Monte Carlo method.1142 The values of gp were expressed iu terms of the force nuutiplicr AZ(f£) (Eq. 8))., The values of $g_{\rm L}$ were expressed in terms of the force multiplier $M(t)$ (Eq. \ref{eq:CAK}) ).1143 Following CAIN we tried. to express M(f) iu terms of a power-law fit of he optical depth parameter £ (Eq. 9))., Following CAK we tried to express $M(t)$ in terms of a power-law fit of the optical depth parameter $t$ (Eq. \ref{eq:tCAK}) ).1144 We found that in the rauge 20 000 <Tig 27 ους. AZ(f) is not accurately fit bv a power-law. since the ionization changes over this critical vanec in Dig.," We found that in the range 20 000 $\le \teff \le$ 27 500, $M(t)$ is not accurately fit by a power-law, since the ionization changes over this critical range in $\teff$."1145 Fortunately. this temperature reeion. M(f) be accurately represeuted im terms of & and o. ie. Therefore. we have calculated models with effective temperatures just below (Tig = 17 500 IK) aud just above Gg = 30 000 I) this critical temperature ranec.," Fortunately, this temperature region, $M(t)$ be accurately represented in terms of $k$ and $\alpha$, i.e. Therefore, we have calculated models with effective temperatures just below $\teff$ = 17 500 K) and just above $\teff$ = 30 000 K) this critical temperature range."1146 Self values of ὃς and AL were thus found in tlie followiug wav:, Self-consistent values of $\vinf$ and $\mdot$ were thus found in the following way:1147"of only ~1 us, instead give an approximation of the temporal extent of the plateau on the main pulse of ~ 55 us2000).. The spectral shape of the emission from the Crab pulsar is thus consistent with being due to incoherent synchrotron radiation from a distribution of relativistic electrons with a sharp low energy cut-off.","of only $\sim1~\mu$ s, instead give an approximation of the temporal extent of the plateau on the main pulse of $\sim$ 55 $\mu$ s. The spectral shape of the emission from the Crab pulsar is thus consistent with being due to incoherent synchrotron radiation from a distribution of relativistic electrons with a sharp low energy cut-off."1148" In order for the rotation of the neutron star to give rise to pulses, relativistic beaming is necessary."," In order for the rotation of the neutron star to give rise to pulses, relativistic beaming is necessary."1149" We denote the frame, in which the total momentum of the relativistic electrons is zero (i.e., the no-streaming frame), with a prime () and let Γ be the Lorentz factor of this frame as measured in the observers frame."," We denote the frame, in which the total momentum of the relativistic electrons is zero (i.e., the no-streaming frame), with a prime $'$ ) and let $\Gamma$ be the Lorentz factor of this frame as measured in the observers frame."1150 A few standard approximations are useful to simplify the treatment. (, A few standard approximations are useful to simplify the treatment. (1151"1) The electron distribution is isotropic and mono-energetic in the primed frame with an electron energy corresponding to a Lorentz factor yj,,. (",1) The electron distribution is isotropic and mono-energetic in the primed frame with an electron energy corresponding to a Lorentz factor $\gamma_{\rm me}'$. (11522) The intensity leaving the source is confined within a cone with opening angle 1/T.,2) The intensity leaving the source is confined within a cone with opening angle $1/\Gamma$.1153 Inside this cone the intensity is constant. (, Inside this cone the intensity is constant. (11543) Frequencies in the two frames are related by v=Εν’.,3) Frequencies in the two frames are related by $\nu = \Gamma \nu '$.1155" Furthermore, Γ>1 will be assumed."," Furthermore, $\Gamma \gg 1$ will be assumed."1156" The observed intensity is then where y=TYie is the Lorentz factor of the radiating electrons as measured in the observers frame, τ is the synchrotron optical depth and m is the mass of the electron."," The observed intensity is then where $\gamma \equiv \Gamma \gamma_{\rm me}'$ is the Lorentz factor of the radiating electrons as measured in the observers frame, $\tau$ is the synchrotron optical depth and $m$ is the mass of the electron."1157 It will be assumed that the emission is produced at a distance R from the neutron star., It will be assumed that the emission is produced at a distance $R$ from the neutron star.1158 Radiation from the streaming electrons is observed from a surface of size απ;/T?., Radiation from the streaming electrons is observed from a surface of size $a \pi R^2 / \Gamma^2$.1159 The value of a is unity for radially streaming electrons and a spherically symmetric source., The value of $a$ is unity for radially streaming electrons and a spherically symmetric source.1160" In many cases, the value of a is likely to be smaller than unity, either due to an actual source size smaller than R/T or the source geometry."," In many cases, the value of $a$ is likely to be smaller than unity, either due to an actual source size smaller than $R/\Gamma$ or the source geometry."1161 The observed flux can then be written, The observed flux can then be written1162circular annulus with mean radius 2° (11 kkpe) centered on NGC 1101 is most likely due to the fact that such a circular region contains cooler raim-pressure stripped gas Crom the trailing side of NGC L101 (the debris tall) as well as the Foruax ICM.,circular annulus with mean radius $2'$ $11$ kpc) centered on NGC 1404 is most likely due to the fact that such a circular region contains cooler ram-pressure stripped gas from the trailing side of NGC 1404 (the debris tail) as well as the Fornax ICM.1163 A single temperature APEC model provides a poor fit to the data inside the edge. as shown in Table L..," A single temperature APEC model provides a poor fit to the data inside the edge, as shown in Table \ref{tab:spectra}."1164 This is not surprising since a second component is warranted to model the coutributiou [rom foreground cluster emission., This is not surprising since a second component is warranted to model the contribution from foreground cluster emission.1165 We model this emission with a separate APEC component with abundance aud temperature fixed at the best fit cluster values., We model this emission with a separate APEC component with abundance and temperature fixed at the best fit cluster values.1166 We find a temperature for the kkeV⋅⋅ ⋅∥∣∣∡∣∣ −⋅∣⊔⋅⇁⊳⊳with an⋅⋅ abundance 0.73. 45; Z..∑∸⋜↕⋜∥∙⋃∢∙≺⇂∐⋃⊳∖≺↵∑≟⋜↕⊳∖⋯⊳∖∐⇂↩∐≺↵≺↵≺∟≺∸≺↵∩⊔≻⋅⋅≻," We find a temperature for the galactic diffuse gas inside the edge of $0.55^{+0.01}_{-0.02}$ keV with an abundance $0.73^{+0.65}_{-0.16}\,\Zs$."1167⋅≻Thefit is n inchauged ib the cluster component. temperature is allowed to vary. although the errors on the ⋅ ↥≺↵≺⇂∢∙∐⇂⊳∖≺↵↕⋅↕↩⋯↥↽≻≺↵⋅⋜⋯⊔⋅↩↸⊥⋅↓↖∖∎∣ ∣↽⋝∣∣∡⊇ ≽↓≽⊔⊊≺↵∖⋝⋜⋃⋅≺↵↥⋜↕⋅∑≟≺↵⋅⊺∐≺↵↕≺↵⋯↥≻≺↵↕⋅⋜⋯⊔⋅≺↵∖∖↽≺↵∐↕," The fit is unchanged if the cluster component temperature is allowed to vary, although the errors on the fitted cluster temperature $1.48^{+0.24}_{-0.22}$ keV) are large."1168≺↵⋜↕⊳∖⋃⋅≺↵↥∩↓⋅∪∐⇂⊳∖≺↵∑≟⋜↕⊳∖; ⋅⋋ ∎↥↓∖⊽∁↽∶⊂⊲↽⊔∩↓↕⊳∖∐↕∑∸∩⋯⇂⋜↕∑≟↕⋅≺↵↩⊔≺↵∐↕∖∖↽∐∐↥↽∐⋅≺↵∖⊽↥∩⋃⊳∖∐≺↵⋜↕⊳∖⋯⋅≺↲⋯≺↵∐↕⊳∖∑⇁⋡↥∖⊽≺↵↥↕↕∐≺↵≺↥∐⇀≺↵↕⋅≺↵⊓∙≺↵⊳∖↥∐↕≺↵⊔∩⊓↲↥⊳∖ ⋜↕∐⇂⊳∖↥↽≻≺↵∢∙↕⋅⋜↕↥≺↵⊸∖⋃⋅⋜↕∢∙↕∩∐↕⋅≺↵∑≟↕∩, The temperature we measure for diffuse gas in NGC 1404 is in good agreement with previous measurements given the differences in the models and spectral extraction regions.1169∐⊳∖⋅⇂⊽⊳∖↥∐∑≟∐⋃∺⇀−∖⊺↥⋟∺↥⋟∁≺⇂⋜↕↕⋜↕⋅∙∣∩⊔≺↵⊳∖≺↵↕⋜↕⋅↸↣∐∫∪⊤⊔∎⋯⊔∐⋜↕∐↕≺↵⋜↕∐ emperature for NGC 1101 of 0.65Mn kkeV: while O'Sullivan (2003) fouud a temperature orolile consistent with isothermal with AT=0.640.01 for radii r<1.6. similar to that [ound » Scharl (2001) using; ACIS-I data.," Using ROSAT PSPC data, Jones (1997) found a mean temperature for NGC 1404 of $0.65^{+0.02}_{-0.01}$ keV; while O'Sullivan (2003) found a temperature profile consistent with isothermal with $kT = 0.6 \pm11700.01$ for radii $r \lesssim 1'.6$, similar to that found by Scharf (2004) using ACIS-I data."1171 We find. however. an abundance A significantly higher hau that [ο by most previous authors C4~O.11Z.. Loewenstein 199[: d—0.16Z... Jones 1997: A~0.35. O'Sullivan 2003). aud more consistent with solar or super- abuudauces expected [or elliptical galaxies (Buote 2002: Brigheuti Mathews 1999).," We find, however, an abundance $A$ significantly higher than that found by most previous authors $A \sim 0.14\,\Zs$, Loewenstein 1994; $A \sim 0.16\,\Zs$ , Jones 1997; $A \sim 0.35$, O'Sullivan 2003), and more consistent with solar or super-solar abundances expected for elliptical galaxies (Buote 2002; Brighenti Mathews 1999)."1172 This discrepancy is probably due to a combination of limited statistics. large heterogeneousextraction," This discrepancy is probably due to a combination of limited statistics, large heterogeneousextraction"1173relatively dense. material in the fireball will be able to cool rapidly down to this temperature before the cooling rate stalls.,relatively dense material in the fireball will be able to cool rapidly down to this temperature before the cooling rate stalls.1174 We approximate a racliatively cooling fireball by maintaining a hot core region which cools acliabatically as it expands., We approximate a radiatively cooling fireball by maintaining a hot core region which cools adiabatically as it expands.1175 Once gas elements cross the boundary. to this region. we assume them to cool immediately to the effective temperature of the photosphere and thereafter adiabatically.," Once gas elements cross the boundary to this region, we assume them to cool immediately to the effective temperature of the photosphere and thereafter adiabatically."1176 We derive the radius of the photospheric surface below. using the blackbody luminosity and the thermal energy. of the central region.," We derive the radius of the photospheric surface below, using the blackbody luminosity and the thermal energy of the central region."1177" Yo lind the photospheric radius rj=(0:25, in our radiative model we calculate the total thermal energy in a sphere of radius η, Lenec. dillerentiating. Racliative cooling at fixed elective temperature 7j, gives and so. using we have the dillerential equation for the core radius as a function of time where We solve. equation (31)) numerically anc plot. the xhaviour for typical parameters in Fig. 2.."," To find the photospheric radius $r_{\rm p}=a_{0} \beta \eta_{\rm p}$ in our radiative model we calculate the total thermal energy in a sphere of radius $r_{\rm p}$ Hence, differentiating, Radiative cooling at fixed effective temperature $T_{\rm p}$ gives and so, using we have the differential equation for the core radius as a function of time where We solve equation \ref{eqn:cordiff}) ) numerically and plot the behaviour for typical parameters in Fig. \ref{fig:tempbnd}."1178 We see how. in he Lagrangian coordinate 4. the boundary migrates inward continually.," We see how, in the Lagrangian coordinate $\eta$, the boundary migrates inward continually."1179 In. Eulerian coordinates. plotted in Fig. 3..," In Eulerian coordinates, plotted in Fig. \ref{fig:abstempbnd},"1180 he boundary is initially acvectecd outwards with the Low., the boundary is initially advected outwards with the flow.1181 When the inward migration exceeds the expansion rate. the ohotosphere turns around. and. begins to collapse.," When the inward migration exceeds the expansion rate, the photosphere turns around and begins to collapse."1182" In both lots the initial conditions for my, have relatively little impact on the behaviour at [ate times.", In both plots the initial conditions for $\eta_{\rm p}$ have relatively little impact on the behaviour at late times.1183 Models with ijjz4 initially are indistinguishable as they rapidly: converge on the same curve., Models with $\eta_{\rm p}\ga4$ initially are indistinguishable as they rapidly converge on the same curve.1184" Lower initial values for rj, also converge. albeit more σον]. on the same evolution."," Lower initial values for $\eta_{\rm p}$ also converge, albeit more slowly, on the same evolution."1185 We plot the temperature profiles at different. times for the radiative model in Fig. 4.., We plot the temperature profiles at different times for the radiative model in Fig. \ref{fig:tprof}.1186 Phe profiles show how the material outside the core region cools very rapidly with distance away from the boundary., The profiles show how the material outside the core region cools very rapidly with distance away from the boundary.1187 As a result. the shell of material with significant temperature outside the core is very thin.," As a result, the shell of material with significant temperature outside the core is very thin."1188 For computational convenience we set a mininimum temperature for any of the gas at 1000 1. In the LPE approximation. the density. and. temperature determine the ionization state of the eas at each point. in space and time through the solution of a network of Saha equations.," For computational convenience we set a minimum temperature for any of the gas at $1~000$ K. In the LTE approximation, the density and temperature determine the ionization state of the gas at each point in space and time through the solution of a network of Saha equations."1189 Atomic level populations are similarly determined through Boltzmann factors and. partition. functions., Atomic level populations are similarly determined through Boltzmann factors and partition functions.1190 Lor purely adiabatie cooling. the temperature retains its initial uniform spatial profile. but decreases with time.," For purely adiabatic cooling, the temperature retains its initial uniform spatial profile, but decreases with time."1191 The LEE ionization is therefore higher in the outer low-clensity regions which also move fastest., The LTE ionization is therefore higher in the outer low-density regions which also move fastest.1192 Thus in the LYE mocdel high ionization emission lines are predicted. to have broader velocity. profiles., Thus in the LTE model high ionization emission lines are predicted to have broader velocity profiles.1193 Once we have determined the evolution of 7 and p with time. we can follow the evolution of the ionization structure," Once we have determined the evolution of $T$ and $\rho$ with time, we can follow the evolution of the ionization structure"1194When comparing models of star-forming regions to observations. it is important to understand how our incomplete understanding of the regions may affect such comparison.,"When comparing models of star-forming regions to observations, it is important to understand how our incomplete understanding of the regions may affect such comparison."1195 Often. the star formation history is poorly constrained. but may be important considering the relatively short timescales of interest of ~10 Myr.," Often, the star formation history is poorly constrained, but may be important considering the relatively short timescales of interest of $\sim10$ Myr."1196 In figure 3. we show the time profiles of kinetic energy ejection from the stellar winds and supernova explosions and of the interstellar mass of ΑΙ., In figure \ref{fig:onecluster} we show the time profiles of kinetic energy ejection from the stellar winds and supernova explosions and of the interstellar mass of $^{26}$ Al.1197 Lines show the three different star formation histories described in section 35 (model D. (model D) and the (model ID.," Lines show the three different star formation histories described in section \ref{sec:models}: (model I), (model I) and the (model II)."1198 The results of all three models are surprisingly. similar: Values for the current and future times are the same within <10%.., The results of all three models are surprisingly similar: Values for the current and future times are the same within $\lesssim$.1199 Some differences appear in the past values. increasing towards the time of formation of subgroup OBId (12 Myr ago).," Some differences appear in the past values, increasing towards the time of formation of subgroup OB1d (12 Myr ago)."1200 We conclude that the properties investigated in this paper are not sensitive to the exact star formation history for regions with ages above 5-6 Myr. and they cannot be used to constrain earlier star formation. accordingly.," We conclude that the properties investigated in this paper are not sensitive to the exact star formation history for regions with ages above 5-6 Myr, and they cannot be used to constrain earlier star formation, accordingly."

Showing the first 1,200 of 10346 lines. Download the file for the rest.