ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 Given the low sigual-to-noise ratio of the echo iu the images iu both bands. we consider our unucertaimties to be quite conservative.," Given the low signal-to-noise ratio of the echo in the images in both bands, we consider our uncertainties to be quite conservative."3 Tere we provide an analysis of the echo and its origin., Here we provide an analysis of the echo and its origin.4 We note that this analvsis differs from that preseuted by Sueenuan (2005)., We note that this analysis differs from that presented by Sugerman (2005).5 We have determined that SN 2003ed is at the exact ceuter of the liebt echo. with uncertainty «0.2 pixel (ο 005}. through comparison of our Suapshot images to the ACS FI35W images obtained by Suuutt et al. (," We have determined that SN 2003gd is at the exact center of the light echo, with uncertainty $< 0.2$ pixel $< 0{\farcs}005$ ), through comparison of our Snapshot images to the ACS F435W images obtained by Smartt et al. ("6200L). when the SN was siguificauth brighter.,"2004), when the SN was significantly brighter."7 The SN itself therefore must be the source of the eclio. which we observe at age f£ after explosion and age 7 after optical maximum.," The SN itself therefore must be the source of the echo, which we observe at age $t$ after explosion and age $\tau$ after optical maximum."8 The observed echo is the product of the iuput, The observed echo is the product of the input9"where N, is the number of true cluster satellite galaxies and is the number of projected field galaxies.",where $N_c$ is the number of true cluster satellite galaxies and $N_f$ is the number of projected field galaxies.10" We can introduceNy the fraction of real cluster satellite as fe(z)=Ne/(Ne+Ng), the BCG alignment from true cluster members as Ye=—45 and the BCG alignment from the projectedκ0;/N. field galaxies as Yyp-Yo0;/N,—45."," We can introduce the fraction of real cluster satellite as $f_c(z) = N_c/(N_c + N_f)$, the BCG alignment from true cluster members as $\gamma_c=\sum_{i=0}^{N_c}\theta_i/N_c - 45$ and the BCG alignment from the projected field galaxies as $\gamma_f=\sum_{j=0}^{N_f}\theta_j/N_f - 45$."11" Substitute these definitions into Equation 5 and take ensemble average of the clusters, we will have: where (...) denotes the average over the cluster ensemble."," Substitute these definitions into Equation \ref{gamma_m} and take ensemble average of the clusters, we will have: where $\left<...\right>$ denotes the average over the cluster ensemble."12" As the mean alignment signal from the field is consistent with zero, the alignment parameter y from the true cluster satellites is related to the measured one through the redshift dependent fraction f.(z)."," As the mean alignment signal from the field is consistent with zero, the alignment parameter $\gamma$ from the true cluster satellites is related to the measured one through the redshift dependent fraction $f_c(z)$ ."13" To the first order approximation, we can separate f.(z) into two parts as f.(z)=feonstXf(z), where fronst is a redshift independent component of the fraction, indicating the “intrinsic” fraction of true satellite based on color selection."," To the first order approximation, we can separate $f_c(z)$ into two parts as $f_c(z) = f_{const} \times f(z)$, where $f_{const}$ is a redshift independent component of the fraction, indicating the “intrinsic” fraction of true satellite based on color selection."14" f(z) is the redshift dependent part, corresponding to the effect we described above."," $f(z)$ is the redshift dependent part, corresponding to the effect we described above."15" Then, the redshift dependence of the measured alignment  will be mainly determined by f(z)."," Then, the redshift dependence of the measured alignment $\gamma$ will be mainly determined by $f(z)$."16" In the GMBCG catalog, we also measured a weighted richness, which takes into account the different degree of overlaps between red sequence and the field galaxies at different redshift (?).."," In the GMBCG catalog, we also measured a weighted richness, which takes into account the different degree of overlaps between red sequence and the field galaxies at different redshift \citep{haocat}."17 The difference between weighted richness and the direct member count richness is a good estimator of the number of projected galaxies due to the effect described above., The difference between weighted richness and the direct member count richness is a good estimator of the number of projected galaxies due to the effect described above.18 The fraction of contamination can therefore be estimated by the ratio of this difference to the direct member count richness., The fraction of contamination can therefore be estimated by the ratio of this difference to the direct member count richness.19" In Figure 20,, we plot the fraction of contamination (1— (f(2))) as a function of redshift in bins of size 0.05."," In Figure \ref{fig:fcz}, we plot the fraction of contamination $1 - \left<f(z)\right>$ ) as a function of redshift in bins of size 0.05."20 The fraction is almost constant except for the lowest redshift bin., The fraction is almost constant except for the lowest redshift bin.21" Again, this cannot explain away the dependence of y on redshift as shown in Figure 10 and Figure 19.."," Again, this cannot explain away the dependence of $\gamma$ on redshift as shown in Figure \ref{fig:gammaz} and Figure \ref{fig:gammaz25}. ."22" Therefore, after considering all the possible systematics known to us, the measured redshift dependence of still cannot be explained."," Therefore, after considering all the possible systematics known to us, the measured redshift dependence of $\gamma$ still cannot be explained."23" In ?,, the authors also reportedΥ a different BCG alignment between one low redshift bin (0.08 - 0.26) and another high redshift bin (0.26 - 0.44), which is consistent with the results we find here."," In \citet{ostholt10}, the authors also reported a different BCG alignment between one low redshift bin (0.08 - 0.26) and another high redshift bin (0.26 - 0.44), which is consistent with the results we find here."24 We measure the satellite alignment and BCG alignment based on a large sample of photometrically selected galaxy clusters from the SDSS DR7., We measure the satellite alignment and BCG alignment based on a large sample of photometrically selected galaxy clusters from the SDSS DR7.25 We detect a satellite alignment only when we use the isphotal PAs., We detect a satellite alignment only when we use the isphotal PAs.26" As we noted in §3.3, the isophotal PA tends to trace the outer profile of the galaxy while the model fit PAs tend to trace the inner part of the galaxy."," As we noted in 3.3, the isophotal PA tends to trace the outer profile of the galaxy while the model fit PAs tend to trace the inner part of the galaxy."27 A direct interpretation of the measurement results could be that the outer part of the satellite galaxy is more susceptible to the the gravitational torque and thus shows an orientation preference toward the BCG., A direct interpretation of the measurement results could be that the outer part of the satellite galaxy is more susceptible to the the gravitational torque and thus shows an orientation preference toward the BCG.28 However the inner part of the galaxy is not affected much by the tidal torque and does not show preference toward the BCG., However the inner part of the galaxy is not affected much by the tidal torque and does not show preference toward the BCG.29 The measured discrepancy of the satellite alignment from different PAs could be a manifestation of the twisting of galaxy shape from inner part to outer part., The measured discrepancy of the satellite alignment from different PAs could be a manifestation of the twisting of galaxy shape from inner part to outer part.30" However, another possibility of this discrepancy could be that the light from BCG contaminates the measurement of the PA based on the isophote fit to the outer region of the galaxy and lead to a ""artificial"" alignment."," However, another possibility of this discrepancy could be that the light from BCG contaminates the measurement of the PA based on the isophote fit to the outer region of the galaxy and lead to a “artificial” alignment."31" By comparing the dependence of ó on BCG apparent and absolute magnitudes, we favor the latter explanation."," By comparing the dependence of $\delta$ on BCG apparent and absolute magnitudes, we favor the latter explanation."32" This means that, though the tidal torque within the galaxy cluster may induce the satellite alignment, we are not yet able to detect them based on our current SDSS data."," This means that, though the tidal torque within the galaxy cluster may induce the satellite alignment, we are not yet able to detect them based on our current SDSS data."33 It will be definitely an interesting question to address with the forthcoming high quality data such as that from the Dark Energy Survey , It will be definitely an interesting question to address with the forthcoming high quality data such as that from the Dark Energy Survey \citep{des05}.34"For the BCG (?)..alignment, by introducing the alignment parameter y, we detect a strong redshift and BCG absolute magnitude dependences of the alignment."," For the BCG alignment, by introducing the alignment parameter $\gamma$, we detect a strong redshift and BCG absolute magnitude dependences of the alignment."35 The redshift dependence cannot be explained by our known systematics., The redshift dependence cannot be explained by our known systematics.36 This result implies that the BCGs orientation is a dynamically evolving process and gets stronger as the cluster system evolves., This result implies that the BCGs orientation is a dynamically evolving process and gets stronger as the cluster system evolves.37" For the dependence of y on the absolute magnitude of BCG, our result is qualitatively consistent with the conclusion that clusters with BCG dominance show stronger BCG alignment in (?).."," For the dependence of $\gamma$ on the absolute magnitude of BCG, our result is qualitatively consistent with the conclusion that clusters with BCG dominance show stronger BCG alignment in \citep{ostholt10}."38" Furthermore, based on a subsample of the BCGs whose stellar masses are available, we show that the BCG alignment signal becomes stronger as the BCG stellar mass increases."," Furthermore, based on a subsample of the BCGs whose stellar masses are available, we show that the BCG alignment signal becomes stronger as the BCG stellar mass increases."39 This result indicates that more massive BCGs lower absolute magnitude) are more likely to align with (withthe major axes of clusters., This result indicates that more massive BCGs (with lower absolute magnitude) are more likely to align with the major axes of clusters.40 We must take great caution when interpreting the dependence of y on BCG absolute magnitude and stellar mass since the purity of the cluster sample may also depend on the BCG absolute magnitude and stellar mass., We must take great caution when interpreting the dependence of $\gamma$ on BCG absolute magnitude and stellar mass since the purity of the cluster sample may also depend on the BCG absolute magnitude and stellar mass.41" As the cluster purity decreases, the alignment signal will decrease too."," As the cluster purity decreases, the alignment signal will decrease too."42" The faintest two bins in Figure 14 show null alignment signal, which may also be due to the significantly decreased cluster purity."," The faintest two bins in Figure \ref{fig:gamma_ramag} show null alignment signal, which may also be due to the significantly decreased cluster purity."43" Nevertheless, we can still see a trend that y increases as the BCG absolute magnitude increases by looking at the bright end of the samplewhere we are confident about the cluster purity."," Nevertheless, we can still see a trend that $\gamma$ increases as the BCG absolute magnitude increases by looking at the bright end of the samplewhere we are confident about the cluster purity."44 Evaluating the cluster purity variation w.r.t BCG absolute magnitude turns out tobe difficult, Evaluating the cluster purity variation w.r.t BCG absolute magnitude turns out tobe difficult45"seen more transparently in the density-corrected V,,,,. method.",seen more transparently in the density-corrected $\vmod$ method.46 The real advantage here is that V4. need only be calculated for each galaxy using the selection r-band Petrosian magnitudes after which the GLF (or GSMF) can be determined straightforwardly using different photometry., The real advantage here is that $\vmod$ need only be calculated for each galaxy using the selection $r$ -band Petrosian magnitudes after which the GLF (or GSMF) can be determined straightforwardly using different photometry.47 When calculating the GLF in a different band (or the GSMF) there is no colour bias in a bin unless a population with a certain colour is only visible over a reduced range of luminosity (mass) within the bin., When calculating the GLF in a different band (or the GSMF) there is no colour bias in a bin unless a population with a certain colour is only visible over a reduced range of luminosity (mass) within the bin.48" Note also the GAMA DDP sample is highly complete, which means thatthe calculation of Padp is robust."," Note also the GAMA DDP sample is highly complete, which means thatthe calculation of $\rho_{\rm ddp}$ is robust."49" Figure 7 shows a comparison between V,,.x and Vinax.", Figure \ref{fig:volumes} shows a comparison between $\vmod$ and $\vmax$ .50" For example, note the flattening of V;,.x in G12 brighter than —15.2 (red line)."," For example, note the flattening of $\vmod$ in G12 brighter than $-15.2$ (red line)."51 This corresponds to the overdensity at z~0.022 with the underdensity beyond., This corresponds to the overdensity at $z\simeq0.022$ with the underdensity beyond.52 Brighter galaxies can be seen further but the corrected volume rises slower than the standard Vinax because the DDP is underdense beyond., Brighter galaxies can be seen further but the corrected volume rises slower than the standard $\vmax$ because the DDP is underdense beyond.53" In order to estimate GLFs, the completeness is assumed to be unity(c;— 1) in this paper with the area of the survey being 143deg? (one third of this for each region)."," In order to estimate GLFs, the completeness is assumed to be unity$c_i=1$ ) in this paper with the area of the survey being $143\,\sqdeg$ (one third of this for each region)."54 Figure 8 shows the 7-band GLF computed using the different volume correction methods., Figure \ref{fig:compare-methods} shows the $i$ -band GLF computed using the different volume correction methods.55" The V;,4,, method produces much better agreement between the regions than the standard Vinax method.", The $\vmod$ method produces much better agreement between the regions than the standard $\vmax$ method.56" The remaining difference between the regions, below <105L in particular, may be the result of the GLF varying between environments or uncertainties in the distances."," The remaining difference between the regions, below $<10^{8}\Lsun$ in particular, may be the result of the GLF varying between environments or uncertainties in the distances."57 The grey lines in Fig., The grey lines in Fig.58 8 represent the GLF using a combined volume over all regions., \ref{fig:compare-methods} represent the GLF using a combined volume over all regions.59" This is obtained by modifying paap(Z1i;Zmax,i)Vmax,i in Eq."," This is obtained by modifying $\rho_{\rm ddp}(z_1; z_{{\rm60 max},i}) \, V_{{\rm max},i}$ in Eq."61" 4 to be a sum over all three regions for each galaxy with zmax,; being different in G09+G15 (r« 19.4) compared to G12 (r« 19.8) (see also Avni&Bahcall1980 for combining samples with different effective volumes)."," \ref{eqn:density-correction} to be a sum over all three regions for each galaxy with $z_{{\rm max},i}$ being different in G09+G15 $r<19.4$ ) compared to G12 $r<19.8$ ) (see also \citealt{AB80} for combining samples with different effective volumes)."62" Hereafter, this combined V;,4, is used."," Hereafter, this combined $\vmod$ is used."63 Note also we show GLFs using solar luminosities because we are working towards the GSMF., Note also we show GLFs using solar luminosities because we are working towards the GSMF.64 The S/N in the 2-band is significantly higher than the SDSS z-band or any of the UKIDSS bands for galaxies in our sample., The S/N in the $i$ -band is significantly higher than the SDSS $z$ -band or any of the UKIDSS bands for galaxies in our sample.65 Thus we use the i-band as the fiducial band from which to apply stellar ratios., Thus we use the $i$ -band as the fiducial band from which to apply stellar mass-to-light ratios.66 First we start by looking at the 7-band and comparing the GLF taken with different photometric apertures., First we start by looking at the $i$ -band and comparing the GLF taken with different photometric apertures.67" Figure 9((a) shows the {-ραπά GLF using photometry from (i) SDSS pipelinePHOTO,, (ii) as run by Hilletal.(2011) and (iii) as run by Kelvinetal.(2011)."," Figure \ref{fig:compare-lf-magtype}( (a) shows the $i$ -band GLF using photometry from (i) SDSS pipeline, (ii) as run by \citet{hill11} and (iii) as run by \citet{kelvin11}."68". For comparison, the result from Lovedayetal.(2012) at z«0.1 using Petrosian magnitudes and SWML method is also shown The difference between the GLFs in Fig. 9(("," For comparison, the result from \citet{loveday12} at $z<0.1$ using Petrosian magnitudes and SWML method is also shown The difference between the GLFs in Fig. \ref{fig:compare-lf-magtype}( ("69a) are generally small except for the The z<0.1 GAMA volume is known to be underdense by about with respect to a larger SDSS volume (see fig.,a) are generally small except for the The $z<0.1$ GAMA volume is known to be underdense by about with respect to a larger SDSS volume (see fig.70 20 of Driver 2011)) whereas the z«0.06 GAMA density is similar to the SDSS volume., 20 of \citealt{driver11}) ) whereas the $z<0.06$ GAMA density is similar to the SDSS volume.71 The faint end differences in Fig. 9((, The faint end differences in Fig. \ref{fig:compare-lf-magtype}( (72a) are generally not significant eerror bars in Fig. 8)),a) are generally not significant error bars in Fig. \ref{fig:compare-methods}) ).73" At the bright end, the differences are because the apertures and Sersic fits are recovering more flux from early-typegalaxies than the Petrosian aperture."," At the bright end, the differences are because the apertures and Sersic fits are recovering more flux from early-typegalaxies than the Petrosian aperture."74 Figure 9((b) compares the GAMA result using Petrosian magnitudes with results using the SDSS NYU-VAGC low-redshift sample (0.0033«z 0.05; Blantonetal. 2005b))., Figure \ref{fig:compare-lf-magtype}( (b) compares the GAMA result using Petrosian magnitudes with results using the SDSS NYU-VAGC low-redshift sample $0.0033 < z < 0.05$ ; \citealt{blanton05nyuvagc}) ).75" Ignoringthe differences below 10"" L, which are because of the differing magnitude limits, the Blantonetal.(20054) GLF (DR2) gives a higher number density below 10°Lo."," Ignoringthe differences below $10^{7.5}\Lsun$ , which are because of the differing magnitude limits, the \citet{blanton05} GLF (DR2) gives a higher number density below $10^{9}\Lsun$ ."76 This can be at least partly explained by the distances used., This can be at least partly explained by the distances used.77" The NYU-VAGC uses distances from the Willicketal.(1997) model, tapering to"," The NYU-VAGC uses distances from the \citet{willick97}78 model, tapering to"79The LIGAS survey (Neugebauer et al.,The IRAS survey (Neugebauer et al.80 1984) discovered many ultraluminous infrared galaxies (ULIICGs) that emit the bulk of their energy. in infrared. (LR) photons., 1984) discovered many ultraluminous infrared galaxies (ULIRGs) that emit the bulk of their energy in infrared (IR) photons.81 Since their bolometric Luminosity and the number density are as high as those of quasars. ULIRCGs are among the most energetic objects in the universe.," Since their bolometric luminosity and the number density are as high as those of quasars, ULIRGs are among the most energetic objects in the universe."82 The most fundamental problem vet to be solved is the energy source of the extremely intense infrared. emission., The most fundamental problem yet to be solved is the energy source of the extremely intense infrared emission.83 NGC 6240. a gravitationallv ineracting svstem with a complex optical morphology (Fosbiuv Wall 1979: Fried Schulz 1983). is à very interesting example of ULIRG.," NGC 6240, a gravitationally interacting system with a complex optical morphology (Fosbury Wall 1979; Fried Schulz 1983), is a very interesting example of ULIRG."84 Lts bolometric luminosity reaches 2.4.1Y? L. (Weight. Joseph. Meikle 1984: z=0.0245 and Lo=50 km s.1 1 are assumed).," Its bolometric luminosity reaches $2.4\times10^{12}$ $L_{\odot}$ (Weight, Joseph, Meikle 1984; z=0.0245 and $H_0=50$ km $^{-1}$ $^{-1}$ are assumed)."85 NGC 6240 is outstanding in several respects., NGC 6240 is outstanding in several respects.86 lis Ils 10S(1) at 2.121j/n and Fell] 1.64421. line luminosities and the ratio of Hs to bolometric luminosities are the largest. currently known (e.g.. van der Werf ct al.," Its $_2$ $1\rightarrow0S(1)$ at $\mu$ m and [FeII] $\mu$ m line luminosities and the ratio of $_2$ to bolometric luminosities are the largest currently known (e.g., van der Werf et al."87 1993)., 1993).88 Further. its stellar velocity dispersion of 360 kms is among the highest values ever found ina galaxy centre (e.g. Dovon et al.," Further, its stellar velocity dispersion of 360 km/s is among the highest values ever found in a galaxy centre (e.g., Doyon et al."89 1994)., 1994).90 The energv source. of the huge li luminosity is controversial., The energy source of the huge IR luminosity is controversial.91 Many. HV spectroscopic suclies (e.g. Genzel ot αἱ., Many IR spectroscopic studies (e.g. Genzel et al.92 1998: Riceway et al., 1998; Ridgway et al.93 1994: Ricke et al., 1994; Rieke et al.94 1985: Weight ot al., 1985; Weight et al.95 1984) have suggested that main energy. source of the Ji emission is starburst: activity. which is presumably a super-starburst induced by a merger of two galaxies (Joseph Wright 1985: Chevalier Clege 1985).," 1984) have suggested that main energy source of the IR emission is starburst activity, which is presumably a super-starburst induced by a merger of two galaxies (Joseph Wright 1985; Chevalier Clegg 1985)."96 The erouncbased: optical spectrum can be classifier as LINER. and iJa interpreted as a resut of shock heating (lleckman ct al.," The ground-based optical spectrum can be classified as LINER, and is interpreted as a result of shock heating (Heckman et al."97 1987)., 1987).98 On the other iand. a significant contribution [roni an active galactic nuceus (ΑΝ) similar to Sevfert. ealaxies was also discovered rom ΕΙ spectroscopy (DePov ct al.," On the other hand, a significant contribution from an active galactic nucleus (AGN) similar to Seyfert galaxies was also discovered from IR spectroscopy (DePoy et al."99 1986)., 1986).100 Another hint o ian AGN in NGC 6240 is the presence of compact bright radio cores (Carral et al., Another hint of an AGN in NGC 6240 is the presence of compact bright radio cores (Carral et al.101 1990. but see Colbert et al., 1990 but see Colbert et al.102 L994)., 1994).103HST discovered a core that is excited higher than LINER. (Itafanelli et al., discovered a core that is excited higher than LINER (Rafanelli et al.104 1997)., 1997).105 X-ray observation provides an important tool. for investigating both the starburst and AGN activity., X-ray observation provides an important tool for investigating both the starburst and AGN activity.106imaging from the VLA FIRST survey (Beckeretal.2003) shows strong emission both in the companion bulge and outside the primary bulge. but not within the primary bulge.,"imaging from the VLA FIRST survey \citep{becker.helfand.ea:first} shows strong emission both in the companion bulge and outside the primary bulge, but not within the primary bulge."107 The primary bulge is much redder than the bulge of any other blue-centered galaxy and has an Ho equivalent width of only iin emission. despite a very blue region immediately surrounding the red core (Fig.," The primary bulge is much redder than the bulge of any other blue-centered galaxy and has an $\alpha$ equivalent width of only in emission, despite a very blue region immediately surrounding the red core (Fig."108 1) and integrated EW(Ha) ~ 6.5 iin emission., 1) and integrated $\alpha$ ) $\sim$ 6.5 in emission.109 Thus although its identifies NGC 5541 as a rare high-luminosity blue-centered galaxy. its low-luminosity companion probably has more similarities to the rest of our blue-centered galaxy sample than NGC 5541 does.," Thus although its identifies NGC 5541 as a rare high-luminosity blue-centered galaxy, its low-luminosity companion probably has more similarities to the rest of our blue-centered galaxy sample than NGC 5541 does."110 NGC 5875A has no UZC companion. but its 2MASS color-composite image reveals a large region with distinct JHK-color on the northeast side of the galaxy. resembling à merging companion.," NGC 5875A has no UZC companion, but its 2MASS color-composite image reveals a large region with distinct JHK-color on the northeast side of the galaxy, resembling a merging companion."111 NGC 7752 appears to be in direct contact with the tidally distorted spiral arm of its larger companion. NGC 7753.," NGC 7752 appears to be in direct contact with the tidally distorted spiral arm of its larger companion, NGC 7753."112 The arm ts not easily visible at the scale and contrast of Fig., The arm is not easily visible at the scale and contrast of Fig.113 |., 1.114"positive. correspondinglv Aj, takes smaller. value and. A, is around 0.5.","positive, correspondingly $\lambda_{\rm b}$ takes smaller value and $\lambda_{\rm g}$ is around $0.5$."115 For stars more massive (han 124M.. A even drops below 0.5 for most J.," For stars more massive than $12M_\odot$ , $\lambda$ even drops below $0.5$ for most $R$."116" The extreme case in our calculation is lor 20... stars. in which both Aj, and A, evolve to be <I in stage 3."," The extreme case in our calculation is for $20M_\odot$ stars, in which both $\lambda_{\rm b}$ and $\lambda_{\rm g}$ evolve to be $\ll 1$ in stage 3."117" To provide easy-to-use formulae of Aj,and Ay. we make polynomial fitting with the following formulation. where y is Àj, or Ay. and is the stellar radius J? in most cases."," To provide easy-to-use formulae of $\lambda_{\rm b}$and $\lambda_{\rm g}$, we make polynomial fitting with the following formulation, where $y$ is $\lambda_{\rm b}$ or $\lambda_{\rm g}$, and $x$ is the stellar radius $R$ in most cases."118" For low-mass stars. we also use the fractional mass of the envelope maj,=MiΤΗ as the fitting variable as suggested hy Webbink(2007)."," For low-mass stars, we also use the fractional mass of the envelope $m_{\rm env} = M_{\rm119env}/M_{\rm donor}$ as the fitting variable as suggested by \citet{web07}."120". In limited caseswe use logAy, instead of Ay, as the y variable during stage 3 when (he value of Aj, is too large. and take 1/À as y and imi, as c in several cases (see Tables 1 and 2. for details)."," In limited caseswe use $\log \lambda_{\rm b}$ instead of $\lambda_{\rm b}$ as the $y$ variable during stage 3 when the value of $\lambda_{\rm b}$ is too large, and take $1/\lambda$ as $y$ and $m_{\rm env}$ as $x$ in several cases (see Tables \ref{tbl1}121 and \ref{tbl2} for details)."122 In Tables 1 and 2 we present the fitting parameters for Pop., In Tables \ref{tbl1} and \ref{tbl2} we present the fitting parameters for Pop.123 I and Pop., I and Pop.124 HE stars. respectively.," II stars, respectively."125 Our caleulations show that stars with different masses have different values of A. and Ais not constant for the same star in different evolutionary stages.," Our calculations show that stars with different masses have different values of $\lambda$, and $\lambda$ is not constant for the same star in different evolutionary stages."126 From Figs., From Figs.127" 1. and 2.. Ay, diverges [rom 0.5 for most AZ ancl 2. and it is obvious that assuming; a constant A=0.5 in population synthesis caleulations is far from fact and therefore lack of reliability."," \ref{fig1}128 and \ref{fig2}, $\lambda_{\rm b}$ diverges from $0.5$ for most $M$ and $R$, and it is obvious that assuming a constant $\lambda = 0.5$ in population synthesis calculations is far from fact and therefore lack of reliability."129 It is also interesting to note that the range of Ay is much narrower than that of Aj.," It is also interesting to note that the range of $\lambda_{\rm g}$ is much narrower than that of $\lambda_{\rm130b}$."131" Of course the actual value of A should lie between A, and Aj, since not all of the internal energvcontributes to the ejection of the envelope (Dewi&Tauris 2000)..", Of course the actual value of $\lambda$ should lie between $\lambda_{\rm g}$ and $\lambda_{\rm b}$ since not all of the internal energycontributes to the ejection of the envelope \citep{dew00}. .132 As we have eiven (he fitting lormmiae for A. the results can be useful for future population svuthesis works.," As we have given the fitting formulae for $\lambda$ , the results can be useful for future population synthesis works."133 However. this approach should be adopted carefully. especially in the cases when (he," However, this approach should be adopted carefully, especially in the cases when the"134data. the Minkowski fuuctionals aud the peak statistics of CAIB maps.,"data, the Minkowski functionals and the peak statistics of CMB maps."135" The standard decomposition of the measured temperature variatious on the skv. AT(0.0). in spherical laruiwnics is ο) = ο. (2) where P/""Cer) ave the associated Legeudre polyuoiuials."," The standard decomposition of the measured temperature variations on the sky, $\Delta T(\theta,\phi)$, in spherical harmonics is ) = ^m(x) }, where $P_\ell^m(x)$ are the associated Legendre polynomials."136" For a «itiunous. ATGeo) function. the coeffients. of decomposition. «των are where 375, deuotes complex conjugation of Y;,,."," For a continuous $\Delta T(x,\phi)$ function, the coefficients of decomposition, $a_{\ell m}$, are where $Y^{*}_{\ell m}$ denotes complex conjugation of $Y_{\ell m}$."137" For nunierica evaluation of the integral Eq(5)) we will use the Gaussian quadratures. a method which was proposed by Gauss in 1511, aud developed later by Christoffel iu 1877."," For numerical evaluation of the integral \ref{eq3}) ) we will use the Gaussian quadratures, a method which was proposed by Gauss in 1814, and developed later by Christoffel in 1877."138 As he iuteeral over .c in Eq(5)) is au iutegral over a polvuonial of ο we may use the following equality (Press et alt? 1992) Wt oY OV o)., As the integral over $x$ in \ref{eq3}) ) is an integral over a polynomial of $x$ we may use the following equality (Press et $^{14}$ 1992) dx ) ) .139 where wy is a proper Gaussian quadrature weighting fuuction., where $w_j$ is a proper Gaussian quadrature weighting function.140" Tere the weighting fiction «;=αμ). aud AT(ej-0))7),,(0).0) are taken at points e; which are the uet of roots of the Legendre polynomialοι. where NV is the maximal rank of the polvuonial uuder consideration."," Here the weighting function $w_j=w(x_j)$ and $\Delta T(x_j,\phi)141Y^{*}_{\ell m}(x_j,\phi)$ are taken at points $x_j$ which are the net of roots of the Legendre polynomial, where $N$ is the maximal rank of the polynomial under consideration."142 It is well known that the equation Py(rj)=O has No muniber of zeros in interval dxc61., It is well known that the equation $P_N(x_j)=0$ has $N$ number of zeros in interval $-1\le x\le 1$.143 For the GaussianLegeudre method Eq(6)). the weighting coefficients ave (Press et alt! 1992) rue?.. where  denotes a derivative.," For the Gaussian–Legendre method \ref{eq4}) ), the weighting coefficients are (Press et $^{14}$ 1992) w_j=, where ${'}$ denotes a derivative."144 They can be calculatedtogether with the set of e; with the gauleg code (Press et alt! 1992. Sec.," They can be calculatedtogether with the set of $x_j$ with the ' code (Press et $^{14}$ 1992, Sec."145 L5)., 4.5).146 Tn the CLESP approach are the trapezoidal pixels bordered by 0 aud o coordinate lines with the pixel ceuters Gi the 0 direction) situated at poiuts with wv;=cos., In the GLESP approach are the trapezoidal pixels bordered by $\theta$ and $\phi$ coordinate lines with the pixel centers (in the $\theta$ direction) situated at points with $x_j=\cos\theta_j$.147 Thus. the interval . lis covered by N vines of tle pixels (details are given in Sec.," Thus, the interval $-1\leq x\leq 1$ is covered by $N$ rings of the pixels (details are given in Sec."148 3)., 3).149 The angular resolution achieved in the measurement of the CAIB data determines the upper Πιτ of sununatioü in Eq. (1)). (xCau.," The angular resolution achieved in the measurement of the CMB data determines the upper limit of summation in Eq. \ref{eq1}) ), $\ell\leq \ell_{max}$."150" To avoid the Nyquist restrictions we use a nunber of pixel vines. NO26,4,"," To avoid the Nyquist restrictions we use a number of pixel rings, $N\geq 2 \ell_{max}$."151 Iu order to make the pixels in the equatorial ring (along the o coordinate) nearly squared. the nuuber of pixels in this direction should be NOsὃν.," In order to make the pixels in the equatorial ring (along the $\phi$ coordinate) nearly squared, the number of pixels in this direction should be $N_\phi^{max}\approx 2N$."152 The muuaber of pixels im otherrings. Α-j M must be deteriuned from the condition of making the pixel sizes as equal as possible with the equatorialrine of pixels.," The number of pixels in otherrings, $N_\phi^j$ , must be determined from the condition of making the pixel sizes as equal as possible with the equatorialring of pixels."153 Fie., Fig.154" 1 shows the weighting coefücients. aj. aud the position of pixel ceuters for the case |— 51, "," \ref{fig_weights} shows the weighting coefficients, $w_j$ , and the position of pixel centers for the case $N=31$ ."155Fie., Fig.156 2 colupares sole features ofthe pixelizatiou schemes used, \ref{fig_cos_theta} compares some features ofthe pixelization schemes used157correction ancl calibrates in wavelength.,correction and calibrates in wavelength.158 We lollowed a similar procedure with the data obtained with WYFFOS. but in this ease we used the general DOFIBERS task. which works similarly to DOIYDRA.," We followed a similar procedure with the data obtained with WYFFOS, but in this case we used the general DOFIBERS task, which works similarly to DOHYDRA."159 Although both tasks allow for sky subtraction. the results were poor. and important residuals of sky lines remained.," Although both tasks allow for sky subtraction, the results were poor, and important residuals of sky lines remained."160 To remove the contribution of these sky lines. we have developed our own procedure to subtract them.," To remove the contribution of these sky lines, we have developed our own procedure to subtract them."161 Basically. it consists in obtaining an average skv spectirum from all fibres placed on the sky in a given configuration.," Basically, it consists in obtaining an average sky spectrum from all fibres placed on the sky in a given configuration."162 Belore subtracting this average. hieh S/N sky. [rom each star spectrum. we need (to know the relation between the intensity of the skv in each fibre (which varies from fibre to fibre due to (he different libre responses) and the average sky.," Before subtracting this average, high S/N sky, from each star spectrum, we need to know the relation between the intensity of the sky in each fibre (which varies from fibre to fibre due to the different fibre responses) and the average sky."163 This relation is a weight (which may depend on wavelength) by which we must multiply (he average sky spectra belore subtracting it from each star., This relation is a weight (which may depend on wavelength) by which we must multiply the average sky spectra before subtracting it from each star.164 To calculate il. we have developed a task (hat finds the weight which minimizes the sky line residuals over the whole spectral region considered.," To calculate it, we have developed a task that finds the weight which minimizes the sky line residuals over the whole spectral region considered."165 As a result of this proceclure. the sky emission lines are removed. very. accurately.," As a result of this procedure, the sky emission lines are removed very accurately."166 Finally. (he normalization was carried out in the same wav as previously described.," Finally, the normalization was carried out in the same way as previously described."167 Examples of 4 stars with different metallicities are shown in Figure 2.., Examples of 4 stars with different metallicities are shown in Figure \ref{spectra}.168 Note how the strength of the CaT lines increases wilh metallicity., Note how the strength of the CaT lines increases with metallicity.169 The radial velocity of each star has been calculated in order (o reject cluster , The radial velocity of each star has been calculated in order to reject cluster non-members.170We used (he EXCOR task in IRLAF. which performs the eross-correlation between the target and template spectra of known radial velocity (Tonry&Davis1979).," We used the FXCOR task in IRAF, which performs the cross-correlation between the target and template spectra of known radial velocity \citep{td79}."171. We selected between 8 and 10 template stars in each run (hat had verv high S/N and covered a wide range of radial velocities., We selected between 8 and 10 template stars in each run that had very high S/N and covered a wide range of radial velocities.172 The velocities were corrected to (the heliocentric reference [rame within ΕΝΟΙ., The velocities were corrected to the heliocentric reference frame within FXCOR.173 The final radial velocity for each star was obtained as the average of the velocities obtained [rom each template. weighted bv the width of correlation peaks.," The final radial velocity for each star was obtained as the average of the velocities obtained from each template, weighted by the width of correlation peaks."174 In the case of observations with slit spectrographers. the star might not be exactly positioned in the centre of the slit.," In the case of observations with slit spectrographers, the star might not be exactly positioned in the centre of the slit."175 This error means a velocity uncertainty given bv p/Ag. where: e is the light speed. p is the spectral resolution given in 1; Ay ds the wavelength of the lines (in this case ~8600 A)). and XO is the angular offset of the star [rom the centre of the slit in aresec.," This error means a velocity uncertainty given by $\Delta v=c\times \Delta \Theta \times176p/\lambda_0$ , where: $c$ is the light speed, $p$ is the spectral resolution given in $^{-1}$; $\lambda_0$ is the wavelength of the lines (in this case $\sim$ 8600 ), and $\Delta \Theta$ is the angular offset of the star from the centre of the slit in arcsec."177 This effect has been described by and Harris&Zaritsky(2006)., This effect has been described by \citet{irwint02} and \citet{hz06}.178. In our case. it may only be significant in the case of the VLT observations.," In our case, it may only be significant in the case of the VLT observations."179 To estimate the offset in this case we used through-slit images obtained at the beginning of the observation of each configuration. taken to check that the stars were positioned in the slits.," To estimate the offset in this case we used through-slit images obtained at the beginning of the observation of each configuration, taken to check that the stars were positioned in the slits."180 In this image we have measured the position of each stellar centroid. which is compared with the position of the slit given in (he header of ihe image.," In this image we have measured the position of each stellar centroid, which is compared with the position of the slit given in the header of the image."181 The difference between both. AO. allows us to caleulate the uncertainty in the measurement of the radial velocity.," The difference between both, $\Delta \Theta$, allows us to calculate the uncertainty in the measurement of the radial velocity."182 This valuechanges Irom one star to another. the error being about 15 kms + on average.," This valuechanges from one star to another, the error being about 15 km $^{-1}$ on average."183 (Bonannoetal.2003).. (Thompson&DuncanRheinhardt2006).," \citep{Bonanno:2003uw}, \citep{ThompsonDuncan1996,Geppert2006}."184. 101° 102 Bonannoetal.(2003))). magnetic provides(Bonazzola&Gourgoulhonmay1996).. X/3-ray Chandrasekhar&Fermi," $10^{13}\,$ $10^{15}\,$ \citet{Miralles2002,Bonanno:2003uw}) \citep{Bonazzola1996}, $\gamma$ \citet{Chandrasekhar1953}."185(1953).. (Ferraro1954;al.1995) Kiuchi&Yoshida2008).. (Roxburgh1966;Haskell2010).," \citep{Ferraro1954, Monaghan1965, Bocquet1995} \citep{Roxburgh1963, Kiuchi2008}, \citep{Roxburgh1966, Haskell2008,186 Tomimura2005, Lander:2009, Ciolfi2009, Ciolfi2010}."187. only half the problem when modelling stellar magnetic fields: one also needs them to be stable over many dynamical timescales. since stellar magnetic fields have been observed to be long-lived.," only half the problem when modelling stellar magnetic fields; one also needs them to be stable over many dynamical timescales, since stellar magnetic fields have been observed to be long-lived."188 This has proved to be a challenging problem for analytic methods. which can only study the initial localised instability and not the resultant field configuration.," This has proved to be a challenging problem for analytic methods, which can only study the initial localised instability and not the resultant field configuration."189 With purely poloidal and purely toroidal fields known to be unstable (Markey&Tayler1973:WrightFlowers&Ruderman 1977).. only mixed-field configurations are likely to exist in stars.," With purely poloidal and purely toroidal fields known to be unstable \citep{Markey1973, Wright1973, Tayler1973,190 Flowers1977}, only mixed-field configurations are likely to exist in stars."191 More recently it has become feasible to use numerical evolutions to study these hydromagnetic instabilities. with the benefit that the global behaviour of the instability may be studied (analytic works rely on local as well as the final outcome of the instability whenanalyses). the field undergoes rearrangement (Lander&Jones2011:Braithwaitesignificant2007:Geppert&Rheinhardt2006;Kiuchietal. 2011).," More recently it has become feasible to use numerical evolutions to study these hydromagnetic instabilities, with the benefit that the global behaviour of the instability may be studied (analytic works rely on local analyses), as well as the final outcome of the instability when the field undergoes significant rearrangement \citep{Lander:2011, Braithwaite2007, Geppert2006,192 Kiuchi2011}."193 Despite this recent progress. there are still very few models of stellar magnetic-field configurations whose stability has been assessed.," Despite this recent progress, there are still very few models of stellar magnetic-field configurations whose stability has been assessed."194 The instability-induced redistribution of magnetic flux is potentially a very violent event and it has been suggested as a trigger mechanism for the giant flares of magnetars (Thompson&Duncan1996)., The instability-induced redistribution of magnetic flux is potentially a very violent event and it has been suggested as a trigger mechanism for the giant flares of magnetars \citep{ThompsonDuncan1996}.195. This redistribution is likely to be accompanied by a significant change to the mass quadrupole moment of a NS. making it a potentially detectable source of gravitational waves (GWs) (Kashiyama&loka2011;CorsiOwen 2011).," This redistribution is likely to be accompanied by a significant change to the mass quadrupole moment of a NS, making it a potentially detectable source of gravitational waves (GWs) \citep{Kashiyama2011,196 Corsi2011}."197 For this reason it is important to understand the frequency. amplitude and duration these GWs may have.," For this reason it is important to understand the frequency, amplitude and duration these GWs may have."198 This paper is organised as follows., This paper is organised as follows.199 In Section 2 we give a description of our computational infrastructure and initial stellar models., In Section 2 we give a description of our computational infrastructure and initial stellar models.200 In Section 3 we present results from our evolutions. showing the generation of an instability and the subsequent reorganisation of the magnetic field into amorestable configuration.," In Section 3 we present results from our evolutions, showing the generation of an instability and the subsequent reorganisation of the magnetic field into amorestable configuration."201 Wealso study the GW emission from the instability and assess its detectability., Wealso study the GW emission from the instability and assess its detectability.202 Conclusions are presented in Section 4., Conclusions are presented in Section 4.203Of ME at AlasSS510°AL. is somewhat dependent on the choice of the outer hreshold density of galaxics.,"of MF at $\Mstar \lesssim 5\times 10^7\,\Msun$ is somewhat dependent on the choice of the outer threshold density of galaxies."204" Figure 7 compares the gas and baryonic (star | gas) AES for the N216L1O series at z=3 (panels a 5). and the redshift evolution o""the barvonic ME from 2.=5 to. =3 in the N216LIO0 (panel ο) ancl N216LI0mc (panel d) runs."," Figure \ref{fig:MF_comp} compares the gas and baryonic (star + gas) MFs for the N216L10 series at $z=3$ (panels $a$ $b$ ), and the redshift evolution of the baryonic MF from $z=5$ to $z=3$ in the N216L10 (panel $c$ ) and N216L10mc (panel $d$ ) runs."205 Llere we show only t1e range of Aag25.0.107AZ. which corresponds to the imiting mass of 32 gas particles.," Here we show only the range of $\Mstar \ge 5.0\times 10^7\,\Msun$, which corresponds to the limiting mass of 32 gas particles."206 Pane (a) shows that more| gas is converted into stars in the runs with metal cooling (:2216L10mc and N216LI0ms comparec o the N216LIO0 run. while panel (5) shows that the) barvonic ALF is similar in all the runs.," Panel $a$ ) shows that more gas is converted into stars in the runs with metal cooling (N216L10mc and N216L10mv) compared to the N216L10 run, while panel $b$ ) shows that the baryonic MF is similar in all the runs."207 As we discussed in 3.3... the IGAL accretion onto galaxies is not so much enhanced. ve rclore z~3 due to relatively low LGAL metallicity. which explains the similarity in the total barvonic ME.," As we discussed in \ref{sec:Evolv4}, , the IGM accretion onto galaxies is not so much enhanced yet before $z\sim 3$ due to relatively low IGM metallicity, which explains the similarity in the total baryonic MF."208 In the runs with metal cooling. the peak of GSME is shifted: toware ligher mass. whereas the peak of eas ME is shifted toware ower mass.," In the runs with metal cooling, the peak of GSMF is shifted toward higher mass, whereas the peak of gas MF is shifted toward lower mass."209 This suggests that the enhanced CGSME a >=3 is clue to the increased SE cllicleney by metal cooling within the galaxies., This suggests that the enhanced GSMF at $z=3$ is due to the increased SF efficiency by metal cooling within the galaxies.210 Again. the apparent enhancement. in he number of low-mass galaxies in the N216L10mc run compared to the N216L10 run is somewhat dependent on he threshold. density of grouping. therefore it. should. be interpreted with caution.," Again, the apparent enhancement in the number of low-mass galaxies in the N216L10mc run compared to the N216L10 run is somewhat dependent on the threshold density of grouping, therefore it should be interpreted with caution."211 As the accretion of GM onto galaxies become more ellicient al ο<3 clue to the increased. LGAL cooling by the metals. we expect that the total harvonic mass of galaxies would be more enhanced at 2=1 than at 2=3.," As the accretion of IGM onto galaxies become more efficient at $z<3$ due to the increased IGM cooling by the metals, we expect that the total baryonic mass of galaxies would be more enhanced at $z=1$ than at $z=3$."212 Figure S. shows the Αποκ at.=3 anced 2=1 in the N288L234 series. and it clearly demonstrates that this expectation is true.," Figure \ref{fig:MF_comp_N288L34} shows the MFs at $z=3$ and $z=1$ in the N288L34 series, and it clearly demonstrates that this expectation is true."213" Here we show only the range of Ala,28.2«107AJ... which corresponds to the limiting mass of 32 gas particles."," Here we show only the range of $\Mgas \ge 8.2\times 10^8\,\Msun$, which corresponds to the limiting mass of 32 gas particles."214 The general trend in the three (star. gas. and total barvon) MES is similar to that we saw in Figure 7.. although the cillerence at 23 between the N288L34 and N288L34mc runs is slightly smaller than in the N2IGLIO series due to poorer resolution.," The general trend in the three (star, gas, and total baryon) MFs is similar to that we saw in Figure \ref{fig:MF_comp}, although the difference at $z=3$ between the N288L34 and N288L34mc runs is slightly smaller than in the N216L10 series due to poorer resolution."215 Fieure SIP shows most. prominently the enhancement of the total barvonic ME at 2=1 in the N288L34mc run owing to the metal cooling., Figure \ref{fig:MF_comp_N288L34}f f shows most prominently the enhancement of the total baryonic MF at $z=1$ in the N288L34mc run owing to the metal cooling.216 In panels (ο) Cf). the N288L34 run actually has a longer tail at he most massive-enc than the N288L34mc run.," In panels $e$ ) $f$ ), the N288L34 run actually has a longer tail at the most massive-end than the N288L34mc run."217 The reason for this feature is not fully clear. but it may. be related to the balance between IGM aceretion and feedback.," The reason for this feature is not fully clear, but it may be related to the balance between IGM accretion and feedback."218 Owing to metal cooling. IGM accretion rate increases in the mc. run. and the SER. is also enhanced. leading to a stronger feedback.," Owing to metal cooling, IGM accretion rate increases in the 'mc' run, and the SFR is also enhanced, leading to a stronger feedback."219 The amount of mass loss is greater in low mass galaxies. but the net heating of IGM is more significant for massive galaxies.," The amount of mass loss is greater in low mass galaxies, but the net heating of IGM is more significant for massive galaxies."220 The mc run has stronger feedback. therefore its feedback. heating may become more significant than ICM acerction for very massive galaxies.," The 'mc' run has stronger feedback, therefore its feedback heating may become more significant than IGM accretion for very massive galaxies."221 The significant IM. heating suppresses the growth of massive-cnd of mass function [from z=3 to >=| and results in shorter tail for the mc run at z=1 as shown in Figure Sec.f. For a fixed galaxy baryonic mass. the enhancement of star formation bv metal cooling would. decrease the gas mass paction. fa.οAdww/Adivaven.," The significant IGM heating suppresses the growth of massive-end of mass function from $z=3$ to $z=1$ and results in shorter tail for the 'mc' run at $z=1$ as shown in Figure \ref{fig:MF_comp_N288L34}e e,f. For a fixed galaxy baryonic mass, the enhancement of star formation by metal cooling would decrease the gas mass fraction, $\fgas \equiv M_{\rm gas} / M_{\rm baryon}$."222 Figure 9 shows fax. as a function of galaxy stellar. mass for the N2IGLIO series., Figure \ref{fig:GFrac_evol_N216L10} shows $\fgas$ as a function of galaxy stellar mass for the N216L10 series.223 ancl (a) shows the data only from. N216L10mc run at >=A. and cach data point corresponds to a simulated galaxy.," Panel $a$ ) shows the data only from N216L10mc run at $z=3$, and each data point corresponds to a simulated galaxy."224" To characterise the distribution. we compute the ollowing two quantities in cach logarithmic stellar mass xn: ""average and ""median."," To characterise the distribution, we compute the following two quantities in each logarithmic stellar mass bin: `average' and `median'."225" The ‘average’ is the ratio of otal gas mass to total barvonic mass for all the galaxies in cach mass bin. Le... 7,οπμ "," The `average' is the ratio of total gas mass to total baryonic mass for all the galaxies in each mass bin, i.e., $\sum_{i}^{} M_{\rm gas, i} / \sum_{i}^{} M_{\rm baryon, i}$."226"The ""median? case is simply the median of fa.. values in cach mass bin.", The `median' case is simply the median of $\fgas$ values in each mass bin.227" Both quantities show a similar trend. however. there is a sharper clrop-olf at. Aa;&2.5101AL. for the ""median case in Figure 9aa. This mass-scale corresponds to 32 star xwiicles in the N2IGLIO series."," Both quantities show a similar trend, however, there is a sharper drop-off at $\Mstar \simeq 2.5 \times 10^{7}\,\Msun$ for the `median' case in Figure \ref{fig:GFrac_evol_N216L10}a a. This mass-scale corresponds to 32 star particles in the N216L10 series."228" We find tha there are many galaxies with fur.=0 above this mass-scale. which causes the sharp drop-olf in the ""median. line."," We find that there are many galaxies with $\fgas = 0$ above this mass-scale, which causes the sharp drop-off in the `median' line."229 Below this imiting mass. galaxies are not resolved. well. which results in an underestimate of star formation and an overestimate of fas.," Below this limiting mass, galaxies are not resolved well, which results in an underestimate of star formation and an overestimate of $\fgas$."230 M we had a higher resolution simulation with finer xuticle masses. this limiting mass-scale would shift to a ower mass.," If we had a higher resolution simulation with finer particle masses, this limiting mass-scale would shift to a lower mass."231 Therefore the location of this sharp drop-olf is currently determined by the resolution of our simulation., Therefore the location of this sharp drop-off is currently determined by the resolution of our simulation.232 Llowever. dark matter halos would stop forming stars at some lower limiting halo mass. if we had an infinitely hieh-resolution simulation. This lower limit to the galaxy mass is presumably. determined. by the photoevaporation of gas by the UV. background: radiation (tees1986:Efstathiou2004:Pontzenctal.2008:Okamotoet 2008).," However, dark matter halos would stop forming stars at some lower limiting halo mass, if we had an infinitely high-resolution simulation, This lower limit to the galaxy mass is presumably determined by the photoevaporation of gas by the UV background radiation \citep{Rees:86, 233Efstathiou:92, Quinn.etal:96,Gnedin:00, Nagamine.etal:04-dla, Pontzen.etal:08,234Okamoto.etal:08}."235.. Recent works suggest that star formation could be suppressed. by the UV backgroundin halos with Mya;1°ALR at zm3.," Recent works suggest that star formation could be suppressed by the UV backgroundin halos with $M_{\rm halo} \lesssim 10^9\,\Msun$ at $z\sim 3$."236" Galaxies with Auc2101AM. would reside in. halos with Alas2210""AL..."," Galaxies with $\Mstar \simeq 2 \times 10^{7}\,\Msun$ would reside in halos with $M_{\rm halo} \approx 2\times 10^9\,\Msun$."237" ""Phe N216LI0 series would resolve such a halo with ~280 dark matter particles. and its mass resolution is actually close to the astrophysical limit [or dwarl galaxy formation at z3."," The N216L10 series would resolve such a halo with $\sim 280$ dark matter particles, and its mass resolution is actually close to the astrophysical limit for dwarf galaxy formation at $z\sim 3$."238 Therefore the sharp drop-oll in sas UU Mau&2sLOτAL. may not be so far [rom the truce answer.," Therefore the sharp drop-off in $\fgas$ at $\Mstar \simeq 2 \times 10^{7}\,\Msun$ may not be so far from the true answer."239 We find that fya. increases with decreasing Maas at al recishifts. regardless of metal cooling ancl wind effects.," We find that $f_{gas}$ increases with decreasing $\Mstar$ at all redshifts, regardless of metal cooling and wind effects."240 “Phis trend. is qualitatively consistent with current observations., This trend is qualitatively consistent with current observations.241 Erbctal.(2006). estimate the eas fraction as a function of stellar mass using the rest-frame UV-selected star-forming ealaxics at z2. and show that the eas fraction decreases with increasing stellar mass.," \citet{Erb.etal:2006} estimate the gas fraction as a function of stellar mass using the rest-frame UV-selected star-forming galaxies at $z \sim 2$, and show that the gas fraction decreases with increasing stellar mass."242 And using the mean gas ane stellar mass. they find the average ων~0.35. which agrees with the predicted: gas fraction for massive galaxies in our simulation.," And using the mean gas and stellar mass, they find the average $f_{gas} \sim 0.35 $, which agrees with the predicted gas fraction for massive galaxies in our simulation."243 In accdition. Gehaetal.(2006). reported. tha the average neutral gas fraction is Cfi)=0.6 for the loca chvarl ealaxies selected. from the Sloan Digital Sky Survey.," In addition, \citet{Geha.etal:06} reported that the average neutral gas fraction is $\langle \fgas \rangle = 0.6$ for the local dwarf galaxies selected from the Sloan Digital Sky Survey."244" In our N216L10 series with metal cooling. the ""average reaches 0.6 for galaxies with AL,210AJ. αἱ 4."," In our N216L10 series with metal cooling, the `average' $\fgas$ reaches 0.6 for galaxies with $\Mstar \simeq 2\times 10^7\,\Msun$ at $z=3$ 4."245" 10bb.ο, dshowtheredshi flevolutiono flan.for the N216L10 series."," \\ref{fig:GFrac_evol_N216L10}b b,c,d show the redshift evolution of $\fgas$for the N216L10 series."246" In the runs with metal cooling (N216L10me and N216LI0mw). fas. is lower than in the N2IGLIO run bv 20—30% at all redshifts. for galaxies with λα=10710"" A4.."," In the runs with metal cooling (N216L10mc and N216L10mv), $\fgas$ is lower than in the N216L10 run by $20-30$ at all redshifts for galaxies with $\Mstar = 10^{7.5} - 10^9\,\Msun$ ."247 This result. suggests. that the metal cooling reduces. a. OWlng to more efficient. star formation., This result suggests that the metal cooling reduces $\fgas$ owing to more efficient star formation.248 The values of. fi; seem to be more convergent . ⋜∐↿↓↕⋖⋅⊔↓⋜↧⊳∖⊳∖↓∖⇁⋖⋅⊣⊾↓⊔⇂∪∫∖⋯↙⇁↓∪⇀∪⋅∃⊳↓⊔⋯," The values of $\fgas$ seem to be more convergent at the massive-end $\Mstar > 10^9\,\Msun$ )."249"⇂∠⊔↿↓∪⊔⊳∖∖⋎⋖⊾∐⊔∠⇂"" .. ⋅"," In addition, we find"250This paper has been concerned with the ellect of PSF anisotropy patterns on systematic errors in weak lensing surveys.,This paper has been concerned with the effect of PSF anisotropy patterns on systematic errors in weak lensing surveys.251 We have suggested the use of galaxy shapes measured in disünct exposures to estimate shear correlations as a way of eliminating the systematic error due to non-recurrent PSF patterns., We have suggested the use of galaxy shapes measured in distinct exposures to estimate shear correlations as a way of eliminating the systematic error due to non-recurrent PSF patterns.252 showed that recurrent PSF patterns can be accurately measured using a Principal Component Approach.," \citet{Ja05}253 showed that recurrent PSF patterns can be accurately measured using a Principal Component Approach."254" By using these two techniques in lensing pipelines, systematic errors due to generic PSF patterns can be interpolated (and therefore corrected) to high accuracy."," By using these two techniques in lensing pipelines, systematic errors due to generic PSF patterns can be interpolated (and therefore corrected) to high accuracy."255" In planning a large-area cosmic shear survey, we have shown that the key factors that enable accurate PSF corrections are: sufficiently many well-measured stars in all parts of the sky; 5-10 exposures per poinüng; sufficiently [ew important principal components, which cannot exceed the number of stars per exposure."," In planning a large-area cosmic shear survey, we have shown that the key factors that enable accurate PSF corrections are: sufficiently many well-measured stars in all parts of the sky; 5-10 exposures per pointing; sufficiently few important principal components, which cannot exceed the number of stars per exposure."256" In addition, the principal components can be estimated better if dense stellar fields are imaged on regular intervals, and if there are few changes in the instrument over the course of the survey (as these can introduce new principal components)."," In addition, the principal components can be estimated better if dense stellar fields are imaged on regular intervals, and if there are few changes in the instrument over the course of the survey (as these can introduce new principal components)."257 Another consideration [or minimizing the number of important principal components is to keep the observing conditions as stable as possible., Another consideration for minimizing the number of important principal components is to keep the observing conditions as stable as possible.258" For each underlying physical cause of PSF variation, one can essentially do a Taylor expansion of the PSF pattern with respect to that variable."," For each underlying physical cause of PSF variation, one can essentially do a Taylor expansion of the PSF pattern with respect to that variable."259 The PCA will need a separate component [or each term in the Taylor expansion which has a significant amplitude., The PCA will need a separate component for each term in the Taylor expansion which has a significant amplitude.260 Thus. one should try to keep such variations (eg.," Thus, one should try to keep such variations (eg."261" locus error, component misalignments, mirror flexure, etc.)"," focus error, component misalignments, mirror flexure, etc.)"262 small enough that one or two terms in the expansion are sufficient to adequately describe the elTect on the PSF pattern., small enough that one or two terms in the expansion are sufficient to adequately describe the effect on the PSF pattern.263 One can estimate what limits are sufficient through spot-diagram ray-tracing programs., One can estimate what limits are sufficient through spot-diagram ray-tracing programs.264 The second goal of this paper was to provide a formalism to estimate residual systematics due to PSF errors., The second goal of this paper was to provide a formalism to estimate residual systematics due to PSF errors.265 The ingredients needed to apply our formalism are an estimate of typical PSF power spectra and of the number of significant principal components of PSF patterns., The ingredients needed to apply our formalism are an estimate of typical PSF power spectra and of the number of significant principal components of PSF patterns.266" For planned surveys, this is best accomplished by generaüng PSF patterns in à given exposure by ray tracing through the telescope opucs."," For planned surveys, this is best accomplished by generating PSF patterns in a given exposure by ray tracing through the telescope optics."267 Mock surveys can then be generated by modeling the atmosphere and the variation of instrumental parameters over the course of the survey., Mock surveys can then be generated by modeling the atmosphere and the variation of instrumental parameters over the course of the survey.268 The resulung models of PSF patterns can be used with the formalism of to find telescope parameters and survey strategy that minimize residual systematics., The resulting models of PSF patterns can be used with the formalism of \\ref{pca} to find telescope parameters and survey strategy that minimize residual systematics.269" The difficulty in gelling reliable estimates of residual systematics will be in including all relevant factors which may affect the PSF, many of which may be subtle and hard to anticipate."," The difficulty in getting reliable estimates of residual systematics will be in including all relevant factors which may affect the PSF, many of which may be subtle and hard to anticipate."270 But the benefit of such an exercise is the ability to optimize instrument and survey parameters for lensing measurements., But the benefit of such an exercise is the ability to optimize instrument and survey parameters for lensing measurements.271" Further, once data is taken, comparison of the measured principal components with the models will help validate the error analysis."," Further, once data is taken, comparison of the measured principal components with the models will help validate the error analysis."272" Our formalism can be applied to survey data to estimate residual systematic errors,", Our formalism can be applied to survey data to estimate residual systematic errors.273" If systematics turn out to be significant, empirical estimation allows one to incorporate them in the error budget lor cosmological parameters."," If systematics turn out to be significant, empirical estimation allows one to incorporate them in the error budget for cosmological parameters."274" In addition, the following tests provide independent checks of the estimate of systematic errors [rom survey data (note that at least the latter two tests can be applied to model PSF patterns for planned surveys as well):"," In addition, the following tests provide independent checks of the estimate of systematic errors from survey data (note that at least the latter two tests can be applied to model PSF patterns for planned surveys as well):"275local universe.,local universe.276 When the R3 distribution is considered. we find the models produce too large a fraction of simulated sources having HR3=-|.," When the $HR3$ distribution is considered, we find the models produce too large a fraction of simulated sources having $HR3 = -1$."277 This is most probably caused by the over-abundance of very faint sources produced by the simulations. related to the XLF mismatch.," This is most probably caused by the over-abundance of very faint sources produced by the simulations, related to the XLF mismatch."278 These sources are detected just above the flux limit in the softer bands. but have count rates which fall below the background level in the hardest band. and hence are measured to have HR3x-|.," These sources are detected just above the flux limit in the softer bands, but have count rates which fall below the background level in the hardest band, and hence are measured to have $HR3 \approx -1$."279 The statistical analysis strongly rejects the R=ACLy) model. in agreement with the findings of a recent study by Treisteretal. (20043... which was based on deep multi-wavelength data in the GOODS fields.," The statistical analysis strongly rejects the $R=R(L_X)$ model, in agreement with the findings of a recent study by \citet{treister04}, which was based on deep multi-wavelength data in the GOODS fields."280 These authors tested the //6(Vjj) model of etal. (2003)... alongside a simpler /CVjj). but found that the latter provided a much better description of the data.," These authors tested the $f(N_H)$ model of \citet{ueda03}, alongside a simpler $f(N_H)$, but found that the latter provided a much better description of the data."281" By examining the subset of sources satisfying the ""hard"" selection criteria. we can compare the distributions of absorption above logN;,=22 that are found in the sample with those predicted bythe models."," By examining the subset of sources satisfying the “hard” selection criteria, we can compare the distributions of absorption above $N_H = 22$ that are found in the sample with those predicted bythe models."282" We have carried out 3D-KS and KS tests on ARI. HR2. and HR3. as before. but only for the ""hard"" selected subsets of the sample and simulations."," We have carried out 3D-KS and KS tests on $HR1$, $HR2$, and $HR3$, as before, but only for the “hard” selected subsets of the sample and simulations."283 The 3D-KS test rejects each of the ΟΛ) models with high confidence. (both with and without a reflection component included in the model spectra).," The 3D-KS test rejects each of the $f(N_H)$ models with high confidence, (both with and without a reflection component included in the model spectra)."284 We haveexamined the individual KS test results to determine the source of this large disparity., We haveexamined the individual $KS$ test results to determine the source of this large disparity.285 We find that the KS probabilities for the best fitting 6=8 model. (with the absorbed power-law spectral model). are 0.0003. 0.76. and 0.12. for HRI. HR2 and HR3 respectively.," We find that the $KS$ probabilities for the best fitting $\beta=8$ model, (with the absorbed power-law spectral model), are 0.0003, 0.76, and 0.12, for $HR1$, $HR2$ and $HR3$ respectively."286 The equivalent probabilities when an additional reflection component isincluded in the model spectra are 0.0002. 0.77. and 0.29.," The equivalent probabilities when an additional reflection component isincluded in the model spectra are 0.0002, 0.77, and 0.29."287" The KS test probabilities do not vary greatly between the different /6N;,) models (excepting the A=0 model).", The $KS$ test probabilities do not vary greatly between the different $f(N_H)$ models (excepting the $R=0$ model).288" The HA2 and HAS distributions of all the ΟΛ) models (excepting the A=QO model) provide rather good matches to the HA? and HR3 distributions found in the ""hard"" subset of the sample.", The $HR2$ and $HR3$ distributions of all the $f(N_H)$ models (excepting the $R=0$ model) provide rather good matches to the $HR2$ and $HR3$ distributions found in the “hard” subset of the sample.289" The ditferences between the ""hard"" subsets of the JON) models are small. due to the rapid decline in the selected fraction of “input” sources for high absorbing columns (see fig. 39)."," The differences between the “hard” subsets of the $f(N_H)$ models are small, due to the rapid decline in the selected fraction of “input” sources for high absorbing columns (see fig. \ref{nh_det_frac}) )."290 This acts to diminish the importance of the ditferences between the JON) models above Ny=107 72., This acts to diminish the importance of the differences between the $f(N_H)$ models above $N_H = 10^{22}$ $^{-2}$.291 The addition of a reflection component to the spectral model improves the KS probability for HR3 by a factor of ~2., The addition of a reflection component to the spectral model improves the KS probability for $HR3$ by a factor of $\sim 2$.292" We see that the mismatch between the AAI distributions is much worse in the ""hard"" subset. compared to the sample as a whole."," We see that the mismatch between the $HR1$ distributions is much worse in the “hard” subset, compared to the sample as a whole."293" This appears to be due to the overproduction of simulated sources having HAL=I. which is more pronounced in the ""hard"" sub-sample."," This appears to be due to the overproduction of simulated sources having $HR1 = 1$, which is more pronounced in the “hard” sub-sample."294" The fraction of the ""hand"" sample with HRI=| is for the field. but ~40% for the model populations."," The fraction of the “hard” sample with $HR1 = 1$ is for the field, but $\sim 40\%$ for the model populations."295 The disparity could be explained if a number of the heavily absorbed AGN have an additional soft X-ray component in their spectra., The disparity could be explained if a number of the heavily absorbed AGN have an additional soft X-ray component in their spectra.296 In order to reproduce the distribution of HAL. this phenomenon should occur in around of the heavily absorbed sources.," In order to reproduce the distribution of $HR1$, this phenomenon should occur in around of the heavily absorbed sources."297 A number of absorbed AGN with excess soft emission have been observed by other authors in samples of spectroscopically identified X-ray sources (e.g. Caccianigaetal.2004... Pageetal. 2005).," A number of absorbed AGN with excess soft emission have been observed by other authors in samples of spectroscopically identified X-ray sources (e.g. \citealt{caccianiga04}, \citealt{page05}) )."298 This excess component could be due to intense starbursts in the host galaxy. or to ditfuse emission surrounding anAGN embedded in a galaxy cluster.," This excess component could be due to intense starbursts in the host galaxy, or to diffuse emission surrounding anAGN embedded in a galaxy cluster."299 Alternatively. it could be scattered radiation from the central engine of the absorbed AGN.," Alternatively, it could be scattered radiation from the central engine of the absorbed AGN."300" For the simplest toy model of a torus with uniformly density. and a typical opening angle. &,. the fraction of AGN that are heavily absorbed is approximately coste,)."," For the simplest toy model of a torus with uniformly density, and a typical opening angle, $\theta_o$, the fraction of AGN that are heavily absorbed is approximately $cos(\theta_o)$."301" So. if we use the size of the ""hard"" fraction of the sample as a measure of the number of absorbed AGN. we can infer a rather wide opening angle of 4,~67."," So, if we use the size of the “hard” fraction of the sample as a measure of the number of absorbed AGN, we can infer a rather wide opening angle of $\theta_o \sim 67\degr$."302" However. this estimate does not take into account the effect of the drop in the selection function toward high Αμ. and can only be seen as an upper limit on &,."," However, this estimate does not take into account the effect of the drop in the selection function toward high $N_H$, and can only be seen as an upper limit on $\theta_o$."303" We estimate the relative selection function for hard sources by counting the fraction of simulated ""hard"" input sources that have output counterparts relative to that for all input sources.", We estimate the relative selection function for hard sources by counting the fraction of simulated “hard” input sources that have output counterparts relative to that for all input sources.304" Applying this correction to the sample. we predict an ""hard"" fraction of ~ 0.8. implying an opening angle of &,~ 37°."," Applying this correction to the sample, we predict an “hard” fraction of $\sim 0.8$ , implying an opening angle of $\theta_o \sim 37\degr$ ."305" If in our correction for the relative selection function. we exclude those sources with absorbing column above log),= 24. where our sample constrains the models only weakly. then we find &,= 52°."," If in our correction for the relative selection function, we exclude those sources with absorbing column above $N_H = 24$ , where our sample constrains the models only weakly, then we find $\theta_o \sol 52\degr$ ."306 We are also able, We are also able307"Mens/Mxray is not only a function of d, but also depends very strongly on R, (or the arc radius r4,).","$m_{\rm lens}/m_{\rm xray}$ is not only a function of $d$, but also depends very strongly on $R_x$ (or the arc radius $r_{\rm arc}$ )."308" Apparently, each cluster in our sample has quite different rare."," Apparently, each cluster in our sample has quite different $r_{\rm arc}$."309" Probably, other mechanisms than the offset effect should play important roles, and the lensing-X-ray mass discrepancy may not be just from one mechanism, but a combination of many effects: (1) The central regions of clusters may be still undergoing dynamical relaxation, and the X-ray gas may not be in good hydrostatic equilibrium."," Probably, other mechanisms than the offset effect should play important roles, and the lensing-X-ray mass discrepancy may not be just from one mechanism, but a combination of many effects: (1) The central regions of clusters may be still undergoing dynamical relaxation, and the X-ray gas may not be in good hydrostatic equilibrium."310" Therefore, large errors could be induced in the X-ray measurement of cluster cores, especially for unrelaxed clusters. ("," Therefore, large errors could be induced in the X-ray measurement of cluster cores, especially for unrelaxed clusters. ("3112) The spherical models are too simple to reflect the real mass distribution of clusters.,2) The spherical models are too simple to reflect the real mass distribution of clusters.312" The use of more realistic mass model could reduce the lens mass within the arc radius by up to 40%, though values of ~20% are more typical (Bartelmann 1995; Allen 1998). ("," The use of more realistic mass model could reduce the lens mass within the arc radius by up to $40\%$, though values of $\sim 20 \%$ are more typical (Bartelmann 1995; Allen 1998). ("313"3) The presence of substructures may complicate our simple spherical lens model, and hence could be a main source of uncertainties in ens.","3) The presence of substructures may complicate our simple spherical lens model, and hence could be a main source of uncertainties in $m_{\rm lens}$."314 The absence of the secondary arc-like images in most arc-cluster systems may indicate the limitations of the spherical mass distribution in the central regions of clusters., The absence of the secondary arc-like images in most arc-cluster systems may indicate the limitations of the spherical mass distribution in the central regions of clusters.315 It should be noted that the mass ratios we obtained here are slightly higher than Allen (1998) and Wu (2000) because they unfortunately used a Hubble constant of Ho=50kms!Mpc!.," It should be noted that the mass ratios we obtained here are slightly higher than Allen (1998) and Wu (2000) because they unfortunately used a Hubble constant of $\rm H_0=50 \, km \,316s^{-1}Mpc^{-1}$."317 The use of Hy)=70kms!Mpc! here will of course make the mass discrepancy problem more pronounced.," The use of $\rm H_0=70 \, km \, s^{-1}Mpc^{-1}$ here will of course make the mass discrepancy problem more pronounced."318" It should be noted that the gas represents only a 10% perturbation due to the small ratio of gas-to-DM in the central region, likewise the offset of the gas is only a small perturbation (less than 10%) to the otherwise concentric matter density or potential."," It should be noted that the gas represents only a $10\%$ perturbation due to the small ratio of gas-to-DM in the central region, likewise the offset of the gas is only a small perturbation (less than $10\%$ ) to the otherwise concentric matter density or potential."319 It is unlikely to create a factor of two difference in the lensing-derived enclosed masses within an arc., It is unlikely to create a factor of two difference in the lensing-derived enclosed masses within an arc.320" To illustrate the lensing effect of the offset perturbation and triaxiality, we show the critical curves in Figure 4."," To illustrate the lensing effect of the offset perturbation and triaxiality, we show the critical curves in Figure 4."321" The solid curves indicate the critical curve of circular NFW plus 6 model without offset, the dotted curves indicate the critical curve of elliptical NFW plus 6 model with offset d=10""."," The solid curves indicate the critical curve of circular NFW plus $\beta$ model without offset, the dotted curves indicate the critical curve of elliptical NFW plus $\beta$ model with offset $d=10''$."322" The square and cross denote the center of dark matter and the hot gas, respectively."," The square and cross denote the center of dark matter and the hot gas, respectively."323" For the NFW profile, c=4.3,r, 516kpc; for the 6 model, B=0.65,r.150kpc."," For the NFW profile, $c=4.3, r_s=516 \rm kpc$ ; for the $\beta$ model, $\beta=0.65, r_c=150 \rm kpc$."324 We also introduce the triaxiality with the ellipticity e=0.15 and position angle 6=30°., We also introduce the triaxiality with the ellipticity $e=0.15$ and position angle $\theta=30^{\circ}$.325" We also assume the lens and source redshifts z;=0.3, z,=1."," We also assume the lens and source redshifts $z_l=0.3$, $z_s=1$."326 We can see that the predicted critical curves (dotted lines) have very similar sizes as the predicted critical curves for a benchmark model (solid lines) with the same mass DM and gas mass but in concentric spheres., We can see that the predicted critical curves (dotted lines) have very similar sizes as the predicted critical curves for a benchmark model (solid lines) with the same mass DM and gas mass but in concentric spheres.327 Early studies have suggested that statistically unrelaxed clusters have larger mass discrepancies than relaxed clusters (Allen 1998; Wu 2000; Richard et al., Early studies have suggested that statistically unrelaxed clusters have larger mass discrepancies than relaxed clusters (Allen 1998; Wu 2000; Richard et al.328 2010)., 2010).329 As Shan et al. (, As Shan et al. (330"2010) have reported, the clusters with large offset of d>10” are all unrelaxed clusters.","2010) have reported, the clusters with large offset of $d>10''$ are all unrelaxed clusters."331" If such offsets exist and are big, then they must come into play in our dynamical studies of galaxy cluster, and should not be ignored, especiallyfor unrelaxed clusters."," If such offsets exist and are big, then they must come into play in our dynamical studies of galaxy cluster, and should not be ignored, especiallyfor unrelaxed clusters."332Several near-infrared surveys (Muenchetal.2001:Oliveira and mid-infrared measurements (Comerónetal.2000:Persi2000;Testietal.2002;Natta2002:Apa2002) indicate the presence of disks around Brown Dwarfs (BDs).,"Several near-infrared surveys \citep{Muench01,Oliveira02,Liu03,Jayawardhana03} and mid-infrared measurements \citep{Comeron00,Persi00,Testi02,Natta02,Apai02} indicate the presence of disks around Brown Dwarfs (BDs)."333 In contrast to infrared emission. submillimeter and millimeter emission 15 certainly always optically thin and is an excellent measure for the total dust mass.," In contrast to infrared emission, submillimeter and millimeter emission is certainly always optically thin and is an excellent measure for the total dust mass."334 An early attempt to detect millimetre continuum emission also from very low-mass stars and suspected BDs was done by Andre&Montmerle(1994)., An early attempt to detect millimetre continuum emission also from very low-mass stars and suspected BDs was done by \citet{Andre94}.335. Probably the most sensitive observationof this kind was carried out by Carpenter(2002) using the OVRO interferometer. however at a relatively long wavelength.," Probably the most sensitive observationof this kind was carried out by \citet{Carpenter02} using the OVRO interferometer, however at a relatively long wavelength."336 We carried out the first successful search for dust continuum emission associated with confirmed BDs. using the bolometer arrays SCUBA at the JCMT and MAMBO at the IRAM 30-m telescope.," We carried out the first successful search for dust continuum emission associated with confirmed BDs, using the bolometer arrays SCUBA at the JCMT and MAMBO at the IRAM 30-m telescope."337 The survey led to the detection of cireumstellar dust around the two young BDs CFHT-BD-Tau 4 and 6613. which have ages below 10 Myrs.," The survey led to the detection of circumstellar dust around the two young BDs CFHT-BD-Tau 4 and 613, which have ages below 10 Myrs."338 In the case of field BDs we obtained upper mass limits of a few Moon masses of dust., In the case of field BDs we obtained upper mass limits of a few Moon masses of dust.339 For BDs in the Pleiades the mass limits are less strict and range 4+ and 7 Earth masses., For BDs in the Pleiades the mass limits are less strict and range 4 and 7 Earth masses.340 We should note that the data presented for CFHT-BD-Tau 4 together with other ground-based and ISO data allowed the first detailed discussion of a complete spectral energy distribution of a BD. ranging from optical to millimeter wavelengths (Pascuecietal.2003).," We should note that the data presented for CFHT-BD-Tau 4 together with other ground-based and ISO data allowed the first detailed discussion of a complete spectral energy distribution of a BD, ranging from optical to millimeter wavelengths \citep{Pascucci03}."341. The detection of these amounts of circumstellar material around two young BDs makes the formation of planets or even planetary systems around BDs a possibility., The detection of these amounts of circumstellar material around two young BDs makes the formation of planets or even planetary systems around BDs a possibility.342 Therefore. search strategies for planets should include BDs.," Therefore, search strategies for planets should include BDs."343 In the case of imaging surveys. they might even be the best targets.," In the case of imaging surveys, they might even be the best targets."344 In. addition. the detection of significant amount. of circumstellar dust carries important information about the formation processes of BDs.," In addition, the detection of significant amount of circumstellar dust carries important information about the formation processes of BDs."345 These detections. together with the discovery of quite a number of BD binaries (Bouyetal.2003:Burgasseretal. 2003).. do not support fragmentation of circumstellar disks as the general process for BD formation.," These detections, together with the discovery of quite a number of BD binaries \citep{Bouy03,Burgasser03}, do not support fragmentation of circumstellar disks as the general process for BD formation."346 Other formation scenarios for BDs (Bateetal.2003:Reipurth&Clarke2001:Watkinsetal.1998) include ejection from multiple systems and erosion of star-forming cloudlets by stellar winds and UV radiation from massive stars.," Other formation scenarios for BDs \citep{Bate03, Reipurth01,Watkins98}347 include ejection from multiple systems and erosion of star-forming cloudlets by stellar winds and UV radiation from massive stars."348 Disks will certainly have different structures depending on the formation mechanism., Disks will certainly have different structures depending on the formation mechanism.349 However. statistics 1s still poor and information about the disk structure from. interferometric observations are needed before one can put more definite observational constraints on BD formation scenarios.," However, statistics is still poor and information about the disk structure from interferometric observations are needed before one can put more definite observational constraints on BD formation scenarios."350 To search for circumstellar material around BDs. we selected relatively young BDs with an age of a few Myrs because these objects should have the highest probability to be associated with disk material.," To search for circumstellar material around BDs, we selected relatively young BDs with an age of a few Myrs because these objects should have the highest probability to be associated with disk material."351 The nine selected objects are located in Taurus. the & Orionis cluster. IC 348. and the Upper Scorpius OB association (Martínetal.2001:BéjarNajitaetal.2000:Luhman1999;Ardila 2000).," The nine selected objects are located in Taurus, the $\sigma$ Orionis cluster, IC 348, and the Upper Scorpius OB association \citep{Martin01,Bejar01,Najita00,Luhman99,Ardila00}."352. For the first three regions. additional selection criteria were the previous detection of Ha emission (Martínetal.2001).. the presence of X-ray emission (Mokler&Stelzer2002;PreibischZin-necker 2001). and the requirement that the objects should be as isolated as possible in order to avoid confusion during the observations with single-dish telescopes.," For the first three regions, additional selection criteria were the previous detection of $\alpha$ emission \citep{Martin01}, the presence of X-ray emission \citep{Mokler02,Preibisch01}, and the requirement that the objects should be as isolated as possible in order to avoid confusion during the observations with single-dish telescopes."353 The three BDs in the Taurus star-forming region are among the youngest BDs of our target list., The three BDs in the Taurus star-forming region are among the youngest BDs of our target list.354 They have ages of about MMyr (Martínetal. 2001).., They have ages of about Myr \citep{Martin01}. .355 The object CFHT-BD-Tau 4 shows the highest Ha emissionamong the Taurus BDs (Martín 2001).. emits X-ray radiation (Mokler&Stelzer2002) and shows mid-infrared excess emission (Pascuecietal. 2003)..," The object CFHT-BD-Tau 4 shows the highest $\alpha$ emissionamong the Taurus BDs \citep{Martin01}, , emits X-ray radiation \citep{Mokler02} and shows mid-infrared excess emission \citep{Pascucci03}. ."356small effect of seeing on the spectrophotomoetry should. not significantly: allect our estimates of the CALR evolution as it does not appear to increase with redshift. or to fainter luxes.,"small effect of seeing on the spectrophotometry should not significantly affect our estimates of the CMR evolution as it does not appear to increase with redshift, or to fainter fluxes."357 Llowever. Figures 1 and 2) also show that the mean GapeeGrab increases with redshift. as does the scatter in his quantity.," However, Figures \ref{sf-z} and \ref{sf-seeing} also show that the mean $g_{spec}-g_{fib}$ increases with redshift, as does the scatter in this quantity."358 This is not related to seeing but might be oe a separate problem with the SDSS spectrophotometry., This is not related to seeing but might be be a separate problem with the SDSS spectrophotometry.359 Further investigation of the gasgrip Olset found. it was correlated with the spectral type classification xvameter. being much greater lor redder galaxies with more negative (ligure 3)).," Further investigation of the $g_{spec}-g_{fib}$ offset found it was correlated with the spectral type classification parameter, being much greater for redder galaxies with more negative (Figure \ref{sf-eclass}) )."360 Note the I2/850 sample all have eclass<0 with a mean of -0.1275., Note the E/S0 sample all have $\rm eclass\leq 0$ with a mean of -0.1275.361 In the red-band the mean FaeePip is also correlated witheclass. although the elfect is smaller and does not increase strongly with redshift.," In the red-band the mean $r_{spec}-r_{fib}$ is also correlated with, although the effect is smaller and does not increase strongly with redshift."362" The dependence on is obviously non-linear and might be better described as eclass"".", The dependence on is obviously non-linear and might be better described as $^2$.363 To understand why gi; might be alfected byeclass. especially at higher redshifts. we examine the spectra. of four representative [2/50 galaxies of dillerenteclass. all at 2om0.25.," To understand why $g_{spec}$ might be affected by, especially at higher redshifts, we examine the spectra of four representative E/S0 galaxies of different, all at $z>0.25$."364 Figure 4. illustrates that a more negative eclass is associated with a lower lux in the rest-frame UV. which at these redshifts is observed in the g-band.," Figure \ref{z0.3spec} illustrates that a more negative eclass is associated with a lower flux in the rest-frame UV, which at these redshifts is observed in the $g$ -band."365 The spectra are particularly noisy at the blue end of the observed: g-band. near 4000A.," The spectra are particularly noisy at the blue end of the observed $g$ -band, near $4000\rm \AA$."366" Flux variations [rom noise at the blue end of the spectrum. would. produce correlated. variations in gio, andeclass.", Flux variations from noise at the blue end of the spectrum would produce correlated variations in $g_{spec}$ and.367 Bul the trend in (gap—drio? With redshift implies that this scatter is not symmetric. but skewed.," But the trend in $\langle g_{spec}-g_{fib}\rangle $ with redshift implies that this scatter is not symmetric, but skewed."368 As a result. [or spectra with very low signal/noise at these wavelengths. the integrated. «ων Hux is. on average. underestimated. by a few times 0.01 mags.," As a result, for spectra with very low signal/noise at these wavelengths, the integrated $g_{spec}$ flux is, on average, underestimated by a few times 0.01 mags."369 Although the reason for this discrepancy in the SDSS spectrophotometry is not known. we can try to correct. for it as follows.," Although the reason for this discrepancy in the SDSS spectrophotometry is not known, we can try to correct for it as follows."370" We begin by assuming that the olfset between the spectra-cerivecd and. fiber magnitude is not. directly sensitive to redshift or wavelength. but depends only (i) the signal/noise in the spectrum. averaged: across the (ii) the tilt of the spectrum across the band. represented bv eclass. (11) à cross-term (eclass"" signal/noise)"," We begin by assuming that the offset between the spectra-derived and fiber magnitude is not directly sensitive to redshift or wavelength, but depends only (i) the signal/noise in the spectrum, averaged across the (ii) the tilt of the spectrum across the band, represented by $^2$ (iii) a cross-term $^2\times$ signal/noise)."371bias toward a negative flux.,bias toward a negative flux.372 There are (wo reasons for the larger error in the measured. growth rate for this run: 1) the equilibrium: velocity gives rise to mumerical diffusion due to the motion of the Πα variables with respect to the grid: and 2) since the erowing modes are being advected in the azimuthal direction. the maximum growth does not occur at the grid scale.," There are two reasons for the larger error in the measured growth rate for this run: 1) the equilibrium velocity gives rise to numerical diffusion due to the motion of the fluid variables with respect to the grid; and 2) since the growing modes are being advected in the azimuthal direction, the maximum growth does not occur at the grid scale."373 The latter effect can be seen in Figure 8:5 several grid cells are required [or a well-resolved wavelength., The latter effect can be seen in Figure \ref{f8}; several grid cells are required for a well-resolved wavelength.374" In order to resolve smaller wavelengths. we have repeated (his run with £,=6. 3 and 1.5."," In order to resolve smaller wavelengths, we have repeated this run with $L_y = 6$ , $3$ and $1.5$."375" The results are plotted in Figure 7 alongwith the results [rom the £,=12 run.", The results are plotted in Figure \ref{f7} alongwith the results from the $L_y = 12$ run.376" The measured erowth rate lor the £,=1.5 run is 0.0024.", The measured growth rate for the $L_y = 1.5$ run is $0.0924$.377 To quantify the ellects of numerical diffusion. we have performed a series of tests similar to Run 2 (external potential in a rotating ΠΙΟ) bul with an overall boost in the azimuthal direction.," To quantify the effects of numerical diffusion, we have performed a series of tests similar to Run 2 (external potential in a rotating frame) but with an overall boost in the azimuthal direction."378 Figure I0. shows measured growth rates as a function of boost al three different nunmerical resolutions., Figure \ref{f10} shows measured growth rates as a function of boost at three different numerical resolutions.379 The largest boost magnitude in (his plot corresponds to the velocity at the mininium in V2 for a run with q=1.5., The largest boost magnitude in this plot corresponds to the velocity at the minimum in $N_x^2$ for a run with $q = 1.5$.380 This highlights the importance of the fluid velocity. wilh respect to the grid in determining numerical camping in ZEUS., This highlights the importance of the fluid velocity with respect to the grid in determining numerical damping in ZEUS.381 To investigate the effect of differential rotation upon the growth of Chis instability. we have performed a series of simulations with nonzero q.," To investigate the effect of differential rotation upon the growth of this instability, we have performed a series of simulations with nonzero $q$."382 Intuitively. one expects the instability to be suppressed when the shear rate is greater than the growth rate. iie. for Ri2—1.," Intuitively, one expects the instability to be suppressed when the shear rate is greater than the growth rate, i.e. for ${\rm Ri} \gtrsim -1$."383 Figure 11. shows growth rates from a series of runs with Α΄ranin>=—0.01 and small. nonzero values of q al three numerical resolutions.," Figure \ref{f11} shows growth rates from a series of runs with $N_{x,min}^2384= -0.01$ and small, nonzero values of $q$ at three numerical resolutions."385 This ligure clearly demonstrates our main result: convective instability is suppressed bv dillerential rotation., This figure clearly demonstrates our main result: convective instability is suppressed by differential rotation.386 The expected growth rate from linear theory (/LN2] ab q= 0) is shown in Figure Ll as a dotted line., The expected growth rate from linear theory $\sqrt{|N_x^2|}$ at $\qe = 0$ ) is shown in Figure \ref{f11} as a dotted line.387 If there is a racial position where g(r)=0 (ie. Ri= —2€). ve at that position looks similar (ο (hat of the previous runs (very little deviationfrom a straight line): these measurements are indicated on the plot with solid points.," If there is a radial position where $\qe(x) = 0$ (i.e., ${\rm Ri} = -\infty$ ), $v_t$ at that position looks similar to that of the previous runs (very little deviationfrom a straight line); these measurements are indicated on the plot with solid points."388 For q20.055 there is no longer any point where g(r)=0: in that case vj was measured at the radial average between the minimum in .V26r) and (he minimuni in g(r). since (his is where the maximum growth occured.," For $q \gtrsim 0.055$ there is no longer any point where $\qe(x) = 0$; in that case $v_t$ was measured at the radial average between the minimum in $N_x^2(x)$ and the minimum in $\qe(x)$, since this is where the maximum growth occured."389 The data for these nmeasurenienis. which are indicated in Fieure 11 with open points. is not as clean as it is for the runs with Ri=—o (see Figure 12)).," The data for these measurements, which are indicated in Figure \ref{f11} with open points, is not as clean as it is for the runs with ${\rm Ri} = -\infty$ (see Figure \ref{f12}) )."390 All of the growth rate measurements in Figure were obtained by a least-squares fit of the data in the range |xLO?<e/6;«€1xLO”., All of the growth rate measurements in Figure \ref{f11} were obtained by a least-squares fit of the data in the range $1 \times 10^{-9} < v_t/\bar{c}_s < 1 \times 10^{-5}$.391" The dashed line in Figure 11. indicates the value of q lor which Ri,,;,,= —1.", The dashed line in Figure \ref{f11} indicates the value of $q$ for which ${\rm Ri}_{min} = -1$ .392 some of the growth in Figure 11. appears to be due (o aliasing., Some of the growth in Figure \ref{f11} appears to be due to aliasing.393 This is a numerical effect, This is a numerical effect394"summarised in Figure 3, which compares the behaviour of InB(—1,0) with that of the DETF FoM. The mostly monotonic relation we see between the DETF and the nested InB(—1,0) FoMs means that a DETF optimized survey will be extremely similar to one optimized with InB(—1,0).","summarised in Figure \ref{fig:NST_DETF2}, which compares the behaviour of $\ln B(-1,0)$ with that of the DETF FoM. The mostly monotonic relation we see between the DETF and the nested $\ln B(-1,0)$ FoMs means that a DETF optimized survey will be extremely similar to one optimized with $\ln B(-1,0)$."395" However the latter FoM provides an absolute scale; in this case InB(—1,0) shows the survey is capable of strongly preferring ACDM when the DETF FoM for the equivalent survey configuration is still around of its optimum."," However the latter FoM provides an absolute scale; in this case $\ln B(-1,0)$ shows the survey is capable of strongly preferring $\Lambda\rm CDM$ when the DETF FoM for the equivalent survey configuration is still around of its optimum."396 This additional information would be invaluable when deciding on a survey's operating mode., This additional information would be invaluable when deciding on a survey's operating mode.397" By deploying the SDDR Gaussian approximation it is possible to perform full MCMC optimizations with InB(—1,0)."," By deploying the SDDR Gaussian approximation it is possible to perform full MCMC optimizations with $\ln B(-1,0)$."398" However, being an approximation it is necessary to establish the impact of this simplification on the resulting Bayes factors."," However, being an approximation it is necessary to establish the impact of this simplification on the resulting Bayes factors."399 Figure 4 compares the Gaussian SDDR calculations with the more accurate nested sampling ones in the case where the upper redshift limit Zmax 15 varied., Figure \ref{fig:zmax_SDnest} compares the Gaussian SDDR calculations with the more accurate nested sampling ones in the case where the upper redshift limit $z_{\rm max}$ is varied.400" We can see that the SDDR InB(-1,0) typically underestimates the Bayes factor"," We can see that the SDDR $\ln B(-1,0)$ typically underestimates the Bayes factor."401" While the assumption of Gaussianity has been seen to be good around the peak of the likelihood (Mukherjeeetal.2006a),, it appears to be less accurate around the tails."," While the assumption of Gaussianity has been seen to be good around the peak of the likelihood \cite{muk2006}, it appears to be less accurate around the tails."402" If the information in the tails is overestimated by this assumption, iif in reality the likelihood falls off more sharply than in the Gaussian approximation, then the average likelihood and therefore evidence for the evolving dark energy model will be overestimated."," If the information in the tails is overestimated by this assumption, if in reality the likelihood falls off more sharply than in the Gaussian approximation, then the average likelihood and therefore evidence for the evolving dark energy model will be overestimated."403 This will result in the underestimation of the Bayes factor we see here., This will result in the underestimation of the Bayes factor we see here.404" It would also explain the increased scatter away from the monotonic relation between the nested InB(—1,0) and the DETF FoM for stronger surveys, clearly seen in Figure 3.."," It would also explain the increased scatter away from the monotonic relation between the nested $\ln B(-1,0)$ and the DETF FoM for stronger surveys, clearly seen in Figure \ref{fig:NST_DETF2}."405" More accurate surveys will have tighter likelihood peaks, and therefore any non-Gaussianity of the tails would be more influential."," More accurate surveys will have tighter likelihood peaks, and therefore any non-Gaussianity of the tails would be more influential."406" Despite this, the general trend is the same, best seen by making a logarithmic plot of the DETF FoM against nested calculations of B, and writing equation 9 for the Gaussian SDDRcalculation of B in terms of the DETF FoM: Figure 5 shows how the nested calculation of InB(—1,0) follows this linear relation well, despite the increased deviations around the highest values."," Despite this, the general trend is the same, best seen by making a logarithmic plot of the DETF FoM against nested calculations of $B$, and writing equation \ref{eq:SDDR2} for the Gaussian SDDRcalculation of $B$ in terms of the DETF FoM: Figure \ref{fig:NST_DETF1} shows how the nested calculation of $\ln407B(-1,0)$ follows this linear relation well, despite the increased deviations around the highest values."408" This implementation of SDDR presents a good alternative to the nested sampling approach, and furthermore it is as quick as the DETF optimization with only a few extra calculations required."," This implementation of SDDR presents a good alternative to the nested sampling approach, and furthermore it is as quick as the DETF optimization with only a few extra calculations required."409" Its underestimation of the Bayes factor is also seen to be almost uniform across the redshift range of Figure 4,, and we therefore infer that it would be simple to calibrate the SDDR FoM to gain more accurate estimates of InB by performing a few nested sampling computations of In B."," Its underestimation of the Bayes factor is also seen to be almost uniform across the redshift range of Figure \ref{fig:zmax_SDnest}, and we therefore infer that it would be simple to calibrate the SDDR FoM to gain more accurate estimates of $\ln B$ by performing a few nested sampling computations of $\ln B$ ."410 The Gaussian SDDR approximation also allows investigation of the, The Gaussian SDDR approximation also allows investigation of the411consistent with classical interstellar dist and grain size estimates in the NLRs of NGC LOGS and Cve A. Thus to first order. assuming that the luminosity in 44151 is anisotropic. the extended micl-IR emission is consistent with heating of dust in the NLR from a central engine.,"consistent with classical interstellar dust and grain size estimates in the NLRs of NGC 1068 and Cyg A. Thus to first order, assuming that the luminosity in 4151 is anisotropic, the extended mid-IR emission is consistent with heating of dust in the NLR from a central engine."412 Another source of mid-IR emission in NGC! 4151 may be from a dusty torus (IRE96)., Another source of mid-IR emission in NGC 4151 may be from a dusty torus (RE96).413 Emission from a dustwv torus may dominate the unresolved. mid-IR. component in 44151., Emission from a dusty torus may dominate the unresolved mid-IR component in 4151.414 It is considered that we view this disk/torus through a line-ol-sight passing near the boundary. edge (Cassidy Raine 1996)., It is considered that we view this disk/torus through a line-of-sight passing near the boundary edge (Cassidy Raine 1996).415 Assuming the torus lies perpendicular to the NLR. its major axis would be oriented in an approximately north-south direction.," Assuming the torus lies perpendicular to the NLR, it's major axis would be oriented in an approximately north-south direction."416 We see no extended emission in Chis direction and can only place an upper limit on the mid-IR. size of the torus of 535 pe based on our resolution limit of ~0753 - 0758., We see no extended emission in this direction and can only place an upper limit on the mid-IR size of the torus of $\lesssim 35$ pc based on our resolution limit of $\thicksim 0\farcs53$ - $0\farcs58$.417 This is consistent with je polarinelry observations and subsequent modelling of Ruiz et al. (, This is consistent with the polarimetry observations and subsequent modelling of Ruiz et al. (4182002) which suggest that the torus size in NGC 4151 is & 30 pe.,2002) which suggest that the torus size in NGC 4151 is $\thickapprox $ 30 pc.419 A direct measurement of the torus may. have been made by N90., A direct measurement of the torus may have been made by N90.420 As previously mentioned. north-south scans by N90 measure (he 11.2 jan emitting region to be 0110-0001 or ~10 pe.," As previously mentioned, north-south scans by N90 measure the 11.2 $\micron$ emitting region to be $\pm 0$ 04 or $\thicksim 10$ pc."421" Based on our ""unresolved"" (PSF) component we therefore place an upper limit on the mid-IR contribution of a dusty torus of <73% of 1e Lotal emission at 10.8 jan and 18.2 jan.", Based on our “unresolved” (PSF) component we therefore place an upper limit on the mid-IR contribution of a dusty torus of $\lesssim 73\%$ of the total emission at 10.8 $\micron$ and 18.2 $\micron$.422 This represents the maximum contribution [rom a dusty torus and does not rule out contribution to the “unresolved mid-IB. emission from a sell-absorbed svnchrotron source., This represents the maximum contribution from a dusty torus and does not rule out contribution to the “unresolved ”mid-IR emission from a self-absorbed synchrotron source.423 Observations of neutral HE and molecular Hà» by Mundell et al. (, Observations of neutral HI and molecular $_{2}$ by Mundell et al. (4241995) ancl Fernandez et al. (,1995) and Fernandez et al. (4251999) respectively. show evidence of a gaseous disk up to 2755 (160 pe) across which may be associated with the torus.,"1999) respectively, show evidence of a gaseous disk up to 5 (160 pc) across which may be associated with the torus."426" This disk is located in approximately a north-south direction and may consist of an ""onion-skin morphology as discussed by Pedlar et al. (", This disk is located in approximately a north-south direction and may consist of an “onion-skin” morphology as discussed by Pedlar et al. (4271998).,1998).428 In this model the gaseous torus contains several lavers (see Figure 5)., In this model the gaseous torus contains several layers (see Figure 5).429 The innermost ring consists ol ionized gas followed bv a ring of neutral HII gas surrounded. by a ring of molecular IH»., The innermost ring consists of ionized gas followed by a ring of neutral HI gas surrounded by a ring of molecular $_{2}$.430" In Pedlars ""onion-skin model the authors further expand on (he subject of anisotropy in NGC! 4151 as discussed by Penston οἱ al. (", In Pedlar's “onion-skin” model the authors further expand on the subject of anisotropy in NGC 4151 as discussed by Penston et al. (4311990).,1990).432 Using observations of Iree-Iree absorption detected al 73 em and 18 em in conjunction with observations of HI by Mundell et al. (, Using observations of free-free absorption detected at 73 cm and 18 cm in conjunction with observations of HI by Mundell et al. (4331995) they estimate the ionizing flux incident on the torus.,1995) they estimate the ionizing flux incident on the torus.434 Assuming a simple Strómmgren model they calculate that the ionizing flux in the plane of the torus is between 210 - 40 times less (han seen from Earth or ~ 100 - 500 times less than seen in the NLR as modelled by Penston et al. (, Assuming a simple Strömmgren model they calculate that the ionizing flux in the plane of the torus is between $\thicksim $ 10 - 40 times less than seen from Earth or $\thicksim $ 100 - 500 times less than seen in the NLR as modelled by Penston et al. (4351990).,1990).436 To test the validity of this model we can use the dust equilibrium equation from Section, To test the validity of this model we can use the dust equilibrium equation from Section437the models of the ONC presented in the first column of Figure 2 all fail to match the Pleiacles. even with this overestimatect loss rate. the couclusion that stellar winds alone canuot explain the observed rotation rates is streuetlenect.,"the models of the ONC presented in the first column of Figure 2 all fail to match the Pleiades, even with this overestimated loss rate, the conclusion that stellar winds alone cannot explain the observed rotation rates is strengthened."438 If the additional loss mechanism is disk locking. it is also difficult to reconcile the observatious if the disk Lifetimes are always less than 3 Myr or can be greater than & Myr.," If the additional loss mechanism is disk locking, it is also difficult to reconcile the observations if the disk lifetimes are always less than 3 Myr or can be greater than 8 Myr."439 The intersection of he constraiuts made by the ONC and Pleiades inodels give us the parameters of δια. aud Tra»=6 Myr for ow prelerrecl model., The intersection of the constraints made by the ONC and Pleiades models give us the parameters of $= 5.4 \omega_\odot$ and $\tau_{max} = 6$ Myr for our preferred model.440 This model. however. is not a unique solution to the ooblem.," This model, however, is not a unique solution to the problem."441 For example. the column of moclels in Figure 2 where τι = 3 Myr for all stars could ιοί be excluded by IWS test at our defined limits.," For example, the column of models in Figure 2 where $\tau_{disk}$ = 3 Myr for all stars could not be excluded by K-S test at our defined limits."442 It is strictly au observational coustraint on 77544 rom IR data that this mocel is cousidered invalid., It is strictly an observational constraint on $\tau_{disk}$ from IR data that this model is considered invalid.443" Diflerent clistributious with other f[unctioual forms of f(rgj,,) OF Ta». combined with different initial conditious such as those presented in 8113. cau be coustructed to compare-— to the data as well."," Different distributions with other functional forms of $f(\tau_{disk})$ or $\tau_{max}$, combined with different initial conditions such as those presented in 4.3, can be constructed to compare to the data as well."444 Further constraiuts ou disk lifetimes and the initial. period distribution can ouly be mace hrough larger statistical samples., Further constraints on disk lifetimes and the initial period distribution can only be made through larger statistical samples.445 The number ONC stars with photometric periods will soon be increased by ~ LOO (Herbst et al., The number ONC stars with photometric periods will soon be increased by $\sim$ 400 (Herbst et al.446 2001)., 2001).447 With this expanded data set. tests like those in 833.1 will jecome a powerful tool tu coustraining augular momentum loss through clisk-lockine.," With this expanded data set, tests like those in 3.4 will become a powerful tool in constraining angular momentum loss through disk-locking."448 One of the reasons for the recent controversy over the observations of the ONC. namely the yunodal period distribution. is uot evideut in the sub3.et of the HRHC cata used in this paper.," One of the reasons for the recent controversy over the observations of the ONC, namely the bimodal period distribution, is not evident in the subset of the HRHC data used in this paper."449 As shown in Figuree 7. the ONC periods used were consistent with the Gaussian birthline model sresentect in 833.[.," As shown in Figure 7, the ONC periods used were consistent with the Gaussian birthline model presented in 3.4."450 At our defiued levels of acceptance. the IX-5 test does not rule out the bypothesis hat the observational distribution was drawn from a uniform distribution as well.," At our defined levels of acceptance, the K-S test does not rule out the hypothesis that the observational distribution was drawn from a uniform distribution as well."451 Our preferred model does not predict that a bimod: distribution would be apparent at 1. Myr or this rauge of masses., Our preferred model does not predict that a bimodal distribution would be apparent at 1 Myr for this range of masses.452 The results reported iu Herbst et al. (, The results reported in Herbst et al. (4532001) shows that the mean period OL stars iu the ONC is mass dependent.,2001) shows that the mean period of stars in the ONC is mass dependent.454 The bunodal period distribution could then be an effect of slotting a wide range of masses in one histogram., The bimodal period distribution could then be an effect of plotting a wide range of masses in one histogram.455 The high mass stars have clillerent evolutionary lune scales. internal angular momeuturm trausport. aud possibly different. clisk-locking lifetimes or initial conditions.," The high mass stars have different evolutionary time scales, internal angular momentum transport, and possibly different disk-locking lifetimes or initial conditions."456 The aloremenutioued increase in the ONC period sample would allow smaller anges of mass to be grouped together in order to test these effects., The aforementioned increase in the ONC period sample would allow smaller ranges of mass to be grouped together in order to test these effects.457 Qur model does predict that the rotation rates of a cluster in the later stages of the distribution ol disk Lifetimes. such as NGC 2261 and NGC 2362 (3.2 and 5.0 Myr respectively). would slow a Xmocality caused by tle spin-up of stars released [rom their disks.," Our model does predict that the rotation rates of a cluster in the later stages of the distribution of disk lifetimes, such as NGC 2264 and NGC 2362 (3.2 and 5.0 Myr respectively), would show a bimodality caused by the spin-up of stars released from their disks."458 Photometric period observations of clusters such as these would be key to further constraints on cisk-locking lifetimes., Photometric period observations of clusters such as these would be key to further constraints on disk-locking lifetimes.459 Another important test would be to incorporate observations of a cluster just beyoud the observed inaximum disk lifetime., Another important test would be to incorporate observations of a cluster just beyond the observed maximum disk lifetime.460" Rotational measurements of stars at this age would coustrain Tas, by comparing uodels of vouuger clusters using the methoc presented here.", Rotational measurements of stars at this age would constrain $\tau_{disk}$ by comparing models of younger clusters using the method presented here.461 Observations at this age would place rther constraints on loss rates from stellar winds since this mechanisin would Lave to account for t| the angular momentum loss from that point to the Pleiades aud Hyades., Observations at this age would place further constraints on loss rates from stellar winds since this mechanism would have to account for all the angular momentum loss from that point to the Pleiades and Hyades.462with two images.,with two images.463 The spectral reduction was performed using the standard tools fromIRAF: zero level exposure. flat-fielding.- cosmic ray removal. aperture selection and sky subtraction using the package.," The spectral reduction was performed using the standard tools from: zero level exposure, flat-fielding, cosmic ray removal, aperture selection and sky subtraction using the package."464 For wavelength calibration. we have used He-Ne-Ar lamp exposures observed at the end of the corresponding night.," For wavelength calibration, we have used He-Ne-Ar lamp exposures observed at the end of the corresponding night."465 The wavelength calibration was performed with a Chebyshev polynomial of 3rd degree and the residuals were kept inside +1.0 wwith an rms scatter ~0.3—0.5Á., The wavelength calibration was performed with a Chebyshev polynomial of 3rd degree and the residuals were kept inside $\pm1.0$ with an rms scatter $\sim 0.3-0.5$.466 A standard star was observed in the beginning and at the end of each night with the same instrumental configuration in order to remove the instrumental response and therefore to transform the spectra to relative flux units., A standard star was observed in the beginning and at the end of each night with the same instrumental configuration in order to remove the instrumental response and therefore to transform the spectra to relative flux units.467 The sky subtracted. wavelength and flux calibrated spectra were used to derive the redshifts.," The sky subtracted, wavelength and flux calibrated spectra were used to derive the redshifts."468 First we obtained a redshift estimate based on the Call H+K doublet. when present. and then we used the cross-correlation technique as implemented in the package (Kurtz Mink 1998)) using an elliptical galaxy template spectrum (Kinney et al. 1996)).," First we obtained a redshift estimate based on the CaII H+K doublet, when present, and then we used the cross-correlation technique as implemented in the package (Kurtz Mink \cite{rvsao}) ) using an elliptical galaxy template spectrum (Kinney et al. \cite{kin}) )."469 To improve the cross-correlation signal. we have masked the wavelength ranges of the strongest sky lines. where residuals from the sky subtraction could occur. and also the region of a strong atmospheric absorption at 7750-7800A.," To improve the cross-correlation signal, we have masked the wavelength ranges of the strongest sky lines, where residuals from the sky subtraction could occur, and also the region of a strong atmospheric absorption at 7750-7800."470. The redshift distributions in each fieldare shown in Fig. 1.., The redshift distributions in each fieldare shown in Fig. \ref{fig:redshifts}.471 To illustrate the redshift space overdensities we have applied ar adaptive kernel smoothing over the redshifts (e.g. Silvermai 1986.. Pisani 1993)).," To illustrate the redshift space overdensities we have applied an adaptive kernel smoothing over the redshifts (e.g. Silverman \cite{sil86}, Pisani \cite{pis93}) )."472 There ts both a clear redshift grouping and a spatial grouping associated with the X-ray emission Ἡ001. aand003.," There is both a clear redshift grouping and a spatial grouping associated with the X-ray emission in, and."473. For these three cases only we show zoomed in an inset a redshift histogram of the overdensity with a fixed bin size., For these three cases only we show zoomed in an inset a redshift histogram of the overdensity with a fixed bin size.474 The derived mean redshift and the velocity dispersion. by means of bi-weighted estimators of location and. scale (Beers et al. 1990)).," The derived mean redshift and the velocity dispersion, by means of bi-weighted estimators of location and scale (Beers et al. \cite{rostat}) ),"475 are shown in Table 2:: the quoted errors are Io bias-accelerated bootstrap errors (Efron Tibshirani 1986))., are shown in Table \ref{tab:spec}; the quoted errors are $1\sigma$ bias-accelerated bootstrap errors (Efron Tibshirani \cite{efr86}) ).476 For aand005.. the peaks in the redshift distribution over the whole FORS field do not correspond to any significant spatial clustering. and no peak can be unambiguously associated with the extended X-ray source.," For and, the peaks in the redshift distribution over the whole FORS field do not correspond to any significant spatial clustering, and no peak can be unambiguously associated with the extended X-ray source."477 Nevertheless. we show in Table 2 the most plausible redshift based on measurements of galaxies spatially coincident with the cluster X-ray emission (see Figs.," Nevertheless, we show in Table \ref{tab:spec}478 the most plausible redshift based on measurements of galaxies spatially coincident with the cluster X-ray emission (see Figs."479 and 8))., \ref{fig:clsd:image} and \ref{fig:clse:image}) ).480 Deriving detailed cluster physical characteristics from the X-ray observations is not the main objective of XMM-LSS., Deriving detailed cluster physical characteristics from the X-ray observations is not the main objective of XMM-LSS.481 Indeed. with exposure times of the order of 10 ks only a small fraction of clusters are expected to have enough photon statisties to allow reliable measurements of the mean temperature. or to distinguish. possible AGN contamination.," Indeed, with exposure times of the order of 10 ks only a small fraction of clusters are expected to have enough photon statistics to allow reliable measurements of the mean temperature, or to distinguish possible AGN contamination."482 Nevertheless. we have derived the temperature and luminosity for the clusters pertaining to this paper and. in some cases. these parameters were well constrained.," Nevertheless, we have derived the temperature and luminosity for the clusters pertaining to this paper and, in some cases, these parameters were well constrained."483 These results however must be taken with caution as in some cases possible AGN contamination cannot be ruled out., These results however must be taken with caution as in some cases possible AGN contamination cannot be ruled out.484 For each cluster an X-ray spectrum was extracted from a region large enough to include the cluster emission., For each cluster an X-ray spectrum was extracted from a region large enough to include the cluster emission.485 A background spectrum was taken from an adjacent annulus., A background spectrum was taken from an adjacent annulus.486 We removed in advance the contribution of all other sources within the cluster and background regions., We removed in advance the contribution of all other sources within the cluster and background regions.487 A photon redistribution matrix (RMF) and ancillary region file (ARF) were created usingXMMSAS:rmfgen/arfgen. including corrections for bad pixels and detector geometry.," A photon redistribution matrix (RMF) and ancillary region file (ARF) were created using, including corrections for bad pixels and detector geometry."488 Finally the spectra from the three instruments MOSI. MOS2 and PN were regrouped to have at least 25 counts per bin.," Finally the spectra from the three instruments MOS1, MOS2 and PN were regrouped to have at least 25 counts per bin."489 The extracted spectra were used to derive the observed characteristics shown in Table 5 without any recourse to a reference model., The extracted spectra were used to derive the observed characteristics shown in Table \ref{tab:x1} without any recourse to a reference model.490 To get the global cluster X-ray characteristics. the binned spectra in each instrument were fitted to a model of thermal plasma emission with photo-electrie absorption using (Arnaud 1996.. also see the for the model andcorresponding references).," To get the global cluster X-ray characteristics, the binned spectra in each instrument were fitted to a model of thermal plasma emission with photo-electric absorption using (Arnaud \cite{xspec}, also see the for the model andcorresponding references)."491 The energy range used in the fit is [0.3—10] keV for MOS instruments. but for PN we used [0.3—7.5] keV in order to avoid an instrumental emission feature at 8—9 keV. We have kept only two free parameters in the fitting: the temperature and the normalisation.," The energy range used in the fit is $[0.3-10]$ keV for MOS instruments, but for PN we used $[0.3-7.5]$ keV in order to avoid an instrumental emission feature at $8-9$ keV. We have kept only two free parameters in the fitting: the temperature and the normalisation."492" The mean Galactic absorption of Ny=2.5x10°"" em? (Dickey Lockman 1990)) the metal abundance of Z=0.270 and the redshift were fixed."," The mean Galactic absorption of $N_H=2.5\times 10^{20}$ $^{-2}$ (Dickey Lockman \cite{nh}) ), the metal abundance of $Z=0.3Z_{\sun}$ and the redshift were fixed."493 For parameter estimation. we used the Cash statistic. modified to allow background subtraction (see the manual).," For parameter estimation, we used the Cash statistic, modified to allow background subtraction (see the manual)."494 The results are shown in Table 4.., The results are shown in Table \ref{tab:x2}. .495 The errors on the temperature are lo. the errors for the flux Fy and the luminosity Ly were calculated varying the normalisation parameter in its lo ," The errors on the temperature are $1\sigma$ , the errors for the flux $F_X$ and the luminosity $L_X$ were calculated varying the normalisation parameter in its $1\sigma$ "496USA Since the description of the Hubble sequence (e.g. Hubble 1926:: deVaucouleurs1959: Sandage&Tam-mann 1981) we have learned that position along. the Hubble sequence correlates with parameters like color. stellar age. and gas fraction. (e.g.. Roberts&Haynes 1994))," Since the description of the Hubble sequence (e.g., \citealt{hub26}; ; \citealt{vau59}; \citealt{san81}) ) we have learned that position along the Hubble sequence correlates with parameters like color, stellar age, and gas fraction (e.g., \citealt{rob94}) )."497 However. morphologies by themselves provide very limited information. as they are scale free and do not include physical parameters such as surface brightnesses. sizes. luminosities and masses.," However, morphologies by themselves provide very limited information, as they are scale free and do not include physical parameters such as surface brightnesses, sizes, luminosities and masses."498 Using the Sloan Digital Sky Survey (SDSS. Yorketal. 2000)). Kauffmannetal.(2003) showed that the main parameter driving galaxy properties 15 stellar mass.," Using the Sloan Digital Sky Survey (SDSS, \citealt{yor00}) ), \cite{kau03} showed that the main parameter driving galaxy properties is stellar mass."499 High mass galaxies are generally red. have old stellar populations and low specific star formation rates (SSERs). while low mass galaxies are generally blue. have young stellar populations and high SSERs.," High mass galaxies are generally red, have old stellar populations and low specific star formation rates (SSFRs), while low mass galaxies are generally blue, have young stellar populations and high SSFRs."500 A key question is what the structure was of the progenitors of low redshift galaxies., A key question is what the structure was of the progenitors of low redshift galaxies.501 Hubble Space Telescope studies out to redshift z~| indicate that the morphological variation ts comparable to that at low redshift (e.g.. Belletal. 2004))," Hubble Space Telescope studies out to redshift $z\sim 1$ indicate that the morphological variation is comparable to that at low redshift (e.g., \citealt{bel04}) )."502 More recent studies of72 galaxies using the HST NICMOS camera have yielded varyingz results. largely due to different selection criteria.," More recent studies of $z > 2$ galaxies using the HST NICMOS camera have yielded varying results, largely due to different selection criteria."503 For example. Papovichetal.(2005) studied the rest-frame optical morphologies of a flux-limited sample of galaxies at zzc2.3 and found that they are generally irregular. Toftetal.(2005).," For example, \cite{pap05} studied the rest-frame optical morphologies of a flux-limited sample of galaxies at $z \approx 2.3$ and found that they are generally irregular. \cite{tof05},"504. on the other hand. investigated the rest-frame optical and UV morphologies of distant red galaxies (DRGs) in the Hubble Ultra Deep Field (HUDF). and found both galaxies with irregular morphologies and galaxies with smooth morphologies.," on the other hand, investigated the rest-frame optical and UV morphologies of distant red galaxies (DRGs) in the Hubble Ultra Deep Field (HUDF), and found both galaxies with irregular morphologies and galaxies with smooth morphologies."505 Additionally. they showed that the rest-frame optical morphologies of these galaxies are much more regular and centrally concentrated than the rest-frame UV morphologies.," Additionally, they showed that the rest-frame optical morphologies of these galaxies are much more regular and centrally concentrated than the rest-frame UV morphologies."506 With the advent of the Wide Field Camera 3 (WFC3). with its vastly improved sensitivity and resolution compared NICMOS. it has become possible to analyze the rest-frame optical structure of high redshift galaxies with an unprecedented level of detail.," With the advent of the Wide Field Camera 3 (WFC3), with its vastly improved sensitivity and resolution compared to NICMOS, it has become possible to analyze the rest-frame optical structure of high redshift galaxies with an unprecedented level of detail."507 Cameronetal.(2010) have used data from the first year of observations of the HUDF and the Early Release Science Field to classify the rest-frame UV and optical morphologies of galaxies up to z—3.5., \cite{cam10} have used data from the first year of observations of the HUDF and the Early Release Science Field to classify the rest-frame UV and optical morphologies of galaxies up to $z\sim 3.5$.508 These authors confirm results by e.g. Krieketal.(2009)... who showed that massive galaxies at formingz>2.3 can galaxiesbe separated into two distinct classes: blue star with irregular morphologies on the one hand. and red quiescent galaxies with smoother morphologies on the other.," These authors confirm results by e.g. \cite{kri09}, who showed that massive galaxies at $z\approx 2.3$ can be separated into two distinct classes: blue star-forming galaxies with irregular morphologies on the one hand, and red quiescent galaxies with smoother morphologies on the other."509 In this Letter. we extend the previous results using the full two-year ultradeep near-infrared (NIR) imaging of the HUDF taken with the HST WFC3.," In this Letter, we extend the previous results using the full two-year ultradeep near-infrared (NIR) imaging of the HUDF taken with the HST WFC3."510 These data are the deepest ever obtained in the NIR and make it possible to analyze the morphologies. colors and structure of galaxies to z~3 in the rest-frame optical.," These data are the deepest ever obtained in the NIR and make it possible to analyze the morphologies, colors and structure of galaxies to $z\sim 3$ in the rest-frame optical."511 Using the incredible sensitivity and angular resolution of the WFC3 images we analyze the rest-frame optical surface brightness profiles of à mass-selected sample of galaxies at z—2., Using the incredible sensitivity and angular resolution of the WFC3 images we analyze the rest-frame optical surface brightness profiles of a mass-selected sample of galaxies at $z\sim 2$.512 We use these profiles to derive structural parameters such às size and profile shape. and obtain rest-frame colorprofiles.," We use these profiles to derive structural parameters such as size and profile shape, and obtain rest-frame colorprofiles."513 We study the correlations between these parameters as a function of redshift in order, We study the correlations between these parameters as a function of redshift in order514using S seconds in order to search for faster variations.,using 8 seconds in order to search for faster variations.515 The correctIv-phased baselines are added to produce. effectively. a phased-array response: since the position of the source is adequately known. the in-phase component then represents an unbiased estimate of its [lux density.," The correctly-phased baselines are added to produce, effectively, a phased-array response; since the position of the source is adequately known, the in-phase component then represents an unbiased estimate of its flux density."516 The typical rms noise on a single 32-seconcl sample when observing in this moce is 6 mJv., The typical rms noise on a single 32-second sample when observing in this mode is 6 mJy.517" Since the estimates are unbiased. the noise level reduces as the square root of the integration time,"," Since the estimates are unbiased, the noise level reduces as the square root of the integration time."518 guez et ((1995) show a map of nearby sources. inclucling the region (45.0|0.06 which has a total Dux. density. of about 5 Jv at this frequency.," guez et (1995) show a map of nearby sources, including the region G45.46+0.06 which has a total flux density of about 5 Jy at this frequency."519 I. lies about 12 aremin from 11915|105 (compared with a full-width to hallpower primary beam of 6 aremin)., It lies about 12 arcmin from 1915+105 (compared with a full-width to half-power primary beam of 6 arcmin).520 Using the IE with the pointing centre on 11915|105 an image of the region shows a response of some 3 mJv at the position of the LL LE region., Using the RT with the pointing centre on 1915+105 an image of the region shows a response of some 3 mJy at the position of the H II region.521" Since 11915|105 is variable and the observations are in any case usually too short for satisfactory mapping. there is à very small aciditional uncertainty in the flux censities when observing in the ""phased. array’ mode: values below about 1 nv may be unreliable."," Since 1915+105 is variable and the observations are in any case usually too short for satisfactory mapping, there is a very small additional uncertainty in the flux densities when observing in the `phased array' mode; values below about 1 mJy may be unreliable."522 Some observations were mace in a slightly more extended array. when this problem is not significant.," Some observations were made in a slightly more extended array, when this problem is not significant."523 The data presented bere run from 1995 Aug LO to 1996 Dee 31., The data presented here run from 1995 Aug 10 to 1996 Dec 31.524 Individual observations were of varving duration. typically between Lh and 6h.," Individual observations were of varying duration, typically between 1h and 6h."525 During intervals of pronounced activity it was often possible to observe every day., During intervals of pronounced activity it was often possible to observe every day.526 Fig., Fig.527 1 shows some 9000 points. cach one being a 5-min integration. over the the whole of this time.," 1 shows some 9000 points, each one being a 5-min integration, over the the whole of this time."528 The overall pattern o£ variations is apparent from this plot. although the details are not.," The overall pattern of variations is apparent from this plot, although the details are not."529 Fig., Fig.530 2 shows a series of individual observations. illustrating the range of behaviours observed.," 2 shows a series of individual observations, illustrating the range of behaviours observed."531 Particular features include: 1., Particular features include: 1.532 Smoothlyv-varving flux density. during major [lares with decav times of hours or davs., Smoothly-varying flux density during major flares with decay times of hours or days.533 The lare starting near ALJD 50275 (1996 July) was characterised. by smooth variations of lux density until it had almost disappeared. at which time the emission became much more crratic.," The flare starting near MJD 50275 (1996 July) was characterised by smooth variations of flux density until it had almost disappeared, at which time the emission became much more erratic."534 2., 2.535 Quasi-periodic oscillations (QPOs) and isolated short Hare events. a selection of which is shown in Fig," Quasi-periodic oscillations (QPOs) and isolated short flare events, a selection of which is shown in Fig."536 : these are discussed further below., 2; these are discussed further below.537 3., 3.538 Very low flux densities between active periods (e.g. ALJD 50105 — 50220. big.," Very low flux densities between active periods (e.g. MJD 50105 – 50220, Fig."539 1)., 1).540 'hese remarkable features were first observed in late 1995. ancl reported in LAU. Circulars (Pooley 1995. 1996).," These remarkable features were first observed in late 1995, and reported in IAU Circulars (Pooley 1995, 1996)."541 One other example has also been reported by guez Mirabel (1997)., One other example has also been reported by guez Mirabel (1997).542 We note the following features: 1., We note the following features: 1.543 Phe periods! vary in the range ο 40 min., The `periods' vary in the range 20 – 40 min.544 The most [requentIy-observed. periods are close to 40 min ancl 25 min: the event reported by guez Mirabel (1097) hack a period. of 30 min., The most frequently-observed periods are close to 40 min and 25 min; the event reported by guez Mirabel (1997) had a period of 30 min.545" “Phere are clear instances when a change in the period occurs during an observation (ος, 1996 Alay 26. 1996 Sep 15). and there are also instances when the gap between the maxima is erratic."," There are clear instances when a change in the period occurs during an observation (e.g. 1996 May 26, 1996 Sep 18), and there are also instances when the gap between the maxima is erratic."546 Isolated. peaks can be characterised. by à. rise-time close to 5 min ancl a decay which is approximately exponential with a time-constant between 12 and. 25 min., Isolated peaks can be characterised by a rise-time close to 5 min and a decay which is approximately exponential with a time-constant between 12 and 25 min.547 When the peaks are close together. they appear as (quasi-sinusuoidal variations. although it is often observed. that the rise is more rapid than the fall of each evele.," When the peaks are close together, they appear as quasi-sinusuoidal variations, although it is often observed that the rise is more rapid than the fall of each cycle."548 We suggest that the events themselves are similar. and they are trigecred by releases of energy. on some short time-scale.," We suggest that the events themselves are similar, and they are triggered by releases of energy on some short time-scale."549 The amplitudes of the individual peaks seldom exceed. 100 mJv (the maximum Ilux density. recorded in the whole of this dataset is 170 mJ)., The amplitudes of the individual peaks seldom exceed 100 mJy (the maximum flux density recorded in the whole of this dataset is 170 mJy).550 Individual sequences of oscillations, Individual sequences of oscillations551halo velocity dispersion can ellectively produce a mildly or non-evolving relation.,halo velocity dispersion can effectively produce a mildly or non-evolving relation.552" We show that this is indeed the case for the empirical scaling that we adopt in this paper with a,xa during mergers.", We show that this is indeed the case for the empirical scaling that we adopt in this paper with $\alpha_* \propto \sigma^{-3}$ during mergers.553 A more physical model might appeal to AGN growth and feedback which are much less ellicient in low mass galaxies. thereby inhibiting quenching. while in massive galaxies. the central black holes are already fully grown and are responsible for quenching the SER.," A more physical model might appeal to AGN growth and feedback which are much less efficient in low mass galaxies, thereby inhibiting quenching, while in massive galaxies, the central black holes are already fully grown and are responsible for quenching the SFR."554 Inhanced merging at high redshift provides the SSER boost that also lends itself to generating enhanced oa{ο in the resulting massive galaxies., Enhanced merging at high redshift provides the SSFR boost that also lends itself to generating enhanced $\alpha/Fe$ in the resulting massive galaxies.555" We predict that there should be rare low mass a/f'e ""refugees"".ὃν perhaps companions of massive IE7ECis. that have avoided the final merging fate and eas blow-out. but nonetheless carry chemical traces of their enhanced SSER. history."," We predict that there should be rare low mass $\alpha/Fe$ ""refugees"", perhaps companions of massive ETGs, that have avoided the final merging fate and gas blow-out, but nonetheless carry chemical traces of their enhanced SSFR history."556 The role of AGN remains to be elucidated., The role of AGN remains to be elucidated.557 Quenching of star formation is Commonly attributed to AGN., Quenching of star formation is commonly attributed to AGN.558 This may be the case for massive galaxies at hieh redshift., This may be the case for massive galaxies at high redshift.559 Llowever AGN may also play a role in boosting star formation in the low mass systems where the SSER is enhanced., However AGN may also play a role in boosting star formation in the low mass systems where the SSFR is enhanced.560 A future test of the role of ACGN will be to examine the residuals of a sample with measured AGN accretion rates and star formation rates in order to see whether for example the Ecdcington ratio correlates. (boosting) or anti-correlates (quenching) with SSER., A future test of the role of AGN will be to examine the residuals of a sample with measured AGN accretion rates and star formation rates in order to see whether for example the Eddington ratio correlates (boosting) or anti-correlates (quenching) with SSFR.561" Our results suggest. that the majority of galaxies with AZ,©10° M. atoc9d are interacting svstenis.", Our results suggest that the majority of galaxies with $M_* \ltsim 10^{9}$ $_{\odot}$ at $z > 4$ are interacting systems.562 This prediction. can be tested with future upcoming observational missions. and should. provide a strong test on the carly build-up of galaxies.," This prediction can be tested with future upcoming observational missions, and should provide a strong test on the early build-up of galaxies."563 In a follow-up paper. we will investigate the individual contribution from. merger triggered star-bursts and GN. with respect to accretion-driven star formation in the context of a full semi-analytic niocel.," In a follow-up paper, we will investigate the individual contribution from merger triggered star-bursts and AGN with respect to accretion-driven star formation in the context of a full semi-analytic model."564 The authors would like to thank Dan Stark for kindly providing the observational data in electronic. form. and useful comments on the draft., The authors would like to thank Dan Stark for kindly providing the observational data in electronic form and useful comments on the draft.565 SIX. acknowledges MM from the the Itoval Society Joint Projects Grant 0500523., SK acknowledges support from the the Royal Society Joint Projects Grant JP0869822.566"The radio pulsation search at the position of hhas been carried out by using the 25-m radio telescope at Nanshan, operated by Urumqi Astronomical Observatory (UAO).","The radio pulsation search at the position of has been carried out by using the 25-m radio telescope at Nanshan, operated by Urumqi Astronomical Observatory (UAO)."567 The observing system has a dual-channel cryogenic receiver that receives orthogonal linear polarizations at 18 cm., The observing system has a dual-channel cryogenic receiver that receives orthogonal linear polarizations at 18 cm.568" After mixing down to an intermediate frequency, the two polarizations are each fed into a filter bank of 128 contiguous channels, each of width 2.5 MHz."," After mixing down to an intermediate frequency, the two polarizations are each fed into a filter bank of 128 contiguous channels, each of width 2.5 MHz."569" The outputs from the channels are then square-law detected, filtered and one-bit sampled at 0.5 ms interval."," The outputs from the channels are then square-law detected, filtered and one-bit sampled at 0.5 ms interval."570 The data streams of all 256 channels are written to disk for subsequent off-line processing., The data streams of all 256 channels are written to disk for subsequent off-line processing.571" For more details about this system, please refer to Wang et al. ("," For more details about this system, please refer to Wang et al. ("5722001).,2001).573" In our observation, we did not find any convincing signal and we placed an upper-limit for any pulsed radio emission of 0.1 mJy at the position ofJ202131."," In our observation, we did not find any convincing signal and we placed an upper-limit for any pulsed radio emission of 0.1 mJy at the position of."5740+402645.. We have also searched for any radio counterpart for wwith the data from the NVSS database. (, We have also searched for any radio counterpart for with the data from the NVSS database. (575Condon et al.,Condon et al.576 1998)., 1998).577" Interestingly, we have identified radio excesses within the y—ray error circle of (see Figure 7))."," Interestingly, we have identified radio excesses within the $\gamma-$ ray error circle of (see Figure \ref{nvss1}) )."578 A 6x arcmin? close-up view centered on the nominal y—ray position of rreported in Abdo et al. (, A $6\times6$ $^{2}$ close-up view centered on the nominal $\gamma-$ ray position of reported in Abdo et al. (5792009a) is displayed in Figure 8..,2009a) is displayed in Figure \ref{nvss2}.580 Radio contours calculated at the levels between 10—25 mJy/beam are overlaid., Radio contours calculated at the levels between $10-25$ mJy/beam are overlaid.581 We have identified a feature with a size of about 3 arcminx1.5 arcmin in the center of this radio map., We have identified a feature with a size of about 3 $\times$ 1.5 arcmin in the center of this radio map.582 The peak of this radio feature is found to be at the south-east from the position ofJ202131., The peak of this radio feature is found to be at the south-east from the position of.583"0+402645.. Apart from the aforementioned feature, another radio excess extends for ~3 arcmin from tto the north-west."," Apart from the aforementioned feature, another radio excess extends for $\sim3$ arcmin from to the north-west."584 Adopting the FWHM of the beam and the rms fluctuation of the image of 45 arcsec and 0.45 mJy/beam respectively (cf., Adopting the FWHM of the beam and the rms fluctuation of the image of 45 arcsec and 0.45 mJy/beam respectively (cf.585 Condon et al., Condon et al.586" 1998), we estimated the flux densities at 1.4 GHz of the southeastern and the northwestern features to be 139+4 mJy and 85+2 mJy respectively."," 1998), we estimated the flux densities at 1.4 GHz of the southeastern and the northwestern features to be $139\pm4$ mJy and $85\pm2$ mJy respectively."587" These correspond to (5.84+0.17)x10!"" ergs cm~? s! and (3.57+0.08)x10!"" ergscm ? s! for an effective bandwidth of 42 MHz respectively.", These correspond to $(5.84\pm0.17)\times10^{-17}$ ergs $^{-2}$ $^{-1}$ and $(3.57\pm0.08)\times10^{-17}$ ergs $^{-2}$ $^{-1}$ for an effective bandwidth of 42 MHz respectively.588 It is interesting to notice that iis located approximately in between this two features., It is interesting to notice that is located approximately in between this two features.589" If such alignment is confirmed, this will suggest a possible bipolar outflow from the pulsar."," If such alignment is confirmed, this will suggest a possible bipolar outflow from the pulsar."590" Unfortunately, the limited angular resolution of NVSS data does not allow us to conclude this possible alignment."," Unfortunately, the limited angular resolution of NVSS data does not allow us to conclude this possible alignment."591 Future observation with the dedicated high resolution aperture synthesis by VLA can help us to confirm (or refute) this suggested scenario., Future observation with the dedicated high resolution aperture synthesis by VLA can help us to confirm (or refute) this suggested scenario.592 With the already publicly available data of the y—ray LAT All-Sky survey we have carried out an analysis of ccentered at the accurate X-ray position derived by analyzing data (see Sec 2.1)., With the already publicly available data of the $\gamma-$ ray LAT All-Sky survey we have carried out an analysis of centered at the accurate X-ray position derived by analyzing data (see Sec 2.1).593 We have studied its y—ray spectral and temporal properties in details., We have studied its $\gamma-$ ray spectral and temporal properties in details.594 In order to get the most significant results for the spectral analysis we took all available events from the start of the LAT All-Sky survey 4 August 2008 until 26 September, In order to get the most significant results for the spectral analysis we took all available events from the start of the LAT All-Sky survey 4 August 2008 until 26 September595see (heir Fig.,see their Fig.596 2: Belt et al. (, 2; Bett et al. (5972007). see their Fie.,"2007), see their Fig."598 13)- the axis ratio q used in (he present paper is equal to the ratio of the semi-major axes c/a in (hese papers., 13)- the axis ratio $q$ used in the present paper is equal to the ratio of the semi-major axes $c/a$ in these papers.599 Thus. either M31 is an unsual galaxy. or the simulations need to include additional physics such as the ellect of barvons that could affect the shape of the halo.," Thus, either M31 is an unsual galaxy, or the simulations need to include additional physics such as the effect of baryons that could affect the shape of the halo."600 Further. a moderate variation in HI gas dispersion results in a less flattened halo as shown in Section 5. point 3.," Further, a moderate variation in HI gas dispersion results in a less flattened halo as shown in Section 5, point 3."601 The III scalehight constraint. as applied in this paper is ideally suited for application to gas-rich. late-tvpe spiral galaxies with an extended III disk.," The HI scalehight constraint as applied in this paper is ideally suited for application to gas-rich, late-type spiral galaxies with an extended HI disk."602" In order to be useful as a constraint. the IHE scale height data should be available bevond 3 - 4 HR, and even Father out in the galaxy."," In order to be useful as a constraint, the HI scale height data should be available beyond 3 - 4 $R_{d}$ and even farther out in the galaxy."603 This is where the disk gravitational force begins to drop out and the dark matter halo takes over., This is where the disk gravitational force begins to drop out and the dark matter halo takes over.604 We note that obtaining the II scale height data is an observationallv challenging task (Sancisi Allen 1979). and therein lies the main diffieultv in using this method.," We note that obtaining the HI scale height data is an observationally challenging task (Sancisi Allen 1979), and therein lies the main difficulty in using this method."605 As far as our work is concerned. the observational data (Braun 1991) gives only three data points bevond Ro — 3424.," As far as our work is concerned, the observational data (Braun 1991) gives only three data points beyond R = $R_{d}$."606" We consider the region only bevond R = 342, following the Galaxy case (Naravan et al.", We consider the region only beyond R = $R_{d}$ following the Galaxy case (Narayan et al.607 2005)., 2005).608 Also. the irregularity or the scatter in (he observed data in (he inner region suggests the presence of a bar or spiral arn or some unknown structure. and is therefore excluded from the analysis.," Also, the irregularity or the scatter in the observed data in the inner region suggests the presence of a bar or spiral arm or some unknown structure, and is therefore excluded from the analysis."609 In Fig.G we illustrate the above point by plotting (he halo surface density within the I scale heieht. as well as the corresponding values for the bulge. stars. and HII gas versus the radius.," In Fig.6 we illustrate the above point by plotting the halo surface density within the HI scale height, as well as the corresponding values for the bulge, stars, and HI gas versus the radius."610 For using the III scale height constraint. the vertical [orce close to the galactic mid-plane is needed. (his is why the surface density of the halo within the ILE scale height is included.," For using the HI scale height constraint, the vertical force close to the galactic mid-plane is needed, this is why the surface density of the halo within the HI scale height is included."611 This figure shows that the halo surface density just begins to take over the stellar density at the point bevond which we do not have any observed data., This figure shows that the halo surface density just begins to take over the stellar density at the point beyond which we do not have any observed data.612 Availability of more data points in (he outer parts. with lower error-bars. is (hus clearly desirable aud would vield a üghter constraint on the halo shape and the density prolile.," Availability of more data points in the outer parts, with lower error-bars, is thus clearly desirable and would yield a tighter constraint on the halo shape and the density profile."613 The calculated rotation curve does not depend on (he shape ol the halo (q)., The calculated rotation curve does not depend on the shape of the halo $q$ ).614 All the q values give equally good fits to the observed data., All the $q$ values give equally good fits to the observed data.615 Surprisingly. the 47 minima for the rotation curve and the IL} scale height data. taken separately. lie on different regions of the grid.," Surprisingly, the ${\chi}^2$ minima for the rotation curve and the HI scale height data, taken separately, lie on different regions of the grid."616 The best-fit to the rotation curve alone gives high values of the central density and small values of core radius., The best-fit to the rotation curve alone gives high values of the central density and small values of core radius.617 The best-fit to the scale height data. on the other hand. gives a lower central density and a larger core radius.," The best-fit to the scale height data, on the other hand, gives a lower central density and a larger core radius."618 Geehan et al. (, Geehan et al. (6192006) obtained a best-Lit pj of 0.033 ΔΙ. * (somewhat higher than the value we get) and /2. of 8.2 kpe. probably. because they had used (he rotation curve as the only constraint.,"2006) obtained a best-fit $\rho_{0}$ of 0.033 $_{\odot}$ $^{-3}$ (somewhat higher than the value we get) and $R_{c}$ of 8.2 kpc, probably because they had used the rotation curve as the only constraint."620 We. on the other hand. have used (wo complementary constraints: (he planar one involving the," We, on the other hand, have used two complementary constraints; the planar one involving the"621the rest-frame UV range. in particular the mid-UV.,"the rest-frame UV range, in particular the mid-UV."622 The first high : red galaxies detected were two fait radio sources frou the Licden-Berkcley Deep. Survey (LBDS): LBDS 53N091 (2—1.55) aud LBDS 53W069 (2 —1.13) (Duulopetal.1996:Spiurad1997:Dun-lopetal. 1999).," The first high $z$ red galaxies detected were two faint radio sources from the Lieden-Berkeley Deep Survey (LBDS): LBDS 53W091 $z=$ 1.55) and LBDS 53W069 $z=$ 1.43) \citep{dunlop96,spinrad97,dunlop99}."623. The aualvsis of these svstenis was soon a subject of much debate., The analysis of these systems was soon a subject of much debate.624" For instance. Spinradctal.(1997) determined an age of 3.5 Cyr for LBDS 53N091. which posed complicatious to explain galaxy formation ""under au Eiustein-De Sitter universe."," For instance, \citet{spinrad97} determined an age of 3.5 Gyr for LBDS 53W091, which posed complications to explain galaxy formation under an Einstein-De Sitter universe."625 This age was soon contested bv a seres of authors (Druzual&Alaeris1997:IIleapetal.1998:Yi2000) that derived much vounger ages (<2 Cyr). which allowed for more comfortable estimates for the formation redshift (i£) of the galaxies.," This age was soon contested by a series of authors \citep{bruzual97,heap98,yi00} that derived much younger ages $<$ 2 Gyr), which allowed for more comfortable estimates for the formation redshift $z_{F}$ ) of the galaxies."626 Subsequeu analvses revived the polemic by coufinüus the first deteriunuations. bo. ascribing ages du excess of 3 Cyr (Nolanetal.2003:PFerreras&Yi 2001).," Subsequent analyses revived the polemic by confirming the first determinations, i.e. ascribing ages in excess of 3 Gyr \citep{nolan03,ferreras04}."627 Aside frou the different inethodologies used for the age deteruriuations. Hf was clear that our poor knowledge of the UV spectrum of the prestunably well understood. MS sars (emsPeterson.Dorman&Rood2001) was (aud still is to some extent) a major drawback that hews prevented the unambiguous deterumination of the main properties (age and chemical colmposition) of these distant svstenis.," Aside from the different methodologies used for the age determinations, it was clear that our poor knowledge of the UV spectrum of the presumably well understood MS stars \citep[e.g.,][]{peterson01} was (and still is to some extent) a major drawback that has prevented the unambiguous determination of the main properties (age and chemical composition) of these distant systems."628 More receutlv. a series of deep surveys have Όσοι conducted. (Cimattietal.2002:Abraham2001:MeCarthyetal.2001) and now iuclude well over 300 svstenis with similar spectrophotometric properties as those of the prototypical LBDS S3WoO9L.," More recently, a series of deep surveys have been conducted \citep{cimatti02,abraham04,mccarthy04} and now include well over 300 systems with similar spectrophotometric properties as those of the prototypical LBDS 53W091."629 Ciiiattietal(2008) presenteκα what perhaps is the best spectrum represeutative of distant red objects., \citet{cimatti08} presented what perhaps is the best spectrum representative of distant red objects.630 Within the Galaxy Mass Assembly ultra-deep Sky. Survey (CALASS) program. thev selected 13 passive galaxies (with 1.3<2 2.0) ou the basis of their red UV color. defined as the magnitude differcuce between two bauds (cach of LOO wwidtl) centered at 200 Yand 3300A.. aud coustructed astacked spectrum that totalled nearly 500. hours of observing time at the Χαν Large Telescope.," Within the Galaxy Mass Assembly ultra-deep Sky Survey (GMASS) program, they selected 13 passive galaxies (with $1.3 < z < 2.0$ ) on the basis of their red UV color, defined as the magnitude difference between two bands (each of 400 width) centered at 2900 and 3300, and constructed a spectrum that totalled nearly 500 hours of observing time at the Very Large Telescope."631 By conrpariue that spectra with single stellar populations (SSPs) from several population svuthesis codes (Bruzuall&Charlot2003:Maraston 2005).. they determined. from the rest-frame UV alone. ages that ranged from 0.7 to 2.8 Cir aud metallicities in the range 0.2 to 1.5 Z..," By comparing that spectrum with single stellar populations (SSPs) from several population synthesis codes \citep{bruzual03,maraston05}, they determined, from the rest-frame UV alone, ages that ranged from 0.7 to 2.8 Gyr and metallicities in the range 0.2 to 1.5 $Z_{\odot}$ ."632 By adding to the comparison near and iid IR photometric data. thewv significantly constrained the ages to L1.6 Cov and fonud that Z=Z.. provided the best results.," By adding to the comparison near and mid IR photometric data, they significantly constrained the ages to 1–1.6 Gyr and found that $Z=Z_{\odot}$ provided the best results."633 Iu Fig. 3..," In Fig. \ref{fig:gmass_seds},"634 we show the CALASSstacked spectrum of the 13 red galaxies (black) together with three different SSPs of various ages and chemical compositions., we show the GMASS spectrum of the 13 red galaxies (black) together with three different SSPs of various ages and chemical compositions.635 As a qualitative demonstration of the AMD in the UV. we uote that the observed spectrum is verv simular to the iuiddle two SSP fluxes constructed with quite differcut parameters.," As a qualitative demonstration of the AMD in the UV, we note that the observed spectrum is very similar to the middle two SSP fluxes constructed with quite different parameters."636 It is bevoud the scope of this paper to discuss any detail ou the procedures so far delevoped to establish the age and chemical composition of distant systems., It is beyond the scope of this paper to discuss any detail on the procedures so far delevoped to establish the age and chemical composition of distant systems.637 We. nevertheless believe that iu general the spectroplotometiic analysis of distant objects has been carried out with stella libraries that might be inadequate. in particular concerning the spectral resolution and capabilities of represcuting real stars.," We, nevertheless, believe that in general the spectrophotometric analysis of distant objects has been carried out with stellar libraries that might be inadequate, in particular concerning the spectral resolution and capabilities of representing real stars."638 Back in 2002 the Stellar Atmospheres aud. Populatious Research Group (GrAPEsfor its designation in spanish at the Tustituto Nacional de Astrofisica. Ópptica Y Llectróunuica initiated a project aimed at providiug updated stellar tools for the analvsis of the UV spectra of a varietv of stellar agerceates. mainly evolved ones.," Back in 2002 the Stellar Atmospheres and Populations Research Group (GrAPEs–for its designation in spanish) at the Instituto Nacional de sica, Ópptica y Electrónnica initiated a project aimed at providing updated stellar tools for the analysis of the UV spectra of a variety of stellar aggregates, mainly evolved ones."639 The overall project consists iu four main steps. παλ] aj- the creation of a theoretical stellar database that we have calledUVBLUE?.. br the conrparison of such data base with observational stellar data. c)- the calculation of a set of svuthetic SEDs of SSPs :id their validation through a comparison with observations of a salmple of Galactic globular clusters. d)- construction of models for dating local cllipticals aud distant τος ealaxies.," The overall project consists in four main steps, namely a)- the creation of a theoretical stellar database that we have called, b)- the comparison of such data base with observational stellar data, c)- the calculation of a set of synthetic SEDs of SSPs and their validation through a comparison with observations of a sample of Galactic globular clusters, d)- construction of models for dating local ellipticals and distant red galaxies."640 In Chavez(2009).. we prescuted a παπα of the results obtained im steps (a) and (b) aud the reacer is referred. to that paper aud the original references for a detailed description of the project (Rodriguez-Merinoetal.2005:Chavezct 2007).," In \citet{chavez09}, we presented a summary of the results obtained in steps (a) and (b) and the reader is referred to that paper and the original references for a detailed description of the project \citep{lino05,chavez07}."641. Tn what follows. we elaborate on the third step.," In what follows, we elaborate on the third step."642 Iu Chavezetal.(2009) we presented the first theoretical analysis of the UV integrated spectra of evolved SSPs (seealsoMarastonetal.2009.forvounepopulatiouxs).., In \citet{chavezetal09} we presented the first theoretical analysis of the UV integrated spectra of evolved SSPs \citep[see also][for young populations]{maraston09}.643 We focused on particular absorption lines aud bleuds to establish. through the use of spectroscopic imdices. their ychavior iu terms of age and chemical composition.," We focused on particular absorption lines and blends to establish, through the use of spectroscopic indices, their behavior in terms of age and chemical composition."644 We identified several interesting tendencies. such as the ow general scusitivity of the indices to age aud the remarkably distinct behavior of the indices Fe 2332 and Fe 2102. at super solar regimes (in fact. we xopose these indicesas a promising tool to establish he age in moetal-nrich svstems).," We identified several interesting tendencies, such as the low general sensitivity of the indices to age and the remarkably distinct behavior of the indices Fe 2332 and Fe 2402, at super solar regimes (in fact, we propose these indicesas a promising tool to establish the age in metal-rich systems)."645 Svuthetic iudices were compared to IUE low resolution observations of prototypical, Synthetic indices were compared to IUE low resolution observations of prototypical646deposition of a significant amount of charges in pixels along the row during the serial read-out process.,deposition of a significant amount of charges in pixels along the row during the serial read-out process.647 These “streak” events were removed by using the program in CIAO., These “streak” events were removed by using the program in CIAO.648 The total available times for cach observation. after the scereeniug. are listed iu Table 1..," The total available times for each observation, after the screening, are listed in Table \ref{obslog}."649 (Jausenctal.2001) also observed SN 1987À aud the 30 Dor region several times: the satellite has a spatial resolution of ~1 and a relatively wide FOV with the radius of15'.," \citep{jansen}650 also observed SN 1987A and the 30 Dor region several times; the satellite has a spatial resolution of $\sim$ and a relatively wide FOV with the radius of."651. We selected wo observations (Observation ID = 0101660301. aud 0113020201: hereafter Obs.3 aud 1D. which cover 303 Dor C and are relatively free from Ligh backeround fares due o low-enerev protous.," We selected two observations (Observation ID = 0104660301 and 0113020201; hereafter Obs.3 and 4), which cover 30 Dor C and are relatively free from high background flares due to low-energy protons."652 The observed dates and argeted positious are shown in Table 1.., The observed dates and targeted positions are shown in Table \ref{obslog}.653 In both observations. only the metal oxide seuiconductors (MOS) CCDs. which have au cucrey range of L110.0 keV and a similar cucrey resolution toChandra. αποetal.2001) were operated in the ull-fiaue mode with the medium filter (Stephanetal.1996:Villa199s) for blocking ultra-violet photous.," In both observations, only the metal oxide semiconductors (MOS) CCDs, which have an energy range of 0.1–10.0 keV and a similar energy resolution to, \citep{turner} were operated in the full-frame mode with the medium filter \citep{stephan,villa} for blocking ultra-violet photons."654 The data reductions aud analyses were nade using the Staudard Analvsis System (SAS: Watson et al 2001) version SLA: we performed the basic pipeline process following the SAS enide., The data reductions and analyses were made using the Standard Analysis System (SAS; Watson et al 2001) version 5.4.1; we performed the basic pipeline process following the SAS guide.655 The background level was larecly changed. particularly in Obs.," The background level was largely changed, particularly in Obs."656 L. heuce we removed the data with a high backeround level (20.6 cuts + iu the 10.015.0 keV baud).," 4, hence we removed the data with a high background level $>$ 0.6 cnts $^{-1}$ in the 10.0–15.0 keV band)."657 The exposure times in cach observation after the screeniues are listed in Table 1.., The exposure times in each observation after the screenings are listed in Table \ref{obslog}.658 Fieve l1 shows the soft (0.72.0 keV) and hard (2.0.7.0 keV) wand iuages around 30 Dor C. in which the two observations (Obs.1 and 2) are combined with a correction of the exposure times.," Figure \ref{images} shows the soft (0.7–2.0 keV) and hard (2.0–7.0 keV) band images around 30 Dor C, in which the two observations (Obs.1 and 2) are combined with a correction of the exposure times."659 A clear shell-like structure with a radius of ~ (UoLO pevadius at the 50 kpc distance) is seen in both bands., A clear shell-like structure with a radius of $\sim$ $R\sim 40$ pc-radius at the 50 kpc distance) is seen in both bands.660 Iu detail. however. the uorphologies are differeut from) each other: the eutire shell is seen im the soft baud. whereas he hard N-vavs are visible oulv at the western vat.," In detail, however, the morphologies are different from each other; the entire shell is seen in the soft band, whereas the hard X-rays are visible only at the western part."661 Catalogned SNRs. the Wouevcomb nebula (SNR 69.3) and SN 1987À are also seen uaiulv iu the soft baud (see Figure 1)).," Catalogued SNRs, the Honeycomb nebula (SNR $-$ 69.3) and SN 1987A are also seen mainly in the soft band (see Figure \ref{images}) )."662 The Nav catures of these objects have been reported with (Deunerlotal.2000) and (Burrowseal.2000:Parket2002:Michael monitoring observatious.," The X-ray features of these objects have been reported with \citep{dennerl}663 and \citep{burrows,park,michael} monitoring observations."664 Iu addition to the diffuse structure. sole poiut-like sources are found inside 30 Dor C. The exposure time of the observations are short. most of the data suffer from a high background. and the spatial resolution is not sufficient.," In addition to the diffuse structure, some point-like sources are found inside 30 Dor C. The exposure time of the observations are short, most of the data suffer from a high background, and the spatial resolution is not sufficient."665" Ποσο, we concentrated on the data for the point-source search anc analysis."," Hence, we concentrated on the data for the point-source search and analysis."666" At first. point sources were searched for with heweedetect softwarcin the 0.58.0 keV baud Πμασος, then manually iuspectecd for any spurious oomt-like structure due mainly to a part of he diffuse enmuüssiou."," At first, point sources were searched for with the in the 0.5–8.0 keV band images, then manually inspected for any spurious point-like structure due mainly to a part of the diffuse emission."667 We lus found six poiut sources with a significance level of 7.06. as shown in Figure 1 aud Table 2..," We thus found six point sources with a significance level of $>$ $\sigma$, as shown in Figure \ref{images} and Table \ref{point}."668 For these six yolut sources. we searched for optical. infrared. and radio counterparts. and found that three (No.l. 3. aud. 1) coincide at the yositions of the xiehtest star clusters: a. 2. and 5 (Lortet&Testor198 L).," For these six point sources, we searched for optical, infrared, and radio counterparts, and found that three (No.1, 3, and 4) coincide at the positions of the brightest star clusters: $\alpha$, $\beta$, and $\gamma$ \citep{lortet}."669. We therefore checked further for any N-ray endssion from the other clusters (8. €. aud C). which are also members of the OB association LII 90 (Lucke&Hodge1970). eunconipassed. by the 30 Dor € shell.," We therefore checked further for any X-ray emission from the other clusters $\delta$ , $\epsilon$, and $\zeta$ ), which are also members of the OB association LH 90 \citep{lucke}670 encompassed by the 30 Dor C shell."671 ILowever. we fouud no excess N-ravs frou these clusters at the 236 limit.," However, we found no excess X-rays from these clusters at the $\sigma$ limit."672 We also searched for N-aay counterparts fromROSAT PSPC aud URI catalogues (Iaberl&Pictsch1999:Sasaki.Haberl.&Pictsch 2000).. but found no candidate.," We also searched for X-ray counterparts from PSPC and HRI catalogues \citep{haberl,sasaki}, but found no candidate."673 Tn the observatious. we can see that the diffuse structure consists of several shell fraeineuts (see Figure 1)). aud the whole structure is widely spread over the two observed regions with different configurations of the CCD types (back- and frout-illunated).," In the observations, we can see that the diffuse structure consists of several shell fragments (see Figure \ref{images}) ), and the whole structure is widely spread over the two observed regions with different configurations of the CCD types (back-illuminated and front-illuminated)."674 Therefore. a spectral analvsis ou allof the diffuse structure is technically and scientifically complicated.," Therefore, a spectral analysis on allof the diffuse structure is technically and scientifically complicated."675For this reason. we divided the diffuse structure iuto four regions (hereafter shells ÀD). as shown in,"For this reason, we divided the diffuse structure into four regions (hereafter shells A–D), as shown in"676The resultiugC» abundance is lavecrOo for ugher trial eniperature.,The resulting abundance is larger for higher trial temperature.677 This is a result of the fact that Iv shell clectrous are increasingly stripped off for higher eniperatures. and hence a higher mon abundance is necessary to account for the observed equivaleut width.," This is a result of the fact that $K-$ shell electrons are increasingly stripped off for higher temperatures, and hence a higher iron abundance is necessary to account for the observed equivalent width."678 The sunallest abuudauce is obtained to be 2.11.17 at a eniperature of 7 keV. which impies the lower limut of the abundance to be 1.35.," The smallest abundance is obtained to be $\pm 1.1\odot$ at a temperature of 7 keV, which implies the lower limit of the abundance to be $\odot$."679 Note. however. that this is a very conservative lower limit. aud the abundance based on the iron omission line is probably several times as large as that of Solar composition.," Note, however, that this is a very conservative lower limit, and the abundance based on the iron emission line is probably several times as large as that of Solar composition."680 This is in conurast to the abundances of CVs which have recently been measured to be xub-Solar. such as 0.63+0.087. for (Fujimoto alc Tshida 1997). 0.1105+ for (Ishida 1997). alc ~O.L+ for SS Cre (Done and Osborne 1997).," This is in contrast to the abundances of CVs which have recently been measured to be sub-Solar, such as $0.63\pm 0.08\odot$ for (Fujimoto and Ishida 1997), $0.4^{+0.2}_{-0.1}\odot$ for (Ishida 1997), and $\sim 0.4\odot$ for SS Cyg (Done and Osborne 1997)."681 A lint for a larger abuudance than Solav is obtained only for (Misaki 1996)., A hint for a larger abundance than Solar is obtained only for (Misaki 1996).682 Since we have obtained the abundance iu the previous section. we have next calculated the bolometric Iuuinositv of the hard N-vav componcut.," Since we have obtained the abundance in the previous section, we have next calculated the bolometric luminosity of the hard X-ray component."683 To do this. we have adopted the volune enüssivitv formmlas of the optically thin plasma approximated by MeCray (1987). but modified to take iuto account the abundance effects.," To do this, we have adopted the volume emissivity formulas of the optically thin plasma approximated by McCray (1987), but modified to take into account the abundance effects."684 where T5 is the plasiua temperature in 109 Ik. The first term on the right haud side is the volume emissivitv for the line cussion which is proportional to the abundance., where $T_6$ is the plasma temperature in $10^6$ K. The first term on the right hand side is the volume emissivity for the line emission which is proportional to the abundance.685 The secoud term represeuts that oftιο frec-free. CLUSSIOL., The second term represents that of the free-free emission.686 Note that the first terii is ereater tiui the second teri. in the rauge T«2 seV. The bolo1ieric linunosity of the uud component Ly is obtained by A+EM. where EM is the emission measure obtained from the spectral fitting or the 0.5 keV component aud the hard excess couponcut separately by asstuuing a distance to the source.," Note that the first term is greater than the second term in the range $T < 2$ keV. The bolometric luminosity of the hard component $L_{\rm H}$ is obtained by $\Lambda \cdot EM$, where $EM$ is the emission measure obtained from the spectral fitting for the 0.8 keV component and the hard excess component separately by assuming a distance to the source."687 The πιοαν thus calculated for the trial teniperatures is otted in the lower pancl of Fig., The luminosity thus calculated for the trial temperatures is plotted in the lower panel of Fig.688" 8. showiug a rather Hat dependence witi temperature in the 730 keV range: Ly-06Ls1079 cre 1,", \ref{AbLumi} showing a rather flat dependence with temperature in the 7–30 keV range: $L_{\rm H}=0.6-1.4\times 10^{30}$ erg $^{-1}$.689 Note hat we have not corrected for reflectionfro t1ο white dwarf surface;, Note that we have not corrected for reflectionfrom the white dwarf surface.690 One can do this by dividiug the above value by 1]ex where ay is the hard N-rav albedo., One can do this by dividing the above value by $1+a_X$ where $a_X$ is the hard X-ray albedo.691 Ins 3... we have obtained the lower lait of the bolometric huninosity othe blackbo«v component Zip to be 2«1077 erg s+ fromROSAT aud siuniltaucous spectral fitting.," In 3.4, we have obtained the lower limit of the bolometric luminosity of the blackbody component $L_{BB}$ to be $2\times 10^{32}$ erg $^{-1}$ from and simultaneous spectral fitting."692 This mcais LaLp>το<cos>., This means $L_{\rm S}/L_{\rm H} > 140/<\cos \theta> $.693 If we also takeICE daadu O accollat x5) Lpp Is constraine iutherauge2 B5«107 ere sf. aud heuce £LsfLy=(110SJO0)/—cos> is obtained.," If we also take data into account 3.5), $L_{BB}$ is constrained in the range $2-5\times 10^{32}$ erg $^{-1}$, and hence $L_{\rm S}/L_{\rm H} = (140-830)/<\cos \theta>$ is obtained."694 Note that wute dyvarf atuosphere models could possibly reduce the himunosity of tιο soft conrponeut. aud thus also LfLy.," Note that white dwarf atmosphere models could possibly reduce the luminosity of the soft component, and thus also $L_{\rm S}/L_{\rm H}$."695 Ins XL we have derived the temperature of the soft blackbody comipoueut to he 15!* eV. The best fit value is outside the usual range derived bv Szkody (1995). namely 2015 eV. Iun estimating the blackbody teiiperature. Szkody (1995) assumed a thermal bremssstrallhime component with a temperature of 10 keV for the lard X-ray. componcnut.," In 3.4, we have derived the temperature of the soft blackbody component to be $15^{+7}_{-5}$ eV. The best fit value is outside the `usual' range derived by Szkody (1995), namely 20–45 eV. In estimating the blackbody temperature, Szkody (1995) assumed a thermal lung component with a temperature of 10 keV for the hard X-ray component."696 However. based on our data we have found a spectral compoucut which can be represented by a R&SS spectrum with KT~ 0.5 keV. The R&SS component with such low cluperature has a forest of wou cussion lines in the L81l keV baud caused by the mon L-shell rausitious (Ravinond and Suuth 1977).," However, based on our data we have found a spectral component which can be represented by a S spectrum with $kT \sim$ 0.8 keV. The S component with such low temperature has a forest of iron emission lines in the 0.8–1 keV band caused by the iron L-shell transitions (Raymond and Smith 1977)."697 ence. a significant amount of the flux iu the 0.52 keV. baud is attributed to the ow temperature R&SS compoucut iu our nocelline.," Hence, a significant amount of the flux in the 0.8–2 keV band is attributed to the low temperature S component in our modelling."698 Note that this cannot happen if we asstue a thermal xemisstrahluug component with a temperature of 10 keV. As a result. the Dlackbody teiiperature. becomes lower han the estimates in Szlsodyv (1995).," Note that this cannot happen if we assume a thermal bremsstrahlung component with a temperature of 10 keV. As a result, the blackbody temperature becomes lower than the estimates in Szkody (1995)."699 Iu analvzingROSAT data. oue usually assumes the cluperature of the hard X-ray. component to be arouud 20 keV (Ramsay 1991. for example).," In analyzing data, one usually assumes the temperature of the hard X-ray component to be around 20 keV (Ramsay 1994, for example)."700 As shown rere. however. this may cause a huge svstemiatic error in evaluating the Iuuiuositv aud the temperature of the soft dlackhody component.," As shown here, however, this may cause a huge systematic error in evaluating the luminosity and the temperature of the soft blackbody component."701 We preseuted ταν data of obtained byΑρα., We presented X-ray data of obtained by.702 From the light curves we find ouly uareinal evidence for orbital intensity modulation which is seen in the light curve below 0.5 keV characterized by the sharp aud deep munima., From the light curves we find only marginal evidence for orbital intensity modulation which is seen in the light curve below 0.5 keV characterized by the sharp and deep minima.703 Frou this energy depenence. we couclude that the intensity modulation is caused mostly bv photoelectric absorption in the pre-shock accretion column. and the accreting pole moves around on the hemisphere visible from the observer. consistent with the conclusions from Cremer. Remillard Notch (1998).," From this energy dependence, we conclude that the intensity modulation is caused mostly by photoelectric absorption in the pre-shock accretion column, and the accreting pole moves around on the hemisphere visible from the observer, consistent with the conclusions from Greiner, Remillard Motch (1998)."704" It is possible that the line of sight absorber is partly ionized or has adistribution in Ny, in the range S107! 7.", It is possible that the line of sight absorber is partly ionized or has adistribution in $N_H$ in the range $^{21}$ $^{-2}$ .705 The X-raw spectruni can be represented by a two teniperature oXticallv thin thermal plasiuna emission model, The X-ray spectrum can be represented by a two temperature optically thin thermal plasma emission model706and { then corresponds to the cooling radius (eg Crawford Fabian 1995b).,and $R$ then corresponds to the cooling radius (eg Crawford Fabian 1995b).707 The second. model emploved is a projected ]xing law. with index fixed at -1.5. and the core radius. /? and normalization left as free parameters.," The second model employed is a projected King law, with index fixed at -1.5, and the core radius $R$ and normalization left as free parameters."708 Given the errors inherent in whether such simple models truly characterize the extended: emission. we do not convolve the extended emission models with the PSE.," Given the errors inherent in whether such simple models truly characterize the extended emission, we do not convolve the extended emission models with the PSF."709 The relative normalization between the PSE and extended components are not always very well determined. so we also derive. what should. be regarded: as a lower limit to the presence of any extended component by assuming the nuclear emission accounts for all the lisht in the X-rav core.," The relative normalization between the PSF and extended components are not always very well determined, so we also derive what should be regarded as a lower limit to the presence of any extended component by assuming the nuclear emission accounts for all the light in the X-ray core."710 We fit the PSE to the quasar racial profile within the inner 15 aresec and then subtract this model and [fit the residuals by cach of the cluster models., We fit the PSF to the quasar radial profile within the inner 1–5 arcsec and then subtract this model and fit the residuals by each of the cluster models.711 We execute these 5 model fits to the profiles out to a radius of 50 arcsec (11 data points). vielding 10. S. and 9 degrees of freedom for the psf onlv. psf|extended component mocdels. and the fit of the extended component model to the residual after subtraction of the normalised URL PSE.," We execute these 5 model fits to the profiles out to a radius of 50 arcsec (11 data points), yielding 10, 8, and 9 degrees of freedom for the psf only, psf+extended component models, and the fit of the extended component model to the residual after subtraction of the normalised HRI PSF."712 We then repeat the fits to the profile out to à racius of 100 aresec (15 data points). vielding 14. 12 and 13 degrees of [reedom to the fits as above.," We then repeat the fits to the profile out to a radius of 100 arcsec (15 data points), yielding 14, 12 and 13 degrees of freedom to the fits as above."713 The fitting analvsis is carried out. first for cach quasar image in the absence of any wobble correction. and then for the images corrected using cdilferent phase intervals.," The fitting analysis is carried out first for each quasar image in the absence of any wobble correction, and then for the images corrected using different phase intervals."714 The detailed results are summarized in Table 2. where the is given for each fit.," The detailed results are summarized in Table 2, where the $\chi^2$ is given for each fit."715 We tabulate the fit parameters of the profile fits out to a radius of 50 arcesec and then LOO aresee in turn: Z? (in aresec) representing either the break in the broken power-law mocel. or the core radius in the Wing law model: the integrated. luminosity from the extended component as a percentage of the total Iuminosity ol the X-ray source: the X-ray luminosities (in the observed nergv. band) of. the quasar component (LyONO ) and that “the cluster component (LA) assuming a power-law of οποίο index 2 and thermal bremsstrahlung emission at a emperature of AZ=4keV respectively. (," We tabulate the best-fit parameters of the profile fits out to a radius of 50 arcsec and then 100 arcsec in turn: $R$ (in arcsec) representing either the break in the broken power-law model, or the core radius in the King law model; the integrated luminosity from the extended component as a percentage of the total luminosity of the X-ray source; the X-ray luminosities (in the observed energy band) of the quasar component $L_X^{QSO}$ ) and that of the cluster component $L_X^{cl}$ ) assuming a power-law of photon index 2 and thermal bremsstrahlung emission at a temperature of $kT=4\keV$ respectively. ("716At the redshift Sour quasars this observed. band. carries about half of the rolometric Luminosity for the thermal spectrum.),At the redshift of our quasars this observed band carries about half of the bolometric luminosity for the thermal spectrum.)717 The errors ave derived from propagating the Ay7=1 confidence limits of the fit parameters., The errors are derived from propagating the $\Delta\chi^2=1$ confidence limits of the fit parameters.718 Errors are not shown when the fit was insulliciently robust to extract errors on all parameters of interest., Errors are not shown when the fit was insufficiently robust to extract errors on all parameters of interest.719 Table 2. however. demonstrates the full range of values obtained from the ten model fits employed. for cach of the phase intervals ancl allows one to assess the variation of cach parameter from the svstematic uncertainties of PSE normalization and extended component model emploved.," Table 2, however, demonstrates the full range of values obtained from the ten model fits employed for each of the phase intervals and allows one to assess the variation of each parameter from the systematic uncertainties of PSF normalization and extended component model employed."720 A comparison of some of the better fits to the radial profile of cach quasar (those shown in bold font in Table 2) are displayed in Figure 2.., A comparison of some of the better fits to the radial profile of each quasar (those shown in bold font in Table 2) are displayed in Figure \ref{fig:profs}.721 These plots clearly show that there are significant dillerences between the PSE-onlv [it to the profile. and the fits that. include a model. for. extended emission.," These plots clearly show that there are significant differences between the PSF-only fit to the profile, and the fits that include a model for extended emission."722 In all this analysis we necessarily assume that any extended component is both centred on the quasar (in no case do we see any evidence for a secondary. oll-centre »eak). and derive its properties such as scale and luminosity assuming that itis at the redshift of the quasar.," In all this analysis we necessarily assume that any extended component is both centred on the quasar (in no case do we see any evidence for a secondary off-centre peak), and derive its properties such as scale and luminosity assuming that it is at the redshift of the quasar."723 The present data cannot rule out a contribution to he extended component of X-ray emission from the active nuclei of close companion galaxies to cach of the quasars., The present data cannot rule out a contribution to the extended component of X-ray emission from the active nuclei of close companion galaxies to each of the quasars.724 Such emission. would. of course. provide further support or a clustered environment.," Such emission would, of course, provide further support for a clustered environment."725 The probability of getting an Unassociated X-ray source within an aperture of 1 square areminute centred. on a quasar is less than LO’. at the lux level of the extended: emission.," The probability of getting an unassociated X-ray source within an aperture of 1 square arcminute centred on a quasar is less than $10^{-3}$, at the flux level of the extended emission."726 Vhus there is little chance of the extended. emission component being due to contamination by fore- or back-ground sources., Thus there is little chance of the extended emission component being due to contamination by fore- or back-ground sources.727 Given dis proximity. to ἃ verv luminous source of photoionizaton. the low ionization state observed in the spatially extended. oxygen line emission around. this 3C48 ος Fabian et al (LOST) to deduce a high density environment around this quasar.," Given its proximity to a very luminous source of photoionizaton, the low ionization state observed in the spatially extended oxygen line emission around this 3C48 led Fabian et al (1987) to deduce a high density environment around this quasar."728 The inferred eas pressure οἱ 10 wwithin oof the quasar core is consistent with confinement of the extended: emission-line region. by an intracluster mediunr There is. however. no strong evidence for a rich cluster of ealaxies [from optical images (Yee. Green Stockman 1986: Yates etal 1989).," The inferred gas pressure of $\times10^5$ within of the quasar core is consistent with confinement of the extended emission-line region by an intracluster medium There is, however, no strong evidence for a rich cluster of galaxies from optical images (Yee, Green Stockman 1986; Yates etal 1989)."729 The fit to the radial profile is substantially improved by he addition of an extended component. the best fits being obtained in all cases when this is represented by a Ixing law.," The fit to the radial profile is substantially improved by the addition of an extended component, the best fits being obtained in all cases when this is represented by a King law."730 The extended component requires à very consistent value for he core radius A of around 5-6 aresee in all fits (1 arcsec corresponds to at the redshilt of the quasar*)). and. accounts. for 10-16 »r cent of the total X-ray source.," The extended component requires a very consistent value for the core radius $R$ of around 5-6 arcsec in all fits (1 arcsec corresponds to at the redshift of the ), and accounts for 10-16 per cent of the total X-ray source."731 The full variation of its uminositv is 5.—10«l0tteres+o. with most of the values derived being to the lower end of this range.," The full variation of its luminosity is $5-10\times10^{44}$, with most of the values derived being to the lower end of this range."732 This quasar lies in a densely clustered. environment (Ellingson 1991: Llintzen 1984). and the racio source has a very complex structure suggestive of dellection. ancl distortion of the radio jet. to. the south-east by. some external medium.," This quasar lies in a densely clustered environment (Ellingson 1991; Hintzen 1984), and the radio source has a very complex structure suggestive of deflection and distortion of the radio jet to the south-east by some external medium."733 The two sides of the radio source show asymmetric Faraday depolarization. which can be interpreted as due to cdilfering lines of sight through a depolarizing cluster medium (Carrington. Conway Leahy 1991).," The two sides of the radio source show asymmetric Faraday depolarization, which can be interpreted as due to differing lines of sight through a depolarizing cluster medium (Garrington, Conway Leahy 1991)."734 Crawford. Fabian (1989) inferred a high gas pressure of over 3.LO {from the ionization state of the extended. line emission, Crawford Fabian (1989) inferred a high gas pressure of over $3\times10^{5}$ from the ionization state of the extended line emission735spends most of its time and emits most of its gravitational radiation while waiting for an encounter rather than curing an interaction. we only include gravitational radiation between encounters.,"spends most of its time and emits most of its gravitational radiation while waiting for an encounter rather than during an interaction, we only include gravitational radiation between encounters."736 To isolate this effect. we run simulations both with and without gravitational radiation.," To isolate this effect, we run simulations both with and without gravitational radiation."737 We include gravitational radiation by utilizing orbit-averaged expressions for the change in seminmajor axis « and eccentricity € with respect to time (Peters1964): and where rp and mag OngZ iy) are the gravitational masses of the binary pair., We include gravitational radiation by utilizing orbit-averaged expressions for the change in semimajor axis $a$ and eccentricity $e$ with respect to time \citep{p64}: : and where $m_{0}$ and $m_{1}$ $m_{0} \ge m_{1}$ ) are the gravitational masses of the binary pair.738 Were C is (he eravitational constant. and ¢ is the speed of light.," Here $G$ is the gravitational constant, and $c$ is the speed of light."739 The orbital elements are evolved until (he next encounter takes place. at a time that we choose randomly from an exponential distribution with a mean encounter time. (Tone)=1/(neso). where n is the number density of objects in the clusters core. vy is the relative velocity. ancl σ is (he cross-section of the binary.," The orbital elements are evolved until the next encounter takes place, at a time that we choose randomly from an exponential distribution with a mean encounter time, $\left<\tau_{\mathrm{enc}}\right> = 1/\left<nv_{\infty}\sigma\right>$, where $n$ is the number density of objects in the cluster's core, $v_{\infty}$ is the relative velocity, and $\sigma$ is the cross-section of the binary."740 If we assume the mass of the binary mg+mq29mo. then where ry is (he maxinmun considered close approach of mis to the binary's center of mass.," If we assume the mass of the binary $m_{0} + m_{1} \gg m_{2}$, then where $r_{p}$ is the maximum considered close approach of $m_{2}$ to the binary's center of mass."741 For a thermal distribution of stellar speeds. ος=(nusma).Uus. Where mass=O4AL is (he average mass of the main sequence star and 04; is (ie main sequence velocity dispersion.," For a thermal distribution of stellar speeds, $v_{\infty} = \left( m_{\mathrm{avg}} / m_{2} \right)^{1/2}742v_{\mathrm{ms}}$, where $m_{\mathrm{avg}} = 0.4~\msun$ is the average mass of the main sequence star and $v_{\mathrm{ms}}$ is the main sequence velocity dispersion."743 In our simulations. the second term of Eq. 3..," In our simulations, the second term of Eq. \ref{crosssection},"744 gravitational focusing. dominates over the first.," gravitational focusing, dominates over the first."745 Averaging over velocity (assiuned to be Maxwellian) we find We then subject the binary to another encounter using orbital parameters adjusted by both the previous encounter and (he gravitational radiation emitted between the encounters., Averaging over velocity (assumed to be Maxwellian) we find We then subject the binary to another encounter using orbital parameters adjusted by both the previous encounter and the gravitational radiation emitted between the encounters.746 This sequence of encounters continues until (he binary merges due to gravitational wave emission., This sequence of encounters continues until the binary merges due to gravitational wave emission.747 If orbital decay is not being caleulated. then we determine that the binary has mergedwhen the randomly drawn encounter time is longer than the timescale to merger. which is approximately," If orbital decay is not being calculated, then we determine that the binary has mergedwhen the randomly drawn encounter time is longer than the timescale to merger, which is approximately"748[actor and is the jet comoving energy density with proton number density i!pedet,"factor and is the jet comoving energy density with proton number density $n'_{\rm p, \, jet}$."749 In the rest frame ol the jet head. the ram-lorce of the ambient medium is where paup=ΠρΠω Is the density of ambient gas around the jet head. is (he advanced. Lorentz [actor of the jet head and μι is the cross-section area of a bow-shock at the end of the jet (ΙΟ ean be larger than the cross-section area of the jet itself. Ajay=πι ).," In the rest frame of the jet head, the ram-force of the ambient medium is where $\rho_{\rm amb} = m_{\rm p} \, n_{\rm amb}$ is the density of ambient gas around the jet head, $\Gamma_{\rm head} \equiv (1 - \beta_{\rm head}^2)^{-1/2}$ is the advanced Lorentz factor of the jet head and $A_{\rm head}$ is the cross-section area of a bow-shock at the end of the jet (which can be larger than the cross-section area of the jet itself, $A_{\rm jet} = \pi R_{\rm jet}^2$ )."750 Hlere we neglect pressure of the non-thermal component within the outer lobe. what will be justified below.," Here we neglect pressure of the non-thermal component within the outer lobe, what will be justified below."751" The ram-force of the ambient medium is balanced by the momentum flix of the jet. where Ty=(1—92,)|? is the bulk Lorentz factor of the jet as measured in the rest frame of the head."," The ram-force of the ambient medium is balanced by the momentum flux of the jet, where $\Gamma_{\rm rel} \equiv (1 - \beta_{\rm rel}^2)^{-1/2}$ is the bulk Lorentz factor of the jet as measured in the rest frame of the head."752 With relation Preter=TheatPict(7j—na) One can therefore find expression for the advance velocity of the jet head where In the non-relativistic Limit with head<jel expression 5 simplifies to the appropriate equation given by Degelman&Ciolli(1989).," With relation $\Gamma_{\rm rel} \, \beta_{\rm rel} = \Gamma_{\rm head} \, \Gamma_{\rm jet} \, ( \beta_{\rm jet} - \beta_{\rm head} )$ one can therefore find expression for the advance velocity of the jet head where In the non-relativistic limit with $\beta_{\rm head} \ll \beta_{\rm jet} \ll 1$ expression 5 simplifies to the appropriate equation given by \citet{beg89}."753. A general formula for Z4 18 derived in. e.g.. Mizutaοἱal.(2004).," A general formula for $\beta_{\rm head}$ is derived in, e.g., \citet{miz04}."754. On the other hand. the brightness asvinnmetry between the head and the possible is related to the velocity 2j«4 and the jet viewing angle @ by," On the other hand, the brightness asymmetry between the head and the possible counter-head is related to the velocity $\beta_{\rm head}$ and the jet viewing angle $\theta$ by"755The central black hole mass can be. obtained. [rom the 1353 ENWILM and the optical luminosity. anc the bulge velocity. dispersion can be indicated by the ΟΠΗΣ ENIM.,"The central black hole mass can be obtained from the $\beta$ FWHM and the optical luminosity, and the bulge velocity dispersion can be indicated by the [OIII] FWHM."756 This provides us the opportunity to investigate the Ay(0 relation in a larger sample of ACGNs with available optical spectra., This provides us the opportunity to investigate the $M_{\rm bh}-\sigma$ relation in a larger sample of AGNs with available optical spectra.757 Moreover. we need to investigate this correlation ina larger sample of radio-loud AXGNs and NLSIs.," Moreover, we need to investigate this correlation in a larger sample of radio-loud AGNs and NLS1s."758 In next section we present the method to estimate the black hole mass. and then our adopted data set.," In next section we present the method to estimate the black hole mass, and then our adopted data set."759 Our results and discussion are given in section 3., Our results and discussion are given in section 3.760 C'onclusion is presented in the last section., Conclusion is presented in the last section.761" All of the cosmological caleulations in this paper assume fy=15kms1Alpe1 Oy,=0.3. Ὃν=0.7."," All of the cosmological calculations in this paper assume $H_{0}=75 \rm {~km ~s^ {-1}~Mpc^{-1}}$, $\Omega_{M}=0.3$, $\Omega_{\Lambda} = 0.7$."762 For the reverberation mapping method. it takes a long-term to simultaneously monitor the variability of the broad emission line and the continuum. and then to obtain the DBLlis size.," For the reverberation mapping method, it takes a long-term to simultaneously monitor the variability of the broad emission line and the continuum, and then to obtain the BLRs size."763 Up to now. there are only 37 ACGNs with the reverberation mapping mass (llo 1998: Wandel et al.," Up to now, there are only 37 AGNs with the reverberation mapping mass (Ho 1998; Wandel et al."764 1999: Ixaspi et al 2000)., 1999; Kaspi et al 2000).765 Fortunately. with the study of the reverberation mapping method. Ixaspi et. al. (," Fortunately, with the study of the reverberation mapping method, Kaspi et al. ("7662000) found an empirical correlation between the DLIts size and the monochromatic luminosity at. SIOOA: where AL4(5100A) can be estimated. from the optical maeinitude by adopting an average optical spectral index of -0.3 and accounting for Galactic redding ancl Ix-correction (Wang Lu 2001).,2000) found an empirical correlation between the BLRs size and the monochromatic luminosity at $\rm{\AA}$: where $\lambda L_{\lambda}(5100 \rm{\AA)}$ can be estimated from the optical maginitude by adopting an average optical spectral index of -0.3 and accounting for Galactic redding and K-correction (Wang Lu 2001).767 Assuming that the LJ: wielths rellect the Ixeplerian velocity of the line-emitting BLR. material around the central black hole. we can estimate the viral black hole Dass where €i is the gravitational constant. V is the velocity of the linc-emitting material.," Assuming that the $\beta$ widths reflect the Keplerian velocity of the line-emitting BLR material around the central black hole, we can estimate the viral black hole mass: where G is the gravitational constant, V is the velocity of the line-emitting material."768 V can be derived from WILL of the Lhe? width., V can be derived from FWHM of the $\beta$ width.769 Assuming the random: orbits. Ixaspi et al.(2000) related Voto ΕΛΛΗΝΑ of 112 line by 1—(/3/2)PWHALy .," Assuming the random orbits, Kaspi et al.(2000) related $V$ to FWHM of $\beta$ line by $V=(\sqrt{3}/2) \rm FWHM_{\rm770[H\beta]}$ ."771 This method to estimate the central black hole masses of AGNs has been discussed by some authors (Wang Lu )01: Dian Zhao 2003b: Bian Zhao 2003c: Shields et al., This method to estimate the central black hole masses of AGNs has been discussed by some authors (Wang Lu 2001; Bian Zhao 2003b; Bian Zhao 2003c; Shields et al.772 )03: Doroson 2003), 2003; Boroson 2003).773 Willams ct al. (, Willams et al. (7742003). presented a sample of 150. low-redshift NLSIs (2< 0.8) found. within the SDSS.,2003) presented a sample of 150 low-redshift NLS1s $z<0.8$ ) found within the SDSS.775 Using the SDSS Query Tool. we downloaded the spectra data and the photometry data of these 150 NLSIs.," Using the SDSS Query Tool, we downloaded the spectra data and the photometry data of these 150 NLS1s."776 We used the 113 EWIIM from their Table. 1., We used the $\beta$ FWHM from their Table 1.777 The value of AL\(SLOOA) is estimated. from the +? magnitude., The value of $\lambda L_{\lambda}(5100 \rm{\AA)}$ is estimated from the $r^{\ast}$ magnitude.778 Fluxes were converted to luminosity using the Schlegel. οἱ al.(1998) maps for correcting lor Galactic absorption., Fluxes were converted to luminosity using the Schlegel et al.(1998) maps for correcting for Galactic absorption.779 We can obtain the central black hole masses in these 150 NLSIs through equation (2) and (3)., We can obtain the central black hole masses in these 150 NLS1s through equation (2) and (3).780 Each spectrum was shifted to the rest frame and we preformed a (quadratic continuum fit., Each spectrum was shifted to the rest frame and we preformed a quadratic continuum fit.781 Using the splot tools in ΗΛΙΟ software. We measured the OLLI] PWLIAL through a Gaussian curve fit to cach OLLI] line.," Using the splot tools in IRAF software, We measured the [OIII] FWHM through a Gaussian curve fit to each [OIII] line."782 “Phe spectrum resolution Rois about 1800. which is equivalent. to 166 kms1.," The spectrum resolution R is about 1800, which is equivalent to 166 $km~ s^{-1}$."783 ‘Phe error of measured OIL]. PWLAL ancl 113 ENTM is aboutL0%., The error of measured [OIII] FWHM and $\beta$ FWHM is about.784. Phe OL] FWILAL is used to estimate the host. velocity dispersion., The [OIII] FWHM is used to estimate the host velocity dispersion.785 Lt is. dillicult to measure OLLI] ENCLAL in three NLSIs of SDSS J010226.31-003904.6. SDSS 0195932105 -004402.2. and SDSS J15324.367-004342.5 because of their OLI] line with irregular profile or. low signal-noise ratio. which are omitted in our discussion.," It is difficult to measure [OIII] FWHM in three NLS1s of SDSS J010226.31-003904.6, SDSS J013521.68 -004402.2, and SDSS J15324.367-004342.5 because of their [OIII] line with irregular profile or low signal-noise ratio, which are omitted in our discussion."786 We listed the NLSIs data in Table 1., We listed the NLS1s data in Table 1.787 bor radio-Ioud and radio-quiet AGNs. we adopted the data of the widths of LL? line anc OLLI] line from. Marziani. et al. (," For radio-loud and radio-quiet AGNs, we adopted the data of the widths of $\beta$ line and [OIII] line from Marziani et al. ("7881996).,1996).789 Marziani et al. (, Marziani et al. (7901996) used a sample of 52 Iow-redshift (2« 0.8) AGNs with available UY and. optical spectra to do à comparative analysis of high-ionization and ow-ionization lines in DLIts.,1996) used a sample of 52 low-redshift $z<0.8$ ) AGNs with available UV and optical spectra to do a comparative analysis of high-ionization and low-ionization lines in BLRs.791 ποιο are 31 racdio-Ioud AXCGNs ancl 21 racio-quict ACGNs in their sample., There are 31 radio-loud AGNs and 21 radio-quiet AGNs in their sample.792 Thes found racio-oucl and. radio-quiet. ACNs show strong cillerence on the dynamic of emission lines in BLRs., They found radio-loud and radio-quiet AGNs show strong difference on the dynamic of emission lines in BLRs.793" The sample is suitable to study the dillerence ifany on Mo,7 relation between raclio-uc and racio-equiet ACGNs.", The sample is suitable to study the difference if any on $M_{bh}-\sigma$ relation between radio-loud and radio-quiet AGNs.794 For EWHLIAL of broad component of LES line. Fell emission and the narrow component were subtracted.," For FWHM of broad component of $\beta$ line, FeII emission and the narrow component were subtracted."795 We obtained. ENIM. of 1135 line from. Column 0) and (12) in Table 8 from Marziani et al. (, We obtained FWHM of $\beta$ line from Column (10) and (12) in Table 8 from Marziani et al. (7961996).,1996).797 The absolute optical B band magnitude for these 52 AGNs are adopted [rom Veron-Cetty Veron (2001)., The absolute optical B band magnitude for these 52 AGNs are adopted from Veron-Cetty Veron (2001).798 The OIL] line widths are adopted. from. Column (17) in Table 5. from Alarziani et al. (, The [OIII] line widths are adopted from Column (17) in Table 5 from Marziani et al. (7991996).,1996).800 Phere are 48 AGNs with available widths of LL? ancl OLLI] line., There are 48 AGNs with available widths of $\beta$ and [OIII] line.801 Using equation (2) and (3). we obtained the central black hole masses of 48 ACGNs in the sample of Marziani et al. (," Using equation (2) and (3), we obtained the central black hole masses of 48 AGNs in the sample of Marziani et al. ("8021996). including 12 flat-spectrum AGNs. IS steep-spectrum AGNs. Is radio-quiet AGNs.,"1996), including 12 flat-spectrum AGNs, 18 steep-spectrum AGNs, 18 radio-quiet AGNs."803 The date are [istecd in Table 2., The date are listed in Table 2.804 In Fig., In Fig.805 1 and Fig., 1 and Fig.806 2. we plot black hole masses estimated from the LL? line width versus the bulge velocity. dispersion obtained from the OLI] line width for the samples of Alarziani ct al. (," 2, we plot black hole masses estimated from the $\beta$ line width versus the bulge velocity dispersion obtained from the [OIII] line width for the samples of Marziani et al. ("8071996). Shields et al. (,"1996), Shields et al. ("8082003). Wang Lu (2001). Nelson (2001). Boroson (2003). and Williams οἱ al. (,"2003), Wang Lu (2001), Nelson (2001), Boroson (2003), and Williams et al. ("8092003).,2003).810 The sample of Shields et al. (, The sample of Shields et al. (8112003) included 49 radio- AGNs and 35 racdio-Ioud Ανν.,2003) included 49 radio-quiet AGNs and 35 radio-loud AGNs.812 Shields et al. (, Shields et al. (8132003) used the LE3 emission line width to investigate the Aia— relation as a function of redshift for an assembled. sample of quasars.,2003) used the $\beta$ emission line width to investigate the $M_{\rm bh}-\sigma$ relation as a function of redshift for an assembled sample of quasars.814 Thes. suggested. that this correlation is not a, They suggested that this correlation is not a815As ow MD2 UV data were obtained im a spectroscopic mode. as well as obtaining the leltcwrve of the reprocessed. burst. we have a unique opportunity to exanuine its spectrum.,"As our MB2 UV data were obtained in a spectroscopic mode, as well as obtaining the lightcurve of the reprocessed burst, we have a unique opportunity to examine its spectrum."816 Fig., Fig.817 LO shows the spectra of the extra light during the first LO0ss of the burst., \ref{BurstSpecFig} shows the spectrum of the extra light during the first s of the burst.818 This was constructed by extracting a series of 1005s sib-spectra using the task and processing them im the same wav as regular spectra., This was constructed by extracting a series of s sub-spectra using the task and processing them in the same way as regular spectra.819 The nou-burst spectrum was defined from 300ss intervals before and after the burst., The non-burst spectrum was defined from s intervals before and after the burst.820 More details of the spectral reduction will be provided in Paper IT., More details of the spectral reduction will be provided in Paper II.821 The burst spectrum appears fo be contiuuuuu dominated with oulv a weak contribution from/ the nes., The burst spectrum appears to be continuum dominated with only a weak contribution from the lines.822 lis particularly strouely cuhanced. aud to a lesser extentAA... but neither dominate the fiux.," is particularly strongly enhanced, and to a lesser extent, but neither dominate the flux."823 The burst is not pronounced at all in oorAA., The burst is not pronounced at all in or.824 The coutimmun shape is consisteut with the burst models described carlicr. beiug well fitted Jn the difereuce between a black body with temperature —2T.000 KI. and one at  δν. The upper temperature corresponds to the expected," The continuum shape is consistent with the burst models described earlier, being well fitted by the difference between a black body with temperature $\sim27,000$ K and one at $\sim18,500$ K. The upper temperature corresponds to the expected"825has abrupt changes of about 90 degrees becoming roughly perpendicular to the jet. direction. during episodes related to enhanced. radio emission and opacity variations.,has abrupt changes of about 90 degrees becoming roughly perpendicular to the jet direction during episodes related to enhanced radio emission and opacity variations.826 These properties may be explained assuming a change between the opticallv-thick ancl optically-thin regime as a consequence of a shock that varies the opacity., These properties may be explained assuming a change between the optically-thick and optically-thin regime as a consequence of a shock that varies the opacity.827 In this context. the luminosity locally increases due to the compression of the plasma in the direction. of the shock propagation. causing the amplification of the perpendicular componen of the magnetic field with respect to the parallel one. anc the EVPA becomes parallel to the direction of the shock propagation.," In this context, the luminosity locally increases due to the compression of the plasma in the direction of the shock propagation, causing the amplification of the perpendicular component of the magnetic field with respect to the parallel one, and the EVPA becomes parallel to the direction of the shock propagation."828 The observed properties may also be explainec as due to a highly ordered magnetic field produced by either an oblique shock or a transverse one propagating down a jet with a curved trajectory., The observed properties may also be explained as due to a highly ordered magnetic field produced by either an oblique shock or a transverse one propagating down a jet with a curved trajectory.829 In. this case the angle of 10 electric vector ancl level of polarization strictly depen on the instantaneous angle formed by the direction. of the shock with our line of sight. thus explaining changes in the polarization angle cdillerent from the 90. degrees xpected during the transition between the opacity regimes.," In this case the angle of the electric vector and level of polarization strictly depend on the instantaneous angle formed by the direction of the shock with our line of sight, thus explaining changes in the polarization angle different from the 90 degrees expected during the transition between the opacity regimes."830 llowever. the aforementioned scenarios cannot describe the source behaviour. alter all the detected Lares and more monitoring multiwavelength campaigns are needed o properly understand the physical processes occurring in US We thank the anonymous referee for reading the manuscript carclully and making valuable suggestions.," However, the aforementioned scenarios cannot describe the source behaviour after all the detected flares and more monitoring multiwavelength campaigns are needed to properly understand the physical processes occurring in this We thank the anonymous referee for reading the manuscript carefully and making valuable suggestions."831 Phe authors are erateful to €. Brunetti for fruitful cliscussion., The authors are grateful to G. Brunetti for fruitful discussion.832 This research ms mace use of data from the ALOJAVE database that. is maintained by the MOJAVI team (Lister et al.," This research has made use of data from the MOJAVE database that is maintained by the MOJAVE team (Lister et al.,"833 2009. AJ. 137. 3718).," 2009, AJ, 137, 3718)."834 The VLBA and VLA are operated by the US ational Raclio Astronomy Observatory which is a facilitv of he National Science Foundation operated under cooperative agreement by Associated Universities. Lac. This research was mace use of the NASA/IPAC Extragalactic Database ED which is operated by the JPL. Californian Institute of ‘Technology. under contract with the National Aeronautics and Space Administration.," The VLBA and VLA are operated by the US National Radio Astronomy Observatory which is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. This research has made use of the NASA/IPAC Extragalactic Database NED which is operated by the JPL, Californian Institute of Technology, under contract with the National Aeronautics and Space Administration."835 ‘To better characterize the evolution of the source structure with a unique approach we re-analvsed. VLBA data at 15 Cllz from the MOJAVIS programme already. published. by Listeretal.(200098) and Lomanetal.(2001)., To better characterize the evolution of the source structure with a unique approach we re-analysed VLBA data at 15 GHz from the MOJAVE programme already published by \citet{lister09b} and \citet{homan01}.836. Data from each epoch were ποσοτος as described in. Section 3.3. providing a homogeneous set of observations with the same data analysis procedure.," Data from each epoch were modelfitted as described in Section 3.3, providing a homogeneous set of observations with the same data analysis procedure."837 The identification ancl monitoring of the source components is critical. when two subsequent epochs are separated by a long time interval., The identification and monitoring of the source components is critical when two subsequent epochs are separated by a long time interval.838 Indeed. if the observation time coverage ds sparse. it becomes very Πο to identify the same component at the various epochs.," Indeed, if the observation time coverage is sparse, it becomes very difficult to identify the same component at the various epochs."839 By comparing the multi-epoch visibility data we found that the source components could be reliably Followed. only in the observations from 1995 July to 1998. December. ancl since 2007.," By comparing the multi-epoch visibility data we found that the source components could be reliably followed only in the observations from 1995 July to 1998 December, and since 2007."840 Between 1995 and 1998 we could identify ancl follow a jet knot for which we derive an angular separation rate, Between 1995 and 1998 we could identify and follow a jet knot for which we derive an angular separation rate841The nature of the CRB 060505 progenitor is currently a topic of hot debate.,The nature of the GRB 060505 progenitor is currently a topic of hot debate.842 GRBs are the signatures of extraordinarily high-cucrey eveuts., GRBs are the signatures of extraordinarily high-energy events.843 Durst leneth distinguishes between “short” (< 28) bursts arising from colmpact-object mergers (Gehrels et al., Burst length distinguishes between “short” $<$ 2 s) bursts arising from compact-object mergers (Gehrels et al.844" 2005) and ""long (2 2 x) bursts with massive core-collapse progenitors (Woosley 1993) that are commonly accompanied by huninous aud broad-lined Type Ic superuovae (Watson et al.", 2005) and “long” $>$ 2 s) bursts with massive core-collapse progenitors (Woosley 1993) that are commonly accompanied by luminous and broad-lined Type Ic supernovae (Watson et al.845 2007)., 2007).846 CRB 060505 has a burst leusth of —1 s. but notably lacks evidence of an accomipauviusg supernova.," GRB 060505 has a burst length of $\sim$ 4 s, but notably lacks evidence of an accompanying supernova."847 Investigations into the host properties of GRD 060505 strongly disagree on the nature of the xoeenitor., Investigations into the host properties of GRB 060505 strongly disagree on the nature of the progenitor.848 Itis unclear whether GRB 060505 originates roni a conipact-object merger. a niswive core-collapse supernova. or a new class of loue-duration GRBs with 10 associated supernovac.," It is unclear whether GRB 060505 originates from a compact-object merger, a massive core-collapse supernova, or a new class of long-duration GRBs with no associated supernovae."849 The nature of CRB 060505 nay have important implications for our classification iid understanding of GRB progenitors., The nature of GRB 060505 may have important implications for our classification and understanding of GRB progenitors.850 GRB 060505 was observed on UTC 2006 May 5 by he Swift Burst Alert Telescope (BAT)(ITulliueer et al., GRB 060505 was observed on UTC 2006 May 5 by the Swift Burst Alert Telescope (BAT) (Hullinger et al.851 2006: ealxyPalmer et al., 2006; Palmer et al.852 2006). associated with the : = SNO 2d0FCRS SI73Z112 (Colless et al.," 2006), associated with the $z$ = 0.0889 galaxy 2dFGRS S173Z112 (Colless et al."853 2002: Ofek et al., 2003; Ofek et al.854 2006: Thóune et al., 2006; Thönne et al.855 200642: Fvubo ct al., 2006a; Fynbo et al.856 2006)., 2006).857 It was initially categorized as a loue-duration GRB based on its ~ ls burst leugth (I&ouveliotou et al., It was initially categorized as a long-duration GRB based on its $\sim$ 4 s burst length (Kouveliotou et al.858 1993)., 1993).859 Thoune Fyubo (2007) fud a lower metallicity and higher rate of star formation at the CRB 060505 burst site when compared with other regions of the host ealaxy., Thönne Fynbo (2007) find a lower metallicity and higher rate of star formation at the GRB 060505 burst site when compared with other regions of the host galaxy.860 Recent investieatious sugeest that long-duratiou GRBs are associated with lovAnetallicitv star-forming environments (Stanek et al., Recent investigations suggest that long-duration GRBs are associated with low-metallicity star-forming environments (Stanek et al.861 2006. Sollerman ct al.," 2006, Sollerman et al."862 2005. Fruchter et al.," 2005, Fruchter et al."863 2006. Ikewlev et al.," 2006, Kewley et al."864 2007. Brown et al.," 2007, Brown et al."865 2007). supporting a core-collapse progenitor scenario for CRB 060505.," 2007), supporting a core-collapse progenitor scenario for GRB 060505."866 Ou the other hand. GRD 060505 mav be the product of à compact-object iierger with a louger-than-average burst duration.," On the other hand, GRB 060505 may be the product of a compact-object merger with a longer-than-average burst duration."867 Short- aud lone-duration CRBs are separated by a burst-duration cut-off of 2 s but there nav be some overlap between these two classes of progenitor events: short-burst progenitors have a chance of vieldiug a burst longer than (IIorvátth 2002).," Short- and long-duration GRBs are separated by a burst-duration cut-off of 2 s, but there may be some overlap between these two classes of progenitor events; short-burst progenitors have a chance of yielding a burst longer than 4 s (Horvátth 2002)."868 Additional support for a conmpact-object merecr xoeenitor for GRB 060505 /includes the progenitor evolutionary timescale. the spiral nature of the lost ealaxy. and the brightuess of the burst reeion.," Additional support for a compact-object merger progenitor for GRB 060505 includes the progenitor's evolutionary timescale, the spiral nature of the host galaxy, and the brightness of the burst region."869 Ofek et al. (, Ofek et al. (8702007) calculate an upper limit of 10 Alyy for he progenitor birth-to-explosiou timescale of the GRD 160505 event.,2007) calculate an upper limit of 10 Myr for the progenitor birth-to-explosion timescale of the GRB 060505 event.871 While this age linut docs not rule out the xossibilitv of a core-collapse progenitor. such a timescale is also consistent with the mereine of two neutron stars or a neutron star-black hole merger. both of which are conrpact object merecr scenarios associated with short musts(Belezvuski et al.," While this age limit does not rule out the possibility of a core-collapse progenitor, such a timescale is also consistent with the merging of two neutron stars or a neutron star-black hole merger, both of which are compact object merger scenarios associated with short bursts (Belczynski et al."872 2006)., 2006).873 The host galaxy of CRB 160505 is categorized as an She spiral. which is uuusual or a lone-duration GRB host ealaxy (Thoune Fyubo 2007).," The host galaxy of GRB 060505 is categorized as an Sbc spiral, which is unusual for a long-duration GRB host galaxy (Thönne Fynbo 2007)."874 Fruchter et -- al.(, Fruchter et al. (8752006) found that loue-diuratiou GRBs favor the reeions of their host galaxies hat are associated with coucentrated populations of young nassve stars (vau deu Παιν Yoon 2007).,2006) found that long-duration GRBs favor the brightest regions of their host galaxies that are associated with concentrated populations of young massive stars (van den Heuvel Yoon 2007).876 The GRB 060505 progenitor region is relatively faint compared to its host ealaxy. supporting a conipact-object merecr progenitor(Ofek et al.," The GRB 060505 progenitor region is relatively faint compared to its host galaxy, supporting a compact-object merger progenitor (Ofek et al."877 2007)., 2007).878" Alternatively, GRB 060505 may. beloug to a new class of long-duration GRBs with no associated supernovae."," Alternatively, GRB 060505 may belong to a new class of long-duration GRBs with no associated supernovae."879 The distribution of knowu GRB burst durations sugecst the existence of a third category of CRBs(Mukhlerjee ot al., The distribution of known GRB burst durations suggest the existence of a third category of GRBs (Mukherjee et al.880 1995. Tlorvatth 2002).," 1998, Horvátth 2002)."881 GRB 060505 is often compared with CRB 06061 La ~102 s burst(Bartheliuv et al.," GRB 060505 is often compared with GRB 060614, a $\sim$ 102 s burst (Barthelmy et al."882 2006) classified as a long GRD with no apparent superuova counterpart - both have been proposed as represents exaluples of a new class of CRBs d.(Fyubo ct al., 2006) classified as a long GRB with no apparent supernova counterpart - both have been proposed as representative examples of a new class of GRBs (Fynbo et al.883 2006 Jakobsson Fyubo 2007. ine ct ," 2006, Jakobsson Fynbo 2007, King et al."8842007)., 2007).885 Schaefer Xiao (2006) sugeest that GRB 060505 is a backeround event that hasbeen associated with 2dFCRS S173Z112 bv coincidence., Schaefer Xiao (2006) suggest that GRB 060505 is a background event that has been associated with 2dFGRS S173Z112 by coincidence.886 However. Watson et al. (," However, Watson et al. ("8872007) estimate that the superposition. of the burst directlv over a star-formüng region of low iuctalliitv would be nureasonably serendipitous.,2007) estimate that the superposition of the burst directly over a star-forming region of low metallicity would be unreasonably serendipitous.888" There are several reasous to believe that the progenitors of long-duration bursts would favor low-metallicity environments,", There are several reasons to believe that the progenitors of long-duration bursts would favor low-metallicity environments.889 Mass loss in late-tvpe massive stars. driven by radiation pressure on spectral lines.," Mass loss in late-type massive stars, driven by radiation pressure on spectral lines,"890while the characteristic timescale of the radiative processes is below 200s (Oke.Giver&Searle1962... Buonauraetal. 1985)).,"while the characteristic timescale of the radiative processes is below $200\mbox{s}$ \citealt{oke1}, \citealt{buon1}) )."891 The cllect of the variable effective. gravity can be characterized. by our Condition HL. which provides information whether QSAA may. be assumed.," The effect of the variable effective gravity can be characterized by our Condition II, which provides information whether QSAA may be assumed."892 The limits are 4.5ems2/25008ο”«14200ems.7/2500s.," The limits are $4.5\mbox{cms}^{-2}/2500\mbox{s} 893 < \vert \partial g_{\rm e}/\partial t \vert <894 14200 \mbox{cms}^{-2}/2500\mbox{s}$."895 ‘Phe upper Limit comes from the rising branch of the light curve. when the main shock hits the atmosphere.," The upper limit comes from the rising branch of the light curve, when the main shock hits the atmosphere."896 In general. the photometric input of the present method is identical with that of the DW. method.," In general, the photometric input of the present method is identical with that of the BW method."897 In. order to obtain the fundamental parameters. radial velocity data and their. problematic conversion to. pulsation velocities are notnecessary.," In order to obtain the fundamental parameters, radial velocity data and their problematic conversion to pulsation velocities are notnecessary."898 On the other hand. 9 and. fy must be differentiated numerically. dilferential quotients are sensitive to the non-valicity of QSAA.," On the other hand, $\vartheta$ and $h_0$ must be differentiated numerically, differential quotients are sensitive to the non-validity of QSAA."899 Our photometric and byerodvnamic considerations revealed empirical quantitative conditions to| find the phase intervals of the pulsation when static model atmospheres of Ixurucz(L997) are satisfactory to derive the variable and non-variable physical parameters. of the pulsating atmosphere., Our photometric and hydrodynamic considerations revealed empirical quantitative conditions to find the phase intervals of the pulsation when static model atmospheres of \citet{kuru1} are satisfactory to derive the variable and non-variable physical parameters of the pulsating atmosphere.900 Outside these intervals. dyvnamical mocel atmospheres are necessary to refine the parameters from QSAA. which is beyond the scope of the present. paper.," Outside these intervals, dynamical model atmospheres are necessary to refine the parameters from QSAA, which is beyond the scope of the present paper."901 The fundamental parameters d. A. Αν ECBV) were determined. using photometric quantities onlv. in phases when the QSAA is à good approximation (ie. both Conditions L and Ll were satisfied).," The fundamental parameters $d$, ${\cal M}$, $[M]$, $E(B-V)$ were determined using photometric quantities only in phases when the QSAA is a good approximation (i.e. both Conditions I and II were satisfied)."902 Phe values obtained from averaging over the entire pulsation evele can be considered as a first approximation only. because QS.AA was assumed in all phases regardless of it being à good or poor approximation.," The values obtained from averaging over the entire pulsation cycle can be considered as a first approximation only, because QSAA was assumed in all phases regardless of it being a good or poor approximation."903 The large error of Ley and (Ady) originates [rom Ad/d.1 of our best value. *] in Table 2.., The large error of $L_{\rm eq}$ and $\langle M_V \rangle$ originates from $\Delta d/d \approx .1$ of our best value $[\ast]$ in Table \ref{tab2}.904 To give an impression on the accuracy of inverting the CBVGe: photometry to physical. parameters. the comparison star DD. |67 TOS was used. because its colours are similar to those of SU Dra (Bareza2002.. Table 3).," To give an impression on the accuracy of inverting the $UBV(RI)_C$ photometry to physical parameters, the comparison star BD +67 708 was used, because its colours are similar to those of SU Dra \citealt{barc0}, Table 3)."905 The results are M]=O77x03. ΗΕV)=000. 9=(1.9132-.002)-10.2? rad loeg—3.504501. 7.= 7505475I. The errors are roughly in the same order of magnitude as those of SU Dra when Conditions E and LE are satisfied.," The results are $[M]=-0.77\pm .03$, $E(B-V)=.000$, $\vartheta=(1.913\pm .002)\times 10^{-10}$ rad, $\log906g=3.59\pm .01$, $T_{\rm e}=7505\pm 5$ K. The errors are roughly in the same order of magnitude as those of SU Dra when Conditions I and II are satisfied."907 Figs., Figs.908. 3cc. d demonstrate that significant corrections must be added to £e. P? ifthe true pulsation velocity and acceleration are required. at QO<or«1.," \ref{fig3}c c, d demonstrate that significant corrections must be added to ${\dot R}$, ${\ddot R}$ if the true pulsation velocity and acceleration are required at $0 \le \tau < 1$."909 Moreover. the triangles show another correction +.6kms3<eu)=hteS3kms| i Od<c06. Le ring)=HASe(Bzxv)hu(BD.Lo is the velocity profile.," Moreover, the triangles show another correction $-4.6\mbox{kms}^{-1} < {\bar v}(R,\varphi)910=h_0^{-1}\partial v/\partial r < 8.3\mbox{kms}^{-1}$ if $0.1 < \varphi < 0.6$, i.e. $v(r,\varphi)=v(R,\varphi)-{\bar v}(R,\varphi)(R-r)h_0(R,\varphi)911+ \cdots$ is the velocity profile."912 In other words. even in the shock free phases. considerable phase- velocity. ancl acceleration gradients exist in the lavers Roof)<r< Rol the line formation.," In other words, even in the shock free phases, considerable phase-dependent velocity and acceleration gradients exist in the layers $R-h_0^{-1} < r < R$ of the line formation."913 The problem of ο= Ois present in all phases. ie. even in the shock free intervals. which are used in modern. DW analyses (e.g. Liu&Janes 1900)).," The problem of ${\bar v}\not=0$ is present in all phases, i.e. even in the shock free intervals, which are used in modern BW analyses (e.g. \citealt{liuj1}) )."914 The non-uniform motion of the outermost layers introduces uncertainty when pulsation velocitics are determined. because the centre of mass velocity ὃς must be subtracted from the observed radial velocities.," The non-uniform motion of the outermost layers introduces uncertainty when pulsation velocities are determined, because the centre of mass velocity $v_\gamma$ must be subtracted from the observed radial velocities."915 A recent exposition of the problem for Cepheid stars is given in Nardettoctal.(2009)., A recent exposition of the problem for Cepheid stars is given in \citet{nard1}.916. ὃν definition. ?.0.)d refer to 0Tow l. while the variable component of the B.radial velocity is an average of velocities (e.g. (9))) over the lavers A?hyrcRie 0Xτο».," By definition $\vartheta,{\dot\vartheta},{\ddot\vartheta}$ refer to $0 \le \tau \ll 1$ , while the variable component of the radial velocity is an average of velocities (e.g. \ref{2.302}) )) over the layers $R-h_0^{-1} \la r < R$ i.e. $0\le \tau \la 0.3$."917" Phe effect on re and d has not vet been studied at all,", The effect on $v_\gamma$ and $d$ has not yet been studied at all.918" Nevertheless. the importance is obvious. since an error of 1lkms+ in e, results in an error Ad/d=0.1 (Gautschy1987)."," Nevertheless, the importance is obvious, since an error of $1\:\mbox{kms}^{-1}$ in $v_\gamma$ results in an error $\Delta d/d \approx 0.1$ \citep{gaut1}."919. There is a considerable uncertainty of er. in the literature. suggesting an error of d as large as a [factor of 2.," There is a considerable uncertainty of $v_\gamma$ in the literature, suggesting an error of $d$ as large as a factor of 2."920 Lt sullices to mention that for SU Dra rm=o161.166.9kmsLowe given by Oke.Giver&Searle(1962) and Liu&Janes(1990) from high dispersion spectra and spectral masking method CORAVEL. respectively.," It suffices to mention that for SU Dra $v_\gamma=-161,-166.9\mbox{kms}^{-1}$ are given by \citet{oke1} and \citet{liuj1} from high dispersion spectra and spectral masking method CORAVEL, respectively."921 Awavy fine structure in the variation of 2 is clearly seen in Figs. 1..," A wavy fine structure in the variation of $R$ is clearly seen in Figs. \ref{fig1},"922 3bb. Standstills are at νο2:0.25.0.55.0.78. when the outward motion is reversed. while the outward motion starts alter short. stancdstills at ο20.45.0.74.0.94-0.98.," \ref{fig3}b b. Standstills are at $\varphi\approx 0.25,0.55,0.78$, when the outward motion is reversed, while the outward motion starts after short standstills at $\varphi\approx 0.45,0.74,0.94\mbox{-}0.98$."923 They are without. doubt real. because the beginnings of the outward motion are connected with significant maxima in Lif).logge).," They are without doubt real, because the beginnings of the outward motion are connected with significant maxima in $T_{\rm e}(\varphi),\log g_{\rm e}(\varphi)$."924 The well known bump ancl hump a yo=O74.0940098 (Smith1995). in the light curve are caused by the precursor and main shocks. respectively.," The well known bump and hump at $\varphi\approx 0.74,0.94\mbox{-}0.98$ \citep{smit1} in the light curve are caused by the precursor and main shocks, respectively."925 A yo&O45. a small change is observable in the slope of the light curve (Bareza&DBenkó2009).," At $\varphi\approx 0.45$, a small change is observable in the slope of the light curve \citep{barc3}."926. ασια. the existence of a shock is à new fincine.," Here, the existence of a shock is a new finding."927 It is a pre-precursor. shock: we propose the designationjaan forit., It is a pre-precursor shock; we propose the designation forit.928 By integrating raclia velocities. authors tend to smooth out the mentioned. [ine structure of motions (e.g. Liu&Janes1990. in the case of SW And).," By integrating radial velocities, authors tend to smooth out the mentioned fine structure of motions (e.g. \citealt{liuj1} in the case of SW And)."929 This practice seems to be unjustifiecd., This practice seems to be unjustified.930 In the interval 45=0.82-0.90. the atmosphere is roughly in standstill. the brightness starts rising. a small depression of Ui).οσα) is visible at 4520.84-0.86. but. τν). is monotonic.," In the interval $\varphi\approx 0.82\mbox{-}0.90$, the atmosphere is roughly in standstill, the brightness starts rising, a small depression of $\vartheta(\varphi),\log g_{\rm e}(\varphi)$ is visible at $\varphi\approx 0.84\mbox{-}0.86$, but $T_{\rm e}(\varphi)$ is monotonic."931 It is not clear whether the small undulation of aeD) around (1.571-1.579)«10.1 is real or not. because the maximal Aloggq=0.116 was found just at y=0.58.," It is not clear whether the small undulation of $\vartheta(\varphi)$ around $(1.571\mbox{-}1.579)\times 10^{-10}$ is real or not, because the maximal $\Delta\log g_{\rm e}=0.116$ was found just at $\varphi=0.88$."932 Surprisingly. in comparison with previous studies. considerabledifferences were. found. —only in. —5. Lag.," Surprisingly, in comparison with previous studies, considerabledifferences were found only in $\langle T_{\rm e}\rangle$, $T_{\rm eq}$."933 This is due to the facet that the interpolatect 1νί} depends on logg.(4) and that the information from a five colour photometry was used in a more complex manner: averaged: value from 30 colour index pairs was utilized., This is due to the fact that the interpolated $T_{\rm e}(\varphi)$ depends on $\log g_{\rm e}(\varphi)$ and that the information from a five colour photometry was used in a more complex manner: averaged value from 30 colour index pairs was utilized.934 The photometry covers the whole spectrum. between 350 and 1000 nm., The photometry covers the whole spectrum between 350 and 1000 nm.935" The use of one colour index only. eg. VoA solely ""because of its apparent merits” (Liu&Janes1990).. can result in systematic error of 7:62)."," The use of one colour index only, e.g. $V-K$ solely “because of its apparent merits” \citep{liuj1}, can result in systematic error of $T_{\rm e}(\varphi)$."936 H0 can. explain he =350 lx dillerence. because in that previous work QSAA was assumed in all phases regardless of violating yoth Conditions E anc Η.," It can explain the $\approx 350$ K difference, because in that previous work QSAA was assumed in all phases regardless of violating both Conditions I and II."937 An inspection of the functions (ESoggeeCli.Cle.ALJ.(Bο derived from the ables (Ixurucz1997). shows that. WVif merely one colour index is to be used. the optimal choice for determining 2. would » Be dee ," An inspection of the functions $\{T_{\rm e}^{(i)}(\log g_{\rm e},{\rm CI}_1,{\rm CI}_2,[M],E(B-V))\}_938{i=1,2}$ derived from the tables \citep{kuru1} shows that, if merely one colour index is to be used, the optimal choice for determining $T_{\rm e}$ would be $R_C-I_C$ ."939Phis is because Fe Feds almost independent of log lor the actual values of Ad] and LUV) of SU Dra., This is because $R_C-I_C$ is almost independent of $\log g_{\rm e}$ for the actual values of $[M]$ and $E(B-V)$ of SU Dra.940 However.ge in phases violating Condition Ll. the sole use of fle:lc would also introduce a systematic error. similarly to the use of V dy.," However, in phases violating Condition I, the sole use of $R_C-I_C$ would also introduce a systematic error, similarly to the use of $V-K$ ."941 There is a remarkable decrease of Ad=200 67pc. AM=0.100.03.44. if our compressible QSAA is substituted. for UA. ie. more physical input is used. in the frame of a one-dimensional model in space.," There is a remarkable decrease of $\Delta d=200\rightarrow94267\mbox{pc}$ , $\Delta {\cal M}=0.10\rightarrow 0.03{\cal M}_\odot$ if our compressible QSAA is substituted for UAA, i.e. more physical input is used in the frame of a one-dimensional model in space."943 Since (10)) was derived. from the dynamic. equation (3)). the mass determination is more accurate from it while the distance is," Since \ref{107a}) ) was derived from the dynamic equation \ref{1.100}) ), the mass determination is more accurate from it while the distance is"944even if &.>1 is satisfied. multiple images can occur only when the source is located within Yer= Yee). where cu is determined. from thelensing equation (eq.|23]]),"even if $\kappa_c>1$ is satisfied, multiple images can occur only when the source is located within $y_\mathrm{cr}=y(x_\mathrm{cr})$ , where $x_\mathrm{cr}$ is determined from thelensing equation (eq.\ref{lenseq1}] ])"945 with dy/d.r=0 Or .r«O0 (this is similar to lensine by NEW halos)., with $dy/dx=0$ for $x<0$ (this is similar to lensing by NFW halos).946 For a singular clensity profile such as the SIS and NEW profiles. the central value is divergent. so &>1 is always satisfied. ancl nuulüple images can be produced [or any given mass.," For a singular density profile such as the SIS and NFW profiles, the central value is divergent, so $\kappa>1$ is always satisfied, and multiple images can be produced for any given mass."947 For densitv profiles with a finite soft core such as the NTIS profile. however. the condition #>1 requires that only halos with nass ereater (han a certain value (determined by &.=1) can produce multiple images.," For density profiles with a finite soft core such as the NTIS profile, however, the condition $\kappa>1$ requires that only halos with mass greater than a certain value (determined by $\kappa_c=1$ ) can produce multiple images."948" This is Clearly shown in Figure 1. where (hree curves lore. =1.1.1.05. and 1.0 are plotted. aud when s,=1.0. only one image is produced."," This is clearly shown in Figure 1, where three curves for $\kappa_c=1.1, 1.05$, and $1.0$ are plotted, and when $\kappa_\mathrm{c}=1.0$, only one image is produced."949 Iu lensing statistics. this requirement will limit the populations of lensing halos to quite a small fraction.," In lensing statistics, this requirement will limit the populations of lensing halos to quite a small fraction."950 Such a conclusion is valid for any lensing halos with a finite soft core. which is discussed in detail later.," Such a conclusion is valid for any lensing halos with a finite soft core, which is discussed in detail later."951" When quasars at redshift 2, are lensed by foreground CDM halos of galaxies ancl clusters ol galaxies. the lensing probability for image separations larger (han A@ is 1984:Schneider.Ehlers.&Faleo1992) where ος) is the redshilt distribution for quasars approximated by a Gaussian model with a mean of 1.27 and a dispersion of 0.95 (IIelbieetal.1999:Marlow2000:etal.2002:Myers 2003)... DP(2) is the proper distance from the observer to thelens located at redshilt z. 5(M.2) is the physical number density of virialized dark halos of masses between 4M and A4M. and B(M.z)isthe magnification bias."," When quasars at redshift $z_{\mathrm{s}}$ are lensed by foreground CDM halos of galaxies and clusters of galaxies, the lensing probability for image separations larger than $\Delta\theta$ is \citep{turner,schne}952 where $\mathcal{P}(z_\mathrm{s})$ is the redshift distribution for quasars approximated by a Gaussian model with a mean of 1.27 and a dispersion of 0.95 \citep{helbig1999,marlow2000,chae02,myers}, $D_{\mathrm{L}}^\mathrm{p}(z)$ is the proper distance from the observer to thelens located at redshift $z$, $\bar{n}(M,z)$ is the physical number density of virialized dark halos of masses between $M$ and $M+dM$, and $B(M,z)$ is the magnification bias."953 The physical number density n(M.z) is related to the comoving number density n(M.z) by n(M.z)=nCAl.2)(1uz) the latter is originally given by Press&Sehechter(1974).. ancl the extended: versionis nCM.z)dM=(poM)fGCM.z)dM. where py is the current mean mass density of the universe and is (he mass function for which we use (he expression given by Jenkinsοἱal.(2001).," The physical number density $\bar{n}(M,z)$ is related to the comoving number density $n(M,z)$ by $\bar{n}(M,z)=n(M,z)(1+z)^3$; the latter is originally given by \citet{press74}, and the extended versionis $n(M,z)dM=(\rho_0/M)f(M,z)dM$, where $\rho_0$ is the current mean mass density of the universe and is the mass function for which we use the expression given by \citet{jenki}."954". In {his expression. A,=0,.f2)/ACAL). in which 9.(2) is the overdensity threshold lor spherical collapse αἱ τους z and ACAL) is the rms of the present variance of the f[Inctuations in a sphere containing a mean mass AL."," In this expression, $\Delta_{\mathrm{z}}=\delta_c(z)/\Delta(M)$, in which $\delta_c(z)$ is the overdensity threshold for spherical collapse at redshift $z$ and $\Delta(M)$ is the rms of the present variance of the fluctuations in a sphere containing a mean mass $M$."955" The overdensity threshokl is given by for the ACDM cosmology(Navarro.Frenk.&White 1997).. where is the linear growth function of the density perturbation (Carroll. 1992).. in which g(r)=0.5r(1/70+200%/140—22/140+P"")* and O(z)=On4+2)°/[L-O402 z:)7]."," The overdensity threshold is given by $\delta_c(z)=1.68/D(z)$ for the $\Lambda$ CDM cosmology\citep{nfw97}, , where $D(z)=g[\Omega(z)]/[g(\Omega_{\mathrm{m}})(1+z)]$ is the linear growth function of the density perturbation \citep{carroll}, , in which $g(x)=0.5x(1/70+209x/140-x^2/140+x^{4/7})^{-1}$ and $\Omega(z)=\Omega_{\mathrm{m}}(1+z)^3956/[1-\Omega_{\mathrm{m}}+\Omega_{\mathrm{m}}(1+z)^3]$ ."957 When we caletdate the variance of the fluctuations ANC(M). we use the fitting formae for the CDM power spectrum P(/)=AET?(&) given by," When we calculate the variance of the fluctuations $\Delta^2(M)$ , we use the fitting formulae for the CDM power spectrum $P(k)=AkT^2(k)$ given by"958cwarfs.,dwarfs.959 We limit the discussion to models with solar metallicity., We limit the discussion to models with solar metallicity.960 The sedimentation parameter of the cloud mocel is fixed at foo=3. which gives a good representation of far-red and photometry of L dwarls (Marley. et al.," The sedimentation parameter of the cloud model is fixed at $f_{\rm sed}=3$, which gives a good representation of far-red and near-IR photometry of L dwarfs (Marley et al."961 2002: Bureasser οἱ al., 2002; Burgasser et al.962 2002) and of (he ammonia cloud deck of Jupiter as well (Ackerman Marley 2001)., 2002) and of the ammonia cloud deck of Jupiter as well (Ackerman Marley 2001).963 For simplicity. we do not take into account the possibility of cloud disruption near the L/T boundary (Durgasser et al.," For simplicity, we do not take into account the possibility of cloud disruption near the L/T boundary (Burgasser et al."964 2002)., 2002).965 The combination of ΗνΑς: photometry aud IRS spectroscopy with eround-based optical and near-IR. data will give the complete spectral energy distributions (SED) of many brown cdwarfs., The combination of IRAC photometry and IRS spectroscopy with ground-based optical and near-IR data will give the complete spectral energy distributions (SED) of many brown dwarfs.966 Empirical bolometric corrections immediately follow as well as the bolometric Iuminosity for objects with known parallaxes., Empirical bolometric corrections immediately follow as well as the bolometric luminosity for objects with known parallaxes.967 An independent determination of Tig (e.g. by fitting spectra wilh models) will give the eravily. radius. and mass of individual brown dwarts.," An independent determination of $\Teff$ (e.g. by fitting spectra with models) will give the gravity, radius, and mass of individual brown dwarfs."968" lt is well known that in the far-red and near-IR. the brightness temperature 7j, οἱ brown clwarls varies stronglv with wavelength due to (he high. contrast between. opacity windows and molecular absorption bands."," It is well known that in the far-red and near-IR, the brightness temperature $T_{\rm br}$ of brown dwarfs varies strongly with wavelength due to the high contrast between opacity windows and molecular absorption bands."969" This is still true in the mid-IR. up to about jam. thereafter T1, gradually decreases to stabilize at ~75% of Tir bevond jam. Only near jan and near sau does Tj, become as large as Tig."," This is still true in the mid-IR up to about $\,\mu$ m, thereafter $T_{\rm br}$ gradually decreases to stabilize at $\sim$ of $\Teff$ beyond $\,\mu$ m. Only near $\,\mu$ m and near $\,\mu$ m does $T_{\rm br}$ become as large as $\Teff$."970 For 4Slogg(ces)5.5. the pressure ad (he mid-IR. photosphere stavs between 0.1 and bar. depending mostly on wavelength. aud surface gravitv and least on Zi.," For $4 \wig< \log g \,({\rm cgs}) \wig< 5.5$, the pressure at the mid-IR photosphere stays between 0.1 and $\,$ bar, depending mostly on wavelength and surface gravity and least on $\Teff$."971 Basically. the mid-IR spectra of brown clwarls ave formed al PSTey and pressures of about bar.," Basically, the mid-IR spectra of brown dwarfs are formed at $T\wig< \Teff$ and pressures of about $\,$ bar."972" Figure 1 identifies (he mid-IR molecular absorbers in a sequence of spectra from 600 (o 2400Ix. By Dar. the most important. absorber is H3O (throughout the entire spectral range. except for two strong molecular bands due to CLL, and δι."," Figure 1 identifies the mid-IR molecular absorbers in a sequence of spectra from 600 to $\,$ K. By far, the most important absorber is $_2$ O throughout the entire spectral range, except for two strong molecular bands due to $_4$ and $_3$."973 Devond jn. all features are due to H5O0. with the exception of a lew weak NII4 bands between 32 and jn for models with TirS800 IN. In the high-7iy spectra. the fundamental band of CO at sam and a weak TiO band at jm are the only features not originating from Π.Ο. The step in the spectrum ~6.5 jm is a IH5O0 feature.," Beyond $\,\mu$ m, all features are due to $_2$ O, with the exception of a few weak $_3$ bands between 32 and $\,\mu$ m for models with $\Teff \wig< 800\,$ K. In the $\Teff$ spectra, the fundamental band of CO at $\,\mu$ m and a weak TiO band at $\,\mu$ m are the only features not originating from $_2$ O. The step in the spectrum $\sim 6.5\,\mu$ m is a $_2$ O feature."974 The TiO band disappears at 2200Ix but the CO band persists down to 900IX in these cloudy models.," The TiO band disappears at $\,$ K but the CO band persists down to $\,$ K in these cloudy models."975 As Zi decreases. new molecular bands appear and steacily increase in strength.," As $\Teff$ decreases, new molecular bands appear and steadily increase in strength."976 The pam band of NI; appears at I. This band is very broad and dominates the spectrum from 3.5 to 1640n ab Teg500 Ix. Weaker bands of NI appear al 900Ix (5.5. Tyan) and 800IN (8.9 jan).," The $\,\mu$ m band of $_3$ appears at $\,$ K. This band is very broad and dominates the spectrum from 8.5 to $\,\mu$ m at $\Teff \le 800\,$ K. Weaker bands of $_3$ appear at $\,$ K (5.5 – $\,\mu$ m) and $\,$ K (3.9 – $\,\mu$ m)."977 The former is superimposed on a, The former is superimposed on a978corresponding to the four main molecular clouds in the whole region.,corresponding to the four main molecular clouds in the whole region.979 Therefore. assuming that each of the four molecular clouds is made from material at the same distance. which ts reasonable given the localized morphology of the emission. each clump is assumed to be at the same distance as the cloud it belongs to (see Table 3)).," Therefore, assuming that each of the four molecular clouds is made from material at the same distance, which is reasonable given the localized morphology of the emission, each clump is assumed to be at the same distance as the cloud it belongs to (see Table \ref{param_nubi}) )."980 This leaves the question of the ambiguity. which we discuss in Sect. ??..," This leaves the question of the ``near-far ambiguity”, which we discuss in Sect. \ref{starformationassociation}."981 The spectrum of the emission of each identified clump was obtained by integrating the 'CO(I-0) data cube in the channels of the emission of the clump. over the area enclosed by the deconvolved contour level of the CO 1-0) emission.," The spectrum of the emission of each identified clump was obtained by integrating the $^{13}$ CO(1-0) data cube in the channels of the emission of the clump, over the area enclosed by the deconvolved contour level of the $^{13}$ CO(1-0) emission."982 The spectra of clump co4 and clump col9 have been derived from the higher velocity resolution (0.5 uns !) data-cube. as discussed in the previous section.," The spectra of clump co4 and clump co19 have been derived from the higher velocity resolution (0.5 km $^{-1}$ ) data-cube, as discussed in the previous section."983 The parameters of each clump were determined by fitting a Gaussian profile to each produced spectrum., The parameters of each clump were determined by fitting a Gaussian profile to each produced spectrum.984 Line profiles showing more than one velocity component were analyzed by fitting more than one Gaussian component. in order to remove the contribution to the emission by other clumps along the line of sight from the emission coming from the clump of interest.," Line profiles showing more than one velocity component were analyzed by fitting more than one Gaussian component, in order to remove the contribution to the emission by other clumps along the line of sight from the emission coming from the clump of interest."985 The results of this analysis are reported in Table 3.., The results of this analysis are reported in Table \ref{param_nubi}.986 Figure 4. shows the APEX 870 ym continuum emission from the same region we observed in the 'CO(1-0) emission line (see Fig. 1))., Figure \ref{identif-cont} shows the APEX 870 $\mu$ m continuum emission from the same region we observed in the $^{13}$ CO(1-0) emission line (see Fig. \ref{integr_tot}) ).987 The data are part of the ATLASGAL project 2009))., The data are part of the ATLASGAL project ).988 The white ellipses represent: 1) the GMC surrounding G19.61-0.23. which is the 33-48 km s! ⋯⋃∣⊜∁∐∣⋅≏∐⋪⊱⊺∐⋋⋖∁∣∪⋯↿⊐⇅∐⋋∁∐⋋⋋⊜∐≣∏⊱⊜∁↾↜∎⋅≱∎⋅≱∷," The white ellipses represent: 1) the GMC surrounding G19.61-0.23, which is the 33–48 km $^{-1}$ molecular gas (cloud 2) discussed in Sect. \ref{kinematics};"989 and 2) the km s! molecular gas (cloud 3) discussed in Sect., and 2) the 54--63 km $^{-1}$ molecular gas (cloud 3) discussed in Sect.990 ?? (see also Fig. 1))., \ref{kinematics} (see also Fig. \ref{integr_tot}) ).991 We decided to use a threshold of 10 «c to identify the different sources in the continuum emission., We decided to use a threshold of 10 $\sigma$ to identify the different sources in the continuum emission.992 In this way. we identified in the APEX continuum emission 14 sources. which aree shown in Fig.," In this way, we identified in the APEX continuum emission 14 sources, which are shown in Fig."993 4. with their respective labels., \ref{identif-cont} with their respective labels.994" Most of the APEX continuum sources have counterparts in one of the FCRAO ""CO(I-0) clumps (see also Fig.", Most of the APEX continuum sources have counterparts in one of the FCRAO $^{13}$ CO(1-0) clumps (see also Fig.995 A3 in the Online Material Sect).," \ref{CO-apex-spitzer} in the Online Material Sect.),"996 with the exception of sources C8 and C9., with the exception of sources C8 and C9.997 Source C8 ts associated with significant emission in the 'CO(1-0) line. but over a region slightly to the south of C8 (see Fig. A3).," Source C8 is associated with significant emission in the $^{13}$ CO(1-0) line, but over a region slightly to the south of C8 (see Fig. \ref{CO-apex-spitzer}) )."998" The ""CO(1-0) emission in this case corresponds to CO clump co7. which “contains” the APEX sources C8 and C7."," The $^{13}$ CO(1-0) emission in this case corresponds to $^{13}$ CO clump co7, which “contains” the APEX sources C8 and C7."999" We thus assume for both C8 and C7 the distance corresponding to ""CO 8.", We thus assume for both C8 and C7 the distance corresponding to $^{13}$ CO 8.1000" C9 is associated with ""CO emission at 62 km s∣ and hence probably to cloud 3.", C9 is associated with $^{13}$ CO emission at 62 km $^{-1}$ and hence probably to cloud 3.1001 Moreover. given the lower resolution of the 'CO data. the continuum sources C3 and C4 correspond both to clump co3 in the FCRAO CO(I-0) emission.," Moreover, given the lower resolution of the $^{13}$ CO data, the continuum sources C3 and C4 correspond both to clump co3 in the FCRAO $^{13}$ CO(1-0) emission."1002 Column 8 of Table 4 indicates the counterpart. if any. of each APEX continuum source. as identified from the comparison between the CO emission and the APEX continuum emission.," Column 8 of Table \ref{param_cont} indicates the counterpart, if any, of each APEX continuum source, as identified from the comparison between the $^{13}$ CO emission and the APEX continuum emission."1003" It 1s worth noting that the two maps (""CO map and APEX continuum maps) have significantly different resolutions. with the APEX resolution being 182 at 870 ym and the FCRAO resolution being 46” at the frequency of the 'CO(1-0) line."," It is worth noting that the two maps $^{13}$ CO map and APEX continuum maps) have significantly different resolutions, with the APEX resolution being $18.\!\!^{\prime\prime}2$ at 870 $\mu$ m and the FCRAO resolution being $^{\prime\prime}$ at the frequency of the $^{13}$ CO(1-0) line."1004 Therefore it is not surprising that the sources identified in the APEX contiuum emission are more compact than the CO clumps (as seen also in Fig. A3)., Therefore it is not surprising that the sources identified in the APEX continuum emission are more compact than the $^{13}$ CO clumps (as seen also in Fig. \ref{CO-apex-spitzer}) ).1005 Moreover. the 870 uim continuum emission probably traces dense cores embedded in the CO(I- 0) clumps.," Moreover, the 870 $\mu$ m continuum emission probably traces dense cores embedded in the $^{13}$ CO(1-0) clumps."1006" For the APEX continuum sources that have a counterpart in the FCRAO ""CO(I-0) emission. we assume as distance the one of the corresponding '*CO(CI-0) clump."," For the APEX continuum sources that have a counterpart in the FCRAO $^{13}$ CO(1-0) emission, we assume as distance the one of the corresponding $^{13}$ CO(1-0) clump."1007 The obtained distances are reported in col., The obtained distances are reported in col.1008 9-10 of Table 4 (see Sect.," 9-10 of Table \ref{param_cont}1009 (see Sect."1010 ?? and Table 3)., \ref{identif} and Table \ref{param_nubi}) ).1011 One of our aims ts to compare the properties of the molecular clumps with and without star formation within them., One of our aims is to compare the properties of the molecular clumps with and without star formation within them.1012" With this in mind. we have compared images from the GLIMPSE 2003)) and MIPSGAL mid infrared surveys 2005)) with both ATLASGAL maps and our FCRAO ""CO data (supplemented by the BU-FCRAO GRS)."," With this in mind, we have compared images from the GLIMPSE ) and MIPSGAL mid infrared surveys ) with both ATLASGAL maps and our FCRAO $^{13}$ CO data (supplemented by the BU-FCRAO GRS)."1013" It is worth recalling that the MIPSGAL 70 jm survey has a ""beam"" of 18"". which is comparable to that of ATLASGAL."," It is worth recalling that the MIPSGAL 70 $\mu$ m survey has a “beam” of $18^{\prime\prime}$, which is comparable to that of ATLASGAL."1014 Moreover. the GLIMPSE 8 um data traces PAH emission excited by UV from OB stars close to GMCs whereas the 24 iim MIPSGAL radiation often traces dust heated by embedded proto-stellar objects.," Moreover, the GLIMPSE 8 $\mu $ m data traces PAH emission excited by UV from OB stars close to GMCs whereas the 24 $\mu$ m MIPSGAL radiation often traces dust heated by embedded proto-stellar objects."1015 Also. the 4.5 uum GLIMPSE data has been found often to trace molecular hydrogen emission associated with outflows.," Also, the 4.5 $\mu$ m GLIMPSE data has been found often to trace molecular hydrogen emission associated with outflows."1016 In Fig., In Fig.1017" A3 (online. version). we superpose FCRAO ""CO and ATLASGAL maps to Spitzer images at 3.6. 8 and 24 um. One sees here that there are several ATLASGAL sources associated with strong continuum emission in the Spitzer bands."," \ref{CO-apex-spitzer} (online version), we superpose FCRAO $^{13}$ CO and ATLASGAL maps to Spitzer images at 3.6, 8 and 24 $\mu$ m. One sees here that there are several ATLASGAL sources associated with strong continuum emission in the Spitzer bands."1018 Table 5. summarizes these associations (within 1) as well as the information about maser emission and HII regions close to the positions of continuum emission., Table \ref{SFassociations} summarizes these associations (within $^{\prime}$ ) as well as the information about maser emission and HII regions close to the positions of continuum emission.1019 Not surprisingly. there is strong mid infrared emission from the vicinity of clumps Cl and C2 which are associated. with the HII region complex G19.61-0.23 but one also notes strong emissio associated with the C7/C8 complex and with CI2.," Not surprisingly, there is strong mid infrared emission from the vicinity of clumps C1 and C2 which are associated with the HII region complex G19.61-0.23 but one also notes strong emission associated with the C7/C8 complex and with C12."1020 In all of these cases. it is reasonable to assume that there is an embedded cluster of young stars producing ultra-violet radiation responsible for exciting the PAH and small grain emission observed at 8 and 24 jim. Less obvious in Fig.," In all of these cases, it is reasonable to assume that there is an embedded cluster of young stars producing ultra–violet radiation responsible for exciting the PAH and small grain emission observed at 8 and 24 $\mu$ m. Less obvious in Fig."1021 is the fact that in many cases there are point-like (< 6 are sec.), \ref{CO-apex-spitzer} is the fact that in many cases there are point-like $<$ 6 arc sec.)1022 continuum sources at 24 jm close to the ATLASGAL 870 micron peaks., continuum sources at 24 $\mu$ m close to the ATLASGAL 870 micron peaks.1023 It is noticeable that there are 3 ATLASGAL sources without clear 24 pm counterparts and we presume this implies a relatively low dust temperature (below 25 K)., It is noticeable that there are 3 ATLASGAL sources without clear 24 $\mu$ m counterparts and we presume this implies a relatively low dust temperature (below 25 K).1024 These are perhaps similar to the infrared dark clouds (RDCs) observed associated with star-forming regions closer to the sun but lacking a strong infrared background., These are perhaps similar to the infrared dark clouds (IRDCs) observed associated with star-forming regions closer to the sun but lacking a strong infrared background.1025 We note also that we have searched without success for extended emission in the 4.5 μπι IRAC band of the type often found associated with outflows in nearby star-forming regions., We note also that we have searched without success for extended emission in the 4.5 $\mu$ m IRAC band of the type often found associated with outflows in nearby star-forming regions.1026 Finally. all the ATLASGAL sources show association with extended Spitzer," Finally, all the ATLASGAL sources show association with extended Spitzer"1027posterior probability distribution (asvimmnetric).,posterior probability distribution (asymmetric).1028 Note that these asvanmnietric distributions arereal ancl not mathematical artifacts: they properly represent our knowledge of the distance and radius. which is not true for least-squares or maximunm-likelihood calculations on the same data.," Note that these asymmetric distributions are and not mathematical artifacts; they properly represent our knowledge of the distance and radius, which is not true for least-squares or maximum-likelihood calculations on the same data."1029 The latter methods assume svinmeltric errors by their verv nature., The latter methods assume symmetric errors by their very nature.1030 Because this situation prevails for only a lew stars in this sample. ancl only for stars with large errors. il has little οδοί on the weighted mean ratios of distances ancl radii quoted in the previous secon.," Because this situation prevails for only a few stars in this sample, and only for stars with large errors, it has little effect on the weighted mean ratios of distances and radii quoted in the previous section."1031 As we did with the distances and radii themselves. we begin by examining the behavior of theratio of the Bavesian uncertainty {ο the linear-bisector uncertaintv for the same Cepheid.," As we did with the distances and radii themselves, we begin by examining the behavior of the of the Bayesian uncertainty to the linear-bisector uncertainty for the same Cepheid."1032 In Figures 7 and 8 we show these ratios for the distance and radius uncertainties plotted against /ogP?., In Figures \ref{sigmadist} and \ref{sigmarad} we show these ratios for the distance and radius uncertainties plotted against $log P$.1033 Unwelghted least-squares fits in these figures vield There is no apparent dependence of these ratios on pulsation period., Unweighted least-squares fits in these figures yield There is no apparent dependence of these ratios on pulsation period.1034 Plots of the ratios ol the distance uncertainties against distance and of the ratios of the radius uncertainties against radius are similarly uninformative., Plots of the ratios of the distance uncertainties against distance and of the ratios of the radius uncertainties against radius are similarly uninformative.1035 The two ratios are. however. highly correlated with each other (22= 0.99) as shown in Figure 9..," The two ratios are, however, highly correlated with each other $R = 0.99$ ) as shown in Figure \ref{sigma_sigma}."1036 Thus the underlviug cause of the larger uneertainties in the Davesian calculation is likely (ο be the same for the distance uicertaintv and radius uncertainty., Thus the underlying cause of the larger uncertainties in the Bayesian calculation is likely to be the same for the distance uncertainty and radius uncertainty.1037 In section 2.1 we noted that the linear-bisector caleulation does not treat (hevariables problem rigorously nor does il properly propagate uncertainty through (he racial velocitv integration., In section 2.1 we noted that the linear-bisector calculation does not treat the problem rigorously nor does it properly propagate uncertainty through the radial velocity integration.1038 The second of these issues will certainly lead to an underestimate of the uncertainties in (he computed clistances and radii., The second of these issues will certainly lead to an underestimate of the uncertainties in the computed distances and radii.1039 Because the Bavesian MICAIC caleulation correctly address these (vo computational issues. we interpret the large ratio of Bavesian to bisector uneertain(y as measuring the amount bv which the linear-biseetor errors have been underestimated.," Because the Bayesian MCMC calculation correctly address these two computational issues, we interpret the large ratio of Bayesian to bisector uncertainty as measuring the amount by which the linear-bisector errors have been underestimated."1040 This interpretation is supported by the fact (hat of the liear-bisector uncertainties isfarger (han ils Bavesian counterpart., This interpretation is supported by the fact that of the linear-bisector uncertainties is than its Bayesian counterpart.1041 Our second result is (hat the linear- calculation underestimates the uncertainties in distance ancl in radius substantially. amounting to factors of 1.46.7 for this dataset.," Our second result is that the linear-bisector calculation underestimates the uncertainties in distance and in radius substantially, amounting to factors of 1.4–6.7 for this dataset."1042 This large range implies that the ratio that is obtained depends on the specifies of the data for the Cepheid which varies from star to star., This large range implies that the ratio that is obtained depends on the specifics of the data for the Cepheid which varies from star to star.1043]xeck I1 NIRSPEC image A and the Subaru IRCS image D.,Keck II NIRSPEC image $A$ and the Subaru IRCS image $B$.1044 These are reproduced in Fig. 3..," These are reproduced in Fig. \ref{ao_core},"1045 where we have marked (wo features that seem to be present in both images., where we have marked two features that seem to be present in both images.1046 Most of the other apparent features in one or the other of the images are likely cue to speckle noise., Most of the other apparent features in one or the other of the images are likely due to speckle noise.1047 The strongest of the “real” [features (aside from the stellar object to the east). labeled α in Fig. 3..," The strongest of the “real” features (aside from the stellar object to the east), labeled $a$ in Fig. \ref{ao_core},"1048 lies within the error bars of the position of the radio core ancl is plausibly to be identified with (he nuclear region of 2294., lies within the error bars of the position of the radio core and is plausibly to be identified with the nuclear region of 294.1049 The position of object « falls near a local minimun in (he //-band image of Qui, The position of object $a$ falls near a local minimum in the $H$ -band image of \citet{qui01} (see Fig.1050rrenbachetal.(2001) (see Fie., \ref{aoimagefig}$ $D$; this weakness may indicate that the nucleus is strongly obscured at shorter wavelengths.1051 LD: hisiwealnessmagyindicatethalthe raysourceinaC 2294isahighlyobscuredquasarwithaluminosilyo[7 10 erg s—1., Such obscuration would be consistent with the conclusion of \citet{fab03} that the central hard X-ray source in 294 is a highly obscured quasar with a luminosity of $\sim10^{45}$ erg ${-1}$.1052 Ifthe radio nucleus lies within the diffuse nebulosity. what is the nature of stellar object to the east?," If the radio nucleus lies within the diffuse nebulosity, what is the nature of stellar object to the east?"1053 The density of star-like objects of similar or greater brightness at A in the field of 2294 is on the order of 10 per square arcinin. so il would be quite unusual for (here {ο be an unrelated object within," The density of star-like objects of similar or greater brightness at $K$ in the field of 294 is on the order of 10 per square arcmin, so it would be quite unusual for there to be an unrelated object within"1054hours.,hours.1055" With both feedback schemes, the accuracy of energy conservation arises because at each simulation step the entire system is integrated."," With both feedback schemes, the accuracy of energy conservation arises because at each simulation step the entire system is integrated."1056" Therefore, all particles are aware of the hydrodynamical state of their neighbours."," Therefore, all particles are aware of the hydrodynamical state of their neighbours."1057 We will develop this argument in more detail in Sec. 3.., We will develop this argument in more detail in Sec. \ref{sec:individual}.1058" Here, we focus on how and why there is agreement between the two schemes."," Here, we focus on how and why there is agreement between the two schemes."1059 It is somehow expected that both methods give the same results., It is somehow expected that both methods give the same results.1060" Indeed, Sedov's initial conditions are the total energy of the explosion and the medium density."," Indeed, Sedov's initial conditions are the total energy of the explosion and the medium density."1061 The only requirement is that a large amount of energy is instantaneously injected in a small but its form is not specified (Landau&Lifshitz1959)., The only requirement is that a large amount of energy is instantaneously injected in a small but its form is not specified \citep{Landau1959}.1062". One can input either all thermal, all kinetic or a combination of both forms and obtain the same similarity solution at any given time."," One can input either all thermal, all kinetic or a combination of both forms and obtain the same similarity solution at any given time."1063" Since the hydrodynamics conservation laws are used to derive the solution, a property of the similarity solution is that the fractions of thermal and kinetic energies of the blast are constant in time."," Since the hydrodynamics conservation laws are used to derive the solution, a property of the similarity solution is that the fractions of thermal and kinetic energies of the blast are constant in time."1064" However, in the numerical integration, a finite time is required to convert one form of energy to the other and reach the energy budget given by the analytic solution (see illustration in Fig. 4))."," However, in the numerical integration, a finite time is required to convert one form of energy to the other and reach the energy budget given by the analytic solution (see illustration in Fig. \ref{fig:concordratio}) )."1065 As long as momentum can be converted into thermal energy by physical processes like e.g. the numerical integration of the conservation laws should reach the similarity solution., As long as momentum can be converted into thermal energy by physical processes like e.g. the numerical integration of the conservation laws should reach the similarity solution.1066 We show in Fig., We show in Fig.1067 3 the time evolution of the energy conservation relative error (given by Eq. 3)), \ref{fig:concordenergy} the time evolution of the energy conservation relative error (given by Eq. \ref{eq:energyconservation}) )1068" for all test simulations, where solid and dashed lines refer to the thermal and kinetic energy injection methods, respectively."," for all test simulations, where solid and dashed lines refer to the thermal and kinetic energy injection methods, respectively."1069 Lines of the same colour are for simulations with the same numerical parameters., Lines of the same colour are for simulations with the same numerical parameters.1070 Energy injection happens at time t=0., Energy injection happens at time $t=0$.1071 We first concentrate on the reference simulation (black lines)., We first concentrate on the reference simulation (black lines).1072" We show in the plot that the violation of energy conservation happens in the early stage of the explosion (tx 1072), when the energy contrast is the largest."," We show in the plot that the violation of energy conservation happens in the early stage of the explosion $t\le10^{-2}$ ), when the energy contrast is the largest."1073" In the thermal case (solid line), there is initially a jump of ~0.15% around t=10~°."," In the thermal case (solid line), there is initially a jump of $\sim0.15$ around $t=10^{-5}$."1074" The conversion of energy into momentum happens very quickly, and after t=4x107 the evolution follows the kinetic case with an offset slowly decreasing."," The conversion of energy into momentum happens very quickly, and after $t=4\times10^{-4}$ the evolution follows the kinetic case with an offset slowly decreasing."1075" At later times, both curves flatten to roughly 0.8%."," At later times, both curves flatten to roughly $0.8$."1076". 'The same behaviour can be seen in the energy variation tests (blue and green lines), where the input energy is decreased by a factor of 10 and 100, respectively."," The same behaviour can be seen in the energy variation tests (blue and green lines), where the input energy is decreased by a factor of 10 and 100, respectively."1077 Decreasing the input energy slows the blast evolution and gives the time offset seen the plot., Decreasing the input energy slows the blast evolution and gives the time offset seen the plot.1078" With constant o, varying the input energy gives similar relative errors, providing an estimate that is independent of the energy value."," With constant $\alpha$, varying the input energy gives similar relative errors, providing an estimate that is independent of the energy value."1079" Moreover, energy conservation is achieved at a comparable level for both thermal and kinetic feedback."," Moreover, energy conservation is achieved at a comparable level for both thermal and kinetic feedback."1080 b)).. with @ and b respectively equal to about 0.2 and 0.8 (Llansen&Staclel2006:: see also Luclowetal.2011. for an alternative expression). although with a substantial scatter this time.,"(r)=a , with $a$ and $b$ respectively equal to about $-0.2$ and $0.8$ \citealt{HS06}; see also \citealt{Ludea11} for an alternative expression), although with a substantial scatter this time."1081 The origin of all these trends is certainly related with the way dark matter clusters., The origin of all these trends is certainly related with the way dark matter clusters.1082 In hierarchical cosmologies. haloes erow through continuous mergers with notably dilleren dynamic effects according to the relative mass of the captured and capturing objects.," In hierarchical cosmologies, haloes grow through continuous mergers with notably different dynamic effects according to the relative mass of the captured and capturing objects."1083 For this reason. it is usually. distinguished between major mergers. with a dramatic effect each. and minor mergers. contributing together with the capture of diluse matter (if anv) to the so-called accretion. responsible of just a smooth secular evolution of the system.," For this reason, it is usually distinguished between major mergers, with a dramatic effect each, and minor mergers, contributing together with the capture of diffuse matter (if any) to the so-called accretion, responsible of just a smooth secular evolution of the system."1084 Some authors have attempted to explain the tvpical halo density profile as the result of repeated major (or intermediate) mergers (Sver&WΜπο1998:Salvador-Soléetal. 2003).," Some authors have attempted to explain the typical halo density profile as the result of repeated major (or intermediate) mergers \citep{SW98,SSM98,Suea00,Dea03}."1085. Others have concentrated instead in the eleets of pure accretion (PA) (Avila-Reeseetal.1998:Nusser&Shethal.2000:Manriquect2003:Ascasibaret2004:Salvador-Solé 2007).," Others have concentrated instead in the effects of pure accretion (PA) \citep{ARea98,NS99,DPea00,metal03,As04,Sea07}."1086. Both extreme scenarios have also been investigated regarding the possible origin of the pseudo phase-space density and. velocity anisotropy profiles (Llansen&Moore2006)., Both extreme scenarios have also been investigated regarding the possible origin of the pseudo phase-space density and velocity anisotropy profiles \citep{HM06}.1087. The PA scenario has received much support from the results by Wang&White(2009). showing that all tvpical halo trends are aroad set in the first generation haloes formed by monolithie collapse (ie. no major merger: only accretion of dilluse matter in warm dark matter cosmologies., The PA scenario has received much support from the results by \citet{WW09} showing that all typical halo trends are already set in the first generation haloes formed by monolithic collapse (i.e. no major merger; only accretion of diffuse matter) in warm dark matter cosmologies.1088 Regarding the shape. CDM haloes are found to be triaxial ellipsoids. with a trend. towards prolate rather than oblate shapes (e.g. Frenketal1988:Dujinski&Culberg1991:Warrenal.1992:ColeLacey1996:Springel2004:Allgoodetal.2006:Llavashi2007:MaccióctStadel2009:Vera-Ciro 20112).," Regarding the shape, CDM haloes are found to be triaxial ellipsoids, with a trend towards prolate rather than oblate shapes (e.g. \citealt{Fea88,dc91,Wa92,CL96,Sp04,All06,Ha07,Macea07,St09,VCea11}) )."1089 Inside cach individual object. the typical minor to major axial ratio takes a roughly uniform vaue of about 0.6. with a slight trend to an outward-decreasing triaxiality (Erenketal1988:Bulock202:Jing&Suto2002:Springelal.2004:IxasunEvrarcl2005:BailinSteinmetz 2011).," Inside each individual object, the typical minor to major axial ratio takes a roughly uniform value of about $0.6$, with a slight trend to an outward-decreasing triaxiality \citep{Fea88,Bull02,JS02,Sp04,KE05,bs05,All06,Ha07,Be07,St09,VCea11}."1090. The main axis is preferentially aligned. at all scales. alorig with the filament. [eeing the halo (e.g. Lemson&Ixaullmann1999:Basilakosοἱ 20113).," The main axis is preferentially aligned, at all scales, along with the filament feeding the halo (e.g. \citealt{LK99,BPYGT06,Patea06,Macea07,Ragea10,VCea11}) )."1091 This indicates that the memory of the preferred. direction of major mergers and accretion is not erased during virialisation (Vera-Ciroctal.2011) or. equivalently. that the shape of virialisecl haloes depends on tja of their seeds.," This indicates that the memory of the preferred direction of major mergers and accretion is not erased during virialisation \citep{VCea11} or, equivalently, that the shape of virialised haloes depends on that of their seeds."1092 Moreover. as haloes are not supported by rotation but by the local anisotropic veocity tensor. the fact that their triaxial shape is related to the shape of protohaloes automatically implies that their kinematies must also be related to it.," Moreover, as haloes are not supported by rotation but by the local anisotropic velocity tensor, the fact that their triaxial shape is related to the shape of protohaloes automatically implies that their kinematics must also be related to it."1093 The seeds of haloes are believed to be peaks (secondary maxima) in the primordial random Caussian density field filtered at the scale of the halo., The seeds of haloes are believed to be peaks (secondary maxima) in the primordial random Gaussian density field filtered at the scale of the halo.1094 Ehe isodensity contours in the immediate vicinity of peaks are triaxial (Doroshkevich1970). and rather prolate with a trend to become more spherical for very high peaks (Bardeenctal.1986: hereafter DDINS)., The isodensity contours in the immediate vicinity of peaks are triaxial \citep{Dor70} and rather prolate with a trend to become more spherical for very high peaks \citealt{BBKS}; hereafter BBKS).1095 As the monolithic collapse of non-spherical systems is highly non-radial (Zeldovich.1970).. giving rise to filaments and riaxial νακο objects.," As well-known, the monolithic collapse of non-spherical systems is highly non-radial \citep{Z70}, giving rise to filaments and triaxial virialised objects."1096 Thus. it is natural to believe that the shape of peaks is somehow translated into that of haloes. in agreement with the above mentioned alignments.," Thus, it is natural to believe that the shape of peaks is somehow translated into that of haloes, in agreement with the above mentioned alignments."1097 A few authors (Leeetal.2005:Rossi2011). have tried to make the ink between the shape of haloes and that of peaks through the modelling of ellipsoidal collapse.," A few authors \citep{Lee05,RST11} have tried to make the link between the shape of haloes and that of peaks through the modelling of ellipsoidal collapse."1098 Unfortunately. these models do not account for the highly non-linear effects of shell-crossing during virialisation. which play a crucial role in setting the inal properties of virialised haloes.," Unfortunately, these models do not account for the highly non-linear effects of shell-crossing during virialisation, which play a crucial role in setting the final properties of virialised haloes."1099 On the other hand. there is in the literature no attempt to relate the kinematics of haloes with the shape of their seeds.," On the other hand, there is in the literature no attempt to relate the kinematics of haloes with the shape of their seeds."1100 In à recent. paper. Salvador-Soléetal... (2012: hereafter SV'AIS) have shown that the kinematics of virialised haloes in (bottom-up) hierarchical cosmologies with dissipationless collisionless dark matter depends on their triaxial shape. contrarilv o their spherically averaged density. profile which does not.," In a recent paper, \citeauthor{Sea12} \citeyear{Sea12}; hereafter SVMS) have shown that the kinematics of virialised haloes in (bottom-up) hierarchical cosmologies with dissipationless collisionless dark matter depends on their triaxial shape, contrarily to their spherically averaged density profile which does not."1101 This allowed ολο to infer. under the assumption of PA. the vpical spherically averaged densitv. profile for haloes from that of peaks in the primordial density field. determined by the »ower-speetrum of density perturbations.," This allowed SVMS to infer, under the assumption of PA, the typical spherically averaged density profile for haloes from that of peaks in the primordial density field, determined by the power-spectrum of density perturbations."1102 Furthermore. SVMS showed that the density profile for haloes having undergone major mergers is indistinguishae from that of haloes &rown by PA. so the model actually holds for all haloes regardless of heir individual aggregation hisOLN.," Furthermore, SVMS showed that the density profile for haloes having undergone major mergers is indistinguishable from that of haloes grown by PA, so the model actually holds for all haloes regardless of their individual aggregation history."1103 In the present. paper. we extend the SVAIS model to the kinematics and triaxial shape of virialisecl objects.," In the present paper, we extend the SVMS model to the kinematics and triaxial shape of virialised objects."1104 Under he PA assumption and neelecting any possible rotation tically induced. by surrounding matter. we derive the halo shape. velocity anisotropy profile and oeudo phase-space density profile from the triaxial shape of peaks. taking into account the ‘all virialisation process.," Under the PA assumption and neglecting any possible rotation tidally induced by surrounding matter, we derive the halo shape, velocity anisotropy profile and pseudo phase-space density profile from the triaxial shape of peaks, taking into account the full virialisation process."1105 We first assume the simple case of PA and then study the foresccable cllects of major mergers., We first assume the simple case of PA and then study the foreseeable effects of major mergers.1106 This allows us to establish the ink between those twpical halo properties and the power-spectrum of density. perturbations., This allows us to establish the link between those typical halo properties and the power-spectrum of density perturbations.1107 The heoretical predictions obtainec when this formalism is applied to CDM. haloes are in good. agreement with the results of numerical simulations., The theoretical predictions obtained when this formalism is applied to CDM haloes are in good agreement with the results of numerical simulations.1108 The paper is organised as follows., The paper is organised as follows.1109 In Section ??.. we derive some general relations valid for triaxial svstems. regardless of whether they are in equilibrium or not.," In Section \ref{axratio}, we derive some general relations valid for triaxial systems, regardless of whether they are in equilibrium or not."1110 Assuming PA. these relations are used. in Section ??.. to make the link between the triaxial shape of a virialised object formed by PA and thatof its seed.," Assuming PA, these relations are used, in Section \ref{eccentricity}, to make the link between the triaxial shape of a virialised object formed by PA and thatof its seed."1111 The tvpical velocity anisotropy and. velocity dispersion profiles for virialised objects are derived in Section ?? from their triaxial shape., The typical velocity anisotropy and velocity dispersion profiles for virialised objects are derived in Section \ref{anisotropy} from their triaxial shape.1112 In Section ??.. we apply the model to CDM," In Section \ref{haloes}, , we apply the model to CDM"1113hiehly relativisüce [low is really the most plausible explanation of the CXO quasar jel observations. aud to look [or possibilities of discriminating between (his aud other models (e.g..Aharonian2002:Dermer&Atovan2002;StawarzOstrowski2002).,"highly relativistic flow is really the most plausible explanation of the CXO quasar jet observations, and to look for possibilities of discriminating between this and other models \citep[e.g.,][]{aha02,der02,sta02}."1114. Analysis of the morphology of the emitting regions constitutes an interesting approach to this problem., Analysis of the morphology of the emitting regions constitutes an interesting approach to this problem.1115 The most apparent characteristic of quasar jets is their knotty morphology with high knot-to-interknot brightness contrast. but also with distinct (in some cases) inter-knot diffuse enussion.," The most apparent characteristic of quasar jets is their knotty morphology with high knot-to-interknot brightness contrast, but also with distinct (in some cases) inter-knot diffuse emission."1116 In addition. knot profiles seem to be lvequencs-ixdependent. and knot extents are similar when observed al radio. optical ancl X-ray. photon energies.," In addition, knot profiles seem to be frequency-independent, and knot extents are similar when observed at radio, optical and X-ray photon energies."1117 Detailed observations of the 3C 273 jet (Jesteretal.2001) reveal also that spectral changes along the flow are not correlated. with brightness changes this may be a general characteristic of these objects., Detailed observations of the 3C 273 jet \citep{jes01} reveal also that spectral changes along the flow are not correlated with brightness changes — this may be a general characteristic of these objects.1118 Finally. in some cases spatial olfsets between the maxima of the N-ray. and radio emission within the knot regions were noted (e.g..PINS1127-145.Siemiginowskaetal.2002).," Finally, in some cases spatial offsets between the maxima of the X-ray and radio emission within the knot regions were noted \citep[e.g., PKS 1127-145,][]{sie02}."1119. It is nol clear whether all of these features can be explained in a Iramework of models involving extended shock waves within continuous jet flow., It is not clear whether all of these features can be explained in a framework of models involving extended shock waves within continuous jet flow.1120 In fact. we argue that the morphological characteristics cannot be explained in this wav. and that substantial modifications of the standard picture are required.," In fact, we argue that the morphological characteristics cannot be explained in this way, and that substantial modifications of the standard picture are required."1121 Such modifications are especially needed if (he X-ray emission of quasar Jets is due to the EIC process., Such modifications are especially needed if the X-ray emission of quasar jets is due to the EIC process.1122 We propose that at least some aspects of the IIST and CXO observations can be understood in terms of intermittent (modulated) jet aclivitv., We propose that at least some aspects of the HST and CXO observations can be understood in terms of intermittent (modulated) jet activity.1123 In this context. we comment on both the external-Compton scenario of quasar jet X-ray emission. and on a model of boundary laver acceleration andresulting high-energv raciation (Stawarz&Ostrowski2002).," In this context, we comment on both the external-Compton scenario of quasar jet X-ray emission, and on a model of boundary layer acceleration andresulting high-energy radiation \citep{sta02}."1124. In particular. in 2 we emphasize the problems with modeling X-ray knots of quasar jets as stationary regions of particle acceleration.," In particular, in 2 we emphasize the problems with modeling X-ray knots of quasar jets as stationary regions of particle acceleration."1125 In 3 we consider the possibility (hat (he knots are moving sources of non-thermal radiation. propose a possible connection of this scenario to models of intermittent jet activity. and discuss the particle acceleration processes possibly involved in such a scenario.," In 3 we consider the possibility that the knots are moving sources of non-thermal radiation, propose a possible connection of this scenario to models of intermittent jet activity, and discuss the particle acceleration processes possibly involved in such a scenario."1126 The discussion ancl final conclusions are presented in 4 and 5. respectively.," The discussion and final conclusions are presented in 4 and 5, respectively."1127 In the most common version of the EIC model. in which the knots are identified with strong stationary shocks through which the jet matter flows continuously. none of the morphological features mentioned in the introduction are straightlorwarcdly expected.," In the most common version of the EIC model, in which the knots are identified with strong stationary shocks through which the jet matter flows continuously, none of the morphological features mentioned in the introduction are straightforwardly expected."1128 The knots appear to be localized along the jet. vet stationary shocks are likely to be highly oblique (with respect to the jet axis) and significantly elongated in the flow direction. if the jel is confined by external pressure (Sanders1933:Ixomissarov&Falle 1997)..," The knots appear to be localized along the jet, yet stationary shocks are likely to be highly oblique (with respect to the jet axis) and significantly elongated in the flow direction, if the jet is confined by external pressure \citep{san83,kom97}. ."1129 Large-scale, Large-scale1130galaxies and smaller than ratios measured for typical type 2 AGNs (usually 0.1. c.g. Robinson ct al. 1987)),"galaxies and smaller than ratios measured for typical type 2 AGNs (usually $>$ 0.1, e.g. Robinson et al. \citeyear{rob87}) )"1131 The emission. lines are narrower in the tidal tail and nuc2 than at the quasar nucleus., The emission lines are narrower in the tidal tail and $nuc2$ than at the quasar nucleus.1132 FWAOLI] = 3302-10 km  and EWIINIGLT2)z 140 km for nuc2: ENILMOLLI] = 310430 Km Land ΜΕ 140 kim + for the tidal tail., FWHM[OIII] = $\pm$ 10 km $^{-1}$ and $\beta$ $\leq$ 140 km $^{-1}$ for $nuc2$; FWHM[OIII] = $\pm$ 30 km $^{-1}$ and $\beta$ $\le$ 140 km $^{-1}$ for the tidal tail.1133 The quasar nucleus shows FEWIIM = 400440 Καὶ 1 and 3804-20 for ΟΠΗ) and 12 respectively., The quasar nucleus shows FWHM = $\pm$ 40 km $^{-1}$ and $\pm$ 20 for [OIII] and $\beta$ respectively.1134 Thus. SDSS J0025-10 is undergoing a merger process with a companion star forming galaxy.," Thus, SDSS J0025-10 is undergoing a merger process with a companion star forming galaxy."1135 We propose that both the companion nucleus and the northern tidal tail are photoionized by voung stars which have probably formed as a consequence of the interaction process., We propose that both the companion nucleus and the northern tidal tail are photoionized by young stars which have probably formed as a consequence of the interaction process.1136 ΑΠΟ] is probably a companion star forming object., $knot1$ is probably a companion star forming object.1137 We find no clear evidence [or a quasar extended ionized nebula along PA 0 or PA 60 at surface brightness levels Z3023.2.10. P erg tem? arcsecE , We find no clear evidence for a quasar extended ionized nebula along PA 0 or PA 60 at surface brightness levels $\ga$ $\sigma$ $\times$ $^{-18}$ erg $^{-1}$ $^{-2}$ $^{-2}$.1138The VET-FOIBS2 broad and narrow band images are shown in Fig., The VLT-FORS2 broad and narrow band images are shown in Fig.1139 6., 6.1140 Xn extended diffuse structure is detected towards the N-W. whose morphology appears more clearly defined in the broad. band image ancl is reminiscent of a tidal tail.," An extended diffuse structure is detected towards the N-W, whose morphology appears more clearly defined in the broad band image and is reminiscent of a tidal tail."1141 A compact knot is also detected to the IE. which appears relatively stronger in the narrow band image.," A compact knot is also detected to the E, which appears relatively stronger in the narrow band image."1142 Vhis suggests that it is a strong lino emitter at the same z as the quasar., This suggests that it is a strong line emitter at the same $z$ as the quasar.1143 The PA 116 slit crosses both the tidal tail ancl the knot., The PA 116 slit crosses both the tidal tail and the knot.1144 The OL 2D spectrum (Fig., The $\beta$ -[OIII] 2D spectrum (Fig.1145 7) shows that the compact knot emits strong lines and. very faint continuum. as expected from the images.," 7) shows that the compact knot emits strong lines and very faint continuum, as expected from the images."1146 Low surface brightness lines are also detected between the quasar and the knot. possibly emitted by an EEL associated with the quasar.," Low surface brightness lines are also detected between the quasar and the knot, possibly emitted by an EELR associated with the quasar."1147 The structure reminiscent of a tidal tail mentioned above emits only faint. dilluse continuum.," The structure reminiscent of a tidal tail mentioned above emits only faint, diffuse continuum."1148 The nuclear line ratios are shown in Table 2., The nuclear line ratios are shown in Table 2.1149 The reddening derived. from the Balmer lines is most. likely wrong. since the galaxy continuum is strong and 1 and LH (not so much 112. which has larger equivalent width) are likely to be strongly. absorbed.," The reddening derived from the Balmer lines is most likely wrong, since the galaxy continuum is strong and $\gamma$ and $\delta$ (not so much $\beta$, which has larger equivalent width) are likely to be strongly absorbed."1150 Given the large uncertainties due to this effect. we will ignore nuclear dust reddening in the diagnostic diagram in this case.," Given the large uncertainties due to this effect, we will ignore nuclear dust reddening in the diagnostic diagram in this case."1151 The knot is dominated by line emission and is not alleetec by this problem: Ly /1E72-0.4643:0.03 is consistent with the case B recombination value 0.47 (Osterbrock 1989))., The knot is dominated by line emission and is not affected by this problem: $\gamma$ $\beta$ $\pm$ 0.03 is consistent with the case B recombination value 0.47 (Osterbrock \citeyear{ost89}) ).1152 It is therefore not reddened., It is therefore not reddened.1153 Three apertures were used to extract. LD spectra from dilferent spatial regions along the slit (Fig., Three apertures were used to extract 1D spectra from different spatial regions along the slit (Fig.1154 7. top): the knot. the quasar and the intermediate region between them.," 7, top): the knot, the quasar and the intermediate region between them."1155 The location of the individual spectra are shown in the diagnostic diagram., The location of the individual spectra are shown in the diagnostic diagram.1156 While the nuclear spectrum. lies very far [from the LU galaxies and is consistent with the AGN models (also Hell is strong. 1115502050.00: Table 2). the knot overlaps with the LLL galaxy region.," While the nuclear spectrum lies very far from the HII galaxies and is consistent with the AGN models (also HeII is strong, $\beta$ $\pm$ 0.06; Table 2), the knot overlaps with the HII galaxy region."1157 For the intermediate region. lower limits are shown. due to the non detection of 1123.," For the intermediate region, lower limits are shown, due to the non detection of $\beta$."1158 Ehe location overlaps with the LILLE galaxy region as well., The location overlaps with the HII galaxy region as well.1159 The lines emitted. by the knot. are. split. into. two kinematics components (see Fig., The lines emitted by the knot are split into two kinematics components (see Fig.1160 Y. top).," 7, top)."1161 The dominant component is very narrow (EWIIM. <120 km s |) and shows very low /113—3.6-E0.3., The dominant component is very narrow (FWHM $\la$ 120 km $^{-1}$ ) and shows very low $\beta$ $\pm$ 0.3.1162 μονο properties and its location on the LIL regionὃν area in the diagnostico diagramso sugeest that the knot is a star forming object where the gas is photoionized by voung stars., These properties and its location on the HII region area in the diagnostic diagrams suggest that the knot is a star forming object where the gas is photoionized by young stars.1163 Lt is redshiftecl by -260+70, It is redshifted by $\pm$ 701164this model is captured by equation 7. (Section 2.1.1)).,this model is captured by equation \ref{eqn:mass2mag} (Section \ref{sec:eqns}) ).1165 For convenience. we invert this equation to obtain where {f(2) is defined by equation 2..," For convenience, we invert this equation to obtain where $H(z)$ is defined by equation \ref{eqn:Hz}."1166 Equation 13 can be used to take à quasar with observed bolometric luminosity Lo at redshift z and predict its halo virial mass. assuming values for parameters 5 (the relationship between virial and circular velocities) and 5 (the Eddington luminosity fraction of the quasar).," Equation \ref{eqn:mag2mass} can be used to take a quasar with observed bolometric luminosity $L_Q$ at redshift $z$ and predict its halo virial mass, assuming values for parameters $\gamma$ (the relationship between virial and circular velocities) and $\eta$ (the Eddington luminosity fraction of the quasar)."1167 Equation 13. is plotted in figure 10.., Equation \ref{eqn:mag2mass} is plotted in figure \ref{fig:evolution}.1168 From this figure alone the quasar host virial mass (either. individual or averaged: over a group) for a given quasar Luminosity and redshift may be simply. reacl oll (solid lines)., From this figure alone the quasar host virial mass (either individual or averaged over a group) for a given quasar luminosity and redshift may be simply read off (solid lines).1169 We emphasise. We discuss the uncertainty on such masses below.," We emphasise, We discuss the uncertainty on such masses below."1170 Also over-plottecl in figure 10. are the corresponding mean space densities of quasar hosts. (dashed lines). calculated. from the quasar luminosity (Section 2.2)). and the black hole mass at fixed. luminosity (horizontal dotted lines). as given by equation 6..," Also over-plotted in figure \ref{fig:evolution} are the corresponding mean space densities of quasar hosts (dashed lines), calculated from the quasar luminosity (Section \ref{sec:selection}) ), and the black hole mass at fixed luminosity (horizontal dotted lines), as given by equation \ref{eqn:LQ}."1171 The spacing of density contours relative to halo mass ughliehts a main result. of this work. which is that the distribution. of the masses of dark matter halos hosting quasars narrows with decreasing redshift.," The spacing of density contours relative to halo mass highlights a main result of this work, which is that the distribution of the masses of dark matter halos hosting quasars narrows with decreasing redshift."1172 This leads to xhaviour such as luminosity dependent. clustering at. high redshift but not at low (see Section. 3.8)). and. luminosity dependent quasar Lifetimes at. low redshift but. not. high (κος Section 3.4)).," This leads to behaviour such as luminosity dependent clustering at high redshift but not at low (see Section \ref{sec:lumclustering}) ), and luminosity dependent quasar lifetimes at low redshift but not high (see Section \ref{sec:lifetimes}) )."1173 Also. as discussed. Section 3.5... the urnover of density contours at zX2 relative to black hole mass demonstrates downsizing in the black hole population.," Also, as discussed Section \ref{sec:BHMF}, the turnover of density contours at $z \simlt 2$ relative to black hole mass demonstrates downsizing in the black hole population."1174 At higher redshifts. rare massive black holes show no downsizing trend. whereas the more common L quasars are predicted to be upsizing. especially at redshifts greater than 2o.," At higher redshifts, rare massive black holes show no downsizing trend, whereas the more common $L^*$ quasars are predicted to be upsizing, especially at redshifts greater than $z \sim 4$."1175 3elore applving our model (particularly equation. 13)) to an observation or set of observations Ἡ djs prudent to understand the limits to which dark matter halo mass can be inferred given both the built in theoretical and observational uncertainties., Before applying our model (particularly equation \ref{eqn:mag2mass}) ) to an observation or set of observations it is prudent to understand the limits to which dark matter halo mass can be inferred given both the built in theoretical and observational uncertainties.1176 Observational error is drawn from local measurements and has been propagated through cach equation appropriately., Observational error is drawn from local measurements and has been propagated through each equation appropriately.1177 Near the characteristic luminosity οἱ the quasar population.; Log1012517h-;L.. the mass error has magnitude 0.32 dex in log units.," Near the characteristic luminosity of the quasar population, $L_Q/\eta\sim 10^{12}h_{70}^{-1}L_\odot$, the mass error has magnitude $0.32$ dex in log units."1178 One magnitude brighter or fainter than this increases the error to 0.34 dex. whereas two magnitudes translates to an error of 0.39 dex.," One magnitude brighter or fainter than this increases the error to $0.34$ dex, whereas two magnitudes translates to an error of $0.39$ dex."1179 While somewhat large at the extremes. this uncertainty is still sullicientlv manageable that tight clustering constraints," While somewhat large at the extremes, this uncertainty is still sufficiently manageable that tight clustering constraints"1180We calibrated the photometry relative to 2MASS.,We calibrated the photometry relative to 2MASS.1181 However. there was uot a sufficient nuuber of nusaturated stars in the field of to do this iu one step.," However, there was not a sufficient number of unsaturated stars in the field of to do this in one step."1182 We therefore used other fields observed ou the same uight over a range of ailnuiasses. uerallv below 1.2.," We therefore used other fields observed on the same night over a range of airmasses, generally below $1.2$."1183 Using only stars that were still in he linear reginae of the detector and were not crowded (16 stars in cach field over 5 fields). we used aperture photometry im with a large aperture of 179 radius and a sky auuulus from 275 to 3δ.," Using only stars that were still in the linear regime of the detector and were not crowded (1–6 stars in each field over 5 fields), we used aperture photometry in with a large aperture of $1\farcs9$ radius and a sky annulus from $2\farcs5$ to $3\farcs8$."1184 We corrected to airinass of 1.0 using approximate airmass cocfitcicuts for he site (0.10. 0.03. and 0.07 + for J. Jf. and AS respectively) aud determined the zero-poiuts for he night.," We corrected to airmass of 1.0 using approximate airmass coefficients for the site (0.10, 0.03, and 0.07 $^{-1}$ for $J$, $H$, and $K_s$ respectively) and determined the zero-points for the night."1185" The final photometry for Hs J=18.590.02. fF=18.35+0.06. and A,=15.398+ 0.06. where the errors are statistical onlv."," The final photometry for is $J=18.59\pm0.02$, $H=18.37\pm0.06$, and $K_s=18.38\pm0.06$ , where the errors are statistical only."1186" We estimate that the uncertainties in the photometric zero points were at nost 0.03 mae for A, aud 11. aud 0.02 for J."," We estimate that the uncertainties in the photometric zero points were at most 0.03 mag for $K_s$ and $H$, and 0.02 for $J$."1187 Spectra of the optical counterpart to wwere taken on the nieht of 1999 July 15 using FORSI at the Very Large Telescope., Spectra of the optical counterpart to were taken on the night of 1999 July 15 using FORS1 at the Very Large Telescope.1188 The setup was tle same as that usedby ?. for a spectroscopic study of the faint neutron star. RN 3751 (Cain 300V with R300. AA//pix dispersion: wwide loue-sht. //pix spatial scale).," The setup was the same as that usedby \citet{2001A&A...378..986V} for a spectroscopic study of the faint neutron star, RX $-$ 3754 (Grism 300V with $R\approx$ 300, /pix dispersion; wide long-slit, /pix spatial scale)."1189 The reduction followed that described by those authors., The reduction followed that described by those authors.1190 Briefly. two 15-nuuute spectra were taken. covering the range of 3600 to aat a resolution of ~12À.. with the slit position angle thosen such that both the counterpart aud star 1 of ? wereσ," Briefly, two 45-minute spectra were taken, covering the range of 3600 to at a resolution of $\sim\!13$, with the slit position angle chosen such that both the counterpart and star 1 of \cite{1993ApJ...411L..83B} were."1191"ον The reductiou involved bias subtraction. sky subtraction.οςδι, aud optimal extraction (7) of the spectra of the counterpart using the spatial profile of star 1."," The reduction involved bias subtraction, sky subtraction, and optimal extraction \citep{1986PASP...98..609H} of the spectra of the counterpart using the spatial profile of star 1."1192 Flux calibration was doue in two steps., Flux calibration was done in two steps.1193" First. we calibrated the fluxes of star 1 using a shorter. 5-uinute spectrum taken through a wide slit (with he instrumental response doeterimüned from two fiux standards: see ὃν, especially their E11)."," First, we calibrated the fluxes of star 1 using a shorter, 5-minute spectrum taken through a wide slit (with the instrumental response determined from two flux standards; see \citealt{2001A&A...378..986V}, especially their 4.4)."1194 Next. we estimated the slit losses by fitting a quadratic fiction to he ratio of the narrow-slit to wide-slit spectra of star 1. and used this to calibrate the fluxes of the counterpart.," Next, we estimated the slit losses by fitting a quadratic function to the ratio of the narrow-slit to wide-slit spectra of star 1, and used this to calibrate the fluxes of the counterpart."1195 Overall. we believe our relative fluxes should be accurate o about between 1500 audAA.," Overall, we believe our relative fluxes should be accurate to about between 4500 and."1196. Shortward ofAA.. the calibration is more uncertain. since it is less clear whether our slit losses are corrected well: the ratio of the narrow- to wide-slit spectra of star 1 shows systematic. ~1056 deviations. likely because the wide-slit spectra were taken at high ainmass.," Shortward of, the calibration is more uncertain, since it is less clear whether our slit losses are corrected well: the ratio of the narrow- to wide-slit spectra of star 1 shows systematic, $\sim\!10$ deviations, likely because the wide-slit spectra were taken at high airmass."1197 The absolute flux calibration is also less certain. since there was some οταν at the start of the nieht.," The absolute flux calibration is also less certain, since there was some cirrus at the start of the night."1198 We find that we have to scale the fluxes up by to match theHST photometry in 82.1., We find that we have to scale the fluxes up by to match the photometry in 2.4.1199 Furthermore. some regions of the spectrm are contaminated by atimospheric absorption aud high backeround we have simply excluded these areas from consideration.," Furthermore, some regions of the spectrum are contaminated by atmospheric absorption and high background – we have simply excluded these areas from consideration."1200— We analysed several observations of wwith theHST. both imaging (WFPC2 and ACS) and spectroscopy (ACS).," We analysed several observations of with the, both imaging (WFPC2 and ACS) and spectroscopy (ACS)."

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