ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 1993: Garnavich et al., 1998; Garnavich et al.3 1998: Perlmutter et al., 1998; Perlmutter et al.4 1993; Riess et al., 1998; Riess et al.5 1993: Perlunitter οἱ al., 1998; Perlmutter et al.6 1999: Ixnop et al., 1999; Knop et al.7 2003: Toury et al., 2003; Tonry et al.8 2003: Barris et al 2004)., 2003; Barris et al 2004).9" The Hubble diagrams derived [rom supernovae have indicated an upward bending curve. interpreted. as acceleration of the expansion rate. along with even more complicated features of ""jerk""."," The Hubble diagrams derived from supernovae have indicated an upward bending curve, interpreted as acceleration of the expansion rate, along with even more complicated features of “jerk”."10 It is important (o explore other interpretations. including possible evolution of supernova or host galaxy characteristics with redshift.," It is important to explore other interpretations, including possible evolution of supernova or host galaxy characteristics with redshift."11 Many papers have explored non-cosmological explanations (Coil et al., Many papers have explored non-cosmological explanations (Coil et al.12 2000: Leibundgut 2001: Sullivan οἱ al., 2000; Leibundgut 2001; Sullivan et al.13 2003: Riess 2004)., 2003; Riess 2004).14 Meanwhile. the high redshift host galaxies have significantly," Meanwhile, the high redshift host galaxies have significantly"15Models (1<107? eg am? st and ς1077 eg cm? +. respectively). so the major heat input is from the cosunic ravs.,"Models $1\times 10^{-22}$ erg $^{-3}$ $^{-1}$ and $1\times 10^{-23}$ erg $^{-3}$ $^{-1}$, respectively), so the major heat input is from the cosmic rays."16 The temperature is high aud the chemistry is held ⋮∎∩⊾⋅∖∶≻⊳down aresto a resultsfractional 18110 5froii COlupares restuts TOLModels 10. 0, The temperature is high and the chemistry is largely suppressed; even CO is held down to a fractional abundance of about $1\times 10^{-10}$.17", The high¢butlow CO — beth have low values abundance leads to a significant IL} abundance.", The high $\zeta$ but low CO abundance leads to a significant $_{3}^{+}$ abundance.18 This suppression of the chemistry for high ¢ is m aerecment with the fudiugs of ο {μου also ?)). Aloceis 0, This suppression of the chemistry for high $\zeta$ is in agreement with the findings of \citet{Lepp96}( (see also \citealt{Lepp98}) ).19 5audand 12 whiclwhich abundance suppressed:of lareclyabouteven CO1 «is Z7 (1. «10. 7 erg curs 7).butstrongly differing values of Q (5 « 10. Ἐν aud 5«10P +. gyespectivelv).," Figure \ref{fig:3} compares results from Models 5 and 12 which both have low values of $H$ $1\times 10^{-22}$ erg $^{-3}$ $^{-1}$ ), but strongly differing values of $\zeta$ $5\times 10^{-17}$ $^{-1}$ and $5\times 10^{-15}$ $^{-1}$, respectively)."20 Both are chemically rich (Model 5 is, Both are chemically rich (Model 5 is21We use the dust opacity from ? without grain mantles or coagulation.,We use the dust opacity from \citet{Ossenkopf94} without grain mantles or coagulation.22" This is reasonable assuming that ice mantles around dust grains have evaporated completely and recently, so that the grains have had no time to coagulate again."," This is reasonable assuming that ice mantles around dust grains have evaporated completely and recently, so that the grains have had no time to coagulate again."23" Since the VLA continuum is dominated by free-free emission, the data are not sensitive to the dust emission and so we cannot constrain the dust optical depth, which is a combination of dust opacity and density, through the dust emission."," Since the VLA continuum is dominated by free-free emission, the data are not sensitive to the dust emission and so we cannot constrain the dust optical depth, which is a combination of dust opacity and density, through the dust emission."24" However, the heating is strongly affected by the dust optical depth."," However, the heating is strongly affected by the dust optical depth."25" The temperature of the ionized gas is assumed to be 104 K, which is the order of magnitude expected from cooling by trace species."," The temperature of the ionized gas is assumed to be $10^4$ K, which is the order of magnitude expected from cooling by trace species."26 A different temperature would require a different electron density to account for the observed fluxes., A different temperature would require a different electron density to account for the observed fluxes.27 The HCN molecular data are from ? and taken from the Cologne Database for Molecular Spectroscopy (??)..," The HCN molecular data are from \citet{HCN_rot_2003} and taken from the Cologne Database for Molecular Spectroscopy \citep{Mueller01,CDMS2_2005}."28 We use an HCN abundance of 10? relative to H5 for our models., We use an HCN abundance of $10^{-5}$ relative to $_2$ for our models.29" Since we mainly constrain the density of HCN, a different abundance would require different dust densities (with the gas/dust mass ratio of 100)."," Since we mainly constrain the density of HCN, a different abundance would require different dust densities (with the gas/dust mass ratio of 100)."30" Dust continuum data (from the SMA) indicate that the resulting dust densities are on the right order of magnitude, which justifies this abundance assumption."," Dust continuum data (from the SMA) indicate that the resulting dust densities are on the right order of magnitude, which justifies this abundance assumption."31 The line radiative transfer assumes LTE (full non-LTE radiative transfer is also planned for RADMC-3D)., The line radiative transfer assumes LTE (full non-LTE radiative transfer is also planned for RADMC-3D).32" LTE is a reasonable assumption for the observed line as HCN thermalizes to the ambient dust temperature: It is vibrationally excited by 14um radiation emitted by warm dust, which is very optically thick at this wavelength due to the high densities (an optical depth of 1 is reached after about 25 AU in a density of 105 cm-?)."," LTE is a reasonable assumption for the observed line as HCN thermalizes to the ambient dust temperature: It is vibrationally excited by $\mu$ m radiation emitted by warm dust, which is very optically thick at this wavelength due to the high densities (an optical depth of 1 is reached after about 25 AU in a density of $10^8$ $^{-3}$ )."33" In this warm and dense environment, also the levels in the ground vibrational state are thermalized by infrared pumping as well as by collisions and radiative excitation."," In this warm and dense environment, also the levels in the ground vibrational state are thermalized by infrared pumping as well as by collisions and radiative excitation."34" Deviations from LTE occur at low temperatures, where the vibrational levels are not populated anyway."," Deviations from LTE occur at low temperatures, where the vibrational levels are not populated anyway."35 The models have no macroscopic velocity field., The models have no macroscopic velocity field.36" We assume a constant intrinsic line width (microturbulence) throughout the source, which reflects internal motions."," We assume a constant intrinsic line width (microturbulence) throughout the source, which reflects internal motions."37" The resulting spectra are shifted by the source velocity (68 km s! for G10.47--0.03, 64 km s! for SgrB2-N, 61 km s! for SgrB2-M Fle, and 71 km s! for SgrB2-M F3)."," The resulting spectra are shifted by the source velocity (68 km $^{-1}$ for G10.47+0.03, 64 km $^{-1}$ for SgrB2-N, 61 km $^{-1}$ for SgrB2-M F1e, and 71 km $^{-1}$ for SgrB2-M F3)."38" To compare the model to the observational data, the synthetic map produced by RADMC-3D, supplemented by distance and coordinate information, is Fourier-transformed, folded with"," To compare the model to the observational data, the synthetic map produced by RADMC-3D, supplemented by distance and coordinate information, is Fourier-transformed, folded with"3925 Μτιμμ.,25 $M_{\rm Earth}$.40 For comparison the mass of the compact disk around IRAS4B inferred from the modeling of high angular resolution dust continuum observations is 0.24 Μο (Jérgensenetal.2009)., For comparison the mass of the compact disk around IRAS4B inferred from the modeling of high angular resolution dust continuum observations is 0.24 $M_\odot$ \citep{evolpaper}.41". Thus, if the H580 emission has its origin in this disk, it arises in a small fraction ~0.03% of the material in the disk."," Thus, if the $_2^{18}$ O emission has its origin in this disk, it arises in a small fraction $\approx 0.03$ of the material in the disk."42" Alternatively, in the absence of such a disk, it is possible that the emission has its origin in the hot inner region of the protostellar envelope where the temperature is z100 K: for a simple power-law envelope density profile reproducing the submillimeter continuum emission for IRAS4B on scales larger than ~1000 AU (2.8 Me within 8000 AU; Jgrgensenetal.2009)), the mass within 25 AU (where the temperature is higher than about 100 K) is about 5x 107Mo, implying a H2O abundance of about 1.5x107>."," Alternatively, in the absence of such a disk, it is possible that the emission has its origin in the hot inner region of the protostellar envelope where the temperature is $\gtrsim 100$ K: for a simple power-law envelope density profile reproducing the submillimeter continuum emission for IRAS4B on scales larger than $\sim$ 1000 AU (2.8 $M_\odot$ within 8000 AU; \citealt{evolpaper}) ), the mass within 25 AU (where the temperature is higher than about 100 K) is about $\times$ $^{-4}~M_\odot$, implying a $_2$ O abundance of about $\times 10^{-5}$."43" However, such a model is not self-consistent on small scales: to fit the observed compact dust continuum emission seen by the interferometer a strong increase in the envelope density on small scales by two orders of magnitude is required — above the already increasing radial density profile (e.g.,Jorgensenetal.2009)."," However, such a model is not self-consistent on small scales: to fit the observed compact dust continuum emission seen by the interferometer a strong increase in the envelope density on small scales by two orders of magnitude is required – above the already increasing radial density profile \citep[e.g.,][]{evolpaper}."44". However, if such a density enhancement was due to a magnetic field wall as discussed above 2008), the H2O abundance would be lower by the same amount, dropping to about 1.5x10~’."," However, if such a density enhancement was due to a magnetic field wall as discussed above \citep{chiang08}, the $_2$ O abundance would be lower by the same amount, dropping to about $\times 10^{-7}$."45 This abundance is low compared to the expectation from the full desorption of the H2O mantles and also lower than the constraints on the H2O abundance in the outer envelopes of the IRAS4 sources where H2O is frozen-out based on ISO-LWS results (Maretetal.2002)., This abundance is low compared to the expectation from the full desorption of the $_2$ O mantles and also lower than the constraints on the $_2$ O abundance in the outer envelopes of the IRAS4 sources where $_2$ O is frozen-out based on ISO-LWS results \citep{maret02}.46". A low H5O abundance in the region of desorption may reflect destruction of H2O by X-rays (Stauberetal.2006),, but the H2O abundance would need to be reduced to the levels of the outer cold envelope where H5O is frozen-out and thus could not provide the compact emission observed here."," A low $_2$ O abundance in the region of grain-mantle desorption may reflect destruction of $_2$ O by X-rays \citep{staeuber06}, but the $_2$ O abundance would need to be reduced to the levels of the outer cold envelope where $_2$ O is frozen-out and thus could not provide the compact emission observed here."47 Models of the chemistry in more evolved disks around pre-main sequence stars (where the envelope has dissipated) show a warm upper layer where H5O gas can exist., Models of the chemistry in more evolved disks around pre-main sequence stars (where the envelope has dissipated) show a warm upper layer where $_2$ O gas can exist.48" Although these models are not fully appropriate for disks in the embedded phase, where UV photons may not be able to freely reach the disk surface and heat the gas, they provide a useful reference point for comparison."," Although these models are not fully appropriate for disks in the embedded phase, where UV photons may not be able to freely reach the disk surface and heat the gas, they provide a useful reference point for comparison."49" If the H2O gas phase abundance is just determined by the balance of photodesorption of H2O ice and freeze-out, typical gaseous H20 column densities at 10-25 AU are a few x10!? cm"", dropping rapidly at larger radii in these models (e.g.,Obergetal.2009),, only slightly lower than those found here."," If the $_2$ O gas phase abundance is just determined by the balance of photodesorption of $_2$ O ice and freeze-out, typical gaseous $_2$ O column densities at 10–25 AU are a few $\times 10^{18}$ $^{-2}$, dropping rapidly at larger radii in these models \citep[e.g.,][]{oberg09h2o}, only slightly lower than those found here."50" Alternatively, the temperatures in the upper layers of the disk may be hot enough to drive an active gas-phase chemistry."," Alternatively, the temperatures in the upper layers of the disk may be hot enough to drive an active gas-phase chemistry."51" Woitkeetal.(2009) find a layer of irradiated hot water at altitudes z/R = 0.1—0.3 extending out to 30 AU where temperatures are K and densities 105—10!? cm?, comparable to the conditions deduced here (see also (2009)))."," \citet{woitke09} find a layer of irradiated hot water at altitudes $z/R$ = 0.1–0.3 extending out to 30 AU where temperatures are 200--1500 K and densities $10^8-10^{10}$ $^{-3}$, comparable to the conditions deduced here (see also \cite{glassgold09}) )."52" The H2O mass in this layer is ~107 Mgasn in their model, about two orders of magnitude lower than derived on basis of the H580 observations presented in this paper."," The $_2$ O mass in this layer is $\sim 10^{-4}$ $M_{\rm Earth}$ in their model, about two orders of magnitude lower than derived on basis of the $_2^{18}$ O observations presented in this paper."53" Because their H2O/H» abundance is only 1076—1075, the inferred total warm H5 mass is comparable."," Because their $_2$ $_2$ abundance is only $10^{-6}-10^{-5}$, the inferred total warm $_2$ mass is comparable."54" The discrepancy between the column densities from these data and those from theSpitzer mid-infrared observations (Watsonetal.2007) remains significant, though."," The discrepancy between the column densities from these data and those from the mid-infrared observations \citep{watson07}55 remains significant, though."56 A possible explanation is that the observations are limited by extinction and thus do not probe the total water column density., A possible explanation is that the mid-infrared observations are limited by extinction and thus do not probe the total water column density.57" Alternatively, a lower temperature of the H2O emitting gas of ~100 K could with an unchanged column density keep the observed H580 line intensity at the same level while decreasing the mid-IR line flux predicted by the model."," Alternatively, a lower temperature of the $_2$ O emitting gas of $\sim 100$ K could with an unchanged column density keep the observed $_2^{18}$ O line intensity at the same level while decreasing the mid-IR line flux predicted by the model."58massive hosts. and matching the observed: quasar space density then requires a higher duty evcle.,"massive hosts, and matching the observed quasar space density then requires a higher duty cycle."59 In this paper. we model Shen et al," In this paper, we model Shen et al."60s (2009a: $809 hereafter) recent measurements of lDuminositv-dependent quasar clustering derived from the quasar redshift) survey (Schneider ct 22007) of the Sloan Digital Sky Survey (SDSS: York et al.,'s (2009a; S09 hereafter) recent measurements of luminosity-dependent quasar clustering derived from the quasar redshift survey (Schneider et 2007) of the Sloan Digital Sky Survey (SDSS; York et al.61 2000) Data Release 5 (DRS: Adelman-AMeCarthy et 22007)., 2000) Data Release 5 (DR5; Adelman-McCarthy et 2007).62 Ross et ((2009) also analyze the clustering of this quasar survey. concentrating on redshift evolution. but here we focus on the SOO results because they isolate the luminosity dependence of clustering.," Ross et (2009) also analyze the clustering of this quasar survey, concentrating on redshift evolution, but here we focus on the S09 results because they isolate the luminosity dependence of clustering."63 Our aim is to answer basic questions about the evolution of the AGN and supermassive DII population at 2.5., Our aim is to answer basic questions about the evolution of the AGN and supermassive BH population at $z \leq 2.5$.64 Does the duty. evele depend. on quasar luminosity and/or redshift?, Does the duty cycle depend on quasar luminosity and/or redshift?65 What is the underlying relation between quasar luminosity and halo mass?, What is the underlying relation between quasar luminosity and halo mass?66 Does it have scatter?, Does it have scatter?67 More generally. what combinations of duty evele and scatter are allowed by the nmieasurements?," More generally, what combinations of duty cycle and scatter are allowed by the measurements?"68" Throughout the paper we adopt ©,,,=0.2 . h=HyflOOkmsMpe|!—0.7. €,=0.0435. ης=0.95. ox=0.78. and the transfer Function of Eisenstein Llu (1999: with zero neutrino contribution) which matches the cosmology used by S00."," Throughout the paper we adopt $\Omega_m=0.26$ , $\Omega_\Lambda=0.74$, $h\equiv H_0/100\, {\rm km\, s^{-1}\, Mpc^{-1}}=0.7$, $\Omega_b=0.0435$, $n_s=0.95$, $\sigma_8=0.78$, and the transfer function of Eisenstein Hu (1999; with zero neutrino contribution), which matches the cosmology used by S09."69 The sample used by 809 is a homogeneous subset ofa catalog of 77.429 spectroscopically identified. quasars brighter than Al;=22. in the redshift range O1zz 5.0.," The sample used by S09 is a homogeneous subset of a catalog of 77,429 spectroscopically identified quasars brighter than $M_i=-22$, in the redshift range $0.1\lesssim z \lesssim705.0$ ."71 Shen οἱ al. (, Shen et al. (722007) computed. the correlation function of the high-redshift quasars at 2=2.9. modeled subsequently by. White et al. (,"2007) computed the correlation function of the high-redshift quasars at $z\ge 2.9$, modeled subsequently by White et al. ("732008) ancl Shankar et al. (,2008) and Shankar et al. (742009€).,2009c).75 Llere instead we focus on the correlation function of lower redshift quasars in the range 0.4x22.5., Here instead we focus on the correlation function of lower redshift quasars in the range $0.4\le z \le 2.5$.76 To probe the luminosity dependence of the bias. S09 divided the Iow-z sample into subsamples containing the fainter half of the quasars. the brighter half of the quasars. and the brightest. of the quasars (see their 22).," To probe the luminosity dependence of the bias, S09 divided the $z$ sample into subsamples containing the fainter half of the quasars, the brighter half of the quasars, and the brightest of the quasars (see their 2)."77 In cach luminosity bin. they computed. the quasar correlation. function.," In each luminosity bin, they computed the quasar correlation function."78 In particular. SOO estimated for the full. sample a mean clustering bias of b=2.16+0.24.2.260.33.4.050.73 for the faint. bright. and brightest subsamples. with median luminosity logLiedfergs|=46.31.46.56. 46.84. We will first compare with their data on the bias by computing models at the average redshift 2=1.45 of their sample (Figure 1)).," In particular, S09 estimated for the full sample a mean clustering bias of $b=2.16\pm 0.24, 2.26\pm 0.33, 4.05\pm 0.73$ for the faint, bright, and brightest subsamples, with median luminosity $\log L_{\rm med}/{\rm erg\, s^{-1}}=46.31, 46.56, 46.84$ , We will first compare with their data on the bias by computing models at the average redshift $z=1.45$ of their sample (Figure \ref{fig|bLz}) )."79 We will then compute the full correlation functions for the fant. bright. and. brightest: subsamples averaged: over the full redshift. distribution of the sample. and compare them with the SOO measurements (Figure 2)).," We will then compute the full correlation functions for the faint, bright, and brightest subsamples averaged over the full redshift distribution of the sample, and compare them with the S09 measurements (Figure \ref{fig|WpYue}) )."80 ὃν imposing a cumulative match between the space densities of quasars and their host. halos. ancl assuming that only a fraction oof halos of a given mass shine as optical quasars at a given time. we can estimate the mean host halo mass given the observed: number density of quasars.," By imposing a cumulative match between the space densities of quasars and their host halos, and assuming that only a fraction of halos of a given mass shine as optical quasars at a given time, we can estimate the mean host halo mass given the observed number density of quasars."81 Formally. this concept reads as (o... White et al.," Formally, this concept reads as (e.g., White et al."82 2008) with e=Ας—2) and y=logM., 2008) with $x=M_i(z=2)$ and $y=\log M$.83 Here (jy.2) is the comoving number density of halos. in units of Alpedex or Ha=TOkms5AlpeJ|. whieh we take from Sheth Tormen (1909). while n(Gr.z) is the comoving number density of quasars (in Mpe7) with absolute magnitude in he range wsur|da.," Here $\Phi(y,z)$ is the comoving number density of halos, in units of ${\rm Mpc^{-3}}\, {\rm dex}^{-1}$ for $H_0=70\, {\rm km\, s^{-1}\, Mpc^{-1}}$, which we take from Sheth Tormen (1999), while $n(x,z)$ is the comoving number density of quasars (in ${\rm Mpc^{-3}}$ ) with absolute magnitude in the range $x \rightarrow x+dx$."84 We take the observed. luminosity unction n(r.2) from Richares ct al. (," We take the observed luminosity function $n(x,z)$ from Richards et al. ("852006). corrected. to our cosmology.,"2006), corrected to our cosmology."86 The quantity lin Eq. (1)), The quantity in Eq. \ref{eq|cummatching}) )87 is the duty evele. ie the fraction of halos hat host quasars shining above a minimum luminosity Juin=Ajauin at redshift 2.," is the duty cycle, i.e., the fraction of halos that host quasars shining above a minimum luminosity $x_{\rm min}=M_{i,{\rm min}}$ at redshift $z$."88 Eq. (1)), Eq. \ref{eq|cummatching}) )89 also takes into account a lognormal scatter with dispersion X (in dex) around the mean quasar Iuninositv-halo massrelation., also takes into account a lognormal scatter with dispersion $\Sigma$ (in dex) around the mean quasar luminosity-halo mass.907.. This scatter includes both the scatter between 1911 mass and halo mass and the scatter between luminosity ancl DII mass (i.c.. in the Exdcdington ratio). and our analysis does not distinguish the two contributions.," This scatter includes both the scatter between BH mass and halo mass and the scatter between luminosity and BH mass (i.e., in the Eddington ratio), and our analysis does not distinguish the two contributions."91 At each redshift. DE. (1))," At each redshift, Eq. \ref{eq|cummatching}) )"92" defines the minimum halo MSS Min Corresponding to the minimum luminosity in the sample rii, (the latter taken from S09).", defines the minimum halo mass $y_{\rm min}$ corresponding to the minimum luminosity in the sample $x_{\rm min}$ (the latter taken from S09).93 We then compute the mean bias 6 associated to a given subsample at. redshift 2 with luminosity. Gres=Adjaneq and minimum Luminosity αμα as with and b(y.2) the halo bias given by Sheth ct al. (," We then compute the mean bias $\bar{b}$ associated to a given subsample at redshift $z$ with luminosity $\langle x \rangle=M_{i, {\rm med}}$ and minimum luminosity $x_{\rm min}$ as with and $b(y,z)$ the halo bias given by Sheth et al. ("942001).,2001).95 We stress here that an upper luminosity limit to the bin. corresponding to an upper cut in halo mass (see footnote 2). does not significantly alter the expected. bias given by Iq. (2)).," We stress here that an upper luminosity limit to the bin, corresponding to an upper cut in halo mass (see footnote 2), does not significantly alter the expected bias given by Eq. \ref{eq|beff}) )."96 To perform a detailed. comparison with the SOO data. for at leastsome of the moclels discussed. below. we also computethe quasar auto- ancl cross-correlation functions for each of S09's redshift and. luminosity bins.," To perform a detailed comparison with the S09 data, for at leastsome of the models discussed below, we also computethe quasar auto- and cross-correlation functions for each of S09's redshift and luminosity bins."97 “Phe quasar auto-correlation function is given by where D(z) is the linear growth factor ofperturbations.," The quasar auto-correlation function is given by where $D(z)$ is the linear growth factor ofperturbations,"9820th solar and solar metallicity respectively (for their case € with Salpeter LME).,20th solar and solar metallicity respectively (for their case C with Salpeter IMF).99 In most of our model fits the metallicity is high. (apparently. higher than solar)., In most of our model fits the metallicity is high (apparently higher than solar).100 Therefore it is not so surprising that this ratio is shallow in our mocels., Therefore it is not so surprising that this ratio is shallow in our models.101 The observed ratio GNY /NZ) [rom regions may not be such a useful constraint to try to match in metal-rich. earlv-tvpe galaxies which formed most of their metals early on.," The observed ratio $\Delta Y/\Delta Z$ ) from regions may not be such a useful constraint to try to match in metal-rich, early-type galaxies which formed most of their metals early on."102 The observed. ratio itself is. not well constrained. with estimates ranging from about 3 to 6 (Pagel et 11992).," The observed ratio itself is not well constrained, with estimates ranging from about 3 to 6 (Pagel et 1992)."103 SNla contribute to the metallicity but not the helium. so they act to. lower the helium-to-metal increase with time.," SNIa contribute to the metallicity but not the helium, so they act to lower the helium-to-metal increase with time."104 IMS. contribute helium. and low mass metals., IMS contribute helium and low mass metals.105 More. metal rich. massive stars. also contribute more helium. ancl metals in winds than co metal poor. massive stars.," More metal rich, massive stars also contribute more helium and metals in winds than do metal poor, massive stars."106 On the other hand. metal rich. massive stars do not form black holes.," On the other hand, metal rich, massive stars do not form black holes."107 The balance of these processes leads to a variable AY/AZ with time and metallicitv., The balance of these processes leads to a variable $\Delta Y/\Delta Z$ with time and metallicity.108 So accurate modelling of the amount and composition of stellar mass loss as a function of star mass ancl metallicity is an important requirement for predicting accurate helium-to-metal enrichment. ratios from chemical evolution models., So accurate modelling of the amount and composition of stellar mass loss as a function of star mass and metallicity is an important requirement for predicting accurate helium-to-metal enrichment ratios from chemical evolution models.109 Ehe strong dependence. of AY/AZ on theoretical assumptions about SNIL explosions limits the usefulness of NYZZ as an observational constraint. on chemical evolution models., The strong dependence of $\Delta Y/\Delta Z$ on theoretical assumptions about SNII explosions limits the usefulness of $\Delta Y/\Delta Z$ as an observational constraint on chemical evolution models.110Survey missions desiencc primarily for observing the continuum radiation at one or more frequencies (for example WALAP (7). Planck (7)). generally produce. as a. by-ooduct a point- or compact-source catalogue (e.g.27) containing positional and (lux information on the detected sources.,"Survey missions designed primarily for observing the continuum radiation at one or more frequencies (for example WMAP \citep{bennett97}, Planck \citep{tauber04}) ), generally produce as a by-product a point- or compact-source catalogue \citep[e.g.\ ][]{lopez07,vielva03}, containing positional and flux information on the detected sources."111 Generally these data have been. or are planned to e. extracted [rom the pixel maps on which the survey data are projected ancl collected.," Generally these data have been, or are planned to be, extracted from the pixel maps on which the survey data are projected and collected."112 The process involves a point-source detection on those maps. followed by an estimate of 16 position and Ilux from the pixels.," The process involves a point-source detection on those maps, followed by an estimate of the position and flux from the pixels."113 There are two intrinsic xoblems here., There are two intrinsic problems here.114 Firstly. cach pixel will represent. a dilferent 'ollection of sean directions.," Firstly, each pixel will represent a different collection of scan directions."115 Secondly. the digitisation on re pixel map will lead. to signal distortion. as centres nel sizes of map-pixels will never coincide accurately. with 1 original size ancl shape of the measured. samples.," Secondly, the digitisation on the pixel map will lead to signal distortion, as centres and sizes of map-pixels will never coincide accurately with the original size and shape of the measured samples."116 When the point-spreac function (PSE) of the instrument is circular symmetric. these problems may be partly overcome.," When the point-spread function (PSF) of the instrument is circular symmetric, these problems may be partly overcome."117 However. any asymmetry in the PSE will lead to a distortion of the accumulated image that is dillicult. if not impossible. to fully incorporate when deriving from the pixel maps the all-ipiportant image parameters: the position and Dux of the source with their formal errors.," However, any asymmetry in the PSF will lead to a distortion of the accumulated image that is difficult, if not impossible, to fully incorporate when deriving from the pixel maps the all-important image parameters: the position and flux of the source with their formal errors."118 LO was also considered. tha pixelisation of the data could have a significant elfect on the derived source parameters and their standard errors., It was also considered that pixelisation of the data could have a significant effect on the derived source parameters and their standard errors.119 Providing accurate anc fully internally consisten positional and [ux information for point sources detected in a survev mission is crucially important for any subsecquen use of those cata., Providing accurate and fully internally consistent positional and flux information for point sources detected in a survey mission is crucially important for any subsequent use of those data.120 Cross identification followed. by. [ux comparisons for dillerent wavelengths is only the mos obvious application allected., Cross identification followed by flux comparisons for different wavelengths is only the most obvious application affected.121 Studies of the dillerent spectra shapes among the cletected sources will rely on. the compatibility anc accuracy of data. obtained. in cdilleren wavelengths to allow for reliable. classification of (newly discovered) objects., Studies of the different spectral shapes among the detected sources will rely on the compatibility and accuracy of data obtained in different wavelengths to allow for reliable classification of (newly discovered) objects.122 We started. the current study with the following hypothesis: Pho question we then asked ourselves was the following:, We started the current study with the following hypothesis: The question we then asked ourselves was the following:123and cylinders are cousidercd as approximations of the observed structures in the IS\[.,and cylinders are considered as approximations of the observed structures in the ISM.124 As selt-exavitatiug entities. they display a density aud pressure profile.," As self-gravitating entities, they display a density and pressure profile."125 It is reasonable o asstune that condeused cores fori out of deusitv euliauceimoents at he ceuters of the GAIC., It is reasonable to assume that condensed cores form out of density enhancements at the centers of the GMC.126 Tere. potential cores experience the highest pressures aud are therefore the locations where clouds ean most easilv become selberavitating.," Here, potential cores experience the highest pressures and are therefore the locations where clouds can most easily become self-gravitating."127 Only those cases are therefore considered iu he model., Only those cases are therefore considered in the model.128 For suuplicitv. the mass aud size of the core is asstuned to be ueglieible o the uass and the exteusion ofthe filaments.," For simplicity, the mass and size of the core is assumed to be negligible to the mass and the extension of the filaments."129 The physical properties of a critical stable spherical GAIC is described by the sue equations as eiven for the cores (Eq., The physical properties of a critical stable spherical GMC is described by the same equations as given for the cores (Eq.130 1 -5))., \ref{eq_coremass} - \ref{eq_meancolumncore}) ).131 Replacing the pressure by the mean ISAT pressure of 2<104Ken. the mass radius relation is iu good agreement with observatious of interstellar molecular clouds (72).," Replacing the pressure by the mean ISM pressure of $2\times 10^4~{\rm K/cm^3}$, the mass radius relation is in good agreement with observations of interstellar molecular clouds \citep{Larson1981}."132 To study the whole rauge of structures frou Bok-elobules to lighly eumibedded cores. I cousider for a οἼνοιι external pressure different extinction values through the fibunents.," To study the whole range of structures from Bok-globules to highly embedded cores, I consider for a given external pressure different extinction values through the filaments."133 Since the ceutral pressure of sclferavitating clouds is related to the colin deusitv at its center. the ceutral pressure is also varied.," Since the central pressure of self-gravitating clouds is related to the column density at its center, the central pressure is also varied."134 The relation for spheres aud cvlnders eiibedded in the ISM. of our Galaxy. is shown in Fig. l., The relation for spheres and cylinders embedded in the ISM of our Galaxy is shown in Fig. \ref{fig_colpresrel}.135 For the same ceutral extinction of a filament. cores situated in cvlnders are subject to a higher ceutral pressure than cores in splieres.," For the same central extinction of a filament, cores situated in cylinders are subject to a higher central pressure than cores in spheres."136 The range of extinction values considered in the paper leads to the situation indicated in Fie. 1..," The range of extinction values considered in the paper leads to the situation indicated in Fig. \ref{fig_colpresrel},"137 where the eravitational state of the spherical filamecuts varies over a wide range from highlv stable to. m some cases. liehly super-critical clouds.," where the gravitational state of the spherical filaments varies over a wide range from highly stable to, in some cases, highly super-critical clouds."138" For the physical solutions of selteravitatiung isothermal cylinders. a similar stability classification as for spheres does not exist as the cloud can always produce by compression a ligher gas pressure at the cloud οσο,"," For the physical solutions of self-gravitating isothermal cylinders, a similar stability classification as for spheres does not exist as the cloud can always produce by compression a higher gas pressure at the cloud edge."139 The exliudrical filaments cau therefore for all cases studied iu the paper be regarded as stable., The cylindrical filaments can therefore for all cases studied in the paper be regarded as stable.140" Cyhuders have a παπα mass-ine deusitv eiven by ον,=2N/G. where Af is the cloud mass. £ is the cloud leugth. aud G is the eravitational constant."," Cylinders have a maximum mass-line density given by $M_{\rm cyl}/L=2K/G$, where $M_{\rm cyl}$ is the cloud mass, $L$ is the cloud length, and $G$ is the gravitational constant."141" The constant A. given by Apply(ini). is the one generally introduced i isothermal cloud inodels where Ap is the Boltzmann coustant. 254, the atomic mass unit. and gr the mean molecular weight."," The constant $K$, given by $k_{\rm B}T/(\mu m_{\rm u})$, is the one generally introduced in isothermal cloud models where $k_{\rm B}$ is the Boltzmann constant, $m_{\rm u}$ the atomic mass unit, and $\mu$ the mean molecular weight."142 This mass-line density 1s only reached in the limut of fuite overpressure (Fischera. im prep.).," This mass-line density is only reached in the limit of infinite overpressure (Fischera, in prep.)."143 By construction. the mass-line density of evliuders with &uite overpressure is lower than the asvauptotic value.," By construction, the mass-line density of cylinders with finite overpressure is lower than the asymptotic value."144 Tf we consider two clouds with the same mass-line density. a higher overpressure corresponds to a lower (effective) gas teiiperature.," If we consider two clouds with the same mass-line density, a higher overpressure corresponds to a lower (effective) gas temperature."145 A change iu the external pressure clearly las no consequence ou the overpressure., A change in the external pressure clearly has no consequence on the overpressure.146 The situation is fundamentally different for spherical clouds where the maxima mass 1s identical to the critical stable mass given bv ALx(TgyVp. Where a hnieher external pressure will chauge the C»gravitational state and can make the cloud unstable.," The situation is fundamentally different for spherical clouds where the maximum mass is identical to the critical stable mass given by $M_{\rm sph} \propto (T/\mu)^2/\sqrt{p_{\rm ext}}$, where a higher external pressure will change the gravitational state and can make the cloud unstable."147 While a cooling of a spherical cloud will consequently lead. to a critical and finally unstable cloud it will lead ouly to a higher eravitational bu still stable state iu the case of evliuders., While a cooling of a spherical cloud will consequently lead to a critical and finally unstable cloud it will lead only to a higher gravitational but still stable state in the case of cylinders.148 I uote that - although a supercritical spherical cloud can )o constructed - Us state can uot be obtained by ποστς of sinple cooling., I note that - although a supercritical spherical cloud can be constructed - this state can not be obtained by means of simple cooling.149 If pressure equilibrium between cloud aud he surrounding iiediuu were assumed cooling of a critical stable cloud would lead to a in the pressuxc at he outskirts., If pressure equilibrium between cloud and the surrounding medium were assumed cooling of a critical stable cloud would lead to a in the pressure at the outskirts.150 A spherical super-critical cloud. assumed to 0 in pressure equilibrium with the surrounding medium also corresponds to a cloud temperature the critical eniperature (Fischera. in prep.).," A spherical super-critical cloud assumed to be in pressure equilibrium with the surrounding medium also corresponds to a cloud temperature the critical temperature (Fischera, in prep.)."151 Cyhudrical selt-gravitatiug clouds of high overpressure are characterized by a steep deusity profile at the outskirts with pxrPerey.," Cylindrical self-gravitating clouds of high overpressure are characterized by a steep density profile at the outskirts with $\rho\propto r^{-4}$ \citep{Stodolkiewicz1963,Ostriker1964}."152 The observed density profile of interstellar clouds as pointed out by ? appears to be less steep and more closely represented by a profile pXr7., The observed density profile of interstellar clouds as pointed out by \citet{FiegePudritz2000a} appears to be less steep and more closely represented by a profile $\rho\propto r^{-2}$.153 Tustabilitices may explain these results as e.g. discussed bv? or ?. which prevent the clouds producing high overpressures.," Instabilities may explain these results as e.g. discussed by \citet{Larson1985} or \citet{FiegePudritz2000b}, which prevent the clouds producing high overpressures."154 However. cases with high overpressure are still useful iu the framework of the radiative transfer problem aud are therefore included in the model.," However, cases with high overpressure are still useful in the framework of the radiative transfer problem and are therefore included in the model."155within the carh-type galaxw popilation have been relatively few 1u nuuber and have often found no sjenificaut trems with local ealaxy density.,within the early-type galaxy population have been relatively few in number and have often found no significant trends with local galaxy density.156 Comparing the morphologics of massive galaxies in the low-redshitt (2 0.165) Abell 901/902. supercluster to those of conrpurable fed samples selected from the Space Telescope A901 Calaxy Evolution Survey 59)... detect no sjeuificaut relationship between salaxw structure and euvironnient wilin the early-type population.," Comparing the morphologies of massive galaxies in the low-redshift $z=0.165$ ) Abell 901/902 supercluster to those of comparable field samples selected from the Space Telescope A901/2 Galaxy Evolution Survey , detect no significant relationship between galaxy structure and environment within the early-type population."157 Focusing ou galaxy eroups identified in the Sloan Digital Skv Survey2000).. a less extreme subdivision of the environnieut distribution. also fud uo significant evidence for a correlation between local euvironimnent and the size or Sérrsic index. within the local carly-type population2010).," Focusing on galaxy groups identified in the Sloan Digital Sky Survey, a less extreme subdivision of the environment distribution, also find no significant evidence for a correlation between local environment and the size or Sérrsic index within the local early-type population."158. Iu contrast. previous studies of brightest cluster calaxics (BCGs) in the local Universe find that BCCs tend to be larger than carly-tyvpes of comparable stellar mass," In contrast, previous studies of brightest cluster galaxies (BCGs) in the local Universe find that BCGs tend to be larger than early-types of comparable stellar mass"159where — dio /c) is (he effective observed. volume used in equation (3)).,where = dt ) is the effective observed volume used in equation \ref{eq:ele}) ).160 To relate this to V. werewrite Eq. (AG))," To relate this to $V$, werewrite Eq. \ref{vobsdef}) )"161 in terms of the spatial coordinates in the blob frame. keeping the time / in the (frame.," in terms of the spatial coordinates in the blob frame, keeping the time $t$ in the frame."162 Since d.e=da/V. dy!=dy and dz!=dz we have: — dl /c) — dto( (25031 /(D)) pu/c) where we assume. without loss of generality. that 1 lies in the wy plane.," Since $dx=dx'/\Gamma$, $dy'=dy$ and $dz'=dz$ we have: = dt ) = dt t ) ) where we assume, without loss of generality, that ${\bf\hat{n}}$ lies in the $x$ $y$ plane."163 Performing the integral over / now vields, Performing the integral over $t$ now yields164these lines are well suited to determination of the CH4 stratospheric abundance.,these lines are well suited to determination of the $_4$ stratospheric abundance.165" We assumed a CH4 abundance of 2 in the deep troposphere, then following the saturation law."," We assumed a $_4$ abundance of 2 in the deep troposphere, then following the saturation law."166" In the stratosphere, the CH4 profile was characterized by its high-altitude mixing ratio (¢cy,) and assumed to follow local saturation below the condensation point near 40 mbar."," In the stratosphere, the $_4$ profile was characterized by its high–altitude mixing ratio $q_{CH_4}$ ) and assumed to follow local saturation below the condensation point near 40 mbar."167 Utilizing the Boudon et al. (, Utilizing the Boudon et al. (168"2010) results on the absolute CH, line strengths and in particular using the high S/N dedicated CH, 120 ym line scan (Fig. 4)),","2010) results on the absolute $_4$ line strengths and in particular using the high S/N dedicated $_4$ 120 $\mu$ m line scan (Fig. \ref{fig:methane}) ),"169" we determined qcu, = (1.5x0.2)x10, consistent with Bézzard et al. ("," we determined $q_{CH_4}$ = $\pm$ $\times$ $^{-3}$, consistent with Bézzard et al. ("1701999b) ((0.5—)x10?) but only marginally with Fletcher et al. (,1999b) $\times$ $^{-3}$ ) but only marginally with Fletcher et al. (1712010) ((0.9:-0.3)x10-?).,2010) $\pm$ $\times$ $^{-3}$ ).172" Because of the progressive increase of the continuum level longwards of 100 um, the CH, features at 137 pm and particularly 159 um are sensitive to the CH4 amount in the lower stratosphere."," Because of the progressive increase of the continuum level longwards of 100 $\mu$ m, the $_4$ features at 137 $\mu$ m and particularly 159 $\mu$ m are sensitive to the $_4$ amount in the lower stratosphere."173" An alternate assumption would be that the CH, is supersaturated there, as could perhaps result from strong convective overshoot."," An alternate assumption would be that the $_4$ is supersaturated there, as could perhaps result from strong convective overshoot."174" This situation leads, however, to unobserved absorption wings at 159 um and to inconsistent mixing ratios for the different lines (Fig. 4))."," This situation leads, however, to unobserved absorption wings at 159 $\mu$ m and to inconsistent mixing ratios for the different lines (Fig. \ref{fig:methane}) )."175" A 1.5x1073 mixing ratio is ~10 times greater than allowed by the 56 K cold trap, and consistent with saturation at 60 K. The most probable origin of this elevated stratospheric abundance is that CHA leaks from the hot (62-66 K at the tropopause) Southern region (Orton et al."," A $\times$ $^{-3}$ mixing ratio is $\sim$ 10 times greater than allowed by the 56 K cold trap, and consistent with saturation at 60 K. The most probable origin of this elevated stratospheric abundance is that $_4$ leaks from the hot (62–66 K at the tropopause) Southern region (Orton et al."176 2007) and is redistributed planetwide by global circulation., 2007) and is redistributed planetwide by global circulation.177" A combined analysis of the PACS, ISO,Spitzer, and AKARI data in terms of stratospheric methane and temperature profile will be performed in the future."," A combined analysis of the PACS, ISO, and AKARI data in terms of stratospheric methane and temperature profile will be performed in the future."178" The presence of HO in giant planet stratospheres, including Neptune's, was established from ISO/SWS 20-45 pum spectra (Feuchtgruber et al."," The presence of $_2$ O in giant planet stratospheres, including Neptune's, was established from ISO/SWS 30–45 $\mu$ m spectra (Feuchtgruber et al."179" 1997), demonstrating the existence of an external oxygen supply."," 1997), demonstrating the existence of an external oxygen supply."180" In Neptune's case, ISO observations determined a (2-4)x10! cm? column density, but did not establish the water vertical profile, a parameter needed to derive the rate at which water is removed by vertical mixing and condensation and to infer the input flux of water."," In Neptune's case, ISO observations determined a $\times$ $^{14}$ $^{-2}$ column density, but did not establish the water vertical profile, a parameter needed to derive the rate at which water is removed by vertical mixing and condensation and to infer the input flux of water."181" More than 20 H5O lines, encompassing over a range in opacity of more than anorder of magnitude (~0.2 to 2.5), are detected in the PACS spectrum."," More than 20 $_2$ O lines, encompassing over a range in opacity of more than anorder of magnitude $\sim$ 0.2 to 2.5), are detected in the PACS spectrum."182" If uniformly mixed above the condensation level near 1.2 mbar, the water mixing ratio is qg,o = (0.85+40.2) ppb, and its column density is (2.1+0.5)x10!4 cm."," If uniformly mixed above the condensation level near 1.2 mbar, the water mixing ratio is $_{H_2O}$ = $\pm$ 0.2) ppb, and its column density is $\pm$ $\times$ $^{14}$ $^{-2}$."183 Following Feuchtgruber et al. (, Following Feuchtgruber et al. (184"1997), we also considered H5O vertical profiles resulting from transport models, characterized by the eddy diffusion coefficient profile (profiles ""A"" and ""B"", see Fig. 2)).","1997), we also considered $_2$ O vertical profiles resulting from transport models, characterized by the eddy diffusion coefficient profile (profiles ""A"" and ""B"", see Fig. \ref{fig:thermal}) )."185" For a given vertical profile, the water amounts we determined from the data were identical, to within 10 %,, to the values inferred from ISO."," For a given vertical profile, the water amounts we determined from the data were identical, to within 10 , to the values inferred from ISO."186" However,"," However,"187only occurs for a small subset of possible How regimes close to density inversion.,only occurs for a small subset of possible flow regimes close to density inversion.188 Steacky flows are the only steady-state processes known {ο be capable of extending scale heights., Steady flows are the only steady-state processes known to be capable of extending scale heights.189 Either the particular [low regimes capable of this occur often in active regions. or the majority οἱ extended pressure scale heights observed in ac(ve regions remain unexplained and (here is another process lengthening scale heights that we haven't vel thought of.," Either the particular flow regimes capable of this occur often in active regions, or the majority of extended pressure scale heights observed in active regions remain unexplained and there is another process lengthening scale heights that we haven't yet thought of."190 The search [or such a process remains a challenge for (he Iuture aud its success would be an important step towards a complete understaiding the plvsics behind (he bulk ecquilibrium of active regions., The search for such a process remains a challenge for the future and its success would be an important step towards a complete understanding the physics behind the bulk equilibrium of active regions.191 ] thank the releree for constructive comments which led (o a substantial improvenient ol the paper. and Markus Aschwanden for encouragement.," I thank the referee for constructive comments which led to a substantial improvement of the paper, and Markus Aschwanden for encouragement."192 This work was conducted while the author was a participant in the National Aeronauties aud Space Administration (NASA) Postdoctoral Program at Goddard Space Flight Center. administered by the National Research Council (NRC) and Oak Ridge Associated Universities (ORAU). and was based at National Solar Observatory. Tucson.," This work was conducted while the author was a participant in the National Aeronautics and Space Administration (NASA) Postdoctoral Program at Goddard Space Flight Center, administered by the National Research Council (NRC) and Oak Ridge Associated Universities (ORAU), and was based at National Solar Observatory, Tucson."193et al.,et al.194 2008. 2010. Lebbre et al.," 2008, 2010, Lèbbre et al."195 2009)., 2009).196 For all these active stars. the origin of the magnetic field is very likely a dynamo.," For all these active stars, the origin of the magnetic field is very likely a dynamo."197" Magnetic fields were also detected iu slowly rotating giants. including EI, Eun. which prescuts a strong maguctic field (Auri¢rre et al."," Magnetic fields were also detected in slowly rotating giants, including EK Eri, which presents a strong magnetic field (Aurièrre et al."198 2008) and Pollux. which presents a very weak magnetic field (Auricire et al.," 2008) and Pollux, which presents a very weak magnetic field (Aurièrre et al."199 20093., 2009).200 These Zeeman-detected evolved stars included oulv intermediate mass objects., These Zeeman-detected evolved stars included only intermediate mass objects.201" Ciureutly. an increasiue miuber of massive stars have oen detected as magnetic. in partieulu thanks to the systematic investigation of the MBMoeS collaboration (ο,ο (απμας et al."," Currently, an increasing number of massive stars have been detected as magnetic, in particular thanks to the systematic investigation of the MiMeS collaboration (e.g. Grunhut et al."202 2009). which concerns main-sequence and ore-nndnu sequence stars.," 2009), which concerns main-sequence and pre-main sequence stars."203 An investigation of the magnetic Ποιος of APCUSAL supereiauts is also under way and first Zecluan detections were presented recently (Curunuhut et al., An investigation of the magnetic fields of AFGKM supergiants is also under way and first Zeeman detections were presented recently (Grunhut et al.204 2010)., 2010).205 Betelecuse appears to be the first M superegiaut ο be detected as magnetic., Betelgeuse appears to be the first M supergiant to be detected as magnetic.206" Deteleeuse is a liehlv variable star iu a genera SCLC, because it ds an nreeular pulsating variable star that presents a wide range of photometric ik spectral variations (Coldbere 1981. Cray 2008)."," Betelgeuse is a highly variable star in a general sense, because it is an irregular pulsating variable star that presents a wide range of photometric and spectral variations (Goldberg 1984, Gray 2008)."207 For the chromospheric lines. which can be tracers of magnetic activity. Ca IT IIIs present variatious (Toussaint ik Reiners. 1989). as well as MeII k (Dupree ct al.," For the chromospheric lines, which can be tracers of magnetic activity, Ca II K present variations (Toussaint and Reimers, 1989), as well as MgII k (Dupree et al."208 1987)., 1987).209 No X-ray emission. which cau be due to coronal heating. could be detected in auyv observation of Deteleeuse. ik very weak upper limits in flux were reached (Aageio et al.," No X-ray emission, which can be due to coronal heating, could be detected in any observation of Betelgeuse, and very weak upper limits in flux were reached (Maggio et al."210 1990. Posson-Brown et al.," 1990, Posson-Brown et al."211 2006)., 2006).212" The reason could be that the magnetic loops are ""buried in the highly exteude chromospheric material as sugeested for cool giants by Avyes et al. ("," The reason could be that the magnetic loops are “buried” in the highly extended chromospheric material, as suggested for cool giants by Ayres et al. ("2132003).,2003).214 Because the rotational period of Betclecuse is expectec to last several τος (2335 davs: AAVSO data. Stothers and Leung 19071: 17 vears: Uitenbrock ct al.," Because the rotational period of Betelgeuse is expected to last several years (2335 days: AAVSO data, Stothers and Leung 1971; 17 years: Uitenbroek et al."215 L998) a classical solar-type dynamo is not expected to operate there., 1998) a classical solar-type dynamo is not expected to operate there.216 Takine its large radius iuto account (R=615 R.. Perrin et al.," Taking its large radius into account (R=645 $R_{\odot}$, Perrin et al."217 2001). the fossil field from a nmüagnetic Inada sequence star would be too diluted to provide an efficient. ronunau as iu Elk Eri CCGSIII/IV. Stepien 1993. Strassineicr et al.," 2004), the fossil field from a magnetic main sequence star would be too diluted to provide an efficient remnant as in EK Eri (G8III/IV, Stepień 1993, Strassmeier et al."218 1999. Auri¢rre et al.," 1999, Aurièrre et al."219 2008)., 2008).220" ""Theoretical oedietions (Schwarzschild 1975) and interferometric observations (6.8. Ilaubois et al.", Theoretical predictions (Schwarzschild 1975) and interferometric observations (e.g. Haubois et al.221 2009. Chiavassa et al.," 2009, Chiavassa et al."222 2010) suggestOO there are large convection cells on the surface of Deteleeuse., 2010) suggest there are large convection cells on the surface of Betelgeuse.223 The 3D convection siulatious of Detelgeuse have already: been carried. out (Frevtag ct al., The 3D convection simulations of Betelgeuse have already been carried out (Freytag et al.224 2002: Dorch 2001) and these studies also Sugeest there are large convective cells aud. furtherinore that à magnetic field could be sustained., 2002; Dorch 2004) and these studies also suggest there are large convective cells and furthermore that a magnetic field could be sustained.225" The Betclecusian dvuame would belong to the class of so-called ""loca snalbseale dyausunos. though the generated magnetic field is both local and large scale (Dorch 2001)."," The Betelgeusian dynamo would belong to the class of so-called “local small-scale dynamos”, though the generated magnetic field is both local and large scale (Dorch 2004)."226 This Isinc of dynamo would work even without rotation (Frevtag et al., This kind of dynamo would work even without rotation (Freytag et al.227 2002) ancl las the sale nature as the loca dynamo. possibly coutributing to the small-scale magnetic ποια on the solu surface (ef," 2002) and has the same nature as the local dynamo, possibly contributing to the small-scale magnetic field on the solar surface (cf."228 Cattaneo 1999)., Cattaneo 1999).229 Dorch (2001) presents a detailed uunerical MIID simulation of Deteleeuse that shows that maguetic spots of strenetl up to 500 CC amay exist but with a mall filline factor., Dorch (2004) presents a detailed numerical MHD simulation of Betelgeuse that shows that magnetic spots of strength up to 500 G may exist but with a small filling factor.230 Our detection aud measurement do prove the existence of a magnetic field on the surface of Betclecus, Our detection and measurement do prove the existence of a magnetic field on the surface of Betelgeuse.231 ΣΑ anouth-scale variation lav have been observed aud has to be confined., A month-scale variation may have been observed and has to be confirmed.232 Variatiou iu the surface pattern on Detelgeuse has been observed on the same fiue scale with interferometry (Wilson et al., Variation in the surface pattern on Betelgeuse has been observed on the same time scale with interferometry (Wilson et al.233 1997)., 1997).234 This time scale is uulikelv to be lmked to the long rotational period and might stem from a local lutrinsic variability iuduced by a local dvuiuuo., This time scale is unlikely to be linked to the long rotational period and might stem from a local intrinsic variability induced by a local dynamo.235 We Zecemanu-detected a magnetic field on the surface of Betelecuse and measured its surface-averaeced longitudinal, We Zeeman-detected a magnetic field on the surface of Betelgeuse and measured its surface-averaged longitudinal236 vois the powerlav exponent of the elliptical mass distribution and fy is a constant.,$\nu$ is the power–law exponent of the elliptical mass distribution and $E_{0}$ is a constant.237" In the analvsis of our results we use the ellipticitv e1""nnbo0X since this is the value that is usually used in the observations."," In the analysis of our results we use the ellipticity $e=1-\frac{b} {a}=\frac {2\epsilon}238{1+\epsilon}$ since this is the value that is usually used in the observations."239 In Appendix A dellection potential and angles for this mass distribution are described., In Appendix \ref {PowerLawDeflection} deflection potential and angles for this mass distribution are described.240 The light distribution of bars has a well-defined. elongated shape. and is non-singular ancl centrally condensed (Sellwood&Wilkinson1993).," The light distribution of bars has a well-defined elongated shape, and is non-singular and centrally condensed \cite{Sellwood1993}."241. It is not straightforward to determine the true form of bar mass distributions from this. so that we have to assume a model.," It is not straightforward to determine the true form of bar mass distributions from this, so that we have to assume a model."242 Very. simple models with these properties of the bar light are the Ferrers profiles (Ferrers1877).," Very simple models with these properties of the bar light are the Ferrers profiles \cite243{Ferrers1877}."244. Phey were used in dynamical studies of bars (Freeman19662.b.c:Martinet&deZeeuwLOSS:SellwoodWilkinson1993) since they can be treated analytically.," They were used in dynamical studies of bars \cite245{Freeman1966,Martinet1988,Sellwood1993} since they can be treated analytically."246" To moclel the surface mass distribution of the bar of 2237|0305 we used tsvo-dimensional Ferrers profiles of the form In this equation. €, and 62 are the coordinates on the sky as measured in a coordinate svstem oriented with the observed major and minor axis of the bar."," To model the surface mass distribution of the bar of 2237+0305 we used two-dimensional Ferrers profiles of the form In this equation, $\theta_1$ and $\theta_2$ are the coordinates on the sky as measured in a coordinate system oriented with the observed major and minor axis of the bar."247" A is à real number. &,; is the central surface density in units of the critical lensing density Mg defined in section 2.1. and e. 6 are the respectively semi-minor axis of the bar."," $\lambda$ is a real number, $\kappa_{\rm c}$ is the central surface density in units of the critical lensing density $\Sigma_{\rm crit}$ defined in section \ref {TheBulge} and $a$, $b$ are the semi-major respectively semi-minor axis of the bar."248 In the analysis we restricted. ourselves {ο moderate exponents A= 0.5. 1 and 2.," In the analysis we restricted ourselves to moderate exponents $\lambda=0.5$ , $1$ and $2$."249 The dellection potential aud angles for integer values of A can be calculated analytically as described in Appencix D.., The deflection potential and angles for integer values of $\lambda$ can be calculated analytically as described in Appendix \ref {FerrersDeflection}.250 For A=0.5 the profiles were constructed. through the numerical superposition of many elliptical slices of constant density (A= 0) and dillerent size (Schramm1994)., For $\lambda=0.5$ the profiles were constructed through the numerical superposition of many elliptical slices of constant density $\lambda=0$ ) and different size \cite {Schramm1994}.251. The lensing influence of the bar can be understood. by considering a system with two shear tensors with shear directions as shown in figure 1. for galaxy. inclination axis and bar (see Schneider. Ehlers Falco (1992) for the definition of the shear tensor).," The lensing influence of the bar can be understood by considering a system with two shear tensors with shear directions as shown in figure \ref {ImageGeometry} for galaxy inclination axis and bar (see Schneider, Ehlers Falco \shortcite {Schneider1992} for the definition of the shear tensor)."252 The resulting shear tensor can be found. by adding up the single tensors and the resulting shear cürection is determined by the shear ratio of the two components., The resulting shear tensor can be found by adding up the single tensors and the resulting shear direction is determined by the shear ratio of the two components.253 A source almost directly behind the core of the lensing galaxy appears lensed with four of the five images in a cross formation aligned with the axes parallel and perpendicular to the resulting shear direction. while the fifth is seen in the centre. (Schneiderοἱaf1992.p252).," A source almost directly behind the core of the lensing galaxy appears lensed with four of the five images in a cross formation aligned with the axes parallel and perpendicular to the resulting shear direction, while the fifth is seen in the centre \cite [p252]{Schneider1992}."254. In the case of 2237|0305. the major axis position angle as found by the one-component lens models (677) can be interpreted to be his resulting shear direction. which almost coincides with he axis through images € and D. The axis through images C and D has cllectively been twisted away from the galaxy inclination axis by the bar.," In the case of 2237+0305, the major axis position angle as found by the one-component lens models $67\degr$ ) can be interpreted to be this resulting shear direction, which almost coincides with the axis through images C and D. The axis through images C and D has effectively been twisted away from the galaxy inclination axis by the bar."255 In figure 2. this twisting is illustrated by plotting the critical lines. caustics and image positions of two barred lenses with identical source positions.," In figure \ref {StrongBar} this twisting is illustrated by plotting the critical lines, caustics and image positions of two barred lenses with identical source positions."256 The caustics are the lines in the source plane that separate regions of clillerent image multiplicity., The caustics are the lines in the source plane that separate regions of different image multiplicity.257 The critical lines are the corresponding lines in the lens plane where pairs of images are created or clestroved (Schneiderefa£1992)., The critical lines are the corresponding lines in the lens plane where pairs of images are created or destroyed \cite {Schneider1992}.258. 1n this figure. the first lens has a weak bar that barely changes the elliptical shape of the bulge’s eritical line or the corresponding diamond shape of the caustic.," In this figure, the first lens has a weak bar that barely changes the elliptical shape of the bulge's critical line or the corresponding diamond shape of the caustic."259 The other bar is significantly more massive: it warps the shape of thesestructures ancl shifts the image positions., The other bar is significantly more massive; it warps the shape of thesestructures and shifts the image positions.260 Our barred galaxy model has ten adjustable paranicters., Our barred galaxy model has ten adjustable parameters.261= ]2pt = 12pt 2.,= 12pt = 12pt 2.262 components spatially varyingUPDATESspectral PLELJILBOS SIMUL.VEIONSthe ANDsimulations RECENTused to create the data for the Planck Satellite presentedobservations., THE SIMULATIONS AND RECENT UPDATES HJLB98 presented the simulations used to create the data for the Planck Satellite observations.263 Here we use the same maps so that easy can be made and we do not include the inputelfects of point sources as this comparisonwas found to have little effect on the reconstructions., Here we use the same input maps so that easy comparison can be made and we do not include the effects of point sources as this was found to have little effect on the reconstructions.264 Figure lshows the six input at 300 Cillz., Figure 1 shows the six input components at 300 GHz.265 We two separate componentsanalyses to test the ellect of relaxing the assumptions performmace about the Galactic , We perform two separate analyses to test the effect of relaxing the assumptions made about the Galactic foregrounds.266The first is simply to assume the incorrect. for the foregrounds.Galactic. foregrounds the this frequencyon spectra, The first is simply to assume the incorrect frequency spectra for the Galactic foregrounds and test the effect that this has on the reconstructions.267 second. is to andassumetest a spatiallyelfect that hasspectral theindex for the reconstructions.Galactic Theforegrounds and try to reconstruct the varving without knowing the form of this spatial variation., The second is to assume a spatially varying spectral index for the Galactic foregrounds and try to reconstruct the components without knowing the form of this spatial variation.268 Figure 2 shows the componentsinput spatial variation in the Galactic dust spectral index., Figure 2 shows the input spatial variation in the Galactic dust spectral index.269 3., 3.270 RESULTS EROSM THIS We first assume that the MIZMGalactic ANALYSIScomponents contributing to the data do not have a well known spectral dependence., RESULTS FROM THE MEM ANALYSIS We first assume that the Galactic components contributing to the data do not have a well known spectral dependence.271 We therefore need to search over a range of spectral indices to find the best result., We therefore need to search over a range of spectral indices to find the best result.272 This is done observing the as a function of spectral index., This is done by observing the $\chi^2$ dependence as a function of spectral index.273 For the frece-[reeby and svnehrotron47 dependenceemission it was found that little cülference in the value was found when the incorrect index was used., For the free-free and synchrotron emission it was found that little difference in the $\chi^2$ value was found when the incorrect spectral index was used.274 The reconstructionsx7 of the other were not spectralaltered in this case but 1e reconstruction of the free-free and componentssvnchrotron were lost., The reconstructions of the other components were not altered in this case but the reconstruction of the free-free and synchrotron were lost.275 However. in re case of varying both the cust emissivity ancl temperature a strong minimum in was seen at the values 3).," However, in the case of varying both the dust emissivity and temperature a strong minimum in $\chi^2$ was seen at the input values (Figure 3)."276 Therefore. it is possible to fit vfor the dust. emission inputusing the cata (Figurealone whereas more," Therefore, it is possible to fit for the dust emission using the data alone whereas more"277"where Gr) is the cimensionless mass interior to .r. in units ο0D,DafDy).","where $m(x)$ is the dimensionless mass interior to $x$, in units of $(c^2/4G)(D_{os}D_{ol}/D_{ls})$."278 A Jensed image ds distorted both racially ancl tangentially with respect to the centre of the lensing potential., A lensed image is distorted both radially and tangentially with respect to the centre of the lensing potential.279 The tangential distortion is the ratio of the tangential size of the image to that of the source: for a sullicientlv. small source it is given. by the ratio of their respective distances from lens centre. τή.," The tangential distortion is the ratio of the tangential size of the image to that of the source; for a sufficiently small source it is given by the ratio of their respective distances from lens centre, $x/y$."280 Similarly. the radial distortion is αμαν. if the source's radial extent. is αμ.," Similarly, the radial distortion is $dx/dy$, if the source's radial extent is $dy$."281 Since magnification is just the ratio of the size of the image to that of the source. it is given by The leneth-to-width ratio of an image whose source is circular is. and is the most commonly. used measure of image distortion.," Since magnification is just the ratio of the size of the image to that of the source, it is given by The length-to-width ratio of an image whose source is circular is, and is the most commonly used measure of image distortion."282" Note that an isothermal density profile. sr)«x pd, implies that dyfade=1 (Equation 7)). i.e. images suller no racial (de)magnification."," Note that an isothermal density profile, $\kappa(x)\propto x^{-1}$ , implies that $dy/dx=1$ (Equation \ref{lens_eq}) ), i.e. images suffer no radial (de)magnification."283 Steeper profiles always result in racially demagnified images. while shallower profiles usually produce raclially magnilied images.," Steeper profiles always result in radially demagnified images, while shallower profiles usually produce radially magnified images."284 Using Equations 4-9 we can calculate all the image properties needed in this paper., Using Equations \ref{mass_dist_proj1}- \ref{LW} we can calculate all the image properties needed in this paper.285 The top panel of Figure 1. shows the relation between the image and source positions. for two values of μυ. of an ESC model.," The top panel of Figure \ref{LWvsx1} shows the relation between the image and source positions, for two values of $\kappa_0$, of an ISC model."286" Supercritical clusters. represented: here. by hy=1. case (solid lines). produce three images if the source impact parameter is smaller than the radial caustic. jy, see Eqn (8.42) of Schneider et al. ("," Supercritical clusters, represented here by $\kappa_0=1.1$ case (solid lines), produce three images if the source impact parameter is smaller than the radial caustic, $y_r$ [see Eqn (8.42) of Schneider et al. ("2871992)].,1992)].288 Suberitical clusters. such as sog=0.9 case (dashed line) always produce one image. and the w-y relation is one-to-one and monotonically increasing.," Subcritical clusters, such as $\kappa_0=0.9$ case (dashed line) always produce one image, and the $x$ $y$ relation is one-to-one and monotonically increasing."289 Figure 2 shows the relation between image magnification and. distortion., Figure \ref{LWvsAmp1} shows the relation between image magnification and distortion.290 “Pwo supercritical cases are shown: solid lines are the three images of a 5023.0. lens. andclot-clash lines are for à πο. lens.," Two supercritical cases are shown: solid lines are the three images of a $\kappa_0$ =3.0 lens, anddot-dash lines are for a $\kappa_0$ =1.1 lens."291 Ehe long-dash line is the single image of a critical lens. 5421.0. while the line is the single image of a 6020.9 lens.," The long-dash line is the single image of a critical lens, $\kappa_0$ =1.0, while the short-dash line is the single image of a $\kappa_0$ =0.9 lens."292 Each lens with Ho291 has three branches corresponding to three images., Each lens with $\kappa_0>1$ has three branches corresponding to three images.293 The primary image. which is formed. at the minimum of the lensing potential see Schneider (1985) and. Blandford Naravan (1986)]. is labeled Lo Phis image appears on the same side of the lens centre as the unlensec source. and is tangentially extended. into an arc. with L/W1.," The primary image, which is formed at the minimum of the lensing potential [see Schneider (1985) and Blandford Narayan (1986)], is labeled I. This image appears on the same side of the lens centre as the unlensed source, and is tangentially extended into an arc, with $L/W>1$."294 lt is always magnified with respect to the source., It is always magnified with respect to the source.295" The image formed. at the sacdedle-point of the lensing potential. sometimes called the ""counter are’. possesses reversed. parity and is labeled LL"," The image formed at the saddle-point of the lensing potential, sometimes called the `counter arc', possesses reversed parity and is labeled II."296 Phe central image. labeled HE. is formed at the maximum of the lensing potential. and is raclially extended. Le. has L/W«1.," The central image, labeled III, is formed at the maximum of the lensing potential, and is radially extended, i.e. has $L/W<1$ ."297 Images HE ancl HE are on the side of the lens opposite to the location of the source., Images II and III are on the side of the lens opposite to the location of the source.298 Note that for very centrally condensed lenses. Le. those with Ho292. image HIE can be demagnified. p<1. if the source is sullicientlv close to the lens centre.," Note that for very centrally condensed lenses, i.e. those with $\kappa_0>2$, image III can be demagnified, $\mu<1$, if the source is sufficiently close to the lens centre."299 The chidden” parameter in this plot is the source position. y.," The `hidden' parameter in this plot is the source position, $y$."300 To illustrate its inlluence on the location of the images. we have plotted the three images of a source at jy=0.010 (empty circles). ancl the three images of a source at y=0.016 (solid. dots). for a 501.1 lens.," To illustrate its influence on the location of the images, we have plotted the three images of a source at $y=0.010$ (empty circles), and the three images of a source at $y=0.016$ (solid dots), for a $\kappa_0$ =1.1 lens."301 As the source approaches the lens centre in projection. images I anc 11 eet very elongated ancl tend to merge along the tangential critical line: while image LL moves close towards the lens centre.," As the source approaches the lens centre in projection, images I and II get very elongated and tend to merge along the tangential critical line; while image III moves close towards the lens centre."302 Notice that the single image branch of a wy«1 lens joins to ancl continues as the branch of the central image. labeled LIL. of the corresponding 20&o lens.," Notice that the single image branch of a $\kappa_0<1$ lens joins to and continues as the branch of the central image, labeled III, of the corresponding $2-\kappa_0$ lens."303 As an example. the image of a wy=0.9 lens (short-dash line)continues as the central image branch of a wy=1.1 lens.," As an example, the image of a $\kappa_0=0.9$ lens (short-dash line)continues as the central image branch of a $\kappa_0=1.1$ lens."304 This can be shown as follows., This can be shown as follows.305 For image position a very close to the lens centre imageὃν magnification.o fe(1wy). has the same numerical value for a αυ as well as a2 wy lens.," For image position $x$ very close to the lens centre image magnification, $\mu\approx(1-\kappa_0)^{-2}$, has the same numerical value for a $\kappa_0$ as well as a $2-\kappa_0$ lens."306 The distortion L/M' of the image located. at. the centre is 1. from symmetry.," The distortion $L/W$ of the image located at the centre is 1, from symmetry."307 Therefore. for small a. the branches of central images of à wy and à 2.wy lens meet at the same point in the logL/W) vs. log(g) diagram.," Therefore, for small $x$, the branches of central images of a $\kappa_0$ and a $2-\kappa_0$ lens meet at the same point in the $(L/W)$ vs. $\mu$ ) diagram."308 The slope of both the branches at this point can be shown to be dog(LAW)/dlog(ya)=i. independent of so. and p: therefore these two branches are continuous.," The slope of both the branches at this point can be shown to be $d\log{(L/W)}/d\log{(\mu)}=-{1\over 2}$, independent of $\kappa_0$, and $p$; therefore these two branches are continuous."309 The most visible feature. in a lensing cluster is the primary arc. since it is always well displaced. from. the cluster centre. is highly elongated. and always magnilied.," The most visible feature in a lensing cluster is the primary arc, since it is always well displaced from the cluster centre, is highly elongated and always magnified."310 For this image. the magnification is an increasing function of distortion.," For this image, the magnification is an increasing function of distortion."311 This is why high magnification is associated with high cistortion of lensed images in galaxy. clusters., This is why high magnification is associated with high distortion of lensed images in galaxy clusters.312 However high magnification need not always imply high distortion., However high magnification need not always imply high distortion.313 Lt is apparent from Figure 2. that subcritical clusters. represented here by a αυ=0.9 case. can produce. highly magnified undistortedimages*.," It is apparent from Figure \ref{LWvsAmp1} that subcritical clusters, represented here by a $\kappa_0=0.9$ case, can produce highly magnified undistorted."314. Por example. if the source is located. closeto the centre of a wy=0.9 lens. its magnification is  100. while its distortion is negligible.," For example, if the source is located closeto the centre of a $\kappa_0=0.9$ lens, its magnification is $\sim$ 100, while its distortion is negligible."315 In fact. the largest. L/M ratio attainedby an image of anv subcritical lens is not greater than L/W= 3. as we now show.," In fact, the largest $L/W$ ratio attainedby an image of any subcritical lens is not greater than $L/W=3$ , as we now show."316 The leneth-to-width ratio of anv image in the [SC cluster model can be derived from Equations 9.. 7.. and 4:," The length-to-width ratio of any image in the ISC cluster model can be derived from Equations \ref{LW}, , \ref{lens_eq}, , and \ref{mass_dist_proj1}; ;"317caused by (he orbital motion is significant.,caused by the orbital motion is significant.318 We have used (he evolution code predictions by Ilowell. Nelson. Rappaport (2001) to estimate the masses of the two components in (he EF En svstem as M4 = 0.6 AL. and Mà = 0.06 AL..," We have used the evolution code predictions by Howell, Nelson, Rappaport (2001) to estimate the masses of the two components in the EF Eri system as $_{\rm 1}$ = 0.6 $_{\sun}$ and $_{\rm 2}$ = 0.06 $_{\sun}$."319 Using an orbital inclination of 45° (see llarrison οἱ al., Using an orbital inclination of $^{\circ}$ (see Harrison et al.320 2003. and references therein). we estimate the radial velocity. semi-amplitude of the secondary in EF Eri to be ky = 340 km |.," 2003, and references therein), we estimate the radial velocity semi-amplitude of the secondary in EF Eri to be $_{\rm 2}$ = 340 km $^{\rm -1}$."321 The full orbital variation corresponds to only about (wo resolution elements in the NURI spectra. but six resolution elements for the Keck spectra.," The full orbital variation corresponds to only about two resolution elements in the NIRI spectra, but six resolution elements for the Keck spectra."322 Thus. to allow us to coadd the individual spectra to search lor features [rom the secondary. star. we have Doppler corrected our data using (his estimated value for Ix».," Thus, to allow us to coadd the individual spectra to search for features from the secondary star, we have Doppler corrected our data using this estimated value for $_{\rm 2}$."323 In our ongoing program of continued. occasional monitoring EF Eri we have obtained a new optical spectrum using the spectrograph in the Red Imaging Low Dispersion (RILD) mode on theNTT.," In our ongoing program of continued, occasional monitoring EF Eri, we have obtained a new optical spectrum using the spectrograph in the Red Imaging Low Dispersion (RILD) mode on the."324 This spectrum. shown in Figure 2. was obtained on 10 August 2002. is a GOO s exposure. and has a resolution of 2.3.," This spectrum, shown in Figure 2, was obtained on 10 August 2002, is a 600 s exposure, and has a resolution of 2.3."325À.. It is interesting to compare this spectrum with those presented in Harrison et al. (, It is interesting to compare this spectrum with those presented in Harrison et al. (3262003). ancl Beuermann et al. (,"2003), and Beuermann et al. ("3272000): the Zeeman absorption features are now more pronounced. and the emission from II I has continued to decline to the point where it is no longer detectable.,"2000): the Zeeman absorption features are now more pronounced, and the emission from H I has continued to decline to the point where it is no longer detectable."328 In the preceding section we noted that we have produced flux-calibrated spectra by using the infrared light curves for EF Evi., In the preceding section we noted that we have produced flux-calibrated spectra by using the infrared light curves for EF Eri.329 We did (his so as to produce a consistent set of data (hat would enable us to ignore slit losses in either set of spectra., We did this so as to produce a consistent set of data that would enable us to ignore slit losses in either set of spectra.330 Comparison of data sets obtained on widely separated epochs like those analvzed here could be compromised by inirmnsic variations in EF Eri., Comparison of data sets obtained on widely separated epochs like those analyzed here could be compromised by intrinsic variations in EF Eri.331 While we are confident about the photometric “stability” of EF En up to. and including (he Gemini data. there is no assurance that EF Eri was in the," While we are confident about the photometric “stability” of EF Eri up to, and including the Gemini data, there is no assurance that EF Eri was in the"332"correlation between n as measured in either FUV or H bands with either logσο or any stellar population parameter, but n measured in the ΝΟΥ band has strong positive correlation with logco (SRCC = 0.65; p«a 0.0001) and weaker but significant correlations with both with [Z/H] (SRCC = 0.45; p= 0.012), and [o/Fe] (SRCC = 0.46; p— 0.010).","correlation between $n$ as measured in either FUV or H bands with either $\log{\sigma_0}$ or any stellar population parameter, but $n$ measured in the NUV band has a strong positive correlation with $\log{\sigma_0}$ (SRCC = 0.65; $p < 0.0001$ ) and weaker but significant correlations with both with [Z/H] (SRCC = 0.45; $p = 0.012$ ), and $\alpha$ /Fe] (SRCC = 0.46; $p = 0.010$ )."333 We suggest that the correlation found by Marino et al. (, We suggest that the correlation found by Marino et al. (334"2011) is dominated by the NUV band, and, as they suggest, is a consequence of the correlation of all of these parameters with the depth of the galaxy potential well.","2011) is dominated by the NUV band, and, as they suggest, is a consequence of the correlation of all of these parameters with the depth of the galaxy potential well."335" The mechanism by which the potential affects n in the NUV band is related to the strong UV to IR colour gradients found in galaxies of lower logoo (Figure 6,, upper right panel) which in turn is related to the strong metallicity gradients in galaxies of intermediate velocity dispersion."," The mechanism by which the potential affects $n$ in the NUV band is related to the strong UV to IR colour gradients found in galaxies of lower $\log{\sigma_0}$ (Figure \ref{fig:GradientPlots}, upper right panel) which in turn is related to the strong metallicity gradients in galaxies of intermediate velocity dispersion."336 The colour gradients show that the stars contributing to the FUV excess are more centrally concentrated than the underlying population., The colour gradients show that the stars contributing to the FUV excess are more centrally concentrated than the underlying population.337 We now attempt to map these regions by subtracting from the GALEX images a model of the underlying population as determined in the H band., We now attempt to map these regions by subtracting from the GALEX images a model of the underlying population as determined in the H band.338" We use to determine n and [ο for the H-band image, then we scale this model to the GALEX images, with the high surface brightness regions masked out."," We use to determine $n$ and $R_e$ for the H-band image, then we scale this model to the GALEX images, with the high surface brightness regions masked out."339 The mask was constructed from the FUV image., The mask was constructed from the FUV image.340 Initially a copy of the FUV image was smoothed with a circular Gaussian kernel of o = 3 pixels (4.5 arcseconds)., Initially a copy of the FUV image was smoothed with a circular Gaussian kernel of $\sigma$ = 3 pixels (4.5 arcseconds).341" All pixels in the smoothed image below a threshold were then set to zero, and the resultant image was used as the mask image forGALFIT,, which ignores in the fit all pixels whose value in the mask is not zero."," All pixels in the smoothed image below a threshold were then set to zero, and the resultant image was used as the mask image for, which ignores in the fit all pixels whose value in the mask is not zero."342" The FUV surface brightness of the mask threshold was set between 26.0 and 27.0 mag arcsec?, and was dependent upon the exposure time of the FUV image."," The FUV surface brightness of the mask threshold was set between 26.0 and 27.0 mag $^{-2}$, and was dependent upon the exposure time of the FUV image."343" was run on both FUV and NUV images using the mask determined in FUV, and with n, RH. and the ellipticity and position angle constrained to the values determined in H. The galaxy centre pixel co-ordinates were constrained to those found from the unmasked FUV and NUV images."," was run on both FUV and NUV images using the mask determined in FUV, and with $n$, $R_e$ and the ellipticity and position angle constrained to the values determined in H. The galaxy centre pixel co-ordinates were constrained to those found from the unmasked FUV and NUV images."344" So effectively we scale the H-band model to the outer regions of the FUV and NUV images, and subtract this scaled model."," So effectively we scale the H-band model to the outer regions of the FUV and NUV images, and subtract this scaled model."345 The residual images now show the spatial distribution of the sources giving rise to the FUV excess., The residual images now show the spatial distribution of the sources giving rise to the FUV excess.346" In Figures B1 to B6 of Appendix B, presented in the online version of the paper only, we show, for a subsample of our galaxies, greyscale images showing the FUV images, FUV residual images, and the residual images in the NUV band obtained by the same process."," In Figures B1 to B6 of Appendix B, presented in the online version of the paper only, we show, for a subsample of our galaxies, greyscale images showing the FUV images, FUV residual images, and the residual images in the NUV band obtained by the same process."347 Most FUV images show an extended FUV excess over the H-band fit at some level., Most FUV images show an extended FUV excess over the H-band fit at some level.348" The NUV residual images show a variety of structures, and provide some indication of the source of the FUV excess emission."," The NUV residual images show a variety of structures, and provide some indication of the source of the FUV excess emission."349" In many galaxies with extended FUV excess (e.g. NGC720, NGC1404, NGC4473, NGC4697 and many other galaxies) the NUV residual image is negative in the core, reflecting the negative"," In many galaxies with extended FUV excess (e.g. NGC720, NGC1404, NGC4473, NGC4697 and many other galaxies) the NUV residual image is negative in the core, reflecting the negative"350In summary. our study shows that SP'T is a suitable approximation for the matter field even at redshift 0. provided a large enough smoothing radius is adopted.,"In summary, our study shows that SPT is a suitable approximation for the matter field even at redshift 0, provided a large enough smoothing radius is adopted."351 However. the Eulerian local bias model can not fully describe the halo density field. which is most evident [rom our by-point comparison in Fig. 10..," However, the Eulerian local bias model can not fully describe the halo density field, which is most evident from our point-by-point comparison in Fig. \ref{fig:dhvsfdmdm_lowdens}."352" We acknowledge support through the SED-'lransregio 33. ""Phe Dark Universe” by the Deutsche lorschungsgemeinschaft (DEC)."," We acknowledge support through the SFB-Transregio 33 ""The Dark Universe"" by the Deutsche Forschungsgemeinschaft (DFG)."353 , \nocite{2007AAS...211.9108J} \nocite{2009ApJ...691..569J} 354where (ΑςΛο is the fiducial value from $2.,where $(\Delta z/R)_0$ is the fiducial value from 2.355 The fractional change in spin frequency is .(2Ar/R). where Ar is the coordinate thickness.," The fractional change in spin frequency is $\beta(2\Delta r/R)$ , where $\Delta r$ is the coordinate thickness."356 Converting to proper thickness Ac involves another factor of V. giving where we define ao as the scaling factor from the fiducial value. and we took M/R20.21 in 82.," Converting to proper thickness $\Delta z$ involves another factor of ${\cal V}$ , giving where we define $\alpha$ as the scaling factor from the fiducial value, and we took $M/R=0.21$ in 2."357 Note that the largest contributions to à. come from rescaling gravity and including the centrifugal force. rather than from general. relativistic effects.," Note that the largest contributions to $\alpha$ come from rescaling gravity and including the centrifugal force, rather than from general relativistic effects."358 Figure 3 shows a as a function of neutron star mass. for EOS APR and EOS L. and in each case for »/=300 and 600Hz.," Figure \ref{fig:corr} shows $\alpha$ as a function of neutron star mass, for EOS APR and EOS L, and in each case for $\nu=300$ and $600\359{\rm Hz}$."360 We also give à in Table l.., We also give $\alpha$ in Table \ref{tab:models}.361 Figure 3. shows that for massive neutron stars with Mz2M ... the frequency shifts calculated in 82 and shown in Figure | should be multiplied by 0.65—0.85 for EOS L. and 0.3-0.4 for EOS APR.," Figure \ref{fig:corr} shows that for massive neutron stars with $M\approx 2362M_\odot$ , the frequency shifts calculated in 2 and shown in Figure 1 should be multiplied by $0.65$ $0.85$ for EOS L, and $0.3$ $0.4$ for EOS APR."363 For a 1.4M.. star. these factors are 1.1—1.7 for EOS L. and 0.7-0.8 for EOS APR.," For a $1.4 M_\odot$ star, these factors are $1.1$ $1.7$ for EOS L, and $0.7$ $0.8$ for EOS APR."364 The largest values ofo are obtained for a low neutron star mass. stiff equation of state. and rapid rotation.," The largest values of $\alpha$ are obtained for a low neutron star mass, stiff equation of state, and rapid rotation."365 However. even à=1.7 for M=14M.. EOS L. and »2600Hz is not large enough to give agreement with the largest observed frequency shifts.," However, even $\alpha=1.7$ for $M=1.4\366M_\odot$, EOS L, and $\nu=600\ {\rm Hz}$ is not large enough to give agreement with the largest observed frequency shifts."367 In Figure 4.. we present some rotational profiles for some specific models.," In Figure \ref{fig:omega}, we present some rotational profiles for some specific models."368 We take the neutron star mass to be 1.4M... the global accretion rate to be 0.1Mya. and agam work in the equatorial plane.," We take the neutron star mass to be $1.4\369M_\odot$, the global accretion rate to be $0.1\ \dot M_{\rm Edd}$, and again work in the equatorial plane."370" We assume that the atmosphere is rigidly-rotating Immediately prior to the burst. and that during the burst. the atmosphere ts radiative and carries a flux equal to the solar-composition Eddington flux at the photosphere (Figg=8.8«107.ei,ergem™ s)."," We assume that the atmosphere is rigidly-rotating immediately prior to the burst, and that during the burst, the atmosphere is radiative and carries a flux equal to the solar-composition Eddington flux at the photosphere $F_{\rm371Edd}=8.8\times 10^{24}\ g_{14}\ {\rm erg\ cm^{-2}\ s^{-1}}$ )."372 For ν=300 and v=600Hz. and for EOS L and EOS APR. we plot the rotational profiles assuming either (1) complete rotational coupling. resulting in rigid rotation across the layer. or (i1) no angular momentum transport. giving a differentially-rotating layer.," For $\nu=300$ and $\nu=600\ {\rm Hz}$, and for EOS L and EOS APR, we plot the rotational profiles assuming either (i) complete rotational coupling, resulting in rigid rotation across the layer, or (ii) no angular momentum transport, giving a differentially-rotating layer."373 If we allow differential rotation to persist. we see that the upper layers of the atmosphere spin down by an amount comparable to or greater than the observed spin changes during bursts.," If we allow differential rotation to persist, we see that the upper layers of the atmosphere spin down by an amount comparable to or greater than the observed spin changes during bursts."374 However. it is not clear why the spin frequency observed should be that of only the outermost layers.," However, it is not clear why the spin frequency observed should be that of only the outermost layers."375 Indeed. CB (33.4) argued that substantial differential rotation would wash out any signal from the deeper cooling layers because of the finite time to transport heat vertically.," Indeed, CB 3.4) argued that substantial differential rotation would wash out any signal from the deeper cooling layers because of the finite time to transport heat vertically."376 We have presented new calculations of the hydrostatic expansion and spin-down of a neutron star atmosphere during a Type I X-ray burst., We have presented new calculations of the hydrostatic expansion and spin-down of a neutron star atmosphere during a Type I X-ray burst.377" Our main conclusion is that hydrostatic expansion is not enough to explain the observed frequency drifts during Type I X-ray bursts if the burning atmosphere rotates rigidly,", Our main conclusion is that hydrostatic expansion is not enough to explain the observed frequency drifts during Type I X-ray bursts if the burning atmosphere rotates rigidly.378 In $2. we showed that Cumming Bildsten (2000) (CB) overestimated the change in the moment of inertia of the atmosphere. obtaining values of spin-down that were a factor of two too large.," In 2, we showed that Cumming Bildsten (2000) (CB) overestimated the change in the moment of inertia of the atmosphere, obtaining values of spin-down that were a factor of two too large."379 Figure | compares the new calculations of spin-down with observations. including recent measurements of large frequency drifts during bursts (Galloway et al.," Figure 1 compares the new calculations of spin-down with observations, including recent measurements of large frequency drifts during bursts (Galloway et al."380 2000: Wijnands et al., 2000; Wijnands et al.381 2001)., 2001).382 We find that the largest observed frequency shift is a factor of 3 or more greater than the theoretical values., We find that the largest observed frequency shift is a factor of 3 or more greater than the theoretical values.383 In $83. we derived the angular momentum conservation law 1n general relativity.," In 3, we derived the angular momentum conservation law in general relativity."384 We calculated the variation of spin frequency with radial distance. «πο/dInr. for a. particle moving with constant angular momentum.," We calculated the variation of spin frequency with radial distance, $d\ln\Omega/d\ln r$ for a particle moving with constant angular momentum."385 In the slow rotation approximation (Q«GM/R*). we obtained the analytic result given by equation (14)). which agrees with recent work by Abramowicz et al. (," In the slow rotation approximation $\Omega^2\ll386GM/R^3$ ), we obtained the analytic result given by equation \ref{eq:slow}) ), which agrees with recent work by Abramowicz et al. ("3872001).,2001).388 For rapidly-rotating stars. we calculated dInQ/dInr by numerically solving for the structure of the neutron star.," For rapidly-rotating stars, we calculated $d\ln\Omega/d\ln389r$ by numerically solving for the structure of the neutron star."390 The correction to the Newtonian angular momentum conservation law. 2(—1/2)(dInOαπ. is shown in Figure 2 for different neutron./ star masses. equations of state and spin frequencies.," The correction to the Newtonian angular momentum conservation law, $\beta=(-1/2)(d\ln\Omega/d\ln r)$, is shown in Figure 2 for different neutron star masses, equations of state and spin frequencies."391 Contrary to the results of Heyl (2000). which were also shown to be incorrect by Abramowicz et al. (," Contrary to the results of Heyl (2000), which were also shown to be incorrect by Abramowicz et al. ("3922001). we find that the general relativistic correction Is small. about5-10%.,"2001), we find that the general relativistic correction is small, about."393. In $4. we calculated the atmospheric expansion and. spin-down. including the effects of rapid rotation and general relativity.," In 4, we calculated the atmospheric expansion and spin-down, including the effects of rapid rotation and general relativity."394 Working in the equatorial plane (in the spirit of CB's calculation. we neglect latitudinal variations in this paper). we calculated the scaling factor © required to rescale our fiducial results of $2 to different neutron star masses. equations of state. and spin frequencies (Figure 3).," Working in the equatorial plane (in the spirit of CB's calculation, we neglect latitudinal variations in this paper), we calculated the scaling factor $\alpha$ required to rescale our fiducial results of 2 to different neutron star masses, equations of state, and spin frequencies (Figure 3)."395 In addition. we presented the rotational profiles for some particular models (Figure 4).," In addition, we presented the rotational profiles for some particular models (Figure 4)."396 We find that the largest spin-down is for rapid rotation. and low mass stars with a stiff equation of state.," We find that the largest spin-down is for rapid rotation, and low mass stars with a stiff equation of state."397 For example. a 1.4 M. star spinning at 600 Hz with the stiff equation of state EOS L has à=1.7.," For example, a 1.4 $M_\odot$ star spinning at 600 Hz with the stiff equation of state EOS L has $\alpha=1.7$."398 However. this is not a large enough factor to bring observations and theory into agreement in Figure 1.," However, this is not a large enough factor to bring observations and theory into agreement in Figure 1."399 The rotational profiles given in Figure 4. show that in principle frequency shifts as large as those observed can be obtained by hydrostatic expansion. if we consider only the outermost layers of the atmosphere. and allow differential rotation.," The rotational profiles given in Figure 4 show that in principle frequency shifts as large as those observed can be obtained by hydrostatic expansion, if we consider only the outermost layers of the atmosphere, and allow differential rotation."400 However. it is not at all obvious why the observed frequency would be that of the outermost shells of the atmosphere. which contain a small amount of the mass. particularly since the energy release is in the deeper layers.," However, it is not at all obvious why the observed frequency would be that of the outermost shells of the atmosphere, which contain a small amount of the mass, particularly since the energy release is in the deeper layers."401 Indeed. CB argued (see their $3.4) that substantial differential rotation in the burning layers would wash out the signal. because of the finite time needed to transport heat vertically in the atmosphere.," Indeed, CB argued (see their 3.4) that substantial differential rotation in the burning layers would wash out the signal, because of the finite time needed to transport heat vertically in the atmosphere."402 Another possible objection to the angular momentum conservation picture was given by CB. who pointed out that if the burning layers are threaded by a large scale poloidal magnetic field. this field will be wound up by the differential rotation during the burst.," Another possible objection to the angular momentum conservation picture was given by CB, who pointed out that if the burning layers are threaded by a large scale poloidal magnetic field, this field will be wound up by the differential rotation during the burst."403" The wound up toroidal field acts back on the shear. halting and reversing its direction in the time for an Alfven wave to cross the atmosphere (see. for example. Spruit 1999),"," The wound up toroidal field acts back on the shear, halting and reversing its direction in the time for an Alfven wave to cross the atmosphere (see, for example, Spruit 1999)."404 For a magnetic field typical of a millisecond radio pulsar. B~~10?G. this timescale is only ~0.01s.," For a magnetic field typical of a millisecond radio pulsar, $B\sim 10^8\ {\rm G}$, this timescale is only $\sim 0.01\ {\rm s}$."405 One possibility is that the surface field is much weaker. B«10°G. allowing shearing to persist.," One possibility is that the surface field is much weaker, $B\lesssim 10^6\ {\rm G}$, allowing shearing to persist."406" Observations of burst oscillations in the accreting millisecond X-ray pulsar SAX J1808.4-3658. which perhaps has a  105-10?G field (Psaltis Chakrabarty 1999), would give an interesting test of this picture."," Observations of burst oscillations in the accreting millisecond X-ray pulsar SAX J1808.4-3658, which perhaps has a $\sim40710^8$ $10^9\ {\rm G}$ field (Psaltis Chakrabarty 1999), would give an interesting test of this picture."408 In't Zand et al. (, In't Zand et al. (4092000) report a marginal detection with. BeppoSAX of oscillations at 400+2Hz during a Type I burst. but are unable to resolve any frequency drift.,"2000) report a marginal detection with BeppoSAX of oscillations at $400\pm 2\ {\rm410Hz}$ during a Type I burst, but are unable to resolve any frequency drift."411 Unfortunately. as yet no burst oscillations have been detectedfrom this sourcewith RXTE.," Unfortunately, as yet no burst oscillations have been detectedfrom this sourcewith RXTE."412 The results we have obtained in thispaper suggest that we may have to look elsewhere for an explanation. of the frequency drifts., The results we have obtained in thispaper suggest that we may have to look elsewhere for an explanation of the frequency drifts.413 Spitkovsky. Levin.Ushomirsky (2001). in a detailed investigation of hydrodynamic flows during Type I| bursts. propose that the frequency drifts may be explained," Spitkovsky, Levin,Ushomirsky (2001), in a detailed investigation of hydrodynamic flows during Type I bursts, propose that the frequency drifts may be explained"414This long campaign was designed to continuously monitor I11H4264-428 al X-ray energies (id at other wavelengths that will be reported on in a forthcoming paper) in an effort to explore variability at multiple timescales.,This long campaign was designed to continuously monitor H1426+428 at X-ray energies (and at other wavelengths that will be reported on in a forthcoming paper) in an effort to explore variability at multiple timescales.415 In spite of the fact that there were no large Lares. relative to those frequently observed for other TeV emitting AGN. the campaign successfully observed. variability with doubling timescales ranging from ο]. day to 22 weeks.," In spite of the fact that there were no large flares, relative to those frequently observed for other TeV emitting AGN, the campaign successfully observed variability with doubling timescales ranging from $\sim$ 1 day to $>$ 2 weeks."416 In several cases. Lhe short timescale flaring was observed on top of the long timescale gradual variations.," In several cases, the short timescale flaring was observed on top of the long timescale gradual variations."417 This tvpe of variability complicates studies of emission mechanisms and should be considered in general. especially lor studies that include non-contemporaneous mul(iwavelength Throughout the entire campaign. a simple power law with galactic absorbtion was able to fit the data well between 2.9 and 24 keV. Prior observations performed by between 1935 and 1994 with ASCA and DDXRT led to similar spectra at some times. but at other times there were some notable differences.," This type of variability complicates studies of emission mechanisms and should be considered in general, especially for studies that include non-contemporaneous multiwavelength Throughout the entire campaign, a simple power law with galactic absorbtion was able to fit the data well between 2.9 and 24 keV. Prior observations performed by \citet{sam97} between 1985 and 1994 with ASCA and BBXRT led to similar spectra at some times, but at other times there were some notable differences."418 At some times. the spectra from Sambrunaetal.(1997) could be fit bv a single power law. but at other times a broken power law (hat became softer al hieher energies was inferred.," At some times, the spectra from \citet{sam97} could be fit by a single power law, but at other times a broken power law that became softer at higher energies was inferred."419 For the part of the spectrum between the break energy and 10 keV. the spectra had a twpical power law index ol ~2.3 above a break οποιον of ~2 keV [or the observations described by (1997).," For the part of the spectrum between the break energy and $\sim$ 10 keV, the spectra had a typical power law index of $\sim$ 2.3 above a break energy of $\sim$ 2 keV for the observations described by \citet{sam97}."420. This is somewhat softer than any of the spectra derived during the present campaign., This is somewhat softer than any of the spectra derived during the present campaign.421 The observations reported by Sambrunaetal.(1097) all show 2-10 keV fluxes that fall within the range of fluxes observed during (his campaien. whereas the spectra οἱ these historical observations are softer (han the more recent observations reported in this paper and in Costamanteetal.(2001).," The observations reported by \citet{sam97} all show 2-10 keV fluxes that fall within the range of fluxes observed during this campaign, whereas the spectra of these historical observations are softer than the more recent observations reported in this paper and in \citet{cos01}."422.. This is most easily interpreted as (nme variability. rather (han interpreting it as a contradiction between (he two results. when consideration is given to the BeppoSAX observations of Costamanteetal.(2001) whieh also leads to a different spectral index ancl when consideration is given to the observed variability during (his four month campaign.," This is most easily interpreted as time variability, rather than interpreting it as a contradiction between the two results, when consideration is given to the BeppoSAX observations of \citet{cos01} which also leads to a different spectral index and when consideration is given to the observed variability during this four month campaign."423 It is also important to note Chat (his has involved a comparison of dilferent instruments with different band passes., It is also important to note that this has involved a comparison of different instruments with different band passes.424 Another interesting feature of the BBNRT observations reported bv Sambrunaetal.(1997). was (he evidence for a spectral line al 220.6 keV. which would imply the presence of absorbing material.," Another interesting feature of the BBXRT observations reported by \citet{sam97} was the evidence for a spectral line at $\approx$ 0.6 keV, which would imply the presence of absorbing material."425 No spectral lines were observed in the 2.9 to 24 keV band covered by the observations presented in this paper (PCA can not observe down to 0.6 keV where the spectral feature was previously The power law spectral index was observed to vary. throughout the range bounded by 1.4640.05 and 2.03250.09., No spectral lines were observed in the 2.9 to 24 keV band covered by the observations presented in this paper (PCA can not observe down to 0.6 keV where the spectral feature was previously The power law spectral index was observed to vary throughout the range bounded by $\pm$ 0.05 and $\pm$ 0.09.426 If one interprets this as being due to a shift in the location of the, If one interprets this as being due to a shift in the location of the427behavior. as suggested by Kalogeraοἱal.(2004).,"behavior, as suggested by \citet{k04}."428. The differences between our work and lxalogeraοἱalM) result Irom the following facts. (, The differences between our work and \citet{k04} result from the following facts. (429"1) We have adopted the DII masses no more ""Mthan a1000AZ. in the caleulations.","1) We have adopted the BH masses no more than $1000\,\ms$ in the calculations."430 With these values. one can actually draw. [rom Fig.," With these values, one can actually draw from Fig."431lin etal.(2004). the similar results as ours. (, 1 in \citet{k04} the similar results as ours. (4322) We assumed tidal capture as the main formation channel of IAIBIL binaries. from which we got the initial orbital periods οἱ ~2—4 clavs: Ixalogeraetal.(2004) favor orbital periods in excess of ~LOO davs. but the duration of the mass transfer episode would decrease to be very short (less (han a few 104 ves). making them difficult to be observed.,"2) We assumed tidal capture as the main formation channel of IMBH binaries, from which we got the initial orbital periods of $\sim 2-4$ days; \citet{k04} favor orbital periods in excess of $\sim 100$ days, but the duration of the mass transfer episode would decrease to be very short (less than a few $10^4$ yrs), making them difficult to be observed."433 1t should be noted that the ealeulated mass transfer rates are long-term. averaged ones.," It should be noted that the calculated mass transfer rates are long-term, averaged ones."434 It is unclear how to relate these secular mass transfer rates to observable instantaneous X-ray humninosities. and to disk instability influenced by (short-term) mass transfer and X- irraciation.," It is unclear how to relate these secular mass transfer rates to observable instantaneous X-ray luminosities, and to disk instability influenced by (short-term) mass transfer and X-ray irradiation."435 Moreover. the mechanisms and criterion for the thermal-viscous instability in irradiated accretion disk are not vet fully. understood.," Moreover, the mechanisms and criterion for the thermal-viscous instability in irradiated accretion disk are not yet fully understood."436 It is premature to predict the instability occurrence [rom only ealeulated mass (transfer rates., It is premature to predict the instability occurrence from only calculated mass transfer rates.437 Another interesting feature is that. if anisotropic (or beamed) emission is associated with mass (ransfer rates comparable to the Edcdington rate. as suggested belore 2001).. our caleulations indicate that IAIBITs may also have anisotropic emission. since {he mass transfer rates can be sufficiently. high to satisfy the condition above.," Another interesting feature is that, if anisotropic (or beamed) emission is associated with mass transfer rates comparable to the Eddington rate, as suggested before \citep[e.g.][]{k01}, our calculations indicate that IMBHs may also have anisotropic emission, since the mass transfer rates can be sufficiently high to satisfy the condition above."438 Llowever. anisolropiec X-rav emission is not preferred in our opinion for persistent ULXs. since the most important stabilizing [actor for disk instability. the efficiency of X-ray. irradiation. will be ereatlv reduced if the emission is beamecl (usually in Che direction perpendicular to the disk plane). and the ULXs would become transient sources.," However, anisotropic X-ray emission is not preferred in our opinion for persistent ULXs, since the most important stabilizing factor for disk instability, the efficiency of X-ray irradiation, will be greatly reduced if the emission is beamed (usually in the direction perpendicular to the disk plane), and the ULXs would become transient sources."439 We have calculated the evolutionary sequences of INIBIT X-ray. binaries formed through tidal capture in dense star clusters. and compared the results with those of SMDIL binaries.," We have calculated the evolutionary sequences of IMBH X-ray binaries formed through tidal capture in dense star clusters, and compared the results with those of SMBH binaries."440 We [found that IMDlIIs seem to be capable of explaining the nature of most Iuminous ULXs. and their companion stus and binary orbits could be similar to those of SMDII-ULXs.," We found that IMBHs seem to be capable of explaining the nature of most luminous ULXs, and their companion stars and binary orbits could be similar to those of SMBH-ULXs."441 We suggest that transient behavior and beamed emission may. be not enough to distinguish between IMDIIs and SMDIIs., We suggest that transient behavior and beamed emission may be not enough to distinguish between IMBHs and SMBHs.442 ] would like to thank Ranold Webbink for helpful discussion. and the referee. Philipp Podsiadlowski for clarifving comments.," I would like to thank Ranold Webbink for helpful discussion, and the referee, Philipp Podsiadlowski for clarifying comments."443 This work was supported by NSFC through. grant number 10025314 and MSTC through grant number NXBRSF G19990754., This work was supported by NSFC through grant number 10025314 and MSTC through grant number NKBRSF G19990754.444"""splitting"" merger treescurves, which cover the range of the dashed curves in Figure 2)).","""splitting"" merger trees, which cover the range of the dashed curves in Figure \ref{f:growth}) )."445 It is worth noting that the curves in Figure 4 are shifted from those in Figure 5 by +0.5—Idex toward higher masses., It is worth noting that the curves in Figure \ref{f:halo_content} are shifted from those in Figure \ref{f:particle_net_accretion} by $\approx0.5-1 dex$ toward higher masses.446" This is expected, as halos accrete most of their final mass M;-o, by definition, when M;>0.1M,~o."," This is expected, as halos accrete most of their final mass $M_{z=0}$, by definition, when $M_z\gtrsim0.1M_{z=0}$."447" This means that the fractions of the different accretion modes in the final halo mass M.-o (Figure 4)) correspond to their fractions in the accretion at M=0.1M,.o (Figure 5)).", This means that the fractions of the different accretion modes in the final halo mass $M_{z=0}$ (Figure \ref{f:halo_content}) ) correspond to their fractions in the accretion at $M\gtrsim0.1M_{z=0}$ (Figure \ref{f:particle_net_accretion}) ).448 From Figures 4 and 5 we can also learn that the fraction of the accretion in the 'stripped' mode is subdominant to that in the 'smooth' mode., From Figures \ref{f:halo_content} and \ref{f:particle_net_accretion} we can also learn that the fraction of the accretion in the 'stripped' mode is subdominant to that in the 'smooth' mode.449" That is, what we could only interpret as 'non-mergers' from the analysis of the merger trees, can now be shown to consist of particles that never to another halo to their accretion."," That is, what we could only interpret as 'non-mergers' from the analysis of the merger trees, can now be shown to consist of particles that never belonged to another halo prior to their accretion."450" In fact, the belonged’stripped’ mass is consistentlyprior ~ of the mass in the *merger’ mode."," In fact, the 'stripped' mass is consistently $\approx1/3$ of the mass in the 'merger' mode."451" Conservatively, the 'stripped'1/3 component is our uncertainty, because our analysis does not indicate how long it has been stripped and what part of it comes from the vicinity of approaching subhalos."," Conservatively, the 'stripped' component is our uncertainty, because our analysis does not indicate how long it has been stripped and what part of it comes from the vicinity of approaching subhalos."452" Indeed, some of these *stripped’ particles arrive as mergers into low-mass halos and after being stripped from them, are re-accreted into more massive halos and tagged there as 'stripped'."," Indeed, some of these 'stripped' particles arrive as mergers into low-mass halos and after being stripped from them, are re-accreted into more massive halos and tagged there as 'stripped'."453" Thus, some of the mass appearing in the merger trees as 'merger mode' is transferred into 'stripped mode' of more massive halos in the analysis."," Thus, some of the mass appearing in the merger trees as 'merger mode' is transferred into 'stripped mode' of more massive halos in the particle analysis."454 This is the reason the red curves are somewhat particlelower than the black dashed ones., This is the reason the red curves are somewhat lower than the black dashed ones.455 We can learn more about this 'cycle' of particles through different halos from Figure 6.., We can learn more about this 'cycle' of particles through different halos from Figure \ref{f:joining_and_leaving}.456" There it is shown that the rate at which particles join and leave their halo is similar to, or even higher than, thenet growth rate, for each of the different modes."," There it is shown that the rate at which particles join and leave their halo is similar to, or even higher than, the growth rate, for each of the different modes."457" As a quantitative example, shown in Figure 6,, the rate of ’smooth’ particles joining their halos at z+0 is =4 times higher than the net growth rate due to smooth accretion, ie. only z33% higher than the leaving’ rate of particles that previously arrived smoothly."," As a quantitative example, shown in Figure \ref{f:joining_and_leaving}, the rate of 'smooth' particles joining their halos at $z\approx0$ is $\approx4$ times higher than the net growth rate due to smooth accretion, i.e. only $\approx33\%$ higher than the 'leaving' rate of particles that previously arrived smoothly."458" These numbers drop toward higher redshift, where the 'cycle' is less significant, e.g. at z&:2 the values are lower roughly by a factor of 2 compared to those shown in Figure 6.."," These numbers drop toward higher redshift, where the 'cycle' is less significant, e.g. at $z\approx2$ the values are lower roughly by a factor of $2$ compared to those shown in Figure \ref{f:joining_and_leaving}."459" Note that all ""leaving' particles leave their halos smoothly, i.e. not as part of a bound subhalo, as such events have already been cleaned at the time of merger tree construction."," Note that all 'leaving' particles leave their halos smoothly, i.e. not as part of a bound subhalo, as such events have already been cleaned at the time of merger tree construction."460 Thus the red curve in Figure 6 shows that there are many particles that arrive via mergers and then stripped off of their subhalos inside the main halos and later leave the main halo 'smoothly'., Thus the red curve in Figure \ref{f:joining_and_leaving} shows that there are many particles that arrive via mergers and then stripped off of their subhalos inside the main halos and later leave the main halo 'smoothly'.461" It seems reasonable to suggest that this cycle is driven, at least partly, by fluctuations of particles that reside close to the halo in and out of the region defined as the halo by the FOF boundaryalgorithm."," It seems reasonable to suggest that this cycle is driven, at least partly, by fluctuations of particles that reside close to the halo boundary in and out of the region defined as the halo by the FOF algorithm."462 This is the reason we focus throughout the paper on the net growth rate., This is the reason we focus throughout the paper on the net growth rate.463 We leave a more detailed study of this cycle to future work., We leave a more detailed study of this cycle to future work.464" In Figure 7 we compare the merger contribution to the accretion rate from our ""splitting"" and ""snipping"" (Fakhouri&Ma2008) trees."," In Figure \ref{f:particles_split_vs_snip} we compare the merger contribution to the accretion rate from our ""splitting"" and ""snipping"" \citep{FakhouriO_07a} trees."465" The ""snipping"" algorithm is the most extreme case of leaving all fragmentations in the trees so that inthe merger tree analysis the merger contribution does not converge(pluses, same as in Figure 2))."," The ""snipping"" algorithm is the most extreme case of leaving all fragmentations in the trees so that inthe merger tree analysis the merger contribution does not converge, same as in Figure \ref{f:growth}) )."466" In contrast, the ""snipping"" merger contribution does not exceed 6096 when the are used (dashed)."," In contrast, the ""snipping"" merger contribution does not exceed $60\%$ when the are used )."467" In fact, it is somewhat lower than in the ""splitting"" case asterisks)"," In fact, it is somewhat lower than in the ""splitting"" case )"468dwarf to be eclipsed. but more likely 7.=79° in order to produce the deep eclipse.,"dwarf to be eclipsed, but more likely $i \simeq 79 \degr$ in order to produce the deep eclipse."469 The inclination cannot be much larger than this. otherwise we would not detect significant X-ray emission outside the eclipse because of strong attenuation by the accretion disc.," The inclination cannot be much larger than this, otherwise we would not detect significant X-ray emission outside the eclipse because of strong attenuation by the accretion disc."470 Are there other evolved WDMT systems among the long period CBSS. or is CAL 87 an exception?," Are there other evolved WDMT systems among the long period CBSS, or is CAL 87 an exception?"471 Cowley et al. (1998)), Cowley et al. \cite{cow98}) )472 suggested that has a low-mass secondary. given its low amplitude radial velocity.," suggested that has a low-mass secondary, given its low amplitude radial velocity."473 Similarly. shows indications that it has a low mass ratio (Diaz Steiner 1995:; Oliveira Steiner 2004)).," Similarly, shows indications that it has a low mass ratio (Diaz Steiner \cite{diaz95}; Oliveira Steiner \cite{oliv}) )."474 From the known systems that belong to the class of CBSS and V Sge stars. six are short period (<6 hr) systemsMus..Pyx..J0439.. J0537.. 0035.. and Ser)) and are therefore WDMT systems.," From the known systems that belong to the class of CBSS and V Sge stars, six are short period $<6$ hr) systems, and ) and are therefore WDMT systems."475 Among the long period objects. four have indications of being WDMT systemsCen..87.. and 83.. see Table 4)). and one has no indication to date of its mass J0513)). while probably has à subgiant secondary (Schmidtke et al. 2000)).," Among the long period objects, four have indications of being WDMT systems, and , see Table \ref{massratio}) ), and one has no indication to date of its mass ), while probably has a subgiant secondary (Schmidtke et al. \cite{schmidtke3}) )."476 The only clear case for a DIMT to date is (Herbig et al. 1965:;, The only clear case for a DIMT to date is (Herbig et al. \cite{herbig};477 Patterson et al. 1998))., Patterson et al. \cite{patter}) ).478 This supports the argument that wind-driven mass transfer (with ten objects) may be the rule and dynamical instability mass transfer (with one object). the exception.," This supports the argument that wind-driven mass transfer (with ten objects) may be the rule and dynamical instability mass transfer (with one object), the exception."479 Another implication is that the CBSS are an old population. instead of a population of intermediate age as previously believed.," Another implication is that the CBSS are an old population, instead of a population of intermediate age as previously believed."480"observations of exoplanets have been obtained with IRAC, we focus on estimating Tug based on brightness temperatures in those four bandpasses.","observations of exoplanets have been obtained with IRAC, we focus on estimating $T_{\rm eff}$ based on brightness temperatures in those four bandpasses."481 The first approach is to simply adopt the brightness temperature of the bandpass closest to the planet's blackbody peak (the black dotted line)., The first approach is to simply adopt the brightness temperature of the bandpass closest to the planet's blackbody peak (the black dotted line).482" If only the four IRAC channels are available, the best one can do is the 3.6 wm measurement, yielding Tag=1925 K. There is —however— some subtlety in estimating the peak wavelength, as this is dependent on knowing the planet’s temperature (and hence Ag and &)priori.."," If only the four IRAC channels are available, the best one can do is the 3.6 $\mu$ m measurement, yielding $T_{\rm eff} = 1925$ K. There is —however— some subtlety in estimating the peak wavelength, as this is dependent on knowing the planet's temperature (and hence $A_{B}$ and $\varepsilon$ )."483" The linear interpolation technique, shown with the red line in Figure 2,, obviates the need for an estimate of the planet’s temperature."," The linear interpolation technique, shown with the red line in Figure \ref{tres3_2pi_TiO.flx}, obviates the need for an estimate of the planet's temperature."484" The brightness temperature is assumed to be constant shortward of the shortest-A observation, and longward of the longest-A observation."," The brightness temperature is assumed to be constant shortward of the $\lambda$ observation, and longward of the $\lambda$ observation."485" Between bandpasses, the brightness temperature changes linearly with A."," Between bandpasses, the brightness temperature changes linearly with $\lambda$."486" As long as the various brightness temperatures do not differ grossly from one another, this technique implicitly gives more weight to observations near the hypothetical blackbody peak."," As long as the various brightness temperatures do not differ grossly from one another, this technique implicitly gives more weight to observations near the hypothetical blackbody peak."487" The bolometric flux of this “model” spectrum is then computed, and admits a single effective temperature, which is Teg=1927 K for the current example."," The bolometric flux of this “model” spectrum is then computed, and admits a single effective temperature, which is $T_{\rm eff} = 1927$ K for the current example."488" Since we hope to apply our routine to planets with well sampled blackbody peaks, we adopt the linear interpolation technique, as it can make use of multiple brightness temperature estimates near the peak."," Since we hope to apply our routine to planets with well sampled blackbody peaks, we adopt the linear interpolation technique, as it can make use of multiple brightness temperature estimates near the peak."489" The two techniques described above produce similar effective temperatures, though —unsurprisingly— neither gives precisely the correct answer."," The two techniques described above produce similar effective temperatures, though —unsurprisingly— neither gives precisely the correct answer."490 But these systematic errors are comparable or smaller than the photometric uncertainty in observations of individual brightness temperatures Table , But these systematic errors are comparable or smaller than the photometric uncertainty in observations of individual brightness temperatures (see Table 1).491"The best IR observations for the nearest,(see brightest1). planetary systems (e.g, HD 189733b and HD 209458b) lead to observational uncertainties of approximately 50 K in brightness temperature."," The best IR observations for the nearest, brightest planetary systems (e.g., HD 189733b and HD 209458b) lead to observational uncertainties of approximately 50 K in brightness temperature."492" For many planets, the uncertainty is 100-200 K. By that metric, either the Wien displacement or the linear interpolation routines give adequate estimates of the effective temperature, with errors of 16 K and 14 K, respectively."," For many planets, the uncertainty is 100–200 K. By that metric, either the Wien displacement or the linear interpolation routines give adequate estimates of the effective temperature, with errors of 16 K and 14 K, respectively."493 We make a more quantitative analysis of the systematic uncertainties involved in the Linear Interpolation temperature estimates as follows., We make a more quantitative analysis of the systematic uncertainties involved in the Linear Interpolation temperature estimates as follows.494" We produce 8800 mock data sets: 100 realizations for 11 models and data in up to 8 wavebands (J, H, K, IRAC, MIPS; Since this numerical experiment chooses random bands from the eight available, the results should not be very different if additional wavebands are considered)."," We produce 8800 mock data sets: 100 realizations for 11 models and data in up to 8 wavebands (J, H, K, IRAC, MIPS; Since this numerical experiment chooses random bands from the eight available, the results should not be very different if additional wavebands are considered)."495 We run our Linear Interpolation technique on each of these and plot in Figure 3 the estimated day-side temperature normalized by the actual model effective temperature versus the number of wavebands used in the estimate., We run our Linear Interpolation technique on each of these and plot in Figure \ref{T_eff_test} the estimated day-side temperature normalized by the actual model effective temperature versus the number of wavebands used in the estimate.496" The temperature estimates cluster near Te«/Teg=1, indicating that the technique is not significantly biased."," The temperature estimates cluster near $T_{\rm est}/T_{\rm eff}=1$, indicating that the technique is not significantly biased."497" The scatter in estimates decreases as more wavebands are used, from a standard deviation of if only a single brightness temperature is used, down to if photometry is acquired in eight bands."," The scatter in estimates decreases as more wavebands are used, from a standard deviation of if only a single brightness temperature is used, down to if photometry is acquired in eight bands."498 We incorporate this systematic error into our analysis by adding it in quadrature to the observational uncertainties described in the following paragraph., We incorporate this systematic error into our analysis by adding it in quadrature to the observational uncertainties described in the following paragraph.499 This has the desirable effect that planets with fewer observations have a larger systematic uncertainty on their effective temperature., This has the desirable effect that planets with fewer observations have a larger systematic uncertainty on their effective temperature.500" In practice, we would like to propagate the photometric uncertainties to the estimate of Tog."," In practice, we would like to propagate the photometric uncertainties to the estimate of $T_{\rm eff}$."501" For the Wien Displacement technique, this uncertainty propagates trivially to the effective temperature."," For the Wien Displacement technique, this uncertainty propagates trivially to the effective temperature."502" For the linear interpolation technique, a Monte Carlo can be used to estimate the uncertainty in Tog: the input eclipse depths are randomly shifted 1000 times in a manner consistent with their photometric uncertainties —assuming Gaussian errors— and the effective temperature is recomputed repeatedly."," For the linear interpolation technique, a Monte Carlo can be used to estimate the uncertainty in $T_{\rm eff}$: the input eclipse depths are randomly shifted 1000 times in a manner consistent with their photometric uncertainties —assuming Gaussian errors— and the effective temperature is recomputed repeatedly."503 The, The504sunmimarized as follows: it is à very good option to model the narrow PSEs present. for example. inT' images because it is numerically well behaved: the Gaussian PSE is a limiting case of the Molfat. PSE (3)ο o6): and the prediction for the PSE due to the theory of atmospheric turbulence can be numerically well approximated by a Mollat. function. with jo4.165.,"summarized as follows: it is a very good option to model the narrow PSFs present, for example, in images because it is numerically well behaved; the Gaussian PSF is a limiting case of the Moffat PSF $\beta\rightarrow\infty$ ); and the prediction for the PSF due to the theory of atmospheric turbulence can be numerically well approximated by a Moffat function with $\beta\sim4.765$."505 For practical purposes we have analysed the elfects of seeing caused by this PSP on the Sérrsic model., For practical purposes we have analysed the effects of seeing caused by this PSF on the Sérrsic model.506 Phe effects on the central intensity. elective radius. » index and mean ellective surface brightness are extensively shown in Figures 3. 4. 5 and 6.," The effects on the central intensity, effective radius, $n$ index and mean effective surface brightness are extensively shown in Figures 3, 4, 5 and 6."507 We have also given an easy. prescription for seeing correction that can be useful for observers in order to obtain the secing-free quantities., We have also given an easy prescription for seeing correction that can be useful for observers in order to obtain the seeing-free quantities.508 Our main results have been to show the importance of taking into account the intrinsic. ellipticities of the objects and the presence of “wines” in the PSPs for the recovery of accurate structural parameter., Our main results have been to show the importance of taking into account the intrinsic ellipticities of the objects and the presence of “wings” in the PSFs for the recovery of accurate structural parameter.509 I0 ijs not sullicient to consider the PSE as Gaussian and assume circular symmetry to model the ellects of seeing on the surface. brightness distribution when the ratio of the cllective radius to the ENIM is small (< 2.5)., It is not sufficient to consider the PSF as Gaussian and assume circular symmetry to model the effects of seeing on the surface brightness distribution when the ratio of the effective radius to the FWHM is small $\leq 2.5$ ).510 We wish to thank Alister W. Graham who kindly proofread versions of this manuscript., We wish to thank Alister W. Graham who kindly proofread versions of this manuscript.511assume aj0 in the foregoing.,assume $a_0=0$ in the foregoing.512 It is interesting to speculate on the possible significance of assuming ay40., It is interesting to speculate on the possible significance of assuming $a_0\ne0$.513 One could interpret the E associated with ajz0 as one way of modeling an unscreened component of the pulsars inductive field., One could interpret the ${\bar E}$ associated with $a_0\ne0$ as one way of modeling an unscreened component of the pulsar's inductive field.514 The systematic acceleration transfers electromagnetic energy into particles., The systematic acceleration transfers electromagnetic energy into particles.515 In à conventional polar-cap model. such acceleration occurs in a gap. and screening of the inductive field results [rom a net charge density in a pair formation front (larding&Muslimov.1998).," In a conventional polar-cap model, such acceleration occurs in a gap, and screening of the inductive field results from a net charge density in a pair formation front \citep{hm98}."516. One motivation for an oscillating model is that such screening is unstable to temporal perturbations. resulting in large-amplitude electric oscillations (Levinsonetal.2005).," One motivation for an oscillating model is that such screening is unstable to temporal perturbations, resulting in large-amplitude electric oscillations \citep{letal05}."517. The build up of à LAEW in an oscillating mocel relies on acceleration bv an incompletely screened electric field., The build up of a LAEW in an oscillating model relies on acceleration by an incompletely screened electric field.518 As in a stationary model. the resulting pair creation should lead to screening of the electric field. and whereas this occurs locally in a stationary model. it corresponds to a svstematic reduction in E. and hence of αμ. in the oscillating model.," As in a stationary model, the resulting pair creation should lead to screening of the electric field, and whereas this occurs locally in a stationary model, it corresponds to a systematic reduction in ${\bar E}$, and hence of $a_0$, in the oscillating model."519 This effect needs to be included in a detailed theory of the instability leading to the LAEW. but we do not attempt a quantitative treatment of this here.," This effect needs to be included in a detailed theory of the instability leading to the LAEW, but we do not attempt a quantitative treatment of this here."520 A particle in à LAEW oscillates about a center that is drifting (except [οι a background particle in the primed frame)., A particle in a LAEW oscillates about a center that is drifting (except for a background particle in the primed frame).521 The displacement about this center is by tre/Q! in the primed frame., The displacement about this center is by $\pm\pi c/\Omega'$ in the primed frame.522 A particle is constrained to move along a magnetic field line Chat is curved. and the neglect of this curvature is valid only if Chis distance is small compared with the radius of curvature of the field line.," A particle is constrained to move along a magnetic field line that is curved, and the neglect of this curvature is valid only if this distance is small compared with the radius of curvature of the field line."523 For a LAEW with a frequency e10°s|. dze/O' is less than a meter. and this condition is well satisfied.," For a LAEW with a frequency $\sim10^9\rm\,s^{-1}$, $\pm\pi c/\Omega'$ is less than a meter, and this condition is well satisfied."524 A test particle has a drift velocity in the primed frame., A test particle has a drift velocity in the primed frame.525 This velocity may be estimated, This velocity may be estimated526was presented by Lebzelteretal.(2008).. introducing a moderate extra-mixing on the AGB.,"was presented by \citet{leb08}, introducing a moderate extra-mixing on the AGB."527 These authors also suggested an increased efficienev. of extra-mixing for increasing values of the envelope C/O ratio. because the bottom of the convective envelope becomes progressively closer to the II-burning shell while the star climbs the AGB.," These authors also suggested an increased efficiency of extra-mixing for increasing values of the envelope C/O ratio, because the bottom of the convective envelope becomes progressively closer to the H-burning shell while the star climbs the AGB."528 For the same reason. the extra-mixing efficiency is expected to increase lor ACB stars of low metallicity. as (he convective envelope becomes hotter for them (Cristalloetal.2009).," For the same reason, the extra-mixing efficiency is expected to increase for AGB stars of low metallicity, as the convective envelope becomes hotter for them \citep{cris}."529. The situation of NGCLOTS is definitely more puzzling (Ledererοἱal.2009):: in that case. a [it to C-rich stars requires the concomitant absence of extra-mixing processes during both the RGB and AGB phases.," The situation of NGC1978 is definitely more puzzling \citep{lederer}: in that case, a fit to C-rich stars requires the concomitant absence of extra-mixing processes during both the RGB and AGB phases."530 Thus. it is hard to find a theoretical recipe suitable to reproduce the isotopic ratios of AGB stars in NCGI978 (both O-rieh and C-rich) without invoking an ad-hoc solution lor this peculiar cluster (seediscussioninLedererοἱal.," Thus, it is hard to find a theoretical recipe suitable to reproduce the isotopic ratios of AGB stars in NCG1978 (both O-rich and C-rich) without invoking an ad-hoc solution for this peculiar cluster \citep[see discussion in][]{lederer}."5312009).. Finally. we would like to comment on the physical origin of extva-mixing on the AGB.," Finally, we would like to comment on the physical origin of extra-mixing on the AGB."532 A popular mechanismis today thermohaline diffusion (Egegletonetal.2006. 2003)..," A popular mechanismis today thermohaline diffusion \citep{egg1,egg2}. ."533object also does uot fit comlortably as au intermediate polar.,object also does not fit comfortably as an intermediate polar.534 Why should it be asvuchronous giver its low accretion rate?, Why should it be asynchronous given its low accretion rate?535 The low |uninosity suggests that V105 Pee might be related to the low accretion rate polar (LARP) systeus found ii the Sloan Digital 5cy Survey sample (Schumal. 2007)...," The low luminosity suggests that V405 Peg might be related to the low accretion rate polar (LARP) systems found in the Sloan Digital Sky Survey sample \citep{schmidtlarp,vogelwx}."536 These appear to be pre-pola‘s that underfill their Roche loyes and are powered by wind accretion via a nagetic siphon from the ate type secondary., These appear to be pre-polars that underfill their Roche lobes and are powered by wind accretion via a magnetic siphon from the late type secondary.537 However. there are siguificau dissinilarities between V105 Pee aud tle LARPs: (1) VIO» Pee does 1ot show the the narrow cyclotron [eatues seen in LARPs. (," However, there are significant dissimilarities between V405 Peg and the LARPs: (1) V405 Peg does not show the the narrow cyclotron features seen in LARPs. ("5382) X-ray 1uuiuosity and accretion ate in VI05 Peg are a least one order of magnitude higher comj»ared to the pre-polars (Seluuidet 2007).. (,"2) X-ray luminosity and accretion rate in V405 Peg are at least one order of magnitude higher compared to the pre-polars \citep{schmidtlarp,vogelwx}. ("5393) The transitions between residual acc'etion aud complete cessation of the mass traustfer are morphologically similar to the high/low stae behavior of AM Her sta*. but have not vet been observed in LARPs. (,"3) The transitions between residual accretion and complete cessation of the mass transfer are morphologically similar to the high/low state behavior of AM Her stars, but have not yet been observed in LARPs. ("5401) The optical mocdulati(i from the eyelotron spots in LARPs teuds to be very sinootli. probably as a consequeuce of wind accretiou.,"4) The optical modulation from the cyclotron spots in LARPs tends to be very smooth, probably as a consequence of wind accretion."541 The high-state light curves of V105 Pee. ou the other hand. show strong flickering. which arises naturally in disk or au accretion streau. either of which would indicate Roche-lobe overflow.," The high-state light curves of V405 Peg, on the other hand, show strong flickering, which arises naturally in disk or an accretion stream, either of which would indicate Roche-lobe overflow."542 Many clisk-accretingOm svstems in this period rangeDm show so-calledsuperhumps. photometric moclulatious at [requencies somewhat cliffere: [rom the orbital frequency (see. ο... aud refereuces therein).," Many disk-accreting systems in this period range show so-called, photometric modulations at frequencies somewhat different from the orbital frequency (see, e.g., \citealt{patt02} and references therein)."543 However. all these systems are much more lumious than V105 Pee.," However, all these systems are much more luminous than V405 Peg."544 It appears that this pleo»nenou arises from disk precession. aud the instabiliy which drives the precession requires the disk to occupy a substantial portion of the Roche lobe radius: this iu turn requires the disk to be persistently bright.," It appears that this phenomenon arises from disk precession, and the instability which drives the precession requires the disk to occupy a substantial portion of the Roche lobe radius; this in turn requires the disk to be persistently bright."545 It is therefore very unlikely that the uou-orbital photometric moculation is a superliump., It is therefore very unlikely that the non-orbital photometric modulation is a superhump.546 I 'V105 Pee is not a magnetic system. then it should have an accretion disk.," If V405 Peg is not a magnetic system, then it should have an accretion disk."547 At low inclination. einissiou lines are generally siugle-peaked. as observed.," At low inclination, emission lines are generally single-peaked, as observed."548 However. the disk hw»otlhiesis does not fit ceufortably with the strong variability of tle eiuissiou-line spectrum seen in Fie.," However, the disk hypothesis does not fit comfortably with the strong variability of the emission-line spectrum seen in Fig."549 DD. the li spectra of dwarf uovae at minimum light tend to e relatively steady., 3; the line spectra of dwarf novae at minimum light tend to be relatively steady.550 Also. if VICο Peg were a disk system. it would be expeced to uudergo dwarf lova eruptious fom time to time. but outbursts have not been recorded.," Also, if V405 Peg were a disk system, it would be expected to undergo dwarf nova eruptions from time to time, but outbursts have not been recorded."551" 1S""D>oO I1ο Warner(1957) relation between 2,4, and outburst. absolte maguitude 34,Inax]* |ogetjer wih our period. «istance. aud iuclhatlon. we esimate that dw:ul uova outbursts [rom this object would reach =9.5. so if outbursts occur they would escape notice ouly if they were very infrequent."," Using the \citet{warn87} relation between $P_{\rm orb}$ and outburst absolute magnitude $M_{V(\rm max)}$, together with our period, distance, and inclination, we estimate that dwarf nova outbursts from this object would reach $V = 9.5$, so if outbursts occur they would escape notice only if they were very infrequent."552 Some cwarf novae. such as WZ See. do outburst ouly every few decades. aud the high-proper-motion star CD2552 (Hessinan&Hopp1990). resembles a dwarf nova spectroscopically but has never been observed to outburst. implying a still longer outburst interval.," Some dwarf novae, such as WZ Sge, do outburst only every few decades, and the high-proper-motion star GD552 \citep{hessmangd552} resembles a dwarf nova spectroscopically but has never been observed to outburst, implying a still longer outburst interval."553 These seldom-outbursting systeus have orbital periods <2 lu. however. much shorter than V105 Pee.," These seldom-outbursting systems have orbital periods $< 2$ hr, however, much shorter than V405 Peg."554 Tappertetal.(2001) Sugeooest that LY UMa (= CW 10154525). wib Posy=0.271 d. may be a long-period example of a dwaT nova which seldom outbursts. but the‘e is no clear evidence for a disk in that system eitler.," \citet{tappertcw1045} suggest that LY UMa (= CW 1045+525), with $P_{\rm orb} = 0.271$ d, may be a long-period example of a dwarf nova which seldom outbursts, but there is no clear evidence for a disk in that system either."555 In sum. we are not able to unambieuously classify V105. Pee as a known type of CV — it is," In sum, we are not able to unambiguously classify V405 Peg as a known type of CV – it is"556"Due to the high uucertainty in the power-law spectral index and to the low level of both S1 aud $2. we estimated their iutenusifies iu the 2-10 keV band bw assuuinmeg a standard factor of couversion from) count rates of 9.5<10 HH, corresponding to au adopted power-law spectral shape of index 0.5.","Due to the high uncertainty in the power-law spectral index and to the low level of both S1 and S2, we estimated their intensities in the 2-10 keV band by assuming a standard factor of conversion from count rates of $9.3557\times 10^{-11}$ , corresponding to an adopted power-law spectral shape of index 0.5."558 The 1-0 uncertainties on the iutensities have been obtained by similarly scaling the errors ou the count rates (Table 1)., The $\sigma$ uncertainties on the intensities have been obtained by similarly scaling the errors on the count rates (Table 1).559 These intensities are reported in Figure 7. along with the WFC lielt curve in the 2-10 keV baud. obtained by binning in intervals of 5-20 seconds the temporal profile reported in Figure 1.," These intensities are reported in Figure 7, along with the WFC light curve in the 2-10 keV band, obtained by binning in intervals of 5-20 seconds the temporal profile reported in Figure 1."560 Differences between these intensities aud those obtained by adopting a bremisstralilung model do not exceed, Differences between these intensities and those obtained by adopting a bremsstrahlung model do not exceed.561 Note that the contribution of the black body component to the itensity of Sl in the 2-10 keV range is negligible., Note that the contribution of the black body component to the intensity of S1 in the 2-10 keV range is negligible.562 The δαν light curve of source S1 measured by the NFIs shows a decay of a factor of two in ~6 months (Fig., The X-ray light curve of source S1 measured by the NFIs shows a decay of a factor of two in $\sim$ 6 months (Fig.563 7h). much slower than X-ray. GRD afterglows so far observed.," 7b), much slower than X-ray GRB afterglows so far observed."564 Assundug. as sugeested by the positional coincidence aud by variability. that S1 dis associated with SN 199s8bw. this is the first detection of mediunu energv X-ray eniüssion from a Type I supernova (there is a unique case of Type I supernova detected i soft N-ravs. the Type Ic SN 1991. Tuuuler et al.," Assuming, as suggested by the positional coincidence and by variability, that S1 is associated with SN 1998bw, this is the first detection of medium energy X-ray emission from a Type I supernova (there is a unique case of Type I supernova detected in soft X-rays, the Type Ic SN 1994I, Immler et al."565 1998a) and the earliest detection of N-ravs after supernova explosion., 1998a) and the earliest detection of X-rays after supernova explosion.566 At the distance of SN 1998bw. 38 Mpc. the Iunuinosity observed in the range 2-10 keV. —Lo7«10! cre sto would be compatible with that of other supernovae detected in the same euergv baud (Ixoliira et al.," At the distance of SN 1998bw, 38 Mpc, the luminosity observed in the range 2-10 keV, $\sim 4-7 \times 10^{40}$ erg $^{-1}$, would be compatible with that of other supernovae detected in the same energy band (Kohmura et al."567 1901: Houck et al., 1994; Houck et al.568 L998: Schlegel 1995. and references therein).," 1998; Schlegel 1995, and references therein)."569 However. the observed Iuuiuositv aud variation thereof represent only au upper lit to the Iuninositv aud a lower lit to the amplitude of N-ray. variability of SN. 1998bw. respectively. due to the possible contribution of its host ealaxy. a face-ou spiral galaxy about one teuth of the size of our Galaxy. which is ouly very mareially resolved iu the BeppoSAX data.," However, the observed luminosity and variation thereof represent only an upper limit to the luminosity and a lower limit to the amplitude of X-ray variability of SN 1998bw, respectively, due to the possible contribution of its host galaxy, a face-on spiral galaxy about one tenth of the size of our Galaxy, which is only very marginally resolved in the BeppoSAX data."570 In fact. à galaxy of that type aud size could casily account for almost all of the N-ray emission served iu November 1998. when the fiux was lowest (sec .g« Fabbiauo 1989).," In fact, a galaxy of that type and size could easily account for almost all of the X-ray emission observed in November 1998, when the flux was lowest (see e.g., Fabbiano 1989)."571" The observed decay of Sl in the 2-10 keV. baud is well fitted by a power-law F(f)~f"" with p=0.16€0.01 (reduced u— 0.2).", The observed decay of S1 in the 2-10 keV band is well fitted by a power-law $F(t) \propto t^{-p}$ with $p = 0.16 \pm 0.04$ (reduced $\chi^2 \simeq 0.7$ ).572 The fit with au exponential luv Fit)xe©? with J=5004100 days has a reduced 4? of 2.1. correspouding to a probability of 10:4 for 2 deerees of freedom. therefore not neelieible (Fig.," The fit with an exponential law $F(t) \propto573e^{-t/\beta}$ with $\beta = 500 \pm 100$ days has a reduced $\chi^2$ of 2.4, corresponding to a probability of $\sim$ for 2 degrees of freedom, therefore not negligible (Fig."574 7b)., 7b).575 Both trends would be similar. considering the unknown dilution by the host ealaxyv of SN 1998). to the N-rav behavior of other supernovac (e... Woluuira et al.," Both trends would be similar, considering the unknown dilution by the host galaxy of SN 1998bw, to the X-ray behavior of other supernovae (e.g., Kohmura et al."576 1991: παπα ct al., 1994; Zimmermann et al.577 1991: IIouck et al., 1994; Houck et al.578 1998) aud. predicted by models of thermal bremisstraliluug of energetic electrons within the circunistellar medium (see c.g... Chevalier Frausson 1991: Chueai Dauzigcr 1991).," 1998) and predicted by models of thermal bremsstrahlung of energetic electrons within the circumstellar medium (see e.g., Chevalier Fransson 1994; Chugai Danziger 1994)."579 The prompt X-ray enmüsson observed for SN 1998bw requires that the circumstellar medium is highly ionized (perhaps by the powerful explosion). to allow the N-ravs to escape so soon after the explosion (see Ziuuunerianu et al.," The prompt X-ray emission observed for SN 1998bw requires that the circumstellar medium is highly ionized (perhaps by the powerful explosion), to allow the X-rays to escape so soon after the explosion (see Zimmermann et al."580 1991). ancl also very dense. as inferred also from the large radio output Usulkarui et al.," 1994), and also very dense, as inferred also from the large radio output (Kulkarni et al."581" 19982: Wicringa. νωπά, Frail 1999)."," 1998a; Wieringa, Kulkarni, Frail 1999)."582 In these coucdcitious. the N-ravs night be produced by the reverse shock which results from the pressure of swept-üp material ou the outeoiug shock aud propagates back iuto the shocked supernova gas (Chevalier Franssou 1991: Schlegel 1995].," In these conditions, the X-rays might be produced by the reverse shock which results from the pressure of swept-up material on the outgoing shock and propagates back into the shocked supernova gas (Chevalier Fransson 1994; Schlegel 1995)."583 The temperature obtained from the thermal bremsstrahhme fit to the BeppoSAN LEC'S—|MECS spectra. admittedly very poorly coustrained. is compatible with that fitted to the medimm or lard X-ray spectra of other supernovae (Iola et al.," The temperature obtained from the thermal bremsstrahlung fit to the BeppoSAX LECS+MECS spectra, admittedly very poorly constrained, is compatible with that fitted to the medium or hard X-ray spectra of other supernovae (Kohmura et al."584 1991: Leising et al., 1994; Leising et al.585 1991: Dota ct al., 1994; Dotani et al.586 1987)., 1987).587 On the other haud. the mildly relativistic couditious evidently present in the expanding shock of ον 199S8bw at early epochs (I&ulleui et al.," On the other hand, the mildly relativistic conditions evidently present in the expanding shock of SN 1998bw at early epochs (Kulkarni et al."588 1998a) aud the acceptable power-law fit obtained for the medii energy ταν spectra nought sugeest that ron-therimal mechauisuis are responsible for the XN-rav οnission such as svuchrotron radiation bv the extremely cherectic electrons. as was modeled for the racio emission by Li aud Chevalier (1999). or inverse Compton scatteriie of relativistic electrous. off optical/UV photons of the thermal ejecta (see Canizares et al.," 1998a) and the acceptable power-law fit obtained for the medium energy X-ray spectra might suggest that non-thermal mechanisms are responsible for the X-ray emission such as synchrotron radiation by the extremely energetic electrons, as was modeled for the radio emission by Li and Chevalier (1999), or inverse Compton scattering of relativistic electrons off optical/UV photons of the thermal ejecta (see Canizares et al."589 1982)., 1982).590 The ταν spectral iudex d8 consistent with that iueasured for tre radio spectrum starting ~15 davs after the explosion (νά ct al., The X-ray spectral index is consistent with that measured for the radio spectrum starting $\sim 15$ days after the explosion (Kulkarni et al.591 199s8a: Wicringa ct al., 1998a; Wieringa et al.592 1999). and wih the slope connecting quasi-simultaneous radio and Xa:Ww odneasureleuts (aον0.8).," 1999), and with the slope connecting quasi-simultaneous radio and X-ray measurements $\alpha \sim 0.8$ )."593 Therefore. it is difficult to «stablish whether the N-ravs are produced through svucwotron or inverse Compton radiation.," Therefore, it is difficult to establish whether the X-rays are produced through synchrotron or inverse Compton radiation."594" Ποπονο, if iuverse Compton losses were dominant. radio cussion production would be rapidly inhibited (Schlegel 1995). coutrary to the observations."," However, if inverse Compton losses were dominant, radio emission production would be rapidly inhibited (Schlegel 1995), contrary to the observations."595 Asstuning the N-vavs have a svuchrotron origin and adopting a single power-law of index o0.8 for the radio-to-N-ray svuchrotron spectrum. we obtain a bolometric luuinosity of ος10! eres 1.," Assuming the X-rays have a synchrotron origin and adopting a single power-law of index $\alpha \sim 0.8$ for the radio-to-X-ray synchrotron spectrum, we obtain a bolometric luminosity of $\sim 9 \times 10^{40}$ erg $^{-1}$."596 Assuming that the radio and X-ray cutting regions are cospatial aud expanding with a speed of ~O.3e (I&ularni ct al., Assuming that the radio and X-ray emitting regions are cospatial and expanding with a speed of $\sim 0.3c$ (Kulkarni et al.597 1998a). we derive a dnagnetic field of 21 Causs. simular to that found for SN 1980I by Canizares ct al. (," 1998a), we derive a magnetic field of $\simlt 1$ Gauss, similar to that found for SN 1980K by Canizares et al. ("5981982) assuniug inverse Compton losses are responsible for the N-xav production.,1982) assuming inverse Compton losses are responsible for the X-ray production.599 However. the Πίος signaleto-noise ratio of the BeppoSAX spectra does not allow us to choose between svuchrotron radiation aud thermal bremsstralling as the uechanuisui for the 1iediumn energv A-rav production.," However, the limited signal-to-noise ratio of the BeppoSAX spectra does not allow us to choose between synchrotron radiation and thermal bremsstrahlung as the mechanism for the medium energy X-ray production."600 The enmüssiou component detected iu the softer part of the BeppoSAN spectrum. if fitted with a black body. las a temperature of —0.1 keV. correspondiug to a black )xdy. total hunuinositv of ~104 ere |.," The emission component detected in the softer part of the BeppoSAX spectrum, if fitted with a black body, has a temperature of $\sim$ 0.1 keV, corresponding to a black body total luminosity of $\sim 10^{41}$ erg $^{-1}$."601" The inferred incar size of the enüttiug region is about one third of he solar radius. too large for a compact object left as a remnant of the supernova explosion. but approximately compatible with the size of the putative acerction disk xoniptlv formed as a consequence of the ""hiyperuova or ""eollapsar phenomenon. of which SN 1998ls might be an example (Pacgvisski 1998: AlacFadven Woosley 1998: Woosley. Eastinan. Sclinicdt 1999a)."," The inferred linear size of the emitting region is about one third of the solar radius, too large for a compact object left as a remnant of the supernova explosion, but approximately compatible with the size of the putative accretion disk promptly formed as a consequence of the “hypernova"" or “collapsar"" phenomenon, of which SN 1998bw might be an example (Paczyńsski 1998; MacFadyen Woosley 1998; Woosley, Eastman, Schmidt 1999a)."602 However. such a compact object or disk could be hardly visible at a so carly epoch. due to the optical thickness of the material cushrouding it.," However, such a compact object or disk could be hardly visible at a so early epoch, due to the optical thickness of the material enshrouding it."603 Black body soft N-rav cluission is not expected frou the supernova itself or from the expanding shell or ejecta. due to nou-equilibrium conditions of the svstem.," Black body soft X-ray emission is not expected from the supernova itself or from the expanding shell or ejecta, due to non-equilibrium conditions of the system."604 However.," However,"605The oscillations of the8 Cep stars are in general understood in terms of a heat mechanism active in the partial tonisation zones of iron-group elements (Moskalik Dziembowks1 1992).,"The oscillations of the$\beta\,$ Cep stars are in general understood in terms of a heat mechanism active in the partial ionisation zones of iron-group elements (Moskalik Dziembowksi 1992)."606 While the majority of detected and well-identified low-order p and g modes is predicted to be excited by non-adiabatic oscillation computations. some excitation problems occurred and remain to be solved for a few well-established observed non-radial mode frequencies. notably the £=|. p» modes of the stars v Eri (Pamyatnykh et 22004) and y Peg (Handler et 22009. Zdravkov Pamyatnykh 2009).," While the majority of detected and well-identified low-order p and g modes is predicted to be excited by non-adiabatic oscillation computations, some excitation problems occurred and remain to be solved for a few well-established observed non-radial mode frequencies, notably the $\ell=1$, $_2$ modes of the stars $\nu\,$ Eri (Pamyatnykh et 2004) and $\gamma\,$ Peg (Handler et 2009, Zdravkov Pamyatnykh 2009)."607 To excite these modes in the models. one would need to increase the opacities of iron-group elements.," To excite these modes in the models, one would need to increase the opacities of iron-group elements."608 In addition. the predicted frequency of this £=|. p» mode for appropriate models was found to be shifted with respect to the observed value for both v Eri and y Peg.," In addition, the predicted frequency of this $\ell=1$, $_2$ mode for appropriate models was found to be shifted with respect to the observed value for both $\nu\,$ Eri and $\gamma\,$ Peg."609 A similar exeitation problem occurred for the star I2LLac (Dziembowski Pamyatnykh 2008; Desmet et 22009)., A similar excitation problem occurred for the star Lac (Dziembowski Pamyatnykh 2008; Desmet et 2009).610 Theory explains the excitation of the observed radial anc pi non-radial modes well for the case studies of seismically modelled8 Cep stars. except for the very massive (M=24 M.) O9V pulsator 446202. for which none of the detectec frequencies is predicted to be excited(Briquet et 22011).," Theory explains the excitation of the observed radial and $_1$ non-radial modes well for the case studies of seismically modelled $\beta\,$ Cep stars, except for the very massive $M\simeq61124\,$ $_\odot$ ) O9V pulsator 46202, for which none of the detected frequencies is predicted to be excited(Briquet et 2011)."612 In particular. the detected radial modes ofa// seismically modelled 6 Cep stars of spectral type B agree with excitatior predictions for these particular modes.," In particular, the detected radial modes of seismically modelled $\beta\,$ Cep stars of spectral type B agree with excitation predictions for these particular modes."613 We are. therefore justified in insisting that the dominant mode of 1180642 be excitec in present-day theoretical computations., We are therefore justified in insisting that the dominant mode of 180642 be excited in present-day theoretical computations.614 To use this requirement as an additional constraint in our stellar modelling. we performed non-adiabatic computations for the radial modes of all the ~55 0000 selected models discussed in the previous section with the code (Dupret 2001. Dupret et 22002).," To use this requirement as an additional constraint in our stellar modelling, we performed non-adiabatic computations for the radial modes of all the $\sim$ 000 selected models discussed in the previous section with the code (Dupret 2001, Dupret et 2002)."615 For ~18 8850 of the models that fit the frequency as a radial mode. this mode is predicted to be excited.," For $\sim$ 850 of the models that fit the frequency as a radial mode, this mode is predicted to be excited."616 The distribution over the various overtones is as follows: 9964 models have the dominant mode excited as fundamental. 6681 as first overtone. 892 as second overtone. and 1324 as fourth overtone.," The distribution over the various overtones is as follows: 9964 models have the dominant mode excited as fundamental, 6681 as first overtone, 892 as second overtone, and 1324 as fourth overtone."617 There are no models with the third overtone excited while there are with an excited fourth overtone., There are no models with the third overtone excited while there are with an excited fourth overtone.618" This may seem strange at first sight. but is explained by the occurrence of a resonance of the type wp,72c."," This may seem strange at first sight, but is explained by the occurrence of a resonance of the type $\omega_{{\rm619 p}_4}\simeq\,2\omega_{{\rm p}_1}$."620" It was already known that à resonance e,=3c, occurs in polytropie models (Van Hoolst 1996)."," It was already known that a resonance $\omega_{{\rm p}_6}\simeq\,3\omega_{{\rm p}_1}$ occurs in polytropic models (Van Hoolst 1996)."621 Near-resonances were also found in that study. in particular the one we also find here on the basis of more realistic models 99 in Van Hoolst 1996).," Near-resonances were also found in that study, in particular the one we also find here on the basis of more realistic models 9 in Van Hoolst 1996)."622 In all the models with the fourth overtone excited. covering the mass interval [16.3.20] M... we also found the fundamental mode at (and quite often also the first overtone) to be excited.," In all the models with the fourth overtone excited, covering the mass interval $[16.3,20]\,$ $_\odot$, we also found the fundamental mode at (and quite often also the first overtone) to be excited."623 This frequency does not occur among the 127 dominant frequencies of 1180642., This frequency does not occur among the 127 dominant frequencies of 180642.624 These high-overtone models are more evolved and in closer agreement with the spectroscopic logg than the models with the fundamental mode interpretation.," These high-overtone models are more evolved and in closer agreement with the spectroscopic $\log\,g$ than the models with the fundamental mode interpretation."625 In the subsequent steps of the modelling procedure. we could not rely on a unique (£.71) identification of the modes corresponding to the observed frequencies. as only limited additional information is available (see reffreqs)).," In the subsequent steps of the modelling procedure, we could not rely on a unique $(\ell,m)$ identification of the modes corresponding to the observed frequencies, as only limited additional information is available (see \\ref{freqs}) )."626 Moreover. the additional modes all have much lower amplitudes than the one of the dominant mode. thus we did not prefer one above the other for the matching procedure.," Moreover, the additional modes all have much lower amplitudes than the one of the dominant mode, thus we did not prefer one above the other for the matching procedure."627 Thus we requested at once that all eight additional frequencies listed in reffreqs were fitted by model frequencies., Thus we requested at once that all eight additional frequencies listed in \\ref{freqs} were fitted by model frequencies.628 We also imposed that the identification of the degree of the mode with frequency is fulfilled ({Ξ0 or 3)., We also imposed that the identification of the degree of the mode with frequency is fulfilled $\ell$ =0 or 3).629 It turned out that this frequency is not a higher overtone radial mode., It turned out that this frequency is not a higher overtone radial mode.630" For the frequencycd. we requested it to have one of the seven (6,μη) combinations listed in reffreqs.."," For the frequency, we requested it to have one of the seven $(\ell,m)$ combinations listed in \\ref{freqs}."631 For each of those possibilities for (£.ΜΗ). we used the rotational splitting along with the V.; value listed in reffreqs and model radius to deduce the shift in. mode frequency implied by rotation. according to the formula (e.g.. Aerts et 22010. Chapter 3). Le. we limited the frequency matching procedure to first-order effects in the rotation frequency. which is consistent with ourgrid. of spherically-symmetric evolutionary models.," For each of those possibilities for $(\ell,m)$, we used the rotational splitting along with the $V_{\rm eq}$ value listed in \\ref{freqs}632 and model radius to deduce the shift in mode frequency implied by rotation, according to the formula (e.g., Aerts et 2010, Chapter 3), i.e., we limited the frequency matching procedure to first-order effects in the rotation frequency, which is consistent with ourgrid of spherically-symmetric evolutionary models."633 In the matching procedure. we screened all the models which excite and fit the dominant radial mode as described in the previous section and fulfilling all the information in reffreqs for the eight additional measured frequencies. after shifting them according to Eq.(1)) and reffreqs..," In the matching procedure, we screened all the models which excite and fit the dominant radial mode as described in the previous section and fulfilling all the information in \\ref{freqs} for the eight additional measured frequencies, after shifting them according to \ref{ledoux}) ) and \\ref{freqs}."634 The quality of the frequency matching was evaluated by the computation of a reduced y statistic. where we used as the error for all the eight frequencies because it is a typical uncertainty on theoretically predicted frequencies for non-rotating main sequence pulsators due to differences in the input physics of the models (e.g.. Moya et 2008).," The quality of the frequency matching was evaluated by the computation of a reduced $\chi^2$ statistic, where we used as the error for all the eight frequencies because it is a typical uncertainty on theoretically predicted frequencies for non-rotating main sequence pulsators due to differences in the input physics of the models (e.g., Moya et 2008)."635 We then considered only those models with y«1 and for which each individual frequency is fitted to better thancd., We then considered only those models with $\chi^2<1$ and for which each individual frequency is fitted to better than.636. The latter constraint was adopted to avoid a rather large mismatch leading to y«1., The latter constraint was adopted to avoid a rather large mismatch leading to $\chi^2<1$.637 In total. 2541 models survived our stringent matching constraints. covering a nass range of [8.1.19.9] M...," In total, 2541 models survived our stringent matching constraints, covering a mass range of $[8.1,19.9]\,$ $_\odot$."638 Among those. some 1000 predict that the dominant frequency Is the fundamental mode. some 1200 that it is instead the first overtone and a few hundred that it is either ps or ps.," Among those, some 1000 predict that the dominant frequency is the fundamental mode, some 1200 that it is instead the first overtone and a few hundred that it is either $_3$ or $_5$ ."639 Six prototypical examples of schematic frequency spectra are show in refbars.., Six prototypical examples of schematic frequency spectra are shown in \\ref{bars}. .640 The four that fit the dominant mode as the radial fundamental. predict that the frequency is an f=2.5+] mode and that the star has an equatorial rotation velocity of kkmss!.," The four that fit the dominant mode as the radial fundamental, predict that the frequency is an $\ell=2, m=+1$ mode and that the star has an equatorial rotation velocity of $^{-1}$ ."641 In the case of the, In the case of the642single clump giant candidate in the fields.,single clump giant candidate in the fields.643" For the UINIDSS-GPS A-band data (he computations are (he same. but with ly/(1,—d)= 0.68. C/—NKyo=0.6640.04 and Mj=—1.6140.03."," For the UKIDSS-GPS $K$ -band data the computations are the same, but with $A_K/(A_J-A_K)=0.68$ , $(J-K)_0=0.66\pm 0.04$ and $M_K=-1.61\pm 0.03$."644 In order to determine the disk edge we computed the distribution in distance for the chuup eiants in each field., In order to determine the disk edge we computed the distribution in distance for the clump giants in each field.645 Thus we coadcded the distance distribution of fields located above and below the plane at same Galactic longitude., Thus we coadded the distance distribution of fields located above and below the plane at same Galactic longitude.646 The coadded distance distribution [or each longitude was analyzed non-parametrically using the local likelihood density estimation method (Loader1996).., The coadded distance distribution for each longitude was analyzed non-parametrically using the local likelihood density estimation method \citep{1996_Loader}.647 Finally. the derivative method was applied for the distribution curve.," Finally, the derivative method was applied for the distribution curve."648 This method is simple and robust. and can be used to detect (he structures in the distance distribution.," This method is simple and robust, and can be used to detect the structures in the distance distribution."649 We defined as the disk edge (he outermost point of minimun derivative in each case., We defined as the disk edge the outermost point of minimum derivative in each case.650 The uncertainties were caleulated with a Monte Carlo procedure. assuming Poisson errors.," The uncertainties were calculated with a Monte Carlo procedure, assuming Poisson errors."651 The uncertainties due to the photometric errors do not produce anv (rend in the caleulations and are much smaller than the statistical error., The uncertainties due to the photometric errors do not produce any trend in the calculations and are much smaller than the statistical error.652 The resulting distance distributions alone different lines of sieht are shown in Fie. 2.., The resulting distance distributions along different lines of sight are shown in Fig. \ref{dist}.653" In all fields there is a censity drop in the clamp giant distribution at a corresponding Galactocentric distance of about 13.9 kpe (assuming J,=8 kpc). as listed in Table 1.."," In all fields there is a density drop in the clump giant distribution at a corresponding Galactocentric distance of about 13.9 kpc (assuming $R_o=8$ kpc), as listed in Table \ref{table}."654 We first noticed (he sharp termination of the clump eiant distribution in the diagram of the VVV field d001 (/.5b=295.4. —1.577). a verv heavily redcdened area located in the outskirts of the Carina star lorming region (Saitoetal.2010)..," We first noticed the sharp termination of the clump giant distribution in the color-magnitude diagram of the VVV field d001 $l, b =655295.4^{\circ}, -1.7^{\circ}$ ), a very heavily reddened area located in the outskirts of the Carina star forming region \citep{2010Msngr.141...24S}."656 Similar behavior is also found in UIKIDSS-GP5 data for different Galactic longitudes 2008)., Similar behavior is also found in UKIDSS-GPS data for different Galactic longitudes \citep{2008MNRAS.391..136L}.657 We studied low-extinction fields across the Milky Way disk (see Table 1))., We studied low-extinction fields across the Milky Way disk (see Table \ref{table}) ).658 When these were available. we selected. pairs of fields located: above and below the plane at the same Galactic longitude. in order to account for the Galactic warp. because if the disk is warped. (he line of sight can leave the stellar clisk before this ends.," When these were available, we selected pairs of fields located above and below the plane at the same Galactic longitude, in order to account for the Galactic warp, because if the disk is warped, the line of sight can leave the stellar disk before this ends."659 For example. at /=300° the mean warp location is 1° below the plane (Robinetal.1992).. so the selected VVV field. d003 is conveniently located to probe the full extent of the disk.," For example, at $l=300^{\circ}$ the mean warp location is $1^{\circ}$ below the plane \citep{1992ApJ...400L..25R}, so the selected VVV field d003 is conveniently located to probe the full extent of the disk."660 At most other longitudes explored here the warp is absent. with the mean plane being at b=0° (Fig. 3)).," At most other longitudes explored here the warp is absent, with the mean plane being at $b=0^{\circ}$ (Fig. \ref{map}) )."661 We have also explored a few other UIXIDSS-GPS fields located at inner longitudes that vield lower distances., We have also explored a few other UKIDSS-GPS fields located at inner longitudes that yield lower distances.662 These fields with /«60* were discarded because they are heavily redclenecl and erowded. and the photometry is not as deep as the rest. presumably due to enhanced contamination ουν the near-sicle of the inner bar.," These fields with $l<60^{\circ}$ were discarded because they are heavily reddened and crowded, and the photometry is not as deep as the rest, presumably due to enhanced contamination from the near-side of the inner bar."663 Svstematic errors such as variations of the recldening law have not been included., Systematic errors such as variations of the reddening law have not been included.664 It is important to note that the present results are independent of models., It is important to note that the present results are independent of models.665Thev rely on basic assunipiions such as that the Lipparcos stellar sample is representative of the entire,They rely on basic assumptions such as that the Hipparcos stellar sample is representative of the entire666AIW dark halo. but a numerical analysis to check this would be interesting.,"MW dark halo, but a numerical analysis to check this would be interesting."667 These arguments make a good though not definitive case that the orbit of LAIC relative to MW has the shape illustrated in Figures 3. ancl 4.., These arguments make a good — though not definitive — case that the orbit of LMC relative to MW has the shape illustrated in Figures \ref{Fig:3} and \ref{Fig:4}.668 An issue to be revisited with better mass models is (hat (his analysis depends on (he assumption that the Magellanic Clouds originated as clumps of matter left little disturbed. by the assembly of the major ealaxies., An issue to be revisited with better mass models is that this analysis depends on the assumption that the Magellanic Clouds originated as clumps of matter left little disturbed by the assembly of the major galaxies.669 An alternative picture in which the Clouds are debris [rom a violent major merger αἱ a more modest redshift (Yang Hammer 2010) is not likely to be found by NNÀM., An alternative picture in which the Clouds are debris from a violent major merger at a more modest redshift (Yang Hammer 2010) is not likely to be found by NNAM.670 This picture will have to be evaluated by other considerations. including observational ancl theoretical studies of the barvonic debris [rom mergers.," This picture will have to be evaluated by other considerations, including observational and theoretical studies of the baryonic debris from mergers."671 The difference between the LMC orbits in the two plausible models (plotted in black) shows that under the cosmological initial condition there still is considerable uncertainty in where LMC was ad redshift z=1., The difference between the LMC orbits in the two plausible models (plotted in black) shows that under the cosmological initial condition there still is considerable uncertainty in where LMC was at redshift $z=1$.672 This might be reduced by tighter modeling of what more distant. galaxies were doing., This might be reduced by tighter modeling of what more distant galaxies were doing.673 Though models 1 and 2 are reasonable fits to the measured proper motions of M33 and 110 as well as LMC. the M33 orbit does not agree with (he proposal by MeConnachie et al. (," Though models 1 and 2 are reasonable fits to the measured proper motions of M33 and IC10 as well as LMC, the M33 orbit does not agree with the proposal by McConnachie et al. ("6742009) that M33 passed close to M31.,2009) that M33 passed close to M31.675 Since the orbits of these two galaxies are sensitive to the orbit of M31 a firmer case For where M32 and IC10 have been awaits a firmer case for the proper motion of M31., Since the orbits of these two galaxies are sensitive to the orbit of M31 a firmer case for where M33 and IC10 have been awaits a firmer case for the proper motion of M31.676 In all five models in Table 1. M31 is moving toward increasing longitude. aud in the (wo most plausible cases (he motion to increasing right ascension is faster than the van der Marel Guhathakurta (2008) estimate.," In all five models in Table 1, M31 is moving toward increasing longitude, and in the two most plausible cases the motion to increasing right ascension is faster than the van der Marel Guhathakurta (2008) estimate."677 Since the transverse motion of M31 is expected to be more sensitive than LAIC (o the mass distribution outside LG a [immer case for the proper motion of M31. and the orbits of M33. and ICTO awaits more detailed mass models that more completely account for the large galaxies exterior (o the Local Group and. equally important. include more of the nearby isolated smaller galaxies that largely serve as test particles.," Since the transverse motion of M31 is expected to be more sensitive than LMC to the mass distribution outside LG a firmer case for the proper motion of M31 and the orbits of M33 and IC10 awaits more detailed mass models that more completely account for the large galaxies exterior to the Local Group and, equally important, include more of the nearby isolated smaller galaxies that largely serve as test particles."678 The analvsis presented here shows that NNÀM will be be well suited [or analyses of these more ambitious mass models. though likely with a more efficient way to minimize the V7 measure of fit and a better strategy to search for acceptable orbits. perhaps along the lines of Peebles et al. (," The analysis presented here shows that NNAM will be be well suited for analyses of these more ambitious mass models, though likely with a more efficient way to minimize the $\chi^2$ measure of fit and a better strategy to search for acceptable orbits, perhaps along the lines of Peebles et al. ("6792001).,2001).680 Most important. of course. will be the lighter constraints from advances in measurements of galaxy distances and proper motions. eround-hased and from the Gaya and SIM lite satellite missions.," Most important, of course, will be the tighter constraints from advances in measurements of galaxy distances and proper motions, ground-based and from the Gaya and SIM lite satellite missions."681 This analvsis is based on a picture for the mass distribution and a cosmology that have passed searching tests., This analysis is based on a picture for the mass distribution and a cosmology that have passed searching tests.682 Bul the cosmology ancl our ideas about how mass is distributed around galaxies still are enormous extrapolations from what actually is well established., But the cosmology and our ideas about how mass is distributed around galaxies still are enormous extrapolations from what actually is well established.683" The apparently successful fit to the motions of the very nearby galaxies is a modest but not trivial addition to our [und of cosmological tests. and a test Chat can and should be considerably improved,"," The apparently successful fit to the motions of the very nearby galaxies is a modest but not trivial addition to our fund of cosmological tests, and a test that can and should be considerably improved."684Compton-thick ACGNs is consistent with the Ly Loop relationship of Goulcing et al. (,Compton-thick AGNs is consistent with the $L_X $ $ L_{\rm [OIV]}$ relationship of Goulding et al. (6852010) when the X-ray clata is corrected for the absorption implied from high-quality X-ray spectroscopy.,2010) when the X-ray data is corrected for the absorption implied from high-quality X-ray spectroscopy.686 Assuming the eniüssion is indeed an isotropic AGN indicator. (c.g. Alelendez et al.," Assuming the emission is indeed an isotropic AGN indicator (e.g., Melendez et al."687 2008: Diamond-Stanic ct al., 2008; Diamond-Stanic et al.688 2009: Coulcing et al., 2009; Goulding et al.689 2010). this suggests that by comparingthe observed: X-rav upper-limit to the intrinsic X-ray luminosity as predicted by our measurements (Lyon). we may infer whether the sources in our sample are indeed Compton-thick AGNs.," 2010), this suggests that by comparingthe observed X-ray upper-limit to the intrinsic X-ray luminosity as predicted by our measurements $L_{\rm x,[OIV]}$ ), we may infer whether the sources in our sample are indeed Compton-thick AGNs."690 Dased on Compton rellection models. Alexander et al. (," Based on Compton reflection models, Alexander et al. ("6912008) predict that the observed.intrinsic N-ray. Εαν ratio inthe 210 keV band fora Compton-thick AGN with Way~1.5.1075em.7 is fxi£αν8M5.,"2008) predict that the observed–intrinsic X-ray flux ratio in the 2–10 keV band for a Compton-thick AGN with $N_H \sim 1.5 \times 10^{24} \pcmsq$ is $f_{\rm X,intr}/f_{\rm X,obs} \approx 15$."692 Hence. we predict that sources with fsiuuiv/foaz15 are likely to be obscured by Compton-thick material.," Hence, we predict that sources with $f_{\rm X,intr}/f_{\rm X,obs} \goa 15$ are likely to be obscured by Compton-thick material."693 For the 14 candidate Conipton-thick ACINs in our sample. we calculate. fsoj using the local relation of 7..," For the 14 candidate Compton-thick AGNs in our sample, we calculate $f_{\rm X,[OIV]}$ using the local relation of \citet{goulding10}."694 We predict intrinsic X-ray luminosities of Lxμοι2(0.1. 26)1057Cres (sec Column 9 of Table 2)).," We predict intrinsic X-ray luminosities of $L_{X{\rm ,predict}} \approx (0.1$ $26) \times69510^{43} \ergps$ (see Column 9 of Table \ref{tab:ir_phot_spec}) )."696 We find that 13 (z90 percent) of the sources exhibit. fxcoc/fiasz15 (seo Column 12 of ‘Table 2)).," We find that 13 $\approx 90$ percent) of the sources exhibit $f_{\rm697 X,[OIV]}/f_{\rm X,obs} \goa 15$ (see Column 12 of Table \ref{tab:ir_phot_spec}) )."698 Furthermore. if we account for the intrinsic scatter within the local relation (+0.3. dex). and conservatively assume that none of the sources which lie within this region are. Compton-thick. we still estimate that at. least 9/14 (zz65 percent) of our candidate Compton-thick AGNSs could be genuine Compton-thick AGNs.," Furthermore, if we account for the intrinsic scatter within the local relation $\approx 0.3$ dex), and conservatively assume that none of the sources which lie within this region are Compton-thick, we still estimate that at least 9/14 $\approx 65$ percent) of our candidate Compton-thick AGNs could be genuine Compton-thick AGNs."699 Lt is also prudent to note that as the observed X-ray [luxes for all of these sources are upper-limits. we cannot exelude the possibility that all of the sources in our sample are Compton-thick AGNs as the implied f&οναν ratio is a lower-Iimit.," It is also prudent to note that as the observed X-ray fluxes for all of these sources are upper-limits, we cannot exclude the possibility that all of the sources in our sample are Compton-thick AGNs as the implied $f_{\rm X,[OIV]}/f_{\rm X,obs}$ ratio is a lower-limit."700 By combining multiple indirect AGN luminosity indicators. particularly those which probe different regions of the central engine. we can place even stronger constraints on whether the AGNs in our sample are Compton thick jin using narrow-line emission alone.," By combining multiple indirect AGN luminosity indicators, particularly those which probe different regions of the central engine, we can place even stronger constraints on whether the AGNs in our sample are Compton thick than using narrow-line emission alone."701 The 6pum continuum luminosity has been shown to provide à good proxy for re LEPLsic AGN luminosity (e.g. Lutz et al.," The $6 \um$ continuum luminosity has been shown to provide a good proxy for the intrinsic AGN luminosity (e.g., Lutz et al."702 2004: 277) ," 2004; \citealt{Maiolino07,Treister08,fiore09}) )."703In Fig., In Fig.704 5bb we again present the observed 2 keV. A-ray upper-limit luminosities from. data but now compare these [uminosities to the ACN continuum luminosity at 6pun derived in Section 3.4. and the Luminosity-depencdent (2). and. Iuminositv-indepencdent (Lutz et al., \ref{fig:6um_xray}b b we again present the observed 2--10 keV X-ray upper-limit luminosities from data but now compare these luminosities to the AGN continuum luminosity at $6 \um$ derived in Section \ref{subsec:6um_emission} and the luminosity-dependent \citep{fiore09} and luminosity-independent (Lutz et al.705 2004) relations derived. using high-quality X-rav data and mid-LIt. SpZzer IRAC photometry and. 190 spectroscopy. respectively.," 2004) relations derived using high-quality X-ray data and mid-IR IRAC photometry and ISO spectroscopy, respectively."706 As noted in Section 23.4.. one of our 14 candidate Compton-thick ACGNs is consistent with rere being Little or no mid-IHt. emission. from an AGN continuum at A~5r 15pun. and we remove this AGN from further analyses in here.," As noted in Section \ref{subsec:6um_emission}, one of our 14 candidate Compton-thick AGNs is consistent with there being little or no mid-IR emission from an AGN continuum at $\lambda \sim 5$ $15 \um$, and we remove this AGN from further analyses in here."707 We conservatively adopt the slightly lower-Iuminosity 6pum relationship of Lutz ct al (2004) to infer the intrinsic. X-ray luminosities of the candidate: Compton-thick AGNs., We conservatively adopt the slightly lower-luminosity $6 \um$ relationship of Lutz et al (2004) to infer the intrinsic X-ray luminosities of the candidate Compton-thick AGNs.708 We estimate intrinsic N-ray luminosities of {νομος7(0.2 30)«107eres (sce Column 10 of ‘Table 2)).," We estimate intrinsic X-ray luminosities of $L_{X {\rm ,predict}} \approx709(0.2$ $30) \times 10^{42} \ergps$ (see Column 10 of Table \ref{tab:ir_phot_spec}) )."710 Eight out of the 13 (260percent) 6pun detected sample members lie in the region expected. for Compton- AGNs (Le. Na<1510em 7i see Column 13 οἱ ‘Table 2)).," Eight out of the 13 $\approx71160$percent) $6 \um$ detected sample members lie in the region expected for Compton-thick AGNs (i.e., $N_H \goa 1.5 \times 10^{24}712\pcmsq$ ; see Column 13 of Table \ref{tab:ir_phot_spec}) )."713 However.if we were to adopt the relationship," However,if we were to adopt the relationship"714" (οιοι,sarsky2000:Ivisonetal.σοι].2002).. Ta. Sullivanetal.(2001).. (Sullivanetal."," \citep[e.g.,][]{Genzel00,Ivison00,Smail02}, $\alpha$ \citet{Hopkins01} \citet{Sullivan01}, \citep{Sullivan01}."7152001).. Πα |On1A3727(0.3<2.(8). (seeCardicletal, $\alpha$ $\lambda$ $0.3<z<0.8$ \citep[see][]{Cardiel03}.716".2003).. (2=0.3) (0.3<2«0.8) Πρ=70 PAIN pe|, Qay=0.3. Q4=0.7."," $z\lesssim 0.3$ $0.3<z<0.8$ $H_0 = 70\,$ $^{-1}$ $^{-1}$ $\Omega_M = 0.3$ $\Omega_\Lambda = 0.7$ \citep[][and references therein]{Hopkins03a}."717 R=22.5 (Coorgakakisetal.1999:Afonso2002).," $R=22.5$ \citep{Georgakakis99, Afonso02}."718. 50005AX8500A.. 1000=Axz7000 (Ceorgakakisetal.1999:Afonso2002)..," $5000 \lesssim \lambda \lesssim 8500\,$ $4000 \lesssim \lambda \lesssim 7000\,$ \citep{Georgakakis99, Afonso02}."719"the evolving Ποιά loops is shown in Fieure S((b) in which we plot the result [rom three simulations wavelengths for the tangled field component (lanelecl field loops"").","the evolving field loops is shown in Figure \ref{fig08}( (b) in which we plot the result from three simulations wavelengths for the tangled field component (tangled field ""loops"")."720 Note that A is defined in Eq (12) and Eq.(13)., Note that $\lambda$ is defined in Eq (12) and Eq.(13).721 We use a sequence of values for wavelength: 2A. A and A/2.," We use a sequence of values for wavelength: $2\lambda$, $\lambda$ and $\lambda/2$."722 Figure S((b) clearly shows (hat smaller field loop A leads to the largest average heat flux. since siialler scale loops will reconnect before large loops for a given magnetic resistivitv.," Figure \ref{fig08}( (b) clearly shows that smaller field loop $\lambda$ leads to the largest average heat flux, since smaller scale loops will reconnect before large loops for a given magnetic resistivity."723 This result demonstrates the link between the nunber of reconnection sites of the field aud heat [Iux., This result demonstrates the link between the number of reconnection sites of the field and heat flux.724 We next analvze (he temperature equilibration in detail., We next analyze the temperature equilibration in detail.725 The averaged temperature difference across the interface is plotted in Figure 7((b)., The averaged temperature difference across the interface is plotted in Figure \ref{fig07}( (b).726 It shows the dillerence between the averaged temperature at the hot side and the cold side., It shows the difference between the averaged temperature at the hot side and the cold side.727 One significant feature in Figure 7T((b) is that the temperature dillerence decreases to a steady value νι in all cases., One significant feature in Figure \ref{fig07}( (b) is that the temperature difference decreases to a steady value $T_{end}$ in all cases.728 This resembles percolation across a membrane which allows a density jump to happen when filtering two fluids., This resembles percolation across a membrane which allows a density jump to happen when filtering two fluids.729 Figure (ο) shows the distance required for the temperature to drop 80 percent at the interface., Figure \ref{fig07}( (c) shows the distance required for the temperature to drop $80$ percent at the interface.730" This distance characterizes the length of the interaction region,", This distance characterizes the length of the interaction region.731 Except for the vertical field case where no heat. transfer is allowed. (he interface is expanding at different rates for different 7? values.," Except for the vertical field case where no heat transfer is allowed, the interface is expanding at different rates for different $R$ values."732 The expansion for all the cases of nonzero H approaches a steady. value which is also a characteristic leature of the temperature equilibration evolution., The expansion for all the cases of nonzero $R$ approaches a steady value which is also a characteristic feature of the temperature equilibration evolution.733 We now analvze the modification of magnetic field configuration curing the evolution., We now analyze the modification of magnetic field configuration during the evolution.734 Throughout our simulations. the local magnetic field is initially a set of complete loops surrounding (he interaction region.," Throughout our simulations, the local magnetic field is initially a set of complete loops surrounding the interaction region."735 Once the energy. transfer begins. the interaction region tends (to expand as discussed previously.," Once the energy transfer begins, the interaction region tends to expand as discussed previously."736 This expansion stretches the field lines on the x direction and distorts these circular loops. eventually inducing magnetic reconnection which oppens up channels connecting the hot and cold regions.," This expansion stretches the field lines on the x direction and distorts these circular loops, eventually inducing magnetic reconnection which oppens up channels connecting the hot and cold regions."737 From the current Jy=|VxBI. we can get information on how tangled the field is.," From the current $J_B = |\curl \textbf{B}|$, we can get information on how tangled the field is."738 Figure 7((d) shows the evolution of, Figure \ref{fig07}( (d) shows the evolution of739where2]ayp ds the coutribution of the fuctuating component of the CAIB. n is the brightuess fluctuations of the Galactic template map (net necessarily iu teiiperature units). à is the cocticient that converts units of the Galactic template iuto antenna temperature and n represents any residual Galactic contribution which is uncorrelated with n,"where$x_{CMB}^i$ is the contribution of the fluctuating component of the CMB, $x_{Gal}^i$ is the brightness fluctuations of the Galactic template map (not necessarily in temperature units), $\alpha$ is the coefficient that converts units of the Galactic template into antenna temperature and $y_{Gal}^i$ represents any residual Galactic contribution which is uncorrelated with $x_{Gal}^i$."740 We consider n aud Xca;g to be randoni variables with zero mean. Le. Xcarjp)=αι)0. and κ and yeu to be coustant vectors.," We consider $\nbf$ and $\xbf_{CMB}$ to be random variables with zero mean, i.e. $\langle \xbf_{CMB} \rangle = \langle \nbf \rangle = 0$, 	and $\xbf_{Gal}$ and $\ybf_{Gal}$ to be constant vectors."741 Thus the data covariance matrix is given by yy where (xearpxXbarg) is the covariance matrix of the CMB aud Gua) is the noise covariance matrix.," Thus the data covariance matrix is given by ^T - ^T = + ^T , where $\langle \xbf_{CMB} \xbf_{CMB}^T \rangle $ is the covariance matrix of the CMB and $\langle \nbf \nbf^T \rangle $ is the noise covariance matrix."742 The uoise in the 19 GIIz map is approximately uncorrelated aud las an amplitude of 7;—2 mk. Therefore. the covariance matrix of this map is SIGH.snas ADuinizius u=(yοκ€lyaxe) vields the nüiuinmnu-variuice estimate of à. ie. Xe]with variance Note that unlike the case in dOC97. there is little contribution from chance aliguients between the CXMB and the various template maps. since the CMD contribution to C is negligible.," The noise in the 19 GHz map is approximately uncorrelated and has an amplitude of $\sigma_i$$\sim$ 2 mK. Therefore, the covariance matrix of this map is _i^2 Minimizing $ \chi^2 \equiv 743 (\ybf - {\alpha} \xbf_{Gal})^T 744 {\bf C}^{-1}745 (\ybf - {\alpha} \xbf_{Gal}) $ yields the minimum-variance estimate of $\alpha$, i.e. = with variance ^2 = Note that unlike the case in dOC97, there is little contribution from chance alignments between the CMB and the various template maps, since the CMB contribution to ${\bf C}$ is negligible."746 If the the noise is correlated or the anisotropy signal is significant. then our C used above will differ from the true covariance matrix. denoted C’.," If the the noise is correlated or the anisotropy signal is significant, then our $\Cbf$ used above will differ from the true covariance matrix, denoted $\Cbf'$."747 Although still provides a reasonable aud uubiased estimate of ad. its variance will be larger than iuplied by(5).. given by Iu the next section. au estimate of Ο is made frou the data and the correspondiug variance of à is evaluated.," Although still provides a reasonable and unbiased estimate of $\alpha$, its variance will be larger than implied by, given by ^2 = In the next section, an estimate of ${\bf C'}$ is made from the data and the corresponding variance of ${\alphaHat}$ is evaluated."748 The 19 GIIZ map has an angular resolution of 3° FWHIAL aud is stored iu 1.97«1.37 pixels (Cottingham 1987: Doughu 1992)., The 19 GHz map has an angular resolution of $^{\circ}$ FWHM and is stored in $1.3^\circ \times 1.3^\circ$ pixels (Cottingham 1987; Boughn 1992).749 The template maps are convolved with a 37 Gaussian beam and regions within 207 and 30° of the Galactic plane are excluded., The template maps are convolved with a $^{\circ}$ Gaussian beam and regions within $^{\circ}$ and $^{\circ}$ of the Galactic plane are excluded.750 To avoid contanunation by zodiacal dust emission. data within 107 of the Ecliptic plane are also excluded from the analysis: although. the results are found to be independent of this cut.," To avoid contamination by zodiacal dust emission, data within $^{\circ}$ of the Ecliptic plane are also excluded from the analysis; although, the results are found to be independent of this cut."751 Off the Galactic plane. the 19 CHIIz map is dominated by the CMD dipole ((=1).," Off the Galactic plane, the 19 GHz map is dominated by the CMB dipole $\l$ =1)."752 On the other haud. because of its planar structure. cussion associated with the Galaxy has a strong quadrupole (f=2) componcut.," On the other hand, because of its planar structure, emission associated with the Galaxy has a strong quadrupole $\l$ =2) component."753 Therefore. the monopole. dipole. aud quadrupole moments are removed from both the 19 CGITz and template maps.," Therefore, the monopole, dipole, and quadrupole moments are removed from both the 19 GHz and template maps."754 As a consequence. the computed a depeuds oulv ou correlated structure iu the maps on augular scales zz907.," As a consequence, the computed $\alphaHat$ depends only on correlated structure in the maps on angular scales $\simlt 90^{\circ}$."755 The 19 CIIz map was cross-correlated with five ciffercut teiiplates: two for cussion. the 108 /MIIZ (TTaslam 1981) and 1120 MITz (Reich aud Reich 1988) survevs: and three to study dust auc free-free cussion. the 100. 110 and Diffuse Infrared Dackground Expernucut (DIRBE) sky maps (Doggess 1992).," The 19 GHz map was cross-correlated with five different templates: two for emission, the 408 MHz (Haslam 1981) and 1420 MHz (Reich and Reich 1988) surveys; and three to study dust and free-free emission, the 100, 140 and Diffuse Infrared Background Experiment (DIRBE) sky maps (Boggess 1992)."756 Table 1 lists the coefficieuts à derived from with errors colpited from(5)., Table 1 lists the coefficients $\alphaHat$ derived from with errors computed from.757. All three DIRBE templates show significant correlations with the 19 GIIz map. while the two templates are found to be ouly mareinally correlated.," All three DIRBE templates show significant correlations with the 19 GHz map, while the two templates are found to be only marginally correlated."758 Also listed in Table 1 are the implied fluctuations in antenna temperature in the 19 GITz map. ie. 62=6654. where σε is the of the teuplate map.," Also listed in Table 1 are the implied fluctuations in antenna temperature in the 19 GHz map, i.e. $\dT = \alphaHat \sigma_{Gal}$ , where $\sigma_{Gal}$ is the of the template map."759" Ifa template map includes a distinct. compouent that is uncorrelated with the 19 GIIz map. then 62 is underestimated by a factor 97,iO6a Where Torah is the of the correlated component of the template map."," If a template map includes a distinct component that is uncorrelated with the 19 GHz map, then $\dT$ is underestimated by a factor $\sigma^{\prime}_{Gal} / \sigma_{Gal}$, where $\sigma^{\prime}_{Gal}$ is the of the correlated component of the template map."760 For this reason. the 9T5 in Table 1 should be considered lower limits.," For this reason, the $\dT$ 's in Table 1 should be considered lower limits."761 As ineutioned above. the errors listed iu Table 1 were computed. from aud are therefore lower limits to the error.," As mentioned above, the errors listed in Table 1 were computed from and are therefore lower limits to the error."762 We now describe a series of tests. performed to estimate the uncertainty in à due to correlated noise aud other svsteimiaties.," We now describe a series of tests, performed to estimate the uncertainty in $\alphaHat$ due to correlated noise and other systematics."763" If the true noise correlation matrix is isotropic. CT,=μμ=RO where 0;; is the angle between pixels / and j. then we can o;o;estimate the uoise correlation function RO) of the 19 GIIz data (after removing the monopole. dipole. aud quackupole) by (0)=Ny,1»-Jil;ícia. where g; is the antenna temperature of the // pixel aud the suni is over all Ng pairs of pixels separated by 0."," If the true noise correlation matrix is isotropic, $C'_{ij} = \expec{n_in_j} = 764	 R(\theta_{ij}) \sigma_i \sigma_j$ where $\theta_{ij}$ is the angle between pixels $i$ and $j$, then we can estimate the noise correlation function $R(\theta)$ of the 19 GHz data (after removing the monopole, dipole, and quadrupole) by $R(\theta) = N_\theta^{-1} 765	 \sum_{ij} y_i y_j /\sigma_i \sigma_j$, where $y_i$ is the antenna temperature of the $i^{th}$ pixel and the sum is over all $N_\theta$ pairs of pixels separated by $\theta$."766 Substituting these relations iuto gives estimates of Ao which are from to larger than those in Table 1., Substituting these relations into gives estimates of $\da$ which are from to larger than those in Table 1.767 As another test of the robustuess of the estimates of o. we employed. Monte Carlo simulations in which the teiiplate maps are sliced iuto eiehteen regions of equal area. each correspouding to a range of Galactic latitude [].," As another test of the robustness of the estimates of $\alphaHat$, we employed Monte Carlo simulations in which the template maps are sliced into eighteen regions of equal area, each corresponding to a range of Galactic latitude $|b|$ ."768 Tuside cach of these regions the pixels are rearrauged in randomorder. so that the latitude dependence is preserved but the longitudinal correlations are destroved.," Inside each of these regions the pixels are rearranged in randomorder, so that the latitude dependence is preserved but the longitudinal correlations are destroyed."769 Repeating this procedure 10080 times vields distributious of a's consistentwith zero mean aud with standard deviations Δάλι1.6 times lareer than the formal errors Aa (see Table 1)., Repeating this procedure 1000 times yields distributions of $\alphaHat$ 's consistentwith zero mean and with standard deviations $\damc\sim 1.6$ times larger than the formal errors $\da$ (see Table 1).770 , 	 771Then we parameterize the environment surrounding each galaxy using the 3-D density contrast computed as: where ρ is the local number density and <p> = 0.05 gal (h! Mpc) represents the mean number density measured in the whole region.,Then we parameterize the environment surrounding each galaxy using the 3-D density contrast computed as: where $\rho$ is the local number density and $<\rho>$ = 0.05 gal $(h^{-1}~$ $)^{-3}$ represents the mean number density measured in the whole region.772" The local number density p around each galaxy is computed within a cylinder with 1 47! Mpc radius and 1000 kms""! half-length, which is large enough to comprise the dispersion of small groups and the newly compressed Finger of Gods of Coma and Abell 1367."," The local number density $\rho$ around each galaxy is computed within a cylinder with 1 $h^{-1}$ Mpc radius and 1000 $\rm km s^{-1}$ half-length, which is large enough to comprise the dispersion of small groups and the newly compressed Finger of Gods of Coma and Abell 1367."773" To take into account boundary effects (the cylinders centered on galaxies near the edges of our sample will partially fall outside the studied volume), for each galaxy we divide p by the fraction of the volume of the cylinder that fall inside the survey borders."," To take into account boundary effects (the cylinders centered on galaxies near the edges of our sample will partially fall outside the studied volume), for each galaxy we divide $\rho$ by the fraction of the volume of the cylinder that fall inside the survey borders."774" We divide the sample in four over-density bins, chosen in order to highlight physically different environments of increasing level of aggregation (see Fig.2)): The UltraLow density bin (UL: 61,1000€ 0) describes the underlying cosmic web; the Low density bin (L: 0«6j,1000€ 4) comprises the filaments in the Great Wall and the loose groups; the High density bin (H: 4<61,1000€ 20) include the cluster outskirts and the significant groups; the UltraHigh density bin (UH: 61,1000> 20) corresponds to the cores of the"," We divide the sample in four over-density bins, chosen in order to highlight physically different environments of increasing level of aggregation (see \ref{fig2}) ): The UltraLow density bin (UL: $\delta_{1,1000}\leq 0$ ) describes the underlying cosmic web; the Low density bin (L: $0 < \delta_{1,1000} \leq 4$ ) comprises the filaments in the Great Wall and the loose groups; the High density bin (H: $4 < \delta_{1,1000} \leq 20$ ) include the cluster outskirts and the significant groups; the UltraHigh density bin (UH: $\delta_{1,1000} > 20$ ) corresponds to the cores of the"775in the view of most people. was suggested. primarily as a replacement for dark matter.,"in the view of most people, was suggested primarily as a replacement for dark matter."776 But more generally. NOND should) not be viewed. simply as an alternative to dark matter: the systematic appearance of the mass discrepancy in astronomical svstenis with low internal accelerations is an indication that Newtonian dynamics or gravity may break down in this limit.," But more generally, MOND should not be viewed simply as an alternative to dark matter; the systematic appearance of the mass discrepancy in astronomical systems with low internal accelerations is an indication that Newtonian dynamics or gravity may break down in this limit."777 MOND primarily acldresses this issue: is physics in the Iow-acceleration regime Newtonian?, MOND primarily addresses this issue: is physics in the low-acceleration regime Newtonian?778 The success of MOND in explaining the scaling properties and observed rotation curves of galaxies suggests that it may not be., The success of MOND in explaining the scaling properties and observed rotation curves of galaxies suggests that it may not be.779 MOND does not rest upon the principle that there is no uncetected or dark matter., MOND does not rest upon the principle that there is no undetected or dark matter.780 Indeed. comparing the density of luminous matter to the barvonic content of the universe implied. by considerations of primordial nucleosynthesis. one can only conclude that there is. as vet. undetected barvonie matter. probably in the formi of clilluse gas in the intergalactic medium.," Indeed, comparing the density of luminous matter to the baryonic content of the universe implied by considerations of primordial nucleosynthesis, one can only conclude that there is, as yet, undetected baryonic matter, probably in the form of diffuse gas in the intergalactic medium."781 Moreover. it is virtually certain that particle dark matter exists in the form of neutrinos: only its contribution to the total mass density of the Universe is unclear.," Moreover, it is virtually certain that particle dark matter exists in the form of neutrinos; only its contribution to the total mass density of the Universe is unclear."782 MOND would be incompatible with the wide-spread existence of dark. matter which clusters on the scale o£ galaxies cold dark matter., MOND would be incompatible with the wide-spread existence of dark matter which clusters on the scale of galaxies– cold dark matter.783 But MOND is not inconsistent with hot dark matter such as 2 ev neutrinos. which can only ageregate on the scale of clusters of galaxies. indeed. | have presented. evidence that this may be the case.," But MOND is not inconsistent with hot dark matter such as 2 ev neutrinos, which can only aggregate on the scale of clusters of galaxies– indeed, I have presented evidence that this may be the case."784 Neutrinos. as particle dark matter. candidates. are unquestionably well-motivated. both from a theoretical point-of-view (they definitely exist). and from an experimental. point-of-view (they have mass).," Neutrinos, as particle dark matter candidates, are unquestionably well-motivated, both from a theoretical point-of-view (they definitely exist) and from an experimental point-of-view (they have mass)."785 No conjectured CDAL particle shares these advantages., No conjectured CDM particle shares these advantages.786 While | do not wish to state that the dark matter in clusters is definitely in the form of 2 ον neutrinos (there is more than enough remaining barvonic matter to make up the missing mass). there are indications that point this wav.," While I do not wish to state that the dark matter in clusters is definitely in the form of 2 ev neutrinos (there is more than enough remaining baryonic matter to make up the missing mass), there are indications that point this way."787 The largest discrepancies are found in the clusters with the largest core radii as would. be the case with neutrinos., The largest discrepancies are found in the clusters with the largest core radii as would be the case with neutrinos.788 The indicated densities of dark matter are comparable to the maximum possible density of 2 ev neutrinos., The indicated densities of dark matter are comparable to the maximum possible density of 2 ev neutrinos.789 The radius-mass relationship for sell-gravitating degenerate neutrino objects forms an envelope for. those clusters with large discrepancies., The radius-mass relationship for self-gravitating degenerate neutrino objects forms an envelope for those clusters with large discrepancies.790 The fact remains that there exists an algorithm. MOND. which allows galaxy rotation curves to be predicted in detail [rom the observed distribution of matter. and it is for these svstems that the kinematic observations are nost precise.," The fact remains that there exists an algorithm, MOND, which allows galaxy rotation curves to be predicted in detail from the observed distribution of matter, and it is for these systems that the kinematic observations are most precise."791 “This fact challenges the current CDM. paracigm. and demands explanation if dark. matter Lies behind. the discrepancy.," This fact challenges the current CDM paradigm, and demands explanation if dark matter lies behind the discrepancy."792 The factor two remaining ciscrepancy in clusters is less challenging for MOND. particularly given that MOND makes no claims about the full material content of the Universe.," The factor two remaining discrepancy in clusters is less challenging for MOND, particularly given that MOND makes no claims about the full material content of the Universe."793 lam grateful to Hans Bobhrinecr for useful discussions ancl for a copy of the thesis of T.H. Reiprich., I am grateful to Hans Böhhringer for useful discussions and for a copy of the thesis of T.H. Reiprich.794 E thank Moti Milgrom for helpful comments on the manuscript., I thank Moti Milgrom for helpful comments on the manuscript.795There is à growing amount of evidence that core-collapse supernovae are asymmetric and that. the core-collapse mechanism itself is responsible for the asymmetry (see Buras et al.,There is a growing amount of evidence that core-collapse supernovae are asymmetric and that the core-collapse mechanism itself is responsible for the asymmetry (see Buras et al.796 2003. Akiyama et al.," 2003, Akiyama et al."797 2003 for more details)., 2003 for more details).798 Several possibilities are explored to account for this observed asymmetry., Several possibilities are explored to account for this observed asymmetry.799 One is associated with the influence of rotation on convection. which seems to be inevitable during the early evolution of proto-neutron stars (PNS).," One is associated with the influence of rotation on convection, which seems to be inevitable during the early evolution of proto-neutron stars (PNS)."800 Convective motions in PNSs are very fast (~10°—10 cm/sec) and. therefore. the convective turnover time is short. ~1LO ms (see. e.g.. Burrows Lattimer 1986).," Convective motions in PNSs are very fast $\sim 10^{8}-10^{9}$ cm/sec) and, therefore, the convective turnover time is short, $\sim 1-10$ ms (see, e.g., Burrows Lattimer 1986)."801 Nevertheless. if angular momentum 1s conserved. the collapsing core can spin up to very short periods ~5LO ms and generate strong differential rotatio.," Nevertheless, if angular momentum is conserved, the collapsing core can spin up to very short periods $\sim 8025-10$ ms and generate strong differential rotation."803 Such fast rotation modifies convection and makes convective motions anisotropic and constrained. to the polar regions (Fryer Heger 2000. Miralles et al.," Such fast rotation modifies convection and makes convective motions anisotropic and constrained to the polar regions (Fryer Heger 2000, Miralles et al."804 2004)., 2004).805 This mechanism ts a natural way to create anisotropic energy and momentum transport by convective motions. that only requires that the angular velocity be of the order of the Brunt-Váusiállá frequency.," This mechanism is a natural way to create anisotropic energy and momentum transport by convective motions, that only requires that the angular velocity be of the order of the Brunt-Väiisällä frequency."806 The other possibility to create asymmetry is the effect of Jets (see. e.g.. Khokhlov et al.," The other possibility to create asymmetry is the effect of jets (see, e.g., Khokhlov et al."807" 1999, Wheeler et al."," 1999, Wheeler et al."808 2002)., 2002).809 Even though the mechanism of jet formation is still unclear. it seems that MHD jets are common in systems where a central body aceretes matter with angular momentum and magnetic field (see. e.g.. Meier at al.," Even though the mechanism of jet formation is still unclear, it seems that MHD jets are common in systems where a central body accretes matter with angular momentum and magnetic field (see, e.g., Meier at al."810 2001). and a core-collapse supernova is such a system.," 2001), and a core-collapse supernova is such a system."811 Calculations have established that nonrelativistic axial jets originating within the collapsed core can initiate a bipolar asymmetric supernova explosion that is consistent with observations (Hwang et al., Calculations have established that nonrelativistic axial jets originating within the collapsed core can initiate a bipolar asymmetric supernova explosion that is consistent with observations (Hwang et al.812 2000)., 2000).813 Another way to generate asymmetry Is associated with the magnetic field that can be an important ingredient of the explosion mechanism (Bisnovatyi-Kogan 1971. Kundt 1976).," Another way to generate asymmetry is associated with the magnetic field that can be an important ingredient of the explosion mechanism (Bisnovatyi-Kogan 1971, Kundt 1976)."814 The toroidal magnetic field can be amplified by differential rotation to such high values that it becomes dynamically important (Ardelyan et al., The toroidal magnetic field can be amplified by differential rotation to such high values that it becomes dynamically important (Ardelyan et al.815 2005)., 2005).816 The effect of the magnetic field on asymmetry of supernovae was considered by Wheeler et al.(2000. 2002) who found that it is possible to produce both a strong toroidal field and an axial jet.," The effect of the magnetic field on asymmetry of supernovae was considered by Wheeler et al.(2000, 2002) who found that it is possible to produce both a strong toroidal field and an axial jet."817 Two-dimensional MHD simulations of core collapse indicate that the shape of shock waves and the neutrinosphere can be modified by the effect of the magnetic field (Kotake et al., Two-dimensional MHD simulations of core collapse indicate that the shape of shock waves and the neutrinosphere can be modified by the effect of the magnetic field (Kotake et al.818 2004. Takiwaki et al.," 2004, Takiwaki et al."819 2004)., 2004).820 The possible presence. of à magnetic field and differential rotation in a core-collapse supernova favours magnetorotational instability (MRI). which can enhance turbulent transport and amplify the magnetic field.," The possible presence of a magnetic field and differential rotation in a core-collapse supernova favours magnetorotational instability (MRI), which can enhance turbulent transport and amplify the magnetic field."821 This instability was considered by Akiyama et al.2003) in. the context of core collapse., This instability was considered by Akiyama et al.(2003) in the context of core collapse.822 The authors argued that instability must occur in core collapse and that it has the capacity to produce fields that are sufficiently strong to affect. if not cause. the explosion.," The authors argued that instability must occur in core collapse and that it has the capacity to produce fields that are sufficiently strong to affect, if not cause, the explosion."823 Thompson et al. (, Thompson et al. (8242005) constructed one-dimensional models. including rotation and magnetic fields. to study the mechanism of energy deposition.,"2005) constructed one-dimensional models, including rotation and magnetic fields, to study the mechanism of energy deposition."825 They explored several mechanism for viscosity and argue that turbulent viscosity caused by the MRI can be most effective., They explored several mechanism for viscosity and argue that turbulent viscosity caused by the MRI can be most effective.826 Numerical simulations provide contradictory conclusions regarding the importance of MRI in core collapse., Numerical simulations provide contradictory conclusions regarding the importance of MRI in core collapse.827 Motseenko et al. (, Moiseenko et al. (8282006) claim that MRI has been found in their 2D simulations. and that it is responsible for a strong amplification of the poloidal magnetic flux.,"2006) claim that MRI has been found in their 2D simulations, and that it is responsible for a strong amplification of the poloidal magnetic flux."829 However. what these authors call MRI is different to standard MRI considered by Velikhov (1959) (see also Balbus Hawley (1991)).," However, what these authors call MRI is different to standard MRI considered by Velikhov (1959) (see also Balbus Hawley (1991))."830 For instance. the instability found by Moiseenko et al (2006) starts to develop only when the ratio of the toroidal and poloidal fields reaches a value of — a few tens.," For instance, the instability found by Moiseenko et al (2006) starts to develop only when the ratio of the toroidal and poloidal fields reaches a value of $\sim$ a few tens."831 On the other hand. the onset of standard MRI in 2D does not depend on the toroidal field at all.," On the other hand, the onset of standard MRI in 2D does not depend on the toroidal field at all."832 The dependence on the ratio of the toroidal and poloidal field is more typical for Tayler instability (Tayler 1973). which is more relevant to the topology of the magnetic field than differential rotation.," The dependence on the ratio of the toroidal and poloidal field is more typical for Tayler instability (Tayler 1973), which is more relevant to the topology of the magnetic field than differential rotation."833 Therefore. it is possible that Moiseenko et al. (," Therefore, it is possible that Moiseenko et al. ("8342006) incorrectly identify instability. and MRI does not occur in their simulations.,"2006) incorrectly identify instability, and MRI does not occur in their simulations."835 Apart from that. Moiseenko et al. (," Apart from that, Moiseenko et al. ("8362006) attributed à rapid growth of the toroidal and poloidal fields to a dynamo driven by the magnetorotational instability.,2006) attributed a rapid growth of the toroidal and poloidal fields to a dynamo driven by the magnetorotational instability.837 This also rise some doubts because of Cowlings's anti-dynamo theorem which states that an axisymmetric dynamo cannot exist (see. e.g.. Shercliff 1965).," This also rise some doubts because of Cowlings's anti-dynamo theorem which states that an axisymmetric dynamo cannot exist (see, e.g., Shercliff 1965)."838 Two-dimensional simulations of core collapse with a strong magnetic field have been performed by Sawai et al. (, Two-dimensional simulations of core collapse with a strong magnetic field have been performed by Sawai et al. (8392005. 2008).,"2005, 2008)."840 They found that the magnetic field can play an important role in the dynamies of the core only if the poloidal field of the progenitor is strong enough (—10/2?—1075 G) but MRI was not seen in the," They found that the magnetic field can play an important role in the dynamics of the core only if the poloidal field of the progenitor is strong enough $\sim 10^{12}-10^{13}$ G), but MRI was not seen in the"841been made at energies above 10. GeV. ancl these are sullicient to constrain a large excess at the shorter bands of the near-H. wavelengths.,"been made at energies above 10 GeV, and these are sufficient to constrain a large excess at the shorter bands of the near-IR wavelengths."842 1n the next section. we first review the caleulations of the buildup of background photons and the phenomenon of gamma-ray attenuation through electron-positron pair-production. and then describe ai model for the SED of the background. component of pop-LLl stars.," In the next section, we first review the calculations of the buildup of background photons and the phenomenon of gamma-ray attenuation through electron-positron pair-production, and then describe a model for the SED of the background component of pop-III stars."843 In Section 3.. we present our results for the limits that can be obtained from observed. gamma-ray sources on he portion of the local EBL that originates from high-redshift. followed by upper bounds on the total rate of ΟΡ star formation.," In Section \ref{sec:results}, we present our results for the limits that can be obtained from observed gamma-ray sources on the portion of the local EBL that originates from high-redshift, followed by upper bounds on the total rate of pop-III star formation."844 Section 4 presents conclusions and the prospects of strengthening our limits with future igh-redshift gamma-ray source detections., Section \ref{sec:disc} presents conclusions and the prospects of strengthening our limits with future high-redshift gamma-ray source detections.845" We assume a ACDAL cosmology with parameters consistent with a maximum likelihood results of Komatsuetal.(2011). in his work: =0.702. Q,=0.0455."," We assume a $\Lambda$ CDM cosmology with parameters consistent with a maximum likelihood results of \citet{komatsu11} in this work: $h=0.702$, $\Omega_b = 0.0455$."846 To examine the effect. that the photon populations created curing reionization have on eamma-rayv propagation. we will develop template SEDs that describe the emissivity. of the universe during these carly times.," To examine the effect that the photon populations created during reionization have on gamma-ray propagation, we will develop template SEDs that describe the emissivity of the universe during these early times."847 These templates can be freely rescaled to simulate varving star-Lormation rate densities., These templates can be freely rescaled to simulate varying star-formation rate densities.848 They. are described in full detail in 82.3.., They are described in full detail in \ref{sec:spectmod}.849 In the following sections. we will treat independently the hypothetical EBL component [rom reionization-cra pop-LLE stars and the component produced. primarily by later population LLL stars.," In the following sections, we will treat independently the hypothetical EBL component from reionization-era pop-III stars and the component produced primarily by later population I/II stars."850 We will distinguish between these by referring to the first as the reionization-cra EBL (r-EBL’) and the second as the post-reionization EBL (Cp-EDBL)., We will distinguish between these by referring to the first as the reionization-era EBL (`r-EBL') and the second as the post-reionization EBL (`p-EBL').851 We emphasize that this work is not intended to comment on the relationship between these components. or the details of how the transition from pop-LLE to population-Ll star formation occurs. but only to examine some possible scenarios for the r-EDL. of which we presently have only indirect evidence.," We emphasize that this work is not intended to comment on the relationship between these components, or the details of how the transition from pop-III to population-II star formation occurs, but only to examine some possible scenarios for the r-EBL, of which we presently have only indirect evidence."852 In general. the EBL in place at a given redshift cy can be calculated by an integral over source terms at all redshifts z29zo. with additional terms describing the ellect of redshift on photon wavelength and Lux redshift (ο-σ.. Somervillectal. 2011)).," In general, the EBL in place at a given redshift $z_0$ can be calculated by an integral over source terms at all redshifts $z>z_0$, with additional terms describing the effect of redshift on photon wavelength and flux redshift (e.g., \citealp{sgpd11}) )."853 where είν.) is the galaxy emissivity at redshift 2 and frequency 7=μή]|zbzo) and didi is the cosmological line clement. defined as for a lat . XCDM universe (Peebles1993).," where $\epsilon(\nu,z)$ is the galaxy emissivity at redshift $z$ and frequency $\nu=\nu_0(1+z)/(1+z_0)$, and $dl/dz$ is the cosmological line element, defined as for a flat $\Lambda$ CDM universe \citep{peebles93}."854". An EBL component originating entirely. above a redshift 2, will evolve only through passive redshifting at 2«σε with an invariant comovine photon number density."," An EBL component originating entirely above a redshift $z_r$ will evolve only through passive redshifting at $z<z_r$, with an invariant comoving photon number density."855" Hf. this component is observed. locally with à spectral energy distribution J!(vy). then the proper tux of these photons at redshift zο If) relers in this case to the EBL produced. by early low metallicity stars. and z; is the end of the era of preeminence of these sources. then it is easy to see that 52) will become an increasingly large fraction of the total background. as z approaches z,."," If this component is observed locally with a spectral energy distribution $J'_\nu(\nu_0)$, then the proper flux of these photons at redshift $z<z_r$ is If $J'_{\nu}$ refers in this case to the EBL produced by early low metallicity stars, and $z_r$ is the end of the era of preeminence of these sources, then it is easy to see that $J'_{\nu}(z)$ will become an increasingly large fraction of the total background as $z$ approaches $z_r$."856" This is due to the fact that the majorityof the background light emerging from resolved. galaxies after reionization in recent mocdels (e.g. Somervilleetal.2011:Domínguezetal.2011:Franceschini.Rocighicro&Vaceari 2008)) comes from redshifts considerably lower than z,."," This is due to the fact that the majorityof the background light emerging from resolved galaxies after reionization in recent models (e.g. \citealp{sgpd11,dominguez11,franceschini08}) ) comes from redshifts considerably lower than $z_r$."857 In the [iducial model of Somervillectal.(2011). for instance. ~75 per cent of p-IEEBL. photons between 0.1 ancl 10 microns are emitted at O«z2. and 96 per cent at aod.," In the fiducial model of \citet{sgpd11}, for instance, $\sim 75$ per cent of p-EBL photons between 0.1 and 10 microns are emitted at $0 < z <2$, and 96 per cent at $z<4$."858 Camma-ganuna scattering into clectron-positron pairs can occur when there is sullicient energy in the center-ol-mass frame of the two-photon system., Gamma-gamma scattering into electron-positron pairs can occur when there is sufficient energy in the center-of-mass frame of the two-photon system.859" Including the effect of interaction angle as measured in the cosmological frame. this condition is where A, and £5 are the photon energies ancl 8 is the angle of incidence. which for our purposes is a random distribution on the unit sphere."," Including the effect of interaction angle as measured in the cosmological frame, this condition is where $E_1$ and $E_2$ are the photon energies and $\theta$ is the angle of incidence, which for our purposes is a random distribution on the unit sphere."860" We can rewrite Equation 4 to define the minimum threshold energy. £i, [or à background photon to interact with a gamma rav of energy. Le. The cross-section for this process is "," We can rewrite Equation \ref{eq:paircre} to define the minimum threshold energy $E_{th}$ for a background photon to interact with a gamma ray of energy $E_{\gamma}$ , The cross-section for this process is \citep{breit&wheeler34,gould&schreder67,madau&phinney96}861 "862The secoud issue is the presence of a substantial eroup of 8CR galaxies with strong broad emission lines.,The second issue is the presence of a substantial group of 3CR galaxies with strong broad emission lines.863 In these objects. the iieasurement of the narrow emission lines is less reliable due to the presence of the strong nuclear continmun and to the complexity of the profiles of the broad lines.," In these objects, the measurement of the narrow emission lines is less reliable due to the presence of the strong nuclear continuum and to the complexity of the profiles of the broad lines."864 Iu particular. as explained in Paper L we expect a ecueral over-estimate of the Hine luminosity.," In particular, as explained in Paper I, we expect a general over-estimate of the line luminosity."865 For this reason we defer the discussion of broac lined objects to Sect. 2.3.., For this reason we defer the discussion of broad lined objects to Sect. \ref {blo}.866 Iu Fig., In Fig.867 3 we show the position of the 3CT sources iu anew diagnostic plane where we compare log [O aand LRI for the 59 narrow line objects for which we are able to measure both values., \ref{lri} we show the position of the 3CR sources in a new diagnostic plane where we compare log [O and LRI for the 59 narrow line objects for which we are able to measure both values.868 The sources are distributed along the edges of the distribution of the SDSS sources. sinularly to the previous diagnostic cdiagrauis.," The sources are distributed along the edges of the distribution of the SDSS sources, similarly to the previous diagnostic diagrams."869 This diagram shows two eroups of ACN: one group with 1 SLRIZ0 and log |O  Land another one with 0.3 SLRIS0.1 and 0.2 Ίου (O XOns., This diagram shows two groups of AGN: one group with $-1\lesssim$ $\lesssim0$ and log [O $\sim1$ and another one with $-0.3\lesssim$ $\lesssim0.1$ and $ 0.2\lesssim$ log [O $ \lesssim0.8$.870 The presence of two populations of AGN is clearly seen in the distribution of the values of the Excitation ludex. shown im Fie. L.," The presence of two populations of AGN is clearly seen in the distribution of the values of the Excitation Index, shown in Fig. \ref{exct},"871 where two separate distributions appear., where two separate distributions appear.872 This result is the analog of the two-horned histograms derived by E06 when slicing the deusity distribution of SDSS sources., This result is the analog of the two-horned histograms derived by \citetalias{kewley06b} when slicing the density distribution of SDSS sources.873 Using the IWAIAD test. for bimodality (Aslanctal.1991) we estimated that the hvpothesis of a sinele Cassia distribution can be rejected at a confidence level of., Using the KMM test for bimodality \citep{ashman94} we estimated that the hypothesis of a single Gaussian distribution can be rejected at a confidence level of.874. The significance level increases to when the two galaxies with extremely low 1ο rratios are excluded from the analysis., The significance level increases to when the two galaxies with extremely low [O ratios are excluded from the analysis.875" The estimated means of the two populations are EL. = 0.63 and EI. = 1.10 for the low aud high excitation sources respectively, with a standard deviation of 0.25."," The estimated means of the two populations are E.I. = 0.63 and E.I. = 1.40 for the low and high excitation sources respectively, with a standard deviation of 0.25."876 We also note that the average rate of correct classification of a galaxy within a eiven group 1s larger than, We also note that the average rate of correct classification of a galaxy within a given group is larger than.877 An additional distinction between objects of high hiis low Excitation ludex is their radio cussion., An additional distinction between objects of high and low Excitation Index is their radio emission.878 We will discuss the connection between radio and optical properties iu more detail later on. but it is useful to anticipate this result.," We will discuss the connection between radio and optical properties in more detail later on, but it is useful to anticipate this result."879 In Fig., In Fig.880 5. wo compare the Excitation Iudex and Ljpug/vLizs. Le. the ratio between their line and total radio (at 178 MITZ) Iuniuosity.," \ref{o3-ei} we compare the Excitation Index and $L_{\rm [OIII]}/\nu L_{178}$, i.e. the ratio between their line and total radio (at 178 MHz) luminosity."881 Iu this diagram. the two populations of galaxies at high aud low values of," In this diagram, the two populations of galaxies at high and low values of"882The major reduction tasks are fix calibration. eain curve (bandpass) correction. SR correction. baseline fitting. and REI detection.,"The major reduction tasks are flux calibration, gain curve (bandpass) correction, SR correction, baseline fitting, and RFI detection."883" The processed spectra are eventually mereed by a eridding tool into a threc-dinensional data cube,", The processed spectra are eventually merged by a gridding tool into a three-dimensional data cube.884 Deviating from the common xpeliue approaches. the EDIITIS reduction is organized in a liehly flexible mamuer.," Deviating from the common pipeline approaches, the EBHIS reduction is organized in a highly flexible manner."885 To uunimize reduudancies. each processing step works as mdepeudeutlv as possible ou the data.," To minimize redundancies, each processing step works as independently as possible on the data."886 To achieve this goal. every correction to be applied⋅ on the data is. described⋅⋅ by a minimal⋅⋅ set of parameters which. is. then stored in. au SOL database.," To achieve this goal, every correction to be applied on the data is described by a minimal set of parameters which is then stored in an SQL database."887 For example. the RFI detection algorvitlin returns a list of spectral channels per spectral dump.," For example, the RFI detection algorithm returns a list of spectral channels per spectral dump."888 Oulv this short list cousistine of a few integer eutries needs to boe stored., Only this short list consisting of a few integer entries needs to be stored.889 Every other processing software cau then casily query the database to obtain these lists aud flag contaminated data., Every other processing software can then easily query the database to obtain these lists and flag contaminated data.890 Also the gain calibration needs only few numbers to store per observation session., Also the gain calibration needs only few numbers to store per observation session.891 Tasks. which rely on calibrated iuput spectra. siuplv read he raw data from disk aud apply the calibration ou-tle-fly.," Tasks, which rely on calibrated input spectra, simply read the raw data from disk and apply the calibration on-the-fly."892 Tfthe iudividual iiodules do uot depend on cach other. this modular approach of the data reduction chain enables to update one single‘ module without the necessity. to re-execute other reduction. tasks.," If the individual modules do not depend on each other, this modular approach of the data reduction chain enables to update one single module without the necessity to re-execute other reduction tasks."893 Tn that case. different tasks can even work iu parallel.," In that case, different tasks can even work in parallel."894 A schematic representation of the EDIIIS data processing chain is shown in reffigdatareductionscheme.., A schematic representation of the EBHIS data processing chain is shown in \\ref{figdatareductionscheme}.895 The picture shows with solid line arrows the flow of the spectral data. while dashed lines show the information exchanec with the databases.," The picture shows with solid line arrows the flow of the spectral data, while dashed lines show the information exchange with the databases."896 Every task stores calculated values m an associated database able. anc call query all other databases as necessary.," Every task stores calculated values in an associated database table, and can query all other databases as necessary."897" Iun coutrast to pipeline approaches. a ucw task is necessary. which⋅⋅ is denoted as -""unerger⋝⋅⊀. to apply all the correction. terius to generate! the final⋅ data set."," In contrast to pipeline approaches, a new task is necessary, which is denoted as “merger”, to apply all the correction terms to generate the final data set."898 After] that. the spectra can be eridded. to a data cubo.," After that, the spectra can be gridded to a data cube."899 As the inteeration time per dump is 500125. a sigiificant amon of data has to )o haudled for the full survey (al)out TTbyte).," As the integration time per dump is $500\,\mathrm{ms}$, a significant amount of data has to be handled for the full survey (about Tbyte)."900 Wo developed serial. aleorithius.. o allow processing of large data sets without the reed to keep them iu the main memory (RAM). which is especially inportaut for the exiddiug task.," We developed serial algorithms, to allow processing of large data sets without the need to keep them in the main memory (RAM), which is especially important for the gridding task."901 Multi-tlhireadiug tecliniques are extensively used το significautlv speed up colmputation on multi-processor/-core platforms., Multi-threading techniques are extensively used to significantly speed up computation on multi-processor/-core platforms.902 Further inrovenient on processing speed is because ofthe database approach which allows the siunultaueous access from inultiple workstations., Further improvement on processing speed is because of the database approach which allows the simultaneous access from multiple workstations.903 The database also oxovides the opportunity to casily query information. e.g... on sky areas already observed (iuchiding visualization). aud allows to backup the database very efficiently.," The database also provides the opportunity to easily query information, e.g., on sky areas already observed (including visualization), and allows to backup the database very efficiently."904 dA typicalκ workx. flow is ias follows., A typical work flow is as follows.905. RETdÀ detectionτου. flux. and gain⋝⋅ curve calibration⋅ are independent.⋅ they canH be processedSS in parallel.," RFI detection, flux, and gain curve calibration are independent, they can be processed in parallel."906ave. From the calibrated spectra. the SR correction is subtracted. baselines are computed. and finally the eridder computes the data cubes.," From the calibrated spectra, the SR correction is subtracted, baselines are computed, and finally the gridder computes the data cubes."907 Towever. an accurate SR correction needs in. principle an iterative approach. where the resulting data of one iteration are fed into au iuproved SR πιο) to be subtracted in the next iteration.," However, an accurate SR correction needs in principle an iterative approach, where the resulting data of one iteration are fed into an improved SR model to be subtracted in the next iteration."908 lu radio astronomy. the sienals of interest are din general polluted by monauade artificial," In radio astronomy, the signals of interest are in general polluted by man-made artificial"909Earth-sun parallax. or stellar lens or source binaries.,"Earth-sun parallax, or stellar lens or source binaries."910 In order to distinguish these from planetary deviations and at the same time to obtain appropriate estimates for the urgency and frequency of second-level follow-up observations. a full real-time modelling taking into account all these effects would be required.," In order to distinguish these from planetary deviations and at the same time to obtain appropriate estimates for the urgency and frequency of second-level follow-up observations, a full real-time modelling taking into account all these effects would be required."911 Optimallv. the prioritization of events would follow the expected constraints on the planet characteristics rather than just maximizing their detectability while ignoring the chances of properly characterizing a potential planet.," Optimally, the prioritization of events would follow the expected constraints on the planet characteristics rather than just maximizing their detectability while ignoring the chances of properly characterizing a potential planet."912 We plan to implement such a system in the near future., We plan to implement such a system in the near future.913 We would like to thank K. Horne. M. F. Bode. S. N. Fraser. C. J. Mottram. T. Naylor. C. Snodgrass. I. A. Steele. P. Wheatley. P.," We would like to thank K. Horne, M. F. Bode, S. N. Fraser, C. J. Mottram, T. Naylor, C. Snodgrass, I. A. Steele, P. Wheatley, J.-P."914 Beaulieu. D. Bennett. P. Fouqué.. N. Kains. C. Vinter and A. Williams for valuable suggestions at various stages.," Beaulieu, D. Bennett, P. Fouqué,, N. Kains, C. Vinter and A. Williams for valuable suggestions at various stages."915 More thanks go to D. Bennett for providing data files and raw seripts for plotting some of the figures., More thanks go to D. Bennett for providing data files and raw scripts for plotting some of the figures.916 We are grateful to the OGLE. MOA. PLANET/RoboNet and MicroFUN teams for providing real-time photometry on ongoing microlensing events and communicating recent developments on suspected anomalies.," We are grateful to the OGLE, MOA, PLANET/RoboNet and MicroFUN teams for providing real-time photometry on ongoing microlensing events and communicating recent developments on suspected anomalies."917 NJR acknowledges financial support by a PPARC PDRA fellowship., NJR acknowledges financial support by a PPARC PDRA fellowship.918 NJR and LW were supported by the European Community's Sixth Framework Marie Curie Research Training Network Programme “ANGLES” (MRTN-CT-2004-505183).," NJR and LW were supported by the European Community's Sixth Framework Marie Curie Research Training Network Programme ""ANGLES"" (MRTN-CT-2004-505183)."919 EK is supported by a PPARC/STFC Advanced Fellowship., EK is supported by a PPARC/STFC Advanced Fellowship.920the diffusion timescale significantly (sec also AlcCowanetal. (2003))).,the diffusion timescale significantly (see also \citet{McGowan:2003a}) ).921 Thus while reprocessing times are of niareginal significance in considering burst reprocessiug. they max be of more iniportance for other applications where further investigation is needed.," Thus while reprocessing times are of marginal significance in considering burst reprocessing, they may be of more importance for other applications where further investigation is needed."922 The corollary of this is that the relatively soft παπαο of bursts may provide the least biased way to isolate light travel time delays aud lence the ideal signal for eclo-tomoeraphy., The corollary of this is that the relatively soft irradiation of bursts may provide the least biased way to isolate light travel time delays and hence the ideal signal for echo-tomography.923 It is interesting to compare the deduced reprocessing teiiperatures with those expected based ou the Nav luniuositv. as this provides a test of the reprocessing efücienev.," It is interesting to compare the deduced reprocessing temperatures with those expected based on the X-ray luminosity, as this provides a test of the reprocessing efficiency."924 We will consider. MD2.. for which the telmperatures are best constrained.," We will consider MB2, for which the temperatures are best constrained."925 For this burst. the persistent huninosity (at G.Skkpe) was 1079 | and the peal burst luminosity was 6.910 d.," For this burst, the persistent luminosity (at kpc) was $2.1\times10^{36}$ $^{-1}$ and the peak burst luminosity was $6.9\times10^{37}$ $^{-1}$."926 hradiation of the companion star is sensitive to the lass ratio. as smaller companions will more readilv be shiclded by the disk.," Irradiation of the companion star is sensitive to the mass ratio, as smaller companions will more readily be shielded by the disk."927 For example. if we take model L(g= O08) aud the typical effective disk opening anele of 12° deduced by deJone.vanParacdijs.&Au-eusteyn(1996) then the compauion would be completely shiclded.," For example, if we take model 1 $q=0.08$ ) and the typical effective disk opening angle of $^{\circ}$ deduced by \citet{deJong:1996a} then the companion would be completely shielded."928 This is clearly not the case. as the companiou can cirectly eclipse the neutron star. but we cannot quantify how directlv it is illuminated.," This is clearly not the case, as the companion can directly eclipse the neutron star, but we cannot quantify how directly it is illuminated."929 Note that the opening angle need not be that of the disk rim. but could represent material in the imuer disk that cau shield the conrpanion.," Note that the opening angle need not be that of the disk rim, but could represent material in the inner disk that can shield the companion."930 For models 2 and 3. calculations are more straightforward aud the differences between the two are less dramatic.," For models 2 and 3, calculations are more straightforward and the differences between the two are less dramatic."931 For a disk opening angle of 6° we expect angeles of incidence of ereater than 157 from. ποια]. Increasing to 607 for opening angles of 12°.," For a disk opening angle of $^{\circ}$ we expect angles of incidence of greater than $^{\circ}$ from normal, increasing to $^{\circ}$ for opening angles of $^{\circ}$."932 We assume an N-vav albedo for the companion of ~0.1 followine deJong.vanParadijs.&Augusteijn(1996).., We assume an X-ray albedo for the companion of $\sim0.4$ following \citet{deJong:1996a}.933 We then expect the highest persistent radiation teniperature ou the companion of depending ou mass ratio (for the range 0.200.31) aud IKI&disk opening anele (Gu the range 12°)., We then expect the highest persistent irradiation temperature on the companion of K depending on mass ratio (for the range 0.20–0.34) and disk opening angle (in the range $^{\circ}$ ).934 This is the temperature at the point closest to the compact object and most of the inradiated region is at temperatures less than this as the angle of incidence is steeper., This is the temperature at the point closest to the compact object and most of the irradiated region is at temperatures less than this as the angle of incidence is steeper.935 At the burst peak we would expect temperatures of IK. For the disk we estimate the estimated teniperature at the disk rii using the semir-enipirical prescription of Dubusetal.(1999). auc Dubusetal.(2001).., At the burst peak we would expect temperatures of K. For the disk we estimate the estimated temperature at the disk rim using the semi-empirical prescription of \citet{Dubus:1999a} and \citet{Dubus:2001a}.936. Απομιιος Dubus’ estimate of the radiation cficiency and a disk radius of 5«101 com we expect a persistent irradiation temperature of 191 auc a peak burst temperature of IKIX. Both of these are the lowest temperatures in the disk. and most of the disk area is hotter than this (the opposite case to that calculated for the companion star).," Assuming Dubus' estimate of the irradiation efficiency and a disk radius of $5\times10^{10}$ cm we expect a persistent irradiation temperature of K and a peak burst temperature of K. Both of these are the lowest temperatures in the disk, and most of the disk area is hotter than this (the opposite case to that calculated for the companion star)."937" For comparison. the persistent luminosity of 2.11076 | corresponds to a mass trausfer rate of ~1.2«1019 ss1,"," For comparison, the persistent luminosity of $2.1\times10^{36}$ $^{-1}$ corresponds to a mass transfer rate of $\sim1.2\times10^{16}$ $^{-1}$."938 For a steady state lobe-filline disk the effective temperature due to viscous heating should be just IKI&. indicating that the disk is in a reginae that can only remain in a hieh state with inadiative heating.," For a steady state lobe-filling disk the effective temperature due to viscous heating should be just K, indicating that the disk is in a regime that can only remain in a high state with irradiative heating."939 Our emlier conclusious that the reprocessed bursts ikelv arise from a combination of oenuission from the conrpanion star and disk are consistent with these calculations., Our earlier conclusions that the reprocessed bursts likely arise from a combination of emission from the companion star and disk are consistent with these calculations.940 Our estimate of the peak reprocessing cluperature is TIN. The irraciiated area of the colupalion star is expected to have temperatures possibly extending up to Is. while the disk could plausibly have temperatures from KI upwarcl.," Our estimate of the peak reprocessing temperature is K. The irradiated area of the companion star is expected to have temperatures possibly extending up to K, while the disk could plausibly have temperatures from K upward."941 The temperature ranges are overlapping. with the ereater distance to the companion offset bv its more direct iluuinatiou. and are consistent with our observations.," The temperature ranges are overlapping, with the greater distance to the companion offset by its more direct illumination, and are consistent with our observations."942 We have reported several siuultaucous X-ray bursts in the low-mass ταν binaryVoL. including the Hehest quality reprocessed optical coverage. aud the only reprocessed UW burst that we are aware of i any source.," We have reported several simultaneous X-ray bursts in the low-mass X-ray binary, including the highest quality reprocessed optical coverage, and the only reprocessed UV burst that we are aware of in any source."943 These results allow a imiore thorough test of the paracdigua Or reprocessing of X-ray bursts. and reprocessing of X-rav enussion in eeueral than previously possible.," These results allow a more thorough test of the paradigm for reprocessing of X-ray bursts, and reprocessing of X-ray emission in general, than previously possible."944 Several sev assertions about reprocessing have been tested., Several key assertions about reprocessing have been tested.945 1) N-ravs are absorbed at relatively high optical deptlis. henualized. aud re-enmütted with a quasi-black body spectrum.," i) X-rays are absorbed at relatively high optical depths, thermalized, and re-emitted with a quasi-black body spectrum."946 By obtaining the UV spectra of the extra ight produced duriiug a burst. we have shown that it is indeed dominated by contmmuu enüssion. aud that he shape of that contimuun is consistent with black ον enussion with temperatures as inferred from the iehteurves of the bursts.," By obtaining the UV spectrum of the extra light produced during a burst, we have shown that it is indeed dominated by continuum emission, and that the shape of that continuum is consistent with black body emission with temperatures as inferred from the lightcurves of the bursts."947 The discrepancy with the optical flux. however. sugeests that a single-teniperature lack body model is not sufficient.," The discrepancy with the optical flux, however, suggests that a single-temperature black body model is not sufficient."948 ü) Reprocessed cussion iu the optical aud UV is aeecd predominantly by Πο travel times rather than x local photon diffusion., ii) Reprocessed emission in the optical and UV is lagged predominantly by light travel times rather than by local photon diffusion.949 This appears to be borne out * our observations as lieht travel times are sufficicut o explain the lags and simearing observed., This appears to be borne out by our observations as light travel times are sufficient to explain the lags and smearing observed.950 Note that lis conclusion (and the preceding oue) may not be true in general. but may be specific to radiation with the spectrum of au N-rav. burst.," Note that this conclusion (and the preceding one) may not be true in general, but may be specific to irradiation with the spectrum of an X-ray burst."951 Warder or softer irradiation is likely to produce a different respousc., Harder or softer irradiation is likely to produce a different response.952 ii) N-ravs are reprocessed both by the accretion disk and by the companion star., iii) X-rays are reprocessed both by the accretion disk and by the companion star.953 This is supported by our observations. as we do appear to see a pliase-depenudenuce of both the lag and the sincaring of the response.," This is supported by our observations, as we do appear to see a phase-dependence of both the lag and the smearing of the response."954 Tf the response cune from the disk alone. we would expect little variation.," If the response came from the disk alone, we would expect little variation."955 If it came from the companion alone. we predict variations in the lag. but not iu the smearing.," If it came from the companion alone, we predict variations in the lag, but not in the smearing."956 The temperatures that both the disk and companion are expected to reach cing a burst are cousisteut witli our observations., The temperatures that both the disk and companion are expected to reach during a burst are consistent with our observations.957" The failure of a single-zone reprocessor model to explain the relative UV. aud. optical fluxes in the burst also supports a mmlti-component response,", The failure of a single-zone reprocessor model to explain the relative UV and optical fluxes in the burst also supports a multi-component response.958 Our observations do not appear to resolve distinct lags from disk and companion. however. possibly a consequence of the long bursts exhibited byVol.," Our observations do not appear to resolve distinct lags from disk and companion, however, possibly a consequence of the long bursts exhibited by."959 Sources which exhibit short duration bursts may be better suited to this analysis., Sources which exhibit short duration bursts may be better suited to this analysis.960 This work iucludes observations with the NASA/ESATelescope. obtained. at STScl. which is operated by AURA uuuder NASA coutract NNÀS5-26555.," This work includes observations with the NASA/ESA, obtained at STScI, which is operated by AURA under NASA contract NAS5-26555."961 Support for pproposal 909398 was provided by NASA through a erant frou STScL RO also acknowledges support by NASA through Hubble Fellowship eraut #IIIIF- awarded by STScI This work uses observations obtained at the Gemini Observatory. which is operated by the AURA Iuc. under a cooperative aerecluent with the NSF on behalf of the Cem," Support for proposal 9398 was provided by NASA through a grant from STScI. RIH also acknowledges support by NASA through Hubble Fellowship grant HF-01150.01-A awarded by STScI. This work uses observations obtained at the Gemini Observatory, which is operated by the AURA Inc., under a cooperative agreement with the NSF on behalf of the Gemini"962Rp = b—|p| on opposite sides of the lens galaxy. as in refplotl..,"$R_{B}$ = $b - |\beta|$ on opposite sides of the lens galaxy, as in \\ref{plot1}."963" The time delay between these two images can be shown to be which depends upon the annulus bounded by the two image positions, as in refplotl.. and as derived in Witt et al. ("," The time delay between these two images can be shown to be which depends upon the annulus bounded by the two image positions, as in \\ref{plot1}, and as derived in Witt et al. ("9642000).,2000).965 A more general approach is to use an effective potential that allows for different slopes (7) for the radial density profile of which the SIS is a special case G7= 2). with more centrally concentrated mass distributions having higher values of 77 (tending to a point mass with 7= 3).," A more general approach is to use an effective potential that allows for different slopes $\eta$ ) for the radial density profile of which the SIS is a special case $\eta=2$ ), with more centrally concentrated mass distributions having higher values of $\eta$ (tending to a point mass with $\eta=3$ )."966 The deflection scale b is given by (e.g. the contribution of Kochanek in Kochanek. Schneider Wambsganss 2004) and the convergence 1s Previous studies have found that lens galaxies are well described by such power-law profiles. in which px7 (e.g. Witt et al.," The deflection scale $b$ is given by (e.g. the contribution of Kochanek in Kochanek, Schneider Wambsganss 2004) and the convergence is Previous studies have found that lens galaxies are well described by such power-law profiles, in which $\rho\propto r^{-\eta}$ (e.g. Witt et al."967 2000; Rusin et al., 2000; Rusin et al.968 2003)., 2003).969" To obtain a time delay from the power-law lens potential. we use the expression detailed in Kockanek (2002): where is. the meanBos surface mass density""M in the annulus bounded by images A and B. in units of the critical surface mass density."," To obtain a time delay from the power-law lens potential, we use the expression detailed in Kockanek (2002): where is the mean surface mass density in the annulus bounded by images A and B, in units of the critical surface mass density."970 In the analysis that follows in $55. we use Qy = 0.3. Q4 = 0.7. Qe = 0. which enter through the angular diameter distances.," In the analysis that follows in 5, we use $\Omega_{M}$ = 0.3, $\Omega_{\Lambda}$ = 0.7, $\Omega_{K}$ = 0, which enter through the angular diameter distances."971 In the preceding section we introduced a spherically symmetric effective potential which will be used to model the lensing galaxy of all systems in the data set. including four-image systems.," In the preceding section we introduced a spherically symmetric effective potential which will be used to model the lensing galaxy of all systems in the data set, including four-image systems."972 Our goal is to obtain an estimate of the average slope of the density profiles using a simple approach. comparing systems in à homogenous manner and without detailed modeling of ellipticity or external shear.," Our goal is to obtain an estimate of the average slope of the density profiles using a $simple$ approach, comparing systems in a homogenous manner and without detailed modeling of ellipticity or external shear."973 We will now. however. briefly discuss the effect these have on the corresponding time delays using Fermat surfaces for illustration.," We will now, however, briefly discuss the effect these have on the corresponding time delays using Fermat surfaces for illustration."974 refplot4. shows four Fermat surfaces. as derived from equation (1). each of which displays a different image configuration dependent on the effective potential and parameters used.," \\ref{plot4} shows four Fermat surfaces, as derived from equation \ref{equ:time}) ), each of which displays a different image configuration dependent on the effective potential and parameters used."975 For all four plots the source position. velocity. dispersion. lens/source redshifts and Hubble constant were kept fixed.," For all four plots the source position, velocity dispersion, lens/source redshifts and Hubble constant were kept fixed."976 We consider the changes in time delays of the images A. B and C. present at the stationary points of the surface (note that there may be other stationary points).," We consider the changes in time delays of the images A, B and C, present at the stationary points of the surface (note that there may be other stationary points)."977 We investigated values of ellipticity up to 0.2. this being a moderate ellipticity for a lens galaxy.," We investigated values of ellipticity up to 0.2, this being a moderate ellipticity for a lens galaxy."978 refplotdaa begins with a standard SIS potential. with a time delay of Δρ = 51.2 days.," \\ref{plot4}a a begins with a standard SIS potential, with a time delay of $\Delta t_{AB}$ = 51.2 days."979 An ellipticity is then introduced into the effective potential (an SIE with € = 0.1). as seen in (b). giving a time delay of Δρ = 57.1 days.," An ellipticity is then introduced into the effective potential (an SIE with $\epsilon$ = 0.1), as seen in (b), giving a time delay of $\Delta t_{AB}$ = 57.1 days."980 Finally. in plots (c) and (d). we consider the impact of changing the slope of the effective potential.," Finally, in plots (c) and (d), we consider the impact of changing the slope of the effective potential."981 Keeping € = 0.2. the slope of the density profile is allowed to change from 7 = 2.0 to 7 = 2.3 (corresponding to a slope of 1.0 to 0.7 1n the effective potential).," Keeping $\epsilon$ = 0.2, the slope of the density profile is allowed to change from $\eta$ = 2.0 to $\eta$ = 2.3 (corresponding to a slope of 1.0 to 0.7 in the effective potential)."982 The time delay is Δρ = 67.9 days and Arye = 48.8 days for the 77 2 2.0 case. and Atyp = 67.2 days and Ary = 46.8 days. for the 7 = 2.3 case.," The time delay is $\Delta t_{AB}$ = 67.9 days and $\Delta t_{AC}$ = 48.8 days for the $\eta$ = 2.0 case, and $\Delta t_{AB}$ = 67.2 days and $\Delta t_{AC}$ = 46.8 days, for the $\eta$ = 2.3 case."983" In the limit 77 tends to 3.0. Ati, = 66.7 days and Atay = 44.5 days."," In the limit $\eta$ tends to 3.0, $\Delta t_{AB}$ = 66.7 days and $\Delta t_{AC}$ = 44.5 days."984 From this we highlight two key features: firstly. the time delays between images A and B change by less than when comparing the SIS to the SIE with a small ellipticity.," From this we highlight two key features: firstly, the time delays between images A and B change by less than when comparing the SIS to the SIE with a small ellipticity."985 Secondly. when we consider the change in the time delays as 7? goes from 2.0 to 2.3. keeping € constant. we observe very little change at all.," Secondly, when we consider the change in the time delays as $\eta$ goes from 2.0 to 2.3, keeping $\epsilon$ constant, we observe very little change at all."986 We pick these particular values for illustrative purposes only., We pick these particular values for illustrative purposes only.987 Indeed. moving beyond 2.3 to higher values of 77 had a similarly small effect.," Indeed, moving beyond 2.3 to higher values of $\eta$ had a similarly small effect."988 As noted by Witt et al. (, As noted by Witt et al. (9892000) for a generalised isothermal lens (allowing for general angular structure irrespective of ellipticity) the Hubble constant is simply related to the image positions and time delay along with the source and lens,2000) for a generalised isothermal lens (allowing for general angular structure irrespective of ellipticity) the Hubble constant is simply related to the image positions and time delay along with the source and lens990where 6 and «2 are the position angles of image and source. respectively. and à is the deflection angle.,"where $\theta$ and $\beta$ are the position angles of image and source, respectively, and $\alpha$ is the deflection angle."991 Integration over the path yields the deflection angle as where all distances are in units of the Schwarzschild radius {τς and wry marks the closest approach of the light ray to the deflector., Integration over the path yields the deflection angle as where all distances are in units of the Schwarzschild radius $R_\mathrm{S}$ and $x_0$ marks the closest approach of the light ray to the deflector.992 If observer. lens. and source happen to fall exactly onto a straight line. the condition for the observation of the source essentially becomes a.=27. where n is the number of turning of the light rays around the black hole (2)..," If observer, lens, and source happen to fall exactly onto a straight line, the condition for the observation of the source essentially becomes $\alpha = 2\upi n$, where $n$ is the number of turning of the light rays around the black hole \citep{Bozza01}."993 For source-lens (line-of-sight projected) separations substantially larger than the Sehwarzschild radius. the magnification of the source star due to strong lensing can be neglected as compared to the weak-field images.," For source-lens (line-of-sight projected) separations substantially larger than the Schwarzschild radius, the magnification of the source star due to strong lensing can be neglected as compared to the weak-field images."994 In this case. the deflection angle is in the order of a&fepeca.," In this case, the deflection angle is in the order of $\alpha\simeq995R_\rmn{E}/a\simeq\sqrt{R_\rmn{S}/a}$."996 With the Schwarzschild radius ἐς to be of the order of kilometersvis and the orbital radius of the order of 10Km. the corresponding angles in the lens equation are in the order of ~10.. and we find ourselves in the small-angle regime.," With the Schwarzschild radius $R_\mathrm{S}$ to be of the order of kilometers and the orbital radius of the order of $10^8~\mbox{km}$, the corresponding angles in the lens equation are in the order of $\sim 10^{-4}$, and we find ourselves in the small-angle regime."997 The proximity of the source star to the lens may also perturb the gravitational lensing effect., The proximity of the source star to the lens may also perturb the gravitational lensing effect.998" Considering a linear perturbation around the Schwarzschild metric in the weak-field limit. the perturbation on the deflection angle relate to the Newtonian potentials as where Ps and c, are the Newtonian gravitational potentials of the source star and the lens. respectively."," Considering a linear perturbation around the Schwarzschild metric in the weak-field limit, the perturbation on the deflection angle relate to the Newtonian potentials as where $\Phi_\rmn{S}$ and $\Phi_\rmn{L}$ are the Newtonian gravitational potentials of the source star and the lens, respectively."999" For a light ray passing near the Einstein radius ή. and source and lens object being separated by about an astronomical unit. one finds a relative perturbation on the deflection angleof where m, and Ad are the mass of source star and the lens. respectively."," For a light ray passing near the Einstein radius $R_\rmn{E}$, and source and lens object being separated by about an astronomical unit, one finds a relative perturbation on the deflection angleof where $m_\star$ and $M$ are the mass of source star and the lens, respectively."1000 With Eq. (3)), With Eq. \ref{re}) )1001 one finds a numerical value of ~LO7. so that the perturbation effect of the companion star does not play a significant role.," one finds a numerical value of $\sim\,10^{-4}$, so that the perturbation effect of the companion star does not play a significant role."1002" Finally we look at the influence of the finite size of the observed source star, which was discussed in detail by 2.."," Finally we look at the influence of the finite size of the observed source star, which was discussed in detail by \citet{WM94}."1003" The relevant parameter p, is the ratio between the angular radius of the source star and the angular Einstein radius. which simplifies to p,=ft,fHip. given that lens and source distances practically coincide."," The relevant parameter $\rho_\star$ is the ratio between the angular radius of the source star and the angular Einstein radius, which simplifies to $\rho_\star = R_\star/R_\rmn{E}$, given that lens and source distances practically coincide."1004" Eliminating the stellar radius in favourof the stellar mass. using 4,/f£.c(m,/M.)7 (2) and using Eq. (3))."," Eliminating the stellar radius in favour of the stellar mass, using $R_\star/R_\odot\simeq(m_\star/M_\odot)^{0.8}$ \citep{rmr} and using Eq. \ref{eq:EinsteinNumerical}) ),"1005 one finds Given that the magnification is limited to which is realised for perfect alignment. the signal amplitude is quite substantially suppressed due to the finite size of main-sequence source stars. unless the star is of low mass and/or the compact object is a massive black hole.," one finds Given that the magnification is limited to which is realised for perfect alignment, the signal amplitude is quite substantially suppressed due to the finite size of main-sequence source stars, unless the star is of low mass and/or the compact object is a massive black hole."1006 As pointed out by 2.. white dwarfs come with a clear advantage of smaller radii. so that larger magnifications occur regularly.," As pointed out by \citet{Mae73}, white dwarfs come with a clear advantage of smaller radii, so that larger magnifications occur regularly."1007" For general separations between lens and source stars. where η denotes the angular separation in units of the angular Einstein radius. the magnification for v4p, is given by where L(A) Av(A and Hl(n:&) are the complete elliptic integral of first. second and third kinds respectively and whereas for #=p,. one finds (2?) The centre of the source star is within the angular Einstein radius of the lens star for angles y=«uuax(e/a."," For general separations between lens and source stars, where $u$ denotes the angular separation in units of the angular Einstein radius, the magnification for $u\neq \rho_\star$ is given by where $E(k)$ $K(k$ and $\Pi(n;k)$ are the complete elliptic integral of first, second and third kinds respectively and whereas for $u=\rho_\star$, one finds \citep{Mae73,Do:thesis}1008 The centre of the source star is within the angular Einstein radius of the lens star for angles $\varphi \leq \varphi_\rmn{max} =1009R_\rmn{E}/a$."1010 Therefore. this condition ean be used as a reference for the magnification to be substantial.," Therefore, this condition can be used as a reference for the magnification to be substantial."1011 We note that the characteristic inclination angle «2: is independent of the distance of the binary system to the observer., We note that the characteristic inclination angle $\varphi_\rmn{max}$ is independent of the distance of the binary system to the observer.1012 We find an order estimate for the fraction of the binary systems with significant magnification signature in their light curves as f=2Suns (7.," We find an order estimate for the fraction of the binary systems with significant magnification signature in their light curves as $f =10132\,\varphi_\rmn{max}/\upi$ ."1014 We further find f.—(2/70(Resa)=(2/7)Ws(t.," We further find $f \sim1015(2/\upi)\,(R_\rmn{E}/a)= (2/\upi)\, \sqrt{2 R_\rmn{S}/a}$."1016 Using the numerical values for the Schwarzschild radiusVf in the order of a few km and @ in the order of one tenth of astronomical unit. the fraction of ραself-lensing binaries with compact objects that provide a signature becomes f—LO+.," Using the numerical values for the Schwarzschild radius in the order of a few km and $a$ in the order of one tenth of astronomical unit, the fraction of self-lensing binaries with compact objects that provide a signature becomes $f \sim 10^{-4}$."1017 Taking 0.4 per cent of binary stars with compact star companions. the probability for the effect to show up amongst all observed stars turns out to be far~4107.," Taking 0.4 per cent of binary stars with compact star companions, the probability for the effect to show up amongst all observed stars turns out to be $f_\rmn{all} \sim 4 \times 10^{-7}$."1018 This number is tiny. but one needs to be aware of the fact that the prospects for observing such an effect crucially depend on the viability of regular monitoring of a huge number of targets. as well as on the frequency of such events to occur.," This number is tiny, but one needs to be aware of the fact that the prospects for observing such an effect crucially depend on the viability of regular monitoring of a huge number of targets, as well as on the frequency of such events to occur."1019" For a binary system. the angular velocity is given by so that the relative transverse velocity of the source with respect to the lens follows as and is therefore determined with the choices of the masses n, and A/ of the components and the orbital radius e."," For a binary system, the angular velocity is given by so that the relative transverse velocity of the source with respect to the lens follows as and is therefore determined with the choices of the masses $m_\star$ and $M$ of the components and the orbital radius $a$."1020 This defines an event time-scale within which the source moves by /?p., This defines an event time-scale within which the source moves by $R_\rmn{E}$ .1021 In fact. the motion can be approximated as uniform. where," In fact, the motion can be approximated as uniform, where"1022(model €i).,(model G).1023 Revnolels (1996) also present results [rom a study of the same ASCA observations. in which they did not detect significant emission associated with the nucleus. although these authors did not account for the possibility of variable clement abundance ratios in their analysis. which provides a crucial step in the modeling (see also Allen 1999).," Reynolds (1996) also present results from a study of the same ASCA observations, in which they did not detect significant emission associated with the nucleus, although these authors did not account for the possibility of variable element abundance ratios in their analysis, which provides a crucial step in the modeling (see also Allen 1999)."1024 To. further illustrate this. we have repeated our analvsis of the power-law component in AIST with the element abundances linked to vary in the same ratio relative to their solar values spectral model DJ.," To further illustrate this, we have repeated our analysis of the power-law component in M87 with the element abundances linked to vary in the same ratio relative to their solar values spectral model D)."1025" Phe best-lit 47. value obtained. with this more. simple nicelel. VO=ISSS. is substantially worse than the value. 47=1468. obtained with spectral model CG. “Phe best-fit parameter values (DL=1.70n"" and ο=L9i7m10 photon tem7s 1 +) are also (slightly) olfset from the results obtained with model €. Such cdillerences demonstrate the need to fully account for the complex temperature structure of the ealaxy/eluster plasma and. possible variations in individual clement abundances ratios when attempting to constrain the power-law emission from such sources."," The best-fit $\chi^2$ value obtained with this more simple model, $\chi^2=1888$, is substantially worse than the value, $\chi^2=1468$, obtained with spectral model G. The best-fit parameter values $\Gamma = 1.70^{+0.27}_{-0.31}$ and $A_1=1.9^{+1.5}_{-0.9} \times 10^{-3}$ photon $^{-1}$ $^{-2}$ $^{-1}$ ) are also (slightly) offset from the results obtained with model G. Such differences demonstrate the need to fully account for the complex temperature structure of the galaxy/cluster plasma and possible variations in individual element abundances ratios when attempting to constrain the power-law emission from such sources."1026 lteynolds (1999) present further constraints on power-law emission from. AIST using observations mace with the Proportional Counter Array (PCA) on the Rossi X-ray Timing Explorer (RATE)., Reynolds (1999) present further constraints on power-law emission from M87 using observations made with the Proportional Counter Array (PCA) on the Rossi X-ray Timing Explorer (RXTE).1027 Phe data presented. by these authors cover the 3.15 keV range and constrain the 2.10 keV Dux of the power-law component to be <41«10.75. for an assumed. photon index P=2.0.," The data presented by these authors cover the $3-15$ keV range and constrain the $2-10$ keV flux of the power-law component to be $< 4.11028\times 10^{-12}$, for an assumed photon index $\Gamma1029=2.0$."1030" This upper limit MNis lower than the measured value of ""oLS7.το107 from the ASCA data (Table 4).", This upper limit is lower than the measured value of $8.7^{+1.7}_{-1.6} \times 10^{-12}$ from the ASCA data (Table 4).1031 The ASCA data also require a significantly [latter photon index lan assumed in the RAPE stud., The ASCA data also require a significantly flatter photon index than assumed in the RXTE study.1032 The best-fitting spectral model for MS? determined rom the ASC'X analysis anc plotted in Fig., The best-fitting spectral model for M87 determined from the ASCA analysis and plotted in Fig.1033 2 shows that 16 extended cluster emission dominates over the power-Inw component in the ASCA spectra across virtually the entire energy range of the detectors., 2 shows that the extended cluster emission dominates over the power-law component in the ASCA spectra across virtually the entire energy range of the detectors.1034 Only at energies o>SO keV. does the power-law component dominate the detected lux., Only at energies $E > 8-9$ keV does the power-law component dominate the detected flux.1035 The much larger field of view of the PCA collimator (1 degrec? ENIM: Jaboca 1996) results in a larger raction of the total cluster Hux (~5 times more) being included. in the detected. spectrum. (the cluster emission extends to a radius of at least 4 degree: Schindler. Binggeli Bobbringer 1999).," The much larger field of view of the PCA collimator $\sim 1$ $^2$ FWHM; Jahoda 1996) results in a larger fraction of the total cluster flux $\sim 5$ times more) being included in the detected spectrum (the cluster emission extends to a radius of at least 4 degree; Schindler, Binggeli Böhhringer 1999)."1036 Thus. the power-law component. as determined from the ASCA data. will not dominate over the cluster emission in the PCA spectrum below an energy of~12.13 keV. Alodelling the extended: plasma emission in a cluster as cool as Vireo Cluster Clable 3) with instruments. like the PCA. restricted. to the (relatively hare) 3 15keV energy range. is dillieult.," Thus, the power-law component, as determined from the ASCA data, will not dominate over the cluster emission in the PCA spectrum below an energy of $\sim 12-13$ keV. Modelling the extended plasma emission in a cluster as cool as Virgo Cluster (Table 3) with instruments like the PCA, restricted to the (relatively hard) $3-15$ keV energy range, is difficult."1037 Phe PCA spectra cannot reliably constrain the multiphase nature of the eas in the cluster core which. as this πάν has shown. can be crucial in constraining the properties of the power-law emission.," The PCA spectra cannot reliably constrain the multiphase nature of the gas in the cluster core which, as this study has shown, can be crucial in constraining the properties of the power-law emission."1038 Llowever. although such considerations may be relevant in interpreting the RAPE results. it remains plausible that the nuclear emission. from AIST may simply have varied between the ASCA observations in 1993 June and the PCA observations macle in 1998 January (Harris 1997. 1998: Psvetanov 1998) The other galaxies discussed. in this paper have not previously been studied in the same detail as AIST and no detections of point-source X-ray emission associated with their nuclei have been reported.," However, although such considerations may be relevant in interpreting the RXTE results, it remains plausible that the nuclear emission from M87 may simply have varied between the ASCA observations in 1993 June and the PCA observations made in 1998 January (Harris 1997, 1998; Tsvetanov 1998) The other galaxies discussed in this paper have not previously been studied in the same detail as M87 and no detections of point-source X-ray emission associated with their nuclei have been reported."1039 However. Di Matteo (19998) present limits on possible nuclear N-ray emission for the three Virgo ellipticals. based on ROSAT 11141. imaging data.," However, Di Matteo (1999a) present limits on possible nuclear X-ray emission for the three Virgo ellipticals, based on ROSAT HRI imaging data."1040" Vhew limits. which are defined at an energv of Γκολ), are vit.<68«101H (Νας 4472). vk.«τὸ10Mo (Νες 4636) and ντ1518 (Νας 4649)."," Their limits, which are defined at an energy of 1keV, are $\nu F_\nu < 6.8 \times 10^{-14}$ (NGC 4472), $\nu1041F_\nu < 7.8 \times 10^{-14}$ (NGC 4636) and $\nu F_\nu <10421.5 \times 10^{-13}$ (NGC 4649)."1043" These limits compare to the measured SCA Iuxes. quoted in the same units. of ££.~6.1.10.+4 [NGC το] vk~16-10P D(NGOC 4636). and vis.~3,510.H L(NGC 4649)."," These limits compare to the measured ASCA fluxes, quoted in the same units, of $\nu F_\nu \sim10446.1 \times 10^{-14}$ (NGC 4472), $\nu F_\nu \sim 1.61045\times 10^{-13}$ (NGC 4636), and $\nu F_\nu \sim 3.51046\times 10^{-14}$ (NGC 4649)."1047 The ASCA measurements for NGC 4472 and 4649 are within the Di Matteo (1999a) limits., The ASCA measurements for NGC 4472 and 4649 are within the Di Matteo (1999a) limits.1048 For NGC 4636. however. the SCA measurement. is approximately twice the ROSAYT limit.," For NGC 4636, however, the ASCA measurement is approximately twice the ROSAT limit."1049 The Di Matteo. (1999a) limits are determined by fitting an analytic Kine model to the observed: X-ray surface brightness profiles ancl determining the maximum additional contribution that can be mace hy a central point source., The Di Matteo (1999a) limits are determined by fitting an analytic King model to the observed X-ray surface brightness profiles and determining the maximum additional contribution that can be made by a central point source.1050 However. these limits are sensitive (ο complexities in the observed surface brightness profiles and. especially for NGC 4636. which exhibits a complex. X-ray morphology in its central regions. the ROSAT limits should be viewed with caution.," However, these limits are sensitive to complexities in the observed surface brightness profiles and, especially for NGC 4636, which exhibits a complex X-ray morphology in its central regions, the ROSAT limits should be viewed with caution."1051 1n contrast to the ASCA results for MIST ancl NGC 4696 (Allen 1999). for which the introduction of individual element abundances as free. parameters in the fits leads to à more significant improvement in the statistical quality of the fits han the introduction of the power-law component. for NGC 4696. the-introduction of the power-Law emission component oovides bv far the most significant improvement. over the asic (wo-lomperature model.," In contrast to the ASCA results for M87 and NGC 4696 (Allen 1999), for which the introduction of individual element abundances as free parameters in the fits leads to a more significant improvement in the statistical quality of the fits than the introduction of the power-law component, for NGC 4696, the-introduction of the power-law emission component provides by far the most significant improvement over the basic two-temperature model."1052 Εις. in determining our results on the abuncances of the individual elements. in ας 4636. we started from the twvo-tempoerature model with he power-law component included. which provides a 47 of 722.6 [or 230 degrees of freedom.," Thus, in determining our results on the abundances of the individual elements in NGC 4636, we started from the two-temperature model with the power-law component included, which provides a $\chi^2$ of 722.6 for 230 degrees of freedom."1053 We then systematically letermined the statistical improvements to the fit obtained w allowing the abundance of cach element. in turn. to be a ree parameter in the analysis.," We then systematically determined the statistical improvements to the fit obtained by allowing the abundance of each element, in turn, to be a free parameter in the analysis."1054 Having identified the element »ovidineg the most significant improvement. the abundance," Having identified the element providing the most significant improvement, the abundance"1055from our Daophot catalog (described in Section 3.2.1). with new single stellar population model predictions from Charlot Bruzual (2009: hereafter CD09. private communication: also see Druzual Charlot 2003) which use the WFEC3 filter transmission curves.,"from our Daophot catalog (described in Section 3.2.1), with new single stellar population model predictions from Charlot Bruzual (2009; hereafter CB09, private communication; also see Bruzual Charlot 2003) which use the WFC3 filter transmission curves."1056" The colors and Iuminosities have been corrected for reddening and extinction in the Milkv Way 0.07. A,=0.213: Schlegel 1998) but not in M83."," The colors and luminosities have been corrected for reddening and extinction in the Milky Way $E(B-V)=0.07$ , $A_V=0.218$; Schlegel 1998) but not in M83."1057 We show predictions from models with zz2xsolar metallicity (the inner portions of M33 have super-solar abundance: Bresolin et 22005)., We show predictions from models with $\approx2\times$ solar metallicity (the inner portions of M83 have super-solar abundance; Bresolin et 2005).1058 We note (he overall exquisite match between the observations and the models. greatly. surpassing those of past observations in the & band using ΛΕΡΟΣ.," We note the overall exquisite match between the observations and the models, greatly surpassing those of past observations in the $U$ band using WFPC2."1059 This bodes well for our ability to age-date the clusters. which is discussed in Section 5.," This bodes well for our ability to age-date the clusters, which is discussed in Section 5."1060 Next. we compare predicted Mn for luminous stars [rom the Padova (e.g. Girardi οἱ 22002: Marigo et 22008). shown as the small filled circles in the upper-right panel of Figure 7.. with the -- cluster colors.," Next, we compare predicted colors for luminous stars from the Padova (e.g., Girardi et 2002; Marigo et 2008), shown as the small filled circles in the upper-right panel of Figure \ref{fig:stvscl1}, with the predicted cluster colors."1061 Predictecl colors for the stars begin al roughly (the same location as for the voungest clusters. in the upper left portion of the Gwo-color diagram. but the two tracks separate for clusters older (han στοκ109 vr. when red supereiants begin to appear.," Predicted colors for the stars begin at roughly the same location as for the youngest clusters, in the upper left portion of the two-color diagram, but the two tracks separate for clusters older than $\approx3\times10^6$ yr, when red supergiants begin to appear."1062" We use (he models as a guide to define four different regions of two-color space: (1) ""cluster space"": region of (wo-color space unique to clusters (5x(V—1)—(UU-B)>2 and 0.33x(V—1)-(U—B)> —0.33) (2) ""star/cluster space’: region of (wo-color space MM both verv voung clusters and very blue stars (5x(V—1)—(U-B)<2 and (U—B)< —0.80) ος ""blue-star space’: region of two-color space unique to luminous. blue stars and 0.33x(V—1)—(/—B)< —0.33) (4) ""vellow-star space"": region of two-color space unique to luminous. vellow stars and 0.33x(V—1)—(C—B)« —0.33) These four regions are somewhat different than those used in the Antennae by Whitmore (2010). primarily because of the significantly. higher quality of the C band observations provided by WECS3 compared with Ες."," We use the models as a guide to define four different regions of two-color space: (1) “cluster space”: region of two-color space unique to clusters $5\times(V\!-\!I) - (U\!-\!B) > 2$ and $0.33\times (V\!-\!I) - (U\!-\!B) > -0.33$ ) (2) “star/cluster space”: region of two-color space containing both very young clusters and very blue stars $5\times(V\!-\!I) - (U\!-\!B) < 2$ and $(U\!-\!B) < -0.80$ ) (3) “blue-star space”: region of two-color space unique to luminous, blue stars $-0.80 < (U\!-\!B) < 0.50$ and $0.33\times (V\!-\!I) - (U\!-\!B) < -0.33$ ) (4) “yellow-star space”: region of two-color space unique to luminous, yellow stars $(U\!-\!B) > 0.50$ and $0.33 \times (V\!-\!I) - (U\!-\!B) < -0.33$ ) These four regions are somewhat different than those used in the Antennae by Whitmore (2010), primarily because of the significantly higher quality of the $U$ band observations provided by WFC3 compared with WFPC2."1063" FigureE 7 shows a series of two-color diagrams.5 divided into four different. intervals of luminosity (down to M,\= —7)."," Figure \ref{fig:stvscl1} shows a series of two-color diagrams, divided into four different intervals of luminosity (down to $M_V = -7$ )."1064" The first two columns show our best (7""Daophot""|see ⊳↔⊲≼↲≺∢∐∪↥⊑↽⊰⋅∃↕⋟≺∢≀↕↴↥≀↧↴↥∪↖≺≟∪↓⋟⋟∖⊽↥≀↧↴↕⋅≺∢↥∏⋟∖⊽∩↲↕⋅⋟∖⊽↕∐⊔∐↲∐∪∐−∐⋯∢↥≼↲≀↧↴↕⋅⊔≼↲∐↕⋝≀↧↴∐≺⇂∐∏≺∢"," The first two columns show our best (“Daophot”—see Section 3.2) catalog of star clusters in the non-nuclear (left) and nuclear (middle) regions,"1065" The first two columns show our best (7""Daophot""|see ⊳↔⊲≼↲≺∢∐∪↥⊑↽⊰⋅∃↕⋟≺∢≀↕↴↥≀↧↴↥∪↖≺≟∪↓⋟⋟∖⊽↥≀↧↴↕⋅≺∢↥∏⋟∖⊽∩↲↕⋅⋟∖⊽↕∐⊔∐↲∐∪∐−∐⋯∢↥≼↲≀↧↴↕⋅⊔≼↲∐↕⋝≀↧↴∐≺⇂∐∏≺∢↥"," The first two columns show our best (“Daophot”—see Section 3.2) catalog of star clusters in the non-nuclear (left) and nuclear (middle) regions,"1066" The first two columns show our best (7""Daophot""|see ⊳↔⊲≼↲≺∢∐∪↥⊑↽⊰⋅∃↕⋟≺∢≀↕↴↥≀↧↴↥∪↖≺≟∪↓⋟⋟∖⊽↥≀↧↴↕⋅≺∢↥∏⋟∖⊽∩↲↕⋅⋟∖⊽↕∐⊔∐↲∐∪∐−∐⋯∢↥≼↲≀↧↴↕⋅⊔≼↲∐↕⋝≀↧↴∐≺⇂∐∏≺∢↥≼"," The first two columns show our best (“Daophot”—see Section 3.2) catalog of star clusters in the non-nuclear (left) and nuclear (middle) regions,"1067" The first two columns show our best (7""Daophot""|see ⊳↔⊲≼↲≺∢∐∪↥⊑↽⊰⋅∃↕⋟≺∢≀↕↴↥≀↧↴↥∪↖≺≟∪↓⋟⋟∖⊽↥≀↧↴↕⋅≺∢↥∏⋟∖⊽∩↲↕⋅⋟∖⊽↕∐⊔∐↲∐∪∐−∐⋯∢↥≼↲≀↧↴↕⋅⊔≼↲∐↕⋝≀↧↴∐≺⇂∐∏≺∢↥≼↲"," The first two columns show our best (“Daophot”—see Section 3.2) catalog of star clusters in the non-nuclear (left) and nuclear (middle) regions,"1068" The first two columns show our best (7""Daophot""|see ⊳↔⊲≼↲≺∢∐∪↥⊑↽⊰⋅∃↕⋟≺∢≀↕↴↥≀↧↴↥∪↖≺≟∪↓⋟⋟∖⊽↥≀↧↴↕⋅≺∢↥∏⋟∖⊽∩↲↕⋅⋟∖⊽↕∐⊔∐↲∐∪∐−∐⋯∢↥≼↲≀↧↴↕⋅⊔≼↲∐↕⋝≀↧↴∐≺⇂∐∏≺∢↥≼↲≀"," The first two columns show our best (“Daophot”—see Section 3.2) catalog of star clusters in the non-nuclear (left) and nuclear (middle) regions,"1069" The first two columns show our best (7""Daophot""|see ⊳↔⊲≼↲≺∢∐∪↥⊑↽⊰⋅∃↕⋟≺∢≀↕↴↥≀↧↴↥∪↖≺≟∪↓⋟⋟∖⊽↥≀↧↴↕⋅≺∢↥∏⋟∖⊽∩↲↕⋅⋟∖⊽↕∐⊔∐↲∐∪∐−∐⋯∢↥≼↲≀↧↴↕⋅⊔≼↲∐↕⋝≀↧↴∐≺⇂∐∏≺∢↥≼↲≀↧"," The first two columns show our best (“Daophot”—see Section 3.2) catalog of star clusters in the non-nuclear (left) and nuclear (middle) regions,"1070" The first two columns show our best (7""Daophot""|see ⊳↔⊲≼↲≺∢∐∪↥⊑↽⊰⋅∃↕⋟≺∢≀↕↴↥≀↧↴↥∪↖≺≟∪↓⋟⋟∖⊽↥≀↧↴↕⋅≺∢↥∏⋟∖⊽∩↲↕⋅⋟∖⊽↕∐⊔∐↲∐∪∐−∐⋯∢↥≼↲≀↧↴↕⋅⊔≼↲∐↕⋝≀↧↴∐≺⇂∐∏≺∢↥≼↲≀↧↴"," The first two columns show our best (“Daophot”—see Section 3.2) catalog of star clusters in the non-nuclear (left) and nuclear (middle) regions,"1071" The first two columns show our best (7""Daophot""|see ⊳↔⊲≼↲≺∢∐∪↥⊑↽⊰⋅∃↕⋟≺∢≀↕↴↥≀↧↴↥∪↖≺≟∪↓⋟⋟∖⊽↥≀↧↴↕⋅≺∢↥∏⋟∖⊽∩↲↕⋅⋟∖⊽↕∐⊔∐↲∐∪∐−∐⋯∢↥≼↲≀↧↴↕⋅⊔≼↲∐↕⋝≀↧↴∐≺⇂∐∏≺∢↥≼↲≀↧↴↕"," The first two columns show our best (“Daophot”—see Section 3.2) catalog of star clusters in the non-nuclear (left) and nuclear (middle) regions,"1072" The first two columns show our best (7""Daophot""|see ⊳↔⊲≼↲≺∢∐∪↥⊑↽⊰⋅∃↕⋟≺∢≀↕↴↥≀↧↴↥∪↖≺≟∪↓⋟⋟∖⊽↥≀↧↴↕⋅≺∢↥∏⋟∖⊽∩↲↕⋅⋟∖⊽↕∐⊔∐↲∐∪∐−∐⋯∢↥≼↲≀↧↴↕⋅⊔≼↲∐↕⋝≀↧↴∐≺⇂∐∏≺∢↥≼↲≀↧↴↕⋅"," The first two columns show our best (“Daophot”—see Section 3.2) catalog of star clusters in the non-nuclear (left) and nuclear (middle) regions,"1073" The first two columns show our best (7""Daophot""|see ⊳↔⊲≼↲≺∢∐∪↥⊑↽⊰⋅∃↕⋟≺∢≀↕↴↥≀↧↴↥∪↖≺≟∪↓⋟⋟∖⊽↥≀↧↴↕⋅≺∢↥∏⋟∖⊽∩↲↕⋅⋟∖⊽↕∐⊔∐↲∐∪∐−∐⋯∢↥≼↲≀↧↴↕⋅⊔≼↲∐↕⋝≀↧↴∐≺⇂∐∏≺∢↥≼↲≀↧↴↕⋅≼"," The first two columns show our best (“Daophot”—see Section 3.2) catalog of star clusters in the non-nuclear (left) and nuclear (middle) regions,"1074" The first two columns show our best (7""Daophot""|see ⊳↔⊲≼↲≺∢∐∪↥⊑↽⊰⋅∃↕⋟≺∢≀↕↴↥≀↧↴↥∪↖≺≟∪↓⋟⋟∖⊽↥≀↧↴↕⋅≺∢↥∏⋟∖⊽∩↲↕⋅⋟∖⊽↕∐⊔∐↲∐∪∐−∐⋯∢↥≼↲≀↧↴↕⋅⊔≼↲∐↕⋝≀↧↴∐≺⇂∐∏≺∢↥≼↲≀↧↴↕⋅≼⋡"," The first two columns show our best (“Daophot”—see Section 3.2) catalog of star clusters in the non-nuclear (left) and nuclear (middle) regions,"1075" The first two columns show our best (7""Daophot""|see ⊳↔⊲≼↲≺∢∐∪↥⊑↽⊰⋅∃↕⋟≺∢≀↕↴↥≀↧↴↥∪↖≺≟∪↓⋟⋟∖⊽↥≀↧↴↕⋅≺∢↥∏⋟∖⊽∩↲↕⋅⋟∖⊽↕∐⊔∐↲∐∪∐−∐⋯∢↥≼↲≀↧↴↕⋅⊔≼↲∐↕⋝≀↧↴∐≺⇂∐∏≺∢↥≼↲≀↧↴↕⋅≼⋡∐"," The first two columns show our best (“Daophot”—see Section 3.2) catalog of star clusters in the non-nuclear (left) and nuclear (middle) regions,"1076" The first two columns show our best (7""Daophot""|see ⊳↔⊲≼↲≺∢∐∪↥⊑↽⊰⋅∃↕⋟≺∢≀↕↴↥≀↧↴↥∪↖≺≟∪↓⋟⋟∖⊽↥≀↧↴↕⋅≺∢↥∏⋟∖⊽∩↲↕⋅⋟∖⊽↕∐⊔∐↲∐∪∐−∐⋯∢↥≼↲≀↧↴↕⋅⊔≼↲∐↕⋝≀↧↴∐≺⇂∐∏≺∢↥≼↲≀↧↴↕⋅≼⋡∐↓"," The first two columns show our best (“Daophot”—see Section 3.2) catalog of star clusters in the non-nuclear (left) and nuclear (middle) regions,"1077" The first two columns show our best (7""Daophot""|see ⊳↔⊲≼↲≺∢∐∪↥⊑↽⊰⋅∃↕⋟≺∢≀↕↴↥≀↧↴↥∪↖≺≟∪↓⋟⋟∖⊽↥≀↧↴↕⋅≺∢↥∏⋟∖⊽∩↲↕⋅⋟∖⊽↕∐⊔∐↲∐∪∐−∐⋯∢↥≼↲≀↧↴↕⋅⊔≼↲∐↕⋝≀↧↴∐≺⇂∐∏≺∢↥≼↲≀↧↴↕⋅≼⋡∐↓↕"," The first two columns show our best (“Daophot”—see Section 3.2) catalog of star clusters in the non-nuclear (left) and nuclear (middle) regions,"1078" The first two columns show our best (7""Daophot""|see ⊳↔⊲≼↲≺∢∐∪↥⊑↽⊰⋅∃↕⋟≺∢≀↕↴↥≀↧↴↥∪↖≺≟∪↓⋟⋟∖⊽↥≀↧↴↕⋅≺∢↥∏⋟∖⊽∩↲↕⋅⋟∖⊽↕∐⊔∐↲∐∪∐−∐⋯∢↥≼↲≀↧↴↕⋅⊔≼↲∐↕⋝≀↧↴∐≺⇂∐∏≺∢↥≼↲≀↧↴↕⋅≼⋡∐↓↕≼"," The first two columns show our best (“Daophot”—see Section 3.2) catalog of star clusters in the non-nuclear (left) and nuclear (middle) regions,"1079" The first two columns show our best (7""Daophot""|see ⊳↔⊲≼↲≺∢∐∪↥⊑↽⊰⋅∃↕⋟≺∢≀↕↴↥≀↧↴↥∪↖≺≟∪↓⋟⋟∖⊽↥≀↧↴↕⋅≺∢↥∏⋟∖⊽∩↲↕⋅⋟∖⊽↕∐⊔∐↲∐∪∐−∐⋯∢↥≼↲≀↧↴↕⋅⊔≼↲∐↕⋝≀↧↴∐≺⇂∐∏≺∢↥≼↲≀↧↴↕⋅≼⋡∐↓↕≼⇂"," The first two columns show our best (“Daophot”—see Section 3.2) catalog of star clusters in the non-nuclear (left) and nuclear (middle) regions,"1080" The first two columns show our best (7""Daophot""|see ⊳↔⊲≼↲≺∢∐∪↥⊑↽⊰⋅∃↕⋟≺∢≀↕↴↥≀↧↴↥∪↖≺≟∪↓⋟⋟∖⊽↥≀↧↴↕⋅≺∢↥∏⋟∖⊽∩↲↕⋅⋟∖⊽↕∐⊔∐↲∐∪∐−∐⋯∢↥≼↲≀↧↴↕⋅⊔≼↲∐↕⋝≀↧↴∐≺⇂∐∏≺∢↥≼↲≀↧↴↕⋅≼⋡∐↓↕≼⇂≺"," The first two columns show our best (“Daophot”—see Section 3.2) catalog of star clusters in the non-nuclear (left) and nuclear (middle) regions,"1081" The first two columns show our best (7""Daophot""|see ⊳↔⊲≼↲≺∢∐∪↥⊑↽⊰⋅∃↕⋟≺∢≀↕↴↥≀↧↴↥∪↖≺≟∪↓⋟⋟∖⊽↥≀↧↴↕⋅≺∢↥∏⋟∖⊽∩↲↕⋅⋟∖⊽↕∐⊔∐↲∐∪∐−∐⋯∢↥≼↲≀↧↴↕⋅⊔≼↲∐↕⋝≀↧↴∐≺⇂∐∏≺∢↥≼↲≀↧↴↕⋅≼⋡∐↓↕≼⇂≺∐"," The first two columns show our best (“Daophot”—see Section 3.2) catalog of star clusters in the non-nuclear (left) and nuclear (middle) regions,"1082" The first two columns show our best (7""Daophot""|see ⊳↔⊲≼↲≺∢∐∪↥⊑↽⊰⋅∃↕⋟≺∢≀↕↴↥≀↧↴↥∪↖≺≟∪↓⋟⋟∖⊽↥≀↧↴↕⋅≺∢↥∏⋟∖⊽∩↲↕⋅⋟∖⊽↕∐⊔∐↲∐∪∐−∐⋯∢↥≼↲≀↧↴↕⋅⊔≼↲∐↕⋝≀↧↴∐≺⇂∐∏≺∢↥≼↲≀↧↴↕⋅≼⋡∐↓↕≼⇂≺∐≼"," The first two columns show our best (“Daophot”—see Section 3.2) catalog of star clusters in the non-nuclear (left) and nuclear (middle) regions,"1083" The first two columns show our best (7""Daophot""|see ⊳↔⊲≼↲≺∢∐∪↥⊑↽⊰⋅∃↕⋟≺∢≀↕↴↥≀↧↴↥∪↖≺≟∪↓⋟⋟∖⊽↥≀↧↴↕⋅≺∢↥∏⋟∖⊽∩↲↕⋅⋟∖⊽↕∐⊔∐↲∐∪∐−∐⋯∢↥≼↲≀↧↴↕⋅⊔≼↲∐↕⋝≀↧↴∐≺⇂∐∏≺∢↥≼↲≀↧↴↕⋅≼⋡∐↓↕≼⇂≺∐≼↲"," The first two columns show our best (“Daophot”—see Section 3.2) catalog of star clusters in the non-nuclear (left) and nuclear (middle) regions,"1084" The first two columns show our best (7""Daophot""|see ⊳↔⊲≼↲≺∢∐∪↥⊑↽⊰⋅∃↕⋟≺∢≀↕↴↥≀↧↴↥∪↖≺≟∪↓⋟⋟∖⊽↥≀↧↴↕⋅≺∢↥∏⋟∖⊽∩↲↕⋅⋟∖⊽↕∐⊔∐↲∐∪∐−∐⋯∢↥≼↲≀↧↴↕⋅⊔≼↲∐↕⋝≀↧↴∐≺⇂∐∏≺∢↥≼↲≀↧↴↕⋅≼⋡∐↓↕≼⇂≺∐≼↲↕"," The first two columns show our best (“Daophot”—see Section 3.2) catalog of star clusters in the non-nuclear (left) and nuclear (middle) regions,"1085" The first two columns show our best (7""Daophot""|see ⊳↔⊲≼↲≺∢∐∪↥⊑↽⊰⋅∃↕⋟≺∢≀↕↴↥≀↧↴↥∪↖≺≟∪↓⋟⋟∖⊽↥≀↧↴↕⋅≺∢↥∏⋟∖⊽∩↲↕⋅⋟∖⊽↕∐⊔∐↲∐∪∐−∐⋯∢↥≼↲≀↧↴↕⋅⊔≼↲∐↕⋝≀↧↴∐≺⇂∐∏≺∢↥≼↲≀↧↴↕⋅≼⋡∐↓↕≼⇂≺∐≼↲↕⋝"," The first two columns show our best (“Daophot”—see Section 3.2) catalog of star clusters in the non-nuclear (left) and nuclear (middle) regions,"1086" The first two columns show our best (7""Daophot""|see ⊳↔⊲≼↲≺∢∐∪↥⊑↽⊰⋅∃↕⋟≺∢≀↕↴↥≀↧↴↥∪↖≺≟∪↓⋟⋟∖⊽↥≀↧↴↕⋅≺∢↥∏⋟∖⊽∩↲↕⋅⋟∖⊽↕∐⊔∐↲∐∪∐−∐⋯∢↥≼↲≀↧↴↕⋅⊔≼↲∐↕⋝≀↧↴∐≺⇂∐∏≺∢↥≼↲≀↧↴↕⋅≼⋡∐↓↕≼⇂≺∐≼↲↕⋝↕"," The first two columns show our best (“Daophot”—see Section 3.2) catalog of star clusters in the non-nuclear (left) and nuclear (middle) regions,"1087" The first two columns show our best (7""Daophot""|see ⊳↔⊲≼↲≺∢∐∪↥⊑↽⊰⋅∃↕⋟≺∢≀↕↴↥≀↧↴↥∪↖≺≟∪↓⋟⋟∖⊽↥≀↧↴↕⋅≺∢↥∏⋟∖⊽∩↲↕⋅⋟∖⊽↕∐⊔∐↲∐∪∐−∐⋯∢↥≼↲≀↧↴↕⋅⊔≼↲∐↕⋝≀↧↴∐≺⇂∐∏≺∢↥≼↲≀↧↴↕⋅≼⋡∐↓↕≼⇂≺∐≼↲↕⋝↕⋅"," The first two columns show our best (“Daophot”—see Section 3.2) catalog of star clusters in the non-nuclear (left) and nuclear (middle) regions,"1088" The first two columns show our best (7""Daophot""|see ⊳↔⊲≼↲≺∢∐∪↥⊑↽⊰⋅∃↕⋟≺∢≀↕↴↥≀↧↴↥∪↖≺≟∪↓⋟⋟∖⊽↥≀↧↴↕⋅≺∢↥∏⋟∖⊽∩↲↕⋅⋟∖⊽↕∐⊔∐↲∐∪∐−∐⋯∢↥≼↲≀↧↴↕⋅⊔≼↲∐↕⋝≀↧↴∐≺⇂∐∏≺∢↥≼↲≀↧↴↕⋅≼⋡∐↓↕≼⇂≺∐≼↲↕⋝↕⋅≼"," The first two columns show our best (“Daophot”—see Section 3.2) catalog of star clusters in the non-nuclear (left) and nuclear (middle) regions,"1089" The first two columns show our best (7""Daophot""|see ⊳↔⊲≼↲≺∢∐∪↥⊑↽⊰⋅∃↕⋟≺∢≀↕↴↥≀↧↴↥∪↖≺≟∪↓⋟⋟∖⊽↥≀↧↴↕⋅≺∢↥∏⋟∖⊽∩↲↕⋅⋟∖⊽↕∐⊔∐↲∐∪∐−∐⋯∢↥≼↲≀↧↴↕⋅⊔≼↲∐↕⋝≀↧↴∐≺⇂∐∏≺∢↥≼↲≀↧↴↕⋅≼⋡∐↓↕≼⇂≺∐≼↲↕⋝↕⋅≼↲"," The first two columns show our best (“Daophot”—see Section 3.2) catalog of star clusters in the non-nuclear (left) and nuclear (middle) regions,"1090" The first two columns show our best (7""Daophot""|see ⊳↔⊲≼↲≺∢∐∪↥⊑↽⊰⋅∃↕⋟≺∢≀↕↴↥≀↧↴↥∪↖≺≟∪↓⋟⋟∖⊽↥≀↧↴↕⋅≺∢↥∏⋟∖⊽∩↲↕⋅⋟∖⊽↕∐⊔∐↲∐∪∐−∐⋯∢↥≼↲≀↧↴↕⋅⊔≼↲∐↕⋝≀↧↴∐≺⇂∐∏≺∢↥≼↲≀↧↴↕⋅≼⋡∐↓↕≼⇂≺∐≼↲↕⋝↕⋅≼↲≸"," The first two columns show our best (“Daophot”—see Section 3.2) catalog of star clusters in the non-nuclear (left) and nuclear (middle) regions,"1091" The first two columns show our best (7""Daophot""|see ⊳↔⊲≼↲≺∢∐∪↥⊑↽⊰⋅∃↕⋟≺∢≀↕↴↥≀↧↴↥∪↖≺≟∪↓⋟⋟∖⊽↥≀↧↴↕⋅≺∢↥∏⋟∖⊽∩↲↕⋅⋟∖⊽↕∐⊔∐↲∐∪∐−∐⋯∢↥≼↲≀↧↴↕⋅⊔≼↲∐↕⋝≀↧↴∐≺⇂∐∏≺∢↥≼↲≀↧↴↕⋅≼⋡∐↓↕≼⇂≺∐≼↲↕⋝↕⋅≼↲≸≟"," The first two columns show our best (“Daophot”—see Section 3.2) catalog of star clusters in the non-nuclear (left) and nuclear (middle) regions,"1092" The first two columns show our best (7""Daophot""|see ⊳↔⊲≼↲≺∢∐∪↥⊑↽⊰⋅∃↕⋟≺∢≀↕↴↥≀↧↴↥∪↖≺≟∪↓⋟⋟∖⊽↥≀↧↴↕⋅≺∢↥∏⋟∖⊽∩↲↕⋅⋟∖⊽↕∐⊔∐↲∐∪∐−∐⋯∢↥≼↲≀↧↴↕⋅⊔≼↲∐↕⋝≀↧↴∐≺⇂∐∏≺∢↥≼↲≀↧↴↕⋅≼⋡∐↓↕≼⇂≺∐≼↲↕⋝↕⋅≼↲≸≟↕"," The first two columns show our best (“Daophot”—see Section 3.2) catalog of star clusters in the non-nuclear (left) and nuclear (middle) regions,"1093" The first two columns show our best (7""Daophot""|see ⊳↔⊲≼↲≺∢∐∪↥⊑↽⊰⋅∃↕⋟≺∢≀↕↴↥≀↧↴↥∪↖≺≟∪↓⋟⋟∖⊽↥≀↧↴↕⋅≺∢↥∏⋟∖⊽∩↲↕⋅⋟∖⊽↕∐⊔∐↲∐∪∐−∐⋯∢↥≼↲≀↧↴↕⋅⊔≼↲∐↕⋝≀↧↴∐≺⇂∐∏≺∢↥≼↲≀↧↴↕⋅≼⋡∐↓↕≼⇂≺∐≼↲↕⋝↕⋅≼↲≸≟↕∪"," The first two columns show our best (“Daophot”—see Section 3.2) catalog of star clusters in the non-nuclear (left) and nuclear (middle) regions,"1094" The first two columns show our best (7""Daophot""|see ⊳↔⊲≼↲≺∢∐∪↥⊑↽⊰⋅∃↕⋟≺∢≀↕↴↥≀↧↴↥∪↖≺≟∪↓⋟⋟∖⊽↥≀↧↴↕⋅≺∢↥∏⋟∖⊽∩↲↕⋅⋟∖⊽↕∐⊔∐↲∐∪∐−∐⋯∢↥≼↲≀↧↴↕⋅⊔≼↲∐↕⋝≀↧↴∐≺⇂∐∏≺∢↥≼↲≀↧↴↕⋅≼⋡∐↓↕≼⇂≺∐≼↲↕⋝↕⋅≼↲≸≟↕∪∐"," The first two columns show our best (“Daophot”—see Section 3.2) catalog of star clusters in the non-nuclear (left) and nuclear (middle) regions,"1095" The first two columns show our best (7""Daophot""|see ⊳↔⊲≼↲≺∢∐∪↥⊑↽⊰⋅∃↕⋟≺∢≀↕↴↥≀↧↴↥∪↖≺≟∪↓⋟⋟∖⊽↥≀↧↴↕⋅≺∢↥∏⋟∖⊽∩↲↕⋅⋟∖⊽↕∐⊔∐↲∐∪∐−∐⋯∢↥≼↲≀↧↴↕⋅⊔≼↲∐↕⋝≀↧↴∐≺⇂∐∏≺∢↥≼↲≀↧↴↕⋅≼⋡∐↓↕≼⇂≺∐≼↲↕⋝↕⋅≼↲≸≟↕∪∐⋟"," The first two columns show our best (“Daophot”—see Section 3.2) catalog of star clusters in the non-nuclear (left) and nuclear (middle) regions,"1096" The first two columns show our best (7""Daophot""|see ⊳↔⊲≼↲≺∢∐∪↥⊑↽⊰⋅∃↕⋟≺∢≀↕↴↥≀↧↴↥∪↖≺≟∪↓⋟⋟∖⊽↥≀↧↴↕⋅≺∢↥∏⋟∖⊽∩↲↕⋅⋟∖⊽↕∐⊔∐↲∐∪∐−∐⋯∢↥≼↲≀↧↴↕⋅⊔≼↲∐↕⋝≀↧↴∐≺⇂∐∏≺∢↥≼↲≀↧↴↕⋅≼⋡∐↓↕≼⇂≺∐≼↲↕⋝↕⋅≼↲≸≟↕∪∐⋟∖"," The first two columns show our best (“Daophot”—see Section 3.2) catalog of star clusters in the non-nuclear (left) and nuclear (middle) regions,"1097" The first two columns show our best (7""Daophot""|see ⊳↔⊲≼↲≺∢∐∪↥⊑↽⊰⋅∃↕⋟≺∢≀↕↴↥≀↧↴↥∪↖≺≟∪↓⋟⋟∖⊽↥≀↧↴↕⋅≺∢↥∏⋟∖⊽∩↲↕⋅⋟∖⊽↕∐⊔∐↲∐∪∐−∐⋯∢↥≼↲≀↧↴↕⋅⊔≼↲∐↕⋝≀↧↴∐≺⇂∐∏≺∢↥≼↲≀↧↴↕⋅≼⋡∐↓↕≼⇂≺∐≼↲↕⋝↕⋅≼↲≸≟↕∪∐⋟∖⇁"," The first two columns show our best (“Daophot”—see Section 3.2) catalog of star clusters in the non-nuclear (left) and nuclear (middle) regions,"1098" The first two columns show our best (7""Daophot""|see ⊳↔⊲≼↲≺∢∐∪↥⊑↽⊰⋅∃↕⋟≺∢≀↕↴↥≀↧↴↥∪↖≺≟∪↓⋟⋟∖⊽↥≀↧↴↕⋅≺∢↥∏⋟∖⊽∩↲↕⋅⋟∖⊽↕∐⊔∐↲∐∪∐−∐⋯∢↥≼↲≀↧↴↕⋅⊔≼↲∐↕⋝≀↧↴∐≺⇂∐∏≺∢↥≼↲≀↧↴↕⋅≼⋡∐↓↕≼⇂≺∐≼↲↕⋝↕⋅≼↲≸≟↕∪∐⋟∖⇁⋅"," The first two columns show our best (“Daophot”—see Section 3.2) catalog of star clusters in the non-nuclear (left) and nuclear (middle) regions,"1099"the form F=Fu(1|z)"". with a best fit to the free parameters o£ Ly = 12 4- 3 Gyr and p= 1.6 + /- 0.4.","the form $\Gamma = \Gamma_{0}(1+z)^{-p}$, with a best fit to the free parameters of: $\Gamma_{0}$ = 12 +/- 3 Gyr and p = 1.6 + /- 0.4."1100 This represents a steep increase in the time taken for galaxies to merge., This represents a steep increase in the time taken for galaxies to merge.1101" We calculate the number of expected mergers GV,,) for a given galaxy between two redshifts using this power law tit.", We calculate the number of expected mergers $N_{m}$ ) for a given galaxy between two redshifts using this power law fit.1102 Specifically we calculate: where L(2) is the characteristic time between mergers. / is the Hubble time. and the parameter (2)=QulPa?|O4]sy|0]beeopp ii.," Specifically we calculate: where $\Gamma(z)$ is the characteristic time between mergers, $t_{H}$ is the Hubble time, and the parameter $E(z) = [\Omega_{M}(1+z)^{3}+\Omega_{k}(1+z)^2+\Omega_{\Lambda}]^{-1/2} = H^{-1}(z)$ ."1103" Calculating this from z 2 3 to z = 0. we obtained a value of |N,,, = 1.7 +/- 0.5 major mergers per galaxy. with 7,, = 0.4 Gyr."," Calculating this from z = 3 to z = 0, we obtained a value of $N_{m}$ = 1.7 +/- 0.5 major mergers per galaxy, with $\tau_{m}$ = 0.4 Gyr."1104 Conselice et al. (, Conselice et al. (1105"2008) tind that galaxies with masses in the range S«logCM./M.)9 and 9«logCAZ./M.)10 have a peak in their merger fraction at around z = 1. with galaxies with stellar masses logCAl,AM.)10 appearing to peak in their merger fraction later. at around z = 2.","2008) find that galaxies with masses in the range $8<\log(M_{*}/M_{\odot})<9$ and $9<\log(M_{*}/M_{\odot})<10$ have a peak in their merger fraction at around z = 1.5, with galaxies with stellar masses $\log(M_{*}/M_{\odot})>10$ appearing to peak in their merger fraction later, at around z = 2."1106" In this paper we have found that for galaxies with log(Al,M.)1l the merger fraction continues to increase out to z  3. indicating that the peak must οσοι at z > 3."," In this paper we have found that for galaxies with $\log(M_{*}/M_{\odot})>11$ the merger fraction continues to increase out to z $\sim$ 3, indicating that the peak must occur at z $>$ 3."1107 This provides further evidence that more massive galaxies undergo a greater number of major mergers earlier than less massive systems., This provides further evidence that more massive galaxies undergo a greater number of major mergers earlier than less massive systems.1108 This method of calculating pair fractions is. based. on noting overdensities of galaxies around host galaxies. based on background counts.," This method of calculating pair fractions is based on noting overdensities of galaxies around host galaxies, based on background counts."1109 However. the clustering of galaxies increases with redshift (see Bell et al.," However, the clustering of galaxies increases with redshift (see Bell et al."1110 2006)., 2006).1111 So. this effect may be partly explained by the correlation function of galaxies increasing with redshift.," So, this effect may be partly explained by the correlation function of galaxies increasing with redshift."1112 Since the parameters of this function are poorly known observationally. no attempt has been made to correct for this issue.," Since the parameters of this function are poorly known observationally, no attempt has been made to correct for this issue."1113 Consequently. our pair fraction results from both the GNS and POWIR surveys may be interpreted as the 2 point correlation at 30 Κρο for these massive galaxies.," Consequently, our pair fraction results from both the GNS and POWIR surveys may be interpreted as the 2 point correlation at 30 kpc for these massive galaxies."1114 This clearly evolves and it is likely true that the actual pair fraction evolves in line with this correlation., This clearly evolves and it is likely true that the actual pair fraction evolves in line with this correlation.1115 Contamination from line of sight projection at scales larger than 30 kpe will be minimised by the fact that we calculate our correction around the galaxies being measured., Contamination from line of sight projection at scales larger than 30 kpc will be minimised by the fact that we calculate our correction around the galaxies being measured.1116 Further. we have recently acquired morphological CAS measurements on the GNS galaxies as well as the POWIR ones.," Further, we have recently acquired morphological CAS measurements on the GNS galaxies as well as the POWIR ones."1117" This gives a consistent merger fraction Cfi,~ 0.3) to the pair methods.", This gives a consistent merger fraction $f_{m} \sim 0.3$ ) to the pair methods.1118 We explore this in a forthcoming paper. and elude to the relation between morphologiocal and pair methods in Conselice. Yang Bluck (2008).," We explore this in a forthcoming paper, and elude to the relation between morphologiocal and pair methods in Conselice, Yang Bluck (2008)."1119 Despite the large errors associated with calculating merger rates. we have demonstrated that there is little or no evolution in the rate of major mergers with redshift.," Despite the large errors associated with calculating merger rates, we have demonstrated that there is little or no evolution in the rate of major mergers with redshift."1120 The maximum evolution permitted by the errors would only amount to increasing the merger rate by a factor of a few., The maximum evolution permitted by the errors would only amount to increasing the merger rate by a factor of a few.1121 Of greater significance. however. is our calculation of the redshift dependence on the characteristic time between mergers. L'(2).," Of greater significance, however, is our calculation of the redshift dependence on the characteristic time between mergers, $\Gamma(z)$."1122 This quantity decreases significantly with redshift., This quantity decreases significantly with redshift.1123 As such. in the early universe (z  3) there was a much shorter time between mergers than there is today.," As such, in the early universe (z $\sim$ 3) there was a much shorter time between mergers than there is today."1124" We derive the major merger fractions for massive (AZ, 10754.) galaxies in the GNS at two redshifts.", We derive the major merger fractions for massive $M_{*} > 10^{11} M_{\odot}$ ) galaxies in the GNS at two redshifts.1125" We find a merger fraction of fi, = 0.19 4/ 0.07 at z = 2.0 and f, = 0.40 44 0.10 at z = 2.6.", We find a merger fraction of $f_{m}$ = 0.19 +/- 0.07 at z = 2.0 and $f_{m}$ = 0.40 +/- 0.10 at z = 2.6.1126 This indicates. when compared to data from Conselice et al. (," This indicates, when compared to data from Conselice et al. ("11272007). De Propis et al. (,"2007), De Propis et al. ("11282007). and POWIR pair fractions (also calculated in this paper) in Fig.,"2007), and POWIR pair fractions (also calculated in this paper) in Fig."1129 2. that there is a strong correlation between merger fraction and redshift for the massive galaxies in our sample.," 2, that there is a strong correlation between merger fraction and redshift for the massive galaxies in our sample."1130" Furthermore. we fit à function of the form 2)"" to our data. and the data from Conselice et al. ("," Furthermore, we fit a function of the form $f_{m}=f_{0}(1+z)^{m}$ to our data, and the data from Conselice et al. ("1131"2007) at lower redshifts for AZ,z-101534. galaxies. finding a best fit to the two free parameters of: fi, = 0.008 +/- 0.003 and m = 3.0 +4 0.4.","2007) at lower redshifts for $M_{*} > 10^{11} M_{\odot}$ galaxies, finding a best fit to the two free parameters of: $f_{0}$ = 0.008 +/- 0.003 and $m$ = 3.0 +/- 0.4."1132 This indicates that the merger fraction for massive galaxies continues to increase out to z  3., This indicates that the merger fraction for massive galaxies continues to increase out to z $\sim$ 3.1133 This implies that more massive galaxies have higher numbers of mergers than less massive ones. since pevious work has found that the merger fraction for lower mass galaxies levels off and declines with increasing redshift in the range z ~~ 1.5 - 2.0 (Conselice et al.," This implies that more massive galaxies have higher numbers of mergers than less massive ones, since pevious work has found that the merger fraction for lower mass galaxies levels off and declines with increasing redshift in the range z $\sim$ 1.5 - 2.0 (Conselice et al."1134 2008)., 2008).1135 We calculate the major merger rate finding no significant evolution from dt « 5 10° Gpe* Gyrtat z= 2.6 to - L2. 10°  Gyr.tat z= 0.5., We calculate the major merger rate finding no significant evolution from $\Re$ $<$ 5 $\times$ $^{5}$ $^{-3}$ $^{-1}$ at z = 2.6 to $\Re$ $<$ 1.2 $\times$ $^{5}$ $^{-3}$ $^{-1}$ at z = 0.5.1136 Moreover. a steep evolution is ruled out.," Moreover, a steep evolution is ruled out."1137 We also calculate the evolution of the characteristic time between mergers L(>). finding a rapid decrease from ~ 12 Gyr at z =Oto ~ L5 Gyr at z = 3.," We also calculate the evolution of the characteristic time between mergers $\Gamma(z)$, finding a rapid decrease from $\sim$ 12 Gyr at z = 0 to $\sim$ 1.5 Gyr at z = 3."1138 This indicates that massive galaxies take onger between individual mergers in the local universe than at high z. but that there are more massive galaxies now than there were in he early universe. so. the rate remains constant.," This indicates that massive galaxies take longer between individual mergers in the local universe than at high z, but that there are more massive galaxies now than there were in the early universe, so, the rate remains constant."1139" By integrating over he best fit to this curve. we calculate the average number of major mergers a massive (A,10734.) galaxy would experience between z= 3 and z 2 0 is N,,, = 1.7 4+/- 0.5."," By integrating over the best fit to this curve, we calculate the average number of major mergers a massive $M_{*} > 10^{11} M_{\odot}$ ) galaxy would experience between z = 3 and z = 0 is $N_{m}$ = 1.7 +/- 0.5."1140 We would like to thank our collaborators on the GNS team. xirticularly Fernando Bruitrago and Ignacio Trujillo. for their work on this project and help in produeing this paper. and Samantha Penny for her assistance.," We would like to thank our collaborators on the GNS team, particularly Fernando Bruitrago and Ignacio Trujillo, for their work on this project and help in producing this paper, and Samantha Penny for her assistance."1141 We also gratefully acknowledge support rom the STFC., We also gratefully acknowledge support from the STFC.1142 REFERENCES Bell. E. Ε. et al..," REFERENCES Bell, E. F. et al.,"1143 2006. ApJ. 652. 270 Bruzual G. Charlot S.. 2003. MNRAS. 344. 1000 Bundy K. et al..," 2006, ApJ, 652, 270 Bruzual G. Charlot S., 2003, MNRAS, 344, 1000 Bundy K. et al.,"1144 2004. ApJL. 601. L123 Bundy K. et al..," 2004, ApJL, 601, L123 Bundy K. et al.,"1145 2006. ApJ. 651. 120 Carlberg R.. 1990. ApJ. 359. LI Conselice C. J.. 2003. ApJS. 147. | Conselice C. J.. 2006. Apt. 639. 120 Conselice C. J.. et al.," 2006, ApJ, 651, 120 Carlberg R., 1990, ApJ, 359, L1 Conselice C. J., 2003, ApJS, 147, 1 Conselice C. J., 2006, ApJ, 639, 120 Conselice C. J., et al."1146 2003. AJ. 126. 1183 Conselice C. 1.. et al.," 2003, AJ, 126, 1183 Conselice C. J., et al."1147 2007. MNRAS. 381. 962 Conselice C. 1.. et al.," 2007, MNRAS, 381, 962 Conselice C. J., et al."1148 2008. MNRAS. 386. 909 Conroy C.. Gunn J. E.. White M.. 2008. submitted to ApJ (arXiv:0809.4261C) Drory N.. 2005. ApJ. 619. L131 Daddi E. et al..," 2008, MNRAS, 386, 909 Conroy C., Gunn J. E., White M., 2008, submitted to ApJ (arXiv:0809.4261C) Drory N., 2005, ApJ, 619, L131 Daddi E. et al.,"1149 2007. Ap]. 670. 156," 2007, ApJ, 670, 156"1150In this section we use the selection criteria outlined. in Section 4 to test the predictions of the AAP function. Eq. 9..,"In this section we use the selection criteria outlined in Section 4 to test the predictions of the AAP function, Eq. \ref{aapfunction},"1151 using the distribution of subhalo pair angles measured in N-boely simulations., using the distribution of subhalo pair angles measured in N-body simulations.1152" The accuracy of this test relies on two Κον variables: the cosmological expansion history assumed. Lf(2) anc the normalizationMIN parameter. a=Ly1(te2Ap, "," The accuracy of this test relies on two key variables: the cosmological expansion history assumed, $H(z)$ and the normalization parameter, $\alpha = H^{-1}_0(\langle \Delta v^2_{\parallel}\rangle/\langle \Delta r^2\rangle)^{1/2}$."1153We consider the impact of uncertainties in each of these variables in turn., We consider the impact of uncertainties in each of these variables in turn.1154 In Section 5.1. we present the measure anisotropic distribution of the orientation of pairs. selectec according to the prescription set out in Section 4. and its firs moment at different redshifts together with the predictec distribution using the AAP function in a ACDAL and in two quintessence dark energy. cosmologies.," In Section \ref{sub3.1} we present the measured anisotropic distribution of the orientation of pairs, selected according to the prescription set out in Section 4, and its first moment at different redshifts together with the predicted distribution using the AAP function in a $\Lambda$ CDM and in two quintessence dark energy cosmologies."1155 In order to tes the ability of the theoretical model to distinguish cilleren cosmologies we will assume perfect knowledge of the correc fi(>) and à in the first instance., In order to test the ability of the theoretical model to distinguish different cosmologies we will assume perfect knowledge of the correct $H(z)$ and $\alpha$ in the first instance.1156 We then consider. how an observer would. measure à and the impact this has on the results. again assuming the correct /4(2).," We then consider how an observer would measure $\alpha$ and the impact this has on the results, again assuming the correct $H(z)$."1157 We relax the assumptions further in Section 5.2. where an incorrect cosmological expansion history is used to analyse the data., We relax the assumptions further in Section \ref{sub3.2} where an incorrect cosmological expansion history is used to analyse the data.1158 ‘This is done by measuring the distribution of subhaloes in the INV and SUCGILA. dark energy. simulations assuming a ACDAL cosmology to infer distances to the pair., This is done by measuring the distribution of subhaloes in the INV and SUGRA dark energy simulations assuming a $\Lambda$ CDM cosmology to infer distances to the pair.1159 We will show that the method. as implemented in 2.. fails to exclude the wrong cosmology.," We will show that the method, as implemented in \citet{2010Natur.468..539M}, fails to exclude the wrong cosmology."1160 Consequently. we propose a new method. which uses the theoretical mocel discussed so [ar but which exploits additional information about à from the numerical simulations.," Consequently, we propose a new method, which uses the theoretical model discussed so far but which exploits additional information about $\alpha$ from the numerical simulations."1161 In Section 5.3 we show that this method can be successfully applied to test dark energy., In Section 5.3 we show that this method can be successfully applied to test dark energy.1162 First of all. we test how the approach discussed in Section 2 can distinguish cdillerent. cosmiologies.," First of all, we test how the approach discussed in Section 2 can distinguish different cosmologies."1163 We put ourselves in the idealised. situation of an observer who knows the correct Cosmological model to compute distances. and. ds able to measure peculiar velocities precisely to find à at each redshift., We put ourselves in the idealised situation of an observer who knows the correct cosmological model to compute distances and is able to measure peculiar velocities precisely to find $\alpha$ at each redshift.1164 In. Fig., In Fig.1165 7 the mean of the redshift. space istributions of subhalo pairs for ACDAL ancl the two uintessence dark energy. models are plotted as a function X redshift., \ref{lcdminvsugra} the mean of the redshift space distributions of subhalo pairs for $\Lambda$ CDM and the two quintessence dark energy models are plotted as a function of redshift.1166 Phe results for ACDAL are the same as those garown in Fig., The results for $\Lambda$ CDM are the same as those shown in Fig.1167 6. for the lower resolution simulation., \ref{3b} for the lower resolution simulation.1168 The nmieasured. sample mean for the INV dark energy. model is ga1own as red-orange circles with error bars while the results for the SUGRA model are shown as green-grev. triangles., The measured sample mean for the INV dark energy model is shown as red-orange circles with error bars while the results for the SUGRA model are shown as green-grey triangles.1169 The predicted AAP function for cach ofthese models. using 10 Correct expansion history and the value for a measured at cach redshift. is shown as a solid red line for the INV model and a solid green. line for the SUGIUX model.," The predicted AAP function for each of these models, using the correct expansion history and the value for $\alpha$ measured at each redshift, is shown as a solid red line for the INV model and a solid green line for the SUGRA model."1170 The uncertainties on the AAP function are plotted. as a red shacled region for the INV mocdel., The uncertainties on the AAP function are plotted as a red shaded region for the INV model.1171 Phe errors for the SUGRA model are similar but are not plotted in Fig., The errors for the SUGRA model are similar but are not plotted in Fig.1172 7. for clarity., \ref{lcdminvsugra} for clarity.1173 Phe errors shown on both mocels for the measured mean and, The errors shown on both models for the measured mean and1174galaxies CE. Sab. Sbe. Sed. Sdm and sb) and 2 AGN.,"galaxies (E, Sab, Sbc, Scd, Sdm and sb) and 2 AGN."1175 At longer wavelengths (5.8 δα) any dust may significantly contribute or even dominate the observed emission.," At longer wavelengths $\rm 5.8 - 24 \, \mu m$ ) any dust may significantly contribute or even dominate the observed emission."1176 Before fitting models to hese wavelengths the stellar contribution is subtracted from the shotometric data by extrapolating the best-fit galaxy template from he previous step., Before fitting models to these wavelengths the stellar contribution is subtracted from the photometric data by extrapolating the best-fit galaxy template from the previous step.1177 The residuals are then fit with a mixture of four emplates: cirrus (2).. AGN dust tori (22).. M882 and 2220 starbursts (2)..," The residuals are then fit with a mixture of four templates: cirrus \citep{Efstathiou2003}, AGN dust tori \citep{rowan1995, Efstathiou1995}, 82 and 220 starbursts \citep{Efstathiou2000}."1178 The modeling above provides both information on he dominant emission mechanism in the optical and the infrared (AGN vs star-formation) and an estimate of the total infrared uminosity. {ος of our sample sources in the wavelength range 3 lI000//m.," The modeling above provides both information on the dominant emission mechanism in the optical and the infrared (AGN vs star-formation) and an estimate of the total infrared luminosity, $L_{TOT}$, of our sample sources in the wavelength range $\rm 3-1000\mu m$."1179 As discussed by ?. {ρω is expected to be accurate within a factor of two., As discussed by \cite{rowan2005} $L_{TOT}$ is expected to be accurate within a factor of two.1180 In this exercise the redshift is fixed to the spectroscopically determined value. if available (8/10 sources).," In this exercise the redshift is fixed to the spectroscopically determined value, if available (8/10 sources)."1181 For the two sources in the sample without spectroscopic redshifts we also estimate photometric redshifts. although we caution that these are likely to be uncertain because of their extreme optical/near-IR colours.," For the two sources in the sample without spectroscopic redshifts we also estimate photometric redshifts, although we caution that these are likely to be uncertain because of their extreme optical/near-IR colours."1182 From the spectroscopic sample we estimate that the fraction of catastrophic redshifts. defined as those with (2...tphotdzu] 0.15. is 38 per cent (3/8).," From the spectroscopic sample we estimate that the fraction of catastrophic redshifts, defined as those with $(z_{spec}-z_{phot})/(1+z_{spec})>0.15$ , is 38 per cent (3/8)."1183" The rms value of the quantity (255,2pber)£CldSupe). after excluding catastrophic failures. is 0.07 and provides an estimate of the accuracy of the photometric redshifts."," The rms value of the quantity $(z_{spec}-z_{phot})/(1+z_{spec})$, after excluding catastrophic failures, is 0.07 and provides an estimate of the accuracy of the photometric redshifts."1184 Figure 3. overplots the best-fit models to the observed SEDs of the red 2MASS sources., Figure \ref{fig_sed} overplots the best-fit models to the observed SEDs of the red 2MASS sources.1185 The derived parameters are presented in Table 3.., The derived parameters are presented in Table \ref{tab_restframe}.1186 In summary. the mid-IR SED of all sources is dominated by hot dust. which is fit by an AGN torus component.," In summary, the mid-IR SED of all sources is dominated by hot dust, which is fit by an AGN torus component."1187 An additional starburst template is required to fit the far-IR data of some sources in Table 3.., An additional starburst template is required to fit the far-IR data of some sources in Table \ref{tab_restframe}.1188 The optical part of the SED is fit with a reddened QSO template adopting the SMC extinction curve of ?.., The optical part of the SED is fit with a reddened QSO template adopting the SMC extinction curve of \cite{Richards2003}.1189 The derived optical extinctions are in the range ly=1[3. 320V)04 Ll., The derived optical extinctions are in the range $A_V=1.3-3.2$ $E(B-V) \approx 0.4-1.1$ ).1190 The nature of the red 2MASS sources is explored by combining information from the optical/near-IR spectroscopy and the broadband UV—to-far-IR photometry., The nature of the red 2MASS sources is explored by combining information from the optical/near-IR spectroscopy and the broadband UV–to–far-IR photometry.1191 There is strong evidence that all sources in the sample are powered by accretion on a central supermassive black hole., There is strong evidence that all sources in the sample are powered by accretion on a central supermassive black hole.1192 Firstly. for seven out of the eight sources for which optical and/or near-IR spectra are available. either from our own observations or from the literature. broad Balmer or Paschen emission lines are found with widths 71000 kkm/s. For more details on the spectroscopic properties of individual objects see the Appendix section.," Firstly, for seven out of the eight sources for which optical and/or near-IR spectra are available, either from our own observations or from the literature, broad Balmer or Paschen emission lines are found with widths $>1000$ km/s. For more details on the spectroscopic properties of individual objects see the Appendix section."1193 Additionally. the red 2MASS sources are luminous in the mid-IR and their SEDs at these wavelengths are fit by the hot dust AGN tori models of ?. and ?..," Additionally, the red 2MASS sources are luminous in the mid-IR and their SEDs at these wavelengths are fit by the hot dust AGN tori models of \cite{rowan1995} and \cite{Efstathiou1995}."1194 The total IR luminosity (3. 10007/n)) of this component is estimated in the range 10172.10 LehLoh4101ores 1) ie. exceeding the limit for either ULIRGs (Ultra-Luminous Infrared Galaxies) or HyLIRGs (Hyper-Luminous Infrared Galaxies).," The total IR luminosity $\rm 3-1000\mu m$ ) of this component is estimated in the range $\rm 10^{12}-10^{14}\, L_{\odot}$ $\rm 4 \times 10^{45} - 41195\times 10^{47}\, \rm erg \, s^{-1}$ ), i.e. exceeding the limit for either ULIRGs (Ultra-Luminous Infrared Galaxies) or HyLIRGs (Hyper-Luminous Infrared Galaxies)."1196 Adopting an AGN bolometric correction factor of Liuτμà3 (eg2). the luminosity interval above exceeds the limit Liu107erg/s. which is often used to differentiate luminous QSOs from Seyfert galaxies.," Adopting an AGN bolometric correction factor of $L_{bol}/L_{IR}\approx 3$ \citep[e.g][]{Risaliti_Elvis2004}, the luminosity interval above exceeds the limit $L_{bol}\ga \rm 10^{46}\,erg/s$, which is often used to differentiate luminous QSOs from Seyfert galaxies."1197 Therefore. in the following we refer to the sample of sources in Table | as 2MASS or red QSOs.," Therefore, in the following we refer to the sample of sources in Table \ref{tab_obs1} as 2MASS or red QSOs."1198 The red optical/near-IR colours of the 2MASS QSOs in Table | can be attributed to either an intrinsically red optical continuum (e.g. 2). synehrotron emission with a turnover frequency in the UV/optical part of the spectrum (e.g.2). or dust reddening.," The red optical/near-IR colours of the 2MASS QSOs in Table 1 can be attributed to either an intrinsically red optical continuum \citep[e.g.][] {Richards2003}, , synchrotron emission with a turnover frequency in the UV/optical part of the spectrum \citep[e.g.][]{Whiting2001} or dust reddening."1199 Each of these possibilities is discussed below., Each of these possibilities is discussed below.1200 Radio selected QSOs from the Parkes half-Jansky flat-spectrum sample (2). have a large spread in the optical/near-IR— colours. with the reddest objects having ὦA>Y (y.," Radio selected QSOs from the Parkes half-Jansky flat-spectrum sample \citep{Drinkwater1997} have a large spread in the optical/near-IR colours, with the reddest objects having $B-K>7$ \citep{Francis2000}."

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