ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 We compute all the corresponudiug likelihood profiles only for + aud. their iuterestiis properties. like the most likely value μαι the mean value μμ the standard deviation Aras of the rye. distributions. the skewuess aad t στον». Qvhich measures the departure from a Gaussian likelibood). Fie. 9..," We compute all the corresponding likelihood profiles only for $ r $ and their interesting properties, like the most likely value $ r_{max} $, the mean value $ r_{mean} $, the standard deviation $ \Delta r_{\max} $ of the $ r_{max} $ distributions, the skewness and the kurtosis, (which measures the departure from a Gaussian likelihood), Fig. \ref{probd}."3 We finally compute the CL. CL. an CL lower bounds for r.," We finally compute the CL, CL, and CL lower bounds for $ r $."4 The probabilities of detection of r are displaved in Fig. 10.., The probabilities of detection of $ r $ are displayed in Fig. \ref{probd2}.5 At the level 'OTCgrotnd residual equal to of the considered tov model. only a CL (o1 sigma) detection is very likeY.," At the level of foreground residual equal to of the considered toy model, only a CL (one sigma) detection is very likely."6 For a CL detection (two sigmas) the level of foreground residual should be reduced to of the cousidered tov uodel. or lower.," For a CL detection (two sigmas) the level of foreground residual should be reduced to of the considered toy model, or lower."7 Leusing actson the B-inodes as a contamination by transforming EAuodes iuto Danodoes., Lensing actson the B-modes as a contamination by transforming E-modes into B-modes.8 It i$ à frequency independent effect while residuals are frequency dependent., It is a frequency independent effect while residuals are frequency dependent.9 Leusiug weakens hesignal around 6~90 where the primordial peak but not iun the small (modes range where the reionization bump dominates., Lensing weakens thesignal around $ \ell \sim 90 $ where the primordial B-modes peak but not in the small $ \ell $ modes range where the reionization bump dominates.10 Ou the other haud foreground residuals are lavecr at σα (6 than at (6~90., On the other hand foreground residuals are larger at small $ \ell $ than at $ \ell \sim 90 $.11 απο] residuaIs and lensing affect the detection of D-1nodoes iu complementary wavs. with the effect of residuals stro1ecr han tha of lensing.," Namely, residuals and lensing affect the detection of B-modes in complementary ways, with the effect of residuals stronger than that of lensing."12 As a consequence. lensing plus residuals can spoil the detection of r even when residuals are assmec. at he level of the considered tov model.," As a consequence, lensing plus residuals can spoil the detection of $ r $ even when residuals are assumed at the level of the considered toy model."13 Ou the contrary. lensing in the absence of residuals still allow ucetection of r.," On the contrary, lensing in the absence of residuals still allows a detection of $ r $."14 For example. several MCMC simulations show that our lower bounds on r are not significantly affeced by lensing in the absence of foreground residuals.," For example, several MCMC simulations show that our lower bounds on $ r $ are not significantly affected by lensing in the absence of foreground residuals."15 Let us 1iake clear. at any vate. that lensing was not considered im he aualvsis ο ther detection probability iu Sect. 7?..," Let us make clear, at any rate, that lensing was not considered in the analysis of the $r-$ detection probability in Sect. \ref{143}."16 Finally.la it should be clear that if the theoretical σοκταλατ 7=ris) of the ΑΙ ΤΕ imodel is imposed on tre ΑΠΟΝΤΟ analysis.la r has always well defined lower bounds regardless of leusiic and/or residuals.," Finally, it should be clear that if the theoretical constraint $ r = r(n_s) $ of the $\Lambda$ $r$ T model is imposed on the MCMC analysis, $ r $ has always well defined lower bounds regardless of lensing and/or residuals."17 The forecasted probability of detecting r is base ou he statistics of the shape of the 7 -IHi«Jibood., The forecasted probability of detecting $ r $ is based on the statistics of the shape of the $r$ -likelihood.18 This sipe determines whether a detection of r cau be clainie wit ra given confidence level., This shape determines whether a detection of $ r $ can be claimed with a given confidence level.19 But real CAD experineuts cal observe only one saie: the observed ska., But real CMB experiments can observe only one sample: the observed sky.20 So. the possibility of inferring + from one single(albeit vory large) nauple depends on the sampe itself. aud therefore. whether k& will be or will be not detected depeuds aso of a quesloni On lick.," So, the possibility of inferring $ r $ from one single(albeit very large) sample depends on the sample itself, and therefore, whether $ r $ will be or will be not detected depends also of a question on luck."21 Th acdition. the restIts for niv skies prescuted im Sect.," In addition, the results for many skies presented in Sect."22 ??. show the consistency of our whole apxoach to determine , \ref{143} show the consistency of our whole approach to determine $ r $.23Finally. iu Sect.," Finally, in Sect."24 τω?) we consider the bias effect in the foreground residuals implemented as a linear perturbation affecting the Cys and explore how the cosmological parameter distributions are affected by the bias., \ref{efbias} we consider the bias effect in the foreground residuals implemented as a linear perturbation affecting the $ C_l'$ s and explore how the cosmological parameter distributions are affected by the bias.25 We implement two extreme casst dn case (1) the bias fluctuates randomly around zero aud in case (d) the bias fluctuates around a non-zero value. saving sienificautly non-zero.," We implement two extreme cases: in case (i) the bias fluctuates randomly around zero and in case (ii) the bias fluctuates around a non-zero value, staying significantly non-zero."26 In case (1) the cosmological parameters are practically unaffected while in case (ii) the peaks of the cosmological parameter distributions are shifted witin one or two signias of tlhe WALAP values., In case (i) the cosmological parameters are practically unaffected while in case (ii) the peaks of the cosmological parameter distributions are shifted within one or two sigmas of the WMAP values.27 Iu. partialar. ris uot auviore detected iu case 11).," In particular,$ r $ is not anymore detected in case (ii)."28 The best aud mean values reported here for r aud the other cosmological paraueters do not correspond to the true sky data but to uock skies generated from the AICAIC simulations as explaiuec above., The best and mean values reported here for $ r $ and the other cosmological parameters do not correspond to the true sky data but to mock skies generated from the MCMC simulations as explained above.29 Nevertheless. the deviatious between the best and the fiducial values are relevant iudicators for ras well as he lower aud upper bounds and the standard deviation.," Nevertheless, the deviations between the best and the fiducial values are relevant indicators for $ r $ as well as the lower and upper bounds and the standard deviation."30 The fact that the fiducial aud mean values of rave very close aud that Arg coincides with the mean value of the standard deviation of + indicate thatPlanck can provide detecfous of high quality., The fact that the fiducial and mean values of $ r $ are very close and that $ \Delta r_{\max} $ coincides with the mean value of the standard deviation of $ r $ indicate that can provide detections of high quality.31 More iu general. our results support the quest for D mode polarization iu fιο clnrent CAIB data and future 2oricuted polarization missionsunder study by both aud (deBernardisetal.2009:Dock 2006)..," More in general, our results support the quest for $B$ mode polarization in the current CMB data and future $B$oriented polarization missionsunder study by both and \citep{2009ExA....23....5D,2006AAS...209.4907B}. ."32" As discussed in the introuction. the effective theoryof inflation within the C-L approach gives precise order of magnitude estimates for fhe spectral iudex ο. the ratio of tensor to scalar fluctuations r aud the ruunius of the spectral iudex do,/dluk (Bovanovslsyetal. 2009)."," As discussed in the introduction, the effective theoryof inflation within the G-L approach gives precise order of magnitude estimates for the spectral index $ n_s $ , the ratio of tensor to scalar fluctuations $ r $ and the running of the spectral index $ dn_s/d \ln k $ \citep{reviu}. ."33. Within the coutext of tιο CEL effective theory of inflation. the work iu Bovanovskyetal. (2006)... (2008a).. Destrietal. (2008b).. Destrietal. (2009)... Bovanovslyctal.(2000). showed that:," Within the context of the G-L effective theory of inflation, the work in \citet{1sN}, , \citet{mcmc1}, , \citet{mcmc2}, , \citet{high}, , \citet{reviu} showed that:"34Orbital eccentricities of extrasolar giant planets can be surprisinglv large compared {ο (heir counterparts in (he solar svstem (see. e.g.. (he review bv Marcy. Cochran. Mavor 2000).,"Orbital eccentricities of extrasolar giant planets can be surprisingly large compared to their counterparts in the solar system (see, e.g., the review by Marcy, Cochran, Mayor 2000)."35 Figure 1. displays the distribution of eccentricities of 93 extrasolar planets. downloaded from the California and Carnegie Planet Search website (http://exoplanets.org)).," Figure \ref{histoecc} displays the distribution of eccentricities of 93 extrasolar planets, downloaded from the California and Carnegie Planet Search website )."36" Aside [rom those ""hot Jupiters"" whose eccentricities were likely clamped by tidal interactions wilh their central stags. most giant planets occupying stellocentric distances between ~0.2 and ~2 AU have eccenlricilies near 0.35. and a few have eccentricities ranging up to 0.93."," Aside from those “hot Jupiters” whose eccentricities were likely damped by tidal interactions with their central stars, most giant planets occupying stellocentric distances between $\sim$ 0.2 and $\sim$ 2 AU have eccentricities near 0.35, and a few have eccentricities ranging up to 0.93."37 A variety of mechanisms have been introduced to excite planetary eccentricities., A variety of mechanisms have been introduced to excite planetary eccentricities.38 These theories can be divided into three categories: those that rely on interactions between the planet and another point mass. be it a star or planet: those Chat rely on interactions between (he planet ancl the circumstellar disk from which that planet coalesced: aud “hybrid” theories that implicate both another body and the disk.," These theories can be divided into three categories: those that rely on interactions between the planet and another point mass, be it a star or planet; those that rely on interactions between the planet and the circumstellar disk from which that planet coalesced; and “hybrid” theories that implicate both another body and the disk."39 Nozai-resonant forcing bv a binary. stellar companion (llolnan. Touma. Tremaine 1997) and violent encounters between. (wo or more planets formed within close proximity (Rasio Ford 1996: Weidenschilling Marzari 1996: Ford. Havlickova. Rasio 2001: Marzari Weidenschilling 2002) belong in the first category.," Kozai-resonant forcing by a binary stellar companion (Holman, Touma, Tremaine 1997) and violent encounters between two or more planets formed within close proximity (Rasio Ford 1996; Weidenschilling Marzari 1996; Ford, Havlickova, Rasio 2001; Marzari Weidenschilling 2002) belong in the first category."40 In the second category. one of the most recent and inclusive studies is by Goldreich Sari (2002). who demonstrate that interactions between a planet and a disk at first-order Lindblad resonances can excite the planets eccentricity provided (hat eccentricitv. exceeds a threshold value.," In the second category, one of the most recent and inclusive studies is by Goldreich Sari (2002), who demonstrate that interactions between a planet and a disk at first-order Lindblad resonances can excite the planet's eccentricity provided that eccentricity exceeds a threshold value."41 In the third category. belongs the formation scenario proposed [or the planetary svstem GJ 376 (Marcy et al., In the third category belongs the formation scenario proposed for the planetary system GJ 876 (Marcy et al.42 2001: Lee Peale 2002): this scenario involves convergent orbital migration of (wo planets. followed by capture of these planets into a mean-molion resonance and continued migration within that resonance.," 2001; Lee Peale 2002); this scenario involves convergent orbital migration of two planets, followed by capture of these planets into a mean-motion resonance and continued migration within that resonance."43 This is a hybricl mechanism because the required planetary. migration is driven bv an underling disk. while each planets eccentricity is directly excited by the other planet.," This is a hybrid mechanism because the required planetary migration is driven by an underlying disk, while each planet's eccentricity is directly excited by the other planet."44 A different hybrid scenario mav have plaved ont for planet c in the svstem Upsilon Andromedae (Butler οἱ al., A different hybrid scenario may have played out for planet c in the system Upsilon Andromedae (Butler et al.45 1999: Chiang. Tabachnik. Tremaine 2001).," 1999; Chiang, Tabachnik, Tremaine 2001)."46 A primordial disk may have clirectly excited the eccenlricily of the outermost planet. d: secular interactions between d and ¢ could then have siphoned olf the eccentricity of the former to grow that of the latter (Chiang Murray 2002).," A primordial disk may have directly excited the eccentricity of the outermost planet, d; secular interactions between d and c could then have siphoned off the eccentricity of the former to grow that of the latter (Chiang Murray 2002)."47 As a bonus. (his mechanism can also explain the heretofore puzzling alignment of orbital apsides exhibited by c and d. This process has been explored both in the adiabatic (Chiang Murray 2002) ancl impulsive (Malhotra 2002) Iimits.," As a bonus, this mechanism can also explain the heretofore puzzling alignment of orbital apsides exhibited by c and d. This process has been explored both in the adiabatic (Chiang Murray 2002) and impulsive (Malhotra 2002) limits."48 Yet another hvbrid mechanism has been introduced by Chiang. Fischer. Thommes (2002. hereafter CFT). who point out that if two planets migrate within a circumstellar disk such (hat their orbital trajectories diverge. then their eccentricities can increase as the planets cross a series of mean-motion resonances.," Yet another hybrid mechanism has been introduced by Chiang, Fischer, Thommes (2002, hereafter CFT), who point out that if two planets migrate within a circumstellar disk such that their orbital trajectories diverge, then their eccentricities can increase as the planets cross a series of mean-motion resonances."49 The closer (he initial ratio of orbital periods, The closer the initial ratio of orbital periods50Since the edge-darkened 11 lobes are contained within the host galaxy. the relevant jet deceleration must take place therein and not far outside in the circumgalactie medium.,"Since the edge-darkened 1 lobes are contained within the host galaxy, the relevant jet deceleration must take place therein and not far outside in the circumgalactic medium."51 But what is the main source for entrainment in 118?, But what is the main source for entrainment in 1s?52 With dust masses between 10° and 10* MM... the IIs refmsxxxx;yabpaininosities) donotshowevidenee forimorcintecstellarinatter( ISMthanthe FR22shavingdustinussesbeticecilu? and 10? MM.. 22 in Haas et al.," With dust masses between $^{\rm 5}$ and $^{\rm 7}$ $_{\odot}$ the 1s \\ref{msxxxx_tab_luminosities}) ) do not show evidence for more matter (ISM) than the 2s having dust masses between $^{\rm 6}$ and $^{\rm53 9}$ $_{\odot}$ 2 in Haas et al."54 2004)., 2004).55 If the 22 dichotomy were due to deceleration of the jetsentrainment. then one would expect the 11s to be less affected. contrary to what is observed.," If the 2 dichotomy were due to deceleration of the jets, then one would expect the 1s to be less affected, contrary to what is observed."56 As one possible way out. the ISM in 22s has to be concentrated in à special geometry. e.g. avoiding a bi-cone. so that the jets are not so much affected.," As one possible way out, the ISM in 2s has to be concentrated in a special geometry, e.g. avoiding a bi-cone, so that the jets are not so much affected."57 Such an explanation. however. 1s questionable. since on HST images FR22s show more disturbed dust structures (de Koff et al.," Such an explanation, however, is questionable, since on HST images 2s show more disturbed dust structures (de Koff et al."58 2000). while 11s appear more regular.," 2000), while 1s appear more regular."59 Thus. that kind of presumably cool ISM. which we can infer via the dust emission. appears not to play a role for the jet entrainment.," Thus, that kind of presumably cool ISM, which we can infer via the dust emission, appears not to play a role for the jet entrainment."60 Current models have considered stellar wind material to be entrained., Current models have considered stellar wind material to be entrained.61 Such material. even if dusty. may be too marginal to show up in our SEDs. which are dominated by the entire dust content.," Such material, even if dusty, may be too marginal to show up in our SEDs, which are dominated by the entire dust content."62 In addition to stellar wind material in the giant elliptical hosts of 11 galaxies the themselves crossing the jet stream could contribute considerably to the material entrained., In addition to stellar wind material in the giant elliptical hosts of 1 galaxies the themselves crossing the jet stream could contribute considerably to the material entrained.63 As a rough estimate. assuming a Jet opening angle of 1* and that the 1077 stars of a giant elliptical galaxy are evenly distributed over the sphere. about 10°? stars lie on the jet trajectory. providing plenty of material. of the order of 10° ... for entrainment.," As a rough estimate, assuming a jet opening angle of $\degr$ and that the $^{\rm 12}$ stars of a giant elliptical galaxy are evenly distributed over the sphere, about $^{\rm 7-8}$ stars lie on the jet trajectory, providing plenty of material, of the order of $^{\rm 7-8}$ $_{\odot}$, for entrainment."64 Then. also the Owen-Ledlow effect can naturally be understood: More luminous hosts contain more starsS and have a larger velocity. dispersion: therefore. the chance that stars cross the jet stream and decelerate the jet increases with host luminosity.," Then, also the Owen-Ledlow effect can naturally be understood: More luminous hosts contain more stars and have a larger velocity dispersion; therefore, the chance that stars cross the jet stream and decelerate the jet increases with host luminosity."65 So far. however. it is not yet clear. what happens with a star approaching the Jet stream and whether a star would survive such an event (e.g. Bednarek Protheroe 1997).," So far, however, it is not yet clear, what happens with a star approaching the jet stream and whether a star would survive such an event (e.g. Bednarek Protheroe 1997)."66 Furthermore. if the dust traces the amount of ISM and if the warm MIR emitting dust indicates also whether there is much [SM in the central region. then. with regard to the more dusty 22s. the 11s suffer a lack of ISM fuel for the immediate accretion region.," Furthermore, if the dust traces the amount of ISM and if the warm MIR emitting dust indicates also whether there is much ISM in the central region, then, with regard to the more dusty 2s, the 1s suffer a lack of ISM fuel for the immediate accretion region."67 This suggests that the black holes of the 11s are fed at a lower accretion rate than those of the 22s., This suggests that the black holes of the 1s are fed at a lower accretion rate than those of the 2s.68 A similar conclusion was reached by Baum et al. (, A similar conclusion was reached by Baum et al. (691995) from the low emission-line luminosity of IIs.,1995) from the low emission-line luminosity of 1s.70 Our IR data of 3CR sources suggest that a combination of central as well as extended differences should be considered for explaining the 22 dichotomy., Our IR data of 3CR sources suggest that a combination of central as well as extended differences should be considered for explaining the 2 dichotomy.71 Furthermore. evolutionary effects could play a role. in the sense that the ΤΙ galaxies could be preferentially old AGN with starving black holes.," Furthermore, evolutionary effects could play a role, in the sense that the 1 galaxies could be preferentially old AGN with starving black holes."72 Since none of the 11 galaxies shows dust properties (like masses and temperatures) comparable to those found for the 22s and quasars. the results from our small randomly selected samples may be valid even more generally.," Since none of the 1 galaxies shows dust properties (like masses and temperatures) comparable to those found for the 2s and quasars, the results from our small randomly selected samples may be valid even more generally."73 Clearly. the phenomena leading to the 22 dichotomy are highly complex. and further data are required. before definite conclusions about these suggestions can be drawn.," Clearly, the phenomena leading to the 2 dichotomy are highly complex, and further data are required, before definite conclusions about these suggestions can be drawn."74 We thank the referee P. Wiita for his constructive suggestions., We thank the referee P. Wiita for his constructive suggestions.75 This work was supported by the Nordrhein-Westfillisehe Akademie der Wissenschaften., This work was supported by the Nordrhein-Westfällische Akademie der Wissenschaften.76is pzz2D(.J+1). and τι is the opacity of the material moving al velocity e (the latter measured in ')).,"is $\nu\approx2 B77(J+1)$, and $\tau_v$ is the opacity of the material moving at velocity $v$ (the latter measured in )."78 Assuming a beam filling factor of 1. the observed main-heam brightness temperature is related to the opacity by where J.C.T) is defined as In the optically thin limit. From (he observations of the emission in (he three transitions of CO il is possible to determine both the excitation temperature and column density of (he outflowing gas using Eqs.," Assuming a beam filling factor of 1, the observed main-beam brightness temperature is related to the opacity by where $J_r(\nu,T)$ is defined as In the optically thin limit, From the observations of the emission in the three transitions of CO it is possible to determine both the excitation temperature and column density of the outflowing gas using Eqs."79" and(3).. and taking Ti,=2.7 Nk. Figure 8. presents plots of the velocity inlegrated emission versus the J quantum number from the blueshifted and redshifted lobes ol both outflows and from the ambient gas."," and, and taking $T_{\rm bg}=2.7$ K. Figure \ref{fig-vels} presents plots of the velocity integrated emission versus the $J$ quantum number from the blueshifted and redshifted lobes of both outflows and from the ambient gas."80 The velocity intervals of integration lor the blueshifted and redshifted emission are [--40.222] and [73.14]|... respectively.," The velocity intervals of integration for the blueshifted and redshifted emission are $[-46,-22]$ and $[-3,14]$, respectively."81 The areas over Which (he emission has been spatially integrated [or the different outflow lobes are shown in Fie. 4.., The areas over which the emission has been spatially integrated for the different outflow lobes are shown in Fig. \ref{fig-outjet}.82" In the positions in which lobes overlap we assumed equal contributions [rom each lobe. except at offset position (Aa=4-20"" λὸ= 20"")) where we assumed that the contribution to the blueshifted emission Irom the NS and SE-NW outllows are in a 2:1 ratio."," In the positions in which lobes overlap we assumed equal contributions from each lobe, except at offset position $\Delta \alpha=+20$ $\Delta83\delta=+20$ ) where we assumed that the contribution to the blueshifted emission from the NS and SE-NW outflows are in a 2:1 ratio."84 Dashed lines show the results of the best [it to the observed integrated emission assuming optically thin conditions and filling factors ol 1., Dashed lines show the results of the best fit to the observed integrated emission assuming optically thin conditions and filling factors of 1.85 The derived CO column densiües and excitation temperatures are given in Table 2.., The derived CO column densities and excitation temperatures are given in Table \ref{param-vels}.86 The parameters for the ambient cloud were derived using the spectra observed at offset, The parameters for the ambient cloud were derived using the spectra observed at offset87of cach physical parameter can be followed closely. Lardeeetal.(1997)..,"of each physical parameter can be followed closely. \citet{hardee97num},"88 for example. investigate the KWH instability in jets by solving he dispersion relations for KL modes over a wide range ο perturbation frequencies.," for example, investigate the KH instability in jets by solving the dispersion relations for KH modes over a wide range of perturbation frequencies."89 However. these studies are [imied to the linear regime of the instability. while the evolution of stellar jets is very. much governed bv nonlinear phenomena (Bodoctal.1994).," However, these studies are limited to the linear regime of the instability, while the evolution of stellar jets is very much governed by nonlinear phenomena \citep{bodo94}."90.. Subsequent studies have followed the growth of the WIE instability. in jets using time-dependent numerical simulations., Subsequent studies have followed the growth of the KH instability in jets using time-dependent numerical simulations.91 Stoneetal.(1997). and Downes&Rav(1998).. to name just a few. impose linear perturbations onto an initially stable set-up to observe the behaviour of the instability into the non-linear regime and the elect it can have in stellar jets.," \citet{stone97} and \citet{downes98}, to name just a few, impose linear perturbations onto an initially stable set-up to observe the behaviour of the instability into the non-linear regime and the effect it can have in stellar jets."92 While many authors have investigated the role of the WI instability in general magnetised. ancl unmagnetise astrophysical [lows (e.g.Franketal.1996:Malagoliepensetal. 1999).. these studies have investigated the Wh instability in the context. of either hyedrodvnamics or idea maegnetohvdrodsnamies (ALD).," While many authors have investigated the role of the KH instability in general magnetised and unmagnetised astrophysical flows \citep[e.g.][]{frank96, mala96, 93hardee97num, downes98, keppens99}, these studies have investigated the KH instability in the context of either hydrodynamics or ideal magnetohydrodynamics (MHD)."94 These. assumptions are. however. not always valid. particularly in. weakly ionisec systems.," These assumptions are, however, not always valid, particularly in weakly ionised systems."95 For example. in molecular. clouds we know tha non-ideal ellects are important at length scales below abou ppc (e.g.Oishi&MacLow2006:Downes2009) and hence it is of interest to explore the KIL instability in the context of either non-icleal MILD or. preferably. fully multilluid MILD.," For example, in molecular clouds we know that non-ideal effects are important at length scales below about pc \citep[e.g.][]{ois06, downes09} and hence it is of interest to explore the KH instability in the context of either non-ideal MHD or, preferably, fully multifluid MHD."96 In recent. vears the emphasis of WL studies has turned to including non-ideal elfects., In recent years the emphasis of KH studies has turned to including non-ideal effects.97 Ixeppensetal.(1999). studied both the linear growth and subsequent. nonlinear saturation of the WIL instability usine resistive ΑΗ numerical simulations., \citet{keppens99} studied both the linear growth and subsequent nonlinear saturation of the KH instability using resistive MHD numerical simulations.98 The inclusion of diffusion allowed for magnetic reconnection ancl non-ideal cllects were observed. through caring instabilities and the formation of magnetic islands., The inclusion of diffusion allowed for magnetic reconnection and non-ideal effects were observed through tearing instabilities and the formation of magnetic islands.99 The case in support of using numerical diffusion in order ο simulate non-ideal MIID elfects was argued the following vear by Jeongetal.(2000).. as analogous to the similar oractice used to simulate non-icleal hycrodyvnaniuc Lows of veh Revnolds number.," The case in support of using numerical diffusion in order to simulate non-ideal MHD effects was argued the following year by \citet{jeong00}, as analogous to the similar practice used to simulate non-ideal hydrodynamic flows of high Reynolds number."100 Ark&Wieehen(2002) examined the case of a xwtiallv ionised clusty plasma. using a multilluid approach in which collisions could be included or ignored.," \citet{birk02} examined the case of a partially ionised dusty plasma, using a multifluid approach in which collisions could be included or ignored."101 Γον founc hat collisions between the neutral [uid and dust. particles could. lead. to the stabilisation of ILE modes of particular wavelengths., They found that collisions between the neutral fluid and dust particles could lead to the stabilisation of KH modes of particular wavelengths.102 Phe unstable modes lecl to a significant loca amplification of the magnetic field. strength. through the formation of vortices and current sheets., The unstable modes led to a significant local amplification of the magnetic field strength through the formation of vortices and current sheets.103 In the nonlinear regime they observed the magnetic [ux being redistribute by magnetic reconnection., In the nonlinear regime they observed the magnetic flux being redistributed by magnetic reconnection.104 It was suggested that this coul be applicable to dense molecular clouds and have importan implications for the magnetic Dux loss problem (Umoebavashi&Nakano 1990)., It was suggested that this could be applicable to dense molecular clouds and have important implications for the magnetic flux loss problem \citep{umebayashi90}.105. A comprehensive study was carried. out by. Wiechen(2006) which demonstrated the ellect of dealing with the plasma using a multifluid scheme., A comprehensive study was carried out by \citet{wiechen06} which demonstrated the effect of dealing with the plasma using a multifluid scheme.106 This study. focused. on the effect of varving the properties of the dust erains., This study focused on the effect of varying the properties of the dust grains.107 The results of the simulations led to the conclusions that more massive dust grains have a stabilising ellect on the svsteni while higher charged numbers have a destabilising elfect., The results of the simulations led to the conclusions that more massive dust grains have a stabilising effect on the system while higher charged numbers have a destabilising effect.108 Lt was found that there is no significant dependence on the charge polarity of the dust., It was found that there is no significant dependence on the charge polarity of the dust.109 Palottietal.(2008) also carried out a series. of simulations using resistive AILLD., \citet{palotti08} also carried out a series of simulations using resistive MHD.110" ""ον found that. following its initial growth. the WIL instability decays at a rate that decreases with decreasing plasma resistivity. at least within the range of resistivities accessible to their simulations."," They found that, following its initial growth, the KH instability decays at a rate that decreases with decreasing plasma resistivity, at least within the range of resistivities accessible to their simulations."111 μον also found that magnetisation increases the efficiency. of momenttun transport. and that the transport increases with decreasing resistivity.," They also found that magnetisation increases the efficiency of momentum transport, and that the transport increases with decreasing resistivity."112 In Jones&Downes(2011.henceforthPaper1). we examine the behaviour of the WIL instability in the presence of multilluid effects., In \citet[henceforth Paper I]{paper1} we examine the behaviour of the KH instability in the presence of multifluid effects.113 We found that. while the linear growth rates of the instability are unalfected by multilluid. effects. the non-linear behaviour was remarkably dillerent.," We found that, while the linear growth rates of the instability are unaffected by multifluid effects, the non-linear behaviour was remarkably different."114 The inclusion of ambipolar diffusion leads to the removal of large quantities of magnetic energy while the Llall effect. if strong enough. proved capable of introducing a dvnamo ellect.," The inclusion of ambipolar diffusion leads to the removal of large quantities of magnetic energy while the Hall effect, if strong enough, proved capable of introducing a dynamo effect."115 This leads to continuing strong growth of the magnetic field well into the non-linear regime and a lack of true saturation of 1ο instability., This leads to continuing strong growth of the magnetic field well into the non-linear regime and a lack of true saturation of the instability.116 In this paper we perform a numerical simulation of 16 complete evolution of the KI instability in a weakly ionised. multilluid. plasma as found in molecular clouds.," In this paper we perform a numerical simulation of the complete evolution of the KH instability in a weakly ionised, multifluid plasma as found in molecular clouds."117 We address the case of a shear laver with a transonic velocity ilference., We address the case of a shear layer with a transonic velocity difference.118 We choose a magnetic field. strength. typical of dense molecular clouds and this vields a velocity dillerence across the shear laver which is highly super-Alfvénnic (see section 2))., We choose a magnetic field strength typical of dense molecular clouds and this yields a velocity difference across the shear layer which is highly super-Alfvénnic (see section \ref{sec:num-setup}) ).119 It is worth noting here that the precise value of 1ο Alfvénn number is known to influence the evolution of the instability (e.g.Jonesetal.LOOT:Batyct2003).," It is worth noting here that the precise value of the Alfvénn number is known to influence the evolution of the instability \citep[e.g.][]{jones97, baty03}."120. Phe work here can be most directly compared to Case 4 of Jones(1997)... although it should be borne in mind that our boundary. conditions are slightly illerent.," The work here can be most directly compared to Case 4 of \citet{jones97}, although it should be borne in mind that our boundary conditions are slightly different."121 Phe. molecular ‘loud material is simulated by four. individual. [uids: a neutral I[uid. an electron. Duid. a positively charged. meta ion [uid and a EHuid of large. negatively charged cust grains.," The molecular cloud material is simulated by four individual fluids: a neutral fluid, an electron fluid, a positively charged metal ion fluid and a fluid of large, negatively charged dust grains."122 The non-ideal effects. of ambipolar diffusion and the Lal ellect are ineluded in the simulation. and their cllect on the inear development. saturation and subsequent behaviour of he instability is analysed in detail.," The non-ideal effects of ambipolar diffusion and the Hall effect are included in the simulation, and their effect on the linear development, saturation and subsequent behaviour of the instability is analysed in detail."123 The aim of this work is to investigate the erowth an saturation of the WIL instability under. the influence of he multifluic effects found in molecular clouds., The aim of this work is to investigate the growth and saturation of the KH instability under the influence of the multifluid effects found in molecular clouds.124 “Phe IW instability is of particular interest as a possible means of converting the ordered. energy. injected into the cloud. by »otostellar jets into the turbulent energy observed., The KH instability is of particular interest as a possible means of converting the ordered energy injected into the cloud by protostellar jets into the turbulent energy observed.125 In Paper ] we ran simulations with parameters chosen to simulate very high. medium and very low magnetic Itevnolds number systems and. with parameters chosen to ensure ambipolar-omünated [lows and Llall-clominated [lows in order to evelop a full understanding of the roles of each.," In Paper I we ran simulations with parameters chosen to simulate very high, medium and very low magnetic Reynolds number systems and with parameters chosen to ensure ambipolar-dominated flows and Hall-dominated flows in order to develop a full understanding of the roles of each."126 In this paper. we investigate the combined cllects of these two muttiflute effects on the instability under. parameters that describe the specific environment. of molecular clouds: and 'ompare these to roles plaved by cach on the development of the instability as studied in Paper L In doing so. we determine the behaviour of the instability in a physical application which. in practice. should. prove observable.," In this paper, we investigate the combined effects of these two multifluid effects on the instability under parameters that describe the specific environment of molecular clouds and compare these to roles played by each on the development of the instability as studied in Paper I. In doing so, we determine the behaviour of the instability in a physical application which, in practice, should prove observable."127 In section 2. we outline the multilluid. equations used bv the code for this analysis. the physical model. being simulated. and the computational parameters emploved.," In section \ref{sec:num-setup} we outline the multifluid equations used by the code for this analysis, the physical model being simulated, and the computational parameters employed."128 Ln section 3. we describe how the ability of the code to simulate the WII instability has been validated. in. both the cases of ideal ALD ancl in the presence of multilluid. effects.," In section \ref{sec:validation-numerics} we describe how the ability of the code to simulate the KH instability has been validated, in both the cases of ideal MHD and in the presence of multifluid effects."129 In, In130plot the density run of the latter (specifically for the a-profile with az1.25 suitable to galactic halos). compared to those of the Einasto. SE. and @NFW amodels.,"plot the density run of the latter (specifically for the $\alpha$ -profile with $\alpha\approx 1.25$ suitable to galactic halos), compared to those of the Einasto, SE, and gNFW models."131 The left and right paucls refer to isotropic and aulsotropic conditions. respectively: the popular NEW profile is also shown for reference.," The left and right panels refer to isotropic and anisotropic conditions, respectively; the popular NFW profile is also shown for reference."132 To make comparisons easier. we plot in the lower panels the correspondiug logarithmic deusitv slopes.," To make comparisons easier, we plot in the lower panels the corresponding logarithmic density slopes."133 It turus out that the closest approximation to the dvuiuuical mode is provide by SE. which shares with it not oulv the central slope ly construction. but also the body aud the outer behaviors.," It turns out that the closest approximation to the dynamical model is provided by SE, which shares with it not only the central slope by construction, but also the body and the outer behaviors."134 The original Eimasto profile provides an acceptable approximation iu the nmüddle aid outer ranges. but not at the center. because of its flatness.," The original Einasto profile provides an acceptable approximation in the middle and outer ranges, but not at the center, because of its flatness."135 On the other haud. the eNFW family provides an acceptable approximation iu the ner and middle ranges. but not in the outskirts where its slope is too flat.," On the other hand, the gNFW family provides an acceptable approximation in the inner and middle ranges, but not in the outskirts where its slope is too flat."136 Finalk. the NEW profile provides an acceptable approximation only in the muddle range.," Finally, the NFW profile provides an acceptable approximation only in the middle range."137 Similar couclusious concern the profi of circular velocities er)—GAr)ír. that are analvticallv dealt with in he Appendix and illustrated in Fie.," Similar conclusions concern the profiles of circular velocities $v_c^2(r)\equiv G\,M(<r)/r$, that are analytically dealt with in the Appendix and illustrated in Fig."138 2., 2.139 We stress that the handy SE representation is convenien in analyzing data iu several coutexts. including: the DAL particle annihilation signal expected from the Calactic Center (see Lapi ct al.," We stress that the handy SE representation is convenient in analyzing data in several contexts, including: the DM particle annihilation signal expected from the Galactic Center (see Lapi et al."140 2010a): rotation curves of dwiuf aud noriual spiral ealaxies (see Salucci et al., 2010a); rotation curves of dwarf and normal spiral galaxies (see Salucci et al.141 2007): individual and statistical properties of elliptical aud spiral ealaxies (see Cook ct al., 2007); individual and statistical properties of elliptical and spiral galaxies (see Cook et al.142 2009): strong and wea- eravitational leusiug (see Lapi οἳ al., 2009); strong and weak gravitational lensing (see Lapi et al.143 20090). currently observed iu clusters (e... Zitrin et al.," 2009b), currently observed in clusters (e.g., Zitrin et al."144 2010) and soon in massive elliptical galaxies (sec discussion by Dradac et al., 2010) and soon in massive elliptical galaxies (see discussion by Bradač et al.145 2009): N-rav e1aüdsslo- ποια the iutrachister plasima (sce Cavaliere ο+ al., 2009); X-ray emission from the intracluster plasma (see Cavaliere et al.146 2009: Fusco-Femiano et al., 2009; Fusco-Femiano et al.147 2009. Lapi et al.," 2009, Lapi et al."148 20105)., 2010b).149" We first stress that the dvuinical model (as well as its approxinations in terms of enipirical models) is in keeping with the basic features of standard DAL Ίνοι, its cold aud collisionless nature."," We first stress that the dynamical model (as well as its approximations in terms of empirical models) is in keeping with the basic features of standard DM, i.e., its cold and collisionless nature."150 Iu fact. it iniplies e)>0 for luge rD rosa behavior expected iu the outskirts for matter dominating the potential well.," In fact, it implies $\sigma_r^2(r)\rightarrow 0$ for large $r\gg r_{-2}$, a behavior expected in the outskirts for matter dominating the potential well."151 At the inner cud. with decreasing à we expect a2(r) to iuerease toward a maxima. corresponding o effective conversion of inflow kinetic iuto random cuerev.," At the inner end, with decreasing $r$ we expect $\sigma_r^2(r)$ to increase toward a maximum, corresponding to effective conversion of inflow kinetic into random energy."152 In fact. toward the center Jeans requires dlogadlogr=>GM(zr6r4 o hold as the eravitational force vanishes there. o the effect that o?(r)wonOh ," In fact, toward the center Jeans requires ${\rm d}\log153\sigma_r^2/{\rm d}\log r = \gamma-GM(<r)/r^2\rightarrow \gamma_a$ to hold as the gravitational force vanishes there, to the effect that $\sigma_r^2(r)\propto r^{\gamma_a}\rightarrow 0$."154"Conceruiue the nature of the DAL he boundary conditions at the center imply a finite. non zero pressure (and cherev density). while along collisional mean free path allows the oressure eradieut dp/dr to diverge,"," Concerning the nature of the DM, the boundary conditions at the center imply a finite, non zero pressure (and energy density), while along collisional mean free path allows the pressure gradient ${\rm d}p/{\rm155d}r$ to diverge."156 Conversely. with a short mean free path A the pressure eradieunt cannot diverge on scales +2Α. where a finite⋅⋅ 07⋅≻ and a flatter 5 apply.," Conversely, with a short mean free path $\lambda$ the pressure gradient cannot diverge on scales $r\ga \lambda$, where a finite $\sigma^2$ and a flatter $\gamma$ apply."157 In :fact. weakly collisional conditions have been proposed to explain the cored light profiles observed m many spheroidal galaxics (see Ostriker 2000).," In fact, weakly collisional conditions have been proposed to explain the cored light profiles observed in many spheroidal galaxies (see Ostriker 2000)."158 Ou approaching the ceuter of a galactic halo. oue expects the basic dynamical model from larec-scale Jeans equilibrium to be altered to an increasing degree by dynamics and/or cherectics related to barvous.," On approaching the center of a galactic halo, one expects the basic dynamical model from large-scale Jeans equilibrium to be altered to an increasing degree by dynamics and/or energetics related to baryons."159 These processes are specifically related to following issues: trausfor of energv/angular moment from barvous to DM during galaxy formation: scouring barvous by the cuerey feedback from central active galactic nuclei: any adiabatiec contraction of the barvons., These processes are specifically related to following issues: transfer of energy/angular momentum from baryons to DM during galaxy formation; scouring baryons by the energy feedback from central active galactic nuclei; any `adiabatic' contraction of the baryons.160" Such issues will be briefly discussed iu turi. with a warning that they cuter increasingly debated eromuds,"," Such issues will be briefly discussed in turn, with a warning that they enter increasingly debated grounds."161 Flatteuiug of the immer density profile may be caused by trausfer of energv and/or angular momentum from the barvous to the DAL during the ealaxy formation process (see EbZaunt et al., Flattening of the inner density profile may be caused by transfer of energy and/or angular momentum from the baryons to the DM during the galaxy formation process (see El-Zant et al.162 2001: Toni et al., 2001; Tonini et al.163 2006. Romano-Diaaz ct al.," 2006, Romano-Díaaz et al."164 2008)., 2008).165 Iu detail. upon transfer of tangential random motions from the barvous to au initiaIv isotropic DM structure. the deusitv in the inuer region 19 expected to behave as Clonini ct al.," In detail, upon transfer of tangential random motions from the baryons to an initially isotropic DM structure, the density in the inner region is expected to behave as (Tonini et al."166" 206) Thus for 3<0 the profile is flattened relative to the original 5,. down to the point o: developiug"," 2006) Thus for $\beta<0$ the profile is flattened relative to the original $\gamma_a$ , down to the point of developing"167compared to the model-atmosphere results.,compared to the model-atmosphere results.168" It’s unclear why the empirical results should show so much greater variation than the models, suggesting that this apparent trend may simply be an artefact of the small sample, or that some additional factor plays an unexpectedly important role."," It's unclear why the empirical results should show so much greater variation than the models, suggesting that this apparent trend may simply be an artefact of the small sample, or that some additional factor plays an unexpectedly important role."169" Baseline parameters of Tog=6113 K (Casagrandeetal. 2010),, logg=4.50, [M/H]=+0.03 (Sousaetal.2008),, vw,—2 !, £/H=1.25 were adopted to construct the reference model atmosphere and intensities for HD 209458."," Baseline parameters of $\Teff = 6113$ K \citep{Casagrande10}, , $\logg =1704.50$, $\MH = +0.03$ \citep{Sousa08}, $\vt = 2$ , $\lH = 1.25$ were adopted to construct the reference model atmosphere and intensities for HD 209458."171 Broad-band limb-darkening was calculated by assuming ‘top hat’ response functions for the photommetric passbands of the Knutsonetal. HST observations., Broad-band limb-darkening was calculated by assuming `top hat' response functions for the metric passbands of the \citeauthor{Knutson07} HST observations.172" The principal results are summarized in Table A2 Additional models were run for T;g=5913,6313; logg=42,48; (/H=0.5; u%=0,4kms‘; and [M/H]=—0.4,+0.4."," The principal results are summarized in Table \ref{tab:A2}173 Additional models were run for $\Teff = 5913, 6313$; $\logg = 4.2,1744.8$; $\lH = 0.5$; $\vt = 0, 4~\kms$; and $\MH = -0.4, +0.4$."175 These ranges allow for quite generous uncertainties in parameters for this well-studied system., These ranges allow for quite generous uncertainties in parameters for this well-studied system.176" The extremes in linear LDCs from the models are for the aand high-gravity models (numerically largest and smallest coefficients, respectively), and these models are used to illustrate plausible ‘error bars’ on the SPAM coefficients in Figs."," The extremes in linear LDCs from the models are for the and high-gravity models (numerically largest and smallest coefficients, respectively), and these models are used to illustrate plausible `error bars' on the SPAM coefficients in Figs."177 6 and 7.., \ref{fig:HD1} and \ref{fig:HD2}. .178 Fig., Fig.179 6 shows results for linear coefficients., \ref{fig:HD1} shows results for linear coefficients.180" The discrepancies between model-atmosphere and photommetric results already noted by Claret (2009;; see also Southworth2008)), on the basis of older persist in the new analysis."," The discrepancies between model-atmosphere and metric results already noted by \citeauthor{Claret09} \citeyear{Claret09}; see also \citealt{Southworth08}) ), on the basis of older persist in the new analysis."181 The comparison for quadratic coefficients is shown in Fig. 7.., The comparison for quadratic coefficients is shown in Fig. \ref{fig:HD2}.182 The variation with wavelength of both ui and u» coefficients is much less for the SPAM coefficients than is found empirically., The variation with wavelength of both $u_1$ and $u_2$ coefficients is much less for the SPAM coefficients than is found empirically.183" However, both sequences run almost parallel to the rotated wi axis, and agreement in the better-determined w» parameter is tolerable at all wavelengths."," However, both sequences run almost parallel to the rotated $w_1$ axis, and agreement in the better-determined $w_2$ parameter is tolerable at all wavelengths."184" In particular, for the ~678 nm passband, which is close to the effective wavelength of the results, the agreement is reasonably good, [(wi,we)=(0.234,0.385),(0.099,0.363) for SPAM and light-curve coefficients, respectively]."," In particular, for the $\sim$ 678 nm passband, which is close to the effective wavelength of the results, the agreement is reasonably good, $(w_1,w_2) = (0.234,0.385), (0.099,0.363)$ for SPAM and light-curve coefficients, respectively]."185 This is in contrast to the results for stars at similar effective temperatures (but is consistent with the result that it is the higher-gravity stars that show the best agreement between models and observations)., This is in contrast to the results for stars at similar effective temperatures (but is consistent with the result that it is the higher-gravity stars that show the best agreement between models and observations).186 Different methods of fitting a given limb-darkening law to a given model-atmosphere intensity distribution lead to quite different numerical coefficients., Different methods of fitting a given limb-darkening law to a given model-atmosphere intensity distribution lead to quite different numerical coefficients.187" Furthermore, the limb-darkening coefficients determined from photometry of exoplanetary transits are functions of impact parameter, and can't reliably be compared directly to any of the standard model-atmosphere characterizations."," Furthermore, the limb-darkening coefficients determined from photometry of exoplanetary transits are functions of impact parameter, and can't reliably be compared directly to any of the standard model-atmosphere characterizations."188" A more direct comparison can be made if the modelintensities are translated into observer space, through the medium of synthetic light-curves."," A more direct comparison can be made if the modelintensities are translated into observer space, through the medium of synthetic light-curves."189" The resulting synthetic-photometry/atmosphere-model (SPAM) limb-darkening coefficients are notsingle-valued, but be compared directly with empirical results."," The resulting synthetic-photometry/atmosphere-model (SPAM) limb-darkening coefficients are notsingle-valued, but be compared directly with empirical results."190bursts al very low flux levels.,bursts at very low flux levels.191 In Figure | we have plotted the cumulative +channel fluence. 37NFi(>ΕΙ} (the fIuence in channels 1 though 4. 20-1000 keV) for the 1293 GRBs in the BATSE 4B catalogue that have a reported [Iuence. as a function of 4d-channel (i.e. total) [Inence Fy.," In Figure 1 we have plotted the cumulative 4-channel fluence, $\sum NF_4(\ge F_4)$ (the fluence in channels 1 though 4, 20-1000 KeV) for the 1293 GRBs in the BATSE 4B catalogue that have a reported fluence, as a function of 4-channel (i.e. total) fluence $F_4$."192 Here the cumulative {hence is defined to be the sum of the fIuences in all bursts brighter than F. We also plot the cumulative 2-channel fluence (channels | and 2. 20 -100 IxeV) for the BATSE 4B catalogue as a [unction of the 2 channel (ence.," Here the cumulative fluence is defined to be the sum of the fluences in all bursts brighter than F. We also plot the cumulative 2-channel fluence (channels 1 and 2, 20 -100 KeV) for the BATSE 4B catalogue as a function of the 2 channel fluence."193" To assist the eve. we plot the cumulative {hence as 6,83UINFSC6:8F3) for the BATSE 2-channel fIuences. which expresses the simplilving assumption that the total {hence is 6.3 times (he 2-channel fIuence. F5."," To assist the eye, we plot the cumulative fluence as $6.8\sum NF_2(\ge 6.8F_2)$ for the BATSE 2-channel fluences, which expresses the simplifying assumption that the total fluence is 6.8 times the 2-channel fluence $F_2$."194 The bolometric correction [actor of 6.8 is motivated by the [act that it is (he average ratio of F1/F5 for the BATSE catalogue., The bolometric correction factor of 6.8 is motivated by the fact that it is the average ratio of $F_4/F_2$ for the BATSE catalogue.195 It can be seen that G.SF> is nearly a proxy for Fy. except that the ratio ΓιFo is somewhat higher (han 6.8 for verv bright bursts. which are probably seen head-on and therefore have harder (han average spectra. and also higher for short bursts. which have very low [Iuences. aud contribute sienilicantlv to the low-fluence population. (," It can be seen that $6.8 F_2$ is nearly a proxy for $F_4$, except that the ratio $F_4/F_2$ is somewhat higher than 6.8 for very bright bursts, which are probably seen head-on and therefore have harder than average spectra, and also higher for short bursts, which have very low fluences, and contribute significantly to the low-fluence population. ("196"That the ratio Fj/F» is lower in the range 10 0-10""erg/cni?s than at the extremes is consistent with the fact that moderate (ence bursts have softer spectra than the bright GRDB. as implied by the Amati relation.)","That the ratio $F_4/F_2$ is lower in the range $10^{-6}$ $10^{-5}$ $^2$ s than at the extremes is consistent with the fact that moderate fluence bursts have softer spectra than the bright GRB, as implied by the Amati relation.)"197 Also plotted is the cumulative fluence vs. fence as recorded by Swill (15-150 IxeV) lor 534 GRBs in the Swilt catalogue with (reported [Inence) as of Sept 1. 2010 as a function the Swilt-recorded (ence. $5NFLFL). with bolometric corrections of 3.15 and 1.5 (see figure caption ancl below).," Also plotted is the cumulative fluence vs. fluence as recorded by Swift (15-150 KeV) for 534 GRBs in the Swift catalogue with (reported fluence) as of Sept 1, 2010 as a function the Swift-recorded fluence, $\sum NF_s(\ge F_s)$, with bolometric corrections of 3.15 and 1.8 (see figure caption and below)."198 As Swift has a larger energv range than channels 12-2 of DATSE. it follows that the bolometrie correction to Swift-measured fInences must be less than 6.8.," As Swift has a larger energy range than channels 1+2 of BATSE, it follows that the bolometric correction to Swift-measured fluences must be less than 6.8."199 As the average (ence was ~3.15 times less than the average DATSE +channel fence. and Swilt sampled a fainter population on average. the bolometric correction should probably be less than 3.15.," As the average Swift-measured fluence was $\sim 3.15$ times less than the average BATSE 4-channel fluence, and Swift sampled a fainter population on average, the bolometric correction should probably be less than 3.15."200" Finally. we may argue that because Swift detects an allskv. equivalent of S40 bursts per vear and a total [lnence of 1.82x10 ""erg/cni? in 534 bursts. the implied allsky [lux is [840/534]xL.82107=2.9 ""erg/eni?v. Because Swift. with proper bolometrie correction. should detect a higher flux than the less sensitive DATSE. it follows that Swift should detect an allskv equivalent of at least 5.3x10. ""erg/eni?v. So the proper bolometrie correction must be at least 5.3/2.9—1.8."," Finally, we may argue that because Swift detects an allsky equivalent of 840 bursts per year and a total fluence of $1.82201\times 10^{-3}$ $^2$ in 534 bursts, the implied allsky flux is $[840/534 ] \times 1.82 \times 10^{-3} =2.9\times20210^{-3}$ $^2$ y. Because Swift, with proper bolometric correction, should detect a higher flux than the less sensitive BATSE, it follows that Swift should detect an allsky equivalent of at least $ 5.3 \times 10^{-3}$ $^2$ y. So the proper bolometric correction must be at least 5.3/2.9=1.8."203 It is clear trom Figure 1 that for any allowed choice of the Swill bolometric correction. the cumulative [ence plateaus al a fIuence of ~10 %ere/em?. which is three orders of magnitude from the minimum.," It is clear from Figure 1 that for any allowed choice of the Swift bolometric correction, the cumulative fluence plateaus at a fluence of $\sim20410^{-5}$ $^2$, which is three orders of magnitude from the minimum."205 Note that choosing the lower limit for the bolometric correction would move the plateau to the right slightly. (hus slightly shortening it. but it would also imply that the allsky [lux in Swift bursts is not senilicantlv higher than in BATSE bursts. which is what the long plateau signifies.," Note that choosing the lower limit for the bolometric correction would move the plateau to the right slightly, thus slightly shortening it, but it would also imply that the allsky flux in Swift bursts is not significantly higher than in BATSE bursts, which is what the long plateau signifies."206 To summarize. the cumulative {hence plateaus near ils maximum value at a (hence that," To summarize, the cumulative fluence plateaus near its maximum value at a fluence that"207galaxy growth and cosmic SFR.,galaxy growth and cosmic SFR.208" Owing to metal cooling, the SFR density increases about at z=3 and about at z=1."," Owing to metal cooling, the SFR density increases about at $z=3$ and about at $z=1$."209" Our results suggest that metal cooling enhances the star formation through two different processes: 1) more efficient conversion of local ISM into stars (i.e., increase of local SF efficiency), and 2) the increase of IGM accretion onto galaxies."," Our results suggest that metal cooling enhances the star formation through two different processes: 1) more efficient conversion of local ISM into stars (i.e., increase of local SF efficiency), and 2) the increase of IGM accretion onto galaxies."210" The former process is in effect essentially at all times at z<15, because the local ISM can be instantaneously enriched by SN explosions."," The former process is in effect essentially at all times at $z\lesssim 15$, because the local ISM can be instantaneously enriched by SN explosions."211" This process enhances the SFR, but does not noticeably change the total baryonic mass of galaxies."," This process enhances the SFR, but does not noticeably change the total baryonic mass of galaxies."212" The latter process, on the other hand, can increase the total baryonic mass of galaxies, as well as enhancing the overall SFR density by supplying more gas for star formation."," The latter process, on the other hand, can increase the total baryonic mass of galaxies, as well as enhancing the overall SFR density by supplying more gas for star formation."213" This process becomes effective only at lower redshifts (z< 3), because it takes some time to enrich the IGM up to Z107?Za."," This process becomes effective only at lower redshifts $z\lesssim 3$ ), because it takes some time to enrich the IGM up to $Z \gtrsim 10^{-2}\Zsun$."214" In this paper, we used two different prescriptions for star formation in the runs with metal cooling: 1) the ‘constant pin’ scheme and 2) the ‘varying pin’ scheme."," In this paper, we used two different prescriptions for star formation in the runs with metal cooling: 1) the `constant $\rhoth$ ' scheme and 2) the `varying $\rhoth$ ' scheme."215" The value of px, was fixed in the former scheme, while it was modulated according to the metallicity in the latter scheme."," The value of $\rhoth$ was fixed in the former scheme, while it was modulated according to the metallicity in the latter scheme."216" Both schemes show similar increase of cosmic SFR density (see Figure 2)), which implies that the overall SF enhancement by metal cooling is not so sensitive to the choice of pin (but with some differences as we discussedin 3.1))."," Both schemes show similar increase of cosmic SFR density (see Figure \ref{fig:sfr_N216L10}) ), which implies that the overall SF enhancement by metal cooling is not so sensitive to the choice of $\rhoth$ (but with some differences as we discussedin \ref{sec:cos_sfr}) )."217" The multiphase ISM model for star formation by Springel&Hernquist(2003a) contains two free parameters: pi and the normalisation of gas consumption time-scale, t$."," The multiphase ISM model for star formation by \citet{Springel.Hernquist:03} contains two free parameters: $\rhoth$ and the normalisation of gas consumption time-scale, $t_\star^0$ ."218For point sources detected αἱ 3.6 and 4.5 wwe find a total 3.6 [flux of 72.4 mJs.,For point sources detected at 3.6 and 4.5 we find a total 3.6 flux of 72.4 mJy.219 of this total flux is from AGB stars and RSGs. which is very similar to the case of WLAL where we found of the flux in point sources was [rom sources brighter than the TRGB.," of this total flux is from AGB stars and RSGs, which is very similar to the case of WLM, where we found of the flux in point sources was from sources brighter than the TRGB."220 The total flux in point sources we measure lor IC 1613 constitutes of the integrated 4.5 Iflux detected byLeeetal.(2006)., The total flux in point sources we measure for IC 1613 constitutes of the integrated 4.5 flux detected by\citet{lee06}.221. Following vanLoonetal.(2005) and adopting an age of the current super-TRGB stellar population of 2 Gyr we find a total stellar mass of {ιτκ 10*M..., Following \citet{van05} and adopting an age of the current super-TRGB stellar population of 2 Gyr we find a total stellar mass of $\times$ $^{7}$.222 This value is a factor of 2.6 higher than the 6.6x 105 eestimatecl by Leeοἱal.(2006)., This value is a factor of 2.6 higher than the $\times$ $^{6}$ estimated by \citet{lee06}.223. Because the vanLoonetal.(2005) method of measuring stellar mass assumes a single-aged stellar population aud is dependent on the age of that population. our stellar mass max be over-estimated since a number of stus above the TRGB in IC 1613 are likely RSGs vounger than 2 Gvr old.," Because the \citet{van05} method of measuring stellar mass assumes a single-aged stellar population and is dependent on the age of that population, our stellar mass may be over-estimated since a number of stars above the TRGB in IC 1613 are likely RSGs younger than 2 Gyr old."224 We present (thermal near-IR. photometry of IC. 1613., We present thermal near-IR photometry of IC 1613.225 These data are compared. with the opticalV andJ photometry of Udalskietal.(2001) and. we find that of the IR detected AGB stars are not detected in the optical and an additional of the AGDs are misidentified as sub-TRGB red giants., These data are compared with the optical and photometry of \citet{uda01} and we find that of the IR detected AGB stars are not detected in the optical and an additional of the AGBs are misidentified as sub-TRGB red giants.226 We show that the optical incompleteness fraction is very well correlated with the [3.6] [4.5] color. which indicates that the optically undetected AGB stars have been reddened by circumstellar material bevond the optical completeness limits.," We show that the optical incompleteness fraction is very well correlated with the $-$ [4.5] color, which indicates that the optically undetected AGB stars have been reddened by circumstellar material beyond the optical completeness limits."227 Our IR. photometry is also compared with the narrowband optical carbou star study of Albertetal.(2000) and we find their study detects of the total AGB population. and their caleulated ΟἱΝΤ ratio is based on of this population.," Our IR photometry is also compared with the narrowband optical carbon star study of \citet{alb00} and we find their study detects of the total AGB population, and their calculated C/M ratio is based on of this population."228 Further. the number of IR detected AGB stars we find for WLM in Jacksonetal.(2007) is in excellent agreement with the recent near-IR study of Valchevaetal. (2007).. who find a CM ratio of 0.58.," Further, the number of IR detected AGB stars we find for WLM in \citet{jac07} is in excellent agreement with the recent near-IR study of \citet{val07}, , who find a C/M ratio of 0.58."229axions.,axions.230 The mass of the axions necessary to fit this discrepancy was 8.5 meV. Later on. the analysis of additional ten years of observations provided a value of Πω=(2.3€1.4)x1078 s/s (Kepler et al.," The mass of the axions necessary to fit this discrepancy was 8.5 meV. Later on, the analysis of additional ten years of observations provided a value of $\dot{\Pi}_{\rm obs} = (2.3 \pm 1.4) \times 10^{-15}$ s/s (Kepler et al."231 2000). closer to the value predicted by the standard theory of evolution of white dwarfs.," 2000), closer to the value predicted by the standard theory of evolution of white dwarfs."232 A detailed seismological analysis (Corrsico et al., A detailed seismological analysis (Córrsico et al.233 2001) found a drift Ila=(3.9+2.3)x107 s/s. where the main sources of uncertainty were due to the mode identification. the mass of the star. the chemical profile and the effective temperature.," 2001) found a drift $\dot{\Pi}_{\rm model} = (3.9234\pm 2.3) \times 10^{-15}$ s/s, where the main sources of uncertainty were due to the mode identification, the mass of the star, the chemical profile and the effective temperature."235 This value suggested that it was no longer necessary to invoke axions to account for the observed cooling rate of white dwarfs. but at the same time the uncertainties were large enough to prevent ruling out their existence.," This value suggested that it was no longer necessary to invoke axions to account for the observed cooling rate of white dwarfs, but at the same time the uncertainties were large enough to prevent ruling out their existence."236 It is important to realize here that the values obtained with Eq. (4)), It is important to realize here that the values obtained with Eq. \ref{eqf}) )237 agreed well with those obtained from the accurate numerical calculations of Corrsico et al. (, agreed well with those obtained from the accurate numerical calculations of Córrsico et al. (2382001).,2001).239 A new analysis including additional five years of observations gave Π=3.57+0.82x107 s/s (Kepler et al., A new analysis including additional five years of observations gave $\dot{\Pi} = 3.57 \pm 0.82 \times 10^{-15}$ s/s (Kepler et al.240 2005). a value that overlaps with the theoretical values obtained by Cérrsico et al. (," 2005), a value that overlaps with the theoretical values obtained by Córrsico et al. ("2412001) and is marginally compatible with the axion luminosity obtained if the axion mass suggested by the luminosity function of white dwarfs. ~4 meV ts adopted.,"2001) and is marginally compatible with the axion luminosity obtained if the axion mass suggested by the luminosity function of white dwarfs, $\sim 4$ meV is adopted."242 Finally. in a recent release that includes yet another five years of observations. Kepler (2009) obtained Π=3.77x0.59107? s/s. Adopting the proper motion correction of Kepler et al. (," Finally, in a recent release that includes yet another five years of observations, Kepler (2009) obtained $\dot{\Pi} = 4.77 \pm 0.59 \times 10^{-15}$ s/s. Adopting the proper motion correction of Kepler et al. ("2432005). we obtain I1=4.07+0.61x107% s/s. a value that is consistent with the existence of the extra cooling term suggested by the luminosity function.,"2005), we obtain $\dot{\Pi} = 4.07 \pm 0.61 \times 10^{-15}$ s/s, a value that is consistent with the existence of the extra cooling term suggested by the luminosity function."244 Figure 1. displays the evolution of the measured value of Il with time., Figure \ref{fig} displays the evolution of the measured value of $\dot\Pi$ with time.245 The jumps between the different observational values reflect the introduction of corrections. like the proper motion correction. and the fact that the phase of the periodicity is affected by a jitter caused by low-amplitude modes. contamination by GII7-BISB. the companion star. use of different telescopes and apertures...that are not well understood yet (Kepler. private communication).," The jumps between the different observational values reflect the introduction of corrections, like the proper motion correction, and the fact that the phase of the periodicity is affected by a jitter caused by low-amplitude modes, contamination by G117–B15B, the companion star, use of different telescopes and that are not well understood yet (Kepler, private communication)."246 Table | displays the axion luminosity and mass necessary to fit the observations when several white dwarf pulsational models are adopted (the values in brackets correspond to the observational uncertainties)., Table \ref{tabg} displays the axion luminosity and mass necessary to fit the observations when several white dwarf pulsational models are adopted (the values in brackets correspond to the observational uncertainties).247 The values of the first row. labeled model C. were obtained using Eq. (4)).," The values of the first row, labeled model C, were obtained using Eq. \ref{eqf}) ),"248 the model of GI17— that best fits the data (Corrsico et al., the model of G117--B15A that best fits the data (Córrsico et al.249 2001) and the previously mentioned axion emission rates of Nakagawa et al. (, 2001) and the previously mentioned axion emission rates of Nakagawa et al. (2501987: 1988).,1987; 1988).251 It is important to realize here that in a completely independent analysis. Bischoff-Kim et al. (," It is important to realize here that in a completely independent analysis, Bischoff-Kim et al. ("252"2008) identified two possible asteroseismological models of G117-B15À. one with a thin hydrogen envelope and the other with a relatively thick hydrogen envelope. with Π2.2.980.17x107% s/s and 1.92+0.26x107"" s/s. respectively.","2008) identified two possible asteroseismological models of G117–B15A, one with a thin hydrogen envelope and the other with a relatively thick hydrogen envelope, with $\dot{\Pi} = 2.98 \pm 0.17 \times 10^{-15}$ s/s and $1.92\pm 0.26 \times 10^{-15}$ s/s, respectively."253 Both values are smaller than the measured ones and indicate that an additional sink of energy Is necessary., Both values are smaller than the measured ones and indicate that an additional sink of energy is necessary.254 Table | shows the luminosity and the mass of the axions necessary to account for the most recent data of Kepler (2009) assuming a temperature of the core of T.=2x10! K in both cases.," Table \ref{tabg} shows the luminosity and the mass of the axions necessary to account for the most recent data of Kepler (2009) assuming a temperature of the core of $T_{\rm255c}=1.2\times 10^7$ K in both cases."256 Recently. Mukadam et al. (," Recently, Mukadam et al. ("2572009) analyzed R 548 (ZZ Ceti itself) and found that its mass lies between 0.55 and 0.58Moe. while the mass of the hydrogen envelope is logMj=—-5.0 and that the best prediction for the rate of change of the period is II=(8.3+0.046)x107P s/s. These results are fully consistent with the values obtained for GII7-BI5A and with those displayed in Table 1..,"2009) analyzed R 548 (ZZ Ceti itself) and found that its mass lies between 0.55 and $0.58\, M_{\sun}$, while the mass of the hydrogen envelope is $\log M_{\rm H}\simeq -5.0$ and that the best prediction for the rate of change of the period is $\dot{\Pi} =(8.3 \pm 0.046) \times 10^{-15}$ s/s. These results are fully consistent with the values obtained for G117–B15A and with those displayed in Table \ref{tabg}."258 The pulsation properties of DBV stars can provide an additional test to the axion hypothesis., The pulsation properties of DBV stars can provide an additional test to the axion hypothesis.259 Since these stars have a hotter core than that of DA white dwarfs. the neutrino luminosity can no longer be neglected.," Since these stars have a hotter core than that of DA white dwarfs, the neutrino luminosity can no longer be neglected."260 and the influence of axions on the pulsation period drift is smaller than. that expected for DA white dwarfs., and the influence of axions on the pulsation period drift is smaller than that expected for DA white dwarfs.261" For instance. a DB white dwarf of M~0.59Mo. an effective temperature 74;~25200 K and a core temperature log7,=7.61 has a luminosity of L~6.3x107Lc, and a neutrino luminosity L,5.1x107Lo."," For instance, a DB white dwarf of $ M \sim 0.59\, M_{\sun}$, an effective temperature $T_{\rm eff}\sim 25\,200$ K and a core temperature $\log T_{\rm c} =2627.61$ has a luminosity of $L \sim 6.3 \times 10^{-2}\, L_{\sun}$ and a neutrino luminosity $L_\nu \sim 5.1 \times 10^{-2}\,L_{\sun}$."263" If an axion mass of 5 meV ts assumed. the axion luminosity amounts La,=6.0x107Le and the corresponding secular change of the pulsation period would be Note that because of the strong dependence of the different luminosities on the core temperature. this prediction is very sensitive to the position in the instability strip and on the particular parameters of the star under study."," If an axion mass of 5 meV is assumed, the axion luminosity amounts $L_{\rm264 ax} = 6.0 \times 10^{-2}\, L_{\sun}$ and the corresponding secular change of the pulsation period would be Note that because of the strong dependence of the different luminosities on the core temperature, this prediction is very sensitive to the position in the instability strip and on the particular parameters of the star under study."265 The only case of DB variable white dwarf that is currently being studied i5 EC20058-5234 (Sullivan 2009). but unfortunately a rate of period change ts not yet available for this star.," The only case of DB variable white dwarf that is currently being studied is EC20058–5234 (Sullivan 2009), but unfortunately a rate of period change is not yet available for this star."266 It has been shown that white dwarf variable GI17-BISAs present value of the secular rate of change of the period of pulsation. 4.07+0.61x107? s/s (Kepler 2009). is consistent with the predictions of the theoretical models. as was anticipated by [sern et al. (," It has been shown that white dwarf variable G117–B15As present value of the secular rate of change of the period of pulsation, $4.07 \pm 0.61 \times 10^{-15}$ s/s (Kepler 2009), is consistent with the predictions of the theoretical models, as was anticipated by Isern et al. ("2671992). if an additional source of cooling like axion emission its included.,"1992), if an additional source of cooling like axion emission is included."268 This result is corroborated by the completely independent analysis of the same star done by Bischoff-Kim et al. (, This result is corroborated by the completely independent analysis of the same star done by Bischoff-Kim et al. (2692008). using the measured rate of period change (3.5740.82107 s/s) obtained previously (Kepler et al.,"2008), using the measured rate of period change $3.57 \pm 0.82 \times27010^{-15}$ s/s) obtained previously (Kepler et al."271 2005)., 2005).272 This means that the conclusion of Cérrsico et al. (, This means that the conclusion of Córrsico et al. (2732001) that 1t was unnecessary to introduce an additional cooling source is no longer valid when the new observational data are taken into account.,2001) that it was unnecessary to introduce an additional cooling source is no longer valid when the new observational data are taken into account.274 This is an important result. as asteroseismological observations of white dwarfs seem to give additional and independent support to the claim of Isern et al. (," This is an important result, as asteroseismological observations of white dwarfs seem to give additional and independent support to the claim of Isern et al. ("2752008: 2009) that the white dwarf luminosity function is better fitted if an additional cooling provided by axions with a mass of a few meV is included in the calculations.,2008; 2009) that the white dwarf luminosity function is better fitted if an additional cooling provided by axions with a mass of a few meV is included in the calculations.27622 pc. respectively.,"22 pc, respectively."277 For high signal-to-noise objects (typically S/N> 30). one can reliably measure 5j down to 0.1 pix. Le. ~2 pe.," For high signal-to-noise objects (typically $S/N \gtrsim 30$ ), one can reliably measure $r_{\mathrm{h}}$ down to 0.1 pix, i.e. $\sim 2$ pc."278 Therefore. it is feasible to measure sizes for extended objects (such as UCDs and bright GCs) from the WFPC2 frames.," Therefore, it is feasible to measure sizes for extended objects (such as UCDs and bright GCs) from the WFPC2 frames."279 To measure the half-light radi 54 of the 26 spectroscopically confirmed objects. we generated ten times sub-sampled PSFs with TinyTim for F555W.," To measure the half-light radii $r_{\mathrm{h}}$ of the 26 spectroscopically confirmed objects, we generated ten times sub-sampled PSFs with TinyTim for $F555W$."280 Each PSF was tailored to the position of the object on the chip., Each PSF was tailored to the position of the object on the chip.281 Utihizirisi the task of the software (?).. this PSF was used to model the object profile as an analytical function convolved with the (model) PSF.," Utilizing the task of the software \citep{1999A&AS..139..393L}, this PSF was used to model the object profile as an analytical function convolved with the (model) PSF."282 When sub-sampling is enabled. TinyTim does not include a convolution with the charge diffusion kernel (CDK). which additionally smears the stellar PSF.," When sub-sampling is enabled, TinyTim does not include a convolution with the charge diffusion kernel (CDK), which additionally smears the stellar PSF."283 Thus. during fitting withishape.. the TinyTim PSF was convolved with a F555W CDK. that simulates blurring caused by charge diffusion which is well understood for the F555W filter.," Thus, during fitting with, the TinyTim PSF was convolved with a $F555W$ CDK, that simulates blurring caused by charge diffusion which is well understood for the $F555W$ filter."284 All objects were modelled with ? profiles with concentrations of the tidal-to-core radius of ο=5.15.30 and 100.," All objects were modelled with \citet{1962AJ.....67..471K} profiles with concentrations of the tidal-to-core radius of $r_{\mathrm{t}}/r_{\mathrm{c}}=5, 15, 30$ and 100."285 We adopted the structural parameter measurements from the best y7 fit model., We adopted the structural parameter measurements from the best $\chi^2$ fit model.286" The output 7j is the η, along the semi-major axis which needs to be corrected for ellipticity and brought to the geometrical mean value effective” 5) by multiplying the square root of the major/minor axis ratio (fordetailsseee.g.Eq.Iin 2).."," The output $r_{\mathrm{h}}$ is the $r_{\mathrm{h}}$ along the semi-major axis which needs to be corrected for ellipticity and brought to the geometrical mean value (""effective"" $r_{\mathrm{h}}$ ) by multiplying the square root of the major/minor axis ratio \citep[for details see e.g. Eq.~1 in][]{2008AJ....135.1858G}."287 Table 2 lists the photometric and structural. properties of the 26 cluster GCs/UCDs., Table \ref{tab:hstucds} lists the photometric and structural properties of the 26 cluster GCs/UCDs.288 The V; magnitudes derived from the HST images are. on average. 0.2-0.4 mag fainter than those measured in the VIMOS pre-images.," The $V_0$ magnitudes derived from the HST images are, on average, 0.2–0.4 mag fainter than those measured in the VIMOS pre-images."289 Reasons for this discrepancy likely include the uncertainty in the VIMOS photometric zeropoints (no photometric standard was taken at the night of the pre-imaging). the different magnitude measurement techniques. and the uncertainty in the magnitude transformation of the HST data.," Reasons for this discrepancy likely include the uncertainty in the VIMOS photometric zeropoints (no photometric standard was taken at the night of the pre-imaging), the different magnitude measurement techniques, and the uncertainty in the magnitude transformation of the HST data."290consideration.,consideration.291 The instability is argued to be a consequence of the reduction of turbulent hydromagnetic pressure by a mean magnetic field and can be understood as follows (Kleeorinetal. 1996)., The instability is argued to be a consequence of the reduction of turbulent hydromagnetic pressure by a mean magnetic field and can be understood as follows \citep{KMR96}.292. The combined Reynolds and Maxwell stress is ρα| O;b?/29.. where tw and b are velocity and magneticbjbifpg fluctuations. respectively. and overbars indicate. averaging.," The combined Reynolds and Maxwell stress is $\overline{\rho u_i u_j}293-\overline{b_i b_j}/\mu_0+\delta_{ij}\overline{\bb^2}/2\mu_0$ , where $\uu$ and $\bb$ are velocity and magnetic fluctuations, respectively, and overbars indicate averaging."294" For isotropic. turbulence. the turbulent hydromagnetie pressure is then Zu,|02/259)."," For isotropic turbulence, the turbulent hydromagnetic pressure is then $\Pturb={\textstyle{1\over3}}(\overline{\rho \uu^2}295+\overline{\bb^2}/2\mu_0)$."296" On the other hand. the total turbulent= περαenergy £L,=l(pu?|b? μι). is nearly conserved because a uniform mean magnetic field does not perform any work: see Brandenburgetal.(2010). for a numerical demonstration."," On the other hand, the total turbulent energy $E_{\rm turb} \equiv \half(\overline{\rho\uu^2}+\overline{\bb^2}/\mu_0)$ , is nearly conserved because a uniform mean magnetic field does not perform any work; see \cite{BKR10} for a numerical demonstration."297 The presence of an additional 1/2 factor in front of the 52/1 term in the for πηγη. but not in that for Z4. implies that the expressiongeneration of magnetic fluctuations results in a reduction of Pause. Phu=b?/241y).," The presence of an additional 1/2 factor in front of the $\overline{\bb^2}/\mu_0$ term in the expression for $\Pturb$, but not in that for $E_{\rm turb}$ ,implies that the generation of magnetic fluctuations results in a reduction of $\Pturb$, $\Pturb={\textstyle{1\over3}}(2E_{\rm turb}-\overline{\bb^2}/2\mu_0)$."298 For anisotropic turbulence this negative οcontribution becomes larger., For anisotropic turbulence this negative contribution becomes larger.299 This physical effect is independent of stratification. but to obtain an instability one needs strong stratification.," This physical effect is independent of stratification, but to obtain an instability one needs strong stratification."300 We speculate that. in the solar context. NEMPI plays a role in formation of active regions from mean fields generated by the solar dynamo.," We speculate that, in the solar context, NEMPI plays a role in formation of active regions from mean fields generated by the solar dynamo."301 Let us now ask whether this instability alone can deseribe the formation of active regions at the solar surface., Let us now ask whether this instability alone can describe the formation of active regions at the solar surface.302 Clearly. the flux concentrations we observe are not strong enough to be noticeable without averaging. while the active regions in the Sun are seen without averaging.," Clearly, the flux concentrations we observe are not strong enough to be noticeable without averaging, while the active regions in the Sun are seen without averaging."303 This suggests that there may be additional mechanisms at work., This suggests that there may be additional mechanisms at work.304 One possibility is that of the magnetic suppression of the convective heat flux that has been invoked to explain the formation of sunspots (Kitchatinov&Mazur2000)., One possibility is that of the magnetic suppression of the convective heat flux that has been invoked to explain the formation of sunspots \citep{KM00}.305 When the mean magnetic field becomes larger than the equipartition field strength. ie.. when NEMPI does not work. and the characteristic spatial scale of the magnetic field is smaller than the density height. it is instead the Parker magnetic buoyancy instability (Parker1966) that is excited.," When the mean magnetic field becomes larger than the equipartition field strength, i.e., when NEMPI does not work, and the characteristic spatial scale of the magnetic field is smaller than the density height, it is instead the Parker magnetic buoyancy instability \citep{Par66} that is excited."306 The presence of a vertical field might also have a strong effect., The presence of a vertical field might also have a strong effect.307 Indeed simulations of convection with an imposed vertical field have produced a segregation into magnetized and (Taoetal.1998:Kitiashvillal.2010) with. unmagnetizedformationregions of flux concentrations. strorΠα» to be noticeable even without averaging.," Indeed simulations of convection with an imposed vertical field have produced a segregation into magnetized and unmagnetized regions \citep{Tao98,KKWM10} with formation of flux concentrations strong enough to be noticeable even without averaging."308 On the other enoughhand NEMPI might become more powerful at stronger stratification., On the other hand NEMPI might become more powerful at stronger stratification.309 Increased stratification clearly has an enhancing effect on the growth rate (Kemeletal.2011).. but the effect on the saturation level has not yet been quantified.," Increased stratification clearly has an enhancing effect on the growth rate \citep{KBKR11}, but the effect on the saturation level has not yet been quantified."310 Furthermore. the interplay between NEMPI and the other effects also needs to be investigated.," Furthermore, the interplay between NEMPI and the other effects also needs to be investigated."311 Our work has established a close link between what can be expected from mean-field studies and what actually happens in DNS., Our work has established a close link between what can be expected from mean-field studies and what actually happens in DNS.312 This correspondence ids particularly important because DNS cannot reach solar parameters in any conceivable future., This correspondence is particularly important because DNS cannot reach solar parameters in any conceivable future.313 Hence a deeper understanding of solar convection can only emerge by studying mean-field models on the one hand and to determine turbulent mean-field coefficients from simulations on the other hand., Hence a deeper understanding of solar convection can only emerge by studying mean-field models on the one hand and to determine turbulent mean-field coefficients from simulations on the other hand.314 This concerns not only the dependence of the mean-field coefficients on parameters such as magnetic Reynolds and Prandtl numbers and scale separation ratio. but also the details of the source of turbulence.," This concerns not only the dependence of the mean-field coefficients on parameters such as magnetic Reynolds and Prandtl numbers and scale separation ratio, but also the details of the source of turbulence."315 In particular. 1t has already been shown that the negative effective magnetic. pressure effect is not unique to forced turbulence. but it also occurs in turbulent convection Kápylietal.(2011).. and thus in an unstably stratified layer.," In particular, it has already been shown that the negative effective magnetic pressure effect is not unique to forced turbulence, but it also occurs in turbulent convection \cite{KBKMR11}, and thus in an unstably stratified layer."316 We emphasize that the present work demonstrates the predictive power of mean-field theory at an advanced level where theory fails (Rüdigeretal.2011) but the spectralquasi-Iinear 7 approach (Rogachevskit&Kleeorin2007) has proven useful.," We emphasize that the present work demonstrates the predictive power of mean-field theory at an advanced level where quasi-linear theory fails \citep{RKS11}317 but the spectral $\tau$ approach \citep{RK07} has proven useful."318 More work using mean-field models ts needed to elucidate details of the mechanism of NEMPI., More work using mean-field models is needed to elucidate details of the mechanism of NEMPI.319 For example. naive thinking suggests that the onset of NEMPI should occur at the depth where the effective magnetic pressure is minimum. but both mean-field models and DNS show that this is not the case.," For example, naive thinking suggests that the onset of NEMPI should occur at the depth where the effective magnetic pressure is minimum, but both mean-field models and DNS show that this is not the case."320 At least at early times. NEMPI appears most pronounced at the top of the domain. while the effective magnetic pressure is usually most negative at the bottom.," At least at early times, NEMPI appears most pronounced at the top of the domain, while the effective magnetic pressure is usually most negative at the bottom."321 On the other hand. the instability is a global one and local considerations such as these are not always meaningful.," On the other hand, the instability is a global one and local considerations such as these are not always meaningful."322 Another question is what happens when the imposed field is replaced by à dynamo-generated one., Another question is what happens when the imposed field is replaced by a dynamo-generated one.323 In that case. the turbulence may be helical and new terms involving current density can occur in the expression for the mean-field stress.," In that case, the turbulence may be helical and new terms involving current density can occur in the expression for the mean-field stress."324 Again. such possibilities are best studied using first the mean-field approach.," Again, such possibilities are best studied using first the mean-field approach."325 We acknowledge the NORDITA dynamo programs of 2009 and 2011 for providing a stimulating scientific , We acknowledge the NORDITA dynamo programs of 2009 and 2011 for providing a stimulating scientific atmosphere.326Computing resources provided by the Swedishatmosphere. National Allocations Committee at the Center for Parallel Computers at the Royal Institute of Technology in Stockholm and the HighPerformance Computing Center North inUmea., Computing resources provided by the Swedish National Allocations Committee at the Center for Parallel Computers at the Royal Institute of Technology in Stockholm and the HighPerformance Computing Center North in.327 This work was supported in part by the European Research Council under the AstroDyn Research Project 2227952., This work was supported in part by the European Research Council under the AstroDyn Research Project 227952.328below 1500 K and at wavelengths shorter than a few gam. This condition is fulfilled only after 10° yr and beyond 0.5 AU in all the solar nebula models used in our calculations.,below 1500 K and at wavelengths shorter than a few $\mu$ m. This condition is fulfilled only after $10^5$ yr and beyond 0.5 AU in all the solar nebula models used in our calculations.329 For H». 1.e. the dominant molecule. the Rayleigh scattering cross section is GU)=849x107?LU(em) (Vardya 1962).," For $_2$, i.e, the dominant molecule, the Rayleigh scattering cross section is $\sigma (\lambda ) = 8.49 \times 10^{-45} / \lambda^4 \rm (cm^2)$ (Vardya 1962)."330 Assuming the illuminating light follows à black body spectrum. the Planck mean cross section as a function of the black body temperature Ty is found to be o(Tp)=1.54x1077T;(em?) (Dalgarno Williams 1962).," Assuming the illuminating light follows a black body spectrum, the Planck mean cross section as a function of the black body temperature $T_B$ is found to be $\sigma(T_B) = 1.54 \times 10^{-42}~ T_B^4 \rm~(cm^2)$ (Dalgarno Williams 1962)."331 Note that. in our case. Tp is not the temperature of the nebula. but rather the effective temperature of the illuminating source. the Sun.," Note that, in our case, $T_B$ is not the temperature of the nebula, but rather the effective temperature of the illuminating source, the Sun."332" With a disks mean molar mass of 2.34g/mol. the mass absorption coefficient is found to be c,(Tg)=3.96x107?T;(em?/g)."," With a disk's mean molar mass of $2.34 \rm ~g/mol$, the mass absorption coefficient is found to be $\sigma_m (T_B) = 3.96 \times 10^{-19}~T_B^4 \rm~(cm^2/g)$."333 Light becomes extinguished close to the star as a result of the high gas density. while the outer regions play only a minor role in the extinction.," Light becomes extinguished close to the star as a result of the high gas density, while the outer regions play only a minor role in the extinction."334 We constructed a grid of nine disk models encompassing the range of thermodynamic conditions that might have taken place during the solar nebula’s evolution., We constructed a grid of nine disk models encompassing the range of thermodynamic conditions that might have taken place during the solar nebula's evolution.335 The three initial disk masses were fixed to 0.01. 0.03 and 0.1 respectively. with 0.01 corresponding to the minimum mass solar nebula (hereafter MMSN) defined by Hayashi (1981).," The three initial disk masses were fixed to 0.01, 0.03 and 0.1 respectively, with 0.01 corresponding to the minimum mass solar nebula (hereafter MMSN) defined by Hayashi (1981)."336" The initial mass of each disk is integrated between 0.25 and 50 AU and the initial gas surface density is given by a power law X«777, with an initial value taken to be X(5.2AU) = 100. 300. and 1000 cem at 5.2 AU for disk masses of 0.01. 0.03 and 0.1M... respectively."," The initial mass of each disk is integrated between 0.25 and 50 AU and the initial gas surface density is given by a power law $\Sigma \propto r^{-3/2}$, with an initial value taken to be $\Sigma (5.2 {\rm AU})$ = 100, 300, and 1000 $^{-2}$ at 5.2 AU for disk masses of 0.01, 0.03 and 0.1, respectively."337 Here. the lifetime of the disk is governed both by viscosity and photoevaporation by the Sun or nearby stars.," Here, the lifetime of the disk is governed both by viscosity and photoevaporation by the Sun or nearby stars."338 On the other hand. the viscosity parameter rules the aceretion velocity of the disk (Eq.," On the other hand, the viscosity parameter rules the accretion velocity of the disk (Eq."339 12) but this latter is found to be low compared to the velocities due to photophoresis and gas drag for particles larger than 1077 m (see Fig., 12) but this latter is found to be low compared to the velocities due to photophoresis and gas drag for particles larger than $^{-4}$ m (see Fig.340 2 for an example of particle velocities due to photophoresis. radiation pressure. residual gravity and accretion flow along their trajectories in the nebula).," 2 for an example of particle velocities due to photophoresis, radiation pressure, residual gravity and accretion flow along their trajectories in the nebula)."341 Here the viscosity parameter is fixed to 7 x 107. ie. a value adopted in works aiming at synthesizing different populations of planets around other stars (Mordasini et al.," Here the viscosity parameter is fixed to 7 $\times$ $^{-3}$, i.e, a value adopted in works aiming at synthesizing different populations of planets around other stars (Mordasini et al."342 2009a. 2009b) and the photoevaporation rate is varied to obtain the appropriate disk lifetimes (1. 3. and 6 Myr for each selected mass).," 2009a, 2009b) and the photoevaporation rate is varied to obtain the appropriate disk lifetimes (1, 3, and 6 Myr for each selected mass)."343 In each case. the lifetime corresponds to the time taken for the mass of the disk (integrated until 50 AU) to decrease to of its initial value.," In each case, the lifetime corresponds to the time taken for the mass of the disk (integrated until 50 AU) to decrease to of its initial value."344 Mousis et al. (, Mousis et al. (3452007) have calculated the optical depth of the disk at 30 AU as a function of time.,2007) have calculated the optical depth of the disk at 30 AU as a function of time.346 They found that even at late epochs. only «0.15€ of the Sun's radiation is available in this region.," They found that even at late epochs, only $\sim$ of the Sun's radiation is available in this region."347 As a result. these authors found that the high extinction induced by H» Rayleigh scattering limits the outward transport of particles only to very short heliocentric distances (typically afew AU) when they are released from the innermost regions.," As a result, these authors found that the high extinction induced by $_2$ Rayleigh scattering limits the outward transport of particles only to very short heliocentric distances (typically a few AU) when they are released from the innermost regions."348 On the other hand. particle transport can be enhanced at larger heliocentric distances when a gap is formed in the inner disk.," On the other hand, particle transport can be enhanced at larger heliocentric distances when a gap is formed in the inner disk."349 In particular. there is a growing body of observational evidence for the existence of disks whose inner few AU are cleared or are strongly depleted of gas (D'Alessio et al.," In particular, there is a growing body of observational evidence for the existence of disks whose inner few AU are cleared or are strongly depleted of gas (D'Alessio et al."350 2005: Sicilia-Aguilar et al., 2005; Sicilia-Aguilar et al.351 2006: Espaillat et al., 2006; Espaillat et al.352 2008; Pontoppidan et al., 2008; Pontoppidan et al.353 2008: Thalmann et al., 2008; Thalmann et al.354 2010)., 2010).355 For this reason. and similar to Mousis et al. (," For this reason, and similar to Mousis et al. ("3562007). we assume here the presence of 1 and 2 AU inner gaps within the nebula during the course of its viscous evolution.,"2007), we assume here the presence of 1 and 2 AU inner gaps within the nebula during the course of its viscous evolution."357 Gaps are prescribed in à way independent of the structure of the disk models used in this work and their sizes remain constant with time., Gaps are prescribed in a way independent of the structure of the disk models used in this work and their sizes remain constant with time.358 As shown in Sect. 4..," As shown in Sect. \ref{res},"359 such an inner hole ts large enough to leave a reasonable fraction of the incoming light to let photophoresis work even in the outer solar system., such an inner hole is large enough to leave a reasonable fraction of the incoming light to let photophoresis work even in the outer solar system.360 Particles considered in our simulations have sizes ranging between 10 and 107'm and are assumed to be spherical and composed of olivine. with a variable porosity.," Particles considered in our simulations have sizes ranging between $^{-5}$ and $^{-1}$ m and are assumed to be spherical and composed of olivine, with a variable porosity."361 Density of aggregates is varied between 500 and 1000 mm., Density of aggregates is varied between 500 and 1000 $^{-3}$.362 The first value corresponds to the random deposition of irregular olivine particles with density of 3300 mm. with a filling factor (Blum Schriippler 2004).," The first value corresponds to the random deposition of irregular olivine particles with density of 3300 $^{\rm-3}$, with a filling factor (Blum Schräppler 2004)."363 The second value corresponds to the average density measured in cometary interplanetary dust particles (Joswiak et al., The second value corresponds to the average density measured in cometary interplanetary dust particles (Joswiak et al.364 2007)., 2007).365 We do not consider particles with sizes lower than 10? m because their path in the nebula is essentially controlled by radiation pressure., We do not consider particles with sizes lower than $^{-5}$ m because their path in the nebula is essentially controlled by radiation pressure.366 Moreover. for objects larger than about 1 m. the radial treatment we apply does no longer hold because the gas grain friction times become comparable to the orbital pertod.," Moreover, for objects larger than about 1 m, the radial treatment we apply does no longer hold because the gas grain friction times become comparable to the orbital period."367 All our calculations are based on the assumption that the disk opacity is essentially caused by Rayleigh scattering and not to dust. implying that the dust size distribution in the nebula is dominated by large particles instead of small particles.," All our calculations are based on the assumption that the disk opacity is essentially caused by Rayleigh scattering and not to dust, implying that the dust size distribution in the nebula is dominated by large particles instead of small particles."368 In the contrary case. smallest aggregates (here 107 m) would create a prominent opacity in the disk. implying that larger aggregates could only migrate outward in the wake of the small ones.," In the contrary case, smallest aggregates (here $^{-5}$ m) would create a prominent opacity in the disk, implying that larger aggregates could only migrate outward in the wake of the small ones."369 Figures 3-6 represent the trajectories of 1077? to 10! m aggregates in the solar nebula that were computed using the defined particle densities anc à set of six disk models that are expected to encompass the range of plausible thermodynamic conditions within the solar nebula (disk masses of 1 MMSN. 3 MMSN. 10 MMSN with lifetimes of | or 6 Myr).," Figures 3–6 represent the trajectories of $^{-5}$ to $^{-1}$ m aggregates in the solar nebula that were computed using the defined particle densities and a set of six disk models that are expected to encompass the range of plausible thermodynamic conditions within the solar nebula (disk masses of 1 MMSN, 3 MMSN, 10 MMSN with lifetimes of 1 or 6 Myr)."370 At the beginning of each computation. the particles start their migration within the disk from the outer edge of the inner gap.," At the beginning of each computation, the particles start their migration within the disk from the outer edge of the inner gap."371 Figure 3 shows that 107—107! m particles with densities of 500 mm that migrate within a disk with a | AU inner, Figure 3 shows that $^{-2}$ $^{-1}$ m particles with densities of 500 $^{-3}$ that migrate within a disk with a 1 AU inner372separation. position angle and flux ratio.,"separation, position angle and flux ratio."373 The average of he teu results eives the final values for the paraicters., The average of the ten results gives the final values for the parameters.374 Figure 9 shows that he residuals after this dual-fit are much better than after the sinele-PSF subtraction described iu the previous section aud in Figure 7.., Figure \ref{companion} shows that the residuals after this dual-fit are much better than after the single-PSF subtraction described in the previous section and in Figure \ref{psf_subtraction}.375 Moreover. the stability of the results for the teu «iffercut PSF stars at each of the six epochs shows that the results are reliable and robust. auk that the thir component livpotesis ds cousistent with the shape of the clongated PSF aud higily probable.," Moreover, the stability of the results for the ten different PSF stars at each of the six epochs shows that the results are reliable and robust, and that the third component hypothesis is consistent with the shape of the elongated PSF and highly probable."376 Table |. eives the fhx ratios between the three conrponeuts of the uultiple svstemi estimated with tus method. as well as the correspondiug differences of ruagnuituce.," Table \ref{flux_ratio} gives the flux ratios between the three components of the multiple system estimated with this method, as well as the corresponding differences of magnitude."377 According to the most receut DUSTY inodoels of Chabrieretal.(2000).. these ¢ifercuces of magnitudes indicate that the three componeuts nst have similar masses.," According to the most recent DUSTY models of \citet{2000ApJ...542..464C}, these differences of magnitudes indicate that the three components must have similar masses."378 A difference of iiagnitue of 1.5 mae in the FelAWW corresponds indeed to a mass ratio of 75. S5 and at respectively 0.5. 1.0. and 5 Cor.," A difference of magnitude of 1.5 mag in the F814W corresponds indeed to a mass ratio of 75, 85 and at respectively 0.5, 1.0, and 5 Gyr."379 The present analysis of the high aneular resolution mages indicates that DENIS-P J020529.115925 is very Likely to be a triple svstem., The present analysis of the high angular resolution images indicates that DENIS-P J020529.0-115925 is very likely to be a triple system.380 Figure Ll shows the Mj. vs Spectral Type relation for all the objects reported bv Dahuetal.(2002) (seco them Tables 1. 2 and 3).," Figure \ref{Mi_spt} shows the $_{\mathrm{I_{C}}}$ vs Spectral Type relation for all the objects reported by \citet{2002AJ....124.1170D} (see their Tables 1, 2 and 3)."381 Asstuning differences of magnitude in Le equal to that repored in Table | for the Faliy filter (FSLIWfiterisclosetoIc.2002). and the DENIS I of the unresolved objects. one ean estimate the spectral tvpes of the three comiponeus.," Assuming differences of magnitude in $_{\mathrm{C}}$ equal to that reported in Table \ref{flux_ratio} for the F814W filter \citep[F814W filter is close to I$_{\mathrm{C}}$, and the DENIS I of the unresolved objects, one can estimate the spectral types of the three components."382 DENTS-P J020529.0-115925 A Is consisteut witl τα L5.5 dwarf. in good agreecimout with the measur‘clment reported by Alartinctal.(1999) aud Cevalleetal.(2002).. and showing that the priunary would be dominating the optical spectrum.," DENIS-P J020529.0-115925 A is consistent with a L5.5 dwarf, in good agreement with the measurement reported by \citet{1999AJ....118.2466M} and \citet{2002ApJ...564..466G}, and showing that the primary would be dominating the optical spectrum."383 D iux C svould be consistent with ~Ls and TU cats respectively. in the Geballeetal.(2002). classification scheme.," B and C would be consistent with $\sim$ L8 and $\sim$ T0 dwarfs respectively, in the \citet{2002ApJ...564..466G} classification scheme."384 Several authors report the detection of methane sorption iu tlje infrared spectrum of P J020529.0-115925 (Delfosseetal.1997:al.2001:Bureasseret 2003)..," Several authors report the detection of methane absorption in the infrared spectrum of DENIS-P J020529.0-115925 \citep{1997A&A...327L..25D, 2001ApJ...561L.115M, 2003ApJ...586..512B}."385" also observed this absorption feaure in the spectrum but attribute it ο II» ratjer than metha1ο,", also observed this absorption feature in the spectrum but attribute it to $_{2}$ rather than methane.386 Durgasseretal.(2002) note that this feature is weak aud variable. aud consider that it does not constitute a clear detection moethaue.," \citet{2002ApJ...564..421B} note that this feature is weak and variable, and consider that it does not constitute a clear detection of methane."387 We note hat if real. this feature could be related to the presence of L8 aud TO companions. alc its variability to some weather effects. already observed in other late L aud T. chwarts by Enochetal.(2003)..," We note that if real, this feature could be related to the presence of L8 and T0 companions, and its variability to some weather effects, as already observed in other late L and T dwarfs by \citet{2003AJ....126.1006E}."388 Dahnctal.(2002) showed that the absolute J aud EK-band magniides of carly T-dwarts are simular to that of late-L dwarfs. so that the contribution of Band C in the infrared can be larger than in the optical.," \citet{2002AJ....124.1170D} showed that the absolute J and K-band magnitudes of early T-dwarfs are similar to that of late-L dwarfs, so that the contribution of B and C in the near-infrared can be larger than in the optical."389" According to the DUSTY nodels (Chabrieral.2000).. and assuniug an age between 1 and 10 Cr. Figure 12. shows that the absolute Mj, maenitude of DENIS-P. J020529.0-115925 A corresponds to an effective. temperature between 19900 E. while D aud C range ETWeCLL Lasoo Ik. These temperatures are consistent with the value reported bv Basrietal.(2000) for fjio unresolved svsteii (1700-1800 INS}. aud show that all compoucuts appear to be clearly substellar."," According to the DUSTY models \citep{2000ApJ...542..464C}, and assuming an age between 1 and 10 Gyr, Figure \ref{teff} shows that the absolute $_{\mathrm{I_{C}}}$ magnitude of DENIS-P J020529.0-115925 A corresponds to an effective temperature between 900 K, while B and C range between 800 K. These temperatures are consistent with the value reported by \citet{2000ApJ...538..363B} for the unresolved system $\sim$ 1800 K), and show that all components appear to be clearly substellar."390 According to the DUSTY models. the stellar/substellar luit is indeed around 2000 Ix at 10 Cer aud 2180 Ik at 1 C. therefore warlucr than any of the componucuts of DENIS-P J020529.0-115925.," According to the DUSTY models, the stellar/substellar limit is indeed around 2000 K at 10 Gyr and 2180 K at 1 Gyr, therefore warmer than any of the components of DENIS-P J020529.0-115925."391 Finally. the proper motion of the object (138liusVr lo and the presence of these strong residuals at six different epochs spread over three vears allow us to rule out definitively the eventuality of a coincidence with some backeround object.," Finally, the proper motion of the object \citep[$\sim$438 mas yr$^{-1}$ , and the presence of these strong residuals at six different epochs spread over three years allow us to rule out definitively the eventuality of a coincidence with some background object."392 The separation between the primary and the secondary changed from ~0%3390 το 072270 between October 2000 aud December 2003. while the separation between the secoud aud the third coniponent is contained between ~O00TS<dpe< 0055 (see Table 5)).," The separation between the primary and the secondary changed from $\sim$ 390 to 270 between October 2000 and December 2003, while the separation between the second and the third component is contained between $\sim$ $\le \delta_{BC} \le$ 055 (see Table \ref{pa_sep}) )."393 As stated by Harrington(1968) aud then Szebewly&Zare(1977) in their analytical study. te systems with moderate eccentricity and equal mass components are stable for ratios between the semiauajor axes of the outer (>) aud the duner orbits (a } eroateor than ayfay 23.2.," As stated by \citet{1968AJ.....73..190H} and then \citet{1977A&A....58..145S} in their analytical study, triple systems with moderate eccentricity and equal mass components are stable for ratios between the semi-major axes of the outer $a_{2}$ ) and the inner orbits $a_{1}$ ) greater than $a_{2}/a_{1} \ge$ 3.2."394 Assmuine that the orbits of DENIS-P JO20529.0-115925 couponents have, Assuming that the orbits of DENIS-P J020529.0-115925 components have395forr weeks.,r weeks.396 It was observed at a wiee range of radio frequencies., It was observed at a wide range of radio frequencies.397and LOA)) obtaining similar results.,and ) obtaining similar results.398 These are comparable to our own observations: CAILA and OSN (1A)). NOT and SPM (8A)). SDSS (3.5A)) and FAST (6A)).," These are comparable to our own observations: CAHA and OSN ), NOT and SPM ), SDSS ) and FAST )."399 Both HO05 and SRROG have3., Both H05 and SRR06 have.4005À.. The S/N continuum levels of the different survevs are also comparable., The S/N continuum levels of the different surveys are also comparable.401 On average the S/N of AGNs in our spectra is 60 with a maximum of the order of 120., On average the S/N of AGNs in our spectra is 60 with a maximum of the order of 120.402 This is comparable to HO05 and SRROG spectra (thev both used SDSS)., This is comparable to H05 and SRR06 spectra (they both used SDSS).403 HIES97 did not published their values., HFS97 did not published their values.404 IIowever their BLAGNs rates are comparable to those of 1105 and SRAR06. suggesting this is nol an issue.," However their BLAGNs rates are comparable to those of H05 and SRR06, suggesting this is not an issue."405 There is no evidence either for a higher galaxy. contamination (ihe amount of galaxy falling into (he aperture) in our samples., There is no evidence either for a higher galaxy contamination (the amount of galaxy falling into the aperture) in our samples.406" Taking into account the slit aperture and distances of the host galaxies in each saniple we find medians of 1 kpe and 1.3 kpe for the HCG. and UZC-CG. respectively,"," Taking into account the slit aperture and distances of the host galaxies in each sample we find medians of 1 kpc and 1.3 kpc for the HCG and UZC-CG, respectively."407 Although the median for IIES97 is lower (0.5 kpe) than for HO5 (7 kpc) the results are similar., Although the median for HFS97 is lower (0.5 kpc) than for H05 (7 kpc) the results are similar.408 Obviously. template subtraction (like we also did) alleviates the differences.," Obviously, template subtraction (like we also did) alleviates the differences."409 We may note also that no relation is observed. in anv of these surveys (including ours). between the frequency of BLAGNs and the redshift of the galaxies where thev are found. which means that nearby galaxies are not more likely DLAGNs than remote ones.," We may note also that no relation is observed, in any of these surveys (including ours), between the frequency of BLAGNs and the redshift of the galaxies where they are found, which means that nearby galaxies are not more likely BLAGNs than remote ones."410 To test if our low number of ον]. could be due (ο a difference in morphologies 2001).. we have divided our (wo samples aud the IIES97 one in three morphology classes: E for early-type galaxies (E-90). Se for earl-tvpe spirals (S0a-5bc). and Sl lor Iate-tvpe spirals (Sc and later).," To test if our low number of Sy1 could be due to a difference in morphologies \citep{sch01}, we have divided our two samples and the HFS97 one in three morphology classes: E for early-type galaxies (E-S0), Se for early-type spirals (S0a-Sbc), and Sl for late-type spirals (Sc and later)."411 For homogeneity sake. all (he morphologies have been taken ουν the Ilvperleda database (Patureletal. 2003)..," For homogeneity sake, all the morphologies have been taken from the Hyperleda database \citep{pat03}. ."412 In Table 3. we give for each morphology. class the fraction of galaxy and the ratios BLAGN/NLAGN and Svl/Sv2., In Table \ref{tbl3} we give for each morphology class the fraction of galaxy and the ratios BLAGN/NLAGN and Sy1/Sy2.413 There are no BLAGNs in late-tvpe spirals in anv sample., There are no BLAGNs in late-type spirals in any sample.414 In the HIES97 sample. the ratio of BLAGN/NLAGN is mareinally higher in the E class while (he ratio Sv1/5V2 is significantly higher. which indicates a definitive increase in DLAGNSs in early-type galaxies.," In the HFS97 sample, the ratio of BLAGN/NLAGN is marginally higher in the E class while the ratio Sy1/Sy2 is significantly higher, which indicates a definitive increase in BLAGNs in early-type galaxies."415 In the two CG samples we almost see an inverse trend: the ratios of DLAGN/NLAGN and ον]ον are both larger iΕν the Se class than in the E one., In the two CG samples we almost see an inverse trend: the ratios of BLAGN/NLAGN and Sy1/Sy2 are both larger in the Se class than in the E one.416 Moreover there is a definite rise in the number of early-(vpT ealaxies in CGs., Moreover there is a definite rise in the number of early-type galaxies in CGs.417 Following the HIIES97 trend. this should have produced more BLAGNs iΕν CGs instead of less.," Following the HFS97 trend, this should have produced more BLAGNs in CGs instead of less."418 This eliminates a difference in morphologies as a possible explanation., This eliminates a difference in morphologies as a possible explanation.419 We also reject the hypothesis of lower sensitivity., We also reject the hypothesis of lower sensitivity.420 Comparing the median Iuminosit 1Εν Ila of the different (vpes of galaxies in our samples with those in the IIES97 sample. lower sensitivity would have translated into higher values in our samples.," Comparing the median luminosity in $\alpha$ of the different types of galaxies in our samples with those in the HFS97 sample, lower sensitivity would have translated into higher values in our samples."421 This is not observed., This is not observed.422" In the HIES97 sample the median Ho Iuminositv of the NLAQNSs is log(Ly,,=38.72 eres +).", In the HFS97 sample the median $\alpha$ luminosity of the NLAGNs is $_{H\alpha} =38.72 $ ergs $^{-1}$ ).423 Our values are comparable: 38.69 for the IICG. and 38.79 for the UZC-CG., Our values are comparable: 38.69 for the HCG and 38.79 for the UZC-CG.424 Finally we have determined the detection limits in our saniplesas in 11οetal. (1997).., Finally we have determined the detection limits in our samplesas in \citet{ho97b}. .425From ZG.V). all thermodvnaimical observables can be caleulated in the usual fashion.,"From $Z(T,V)$, all thermodynamical observables can be calculated in the usual fashion."426 Thus = y gives the energv densitv. and the pressure.," Thus = )_V gives the energy density, and P = T )_T the pressure."427 For the study of critical behaviour. long range correlations ancl multi-particle interactions are of crucial importance: hence perturbation theory cannot be used.," For the study of critical behaviour, long range correlations and multi-particle interactions are of crucial importance; hence perturbation theory cannot be used."428 The necessary non-perturbative regularisation scheme is provided by the lattice formulation of QCD [7]: it leads to a form which can be evaluated numerically by computer simulation .., The necessary non-perturbative regularisation scheme is provided by the lattice formulation of QCD \cite{Wilson}; it leads to a form which can be evaluated numerically by computer simulation \cite{Creutz}.429 The caleulational methods anc techniques of finite temperature lattice QCD form a challenging subject on ils own. which certainly surpasses (he scope ol (his survey.," The calculational methods and techniques of finite temperature lattice QCD form a challenging subject on its own, which certainly surpasses the scope of this survey."430 We therefore restrict. ourselves here to a summary. of the main results obtained so far: for more details. we refer to excellent recent surveys and reviews [9]..," We therefore restrict ourselves here to a summary of the main results obtained so far; for more details, we refer to excellent recent surveys and reviews \cite{lattice}."431 The first variable considered in finite temperature lattice QCD is Che deconfinement measure provided by the Polyakov loop |10.L| LOT) where V(i) is the potential between a static quark-antiquark pair separated by a distance r.," The first variable considered in finite temperature lattice QCD is the deconfinement measure provided by the Polyakov loop \cite{Larry,Kuti}432 L(T) where $V(r)$ is the potential between a static quark-antiquark pair separated by a distance $r$."433 In pure gauge theory. without light quarks. V(r)» or. where o is the string (tension: hence here V(2e)=x. πο that £—0.," In pure gauge theory, without light quarks, $V(r) \sim \sigma r$ , where $\sigma$ is the string tension; hence here $V(\infty)= \infty$, so that $L=0$."434 In a deconfined medium. colour screening among the gluons leads to a melting of the string. which makes V(r) finite al large 7: hence now L does not vanish.," In a deconfined medium, colour screening among the gluons leads to a melting of the string, which makes $V(r)$ finite at large $r$; hence now $L$ does not vanish."435 It thus becomes an order parameter like (he magnetisalion in (he Ising model: for the temperature range 0<7x7. we have L=0 and hence confinement. while lor 7.« Lowe have L>0 and deconfinement.," It thus becomes an `order parameter' like the magnetisation in the Ising model: for the temperature range $0 \leq T \leq T_c$, we have $L=0$ and hence confinement, while for $T_c < T$ we have $L>0$ and deconfinement."436 The temperature 7). al which £L becomes finite thus defines the onset of deconfimement., The temperature $T_c$ at which $L$ becomes finite thus defines the onset of deconfinement.437 In the large quark mass limit. QCD reduces to pure SU(3) gauge (heory. which is invariant under a global Za symmetry.," In the large quark mass limit, QCD reduces to pure $SU(3)$ gauge theory, which is invariant under a global $Z_3$ symmetry."438 The Polvakov loop provides a measure of thestate of the system under this symmetry: it vanishes [or Z4 svmmetrie states and becomes finite when, The Polyakov loop provides a measure of thestate of the system under this symmetry: it vanishes for $Z_3$ symmetric states and becomes finite when439throughout the protogalaxv?,throughout the protogalaxy?440 Iuhomoseneous ήπιο may create pockets of enhanced curichiment. with a metallicity wich ereater than Z...," Inhomogeneous mixing may create pockets of enhanced enrichment, with a metallicity much greater than $Z_{\odot}$."441 The degree of mixine or chuupiness of the ietal distribution inside the protogalaxy will be investigated in greater detail iu later work., The degree of mixing or clumpiness of the metal distribution inside the protogalaxy will be investigated in greater detail in later work.442 Our numerical integratious are run for both standard solar (seeCrevesse&Sauval1998) aud PISN ietal abundance patterns., Our numerical integrations are run for both standard solar \citep[see][]{GS98} and PISN metal abundance patterns.443" PISN patterns are frou Ueeer&Woosley(2002) for a 150 and 250ΑΕ, progenitor SN (corresponding to a 75 and 125AL. heli core. respectively)."," PISN patterns are from \citet{HW02} for a 150 and $250\, M_\odot$ progenitor SN (corresponding to a 75 and $125 \,M_\odot$ helium core, respectively)."444 Table 1. represents the ταν density Gin cn 7) of metallic species given a lydrogen uber deusity of Leu7.," Table \ref{tab:abundance_pattern} represents the number density (in $\text{cm}^{-3}$ ) of metallic species given a hydrogen number density of $1\, \text{cm}^{-3}$."445 The PISN values ave computed with the same overall mass fraction in metals. but differiug elemental proportions compared to the Sun.," The PISN values are computed with the same overall mass fraction in metals, but differing elemental proportions compared to the Sun."446" The rate of photoionization of a species το) for an optically thin gas is given by (6.8...Osterbrock1989) where J,=—↽10⋅≽21500988tam7Uzlay bis. he mean intensity. o(7} is the frequency depeudeut photoionization cross section. aud the integration rus your the threshold photoionization frequency. ÁJj4. to infinity."," The rate of photoionization of a species $R_{\text{photo}}$ ) for an optically thin gas is given by \citep[e.g.,][]{OST89}447 where $J_{\nu} = 10^{-21}\,J_{21}\,\text{ergs}\, \text{s}^{-1} \,\text{cm}^{-2}\, \text{Hz}^{-1}\, \text{sr}^{-1}$ is the mean intensity, $\sigma(\nu)$ is the frequency dependent photoionization cross section, and the integration runs from the threshold photoionization frequency, $\nu_{\text{th}}$ , to infinity."448 In the case of metallic photoiouizatious which are doimunuaut (see Section 2.2]). we run this integration ο rq. the ionization threshold of hydrogen. as hydrogen ioniziug photons are effectively shiclded by the ICAL prior o reionizatiou.," In the case of metallic photoionizations which are dominant (see Section \ref{sec:heating_processes}) ), we run this integration to $\nu_{\text{H}}$, the ionization threshold of hydrogen, as hydrogen ionizing photons are effectively shielded by the IGM prior to reionization."449 Photoionizatiou cross-sectious for C. Si. Fe. and ο are taken from the fits of Verneretal. (1996). ," Photoionization cross-sections for C, Si, Fe, and O are taken from the fits of \citet{VER96}. ."450"For our incident spectrum. we use thermal Planck spectra with T.=10! and 10*K aud a power law spectrum. J,x ντ, Asin "," For our incident spectrum, we use thermal Planck spectra with $T_{*}=10^{4} $ and $10^{5}\,\text{K}$ and a power law spectrum, $J_{\nu} \propto \nu^{-1}$ ."451Bronun&Loeb(2003a).. we normalize these spectra at the Lyman limit Όσο.," As in \citet{BL03}, we normalize these spectra at the Lyman limit by $J_{21}$."452 The photodissociation of IT» is a more complicated process., The photodissociation of $\textrm{H}_2$ is a more complicated process.453 It occurs through the two-step Solomon process (Stecher&Williams1967) by photons in the LW bands. 11.2)13.6eV.," It occurs through the two-step Solomon process \citep{SW67} by photons in the LW bands, $11.2 - 13.6 \,\text{eV}$."454" A commonly used approxiniatiou for this rate of dissociation. Rajni. is given by ~138<1094, where A, is the wean intensity at 12.1 eV. the mean energy of a LAV baud photon (secAbeletal. 1997)."," A commonly used approximation for this rate of dissociation, $R_{\text{diss}, \htwoeq}$, is given by $\sim 1.38 \times 10^{9} J_{\bar{\nu}}$ where $J_{\bar{\nu}}$ is the mean intensity at 12.4 eV, the mean energy of a LW band photon \citep[see][]{AB97}."455. We assume the photocissociation rate of TID equals that of IT»., We assume the photodissociation rate of HD equals that of $\textrm{H}_2$ .456 At high column densities. Πο can be particularly effective at shielding itself from LAV radiation which cau sieuificautlv alter its photodissociation rate (e.9..Oh&Taian 2002).," At high column densities, $\textrm{H}_2$ can be particularly effective at shielding itself from LW radiation which can significantly alter its photodissociation rate \citep[e.g.,][]{OH02}."457" Draine&Bertoldi(1996) provide an i»proxination for the shiekdiug factor such that aii;κ Fas Where fanaacnmdu[l.0.OV,10-0.2)Urs with Ay, being the coluun deusitv of IT."," \citet{DB96} provide an approximation for the shielding factor such that $R_{\text{diss}} \propto f_{\text{shield}}$ , where $f_{\text{shield}} \simeq \text{min}[1.0, (N_{\htwoeq}/10^{14}\text{cm}^{-2})^{-0.75}]$ with $N_{\htwoeq}$ being the column density of $\textrm{H}_2$."458 However. this applies to a static. cold medium.," However, this applies to a static, cold medium."459 If the LAW bands are Doppler shifted by large thermal or bulk motions. the shielding rate will be much lower.," If the LW bands are Doppler shifted by large thermal or bulk motions, the shielding rate will be much lower."460 Tn in accreting protogalaxy. where large-scale velocity eradieuts reach ~20kns  selfshiclding will certainly be overestimated within this prescription.," In in accreting protogalaxy, where large-scale velocity gradients reach $\sim 20 \;\text{km} \;\text{s}^{-1}$ , self-shielding will certainly be overestimated within this prescription."461" Taking thermal broadening iuto consideration. Draine&Bertoldi(1996) provide another fit to the shiclding factor as where c=Ny, aud bj=b1Uemst."," Taking thermal broadening into consideration, \citet{DB96} provide another fit to the shielding factor as where $x = N_{\htwoeq}$ and $b_{5} = b / 10^{5}\; \text{cm}\; \text{s}^{-1}$."462 We follow Alm&Shapiro(2007) in setting b=9.12lans|. as their plysical svsteimi is approximately simular to ours.," We follow \citet{AS07} in setting $b = 9.12\; \text{km}\; \text{s}^{-1}$, as their physical system is approximately similar to ours."463 Although this will still overestimate the amount of self-shiekdiug when bulk motions dominate. it is an iuprovenient over the previous fit aud will be used iu computing our value of IT» selt-slicldiug.," Although this will still overestimate the amount of self-shielding when bulk motions dominate, it is an improvement over the previous fit and will be used in computing our value of $\textrm{H}_2$ self-shielding."464 The radiation field preseut iun these lieh redshift protogalaxies is uncertain. owiug to the contribution from the external. elobal ICAL field. aud the local field produced by internalPop IIL/II stars.," The radiation field present in these high redshift protogalaxies is uncertain, owing to the contribution from the external, global IGM field, and the local field produced by internalPop III/II stars."465" One can estimate. at +=10. that the intensity just above the Lyman Πατ, Jj. necessaryto relouize the universe is ~LO (Bromun&Loeb2003a)."," One can estimate, at $z=10$, that the intensity just above the Lyman limit, $J^{+}_{21}$, necessaryto reionize the universe is $\sim 40$ \citep{BL03}."466". However. photons with enereies below the Lyauiu limit are virtually free to escape their host halo. so that the correspouding iuteusity. οι. which includesthe IL, dissociating LAW bands. could potentially be fd~100 times higher. where fie is the escape fraction ofITHioniziug plotous (Wood&Loch2000)."," However, photons with energies below the Lyman limit are virtually free to escape their host halo, so that the corresponding intensity, $J^{-}_{21}$, which includesthe $\textrm{H}_2$ dissociating LW bands, could potentially be $f_{\text{esc}}^{-1} \sim 100$ times higher, where $f_{\rm esc}$ is the escape fraction of H-ionizing photons \citep{WL00}."467. Other receut estimates (Razommov&SouunerLarscu2009:WiseCen2009) have found f;~0.25 in chwart ealaxies at lieh redshift.," Other recent estimates \citep{RS09,Wise:09} have found $f_{\text{esc}} \sim 0.25-1$ in dwarf galaxies at high redshift."468 Finally. the LW background cau be elevated: orders of mmaeuitucde above the elobal average LW Ποια in clustered halos (Dijkstraetal.2008:Whalenetal.2000)...," Finally, the LW background can be elevated orders of magnitude above the global average LW field in clustered halos \citep{Dijk08, WHA08,JOH08, AH09, SHA09} ."469" For this study we take so,=10 and Jo=104. representing small and large radiation fields which could be realistically present at this epoch."," For this study, we take $J_{21} = 10$ and $J_{21} = 10^{4}$, representing small and large radiation fields which could be realistically present at this epoch."470 We now consider the case of a cold accretion stream which is shock heated in the center of a primorcial protogalaxy., We now consider the case of a cold accretion stream which is shock heated in the center of a primordial protogalaxy.471 In Section Ll we derive a simple criterion for when the post-shock region will fragment based ou the free-fall and sound crossing times., In Section \ref{sec:frag_criteria} we derive a simple criterion for when the post-shock region will fragment based on the free-fall and sound crossing times.472 Section. 1.2 describes the thermal evolution of the post-shock region. and preseuts the fragmentation mass scale for different parameter choices. whereas Section 1.3> outlines a simple analytical model for the critical mctallicity iu inolecule-free regine.," Section \ref{sec:results} describes the thermal evolution of the post-shock region, and presents the fragmentation mass scale for different parameter choices, whereas Section \ref{sec:toy_model} outlines a simple analytical model for the critical metallicity in molecule-free regime."473 To derive a rough estimate of when fragmentation will occur. we consider the growth of the shocked gas region within our one-zone nodoel.," To derive a rough estimate of when fragmentation will occur, we consider the growth of the shocked gas region within our one-zone model."474" Following the shock that terminates the accretion stream near the ceuter of the protogalaxw. the eas begius to cool off isobarically (seeShapiro&Kaug19857:Clarkeτοι2003). from the virial temperature of the halo. Ti,iunc.2ky~IS. where ji=0.6pug is the mean molecular weielt in :MAO]the mauuaediate post-shock οas."," Following the shock that terminates the accretion stream near the center of the protogalaxy, the gas begins to cool off isobarically \citep[see][]{SK87, CB03} from the virial temperature of the halo, $T_{\text{vir}} = \onehalf \mu m_p v_{\text{vir}}^{2} / k_{\text{B}} \simeq 2\times 10^{4} \mu_{0.6} M_8^{2/3}[(1+z)/10] \,\text{K}$, where $\mu=0.6\,\mu_{0.6}$ is the mean molecular weight in the immediate post-shock gas."475 Applving the standard Jeans analysis for gravitational instability. we take it that fragmentation occurs when the ever-increasing sound crossing time equals the decreasing free fall time of the post-shock region.," Applying the standard Jeans analysis for gravitational instability, we take it that fragmentation occurs when the ever-increasing sound crossing time equals the decreasing free fall time of the post-shock region."476" Specifically. we exanune three time scales: the cooling time. feo)& T). the free-fall tine. fgg=Ox326p)! 3, and the souud-crossiug time. tf.2 Le. where L is the leneth ofthe shocked slab. AC.D) the voluuetrie cooling rate. ande,=(5kppinu)? the sound speed."," Specifically, we examine three time scales: the cooling time, $t_{\text{cool}} \simeq\frac{3}{2}k_{\text{B}}Tn_{\text{tot}}/\Lambda(n, T)$ , the free-fall time, $t_{\rm ff} = (3\pi/32G\rho)^{1/2}$ , and the sound-crossing time, $t_{\rm s}477\simeq L/c_{\rm s}$ , where $L$ is the length ofthe shocked slab, $\Lambda(n,T)$ the volumetric cooling rate, and $c_{\text{s}} = (\gamma k_{\text{B}} T/\mu m_p)^{1/2}$ the sound speed."478 The density py isrelated tothe instantaneous post- density py via polCintall|Caboek)=PL Cock: , The pre-shock density $\rho_0$ isrelated tothe instantaneous post-shock density $\rho_1$ via $\rho_{0}(v_{\text{infall}} + v_{\text{shock}}) = \rho_1v_{\text{shock}}$ .4791nco the shock is strong. py py.," Since the shock is strong, $\rho_1\sim 4\rho_0$ ."480 Tf tlhe post shock gas, If the post shock gas481"et ((2011), the BBAL fraction is a constant for the most luminous quasars.","et (2011), the BAL fraction is a constant for the most luminous quasars."482" Moreover, if the trend of increasing fraction with luminosity is really due to the S/N of quasar spectra, it indicates that the intrinsic LoBAL fractions are close to ~18 percent."," Moreover, if the trend of increasing fraction with luminosity is really due to the S/N of quasar spectra, it indicates that the intrinsic LoBAL fractions are close to $\sim$ 18 percent."483 This is not consistent with our Model I prediction after taking the obscuration effects into account., This is not consistent with our Model I prediction after taking the obscuration effects into account.484" In the rest of the paper, we assume that the S/N has a small effect on the observed fractions in the luminosity range of our sample."," In the rest of the paper, we assume that the S/N has a small effect on the observed fractions in the luminosity range of our sample."485" We add another LoBAL component to our geometric model (Model II), based on the larger observed LoBAL fractions at high IR luminosities and the large x? values from a pure geometric fit in Fig."," We add another LoBAL component to our geometric model (Model II), based on the larger observed LoBAL fractions at high IR luminosities and the large $\chi^2$ values from a pure geometric fit in Fig."486 3 (left)., \ref{fig:thr} (left).487 We call this component the evolutionary component., We call this component the evolutionary component.488" We model the evolutionary component as having a power-law luminosity function only at high luminosities, ®gvo=ogvoL only when Mx,<—29.5."," We model the evolutionary component as having a power-law luminosity function only at high luminosities, $\Phi_{EVO} = \Phi_{0, EVO} L^{\alpha}$ only when $M_{K_s} \le -29.5$."489" We fit the observed LoBAL fractions from the g to Ks, bands using Model II, and obtain considerably better fits."," We fit the observed LoBAL fractions from the $g$ to $K_s$ bands using Model II, and obtain considerably better fits."490 We show the Model II fits in Figs., We show the Model II fits in Figs.491" 3 (right) and 5 (left), and list the fitting results in Table 2.."," \ref{fig:thr} (right) and \ref{fig:fiv} (left), and list the fitting results in Table \ref{tab:ifrac}."492" The intrinsic fractions from the geometric component are 3.3+0.4, 5.40.5, and 1.3+0.3 per cent for B-LoBALs, AI-LoBALs, and FeLoBALs, respectively, and they are all smaller than the intrinsic fractions obtained from a pure geometric model fit (Model I)."," The intrinsic fractions from the geometric component are $\pm$ 0.4, $\pm$ 0.5, and $\pm$ 0.3 per cent for BI-LoBALs, AI-LoBALs, and FeLoBALs, respectively, and they are all smaller than the intrinsic fractions obtained from a pure geometric model fit (Model I)."493" The fractions for the evolutionary component are functions of luminosities, and the total intrinsic fractions are the sum of the two components."," The fractions for the evolutionary component are functions of luminosities, and the total intrinsic fractions are the sum of the two components."494The parameters of the evolutionary,The parameters of the evolutionary495observations of M87 during the flaring period of HST-1 by Cheungetal.(2007).,observations of M87 during the flaring period of HST-1 by \cite{che07}.496". The VLBA observations show that the resolved subcomponent a moves downstream at ~2.49c at P.A.~295° initially, and then deflect to the direction of ~289° with apparent speed of 1.416, differing to the overall jet direction of 290°.In addition, the other two subcomponents b and c move down the jet at P.A.~279°, and the routes also appear not straight."," The VLBA observations show that the resolved subcomponent $a$ moves downstream at $\sim2.49c$ at $\rm{P.A.\simeq295^\circ}$ initially, and then deflect to the direction of $\sim289^\circ$ with apparent speed of $\sim1.41c$, differing to the overall jet direction of $290^\circ$ .In addition, the other two subcomponents $b$ and $c$ move down the jet at $\rm{P.A.\simeq279^\circ}$, and the routes also appear not straight."497" It can be interpreted that different emission features may gain energy across different part of its cross-sectional area, and trace down the different subset of streamlines, and the changes in apparent speed may mainly attribute to the orientation change down the jet."," It can be interpreted that different emission features may gain energy across different part of its cross-sectional area, and trace down the different subset of streamlines, and the changes in apparent speed may mainly attribute to the orientation change down the jet."498" Giovanninietal.(2011) presented an e-EVN image at epoch 2010 Jan. 27, which shows a significant orientation difference of the substructures within HST-1 to that at epochs by 2007 given in Cheungetal. (2007)."," \cite{gio11} presented an e-EVN image at epoch 2010 Jan. 27, which shows a significant orientation difference of the substructures within HST-1 to that at epochs by 2007 given in \cite{che07}."499". If the helical magnetic field around HST-1 do exists, each subcomponent may follow different subset of spiral streamlines down the jet, and with time, result in the significant orientation change of the substructures within it."," If the helical magnetic field around HST-1 do exists, each subcomponent may follow different subset of spiral streamlines down the jet, and with time, result in the significant orientation change of the substructures within it."500 All these effectively strengthens the argument that a helical magnetic field around HST-1 plays an important role in these phenomena., All these effectively strengthens the argument that a helical magnetic field around HST-1 plays an important role in these phenomena.501" The approximate 100 pc scale of the disk of ionized gas observed in M87 by HST (Fordetal.1994) may indicate to some extent the presence of helical magnetic fields around HST-1, which is also about 100 pc away from the active centre (Stawarzetal.2006)."," The approximate 100 pc scale of the disk of ionized gas observed in M87 by HST \citep{for94} may indicate to some extent the presence of helical magnetic fields around HST-1, which is also about 100 pc away from the active centre \citep{sta06}."502". Fractional polarization reflects the degree of magnetic field order, which may be affected by Faraday rotation and the medium opacity in the passage to the observer (Homanetal. 2009), and polarization level variability is argued to arise from the source itself as well as its immediate surrounding medium (Homanetal.2009)."," Fractional polarization reflects the degree of magnetic field order, which may be affected by Faraday rotation and the medium opacity in the passage to the observer \citep{hom09}, and polarization level variability is argued to arise from the source itself as well as its immediate surrounding medium \citep{hom09}."503". We show the variations of the fractional polarization in the bottom panel of Fig. 3,,"," We show the variations of the fractional polarization in the bottom panel of Fig. \ref{fig3},"504 which shows that the fractional polarization varies in a quite complex way., which shows that the fractional polarization varies in a quite complex way.505" However, it is quite affirmative that the fractional polarization roughly minimizes in the peaking stage, and is relatively low in the rising stage, and high in the decaying stage."," However, it is quite affirmative that the fractional polarization roughly minimizes in the peaking stage, and is relatively low in the rising stage, and high in the decaying stage."506 That is to say that the depolarization effect due to Faraday rotation and medium opacity is relatively strong in the rising stage of the major outburst., That is to say that the depolarization effect due to Faraday rotation and medium opacity is relatively strong in the rising stage of the major outburst.507 Faraday rotation is often detected from jet emission in radio-loud AGNs., Faraday rotation is often detected from jet emission in radio-loud AGNs.508" Zavala&Taylor(2004,2005) suggested that it occurs external to the jet by excluding several other identities such as broad and narrow line regions, and giving evidence of high fractional polarization to rule out internal Faraday rotation in 3C 273, while internal Faraday rotation gets supported in model-fitting to the full polarization spectra of 3 jet components simultaneously in a consistent physical picture in 3C 279 (Homanetal.2009)."," \cite{zav04,zav05} suggested that it occurs external to the jet by excluding several other identities such as broad and narrow line regions, and giving evidence of high fractional polarization to rule out internal Faraday rotation in 3C 273, while internal Faraday rotation gets supported in model-fitting to the full polarization spectra of 3 jet components simultaneously in a consistent physical picture in 3C 279 \citep{hom09}."509". The rotation measure can be expressed as RMοςfN(s)B-ds, where N is the electron number density, is the magnetic field, and is the emission path to the observer."," The rotation measure can be expressed as $\rm{RM\propto\int N(\textbf{s})\textbf{B}\cdot d\textbf{s}}$, where N is the electron number density, is the magnetic field, and is the emission path to the observer."510" Obviously, RM may provide constraints on number density and magnetic field in the passage, which is here obtained by fitting the observed EVPAs over 3 wavebands with Faraday wavelength square law."," Obviously, RM may provide constraints on number density and magnetic field in the passage, which is here obtained by fitting the observed EVPAs over 3 wavebands with Faraday wavelength square law."511" The RM variation with time for HST-1 is shown in Fig. 4,"," The RM variation with time for HST-1 is shown in Fig. \ref{fig4},"512" in which the top right inset gives the fit of the observed EVPAs in deg to the squared wavelength in cm?, as an example, at epoch 2003 Aug. 24."," in which the top right inset gives the fit of the observed EVPAs in deg to the squared wavelength in $\rm{cm^2}$, as an example, at epoch 2003 Aug. 24."513 One can find that the EVPAs obey the A? Faraday rotation, One can find that the EVPAs obey the $\lambda^2$ Faraday rotation514There are inhereut difficulties in defining enerev in COR. essentially due to its ,"There are inherent difficulties in defining energy in GR, essentially due to its non-localizability."515For OLE. we shall adopt the definition given by Brown aud York|10].," For QLE, we shall adopt the definition given by Brown and ."516. where Bis the two dimeusiou spherical surface. 0 is the determinant of the 2anetric on DB. N is the trace of the extrinsic curvature of B. aud Avy is a reference terii that is used to normalize the energv with respect to a reference space-time. not necessarily flat.," where $B$ is the two dimension spherical surface, $\sigma$ is the determinant of the 2-metric on $B$, $K$ is the trace of the extrinsic curvature of $B$, and $K_0$ is a reference term that is used to normalize the energy with respect to a reference space-time, not necessarily flat."517 To the eiven metric eq.33)). A is even by Forspace-times that are asvurptoticallv fat iu spacelike directions. the QLE eq.(31)) with B at spatial infinity agrees with the ADM.," To the given metric \ref{metric}) ), $K$ is given by Forspace-times that are asymptotically flat in spacelike directions, the QLE \ref{QLE}) ) with $B$ at spatial infinity agrees with the ADM."518"energy|ü].. Now. we chose the Avy is as follows The QLE of the black hole reads Specifically, for Beissuer-Nordstróuun black hole. where where M. and Q are the mass aud the charge ofthe hole respectively. aud when Q=0. the metric of (33)) reduces into Seluvarzschild’s."," Now, we chose the $K_0$ is as follows The QLE of the black hole reads Specifically, for Reissner-Nordströmm black hole, where where $M$ and $Q$ are the mass and the charge ofthe hole respectively, and when $Q=0$, the metric of \ref{metric}) ) reduces into Schwarzschild's."519 Obvious. as roo} x. vDir)lMyr. and hence Lr>x)orE=M. ic. the ADM-anass of the Reissuer-Nordstromun black hole.," Obvious, as $r\rightarrow \infty$ , $\sqrt{D(r)}\rightarrow 1-M/r$, and hence $E(r\rightarrow520\infty)_{QLE}=M$, i.e, the ADM-mass of the Reissner-Nordströmm black hole."521 And as r—ry. we have Diry)=0 auc We have mentioned iu the Iutroduction that according to the quantum principle. the quautuni state energv £ aud its conjugate time Ff can not be simultancously measured exactlv(Heiseubere uncertainty principle).," And as $r=r_H$, we have $D(r_H)=0$ and We have mentioned in the Introduction that according to the quantum principle, the quantum state energy $E$ and its conjugate time $t$ can not be simultaneously measured exactly(Heisenberg uncertainty principle)."522 Namely treating £ aud τας operators. we have [r.E]—j," Namely, treating $E$ and $t$ as operators, we have $[t,E]=i$."523" Given the relation 101. we must conclude that the uncertaiutv of £ imply that of ry. and then we have Note this non-commitative relation is iudepenudeut ou the parametersof the black hole. and the comespoudiug uncertainty relation is (Αλνο,P n."," Given the relation \ref{11}) ), we must conclude that the uncertainty of $E$ imply that of $r_H$, and then we have Note this non-commutative relation is independent on the parametersof the black hole, and the corresponding uncertainty relation is $(\Delta t)(\Delta r)|_{r\sim r_H}\sim l_p^2$ ."524 Iu other hands. dueto quaüitun measurement effects. ry spread mto a range of {ryAoeg| Ar}.," In other hands, dueto quantum measurement effects, $r_H$ spread into a range of $\{r_H-\Delta r,r_H+\Delta r\}$ ."525 Thus 11) extends iuto, Thus \ref{trn}) ) extends into526JEM-X and ISGRI instruments of INTEGRAL.,JEM-X and ISGRI instruments of INTEGRAL.527 Using the same data anc analysis procedures as ?.. we could not find any spectral transitions either in the lightcurve or by plotting fluxes in different energy bands versus each other.," Using the same data and analysis procedures as \citet{2005A&A...442L..15P}, we could not find any spectral transitions either in the lightcurve or by plotting fluxes in different energy bands versus each other."528 The result does not change with addition of newest RKTE/ASM. MAXI or INTEGRAL data or by extending the analysis up to higher energy bands.," The result does not change with addition of newest RXTE/ASM, MAXI or INTEGRAL data or by extending the analysis up to higher energy bands."529 Although ? ruled out possible instrumental effects on the basis of their analysis of the ASM data of some other sources for the same time interval as for XX-3. we suggest that systematic and/or analysis effects are responsible for the previously reported appearance of the two spectral states.," Although \citet{2005A&A...442L..15P} ruled out possible instrumental effects on the basis of their analysis of the ASM data of some other sources for the same time interval as for X-3, we suggest that systematic and/or analysis effects are responsible for the previously reported appearance of the two spectral states."530 To clarify this issue we have contacted the ASM instrument team inquiring whether any substantial recalibration of ASM data took place after the work of ?.., To clarify this issue we have contacted the ASM instrument team inquiring whether any substantial recalibration of ASM data took place after the work of \citet{2005A&A...442L..15P}.531" According to them. major calibrational changes occurred around MJD 51956 when telemetry modes switched from ASM ""Position Histogram” to ASM Event mode."," According to them, major calibrational changes occurred around MJD 51956 when telemetry modes switched from ASM ""Position Histogram"" to ASM Event mode."532 ASM camera 1] was mainly influenced by this change and a discontinuity around that time might have led to a change in the observed fluxes as reported in ?.., ASM camera 1 was mainly influenced by this change and a discontinuity around that time might have led to a change in the observed fluxes as reported in \citet{2005A&A...442L..15P}.533 However. the spectral discontinuity was seen in each ASM camera separately for XX-3. but not seen at all for a set of other pulsars.," However, the spectral discontinuity was seen in each ASM camera separately for X-3, but not seen at all for a set of other pulsars."534 Additionally. the data software ran through major updates in April 2005 and 2007.," Additionally, the data software ran through major updates in April 2005 and 2007."535 This could have also led to the reported behavior if the data for XX-1. XX-1. and XX-] used by ? to check for possible instrumental effects were downloaded after the software update.," This could have also led to the reported behavior if the data for X-1, X-1, and X-1 used by \citet{2005A&A...442L..15P} to check for possible instrumental effects were downloaded after the software update."536 The instrument team also generally claimed that although it is now difficult to check if the recalibration or data analysis software updates could lead to the reported effect. the regular improvement of the ASM calibration over time suggests that any later analysis is generally more reliable as the earlier one.," The instrument team also generally claimed that although it is now difficult to check if the recalibration or data analysis software updates could lead to the reported effect, the regular improvement of the ASM calibration over time suggests that any later analysis is generally more reliable as the earlier one."537"on an eccentric orbit, and observations indicate that it may have a non-equilibrium atmosphere (Stevensonetal. 2010).","on an eccentric orbit, and observations indicate that it may have a non-equilibrium atmosphere \citep{Stevenson_2010}."538". There is no reason, on the other hand, that planets shouldn’t lie below the red dotted line in Figure 7:: all it would take is non-zero Bond albedo."," There is no reason, on the other hand, that planets shouldn't lie below the red dotted line in Figure \ref{beta_vs_T0}: all it would take is non-zero Bond albedo."539" That said, only 3 of the 24 planets we consider are in this region, with the greatest outlier being HD 80606b, a planet on an extremely eccentric orbit with superior conjunction nearly coinciding with periastron."," That said, only 3 of the 24 planets we consider are in this region, with the greatest outlier being HD 80606b, a planet on an extremely eccentric orbit with superior conjunction nearly coinciding with periastron."540" As such, it is likely that much of the energy absorbed by the planet at that point in its orbit performs mechanical work (speedingupwinds,puffingtheplanet,etc.SeealsoCowan&Agol2010) rather than merely warming the gas."," As such, it is likely that much of the energy absorbed by the planet at that point in its orbit performs mechanical work \citep[speeding up winds, puffing up the planet, etc. See also][]{Cowan_2010} rather than merely warming the gas."541 Gl 436b and HD 80606b are denoted by red x’s in Figure 7.., Gl 436b and HD 80606b are denoted by red x's in Figure \ref{beta_vs_T0}. .542" The gray points in Figure 7 indicate the default values (using only observations with A>0.8 micron) for the four planets whose optical eclipse depths may be probing thermal emission rather than just reflected light (from left to right: TrES-2b, CoRoT-2b, CoRoT-1b, HAT-P-7b)."," The gray points in Figure \ref{beta_vs_T0} indicate the default values (using only observations with $\lambda > 0.8$ micron) for the four planets whose optical eclipse depths may be probing thermal emission rather than just reflected light (from left to right: TrES-2b, CoRoT-2b, CoRoT-1b, HAT-P-7b)."543" For these planets we have here elected to use all available flux ratios optical observations potentially contaminated by (includingreflected light) to estimate the day-side bolometric flux and effective temperature, shown as black points in Figure 7.."," For these planets we have here elected to use all available flux ratios (including optical observations potentially contaminated by reflected light) to estimate the day-side bolometric flux and effective temperature, shown as black points in Figure \ref{beta_vs_T0}."544" If one takes these day-side effective temperature estimates at face value, it appears that the planets with Τεοϱ«2400 K exhibit a wide-variety of redistribution efficiencies Bond albedos, but are consistent with Ap=0."," If one takes these day-side effective temperature estimates at face value, it appears that the planets with $T_{\varepsilon=0}<2400$ K exhibit a wide-variety of redistribution efficiencies and/or Bond albedos, but are consistent with $A_{B}=0$."545" It is and/orworth noting that many of the best characterized planets in this region have Ta/To~0.75, and this accounts for the sharp peak in the dotted line of Figure 5 at εξ0.75."," It is worth noting that many of the best characterized planets in this region have $T_{\rm d}/T_{0}\approx 0.75$, and this accounts for the sharp peak in the dotted line of Figure \ref{all_R50_N0_both_circulation_hist} at $\varepsilon=0.75$."546" The hottest 6 planets, on the other hand, have uniformly high Ta/To, indicating that they have both low Bond albedo low redistribution efficiency."," The hottest 6 planets, on the other hand, have uniformly high $T_{\rm d}/T_{0}$, indicating that they have both low Bond albedo low redistribution efficiency."547" These planets must not have the high-altitude, reflective silicate clouds hypothesized in Sudarskyetal.(2000)."," These planets must not have the high-altitude, reflective silicate clouds hypothesized in \cite{Sudarsky_2000}."548". But this conclusion is dependent on how one interprets the observations of HAT-P-7b: if the large optical flux ratio is due to reflected light, then this planet is cooler than we think, and even the hottest transiting planets exhibit a variety of behaviors."," But this conclusion is dependent on how one interprets the observations of HAT-P-7b: if the large optical flux ratio is due to reflected light, then this planet is cooler than we think, and even the hottest transiting planets exhibit a variety of behaviors."549" We have described how to estimate a planet's incident power budget (Το), where the uncertainties are driven by the uncertainties in the host star's effective temperature and size, as well as the planet’s orbit."," We have described how to estimate a planet's incident power budget $T_{0}$ ), where the uncertainties are driven by the uncertainties in the host star's effective temperature and size, as well as the planet's orbit."550 We then described a model-independent technique to estimate the effective temperature of a planet based on planet/star flux ratios obtained at various wavelengths., We then described a model-independent technique to estimate the effective temperature of a planet based on planet/star flux ratios obtained at various wavelengths.551" When the observed day-side and night-side effective temperatures are compared, one can constrain a combination of the planet's Bond albedo, Ag, and its recirculation efficiency, ε."," When the observed day-side and night-side effective temperatures are compared, one can constrain a combination of the planet's Bond albedo, $A_{B}$, and its recirculation efficiency, $\varepsilon$."552 We applied this analysis on 24 known transiting planets with measured infrared eclipse depths., We applied this analysis on 24 known transiting planets with measured infrared eclipse depths.553 Our principal results are: 1., Our principal results are: 1.554 Essentially all of the planets are consistent with low Bond albedo., Essentially all of the planets are consistent with low Bond albedo.555 2., 2.556" We firmly rule out the “null hypothesis"", whereby all transiting planets can be fit by a single Ap and e."," We firmly rule out the “null hypothesis”, whereby all transiting planets can be fit by a single $A_{B}$ and $\varepsilon$."557" It is not immediately clear whether this stems from differences in Bond albedo, recirculation efficiency, or both."," It is not immediately clear whether this stems from differences in Bond albedo, recirculation efficiency, or both."558 3., 3.559" In the few cases where it is possible to unambiguously infer an albedo based on optical eclipse depths, they are extremely low, implying correspondingly low Bond albedos (« 10%))."," In the few cases where it is possible to unambiguously infer an albedo based on optical eclipse depths, they are extremely low, implying correspondingly low Bond albedos $<10$ )."560" If one adopts such low albedos for all the planets in our sample, the discrepancies in day-side effective temperature must be due to differences in recirculation efficiency."," If one adopts such low albedos for all the planets in our sample, the discrepancies in day-side effective temperature must be due to differences in recirculation efficiency."561 4., 4.562 These differences in recirculation efficiency do not appear to be correlated with the presence or absence of a stratospheric inversion., These differences in recirculation efficiency do not appear to be correlated with the presence or absence of a stratospheric inversion.563 5., 5.564 Planets cooler than Τε.ο=2400 K exhibit a wide variety of circulation efficiencies that do not appear to be correlated with equilibrium temperature., Planets cooler than $T_{\varepsilon=0}=2400$ K exhibit a wide variety of circulation efficiencies that do not appear to be correlated with equilibrium temperature.565" Alternatively, these planets may have different (but generally low) albedos."," Alternatively, these planets may have different (but generally low) albedos."566 Planets hotter than Τεϱ=2400 K have uniformly low redistribution efficiencies and albedos., Planets hotter than $T_{\varepsilon=0}=2400$ K have uniformly low redistribution efficiencies and albedos.567 The apparent decrease in advective efficiency with increasing planetary temperature remains unexplained., The apparent decrease in advective efficiency with increasing planetary temperature remains unexplained.568" One hypothesis, mentioned earlier, is that TiO and VO would provide additional optical opacity in atmospheres hotter than T~1700 K, leading to temperature inversions and reduced heat recirculation on these planets (Fortneyetal.2008)."," One hypothesis, mentioned earlier, is that TiO and VO would provide additional optical opacity in atmospheres hotter than $T\sim1700$ K, leading to temperature inversions and reduced heat recirculation on these planets \citep{Fortney_2008}."569". But if our sample shows any sharp change it behavior it occurs near 2400 K, rather than 1700 K. One could invoke another optical absorber, but in any case the lack of correlation. —pointed out in this work and elsewhere— between the presence of a temperature inversion and the efficiency of heat recirculation makes this explanation suspect."," But if our sample shows any sharp change it behavior it occurs near 2400 K, rather than 1700 K. One could invoke another optical absorber, but in any case the lack of correlation ---pointed out in this work and elsewhere— between the presence of a temperature inversion and the efficiency of heat recirculation makes this explanation suspect."570 Another possible explanation for the observed trend is that the hottestplanets have the most ionized atmospheres and may suffer the most severe magnetic drag (Pernaetal. 2010).., Another possible explanation for the observed trend is that the hottestplanets have the most ionized atmospheres and may suffer the most severe magnetic drag \citep{Perna_2010}. .571ereat deal about the internal structure of more massive aand ssvstenis aud about the connection between these systems aid the population of high. redshilt galaxies.,great deal about the internal structure of more massive and systems and about the connection between these systems and the population of high redshift galaxies.572 We thank Eric Liuder for useful discussions., We thank Eric Linder for useful discussions.573 This work was supported by NASA Astropliysical Theory Grants NAG5-3922. NAC5-3820. and NACÓ-3111. by NASA Loug-Terii Space Astrophysics Grant NACG5-3525. and by the NSF uuder grants ASCOJ3-Is155. ACIO6-19010. aud. AST-OS802568.," This work was supported by NASA Astrophysical Theory Grants NAG5-3922, NAG5-3820, and NAG5-3111, by NASA Long-Term Space Astrophysics Grant NAG5-3525, and by the NSF under grants ASC93-18185, ACI96-19019, and AST-9802568."574 Garcduer was supported under NASA Crant NCE5-50078 and NSF Award DCE-O071228 for the curation of this work., Gardner was supported under NASA Grant NGT5-50078 and NSF Award DGE-0074228 for the duration of this work.575 The simulatious were perforiued at the Sau Diego Supercomputer Center., The simulations were performed at the San Diego Supercomputer Center.576quasars are shown to be located in slightly more overdense environments than the dimmer quasars.,quasars are shown to be located in slightly more overdense environments than the dimmer quasars.577 At scale of 21.0htApe. the brighter quasars are located in environments with overdensity 1.5 (mes Chat of (he climmer quasars.," At scale of $R\approx 1.0\Mpchseventy$, the brighter quasars are located in environments with overdensity 1.5 times that of the dimmer quasars."578 The brighter quasars have environments with overdensity 1.4 (mes (he overdensity of dimmer quasar environments al a scale of Rx250ho!kpe. and then the ratio begins to drop toward unity al the innermost scales.," The brighter quasars have environments with overdensity 1.4 times the overdensity of dimmer quasar environments at a scale of $R\approx250\kpchseventy$, and then the ratio begins to drop toward unity at the innermost scales."579 llowever. the large errors are nearly consistent with unity on all scales we measure.," However, the large errors are nearly consistent with unity on all scales we measure."580 It appears. therefore. that there is again slight evidence for some redshift evolution of Type I quasar environments. but it is mainly manilested al the highest redshilt range.," It appears, therefore, that there is again slight evidence for some redshift evolution of Type I quasar environments, but it is mainly manifested at the highest redshift range."581 This emphasizes the need for additional studies of the environments around higher redshift Type I quasars., This emphasizes the need for additional studies of the environments around higher redshift Type I quasars.582 We caution that the increased overdensity at higher redshift may be influenced by the fact that there are nearly thiree times (he number of brighter quasars as cimmer quasars in (he interval 0.45<z0.6 (see Table 2))., We caution that the increased overdensity at higher redshift may be influenced by the fact that there are nearly three times the number of brighter quasars as dimmer quasars in the interval $0.45 < z \leqslant 0.6$ (see Table \ref{table_Fig9Details}) ).583 In the range 0.3<20.45. the number of bright quasars is closer to the number of dim quasars. while in the range 0.15<2x0.3. (he dim quasars outinnber (he bright quasars by more (han a factor of two.," In the range $0.3 < z \leqslant 0.45$, the number of bright quasars is closer to the number of dim quasars, while in the range $0.15 < z \leqslant 0.3$, the dim quasars outnumber the bright quasars by more than a factor of two."584 The change in overdensity ratio will also be affected by the change in mean luminosity of the dimmer quasar sample with increasing redshift., The change in overdensity ratio will also be affected by the change in mean luminosity of the dimmer quasar sample with increasing redshift.585 While the bright quasar luminosity changes only by 0.07 magnitudes. (he mean dim quasar Iuminositv changes by 0.17 magnitudes.," While the bright quasar luminosity changes only by 0.07 magnitudes, the mean dim quasar luminosity changes by 0.17 magnitudes."586 Therefore we cannot draw strong conclusions. but reiterate the need for higher precision and higher redshift measurements of quasar environments.," Therefore we cannot draw strong conclusions, but reiterate the need for higher precision and higher redshift measurements of quasar environments."587 Our work sheds new light on the nature of AGN environments and their relationship to the (vpe. huninosity. ancl redshift of the AGN itself.," Our work sheds new light on the nature of AGN environments and their relationship to the type, luminosity, and redshift of the AGN itself."588 We have used larger samples of AGN targets and imposed a photometric redshift eut on the nearby photometric galaxies in orcler (o minimize projection effects ancl to account for redshift evolution of the photometric galaxy sample., We have used larger samples of AGN targets and imposed a photometric redshift cut on the nearby photometric galaxies in order to minimize projection effects and to account for redshift evolution of the photometric galaxy sample.589 By using photometric redshift cults. we obtain more realistic overclensily estimates and errors for the local environments of AGN of various Iuminosities and types.," By using photometric redshift cuts, we obtain more realistic overdensity estimates and errors for the local environments of AGN of various luminosities and types."590 There are (wo main pictures through which observed differences in AGN can be interpreted., There are two main pictures through which observed differences in AGN can be interpreted.591 In (he merger models presented by Hopkiusetal.(2006).. differing fueling mechanisms (rigeer AGN activity at different luminosities.," In the merger models presented by \citet{Hopkins2006}, differing fueling mechanisms trigger AGN activity at different luminosities."592 Unified models such as those presented by or Elvis(2000) ascribe observed dillerences in AGN to viewing angle or structure., Unified models such as those presented by \citet{Antonucci} or \citet{Elvis} ascribe observed differences in AGN to viewing angle or structure.593 These pictures are not mutually exclusive: in fact. we show that the interdependency between the variables of (wpe. Iuminosity. and redshift play into the subtleties of distinguishing the pictures based on environment overdensity measurements.," These pictures are not mutually exclusive; in fact, we show that the interdependency between the variables of type, luminosity and redshift play into the subtleties of distinguishing the pictures based on environment overdensity measurements."594Figure 4 shows the distribution of richness for the SLACS lenses and the SDSS comparison sample: a Ίντο test cannot distinguish between the distributions.,Figure \ref{figure_comp_rich} shows the distribution of richness for the SLACS lenses and the SDSS comparison sample; a K-S test cannot distinguish between the distributions.595 The lenses lie in typical environments and there is not a strong correlation between the elobal richness ancl the density slope for the SLACS lenses., The lenses lie in typical environments and there is not a strong correlation between the global richness and the density slope for the SLACS lenses.596 Vhree of the systems. SDSSJ1I330-0148. SDSSJ1420|6019. and $D55J2321-0039. are at lower redshifts than the other lenses and their fields have nearly complete SDSS spectroscopy down tor=ris|2.5.," Three of the systems, SDSSJ1330-0148, SDSSJ1420+6019, and SDSSJ2321-0939, are at lower redshifts than the other lenses and their fields have nearly complete SDSS spectroscopy down to $r = r_{lens} + 2.5$."597 We use the SDSS redshifts to determine group properties for these lens fields., We use the SDSS redshifts to determine group properties for these lens fields.598" There is one spectroscopically identified: companion within LOO Kpe of SDSSJ1330-0148 but. no spectroscopic neighbours are found for the other two svstems. tentatively confirming the binary interpretation of IN, for these three systems."," There is one spectroscopically identified companion within 100 kpc of SDSSJ1330-0148 but no spectroscopic neighbours are found for the other two systems, tentatively confirming the binary interpretation of $N_w$ for these three systems."599 However. due to the inability to closely pack fibres on the SDSS spectrograph. the local environments of these lenses are not completely probed: spectroscopically.," However, due to the inability to closely pack fibres on the SDSS spectrograph, the local environments of these lenses are not completely probed spectroscopically."600 One of the systems. SDSSJ1420|6019. appears to be isolated and no group is found to be associated with the lens.," One of the systems, SDSSJ1420+6019, appears to be isolated and no group is found to be associated with the lens."601 For the remaining two lens systems. we determine the eroup velocity dispersion using the biweight estimate of the velocity distribution (Beersetal.1990).. and the lens offset is determined. with respect to the median. position of all identified group members (Table 2)).," For the remaining two lens systems, we determine the group velocity dispersion using the biweight estimate of the velocity distribution \citep{beers}, and the lens offset is determined with respect to the median position of all identified group members (Table \ref{table_groups}) )."602 The LOS ‘contamination’ for a lens can be quantified. by summing the number of objects within an aperture around he lensing galaxy., The LOS `contamination' for a lens can be quantified by summing the number of objects within an aperture around the lensing galaxy.603 We use the SDSS photometric recdshift catalogue to exclude local galaxies with redshifts ο<0.001 hat cdo not stronely influence the lensing., We use the SDSS photometric redshift catalogue to exclude local galaxies with redshifts $z < 0.001$ that do not strongly influence the lensing.604 We then count all xickground galaxies with ollscts less than 30 aresec from the ens and compare this sum with background galaxy. counts in non-lens fields., We then count all background galaxies with offsets less than 30 arcsec from the lens and compare this sum with background galaxy counts in non-lens fields.605 The SDSS comparison saniple for cach ens contains 200 galaxies at the same redshift as the lens and with approximately the same luminosity and: velocity dispersion., The SDSS comparison sample for each lens contains 200 galaxies at the same redshift as the lens and with approximately the same luminosity and velocity dispersion.606 “Phe mean. median. and standard. deviation of he comparison samples are tabulated with the lens data in ‘Table 3..," The mean, median, and standard deviation of the comparison samples are tabulated with the lens data in Table \ref{table_lineofsight}."607 Phe most significant deviation between the lenses and comparison fields is less than 1.5 σ and there is not a systematic olfset., The most significant deviation between the lenses and comparison fields is less than 1.5 $\sigma$ and there is not a systematic offset.608 Note that our comparison is between the LOS of a SLACS lens and the lines of sight to other SDSS massive earlv-tvpe galaxies: random lines of sight might be more or less dense., Note that our comparison is between the LOS of a SLACS lens and the lines of sight to other SDSS massive early-type galaxies; random lines of sight might be more or less dense.609 We find that the global environments of the SLACS lenses are twpical of other massive early-tvpe galaxies found in the SDSS., We find that the global environments of the SLACS lenses are typical of other massive early-type galaxies found in the SDSS.610 Two of the steeper than isothermal svstenis lic in very over-dense regions but the remaining lenses all have richness values that fall near the peak of the richness distribution (Figure 4))., Two of the steeper than isothermal systems lie in very over-dense regions but the remaining lenses all have richness values that fall near the peak of the richness distribution (Figure \ref{figure_comp_rich}) ).611 Furthermore. the suggestion that the οἱλος lenses are alfected by LOS contamination does not seem to be merited by the data.," Furthermore, the suggestion that the SLACS lenses are affected by LOS contamination does not seem to be merited by the data."612 While there are other ealaxies along the lines of sight to the lens svstems. the LOS densities do not significantly deviate [rom the densities along comparable lines of sight.," While there are other galaxies along the lines of sight to the lens systems, the LOS densities do not significantly deviate from the densities along comparable lines of sight."613 We therefore expect. that theparameter estimates should not be alfected as proposed bv Guimaràes&Sodré (2007).., We therefore expect that theparameter estimates should not be affected as proposed by \citet{guimaraes}. .614The Schwinger mechanism of pair production (Schwinger1951).. first proposed to study the production of electron-positron. pairs in a strong and unilorm electric [fiekl. has been applied to many problems in contemporary physics.,"The Schwinger mechanism of pair production \citep{Sch51}, first proposed to study the production of electron-positron pairs in a strong and uniform electric field, has been applied to many problems in contemporary physics."615 Strong electromagnetic [fields lead to {wo physically important phenomena: pair production and vacuum polarization., Strong electromagnetic fields lead to two physically important phenomena: pair production and vacuum polarization.616 A strong electric field makes the quantum electrodvnanmic vacuum (QED) unstable. and consequently it decavs by emitting a significant number of boson or fermion pairs (Greinerοἱal.1985).," A strong electric field makes the quantum electrodynamic vacuum (QED) unstable, and consequently it decays by emitting a significant number of boson or fermion pairs \citep{Gr85}."617". For a spin 1/2 particle Schwinger's predicted production rate per unit time and volume wis given by (Schwinger1951:Solleletal.1952) where i, and e are (he electron mass and charge. respectively. A; is (he (rausverse momentum and Ly is the (constant) electric fiekd."," For a spin $1/2$ particle Schwinger's predicted production rate per unit time and volume $w$ is given by \citep{Sch51,So82}618 where $m_{e}$ and $e$ are the electron mass and charge, respectively, $k_{i}$ is the transverse momentum and $E_0$ is the (constant) electric field."619 In the present paper we use units so (hat h=e=hy=1., In the present paper we use units so that $\hbar =c =k_B =1$.620 In these units. e is equal to al’? and 1 MeV5.064x10* [m|!," In these units, $e$ is equal to $\alpha^{1/2}$ and $1$ $=5.064\times 10^{-3}$ $^{-1}$."621 In most of the physical applications the proper time method introduced by has been used to calculate the pair production rate., In most of the physical applications the proper time method introduced by \citet{Sch51} has been used to calculate the pair production rate.622 The real part of the effective action leads to vacuum polarization and the imaginary part to pair production., The real part of the effective action leads to vacuum polarization and the imaginary part to pair production.623 Though that method is conceptually well defined ancl technically rigorous. it is generally difficult to apply 1 to concrete physical problems such as inhomogeneous electromagnetic fields.," Though that method is conceptually well defined and technically rigorous, it is generally difficult to apply it to concrete physical problems such as inhomogeneous electromagnetic fields."624 Schwinger's result. was generalized to electric fields Ly=FE(vr). which depend upon either Leht cone coordinates re—tydag. bul not upon both. in Tomarasetal.(2000).," Schwinger's result was generalized to electric fields $E_3=E_3\left(x_{\pm }\right)$, which depend upon either light cone coordinates $x_{\pm }=x_3\pm x_0$, but not upon both, in \citet{To00}."625. The form of the result is exactly the same as in (he original formula given by Eq. (11)., The form of the result is exactly the same as in the original formula given by Eq. \ref{prod}) ).626 The case of electric fields depending on both. and.r. by=Bytror) was considered in Avanatal.(2003).," The case of electric fields depending on both $x_+$ and $x_{-}$, $E_3=E_3\left(x_+,x_{-}\right)$ was considered in \citet{Av03}."627. An alternative approach to pair creation was initiated by Casherοἱal.(L979.1930).. who re-derived Sehwingers pair production rate by senii-classical tunnelling. calculations.," An alternative approach to pair creation was initiated by \citet{Ca79,Ca80}, who re-derived Schwinger's pair production rate by semi-classical tunnelling calculations."628 The boson and fermion pair production rate by strong static uniform or inhomogeneous electric fields was derived. in terms of instanton tunnelling through potential barriers in the space-dependent gauge. in IximandPage(2002).," The boson and fermion pair production rate by strong static uniform or inhomogeneous electric fields was derived, in terms of instanton tunnelling through potential barriers in the space-dependent gauge, in \citet{Kim02}."629. The Schwinger mechanism for particle production in a strong; and uniform electric field for an infinite svstem was generalized (ο the case were the strong field is confined between two plates separated by a finite distance by WanganclWong(1988)., The Schwinger mechanism for particle production in a strong and uniform electric field for an infinite system was generalized to the case were the strong field is confined between two plates separated by a finite distance by \citet{Wa88}.630. The production rates. obtained by solving the Nlein-Gordon and Dirac equations in a linear vector potential. can be expressed in an exact analvtical Form.," The production rates, obtained by solving the Klein-Gordon and Dirac equations in a linear vector potential, can be expressed in an exact analytical form."631 The numerical evaluations of (he production rates have shown large deviations [rom the Schwinger formula. thus indicating a large finite size effect in," The numerical evaluations of the production rates have shown large deviations from the Schwinger formula, thus indicating a large finite size effect in"632"divideds at z—0.5 and Ad,—9LOMt AXIAL..",divided at $z=0.5$ and $M_*=9\times10^{10}$ $_\odot$.633" Figure"" 3 shows the average SELL for cach sub-saniple. rebinned to a common resolution of five blocks."," Figure \ref{SFHs} shows the average SFH for each sub-sample, rebinned to a common resolution of five blocks."634 In the averaging. we normalised the SELL of cach galaxy to units of fractional total stellar mass formed per fractional age so that the integral of SELL over fractional age (i.c.. the total stellar mass) is equal to unity.," In the averaging, we normalised the SFH of each galaxy to units of fractional total stellar mass formed per fractional age so that the integral of SFH over fractional age (i.e., the total stellar mass) is equal to unity."635 The most striking feature seen in the plots is the dillerence between the low and high mass sub-saniples., The most striking feature seen in the plots is the difference between the low and high mass sub-samples.636 On average. both low mass SEIS are dominated by a late burst of strong star formation activity accounting for 40% of the otal stellar mass.," On average, both low mass SFHs are dominated by a late burst of strong star formation activity accounting for $\sim 40\%$ of the total stellar mass."637 Conversely. both high mass SELIs show hat a much smaller fraction of stellar mass (~5 104) is created during this last. period. the majority of mass being ormed at earlier times.," Conversely, both high mass SFHs show that a much smaller fraction of stellar mass $\sim 5 -63810\%$ ) is created during this last period, the majority of mass being formed at earlier times."639Another obvious cllect seen in Figure 3. is that. the igh mass sources exhibit a more prominent dillerence in heir SELIs in moving from high to low redshifts than the ow mass sources.,Another obvious effect seen in Figure \ref{SFHs} is that the high mass sources exhibit a more prominent difference in their SFHs in moving from high to low redshifts than the low mass sources.640 The high mass sources have therefore. by his definition. undergone more evolution.," The high mass sources have therefore, by this definition, undergone more evolution."641 To quantily the signilieance of this. we computed the reduced. X7 statistic oetween the low anc high. redshift SELHIs for the low and ligh mass sub-samples in turn.," To quantify the significance of this, we computed the reduced $\chi^2$ statistic between the low and high redshift SFHs for the low and high mass sub-samples in turn."642 For the high mass SELIs. the statistic is A7—3.57£0.63 compared to 47=0.51+0.63 or the low mass ΕΠΣ.," For the high mass SFHs, the statistic is $\chi^2_r=3.57\pm0.63$ compared to $\chi^2_r=0.51\pm0.63$ for the low mass SFHs."643 Phe change at high mass is therefore significant at the ~30 level whereas the [ow mass source SELs are consistent with no change., The change at high mass is therefore significant at the $\sim 3 \sigma$ level whereas the low mass source SFHs are consistent with no change.644 This is svnonvmous with downsizing where the instantaneous star formation rate in high mass galaxies evolves more strongly than that in low mass systems (e.g.Lleavensetal.2004).," This is synonymous with downsizing where the instantaneous star formation rate in high mass galaxies evolves more strongly than that in low mass systems \citep[e.g.,][]{heavens04}."645. The SELIs computed in terms of fractional mass and fractional galaxy age are a very useful diagnostic since they cllectively normalise out thelarge scatter in mass and redshift present in the necessarily coarsely binned sub-samples., The SFHs computed in terms of fractional mass and fractional galaxy age are a very useful diagnostic since they effectively normalise out thelarge scatter in mass and redshift present in the necessarily coarsely binned sub-samples.646 This makes the mean trends more Conspicuous., This makes the mean trends more conspicuous.647 llowever. to compare with more traditional studies of the evolution of star formation. we estimated. instantaneous absolute SERs.," However, to compare with more traditional studies of the evolution of star formation, we estimated instantaneous absolute SFRs."648" For each source. we computed. a ""pseudo-instantaneous! SER by dividing the absolute stellar mass created in the last SELL block by the real time spanned by the block."," For each source, we computed a `pseudo-instantaneous' SFR by dividing the absolute stellar mass created in the last SFH block by the real time spanned by the block."649 We found that the pseudo-instantaneous SER for the high mass sources changed [rom 75226 MM. ver+ at high redshifts to 2045 MAL. at low redshifts., We found that the pseudo-instantaneous SFR for the high mass sources changed from $75\pm26$ $_\odot$ $^{-1}$ at high redshifts to $20\pm5$ $_\odot$ $^{-1}$ at low redshifts.650 In comparison. the change for the low mass sources is from from 432 23MM. + at high redshifts to Ὁ2 MM. vr+ at low redshifts.," In comparison, the change for the low mass sources is from from $43\pm23$ $_\odot$ $^{-1}$ at high redshifts to $9\pm2$ $_\odot$ $^{-1}$ at low redshifts."651 Phe conclusion is therefore that we detect no significant cdillerence in the evolution of the pseudo-instantaneous SER between the high and low mass sources., The conclusion is therefore that we detect no significant difference in the evolution of the pseudo-instantaneous SFR between the high and low mass sources.652 ‘Lo detect an absolute trend such as this. more sources would be required to enable finer binning in mass and redshift.," To detect an absolute trend such as this, more sources would be required to enable finer binning in mass and redshift."653 An interesting point to note is that the rate of formation of stellar mass. which is highest at carly and at late times in the high mass. high redshift sub-sample. is very. similar to that measured by Dyectal.(2008). for jin selected sources.," An interesting point to note is that the rate of formation of stellar mass, which is highest at early and at late times in the high mass, high redshift sub-sample, is very similar to that measured by \citet{dye_et_al08} for $\,\mu$ m selected sources."654" This is perhaps not too surprising given the large overlap of this sub-sample with the sam sample which has à median value of redshift and log,CM/M..) of 1.621.0 and 11.5d:0.5 respectively. where the errors give the standard deviation."," This is perhaps not too surprising given the large overlap of this sub-sample with the $\,\mu$ m sample which has a median value of redshift and $\log_{10}$ $/$ $_\odot)$ of $1.6\pm1.0$ and $11.5\pm0.5$ respectively, where the errors give the standard deviation."655 Ehe fact that such a large stellar. population was already in place at higher redshifts suggests that the peak star formation rate occurred significantly earlier in the history of the Universe for high mass systems than for low mass svstems., The fact that such a large stellar population was already in place at higher redshifts suggests that the peak star formation rate occurred significantly earlier in the history of the Universe for high mass systems than for low mass systems.656 This behaviour was observed by al.(2004) [or optically selected galaxies., This behaviour was observed by \citet{heavens04} for optically selected galaxies.657 To verily the robustness of our results. we conduct a series of tests.," To verify the robustness of our results, we conducted a series of tests."658 The first was to see if the inferred. SELIS are intrinsic or merely the effect. of reddening., The first was to see if the inferred SFHs are intrinsic or merely the effect of reddening.659 For example. an intrinsically late-type galaxy with strong recdcdening coulc give rise to a reconstructed SEL with artificially suppressec late star formation.," For example, an intrinsically late-type galaxy with strong reddening could give rise to a reconstructed SFH with artificially suppressed late star formation."660 We therefore plotted the fraction of mass formed in the last of cach galaxy’s history. Maz against ly.," We therefore plotted the fraction of mass formed in the last of each galaxy's history, $_{10\%}$ , against $A_V$ ."661 Since late activity strongly dominates the shape, Since late activity strongly dominates the shape6622010).. the data of X-ray gas mass [fraction in elusters (Allenetal.2004.2008:Ettori2009) and gravitational lensing data 2002:Cao&Zhu 2011)..,", the data of X-ray gas mass fraction in clusters \citep{Allen04,Allen08,Ettori09} and gravitational lensing data \citep{Zhu98,Sereno02,Cao11b}."663 This work was supported by the National Natural Science Foundation of China under the Disünguished Young Scholar Grant 10825312 and Grant 11073005. (he Ministry of Science and Technology national basic science Program (Project 973) under Grant No.2007CD8315401. the Fundamental Research Funds for the Central Universities and Scientific Research Foundation ol Beijing Normal University.," This work was supported by the National Natural Science Foundation of China under the Distinguished Young Scholar Grant 10825313 and Grant 11073005, the Ministry of Science and Technology national basic science Program (Project 973) under Grant No.2007CB815401, the Fundamental Research Funds for the Central Universities and Scientific Research Foundation of Beijing Normal University."664these results in Section 4.1 below.,these results in Section \ref{mass} below.665 Results calculated from our data are presented in Table 1.., Results calculated from our data are presented in Table \ref{coreprop}.666 Here. Core B is located to the north of Core A (Fig. 3))," Here, Core B is located to the north of Core A (Fig. \ref{model3176}) )"667 and. although it is the more extended of the two. 1t is actually fainter than Core A. Neither core can be seen in emission at wavelengths shorter than ym. A distance of kkpe is assumed (?)..," and, although it is the more extended of the two, it is actually fainter than Core A. Neither core can be seen in emission at wavelengths shorter than $\mu$ m. A distance of kpc is assumed \citep{simon06b}."668 No previously calculated masses are available for these cores., No previously calculated masses are available for these cores.669 A third core in this cloud. located to the south of Core A. is not modelled here due to a bright 84m source at the same position. implying the core may have an internal heating source.," A third core in this cloud, located to the south of Core A, is not modelled here due to a bright $\mu$ m source at the same position, implying the core may have an internal heating source."670 A possible fourth core exists to the north of Core B. we ignore this as 506 state that it belongs to a different IRDC with no known distance.," A possible fourth core exists to the north of Core B, we ignore this as S06 state that it belongs to a different IRDC with no known distance."671 Results calculated from our data are presented in Table 1.., Results calculated from our data are presented in Table \ref{coreprop}.672 We model the cores in two different ways: first. using a greybody single-temperature fit. and second. usingthe 3D Monte Carlo radiative transfer code. (???)..," We model the cores in two different ways: first, using a greybody single-temperature fit, and second, usingthe 3D Monte Carlo radiative transfer code, \citep{stamatellos03, stamatellos05, stamatellos10}."673 The flux density. integrated over twice the FWHM of each core using an elliptical aperture. was measured in all five FIR maps (see Table 2)) and an SED (spectral energy distribution) was plotted.," The flux density, integrated over twice the FWHM of each core using an elliptical aperture, was measured in all five FIR maps (see Table \ref{flux}) ) and an SED (spectral energy distribution) was plotted."674 These flux densities have been background subtracted. where the background was defined using an off-cloud. elliptical aperture.," These flux densities have been background subtracted, where the background was defined using an off-cloud, elliptical aperture."675 For example. with GO31.03+00.76 the area to the right of Core B was used.," For example, with G031.03+00.76 the area to the right of Core B was used."676 The background subtraction removed up to of the original flux. the exception being at um where over of the original flux was removed.," The background subtraction removed up to of the original flux, the exception being at $\mu$ m where over of the original flux was removed."677 A single- greybody (modelling thermal emission from cold dust) was fitted (using MPFit: ?)) to each core. shown as a dashed line in Fig. 4..," A single-temperature greybody (modelling thermal emission from cold dust) was fitted (using MPFit; \citealp{sedfit}) ) to each core, shown as a dashed line in Fig. \ref{seda}."678" This has the form where: F, is the flux density at frequency v: B,(T) i8 the blackbody function at temperature 7: Q ts the solid angle subtended at the observer by the source: 2715 1s the mass of a hydrogen molecule: is the mass fraction of hydrogen and κι Is the dust mass opacity (e.g. 22))."," This has the form where: $F_{\nu}$ is the flux density at frequency $\nu$; $B_{\nu}(T)$ is the blackbody function at temperature $T$; $\Omega$ is the solid angle subtended at the observer by the source; $m_H$ is the mass of a hydrogen molecule; is the mass fraction of hydrogen and $\kappa_\nu$ is the dust mass opacity (e.g. \citealt{kirk10, wardthompson10}) )."679" &, is given by where f. the dust emissivity index. was set to 1.85 (?).."," $\kappa_\nu$ is given by where $\beta$, the dust emissivity index, was set to 1.85 \citep{ossenkopf94}."680 The model was fitted between jm and jm. with the flux density at jm being used as an upper limit. as the cores are not visible at this wavelength.," The model was fitted between $\mu$ m and $\mu$ m, with the flux density at $\mu$ m being used as an upper limit, as the cores are not visible at this wavelength."681 The temperature was allowed to vary over a range KK. The best fit temperatures for the cores are given in Table I., The temperature was allowed to vary over a range K. The best fit temperatures for the cores are given in Table \ref{coreprop}.682 The cores were modelled usingPHAETHON.. a 3D Monte Carlo radiative transfer code.," The cores were modelled using, a 3D Monte Carlo radiative transfer code."683 The code uses luminosity packets to represent the ambient radiation field in the system., The code uses luminosity packets to represent the ambient radiation field in the system.684 These packets are injected into the system where they interact (are absorbed. re-emitted or scattered) with it stochastically.," These packets are injected into the system where they interact (are absorbed, re-emitted or scattered) with it stochastically."685 The ambient radiation field is taken to be a multiple of a modified version of the ? interstellar radiation field. which gives a good approximation to the radiation field in the solar neighbourhood.," The ambient radiation field is taken to be a multiple of a modified version of the \citet{black94} interstellar radiation field, which gives a good approximation to the radiation field in the solar neighbourhood."686 The input variables of the code are the strength of the ambient radiation field. the density profile. the size and geometry of the core (1e. spherical. flattened or cometary) and the dust properties of the system.," The input variables of the code are the strength of the ambient radiation field, the density profile, the size and geometry of the core (i.e. spherical, flattened or cometary) and the dust properties of the system."687 The code calculates the temperature profile of the system as well as SEDs and intensity maps. at different wavelengths and viewing angles.," The code calculates the temperature profile of the system as well as SEDs and intensity maps, at different wavelengths and viewing angles."688 All six cores showed some measure of eccentricity in the observations and so were modelled with a flattened geometry — see ?? for details.," All six cores showed some measure of eccentricity in the observations and so were modelled with a flattened geometry — see \citet{stamatellos04, stamatellos10} for details."689 In this case the density profile is given by: where is the radial distance. 4 is the polar angle and Ro is the flattening radius (i.e. the radial distance for which the central density is approximately constant).," In this case the density profile is given by: where is the radial distance, $\theta$ is the polar angle and $R_0$ is the flattening radius (i.e. the radial distance for which the central density is approximately constant)."690 ΠΟ(Π2) is the central density. which ts controlled as an input variable.," $_0$ $_2$ ) is the central density, which is controlled as an input variable."691 is a factor that controls the equatorial to polar optical depth ratio and determines how flattened the core is., is a factor that controls the equatorial to polar optical depth ratio and determines how flattened the core is.692 determines how quickly the optical depth changes from equator to pole. and was set to 2," determines how quickly the optical depth changes from equator to pole, and was set to 2."693 The FWHM of the major axis of each observed core was measured at 250 jm and used as the model core’s semi-major axis., The FWHM of the major axis of each observed core was measured at 250 $\mu$ m and used as the model core's semi-major axis.694 The flattening radius. Ro.. was set at one tenth of this," The flattening radius, , was set at one tenth of this"695some problems have been pointed out for this method.,some problems have been pointed out for this method.696" For instance, the relation between the UV slope § (or equivalently, FUV-NUV color) and the FIR-FUV flux ratio Legi/Lruv (often referred to as the IRX- relation) is frequently used to correct the extinction, but this relation is not always the same for various categories of star-forming galaxies etal. 2010a)."," For instance, the relation between the UV slope $\beta$ (or equivalently, $-$ NUV color) and the FIR-FUV flux ratio $\lir/\luv$ (often referred to as the $\beta$ relation) is frequently used to correct the extinction, but this relation is not always the same for various categories of star-forming galaxies \citep[e.g.][]{buat05,boissier07,boquien09,takeuchi10a}."697". Instead, the total SFR obtained from the FUV and FIR luminosities would be a more reliable measure of the SFR since both are directly observable values (e.g.Iglesias-Páramoetal.2004;Buat2005;2006;2007a,b;Takeuchi2010a)."," Instead, the total SFR obtained from the FUV and FIR luminosities would be a more reliable measure of the SFR since both are directly observable values \citep[e.g.][]{iglesias04, buat05, iglesias06, buat07a, buat07b, takeuchi10a}."698". Assuming a constant SFR over 105yr, and Salpeter initial mass function (Salpeter1955,massrange:0.1-1100 Mo), we have the relation between the SFR and Lruv For the FIR, to transform the dust emission to the SFR, we assume that all the stellar light is absorbed by dust."," Assuming a constant SFR over $10^8 \mbox{yr}$, and Salpeter initial mass function \citep[][mass range: $0.1\mbox{--}1 , we have the relation between the SFR and $\luv$ For the FIR, to transform the dust emission to the SFR, we assume that all the stellar light is absorbed by dust."699" Then, we obtain the following formula under the same assumption for both the SFR history and the IMF as those of the FUV, Here, 77 is the fraction of the dust emission by old stars which is not related to the current SFR (Hirashita,Buat,&Inoue2003),, and Ίντι is the FIR luminosity integrated over A=8-1000 jum. Thus, the total SFR is simply (glesias-Paramoetal.2006)."," Then, we obtain the following formula under the same assumption for both the SFR history and the IMF as those of the FUV, Here, $\eta$ is the fraction of the dust emission by old stars which is not related to the current SFR \citep{hirashita03}, and $\ltir$ is the FIR luminosity integrated over $\lambda = 8 \mbox{--} 1000\;\mu$ m. Thus, the total SFR is simply \citep{iglesias06}."700". Since the total SFR is basically estimated from the luminosities at FUV and FIR (note that and SFRaustος Drip), the estimation of the PDF of the total SFR reduces to the estimation of the FIR-FUV BLF 2010b)."," Since the total SFR is basically estimated from the luminosities at FUV and FIR (note that $\sfruv \propto \luv$ and $\sfrir \propto \ltir$ ), the estimation of the PDF of the total SFR reduces to the estimation of the FIR-FUV BLF \citep[e.g.][]{takeuchi10b}."701". Another direct application is the distribution of the specific SFR (SSFR), SFR/M.. where ΛΜ. is the total stellar mass of a galaxy."," Another direct application is the distribution of the specific SFR (SSFR), $\mbox{SFR}/M_*$ where $M_*$ is the total stellar mass of a galaxy."702" The SSFR has gained much attention in the last decade, since the relation between M.. and the SSFR of galaxies turns out to be a very important clue to understand the SF history of galaxies: more massive galaxies have ceased their SF activity earlier in the cosmic time than less massive galaxies (downsizinginredshift:e.g.Cowieetal.1996;Boselli2001;Heavens2004;Feulner2005;NoeskePanteretal.2007;Damen2009a,b,among others)."," The SSFR has gained much attention in the last decade, since the relation between $M_*$ and the SSFR of galaxies turns out to be a very important clue to understand the SF history of galaxies: more massive galaxies have ceased their SF activity earlier in the cosmic time than less massive galaxies \citep[downsizing in redshift: e.g.][among others]{cowie96,boselli01,heavens04,703feulner05,noeske07a,noeske07b,panter07,damen09a,damen09b}."704". For a comprehensive summary of the downsizing, readers are encouraged to read Introduction of Fontanotetal.(2009)."," For a comprehensive summary of the downsizing, readers are encouraged to read Introduction of \citet{fontanot09}."705". Despite of its importance, the treatment of multiwavelength data for this analysis is inevitably complicated and does not seem to be well understood, because we must deal with the data related to SFR and M.. estimation."," Despite of its importance, the treatment of multiwavelength data for this analysis is inevitably complicated and does not seem to be well understood, because we must deal with the data related to SFR and $M_*$ estimation."706" This might be, at least partially, the reason why the quantitative values of the M..-SSFR relation are different among different studies."," This might be, at least partially, the reason why the quantitative values of the $M_*$ –SSFR relation are different among different studies."707" As may easily guess after the above discussions, the M..-SSFR relation can be reduced to the relation between a luminosity at a certain mass-related band (often near IR bands) and a SF-related one (FUV, FIR, etc.)"," As may easily guess after the above discussions, the $M_*$ –SSFR relation can be reduced to the relation between a luminosity at a certain mass-related band (often near IR bands) and a SF-related one (FUV, FIR, etc.)"708" Then, we can model, for example, a Li —L'rrn bivariate luminosity function (Lx: K-band to examine the observed relation including all the selection effects."," Then, we can model, for example, a $L_K$ $\ltir$ bivariate luminosity function $L_K$: -band to examine the observed relation including all the selection effects."709" This is particularly useful for this topic, since Takeuchietal.(2010b) found that the SFRF cannot be described by the Schechterfunction unlike the assumptions adopted in previous studies, but much more similar to the Saunders IR LF [Eq. (36))]."," This is particularly useful for this topic, since \citet{takeuchi10b} found that the SFRF cannot be described by the Schechterfunction unlike the assumptions adopted in previous studies, but much more similar to the Saunders IR LF [Eq. \ref{eq:saunders}) )]."710 The selection effect would be more complicated than, The selection effect would be more complicated than711For the error of SAIBLL mass. MeCGill et al.,"For the error of SMBH mass, McGill et al."712 2008 have compared 12 formulae taken [rom the literature. showing that SMDII mass estimates can diller on average 0.13£0.05 or 0.38c0.05 dex in the case of the same or cillerent virial coellicient. respectively.," 2008 have compared 12 formulae taken from the literature, showing that SMBH mass estimates can differ on average $0.13 \pm 0.05$ or $0.38 \pm 0.05$ dex in the case of the same or different virial coefficient, respectively."713 For Sevfert 2 galaxies. we used SMDII mass data (Bian&Gu2007) whose mean error was within a factor of 1.6.," For Seyfert 2 galaxies, we used SMBH mass data \citep{BG07} whose mean error was within a factor of 1.6."714 These were estimated from the SAIBLE massstellar velocity dispersion relation. (Tremaineetal. 2002)., These were estimated from the SMBH mass–stellar velocity dispersion relation \citep{Tr02}.715. Since the PALL molecules are excited by far-UV. photons in the photo-dissociation region around. the LIL region. and strong PALL emission is often observed.from even a weak starburst (Imanishi2002).. we ean use PALL emission as an indicator of starburst activity.," Since the PAH molecules are excited by far-UV photons in the photo-dissociation region around the HII region, and strong PAH emission is often observedfrom even a weak starburst \citep{Im02}, we can use PAH emission as an indicator of starburst activity."716 We used the PALL emission estimated by Watabe.Ixawalkatiu.&Lmanishi(2008). for Sevlert galaxies (6.2. 7.7. and 11.3 p/m) and Shietal. [or PO-QSOs (7.7. and 11.3 jn).," We used the PAH emission estimated by \citet{Wa08} for Seyfert galaxies (6.2, 7.7, and 11.3 $\mu$ m) and \citet{Sh07} for PG-QSOs (7.7, and 11.3 $\mu$ m)."717 We select the 11.3. sam PALL emission., We select the 11.3 $\mu$ m PAH emission.718 The. 7.7 ja PALL emission ijs sometimes allected by the broad and strong 9.7 (mn silicate absorption. especially in Sevfert 2 galaxies.," The 7.7 $\mu$ m PAH emission is sometimes affected by the broad and strong 9.7 $\mu$ m silicate absorption, especially in Seyfert 2 galaxies."719 μις. it could. be cifficult to distinguish between 7.7 pm. PALL emission and 9.7 jun silicate absorption.," Thus, it could be difficult to distinguish between 7.7 $\mu$ m PAH emission and 9.7 $\mu$ m silicate absorption."720 PALL emission. was obtained with the Infrared Spectrograph (URS:Louck2004). (Wernerctal.2004)., PAH emission was obtained with the Infrared Spectrograph \citep[IRS;][]{Ho04} \citep{We04}.721. For Seyfert) galaxies. since the PALL emission was observed. with the slit-scan mode (PID 3269. PLE J. Gallimore). the entire host galaxy regions of the Sevfert galaxies were covered.," For Seyfert galaxies, since the PAH emission was observed with the slit-scan mode (PID 3269, PI: J. Gallimore), the entire host galaxy regions of the Seyfert galaxies were covered."722 For PG-OSOs. PALL emission was obtained by the slit width of Short-Low (SL) (SL1: 37.7. SL2: 37.6) and Long-LowtLL) (LLL: 107.7. LL2: 107.5) modules (forPLDanclPLseeShietal.2007).," For PG-QSOs, PAH emission was obtained by the slit width of Short-Low (SL) (SL1: $\arcsec$ .7, SL2: $\arcsec$ .6) and Long-Low(LL) (LL1: $\arcsec$ .7, LL2: $\arcsec$ .5) modules \citep[for PID and PI, see][]{Sh07}."723. The SL slit width is roughly. comparable to the effective racius of PG-QSO host galaxies (CGiuvon.Sanders.&Stock-ton2006). and several hundred-parsec to. kiloparsec-scale starbursts have been considered. as the origin. of the radiation in. PO-QSOs (Llaasctal.2003:Barthel2006:Netzerοἱal. 2007).," The SL slit width is roughly comparable to the effective radius of PG-QSO host galaxies \citep{Gu06} and several hundred-parsec to kiloparsec-scale starbursts have been considered as the origin of the far-infrared radiation in PG-QSOs \citep{Ha03,Ba06,Ne07}."724. Thus. we consider that these slit observations cover almost all starburst activity in PO-QSOs host galaxies.," Thus, we consider that these slit observations cover almost all starburst activity in PG-QSOs host galaxies."725 We used host. galaxy morphology classifications for PC-OSOs based on the literature. evaluated by 2D 47 fitting of the obtained image (references. Listed in ‘Table 1).," We used host galaxy morphology classifications for PG-QSOs based on the literature, evaluated by 2D $\chi^2$ fitting of the obtained image (references listed in Table 1)."726 We carefully checked the morphology classifications ancl defined a host galaxy as elliptical- or cisk-dominated only in cases for which the literature listed said galaxy as only elliptical or disk. respectively.," We carefully checked the morphology classifications and defined a host galaxy as elliptical- or disk-dominated only in cases for which the literature listed said galaxy as only elliptical or disk, respectively."727 We also defined a bulge | disk host galaxy in cases where a 2D [it favored a two-component (bulge | disk) model. or in cases where the morphology decision given in the literature varied (see Table 1).," We also defined a bulge + disk host galaxy in cases where a 2D fit favored a two-component (bulge + disk) model, or in cases where the morphology decision given in the literature varied (see Table 1)."728 We also used: a homogeneous morphology classification criterion to check our results. by separately examining objects classified only by Guvon.Sanders.&Stockton (2006)..," We also used a homogeneous morphology classification criterion to check our results, by separately examining objects classified only by \citet{Gu06}. ."729 This sample consisted of a number of PG-OSOs (20 objects) investigated by near-infrared AO imaging with the Cemini-N and Subaru Telescope., This sample consisted of a number of PG-QSOs (20 objects) investigated by near-infrared AO imaging with the Gemini-N and Subaru Telescope.730 For the Sevfert. galaxies. since their hosts are almost all spiral galaxies1999).. we assumed that their morphologies were clisk-clomiinetος.," For the Seyfert galaxies, since their hosts are almost all spiral galaxies, we assumed that their morphologies were disk-dominated."731 We plotted the 11.3 jam PALL luminosity ancl SALBLE mass μα»eciving the host galaxy morphology in Figure 1.., We plotted the 11.3 $\mu$ m PAH luminosity and SMBH mass specifying the host galaxy morphology in Figure \ref{fig1}.732 Phe left and the right panels of this figure show that the morphology Jassification is used Table 1 and only Cuvon.Sanders.&Stockton(2006).. respectively.," The left and the right panels of this figure show that the morphology classification is used Table 1 and only \citet{Gu06}, respectively."733 We applied detailed statistical tests about the dillerence of these. distributions (Lakeuchi et al., We applied detailed statistical tests about the difference of these distributions (Takeuchi et al.734 20090 in. prep.), 2009 in prep.).735 To summarize. the SMDBILI mass. distributions of the elliptical- and disk-dominated host galaxies are significantly dillerent.," To summarize, the SMBH mass distributions of the elliptical- and disk-dominated host galaxies are significantly different."736 However. the dillerence of the PALL luminosity. is not. very clear. (," However, the difference of the PAH luminosity is not very clear. ("737We showed this statistical analysis in Appendix.),We showed this statistical analysis in Appendix.)738 Averaged SAIBLE mass ancl its dispersions are <logMpy/Al.»=S42(+0-44) anc 7.48(£0.36) for the elliptical- and. cisk-clominated host. galaxies. respectively.," Averaged SMBH mass and its dispersions are $<\log M_{\rm BH}/M_{\odot}> = 8.42\, (\pm 0.44) $ and $7.48\, (\pm 0.36)$ for the elliptical- and disk-dominated host galaxies, respectively."739 Also. bulge | disk host galaxies are distributed in both the elliptical- ancl the cisk-dominated host galaxy regions.," Also, bulge + disk host galaxies are distributed in both the elliptical- and the disk-dominated host galaxy regions."740 1n particular. for the cisk-dominated host galaxy. although the PALL luminosity increases by about three orders. of magnitude. SMDII mass increases by only about one order.," In particular, for the disk-dominated host galaxy, although the PAH luminosity increases by about three orders of magnitude, SMBH mass increases by only about one order."741 These results indicate that the final SALBIL mass is strongly connected with host galaxy morphologv: the SMDBIIL of a disk-dominated host galaxy is suppressed. while a more massive SMDII can form in an elliptical-dominated: host ealaxv.," These results indicate that the final SMBH mass is strongly connected with host galaxy morphology; the SMBH of a disk-dominated host galaxy is suppressed, while a more massive SMBH can form in an elliptical-dominated host galaxy."742 In order to remove the cillerences in observations ancl morphology classification. methods. we checked: our lindings usingcata from Ciuvon.Sanders.&Stockton only in the right panel of Figure 1.," In order to remove the differences in observations and morphology classification methods, we checked our findings using data from \citet{Gu06} only in the right panel of Figure 1."743 Although the sample size decreases. the tendency of our results does not change: <logMpy/Al.»=SA0(40-41) and. 7.432(£0.34) for the elliptical ancl clisk-clominatec host galaxies. respectively.," Although the sample size decreases, the tendency of our results does not change; $<\log M_{\rm BH}/M_{\odot}> = 8.40 \,(\pm 0.41) $ and $7.42\, (\pm 0.34)$ for the elliptical- and disk-dominated host galaxies, respectively."744 ‘Yo interpret our findings. we must consider the SMDIL erowth mechanism including both the host starburst elfects and the host galaxy morphology.," To interpret our findings, we must consider the SMBH growth mechanism including both the host starburst effects and the host galaxy morphology."745 Although galaxy. mergers (e.g...Hernquist1980). and stellar bars (e...Noguchi1988) have also been considered as SMDBII growth mechanism candidates. the relationship between final SMDII. mass and these mechanisms is still unknown.," Although galaxy mergers \citep[e.g.,][]{He89} and stellar bars \citep[e.g.,][]{No88} have also been considered as SMBH growth mechanism candidates, the relationship between final SMBH mass and these mechanisms is still unknown."746 Therefore. dt. is difficult to explain the dillerence in SMDBILI mass for the same starburst luminosity range using these mechanisms.," Therefore, it is difficult to explain the difference in SMBH mass for the same starburst luminosity range using these mechanisms."747 ‘Thus. in order to relate the host starburst ancl host galaxy morphology with SALBIL formation. we focused on the racliation-hyclrodvnamic ellect from the host starburst.," Thus, in order to relate the host starburst and host galaxy morphology with SMBH formation, we focused on the radiation-hydrodynamic effect from the host starburst."748 The raciation drag is a relativistic effect known as the Povnting- effect., The radiation drag is a relativistic effect known as the Poynting-Robertson effect.749 It is a possible mechanism for extracting angular momentum from the eas and driving SMDLII mass accretion (Umemura.Fukue.&MineshigeLOOT:Umoemura 2002)..," It is a possible mechanism for extracting angular momentum from the gas and driving SMBH mass accretion \citep{Um97,Um01,KU02}. ."750 Final SMDLLI mass is connected. with the absorption ellicieney of the amount of radiation energv [rom the starburst., Final SMBH mass is connected with the absorption efficiency of the amount of radiation energy from the starburst.751 This radiation drag clliciency is strongly. alfected by host ecometry (Umoemura. 1999).," This radiation drag efficiency is strongly affected by host geometry \citep{Um97,Um98,Oh99}. ."752" The future space mission will be able ton10Ο, with uuprec‘dented auguar resolution aud seusitivity. he cosmic 1icrowave backgrotud (CAIB) auisoticypy and oobludzation at 9 frequencies in the range 3085 πο."," The future space mission will be able to measure, with unprecedented angular resolution and sensitivity, the cosmic microwave background (CMB) anisotropy and polarization at 9 frequencies in the range 30–857 GHz."753" Iu colmbination with balOOborne experiueuts such asANC. MANIALA-L. and the recently auuched space nission., these observational cata will oovide a uuique base for iucSsigation of the history and he largescae structure formaion of the Cuiversο"," In combination with balloon–borne experiments such as, -1, and the recently launched space mission, these observational data will provide a unique base for investigation of the history and the large–scale structure formation of the Universe."754 The accuracy of the cosimoogical parameter exraction auned for the ission ds determijd. by he correspoding accuracy of the systematic effects., The accuracy of the cosmological parameter extraction planned for the mission is determined by the corresponding accuracy of the systematic effects.755 Systematic errors can be ore of the most nuportant sources of errors for high iuultipole rauge of tιο CU) yoOWCT spectimi (CMaudolesieal. 2000))., Systematic errors can be one of the most important sources of errors for high multipole range of the $C(l)$ power spectrum \cite{mandolesi}) ).756 It is wel known hat extraction of the iufornation about cosological uwanieters slchi as barvonuic «cusity Os. cold dark luatter density Quay. IIubble coustaut Fy. aud so οἱ1 needs adclitioral information about the statistical characteristics of the neasured CALB anisotropy signal frou he sia.," It is well known that extraction of the information about cosmological parameters such as baryonic density $\Omega_b$, cold dark matter density $\Omega_{cdm}$, Hubble constant $H_0$, and so on, needs additional information about the statistical characteristics of the measured CMB anisotropy signal from the sky."757 The pive CMB signal is assumed to be a reization of a raido Gaussian signal ou the sphere wit) power spectruu C(H., The pure CMB signal is assumed to be a realization of a random Gaussian signal on the sphere with power spectrum $C(l)$.758 The Caussianity of the CMD signed nieans hat all its statistical properties are specified by is power spectruu CU). which depend ou 7 aud not ou the phases.," The Gaussianity of the CMB signal means that all its statistical properties are specified by its power spectrum $C(l)$, which depend on $l$ and not on the phases."759 lutje frünework of the CMD observations the signal neasured by cifferent iustruiments at different frecuencles. iowever. dispavs sole peculiarities iu observatlonal as well as iu foreground manifestations.," In the framework of the CMB observations the signal measured by different instruments at different frequencies, however, displays some peculiarities in observational as well as in foreground manifestations."760 This is why :Vvaricty of the methods of the correct information extraction roni the CAB data sets are now uier discussion., This is why a variety of the methods of the correct information extraction from the CMB data sets are now under discussion.761" All hese methods are somewhat complementary to each other in the future highly sensitive €""ID. experiments. due to different sensitivity of the iehods to «liffereut characteristics of the signal."," All these methods are somewhat complementary to each other in the future highly sensitive CMB experiments, due to different sensitivity of the methods to different characteristics of the signal."762 From a theoretical point of view. the power s])octruni of the true CMD signal is indepencden of FourkYo rlues. ucaning thati does uot depend on the aziuthal iuuber a.," From a theoretical point of view, the power spectrum of the true CMB signal is independent of Fourier rings, meaning thatit does not depend on the azimuthal number $m$."763" For a flat patch of the xsv df correspouds o homogeneity and isotropy of the signal without angular dependeacy of the power spectrmu C(k) on ϐ=mIk, kwwre k=(hy.ky)"," For a flat patch of the sky it corresponds to homogeneity and isotropy of the signal, without angular dependency of the power spectrum $C({\bf k})$ on $\theta=\tan^{-1}({k_y}/{k_x})$ , where ${\bf k}=(k_x,k_y)$."764 In reality. the CMD signal frou the sky has a iore complicated structure reflecting some artifacts of the observation aud cifferent sinds of foreerouxd coutzuuinations. which can desrov the isotropy of the power spectrum.," In reality, the CMB signal from the sky has a more complicated structure reflecting some artifacts of the observation and different kinds of foreground contaminations, which can destroy the isotropy of the power spectrum."765" We will focus o jon few iuportant sources causing artificial ajsotropy ofthe map: (1) ""nou-Caussiaitv Gulomoegcucity aud anisotropy) of t1e foregrounds iu the map: 11) asvmuuctry of the bei shape. which is now the standard part of investigation on systematic effcvets: (1) correlations of the iunstiiuncental )jxel) noise: (iv) low multipole modes. c.g. 72LO for the whole sky (&Ox 1. where O is he linear size of the"," We will focus on a few important sources causing artificial anisotropy of the map: (i) “non-Gaussianity” (inhomogeneity and anisotropy) of the foregrounds in the map; (ii) asymmetry of the beam shape, which is now the standard part of investigation on systematic effects; (iii) correlations of the instrumental (pixel) noise; (iv) low multipole modes, e.g. $l \sim 2-10$ for the whole sky $k\Theta \simeq 1$ , where $\Theta$ is the linear size of the"766"be taken in the practical implementation of the method (e.g., the proper definition of the individual regions is a crucial and beyond this one needs to be highly aware of its step),limitations.","be taken in the practical implementation of the method (e.g., the proper definition of the individual regions is a crucial step), and beyond this one needs to be highly aware of its limitations."767" On a more detailed level, we derived the equations for the ILC weights based on Lagrange multipliers, which were also discussed by Tegmark "," On a more detailed level, we derived the equations for the ILC weights based on Lagrange multipliers, which were also discussed by Tegmark (1998)."768"While a non-linear search algorithm is based on (1998).iterations, this method solves one single linear system of equations, and is therefore much faster."," While a non-linear search algorithm is based on iterations, this method solves one single linear system of equations, and is therefore much faster."769 This is important when generating Monte Carlo simulations., This is important when generating Monte Carlo simulations.770" Subsequently, we discussed how to produce realistic simulations of the ILC map, and used these simulations to study the properties of the method itself, with particular emphasis on the sensitivity to noise and sky cuts."," Subsequently, we discussed how to produce realistic simulations of the ILC map, and used these simulations to study the properties of the method itself, with particular emphasis on the sensitivity to noise and sky cuts."771" The method was applied to the real data, and the resultant LILC map was determined to have properties similar to the TCM map, but somewhat different from the Bennettetal.(2003b) WILC map."," The method was applied to the real data, and the resultant LILC map was determined to have properties similar to the TCM map, but somewhat different from the \citet{bennett:2003b} WILC map."772" We also computed ILC weights for four quadrants of the sky, and found that the south-eastern Galactic quadrant has significantly different properties than the other three, possibly shedding new light on the asymmetry issue discussed by Eriksenetal.(2004a)."," We also computed ILC weights for four quadrants of the sky, and found that the south-eastern Galactic quadrant has significantly different properties than the other three, possibly shedding new light on the asymmetry issue discussed by \citet{Eriksen:2004a}."773". Finally, as a comment to the on-going debate on the nature of the large-angular scale anisotropy, we investigated the implications of the LILC map for estimates of the quadrupole and octopole modes, and found that the new quadrupole moment increases from 195LK to 351μμ. which is a perfectly acceptable amplitude compared to the best-fit spectrum."," Finally, as a comment to the on-going debate on the nature of the large-angular scale anisotropy, we investigated the implications of the LILC map for estimates of the quadrupole and octopole modes, and found that the new quadrupole moment increases from $195\;\mu774\textrm{K}$ to $351\;\mu \textrm{K}$, which is a perfectly acceptable amplitude compared to the best-fit spectrum."775" However, the alignment between the quadrupole and the octopole is stronger in our map than in the WILC and the TCM."," However, the alignment between the quadrupole and the octopole is stronger in our map than in the WILC and the TCM."776" We also pointed out that the 6--5 and 6 modes are most peculiar in their symmetry properties, as only of the simulations have a more spherically symmetric /=5 mode than the data, and a more planar £=6 mode."," We also pointed out that the $\ell=5$ and 6 modes are most peculiar in their symmetry properties, as only of the simulations have a more spherically symmetric $\ell=5$ mode than the data, and a more planar $\ell=6$ mode."777" Further, since we have access to the full Sky, these modes are all independent under the Gaussian, random-phase hypothesis, and the probabilities therefore accumulate quite straightforwardly."," Further, since we have access to the full sky, these modes are all independent under the Gaussian, random-phase hypothesis, and the probabilities therefore accumulate quite straightforwardly."778" The major caveat, however, is that many of these measurements are derived from maps with complex foreground and noise properties, and definitive cosmological conclusions therefore remain elusive."," The major caveat, however, is that many of these measurements are derived from maps with complex foreground and noise properties, and definitive cosmological conclusions therefore remain elusive."779" Better foreground correction methods are required, or, alternatively, methods for studying the same properties on a cut sky should be developed."," Better foreground correction methods are required, or, alternatively, methods for studying the same properties on a cut sky should be developed."780" This work is already under way, and will be published in a future paper."," This work is already under way, and will be published in a future paper."781" Returning to the ILC method, one may question whether the minimum variance criterion in itself is a meaningful measure of performance."," Returning to the ILC method, one may question whether the minimum variance criterion in itself is a meaningful measure of performance."782" As we have seen, this criterion implies a trade-off between suppressing noise and foregrounds, and moderate levels of foregrounds are often accepted in order to suppress noise."," As we have seen, this criterion implies a trade-off between suppressing noise and foregrounds, and moderate levels of foregrounds are often accepted in order to suppress noise."783 For most practical cosmological analyses this is not likely to be acceptable; noise is more easily quantified than residual foregrounds., For most practical cosmological analyses this is not likely to be acceptable; noise is more easily quantified than residual foregrounds.784" Note therefore that although we do provide a copy of the LILC map at H.K.E.’s homepage®,, we strongly advise against using it for purposes beyond visual presentation, for which, of course, the official WILC map is perfectly acceptable."," Note therefore that although we do provide a copy of the LILC map at H.K.E.'s home, we strongly advise against using it for purposes beyond visual presentation, for which, of course, the official WILC map is perfectly acceptable."785Dikpati et al (2006) first used a flux transport dvnanmo calibrated to the Sun (Dikpati et al 2004) to simulate and predict solar evele peaks from the record of past surface magnetic field patterns.,Dikpati et al (2006) first used a flux transport dynamo calibrated to the Sun (Dikpati et al 2004) to simulate and predict solar cycle peaks from the record of past surface magnetic field patterns.786 This was done mathematically by forcing the diamo equations at the top boundary. wilh a forcing function derived from past surface magnetic fields.," This was done mathematically by forcing the dynamo equations at the top boundary, with a forcing function derived from past surface magnetic fields."787 Flux transport dvnamos. and indeed all dvnanmos. have their own unlorced. usually complex [requencies of excitation (hat are commonly found by. treating the diano equations as an eigenvalue problem.," Flux transport dynamos, and indeed all dynamos, have their own unforced, usually complex frequencies of excitation that are commonly found by treating the dynamo equations as an eigenvalue problem."788 Many naturally occurring and man-made svstems have such properties., Many naturally occurring and man-made systems have such properties.789 When a physical system (hat has natural [reqencies is excited by external forcing whose own frequency is close to one of the natural ones. there can be resonance produced.that is.," When a physical system that has natural freqencies is excited by external forcing whose own frequency is close to one of the natural ones, there can be resonance produced–that is,"790"for globular clusters, since there is no firm conclusion that massive black holes’ masses scale with the mass of the stellar component as Mpy=107?Mana,","for globular clusters, since there is no firm conclusion that massive black holes' masses scale with the mass of the stellar component as $M_{\rm BH}=10^{-3} M_{\rm stellar}$."791" For galaxies we assume instead an upper limit to the massive black hole mass corresponding to Mpy=2x107?Mana, à lower limit of 100Me for dSph and nuclear clusters and a lower limit of 10*M for early type galaxies."," For galaxies we assume instead an upper limit to the massive black hole mass corresponding to $M_{\rm BH}=2 \times 10^{-2} M_{\rm stellar}$, a lower limit of $100\msun$ for dSph and nuclear clusters and a lower limit of $10^4\msun$ for early type galaxies."792 We complete the exercise by adding observational results for a sample of 29 early type galaxies where both dynamical black hole mass and X-ray luminosity (Pellegrini2010) are available alsoSoriaetal.2006a;Gültekinetal.2009)..," We complete the exercise by adding observational results for a sample of 29 early type galaxies where both dynamical black hole mass and X–ray luminosity \citep{Pellegrini2010} are available \citep[see also][]{Soria2006a,Gultekin2009b}."793 24 of these(see galaxies also report the stellar mass of the bulge (Marconi&Hunt2003)., 24 of these galaxies also report the stellar mass of the bulge \citep{MarconiHunt2003}.794. For those galaxies where the bulge mass is unavailable we derive stellar masses from B-band magnitudes., For those galaxies where the bulge mass is unavailable we derive stellar masses from B-band magnitudes.795" For these galaxies we also derive B-band luminosities directly from Ly (Gültekinetal.2009),, assuming B—V=1 (Colemanetal.1980),, and we check that our choice of a mass- ratio of 5 agrees well with this complementary technique to derive Lg."," For these galaxies we also derive B-band luminosities directly from $L_V$ \citep{Gultekin2009}, assuming $B-V=1$ \citep{Coleman1980}, and we check that our choice of a mass-to-light ratio of 5 agrees well with this complementary technique to derive $L_B$."796 Figure 5 compares the luminosities we predict for these galaxies to the measured X-ray luminosity of the galaxies (or upper limits)., Figure \ref{LE} compares the luminosities we predict for these galaxies to the measured X-ray luminosity of the galaxies (or upper limits).797" In agreement with the conclusions of Pellegrini(2005) and Soriaetal.(2006b) the radiatively inefficient case best fits the luminosity of most systems, except the most luminous ones."," In agreement with the conclusions of \cite{pellegrini2005} and \cite{Soria2006b} the radiatively inefficient case best fits the luminosity of most systems, except the most luminous ones."798" Overall, even the radiatively inefficient case slightly overestimates the luminosity, at least at the high mass end, and we find that, for instance, 7x=0.03 provides a much better fit."," Overall, even the radiatively inefficient case slightly overestimates the luminosity, at least at the high mass end, and we find that, for instance, $\eta_{\rm X}=0.03$ provides a much better fit."799 As discussed by Pellegrini (2010) there seems to be a smooth transition between radiatively inefficient and radiatively efficient accretion., As discussed by Pellegrini (2010) there seems to be a smooth transition between radiatively inefficient and radiatively efficient accretion.800" We also estimate the X-ray luminosities for Milky Way dSphs with stellar mass 10?Mo, where we use directly Rnait and Macenac from Walkeretal.(2010)."," We also estimate the X–ray luminosities for Milky Way dSphs with stellar mass $>10^5 \, \msun$, where we use directly $R_{\rm half}$ and $M_{\rm stellar}$ from \cite{Walker2010}."801". We assume in one case that Mgy=107?Metenar, and in another case that black holes have a fixed massive black hole mass of 10°Mo, based on models presented in VanWassenhoveetal. (2010)."," We assume in one case that $M_{\rm BH}=10^{-3} M_{\rm stellar}$, and in another case that black holes have a fixed massive black hole mass of $10^5 \msun$, based on models presented in \cite{svanwas2010}."802. We note that in all these cases the X— luminosities for massive black holes in dwarf galaxies are below 1099?ergs-!.," We note that in all these cases the X--ray luminosities for massive black holes in dwarf galaxies are below $10^{35} {\rm erg\, s^{-1}}$."803 Figure 6 summarizes our primary results; predicted X-ray luminosities for different stellar systems., Figure \ref{lum} summarizes our primary results; predicted X-ray luminosities for different stellar systems.804 We have developed a simple model to estimate the level of accretion fueled by recycled stellar winds on black holes hosted in stellar systems of different types., We have developed a simple model to estimate the level of accretion fueled by recycled stellar winds on black holes hosted in stellar systems of different types.805 Let us examine the various assumptions of our models to question if our approach is too conservative., Let us examine the various assumptions of our models to question if our approach is too conservative.806" To model the accretion rate we need a stellar density profile, (2) physical size and mass of a (1)system, (3) a total mass loss from stars (which depends on their age and luminosity), and (4) a velocity of stellar wind."," To model the accretion rate we need (1) a stellar density profile, (2) physical size and mass of a system, (3) a total mass loss from stars (which depends on their age and luminosity), and (4) a velocity of stellar wind."807" Regarding points and (4), we note that our choice of stellar ages and mass-to-light(3) ratios are already quite optimistic (except for the case of globular clusters and early type galaxies, but we note that our results for globulars are consistent with the estimate of Miller Hamilton 2002), and for most massive black holes in massive stellar systems the wind velocity is not highly"," Regarding points (3) and (4), we note that our choice of stellar ages and mass-to-light ratios are already quite optimistic (except for the case of globular clusters and early type galaxies, but we note that our results for globulars are consistent with the estimate of Miller Hamilton 2002), and for most massive black holes in massive stellar systems the wind velocity is not highly"808This Q(H) value is larger than the value for the Orion Nebula of 7.8x1035 photons 1 found by Peimbertetal.(1975) from early radio continuum observations and the value for the Orion Nebula of 1.1x1015 found by vanderWerf&Goss(1989) from their VLA study.,This Q(H) value is larger than the value for the Orion Nebula of $7.8\times 10^{48}$ photons $^{-1}$ found by \citet{pei75} from early radio continuum observations and the value for the Orion Nebula of $1.1\times 10^{49}$ found by \citet{vdw89} from their VLA study.809" The Orion Nebula Q(H) values are in approximate agreement with those expected from dominant photoionization of that object being by aandA,, where the expected Q(H) for the stars are 6x1015 photons s! and 1.5x1015 photon rrespectively, using the calibration of Heapetal.(2006)."," The Orion Nebula Q(H) values are in approximate agreement with those expected from dominant photoionization of that object being by and, where the expected Q(H) for the stars are $6\times 10^{48}$ photons $^{-1}$ and $1.5\times 10^{48}$ photon respectively, using the calibration of \citet{srh06}."810. The fact that the predicted stellar value of Q(H) is smaller than that derived for the nebula probably indicates the uncertainty in the calibration or that the true spectral type is slightly earlier., The fact that the predicted stellar value of Q(H) is smaller than that derived for the nebula probably indicates the uncertainty in the calibration or that the true spectral type is slightly earlier.811" One can also estimate the electron density from a knowledge of the surface brightness, the emissivity in the lline and the geometry."," One can also estimate the electron density from a knowledge of the surface brightness, the emissivity in the line and the geometry."812" For the constant density shell model the electron density (πιο) will be n2—4n S(H))/[o$fs 8(Rmax-Rpea)}, assuming that all the free electrons arise from the photoionization of hydrogen, a very good approximation in this low-ionizationization region where helium is neutral (as indicated by the very weak or absent Hel 5876 lline)."," For the constant density shell model the electron density $n\rm _{e}$ ) will be $n\rm _{e}^{2}$ $\pi$ $\rm \alpha ^{eff}_{H\beta}$ $\rm _{max}$ $\rm _{peak}$ )], assuming that all the free electrons arise from the photoionization of hydrogen, a very good approximation in this low-ionizationization region where helium is neutral (as indicated by the very weak or absent HeI 5876 line)."813" Using the previous values and adopting a5—3.63x107!“ em? s! from (2006) yields n,—3.2 ffor the region of Barnard's Loop that we have observed and 0.7 Που the Madsenetal.(2006) western arc.", Using the previous values and adopting $\rm \alpha ^{eff}_{H\beta}$ $3.63\times 10^{-14}$ $^{3}$ $^{-1}$ from \citet{agn3} yields $n\rm _{e}$ =3.2 for the region of Barnard's Loop that we have observed and 0.7 for the \citet{mad06} western arc.814 These numbers are similar to the density n.=2.0 derived by Heilesetal.(2000) from combined optical and radio data over large samples in Barnard's Loop., These numbers are similar to the density $n\rm _{e}$ =2.0 derived by \citet{carl00} from combined optical and radio data over large samples in Barnard's Loop.815shallower than isothermal.,shallower than isothermal.816 Munoz.IXochanek.&Keeton(2001) reached a similar conclusion about the particular radio lens B1933+503., \citet{mkk01} reached a similar conclusion about the particular radio lens B1933+503.817 Keeton(2002) found Chat the distribution ol stars observed in HST images of nearby early-(wpe galaxies is often sufficiently concentrated to suppress the central image without recourse to dark matter., \citet{keeton02} found that the distribution of stars observed in HST images of nearby early-type galaxies is often sufficiently concentrated to suppress the central image without recourse to dark matter.818 We describe our observations of in 2.. and our interpretation of the results in8 3.," We describe our observations of in \ref{sec:observations}, and our interpretation of the results in \ref{sec:interpretation}."819 In 4.. we compute lens models for this svstem under (the two different hypotheses for the nature of the central component.," In \ref{sec:models}, we compute lens models for this system under the two different hypotheses for the nature of the central component."820 We consider density distributions (hat are scale-Iree power laws. ancl also determine the required properties of a constant-density core or an inner cusp.," We consider density distributions that are scale-free power laws, and also determine the required properties of a constant-density core or an inner cusp."821 Finally. in Hr5.. we summarize our conclusions and discuss Iuture observations (hat could test more definitively whether PAIN J16320033 is a (tBiree-image quasar.," Finally, in \ref{sec:summary}, we summarize our conclusions and discuss future observations that could test more definitively whether PMN J1632–0033 is a three-image quasar."822 We observed with the VLBA on 2002 March 14 and 15. for one eight-hour session each day.," We observed with the VLBA on 2002 March 14 and 15, for one eight-hour session each day."823 On the first day. the array included one VLA antenna in place of the VLBA antenna at Pie Town. but on the second daw. the array consisted of the usual ten antennas.," On the first day, the array included one VLA antenna in place of the VLBA antenna at Pie Town, but on the second day, the array consisted of the usual ten antennas."824 During both sessions we alternated between observations at the standard 8.4 GlIz (3.6 em) band and the standard 1.7 GlIz (18 em) band., During both sessions we alternated between observations at the standard 8.4 GHz (3.6 cm) band and the standard 1.7 GHz (18 cm) band.825 For both bands. the observing bandwidth of 32 MIIz per polarization was divided into 4 sub-bands.," For both bands, the observing bandwidth of 32 MHz per polarization was divided into 4 sub-bands."826 Both senses of polarization were recorded with 2-bit sampling., Both senses of polarization were recorded with 2-bit sampling.827 The data were correlated in Socorro. New Mexico. producing 16 channels of width 500 kIIz [rom each sub-band. with an integration time of one second.," The data were correlated in Socorro, New Mexico, producing 16 channels of width 500 kHz from each sub-band, with an integration time of one second."828 Calibration was performed with using standard procedures., Calibration was performed with using standard procedures.829 We used the observations of to solve for residual delavs. rates. ancl phases directly (rather than using with a [ringe-littng solution interval of 2 minutes.," We used the observations of to solve for residual delays, rates, and phases directly (rather than using phase-referencing), with a fringe-fitting solution interval of 2 minutes."830 We used the multiple-field deconvolution algorithm available in to deconvolve a field centered on A and. simultaneously. a field of the same size centered on the mid-point between D and C. For the 8.4 GUz data. the fields were 1024x with a scale of 0.2 mas !.," We used the multiple-field deconvolution algorithm available in to deconvolve a field centered on A and, simultaneously, a field of the same size centered on the mid-point between B and C. For the 8.4 GHz data, the fields were $1024\times 1024$ with a scale of 0.2 mas $^{-1}$."831 For the 1.7 Gllz data. the fields were 512x with a scale of 1.0 mas |.," For the 1.7 GHz data, the fields were $512\times 512$ with a scale of 1.0 mas $^{-1}$."832 At first. the data trom each day were analvzed separately.," At first, the data from each day were analyzed separately."833 Once we verified that the results of the (wo sessions were consistent. we combined the visibility data from each frequency to produce final maps.," Once we verified that the results of the two sessions were consistent, we combined the visibility data from each frequency to produce final maps."834 The data were sel-calibrated. based on (le model derived [rom (he preliminary maps. wilh a 15-second solution interval.," The data were self-calibrated, based on the model derived from the preliminary maps, with a 15-second solution interval."835 The final 1.7 Giz maps are shown, The final 1.7 GHz maps are shown836"morecomplex boundary patterns develop, clarifying that turbulence doesnot stem from adirectinfluenceofthephotosphericvelocitypatternbutitis due tothe inherent nonlinear properties ofthesystem.","The dynamics are integrated, as in our previous works, using the equations of RMHD \citep{kp74,str76,mon82}, which are well suited for a plasma embedded in a strong axial magnetic field."837" TheParker Scenario forcoronal heating has with magnetic forcing ( romez)| L997; 1998; EinaudiVelli||1999) and shell models (Nigroet al, IBuchlin& Velli .. energy release,"," In dimensionless form they are given by: where $\mathbf{u_{_\perp}}$ and $\mathbf{b_{_\perp}}$ are the velocity and magnetic fields components orthogonal to the axial field, $p$ is the kinetic pressure."838" peak dissipation, and duration, ina way reminiscentof, and consistentwith, thedistribution of flaresin the solar corona. An analytical model ofa forced system", The gradient operator has components only in the perpendicular $x$ $y$ planes while the linear term $\propto \partial_z$ couples the planes along the axial direction through a wave-like propagation at the Alfvénn speed $c_A$.839 very similarto thesimulation presented herewas proposedby [Heyvaerts| (1992).andrecentlyextendedtotheanisotropic turbulence regime by with same MH," Incompressibility in RMHD equations follows from the large value of the axial magnetic fields \citep{str76} and they remain valid also for low $\beta$ systems \citep{zm92,bns98} such as the corona."840Dsystem threaded−−bya strong axial magnetic field incartesian geometry andapplyat thetop andbottom boundaries two 1D velocityfields ofopposite directionand assumedthat the sheared structure that developsinthe coronathen dissipatesviaan effective “turb," To render the equations nondimensional, we have first expressed the magnetic field as an Alfvénn velocity $b \rightarrow b/\sqrt{4\pi \rho_0}$ ], where $\rho_0$ is the density supposed homogeneous and constant, and then all velocities have been normalized to the velocity $u^{\ast} = 1\ km\, s^{-1}$, the order of magnitude of photospheric convective motions."841"ulent resistivity” providedbya cascade,so dissipative equilibriumis setupin which shearingis balancedby slippage providedbythe turbulence.", Lengths and times are expressed in units of the perpendicular length of the computational box $\ell^{\ast} = \ell$ and its related crossing time $t^{\ast} = \ell^{\ast}/u^{\ast}$.842"This amounts essentiallyto a one-point closure model of MHD turbulence where turbulenceacts onlyon very small-scales (Biskamp]2003),,whilethe large-scales remain laminarand indeed withthe same large-scal"," As a result, the linear terms $\propto \partial_z$ are multiplied by the dimensionless Alfvénn velocity $c_A = v_A/u^{\ast}$, where $v_A = B_0/\sqrt{4\pi \rho_0}$ is the Alfvénn velocity associated with the axial magnetic field."843"e magnetic structure. Markovian approximation (EDQNM) 1976) to estimatethe effective cascadeand dissipation forthe given driving shear, and thisallow themto developa"," The majority of the simulations performed [specifically runs A–E (see table \ref{tbl}) )] use a standard simplified diffusion model, in which both the magnetic resistivity $\eta$ and viscosity $\nu$ are constant and uniform."844" heating theoryin which theonly free parameter is the equivalent Kolmogorov constant. In contrast, shear flow. As a result "," The kinetic and magnetic Reynolds numbers are then given by: where $c$ is the speed of light, and numerically they are given the same value $Re=Re_{_m}$ ."845|Heyvaerts&Priest} (1992) overestimate the heatingrateas , In equations \ref{eq:eq1}) \ref{eq:eq2}) ) this case is realized for $n=1$ with $Re_{_1} = Re$.846laminard ynamics would lead toa higher energy injection (Poyntingflux). More recently have proposedthe so-called “secondary instabil, The index $n$ is called and for $n > 1$ the dissipative terms in \ref{eq:eq1}) \ref{eq:eq2}) ) correspond to so-called hyperdiffusion \citep{bis03}.847ity”asa leading mechanismoperating in the ParkerScena," We use hyperdiffusion, with $n=4$, only in runs F and G (table \ref{tbl}) ) dedicated to study the energy spectra."848"rio, responsible for the rapid releaseof energy.In their view, disruption on idealtime-scale must ariseafter some time while slow quasi-steady reconnection allows magnetic ener"," Hyperdiffusion is used because, even with a grid of $512 \times 512$ points in the x-y plane (the highest resolution grid we used for the plane), the timescales associated with ordinary diffusion are small enough to affect the large-scale dynamics and render difficult the resolution of an inertial range."849gyto continue to accumulatein the system.In their viewthe system evolution maybe described bya sequenceof equilibria destabilized bymagnetic reconnection. The bulk ofnumerical simulations performed," The diffusive time $\tau_{_n}$ at the scale $\lambda$ associated with the dissipative terms used in equations \ref{eq:eq1}) \ref{eq:eq2}) ) is given by For $n=1$ the diffusive time decreases relatively slowly toward smaller scales, while for $n=4$ it decreases far more rapidly."850" by 1996); &Gomez) (1997); |Georgoulis et al| (1998); system does not evolvethrough asequence ofequilibria, rathermore complex", As a result for $n=4$ we have longer diffusive timescales at large spatial scales and diffusive timescales similar to the case with $n=1$ at the resolutionscale.851" dynamics develop. The initial setup ofthe also simulation similarpresented thein implemented in this is but,very besides the tolower one paper resolutiondiffusion, theandtherefore interval thehigherfor which influencethey ofadvancenumerical the istime compared with coronal loopsand equationsactive region tootime-scales. short These leads them claim currentonly representativesheet collapse.ofThis smallevolution class isofnot ge"," Numerically we require the diffusion time at the resolution scale $\lambda_{min} = 1/N$, where N is the number of grid points, to be of the same order of magnitude for both normal and hyperdiffusion, i.e., Then for a numerical grid with $N=512$ points that requires a Reynolds number $Re_{_1} = 800$ with ordinary diffusion we can implement $Re_{_{4}} \sim 10^{19}$ (table \ref{tbl}) ), removing diffusive effects at the large scales and allowing (if present) the resolution of an inertial range."852"neric,symmetric but isboundary patterns, a whichvery admit coronal equilibria atvelocity alltimes. Wewillthose tothis question detailed discussion inreturnthe conclusion. andThe amore is organized follows. In § thebasic papergoverning equations asand boundary wecondi"," We solve numerically equations \ref{eq:eq1}) \ref{eq:eq3}) ) written in terms of the potentials of the orthogonal velocity and magnetic fields [see \cite{rved07,rved08} for a more detailed description of the numerical code] in Fourier space, we advance the Fourier components in the $x$ - and $y$ -directions of the scalar potentials."853"tions,describe well the code used tointegrate them. In as§B] discussnumerical the forsimulations andbrieflywe summarize initialtheconditionslinear stage dynamicsour extensively"," Along the $z$ -direction, no Fourier transform is performed so that we can impose non-periodic boundary conditions \ref{par3}) ), and a central second-order finite-difference scheme is used."854" detailed in (2008),, morein § Ml outline main points of|Heyvaerts &"," In the $x$ $y$ plane, a Fourier pseudospectral method is implemented."855while Priest (1992)) we tothe thiswork. Theresults o, Time is discretized with a third-order Runge-Kutta method.856"fnumerical simulations relevant presentedin 8B],while thefinaloursection is devoted toare of theimpact of work"," At time $t=0$ we start our simulations with a uniform and homogeneous magnetic field along the axial direction $\mathbf{B} = B_0\, \mathbf{\hat{e}_z}$."857 our conclusions coronal physics. anddiscussion thison 2. GOVERNINGEQUATIONS Cartesian box with an orthogonalloop cross axiallysection elongated ofsize£ and anaxial lengthLembedded inan homogeneous and unif," The orthogonal component of the velocity and magnetic fields are zero inside our computational box $\mathbf{u_{_\perp}}=\mathbf{b_{_\perp}}=0$, while at the top and bottom planes a large-scale velocity pattern is imposed \ref{eq:f0}) \ref{eq:f1}) ) or \ref{eq:f0}) \ref{eq:f2}) )] and kept."858"orm axial magneticfield Bo= é,aligned along the z-direction. curvature effect Boisneglected. ", We briefly summarize and extend to the shear forcing considered in this paper the linear stage analysis covered in more detail in \cite{rved08}. .859"Thetopand bottomAny plates (z —0 andL) the photospheric surfaces wherewe impose, asrepresent boundary conditions, motions."," In general for an initial interval of time smaller than the nonlinear timescale $t < \tau_{nl}$, nonlinear terms in equations \ref{eq:eq1}) \ref{eq:eq3}) ) can be neglected and the equations linearized."860 Alongvelocitythex andy patternsdirections mimicking periodic photospheric boundary conditions are At the plateimp, For simplicity we will at first neglect also the diffusive terms and consider their effect in the second part of this section.861"lemented.z—Lwea sinusoidal shear flowwith top wavenumber 4 impose (a 1) ul(x,y) =sin xizx &y. (1) Atthe bottom plate z = 0we generally imposea vanishing velocity α (x,y)=0, (2) exceptin one simulation [runF (table u? =— sin &y. (3) (z,y) (Ame) Here is the unitary vector directed along they direction,éy while theflow is sheared along zr."," The solution during the linear stage for generic boundary velocity forcings, $\mathbf{u^L}$ and $\mathbf{u^0}$ respectively at the top and bottom planes $z=L$ and $0$ , is given by: where $\tau_A = L/v_A$ is the Alfvénn crossing time along the axialdirection $z$ .The magnetic field grows linearly in time, while the velocity field is stationary and the order of magnitude of itsrms is determined by the boundary"862vacuunm decayvs takes place near z~1. too late to affect bie-baug nucleosyuthesis (BBN} or large-scale structure formation (LSS).,"vacuum decays takes place near $z\sim1$, too late to affect big-bang nucleosynthesis (BBN) or large-scale structure formation (LSS)."863 Lower linits on the age of the universe. however. put weak coustraimts ou the primary free parameter of the theory (a de Sitter-like length paraueter L). and these bounds are improved somewhat bv data ou the imagnuitude- relation for Type Ia superuovae.," Lower limits on the age of the universe, however, put weak constraints on the primary free parameter of the theory (a de Sitter-like length parameter $L$ ), and these bounds are improved somewhat by data on the magnitude-redshift relation for Type Ia supernovae."864 Taken together with the solarsvstem tests. we tentatively couclude that available astroplivsical data are consistent with a universe with one (or more) extra dinienusions.," Taken together with the solar-system tests, we tentatively conclude that available astrophysical data are consistent with a universe with one (or more) extra dimensions."865 A starting point for cosinological investigations in 5D theory is the metric in canonical form (Alashhoon et al., A starting point for cosmological investigations in 5D theory is the metric in canonical form (Mashhoon et al.866 199L): where £ is a constant with dimensions of leneth (akin to the de Sitter radius Ain standard cosmology)., 1994): where $L$ is a constant with dimensions of length (akin to the de Sitter radius $L_d=\sqrt{3/\Lambda}$ in standard cosmology).867 The 5D line clement contains the LD one: There is no loss of generality to this point: five available degrees of coordinate freedom. have been used to set the electromagnetic potentials (yi) to zero and to set the scalar potential (g411) to a coustaut iu Eq. (1))., The 5D line element contains the 4D one: There is no loss of generality to this point; five available degrees of coordinate freedom have been used to set the electromagnetic potentials $g_{4\mu}$ ) to zero and to set the scalar potential $g_{44}$ ) to a constant in Eq. \ref{5dmetric}) ).868 It is. however. necessary to retain (-dependence in the ID ietric tensor in order to preserve this ecuerality (Overduin Wessou 1997).," It is, however, necessary to retain $\ell$ -dependence in the 4D metric tensor in order to preserve this generality (Overduin Wesson 1997)."869 Under the restriction to 5D conformal flatuess. and the natural assumption that all test particles (niassive as well as niassless) move along null geodesics in 5D (i.c.. 4$?= 0). Mashlioon Wessou (2001) have shown that A in 1D drops expoucutially with proper tine s: Physically. this variation arises because we require the 5D field equations to satisfv eeneral covariance in five. uot four dimensions.," Under the restriction to 5D conformal flatness, and the natural assumption that all test particles (massive as well as massless) move along null geodesics in 5D (i.e., $dS^2=0$ ), Mashhoon Wesson (2004) have shown that $\Lambda$ in 4D drops exponentially with proper time $s$: Physically, this variation arises because we require the 5D field equations to satisfy general covariance in five, not four dimensions."870The canonical metric (1)) is mvariaut with respect to translations along the (-axis. so (- or eanec-depencdence then necessarily appears in the LD field equations.,"The canonical metric \ref{5dmetric}) ) is invariant with respect to translations along the $\ell$ -axis, so $\ell$ - or gauge-dependence then necessarily appears in the 4D field equations."871 We lave used the LD metre to re-express this dependence in terms of proper time s rather than ((, We have used the 4D metric to re-express this dependence in terms of proper time $s$ rather than $\ell$.872" There are two cases: iu the first Coen in the exponent). A decays asviuptoticallv to the small finite value 3/L7 as s3oo, While iu the secoud (1° sign) it vanishes in this lt."," There are two cases: in the first $-$ ' sign in the exponent), $\Lambda$ decays asymptotically to the small finite value $3/L^2$ as $s\rightarrow\infty$, while in the second $+$ ' sign) it vanishes in this limit."873 Measurements tell us that Ais small at present. but are not precise enoueh to discriminate between a coustaut value aud oue that is still decaving on cosmological timescales.," Measurements tell us that $\Lambda$ is small at present, but are not precise enough to discriminate between a constant value and one that is still decaying on cosmological timescales."874 Therefore we retain both possibilities in what follows., Therefore we retain both possibilities in what follows.875 Oue wav to constrain proposals of this kind is to ask what A decays n£o. If matter or radiation. then stroug constraiuts cau be placed ou the theory usimg experiucutal," One way to constrain proposals of this kind is to ask what $\Lambda$ decays If matter or radiation, then strong constraints can be placed on the theory using experimental"876lu uost of the cosinological studies. dark matter particles are treated as collisionless particles.,"In most of the cosmological studies, dark matter particles are treated as collisionless particles."877 For instance. to describe the cosmological cleusity evolution. collisionless Boltzimaun ecuation is adopte.," For instance, to describe the cosmological density evolution, collisionless Boltzmann equation is adopted."878 In. cosmological N-body simualions. a group of collisioiless dark matter particles. are 'epresented by a siugle collisionless particle in the computer ron the coarse-graiued point of view.," In cosmological N-body simulations, a group of collisionless dark matter particles, are represented by a single collisionless particle in the computer from the coarse-grained point of view."879 In the treatment by the Boltzinaun ecuation. in which the distribution functiji is defiued iu a dhase space. the particle Inass aul staistical weight are exdlicitly dealt. with. athough the dark hatter particles are still regarded as €assical particles witlout iiteraction excex for [n]eανν.," In the treatment by the Boltzmann equation, in which the distribution function is defined in a phase space, the particle mass and statistical weight are explicitly dealt with, although the dark matter particles are still regarded as classical particles without interaction except for gravity."880 Iu he coarse-galned view adopted by N-body simulatious. there is no particle iuloruiatjon aud only he global inass «eusity distribution is obtainec.," In the coarse-grained view adopted by N-body simulations, there is no particle information and only the global mass density distribution is obtained."881 However. by adopting the assumption that dark matte| particles are collisioness Classical yarticles. we migit have lost basic physics li SOMME cases.," However, by adopting the assumption that dark matter particles are collisionless classical particles, we might have lost basic physics in some cases."882 At hi[uneh uumber cdensities aid relatively Ow temperature. low-tuass elementary particles. experieuk'e quatum statistical «legeneracy due to incdistinguishability. of ideical particles.," At high number densities and relatively low temperature, low-mass elementary particles, experience quantum statistical degeneracy due to indistinguishability of identical particles."883 Εςy instance. it. used o be well known that the neutrino jack body iu the early uiiverse was partially degenerate (Weliberg1962).," For instance, it used to be well known that the neutrino black body in the early universe was partially degenerate \citep{Weinberg1962}."884. Neutrinos are fermions aud the radiation pressuὁ of the neutrino black body can be interpreted. as the combination degeneracy pressure aid tjerial pressure., Neutrinos are fermions and the radiation pressure of the neutrino black body can be interpreted as the combination degeneracy pressure and thermal pressure.885 As we discuss laer iu this paper. massive relic neutrinos are likely to remain partialy cegeuerate. after decoupling ad even alter they become nourelaivistic uncer adiabatic expansiou.," As we discuss later in this paper, massive relic neutrinos are likely to remain partially degenerate, after decoupling and even after they become nonrelativistic under adiabatic expansion."886 Alte ‘nonlinear evoluion ofa high-deusity part of the tliverse. we might see a hieh coucentration of dark 1matter particles arouixd the center oL a cluster «X galaxies.," After nonlinear evolution of a high-density part of the universe, we might see a high concentration of dark matter particles around the center of a cluster of galaxies."887 If dark matter particles are composed at least. partialy of Leht fermiouss (e.g. neutrios). their degeneracy pressure may be large enough to support tie clensity structure near the ceiter of the cluster against gravity.," If dark matter particles are composed at least partially of light fermions (e.g. neutrinos), their degeneracy pressure may be large enough to support the density structure near the center of the cluster against gravity."888 A system supported yy degeneracy pressure of fernious. πό as a white «να [ου a neutron star. is laown to have a [lat-top density prolie.," A self-gravitating system supported by degeneracy pressure of fermions, such as a white dwarf or a neutron star, is known to have a flat-top density profile."889 This is our notivation to explore tie possibility tliat recent results regardiug the 1jass profiles of cluste5 ol galaxies obtained by gravitational lensiug (Tyson.Wochauski.&dellAtloiio1998:Saxlοἱal.2002.20(Ji:Broadhurstet2005a.b) might be explained by tle degeueracy pressire of ight [e‘uO da‘ko matter particles.," This is our motivation to explore the possibility that recent results regarding the mass profiles of clusters of galaxies obtained by gravitational lensing \citep{Tyson98,Sand02,Sand04,TB05A,TB05B} might be explained by the degeneracy pressure of light fermionic dark matter particles."890 1 this paper. usiig a plenomenological equation of state (EOS) that desc‘ibes the physical itions betwee1 fully degenerate fermionic gas and the classical ideal gas. we irtegrate the ion of hydrostatic equilib‘itm. under the siuple assimption that the lox‘al kinetic enerey ‘lassical particle is equal ο its gravitaional energy determined by the 3D eucirelecl mass.," In this paper, using a phenomenological equation of state (EOS) that describes the physical conditions between fully degenerate fermionic gas and the classical ideal gas, we integrate the equation of hydrostatic equilibrium, under the simple assumption that the local kinetic energy of a classical particle is equal to its gravitational energy determined by the 3D encircled mass."891 Our 10461 is expected to be valid only near the co ‘eof a cluster where dyuunical equilibrium is possidy achieved., Our model is expected to be valid only near the core of a cluster where dynamical equilibrium is possibly achieved.892 For pure fermious. the votune density prolile is uniquely determiued by three parameters. tlie centra density. p(0). and the ‘operties of dark matter particles. uaimely. the mass. nmi. aud statistical weight. g.," For pure fermions, the volume density profile is uniquely determined by three parameters, the central density, $\rho(0)$, and the properties of dark matter particles, namely, the mass, $m$, and statistical weight, $g$."893 To compare our model with observatlons. we snotXhly connect our moclel volume deusity profile describing the jnler region to a volume density. profile «erived from the observed column deusity profile by assumit& splerical sviumetry at a raditis near he Einstein," To compare our model with observations, we smoothly connect our model volume density profile describing the inner region to a volume density profile derived from the observed column density profile by assuming spherical symmetry at a radius near the Einstein"894We have measured the non-axisvmmetryv in the mass distribution within the central few kpe of advanced mergers of galaxies which have merged into a single nucleus but have indications of interactions including tidal tails.,We have measured the non-axisymmetry in the mass distribution within the central few kpc of advanced mergers of galaxies which have merged into a single nucleus but have indications of interactions including tidal tails.895 The main results obtained are: Phe mergers show strong non-axisvmimetry - with the centres of isophotes showing a sloshing by ~32030% within the central 1 kpe., The main results obtained are: The mergers show strong non-axisymmetry - with the centres of isophotes showing a sloshing by $\sim 20-30 \%$ within the central 1 kpc.896 The asymmetry is also high. as measured by the Fourier amplitudes of the central light distribution.," The asymmetry is also high, as measured by the Fourier amplitudes of the central light distribution."897 The typical fractional lopsiclecl amplitude (AL) within the central 5 kps is found to be high ~ 0.12 eoing upto 0.2. while the typical As values are higher ~0.2 going upto 0.3.," The typical fractional lopsided amplitude $_1$ ) within the central 5 kps is found to be high $\sim$ 0.12 going upto 0.2, while the typical $_2$ values are higher $\sim 0.2$ going upto 0.3."898 This implies the presence of bars as in Arp 160. Arp 162. and Arp 163 or thick disces as in the rest of the sample. both of which are unexpected in mergers with elliptical. profiles or in no-Lit. unrelaxed galaxies.," This implies the presence of bars as in Arp 160, Arp 162, and Arp 163 or thick discs as in the rest of the sample, both of which are unexpected in mergers with elliptical profiles or in no-fit, unrelaxed galaxies."899 The corresponding values especially for the lopsidedness for a control sample of non-merger galaxies are smaller by a factor of 2-4. this confirms that the high central asymmetry in mergers discovered and measured in this paper can be truly attributed to the merger history.," The corresponding values especially for the lopsidedness for a control sample of non-merger galaxies are smaller by a factor of 2-4, this confirms that the high central asymmetry in mergers discovered and measured in this paper can be truly attributed to the merger history."900 The ratio of masses of galaxies undergoing the merger does not have a strong influence on the value of the central asvmmetrv once the outer regions have relaxed. (Sections 1 and 4.2)., The ratio of masses of galaxies undergoing the merger does not have a strong influence on the value of the central asymmetry once the outer regions have relaxed (Sections 1 and 4.2).901 The stage of merger. however. does seem to be significant because the ealaxices where the outer regions are non-relaxed. show a higher amplitude of asvnimetry in the inner regions (Section 4.2).," The stage of merger, however, does seem to be significant because the galaxies where the outer regions are non-relaxed, show a higher amplitude of asymmetry in the inner regions (Section 4.2)."902 The mergers are about 1-2 Gyr old as shown by the N- simulations (Bournaud ct al 2004)., The mergers are about 1-2 Gyr old as shown by the N-body simulations (Bournaud et al 2004).903 Thus in all cases studied. the central asymmetry. appears to be long-lived. lasting for over LOO local cvnamical timescales.," Thus in all cases studied, the central asymmetry appears to be long-lived, lasting for over 100 local dynamical timescales."904 This can be important for the dynamical evolution of the central regions of mergers., This can be important for the dynamical evolution of the central regions of mergers.905 We are grateful to the referee. Robert Jedrzejewski. for constructive comments anc particularly for suggesting that we add a comparison with a control sample of non-merger galaxies.," We are grateful to the referee, Robert Jedrzejewski, for constructive comments and particularly for suggesting that we add a comparison with a control sample of non-merger galaxies."906 This publication makes use of data products from the Two Micron. All Sky Survey (2\LASS). which is a joint project of the University of Massachusetts and the Infrared Processing anc Analysis Center/California Institute. of ‘Technology. funded by the National Aeronautics and Space Administration and the National Science Foundation.," This publication makes use of data products from the Two Micron All Sky Survey (2MASS), which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation."907 The details of sloshing as well as the non-axisvnimictric Fourier amplitudes obtained for cach galaxy in Section 3 are sumnmarised below: 1., The details of sloshing as well as the non-axisymmetric Fourier amplitudes obtained for each galaxy in Section 3 are summarised below: 1.908 Arp 221: Phe coordinates of the centre remain constant in the inner 4 and change bevond that.," Arp 221: The coordinates of the centre remain constant in the inner 4"" and change beyond that."909 Phe non-axisvnunetric analysis shows that the As. A. and AY values are small while Ay shows a maximum of 0.25 at S7," The non-axisymmetric analysis shows that the $_2$, $_3$ and $_4$ values are small while $_1$ shows a maximum of 0.25 at 8""."910 2., 2.911 Arp 222:H Phe coordinates of the centre remain constantin the inner 207 and change bevond that.," Arp 222: The coordinates of the centre remain constantin the inner 20"" and change beyond that."912 This galaxy has very low Ay values., This galaxy has very low $_1$ values.913 As maintains a constant. value of 0.3 from the center to about 307.," $_2$ maintains a constant value of 0.3 from the center to about 30""."914 Phe As and Ay values are both very small., The $_3$ and $_4$ values are both very small.915 3., 3.916 Arp 225: The coordinates of the centre are constant in the inner IS”.," Arp 225: The coordinates of the centre are constant in the inner 18""."917" This galaxy shows low values of Ay. A; and A, but high As values."," This galaxy shows low values of $_1$, $_3$ and $_4$ but high $_2$ values."918 The behaviour of A» is similar to that seen in Arp 222., The behaviour of $_2$ is similar to that seen in Arp 222.919 As maintains a value of 0.3 in the inner 45°.," $_2$ maintains a value of 0.3 in the inner 45""."920 4., 4.921" AM 0612-3 There is no substantial change in the coordinates of the center. with a total change of 1 pixel for xO and νο,"," AM 0612-373: There is no substantial change in the coordinates of the center, with a total change of 1 pixel for x0 and y0."922 The value of Ay is low. while Ao is quite high. peaking at 0.6 at 157.," The value of $_1$ is low, while $_2$ is quite high, peaking at 0.6 at 15""."923 Phe As and Ay values are fairly. high., The $_3$ and $_4$ values are fairly high.924 Class LL galaxies: 5., Class II galaxies: 5.925 Arp 162: The centre co-ordinates xO. and vO are constant in the inner 12.," Arp 162: The centre co-ordinates x0, and y0 are constant in the inner 14""."926" The values of A, and As are extremely small.", The values of $_1$ and $_3$ are extremely small.927 Phe amplitude As starts olf at about 0.2 between 207 and then increases to 0.3 beyond that. while Ay is low in the inner 20° and then increases.," The amplitude $_2$ starts off at about 0.2 between 6""-20"" and then increases to 0.3 beyond that, while $_4$ is low in the inner 20"" and then increases."928 The phase angle is nearly constant throughout for the m=2 and 4 components., The phase angle is nearly constant throughout for the m=2 and 4 components.929 6., 6.930 Arp 212: The centre co-ordinates xO. and vO remain constant in the inner 6 and then change substantially.," Arp 212: The centre co-ordinates x0, and y0 remain constant in the inner 6"" and then change substantially."931 AL A coefficients show (nearly) double-peaked behaviour., All A coefficients show (nearly) double-peaked behaviour.932 The values of the A coellicients decrease in the order: Ay c As a Aa zx Aa., The values of the A coefficients decrease in the order: $_1$ $>$ $_2$ $>$ $_3$ $>$ $_4$.933 7., 7.934 Arp 224: The centre (x0. V0) remains constant in the inner 6.," Arp 224: The centre (x0, y0) remains constant in the inner 6""."935 Phe value of Ay is high showing a peak of 0.3 at 127.," The value of $_1$ is high showing a peak of 0.3 at 12""."936 In this case also. Ay > As c Ay >» Ay.," In this case also, $_1$ $>$ $_2$ $>$ $_3$ $>$ $_4$."937 Class LLL galaxies: S., Class III galaxies: 8.938 Arp 160: Phis shows a constantly changing centre (x0. vO) for the subsequent isophotes.," Arp 160: This shows a constantly changing centre (x0, y0) for the subsequent isophotes."939 The values of As are also high with a peak of 0.45 at 107," The values of $_2$ are also high with a peak of 0.45 at 10""."940 9., 9.941 Arp 163: ‘This also shows a constantly. changing centre (xO and v0) for the nearby isophotes., Arp 163: This also shows a constantly changing centre (x0 and y0) for the nearby isophotes.942 The value of the ni-2 amplitude As is the strongest. with a maximum of 0.4 between 107-147.," The value of the m=2 amplitude $_2$ is the strongest, with a maximum of 0.4 between 10""-14""."943 Phe value of Ay peaks at 0.3 at 67 and Ay peaks at 0.3 at 127.," The value of $_1$ peaks at 0.3 at 6"", and $_4$ peaks at 0.3 at 14""."944 The value of As is small at all raclil., The value of $_3$ is small at all radii.945 0., 10.946 Arp 209: The centre co-ordinates are constant in the inner 4°. ancl vary thereafter.," Arp 209: The centre co-ordinates are constant in the inner 4"", and vary thereafter."947 The values of Ay. As and A; are high.," The values of $_1$, $_2$ and $_3$ are high."948 1., 11.949 Arp 254: This shows changing co-ordinates for the centre., Arp 254: This shows changing co-ordinates for the centre.950" The values of As and Ay are large as compared to the values of X, and Xa.", The values of $_2$ and $_4$ are large as compared to the values of $_1$ and $_3$ .951 2., 12.952 AM 1045-433: Ehis is à Toomre sequence galaxy., AM 1045-433: This is a Toomre sequence galaxy.953 Here the co-ordinates of the centre (xO and vO) show a change from the innermost region itself., Here the co-ordinates of the centre (x0 and y0) show a change from the innermost region itself.954 Phe value of A» is high with a peak value of 0.5 at 207.," The value of $_2$ is high with a peak value of 0.5 at 20""."955 This galaxy shows the following values for the Fourier amplitudes: As IUDA, This galaxy shows the following values for the Fourier amplitudes: $_2$ $>$ $_3$ $>$ $_4$ $>$ $_1$ .956The VJ combination is so cllective because. the spectral energy distribution of stars with similar V-J colours to quasars (principally those of spectral types Ix and M) turn over in the HE band (Fig.,The VJK combination is so effective because the spectral energy distribution of stars with similar V-J colours to quasars (principally those of spectral types K and M) turn over in the H band (Fig.957 1)., 1).958 The J and Ix. bands stracdelle the break point. providing the discriminatory power of the technique. so utilising LEband magnitudes in place of J or Ix is not viable.," The J and K bands straddle the break point, providing the discriminatory power of the technique, so utilising H–band magnitudes in place of J or K is not viable."959 A limit to the clleetiveness of the KN method using V. J. and Ix. passbands occurs at. redshifts 23.5 where absorption by the Lya forest is present. over much of the wavelength range included in the V.filter.," A limit to the effectiveness of the KX method using V, J, and K passbands occurs at redshifts $z>3.5$ where absorption by the $\alpha$ forest is present over much of the wavelength range included in the V–filter."960 Quasars start to become redder in. V-J. moving vertically in the VJIx. cliagram and approaching the stellar locus.," Quasars start to become redder in V-J, moving vertically in the VJK diagram and approaching the stellar locus."961 In Figure 2 the triangle marks the colours of a quasar of redshift =4.5. which lies below the colour selection boundary cause. Of this absorption.," In Figure 2 the triangle marks the colours of a quasar of redshift $z=4.5$, which lies below the colour selection boundary because of this absorption."962 Substituting the It or IE filter or V would extend the ellectiveness of the KN method to redshifts bevond 2=4., Substituting the R or I filter for V would extend the effectiveness of the KX method to redshifts beyond $z=4$.963 At the end of this section we reemphasise the dillerence tween the elfects. of reddening and extinction. on. the completeness of quasar surveys., At the end of this section we reemphasise the difference between the effects of reddening and extinction on the completeness of quasar surveys.964 Some optical survey methods. including the multicolour method ancl emission-ine searches (but excluding the ΕΝ method). are also argelv insensitive to reddening.," Some optical survey methods, including the multicolour method and emission-line searches (but excluding the UVX method), are also largely insensitive to reddening."965 The advantage of the WX method. over all optical survey methods is the reduced extinction in the Ix band. rather than simply the ability to ind reddened quasars. Le. à much larger fraction of quasars sullering extinction. will be included. in the Ix.band. Huximited sample.," The advantage of the KX method over all optical survey methods is the reduced extinction in the K band, rather than simply the ability to find reddened quasars, i.e. a much larger fraction of quasars suffering extinction will be included in the K–band, flux--limited sample."966 The proposed. UINIICE widefield nearinfrared camera will image 0.2 square degrees per exposure., The proposed UKIRT wide–field near–infrared camera will image 0.2 square degrees per exposure.967 One of its goals is a moderately deep survey over à substantial fraction of he area of the Sloan Digital Sky Survey (SDSS) accessible w UII. Le. thousands of square degrees. to a depth of WK=19 with a signaltonoise ratio of ~10.," One of its goals is a moderately deep survey over a substantial fraction of the area of the Sloan Digital Sky Survey (SDSS) accessible by UKIRT, i.e. thousands of square degrees, to a depth of K=19 with a signal–to–noise ratio of $\sim 10$."968 Such a survey would contain many thousands of quasars., Such a survey would contain many thousands of quasars.969 Here weconsider he effectiveness of this survey for finding clampecl Lye ealaxies and gravitational lenses. especially examples where he background. quasar had. been dimmed: by dust in the intervening galaxy.," Here weconsider the effectiveness of this survey for finding damped $\alpha$ galaxies and gravitational lenses, especially examples where the background quasar had been dimmed by dust in the intervening galaxy."970 A survey for DLAs requires samples of highredshift zz2 uasars. since for groundbased spectroscopy DLAs are only etectable at z1.85.," A survey for DLAs requires samples of high–redshift $z \ga 2$ quasars, since for ground–based spectroscopy DLAs are only detectable at $z>1.8$."971 The number of DLAs catalogued in 1e literature is approaching 100., The number of DLAs catalogued in the literature is approaching 100.972 Therefore. to. provide a substantial advance. à survey that produces more than 300 DLAs is desirable.," Therefore, to provide a substantial advance, a survey that produces more than 300 DLAs is desirable."973 For à given survey area we can compute 10 Ix-band. [lux limit that will provide sullicient. quasars to xoduce a sample of DLAs of this size., For a given survey area we can compute the K-band flux limit that will provide sufficient quasars to produce a sample of DLAs of this size.974 We can then verily iat this [lux limit is sulliciently bright. sav Itc20. to allow ughresolution spectroscopy on an Smetre class telescope or the measurement of the absorber metallicities.," We can then verify that this flux limit is sufficiently bright, say $\le20$, to allow high–resolution spectroscopy on an 8–metre class telescope for the measurement of the absorber metallicities."975 For the calculation. we take an area of 4000. square degrees over à region in common with the SDSS., For the calculation we take an area of 4000 square degrees over a region in common with the SDSS.976 An advantage of covering the SDSS area is that lowresolution spectra of most of the bright IKXN.selected quasar candidates will exist in. the SDSS database., An advantage of covering the SDSS area is that low–resolution spectra of most of the bright KX–selected quasar candidates will exist in the SDSS database.977 Taking the quasar luminosity function of Warren. Llewett and Osmer (1904) we can compute the surface density of highredshift quasars as a function of Ro magnitude.," Taking the quasar luminosity function of Warren, Hewett and Osmer (1994) we can compute the surface density of high–redshift quasars as a function of R magnitude."978 We then convert to Ix assuming a mean colour of I-Ix—2.2., We then convert to K assuming a mean colour of R-K=2.2.979 We then estimate the number of DLAs bv assuming a line density dpídz=0.055(1|ο.) (Wolfe et al., We then estimate the number of DLAs by assuming a line density $dn/dz=0.055(1+z)^{1.15}$ (Wolfe et al.980 1995) and supposing that DLAs can be detected [rom the quasar emission redshift down to z— L8., 1995) and supposing that DLAs can be detected from the quasar emission redshift down to $z=1.8$ .981 Over 4000 square degrees. to K=16.0. we estimate there," Over 4000 square degrees, to K=16.0, we estimate there"982In RASO9 we describe the iterative method that can be used for constructing an equilibrium N-body system with à given mass distribution. following given. kinematical constraints.,"In RAS09 we describe the iterative method that can be used for constructing an equilibrium $N$ -body system with a given mass distribution, following given kinematical constraints."983 The same conceptually method. with only relatively. minor modifications ean be applied for the construction of the gaseous disk.," The same conceptually method, with only relatively minor modifications can be applied for the construction of the gaseous disk."984 It relies on constrained (or guided) evolution., It relies on constrained (or guided) evolution.985 When constructing the equilibrium N-body system. we let it evolve. and during this evolution we fix the desired mass distribution and kinematics (see RASO9).," When constructing the equilibrium $N$ -body system, we let it evolve, and during this evolution we fix the desired mass distribution and kinematics (see RAS09)."986 This will be the same for the gaseous disk. except that now we do not fix the full mass distribution. but only the projected surface density.," This will be the same for the gaseous disk, except that now we do not fix the full mass distribution, but only the projected surface density."987 The general scheme of the iterative method is outlined in Fig. 1.., The general scheme of the iterative method is outlined in Fig. \ref{fig_scheme}.988 We start from some initial system. which is the starting point of the iterative procedure.," We start from some initial system, which is the starting point of the iterative procedure."989 We then let the system go through a sequence of evolutionary steps of short duration., We then let the system go through a sequence of evolutionary steps of short duration.990 At the end of each one of these steps. and before the new evolutionary step Is started. we “set” the chosen parameters or quantities to the desired values (see RASO9).," At the end of each one of these steps, and before the new evolutionary step is started, we “set” the chosen parameters or quantities to the desired values (see RAS09)."991 We repeat this iteration procedure a number of times. alternating one evolution phase and one phase during which the necessary parameters are set. until we come sufficiently near to the desired equilibrium state.," We repeat this iteration procedure a number of times, alternating one evolution phase and one phase during which the necessary parameters are set, until we come sufficiently near to the desired equilibrium state."992" In practice. to apply this general scheme we need to define which initial model we will use. and. most important. which parameters we want to ""fix"" during the iterative procedure."," In practice, to apply this general scheme we need to define which initial model we will use, and, most important, which parameters we want to “fix” during the iterative procedure."993 Let us now describe how we will apply this iterative method to the construction of an equilibrium gaseous disk., Let us now describe how we will apply this iterative method to the construction of an equilibrium gaseous disk.994" Our initial model is a gaseous disk with a given surface density X,(R).", Our initial model is a gaseous disk with a given surface density $\Sigma_g(R)$.995 The vertical coordinates of the particles can be arbitrarily chosen (for example equal to zero)., The vertical coordinates of the particles can be arbitrarily chosen (for example equal to zero).996 Equally arbitrary. the tangential velocity of each particle is set equal to the circular velocity and the vertical and radial velocities are set equal to zero.," Equally arbitrary, the tangential velocity of each particle is set equal to the circular velocity and the vertical and radial velocities are set equal to zero."997" The circular velocity is calculated from the total potential. which is the sum of @,.,. due to the adopted mass distribution of the collisionless part. and the potential generated by the initial distribution of the gas."," The circular velocity is calculated from the total potential, which is the sum of $\Phi_{ext}$, due to the adopted mass distribution of the collisionless part, and the potential generated by the initial distribution of the gas."998 At this stage 1t is not necessary to caleulate the circular velocity very accurately., At this stage it is not necessary to calculate the circular velocity very accurately.999 Even if we set the azimuthal velocities equal to twice or to half of the circular velocity. the iterative method will converge to the same result.," Even if we set the azimuthal velocities equal to twice or to half of the circular velocity, the iterative method will converge to the same result."1000 In the case of a non-isothermal system the thermal energies of the particles can be arbitrarily chosen., In the case of a non-isothermal system the thermal energies of the particles can be arbitrarily chosen.1001 This model will be the starting point for the iterative procedure (see Fig. 1))., This model will be the starting point for the iterative procedure (see Fig. \ref{fig_scheme}) ).1002 Having thus obtained the starting model. we start the iterative procedure. which consists of a sequence of evolutionary steps of short duration. followed by steps during which some parameters or quantities are fixed. and this until a near equilibrium model is obtained.," Having thus obtained the starting model, we start the iterative procedure, which consists of a sequence of evolutionary steps of short duration, followed by steps during which some parameters or quantities are fixed, and this until a near equilibrium model is obtained."1003 In this example we fix the following parameters: This means that we do not fix the vertical distribution of the particles. letting it adjust itself to hydrostatic equilibrium.," In this example we fix the following parameters: This means that we do not fix the vertical distribution of the particles, letting it adjust itself to hydrostatic equilibrium."1004 To fix the surface density in the gaseous disk at the end of an evolutionary step we proceed as follows., To fix the surface density in the gaseous disk at the end of an evolutionary step we proceed as follows.1005 We construct à gaseous disk with the desired surface density. but with velocities and vertical coordinates chosen according to the velocities and the vertical coordinates of the disk resulting from the evolution step.," We construct a gaseous disk with the desired surface density, but with velocities and vertical coordinates chosen according to the velocities and the vertical coordinates of the disk resulting from the evolution step."1006 We first construct a new gaseous disk with the desired surface density profile., We first construct a new gaseous disk with the desired surface density profile.1007" We then ""transfer"" the velocity distribution and the distribution of the vertical coordinates of the particles from the system obtained from the evolution to this new system. using the ""transfer"" algorithm described in RASO9 (see Sect."," We then “transfer” the velocity distribution and the distribution of the vertical coordinates of the particles from the system obtained from the evolution to this new system, using the “transfer” algorithm described in RAS09 (see Sect."1008 2.2 in that paper)., 2.2 in that paper).1009 The basic idea of this algorithm is very simple. namely we assign to the new-model particles the velocities of those particles from the old model that are “nearest to the ones in the new model. the definition of nearest depending on the problem at hand.," The basic idea of this algorithm is very simple, namely we assign to the new-model particles the velocities of those particles from the old model that are “nearest” to the ones in the new model, the definition of nearest depending on the problem at hand."1010" In the present case we need to ""transfer"" the vertical coordinate of the particle together with the velocities.", In the present case we need to “transfer” the vertical coordinate of the particle together with the velocities.1011 Since our model Is axisymmetric. we need to search for the nearest particle in the one-dimensional space R. where R is the cylindrical radius.," Since our model is axisymmetric, we need to search for the nearest particle in the one-dimensional space $R$, where $R$ is the cylindrical radius."1012 This implicitly fixes the condition of axisymmetry., This implicitly fixes the condition of axisymmetry.1013 The vertical coordinate should not be taken into account during the search for the nearest neighbour because we copy it from the evolved model particle to the new model particle together with the velocities., The vertical coordinate should not be taken into account during the search for the nearest neighbour because we copy it from the evolved model particle to the new model particle together with the velocities.1014 In the case of non-isothermal gas. the thermal energy of the particle should be copied together with the velocities and the vertical coordinate.," In the case of non-isothermal gas, the thermal energy of the particle should be copied together with the velocities and the vertical coordinate."1015 The algorithm for constructing the equilibrium N-body system with given parameters and constraints is described in RASO9 and is not altered by the presence of the gaseous component., The algorithm for constructing the equilibrium $N$ -body system with given parameters and constraints is described in RAS09 and is not altered by the presence of the gaseous component.1016 We simply need to take into account the gravitational acceleration caused by the gaseous component when creating the collisionless components. since 1t will act on them as an external potential.," We simply need to take into account the gravitational acceleration caused by the gaseous component when creating the collisionless components, since it will act on them as an external potential."1017 However. because we initially know only the surface density of the gaseous disk. we cannot calculate the three-dimensional gravitational acceleration.," However, because we initially know only the surface density of the gaseous disk, we cannot calculate the three-dimensional gravitational acceleration."1018 We need. therefore. to construct the equilibrium model of the gaseous disk first. before that of the collisionless components.," We need, therefore, to construct the equilibrium model of the gaseous disk first, before that of the collisionless components."1019 After constructing this model we have the full mass nodel of the, After constructing this model we have the full mass model of the1020as well.,as well.1021 The degeneracy can not be removed even using the SED (Fis.7)) which is simular in the two moclels (Lyra/L.=ON0.1 A) and it is ouly roughlv consistent with the photometric values., The degeneracy can not be removed even using the SED \ref{fig:MWC480_vis2}) ) which is similar in the two models $L_{NIR}/L_{\star} = 0.18\%-0.14\%$ ) and it is only roughly consistent with the photometric values.1022 AB Auris the oulv IL&e star that cannot be fitted with the INO» models., AB Aur is the only HAe star that cannot be fitted with the IN05 models.1023 The PTT visibilities require a face-on rini. consistent with the iuclinatiou derived from large-scale nuages m scattered light (Grady et al.," The PTI visibilities require a face-on rim, consistent with the inclination derived from large-scale images in scattered light (Grady et al."1024 1999: Fuisaecawa et al., 1999; Fukagawa et al.1025 2001) aud at millimeter waveleneths (Corder et al., 2004) and at millimeter wavelengths (Corder et al.1026 2005: Piéttu et al., 2005; Piéttu et al.1027 2005)., 2005).1028" For these inclinatious. the V? data imply a verv sinall πο radius; about two times smaller that the smallest /,;,, obtained using the INOS model (see Fie.s)}."," For these inclinations, the $V^2$ data imply a very small inner radius, about two times smaller that the smallest $R_{rim}$ obtained using the IN05 model (see \ref{fig:ABAur_vis2}) )."1029" If. to put the discrepancy m a more physical coutest. we take Τρηρ as a free parameter. we find good agreciuent with the PTT data for 7,44,2800 (dashed line). a value by far too high not oulv for silicates but also for auv other type of grains (οι, Pollack et al."," If, to put the discrepancy in a more physical context, we take $T_{evp}$ as a free parameter, we find good agreement with the PTI data for $T_{evp}\sim 2800K$ (dashed line), a value by far too high not only for silicates but also for any other type of grains (e.g., Pollack et al."1030 1991)., 1994).1031 The situation becames even less clear if we consider also the IOTÀ observations (squared points). since they seeni to indicate the presence of a iore inclined disk. with an inucr radius between 0.268U aud O.5LAU.," The situation becames even less clear if we consider also the IOTA observations (squared points), since they seem to indicate the presence of a more inclined disk with an inner radius between 0.26AU and 0.51AU."1032 No additional information can be obtained from the analysis of the spectral energy distribution. since all the iuuer ria models wih an effective temperature between 195001 aud 250018 are compatible with the photometric data.," No additional information can be obtained from the analysis of the spectral energy distribution, since all the inner rim models with an effective temperature between 1500K and 2500K are compatible with the photometric data."1033 We will come back to AB Aur in 86., We will come back to AB Aur in 6.1034 Fits to the same interferometric data analyzed im refsec:it— have been obtained by Eisner et al. (, Fits to the same interferometric data analyzed in \\ref{sec:fit} have been obtained by Eisner et al. (1035"2001. hereafter. EO1) assuming a toroidal shape for the imner ""Upuffed-up riu. based on the simplified DDNOL model.","2004, hereafter E04) assuming a toroidal shape for the inner “puffed-up” rim, based on the simplified DDN01 model."1036 Tn these fits. the free parameters are the location of the riu Πρι aud the two observational parameters. ¢ and PA.," In these fits, the free parameters are the location of the rim $\Rrim$ and the two observational parameters, $\iota$ and $PA$."1037 The EOL results are shown in Table 2., The E04 results are shown in Table 2.1038 We note that for three objects (AWC 758. VV Ser and CQ Tau) the EOL inclinations ire in agreement within the errors with the values obtained with the INOS model. while for the other two (V1295 Aql and MWC. 180) the EOL / estimaes are consistent with the lowest value of the rauge derived in this paper.," We note that for three objects (MWC 758, VV Ser and CQ Tau) the E04 inclinations are in agreement within the errors with the values obtained with the IN05 model, while for the other two (V1295 Aql and MWC 480) the E04 $\iota$ estimates are consistent with the lowest value of the range derived in this paper."1039" The largest differcuces are in the derived values of ΠΠ2EPH he INOS iuner radi are ahwavs huger than EOL results. with a maximum difference of a factor ~3 if we consider our maxiumuni /7,;, iu the MAVC 150 system."," The largest differences are in the derived values of $R_{rim}$: the IN05 inner radii are always larger than E04 results, with a maximum difference of a factor $\sim 3$ if we consider our maximum $\Rrim$ in the MWC 480 system."1040 While or CQ Tan the two values are almost the same. for all the other stars the difference is a factor 1.5 anc 2.," While for CQ Tau the two values are almost the same, for all the other stars the difference is a factor 1.5 and 2."1041 This discrepancy is mainly due to the difference bewee1 ENOD and EOL models., This discrepancy is mainly due to the difference between IN05 and E04 models.1042 I1 particular. in INOS. the curved shape of the enüttiug srface is seltf-eonsistentlv Caculaed. allowing a more correct deteriuination of the dependence of the rini emissiou on the inclination of the disk.," In particular, in IN05, the curved shape of the emitting surface is self-consistently calculated, allowing a more correct determination of the dependence of the rim emission on the inclination of the disk."1043 Moreover. the INO5 model takes iuto account the effect of the radiation transport within the disk. even if iu an approxinate wav (see Appecudix A in INO5).," Moreover, the IN05 model takes into account the effect of the radiation transport within the disk, even if in an approximate way (see Appendix A in IN05)."1044 This supplementary heating is neglected by EOL who calculate the ¢ust temperature taking iuto account ouly the direct stellar radiation.," This supplementary heating is neglected by E04, who calculate the dust temperature taking into account only the direct stellar radiation."1045" The ratio between the two values of £,.;,, is Given by the relation where the e. &,;,,rin aud T2.,copP are the values used by EOL ⋜⋯≼↧↑↕∐∖↕∐∐↸∖↥⋅↥⋅⋜∥∐∏↴∖↴∫↿⋟∣⋅∣⇁⋯↕↴∖↴∶↴∙⊾↕↖↽↸∖∐↴⋝⋅↖⇁↑∐↸∖↥⋅↸∖↕⋜↧↑↕∪∐ Asstuning the same value of the dust eimissivitv (e=€). the ratio ΠρRy, is ~1 for ε<<l."," The ratio between the two values of $\Rrim$ is given by the relation where the $\hat\epsilon$, $\hat{R}_{rim}$ and $\hat{T}_{evp}^2$ are the values used by E04 and the inner radius $\hat{R}_{rim}$ is given by the relation Assuming the same value of the dust emissivity $\epsilon=\hat{\epsilon}$ ), the ratio $\Rrim/\hat{R}_{in}$ is $\sim1$ for $\epsilon<<1$ ."1046 The difference increases for larger € and is maxiuuin when ε aud € are very different., The difference increases for larger $\epsilon$ and is maximum when $\epsilon$ and $\hat\epsilon$ are very different.1047" Finally. there also differences due to the fact that E01 ases T5224, (ors equivalently. Πρ). as a free ΓΕποκ... while iu the INO5 model Zi. is sltcousisteutlv deteriunued starine from the choice of he type of eraius aud the gas density in the disk (see Eq.2))."," Finally, there also differences due to the fact that E04 assumes $T_{evp}$ (or, equivalently, $\Rrim$ ) as a free parameter, while in the IN05 model $T_{evp}$ is self-consistently determined starting from the choice of the type of grains and the gas density in the disk (see \ref{eq:Tevp}) )."1048" For all our target stars. the resulting values of T5, vary heween 1101 and 11ου. aud are in some cases senificautlv differeut from those eiven by EOL."," For all our target stars, the resulting values of $T_{evp}$ vary between 1370K and 1460K, and are in some cases significantly different from those given by E04."1049" The results presented in refseciit show that. with the exception of AB Aur. the INOS self-consisteut models of the ""puffed-up inner rim can explain the available observations. both visibilities and SEDs. of Πδο stars."," The results presented in \\ref{sec:fit} show that, with the exception of AB Aur, the IN05 self-consistent models of the “puffed-up” inner rim can explain the available observations, both visibilities and SEDs, of HAe stars."1050 They can be used. to derive information about the properties of the dust present iu the innermost region of the circumstellar disk. the location of the inner riu and the orieutation of the disk ou the slo. WINE a Wud uuuber of assuuptions.," They can be used to derive information about the properties of the dust present in the innermost region of the circumstellar disk, the location of the inner rim and the orientation of the disk on the sky, using a minimum number of assumptions."1051 As shown in rofsecifit.. the INOS models reproduce the interferometric data uuder the assumption that the most refractory dust in the inner disk is made of silicates. with properties typical of astronomical silicates (Weimeartucr Draine 2OOL)).," As shown in \\ref{sec:fit}, the IN05 models reproduce the interferometric data under the assumption that the most refractory dust in the inner disk is made of silicates, with properties typical of astronomical silicates (Weingartner Draine \cite{WD01}) )."1052 Iu our cases. grain sizes larecr than ~1.224 anre C1her required by or cousisteut with the observations.," In four cases, grain sizes larger than $\sim 1.2$ are either required by or consistent with the observations."1053 Onlv in one case are the data better fitted with a~ 0.3422. Caius 1n the riiare thus larger. aud often much larger. than eraius m the iutorsellar medi (a= μια. WeineartnerC» Draine 2001)). coufirmine," Only in one case are the data better fitted with $a \sim10540.2-0.3\mu$ m. Grains in the rimare thus larger, and often much larger, than grains in the interstellar medium $a=0.01-0.1\mu$ m, Weingartner Draine \cite{WD01}) ), confirming"1055 Onlv in one case are the data better fitted with a~ 0.3422. Caius 1n the riiare thus larger. aud often much larger. than eraius m the iutorsellar medi (a= μια. WeineartnerC» Draine 2001)). coufirmineC," Only in one case are the data better fitted with $a \sim10560.2-0.3\mu$ m. Grains in the rimare thus larger, and often much larger, than grains in the interstellar medium $a=0.01-0.1\mu$ m, Weingartner Draine \cite{WD01}) ), confirming"1057 Onlv in one case are the data better fitted with a~ 0.3422. Caius 1n the riiare thus larger. aud often much larger. than eraius m the iutorsellar medi (a= μια. WeineartnerC» Draine 2001)). coufirmineC»," Only in one case are the data better fitted with $a \sim10580.2-0.3\mu$ m. Grains in the rimare thus larger, and often much larger, than grains in the interstellar medium $a=0.01-0.1\mu$ m, Weingartner Draine \cite{WD01}) ), confirming"1059shown.,shown.1060" fyCV) and fix,(οι). have been caleulatecl for periods of 1 decade. corresponding approximately to the total 2237|0305 monitoring period. as well as a 6 month period which corresponds to a single observing season."," $h_{N}\left(N\right)$ and $h_{N_{tot}}\left(N_{tot}\right)$ have been calculated for periods of 1 decade, corresponding approximately to the total Q2237+0305 monitoring period, as well as a 6 month period which corresponds to a single observing season."1061 We find that the event rates should be highest in image D. corresponding to the higher expected magnification.," We find that the event rates should be highest in image D, corresponding to the higher expected magnification."1062 ‘This is in contrast to the observed. behaviour of image D which has been relatively faint for the period of monitoring. suggesting that the source may currently reside in a sparse region of the corresponding caustic network.," This is in contrast to the observed behaviour of image D which has been relatively faint for the period of monitoring, suggesting that the source may currently reside in a sparse region of the corresponding caustic network."1063 Lt is important to note however that the non-observation of a LEME in any image over the time that Q2237|0305 has been monitorec should not be surprising. since the modes of all individua image histograms are zero.," It is important to note however that the non-observation of a HME in any image over the time that Q2237+0305 has been monitored should not be surprising, since the modes of all individual image histograms are zero."1064 This ollers an alternative to the explanation given by Witt Mao (1994) that the lack of variability in images € and D (which persisted following the publication of that paper) is the result of an alignmen between the transverse velocity ancl the caustic clustering., This offers an alternative to the explanation given by Witt Mao (1994) that the lack of variability in images C and D (which persisted following the publication of that paper) is the result of an alignment between the transverse velocity and the caustic clustering.1065 The probability. distributions of microlensing naiccle parameters that have been usec to caleulate the even rates have been obtained from the observed. light curves., The probability distributions of microlensing model parameters that have been used to calculate the event rates have been obtained from the observed light curves.1066 Llowever these statistics are derived. primarily [rom the, However these statistics are derived primarily from the1067"For (is purpose. let us define a 4-dimensional vector space spanned by the four variables. Y)— Mu. Yo=ry. Ya=Των. anc Y;—rppy. wherein each data set is represented by a vector 1.2....95 denoting the data πήραν,","For this purpose, let us define a 4-dimensional vector space spanned by the four variables, $Y_1=kT_{\rm in}$ , $Y_2=r_{\rm in}$, $Y_3=kT_{\rm BB}$, and $Y_4=r_{\rm BB}$, wherein each data set is represented by a vector with $i=1, 2, .., 95$ denoting the data number."1068" Let us also define the average vector =SIV)/95{ο03.03.01). and the zero-mean vectors. eG)—V()—(y= Then. a ""distance"" D(i) of the vector ve(i). from the origin. iscalculated as standard deviation in yiG) around the origin (or in Y;(/) around its mean ΟΥ]."," Let us also define the average vector $\langle \vec{V} \rangle = \Sigma_{i=1}^{95} \vec{V(i)}/951069 \equiv \left\{\langle Y_1 \rangle, \langle Y_2 \rangle,1070 \langle Y_3 \rangle, \langle Y_4 \rangle \right\}$, and the zero-mean vectors, $\vec{v(i)} = \vec{V(i)} - \langle \vec{V} \rangle1071 \equiv \left\{y_1(i), y_2(i), y_3(i), y_4(i) \right\}$ Then, a “distance"" $D(i)$ of the vector $\vec{v(i)}$, measured from the origin, iscalculated as tandard deviation in $y_k(i)$ around the origin [or in $Y_k(i)$ around its mean $\langle Y_k \rangle$ ]."1072 Finally. we calculate the number V(<D) of those data points of which the distance D() is less (han a given value D.," Finally, we calculate the number $N(<D)$ of those data points of which the distance $D(i)$ is less than a given value $D$."1073 Figure 8 shows the normalized data point number .N(«D)/95 [rom equation (11)) as a function of D. over the range of N/95=0.2—0.8 (or N=23— 16).," Figure \ref{fig:fractal} shows the normalized data point number $N(<D)/95$ from equation \ref{eq:distance}) ) as a function of $D$, over the range of $N/95 = 0.2-0.8$ (or $N =23-76$ )."1074" IE (he variations nre controlled by ài(1<nx4) independeni parameters. we expect (he vectors e(1).v(1)...(95) to form a n-dimensional subspace in the vector space. so that W(<D) should increase as xD""."," If the variations are controlled by $n~(1\le n \le4) $ independent parameters, we expect the vectors $\vec{v(1)}, \vec{v(1)}, ... \vec{v(95)}$ to form a $n$ -dimensional subspace in the vector space, so that $N(<D)$ should increase as $\propto D^n$."1075 Indeed. Figure 8 reveals a tight power-law relation as since (his with »= 2. we inler thal the spectral behavior in the upper-banana state of 4U 1608522 has elfectivelv. (vo degrees of freedom.," Indeed, Figure \ref{fig:fractal} reveals a tight power-law relation as Since this with $n=2$ , we infer that the spectral behavior in the upper-banana state of 4U 1608–522 has effectively two degrees of freedom."1076 Of the two independent variables describing the spectral variability 3.4)). one is obviously the total luminosity Lig. or nearly equivalently. (he mass accretion rate M.," Of the two independent variables describing the spectral variability \ref{subsec:dof}) ), one is obviously the total luminosity $L_{\rm tot}$, or nearly equivalently, the mass accretion rate $\dot{M}$."1077 Actually in Figure 6 (or Figure 7). the four quantities are all observed to depend primarily on Lu (ov M).," Actually in Figure 6 (or Figure 7), the four quantities are all observed to depend primarily on $L_{\rm tot}$ (or $\dot{M}$ )."1078 However. they show significant scatters around the £L -dependentcorrelation. so that none of them can be regarded as a single-valued [unetion of Ly. (or M).," However, they show significant scatters around the $L_{\rm tot}$ -dependent, so that none of them can be regarded as a single-valued function of $L_{\rm tot}$ (or $\dot{M}$ )."1079 This is consistent with (hepresence of the second degree of freedom 3., This is consistent with thepresence of the second degree of freedom .1080"4. In order to identify what is causing (his extra Ireedonm. we remove the L,-dependence from the behavior of the four model parameters. and study (heresidual variations."," In order to identify what is causing this extra freedom, we remove the $L_{\rm tot}$ -dependence from the behavior of the four model parameters, and study theresidual variations."1081of the [OZ|AG300 and Jo lines from this svstem. which should be useful in resolving the issue.,"of the $[OI] \lambda{6300}$ and $H\alpha$ lines from this system, which should be useful in resolving the issue."1082 The 2.2 arcsec separation between the quasar and he absorber correspouds to a linear separation of 9.8 spe between their lines of sieht at the redshift of the absorber (assunmudüng a fat FRW Universe. with Πρ=το 1).," The 2.2 arcsec separation between the quasar and the absorber corresponds to a linear separation of 9.8 kpc between their lines of sight at the redshift of the absorber (assuming a flat FRW Universe, with $H_01083 = 75$ $^{-1}$ )."1084 Although we cannot rule out the »ossibilitv. tha the absorbing galaxy is uot object A. mt some füuter companion galaxy. the smal projected separation between object A and the QSO makes it likely hat the absorption arises in object A itself," Although we cannot rule out the possibility that the absorbing galaxy is not object A, but some fainter companion galaxy, the small projected separation between object A and the QSO makes it likely that the absorption arises in object A itself."1085 We note that here is a faint object 17 north of A aud 27 east of the quasar. barely visible iu Fie. 2..," We note that there is a faint object 1” north of A and 2” east of the quasar, barely visible in Fig. \ref{fig:image}."1086" This svstem is about 2 nagnitudes fainter than object A and considerably more diffuse,", This system is about 2 magnitudes fainter than object A and considerably more diffuse.1087 It is unclear whether this object is in the vicinity of the QSO or a companion to object. A or. indeed. an iuterloper not associated with either svstenm.," It is unclear whether this object is in the vicinity of the QSO or a companion to object A or, indeed, an interloper not associated with either system."1088 Our optical photometry shows that object À has LονL*., 	Our optical photometry shows that object A has $L \sim L^\star$.1089 This is cousisteut with the results of Rao Briees (1993) who used a survev of the III conteut of =0 optically bright ealaxies. to conclide that the cross section for DLA absorption peaks at this luminosity.," This is consistent with the results of Rao Briggs (1993) who used a survey of the HI content of $z=0$ optically bright galaxies, to conclude that the cross section for DLA absorption peaks at this luminosity."1090 Note. however. that Roscubere Schucider (2001) arene that a substantial contribution to the DLA cross-section is provided by optically faint galaxies. based ou a blind 21-cn survey at 2=0.," Note, however, that Rosenberg Schneider (2001) argue that a substantial contribution to the DLA cross-section is provided by optically faint galaxies, based on a blind 21-cm survey at $z=0$."1091 The latter is also cousisteut with optical searches for the counterparts of low redshift DLAs. which have shown that the absorbers arise in galaxies with a wide range of Iuninosities.," The latter is also consistent with optical searches for the counterparts of low redshift DLAs, which have shown that the absorbers arise in galaxies with a wide range of luminosities."1092 Cheungalur Iauckar (2000) found that low spin temperatures (Z5x5300 IK) were obtained in the few cases where the absorber was ideutified to be a spiral galaxy: such temperatures are typical of the Milkv. Way aud local spirals (see also Ikauckar Chenusalur (2001))., Chengalur Kanekar (2000) found that low spin temperatures $T_{\rm s} \la 300$ K) were obtained in the few cases where the absorber was identified to be a spiral galaxy; such temperatures are typical of the Milky Way and local spirals (see also Kanekar Chengalur (2001)).1093" IHTowever. he majority of DLAs were found to have ar higher spin eniperatures. 7;Zi1000 IK. Ileher T, values are to be expected in sinaller svstenis ike dwarf galaxies. whose ow inctallicities aud pressures are nof conducive to the ormnation of the cold phase of HII. (Wolfireetal. 1995)): such systems hence have a higher fraction of warm gas as compared to normal spirals. and therefore. a high spin eniperature."," However, the majority of DLAs were found to have far higher spin temperatures, $T_{\rm s} \ga 1000$ K. Higher $T_{\rm s}$ values are to be expected in smaller systems like dwarf galaxies, whose low metallicities and pressures are not conducive to the formation of the cold phase of HI \cite{wolfire95}) ); such systems hence have a higher fraction of warm gas as compared to normal spirals, and therefore, a high spin temperature."1094 Ou the other haud. bright galaxies teud to rave high masses. auc hence both higher ietallicitics and ceutral pressures. contributing to the formation of he cold phase of jeutral hydrogen.," On the other hand, bright galaxies tend to have high masses, and hence both higher metallicities and central pressures, contributing to the formation of the cold phase of neutral hydrogen."1095" The high luuinosity of object À thus indicates that it is likely to have a ow spin temperature C5300 I) aud hence. a relatively ow cohuun densityH Vy,τX5&E1079PP2"," The high luminosity of object A thus indicates that it is likely to have a low spin temperature $\la 300$ K) and hence, a relatively low column density $N_{\rm HI} \la 5 \times 10^{20}$."1096 Tt would ο interesting to test this conjecture by means of IIST observatious in the Lyra liue. as well as to directly deteriuue the moetalliitv of the absorber through high resolutiou absorption studies.," It would be interesting to test this conjecture by means of HST observations in the $\alpha$ line, as well as to directly determine the metallicity of the absorber through high resolution absorption studies."1097 Iu à subsequent paper. we plan o compare the metallicity as computed from such a ligh resolution absorption spectrum to the metallicity measured frou the cussion lines.," In a subsequent paper, we plan to compare the metallicity as computed from such a high resolution absorption spectrum to the metallicity measured from the emission lines."1098 21e absorption frou 1213- has recently been iudepenudoeutlv detected by Lane et al. (, 21cm absorption from 1243-072 has recently been independently detected by Lane et al. (10992001) using the WSRT.,2001) using the WSRT.1100faster than linearly.,faster than linearly.1101 Only smaller mass black holes (less than a few times 105 solar masses) may have limit evele instability timescales of just a few vears., Only smaller mass black holes (less than a few times $10^7$ solar masses) may have limit cycle instability timescales of just a few years.1102 Leven considering the uncertainties in the absolute values of the predicted critical luminosity that come from uncertainties in the black hole mass and spin. it would be interesting to search [or any evidence of the predicted. behaviour by looking at distribution of observed. disk luminosities in large samples of AGN with available estimates of the central black hole miss.," Even considering the uncertainties in the absolute values of the predicted critical luminosity that come from uncertainties in the black hole mass and spin, it would be interesting to search for any evidence of the predicted behaviour by looking at distribution of observed disk luminosities in large samples of AGN with available estimates of the central black hole mass."1103~ 0 represents a purely exponential or disk-like profile).,$\sim$ 0 represents a purely exponential or disk-like profile).1104 Past work (e.g.Kavirajetal.2007a) has successfully used this parameter as a measure of morphology in large galaxy samples., Past work \citep[e.g.][]{Kav07} has successfully used this parameter as a measure of morphology in large galaxy samples.1105 In Figure 2 we plot the in the r band of our sample., In Figure \ref{fig:frac} we plot the in the $r$ band of our sample.1106" All our SPMs have a greater than 0.5 (ie. they are dominated by the ‘bulge-like’ profile), with most of them higher than 0.8, which is consistent with the results of our visual classification."," All our SPMs have a greater than 0.5 (i.e. they are dominated by the `bulge-like' profile), with most of them higher than 0.8, which is consistent with the results of our visual classification."1107" Note that not all postmergers with high values of from the original sample of 370 were in fact bulge-dominated when inspected visually, a further example of the utility of employing visual inspection in conjunction with automatic We begin by exploring the local environments of our SPMs, using the environment parameter (ps) defined by Schawinskietal. (2007a)."," Note that not all postmergers with high values of from the original sample of 370 were in fact bulge-dominated when inspected visually, a further example of the utility of employing visual inspection in conjunction with automatic We begin by exploring the local environments of our SPMs, using the environment parameter $\rho_g$ ) defined by \cite{Sch07}."1108". This is defined as a weighted sum of all the neighbours within the ellipse where rq is the distance on the sky in Mpc to each surrounding galaxy, rz is the distance along the line-of-sight in Mpc to each surrounding galaxy, and σ is the radius."," This is defined as a weighted sum of all the neighbours within the ellipse where $r_a$ is the distance on the sky in Mpc to each surrounding galaxy, $r_z$ is the distance along the line-of-sight in Mpc to each surrounding galaxy, and $\sigma$ is the radius."1109 The parameter cz scales the value of o along the line of sight to compensate for the ‘finger of god’ effect (see Schawinski et al., The parameter $c_z$ scales the value of $\sigma$ along the line of sight to compensate for the `finger of god' effect (see Schawinski et al.1110 2007 for moredetails)?., 2007 for more.1111. According to this definition a galaxy with pg=0 typically has no neighbours ina c radius., According to this definition a galaxy with $\rho_g=0$ typically has no neighbours in a $\sigma$ radius.1112" Values in the range 0<p,<0.1 are consistent with a field environment."," Values in the range $ 0 \textless1113\rho_g \textless 0.1$ are consistent with a field environment."1114" Galaxies with 0.1<pg<1 are in a group environment, while anything larger typically corresponds to clusters."," Galaxies with $0.1 \textless \rho_g \textless 1$ are in a group environment, while anything larger typically corresponds to clusters."1115" We find that two galaxies in our SPM sample inhabit clusters (pg> 1), while the rest are split between groups and the field."," We find that two galaxies in our SPM sample inhabit clusters $\rho_g > 1$ ), while the rest are split between groups and the field."1116 This result is expected since the high peculiar velocities of the galaxies in dense environments such as clusters make collisions unlikely., This result is expected since the high peculiar velocities of the galaxies in dense environments such as clusters make collisions unlikely.1117" Similarly, in very sparse environments there are not enough galaxies around to produce many merger events, so a post-merger population spread between intermediate and low-density environments is reasonable."," Similarly, in very sparse environments there are not enough galaxies around to produce many merger events, so a post-merger population spread between intermediate and low-density environments is reasonable."1118 The environment parameter values for the sample are shown in Figure 3.., The environment parameter values for the sample are shown in Figure \ref{fig:Rho}. .1119location) produce measurable systematic biasses to within the +0.!—mag fitting uncertainties built into the GCLF method.,location) produce measurable systematic biasses to within the $\pm0.1-$ mag fitting uncertainties built into the GCLF method.1120 We therefore adopt the last of the determinations listedabove (jr=4.06£0.11). which has the highest internal precision and greatest statistical security of sample size.," We therefore adopt the last of the determinations listedabove $\Delta\mu = 4.06 \pm 0.11$ ), which has the highest internal precision and greatest statistical security of sample size."1121" Adding this to our adopted Virgo distance modulus, we obtain j/(Coma) =35.0540.12 or d=(102£6) Mpe (where the quoted error represents only the internal uncertainty of the method)."," Adding this to our adopted Virgo distance modulus, we obtain $\mu$ (Coma) $= 35.05 \pm 0.12$ or $d = (102 \pm 6)$ Mpc (where the quoted error represents only the internal uncertainty of the method)."1122 Earlierliterature (see. e.g.. Capaccioletal.1990:: Sandage&Tammann 1990: vandenBergh1992 for reviews of a range of methods) tended to give qi(Coma — Virgo) in the range 3.723.8.," Earlierliterature (see, e.g., \cite{cap90}; \cite{san90}; \cite{van92} for reviews of a range of methods) tended to give $\Delta \mu$ (Coma $-$ Virgo) in the range $3.7 - 3.8$."1123" However. our determination of 4.06 is similar to other, more recent determinations that rely directly on the giant ellipticals: for example. SBF analysis of ellipticals in Coma and Leo I (Thomsenetal. 1997)) and the fundamental plane comparison for the Leo and Coma ellipticals (Hjorth&Tanvir 1997)) give Aj«Coma — Leo) ~4.8—4.9."," However, our determination of 4.06 is similar to other, more recent determinations that rely directly on the giant ellipticals: for example, SBF analysis of ellipticals in Coma and Leo I \cite{tho97}) ) and the fundamental plane comparison for the Leo and Coma ellipticals \cite{hjo97}) ) give $\Delta \mu$ (Coma $-$ Leo) $\simeq 4.8 - 4.9$."1124" Subtracting Aj:(Virgo — Leo) 0.87E0.1 (Ferrareseetal. 1999a)) then gives Ay——4.0 to 4.1 for the Virgo-to-Coma step, in agreement with our findings."," Subtracting $\Delta \mu$ (Virgo $-$ Leo) $ = 0.87 \pm 0.1$ \cite{fer99a}) ) then gives $\Delta \mu \simeq 4.0$ to 4.1 for the Virgo-to-Coma step, in agreement with our findings."1125 The GCLF turnover luminosity that we implicitly adopt along with this distance calibration 19.alone. My.=—7.26+0.06 (internal uncertainty).," The GCLF turnover luminosity that we implicitly adopt along with this distance calibration is, $M_V^0 = -7.26 \pm 0.06$ (internal uncertainty)."1126" For Fornax alone, our turnover luminosity would be Mi,2—7.45+0.06."," For Fornax alone, our turnover luminosity would be $M_V^0 = -7.45 \pm 0.06$."1127 The true external uncertaintics on both of these estimates. particularly for Fornax. are likely to be near +0.2 mag.," The true external uncertainties on both of these estimates, particularly for Fornax, are likely to be near $\pm0.2$ mag."1128 We can now estimate Ho., We can now estimate $H_0$.1129 The redshift of Coma corrected for Local Group peculiar motion (ο.σ.. Colless&Dunn 1996)) is cz27100 km s'!. with a likely uncertainty of +200 km s' taking into account the degree to which the peculiar velocities of the Milky Way and Local Supercluster relative to the CMB are known.," The redshift of Coma corrected for Local Group peculiar motion (e.g., \cite{col96}) ) is $cz = 7100$ km $^{-1}$, with a likely uncertainty of $\pm 200$ km $^{-1}$ taking into account the degree to which the peculiar velocities of the Milky Way and Local Supercluster relative to the CMB are known."1130 We note that this mean Coma velocity explicitly excludes the outlying NGC 4839 subgroup. which would have biased the mean to slightly higher levels (see Colless&Dunn 1996)).," We note that this mean Coma velocity explicitly excludes the outlying NGC 4839 subgroup, which would have biased the mean to slightly higher levels (see \cite{col96}) )."1131" From Hubble's law, cz=Ho:d. we obtain Corrections for the geometric curvature parameter qo are negligible Gf gp is in the range ~— 0.00.5. at the Coma redshift of z=0.0237 the resulting uncertainty in Hy is only 0.3 percent)."," From Hubble's law, $cz = H_0 \cdot d$, we obtain Corrections for the geometric curvature parameter $q_0$ are negligible (if $q_0$ is in the range $\sim 0.0 - 0.5$ , at the Coma redshift of $z = 0.0237$ the resulting uncertainty in $H_0$ is only 0.3 percent)."1132" Putting in our distance modulus and redshift for Coma, we obtain H,269 kms! Mpc!."," Putting in our distance modulus and redshift for Coma, we obtain $H_0 = 69$ km $^{-1}$ $^{-1}$ ."1133 The net uncertainty in our result must include not, The net uncertainty in our result must include not1134accretion disk or torus.,accretion disk or torus.1135 A similar state is expected from tidal break-up of a neutron star by a Ixerr black hole (Paezyuiski1991:vanPutten1999).," A similar state is expected from tidal break-up of a neutron star by a Kerr black hole \citep{pac91,mvp99b}."1136. Ultrarelativistic leptomie outflows which form the input to GBRs may be powered by black hole-spin in the presence of magnetic fields (vanPutten2000a.b:Heyl2000).," Ultrarelativistic leptonic outflows which form the input to GBRs may be powered by black hole-spin in the presence of magnetic fields \citep{mvp00a,mvp00b,hey00}."1137. Long/short GRBs can hereby be associated with magnetic regulated suspeuded/hyper-accretion onto rapidly/slowly spiuniug black holes (vanPutten&Ostriker2000)., Long/short GRBs can hereby be associated with magnetic regulated suspended/hyper-accretion onto rapidly/slowly spinning black holes \citep{mvp00c}.1138. For loug bursts. the suspended accretion state asts for the duration of spiu-down of the black hole. whereby the surrouudiug maguetizecl matter 'eceives a powerful torque J=—5 from the auglar momentum J); of the black hole (vanPuttenPutten1999:Brownetal.2001) which arrests the inflow.," For long bursts, the suspended accretion state lasts for the duration of spin-down of the black hole, whereby the surrounding magnetized matter receives a powerful torque $T=-\dot{J}_H$ from the angular momentum $J_H$ of the black hole \citep{mvp99a,mvp99b,bro01} which arrests the inflow."1139 The black hole »erforms approximately isotropic work in powering both the outflow aud the Maxwell stresses onto he torus., The black hole performs approximately isotropic work in powering both the outflow and the Maxwell stresses onto the torus.1140 This suggestsMO to consider the possibility that the torus re-radiates this output. in part. in gravitational-wave emissions as it develops non-axisyimauetric iustabilities.," This suggests to consider the possibility that the torus re-radiates this output, in part, in gravitational-wave emissions as it develops non-axisymmetric instabilities."1141 Here. we show that gravitational wave-einissions are expected in[un suspeuded accretion as a collateral feature to long GRB-alterelow emissious.," Here, we show that gravitational wave-emissions are expected in suspended accretion as a collateral feature to long GRB-afterglow emissions."1142 This feature is it —jay ways sunilar to pulsars. which are well-kuown to radiate predominantly in gravitational waves Teukolsky 1983).," This feature is in many ways similar to new-born pulsars, which are well-known to radiate predominantly in gravitational waves \citep{sha83}."1143. The approximately isotropic work performed by the black hole takes place over intercounecting magnetic fiekl-lines regulated by the magnetic moment of the black hole in equilibrium with the torus maguetospliere (WaldL97Ll:DokuchaeyLOST:vauPutten2000b:Leeetal.2001).," The approximately isotropic work performed by the black hole takes place over interconnecting magnetic field-lines regulated by the magnetic moment of the black hole in equilibrium with the torus magnetosphere \citep{wal74,dok87,mvp00b,lee01}."1144. These lines comprise a torus innagnuetospliere supported by surrouucdiug baryouic matter aud open Geld-lines to infinity. as schematically indicated in Figure 1.," These field-lines comprise a torus magnetosphere supported by surrounding baryonic matter and open field-lines to infinity, as schematically indicated in Figure 1."1145 The latter field-lines are eudowed with coujugate raciative-radiative boundary conditions. whereas the former have racliative-Dirichlet boundary couditious.," The latter field-lines are endowed with conjugate radiative-radiative boundary conditions, whereas the former have radiative-Dirichlet boundary conditions."1146 These different boundary conditions introduce interactions which will differ in details. e.g: leptonie outflow to infinity and Maxwell stresses outo the torus. respectively.," These different boundary conditions introduce interactions which will differ in details, e.g.: leptonic outflow to infinity and Maxwell stresses onto the torus, respectively."1147 Nevertheless. the work performed per solid angle into these different fiekl-lines is expected to be rather similar.," Nevertheless, the work performed per solid angle into these different field-lines is expected to be rather similar."1148 The magnetic connection of the black hole to the inner face of the inecdiates Maxwell stresses by equivalence in poloidal topology to pulsar inaguetospheres., The magnetic connection of the black hole to the inner face of the mediates Maxwell stresses by equivalence in poloidal topology to pulsar magnetospheres.1149" Au aligned rotator radiates Maxwell stresses to iufinityH accordingH to —4,=>0,45. where the subscriptH p refersH to the appropriateH pulsar values (CtoldreichandJulian1969)."," An aligned rotator radiates Maxwell stresses to infinity according to $-\dot{J}_{p}=\Omega_{p} A_p^2$, where the subscript $p$ refers to the appropriate pulsar values \citep{gol69}."1150". Analogously. causal Maxwell stresses are set up between the black hole and the inner face of the torus according to (adapted [rom Ostriker (2000))) where £25 denotes the augular velocity of the torus aud its similarly shaped force-Dree nuaguetospliere. aud 2afy,A denotes the flux in interconnecting magnetic field-lines - 274 representing the net"," Analogously, causal Maxwell stresses are set up between the black hole and the inner face of the torus according to (adapted from \cite{tho86,mvp00c}) ) where $\Omega_T$ denotes the angular velocity of the torus and its similarly shaped force-free magnetosphere, and $2\pi f_HA$ denotes the flux in interconnecting magnetic field-lines - $2\pi A$ representing the net"1151nucleon) at 75=9.,nucleon) at $T_9 = 9$.1152 Iu this study. Y; is taken to be 0.1. according to the core-collapse simulation iu," In this study, $Y_{e}$ is taken to be 0.4, according to the core-collapse simulation in."1153 LebsinWana thoteimperaturcambdesaityerdsottübe ο(dto 1 Fagecstod.Coco decreases to 1.0. im order to ninüc the effect of the slower outgoing ejecta behind the shock.," As in, the temperature and density are set to be constant when $T_9$ decreases to $1.0$, in order to mimic the effect of the slower outgoing ejecta behind the shock."1154 The uucleosvuthesis results for models B2-Bh. C2-C5. aud. D2-D5 (Table 1) are shown iu Figure 3. as a function of atomic mass nunber.," The nucleosynthesis results for models B2-B5, C2-C5, and D2-D5 (Table 1) are shown in Figure 3, as a function of atomic mass number."1155 For anisotropic wind models with Ro=12kin (D2-Bh). the effect of anisotropic neutrino ciission is evident.," For anisotropic wind models with $R_2 = 12\, \mathrm{km}$ (B2-B5), the effect of anisotropic neutrino emission is evident."1156 A factor of three or four iucrease in Li» (B38 aud Blin Table 1) leads tosee150.160.N4 and nga3lius. resulting in- the r--process uucleosvuthesis (Fie.," A factor of three or four increase in $L_{\nu 2}$ (B3 and B4 in Table 1) leads to $s1157\approx 150-160\, N_A\, k$ and $\tau_\mathrm{dyn} \approx 3-4\,1158\mathrm{ms}$, resulting in the -process nucleosynthesis (Fig."1159 3)., 3).1160 For model Bh. the lieh cutropy (= 180.N yA) and short dyuunic timescale (=1.65 113) of the wind dive the nuclear matter to the actinide region.," For model B5, the high entropy $= 180\, N_A\, k$ ) and short dynamic timescale $= 1.65\, \mathrm{ms}$ ) of the wind drive the nuclear matter to the actinide region."1161" The neutrou-to-secd abundance ratio at the beeiuuing of the r--process. defined as Ty=2.5. is 3,/Y,=176 aud the final averagel niass nuinver of heavy nuclei wi hZ>2 is Gl;=230 (Table 1)."," The neutron-to-seed abundance ratio at the beginning of the -process, defined as $T_9 =11622.5$, is $Y_n/Y_h = 176$ and the final averaged mass number of heavy nuclei with $Z > 2$ is $\langle A_h \rangle = 230$ (Table 1)."1163" For the iueels with Ry=kin (C2-€'5). the r-process still takes place when £,2 Is our or five times ligjer than L, Quodels Cl anc LCh)."," For the models with $R_2 = 15\, \mathrm{km}$ (C2-C5), the -process still takes place when $L_{\nu 2}$ is four or five times higher than $L_\nu$ (models C4 and C5)."1164 For Ro=20lau (D2-D5). the effect of arisotropic neutrino enussion is not important aud the nucleosvuthesis results are uot seuifcantlv different from the isotropic cases (A1-A5).," For $R_2 = 20\, \mathrm{km}$ (D2-D5), the effect of anisotropic neutrino emission is not important and the nucleosynthesis results are not significantly different from the isotropic cases (A1-A5)."1165 Iun thisLetter. the effects of anisotropy in neutiiuo emission for the r-—process nucleosvuthliesis in proto-neutrou-star winds were examined. usus the spherically sxainietric. steady outflow. mode of neutrino-cdiiven winds.," In this, the effects of anisotropy in neutrino emission for the -process nucleosynthesis in proto-neutron-star winds were examined, using the spherically symmetric, steady outflow model of neutrino-driven winds."1166" It was shown that stroug anisotropy.δές, cau be au additional energy source to heat the wine material."," It was shown that strong anisotropy, can be an additional energy source to heat the wind material."1167 A factor of four or five cnhancemenu iu neutrino πιο results iu the sjeuificaut increase of entropy and shorteuiug of dynamic timescale of outgoiug neutrimo-lheatec ejecta., A factor of four or five enhancement in neutrino luminosity results in the significant increase of entropy and shortening of dynamic timescale of outgoing neutrino-heated ejecta.1168 This is inanly due to the neutinuo heating from annihilation of neutriuo-antincutrino pairs iuto clectron-positron pairs as a result of anisotropic neutrino enuüssion., This is mainly due to the neutrino heating from annihilation of neutrino-antineutrino pairs into electron-positron pairs as a result of anisotropic neutrino emission.1169" This provides the physical condition suitable for the robust :—process, producing the third abundance peak (A=195) and bevoud."," This provides the physical condition suitable for the robust -process, producing the third abundance peak $A = 195$ ) and beyond."1170 Tt is conceivable that asvnuuetrie neutriuo Cluission can be associated with the anisotropic natter distribution near the neutrino sphere., It is conceivable that asymmetric neutrino emission can be associated with the anisotropic matter distribution near the neutrino sphere.1171 As that 16 non-sphlierical neutriuo sphere owing to rapid rotation leads to anisotropic neutrino heating Naath the pole-to-equator ratio of a few to more iui 10.," As an example, suggested that the non-spherical neutrino sphere owing to rapid rotation leads to anisotropic neutrino heating with the pole-to-equator ratio of a few to more than 10."1172 This may result iu strong contrast iu retiring chussion on the neutrmo sphere. which rns an “lot spot arouud the rotational axis.," This may result in strong contrast in neutrino emission on the neutrino sphere, which forms an “hot spot” around the rotational axis."1173 À recent work with more sophisticated jeutrino-trausport scheme by showed. however. that the pole-to-equator flux ratio ds at most a factor of two. even for a rather rapidly rotating core.," A recent work with more sophisticated neutrino-transport scheme by showed, however, that the pole-to-equator flux ratio is at most a factor of two, even for a rather rapidly rotating core."1174 This is a consequence that he radiation ποια is smootheued by the παν jeutrino sources above the neutrino sphere (e.e.. convective bubbles) at the carly phase (<Is after core bounce).," This is a consequence that the radiation field is smoothened by the many neutrino sources above the neutrino sphere (e.g., convective bubbles) at the early phase $< 1\, \textrm{s}$ after core bounce)."1175 Nevertheless. all the couvective »bbles are evacuated during the late wind plase (~ 10s) aud a strong contrast of ιοπο flux uight foriu on the ueutriuo sphere for a rapidly rotating core.," Nevertheless, all the convective bubbles are evacuated during the late wind phase $\sim 10\, \textrm{s}$ ) and a strong contrast of neutrino flux might form on the neutrino sphere for a rapidly rotating core."1176 Another possibilitv of anisotroye neutrino (quission nieht be due a elobal fiui oeistabilities of neutrino-heated matter as observed i imuulti-dimensional lvdrocdvuamic simulations., Another possibility of anisotropic neutrino emission might be due a global fluid instabilities of neutrino-heated matter as observed in multi-dimensional hydrodynamic simulations.1177 Receut works have shown that hivdrodyviiuaulc mstabilities can lead to low-mode (7=1 in terms of an expansion iu spherical harmonics of order 7) oscillation of the couvective fluid flow iu the jieutriino-heated laver behind the shock2006)., Recent works have shown that hydrodynamic instabilities can lead to low-mode $l = 1$ in terms of an expansion in spherical harmonics of order $l$ ) oscillation of the convective fluid flow in the neutrino-heated layer behind the shock.1178". The presence of such a low couvective uode results in the pair of a single outfow aud a iurow accretion flow that creates the. ""hot spot on the neutron star surface.", The presence of such a low convective mode results in the pair of a single outflow and a narrow accretion flow that creates the “hot spot” on the neutron star surface.1179 It should be noted. rowever. that the two-dimensional simulatious bv showed tha jo andsotropv of the accretion. luminosity owing to this flow iypears to be oulv a few perceut (at least curing the early phase up to ~Ls after core bounce).," It should be noted, however, that the two-dimensional simulations by showed that the anisotropy of the accretion luminosity owing to this flow appears to be only a few percent (at least during the early phase up to $\sim 1\, \textrm{s}$ after core bounce)."1180 A future investigation8 relevant for the wind phase (c1. 10s) will be needed to exiunine the degree of anisotropic neutro cluission from such au accretion flow.," A future investigation relevant for the wind phase $\sim 1-10\, \textrm{s}$ ) will be needed to examine the degree of anisotropic neutrino emission from such an accretion flow."1181 (νο one of the above (or another uukuown) miechanisni works. a coustraiunt for the r-—process iav be obtained from the condition that creates," Given one of the above (or another unknown) mechanism works, a constraint for the -process may be obtained from the condition that creates"1182These can be combined to obtain the normalizations for the mass. aud for the kinetic aud thermal energies. of the bubble: The power of à in the square brackets imdicates how cach integral scales im a normalization.,"These can be combined to obtain the normalizations for the mass, and for the kinetic and thermal energies, of the bubble: The power of $\alpha$ in the square brackets indicates how each integral scales in a normalization."1183 The full equations for the mass. kinetic aud thermal energies. in the bubble are The mass in the USW (SSW) reeion. Mua (Ma). Is obtained through the replacement of i in Eq.," The full equations for the mass, kinetic and thermal energies, in the bubble are The mass in the USW (SSW) region, $M_{\rm usw}$ $M_{\rm ssw}$ ), is obtained through the replacement of $m$ in Eq."1184 21 with Basse (Due). Where the integral is evaluated frou 1=0 tor—vu (frome=su foc tea).," \ref{eq:mbub} with $m_{\rm usw}$ $m_{\rm ssw}$ ), where the integral is evaluated from $x=0$ to $x=x_{\rm is}$ (from $x=x_{\rm is}$ to $x=x_{\rm cd}$ )."1185" The total mass carried from the star lov its wind is The degree of imass-loading in the bubble. Pj,. cal be neasured bv the ratio AMj,/AA."," The total mass carried from the star by its wind is The degree of mass-loading in the bubble, $\Phi_{\rm b}$, can be measured by the ratio $M_{\rm b}/M_{\rm w}$ ."1186 Starting with the expression for M. text following Eq. 101).," Starting with the expression for $M_{\rm sh}$, text following Eq. \ref{eq:cons_mtm}) ),"1187 using Eq., using Eq.1188 to express req du ternis of eg. emiploviug Eq.," \ref{eq:sim_r} to express $r_{\rm cd}$ in terms of $x_{\rm cd}$, employing Eq."1189 18. to rewrite po in terms of 0. and using Eq.," \ref{eq:theta_form} to rewrite $\rho_{0}$ in terms of $\theta$, and using Eq."1190 11 and the definition of . we find The ratio of the «πρτης mass in the shell to the bubble mass is hence: The kinetic energy of the shell is AE=iMac.," \ref{eq:mdotc} and the definition of $\Xi$, we find The ratio of the swept-up mass in the shell to the bubble mass is hence: The kinetic energy of the shell is $KE_{\rm sh} = \frac{1}{2}1191M_{\rm sh}v_{\rm cd}^{2}$."1192 Using Eqs. 28. 13. 20.," Using Eqs. \ref{eq:m_sh}, \ref{eq:edot}, \ref{eq:scale_trans},"1193 and δ through 10 we obtain We can also calculate the pd work doue ou the shocked iutercliump medimm in compressing it into a neeligibly thin shell., and \ref{eq:ode1_evap} through \ref{eq:ode3_evap} we obtain We can also calculate the $pdV$ work done on the shocked interclump medium in compressing it into a negligibly thin shell.1194 The initial euergw per uuit mass of the interchuup eas inuucdiately after passing through the forward shock is: where here ey is the post-shock flow velocity (=inu) aud py aud py are the post-shock pressure and deusity., The initial energy per unit mass of the interclump gas immediately after passing through the forward shock is: where here $v_{1}$ is the post-shock flow velocity $=\frac{3}{4} v_{\rm cd}$ ) and $p_{1}$ and $\rho_{1}$ are the post-shock pressure and density.1195" If we asstune that the pressure and velocity of the surrounding medi are both negligible. the yost-shock pressure is p=Byres,."," If we assume that the pressure and velocity of the surrounding medium are both negligible, the post-shock pressure is $p_{1} = \frac{3}{4}\rho_{0}r^{\beta}_{\rm cd} v_{\rm cd}^{2}$."1196 Substituting for p into Eq. 31..," Substituting for $p_{1}$ into Eq. \ref{eq:energ},"1197 we find that the su of the kinetic aud thermal energies per uuit mass behind a strongshock is £4=inp02, we find that the sum of the kinetic and thermal energies per unit mass behind a strongshock is $E_{1} = \frac{9}{16}v_{\rm cd}^{2}$.1198 From our earlier assuiuptious. the swept up eas ends up with a velocity ο=(oq it is accelerated) aud no mterual energv.," From our earlier assumptions, the swept up gas ends up with a velocity $v=v_{\rm cd}$ it is accelerated) and no internal energy."1199 Hence. the finala energy per unit. mass isB Ly=iP ," Hence, the final energy per unit mass is $E_{2} = \frac{1}{2}v_{\rm cd}^{2}$."1200Therefore theeuergy radiated away is E44;=EME=e)16142οἱ per unit mass., Therefore theenergy radiated away is $E_{rad} = E_{1}-E_{2} = \frac{1}{16} v_{\rm cd}^{2}$ per unit mass.

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