ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 These differences are caused bv the enhanced (turbulent diffusion of dust particle motions through5 enhanced 5eas drag., These differences are caused by the enhanced turbulent diffusion of dust particle motions through enhanced gas drag.3el Indeed. Fiewe lice shows that the turbulent seattering ci dominates over the steady migration ey in most areas of the simulation box.," Indeed, Figure \ref{fig:t01-dust}c c shows that the turbulent scattering $v_{\rm t}$ dominates over the steady migration $v_{\rm f}$ in most areas of the simulation box."4 Figure 11bb shows the estimated. radial velocity of particles vy., Figure \ref{fig:t01-dust}b b shows the estimated radial velocity of particles $v_{\rm d}$.5" The radial velocity of the simulated particles. ¢,. are also shown by dots."," The radial velocity of the simulated particles, $v_{x}$, are also shown by dots."6 Although dust particles ave swept out of the unstable region. in most parts of the unstable region. max[e4]>0 and min|e4]<0 are satisfied. so the dust particles are broadly distributed in (he stable region with lower concentration.," Although dust particles are swept out of the unstable region, in most parts of the unstable region, $v_{\rm d}] > 0$ and $v_{\rm d}] < 0$ are satisfied, so the dust particles are broadly distributed in the stable region with lower concentration."7 Nevertheless. identity of the clump with the highest dust concentration is sill maintained (Figure 12aa).," Nevertheless, identity of the clump with the highest dust concentration is still maintained (Figure \ref{fig:t01-clump}a a)."8 Indeed the velocity dispersion around center of the traced clump shown is not increased significantly (Figure 12bb)., Indeed the velocity dispersion around center of the traced clump shown is not increased significantly (Figure \ref{fig:t01-clump}b b).9 We also run a high global pressure gradient model (2=—0.10)., We also run a high global pressure gradient model $\beta=-0.10$ ).10 Though the inwud migration of dust particles becomes faster on average. the maximunm density is unclianged because (he remnant turbulence that scatters the dust particles in the dust concentrated region is the dominant [actor for this τε)=0.1 case.," Though the inward migration of dust particles becomes faster on average, the maximum density is unchanged because the remnant turbulence that scatters the dust particles in the dust concentrated region is the dominant factor for this $\tau_f\Omega=0.1$ case."11 Recent works (e.g..Johansen&Youdin2007) proposed that turbulence itself concentrates dust particles in turbulent eddies.," Recent works \citep[e.g.,][]{joh07a} proposed that turbulence itself concentrates dust particles in turbulent eddies."12 In their models. lifetime of the eddies has to be longer than the timescale to form dense enough particle clumps lor formation of planetesimals.," In their models, lifetime of the eddies has to be longer than the timescale to form dense enough particle clumps for formation of planetesimals."13 On the other hand. our model proposes another path to accumulate dust particles Chat turbulence plavs a role in transformation of the nearly Ixeplerian gas [low into (he quasi-steady flow wilh a local rigid rotation region.," On the other hand, our model proposes another path to accumulate dust particles that turbulence plays a role in transformation of the nearly Keplerian gas flow into the quasi-steady flow with a local rigid rotation region."14 Because the dust particles accumulate near the outer edge of super-Ixeplerian parts produced by the rigid rotation aud the flow pattern is quasi-steady. ihe timeseale problem does not exist in our model.," Because the dust particles accumulate near the outer edge of super-Keplerian parts produced by the rigid rotation and the flow pattern is quasi-steady, the timescale problem does not exist in our model."15 Actually. in the case of model-s40. and model-t01 with f«c0.096. the same chunp with the highest density is maintained until the end of simulations (/€9 80).," Actually, in the case of model-s40 and model-t01 with $R_{\rm m,ave} \simeq 0.096$, the same clump with the highest density is maintained until the end of simulations $t \Omega \simeq 80$ )."16 llowever. in our model. as A44: increases 0o unity. stronger residual turbulence may destroy the chunps. although the clumps are repeatedly created. which may inhibit planetesimal formation.," However, in our model, as $R_{\rm m,ave}$ increases to unity, stronger residual turbulence may destroy the clumps, although the clumps are repeatedly created, which may inhibit planetesimal formation."17" Ilere. we examine the cases with larger A224, (but still H4,< 1) to find the critical value of Ryaye for persistent clumping."," Here, we examine the cases with larger $R_{\rm m,ave}$ (but still $R_{\rm m,ave}<1$ ) to find the critical value of $R_{\rm m,ave}$ for persistent clumping."18" In moclel-s055. the width of the stable region L, is one eighth of modelst0."," In model-s055, the width of the stable region $L_{\rm s}$ is one eighth of model-s40."19 Accordingly. Haas=0.64 compared (to 0.096 of model-s40.," Accordingly, $R_{\rm m,ave}=0.64$ compared to 0.096 of model-s40."20 Figure 13aa shows that the AUR turbulence, Figure \ref{fig:s055-3D}a a shows that the MRI turbulence21be intrinsically faint (e.g. Kolb 1993: Howelletal. 1997)): Pretoriusctal.(2007a) and Pretorius&Ixnigge(2008b) find that. although an as vet undetected fant CV population cannot dominate the overall population to. the extent predicted. observed. CV. samples are nevertheless strongly biased against [aint svstemis.,"be intrinsically faint (e.g. \citealt{Kolb93}; ; \citealt{howell2}) ); \cite{PretoriusKniggeKolb07} and \cite{halpha2} find that, although an as yet undetected faint CV population cannot dominate the overall population to the extent predicted, observed CV samples are nevertheless strongly biased against faint systems."22 The faintest secular average Lx expected ofCVs can be estimated from the gravitational radiation-driven AZ., The faintest secular average $L_X$ expected of CVs can be estimated from the gravitational radiation-driven $\dot{M}$.23 We find that the Patterson&Rav-mone(1985a). relation between Lx and Al predicts that the majority ofCVs in the theoretical population of Ixolb(1993) should have time-averaged X-ray luminosities ofa lew times 10o0eres+ and higher.," We find that the \cite{PattersonRaymond85a} relation between $L_X$ and $\dot{M}$ predicts that the majority of CVs in the theoretical population of \cite{Kolb93} should have time-averaged X-ray luminosities of a few times $10^{29}\,\mathrm{erg\,s^{-1}}$ and higher."24". In intrinsically⋠⋠⋠ faintD. ""CVs. however. the rate of transfer of material onto the white ονα surface (which determines Lx). is not the the same as the secular AL. since these svstems are dwarf novae."," In intrinsically faint CVs, however, the rate of transfer of material onto the white dwarf surface (which determines $L_X$ ), is not the the same as the secular $\dot{M}$, since these systems are dwarf novae."25 HU is possible that. in the faintest CVs. hardly any material reaches the white dwarf surface during quiescence. so that they may. spend most of their time at very faint Ly (perhaps with X-ray emission from the donor star being brighter than from the accretion Low).," It is possible that, in the faintest CVs, hardly any material reaches the white dwarf surface during quiescence, so that they may spend most of their time at very faint $L_X$ (perhaps with X-ray emission from the donor star being brighter than from the accretion flow)."26 The faintest. short-period CVs in our sample have luminosities of a few times 10eres+.," The faintest short-period CVs in our sample have luminosities of a few times $10^{30}\,\mathrm{erg\,s^{-1}}$."27 Several intrinsically faint. short-periocd systems are now known to have Ly<10erests (κου Byeklingetal2010... as well as Peter Wheatles. publie )).," Several intrinsically faint, short-period systems are now known to have $L_X<10^{29}\,\mathrm{erg\,s^{-1}s}$ (see \citealt{Byckling10}, as well as Peter Wheatley, public )."28 Lt is not known how intrinsically common such systems are. but they may. well dominate the population.," It is not known how intrinsically common such systems are, but they may well dominate the population."29 The standard. theory of CV evolution predicts that 2704 of CVs are period. bouncers citealtIxolb03))., The standard theory of CV evolution predicts that $\simeq$ of CVs are period bouncers \\citealt{Kolb93}) ).30 Using the observed mass-radius relationship of CV donors. Ixniggo.ctal.(2011) predict an even arecr fraction. of period bouncers.," Using the observed mass-radius relationship of CV donors, \cite{KBP11} predict an even larger fraction of period bouncers."31 Observations are also now indicating a large population of intrinsically faint CVs (probably both normal short-period CVs and. period. x»incers)., Observations are also now indicating a large population of intrinsically faint CVs (probably both normal short-period CVs and period bouncers).32 First. Gansickeetal.(2009). find a large number of intrinsically faint CVs at the shortest. orbital periods.," First, \cite{Gansicke09} find a large number of intrinsically faint CVs at the shortest orbital periods."33 Furthermore. several period bouncers ancl good candidate »eriod. bouncers are now known citealtLittlefairDhillonMarsh06:::— Littlefairοal.2008: Patterson2011)). and Patterson(2011). argue that these systems may be common enough to make up most of the intrinsic population.," Furthermore, several period bouncers and good candidate period bouncers are now known \\citealt{LittlefairDhillonMarsh06}; \citealt{LittlefairDhillonMarsh08}; \citealt{Patterson11}) ), and \cite{Patterson11} argue that these systems may be common enough to make up most of the intrinsic population."34 Two (related) properties of the sample used here show hat it probably. does not. fairly represent. the underlying population: it contains no faint short-period. CVs. and it obabls contains no period bouncers (see Section 2)).," Two (related) properties of the sample used here show that it probably does not fairly represent the underlying population: it contains no faint short-period CVs, and it probably contains no period bouncers (see Section \ref{sec:sample}) )."35 The ack of period bouncers alone likely means that it has missed ab least half the intrinsic population., The lack of period bouncers alone likely means that it has missed at least half the intrinsic population.36 Furthermore. it is disconcerting that the faintest member of our sample. and herefore the svstem that dominates our p measurement. is a lone-period CV. EXDra.," Furthermore, it is disconcerting that the faintest member of our sample, and therefore the system that dominates our $\rho$ measurement, is a long-period CV, EX."37. Population svnthesis models owediet that at most a few percent of all CVs are above he period σαρ (Ixolb1993 finds less than 1l'A.. while Ixniggeetal.2011. predict. 320).," Population synthesis models predict that at most a few percent of all CVs are above the period gap \citealt{Kolb93} finds less than , while \citealt{KBP11} predict )."38 Although we find. that ong-period systems account for. slightly. more than of our total space density. the data do not rule out these heoretical predictions.," Although we find that long-period systems account for slightly more than of our total space density, the data do not rule out these theoretical predictions."39" For example. using the Ixnigeeοἱal.(2011). fraction of long-period systems. ancl assuming hat we have not significantly under-estimated. the space density of long-period CVs. the space density of short-period. CVs dis 02«10""pe(97/3)e&67pe. 7."," For example, using the \cite{KBP11} fraction of long-period systems, and assuming that we have not significantly under-estimated the space density of long-period CVs, the space density of short-period CVs is $\simeq 2 \times 10^{-6}\,\mathrm{pc^{-3}}(97/3) \simeq 6 \times 10^{-5}\,\mathrm{pc^{-3}}$ ."40 Using the upper limit on p from Section 5.1..« we find that a short- CY population of this size could. escape detection in the two surveys. provided that the systems have ἅlOeres+ (for the simple case of a hypothetical Lx population of faint. undetected CVs).," Using the upper limit on $\rho$ from Section \ref{sec:limits}, we find that a short-period CV population of this size could escape detection in the two surveys, provided that the systems have $L_X \la 8 \times 10^{28}\,\mathrm{erg\,s^{-1}}$ (for the simple case of a hypothetical $L_X$ population of faint, undetected CVs)."41 Clearly. i£ CVs are arbitrarily faint in N-ravs. the data allow for an arbitrarily large population to escape detection.," Clearly, if CVs are arbitrarily faint in X-rays, the data allow for an arbitrarily large population to escape detection."42 Llowever. we can also choose to place a restriction in ternis of what we might consider reasonable X-ray Iuminosities or active CVs.," However, we can also choose to place a restriction in terms of what we might consider reasonable X-ray luminosities for active CVs."43" For example. if we integrate the it power law Luminosity function over the range 28.7< (this is a luminosity range where CVs are known to exist. but where we detect. none) we ind po=1.2;10.""pe for svstems at those luminosities. a factor of almost 3 larger than our.po estimate from the detected. CVs."," For example, if we integrate the best-fit power law luminosity function over the range $28.7<\mathrm{log}(L_X/\mathrm{erg\,s^{-1}})<29.7$ (this is a luminosity range where CVs are known to exist, but where we detect none), we find $\rho_0=1.2 \times 10^{-5}\,\mathrm{pc^{-3}}$ for systems at those luminosities, a factor of almost 3 larger than our$\rho_0$ estimate from the detected CVs."44 Thisagain indicates that it is reasonable to hink that our po estimate is low by a factor of more than 2, Thisagain indicates that it is reasonable to think that our $\rho_0$ estimate is low by a factor of more than 2.45 We find that a power law X-ray luminosityfunction, We find that a power law X-ray luminosityfunction46turbulence in the Local Clouds of the VLISM resembles the turbulence in the solar wind and solar corona.,turbulence in the Local Clouds of the VLISM resembles the turbulence in the solar wind and solar corona.47 The Verv Local Interstellar Medium (VLISM) is loosely defined: as the interstellar medium within about 15 parsecs of the Sun., The Very Local Interstellar Medium (VLISM) is loosely defined as the interstellar medium within about 15 parsecs of the Sun.48 One of the interesting aspects of the VLISM is that it contains about 15 clouds with diameters of a few parsecs (RecllieldandLinsky2005)., One of the interesting aspects of the VLISM is that it contains about 15 clouds with diameters of a few parsecs \citep{Redfield08a}.49. It appears Chat the Sun is near the interface and region of interaction of (wo of these clouds. the Local Interstellar Cloud. or LIC. and the G cloud (BedtieldandLinskv2008)..," It appears that the Sun is near the interface and region of interaction of two of these clouds, the Local Interstellar Cloud, or LIC, and the G cloud \citep{Redfield08a}."50 Reviews ol (he properties of these clouds may be found in Frisch.(2000).. Redlield(2009).. and (2011).," Reviews of the properties of these clouds may be found in \cite{Frisch00}, , \cite{Redfield09}, and \cite{Frisch11}."51. Most of the information we have about these clouds comes from UV and visible wavelength spectroscopy., Most of the information we have about these clouds comes from UV and visible wavelength spectroscopy.52 Absorption lines attributable to these clouds are measured. along lines of sight to nearby stars wilh precisely known distances., Absorption lines attributable to these clouds are measured along lines of sight to nearby stars with precisely known distances.53 Properties of these clouds are deduced [rom the Doppler shift. strength. ancl width of the spectral lines.," Properties of these clouds are deduced from the Doppler shift, strength, and width of the spectral lines."54 These clouds are plasmas because absorption lines of ious as well as neutral atoms are observed: (he ionization fraction is about 50 (ReclfieldandFaleon3005].., These clouds are plasmas because absorption lines of ions as well as neutral atoms are observed; the ionization fraction is about 50 \citep{Redfield08b}.55 Although the information available on these clouds is not as extensive as for the solar wind or solar corona. it is sufficient to. place the Local Clouds among the best-diagnosed astrophysical plasmas.," Although the information available on these clouds is not as extensive as for the solar wind or solar corona, it is sufficient to place the Local Clouds among the best-diagnosed astrophysical plasmas."56 There are several reasons for this state of affairs., There are several reasons for this state of affairs.57 First. because (he absorption lines are nieasured in (he spectra of nearby stars wilh precisely known distances. the spatial extent of the clouds is well determined.," First, because the absorption lines are measured in the spectra of nearby stars with precisely known distances, the spatial extent of the clouds is well determined."58 Second. the neutral component of the clouds [lows into the inner solar svstem. where it can be measured in situ 2009).," Second, the neutral component of the clouds flows into the inner solar system, where it can be measured in situ \citep[e.g.][]{Moebius09}."59. Finally. the heliosphere is embedded in one of these clouds. the LIC cloud. and the solar wind interacts with it.," Finally, the heliosphere is embedded in one of these clouds, the LIC cloud, and the solar wind interacts with it."60 The shape and other characteristics of the solar wind interaction provide constraints on the LIC cloud properties (Lallementetal2005;Opher2009).," The shape and other characteristics of the solar wind interaction provide constraints on the LIC cloud properties \citep{Lallement05,Opher09}."61. The mean plasma properties of the turbulent clouds are given in Table 1 2003)..," The mean plasma properties of the turbulent clouds are given in Table 1 \citep[adapted from][]{Redfield08a,Redfield08b}."62 Information on turbulence in the Local Clouds is discussed in Redfield (2004)., Information on turbulence in the Local Clouds is discussed in \cite{Redfield04}.63. Such information is retrievable because the absorption line width 6 can be measured for transitions of several atoms or ions., Such information is retrievable because the absorption line width $b$ can be measured for transitions of several atoms or ions.64 ReclfieldandLinsky(2004) fit the line width data for each line ofsight and Doppler component to the formula, \cite{Redfield04} fit the line width data for each line ofsight and Doppler component to the formula65number too small to give meaningful results to study their radial distributions.,number too small to give meaningful results to study their radial distributions.66 It dis very likely that the majority of cluster RGB variables ave brighter than our magnitude limit., It is very likely that the majority of cluster RGB variables are brighter than our magnitude limit.67 A shorter exposure search lor variability amone 47 Tuc RGB stars has recently been started by Ixiss et al (2003. private communication. also with WEI on the MSSSO 40-inch). ancl our LPV sample will overlap somewhat with their results.," A shorter exposure search for variability among 47 Tuc RGB stars has recently been started by Kiss et al (2003, private communication, also with WFI on the MSSSO 40-inch), and our LPV sample will overlap somewhat with their results."68 This should allow a more accurate study into the eluster LPV radial distribution., This should allow a more accurate study into the cluster LPV radial distribution.69 A small number of other variables were also discovered in our dataset. including two Cepheids. four ὁ Scuti stars. and an anomalous short-period red variable. which is a likely SAIC star.," A small number of other variables were also discovered in our dataset, including two Cepheids, four $\delta$ Scuti stars, and an anomalous short-period red variable, which is a likely SMC star."70 The two Cepheids (V24 and. V37) are identified from their position in the schematie cluster CMD (Fig.11))., The two Cepheids (V24 and V37) are identified from their position in the schematic cluster CMD \ref{linecmd}) ).71 They are significantly brighter and redder than the RR Lyrae stars. but ave of short period (O.387d ancl 2.572d respectively) lor Cepheids. and as such could be classified as anomalous.," They are significantly brighter and redder than the RR Lyrae stars, but are of short period (0.387d and 2.572d respectively) for Cepheids, and as such could be classified as anomalous."72 V24 has been tentatively identified as a Tvpell Cepheid based on the secondary variation seen on (he lightcurve at phase 70.5., V24 has been tentatively identified as a TypeII Cepheid based on the secondary variation seen on the lightcurve at phase $\sim$ 0.5.73 We detected four 0 Seni stars in our search (V35. V54. V67 and V30).," We detected four $\delta$ Scuti stars in our search (V35, V54, V67 and V80)."74 All are certainly members of the SAIC. as thev have Ve21.," All are certainly members of the SMC, as they have $\sim$ 21."75 This is at the limit of our detectabilitv. but they were found due to their large amplitude of variation.," This is at the limit of our detectability, but they were found due to their large amplitude of variation."76 V35.V54 and V6T all have very short periods <Q.1d. typical of ὁ Seuti stars.," V35,V54 and V67 all have very short periods $<$ 0.1d, typical of $\delta$ Scuti stars."77 V80 has a period that is longer. at 0.2142. and is among the faintest variables in our catalogue αἱ V~22.," V80 has a period that is longer, at 0.2144d, and is among the faintest variables in our catalogue at $\sim$ 22."78 It has been classified as ad Seuli star due to the shape of the lighteurve. ancl the amplitude of variation.," It has been classified as a $\delta$ Scuti star due to the shape of the lightcurve, and the amplitude of variation."79 The 9 seuli liehteurves presented here show a significant amount of scatter. which is attributed to photometric scatter caused by the faintuess of the sample.," The $\delta$ Scuti lightcurves presented here show a significant amount of scatter, which is attributed to photometric scatter caused by the faintness of the sample."80 To investigate the possibility of multi-periodicitv. (he periodograms for (hese four stars were compared to those of non-variables of the same magnitude.," To investigate the possibility of multi-periodicity, the periodograms for these four stars were compared to those of non-variables of the same magnitude."81 The lighteurves were phase-wrapped {ο all significant, The lightcurves were phase-wrapped to all significant82any claim of significance.,any claim of significance.83 The period is also suspiciously close to one vear and might be an artefact. of the data reduction., The period is also suspiciously close to one year and might be an artefact of the data reduction.84 In Section 3.1. we showed that LALCAIC periodogram peaks exhibit a well defined. statistical bias towards high eccentricity. in the absence of a real periodic signal., In Section \ref{sec:eccBias} we showed that HMCMC periodogram peaks exhibit a well defined statistical bias towards high eccentricity in the absence of a real periodic signal.85 To mümic a circular. velocity orbit the noise points need to be correlated. over a larger fraction of the orbit than they do to mimic a highly eccentric orbit., To mimic a circular velocity orbit the noise points need to be correlated over a larger fraction of the orbit than they do to mimic a highly eccentric orbit.86 For this reason it is more likely that noise will give rise to spurious highly eccentric orbits than low cecentricity orbits., For this reason it is more likely that noise will give rise to spurious highly eccentric orbits than low eccentricity orbits.87 Is there a similar or stronger bias when there is a real periodic signal?, Is there a similar or stronger bias when there is a real periodic signal?88 Based on the above explanation. of the bias we would. expect noise to conspire to increase the eccentricity of detected periodogram peaks associated with the real periodic signals., Based on the above explanation of the bias we would expect noise to conspire to increase the eccentricity of detected periodogram peaks associated with the real periodic signals.89 Our expectation is that the importance of this bias will be dependent on the strength of the signal ancl possibly on the number of observed. periods7., Our expectation is that the importance of this bias will be dependent on the strength of the signal and possibly on the number of observed periods.90.. For very. strong signals like the 1078 day period we would expect the bias to be very small., For very strong signals like the 1078 day period we would expect the bias to be very small.91 For very weak signals the bias might well be approximated by the no real periodic signal eccentricity bias which we quantified earlier., For very weak signals the bias might well be approximated by the no real periodic signal eccentricity bias which we quantified earlier.92 As we have seen. in the case of," As we have seen, in the case of"93a statistic (the correlation function and its relative bias) as a Function of number of subhalos for fixed mass.,a statistic (the correlation function and its relative bias) as a function of number of subhalos for fixed mass.94 Either way we have removed the dependence on mass for the purposes of our analvsis., Either way we have removed the dependence on mass for the purposes of our analysis.95" Once we have a halo catalogue and have enumerated. the subhalos per halo. we would like to break up our full sample into high and low occupation halos. where ""occupation"" is simply the number of subhalos (we do not dillerentiate between central subhalos or satellites)."," Once we have a halo catalogue and have enumerated the subhalos per halo, we would like to break up our full sample into high and low occupation halos, where “occupation” is simply the number of subhalos (we do not differentiate between central subhalos or satellites)."96 In order to avoid dependence of properties (such as clustering) on halo mass. we would like to somehow make the sample be effectively. at. fixed. halo mass.," In order to avoid dependence of properties (such as clustering) on halo mass, we would like to somehow make the sample be effectively at fixed halo mass."97 One possible approach involves applying an upper and lower mass threshold to the halo sample and. then ordering the remaining halos by occupation., One possible approach involves applying an upper and lower mass threshold to the halo sample and then ordering the remaining halos by occupation.98 There are two disadvantages with this., There are two disadvantages with this.99 First. applving mass cuts in this way will reduce the number of halos available for study. perhaps cramatically if the mass window allowed is narrow.," First, applying mass cuts in this way will reduce the number of halos available for study, perhaps dramatically if the mass window allowed is narrow."100 Second. ifthe mass window is not very narrow one could legitimately. worry Chat dependence on halo mass will still creep in. as there is obviously a strong dependence of halo occupation and halo mass.," Second, if the mass window is not very narrow one could legitimately worry that dependence on halo mass will still creep in, as there is obviously a strong dependence of halo occupation and halo mass."101 This means that for such a mass window. the top sav of halos by occupation could. be significantly more massive than the bottom1064.," This means that for such a mass window, the top say of halos by occupation could be significantly more massive than the bottom."102. We avoid both of these problems by instead. breaking our full halo sample into a large number of narrow bins in mass., We avoid both of these problems by instead breaking our full halo sample into a large number of narrow bins in mass.103 In each one of the mass bins. we order the halos by occupation number per unit mass. choosing the top of halos. top 10 and so on.," In each one of the mass bins, we order the halos by occupation number per unit mass, choosing the top of halos, top 10 and so on."104 When making a sample of halos chosen bv occupation we then take the required. fraction from each mass bin. so that we are left. with a sample that spans the entire mass range. but that was chosen by occupation at fixed halo mass.," When making a sample of halos chosen by occupation we then take the required fraction from each mass bin, so that we are left with a sample that spans the entire mass range, but that was chosen by occupation at fixed halo mass."105" We have tried. varving the width of the mass bins. Alog,(AL). finding that below Alog,(42)=0.5 our results are independent. of its value (ve use Alog),ή= 0.2)."," We have tried varying the width of the mass bins, $\Delta\log_{10}(M)$, finding that below $\Delta\log_{10}(M)=0.5$ our results are independent of its value (we use $\Delta\log_{10}(M)=0.2$ )."106 We make first use of our set of halos ranked by occupation at fixed halo mass in Section 2.4 below when plotting their spatial distribution., We make first use of our set of halos ranked by occupation at fixed halo mass in Section 2.4 below when plotting their spatial distribution.107 Phe main use for this type of subsample will however be in Section 4 when we examine clustering., The main use for this type of subsample will however be in Section 4 when we examine clustering.108 It will be useful to us to also look at halos ranked bv mass for a fixed number of subhalos., It will be useful to us to also look at halos ranked by mass for a fixed number of subhalos.109 In this case we will use the same technique. breaking the sample into a Large number of narrow bins. but this time in subhalo number.," In this case we will use the same technique, breaking the sample into a large number of narrow bins, but this time in subhalo number."110 As an example of our categorization of halos by occupation we show in Figure 1 the spatial distribution of high and low occupation halos., As an example of our categorization of halos by occupation we show in Figure \ref{slice} the spatial distribution of high and low occupation halos.111 Here high occupation halos are the top by number of subhalos per unit mass at. fixed. mass.," Here high occupation halos are the top by number of subhalos per unit mass at fixed mass,"112order polynomials for each parameter. finding that second-order or higher dependencies for some parameters. even if improved. agreement with the observations for the stars under consideration. led to unphysical shapes in poorly constrained regions of the parameter space.,"order polynomials for each parameter, finding that second-order or higher dependencies for some parameters, even if improved agreement with the observations for the stars under consideration, led to unphysical shapes in poorly constrained regions of the parameter space."113 After some experimentation. the adopted. polynomials were second order in temperature (η= 2). zero-th order in surface gravity (0i— 0). and up to first order in metallicity (fh=1 for grids #11. 2 and 3. but f=0 for grids #44 anc 5).," After some experimentation, the adopted polynomials were second order in temperature $n=2$ ), zero-th order in surface gravity $m=0$ ), and up to first order in metallicity $h=1$ for grids 1, 2 and 3, but $h=0$ for grids 4 and 5)."114 Phe polynomial mocel for the ratio of observed. and synthetic spectra was then used to correct the svnthetic eric. aM new svnthetie spectra for the parameters of the MILIZS stars were derived. by quadratic Bezier interpolation.," The polynomial model for the ratio of observed and synthetic spectra was then used to correct the synthetic grid, and new synthetic spectra for the parameters of the MILES stars were derived by quadratic Bezier interpolation."115 As expected the corrections tightened. made more symmetric. and centred closer to zero the distributions of residuals.," As expected the corrections tightened, made more symmetric, and centred closer to zero the distributions of residuals."116 Particularly large residuals remain after the correction or some stars with cool temperatures ancl low &ravities. suggesting that these stars are somewhat singular. or hat their assigned parameters are wrong.," Particularly large residuals remain after the correction for some stars with cool temperatures and low gravities, suggesting that these stars are somewhat singular, or that their assigned parameters are wrong."117 To improve CONSISLCDEY. we recetermined. the atmospheric parameters or all stars by using the most recent version of the optimisation code «iscussed by Allende Prieto et al. (," To improve consistency, we redetermined the atmospheric parameters for all stars by using the most recent version of the optimisation code discussed by Allende Prieto et al. ("1182004. 2006. 2008. 2009). and exelude a few stars which could not be it reasonably well.,"2004, 2006, 2008, 2009), and exclude a few stars which could not be fit reasonably well."119 Fig., Fig.120 2 illustrates the comparison between he old and the recderivecl parameters for eric 2., 2 illustrates the comparison between the old and the rederived parameters for grid 2.121 Robust estimates of the mean and the standard cleviation (half o£ he width of the distribution after discarding 15.85 of the sample on cach end) between the MILES parameters and the redeterminations are given in “Table 2. which also includes the numbers of surviving library stars within each of the subericls.," Robust estimates of the mean and the standard deviation (half of the width of the distribution after discarding 15.85 of the sample on each end) between the MILES parameters and the redeterminations are given in Table 2, which also includes the numbers of surviving library stars within each of the subgrids."122 The parameters. provided. with MILIZS. (Cenarro et al., The parameters provided with MILES (Cenarro et al.123 2007) have been compiled from the literature. ane subsequently homogenised by identifying and removing systematics across data sets (C'enarro. οἱ al.," 2007) have been compiled from the literature, and subsequently homogenised by identifying and removing systematics across data sets (Cenarro et al."124 2001)., 2001).125 The metallicities in this compilation are mainly from hieh-resolution studies. and therefore reflect measurements fron iron lines.," The metallicities in this compilation are mainly from high-resolution studies, and therefore reflect measurements from iron lines."126 Our model spectra have simply solar scaled meta abundances and. interestingly. if the corrections introduce are. independent of Fe/H]. ie. =0. our rederive metallicities are systematically higher than those in the AMILLIZS catalogue for metal-poor stars.," Our model spectra have simply solar scaled metal abundances and, interestingly, if the corrections introduced are independent of [Fe/H], i.e. $h=0$, our rederived metallicities are systematically higher than those in the MILES catalogue for metal-poor stars."127 With fo0. such a trend disappears. as the corrections partially accoun for the relative strengthening of the features. produced. by a elements relative to iron.," With $h>0$, such a trend disappears, as the corrections partially account for the relative strengthening of the features produced by $\alpha-$ elements relative to iron."128 Phe polvnomial fittinge usinge the algorithmo> describe in Section 2 was then repeated. using the original grid. of synthetic spectra and the rederived atmospheric parameters.," The polynomial fitting using the algorithm described in Section \ref{procedure}129 was then repeated using the original grid of synthetic spectra and the rederived atmospheric parameters."130" and its determinant 4 is — J-—1| - IO where z=re"",","g = +, and its determinant $J$ is J = 1 - - + ) where $z = r e^{i\theta}$."131 The critical condition is given bv coe LqAd, The critical condition is given by = r^2 -.132) From the simple graph of the RIIS. it can be seen that there is a solution space in the neighborhood of r=1.," From the simple graph of the RHS, it can be seen that there is a solution space in the neighborhood of $r=1$."133 Set r=1+0 and find 9 using eq.(A)) to obtain r= 1 +2, Set $r = 1 + \delta$ and find $\delta$ using \ref{eqBiJ}) ) to obtain r = 1 +.1342(À5) €cos286—lH is a peanut-shape curve squeezed along the imaginary axis even though the small coefficient e/2(7 makes it difficult to discern from a circle. 0=0. 7/2. π.," It is a peanut-shape curve squeezed along the imaginary axis even though the small coefficient $\epsilon/2\ell^2$ makes it difficult to discern from a circle. $\theta =0$, $\pi/2$, $\pi$,"135 and 32/2 are the precusps., and $3\pi/2$ are the precusps.136 H can be confirmed by ealeulating OJ as it was done for an arbitrary d in the main text., It can be confirmed by calculating $\partial_- J$ as it was done for an arbitrary $d$ in the main text.137 The cusps are (wo on (he real axis and (wo on (he imaginaray axis., The cusps are two on the real axis and two on the imaginaray axis.138 In order to estimate the size of (he caustic. measure (he cusp-lo-cusp distances on the real axis and on the imaginary axis.," In order to estimate the size of the caustic, measure the cusp-to-cusp distances on the real axis and on the imaginary axis."139" ia : vw, =+(AG) = TW = cHT) The quaroid is equilateral and its orientation is opposite to the critical curve.", = _0 - = = - = -i The quaroid is equilateral and its orientation is opposite to the critical curve.140 The diagonal length of the quadroicd will be comapred to that of the large separation DSTP lens caustics., The diagonal length of the quadroid will be comapred to that of the large separation DSTP lens caustics.141 — — i, = = =142 — — ic, = = =143As cosmic microwave background (CMB) travel through the diffuse hot gas comprising the bulk of photonsbaryons in clusters. a fraction of them are upscattered the in à galaxyprocess called the thermal Sunyaev-Zel'dovich by(tSZ) gaseffect (?)..,"As cosmic microwave background (CMB) photons travel through the diffuse hot gas comprising the bulk of baryons in galaxy clusters, a fraction of them are upscattered by the gas in a process called the thermal Sunyaev-Zel'dovich (tSZ) effect \citep{1970Ap&SS...7....3S}."144 This scattering produces a unique spectral signature in the CMB. with a decrement in thermodynamic temperature below v~220 GHz. and an excess above.," This scattering produces a unique spectral signature in the CMB, with a decrement in thermodynamic temperature below $\nu145\sim 220$ GHz, and an excess above."146 The tSZ effect is typically seen on are-minute scales. and is referred to às à secondary anisotropy. às it originates between us and the surface of last scattering. unlike the primary CMB anisotropies.," The tSZ effect is typically seen on arc-minute scales, and is referred to as a secondary anisotropy, as it originates between us and the surface of last scattering, unlike the primary CMB anisotropies."147 In the non-relativistic limit. the tSZ is directly proportional to the integrated electron pressure along the line-of-sight.," In the non-relativistic limit, the tSZ is directly proportional to the integrated electron pressure along the line-of-sight."148 It typically traces out the spatial distribution of clusters and groups. since the hot intracluster medium (ICM) dominates the line-of-sight pressure integral.," It typically traces out the spatial distribution of clusters and groups, since the hot intracluster medium (ICM) dominates the line-of-sight pressure integral."149 Thus. the tSZ provides an excellent tool to examine the bulk of cluster baryons.," Thus, the tSZ provides an excellent tool to examine the bulk of cluster baryons."150 Found at the intersections of filaments in the cosmic web (2).. clusters form at sites of constructive interference of long waves in the primordial density fluctuations.the coherent peak-patches (22)..," Found at the intersections of filaments in the cosmic web \citep{1996Natur.380..603B}, clusters form at sites of constructive interference of long waves in the primordial density fluctuations,the coherent peak-patches \citep{1986ApJ...304...15B,1996ApJS..103....1B}."151 Clusters are sign posts for the growth of structure in the Universe. and are a potentially powerful tool for probing underlying cosmological parameters. such as w. the dark energy to-density ratio.," Clusters are sign posts for the growth of structure in the Universe, and are a potentially powerful tool for probing underlying cosmological parameters, such as $w$, the dark energy pressure-to-density ratio."152 The of the tSZ effect is extremely sensitive to angularcosmologicalpower spectrumparameters like oy. the root mean square (RMS) amplitude of the (Iinearized) density fluctuations on 8/r! Mpe scales.," The angular power spectrum of the tSZ effect is extremely sensitive to cosmological parameters like $\sigma_8$, the root mean square (RMS) amplitude of the (linearized) density fluctuations on $h^{-1}$ Mpc scales."153 In fact. the amplitude of the tSZ power spectrum scales at least as steeply as the seventh power of oy (222?) and improving the constraints on ay will aid in breaking the degeneracies found between oy and w when using only primary CMB constraints.," In fact, the amplitude of the tSZ power spectrum scales at least as steeply as the seventh power of $\sigma_8$ \citep{2002ASPC..257...15B,2002MNRAS.336.1256K,2005ApJ...626...12B,2011ApJ...727...94T}154 and improving the constraints on $\sigma_8$ will aid in breaking the degeneracies found between $\sigma_8$ and $w$ when using only primary CMB constraints."155 An advantage of using the tSZ angular power spectrum over counting clusters is that no explicit measurement of cluster masses is required., An advantage of using the tSZ angular power spectrum over counting clusters is that no explicit measurement of cluster masses is required.156 Also. lower mass. and therefore fainter. clusters that may not be significantly detected as 1individual objects in CMB maps contribute to this statistical signal.," Also, lower mass, and therefore fainter, clusters that may not be significantly detected as individual objects in CMB maps contribute to this statistical signal."157 However. disadvantages of using the tSZ angular power spectrum include potential contamination from point sources ard that no redshift information from the clusters is used.," However, disadvantages of using the tSZ angular power spectrum include potential contamination from point sources and that no redshift information from the clusters is used."158 Previous observations by the Berkeley-Illinois-Maryland Association (BIMA.?).. the Atacama Path-finding Experiment (APEX-SZ.?).. the Quest at DASI (QUaD.?).. Arc-minute Cosmology Bolometer Array Receiver (ACBAR.?).. and the Cosmic Background Imager (CBI.?) all measured excess power above that expected from primary anisotropies. which have been attributed to some combination of the tSZ effect and point source contamination.," Previous observations by the Berkeley-Illinois-Maryland Association \citep[BIMA,][]{2006ApJ...647...13D}, the Atacama Path-finding Experiment \citep[APEX-SZ,][]{2009ApJ...701.1958R}, the Quest at DASI \citep[QUaD,][]{2009ApJ...700L.187F}, Arc-minute Cosmology Bolometer Array Receiver \citep[ACBAR,][]{2009ApJ...694.1200R}, and the Cosmic Background Imager \citep[CBI,][]{2009arXiv0901.4540S} all measured excess power above that expected from primary anisotropies, which have been attributed to some combination of the tSZ effect and point source contamination."159 The measurements from these experiments provided upper limits to the tSZ power spectrum amplitude., The measurements from these experiments provided upper limits to the tSZ power spectrum amplitude.160 More recently. the Atacama Cosmology Telescope (ACT.??) and the South Pole Telescope (SPT.???) have detected the SZ effect in the CMB powerspectrum!.," More recently, the Atacama Cosmology Telescope \citep[ACT,][]{2010ApJ...722.1148F,2010arXiv1009.0866D} and the South Pole Telescope \citep[SPT,][]{2010ApJ...719.1045L,2010arXiv1012.4788S,2011arXiv1105.3182K} have detected the SZ effect in the CMB power."161". The results from ACT and SPT emphasize that the ""sweet spot"" for measuring the tSZ signal is between (~20004000.", The results from ACT and SPT emphasize that the “sweet spot” for measuring the tSZ signal is between $\ell \sim 2000 - 4000$.162 Silk (?) suppresses the of primary anisotropies— so that dampingtheir contributions to the power spectrum are much smaller than the tSZ contribution at even higher (.," Silk damping \citep{1968ApJ...151..459S}163 suppresses the power of primary anisotropies so that their contributions to the power spectrum are much smaller than the tSZ contribution at even higher $\ell$ ."164 At these scales there are important additional contributions to the power, At these scales there are important additional contributions to the power165respectively with the inverse-variance weighting where/ corresponds to one smoothing scale and Nici represents the number of scales used in the combination.,respectively with the inverse-variance weighting where$i$ corresponds to one smoothing scale and $N_{\rm fwhm}$ represents the number of scales used in the combination.166 The combined x7 is then computed This combination makes an integrated estimation of wwhich includes the non-Gaussian signal at several cilferent scales with a mild weighting., The combined $\chi^2$ is then computed This combination makes an integrated estimation of which includes the non-Gaussian signal at several different scales with a mild weighting.167 We first compare the observed. results with our Gaussian model predictions., We first compare the observed results with our Gaussian model predictions.168 In this case. we perform. 10240 Gaussian simulations of the VVW-band. properties.," In this case, we perform 10240 Gaussian simulations of the VW-band properties."169 Dilferent. base-masks. as well as the mecdian-ilter. are applied. independently to both the real and the simulated: skies to study the foreground. effect. on the skeleton results.," Different base-masks, as well as the median-filter, are applied independently to both the real and the simulated skies to study the foreground effect on the skeleton results."170 Phe corresponding X7 values are then computed to enable the frequentist test., The corresponding $\chi^2$ values are then computed to enable the frequentist test.171 For each smoothing scale. the skeleton length departure from the Gaussian expectation. ALG.Üpwgar)=ZG.PpwHa)CC(pBrew D. is computed. from samples obtained with the WOT5B masked. maps.," For each smoothing scale, the skeleton length departure from the Gaussian expectation, $\Delta \mathcal{L}(\nu,\theta_{\rm FWHM}) =172\mathcal{L}(\nu,\theta_{\rm FWHM})-\langle \mathcal{L}^{\rm173G}(\nu,\theta_{\rm FWHM}) \rangle$ , is computed from samples obtained with the KQ75B masked maps."174 The results are shown in the lef two columns (for both the dillerential ancl cumulative distributions) of Figure 5. for Gps;=0764. 0785. 1228. 1770. 2798 and 3740.," The results are shown in the left two columns (for both the differential and cumulative distributions) of Figure \ref{fig_dske_KQ75} for $\theta_{\rm FWHM}175= 0\fdg64$, $0\fdg85$, $1\fdg28$ , $1\fdg70$, $2\fdg98$ and $3\fdg40$."176 The στον bands demonstrate the le and 20 confidence regions of the Gaussian. prediction., The grey bands demonstrate the $1\sigma$ and $2\sigma$ confidence regions of the Gaussian prediction.177 The observed ones are rebinned to 25 bins and depicted by filled circles with the lo-error bar of each bin., The observed ones are rebinned to 25 bins and depicted by filled circles with the $1\sigma$ -error bar of each bin.178 The rebinning is necessary since the clilferential skeleton elistribution is relatively. noisy., The rebinning is necessary since the differential skeleton distribution is relatively noisy.179" In the case of the cumulative distributions. AL,(7) for WALTPS5. some features consistent with a positive value are observed. albeit within the de Caussian confidence. level."," In the case of the cumulative distributions, $\Delta180\mathcal{L}_{a}(\nu)$ for 5, some features consistent with a positive value are observed, albeit within the $1\sigma$ Gaussian confidence level."181 Phe behaviour of the dilferential distribution. ALsz). supports this inference. —despite the existence of a higher level of Luctuations.," The behaviour of the differential distribution, $\Delta \mathcal{L}_{d}(\nu)$, supports this inference despite the existence of a higher level of fluctuations."182 Llowever. there aredifferences between the new results ancl the corresponding WAZLAPIL ones (Eriksenetal.2004).," However, there aredifferences between the new results and the corresponding 1 ones \citep{Eriksen_etal_2004}."183. For cach smoothing scale. the latter show a LIe-Ievel peak around 7=0 while the neighbouring troughs show less Ductuations especially in the vol region.," For each smoothing scale, the latter show a $1\sigma$ -level peak around $\nu=0$ while the neighbouring troughs show less fluctuations especially in the $\nu>1$ region."184 In contrast. asshown in Figure 5. (the left two columns). the former's peak is less apparent but the troughs are much more distinct particularly. for. Opwgsr=—1728 and. 1770.," In contrast, asshown in Figure \ref{fig_dske_KQ75} (the left two columns), the former's peak is less apparent but the troughs are much more distinct particularly for $\theta_{\rm FWHM}=1\fdg28$ and $1\fdg70$ ."185 The comparison between WALL?IL and our new results is shown inFigure 7? [or psg;= 0764. 0785 and 1:2 ," The comparison between 1 and our new results is shown inFigure \ref{fig_syseff} for $\theta_{\rm186FWHM}=0\fdg64$ , $0\fdg85$ and $1\fdg28$ ."187There are several possibilities associated: with such a discrepancy., There are several possibilities associated with such a discrepancy.188Nem berms of equation (8)) are uncorrelated for different pulsars. but the second. term of (his equation provides a common change of periods ancl period derivatives for all objects.,"$\eta_{em}$ terms of equation \ref{eq_gwshift}) ) are uncorrelated for different pulsars, but the second term of this equation provides a common change of periods and period derivatives for all objects."189 The difference between the expected and the measured values of the period derivatives in individual objects. sueh as those listed in Table 1. can be directly used to constrain the enerev densitv in gravitational waves in this frequency regime (Bertolli&Weisberg1989:ThorsettDewey 1996).. giving Qeayh?<0.04 1996).," The difference between the expected and the measured values of the period derivatives in individual objects, such as those listed in Table 1, can be directly used to constrain the energy density in gravitational waves in this frequency regime \citep{bert83, tayl89, thor96}, giving $\Omega_{GW} h^2 \la 0.04$ \citep{thor96}."190. The accuracy of the AP/P measurement for PSR 1010-10 (which dominated this constraint) has improved by about a factor of three since the publication by Thorsett (1996).. so the current upper limit on Qc?xGXP/P)? is approximately an order of magnitude better.," The accuracy of the $\Delta \dot{P}/P$ measurement for PSR B1913+16 (which dominated this constraint) has improved by about a factor of three since the publication by \citet{thor96}, so the current upper limit on $\Omega_{GW}h^2 \propto (\Delta \dot{P}/P)^2$ is approximately an order of magnitude better."191 In contrast to the case of the peculiar solar acceleration. the ellect of eravitational waves in this frequency range on liming measurements does not depend on the position on the sky. so it cannot be extracted statistically [rom the imine data as we did in Seclion 2 [or the solar acceleration.," In contrast to the case of the peculiar solar acceleration, the effect of gravitational waves in this frequency range on timing measurements does not depend on the position on the sky, so it cannot be extracted statistically from the timing data as we did in Section \ref{sec_stat} for the solar acceleration."192 Finally. for very. low frequency gravitational waves (f.<c/d) the size of the ‘detector’ (ihe solar svstem and (he pulsars) is smaller than the wavelength of the waves. and it can be shown that. to first order in η. the change in the observed period of the signals is where n; are the spatial components of the unit vector in the direction to the pulsar and jj are (he spatial components of (he metric perturbation taken at the observers position.," Finally, for very low frequency gravitational waves $f\la c/d$ ) the size of the `detector' (the solar system and the pulsars) is smaller than the wavelength of the waves, and it can be shown that, to first order in $\eta$, the change in the observed period of the signals is where $n_i$ are the spatial components of the unit vector in the direction to the pulsar and $\eta_{ij}$ are the spatial components of the metric perturbation taken at the observer's position."193 This reeime can be probed both with individual objects (by taking a time derivative of eq., This regime can be probed both with individual objects (by taking a time derivative of eq.194 9. and using limits on AP [rom Table 1) and in the statistical sense using AISPs since the ellect is expected to increase with distance., \ref{eq_gwlong} and using limits on $\Delta \dot{P}$ from Table 1) and in the statistical sense using MSPs since the effect is expected to increase with distance.195 In the latter case. one must be aware (hal a systematic dependence on the clistance may be introduced when applying (he proper motion correction to the observed values PUP. since pr; are (vpically not known for more distant objects.," In the latter case, one must be aware that a systematic dependence on the distance may be introduced when applying the proper motion correction to the observed values $\dot{P}'_i/P_i$, since $\mu_i$ are typically not known for more distant objects."196 For the subset of MSPs wilh measured proper motions. the correlation οἱ D/D; versus d; is present al less (han confidence level (using the rank correlation test).," For the subset of MSPs with measured proper motions, the correlation of $\dot{P}_i/P_i$ versus $d_i$ is present at less than confidence level (using the rank correlation test)."197 For individual objects. the amplitude of the metric perturbation is best constrained. with PSR J17134-074T and PSR D19134-16 and is consistent with 0 within l.lo.," For individual objects, the amplitude of the metric perturbation is best constrained with PSR J1713+0747 and PSR B1913+16 and is consistent with 0 within $\sigma$."198 Using equation (9)) ancl (hie expression for enerev clensily of gravitational waves (e.g.. Detweiler 1979)) we can place an upper limit on the energy density of very low Irequency waves: With the best accuracy of oj4/DPc1x10.19P ! for objects in Table 1. equation (10))," Using equation \ref{eq_gwlong}) ) and the expression for energy density of gravitational waves (e.g., \citealt{detw79}) ) we can place an upper limit on the energy density of very low frequency waves: With the best accuracy of $\sigma_{tot}/P\simeq 1\times 10^{-19}$ $^{-1}$ for objects in Table 1, equation \ref{eq_fof}) )"199summarizes using histograms the current distributions of reported spins: clearly there is a bias towards higher spin measurements. which is to be expected since these cases should correspond to the strongest observational effects.,"summarizes using histograms the current distributions of reported spins; clearly there is a bias towards higher spin measurements, which is to be expected since these cases should correspond to the strongest observational effects."200 In the following we shall compare these reported spin measurements with estimates of the jet power in the hard state. and both jet speed and power in transient outbursts.," In the following we shall compare these reported spin measurements with estimates of the jet power in the hard state, and both jet speed and power in transient outbursts."201 Most of the sources with reported spin measurements have radio and/or near-infrared measurements which allow estimates of the jet power., Most of the sources with reported spin measurements have radio and/or near-infrared measurements which allow estimates of the jet power.202 Note that in these histograms and the subsequent analyses. we do not use the spin measurements reported by Zhang et al. (," Note that in these histograms and the subsequent analyses, we do not use the spin measurements reported by Zhang et al. ("2031997). although we do list them in table |.,"1997), although we do list them in table 1."204 This is because they are likely to have been superceded by more recent retfinements of the disc-fitting method. although in some cases their measurements are in agreement with more recent fits (see e.g. discussion in McClintock et al.," This is because they are likely to have been superceded by more recent refinements of the disc-fitting method, although in some cases their measurements are in agreement with more recent fits (see e.g. discussion in McClintock et al."205 2006)., 2006).206 In the hard state. we can only really compare jet power. and not speed. between sources to see if it correlates with estimates of black hole spin.," In the hard state, we can only really compare jet power, and not speed, between sources to see if it correlates with estimates of black hole spin."207 We note that the analyses of Gallo. Fender Pooley (2003) and Heinz Merloni (2004) already indicate that the range of Lorentz factors of such hard state jets is likely to be small (although the absolute value is as yet undetermined).," We note that the analyses of Gallo, Fender Pooley (2003) and Heinz Merloni (2004) already indicate that the range of Lorentz factors of such hard state jets is likely to be small (although the absolute value is as yet undetermined)."208 Therefore we can immediately conclude that if the reported range of spins in the, Therefore we can immediately conclude that if the reported range of spins in the209The generic model for radio galaxies assumes that twin jets cianatine from an active galactic uucleus propagate outward in two opposite directions.,The generic model for radio galaxies assumes that twin jets emanating from an active galactic nucleus propagate outward in two opposite directions.210" The jets. which initially propagate at a relativistic προσ, interact with the stirounding medimm leading to formation of a diffuse emission region."," The jets, which initially propagate at a relativistic speed, interact with the surrounding medium leading to formation of a diffuse emission region."211 Badio galaxies appear to have two classes: low- and high-huuiuositv radio ealaxics. conunouly referred to as ER I aud II sources. respectively (Fauaroff&Riley1971).," Radio galaxies appear to have two classes: low- and high-luminosity radio galaxies, commonly referred to as FR I and II sources, respectively \citep{fr74}."212 The jets iu ligh-lhuuinosity radio galaxies have relatively homogeuecous morphology: they are well collamated aud propagate through the strounding medium initfiallv iu the cores. then halos of their parent galaxies aud then the intergalactie media (ICM)creating pair of large lobes.," The jets in high-luminosity radio galaxies have relatively homogeneous morphology; they are well collimated and propagate through the surrounding medium—initially in the cores, then halos of their parent galaxies and then the intergalactic medium (IGM)—creating pair of large lobes."213 The jets are dim until the eud of the lobes where there are bright hot spots., The jets are dim until the end of the lobes where there are bright hot spots.214 Classical double radio sources ave a typical exanple of this class., Classical double radio sources are a typical example of this class.215 Dv contrast. low-huuinositv radio galaxies are characterized by jets that are bright close to the micleus of thei pareut galaxy.," By contrast, low-luminosity radio galaxies are characterized by jets that are bright close to the nucleus of their parent galaxy."216 The jets have diverse norphologics. a feature that can be interpreted as deceleration of jets due to eutrainmenut of the external uediuu.," The jets have diverse morphologies, a feature that can be interpreted as deceleration of jets due to entrainment of the external medium."217 The jets are initially laminar near the nucleus and then subject to turbulent disruption when passing hrough the fare region that is thought to be the main acceleration site for relativistic particles., The jets are initially laminar near the nucleus and then subject to turbulent disruption when passing through the flare region that is thought to be the main acceleration site for relativistic particles.218 The jets bevoud he flare region spread out. reseiniblins smoke arising roni a chimmeyv nüxiug with the ambicut wedi.," The jets beyond the flare region spread out, resembling smoke arising from a chimney mixing with the ambient medium."219 The key issues duo the understanding of radio ealaxies include the evolution of radio galaxies aud the nuderlining plivsics that distinguishes these two classes., The key issues in the understanding of radio galaxies include the evolution of radio galaxies and the underlining physics that distinguishes these two classes.220 One sugecstion is that these two classes of source ire intrinsically different. primarily in their jet αναος. evolving along different tracks (Jackson&Wall1999).," One suggestion is that these two classes of source are intrinsically different, primarily in their jet dynamics, evolving along different tracks \citep{jw99}."221".. However. there are sugeestions that some of the hieh-""uimositv radio sources with weal. jets mav evolve iuto ow-luuinosity sources (CGopaldrishua&Wita1987.1988:Ἱναίκο&Best 2007)."," However, there are suggestions that some of the high-luminosity radio sources with weak jets may evolve into low-luminosity sources \citep{gw87,gw88,kb07}."222. Some radio sources exhibit uixed features of FR Is and Ws., Some radio sources exhibit mixed features of FR Is and IIs.223 For example. there are souces with oue-side jet showing the FR I features and he other showing the FR II features.," For example, there are souces with one-side jet showing the FR I features and the other showing the FR II features."224 This leads to an opinion that such classification may uot be clear cut as xeviouxlv thought Uxaiser&Best2007)., This leads to an opinion that such classification may not be clear cut as previously thought \citep{kb07}.225 It is well accepted that the radio cimission in radio ealaxies is due to svuchnrotrou radiation by relativistic clectrous (or positrons) injected from the jets., It is well accepted that the radio emission in radio galaxies is due to synchrotron radiation by relativistic electrons (or positrons) injected from the jets.226" The total svuchrotron power P, evolves with time as the injection of a nüxture of kinetic energv and magnetic energv colpctes against the losses due to volume expansion aud radiation.", The total synchrotron power $P_\nu$ evolves with time as the injection of a mixture of kinetic energy and magnetic energy competes against the losses due to volume expansion and radiation.227 When the losses dominate. the total power is a decreasing function of time as the source ages.," When the losses dominate, the total power is a decreasing function of time as the source ages."228 Since the typical evolutionary time scale is ~LOSyr. it is not practical to mcasure how the total power changes in time directly Jay observations.," Since the typical evolutionary time scale is $\sim 10^8\,\rm yr$, it is not practical to measure how the total power changes in time directly by observations."229 One may study the temporal evolution of radio galaxies from the total spectral power. D. as a function of the sources near size (Shiklovskii 1963).," One may study the temporal evolution of radio galaxies from the total spectral power, $P_\nu$, as a function of the source's linear size \citep{s63}."230. The linear size here is defined as the cimension of the lobe along the jet axis., The linear size here is defined as the dimension of the lobe along the jet axis.231" Since the linear size D Increases as the source expands. a radio source should evolve along a particular track in the P, D diagram."," Since the linear size $D$ increases as the source expands, a radio source should evolve along a particular track in the $P_\nu$ $D$ diagram."232 There are παν discussions in the literature on the time evolution of Lieh-luuinosity radio galaxies (or FR II sources) (saiseretal.1997:DIundell.Rawlings&Willott1999:Manolakou&Ixirk 2002).," There are many discussions in the literature on the time evolution of high-luminosity radio galaxies (or FR II sources) \citep{ketal97,betal99,mk02}."233. In the existing models. there are three relevant regions where the plysical processes determine the evolution of the source.," In the existing models, there are three relevant regions where the physical processes determine the evolution of the source."234 These, These235in Eq. 7..,in Eq. \ref{sig}.236 Marinoni Buzzi set the first. term on the right hand side of Eq., Marinoni Buzzi set the first term on the right hand side of Eq.237 7. to zero on the assumption that the comoving separation of pairs and their radial peculiar velocities are uncorrelated. (Ae)27)=0.," \ref{sig} to zero on the assumption that the comoving separation of pairs and their radial peculiar velocities are uncorrelated, $\langle \Delta v_{\parallel}/\Delta r\rangle=0$."238 We shall discuss this assumption further in Section 4., We shall discuss this assumption further in Section 4.239" The original Alcock-Paczvnski test. when applied to a spherical object. measures a distortion parameter. the ratio of the tangential and racial clistances. which is proportional to Da(z)I(z) and is unity if the correct. cosmological model is assumed and there are no redshift, space effects i.c. there is no distortion. of the spherical object."," The original Alcock-Paczynski test, when applied to a spherical object, measures a distortion parameter, the ratio of the tangential and radial distances, which is proportional to $D_A(z) H(z)$ and is unity if the correct cosmological model is assumed and there are no redshift space effects i.e. there is no distortion of the spherical object."240" The Alcock-DPaczynski test. applied in this paper compares the distribution of pair angles in real and redshift space in the distant observer approximation. drja,8drj. which gives rise to a distortion parameter which is independent of D4."," The Alcock-Paczynski test applied in this paper compares the distribution of pair angles in real and redshift space in the distant observer approximation, ${\rm{d}}r_{\perp ,\mbox{\tiny obs}} \approx {\rm{d}}r_{\perp}$, which gives rise to a distortion parameter which is independent of $D_A$."241 The distortion is estimated. after modelling redshift space ellects. by comparingthe distribution of the angles / and 7. and only depends on Lf(2).," The distortion is estimated, after modelling redshift space effects, by comparingthe distribution of the angles $t$ and $\tau$, and only depends on $H(z)$."242 Using pairs of galaxies in a survey. an observer can measure the average orientation using Eq.," Using pairs of galaxies in a survey, an observer can measure the average orientation using Eq."243 1 which should oe equal to the AAP funetion in Eq., \ref{sin2t} which should be equal to the AAP function in Eq.244 9 if the correct cosmology is assumed and the observer is able to measure o precisely in order to fully svecify Wir)., \ref{aapfunction} if the correct cosmology is assumed and the observer is able to measure $\alpha$ precisely in order to fully specify $\Psi(\tau)$.245 In this paper we »erform this exact test using pairs of subhaloes in N-boely simulations of cillerent Cosmeogies., In this paper we perform this exact test using pairs of subhaloes in N-body simulations of different cosmologies.246" In practise in a galaxy survey the parameter à can be determined in two wavs: irstlv. ad low redshifts. where the peculiar velocities of the our can be measured by combining a redshift: independent distance measurement. e.g. Luminosity distances from Type la supernovae. the ""Tulls-Fisher relation or the D,σ relation (sece.g.2???)). with the measured. redshift of the galaxy."," In practise in a galaxy survey the parameter $\alpha$ can be determined in two ways: firstly, at low redshifts, where the peculiar velocities of the pair can be measured by combining a redshift independent distance measurement, e.g. luminosity distances from Type Ia supernovae, the Tully-Fisher relation or the $D_n - \sigma$ relation \citep[see e.g.][]{2000ApJ...544..636C, 2000AJ....120...95D,2000AJ....119..102B,2000ASPC..201..254B}, with the measured redshift of the galaxy."247" Phe uncertainties associated: with the redshift independent. Luminosity distance measurementsare large. ~1020 for the Tullv-EFisher or D,0 relations. and ~510% for supernovae or the surface. brightness fluctuation method (27).. T"," The uncertainties associated with the redshift independent luminosity distance measurementsare large, $\sim 10-20$ for the Tully-Fisher or $D_n - \sigma$ relations, and $\sim 5-10$ for supernovae or the surface brightness fluctuation method \citep{2001astro.ph.10344B, 2001ApJ...546..681T}."248hese uncertainties on the redshift independent distance measurements. propagate into larger errors for the peculiar velocities. making it almost impossible to accurately measure the peculiar velocity ofa single galaxy.," These uncertainties on the redshift independent distance measurements propagate into larger errors for the peculiar velocities, making it almost impossible to accurately measure the peculiar velocity of a single galaxy."249 The second. method to determine à observationallv. which we shall assess in this paper after considering the ideal case of measuring à. [rom the simulations using Eq.," The second method to determine $\alpha$ observationally, which we shall assess in this paper after considering the ideal case of measuring $\alpha$ from the simulations using Eq."250 S. is to fit to the measured distribution of pairs at each redshift using Eq. 6..," 8, is to fit to the measured distribution of pairs at each redshift using Eq. \ref{dist}."251 One of the key assumptions made by. Marinoni Buzzi is that the normalization factor a is constant for all redshifts and for dillerent. galaxy selections., One of the key assumptions made by Marinoni Buzzi is that the normalization factor $\alpha$ is constant for all redshifts and for different galaxy selections.252 At 2=0. Alarinoni juzzi obtained a=5.79Uo. using binaries in the SDSS (?)..," At $z \approx 0$, Marinoni Buzzi obtained $\alpha = 5.79^{+0.32}_{-0.35}$, using binaries in the SDSS \citep{2009ApJS..182..543A}."253 Marinoni Buzzi obtained this value by fitting Iq., Marinoni Buzzi obtained this value by fitting Eq.254 6 to the observed distribution at z0., \ref{dist} to the observed distribution at $z \approx 0$.255 We explicitly test this assumption in this paper where it is possible to measure a directly. from the N-body simulations at. cach recishift., We explicitly test this assumption in this paper where it is possible to measure $\alpha$ directly from the N-body simulations at each redshift.256 We can also compare the predictions of the AAP function using the best fit value for a obtained at z=0. instead of normalizing the function at each redshift.," We can also compare the predictions of the AAP function using the best fit value for $\alpha$ obtained at $z=0$, instead of normalizing the function at each redshift."257 Phis will allow us to see if the value of à really is independent of redshift., This will allow us to see if the value of $\alpha$ really is independent of redshift.258 As a test of the method: proposed. by. Marinoni Buzzi which was outlined in Section 2. we apply it to cdillerent cosmologies. focussing on quintessence models.," As a test of the method proposed by Marinoni Buzzi which was outlined in Section 2, we apply it to different cosmologies, focussing on quintessence models."259 In Section 3.1 we discuss the two quintessence dark energy models we take as examples and highlight the main cillerences between these and the concordance cosmological model., In Section \ref{sub20} we discuss the two quintessence dark energy models we take as examples and highlight the main differences between these and the concordance cosmological model.260 In Section 3.2 we describe the simulations carried out., In Section \ref{sim21} we describe the simulations carried out.261 Numerous quintessence dark energy models. have been considered as an alternative to the concordance cosmology (sce(eg.7777).," Numerous quintessence dark energy models have been considered as an alternative to the concordance cosmology \citep[see e.g.][]{Ratra:1987rm, Ferreira:1997hj, Copeland:2006wr, 2008MPLA...23.1252M}."262 We focus on two interesting. examples which are representative of a wider class of quintessence models. scalar fields which evolve in time. which are viable alternative cosmologies.," We focus on two interesting examples which are representative of a wider class of quintessence models, scalar fields which evolve in time, which are viable alternative cosmologies."263 One of the models we consider has substantial dilferences to CDM and can be considered. as an dark energy. model which features non-negligible amounts of dark energy at high redshifts., One of the models we consider has substantial differences to $\Lambda$ CDM and can be considered as an dark energy model which features non-negligible amounts of dark energy at high redshifts.264 This quintessence dark energy model features an exponential term in the scalar field potential which pushes the dark energy. equation. of state (ο dy=O82 today. (7)..., This quintessence dark energy model features an exponential term in the scalar field potential which pushes the dark energy equation of state to $w_0 =-0.82$ today \citep{Brax:1999gp}.265 We refer to this model as the SUCGIUA model., We refer to this model as the SUGRA model.266 Phe second quintessence dark energy mocel. which we refer to as INV. has been shown to produce a similar expansion history and non-linear growth of structure to those in à ACDAL cosmologyv. (27). ancl will provide a measure of the sensitivity of the test we perform in this paper.," The second quintessence dark energy model, which we refer to as INV, has been shown to produce a similar expansion history and non-linear growth of structure to those in a $\Lambda$ CDM cosmology \citep{2010MNRAS.401.2181J, 2011MNRAS.410.2081J} and will provide a measure of the sensitivity of the test we perform in this paper."267 The INW model has an inverse power law potential Vie)=A?1o for the scalar field 6 €2).., The INV model has an inverse power law potential $V(\phi) = \Lambda^{\beta +4}/\phi$ for the scalar field $\phi$ \citep{Zlatev:1998tr}.268 The values of the constants A and 3 are fixed by the current value of the dark energy density. (seee.g.?).., The values of the constants $\Lambda$ and $\beta$ are fixed by the current value of the dark energy density \citep[see e.g.][]{Corasaniti:2002vg}.269 The dark energy equation ofstate for these quintessence models can be accurately described. over a wide range of redshifts using four parameters (2).., The dark energy equation of state for these quintessence models can be accurately described over a wide range of redshifts using four parameters \citep{Corasaniti:2002vg}. .270 The variables used are: wy. Che current dark energy equation of state: ty. the value of w during the matter dominated era: egy. the scale factor at which the dark energy equation of state changes [rom its value during the matter dominated era to its present value. and Ag. the width of the transition in the expansion factor.," The variables used are: $w_0$, the current dark energy equation of state; $w_{\rm{m}}$, the value of $w$ during the matter dominated era; $a_{\rm{m}}$, the scale factor at which the dark energy equation of state changes from its value during the matter dominated era to its present value, and $\Delta_{\rm{m}}$, the width of the transition in the expansion factor."271" For the SUGRA model these parameters are wy=O.S2.0y,=O.1S.ay,0.1 and Ay,=0.7."," For the SUGRA model these parameters are $w_{0} = -0.82 , w_{\rm{m}} =272-0.18, a_{\rm{m}} = 0.1$ and $\Delta_{\rm{m}} = 0.7$."273" For the INV model the values of the parameters are wy= and Ay,=0.4 (?).."," For the INV model the values of the parameters are $w_{0} = -0.79 , w_{\rm{m}} = 274-0.67, a_{\rm{m}} = 0.29$ and $\Delta_{\rm{m}} = 0.4$ \citep{2010MNRAS.401.2181J}."275 The cark energv models have cdillerentexpansion histories to ACDAL and so when compared to the currently available observations maw favour different best fitting values of the cosmological parameters (sec7.fora cliscussion).., The dark energy models have differentexpansion histories to $\Lambda$ CDM and so when compared to the currently available observations may favour different best fitting values of the cosmological parameters \citep[see][for a discussion]{2010MNRAS.401.2181J}.276" As our starting point. we consider a ACDAL model with the following cosmological parameters: O4,= 0.26. Opp=0.74. O4,=0.044. fF=0.715. where Lf,=1007 km/s/Mpce and a spectral tilt of ης0.96 (?).."," As our starting point, we consider a $\Lambda$ CDM model with the following cosmological parameters: $\Omega_{\rm m} = 0.26$ , $\Omega_{\rm{DE}}=0.74$, $\Omega_{\rm b} = 0.044$, $h = 0.715$, where $H_0 = 100h$ km/s/Mpc and a spectral tilt of $n_{\mbox{s}} =0.96$ \citep{2009MNRAS.400.1643S}."277" The linear theory rms fluctuation in spheres of radius Sf1 Alpe is set to be a,= OS.", The linear theory rms fluctuation in spheres of radius 8 $h^{-1}$ Mpc is set to be $\sigma_8 = 0.8$ .278" In the simulations. discussed in this paper. the ACDAL values for Qu, and. dfy were used for the INV dark energy model while for the SUGRA model the bestfit parameters usec were Quy,=0.243 and ll,= 67.73km/s/Alpe (κου?.formore details)... "," In the simulations discussed in this paper, the $\Lambda$ CDM values for $\Omega_{\rm m}$ and $H_0$ were used for the INV dark energy model while for the SUGRA model the bestfit parameters used were $\Omega_{\rm m} = 0.243$ and $H_0 = 67.73$ km/s/Mpc \citep[see][ for more details]{2010MNRAS.401.2181J}. ."279Both of these models are consistent with current observations of Supernovac Tvpe la lighteurves (?).. barvonic acoustic oscillations (??) and the WALAP 7 vear measurements of the cosmic microwave background (2)...," Both of these models are consistent with current observations of Supernovae Type Ia lightcurves \citep{Kowalski:2008ez}, , baryonic acoustic oscillations \citep{Percival:2007yw, 2009MNRAS.400.1643S} and the WMAP 7 year measurements of the cosmic microwave background \citep{2010arXiv1001.4538K}. ."280 A detailed study of, A detailed study of281inside the Bubble aud outside is AJT/II=cect6.54L5.,inside the Bubble and outside is $\Delta H/H = 6.5\pm1.8\%$.282 If correct. this could have a dramatic ou the derived cosinological paraicters (Jhaetal.2006.Fie 17). especially for those studies that extend their local sunuple down below :«0.015.," If correct, this could have a dramatic effect on the derived cosmological parameters \citep[Fig28317]{JhaRieKir06}, especially for those studies that extend their local sample down below $z<0.015$."284" However. the ""IIubble Bubble” was not coufirmed by Cüovanellietal.(1999) who found AJI/II=1.042. using the Tull-Fisher (TF) peculiar velocities. nor ""by IIudsonetal.(2001) who found AJI7/II=2.31.9% using the Fundamental Plane (FP) distances."," However, the “Hubble Bubble” was not confirmed by \cite{GioDalHay99} who found $\Delta H/H = 1.0\pm2.2$ using the Tully-Fisher (TF) peculiar velocities, nor by \cite{HudSmiLuc04} who found $\Delta H/H = 2.3\pm1.9\%$ using the Fundamental Plane (FP) distances."285" According to equation L.. a mean underdeusitv of IRAS galaxies of order — within 7100 wwould be needed to generate the ""IIubble Bubble” quoted by Jhaetal. (2006)..."," According to equation \ref{eq_pvel}, , a mean underdensity of IRAS galaxies of order $\sim$ within 7400 would be needed to generate the “Hubble Bubble” quoted by \cite{JhaRieKir06}. ."286 ITowever. we fiud that the IRAS PSCz deusity i of Brauchinictal.(1999). is uot underdeuse im this distance range: iustead it is wildly overdeuse (hy a few percent) within 7100 citep|scealso||Figure2]Dra TeoFre99..," However, we find that the IRAS PSCz density field of \cite{BraTeoFre99} is not underdense in this distance range; instead it is mildly overdense (by a few percent) within 7400 \\citep[see also][Figure 2]{BraTeoFre99}."287 As a further cross- when we refit the Jhaetal.(2006). data after having subtracted the predictions of the BOS fow model. the “Bubble” remains mn the Jhaetal.(2006) data.," As a further cross-check, when we refit the \cite{JhaRieKir06} data after having subtracted the predictions of the B05 flow model, the “Bubble” remains in the \cite{JhaRieKir06} data."288 Thus. the Jha ot al “Bubble” cannot be explained bx local structure. unless that structure is not traced bv IRAS ealaxics.," Thus, the Jha et al “Bubble” cannot be explained by local structure, unless that structure is not traced by IRAS galaxies."289" Moreover. when we analyze the 99 SNe within 15000 ffrom Touryetal.(2003) in the same wav. we fiud no evidence of a significant ""Ἡπυυ]ο Bubble” (ΔΙ L.542.0%)). in agreement with the results from TF and EP;survevs,"," Moreover, when we analyze the 99 SNe within 15000 from \cite{Tonry03ApJ} in the same way, we find no evidence of a significant “Hubble Bubble” $\Delta H/H = 1.5\pm2.0$ ), in agreement with the results from TF and FP surveys."290 The Tourvetal.(2003). sample aud that of Jhaetal.(2006) have 67 SNe in conunon., The \citet{Tonry03ApJ} sample and that of \cite{JhaRieKir06} have 67 SNe in common.291 The high deeree of overlap suggests that the difference lies iu the different iiethods for converting the photometrv ito SN distance moduli., The high degree of overlap suggests that the difference lies in the different methods for converting the photometry into SN distance moduli.292 A local large-scale flow can also introduce systematic errors if the low-z sample is biased in its sky coverage: in this case. an uncorrected dipole term can corrupt the monopole term. which then biases the cosinological parameters.," A local large-scale flow can also introduce systematic errors if the low-z sample is biased in its sky coverage: in this case, an uncorrected dipole term can corrupt the monopole term, which then biases the cosmological parameters."293" For the large-scale flow directions cousidered here. this does not appear to affect the AOG sample: we note that the PBF-corrected case has similar cosimnological parazuueters to the ""No Flow” case."," For the large-scale flow directions considered here, this does not appear to affect the A06 sample: we note that the PBF-corrected case has similar cosmological parameters to the “No Flow” case."294 However. if coherent flows exist ou large scales. this may affect surveys with unbalanced sky coverage. such as the SN Factory (Alderingetal.2002) or the SDSS SNsuvey?.," However, if coherent flows exist on large scales, this may affect surveys with unbalanced sky coverage, such as the SN Factory \citep{Aldering02SPIE} or the SDSS SN."295", The most promusiug approach to treating the effect of large-scale flows is a more sophisticated version of the analysis presented here: combine low-redshift SNe with other low-vedshitt peculiar velocity tracers. such as Tully-Fisher SET|| survey (Mastersetal.2006). aud the NOAO Funcdameutal Plane Survey (S11ithetal.200180). and use these data to constrain the parameters ofthe flow model (67 and the residual large-scale flow V) directly."," The most promising approach to treating the effect of large-scale flows is a more sophisticated version of the analysis presented here: combine low-redshift SNe with other low-redshift peculiar velocity tracers, such as Tully-Fisher SFI++ survey \citep{MasSprHay06} and the NOAO Fundamental Plane Survey \citep{SmiHudNel04}, and use these data to constrain the parameters of the flow model $\beta$ and the residual large-scale flow $\bvec{V}$) directly."296 One can then mareinalize over theparamcters ofthe flow model while fittiug the cosmological paraiiceters to the low- aud high-: SNe., One can then marginalize over theparameters of the flow model while fitting the cosmological parameters to the low- and $z$ SNe.297"GTo 1.3 keV). We hence consider (hat the ""soft component"" is approximated by an MCD model with 475,~ 1.7 keV. The middle two spectra (Spec D and C) in Figure 2. have relatively similar shapes. although their intensities are different.","$kT_{\rm BB} \sim$ 1.3 keV), We hence consider that the “soft component” is approximated by an MCD model with $kT_{\rm in} \sim$ 1.7 keV. The middle two spectra (Spec B and C) in Figure \ref{fig:spec_1608_upper1} have relatively similar shapes, although their intensities are different."298 As shown in Figure ??.. their difference spectrum (Spec 3) is in [act softer than Spee 1. while harder than Spec 2.," As shown in Figure \ref{fig:spec_1608_upper4}, their difference spectrum (Spec 3) is in fact softer than Spec 1, while harder than Spec 2."299 If we employ the BB or MCD model to fit the spectrum. the temperatures are obtained as Api~ 2.1 keV or Kj~ 3.0 keV. respectively: these values are somewhat different [rom those derived with Spec 1 and spec 2 (Table 2)). although the fits are both acceptable.," If we employ the BB or MCD model to fit the spectrum, the temperatures are obtained as $kT_{\rm BB} \sim$ 2.1 keV or $kT_{\rm in} \sim$ 3.0 keV, respectively; these values are somewhat different from those derived with Spec 1 and Spec 2 (Table \ref{tab:spec_1608_upper}) ), although the fits are both acceptable."300 Then. we may adopt a composite model which consists of the soft MCD and the hard BB models. hereafter \ICD+BB model. with ATi fixed at 1.7 keV and App fixed at 2.5 keV. but the component normalizations are left [ree to vary.," Then, we may adopt a composite model which consists of the soft MCD and the hard BB models, hereafter MCD+BB model, with $kT_{\rm in}$ fixed at 1.7 keV and $kT_{\rm BB}$ fixed at 2.5 keV, but the component normalizations are left free to vary."301.. We subject the (wo components to a common absorption., We subject the two components to a common absorption.302 This two component model has been found to successfully represent the difference spectrum as well., This two component model has been found to successfully represent the difference spectrum as well.303 The estimated absorption column density is roughly consistent with 0.8x1077 7., The estimated absorption column density is roughly consistent with $0.8 \times 10^{22}$ $^{-2}$.304" The result obtained with the DD modeling is consistent with a report by Makishimaοἱal.(1939): namely, if emploving a single BB model to represent (the difference spectrum at the time when (he intensity. varies simultaneously all over the energy band. the DD temperature turns out to be the intermediate between those of the soft MCD model of Spec 2 aud the hard BB οἱ spec 1."," The result obtained with the BB modeling is consistent with a report by \citet{makishima_gx3+1}; namely, if employing a single BB model to represent the difference spectrum at the time when the intensity varies simultaneously all over the energy band, the BB temperature turns out to be the intermediate between those of the soft MCD model of Spec 2 and the hard BB of Spec 1."305 The results obtained so far are all consistent with the Eastern model. where (he spectra consist of the soft MCD and the hard BB components.," The results obtained so far are all consistent with the Eastern model, where the spectra consist of the soft MCD and the hard BB components."306 Since the variability of only the MCD component (Spec B) is first revealed. it is (thought that the behavior is rarer (han (that of the BB.," Since the variability of only the MCD component (Spec B) is first revealed, it is thought that the behavior is rarer than that of the BB."307 The too high an absorption value of Spec 1 may be explained away if the soft NCD component also varies slightly between the two brightest spectra., The too high an absorption value of Spec 1 may be explained away if the soft MCD component also varies slightly between the two brightest spectra.308" To confirm these inferences, we applied the Eastern model to the original four energy. spectra in Figure 2.. with the absorption column density fixed al 0.8x1077 7."," To confirm these inferences, we applied the Eastern model to the original four energy spectra in Figure \ref{fig:spec_1608_upper1}, with the absorption column density fixed at $0.8 \times 10^{22}$ $^{-2}$."309 We added a narrow Gaussian component. lo represent an Fe-Ix enission line al ~ 6.6 keV. Because of the limited energy resolution of the PCA. the center energv and the width of the Gaussian model were constrained to [all in the range of 6.4:6.9 keV and <0.2 keV. respectively.," We added a narrow Gaussian component, to represent an Fe-K emission line at $\sim$ 6.6 keV. Because of the limited energy resolution of the PCA, the center energy and the width of the Gaussian model were constrained to fall in the range of 6.4–6.9 keV and $\le 0.2$ keV, respectively."310 by a linear combination (though with different weights) of the soft component a lc dl keV MCD. and the hard component identifiable with a /pi~ 2.5 keV DD.," by a linear combination (though with different weights) of the soft component a $kT_{\rm in} \sim$ 1.7 keV MCD, and the hard component identifiable with a $kT_{\rm BB} \sim$ 2.5 keV BB."311 Then. adding a narrow Gaussiaui component to represent an Fe-Ix line emission line al G7 keV. we fitted (hefour spectra with this composite model. denoted MCD--DDB-4-Gau model.," Then, adding a narrow Gaussian component to represent an Fe-K line emission line at 6–7 keV, we fitted thefour spectra with this composite model, denoted MCD+BB+Gau model."312" The results are shown in Figure 55. and Table 3: (there. rj, is (he innermost radius of (he accretion disk for an assumed inclination angle /= O°. and rpp is that of the BB model assuming"," The results are shown in Figure \ref{fig:spec_1608_upper5} and Table \ref{tab:spec_1608_upper2}; there, $r_{\rm in}$ is the innermost radius of the accretion disk for an assumed inclination angle $i = 0\arcdeg$ , and $r_{\rm BB}$ is that of the BB model assuming"313Cenerallv. i aud a are the functions of Macao.,"Generally, $\mu$ and $\alpha$ are the functions of $\dot M_{\rm accretion}$."314 For siuplieitv. we take them as coustauts if Afgeeretion=Massi ab ," For simplicity, we take them as constants if $\dot M_{\rm accretion} \ge \dot M_{\rm critical}$ ."315When the accretion rate falls down below Mojriceat. the dujection of jets is turned off," When the accretion rate falls down below $\dot M_{\rm critical}$, the injection of jets is turned off."316 Mic expresses the critical accretion rate at which the central aceretion flow changes its characteristics dramatically., $\dot M_{\rm critical}$ expresses the critical accretion rate at which the central accretion flow changes its characteristics dramatically.317 Such transition would occur iu a byper-acereting disk by the strong dependence of neutrino cooling ou the mass accretion rate (Poplam. Woosley. Frver. 1999).," Such transition would occur in a hyper-accreting disk by the strong dependence of neutrino cooling on the mass accretion rate (Popham, Woosley, Fryer, 1999)."318 We set EPAal=O2AL.s +., We set $\dot M_{\rm critical} = 0.2 \msun$ $^{-1}$ .319 For the relation between o. aud gi. we set p—1060. so that euao15s Lom 3 for all the models.," For the relation between $\alpha$ and $\mu$, we set $\mu = 10 \alpha$, so that $v_{\rm jet} \sim 1.3 \times 10^{10}$ cm $^{-1}$ for all the models."320 Our models are παπασος in the first five σος of Table 1., Our models are summarized in the first five columns of Table 1.321 For the progenitor models. we take the 16AL.. aud SAL. Te cores of stis with να=10M. aud 92511... respectively. from the solar iietalicitv models of Nomoto Uashimoto (1988).," For the progenitor models, we take the $16\msun$ and $8\msun$ He cores of stars with $M_{\rm ZAMS} =40\msun$ and $25\msun$, respectively, from the solar metalicity models of Nomoto Hashimoto (1988)."322 The U-rich envelope in the progenitor star is removed aud the remaining Πο star is mapped onto the nunernrcal exids with the outer radi AH.=3.7 aud 6.7« οσα for LOAL.. aud 254L... respectively.," The H-rich envelope in the progenitor star is removed and the remaining He star is mapped onto the numerical grids with the outer radii $R_{*} = 3.7$ and $6.7 \times 10^{10}$ cm for $40\msun$ and $25\msun$, respectively."323 With the parameterization described above. we follow hbydrodvuaimics of the explosion.," With the parameterization described above, we follow hydrodynamics of the explosion."324 At cach time step. we conrpute NLvcovetiom at the iuner boundary. and then update the jet properties and the mass of the central ronunant (Magma) at the next step.," At each time step, we compute $\dot M_{\rm accretion}$ at the inner boundary, and then update the jet properties and the mass of the central remnant $M_{\rm REM}$ ) at the next step."325 To determine the final central ront mass aud the composition in the ejected luaterials. if is necessary to follow the lydrodvuanics until HAN beconies very πα] aud the ejecta reaches homologous expansion.," To determine the final central remnant mass and the composition in the ejected materials, it is necessary to follow the hydrodynamics until $\dot M_{\rm accretion}$ becomes very small and the ejecta reaches homologous expansion."326 This is done bv expaucding the nunerical erids and adding the exponential atmosphere above the surface of the Πο star when the leading edge of the jets reaches the outer boundary., This is done by expanding the numerical grids and adding the exponential atmosphere above the surface of the He star when the leading edge of the jets reaches the outer boundary.327 The bydrodvuamical evolution is followed up to 10~100 secouds m most ruus. so that the expansion becomes nearly homologous.," The hydrodynamical evolution is followed up to $40 \sim 100$ seconds in most runs, so that the expansion becomes nearly homologous."328 Roe’s scheme based on Biemiaun solver is applied to a two-dimensional Eulerian bycrodvuamical code (IHachisu et al., Roe's scheme based on Riemann solver is applied to a two-dimensional Eulerian hydrodynamical code (Hachisu et al.329 1992. 1991).," 1992, 1994)."330 Typically 100.20 zones are used in spherical polar coordinate cescritisized logaxithiicallv iu the radial direction., Typically $100 \times 30$ zones are used in spherical polar coordinate descritisized logarithmically in the radial direction.331 This relatively coarse zouiug is due to the small time steps imposed at the iuuer boundary as a cousequence of large ci; , This relatively coarse zoning is due to the small time steps imposed at the inner boundary as a consequence of large $v_{\rm jet}$.332A typical time step is At=RyAOlye~(0.57730s 3 om slj[«101 seconds.," A typical time step is $\Delta t = R_0 \Delta \theta / v_{\rm jet} 333\sim (0.5 \pi/30 \times 10^8$ $)/(1.3 \times 10^{10}$ cm $^{-1}) 334\sim 4 \times 10^{-4}$ seconds."335 We have set the CFL πο to be 0.1 so that the calculations are stable. which males Af~p107 seconds.," We have set the CFL number to be 0.1 so that the calculations are stable, which makes $\Delta t \sim 4 \times 10^{-5}$ seconds."336 As mentioned above. we have to follow the evolution up to 100 seconds. so that more than 10 time steps are needed to ui oue model.," As mentioned above, we have to follow the evolution up to $\sim 100$ seconds, so that more than $10^6$ time steps are needed to run one model."337 Also. we need to yun many models (about 10 models: sce Table 1) to investigate the outcome with various jet properties.," Also, we need to run many models (about 10 models: see Table 1) to investigate the outcome with various jet properties."338 Iu addition. the wmmber of points to calculate uucleosvuthlesis should be proportional to the uuuber of the meshes used in the livdrodyvnuauic caleulation. which puts another ποσα for computational time for a higher resolution run.," In addition, the number of points to calculate nucleosynthesis should be proportional to the number of the meshes used in the hydrodynamic calculation, which puts another need for computational time for a higher resolution run."339 Despite the practical dif&culties mentioned above. the coarse zonimg is plhnwsieallv little justifiable.," Despite the practical difficulties mentioned above, the coarse zoning is physically little justifiable."340 We lave performed a convergence test by running model LOA with lower and higher resolutious in Appendix A. We have found that the results do uot chauge significantly. if the uunuber of the meshes is greater than 100ς30 (sce Appendix A for the details).," We have performed a convergence test by running model 40A with lower and higher resolutions in Appendix A. We have found that the results do not change significantly, if the number of the meshes is greater than $100 \times 30$ (see Appendix A for the details)."341 We curplov equation of state incliding radiation aud elo pais im an approximated analytical form (Fretburehaus et al., We employ equation of state including radiation and $^{+}$ $^{-}$ pairs in an approximated analytical form (Freiburghaus et al.342 1999)., 1999).343 The inteerated form of Poisson equation (Ilachisu 1986) handles with both self eravity of a stellar mantle and eravity of a central point mass (in Newtouian limit)., The integrated form of Poisson equation (Hachisu 1986) handles with both self gravity of a stellar mantle and gravity of a central point mass (in Newtonian limit).344 Iu the lbycrodvuamical calculations. the energies generated by nuclear reactions are onütted.," In the hydrodynamical calculations, the energies generated by nuclear reactions are omitted."345 This is justified by the following reason: We have used Ie star models. so that the original composition of the materials which bas burued iuto 7 Ni is heavier than ‘Te.," This is justified by the following reason: We have used He star models, so that the original composition of the materials which has burned into $^{56}$ Ni is heavier than $^{4}$ He."346" The enerey ecnuerated by the reactions is therefore at ost NEN10 eres (ΛΙ ΟΟΝΙ ΛΙ. ). aud even siunaller iu a tvpical ease because most of the materials burned into 7?Ni are javier than 190. Because ALON) is of the order of VIAL... This enerev is about 10)20% for the models with Es,~Laud amueh smaller for the models with E51>10."," The energy generated by the reactions is therefore at most $3 \times 10^{51}$ ergs $/$ $M$ $^{56}$ $/\msun$ ), and even smaller in a typical case because most of the materials burned into $^{56}$ Ni are heavier than $^{16}$ O. Because $M$ $^{56}$ Ni) is of the order of $0.1\msun$, This energy is about $10 - 20$ for the models with $E_{51} \sim 1$ and much smaller for the models with $E_{51} 347\gsim 10$."348 With the lvdrodvnuamical calculation. woe trace hermodvnamical histories of individual Lagrangian elements.," With the hydrodynamical calculation, we trace thermodynamical histories of individual Lagrangian elements."349 3000) particles are used for stellar imautle., 3000 particles are used for stellar mantle.350 At the base of the jet. new particles flow iuto the unuerical domain. aud are also traced.," At the base of the jet, new particles flow into the numerical domain, and are also traced."351 These histories are used to caleulate uucleosvuthesis as post-processing., These histories are used to calculate nucleosynthesis as post-processing.352 The reaction network includes 222 isotopes up to “Ce (lis. Thiclemamu 1996. 1999).," The reaction network includes 222 isotopes up to $^{71}$ Ge (Hix, Thielemann 1996, 1999)."353 The initial compositions of the particles in the processing are taken as follows: Because of the lavee unecrtainty in the initia composition of the jet material. we restrict ourselves iu his paper to parameter space where the mass of the isotopes newly svuthesized in the shocked stellar wautles overwhelins the mass contained iu the jets.," The initial compositions of the particles in the post-processing are taken as follows: Because of the large uncertainty in the initial composition of the jet material, we restrict ourselves in this paper to parameter space where the mass of the isotopes newly synthesized in the shocked stellar mantles overwhelms the mass contained in the jets."354 We postpone he whole survey. such as very massive jets. to future works.," We postpone the whole survey, such as very massive jets, to future works."355 This should require to follow the accretion process o determined the initial composition and will involve he physics neglected imthe prescut study. c.g. angular nomenti transport. nuclear cucrey eeueration. and cooling by photocdisintegration aud ucutring enüssions. as well as lighly resolved ποΊσα simulation around the ceutral remuaut.," This should require to follow the accretion process to determined the initial composition and will involve the physics neglected inthe present study, e.g., angular momentum transport, nuclear energy generation, and cooling by photodisintegration and neutrino emissions, as well as highly resolved numerical simulation around the central remnant."356 We perform lvdrocdvuamic calculations for tle models in Table 1., We perform hydrodynamic calculations for the models in Table 1.357 The models are named with the nuubers, The models are named with the numbers358spectral type and its neighbours 1s about 0.2 mag. so this value was assumed in all subsequent caleulations.,"spectral type and its neighbours is about 0.2 mag, so this value was assumed in all subsequent calculations."359 This error of 0.2 mag corresponds to an error of iin distance (see reftable:comparison.. 7th column).," This error of 0.2 mag corresponds to an error of in distance (see \\ref{table:comparison}, 7th column)."360 The corresponding error in the parallax was used for the correction of the relative parallaxes., The corresponding error in the parallax was used for the correction of the relative parallaxes.361 Given the relation between parallax and distance. the error in the former is not symmetric 1f that of the former ts.," Given the relation between parallax and distance, the error in the former is not symmetric if that of the former is."362 The asymmetric nature of the parallax error is represented in column 8 of reftable:comparison.., The asymmetric nature of the parallax error is represented in column 8 of \\ref{table:comparison}.363 The errors given in reftable:comparison do not represent the overall error., The errors given in \\ref{table:comparison} do not represent the overall error.364 A main source of error will most likely be the photometry. which is not of the highest precision.," A main source of error will most likely be the photometry, which is not of the highest precision."365 Moreover. our spectra do not allow us to determine the exact evolutionary status of the objects. which influences the accuracy of the absolute magnitude.," Moreover, our spectra do not allow us to determine the exact evolutionary status of the objects, which influences the accuracy of the absolute magnitude."366 For the same reason. the influence of metallicity cannot be taken into account. and all stars are assumed to be of solar abundance.," For the same reason, the influence of metallicity cannot be taken into account, and all stars are assumed to be of solar abundance."367 Adding these uncertainties with some margin leads to an overall error in distance of20-30%.. with the stars Ref7-9 having the larger errors. since we only have one spectrum (red of Ref7. blue for the other two) for these objects.," Adding these uncertainties with some margin leads to an overall error in distance of, with the stars Ref7-9 having the larger errors, since we only have one spectrum (red of Ref7, blue for the other two) for these objects."368 Since the parallax is the reciprocal of the distance. the stars with a large distance are the more reliable ones. especially the two giants (Ref3 and 5).," Since the parallax is the reciprocal of the distance, the stars with a large distance are the more reliable ones, especially the two giants (Ref3 and 8)."369 Our astrometric measurements used Ir in position mode to observeREJ0317-853..9802.. and the associated reference field stars.," Our astrometric measurements used 1r in position mode to observe, and the associated reference field stars."370 At each of the three epochs. two," At each of the three epochs, two"371magnitude relation varving with metallicity.,magnitude relation varying with metallicity.372 Hence them salple is dominated by what we usually call the thick disc population., Hence their sample is dominated by what we usually call the thick disc population.373 They deduce an IME slope of a=0.10 or a=0.17 with or without the metallicity eradieut taken into account., They deduce an IMF slope of $\alpha=-0.10$ or $\alpha=-0.47$ with or without the metallicity gradient taken into account.374" 1ic saniple considered. m this paper Ts significantly ifferent. frou the UST sample. as it is dominated by stars at distances. above the plane of. -150 to 150 pe withH a mean distance of 350 pe for stars at r=1.6 and 210 pe for stars having ri""=2.0."," The sample considered in this paper is significantly different from the HST sample, as it is dominated by stars at distances above the plane of 150 to 450 pc with a mean distance of 350 pc for stars at $r'-i'=1.6$ and 210 pc for stars having $r'-i'=2.0$."375 This has two consequences: 1) the sample is less biased by unresolved binaries aud 2) it is dominated by the normal thin dise population aud more comparable with the local sample which is used. to eternune the LE in the solar neighbourhood (Reid et al. 2001))., This has two consequences: 1) the sample is less biased by unresolved binaries and 2) it is dominated by the normal thin disc population and more comparable with the local sample which is used to determine the LF in the solar neighbourhood (Reid et al. \cite{Reid2004}) ).376 Revlé Robin (2001)) have performed the first etevinination of the thick disc IMF from a αμdirectional analysis of star counts., Reylé Robin \cite{Reyle2001}) ) have performed the first determination of the thick disc IMF from a multi-directional analysis of star counts.377" They obtained au IMF.— dINidinxii""7 in the wass range 0.2<a<OSM. which is in agreciment with the IME deduced by Zheng et al. (20013) "," They obtained an IMF $dN/dm \propto m^{-0.5}$ in the mass range $0.2<m<0.8\Msun$, which is in agreement with the IMF deduced by Zheng et al. \cite{Zheng}) )"378from the IST sample. reinforcing the ideas that: firstly Zheug et al. (20011) ," from the HST sample, reinforcing the ideas that: firstly Zheng et al. \cite{Zheng}) )"379lave measured the thick dise IME. rather than the thin disc one: secondly the thin disc aud thick disc have different IME slopes at low masses.," have measured the thick disc IMF, rather than the thin disc one; secondly the thin disc and thick disc have different IMF slopes at low masses."380 The IME found by Revlé Robin (2001)) iu the thick dise is well iu agreement with the one determined in globular clusters (Paresece De Marchi 2000)) and VAiguificautly different frour the one found in the local thin isc (Ixyoupa 2001))., The IMF found by Reylé Robin \cite{Reyle2001}) ) in the thick disc is well in agreement with the one determined in globular clusters (Paresece De Marchi \cite{Paresece}) ) and significantly different from the one found in the local thin disc (Kroupa \cite{Kroupa2001}) ).381 The origin of the thick dise has loug been a matter of. debate., The origin of the thick disc has long been a matter of debate.382 Nowadays- favoured. scenariM explain: the thic:- diseR by one or more accretionsR of tealaxy satellitesR at ey epochs of the CGalaxvs formation. or bv star formation fron gas accreted. during a chaotic period of hierarchical clustering:e (Brook et al. 2 200L)).," Nowadays favoured scenarii explain the thick disc by one or more accretions of galaxy satellites at early epochs of the Galaxy's formation, or by star formation from gas accreted during a chaotic period of hierarchical clustering (Brook et al. \cite{Brook2004}) )."383. The thick disc ↴↴is old and metal poor relative to the sun and it is also euliauced iu alpha clemeuts., The thick disc is old and metal poor relative to the sun and it is also enhanced in alpha elements.384 Abundance determinations (Cratton ot al. 2000)), Abundance determinations (Gratton et al. \cite{Gratton2000}) )385 also show that there has been a discoutinuity iu the star formation between the thick disc aud the thin disc of at least 1 Cr., also show that there has been a discontinuity in the star formation between the thick disc and the thin disc of at least 1 Gyr.386 The conditions of star formation at the epoch of thick dixe formation were clearly different. from the present. conditions iu the thin disc., The conditions of star formation at the epoch of thick disc formation were clearly different from the present conditions in the thin disc.387 Larson (2005) has analysed the pliysical couditious requiredfor the thermal couplingof eas aud dust iu cloud fragmientatiou., Larson (2005) has analysed the physical conditions required for the thermal coupling of gas and dust in cloud fragmentation.388" Πο studied the roles of the metallicity. backeround radiation and dust cuvironment ou the Jeans mass, hence on the typical mass of the stars formed."," He studied the roles of the metallicity, background radiation and dust environment on the Jeans mass, hence on the typical mass of the stars formed."389 The conibiued effects ofthe metallicity aud the possible lack of dust at cosmological epochs could increase the peak ass of the IMF relative to the present one., The combined effects of the metallicity and the possible lack of dust at cosmological epochs could increase the peak mass of the IMF relative to the present one.390 Moreover as the cosmic background temperature was higher iu the past. a higher Πα cloud temperature exists. which also nuples a higher Jeans mass.," Moreover as the cosmic background temperature was higher in the past, a higher minimum cloud temperature exists, which also implies a higher Jeans mass."391 These conditions may well explain the fact that the IME found iu the thick dise has a typical mass higher than the thin disc. aud is deficient in the very low mass stars which are fod iu the present disk ME.," These conditions may well explain the fact that the IMF found in the thick disc has a typical mass higher than the thin disc, and is deficient in the very low mass stars which are found in the present disk MF."392" qi have presented an zualvsis of the stellar populations iu μια CEIDTLS, usinet[m] cataloeues[m]t and imaeesoo roni the first public data release.", We have presented an analysis of the stellar populations in the CFHTLS using catalogues and images from the first public data release.393 Our population svuthesis approach allowed us to test stellar Wbrarics aud to icdeutity ciffereut Sellar types aud Calaxy components using colour-colour diagrams., Our population synthesis approach allowed us to test stellar libraries and to identify different stellar types and Galaxy components using colour-colour diagrams.394 We discuss the locations of various stellar species such ax white dwarfs. late-type and σος. and binary systenus in the MEGACAM filter/detector conmibination.," We discuss the locations of various stellar species such as white dwarfs, late-type and brown dwarfs and binary systems in the MEGACAM filter/detector combination."395 The contamination of the stellar sample by quasars and compact ealaxies is quantified usine spectroscopic data from the VIAMIOS-VLT Deep Survey (WWDS)., The contamination of the stellar sample by quasars and compact galaxies is quantified using spectroscopic data from the VIMOS-VLT Deep Survey (VVDS).396 The percentage of the galaxy coutamination depends very iumch on the 7— colour and cau reach a maxima of for //«22.0 andr’ i«0.5.," The percentage of the galaxy contamination depends very much on the $r'-i'$ colour and can reach a maximum of for $i' < 22.0$ and $r'-i' <3970.5$."398 Our iain conclusions concern the bDuninositv and ass fiction (ME) at low mass for the dise population., Our main conclusions concern the luminosity and mass function (MF) at low mass for the disc population.399 This data set favours an MF slope of a=2.5+1.0 for a<0.25 ου a=3.041.0 for η«0.2 which although steep compared with previous investigations fom other deep imaging surveys (such as Zhene et al., This data set favours an MF slope of $\alpha=2.5 \pm 1.0$ for $m< 0.25$ or $\alpha=3.0 \pm 1.0$ for $m<$ 0.2 which although steep compared with previous investigations from other deep imaging surveys (such as Zheng et al.400 who used IST images) is still in agreement with local determuuatious of the IMF., who used HST images) is still in agreement with local determinations of the IMF.401 This discrepaucy can be explained by differences in the mean age and physical conditious of star formation of the samples. one! beingius at about LE1 pekpe or more where the thick discdix »pulatiouPOPE is expected] to dominate.‘ ‘and ours ιοo κ 1-45150-150 e.and dominatedmate An- hi. thin1 disc.," This discrepancy can be explained by differences in the mean age and physical conditions of star formation of the samples, one being at about 1 kpc or more where the thick disc population is expected to dominate, and ours being at 150-450 pc and dominated by the thin disc."402isc This‘Luis atdiscrepancy ..... the thin disc aud ttick disc. IMES could be explained if for plivsical reasons (for example. lack of dust. higher temperature backgound radiation or metallicity)D. verv low mass star formation.: has been less efficient at the epoch of the thick dise formation.," This discrepancy between the thin disc and thick disc IMFs could be explained if for physical reasons (for example, lack of dust, higher temperature backgound radiation or metallicity) very low mass star formation has been less efficient at the epoch of the thick disc formation."403 The new IME as determined here cannot he extrapolated to masses below 0.1AD., The new IMF as determined here cannot be extrapolated to masses below 0.1.404.. It is probable from the nmuubers of known brown dwrfs in chisters that the PUP starts to decrease near the HW burning limit (IKroupa 2001))., It is probable from the numbers of known brown dwarfs in clusters that the IMF starts to decrease near the H burning limit (Kroupa \cite{Kroupa2001}) ).405 In futuro papers we plan a more detailed analysis of these stellar populations. tn particular the IME. at low lasses of the disk. thick disk and spheroid and tlic old population density distribution up to several teus of kiloparsees.," In future papers we plan a more detailed analysis of these stellar populations, in particular the IMF at low masses of the disk, thick disk and spheroid and the old population density distribution up to several tens of kiloparsecs."406 This müght be performed using more accurate star- ealaxy separation and by accounting for binary frequency im the modelling., This might be performed using more accurate star-galaxy separation and by accounting for binary frequency in the modelling.407 The combination of multibaud wide survey coverageo together with proper motions will euable ux to count thick dise and halo white dwarts. and to constrain on the fraction of baryouic dark matter preseut in the form of stellar reninauts.," The combination of multiband wide survey coverage together with proper motions will enable us to count thick disc and halo white dwarfs, and to constrain on the fraction of baryonic dark matter present in the form of stellar remnants."408(peculiar) motion of the Sun with respect to the LSR. which makes (he Sun's orbit to be and non-planar.,"(peculiar) motion of the Sun with respect to the LSR, which makes the Sun's orbit to be non-circular and non-planar."409" We adopt a solar peculiar velocity of V,=(10.0.5.3.7.2) as given by (Dehnen&Binney1993)."," We adopt a solar peculiar velocity of $\vec{V}_\sun=(10.0,5.3,7.2)$ as given by \citep{deh}."410. The absolute value of the rotational velocity of the LShR ls = ( ( )1993)., The absolute value of the rotational velocity of the LSR is = ( ( ).411. The galactocentrie acceleration resulting from this circular motion is (E73 uu y. and the maximun value of a proper motion caused by this acceleration is (ESI πα...(Cus (9)) the maxinmnmn proper motion is achieved [or objects Iving on the great circle orthogonal to the direction to the galactic center.," The galactocentric acceleration resulting from this circular motion is ( ( )^2, and the maximum value of a proper motion caused by this acceleration is ( ( ) the maximum proper motion is achieved for objects lying on the great circle orthogonal to the direction to the galactic center."412 The proper motion vectors from this largest component of the LSR. acceleration are directed toward the galactic center (see Fig. 1))., The proper motion vectors from this largest component of the LSR acceleration are directed toward the galactic center (see Fig. \ref{pmfield.fig}) ).413 In order (o estimate the magnitude of (he secular aberration caused by the peculiar acceleration of the solar svstem with respect to the LSR. we emplov the classic epicycle approximation for the planar motion of the Sun. aud a harmonic force approximation for its vertical oscillation about the ealactic plane (Marochnik&Suchkov1984:BinneyMerrifield 1993).," In order to estimate the magnitude of the secular aberration caused by the peculiar acceleration of the solar system with respect to the LSR, we employ the classic epicycle approximation for the planar motion of the Sun, and a harmonic force approximation for its vertical oscillation about the galactic plane \citep{marsuch,binney}."414. The peculiar velocity components in this model are (Makarovetal. 2004):, The peculiar velocity components in this model are \citep{mo}: :415against the detection of the nonlinear P-L relation.,against the detection of the nonlinear P-L relation.416 It has been suggested that the nonlinearity of the LMC P-L relation is due to the relatively small nuuber of the lone period Cepheids in the OGLE and MACIIO saluples. aud this nonlinear feature will eo away if more long period Cepheids are added to the samples.," It has been suggested that the nonlinearity of the LMC P-L relation is due to the relatively small number of the long period Cepheids in the OGLE and MACHO samples, and this nonlinear feature will go away if more long period Cepheids are added to the samples."417 Tanunann&Reindl(2002) and Wanbur&Necowo(2001) usingo the OGLE dataalone already suggestedoo the LAIC P-L relation is nonlinemr., \citet{tam02} and \citet{kan04} using the OGLE data already suggested the LMC P-L relation is nonlinear.418 SandageoOetal.(2001) tried to züiueliorate the shortageoO of lonec» period Cepheid by including additional Cepheids from literature to expand the OGLE sample., \citet{san04} tried to ameliorate the shortage of long period Cepheid by including additional Cepheids from literature to expand the OGLE sample.419 They found the nonlinear LAIC P-L relatiou was still evident., They found the nonlinear LMC P-L relation was still evident.420 The nuuber of long period Cepheids will not be the same as the short period Cepheids., The number of long period Cepheids will not be the same as the short period Cepheids.421 This is not a surprise. as argued in Necowctal.(2005).. because iu general the mass is lugher for longer period Cepheids.," This is not a surprise, as argued in \citet{nge05}, because in general the mass is higher for longer period Cepheids."422 The consequence is that there are a fewer uunnber of long period Cepheids (due to initial mass function) aud the long period Cepheids will cross the instability in a shorter amount of time (Bonoctal.20003., The consequence is that there are a fewer number of long period Cepheids (due to initial mass function) and the long period Cepheids will cross the instability in a shorter amount of time \citep{bon00}.423. These two effects have linited the uuuber of long period Cepheids preseut in the LAIC (or in any galaxy)., These two effects have limited the number of long period Cepheids present in the LMC (or in any galaxy).424 Despite the fact that the F-test first used in Iiubur&Necow(2001) sensitive to both the uunuber aud nature of Cepheids on cither side of the period cut. we will demonstrate that the sample selection iu general will not affect the detection of a nonlinear LMC P-L relation.," Despite the fact that the $F$ -test first used in \citet{kan04} sensitive to both the number and nature of Cepheids on either side of the period cut, we will demonstrate that the sample selection in general will not affect the detection of a nonlinear LMC P-L relation."425 The published V-baud mean magnitudes from various sources. as given below. will be used for this test because there is a vast amount of data available iu the V-banud.," The published $V$ -band mean magnitudes from various sources, as given below, will be used for this test because there is a vast amount of data available in the $V$ -band."426 Following Udalskietal.(1999a) aud Necowctal.(2005).. Cepheids with log(P)«0.L were removed from the samples to avoid contamination from first overtone Cepheids.," Following \citet{uda99a} and \citet{nge05}, Cepheids with $\log(P)<0.4$ were removed from the samples to avoid contamination from first overtone Cepheids."427 The plots of these samples (uot shown) reveal that some of the obvious outliers should be removed., The plots of these samples (not shown) reveal that some of the obvious outliers should be removed.428 We use the siguma-clipping algorithin to remove these outliers (Udalskictal.1999a)., We use the sigma-clipping algorithm to remove these outliers \citep{uda99a}.429. First we fit a standard regression to all Cepheids in the samples and οtain the 0 ( = Root Alcan Square. or total dispersion). then those outhers with a dispersion morethan Vo from the fitted regression line are removed.," First we fit a standard regression to all Cepheids in the samples and obtain the $\sigma$ ( = Root Mean Square, or total dispersion), then those outliers with a dispersion morethan $X\sigma$ from the fitted regression line are removed."430 We adopt a novice value of .X=2.5 in our test. which is also sed by the OGLE team (Udalskietal.1999a).," We adopt a novice value of $X=2.5$ in our test, which is also used by the OGLE team \citep{uda99a}."431. We then re-fit the reeression to the short aud lone period Cepheids aud apply the F-test as done in Ikaubur&Necow(2001) and Necowctal.(2005)., We then re-fit the regression to the short and long period Cepheids and apply the $F$ -test as done in \citet{kan04} and \citet{nge05}.432. For our siuuple. £—3 at 95 per cout confidence level. heuce if £73 then the P-L relation is uoulinear.," For our sample, $F\sim3$ at 95 per cent confidence level, hence if $F>3$ then the P-L relation is nonlinear."433" The results are summarized in Table Ἐν, ", The results are summarized in Table \ref{tab1}. .434From this table it can be seen that the nonlinear P-L is clearly evideut from the, From this table it can be seen that the nonlinear P-L is clearly evident from the435"These two equations show how the measured /,, and V, arecontaminated by {εςQ,.U, and V, depending on the values of the D-terms.","These two equations show how the measured $I_m$ and $V_m$ arecontaminated by $I_s, Q_s, U_s$ and $V_s$ depending on the values of the D-terms."436" To measure the linear polarization components. Q,,and U,,. the measurements VyViTIuV. and (VnV;−Iu are made using a multiplying polarimeter."," To measure the linear polarization components, $Q_m$and $U_m$, the measurements $\widetilde V_R \widetilde V_L^*+\widetilde V_L\widetilde V_R^*$ and $i\left(\widetilde V_R\widetilde V_L^*-\widetilde V_L\widetilde V_R^*\right) $ are made using a multiplying polarimeter."437 The outputs of the Vi)multipliers in the polarimeter are related to the incoming electric fields by The Eqs., The outputs of the multipliers in the polarimeter are related to the incoming electric fields by The Eqs.438 can be expressed in terms of Stokes parameters or in terms of linearly polarized flux density., can be expressed in terms of Stokes parameters or in terms of linearly polarized flux density.439" By assuming that Ss""m6o=gu and yo=ye (standard procedure at Effelsberg). it Iss possible to apply to both the Q and U channels the same calibration factor. according to the following where Q, and U, Po.are the Teal signals coming through the ο and U channels and measured at the end of the backend."," By assuming that $g_Q=g_U$ and $\gamma_Q=\gamma_U$ (standard procedure at Effelsberg), it is possible to apply to both the Q and U channels the same calibration factor, according to the following where $Q_c$ and $U_c$ are the Tcal signals coming through the $Q$ and $U$ channels and measured at the end of the backend."440 The Teal is applied analogously to Eqs., The Tcal is applied analogously to Eqs.441(A2).. The ratio between the {ως value and the corresponding measured voltage gives the conversion factor K/V to be applied to the on-source Q and U measurements Discarding the terms of order > 3 the following is obtained The channels Q and U could also be calibrated separately., The ratio between the $I_{lpc}$ value and the corresponding measured voltage gives the conversion factor $K/V$ to be applied to the on-source $Q$ and $U$ measurements Discarding the terms of order $\geq$ 3 the following is obtained The channels Q and U could also be calibrated separately.442 In this case in Eqs., In this case in Eqs.443 two different denominators. one for each channel. would be present.," two different denominators, one for each channel, would be present."444 With Eqs., With Eqs.445 and we have all 16 elements of the Mülller matrix in terms of D-terms. required to relate measured and true Stokes parameters.," and we have all 16 elements of the Mülller matrix in terms of D-terms, required to relate measured and true Stokes parameters."446 From Eqs. (," From Eqs. ,"447A3).. and recalling the definition (5).. the coefficients. of the instrumental Mülller matrix T can be summarized as," and recalling the definition , the coefficients of the instrumental Mülller matrix $\mathbf{T}$ can be summarized as"448underneath (Chandrasekhar1961).,underneath \citep{CHAN1961}.449. In the case where 4A—1 the formation of rising bubbles and Falling spikes is common (Daly1967)., In the case where $A \rightarrow 1$ the formation of rising bubbles and falling spikes is common \citep{DALY1967}.450. Stone&Gardiner(2007) investigated (he impact of shear in the magnetic field across the contact discontinuityv. finding that. this suppressed the small wavenumbers creating wider filamentary structures.," \cite{Stone2007} investigated the impact of shear in the magnetic field across the contact discontinuity, finding that this suppressed the small wavenumbers creating wider filamentary structures."451 Recent observations by Bergerαἱal.(2010). of dark upllows that. propagate from underdense bubbles through quiescent prominences appear to be the observational signature of the havleigh-Tavlor instability in quiescent. prominences., Recent observations by \cite{BERG2010} of dark upflows that propagate from underdense bubbles through quiescent prominences appear to be the observational signature of the Rayleigh-Taylor instability in quiescent prominences.452 Quiescent prominences are large structures of relatively cool (10000 1995))). dense (~I10!*em. ? plasma. that exist in quiet regions of the solar corona. predominantly al high heliographic latitudes.," Quiescent prominences are large structures of relatively cool \citep[10000 K][]{TH1995}) ), dense \citep[$\sim 10^{11}$ $^{-3}$ plasma, that exist in quiet regions of the solar corona, predominantly at high heliographic latitudes."453 Using a characteristic gas pressure of 0.6dynem7 (liravama1986) and magnetic field of 3—30 G (Lerov1989).. gives a plasma ο~ 0.01-1.," Using a characteristic gas pressure of $0.6~dyn~cm^{-2}$ \citep{HIR1986} and magnetic field of $3 \sim 30$ G \citep{LER1989}, gives a plasma $\beta \sim 0.01$ $1$."454 Linear magnetohvdrostatic modelling of a quiet region filament has shown plasma ο<1 and strong departures [rom [orce-[ree magnetic field 2008)., Linear magnetohydrostatic modelling of a quiet region filament has shown plasma $\beta \leq 1$ and strong departures from force-free magnetic field \citep{DUD2008}.455. Globally . quiescent prominences are incredibly stable structures (hat often exist in the corona for weeks.," Globally , quiescent prominences are incredibly stable structures that often exist in the corona for weeks."456 In contrast to this global stability. locally quiescent prominences are hiehlv dynamic phenomena.," In contrast to this global stability, locally quiescent prominences are highly dynamic phenomena."457 Observations of quiescent prominences have shown downllows (Engvold1981).. vortices of approximately 10? kin xLO? km in size and a bubble of size 2800 km forming a kevhole shape with a brieht center with velocities of kkmi +.," Observations of quiescent prominences have shown downflows \citep{ENG1981}, vortices of approximately $10^5$ km $\times 10^5$ km in size \citep{LZ1984} and a bubble of size $2800$ km forming a keyhole shape with a bright center \citep{DT2008} with velocities of km $^{-1}$."458 There are many reviews that give a full description of the current. understanding of the structure and dynamics of quiescent. prominences example.Tancdbere-Tanssen1995:Labrosseetal.2010:Mackay. 2010).," There are many reviews that give a full description of the current understanding of the structure and dynamics of quiescent prominences \citep[see, for example,][]{TH1995,LAB2010,MAC2010}."459. Observations by the Solar Optical Telescope (Ixosugiatal.2007) on the IHinocde satellite CIsunetaetal.2007) have shown that on a small scale quiescent prominences are highly dvnamic and unstable phenomena., Observations by the Solar Optical Telescope \citep{KOS2007} on the Hinode satellite \citep{TSU2007} have shown that on a small scale quiescent prominences are highly dynamic and unstable phenomena.460 Bergeretal.(2008) ancl Dergeratal.(2010). reported dark plumes that propagated from. large bubbles (approximately 10 MMmr in size) that form at the base of some quiescent prominences., \cite{BERG2008} and \cite{BERG2010} reported dark plumes that propagated from large bubbles (approximately $10$ Mm in size) that form at the base of some quiescent prominences.461 Plumes form at the bubble prominence boundary and (hen flow through a height of approximately MMm belore dispersing into the background. prominence material (see Figure 1))., Plumes form at the bubble prominence boundary and then flow through a height of approximately Mm before dispersing into the background prominence material (see Figure \ref{obs_bubble}) ).462 Observations imply that the plumes and the cavities have a column density about 20% of the prominence density 2008)., Observations imply that the plumes and the cavities have a column density about $20$ of the prominence density \citep{HEINZEL2008}.463. The dark upllows maintained an almost constant velocity of approximately 20kkmss ! throughout their rise phase., The dark upflows maintained an almost constant velocity of approximately $20$ $^{-1}$ throughout their rise phase.464 Often these plumes would separate [rom the large scale bubble forming smaller bubbles inside (he prominence material., Often these plumes would separate from the large scale bubble forming smaller bubbles inside the prominence material.465 Dergeretal. presents observations of large scale prominence bubbles using the Atmospheric Imaging Assembly (ALA) on the Solar Dynamics Observatory (5DO) that show the temperature of the material inside the bubble to be >250.000 Ix.," \cite{BERG2011} presents observations of large scale prominence bubbles using the Atmospheric Imaging Assembly (AIA) on the Solar Dynamics Observatory (SDO) that show the temperature of the material inside the bubble to be $>250,000$ $K$ ."466Exposed water ice on main-belt asteroids is Caermocdvnamically unstable. on timescales that are very short compared to the age of the Solar svstem.,"Exposed water ice on main-belt asteroids is thermodynamically unstable, on timescales that are very short compared to the age of the Solar system."467 Ice is therelore not expected on, Ice is therefore not expected on468Comparing equation (127)) with equation (113)). one can see (hat the ellective bending constant is given bv This is the same result that we have obtainedin section 3..,"Comparing equation \ref{app3-z5}) ) with equation \ref{app3-z0}) ), one can see that the effective bending constant is given by This is the same result that we have obtainedin section \ref{results}. ."469are indistinguishable from the nearby dust. emission in the (PALL S yam)160 pm ratio maps.,are indistinguishable from the nearby dust emission in the (PAH 8$\mu$ m)/160 $\mu$ m ratio maps.470 Nonetheless. keep in mind that enhancements/ in the (PALL S j/m)/160 jim ratios are still visible in the large scale structures such as the spiral arms in NGC 3031 and NGC 69046.," Nonetheless, keep in mind that enhancements in the (PAH 8 $\mu$ m)/160 $\mu$ m ratios are still visible in the large scale structures such as the spiral arms in NGC 3031 and NGC 6946."471 Figure 5. shows how the (PALES sam)/160 jim surface brightness ratio varies with 160 jun surface brightness among the sample galaxies. and the slopes ancl intrinsic scatter for the best fit lines as well as Spearman's correlation coelTicients for the data are given in Table 5..," Figure \ref{f_pahvs160} shows how the (PAH 8 $\mu$ m)/160 $\mu$ m surface brightness ratio varies with 160 $\mu$ m surface brightness among the sample galaxies, and the slopes and intrinsic scatter for the best fit lines as well as Spearman's correlation coefficients for the data are given in Table \ref{t_pahvs160}."472 Again. the best fitting lines are determined using uncertainties in both the x- and v-directions to weight the data.," Again, the best fitting lines are determined using uncertainties in both the x- and y-directions to weight the data."473 For all galaxies in the sample. the (PALL S j/m)/160 pm ratio generally increases as the 160 jm surface brightness increases. although the slopes of the relations are relatively shallow for some galaxies. such as NGC 3031. NGC 3351. and NGC 4725.," For all galaxies in the sample, the (PAH 8 $\mu$ m)/160 $\mu$ m ratio generally increases as the 160 $\mu$ m surface brightness increases, although the slopes of the relations are relatively shallow for some galaxies, such as NGC 3031, NGC 3351, and NGC 4725."474 UW the slopes of the best fit lines in Figure 5 were equivalent to 0. this would. indicate that a one-to-one correspondence exists between the PALL S and. 160 pena bands.," If the slopes of the best fit lines in Figure \ref{f_pahvs160} were equivalent to 0, this would indicate that a one-to-one correspondence exists between the PAH 8 and 160 $\mu$ m bands."475 Llowever. since the slopes are instead all positive. this indicates that the colours change from low to high surface brightness regions.," However, since the slopes are instead all positive, this indicates that the colours change from low to high surface brightness regions."476 The scatter in the data around the best [it lines eenerallv appears to be at the level in many cases., The scatter in the data around the best fit lines generally appears to be at the level in many cases.477 According to the intrinsic scatter measurement used. here. the seatter in many of the plots can be explained. mostly bv uncertainties in the measurements.," According to the intrinsic scatter measurement used here, the scatter in many of the plots can be explained mostly by uncertainties in the measurements."478 For most. galaxies. the intrinsic scatter measurements in Table ο are either similar to or notably lower than the values in Table 3..," For most galaxies, the intrinsic scatter measurements in Table \ref{t_pahvs160}479 are either similar to or notably lower than the values in Table \ref{t_pahvs24}."480 Decause the data used for Tables 3. and 5 were measured in images that were degraded to the resolution of the 160 jum images. resolution ellects should. not be a factor in this comparison.," Because the data used for Tables \ref{t_pahvs24} and \ref{t_pahvs160} were measured in images that were degraded to the resolution of the 160 $\mu$ m images, resolution effects should not be a factor in this comparison."481 lence. this comparison between the intrinsic scatter measurements demonstrates quantitatively that the relation between PALL S ancl 160 jm emission may exhibit less scatter than the relation between PALL 8 and 24 jun emission.," Hence, this comparison between the intrinsic scatter measurements demonstrates quantitatively that the relation between PAH 8 and 160 $\mu$ m emission may exhibit less scatter than the relation between PAH 8 and 24 $\mu$ m emission."482 Also note that very low and very high surface brightness 45 aresce regions in NGC 5194 and NGC 5055 fall below the best fit line., Also note that very low and very high surface brightness 45 arcsec regions in NGC 5194 and NGC 5055 fall below the best fit line.483 A related phenomenon is visible in NGC 1725. where the 45 aresee regions within the inner ring Fall below the best fit line in Figure 5..," A related phenomenon is visible in NGC 4725, where the 45 arcsec regions within the inner ring fall below the best fit line in Figure \ref{f_pahvs160}."484 The disparity in the slopes between the high and low surface brightness data for some galaxies demonstrates that the (PALL S μαι)/160 p/m ratio either stops rising or decreases in the high surface brightness centres of the galaxies. as can also be seen in the maps of the (PALL 8 jam)/160 pam ratio in Figure 1. and in the plots of the (PALES sam)/160 pim ratio versus radius in Figure 6..," The disparity in the slopes between the high and low surface brightness data for some galaxies demonstrates that the (PAH 8 $\mu$ m)/160 $\mu$ m ratio either stops rising or decreases in the high surface brightness centres of the galaxies, as can also be seen in the maps of the (PAH 8 $\mu$ m)/160 $\mu$ m ratio in Figure \ref{f_map} and in the plots of the (PAH 8 $\mu$ m)/160 $\mu$ m ratio versus radius in Figure \ref{f_pah160vsdist}."485 Figure 1. illustrates how the (PALL 8. sam)/160 iim ratio may peak outside the nuclei of nearby galaxies., Figure \ref{f_map} illustrates how the (PAH 8 $\mu$ m)/160 $\mu$ m ratio may peak outside the nuclei of nearby galaxies.486 From the ratio maps alone. it is apparentthat the (PALL S μπι)/160 jm ratio does not. necessarily monotonically decrease from the nuclei to the edges of the optical disces as was suggested by Bendoetal.(2006).," From the ratio maps alone, it is apparentthat the (PAH 8 $\mu$ m)/160 $\mu$ m ratio does not necessarily monotonically decrease from the nuclei to the edges of the optical discs as was suggested by \citet{betal06}."487. Both Figure 6.. which plots the (PALL δ jm)/160. pmi ratio versus deprojected ealactocentric radius for 45 aresec regions in these galaxies. and “Table 6.. which gives the slopes and intrinsic scatter measurements for the best fit lines in Figure G6 as well," Both Figure \ref{f_pah160vsdist}, , which plots the (PAH 8 $\mu$ m)/160 $\mu$ m ratio versus deprojected galactocentric radius for 45 arcsec regions in these galaxies, and Table \ref{t_pah160vsdist}, , which gives the slopes and intrinsic scatter measurements for the best fit lines in Figure \ref{f_pah160vsdist} as well"488was accordingly taken to be £0.09.,was accordingly taken to be $\pm$ 0.09.489 We used the above results for density. temperatures. and ICE determinations to derive new values for the O/T] anc N/O ratios lor our sample objects.," We used the above results for density, temperatures, and ICF determinations to derive new values for the O/H and N/O ratios for our sample objects."490 The corresponding uncertainties were obtained using standard error propagation. where (he quantities considered in our estimation of the abundance errors is given in Table 4..," The corresponding uncertainties were obtained using standard error propagation, where the quantities considered in our estimation of the abundance errors is given in Table \ref{error}."491 The «quantües listed in column (1) were assumed to be functions of the variables given in column (2)., The quantities listed in column (1) were assumed to be functions of the variables given in column (2).492 Note that because depends on ancl visa versa. and since in addition. had to be assumed for a significant number of objects (see below). does not appear in Table 4..," Note that because depends on and visa versa, and since in addition, had to be assumed for a significant number of objects (see below), does not appear in Table \ref{error}."493 For each object in our sample. Table 5. gives (he object name in column (1). in column (2).2)..TO)... and in columns (3). (4). and (5). respectively. and 7/IL .and in columns (6). (7). and (8). respectively.," For each object in our sample, Table \ref{ionabun} gives the object name in column (1), in column (2), and in columns (3), (4), and (5), respectively, and $^+$ $^+$, $^{+2}$ $^+$, and $^{+}$ $^+$ in columns (6), (7), and (8), respectively."494" Our final abundance results are given in Table 6.. which lists object name in column (1). references for the observed emission-line strengths in column (2). our derived values lor sa and log(N/O) x¢ in columns (3) and (4). and literature values and relerences in columns (5). (6). aud (7). respectively,"," Our final abundance results are given in Table \ref{bigtable}, which lists object name in column (1), references for the observed emission-line strengths in column (2), our derived values for $\pm~\sigma$ and log(N/O) $\pm~\sigma$ in columns (3) and (4), and literature values and references in columns (5), (6), and (7), respectively."495 Figures 9 and 10 leature comparisons of our Ο/Η and N/O values (vertical axes) against published values., Figures \ref{oldnew_o2h} and \ref{oldnew_n2o} feature comparisons of our O/H and N/O values (vertical axes) against published values.496 The diagonals show points of one-to-one correspondence., The diagonals show points of one-to-one correspondence.497 Our O/II values are systematically lower will respect to past calculations due primarily to our new temperature scheme for calculating ., Our O/H values are systematically lower with respect to past calculations due primarily to our new temperature scheme for calculating $^+$ $^+$.498 ILowever. in general. the error bars show agreement between our results and literature values.," However, in general, the error bars show agreement between our results and literature values."499 Our N/O values are also offset (higher bv ~ 0.05 to 0.1 dex) due the use of new temperature parameltrizations and an ICE. lor obtaining N/O. In Figure ll.. we plot our uncertainties in log(N/O) against corresponding literature values.," Our N/O values are also offset (higher by $\sim$ 0.05 to 0.1 dex) due the use of new temperature parametrizations and an ICF for obtaining N/O. In Figure \ref{oldnew_sigma_n2o}, we plot our uncertainties in log(N/O) against corresponding literature values."500 Some of the published uncertainties were estimated using Monte Carlo simulations lo propagate the errors in (he relevant line strengths. (Campbelletal.&Skillman 1996).. ancl thus points occupy. both sides of the diagonal due to the random nature of (he latter technique.," Some of the published uncertainties were estimated using Monte Carlo simulations to propagate the errors in the relevant line strengths \citep{campbell86, kobulnicky96}, and thus points occupy both sides of the diagonal due to the random nature of the latter technique."501 We point out that log(N/O) values with small uncertainties eenerallv correspond to objects with small uncertainties in relevant emission-line strengths., We point out that log(N/O) values with small uncertainties generally correspond to objects with small uncertainties in relevant emission-line strengths.502 The tendency for our error estimates (o svstematically exceed published ones is primarily due to the contribution of ICF uncertainty for each of our objects., The tendency for our error estimates to systematically exceed published ones is primarily due to the contribution of ICF uncertainty for each of our objects.503 However. we strongly argue (hat inclusion of this additional factor produces more realistic uncertainties (han Chose," However, we strongly argue that inclusion of this additional factor produces more realistic uncertainties than those"504observations aud the search for an optical counterpart to the X-ray source.,observations and the search for an optical counterpart to the X-ray source.505 Our results and their implications are ciseussed im LI., Our results and their implications are discussed in 4.506 The X-ray observations were obtained with the ROSAT AN-Rav Telescope CTPrimnuper et 11991) iu combination with the Ihebh-Resolution Jaeger (IRI. David ct 11995).," The X-ray observations were obtained with the ROSAT X-Ray Telescope (Trümmper et 1991) in combination with the High-Resolution Imager (HRI, David et 1995)."507 The los of the observations is eiven iu Table 1: the last entry in that table is the oue obtained near the BeppoSAX observations. the other entries refer to earlier observations in the ROSAT data archive.," The log of the observations is given in Table \ref{tablog}; the last entry in that table is the one obtained near the BeppoSAX observations, the other entries refer to earlier observations in the ROSAT data archive."508 The standard data reduction was done with the Extended Scicutific Aalysis Svstena (Zinuucrinann et 11996)., The standard data reduction was done with the Extended Scientific Analysis System (Zimmermann et 1996).509 To take inO account f re-calibration of the pixel size (lasinger et 11998). we uultiplv the ον pixel coordinates of eac1i photon wihi respect to the URI ceuter with 0.9972," To take into account the re-calibration of the pixel size (Hasinger et 1998), we multiply the $x,y$ pixel coordinates of each photon with respect to the HRI center with 0.9972."510 Then a senich Or sources Is ας by comparing counts in a box wihi he counts in a rineC» surroundiugC» it. aud by moving tlus detection box across the inage.," Then a search for sources is made by comparing counts in a box with the counts in a ring surrounding it, and by moving this detection box across the image."511 The sources thus detected are excised from the image aud backerounuc nap is nade for the remaining photons., The sources thus detected are excised from the image and a background map is made for the remaining photons.512 A search for sources is uade by comparing the nuuber of photons iu a moving )ox With resect to the munor expected on the basis of he backerorud map., A search for sources is made by comparing the number of photons in a moving box with respect to the number expected on the basis of the background map.513 Finally. at cach position in which a source was found. a maniuuu-likelihood technique is used to coixwe the observed photon distribution with he poiut spread fiction o: the IIRI (Cruddace et 119855).," Finally, at each position in which a source was found, a maximum-likelihood technique is used to compare the observed photon distribution with the point spread function of the HRI (Cruddace et 1988)."514 The resulting countraes for significant detections near the centre of cach image are eiven in Table 1, The resulting countrates for significant detections near the centre of each image are given in Table \ref{tablog}.515 No source is detected in the 1998 Sep & observation., No source is detected in the 1998 Sep 8 observation.516" For a poiut source at the center of the image. oof the photous arrive within a circle with a 5"" yadinIn. in stable TRI poiitings (David et 11995)."," For a point source at the center of the image, of the photons arrive within a circle with a $''$ radius, in stable HRI pointings (David et 1995)."517 At the time of «observatioi the ROSAT satellite poiutiug was experiencing cdiffüct]ties. effectively. exteudiug the radius of the point sprcad function. by a few ircseconds.," At the time of observation the ROSAT satellite pointing was experiencing difficulties, effectively extending the radius of the point spread function by a few arcseconds."518" We therefore search a circle with a 10"" radius around the center of 6610 (according to Picard JJohustou 1995: see roftabpos)). oulv five photons are detected."," We therefore search a circle with a $''$ radius around the center of 6440 (according to Picard Johnston 1995; see \\ref{tabpos}) ), only five photons are detected."519" The iain of five photoIs ¢etected remains if we move the center of the circle to anv location withiu 30"" of the nominal cluster. centre. lus allowing for possible inaccurate reconstructioiof the satellite poiutiug."," The maximum of five photons detected remains if we move the center of the circle to any location within $''$ of the nominal cluster centre, thus allowing for possible inaccurate reconstruction of the satellite pointing."520 For an expeced number of 10 piotons. the Poisson xobabilitv. of dcAtecting 5 or fewer plotous is ," For an expected number of 10 photons, the Poisson probability of detecting 5 or fewer photons is ."521We hus take LO plMons as the 2-0 upper linüt. which for he exposure of ss IVES an upper lait for the count ratee of O.005ctssτ," We thus take 10 photons as the $\sigma$ upper limit, which for the exposure of s gives an upper limit for the count rate of $\cts$."522", To convert this couutrate ito a huuimositvowoe use one of the fits made to the BeppoSAX data win f Zaud et ((1999). aa suum O |n black body with temperature AL=0.51 κο aud brenissrahluus» spectrum with temperature 16.6 kkeV. sorbed by a ¢ola Nyy6.9«10?tan7."," To convert this countrate into a luminosity we use one of the fits made to the BeppoSAX data by in 't Zand et (1999), a sum of a black body with temperature $kT=0.84$ keV and a bremsstrahlung spectrum with temperature $46.6$ keV, absorbed by a column $N_H=6.9\times10^{21}\cmsq$."523" Iu he OSAT baudpas of O.5-2.5kkeV the ΠΠντΓηug xd blackbody components contribute SN) and 17 respectively, to tie total dux."," In the ROSAT bandpass of keV the bremsstrahlung and blackbody components contribute 83 and 17 , respectively, to the total flux."524 For this s)ectiui. the up201’ lait of ctss Liu the URI corresponds to an Narav nünositv of 6«LOeres1 between 0.5 and 2.5 keV. Or 1.5«lo?lores between 2 aud 10 keV. Note tha 1o OSAT ranec froni kkeV is effectively linuted to above O.5kkeV because of the hieh reddening.," For this spectrum, the upper limit of $\cts$ in the HRI corresponds to an X-ray luminosity of $6\times 10^{33}\ergs$ between 0.5 and 2.5 keV, or $1.5\times 10^{34}\ergs$ between 2 and 10 keV. Note that the ROSAT range from keV is effectively limited to above keV because of the high reddening."525 Since SAN measures the flux down to 2 keV. the estimates of the ROSAT flux are quite accurate.," Since SAX measures the flux down to 2 keV, the estimates of the ROSAT flux are quite accurate."526 This nuplies that the flux of the transient iu NGC66LL0 droppedby a factor 250 or more between the BeppoSAX observation ou Aug26 aud the ROSAT URI observation ou Sep 8., This implies that the flux of the transient in 6440 dropped by a factor 250 or more between the BeppoSAX observation on Aug 26 and the ROSAT HRI observation on Sep 8.527" The ROSAT data archive contains several litherto nupublished observatious of ""66LI0 made with the ROSAT IIRI after the 1991 observation reported ly Joinston et ((1995).", The ROSAT data archive contains several hitherto unpublished observations of 6440 made with the ROSAT HRI after the 1991 observation reported by Johnston et (1995).528 A list of all ROSAT observations is given in 1t ftablog.., A list of all ROSAT observations is given in \\ref{tablog}.529 We rave analyzed cach observation separatelv with the stanard procedure. and detect the source iu NOC66LL0 iu he 1993 observation audin the Sep 1991 observation. iin the observations with the longer CN)osure times.," We have analyzed each observation separately with the standard procedure, and detect the source in 6440 in the 1993 observation and in the Sep 1994 observation, in the observations with the longer exposure times."530 Iu the shorter observations. we only obtain upper liits.," In the shorter observations, we only obtain upper limits."531" From the olserved. uber —of: counts iu a cncle with 5"" radius near the cluster we derive an upper linit to the couutrate of 8 counts for the ceutral source for both the 1992 and the March 1991 o)bservatikDI", From the observed number of 3 counts in a circle with $''$ radius near the cluster center we derive an upper limit to the countrate of 8 counts for the central source for both the 1992 and the March 1994 observation.532R Thethree detections are compatible witha coustan countrate. at a level below the derived," Thethree detections are compatible witha constant countrate, at a level below the derived"533 , 534states low-hard and ligh-soft simular to NX-1 and has been observed up to 500 keV during the flare modo.,states low-hard and high-soft similar to X-1 and has been observed up to 500 keV during the flare mode.535 The quasi-periodic oscillatious with periods between 50 1500 s are the kev characteristics of the source (vau der Whs Jausou 1985)., The quasi-periodic oscillations with periods between 50 $--$ 1500 s are the key characteristics of the source (van der Klis Janson 1985).536 A detailed analysis of the. X-rav spectrin sugeests that the total no of ταν photons seenis to be conserved at all times irrespective of the state aud the observed spectrum is cousistent with a thermal source embedded ii a hot plasma aud enveloped iu a cold hydrogen shell (Mauchauda 2002)., A detailed analysis of the X-ray spectrum suggests that the total no of X-ray photons seems to be conserved at all times irrespective of the state and the observed spectrum is consistent with a thermal source embedded in a hot plasma and enveloped in a cold hydrogen shell (Manchanda 2002).537 The X-ray light curve of the source in the 2-12 keV baud from the RNTE/ÀASM data shows frequent spectral changes between the high-soft to low-hard states thereby sueecsting large. changes in the accretion rate on to the compact object., The X-ray light curve of the source in the 2-12 keV band from the RXTE/ASM data shows frequent spectral changes between the high-soft to low-hard states thereby suggesting large changes in the accretion rate on to the compact object.538 At radio wavelengths. XX-3 is the most huuinous A-rav binary du both its quiescent and flaring states (Waltman et al.," At radio wavelengths, X-3 is the most luminous X-ray binary in both its quiescent and flaring states (Waltman et al."539 1995)., 1995).540" IIuge radio outbursts have becu reported in NN-39 durus which the fux density can increase up to levels of ~20JJv: radio cussion is suppressed (""queuched""} to levels below nuuJx for some clays fore large radio flares (Waltinan ct al.", Huge radio outbursts have been reported in X-3 during which the flux density can increase up to levels of $\sim$ Jy; radio emission is suppressed (“quenched”) to levels below mJy for some days before large radio flares (Waltman et al.541 1991)., 1994).542 Jet-ike structures with repeated relativistic ejection have )een observed at various radio frequencies (6.8. Schalinski et al., Jet-like structures with repeated relativistic ejection have been observed at various radio frequencies (e.g. Schalinski et al.543 1998)., 1998).544 Ou an are-secoud scale. two-sidec jets have con seen from the source in the N-S orientation. whereas a highh-relativistic (9 2 0.81) one-sidedjet with the same orientation has been reported on qulli-arcsec scales with he VLBA ct al.," On an arc-second scale, two-sided jets have been seen from the source in the N-S orientation, whereas a highly-relativistic $\beta$ $\ge$ 0.81) one-sided jet with the same orientation has been reported on milli-arcsec scales with the VLBA et al."545 2001: Mioduszewski et al., 2001; Mioduszewski et al.546 2001)., 2001).547 Iu the Table 2 above we lave σπαΊος the radio flux deusities of the source as measured during various observations with CAIRT aud from the Ryle Telescope data., In the Table 2 above we have summarized the radio flux densities of the source as measured during various observations with GMRT and from the Ryle Telescope data.548 Fig., Fig.549 6 shows a fiuxflux plot for (νοκ for the GAIRT and 15-GIIz data. and Fig.," 6 shows a flux–flux plot for X-3 for the GMRT and 15-GHz data, and Fig."550 7 shows the 15-CIIz and RNTE ASM data for the whole period., 7 shows the 15-GHz and RXTE ASM data for the whole period.551 The timing of the GAIRT observations is again marked with vertical lines in Fig., The timing of the GMRT observations is again marked with vertical lines in Fig.552 7., 7.553 The last 1 GAIRT observations. all at GCIIz. were made during the high-soft state.," The last 4 GMRT observations, all at GHz, were made during the high-soft state."554" The mean fiux density at that frequency was ΗΝ, compared with Tuunaty for the 6 xevious data points: the 15-GIIz uean value was also üeher. 150nunJy compared withwi TluunJv for the correspouding 6 data points."," The mean flux density at that frequency was mJy, compared with mJy for the 6 previous data points; the 15-GHz mean value was also higher, mJy compared with mJy for the corresponding 6 data points."555 We note hat the radio/N-rav correlation is in the opposite ποσο o that for NN-1., We note that the radio/X-ray correlation is in the opposite sense to that for X-1.556" MeColloush et al (1999) repor both anuti-correlatious (in the quiescent state) aud correlations (n the flaring state) between the hard ταν flux kkeV. as measured x DATSE) aud the cn-wave radio flux «eusitv of δν,"," McCollough et al (1999) report both anti-correlations (in the quiescent state) and correlations (in the flaring state) between the hard X-ray flux keV, as measured by BATSE) and the cm-wave radio flux density of X3."557 We investigated the possibility that RISS mught be nuportaut iu the case of XNN3., We investigated the possibility that RISS might be important in the case of X3.558 The propagation conciJos are more severe than for the case of NX-1: the path leusth is much lounger. and it has been kuownun for some tine (e.g. Wilkmson ct al. 1991) that the scatter-broadening for this source ds extreme.," The propagation conditions are more severe than for the case of X-1: the path length is much longer, and it has been known for some time (e.g. Wilkinson et al, 1994) that the scatter-broadening for this source is extreme."559 The NE2001 model is cousisteut: it sugeests angular broadening of 20.59. aaresec at 0.61. GGITz.," The NE2001 model is consistent: it suggests angular broadening of 20.59, arcsec at 0.61, GHz."560 The correspouding timescales would be many vears. and the narrow scintillation bandwidth ΠΠ) would suppress anv observed scintillation.," The corresponding timescales would be many years, and the narrow scintillation bandwidth Hz) would suppress any observed scintillation."561 We conclude that RISS is uot relevant to this study of NX-3., We conclude that RISS is not relevant to this study of X-3.562 To look for correlation between the radio emiüssiou fron the source with its X-ray cussion characteristics. we have plotted the RNTE/ASAI X-ray light curve for NN-3 in Fie.," To look for correlation between the radio emission from the source with its X-ray emission characteristics, we have plotted the RXTE/ASM X-ray light curve for X-3 in Fig."563 7 along with the radio data., 7 along with the radio data.564 The timing of the CAIRT observations is shown by the vertical lines., The timing of the GMRT observations is shown by the vertical lines.565 It can be seen that no large flares were observed dunue this interval., It can be seen that no large flares were observed during this interval.566 The radio Cluission is iu the “quiescent” state. typically 50 to muuJy at 15 GIIz.," The radio emission is in the `quiescent' state, typically 50 to mJy at 15 GHz."567 For the last mouth or so of this time- the N-rav spectrum softens: the RATE ASAI ratio IIR2 falls consistently below 2. aud the radio euiussion starts to become more erratic.," For the last month or so of this time-range, the X-ray spectrum softens: the RXTE ASM ratio HR2 falls consistently below 2, and the radio emission starts to become more erratic."568 This behaviour faced away after another nouth or so. aud the source returued to the quiescent state.," This behaviour faded away after another month or so, and the source returned to the quiescent state."569 As seen from the data in Table 2 and Fig., As seen from the data in Table 2 and Fig.570 6. NN-3 Is a persistcut radio source at all wavelengths.," 6, X-3 is a persistent radio source at all wavelengths."571 NX-3 ds amore luninous at higher frequencies., X-3 is more luminous at higher frequencies.572 The data in Table 2 clearly indicates a low frequenev turi-over in the ποος spectrmm below Πε., The data in Table 2 clearly indicates a low frequency turn-over in the source spectrum below GHz.573 Às discussed earlier. such schaviour can arise due to svuchrotrou self absorption of the compact radio emüttiug plasima in an optically tick imediuu.," As discussed earlier, such behaviour can arise due to synchrotron self absorption of the compact radio emitting plasma in an optically thick medium."574 The observed variability. of the flux ceusi vods consistent with tje asstuuption of a discrete cjection/plasimoid in adiabatic expansion., The observed variability of the flux density is consistent with the assumption of a discrete ejection/plasmoid in adiabatic expansion.575 The, The576During most of the previous decade Lye emission was considered an inefficient. survey method for high-redshift galaxies due to a number of unsuccessful surveys (e.g. Prichet 1994 and references therein).,During most of the previous decade $\alpha$ emission was considered an inefficient survey method for high-redshift galaxies due to a number of unsuccessful surveys (e.g. Prichet 1994 and references therein).577 It is now clear that the first surveys for Lyn emitters were unsuccessful mainly because they reached significantly too shallow detection limits., It is now clear that the first surveys for $\alpha$ emitters were unsuccessful mainly because they reached significantly too shallow detection limits.578 The theoretical expectation was that todays large ellipticals formed in a fast. monolithic collapse (e.g. Patridge Peebles 1967).," The theoretical expectation was that todays large ellipticals formed in a fast, monolithic collapse (e.g. Patridge Peebles 1967)."579 In the hierarchical picture of galaxy formation the high-redshift galaxies are smaller and hence fainter than expected when the first surveys were planned., In the hierarchical picture of galaxy formation the high-redshift galaxies are smaller and hence fainter than expected when the first surveys were planned.580 The main advantage of LBG surveys is that they probe a very large volume and hence provide a large number of galaxies per field., The main advantage of LBG surveys is that they probe a very large volume and hence provide a large number of galaxies per field.581 However. there is a number of studies that are most efficiently done with LEGOs as probes: LEGOs can be used to probe the faint end of the luminosity function (Fynbo et al.," However, there is a number of studies that are most efficiently done with LEGOs as probes: LEGOs can be used to probe the faint end of the luminosity function (Fynbo et al."582 2001): LEGOs can be detected and spectroscopically confirmed at both lower (Fynbo et al., 2001); LEGOs can be detected and spectroscopically confirmed at both lower (Fynbo et al.583" 1999, 2002) and higher redshifts (Dey et al."," 1999, 2002) and higher redshifts (Dey et al."584 1998; Ellis et al., 1998; Ellis et al.585 2001: Venemans et al., 2001; Venemans et al.586 2002: Hu et al., 2002; Hu et al.587 2002: Taniguchi et al., 2002; Taniguchi et al.588 2003) than is currently possible with techniques based on the continuum: the large space density reachable with surveys for LEGOs allows a detailed study of the underlying large scale structure and to probe the environments of other high-redshift objects such as radio galaxies (Kurk et al., 2003) than is currently possible with techniques based on the continuum; the large space density reachable with surveys for LEGOs allows a detailed study of the underlying large scale structure and to probe the environments of other high-redshift objects such as radio galaxies (Kurk et al.589 2000; Venemans et al., 2000; Venemans et al.590 2002). Gamma Ray Burst host galaxies (Fynbo et al.," 2002), Gamma Ray Burst host galaxies (Fynbo et al."591 2002) or QSO absorbers (e.g. Meller Warren 1993. Francis et al.," 2002) or QSO absorbers (e.g. ller Warren 1993, Francis et al."592 1995; and this paper)., 1995; and this paper).593 The optimal way to proceed with Lya surveys seems to be the use of large area cameras on 8-m class telescopes., The optimal way to proceed with $\alpha$ surveys seems to be the use of large area cameras on 8-m class telescopes.594 First results regarding the luminosity function and clustering properties of LEGOs using the Suprime Camera (Miyazaki et, First results regarding the luminosity function and clustering properties of LEGOs using the Suprime Camera (Miyazaki et595were (hen flatfielded by clividing by the internal «ΟΠΗ lamp frame.,were then flatfielded by dividing by the internal continuum lamp frame.596 Object and telluric calibration spectra in each echelle order were extracted from a spatial profile that was fixed al z2.5 pixels (2:075) about the prolile peak., Object and telluric calibration spectra in each echelle order were extracted from a spatial profile that was fixed at $\pm$ 2.5 pixels $\pm 0\farcs5$ ) about the profile peak.597 The object and telluric spectra extracted ad each nod position were wavelength calibrated. using selected tellurie absorption lines (Lor orders 33. 34. and 35) with wavelengths taken from the LITRAN database (Rothman et 11998). and emission lines of Areon. Krypton. Xenon. and Neon from exposures in the internal lamp spectra (for orders 36. 37. and 38).," The object and telluric spectra extracted at each nod position were wavelength calibrated using selected telluric absorption lines (for orders 33, 34, and 35) with wavelengths taken from the HITRAN database (Rothman et 1998), and emission lines of Argon, Krypton, Xenon, and Neon from exposures in the internal lamp spectra (for orders 36, 37, and 38)."598 Telluric features in each of the four nod positions were removed fom our object spectra by dividing by the spectrum of the telluric standard star obtained at a similar nod position., Telluric features in each of the four nod positions were removed from our object spectra by dividing by the spectrum of the telluric standard star obtained at a similar nod position.599 Order 35 contned emission Irom Dr? in our telluric standard., Order 35 contained emission from $\gamma$ in our telluric standard.600 To avoid introducing spurious structure in the object spectra. we divided bv the telluric standard to correct [ον telluric absorption only in regions far from the Bro line.," To avoid introducing spurious structure in the object spectra, we divided by the telluric standard to correct for telluric absorption only in regions far from the $\gamma$ line."601 Residual telluric features are therefore present in the spectral region within 415 kms+ ofthe Dr 5 line center (2.1638 — jm)., Residual telluric features are therefore present in the spectral region within $\sim$ 415 $\kms$ of the Br $\gamma$ line center (2.1638 – $\micron$ ).602 Waveleneth calibrated spectra al different nod positions in each order were summed and then multiplied by a blackbody of KIX to restore the true continuum shape after division bv the D2V telluric standard., Wavelength calibrated spectra at different nod positions in each order were summed and then multiplied by a blackbody of K to restore the true continuum shape after division by the B2V telluric standard.603 The fIux level in the V1331 spectrum was estimated bv the conversion from observed counts in the observations of the standard toits 2ALASS A- magnitude Gay = 4.48: JJv). and assuming; an equal slit loss between the stancard and object observations.," The flux level in the V1331 spectrum was estimated by the conversion from observed counts in the observations of the standard to its 2MASS $K$ -band magnitude $m_K$ = 4.48; Jy), and assuming an equal slit loss between the standard and object observations."604 The MWCHS0AIWCAS0 observationsobservation werere reduced using a similar prprocedure., The MWC480 observations were reduced using a similar procedure.605lure. Since (1these bservatiolobservations made use of (he improved NIRSPEC array. there were significantly fewer bad. pixels.," Since these observations made use of the improved NIRSPEC array, there were significantly fewer bad pixels."606 Thus. bad pixels were individually identified and their values fixed bv interpolation using the IRAF task “fixpix”.," Thus, bad pixels were individually identified and their values fixed by interpolation using the IRAF task “fixpix""."607" The observations of AIWC! 480 were taken with a wider slit (3-pixel. 07432) and in windy conditions with poor seeing. compared to V1331 (νο,"," The observations of MWC 480 were taken with a wider slit (3-pixel, $\farcs$ 432) and in windy conditions with poor seeing, compared to V1331 Cyg."608 As a result. spectral images of MWC 480 and the tellurie standard star (IR 1412) that were observed at similar beam positions were sumed together without offsets. and their spectra were extracted from a relatively wide (£5 pixels) spectral profile.," As a result, spectral images of MWC 480 and the telluric standard star (HR 1412) that were observed at similar beam positions were summed together without offsets, and their spectra were extracted from a relatively wide $\pm$ 5 pixels) spectral profile."609" Good signal-to-noise in the exposures of (he arc lamps (i.e. Ar. νε, Xe. and Ne) permitted wavelength calibration of all orders except order 33. where telluric absorption lines were used."," Good signal-to-noise in the exposures of the arc lamps (i.e. Ar, Kr, Xe, and Ne) permitted wavelength calibration of all orders except order 33, where telluric absorption lines were used."610 Telluric features in the IWC 480 spectra were removed by dividing by the spectrum of the standard star (II. 1412) obtained at a similar nod position., Telluric features in the MWC 480 spectra were removed by dividing by the spectrum of the standard star (HR 1412) obtained at a similar nod position.611 Several weak stellar absorplion lines were present in (he standard star spectrum., Several weak stellar absorption lines were present in the standard star spectrum.612 These were modeled and, These were modeled and613medium of Miller Cox (1993). which took into account the absorption of UV radiation by clouds with density larger than the surrounding medium in a statistical wav.,"medium of Miller Cox (1993), which took into account the absorption of UV radiation by clouds with density larger than the surrounding medium in a statistical way."614 In Fig., In Fig.615 7 the vertical distribution of the mean LIL (solid lines) and. LILLE (dottec Lines) number densities is shown. for runs A and D with the above μι. in the case of a Gaussian (top panel) and. fractal (bottom panel). density fielcl at clifferent times after the source turn on.," \ref{fig07} the vertical distribution of the mean HI (solid lines) and HII (dotted lines) number densities is shown, for runs A and B with the above $N_{HI}$, in the case of a Gaussian (top panel) and fractal (bottom panel) density field at different times after the source turn on."616 For both, For both617"Llere δν,; denotes the resulting. value of ⋅∕v7... when wesubstitute. 5,, ∕⋅for 5, ∕⋠in equation. (AL)).","Here $\nu'_{cr,m}$ denotes the resulting value of $\nu'_{cr,e}$ when wesubstitute $\gamma'_m$ for $\gamma'_e$ in equation \ref{nume}) )."618 Ht surfaces⋅ when we switch. integration. variables. from⋅ .∕ to ∕vy...," It surfaces when we switch integration variables from $\gamma'_e$ to $\nu'_{cr,e}$."619 The auxiliary function Q is defined as In practice. the computer code uses lookup tables for £67). PGr) and ρω).," The auxiliary function $Q$ is defined as In the limit of small and large $x$, $Q(x)$ behaves as follows: In practice, the computer code uses lookup tables for $F(x)$ , $\mathcal{P}(x)$ and $Q(x)$ ."620 The three functions have been plotted in figure CX1)) (Q for both p=2.2 and p= 2.8). allowing for comparison between the spectra from a single electron. an angle-averaged electron and an ensemble electron.," The three functions have been plotted in figure \ref{FPQplot}) ) $Q$ for both $p = 2.2$ and $p = 2.8$ ), allowing for comparison between the spectra from a single electron, an angle-averaged electron and an ensemble electron."621 Η the only. processes that are of importance are svnchrotron emission and acliahatic cooling. the evolution of the Lorentz [actor of a single electron is described by where er denotes the Thomson cross section.," If the only processes that are of importance are synchrotron emission and adiabatic cooling, the evolution of the Lorentz factor of a single electron is described by where $\sigma_T$ denotes the Thomson cross section."622 In Ciranot&Sari(2002). this cdillerential equation is applied to the DM solution by expressing it in terms of the self-similar variable and solving it analytically., In \cite{Granot2002} this differential equation is applied to the BM solution by expressing it in terms of the self-similar variable and solving it analytically.623 In our case we can use eq. CX12)), In our case we can use eq. \ref{gamma_m_equation}) )624" to establish +5,; directly behind the shock front and initially put 55. the upper cut-off Lorentz [actor due to cooling. at a sullicienthy large value (instead. of infinity)."," to establish $\gamma'_m$ directly behind the shock front and initially put $\gamma'_M$, the upper cut-off Lorentz factor due to cooling, at a sufficiently large value (instead of infinity)."625 SullicientIx large for example can be taken such that with c some tolerance lor the error in the energy., Sufficiently large for example can be taken such that with $\epsilon$ some tolerance for the error in the energy.626" The real 55, will quickly catch up with the approximated +4). as can be seen from equation (D1))."," The real $\gamma'_M$ will quickly catch up with the approximated $\gamma'_M$ , as can be seen from equation \ref{evolution_equation}) )."627 The analytical solutionfor the particle distribution in the DM caseis given by, The analytical solutionfor the particle distribution in the BM caseis given by628al distance . (hen it contains a total number of particles and has emission measure where n is the mean mass per particle.,at distance $x$ then it contains a total number of particles and has emission measure where $m$ is the mean mass per particle.629" Using equation (17)) these vield where .V,=2x1Dpe""E and where EM,=2xRP(Eyl, "," Using equation \ref{rhod}) ) these yield where $N_o=2\pi R^3\frac {\rho_o}{m}$, and where $EM_o=2\pi R^3 (\frac {\rho_o}{m})^2$."630Following the Brown&McLean(1977). formulation. (he scattering polarization is T7(l- 3D)sin?;. where 7 is optical depth. P is the shape factor of the disk and 7 is the inclination angle.," Following the \citet{brown77} formulation, the scattering polarization is $P=\tau (1-3\Gamma)\sin^2 i$ , where $\tau$ is optical depth, $\Gamma$ is the shape factor of the disk and $i$ is the inclination angle."631 Assuming the disk to be a slab with constant thickness //=Hh and including the finite source depolarization [actor D=/1—R?/r?γι1/4? 1939).. then we have the optical depth 7. Sepp. ⋅↴ − − − ⊔∐↲≼∐⊳∖⇁↳↽⋅≀↧↴∐≼⇂∕∣↥⊳∖⊽⊔∐↲≺∢∪⋝∖⊽↕∐≼↲∪↓≯⊔∐↲≀↧↴∐≸≟↥≼↲⊳∖⇁∣↽≻≼↲↥∖∖⊽≼↲≼↲∐⊔∐↲↕∐≺∢↕≼⇂≼↲∐↥∐↖⊂↽↔↴↥∐∩≻⊔∐↲≼∐⋝∖⊽↳↽≀↧↴∐≺⇂⊔∐↲ ↕⋅∪↥≀↧↴∐∪∐≀↧↴↥≀↧↴⇀↸↕⊳∖⇁⋅↼≚⊳∖⊽↥∐⇀∖↕⊺∐⋅∖∖↽≼↲∐≼↲↖⊂↽↔↴↥≼↲≺∢," Assuming the disk to be a slab with constant thickness $H=Rh$ and including the finite source depolarization factor $D=\sqrt632{1-R^2/r^2}=\sqrt{1-1/x^2}$ \citep{cassi87,brown89}, then we have the optical depth $\tau$, where $\tau_o=\frac {3\sigma_T R}{16}\frac{\rho_o}{ m}$, $\sigma_T$ is Thomson cross section, $n=\rho_D/m$ is the electron density of the disk, and $\mu$ is the cosine of the angles between the incident light to the disk and the rotational axis."633↥⊔∐↲≀↧↴∣↽≻⊳∖⇁∪↕⋅↕↽≻∐∪∐≀↧↴∐≼⇂⊳∖⊽∏↕↽≻↕↽≻∪⋝∖⊽≼↲≀↧↴↓≯∏∐⋡∖↽↕∪∐↕∠≼↲≼⇂≼∐⊳∖⇁↕≶⋅," As in MTD, we neglect the absorption and suppose a fully ionized disk."634↴∏∐↲, The635channels using this method.,channels using this method.636 As can be seen each of the channels have been reconstructed. very. well (the dust templates have been added together to allow a with the input maps of Figure 1)., As can be seen each of the channels have been reconstructed very well (the dust templates have been added together to allow a comparison with the input maps of Figure 1).637 Indeed. the error on the CMD comparisonreconstruction is still ομ]ν which is the same as in the case ofa single dust channel perwith pixelknown emissivity (ΕΤΟΣ).," Indeed, the error on the CMB reconstruction per pixel is still $6\mu$ K which is the same as in the case of a single dust channel with known emissivity (HJLB98)."638 Vhis should be contrasted with the 1θμ]ν error obtained by performing the analysis with only one dust template (as in JL205) assuming a spectral index of 2.0., This should be contrasted with the $10\mu$ K error obtained by performing the analysis with only one dust template (as in HJLB98) assuming a spectral index of 2.0.639 The free-free. svnchrotron ancl thermal SZ have been reconstructed to à lower amplitude than the input map (this is because most of the information on these foregrounds occur at the lower frequencies of the Planck Survevor which have lower resolutions: sec ILJLB98).," The free-free, synchrotron and thermal SZ have been reconstructed to a lower amplitude than the input map (this is because most of the information on these foregrounds occur at the lower frequencies of the Planck Surveyor which have lower resolutions; see HJLB98)."640 The kinetic SZ is not reconstructed. to a very high. and only features associated with strong thermal SZ elfects are significance.reconstructed (see LEJEDON)., The kinetic SZ is not reconstructed to a very high significance and only features associated with strong thermal SZ effects are reconstructed (see HJLB98).641This estimate for the size of the flaring region has becu obtained under a few assuuptious which deserve some cohunents.,This estimate for the size of the flaring region has been obtained under a few assumptions which deserve some comments.642 First. we have cousidered a flare occuring iu a single loo»," First, we have considered a flare occurring in a single loop."643 This may uot hold true for such an intense aud oue-lasti1 fiare. Which may perhaps be described more oxoperlv as à ποπρο flare. cousistiie of progressively reconnecting higher and higher loops.," This may not hold true for such an intense and long-lasting flare, which may perhaps be described more properly as a two-ribbon flare, consisting of progressively reconnecting higher and higher loops."644 Nevertheless. it often occurs in solar ποτοι flares hat the rise phase uostlv involves a dominant loop structure. aud then nevaditalv extends to others citealpaa2 )013).," Nevertheless, it often occurs in solar two-ribbon flares that the rise phase mostly involves a dominant loop structure, and then gradually extends to others \\citealp{aa2001}) )."645 We nay associate the estimated length ο such donmunuanut structure., We may associate the estimated length to such dominant structure.646 Anoher müuplicit nou-trivial assmnuption is that of a heatiis pulse coustautlv high during the rise phase., Another implicit non-trivial assumption is that of a heating pulse constantly high during the rise phase.647 Tudeed. a gradually increasing heating function may drive he observed eradual rise of the Lelt curve. invalidating he estimations made above.," Indeed, a gradually increasing heating function may drive the observed gradual rise of the light curve, invalidating the estimations made above."648 However. in such a case we should observe also a gradual increase of the temperature. while the i]idicatiojs are for a sudden jmp of the cluperature to the flare value. which is more typical of a heating pulse.," However, in such a case we should observe also a gradual increase of the temperature, while the indications are for a sudden jump of the temperature to the flare value, which is more typical of a heating pulse."649 We uav be therefore quie confident that ιο total loop leugth i2.10H Cni.," We may be therefore quite confident that the total loop length is $\simeq 2650\times 10^{11}$ cm."651 Tf we asstme a loop aspect R/L~0.1. where Π> is re radius of the loop cross-section. assuied circular aud constant along the oop. we obtain a total loop volume Proxτή Clu? a WANT enission nieasure of 2.6&pl > tion dupies A niaxiumui average loop plasina density of ~2«10 ban3 and a maxiuun pressure of the order of 10 dvne D 7.," If we assume a loop aspect $R/L \sim 0.1$, where $R$ is the radius of the loop cross-section, assumed circular and constant along the loop, we obtain a total loop volume $V \sim 6 \times 10^{31}$ $^3$; a maximum emission measure of $\sim 2.6 \times 10^{54}$ $^{-3}$ then implies a maximum average loop plasma density of $\sim 2 \times65210^{11}$ $^{-3}$ and a maximum pressure of the order of $10^4$ dyne $^{-2}$ ."653 This value is compatible with the equilibrium pressure obtained frou loop scaine laws (Rosneretal. 1978)) aud cousisteut wit1i the hypothesis of the loop at Παπά X-rav huninosity beime close to equilibriu coxditious., This value is compatible with the equilibrium pressure obtained from loop scaling laws \citealp{rtv78}) ) and consistent with the hypothesis of the loop at maximum X-ray luminosity being close to equilibrium conditions.654 Iun order to confine a plasma at such a pressure. a inaenetic field of more tman e500 Cass is required.," In order to confine a plasma at such a pressure, a magnetic field of more than $\sim 500$ Gauss is required."655 The origin of such a field i) stars that are thought to be tilly or uearly-fully radiative is ptzzlug., The origin of such a field in stars that are thought to be fully or nearly-fully radiative is puzzling.656 Iu low-imass stars the presence of a significant convection zone supports the dynamo mechauisin that can generate the confining magnetic fields at the origin o| the rav flare events. but according to classical m0¢lols. pre- star with masses dn excess of 2 M: are expected to follow fully radiative tracks once tf1e qlasistatic contraction has euded.," In low-mass stars the presence of a significant convection zone supports the dynamo mechanism that can generate the confining magnetic fields at the origin of the X-ray flare events, but according to classical models, pre-main-sequence star with masses in excess of 2 $M_{\sun}$ are expected to follow fully radiative tracks once the quasi-static contraction has ended."657 Palla&Stahler(1990) have nude the sugeestionCoco that the surface activity aid winds observed in Tarbie Ac/Be Way be related fo f1ο presence of an outer colnvecjon zone., \cite{ps90} have made the suggestion that the surface activity and winds observed in Harbig Ae/Be may be related to the presence of an outer convection zone.658 Iu their interpretation. this αςoxvection zone results from the subsurface shell burning of residual deuteruu which was accreted «ming the protostar pliase.," In their interpretation, this convection zone results from the subsurface shell burning of residual deuterium which was accreted during the protostar phase."659 Nevertheless Palla&Staller(1993) reconsider their hypothesis. a1Lexplain that accordiie to their models the retrea of the proto-star outer couvection zone docs last a substantial fraction of the preauairsequeuce lifetime of au intermeciaο lnass star.," Nevertheless \cite{ps93}660 reconsider their hypothesis, and explain that according to their models the retreat of the proto-star outer convection zone does last a substantial fraction of the pre-main-sequence lifetime of an intermediate mass star."661 Diving his retreat. however. the effective fc‘perature remains rclatively low. so that the star wouk not be observed witran A or D specral type.," During this retreat, however, the effective temperature remains relatively low, so that the star would not be observed with an A or B spectral type."662 Thev coiclude that the preseice in Herbie Ae‘Be stars of surface| activitv aud strong winds is not linke to an otter convection zone. since tlieir model shows tlat such couvectiojiondbwayvs vanishes with t1e Visine effective (‘perature.," They conclude that the presence in Herbig Ae/Be stars of surface activity and strong winds is not linked to an outer convection zone, since their model shows that such convection always vanishes with the rising effective temperature."663 Receutly Siessctal(2000) lavo presened calculatiois of pre-niadi-sequence evolulonarv tracks for ow- and iutermediate-nuass stars., Recently \cite{sdf00} have presented calculations of pre-main-sequence evolutionary tracks for low- and intermediate-mass stars.664 These models precict he existeice of a thin convective cuvelo»( in voung AB stars., These models predict the existence of a thin convective envelope in young AB stars.665 In their review. Favata&Micela(203) sugeest that his thin couvective envelope. of roughly 2.LO? times he stellar radius. could be at the origin of a low-coronal activity (at the level of the observed πάπια for solar vpe stars) in Altair (ATV) aud lus explain the source N-rav luminosity of Lx=3<10?Tored.," In their review, \cite{fm03} suggest that this thin convective envelope, of roughly $2 \times 10^{-3}$ times the stellar radius, could be at the origin of a low-coronal activity (at the level of the observed minimum for solar type stars) in Altair (A7V) and thus explain the source X-ray luminosity of $L_{\rm X} = 3 \times66610^{27}$."667 According to the same imodels a star with mass LO AL:. the κιune ietallicitv of the Sun aud an age of 10 uillion years. would have a spectral type AG. à Iuninositv of 12 L;. not too far from the one of V892 Tau. iud a convective envelope of a fraction oa 0018 its raclius.," According to the same models a star with mass 1.9 $M_{\sun}$, the same metallicity of the Sun and an age of 10 million years, would have a spectral type A6, a luminosity of 12 $L_{\sun}$, not too far from the one of V892 Tau, and a convective envelope of a fraction of 0.0018 its radius."668 Since 1e niodel prelicts a stellar radis of 1.2«LotLoan. the size of the convective region wotld be 2.2«10ys cn (~ Rs.)," Since the model predicts a stellar radius of $1.2 \times66910^{11}$ cm, the size of the convective region would be $2.2\times67010^8$ cm $\sim$ $R_{\sun}$ )."671 Tt is not clear whether such a thin convective welope. that may be sufficieu to generate the low «€wonal activity mnuvokec to explaiu the 3 to 1 order of -magnitude faiter X-ray cussion of a man secποιος A ar. cadi sustain the dxiuo action necessary f» explain je strong X-rav activity of V892 Tan.," It is not clear whether such a thin convective envelope, that may be sufficient to generate the low coronal activity invoked to explain the 3 to 4 order of magnitude fainter X-ray emission of a main sequence A star, can sustain the dynamo action necessary to explain the strong X-ray activity of V892 Tau."672 Dudeed. YOU OUr flare model we derive a flare oop leugth of ὃν101. oun.," Indeed, from our flare model we derive a flare loop length of $\simeq 2\times 10^{11}$ cm."673 This is comparabe to the stellar radius aud corresponds oa size of ~500 times the hin convective euveope., This is comparable to the stellar radius and corresponds to a size of $\sim 500$ times the thin convective envelope.674 An alteruative imechauisni fo sustain the cdynanaio activity in these xecdowinautly radiative stars las been xoposed by Tout&Pringe(1995)., An alternative mechanism to sustain the dynamo activity in these predominantly radiative stars has been proposed by \cite{tp95}.675. They argue that dviuainio activity can be ststained in AB stars for a substantial fraction oftieir preanain-sequence life time by apping the initial stelar differcutial rotation or shear CLOTSV., They argue that dynamo activity can be sustained in AB stars for a substantial fraction of their pre-main-sequence life time by tapping the initial stellar differential rotation – or shear energy.676 We have analysed the lieht curves and spectral data of the system V892 Tau and V892 Tau NE ina 115 ks exposure and 2 cousecutive cexposures of 7 land L5 ks (nominal)., We have analysed the light curves and spectral data of the system V892 Tau and V892 Tau NE in a 18 ks exposure and 2 consecutive exposures of 74 and 45 ks (nominal).677 In the data. the Herbig Ac star V892 Tau iswell resolved from the low niass later type apparent coniauion V892 Tau NE.," In the data, the Herbig Ae star V892 Tau iswell resolved from the low mass later type apparent companion V892 Tau NE."678 During the, During the679et al. (,et al. (6802001) with LIE detections.,2001) with HI detections.681 An exponential law fails to fit the ealaxy simultaneously at both small anc laree radii. at a high level of significance: the reduced 47 (v7 = 10 degrees of freedom) for the r+1 and exponential fits ⋠⋅⋠in Figure 3 are 0.85 and 131 respectively.," An exponential law fails to fit the galaxy simultaneously at both small and large radii, at a high level of significance: the reduced $\chi^2$ $\nu$ = 10 degrees of freedom) for the $r^{1/4}$ and exponential fits in Figure 3 are 0.85 and 131 respectively."682 Phe central surface-brightness derived from the r3 fit at radii larger than one aresecond (corresponding to the seeing radius) is fog = 15.2 mag 7., The central surface-brightness derived from the $r^{1/4}$ fit at radii larger than one arcsecond (corresponding to the seeing radius) is $\mu_{0R}$ = 15.2 mag $^{-2}$.683 This extrapolated value is very much higher than themeasured central surface brightnesses of about. fro = 19.5 mag 2, This extrapolated value is very much higher than the central surface brightnesses of about $\mu_{0R}$ = 19.5 mag $^{-2}$.684" We can infer the star formation rate in Ark 1460. from measurements of the OLL line equivalent width (46.X: ""ustilnik et al.", We can infer the star formation rate in Mrk 1460 from measurements of the OII line equivalent width (46; Pustilnik et al.685 1999) and also the 1.4 C€llz continuum lux (Section 2.3. Verheijen et al.," 1999) and also the 1.4 GHz continuum flux (Section 2.3, Verheijen et al."686 2001)., 2001).687 Both sets of measurements directly. probe high-mass stars and. their remnants and derivations of the star formation rate [rom hese measurements therefore require very substantial corrections for low-mass stars. which dominate the total mass.," Both sets of measurements directly probe high-mass stars and their remnants and derivations of the star formation rate from these measurements therefore require very substantial corrections for low-mass stars, which dominate the total mass."688 Assuming a Salpeter (1955) stellar. initial mass unction. and the OIL line calibration of Gallego (1998). he current. star formation rate in Markarian 1460 is 00M.vr ," Assuming a Salpeter (1955) stellar initial mass function and the OII line calibration of Gallego (1998), the current star formation rate in Markarian 1460 is $0.09 \,{\rm M}_{\odot} {\rm yr}^{-1}$."689"Assuming the same stellar initial mass ""unction and the calibration of Cram et al. (", Assuming the same stellar initial mass function and the calibration of Cram et al. (6901998). the 36 upper limit on the star formation rate derived from the 1.4 Gllz measurements described in Section 2.3 is 0.1Mor4 ,"1998), the $\sigma$ upper limit on the star formation rate derived from the 1.4 GHz measurements described in Section 2.3 is $0.11 \,{\rm M}_{\odot} {\rm yr}^{-1}$."691Deriving abundances from. emission-line properties is complicated and a detailed: analysis requires many more measurements than are available for this galaxy (Stasinska Leitherer. 1996)., Deriving abundances from emission-line properties is complicated and a detailed analysis requires many more measurements than are available for this galaxy (Stasinska Leitherer 1996).692 However. the following simple analysis IS sUgeestec-," However, the following simple analysis is suggested."693 From the Dux ratios H]J/IE3 and LU/LE7 (Dustilnik et al., From the flux ratios $\beta$ and $\beta$ (Pustilnik et al.694 1999). the abundance ratios /11 and Hare 3.7 5 7 and 46 s 7. leading to a value of the ionized gas oxvgen abundance of O/LE = 8.3 « 7.," 1999), the abundance ratios $^{+}$ /H and $^{++}$ /H are 3.7 $\times$ $^{-5}$ and 4.6 $\times$ $^{-5}$, leading to a value of the ionized gas oxygen abundance of O/H = 8.3 $\times$ $^{-5}$."695 In this calculation we follow “Tully et al. (, In this calculation we follow Tully et al. (6961981) and adopt a normal Whitford (1958) reddening curve.,1981) and adopt a normal Whitford (1958) reddening curve.697 LE the. heavy element abundance is proportional to the oxvgen abundance. the total metallicity of the ionized eas in Alrk 1460 is then about 0.1 solar CXneders Grevesse 1989).," If the heavy element abundance is proportional to the oxygen abundance, the total metallicity of the ionized gas in Mrk 1460 is then about 0.1 solar (Anders Grevesse 1989)."698 The colours of this galaxy are: ο[22083. BR1—0:31. and 4/— A'—191.," The colours of this galaxy are: $B-R=0.83$, $R-I=0.31$, and $I-K^{\prime}$ =1.91."699" The fA! colour is derived using aperture magnitudes within the A"" 2-0 isophote: this ensures that we are measuring the same part of the galaxy in both filters aud does not require us to make corrections for light lost. below the sky at large radius in the A image.", The $I-K^{\prime}$ colour is derived using aperture magnitudes within the $K^{\prime}$ $\sigma$ isophote; this ensures that we are measuring the same part of the galaxy in both filters and does not require us to make corrections for light lost below the sky at large radius in the $K^{\prime}$ image.700 These optical colours suggest an age of approximately 1.8 Gyr if the galaxy has been forming stars either in an instantaneous burst at this time in the past or continuously with an exponential star-formation history profile with e-folcing time 1 Gwr. given the models of Bruzual Charlot (1993). assuming a Salpeter (1955) stellar. initial mass function from 0.1 AL. to 100 AL. ). negligible internal extinction and a metallicity of 0.4 solar.," These optical colours suggest an age of approximately 1.3 Gyr if the galaxy has been forming stars either in an instantaneous burst at this time in the past or continuously with an exponential star-formation history profile with $e$ -folding time 1 Gyr, given the models of Bruzual Charlot (1993), assuming a Salpeter (1955) stellar initial mass function from 0.1 $_{\odot}$ to 100 $_{\odot}$ ), negligible internal extinction and a metallicity of 0.4 solar."701 Phe £0A colour above is. however. too red by about 0.7 magnitudes to be produced by the stars [from this burst alone.," The $I-K^{\prime}$ colour above is, however, too red by about 0.7 magnitudes to be produced by the stars from this burst alone."702 This might sugeest the presence ofa population of older stars which only contribute in a small way to the optical D'uxes., This might suggest the presence of a population of older stars which only contribute in a small way to the optical fluxes.703 Probably the, Probably the704explosions are more easier to be obtained for higher neutrino luminosity.,explosions are more easier to be obtained for higher neutrino luminosity.705" As is well known, the combination of (e,,) and L,, is an important quantity to diagnose the success or failure of explosions, because the neutrino heating rate in the so-calledgain region, Q7, is proportional to (&)Ly, (e.g., equation (23)in Janka (2001)))."," As is well known, the combination of $\bracket{\epsilon_{\nu_x}}$ and $L_{\nu_x}$ is an important quantity to diagnose the success or failure of explosions, because the neutrino heating rate in the so-calledgain region, $Q_\nu^+$, is proportional to $\bracket{\epsilon_{\nu_x}^2} L_{\nu_x}$ (e.g., equation (23) in \citet{jank01}) )."706" Figure 6 shows Eg, as a function of (e,L,,.", Figure \ref{fig:Ediag} shows $E_\mathrm{diag}^\infty$ as a function of $\bracket{\epsilon_{\nu_x}}^2L_{\nu_x}$.707" Note in the plot that we set the horizontal axis not as (εν)Ly, but as (c,,)?Ly, so that we can deduce the lodipgowin3xdepent dence more clearly andeasily®.", Note in the plot that we set the horizontal axis not as $\bracket{\epsilon_{\nu_x}^2}L_{\nu_x}$ but as $\bracket{\epsilon_{\nu_x}}^2L_{\nu_x}$ so that we can deduce the following dependence more clearly and.708". In this figure, let us fitst focus on red pluses, green crosses,by and blue squares whose difference is characterized s (2D results (filled circles) will be mentioned in the "," In this figure, let us first focus on red pluses, green crosses, and blue squares whose difference is characterized by $t_s$ (2D results (filled circles) will be mentioned in the later section)."709"L,-5x10b (1)p, "," Red $t_s=$ 100 ms), green $t_s=$ 150 ms), and blue $t_s=$ 200 ms) points have a clear correlation with $\bracket{\epsilon_{\nu_x}}^2L_{\nu_x}$."710"Orange and light-blue regions represent ón-explodng regions for red and blue points, f.."," Orange and light-blue regions represent the non-exploding regions for red and blue points, respectively."711 indicating that the critical values of .," Both of them show that the minimum $E_\mathrm{diag}^\infty$ decreases with $t_s$, indicating that the critical values of $\bracket{\epsilon_\nu}^2L_\nu$ for explosion sharply depends on $t_s$."712 This is S tain a er , This is because the mass outside the shock wave gets smaller with time so that the minimum energy to blow up star gets smaller too.713Ej.," By the same reason, $E_\mathrm{diag}$ becomes larger as $t_s$ becomes smaller given the same $\bracket{\epsilon_{\nu_x}}^2L_{\nu_x}$."714 the earlier spectral swapping is MEO," To obtain a larger $E_\mathrm{diag}^\infty$, the earlier spectral swapping is more preferential."715"""Figureshows 7 the neutrino heating rate and the density distribution of NH13R30E13T1008S for 10 ms and 250 ms after t, (=100 ms after the bounce).", Figure \ref{fig:edot} shows the neutrino heating rate and the density distribution of NH13R30E13T100S for 10 ms and 250 ms after $t_s$ (=100 ms after the bounce).716" As the shock wave propagates outward, the density in the gain region sharply drops (e.g., 100-200km, dashed blue line), leading to the suppression of the heating rate (dashed red line)."," As the shock wave propagates outward, the density in the gain region sharply drops (e.g., 100-200km, dashed blue line), leading to the suppression of the heating rate (dashed red line)."717 This is the reason of the saturation in Egjag as shown in Figure 4.., This is the reason of the saturation in $E_\mathrm{diag}$ as shown in Figure \ref{fig:time_ev}.718 The remnant mass is an important indicator to diagnose the consequences of the explosion in producing either a neutron star or a black hole., The remnant mass is an important indicator to diagnose the consequences of the explosion in producing either a neutron star or a black hole.719" The last two lines in Table 1 show the integrated masses in the regions of p>1010 g cm? at t—t, and t= oo.", The last two lines in Table \ref{tab:models} show the integrated masses in the regions of $\rho\ge 10^{10}$ g $^{-3}$ at $t=t_s$ and $t=\infty$ .720 The latter one is estimated by the fitting as where c and d are the fitting parameters., The latter one is estimated by the fitting as where $c$ and $d$ are the fitting parameters.721" For the exploding models, Mpg becomes generally smaller than Mis!* because of the mass ejection."," For the exploding models, $M_{10}^\infty$ becomes generally smaller than $M_{10}^{t=t_s}$ because of the mass ejection."722 Exceptions, Exceptions723features with orbital phase (Section 3.4).,features with orbital phase (Section 3.4).724 Each hemisphere is assumed to have uniform absorption. and we relate Lsfe to the mass ratio q using (I5eeleton. 1983).," Each hemisphere is assumed to have uniform absorption, and we relate $R_2/a$ to the mass ratio $q$ using (Eggleton, 1983)."725 Consider the conservative mass transfer equation. where hj ds the radius of the Roche Lobe. J is the orbital angular momentum. and. -Mo is the instantanecga mass transfer rate (Frank. Wine Raine 1992).," Consider the conservative mass transfer equation, where $_L$ is the radius of the Roche Lobe, $J$ is the orbital angular momentum, and $\dot{M_2}$ is the instantaneous mass transfer rate (Frank, King Raine 1992)."726 When αςΛοΑΙ)«5/6 then Rp70. so the toche lobe expands. reducing the mass transfer. ancl the system is stable.," When $q(=M_2/M_1)<5/6$ then $\dot{R_L}>0$, so the Roche lobe expands, reducing the mass transfer, and the system is stable."727 In order to sustain long lived mass transfer he secondary star must expand. in size relative to. the toche lobe. otherwise the lobes detach from the star and mass transfer stops.," In order to sustain long lived mass transfer the secondary star must expand in size relative to the Roche lobe, otherwise the lobes detach from the star and mass transfer stops."728 Evolution of the secondary. star is one xossibilitv. but for the secondary to evolve within the age of he Galaxy. it must be spectral tvpe GO or earlier (Patterson 1984).," Evolution of the secondary star is one possibility, but for the secondary to evolve within the age of the Galaxy, it must be spectral type G0 or earlier (Patterson 1984)."729 Most €V secondaries have spectral types later than GO. so a more likely solution for stable mass transfer. is angular momentum loss due to either gravitational radiation and/or magnetic braking.," Most CV secondaries have spectral types later than G0, so a more likely solution for stable mass transfer is angular momentum loss due to either gravitational radiation and/or magnetic braking."730 Phe loss of angular momentunir shrinks the binary system therefore enablingsustained mass transfer to occur., The loss of angular momentum shrinks the binary system therefore enablingsustained mass transfer to occur.731" When q>»5/6 then ""m<0. and the Roche lobe shrinks."," When $q>5/6$ then $\dot{R_L}<0$, and the Roche lobe shrinks."732 Mass transfer will therefore increase. and the svsteni will become unstable unless the secondary star can contract rapidly enough to keep its radius smaller than the radius of the Roche lobe.," Mass transfer will therefore increase, and the system will become unstable unless the secondary star can contract rapidly enough to keep its radius smaller than the radius of the Roche lobe."733 I£ the secondary star obevs the main sequence mass-racdius relation f»-xAle. and the radius of the star responds to changes in its mass on a thermal time scale. Equation 6. becomes. vielding a critical upper mass ratio (goa).," If the secondary star obeys the main sequence mass-radius relation $R_2\propto M_2$, and the radius of the star responds to changes in its mass on a thermal time scale, Equation \ref{e7} becomes, yielding a critical upper mass ratio $q_{crit}$ )."734 When q> the secondary star will not shrink rapidly enough to keep pace with the Roche lobe., When $q>4/3$ the secondary star will not shrink rapidly enough to keep pace with the Roche lobe.735 Phere will be à spontaneous overllow ancl mass transfer becomes unstable., There will be a spontaneous overflow and mass transfer becomes unstable.736 The secondary star in a CV is a late type low mass star with a deep convective envelope. ancl therefore. loses mass on a clynamical time scale governed by the stars aciabatic response.," The secondary star in a CV is a late type low mass star with a deep convective envelope, and therefore loses mass on a dynamical time scale governed by the star's adiabatic response."737" Considering a complete polvtrope with a polvtropic index of n=3/2 (Iljellming Webbink 1987). the mass-radius relation for the secondary star becomes RoxAL,L7 and hence Equation 6 becomes. producing a lower mass ratio limit ($44,5:,)."," Considering a complete polytrope with a polytropic index of $n=3/2$ (Hjellming Webbink 1987), the mass-radius relation for the secondary star becomes $R_2\propto738M_2^{-1/3}$, and hence Equation \ref{e7} becomes, producing a lower mass ratio limit $q_{ad,fc}$ )."739 When qc2/8 the star can not remain within its Roche lobe in hvdrostatic equilibrium. ancl mass transfer. occurs. on dyvnamical time scales.," When $q > 2/3$ the star can not remain within its Roche lobe in hydrostatic equilibrium, and mass transfer occurs on dynamical time scales."740 When gq«2/3. the star becomes stable on a dynamical time scale and mass transfer occurs due to the slow expansion of the star via nuclear evolution or angular momentum loss causing the Roche lobe to contract.," When $q < 2/3$, the star becomes stable on a dynamical time scale and mass transfer occurs due to the slow expansion of the star via nuclear evolution or angular momentum loss causing the Roche lobe to contract."741 The secondary star in RW Tri. may not. be. fully convective so the true adiabatic mass ratio will be higher., The secondary star in RW Tri may not be fully convective so the true adiabatic mass ratio will be higher.742" In the case where the secondary star has a convective envelope. but a vacliative core. the mass-racius relation becomes Aly”.Les leading. to a mass ratio. of. qi,=1 for. the adiabatic. response (ILellming Webbink 1987)."," In the case where the secondary star has a convective envelope, but a radiative core, the mass-radius relation becomes $R_2\propto M_2^{1/3}$ , leading to a mass ratio of $q_{ad,rc}=1$ for the adiabatic response (Hjellming Webbink 1987)."743 We first calculate the mass ratio of RW ‘Tri using the various estimates of the component star radial velocity zumplitudes., We first calculate the mass ratio of RW Tri using the various estimates of the component star radial velocity amplitudes.744 The most reliable. estimate for the secondary star velocity is [rom the W-baned data because there is not enough detail in the I-band data to be sure that they are not allected by elluric lines and background emission etc., The most reliable estimate for the secondary star velocity is from the K-band data because there is not enough detail in the I-band data to be sure that they are not affected by telluric lines and background emission etc.745 When combined with the ραπ secondary. star velocity. (221+429km). he various estimates of the primary star velocity amplitude discussed in Section 4.1 lead to a range of mass ratios of ks3 as expressed in Table 4 (column +).," When combined with the K-band secondary star velocity $221\pm29$ km/s), the various estimates of the primary star velocity amplitude discussed in Section 4.1 lead to a range of mass ratios of $0.8-1.3$ as expressed in Table \ref{t3} (column 4)."746" The AN, velocity values that are most likely to reflect the motion of the white ciwarf are the UV absorption ines of Mason (2002). and the Le LL emission lines of Still (1995). because they both originate in regions close to the white chwarl."," The $K_1$ velocity values that are most likely to reflect the motion of the white dwarf are the UV absorption lines of Mason (2002), and the He II emission lines of Still (1995), because they both originate in regions close to the white dwarf."747 Fhese velocities therefore give us acmost likely’ mass ratio in the range 1.001.3., These velocities therefore give us a `most likely' mass ratio in the range $1.0-1.3$.748" To consider the ellects of the ""Ix-correction on our most. likely mass ratio range. we use Equation 3.2 and 5.. and f—0.25 with q-—1.01.3. which corresponds to a range in A of ~19% to ~24."," To consider the effects of the “K-correction” on our most likely mass ratio range, we use Equation \ref{extra2} and \ref{eadded}, and $f\sim0.25$ with $q=1.0-1.3$, which corresponds to a range in $\Delta K$ of $\sim 19\%$ to $\sim24\%$."749 Thus after applying the most likely value for the secondary star heating the value of A» in RAVTri is ~ liskni/s. implying a revised mass ratio. d. in the range 1317 (Yable 4.. column 5).," Thus after applying the most likely value for the secondary star heating the value of $K_2$ in RWTri is $\sim178$ km/s, implying a revised mass ratio, $q$, in the range $1.2-1.7$ (Table \ref{t3}, column 5)."750 Alternatively we can caleulate the mass ratio of RW ‘Tri using the rotational broadening of the secondary star. independent of Ay.," Alternatively we can calculate the mass ratio of RW Tri using the rotational broadening of the secondary star, independent of $K_1$ ."751 Assuming that the secondary star rotates in phase with the binary orbit we use. where fo/a@ is found using Equation 5..," Assuming that the secondary star rotates in phase with the binary orbit we use, where $R_2/a$ is found using Equation \ref{eadded}. ."752 The results are shown in Figure 9 where the solid line represents the A» , The results are shown in Figure \ref{f7b} where the solid line represents the $K_2$ 753Py/P—1 and « for P2 and Pl are shown in Fig.,$P_K/P - 1$ and $a$ for P2 and P1 are shown in Fig.754 1 with their 16 error bars.," \ref{fig:period} with their $1\,\sigma$ error bars."755 The orbital periods are clearly shorter than the Ixepleriau values (by 2.160 and 3.26 lor P2 aud PI. respectively).," The orbital periods are clearly shorter than the Keplerian values (by $2.1\,\sigma$ and $3.2\,\sigma$ for P2 and P1, respectively)."756 Ou the other hand. Pg/P—1 for P2 is in excellent agreement within 0.[Lo) with the analytic result. aud that for PI is in reasouable agreement (within 1.60) with the analytic result.," On the other hand, $P_K/P - 1$ for P2 is in excellent agreement (within $0.4\,\sigma$ ) with the analytic result, and that for P1 is in reasonable agreement (within $1.6\,\sigma$ ) with the analytic result."757 The remainine discrepancy for Pl may be simply statistical. but it could also be due to the assumption in the fitting that the orbit is au unperturbed Ixepleriau orbit (see below for more details ou the expected uou-Ixepleriau behaviors).," The remaining discrepancy for P1 may be simply statistical, but it could also be due to the assumption in the fitting that the orbit is an unperturbed Keplerian orbit (see below for more details on the expected non-Keplerian behaviors)."758" With α fom Table Ἰ as Ry lor P2 aud Pl and aefin,=0.1165. we evaluate τν ny (Eq. [7]."," With $a$ from Table \ref{table1} as $R_0$ for P2 and P1 and $m_c/m_p =7590.1165$, we evaluate $P_K = P_{pc} (a/a_{pc})^{3/2}$ , $n_0/n_K$ (Eq. \ref{n0}] ]),"760 &o/n CEq. [22].," $\kappa_0/n_K$ (Eq. \ref{kappa0}] ]),"761 and ήν (Eq. [32] , and $\nu_0/n_K$ (Eq. \ref{nu0}] ])762for the analytic theory. and they are listed in Table 2..," for the analytic theory, and they are listed in Table \ref{table2}."763 The precession of the periapse is prograde with period aud 5280 days for P2 aud PL. respectively.," The precession of the periapse is prograde with period $2\pi/|\dot{\varpi}| = 2\pi/|n_0 - \kappa_0| = 1740$ and $5280\,$ days for P2 and P1, respectively."764 The nodal precession bas a similar period 27/|Q=DcZH/ngL770 aud 5330 days for P2 aud PL. respectively) but it is retrograde.," The nodal precession has a similar period $2\pi/|\dot{\Omega}| =7652\pi/|n_0 - \nu_0| = 1770$ and $5330\,$ days for P2 and P1, respectively) but it is retrograde."766 The periapse aud nodal precessious at uearly equal rates in opposite directions aud tle mean motion are similar to the behaviors of orbits arouud au oblate planet. (see. e.g.. Section 6.11 of MurrayaudDermott 1999)).," The periapse and nodal precessions at nearly equal rates in opposite directions and the faster-than-Keplerian mean motion are similar to the behaviors of orbits around an oblate planet (see, e.g., Section 6.11 of \citealt{mur99}) )."767 This cau be uuderstood [rom the fact that the (pe/fR)-> 4tT‘us in the axisyiumetric components of the potential. yg aud Poy in Eqs. (7))," This can be understood from the fact that the $(a_{pc}/R)^2$ terms in the axisymmetric components of the potential, $\Phi_{00}$ and $\Phi_{20}$ in Eqs. \ref{Phi00}) )"768 aud (11)). are identical to the Jo terms of an oblate planet with Jo=mimef[26g>Tan).," and \ref{Phi20}) ), are identical to the $J_2$ terms of an oblate planet with $J_2 =769m_p m_c/[2 (m_p + m_c)^2]$."770 For the remaiuder of this paper we use Jacobi coordinates where the position of Charon is relative to Pluto. the position of the inuer satellite P2 is relative to the center of mass of aud the position of the outer satellite PI is relative to the center of mass of ," For the remainder of this paper we use Jacobi coordinates where the position of Charon is relative to Pluto, the position of the inner satellite P2 is relative to the center of mass of Pluto-Charon, and the position of the outer satellite P1 is relative to the center of mass of Pluto-Charon-P2."771Jacobi coordinates are the uatural generalization of the coordinates used in Section 2 (where the position of PI is relative to the center of mass of Pluto-Charou) when P2 aud PI are not test particles. and they reduce to the coordiuates used tu Section 2 iu the test-particle limit.," Jacobi coordinates are the natural generalization of the coordinates used in Section 2 (where the position of P1 is relative to the center of mass of Pluto-Charon) when P2 and P1 are not test particles, and they reduce to the coordinates used in Section 2 in the test-particle limit."772" Prom- P, aud dpe inn Table 41.. we adopt Gm,Y,+in.)=(22íi/HPy)>αρ.5—9.71791-—-—4x10ni?3sL7? (or; mpbay=41.1565-pn-x40221077 kg for. C:=6.672>pax10Hay*ke3ts9 7)."," From $P_{pc}$ and $a_{pc}$ in Table \ref{table1}, we adopt $G (m_p + m_c) = (2\pi/P_{pc})^2 a_{pc}^3 =7739.71791 \times 10^{11}\,{\rm m}^3\,{\rm s}^{-2}$ (or $m_p + m_c = 1.4565 \times 10^{22}\,$ kg for $G = 6.672 \times 10^{-11}\,{\rm m}^3\,{\rm kg}^{-1}\,{\rm s}^{-2}$ )."774 ForE the mass ratio⋅ Πο/bp. we use the best-fit value 0.1165 from BOYYS.," For the mass ratio $m_c/m_p$, we use the best-fit value $0.1165$ from BGYYS."775 We generate the initial position aud velocity of Cliarou relative to Pluto by using the orbital parameters in Table 1. at epoch JD 21252600.5 as the osculatiug Ixepleriaur orbital parameters., We generate the initial position and velocity of Charon relative to Pluto by using the orbital parameters in Table \ref{table1} at epoch JD 2452600.5 as the osculating Keplerian orbital parameters.776 The orbits of P2 and PI are sulficiently non-Ixepleriau even iu tlie test-particle limit that. if we," The orbits of P2 and P1 are sufficiently non-Keplerian even in the test-particle limit that, if we"777significant role in the dynamics of the supernova and perhaps in the revival of the shockwave (e.g.Colgate&White1966:BetheWil-son1985).,"significant role in the dynamics of the supernova and perhaps in the revival of the shockwave \citep[e.g.][]{colgate66,bethewilson85}."778". Specitically. the “neutrino mechanism”. as formulated by Burrows&Goshy(1993)., states that the steady-state accretion through the shock turns into an explosion when Ly...care exceeds a critical value. 5,7""..."," Specifically, the “neutrino mechanism”, as formulated by \citet{bg93}, states that the steady-state accretion through the shock turns into an explosion when $\lcore$ exceeds a critical value, $\lcrit$."779 In Pejeha&Thompson(2012) thereafter PaperD) we showed using steady-state calculations that L7! is equivalent to reaching max(οςfor.)e0.19 in the accretion flow. where es is the sound speed and 0... is the local escape velocity.," In \citet{pejcha12} (hereafter \citetalias{pejcha12}) ) we showed using steady-state calculations that $\lcrit$ is equivalent to reaching $\max\,(c_S^2/\vesc^2) \simeq 0.19$ in the accretion flow, where $c_S$ is the sound speed and $\vesc$ is the local escape velocity."780" This ""antesonic"" condition is a manifestation of the inabilitya T the flow to satisfy both the shock jump conditions and the Euler equations for the accretion flow simultaneously (Yamasaki&Ya-mada2005:Fernández 2012)."," This “antesonic” condition is a manifestation of the inability of the flow to satisfy both the shock jump conditions and the Euler equations for the accretion flow simultaneously \citep{yamasaki05,fernandez12}."781". We also determined the dependence of LY""... on the key parameters of the problem. including the energies of the neutrinos over a wide range of parameter values."," We also determined the dependence of $\lcrit$ on the key parameters of the problem, including the energies of the neutrinos over a wide range of parameter values."782 Specifically. and most importantly for this paper. we found that Lius. ds proportional to the inverse square of the (. ands. energies. us expected from the heating rate.," Specifically, and most importantly for this paper, we found that $\lcrit$ is proportional to the inverse square of the $\nue$ and $\nuebar$ energies, as expected from the heating rate."783 There are a number of time-dependent multi-dimensional effects that might modify the transition from accretion to explosion., There are a number of time-dependent multi-dimensional effects that might modify the transition from accretion to explosion.784 For example. accretion luminosity from cooling of the accretion flow is an important contribution to LMore (PaperD. and accretion simultaneously powering an asymmetric explosion is possible only in 2D and 3D (e.g.Burrowsetal.2006:Marek&Janka2009:Suwa2010).," For example, accretion luminosity from cooling of the accretion flow is an important contribution to $\lcrit$ \citepalias{pejcha12} and accretion simultaneously powering an asymmetric explosion is possible only in 2D and 3D \citep[e.g.][]{burrows06,marek09,suwa10}."785. Furthermore. close to the critical condition for explosion the shock surface often exhibits oscillations that feed back on the neutrino emission (e.g.Murphy&Burrows2008:MarekJanka2009:Nordhausetal.2010:Hanke2011). potentially modifying LMop," Furthermore, close to the critical condition for explosion the shock surface often exhibits oscillations that feed back on the neutrino emission \citep[e.g.][]{murphy08,marek09,nordhaus10,hanke11} potentially modifying $\lcrit$."786 At least in ID.these oscillations seem to occur only very close to the steady-state value of LUap (Fernandez20123.," At least in 1D,these oscillations seem to occur only very close to the steady-state value of $\lcrit$ \citep{fernandez12}."787 The steady-state calculation is thus useful way to estimate Li)Hus and to examine effects of modified physics on the critical condition for supernova explosion., The steady-state calculation is thus useful way to estimate $\lcrit$ and to examine effects of modified physics on the critical condition for supernova explosion.788 Within the parameterization of the neutrino mechanism of Burrows&Goshy(1993). the failure of supernova simulations implies. by detinition. that the neutrino luminosities in the models never reach Li.iie," Within the parameterization of the neutrino mechanism of \citet{bg93}, the failure of supernova simulations implies, by definition, that the neutrino luminosities in the models never reach $\lcrit$."789 For successful explosions. either (i) L7;Mae needs to be decreased or (i) Licore Increased.," For successful explosions, either (i) $\lcrit$ needs to be decreased or (ii) $\lcore$ increased."790" As an example of the former. multi-dimensional effects like convection and SAST decrease L/775,,,. CYamasaki&Yamada2005. by making the heating more efficient (e.g.Herantetal.2004:Burasetal. 2006).."," As an example of the former, multi-dimensional effects like convection and SASI decrease $\lcrit$ \citep{yamasaki05,yamasaki06,murphy08,nordhaus10,hanke11,takiwaki12} by making the heating more efficient \citep[e.g.][]{herant94,bhf95,janka96,fryer04,buras06a}."791 As an example of the latter. Ly.core can be enhanced by convection inside the PNS (e.g.Wilson&Mayle 1996).," As an example of the latter, $\lcore$ can be enhanced by convection inside the PNS \citep[e.g.][]{wilson88,bruenn96,keil96}."792. Another option is that cooling becomes less efficient in 2 and 3 spatial dimensions causing a decrease of LY!Maye (PaperD., Another option is that cooling becomes less efficient in $2$ and $3$ spatial dimensions causing a decrease of $\lcrit$ \citepalias{pejcha12}.793 Most of the heating below the shock occurs due to absorption of v. and £. on neutrons and protons. while the 74 escape without much interaction.," Most of the heating below the shock occurs due to absorption of $\nue$ and $\nuebar$ on neutrons and protons, while the $\nux$ escape without much interaction."794" However. due to the high density of neutrinos in his region. self-interaction between neutrinos becomes important and ean lead to a range of phenomena called “collective neutrino oscillations"" (e.g.Pantaleone1992:Duanetal.2006.2010)."," However, due to the high density of neutrinos in this region, self-interaction between neutrinos becomes important and can lead to a range of phenomena called “collective neutrino oscillations” \citep[e.g.][]{pantaleone92,duan06,duan10}."795. In j»urticular. there is a possibility of an instability (Dasgupta2009) that exchanges part of the 74 spectra with the vu. and f. spectra.," In particular, there is a possibility of an instability \citep{dasgupta09} that exchanges part of the $\nux$ spectra with the $\nue$ and $\nuebar$ spectra."796 If the luminosities and energies of ἐκ... and vy are right. his can produce significantly more heating below the shock than calculations neglecting neutrino oscillations. Le. effective Licore is increased byCvO.," If the luminosities and energies of $\nue$, $\nuebar$, and $\nux$ are right, this can produce significantly more heating below the shock than calculations neglecting neutrino oscillations, i.e., effective $\lcore$ is increased by."797". Specifically. a strong effect on heating can be expected if luminosities are similar and vy have significantly ligher energies than £. and v,.."," Specifically, a strong effect on heating can be expected if luminosities are similar and $\nux$ have significantly higher energies than $\nue$ and $\nuebar$."798 The exact values of these quantities and their mutua ratios are model-dependent (e.g.Thompsonal.2010).. Chakraboryetal.(01lab). Dasguptaetal.(2012). Suwaetal.(2011.," The exact values of these quantities and their mutual ratios are model-dependent \citep[e.g.][]{thompson03,marek09,fischer10,fischer12,hudepohl10}. \citet{chakraborty11a,chakraborty11b}, \citet{dasgupta12}, \citet{suwa11},"799 and Sarikasetal.(011). have investigated the role of iin the core-colapse simulations of several progenitor models., and \citet{sarikas11} have investigated the role of in the core-collapse simulations of several progenitor models.800 They found that there are a number of multi-angle effects. especially the effect of matter suppression. that can reduce or entirely eliminaeCvO.," They found that there are a number of multi-angle effects, especially the effect of matter suppression, that can reduce or entirely eliminate."801". We address the issue of increased neutrino jeating due to aand matter suppression without reference to detailed supernova models and we evaluate them at Li""Peor. Which separates accretion rom explosion."," We address the issue of increased neutrino heating due to and matter suppression without reference to detailed supernova models and we evaluate them at $\lcrit$, which separates accretion from explosion."802 We treat the oscillation physics in a schematic way and the supernova physies using a steady state model developed in PaperI.., We treat the oscillation physics in a schematic way and the supernova physics using a steady state model developed in \citetalias{pejcha12}.803 Although this approach is less detailed than some recent wipers. e.g.. (e.g.Chakrabortyetal.201La.b:Dasgupta2012:Sarikasetal.2011). it allows for a parametric study to determine he potential role of iin shock reheating. and its dependence on the progenitor mass. radius. and accretion rate for a very broad range of parameters and without being tied to any particular progenitor model or simulation setup.," Although this approach is less detailed than some recent papers, e.g., \citep[e.g.][]{chakraborty11a,chakraborty11b,dasgupta12,sarikas11}, it allows for a parametric study to determine the potential role of in shock reheating, and its dependence on the progenitor mass, radius, and accretion rate for a very broad range of parameters and without being tied to any particular progenitor model or simulation setup."804 The remainder of our paper is organized as follows., The remainder of our paper is organized as follows.805 In Section 2.. we describe our steady state model for the accretion flow based on PaperL. and a scheme for collective neutrino oscillations based on Dasguptaetal.(2012).," In Section \ref{sec:method}, we describe our steady state model for the accretion flow based on \citetalias{pejcha12}, and a scheme for collective neutrino oscillations based on \citet{dasgupta12}."806. We present our results in Section 3.., We present our results in Section \ref{sec:results}.807" We quantify the changes to 777, and the shock radii. and compare the magnitude of the effect of tto other known pieces of physies."," We quantify the changes to $\lcrit$ and the shock radii, and compare the magnitude of the effect of to other known pieces of physics."808 We also estimate the importance of multi-angle effects showing that they suppress iin the region of parameter space where they might otherwise be strong., We also estimate the importance of multi-angle effects showing that they suppress in the region of parameter space where they might otherwise be strong.809 In Section 4.. we conclude with a discussion and review of our results.," In Section \ref{sec:disc}, we conclude with a discussion and review of our results."810 In this Section we tirst describe the hydrodynamic equations that we shall solve. their boundary conditions. and the input neutrino physics (Section 2.1)).," In this Section we first describe the hydrodynamic equations that we shall solve, their boundary conditions, and the input neutrino physics (Section \ref{sec:hydro}) )."811 We describe our scheme of coupling the eeffects to the hydrodynamical equations in Section 2.2..., We describe our scheme of coupling the effects to the hydrodynamical equations in Section \ref{sec:cno}.812" Our combination of steady-state approach and simple treatment of aallows us to calculate £77""... quantify the maximum possible effect of oon £577, as a function of boundary conditions. and set limits on the parameter space. which can then be probed with more realistic methods."," Our combination of steady-state approach and simple treatment of allows us to calculate $\lcrit$ quantify the maximum possible effect of on $\lcrit$ as a function of boundary conditions, and set limits on the parameter space, which can then be probed with more realistic methods."813" We use the code developed in PaperI. to calculate the structure of the steady-state accretion flow between the neutrinosphere at radius r7, and the standoff accretion shock at rs assuming spherical symmetry by solving the time-independent Euler equations", We use the code developed in \citetalias{pejcha12} to calculate the structure of the steady-state accretion flow between the neutrinosphere at radius $\rnu$ and the standoff accretion shock at $\rs$ assuming spherical symmetry by solving the time-independent Euler equations814curves is found by ruunimg mauv simulations for various initial densities and metallicities. wutil they satisfv the fraginentation criterion (C— E44) at Ζ and density ng.,"curves is found by running many simulations for various initial densities and metallicities, until they satisfy the fragmentation criterion ${\cal L} = \Gamma_{\rm ad}$ ) at $Z_{\rm crit}$ and density $n_f$."815 The double-valucducss 3i imnauy of the parabolic curves is explained by Figure [. which shows the cooling rates and equilibria for gas with »;= lcm?5m and three mictallicitics.," The double-valuedness in many of the parabolic curves is explained by Figure \ref{fig:coolingequilib}, which shows the cooling rates and equilibria for gas with $n_i = 1$ $^{-3}$ and three metallicities."816 Table 2 summuarizes the results of Figure 3. by choosing three particular values of temperature and deusity relevant for this studyw., Table \ref{tab:lowhighdcritm} summarizes the results of Figure \ref{fig:paracoolmcool} by choosing three particular values of temperature and density relevant for this study.817 The first coluunu shows the temperature and density of the eas., The first column shows the temperature and density of the gas.818 For the low-deusity case. we choose the set of three curves corresponding to an initial density of 0.1 7. while the high-density case starts at 105 3.," For the low-density case, we choose the set of three curves corresponding to an initial density of 0.1 $^{-3}$, while the high-density case starts at $10^4$ $^{-3}$."819 We beein at 7;=200 Ix. aud after the eas cools down. we choose two more temperatures. 150 I& aud 100 I and their corresponding densities.," We begin at $T_i = 200$ K, and after the gas cools down, we choose two more temperatures, 150 K and 100 K and their corresponding densities."820 The next four columns show the metallicity at those temperatures and deusities during fragmentation., The next four columns show the metallicity at those temperatures and densities during fragmentation.821 In the fourth coluun. all metal lines are included in the cooling function.," In the fourth column, all metal lines are included in the cooling function."822"The last column shows the Jeaus mass. fp, at fragmentation. taken from ?.. where Thay is the temperature at fraeieutation aud ay is the hydrogen nuuber density.","The last column shows the Jeans mass, $M_J \propto T^{3/2}/\rho^{1/2}$ , at fragmentation, taken from \cite{CB03}, where $T_{\rm{frag}}$ is the temperature at fragmentation and $n_H$ is the hydrogen number density."823 The ατα critical uectallicitics are calculated from Figure 3 and shown in Figure 5.., The minimum critical metallicities are calculated from Figure \ref{fig:paracoolmcool} and shown in Figure \ref{fig:minimetallicity}.824 The bottom panel of Figure 5 shows two sets of curves. to illustrate the sleht differences in fragiieutation criteria when one equates Pag to cooling bv inetals-ouly (dashed dines) aud to total cooling (solid lines).," The bottom panel of Figure \ref{fig:minimetallicity} shows two sets of curves, to illustrate the slight differences in fragmentation criteria when one equates $\Gamma_{\rm ad}$ to cooling by metals-only (dashed lines) and to total cooling (solid lines)."825 In both cases. oue cun see the transition frou non-LTE to LTE of particular ciissiou lues.," In both cases, one can see the transition from non-LTE to LTE of particular emission lines."826 The iminimuuni value in each curve corresponds to the critical deusity of the line (see Table 1))., The minimum value in each curve corresponds to the critical density of the line (see Table \ref{tab:mabundances}) ).827 Thecurves turn around when collisional de-excitation of the lues starts to dominate for each metal., Thecurves turn around when collisional de-excitation of the lines starts to dominate for each metal.828 The volume cooling- rate then scales as à» rather than D»7., The volume cooling rate then scales as $n$ rather than $n^2$.829 Thed cooling: eficiency is reduced. aud. higher abundanuces of metals are needed to reach fragmentation.," The cooling efficiency is reduced, and higher abundances of metals are needed to reach fragmentation."830 Table 23. shows the values of the inuumnmui critical ietallicities for the fracmentation criterion. and for several values of gas density.," Table \ref{tab:minimumcritical} shows the values of the minimum critical metallicities for the fragmentation criterion, and for several values of gas density."831 We choose a range iu deusities. from na=Ol cm C. just below the mean density of eas iu viralized halos at += 20. up to," We choose a range in densities, from $n = 0.1$ $^{-3}$ , just below the mean density of gas in virialized halos at $z = 20$ , up to"832"The ADAF accretion rates derived at 8.5 GHz. in both normalized (ir) and absolute (AL, form. have cousequences for the predicted levels of X-ray emission from these quiescent elliptica galaxies. aud these predicted levels must not violate the observed levels.","The ADAF accretion rates derived at 8.5 GHz, in both normalized $\dot{m}_{\rm A}$ ) and absolute $\dot{M}_{\rm A}$ ) form, have consequences for the predicted levels of X-ray emission from these quiescent elliptical galaxies, and these predicted levels must not violate the observed levels."833 Only oue galaxy. 11291. is a weak X-ray emitter aud the other three remain undetected in the ROSAT All Sky Survey (Beuiugetal.1999).," Only one galaxy, 4291, is a weak X-ray emitter and the other three remain undetected in the ROSAT All Sky Survey \citep{beu99}."834. That survey was conducted with the Position Sensitive Proportional Counter at soft. X-rays (0.5-2 keV uid at an angular resolution of 0.5., That survey was conducted with the Position Sensitive Proportional Counter at soft X-rays (0.5-2 keV) and at an angular resolution of $\sim 0.5\arcmin$.835 The table gives values for. or upper limits to. the observed soft. X-ray. luminosities. Lgvss. scaled to the Magorrianetal.(1995) distances.," The table gives values for, or upper limits to, the observed soft X-ray luminosities, $L_{\rm836RASS}$, scaled to the \citet{mag98} distances."837 No deprojection analysis has yet been attempted for 11291. since no ROSAT data [rom the High Resolution Lnager are available.," No deprojection analysis has yet been attempted for 4291, since no ROSAT data from the High Resolution Imager are available."838 Data at hard X-rays (2-10 keV) are also lackiug., Data at hard X-rays (2-10 keV) are also lacking.839 Au elliptical galaxy harboring an ADAF will be a source of X-rays from the ADAF itself aud [rom the galaxys interstellar tmecium., An elliptical galaxy harboring an ADAF will be a source of X-rays from the ADAF itself and from the galaxy's interstellar medium.840 Each photon source will be discussed in turn., Each photon source will be discussed in turn.841 The normalized ADAF accretion rates derived at 8.5 GHz are so low that bremsstrahlung emission. not inverse Compton scattering. will dominate the ADAEs X-rays (Mahadevan 1998).," The normalized ADAF accretion rates derived at 8.5 GHz are so low that bremsstrahlung emission, not inverse Compton scattering, will dominate the ADAF's X-rays \citep{mah97,yi98}."842.. The latter authors provide an expression for the bremsstrahlung Iuminosity of a canonical ADAF that. at the T. adopted for Equation (1). reduces to at a fiducial soft. X-ray. frequency of v=2.12xLOM Hz: and reduces to at a fiducial hard.X-ray. frequency of vy=1.45x107 Hz.," The latter authors provide an expression for the bremsstrahlung luminosity of a canonical ADAF that, at the $T_e$ adopted for Equation (1), reduces to at a fiducial soft X-ray frequency of $\nu = 2.42\times10^{17}$ Hz; and reduces to at a fiducial hardX-ray frequency of $\nu = 1.45\times10^{18}$ Hz."843 Applying the tabulated values for my aud mia to Equatious (2) aud (3) vields the tabulated preclictious for the soft aud harc X-ray luminosities of the ADAFs., Applying the tabulated values for $m_8$ and $\dot{m}_{\rm A}$ to Equations (2) and (3) yields the tabulated predictions for the soft and hard X-ray luminosities of the ADAFs.844 The predicted Iuminosities at 1 keV are consistent with the published ROSAT limits for 11561. 11621. aud 11660. as well as for the ROSAT detection of [1291 but only if that detection is domiuated by the galaxys interstellar inecdiuum rather than by its ADAF (Beuiugetal.1999).," The predicted luminosities at 1 keV are consistent with the published ROSAT limits for 4564, 4621, and 4660, as well as for the ROSAT detection of 4291 but only if that detection is dominated by the galaxy's interstellar medium rather than by its ADAF \citep{beu99}."845. Note further that the ADAFs are expected to be six times more Iuininous at hard than at soft. X-rays. so these galaxies must must be cousidered prime targets for observations iu the 2-10 keV region with the Advanced Satellite for Cosmologyand. Astrophysics (Tanaka.Inoue.&Holt1991).," Note further that the ADAFs are expected to be six times more luminous at hard than at soft X-rays, so these galaxies must must be considered prime targets for observations in the 2-10 keV region with the Advanced Satellite for Cosmologyand Astrophysics \citep{tan94}."846. Solt X-rays can also arise from au elliptical’s general interstellar mecdituu (Fabian&CanizaresMahacevanL907:DiMatteoetal. 2000).," Soft X-rays can also arise from an elliptical's general interstellar medium \citep{fab88,mah97,dim00}."847. For the galaxies in this study. a Bondi analysis of that medium can produce an estimate for the Bondi accretion rate. Alp. which can then be compared with the absolute ADAF accretion rate. Aly. derived at 8.5 GHz.," For the galaxies in this study, a Bondi analysis of that medium can produce an estimate for the Bondi accretion rate, $\dot{M}_{\rm B}$, which can then be compared with the absolute ADAF accretion rate, $\dot{M}_{\rm A}$ , derived at 8.5 GHz."848 The black hole masses from Magorrianetal.(1998).. in combination with 77=1 being typical for elliptical galaxies (DiMatteoetal.2000).. results in the Boncli radii listed in the table.," The black hole masses from \citet{mag98}, in combination with $T_7 =8491$ being typical for elliptical galaxies \citep{dim00}, results in the Bondi radii listed in the table."850 Assuming further that the pressure. P=10°2 * K.at the Boudi radius satisfies 2;=1—10 (DiMatteoetal.2000).. then the table gives the correspouclit£& range in Boucdi accretion rates. Adp.," Assuming further that the pressure, $P = 10^6 P_6$ $^{-3}$ K, at the Bondi radius satisfies $P_6 = 1-10$ \citep{dim00}, then the table gives the corresponding range in Bondi accretion rates, $\dot{M}_{\rm B}$ ."851 The Bondi rate estimates for P;=1 are generally consistent. with the limits on the absoluteADAF rates. Aa. imposed," The Bondi rate estimates for $P_6852= 1$ are generally consistent with the limits on the absoluteADAF rates, $\dot{M}_{\rm A}$ , imposed"853clusters reside. along with many metal-poor clusters).,"clusters reside, along with many metal-poor clusters)."854 As described in Paper I. for the bulge clusters only skv spectra far [rom the bulge of M31. were used.," As described in Paper II, for the bulge clusters only sky spectra far from the bulge of M31 were used."855 A separate offset exposure for such fields. taken concurrently and about 5” offset [rom the targets. was reduced in a similar wav (so (hat contemporaneous sky subtraction was performed for on- and off-target exposures). and then these off-target local background spectra were subtracted [rom the on-largel.," A separate offset exposure for such fields, taken concurrently and about $\arcsec$ offset from the targets, was reduced in a similar way (so that contemporaneous sky subtraction was performed for on- and off-target exposures), and then these off-target local background spectra were subtracted from the on-target."856 Relative (lux calibration. aimed at removing the signatures of instrumental ancl abmospheric transmission. was achieved using observations of fIux stanclards.," Relative flux calibration, aimed at removing the signatures of instrumental and atmospheric transmission, was achieved using observations of flux standards."857 The MW GC spectra were collected with the CTIO Blanco 4 m telescope. equipped with the Ritchey-Chréttien spectrograph. mounted at the telescopes Casseerain locus.," The MW GC spectra were collected with the CTIO Blanco 4 m telescope, equipped with the Ritchey-Chréttien spectrograph, mounted at the telescope's Cassegrain focus."858 Given the extended nature of Galactic GCs. observations were executed by drift scanning the targets with a 5'.5-long slit. over the range of x one GC core radius. r.. taken from Ilarris(1996).," Given the extended nature of Galactic GCs, observations were executed by drift scanning the targets with a $\arcmin$ .5-long slit, over the range of $\pm$ one GC core radius, $r_c$, taken from \cite{ha96}."859. Additional exposures in areas surrounding the target GCs were obtained for background-subtraction purposes., Additional exposures in areas surrounding the target GCs were obtained for background-subtraction purposes.860 One-dimensional spectra were extracted by coadcding the columns contained within a €~lr. spatial window centered on (he peak of each GC's light profile.," One-dimensional spectra were extracted by coadding the columns contained within a $\pm\,\sim\,1\,r_c$ spatial window centered on the peak of each GC's light profile."861 Therefore. for most GCs. the 1-D spectra sample a core radius-sized square spatial region (butseeSchiavonetal.2005.lorexceptions).," Therefore, for most GCs, the 1-D spectra sample a core radius-sized square spatial region \citep[but see ][for exceptions]{s05}."862 No significant. variations in Lick index measurements were found. between spectra (hat sample different spatial regions. for anv of the 9 GCs [or which such spectra were available.," No significant variations in Lick index measurements were found between spectra that sample different spatial regions, for any of the 9 GCs for which such spectra were available."863 The spectra. were wavelength-calibrated in the usual fashion., The spectra were wavelength-calibrated in the usual fashion.864 The resulüng 1D waveleneth-calibrated spectra cover the region between 3360 and 6430 A. with a spectral dispersion of L A ! and a resolution of ~ 3.1 A.," The resulting 1D wavelength-calibrated spectra cover the region between 3360 and 6430 ${\rm\AA}$, with a spectral dispersion of 1 ${\rm\AA}$ $^{-1}$ and a resolution of $\sim$ 3.1 ${\rm\AA}$."865 Relative [αν calibration was achieved in the usual fashion. using observations of spectrophotometric standards.," Relative flux calibration was achieved in the usual fashion, using observations of spectrophotometric standards."866 Even though the two sets of GC spectra were obtained with different instruments.," Even though the two sets of GC spectra were obtained with different instruments,"867period.,period.868 There is also no evidence for the secondary minima being shifted from phase 0.5. implying that eccentricity is negligible.," There is also no evidence for the secondary minima being shifted from phase 0.5, implying that eccentricity is negligible."869 Our time-resolved spectroscopic dataset consists of 38 observations covering the wavelength rangeΑΑ.. of which six were taken during secondary eclipse when the wo stars have very similar velocities.," Our time-resolved spectroscopic dataset consists of 38 observations covering the wavelength range, of which six were taken during secondary eclipse when the two stars have very similar velocities."870 We have measured radial velocities (RVs) from the remaining 32 spectra. concentrating on he wwavelength range which contains a multitude of spectral lines but avoids the very broad H feature.," We have measured radial velocities (RVs) from the remaining 32 spectra, concentrating on the wavelength range which contains a multitude of spectral lines but avoids the very broad $\gamma$ feature."871 We have considered hree different methods of measuring the velocity amplitudes of he component stars of CCet. and this redundancy allows consistency checks and the assignment of robust measurement uncertainties.," We have considered three different methods of measuring the velocity amplitudes of the component stars of Cet, and this redundancy allows consistency checks and the assignment of robust measurement uncertainties."872 A large number of standard stars were observed using the same observational setup as for our target star., A large number of standard stars were observed using the same observational setup as for our target star.873 Inspection of these yielded five which have a similar appearance to the spectra of the components of CCet: 339945 (spectral type VV). 332115(AS8 TV). 337594 VVs). 9905 ITV» and 224740 TEV).," Inspection of these yielded five which have a similar appearance to the spectra of the components of Cet: 39945 (spectral type V), 32115 IV), 37594 Vs), 905 IV) and 24740 IV)."874 These will be used as template spectra in the analyses below., These will be used as template spectra in the analyses below.875 Numerical cross-correlation (Simkin1974:Tonry&Davis1979) is a standard approach for measuring RVs from the spectra of celestial objects.," Numerical cross-correlation \citep{Simkin74aa,TonryDavis79aa} is a standard approach for measuring RVs from the spectra of celestial objects."876 We used our own implementation ofthis method(ONECOR: Southworth&Clausen 2007)) after binning all spectra onto a common logarithmic wavelength scale., We used our own implementation ofthis method; \citealt{MeClausen07aa}) ) after binning all spectra onto a common logarithmic wavelength scale.877 The cross-correlation functions (CCFs) were interactively assigned weights based on two factors: signal to noise and the velocity separation of the components of CCet., The cross-correlation functions (CCFs) were interactively assigned weights based on two factors: signal to noise and the velocity separation of the components of Cet.878 These weights were fixed for all subsequent analyses. and we have verified that their precise values do not have a significant effect on the resulting RVs.," These weights were fixed for all subsequent analyses, and we have verified that their precise values do not have a significant effect on the resulting RVs."879 Each template spectrum was cross-correlated against the spectra of CCet. and the positions of the two peaks were measured using quadratic interpolation.," Each template spectrum was cross-correlated against the spectra of Cet, and the positions of the two peaks were measured using quadratic interpolation."880 The resulting RVs were fitted with spectroscopic orbits using the code., The resulting RVs were fitted with spectroscopic orbits using the code.881 Orbits were fitted for the two stars separately (see Southworthetal.2004a and Popper&Hill 1991»)., Orbits were fitted for the two stars separately (see \citealt{Me++04mn} and \citealt{PopperHill91aj}) ).882 Fits including orbital eccentricity yielded values which were small and not significantly different from zero. as expected from the period study refsec:period)}. so our final results were calculated with eccentricity fixed at zero.," Fits including orbital eccentricity yielded values which were small and not significantly different from zero, as expected from the period study \\ref{sec:period}) ), so our final results were calculated with eccentricity fixed at zero."883 The outcome of this analysis was velocity amplitude measurements for the two of CCet CAy and Aq) and for each of the five template spectra reftab:K IK)., The outcome of this analysis was velocity amplitude measurements for the two of Cet $K_{\rm A}$ and $K_{\rm B}$ ) and for each of the five template spectra \\ref{tab:k1k2}) ).884 RVs found from cross-correlation analyses are known to show slight biases due to effects such as line blending (Petrie&An-drews1966) and individual spectral lines being Doppler-shifted into or out of the considered wavelength range (e.g.Torresetal.1997:Clausenetal. 2008)..," RVs found from cross-correlation analyses are known to show slight biases due to effects such as line blending \citep{PetrieAndrews66aa} and individual spectral lines being Doppler-shifted into or out of the considered wavelength range \citep[e.g.][]{Torres+97aj,Clausen+08aa}."885 These biases can be measured and thus removed by constructing synthetic composite spectra with known RVs and measuring them in the same way as the observed spectra., These biases can be measured and thus removed by constructing synthetic composite spectra with known RVs and measuring them in the same way as the observed spectra.886 We have performed this analysis using our five observed template spectra and the method discussed by Southworth&Clausen (2007)..., We have performed this analysis using our five observed template spectra and the method discussed by \citet{MeClausen07aa}.887 We find that removing these biases from the measured RVs results in velocity amplitudes whose values are almost unchanged but whose uncertainties are noticeably lower: the results are given in reftab:Kk HK2.., We find that removing these biases from the measured RVs results in velocity amplitudes whose values are almost unchanged but whose uncertainties are noticeably lower; the results are given in \\ref{tab:k1k2}.888. The algorithm. introduced by Zucker&Mazeh(1994) calculates a two-dimensional CCF for a double-lined spectrum using two template spectra.," The algorithm, introduced by \citet{ZuckerMazeh94apj} calculates a two-dimensional CCF for a double-lined spectrum using two template spectra."889 This approach is aimed at avoiding line blending when the two target stars have quite different spectral characteristics. although Southworth&Clausen(2007) found that it is no better than for spectroscopic binaries containing two similar stars.," This approach is aimed at avoiding line blending when the two target stars have quite different spectral characteristics, although \citet{MeClausen07aa} found that it is no better than for spectroscopic binaries containing two similar stars."890 This is the case with CCet. but the relatively low rotational velocities of its components mean that line blending is not a significant problem.," This is the case with Cet, but the relatively low rotational velocities of its components mean that line blending is not a significant problem."891 We used our own implementation of (Southworthal.20040) and the same method and template stars as for in deriving A and wp., We used our own implementation of \citep{Me++04mn} and the same method and template stars as for in deriving $K_{\rm A}$ and $K_{\rm B}$ .892 This process included the measurement and removal of RV biases. using synthetic spectra constructed from the observed template spectra.," This process included the measurement and removal of RV biases, using synthetic spectra constructed from the observed template spectra."893 In each case we, In each case we894and spatially-correlated signals from one another.,and spatially-correlated signals from one another.895 The degeneracy caused by not being able to retrieve the component's signs or amplitudes can be circumvented in two ways: 1) The separated signals are used to construct a linear transformation to filter the astrophysical signal from the originally observed data and hence preserve all scaling information; 2) The separated astrophysical signal is not used directly but instead all systematic noise components are combined to form a ‘systematic noise model’ which can then be used to correct the original observed data., The degeneracy caused by not being able to retrieve the component's signs or amplitudes can be circumvented in two ways: ) The separated signals are used to construct a linear transformation to filter the astrophysical signal from the originally observed data and hence preserve all scaling information; ) The separated astrophysical signal is not used directly but instead all systematic noise components are combined to form a `systematic noise model' which can then be used to correct the original observed data.896 We have explored the efficiency of the signal de-trending on two simulated and two HST/NICMOS data sets with different types of systematic noise due to different grisms., We have explored the efficiency of the signal de-trending on two simulated and two HST/NICMOS data sets with different types of systematic noise due to different grisms.897 The simulations demonstrate the two methods of de-trending the data in an idealised case and explore the efficiency of the signal separation in the presence of varying Gaussian noise in the data., The simulations demonstrate the two methods of de-trending the data in an idealised case and explore the efficiency of the signal separation in the presence of varying Gaussian noise in the data.898" In the instantaneous mixing model employed here, Gaussian noise sources are only indirectly allowed and can interfere with the effectiveness of separating non-Gaussian vectors."," In the instantaneous mixing model employed here, Gaussian noise sources are only indirectly allowed and can interfere with the effectiveness of separating non-Gaussian vectors."899 We tested this point by adding additional Gaussian noise components of variable amplitude to the simulations but did not observe any significant reductions in the signal separation efficiency., We tested this point by adding additional Gaussian noise components of variable amplitude to the simulations but did not observe any significant reductions in the signal separation efficiency.900 We proceeded to analyse two HST/NICMOS data sets: the primary eclipses of HD189733b and XO1b., We proceeded to analyse two HST/NICMOS data sets: the primary eclipses of HD189733b and XO1b.901 For both data sets we find the2 to yield better results., For both data sets we find the to yield better results.902" In the case of HD189733b, we can achieve a near perfect de-correlation of astrophysical signal and systematic noise and no further steps are necessary to the de-correlation process."," In the case of HD189733b, we can achieve a near perfect de-correlation of astrophysical signal and systematic noise and no further steps are necessary to the de-correlation process."903 A more in depth discussion of this data set and HST/NICMOS systematics is beyond the scope of this publication., A more in depth discussion of this data set and HST/NICMOS systematics is beyond the scope of this publication.904 In the case of XO1b the de-correlation is significant but incomplete., In the case of XO1b the de-correlation is significant but incomplete.905 The difference in maximum de-correlation achievable can be attributed to the systematic noise sources being strong functions of wavelength in the case of HD189733b whilst almost with constant weighting (ay; in equation 2)) in the case of XO1b., The difference in maximum de-correlation achievable can be attributed to the systematic noise sources being strong functions of wavelength in the case of HD189733b whilst almost with constant weighting ${a}_{kl}$ in equation \ref{intro2}) ) in the case of XO1b.906" Whenever systematics have constant weighting per channel observed (2) and/or time, it becomes very difficult for PCA or ICA based approaches to de-correlate the signal from the systematics."," Whenever systematics have constant weighting per channel observed $x_{k}$ ) and/or time, it becomes very difficult for PCA or ICA based approaches to de-correlate the signal from the systematics."907 Here auxiliary information of the instrument is, Here auxiliary information of the instrument is908The light curve for J060938—333508 (Fig. 27)),The light curve for $-$ 333508 (Fig. \ref{fig:J060938-333508}) )909 shows MOST and NVSS non-detections followed by a single MOST detection., shows MOST and NVSS non-detections followed by a single MOST detection.910" Unlike the vast majority of sources in the MOST archive, the MOST contours appear rotated with respect to the MOST beam possibly indicating a change in flux density over the 12 hr synthesis time."," Unlike the vast majority of sources in the MOST archive, the MOST contours appear rotated with respect to the MOST beam possibly indicating a change in flux density over the 12 hr synthesis time."911" The MOST contours are centred 9 arcsec from the centre of Fairall 1138, a galaxy with spectral type SBab D (?) and with redshift z=0.037 (?).."," The MOST contours are centred 9 arcsec from the centre of Fairall 1138, a galaxy with spectral type SBab D \citep{Dressler88} and with redshift $z=0.037$ \citep{1998AJ....115..418D}."912" Assuming the radio source and galaxy are associated, the inferred isotropic radio luminosity from the brightest epoch (2004 December 9) is Ly~6x10?ergs!Hz! at 843 MHz."," Assuming the radio source and galaxy are associated, the inferred isotropic radio luminosity from the brightest epoch (2004 December 9) is $L_{\nu} \simeq 6 \times 10^{29} \unit{erg~s^{-1}~Hz^{-1}}$ at 843 MHz."913" 'The offset from the centre of the optical galaxy, and the fact that spiral galaxies rarely contain an AGN argues against an AGN source for the radio variability."," The offset from the centre of the optical galaxy, and the fact that spiral galaxies rarely contain an AGN argues against an AGN source for the radio variability."914" The spectral luminosity is very high for à RSN and we are unable to discriminate between Type Ib/c or Type II RSNe by the light curve time-scales, as the time interval between the detection and non-detection epochs is too large."," The spectral luminosity is very high for a RSN and we are unable to discriminate between Type Ib/c or Type II RSNe by the light curve time-scales, as the time interval between the detection and non-detection epochs is too large."915 The spectral luminosity of J060938—333508 is within the range of GRB afterglows., The spectral luminosity of $-$ 333508 is within the range of GRB afterglows.916" It is also within the error circle of GRB 940526B, which occurred after the MOST non-detection in 1993, and 10 years before the MOST detection."," It is also within the error circle of GRB 940526B, which occurred after the MOST non-detection in 1993, and 10 years before the MOST detection."917" If J060938—333508 is the radio afterglow of GRB 940526B, then the radio detection 10 years after the gamma ray event is unlike known GRB afterglows, which typically peak at 843 MHz a few weeks after the explosion and fade over about 3 years."," If $-$ 333508 is the radio afterglow of GRB 940526B, then the radio detection 10 years after the gamma ray event is unlike known GRB afterglows, which typically peak at 843 MHz a few weeks after the explosion and fade over about 3 years."918 We consider an association of GRB 940526B and J060938—333508 unlikely., We consider an association of GRB 940526B and $-$ 333508 unlikely.919 We consider an unusual stellar event in Fairall 1138 as the likely interpretations of this source., We consider an unusual stellar event in Fairall 1138 as the likely interpretations of this source.920 The light curve for SUMSS J055712—381106 (Fig. 28)), The light curve for SUMSS $-$ 381106 (Fig. \ref{fig:J055712-381105}) )921" shows an NVSS detection followed by a MOST detection approximately 10 years later and then a non-detection 6 days after that, consistent with either a flaring source or a highly variable source occasionally appearing above our sensitivity limit."," shows an NVSS detection followed by a MOST detection approximately 10 years later and then a non-detection 6 days after that, consistent with either a flaring source or a highly variable source occasionally appearing above our sensitivity limit."922 The MOST contours appear slightly elongated and rotated with respect to the MOST beam possibly indicating achange in flux density over the 12 hr synthesis time., The MOST contours appear slightly elongated and rotated with respect to the MOST beam possibly indicating a change in flux density over the 12 hr synthesis time.923 Flaring or scintillating AGN or flaring radio stars are possible counterparts with these properties., Flaring or scintillating AGN or flaring radio stars are possible counterparts with these properties.924" The SuperCOSMOS B image shows what appears to be a blend of three objects, a star-like object to the south, a faint star-like object immediately to its north, and an extended object to the north-east."," The SuperCOSMOS B image shows what appears to be a blend of three objects, a star-like object to the south, a faint star-like object immediately to its north, and an extended object to the north-east."925 The MOST and NVSS radio sources cannot be conclusively associated with any of the three sources in the optical, The MOST and NVSS radio sources cannot be conclusively associated with any of the three sources in the optical926Yusifov. LAL. Alpar. M.A.. Gokk. F.. Guseinov. O.IL 1995. ΜΙΑ. Alpar. U.. Iizilogllu. J. van Paraclijs (eds.),"Yusifov, I.M., Alpar, M.A., Gökk, F., Guseinov, O.H. 1995, M.A. Alpar, Ü.. loğllu, J. van Paradijs (eds.)"927 The Lives of the Neutron Stars. P.201. Dordrecht: Kluwer.," The Lives of the Neutron Stars, P.201, Dordrecht: Kluwer."928relative to the mean age remains constant.,relative to the mean age remains constant.929 In the Appendix this effect is demonstrated analytically., In the Appendix this effect is demonstrated analytically.930 Only in models with mild morphological evolution to z21 (indicated by the broken lines in refmodeldata.plot)) we find an increase of the scatter with redshift., Only in models with mild morphological evolution to $z=1$ (indicated by the broken lines in \\ref{modeldata.plot}) ) we find an increase of the scatter with redshift.931 In these models the scatter is very low at z=0. and at z>0.5 reaches values similar to those in models with strong morphological evolution.," In these models the scatter is very low at $z=0$, and at $z>0.5$ reaches values similar to those in models with strong morphological evolution."932 The progenitor bias of the models is shown in panel (c)., The progenitor bias of the models is shown in panel (c).933 We define the progenitor bias at given redshift as the difference between the M/L ratio of early-type galaxies and the W/L ratio of all progenitors of present-day early-type galaxies., We define the progenitor bias at given redshift as the difference between the $M/L$ ratio of early-type galaxies and the $M/L$ ratio of all progenitors of present-day early-type galaxies.934 This is the “error” m the observed M/L ratio that is caused by the late addition of early-type galaxies to the sample., This is the “error” in the observed $M/L$ ratio that is caused by the late addition of early-type galaxies to the sample.935 As the figure shows. the bias increases with increasing tranformation time scale 7 and increasing. f...," As the figure shows, the bias increases with increasing tranformation time scale $\taustop$, and increasing $f_*$."936 Both parameters also cause the scatter to (op.increase., Both parameters also cause the scatter to increase.937 For models with strong morphological evolution the progenitor bias can be approximated by This approximation is accurate to <10 This result suggests that the progenitor bias can be estimated on the basis of the observed transformation rate. and the observed scatter.," For models with strong morphological evolution the progenitor bias can be approximated by This approximation is accurate to $\lesssim 10$ This result suggests that the progenitor bias can be estimated on the basis of the observed transformation rate, and the observed scatter."938 The star formation history ας the individual galaxies. as parametrized by f... is not needed to estimate the effect.," The star formation history is the individual galaxies, as parametrized by $f_*$, is not needed to estimate the effect."939 This 1s à very useful result. as it is difficult to constrain the value of f. directly from the observed colors and luminosities.," This is a very useful result, as it is difficult to constrain the value of $f_*$ directly from the observed colors and luminosities."940 Panels (d). (e). and (f) show the effect of changing the time of onset of star formation fa44. While keeping the star formatio history constant at. f.=0.5 (Le. approximately constant star formation from £4 to 44).," Panels (d), (e), and (f) show the effect of changing the time of onset of star formation $\tstart$, while keeping the star formation history constant at $f_*=0.5$ (i.e., approximately constant star formation from $\tstart$ to $\tstop$ )."941 The evolution of the mean M/L ratio for the vartous models is shown in panel (f)., The evolution of the mean $M/L$ ratio for the various models is shown in panel (f).942 The evolutio is very sensitive to the time of onset of star formation: there is an almost linear relation between the time when star formatio commences and the rate of M/L evolution., The evolution is very sensitive to the time of onset of star formation: there is an almost linear relation between the time when star formation commences and the rate of $M/L$ evolution.943 The reason for this behaviour is that the mean age of the stellar population in all galaxies is lower for higher values of 44., The reason for this behaviour is that the mean age of the stellar population in all galaxies is lower for higher values of $\tstart$.944 As will be shown 1 the observed evolution of the mean M/L ratio places strong constraints on the time when star formation commenced in early-type galaxies., As will be shown in \\ref{mc.sec} the observed evolution of the mean $M/L$ ratio places strong constraints on the time when star formation commenced in early-type galaxies.945 The scatter and the progenitor bias are shown in panels (e) and (f)., The scatter and the progenitor bias are shown in panels (e) and (f).946 They both depend on the value of t44. such that the scatter is higher and the progenitor bias stronger for later onset of star formation.," They both depend on the value of $\tstart$, such that the scatter is higher and the progenitor bias stronger for later onset of star formation."947 As a result of this dual dependence the relation between the progenitor bias and the observed scatter refprogz.eq)) Is not very sensitive to the value of t4. once again indicating that the observed rate of morphological evolution and the observed scatter suffice to estimate the progenitor bias.," As a result of this dual dependence the relation between the progenitor bias and the observed scatter \\ref{progz.eq}) ) is not very sensitive to the value of $\tstart$, once again indicating that the observed rate of morphological evolution and the observed scatter suffice to estimate the progenitor bias."948 The models deseribed in the previous Section can be applied to observations of early-type galaxies in. clusters at I., The models described in the previous Section can be applied to observations of early-type galaxies in clusters at $0<z<1$ .949 Parameters to fit are the evolution of the early-type galaxy fraction. the mean M/Lp ratio. as determined from the Fundamental Plane. the scatter in Πρ. and the scatter in the color-magnitude relation.," Parameters to fit are the evolution of the early-type galaxy fraction, the mean $M/L_B$ ratio, as determined from the Fundamental Plane, the scatter in $M/L_B$, and the scatter in the color-magnitude relation."950 Free parameters are the morphological transformation rate (parameterized by Tap). and the star formation histories of galaxies prior to the transformations (parameterized by f£. and tua).," Free parameters are the morphological transformation rate (parameterized by $\taustop$ ), and the star formation histories of galaxies prior to the transformations (parameterized by $\fstar$ and $\tstart$ )."951 The evolution of the early-type galaxy fraction in clusters is shown in refbestfit.plot((a) (taken from van Dokkum et 22000)., The evolution of the early-type galaxy fraction in clusters is shown in \\ref{bestfit.plot}( (a) (taken from van Dokkum et 2000).952 Data points are from Dressler (1980). Andreon. Davoust. Heim (1997). Dressler et ((1997). Lubin et ((1998). Fabricant et ((2000). and van Dokkum et ((2000).," Data points are from Dressler (1980), Andreon, Davoust, Heim (1997), Dressler et (1997), Lubin et (1998), Fabricant et (2000), and van Dokkum et (2000)."953 The early-type fraction decreases by a factor ~2 from z20 to zz1., The early-type fraction decreases by a factor $\sim 2$ from $z=0$ to $z=1$.954 The scatter around the downward trend is significant. and it will be interesting in the future to explore systematic differences in the evolution depending on cluster type.," The scatter around the downward trend is significant, and it will be interesting in the future to explore systematic differences in the evolution depending on cluster type."955 In this Section we do not distinguish elliptical galaxies and SO galaxies within the class of early-type galaxies., In this Section we do not distinguish elliptical galaxies and S0 galaxies within the class of early-type galaxies.956 In refESO.sec we explore models in which both classes are modeled separately., In \\ref{ES0.sec} we explore models in which both classes are modeled separately.957 The evolution of the early-type galaxy fraction is possibly influenced by the inclusion of low mass galaxies undergoing star bursts., The evolution of the early-type galaxy fraction is possibly influenced by the inclusion of low mass galaxies undergoing star bursts.958 Since the samples are magnitude selected. the presence of such galaxies at high redshift would decrease the fraction of early-type galaxies. and would be unrelated to the evolution of massive galaxies.," Since the samples are magnitude selected, the presence of such galaxies at high redshift would decrease the fraction of early-type galaxies, and would be unrelated to the evolution of massive galaxies."959 For the cluster at z=0.83 we have a large data set of confirmed members with accurate colors (van Dokkum et 22000). and we tested the importance of this effect by determining the early-type galaxy fraction among red galaxies alone.," For the cluster at $z=0.83$ we have a large data set of confirmed members with accurate colors (van Dokkum et 2000), and we tested the importance of this effect by determining the early-type galaxy fraction among red galaxies alone."960 If we limit the analysis to red galaxies with (U—B).>0.3 the early-type fraction changes from mass galaxies has a minor effect on the fraction of early-type galaxies., If we limit the analysis to red galaxies with $(U-B)_z >0.3$ the early-type fraction changes from mass galaxies has a minor effect on the fraction of early-type galaxies.961 Other effects may have the opposite effect., Other effects may have the opposite effect.962 As an example. biases introduced by the selection of the clusters themselves probably cause us to underestimate the evolution of the early-type galaxy fraction (see. e.g.. Kauffmann 1995).," As an example, biases introduced by the selection of the clusters themselves probably cause us to estimate the evolution of the early-type galaxy fraction (see, e.g., Kauffmann 1995)."963" The evolution of the rest frame W/L, ratio with redshift is shown in refbestfit.plot((b) and is taken from van Dokkum et ((19982).", The evolution of the rest frame $M/L_B$ ratio with redshift is shown in \\ref{bestfit.plot}( (b) and is taken from van Dokkum et (1998a).964 Data are from Jorrgensen et ((1996). van Dokkum Franx (1996). Kelson et ((1997). and van Dokkum et ((1998a).," Data are from rgensen et (1996), van Dokkum Franx (1996), Kelson et (1997), and van Dokkum et (1998a)."965 The M/L ratio evolution is derived from the evolution of the zeropoint of the Fundamental Plane relation (see van Dokkum Franx 1996)., The $M/L$ ratio evolution is derived from the evolution of the zeropoint of the Fundamental Plane relation (see van Dokkum Franx 1996).966 The evolution is well determined. because the Fundamental Plane has very small scatter.," The evolution is well determined, because the Fundamental Plane has very small scatter."967 The seatter in InM/Lg) is shown in refbestfit.plot((c)., The scatter in $\ln (M/L_B)$ is shown in \\ref{bestfit.plot}( (c).968 The data point at ς O is from Jérrgensen et ((1996)., The data point at $z\approx 0$ is from rgensen et (1996).969 Data points at higher redshift are from Kelson et ((2000) (z2 0.33). Kelson et ((1997) (z2 0.58). and van Dokkum et ((1998a) (z= 0.83).," Data points at higher redshift are from Kelson et (2000) $z=0.33$ ), Kelson et (1997) $z=0.58$ ), and van Dokkum et (1998a) $z=0.83$ )."970 The highest redshift points have considerable uncertainty. because theyare derived from small samples.," The highest redshift points have considerable uncertainty, because theyare derived from small samples."971 The scatter in the UL—B color-magnitude relation is taken from van Dokkum et ((2000) and shown in refbestfit.plot((d)., The scatter in the $U-B$ color-magnitude relation is taken from van Dokkum et (2000) and shown in \\ref{bestfit.plot}( (d).972 Data are from Stanford et ((1998). Bower. Lucey. Ellis (1992). Ellis et ((1997). van Dokkum et ((1998b). and vanDokkum et ((2000).," Data are from Stanford et (1998), Bower, Lucey, Ellis (1992), Ellis et (1997), van Dokkum et (1998b), and vanDokkum et (2000)."973 The observations were brought to à common (rest frame) band by using o(U— and e(U—B)Z0.66(U ). as derived from the Worthey (1994) models.," The observations were brought to a common (rest frame) band by using $\sigma (U-B) = 1.4 \sigma (B-V)$ and $\sigma (U-B) = 0.6 \sigma (U-V)$ , as derived from the Worthey (1994) models."974 The scatter is —Vroughly constant with redshift. at σι—B)~0.03 magnitudes.," The scatter is roughly constant with redshift, at $\sigma (U-B) \approx 0.03$ magnitudes."975We applied our orbit recovery technique to nine Milky,We applied our orbit recovery technique to nine Milky976for galaxies fünter than My=21.,for galaxies fainter than $M_K=-21$.977 This treud is hardly seuificaut., This trend is hardly significant.978 The fact that theεως and € estimates are very close means that tlrere are no artifacts due to clustering., The fact that the$1/V_{\rm max}$ and $C^-$ estimates are very close means that there are no artifacts due to clustering.979 0.15ca Tn Table 3H) we list the pax:uneters of the STY estimate or the [0.1] aud [1.2| samples.," 0.15cm In Table \ref{tab_lfk_sty} we list the parameters of the STY estimate for the $[0,1]$ and $[1,2]$ samples."980 The most impressive results we can uote from Fie., The most impressive results we can note from Fig.981 11 are the very wide range of absolute maguitudes covered by the data aud the »ossibilitv of Comptine for the first time the NIR LES at redshifts iu the raneoe [1.2]. where many difficulties arise or the traditional spectrosccpy.," \ref{lf_k_hdfns} are the very wide range of absolute magnitudes covered by the data and the possibility of computing for the first time the NIR LFs at redshifts in the range $[1,2]$, where many difficulties arise for the traditional spectroscopy."982 Moreover. this redshift range is of paraniotit importance in the study of galaxy onmuation aud evohion. as we will discuss iu Sect. 6..," Moreover, this redshift range is of paramount importance in the study of galaxy formation and evolution, as we will discuss in Sect. \ref{discuss}."983 In Fig., In Fig.984" 15 We SILILewize the results given in Table .. showi18o 16 60 alu| AI,-(AB)ACAD) parameterst arc1 heir respective errors as a fππποτίοι of redshift. derived or the two adopte cosimologies."," \ref{zalpham} we summarize the results given in Table \ref{tab_lfk_sty}, showing the $\alpha$ and $M^*_K({\rm AB})$ parameters and their respective errors as a function of redshift, derived for the two adopted cosmologies."985 We also compu LFs in tl1ο J-band., We also computed LFs in the $J$ -band.986" In this case. we selected eaaxies the J filter when considering the lowest redshift bi MN .cwlhDereas wο estimated. the J-baud i1 the highes redsdlüt range (2phor© [L.2]) using the A, bid seleced subsuuples."," In this case, we selected galaxies in the $J$ filter when considering the lowest redshift bin [0,1], whereas we estimated the $J$ -band in the highest redshift range $z_{\rm phot} \in [1,2]$ ) using the $K_s$ -band selected subsamples."987 Iu his wav we select the object.. approxiuatelv i itie J-baud rest-frame aud we can check if the assuniptiolis made for t1ο A baud LE computation were safe., In this way we select the objects approximately in the $J$ -band rest-frame and we can check if the assumptions made for the $K_s$ band LF computation were safe.988" We seleced objects inthe IIDE-N with J<21.6 oe1i the redsüft range |0.1] arc Lwith A,x 21in :=[1.2]. COLYYCSDOLKΠιο to objects witi S/N&3."," We selected objects in the HDF-N with $J989\le 24.6$ in the redshift range $[0,1]$ and with $K_s \le 24$ in $z=[1,2]$, corresponding to objects with $S/N \ge 3$."990" At these limits the colours iu the IIDE-N anc LIIDF-S are very simular: at J—21.6. the mean ssi, id1 [0.1] is 0.57 in the HIDE-N and 0.50 i the IIDE-S: at Ay=21 the mean Ley)Iv in;=[1.2] is 1.65 in the IIDE-N aud it is 1.85 in the IIDE-S. The values of VYVinax? are 0.56.0.13 in he redshitt ranges thorC[O.1) anel |1.2]. respectively. for he ITIDE-N. and 0.51.0.17 int 1C sade redshift ranges for he IIDE-S. Iu Fig."," At these limits the colours in the HDF-N and HDF-S are very similar: at $J = 24.6$, the mean $I_{814}-J$ in $[0,1]$ is $0.57$ in the HDF-N and $0.50$ in the HDF-S; at $K_s = 24$ the mean $I_{814}-K$ in $z=[1,2]$ is $1.65$ in the HDF-N and it is $1.85$ in the HDF-S. The values of $\left<V/V_{\rm max}\right>$ are $0.56, 0.43$ in the redshift ranges $z_{\rm phot} \in [0,1]$ and $[1,2]$ , respectively, for the HDF-N, and $0.51, 0.47$ in the same redshift ranges for the HDF-S. In Fig."991 16 we ]dot the LFs obtained with the ado]ated parauetiric aud noL parametric imetrods in he redshitt ranges [U.1] aud |:2|. as well as the Cole et ((2001)) local LF estimate in the 2dFCRS. x1OWL as a reference.," \ref{lf_j_hdfns} we plot the LFs obtained with the adopted parametric and non parametric methods in the redshift ranges $[0,1]$ and $[1,2]$, as well as the Cole et \cite{cole1}) ) local LF estimated in the 2dFGRS, shown as a reference."992" Oi estimate and he Cole et ((2001)) 01ο, suitablv transforued in AB inaguitudes (AM,=—21.10. 0.03. o=(0.0108 computed with cosinclogy 09=1.04=0 and only f-correction to iatch the same conditiojs we used}. seen to be iu disagreement. mainviu he normalization."," Our estimate and the Cole et \cite{cole1}) ) one, suitably transformed in AB magnitudes $M^*_J=-21.40$, $\alpha=-0.93$ , $\phi^*=0.0108$ computed with cosmology $\Omega_0=1, \Omega_\Lambda=0$ and only $k$ -correction to match the same conditions we used), seem to be in disagreement, mainly in the normalization."993 IToxees«y. the conrxuison between our LF estimate obtained iu tιο flat A-cdomiunated cosiioουν and the analogous one ccmuputed by Cole et al.," However, the comparison between our LF estimate obtained in the flat $\Lambda$ -dominated cosmology and the analogous one computed by Cole et al."994 2001 outiallv iitieates the difference., \cite{cole1} partially mitigates the difference.995 Table 4| contains he values of the Scheciter xuadneters o ‘the J-haud LF obtained in the two redslift ranges for the IIDE-N aud IIDE-S. We have also compted he LF iu the Z7 aud £ baids for the IIDE-N aud IIDE-S catalogues., Table \ref{tab_lfj_sty} contains the values of the Schechter parameters of the $J$ -band LF obtained in the two redshift ranges for the HDF-N and HDF-S. We have also computed the LF in the $H$ and $I$ bands for the HDF-N and HDF-S catalogues.996 Ii all cases. we found simular results for the wo fields.," In all cases, we found similar results for the two fields."997 We estimated LEs in two cosmologies: the “old” Standard CDM wih Oy=I aud O4=0. aud a flat cosinological coustant donmünated motel. that nowadays is the inost accepted one. with 04=L3 and O4— 0.7.," We estimated LFs in two cosmologies: the “old” Standard CDM with $\Omega_0=1$ and $\Omega_\Lambda=0$, and a flat cosmological constant dominated model, that nowadays is the most accepted one, with $\Omega_0=0.3$ and $\Omega_\Lambda=0.7$ ."998 The iuflueuce of cosmology in the photoletric redshift computatiou is uceelieible. as discussed ba* Dolzonella et (20003). thus we used the same photonetric redshifts to estimate the LFs in different cosinologles.," The influence of cosmology in the photometric redshift computation is negligible, as discussed by Bolzonella et \cite{hyperz}) ), thus we used the same photometric redshifts to estimate the LFs in different cosmologies."999 When LFs are comp.ted at low redshifts. we expect little or no differences in the estimates. as in the caseofthe 24FGRS by Cole et ((2001)). where the difference," When LFs are computed at low redshifts, we expect little or no differences in the estimates, as in the caseofthe 2dFGRS by Cole et \cite{cole1}) ), where the difference"1000The secondary. Roche-lobe-lilling stars in CVs are kev to our understanding of the origin. evolution and behaviour of this class of interacting binary.,"The secondary, Roche-lobe-filling stars in CVs are key to our understanding of the origin, evolution and behaviour of this class of interacting binary."1001 Fo best study the secondary stars in CVs. we would ideally like direct images of the stellar surface.," To best study the secondary stars in CVs, we would ideally like direct images of the stellar surface."1002 This is currently impossible. however. as typical CV. secondary stars have raclii of 400 000 km ancl distances of 200 xc. which means that to detect a feature covering 20 per cent of the star's surface requires a resolution of approximately l microarcsecond. LO 000 times greater than the dilfraction-imited resolution ofthe world's largest telescopes.," This is currently impossible, however, as typical CV secondary stars have radii of 400 000 km and distances of 200 pc, which means that to detect a feature covering 20 per cent of the star's surface requires a resolution of approximately 1 microarcsecond, 10 000 times greater than the diffraction-limited resolution of the world's largest telescopes."1003 ? and ?.iereafterreferredtoasPaperL described a way around this oblenm: using an indirect. imaging technique calledfomography which uses phasc-resolved spectra to reconstruct he line intensity distribution on the surface of the secondary star.," \citet{rutten94} and \citet[hereafter referred to as Paper1004I]{watson01} described a way around this problem using an indirect imaging technique called which uses phase-resolved spectra to reconstruct the line intensity distribution on the surface of the secondary star."1005 Obtaining surface images of the secondary star in CVs ias far-reaching implications., Obtaining surface images of the secondary star in CVs has far-reaching implications.1006 For example. a knowledge of the irradiation pattern on the inner hemisphere of the secondary star in CVs is essential if one is to calculate stellar masses accurately enough to test binary star evolution models. (see. 2)).," For example, a knowledge of the irradiation pattern on the inner hemisphere of the secondary star in CVs is essential if one is to calculate stellar masses accurately enough to test binary star evolution models (see \citealt{smith98}) )."1007 Furthermore. the irradiation. pattern provides information on the geometry of the accreting structures around the white dwarf (see ?)).," Furthermore, the irradiation pattern provides information on the geometry of the accreting structures around the white dwarf (see \citealt{smith95}) )."1008 In this paper we present new Roche tomograms of the secondary star in the dwarf nova IP Pee. and the magnetic CVs AAL Her anc QQ Vul in the light of the Na E AASISA3.8195 absorption doublet.," In this paper we present new Roche tomograms of the secondary star in the dwarf nova IP Peg, and the magnetic CVs AM Her and QQ Vul in the light of the Na I $\lambda\lambda$ 8183,8195 absorption doublet."1009 In. addition. we also present a Roche tomogram of the magnetic CV LIU Aqr in the light of the Le LE A4686. emission. line component known to originate [rom the secondary star.," In addition, we also present a Roche tomogram of the magnetic CV HU Aqr in the light of the He II $\lambda$ 4686 emission line component known to originate from the secondary star."1010 These tomograms allow a study of the irradiation. pattern on the secondary stars as well as providing measurements of the binary parameters for all four CVs., These tomograms allow a study of the irradiation pattern on the secondary stars as well as providing measurements of the binary parameters for all four CVs.1011 The spectra of OX Vul and LIU Λα were taken on the 3.5-m telescope at Calar Alto and full details of the observations, The spectra of QQ Vul and HU Aqr were taken on the 3.5-m telescope at Calar Alto and full details of the observations1012bbulge and its immediate implications.,bulge and its immediate implications.1013 We οποίο our statistical error estimates at the confidence level., We quote our statistical error estimates at the confidence level.1014 Our X-ray study was based on 31 ACIS archival observations of (taken by 2005., Our X-ray study was based on 31 ACIS archival observations of taken by 2005.1015 The majority (21 out of 31) of these observations were taken with the ACIS-I array ancl aimed toward the bbulge with the aim-points located within 1’ from the galactic center., The majority (21 out of 31) of these observations were taken with the ACIS-I array and aimed toward the bulge with the aim-points located within $^\prime$ from the galactic center.1016 To maximize the coverage and uniformity of the combined field. we utilized data only from the front-illnuminated CCDs (the ACIS-I array and the $2 chips) of the 21 observations.," To maximize the coverage and uniformity of the combined field, we utilized data only from the front-illuminated CCDs (the ACIS-I array and the S2 chips) of the 21 observations."1017 For same reason. we also included. I-chip data from four ACIS-8 observations.," For same reason, we also included I-chip data from four ACIS-S observations."1018 These data together cover a field of ro ουδ around the center ofM31., These data together cover a field of $r\sim$ $^\prime$ around the center of.1019".. Furthermore. for local sky background. determination. we used six additional ACIS-I observations which were aimed toward an ""of(L-füekl ~20! southwest to the center."," Furthermore, for local sky background determination, we used six additional ACIS-I observations which were aimed toward an “off-field” $\sim$$20^\prime$ southwest to the center."1020 We reprocessed the data using CIAO (version 3.3). following the ACIS data analvsis guide.," We reprocessed the data using CIAO (version 3.3), following the ACIS data analysis guide."1021 We generated count ancl exposure maps [ον each observation in the 0.5-1. 1-2. 2-4 and 4-8 keV bands.," We generated count and exposure maps for each observation in the 0.5-1, 1-2, 2-4 and 4-8 keV bands."1022 Corresponding instrumental background maps were generated from the “stowed” data. after calibrating the 10-12 keV count rate with individual observations.," Corresponding instrumental background maps were generated from the “stowed” data, after calibrating the 10-12 keV count rate with individual observations."1023 The total effective exposure is 295 ks in the central region and gradually drops to < 20 ks at radii rZ10’., The total effective exposure is $\sim$ 95 ks in the central region and gradually drops to $\lesssim$ 20 ks at radii $r \gtrsim 10^\prime$.1024 Following a procedure detailed in Wang (2004). we performed source detection in the κο (0.5-2 keV). hard (2-8 keV) and broad (0.5-8 keV) bands.," Following a procedure detailed in Wang (2004), we performed source detection in the soft (0.5-2 keV), hard (2-8 keV) and broad (0.5-8 keV) bands."1025 With a local false detection probability Px10.5. a total of 305 sources are detected in the field.," With a local false detection probability $P \leq 10^{-6}$, a total of 305 sources are detected in the field."1026 To study the unresolved X-ray emission. we excluded each of (he sources from maps of individual observations with circular regions enclosing ~97% of the source counts.," To study the unresolved X-ray emission, we excluded each of the sources from maps of individual observations with circular regions enclosing $\sim$ of the source counts."1027 The residual of (his source removal contributes about. of the remaining unresolved X-ray emission in the field., The residual of this source removal contributes about of the remaining unresolved X-ray emission in the field.1028 The maps were (hen reprojected to generate combined images in the four bands., The source-removed maps were then reprojected to generate combined images in the four bands.1029 We [further statistically corrected for the variation of the detection incompleteness across the field. to a common detection limit of 8x10?!eress| (0.5-8 keV).," We further statistically corrected for the variation of the detection incompleteness across the field, to a common detection limit of $\times10^{34}{\rm~ergs~s^{-1}}$ (0.5-8 keV)."1030 Decause of the relatively flat luminosity function of the sources (mostly LAINBs: Li et al., Because of the relatively flat luminosity function of the sources (mostly LMXBs; Li et al.1031 2007 in preparation: see also Voss CGilfanov 2007). the correction. (normalized. according to the 2ALASS K-band intensitv: Fig.," 2007 in preparation; see also Voss Gilfanov 2007), the correction (normalized according to the 2MASS K-band intensity; Fig."1032 Jaa: Jarrett et al., \ref{fig:unr}a a; Jarrett et al.1033 2003) typically amounts to less than of the unresolved emission., 2003) typically amounts to less than of the unresolved emission.1034 For the same reason. the residual contribution [vont LAINBs at lower luminosities," For the same reason, the residual contribution from LMXBs at lower luminosities"1035derived an EBL of 0.71-1.18. Wi? for the ALOG model in the UV band. while t and [S07 ones give 2.66 aud 3.26 (MUAm?/Sri;MORGANA respectively.,"derived an EBL of 0.71-1.18 $nW/m^2/Sr$ for the M06 model in the UV band, while the and K07 ones give 2.66 and 3.26 $nW/m^2/Sr$, respectively."1036 To sunmuarize the main results of the paper: A correct physical description of the MoACN feedback. dust properties aud star formation in the models is fundamental to cusure a reasonable agreement of the model predictions at the faint cud of the galaxy counts.," To summarize the main results of the paper: A correct physical description of the AGN feedback, dust properties and star formation activities in the models is fundamental to ensure a reasonable agreement of the model predictions at the faint end of the galaxy counts."1037 Adding colour information for ealaxies with UV enuüssiou as faiut as CU=2728 nuples very deep observations in the red bands which are feasible with several hours of integration at Sin class telescopes., Adding colour information for galaxies with UV emission as faint as $U=27-28$ implies very deep observations in the red bands which are feasible with several hours of integration at 8m class telescopes.1038 Very deep multicolour information ou areas of the order of the square deeree cau help in extracting plivsical information ou the star formation historv of the dwarf population at intermediate and high redshifts., Very deep multicolour information on areas of the order of the square degree can help in extracting physical information on the star formation history of the dwarf population at intermediate and high redshifts.1039the QSO.,the QSO.1040 Our toy model assumes a simple cut-off radius inside of which no absorbers can exist. and beyond which power-law clustering dominates.," Our toy model assumes a simple cut–off radius inside of which no absorbers can exist, and beyond which power-law clustering dominates."1041 In a more realistic model. there might be variable cut-off radius (au) dependent on the density of the absorbing cloud.," In a more realistic model, there might be variable cut–off radius $R_{\rm cut}$ ) dependent on the density of the absorbing cloud."1042 Such models are beyond the scope of the present analysis., Such models are beyond the scope of the present analysis.1043 We note that a small offset remains between the line-of-sight distributions predicted by our model and the the observed one., We note that a small offset remains between the line-of-sight distributions predicted by our model and the the observed one.1044 The magnitude of the observed offset is around KKm/s or MMpc. and may be accounted for by the fact that galaxies in the vicinity of the QSO will have a net motion caused by infall into potential well of the QSO host halo.," The magnitude of the observed offset is around km/s or Mpc, and may be accounted for by the fact that galaxies in the vicinity of the QSO will have a net motion caused by infall into potential well of the QSO host halo."1045 This will alter the observed shape and peak position of the absorber distribution., This will alter the observed shape and peak position of the absorber distribution.1046 A full treatment of infall requires detailed cosmological simulations. and will be addressed in future work.," A full treatment of infall requires detailed cosmological simulations, and will be addressed in future work."1047 On the observational side. it is clear that a careful correction of the QSO redshifts for the effect of the blue-shifting of emission lines is warranted in order to constrain the detailed shape of the aabsorber distribution.," On the observational side, it is clear that a careful correction of the QSO redshifts for the effect of the blue-shifting of emission lines is warranted in order to constrain the detailed shape of the absorber distribution."1048 Follow-up observations in the near infra-red of the aand eemission lines in a relatively large sample of high-z QSOs would provide a very useful basis for measuring these effects., Follow-up observations in the near infra-red of the and emission lines in a relatively large sample of $z$ QSOs would provide a very useful basis for measuring these effects.1049 The increase in number of QSOs from SDSS DR3 to SDSS DR7 will also further enable us to constrain the precise shape of the velocity distribution. and the fraction of dense absorbers which survive the ionising radiation of the QSO.," The increase in number of QSOs from SDSS DR3 to SDSS DR7 will also further enable us to constrain the precise shape of the velocity distribution, and the fraction of dense absorbers which survive the ionising radiation of the QSO."1050 We have used a cross-correlation analysis of QSO-absorber pairs to measure the strength of narrow absorber clustering around QSOs., We have used a cross-correlation analysis of QSO-absorber pairs to measure the strength of narrow absorber clustering around QSOs.1051 A simple model to convert the 3-D distribution of QSO-absorber separations into a line-of-sight distribution in velocity space is presented., A simple model to convert the 3-D distribution of QSO-absorber separations into a line-of-sight distribution in velocity space is presented.1052 Our modelling allows us to reach the following conclusions for ssystems: For aabsorbers we find: In the future. the larger absorber samples provided by later releases of the SDSS survey data. improved methods for obtaining reliable QSO redshifts. and investigations of ionisation and line width trends with velocity. will contribute substantially to isolating the physical processes responsible for QSO outflows detected through narrow absorption lines.," Our modelling allows us to reach the following conclusions for systems: For absorbers we find: In the future, the larger absorber samples provided by later releases of the SDSS survey data, improved methods for obtaining reliable QSO redshifts, and investigations of ionisation and line width trends with velocity, will contribute substantially to isolating the physical processes responsible for QSO outflows detected through narrow absorption lines."1053 We would like to thank Craig Hogan. Stuart Sim. Philip Best. Jeremy Blaizot. Cheng Li. and Robert Brunner or useful discussions and comments.," We would like to thank Craig Hogan, Stuart Sim, Philip Best, Jeremy Blaizot, Cheng Li, and Robert Brunner for useful discussions and comments."1054 This paper made use of the IDL MPFIT package by Craig) Markwardt rttp://cow.physics.wisc.edu/ eraign/idl/. Funding for the SDSS and SDSS-II has been provided by he Alfred P. Sloan Foundation. the Participating Institutions. the ational Science Foundation. the U.S. Department of Energy. he National Aeronautics and Space Administration. the Japanese lonbukagakusho. the Max Planck Society. and the Higher Edueation Funding Council for England.," This paper made use of the IDL MPFIT package by Craig Markwardt http://cow.physics.wisc.edu/ craigm/idl/. Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England."1055 The SDSS Web Site is rtp://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions., The SDSS Web Site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions.1056 The Participating Institutions are the American Museum of Natural History. Astrophysical Institute Potsdam. University of Basel. University of Cambridge. Case Western Reserve University. University of Chicago. Drexel University. Fermilab. the Institute for Advanced Study. the Japan Participation Group. Johns Hopkins University. he Joint Institute for Nuclear Astrophysics. the Kavli Institute or Particle Astrophysics and Cosmology. the Korean Scientist Group. the Chinese Academy of Sciences (LAMOST). Los Alamos ational Laboratory. the Max-Planck-Institute for Astronomy (ΜΡΙΑ). the Max-Planck-Institute for Astrophysics (MPA). New Texico State University. Ohio State University. University of Pittsburgh. University of Portsmouth. Princeton University. he United States Naval Observatory. and the University of Washington.," The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington."1057luminosity. of both AGN ancl quiescent nearby galaxies appears to be confined between two radio-power limits.,luminosity of both AGN and quiescent nearby galaxies appears to be confined between two radio-power limits.1058" The lower radio-power limit defines the minimum raclio luminosity that can be emitted by a given black-hole mass. and is well described by a relation of the form LsegsκAM,» in good agreement with the correlation originally observed. for nearby quiescent galaxies by Franceschini. Verecllone Fabian (1998)."," The lower radio-power limit defines the minimum radio luminosity that can be emitted by a given black-hole mass, and is well described by a relation of the form $L_{5GHz} \propto M_{bh}^{2.5}$ , in good agreement with the correlation originally observed for nearby quiescent galaxies by Franceschini, Vercellone Fabian (1998)."1059 Phe upper radio-power limit ooposed by Dunlop AleLure (2003) appears to be well described by a relation of the same functional form. olfset rom the lower limit by some 5 decades in radio luminosity.," The upper radio-power limit proposed by Dunlop McLure (2003) appears to be well described by a relation of the same functional form, offset from the lower limit by some 5 decades in radio luminosity."1060 1n contrast. the recent studies of Ho (2002) and Woo Urry (2002) find no convincing evidence for a correlation between Xack-hole mass and radio Luminosity. in ssumples comprising a range in nuclear activity [rom local quiescent galaxies up o and including powerful quasars.," In contrast, the recent studies of Ho (2002) and Woo Urry (2002) find no convincing evidence for a correlation between black-hole mass and radio luminosity, in samples comprising a range in nuclear activity from local quiescent galaxies up to and including powerful quasars."1061 In this section we investigate whether there is a correlation between black-hole mass and. racio luminosity within the ZP5 radio-galaxy sample., In this section we investigate whether there is a correlation between black-hole mass and radio luminosity within the ZP5 radio-galaxy sample.1062 In contrast to previous studies. the majority. of which have been based. on high requeney (5-Cillz) radio Iuminosity. the ZP5 radio-galaxy sample allows us to test lor à correlation between black-role mass and extended low-frequeney (151-MlIZ) racio uminositv.," In contrast to previous studies, the majority of which have been based on high frequency (5-GHz) radio luminosity, the ZP5 radio-galaxy sample allows us to test for a correlation between black-hole mass and extended low-frequency (151-MHz) radio luminosity."1063 Fhis distinction is potentially important. given hat Liziuuz is less alfected by beaming than τομ. (og., This distinction is potentially important given that $L_{151MHz}$ is less affected by beaming than $L_{5GHz}$ (eg.1064 Jarvis MeLure 2002) and has a close relationship to the inic-averaged kinetic energy of the jets (c.g. Rawlings Saunders 1991)., Jarvis McLure 2002) and has a close relationship to the time-averaged kinetic energy of the jets (e.g. Rawlings Saunders 1991).1065 The results. presented. thus far are consistent. with a picture in which extended. low-L[requeney radio Luminosity seales roughly with host-galaxv luminositv/mass., The results presented thus far are consistent with a picture in which extended low-frequency radio luminosity scales roughly with host-galaxy luminosity/mass.1066 dn combination with the latest. determination. of the A2 relation (Willott et al., In combination with the latest determination of the $K-z$ relation (Willott et al.1067 2003) it appears that the most powerful 3C-class radio galaxies reside in galaxies with R band luminosities of ~4L°. while the lower-lumuinosity 6C and TC-class radio ὃνgalaxies typically inhabit hosts with uminosities of 23L* and z2L* respectively.," 2003) it appears that the most powerful 3C-class radio galaxies reside in galaxies with $R-$ band luminosities of $\simeq 4L^{\star}$, while the lower-luminosity 6C and 7C-class radio galaxies typically inhabit hosts with luminosities of $\simeq 3L^{\star}$ and $\simeq 2L^{\star}$ respectively."1068 At present it is unclear how the TOOT sub-sample its within this picture., At present it is unclear how the TOOT sub-sample fits within this picture.1069 It can be seen from the results oesented in “Table 4. that the POO galaxies co not appear to follow the rough scaling between extended. racio uminosity anc host-galaxy luminosity apparent in the BCRR. GCE and TORS sub-samples.," It can be seen from the results presented in Table \ref{tab4} that the TOOT galaxies do not appear to follow the rough scaling between extended radio luminosity and host-galaxy luminosity apparent in the 3CRR, 6CE and 7CRS sub-samples."1070 Lacteed. the mean uminositv of the “POO sub-sample (3.28+0.5447) is ereater than that of both the TORS and GCL sub-samples. and is consistent with the low-recshilt results of Owen Laing (1989) that fat coublejet/PRL sources reside in hosts which are on average 20.5 magnitudes brighter than those of classical doublesRIL sources of comparable racio luminosity.," Indeed, the mean luminosity of the TOOT sub-sample $3.28\pm0.54 L^{\star}$ ) is greater than that of both the 7CRS and 6CE sub-samples, and is consistent with the low-redshift results of Owen Laing (1989) that fat double/jet/FRI sources reside in hosts which are on average $\simeq10710.5$ magnitudes brighter than those of classical double/FRII sources of comparable radio luminosity."1072 However. as was mentioned in Section 2. the TOOT sub-sample was drawn from a preliminary version of the survey and it is unclear at the time of writing to what extent the current TOOT sub-sample is biased bv the exclusion of the optically faintest sources.," However, as was mentioned in Section 2, the TOOT sub-sample was drawn from a preliminary version of the survey and it is unclear at the time of writing to what extent the current TOOT sub-sample is biased by the exclusion of the optically faintest sources."1073 With this in mind. panel A of Fig 10. shows 151-MllIz radio luminosity versus estimated black-hole mass for the full ZP5 sample. where the black-hole mass estimates have been derived via the Mebure Dunlop (2002) ManAdmits. relation as described in Section S.," With this in mind, panel A of Fig \ref{fig10} shows 151-MHz radio luminosity versus estimated black-hole mass for the full ZP5 sample, where the black-hole mass estimates have been derived via the McLure Dunlop (2002) $M_{bh}-M_{bulge}$ relation as described in Section 8."1074" Taken as a whole. there is only a weak (i7,=0.35.p0.027. 2.20) correlation between black-hole mass and radio luminosity within the ZP5 sample."," Taken as a whole, there is only a weak $r_{s}=0.35, p=0.027$, $2.2\sigma$ ) correlation between black-hole mass and radio luminosity within the ZP5 sample."1075" Llowever. as suggested: previously. it can be seen from panel A of Fig 10. that the apparent weakness of the Lis,Mo, correlation displayed by the full ZP5 sample is due. at least in part. to the inclusion of the eleven POO'T objects."," However, as suggested previously, it can be seen from panel A of Fig \ref{fig10} that the apparent weakness of the $L_{151}-M_{bh}$ correlation displayed by the full ZP5 sample is due, at least in part, to the inclusion of the eleven TOOT objects."1076" ‘To investigate the possible inlluence of radio structure and nuclear spectral type we have also plotted in Fig 10 the Lis)—Ads, relation for two sub-sets of the ZP5 sample.", To investigate the possible influence of radio structure and nuclear spectral type we have also plotted in Fig \ref{fig10} the $L_{151}-M_{bh}$ relation for two sub-sets of the ZP5 sample.1077" In panel B of Fig LO we show the Lis,AM, relation for those objects which display high-excitation nuclear spectra (LIEG) only.", In panel B of Fig \ref{fig10} we show the $L_{151}-M_{bh}$ relation for those objects which display high-excitation nuclear spectra (HEG) only.1078 As is suggested by the figure. this sub-sample," As is suggested by the figure, this sub-sample"1079additional optical images around five slightly more compact radio sources (also from the sample of 26 sources) to search for optical counterparts.,additional optical images around five slightly more compact radio sources (also from the sample of 26 sources) to search for optical counterparts.1080 These sources are not located in nearby galaxy clusters and their nature remains unclear., These sources are not located in nearby galaxy clusters and their nature remains unclear.1081 We end with à discussion and conclusions in Sects., We end with a discussion and conclusions in Sects.1082 5 and 6.., \ref{sec:discussion} and \ref{sec:conclusion}.1083" Throughout this paper. we assume à ACDM cosmology with Ho=71 km s! Mpc!. Q,,=0.3. and Q4=0.7."," Throughout this paper, we assume a $\Lambda$ CDM cosmology with $H_{0} = 71$ km $^{-1}$ $^{-1}$, $\Omega_{m} = 0.3$, and $\Omega_{\Lambda} = 0.7$."1084 All images are in the J2000 coordinate system., All images are in the J2000 coordinate system.1085 Radio continuum observations with the GMRT at 325 MHz were carried out on 14. 15. and 17 May. 2009.," Radio continuum observations with the GMRT at 325 MHz were carried out on 14, 15, and 17 May, 2009."1086 Both upper (USB) and lower (LSB) sidebands (IFs. which included RR and LL polarizations) were recorded with a total bandwidth of 32 MHz.," Both upper (USB) and lower (LSB) sidebands (IFs, which included RR and LL polarizations) were recorded with a total bandwidth of 32 MHz."1087 The observations were carried out in spectral line mode with 128 channels per IF to facilitate the removal of radio frequency interference (RFI) and reduce the effect of bandwidth smearing., The observations were carried out in spectral line mode with 128 channels per IF to facilitate the removal of radio frequency interference (RFI) and reduce the effect of bandwidth smearing.1088 The integration time per visibility was 8 sec., The integration time per visibility was 8 sec.1089 Each source was observed for about 4 hrs in total., Each source was observed for about 4 hrs in total.1090 The data were reduced with the NRAO Astronomical Image Processing System (AIPS) package., The data were reduced with the NRAO Astronomical Image Processing System (AIPS) package.1091 The data was visually inspected for the presence of ΕΚΕΙ. which was subsequently removed (re.. “flagged™).," The data was visually inspected for the presence of RFI, which was subsequently removed (i.e., “flagged”)."1092 We curied out an amplitude and phase calibration on the flux and bandpass calibrators 3C147 and 3C286 on a timescale of 8 sec., We carried out an amplitude and phase calibration on the flux and bandpass calibrators 3C147 and 3C286 on a timescale of 8 sec.1093 For this. we chose three neighboring frequency channels free of RFI.," For this, we chose three neighboring frequency channels free of RFI."1094 These gain solutions were applied before determining the bandpass response of the antennas., These gain solutions were applied before determining the bandpass response of the antennas.1095 This assures that any amplitude and/or phase variations during the scans on the calibrators are corrected before determining the bandpass solutions., This assures that any amplitude and/or phase variations during the scans on the calibrators are corrected before determining the bandpass solutions.1096 At higher frequencies (e.g.. 1.4 GHz). both amplitude and phases are assumed to be constant during bandpass calibration.," At higher frequencies (e.g., 1.4 GHz), both amplitude and phases are assumed to be constant during bandpass calibration."1097 However. for the GMRT observingσι at low frequencies. this assumption is not always valid and can affect the quality of the bandpass solutions as well as the determination of the flux seale.," However, for the GMRT observing at low frequencies, this assumption is not always valid and can affect the quality of the bandpass solutions as well as the determination of the flux scale."1098 After correcting for the bandpass response. both the amplitude and phase solutions for both primary and secondary calibrators were determined but in this case using the full channel range.," After correcting for the bandpass response, both the amplitude and phase solutions for both primary and secondary calibrators were determined but in this case using the full channel range."1099 The fluxes of the primary calibrators were set according to the ? extension to the ? scale., The fluxes of the primary calibrators were set according to the \cite{perleyandtaylor} extension to the \cite{1977A&A....61...99B} scale.1100 The flux densities for the secondary calibrators were bootstrapped from the primary calibrators., The flux densities for the secondary calibrators were bootstrapped from the primary calibrators.1101 The amplitude and phase solutions were interpolated and applied to the target sources., The amplitude and phase solutions were interpolated and applied to the target sources.1102" Some targets were observed over multiple days (observing runs). the resulting different data sets were combined with the AIPS task '""DBCON':."," Some targets were observed over multiple days (observing runs), the resulting different data sets were combined with the AIPS task `DBCON'."1103 For each of the target sources. we created a model of the surrounding field using the NVSS survey with a spectral index scaling of —0.7.," For each of the target sources, we created a model of the surrounding field using the NVSS survey with a spectral index scaling of $-0.7$."1104 We carried out à phase-only self-calibration against this model to improve the astrometric accuracy., We carried out a phase-only self-calibration against this model to improve the astrometric accuracy.1105 This was followed by several rounds of phase self-calibration and two final rounds of amplitude and phase self-calibration., This was followed by several rounds of phase self-calibration and two final rounds of amplitude and phase self-calibration.1106 To produce the images. we used the polyhedron method (??) to minimize the effects of non-coplanar baselines.," To produce the images, we used the polyhedron method \citep{1989ASPC....6..259P, 1992A&A...261..353C} to minimize the effects of non-coplanar baselines."1107 The model was then subtracted from the data. a step that facilitated the removal of additional. RFI or baselines with. problems.," The model was then subtracted from the data, a step that facilitated the removal of additional RFI or baselines with problems."1108 Final images were made using robust weighting (robust20.5.?)..," Final images were made using robust weighting \citep[robust = 0.5,][]{briggs_phd}."1109 Images were cleaned using the automatic clean-box windowing algorithm in AIPS and cleaned down to 2 times the rms noise level (σημ) within the clean boxes., Images were cleaned using the automatic clean-box windowing algorithm in AIPS and cleaned down to $2$ times the rms noise level $2\sigma_{\mathrm{rms}}$ ) within the clean boxes.1110 The final images were corrected for the primary beamresponse-., The final images were corrected for the primary beam.1111. The uncertainty in the calibration of the absolute flux-scale ts in the range 5—10%. see ?..," The uncertainty in the calibration of the absolute flux-scale is in the range $5-10\%$, see \cite{2004ApJ...612..974C}."1112 The resulting noise levels and beam sizes are shown in Table 1.., The resulting noise levels and beam sizes are shown in Table \ref{tab:gmrtobservations}.1113 Radio observations at 610 MHz were taken with the GMRT in February and November 2008 of the sources in Table l.., Radio observations at $610$ MHz were taken with the GMRT in February and November 2008 of the sources in Table \ref{tab:gmrtobservations}.1114 The reduction of these observations is similar to the GMRT 325 MHz data and is described in more detail in ?.., The reduction of these observations is similar to the GMRT 325 MHz data and is described in more detail in \cite{2009A&A...508...75V}.1115 We used these images to create the spectral index maps., We used these images to create the spectral index maps.1116 We carried out L-band observations of four sources with the VLA (see Table 2))., We carried out L-band observations of four sources with the VLA (see Table \ref{tab:vlaobservations}) ).1117 The observations were taken in standard continuum mode with two IFs. each having a bandwidth of 50 MHz recording all polarization products (RR. LL. RL. and LR).," The observations were taken in standard continuum mode with two IFs, each having a bandwidth of 50 MHz recording all polarization products (RR, LL, RL, and LR)."1118 Gain solutions were determined for the calibrator sources and transferred to the target sources., Gain solutions were determined for the calibrator sources and transferred to the target sources.1119 The fluxes for the primary calibrators were set according to the ? extension to the ? scale., The fluxes for the primary calibrators were set according to the \cite{perleyandtaylor} extension to the \cite{1977A&A....61...99B} scale.1120 The effective feed polarization parameters (the leakage terms or D-terms) were found by observing the phase calibrator over a wide range of parallactic angles and simultaneously solving for the unknown polarization properties of the source., The effective feed polarization parameters (the leakage terms or D-terms) were found by observing the phase calibrator over a wide range of parallactic angles and simultaneously solving for the unknown polarization properties of the source.1121 The polarization angles were set using the polarized sources 3C286 and 3C138., The polarization angles were set using the polarized sources 3C286 and 3C138.1122 For the R-L phase difference. we assumed values of —66.0 and 15.0 deg for 3C286 and 3C138. respectively.," For the R-L phase difference, we assumed values of $-66.0$ and $15.0$ deg for 3C286 and 3C138, respectively."1123 Stokes Q and U images were compiled for each source., Stokes Q and U images were compiled for each source.1124 From the Stokes Q and U images. the polarization angles (Y) were determined (V=4arctan (U/Q)).," From the Stokes Q and U images, the polarization angles $\Psi$ ) were determined $\Psi = \frac{1}{2} \arctan{(U/Q})$ )."1125 Total polarized intensity (P) images were also made (P=VQ+ U7)., Total polarized intensity $P$ ) images were also made $P = \sqrt{Q^2 + U^2}$ ).1126 The polarization fraction were found by dividing the total polarized intensity by the total intensity (Stokes D image Q7+ U7/D)., The polarization fraction were found by dividing the total polarized intensity by the total intensity (Stokes I) image $ \sqrt{Q^2 + U^2}$ /I).1127EE pli ipeum,_2 = ( ) ds.1128 Note that X aud X» depend ou the density aud magnetic structure of the cloud. but not the eraiu properties.," Note that $\Sigma$ and $\Sigma_2$ depend on the density and magnetic structure of the cloud, but not the grain properties."1129 The polarization percentage is defined by p27 where Q. C. and Fare obtained by παπάς equations L.. 5.. and 3.1 over erain species j.," The polarization percentage is defined by , where $Q$ , $U$, and $I$ are obtained by summing equations \ref{eq:Q}, , \ref{eq:U}, and \ref{eq:I} over grain species $j$ ."1130 It is easy to show that equation 3.1 becomes where (a) is a weighted iieau of 6j defiued as follows: Equations 6.. 7.. aud 3.10 show that the polarization pattern is determined by the deusitv aud magnetic structure of the eas. plus a single paramucter £05 related to the grain cross-sections aud aliguinenut properties.," It is easy to show that equation \ref{eq:pdef} becomes where $\meanalpha$ is a weighted mean of $\alphaj$ defined as follows: Equations \ref{eq:q}, \ref{eq:u}, and \ref{eq:p} show that the polarization pattern is determined by the density and magnetic structure of the gas, plus a single parameter $\meanalpha$ related to the grain cross-sections and alignment properties."1131 We estimate (a; as follows., We estimate $\meanalpha$ as follows.1132 We assume that the optimal maguetic field geometry. ii which +=0 and oe—const. gives rise to the maxi polarizationpercentagepray that is normallyobserved.," We assume that the optimal magnetic field geometry, in which $\gamma=0$ and $\psi=const$, gives rise to the maximum polarizationpercentage$p_{max}$ that is normallyobserved."1133 TheaNpolarization percentage is obtained from equation 3.1.. with the help of equations 6 aud 7:," Themaximumpolarization percentage is obtained from equation \ref{eq:p}, , with the help of equations $\ref{eq:q}$ and \ref{eq:u}: :"1134by 15-60 minutes.,by 15-60 minutes.1135 This is done to maximize the sensitivity to motion of solar svstem objects but also to benefit the detection of short period stellar variability., This is done to maximize the sensitivity to motion of solar system objects but also to benefit the detection of short period stellar variability.1136 The universal cadence excludes visits of 21.000 square degrees around the galactic center because of erowcding.," The universal cadence excludes visits of $\sim$ 1,000 square degrees around the galactic center because of crowding."1137 To simulate this universal cadence. we made use of the thal serves to evaluate the suitability of the scanning model and to (quantify the vield for individual scientific goals of the survey (7.83.1)..," To simulate this universal cadence, we made use of the that serves to evaluate the suitability of the scanning model and to quantify the yield for individual scientific goals of the survey \citepalias[\S3.1]{LSSTbook}."1138 The simulator provides an array of heliocentric Julian dates (ILJD) at which a given field will be observed., The simulator provides an array of heliocentric Julian dates (HJD) at which a given field will be observed.1139 We split the southern sky uniformly in declination: where .N is (he number of declination bands., We split the southern sky uniformly in declination: where $N$ is the number of declination bands.1140 The i-th band is then split into M; right ASCELISIONS: The factor 1.3 in the expression for M; makes the distribution in a denser to account for the pronounced universal cadence variability along a., The $i$ -th band is then split into $M_i$ right ascensions: The factor $1.3$ in the expression for $M_i$ makes the distribution in $\alpha$ denser to account for the pronounced universal cadence variability along $\alpha$.1141 Sky partitioning in this wav vielded 1558 [fields [or --30. covering all right ascensions and declinations between —90* and 10.," Sky partitioning in this way yielded 1558 fields for $N=30$, covering all right ascensions and declinations between $-90^\circ$ and $10^\circ$."1142 Fig., Fig.1143 2. depicts the number of visits per field in the r band., \ref{EB_fig_skymap} depicts the number of visits per field in the $r$ band.1144 The numbers tvpically vary from almost GOO points per lighteurve close to (he celestial equator. down to," The numbers typically vary from almost 600 points per lightcurve close to the celestial equator, down to"1145nuaee (Milios 2005).,image (Mihos 2005).1146 The nearby galaxy PGC 11098 (VCCILIS) also has a small stream emanatiug from it (Region 5)., The nearby galaxy PGC 41098 (VCC1148) also has a small stream emanating from it (Region 5).1147 There is a hint that this stream coutimucs to the northeast. ruining through the radial stream. aud connecting up with the N Phune (Region [). but this is just at our surface brightness limit we do uot consider it firmly enouch detected to photomoeter.," There is a hint that this stream continues to the northeast, running through the radial stream, and connecting up with the N Plume (Region 4), but this is just at our surface brightness limit we do not consider it firmly enough detected to photometer."1148 The Iuuinosity and λα surface brightuess of the detected features are given iu Table 1.., The luminosity and maximum surface brightness of the detected features are given in Table \ref{m87tab}.1149 To assess the autheuticitv of all these features. aud avoid confusiou with galactic cirrus. we have compared hem to far infrared IRIS observations over the same area (Miville-Descheuues Lagache 2005).," To assess the authenticity of all these features, and avoid confusion with galactic cirrus, we have compared them to far infrared IRIS observations over the same area (Miville-Deschênnes Lagache 2005)."1150 While the spatial resolution of the IRIS data is oulwLX... we fiud 10 correlation with regions of suspected galactic dust contamination. and are confident that these features are rue stellar features around MST.," While the spatial resolution of the IRIS data is only, we find no correlation with regions of suspected galactic dust contamination, and are confident that these features are true stellar features around M87."1151 Again. however. since we are explicitly avoiding the dust-coutaminated regeious o the southeast of AIST. our catalog of features is likely uuderestimating the total structure around ALS7.," Again, however, since we are explicitly avoiding the dust-contaminated regions to the southeast of M87, our catalog of features is likely underestimating the total structure around M87."1152 The long linear streams to the northwest of MBST. are sugecstive of simall satellites falling iu ou radial orbits. or onu inore tangential orbits viewed alone the orbital plane.," The long linear streams to the northwest of M87 are suggestive of small satellites falling in on radial orbits, or on more tangential orbits viewed along the orbital plane."1153 The larger NW Stream (Reeious 112) crosses the galaxy pair NGC 1158/61., The larger NW Stream (Regions 1+2) crosses the galaxy pair NGC 4458/61.1154 These two galaxies have a velocity difference of 1300 |au/s and are not likely eusaged iu any slow mutual interaction that would draw out loug tidal tails., These two galaxies have a velocity difference of 1300 km/s and are not likely engaged in any slow mutual interaction that would draw out long tidal tails.1155 It is possible. however. that the stripping of one of these galaxies as it orbits in the potential well of the cluster could have giveu rise to the NW Stream.," It is possible, however, that the stripping of one of these galaxies as it orbits in the potential well of the cluster could have given rise to the NW Stream."1156 The thinner WNW Stream (Region 3). projects across the dwarf galaxy VCC 1119. aud again could be duc to stripping of this galaxy as it orbits M87.," The thinner WNW Stream (Region 3), projects across the dwarf galaxy VCC 1149, and again could be due to stripping of this galaxy as it orbits M87."1157 The surface brightness profiles of M81 and M86 overlap at large radii Gwhere 25) and thus cannot be fit independeutlv., The surface brightness profiles of M84 and M86 overlap at large radii (where $\ga 25$ ) and thus cannot be fit independently.1158 We have µνenmiploved. an iterative process. bv alternately fitting and subtracting both galaxies.," We have employed an iterative process, by alternately fitting and subtracting both galaxies."1159 Our fit show that MSIE is better fit with a fixed center (a =12:25:03.8. 6= |12:53:13.2 T2000) and that AfSG best fit isophotes have a ceuter that drifts south cast sabout 150 aresecouds from the initial center of (a =12:26:11.8. 8 =|12:56:16.6 J2000).," Our fits show that M84 is better fit with a fixed center $\alpha=$ 12:25:03.8, $\delta=$ +12:53:13.2 J2000) and that M86's best fit isophotes have a center that drifts south east about $150$ arcseconds from the initial center of $\alpha=$ 12:26:11.8, $\delta=$ +12:56:46.6 J2000)."1160 The ceutroid diiff is small at high surface brishtuess. but is more significant for the faint outer isophotes.," The centroid drift is small at high surface brightness, but is more significant for the faint outer isophotes."1161" At far= 25. the ceuter has drifted less than 107, auc the more significant drifting occurs fainter than j= 27."," At = 25, the center has drifted less than $10''$, and the more significant drifting occurs fainter than = 27."1162 We begin our iterative process by masking ALS6 and making au initial fit to AIS with limited radial extent.," We begin our iterative process by masking M86 and making an initial fit to M84, with limited radial extent."1163 We subtract this MSL fit L.from the nuage. mask the residuals near MISts center. unmask ALS6. and make au initial fit to M86.," We subtract this M84 fit from the image, mask the residuals near M84's center, unmask M86, and make an initial fit to M86."1164 We then subtract the M86 ft from the original iniage. again masking the iucr residual. aud make a new fit to M81. over a larger radial ranec.," We then subtract the M86 fit from the original image, again masking the inner residual, and make a new fit to M84, over a larger radial range."1165" We continue this iterative process for 5 steps. uutil we have fit both galaxies out to Raj,= ffor MISG and Reyyy= Που M81."," We continue this iterative process for 5 steps, until we have fit both galaxies out to $\rsma =$ for M86 and $\rsma =$ for M84."1166 Because of the complexity of the fitting process. and the crowded nature of the field surromnding ALS1 aud AISG. our fits do not extend to the nominal limit of µη 29.," Because of the complexity of the fitting process, and the crowded nature of the field surrounding M84 and M86, our fits do not extend to the nominal limit of = 29."1167 As noted above. we find that as we reach jr 27. the ceutroid of the ft begius drifting siguificautly. at about he same point where the isoplotes beein cucoupassine other galaxies in the field.," As noted above, we find that as we reach = 27, the centroid of the fit begins drifting significantly, at about the same point where the isophotes begin encompassing other galaxies in the field."1168 We therefore take this brighter iudt of p— 27 as the liit of our fitting process when extracting the analytic profile fits. aud show this as our outermost isoplote in Figure L.," We therefore take this brighter limit of = 27 as the limit of our fitting process when extracting the analytic profile fits, and show this as our outermost isophote in Figure \ref{subtract_m84m86m89}."1169 The isophotal ELLIPSE fits for both M81 and M86 are shown in Figure 2.., The isophotal ELLIPSE fits for both M84 and M86 are shown in Figure \ref{allfits}.1170 We compare our surface brightness. ellipticity. aud xositiou angle profiles with those of Caon (1990). Poletier (1990). and I&09 in B8. R. and V. bauds. respectively.," We compare our surface brightness, ellipticity, and position angle profiles with those of Caon (1990), Peletier (1990), and K09 in $B$, $R$, and $V$ bands, respectively."1171 For M8SÍ. we again find good agrecment )etwoeen those studies aud ours. save for discrepancies in. the position⋅⋅ angle ucar Fi17d.," For M84, we again find good agreement between those studies and ours, save for discrepancies in the position angle near $\rsma^{1/4}\sim 4$."1172 Tn this. region.. rowever. the ellipticity is so close to zero that the exact value of the position angle has little weaning.," In this region, however, the ellipticity is so close to zero that the exact value of the position angle has little meaning."1173 The Sérrsic and 2dV fits for MBS1 (given in Table 2)) vield a total unumnositv of 7.2 and 6.5 «101E... respectively. aud iu he 2dV fit the outer component carrics of the total unmdnositv.," The Sérrsic and 2dV fits for M84 (given in Table \ref{sbfits}) ) yield a total luminosity of 7.2 and 6.5 $\times 10^{10} L_{\sun}$ respectively, and in the 2dV fit the outer component carries of the total luminosity."1174 For Ms6. the comparison between our profiles aud hose previously published is) eood throughout.," For M86, the comparison between our profiles and those previously published is good throughout."1175 Iu articular we uote that the hup in the surface xiehtuess profile of M86. near IRAN~d ds also seeu in the M86 profile of IK09., In particular we note that the hump in the surface brightness profile of M86 near $\rsma^{1/4}\sim 4$ is also seen in the M86 profile of K09.1176 This feature complicates the analytic fitting process (Table 2)). vielding u values sjenificautle worse thin for any other galaxy in our saluple.," This feature complicates the analytic fitting process (Table \ref{sbfits}) ), yielding $\chi^2$ values significantly worse than for any other galaxy in our sample."1177 Our Sévrsic fit differs dramatically from that of 09. but as IK09 shows. the rauge of radii chosen to fit he profile has a significant effect on the fit parameters.," Our Sérrsic fit differs dramatically from that of K09, but as K09 shows, the range of radii chosen to fit the profile has a significant effect on the fit parameters."1178" 1909 do not fit past Ria—3,5, and so their fit excludes he hump."," K09 do not fit past $\rsma^{1/4} = 3.5$, and so their fit excludes the hump."1179 If sve Bit our fif to a similar range. our fit xuinueters more closely match those of I&09.," If we limit our fit to a similar range, our fit parameters more closely match those of K09."1180 The 2dV fit is similarly poor. consisting of a small high surface xiehtuess immer component. and an outer component which contains of the light.," The 2dV fit is similarly poor, consisting of a small high surface brightness inner component, and an outer component which contains of the light."1181 Civen the actual shape of the profile. we do not consider this 2dV fit to be physically mieaniusful.," Given the actual shape of the profile, we do not consider this 2dV fit to be physically meaningful."1182 The total huuinositv of MBSG is 9.3 and 9.2 «1019E. under the Séórrsie aud 2dV fits. respectively.," The total luminosity of M86 is 9.3 and 9.2 $\times 10^{10} L_{\sun}$ under the Sérrsic and 2dV fits, respectively."1183 We subtract the combined M86 aud MSIE models frou the original mage. vieldiug the residual iiage shown im Figure L.," We subtract the combined M86 and M84 models from the original image, yielding the residual image shown in Figure \ref{subtract_m84m86m89}."1184 We note that in this case the mask displaved ou the final residuals is a subset of the mask that is used in the fitting procedure., We note that in this case the mask displayed on the final residuals is a subset of the mask that is used in the fitting procedure.1185 The bright galaxies south aud cast of M86 have all been ageressively masked in the analysis. but are displaved im this niase for clarity.," The bright galaxies south and east of M86 have all been aggressively masked in the analysis, but are displayed in this image for clarity."1186 Iu the residual image. we mnunediatelv note the piuxclhiecl-like fins ceutered on M86. which are indicators of the boxy isophotes noted by Peletier (1990).," In the residual image, we immediately note the pinwheel-like fins centered on M86, which are indicators of the boxy isophotes noted by Peletier (1990)."1187 These features are usually represeuted as azimuthal Al Fourier colponcuts. bevoud a pure clliptical model.," These features are usually represented as azimuthal A4 Fourier components, beyond a pure elliptical model."1188 Since we do not inchide these hieher-order Fourier terms in our, Since we do not include these higher-order Fourier terms in our1189(Socderblou et al.,(Soderblom et al.1190 1991). have photometric metallicities lower than the spectroscopic values by a constant amount A.," 1991), have photometric metallicities lower than the spectroscopic values by a constant amount $\Delta$."1191 Infact. A is likely to depeud ou logRi. but for the sake of simplicity we shall adopt here an average value eiven by where \(logPu is the distribution of stellar chromospheric activity. that can be found from the combined data of Soderbloin (1985)) anc IHeurv et al. (1996)).," Infact, $\Delta$ is likely to depend on $\log R'_{\rm HK}$, but for the sake of simplicity we shall adopt here an average value given by where $\chi(\log R'_{\rm HK})$ is the distribution of stellar chromospheric activity, that can be found from the combined data of Soderblom \cite{soder})) and Henry et al. \cite{HSDB}) ),"1192 auc A is estimated by usine Eq. (, and $\Delta$ is estimated by using Eq. (11935) of Rocha- Maciel (1998)).,5) of Rocha-Pinto Maciel \cite{RPM98}) ).1194 Using Eq. (1)).," Using Eq. \ref{deltamean}) ),"1195 we have A=0.119 dex., we have $\bar\Delta=0.149$ dex.1196 The normalized photometric mctallicity distibution of he active stars. D(OFe/TII]). frou: Rocha-Pinto Maciel (1998)). is shown in Table 3..," The normalized photometric metallicity distribution of the active stars, ${\cal D}({\rm [Fe/H]})$, from Rocha-Pinto Maciel \cite{RPM98}) ), is shown in Table \ref{xdist}."1197 Tustead of ideutifving he active stars in the data sample. the approach we inve taken here assumes that a fraction c of the total iiber of stars in the sample (Npor) are active stars.," Instead of identifying the active stars in the data sample, the approach we have taken here assumes that a fraction $c$ of the total number of stars in the sample $N_{\rm tot}$ ) are active stars."1198 Therefore. the umuber of active stars in each metallicity dn is eMSQPX[Fe/II]). aud to correct the metallicity distribution. these active stars should be allocated to more uetalrich bius bv an amount of A.," Therefore, the number of active stars in each metallicity bin is $cN_{\rm tot}{\cal D}({\rm [Fe/H]})$, and to correct the metallicity distribution, these active stars should be allocated to more metal-rich bins by an amount of $\bar\Delta$."1199 The fraction e is Likely to depend ou the spectral type considered. as the chromospheric activity is thought to be caused by the interaction between the stellar rotation aud the convection iu the stella envelope.," The fraction $c$ is likely to depend on the spectral type considered, as the chromospheric activity is thought to be caused by the interaction between the stellar rotation and the convection in the stellar envelope."1200 The decrease of the outer convective zone towards hotter stars iudicates that vouug hotter stars do not show mach activity (Elearoy et al. 19973)., The decrease of the outer convective zone towards hotter stars indicates that young hotter stars do not show much activity y et al. \cite{elgaroy}) ).

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