ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 However. this too is unlikely.," However, this too is unlikely."3 It is clilficult to configure Sgr's geometry so that tidal arms are further away than the Ser core., It is difficult to configure Sgr's geometry so that tidal arms are further away than the Sgr core.4 In the enc. we conclude that the most likely explanation for the distance discrepancy between the Ser debris and M54 is that M54 is. in fact. in [ront of the main body of Ser.," In the end, we conclude that the most likely explanation for the distance discrepancy between the Sgr debris and M54 is that M54 is, in fact, in front of the main body of Sgr."5 The mean distance modulus of the Ser clusters is 17.22. shorter than the Paper IV. distance of 11.27. mostly because of the short distance we measure lor Terzan 7.," The mean distance modulus of the Sgr clusters is 17.22, shorter than the Paper IV distance of 17.27, mostly because of the short distance we measure for Terzan 7."6 Dropping Terzan 7 sets ihe mean distance modulus to 17.30., Dropping Terzan 7 sets the mean distance modulus to 17.30.7 The CMD background features have a mean distance of 17.37 and a dispersion of 0.04. indicating a Ser distance modulus between 17.32 and 17.42 (assuming a 0.05 magnitude relative uncertainty). corresponding to a linear distance of 29-30 kpe.," The CMD background features have a mean distance of 17.37 and a dispersion of 0.04, indicating a Sgr distance modulus between 17.32 and 17.42 (assuming a 0.05 magnitude relative uncertainty), corresponding to a linear distance of 29-30 kpc."8 Increasing the Ser distance. however. might change the assumed Ser populations.," Increasing the Sgr distance, however, might change the assumed Sgr populations."9 The Ser populations that we use to measure the clistance of the background main sequence features were constrained in Paper IV. based on the assumption that thev were at the same distance as M54., The Sgr populations that we use to measure the distance of the background main sequence features were constrained in Paper IV based on the assumption that they were at the same distance as M54.10 If the Ser populations were more distant. however. this would alter the ages and metallicities of the Ser populations described in Paper IV. which were based on the bluer MSTOs and RGBs of Ser. rather than the M54-dominated. AIS.," If the Sgr populations were more distant, however, this would alter the ages and metallicities of the Sgr populations described in Paper IV, which were based on the bluer MSTOs and RGBs of Sgr, rather than the M54-dominated MS."11 This could. in turn. change the distances measured for the background features from isochrone fitting.," This could, in turn, change the distances measured for the background features from isochrone fitting."12 llowever. our analvsis indicates (hat (hese changes to the measured Ser stellar populations would be minor.," However, our analysis indicates that these changes to the measured Sgr stellar populations would be minor."13 If we give Ser a line-of-distance distance modulus of (2— Afjy=17.39. we could easily align the intermediate isochrones with the observed Ser CMD features by decreasing (heir ages by 0.5-1 Gyr and perhaps increasing their abundanees by (ο 0.1 dex (see Figure 15)).," If we give Sgr a line-of-distance distance modulus of $(m-M)_0$ =17.39, we could easily align the intermediate isochrones with the observed Sgr CMD features by decreasing their ages by 0.5-1 Gyr and perhaps increasing their abundances by to 0.1 dex (see Figure \ref{f:sgrmove}) )."14 This would have little effect on the CMD background. feature distances., This would have little effect on the CMD background feature distances.15 Although the stellar population analvsis of Paper IV. was based on the MSTO and RGB. the distances in this paper were measured based solely on main sequence fitting.," Although the stellar population analysis of Paper IV was based on the MSTO and RGB, the distances in this paper were measured based solely on main sequence fitting."16 Altering, Altering17determined the distance from the presence of interstellar Ca and Na absorption features in the spectrum and obtained270+120 pc based on the interstellar absorption column (Sect. 2.8)).,determined the distance from the presence of interstellar Ca and Na absorption features in the spectrum and obtained$270\pm120$ pc based on the interstellar absorption column (Sect. \ref{sec:interstAbsDist}) ).18" In summary, we argue in favor of a distance of ~270 pc as the most likely value."," In summary, we argue in favor of a distance of $\approx 270$ pc as the most likely value."19" Because oorbits its host star at a distance of only 0.03 AU, it is immersed in an enormous high-energy radiation field."," Because orbits its host star at a distance of only $0.03$ AU, it is immersed in an enormous high-energy radiation field."20" According to CoRoT-2A’ss X-ray luminosity, the X-ray flux at the distance of CoRoT-2b’ss orbit amounts tos!,, which is five orders of magnitude larger than the solar X-ray flux received by Earth."," According to s X-ray luminosity, the X-ray flux at the distance of s orbit amounts to, which is five orders of magnitude larger than the solar X-ray flux received by Earth."21 This amount of ionizing radiation can have a significant influence on the structure and evolution of the planetary atmosphere., This amount of ionizing radiation can have a significant influence on the structure and evolution of the planetary atmosphere.22" ? found that the extent of the atmospheres of hot Jovian exoplanets can exceed the Roche lobe, leading to evaporation of planetary material by an interaction with the stellar wind."," \citet{Schneider1998} found that the extent of the atmospheres of hot Jovian exoplanets can exceed the Roche lobe, leading to evaporation of planetary material by an interaction with the stellar wind."23" Indeed, extended atmospheres of extrasolar planets were found for HD 209458 b (??) and HD 189733b (?).."," Indeed, extended atmospheres of extrasolar planets were found for HD 209458 b \citep{Vidal-Madjar2003,Linsky2010} and HD 189733b \citep{LecavelierDesEtangs2010}."24 ? analyzed a sample of planetary systems., \citet{SanzF2010} analyzed a sample of planetary systems.25 The authors come to the conclusion that erosion triggered by stellar high-energy illumination has a detectable influence on the observed mass distribution of exoplanets., The authors come to the conclusion that erosion triggered by stellar high-energy illumination has a detectable influence on the observed mass distribution of exoplanets.26" This gives rise to an ""erosion line”, below which ? the large majority of the planets in their sample."," This gives rise to an “erosion line”, below which \citet{SanzF2010} the large majority of the planets in their sample."27" To estimate the mass loss induced by the X-ray and extreme-UV (EUV) irradiation, we used Eq."," To estimate the mass loss induced by the X-ray and extreme-UV (EUV) irradiation, we used Eq."28" 2 from ?,, viz."," 2 from \citet{SanzF2011}, viz."29" where Fxuy is the sum of the stellar X-ray and EUV flux at the planetary orbit, G is the gravitational constant, and ρ is the density of the planet (all in cgs units)."," where $F_\mathrm{XUV}$ is the sum of the stellar X-ray and EUV flux at the planetary orbit, $G$ is the gravitational constant, and $\rho$ is the density of the planet (all in cgs units)."30" Because there are no EUV data of aavailable, we use Eq."," Because there are no EUV data of available, we use Eq."31" 3 from ?,, which provides a relation between X-ray and EUV luminosity calibrated with their sample of objects, to obtain an estimate of 4.3x10? ffor the expected EUV flux at the distance ofCoRoT-2b."," 3 from \citet{SanzF2011}, which provides a relation between X-ray and EUV luminosity calibrated with their sample of objects, to obtain an estimate of $4.3\times10^5$ for the expected EUV flux at the distance of."32". Substituting the parameters for citep[][Table 1]Alonso2008,, we obtained a mass-loss rate of 4.5x10!? ss! or 7.3x10-? My GGa""! for the planet."," Substituting the parameters for \\citep[][Table~1]{Alonso2008}, we obtained a mass-loss rate of $4.5\times 10^{12}$ $^{-1}$ or $7.3\times 10^{-2}$ $_\mathrm{J}$ $^{-1}$ for the planet."33" Given the uncertainties, this value remains a coarse estimate, but places cclearly above the erosion line, which, according to ?,, may be explained by the youth of the system."," Given the uncertainties, this value remains a coarse estimate, but places clearly above the erosion line, which, according to \citeauthor{SanzF2010}, may be explained by the youth of the system."34" We note, however, that by using different assumptions for the extent of CoRoT-2b'ss atmosphere (?,Eq.1), the mass-loss rate may be increased by up to one order of magnitude."," We note, however, that by using different assumptions for the extent of s atmosphere \citep[][Eq.~1]{SanzF2010}, the mass-loss rate may be increased by up to one order of magnitude."35" Moreover, the effects leading to planetary mass loss are not yet well understood."," Moreover, the effects leading to planetary mass loss are not yet well understood."36 An important consequence of our analysis is that the ssystem may extend far beyond the planetary orbit., An important consequence of our analysis is that the system may extend far beyond the planetary orbit.37" CoRoT-2A'ss visual companion, J19270636+0122577,, may actually also be a physical companion, forming a wide binary pair withCoRoT-2A."," s visual companion, , may actually also be a physical companion, forming a wide binary pair with."38. We obtained and analyzed the first low-SNR UVES spectrum of the companion., We obtained and analyzed the first low-SNR UVES spectrum of the companion.39 ? already noticed that the companion may be a late-K or early-M-type star at about the same distance asCoRoT-2A.., \citet{Alonso2008} already noticed that the companion may be a late-K or early-M-type star at about the same distance as.40" We measured the companion's radial velocity and found a value of 23.9+0.4s, which is close to CoRoT-2A’ss radial velocity."," We measured the companion's radial velocity and found a value of $23.9\pm0.4$, which is close to s radial velocity."41" By modeling the TiO bands present in the spectrum, we determined an effective temperature between 3900 and 4100 K. Wide lines of were used to infer a surface gravity of logg—4.74."," By modeling the TiO bands present in the spectrum, we determined an effective temperature between 3900 and 4100 K. Wide lines of were used to infer a surface gravity of $\log{g}=4.74$."42" Consulting the evolutionary tracks of ? at an estimated age of 200 Ma, we find that the companion is likely to be a star of spectral type K9, which is gravitationally bound toCoRoT-2A."," Consulting the evolutionary tracks of \citet{Siess2000} at an estimated age of $200$ Ma, we find that the companion is likely to be a star of spectral type K9, which is gravitationally bound to."43. This would make oone of about 40 known binary systems harboring an exoplanet (?).., This would make one of about 40 known binary systems harboring an exoplanet \citep{Mugrauer2009}.44" If this hypothesis withstands further observational tests, it would challenge our understanding of the ssystem, in particular, the age of the system."," If this hypothesis withstands further observational tests, it would challenge our understanding of the system, in particular, the age of the system."45" From the ddata we derived an upper limit of ffor the X-ray luminosity of the companion, and the ? evolutionary tracks suggest an absolute bolometric luminosity of 6.8 mag."," From the data we derived an upper limit of for the X-ray luminosity of the companion, and the \citeauthor{Siess2000} evolutionary tracks suggest an absolute bolometric luminosity of $6.8$ mag."46" Combining these numbers, we obtain—5.8,, making the companion a star much less active thanCoRoT-2A."," Combining these numbers, we obtain, making the companion a star much less active than."47". From our spectral analysis, we concluded that hhas an age between 100 and 300 Ma."," From our spectral analysis, we concluded that has an age between $100$ and $300$ Ma."48" Assuming that the companion is physically bound and has the same age asCoRoT-2A,, we would expect an X-ray flux significantly higher than observed in our ppointing."," Assuming that the companion is physically bound and has the same age as, we would expect an X-ray flux significantly higher than observed in our pointing."49" From the study of X-ray emission of members of the Pleiades cluster, ? find typical X-ray luminosities for K-stars of logLx=29.4sl, which is more than two orders of magnitude above our upper limit for the companion."," From the study of X-ray emission of members of the Pleiades cluster, \citet{Micela1996} find typical X-ray luminosities for K-stars of $\log{L_\mathrm{X}}=29.4$, which is more than two orders of magnitude above our upper limit for the companion."50" We therefore conclude that either the companion has never been an active X-ray source, which seems unusual for a young late-type star, or that the activity of the companion has already dropped to a moderate level."," We therefore conclude that either the companion has never been an active X-ray source, which seems unusual for a young late-type star, or that the activity of the companion has already dropped to a moderate level."51" Given the upper limit for the X-ray luminosity, the companion may be an evolved K-type star similar to those found in the solar neighborhood (?).."," Given the upper limit for the X-ray luminosity, the companion may be an evolved K-type star similar to those found in the solar neighborhood \citep{Schmitt1995}."52" This also agrees with the upper limit on its rotational velocity of vsini«10kms~!;; neglecting the unknown inclination, this would be a value typical for K-type stars on the main-sequence (?,p.389,Table15.8).."," This also agrees with the upper limit on its rotational velocity of $v\sin{i}<10$; neglecting the unknown inclination, this would be a value typical for K-type stars on the main-sequence \citep[][p.~389, Table~15.8]{AllenEd4}."53" We speculate that the ssystem, if bound, should be old enough to let the K-star become sufficiently inactive, while the G-star rremained more active, maybe through an interaction with its close-in planet."," We speculate that the system, if bound, should be old enough to let the K-star become sufficiently inactive, while the G-star remained more active, maybe through an interaction with its close-in planet."54" This hypothesis is backed by the recent results presented by ?,, who reported on a discrepancy between different age estimations of the host stars of the planetary systems WASP-18 and WASP-19."," This hypothesis is backed by the recent results presented by \citet{Brown2011}, who reported on a discrepancy between different age estimations of the host stars of the planetary systems WASP-18 and WASP-19."55 Both stars harbor a close-in hot Jupiter and appear to be older than attested by their gyrochronological age., Both stars harbor a close-in hot Jupiter and appear to be older than attested by their gyrochronological age.56 ? suggested that an inward migration of the hot Jupiters has caused a spin-up of their host stars via tidal interaction., \citet{Brown2011} suggested that an inward migration of the hot Jupiters has caused a spin-up of their host stars via tidal interaction.57" Alternatively, or even additionally, interactions between the planetary andstellar magnetic fields may have reduced the stellar angular- loss as proposed by ?.."," Alternatively, or even additionally, interactions between the planetary andstellar magnetic fields may have reduced the stellar angular-momentum loss as proposed by \citet{Lanza2010}. ."58 The ssystem is, The system is59(b) determinations of cosmological parameters. via &ravitational lensing measurements: (c) accurate measurements of the Sunvaev-Zel'dovich (d) observation of CAIBL. Doppler peaks by the MAD and satellites.,(b) determinations of cosmological parameters via gravitational lensing measurements; (c) accurate measurements of the Sunyaev-Zel'dovich (d) observation of CMBR Doppler peaks by the MAP and satellites.60 This will only determine parameters in the neighbourhood of ς=1000. but is independent. of source evolution all the same. (," This will only determine parameters in the neighbourhood of $z = 1000$, but is independent of source evolution all the same. ("61o) the increasing number of source evolution studies that look for tell-tale signs of carly stages of galaxy evolution. such as intense star formation. etc.,"e) the increasing number of source evolution studies that look for tell-tale signs of early stages of galaxy evolution, such as intense star formation, etc."62 Once again. the FLAW assumption is usually if not always mace in analyses of these cllects.," Once again, the FLRW assumption is usually if not always made in analyses of these effects."63 A re-analysis that permits inhomogeneity would be very worthwhile. as these techniques may well provide information complementary to the principal cosmological measures. that would help separate out the effects. of cosmic evolution. spatial inhomogeneity. anc source evolution.," A re-analysis that permits inhomogeneity would be very worthwhile, as these techniques may well provide information complementary to the principal cosmological measures, that would help separate out the effects of cosmic evolution, spatial inhomogeneity, and source evolution."64 Some of these issues are discussed in(5)., Some of these issues are discussed in.65. In fact. it is already dillicult to constrain the values of fly. qo and A within a homogeneous dust. model. because of the uncertainty in source evolution. as pointed out in(31).," In fact, it is already difficult to constrain the values of $H_0$ , $q_0$ and $\Lambda$ within a homogeneous dust model because of the uncertainty in source evolution, as pointed out in."66. In this case the value of A allects the time evolution of the scale factor. and so the deviation. of the angular diameter-redshift. relation. from. expectation for a A=0 FLEW model could. be due to non-zero A or to source evolution.," In this case the value of $\Lambda$ affects the time evolution of the scale factor, and so the deviation of the angular diameter-redshift relation from expectation for a $\Lambda=0$ FLRW model could be due to non-zero $\Lambda$ or to source evolution."67 Similarly the possible presence of non-baryonic dark matter or for that matter. the possibility that eravity obeys field equations other than Einstein's could significantly alfect the cosmic time evolution. and introduce further uncertainty.," Similarly the possible presence of non-baryonic dark matter — or for that matter, the possibility that gravity obeys field equations other than Einstein's — could significantly affect the cosmic time evolution, and introduce further uncertainty."68 The introduction. of multi-colour observations σος not resolve the problem in any simple wav., The introduction of multi-colour observations does not resolve the problem in any simple way.69 1 we have observations in various colour bands sav UU B& V then we must replace the source luminosity evolution ΠΟΙΟ bv a set of evolution functions for the luminosity in each colour., If we have observations in various colour bands — say U B V — then we must replace the source luminosity evolution function by a set of evolution functions for the luminosity in each colour.70 hus. if we find deviations of the observations from FLEW expectations. we still have a freedom to attribute this either to inhomogencity or to source evolution.," Thus, if we find deviations of the observations from FLRW expectations, we still have a freedom to attribute this either to inhomogeneity or to source evolution."71 Its true that voung ealaxies with lots of star formation are very blue., It's true that young galaxies with lots of star formation are very blue.72 Sut. having introduced. colour observations. and. permitted evolution in colour. we must also adimit the possibilitv of spatial inhomoseneities in the intrinsic colours of sources.," But, having introduced colour observations, and permitted evolution in colour, we must also admit the possibility of spatial inhomogeneities in the intrinsic colours of sources."73 We come back to the same problem are the cillerences between observations in cdillerent colours clue to. source evolution or spatial inhomogeneity?, We come back to the same problem — are the differences between observations in different colours due to source evolution or spatial inhomogeneity?74 The only dilference here is that cosmic evolution is fairly casily factored out. as the redshift’ is measured.," The only difference here is that cosmic evolution is fairly easily factored out, as the redshift is measured."75 We are not here asserting that the observable universezs inhomogeneous. nor are we suggesting that source evolution studies that assume homosenity are not worthwhile.," We are not here asserting that the observable universe inhomogeneous, nor are we suggesting that source evolution studies that assume homogenity are not worthwhile."76 The purpose of this paper is to emphasise that we don't =ave unquestionable evidence for spatial homogeneity: ancl wl we can't have a good demonstration of homogeneity or even homogeneity on average without a reliable Ἰσοῦν Of source evolution. supported. by. measurements mt are independent of cosmological model. and/or cosmic distance measures that don't depend. on knowing the uminosity evolution of sources.," The purpose of this paper is to emphasise that we don't have unquestionable evidence for spatial homogeneity; and that we can't have a good demonstration of homogeneity — or even homogeneity on average — without a reliable theory of source evolution, supported by measurements that are independent of cosmological model, and/or cosmic distance measures that don't depend on knowing the luminosity evolution of sources."77" Our best basis for assuming spatial homogeneity is the Stoeger-Maartens-Ellis theorem or ""almost EOS theorem(32). which savs that. if the universe is expanding and the CMDIU (cosmic microwave background. radiation) is almost isotropic for all observers since decoupling. then the universe is almost homogeneous. and more specifically. the scale of CMDlIt anisotropy puts a limit on the cegree> of cosmic inhomogeneity."," Our best basis for assuming spatial homogeneity is the Stoeger-Maartens-Ellis theorem or “almost EGS theorem"", which says that, if the universe is expanding and the CMBR (cosmic microwave background radiation) is almost isotropic for all observers since decoupling, then the universe is almost homogeneous, and more specifically, the scale of CMBR anisotropy puts a limit on the degree of cosmic inhomogeneity."78oO But2 this result depends on a weak form of the Copernican principle: aud however convincinge that principle is in ὃνgeneral terms. we shouldn't overstate it.," But this result depends on a weak form of the Copernican principle; and however convincing that principle is in general terms, we shouldn't overstate it."79 This line of thought savs that the earth is just another planet around the sun. but it doesn't sav alb planets are the same size or composition.," This line of thought says that the earth is just another planet around the sun, but it doesn't say all planets are the same size or composition."80 Lt says that our galaxy and our supercluster are one among many. but allows several tvpes of galaxy. and considerable variety in galaxy clustering.," It says that our galaxy and our supercluster are one among many, but allows several types of galaxy and considerable variety in galaxy clustering."81 Thus the principle does not. insist on uniformity on any scale. or even that the observable portion ofthe universe has a density particularly close to the “global average assuming we can define such a thing.," Thus the principle does not insist on uniformity on any scale, or even that the observable portion of the universe has a density particularly close to the “global average"" — assuming we can define such a thing."82 Anc above all. while it may be true in the real universe. it is also possible that this is not so.," And above all, while it may be true in the real universe, it is also possible that this is not so."83 We are entitled. to deduce homogeneity on the basis of untested philosophical principles. such as a Copernican principle: but we must be quite clear what we are doing when we make such a deduction. anc how it relates to possible observational tests.," We are entitled to deduce homogeneity on the basis of untested philosophical principles, such as a Copernican principle; but we must be quite clear what we are doing when we make such a deduction, and how it relates to possible observational tests."84 This paper helps throw light on the latter issue., This paper helps throw light on the latter issue.85 We thank Igor Darashenkov and Ronnie Becker for advice on existence of solutions. and Alan Coley and Bruce Bassett for helpful comments.," We thank Igor Barashenkov and Ronnie Becker for advice on existence of solutions, and Alan Coley and Bruce Bassett for helpful comments."86 GERI and CLL thank the FRDfor research grants., GFRE and CH thank the FRDfor research grants.87 (Strongetal.2007)., \citep{strong2007}.88. E>200 (Schlickeiser2002)..," $E>200$ \citep{julias_review}, \citep{schlickeiser2002}."89NIR results generally compare well to those of ? for the same galaxies.,NIR results generally compare well to those of \cite{Silva2008} for the same galaxies.90 Fig., Fig.91 7 presents the correlation between the optical and NIR central velocity dispersions for 19galaxies of our sample., \ref{corrCOoptical} presents the correlation between the optical and NIR central velocity dispersions for 19 galaxies of our sample.92 The solid line shows the best fit. with a slope consistent with |. an intercep consistent with O and a reduced X7 of 1.09.," The solid line shows the best fit, with a slope consistent with 1, an intercept consistent with 0 and a reduced $\chi^2$ of 1.09."93 The absence of a σ- confirms the findings by? and further generalizes their results due to the statistical completeness of this study. but does no agree with ?..," The absence of a $\sigma$ -discrepancy confirms the findings by \cite{Silva2008} and further generalizes their results due to the statistical completeness of this study, but does not agree with \cite{Silge2003}. ."94 Their best-fitting line had a slope of 1.189+0.084 and an intercept of S.6+12.4., Their best-fitting line had a slope of $1.189\pm0.084$ and an intercept of $-8.6\pm12.4$.95" 9 had difficulties in determining the velocity dispersions for galaxies with e,)kms.I and noted that the results of ~50r GOkms| are only rough estimates.", \cite{Kuntschner2000} had difficulties in determining the velocity dispersions for galaxies with $\sigma_{\rm opt}<70~\text{km s}^{-1}$ and noted that the results of $\sim50-60~\text{km s}^{-1}$ are only rough estimates.96" However. excluding the galaxies with m,«TOkms+ does not change the results significantly."," However, excluding the galaxies with $\sigma_{\rm opt}<70~\text{km s}^{-1}$ does not change the results significantly."97 Fig., Fig.98 8. presents a histogram of the fractional difference between NIR and optical measurements of dispersion., \ref{histogramfracdiff} presents a histogram of the fractional difference between NIR and optical measurements of dispersion.99 The median fractional difference between the optical and the NIR velocity dispersions is6.. the mean fractional difference is3.," The median fractional difference between the optical and the NIR velocity dispersions is, the mean fractional difference is."1009%.. found a median difference of —11%.. opposite to theoretical expectations (2) and to our results.," found a median difference of $-11$, opposite to theoretical expectations \citep{Baes2002} and to our results."101 It is not immediately clear why ?— found that NIR velocity dispersion measurements arelower than optical dispersion measurements., It is not immediately clear why \cite{Silge2003} found that NIR velocity dispersion measurements arelower than optical dispersion measurements.102 One possible reason could be the different spatial range used by ?:: Fig., One possible reason could be the different spatial range used by \cite{Silge2003}: Fig.103 | indicates that velocity dispersions can decrease for higher spatial ranges., \ref{dispersionextractionwindow} indicates that velocity dispersions can decrease for higher spatial ranges.104" The average spatial width in is ~ 12"". which may be the reason for their difference between NIR and optical velocity dispersions."," The average spatial width in \cite{Silge2003} is $\sim$ $''$, which may be the reason for their difference between NIR and optical velocity dispersions."105" In order to investigate this possibility. we recalculated the NIR velocity dispersions for all galaxies in our sample. now using an extraction window of 2"" "," In order to investigate this possibility, we recalculated the NIR velocity dispersions for all galaxies in our sample, now using an extraction window of $1''\times12''$ ."106The best-titting line. with a reduced \7 of 1.35. is fully consistent with Eq.2.," The best-fitting line, with a reduced $\chi^2$ of 1.35, is fully consistent with Eq. \ref{eq:corrCOopt}."107., Fig.108" indeedFig. "" suggests an increase of the slope of ?CJA. whichis W we find."," \ref{dispersionextractionwindow} suggests an increase of the slope of $\sim 4\%$, which is indeed what we find."109"+ Nonetheless.""m a ~20% effect is needed to explain the results found by 9. SO We exclude that the extraction width is responsible for the discrepancy."," Nonetheless, a $\sim 20\%$ effect is needed to explain the results found by \cite{Silge2003}, so we exclude that the extraction width is responsible for the discrepancy."110 Another possible explanation for the discrepancy could be the choice of the templates: Fig., Another possible explanation for the discrepancy could be the choice of the templates: Fig.111 3 showed that the measured velocity dispersion depends strongly on the equivalent width of the CO band of the template., \ref{EW_sigma_IC1963} showed that the measured velocity dispersion depends strongly on the equivalent width of the CO band of the template.112 ? usedtemplates with equivalent widths ranging from less than 5 to over 20 A., \cite{Silge2003} usedtemplates with equivalent widths ranging from less than 5 to over 20 .113. So far. we have only used the average K giant template with an equivalent width of 8.99 Α.," So far, we have only used the average K giant template with an equivalent width of 8.99 ."114". So far. we have only used the average K giant template with an equivalent width of 8.99 Α.,"," So far, we have only used the average K giant template with an equivalent width of 8.99 ."115A correlation between H» and NH; column densities is also seen. although there is somewhat more scatter in the plotted points.,"A correlation between $_2$ and $_3$ column densities is also seen, although there is somewhat more scatter in the plotted points."116 This likely reflects variation in the fractional abundance of ammonia from source to source., This likely reflects variation in the fractional abundance of ammonia from source to source.117 À mean fractional abundance of tto H» is 2.6 x . typical for most observations of protostellar regions.," A mean fractional abundance of to $_2$ is 2.6 $\times$ $^{-8}$, typical for most observations of protostellar regions."118 Using a combination of mid-infrared. submillimetre and radio images. and CO molecular line data presented in earlier works (22? we have retined the original sample of 44 BRCs.," Using a combination of mid-infrared, submillimetre and radio images, and CO molecular line data presented in earlier works \citep{Morgan2004,Morgan2008,Morgan2009}, we have refined the original sample of 44 BRCs."119 Our ettorts iive )..identified 26 bright-rimmed clouds in which the data are consistent with the hypothesis that any observed star formation is ikely to have been triggered., Our efforts have identified 26 bright-rimmed clouds in which the data are consistent with the hypothesis that any observed star formation is likely to have been triggered.120 Within this retined sample we have detected strong ammonia emission towards 15., Within this refined sample we have detected strong ammonia emission towards 15.121 In combination with he submillimetre continuum and CO line emission results of ? and ? respectively. in addition to outflow and maser detections from he literature. our ammonia detections leave little doubt of the star-orming nature of these sources.," In combination with the submillimetre continuum and CO line emission results of \citet{Morgan2008} and \citet{Morgan2009} respectively, in addition to outflow and maser detections from the literature, our ammonia detections leave little doubt of the star-forming nature of these sources."122 Having already established the ikelihood that these sources represent photoionisation-triggering wocesses in progress. these [5 sources are some of the best examples yet known of the RDI process.," Having already established the likelihood that these sources represent photoionisation-triggering processes in progress, these 15 sources are some of the best examples yet known of the RDI process."123 An investigation of our samples. separated based upon riggered status. indicates a bimodality within observations of he turbulent velocity dispersion.," An investigation of our samples, separated based upon triggered status, indicates a bimodality within observations of the turbulent velocity dispersion."124 Those sources which have been identified as likely triggered in nature show typically supersonic urbulent velocity dispersions., Those sources which have been identified as likely triggered in nature show typically supersonic turbulent velocity dispersions.125 While non-triggered sources are more often found to be subsonic., While non-triggered sources are more often found to be subsonic.126 This disparity may stem from the oresenee of shocks. traversing the clouds in the triggered sample.," This disparity may stem from the presence of shocks, traversing the clouds in the triggered sample."127 It is also possible that the higher observed velocity dispersion in the riggered sample is simply due to the higher occurence of outflows ‘ound in that sample., It is also possible that the higher observed velocity dispersion in the triggered sample is simply due to the higher occurence of outflows found in that sample.128 It is tempting to draw conclusions of ditfering johysieal processes occuring within our triggered and non-triggered samples., It is tempting to draw conclusions of differing physical processes occuring within our triggered and non-triggered samples.129 However. we are not able to determine the true cause of his finding without mapping of molecular emission in these clouds.," However, we are not able to determine the true cause of this finding without mapping of molecular emission in these clouds."130 The authors would like to thank an anonymous referee for a careful examination of this work which has resulted in considerable improvements., The authors would like to thank an anonymous referee for a careful examination of this work which has resulted in considerable improvements.131 We would like to thank the helpful of statfthe Green Bank Telescope and Bill Saxton for his assistance in creating Fig.1., We would like to thank the helpful staff of the Green Bank Telescope and Bill Saxton for his assistance in creating Fig.1.132 LKM is supported by a STFC postdoctoral grant (ST/GOOIH847/1)., LKM is supported by a STFC postdoctoral grant (ST/G001847/1).133 JSU is supported by a CSIRO OCE postdoctoral grant., JSU is supported by a CSIRO OCE postdoctoral grant.134 This research would not have been possible without the SIMBAD astronomical database service operated at CDS. Strasbourg. France and the NASA Astrophysies Data System Bibliographie Services.," This research would not have been possible without the SIMBAD astronomical database service operated at CDS, Strasbourg, France and the NASA Astrophysics Data System Bibliographic Services."135 This research makes use of data products from the MSX and 2MASS and GLIMPSE Surveys. which is are joint projects of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology. funded by the National Aeronautics and Space Administration and the National Science Foundation.," This research makes use of data products from the MSX and 2MASS and GLIMPSE Surveys, which is are joint projects of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation."136 Several sources were detected in the (3.3) and (4.4) rotational transitions of ammonia.," Several sources were detected in the (3,3) and (4,4) rotational transitions of ammonia."137 Spectra of these sources are presented in Figs., Spectra of these sources are presented in Figs.138 ?? and ?? and relevant parameters are listed in Table ΑΙ. RMS values of these observations are presented in Table A2..," \ref{img:33Spectra} and \ref{img:44Spectra} and relevant parameters are listed in Table \ref{tbl:3344}, RMS values of these observations are presented in Table \ref{tbl:non-detections3344}."139 Those sources detected in the (3.3) line of ammonia were examined for signs of masing.," Those sources detected in the (3,3) line of ammonia were examined for signs of masing."140 If masing is occuring in this transition then the brightness temperature of that source would be larger than the brightness temperature in the (1.1) transition and comparable to the (1.1) Kinetic temperature (e.g. 2).," If masing is occuring in this transition then the brightness temperature of that source would be larger than the brightness temperature in the (1,1) transition and comparable to the (1,1) kinetic temperature (e.g. \citealt{Kuiper1995}) )."141 However. none of our sources show such symptoms.," However, none of our sources show such symptoms."142 The (+4) line of ammonia may often be observed toward warmer cores (e.g. 2)). only one of our sources provided a detection in this line. SFO 14.," The (4,4) line of ammonia may often be observed toward warmer cores (e.g. \citealt{Longmore2007}) ), only one of our sources provided a detection in this line, SFO 14."143 This core is indeed one of the warmer sources in our sample at ~26K., This core is indeed one of the warmer sources in our sample at $\sim$ 26K.144picture implied by Fig. 1..,picture implied by Fig. \ref{f1}.145 If anything. not only will the subsurface strata be quite great 1n number (instead of the single stratum shown in Fig. 1)).," If anything, not only will the subsurface strata be quite great in number (instead of the single stratum shown in Fig. \ref{f1}) ),"146 but also each stratum will have complex gradients in space., but also each stratum will have complex gradients in space.147 This will cause for much difficulty in devising an accurate theoretical model for the physics of reflection seismics., This will cause for much difficulty in devising an accurate theoretical model for the physics of reflection seismics.148 This fact can be amply illustrated even by considering the very simple case of a single dipping interface with a constant spatial gradient., This fact can be amply illustrated even by considering the very simple case of a single dipping interface with a constant spatial gradient.149 When the reflecting interface is inclined at a constant angle 0. with respect to the horizontal. as it has been shown in Fig. 3..," When the reflecting interface is inclined at a constant angle $\theta$, with respect to the horizontal, as it has been shown in Fig. \ref{f2},"150 it will be necessary to make suitable modifications in the analysis presented in Section 1.. to retain the canonical form of the hyperbolic normal moveout equation that Eq. (1))," it will be necessary to make suitable modifications in the analysis presented in Section \ref{sec1}, to retain the canonical form of the hyperbolic normal moveout equation that Eq. \ref{hyper1}) )"151 represents., represents.152 This can indeedbe achieved by noting in Fig., This can indeedbe achieved by noting in Fig.153" 3 that the perpendicular distance from the source to the reflector. SN=4. the source-to-receiver distance. SR=ur. and the total travel path. SD,|D4R=cf."," \ref{f2} that the perpendicular distance from the source to the reflector, $\overline{\mrm{SN}} = d$, the source-to-receiver distance, $\overline{\mrm{SR}} = x$, and the total travel path, $\overline{\mrm{SD_1}} + \overline{\mrm{D_1 R}} = vt$."154 With this information. even upon accounting for the dip in the reflector. the invariant canonical form of the hyperbola can be obtained as with .c and ty being defined by the transformations. τμ2dsin0 and ty=(2dcos0)f c. respectively.," With this information, even upon accounting for the dip in the reflector, the invariant canonical form of the hyperbola can be obtained as with $\bar{x}$ and $\bar{t}_0$ being defined by the transformations, $\bar{x} = x - 2 d \sin \theta$ and $\bar{t}_0 =(2d\cos \theta)/{v}$ , respectively."155 From Eq. (4)).," From Eq. \ref{hyper2}) ),"156" the coordinates of the maximum point of the hyperbola (αμ.f,,) 1n the à—£ plane (with £ increasing in the downward direction) will be given by the condition ατα.=0."," the coordinates of the maximum point of the hyperbola $(x_{\mrm m},t_{\mrm m})$ in the $x$ $t$ plane (with $t$ increasing in the downward direction) will be given by the condition ${\mrm d}t/{\mrm d}x = 0$."157 This will place the peak of the hyperbola at (2dsin0.ty).," This will place the peak of the hyperbola at $(-2 d \sin \theta , \bar{t}_0)$."158 Going back to the case of the horizontal reflector (0=0). given by Eq. (1)).," Going back to the case of the horizontal reflector $(\theta = 0)$, given by Eq. \ref{hyper1}) ),"159 the peak of the hyperbola here is to be seen at (0.ty).," the peak of the hyperbola here is to be seen at $(0, t_0)$."160 Therefore. a distinct shift ts seen to arise because of the dip of the subsurface reflector. and this shift has been shown by the position of the dotted hyperbola in Fig. 2..," Therefore, a distinct shift is seen to arise because of the dip of the subsurface reflector, and this shift has been shown by the position of the dotted hyperbola in Fig. \ref{f15}."161 The locus of this shift can also be traced on the .—-f plane., The locus of this shift can also be traced on the $x$ $t$ plane.162" Noting that the coordinates of the maximum of the normal moveout hyperbola aregiven by c,=—2dsn0 and f,= fy.one could. by making use of the standard trigonometric. result. iu202@|cos?D0=4 1. derive. the condition."," Noting that the coordinates of the maximum of the normal moveout hyperbola aregiven by $x_{\mrm m}=-2d\sin \theta$ and $t_{\mrm m}=\bar{t}_0$ ,one could, by making use of the standard trigonometric result, $\sin^2 \theta + \cos^2 \theta = 1$ , derive the condition,"163" Noting that the coordinates of the maximum of the normal moveout hyperbola aregiven by c,=—2dsn0 and f,= fy.one could. by making use of the standard trigonometric. result. iu202@|cos?D0=4 1. derive. the condition.l"," Noting that the coordinates of the maximum of the normal moveout hyperbola aregiven by $x_{\mrm m}=-2d\sin \theta$ and $t_{\mrm m}=\bar{t}_0$ ,one could, by making use of the standard trigonometric result, $\sin^2 \theta + \cos^2 \theta = 1$ , derive the condition,"164" Noting that the coordinates of the maximum of the normal moveout hyperbola aregiven by c,=—2dsn0 and f,= fy.one could. by making use of the standard trigonometric. result. iu202@|cos?D0=4 1. derive. the condition.ll"," Noting that the coordinates of the maximum of the normal moveout hyperbola aregiven by $x_{\mrm m}=-2d\sin \theta$ and $t_{\mrm m}=\bar{t}_0$ ,one could, by making use of the standard trigonometric result, $\sin^2 \theta + \cos^2 \theta = 1$ , derive the condition,"165" Noting that the coordinates of the maximum of the normal moveout hyperbola aregiven by c,=—2dsn0 and f,= fy.one could. by making use of the standard trigonometric. result. iu202@|cos?D0=4 1. derive. the condition.ll."," Noting that the coordinates of the maximum of the normal moveout hyperbola aregiven by $x_{\mrm m}=-2d\sin \theta$ and $t_{\mrm m}=\bar{t}_0$ ,one could, by making use of the standard trigonometric result, $\sin^2 \theta + \cos^2 \theta = 1$ , derive the condition,"166nova rale per unit luminosity. or if the nova rate is influenced by the mass of the host ealaxv.,"nova rate per unit luminosity, or if the nova rate is influenced by the mass of the host galaxy."167 We used the SITe based 1024x1024 pixel CCD camera on the Tenagra 0.8 m telescope for our observations of the local group dwarls., We used the SITe based 1024x1024 pixel CCD camera on the Tenagra 0.8 m telescope for our observations of the local group dwarfs.168 This configuration vields a pixel scale of Q78ST t and a field size of 15 on a side. allowing us to cover each galaxy in ils entirety for each epoch of observation.," This configuration yields a pixel scale of 87 $^{-1}$ and a field size of 15' on a side, allowing us to cover each galaxy in its entirety for each epoch of observation."169" The majority of the survey observations were taken through a standard Johnson V filter,", The majority of the survey observations were taken through a standard Johnson V filter.170 This filler was chosen to maximize (he sensitivity of the telescope and detector combination., This filter was chosen to maximize the sensitivity of the telescope and detector combination.171 Once a nova was discovered. we initiated additional observations through the standard Johnson D filter to derive nova colors.," Once a nova was discovered, we initiated additional observations through the standard Johnson B filter to derive nova colors."172" Each individual exposure was 300s. except for M32 which required a shorter exposure time of 150s to avoid saturating the nuclear region,"," Each individual exposure was 300s, except for M32 which required a shorter exposure time of 150s to avoid saturating the nuclear region."173 We attempted to have 15 minutes total exposure time per epoch., We attempted to have 15 minutes total exposure time per epoch.174 Most epochs reached this goal. with only a lew having less exposure time.," Most epochs reached this goal, with only a few having less exposure time."175 The seeing for our observations had a median of 2755 and ranged [from 1777 to 4755., The seeing for our observations had a median of 5 and ranged from 7 to 5.176 Our survey ran [rom October 04. 2003 (JD 2452916.3) to February 13. 2004 (JD 2453053.6) covering a total of 136.8 davs.," Our survey ran from October 04, 2003 (JD 2452916.8) to February 18, 2004 (JD 2453053.6) covering a total of 136.8 days."177 An additional epoch in the I-band was generously obtained for us bv John Thorstensen using the Echelle direct CCD camera on the Hiltner 2.4m telescope., An additional epoch in the I-band was generously obtained for us by John Thorstensen using the Echelle direct CCD camera on the Hiltner 2.4m telescope.178 In addition. he was able to obtain (wo spectra using the Mocdspec on the 2.4m on JD 2453017.60 and two spectra on JD 2453022.60. allowing us to confirm the nature of the M22 nova.," In addition, he was able to obtain two spectra using the Modspec on the 2.4m on JD 2453017.60 and two spectra on JD 2453022.60, allowing us to confirm the nature of the M32 nova."179 We were also fortunate that7787 images were available in the archive of both novapositionst., We were also fortunate that images were available in the archive of both nova.180. For M32 nova 1 we used WEDPC? images taken on JD, For M32 nova 1 we used WFPC2 images taken on JD181We find a large difference in the number density of blue galaxies as predicted by the SAM and observed in the VVDS-Deep.,We find a large difference in the number density of blue galaxies as predicted by the SAM and observed in the VVDS-Deep.182" While the trends with redshift are rather similar, the SAM predicts more blue galaxies than observed over the whole redshift interval 0.2<z1.6 in the VVDS-Deep."," While the trends with redshift are rather similar, the SAM predicts more blue galaxies than observed over the whole redshift interval $0.2<z<1.6$ in the VVDS-Deep."183 In the observations we find the presence of an already significant number of red galaxies at z~1.5., In the observations we find the presence of an already significant number of red galaxies at $z\simeq1.5$.184 This number increases until z~0.8 and then slightly decreases with cosmic time., This number increases until $z\simeq0.8$ and then slightly decreases with cosmic time.185" In contrast, the SAM predicts a monotonic increase with time of the number of red galaxies."," In contrast, the SAM predicts a monotonic increase with time of the number of red galaxies."186" Above z~0.8, the total number of red galaxies is smaller in the model than in the observations but the trend reverses at later epochs, where the total number of red VVDS-Deep galaxies starts to decline and that of red model galaxies continues to rise slowly."," Above $z\simeq0.8$, the total number of red galaxies is smaller in the model than in the observations but the trend reverses at later epochs, where the total number of red VVDS-Deep galaxies starts to decline and that of red model galaxies continues to rise slowly."187 These same problems are evident when looking at the fractions of the two populations (bottom panel in Fig. 8))., These same problems are evident when looking at the fractions of the two populations (bottom panel in Fig. \ref{fraction}) ).188" The SAM predicts a monotonic decrease (increase) of the fraction of blue (red) galaxies with time at variance with VVDS-Deep sample, in which this trend reverses at z<0.8."," The SAM predicts a monotonic decrease (increase) of the fraction of blue (red) galaxies with time at variance with VVDS-Deep sample, in which this trend reverses at $z<0.8$."189" Note that we discuss the variation with cosmic time of the number and fraction of red and blue galaxies in terms of increase or decrease in a given apparent magnitude range, which does not necessarily imply increase or decrease in number density at these redshifts."," Note that we discuss the variation with cosmic time of the number and fraction of red and blue galaxies in terms of increase or decrease in a given apparent magnitude range, which does not necessarily imply increase or decrease in number density at these redshifts."190" At redshifts higher than z~0.8, the number of red galaxies is slightly lower in the SAM with respect to observations, while blue galaxies appear to be significantly more abundant at all cosmic epochs."," At redshifts higher than $z\simeq0.8$, the number of red galaxies is slightly lower in the SAM with respect to observations, while blue galaxies appear to be significantly more abundant at all cosmic epochs."191" This indicates that the overabundance of galaxies previously seen in the redshift distribution below z=~0.8— Lin the SAM (Fig. 5)),"," This indicates that the overabundance of galaxies previously seen in the redshift distribution below $z\simeq 0.8-1$ in the SAM (Fig. \ref{Nz_comp}) ),"192 is due to the presence of a larger number of both blue (true at all redshifts for this colour) and red galaxies., is due to the presence of a larger number of both blue (true at all redshifts for this colour) and red galaxies.193" The difference in the variation with cosmic time of the fraction of red and blue galaxies and of the shape of the rest- B—I colour distribution in the SAM, suggests that these populations may have different histories of formation and evolution than in the VVDS-Deep."," The difference in the variation with cosmic time of the fraction of red and blue galaxies and of the shape of the rest-frame $B-I$ colour distribution in the SAM, suggests that these populations may have different histories of formation and evolution than in the VVDS-Deep."194" In particular, SAM red galaxies may start to form at later epochs and be forming continuously and more efficiently up to present day, in contrast with what appears to be happen to VVDS-Deep galaxies."," In particular, SAM red galaxies may start to form at later epochs and be forming continuously and more efficiently up to present day, in contrast with what appears to be happen to VVDS-Deep galaxies."195 The clustering properties of galaxies provide strong constraints on galaxy formation models as they encode important information on how galaxies populate dark matter haloes., The clustering properties of galaxies provide strong constraints on galaxy formation models as they encode important information on how galaxies populate dark matter haloes.196" We compare in this section the galaxy clustering as inferred from the two-point correlation function in the SAM with VVDS-Deep measurements, for the global population of 17.5«I24 galaxies."," We compare in this section the galaxy clustering as inferred from the two-point correlation function in the SAM with VVDS-Deep measurements, for the global population of $17.5<I<24$ galaxies."197" We estimate the real-space galaxy clustering using the standard projected two-point correlation function, w,(rp), that corrects for redshift-space distortions due to galaxy peculiar motions."," We estimate the real-space galaxy clustering using the standard projected two-point correlation function, $w_p(r_p)$, that corrects for redshift-space distortions due to galaxy peculiar motions."198" This is obtained by splitting the galaxy separation vector into two components, r, and 7, perpendicular and parallel to the line of sight respectively (??),, and projecting the two-dimensional two-point correlation function &(rp,7) along the line-of-sight: We use the standard ? estimator to compute &(rp,7)."," This is obtained by splitting the galaxy separation vector into two components, $r_p$ and $\pi$, perpendicular and parallel to the line of sight respectively \citep{peebles80,fisher94}, and projecting the two-dimensional two-point correlation function $\xi(r_p,\pi)$ along the line-of-sight: We use the standard \citet{landy93} estimator to compute $\xi(r_p,\pi)$."199" In practice, to obtainw,(rp),, we integrate E(rp,zt) up to πιω=20h! Mpc."," In practice, to obtain, we integrate $\xi(r_p,\pi)$ up to $\pi_{max}=20~h^{-1}~Mpc$ ."200" We adopt this value because we find that, given the volume of the survey, this value is large enough so as to minimise the noise introduced at large a by the uncorrelated pairs in the data (?).."," We adopt this value because we find that, given the volume of the survey, this value is large enough so as to minimise the noise introduced at large $\pi$ by the uncorrelated pairs in the data \citep[][]{pollo05}."201" Errors in the VVDS-Deep are estimated through the blockwise bootstrap resampling technique (e.g. ?), which allows us to account for sample variance in the field and provides fair error estimates, very similar to those obtained using the Jackknife resampling technique (?).."," Errors in the VVDS-Deep are estimated through the blockwise bootstrap resampling technique \citep[e.g.][]{porciani02}, which allows us to account for sample variance in the field and provides fair error estimates, very similar to those obtained using the Jackknife resampling technique \citep{norberg09}."202" Since the transverse dimension of the survey is small, to generate the different resamplings we divide each sample in slices along the radial direction (e.g.??).."," Since the transverse dimension of the survey is small, to generate the different resamplings we divide each sample in slices along the radial direction \cite[e.g.][]{delatorre09,meneux09}."203" For each of our samples, we use 300 resamplings by bootstrapping 6 slices of equal volume."," For each of our samples, we use $300$ resamplings by bootstrapping $6$ slices of equal volume."204 We estimated the errors in the SAM by computing the field-to-field variance among the 100 mock samples., We estimated the errors in the SAM by computing the field-to-field variance among the 100 mock samples.205 We explicitly verified that the bootstrap error estimates agree with the ensemble errors obtained from the mock samples., We explicitly verified that the bootstrap error estimates agree with the ensemble errors obtained from the mock samples.206of compact object binaries in Figures2. - 4 in the space spanned by the initial eccentricity and initial gravitational wave frequency. which is twice the orbital frequency.,"of compact object binaries in Figures\ref{Initial_nsns} - \ref{Initial_bhbh} in the space spanned by the initial eccentricity and initial gravitational wave frequency, which is twice the orbital frequency."207 Each panel in theses figures corresponds to a different model labeled as listed in Table 2.., Each panel in theses figures corresponds to a different model labeled as listed in Table \ref{Models}.208 The case of the NS-NS systems is shown in Figure 2.., The case of the NS-NS systems is shown in Figure \ref{Initial_nsns}.209 The boundary of the region populated by the systems on the left-hand side corresponds to the requirement that we only consider binaries that nerge within a Hubble time., The boundary of the region populated by the systems on the left-hand side corresponds to the requirement that we only consider binaries that merge within a Hubble time.210 The bulk of the binaries shown in each panel correspond to those that have undergone one CE phase in their evolution., The bulk of the binaries shown in each panel correspond to those that have undergone one CE phase in their evolution.211" The top row corresponds to the models AZK. AZk. AzK. and Azk. in which we allow the binaries to cross through the common envelope with the donor on the Hertzsprung gap. denoted by “+"" in Table 2.."," The top row corresponds to the models AZK, AZk, AzK, and Azk, in which we allow the binaries to cross through the common envelope with the donor on the Hertzsprung gap, denoted by ""+"" in Table \ref{Models}."212 These binaries may undergo a second common envelope phase with a helium star companion., These binaries may undergo a second common envelope phase with a helium star companion.213 At the second CE stage. the orbit is tightened even more leading to formation of the stripe in the diagram stretching from ονx107? Hz at ex1077.," At the second CE stage, the orbit is tightened even more leading to formation of the stripe in the diagram stretching from $f_{GW}\approx 10^{-2}$ Hz at $e\approx 10^{-2}$."214 In these models. the initial distribution in the space of gravitational wave frequency versus eccentricity 1s bimodal.," In these models, the initial distribution in the space of gravitational wave frequency versus eccentricity is bimodal."215 The influence of the value of the kick velocity has a small impact on the shape of distributions presented in Figure 2. as can be seen by comparing the data in plots labeled as either K-large kicks or k-small kicks., The influence of the value of the kick velocity has a small impact on the shape of distributions presented in Figure \ref{Initial_nsns} as can be seen by comparing the data in plots labeled as either K-large kicks or k-small kicks.216 For BH-NS systems. presented in Figure 3.. and BH-BH binaries. in Figure 4.. we present the results of six out of eight models. since in models BZK and BZk. almost no binaries are formed in our simulations that involve 2x10° initial binaries.," For BH-NS systems, presented in Figure \ref{Initial_nsbh}, and BH-BH binaries, in Figure \ref{Initial_bhbh}, we present the results of six out of eight models, since in models BZK and BZk, almost no binaries are formed in our simulations that involve $2\times 10^6$ initial binaries."217 For BH-NS and BH-BH binaries. the formation of ultra-compact binaries 1s not expected.," For BH-NS and BH-BH binaries, the formation of ultra-compact binaries is not expected."218 The formation of NS-NS ultra-compact systems in very close orbits is the consequence of the final CE episode. which ts initiated by a low-mass helium (2-4 M.) star and its NS companion (1.4 4).," The formation of NS-NS ultra-compact systems in very close orbits is the consequence of the final CE episode, which is initiated by a low-mass helium (2-4 $M_{\odot}$ ) star and its NS companion $1.4\, M_{\odot}$ )."219 Since the donor is about twice as massive as its companion. the CE phase ts initiated by the non-stable mass transfer and the orbit significantly decreased in size.," Since the donor is about twice as massive as its companion, the CE phase is initiated by the non-stable mass transfer and the orbit significantly decreased in size."220 For more massive BH-BH/BH-NS binaries. helium stars are on average More massive (M»3—4M.) and do not expand (so no CE phase). and even if à low mass helium star forms. then its companion is a BH (M>3M..). so most likely instead of CE the RLOF ts stable and does not lead to orbital decay (mass ratio ~1).," For more massive BH-BH/BH-NS binaries, helium stars are on average more massive $M>3-4\, M_{\odot}$ ) and do not expand (so no CE phase), and even if a low mass helium star forms, then its companion is a BH $M>3\, M_{\odot}$ ), so most likely instead of CE the RLOF is stable and does not lead to orbital decay (mass ratio $\sim 1$ )."221 Very few systems (e.g.. models AzK or Azk) produce ultra-compact BH-NS/BH-BH binaries for very special cases of binary evolution.," Very few systems (e.g., models AzK or Azk) produce ultra-compact BH-NS/BH-BH binaries for very special cases of binary evolution."222 In the case of BH-BH binaries. shown in Figure + we present only six models. since models BZK and BZk do not lead to the formation of BH-BH binaries (?)..," In the case of BH-BH binaries, shown in Figure \ref{Initial_bhbh} we present only six models, since models BZK and BZk do not lead to the formation of BH-BH binaries \citep{2007ApJ...662..504B}."223 In all models. there is an enhanced density of systems formed with ο=0.1 at approximately 107Hz<fw107?Hz.," In all models, there is an enhanced density of systems formed with $e\approx 0.1$ at approximately $10^{-5}\,{\rm Hz} < f_{GW} < 10^{-4}\,{\rm Hz}$."224 In these systems. the second black hole has formed via direct collapse.," In these systems, the second black hole has formed via direct collapse."225 When treating the direct collapse. we assume that of the mass escapes in the form of neutrinos and possibly gravitational waves.," When treating the direct collapse, we assume that of the mass escapes in the form of neutrinos and possibly gravitational waves."226 Hence. the gravitational mass of the BH is lower than the baryon mass of the collapsing star.," Hence, the gravitational mass of the BH is lower than the baryon mass of the collapsing star."227 This introduces a small eccentricity z0.1 since the systems were circularized in the mass transfer prior to the collapse and the formation of the second BH., This introduces a small eccentricity $\approx 0.1$ since the systems were circularized in the mass transfer prior to the collapse and the formation of the second BH.228 Por the detection of gravitational waves. it is Important to know the eccentricity of a binary at the time it enters the sensitivity window of the detector.," For the detection of gravitational waves, it is important to know the eccentricity of a binary at the time it enters the sensitivity window of the detector."229 We consider three cases that correspond approximately to three types of detectors., We consider three cases that correspond approximately to three types of detectors.230 In Figure 5.. we show the eccentricity distributions at 0.3 Hz (bottom horizontal axis) and 3 Hz (top horizontal axis) corresponding approximately to the ET and DECIGO detectors.," In Figure \ref{Results}, we show the eccentricity distributions at 0.3 Hz (bottom horizontal axis) and 3 Hz (top horizontal axis) corresponding approximately to the ET and DECIGO detectors."231 The results for the Advanced LIGO/VIRGO can be easily obtained by rescaling the horizontal axis., The results for the Advanced LIGO/VIRGO can be easily obtained by rescaling the horizontal axis.232 The shape of the eccentricity distributions at the moment that the binary enters the given detector band follows from the corresponding initial distribution., The shape of the eccentricity distributions at the moment that the binary enters the given detector band follows from the corresponding initial distribution.233 However. one must note that for each type of binary there is a different natural timescale and frequency. because of the different mass scales of each binary.," However, one must note that for each type of binary there is a different natural timescale and frequency, because of the different mass scales of each binary."234 We present the results for the DECIGO detector and add appropriate numbers for the ET in parentheses., We present the results for the DECIGO detector and add appropriate numbers for the ET in parentheses.235 For the NS-NS binaries shown in the top panel of Figure 5.. the distribution is either centered on e=1077 (ET: 107) for the models BZK. BZk. BzK. and Bzk. where we do not allow the formation of ultra-compact binaries 1n a second CE phase.," For the NS-NS binaries shown in the top panel of Figure \ref{Results}, the distribution is either centered on $e\approx 10^{-4}$ (ET: $10^{-5}$ ) for the models BZK, BZk, BzK, and Bzk, where we do not allow the formation of ultra-compact binaries in a second CE phase."236 The remaining models AZK. AZk. AzK. and Azk contain another component centered roughly at e=107 (ET: 107).," The remaining models AZK, AZk, AzK, and Azk contain another component centered roughly at $e\approx 10^{-4}$ (ET: $10^{-3}$ )."237 This additional component represent the ultra-compact binaries that have experienced two episodes of mass transfer in their evolutionary history and were already very tight at the second supernova explosion., This additional component represent the ultra-compact binaries that have experienced two episodes of mass transfer in their evolutionary history and were already very tight at the second supernova explosion.238 The mixed BH-NS binaries. shown in the middle panel of Figure 5. exhibit a distribution of eccentricity centered at e=3x107? (ET: 3x10 9). while the eccentricity BH-BH binaries. shown in the bottom panel of Figure 5. lie between e=x10 (ET: 1077) and e=x10 (ET: 107).," The mixed BH-NS binaries, shown in the middle panel of Figure \ref{Results} exhibit a distribution of eccentricity centered at $e\approx 3\times 10^{-5}$ (ET: $3\times10^{-6}$ ), while the eccentricity BH-BH binaries, shown in the bottom panel of Figure \ref{Results} lie between $e\approx \times 10^{-6}$ (ET: $10^{-7}$ ) and $e\approx \times 10^{-4}$ (ET: $10^{-5}$ ) ."239 For the Advanced LIGO/VIRGO detectors where we assume that the low frequency boundary lies at = 30 Hz. the," For the Advanced LIGO/VIRGO detectors where we assume that the low frequency boundary lies at $\approx$ 30 Hz, the"240With the addition of Ry» we now have seven free parameters that define our rest-frame moclels for both οjects.,With the addition of $\mathcal{R}_f$ we now have seven free parameters that define our rest-frame models for both objects.241 If the two SNe are iu act plysically sinilar. and if we have enessed correctly about Vy. Vy aud Ry. then we should expect to see the sale fux values as a function of wavelength aud time: fy(A.f£)=Ryf).," If the two SNe are in fact physically similar, and if we have guessed correctly about $\bfvartheta_X$ , $\bfvartheta_Y$ and $\mathcal{R}_f$, then we should expect to see the same flux values as a function of wavelength and time: $f_X(\lambda,t) = \mathcal{R}_f \cdot f_Y(\lambda, t)$."242 This iicaus that we can compute a posterior likelihood for cach set of model parameters in the same mannerthat was used for Eq.1 2.. 7. ?," This means that we can compute a posterior likelihood for each set of model parameters in the same mannerthat was used for Eq.\ref{eqn:p(D|theta,Mj)}: :"243 (777T). (?7).. (1).," \ref{eqn:p(D|varthetaX,varthetaY,Rf)}244 \ref{sec:ParameterEstimation}. \ref{eqn:p(theta|D,Mj)}."245 (7)..," \citet{Hsiao:2007} \citet{Nugent:2002} \citep{Blondin:2006,Bronder:2008,Foley:2008,Sullivan:2009}, \citep{Ellis:2008}, \citep{Foley:2008a}. \citep{Guy:2007}."246of mnassive star formation.,of massive star formation.247 For example. ? use iitial mean volume aud column densities of 1.31019 e cl3 (3.3.10! 2) and 0.26 ο 7. respectively: 2 use 3.9.10 σαιP (0.0&107 em 2) and 0.026 ο 7.," For example, \citet{bonnell03a} use initial mean volume and column densities of $1.3\times 10^{-19}$ g $^{-3}$ $3.3\times 10^4$ $^{-3}$ ) and $0.26$ g $^{-2}$ , respectively; \citet{peters10b} use $3.9\times 10^{-21}$ g $^{-3}$ $1.0\times 10^3$ $^{-3}$ ) and $0.026$ g $^{-2}$."248 However. our parameter choices are Ίο closer to what is actually observed in regious of massive star formation.," However, our parameter choices are much closer to what is actually observed in regions of massive star formation."249 For example. in their survev of 116 Souther massive star-forming regions. ? find a typical mass and radius of 5000. AL. and 0.L pce. corresponding to a volume density of 1.2«1ο οσα P (3.0ς10* 3) and a col deusity o£ 2.1. ο 2. similar to what we use.," For example, in their survey of $146$ Southern massive star-forming regions, \citet{faundez04a} find a typical mass and radius of $5000$ $\msun$ and $0.4$ pc, corresponding to a volume density of $1.2\times 10^{-18}$ g $^{-3}$ $3.1\times 10^5$ $^{-3}$ ) and a column density of $2.1$ g $^{-2}$ , similar to what we use."250" Ory initial cloud las a deusitv structure described by where s ds the distance from the cloud center aud poo6S,/((2?91)R.|=16.10% g ® is ie core densitv.", Our initial cloud has a density structure described by where $r$ is the distance from the cloud center and $\rho_c = 6\Sigma_c/[(2^{2.5}-1) R_c]=1.6\times 10^{-18}$ g $^{-3}$ is the core density.251 Thus our deusity profile consists of a constant deusitv iu the πιο half of the radius. coupled with a powerlaw falloff in the outer half of je radius.," Thus our density profile consists of a constant density in the inner half of the radius, coupled with a powerlaw falloff in the outer half of the radius."252 Outside this cloud we place a low density züubieut medium with a deusitv that is LOO times sinialler iui the cloud edge density., Outside this cloud we place a low density ambient medium with a density that is 100 times smaller than the cloud edge density.253 We choose this density structure because observations indicate the preseuce of avoughly kcD deusity gradient ou laree-scales in star-ornüue clumps (e.g.2?272777)..," We choose this density structure because observations indicate the presence of a roughly $r^{-1.5}$ density gradient on large-scales in star-forming clumps \citep[e.g.][]{caselli95a, beuther02c, beuther05b, beuther06a, mueller02a, sridharan05a}."254 By choosing a fat iuner density profile. however. we minimize tidal forces in the cloud core. thereby eusuriug maxinunm opportunity for ragnieutation.," By choosing a flat inner density profile, however, we minimize tidal forces in the cloud core, thereby ensuring maximum opportunity for fragmentation."255" We initialize the cloud velocity with a Caussian-vaudom velocity field with a power spectrmu P(k)kD aud a one-dimensionalHB velocityH dispersion.- o,=GM,OR.=2.9 lan |.", We initialize the cloud velocity with a Gaussian-random velocity field with a power spectrum $P(k)\propto k^{-2}$ and a one-dimensional velocity dispersion $\sigma_c = \sqrt{G M_c/ 2 R_c}=2.9$ km $^{-1}$.256" The corresponding virial parameter is a=5o2GA,R=. so that the turbuleut kinetic energv is larger than the potential caereyv at time zero."," The corresponding virial parameter is $\alpha = 5 \sigma_c^2 G M_c/R_c = 5$, so that the turbulent kinetic energy is larger than the potential energy at time zero."257 However. we do not iuchude auv feedback processes wwinds or IT regions) capable of diviug the turbulence. nor do we have other potential driving niechanisnis. such as a turbulent cascade frou larecr scales or ongoing Πα.," However, we do not include any feedback processes winds or H regions) capable of driving the turbulence, nor do we have other potential driving mechanisms, such as a turbulent cascade from larger scales or ongoing infall."258 As a result. the turbulence nucdereocs a rapid decay. whichquickly reuders the cloud evavitationally bound.," As a result, the turbulence undergoes a rapid decay, whichquickly renders the cloud gravitationally bound."259" Throughout the computational domain. we initialize the raciation energy density to that of a blackbody with a temperature T,=10 K. Thus we have E=aT!τούς10H ere ."," Throughout the computational domain, we initialize the radiation energy density to that of a blackbody with a temperature $T_r = 10$ K. Thus we have $E = a T_r^4 = 7.56 \times 10^{-11}$ erg $^{-3}$."260" Similarly. we initialize the eas teniperature within the cloud (re<R.) to LT,=10 Is.Outside the cloud (e2: ΠΠ). we set the temperature to T,=1000 Ts. Since the density outside the cloud is 1/100 hat of the densivat the cloud edge. tjs ensures thermal oyessure balance across the cloud boindary."," Similarly, we initialize the gas temperature within the cloud $r<R_c)$ to $T_g = 10$ K.Outside the cloud $r>R_c$ ), we set the temperature to $T_g = 1000$ K. Since the density outside the cloud is $1/100$ that of the density at the cloud edge, this ensures thermal pressure balance across the cloud boundary."261" We also set he Planck aud Rosselaud opacities of the material with T,>DOO K and p<24%p,./50 to zero. to ensure that he host ambient imnediun does not interact with the radiation feld. aud is not able to cool."," We also set the Planck and Rosseland opacities of the material with $T_g > 500$ K and $\rho < 2^{-1.5}\rho_c/50$ to zero, to ensure that the host ambient medium does not interact with the radiation field, and is not able to cool."262 The suaulatiouns we present in this paper use the ORION adaptive mesh refinement code., The simulations we present in this paper use the ORION adaptive mesh refinement code.263 The mmucrical method is uearly ideutical to that in our previous papers (ee.77777).," The numerical method is nearly identical to that in our previous papers \citep[e.g.][]{krumholz07a, krumholz09c, krumholz10a, myers11a, cunningham11a}."264 Tere we only sununarize the physics. and we refer readers to the numerical method papers referenced in Section 2.3. for a full description of ORION' workings.," Here we only summarize the physics, and we refer readers to the numerical method papers referenced in Section \ref{sec:numerics} for a full description of ORION's workings."265 ORION worksby solving the equations ofs compressible eas dynamics chiding scleravitv. raciative transfer. and radiatiug star particles. all on an adaptive eid.," ORION worksby solving the equations of compressible gas dynamics including self-gravity, radiative transfer, and radiating star particles, all on an adaptive grid."266 Iu our computational domain. we describe every cell with a vector of conserved. quantities (p.pv.pc. E). where pis the density. pois the momentum density. pe is the total internal plus kinetic gas energy density. and E is the radiation energv density in the rest frame of the computational exid.," In our computational domain, we describe every cell with a vector of conserved quantities $(\rho, \rho\vecv, \rho e, E)$ , where $\rho$ is the density, $\rho\vecv$ is the momentum density, $\rho e$ is the total internal plus kinetic gas energy density, and $E$ is the radiation energy density in the rest frame of the computational grid."267 In addition to eas quantities. wealso track an arbitrary number of point mass star particles. cach of whichis described bv a position z;. a moment p;. and an instantancous huninosity L;. wherethe subscript / refers to the particle muuber.," In addition to gas quantities, wealso track an arbitrary number of point mass star particles, each of whichis described by a position $\vecx_i$ , a momentum $\vecp_i$ , and an instantaneous luminosity $L_i$ , wherethe subscript $i$ refers to the particle number."268 Given this description of the problem. the full set. of evolution equations is," Given this description of the problem, the full set of evolution equations is"269accordance with those found theoretically by Oh and observationally by Grillmairetal.(1905).,accordance with those found theoretically by \cite{OhLin92} and observationally by \cite{Grillmair95}. .270are niore stronely clustered on small scales.,are more strongly clustered on small scales.271 Likewise. measurements of the stellar mass function at slightly lower redshift (2~0.5) also suggest a variation iu the shape of the mass function with local cuviroument2010).," Likewise, measurements of the stellar mass function at slightly lower redshift $(z \sim 0.5)$ also suggest a variation in the shape of the mass function with local environment."272. Thus. when looking to quantify environmental dependencies at fixed stellar mass. the use of broad stellar mass bins (ess those used by 2009.. 2009.. 2009..2009... and 2010)) or siniple mass-limuted siuuple solectious is inappropriate as both approaches injMieitlv assume that there is no variation in the stellar nass function with cnviromment.," Thus, when looking to quantify environmental dependencies at fixed stellar mass, the use of broad stellar mass bins (e.g., those used by , , , and ) or simple mass-limited sample selections is inappropriate as both approaches implicitly assume that there is no variation in the stellar mass function with environment."273 Iu the following stbscction. we develop improved techniques that account for the apparent environmental depeudeuce of the shape of the stellar mass fuuction. thereby enabling an unbiased analysis of the color-deusity relation at fixed stellar mass.," In the following subsection, we develop improved techniques that account for the apparent environmental dependence of the shape of the stellar mass function, thereby enabling an unbiased analysis of the color-density relation at fixed stellar mass."274 The ultimate goal of this work is not to study the correlation between stellar mass and euvironnieut. but rather to investigate the relationship between galaxy color and cuviroument at fixed stellar mass.," The ultimate goal of this work is not to study the correlation between stellar mass and environment, but rather to investigate the relationship between galaxy color and environment at fixed stellar mass."275 But as shown in the above analvsis. we must be careful to account for the weak correlation between stellar mass aud overdensity even with stellar mass bins as narrow as 0.5 dex.," But as shown in the above analysis, we must be careful to account for the weak correlation between stellar mass and overdensity even with stellar mass bins as narrow as $0.5$ dex."276 Thus. we now select those galaxies within the top 10€ of the overdensity distribution for all galaxies at 10.6<logy(AL./h2M)Hl aud 0.75«:1.05 (the same high-deusity subsample of 159 ealaxies). aud from the corresponding bottom 50% of the overdensity distribution we randomly draw 1000 subsunuples (each composed of 159 ealaxies) so as to match the joiut redshift and stellar mass distributions of the galaxies im the high-density subsiiple.," Thus, we now select those galaxies within the top $10\%$ of the overdensity distribution for all galaxies at $10.6 < \log_{10}({\rm M}_{*} /277h^{-2}\ {\rm M}_{\sun}) < 11.1$ and $0.75 < z < 1.05$ (the same high-density subsample of $159$ galaxies), and from the corresponding bottom $50\%$ of the overdensity distribution we randomly draw 1000 subsamples (each composed of $159$ galaxies) so as to match the joint redshift and stellar mass distributions of the galaxies in the high-density subsample."278 Members of the low-deusity subsample are drawn raucomlyfrou within a two-dimensional window with dimeusious of Az?<1:410! and Alogy(Al52οng0? ofarandomly-sclected object in the hieh-deusitv suo»unple.," Members of the low-density subsample are drawn randomlyfrom within a two-dimensional window with dimensions of $\Delta z^2 < 4 \cdot 10^{-4}$ and $\Delta \log_{10}({\rm M}_{*})^2 <2795 \cdot 10^{-5}$ of a randomly-selected object in the high-density subsample."280 Varvine the size of this window bv factors of a few im each dimension has uo sienificaut effect ou our results;, Varying the size of this window by factors of a few in each dimension has no significant effect on our results.281 Caven the random nature of the matching. some objects are repeated iu the low-density subsamples.," Given the random nature of the matching, some objects are repeated in the low-density subsamples."282 However. for cach subsample of 159 ealaxics. ~90% of the ealaxies are unique: requiring all iienibers of a subsample to be unique would skew the statistics1981).," However, for each subsample of $159$ galaxies, $\sim \!28390\%$ of the galaxies are unique; requiring all members of a subsample to be unique would skew the statistics."284. By matching our hiegh- aud low-density subsamples in stellar mass as well as redshift. we are able to effectively study the correlation between ealaxy properties such as color and euvironment at fixed stellar mass.," By matching our high- and low-density subsamples in stellar mass as well as redshift, we are able to effectively study the correlation between galaxy properties such as color and environment at fixed stellar mass."285 As shown in Figures Lo aud 5.. we find a siguificaut relationship at 2~0.9 between rest-frame C2B color and local galaxy overdensity at fixed stellar mass for galaxies with 10.6<logyAL/h?M.) 11.1.," As shown in Figures \ref{color_fig} and \ref{color_fig2}, we find a significant relationship at $z \sim 0.9$ between rest-frame $U-B$ color and local galaxy overdensity at fixed stellar mass for galaxies with $10.6 < \log_{10}({\rm M}_{*} / h^{-2}\ {\rm M}_{\sun}) <28611.1$ ."287 The cumulative color distributions for the two subsamples drawn from separate cuviromment reeginies are sieuiBcantlv distinct. with the salaxies in liegh-density environments skewed towards redder rest-frame colors.," The cumulative color distributions for the two subsamples drawn from separate environment regimes are significantly distinct, with the galaxies in high-density environments skewed towards redder rest-frame colors."288 The ΛΙΑΝ C test confruis what is apparcut iu Figure L. vieldiug Pr-«0.002 when comparing the color distributions of the lieh- aud low-density subsamples: hese color distributions are distinct at 22360 confidence.," The WMW $U$ test confirms what is apparent in Figure \ref{color_fig}, yielding $P_{U} < 0.002$ when comparing the color distributions of the high- and low-density subsamples: these color distributions are distinct at $> \! 3\sigma$ confidence."289 Dv construction. the corresponding stellar mass aud redshift distributions are indistineuishable (see iuset ots in refeoloryig)).avthPy oo~Li? and Py~—0.19. respectively.," By construction, the corresponding stellar mass and redshift distributions are indistinguishable (see inset plots in \\ref{color_fig}) ), with $P_{U} \sim 0.47$ and $P_{U} \sim 0.49$, respectively."290 Tn Figure 5.. we show the distribution of differences vetween the Hodges-Lelinaun estimator of the mean £7D color. stellar mass. and redshift for the hieh-deusity subsample relative to the corresponding estimator of the uean for the 1000 low-density subsiuuples.," In Figure \ref{color_fig2}, we show the distribution of differences between the Hodges-Lehmann estimator of the mean $U-B$ color, stellar mass, and redshift for the high-density subsample relative to the corresponding estimator of the mean for the $1000$ low-density subsamples."291" The median differences in stellar mass aud redshift are cousisteut witli zero. Av~~1-10t40,009 and Alog,,(AL/h2M.)τν1.0032E0.012. while the median offset i rest-frame color is ΑιB)~0.03350.013 such that galaxies in hieli-density cavirons are typically redder im color at fixed stellar mass aud redshift."," The median differences in stellar mass and redshift are consistent with zero, $\Delta z \sim -1 \cdot 10^{-4} \pm 0.009$ and $\Delta \log_{10}({\rm M}_{*} / h^{-2}\ {\rm M}_{\sun}) \sim 0.003 \pm2920.012$ , while the median offset in rest-frame color is $\Delta(U-B)293\sim 0.033 \pm 0.013$ such that galaxies in high-density environs are typically redder in color at fixed stellar mass and redshift."294 Similarly. the aritlauetic means of the two color distri]xitious are accordingly fouud to be distiuct at 23.50 (see Table 2)).," Similarly, the arithmetic means of the two color distributions are accordingly found to be distinct at $\gtrsim \! 3.5295\sigma$ (see Table \ref{res_tab2}) )."296 Altogether. the DEEP2 data show a robust color-density relation at fixed stellar nass at 2~0.9 for galaxies in the stellar mass regine of 10.6<logy(ALfh2AL.)«11.1.," Altogether, the DEEP2 data show a robust color-density relation at fixed stellar mass at $z \sim 0.9$ for galaxies in the stellar mass regime of $10.6 < \log_{10}({\rm297 M}_{*} / h^{-2}\ {\rm M}_{\sun}) < 11.1$."298 To test the robustuess of our results to the warticularitics of the sample selection. we repeat the analysis described above for several suuples spanning varving redshift and stellar mass regimes.," To test the robustness of our results to the particularities of the sample selection, we repeat the analysis described above for several samples spanning varying redshift and stellar mass regimes."299 For example. woadenimes the redshift rauge over which we select ealaxies to (0.75.i«1.25. thereby increasing he size of the sample. we again find a statistically sjeuificaut relationship between rest-frame color aud eunvironnient within our adopted stellar mass bin of 10.6<logy2AL.) 111.," For example, broadening the redshift range over which we select galaxies to $0.75 < z < 1.25$, thereby increasing the size of the sample, we again find a statistically significant relationship between rest-frame color and environment within our adopted stellar mass bin of $10.6 <300\log_{10}({\rm M}_{*} / h^{-2}\ {\rm M}_{\sun}) < 11.1$ ."301 For the 211 galaxies in the high-deusitv(AL./h regime (again the highest 105€ of he overdensity distribution) at 0.75<i«1.25. the cumulative distribution of ( B color is skewed towards redder colors relative to the comparison set of galaxiesin owdensity environments viclding Pr«0.01 and with he means ofthe two color distributions distinct at à ~30 evel.," For the $211$ galaxies in the high-density regime (again the highest $10\%$ of the overdensity distribution) at $0.75 < z < 1.25$, the cumulative distribution of $U-B$ color is skewed towards redder colors relative to the comparison set of galaxiesin low–density environments, yielding $P_{U} < 0.01$ and with the means of the two color distributions distinct at a $\sim \! 3\sigma$ level."302 In Table 2.. we list the results from similar analyses of several other ealaxy samples.," In Table \ref{res_tab2}, we list the results from similar analyses of several other galaxy samples."303 When wvarviug the redshift aud/or stellay mass reginies probed. we continue ο fiud a significant color-density relation at fixed stellar nass at 2c d.," When varying the redshift and/or stellar mass regimes probed, we continue to find a significant color-density relation at fixed stellar mass at $z \sim 1$ ."304 This result is found to hold even at slightly lower masses: restricting to onlv those galaxies with 10.2<logy(AL/h2.NL.)10.7 (a sample with a quedian stellar mass of log44(M./h2ATLYSdO D). we again fud that redder galaxies teud to favor overdense reeions at fixed stellar mass aud redshift.," This result is found to hold even at slightly lower masses; restricting to only those galaxies with $10.2 < \log_{10}({\rm M}_{*} / h^{-2}\ {\rm M}_{\sun}) < 10.7$ (a sample with a median stellar mass of $\log_{10}({\rm M}_{*} /305h^{-2}\ {\rm M}_{\sun}) \sim 10.4$ ), we again find that redder galaxies tend to favor overdense regions at fixed stellar mass and redshift."306 As shown in Figure Lb. we find that there exists a correlation between rest-frame C——DB color and local galaxy. overdensity within the highanass (logyAL/h2M.)~ LOS) segment of the galaxy »pulatioun at 2~(0.9 such that red galaxies favor üueher-«deusitv euvironnieuts at fixed stellar mass.," As shown in Figure \ref{color_fig}, we find that there exists a correlation between rest-frame $U-B$ color and local galaxy overdensity within the high-mass $\log_{10}({\rm M}_{*} / h^{-2}\307{\rm M}_{\sun}) \sim 10.8$ ) segment of the galaxy population at $z308\sim 0.9$ such that red galaxies favor higher-density environments at fixed stellar mass."309 As roted iu Section 1. several receut studies utilizing data von VVDS aud zCOSAIOS have coucluded that nosuch correlation exists within this stellar mass and redshift reenne2009).," As noted in Section \ref{sec_intro}, , several recent studies utilizing data from VVDS and zCOSMOS have concluded that nosuch correlation exists within this stellar mass and redshift regime."310. Tere. we discussthe likely reasous for the discrepancy οποσα these conclusions aud our results.," Here, we discussthe likely reasons for the discrepancy between these conclusions and our results."311 It is highly unlikely that the hiehlv significant color- relation at fixed stellar mass within the DEEP2, It is highly unlikely that the highly significant color-density relation at fixed stellar mass within the DEEP2312Dillereuce in composition of the core—whether these heavy elements are mostly “ices” (a mixture of water. ammonia and methane in their [unknown] high pressure. relatively high temperature form or “rocks” (a mixture of refractory materials including mostly silicates)—:Tects the radius of the planet by 10 to20%.,"Difference in composition of the core—whether these heavy elements are mostly “ices” (a mixture of water, ammonia and methane in their [unknown] high pressure, relatively high temperature form) or “rocks” (a mixture of refractory materials including mostly silicates)—affects the radius of the planet by 10 to."313. For comparison. the interiors of Uranus aud. Neptune are consistent wi beiug mostly made of “lees” (e.g..Podolak.&Marley2000).," For comparison, the interiors of Uranus and Neptune are consistent with being mostly made of “ices” \citep[e.g.,][]{PPM00}."314. Figure 1. thus coufirms the ueed for a substautial amouut of heavy elements in HD119026b when adopting a standard evoluti scenario., Figure \ref{fig:evol_std} thus confirms the need for a substantial amount of heavy elements in HD149026b when adopting a standard evolution scenario.315 Quantitatively. this implies core masses between Ll and in good agreement wi Satoetal.(2005) aud Fortueyetal.(2006).," Quantitatively, this implies core masses between 41 and $_\oplus$ in good agreement with \citet{Sato05} and \cite{Fortney06}."316. In particular. the latter yields values between 60 aie .," In particular, the latter yields values between 60 and $_\oplus$."317 The differeuce is due to the fact that in order to coustrain more strictly the miuimuui mass of heavy elements present in the planet. we used a low value of the atmospheric temperature.," The difference is due to the fact that in order to constrain more strictly the minimum mass of heavy elements present in the planet, we used a low value of the atmospheric temperature."318 We now investigate the hypothesis that the planet may have cooled far from its parent. star before suddenly being sent into the presently observed 0.016 AU orbit., We now investigate the hypothesis that the planet may have cooled far from its parent star before suddenly being sent into the presently observed 0.046 AU orbit.319 The reason for this sudden eveut is to be determined. but coukl be due to dynamical plauet-plauet interactions (see section 1L.1.2)).," The reason for this sudden event is to be determined, but could be due to dynamical planet-planet interactions (see section \ref{sec:late_Z_supply}) )."320 In terms of evolutio. the planet is allowed to cool more rapidly duriug the tiiie-period wheu it is far from tlie parent star.," In terms of evolution, the planet is allowed to cool more rapidly during the time-period when it is far from the parent star."321 The sudden inward migration iudeed vield aui expausion of the planet but it παν be limited to the outer layers aud thus be relatively stall (Burrowsetal.2000)., The sudden inward migration indeed yield an expansion of the planet but it may be limited to the outer layers and thus be relatively small \citep{Burrows00}.322. We want to investigate whether the present mass aucl radius are compatible with a relatively small Core., We want to investigate whether the present mass and radius are compatible with a relatively small core.323 We thus calculate evolution models similar to those in the previous section. but using 100Ix aud an atinospheric modelbased ou simplified radiative transfer calculations of an isolated atmosphere (seeSauiouetal.1996:Cruillot2005).," We thus calculate evolution models similar to those in the previous section, but using $T_{\rm eq}=100\,$ K and an atmospheric modelbased on simplified radiative transfer calculations of an isolated atmosphere \citep[see][]{Saumon96,Guillot05}."324. Based ou these calculations. we obtain generally a much faster conutraetiou of the planet: a less than 30M core can account for the observed radius.," Based on these calculations, we obtain generally a much faster contraction of the planet; a less than $\mearth$ core can account for the observed radius."325 However. we have to include reheating of the outer shell of the envelope.," However, we have to include reheating of the outer shell of the envelope."326 This shell is approximatively defined by the region whose temperature is lower (lau the new equilibrium temperature. ΝΑ. Based on our calculations. tliis corresponds to a pressure level of —10 kkbar.," This shell is approximatively defined by the region whose temperature is lower than the new equilibrium temperature, K. Based on our calculations, this corresponds to a pressure level of $\sim$ kbar."327 A simple estimation of the reheating timescale of the outer shell suggests that we have to include this elfect., A simple estimation of the reheating timescale of the outer shell suggests that we have to include this effect.328 Using equations of radiative diffusion aud euergy couservatiou. we estimate tliat the reheating timescale of a laver of pressure Z. temperature 7. opacity # and heat capacity ey is to first order inclepeudent of its initial temperature auc equal to: where α is the radiation density coustant. c the speed of light. aud gthe planets gravity (assumed uniform).," Using equations of radiative diffusion and energy conservation, we estimate that the reheating timescale of a layer of pressure $P$, temperature $T$, opacity $\kappa$ and heat capacity $c_p$ is to first order independent of its initial temperature and equal to: where $a$ is the radiation density constant, $c$ the speed of light, and $g$the planet's gravity (assumed uniform)."329 This expression is cousistent with direct simulations by (2005).., This expression is consistent with direct simulations by \citet{IBG05}. .330 This timescale is about LOS years for &zzlem?g |. Pz 10kkbar. g=1550ems 7," This timescale is about $10^8\,$ years for $\kappa\approx 1\,\rm cm^2\,g^{-1}$ , $P\approx 10$ kbar, $g\approx 1550\rm\,cm\,s^{-2}$ ,"331 This timescale is about LOS years for &zzlem?g |. Pz 10kkbar. g=1550ems 7.," This timescale is about $10^8\,$ years for $\kappa\approx 1\,\rm cm^2\,g^{-1}$ , $P\approx 10$ kbar, $g\approx 1550\rm\,cm\,s^{-2}$ ,"332"shocks and convective motions, pushing gas outside the virial radius.","shocks and convective motions, pushing gas outside the virial radius."333" One can see from the local baryon fraction profile in Figure 12 that this gas accumulates in a region between 1 to 2 virial radii around the cluster, beyond which the cumulated baryon fraction converge to the universal one."," One can see from the local baryon fraction profile in Figure \ref{fig:BaryonFraction} that this gas accumulates in a region between 1 to 2 virial radii around the cluster, beyond which the cumulated baryon fraction converge to the universal one."334" Our SF model compares very well to the AMR simulation performed by ?,, showing slight excess of baryon at the virial radius."," Our SF model compares very well to the AMR simulation performed by \cite{Kravtsov:2005p702}, showing a slight excess of baryon at the virial radius."335" From these standarda galaxy formation models, we obtain gas properties that compare favorably to X-ray data (?).."," From these standard galaxy formation models, we obtain gas properties that compare favorably to X-ray data \citep{Nagai:2007p712}."336" We see indeed in Figure 12 that in the SF model, the gas mass fraction is slowly decreasing towards the center, with a significant deficit at the virial radius."," We see indeed in Figure \ref{fig:BaryonFraction} that in the SF model, the gas mass fraction is slowly decreasing towards the center, with a significant deficit at the virial radius."337 This behavior is traditionally explained by the joint effect of cooling and star formation (?).., This behavior is traditionally explained by the joint effect of cooling and star formation \citep{Voit:2001p1750}.338" The price to pay is however to form too many stars and cold gas in the cluster, as confirmed by previous numerical models (??7).."," The price to pay is however to form too many stars and cold gas in the cluster, as confirmed by previous numerical models \citep{Borgani:2004p1066, Kravtsov:2005p702, Borgani:2009p728}."339" Our simple Quenching model is making things better for the stellar component, but now the gas mass distribution is too concentrated (see Fig.+12))."," Our simple Quenching model is making things better for the stellar component, but now the gas mass distribution is too concentrated (see \ref{fig:BaryonFraction}) )."340 Only with AGN feedback can we obtain a small stellar mass fraction and in the same time a small gas fraction., Only with AGN feedback can we obtain a small stellar mass fraction and in the same time a small gas fraction.341" We note however that, in our AGN model, the gas mass profile is not as steep as suggested by X-ray data."," We note however that, in our AGN model, the gas mass profile is not as steep as suggested by X-ray data."342 We could probably reproduce the gas profile of, We could probably reproduce the gas profile of343resultss are typical for the class of polar disk galaxies as whole.,s are typical for the class of polar disk galaxies as whole.344"Applications of this algorithm to synthetic data show that the known, simulated cluster lenses are accurately reproduced, although intrinsic ellipticities, measurement and shot noise inevitably lead to a considerable noise level of the reconstruction in the case of realistic data.","Applications of this algorithm to synthetic data show that the known, simulated cluster lenses are accurately reproduced, although intrinsic ellipticities, measurement and shot noise inevitably lead to a considerable noise level of the reconstruction in the case of realistic data."345" Still, the quantitative analysis of our convergence maps shows a very good agreement with the expected result."," Still, the quantitative analysis of our convergence maps shows a very good agreement with the expected result."346" An application to the galaxy cluster MS 2137 qualitatively confirms the results of earlier, parametric studies that show an almost"," An application to the galaxy cluster MS 2137 qualitatively confirms the results of earlier, parametric studies that show an almost"347w BurbidgeaudΠαν(1990).,by \citet{bur90}.348. Nor does it link he quantized redshifts found in quasars to the quantized ‘velocities’ found by Tifft(1996.1997) o be present in galaxies.," Nor does it link the quantized redshifts found in quasars to the quantized 'velocities' found by \citet{tif96,tif97} to be present in galaxies."349 Ou the other hand. the intrinsic redshift distribution predicted by the Ζω relation given x equ thas been found here to show a siguificaut correlation with both observed redshift distributions.," On the other hand, the intrinsic redshift distribution predicted by the $_{iQ}$ relation given by eqn 4 has been found here to show a significant correlation with both observed redshift distributions."350 This relation (for No = 1) also predicts the 1.062 periodicity betwee2. 1G and z = 0.62 (DurbidgeandHewitt1990)., This relation (for $N$ = 1) also predicts the 0.062 periodicity between z = 0.06 and z = 0.62 \citep{bur90}.351. I has also been shown (Bell2002d) that there is a direct liuk )etwoeen the quasar iutrIsic recshifts predicted woequ band the “velociV periodicities reported in galaxies by Tifft.," It has also been shown \citep{bel02d} that there is a direct link between the quasar intrinsic redshifts predicted by eqn 4 and the ""velocity"" periodicities reported in galaxies by Tifft."352 Recently Foschinietal.(2002) have reported hat they have found a BL Lac object (z = 1.13) line in the direction of NGC 1698 (z = 40033)., Recently \citet{fos02} have reported that they have found a BL Lac object (z = 0.43) lying in the direction of NGC 4698 (z = 0.0033).353 Althoueh this object is assumed to be a vackerouud object by these investigators. if it were actually located in the galaxy it would have to lave an iutriusic redshift near z — 0.13. assuniug hat its Lo-s ejection velocity is s122ll.," Although this object is assumed to be a background object by these investigators, if it were actually located in the galaxy it would have to have an intrinsic redshift near z = 0.43, assuming that its l-o-s ejection velocity is small."354 Since this intrinsic redshift value corresponds closely to the intrinsic redshift precicted by equ 5 for η = 3. or 4o{l.3)=0.131 (Bell2002d.Table2).. we «οσον that the possibility that this object is associated with NGC L698 cannot vet be ruled out.," Since this intrinsic redshift value corresponds closely to the intrinsic redshift predicted by eqn 5 for $n$ = 3, or $_{\rm iQ}[1,3] = 0.434$ \citep[Table 2]{bel02d}, we suggest that the possibility that this object is associated with NGC 4698 cannot yet be ruled out."355 The I&ulsson intrinsic redshift relation docs not predict this intrinsic redshift value., The Karlsson intrinsic redshift relation does not predict this intrinsic redshift value.356 Finally. we make the followiig two comuaenuts.," Finally, we make the following two comments."357 Since the distribution of ΟΤΙ «nuasar redshifts in Fig 7 was the distribution that was used mitiallv to define t1ο I&arlsson relatio Lit is somewhat surprising trat it does not show a niore significant correlation coefficient.," Since the distribution of 574 quasar redshifts in Fig 7 was the distribution that was used initially to define the Karlsson relation, it is somewhat surprising that it does not show a more significant correlation coefficient."358 On the other haud. since the Σω relation was defined using a couipletely independent data sample. the correlation analysis carried out here between he zio redshifts aud the INarlsson distributiou in Fie 7 cau be considered as an independent test of the z;o relation.," On the other hand, since the $_{iQ}$ relation was defined using a completely independent data sample, the correlation analysis carried out here between the $_{iQ}$ redshifts and the Karlsson distribution in Fig 7 can be considered as an independent test of the $_{iQ}$ relation."359 It appears to have passed. this test successfully., It appears to have passed this test successfully.360 We lave carried out correlation analyses on two cdlifferent observed redshift distributions. comparing them to the intrinsic redshift distributions predicted by the warlsson intrinsic redshift relation. and bv the zig = 0.62LNV - OA] relation.," We have carried out correlation analyses on two different observed redshift distributions, comparing them to the intrinsic redshift distributions predicted by the Karlsson intrinsic redshift relation, and by the $_{iQ}$ = $N$ - $M_{N}$ ] relation."361On the other baud. the neutrino temperature then was Therefore the degree of degeneracy is given by which indicates moderate clegeneracy.,"On the other hand, the neutrino temperature then was Therefore the degree of degeneracy is given by which indicates moderate degeneracy."362 Under adiabatic expansion. this degree of degeneracy is unlikely to chanee. while neutrinos are relativistic.," Under adiabatic expansion, this degree of degeneracy is unlikely to change, while neutrinos are relativistic."363" There is a transition from the relativistic to uourelativistic"". regime. when μή=>mc.", There is a transition from the relativistic to nonrelativistic regime when $k_B T = m c^2$.364" Below Or al ty,&Oix 107. where η is uuits of eV. neutrinos become nonrelativistic."," Below or at $z_{tr} \approx 6 m \times 10^3$ , where $m$ is units of eV, neutrinos become nonrelativistic."365 Then the expressions for both Feriui level and neutriuo temperature change. but they have the same depeudence on (14-2).," Then the expressions for both Fermi level and neutrino temperature change, but they have the same dependence on $(1+z)$."366 As long as local gravity is negligible. nonrelativistic adiabatic expansion is assumed below Ti». 2 — So the degreefae) ofdegeneracye is," As long as local gravity is negligible, nonrelativistic adiabatic expansion is assumed below $T_{tr}$, and or So the degree ofdegeneracy is"367"(4) The aceuraey of recent. parameter measurements is generally what should be expected based on the quoted error bars Le. the error. bars overall are neither understimatec nor overestimated (an accuracy. Vy,=1.0. within the Poisson uncertainty on the measurement).","(4) The accuracy of recent parameter measurements is generally what should be expected based on the quoted error bars i.e. the error bars overall are neither understimated nor overestimated (an accuracy, $N_{\sigma}=1.0$, within the Poisson uncertainty on the measurement)."368 Belore 2000. the accuracy Nz as closer to 2. indicating unelerestimation of the error bars by a factor of 2.," Before 2000, the accuracy $N_{\sigma}$ as closer to 2, indicating underestimation of the error bars by a factor of 2."369 Overall. there is a small non- tail to the error distributions (we find that 20% of measurements are more that 20 away [rom the true values. (," Overall, there is a small non-Gaussian tail to the error distributions (we find that $20\%$ of measurements are more that $2\sigma$ away from the true values. ("3705) The accuracy of most methods. has become consistent with Ας=LO. with the historically mos innaccurate parameter measurement technique being the use of galaxy peculiar velocities.,"5) The accuracy of most methods has become consistent with $N_{\sigma}=1.0$, with the historically most innaccurate parameter measurement technique being the use of galaxy peculiar velocities."371 Measurements of O3; and particularly ον mace since 2000 tend to have accuracy IN significantly [ess than 1.0. indicating “confirmation bias” αποου an overestimation of error bar sizes.," Measurements of $\Omega_{M}$ and particularly $\Omega_{\Lambda}$ made since 2000 tend to have accuracy $N_{\sigma}$ significantly less than 1.0, indicating “confirmation bias” and/or an overestimation of error bar sizes."372 Over the 20 vear period covered in this study. it is apparen that many of the parameters in what is now the concordance CDAL cosmological model. went. from. the status of no information or only limits to being known at the 104 leve or better.," Over the 20 year period covered in this study, it is apparent that many of the parameters in what is now the concordance CDM cosmological model went from the status of no information or only limits to being known at the $10\%$ level or better."373 Lt is also apparent from Figure 2 that there was a “eolden age” of parameter measurements. between 1995 and ~2005 during which the number of publishec measurements peaked sharply and then declined., It is also apparent from Figure 2 that there was a “golden age” of parameter measurements between $\sim 1995$ and $\sim 2005$ during which the number of published measurements peaked sharply and then declined.374 This seems to indicate that for many purposes (such as the use of a background. cosmology in galaxy formation moclels). the precision to which the ACDAL parameters were known by the time of the List WALAD results is sullicient. and many of the reasons for pinning down the miocel better had. diminishes alter tha," This seems to indicate that for many purposes (such as the use of a background cosmology in galaxy formation models), the precision to which the $\Lambda$ CDM parameters were known by the time of the first WMAP results is sufficient, and many of the reasons for pinning down the model better had diminished after that."375 This said. however. the exception to this rule. measurements of wy (which are still rising in terms of number per vear at the end of our study) seems to poin o à coming new cra in parameter measurement.," This said, however, the exception to this rule, measurements of $w_{0}$ (which are still rising in terms of number per year at the end of our study) seems to point to a coming new era in parameter measurement."376 Certainly.μ he motivation for the large number of ongoing ancl future arge-scale structure. lensing and other surveys is to hun or the signatures of dynamical dark energy. and. moclified eravity. and given the number of researchers carrying ou hese studies it is likely that measurements will continue O vise.," Certainly, the motivation for the large number of ongoing and future large-scale structure, lensing and other surveys is to hunt for the signatures of dynamical dark energy and modified gravity, and given the number of researchers carrying out these studies it is likely that measurements will continue to rise."377 Many. parameters which we have not catalogued are now within reach of quantitiative study., Many parameters which we have not catalogued are now within reach of quantitiative study.378 These include he moclified gravity parameter. Le; (eves 2010) and the time derivative of the equation of state parameter. ts.," These include the modified gravity parameter, $E_{G}$ (Reyes 2010) and the time derivative of the equation of state parameter, $w_{a}$."379 Measurements of such parameters involve searching for deviations from the concordance CDAL model and fall into a dillerent category. from most of the parameters we have studied in this paper., Measurements of such parameters involve searching for deviations from the concordance CDM model and fall into a different category from most of the parameters we have studied in this paper.380 Lollationary parameters such as the non-Gaussianity (NL. or tensor to scalar ratio r will pinned down with higher precision in the future. and these should also represent a growth area.," Inflationary parameters such as the non-Gaussianity fNL, or tensor to scalar ratio $r$ will pinned down with higher precision in the future, and these should also represent a growth area."381 The motivation for most future measurements being largely. framed in terms of a quest for fundamental physics. it would be logical to assume that they will continue until the cause for the Universe's acceleration," The motivation for most future measurements being largely framed in terms of a quest for fundamental physics, it would be logical to assume that they will continue until the cause for the Universe's acceleration"382The 0.510 keV luminosity of the hard component [found in the VAL-Nerlon data. represented by the LMXD model. becomes 3.7x107 erg ! when integrated over the 6' racius.,"The 0.5–10 keV luminosity of the hard component found in the ${\it XMM}$ ${\it Newton}$ data, represented by the LMXB model, becomes $3.7 \times 10^{38}$ erg $^{-1}$ when integrated over the $6\arcmin$ radius."383" It is primarily attributable to the spill-over from the excluded point sources erg 1) § 3.2). with a smaller contribution from unresolved [aint sources (<5xLO erg "")D)."," It is primarily attributable to the spill-over from the excluded point sources $\sim 2.6 \times 10^{38}$ erg $^{-1}$; $\S$ 3.2), with a smaller contribution from unresolved faint sources $\lesssim 5 \times 10^{37}$ erg $^{-1}$ )."384" After subtracting these two estimates. we are left with an unexplained hard-component huninosity of ~GxLO"" eves tin the VALA/-New/on spectra of the diffuse emission."," After subtracting these two estimates, we are left with an unexplained hard-component luminosity of $\sim 6 \times 10^{37}$ erg $^{-1}$ in the ${\it XMM}$ ${\it Newton}$ spectra of the diffuse emission."385" Similarly. the Iuminositv of the hard component integrated over the 3’ radius derived from the Chandra data. 1.3109 erg s.|, exceeds the sum of the spill-over (~4.5x10* eres 1) and unresolved sources (<1xLO""i erg 1) as described in § 4."," Similarly, the luminosity of the hard component integrated over the $3\arcmin$ radius derived from the ${\it Chandra}$ data, $1.3 \times 10^{38}$ erg $^{-1}$, exceeds the sum of the spill-over $\sim 4.5 \times 10^{37}$ erg $^{-1}$ ) and unresolved sources $\lesssim 1 \times 10^{37}$ erg $^{-1}$ ) as described in $\S$ 4."386 These [acts suggests the presence of vel another. rather hot. diffuse emission in the central region of M 91.," These facts suggests the presence of yet another, rather hot, diffuse emission in the central region of M 31."387 In a detailed examination of the .XA/M Νεο) diffuse spectra (Figure 5)). we find ahint of excess just below 7 keV. which may correspond to Ee-Ix lines.," In a detailed examination of the ${\it XMM}$ ${\it Newton}$ diffuse spectra (Figure \ref{fig:0.4-7keV}) ), we find ahint of excess just below 7 keV, which may correspond to Fe-K lines."388 Ixdeed. a single PL fit io the 3.7 keV portion of the VALAL-New/lon spectra within 6. with 2/d.o.[. == 165/159. is improved to \7/d.o.f. == 152/157. by adding a narrow Gaussian with an equivalent width 1212 eV and a center οποιον of 6.64ing keV. According to an F-test. the Gaussian line is Significant at a > confidence level.," Indeed, a single PL fit to the 3–7 keV portion of the ${\it XMM}$ ${\it Newton}$ spectra within $\arcmin$, with $\chi^{2}$ = 165/159, is improved to $\chi^{2}$ = 152/157, by adding a narrow Gaussian with an equivalent width $121^{+59}_{-56}$ eV and a center energy of $6.64^{+0.07}_{-0.09}$ keV. According to an ${\it F}$ -test, the Gaussian line is significant at a $>$ confidence level."389 Moreover. if we add one more MIXL. component to the LMXD-3MBNKL model in & 3.3. where the metal abundances other than nitrogen of all the four MIXL components are fixed al 0.3 solar units referring to Oxveen abuncdances of planetary. nebulae in the bulge of M31 (Jacobyand.Ciardullo1999).. (he entire 0.47 keV XAMM- Neiebon spectra in the 6 radius is reproduced better (A? ddecreasing to 768/701 from 792/703). with insignificant changes in (he parameters of the other MIXL components.," Moreover, if we add one more MKL component to the LMXB+3MKL model in $\S$ 3.3, where the metal abundances other than nitrogen of all the four MKL components are fixed at 0.3 solar units referring to Oxygen abundances of planetary nebulae in the bulge of M31 \citep{M31_abu_Jacoby}, the entire 0.4–7 keV ${\it XMM}$ ${\it Newton}$ spectra in the $\arcmin$ radius is reproduced better $\chi^{2}$ decreasing to 768/701 from 792/703), with insignificant changes in the parameters of the other MKL components."390 The temperature and luminosity of the added fourth MIXL have been obtained as 3.7.13 keV and (1.120.4)xLO erg ! respectively. within the 6 radius.," The temperature and luminosity of the added fourth MKL have been obtained as $3.7^{+1.4}_{-0.7}$ keV and $(1.1\pm0.4) \times 10^{38}$ erg $^{-1}$ respectively, within the $\arcmin$ radius."391 The inferred luminosity of this hot AINL component agrees with the unexplained hard-component luminosity., The inferred luminosity of this hot MKL component agrees with the unexplained hard-component luminosity.392 Although the Chandra specirum within 3° does not clearly reveal the Fe-Ix line. the same analvsis vields a hot MIXL temperature of >5 keV and a Iuminosity of (321)x10 erg |.," Although the ${\it Chandra}$ spectrum within $\arcmin$ does not clearly reveal the Fe-K line, the same analysis yields a hot MKL temperature of $> 5$ keV and a luminosity of $(3\pm1) \times 10^{37}$ erg $^{-1}$."393 The center enerev of the Fe-Ix line. (he implied temperature (several keV). and the luminosity of this hot and possible extended thermal emission are similar to those of the hot component of the Galactic ridee emission (Ixovanmaοἱal.1986:Kaneda and the Galactic bulge emission (INokubun 2001)..," The center energy of the Fe-K line, the implied temperature (several keV), and the luminosity of this hot and possible extended thermal emission are similar to those of the hot component of the Galactic ridge emission \citep{ridge_Koyama,ridge_Kaneda,ridge_Valinia} and the Galactic bulge emission \citep{bulge_Kokubun}. ."394 The soft X-ray (S 2 keV) spectra of the diffuse emission generally require more than one temperature components. even if we tse relatively narrow (1' ~ 0.2 kpc) annular regions.," The soft X-ray $\lesssim$ 2 keV) spectra of the diffuse emission generally require more than one temperature components, even if we use relatively narrow $\arcmin$ $\sim$ 0.2 kpc) annular regions."395The sightline toward IID 27778 has N(CO) = 2.5x10! 7 elal.1936): this is the largest CO column density among our six sightlines by about a factor ol 10.,"The sightline toward HD 27778 has N(CO) = $2.5 \times 39610^{16}$ $^{-2}$ \citep{fed94,jos86}; this is the largest CO column density among our six sightlines by about a factor of 10."397 Other C-bearing molecules ean be ignored because their abundances are insignificant compared to CO., Other C-bearing molecules can be ignored because their abundances are insignificant compared to CO.398 For example. CLL CN. Cs and Cy toward ID 27778 contribute a total C column densitv of only L3x10! 7 (Okaetal.2003).," For example, CH, CN, $_{2}$ and $_{3}$ toward HD 27778 contribute a total C column density of only $1.8 \times 10^{14}$ $^{-2}$ \citep{oka03}."399. None of the sightlines contains an appreciable amount of neutral C: each has à NGC 1) that is less than 5x1012 em7., None of the sightlines contains an appreciable amount of neutral C; each has a N(C ) that is less than $5 \times 10^{15}$ $^{-2}$.400 The final source that can contribute significantly to the total £as-phase C abundance is excited Ci. HD 37061 is the only sightline for which an excited CU] absorption feature was detected., The final source that can contribute significantly to the total gas-phase C abundance is excited C. HD 37061 is the only sightline for which an excited C ] absorption feature was detected.401 Two features out of the 63.42 1 energv level. at 2326.1126 aand 2328.8374 were detected and measured to have equivalent widths of 1.0140.26 and 0.8940.21má... respectively.," Two features out of the 63.42 $^{-1}$ energy level, at 2326.1126 and 2328.8374 were detected and measured to have equivalent widths of $1.01 \pm 0.26$ and $0.89 \pm 0.21$, respectively."402 The equivalent widths for these lines are nearly equal although the oscillator strengtlis reported in Morton (2003) suggest that the A2326 feature should be approximately twice the strength. of A2328.., The equivalent widths for these lines are nearly equal although the oscillator strengths reported in Morton (2003) suggest that the $\lambda2326$ feature should be approximately twice the strength of $\lambda2328$.403 This leads to a large uncertainiv in the calenlatecd C dr abundance: the weighted average of the two features gives a column density of Χίος LOM., This leads to a large uncertainty in the calculated C $^{*}$ abundance; the weighted average of the two features gives a column density of N(C $^{*}) = 4.65 \pm 0.84 \times 10^{17}$ .404 This column density is consistent with the crude estimate possible for the C 11A1335 damping wines.," This column density is consistent with the crude estimate possible for the C $^{*} 405\lambda 1335$ damping wings."406 This suggests that. toward HD 37061 approximately of the eas-phase C is in an excited state (see Table 2)., This suggests that toward HD 37061 approximately of the gas-phase C is in an excited state (see Table 2).407 Table 2 gives a summary of the interstellar gas-phiase carbon measurements aud column densities for each sightline in this study., Table 2 gives a summary of the interstellar gas-phase carbon measurements and column densities for each sightline in this study.408 The C i1] equivalent widths and resulting column densities are the averages from (he three independent analyses., The C ] equivalent widths and resulting column densities are the averages from the three independent analyses.409 The reported lo uncertainties are the largest from (he three independent determinations., The reported $\sigma$ uncertainties are the largest from the three independent determinations.410 The (hree measurements for each sightline all agreed. with each other within the reported lo uncertainties., The three measurements for each sightline all agreed with each other within the reported $\sigma$ uncertainties.411 The weakness of the C iu] A2325 transition allows abundances for this ion to be determined directly from the weak line limit., The weakness of the C ] $\lambda2325$ transition allows abundances for this ion to be determined directly from the weak line limit.412 We use the oscillator strength reported in Morton (2003: log [A=—3.954)., We use the oscillator strength reported in Morton (2003; log $\lambda = -3.954$ ).413 The lower limit of 0.5 rreported in Table 2 for the equivalent width in the IID 27778 spectrum is approximately a 3c limit., The lower limit of 0.5 reported in Table 2 for the equivalent width in the HD 27778 spectrum is approximately a $\sigma$ limit.414 To check that such a feature would be identifiable in the spectrum. we produced a svnthetie absorption feature of 0.5 and the width of the interstellar O absorption: the synthetic feature was easily visible giving us confidence that our limit is conservative.," To check that such a feature would be identifiable in the spectrum, we produced a synthetic absorption feature of 0.5 and the width of the interstellar O absorption; the synthetic feature was easily visible giving us confidence that our limit is conservative."415 In order to consolidate all of the C absorption measurements using unilorm atomic constants. we eive a summary of previous interstellar gas-phase carbon measurements updated," In order to consolidate all of the C absorption measurements using uniform atomic constants, we give a summary of previous interstellar gas-phase carbon measurements updated"416NGCB55506 is a spiral galaxy with a Sevfert 2 nucleus.,5506 is a spiral galaxy with a Seyfert 2 nucleus.417 The central racio structure was studied by Ulvestadetal. and Ungeretal.(1986). by VLA and. MERLIN observations., The central radio structure was studied by \citet{ulvestad81} and \citet{unger86} by VLA and MERLIN observations.418 Lt shows cilluse feat bubble-likeextending to the north-west of athe unresolved nucleus., It shows a diffuse bubble-like feature extending to the north-west of the unresolved nucleus.419 ureAt 5 CLL Wehrle&Morris(1987). found a low-surlace brightness halo enshroucding the central Alulti-frequeney observations of the nucleus with the PTL (Sadleretal.1995). showed that it has a convex spectrum., At 5 GHz \citet{wehrle87} found a low-surface brightness halo enshrouding the central Multi-frequency observations of the nucleus with the PTI \citep{sadler95} showed that it has a convex spectrum.420 Pe-scale VLBI observations at 18. 6 and 3.6 em (Middelbergetal.2004). could resolve the nucleus in three main components roughly aligned in the cast-west direction and extending within an area ol about 50 imas (~ 6 pc).," Pc-scale VLBI observations at 18, 6 and 3.6 cm \citep{middelberg04}421 could resolve the nucleus in three main components roughly aligned in the east-west direction and extending within an area of about 50 mas $\sim$ 6 pc)."422 The flattish spectrum cdisplaved by the brightest component suggests that itis the true source core., The flattish spectrum displayed by the brightest component suggests that it is the true source core.423We have examined (he average fractional polarization as a function of radio aud optical class.,We have examined the average fractional polarization as a function of radio and optical class.424 We show in Figure 12 the distributions for the compact svainnmetrie (cso) ancl (1d) objects at 14.5 and 4.8 Gllz., We show in Figure 12 the distributions for the compact symmetric (cso) and lobe-dominated (ld) objects at 14.5 and 4.8 GHz.425 These eroups are comprised almost exclusively of galaxies. and. with the exception of 07234-6719. they have steep total flux density spectra.," These groups are comprised almost exclusively of galaxies, and, with the exception of 0723+679, they have steep total flux density spectra."426 For comparison. (he distributions are shown for the flat spectrum QSOs and BL Lacs in Figure 13.," For comparison, the distributions are shown for the flat spectrum QSOs and BL Lacs in Figure 13."427 The number of BL Lacs is small in the sample. but a distribution based on a laveer fIux-limited sample of BL Lacs ean be found in Alleretal.(1999).," The number of BL Lacs is small in the sample, but a distribution based on a larger flux-limited sample of BL Lacs can be found in \citet{all99}."428. We note that the QSO 0723+679 is included in both sets of distributions since its properties place it in both categories: i( is classed as an Id object based on its radio morphology while we find. that the spectral index is flat in the centimeter band., We note that the QSO 0723+679 is included in both sets of distributions since its properties place it in both categories: it is classed as an ld object based on its radio morphology while we find that the spectral index is flat in the centimeter band.429 The esos are well-known to have very. low degrees of polarization at 4.8 Gllz (Stangellinietal...1993)... and (his result. combined with recent VLBA observations identilving low values of the polarization at 8.4 GlIz. have been used (o argue that these objects are depolarized by Faraday rotation in a circummnmiclear torus (PeckandTavlor|2000).," The csos are well-known to have very low degrees of polarization at 4.8 GHz \citep{stan98}, and this result, combined with recent VLBA observations identifying low values of the polarization at 8.4 GHz, have been used to argue that these objects are depolarized by Faraday rotation in a circumnuclear torus \citep{pec00}."430. This interpretation is consistent. with the waveleneth-dependent fractional polarizations that we finc., This interpretation is consistent with the wavelength-dependent fractional polarizations that we find.431 In Table 3 we summarize our results on polarization for the lobe-dominated objects in (his sample., In Table 3 we summarize our results on polarization for the lobe-dominated objects in this sample.432 The detailed polarization structure and spectral variations within the lobes aud central regions have been studied with observations from the VLA and sophisticated analysis tools (IXatz-Stoneetal.1999)., The detailed polarization structure and spectral variations within the lobes and central regions have been studied with observations from the VLA and sophisticated analysis tools \citep{kat99}.433. In the ease of the ER. Is. such data have revealed sheath-like polarization structure in some objects (1lardeastleetal.1996). and complicated spectra eradients in FR IIs (Treicheletal.2001).," In the case of the FR Is, such data have revealed sheath-like polarization structure in some objects \citep{har96}434 and complicated spectral gradients in FR IIs \citep{tre01}."435. However. our integrated measurements can be used (o identily class differences.," However, our integrated measurements can be used to identify class differences."436 We list optical class in column 2. and average [ractiona polarization corrected for bias at 4.5 and 14.5 Gllz in columns 3 and 4 respectively.," We list optical class in column 2, and average fractional polarization corrected for bias at 4.8 and 14.5 GHz in columns 3 and 4 respectively."437 An indicator of the spectrum of the polarized flux (note that (this is not fractional polarization) is given in column 5: these are denoted bv flat. inverted. or steep (E. I. 5). based on visua inspection of the longterm light curves.," An indicator of the spectrum of the polarized flux (note that this is not fractional polarization) is given in column 5: these are denoted by flat, inverted, or steep (F, I, S), based on visual inspection of the longterm light curves."438 In some cases (he spectrum has changed with time: in (hese cases (e.g. 06054-4380) we list two classes. with the first denoting the most characteristic spectral behavior during the full Gime window of the study.," In some cases the spectrum has changed with time; in these cases (e.g. 0605+480) we list two classes, with the first denoting the most characteristic spectral behavior during the full time window of the study."439 FIR class is listed in column 6., FR class is listed in column 6.440" For the FR II class objects we list in column 7 the projected. linear size (taken [rom the compilation of Nilsson(1998) which assumes //—50 km !Mpe. | and q,=0.5."," For the FR II class objects we list in column 7 the projected linear size taken from the compilation of \citet{nils98}441 which assumes $H$ =50 km $^{-1}$ $^{-1}$ and $q_o$ =0.5."442" For the FR Is we give projected leneth of the brighter jet originally tabulated in but modified to a value of [15-50 km tMpe ! by Hardcastleetal.(1996). and assuming q,-—0.5."," For the FR Is we give projected length of the brighter jet originally tabulated in \citet{bri84} but modified to a value of $H$ =50 km $^{-1}$ $^{-1}$ by \citet{har96}443 and assuming $q_o$ =0.5."444 In the three EH. Is in the PR sample the spectra of the polarized flix are steep., In the three FR Is in the PR sample the spectra of the polarized flux are steep.445 In the case of (he FR Us we find a range of behaviors: half of the sources have fIat-to-invertecd, In the case of the FR IIs we find a range of behaviors: half of the sources have flat-to-inverted446Curvature radiation is a widely discussed process to explain the observed emission [rom (he maguelosphere of pulsars.,Curvature radiation is a widely discussed process to explain the observed gamma-ray emission from the magnetosphere of pulsars.447 In this section we discuss the difficulty of invoking curvature radiation as (he emission process that explains the observed. pulsed enussion from the Crab pulsar above 100 GeV. We assunie an outer gap scenario with (he accelerating electric field being parallel to the magnetic field Chengetal.(1956).., In this section we discuss the difficulty of invoking curvature radiation as the emission process that explains the observed pulsed emission from the Crab pulsar above 100 GeV. We assume an outer gap scenario with the accelerating electric field being parallel to the magnetic field \cite{1986ApJ...300..500C}.448 In the electric field a beam of charged particles accelerates hereafter primary beam that has à particle density. which is of the order of the Goldreich- density ney (Goldreich&Julian1969).," In the electric field a beam of charged particles accelerates – hereafter primary beam – that has a particle density, which is of the order of the Goldreich-Julian density $n_{GJ}$ \citep{GoldreichJulian}."449. The primary beam loses a significant amount of its energv (rough various radiative processes of which the curvature emission aud the IC- pair production are the dominant ones Arons(1983):Cheng&Ruderman(1977).," The primary beam loses a significant amount of its energy through various radiative processes of which the curvature emission and the IC-induced pair production are the dominant ones \cite{1983ApJ...266..215A,cr77}."450. The pair-production process results in the formation of a second population of particles hereafter secondary plasma. which has a higher particle density (han the primary beam but a smaller bulk Lorentz factor.," The pair-production process results in the formation of a second population of particles – hereafter secondary plasma –, which has a higher particle density than the primary beam but a smaller bulk Lorentz factor."451 Within this outer-gap framework we derive a general upper limit of the break in the curvature radiation spectrum (hat is emitted by particles within the outer gap of the Crab pulsar., Within this outer-gap framework we derive a general upper limit of the break in the curvature radiation spectrum that is emitted by particles within the outer gap of the Crab pulsar.452 The limit we obtain is independent of the particular details of the acceleration mechanism of the primary beam., The limit we obtain is independent of the particular details of the acceleration mechanism of the primary beam.453 In our argument we follow a similar approach that has been applied before in the discussion of the svuchrotron emission from pulsar wind nebulae by deJageretal.(1996). and Lyutikoy(2010).., In our argument we follow a similar approach that has been applied before in the discussion of the synchrotron emission from pulsar wind nebulae by \cite{1996ApJ...457..253D} and \cite{2010MNRAS.405.1809L}.454 Within the outer eap. the charged particles follow the curved magnetic field lines ancl. therefore. emit eurvature-radiation photons.," Within the outer gap, the charged particles follow the curved magnetic field lines and, therefore, emit curvature-radiation photons."455" The curvature radiation spectrum emitted by monoenereelic particles has a break at energy. ey. (Zheleznvakov.1996) where /2. is (he curvature radius of the magnetic field lines. aud >, is the Lorentz [nctor of (he radiating particles."," The curvature radiation spectrum emitted by monoenergetic particles has a break at energy $\epsilon_{br}$ \citep{1996ASSL..204.....Z}456 = _b^3, where $R_c$ is the curvature radius of the magnetic field lines, and $\gamma_b$ is the Lorentz factor of the radiating particles."457" An upper limit of 5; is set bv the constraint that while the particles accelerate they radiate and. therefore. the maximum value of 5, is obtained. when acceleration gains are"," An upper limit of $\gamma_b$ is set by the constraint that while the particles accelerate they radiate and, therefore, the maximum value of $\gamma_b$ is obtained when acceleration gains are"458a fit by comparing the obtained parameters with those used as input for the simulations.,a fit by comparing the obtained parameters with those used as input for the simulations.459" Instead, we use the reduced x? for each of the 960 fits to decide whether a fit is acceptable or not."," Instead, we use the reduced $\chi^2$ for each of the 960 fits to decide whether a fit is acceptable or not."460 We obtain values between 0.88 and 357., We obtain values between 0.88 and 357.461" In addition, we examine the residuals of each fit by eye, dividing them into two categories: A set of fits for which the residuals do not visually show obvious correlations and a set for which it is apparent that the chosen gravitational potential model is not adequate."," In addition, we examine the residuals of each fit by eye, dividing them into two categories: A set of fits for which the residuals do not visually show obvious correlations and a set for which it is apparent that the chosen gravitational potential model is not adequate."462 Figure 5 shows typical examples of the residuals from three simulations., Figure \ref{fig:residuals} shows typical examples of the residuals from three simulations.463 Each of the simulated data sets has 418+1 astrometric data points and 142c1 radial velocity measurements., Each of the simulated data sets has $418\pm 1$ astrometric data points and $142\pm 1$ radial velocity measurements.464 The exact numbers vary due to the random variations of the sampling pattern., The exact numbers vary due to the random variations of the sampling pattern.465" Given that our fits have 13 free parameters, the number of degrees of freedom is naor©2x4184-142—13 965."," Given that our fits have 13 free parameters, the number of degrees of freedom is $n_\mathrm{dof}\approx 2\times 418+142-13=965$ ."466 Figure 6 shows the distribution of reduced X? together with the flag whether a given fit is acceptable or not., Figure \ref{fig:dist} shows the distribution of reduced $\chi^2$ together with the flag whether a given fit is acceptable or not.467" Clearly, the reduced x? can be used as discriminator."," Clearly, the reduced $\chi^2$ can be used as discriminator."468" The largest reduced X? corresponding to fit classified as ’acceptable’ is 1.36, the smallest reduced x? acorresponding to a fit classified as ’not acceptable’ is 1.12."," The largest reduced $\chi^2$ corresponding to a fit classified as 'acceptable' is 1.36, the smallest reduced $\chi^2$ corresponding to a fit classified as 'not acceptable' is 1.12."469" The optimum cut is at a reduced X? of 1.22, yielding as many good fits above as bad fits below the threshold."," The optimum cut is at a reduced $\chi^2$ of 1.22, yielding as many good fits above as bad fits below the threshold."470 The total number of fits misclassified by this cut is 41., The total number of fits misclassified by this cut is 41.471 The total number of bad fits is 409 and correspondingly 551 fits have a reduced X? below the threshold., The total number of bad fits is 409 and correspondingly 551 fits have a reduced $\chi^2$ below the threshold.472" Hence, the IBH would be detectable from the data in 224396 of the cases."," Hence, the IBH would be detectable from the data in $\approx$ of the cases."473 We find a dependence of the fraction of bad fits on the assumed mass for the IBH., We find a dependence of the fraction of bad fits on the assumed mass for the IBH.474" For q=10~*, 2.5x107?, 5x102, 107? the percentage of detectable IBHs is15%,,39%,,51%,, and 66%,, respectively."," For $q=10^{-4}$, $2.5\times 10^{-3}$, $5\times 10^{-3}$, $10^{-3}$ the percentage of detectable IBHs is, and , respectively."475 Having a reduced χ>1.22 corresponds formally to a 4.70 detection of the effects of the IBH for nao:= 965., Having a reduced $\chi^2 \geq 1.22$ corresponds formally to a $4.7\sigma$ detection of the effects of the IBH for $n_\mathrm{dof}=965$ .476" In reality, there will be perturbing effects such as confusion events, recognised or unrecognised."," In reality, there will be perturbing effects such as confusion events, recognised or unrecognised."477" Hence, the actual x? might be larger than in the simulations and the simple Gaussian statistics will not apply"," Hence, the actual $\chi^2$ might be larger than in the simulations and the simple Gaussian statistics will not apply."478 We are nevertheless confident that by observing the astrometric (and photometric) residuals as a function of time the effects of an IBH can be disentangled from confusion events., We are nevertheless confident that by observing the astrometric (and photometric) residuals as a function of time the effects of an IBH can be disentangled from confusion events.479 The patterns of the residuals contain more information than a single x? value., The patterns of the residuals contain more information than a single $\chi^2$ value.480 In Figure 7 we examine the dependence of the reduced X? on the black hole binary parameters., In Figure \ref{fig:dist2} we examine the dependence of the reduced $\chi^2$ on the black hole binary parameters.481" The left panel in the first row shows that the fits on average get worse when the mass of the assumed IBH is increased, as expected."," The left panel in the first row shows that the fits on average get worse when the mass of the assumed IBH is increased, as expected."482 The right panel in the first row shows that a value for the semi major axis of the IBH around z1mpc leads on average to the worst fits., The right panel in the first row shows that a value for the semi major axis of the IBH around $\approx 1\mpc$ leads on average to the worst fits.483" 'These two parameters correlate actually best with the reduced x?, and in Figure 8 we show the reduced x? in the Mipu-a-plane."," These two parameters correlate actually best with the reduced $\chi^2$, and in Figure \ref{fig:dist3} we show the reduced $\chi^2$ in the $M_\mathrm{IBH}$ $a$ -plane."484 The unacceptable fits occupy a well-defined region in this plot., The unacceptable fits occupy a well-defined region in this plot.485" The goodness of the fits, on the other hand, is fairly independent of the eccentricity of the IBH orbit (second row of Figure 7,, left panel)."," The goodness of the fits, on the other hand, is fairly independent of the eccentricity of the IBH orbit (second row of Figure \ref{fig:dist2}, , left panel)."486 The right panel in the second row shows that the periapsis distance p=a(1—e) of the IBH isa less good predictor for the fit than the semi major axis.," The right panel in the second row shows that the periapsis distance $p=a\,(1-e)$ of the IBH is a less good predictor for the fit than the semi major axis."487 The reduced X?does not correlate with the finite set of orbital, The reduced $\chi^2$does not correlate with the finite set of orbital488"The paper by vonHippel(1998) lists 10 white dwarfs that we call henceforth the ""classical"" Hyades white dwarfs.",The paper by \citet{1998AJ....115.1536V} lists 10 white dwarfs that we call henceforth the “classical” Hyades white dwarfs.489 There are seven single white dwarfs and three in binary systems., There are seven single white dwarfs and three in binary systems.490 We list them with their primary identifiers in SIMBAD (Data base of the Centre de Donnéees astronomiques de Strasbourg. CDS).," We list them with their primary identifiers in SIMBAD (Data base of the Centre de Donnéees astronomiques de Strasbourg, CDS)."491 The seven single white dwarfs are EGGR 26. 29. 36. 37. 39. 42. and 316.," The seven single white dwarfs are EGGR 26, 29, 36, 37, 39, 42, and 316."492 The three stars in binary systems are HR 1358. EGGR 38. and V47] Tau.," The three stars in binary systems are HR 1358, EGGR 38, and V471 Tau."493 Data for these stars are given in Table | (the first ten rows)., Data for these stars are given in Table \ref{table:1} (the first ten rows).494 In some cases there is no consistency about actual membership in the cluster., In some cases there is no consistency about actual membership in the cluster.495 For instance. Weidemannetal.(1992) exclude EGGR 29 from membership. because they put it at 60 pe. where its tangential velocity would be discordant from the bulk tangential velocity. whereas DeGennaroetal.(2009) used it for their determination of the white dwarf age of the Hyades.," For instance, \citet{1992AJ....104.1876W} exclude EGGR 29 from membership, because they put it at 60 pc, where its tangential velocity would be discordant from the bulk tangential velocity, whereas \citet{2009ApJ...696...12D} used it for their determination of the white dwarf age of the Hyades."496 Reid(1992) lists two additional candidates RHya 102 and RHya 145., \citet{1992MNRAS.257..257R} lists two additional candidates RHya 102 and RHya 145.497 He also examined all candidates for Hyades white dwarfs proposed by vanAltena(1969).. and discarded all of them except vA54 and vA71. which were outside his view.," He also examined all candidates for Hyades white dwarfs proposed by \citet{1969AJ.....74....2V}, and discarded all of them except vA54 and vA71, which were outside his field-of-view."498 We discuss these four objects in Sect. 4.., We discuss these four objects in Sect. \ref{individual}.499 Throughout the paper we use the following abbreviations for star names: In Paper I we described in detail how we selected MS (main sequence) Hyades candidates from their kinematic and photometric properties in the PPMXL catalogue (Róser.Dem-leitner&Schilbach. 2010).., Throughout the paper we use the following abbreviations for star names: In Paper I we described in detail how we selected MS (main sequence) Hyades candidates from their kinematic and photometric properties in the PPMXL catalogue \citep{2010AJ....139.2440R}.500 More specifically. we used the Carlsberg-UCAC (CU) subset containing improved proper motions and photometry by including UCACS3 (Zachariasetal.2010) and CMCI4. Carlsberg Meridian Catalog 14. (CopenhagenUniv.Obs.etal..2006).," More specifically, we used the Carlsberg-UCAC (CU) subset containing improved proper motions and photometry by including UCAC3 \citep{2010AJ....139.2184Z} and CMC14, Carlsberg Meridian Catalog 14, \citep{2006yCat.1304....0C}."501. Paper I also contains a description of the convergent point method. which served as a baseline for the selection.," Paper I also contains a description of the convergent point method, which served as a baseline for the selection."502 For our general selection process we did not permit the tangential motion to differ from the one given by the bulk motion of the cluster by more than 4 kms7!. and we considered only stars closer than 30 pe from the cluster centre.," For our general selection process we did not permit the tangential motion to differ from the one given by the bulk motion of the cluster by more than 4 $\rm{km\,s}^{-1}$, and we considered only stars closer than 30 pc from the cluster centre."503 The stars had to be in the CU subset to PPMXL to ensure that they have CMCI4 and/or 2MASS (Skrutskieetal..2006) measurements., The stars had to be in the CU subset to PPMXL to ensure that they have CMC14 and/or 2MASS \citep{2006AJ....131.1163S} measurements.504 These kinematic selection criteria were fulfilled by 15757 stars out of the 140 million contained in the CU subset. which were shown in Fig.," These kinematic selection criteria were fulfilled by 15757 stars out of the 140 million contained in the CU subset, which were shown in Fig."505 | of Paper I. Two features from the kinematic selection via the convergent por= method are worth to be explained in more detail., 1 of Paper I. Two features from the kinematic selection via the convergent point method are worth to be explained in more detail.506 First. for each candidate that i5 supposed to share the bulk space motion of the cluster. the convergent point method predicts a radial velocity that only depends on the position a.o of the star.," First, for each candidate that is supposed to share the bulk space motion of the cluster, the convergent point method predicts a radial velocity that only depends on the position $\alpha, \delta$ of the star."507 In consequence. the radial velocity of each candidate has to be measured to confirm it is still member.," In consequence, the radial velocity of each candidate has to be measured to confirm it is still member."508 Second. the convergent point method attributes (predicts) a so-called secular parallax to each candidate by minimising the difference between the space motion of the cluster centre and the space motion of a candidate star.," Second, the convergent point method attributes (predicts) a so-called secular parallax to each candidate by minimising the difference between the space motion of the cluster centre and the space motion of a candidate star."509 In a very strict sense the secular parallax is not the least-squares solution in the plane perpendicular to the line-of-sight. but this difference is small in all practical cases.," In a very strict sense the secular parallax is not the least-squares solution in the plane perpendicular to the line-of-sight, but this difference is small in all practical cases."510 So. the second confirmation of membership comes from an independent measurement of the distance to the star.," So, the second confirmation of membership comes from an independent measurement of the distance to the star."511 If the result of this independent distance determination does not confirm the prediction. this means in turn that the difference in space motion between the bulk of the cluster and the candidate increases.," If the result of this independent distance determination does not confirm the prediction, this means in turn that the difference in space motion between the bulk of the cluster and the candidate increases."512 This may rule out a given star as a member candidate., This may rule out a given star as a member candidate.513 As an independent check of the predicted distances of kinematic candidates. we can consider their location in different colour-absolute-magnitude diagrams.," As an independent check of the predicted distances of kinematic candidates, we can consider their location in different colour-absolute-magnitude diagrams."514" In Paper I we used B.V-photometry for bright stars: for stars fainter than My,=4 the basic photometric data were r from CMC14 and JHK,."," In Paper I we used $B,V$ -photometry for bright stars; for stars fainter than $M_{K_s} = 4$ the basic photometric data were $r'$ from CMC14 and $JHK_s$."515 Only for 724 out of 15757 kinematic candidates. the membership was confirmed by photometric selection in Paper I. The procedure adopted in Paper I is a two-step procedure.," Only for 724 out of 15757 kinematic candidates, the membership was confirmed by photometric selection in Paper I. The procedure adopted in Paper I is a two-step procedure."516 The first step is the kinematic selection. and the second is the check of kinematically predicted distances with photometric ones. Le. à comparison with isochrones.," The first step is the kinematic selection, and the second is the check of kinematically predicted distances with photometric ones, i.e. a comparison with isochrones."517 In principle. the same approach could be applied to find white dwarfs among kinematic candidates.," In principle, the same approach could be applied to find white dwarfs among kinematic candidates."518 This would require an all-sky. accurate. multi (at least two)-colour photometric survey.," This would require an all-sky, accurate, multi (at least two)-colour photometric survey."519 Concentrating on a 30 pe radius around the centre of the Hyades. such a survey should at least cover of the celestial sphere or 5000 square degrees.," Concentrating on a 30 pc radius around the centre of the Hyades, such a survey should at least cover of the celestial sphere or 5000 square degrees."520 The only survey that fulfils this requirement is 2MASS in the near-infrared., The only survey that fulfils this requirement is 2MASS in the near-infrared.521 However. even at the central distance of the Hyades (46.3 pe). white dwarfs will be at the limiting magnitude of 2MASS and also of CMCI4. where the photometric quality becomes very poor.," However, even at the central distance of the Hyades (46.3 pc), white dwarfs will be at the limiting magnitude of 2MASS and also of CMC14, where the photometric quality becomes very poor."522 Therefore. we introduced an intermediate step. in which all kinematic candidates from Paper | were cross-mateched with the white dwarf catalogues by Luyten (VizieR Online Data Catalog HI/70) and MeCook&Sion(1999).. the updated version (VizieR Online Data Catalog IH/235B).," Therefore, we introduced an intermediate step, in which all kinematic candidates from Paper I were cross-matched with the white dwarf catalogues by Luyten (VizieR Online Data Catalog III/70) and \citet{1999ApJS..121....1M}, the updated version (VizieR Online Data Catalog III/235B)."523 Each match was individually checked using the VizieR data base from the CDS., Each match was individually checked using the VizieR data base from the CDS.524 After rejecting obvious red dwarfs (from Luyten candidates). we identified 20 white dwarfs that passed the," After rejecting obvious red dwarfs (from Luyten candidates), we identified 20 white dwarfs that passed the"525prompt emission (Ghisellinietal.2007) or up-scattered forward-shock emission 2001).,prompt emission \citep{ghisellini07} or up-scattered forward-shock emission \citep{panaitescu07}.526 From the point of microphysies in the hyvdrodyvnanmic evolution. the nature of coupling between the electrons. protons and magnetic field is complex (Chiang&Dermer1999).," From the point of microphysics in the hydrodynamic evolution, the nature of coupling between the electrons, protons and magnetic field is complex \citep{chiang99}."527 Usually the simple wav is (o assume the equipartition between electrons. protons and magnetic field (Danaiteseu&Mészázros2006).," Usually the simple way is to assume the equipartition between electrons, protons and magnetic field \citep{panaitescu98}."528". ILowever. in (his Letter. we propose (hat the kinetic energv of (he relativistic shocks in the plasma has been converted to the internal energy. as three parts: (1) 25. which is theenergy of magnetic field: (2) 7, and τρ. it means that the electrons and protons/positrons are accelerated by the shocks. normally. (his is (he process of first-order Fermi acceleration: (3) z,. which presents the turbulent energy. and (his energy would sustain a relatively long time (see Section 2)."," However, in this Letter, we propose that the kinetic energy of the relativistic shocks in the plasma has been converted to the internal energy as three parts: (1) $\varepsilon_B$, which is theenergy of magnetic field; (2) $\varepsilon_e$ and $\varepsilon_p$, it means that the electrons and protons/positrons are accelerated by the shocks, normally, this is the process of first-order Fermi acceleration; (3) $\varepsilon_t$, which presents the turbulent energy, and this energy would sustain a relatively long time (see Section 2)."529 The last part has not been taken into account bv the former research., The last part has not been taken into account by the former research.530 In our novel scenario. the relativistic electrons accelerated by the first-order Fermi acceleration emit the gamma-ray by svinchrotron radiation. alter the decrease of the prompt emission tail which is shown as the deep decay in (he early N-rax light curve. indicating that the internal shocks are abated. the follow-up turbulence and its effects might be dominated.," In our novel scenario, the relativistic electrons accelerated by the first-order Fermi acceleration emit the gamma-ray by synchrotron radiation, after the decrease of the prompt emission tail which is shown as the deep decay in the early X-ray light curve, indicating that the internal shocks are abated, the follow-up turbulence and its effects might be dominated."531 The turbulence could transfer its energv (o the electrons via Fermi acceleration. which is also called as the stochastic acceleration.," The turbulence could transfer its energy to the electrons via second-order Fermi acceleration, which is also called as the stochastic acceleration."532 Therelore. in this turbulent region. due to the resonant interaction between electrons and plasma waves. the electrons buried in the magnetic field are re-accelerated by the stochastic acceleration.," Therefore, in this turbulent region, due to the resonant interaction between electrons and plasma waves, the electrons buried in the magnetic field are re-accelerated by the stochastic acceleration."533 The enussion of these electrons dominates (he shallow decay phase. until the turbulent. energy dissipates and the external shock sweeps (he surround medium thus the deep decay appears again.," The emission of these electrons dominates the shallow decay phase, until the turbulent energy dissipates and the external shock sweeps the surround medium thus the deep decay appears again."534 In Section 2. we review the Fokker-Planck equation and list the coefficients associated with the turbulent term.," In Section 2, we review the Fokker-Planck equation and list the coefficients associated with the turbulent term."535" In Section 3. the turbulent. parameter τι, as same as z, and τμ. is introduced."," In Section 3, the turbulent parameter $\varepsilon_t$, as same as $\varepsilon_e$ and $\varepsilon_B$, is introduced."536 Due to the turbulence. these microphvsical parameters evolved with time are constrained by (he process of stochastic acceleration.," Due to the turbulence, these microphysical parameters evolved with time are constrained by the process of stochastic acceleration."537 Finally. we select these relations to reproduce the feature of shallow decay.," Finally, we select these relations to reproduce the feature of shallow decay."538 The discussions are given in Section 4., The discussions are given in Section 4.539 The stochastic acceleration was suggested as an non-neglected mechanism to produce the high energv particles in GRBs (Wasman1995;Dermer&IIumi2001).," The stochastic acceleration was suggested as an non-neglected mechanism to produce the high energy particles in GRBs \citep{waxman95,dermer01}."540. The numerical simulation has confirmed (hat the stochastic acceleration in the relativistic shocks plavs an important role on the particle energy distribution and evolution (Virtanen&Vainio2005 ).., The numerical simulation has confirmed that the stochastic acceleration in the relativistic shocks plays an important role on the particle energy distribution and evolution \citep{virtanen05}. .541 In general. (he charge particles ave expected to be accelerated through resonant interactions," In general, the charge particles are expected to be accelerated through resonant interactions"542The UV spectrum of the z=2.3 galaxy BX418 from Erbetal.(2010) (shown in Figure 7)) has a very weak stellar wind line with a P Cygni profile and strong and broad emission.,The UV spectrum of the $z=2.3$ galaxy BX418 from \citet{erb} (shown in Figure \ref{bx418}) ) has a very weak stellar wind line with a P Cygni profile and strong and broad emission.543 There is clearly a narrow nebular component superposed on the broader stellar emission line., There is clearly a narrow nebular component superposed on the broader stellar emission line.544 This indicates a very hard ionising spectrum present within the galaxy., This indicates a very hard ionising spectrum present within the galaxy.545" The line implies that the metallicity must be low, especially in carbon, suggesting a metallicity range of 0.001 to 0.004 (i.e. significantly sub-Solar)."," The line implies that the metallicity must be low, especially in carbon, suggesting a metallicity range of $0.001$ to $0.004$ (i.e. significantly sub-Solar)."546 However the more prominent profile implies a slightly higher (but still sub-Solar) carbon abundance in this source., However the more prominent profile implies a slightly higher (but still sub-Solar) carbon abundance in this source.547" As is the case for the Shapley et al composite, matching both lines simultaneously requires the presence of both a reduced relative carbon abundance and QHE in the population synthesis model."," As is the case for the Shapley et al composite, matching both lines simultaneously requires the presence of both a reduced relative carbon abundance and QHE in the population synthesis model."548" In Figure 8 we consider the 8 o'clock arc, à z— lensed Lyman break galaxy, with a rest-frame UV spectrum obtained by Dessauges-Zavadskyetal.(2010)."," In Figure \ref{8oclockarc} we consider the 8 o'clock arc, a $z=2.7$ lensed Lyman break galaxy, with a rest-frame UV spectrum obtained by \citet{2010A&A...510A..26D}."549". This galaxy has reported metallicities higher than others in this sample (Solar, or near-Solar) and has also been reported as relatively massive and dusty (M.4x10! MMo, V)~0.67, see2010)."," This galaxy has reported metallicities higher than others in this sample (Solar, or near-Solar) and has also been reported as relatively massive and dusty \citep[M$_\ast\sim4\times10^{11}$ $_\odot$, $\sim$ 0.67, see."550" In this context, its rest-UV spectrum is somewhat surprising."," In this context, its rest-UV spectrum is somewhat surprising."551" As in the case of BX418, the 8 o'clock arc has a very weak stellar wind line (the absorption is dominated by the narrow nebular component), but strong and broad emission, without any obvious nebular component."," As in the case of BX418, the 8 o'clock arc has a very weak stellar wind line (the absorption is dominated by the narrow nebular component), but strong and broad emission, without any obvious nebular component."552" The lack of a strong wind line indicates that the preferred metallicity in the regions dominating the rest-UV emission must be low, especially in carbon, suggesting a metallicity range of 0.001 to 0.004, with higher metallicities within this range requiring areduced [C/O]"," The lack of a strong wind line indicates that the preferred metallicity in the regions dominating the rest-UV emission must be low, especially in carbon, suggesting a metallicity range of $0.001$ to $0.004$ , with higher metallicities within this range requiring areduced [C/O]"553 jon αἱ a resolution of ,$\mu$ m at a resolution of $^{-1}$.554Gold mirrors have been used as references., Gold mirrors have been used as references.555 A turnable grid polarizer on polvetlvlene substrate positioned at the entrance of the saniple compartinent was used to select polarization directions parallel ancl normal to the plane of incidence., A turnable grid polarizer on polyethylene substrate positioned at the entrance of the sample compartment was used to select polarization directions parallel and normal to the plane of incidence.556" reff: Refealeshowsre [leelancespeetrao[caleileint Betessary —]20,mr range which comprises all IR bands of (his mineral.", \\ref{f:Ref_Calc} shows reflectance spectra of calcite in the $\mu$ m range which comprises all IR bands of this mineral.557 In the case of the rellectance for the ordinary rav (IELLc). an olfset olf 1.0 has been added to all rellectance values.," In the case of the reflectance for the ordinary ray $\bot$ c), an offset of 1.0 has been added to all reflectance values."558" The different. linestvles correspond to the different. temperatures NIN) as indicated,", The different linestyles correspond to the different temperatures K) as indicated.559 For the ordinarv rav. [five reflection bands can be discerned in (he infrared spectrum of caleite. which are centered. al 6.8. 14.0. 30.7. 44.0 and jm for room temperature.," For the ordinary ray, five reflection bands can be discerned in the infrared spectrum of calcite, which are centered at 6.8, 14.0, 30.7, 44.0 and $\mu$ m for room temperature."560 For the extraordinary rax. the respective reflectance band. positions amount to 11.4. 29.6 and mi (again for room temperature).," For the extraordinary ray, the respective reflectance band positions amount to 11.4, 29.6 and $\mu$ m (again for room temperature)."561" In rel: Belpof..therefleclancespectraofdoloim it car AW,"," In \\ref{f:Ref_Dol}, the reflectance spectra of dolomite are plotted on the same scale as for calcite."562" lar, Smau ilehasasti"," Dolomite has a slightly more complex band pattern than calcite, which is a consequence of its comparatively reduced lattice symmetry mentioned above."563qhlly. for the ordinary ray (al T — IXIX). while for the extraordinarv rav. the respective positions are 11.3. 25.4. 31.6. 56.7 and jum. For the cryogenic measurements. the experimental setup was (he lollowing: {he samples have been placed into a contimious-flow liuid-helium eryostat with contact-gas cooling (CrvoVac IARONTI Spectro D) equipped with polvethylene windows.," The reflectance maxima are located at 6.6, 13.8, 25.5, 38.4 and $\mu$ m for the ordinary ray (at T = K), while for the extraordinary ray, the respective positions are 11.3, 25.4, 31.6, 56.7 and $\mu$ m. For the cryogenic measurements, the experimental setup was the following: the samples have been placed into a continuous-flow liquid-helium cryostat with contact-gas cooling (CryoVac KONTI Spectro B) equipped with polyethylene windows."564 It was inserted into the FTIR spectrometer's saniple compartiment at (he same position where (he room temperature reflection measurements had been performed., It was inserted into the FTIR spectrometer's sample compartment at the same position where the room temperature reflection measurements had been performed.565 The crvostal windows did not allow measurements ab wavelengths shorter than yam. The crvostal possesses (wo sample mols which can alternatinglv be moved into the inlrared. beam. thus allowing subsequent measurements on (he sample and the relerence miror αἱ each Lenperalture.," The cryostat windows did not allow measurements at wavelengths shorter than $\mu$ m. The cryostat possesses two sample mounts which can alternatingly be moved into the infrared beam, thus allowing subsequent measurements on the sample and the reference mirror at each temperature."566" A third measurement with Che sample being tilted to suppress the reflection was (again. ad each temperature) in order to clelermine the reflectivity of the ervostat windows (""zero signal). which had to be subtracted from both the sample and (he reference spectra."," A third measurement with the sample being tilted to suppress the reflection was necessary (again at each temperature) in order to determine the reflectivity of the cryostat windows (“zero signal”), which had to be subtracted from both the sample and the reference spectra."567 The temperature was controlled bv means of a CrvoVac temperature controller. using an ohmic heater and The teniperatiures have been stable to about 40.5 Ix. cluring ihe measurements., The temperature was controlled by means of a CryoVac temperature controller using an ohmic heater and The temperatures have been stable to about $\pm$ 0.5 K during the measurements.568 Spectra have been taken al 200IXIx. IXIX. ancl LOWS during cooling down the samples.," Spectra have been taken at K, K, and K during cooling down the samples."569 Two cooling evcles have been BEBE PRU UD polarizer orientations., Two cooling cycles have been carried out for each sample with the two polarizer orientations.570" The wavelength- and temperature-clepencent reflectances have been ealeulated by dividing the ""zero-corrected” sample and reference spectra αἱ each temperature.", The wavelength- and temperature-dependent reflectances have been calculated by dividing the ``zero-corrected'' sample and reference spectra at each temperature.571 It is found that both for dolomite aud caleile all bands in the above indicated wavelength range undergo a shift to shorter wavelengths. a bandwidth decrease. and band streneth increase with decreasing temperatures.," It is found that both for dolomite and calcite all bands in the above indicated wavelength range undergo a shift to shorter wavelengths, a bandwidth decrease and band strength increase with decreasing temperatures."572 These effects are especially significant for caleite's. yan reflectance band and for dolomite's jmi reflectance band., These effects are especially significant for calcite's $\mu$ m reflectance band and for dolomite's $\mu$ m reflectance band.573 A more detailed discussion is given In 83., A more detailed discussion is given in 3.574"CGomma-ray. bursts. (CltDs). are the most energetic. explosions. nin the universe.. which. release large amount of energv up to LOuu eres in: only O.OL 10""» seconds in. the form⋅ of⋅ gamma-ray emissions.2. and thev show violent. time. variabilities in their emissions (Af lmisec)","Gamma-ray bursts (GRBs) are the most energetic explosions in the universe, which release large amount of energy up to $10^{51}$ ergs in only 0.01 – $10^3$ seconds in the form of gamma-ray emissions, and they show violent time variabilities in their emissions $\delta t\sim 1{\rm msec}$ )."575 Although the central engine. of GRBs is totally hidden. from. our view. according to their enormous power. it is often argued that relativisticMN phenomena should. be involved.," Although the central engine of GRBs is totally hidden from our view, according to their enormous power, it is often argued that relativistic phenomena should be involved."576. mThe most popular model for the central engines. of GRBs is a hyperacercting black hole model (Naravan et al., The most popular model for the central engines of GRBs is a hyperaccreting black hole model (Narayan et al.577 1992. 2001).," 1992, 2001)."578 In this model. the energy. of relativistic jets that makes intense eamma-ray emissions is produced. via the accretion of a massive disk. (0.1 TAL.) onto a stellar-mass black hole.," In this model, the energy of relativistic jets that makes intense gamma-ray emissions is produced via the accretion of a massive disk $0.1-1M_{\odot}$ ) onto a stellar-mass black hole."579 Such systems are expected. after several energetic phenomena such as mergers of double neutron star binaries (Eichler et al., Such systems are expected after several energetic phenomena such as mergers of double neutron star binaries (Eichler et al.580 1989). neutron. star/black hole binaries (DPaczvsski 1991). white dwarl/black hole binaries (Eryer et al.," 1989), neutron star/black hole binaries (Paczyńsski 1991), white dwarf/black hole binaries (Fryer et al."581 1999). black hole/lle star binaries (liver Woosley 1998). ancl failed supernovae (or collapsars: Woosley 1993: Paczviisski 1998: Alackadven Woosley 1999).," 1999), black hole/He star binaries (Fryer Woosley 1998), and failed supernovae (or collapsars; Woosley 1993; Paczyńsski 1998; MacFadyen Woosley 1999)."582 Their mass accretion rate is supposed to be as high as 0.011044.s.+. and then the accretion Hows become so optically thick that photons are almost trapped in. the Lows.," Their mass accretion rate is supposed to be as high as $0.01-10M_{\odot}{\rm s}^{-1}$, and then the accretion flows become so optically thick that photons are almost trapped in the flows."583 qsTherefore⋅ radiativeMM cooling. is. not ellicients in. this. case., Therefore radiative cooling is not efficient in this case.584" Alternativelv.... since. the densityul ancl temperature. can become very. ---high (pleEem . ""M210In Ix). the cooling. via. thermal neutrinoQU emissions will become ellicient."," Alternatively, since the density and temperature can become very high $\rho \gtrsim 10^7{\rm g}~{\rm cm}^{-3}$ , $T\gtrsim 10^{10}{\rm K}$ ), the cooling via thermal neutrino emissions will become efficient."585" Such disks (or llows) are called ""INeutrino-Dominated. Aceretion. Flows” (NDAs).", Such disks (or flows) are called “Neutrino-Dominated Accretion Flows” (NDAFs).586 This neutrino emissions may provide the energy. deposition enough to making relativistic jet by neutrino annihilation above the disk (Popham ct al., This neutrino emissions may provide the energy deposition enough to making relativistic jet by neutrino annihilation above the disk (Popham et al.587 1999)., 1999).588 The steady. structure of NDAEs has been studied by many authors (Popham et al., The steady structure of NDAFs has been studied by many authors (Popham et al.589 1999: Naravan et al., 1999; Narayan et al.590 2001: Ixohri Alineshige 2002 (hereafter IXKMO2): Di Matteo et al., 2001; Kohri Mineshige 2002 (hereafter KM02); Di Matteo et al.591 2002: Wohri et al., 2002; Kohri et al.592 2005: Gu et al., 2005; Gu et al.593 2006: Chen Beloborocoy 2007: Liu et al., 2006: Chen Beloborodov 2007; Liu et al.594 2007: Ixawanaka Mineshige 2007: see also Chapter 10.6 of Ixato et al, 2007; Kawanaka Mineshige 2007; see also Chapter 10.6 of Kato et al.595 2008)., 2008).596 As for their time-dependent behavior. some authors performed:⋅ hvdrodynamical. simulations. including.: neutrino cooling (Itulfert Janka 1999: Janka οἱ al.," As for their time-dependent behavior, some authors performed hydrodynamical simulations including neutrino cooling (Ruffert Janka 1999; Janka et al."597 1990: Proga et al., 1999; Proga et al.598 2003: Lee et al., 2003; Lee et al.599 2004: Itosswog 2005: Fujimoto et al., 2004; Rosswog 2005; Fujimoto et al.600 2006: Sctiawan et al., 2006; Setiawan et al.601 2006: Nagatalki et al., 2006; Nagataki et al.602 2007: Shibata et al., 2007; Shibata et al.603 2007: Metzger et al., 2007; Metzger et al.604 2008: Sekiguchi Shibata 2010: Carballido Lee 2010: Taylor et al., 2008; Sekiguchi Shibata 2010; Carballido Lee 2010; Taylor et al.605 2011). and some authors investigated analvticallv the disk. instabilities which may," 2011), and some authors investigated analytically the disk instabilities which may"606of brown dwarf companions compared to FGIN companions plays an important role in our calculations.,of brown dwarf companions compared to FGK companions plays an important role in our calculations.607 One of the peculiar properties of brown cwarf companions discovered by radial velocity survevs is (hat (here is a definite paucity of close brown cdwarl secondaries to main-sequence primaries., One of the peculiar properties of brown dwarf companions discovered by radial velocity surveys is that there is a definite paucity of close brown dwarf secondaries to main-sequence primaries.608 The mass function of binary companions to nearby solar stars shows a clear gap between the planetary ancl stellar mass ranges., The mass function of binary companions to nearby solar stars shows a clear gap between the planetary and stellar mass ranges.609" This is known as the “brown dwarl desert"" (Halbwachsetal.2000:Gizis2001)."," This is known as the “brown dwarf desert” \citep{halb00,giz01}."610. Observationallv. the brown chwarl desert is evident in spectroscopic binaries. even though today’s survevs are sensitive enough to detect these close substellar companions.," Observationally, the brown dwarf desert is evident in spectroscopic binaries, even though today's surveys are sensitive enough to detect these close substellar companions."611 IH is possible that the brown dwarf desert reflects fundamentally different formation processes for planets aud for binary stellar companions., It is possible that the brown dwarf desert reflects fundamentally different formation processes for planets and for binary stellar companions.612" The question as to how far this scarcity. of brown dwarl companions extends is still uncertain,", The question as to how far this scarcity of brown dwarf companions extends is still uncertain.613 Gizisοἱal.(2001) estimate that brown dwarl companions with large periastron distance (A=as(1—ου)>1000 AU) are at least 4 times more frequent than those at shorter separations (A«3 AU).," \citet{giz01} estimate that brown dwarf companions with large periastron distance $\Delta=a_2(1-e_2)>1000\,$ AU) are at least 4 times more frequent than those at shorter separations $\Delta<3\,$ AU)."614 Searches for brown dwarl companions within 1—100 AU of a primary have had litle success. although the stellar companion frequency. peaks in this range (Duquennov&Mayor1991:FischerMarcy 1992)...," Searches for brown dwarf companions within $1-100\,$ AU of a main-sequence primary have had little success, although the stellar companion frequency peaks in this range \citep{duq91, fisch92}. ."615 The frequency of brown dwarl companions within 100—1000 AU has not vet been well constrained either 2001).," The frequency of brown dwarf companions within $100-1000\,$ AU has not yet been well constrained either \citep{giz01}."616". Here we define a2»,5pb to be the upper bound of the brown dwarf desert."," Here we define $a_{2\rm ,BD}$ to be the upper bound of the brown dwarf desert."617 The minimum upper bound espp23 AU is quite well established (IIalbwaehsetal.2000).," The minimum upper bound $a_{2,\rm BD}\simeq3\,$ AU is quite well established \citep{halb00}."618. By using the astromeltric data from IHipparcos. Halbwachs et sshowed (hat most of the candidate close brown clwarl secondaires with Assin/ between 0.01. and 0.08AL. have actual masses above the substellar limit of 0.08M...," By using the astrometric data from Hipparcos, Halbwachs et showed that most of the candidate close brown dwarf secondaries with $M_2\sin{i}$ between $0.01\,$ and $0.08\,M_\odot$ have actual masses above the substellar limit of $0.08\,M_\odot$."619 This result ruled ont the majority of the candidate close brown cwarf companions and (therefore established (he size of the brown dwarf desert to be at least a few AU., This result ruled out the majority of the candidate close brown dwarf companions and therefore established the size of the brown dwarf desert to be at least a few AU.620 IIowever. there are a few exceptions within (his range. particularly the recently discovered companion to WD 137510 (Az1.6 AU) (Endletal.2004).," However, there are a few exceptions within this range, particularly the recently discovered companion to HD 137510 $\Delta \approx 1.6\,$ AU) \citep{endl04}."621.. This companion has a mass between 26 and 61M; with a probabilitv: thus it is very likely a substellar object.," This companion has a mass between 26 and $\,M_{\rm J}$ with a probability; thus it is very likely a substellar object."622" This new ""oasis"" in the brown dwarf desert poses an interesting problem in our simulations.", This new “oasis” in the brown dwarf desert poses an interesting problem in our simulations.623 We have tested models with different radial extents for the brown cdwaarl desert. corresponding to dep— 10. 100. and 1000 AU.," We have tested models with different radial extents for the brown dwarf desert, corresponding to $a_{2,\rm BD}=$ 10, 100, and $1000\,$ AU."624 The frequency of brown dwarf companions outside (he brown dwarf desert is also not vel well constrained., The frequency of brown dwarf companions outside the brown dwarf desert is also not yet well constrained.625 From (he observations of main-sequence potential primary stars by the Two Micron. All-Skv Survey. (241ASS). Gizis οἱ citepgiz0l estimated the frequency of brown dwarf companions to FMO primaries al vide separations to be δήd:14%.," From the observations of main-sequence potential primary stars by the Two Micron All-Sky Survey (2MASS), Gizis et \\citep{giz01} estimated the frequency of brown dwarf companions to F–M0 primaries at wide separations to be $18\%\pm14\%$."626 In one of our simulations. the effect of different frequencies of brown dwarf companions isspecifically investigated.," In one of our simulations, the effect of different frequencies of brown dwarf companions isspecifically investigated."627 Typically. à hieher proportion of brown cdwarf companions in a sample leads to longer average Ixozai oscillation periods. which in," Typically, a higher proportion of brown dwarf companions in a sample leads to longer average Kozai oscillation periods, which in"628Statistical observations of the redshilted 21-cm. emission from neutral hydrogen during the epoch of reionisation (EoR) promise to provide a wealth of information. about the properties of neutral hydrogen. at high redshift. as well as some of the funcamental astrophysics behind the rejonisation process and the first luminous objects.,"Statistical observations of the redshifted 21-cm emission from neutral hydrogen during the epoch of reionisation (EoR) promise to provide a wealth of information about the properties of neutral hydrogen at high redshift, as well as some of the fundamental astrophysics behind the reionisation process and the first luminous objects."629 While density. perturbations in the matter distribution. mediate Iluctuations in the 21-cm signal both prior to and following reionisation. curing the reionisation era the relation between the 21-cm power spectrum and the underlying matter power spectrum is complex and. in its late stages. dominated bv the formation of large ionisecl “bubbles” (22)...," While density perturbations in the matter distribution mediate fluctuations in the 21-cm signal both prior to and following reionisation, during the reionisation era the relation between the 21-cm power spectrum and the underlying matter power spectrum is complex and, in its late stages, dominated by the formation of large ionised “bubbles"" \citep{furl2004b,mcquinn2006}."630 These bubbles of ionised hydrogen imprint features on the 21-cm power spectrum that rellect the luminosity and. clustering of ionising sources responsible for reionisation., These bubbles of ionised hydrogen imprint features on the 21-cm power spectrum that reflect the luminosity and clustering of ionising sources responsible for reionisation.631 The 21-cni power spectrum can be used as a statistical test to distinguish candidate reionisation. models. as well as to constrain the history and morphology of reionisation (?)..," The 21-cm power spectrum can be used as a statistical test to distinguish candidate reionisation models, as well as to constrain the history and morphology of reionisation \citep{barkana2009}."632 Aleasuring this weal cosmic signal will be challenging however. owing to contamination from a large number of astrophysical and non-astrophysical components.," Measuring this weak cosmic signal will be challenging however, owing to contamination from a large number of astrophysical and non-astrophysical components."633 Indeed. astrophysical foregrounds— are typically— brighter than the cosmological 21-cm signal by 4.5) orders of magnitude (see.e.g.??7).," Indeed, astrophysical foregrounds are typically brighter than the cosmological 21-cm signal by 4–5 orders of magnitude \citep[see, e.g.,][]{dimatteo2002,oh2003}."634 Some of these loreerouncls also. have bright polarised counterparts., Some of these foregrounds also have bright polarised counterparts.635 As a result. significant contamination will occur in the non-polariscd," As a result, significant contamination will occur in the non-polarised"636On the basis of the principle. one expects (hat the relation holds for large s |?]..,"On the basis of the principle, one expects that the relation holds for large $s$ \cite{foot3}."637 Thus. for along DNA we can employ the approximation H and substitute ó(s) into equation (94)) to gel To calculate the partition function. we express the tota] energy in ternis of Fourier components of ds. aud dy.," Thus, for a long DNA we can employ the approximation \cite{foot4}638 and substitute $\phi (s)$ into equation \ref{app3-E1-1}) ) to get To calculate the partition function, we express the total energy in terms of Fourier components of $\hat{d}_{3\,x}$ and $\hat{d}_{3\,y}$."639" The Fourier transform of di,+iday is given by where qj)= a "," The Fourier transform of $\hat{d}_{3\,x}+i\,\hat{d}_{3\,y}$ is given by where $q_j=\frac{2\,j\,\pi}{L}$ ."640"Using the properties of Fourier transformation. we obtain H ancl where qj, is the closest to 25 We denote the real and imaginary. parts of a; as ;. and 7; respectively."," Using the properties of Fourier transformation, we obtain \cite{Nelson}641 and where $q_{j_0}$ is the closest to $2\omega_0$ We denote the real and imaginary parts of $a_j$ as $R_j$, and $I_j$ ,respectively."642 Then the total energv of the DNA can be written in the form with, Then the total energy of the DNA can be written in the form with643One of Spitzers most intriguing discoveries is the extreme level of zodiacal emission around (he nearby (12.6 pe) IXQV star ILD69530.,One of Spitzer's most intriguing discoveries is the extreme level of zodiacal emission around the nearby (12.6 pc) K0V star HD69830.644 The dust cloud around ILD69830 is approximately 1.400 times brighter than the emission of our own zodiacal cloud. aud shows a plethora of solid state features attributable to small. hot. ervstalline silicate grains located «1I AU from the parent star2005).," The dust cloud around HD69830 is approximately 1,400 times brighter than the emission of our own zodiacal cloud and shows a plethora of solid state features attributable to small, hot, crystalline silicate grains located $<$ 1 AU from the parent star."645. Such intense emission from dust in (he inner solar system is exceedingly rare. detectable in only ~1'% of the mature stus surveved by Spitzer2009).," Such intense emission from dust in the inner solar system is exceedingly rare, detectable in only $\sim$ of the mature stars surveyed by Spitzer."646. Interest in this cloud and its link to the evolution of planetary svstems was greatly heightened by the discovery. of three Neptune-mmass planets orbiting within 0.6 AU of the star2006)., Interest in this cloud and its link to the evolution of planetary systems was greatly heightened by the discovery of three Neptune-mass planets orbiting within 0.6 AU of the star.647. One of the major unanswered questions about (his svstem is whether the dust seen by Spitzer comes from collisions within a particularly massive asteroid belt or [rom a swarm of comets released bv planet-disk interactions., One of the major unanswered questions about this system is whether the dust seen by Spitzer comes from collisions within a particularly massive asteroid belt or from a swarm of comets released by planet-disk interactions.648 The Spitzer follow-up observations described here include hieh signal to noise (8NR). low and high spectral resolution observations of the dust disk to help distinguish. between (hese two alternatives.," The Spitzer follow-up observations described here include high signal to noise (SNR), low and high spectral resolution observations of the dust disk to help distinguish between these two alternatives."649 Five repeats of the spectral observations over 12 months were designed (o search for small variations that might be expected fom a dust cloud evolving on a dvnamical time scale of less than 1 vear., Five repeats of the spectral observations over 12 months were designed to search for small variations that might be expected from a dust cloud evolving on a dynamical time scale of less than 1 year.650 Overall. the cata described here span more than 4 νους of Spitzer observations from 2004 (o 2008 and extend as [ar back as a 1983 detection bv IRAS at 25 jm. In this paper we use new Spitzer data to refine our assav of the mineralogical and gaseous components of the ILD69530 disk and look for temporal variations in (he disk emission that might occur on dynamical or dust replenishment Gimescales. from 1. vear to over 1.000 vears.," Overall, the data described here span more than 4 years of Spitzer observations from 2004 to 2008 and extend as far back as a 1983 detection by IRAS at 25 $\mu$ m. In this paper we use new Spitzer data to refine our assay of the mineralogical and gaseous components of the HD69830 disk and look for temporal variations in the disk emission that might occur on dynamical or dust replenishment timescales, from 1 year to over 1,000 years."651 Observations of voung protoplanetary disks can exhibit dramatic changes in the shape of their Spitzer/IRS spectra, Observations of young protoplanetary disks can exhibit dramatic changes in the shape of their Spitzer/IRS spectra652The behaviour of the intrinsic dispersion of the FJR and the KR have not been studied thoroughly because it is considered that there ts a third variable which causes most of the intrinsic. dispersion. in. both these relations.,The behaviour of the intrinsic dispersion of the FJR and the KR have not been studied thoroughly because it is considered that there is a third variable which causes most of the intrinsic dispersion in both these relations.653" The intrinsic. dispersion of the FP has not been thoroughly studied because. it has been traditionally thought. small (O.1 dex. Kjyergaardetal. 1993... Jorgensenetal. 1996.. Kelsonetal. 1997.. Jorgensenetal.1999., Blakesleeetal. 2002.. Bernardietal. 2003c.. Redaetal. 2005.. Jorgensenetal. 2006)."," The intrinsic dispersion of the FP has not been thoroughly studied because, it has been traditionally thought small $\sim 0.1$ dex, \cite{kja93}, , \cite{jor96}, , \cite{kel97}, , \cite{jor99}, \cite{bla02}, \cite{ber03c}, \cite{red05}, \cite{jor06}) )."654 However. some studies show that the intrinsic dispersion. values are far from being small (~0.3 dex. Benderetal.1992:; LaBarberaetal. 2003. Nigoche-Netroetal. 2009)).," However, some studies show that the intrinsic dispersion values are far from being small $\sim0.3$ dex, \cite{ben92}; \cite{lab03}; \cite{nig09}) )."655 This. relatively high dispersion causes that the galaxy distribution in the space that defines the structural relations follows a surface whose thickness is determined by this dispersion.," This, relatively high dispersion causes that the galaxy distribution in the space that defines the structural relations follows a surface whose thickness is determined by this dispersion."656 Recent works (Nigoche-Netro2007:: Nigoche-Netro et al., Recent works \cite{nig07b}; Nigoche-Netro et al.657 2008: 2009: 2010) have shown that the intrinsic dispersion is also affected by the geometrical effect., 2008; 2009; 2010) have shown that the intrinsic dispersion is also affected by the geometrical effect.658 However. Nigoche-Netro et al. (," However, Nigoche-Netro et al. ("6592010) have found that differences in the value of the intrinsic. dispersion. for different samples of galaxies do not disappear as the magnitude range diminishes.,2010) have found that differences in the value of the intrinsic dispersion for different samples of galaxies do not disappear as the magnitude range diminishes.660 They find that the exact value for the intrinsic dispersion. is obtained when AM=0., They find that the exact value for the intrinsic dispersion is obtained when $\Delta M = 0$.661 The intrinsic dispersion for this extreme case would be defined as the standard deviation of the distribution of the points at constant magnitude., The intrinsic dispersion for this extreme case would be defined as the standard deviation of the distribution of the points at constant magnitude.662 Hence. Nigoche-Netro et al. (," Hence, Nigoche-Netro et al. ("6632010) consider that an appropriate method for obtaining physical informatior for a sample of galaxies is to find its intrinsic. dispersion at each nagnitude value and then perform comparisons of this dispersion at different luminosities. wavelengths. redshifts. or environments.,"2010) consider that an appropriate method for obtaining physical information for a sample of galaxies is to find its intrinsic dispersion at each magnitude value and then perform comparisons of this dispersion at different luminosities, wavelengths, redshifts, or environments."664 In light of this. in this paper we carry out a study of the behaviour of the intrinsic dispersion of the FJR as a function of luminosity. mass and redshift for a sample of ETGs selected from the SDSS-DR7 archive.," In light of this, in this paper we carry out a study of the behaviour of the intrinsic dispersion of the FJR as a function of luminosity, mass and redshift for a sample of ETGs selected from the SDSS-DR7 archive."665 In 2 we present the galaxy sample used to study the intrinsic dispersion of the FJR. the calculation of the intrinsic dispersion and the analysis of the behaviour of the intrinsic dispersion as a function of the luminosity. mass and redshift.," In 2 we present the galaxy sample used to study the intrinsic dispersion of the FJR, the calculation of the intrinsic dispersion and the analysis of the behaviour of the intrinsic dispersion as a function of the luminosity, mass and redshift."666 In 3 we present a discussion of the most important results of this paper., In 3 we present a discussion of the most important results of this paper.667 Finally in 4 we present our conclusions., Finally in 4 we present our conclusions.668 We use a sample of ETGs from the Seventh Data Release of the SDSS (Yorketal.2000:; Abazajianetal. 2009)) in. g and r filters., We use a sample of ETGs from the Seventh Data Release of the SDSS \cite{yor00}; \cite{aba09}) ) in $g$ and $r$ filters.669 This sample contains approximately 90 000 galaxies in each filter. distributed in a redshift interval 0.01.<z0.35 and within a magnitude range AM~7 mag.," This sample contains approximately 90 000 galaxies in each filter, distributed in a redshift interval $0.01 < z < 0.35$ and within a magnitude range $\Delta M\sim 7$ $mag$."670 The sample selection procedure was based on the Bernardi et al. (, The sample selection procedure was based on the Bernardi et al. (6712003a) and Hyde Bernardi (2009) selection criteria (see Nigoche-Netroetal. 2010).,2003a) and Hyde Bernardi (2009) selection criteria (see \cite{nig10}) ).672 Hereinafter we will refer to it as the total SDSS sample., Hereinafter we will refer to it as the total SDSS sample.673 Given that the total sample spans a relatively ample redshift range. it is affected by the Malmquist bias.," Given that the total sample spans a relatively ample redshift range, it is affected by the Malmquist bias."674 To avoid this bias. we use a volume-limited sample of approximately 17 000 ETGs with 0.04 €ςx 0.08 in the g and r filters.," To avoid this bias, we use a volume-limited sample of approximately 17 000 ETGs with 0.04 $\leq\;z\;\leq$ 0.08 in the $g$ and $r$ filters."675" This subsample covers a magnitude range <AM> ~4.5 mag (-18.52M,>—23.0) in both filters and we refer to it as the homogeneous SDSS sample.", This subsample covers a magnitude range $<\Delta M>$ $\sim 4.5$ $mag$ $-18.5 \ge M_{g} > -23.0$ ) in both filters and we refer to it as the homogeneous SDSS sample.676" This sample is complete approximately for M,<—20.0.", This sample is complete approximately for $M_{g} \leq -20.0$.677 In recent papers (Nigoche-Netro2007:; Nigoche-Netro et al., In recent papers \cite{nig07b}; Nigoche-Netro et al.678 2008: 2009: 2010) it has been demonstrated that due to the geometrical effect. it is risky to draw conclusions about the physical properties of galaxies by comparing the slopes of the structural relations for magnitude ranges of different widths or for magnitude ranges of the same width but of different luminosity. because. with the exception of the full magnitude interval. there is no ideal width at which comparisons should be made.," 2008; 2009; 2010) it has been demonstrated that due to the geometrical effect, it is risky to draw conclusions about the physical properties of galaxies by comparing the slopes of the structural relations for magnitude ranges of different widths or for magnitude ranges of the same width but of different luminosity, because, with the exception of the full magnitude interval, there is no ideal width at which comparisons should be made."679 So that using the slopes of the structural relations to find intrinsic differences among samples of galaxies Is a delicate matter. and the results might be non conclusive.," So that using the slopes of the structural relations to find intrinsic differences among samples of galaxies is a delicate matter, and the results might be non conclusive."680 This procedure should be supplemented by an alternative corroborative method., This procedure should be supplemented by an alternative corroborative method.681 Nigoche-Netro et al. (, Nigoche-Netro et al. (6822010) demonstrate that the intrinsic dispersion values at constant magnitude ts an appropriate method for obtaining physical information on a sample of galaxies.,2010) demonstrate that the intrinsic dispersion values at constant magnitude is an appropriate method for obtaining physical information on a sample of galaxies.683 In the next sections we will use this method to try to find differences among the structural properties of galaxies belonging to different samples., In the next sections we will use this method to try to find differences among the structural properties of galaxies belonging to different samples.684 Some papers from the literature have studied the intrinsic dispersion of the structural. relations as a function. of the luminosity (Benderetal.1992:; J@rgensenetal. 1996.. Hyde&Bernardi 2009::. Nigoche-Netroetal. 2010)).," Some papers from the literature have studied the intrinsic dispersion of the structural relations as a function of the luminosity \cite{ben92}; \cite{jor96}, \cite{hyd09}; \cite{nig10}) )."685 Those works reveal that the intrinsic dispersion for bright galaxies is smaller than that for faint galaxies., Those works reveal that the intrinsic dispersion for bright galaxies is smaller than that for faint galaxies.686 However. these works have made comparisons of the intrinsic dispersion on wide magnitude ranges. so that. these results are affected by the geometrical effect.," However, these works have made comparisons of the intrinsic dispersion on wide magnitude ranges, so that, these results are affected by the geometrical effect."687 An appropriate analysis requires the calculation of the intrinsic dispersion at constant magnitude., An appropriate analysis requires the calculation of the intrinsic dispersion at constant magnitude.688 In Figure | we show the behaviour of the intrinsic dispersion of the FIR (σα) in very narrow magnitude ranges for the homogeneous and total samples from the SDSS in the filter., In Figure 1 we show the behaviour of the intrinsic dispersion of the FJR $\sigma_{log(\sigma_{0})}$ ) in very narrow magnitude ranges for the homogeneous and total samples from the SDSS in the $g$ filter.689" This figure shows the data for the homogeneous sample (Red Diamonds) where it is clearly seen that in the regime M,< —20. where the sample is complete. the intrinsic. dispersion value changes systematically as weconsider brightergalaxies. andthat the distribution of brighter galaxies presents a lower value for the intrinsic dispersion than the value presented by"," This figure shows the data for the homogeneous sample (Red Diamonds) where it is clearly seen that in the regime $M_{g} \lesssim -20$ , where the sample is complete, the intrinsic dispersion value changes systematically as weconsider brightergalaxies, andthat the distribution of brighter galaxies presents a lower value for the intrinsic dispersion than the value presented by"690 5)).,\ref{fig:Ha-synoptic}) ).691 These spectral features suggest a dAle classification of GSC 2314-0530., These spectral features suggest a dMe classification of GSC 2314-0530.692 The spectral contribution of the secondary. component is visible only in the Ha line (Fig. 5))., The spectral contribution of the secondary component is visible only in the $\alpha$ line (Fig. \ref{fig:Ha-synoptic}) ).693 That is why we determined. the racial velocities of the two stellar components by fitting the Lla lines at each phase with Gaussians (Pie. 7))., That is why we determined the radial velocities of the two stellar components by fitting the $\alpha$ lines at each phase with Gaussians (Fig. \ref{fig:Ha-fit}) ).694 ‘Table 4 anc Figure S. present the radial velocities of the stellar components of GSC 2314-0530., Table \ref{tab:radvel} and Figure \ref{fig:RV} present the radial velocities of the stellar components of GSC 2314-0530.695 Eheir fit corresponds to values Ay=ising2100.732 kms J|. Ao=VosiniPILZ45.8 km n ⋜⋯∠⇂⇖⊓⊳∖↓⊔∣∶⊳⊀⇁1245.3 kms +.," Their fit corresponds to values $K_{1}=V_{1}\sin i = 109.7\pm3.2$ km $^{-1}$, $K_{2} = V_{2}\sin i = 211.3\pm5.8$ km $^{-1}$ and $V_{0}\sin i696=-1.2\pm5.7$ km $^{-1}$."697 They lead to mass ratio q=0.519+0.029 and binary separation asin;=1.22£0.04 Rh..., They lead to mass ratio $q=0.519\pm0.029$ and binary separation $a \sin i=1.22\pm0.04$ $_{\sun}$.698 The qualitative analysis of the new photometric data (Fie. 4)), The qualitative analysis of the new photometric data (Fig. \ref{fig:folded}) )699 leads to several conclusions., leads to several conclusions.700 In order to determine the global parameters. of GSC 2314-0530 we modeled. our VA folded. curves simultaneously. using the software PLIIOEBE by the following procedure., In order to determine the global parameters of GSC 2314-0530 we modeled our $VRI$ folded curves simultaneously using the software PHOEBE \citep{prsa05} by the following procedure.701Even though the analytic estimates presented. here are only approximate. they serve to highlight the low probability,"Even though the analytic estimates presented here are only approximate, they serve to highlight the low probability"702 2004b)).,\cite{napiwotzki04b}) ).703" The RVs of the GMOS spectra have been measured by fitting three Gaussians to the H, line.", The RVs of the GMOS spectra have been measured by fitting three Gaussians to the $H_{\rm \gamma}$ line.704 Three functions are used to match the continuum. the line and the line core. respectively and mimic the typical Voigt profile of spectral lines.," Three functions are used to match the continuum, the line and the line core, respectively and mimic the typical Voigt profile of spectral lines."705 The profiles are fitted to all suitable lines simultaneously using y-minimization and the RV shift with respect to the rest wavelengths is measured., The profiles are fitted to all suitable lines simultaneously using $\chi^{2}$ -minimization and the RV shift with respect to the rest wavelengths is measured.706 The RVs and formal Lc-errors are given in Appendix AppendixB:.., The RVs and formal $1\sigma$ -errors are given in Appendix \ref{app:RV}.707 Assuming circular orbits sine curves were fitted to the RV data points in fine steps over a range of test periods., Assuming circular orbits sine curves were fitted to the RV data points in fine steps over a range of test periods.708 For each period the y of the best fitting sine curve was determined., For each period the $\chi^{2}$ of the best fitting sine curve was determined.709 The result is similar to a power spectrum with the lowest y indicating the most likely period (see Fig. 4))., The result is similar to a power spectrum with the lowest $\chi^{2}$ indicating the most likely period (see Fig. \ref{chi}) ).710 In order to estimate the significance of the orbital solutions and the contributions of systematic effects to the error budget. we 1ormalised the y of the most probable solution by adding systematic errors in quadrature until the reduced y reached =1.0.," In order to estimate the significance of the orbital solutions and the contributions of systematic effects to the error budget, we normalised the $\chi^{2}$ of the most probable solution by adding systematic errors in quadrature until the reduced $\chi^{2}$ reached $\simeq1.0$."711 Using these modified uncertainties we performed Monte Carlo simulations for the most likely periods., Using these modified uncertainties we performed Monte Carlo simulations for the most likely periods.712 For each sinulation a randomised set of RVs was drawn from Gaussian distributions with central value and width corresponding to the RV measurements and the analysis repeated., For each simulation a randomised set of RVs was drawn from Gaussian distributions with central value and width corresponding to the RV measurements and the analysis repeated.713 From these simulations the probabilities for the orbital periods to deviate from our best solution by more than 1% or 10% were calculated., From these simulations the probabilities for the orbital periods to deviate from our best solution by more than $1\%$ or $10\%$ were calculated.714 of oo... burst hare sto these rindeed z tis , $-$ $-$ $\approx$ 715accounted for.,accounted for.716 The largest of these are obtained by conmgxuius the BOF model with the NF scenario., The largest of these are obtained by comparing the B07 model with the NF scenario.717 This colmparison viclds Awpyr[0.010 and AO4pyr 0.039.," This comparison yields $\Delta w_{B07} = +0.040$ and $\Delta\Omega_{\Lambda,B07}718= -0.039$ ."719 The same comparison for the BOS model. which is only slightlypreferred by the \? statistic over model Boz. produces At’py;=|0.027 and Δονpus=0.026.," The same comparison for the B05 model, which is only slightlypreferred by the $\chi^2$ statistic over model B07, produces $\Delta720w_{B05} = +0.027$ and $\Delta\Omega_{\Lambda,B05} = -0.026$."721" The systematic offsets for O,, are all 0.001 or less, demonstrating the iuscnsitivity of this parameter to peculiar velocities."," The systematic offsets for $\Omega_m$ are all $0.004$ or less, demonstrating the insensitivity of this parameter to peculiar velocities."722" This is due to the BAO prior which is insensitive to local flow aud provides a uch stronger constraint for O,, than for w or Qy (see ANG. Figures 5 and 6G)."," This is due to the BAO prior which is insensitive to local flow and provides a much stronger constraint for $\Omega_m$ than for $w$ or $\Omega_\Lambda$ (see A06, Figures 5 and 6)."723 The systematic effect of different flow models is at the level of ΕΕ in dw., The systematic effect of different flow models is at the level of $\pm0.04$ in $w$.724 This is simaller than the level of random error m ow. which is larecly due to the stnall uunubers of bigh- aud low-redshift SNe.," This is smaller than the level of random error in $w$, which is largely due to the small numbers of high- and low-redshift SNe."725 However. compared to other svstemiaties discussed in. A06. which total Aw=40.051. the svstemiatic effect of large-scale Hows is iniportaut.," However, compared to other systematics discussed in A06, which total $\Delta w = \pm0.054$, the systematic effect of large-scale flows is important."726 Wood-Vaseyetal.(2007.Table5) list 16 sources of svsteimatie error which total Aw=£0.13., \citet[Table 5]{Wood-Vasey07astroph} list 16 sources of systematic error which total $\Delta w = \pm 0.13$.727 Aside froin three imuethod-depeudenut svsteiaties and the photometric zero-point error. they are all smaller than he flaw systematic.," Aside from three method-dependent systematics and the photometric zero-point error, they are all smaller than the flow systematic."728" As the uunuber of SNe coutinucs to lncreaSC. and understanding of other svstematics (6.8. photometric zero-poiuts) nmuproves. if is possible that arge-scale flows will become oue of the dominant sources of svstematic πουΤαλατν,"," As the number of SNe continues to increase, and understanding of other systematics (e.g. photometric zero-points) improves, it is possible that large-scale flows will become one of the dominant sources of systematic uncertainty."729 The peculiar velocities of SN host galaxies arise roni large-scale structures over a range of scales., The peculiar velocities of SN host galaxies arise from large-scale structures over a range of scales.730 The conmpoueut arising from siall-scale. local structure is he least important: it is essentially a random variable which is reduced by VN.," The component arising from small-scale, local structure is the least important: it is essentially a random variable which is reduced by $\sqrt{N}$."731 More problematic is the laree-scale coherent component., More problematic is the large-scale coherent component.732 Such a larec-scale componoeut can fake several forms: an overdeusitv or uudoerdeusitv: a large-scale dipole. or “bulls” flow.," Such a large-scale component can take several forms: an overdensity or underdensity; a large-scale dipole, or “bulk” flow."733" The existence of a large-scale. but local (<τος 1j) underdeusitv. or ""IIbde Bubble” was first discussed. by. Zeliavietal.(1998) ε"," The existence of a large-scale, but local $<7400$ ) underdensity, or “Hubble Bubble” was first discussed by \cite{ZehRieKir98}. ."734ν Boeceutlv Jhactal. have re-enforced this claim with a larger SN data set: they find that the difference 11i the IHIubble coustaut, Recently \cite{JhaRieKir06} have re-enforced this claim with a larger SN data set: they find that the difference in the Hubble constant735Recent observations of the Hubble relation of distant Type Ia supernovae (SNe la) have provided strong evidence for acceleration of the present universe (Riess et al.,Recent observations of the Hubble relation of distant Type Ia supernovae (SNe Ia) have provided strong evidence for acceleration of the present universe (Riess et al.736 1998; Perlmutter et al., 1998; Perlmutter et al.737 1999)., 1999).738 The observations of the spectrum of cosmic microwave background (CMB) anisotropies (Spergel et al., The observations of the spectrum of cosmic microwave background (CMB) anisotropies (Spergel et al.739 2003:2007). large-scale structure (LSS) (Tegmark et al.," 2003;2007), large-scale structure (LSS) (Tegmark et al."740 2004; Eisenstein et al., 2004; Eisenstein et al.741 2005) and the distance-redshift relation to X-ray galaxy clusters (Allen et al., 2005) and the distance-redshift relation to X-ray galaxy clusters (Allen et al.742 2004; 2007) also confirm that the universe is accelerating., 2004; 2007) also confirm that the universe is accelerating.743 Possible explanations for the acceleration have been proposed., Possible explanations for the acceleration have been proposed.744 À negative pressure term called dark energy is taken into account. such as the cosmological constant model with equation of state w=p/p=—] (Weinberg 1989). an evolving scalar field (Peeble Ratra. 1988. Caldwell et al.," A negative pressure term called dark energy is taken into account, such as the cosmological constant model with equation of state $w=p/\rho =-1$ (Weinberg 1989), an evolving scalar field (Peeble Ratra, 1988, Caldwell et al."745 1998). the phantom energy for which the sum of the pressure and energy density is negative. and the Chaplygin gas (Kamenshehik et al.," 1998), the phantom energy for which the sum of the pressure and energy density is negative, and the Chaplygin gas (Kamenshchik et al."746 2001)., 2001).747 All the above models for acceleration are obtained by introducing a new energy component called dark energy., All the above models for acceleration are obtained by introducing a new energy component called dark energy.748 Alternative models. in which gravity is modified. can also drive the universe acceleration. e.g.. the Dvali-Gabadadze-Porrati (DGP) model (Dvali et al.," Alternative models, in which gravity is modified, can also drive the universe acceleration, e.g., the Dvali-Gabadadze-Porrati (DGP) model (Dvali et al."749 2000: Deffayet et al., 2000; Deffayet et al.750 2002). Cardassian expansiot model (Freese Lewis 2002; Wang et al.," 2002), Cardassian expansion model (Freese Lewis 2002; Wang et al."751 2003). and the f(R) gravity model (Vollick 2003: Carroll et al.," 2003), and the f(R) gravity model (Vollick 2003; Carroll et al."752 2004)., 2004).753 These two families of models. dark energy and modified gravity. are fundamentally different.," These two families of models, dark energy and modified gravity, are fundamentally different."754 An important questio is whether it is possible to distinguish between the modified gravity and dark energy models that have nearly the same cosmic expansion history., An important question is whether it is possible to distinguish between the modified gravity and dark energy models that have nearly the same cosmic expansion history.755 Many works have been done o this topic., Many works have been done on this topic.756 A usually-discussed quantity is the growth rate of cosmological density perturbations. which should be differe:= in the models depending on different gravity theory even if they have an identical cosmic expansion history.," A usually-discussed quantity is the growth rate of cosmological density perturbations, which should be different in the models depending on different gravity theory even if they have an identical cosmic expansion history."757 Recently. there have been extensive discussions on discriminating dark energy and modified gravity models using the matter density perturbations growth factor (Linder 2005).," Recently, there have been extensive discussions on discriminating dark energy and modified gravity models using the matter density perturbations growth factor (Linder 2005)."758 But Kunz and Sapone (2007) demonstrated that the growth factor is not sufficient to distinguish between modified gravity and dark energy (Kunz Sapone 2007)., But Kunz and Sapone (2007) demonstrated that the growth factor is not sufficient to distinguish between modified gravity and dark energy (Kunz Sapone 2007).759 They found that a generalized dark energy model can match the growth rate of the Dvali-Gabadadze-Porrati model and reproduce the 31 dimensional metric perturbations., They found that a generalized dark energy model can match the growth rate of the Dvali-Gabadadze-Porrati model and reproduce the 3+1 dimensional metric perturbations.760 On the other hand. the statefinder pair Gs) has also been proposed to distinguish between the models. where r2üjaH? and s=(r—D/3(1/2).," On the other hand, the statefinder pair $r,s$ ) has also been proposed to distinguish between the models, where $r\equiv761\dot{\ddot{a}}/aH^3$ and $s\equiv (r-1)/3(q-1/2)$."762 Sahni et al. (, Sahni et al. (7632003) demonstrated that the statefinder diagnostic could effectively discriminate different forms of dark energy (Sahni et al.,2003) demonstrated that the statefinder diagnostic could effectively discriminate different forms of dark energy (Sahni et al.764 2003)., 2003).765 Alam et al. (, Alam et al. (7662003) investigated the cosmological constant. quintessence. Chaplygin gas. and braneworld nodels using the statefinder diagnostic. and found that the statefinder pair could differentiate these models (Alam et al.,"2003) investigated the cosmological constant, quintessence, Chaplygin gas, and braneworld models using the statefinder diagnostic, and found that the statefinder pair could differentiate these models (Alam et al."767 2003)., 2003).768 Different cosmological models exhibit qualitatively different trajectories of evolution in the r—s plane., Different cosmological models exhibit qualitatively different trajectories of evolution in the $r-s$ plane.769 The statefinder diagnostic has been extensively used in many models (Gorint et al., The statefinder diagnostic has been extensively used in many models (Gorini et al.770 2003)., 2003).771 But the statefinder pair is difficult to measure by cosmological observations (Visser 2004; Cattoénn Visser 2007)., But the statefinder pair is difficult to measure by cosmological observations (Visser 2004; Cattoënn Visser 2007).772 The present values of cosmographie parameters can be determined from observations (Riess et al., The present values of cosmographic parameters can be determined from observations (Riess et al.773 2004: Visser 2004)., 2004; Visser 2004).774 Caldwell Kamionkowski (2004) showed the jerk parameter could probe the spatial curvature of the universe (Caldwell Kamionkowski 2004)., Caldwell Kamionkowski (2004) showed the jerk parameter could probe the spatial curvature of the universe (Caldwell Kamionkowski 2004).775 The deceleration. jerk and snap parameters are related to the second. third and fourth derivative of the scale factor respectively.," The deceleration, jerk and snap parameters are related to the second, third and fourth derivative of the scale factor respectively."776 Visser (2004) expanded the Hubble law to fourth order in redshift including the snap parameter and put constraints on the deceleration and jerk parameters using Se la (Visser 2004)., Visser (2004) expanded the Hubble law to fourth order in redshift including the snap parameter and put constraints on the deceleration and jerk parameters using SNe Ia (Visser 2004).777 Rapetti et al. (, Rapetti et al. (7782007) constrained the deceleration and jerk parameters from SNe la and X-ray cluster gas mass fraction measurements.,2007) constrained the deceleration and jerk parameters from SNe Ia and X-ray cluster gas mass fraction measurements.779 For a redshift range of SNe Ia the terms beyond the cubic. power of Hubble law can be neglected., For a redshift range of SNe Ia the terms beyond the cubic power of Hubble law can be neglected.780 In order to put a narrow constraint on the snap parameter. we need high-redshift objects.," In order to put a narrow constraint on the snap parameter, we need high-redshift objects."781 GRBs may be a useful tool., GRBs may be a useful tool.782 GRBs can be detectable out to very high redshifts (Ciardi Loeb 2000)., GRBs can be detectable out to very high redshifts (Ciardi Loeb 2000).783 The farthest burst detected so far is GRB 090423. which is at z=8.2 (Olivares et al.," The farthest burst detected so far is GRB 090423, which is at $z=8.2$ (Olivares et al."784 2009)., 2009).785 A lot of work in this so-called has been published (Dai. Liang Xu 2004: Ghirlanda et al.," A lot of work in this so-called has been published (Dai, Liang Xu 2004; Ghirlanda et al."786 2004: Di Girolamo et al., 2004; Di Girolamo et al.787as it- has been typically. doue forB confined*fares.. e.g. Svlwester et al.,"as it has been typically done for confined, e.g. Sylwester et al."788 1993. Reale et al.," 1993, Reale et al."789 1997). iu ordY to conpare this work with previous work to model stellar fiare decay (Reale et al.," 1997), in order to compare this work with previous work to model stellar flare decay (Reale et al."790 1997. Reale Micela 1998. Favata οσο 1999).," 1997, Reale Micela 1998, Favata Schmitt 1999)."791 Tjs diagram is used as a diagnostics of the possible prexsauce of sustained heating durug the ecay (Sylwester et :d., This diagram is used as a diagnostics of the possible presence of sustained heating during the decay (Sylwester et al.792 1993)., 1993).793 The upper pane of Fig., The upper panel of Fig.794 Ss shows he path o the --‘eference nou-coufiued fiue in the dejdtv-tenipor:ture lagrana. and. for comparison. the one of 16 confined flare.," \ref{fig:nt} shows the path of the reference non-confined flare in the density-temperature diagram, and, for comparison, the one of the confined flare."795 We first notice that he 1iaxiuua best fif temiperatire of he nou-confined flare (~L MIS) is iuli lower thai the rue lnaxinuun tenmperature (see Table ] )). bv more than a factor 2.," We first notice that the maximum best fit temperature of the non-confined flare $\sim 4$ MK) is much lower than the true maximum temperature (see Table \ref{tab:sim}) ), by more than a factor 2."796 The reason is that the best-fi eni])orature is a weighted average owY the cutting reeicπα. Which is uuch arvecr and cooler theui the directly heaed region: d1 the atter the temperature is close to the ο maxi teloserature.," The reason is that the best-fit temperature is a weighted average over the emitting region, which is much larger and cooler than the directly heated region; in the latter the temperature is close to the plasma maximum temperature."797 We eud up with an “observed” temperature well below typical flare temperatures. although there is plasua above 10 MIS aud the rate of cucrey released is enough to produce a πιοπα (AL GOES class) solar flare. as the confined oue srown in the figure. with peak plana teniperatures around 20 ME.," We end up with an “observed"" temperature well below typical flare temperatures, although there is plasma above 10 MK and the rate of energy released is enough to produce a medium (M GOES class) solar flare, as the confined one shown in the figure, with peak plasma temperatures around 20 MK."798 The euissiou measure values of the reference mocks dare lower. bv a factor 5. than those oftre confined 1oel flare. wit La naniun value of 3«10! 5m versus ~1.6<1Qi 5m ," The emission measure values of the reference model are lower, by a factor 5, than those of the confined model flare, with a maximum value of $\sim 3 \times 10^{47}$ $^{-3}$ versus $\sim 1.6 \times 10^{48}$ $^{-3}$."799The flare path i the diagran ds differen from the one of the confines| flare in the heating yhase: the eniüsson nmeasure reaches VOYV 8OOlL its iuaxinunna aud the1 eradually decreases (leftwars). aud the temperature slightly fluctuates. whereas the inodel of confined flare shows increasing conüss3on naeasure a constaut temperature (CJakiuiec at al.," The flare path in the diagram is different from the one of the confined flare in the heating phase: the emission measure reaches very soon its maximum and then gradually decreases (leftwards), and the temperature slightly fluctuates, whereas the model of confined flare shows increasing emission measure at constant temperature (Jakimiec at al."800 1992). as also observed iu luaiv solar flares (Svlwester et al.," 1992), as also observed in many solar flares (Sylwester et al."801 1993)., 1993).802 T15 path is much more “standard” im the decay phase: temperature alc enission measure both decrease. along the line with," The path is much more ""standard"" in the decay phase: temperature and emission measure both decrease, along the line with"803gaseous disk and can construct all other components of the galaxy. taking into account the acceleration generated by the gaseous disk.,"gaseous disk and can construct all other components of the galaxy, taking into account the acceleration generated by the gaseous disk."804 In this section we elaborate a few important technical points. useful to anybody wishing to apply the iteration method.," In this section we elaborate a few important technical points, useful to anybody wishing to apply the iteration method."805" The iterative method has two free parameters: the duration of each iteration. fj; and the number of neighbours used in the ""transfer"" algorithm. 7,5 (see section 2.1. of this paper and section 2.2 of RASO9)."," The iterative method has two free parameters: the duration of each iteration, $t_i$, and the number of neighbours used in the “transfer” algorithm, $n_{nb}$ (see section \ref{s_gmethod} of this paper and section 2.2 of RAS09)."806 The choice of these parameters was discussed in RASO9 section 2.5., The choice of these parameters was discussed in RAS09 section 2.5.807 We choose both these parameters empirically., We choose both these parameters empirically.808" In all experiments discussed in. this article we use 1,5""=IO.", In all experiments discussed in this article we use $n_{nb}=10$.809 We construct each component of the galaxy separately in the rigid potential of all other components., We construct each component of the galaxy separately in the rigid potential of all other components.810 So in the iterative method when we calculate the evolution of the system during the iteration time. we do it in the presence of the appropriative external potential.," So in the iterative method when we calculate the evolution of the system during the iteration time, we do it in the presence of the appropriative external potential."811 This can be done either by introducing an analytical external. potential. or by adding the component(s) that create this external potential as a rigid N-body system.," This can be done either by introducing an analytical external potential, or by adding the component(s) that create this external potential as a rigid $N$ -body system."812 In the current work we use the latter., In the current work we use the latter.813 For example. to include the external potential due to the halo. we simply add rigid particles to the system according to the mass distribution of the halo.," For example, to include the external potential due to the halo, we simply add rigid particles to the system according to the mass distribution of the halo."814 When creating the collisionless components we follow the evolution using the public versionof the gyrfaleon N-body code (Dehnen.2000.2002).," When creating the collisionless components we follow the evolution using the public versionof the gyrfalcon $N$ -body code \citep{D00,815 D02}."816. For the gaseous disk we need an appropriate SPH code., For the gaseous disk we need an appropriate SPH code.817 For the isothermal gas we use the public version of the GADGET? code (Springel.2005) and for the multiphase gas code with sub-grid resolution physics we use a private version of GADGET? kindly provided by V. Springel and deseribed in Springel&Hernquist(2003)., For the isothermal gas we use the public version of the GADGET2 code \citep{S05} and for the multiphase gas code with sub-grid resolution physics we use a private version of GADGET2 kindly provided by V. Springel and described in \cite{SH03}.818. We still need to decide when the iteration procedure will be stopped., We still need to decide when the iteration procedure will be stopped.819 We can assume that the iterative process has converged when the system does not change by more than a pre-set amount during one single iteration., We can assume that the iterative process has converged when the system does not change by more than a pre-set amount during one single iteration.820 We check this convergence by comparing different parameters of the system in the beginning and in the end of a single short- evolution step. using a modification of the y test (see Appendix Appendix A:)).," We check this convergence by comparing different parameters of the system in the beginning and in the end of a single short-term evolution step, using a modification of the $\chi^2$ test (see Appendix \ref{s_app}) )."821 In this section we consider an example of a model constructed by means of the method deseribed above., In this section we consider an example of a model constructed by means of the method described above.822 This model is axisymmetric and has an isothermal gaseous disk., This model is axisymmetric and has an isothermal gaseous disk.823 It consists of three components: the gaseous disk. the stellar disk. and the halo.," It consists of three components: the gaseous disk, the stellar disk, and the halo."824 To start. we need to define the mass distribution in both of the non-dissipative components and the projected surface density in the gaseous disk.," To start, we need to define the mass distribution in both of the non-dissipative components and the projected surface density in the gaseous disk."825" The stellar disk model is an exponential disk with a density where M, is the total disk mass. R, is the disk scale length. cy ds its scale height and R is the cylindrical radius."," The stellar disk model is an exponential disk with a density where $M_d$ is the total disk mass, $R_d$ is the disk scale length, $z_d$ is its scale height and $R$ is the cylindrical radius."826" The halo model is a truncated NEW halo (Navarroetal.1996)) where /y, 1s the halo scale length. Cy is a parameter defining the mass of the halo and ny, is the truncation radius of the halo."," The halo model is a truncated NFW halo \citealt{N96}) ) where $r_h$ is the halo scale length, $C_h$ is a parameter defining the mass of the halo and $r_{\rm th}$ is the truncation radius of the halo."827 Similarly to the stellar disk. the gaseous disk has an exponential projected surface density profile scale length.," Similarly to the stellar disk, the gaseous disk has an exponential projected surface density profile where $M_g$ is the total mass of the gaseous disk and $R_g$ is its scale length."828 We still need to adopt specific values for the present example., We still need to adopt specific values for the present example.829" In the above we take My=5-10Mi. Ry=3kpe. xo=0.6kpe: ry=12kpe. C,=0.0019-I0'?M./kpe?. rn=40kpe: M,=0.5-10!""Ms. Κι=3kpe."," In the above we take $M_d= 5 \cdot 10^{10} \; {\rm M}_{\odot}$, $R_d = 3 \;\rm kpc$, $z_0=0.6 \;\rm kpc$; $r_h=12 \;\rm kpc$, $C_h=0.0019 \cdot 10^{10} \rm M_{\odot}/kpc^3$, $r_{\rm th}=40830\;\rm kpc$; $M_g= 0.5 \cdot 10^{10} \; {\rm M}_{\odot}$, $R_g = 3831\;\rm kpc$."832 We set the temperature of the isothermal gas to 7=10000K., We set the temperature of the isothermal gas to $T=10000 \;\rm K$.833 Note that the mass of the gaseous disk is of the stellar disk mass., Note that the mass of the gaseous disk is of the stellar disk mass.834 For the chosen parameters. the total mass of the halo is Myοὐx4.9-M.," For the chosen parameters, the total mass of the halo is $M_h \approx 4.9 \cdot M_d$."835" In this specific example we chose NV,=100000. Ny=200000. N,=980311 for the number of particles in the gaseous disk. the stellar disk. and the halo. respectively."," In this specific example we chose $N_g=100000$, $N_d=200000$, $N_h=980311$ for the number of particles in the gaseous disk, the stellar disk, and the halo, respectively."836 With these numbers. the mass of the particles in the stellar disk and in the halo is the same.," With these numbers, the mass of the particles in the stellar disk and in the halo is the same."837" We use the GADGET system of units. where the unit of length is Ξ|kpe. the unit of velocity is i,=1km/sec. the unit of mass is u,,=10!""M. and consequently the unit of time is 4,=0.98 Gyr."," We use the GADGET system of units, where the unit of length is $u_l=1 \;\rm kpc$, the unit of velocity is $u_v=1 \;\rm km/sec$, the unit of mass is $u_m = 10^{10}838\;\rm M_{\odot}$ and consequently the unit of time is $u_t \approx8390.98 \;\rm Gyr$ ."840" For simplicity. when we convert this time unit into gigayears we assume that a,=|Gyr."," For simplicity, when we convert this time unit into gigayears we assume that $u_t=1 \;\rm Gyr$."841 We also need to select the kinematic constrains for the stellar components (see RASO9)., We also need to select the kinematic constrains for the stellar components (see RAS09).842 We created the disk with the following velocity dispersion profile where op Is the radial velocity dispersion., We created the disk with the following velocity dispersion profile where $\sigma_R$ is the radial velocity dispersion.843 When constructing the halo. we did not impose any specific kinematic constraints.," When constructing the halo, we did not impose any specific kinematic constraints."844 Instead. we aimed for a model not far from isotropic (see RASO9).," Instead, we aimed for a model not far from isotropic (see RAS09)."845 As noted in section 2.1.. we should first construct. the equilibrium. model of the gaseous disk with the desired projected surface density embedded in the rigid potential generated by the halo and the stellar disk. as deseribed in section 2.1..," As noted in section \ref{s_gmethod}, we should first construct the equilibrium model of the gaseous disk with the desired projected surface density embedded in the rigid potential generated by the halo and the stellar disk, as described in section \ref{s_gmethod}. ."846 To achieve this. we made 50 iterations. each with t;=0.02Gyr.," To achieve this, we made 50 iterations, each with $t_i = 0.02 \; \rm Gyr$."847 We note that ¢; should be shorter than the time scale of the strong instability developing in the system under construction., We note that $t_i$ should be shorter than the time scale of the strong instability developing in the system under construction.848 In our case the gaseous disk forms strong spirals relatively fast (see fig. 2))., In our case the gaseous disk forms strong spirals relatively fast (see fig. \ref{fig_gas.iso}) ).849 It is why we have to choose relatively short f; in this case., It is why we have to choose relatively short $t_i$ in this case.850 After constructing the equilibrium gaseous disk. we have the full mass model of the galaxy. and we can apply the algorithm for constructing the equilibrium models of the stellar disk and the halo (RASO9).," After constructing the equilibrium gaseous disk, we have the full mass model of the galaxy, and we can apply the algorithm for constructing the equilibrium models of the stellar disk and the halo (RAS09)."851 Let us first describe the stellar disk construction., Let us first describe the stellar disk construction.852 Our initial model was a cold disk. where all particles. move on circularorbits.," Our initial model was a cold disk, where all particles move on circularorbits."853 We made 50 iterations. each with 5;= Gyr.," We made $50$ iterations, each with $t_i=0.25 \; \rm Gyr$ ."854 The integration step and softening length were, The integration step and softening length were855to be Γ=5/3.,to be $\Gamma = 5/3$.856 In both cases the «M distribution was of the form with A=1 for solution (a). and A=50 for solution (5) (notice that κ is a dimensionless quantity).," In both cases the $\kappa \dot M$ distribution was of the form with $A = 1$ for solution $(a)$ , and $A = 50$ for solution $(b)$ (notice that $\kappa \dot M$ is a dimensionless quantity)."857 When deriving Eqs. (6)). (11))," When deriving Eqs. \ref{ac}) ), \ref{aj}) )"858 and (13)) we have assumed that |]«rw., and \ref{al}) ) we have assumed that $|U| \ll r \omega$.859 Having obtained solutions to this system of equations. it remains to be checked if this condition ts satisfied.," Having obtained solutions to this system of equations, it remains to be checked if this condition is satisfied."860 For solutions depicted on Figs. 2-, For solutions depicted on Figs. \ref{fig_rho_thin}-861-4 and 5--7 rw=vconst. so we are mainly interested in the distribution of |U|.," \ref{fig_psi_thin} and \ref{fig_rho}- \ref{fig_psi} $r \omega = v = \mathrm{const}$, so we are mainly interested in the distribution of $|U|$."862 This can be computed from Eq. (8)), This can be computed from Eq. \ref{bt}) )863 basing on the density distribution and the assumed nàss accretion rate M. (, basing on the density distribution and the assumed mass accretion rate $\dot M$ . (864Note that in the process of finding the numerical solution we have to supply values of the product «M.,Note that in the process of finding the numerical solution we have to supply values of the product $\kappa \dot M$.865 It is only now that we have to split this product and provide values of « and M separately.), It is only now that we have to split this product and provide values of $\kappa$ and $\dot M$ separately.)866 Fig., Fig.867 8 show the graphs of [U]|/Gco) for solutions presented on Figs. —L, \ref{fig_rad_vel} show the graphs of $|U|/(r \omega)$ for solutions presented on Figs. \ref{fig_rho_thin}-868 and 5--7 respectively., \ref{fig_psi_thin} and \ref{fig_rho}- \ref{fig_psi} respectively.869 Clearly. values of [U] are orders of nagnitude smaller than values of rc.," Clearly, values of $|U|$ are orders of magnitude smaller than values of $r \omega$."870 Given a solution. one can find other useful quantities describing the entire configuration.," Given a solution, one can find other useful quantities describing the entire configuration."871 These are. in particular. the nass of the fluid. Myuig and the total luminosity L.," These are, in particular, the mass of the fluid $M_\mathrm{fluid}$ and the total luminosity $L$."872 We get for solution (4): Mayiq=+8Me and L=2.2-10°Le., We get for solution $(a)$: $M_\textrm{fluid} = 48 M_{\astrosun}$ and $L = 2.2 \cdot 10^3 L_{\astrosun}$.873 Solution (5) in turn is characterized by Mayjq=55Me and L=1.2107 Lo., Solution $(b)$ in turn is characterized by $M_\textrm{fluid} = 55 M_{\astrosun}$ and $L = 1.2 \cdot 10^5 L_{\astrosun}$ .874 otice that these luminosities are smaller than the Eddington limit for the whole system consisting of the central mass and the disk., Notice that these luminosities are smaller than the Eddington limit for the whole system consisting of the central mass and the disk.875 Assuming the perfect gas approximation and a value of the mean molecular weight of the gas µ. we can also find the distribution of the gas temperature where Kg denotes the Boltzmann constant.," Assuming the perfect gas approximation and a value of the mean molecular weight of the gas $\mu$, we can also find the distribution of the gas temperature where $k_\mathrm{B}$ denotes the Boltzmann constant."876 The maximal value of the gas temperature obtained for solution (e) 1s T=1.3- 10°K., The maximal value of the gas temperature obtained for solution $(a)$ is $T_\mathrm{max} = 1.3 \cdot 10^7 \mathrm{K}$ .877 For solution (5) it is of order Τιμ.=1.4-10:Κ., For solution $(b)$ it is of order $T_\mathrm{max} = 1.4 \cdot 10^7 \mathrm{K}$.878 In both cases the mean molecular weight was assumed to be He=1/2 corresponding to the gas consisting of fully ionized hydrogen., In both cases the mean molecular weight was assumed to be $\mu = 1/2$ corresponding to the gas consisting of fully ionized hydrogen.879 From a given solution one can also obtain the emissivity “We have checked that it is concentrated only around the equatorial plane. and its values are increasing towards the inner disk boundary rip.," From a given solution one can also obtain the emissivity We have checked that it is concentrated only around the equatorial plane, and its values are increasing towards the inner disk boundary $r_\mathrm{in}$."880 Parameters characterizing a handful of disk solutions are collected in Table |.., Parameters characterizing a handful of disk solutions are collected in Table \ref{tabelka}.881 These solutions were obtained for M.= Mg. V=5/3 and v-const rotation.," These solutions were obtained for $M_\mathrm{c} = M_{\astrosun}$ , $\Gamma = 5/3$ and $v$ -const rotation."882 The assumed mass aecretion rate function is given by formula (34)). and the value of the mean molecular weight used to compute the maximal temperature within the disk is μ—1/2.," The assumed mass accretion rate function is given by formula \ref{accretion_f}) ), and the value of the mean molecular weight used to compute the maximal temperature within the disk is $\mu = 1/2$."883 For each set of parameters Απ. Row and Pinay two solutions are computed: one corresponding to A=| and the second corresponding to A-50.," For each set of parameters $R_\mathrm{in}$, $R_\mathrm{out}$ and $\rho_\mathrm{max}$ two solutions are computed: one corresponding to $A = 1$ and the second corresponding to $A = 50$."884 We have formulated a consistent model of a selfgravitating dise with a steadily accreting matter., We have formulated a consistent model of a selfgravitating disc with a steadily accreting matter.885 The radiation emitted by the disk interacts with the infalling gas by the Thompson scattering., The radiation emitted by the disk interacts with the infalling gas by the Thompson scattering.886 The aceretion mass rate flux density is chosen in a way that allows for a slow radial drift of gas concentrated in the equatorial plane., The accretion mass rate flux density is chosen in a way that allows for a slow radial drift of gas concentrated in the equatorial plane.887 We investigate several standard rotation laws., We investigate several standard rotation laws.888 It appears that the conservation laws of the energy and the momentum together with the assumption. of approximate stationarity suffice to obtain the structure of the disk., It appears that the conservation laws of the energy and the momentum together with the assumption of approximate stationarity suffice to obtain the structure of the disk.889 The emissivity index of accreting matter can be deduced after solving equations of the model., The emissivity index of accreting matter can be deduced after solving equations of the model.890 The approximation of stationarity demands that the radial inflow speed of matter has to be negligible in comparison with the rotational velocity of the gas in the disk., The approximation of stationarity demands that the radial inflow speed of matter has to be negligible in comparison with the rotational velocity of the gas in the disk.891 The secular change in the mass of the central accreting object should also be negligible., The secular change in the mass of the central accreting object should also be negligible.892 These two assumptions have been verified post factum in the sample of solutions presented in this paper., These two assumptions have been verified post factum in the sample of solutions presented in this paper.893 The mathematical description of the radiating disk reduces to a par of elliptic partial differential equations., The mathematical description of the radiating disk reduces to a pair of elliptic partial differential equations.894 They can be solved iteratively in a way similar to that routinely used in the literature when finding selfgravitating equilibria of on-radiating gas (cf.Ostriker&Mark.1968;EriguchiMüller.1985:Nishida.Eriguchi&Lanza. 1992).," They can be solved iteratively in a way similar to that routinely used in the literature when finding selfgravitating equilibria of non-radiating gas \citep[cf.][]{ostriker_mark_1968, eriguchi_muller_1985, nishida_eriguchi_lanza_1992}."895. In our case each iteration step consist of finding new distributions of the density. the gravitational potential and the radiation potential.," In our case each iteration step consist of finding new distributions of the density, the gravitational potential and the radiation potential."896 One of the main results of this paper ts that this procedure umerically converges., One of the main results of this paper is that this procedure numerically converges.897" As a result we recover rigorously the picture of ""Polish donuts” predicted by Paezynsski and his coworkers (Paezyíski.1978:Paezynski&Wiita.1980;Qianetal..2009) for radiating disks."," As a result we recover rigorously the picture of “Polish donuts” predicted by Paczyńsski and his coworkers \citep{Paczynski78, Wiita, Qian} for radiating disks."898 Let us point out that analytic results can be obtained in. simplifiec cases., Let us point out that analytic results can be obtained in simplified cases.899 We investigate the influence of the emitted radiation onto the disk structure in the test fluid approximation., We investigate the influence of the emitted radiation onto the disk structure in the test fluid approximation.900 The interesting conclusion ts that approximately stationary solutions do exist only when the mass accretion (and thus the Juminosity) is not too large., The interesting conclusion is that approximately stationary solutions do exist only when the mass accretion (and thus the luminosity) is not too large.901 This intuitively well understood feature of solutions has been revealed also in our numerical analysis of heavy selfgravitating disks., This intuitively well understood feature of solutions has been revealed also in our numerical analysis of heavy selfgravitating disks.902 A future investigation of our model can be aimed in two directions. the study of stability of disks and the formulation of a general-relativistic version.," A future investigation of our model can be aimed in two directions, the study of stability of disks and the formulation of a general-relativistic version."903 Unlike for the standard models. the structure of our Newtonian disks is dependent on the accretio flux and radiation.," Unlike for the standard models, the structure of our Newtonian disks is dependent on the accretion flux and radiation."904 We have discovered that Bondi-type. spherically symmetric solutions are stable also in the selfgravitating regime (Mach&Malec.2008).," We have discovered that Bondi-type, spherically symmetric solutions are stable also in the selfgravitating regime \citep{MM08}."905. The Bondi accretio models are spherically symmetric in. contrast. to accreting disks. but they share with our model the property that their structure depends on the aceretion. and that can have a stabilizig effect also in the nonspherical case.," The Bondi accretion models are spherically symmetric in contrast to accreting disks, but they share with our model the property that their structure depends on the accretion, and that can have a stabilizing effect also in the nonspherical case."906 Thus we expect that solutions that are discussed in this paper could appear to bestable., Thus we expect that solutions that are discussed in this paper could appear to bestable.907 There are two extremal classesof general-relativistic radiating accretion disks., There are two extremal classesof general-relativistic radiating accretion disks.908" Disks characterized by the size of inner boundary muchlarger than 2GM,/c (quasi-Newtonian case). where M, is the central mass. should have a structure similar to the ones presented in this paper."," Disks characterized by the size of inner boundary muchlarger than $2 G M_\mathrm{c}/c^2$ (quasi-Newtonian case), where $M_\mathrm{c}$ is the central mass, should have a structure similar to the ones presented in this paper."909 However. their stability properties can still be different due to the influence of gravitational radiation.," However, their stability properties can still be different due to the influence of gravitational radiation."910 Disks that are inherently relativistic.," Disks that are inherently relativistic,"911The Panoramic Survey Telescope And Rapid Response Svstem (Pan-STARBS. ?)) is a pioneering wide-field. multi-filter. multi-epoch astronomical survey program.,"The Panoramic Survey Telescope And Rapid Response System (Pan-STARRS, \citealt{Kaiser2002}) ) is a pioneering wide-field, multi-filter, multi-epoch astronomical survey program."912 The project is plauned (o consist of four (wo-meter class telescopes operating Irom the ILawaiiun Islands., The project is planned to consist of four two-meter class telescopes operating from the Hawaiian Islands.913 The first of these. the Pan-STARRSI1 telescope (PSI). has recently began full science operations on Mav the 15th 2010 on llaleakala on Mani ancl is operated by (he LL Science Consortium.," The first of these, the 1 telescope (PS1), has recently began full science operations on May the 15th 2010 on Haleakalā on Maui and is operated by the 1 Science Consortium."914 The largest of the PSI surveys is the 33 Survey which is planned to cover the entire sky visible from Lawaii (37 steradiaus in area. 0> —30°) in five fillers (g. r. 7. z and y) wilh pairs of observations in each filter being taken al six different epochs.," The largest of the PS1 surveys is the $\pi$ Survey which is planned to cover the entire sky visible from Hawai`i $\pi$ steradians in area, $\delta > -30^{\circ}$ ) in five filters $g$, $r$, $i$, $z$ and $y$ ) with pairs of observations in each filter being taken at six different epochs."915 This will allow (he survey to serve a range of science goals by both stacking individual exposures for deep images and using multiple epochs to identify moving or variable objects., This will allow the survey to serve a range of science goals by both stacking individual exposures for deep images and using multiple epochs to identify moving or variable objects.916 50 lar the data available have been used to search for Trans-Neptunian Objects (2)) and supernovae (e.g. 72))., So far the data available have been used to search for Trans-Neptunian Objects \citealt{Wang2009}) ) and supernovae (e.g. \citealt{Botticella2010}) ).917 One of the kev science areas where P51 aims (o contribute is Che study of the local low bhuninosity population., One of the key science areas where PS1 aims to contribute is the study of the local low luminosity population.918 The unique combination of a wide field. multiple," The unique combination of a wide field, multiple"919remained.,remained.920 Also. the observed (1.9. absorbed) luminosities £1. are correlated with LP. but the VyLP dependence leads to a ‘shallower’ correlation between {μι and EL.," Also, the observed (i.e. absorbed) luminosities $\Labs$ are correlated with $\Gamma$, but the $\NH - \Gamma$ dependence leads to a `shallower' correlation between $\Labs$ and $\Gamma$."921 Therefore. we conclude that the LxV correlations are real.," Therefore, we conclude that the $\Lx-\Gamma$ correlations are real."922 Tf the NyLE correlation is indeed artificial. then there must be a low-energy break in the power-law component below ~1 keV in these spectra.," If the $\NH - \Gamma$ correlation is indeed artificial, then there must be a low-energy break in the power-law component below $\sim 1$ keV in these spectra."923 This could be then be interpreted as a sign that this component arises from Comptonization of the dise photons in à ‘corona’ surrounding the source., This could be then be interpreted as a sign that this component arises from Comptonization of the disc photons in a `corona' surrounding the source.924 It is also possible. however. that the correlation between Ny and D has a physical origin. for example a growing luminosity might lead to a stronger outflow and therefore to a denser environment.," It is also possible, however, that the correlation between $\NH$ and $\Gamma$ has a physical origin, for example a growing luminosity might lead to a stronger outflow and therefore to a denser environment."925 In general. all the sources that have luminositiesabove ~3«LOeres| show a power-law type spectra.," In general, all the sources that have luminosities $\sim 3 \times 10^{39} \, \ergs$ show a power-law type spectra."926 In contrast. the three sources with luminositiesbelow ~3.LO’eres| have non-power-law tor thermal) type spectra (see next subsection).," In contrast, the three sources with luminosities $\sim 3 \times 10^{39} \, \ergs$ have non-power-law (or thermal) type spectra (see next subsection)."927 An exception to this ‘rule’ is NGC 1313 ULX-2 which has non-power-law type spectra at high luminosities and power-law type spectra at lower luminosities very much like the very high state spectra of XTE 11550-564 (Kubota&Done 2004)., An exception to this `rule' is NGC 1313 ULX-2 which has non-power-law type spectra at high luminosities and power-law type spectra at lower luminosities very much like the very high state spectra of XTE J1550-564 \citep{KD04}.928. In some sources. both and models give statistically acceptable (or equally good) fits.," In some sources, both and models give statistically acceptable (or equally good) fits."929 We assign them to a non-power-law type because their variability is consistent with Galactic black hole binaries («BHB) when modelled usingDISKBD., We assign them to a non-power-law type because their variability is consistent with Galactic black hole binaries (BHB) when modelled using.930 Also. a simple absorbed model does not provide statistically acceptable tits for NGC 6946 X-6. but the model gives good fits for most observations (see Sect.," Also, a simple absorbed model does not provide statistically acceptable fits for NGC 6946 X-6, but the model gives good fits for most observations (see Sect."931 3.3 and Table A L3)., \ref{soft_excess} and Table \ref{bestfits}) ).932 We therefore assign this source to a power-law type., We therefore assign this source to a power-law type.933 Four out of the 7 ULXs with the Zx—E correlation (NGC 1313 ULX-I. Holmberg II ULX-I. Holmberg IX ULX-1 and NGC 5204 ULX-I) show also signs of spectral pivoting.," Four out of the 7 ULXs with the $\Lx-\Gamma$ correlation (NGC 1313 ULX-1, Holmberg II ULX-1, Holmberg IX ULX-1 and NGC 5204 ULX-1) show also signs of spectral pivoting."934 Similar pivoting has been also observed in Cyg X-I (Zdziarskietal.2002). and several AGNS (seee.g.Zdziarskietal.2003.table|.andreferences therein)...," Similar pivoting has been also observed in Cyg X-1 \citep{Z02} and several AGNs \citep[see e.g.][ table 1, and references therein]{Z03}."935 The pivoting is clearly seen for NGC 5204 ULX-1 at keV (see Fig. 20) , The pivoting is clearly seen for NGC 5204 ULX-1 at $\sim 5.5$ keV (see Fig. \ref{pivoting}) )936and the three high luminosity observations of Holmberg II ULX-1 seem to pivot at ~3.5 keV. The pivoting in NGC 1313 ULX-I and Holmberg IX ULX-1 occur at the boundary of the energy range at 9 and 10 keV. respectively.," and the three high luminosity observations of Holmberg II ULX-1 seem to pivot at $\sim 3.5$ keV. The pivoting in NGC 1313 ULX-1 and Holmberg IX ULX-1 occur at the boundary of the energy range at $\sim 9$ and $10$ keV, respectively."937 To evaluate whether these pivots are real. wealso show in Fig.," To evaluate whether these pivots are real, wealso show in Fig."938" | the dependences between the luminosity in a given energy band G7,.E») and the photon index expected for a pivoting power-law (Zdziarskietal.2003): AxD = where 2 is the distance. ZE,5 is the flux in the selected energy band and C' is a constant."," \ref{pofitresults} the dependences between the luminosity in a given energy band $E_1,E_2$ ) and the photon index expected for a pivoting power-law \citep{Z03}: = D^2 = C where $D$ is the distance, $F_{E_1 - E_2}$ is the flux in the selected energy band and $C$ is a constant."939 Equation (I9) gives à. good representation of the observed LxE relation for all these pivoting ULXs., Equation \ref{Fgamma}) ) gives a good representation of the observed $\Lx-\Gamma$ relation for all these pivoting ULXs.940 We therefore conclude. that the pivoting is most likely real even in the cases of NGC 1313 ULX-1I and Holmberg IX ULX-I.," We therefore conclude, that the pivoting is most likely real even in the cases of NGC 1313 ULX-1 and Holmberg IX ULX-1."941 However. when the spectrum gets very soft at DL=3. NGC 1313 ULX-I. Holmberg II ULX-1 and NGC 5204 ULX-1I also show deviations from this dependence.," However, when the spectrum gets very soft at $\Gamma \gtrsim 3$, NGC 1313 ULX-1, Holmberg II ULX-1 and NGC 5204 ULX-1 also show deviations from this dependence."942 These deviations to the low/soft states (Dewanganetal.2004).. are similar to those seen in Galactic BHBs (seeZdziarskietal.2002.fig.162).," These deviations to the low/soft states \citep{DM04}, are similar to those seen in Galactic BHBs \cite[see][ fig. 16a]{Z02}."943 The process producing the observed power-law type spectrum is most likely Compton up-scattering of soft dise photons in a hot plasma surrounding the inner part of the disc., The process producing the observed power-law type spectrum is most likely Compton up-scattering of soft disc photons in a hot plasma surrounding the inner part of the disc.944 The observed Lx1. correlation and the pivoting in the sources can be explained by variability of the luminosity of the soft dise photons., The observed $\Lx-\Gamma$ correlation and the pivoting in the sources can be explained by variability of the luminosity of the soft disc photons.945 A larger dise luminosity leads to a softer X-ray spectrum (CZdziarskietal.2003)., A larger disc luminosity leads to a softer X-ray spectrum \citep{Z03}.946. An example of such variability for a constant hot-plasma luminosity is given in fig., An example of such variability for a constant hot-plasma luminosity is given in fig.947 3 of Zdziarski&Grandi(2001) for 3C 120., 3 of \citet{ZG01} for 3C 120.948 The similarity of this source to NGC 5204 ULX- (and the other 3 ULXs with pivoting) is remarkable (see Fig. 29., The similarity of this source to NGC 5204 ULX-1 (and the other 3 ULXs with pivoting) is remarkable (see Fig. \ref{pivoting}) ).949 Transition to the low/soft state can be associated with the decreasing luminosity of the hot plasma (corona) with the nearly constant dise luminosity., Transition to the low/soft state can be associated with the decreasing luminosity of the hot plasma (corona) with the nearly constant disc luminosity.950 The highest quality data also seems to show a break/cutoff in the power-law component above ~3 keV (Stobbartetal.2006:Gladstoneetal. 2009).," The highest quality data also seems to show a break/cutoff in the power-law component above $\sim 3$ keV \citep{SRW06,GRD09}."951. This could be then interpreted as a sign of a cool and optically thick corona (Gladstoneetal.2009)., This could be then interpreted as a sign of a cool and optically thick corona \citep{GRD09}.952 Unfortunately the limited observing band of and and the typical data quality in our sample do not allow us to see these high energy breaks/cutoffs in most of these data., Unfortunately the limited observing band of and and the typical data quality in our sample do not allow us to see these high energy breaks/cutoffs in most of these data.953 A dedicated monitoring campaing of these power-law type ULXs would help us to check whether these breaks are always present. which would be highly useful in order to understand the nature of the emission mechanisms in ULXs.," A dedicated monitoring campaing of these power-law type ULXs would help us to check whether these breaks are always present, which would be highly useful in order to understand the nature of the emission mechanisms in ULXs."954 Out of the selected 11 ULXs. four ULXs can be adequately fitted with an absorbed MCD model.," Out of the selected 11 ULXs, four ULXs can be adequately fitted with an absorbed MCD model."955 These sources include the two ULXs that show the LxEL anti-correlation (NGC 253 X-2 and NGC 1313 X-2) and the two low-luminosity ULXs (NGC 253 X-4 and NGC 253 X-9)., These sources include the two ULXs that show the $\Lx-\Gamma$ anti-correlation (NGC 253 X-2 and NGC 1313 X-2) and the two low-luminosity ULXs (NGC 253 X-4 and NGC 253 X-9).956 The resulting fits are shown in a luminosity- (hereafter £9 7) diagram in Fig., The resulting fits are shown in a luminosity-temperature (hereafter $L-T$ ) diagram in Fig.957 3. together with the observations on known BHBs adopted from Gierliiski&Done (2004)..., \ref{dbbfits} together with the observations on known BHBs adopted from \citet{GD04}. .958 These four ULXs follow the behaviour seen in BHBs., These four ULXs follow the behaviour seen in BHBs.959 The properties of the sources can be summarised as follows., The properties of the sources can be summarised as follows.960where «;.f and A are coustauts and (41/2.2.,"where $ c_i, \ell$ and $\lambda$ are constants and $\ell\neq961-1/2, 2$ ."962" Since B—0 aud 7=0 for Nocther sviuunetrv without eauge term. the parameters ej.ος and e, should vauish."," Since $B=0$ and $\tau=0$ for Noether symmetry without gauge term, the parameters $c_1, c_3$ and $c_4$ should vanish."963 This case has been studied iu (RoshanaudS, This case has been studied in \cite{fat}.964hojai2005). Taking o=yo in the Lagrangian (6)) and doing the above calculations again. the obtained form of aaud Jj generalizes the ones found in Ref.(RoshanandShojai2008) which are represcuted as A and DB in this reference).," Taking $\phi =965\varphi^2$ in the Lagrangian \ref{lag}) ) and doing the above calculations again, the obtained form of $\alpha$and $\beta$ generalizes the ones found in \cite{fat} (which are represented as $A$ and $B$ in this reference)."966 It is seen from (23))-(25)) that the Lagrangian (6)) adits Nocther svuunetry ecucrators The correspondiug Lie algebra has the following commutators: The first iutegrals associated with X; are Tere the coustaut parameter e; is assuniecd to be zero in the gauge function B., It is seen from \ref{alpha}) \ref{vec2}) ) that the Lagrangian \ref{lag}) ) admits Noether symmetry generators The corresponding Lie algebra has the following non-vanishing commutators: The first integrals associated with ${\bf X_{i}}$ are Here the constant parameter $c_{4}$ is assumed to be zero in the gauge function $B$.967 We note that the first iuteeral (32)) is related with the (7)). so that the fixst iteeral £4. vanishes.," We note that the first integral \ref{frstI-1}) ) is related with the \ref{E-L}) ), so that the first integral $I_{1}$ vanishes."968 As an inverse problem of finding FCR) Lagrangian. it is only required to eive C(47).," As an inverse problem of finding $f(\mathcal{R})$ Lagrangian, it is only required to give $U(\varphi)$."969 Using the algebraic relation it is possible to solve fUR). whereRo=«(0) aud o=fr.," Using the algebraic relation it is possible to solve $f(\mathcal{R})$, where$\mathcal{R}=\chi(\phi)$ and $\phi = f_{\mathcal{R}}$."970 Putting the potential (26)) iuto Eq. (35)), Putting the potential \ref{pot}) ) into Eq. \ref{pot-bag}) )971 vields Thus. it is straightforward to eet the followingtwo solutious frou Eq. (36))," yields Thus, it is straightforward to get the followingtwo solutions from Eq. \ref{defe}) )"972 for FUR.) where pif)∣=2(f|↽1)Yesamoi]38πι. Ry isa. constant aud {σε1.1/2.," for $f(\mathcal{R})$ where $p(\ell)= 2(\ell +1) \left[ \frac{\lambda 3^{-3/(2 \ell973-1)}}{1- 2\ell} \right]^{\frac{2 \ell -1}{2(\ell+1)}}$, $R_{0}$ is a constant and $\ell\neq -1, 1/2$ ."974 Iu the following subsectious. considering FÜR.) given by 07)) aud (38)). we will search the exact solution for cosmic scale factor.," In the following subsections, considering $f(\mathcal{R})$ given by \ref{form1}) ) and \ref{form2}) ), we will search the exact solution for cosmic scale factor."975 For a aud 3 given by (23))-(21)) and Eq. (37)).," For $\alpha$ and $\beta$ given by \ref{alpha}) \ref{beta}) ) and Eq. \ref{form1}) ),"976 it is appeared the sineularitics for the values of (=1/2 and (=~1., it is appeared the singularities for the values of $\ell =-1/2$ and $\ell = -1$.977 For these values of f. after solving Eq.(36)) one has the sameform with (38)) for FUR).," For these values of $\ell$, after solving \ref{defe}) ) one has the sameform with \ref{form2}) ) for $f(\mathcal{R})$ ."978 Usine the trace relation (1)) and o=fr we obtain where (tjDre;Spit)Lilουpico16]|1)=|1ls2: .((x— lfl.," Using the trace relation \ref{trace}) ) and $\phi=f_{\mathcal{R}}$ we obtain where $r(\ell)=\frac{3979p(\ell)}{2(\ell+1)}[\frac{2\kappa\rho_{m0}(\ell+1)}{p(\ell)(4\ell+1)}]^{\frac{1-2\ell}{3}}$ , $\ell \neq -1/4$ ."980 Ience. the Noetherfirst integrals (: 339) and (31)) cau be written as Now the Eq.(10)) can be used to find out the time dependence of the cosmic scale factor as," Hence, the Noetherfirst integrals \ref{frstI-2}) ) and \ref{frstI-3}) ) can be written as Now the \ref{frstI-22}) ) can be used to find out the time dependence of the cosmic scale factor as"981There are several reasons for this.,There are several reasons for this.982 First. at ~£000 davs IXF99 fud that almost half of the Iuuinosity from the supernova is emereimes in this line.," First, at $\sim 4\,000$ days KF99 find that almost half of the luminosity from the supernova is emerging in this line."983 Second. because the iron lines are oulv little affected by freeze-out they are eood tracers of the instantancous euerev deposition. aud the flux of [Fe II| 25.9950 is therefore alinost proportional to MUT).," Second, because the iron lines are only little affected by freeze-out they are good tracers of the instantaneous energy deposition, and the flux of [Fe II] $\mum$ is therefore almost proportional to $\Ti44$."984 This. lis liue is foiiied. through collisional excitations and is therefore iusensifive to uncertainties in atomic data involved iu calculating the recombination cascade.," Third, this line is formed through collisional excitations and is therefore insensitive to uncertainties in atomic data involved in calculating the recombination cascade."985 Iu a preliminary analysis. Borkowski et al. (," In a preliminary analysis, Borkowski et al. ("9861997) find that their Infrared Space Observatory (ISO: Kessler et al.,1997) find that their Infrared Space Observatory (ISO; Kessler et al.987 1996) observations eive an upper luit on the line fux which correspouds to ouly 1.5«10°4 , 1996) observations give an upper limit on the line flux which corresponds to only $1.5 \times 10^{-5} \Msun$.988Tere we report on observations we have made with ISO., Here we report on observations we have made with ISO.989 Although we have observed the supernova over the eutire wavelength rauge 2.38.—10741. we will couceutrate our discussion on the region. 232T. where the strongest cussion lines are expected to cierec.," Although we have observed the supernova over the entire wavelength range $2.38 - 197 \mum$, we will concentrate our discussion on the region, $23 - 27 \mum$, where the strongest emission lines are expected to emerge."990 We compare these observations with theorctical uodeliug., We compare these observations with theoretical modeling.991 We also briefly discuss our observations at longer waveleneths where we detect eniüssion originating from elsewhere im the LMC., We also briefly discuss our observations at longer wavelengths where we detect emission originating from elsewhere in the LMC.992 We have used ISO to. observe SN. 1987À on several occasions., We have used ISO to observe SN 1987A on several occasions.993 Both the Short Wavelength Spectrograph (SWS: de Caaamy ct al., Both the Short Wavelength Spectrograph (SWS; de Graauw et al.994 1996) aud the Long Wavelength Spectrograph (LAVS: Cleeeao et al., 1996) and the Long Wavelength Spectrograph (LWS; Clegg et al.995 1996) were used. aud Table 1 sunmniarizes our observations.," 1996) were used, and Table 1 summarizes our observations."996 We will conceutrate here mainly on the SWS observation from [| February. 1998 (Sect.," We will concentrate here mainly on the SWS observation from 4 February, 1998 (Sect."997 2.1). though we provide a cousistenev check of this observation against our other SWS observations.," 2.1), though we provide a consistency check of this observation against our other SWS observations."998 The LAYS data are discussed ii Sect., The LWS data are discussed in Sect.999 2.2., 2.2.1000 The SWS observation ou [ February. 1998 was mace iu the SWSOL mode with speed [ aud was centered on the position of SN 1987À. ie. R.A. = 5h 351 28.058: Decl.," The SWS observation on 4 February, 1998 was made in the SWS01 mode with speed 4 and was centered on the position of SN 1987A, i.e., R.A. = 5h 35m 28.05s; Decl."1001" = 69"" 16 1176L: 672000.0).", = $-69^{\rm o}$ $\arcmin$ $\farcs$ 64; (J2000.0).1002 SWSOL provides spectra whic[um together cover the eutire waveleneth region between 2.38 15.2;nu., SWS01 provides spectra which together cover the entire wavelength region between $2.38 - 45.2 \mum$ .1003 However. as our models predict [Fe I| 21.05704 and [Fe II] 25.995 to be by far the strongest eniissio- lines from the supernova at this epoch (dav 39999: see Sect.," However, as our models predict [Fe I] $\mum$ and [Fe II] $\mum$ to be by far the strongest emission lines from the supernova at this epoch (day 999; see Sect."1004 3). we have concentrated ou measuring the fiux in the wavelength range inclicding these two mes.," 3), we have concentrated on measuring the flux in the wavelength range including these two lines."1005 This range. between 22.527.54nu. is covered by band 3D of SWS.," This range, between $22.5 - 27.5 \mum$, is covered by band 3D of SWS."1006 The reductions were made using the SWS Iuteractive Analysis software system (SIA) available at ISO Spectrometer Data Center TSOSDC) at the Max Plauck Tustitut fiuy extraterrestrische Physik iu Garching (AIPE)., The reductions were made using the SWS Interactive Analysis software system (SIA) available at ISO Spectrometer Data Center (ISOSDC) at the Max Planck Institut fürr extraterrestrische Physik in Garching (MPE).1007 The most receu set of calibration files equivalent to off-ine processing (OLP/pipeliue) version 7.0 was used., The most recent set of calibration files equivalent to off-line processing (OLP/pipeline) version 7.0 was used.1008 The interactive reduction allows special care to be given to dark subtractions. which is of particular iutercst when neasuring low flux levels.," The interactive reduction allows special care to be given to dark subtractions, which is of particular interest when measuring low flux levels."1009 Flat fielding was also applied. mt we have uot mace any fringe corrections since the fringes at low flux levels disappear in the noise.," Flat fielding was also applied, but we have not made any fringe corrections since the fringes at low flux levels disappear in the noise."1010 Iu Fig., In Fig.1011 l woe present a fully reduced spectra of SN 198TÀ for baud 3D. Although the nominal instrmuental resolution. of SWS is Roz1000. the slowest SWSUI node with speed [ degraces this bv a factor of 2.," 1 we present a fully reduced spectrum of SN 1987A for band 3D. Although the nominal instrumental resolution of SWS is $R \approx 1\,000$, the slowest SWS01 mode with speed 4 degrades this by a factor of 2."1012" We wave therefore averaged the spectrum with a biu size of 0.052,n1u. corresponding to 600650kms! for the wo lines of interest."," We have therefore averaged the spectrum with a bin size of $\mum$, corresponding to $600 - 650 \kms$ for the two lines of interest."1013 As the lines could exteud to well above +2000kns3 this resolution should be sufficient o resolve the lines.," As the lines could extend to well above $\pm 2\,000 \kms$ this resolution should be sufficient to resolve the lines."1014 However. neither [Fe I] LO5jmu nor Fe HI] 25.9951 are seen in the spectrin.," However, neither [Fe I] $\mum$ nor [Fe II] $\mum$ are seen in the spectrum."1015 The ‘features’ hat do appear around ~23.5 and 25.702 are iiost likely due to instrumental effects. as they are rather robust in he sense that they appear iu many detectors andin both up and down scans.," The `features' that do appear around $\sim 23.5$ and $25.7 \mum$ are most likely due to instrumental effects, as they are rather robust in the sense that they appear in many detectors andin both up and down scans."1016 They are certainly not duc to fringes.," They are certainly not due to fringes,"1017spectroscopic surface gravity.,spectroscopic surface gravity.1018 Here it is worth summarizing our method and emphasizing one aspect of it before presenting one more result., Here it is worth summarizing our method and emphasizing one aspect of it before presenting one more result.1019 We started out by fixing the helium envelope parameters to the values that fit the time dependent diffusion calculations of Dehner Kawaler (1995) but when we zoomed in on the promising part of parameter space (grid 2 in table 2)). we relaxed the parameter that sets the thickness of the pure helium envelope.," We started out by fixing the helium envelope parameters to the values that fit the time dependent diffusion calculations of Dehner Kawaler (1995) but when we zoomed in on the promising part of parameter space (grid 2 in table \ref{t2}) ), we relaxed the parameter that sets the thickness of the pure helium envelope."1020 We also never fixed the effective temperature and treated it as à free parameter within à reasonable range., We also never fixed the effective temperature and treated it as a free parameter within a reasonable range.1021 We now come back to Fig. 1..," We now come back to Fig. \ref{f1},"1022 which actually shows quite an interesting result., which actually shows quite an interesting result.1023 On that graph. we show the helium abundance profile for our best fit model along with the profile calculated by Dehner Kawaler (1995).," On that graph, we show the helium abundance profile for our best fit model along with the profile calculated by Dehner Kawaler (1995)."1024 Two things match beautifully: 1) The profiles themselves (of course the base of the mixed He/C layer matches perfectly because we fixed that. but the base of the pure helium layer was eventually allowed to vary) and 2) The effective temperature.," Two things match beautifully: 1) The profiles themselves (of course the base of the mixed He/C layer matches perfectly because we fixed that, but the base of the pure helium layer was eventually allowed to vary) and 2) The effective temperature."1025 The latter was allowed to vary between KK and KK and settled on KK. This last result may be evidence that the calculations of time dependent diffusion caleulations of Dehner Kawaler (1995). as well as others since then e.g. Althaus et al. (," The latter was allowed to vary between K and K and settled on K. This last result may be evidence that the calculations of time dependent diffusion calculations of Dehner Kawaler (1995), as well as others since then e.g. Althaus et al. ("10262005) describe the evolution of PGI159 stars well.,2005) describe the evolution of PG1159 stars well.1027 However. we also need to look at what the core structure is.," However, we also need to look at what the core structure is."1028 Does it agree with stellar evolution calculations?, Does it agree with stellar evolution calculations?1029 The answer there is not quite as positive., The answer there is not quite as positive.1030 We find a central oxygen abundance of 0.60., We find a central oxygen abundance of 0.60.1031 With the standard reaction rates and treatment for convection. we expect the central abundance for a white dwarf of mass 0.550 AL.. to be between ~0.5 and ~0.9 (Althaus et al.," With the standard reaction rates and treatment for convection, we expect the central abundance for a white dwarf of mass 0.550 $M_\odot$ to be between $\sim 0.8$ and $\sim 0.9$ (Althaus et al."1032 2010; Salaris et al., 2010; Salaris et al.1033 1997)., 1997).1034 Perhaps more importantly. as our models are highly sensitive to that parameter. (Bischoff-Kim Metealfe 2011). the location of the edge of the homogeneous core is further inward than what stellar evolution calculations find.," Perhaps more importantly, as our models are highly sensitive to that parameter (Bischoff-Kim Metcalfe 2011), the location of the edge of the homogeneous core is further inward than what stellar evolution calculations find."1035 In this paper. we took three different approaches using the pulsations to determme an effective temperature for JJ19294+4447: 1) Through a quick inspection of the pulsation spectrum. noting that low period modes were observed. 2) using average period spacing arguments. and 3) by performing asteroseismic fits of the period spectrum.," In this paper, we took three different approaches using the pulsations to determine an effective temperature for J1929+4447: 1) Through a quick inspection of the pulsation spectrum, noting that low period modes were observed, 2) using average period spacing arguments, and 3) by performing asteroseismic fits of the period spectrum."1036 All three point to an effective temperature more similar to 220058-5234's and inconsistent with the spectroscopic value of T.=219003:750 KK. A well-calibrated high-S/N spectrum is urgently needed to settle the temperature issue., All three point to an effective temperature more similar to 20058-5234's and inconsistent with the spectroscopic value of $\rm T_{eff}=24900 \pm 750$ K. A well-calibrated high-S/N spectrum is urgently needed to settle the temperature issue.1037 We performed an asteroseismic analysis of JJ1929-4447. a DBV discovered in the field of view of the satellite.," We performed an asteroseismic analysis of J1929+4447, a DBV discovered in the field of view of the satellite."1038 We find strong evidence that the star is à hot DBV., We find strong evidence that the star is a hot DBV.1039 Our models also support the time dependent diffusion calculations of Dehner Kawaler (1995). though more positive results from the study of other DBVs are needed to further support these results.," Our models also support the time dependent diffusion calculations of Dehner Kawaler (1995), though more positive results from the study of other DBVs are needed to further support these results."1040 Also. it would be worth approaching the problem from another angle.," Also, it would be worth approaching the problem from another angle."1041 In section 3.2. we made the somewhat arbitrary choice of fixing the envelope parameters and allowing the core parameters to vary., In section \ref{grids} we made the somewhat arbitrary choice of fixing the envelope parameters and allowing the core parameters to vary.1042 We would most likely learn a lot by trying to fix the core parameters to those expected from stellar evolution (e.g. Althaus et al., We would most likely learn a lot by trying to fix the core parameters to those expected from stellar evolution (e.g. Althaus et al.1043 2010: Salaris et al., 2010; Salaris et al.1044 1997) and allow the envelope parameters to freely vary over the entire reasonable range., 1997) and allow the envelope parameters to freely vary over the entire reasonable range.1045 Continuous observations with the satellite may also reveal more modes. hidden in noise at the current. S/N level. allowing 6 parameter fits.," Continuous observations with the satellite may also reveal more modes, hidden in noise at the current S/N level, allowing 6 parameter fits."1046 The discovery of a hot DBV is significant. as it gives us another chance to study plasmon neutrino emission from white dwarfs.," The discovery of a hot DBV is significant, as it gives us another chance to study plasmon neutrino emission from white dwarfs."1047 At KK. JJ19294+4447 should be radiating as much energy through the emission of photons as through the emission of plasmon neutrinos (Winget et al.," At K, J1929+4447 should be radiating as much energy through the emission of photons as through the emission of plasmon neutrinos (Winget et al."1048 2004)., 2004).1049 The extra cooling due to neutrinos is therefore easily detectable if one could measure the cooling rate for the star with any significance., The extra cooling due to neutrinos is therefore easily detectable if one could measure the cooling rate for the star with any significance.1050 An observed period change in any of the modes can be a reliable estimator for the cooling rate. and only requires that at least one of the observed modes are phase-stable over a sufficient number of years to detect the variation.," An observed period change in any of the modes can be a reliable estimator for the cooling rate, and only requires that at least one of the observed modes are phase-stable over a sufficient number of years to detect the variation."1051 If. is permitted to maintain observations of WD J1929+4447 for a period of five years. the cooling rate should be determined to a sufficient precision to establish the respective contributions from thermal radiation and plasmon neutrinos.," If is permitted to maintain observations of WD J1929+4447 for a period of five years, the cooling rate should be determined to a sufficient precision to establish the respective contributions from thermal radiation and plasmon neutrinos."1052The full range of products for patch A aud D iu the form of astrometric and photometric calibrated pixel naps. object catalogs. candidate target lists aud line co-added section iÓuages can be found at release.itin.,"The full range of products for patch A and B in the form of astrometric and photometric calibrated pixel maps, object catalogs, candidate target lists and on-line co-added section images can be found at release.html”."1053 New products. will be added incrementally as they become avaialble., New products will be added incrementally as they become avaialble.1054 Further oeformation on the project are available ou the World Wide Web at Αμο/CIS-, Further information on the project are available on the World Wide Web at www.eso.org/eis”.1055 , 1056 Using T?! and assunius LTE excitation. the total INCO column densities are 0.2-0.8. 1-1.9 and 1.5-3.8 (n units of 1077. 351) for min. Bl. and B2. respectively.," Using $_{ex}^{54}$ and assuming LTE excitation, the total HNCO column densities are 0.2-0.8, 1-1.9 and 1.5-3.8 (in units of $10^{13}$ ) for mm, B1, and B2, respectively."1057 Since the excitation is similar in Bl aud D2. the highest line intensities measured towards B2 translate iuto larger cohuun deusities. m contrast to the CO σοι deusitv which is a factor of 2 lower in D2 (?)..," Since the excitation is similar in B1 and B2, the highest line intensities measured towards B2 translate into larger column densities, in contrast to the CO column density which is a factor of 2 lower in B2 \citep{Bachiller97}."1058 Iu addition. we have studied the TNCO excitation using (?).. which is a nou-LTE excitation and radiative transfer code that decouples the statistical equilibrium and the radiative transfer equations using the escape probability method.," In addition, we have studied the HNCO excitation using \citep{vanderTak07}, which is a non-LTE excitation and radiative transfer code that decouples the statistical equilibrium and the radiative transfer equations using the escape probability method."1059 The caleulatious assume lines of a even width aud rectangular shape., The calculations assume lines of a given width and rectangular shape.1060 Therefore. the chanec of the optical depth over the profile is not taken iuto account.," Therefore, the change of the optical depth over the profile is not taken into account."1061 This is not a problem if the opacity of the lines is not verv high., This is not a problem if the opacity of the lines is not very high.1062 We have used the TNCO-H» collisional COefficients listed in the database (?).., We have used the $_2$ collisional coefficients listed in the database \citep{Schoier05}.1063" The colputatio suse a backeround temperature of 2.73 Is. We have modeled the me fluxes (or integrated mteusities) as a function of the hivdroeen. volume clousity (yy, ). the IINCO coluun density GVjjr veo). the uu‘tic temperature Gy) and the velocity dispersion."," The computations use a background temperature of 2.73 K. We have modeled the line fluxes (or integrated intensities) as a function of the hydrogen volume density $n_{H_{2}}$ ), the HNCO column density $N_{HNCO}$ ), the kinetic temperature $T_K$ ) and the velocity dispersion."1064 The rauge of hivdroex‘ll deusities used is 10710% aaL that of NHNe© Is ↽10-72+1057., The range of hydrogen densities used is $10^3-10^6$ and that of $N_{HNCO}$ is $10^{12}-10^{15}$.1065 Two: kinetic. teniperatures have been considered: a low kinetic temperature (30 Is). oulv slightly higver than the excitation temperature derivxl with he IENC'O lines and a mach higher temperature (250 Ix). since the actual eas temperature 1 the shocked gas can be conskerably higher than the IENC'O. excitation te11])oratures.," Two kinetic temperatures have been considered: a low kinetic temperature (30 K), only slightly higher than the excitation temperature derived with the HNCO lines and a much higher temperature (250 K), since the actual gas temperature in the shocked gas can be considerably higher than the HNCO excitation temperatures."1066 These temperatures probably cover fje different plivsical couditious of L1157au nand the shockexl sources Dl aid D2., These temperatures probably cover the different physical conditions of L1157-mm and the shocked sources B1 and B2.1067" We have comted models wihi veocity dispersions (linewidths) from Ἰ to 6 which cover the neasured range of liuewidt isin the thre"" observed posiions."," We have computed models with velocity dispersions (linewidths) from 1 to 6, which cover the measured range of linewidths in the three observed positions."1068 In the range of pwsical conditioIs COupatible wih the observations. the οoicitv at the peeus of the lines is low.," In the range of physical conditions compatible with the observations, the opacity at the peak of the lines is low."1069 Therefore. the predicted iuteeratexl lutcnsitics are independent of the actual linewidth used O COupute the nocdels.," Therefore, the predicted integrated intensities are independent of the actual linewidth used to compute the models."1070 For iustance. the figures discussed beow have been computed with a linewidth of 5.," For instance, the figures discussed below have been computed with a linewidth of 3."1071 We have based our analysis on the two lowest lines. which are detected towards the three observed. positions.," We have based our analysis on the two lowest lines, which are detected towards the three observed positions."1072 Figure b shows the model predictions for the tto, Figure \ref{fig:radex1} shows the model predictions for the to1073"5 and 10 are obviously more scattered (han the data with 7,4,,/0; greater than 10.",5 and 10 are obviously more scattered than the data with $\tau_{max}/\sigma_\tau$ greater than 10.1074" This implies that the signal-to-noise is too low to obtain reliable (p) estimates when Toss/0,<10.", This implies that the signal-to-noise is too low to obtain reliable $\langle\rho\rangle$ estimates when $\tau_{max}/\sigma_\tau <10$.1075 We therefore tabulate in Tables 1-- 3. the (pj values only [or those observations where Τσ.210., We therefore tabulate in Tables \ref{obstab}- - \ref{charmtab} the $\langle\rho\rangle$ values only for those observations where $\tau_{max}/\sigma_\tau >10$.1076 Focusing exclusively on (he higher significance data in Figure 7.. il is apparent that the different dusty rings have different distributions of (p). The F-ring distribution peaks around 0.9. but extends [rom below 0.8 to about 1.0.," Focusing exclusively on the higher significance data in Figure \ref{rhodist}, it is apparent that the different dusty rings have different distributions of $\langle\rho\rangle.$ The F-ring distribution peaks around 0.9, but extends from below 0.8 to about 1.0."1077 The three clear measurements of (p) from the Charming Ringlet all fall between 0.8 and 0.9. and therefore overlap the F-ring distribution.," The three clear measurements of $\langle\rho\rangle$ from the Charming Ringlet all fall between 0.8 and 0.9, and therefore overlap the F-ring distribution."1078 However. the Encke Gap ringlets seem to have (p) values between 0.95 and 1. which is clearly higher (han (tvpical values for the F ring.," However, the Encke Gap ringlets seem to have $\langle\rho\rangle$ values between 0.95 and 1, which is clearly higher than typical values for the F ring."1079 Figure 8 shows the (p) values versus the equivalent depth for the dilferent rines (computed using Equation 2. and the same radial ranges as emploved in the calculations of (pj)., Figure \ref{rhoscat} shows the $\langle\rho\rangle$ values versus the equivalent depth for the different rings (computed using Equation \ref{eqdepth} and the same radial ranges as employed in the calculations of $\langle\rho\rangle$ ).1080 This plot demonstrates that the spectral differences between the Encke Gap ringlets and the F ring cannot be entirely. ascribed to differences in these fealtves’ average optical deptlis., This plot demonstrates that the spectral differences between the Encke Gap ringlets and the F ring cannot be entirely ascribed to differences in these features' average optical depths.1081 Even though the F ring's equivalent depth is almost always higher (han the Encke Gap ringlets. (here are cases where (he equivalent depth of these features are comparable to each other. and even in these situations the (p) values of the Encke Gap ringlets are svstematically hieher than those of the F ring.," Even though the F ring's equivalent depth is almost always higher than the Encke Gap ringlets, there are cases where the equivalent depth of these features are comparable to each other, and even in these situations the $\langle\rho\rangle$ values of the Encke Gap ringlets are systematically higher than those of the F ring."1082 The Encke Gap ringlets and the F ring would therelore appear to have svstematically different particle size distributions (see also Figure 9 below)., The Encke Gap ringlets and the F ring would therefore appear to have systematically different particle size distributions (see also Figure \ref{rhotrend} below).1083 Since there is no evidence for a spike in the optical depth at 3.1 san in any of the dusty rings (see Figure 6)). thev all are probably depleted in sub-micron particles (cl.," Since there is no evidence for a spike in the optical depth at 3.1 $\mu$ m in any of the dusty rings (see Figure \ref{ocetspec}) ), they all are probably depleted in sub-micron particles (cf."1084 Figure 5))., Figure \ref{plmod}) ).1085 However. the higher (p) values in the Encke Gap ringlets (corresponding to a weaker opacity dip at 2.87 jm) iniplies that these ringlets have a smaller fraction of particles in the 1-10 jm range.," However, the higher $\langle\rho\rangle$ values in the Encke Gap ringlets (corresponding to a weaker opacity dip at 2.87 $\mu$ m) implies that these ringlets have a smaller fraction of particles in the 1-10 $\mu$ m range."1086 The size distribution of grains larger than 10 jn in the Encke Gap ringlets is therefore probably not as steep as itis for the (vpical F ring or (he Charming Rinelet., The size distribution of grains larger than 10 $\mu$ m in the Encke Gap ringlets is therefore probably not as steep as it is for the typical F ring or the Charming Ringlet.1087 In addition to the systematic dilference between the F ring and the Encke Gap ringlets. the finite widths of the (p) distributions in Figure 7 also suggest that there are significant spectral and particle-size variations within each ring.," In addition to the systematic difference between the F ring and the Encke Gap ringlets, the finite widths of the $\langle\rho\rangle$ distributions in Figure \ref{rhodist} also suggest that there are significant spectral and particle-size variations within each ring."1088" Further evidence for such variations can be found in Figures 9 and 10.. which show sinele-sample estimates of p versus optical depth derived [rom occultations of the star ο Ceti. which were obtained αἱ a very low ring opening angle of 3.5"" aud hence provide exceptionally hieh sienal-to-noise data for these rings."," Further evidence for such variations can be found in Figures \ref{rhotrend} and \ref{ocettrend}, which show single-sample estimates of $\rho$ versus optical depth derived from occultations of the star $o$ Ceti, which were obtained at a very low ring opening angle of $^\circ$ and hence provide exceptionally high signal-to-noise data for these rings."1089 In both the Encke Gap ringlet ancl the F ring data there are clear trends of increasing p with increasing optical depth., In both the Encke Gap ringlet and the F ring data there are clear trends of increasing $\rho$ with increasing optical depth.1090 The denser parts of these rings therefore havea smaller fraction of 1-10 micron particles. which would suggest that smaller grains are more widely dispersed in (hese rings than (he larger ones.," The denser parts of these rings therefore havea smaller fraction of 1-10 micron particles, which would suggest that smaller grains are more widely dispersed in these rings than the larger ones."1091 Note that in spite of these trends. Figure 9. demonstrates (hat svstenmatic differences between (he Encke Gap and F ring persist even al (he level of single-sample estimates of p.," Note that in spite of these trends, Figure \ref{rhotrend}1092 demonstrates that systematic differences between the Encke Gap and F ring persist even at the level of single-sample estimates of $\rho$ ."1093Also alt the aceretion shock. e.(ry)=(Vor;(tsfive)Vc(ri). which after some rearrangement gives Eliminatinge V.«( between equations Bl and D2 egives where V?B.=—H1)Bree? (v⋅i)—-441)LnVo/r? and 52v.,"Also at the accretion shock, $v_{\perp}\left(r_s\right)=v_s\vec{\nabla _{\perp}}\delta r_s=1094\left(v_s/i\omega\right)\vec{\nabla _{\perp}}v_r\left(r_s\right)$, which after some rearrangement gives Eliminating $\vec{\nabla _{\perp}}\cdot\vec{v_{\perp}}$ between equations B1 and B2 gives where $\nabla _{\perp}^2B_{\pm} = -l\left(l+1\right)B_{\pm}/r^2$, $\nabla _{\perp}^2\left(\vec{\nabla _{\perp}}\cdot1095\vec{v_{\perp}}\right) = -l\left(l+1\right)\left(\vec{\nabla _{\perp}}\cdot1096\vec{v_{\perp}}\right)/r^2$ and $1/L^{\prime}=1/L+5/2r$ ."1097 The interior boundary. and hence the boundary. conditions here. are less well defined in our model.," The interior boundary, and hence the boundary conditions here, are less well defined in our model."1098 We are assuming that the region where strong neutrino cooling sets in and causes (he accreting matter to decouple from (he hot postshock flow will give a boundary from which waves can reflect. Vishniac&Rau(1989).," We are assuming that the region where strong neutrino cooling sets in and causes the accreting matter to decouple from the hot postshock flow will give a boundary from which waves can reflect. \citet{vishniac89},"1099". considering a plane parallel shock. assume a constant pressure boundary condition. 0=—05;/Lοζω, "," considering a plane parallel shock, assume a constant pressure boundary condition, $\delta =-\delta r_i/L=-v_r/i\omega L$."1100We assume something similar: We do not take the local value of £ in this boundary condition. but take the same value as asstuned above al the forward shock. modified by a constant à which we vary to find the best match to the /=0 stabilitv.," We assume something similar; We do not take the local value of $L$ in this boundary condition, but take the same value as assumed above at the forward shock, modified by a constant $a$ which we vary to find the best match to the $l=0$ stability."1101" In any case. 0(7j)=0,(ri)freak(ry)<<-0,fie as il must be. because the background density increases signilicantly over (hat predicted by the Bernoulli model due to radiative cooling by neutrino emission."," In any case, $\delta\left(r_i\right)=-v_r\left(r_i\right)/i\omega aL\left(r_s\right)1102<<-v_r\left(r_i\right)/i\omega L\left(r_i\right)$ as it must be, because the background density increases significantly over that predicted by the Bernoulli model due to radiative cooling by neutrino emission."1103 We prefer (o cast the interior boundary. condition in terms of L ancl r evaluated at the outer shock. because of the algebraic simplification it produces. ancl (he somewhat easier conditions requirecl (o keep ihe /=0 mode stable.," We prefer to cast the interior boundary condition in terms of $L$ and $r$ evaluated at the outer shock, because of the algebraic simplification it produces, and the somewhat easier conditions required to keep the $l=0$ mode stable."1104 It is clear [rom the work of various authors Nakayama.(e.g.1992):Goshy(e.g.1993):Yamasaki&Yamada2005) that this must be true.," It is clear from the work of various authors \citet[e.g.][]{nakayama92,burrows93,yamasaki05}1105 that this must be true."1106 These last (wo references. in particular. include considerably more physics. ancl are able to predict the shock radius. rather than just specilving it as we do. but thev only (reat radial stability.," These last two references, in particular, include considerably more physics, and are able to predict the shock radius, rather than just specifying it as we do, but they only treat radial stability."1107 Consequently we have, Consequently we have1108The radio source B0605-085 (OH 010) is a very bright at centimeter and millimeter wavelengths quasar with a redshift of 0.872 (Stickel et al.,The radio source $-$ 085 $OH~010$ ) is a very bright at centimeter and millimeter wavelengths quasar with a redshift of 0.872 (Stickel et al.1109 1993)., 1993).1110 B0605-085 was studied in X-ray and optical wavelengths with andHST telescopes by Sambruna et al. (, $-$ 085 was studied in X-ray and optical wavelengths with and telescopes by Sambruna et al. (11112004) and is one of a few quasars which jets have been detected in the X-rays.,2004) and is one of a few quasars which jets have been detected in the X-rays.1112 Very Long-Baseline Interferometry (VLBI) observations revealed a complex structure of the radio jet of the quasar. with multiple bends and curves at scales from parsecs to kiloparsees.," Very Long-Baseline Interferometry (VLBI) observations revealed a complex structure of the radio jet of the quasar, with multiple bends and curves at scales from parsecs to kiloparsecs."1113 High-resolution space VLBI observations show that the inner jet extends in the south-east direction and at ~0.2 mas 1t turns to the north-east (Scott et al., High-resolution space VLBI observations show that the inner jet extends in the south-east direction and at $\sim$ 0.2 mas it turns to the north-east (Scott et al.1114 2004)., 2004).1115 When observed at centimeter wavelengths the outer part of the jet continues to extend south-east with multiple turns and at kilo-parsec scales it goes eastwards with a south-east bend at ~3 areseconds (Cooper et al., When observed at centimeter wavelengths the outer part of the jet continues to extend south-east with multiple turns and at kilo-parsec scales it goes eastwards with a south-east bend at $\sim$ 3 arcseconds (Cooper et al.1116 2007)., 2007).1117 The kinematics of B0605—085 jet was studied by Kellermann et al. (, The kinematics of $-$ 085 jet was studied by Kellermann et al. (11182004) at 2 em as part of the MOJAVE 2- survey.,2004) at 2 cm as part of the MOJAVE 2-cm survey.1119 Based on three epochs of observations (1996. 1999 and 2001). two jet components were found at 1.6 and 3.8 mas distance from the radio core with moderate apparent speeds of 0.1020.21c and 0.18+0.02c. respectively.," Based on three epochs of observations (1996, 1999 and 2001), two jet components were found at 1.6 and 3.8 mas distance from the radio core with moderate apparent speeds of $\pm$ 0.21c and $\pm$ 0.02c, respectively."1120 The kinematics of Β0605--055 and its components accelerations were also studied by Lister et al. (, The kinematics of $-$ 085 and its components accelerations were also studied by Lister et al. (11212009) and Homan et al. (,2009) and Homan et al. (11222009) as part of the sample of 135 radio-loud active galactic nuclei.,2009) as part of the sample of 135 radio-loud active galactic nuclei.1123 However. only average acceleration of jet components have been discussed in these papers.," However, only average acceleration of jet components have been discussed in these papers."1124 The total flux-density radio light curves of Β0605--055 from University of Michigan Radio Astronomical Observatory (e.g.. Aller et al.," The total flux-density radio light curves of $-$ 085 from University of Michigan Radio Astronomical Observatory (e.g., Aller et al."1125 1999) show hints of periodic variability., 1999) show hints of periodic variability.1126 Several outbursts appeared in the source at regular intervals., Several outbursts appeared in the source at regular intervals.1127 Periodic variability of active galactic nuclei is a fascinating topic which ts not well understood at the moment., Periodic variability of active galactic nuclei is a fascinating topic which is not well understood at the moment.1128 Only a few active galaxies show evidence for possible periodicity in radio light curves (e.g.. Raiteri et al.," Only a few active galaxies show evidence for possible periodicity in radio light curves (e.g., Raiteri et al."1129 2001. Aller et al.," 2001, Aller et al."1130 2003. Kelly et al.," 2003, Kelly et al."1131 2003. Ciaramella et al.," 2003, Ciaramella et al."1132 2004. Villata et al.," 2004, Villata et al."1133 2004. Kadler et al.," 2004, Kadler et al."1134 2006. Kudryavtseva Pyatunina 2006. Qian et al.," 2006, Kudryavtseva Pyatunina 2006, Qian et al."1135 2007. Villata et al.," 2007, Villata et al."1136 2009)., 2009).1137" Various mechanisms might cause periodic appearance of outbursts in radio wavelength. such as helical movement of jet components (e.g.. Camenzind Krockenberger 1992. Villata Raiteri 1999, Ostorero et al."," Various mechanisms might cause periodic appearance of outbursts in radio wavelength, such as helical movement of jet components (e.g., Camenzind Krockenberger 1992, Villata Raiteri 1999, Ostorero et al."1138 2004). shock waves propagation (e.g.. Gómmez et al.," 2004), shock waves propagation (e.g., Gómmez et al."1139 1997). aceretion dise instabilities (e.g.. Honma et al.," 1997), accretion disc instabilities (e.g., Honma et al."1140 1991. Lobanov Roland 2005). jet precession (e.g.. Stirling et al.," 1991, Lobanov Roland 2005), jet precession (e.g., Stirling et al."1141 2003. Bach et al.," 2003, Bach et al."1142 2006. Britzen et al.," 2006, Britzen et al."1143 2010). or they even might be indirectly caused by a secondary black hole rotating around the primary super-massive black hole in the center (e.g.. Lehto Valtoner 1996. Rieger Mannheim 2000).," 2010), or they even might be indirectly caused by a secondary black hole rotating around the primary super-massive black hole in the center (e.g., Lehto Valtonen 1996, Rieger Mannheim 2000)."1144 However. investigation of repeating processes in active galaxies is extremely complicated due to various factors.," However, investigation of repeating processes in active galaxies is extremely complicated due to various factors."1145 The first complicity is that a light curve Is usually a mixture of flares which are most likely not caused solely by one effect., The first complicity is that a light curve is usually a mixture of flares which are most likely not caused solely by one effect.1146 Outbursts might be caused by multiple shock waves propagation. changes of the viewing angle or other conditions in the jet. such as magnetic field or electron density.," Outbursts might be caused by multiple shock waves propagation, changes of the viewing angle or other conditions in the jet, such as magnetic field or electron density."1147 Looking for periodicity is also complicatec with possible quasi-periodic nature of variability (e.g.. OJ 287. Kidger 2000 and references therein) and long-term nature of periods. when the observed timescales are of the order of tens of years and really long observations are necessary in order to detect such timescales.," Looking for periodicity is also complicated with possible quasi-periodic nature of variability (e.g., OJ 287, Kidger 2000 and references therein) and long-term nature of periods, when the observed timescales are of the order of tens of years and really long observations are necessary in order to detect such timescales."1148 In this paper we aim to study the probable periodic nature of the radio total flux-density variability of the quasar B0605—085 and to check what might be a possible reason for it. investigating the movement of the Jet components with high-resolution VLBI observations together with an analysis of spectral indexes and opacity of B0605—085.," In this paper we aim to study the probable periodic nature of the radio total flux-density variability of the quasar $-$ 085 and to check what might be a possible reason for it, investigating the movement of the jet components with high-resolution VLBI observations together with an analysis of spectral indexes and opacity of $-$ 085."1149 The structure of this paper is organized às follows: in Sect., The structure of this paper is organized as follows: in Sect.1150 2 we describe the total flux-density variability of Β0605--055 and focus on periodicity analysis. spectral changes and frequency-dependent time lags of the flares.," 2 we describe the total flux-density variability of $-$ 085 and focus on periodicity analysis, spectral changes and frequency-dependent time lags of the flares."1151 In Sect., In Sect.1152 3 parsec-scale jet kinematics of B0605—085 is. presented., 3 parsec-scale jet kinematics of $-$ 085 is presented.1153 In Sect., In Sect.1154 + we apply a precession model to the trajectory of Β0605--055 jet component., 4 we apply a precession model to the trajectory of $-$ 085 jet component.1155 In Sect., In Sect.1156 5 we discuss and present, 5 we discuss and present1157barvon. wilh barvon number vl.,"baryon, with baryon number $A$."1158 This structure of the quarks leads (o a net positive charge inside (he star., This structure of the quarks leads to a net positive charge inside the star.1159 Since stars in (heir lowest energy state are supposed to be charge neutral. electrons must balance (he net positive quark charge in strange matter stus.," Since stars in their lowest energy state are supposed to be charge neutral, electrons must balance the net positive quark charge in strange matter stars."1160 The electrons. being bounded to the quark matter by the electromagnetic interaction and not by the strong force. are able to move [freely across the quark surface. but clearly cannot move to infinity because of the electrostatic attraction of quarks.," The electrons, being bounded to the quark matter by the electromagnetic interaction and not by the strong force, are able to move freely across the quark surface, but clearly cannot move to infinity because of the electrostatic attraction of quarks."1161 The electron distribution extends up to ~10* [m above the quark surface., The electron distribution extends up to $\sim 10^{3}$ fm above the quark surface.1162 The Coulomb barrier at the quark surface of a hot strange star may also be a powerful source of pairs. which are created in the extremely strong electric Ποια of (he barrier.," The Coulomb barrier at the quark surface of a hot strange star may also be a powerful source of }$ pairs, which are created in the extremely strong electric field of the barrier."1163 At surface temperatures of around. 10! IX. the luminosity of the outflowing plasma may be of the order ~10°! !1998)..," At surface temperatures of around $10^{11}$ K, the luminosity of the outflowing plasma may be of the order $\sim 10^{51}$ $^{-1}$."1164 Moreover. as shown by(2002).. the thermal Iuminositv [rom the star surface. due to both photon emission and € pair production may be. for about one day for normal quark matter and for up to a ΠΙΟΤΘ vears for superconducting quark matter. orders of magnitude higher (han the Eddineton limit.," Moreover, as shown by, the thermal luminosity from the star surface, due to both photon emission and $e^{+}e^{-}$ pair production may be, for about one day for normal quark matter and for up to a hundred years for superconducting quark matter, orders of magnitude higher than the Eddington limit."1165 It is the purpose of the present paper to reconsider the problem of the photon enissivilv. via bremisstralilung radiation. of (he quark stars.," It is the purpose of the present paper to reconsider the problem of the photon emissivity, via bremsstrahlung radiation, of the quark stars."1166 Equilibrium radiation. transmitted through the surface. is dominant at temperatures T>2xLO! KI. while below this temperature the bremsstrahlung radiation from the surface laver prevails.," Equilibrium radiation, transmitted through the surface, is dominant at temperatures $T>2\times 10^{10}$ K, while below this temperature the bremsstrahlung radiation from the surface layer prevails."1167 Ilence bremsstrahlung is the main source of radiation for cold quark stars., Hence bremsstrahlung is the main source of radiation for cold quark stars.1168 This electromagnetic radiation is generated in the dense medium at the stellar surface in which extremely relativistic quarks move., This electromagnetic radiation is generated in the dense medium at the stellar surface in which extremely relativistic quarks move.1169 In the 1950's predicted that the cross section lor bremsstrahlung from hiehlv relativistic particles in dense media is suppressed. due to (he interference between amplitudes of nearby interactions.," In the 1950's predicted that the cross section for bremsstrahlung from highly relativistic particles in dense media is suppressed, due to the interference between amplitudes of nearby interactions."1170 The suppression has its roots in the uncertainty. principle., The suppression has its roots in the uncertainty principle.1171 The kinematics of the bremsstrahlung requires Chat the longitudinal momentum (ransler between (he fixed and the scattered particles must be small., The kinematics of the bremsstrahlung requires that the longitudinal momentum transfer between the fixed and the scattered particles must be small.1172 On the other hand the uncertainty principle requires that (he interaction must occur over a large longitudinal distance scale (formation zone)., On the other hand the uncertainty principle requires that the interaction must occur over a large longitudinal distance scale (formation zone).1173 If the charged particle Coulomb scatters while traversing (his zone. the bremsstrahlung amplitude Irom before and alter the scattering can interfere. reducing the amplitude for photon emission1999).," If the charged particle Coulomb scatters while traversing this zone, the bremsstrahlung amplitude from before and after the scattering can interfere, reducing the amplitude for photon emission."1174. This effect has been recently confirmed experimentally for the bremsstrahlung emission ol electrons in different materials al a accuracy level1995)., This effect has been recently confirmed experimentally for the bremsstrahlung emission of electrons in different materials at a accuracy level.1175.. Since the surface of the quark star consists of a very dense medium. with density of the orcer 4xBe4x011. multiple collisions of the electromagneticallv radiating particle lead to a signilicant suppression of the quark-quark bremsstrahlung.," Since the surface of the quark star consists of a very dense medium, with density of the order $4\times B\approx4\times 10^{14}$, multiple collisions of the electromagnetically radiating particle lead to a significant suppression of the quark-quark bremsstrahlung."1176 By adopting a simple model for the elastic scattering of quarks. we derive (he spectrum of the classical bremsstrahlilung radiation and (he emissivity of the quark matter. by considering (he multiple scattering effects in the electromagnetic radiation of quark matter.," By adopting a simple model for the elastic scattering of quarks, we derive the spectrum of the classical bremsstrahlung radiation and the emissivity of the quark matter, by considering the multiple scattering effects in the electromagnetic radiation of quark matter."1177 For the range of densities existing, For the range of densities existing1178take account for the effective spatial resolution of the X-ray and data (FWITMD = 079 |—0.6° iu position angle in the azimuthal profiles} for the XN-rav aud 175 for the data). aud compared by eve with the data.,"take account for the effective spatial resolution of the X-ray and data (FWHM = $0\farcs9$ $\equiv0.6\degr$ in position angle in the azimuthal profiles] for the X-ray and $1\farcs5$ for the data), and compared by eye with the data."1179 We primarily attempt to match the position. width aud intensity of the eastern linib. eiven the more confused state of the western side of the profiles.," We primarily attempt to match the position, width and intensity of the eastern limb, given the more confused state of the western side of the profiles."1180 The relative intensity of the eastern hub with respect to the central surface brightuess mudi then constrains the cmussivity of auv material within the core of the outflow., The relative intensity of the eastern limb with respect to the central surface brightness minimum then constrains the emissivity of any material within the core of the outflow.1181 The best fit-by-eve shell models are shown in Fig., The best fit-by-eye shell models are shown in Fig.1182 6., 6.1183 Attempting to better latch the inteusitv of the western Linh would iucrease tle peak-to-core mteusitv contrast aud lead to lower values of LosLua, Attempting to better match the intensity of the western limb would increase the peak-to-core intensity contrast and lead to lower values of $I_{\rm core}/I_{\rm shell}$.1184" Both the N-rav aud the data are cousisteut with a hollow (Zo,uua = 0) conical outflow with uj=26"" and Ooo.= 20°.", Both the X-ray and the data are consistent with a hollow $I_{\rm core}/I_{\rm shell}$ = 0) conical outflow with $\theta_{\rm shell} = 26\degr$ and $\theta_{\rm core} = 20\degr$ .1185 The masxinuun value of Loreτοι consistent with the data is ~0.2 (N-rav) or ~0.1 (IIn))., The maximum value of $I_{\rm core}/I_{\rm shell}$ consistent with the data is $\sim 0.2$ (X-ray) or $\sim 0.1$ ).1186 Both the N-rav and eiiissiou iust therefore arise predominantly in a thin boundary laver. between a faster and/or hot teuuous wind of SN-ejecta (that iuvisibly fills the core of the outflow). and deuse cool ambicut ISM. strounding the walls of the cavity.," Both the X-ray and emission must therefore arise predominantly in a thin boundary layer, between a faster and/or hot tenuous wind of SN-ejecta (that invisibly fills the core of the outflow), and dense cool ambient ISM surrounding the walls of the cavity."1187 We looked for spectral variation between the ceuter and walls of the southern outflow couc. m an effort to detect hotter gas from within the cone. but found uo statistically siguificaut differcuces.," We looked for spectral variation between the center and walls of the southern outflow cone, in an effort to detect hotter gas from within the cone, but found no statistically significant differences."1188 We divided the limb brightened reeion iuto three sectors. corresponding to the caster Iuub. the low surface brightuess core. aud the western lim. based on the azimuthal profile shown in Fie.," We divided the limb brightened region into three sectors, corresponding to the eastern limb, the low surface brightness core, and the western limb, based on the azimuthal profile shown in Fig."1189 6., 6.1190 As there were too few counts in these sub-reeious for spectral fitting we constructed a harducss ratio Q from the backeround subtracted count rates in the two energv bands 0.3 Li keV aud 1.1 2.0 keV. and calculated (Q for the entire limb brightened region. as well as the three sub-regions (see Table.," As there were too few counts in these sub-regions for spectral fitting we constructed a hardness ratio $Q$ from the background subtracted count rates in the two energy bands 0.3 -- 1.1 keV and 1.1 – 2.0 keV, and calculated $Q$ for the entire limb brightened region, as well as the three sub-regions (see Table."1191 2)., 2).1192 Simulations with had shown this choice of euergv. bauds to be reasonablv seusitive to changes im spectral hirdness for thermal enüssion with temperature AT—0.1 to 3.0 keV aud bydrogen coluuus of between a few «1029 to a few «102!e.2., Simulations with had shown this choice of energy bands to be reasonably sensitive to changes in spectral hardness for thermal emission with temperature $kT \sim 0.1$ to $3.0$ keV and hydrogen columns of between a few $\times 10^{20}$ to a few $\times 10^{21} \pcmsq$.1193 This liarduess ratio Is more sensitive to temperature variation than usus a simple ratio of 0.3 2.0 keV verses 2.0 - 8.0 keV count rates. for example.," This hardness ratio is more sensitive to temperature variation than using a simple ratio of 0.3 – 2.0 keV verses 2.0 - 8.0 keV count rates, for example."1194 Both the Πιο and core of the Iuub brightened region have hardness ratios statistically iucistinguisliable from oue another or from the region as a whole., Both the limbs and core of the limb brightened region have hardness ratios statistically indistinguishable from one another or from the region as a whole.1195 This is consistent with the majority of the emission. even within the projected ceuter of the outflow cone. being from the bright walls of the cavity.," This is consistent with the majority of the emission, even within the projected center of the outflow cone, being from the bright walls of the cavity."1196 Nevertheless. the nucertaimty in the harducss ratio of the core region is large enough to correspond to an uncertainty iu teniperature (from the nominal AKT.—0.6 keV) of approximately a factor Two.," Nevertheless, the uncertainty in the hardness ratio of the core region is large enough to correspond to an uncertainty in temperature (from the nominal $kT \sim 0.6$ keV) of approximately a factor two."1197 The spectral wnitormitv of the southern outflow cone allows us to interpret variations iu surface briehtuess directly απ variations du. cluuission inteeral (EI = πο , The spectral uniformity of the southern outflow cone allows us to interpret variations in surface brightness directly as variations in emission integral (EI = $\int n_{\rm e} n_{\rm H} dV$ ).1198"Attcupting to explain the central surface-brightuess decrement of ~50 GO. with respect to the apparent walls of the cone. as being purely due to absorption would require an order-oFmaguitude increase in absorption coluun iu front of the center of the cone,"," Attempting to explain the central surface-brightness decrement of $\sim 50$ – $60$, with respect to the apparent walls of the cone, as being purely due to absorption would require an order-of-magnitude increase in absorption column in front of the center of the cone."1199 This would also make the surprising deeree of sinularity between the and. X-ray azimuthal profiles an astounding coincidence. which secs unlikely.," This would also make the surprising degree of similarity between the and X-ray azimuthal profiles an astounding coincidence, which seems unlikely."1200 For example. assunuüne cussion from a hot plasma with xuanmeters equal to the best-fit model for the CLB region (see Table.," For example, assuming emission from a hot plasma with parameters equal to the best-fit model for the CLB region (see Table."

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