ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2" The simple analytical form of the adopted rotation curve (25)) allows us to calculate explicitly the value of the ""observed"" parameter «4, defined in Eq. (A13)):"," The simple analytical form of the adopted rotation curve \ref{paramprof}) ) allows us to calculate explicitly the value of the “observed"" parameter $\alpha_{obs}$ defined in Eq. \ref{alphaobs}) ):"3 where yx0.577 denotes the Euler gamma constant. thus Qop(t=1)1.59: the following discussion will be based on the use of this value of apy.," where $\gamma \approx 0.577$ denotes the Euler gamma constant, thus $\alpha_{obs}(\tau = 1) \approx 1.59$; the following discussion will be based on the use of this value of $\alpha_{obs}$."4 Note also that. for a given value of r. the rotation curve (25)) will admit a well-defined decomposition.," Note also that, for a given value of $\tau$, the rotation curve \ref{paramprof}) ) will admit a well-defined decomposition."5" In practice. before carrying out any detailed decomposition. we may introduce. as à simple definition of maximum-disk. the disk characterized by the value of the dimensionless weight £,,,.(7) that gives. without any dark matter contribution. the best fit to the inner rotation curve in the interval [O.Ro]."," In practice, before carrying out any detailed decomposition, we may introduce, as a simple definition of maximum-disk, the disk characterized by the value of the dimensionless weight $\beta_{max}(\tau)$ that gives, without any dark matter contribution, the best fit to the inner rotation curve in the interval $\left[0,R_{\Omega}\right]$."6 Note that this maximum-disk decomposition is designed in such a way to recover the central gradient of the rotation curve., Note that this maximum-disk decomposition is designed in such a way to recover the central gradient of the rotation curve.7 Sometimes a different definition is used. by referring to the stellar disk which reaches the asymptotic rotation velocity in correspondence of the maximum of its rotation curve.," Sometimes a different definition is used, by referring to the stellar disk which reaches the asymptotic rotation velocity in correspondence of the maximum of its rotation curve."8 This definition gives higher values ofB (Bing.310 for an exponential disk). but it is completely independent of the properties of the central part of the rotation curve.," This definition gives higher values of $\beta$ $\beta_{max}\approx 10$ for an exponential disk), but it is completely independent of the properties of the central part of the rotation curve."9 For r given by equation (26)). we find this value of B identifies an important reference value to which the results obtained from the self-consistent decomposition will thus be compared.," For $\tau$ given by equation \ref{taucorr}) ), we find this value of $\beta$ identifies an important reference value to which the results obtained from the self-consistent decomposition will thus be compared."10 We recall that 8=5 Is approximately in the middle of the parameter range discussed and explored in Sect. ?2.., We recall that $\beta=5$ is approximately in the middle of the parameter range discussed and explored in Sect. \ref{shaperc}.11 The properties of the self-consistent models constructed in the present paper are best illustrated by describing their ability to fit the just described representative idealized case in comparison to a fit performed by more standard parametric analyses., The properties of the self-consistent models constructed in the present paper are best illustrated by describing their ability to fit the just described representative idealized case in comparison to a fit performed by more standard parametric analyses.12 For both methods the goodness of a disk-halo decomposition. defined by a pair (α.8). is quantified by the function that is the integrated squared residuals between the “observed rotation curve and the rotation curve calculated from the model ωνηVpas ," For both methods the goodness of a disk-halo decomposition, defined by a pair $(\alpha,\beta)$, is quantified by the function that is the integrated squared residuals between the “observed"" rotation curve and the rotation curve calculated from the model $V_{mod} = \sqrt{{V}^2_D + V_{DM}^2}$."13The cut of the integration at seven exponential lengths is a reasonable choice. consistent with the analysis of Sect. 22...," The cut of the integration at seven exponential lengths is a reasonable choice, consistent with the analysis of Sect. \ref{flat} ."14 In this preliminary test we do not treat the asymptotic velocity as an additional free parameter of the model., In this preliminary test we do not treat the asymptotic velocity as an additional free parameter of the model.15 In other words. we just analyze the deviations defined by Eq. (," In other words, we just analyze the deviations defined by Eq. ("1629) in the (o.f) plane. at fixed V.,"29) in the $(\alpha, \beta)$ plane, at fixed $V_{\infty}$."17 The asymptotic velocity will be kept as a free parameter in Sect., The asymptotic velocity will be kept as a free parameter in Sect.18 5.2. for the case of NGC 3198.," 5.2, for the case of NGC 3198."19 The results obtained from the standard parametric decomposition are shown in Fig. 10..," The results obtained from the standard parametric decomposition are shown in Fig. \ref{parametric},"20 which clearly exhibits the disk-halo degeneracy pattern., which clearly exhibits the disk-halo degeneracy pattern.21 In particular. consider the contour marked by 0.02.," In particular, consider the contour marked by $0.02$."22 A sizable diagonal strip in parameter space consists of points that are basically equivalent from the point of view of the quality of the fit. even though they correspond to models that are physically very different. ranging from fairly light disks up to maximum-disk solutions (with 8 changing by a factor higher than ten. from =0.5 to = 6.5).," A sizable diagonal strip in parameter space consists of points that are basically equivalent from the point of view of the quality of the fit, even though they correspond to models that are physically very different, ranging from fairly light disks up to maximum-disk solutions (with $\beta$ changing by a factor higher than ten, from $\approx 0.5$ to $\approx 6.5$ )."23 In contrast. Fig.," In contrast, Fig."24 11. shows the contours of function (29)) for the case in which the model rotation curve is calculated using the self-consistent method presented in this paper., \ref{nparametric} shows the contours of function \ref{deviat}) ) for the case in which the model rotation curve is calculated using the self-consistent method presented in this paper.25 The plot ranges and the values of the solid line contours plotted in Fig., The plot ranges and the values of the solid line contours plotted in Fig.26 10. and Fig., \ref{parametric} and Fig.27 ΤΙ are the same., \ref{nparametric} are the same.28 The self-consistent models give a better disk-halo decomposition for three distinct, The self-consistent models give a better disk-halo decomposition for three distinct29the GGHz light curve.,the GHz light curve.30 The UMRAO monitoring of aat GGHz and GGHz started respectively in 1974 and in 1978., The UMRAO monitoring of at GHz and GHz started respectively in 1974 and in 1978.31 The 5GGHz and the GGHz light curves contain mainly these observations., The GHz and the GHz light curves contain mainly these observations.32 Details on the instrumentation and the calibration used at the UMRAO are given by Aller et al. (1985)), Details on the instrumentation and the calibration used at the UMRAO are given by Aller et al. \cite{AAL85}) )33 together with the data obtained until 1984., together with the data obtained until 1984.34 We do not include here the polarization observations. which are publicly available at the UMRAO Database Interface on the WWW at http://www.astro.Isa.umich.edu/obs/radiotel/umrao.html.," We do not include here the polarization observations, which are publicly available at the UMRAO Database Interface on the WWW at http://www.astro.lsa.umich.edu/obs/radiotel/umrao.html."35 Shorter wavelengths radio observations at 22.2 and GGHz were performed since 1980 both with the mm telescope of the Metsiihhovi Radio Observatory. Finland and with the 22mm telescope of the Crimean Astrophysical Observatory. Ukraine.," Shorter wavelengths radio observations at 22.2 and GHz were performed since 1980 both with the m telescope of the Metsähhovi Radio Observatory, Finland and with the m telescope of the Crimean Astrophysical Observatory, Ukraine."36 The GGHz and GGHz light curves are very well sampled since 1986 except for a gap in the summer of 1994 due to the replacement of the Metsihhovi antenna (see Fig. 2))., The GHz and GHz light curves are very well sampled since 1986 except for a gap in the summer of 1994 due to the replacement of the Metsähhovi antenna (see Fig. \ref{lcrmm}) ).37 The observations during 1980-85 and during 1985-90 are respectively published in Salonen et al. (1987)), The observations during 1980–85 and during 1985–90 are respectively published in Salonen et al. \cite{STU87}) )38 and in Terássranta et al. (1992)).," and in Terässranta et al. \cite{TTV92}) ),"39 together with details on the measurement methods and the calibrations., together with details on the measurement methods and the calibrations.40 Calibrations at GGHz were usually performed with the nearby source 2274 AA. M887). whose flux was taken to be Hy.," Calibrations at GHz were usually performed with the nearby source 274 A, 87), whose flux was taken to be Jy."41 Since there might have been a recent outburst in 2274. the GGHz data from Metsiihhovi presented here are only calibrated with the primary calibrator 221.," Since there might have been a recent outburst in 274, the GHz data from Metsähhovi presented here are only calibrated with the primary calibrator 21."42 We therefore have the same calibration procedure at 22 and GGHz., We therefore have the same calibration procedure at 22 and GHz.43 The differences between the two calibrations are generally within the uncertainties., The differences between the two calibrations are generally within the uncertainties.44 Daily observations of wwere performed by the Green Bank Interferometer (GBI) at GGHz and at GGHz from 1979 to 1988., Daily observations of were performed by the Green Bank Interferometer (GBI) at GHz and at GHz from 1979 to 1988.45 This huge data set was published by Waltman et al. (1991))., This huge data set was published by Waltman et al. \cite{WFJ91}) ).46 Additional observations carried out with new receivers at GGHz and at GGHz from 1989 to 1994 are also included in the database., Additional observations carried out with new receivers at GHz and at GHz from 1989 to 1994 are also included in the database.47 The GBI light curves display brightness dips. which occur when the sun is too close to oon the sky.," The GBI light curves display brightness dips, which occur when the sun is too close to on the sky."48 Since the GBI is an interferometer. 1t does not measure the total flux of an extended source like 273c. It is therefore difficult to compare the GBI measurements with single dish telescope observations.," Since the GBI is an interferometer, it does not measure the total flux of an extended source like c. It is therefore difficult to compare the GBI measurements with single dish telescope observations."49 For clarity. the GBI data are stored in separate files.," For clarity, the GBI data are stored in separate files."50 Other repeated radio observations from. the. literature were added to the database., Other repeated radio observations from the literature were added to the database.51 Observations at 2.7. 4.75 and GGHz from the mm telescope at Effelsberg. Germany reported in von Montigny et al. (1997))," Observations at 2.7, 4.75 and GHz from the m telescope at Effelsberg, Germany reported in von Montigny et al. \cite{VAA97}) )"52 were added to the GGHz. the GGHz and the GGHz light curves respectively.," were added to the GHz, the GHz and the GHz light curves respectively."53 The GGHz and 10GGHz light curves also contall earlier observations at GGHz and at GGHz from the mm telescope of the Algonquin Radio Observatory (Medd et al. 1972:;, The GHz and GHz light curves also contain earlier observations at GHz and at GHz from the m telescope of the Algonquin Radio Observatory (Medd et al. \cite{MAH72};54 Andrew et al. 1978))., Andrew et al. \cite{AMH78}) ).55 Observations at 7.8. 7.9 and GGHz from the mm antenna of the Haystack Radio Observatory are included in the GGHz and in the GGHz light curves (Allen Barrett 1966:; Dent Kapitzky 1976:: Dent Kojoian 1972:: Dent et al. 1974)).," Observations at 7.8, 7.9 and GHz from the m antenna of the Haystack Radio Observatory are included in the GHz and in the GHz light curves (Allen Barrett \cite{AB66}; Dent Kapitzky \cite{DK76}; Dent Kojoian \cite{DK72}; Dent et al. \cite{DKK74}) )."56 We also added to the GGHz and GGHz light curves the 22 and GGHz observations from the mm Itapetinga radio telescope. Brazil (Botti Abraham 1988)) and the GGHz observations from the UMRAO (Haddock et al. 1987)).," We also added to the GHz and GHz light curves the 22 and GHz observations from the m Itapetinga radio telescope, Brazil (Botti Abraham \cite{BA88}) ) and the GHz observations from the UMRAO (Haddock et al. \cite{HAA87}) )."57 Finally. we included in the GGHz light curve a few earlier observations at 31.4GGHz made with the mm antenna of the National Radio Astronomical Observatory (NRAO) at Kitt Peak (Dent Hobbs 1973)).," Finally, we included in the GHz light curve a few earlier observations at GHz made with the m antenna of the National Radio Astronomical Observatory (NRAO) at Kitt Peak (Dent Hobbs \cite{DH73}) )."58 We did not include all the isolated observations from early radio catalogues., We did not include all the isolated observations from early radio catalogues.59 We added only the flux measurements reported by Kühhr et al. (1981)).," We added only the flux measurements reported by Kühhr et al. \cite{KWP81}) ),"60 since they are all recalibrated to the scale of Baars et al. (1977)).," since they are all recalibrated to the scale of Baars et al. \cite{BGP77}) ),"61 and the total flux densities (core plus jet) reported by Conway et al. (1993))., and the total flux densities (core plus jet) reported by Conway et al. \cite{CGP93}) ).62 At very low frequency (< 330MMHz). we added the observations fron= Braude et al. (1979)).," At very low frequency $<$ MHz), we added the observations from Braude et al. \cite{BMS79}) ),"63 but multiplied by the scaling factor of 1.23 used for other objects by Kühhr et al. (1981))., but multiplied by the scaling factor of 1.23 used for other objects by Kühhr et al. \cite{KWP81}) ).64 In the MMHz range other isolated observations are from Artyukh (1984)). Dennison et al. (1981)).," In the MHz range other isolated observations are from Artyukh \cite{A84}) ), Dennison et al. \cite{DBL81}) ),"65 Fanti et al. (1979.. 1981)).," Fanti et al. \cite{FFM79}, , \cite{FFF81}) ),"66 Fisher Erickson (1980)) and Hunstead (1972))., Fisher Erickson \cite{FE80}) ) and Hunstead \cite{H72}) ).67 Above GGHz. some isolated radio observations were found in Jones et al. (1981)).," Above GHz, some isolated radio observations were found in Jones et al. \cite{JRO81}) ),"68 Landau et al. (1983)), Landau et al. \cite{LJE83}) )69 and Lichti et al. (1995))., and Lichti et al. \cite{LBC95}) ).70 All these data were included in the respective light curves., All these data were included in the respective light curves.71 The radio light curves of aat GGHz. GGHz and GGHz are shown in Fig. 2..," The radio light curves of at GHz, GHz and GHz are shown in Fig. \ref{lcrmm}."72 The contribution from the jet 2273A) was derived from Fig., The contribution from the jet 273A) was derived from Fig.73 Al of Conway et al. (1993))., A1 of Conway et al. \cite{CGP93}) ).74 It is a broken power law with a spectral index oj of 0.67 below MMHz (29.0JJy) and of 0.85 at higher frequencies., It is a broken power law with a spectral index $\alpha\dmrm{jet}$ of 0.67 below MHz Jy) and of 0.85 at higher frequencies.75 The flux density of 2273A declines strongly in the infrared-to-optical domain with εντον 7 44. as shown in Fig.," The flux density of 273A declines strongly in the infrared-to-optical domain with $\alpha\dmrm{jet}$ $\sim$ 4, as shown in Fig."76 Af of Meisenheimer et al. (1989))., 4f of Meisenheimer et al. \cite{MRH89}) ).77 Fig., Fig.78 6 shows that the jet component is dominant below ~ GGHz. whereas it becomes negligible (< All the millimetre/submillimetre (mm/submm) observations of wwere grouped together into seven light curves: mmm GGHz). mmm GGHz). mmm GGHz). mmm. mmm. mmm and mmm (see Table 1).," \ref{avspect} shows that the jet component is dominant below $\sim$ GHz, whereas it becomes negligible $<$ All the millimetre/submillimetre (mm/submm) observations of were grouped together into seven light curves: mm GHz), mm GHz), mm GHz), mm, mm, mm and mm (see Table \ref{tabrmm}) )."79 The mmm light curve is shown in Fig. 2.., The mm light curve is shown in Fig. \ref{lcrmm}.80 All the submillimetre observations. as well as most observations at. mmm. 1.3mmm and 2.0mmm were performed on Mauna Kea. Hawai.," All the submillimetre observations, as well as most observations at mm, mm and mm were performed on Mauna Kea, Hawaii."81 The QMC/Oregor photometer (Ade et al. 1954)), The QMC/Oregon photometer (Ade et al. \cite{AGC84}) )82 was used on the 3.8mm United Kingdom Infrared Telescope (UKIRT) until 1985., was used on the m United Kingdom Infrared Telescope (UKIRT) until 1985.83 Since January 1986. à new common user photometer UKT14 (Dunean et al. 1990))," Since January 1986, a new common user photometer UKT14 (Duncan et al. \cite{DSR90}) )"84 was installed on the UKIRT. before being moved in March 1988 to the 15mm James Clerk Maxwell Telescope (JCMT).," was installed on the UKIRT, before being moved in March 1988 to the m James Clerk Maxwell Telescope (JCMT)."85 Finally. in July 1996. UKT14 was replacec on the JCMT by the Submillimetre Common-User Bolometer Array (SCUBA). described by Robson et al. (1998)).," Finally, in July 1996, UKT14 was replaced on the JCMT by the Submillimetre Common-User Bolometer Array (SCUBA), described by Robson et al. \cite{R98}) )."86 Details οἱ the observations performed with the UKTI4 photometer both on the JCMT and the UKIRT. as well as calibration techniques are given by Robson et al. (1993)).," Details on the observations performed with the UKT14 photometer both on the JCMT and the UKIRT, as well as calibration techniques are given by Robson et al. \cite{RLG93}) )."87 The earlier observatior techniques with the QMC/Oregon photometerare described i Robson et al. (1983))., The earlier observation techniques with the QMC/Oregon photometerare described in Robson et al. \cite{RGC83}) ).88made by registering to the V frame then binning 3x3.,made by registering to the $V$ frame then binning 3x3.89 An example of a spatial map is shown in Figure 1., An example of a spatial map is shown in Figure 1.90 It is also possible to plot spatial color versus surface brightness (i.e. pixel color versus that pixels surface brightness in V)., It is also possible to plot spatial color versus surface brightness (i.e. pixel color versus that pixels surface brightness in $V$ ).91 An example of that type of analysis is shown in 833.5., An example of that type of analysis is shown in 3.5.92" A subset of the sample had been previously imaged in V—I (Pildis, Schombert Eder 1997)."," A subset of the sample had been previously imaged in $V-I$ (Pildis, Schombert Eder 1997)."93" While those colors are less accurate, their total values will be compared to the B—V colors in 833.4 and are found listed in Table 1."," While those colors are less accurate, their total values will be compared to the $B-V$ colors in 3.4 and are found listed in Table 1."94 Spatial V—I color maps are made and re-pixeled to the same orientation and scale of the newer B—V frames., Spatial $V-I$ color maps are made and re-pixeled to the same orientation and scale of the newer $B-V$ frames.95" This allows for a comparison of B—V and V—I not only in total colors and color profiles, put also on a pixel-by-pixel basis."," This allows for a comparison of $B-V$ and $V-I$ not only in total colors and color profiles, put also on a pixel-by-pixel basis."96Figure 7 is a “residual map”. demonstrating the difference between the observed 2 tuage aud a modelled one consisting of pure elliptical isophotes.,"Figure \ref{resid} is a ""residual map"", demonstrating the difference between the observed $R$ image and a modelled one consisting of pure elliptical isophotes."97 The “residual maps in all four filters are similar aud look like the Fig.," The ""residual maps"" in all four filters are similar and look like the Fig."98 3b from the paper of Wirth et al. (1985)), 3b from the paper of Wirth et al. \cite{wsb85}) )99 though Wirth et al., though Wirth et al.100 subtracted mediau-snoothed images. not modelled oues.," subtracted median-smoothed images, not modelled ones."101 With et al. (1985)), Wirth et al. \cite{wsb85}) )102 have interpreted the spiral absorption features of their Fig., have interpreted the spiral absorption features of their Fig.103 3b as dust arms., 3b as dust arms.104 We reach the same conclusion., We reach the same conclusion.105 Figure 6 is fully cousistent with earlier pliotoietric results for the central part of (see. for example. CFUT data in the work of Bacon et al. 1991)).," Figure \ref{isopar} is fully consistent with earlier photometric results for the central part of (see, for example, CFHT data in the work of Bacon et al. \cite{bemn94}) ),"106 though we would like to no| that boxiuess of the iuner isoplotes of is shown here for he first time., though we would like to note that boxiness of the inner isophotes of is shown here for the first time.107 There are also soie details of the radia profiles of PA. aud (1bía) which were not discussed earlier., There are also some details of the radial profiles of $P.A.$ and $(1-b/a)$ which were not discussed earlier.108 Over al the four spectral bands the major seni-axis ranee of Hs characterized by a local mast of ellipticity which reaches 0.2 auc by a local minima iu the position angle which oscillates between aand cclose enough to the oricutation of the line of nodes of the disk. PA.= 387.," Over all the four spectral bands the major semi-axis range of is characterized by a local maximum of ellipticity which reaches 0.2 and by a local minimum in the position angle which oscillates between and close enough to the orientation of the line of nodes of the disk, $P.A.=38\degr$ ."109 The same radius interval is characterized by a αια higher than outside. eq/0 is less hanLI.," The same radius interval is characterized by a $a_4/a$ higher than; outside, $a_4/a$ is less than."110.. This neaus that in the radius rauge of Wwe νου. a stellar disk. whose plane ds close tfo or even coincides with the global aue of the Ooealaxy., This means that in the radius range of we see a stellar disk whose plane is close to or even coincides with the global plane of the galaxy.111 One ist ↘↽↸∖↸∖↻↕∐∐∐∐≼↧↑∐⋜↧↑↑↕∐∖↸⊳↸∖∐⊓⋅⋜↧↕↥⋅↸∖∶↴⋁↕∪↕∪↕⋟ is) photometrically dominated by the bulee (ijimaetal. 1976))., One must keep in mind that the central region of is photometrically dominated by the bulge \cite{jap76}) ).112" At the distance of the major seuii-axi« of ccorresponds to a imetric radius of 85 pc. therefore we deal with a so called nuclear disk: simular disks were earlier found in some other emlv-tvpe spiral galaxies. particularly, i (Burkhead 19913)."," At the distance of the major semi-axis of corresponds to a metric radius of 85 pc, therefore we deal with a so called nuclear disk; similar disks were earlier found in some other early-type spiral galaxies, particularly, in \cite{burk}) )."113 In Fig., In Fig.114 7 one can see two dark (dust?), \ref{resid} one can see two dark (dust?)115 spiral müniuius located also in the same radius rauge., spiral miniarms located also in the same radius range.116" Besides that. over the same radius range a noticeable eiission line |OITI|A5007 is seen in our spectra (in the very center of31. r«D"". enission lines are abseut according to the claims of Bacon ( al. 199 D)."," Besides that, over the same radius range a noticeable emission line $\lambda 5007$ is seen in our spectra (in the very center of, $r < 5\arcsec$, emission lines are absent according to the claims of Bacon et al. \cite{bemn94}) )."117 We cau conclude that the nuclear stellar disk of contains also dust and ionized gas., We can conclude that the nuclear stellar disk of contains also dust and ionized gas.118 Lonizatiou nuelt be due to shocks because. according to Ciardullo ct al. (1988)).," Ionization might be due to shocks because, according to Ciardullo et al. \cite{ciar}) ),"119 the nitrogen emission line AG583 is everywhere stronger than fa inside kc=1’., the nitrogen emission line $\lambda 6583$ is everywhere stronger than $H\alpha$ inside $r=1\arcmin$.120 Thouel3... the most nearby spiral galaxy. has been studied for a lone time and with munatched spatial resolution. the true structure of its central region is still a puzzle.," Though, the most nearby spiral galaxy, has been studied for a long time and with unmatched spatial resolution, the true structure of its central region is still a puzzle."121 The large amount of accumulated observational data hasled to reject mau models. even regarded earlier ax reasonable ones.," The large amount of accumulated observational data hasled to reject many models, even regarded earlier as reasonable ones."122 Our work contributes to this process., Our work contributes to this process.123 found in a few clusters incliding MBS7/Virgo (Forman ot 22005). Indra A (Nulseu ct 220054). Hercules A (Nulseu et 22005b). aud MS0735.6|72121 (AI¢eNamara et 22005).," found in a few clusters including M87/Virgo (Forman et 2005), Hydra A (Nulsen et 2005a), Hercules A (Nulsen et 2005b), and MS0735.6+7421 (McNamara et 2005)."124 These shocks were fairly sveak with Mach uunbers iu the rauge of 1.2 aud 1.7 (see MeNiuuara Nulseu 2007 for a review)., These shocks were fairly weak with Mach numbers in the range of 1.2 and 1.7 (see McNamara Nulsen 2007 for a review).125 Ripple features in the N-rav surface brightness resulting from the propagation of veak shocks or sound waves as seeu iu a loug observation of Perseus (Fabian et 22003. 2006) may also coutribute to heating.," Ripple features in the X-ray surface brightness resulting from the propagation of weak shocks or sound waves as seen in a long observation of Perseus (Fabian et 2003, 2006) may also contribute to heating."126 Energy iuput from buovautlv rising bubbles of relativistic plasina (6.2.. Churazov ct 22002). weak shocks (c.g.. Revnolds. Heinz. Beegchuan 2001). and the propagation of sound or pressure waves are able to offset cooling.," Energy input from buoyantly rising bubbles of relativistic plasma (e.g., Churazov et 2002), weak shocks (e.g., Reynolds, Heinz, Begelman 2001), and the propagation of sound or pressure waves are able to offset cooling."127 Abell 2052 is a moderately rich. cooling flow cluster at a redshift of τ=04019815.," Abell 2052 is a moderately rich, cooling flow cluster at a redshift of $z=0.0348$."128 A powerful radio source. 3C 317. is hosted by the central cD galaxy. UGC 09799.," A powerful radio source, 3C 317, is hosted by the central cD galaxy, UGC 09799."129 Abell 2052 was previously observed in the N-vav with Einstein (White. Jones. Forman 1997).ROSA (Peres et 11998. Rizza et 22000). (White 2000). andChandra (Blanton ot 22001. 2003).," Abell 2052 was previously observed in the X-ray with $Einstein$ (White, Jones, Forman 1997), (Peres et 1998, Rizza et 2000), (White 2000), and (Blanton et 2001, 2003)."130 We present a deep observation of Abell 2052. combining the earlier Cvele 1 data with data from Cycle 6.," We present a deep observation of Abell 2052, combining the earlier Cycle 1 data with data from Cycle 6."131 This longer observation reveals probable shock features exterior to the bubble rius that contribute to heating im the cluster center., This longer observation reveals probable shock features exterior to the bubble rims that contribute to heating in the cluster center.132" We assume ZI,=10 kan + Πο |. Qa,—0.3. and Q4—0.7 (1""=0.69 κος at += 0.0318) throughout."," We assume $H_{\circ}=70$ km $^{-1}$ $^{-1}$ , $\Omega_{M}=0.3$, and $\Omega_{\Lambda}=0.7$ $1\arcsec = 0.69$ kpc at $z = 0.0348$ ) throughout."133 Errors are given at the 90% confidence level unless otherwise stated., Errors are given at the $90\%$ confidence level unless otherwise stated.134 Abcll 2052 was observed withChandra using the ACTS- detector on 2000 September 3 for a total of 36.751 seconds aud ou 2006 March 21 for 128.630 seconds.," Abell 2052 was observed with using the ACIS-S detector on 2000 September 3 for a total of 36,754 seconds and on 2006 March 24 for 128,630 seconds."135 The events from the 2000 data were telemietered in Faint mode and the eveuts from thelonger exposure were, The events from the 2000 data were telemetered in Faint mode and the events from thelonger exposure were136These successful first applications of the FGLR-method for distance determinations indicate the very promising potential of the method to provide an independent constraint on the extragalactic distance scale.,These successful first applications of the FGLR-method for distance determinations indicate the very promising potential of the method to provide an independent constraint on the extragalactic distance scale.137" In this section we use the results from the BSG studies to discuss Cepheid distances and the ""standard"" approach for their metallicity correction.", In this section we use the results from the BSG studies to discuss Cepheid distances and the “standard” approach for their metallicity correction.138 We start with M81 (the discussion presented here closely follows the one given by Kudritzkietal. 2011))., We start with M81 (the discussion presented here closely follows the one given by \citealt{kud11}) ).139 In addition to the HST Key Project work on M81 (Freedmanetal.1994.2001) there are two recent Cepheid studies by MeCommiasetal.(2009) and by Gerkeetal.(2010.," In addition to the HST Key Project work on M81 \citep{freedman94, freedman01} there are two recent Cepheid studies by \citet{mccommas09} and by \citet{gerke11}."140.. MeCommasetal.(2009) use HST light curves of 11 fundamental and two first overtone short period Cepheids 1n the outer disk of M8] at ~ 13.5 kpe galactocentric distance., \citet{mccommas09} use HST light curves of 11 fundamental and two first overtone short period Cepheids in the outer disk of M81 at $\sim$ 13.5 kpc galactocentric distance.141 Gerkeetal.(2011) investigate 107 long period Cepheids observed with the LBT in a galactocentric range of 3.5 to 10.5 kpe with ground-based B. V. I photometry.," \citet{gerke11} investigate 107 long period Cepheids observed with the LBT in a galactocentric range of 3.5 to 10.5 kpc with ground-based B, V, I photometry."142 Applying the Wesenheit VI method. both studies obtain a distance modulus relative to the LMC which is 0.17 mag longer than the BSG result.," Applying the Wesenheit VI method, both studies obtain a distance modulus relative to the LMC which is 0.17 mag longer than the BSG result."143 However. this is based on a metallicity correction Ate = YZ] - rare). which is motivated by the fact that the inner field Cepheids observed by the KP yield a distance modulus. which is 0.23 mag shorter relative to the outer fields without such a correction applied.," However, this is based on a metallicity correction $\Delta \mu$ = $\gamma$ ([Z] - $_{LMC}$ ), which is motivated by the fact that the inner field Cepheids observed by the KP yield a distance modulus, which is 0.23 mag shorter relative to the outer fields without such a correction applied."144 They use Zaritskyetal.(1994). for metallicity [Z] and the metallicity gradient and rage —-0.19 for the LMC oxygen abundance (see section 4. 2nd to last paragraph).," They use \citet{zaritsky94} for metallicity [Z] and the metallicity gradient and $_{LMC}$ =-0.19 for the LMC oxygen abundance (see section 4, 2nd to last paragraph)."145 This metallicity gradient requires a highly negative value of y. y = -0.55 mag dex7!. to account for the inner and outer field Cepheid distance moduli differences.," This metallicity gradient requires a highly negative value of $\gamma$, $\gamma$ = -0.55 mag $^{-1}$, to account for the inner and outer field Cepheid distance moduli differences."146 Applying the BSG metallicity gradient would require an even more negative value of y. namely y= -0.65 mag .," Applying the BSG metallicity gradient would require an even more negative value of $\gamma$, namely $\gamma$ = -0.65 mag $^{-1}$."147 Moreover. the LMC oxygen abundance in these corrections is too large compared with the LMC oxygen abundance of B-stars found by Hunteretal.(2007). ([Z]rajc = -0.36 dex). the iron abundances of LMC Cepheids determined by Romanielloetal.(2008) and Lucketal.(1998) με -0.33 dex). and the LMC region oxygen abundances obtained by Bresolin(2011). ϱΖ]ιμο = -0.33 dex).," Moreover, the LMC oxygen abundance in these corrections is too large compared with the LMC oxygen abundance of B-stars found by \citet{hunter07} $_{LMC}$ = -0.36 dex), the iron abundances of LMC Cepheids determined by \citet{romaniello08} and \citet{luck98} $_{LMC}$ = -0.33 dex), and the LMC region oxygen abundances obtained by \citet{bresolin11} $_{LMC}$ = -0.33 dex)."148 This means that with the BSG metallicity values in M81 the Cepheids in the outer field have a metallicity 0.11 dex higher than the LMC., This means that with the BSG metallicity values in M81 the Cepheids in the outer field have a metallicity 0.11 dex higher than the LMC.149 If one would apply the metallicity correction with y = -0.65 mag dex7! accordingly. this would enlarge the distance modulus by another 0.07 mag.," If one would apply the metallicity correction with $\gamma$ = -0.65 mag $^{-1}$ accordingly, this would enlarge the distance modulus by another 0.07 mag."150 However. with such a large negative value of y It is important to note that this empirical correction. which claims that Cepheids become brighter with increasing metallicity. is in striking disagreement with pulsation theory. which predicts exactly the opposite. namely that the Cepheid brightness decreases with increasing metallicity (FiorentinoBonoetal.2008).," However, with such a large negative value of $\gamma$ it is important to note that this empirical correction, which claims that Cepheids become brighter with increasing metallicity, is in striking disagreement with pulsation theory, which predicts exactly the opposite, namely that the Cepheid brightness decreases with increasing metallicity \citep{fiorentino02, marconi05, fiorentino07, bono08}."151. It also disagrees with the recent high S/N. high spectral resolution quantitative spectroscopy in the Milky Way and the LMC carried out by Romanielloetal.(2008).. which confirms the prediction by pulsation theory.," It also disagrees with the recent high S/N, high spectral resolution quantitative spectroscopy in the Milky Way and the LMC carried out by \citet{romaniello08}, which confirms the prediction by pulsation theory."152 According to this work. the value of y should be positive and not negative.," According to this work, the value of $\gamma$ should be positive and not negative."153 We also note that Uetal.(2009) have demonstrated from their quantitative spectroscopy of blue supergiants in M33 that the difference of distance moduli between inner field and outer field Cepheids found by Scoweroft would require a y-value of -0.55 mag dex7!., We also note that \citet{u09} have demonstrated from their quantitative spectroscopy of blue supergiants in M33 that the difference of distance moduli between inner field and outer field Cepheids found by \citet{scowcroft09} would require a $\gamma$ -value of -0.55 mag $^{-1}$.154 Even worse. Bresolinetal.(2010) re-determined region abundances in M33 using auroral lines and applying their abundance gradient to the Cepheid fields in M33 yields y = - 1.2 mag dex”!] (see discussion in Bresolin201 1)).," Even worse, \cite{bresolin10} re-determined region abundances in M33 using auroral lines and applying their abundance gradient to the Cepheid fields in M33 yields $\gamma$ = - 1.2 mag $^{-1}$ (see discussion in \citealt*{bresolin11}) )."155 Another galaxy where the comparison of Cepheids in the inner and outer fields leads to a significantly different distance modulus is the maser galaxy NGC 4258., Another galaxy where the comparison of Cepheids in the inner and outer fields leads to a significantly different distance modulus is the maser galaxy NGC 4258.156 This galaxy is of particular importance. since it has been used as the new anchor point for the extragalactic distance scale by Riessetal.(2009a.b.2011) because of its accurately known distance from the Keplerian motion of water masers orbiting the central black hole (Humphreysetal.2008).," This galaxy is of particular importance, since it has been used as the new anchor point for the extragalactic distance scale by \citet{riess09a, riess09b, riess11} because of its accurately known distance from the Keplerian motion of water masers orbiting the central black hole \citep{humphreys08}."157. Maerietal.(2006) based on the region strong line method oxygen abundances by Zaritskyetal.(1994) derived a y- value of -0.29 mag dex~!., \citet{macri06} based on the region strong line method oxygen abundances by \citet{zaritsky94} derived a $\gamma$ -value of -0.29 mag $^{-1}$ .158 However. most recently. Bresolin(2011) re-determined the region metallicities 1n. this galaxy including the observation of auroral lines in a few cases.," However, most recently, \cite{bresolin11} re-determined the region metallicities in this galaxy including the observation of auroral lines in a few cases."159 This led to a downward substantial revision of the metallicity. which seems to be close to the LMC and not strongly super-solar. and a very shallow abundance gradient.," This led to a downward substantial revision of the metallicity, which seems to be close to the LMC and not strongly super-solar, and a very shallow abundance gradient."160 Based on these results. Bresolin(2011) show that y = - 0.69 mag dex-! would be needed to explain the distance modulus difference between inner and outer fields. again a value much too negative. when compared with pulsation theory and observational work on Milky Way and LMC Cepheids.," Based on these results, \cite{bresolin11} show that $\gamma$ = - 0.69 mag $^{-1}$ would be needed to explain the distance modulus difference between inner and outer fields, again a value much too negative, when compared with pulsation theory and observational work on Milky Way and LMC Cepheids."161 While the improved region work on this important galaxy still awaits an independent confirmation through a study of BSGs. it is an additional clear indication of a systematic effect on Cepheid distance moduli. not understood at this point.," While the improved region work on this important galaxy still awaits an independent confirmation through a study of BSGs, it is an additional clear indication of a systematic effect on Cepheid distance moduli not understood at this point."162 Majaessetal.(2011) discussthe large metallicity corrections suggested by Gerkeetal. and by the recent HST/ACS Cepheid study of M101, \citet{majaess11} discussthe large metallicity corrections suggested by \citet{gerke11} and by the recent HST/ACS Cepheid study of M101163between radial bins.,between radial bins.164 Another is the fact that such a scheme results in necessarily wider radial bins. which causes the clustering signal to be diluted.," Another is the fact that such a scheme results in necessarily wider radial bins, which causes the clustering signal to be diluted."165 We do not feel that either is a large problem., We do not feel that either is a large problem.166 Applying the more traditional top-hat binning scheme to photometric surveys necessarily results in overlapping radial bins (due to photometric redshift errors) and there will always be considerable covariance between radial bins selected with photometric redshifts — we do not think that pair-centre binning will make this problem considerably worse., Applying the more traditional top-hat binning scheme to photometric surveys necessarily results in overlapping radial bins (due to photometric redshift errors) and there will always be considerable covariance between radial bins selected with photometric redshifts — we do not think that pair-centre binning will make this problem considerably worse.167 The dilution effect can be mitigated by imposing a maximum separation between the pairs included in a pair-centre bin: we call this constrained pair-centre binning., The dilution effect can be mitigated by imposing a maximum separation between the pairs included in a pair-centre bin: we call this constrained pair-centre binning.168 As can be seen by comparing the middle and right-hand panels of Figs., As can be seen by comparing the middle and right-hand panels of Figs.169 14 and 15. imposing such a constraint increases the expected signal while not causing a significant change in the effects of redshift-space distortions.," \ref{fig:xi-des}170 and \ref{fig:xi-dess}, imposing such a constraint increases the expected signal while not causing a significant change in the effects of redshift-space distortions."171 More detailed studies of these effects are warranted. but we are confident that the reduction in the redshift distortion effect we observe when utilising pair-centre binning wil make this scheme considerably preferable to a top-hat binning scheme.," More detailed studies of these effects are warranted, but we are confident that the reduction in the redshift distortion effect we observe when utilising pair-centre binning will make this scheme considerably preferable to a top-hat binning scheme."172 Pair-centre binning completely removes the effect of redshif distortions when given a uniform galaxy distribution., Pair-centre binning completely removes the effect of redshift distortions when given a uniform galaxy distribution.173 Such perfec distributions do not exist — most galaxy samples selections are based on an apparent magnitude limit — and thus realistic radia distributions of galaxies are more complicated., Such perfect distributions do not exist — most galaxy samples selections are based on an apparent magnitude limit — and thus realistic radial distributions of galaxies are more complicated.174 However. we have argued that if galaxy samples selected based on an apparen magnitude limit are cut back so that no galaxies A-corrected galaxies are missing from the sample. then this does not matter: the boundaries of the bins are either in real-space. or based on pair- neither of which introduces redshift distortion effects.," However, we have argued that if galaxy samples selected based on an apparent magnitude limit are cut back so that no galaxies $k$ -corrected galaxies are missing from the sample, then this does not matter: the boundaries of the bins are either in real-space, or based on pair-centres, neither of which introduces redshift distortion effects."175 We have argued. and it is clear from previous work. that any interpretation of projected clustering measurements must account for redshift space distortions.," We have argued, and it is clear from previous work, that any interpretation of projected clustering measurements must account for redshift space distortions."176 In fact. comparing correlation functions calculated using different binning schemes might actually prove to provide a mechanism for measuring the amplitude of the redshift-space distortions.," In fact, comparing correlation functions calculated using different binning schemes might actually prove to provide a mechanism for measuring the amplitude of the redshift-space distortions."177 This is beyond the scope of our current draft. and we leave this for subsequent work.," This is beyond the scope of our current draft, and we leave this for subsequent work."178 To quantify the effect of redshift-space distortions for future survevs. we have used the expected radial selection. function and photometric redshift distribution for the Dark Energy Survey ο. predict the effect of redshift-space distortions on projected clustering measurements.," To quantify the effect of redshift-space distortions for future surveys, we have used the expected radial selection function and photometric redshift distribution for the Dark Energy Survey to predict the effect of redshift-space distortions on projected clustering measurements."179 This analysis is also relevant to other jxlanned surveys such as PanStarrs and the LSST. which will have similar radial selection functions.," This analysis is also relevant to other planned surveys such as PanStarrs and the LSST, which will have similar radial selection functions."180 We have contrasted two differen ypes of binning: top-hat — in which we only allow galaxies between a given radial bound to enter our sample— and pair-centre — in which we only count galaxy pairs with an average radia yosition that Hes within our bounds., We have contrasted two different types of binning: top-hat — in which we only allow galaxies between a given radial bound to enter our sample— and pair-centre — in which we only count galaxy pairs with an average radial position that lies within our bounds.181 For typical bin widths that wil be applied to these surveys. we find that top-hat binning in the radia direction leaves a strong signal from redshift-space distortions.," For typical bin widths that will be applied to these surveys, we find that top-hat binning in the radial direction leaves a strong signal from redshift-space distortions."182 Using a pair-centre binning scheme reduces the redshift-space distortion signal. by as much as 80% in realistic situations (see Fig. 145) ," Using a pair-centre binning scheme reduces the redshift-space distortion signal, by as much as $\%$ in realistic situations (see Fig. \ref{fig:xi-des}) )"183and should therefore allow the measurements to be more sensitive to the cosmological parameters one wishes to constrain., and should therefore allow the measurements to be more sensitive to the cosmological parameters one wishes to constrain.184 In this analysis. we have only considered the simplitied situation where the redshift-space distortions act along one axis of a Cartesian basis.," In this analysis, we have only considered the simplified situation where the redshift-space distortions act along one axis of a Cartesian basis."185 However. the arguments we have put forward in favour of pair-centre binning do not rely on this assumption. and will remain valid even when wide-angle effects are included in any analysis.," However, the arguments we have put forward in favour of pair-centre binning do not rely on this assumption, and will remain valid even when wide-angle effects are included in any analysis."186 The authors thank the UK Science and Technology Facilities Research Council for financial support., The authors thank the UK Science and Technology Facilities Research Council for financial support.187 WIP is also grateful for support from the Leverhulme Trust and the European Research Council., WJP is also grateful for support from the Leverhulme Trust and the European Research Council.188 Simulated data was ealeulated. and analysed using the COSMOS Altix 3700 supercomputer. a UK-CCC facility supported by HEFCE and STFC in cooperation with CGI/Intel.," Simulated data was calculated and analysed using the COSMOS Altix 3700 supercomputer, a UK-CCC facility supported by HEFCE and STFC in cooperation with CGI/Intel."189 We thank the DES Large-Scale Structure working group members. and especially Enrique Gaztanaga. for many helpful discussions.," We thank the DES Large-Scale Structure working group members, and especially Enrique Gaztanaga, for many helpful discussions."190 We also thank the referee for carefully reading our manuscript and providing excellent suggestions for improvements., We also thank the referee for carefully reading our manuscript and providing excellent suggestions for improvements.191WD.,WD.192" Ποπονα, the issue of whether the debris disk cau sustain the high metal accretion rates Mz up to several S10) os} inferred iu some systems lias not been clear for a long time."," However, the issue of whether the debris disk can sustain the high metal accretion rates $\dot M_Z$ up to several $\times 10^{10}$ g $^{-1}$ inferred in some systems has not been clear for a long time."193 Receutly Rafikov (20112: hereafter R11) showed that coupling of the disk to stellar radiation via the Povuting-Robertson (PR) effect (Burns L979) can result in metal accretion rates Mz~10s gs Ll., Recently Rafikov (2011a; hereafter R11) showed that coupling of the disk to stellar radiation via the Poynting-Robertson (PR) effect (Burns 1979) can result in metal accretion rates $\dot M_Z \sim 10^8$ g $^{-1}$.194 Later Rafikov (2011b) has also demoustrated that under certain circumstances even higher values of Mz cau arise from the interaction between the debris disk aud metal eas that is produced by the sublimation at ει, Later Rafikov (2011b) has also demonstrated that under certain circumstances even higher values of $\dot M_Z$ can arise from the interaction between the debris disk and metal gas that is produced by the sublimation at $R_{in}$.195 The model of radiatively driven accretion of R11 did not cover the huge scale evolution of the debris disk resulting from the PR drag. and made certain assuniptious (c.e. hieh optical depths of the disk) which were not rigorously verified.," The model of radiatively driven accretion of R11 did not cover the large scale evolution of the debris disk resulting from the PR drag, and made certain assumptions (e.g. high optical depths of the disk) which were not rigorously verified."196 The goal of this work is to extend the analysis of R11 and to develop a detailed elobal model of the compact debris disk evolution caused by the PR drag., The goal of this work is to extend the analysis of R11 and to develop a detailed global model of the compact debris disk evolution caused by the PR drag.197 The paper is organized as follows., The paper is organized as follows.198 Iu refsectitheorv owe outline the basic picture of the PR-driven debris aceretiou and derive master equation (18)) that describes elobal evolution of the disk., In \\ref{sect:theory} we outline the basic picture of the PR-driven debris accretion and derive master equation \ref{eq:1}) ) that describes global evolution of the disk.199 We then explore in refsectilow both analytically and nuuerieallv the evolution of a low mass. optically thin disk of debris.," We then explore in \\ref{sect:low} both analytically and numerically the evolution of a low mass, optically thin disk of debris."200" In refsectihieh πο study global evolution of massive. optically thick debris disks starting with different initial spatial distributions of debris around the WD (vine-like. retsubsectilarec, arrow... LAO. ordishkοι refsubsect :disk)ytosccthecf feetoutheglobaldishecolution"," In \\ref{sect:high} we study global evolution of massive, optically thick debris disks starting with different initial spatial distributions of debris around the WD (ring-like, \\ref{subsect:large_narrow}, \ref{subsect:small}, or disk-like, \\ref{subsect:disk}) ) to see the effect on the global disk evolution."201 W etlscussourresultsumltheirobservationalimplicationsint disc., We discuss our results and their observational implications in \\ref{sect:disc}.202" Iu the following we consider an axisviunietrie disk of particles extending frou R;, to Rove in radius.", In the following we consider an axisymmetric disk of particles extending from $R_{in}$ to $R_{out}$ in radius.203" The ier radius nav coincide with the sublimation radius A, at which the effective temperature of particles equals the sublimation temperature Ti: 2 2 3.) where (δὲ, is the WD radius. 7,z:1500 Is for silicate erains. and Z,,=T,/(10! Is) is the normalized stellar temperature 7i."," The inner radius may coincide with the sublimation radius $R_s$ , at which the effective temperature of particles equals the sublimation temperature $T_s$: 22 ^2 )^2, where $R_\star$ is the WD radius, $T_s\approx 1500$ K for silicate grains, and $T_{\star,4}\equiv T_\star/(10^4$ K) is the normalized stellar temperature $T_\star$."204" Taking R,zO.OLR.. one funds Ryzm0.2 Ro. in agreement with observationallv iuferred mner radii of compact debris disks (Jura 2007. 20092)."," Taking $R_\star\approx 0.01R_\odot$ one finds $R_s\approx 0.2$ $_\odot$, in agreement with observationally inferred inner radii of compact debris disks (Jura 2007, 2009a)."205 When particles reach the sublimation radius they produce metallic eas. which joius the gaseous disk extending down to the WD surface.," When particles reach the sublimation radius they produce metallic gas, which joins the gaseous disk extending down to the WD surface."206 Metal accretion outo the WD surface proceeds through this clisk., Metal accretion onto the WD surface proceeds through this disk.207 Although this metal gas also spreads outward frou the sublination radius (CMelis 2010) aud under certain eireunistauces ean substantially affect debris disk evolution (Bafikov 2011b). in this work. following R11. we concentrate onlv on effects associated with the PR drag.," Although this metal gas also spreads outward from the sublimation radius (Melis 2010) and under certain circumstances can substantially affect debris disk evolution (Rafikov 2011b), in this work, following R11, we concentrate only on effects associated with the PR drag."208 Thus. here we neelect presence of the eas exterior of Fouad its iuteraction with the debris disk.," Thus, here we neglect presence of the gas exterior of $R_s$ and its interaction with the debris disk."209 According to Rafikov (2011b) this is a valid approxiuation as long as the viscous timescale in the gaseous disk is shorter than the time on which this disk cau be replenished by the sublimation of debris., According to Rafikov (2011b) this is a valid approximation as long as the viscous timescale in the gaseous disk is shorter than the time on which this disk can be replenished by the sublimation of debris.210" Then the eas does not acciuulate at rzFR, aud its density is always low cuough for the eas drag to not affect the debris disk appreciably.", Then the gas does not accumulate at $r\approx R_{in}$ and its density is always low enough for the gas drag to not affect the debris disk appreciably.211 We characterize the disk at cach point by its surface density X(r) aud optical depth where p ds the bulk ceusity of particles aud «is their characteristic size., We characterize the disk at each point by its surface density $\Sigma(r)$ and optical depth = where $\rho$ is the bulk density of particles and $a$ is their characteristic size.212 The particle size e is not well constrained by the existing observations. but its actual value becomes important only for low mass disks with stnall 7. see §3..," The particle size $a$ is not well constrained by the existing observations, but its actual value becomes important only for low mass disks with small $\tau$, see \ref{sect:low}."213" Following Friedjung (1985) aud RIL we represent iracdiation of the disk by the WD using a single incidence auele à at each radius + from the disk (the so-called ""h]unp-post dhunination model described iu R11): attr) where R&R, is the radius of the star.", Following Friedjung (1985) and R11 we represent irradiation of the disk by the WD using a single incidence angle $\alpha$ at each radius $r$ from the disk (the so-called “lamp-post” illumination model described in R11): (r) where $R_{\star}$ is the radius of the star.214 We can then introduce 7| according to the following definition:, We can then introduce $\tau_\parallel$ according to the following definition:.215 This variable is very important for our subsequent analysis., This variable is very important for our subsequent analysis.216 In the following we will call the disk optically thick or thin based ou whether 7) aud uot 7 is greater or sunaller than uit., In the following we will call the disk optically thick or thin based on whether $\tpar$ and not $\tau$ is greater or smaller than unity.217" R11 demoustrated that the mass accretion rate AL through the disk of solids dviven by the PR drag may be written as Tere L, is the WD Iuuinuosity. € is the speed of light and function eives the fraction of incoming starlight that is absorbed by thedisk."," R11 demonstrated that the mass accretion rate $\dot M$ through the disk of solids driven by the PR drag may be written as M(r)= (r) Here $L_{\star}$ is the WD luminosity, $c$ is the speed of light and function _r = 1 - gives the fraction of incoming starlight that is absorbed by thedisk."218 It is iustructive to examine different hnuuits of the expression (5))., It is instructive to examine different limits of the expression \ref{eq:mdot}) ).219 If the disk isoptically thick to iucideut stellar radiation. 7)291 (which cannot be the case everywhere at all times. as we will see below). then the," If the disk isoptically thick to incident stellar radiation, $\tau_\parallel\gg 1$ (which cannot be the case everywhere at all times, as we will see below), then the"220(2008).,.221". In order to take into account the isotopic effect. we correct the energies of the P,» and of the Ps;s levels of “Lit using the values of the isotopic shifts in the Dj and Ds lines listed in Table 1.."," In order to take into account the isotopic effect, we correct the energies of the$^2$ $_{1/2}$ and of the $^2$ $_{3/2}$ levels of $^6$ Li using the values of the isotopic shifts in the $_1$ and $_2$ lines listed in Table \ref{tab:phys-prop}."222 The HFS Hamiltonian. describing the interaction between the nuclear spin and the electronic angular momentum. can be expressed as a series of electric and magnetic multipoles (see.forexample.Kopfermann1958).," The HFS Hamiltonian, describing the interaction between the nuclear spin and the electronic angular momentum, can be expressed as a series of electric and magnetic multipoles \citep[see, for example,][]{Kop58}."223 We calculate the energies of the HFS F-levels using the values of the magnetic dipole and of the electric quadrupole HFS constants (usually indicated with the symbols <A and 8. respectively) listed in Table I..," We calculate the energies of the HFS $F$ -levels using the values of the magnetic dipole and of the electric quadrupole HFS constants (usually indicated with the symbols $\mathcal{A}$ and $\mathcal{B}$, respectively) listed in Table \ref{tab:phys-prop}."224 We recall that in the absence of magnetic fields. using Dirac’s notation. the energy eigenvectors can be written in the form ja//Ff>. where « represents a set of inner quantum numbers (specifying the configuration and. if the atomic system is deseribed by the L-S coupling scheme. the total electronic orbital and spin angular momenta). / is the total electronic angular momentum quantum number. while F and f are the quantum numbers associated with the total angular momentum operator (electronic plus nuclear: and with its projection along the quantization axis. respectively.," We recall that in the absence of magnetic fields, using Dirac's notation, the energy eigenvectors can be written in the form $|\alpha J I F f >$, where $\alpha$ represents a set of inner quantum numbers (specifying the configuration and, if the atomic system is described by the $L$ $S$ coupling scheme, the total electronic orbital and spin angular momenta), $J$ is the total electronic angular momentum quantum number, while $F$ and $f$ are the quantum numbers associated with the total angular momentum operator (electronic plus nuclear: ), and with its projection along the quantization axis, respectively."225"ΤΠ). The Grotrian diagrams showing the various HFS F-levels of the two isotopes. and the HFS components of the D, and D» lines are shown in the upper panel of Figure 2.."," The Grotrian diagrams showing the various HFS $F$ -levels of the two isotopes, and the HFS components of the $_1$ and $_2$ lines are shown in the upper panel of Figure \ref{fig:grotrian}."226 In the lower panels of Figure 2. the laboratory positions of the various HFS components are shown., In the lower panels of Figure \ref{fig:grotrian} the laboratory positions of the various HFS components are shown.227" Since the isotopic shifts are of the same order of magnitude às the frequency separation between the two D-lines. the D, line of “Li falls almost at the same wavelength as the D» line of °Li (see panels and c of Figure 2)."," Since the isotopic shifts are of the same order of magnitude as the frequency separation between the two D-lines, the $_1$ line of $^7$ Li falls almost at the same wavelength as the $_2$ line of $^6$ Li (see panels and of Figure \ref{fig:grotrian}) )."228 We observe that in both isotopes the ground level splits into two HFS F-levels., We observe that in both isotopes the ground level splits into two HFS $F$ -levels.229 The splitting between these two levels is much larger than that, The splitting between these two levels is much larger than that230"instantly removed as it arrives, while (ii) the outer grid point is placed at such a large radius, typically 1015 cm, that during the course of the run the outer edge of the spreading fall-back disk never reaches it.","instantly removed as it arrives, while (ii) the outer grid point is placed at such a large radius, typically $10^{13}$ cm, that during the course of the run the outer edge of the spreading fall-back disk never reaches it."231 The range in disk radii necessitates ~large1500dynamic—3000 grid points., The large dynamic range in disk radii $r_{\rm outer}/r_{\rm inner}$ necessitates $\sim1500-3000$ grid points.232" In addition, no router/Tinnerfresh material is added during a run."," In addition, no fresh material is added during a run."233" Thus the evolution is set entirely by gradients within the disk, unlike the standard Shakura-Sunyaev disk fed at a constant rate in the outer edge which approaches a steady-state M(r)= constant with time."," Thus the evolution is set entirely by gradients within the disk, unlike the standard Shakura-Sunyaev disk fed at a constant rate in the outer edge which approaches a steady-state ${\dot M}(r)=$ constant with time."234" -0.065 cm LGRBs are thought to be associated with the explosions of massive stars (MacFadyen Woosley 1999, Woosley Heger 2006)."," -0.065 cm LGRBs are thought to be associated with the explosions of massive stars (MacFadyen Woosley 1999, Woosley Heger 2006)."235 The initial failure of the SN is the reason for the GRB in the collapsar model., The initial failure of the SN is the reason for the GRB in the collapsar model.236" The hosts for IGRBs tend to be subluminous, irregular galaxies rich in star formation (Fruchter et al."," The hosts for lGRBs tend to be subluminous, irregular galaxies rich in star formation (Fruchter et al."237 2006)., 2006).238 If the long-term X-ray light curves of GRBs are indicative of feeding from a fall-back accretion, If the long-term X-ray light curves of GRBs are indicative of feeding from a fall-back accretion239The damping of Neptune’s eccentricity ew or inclination iw affects the secular excitation of the planetesimals in two regimes: slow and fast.,The damping of Neptune's eccentricity $e_N$ or inclination $i_N$ affects the secular excitation of the planetesimals in two regimes: slow and fast.240" We summarize constraints on Neptune’s eccentricity and inclination in Table 1 In the slow regime, ey or iw damps on a timescale Το or τι, respectively, longer than the time (527/gKBO) for e or i to reach its maximum value."," We summarize constraints on Neptune's eccentricity and inclination in Table \ref{tab:constrain}241 In the slow regime, $e_N$ or $i_N$ damps on a timescale $\tau_e$ or $\tau_i$, respectively, longer than the time $\frac{1}{2} 2\pi/g_{\rm KBO}$ ) for $e$ or $i$ to reach its maximum value."242" Because each planetesimal has an initial =0)0, its free inclination ifree and eccentricityi(£=0) ege,=e(t are set by Neptune’s initial en(t=0) and in(t=0)."," Because each planetesimal has an initial $i (t=0) = e (t=0)= 0$ , its free inclination $\ifree$ and eccentricity $\efree$ are set by Neptune's initial $e_N (t=0)$ and $i_N (t=0)$."243" In this slow regime, the planetesimal's ife¢ and ege, are conserved."," In this slow regime, the planetesimal's $\ifree$ and $\efree$ are conserved."244" As ey and iy damp, the planetesimal’s forced eccentricity eforceqa and inclination iforceq decrease, and the total eccentricity e and inclination i of the planetesimal approach ege, and 5free-"," As $e_N$ and $i_N$ damp, the planetesimal's forced eccentricity $\eforced$ and inclination $\iforced$ decrease, and the total eccentricity $e$ and inclination $i$ of the planetesimal approach $\efree$ and $\ifree$."245" Thus, in the slow regime, the planetesimals will evolve to a value below i«6? if iw<6°."," Thus, in the slow regime, the planetesimals will evolve to a value below $i < 6^\circ$ if $i_N < 6^\circ$."246" To satisfy our conservative criteria established in Section 3.1,, which requires planetesimals with 42.5«a45 AU to remain at e«0.1, Neptune's eccentricity must stay below 0.18 at 20 AU and 0.12 at 30 AU."," To satisfy our conservative criteria established in Section \ref{sec:obs}, which requires planetesimals with $42.5 < a < 45$ AU to remain at $e<0.1$, Neptune's eccentricity must stay below 0.18 at 20 AU and 0.12 at 30 AU."247" Thus in the slow damping case, there is a strong constraint 1)) on the maximum eccentricity and inclination at(Table which Neptune can remain over long timescales."," Thus in the slow damping case, there is a strong constraint (Table \ref{tab:constrain}) ) on the maximum eccentricity and inclination at which Neptune can remain over long timescales."248 Note that these values are twice the values given in Section 4.2.., Note that these values are twice the values given in Section \ref{subsec:evolve}.249" This is because in the slow damping regime, the planetesimals will evolve to Cfree=Cforcea(t and Uree=forced0), whereas if ey and iy remain0) high indefinitely, the(t planetesimals’ e and i continue to oscillate, reaching a maximum of 2€forced and 2itorced-"," This is because in the slow damping regime, the planetesimals will evolve to $\efree = \eforced(t=0)$ and $\ifree = \iforced(t=0)$, whereas if $e_N$ and $i_N$ remain high indefinitely, the planetesimals' $e$ and $i$ continue to oscillate, reaching a maximum of $2\eforced$ and $2\iforced$."250" If ew and iy damp in the fast regime, on a timescale shorter than the secular excitation time, ifree and etree are not conserved."," If $e_N$ and $i_N$ damp in the fast regime, on a timescale shorter than the secular excitation time, $\ifree$ and $\efree$ are not conserved."251 The planetesimal's total e and i are frozen at the values they reach after approximately one damping time., The planetesimal's total $e$ and $i$ are frozen at the values they reach after approximately one damping time.252 Fig., Fig.253 9 illustrates the behavior of the planetesimals in this regime in integrations in which Neptune's eccentricity orinclination damps., \ref{fig:idamp} illustrates the behavior of the planetesimals in this regime in integrations in which Neptune's eccentricity orinclination damps.254" Neptune's orbit could have been even more eccentric and inclined than in the slow regime if ey and iy damped quickly (Table 1,, right column)."," Neptune's orbit could have been even more eccentric and inclined than in the slow regime if $e_N$ and $i_N$ damped quickly (Table \ref{tab:constrain}, right column)."255" If the planetesimal has not yet reached the maximum of its secular cycle after one damping time, instead of converging to the ege, and ifree Set by initial conditions, the planetesimal evolves to €fnal=free and gna]=freesin(gknoTi) (see?,foradetailedsin(gKBOTe)explanationand"," If the planetesimal has not yet reached the maximum of its secular cycle after one damping time, instead of converging to the $\efree$ and $\ifree$ set by initial conditions, the planetesimal evolves to $e_{\rm final} = \efree \sin(\gkbo \tau_e )$ and $i_{\rm final} =\ifree \sin(\gkbo \tau_i )$ \citep[see][for a detailed explanation and justification]{2012D}."256 Consider again a planetesimal at 42.5 AU., Consider again a planetesimal at 42.5 AU.257" If justification)..Neptune's eccentricity and inclination damp on timescale of 7= 0.32 Myr,the final eccentricity and ainclination of the planetesimal are reduced by a factorof sin(gkgoT)= compared to the slow damping case."," If Neptune's eccentricity and inclination damp on a timescale of $\tau = $ 0.32 Myr,the final eccentricity and inclination of the planetesimal are reduced by a factorof $\sin(\gkbo \tau) = 0.5$ compared to the slow damping case."258" Thus the planetesimals will evolve to a value below i«6? if iw«6°/0.5= 12°.To satisfy our conservative criteria established in Section 3.1,, which requires planetesimals with 42.5«a45 AU to remain at e« 0.1, ey must stay below 0.18/0.5—0.36 at 20 AU and 0.12/0.5—0.24 "," Thus the planetesimals will evolve to a value below $i < 6^\circ$ if $i_N < 6^\circ/0.5 = 12^\circ$ To satisfy our conservative criteria established in Section \ref{sec:obs}, , which requires planetesimals with $42.5 < a < 45$ AU to remain at $e < 0.1$ $e_N$ must stay below $0.18/0.5 = 0.36$ at 20 AU and $0.12/0.5 = 0.24$ "259about the absolute level of obscuration (the embedded prolostars show comparable silicate feature depths).,about the absolute level of obscuration (the embedded protostars show comparable silicate feature depths).260 An alternative explanation might be that deeply obsenrecd ULIRGs and our z: 422 sources simply have a higher proportion of hydrocarbons., An alternative explanation might be that deeply obscured ULIRGs and our $z$ $\sim$ 2 sources simply have a higher proportion of hydrocarbons.261 For example. bombardinent with II atoms can hydrogenate amorphous carbon grains increasing the ILAC-to-silicate ratio (seee.g.Grishko&Dulev2000;Duleyetal. 2005).," For example, bombardment with H atoms can hydrogenate amorphous carbon grains increasing the HAC-to-silicate ratio \citep[see e.g.][]{gd00,duley05}."262. Various other processes can be important. s...," Various other processes can be important, s.a."263 UV radiation processing of ice mantles can lead to relractory materials on (he grain surfaces (hat lead to the aabsorption feature (Greenbergetal.1995).. consistent wilh the somewhat weaker ice features.," UV radiation processing of ice mantles can lead to refractory materials on the grain surfaces that lead to the absorption feature \citep{greenberg95}, consistent with the somewhat weaker ice features."264 Ultimately. the degree of WAC absorption depends on the balance of processes that support hydrocarbon generation to those that suppress it (s.a.," Ultimately, the degree of HAC absorption depends on the balance of processes that support hydrocarbon generation to those that suppress it (s.a."265 converte hydrocarbons (o aromatics)., converting hydrocarbons to aromatics).266 It is not unreasonable to suppose that such processes might be more efficient in our sources (han the tvpical Milkv Way sources., It is not unreasonable to suppose that such processes might be more efficient in our sources than the typical Milky Way sources.267 The geometric explanation is simpler ancl therefore favored. however. a difference in composition cannot be excluded.," The geometric explanation is simpler and therefore favored, however, a difference in composition cannot be excluded."268 refice;ZshowstheratioofIhe3.0 Πορ feature optical depth to the ssilicate dust optical depth., \\ref{ice_si} shows the ratio of the ice feature optical depth to the silicate dust optical depth.269 As before. we compare our sample with both local ULIRGs and ihe data for MW stars.," As before, we compare our sample with both local ULIRGs and the data for MW stars."270 We find that unlike the case lor the ILAC-to-silicate ratio which is remarkably similar across [or all available MW. sources. the ice-to-silieate ratio shows a wide spread of more (han an order of magnitude.," We find that unlike the case for the HAC-to-silicate ratio which is remarkably similar across for all available MW sources, the ice-to-silicate ratio shows a wide spread of more than an order of magnitude."271 This ratio is strongly. dependent on the ice mantle (hickuess (e.g.Ossenkopf&Henning1994:Zinoveva2005).. but radiative (ransler details following the arguments presented in (he previous section likely dominate.," This ratio is strongly dependent on the ice mantle thickness \citep[e.g.][]{oss94,zinoveva05}, but radiative transfer details following the arguments presented in the previous section likely dominate."272 When we consider only the sources with red sspectra. and where both ice and silicate optical depths are available. we find that IRASO8572+3915 has T.9/7o.7 00.08. and IRAS19254-7245 has 744/794; 00.15.," When we consider only the sources with red spectra, and where both ice and silicate optical depths are available, we find that IRAS08572+3915 has $\tau_{3.0}/\tau_{9.7}$ 0.08, and IRAS19254-7245 has $\tau_{3.0}/\tau_{9.7}$ 0.15."273 Although a much Larger sampling is needed. (his suggests (especially in conjunction wilh our own sample) Chat sources with redder sslopes have lower observed ssilicate ratios.," Although a much larger sampling is needed, this suggests (especially in conjunction with our own sample) that sources with redder slopes have lower observed silicate ratios."274[daG65s83 map (Fig. 10)) (,6583 map (Fig. \ref{fig:otherlines}) ) (275for which the surrounding continuum is essentially featureless).,for which the surrounding continuum is essentially featureless).276 Phe match is excellent (see Fig. 11)).," The match is excellent (see Fig. \ref{fig:NImap}) ),"277 particularly when considering the low Lo-noise ratio of the residual Ica55200 line spectra., particularly when considering the low signal-to-noise ratio of the residual 5200 line spectra.278 The rratio ranges from 21 at the centre to z1.4-1.5 in the arms. corresponding to electron densities IN. of 500 aand less than 100 ((low density. limit). respectively.," The / ratio ranges from $\simeq$ 1 at the centre to $\simeq$ 1.4-1.5 in the arms, corresponding to electron densities $N_e$ of 500 and less than 100 (low density limit), respectively."279 Lhe rratio ds roughly constant over the Ποιά of view. with values between 2 and 2.2.," The / ratio is roughly constant over the field of view, with values between 2 and 2.2."280 This seems to contracict the measurements made by Zeilinger et al. (, This seems to contradict the measurements made by Zeilinger et al. (2811996). who reported vvalues as high as SN at the centre. a factor of two higher han ours at the centre.,"1996), who reported / values as high as 8 at the centre, a factor of two higher than ours at the centre."282 We suggest that this cliscrepaney is mainlv due to the fact that Zeilinger et al. (, We suggest that this discrepancy is mainly due to the fact that Zeilinger et al. (2831996). cid not flux-calibrate their spectra (which were taken for the »urpose of measuring eas kinematics) anc did not correct hem for the underlving (Ho) stellar absorption.,1996) did not flux-calibrate their spectra (which were taken for the purpose of measuring gas kinematics) and did not correct them for the underlying $\alpha$ ) stellar absorption.284 The Bux distribution of the lines is less centrally peaked than that of the lines. with the rratio ranging from 0.4 at the location of the nucleus to 7«0.65 in the armis.," The flux distribution of the lines is less centrally peaked than that of the lines, with the / ratio ranging from $\simeq$ 0.4 at the location of the nucleus to $\simeq$ 0.65 in the arms."285 This is usually interpreted as a decrease of the comission in the dense nuclear regions. due to the lower critical electronic densities of the ines with respect to the ine doublet. (NO=1.9 Wwe. 1: and 5 Tor the u]AGTIT.. aand ines. respectively).," This is usually interpreted as a decrease of the emission in the dense nuclear regions, due to the lower critical electronic densities of the lines with respect to the line doublet $N_e^{crit} = 2861.9$ $\times$, 1.2 $\times$ and 8 $\times$ for the , and lines, respectively)."287 The flux integrated over à rraciius from the nucleus is c 1.9. is ΑΝ μα ο Ετος is W contribution from the central unresolved. peak.," The flux integrated over a radius from the nucleus is $\simeq$ 1.9 $\times$ $^2$ W, with a $\simeq$ 4.7 $\times$ $^2$ W contribution from the central unresolved peak."288 Assuming a uniform electron density IN. = 100 aand a pure hydrogen gas. this corresponds to a mass of ionized.. σας in. the arms of ⋅⋅GS ssolar masses.," Assuming a uniform electron density $N_e$ = 100 and a pure hydrogen gas, this corresponds to a mass of ionized gas in the arms of 6.8 $\times$ solar masses."289 For the central unresolved peak and assuming this time an electron density of 500 we obtain à mass of ionized gas of 4.43. ssolar masses.," For the central unresolved peak and assuming this time an electron density of 500, we obtain a mass of ionized gas of 4.4 $\times$ solar masses."290 Note that the quoted ionized eas masses are inversely proportional to the value of IN..., Note that the quoted ionized gas masses are inversely proportional to the value of $N_e$.291 The emission-line velocity and velocity dispersion. maps are shown in Fie. 12.., The emission-line velocity and velocity dispersion maps are shown in Fig. \ref{fig:gaskin}.292 The velocity field exhibits strong disturbances following the spiral-Hike distribution of the gas., The velocity field exhibits strong disturbances following the spiral-like distribution of the gas.293 There is a strong hint lor eas streaming on the inner side of the south-western arm. where the emission lines exhibit a complex structure probably resulting from the superposition of several kinematical components (Fig. 9)).," There is a strong hint for gas streaming on the inner side of the south-western arm, where the emission lines exhibit a complex structure probably resulting from the superposition of several kinematical components (Fig. \ref{fig:NIIwithspec}) )."294 This widening of the lines (m4.250 13) is also observed on the inner side of the north-castern arm. as emphasized in the dispersion map (Fig. 12)).," This widening of the lines $\sigma_{\rm gas} > 250$ ) is also observed on the inner side of the north-eastern arm, as emphasized in the dispersion map (Fig. \ref{fig:gaskin}) )."295 Using the high-resolution. ΛΕΡΟΣ narrow-banel image of NGC 2974 shown in Fig. 3..," Using the high-resolution /WFPC2 narrow-band image of NGC 2974 shown in Fig. \ref{fig:HSTimages},"296 we applied the method pioneered by Ferruit (1999) to deconvolve our merged clelatacube (see also Emisellem Ferruit 2000)., we applied the method pioneered by Ferruit (1999) to deconvolve our merged datacube (see also Emsellem Ferruit 2000).297 Pwo methocs were tested: a pure. Lucy. deconvolution. and a weakly euicded” Luey deconvolution. in which the narrow-band HST/NVPC2 image is used to constrain the integrated Lux in the deatacube.," Two methods were tested: a pure Lucy deconvolution, and a “weakly guided” Lucy deconvolution in which the narrow-band /WFPC2 image is used to constrain the integrated flux in the datacube."298 In both cases. we performed 300 iterations after which the gain in resolution was found not to compensate the increase in noise level.," In both cases, we performed 300 iterations after which the gain in resolution was found not to compensate the increase in noise level."299 Dilferences between the results of the two deconvolutions were not significant. except for a slight reduction of the high-frequeney features in the weakly euiced case.," Differences between the results of the two deconvolutions were not significant, except for a slight reduction of the high-frequency features in the weakly guided case."300 We therefore favour the latter. the analysis of which will be presented here.," We therefore favour the latter, the analysis of which will be presented here."301 The final resolution of the cdeconvolved clatacube. evaluated from the central peak (unresolved in the WEPC2 |Lea image). isΠΡΙ HM.," The final resolution of the deconvolved datacube, evaluated from the central peak (unresolved in the WFPC2 $+$ image), is $0\farcs35$ FWHM."302" ALapso fthedceconvol veddatacube. namelythe aandlla [flidistribition. thegasveloci yanddispersionmaps. areshouniniig, 13.."," Maps of the deconvolved datacube, namely the and flux distribution, the gas velocity and dispersion maps, are shown in Fig. \ref{fig:decmaps}."303 The two spiral arms are nicely revealed. as well as the central concentration which is now highly: contrasted.," The two spiral arms are nicely revealed, as well as the central concentration which is now highly contrasted."304 The velocity field shows strong streaming motions along the arms. with peak velocities of 211 and 264+.," The velocity field shows strong streaming motions along the arms, with peak velocities of $-$ 211 and 264."305 More interestingly. the dispersion is very high on the inner side of both arms. confirming the picture seen before deconvolution (sce Fig. 12)).," More interestingly, the dispersion is very high on the inner side of both arms, confirming the picture seen before deconvolution (see Fig. \ref{fig:gaskin}) ),"306 reaching values greater than 300., reaching values greater than 300.307.. The eas kinematics will be further discussed in Sect., The gas kinematics will be further discussed in Sect.308 4.3. in view of a density wave model., \ref{sec:wave} in view of a density wave model.309 In this Section. we present new cvnamical models for the stellar and. gas components in the central region of NGC 2074. using our new two-dimensional data as well as published. kinematics.," In this Section, we present new dynamical models for the stellar and gas components in the central region of NGC 2974, using our new two-dimensional data as well as published kinematics."310 The first step in this modelling process is to obtain a realistic threec-dimensional representation of the luminosity and mass distribution of the galaxy [from the very centre to the outer region., The first step in this modelling process is to obtain a realistic three-dimensional representation of the luminosity and mass distribution of the galaxy from the very centre to the outer region.311 We used the Multi-Gaussian. Expansion method. (Monnet. Bacon Emsellem1992: Emisellen 1994) to build a photometric for the cleconvolved surface. brightness of Νας 2974.," We used the Multi-Gaussian Expansion method (Monnet, Bacon Emsellem1992; Emsellem 1994) to build a photometric for the deconvolved surface brightness of NGC 2974."312 the combination of a ground-based. £ band image taken at, the combination of a ground-based $I$ band image taken at313formed in the wake of the runaway star DN.,formed in the wake of the runaway star BN.314 From the proper motion of BN and the projected separation from the Northern tip of Stream X we can infer a timescale of 200 vr., From the proper motion of BN and the projected separation from the Northern tip of Stream A we can infer a timescale of 200 yr.315 This may correspon to à cooling time. a formation time for OLL or a time for population inversion to be established Following the passage of BN.," This may correspond to a cooling time, a formation time for OH, or a time for population inversion to be established following the passage of BN."316 Fie., Fig.317 l shows tha the proper motions of BN ancl sources ] and n project back to à position on the sky near the base of Stream A. in a reeion largely clear of OLL masers.," \ref{ra-dec} shows that the proper motions of BN and sources I and n project back to a position on the sky near the base of Stream A, in a region largely clear of OH masers."318 This position is significanty displaced 7 aresec Northwest of the centre of the OLI maser torus., This position is significantly displaced $\sim$ 4 arcsec Northwest of the centre of the OH maser torus.319 I has been suggested that BN and sources Land n originally belonged to a multiple stellar system that. clisintegrated 7500. vr ago., It has been suggested that BN and sources I and n originally belonged to a multiple stellar system that disintegrated $\sim$ 500 yr ago.320 The disintegration could have due to a close dvnamical interaction. as suggested bv Gómez et al. (," The disintegration could have due to a close dynamical interaction, as suggested by Gómmez et al. ("321in. press). or it could have been due to a merger event that also produced the molecular outflow. as suggested. by Bally Zinnecker (2005).,"in press), or it could have been due to a merger event that also produced the molecular outflow, as suggested by Bally Zinnecker (2005)."322 Alternatively. Tan (2004) has proposed that BN was ejected [rom the 4! Ori € system ~4000 vr ago.," Alternatively, Tan (2004) has proposed that BN was ejected from the $\theta^{1}$ Ori C system $\sim$ 4000 yr ago."323 Our data do not distinguish unambiguously between these possibilities., Our data do not distinguish unambiguously between these possibilities.324 Llowever the fact that the large-scale OLL maser torus is centred. on source ] slightly favours Tan's scenario. with BN being a passing runaway from the 6+ Ori C svsten.," However the fact that the large-scale OH maser torus is centred on source I slightly favours Tan's scenario, with BN being a passing runaway from the $\theta^{1}$ Ori C system."325 The other large-scale feature Are D encloses Hic6. which is one of the cooler mid-LHt sources. with polarization that is consistent with external illumination and with no evidence ob embedded bright stars (Shuping et al.," The other large-scale feature Arc B encloses IRc6, which is one of the cooler mid-IR sources, with polarization that is consistent with external illumination and with no evidence of embedded bright stars (Shuping et al."326 2004 and references therein)., 2004 and references therein).327 This suggests that Are D might be associated with a photodissociation zone around UG., This suggests that Arc B might be associated with a photodissociation zone around IRc6.328" In further support of this there is strong emission from CIIGCII at the position of Htc6. implying densities of at. leas 10"" ? (Wilner. Wright Plambeck 1996)."," In further support of this there is strong emission from $_{3}$ CH at the position of IRc6, implying densities of at least $^{6}$ $^{-3}$ (Wilner, Wright Plambeck 1996)."329 The large-scale maser structures found in Orion-BN/IXL are similar in scale to OLL maser structures recently reported in W3(COLD., The large-scale maser structures found in Orion-BN/KL are similar in scale to OH maser structures recently reported in W3(OH).330 Wright et al. (, Wright et al. (3312004a.b) noted several ares of 18-cm masers. which they interpreted as propagating shocks.,"2004a,b) noted several arcs of 18-cm masers, which they interpreted as propagating shocks."332 Llarvey-Smiuth Cohen (2005) found a low brightness filament of excited. OLL 4765-MlIz emission. stretching for ~2200 au and clearly related. in its morphology to some of the erounc-state OLL ares at. 18-0. wavelength., Harvey-Smith Cohen (2005) found a low brightness filament of excited OH 4765-MHz emission stretching for $\sim$ 2200 au and clearly related in its morphology to some of the ground-state OH arcs at 18-cm wavelength.333 The structures seen in Orion are similar in linear scale., The structures seen in Orion are similar in linear scale.334 The individual maser spots in Stream A and Are B are. well separated on the sky for the most part. but are nevertheless likely to be simply the high-gain cores of an extended stream of maser emission.," The individual maser spots in Stream A and Arc B are well separated on the sky for the most part, but are nevertheless likely to be simply the high-gain cores of an extended stream of maser emission."335 The tvpical flux densities of ~O.1 Jv correspond to brightness temperatures ofat least ~3. 107 Ix. All these large-scale features in Orion and W3(OLLD) are relatively weak and therefore below the sensitivies of earlier surveys. for the most part.," The typical flux densities of $\sim$ 0.1 Jy correspond to brightness temperatures of at least $\sim$ $\times$ $^{5}$ K. All these large-scale features in Orion and W3(OH) are relatively weak and therefore below the sensitivies of earlier surveys, for the most part."336 Deeper observations ofother well-known OLL maser sources are needed to establish just how common such features are., Deeper observations of other well-known OH maser sources are needed to establish just how common such features are.337 The ΟΗ 1612-Mllz masers have ao more widespread distribution. than the other ΟΙ masers. and cilferent kinematics (Section 3.2)).," The OH 1612-MHz masers have a more widespread distribution than the other OH masers, and different kinematics (Section \ref{kinematics}) )."338 This suggests that they trace a region with dillerent physical conditions., This suggests that they trace a region with different physical conditions.339" Gray. Field Docl (1992) eive the following conditions for strong 1612-MllIz masers: molecular hydrogen density ng, 5 nog 60 eas kinetic temperature {ος Wk. dust emperature at maser site Zi 30 Ix. external radiation field Tí SOW and. velocity shift AV 2.0 +."," Gray, Field Doel (1992) give the following conditions for strong 1612-MHz masers: molecular hydrogen density $n_{\rm H_{2}}$ $^{-3}$, $n_{\rm OH}$ 60 $^{-3}$, gas kinetic temperature $T_{\rm k}$ =30 K, dust temperature at maser site $T_{\rm d}$ 30 K, external radiation field $T_{\rm x}$ 80 K and velocity shift $\Delta V$ 2.0 $^{-1}$."340 This is cooler han tvpical for OLL masers. but is consistent with the ocation of these particular 1612-MlIz masers further than normal from the main source of infrared. luminosity.," This is cooler than typical for OH masers, but is consistent with the location of these particular 1612-MHz masers further than normal from the main source of infrared luminosity."341 “Phe velocity. eracient needed for strong maser action is also consistent with the association of these masers with shocked eas in the molecular outllow (Section 3.3.2))., The velocity gradient needed for strong maser action is also consistent with the association of these masers with shocked gas in the molecular outflow (Section \ref{nearIR}) ).342 We note a further possible positional association between the 1612-MlIz masers and the methanol 6.7-Cillz masers recently discovered. by Voronkoy et al. (, We note a further possible positional association between the 1612-MHz masers and the methanol 6.7-GHz masers recently discovered by Voronkov et al. (3432005).,2005).344 In Fig., In Fig.345 11 we show the positions ancl velocities of the two species., \ref{methanol} we show the positions and velocities of the two species.346" There is a clear region of overlap centred around RA (J2000) = 0535"" 14255. Dee. (92000) = -05°222/44599 and Yi,— [75 km s!."," There is a clear region of overlap centred around RA (J2000) = $^{\rm h}$ $^{\rm m}$ 5, Dec. (J2000) = 9 and $V_{\rm lsr}$ = +7.5 km $^{-1}$."347 The 6.7-Gllz positions have errors of ~2 arcsec., The 6.7-GHz positions have errors of $\sim$ 2 arcsec.348 Lt will be important. to make 6.7- measurements of higher precision to examine this correspondence more. closely., It will be important to make 6.7-GHz measurements of higher precision to examine this correspondence more closely.349 “Phe positions of 25-Cillz masers from Johnston et al. (, The positions of 25-GHz masers from Johnston et al. (350L997. 1992) are also shown in the figure for completeness.,"1997, 1992) are also shown in the figure for completeness."351 Only one of these falls in the region of interest., Only one of these falls in the region of interest.352 We note that there is no association with the OLI mainline masers., We note that there is no association with the OH mainline masers.353 This is consistent with the 25-CGllz masers being class E masers. which are thought to be collisionally pumped (cf.," This is consistent with the 25-GHz masers being class I masers, which are thought to be collisionally pumped (cf."354 Crage et al., Cragg et al.355 2002)., 2002).356 The 6.7-Gllz maser transition is the prototype class Lb maser. usually thought to be radiatively pumped.," The 6.7-GHz maser transition is the prototype class II maser, usually thought to be radiatively pumped."357 The 6.7-CGllz masers in Orion are of therefore of interest. because of their apparent association with 25-Gllz masers., The 6.7-GHz masers in Orion are of therefore of interest because of their apparent association with 25-GHz masers.358 Voronkov et al., Voronkov et al.359 have considered. the pumping requirements for the coexistence of both types of methanol maser and find. that both tvpes can occur simultaneously. at. low temperature (~60 Ix) and low molecular hydrogen density (107 em.?)., have considered the pumping requirements for the coexistence of both types of methanol maser and find that both types can occur simultaneously at low temperature $\sim$ 60 K) and low molecular hydrogen density $\sim$ $^{5}$ $^{-3}$ ).360 These conditions are not too cdissimilar to those needed for strong 1612-Mllz masers. as given earlier.," These conditions are not too dissimilar to those needed for strong 1612-MHz masers, as given earlier."361 In. summary. it appears that in Orion we may have the first examples of both methanol class HL and OLL ground. state masers located far from the main source of infrared luminosity. and. associated instead with the interaction between the molecular outflow and the surrounding gas.," In summary, it appears that in Orion we may have the first examples of both methanol class II and OH ground state masers located far from the main source of infrared luminosity, and associated instead with the interaction between the molecular outflow and the surrounding gas."362" The proplyvds originally designated LV. 16 within the Orion '""Trapezium. cluster are those most likely to exhibit. maser emission for they are irradiated by the intense field of the O6.5 star 65 Ori C. Of these LV. 1. now resolved as a binary proplvd (168326 NW SE) by ODell Wen (1904). and LV 2 (proplvd. 167-317 of O'Dell Wen 1994) have been most intensively observed. (Graham ct al."," The proplyds originally designated LV 1–6 within the Orion Trapezium cluster are those most likely to exhibit maser emission for they are irradiated by the intense field of the O6.5 star $\theta^{1}$ Ori C. Of these LV 1, now resolved as a binary proplyd (168–326 NW SE) by O'Dell Wen (1994), and LV 2 (proplyd 167-317 of O'Dell Wen 1994) have been most intensively observed (Graham et al."363 2002: Henney et al., 2002; Henney et al.364 2002 respectively)., 2002 respectively).365 The S. 101. em radius LY 2 was shown by Hennev et al. (, The $\times$ $^{14}$ cm radius LV 2 was shown by Henney et al. (3662002) to be irradiated by a fux of 10t em7 ! Lyman photons.,2002) to be irradiated by a flux of $\times$ $^{4}$ $^{-2}$ $^{-1}$ Lyman photons.367 These. produce an ionisee skin with, These produce an ionised skin with368particle acceleration case.,particle acceleration case.369 The harder spectrum could suggest non-linear shock effects in jets where the CR pressure is nonnegligible (Ellison2001)., The harder spectrum could suggest non-linear shock effects in jets where the CR pressure is nonnegligible \citep{ell01}.370. This 15 consistent with the fact that the necessary CR energy is comparable to the total energy of jets. E—Ej.," This is consistent with the fact that the necessary CR energy is comparable to the total energy of jets, $E \sim E_j$."371 In Figure 3.. we also show the synchrotron and IC emission from decaypositrons in. equation. (11)). which have an energy comparable to that of decay gamma-rays.," In Figure \ref{fig:flux}, we also show the synchrotron and IC emission from decaypositrons in equation \ref{eq:Cob+}) ), which have an energy comparable to that of decay gamma-rays."372" The positron spectrum is dN,xz,""dz, for Duacccy and dN,xoPde, for 7,«oe<Say.", The positron spectrum is $dN_e \propto \varepsilon_e^{-p} d\varepsilon_e$ for $\Gamma m_e c^2< \varepsilon_e < \varepsilon_p$ and $dN_e \propto \varepsilon_e^{-p-1} d\varepsilon_e$ for $\varepsilon_p < \varepsilon_e < \varepsilon_{\max}$.373" Thesynchrotron frequency is ο—007¢(2./0.1TeVY eV while the IC frequency is p~9ecypgCosΠω].109(5,/0.ITeV eV where we consider cosmic microwave background (CMB). às main target photons (lokaetal.2004)."," Thesynchrotron frequency is $\nu^{\rm syn}=q B \varepsilon_e^2/2\pi m_e^3 c^5374\sim 10^{-4} B_{-6} (\varepsilon_e/0.1{\rm TeV})^2$ eV while the IC frequency is $\nu^{\rm IC} \sim 9 \epsilon_{\rm CMB} (\varepsilon_e/m_e c^2)^2375\sim 10^8 (\varepsilon_e/0.1{\rm TeV})^2$ eV where we consider cosmic microwave background (CMB) as main target photons \citep{ioka04}."376". However the cooling time {=mzloepz.U—107(,/0.1TeVyUl yr. is. usually longer than the decay time £. in equation (13) for s,«sg~10 TeV where U is the total energy density of magnetic fields and CMB."," However the cooling time $t_c = 3 m_e^2 c^3/4 \sigma_T \varepsilon_{e} U377\sim 10^7 (\varepsilon_e/0.1{\rm TeV})^{-1} U_{-12}^{-1}$ yr is usually longer than the decay time $t_\gamma$ in equation \ref{eq:tga}) ) for $\varepsilon_e < \varepsilon_{\max} \sim 10$ TeV where $U$ is the total energy density of magnetic fields and CMB."378" Then the luminosity is suppressed by [fto1007(e10yr)c,/0.TTeV)U.45 compared with decay gamma-rays in equation. (15))."," Then the luminosity is suppressed by $t_\gamma/t_c \sim 10^{-2} (t_\gamma/10^5{\rm yr}) 379(\varepsilon_e/0.1{\rm TeV}) U_{-12}$ compared with decay gamma-rays in equation \ref{eq:lumi}) )."380 This is favorable for the interpretation of such sources as TeV unlDs., This is favorable for the interpretation of such sources as TeV unIDs.381 Note that the ~eV photons by decay positrons come from an extended region in. which the optical background dominates the remnant flux., Note that the $\sim$ eV photons by decay positrons come from an extended region in which the optical background dominates the remnant flux.382 The accelerated RI CRs may suffer the adiabatic energy losses during the expansion of the remnant (Rachen&Mészáros 1998).. which will greatly suppress the RI emission.," The accelerated RI CRs may suffer the adiabatic energy losses during the expansion of the remnant \citep{Rachen:1998fd}, which will greatly suppress the RI emission."383 This is a potential problem for the RI decay model., This is a potential problem for the RI decay model.384 However the CR escape from a remnant is not fully understood yet., However the CR escape from a remnant is not fully understood yet.385 For instance. it is common to assume the free escape of CRs in models where the GRB reverse shocks are the sites for the ultra high energy CR production (e.g..Waxman2006;etal. 2008)..," For instance, it is common to assume the free escape of CRs in models where the GRB reverse shocks are the sites for the ultra high energy CR production \citep[e.g.,][]{Waxman:2004ez,minn08}. ."386 In the same sense. the RI decay model is a viable possibility for TeV unIDs.," In the same sense, the RI decay model is a viable possibility for TeV unIDs."387 We have discussed the TeV gamma-ray emission from the z decay. 3 decay and the radio-isotope (RI) decay mechanisms in GRB and/or hypernova remnants. in. their possible role as TeV unIDs.," We have discussed the TeV gamma-ray emission from the $\pi^0$ decay, $\beta$ decay and the radio-isotope (RI) decay mechanisms in GRB and/or hypernova remnants, in their possible role as TeV unIDs."388 There is evidence that typical GRBs predominantly occur in galaxies with less metals than our own (Fruchteretal.2006:Stanek2006).. although the correlation between the host metallicity and the GRB energy Is not confirmed (Savaglioetal.2008a.b).," There is evidence that typical GRBs predominantly occur in galaxies with less metals than our own \citep{fru06,sta06}, although the correlation between the host metallicity and the GRB energy is not confirmed \citep{sav08a,sav08b}."389. On the other hand broad-lined SNe Ie also inhabit more metal-rich galaxies (Modjazetal.2008).. suggesting that at least hypernovae and possibly GRB/SNe with LL Jets can occur in our Galaxy.," On the other hand broad-lined SNe Ic also inhabit more metal-rich galaxies \citep{mod08}, suggesting that at least hypernovae and possibly GRB/SNe with LL jets can occur in our Galaxy."390 In addition. the evidence that GRBs occur in low metal regions could be biased because the GRBs in the metal rich region tend to have no optical afterglows due to the dust absorption (1.e.. dark GRBs. which ts about half of all GRBs).," In addition, the evidence that GRBs occur in low metal regions could be biased because the GRBs in the metal rich region tend to have no optical afterglows due to the dust absorption (i.e., dark GRBs, which is about half of all GRBs)."391 Then it becomes difficult to identify the hosts for measuring the metal abundance., Then it becomes difficult to identify the hosts for measuring the metal abundance.392 To discrimmate amongst these models. the imaging of the gamma-ray morphology would be useful.," To discriminate amongst these models, the imaging of the gamma-ray morphology would be useful."393" The z"" decay model predicts a shell structure. since the density inside the remnants is low, while the |. decay model predicts an elongated structure. and the RI decay model predicts a center-filled structure."," The $\pi^0$ decay model predicts a shell structure, since the density inside the remnants is low, while the $\beta$ decay model predicts an elongated structure, and the RI decay model predicts a center-filled structure."394 For remnant ages fa<10 yr. the SNR may be observed also at other wavelengths.," For remnant ages $t_{\rm age}< 10^5$ yr, the SNR may be observed also at other wavelengths."395" HESS J1731-347 may be such an example. which ts likely to be an old SNR with a large gamma-ray to radio flux ratio [ων/Fa,~33 (Tianetal.2008)."," HESS J1731-347 may be such an example, which is likely to be an old SNR with a large gamma-ray to radio flux ratio $F_{\rm TeV}/F_{\rm radio}\sim 33$ \citep{tian08}."396 HESS 11834-087 may be also an old remnant with an elongated gamma-ray emission outside the SNR (Aharonianetal.2006).. which could be interpreted in the conetxt of a ./-decay model (but see also Mukherjeeet(2008))).," HESS J1834-087 may be also an old remnant with an elongated gamma-ray emission outside the SNR \citep{aha06}, which could be interpreted in the conetxt of a $\beta$ -decay model (but see also \citet{muk08}) )."397 The x? decay model predicts detectable GeV emission if the spectral index of 2.1-2.4 continues down to the GeV region (see Fig. 3))., The $\pi^0$ decay model predicts detectable GeV emission if the spectral index of $2.1$ $2.4$ continues down to the GeV region (see Fig. \ref{fig:flux}) ).398" Other models predict relatively low levels of GeV emission (Fig.3::2006). although rare young remnants may be bright if ©,~20GeV(rIOyr) in the RI model."," Other models predict relatively low levels of GeV emission \citep[Fig.~\ref{fig:flux};, although rare young remnants may be bright if $\varepsilon_p \sim 20 {\rm GeV} (t/10^4 {\rm yr})$ in the RI model."399 This may be tested by the Fermi satellite., This may be tested by the Fermi satellite.400" Note that the GRB prompt and afterglow emission. will mask the very early RI decay emission, which becomes prominent later."," Note that the GRB prompt and afterglow emission will mask the very early RI decay emission, which becomes prominent later."401 The implied TeV neutrino flux (~ gamma-ray flux) is not enough for detection by current facilities., The implied TeV neutrino flux $\sim$ gamma-ray flux) is not enough for detection by current facilities.402 However. in thefuture one may in principle test models through the flavor ratio.," However, in thefuture one may in principle test models through the flavor ratio."403" We expect z.»ptt,>+rἘνtu, in the z decay model. no neutrinos in the .} decay model (since neutrinos are beamed and usually off-axis). and Re”Ee*p, in the RI decay model."," We expect $\pi^{+} \to \mu^{+} + \nu_{\mu}404\to e^+ + \nu_e + \bar \nu_{\mu} + \nu_{\mu}$ in the $\pi^0$ decay model, no neutrinos in the $\beta$ decay model (since neutrinos are beamed and usually off-axis), and ${}^{56}{\rm Co} \to {}^{56}{\rm Fe}^{*} + e^{+} + \nu_e$ in the RI decay model."405 As discussed at the end of 22.. the radio observations limit the (e/p)joc;v ratio to S10 in the z decay model.," As discussed at the end of \ref{sec:pi}, the radio observations limit the $(e/p)_{10{\rm GeV}}$ ratio to $\lesssim 10^{-3}$ in the $\pi^0$ decay model."406 For the RI decay model. the CRs need to freely escape from the acceleration site before suffering the adiabatic energy losses (see the end of ??)).," For the RI decay model, the CRs need to freely escape from the acceleration site before suffering the adiabatic energy losses (see the end of \ref{sec:ri}) )."407 The implied 8$CR energy budget is less than ~10%(10timesenergy)«(107rate) of the standard SN CR energy budget in our models.," The implied CR energy budget is less than $\sim 10\%408\sim (10\ {\rm times}\ {\rm energy}) \times (10^{-2}\ {\rm times}\ 409{\rm rate})$ of the standard SN CR energy budget in our models."410 The CRs above the knee at 3«I0P eV. however. could be produced mainly by extragalactic and/or Galactic GRBs/hypernovae (Wicketal. 2008)..," The CRs above the knee at $\sim 3 \times 10^{15}$ eV, however, could be produced mainly by extragalactic and/or Galactic GRBs/hypernovae \citep{wic04,minn06,wan07,bud08}. ."411 The chemical composition is increasingly richerin heavy nuclei above the knee ~3«10 eV to the second knee ~6«10! eV (Antonietal.2005:Abbasi 2005).. and possibly above ~3«10'? eV (Ungeretal. 2007)..," The chemical composition is increasingly richerin heavy nuclei above the knee $\sim 3 \times 10^{15}$ eV to the second knee $\sim 6 \times 10^{17}$ eV \citep{ant05,abb05}, , and possibly above $\sim 3 \times 10^{19}$ eV \citep{ung07}. ."412 These may be accelerated by Jets as in the RI decay model., These may be accelerated by jets as in the RI decay model.413 The GRB remnants may be also responsible. for the excesses of cosmic-ray positrons and electrons recently observed by the PAMELA and ATIC/PPB-BETS experiments, The GRB remnants may be also responsible for the excesses of cosmic-ray positrons and electrons recently observed by the PAMELA and ATIC/PPB-BETS experiments414The Cold Neutral Medii: (CNM) is easily studied with the 21-cu line absorption because the II opacity .OAXUIDS shove N(WD is the column density aud T the temperature.,"The Cold Neutral Medium (CNM) is easily studied with the 21-cm line absorption because the HI opacity $\propto {N({\rm HI}) \over T}$, where $N({\rm HI})$ is the column density and $T$ the temperature."415 The CNALD has been au inportaut subfield for the interstellar medi (ISM) in general aud radio astronomy in particular., The CNM has been an important subfield for the interstellar medium (ISM) in general and radio astronomy in particular.416 Theoretically the CNAL is understood as being oue of two thermal equilibria states of the neutral medimu (Fieldetal.1969:Melee&Os-triker1977:Wolfireetal. 2003).," Theoretically the CNM is understood as being one of two thermal equilibrium states of the neutral medium \citep{Field69,McKee77a,Wolfire03}."417". McIvee&Ostriker(1977) sununarized the expected properties for the CNAL clouds: a coustaut deusitv of 12 αμὉ, temperature of 80 I. cloud size between 0.1 aud 10 pe (with the mean value of 1.6 pc). the III cobuuu density ranging between 6.5s107? aud 1273«1079 cur2. with the mean value of 27<Lat? cm7."," \cite{McKee77a} summarized the expected properties for the CNM clouds: a constant density of 42 $^{-3}$, temperature of 80 K, cloud size between 0.4 and 10 pc (with the mean value of 1.6 pc), the HI column density ranging between $6.5\times10^{19}$ and $173\times10^{19}$ $^{-2}$, with the mean value of $27\times10^{19}$ $^{-2}$."418 Although thermal properties of the CNA aro VON well understood theoretically and observationally. its other aspects remain iuvsterious and not wellbstudied. primarily because of a paucity of observational knowledge.," Although thermal properties of the CNM are very well understood theoretically and observationally, its other aspects remain mysterious and not well-studied, primarily because of a paucity of observational knowledge."419 This observational paucity inchides such very basics as cloud shapes (morphology) aud the coblunn-deusity distribution: acconrpauiviug it is the theoretical paucity involving production mechanism of the CNAL. the dynamic equilibriuu between the CNAL and its enviroment (specifically. condensation. evaporation. aud turbulent musing). aud the time scales for formation aud destruction.," This observational paucity includes such very basics as cloud shapes (morphology) and the column-density distribution; accompanying it is the theoretical paucity involving production mechanism of the CNM, the dynamic equilibrium between the CNM and its environment (specifically, condensation, evaporation, and turbulent mixing), and the time scales for formation and destruction."420 Two important recent observational works are stimulating further work on this topic., Two important recent observational works are stimulating further work on this topic.421 One is the \Gllennimu Survey of 21-àà line absorption. of which he latest paper(Ileiles Trolaud 2005: ITT05) provides statistical distributions of the fundamental parameters: cohunn density. temperature. turbulence. aud magnetic field.," One is the Millennium Survey of 21-cm line absorption, of which the latest paper (Heiles Troland 2005; HT05) provides statistical distributions of the fundamental parameters: column density, temperature, turbulence, and magnetic field."422" The secoud is the detection of reliable. very weak "" ibsorption lines towards three high-latitude sources mBraun&Ἱναιοκα(2001) aud Braun [auckar DR05)."," The second is the detection of reliable, very weak HI absorption lines towards three high-latitude sources by \cite{Braun04} and Braun Kanekar (2005; BK05)."423 These latest very seusitive. HT absorption observations were undertaken with the Westerbork radio elescope. in the directions of four continuni sources. all located at high Calactic latitude (b~ 8073) aud relatively close to each other.," These latest very sensitive HI absorption observations were undertaken with the Westerbork radio telescope, in the directions of four continuum sources, all located at high Galactic latitude $b\sim80$ ) and relatively close to each other."424 The peak HI cussion iu hese cirections is van low. 25 I& oulv.," The peak HI emission in these directions is very low, 2–5 K only."425 For three out of our sources multiple absorption lines were detected. with he peak optical depth of only 0.1 to2%.," For three out of four sources multiple absorption lines were detected, with the peak optical depth of only 0.1 to."426. DIx05 discovered. cold IIT. clouds with the lowest III column densities ever detected for cold iuterstellar clouds. nore than 30 times lower than what is expected for the smallest CNALD clouds.," 	BK05 discovered cold HI clouds with the lowest HI column densities ever detected for cold interstellar clouds, more than 30 times lower than what is expected for the smallest CNM clouds."427 Fascinated by the discoveries of DI&05. and desiring to confirm their reality. we repeated heir observations for two sources; 3C286 and 3C287. with he Arecibo telescope.," Fascinated by the discoveries of BK05, and desiring to confirm their reality, we repeated their observations for two sources, 3C286 and 3C287, with the Arecibo telescope."428 We casily coufirmed fincdines by BISOS for 3€286., We easily confirmed findings by BK05 for 3C286.429 Against 30287 we see only a weak feature with too little signal/noise to iuclude im our discussion., Against 3C287 we see only a weak feature with too little signal/noise to include in our discussion.430 Iu this paper we report on the Arecibo observations of 30286 and 3C287 and discuss müplicatious of these findiugs., 	In this paper we report on the Arecibo observations of 3C286 and 3C287 and discuss implications of these findings.431 Our main ain is to cuphasize the existence of cold CNAL clouds with the IIT cola deusities ~1055 7. to discuss these. data in the context of previous observational results. and to initiate discussion on the possible origin of these clouds. as well as their importance in the ISAL.," Our main aim is to emphasize the existence of cold CNM clouds with the HI column densities $\sim10^{18}$ $^{-2}$, to discuss these data in the context of previous observational results, and to initiate discussion on the possible origin of these clouds, as well as their importance in the ISM."432 Iu Section 2 we briefly outline our observing and data processing methods., In Section 2 we briefly outline our observing and data processing methods.433 Section presents basic properties of cold HI clouds iu he directious of 3C286 and 30287., Section 3 presents basic properties of cold HI clouds in the directions of 3C286 and 3C287.434 À comparison of frese Clouds with CNM compoucuts forud iu previous observational studies is even m Section 1., A comparison of these clouds with CNM components found in previous observational studies is given in Section 4.435 Iu Section5 we discuss several different possibilities for he formation of these clouds., In Section 5 we discuss several different possibilities for the formation of these clouds.436 The observations were conducted with t1ο Arecibo, 	The observations were conducted with the Arecibo.437 Several hours of observiug tine were erauted at the discretion o “the Arecibo Observatory Director Sixto Gonzalez to evaluate the viability of future very seusitive III absorption measurements., Several hours of observing time were granted at the discretion of the Arecibo Observatory Director Sixto Gonzalez to evaluate the viability of future very sensitive HI absorption measurements.438 The observing procedure was the same as in Ποιος&Trolaud(2003a)., The observing procedure was the same as in \cite{Heiles03a}.439. A specific observing pattern. developed in Heiles&Trolaud(2003a).. was performed to cstimate the expected? TL cussion profile.," A specific observing pattern, developed in \cite{Heiles03a}, was performed to estimate the `expected' HI emission profile."440 This pattern geuerates oue on-source spectrum and 16 off-source spectra which are used to derive first aud second derivatives of the ITE emission on the sky., This pattern generates one on-source spectrum and 16 off-source spectra which are used to derive first and second derivatives of the HI emission on the sky.441subject of a future paper.,subject of a future paper.442" The equivalent widths of the H, emission components are related to the mass loss rates in OB stars (Leitherer 1988).", The equivalent widths of the $_{\alpha}$ emission components are related to the mass loss rates in OB stars (Leitherer 1988).443" The H, emission component in [22023 has an equivalent width (W, = ) comparable to that of the OSI star. HD152408 (W, = )."," The $_{\alpha}$ emission component in I22023 has an equivalent width $_{\lambda}$ = ) comparable to that of the O8I star, HD152408 $_{\lambda}$ = )."444" From this. we estimate a mass loss rate of 1.23 107? Mayr""! (Leitherer 1988)."," From this, we estimate a mass loss rate of $\times$ $^{-5}$ $_{\odot}$ $^{-1}$ (Leitherer 1988)."445 However. this value may be treated with caution.," However, this value may be treated with caution."446" In 122023. the large equivalent width of the H, emission component may be due to a large amount of gas in its circumstellar envelope or the presence of a bipolar envelope (Volk et al."," In I22023, the large equivalent width of the $_{\alpha}$ emission component may be due to a large amount of gas in its circumstellar envelope or the presence of a bipolar envelope (Volk et al."447 2004) and may not be directly related to the mass loss rate., 2004) and may not be directly related to the mass loss rate.448 DIBs.5780.410A.... . —.. and were identified in the spectrum of the star (Table 2).," DIBs, and were identified in the spectrum of the star (Table 2)."449 They have also been identified in other hot post-AGB stars e.g. IRASO1005+7910 (Klochkova et al., They have also been identified in other hot $-$ AGB stars e.g. IRAS01005+7910 (Klochkova et al.450 2002). IRAS13266-5551] IRASI7311—4924 (Sarkar et al.," 2002), $-$ 5551 $-$ 4924 (Sarkar et al."451 2005)., 2005).452sample calculated by this method: mesL<0.4.,sample calculated by this method: $\frac{L_{bol.}}{L_{Edd}} \lesssim 0.4$.453 The lower part ofM ligure 5 shows the histogram ol the Eddington ratios calculated in this section., The lower part of figure \ref{fig5} shows the histogram of the Eddington ratios calculated in this section.454" The results from the (wo methods of black hole mass caleulation agree: radio-Ioud AGN are powered by very massive central black holes. (vpically with M,>107.. and more often wilh A,~10M..."," The results from the two methods of black hole mass calculation agree: radio-loud AGN are powered by very massive central black holes, typically with $M_{\bullet} > 10^8 M_{\odot}$, and more often with $M_{\bullet} \sim 10^9 M_{\odot}$."455 These results are generally consistent with the black hole masses derived [or luminous raciio-loud AGN in other studies., These results are generally consistent with the black hole masses derived for luminous radio-loud AGN in other studies.456 Falomo.Ixotilaànen&Treves(2002) [ind masses in the range 5x10M. to 9xLOSAL. [or their sample of 7 low-redshift (2<0.055) BL Lacs. calculated from spectroscopic measurements of stellar velocity dispersion.," \citet{Falomo} find masses in the range $5\times 10^7 M_{\odot}$ to $9 \times 10^8 M_{\odot}$ for their sample of 7 low-redshift $z < 0.055$ ) BL Lacs, calculated from spectroscopic measurements of stellar velocity dispersion."457 These fall within the range of masses found for our sample of BL Lacs via the velocity dispersion relation. although they tend toward the low-mass end of that range.," These fall within the range of masses found for our sample of BL Lacs via the velocity dispersion relation, although they tend toward the low-mass end of that range."458 This may indicate an evolutionary or selection effect. between (he (wo epochs studied., This may indicate an evolutionary or selection effect between the two epochs studied.459 MeLure&Dunlop(2001). find black hole masses in the range 2x10M. to 2x10M. [or a sample of 22 radio-loud quasars. determined through reverberation mapping.," \citet{McLure3} find black hole masses in the range $2\times 10^8460M_{\odot}$ to $2\times 10^9 M_{\odot}$ for a sample of 22 radio-loud quasars, determined through reverberation mapping."461 These are consistent will the masses found for our high-power sample., These are consistent with the masses found for our high-power sample.462 Our results support the idea that. although some radio-quiet objects may host very massive central black holes (Dunlopetal.2002).. luminous radio sources may require them.," Our results support the idea that, although some radio-quiet objects may host very massive central black holes \citep{Dunlop}, luminous radio sources may require them."463 Dunlop οἱ al., Dunlop et al.464 suggest a black hole mass threshold [or radio-Ioud AGN of 5x109... which is supported by the black hole masses derived [rom bulge Iuminosity in this study.," suggest a black hole mass threshold for radio-loud AGN of $5 \times 10^8 M_{\odot}$, which is supported by the black hole masses derived from bulge luminosity in this study."465" Masses derived in this study via the M, σ, relation suggest a threshold of ~1x10M...", Masses derived in this study via the $M_{\bullet}$ $\sigma_e$ relation suggest a threshold of $\sim 1\times 10^8 M_{\odot}$.466 Whatever its value. we find that neither the threshold nor the distribution of black hole masses in raclio-loud AGN depends on the actual level of radio emission. within the range represented bv these radio sources. or on the overall energv output of the nucleus.," Whatever its value, we find that neither the threshold nor the distribution of black hole masses in radio-loud AGN depends on the actual level of radio emission, within the range represented by these radio sources, or on the overall energy output of the nucleus."467 As a consequence. radio-Ioud AGN exhibit an extremely broad range of accretion rates: from petσοκ10 to fen~1.0.," As a consequence, radio-loud AGN exhibit an extremely broad range of accretion rates; from $\frac{L_{bol.}}{L_{Edd}} \lesssim 2\times 10^{-4}$ to $\frac{L_{bol.}}{L_{Edd}} \sim 1.0$."468 Across this range the host galaxies span a remarkably light range of high stellar Iuminosities all within one magnitude of brightest. cluster galaxies suggesting that. al least for raclio-loud AGN. there is al most a very weak relation between (he properties of (he host galaxy and both the overall rate ancl the efficiency ol fuelling of the black hole.," Across this range the host galaxies span a remarkably tight range of high stellar luminosities — all within one magnitude of brightest cluster galaxies — suggesting that, at least for radio-loud AGN, there is at most a very weak relation between the properties of the host galaxy and both the overall rate and the efficiency of fuelling of the black hole."469 (5) Ίσα (08).,= ( ] ( ).470" so long as E.>me*/2h?z13.7eV.? Here, the factor Ce=7.40x10!!(n./cm?) eV. In this case, σεεοςE?lnE, so heating is somewhat more important at high energies, although σεε Still falls off by one power of energy faster than the ionization and excitation cross-sections."," so long as $E > me^4/2 \hbar^2 \approx 13.7 \eV$ Here, the factor $\zeta_e = 7.40 \times 10^{-11} (n_e/{\rm cm}^{-3})$ eV. In this case, $\sigma_{ee} \propto E^{-2} \ln E$, so heating is somewhat more important at high energies, although $\sigma_{ee}$ still falls off by one power of energy faster than the ionization and excitation cross-sections."471" Note that, when plasma effects are included, the cross-section is independent of the temperature of the gas, so we need not specify it in our calculations."," Note that, when plasma effects are included, the cross-section is independent of the temperature of the gas, so we need not specify it in our calculations."472" We use equation (12)) in our fiducial calculations, following ?.."," We use equation \ref{eq:coul-log}) ) in our fiducial calculations, following \citet{xu91}."473" Ignoring collective effects reduces the fraction of incident energy deposited as heat at E=100eV by a few percent, and it correspondingly increases the fractions of energy deposited in ionization and excitation."," Ignoring collective effects reduces the fraction of incident energy deposited as heat at $E \ga 100 \eV$ by a few percent, and it correspondingly increases the fractions of energy deposited in ionization and excitation."474 The density can also play a second role in collisional de-excitation of the target atoms and in populating the upper levels of the atoms (provided also that the temperature is sufficiently large)., The density can also play a second role in collisional de-excitation of the target atoms and in populating the upper levels of the atoms (provided also that the temperature is sufficiently large).475 This requires n>>10?cm? so is not important for the IGM., This requires $n \gg 10^8 \cmden$ so is not important for the IGM.476 But we caution readers against trusting our results in such environments., But we caution readers against trusting our results in such environments.477 We now present our main results., We now present our main results.478" As a reminder, we use 10° Monte Carlo trials for each electron energy (which ranges from 10-9900 eV), and we explicitly follow all secondary electrons and photons."," As a reminder, we use $10^5$ Monte Carlo trials for each electron energy (which ranges from $10$ –9900 eV), and we explicitly follow all secondary electrons and photons."479" We take f=0.05 and set the density of the background gas to be the mean cosmic density at z=10, but we saw above that the results are very insensitive to these parameters."," We take $f=0.05$ and set the density of the background gas to be the mean cosmic density at $z=10$, but we saw above that the results are very insensitive to these parameters."480 The primary input parameters are then the initial electron energy and the ionization fractions., The primary input parameters are then the initial electron energy and the ionization fractions.481" For the latter, we let x; be the density of HII relative to the total hydrogen density and assume that this is also the fraction of helium in the form of Hell, with zero Helll."," For the latter, we let $x_i$ be the density of HII relative to the total hydrogen density and assume that this is also the fraction of helium in the form of HeII, with zero HeIII."482" We present our results in terms of energy deposition fractions, with fion, feat, and fexcite the fractions of the initial energy that goes into ionization, heating, and HI line photons generated by collisional (Note that line photons from helium are transformed into ionizing photons and so deposit their energy in other ways, implicit in our code.)"," We present our results in terms of energy deposition fractions, with $f_{\rm ion}$, $f_{\rm heat}$, and $f_{\rm excite}$ the fractions of the initial energy that goes into ionization, heating, and HI line photons generated by collisional (Note that line photons from helium are transformed into ionizing photons and so deposit their energy in other ways, implicit in our code.)"483 We also let fLya be the fraction of energy deposited in HI photons., We also let $f_{\rm Ly\alpha}$ be the fraction of energy deposited in HI photons.484 We have verified explicitly that our code conserves energy throughout the entire interaction cycle., We have verified explicitly that our code conserves energy throughout the entire interaction cycle.485" Figure 1 shows these fractions, as a function of photon energy, in a medium with σι=0.01."," Figure \ref{fig:xh099} shows these fractions, as a function of photon energy, in a medium with $x_i=0.01$."486" The thick solid, dashed, and dotted curves Show fion, fheat, and fexcite, respectively."," The thick solid, dashed, and dotted curves show $f_{\rm ion}$, $f_{\rm heat}$, and $f_{\rm excite}$, respectively."487" The thin solid and dot-dashed curves show explicitly the fractions of energy going into HI and Hel ionization, respectively. ("," The thin solid and dot-dashed curves show explicitly the fractions of energy going into HI and HeI ionization, respectively. ("488The fraction going into Hell ionization is <1% throughout.),The fraction going into HeII ionization is $\ll 1\%$ throughout.)489" Finally, the thin dotted curve Shows frya."," Finally, the thin dotted curve shows $f_{\rm Ly\alpha}$."490 The structure of the curves is relatively easy to understand., The structure of the curves is relatively easy to understand.491" Electrons with E«10.2eV are unable to interact with any atoms or ions, so all of the energy is deposited as heat."," Electrons with $E<10.2 \eV$ are unable to interact with any atoms or ions, so all of the energy is deposited as heat."492" As F increases, more and more excitation and ionization processes become available, so the energy injected as heat decreases."," As $E$ increases, more and more excitation and ionization processes become available, so the energy injected as heat decreases."493" Interestingly, even with this large of a neutral fraction, the individual line thresholds do not introduce discrete features into the deposition fractions, and all of the parameters depend smoothly on energy."," Interestingly, even with this large of a neutral fraction, the individual line thresholds do not introduce discrete features into the deposition fractions, and all of the parameters depend smoothly on energy."494" At higher energies, where no additional processes become available, the fractions vary only slowly, eventually approaching reasonably constant values at E~ 1-10keV, where ionization, heating, and excitation split roughly equally."," At higher energies, where no additional processes become available, the fractions vary only slowly, eventually approaching reasonably constant values at $E \sim 1$ $10 \keV$, where ionization, heating, and excitation split roughly equally."495" As pointed out by ?,, the naive expectation from the Bethe approximation(with c;,«cxE~'lnE for ionization and excitation and σεεο.E~*?InE for heating), that less and less heating should occur at high photon energies, is false."," As pointed out by \citet{shull85}, the naive expectation from the Bethe approximation(with $\sigma_{i,e} \propto E^{-1} \ln E$ for ionization and excitation and $\sigma_{ee} \propto E^{-2} \ln E$ for heating), that less and less heating should occur at high photon energies, is false."496" This is because each ionization produces a moderate energy secondary electron (typically ~10eV, but occasionally much larger)."," This is because each ionization produces a moderate energy secondary electron (typically $\sim 10 \eV$, but occasionally much larger)."497" A large fraction of the primary's energy is lost through these intermediaries, who in turn lose most of their energy to heat, making the behavior at high energies much less variable than one would expect."," A large fraction of the primary's energy is lost through these intermediaries, who in turn lose most of their energy to heat, making the behavior at high energies much less variable than one would expect."498 Figures 2 and 3 show the energy deposition fractions for a range of z;., Figures \ref{fig:ion-heat} and \ref{fig:excite-lya} show the energy deposition fractions for a range of $x_i$.499 The first panel shows fios., The first panel shows $f_{\rm ion}$.500" For small x;, the ionization thresholds imprint features on the curves."," For small $x_i$, the ionization thresholds imprint features on the curves."501" At high energies, fion~0.4 at small ionized fractions and rapidly approaches zero as x; increases."," At high energies, $f_{\rm ion} \sim 0.4$ at small ionized fractions and rapidly approaches zero as $x_i$ increases."502 The behavior at very high energies sets an upper limit to the total energy invested in ionization., The behavior at very high energies sets an upper limit to the total energy invested in ionization.503 The left panel of Figure 3 shows the corresponding fractions lost to collisionally excited HI line photons., The left panel of Figure \ref{fig:excite-lya} shows the corresponding fractions lost to collisionally excited HI line photons.504 Note the line structure apparent at z;<10?; the features are separated by ~10eV and correspond to multiple excitations of HI atoms., Note the line structure apparent at $x_i \le 10^{-3}$; the features are separated by $\sim 10 \eV$ and correspond to multiple excitations of HI atoms.505" Although the structure around these features appears noisy, it is real and remains unchanged in other Monte Carlo tests."," Although the structure around these features appears noisy, it is real and remains unchanged in other Monte Carlo tests."506" However, as noted above these features blend together by x;~ 10?."," However, as noted above these features blend together by $x_i \sim 10^{-2}$ ."507" Note that collisional excitation becomes important at lower photon energies than does ionization, because the lines require less energy; in nearly neutral"," Note that collisional excitation becomes important at lower photon energies than does ionization, because the lines require less energy; in nearly neutral"508"using the RMS value of pv?/(poc2), to correspond to the SPH average.","using the RMS value of $\rho v^{2}/(\rho_{0} c_{s}^{2})$, to correspond to the SPH average."509 The Mach number evolution (Fig. 1)), The Mach number evolution (Fig. \ref{fig:vrms}) )510" is similar in both codes and at all resolutions up to around 4 tg, at which point all calculations show variations of order from each other."," is similar in both codes and at all resolutions up to around 4 $t_{d}$, at which point all calculations show variations of order from each other."511" No clear trends either between codes or with resolution are apparent, indicating that the variation observed is due to the stochastic nature of fully-developed turbulence producing different though statistically similar evolution (see Fig."," No clear trends either between codes or with resolution are apparent, indicating that the variation observed is due to the stochastic nature of fully-developed turbulence producing different though statistically similar evolution (see Fig."512 3 for the evidence for this in the density field)., \ref{fig:coldens512} for the evidence for this in the density field).513" It is these intermittent fluctuations that make turbulence code comparisons based on snapshot-to-snapshot comparison difficult, because the instantaneous turbulence field will quickly diverge between different codes in the fully developed regime because of the chaotic nature of the turbulence (see projections and slices for t22ta comparing the SPH and grid results)."," It is these intermittent fluctuations that make turbulence code comparisons based on snapshot-to-snapshot comparison difficult, because the instantaneous turbulence field will quickly diverge between different codes in the fully developed regime because of the chaotic nature of the turbulence (see projections and slices for $t \gtrsim 2 t_{d}$ comparing the SPH and grid results)."514 The evolution of maximum density (Fig. 2)), The evolution of maximum density (Fig. \ref{fig:rhomax}) )515" shows strong time variability in all six calculations, similar to the results shown in ?,Fig.2 and ?,Fig.2.."," shows strong time variability in all six calculations, similar to the results shown in \citet[][Fig.~2]{kritsuketal07} and \citet[][Fig.~2]{FederrathKlessenSchmidt2009}."516" For isothermal flows arbitrarily large density fluctuations can be produced, though with vanishingly small probability as can be inferred from the log-normal form of the PDF."," For isothermal flows arbitrarily large density fluctuations can be produced, though with vanishingly small probability as can be inferred from the log-normal form of the PDF."517" This simply reflects the highly intermittent nature of the density fluctuations in supersonic, turbulent flows."," This simply reflects the highly intermittent nature of the density fluctuations in supersonic, turbulent flows."518" The maximum density is a clear function of resolution in each code, showing no signs of convergence, as one might expect seeing as we are sampling the very highest data point in the PDF."," The maximum density is a clear function of resolution in each code, showing no signs of convergence, as one might expect seeing as we are sampling the very highest data point in the PDF."519 The results also demonstrate the evidently higher mass resolution in the SPH code: at 128? particles the maximum density resolvable in SPH is roughly similar to that resolved at 512? on the grid., The results also demonstrate the evidently higher mass resolution in the SPH code: at $128^{3}$ particles the maximum density resolvable in SPH is roughly similar to that resolved at $512^{3}$ on the grid.520 Using 512? SPH particles the maximum density resolved at RMS Mach 10 is roughly three-and-a-half orders of magnitude above the mean density which one might therefore expect to be similar to the mass resolution in a 2048? grid-based calculation., Using $512^{3}$ SPH particles the maximum density resolved at RMS Mach 10 is roughly three-and-a-half orders of magnitude above the mean density which one might therefore expect to be similar to the mass resolution in a $2048^{3}$ grid-based calculation.521" The projected column density fields at the highest resolution (512?) are shown forPHANTOM,, and the density field computed from the tracer particles in Fig."," The projected column density fields at the highest resolution $512^{3}$ ) are shown for, and the density field computed from the tracer particles in Fig."522" 3 (left, middle and right columns, respectively), at intervals of At—1t4 for the first four dynamical times."," \ref{fig:coldens512} (left, middle and right columns, respectively), at intervals of $\Delta t= 1 t_{d}$ for the first four dynamical times."523 The column density plots for SPH have been produced directly from the particles to a 2D pixel map using the visualisation tool (?) whilst the grid based results have been integrated through the grid., The column density plots for SPH have been produced directly from the particles to a 2D pixel map using the visualisation tool \citep{splashpaper} whilst the grid based results have been integrated through the grid.524 We show the integration through the z-direction in the codes., We show the integration through the $z$ -direction in the codes.525" At early times the calculations show clear agreement in the location of individual shocks (£=lta, top row) and in the development of large scale structures (&.=2t4, second row)."," At early times the calculations show clear agreement in the location of individual shocks $t=1 t_{d}$, top row) and in the development of large scale structures $t=2 t_{d}$, second row)."526" By t=Atq (fourth row) there is no longer clear correspondence even at the largest scales between codes, in agreement with the observed deviations in the time evolution of the RMS Mach number around this time (Fig. 1))."," By $t=4 t_{d}$ (fourth row) there is no longer clear correspondence even at the largest scales between codes, in agreement with the observed deviations in the time evolution of the RMS Mach number around this time (Fig. \ref{fig:vrms}) )."527" In terms of resolution, high-density structures appear better resolved in the SPH calculations at the same number of computational elements."," In terms of resolution, high-density structures appear better resolved in the SPH calculations at the same number of computational elements."528" However, the grid results tend to show better resolution of features in low density regions, as one might expect since in SPH the resolution is preferentially shifted from low density regions towards high density regions."," However, the grid results tend to show better resolution of features in low density regions, as one might expect since in SPH the resolution is preferentially shifted from low density regions towards high density regions."529 The excellent agreement between codes in the development of individual shock structures within the first dynamical times (top row) enabled us to make a very detailed comparison of features between codes which proved to be very helpful in the comparison process., The excellent agreement between codes in the development of individual shock structures within the first dynamical times (top row) enabled us to make a very detailed comparison of features between codes which proved to be very helpful in the comparison process.530" In particular it highlighted that, with the parameters we were initially using, some of the dense structures created by the collision of one or more shocks were rapidly losing definition in the SPH results, resulting in a noisy density field that was rather unlike the grid results (this is shown in more detail in Appendix A))."," In particular it highlighted that, with the parameters we were initially using, some of the dense structures created by the collision of one or more shocks were rapidly losing definition in the SPH results, resulting in a noisy density field that was rather unlike the grid results (this is shown in more detail in Appendix \ref{sec:viscosity}) )."531" The problem could be easily traced to be caused by particles penetrating or “overshooting” the shock front in these high Mach number shocks, a problem which the non-linear 3 (von-Neumann-Richtmyer) term in the SPH artificial viscosity (Eqs. 9--10))"," The problem could be easily traced to be caused by particles penetrating or “overshooting” the shock front in these high Mach number shocks, a problem which the non-linear $\beta$ (von-Neumann-Richtmyer) term in the SPH artificial viscosity (Eqs. \ref{eq:qvisc}- \ref{eq:vsig}) )"532 was designed to prevent (see?).., was designed to prevent \citep[see][]{monaghan89}.533" The problem was thus easily fixed by using a larger value for 2,;,..", The problem was thus easily fixed by using a larger value for $\beta_{visc}$.534" We have therefore used υιοε=4 throughout the paper, rather than the nominal B,;;.=2 which is widely used — and sufficient — for low Mach number calculations."," We have therefore used $\beta_{visc} = 4$ throughout the paper, rather than the nominal $\beta_{visc} = 2$ which is widely used — and sufficient — for low Mach number calculations."535 It should be noted that this makes very little difference to the overall dissipation rate since the linear viscosity term (o) dominates the numerical dissipation rate almost everywhere except at very strong divergence in the velocity field (where particle penetration can occur)., It should be noted that this makes very little difference to the overall dissipation rate since the linear viscosity term $\alpha$ ) dominates the numerical dissipation rate almost everywhere except at very strong divergence in the velocity field (where particle penetration can occur).536 Comparing the projected column density fields calculated using the tracer particles in the calculation (right column) to, Comparing the projected column density fields calculated using the tracer particles in the calculation (right column) to537 as a whole., as a whole.538 The IL I A 1215 absorption line iu Damped a svstenis. (DLAs. loge NOI 1)220.3). aud sub-DLAs 01ος. N(II I):20.3) can be fit for accurate colin density imcasurcuicuts due to the exteuded damping wines in the profile.," The H I $\lambda$ 1215 absorption line in Damped $\alpha$ systems (DLAs, log N(H $>$ 20.3) and sub-DLAs $<$ log N(H $<$ 20.3) can be fit for accurate column density measurements due to the extended damping wings in the profile."539 DLAs and sub-DLA svsteiis have been shown to contain the majority of the neutral gas in the Universe (Wolfeetal.1995:Péroux2003h:al. 2009)..," DLAs and sub-DLA systems have been shown to contain the majority of the neutral gas in the Universe \citep{Wol95, Per03b, Pro05, Not09b}."540 The DLAs are of particular importance for galactic chemical evolution studies., The DLAs are of particular importance for galactic chemical evolution studies.541" With such hieh cobhuun densities. the absorption lines from metal atoms are easily visible,"," With such high column densities, the absorption lines from metal atoms are easily visible."542 Also. svstenis with high column deusities are expected to remain mainly neutral due to self shiclding. alleviating the need for uucertaiu ionization corrections to the abundances.," Also, systems with high column densities are expected to remain mainly neutral due to self shielding, alleviating the need for uncertain ionization corrections to the abundances."543 There is still nmumeh debate as to the nature of the ealaxies hosting DLAs and sub-DLAs., There is still much debate as to the nature of the galaxies hosting DLAs and sub-DLAs.544 Even at low redshift. finding a faint galaxy near the bright poiut source of the QSO is challenging.," Even at low redshift, finding a faint galaxy near the bright point source of the QSO is challenging."545 At higher redshift. the cosmological dimaningof surface brielituess (jiX(L| :)!) makes galaxy detectious even more difficult.," At higher redshift, the cosmological dimming of surface brightness $\mu\propto(1+z)^4$ ) makes galaxy detections even more difficult."546 Nonetheless. these svstenis are a unique laboratory to study the ISM of galaxies over a wide range of redshifts.," Nonetheless, these systems are a unique laboratory to study the ISM of galaxies over a wide range of redshifts."547Gaussian lies along the .r-axis and the shortest axis along the z- so that 0.σα<p1.,"Gaussian lies along the $x$ -axis and the shortest axis along the $z$ -axis, so that $0\le q\le p\le 1$."548 The two usual polar coordinates (8.0) define the orientation of the line-of-sight with respect to the principal axes of the object.," The two usual polar coordinates $(\theta,\phi)$ define the orientation of the line-of-sight with respect to the principal axes of the object."549 Another angle c is required to specify the rotation of the object around the line-of-sight. and uniquely detine the orientation in space of the Gr.jy.2) coordinate system.," Another angle $\psi$ is required to specify the rotation of the object around the line-of-sight, and uniquely define the orientation in space of the $(x,y,z)$ coordinate system."550 This angle c is defined by the requirement that the + axis project onto the ;/ axis. or equivalently that the ο axis lies in the Gr.y) plane.," This angle $\psi$ is defined by the requirement that the $z$ axis project onto the $y'$ axis, or equivalently that the $x'$ axis lies in the $(x,y)$ plane."551 Once the viewing angles (4.0.c) have been assiumed.. given the observed axial ratio q' forthe Gaussian. the intrinsic axial ratios p and q ean be found using relations valid for general ellipsoidal bodies (e.g.. de Zeeuw Franx 1989) where 0=1.q'7.," Once the viewing angles $(\theta,\phi,\psi)$ have been , given the observed axial ratio $q'$ for the Gaussian, the intrinsic axial ratios $p$ and $q$ can be found using relations valid for general ellipsoidal bodies (e.g., de Zeeuw Franx 1989) where $\delta'=1-q'^2$."552 It should be noted that in general a solution may not be found for all assumed viewing angles (e.g.. Bertola et 11991).," It should be noted that in general a solution may not be found for all assumed viewing angles (e.g., Bertola et 1991)."553 If a triaxial deprojection is sought for the galaxy. then the viewing angles have to be the same for all the Gaussians and the permissible viewing angles for the object. assumed to be triaxial. will lie in the intersection of the permissible viewing angles of euch Gaussian (cf.," If a triaxial deprojection is sought for the galaxy, then the viewing angles have to be the same for all the Gaussians and the permissible viewing angles for the object, assumed to be triaxial, will lie in the intersection of the permissible viewing angles of each Gaussian (cf."554 Williams 198, Williams 1981).555 If an acceptable MGE model can be obtained by fixing the PA wy of all the Gaussians to the same value c. then the object can be deprojected by assuming it is axisymmetric (triaxial solutions yowever can be excluded FFranx 1988].," If an acceptable MGE model can be obtained by fixing the PA $\psi_j$ of all the Gaussians to the same value $\psi$, then the object can be deprojected by assuming it is axisymmetric (triaxial solutions however can be excluded Franx 1988])."556 In this case the ormulae of the previous section simplify considerabuc, In this case the formulae of the previous section simplify considerably.557 In the oblate axisymmetric case (p— 1). once an inclination i>0 (for?= Othe deprojection is degenerate) has been assumed or the galaxy 6.=90° corresponding to edge-on). one has: while in the prolate axisymmetric case (p= q) The oblate MGE deprojection above is only defined if cosseq7 for all Gaussians.," In the oblate axisymmetric case $p=1$ ), once an inclination $i>0$ (for $i=0$ the deprojection is degenerate) has been assumed for the galaxy $i=90^\circ$ corresponding to edge-on), one has: while in the prolate axisymmetric case $p=q$ ) The oblate MGE deprojection above is only defined if $\cos^2 i<q'^2_j$ for all Gaussians."558 This means that the flattest Gaussian in an MGE fit dictates the minimum possible inclination for which the MGE model ean be used in a dynamical model., This means that the flattest Gaussian in an MGE fit dictates the minimum possible inclination for which the MGE model can be used in a dynamical model.559 However since the Gaussian components don't necessarily have physical significance one don't want to base any conclusion of a dynamical model on this minimum inclination., However since the Gaussian components don't necessarily have physical significance one don't want to base any conclusion of a dynamical model on this minimum inclination.560 One simple way to avoid this problem consists in trying to increase the minimum axial ratio q' allowed in the MGE fit until the X7 increases significantly or the galaxy contour cannot be accurately reproduced any more with any number of Gaussians., One simple way to avoid this problem consists in trying to increase the minimum axial ratio $q'$ allowed in the MGE fit until the $\chi^2$ increases significantly or the galaxy contour cannot be accurately reproduced any more with any number of Gaussians.561 This Gi Will provide a good estimate of the minimum inclination for which the given galaxy. assumed to be axisymmetric. can be deprojected.," This $q'_{\rm max}$ will provide a good estimate of the minimum inclination for which the given galaxy, assumed to be axisymmetric, can be deprojected."562 Independently from an actual MGE tit. the limit to the above (duas is Set by the axial ratio q’ of the ellipse having the same curvature of the galaxy isophotes along the major axis. at the point of maximum curvature.," Independently from an actual MGE fit, the limit to the above $q'_{\rm max}$ is set by the axial ratio $q'$ of the ellipse having the same curvature of the galaxy isophotes along the major axis, at the point of maximum curvature."563 In fact there has to be at least one Gaussian flat enough to reproduce the maximum curvature along the major axis., In fact there has to be at least one Gaussian flat enough to reproduce the maximum curvature along the major axis.564 The potential generated by a triaxial Gaussian mass distribution of the form given in equation (62). can be evaluated using the classical Chandrasekhar (1969) formulae for densities stratified on similar concentric ellipsoids (see Binney Tremaine 1987. p. 61).," The potential generated by a triaxial Gaussian mass distribution of the form given in equation \ref{eq:density}) ), can be evaluated using the classical Chandrasekhar (1969) formulae for densities stratified on similar concentric ellipsoids (see Binney Tremaine 1987, p. 61)."565 In the MGE case the potential can be written as a one-dimensional 1) integral wheres =1ιοί q.Gisthe gravitational constant and Y is the mass-to-light-ratio.," In the MGE case the potential can be written as a one-dimensional (1D) integral where $\delta=1-p^2$, $\epsilon=1-q^2$, G is the gravitational constant and $\Upsilon$ is the mass-to-light-ratio."566 For oblate axisymmetric models (p= 1) this reduces to In the spherical ease (p=q 1) to Already for So&[i the error function ertRB(2σ)] —]to 16 digits accuracy and the spherical MGE potential can be replaced with high precision by the potential of a point mass enclosing the total mass 4=YL of the Gaussian component., For oblate axisymmetric models $p=1$ ) this reduces to In the spherical case $p=q=1$ ) to Already for $8\sigma\la R$ the error function ${\rm erf}[R/(\sqrt{2}\ \sigma)]=1$ to 16 digits accuracy and the spherical MGE potential can be replaced with high precision by the potential of a point mass enclosing the total mass ${\cal M}=\Upsilon L$ of the Gaussian component.567 Since the σ of the Gaussians in an MGE fit span various orders of magnitude in size. asymptotic expressions can also be conveniently used to estimate the triaxial or axisymmetric potential of equations CLE) and (123) at very small and very large radii as done in Cappellari et (2002).," Since the $\sigma$ of the Gaussians in an MGE fit span various orders of magnitude in size, asymptotic expressions can also be conveniently used to estimate the triaxial or axisymmetric potential of equations \ref{eq:pot_tri}) ) and \ref{eq:pot_axis}) ) at very small and very large radii as done in Cappellari et (2002)."568 We start by considering the MGE fit to. galaxies without isophote twists., We start by considering the MGE fit to galaxies without isophote twists.569" The determination of an axisymmetric MGE parametrization from the photometry. namely the fit of à sum of Gaussians with the same centre and PA. to a galaxy image seems to be a very simple problem that can be efficiently solved with general nonlinear minimization algorithms,"," The determination of an axisymmetric MGE parametrization from the photometry, namely the fit of a sum of Gaussians with the same centre and PA, to a galaxy image seems to be a very simple problem that can be efficiently solved with general nonlinear minimization algorithms."570 We assume for simplicity that the PA cof all Gaussians is known., We assume for simplicity that the PA $\psi$ of all Gaussians is known.571 We don't fit c since it is very easily measured before fitting., We don't fit $\psi$ since it is very easily measured before fitting.572 We found it fast and accurate to determine it fromthe weighted second moments of the surface brightness above a given level. as done by automatic galaxy extraction. packages (e.g. Bertin Arnouts 1996).," We found it fast and accurate to determine it fromthe weighted second moments of the surface brightness above a given level, as done by automatic galaxy extraction packages (e.g., Bertin Arnouts 1996)."573 It may also be measured with standard, It may also be measured with standard574layer of dust causes a large temperature gradient.,layer of dust causes a large temperature gradient.575 Following this result. we attributed a value of 0.01 W K! m' to the thermal conductivity of a crust composed only of silicatic particles.," Following this result, we attributed a value of 0.01 W $^{-1}$ $^{-1}$ to the thermal conductivity of a crust composed only of silicatic particles."576" In. the case of the ""organic"" distribution. lacking for direct measurements. we deduced the physical properties from the results of the laboratory experiments conducted at the Space Research Institute of Graz (Kómmle et al. 1996))."," In the case of the ""organic"" distribution, lacking for direct measurements, we deduced the physical properties from the results of the laboratory experiments conducted at the Space Research Institute of Graz (Kömmle et al. \cite{koemle}) )."577 The thermal evolution of an analogue of cometary material composed of a mixture of minerals. ices and hydrocarbons has been studied. obtaining a sort of cohesive crust composed of minerals glued together by organics.," The thermal evolution of an analogue of cometary material composed of a mixture of minerals, ices and hydrocarbons has been studied, obtaining a sort of cohesive crust composed of minerals glued together by organics."578 This kind of crust has a thermal conductivity higher than that of silicatic crust. and also has a greater cohesive strength: an admixture with organic material raises crust conductivity of one order of magnitude or more with respect to a crust composed of silicatic grains.," This kind of crust has a thermal conductivity higher than that of silicatic crust, and also has a greater cohesive strength: an admixture with organic material raises crust conductivity of one order of magnitude or more with respect to a crust composed of silicatic grains."579" So. our ""organic"" crust is characterized by a higher thermal conductivity than the ""silicatic one: we attributed to a crust mainly composed of organic particles a value of 0.2 W K! m*'. At the beginning of computations the dust particles are embedded in the porous ice."," So, our ""organic"" crust is characterized by a higher thermal conductivity than the ""silicatic"" one: we attributed to a crust mainly composed of organic particles a value of 0.2 W $^{-1}$ $^{-1}$ At the beginning of computations the dust particles are embedded in the porous ice."580 When the ice sublimates the embedded particles become free. in a number proportional to the amount of sublimated ice. and can undergo the drag exerted by the gas flux.," When the ice sublimates the embedded particles become free, in a number proportional to the amount of sublimated ice, and can undergo the drag exerted by the gas flux."581" Average pore size is increasing due to the ice sublimation: a “pore widening factor"" proportional to the amount of sublimated ice is locally applied to the pore average size."," Average pore size is increasing due to the ice sublimation: a ""pore widening factor"" proportional to the amount of sublimated ice is locally applied to the pore average size."582 In this way we are taking into account that a sublimating ice produces holes and cavities. and as a consequence free particles can move towards the surface (particles can move and be blown off only if their size is less than the local average pore size!).," In this way we are taking into account that a sublimating ice produces holes and cavities, and as a consequence free particles can move towards the surface (particles can move and be blown off only if their size is less than the local average pore size!)."583 Free particles that are found close to the surface can move toward the surface and be blown off or accumulate to form a dust mantle., Free particles that are found close to the surface can move toward the surface and be blown off or accumulate to form a dust mantle.584 Free particles are noving under the opposite effects of gravity and gas flux: only grains smaller than the pore average size can move toward the surface in the pore system., Free particles are moving under the opposite effects of gravity and gas flux; only grains smaller than the pore average size can move toward the surface in the pore system.585 When the 1ce is condensing. a proportional amount of free particles become embedded and the pores becomes smaller (porosity To determine how many particles can be blown off to contribute to dust flux. and how many can instead be accumulated on the surface. the different forees acting on the single grain are compared. obtaining for each distribution a critical radius. depending on grain density.," When the ice is condensing, a proportional amount of free particles become embedded and the pores becomes smaller (porosity To determine how many particles can be blown off to contribute to dust flux, and how many can instead be accumulated on the surface, the different forces acting on the single grain are compared, obtaining for each distribution a critical radius, depending on grain density."586" The critical radius represents the radius of the largest particle that can leave the surface of the comet: G is the gravitational constant. M, the mass of the comet. R, its radius. w its angular rotation velocity. ο the dust grain density. Φ/ο is the gas flux. and Vy, the velocity of the gas flux."," The critical radius represents the radius of the largest particle that can leave the surface of the comet: where $G$ is the gravitational constant, $M_n$ the mass of the comet, $R_n$ its radius, $\omega$ its angular rotation velocity, $\rho_{dust}$ the dust grain density, $\Phi_{H_{2}O}$ is the gas flux, and $V_{H_{2}O}$ the velocity of the gas flux."587 In the Eq. (5)), In the Eq. \ref{rstar}) )588 the numerator represents the lifting force exerted by the outflowing gases. and the denominator represents the gravitational attraction. corrected by the centrifugal force.," the numerator represents the lifting force exerted by the outflowing gases, and the denominator represents the gravitational attraction corrected by the centrifugal force."589 At each time step the number of free dust particles for each size class and the value of the critical radius are computed., At each time step the number of free dust particles for each size class and the value of the critical radius are computed.590 All the free particles with radius à.<a are considered ejected (blown off) and contribute to the dust flux. while those with &.>e accumulate on the surface.," All the free particles with radius $a~<~a^*$ are considered ejected (blown off) and contribute to the dust flux, while those with $a~\geq~a^*$ accumulate on the surface."591 This refractory surface layer (dust mantle) is not necessarily stable. and can be later on blown off if the gas flux is strong enough.," This refractory surface layer (dust mantle) is not necessarily stable, and can be later on blown off if the gas flux is strong enough."592 It could also increase in thickness 1f more and more particles are not able to leave the surface. substantially reducing and then quenching the gas flux.," It could also increase in thickness if more and more particles are not able to leave the surface, substantially reducing and then quenching the gas flux."593" Dust mantle compaction due to a volume reduction when ice is sublimated ts taken into account,", Dust mantle compaction due to a volume reduction when ice is sublimated is taken into account.594 If the dust mantle is not too thick the gas flux from the interior is able to entrain a dust flux. so it is possible to have a dust flux even when there is no ice left on the In this way. even an originally homogeneous body becomes quickly highly inhomogeneous: composition. density and porosity are changing with depth.," If the dust mantle is not too thick the gas flux from the interior is able to entrain a dust flux, so it is possible to have a dust flux even when there is no ice left on the In this way, even an originally homogeneous body becomes quickly highly inhomogeneous: composition, density and porosity are changing with depth."595 A thermal model depends not only on the assumptions of the model itself. but also on the values attributed to the initial parameters.," A thermal model depends not only on the assumptions of the model itself, but also on the values attributed to the initial parameters."596 These parameters describe the orbit. the initial state of the body and the properties of the matter of which it is composed.," These parameters describe the orbit, the initial state of the body and the properties of the matter of which it is composed."597 They are defined or derived. when possible. from observation and laboratory experiments.," They are defined or derived, when possible, from observation and laboratory experiments."598" A given set of these parameters define a ""Case""."," A given set of these parameters define a ""Case""."599 By changing a small number of these parameters. and keeping fixed all the rest. we can build different Cases that are the subject of the To apply the above described model to a real case we need to define the characteristics of the body that we want to simulate. assuming an mitial structure and composition.," By changing a small number of these parameters, and keeping fixed all the rest, we can build different Cases that are the subject of the To apply the above described model to a real case we need to define the characteristics of the body that we want to simulate, assuming an initial structure and composition."600 As for the real case. we chose to simulate the behaviour of P/2005 Ul] (Read).," As for the real case, we chose to simulate the behaviour of P/2005 U1 (Read)."601 The results of this simulation can be applied also to the other MBCs known until now. because orbits and sizes are reasonably similar.," The results of this simulation can be applied also to the other MBCs known until now, because orbits and sizes are reasonably similar."602 As written before. we start from the assumption that the model body has a cometary nature. that is 1t is composed of ice and dust grains.," As written before, we start from the assumption that the model body has a cometary nature, that is it is composed of ice and dust grains."603 A further assumption is being made that the surface of the body is covered by a devolatilized mantle. and that a recently happened impact has opened a crater in this mantles.," A further assumption is being made that the surface of the body is covered by a devolatilized mantle, and that a recently happened impact has opened a crater in this mantles."604 As a consequence. the heat from the Sun is now able to reach ice-rich layers. so triggering a cometary-like activity (sublimating gas entraining dust particles).," As a consequence, the heat from the Sun is now able to reach ice-rich layers, so triggering a cometary-like activity (sublimating gas entraining dust particles)."605 At the beginning of the simulation. the immediate effects of the impact (release of heat) have already As for the composition and physical properties. it is difficult to make safe assumptions.," At the beginning of the simulation, the immediate effects of the impact (release of heat) have already As for the composition and physical properties, it is difficult to make safe assumptions."606 We have no reason to think. anyway. that these bodies are absolutely similar to the classical comets (Jupiter-family. Halley-family and Long Period comets). because their origin and evolution history ts different.," We have no reason to think, anyway, that these bodies are absolutely similar to the classical comets (Jupiter-family, Halley-family and Long Period comets), because their origin and evolution history is different."607 They formed closer to the Sun than the comets now stocked in the Kuiper Belt or Oort cloud., They formed closer to the Sun than the comets now stocked in the Kuiper Belt or Oort cloud.608 During the Solar System formation period materials from different distances, During the Solar System formation period materials from different distances609using ¢ Gem data.,using $\zeta$ Gem data.610 In this case we used photometry from Wisniewski&Johnson(1968). and Aloffeti&Barnes (1984).., In this case we used photometry from \citet{wj68} and \citet{mb84}. .611 In Table 8. we compare the derived surface brightness relations to similar relations from work based on non-variable supergiants (Fouque&Gieren1997) and other Cepheid observations (Nordegrenetal.2001)., In Table \ref{tab:sb} we compare the derived surface brightness relations to similar relations from work based on non-variable supergiants \citep{fg97} and other Cepheid observations \citep{nordgren01}.612. The Fy vs. V—HR fits can also be compared with the Gieren(1988) result Chat the slope of the V—H surface brightness relation (c) is weakly dependent on pulsational period (2?) according to which for a Aql predicts e=—0.376 and for ¢ Gem ¢=—0.319., The $F_{V}$ vs. $V-R$ fits can also be compared with the \citet{gieren88} result that the slope of the $V-R$ surface brightness relation (c) is weakly dependent on pulsational period $P$ ) according to which for $\eta$ Aql predicts $c = -0.376$ and for $\zeta$ Gem $c = -0.379$.613 These comparisons reveal generally good agreement between (he various relations in Table &.., These comparisons reveal generally good agreement between the various relations in Table \ref{tab:sb}.614 The relation between pulsational period and Cepheid radius has received considerable altention in the literature. primarily because early results based on dillerent techniques were discrepant (Fernie1984:Molfett&Barnes1987).," The relation between pulsational period and Cepheid radius has received considerable attention in the literature, primarily because early results based on different techniques were discrepant \citep{fernie84,mb87}."615. Period-radius relations are also useful in that they can indicate pulsation mode., Period-radius relations are also useful in that they can indicate pulsation mode.616 This is important for calibrating period-Iuminosity relations since different modes will vield different relations (Feast )..," This is important for calibrating period-luminosity relations since different modes will yield different relations \citep{fc97,nordgren01}."617 In Fig., In Fig.618 5. we compare our measured Cepheicl diameters to (he values predicted from a range of techniques: Dono.Caputo.&Marconi(1998) calculate a period-radius relation from [ull-amplitude. nonlinear. convective models for a range of metallicities ancl stellar masses.," \ref{fig:rad} we compare our measured Cepheid diameters to the values predicted from a range of techniques: \citet{bono98} calculate a period-radius relation from full-amplitude, nonlinear, convective models for a range of metallicities and stellar masses."619 Gieren.Molffett.&Barnes(1999) use the surface brightness technique based on W aud V—£2 photometry and (he Fouque&Gieren(1997). result to derive radii lor 116 Cepheids in the Galaxy and the Magellanie Clouds., \citet{gmb99} use the surface brightness technique based on $V$ and $V-R$ photometry and the \citet{fg97} result to derive radii for 116 Cepheids in the Galaxy and the Magellanic Clouds.620 They find an intrinsic width in their relationof z:0.03 in log h. Lanev&Stobie(1995) also use the surface brightness techuique for estimating, They find an intrinsic width in their relationof $\pm 0.03$ in log R. \citet{laney95} also use the surface brightness technique for estimating621of galaxies ancl even among the YSC's formed within one global galaxy-wide starburst.,of galaxies and even among the YSCs formed within one global galaxy-wide starburst.622 During a strong burst. typically lasting a few 100 vr in a massive gas-rich. ealaxy. a significant. increase of the ISM abundance may occur (Eritzev. Alvensleben Gerhardt 1994. their Fig.," During a strong burst, typically lasting a few $\times 10^8$ yr in a massive gas-rich galaxy, a significant increase of the ISM abundance may occur (Fritze–v. Alvensleben Gerhardt 1994, their Fig."623 12b)., 12b).624 Meanwhile. some fraction of the gas enriched. by dying first-generation. burst stars may well be shock-compressed to cool fast enough to be built into later generations of stars or clusters produced in the burst.," Meanwhile, some fraction of the gas enriched by dying first-generation burst stars may well be shock-compressed to cool fast enough to be built into later generations of stars or clusters produced in the burst."625 The same effect may occur when multiple bursts occur in a series of close encounters between two galaxies before their final merger., The same effect may occur when multiple bursts occur in a series of close encounters between two galaxies before their final merger.626 Hence. in extended: starburst: episodes. metallicity differences between YSC's formed carly on and [ate in the burst phase may be expected.," Hence, in extended starburst episodes metallicity differences between YSCs formed early on and late in the burst phase may be expected."627 Precise (relative) metallicity determinations for individual YSCs are not only important to study the questions raised. above. but also for the correct. derivation of ages [from broad-band colours.," Precise (relative) metallicity determinations for individual YSCs are not only important to study the questions raised above, but also for the correct derivation of ages from broad-band colours."628 Dust extinction is often very important in YSC systems., Dust extinction is often very important in YSC systems.629 In particular the voungest post-burst. galaxies ancl galaxies with ongoing starbursts often show strong ancl patchy dust structures ancl morphologies., In particular the youngest post-burst galaxies and galaxies with ongoing starbursts often show strong and patchy dust structures and morphologies.630 For instance. the voungest clusters in the overlap region of the two ealactic clises in the Antennac galaxies are completely obscurecl in the optical anc can only be detected. in near or miüd-infrared observations (Mirabel et al.," For instance, the youngest clusters in the overlap region of the two galactic discs in the Antennae galaxies are completely obscured in the optical and can only be detected in near or mid-infrared observations (Mirabel et al."631 1998. Mengel et al.," 1998, Mengel et al."632 2001)., 2001).633 Older merger remnants like NGC 7252 or NGC 3921 seem to have own their inner regions clear of all the gas left over from intense star formation during the burst (e.g... Schweizer et al.," Older merger remnants like NGC 7252 or NGC 3921 seem to have blown their inner regions clear of all the gas left over from intense star formation during the burst (e.g., Schweizer et al."634 1996)., 1996).635 Extinction estimates towards individual YSC's are therefore as important as individual metallicity estimates in order to obtain reliable ages and to be able to derive an age-normatised CLE or YSC mass function., Extinction estimates towards individual YSCs are therefore as important as individual metallicity estimates in order to obtain reliable ages and to be able to derive an age-normalised CLF or YSC mass function.636 Inclividual YSC spectroscopy. feasible today with Sm-class telescopes for the nearest systems. is very time-consuming. since observations of large numbers of clusters are required to obtain statistically significant results.," Individual YSC spectroscopy, feasible today with 8m-class telescopes for the nearest systems, is very time-consuming, since observations of large numbers of clusters are required to obtain statistically significant results."637 Multi-passbauxd imaging is à very interesting and useful alternative. as we will show below. in particular if it includes coverage of near-infrared (NIR) and/or ultraviolet. (UV) wavelengths.," Multi-passband imaging is a very interesting and useful alternative, as we will show below, in particular if it includes coverage of near-infrared (NIR) and/or ultraviolet (UV) wavelengths."638 The large majority of extragalactic star cluster studies done to date have essentially used two or three-passbancl aperture photometry. combined with theoretical stellar population synthesis models to obtain age estimates.," The large majority of extragalactic star cluster studies done to date have essentially used two or three-passband aperture photometry, combined with theoretical stellar population synthesis models to obtain age estimates."639 Phe accuracy to which this can be done obviously depends on the nuniber of different (broac-band) filters available as well as. crucially. on the actual wavelengths and wavelength range. covered by the observations. and on the PSE size compared to the cluster surface density. profile (ie. on how close to the observations were taken to the confusion limit for these clusters).," The accuracy to which this can be done obviously depends on the number of different (broad-band) filters available as well as, crucially, on the actual wavelengths and wavelength range covered by the observations, and on the PSF size compared to the cluster surface density profile (i.e., on how close to the observations were taken to the confusion limit for these clusters)."640 In this paper we assess the systematic uncertainties in age. extinction and metallicity determinations for YSC systems inherent to the use of broad-band. integrated colours.," In this paper we assess the systematic uncertainties in age, extinction and metallicity determinations for YSC systems inherent to the use of broad-band, integrated colours."641 We have ceveloped an evolutionary svnthesis optimisation technique that can be applied to photometric nmieasurements in à given number NON&4) of broad-band passbands., We have developed an evolutionary synthesis optimisation technique that can be applied to photometric measurements in a given number $N (N \ge 4)$ of broad-band passbands.642 “Phe optimisation routine then. simultaneously determines the best combination of age. extinction. and metallicity. from a comparison with the most. up-to-date Gotttingen simple stellar population (SSP) mocdels (Schulz et al.," The optimisation routine then simultaneously determines the best combination of age, extinction and metallicity from a comparison with the most up-to-date Götttingen simple stellar population (SSP) models (Schulz et al."643 2002). to which we have added the contributions of an exhaustive set of gaseous emission. lines. ancl gaseous continuum emission. GXndeors. Eritzev. Alvensleben cle Cirijs 2002. Anders Fritzev. Alvensleben 2003).," 2002), to which we have added the contributions of an exhaustive set of gaseous emission lines and gaseous continuum emission (Anders, Fritze–v. Alvensleben de Grijs 2002, Anders Fritze–v. Alvensleben 2003)."644 We also compare these results with similar determinations based on w Starburst99 SSP models (Leitherer et al., We also compare these results with similar determinations based on the Starburst99 SSP models (Leitherer et al.645 1999). but assuming fixed. solar metallicity for our sample clusters.," 1999), but assuming fixed, solar metallicity for our sample clusters."646 Although this is an often-used assumption. we will show that us introduces significant systematic cllects in the final age istribution. and therefore also in the mass clistribution.," Although this is an often-used assumption, we will show that this introduces significant systematic effects in the final age distribution, and therefore also in the mass distribution."647 We decided to focus our ellorts on the nearby. well-studied starburst galaxy NGC 3310. known to harbour large numbers of voung star clusters. for which multi-passband observations from the near-UV to the NIU are. reaclily available from theHS Data Archive (Section 2:: see also Elmeercen et al.," We decided to focus our efforts on the nearby, well-studied starburst galaxy NGC 3310, known to harbour large numbers of young star clusters, for which multi-passband observations from the near-UV to the NIR are readily available from the Data Archive (Section \ref{obs.sect}; see also Elmegreen et al."648 2002. hereafter. E02).," 2002, hereafter E02)."649 In Section 4d. we first place the NGC 3310 starburst in its physical context., In Section \ref{ngc3310.sect} we first place the NGC 3310 starburst in its physical context.650 We then discuss the derived age distribution of the cluster population. which we extend compared to previous work. in terms of the evolution of the CLE and the interaction stage of its parent galaxy in Sections 5. and 6...," We then discuss the derived age distribution of the cluster population, which we extend compared to previous work, in terms of the evolution of the CLF and the interaction stage of its parent galaxy in Sections \ref{agedet.sec} and \ref{interpretation.sec}. ."651 We summarise our main results and conclusions in Section 7.., We summarise our main results and conclusions in Section \ref{summary.sect}.652 Finally. we will apply our knowledge of the svstematic uncertainties eained in this paper to a larger sample of nearby starburst and interacting galaxies drawn from theUST GO-s5645 programme (Winclhorst ct al.," Finally, we will apply our knowledge of the systematic uncertainties gained in this paper to a larger sample of nearby starburst and interacting galaxies drawn from the GO-8645 programme (Windhorst et al."653 2002) in Papers HE ancl HI (de Cirijs et al..," 2002) in Papers II and III (de Grijs et al.,"654 in prep.)., in prep.).655 NGC 3310 is a representative member of the class of galaxies often showing signs of active starbursts and recently formed star clusters., NGC 3310 is a representative member of the class of galaxies often showing signs of active starbursts and recently formed star clusters.656 The galaxy may have been a normal. quiescent Sbe-tvpe galaxy before it started to produce large numbers of new stars. possibly due to the merger with a gas-rich metallicity companion (cf.," The galaxy may have been a normal, quiescent Sbc-type galaxy before it started to produce large numbers of new stars, possibly due to the merger with a gas-rich low-metallicity companion (cf."657 Ixobulnicky Skillman 1995)., Kobulnicky Skillman 1995).658 As part ofHST programme CGO-8645.. we. obtained observations of NGC 3310 through the E300. ΟΡΝΤΟ and Fsi4Ww filters (Winchorst ct al.," As part of programme GO-8645, we obtained observations of NGC 3310 through the F300W (“UV”) and F814W filters (Windhorst et al."659 2002). with the galaxy centre located on chip 3 of the Wide Field. Planetary Camera 2 (WEPC?).," 2002), with the galaxy centre located on chip 3 of the Wide Field Planetary Camera 2 )."660 Observations in aclelitional passbancds were obtained from theHST Data Archive., Observations in additional passbands were obtained from the Data Archive.661 ln order to obtain the largest common Ποιά of view (FoV) in the optical wavelength range. we restricted these archival data to be taken with theWEPC2.," In order to obtain the largest common field of view (FoV) in the optical wavelength range, we restricted these archival data to be taken with the."662 In addition. we obtained archival. NIIS. images taken with the Near-IEnfrared. Cameraand. Multi-Object. Spectrometers. (NICAIOS) camera. 2.," In addition, we obtained archival NIR images taken with the Near-Infrared Cameraand Multi-Object Spectrometer's (NICMOS) camera 2,"663The results for our cosmological parameters are shown in Fieure 6.. where we plot the nunmber of supernovae that could be observed per vear ancl per square degree.,"The results for our cosmological parameters are shown in Figure \ref{fig:snr}, where we plot the number of supernovae that could be observed per year and per square degree."664 Note that this ligure does not incorporate magnitude limits or observational selection functions. but does simply show the predicted number of supernovae (hat can in principle be observed.," Note that this figure does not incorporate magnitude limits or observational selection functions, but does simply show the predicted number of supernovae that can in principle be observed."665 The redshift distribution of SNe follows the star formation rate. peaking αἱ 25 for Pop II. and showing the same break al 2=30 lor PISNe as in Figure 2..," The redshift distribution of SNe follows the star formation rate, peaking at $z\sim5$ for Pop II, and showing the same break at $z=30$ for PISNe as in Figure \ref{fig2}."666 We expect the transition from preclominantiv PISNe to Pop II SNe to occur around a redshift of 2~15—20 (see Figure 4)). and we therelore show the rates for both tvpes of supernova in this redshift range.," We expect the transition from predominantly PISNe to Pop II SNe to occur around a redshift of $z\sim66715-20$ (see Figure \ref{fig:metal}) ), and we therefore show the rates for both types of supernova in this redshift range."668 As this transition occurs. we expect the Pop II SN rate to gradually drop below the solid line towards hieher redshifts as Pop II star formation switches off.," As this transition occurs, we expect the Pop II SN rate to gradually drop below the solid line towards higher redshifts as Pop II star formation switches off."669 Similarly we expect the Pop HI (Pop IL5) rate to drop below the dashed (dotted) line towards lower recdshilts as Pop III star formation ceases., Similarly we expect the Pop III (Pop II.5) rate to drop below the dashed (dotted) line towards lower redshifts as Pop III star formation ceases.670 We do not expect anv VAISs at ο<15. but we extend our caleulation down to z=7 because the reionization of the universe al roughly this recshilt provides a robust lower limit for the end of VAIS formation (e.g..Ohetal.2001).," We do not expect any VMSs at $z\la 15$, but we extend our calculation down to $z=7$ because the reionization of the universe at roughly this redshift provides a robust lower limit for the end of VMS formation \citep[e.g.,][]{Ohetal01}."671. That the PISN and Pop IE ον rates are so similar ad the transition redshilts is because the star mamation rate for Pop III al z15 which we predict analytically is similar (o the rate (for Pop II) found in the simulations of Springel&IHernequist. (see Figure 1))., That the PISN and Pop II SN rates are so similar at the transition redshifts is because the star formation rate for Pop III at $z\sim15$ which we predict analytically is similar to the rate (for Pop II) found in the simulations of \citeauthor{SprHer02} (see Figure \ref{fig1}) ).672 Again. we Mnphasize (hat the break in the VMS supernova rate at z=30 is artificially sharp. reflecting the abrupt transition in (he underlving star formation rate.," Again, we emphasize that the break in the VMS supernova rate at $z=30$ is artificially sharp, reflecting the abrupt transition in the underlying star formation rate."673 In terms of total numbers of supernovae. we predict ~2x10 PISNe per vear over je whole skv(above 2= 15). or about 50 per square degree per vear.," In terms of total numbers of supernovae, we predict $\sim 2\times10^6$ PISNe per year over the whole sky(above $z=15$ ), or about 50 per square degree per year."674 This still comprises only ~0.4 of all supernovae. as we find ~4x105 SNell per νου (all skv). a value comparable (ο previous estimates (Miralda-Escudé&Rees1997:Macdauetal.1993).," This still comprises only $\sim 0.4$ of all supernovae, as we find $\sim 4\times 10^8$ SNeII per year (all sky), a value comparable to previous estimates \citep{MirRee97,MadDelPan98}."675.. This number can be understood by a simple order of magnitude estimate as follows., This number can be understood by a simple order of magnitude estimate as follows.676" About of the barvons in (he universe are in stus by the present time. giving a local density in stus of p,c0.10rpua0GX105NL,/Mpc* for our cosmological parameters (Peebles1993)."," About of the baryons in the universe are in stars by the present time, giving a local density in stars of $\rho_* \simeq 0.1\Omega_b \rho_{\rm crit}677 \sim 6\times 10^8 \;\msun/{\rm Mpc^3}$ for our cosmological parameters \citep{Pee93}."678. The size ol the observable universe is 10 Gpe out to z=5 (most of the star formation happens later (han 2=5 because there is very little physical time belore (his). so the total mass in stars in (his volume. ignoring redshift evolution effects. is ~107M...," The size of the observable universe is $\sim 10$ Gpc out to $z=5$ (most of the star formation happens later than $z=5$ because there is very little physical time before this), so the total mass in stars in this volume, ignoring redshift evolution effects, is $\sim 10^{21.5}\;\msun$."679" About of the lass in stars goes into stars which can explode. sothe mass in supernovae is ~107ML,,"," About of the mass in stars goes into stars which can explode, sothe mass in supernovae is $\sim 10^{20.5}\;\msun$."680 The mass weighted average for a supernova progenitors mass is e30 M... and (he age of (he universe is 14 Gyr.," The mass weighted average for a supernova progenitor's mass is $\sim30\;\msun$ , and the age of the universe is $14\;{\rm Gyr}$ ."681 The number of supernovae per vear is then, The number of supernovae per year is then682NSERC and ολα.,NSERC and CIfAR.683 CAV acknowledges support from NSF eraut. AST-0909198., GW acknowledges support from NSF grant AST-0909198.684 Facilities:S," Facilities:,"685 Facilities:Sp," Facilities:,"686 Facilities:Spi," Facilities:,"687 Facilities:Spit," Facilities:,"688 Facilities:Spitz," Facilities:,"689 Facilities:Spitze," Facilities:,"690 Facilities:Spitzer," Facilities:,"691 Facilities:Spitzer.," Facilities:,"692 Facilities:Spitzer..," Facilities:,"693 Facilities:Spitzer...," Facilities:,"694be quantified by a luminosity-weighted age fractional change right).,be quantified by a luminosity-weighted age fractional change ).695 However. these galaxies can still accomodate the tight CM relation found in local clusters right).," However, these galaxies can still accomodate the tight CM relation found in local clusters )."696 In the framework of current models of star formation. one could accomodate this trend with lower star formation efficiencies in fainter galaxies. also resulting in a significant change with redshift of the slope of the correlation between mass-to-light ratio and mass (Ferreras Silk 2000).," In the framework of current models of star formation, one could accomodate this trend with lower star formation efficiencies in fainter galaxies, also resulting in a significant change with redshift of the slope of the correlation between mass-to-light ratio and mass (Ferreras Silk 2000)."697 This would imply that in the latest merging stages the less massive early-type systems could still undergo some star formation. whereas more massive galaxies would just merge stars and hot gas. without triggering star formation.," This would imply that in the latest merging stages the less massive early-type systems could still undergo some star formation, whereas more massive galaxies would just merge stars and hot gas, without triggering star formation."698 The fact that the method presented here ts very sensitive to small fractions of young stars poses a strong constraint on recent star formation in massive ellipticals., The fact that the method presented here is very sensitive to small fractions of young stars poses a strong constraint on recent star formation in massive ellipticals.699 We should emphasize that our claim only applies to the scatter at faint magnitudes. since red faint galaxies might lie beyond the detection limit of the archival F300W images used here.," We should emphasize that our claim only applies to the scatter at faint magnitudes, since red faint galaxies might lie beyond the detection limit of the archival F300W images used here."700 There are two possible alternatives to explain the blueness of these faint early-type systems., There are two possible alternatives to explain the blueness of these faint early-type systems.701 However. one can argue against them for the following reasons:," However, one can argue against them for the following reasons:"702since strong HICN emission is detected.,since strong HCN emission is detected.703 has a CLII;CN 11)/7CO (2.1) integrated intensitv ratio of 0.005. in good agreement with the value of 0.043 in 2008).," has a $_3$CN $^{13}$ CO (2–1) integrated intensity ratio of 0.058, in good agreement with the value of 0.043 in \citep{he08}."704 Strong C'S emission has been detected in our survey., Strong CS emission has been detected in our survey.705 According to (1993).. CS can be rapidly destroved by shocks which might occur after a star leaves the AGB stage and ejects material in a very fast wind (Ilerpinetal.2002).," According to \citet{willacy98}, CS can be rapidly destroyed by shocks which might occur after a star leaves the AGB stage and ejects material in a very fast wind \citep{herpin02}."706. Therefore. the high abundance of CS in suggests that shocks are not important for the chemistry in this C-rich envelope.," Therefore, the high abundance of CS in suggests that shocks are not important for the chemistry in this C-rich envelope."707 Three refractory Si-bearing species (SiO. SiS. and S1Cs) were detected in 6.," Three refractory Si-bearing species (SiO, SiS, and $_2$ ) were detected in ."708. Although other Si-bearing species were detected in (Cernicharoetal.2000).. emission from the other Si-bearing species is relatively faint and should be below the detection limit of our observations of 6.," Although other Si-bearing species were detected in \citep{cernicharo00}, emission from the other Si-bearing species is relatively faint and should be below the detection limit of our observations of ."709. We find that the abunclances of SiO and SiCs in are similar to those in determined by Ileetal.(2008)., We find that the abundances of SiO and $_2$ in are similar to those in determined by \citet{he08}.710. Although the situation may be complicated by optical depth effects. the WON/SiO line intensity ratio has (he potential to provide a useful tool to discriminate between C-riehi and O-rich envelopes and is a good (racer of mass loss rate for AD and ο stars (seee.g.Diegingetal.2000).," Although the situation may be complicated by optical depth effects, the HCN/SiO line intensity ratio has the potential to provide a useful tool to discriminate between C-rich and O-rich envelopes and is a good tracer of mass loss rate for M and S stars \citep[see e.g.][]{bieging00}."711. The HCN (82)/SiO (65) intensity ratio in is 8.4. in good agreement the value of 9.7 in (IIeetal.2008).," The HCN (3–2)/SiO (6–5) intensity ratio in is 8.4, in good agreement the value of 9.7 in \citep{he08}."712. There is no evidence showing that the ION/SiO line intensity ratio has dependance on (he mass loss rate of C-rich stars., There is no evidence showing that the HCN/SiO line intensity ratio has dependance on the mass loss rate of C-rich stars.713 GonzálezDelgadoetal.(2003) ancl Schoieretal.(2006) found a correlation between the mass loss rate and the SiO abundance for AGB stars., \citet{gonzalez03} and \citet{schoier06} found a correlation between the mass loss rate and the SiO abundance for AGB stars.714 This is described as of SiO molecules onto dust grains., This is described as freeze-out of SiO molecules onto dust grains.715 The similarity of the SiO abundances in and suggests that the depletion of SiO onto dust grains might be insignificant for the two C-rich envelopes., The similarity of the SiO abundances in and suggests that the depletion of SiO onto dust grains might be insignificant for the two C-rich envelopes.716 Our observations show that the SiS abundance in is lower than that in IRC+10216., Our observations show that the SiS abundance in is lower than that in .717. The Sis (14.13)/SiO (65) intensity ratio in is 1.1. about half of that in found by IIeetal. (2008)..," The SiS (14–13)/SiO (6–5) intensity ratio in is 1.1, about half of that in found by \citet{he08}. ."718 Schóieretal.(2007) cidnot finda strong correlation between tlie massloss rate and the SiS abundance. suggesting," \citet{schoier07} didnot finda strong correlation between the massloss rate and the SiS abundance, suggesting"719stars in individual LMC clusters as given in Grocholski et al.,stars in individual LMC clusters as given in Grocholski et al.720 have not been corrected for age and metallicity according to the formulation given by those authors. as this actually. increases the dispersion in distance modulus.," have not been corrected for age and metallicity according to the formulation given by those authors, as this actually increases the dispersion in distance modulus."721 Combining the mean Weyiss magnitudes for. the solar. neighbourhood and the LALC gives an uncorrected LAIC clistance modulus of 1S.505+0.019., Combining the mean $_{2MASS}$ magnitudes for the solar neighbourhood and the LMC gives an uncorrected LMC distance modulus of $\pm$ 0.019.722 Applying Ix-band corrections for the age and. metallicity cillerences between LAIC ancl solar-neighborhooc red. clump populations of -0.03 (Salaris Cirarcli 2002) gives a truc LALC Ix-band distance modulus of LS.4A75-40.0 21. where we have somewhat arbitrarily allowed for an uncertainty of 0.01. mag in the population correction.," Applying K-band corrections for the age and metallicity differences between LMC and solar-neighborhood red clump populations of -0.03 (Salaris Girardi 2002) gives a 'true' LMC K-band distance modulus of $\pm$ 0.021, where we have somewhat arbitrarily allowed for an uncertainty of 0.01 mag in the population correction."723 The only L-band mean magnitude for LMC red clump stars currently available in the literature is ονiss=17.03+0.06 from Ixoerwer (2009)., The only H-band mean magnitude for LMC red clump stars currently available in the literature is $H_{2MASS} = 17.03\pm0.06$ from Koerwer (2009).724 On the assumption that H-Ix. is about equal in LMC anc solar neighborhoot red clump stars (given that H-Ix. is insensitive to. both temperature and metallicity). we apply the same population correction as for Ix to get an L-band LAC modulus of 1S8.49+0.06. in good agreement with the K-band value bu much less tightly. constrained.," On the assumption that H-K is about equal in LMC and solar neighborhood red clump stars (given that H-K is insensitive to both temperature and metallicity), we apply the same population correction as for K to get an H-band LMC modulus of $\pm$ 0.06, in good agreement with the K-band value but much less tightly constrained."725 For LMC red clump stars in the J band. we have use the values given by Szewezvk et al. (," For LMC red clump stars in the J band, we have used the values given by Szewczyk et al. ("7262008). as neither Alves et al. (,"2008), as neither Alves et al. ("7272002) nor CGrocholski et al. (,2002) nor Grocholski et al. (7282007) provide J-baux measurements.,2007) provide J-band measurements.729 We get a mean Joyass for LMC red clump stars of 4040.02. and hence anuncorrcehed LM clistance nmiocdulus of 15.950.009.," We get a mean $_{2MASS}$ for LMC red clump stars of $\pm$ 0.02, and hence an LMC distance modulus of $\pm$ 0.03."730 Ehe ciscrepaney between this ane the corrected. Ix-band: modulus is unsurprising. since the mean οτί for τος clump stars in the LAIC is about 0.13 bluer than in the solar neighbourhood. indicating that a substantial population correction would. be required.," The discrepancy between this and the corrected K-band modulus is unsurprising, since the mean J-K for red clump stars in the LMC is about 0.13 bluer than in the solar neighbourhood, indicating that a substantial population correction would be required."731 Our results suggest that this correction would lie roughly halfway between the value for E (0.2. Cirardi Salaris 2001) and Ix (-0.03. Salaris Cirardi 2002).," Our results suggest that this correction would lie roughly halfway between the value for I (0.2, Girardi Salaris 2001) and K (-0.03, Salaris Girardi 2002)."732 The mean red clump absolute magnitude in Ix derived above is consistent with that of Alves (2000). although an exact comparison is dillicult. given the absence of a well-defined: standard svstem in the data used there.," The mean red clump absolute magnitude in K derived above is consistent with that of Alves (2000), although an exact comparison is difficult given the absence of a well-defined standard system in the data used there."733 Our result is. however. somewhat brighter than that derived. by CGroenewegen (2008).," Our result is, however, somewhat brighter than that derived by Groenewegen (2008)."734 This is not surprising in view of the rend toward fainter absolute magnitude with decreasing »wallax seen in our own data., This is not surprising in view of the trend toward fainter absolute magnitude with decreasing parallax seen in our own data.735 Alves’ sample include a range of parallaxes similar to that used here. while CGroenewegen's sample included. only. stars more. distan han those we observed.," Alves' sample included a range of parallaxes similar to that used here, while Groenewegen's sample included only stars more distant than those we observed."736 The hypothesis considered. by CGroenewegen. that a bias might be present in his resul »ecause ofa lack of data for bright nearby rec clump stars. is hus confirmed.," The hypothesis considered by Groenewegen, that a bias might be present in his result because of a lack of data for bright nearby red clump stars, is thus confirmed."737 As all three studies use the same definition of the red clump (ice. Paezvisski Stanck 1998). this is no a [actor in the comparison.," As all three studies use the same definition of the red clump (i.e. Paczyńsski Stanek 1998), this is not a factor in the comparison."738 Thecorrected distance to the LMC derived: above is in good agreement with the Ix-band. red. clump distance derived by Alves ct al. (, The distance to the LMC derived above is in good agreement with the K-band red clump distance derived by Alves et al. (7392002) (18.494+0.03). which includes the same Salaris Girardi (2002) population correction.,"2002) $\pm$ 0.03), which includes the same Salaris Girardi (2002) population correction."740 Our distance is in excellent. agreement with Dietrzvsski. Gieren and Uelalski (2003) (18.50+0.01). who applied no correction for population dillerences.," Our distance is in excellent agreement with Pietrzyńsski, Gieren and Udalski (2003) $\pm$ 0.01), who applied no correction for population differences."741 Red clump LMC distances derived. using V. and | magnitudes would need. much larger anc more uncertain corrections [ου abundance and age cllects. and are best excluded. from comparison (Pictrzvisski et al.," Red clump LMC distances derived using V and I magnitudes would need much larger and more uncertain corrections for abundance and age effects, and are best excluded from comparison (Pietrzyńsski et al."742 2010)., 2010).743 While the K-band correction undoubtedly has some uncertainty attached. the correction itself is quite small.," While the K-band correction undoubtedly has some uncertainty attached, the correction itself is quite small."744 Thewnecorrected Ix-band. Cepheicl distance moduli. of Is.48+0.04 (Benedict ct al., The K-band Cepheid distance moduli of $\pm$ 0.04 (Benedict et al.745 2007) and IS470.03 (van Lecuwen οἱ al., 2007) and $\pm$ 0.03 (van Leeuwen et al.746 2007) are [likewise in excellent. agreement. especially with our eorreched distance.," 2007) are likewise in excellent agreement, especially with our distance."747 Phe uncorrected V-band and. Wis; distance moduli from Beneclict et al. (, The uncorrected V-band and $_{VI}$ distance moduli from Benedict et al. (7482007). 18.50 0.03 ancl IS.520.06. and the Wi modulus from van Leeuwen et al. (,"2007), 18.50 $\pm$ 0.03 and $\pm$ 0.06, and the $_{VI}$ modulus from van Leeuwen et al. ("7492007). 18.52zE0.03. are slightly larger. but LAIC Cepheids have long been known to be bluer at a given. period than Cepheids in the solar neighbourhood (Gascoigne Iron 1965. Laney Stobie 150. 1904). so this small dillerence is in the expected sense. though hardly significant.,"2007), $\pm$ 0.03, are slightly larger, but LMC Cepheids have long been known to be bluer at a given period than Cepheids in the solar neighbourhood (Gascoigne Kron 1965, Laney Stobie 1986, 1994), so this small difference is in the expected sense, though hardly significant."750 Agreement with the Cepheid moduli apparently also implies good agreement with the most recent RR Lyrac results from LIST parallaxes (Benedict AleArthur 2011)., Agreement with the Cepheid moduli apparently also implies good agreement with the most recent RR Lyrae results from HST parallaxes (Benedict McArthur 2011).751 bor Twpe Ib Cepheids. the latest results (Alatsunaga. Feast Alenzies 2009) give LS4640.10. which is in. very good agreement although considerably less precise.," For Type II Cepheids, the latest results (Matsunaga, Feast Menzies 2009) give $\pm$ 0.10, which is in very good agreement although considerably less precise."752 This supersedes the earlier result (Feast ct al., This supersedes the earlier result (Feast et al.753 2008). which eave a rather smaller nioclulus.," 2008), which gave a rather smaller modulus."754 Results from LMC eclipsing binaries are rather sparse. and only one result is available for a binary where empirical surface brightnesses are available (Pietrzvásski ct al.," Results from LMC eclipsing binaries are rather sparse, and only one result is available for a binary where empirical surface brightnesses are available (Pietrzyńsski et al."755 2009)., 2009).756 Agreement between their value for the LMC modulus (18.50+0.06) anc ours is reasonable enough. but a [final comparison will have to wait until results for the remaining seven binaries in that phase of the Araucaria Project are available.," Agreement between their value for the LMC modulus $\pm$ 0.06) and ours is reasonable enough, but a final comparison will have to wait until results for the remaining seven binaries in that phase of the Araucaria Project are available."757 Neat-LR. observations of 226 red clump stars as bright as A=0.3 have resulted in a determination of the local mean absolute magnitude in οντως and Keayyess accurate to +0.02 mag.," Near-IR observations of 226 red clump stars as bright as $K =758-0.3$ have resulted in a determination of the local mean absolute magnitude in $_{2MASS}$ and $_{2MASS}$ accurate to $\pm0.02$ mag."759 A comparison with Ix-band absolute magnitudes for LMC red. clump stars from the literature implies an LAIC distance. modulus. of 18.5030.02. (uncorrected). or 18.472E0.02 (corrected by the value given in Salaris Girardi 2002).," A comparison with K-band absolute magnitudes for LMC red clump stars from the literature implies an LMC distance modulus of $\pm0.02$ (uncorrected), or $\pm0.02$ (corrected by the value given in Salaris Girardi 2002)."760 Comparison of this result touncorrecled Copheid. PL-relation clistance moduli in the Ix-band. (van Leeuwen et al., Comparison of this result to Cepheid PL-relation distance moduli in the K-band (van Leeuwen et al.761 2007. )onedict et al.," 2007, Benedict et al."762 2007) suggests that metallicity corrections to distance moduli derived [rom near-H Cepheid PL relations may not be very significant. at least for abundances between those in the solar neighbourhood and in the LAIC.," 2007) suggests that metallicity corrections to distance moduli derived from near-IR Cepheid PL relations may not be very significant, at least for abundances between those in the solar neighbourhood and in the LMC."763 1n addition. the agreement between our cistance moclulus and those derived from Cepheid Wy; PL relations (van Lecuwen et al.," In addition, the agreement between our distance modulus and those derived from Cepheid $_{VI}$ PL relations (van Leeuwen et al."764 2007. Denedict et al.," 2007, Benedict et al."765 2007) suggests that )ono et al. (, 2007) suggests that Bono et al. (7662010) may be correct in arguing that metallicity corrections to distances from. Cepheid. Wesenheit (VI) PL relations may be fairly negligible.,2010) may be correct in arguing that metallicity corrections to distances from Cepheid Wesenheit (VI) PL relations may be fairly negligible.767 Aluch the sameholds for the V-band PLrelation (Benedict ο al., Much the sameholds for the V-band PLrelation (Benedict et al.768 2007). and these conclusions are strengthened by the recent results from RR Lyraes. Type LH," 2007), and these conclusions are strengthened by the recent results from RR Lyraes, Type II"769simplicity. we retain only the scattering term in. equation (7)). reducing it to In the 3l limit. equations (9)) and (10)) lead to an exponential growth of the pairdensity ancl velocity: for .r29r. where is the leneth-seale for pair loading.,"simplicity, we retain only the scattering term in equation \ref{dPdxa}) ), reducing it to In the $\beta \ll 1$ limit, equations \ref{dndxb}) ) and \ref{dPdxb}) ) lead to an exponential growth of the pairdensity and velocity: for $x > x_\pm$, where is the length-scale for pair loading."770" For a GRB of isotropic-cquivalent output energy. £-. equation (5)) gives for the acceleration length-scale at racius r where A=efl|2) is the geometrical thickness of he GARB front. % being the observed burst. duration. 2 the GIUDs redshift. and the usual scaling .X,,=V/10"" was used."," For a GRB of isotropic-equivalent output energy $E_\gamma$, equation \ref{lambda}) ) gives for the acceleration length-scale at radius $r$ where $\Delta = cT/(1+z)$ is the geometrical thickness of the GRB front, $T$ being the observed burst duration, $z$ the GRB's redshift, and the usual scaling $X_n = X/10^n$ was used."771 From equation (11)) we see that the wind acceleration ength-scale wv... defined by +Grae)=2 isa factor of a [ow arecr than wa.," From equation \ref{nb}) ) we see that the wind acceleration length-scale $x_{acc}$, defined by $\gamma (x_{acc}) = 2$ is a factor of a few larger than $x_\pm$ ."772" A simple estimate of uric. can be obtained ον equating the momentum deposited by photon scattering Dacelerpraes)PyzomeoeccEie)2=DacezynoscerefA} (considering that all photons have the same energy mocz,) with the momentum (acct|pectpemye of the medium. (assuming that the wind mass density. is dominated by the protons. Gru)Kp(rocnpsme). and that nyCroce) 8): Then equation (13)) shows that the wind is accelerated to a relativistic speed for radii smaller than >Meee We Can solve the pair density ancl momentun equations together to obtain nGr) ων"," A simple estimate of $x_{acc}$ can be obtained by equating the momentum deposited by photon scattering $\npair_{acc} (\sigma_T x_{acc})773(F_p \epsilon_p m_e c^2/c^2) = \npair_{acc}\epsilon_p(m_e c)(x_{acc}/\lambda)$ (considering that all photons have the same energy $m_e c^2 \epsilon_p$ ) with the momentum $(\npair_{acc} m_e +774n_{p,acc} m_p) c \sim \next m_p c$ of the medium (assuming that the wind mass density is dominated by the protons, $\npair (x_{acc}) \ll n_p(x_{acc})775(m_p/m_e)$, and that $n_p(x_{acc}) \approx \next$ ): Then equation \ref{xpm}) ) shows that the wind is accelerated to a relativistic speed for radii smaller than For $x \gg x_{acc}$ we can solve the pair density and momentum equations together to obtain $\npair(x)$ $\gamma(x)$."776" We consider a power-law solution of the form Substituting this into equations (9)) and (10)). and assuming that the mass density is dominated by protons Lc. the number of pairs per proton is much less than mpm... we obtain where yourfoc. og]Lmoraesfru is à constant independent of c. and inu;s ds determined. by the condition that the pair creation optical depth for a photon scattered at a; of energy ~cy. is unity between vii, and ir tine ds determined by thefollowing equation ὃν substituting (16)) in the above equation we find Minin explicitly Or Lt follows from equation (18)) that Furthermore. there are two cases to be considered. for the integral in equation (17)) | one of which is ej2(aDaszc 1."," We consider a power-law solution of the form Substituting this into equations \ref{dndxb}) ) and \ref{dPdxb}) ), and assuming that the mass density is dominated by protons i.e., the number of pairs per proton is much less than $m_p/m_e$, we obtain where $y\equiv x/x_{acc}$ , $\eta\equiv x_{acc}/x_\pm$ is a constant independent of $x$, and $x_{min}$ is determined by the condition that the pair creation optical depth for a photon scattered at $x_{min},777$ of energy $\sim \epsilon_p$, is unity between $x_{min}$ and $x$ ; $x_{min}$ is determined by thefollowing equation By substituting \ref{sola}) ) in the above equation we find $x_{min}$ explicitly or It follows from equation \ref{dPdxc}) ) that Furthermore, there are two cases to be considered for the integral in equation \ref{dndxc}) ) – one of which is $a_1-2(\alpha+1)a_2>-1$ ."778 The integral in this case is dominated by the upper limit. and by equating the exponents of y on the two sides of the equation we find ad=1.," The integral in this case is dominated by the upper limit, and by equating the exponents of $y$ on the two sides of the equation we find $\alpha a^2 = 1$."779 This together with equation (22)) implies that a<1/2. which is not a case of interest for GRBs since the high energy spectral index. for GRBs has à2 1.," This together with equation \ref{rela}) ) implies that $\alpha<1/2$, which is not a case of interest for GRBs since the high energy spectral index for GRBs has $\alpha>1$ ."780 The other possibility is that αι2(al)ro<— l.andinthis case pair production is dominated by photons scattered at the smallest. ie. at ai.," The other possibility is that $a_1-2(\alpha+1)a_2<-1$ , and in this case pair production is dominated by photons scattered at the smallest $x$ i.e. at $x_{min}$."781" Making use of the expression for ric, (eq. 21))", Making use of the expression for $x_{min}$ (eq. \ref{xmin}) )782" in equation (17)). and setting the exponent of y to zero results in Solving for e, and e» from equations (22)) and (23)) we lind In other words the solution for n and 5 are given by with ol)~expt). the density at ra... and clo~ 4."," in equation \ref{dndxc}) ), and setting the exponent of $y$ to zero results in Solving for $a_1$ and $a_2$ from equations \ref{rela}) ) and \ref{relb}) ) we find In other words the solution for $\npair$ and $\gamma$ are given by with $A_1\sim n\exp(\eta)$, the density at $x_{acc}$, and $A_2\sim 4$ ."783 X somewhat more accurate expression for ely ancl ele can beobtained by combining equations (17)). (18)) (24)).," A somewhat more accurate expression for $A_1$ and $A_2$ can beobtained by combining equations \ref{dndxc}) ), \ref{dPdxc}) ) \ref{solb}) )."784 The result in Beloborocdoy (2002)is à special case (a= 1) of the solution presented. here., The result in Beloborodov (2002)is a special case $\alpha=1$ ) of the solution presented here.785 Equations (4)) and (7)) were derived under the assumptions of planar ecometry and. stationary solution in the a, Equations \ref{dndxa}) ) and \ref{dPdxa}) ) were derived under the assumptions of planar geometry and stationary solution in the $x$ -coordinate.786 Dueto the spherical expansion.the rate of momentum deposition decreases as r while the rate," Dueto the spherical expansion,the rate of momentum deposition decreases as $r^{-2}$ , while the rate"787to the carbon detected in the hieh-: IGAL particularly: at;Z6.,"to the carbon detected in the $z$ IGM, particularly at $z \ga 6$."788 Àn alternate interpretation of Table 1. assuniug that the ICAL is relatively uniforiilv euxielied by volume. is that Z= stars (1100 37.) created the ICM metals aud consequently. reionization may occur early.," An alternate interpretation of Table 1, assuming that the IGM is relatively uniformly enriched by volume, is that $Z=0$ stars (1–100 $M_\odot$ ) created the IGM metals and consequently, reionization may occur early."789 This is because the values of NyeNy (0 30.220) generated by these stars In association with the detected: Zj well exceeds that required for a late IT I reionization at :~6., This is because the values of $N_{\rm Lyc}/N_{\rm b}$ $\sim$ 30–220) generated by these stars in association with the detected $Z_{\rm IGM}$ well exceeds that required for a late H I reionization at $z \sim 6$.790 If clusters of such stars are respousible for both the reiouization ancl inetal eurichiment of the ICONE. they should be easily detected by future missions such as the IWST (Tiuuulinsouetal.2003. 2001).. aud the amount of star formation at 29 is potentially significant (81).," If clusters of such stars are responsible for both the reionization and metal enrichment of the IGM, they should be easily detected by future missions such as the JWST \citep{tsv,tgs}, and the amount of star formation at $z \ga 9$ is potentially significant 1)."791 Lastly. despite their lieh ionizing photonrete. VAISS are efficicut at ecnerating total ionizing radiationmass than are ποτάπου stars in a prescut-dav IME. owing to the ercatly boosted metal vield from a top-heavy IMFE. (," Lastly, despite their high ionizing photon, VMSs are efficient at generating total ionizing radiation than are metal-free stars in a present-day IMF, owing to the greatly boosted metal yield from a top-heavy IMF. ("792Both of these stellar populations. however. have approximately equal ο the difference being largest when IMSs are excluded. or equivaleutly at 2= 6.),"Both of these stellar populations, however, have approximately equal $\eta_{\rm Lyc, C}$, with the difference being largest when IMSs are excluded, or equivalently at $z793\ga 6$ .)"794 Therefore. VMSs are not necessarily preferred as a more efficient source of ionizing radiation at carly epochs ou nucleosvuthetie grounds in association with a eiven detected level of IGM. cuvichmenut. auc possibly based ou reionization requirements as well (sec. e.g.. SomervilleLivio 2003)).," Therefore, VMSs are not necessarily preferred as a more efficient source of ionizing radiation at early epochs on nucleosynthetic grounds in association with a given detected level of IGM enrichment, and possibly based on reionization requirements as well (see, e.g., \citealt{somerville2}) )."795 Furthermore. recent studies (e.g... Sclineideretal 2002)) indicate that the transition from a top- to a preseut-dav IMIF occurs at gas metallicities of about 10τσ.," Furthermore, recent studies (e.g., \citealt{schneider}) ) indicate that the transition from a top-heavy to a present-day IMF occurs at gas metallicities of about $10^{-4} Z_\odot$."796 If this were true. then we can scale the uuubers for VMSs in Table 1 down by 1.5 orders of magnitude. and derive that VMSS may produce oulv ~ 0.35 jonizine photous per barvou for au ICAL metallicity of 10.!Z.. before they pollute thei cuviromments aud cease forming.," If this were true, then we can scale the numbers for VMSs in Table 1 down by 1.5 orders of magnitude, and derive that VMSs may produce only $\sim$ 0.35 ionizing photons per baryon for an IGM metallicity of $10^{-4} Z_\odot$ before they pollute their environments and cease forming."797 We eniplasize. however. that VMSs may still be iuportaut for reiouization alone. given the right combination of conditions. owing to their hieh ioniziug rates.," We emphasize, however, that VMSs may still be important for reionization alone, given the right combination of conditions, owing to their high ionizing rates."798 The conversion between νο and NiveNy does not account for the relative propagation timescales of metals and photons from starforiiing reeious to the ICAL which will nupact the evolution of ICAL abundance ratios between individual elements. c.g.. [C/O].," The conversion between $\eta_{\rm Lyc}$ and $N_{\rm Lyc}/N_{\rm b}$ does not account for the relative propagation timescales of metals and photons from starforming regions to the IGM, which will impact the evolution of IGM abundance ratios between individual elements, e.g., [C/O]."799 Furthenuiore. the definition of gp nupliitle assumes the instantancous creation of the metals.," Furthermore, the definition of $\eta_{\rm Lyc}$ implicitly assumes the instantaneous creation of the metals."800 This is not necessarily true at high redshifts. c.g. to generate sufficicut carbon at 2— 36 requires the star formation to have occurred at 2 69.," This is not necessarily true at high redshifts, e.g., to generate sufficient carbon at $z \sim$ 3–6 requires the star formation to have occurred at $z \ga$ 6–9."801 As we noted earlier. this becomes particularly problematic for the transport of the carbon to the ICM through SN-driven winds.," As we noted earlier, this becomes particularly problematic for the transport of the carbon to the IGM through SN-driven winds."802 We explore the cosmological relevance of these timescale issucs in inore detail in a forthcoming paper., We explore the cosmological relevance of these timescale issues in more detail in a forthcoming paper.803 We are grateful το Jason Tunliuson for valuable input aud calculations., We are grateful to Jason Tumlinson for valuable input and calculations.804 We thank Alike Shull aud Jessica Roscuberg for mau helpful discussions. and Danicl Schaerer. Alessandro Chief. Oscar Straniero aud Sara Ellisou for useful correspoudence.," We thank Mike Shull and Jessica Rosenberg for many helpful discussions, and Daniel Schaerer, Alessandro Chieffi, Oscar Straniero and Sara Ellison for useful correspondence."805 We thank our anonviuous referee for helpful sugeestious which improved the manuscript., We thank our anonymous referee for helpful suggestions which improved the manuscript.806 À. V. eratefullv acknowledges the support of NSF eraut. AST-0201670., A. V. gratefully acknowledges the support of NSF grant AST-0201670.807. J. W. T. acknowledges the support of DOE eraut. DE-ECGO2-91ER10606 in Nuclear Physics and Astrophysics at The University of Chicago., J. W. T. acknowledges the support of DOE grant DE-FG02-91ER40606 in Nuclear Physics and Astrophysics at The University of Chicago.808the calculation of optical depths.,the calculation of optical depths.809" This calculation requires a specification of the density field at all locations, which can be given by the SPH formalism."," This calculation requires a specification of the density field at all locations, which can be given by the SPH formalism."810" The definition of a scalar field using an SPH particle distribution is where is the value of at the location of particlejj., is the mass of particle77,, is the density of particlej7,, and )isthesmoothingkernel(orinterpolatingkernel)."," The definition of a scalar field using an SPH particle distribution is where is the value of at the location of particle, is the mass of particle, is the density of particle, and is the smoothing kernel (or interpolating kernel)."811"Thesummationisty, ~~ nearest neighbour particles to the location ).", The summation is typically over nearest neighbour particles to the location.812".Thesmoothing lengthof particlejj,,hh;,, is defined such that a sphere of radius will contain the nearest neighbour particles tojj."," The of particle, is defined such that a sphere of radius will contain the nearest neighbour particles to."813". For example, to calculate density, substitute):: The sphere that contains the nearest neighbours (i.e. a sphere of radius 22h;)) is referred to as the volume..There is a subtlety to equation (16)) that should be noted, relating to which value of to use."," For example, to calculate density, substitute: The sphere that contains the nearest neighbours (i.e. a sphere of radius ) is referred to as the .There is a subtlety to equation \ref{eq:rhocalc}) ) that should be noted, relating to which value of to use."814" There are now two means by which to estimate density: the first is the so-called ""gather"" method, where the smoothing length is defined for the locationTTj, and Where the index refers to all particles which are contained within a radius of the locationrr;."," There are now two means by which to estimate density: the first is the so-called “gather” method, where the smoothing length is defined for the location, and Where the index refers to all particles which are contained within a radius of the location."815". The second method (which is used in this work and in ?)) is the ""scatter"" method.", The second method (which is used in this work and in \citealt{SPHRAY}) ) is the “scatter” method.816" The smoothing length is used - in this formalism, the density at any one location is calculated by adding the contributions from particles whose smoothing volume intersects the location: In the context of ray tracing, the density along the ray is affected only by particles with smoothing volumes that intersect it (see Figure 2))."," The smoothing length is used - in this formalism, the density at any one location is calculated by adding the contributions from particles whose smoothing volume intersects the location: In the context of ray tracing, the density along the ray is affected only by particles with smoothing volumes that intersect it (see Figure \ref{fig:scatter}) )."817" By determining which particles intersect the ray, the rest of the particle distribution can be ignored for the purposes of calculating optical depth, reducing computational expense (whereas with the gather method, the ensemble of particles contributing to the calculation changes significantly with position, and requires the inclusion of a larger subset of SPH particles to perform the calculation)."," By determining which particles intersect the ray, the rest of the particle distribution can be ignored for the purposes of calculating optical depth, reducing computational expense (whereas with the gather method, the ensemble of particles contributing to the calculation changes significantly with position, and requires the inclusion of a larger subset of SPH particles to perform the calculation)."818" Using the scatter method, the column density Jalongtherayis Which can be rearranged to give The integral is now decomposed into integrals, where is the number of particles intersected by the ray."," Using the scatter method, the column density along the ray is Which can be rearranged to give The integral is now decomposed into integrals, where is the number of particles intersected by the ray."819 Each integral is defined by the impact parameter (see Figure 2))., Each integral is defined by the impact parameter (see Figure \ref{fig:scatter}) ).820" The calculation itself can be performed for a smoothing volume of1,, and scaled upwards (this is due to the construction of the smoothing kernel)."," The calculation itself can be performed for a smoothing volume of, and scaled upwards (this is due to the construction of the smoothing kernel)."821 The entire optical depth calculation has been decomposed into the repetition of a single algorithm for calculating the optical depth through a single smoothing volume., The entire optical depth calculation has been decomposed into the repetition of a single algorithm for calculating the optical depth through a single smoothing volume.822 This calculation will nowbe expounded., This calculation will nowbe expounded.823 Consider Figure 3.., Consider Figure \ref{fig:sphere}.824 The ray (with direction vector )))intersectsthespherewithimpactparameterbb., The ray (with direction vector ) intersects the sphere with impact parameter.825". If the ray penetrates a distance into the sphere (out of total possible distance ss)), then the integral can be defined analytically,a given the functional form of )."," If the ray penetrates a distance into the sphere (out of a total possible distance ), then the integral can be defined analytically, given the functional form of ."826.defining, defining827of that clement was maintained. as a free parameter. ancl the process repeated to determine the clement providing the next most significant improvement.,"of that element was maintained as a free parameter, and the process repeated to determine the element providing the next most significant improvement."828 1n agreement with the results for AIST and NGC 4696. we find that the most significant. improvements in the fit to the NGC 4636 data are obtained by including the abundances of Si. Mg and S as free fit parameters (the measured 47.2 value is. reduced from. -722.6 to 475.0. for the introduction. of only three extra fit) parameters)," In agreement with the results for M87 and NGC 4696, we find that the most significant improvements in the fit to the NGC 4636 data are obtained by including the abundances of Si, Mg and S as free fit parameters (the measured $\chi^2$ value is reduced from 722.6 to 475.0, for the introduction of only three extra fit parameters)."829 At this »ont. including the abundances of further elements as fit xuvameters did. not lead to such significant. improvements and. due to the already complex nature of the best-fit moc1. we forced the abuncanees of all other elements to vary with he same ratio relative to their solar values (cllectively tving he abundances to that of iron. the clement to which the ASCA cata are most. sensitive).," At this point, including the abundances of further elements as fit parameters did not lead to such significant improvements and, due to the already complex nature of the best-fit model, we forced the abundances of all other elements to vary with the same ratio relative to their solar values (effectively tying the abundances to that of iron, the element to which the ASCA data are most sensitive)."830 We note. however. that including the abundances of Na and. O as further free fit xwameters did. lead. to formally significant improvements. with reductions in X7 of ~20 and 30. respectively.," We note, however, that including the abundances of Na and O as further free fit parameters did lead to formally significant improvements, with reductions in $\chi^2$ of $ \sim 20$ and 30, respectively."831 Llowever. due to the systematic uncertainties in the NCC 4636 spectra at low energies (Section 3.3). which elfect the measured O abundance. and the fact that the Na abundance fits to an un-physically high. value (5 times solar). the metallicities of these elements were not included as free. parameters in our final analysis).," However, due to the systematic uncertainties in the NGC 4636 spectra at low energies (Section 3.3), which effect the measured O abundance, and the fact that the Na abundance fits to an un-physically high value $\sim 5$ times solar), the metallicities of these elements were not included as free parameters in our final analysis)."832 Phe measured. clement abundances for NGC 4636. as a fraction of their solar photospheric values defined by Anders Crevesse (1989). are Zp.=0.62un οσο Zu=0.96fr and Za=149.525.," The measured element abundances for NGC 4636, as a fraction of their solar photospheric values defined by Anders Grevesse (1989), are $Z_{\rm Fe} = 0.62^{+0.13}_{-0.09}$, $Z_{\rm Mg} =8330.93^{+0.19}_{-0.15}$, $Z_{\rm Si} = 0.96^{+0.18}_{-0.12}$ and $Z_{\rm834S} = 1.49^{+0.27}_{-0.22}$."835 These results are in reasonable agreement with those of Matsushita C1997) and. Buote (1999)., These results are in reasonable agreement with those of Matsushita (1997) and Buote (1999).836 Scaling our measured abundance ratios to the meteoric abundance scale of Anders Crevesse (1989) we determine Me/Fe] ~0.00. διο ~0.02 and. S/Ee]-0.16.," Scaling our measured abundance ratios to the meteoric abundance scale of Anders Grevesse (1989) we determine [Mg/Fe] $\sim 0.00$, [Si/Fe] $\sim 0.02$ and $\sim 0.16$."837 Comparing these values with the supernova vield. models of Nagataki Sato (1998). our observed Si/Fe] ratio implies a mass fraction of the iron enrichment due to type Ia supernova. MiosniafMerete in the range 0.55rr0.9 (where the limits cover the full range of models examined by these authors).," Comparing these values with the supernova yield models of Nagataki Sato (1998), our observed [Si/Fe] ratio implies a mass fraction of the iron enrichment due to type Ia supernova, $M_{\rm Fe,SNIa}/M_{\rm Fe,total}$, in the range $0.55-0.9$ (where the limits cover the full range of models examined by these authors)."838 For spherical type HE supernovae. a mass fraction in the range AlpeNia/MpeaonavOT0.85 is preferred.," For spherical type II supernovae, a mass fraction in the range $M_{\rm Fe,SNIa}/M_{\rm Fe,total} \sim 0.7-0.85$ is preferred."839 Further comparison of our Si/Fe] constraint with the supernovae nmicdels. discussed. by Gibson (1997). also. requires Miosnia~0.50.7.," Further comparison of our [Si/Fe] constraint with the supernovae models discussed by Gibson (1997) also requires $M_{\rm Fe,SNIa} \sim 0.5-0.7$."840 However. the observed S/Ec] and Me/Fe] ratios favour a mass fraction due to type la supernovae of &0.5 (Gibson 1991).," However, the observed [S/Fe] and [Mg/Fe] ratios favour a mass fraction due to type Ia supernovae of $\approxlt 0.5$ (Gibson 1997)."841 We have presented detections of harc N-rav emission components in the spectra of six. nearby giant elliptical ealaxies observed. with ASC'A.," We have presented detections of hard X-ray emission components in the spectra of six, nearby giant elliptical galaxies observed with ASCA."842" The galaxies exhibit clear. dynamical evidence for supermassive (107 afew 10"" )) black holes in their nuclei."," The galaxies exhibit clear, dynamical evidence for supermassive $10^8-$ a few $10^9$ ) black holes in their nuclei."843 Phe hare X-ray. emission can be parameterizecl by power-law mocels with photon indices. DL-061.5 (mean value 1.2). and luminosities. Exi407.26.H107is)215 5. or thermal bremsstrahlung models with electron. temperatures. AT10 keV. Such properties identify these galaxies as a new class of accreting X-ray source. with X-ray. spectra significantly harder than those of Seyfert nuclei. typical binary X-ray sources and low-luminosity AGN. and bolometric luminosities comparatively dominated bv their X-ray emission.," The hard X-ray emission can be parameterized by power-law models with photon indices, $\Gamma =8440.6-1.5$ (mean value 1.2), and luminosities, $L_{\rm X,1-10} \sim 2.6845\times 10^{40}-2.1 \times 10^{42}$ , or thermal bremsstrahlung models with electron temperatures, $kT > 10$ keV. Such properties identify these galaxies as a new class of accreting X-ray source, with X-ray spectra significantly harder than those of Seyfert nuclei, typical binary X-ray sources and low-luminosity AGN, and bolometric luminosities comparatively dominated by their X-ray emission."846 We have argued. that the hard X-ray. emission. is likely to be due to acerction onto the central. supermassive black holes. via low-racliative cllicicney Lows. coupled with strong outllows.," We have argued that the hard X-ray emission is likely to be due to accretion onto the central, supermassive black holes, via low-radiative efficiency flows, coupled with strong outflows."847 Within such models. the hard. X-ray emission. originates [rom bremsstrahlung processes in the racliatively-clominant. outer regions of the accretion lows. (," Within such models, the hard X-ray emission originates from bremsstrahlung processes in the radiatively-dominant, outer regions of the accretion flows. ("848Detailed modeling. and discussion of these issues are presented by Di Matteo 1999.,Detailed modeling and discussion of these issues are presented by Di Matteo 1999b).849 For the case of M87. the lux of the hard component was shown to be in good agreement with the nuclear X-rav [lux determined from earlier ROSAT LIBRI observations. which were able to resolve knot A in the jet from the nuclear emission component.," For the case of M87, the flux of the hard component was shown to be in good agreement with the nuclear X-ray flux determined from earlier ROSAT HRI observations, which were able to resolve knot A in the jet from the nuclear emission component."850 We have stressed the importance of accounting for the complex temperature structure. intrinsic absorption and variable clement abundance ratios in the analysis of the ASC'X spectra.," We have stressed the importance of accounting for the complex temperature structure, intrinsic absorption and variable element abundance ratios in the analysis of the ASCA spectra."851 We confirmed results showing that the application of such models leads to measurements of approximately solar emission-weighted. metallicities for the X-ray gas in the galaxies., We confirmed results showing that the application of such models leads to measurements of approximately solar emission-weighted metallicities for the X-ray gas in the galaxies.852 We also presented detailed results on the individual element abundances in NGC 4636., We also presented detailed results on the individual element abundances in NGC 4636.853 Future observations at high spatial resolution with the Chandra Observatory will be crucial in establishing the contributions [from the various N-ray emission. mechanisms esent in elliptical galaxies and unambiguously identifving he origin of the hard. N-rav. components., Future observations at high spatial resolution with the Chandra Observatory will be crucial in establishing the contributions from the various X-ray emission mechanisms present in elliptical galaxies and unambiguously identifying the origin of the hard X-ray components.854 Decp X-ray spectroscopy with NMM ancl ASTRO-E will allow us to examine variability. in the X-ray emission. (which. should x: slower in sources where the X-rav emission originates rom the outer regions of low racliative-cllicicney accretion lows than in typical Sevfert nuclei) and to search for road. iron emission features associated with the power-law components.," Deep X-ray spectroscopy with XMM and ASTRO-E will allow us to examine variability in the X-ray emission (which should be slower in sources where the X-ray emission originates from the outer regions of low radiative-efficiency accretion flows than in typical Seyfert nuclei) and to search for broad, iron emission features associated with the power-law components."855 The detection of such broad emission features would argue against the simple. low-racliative ellicienev accretion models discussed. here. ancl require the presence of significant amounts of cold. reflecting material close to the central black holes.," The detection of such broad emission features would argue against the simple, low-radiative efficiency accretion models discussed here, and require the presence of significant amounts of cold, reflecting material close to the central black holes."856 The discovery of hard X-ray emission components in the spectra of nearby elliptical galaxies containing supermassive jack holes provides important new constraints on the accretion processes in these systenis., The discovery of hard X-ray emission components in the spectra of nearby elliptical galaxies containing supermassive black holes provides important new constraints on the accretion processes in these systems.857 Our results are relevant o understanding the demise of quasars (which could Xausiblv be due to a change in the dominant. acerction mode in ellipticals over the history of the Universe) and. ultimately. the origin of the hard (DL~ 1.4) Cosmic X-ray Backeround Di Matteo Fabian 1997b).," Our results are relevant to understanding the demise of quasars (which could plausibly be due to a change in the dominant accretion mode in ellipticals over the history of the Universe) and, ultimately, the origin of the hard $\Gamma \sim 1.4$ ) Cosmic X-ray Background Di Matteo Fabian 1997b)."858 These issues. and others. will be explored in future papers (Di Matteo 1990b: Di Matteo Allen 1999).," These issues, and others, will be explored in future papers (Di Matteo 1999b; Di Matteo Allen 1999)."859Upon examination of the one-dimensional beta fits and their reduced y statistics. it appeared as though the beta model fits derived from Sherpa were not statistically robust.,"Upon examination of the one-dimensional beta fits and their reduced $\chi^{2}$ statistics, it appeared as though the beta model fits derived from Sherpa were not statistically robust."860 The reduced y for these fits was often above 2. and although others have used similar results (2).. 1t was judged necessary to find a second method used as to of independently verify the profiles.," The reduced $\chi^{2}$ for these fits was often above 2, and although others have used similar results \citep{Sakelliou}, it was judged necessary to find a second method used as to of independently verify the profiles."861 Therefore. a second set of temperature and iron profiles were calculated with the same set of data.," Therefore, a second set of temperature and iron profiles were calculated with the same set of data."862 The second method used was to divide the cluster into radial regions not by a constant length scale. but instead by giving each region a constant number of counts.," The second method used was to divide the cluster into radial regions not by a constant length scale, but instead by giving each region a constant number of counts."863" The furthest extent of spectral extraction was also determined by the net counts in a 2.55 wide region,", The furthest extent of spectral extraction was also determined by the net counts in a 5 wide region.864" If the net counts next the 2.""55 wide region out ever dropped below 20 for or 100 for data. then this defined the edge of the cluster due to their low signal-to-noise ratio of the regions beyond this point."," If the net counts next the 5 wide region out ever dropped below 20 for or 100 for data, then this defined the edge of the cluster due to their low signal-to-noise ratio of the regions beyond this point."865 The four calculated counts regions for each cluster are listed in Table 3.., The four calculated counts regions for each cluster are listed in Table \ref{Table3}.866 Dividing the cluster in this manner also allows for all of the spectra for one cluster to be comparably significant instead of having a wide disparity in spectral quality., Dividing the cluster in this manner also allows for all of the spectra for one cluster to be comparably significant instead of having a wide disparity in spectral quality.867 The spectra were extracted in exactly the same manner as the core radius spectra. which will be described in detail in $2.5...," The spectra were extracted in exactly the same manner as the core radius spectra, which will be described in detail in \ref{spectrasec}."868 This process of sub-dividing the cluster will be called the counts profile or counts hereafter.," This process of sub-dividing the cluster will be called the counts profile or counts radius, hereafter."869 They will also be listed às 7j. 7s.73.and ry as an abbreviation in the tables. particularly in Table 3 The radial profiles in each cluster are compared in two ways in Tables 3 4..," They will also be listed as $r_{\rm{1}}, r_{\rm{2}}, r_{\rm{3}}$, and $r_{\rm{4}}$ as an abbreviation in the tables, particularly in Table \ref{Table3}870 The radial profiles in each cluster are compared in two ways in Tables \ref{Table3} \ref{Table4}."871 Table 3 shows the extents of each individual counts region as well as the calculated core radius and virial radius fgg 1n areseconds., Table \ref{Table3} shows the extents of each individual counts region as well as the calculated core radius and virial radius $r_{200}$ in arcseconds.872 Table 4. shows the average core and counts regions in terms of kpe., Table \ref{Table4} shows the average core and counts regions in terms of kpc.873 It was found that there were insignifica5 differences between the two radit on average. except foSB the very outer region.," It was found that there were insignificant differences between the two radii on average, except for the very outer region."874 The outermost counts regions are usually much wider than 2r. (see the averages given 1 Table 4 )., The outermost counts regions are usually much wider than $_{\rm c}$ (see the averages given in Table \ref{Table4}) ).875 Therefore. the average temperature and iro abundance measurements should be strongly correlatec between the core and counts radius. with differences only being expected in the outermost regions.," Therefore, the average temperature and iron abundance measurements should be strongly correlated between the core and counts radius, with differences only being expected in the outermost regions."876 Also included i Table 3is the calculated virial radius in are seconds., Also included in Table \ref{Table3} is the calculated virial radius in arc seconds.877 The virial radius is calculated as found in ?.. divided by 1.4 to take into account the difference between cosmologies (Ho=S0 km s! Mpe7! in ?. while Ho=71 km s Mpc! here).," The virial radius is calculated as found in \cite{Jones}, divided by 1.4 to take into account the difference between cosmologies ${H}_{0} = 50$ km $^{-1}$ $^{-1}$ in \cite{Jones} while $H_{0} = 71$ km $^{-1}$ $^{-1}$ here)."878 The formula itself is given as and the temperature used was the overall temperature measured by the procedure described in § 2.5.., The formula itself is given as and the temperature used was the overall temperature measured by the procedure described in $\S$ \ref{spectrasec}. .879 This, This880Both cases were evaluated together with the CPL parametrization (Eq. 7)).,Both cases were evaluated together with the CPL parametrization (Eq. \ref{eq:cpl}) ).881 We performed a MCMC run by introducing the modified CAMB routines and the new parametrization for w(z) in the COSMOMC code., We performed a MCMC run by introducing the modified CAMB routines and the new parametrization for $w(z)$ in the COSMOMC code.882" The total parameter space directly constrained was then p={Q,h?,Q.h7,0,T,Aj,n, wo,w1)."," The total parameter space directly constrained was then $\{\Omega_b h^2, \Omega_c h^2, \theta, \tau, A_s, n_s,$ $w_0, w_1 \}$."883 We used the matter power spectrum from Tegmarketal.2006 to account for the SDSS LRG data., We used the matter power spectrum from \cite{T06} to account for the SDSS LRG data.884 The modeling for non linear effects and scale dependent bias was done with a Q-model (Coleetal. 2005)) as explained above., The modeling for non linear effects and scale dependent bias was done with a Q-model \cite{Cole05}) ) as explained above.885" Since we are interested in models with w(z)«—1 in order to determine a valid figure of merit, dark energy perturbations were ""turned off"" when solving for CMB and matter power spectrum."," Since we are interested in models with $w(z)<-1$ in order to determine a valid figure of merit, dark energy perturbations were “turned off” when solving for CMB and matter power spectrum."886 The obtained results on all parameters are summarized in Table 1.., The obtained results on all parameters are summarized in Table \ref{Tablew0w1}.887 All these constraints on individual parameters were obtained by marginalization over other parameters., All these constraints on individual parameters were obtained by marginalization over other parameters.888" For comparison reasons, the last column shows the results where w is a constant value (no evolution)."," For comparison reasons, the last column shows the results where $w$ is a constant value (no evolution)."889 The constraints on nearly all parameters remain essentially identical., The constraints on nearly all parameters remain essentially identical.890" Of course, the main exception regards parameters that govern the equation of state itself, which have a bigger uncertainty compared to a constant w."," Of course, the main exception regards parameters that govern the equation of state itself, which have a bigger uncertainty compared to a constant $w$ ."891" Considering the parametrization of a smooth transition with either Il=1 or Γ=0.85 results in some small changes in the preferred values and the uncertainties, which seem to be smaller when Γ=0.85."," Considering the parametrization of a smooth transition with either $\Gamma=1$ or $\Gamma=0.85$ results in some small changes in the preferred values and the uncertainties, which seem to be smaller when $\Gamma=0.85$."892 The 2D marginalized contours at and 95 confidence level are presented in Fig. 3.., The 2D marginalized contours at and 95 confidence level are presented in Fig. \ref{fig:w0w1}.893" Again, the slightly different values of the Γ parameter have an effect on the derived constraints on wo— wi, although it is rather small."," Again, the slightly different values of the $\Gamma$ parameter have an effect on the derived constraints on $w_0-w_1$ , although it is rather small."894" Finally, we notice that using the parametrization given by Eq."," Finally, we notice that using the parametrization given by Eq."895 8 with Γ=0.85 provides very similar constraints to a pure CPL parametrization., \ref{wqz} with $\Gamma=0.85$ provides very similar constraints to a pure CPL parametrization.896 The Dark Energy Task Force report (Albrechtetal. 2006)) introduced a numerical quantity to determine the capacity of future surveys in constraining dark energy models., The Dark Energy Task Force report \cite{DETF}) ) introduced a numerical quantity to determine the capacity of future surveys in constraining dark energy models.897 This numerical quantity is referred to as the figure of merit (f.o.m.), This numerical quantity is referred to as the figure of merit (f.o.m.)898 for a given experiment or combination of experiments and is defined as the reciprocal of the area of the marginalized 2D region contour at 95 confidence in the wo—w; parameter space., for a given experiment or combination of experiments and is defined as the reciprocal of the area of the marginalized 2D region contour at 95 confidence in the $w_0-w_1$ parameter space.899 In terms of the f.o.m., In terms of the f.o.m.900" for the present day data, the obtained values are summarized in the following table These values can thus be used to compare the improvement of future experiments in constraining dark energy evolution on Hubble timescales."," for the present day data, the obtained values are summarized in the following table These values can thus be used to compare the improvement of future experiments in constraining dark energy evolution on Hubble timescales."901" For more rapid transitions, one has to consider higher values of I, which is done in the next section."," For more rapid transitions, one has to consider higher values of $\Gamma$, which is done in the next section."902" In this section we examine what constraints can be derived when a rapid transition in the equation of state of dark energy (T=5) is considered, using the full data sets presented above."," In this section we examine what constraints can be derived when a rapid transition in the equation of state of dark energy $\Gamma=5$ ) is considered, using the full data sets presented above."903 Only models with w(z)>—1 were constrained by including DE perturbations when solving the total perturbations equations with CAMB., Only models with $w(z)>-1$ were constrained by including DE perturbations when solving the total perturbations equations with CAMB.904" For each case we ran one long chain, using the Rafetery-Lewis diagnostic to check for convergence."," For each case we ran one long chain, using the Rafetery-Lewis diagnostic to check for convergence."905" As for the LRG SDSS data, we used the data on the matter power spectrum as implemented in COSMOMC with a Q-model to correct for non-linear effects."," As for the LRG SDSS data, we used the data on the matter power spectrum as implemented in COSMOMC with a Q-model to correct for non-linear effects."906" Finally, we restricted ourselves to a flat Universe (€),=0) for simplicity reasons."," Finally, we restricted ourselves to a flat Universe $\Omega_k=0$ ) for simplicity reasons."907" As seen above, for transitions to w..=—1, the matter correlation function shows a different sensitivity to the initial value w,."," As seen above, for transitions to $w_-=-1$, the matter correlation function shows a different sensitivity to the initial value $w_+$."908" We considered then three distinct transitions by setting w_=—1 and three low values for w, (0,—0.1 and —0.2)."," We considered then three distinct transitions by setting $w_-=-1$ and three low values for $w_+$ $0, -0.1$ and $-0.2$ )."909 In each case the objective is to get constraints on the transition epoch (αι). the value a;=0 corresponding to the standard concordance model.," In each case the objective is to get constraints on the transition epoch $a_t$ ), the value $a_t= 0$ corresponding to the standard concordance model."910" As w, approaches 0 the contribution of dark energy at high redshifts remains non vanishing, allowing us to investigate its possible influence at earlier epochs."," As $w_+$ approaches $0$ the contribution of dark energy at high redshifts remains non vanishing, allowing us to investigate its possible influence at earlier epochs."911" Four different data combinations were used to constrain this model, CMB, CMB+SN Ia, CMB+P(k) and finally CMB+P(k)+ SN Ia. The results of the mean posterior values and confidence intervals on each parameter are summarized in Table 2.."," Four different data combinations were used to constrain this model, CMB, CMB+SN Ia, CMB+P(k) and finally CMB+P(k)+ SN Ia. The results of the mean posterior values and confidence intervals on each parameter are summarized in Table \ref{Table_wi02wf1}."912" The posterior distribution in some parameter is clearly non-Gaussian, so in some cases the lo error bars are quoted using asymmetrical limits."," The posterior distribution in some parameter is clearly non-Gaussian, so in some cases the $\sigma$ error bars are quoted using asymmetrical limits."913 Fig., Fig.914" 4 shows the contours in the space of Oo—a;, on which the effect of the different data combinations on these two parameters can be appreciated."," \ref{fig:Ol_at_1} shows the contours in the space of $\Omega_Q-a_t$, on which the effect of the different data combinations on these two parameters can be appreciated."915" This figure shows that the combination of the WMAPS data on the CMB with supernovae already constrains the possible transition to be at a;«0.6 at the two sigma level confidence region), or in redshift space z,>0.7."," This figure shows that the combination of the WMAP5 data on the CMB with supernovae already constrains the possible transition to be at $a_t<0.6$ at the two sigma level confidence region), or in redshift space $z_t>0.7$."916" When the matter power spectrum data is added, some small reduction on the allowed region in the transition parameter a, is observed."," When the matter power spectrum data is added, some small reduction on the allowed region in the transition parameter $a_t$ is observed."917" Surprisingly, the combination CMB+P(k) without supernovae leads to a better constraint on the transition epoch."," Surprisingly, the combination CMB+P(k) without supernovae leads to a better constraint on the transition epoch."918" This result is not intuitive, sinceas demonstrated in the previous section, one obtains only negligible differences in the matter correlation function shape by changing the transition epoch."," This result is not intuitive, sinceas demonstrated in the previous section, one obtains only negligible differences in the matter correlation function shape by changing the transition epoch."919 The cause for this reduction of the allowed transition redshift is actuallydue, The cause for this reduction of the allowed transition redshift is actuallydue920In FigureOo 3.. we show a selection of two-point correlation fictions derived from theWAZAP. data.,"In Figure \ref{fig:twopt_auto}, we show a selection of two-point correlation functions derived from the data."921 Specifically. all available Wa. Q and V. auto-correlatious are shown. in addition to the eross-correlations between the Wwe aud VW bands.," Specifically, all available $Ka$ , $Q$ and $V$ auto-correlations are shown, in addition to the cross-correlations between the $Ka$ and $W$ bands."922 Table 1 shows the \? sieuificauces for all possible two-point fuuctious from the available data. (," Table \ref{tab:twopt}923 shows the $\chi^2$ significances for all possible two-point functions from the available data. ("924Note that ouly unique combinations are actually shown: empty table cells iudicate that the same colubinatious may be fouud elsewhere iu the table.,Note that only unique combinations are actually shown; empty table cells indicate that the same combinations may be found elsewhere in the table.925 For example. TQ aud QI are ideutical for auto-correlatious. but ciffereut for cross-correlations.)," For example, IQ and QI are identical for auto-correlations, but different for cross-correlations.)"926 Starting with the pure intensity correlations shown in the top row of Figure 3.. we recognize the by now well-known behavior of the CAIB temperature two-poiut function. observed both byCOBE (e.s..Bennettctal.1991) audWAZAP (c.e..Spereeletal. 2003): at small aneular separations. it is slightly low compared to the ACDM inodel. and at separations lareer than 607. very close to zero.," Starting with the pure intensity correlations shown in the top row of Figure \ref{fig:twopt_auto}, we recognize the by now well-known behavior of the CMB temperature two-point function, observed both by \citep[e.g.,][]{bennett:1994} and \citep[e.g.,][]{spergel:2003}: : at small angular separations, it is slightly low compared to the $\Lambda$ CDM model, and at separations larger than $60^{\circ}$, very close to zero."927 This peculiar behavior has attracted the interest of both experimentalists aud theorists. aud some have suggested that this could be the signature of a closed topological space.," This peculiar behavior has attracted the interest of both experimentalists and theorists, and some have suggested that this could be the signature of a closed topological space."928 However. from the view of a simple 4? test. this function remains consistent with the simplest ACDALT model at the level.," However, from the view of a simple $\chi^2$ test, this function remains consistent with the simplest $\Lambda$ CDM model at the level."929 Next. looking at the tempcrature-polarization (IL-Q/U) cross-correlations we see that the overall behavior of the Q-. V. and Wa«W band functions are quite different.," Next, looking at the temperature-polarization (I-Q/U) cross-correlations we see that the overall behavior of the $Q$ -, $V$, and $Ka \times W$ band functions are quite different."930 This indicates that theWAZAP data still are too noise dominated to extract high-sensitivity cosmological information from individual bands., This indicates that the data still are too noise dominated to extract high-sensitivity cosmological information from individual bands.931 This is also reflected in the second and third cohuuus of Table 1.. where there is a significant scatter between the different results.," This is also reflected in the second and third columns of Table \ref{tab:twopt}, where there is a significant scatter between the different results."932 Towever. we do see that all results are iu good agereemoenut with the expectations. indicating that the noise model is satisfactory.," However, we do see that all results are in good agreement with the expectations, indicating that the noise model is satisfactory."933 The three bottoni rows of Figure 2. show the pure polarization correlation functions. which are the main target in this paper.," The three bottom rows of Figure \ref{fig:twopt_auto} show the pure polarization correlation functions, which are the main target in this paper."934 And here we see several interesting features., And here we see several interesting features.935 First. we recognize a sharp feature in the UU correlation function at ~111.," First, we recognize a sharp feature in the UU correlation function at $\sim141^{\circ}$."936 This is the angular separation between the A- and D sides ofthe differcutialWALA detectors. and it was also seen in the pure noise teiiperatureP two-point correlation function in the WAZAP data (Eriksenetal.2005).," This is the angular separation between the A- and B sides of the differential detectors, and it was also seen in the pure noise temperature two-point correlation function in the first-year data \citep{eriksen:2005}."937. However. even nore interesting ds the overall very pronounced large-scale excesses seen iu the QQ and UU fictions: both the Q- aud V-baud functions lie mostly within the 26-3e confidence regious. aud the overall aerectuent with the simulations appears quite poor.," However, even more interesting is the overall very pronounced large-scale excesses seen in the QQ and UU functions: both the $Q$ - and $V$ -band functions lie mostly within the $2\sigma$ $3\sigma$ confidence regions, and the overall agreement with the simulations appears quite poor."938 Again. this is strongly reflected in Table 1: all OQ correlations are anomalous at iiore than couficence. and all UU correlations at more than confidence.," Again, this is strongly reflected in Table \ref{tab:twopt}: all QQ correlations are anomalous at more than confidence, and all UU correlations at more than confidence."939 In the case of the TT band. which happens to be the most anomalous of any band. we have good reasons to expect such behavior.," In the case of the $W-$ band, which happens to be the most anomalous of any band, we have good reasons to expect such behavior."940 This band has a significantly higher 1/7 kuce frequency than any other baud (Jarosiketal.2003).. with the IL differencing assenibly. haviug the highest.," This band has a significantly higher $1/f$ knee frequency than any other band \citep{jarosik:2003}, with the $W$ 4 differencing assembly having the highest."941 As a result. theWAZAP team has chosen not to use this baud for cosmological analysis in polarization.," As a result, the team has chosen not to use this band for cosmological analysis in polarization."942 But the anomalous behavior of the Q aud V. bands is a priori not expected: these are used for cosinological analysis by theWALA team aud should be clean., But the anomalous behavior of the $Q$ and $V$ bands is a priori not expected; these are used for cosmological analysis by the team and should be clean.943 We Phave also generated an ensemble of noisc-oulv simulations. and computed the tvo-poiut fictions from hese.," We have also generated an ensemble of noise-only simulations, and computed the two-point functions from these."944 The corresponding 4? fractions are listed) in xmwentheses in Table 1 for the pure polarization modes.," The corresponding $\chi^2$ fractions are listed in parentheses in Table \ref{tab:twopt}945 for the pure polarization modes."946 Tere we see that. eenerallv speaking. the noisc-oulv wpothesis performs almost. but not quite. as well as he signal-plus-uoise hypothesis.," Here we see that, generally speaking, the noise-only hypothesis performs almost, but not quite, as well as the signal-plus-noise hypothesis."947 This is simply due to he fact that theWAZAP polarization data are stronely dominated by the correlated noise. and it is very difficult roni a correlation fiction point of view to distinguish yetwoeen a small signal component aud a large-scale noise Huctuation.," This is simply due to the fact that the polarization data are strongly dominated by the correlated noise, and it is very difficult from a correlation function point of view to distinguish between a small signal component and a large-scale noise fluctuation."948 The anomalous behavior seen in the Q- aud V-baud two-point functions clearly ueeds an explanation., The anomalous behavior seen in the $Q$ - and $V$ -band two-point functions clearly needs an explanation.949 Aud typically. when such unexpected behavior is observed. oue of the the first issues fo consider is residual foregrounds.," And typically, when such unexpected behavior is observed, one of the the first issues to consider is residual foregrounds."950 To check whether this may be a relevant issue. we first sinplwv compute the cross-correlation fictions between each of the three frequency bauds (va. Q. aud V) aud the two available foreground templates (svuchrotron aud dust).," To check whether this may be a relevant issue, we first simply compute the cross-correlation functions between each of the three frequency bands $Ka$, $Q$, and $V$ ) and the two available foreground templates (synchrotron and dust)."951 This is done both for the realWALAP data aud the simulated cuscuibles. aud the agreement between the (pure CAMIB | noise) sinulatious aud theWAZAP data is again quoted iu terms of a 47 fraction.," This is done both for the real data and the simulated ensembles, and the agreement between the (pure CMB $+$ noise) simulations and the data is again quoted in terms of a $\chi^2$ fraction."952 The results from these calculations are as follows: or the Wa baud. we find that the 47 siguificauces are 451 and 0.21 for svuchrotron and dust. respectively. indicating no significaut foreground detection iu this case.," The results from these calculations are as follows: for the $Ka$ band, we find that the $\chi^2$ significances are 0.51 and 0.24 for synchrotron and dust, respectively, indicating no significant foreground detection in this case."953" dElowever. for the (Q band the corresponding Munbers are (0.05. and ~0.005. corresponding to correlations statistically significant at 26 and ~3 respectively,"," However, for the $Q$ band the corresponding numbers are 0.05 and $\sim0.005$, corresponding to correlations statistically significant at $2\sigma$ and $\sim3\sigma$, respectively."954 For the V. baud. the uunbers are 0.05 and 1.02. sienificant at 20 or more.," For the $V$ band, the numbers are 0.05 and 0.02, significant at $2\sigma$ or more."955" To study theseforeeround correlations further. we conrpute the two-poiut functions from the foreground cluplates directly, and fit these to the observed correlation functions with a single free ampltucle for cach cluplate. A, and Aq. bv minimizine Tere. αμ.) is the correlation function mean aud οι=—(GC)p)Cu)pU) ds the covariance iatrix. both quantities obtained from the noise simuulatious."," To study theseforeground correlations further, we compute the two-point functions from the foreground templates directly, and fit these to the observed correlation functions with a single free amplitude for each template, $A_{\textrm{s}}$ and $A_{\textrm{d}}$, by minimizing Here, $C_{\textrm{sim}}(b)$ is the correlation function mean and $\Sigma_{\textrm{sim}}(b, b') = \bigl<(C(b) -\mu(b))(C(b')-\mu(b'))\bigr>$ is the covariance matrix, both quantities obtained from the noise simulations."956 The iudices 6.0% run over all possible pure polarization two-poiut bius (.6.. both angular bius and QQ. QU. and UU correlations).," The indices $b, b'$ run over all possible pure polarization two-point bins (i.e., both angular bins and QQ, QU, and UU correlations)."957 The resulting best-fit amplitudes from this caleulatiou for [να Q- aud V. bands are shown in Table 2..," The resulting best-fit amplitudes from this calculation for $Ka$ -, $Q$ - and $V$ bands are shown in Table \ref{tab:amp_marg_conf}."958 Tere. we again see that the /va-hand amplitudes are ecucrally significantly lower than those of the Q and V lands. (," Here, we again see that the $Ka$ -band amplitudes are generally significantly lower than those of the $Q$ and $V$ bands. ("959Note that the uncertainties quoted iu this table ouly iuchide statistical errors. not systematic errors.,"Note that the uncertainties quoted in this table only include statistical errors, not systematic errors."960The sienificances should thereforenot be considered as true detection levels. but are only sugecstive.},"The significances should thereforenot be considered as true detection levels, but are only suggestive.)"961 In Figure L.the fitted correlation functious are compared to the observed functions.," In Figure \ref{fig:amp_tp}, the fitted correlation functions are compared to the observed functions."962 First. the red curve shows the functions derived from the actual WAZAP data. with grav bands iudicatiung the lo uncertainties derived from smniulatious.," First, the red curve shows the functions derived from the actual data, with gray bands indicating the $1\sigma$ uncertainties derived from simulations."963 The blue curve shows the mean correlation function of the simnulatious. Cu tb).," The blue curve shows the mean correlation function of the simulations, $C_{\textrm{sim}}(b)$ ,"964The principal obstacle to the development of three-dimensional turbulence ancl a cascade to small scales is the stable stratification.,The principal obstacle to the development of three-dimensional turbulence and a cascade to small scales is the stable stratification.965 The kinetic energy. available in the vertical wind shear must be greater (han the potential energy. requirecl to mix the atmosphere., The kinetic energy available in the vertical wind shear must be greater than the potential energy required to mix the atmosphere.966 The ratio of these energies is quantified bv the Richardson number £2;=N?/(0U/Or). where N is the frequency and U is the horizontal velocity.," The ratio of these energies is quantified by the Richardson number $Ri\equiv N^2/(\partial U/\partial r)^2$, where $N$ is the frequency and $U$ is the horizontal velocity."967 A requirement for XII instability in vertical planes is that 227<1/4 somewhere in the flow. at least under adiabatic ancl inviscid conditions (Drazin&Reid1981).," A requirement for KH instability in vertical planes is that $Ri<1/4$ somewhere in the flow, at least under adiabatic and inviscid conditions \citep{Drazin_Reid81}."968. It would be Πορ if numerical researchers would report the values of Aj achieved in their simulations., It would be helpful if numerical researchers would report the values of $Ri$ achieved in their simulations.969" For an isothermal atmosphere with density and pressure scale height /7,=c2/59. the condition Ri«+ is equivalent to so Wilh 5zz7/5 as for nondegenerate molecular hydrogen. the flow must be (ransonic or else change on a scale smaller (han the scale height in order (hat A27<1/4."," For an isothermal atmosphere with density and pressure scale height $H_p=\cs^2/\gamma g$, the condition $Ri<\frac{1}{4}$ is equivalent to so with $\gamma\approx 7/5$ as for nondegenerate molecular hydrogen, the flow must be transonic or else change on a scale smaller than the scale height in order that $Ri<1/4$."970 But it is possible (hat instability max occur at larger Richardson number in the presence of radiative diffusion., But it is possible that instability may occur at larger Richardson number in the presence of radiative diffusion.971 Other instabilities that may be relevant are the baroclinic instability (Pecllosky1987:Vallis 2006).. the Goldreich-Schubert-Fricke instability (Goldreich&Sehubert1967:Fricke1968). and perhaps even (he magnetorotational instability. (Balbus&Lawley1991) if the shear extends {ο such a depth that the atmosphere becomes substantially conducting. aud if the shear has the right sign.," Other instabilities that may be relevant are the baroclinic instability \citep{Pedlosky_book,Vallis_book}, the Goldreich-Schubert-Fricke instability \citep{GoldreichSchubert67,Fricke68}, and perhaps even the magnetorotational instability \citep{balbus91} if the shear extends to such a depth that the atmosphere becomes substantially conducting, and if the shear has the right sign."972 It is bevond the scope of this note to assess the importance of these instabilities for controlling the speed of the circulation., It is beyond the scope of this note to assess the importance of these instabilities for controlling the speed of the circulation.973 Nevertheless. we will discuss the GSF instability briefly because it is illustrative and must surely occur at some level.," Nevertheless, we will discuss the GSF instability briefly because it is illustrative and must surely occur at some level."974 The GSF instability is enabled by thermal diffusion in baroclinic atmospheres of negligible viscosity that do not rotate on evlinders. 0O/0z40. even if the atmosphere is dynamically. stable according to Hollands Criterion (Tassoul1973).. i.e. baroclinically stable.," The GSF instability is enabled by thermal diffusion in baroclinic atmospheres of negligible viscosity that do not rotate on cylinders, $\partial\Omega/\partial z\ne0$, even if the atmosphere is dynamically stable according to lland's Criterion \citep{Tassoul78}, i.e. baroclinically stable."975" The instability is aNISVInInelric., and the maximum erowth rate is expressed in terms of the evlindrical radius zc and angular momentum per unit mass j=zOQ by but this is approached only al wavelengths A<2z(,/N)*7. where y=166T""/35qPe,ep)paa/p) is the thermal diffusivitv. so that radiative diffusion undercuts the restoring force of buovancv."," The instability is axisymmetric, and the maximum growth rate is expressed in terms of the cylindrical radius $\varpi$ and angular momentum per unit mass $j=\varpi^2\Omega$ by but this is approached only at wavelengths $\lambda\lesssim2\pi(\chi/N)^{1/2}$, where $\chi=16\sigma976T^3/3\kappa\rho^2c_v\sim (c/\kappa\rho)(p_{\rm rad}/p)$ is the thermal diffusivity, so that radiative diffusion undercuts the restoring force of buoyancy."977 Thus A<LHkm(íp/bar)Is/fone!) ΙΩΝ)”.," Thus $\lambda\lesssim 1\,{\rm km}\,(p/{\rm978 bar})^{-1}(\kappa/{\rm cm^2\,g^{-1}})^{-1/2} (T/10^3{\rm K})^2$ ."979 Such a wavelength would not be resolved by elobal simulations., Such a wavelength would not be resolved by global simulations.980" One müght expect the GSF instabilities {ο saburate nonlinearly at displacements £~A due to nonaxisvmmetric IKelvin-IHelmholtz instabilities acting on the risingand falling ""fingers. which carry opposilely signed eulerian"," One might expect the GSF instabilities to saturate nonlinearly at displacements $\xi\sim\lambda$ due to nonaxisymmetric Kelvin-Helmholtz instabilities acting on the risingand falling “fingers,” which carry oppositely signed eulerian"981One possibility is that the emission is extended beyond the slit adopted in these observations.,One possibility is that the emission is extended beyond the slit adopted in these observations.982 Spatially extended emission can certainly arise in outflow sources. as demonstrated by vanBoekeletal.(2009) ancl by our sample of optically thick dust disks (see Sect. ??)).," Spatially extended emission can certainly arise in outflow sources, as demonstrated by \citet{van09} and by our sample of optically thick dust disks (see Sect. \ref{Sect:thick}) )."983 However. no jets have been reported toward TW Iva and T Cha (Azevedo1993) and only a compact (8-LOmimas) outflow in Ha has been detected toward CS Cha (Takamietal.2003).," However, no jets have been reported toward TW Hya and T Cha \citep{azevedo07,alcala93} and only a compact mas) outflow in $\alpha$ has been detected toward CS Cha \citep{takami03}."984. In Sect., In Sect.985 ?? we also show (hat jets/oullows are not likely to be the main source of emission in transition objects., \ref{sect:jets} we also show that jets/outflows are not likely to be the main source of emission in transition objects.986 Another explanation for the Spitzer-VLT {his dilference is line and/or continuum variability., Another explanation for the Spitzer-VLT flux difference is line and/or continuum variability.987 At least for CS Cha and TW Ilva we know that line/contimmun variability measured from 2-epochs of Spitzer spectra is ~30%.. similar to the {his differences from the VLT and Spitzer spectra.," At least for CS Cha and TW Hya we know that line/continuum variability measured from 2-epochs of Spitzer spectra is $\sim$, similar to the flux differences from the VLT and Spitzer spectra."988 We should also keep in mind that at the distance of TW Iva and T. Cha (Table 4)) our slit just covers out to 10 AAU from the central stars., We should also keep in mind that at the distance of TW Hya and T Cha (Table \ref{table:modelparameters}) ) our slit just covers out to $\sim$ AU from the central stars.989 As discussed later even emission from the disk surface can extend bevond several tens of AU., As discussed later even emission from the disk surface can extend beyond several tens of AU.990 Further observations with wider slits and different orientation angles are necessary to constrain the spatial extension of the emission., Further observations with wider slits and different orientation angles are necessary to constrain the spatial extension of the emission.991 The most important result from the VISIR spectra is that the measured lines of transilion disks are relatively narrow (ranging [rom ~14kkin/s to 740 kkin/s) and peaked near the stellar velocity (see Table 3))., The most important result from the VISIR spectra is that the measured lines of transition disks are relatively narrow (ranging from $\sim$ km/s to $\sim$ km/s) and peaked near the stellar velocity (see Table \ref{table:results}) ).992 These line characteristics are consistent with a cisk origin [or the emission?., These line characteristics are consistent with a disk origin for the .993. We note that TW IIva. whose disk is almost seen face-on (441°. Pontoppidanetal. 2008)). has (he narrower line width.," We note that TW Hya, whose disk is almost seen face-on $4\pm 1^{\circ}$, \citealt{pontoppidan08}) ), has the narrower line width."994 The inclinations of the disks around Cs Cha and T Cha are not well constrained but likely closer to edge-on., The inclinations of the disks around CS Cha and T Cha are not well constrained but likely closer to edge-on.995 successfully model the SED of CS Cha with a disk viewed at aninclination of 607., \citet{espaillat07} successfully model the SED of CS Cha with a disk viewed at aninclination of $^\circ$ .996The star formation history (SEID) of galaxies is a key ingredient in describing thei evolution.,The star formation history (SFH) of galaxies is a key ingredient in describing their evolution.997 From an observational point of view. the SELL can be studied: by measuring the integrated. light of the galaxy population as a whole or of a homogeneous sample of galaxies at cilferent redshifts. at wavelengths associated with massive star formation (e.g.. Madau. Pozzetti Dickinson 1998: Lilly et al.," From an observational point of view, the SFH can be studied by measuring the integrated light of the galaxy population as a whole or of a homogeneous sample of galaxies at different redshifts, at wavelengths associated with massive star formation (e.g., Madau, Pozzetti Dickinson 1998; Lilly et al."998 1998)., 1998).999 An alternative method. which avoids the dillieulties in selecting a homogeneous sample of galaxies. determines the SELL of a specific galaxy using multi-band. photometry and chemical abuncances combined. with population synthesis models.," An alternative method, which avoids the difficulties in selecting a homogeneous sample of galaxies, determines the SFH of a specific galaxy using multi-band photometry and chemical abundances combined with population synthesis models."1000 In. the case of the Milky Way (MW the large amount of available data. allows to qualitatively constrict the input SEES of these methods with some accuracy (e.g.. Prantzos Aubert 1995: Chiappini. AMatteucci. Gratton 1997: C'arigi 1997: Boissier Prantzos 1999).," In the case of the Milky Way (MW), the large amount of available data allows to qualitatively constrict the input SFHs of these methods with some accuracy (e.g., Prantzos Aubert 1995; Chiappini, Matteucci, Gratton 1997; Carigi 1997; Boissier Prantzos 1999)."1001 On the same line of multi-band. photometry. but with higher precision. the SEL of à system can be. obtained through the study. of its resolved. stellar population.," On the same line of multi-band photometry, but with higher precision, the SFH of a system can be obtained through the study of its resolved stellar population."1002 This allows to construct colour-magnituce cliagrams. which contain detailed information on the SELL behind such diagrams.," This allows to construct colour-magnitude diagrams, which contain detailed information on the SFH behind such diagrams."1003 LInverting the problem however. is not. trivial. with the answer depending sensitively on the assumed metallicity of the object being studied at every time. ic.. the enrichment history.," Inverting the problem however, is not trivial, with the answer depending sensitively on the assumed metallicity of the object being studied at every time, i.e., the enrichment history."1004 The accuracy of these infercnees being aso crucially determined by the depth and error level of he observations. these requirements have so far severely constrained the applicability. of such direct. inferences to only a handful of astrophysical systems.," The accuracy of these inferences being also crucially determined by the depth and error level of the observations, these requirements have so far severely constrained the applicability of such direct inferences to only a handful of astrophysical systems."1005 Still. such methods jwe recently been applied to svstems where the metallicity ws been independently determined. and where high quality data exist.," Still, such methods have recently been applied to systems where the metallicity has been independently determined, and where high quality data exist."1006 Examples being the works of Chiosi et al. (, Examples being the works of Chiosi et al. (10071989). Aparicio et al. (,"1989), Aparicio et al. ("10081990) ancl Mould ct al. (,1990) and Mould et al. (10091997) using Alagellanie and local star clusters. ancl Mighell Butcher (1992). Smeecker-Llane et al. (,"1997) using Magellanic and local star clusters, and Mighell Butcher (1992), Smecker-Hane et al. ("10101994). Tolstoy Saha (1996). Aparicio CGallart (1995). Mighell (1997) and Lernancdez et al. (,"1994), Tolstoy Saha (1996), Aparicio Gallart (1995), Mighell (1997) and Hernandez et al. ("10112000a) using local dSph's.,2000a) using local dSph's.1012 With the coming of high equality photometric data from the Llipparcos satellite. colour magnitude diagram inversion methods using rigorous statistical analysis Clolstov," With the coming of high quality photometric data from the Hipparcos satellite, colour magnitude diagram inversion methods using rigorous statistical analysis (Tolstoy"1013lind a value of XN~0.8.,find a value of $\rm X \simeq 0.8$.1014 This caleulation also requires an extrapolation from the CO(2-1) measurements to the CO(1-0) luminosity., This calculation also requires an extrapolation from the CO(2-1) measurements to the CO(1-0) luminosity.1015" Assuming constant brightness temperature and using a value of X appropriate to ULIRGs leads to molecular gas masses of about 5x10!"" AL. for the CO emitting components in 12020725 and 13350417.", Assuming constant brightness temperature and using a value of X appropriate to ULIRGs leads to molecular gas masses of about $5\times10^{10}$ $_\odot$ for the CO emitting components in 1202–0725 and 1335–0417.1016 We can also calculate the gravitational masses using the observed sizes and line widtlis for the sources. and assuming a disk of gas in Ixeplerian rotation.," We can also calculate the gravitational masses using the observed sizes and line widths for the sources, and assuming a disk of gas in Keplerian rotation."1017" For 120201725 south we use a line width of 190 lan ! and a radius corresponding to half the separation of the two components = 0.15"" = 1.1 kpc. leading to an enclosed mass of 0.23x10!"" 707) M..."," For 1202–0725 south we use a line width of 190 km $^{-1}$ and a radius corresponding to half the separation of the two components = $''$ = 1.1 kpc, leading to an enclosed mass of $0.23 \times 10^{10}$ $^{-2}(i)$ $_\odot$."1018" For 13350417 we do not have spatially resolved spectroscopy. so we adopt a line width of 420 km | and a radius of half the separation of the two components = 0.65"" = 4.7 kpc. leading to an enclosed mass of 4.8xLOM 26) M."," For 1335–0417 we do not have spatially resolved spectroscopy, so we adopt a line width of 420 km $^{-1}$ and a radius of half the separation of the two components = $''$ = 4.7 kpc, leading to an enclosed mass of $4.8 \times 10^{10}$ $^{-2}(i)$ $_\odot$."1019 An upper limit to / can be derived by assuming that the molecular gas mass dominates the total enclosed mass., An upper limit to $i$ can be derived by assuming that the molecular gas mass dominates the total enclosed mass.1020 Using X=0.8 for 12020725 south we find 7<12. while for 13350417 we lind 7<43°.," Using $\rm X = 0.8$ for 1202–0725 south we find $i \le 12^o$, while for 1335–0417 we find $i \le 43^o$."1021 These small angles lead (o a sienilicant problem in thatthe implied rotational velocities are then extremely large. > 400 km 4.," These small angles lead to a significant problem in thatthe implied rotational velocities are then extremely large, $\ge$ 400 km $^{-1}$."1022 To obtain rotational velocities of ~250 km !. more typical of large spiral galaxies. would require a further reduction in the conversion factor to X.<0.2.," To obtain rotational velocities of $\sim 250$ km $^{-1}$, more typical of large spiral galaxies, would require a further reduction in the conversion factor to $\rm X \le 0.2$."1023 IIowever. such a low X value would violate (he minimun mass conditions dictated by optically Chin CO emission. for which X~0.35 for an excitation temperature of 50 Ix. and assuming a Galactic CO abundance (Solomon οἱ al.," However, such a low X value would violate the minimum mass conditions dictated by optically thin CO emission, for which $\rm X \sim 0.35$ for an excitation temperature of 50 K and assuming a Galactic CO abundance (Solomon et al."1024 1997)., 1997).1025 It max be that these svstems are extremely massive. or perhaps that (he apparent CO lIunminosities are magnified by gravitational lensing (see section 6).," It may be that these systems are extremely massive, or perhaps that the apparent CO luminosities are magnified by gravitational lensing (see section 6)."1026" We now consider the continuunrto-line ratio: —552—,", We now consider the continuum-to-line ratio: ${{L_{\rm FIR}}\over{L'_{\rm CO(1-0)}}}$ .1027 A non-linear relationship, A non-linear relationship1028»oint that it is possible for gas physics to significantly change the Einstein racius of massive clusters. even without caving a central barvon concentration.,"point that it is possible for gas physics to significantly change the Einstein radius of massive clusters, even without leaving a central baryon concentration."1029 Finally. we note that rani pressure stripping of hot accreted barvons. which make up the majority (~80hanvon ) o£ he cluster barvons. may help to reduce the central raction.," Finally, we note that ram pressure stripping of hot accreted baryons, which make up the majority $\sim 80\%$ ) of the cluster baryons, may help to reduce the central baryon fraction."1030 Indeed. cluster simulations find a reduced barvon Traction atorMeir20.2 (c.g.]xravtsovetal.2005:Dolagal.2009) and match better the barvonie fraction. inferred rom X-rav observations (Vikhlininetal.," Indeed, cluster simulations find a reduced baryon fraction at $r/\rv \la 0.2$ \citep[e.g.,][]{Kravtsov,Dolag} and match better the baryonic fraction inferred from X-ray observations \citep{Vikhlinin}."1031206)9).. RB is grateful. for the kind. hospitality of the. at the Larvarel-Smithsonian CLA. ancl also acknowledges support by the Moore. Distinguished Scholar program at Caltech ancl the John Simon Guggenheim Memorial Foundation.," RB is grateful for the kind hospitality of the at the Harvard-Smithsonian CfA, and also acknowledges support by the Moore Distinguished Scholar program at Caltech and the John Simon Guggenheim Memorial Foundation."1032 This work was supported in part by NASBA grant. NNNOSALA3Cἐν by Harvard. University funcls and by BSE grant. 2004386," This work was supported in part by NASA grant NNX08AL43G, by Harvard University funds and by BSF grant 2004386."1033The 1.4 Gllz VLA image of ? shows a faint jet-like extension to the southeast. while the 8.4 Gllz VLA map of ? shows only the unresolved core.,"The 1.4 GHz VLA image of \citet{Giroletti04a} shows a faint jet-like extension to the southeast, while the 8.4 GHz VLA map of \citet{Patnaik92} shows only the unresolved core."1034 The source is quite core-dominated in our VLDI image (Fig. 6)).," The source is quite core-dominated in our VLBI image (Fig. \ref{fig:0929}) ),"1035 but also shows a clear jet to the southeast. well aligned with the structure observed by 2..," but also shows a clear jet to the southeast, well aligned with the structure observed by \citet{Giroletti04a}."1036" The VLBI core displavs the verv hieh fractional polarization of m,=15%. while no polarization was detected in the jet."," The VLBI core displays the very high fractional polarization of $m_c=15\%$, while no polarization was detected in the jet."1037"SED model does not, on average, seem to provide a closer fit.","SED model does not, on average, seem to provide a closer fit."1038 The relatively good fit provided by the isothermal SED model is probably due to most of our sample consisting of low redshift galaxies and therefore that we do not probe much of the Wien part of the galaxy SED., The relatively good fit provided by the isothermal SED model is probably due to most of our sample consisting of low redshift galaxies and therefore that we do not probe much of the Wien part of the galaxy SED.1039 In Fig., In Fig.1040" 2, we summarize our results and compare the H-ATLAS dust temperatures with dust temperatures in the literature for a variety of sub-mm bright galaxies."," 2, we summarize our results and compare the H-ATLAS dust temperatures with dust temperatures in the literature for a variety of sub-mm bright galaxies."1041 These samples are: (i) the sources in BLAST detected above 5c in at least one of the BLAST bands with either a COMBO-17 (Wolf et al., These samples are: (i) the sources in BLAST detected above $\sigma$ in at least one of the BLAST bands with either a COMBO-17 (Wolf et al.1042 2004) or a SWIRE photometric redshift (Rowan-Robinson et al., 2004) or a SWIRE photometric redshift (Rowan-Robinson et al.1043 2008) and Spitzer-MIPS 70 and 160 um fluxes (Dye et al.," 2008) and -MIPS $70$ and $160\,\mu$ m fluxes (Dye et al."1044 2009; 6=1.5 fixed); (ii) local ULIRGS observed with SCUBA at 450 and 850 um and complemented with IRAS 60 and 100 um fluxes (Clements et al.," 2009; $\beta=1.5$ fixed); (ii) local ULIRGS observed with SCUBA at $450$ and $850\,\mu$ m and complemented with IRAS $60$ and $100\,\mu$ m fluxes (Clements et al."1045 2010; 6 varied); (iii) SCUBA sub-mm galaxies detected at better than 3σ at 850 um and having redshifts determined from Keck-I spectroscopy (Chapman et al.," 2010; $\beta$ varied); (iii) SCUBA sub-mm galaxies detected at better than $\sigma$ at $850\,\mu$ m and having redshifts determined from Keck-I spectroscopy (Chapman et al."1046 2005; 6=1.5 fixed); and (iv) local IRAS-selected galaxies with 60 and 100 um fluxes complemented with SCUBA 850 um (Dunne et al.," 2005; $\beta=1.5$ fixed); and (iv) local IRAS-selected galaxies with 60 and $100\,\mu$ m fluxes complemented with SCUBA $850\,\mu$ m (Dunne et al."1047 2000; β varied)., 2000; $\beta$ varied).1048" In Table 1, we list average dust temperatures as a function of redshift for several bins in redshift for both H-ATLAS only and all of the combined sub-mm galaxy samples, including H-ATLAS, plotted in Fig."," In Table 1, we list average dust temperatures as a function of redshift for several bins in redshift for both H-ATLAS only and all of the combined sub-mm galaxy samples, including H-ATLAS, plotted in Fig."1049 2., 2.1050" We do not find any evolution in the H-ATLAS dust temperature with redshift, though some evolution is inferred by BLAST measurements (Dye et al."," We do not find any evolution in the H-ATLAS dust temperature with redshift, though some evolution is inferred by BLAST measurements (Dye et al."1051 2009; Pascale et al., 2009; Pascale et al.1052" 2009), where sources at higher redshift had higher temperature in agreement with the radio-identified submillimeter-selected galaxies (SMGs) found with SCUBA (Chapman et al."," 2009), where sources at higher redshift had higher temperature in agreement with the radio-identified submillimeter-selected galaxies (SMGs) found with SCUBA (Chapman et al."1053 2005; Ivison et al., 2005; Ivison et al.1054 2010; Kovacs et al., 2010; Kovacs et al.1055 2006; Coppin et al., 2006; Coppin et al.1056 2008)., 2008).1057" While we find remarkable consistency between the average dust temperatures for our H-ATLAS sample as a function of redshift, these average values are not necessarily in agreement with other sub-mm galaxy subsamples in the literature, mostly due to selection effects."," While we find remarkable consistency between the average dust temperatures for our H-ATLAS sample as a function of redshift, these average values are not necessarily in agreement with other sub-mm galaxy subsamples in the literature, mostly due to selection effects."1058" For example, the SCUBA ULIRGS have an average temperature of (43+7)K. These sources were selected using IRAS 60um data and IRAS selected sources are known to be biased towards higher temperatures."," For example, the SCUBA ULIRGS have an average temperature of $(43 \pm 7)$ K. These sources were selected using IRAS $60\,\mu$ m data and IRAS selected sources are known to be biased towards higher temperatures."1059" Optically-selected low-redshift sub-mm galaxies are known to have colder temperatures consistent with our findings (e.g., Willmer et al."," Optically-selected low-redshift sub-mm galaxies are known to have colder temperatures consistent with our findings (e.g., Willmer et al."1060 2009; Vlahakis et al., 2009; Vlahakis et al.1061 2005)., 2005).1062" The large expected sample of sources from the 550 deg.? of H-ATLAS will enable more detailed studies in the future, without the biases associated with selections of various sub-samples, including our own."," The large expected sample of sources from the 550 $^2$ of H-ATLAS will enable more detailed studies in the future, without the biases associated with selections of various sub-samples, including our own."1063" While we show results here with B=1.5 fixed, when fitting for & and Ty we found 8=1.4+0.1, consistent with 6=1.3 found in Dunne et al. ("," While we show results here with $\beta=1.5$ fixed, when fitting for $\beta$ and $T_{\rm d}$ we found $\beta = 1.4 \pm 0.1$, consistent with $\beta=1.3$ found in Dunne et al. ("10642000).,2000).1065 In Fig., In Fig.1066" 3, we plot the dust temperature versus FIR luminosity by integrating model SEDs between 8 and 1100 um for the H-ATLAS subsample."," 3, we plot the dust temperature versus FIR luminosity by integrating model SEDs between 8 and 1100 $\mu$ m for the H-ATLAS subsample."1067 Luminosities for other samples are from the literature., Luminosities for other samples are from the literature.1068" Fitting for a relation of the form Ty=+alog(Lrig/ Lo), we find Το= —20.5K and a=4.4 (see, Fig."," Fitting for a relation of the form $T_{\rm d}={T_{\rm 0}}+\alpha\log(L_{FIR}/L_{\odot})$ , we find ${T_{\rm 0}}=-20.5$ K and $\alpha=4.4$ (see, Fig."1069 4)., 4).1070 The value of log(Lr;g/Lo) is on average 10.9+0.8 for our sample., The value of $\log(L_{FIR}/L_{\odot})$ is on average $10.9\pm0.8$ for our sample.1071 This relation is consistent with the BLAST data (Dye et al., This relation is consistent with the BLAST data (Dye et al.1072 2009)., 2009).1073" Since most of our sources lack redshifts, we consider another example application of our colour diagram and infer the statistical redshift distribution N(z) for the source samples plotted in Fig."," Since most of our sources lack redshifts, we consider another example application of our colour diagram and infer the statistical redshift distribution $N(z)$ for the source samples plotted in Fig."1074 1., 1.1075 We do this by first gridding the colour-colour plane along the SED tracks into redshift bins., We do this by first gridding the colour-colour plane along the SED tracks into redshift bins.1076 We then convert the number of sources within a grid region of colours to a binned redshift distribution (Hughes et al., We then convert the number of sources within a grid region of colours to a binned redshift distribution (Hughes et al.1077 2002)., 2002).1078 This method is equivalent to extracting the redshift probability distribution function for the whole sample if we had simply fitted SEDs to individual fluxes and taken the sum of the redshift probabilities of each source., This method is equivalent to extracting the redshift probability distribution function for the whole sample if we had simply fitted SEDs to individual fluxes and taken the sum of the redshift probabilities of each source.1079" While the redshift for an individual galaxy is largely uncertain, and sensitive to the SEDs used, the statistical redshift distribution we extract should be a reasonable estimate of the true distribution of the source sample."," While the redshift for an individual galaxy is largely uncertain, and sensitive to the SEDs used, the statistical redshift distribution we extract should be a reasonable estimate of the true distribution of the source sample."1080 Figure 4 shows the redshift distribution for SPIRE sources detected in all 3 bands (Fig., Figure 4 shows the redshift distribution for SPIRE sources detected in all 3 bands (Fig.1081 1(a))., 1(a)).1082" For the sample of 1686 sources with flux densities above 35 mJy at 350 um and above 3o0 at 250 and 500m, we find the average redshift to be 2.2+ 0.6."," For the sample of 1686 sources with flux densities above 35 mJy at $350\,\mu$ m and above $\sigma$ at $250$ and $500\,\mu$ m, we find the average redshift to be $2.2 \pm 0.6$ ."1083 This is consistent with the average redshift of, This is consistent with the average redshift of1084For these objects. most of the euergv radiated bv the central star is absorbed by the circumstellar dust shell and recadiatedoas thermal cutission. predonmiünautlv by amorphous silicates.,"For these objects, most of the energy radiated by the central star is absorbed by the circumstellar dust shell and re-radiated as thermal emission, predominantly by amorphous silicates."1085 Amorphous silicates have strong catures at 10 and LS jan. The current objects cau be ordered by increasing optical depth of those features. which aerees with ordering bv increasing waveleugth of he peak of he SED.," Amorphous silicates have strong features at 10 and 18 $\mu$ m. The current objects can be ordered by increasing optical depth of those features, which agrees with ordering by increasing wavelength of the peak of the SED."1086 When the 10-1. feature becomes optically thick. the enerev from the central star must ve re-raciated at even longer wavoeleugths. therefore the )ea position shifts towards 30 gan (seo Fig. 1)).," When the $\mu$ m feature becomes optically thick, the energy from the central star must be re-radiated at even longer wavelengths, therefore the peak position shifts towards 30 $\mu$ m (see Fig. \ref{fig1}) )."1087 It is yvclieved that the low amass loss rate Miras evolve iuto Yeh mass loss rate ΟΠΠ stars. while the IRAS colors indicate that the peak of the dust emission shifts towards ouecr waveleneths (van der Veen Παπιο 198s)).," It is believed that the low mass loss rate Miras evolve into high mass loss rate OH/IR stars, while the IRAS colors indicate that the peak of the dust emission shifts towards longer wavelengths (van der Veen Habing \cite{vanderveen}) )."1088 With Increasing nass loss rate the characteristic density in the wind will increase. increasing the optical depth towards he ceutral star.," With increasing mass loss rate the characteristic density in the wind will increase, increasing the optical depth towards the central star."1089 This evolution can be found im the oxygen-rich AGB stars in our sample., This evolution can be found in the oxygen-rich AGB stars in our sample.1090 Iu Fig., In Fig.1091 6 the objects are plotted iu the same order as in Fig. 1.. ," \ref{ovcrystal} the objects are plotted in the same order as in Fig. \ref{fig1}, ,"1092"however. the intensities are now in £, units. and normalized with respect to the measured maximal intensity."," however, the intensities are now in $F_\nu$ units, and normalized with respect to the measured maximum intensity."1093 The 10-410 feature of Mira is completely in cluission: for WAN Pse and CRL 2199. the 10-10 feature is partially self-absorbed.," The $\mu$ m feature of Mira is completely in emission; for WX Psc and CRL 2199, the $\mu$ m feature is partially self-absorbed."1094 For the OIT/IR. stars OITIO1.9. OITI27.5. OII26.5. AFGL 5379 and OID32.8. the 10-412 feature is completely in absorption. with optical depths rangiug fron l.l for OIILOLO to 3.6 for OID2.5.," For the OH/IR stars OH104.9, OH127.8, OH26.5, AFGL 5379 and OH32.8, the $\mu$ m feature is completely in absorption, with optical depths ranging from 1.1 for OH104.9 to 3.6 for OH32.8."1095 A detailed aualvsis of the amorphous silicate features will be presented in a future paper (Ikeniper et al. in preparation).," A detailed analysis of the amorphous silicate features will be presented in a future paper (Kemper et al, in preparation)."1096 As the optical depth increases. some structure becomes apparent iu the 20.15 pau region.," As the optical depth increases, some structure becomes apparent in the 20–45 $\mu$ m region."1097 Iu the lower iass-loss rate objects. strong enuüssiou features due to amorphous silicates are present. but there are no obvious uarrow features at AN>20 μπι. For the redder objects. we fud that the amorphous silicates features are(self-)absorbed.. and that ποιο structure is apparent at wavelengths Αα.>20 san. These narrow features can be identified as crystalline silicates. both olivines aud pyroxenes (Waters ct al. 1996)).," In the lower mass-loss rate objects, strong emission features due to amorphous silicates are present, but there are no obvious narrow features at $\lambda > 20$ $\mu$ m. For the redder objects, we find that the amorphous silicates features are, and that some structure is apparent at wavelengths $\lambda > 20$ $\mu$ m. These narrow features can be identified as crystalline silicates, both olivines and pyroxenes (Waters et al. \cite{waters96}) )."1098 The identifications are based on laboratory spectra of crystalline silicates (Jaeecr ct al. 1998:, The identifications are based on laboratory spectra of crystalline silicates (Jägger et al. \cite{jaeger};1099 voile et al. 1993..," Koike et al. \cite{koike},"1100 I&oike Shibai 1998)) aud simular bauds secu in other objects on which detailed studies have been performed. ie. AFGL 1106 (Molster et al. 1999a)}) ," Koike Shibai \cite{koike98}) ) and similar bands seen in other objects on which detailed studies have been performed, i.e. AFGL 4106 (Molster et al. \cite{molster}) )"1101aud to ΠΟ 15677 (Voors 1999))., and to HD 45677 (Voors \cite{voors}) ).1102 The dashed lines iu Fie., The dashed lines in Fig.1103 6 represent the position of some muportaut crvstalliue silicate complexes. which are listed in Table L. ," \ref{ovcrystal} represent the position of some important crystalline silicate complexes, which are listed in Table \ref{xtab}. ."1104These crystalline silicate features are found i clussion at the longest waveleugths but sometimes in absorption at somewhat shorter wavelengths. for example the 23.6 pau olivine feature in OIT32.8 and in OII26.5 (see Fig. 6)).," These crystalline silicate features are found in emission at the longest wavelengths but sometimes in absorption at somewhat shorter wavelengths, for example the 23.6 $\mu$ m olivine feature in OH32.8 and in OH26.5 (see Fig. \ref{ovcrystal}) )."1105 The OILI/IR stars presented here are the oulv objects Known to exhibit crystalline silicates in absorption outside the 8-13 pon waveleneth region., The OH/IR stars presented here are the only objects known to exhibit crystalline silicates in absorption outside the 8-13 $\mu$ m wavelength region.1106 For OT32.8 this was already reported by Waters Molster (1999)) iu compariso- with AFCGL 1106., For OH32.8 this was already reported by Waters Molster \cite{wamo}) ) in comparison with AFGL 4106.1107 The presence of the most nuportaut crystalline silicate features is mdicated im Table l1 for all he sources im our sample., The presence of the most important crystalline silicate features is indicated in Table \ref{xtab} for all the sources in our sample.1108 Note that those features are detected bv close examination of the spectrum: not all catures are visible iu the overview figures preseuted im his paper., Note that those features are detected by close examination of the spectrum; not all features are visible in the overview figures presented in this paper.1109 Detailed modelling of the wealth of crystalline 4.ilicate features shown by the individual objects is deferred o a future paper., Detailed modelling of the wealth of crystalline silicate features shown by the individual objects is deferred to a future paper.1110 The crystalline silicate features tend to appear iu hose sources having ereater optical depth at 10 san. However. the sharpucss of the crystalline silicate features shows a large variation.," The crystalline silicate features tend to appear in those sources having greater optical depth at 10 $\mu$ m. However, the sharpness of the crystalline silicate features shows a large variation."1111 The sharpucss is expected to be determined by properties of the crystalline silicates. such as the presence of impurities. the shape of the dust grains. and ureenlaritics iu the lattice structure.," The sharpness is expected to be determined by properties of the crystalline silicates, such as the presence of impurities, the shape of the dust grains, and irregularities in the lattice structure."1112 The spectra. of AFGL 5379 does not show the sharp crystalline peaks ound in the spectra of the other OIL/IR stars auc in the spectra of AFGL 1106 and ΠΟ 15677. but the shapes of its catures do resemble the laboratory spectra of crystalline silicates (Jaeecrao ot al. 1998)).," The spectrum of AFGL 5379 does not show the sharp crystalline peaks found in the spectra of the other OH/IR stars and in the spectra of AFGL 4106 and HD 45677, but the shapes of its features do resemble the laboratory spectra of crystalline silicates (Jägger et al. \cite{jaeger}) )."1113 This sueecstsee hat the dust eraius around these objects exhibit differences im he properties of the lattice structure. such as inpurities. roles. aud edge effects due to erain size.," This suggests that the dust grains around these objects exhibit differences in the properties of the lattice structure, such as impurities, holes, and edge effects due to grain size."1114 The appearauce of the crystalline silicate cussion features iu the redder sources in our sample confirms the relationship between dust crystallinity and cuvelope colour temperature. and hence mass-loss rate. identified by Waters et al. (1996)).," The appearance of the crystalline silicate emission features in the redder sources in our sample confirms the relationship between dust crystallinity and envelope colour temperature, and hence mass-loss rate, identified by Waters et al. \cite{waters96}) )."1115" Specifically, there secius to be a threshold value for the lass loss rate above which the crystalline silicate features appear in the spectrum."," Specifically, there seems to be a threshold value for the mass loss rate above which the crystalline silicate features appear in the spectrum."1116" Ποπονο, above this threshold value. the streneth and width of the features secu to be uncorrelated to the mass loss rate."," However, above this threshold value, the strength and width of the features seem to be uncorrelated to the mass loss rate."1117 Fie., Fig.1118 7 prescuts a inore detailed overview of the location ofthe crystalline silicate features., \ref{oh104} presents a more detailed overview of the location ofthe crystalline silicate features.1119 Tn the upper panel. theupper spectrum is that of OTLOL9.," In the upper panel, theupper spectrum is that of OH104.9."1120 The solid line represents the coutinuu fit obtained using the method described above., The solid line represents the continuum fit obtained using the method described above.1121 At longer wavelcneths the, At longer wavelengths the1122increases by a factor 16.,increases by a factor 16.1123 This is in reasonable agreement with the theoretical value and the expected behaviour with changing resolution. confirming that the NTST is triggered in our simulations.," This is in reasonable agreement with the theoretical value and the expected behaviour with changing resolution, confirming that the NTSI is triggered in our simulations."1124 Fig., Fig.1125 8 also shows that the saturation amplitude is somewhat smaller as the resolution is increased (compare also the bottom left and right panels of Fig. 7)), \ref{fig:NTSI} also shows that the saturation amplitude is somewhat smaller as the resolution is increased (compare also the bottom left and right panels of Fig. \ref{fig:evolution}) )1126 and that it converges to a resolution- value., and that it converges to a resolution-independent value.1127 The numerical simulations show that the initial perturbations are preferentially located off the binary axis. have an oscillatory behaviour with a small wavelength and grow faster when the spatial resolution is increased (Fig. 7)).," The numerical simulations show that the initial perturbations are preferentially located off the binary axis, have an oscillatory behaviour with a small wavelength and grow faster when the spatial resolution is increased (Fig. \ref{fig:evolution}) )."1128 The rapid development of these perturbations is consistent with a linear instability., The rapid development of these perturbations is consistent with a linear instability.1129 These properties are reminiscent of the TAI., These properties are reminiscent of the TAI.1130 The TAT studied by ?? is an overstability with an oscillation frequency of the velocity perturbations x1/A.," The TAI studied by \citet{1993A&A...267..155D,1996ApJ...461..927D} is an overstability with an oscillation frequency of the velocity perturbations $\propto 1/\lambda$."1131 The growth timescale is xV/A and indeed smaller wavelength perturbations grow faster at higher resolution., The growth timescale is $\propto \sqrt{\lambda}$ and indeed smaller wavelength perturbations grow faster at higher resolution.1132 ? noted that the growth is limited by pressure effects and that the TAI grows faster than the NTSI when Here. / is the minimum distance along the contact discontinuity (/=0 on the binary axis) beyond which the TAT can develop for a given wavelength A.," \citet{1994ApJ...428..186V} noted that the growth is limited by pressure effects and that the TAI grows faster than the NTSI when Here, $l$ is the minimum distance along the contact discontinuity $l=0$ on the binary axis) beyond which the TAI can develop for a given wavelength $\lambda$."1133" The relevant wavelengths are smaller than #2, and larger than the shell width L~42, /A4>. with the smaller scales growing faster."," The relevant wavelengths are smaller than $R_s$ and larger than the shell width $L\sim R_s/\mathcal{M}^2$ , with the smaller scales growing faster."1134 The instability develops preferentially along the wings (?).., The instability develops preferentially along the wings \citep{1998NewA....3..571B}.1135 The presence of the TAI closer to the binary axis at the highest resolution may explain why the growth rate of the NTSI (see Fig. 8)), The presence of the TAI closer to the binary axis at the highest resolution may explain why the growth rate of the NTSI (see Fig. \ref{fig:NTSI}) )1136 does not perfectly match the theoretical value., does not perfectly match the theoretical value.1137 Despite the similarities. we could not formally identify the TAT.," Despite the similarities, we could not formally identify the TAI."1138 One difficulty is that we were not able to quantify the growth rates as several modes interact quickly and make the linear phase very short., One difficulty is that we were not able to quantify the growth rates as several modes interact quickly and make the linear phase very short.1139 Another is that we found that our initial velocity profile along the shock is inconsistent with the equilibrium solution proposed by ?.., Another is that we found that our initial velocity profile along the shock is inconsistent with the equilibrium solution proposed by \citet{1993A&A...267..155D}.1140 This was corrected by ? but they concluded that the set of equations used by ?. led to inconsistencies in the dispersion relations. casting doubt on the theoretical rates to expect.," This was corrected by \citet{1998MNRAS.298.1021M} but they concluded that the set of equations used by \citet{1993A&A...267..155D} led to inconsistencies in the dispersion relations, casting doubt on the theoretical rates to expect."1141 We suggest that it 1s not possible to neglect. as was done. the derivatives 0/00 in the equations (6 corresponds to the polar angle to the binary axis with the origin at the stagnation point). since there is a significant change in the azimuthal speed of the incoming flow as it is decelerated and redirected along the shock.," We suggest that it is not possible to neglect, as was done, the derivatives $\partial/\partial \theta$ in the equations $\theta$ corresponds to the polar angle to the binary axis with the origin at the stagnation point), since there is a significant change in the azimuthal speed of the incoming flow as it is decelerated and redirected along the shock."1142 Although our results still support the presence in the simulations of some form of the TAT. the simulations also show that the saturation amplitude of this instability is low compared to the NTSI.," Although our results still support the presence in the simulations of some form of the TAI, the simulations also show that the saturation amplitude of this instability is low compared to the NTSI."1143 In all the simulations we performed. the non-linear evolution was dominated by the large scale. high amplitude perturbations induced by the NTSI.," In all the simulations we performed, the non-linear evolution was dominated by the large scale, high amplitude perturbations induced by the NTSI."1144 At best. the TAI may play a role in the early stages as a seed instability for the NTST. as described in refntsi..," At best, the TAI may play a role in the early stages as a seed instability for the NTSI, as described in \\ref{ntsi}."1145 In real systems the velocities of the winds are never exactly equal and the contact discontinuity is subject to the KHI., In real systems the velocities of the winds are never exactly equal and the contact discontinuity is subject to the KHI.1146 Even or a 1 velocity difference between the winds. this instability jeoretically has a larger growth rate than the TAI and NTSI.," Even for a $1\%$ velocity difference between the winds, this instability theoretically has a larger growth rate than the TAI and NTSI."1147 Fig., Fig.1148 9 compares simulations for ;j=1 with equal winds or ey.=Brox. ραubject to the KHI.," \ref{fig:NTSI_KH} compares simulations for $\eta=1$ with equal winds or $v_{1\infty}=2v_{2\infty}$, subject to the KHI."1149 We also include here a map of the r.m.s., We also include here a map of the r.m.s.1150 of 18. Velocity fluctuations observed over a long averaging period., of the velocity fluctuations observed over a long averaging period.1151 There is little difference in the outcome between equal winds and rx=25x. either in the appearance of the turbulent region op row) or in the r.m.s.," There is little difference in the outcome between equal winds and $v_{1\infty}=2v_{2\infty}$, either in the appearance of the turbulent region (top row) or in the r.m.s."1152 of the perturbations (second row)., of the perturbations (second row).1153 If anything. the KHI seems to increase slightly the region where strong fluctuations occur.," If anything, the KHI seems to increase slightly the region where strong fluctuations occur."1154 The NTSI dominates the final non-linear phase even when the KHI is initially present., The NTSI dominates the final non-linear phase even when the KHI is initially present.1155 The r.m.s., The r.m.s.1156 values close to one are the expected outcome of the NTSI (2).., values close to one are the expected outcome of the NTSI \citep{1994ApJ...428..186V}.1157 We found the same results for simulations with 7=1/16 0.0625., We found the same results for simulations with $\eta=1/16=0.0625$ .1158 The corresponding density maps and velocity perturbations are given in the bottom two rows of Fig. 9.., The corresponding density maps and velocity perturbations are given in the bottom two rows of Fig. \ref{fig:NTSI_KH}.1159 The NTSI was studied theoretically for planar shocks but the ;j=0.0625 simulations show it is also present and dominant when the shock is curved. although following it requires high numerical resolutions.," The NTSI was studied theoretically for planar shocks but the $\eta=0.0625$ simulations show it is also present and dominant when the shock is curved, although following it requires high numerical resolutions."1160 The simulations were performed with ο=12S and 5 levels of refinement in a box of size Sa., The simulations were performed with $n_x=128$ and 5 levels of refinement in a box of size $8a$.1161 For lower resolutions the NTSI is not triggered and the final result is stable (the same is observed for η= 1)., For lower resolutions the NTSI is not triggered and the final result is stable (the same is observed for $\eta=1$ ).1162 The density maps for equal winds and ep.=204 look similar., The density maps for equal winds and $v_{1\infty}=2v_{2\infty}$ look similar.1163 The highest velocity perturbations are at the same location but the r.m.s values are higher when an initial shear is present., The highest velocity perturbations are at the same location but the r.m.s values are higher when an initial shear is present.1164 We conclude that having a velocity shear in a thin shell increases the amplitude of the perturbations but does not affect much the morphology of the unstable flow. which is mostly set by the NTSI.," We conclude that having a velocity shear in a thin shell increases the amplitude of the perturbations but does not affect much the morphology of the unstable flow, which is mostly set by the NTSI."1165 This is consistent with ? who concluded from their simulations of perturbed slabs that the KHI does not strongly modify the outcome of the NTSI., This is consistent with \citet{1996NewA....1..235B} who concluded from their simulations of perturbed slabs that the KHI does not strongly modify the outcome of the NTSI.1166 Pressure has a stabilising effect on both instabilities., Pressure has a stabilising effect on both instabilities.1167 We performed a simulation. with αι Μο with all other physical and numerical parameters identical to those of the jj= lori.=rox simulations.," We performed a simulation with $\mathcal{M}_1$ $\mathcal{M}_2$ $6$ with all other physical and numerical parameters identical to those of the $\eta=1$, $v_{1\infty}=v_{2\infty}$ simulations."1168 Both instabilities are seen to develop but more slowly., Both instabilities are seen to develop but more slowly.1169 Keeping the wind velocity constant. a lower Mach number implies a higher sound speed but the thickness of the shell increases faster so that the growth timescale of the NTSI ονἐςx 1/.MD is longer.," Keeping the wind velocity constant, a lower Mach number implies a higher sound speed but the thickness of the shell increases faster so that the growth timescale of the NTSI $\propto L/c_s\propto 1/{\cal M}$ ) is longer."1170 The NTSI is also harder to trigger as it requires a perturbation of amplitude comparable to the size of theshell., The NTSI is also harder to trigger as it requires a perturbation of amplitude comparable to the size of theshell.1171 The TAT develops more slowly as pressure suppresses the development, The TAI develops more slowly as pressure suppresses the development1172In the case of dy angle the situation is more complicated.,In the case of $\delta_D$ angle the situation is more complicated.1173 Iowever. if we restrict our analvsis only to the case of the absolute value of dy angle. then we could neglect As; and Aso coellicients. because (they are equal to zero (see also (Flin2004.2005.2006. 2007))).," However, if we restrict our analysis only to the case of the absolute value of $\delta_D$ angle, then we could neglect $\Delta_{21}$ and $\Delta_{22}$ coefficients, because they are equal to zero (see also \citep{f4,Aryal04,Aryal05a,Aryal06,Aryal07}) )."1174" In that case Ay is reduced to |Ay]. while A. now denoted as A... is (he function of coefficients Ay, ancl Ay only."," In that case $\Delta_1$ is reduced to $|\Delta_{11}|$, while $\Delta$, now denoted as $\Delta_c$, is the function of coefficients $\Delta_{11}$ and $\Delta_{12}$ only."1175 However. please note that 244 and Ays are not independent of each other (Gocdlowski1994).," However, please note that $\Delta_{11}$ and $\Delta_{12}$ are not independent of each other \citep{g3}."1176. We also performed the investigation of the linear regression given by y=αν+h counted for various parameters., We also performed the investigation of the linear regression given by $y=aN+b$ counted for various parameters.1177 These were carried out [ον each investigated angle separately., These were carried out for each investigated angle separately.1178" We studied the linear regression between: the values of different statistics A7. A,σκι). A/o(A) and the number of analvzed galaxies in each particular cluster."," We studied the linear regression between: the values of different statistics $\chi^2$, $\Delta_1/\sigma(\Delta_1)$, $\Delta/\sigma(\Delta)$ and the number of analyzed galaxies in each particular cluster."1179 In the case of dp. the values of statistics: A7. Nga/oGNu). Ap/o0GN) and the number of analyzed galaxies in each particular cluster were considered.," In the case of $\delta_D$, the values of statistics: $\chi^2$, $|\Delta_{11}/\sigma(\Delta_{11})|$, $\Delta_c/\sigma(\Delta_c)$ and the number of analyzed galaxies in each particular cluster were considered."1180 We assumed that the theoretical. uniform. random distribution contains the same number of objects as the observed one.," We assumed that the theoretical, uniform, random distribution contains the same number of objects as the observed one."1181 Our null hvpothesis ff) is that the distribution is a random one., Our null hypothesis $H_0$ is that the distribution is a random one.1182 In such a case the statistics /=a/o(a) has Students distribution with u—2 degrees of freedom. where vw is the number of analvzed clusters.," In such a case the statistics $t=a/\sigma(a)$ has Student's distribution with $u-2$ degrees of freedom, where $u$ is the number of analyzed clusters."1183 It means (hat we tested Lf) hypothesis that /=0 against //4 hypothesis that />0., It means that we tested $H_0$ hypothesis that $t=0$ against $H_1$ hypothesis that $t>0$.1184" In order to reject the Lf) hypothesis. (he value of the observed statistics / should be greater than /,,.."," In order to reject the $H_0$ hypothesis, the value of the observed statistics $t$ should be greater than $t_{cr}$."1185 Our sample has PAT clusters., Our sample has 247 clusters.1186" For this sample. at the significance level a= 0.05. the value /,,.= 1.651. while for the sample of OF clusters with known values of velocity dispersion. the value /,,.=1.660."," For this sample, at the significance level $\alpha=0.05$ , the value $t_{cr} = 1.651$ , while for the sample of 97 clusters with known values of velocity dispersion, the value $t_{cr} = 1.660$."1187 Sinularly. using linear regression we looked lor possible relations between the values of applied statistics: A7. Ay/o(Ay) and A/o(A) (or A7. Nu/o(Au) and a./o(6N.) in the ease of dp angle) and the DM type of each cluster.," Similarly, using linear regression we looked for possible relations between the values of applied statistics: $\chi^2$, $\Delta_1/\sigma(\Delta_1)$ and $\Delta/\sigma(\Delta)$ (or $\chi^2$, $|\Delta_{11}/\sigma(\Delta_{11})|$ and $\Delta_c/\sigma(\Delta_c)$ in the case of $\delta_D$ angle) and the BM type of each cluster."1188 The linear regression between values of above mentioned statistics ancl velocity dispersion of galaxies inside cluster was also examined., The linear regression between values of above mentioned statistics and velocity dispersion of galaxies inside cluster was also examined.1189 The linearregression analvses were performedindependently for (he sample containing, The linearregression analyses were performedindependently for the sample containing1190Nuclear radio emission ts almost invariably associated with the presence of an active galactic nucleus (AGN) and this is an indication that the process of accretion onto a supermassive black hole (SMBH) naturally produces a signature in the form of radiation in the radio domain.,Nuclear radio emission is almost invariably associated with the presence of an active galactic nucleus (AGN) and this is an indication that the process of accretion onto a supermassive black hole (SMBH) naturally produces a signature in the form of radiation in the radio domain.1191 The separation between radio-loud (RL) and radio-quiet (RQ) AGNs ts in fact only a measure of the relative flux in the radio band with respect to the optical or X-ray nucleus (Kellermannetal.1994;Terashima&Wilson 2003):: but also RQ AGNs. when studied at sufficient depth. usually show the presence at least of a nuclear radio component (e.g..Ulvestad&Wilson1989:Na-garetal. 2005).," The separation between radio-loud (RL) and radio-quiet (RQ) AGNs is in fact only a measure of the relative flux in the radio band with respect to the optical or X-ray nucleus \citep{kellermann94,terashima03}; but also RQ AGNs, when studied at sufficient depth, usually show the presence at least of a nuclear radio component \citep[e.g.,][]{ulvestad89,nagar05}."1192. For RL AGNs the radio core results from synchrotron emission produced by the unresolved base of their jets: for RQ AGNSs the situation is more controversial and it has been recently proposed. besides the possibility of a Jet origin. that their radio nuclei are the manifestation of the presence of a thermal outflow or of an active disk corona (Blundell&Kuncic2007;LaorBehar2008) When combined to the very limited effects that absorption has on radio waves. the study of radio emission provides. in principle. a very powerful tool to detect accretion onto SMBH and. consequently. to establish when a SMBH is present in à given galaxy.," For RL AGNs the radio core results from synchrotron emission produced by the unresolved base of their jets; for RQ AGNs the situation is more controversial and it has been recently proposed, besides the possibility of a jet origin, that their radio nuclei are the manifestation of the presence of a thermal outflow or of an active disk corona \citep{blundell07,laor08}1193 When combined to the very limited effects that absorption has on radio waves, the study of radio emission provides, in principle, a very powerful tool to detect accretion onto SMBH and, consequently, to establish when a SMBH is present in a given galaxy."1194" However. to take full advantage of this approach. we must reach a much deeper understanding of what determines the radio luminosity of a given galaxy and how this ts related to its level of accretion,"," However, to take full advantage of this approach, we must reach a much deeper understanding of what determines the radio luminosity of a given galaxy and how this is related to its level of accretion."1195 A large effort has been dedicated to explore the connection between the host properties (mostly from an optical point of view) and its radio emission., A large effort has been dedicated to explore the connection between the host properties (mostly from an optical point of view) and its radio emission.1196 Already. from the pioneering study by Auriemmaetal.(1977) it was clear that more massive galaxies have on average a higher radio lummosity than smaller galaxies. while apparently there are no distinctions between clusters and non-clusters members (Ledlow&Owen1996).," Already from the pioneering study by \citet{auriemma77} it was clear that more massive galaxies have on average a higher radio luminosity than smaller galaxies, while apparently there are no distinctions between clusters and non-clusters members \citep{ledlow96}."1197 The radio luminosity functions (RLFs) of galaxies of different optical magnitudes are similar but they differ strongly in their scaling., The radio luminosity functions (RLFs) of galaxies of different optical magnitudes are similar but they differ strongly in their scaling.1198 More recent studies confirm the early results. indicating that the normalization of the RLF scales with the host luminosity as L? (e.g.Bestetal.2005:Mauch&Sadler 2007).," More recent studies confirm the early results, indicating that the normalization of the RLF scales with the host luminosity as $\sim$ $^{2.5}$ \citep[e.g.,][]{best05b,mauch07}."1199. However. galaxies of given optical magnitude show a very large range of radio power. more than 5 orders of magnitude. and the relation between the radio and optical luminosity can only be described in terms of a probability distribution.," However, galaxies of given optical magnitude show a very large range of radio power, more than 5 orders of magnitude, and the relation between the radio and optical luminosity can only be described in terms of a probability distribution."1200 These studies focused mostly on massive galaxies and had a relatively high threshold for the radio detection., These studies focused mostly on massive galaxies and had a relatively high threshold for the radio detection.

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