ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2". Generally. in addition to the “accretion torque"" z,=AlVON,I (e.g.Mattetal.2010). the disc-magnetosphere coupling can cause an additional “magnetic torque.” which is strongly dependent on the nature of the interaction and varies significantly between the models."," Generally, in addition to the “accretion torque"" $\tau_{\rm a} = \dot{M}\sqrt{G \Mns \Rt}$ \citep[e.g.][]{MP10}, the disc–magnetosphere coupling can cause an additional “magnetic torque,"" which is strongly dependent on the nature of the interaction and varies significantly between the models."3" Nevertheless. it can be concluded that small. variations of Ay, independent of the mass accretion rate (as observed here for 11808.4—3658)) can cause the NS spin-up or spin-down depending on the geometry and position of /7,, relative to 22..."," Nevertheless, it can be concluded that small variations of $\Rm$ independent of the mass accretion rate (as observed here for ) can cause the NS spin-up or spin-down depending on the geometry and position of $\Rm$ relative to $\Rco$."4 Also the data suggests. that only those models that predict that w8: w.dnthe magnetosphere can be valid to explain the observed spectral transition.," Also the data suggests, that only those models that predict that $\omega \approx \omegans$ in the magnetosphere can be valid to explain the observed spectral transition."5 So observations of AMPs — as presented here — can be used to test different hypothesis and constrain the nature of the disc-magnetosphere coupling., So observations of AMPs – as presented here – can be used to test different hypothesis and constrain the nature of the disc–magnetosphere coupling.6 Although the pulse amplitude dropped significantly. the pulse phase remained constant during the transition.," Although the pulse amplitude dropped significantly, the pulse phase remained constant during the transition."7 This is actually not surprising. based on the fact that the magnetic inclination seems to be about ϐzz10.," This is actually not surprising, based on the fact that the magnetic inclination seems to be about $\theta \approx 10\degr$."8" As the hotspot shape is most likely close to a ring (Romanovaetal.2004). the change in 7, shouldonly affect the location of the inner edge of the hotspot pin. but not change the location of the hotspot on the NS surface."," As the hotspot shape is most likely close to a ring \citep{RU04}, the change in $\Rm$ shouldonly affect the location of the inner edge of the hotspot $\rhoin$, but not change the location of the hotspot on the NS surface."9 However. the situation might be different for other AMPs. where 9 can be larger.," However, the situation might be different for other AMPs, where $\theta$ can be larger."10" For such AMPs. the hotspot shapes are most certainly not symmetric (Romanovaetal.2004)... and changes in Ay, might result in a change in the shape. size. latitude and —most importantly— the hotspot longitude."," For such AMPs, the hotspot shapes are most certainly not symmetric \citep{RU04}, and changes in $\Rm$ might result in a change in the shape, size, latitude and –most importantly– the hotspot longitude."11 Shifts in the hotspot longitude can especially cause large jumps in the observed pulse phases (seeLambetal.2009.for discussion)., Shifts in the hotspot longitude can especially cause large jumps in the observed pulse phases \citep[see][for discussion]{LBW09}.12" We speculate that such /7,,— motion of the hotspots Cand the associated phase jumps) could be the origin of at least part of the timing noise in AMPs.", We speculate that such $\Rm$ --dependent motion of the hotspots (and the associated phase jumps) could be the origin of at least part of the timing noise in AMPs.13 Observationally. such mechanism could cause the outliers in the ray flux — phase residual relations in XTE 11807—294 (Riggio2008:Patrunoetal.2009c. 2010b).. XTE 70929—314 (Gallowayetal.2002:Patruno20090). and IGR. 117511—3057 (Riggioetal.201 12: Ibragimovetal.201 13). whereas the overall X-ray flux — phase residual trends can be caused by AXI-dependent motion of the hotspots (Lambetal.2009:Patruno2009c.2010b).," Observationally, such mechanism could cause the outliers in the X-ray flux – phase residual relations in XTE J1807–294 \citep{RDB08,PWvdK09,PHW10}, XTE J0929–314 \citep{GC02,PWvdK09} and IGR J17511–3057 \citealt{RPB11}; \citealt{IKP11}) ), whereas the overall X-ray flux – phase residual trends can be caused by $\Mdot$ –dependent motion of the hotspots \citep{LBW09,PWvdK09,PHW10}."14. Also. we stress that an additional contribution to the timing noise can be caused by AXI-dependent variation of the truncation radius £2). as it affects the visibility of the secondary spot (Ibragimov&Pouta- ," Also, we stress that an additional contribution to the timing noise can be caused by $\Mdot$ –dependent variation of the truncation radius $\Rt$, as it affects the visibility of the secondary spot \citep{IP09,PIA09}. ."15These factors do not however exclude the possibility that some AMPs do spin-up during X-ray outbursts (as is most likely the case with IGR 7002914-5934. e.g. Falangaetal.2005:Burderi," These factors do not however exclude the possibility that some AMPs do spin-up during X-ray outbursts (as is most likely the case with IGR J00291+5934, e.g. \citealt{FKP05,BDL07,Pat10b,HGC11,PRB11}) )."16"where = Gor. Hatton, =V all — 3) 68",where = ) - _l) = V ( - ) ].176) Süll using V.=400 [m?. the relative probability is plotted as a [unction of yp in Fig.," Still using $V = 400$ $^3$, the relative probability is plotted as a function of $\eta$ in Fig."18 8 for several values of T'€7)., 8 for several values of $T \le T_c$.19 For T'>0.67. there is more than a probability to find the svstem with any value of 7 in the range from -0.2 to 0.2., For $T \ge 0.6T_c$ there is more than a probability to find the system with any value of $\eta$ in the range from -0.2 to 0.2.20 A major reason that this probability distribution is so Hat is due to the large value of the exponent ¢=5.81526., A major reason that this probability distribution is so flat is due to the large value of the exponent $\sigma = 5.815 \approx 6$.21 This is in contrast to the mean field models which have &=4., This is in contrast to the mean field models which have $\sigma = 4$.22 For a smaller. probably more realistic volume [rom the perspective of nuclear collisions. the f[Inctuations would be even greater.," For a smaller, probably more realistic volume from the perspective of nuclear collisions, the fluctuations would be even greater."23 The magnitude of these fInetuations suggests that it is difficult to probe the properties of the matter very close to the chiral critical point., The magnitude of these fluctuations suggests that it is difficult to probe the properties of the matter very close to the chiral critical point.24SMM 4 no reasonable estimate could be obtained because of the large error in ts).,SMM 4 no reasonable estimate could be obtained because of the large error in $\tau_8$ ).25 On the other hand. the estimates with moderate formal errors in the central and northern part of the cloud suggest low temperatures of slightly above 10 K. It should be noted. however. that there are large uncertainties concerning the dust opacities and the determination of the rs.," On the other hand, the estimates with moderate formal errors in the central and northern part of the cloud suggest low temperatures of slightly above 10 K. It should be noted, however, that there are large uncertainties concerning the dust opacities and the determination of the $\tau_8$."26 This issue will be raised again in Sect., This issue will be raised again in Sect.27 6.2., 6.2.28 In view of these uncertainties. dust temperatures estimated above should be compared with previous temperature determinations from molecular lines.," In view of these uncertainties, dust temperatures estimated above should be compared with previous temperature determinations from molecular lines."29 Observations towards several other IRDC clumps (H2CO. Careyetal. 1998:: CH;CCH. Teyssieretal.2002:: NHs.. Pillaietal.200601: Sakaietal. 2008)) provide gas kinetic temperatures of Thin10—20 K. The assumption that 74Thin ds probably valid in dense clouds (4(H:)=10° em e.g. Goldsmith&Langer 1978)).," Observations towards several other IRDC clumps $_2$ CO, \cite{carey1998}; ; $_3$ CCH, \cite{teyssier2002}; $_3$ , \cite{pillai2006b}; \cite{sakai2008}) ) provide gas kinetic temperatures of $T_{\rm kin}\approx10-20$ K. The assumption that $T_{\rm d}=T_{\rm kin}$ is probably valid in dense clouds $n({\rm H_2})\gtrsim10^5$ $^{-3}$; e.g., \cite{goldsmith1978}) )."30 Based on these considerations. we assume in what follows that in general 7415 K. Exceptions are made in the cases of two IRAS sources. for which temperatures can be derived from thespectral energy," Based on these considerations, we assume in what follows that in general $T_{\rm d}=15$ K. Exceptions are made in the cases of two IRAS sources, for which temperatures can be derived from thespectral energy"31sown ciwarfs.,brown dwarfs.32 The CPAPIR filters iatch those of he Mauna Ikea (ΑΠΟ) system (Simons&Tolku-maga2002:Tokunagaetal. 2002).," The CPAPIR filters match those of the Mauna Kea (MKO) system \citep{Simons2002, Tokunaga2002}."33.. The unresolve photometry leasurements were performed through aperture photometry (radius of one FWIIM) and are reported iu Tables 2. and 3.., The unresolved photometry measurements were performed through aperture photometry (radius of one FWHM) and are reported in Tables \ref{tbl-1} and \ref{tbl-2}.34 The zero points were se wv using all 2MMASS stars in the Point Source Catalog within an 8’ radius around the targets, The zero points were set by using all 2MASS stars in the Point Source Catalog within an $8\arcmin$ radius around the targets.35 We couvertes he 2\IASS inagnitudes into the Mauna Kea syste using the Leeeettetal.(2006) polvuouual relations., We converted the 2MASS magnitudes into the Mauna Kea system using the \citet{Leggett2006} polynomial relations.36 The uncertainties ou the zero points (tvpically ~1%) were determined from the dispersion of differences to the median divided by the square root of the number of calibration stars., The uncertainties on the zero points (typically $\sim1\%$ ) were determined from the dispersion of differences to the median divided by the square root of the number of calibration stars.37 For comparison with BDs in the literature. the Mauna Ikea system magnitudes determined for both binaries were converted back into the 2\LASS svstem using the NIRI spectra and the procedure described iu Steplicus&Leeectt (2001).," For comparison with BDs in the literature, the Mauna Kea system magnitudes determined for both binaries were converted back into the 2MASS system using the NIRI spectra and the procedure described in \citet{Stephens2004}."38. The corrections derived frou. this procedure match those eiven by the polynomial relations of Stephens&Leggett(2001). to within for the J aud II buds., The corrections derived from this procedure match those given by the polynomial relations of \citet{Stephens2004} to within for the $J$ and $H$ bands.39 Remarkably. the A-baud correction differs by ο... for both components as the A- baud portion of their spectra peaks at a slightly bluer wavelength compared to field objects of similar spectral types (sce iu particular J1501-0135D in refüe3))," Remarkably, the $K$ -band correction differs by $\sim10\%$ for both components as the $K$ -band portion of their spectra peaks at a slightly bluer wavelength compared to field objects of similar spectral types (see in particular B in \\ref{fig3}) )."40 Both objects are therefore brighter iu the slightly bluer Aio compared to Aoxtss., Both objects are therefore brighter in the slightly bluer $K_{\rm MKO}$ compared to $K_{\rm 2MASS}$.41 The CPAPIR discovery (2006) aud follow-up (2009) datasets were used to measure the proper motion of both pairs., The CPAPIR discovery (2006) and follow-up (2009) datasets were used to measure the proper motion of both pairs.42 The proper motion of field stars (Zachariasctal.2005) has been taken iuto account and. for both binarics. we corrected the proper motion measurement for the parallax estimated from the photometric distance.," The proper motion of field stars \citep{Zacharias2005} has been taken into account and, for both binaries, we corrected the proper motion measurement for the parallax estimated from the photometric distance."43 These corrections are smaller than 5 mas/vr in both spatial directions and sualler than the astrometric accuracy., These corrections are smaller than 5 mas/yr in both spatial directions and smaller than the astrometric accuracy.44 Tables 20 aud 23. report the measured proper motions., Tables \ref{tbl-1} and \ref{tbl-2} report the measured proper motions.45 A search for coninon proper motion stars within a radius was performed using the NLTT (Salim&Could2003) catalog., A search for common proper motion stars within a radius was performed using the NLTT \citep{Salim2003} catalog.46 No object was found to have a common PAL with either binary., No object was found to have a common PM with either binary.47 We note that NLTT39039 lies ποπ and has a simular PM. but our analysis rules-out a conunon PM.," We note that NLTT39039 lies from and has a similar PM, but our analysis rules-out a common PM."48 The velatively wide physical separation of ατα: ünarv (exceeded only by the SDSS1116|I3AB syste. Birninghametal. 20103) leaves room for higher-order uultiplicitv for both systems.," The relatively wide physical separation of either binary (exceeded only by the SDSS1416+13AB system, \citealt{Burningham2010}) ) leaves room for higher-order multiplicity for both systems."49 The case for a higher-order uultiple is further strengthened for jby dts large flux ratio., The case for a higher-order multiple is further strengthened for by its large flux ratio.50 Furthermore. adaptive optics observations provide accurate differential plotometiv hat can be combined with unresolved photometry for absolute flux ineasurements of madiidual componcuts.," Furthermore, adaptive optics observations provide accurate differential photometry that can be combined with unresolved photometry for absolute flux measurements of individual components."51 Both targets are too faint at visible wavelengths for watural euide star AO observations and ucither las a xieht enoush nearby star for that purpose., Both targets are too faint at visible wavelengths for natural guide star AO observations and neither has a bright enough nearby star for that purpose.52 However. hey do both have nearby enide stars that are sufficiently xieht to enable LCS AO operation.," However, they do both have nearby guide stars that are sufficiently bright to enable LGS AO operation."53 We obtained J. Z7 and πασάς of at the Gemini North telescope using the NIRI nnager in its £/32 coufieuration with the Altair AO system operated iu LOGS mode.," We obtained $J$, $H$ and imaging of at the Gemini North telescope using the NIRI imager in its f/32 configuration with the Altair AO system operated in LGS mode."54 Altair was used with its field leus that siguiicautlv reduces the anisoplanatisia effects, Altair was used with its field lens that significantly reduces the anisoplanatism effects.55" The tip-tilt star (USNO-DBI.O Oss0256280, R=16.5: Monetetal. 2003)) was located ffrom our target. at the workable limut of the system."," The tip-tilt star (USNO-B1.0 0884-0256280, $R=16.5$; \citealt{Monet2003}) ) was located from our target, at the workable limit of the system."56 We therefore had to offset from the ceuter of the field., We therefore had to offset from the center of the field.57 The nuages were reduced iun a standard manner: a skv maage was constructed from the median combination of the dithered science sequence. then science duages were sky subtracted aud divided by a dome flat.," The images were reduced in a standard manner: a sky image was constructed from the median combination of the dithered science sequence, then science images were sky subtracted and divided by a dome flat."58 The images were then registered to a common center aud median combined., The images were then registered to a common center and median combined.59" For cach filter. a set of 9 [5-8 images dithered over a 2.5"" ppatteru was taken."," For each filter, a set of 9 45-s images dithered over a $2.5$ pattern was taken."60 The separation aud position angle of the binary were taken to be the mean of the values measured in the individual fframes and the wneertaimty was derived from the standard deviation of the individual values., The separation and position angle of the binary were taken to be the mean of the values measured in the individual frames and the uncertainty was derived from the standard deviation of the individual values.61 Note that the NIRI Altair plate scale has not been fully characterized. we asuunied a pixel scale of and adopted a rather conservative unecrtainty in the separation of the binary.," Note that the NIRI Altair plate scale has not been fully characterized, we assumed a pixel scale of and adopted a rather conservative uncertainty in the separation of the binary."62 The resulting nuage of the pair is shown iu rofüel.., The resulting image of the pair is shown in \\ref{fig1}.63 The PSF cloneation is due to the sub-optimal LCS coufiguration., The PSF elongation is due to the sub-optimal LGS configuration.64 wovas observed on 2008 April OL and May 29 using the sodium LOS AQ system of the LO-meter Iseck II Telescope ou Manna Wea. Παν (vau.Dainetal.2006:Wizinowichetal. 2006).," was observed on 2008 April 01 and May 29 using the sodium LGS AO system of the 10-meter Keck II Telescope on Mauna Kea, Hawaii \citep{vanDam2006, Wizinowich2006}."65. Conditions were photometric for both runs., Conditions were photometric for both runs.66 The facility NIRC2 IR camera was used both in narrow oon a side) aud wide oon a side) feld-of-view modes., The facility NIRC2 IR camera was used both in narrow on a side) and wide on a side) field-of-view modes.67 The LOS provided the wavefrout reference. source for AO correction. with the exceptionof tip-tilt motion.," The LGS provided the wavefront reference source for AO correction, with the exceptionof tip-tilt motion."68 Tip-tilt aberrations aud quasi-static changes in the amaee of the LOS as secu by, Tip-tilt aberrations and quasi-static changes in the image of the LGS as seen by69he first (Pop.,the first (Pop.70 HI) stars have exploded: as SNe. given the relatively small binding energy of Population LLL DAL halos (Ciardi οἱ al.," III) stars have exploded as SNe, given the relatively small binding energy of Population III DM halos (Ciardi et al."71 2000)., 2000).72 We here consider the limiting case in which all theLl» as been radiatively destroved by the presence of a soft UV. ickeround., We here consider the limiting case in which all the$_{2}$ has been radiatively destroyed by the presence of a soft UV background.73 I» molecules are very vulnerable to photons with energies below the Lyman limit., $_{2}$ molecules are very vulnerable to photons with energies below the Lyman limit.74 Even before the universe has been reionized. a pervasive. soft. UV radiation ield could. therefore. have been established. (eg. Cardi et al.," Even before the universe has been reionized, a pervasive, soft UV radiation field could therefore have been established (e.g., Ciardi et al."75 2000)., 2000).76 Metals consequently. provide the only. cooling at emperatures 2S107 Hx. Other important roles in mocifving the physics of star ormation might be attributable to magnetic fields. or to he onset of turbulence.," Metals consequently provide the only cooling at temperatures $T\la 10^{4}$ K. Other important roles in modifying the physics of star formation might be attributable to magnetic fields, or to the onset of turbulence."77 Both these effects are believed. to » unimportant in the formation of the very first stars (e.g. Loeb 1998). but it will be interesting to explore their role in orming the second. generation of stars in future work.," Both these effects are believed to be unimportant in the formation of the very first stars (e.g., Loeb 1998), but it will be interesting to explore their role in forming the second generation of stars in future work."78 vevious work on this question has focused on. the chemical and thermal history of the gas. emploving a simple one-zone model for the dynamical evolution of the collapsing cloud (e.g. Silk 1977: Yoshii Sabano 1980: Lin Murray 1992: Nishi ‘Tashiro 2000: Omukai 2000).," Previous work on this question has focused on the chemical and thermal history of the gas, employing a simple one-zone model for the dynamical evolution of the collapsing cloud (e.g., Silk 1977; Yoshii Sabano 1980; Lin Murray 1992; Nishi Tashiro 2000; Omukai 2000)."79 Following the collapse to the point where the gas becomes opaque. Omukai (2000) argues that the resulting mass of the protostellar core is independent of metallicity.," Following the collapse to the point where the gas becomes opaque, Omukai (2000) argues that the resulting mass of the protostellar core is independent of metallicity."80 The final stellar mass. however. is expected to have no direct relation to the initial (core) mass. and is mainly determined by the continued accretion onto the protostellar core.," The final stellar mass, however, is expected to have no direct relation to the initial (core) mass, and is mainly determined by the continued accretion onto the protostellar core."81 Our approach. based on full three-dimensional numerical simulations of a collapsing primorclial cloud. allows for the ereation of sink particles and is thus well suited to address the complex physics of accretion.," Our approach, based on full three-dimensional numerical simulations of a collapsing primordial cloud, allows for the creation of sink particles and is thus well suited to address the complex physics of accretion."82 The paper is organized as follows., The paper is organized as follows.83 In 82. we present our numerical methodology.," In 2, we present our numerical methodology."84 The choice and justification for the initial conditions. and the results of the simulation are discussed in 83.," The choice and justification for the initial conditions, and the results of the simulation are discussed in 3."85 We summarize our findings. and address their implications in the final section.," We summarize our findings, and address their implications in the final section."86 The evolution of the dark matter and gas components is calculated with a version of TRIISPLL (Hernquist Ixatz 989). combining the smoothec particle hvedrodynamics (SPL) method with a hierarchical (tree) gravity solver (see Dromm. Coppi. Larson 2001 for further details).," The evolution of the dark matter and gas components is calculated with a version of TREESPH (Hernquist Katz 1989), combining the smoothed particle hydrodynamics (SPH) method with a hierarchical (tree) gravity solver (see Bromm, Coppi, Larson 2001 for further details)."87 Here. we discuss the additions to the code which are necessary. [or he investigation of low metallicity eas.," Here, we discuss the additions to the code which are necessary for the investigation of low metallicity gas."88 Phese are a method ο treat the radiative cooling of the gas. and a technique ο create sink particles.," These are a method to treat the radiative cooling of the gas, and a technique to create sink particles."89 The thermal evolution of the gas is governed by the equation: where D/D/ is the usual Lagrangian time derivative. DP and p are the gas pressure and density. 8 ds.the specilie internal energv (in erg 7). and D and A are the contributions from radiative heating and cooling. respectively (in units oferg 5s. 1).," The thermal evolution of the gas is governed by the equation: where ${\rmn D}/{\rmn D}t$ is the usual Lagrangian time derivative, $P$ and $\rho$ are the gas pressure and density, $u$ isthe specific internal energy (in erg $^{-1}$ ), and $\Gamma$ and $\Lambda$ are the contributions from radiative heating and cooling, respectively (in units of erg $^{-3}$ $^{-1}$ )."90 Phe first termi on the right-hand side describes adiabatie cooling due to expansion or heating due to compression., The first term on the right-hand side describes adiabatic cooling due to expansion or heating due to compression.91 We now discuss the relevant radiative processes., We now discuss the relevant radiative processes.92 We use the cooling. function. of Rücotti. Ferrara Miniati (1997) which includes cooling by fine structure and metastable lines of €. N. O. Fe. S. and Si.," We use the cooling function of Ricotti, Ferrara Miniati (1997) which includes cooling by fine structure and metastable lines of C, N, O, Fe, S, and Si."93 lonization equilibrium. is supposed. to be maintained hy cosmic rays that we assume to be associated with the heavy. element production by SNe., Ionization equilibrium is supposed to be maintained by cosmic rays that we assume to be associated with the heavy element production by SNe.94 The (primary) cosmic ray. ionization rate is scaled from the Galactic value. eg=L8;10 ts+ (Melxee 1995). by the factor Z/Z.. where Z. is the solar metallicitv.," The (primary) cosmic ray ionization rate is scaled from the Galactic value, $\zeta_{CR} = 1.8 \times 10^{-17}$ $^{-1}$ (McKee 1995), by the factor $Z/Z_{\odot}$, where $Z_{\odot}$ is the solar metallicity."95 Phe same scaling with Z is used to derive the cdust-to-gas ratio. which we take locally to be equal to 1/160.," The same scaling with $Z$ is used to derive the dust-to-gas ratio, which we take locally to be equal to 1/160."96 Again. the rationale is that dust at high redshift can only be formed in the ejecta of primordial Pype HE SNe (CTodini Ferrara 2001): hence. its production occurs simultaneously with the injection of heavy elements into the intergalactic mecdium (16M).," Again, the rationale is that dust at high redshift can only be formed in the ejecta of primordial Type II SNe (Todini Ferrara 2001); hence, its production occurs simultaneously with the injection of heavy elements into the intergalactic medium (IGM)."97 Dust. however. is only mareinally important [or the cooling (via electron. recombinations on positively charged. grains) at the low heavy clement abuncances we are interested in.," Dust, however, is only marginally important for the cooling (via electron recombinations on positively charged grains) at the low heavy element abundances we are interested in."98 In Figure 1. we show the resulting cooling function for two cillerent metallicities.," In Figure 1, we show the resulting cooling function for two different metallicities."99 Since radiative cooling. to. temperatures. below that of the cosmic microwave background. (CMD). ον=27WKOL| z). is thermodynamically not. possible. we write for the cooling term For T«Toug. radiative cooling consequently. turns into heating.," Since radiative cooling to temperatures below that of the cosmic microwave background (CMB), $T_{\rmn CMB}=2.7\mbox{\,K}(1+z)$ , is thermodynamically not possible, we write for the cooling term For $T < T_{\rmn CMB}$, radiative cooling consequently turns into heating."100 This approximate treatment ensures that 7°> Toug. unless cooling proceeds via adiabatie expansion.," This approximate treatment ensures that $T\geq T_{\rmn CMB}$ , unless cooling proceeds via adiabatic expansion."101 At 2X 30. gas temperatures are therefore. limited. to 77κ Ix. justifving the neglect. of cooling due to molecules.," At $z\ga 30$ , gas temperatures are therefore limited to $T \ga 90$ K, justifying the neglect of cooling due to molecules,"102vears [rom 1980 to 2001.,years from 1980 to 2001.103 Phis unbroken sequence normally included 4 sky limited: exposures in both £2; and. /? each vear. but in à few vears it was only possible to obtain one plate in one or both of the passbands.," This unbroken sequence normally included 4 sky limited exposures in both $B_{J}$ and $R$ each year, but in a few years it was only possible to obtain one plate in one or both of the passbands."104 Details of all the plates used in this paper are given in Table 1 of the Appendix., Details of all the plates used in this paper are given in Table 1 of the Appendix.105 The carly plates (up to 1992) were measured with the COSMOS measuring machine. and after that with SuperCOSMOS at the Roval Observatory. Exünburgh.," The early plates (up to 1992) were measured with the COSMOS measuring machine, and after that with SuperCOSMOS at the Royal Observatory, Edinburgh."106 The survey area was confined to a square area of 19 deg? in the centre of the Ποιά to avoid. problems with vignetting and other oll-axis clleets., The survey area was confined to a square area of 19 $^{2}$ in the centre of the field to avoid problems with vignetting and other off-axis effects.107" Approximately 180.000 objects were detected in this area to a limit of D,=21.5."," Approximately 180,000 objects were detected in this area to a limit of $B_{J} \approx 21.5$."108 The / plates went to a limit ol f?zz20.5., The $R$ plates went to a limit of $R \approx 20.5$.109 The plates were paired up to. give around LOO photometric measures in each of By and £2 for every objec on the plate where a detection was made., The plates were paired up to give around 100 photometric measures in each of $B_{J}$ and $R$ for every object on the plate where a detection was made.110 Because variability was the main interest for these data. the measures were firs reduced to a common photometric zero point using loca standards.," Because variability was the main interest for these data, the measures were first reduced to a common photometric zero point using local standards."111 Phese transformed measures were then calibratec with a CCD standards (Hawkins1996).. giving a tvpica relative photometric error of 0.08 mag for cach plate.," These transformed measures were then calibrated with a CCD standards \cite{h96}, giving a typical relative photometric error of 0.08 mag for each plate."112 For most vears where + plates were available this error reduce to 0.04. mag., For most years where 4 plates were available this error reduced to 0.04 mag.113 A more detailed. discussion. of these errors is given. bv. Hawkins (1996) anc references. therein., A more detailed discussion of these errors is given by Hawkins (1996) and references therein.114 The absolute photometric errors across the field are somewha larger than this. but are hard to pin down precisely without a eric of standards covering the whole field.," The absolute photometric errors across the field are somewhat larger than this, but are hard to pin down precisely without a grid of standards covering the whole field."115 They are however not significant for the present investigation where relative change in brightness is being analysed., They are however not significant for the present investigation where relative change in brightness is being analysed.116 The quasars for the sample were selected by a number of methods including ultra-violet excess. variability. objective prism. and red clrop-out.," The quasars for the sample were selected by a number of methods including ultra-violet excess, variability, objective prism, and red drop-out."117 Of the estimated. ISOO quasars in the field. some 1200 now have redshifts in the range 0.1<2o 4.5.," Of the estimated 1800 quasars in the field, some 1200 now have redshifts in the range $0.1 < z < 4.5$ ."118 From this parent population a number of complete samples have been constructed: according to. well-defined selection criteria (Llawkins2000)., From this parent population a number of complete samples have been constructed according to well-defined selection criteria \cite{h00}.119". Phe light curves now span 26 vears in the D, passband. and 21 vears in both D; and R."," The light curves now span 26 years in the $B_{J}$ passband, and 21 years in both $B_{J}$ and $R$."120 Nearly all quasars discovered by colour techniques have varied by more than 0.35 mag. the threshold. for detection by variability.," Nearly all quasars discovered by colour techniques have varied by more than 0.35 mag, the threshold for detection by variability."121 The statistics of this are ciscussecl in more detail by Hawkins (2000)., The statistics of this are discussed in more detail by Hawkins (2000).122 The quasar light. curves in this survey appear to be most useful on a timescale of 5 vears or more., The quasar light curves in this survey appear to be most useful on a timescale of 5 years or more.123 Short term. variations were studied by taking 16 exposures over six months in 1984., Short term variations were studied by taking 16 exposures over six months in 1984.124 Typical light curves are illustrated by Lawkins (1996). and analvsis shows that very [ew of the quasars in the sample vary by more than 0.1 mag over this period. This is too close to the photometric errors on the measurements to be useful for statistical analysis.," Typical light curves are illustrated by Hawkins (1996), and analysis shows that very few of the quasars in the sample vary by more than 0.1 mag over this period, This is too close to the photometric errors on the measurements to be useful for statistical analysis."125 In fact the median amplitude for quasar variation is about 0.6 mag. and most quasars in the sample take a few vears to achieve this (Llawkins2000).," In fact the median amplitude for quasar variation is about 0.6 mag, and most quasars in the sample take a few years to achieve this \cite{h00}."126. lt was stated by Llawkins (1996) that the variation of most quasars appears to be nearly. achromatic. and. indeed it is not cdillieult to find examples of quasar light curves which show no measurable colour change even with large changes in amplitude.," It was stated by Hawkins (1996) that the variation of most quasars appears to be nearly achromatic, and indeed it is not difficult to find examples of quasar light curves which show no measurable colour change even with large changes in amplitude."127 Four such cases are shown in Fig. 1..," Four such cases are shown in Fig. \ref{fig:fig1},"128 and it will be seen that although there is some scatter between blue and red magnitudes in individual vears. there is no svtematic change in colour with brightness.," and it will be seen that although there is some scatter between blue and red magnitudes in individual years, there is no sytematic change in colour with brightness."129 At the other extreme. there are quasars which show light curves of very different character in blue and rec passbands (Hawkins1998).," At the other extreme, there are quasars which show light curves of very different character in blue and red passbands \cite{h98}."130. The long term (several vears) variation of most quasars is near to being achromatic. but close examination of the light curves shows small clepartures from this simple picture.," The long term (several years) variation of most quasars is near to being achromatic, but close examination of the light curves shows small departures from this simple picture."131 lig., Fig.132 2 shows six typical quasar light curves which illustrate this., \ref{fig:fig2} shows six typical quasar light curves which illustrate this.133" Ht will be seen that although there is no systematic colour change between maximum and minimum brightness. sharp features in the blue light curves tend to be slightly ""meared out” in the red."," It will be seen that although there is no systematic colour change between maximum and minimum brightness, sharp features in the blue light curves tend to be slightly `smeared out' in the red."134 Also. there are occasional small isolated. fluctuations on a timescale of a vear in either passband which are not mirrored in the other colour.," Also, there are occasional small isolated fluctuations on a timescale of a year in either passband which are not mirrored in the other colour."135 One tvpe of variation which is rarely seen in the quasar population is the strictly chromatic variability observed. for NGC 5548 (Claveletal.1991)., One type of variation which is rarely seen in the quasar population is the strictly chromatic variability observed for NGC 5548 \cite{c91}.136. Alost statistical analysis of AGN light curves until recently was carried out by calculating the structure function (Cristianietal.1996:Look1994). or auto-correlation unction (Llawkins1996).," Most statistical analysis of AGN light curves until recently was carried out by calculating the structure function \cite{c96,h94} or auto-correlation function \cite{h96}."137. The idea was to characterise the imescale or amplitude by reference to the shape of these unctions. but the early results did not shed much light on hese or any other parameters.," The idea was to characterise the timescale or amplitude by reference to the shape of these functions, but the early results did not shed much light on these or any other parameters."138 “Phere were several problems o overcome., There were several problems to overcome.139 Perhaps the most important one concerns the imescale covered. by the observations., Perhaps the most important one concerns the timescale covered by the observations.140 Inspection. of the ight curves in Figs 1l and 2 strongly suggests power on a imescale of decades or more. and recent work has confirmed his (Hawkins2001).," Inspection of the light curves in Figs 1 and 2 strongly suggests power on a timescale of decades or more, and recent work has confirmed this \cite{h01}."141. To properly measure the timescale of variation it is clear that à run of data covering many tens of vears is ideally needed., To properly measure the timescale of variation it is clear that a run of data covering many tens of years is ideally needed.142 Although this ideal has vet to be achieved. the survey on which the present analysis is based &oes a long wav to addressing the problem.," Although this ideal has yet to be achieved, the survey on which the present analysis is based goes a long way to addressing the problem."143 Another problem with early datasets was the lack of homogeneous. regular monitoring.," Another problem with early datasets was the lack of homogeneous, regular monitoring."144 Without this. time series analysis becomes difficult. with spurious features and aliassing dominating the results.," Without this, time series analysis becomes difficult, with spurious features and aliassing dominating the results."145 Lt is also important to have a large sample of light curves covering a large span of AGN redshift and luminosity to enable subsamples to be analysed and compared., It is also important to have a large sample of light curves covering a large span of AGN redshift and luminosity to enable subsamples to be analysed and compared.146 Again. this survey marks a major improvement on earlier work.," Again, this survey marks a major improvement on earlier work."147 Another area of dilliculty concerns the procedures which have been used to analyse light curves., Another area of difficulty concerns the procedures which have been used to analyse light curves.148 The irregular pattern of observations in the monitoring programmes has led. to the choice of structure or. auto-correlations functions as, The irregular pattern of observations in the monitoring programmes has led to the choice of structure or auto-correlations functions as149"the central source, or a short lived central explosion that produces ejecta with some distribution of Lorentz factor (LF). cf. (Nouseketal.2005:PanaitescuZhang2005).","the central source, or a short lived central explosion that produces ejecta with some distribution of Lorentz factor (LF), cf. \citep{Nousek05,Panaitescu05,Zhang05}."150". In either of these scenarios the deceleration of the afterglow shock is reduced due to the energy being added to it, and this in turn produces a slowly declining light curve."," In either of these scenarios the deceleration of the afterglow shock is reduced due to the energy being added to it, and this in turn produces a slowly declining light curve."151" Slow decline of the early optical lightcurve was also reported before theSwift era, although quite rarely, c.g. GRB 021004 (Foxetal.2003)."," Slow decline of the early optical lightcurve was also reported before the era, although quite rarely, e.g. GRB 021004 \citep{Fox03}."152. Li&Chevalier(2003) have made a good case that the slowly declining early optical ightcurve of GRB 021004 could naturally occur for a stellar wind type external medium when the optical band is below the characteristic synchrotron frequency (and above the cooling break frequency)., \citet{LC03} have made a good case that the slowly declining early optical lightcurve of GRB 021004 could naturally occur for a stellar wind type external medium when the optical band is below the characteristic synchrotron frequency (and above the cooling break frequency).153" However, this explanation is unlikely to work for the slowly declining X-ray lightcurves since the X-ray band at —| hr after a GRB is expected to lie well above the synchrotron characteristic frequency, and furthermore there is no evidence for a change in the spectral slope across the break in the X-ray lighteurve at ρω»."," However, this explanation is unlikely to work for the slowly declining X-ray lightcurves since the X-ray band at $\sim1541\;$ hr after a GRB is expected to lie well above the synchrotron characteristic frequency, and furthermore there is no evidence for a change in the spectral slope across the break in the X-ray lightcurve at $t_{\rm break,2}$."155" Foxetal.(2003) argued that the early flat optical lightcurve of GRB 021004 is either due to energy injection into the afterglow shock, or due to angular inhomogeneity (patehyshell”;Kumar&Piran2000)."," \citet{Fox03} argued that the early flat optical lightcurve of GRB 021004 is either due to energy injection into the afterglow shock, or due to angular inhomogeneity \citep[``patchy156shell'';][]{KP00}."157. The latter was favored as it also provided a good explanation for the fluctuations (or “bumps”) that appear later in the optical lightcurve of GRB 021004 (seealsoNakar.Piran&Granot2003).," The latter was favored as it also provided a good explanation for the fluctuations (or “bumps”) that appear later in the optical lightcurve of GRB 021004 \citep[see158also][]{NPG03}."159". However, the sparse early afterglow data in thepre-Swiff era made it difficult to distinguish between the different explanations."," However, the sparse early afterglow data in the era made it difficult to distinguish between the different explanations."160" A long lived activity of the central source is not very appealing since it would require the source to be active up to several hours after the GRB, with a very smooth temporal behavior, where most of the energy is in the outflow that is ejected around fp»~10 s (seehoweverDai2004):: this makes the problem of the observed high efficiency for converting kinetic energy to gamma-ray radiation much worse (Nouscketal.2005)."," A long lived activity of the central source is not very appealing since it would require the source to be active up to several hours after the GRB, with a very smooth temporal behavior, where most of the energy is in the outflow that is ejected around $t_{\rm break,2}\sim16110^4\;$ s \citep[see however][]{Dai04}; this makes the problem of the observed high efficiency for converting kinetic energy to gamma-ray radiation much worse \citep{Nousek05}."162". Another interesting way to produce an early flat phase in the afterglow light curve (Eichler&Granot2005) is by a line of sight that is slightly outside the (sharp) edge of a roughly uniform jet (Granotetal.2002;Granot,Ramirez-Ruiz&Perna2005)."," Another interesting way to produce an early flat phase in the afterglow light curve \citep{EG05}163 is by a line of sight that is slightly outside the (sharp) edge of a roughly uniform jet \citep{Granot02,GR-RP05}."164". This would, however, naturally be accompanied by a weaker and softer prompt emission, perhaps resulting in an X-ray flash or X-ray rich GRB rather than a classical GRB; the more pronounced this effect 1s the flatter and longer lived the slow X-ray afterelow decay phase should be."," This would, however, naturally be accompanied by a weaker and softer prompt emission, perhaps resulting in an X-ray flash or X-ray rich GRB rather than a classical GRB; the more pronounced this effect is the flatter and longer lived the slow X-ray afterglow decay phase should be."165" Initial inspection of the data does not show such a correlation, suggesting that viewing angle effects are probably not the predominant cause of the early slow decay phase in the X-ray afterglows, at least under the simplest It is natural to expect that matter cjected in any explosion will have a range of velocities or"," Initial inspection of the data does not show such a correlation, suggesting that viewing angle effects are probably not the predominant cause of the early slow decay phase in the X-ray afterglows, at least under the simplest It is natural to expect that matter ejected in any explosion will have a range of velocities or"166The classification of short and long GRBs was introduced before the discovery of GRB afterglows (Costaetal.1997) on the basis of their observed duration: AT.«2 s for the short GRBs and AT>2 s for the long ones (Kouveliotouetal. 1993).,The classification of short and long GRBs was introduced before the discovery of GRB afterglows \citep{costa} on the basis of their observed duration: $\Delta T < 2$ s for the short GRBs and $\Delta T > 2$ s for the long ones \citep{k93}.167. A possible connection. between duration. and spectral hardness was also proposed (Kouveliotouetal.1993;Tavani 1998).," A possible connection between duration and spectral hardness was also proposed \citep{k93,t98}."168". In addition. “long” GRBs display an evident hard-to-soft transition and a time lag between the peak luminosities in different contiguous energy bands. the so-called ""spectral lag"". absent in the ""short ones (Norris2002)."," In addition, “long” GRBs display an evident hard-to-soft transition and a time lag between the peak luminosities in different contiguous energy bands, the so-called “spectral lag”, absent in the “short” ones \citep{n02}."169" Following the afterglow discovery and the spectral distribution detected by the satellite. another characteristic was introduced to discriminate between “short” and “long” GRBs,"," Following the afterglow discovery and the spectral distribution detected by the satellite, another characteristic was introduced to discriminate between “short” and “long” GRBs."170" The afterglow was observed for the ""long"" GRBs only. which Were assumed to be generated in the collapse of massive stars (the""eollapsars"".seeWoosley&Bloom2009) and to oceur in. star-forming regions."," The afterglow was observed for the “long” GRBs only, which were assumed to be generated in the collapse of massive stars \citep[the ``collapsars'', see][]{wb06} and to occur in star-forming regions."171 The crucial point in that scenario was that “long” GRBs are intrinsically connected with supernovae (SN) events. “, The crucial point in that scenario was that “long” GRBs are intrinsically connected with supernovae (SN) events. “172Short” GRBs were instead assumed to originate in coalescing neutron star binaries (seee.g..Gehrelsetal.2009.andreferences therein)...,"Short” GRBs were instead assumed to originate in coalescing neutron star binaries \citep[see e.g.,][and references therein]{ga09}."173 The first anomaly of this classification was already present in data. but was identified only years later by Norris&Bonnell (2006).," The first anomaly of this classification was already present in data, but was identified only years later by \citet{nb06}."174. They noticed the existence of hybrid sources with an occasional. softer. prolonged emission lasting tenths of seconds in the gamma-ray energy band. following an initial spike-like emission comprising an otherwise short burst.," They noticed the existence of hybrid sources with an occasional, softer, prolonged emission lasting tenths of seconds in the gamma-ray energy band, following an initial spike-like emission comprising an otherwise short burst."175 The observations by further infringed the short/long dichotomy in many ways: some short duration GRBs were observed to be followed by an X-ray afterglow (first GRB 050509B observed bySwift. see Gehrelsetal.2005.. and. two months later. GRB 050709 observed byHETE-2.. see Villasenoretal. 2005)); some nearby long-duration GRBs were also observed to be not associated with SN (GRB 060614. DellaValleetal.2006:Fynbo2006:Gal-Yametal. 2006.. and GRB 060505. Xuetal. 2009)).," The observations by further infringed the short/long dichotomy in many ways: some short duration GRBs were observed to be followed by an X-ray afterglow (first GRB 050509B observed by, see \citealp{ge05}, and, two months later, GRB 050709 observed by, see \citealp{villasenor}) ); some nearby long-duration GRBs were also observed to be not associated with SN (GRB 060614, \citealp{d06,f06,ga06}, and GRB 060505, \citealp{xu09}) )."176 GRB 071227 also presents some intriguing anomalies., GRB 071227 also presents some intriguing anomalies.177" As for the ""Norris and Bonnel” GRBs. its BAT light curve shows in the 15-150 keV range a multi-peaked structure lasting Zoo=(1.80.4) s. followed by an extended but much softer emission up to f+100 s (D'Avanzoetal.2009).."," As for the “Norris and Bonnel” GRBs, its BAT light curve shows in the $15$ $150$ keV range a multi-peaked structure lasting $T_{90}=(1.8\pm0.4)$ s, followed by an extended but much softer emission up to $t_0+100$ s \citep{D09}."178 A fading X-ray (0.3-- 10 keV) and a faint optical afterglow have also been identified., A fading X-ray $0.3$ $10$ keV) and a faint optical afterglow have also been identified.179" The optical afterglow emission allowed to measure its redshift. =0.383. and therefore its isotropic equivalent energy. E;,,=5.8x10°° erg in 20-1300 keV (D'Avanzoetal.2009)."," The optical afterglow emission allowed to measure its redshift, $z=0.383$, and therefore its isotropic equivalent energy, $E_{iso}=5.8\times10^{50}$ erg in $20$ $1300$ keV \citep{D09}."180. The observed X-ray and optical afterglow Is superimposed on the plane of the host galaxy. at (15.0+2.2) kpe from its center.," The observed X-ray and optical afterglow is superimposed on the plane of the host galaxy, at $(15.0\pm2.2)$ kpc from its center."181 On the basis of these characteristics. GRB 071227 has been classified as a short burst.," On the basis of these characteristics, GRB 071227 has been classified as a short burst."182" This statement is supported by other main features: If we consider the first and apparently predominant short-duration episode. it does not fulfill the Amati relation between the isotropic equivalent radiated energy of the prompt emission £;,, and the cosmological rest-frame vF, spectrum peak energy Εν (Amatietal.2002:Am-ati2006:Amatietal.2007. 2009)."," This statement is supported by other main features: If we consider the first and apparently predominant short-duration episode, it does not fulfill the Amati relation between the isotropic equivalent radiated energy of the prompt emission $E_{iso}$ and the cosmological rest-frame $\nu F_{\nu}$ spectrum peak energy $E_{p,i}$ \citep{A02,A06b,a07,A09}."183. The spectral lag of the first spike-like emission in 25-50 keV to 100-350 keV bands is consistent with zero (Sakamotoetal.2007)., The spectral lag of the first spike-like emission in $25$ $50$ keV to $100$ $350$ keV bands is consistent with zero \citep{sa07}.184. Multiwavelength observations performed over many days have displayed that there 1s no association with a Ib/c hypernova. the type of SN generally observed with GRBs. even if it is a nearby burst and its isotropic energy 1s compatible with that of other GRBs associated with them (D'Avanzoetal.2009).. although the upper limits are not deep enough to rule out a low-energetic core-collapse event.," Multiwavelength observations performed over many days have displayed that there is no association with a Ib/c hypernova, the type of SN generally observed with GRBs, even if it is a nearby burst and its isotropic energy is compatible with that of other GRBs associated with them \citep{D09}, although the upper limits are not deep enough to rule out a low-energetic core-collapse event."185 Nevertheless. the explosion of this burst in a star-forming region of a spiral galaxy. and its prolonged tail of emission. makes it most likely to be a long burst.," Nevertheless, the explosion of this burst in a star-forming region of a spiral galaxy, and its prolonged tail of emission, makes it most likely to be a long burst."186 In this paper. we show that all these ambiguities and peculiarities can be explained in the framework of the fireshell model if we assume GRB 071227 to be a short burst. in which the first spike-like emission coincides with the P-GRB and the prolonged softer tail with the peak of the extended afterglow emitted in a low CircumBurst Medium (CBM) density region.," In this paper, we show that all these ambiguities and peculiarities can be explained in the framework of the fireshell model if we assume GRB 071227 to be a short burst, in which the first spike-like emission coincides with the P-GRB and the prolonged softer tail with the peak of the extended afterglow emitted in a low CircumBurst Medium (CBM) density region."187 We show. moreover. that this tail satisfies the Amati relation. and this ts consistent with our interpretation.," We show, moreover, that this tail satisfies the Amati relation, and this is consistent with our interpretation."188" Within the fireshell model (Ruffinietal..2002.2004.2005. 2005a.b).. all GRBs originate from an optically thick e= plasma of total energy £7,(4, 1n the range"," Within the fireshell model \citep{R02,R04,R05,R09,B05,Bia05}, , all GRBs originate from an optically thick $e^\pm$ plasma of total energy $E_{tot}^{e^\pm}$ in the range"189directly in (the three-dimensional space using a variety of density thresholds ranging from 10nq: to 1280nope Wilh increments by a factor of 2.,directly in the three-dimensional space using a variety of density thresholds ranging from $10~n_{aver}$ to $1280~n_{aver}$ with increments by a factor of 2.190" We make the simple assumption that a threshold of 20n,,,,=10 * is of the order of the excitation density for the NIL; (J— K)-(.1) transition. whereas a threshold of 1602,,,,=8x107 ?* is of the order ol the excitation density for the (1-0) Nel] emission line."," We make the simple assumption that a threshold of $20~n_{aver}=10^{4}$ $^{-3}$ is of the order of the excitation density for the $_{3}$ $J-K$ )=(1,1) transition, whereas a threshold of $160~n_{aver}=8 \times 10^{4}$ $^{-3}$ is of the order of the excitation density for the (1-0) $_{2}$ $^{+}$ emission line."191 Below these values. it is assumed that the molecules are under-excitecl and (hat there is no emission in the considered lines.," Below these values, it is assumed that the molecules are under-excited and that there is no emission in the considered lines."192 The clump-finding algorithm (takes into account the periodicity of the simulation box ancl (hus. of cores that extend across the box boundaries.," The clump-finding algorithm takes into account the periodicity of the simulation box and thus, of cores that extend across the box boundaries."193 In this section. we briefly summarize some of the basic properties of simulations 1 and D2 in terms of their respective populations of cores identilied at the selected. density thresholds.," In this section, we briefly summarize some of the basic properties of simulations B1 and B2 in terms of their respective populations of cores identified at the selected density thresholds."194 As time evolves. turbulence decavs in the box and the sonic Mach. number decreases from ME—10 at /=0 to. M=[5.28. 3.54. 2.97. 3.08. 3.28. 3.36] at 1=[0.087.0.226.0.293.022ye6.0.4 is run Bl and to M —[3.61. 3.37. 2.89. 2.89. 2.59. 2.73] al /=οστ0.280.0.351.0.3173.0.420.0.486] in model D2.," As time evolves, turbulence decays in the box and the sonic Mach number decreases from ${\cal M}=10$ at $t=0$ to ${\cal M}$ =[5.28, 3.54, 2.97, 3.08, 3.28, 3.36] at $t=[0.087, 0.226, 0.293, 0.356, 0.410, 0.424]~t_{ff,cl}$ is run B1 and to ${\cal M}$ =[3.61, 3.37, 2.89, 2.89, 2.59, 2.73] at $t=[0.257, 0.280, 0.351, 0.373, 0.420, 0.486]$ in model B2."195 By /~0.42Γεω the rims Mach number has decayed faster in model D2 to a value of 2.6 and which is comparable to the riis Mach. number in the Ophiucus cloud feo. Enoch et al.," By $t \sim 0.42~t_{ff,cl}$, the $rms$ Mach number has decayed faster in model B2 to a value of $2.6$ and which is comparable to the $rms$ Mach number in the Ophiucus cloud (e.g., Enoch et al."196 2007 based on the COMPLETE survey. Ridge et al.," 2007 based on the COMPLETE survey, Ridge et al."197 2006) as compared to à value of ~3 in run Bl which is comparable to the rms Mach number in the Perseus noleular cloud. (Enoch et al., 2006) as compared to a value of $\sim 3$ in run B1 which is comparable to the $rms$ Mach number in the Perseus molcular cloud (Enoch et al.198 2007. Pineda οἱ al.," 2007, Pineda et al."1992008)5.. In both runs. the Mach numbers increases again at later stages because the rms velocity becomes increasingly dominated bv the large velocity components in the collapsing cores.," In both runs, the Mach numbers increases again at later stages because the $rms$ velocity becomes increasingly dominated by the large velocity components in the collapsing cores."200 Tabs. 1-, Tabs. \ref{table1}-201"4. display the riis Mach 1unbers. the numbers of C20 cores (cores identified at a density threshold of 20μυ) and the C160 cores (cores identified at a density threshold of 160 05,4). the peak density in the box in units of the average density. the median mass of the cores. their median sizes (taken to be (he cubie root of the cores volumes). their median specific angular momentum. and (heir median rotational parameter (see below lor definition) at (wo selected. nearly similar. epochs."," \ref{table4} display the $rms$ Mach numbers, the numbers of C20 cores (cores identified at a density threshold of $20~n_{aver}$ ) and the C160 cores (cores identified at a density threshold of $160~n_{aver}$ ), the peak density in the box in units of the average density, the median mass of the cores, their median sizes (taken to be the cubic root of the cores volumes), their median specific angular momentum, and their median rotational parameter (see below for definition) at two selected, nearly similar, epochs."202" At early epochs (i.e.. when /S0.35 pp4). the peak density in the simulation box. associated with the most massive cores is of the order of a few LO""n4, a few LO? oM"" which is characteristic of the densities of gravitationally bound cores (e.g.. Lee et al."," At early epochs (i.e., when $t \lesssim~0.35~t_{ff,cl}$ ), the peak density in the simulation box, associated with the most massive cores is of the order of a few $10^{3}~n_{aver} \sim$ a few $10^{5}$ $^{-3}$ which is characteristic of the densities of gravitationally bound cores (e.g., Lee et al."203 2001:, 2001;204the shock front (e.g.. Frederiksen et al.,"the shock front (e.g., Frederiksen et al."205 2004: Kato 2005: Chang et al., 2004; Kato 2005; Chang et al.206 2008: Haugbolle 2010)., 2008; Haugbolle 2010).207 The characteristic scale of the magnetic fields is the order of skin depth as predicted. by the analvsis of Weibel instability., The characteristic scale of the magnetic fields is the order of skin depth as predicted by the analysis of Weibel instability.208" Then. the wavelength of (urbulent magnetic field Ay is described by using a coefficient # as where xy. is the plasma frequency. and Pi, is the relative. Lorentz factor between colliding shells."," Then, the wavelength of turbulent magnetic field $\lambda_{\mathrm{B}}$ is described by using a coefficient $\kappa$ as where $\omega_{\mathrm{pe}}$ is the plasma frequency, and $\Gamma_{\mathrm{int}}$ is the relative Lorentz factor between colliding shells."209 The energv conversion fraction into the magnetic fields is 107—0.1. where D?/8z is energy. density of magnetic fields. and Dunne is the kinetic enerev densitv of the shell.," The energy conversion fraction into the magnetic fields is $10^{-3}-0.1$, where $B^2/8\pi$ is energy density of magnetic fields, and $\Gamma_{\mathrm{int}} n m_{\mathrm{p}} c^2$ is the kinetic energy density of the shell."210 The Lorentz [actor of electrons is similar to Dj. and that & ds (vpically LO from the result of PIC simulations. the strength. parameter @ can be estimated as Thus. the assumption α«1l on which jitter radiation and DSR. weak random field regime are based is not necessarily valid when we consider the radiation from the internal shock region of GRB.," The Lorentz factor of electrons is similar to $\Gamma_{\mathrm{int}}$, and that $\kappa$ is typically $10$ from the result of PIC simulations, the strength parameter $a$ can be estimated as Thus, the assumption $a\ll1$ on which jitter radiation and DSR weak random field regime are based is not necessarily valid when we consider the radiation from the internal shock region of GRB."211 Fleishman Urtiev (2010) calculated the radiation spectrum lor α>1 using a statistical method. but their treatment of the. “small scale component” is somewhat arbitrary.," Fleishman Urtiev (2010) calculated the radiation spectrum for $a>1$ using a statistical method, but their treatment of the ""small scale component"" is somewhat arbitrary."212 They introduced the critical wavelength A44 aud called components wilh AxA4 the small scale component”. where Àj Obevs the inequality (Toptvgin Fleishman 1937).," They introduced the critical wavelength $\lambda_{\mathrm{crit}}$ and called components with $\lambda \leq \lambda_{\mathrm{crit}}$ the ""small scale component"", where $\lambda_{\mathrm{crit}}$ obeys the inequality (Toptygin Fleishman 1987)."213 The inequality can be transformed to . πο that the division through Apia may be ambiguous when we caleulate the radiation spectrum for 1.«a5.," The inequality can be transformed to $1\ll \lambda_{\mathrm{crit}}e|B|/mc^2 \ll \gamma$ , so that the division through $\lambda_{\mathrm{crit}}$ may be ambiguous when we calculate the radiation spectrum for $1<a<\gamma$."214 The svuthetic spectra from PIC simulations were calculated. recently (e.g.. Hecdedal 2005: Sironi Spitkovsky 2009: Frederiksen 2010: Reville Wirk 2010: Nishikawa et al 2011).," The synthetic spectra from PIC simulations were calculated recently (e.g., Hededal 2005; Sironi Spitkovsky 2009; Frederiksen 2010; Reville Kirk 2010; Nishikawa et al 2011)."215 Althogh their magnetic fields are realistic ancl sell-consistent. it is inevitable that the fields are described bv discrete cells in PIC simulation.," Althogh their magnetic fields are realistic and self-consistent, it is inevitable that the fields are described by discrete cells in PIC simulation."216 Reville Ixirk (2010) developed an alternative method of caleulation of radiation spectra that uses the concept of photon, Reville Kirk (2010) developed an alternative method of calculation of radiation spectra that uses the concept of photon217is however enough to compensate the deficit of Type-I. galaxies in the GAS runs.,is however enough to compensate the deficit of Type-1 galaxies in the GAS runs.218 As explained in Sec. 2..," As explained in Sec. \ref{sec:sims},"219 we have considered as genuine substructures all those with at least 32 bound particles., we have considered as genuine substructures all those with at least 32 bound particles.220" Our resolution limit for the galaxy stellar mass is therefore Mai,στ325Myaofs&7o10h1M. (with fiu;= 0.17."," Our resolution limit for the galaxy stellar mass is therefore $M_{\rm star} \simeq22132 \times M_{\rm part} \times f_{\rm bar} \simeq 7 \times 10^9 h^{-1} M_\odot$ (with $f_{\rm bar} = 0.17$ )."222 This value is close to the peak of the differential mass functions shown in the upper panels of Figure 3.., This value is close to the peak of the differential mass functions shown in the upper panels of Figure \ref{fi:MFS}.223 All galaxies below this mass limit were born in fully resolved haloes. but were not able to transform all their baryons into stars (e.g. because their parent halo was accreted onto a bigger system. their gas reservoir was stripped and their star formation activity suppressed. or because they are young gas-rich galaxies in haloes that formed relatively late).," All galaxies below this mass limit were born in fully resolved haloes, but were not able to transform all their baryons into stars (e.g. because their parent halo was accreted onto a bigger system, their gas reservoir was stripped and their star formation activity suppressed, or because they are young gas-rich galaxies in haloes that formed relatively late)."224 Figure 4. shows the density profile of all galaxies within reo from the DM (black solid lines) and the GAS (red dot-dashed lines) runs., Figure \ref{fi:rad_prof} shows the density profile of all galaxies within $r_{200}$ from the DM (black solid lines) and the GAS (red dot-dashed lines) runs.225 Solid lines show the average obtained by stacking the profiles of the four clusters used in this study. while shaded regions show the minimum and maximum value obtained for the simulated clusters.," Solid lines show the average obtained by stacking the profiles of the four clusters used in this study, while shaded regions show the minimum and maximum value obtained for the simulated clusters."226 As for Figure 3.. we show the density protile corresponding to the whole galaxy population in the left panel. and the contributions from Type-2 and non-Type-2 galaxies in the central and left panels respectively.," As for Figure \ref{fi:MFS}, we show the density profile corresponding to the whole galaxy population in the left panel, and the contributions from Type-2 and non-Type-2 galaxies in the central and left panels respectively."227 All profiles have been normalised to the mean galaxy density within r»oo. and correspond to the galaxies identitied at =0.," All profiles have been normalised to the mean galaxy density within $r_{200}$, and correspond to the galaxies identified at $z=0$."228 Inall panels. the dashed green line shows the average DM protile of the simulated clusters. normalised to match the density protile of the galaxies in the inner bin.," In all panels, the dashed green line shows the average DM profile of the simulated clusters, normalised to match the density profile of the galaxies in the inner bin."229 The galaxy density profile is dominated by the Type-2 galaxy population at all radii. and follows very nicely the underlying DM profile. in agreement with what found by ?..," The galaxy density profile is dominated by the Type-2 galaxy population at all radii, and follows very nicely the underlying DM profile, in agreement with what found by \citet{Gao_etal_2004}."230 By definition. the central Type-O galaxies populate the innermost bin in Figure 4..," By definition, the central Type-0 galaxies populate the innermost bin in Figure \ref{fi:rad_prof}."231 The right panel of this figure shows that Tvpe-1 galaxies tend to avoid the central cluster regions. where they are efficiently destroyed by the intense tidal field of the parent halo.," The right panel of this figure shows that Type-1 galaxies tend to avoid the central cluster regions, where they are efficiently destroyed by the intense tidal field of the parent halo."232" The radial profile of Type- galaxies is ""anti-biased relative to the dark matter profile in the inner regions. as expected from studies of dark matter substructures (99"," The radial profile of Type-1 galaxies is `anti-biased' relative to the dark matter profile in the inner regions, as expected from studies of dark matter substructures \citep{Ghigna_etal_2000,2004MNRAS.349.1101D}."233 The agreement between the DM and GAS runs is quite good., The agreement between the DM and GAS runs is quite good.234 The only notable difference is a small shift towards the centre for the positions of Type-| galaxies in the GAS runs., The only notable difference is a small shift towards the centre for the positions of Type-1 galaxies in the GAS runs.235 We have verified. however. that this difference is due to a single galaxy which is found closer to the centre in the GAS run of the cluster g72.," We have verified, however, that this difference is due to a single galaxy which is found closer to the centre in the GAS run of the cluster g72."236 The shift is due to the influence of the gas on the orbit of substructures. as we will discuss in the following.," The shift is due to the influence of the gas on the orbit of substructures, as we will discuss in the following."237 The good agreement for the radial distribution of Type-2 galaxies in the two sets of runs used in this study is not obvious., The good agreement for the radial distribution of Type-2 galaxies in the two sets of runs used in this study is not obvious.238 We recall that the positions of Type-2 galaxies are given by the updated positions of the particles that were the most bound particles of the parent substructure. before their masses were reduced below the resolution limit of the simulation.," We recall that the positions of Type-2 galaxies are given by the updated positions of the particles that were the most bound particles of the parent substructure, before their masses were reduced below the resolution limit of the simulation."239 The agreement between the DM and GAS runs therefore implies that the presence of gas in the simulation does not significantly alter the distribution of those particles. which trace the spatial distribution of DM particles.," The agreement between the DM and GAS runs therefore implies that the presence of gas in the simulation does not significantly alter the distribution of those particles, which trace the spatial distribution of DM particles."240 In the previous section. we have shown that the cluster galaxy population resulting from the model employed in this study is dominated in number by Type-2 galaxies.," In the previous section, we have shown that the cluster galaxy population resulting from the model employed in this study is dominated in number by Type-2 galaxies."241 Model predictions for this galaxy population are very sensitive to the residual merging times that are assigned to Type-2 galaxies when their parent dark matter subhaloes are stripped below the resolution limit of the simulation., Model predictions for this galaxy population are very sensitive to the residual merging times that are assigned to Type-2 galaxies when their parent dark matter subhaloes are stripped below the resolution limit of the simulation.242be valuable in this regard.,be valuable in this regard.243 An important question concerns the ratio of Iuminosities between the two nuclei., An important question concerns the ratio of luminosities between the two nuclei.244" Using 25,0m imaging. Soiler οἱ al. ("," Using $\mu$ m imaging, Soifer et al. ("2451999) measured a 3:1 ratio. with the western nucleus being (he stronger.,"1999) measured a 3:1 ratio, with the western nucleus being the stronger."246 Since most of the luminosity of Arp 220 emerges at longer wavelengths (around 100jmi). and since there is evidence for significant opacity al 25/0. (Soifer οἱ al.," Since most of the luminosity of Arp 220 emerges at longer wavelengths (around $\mu$ m), and since there is evidence for significant opacity at $\mu$ m (Soifer et al."247 2002). the infrared evidence strongly suggests a 3:1 luminosity ratio. but is not conclusive. and does not dictate an origin (AGN or starburst) for the buminosity.," 2002), the infrared evidence strongly suggests a 3:1 luminosity ratio, but is not conclusive, and does not dictate an origin (AGN or starburst) for the luminosity."248 The RSN data presented here support a roughly 3:1 ratio of starburst luminosities between (he nuclei., The RSN data presented here support a roughly 3:1 ratio of starburst luminosities between the nuclei.249 The dillerent rates in the east and the west (1/yr and 2/vr respectively). while obviously very poorly determined due (to small number statistics. are roughly consistent with ratio of luminosities (2.7) assumed in 4.2.1 for testing (he hypothesis that the eastern nucleus differs from the west only in starburst intensity and (vpical RSN ages.," The different rates in the east and the west (1/yr and 3/yr respectively), while obviously very poorly determined due to small number statistics, are roughly consistent with ratio of luminosities (2.7) assumed in 4.2.1 for testing the hypothesis that the eastern nucleus differs from the west only in starburst intensity and typical RSN ages."250 Future monitoring will quickly refine (his statistical result., Future monitoring will quickly refine this statistical result.251 The apparent agreement between infrared and RSN evidence for a 3:1 ratio lends weight to the hypothesis that the bolometric luminosity of Arp 220 is dominated by starburst activity., The apparent agreement between infrared and RSN evidence for a 3:1 ratio lends weight to the hypothesis that the bolometric luminosity of Arp 220 is dominated by starburst activity.252 If AGN activity were a major contributor. one would expect the overall ratio to differ [rom the ratio based solely on starburst activity.," If AGN activity were a major contributor, one would expect the overall ratio to differ from the ratio based solely on starburst activity."253 Although requiring confirmation with more data unaffected by opacity. this appears not to be Che case: starburst activity (traced by radio supernovae vields the same luminosity ratio as a method (IR. imaging) which is blind to the luminosity source.," Although requiring confirmation with more data unaffected by opacity, this appears not to be the case; starburst activity traced by radio supernovae yields the same luminosity ratio as a method (IR imaging) which is blind to the luminosity source."254 A supernova origin for the svnchrotron plasma responsible for the diffuse continuum enission is stronelv supported by our data., A supernova origin for the synchrotron plasma responsible for the diffuse continuum emission is strongly supported by our data.255 We see a detailed correspondence between the properties of the supernova aggregations and (he diffuse emission regions. consistent with diffusion of supernova renmnant relativistic electrons into the interstellar medium.," We see a detailed correspondence between the properties of the supernova aggregations and the diffuse emission regions, consistent with diffusion of supernova remnant relativistic electrons into the interstellar medium."256 The degree of correspondence suggests that the electrons are not diffusing very far. most likely due to relatively short svnchrotron lifetimes of the electrons.," The degree of correspondence suggests that the electrons are not diffusing very far, most likely due to relatively short synchrotron lifetimes of the electrons."257 The ISM density could also be involved. since it mav influence both the local star formation rate and the local svnchrotron emissivity when seeded with SN. electrons.," The ISM density could also be involved, since it may influence both the local star formation rate and the local synchrotron emissivity when seeded with SNR electrons."258 This emission is of the kind expected to conform to the well-known FIRradio correlation.," This emission is of the kind expected to conform to the well-known FIR/radio correlation,"259"where p,,—po(0).uy,wo(0).eu,e.(O) are the nudplane values of the equilibrium density. pseudo-enthalpy and sound speed.","where $\rho_m\equiv \rho_0(0),~w_m\equiv w_0(0),~c_{sm}\equiv260c_s(0)$ are the midplane values of the equilibrium density, pseudo-enthalpy and sound speed."261 We define the three-dimensional analogue of Toonmre's parameter as which is a measure of disc self-gravitv (from. now on until Section. 6. we will use Qso without subscript everywhere. so it) should not be confused. with the 2D ‘Toomre’s parameter).," We define the three-dimensional analogue of Toomre's parameter as which is a measure of disc self-gravity (from now on until Section 6, we will use $Q_{3D}$ without subscript everywhere, so it should not be confused with the 2D Toomre's parameter)."262 Using that at.the midplane cingfdz(0)=0. we can derive from equations (5-7) a single equation for the normalized. pseudo-enthalpy The normalized. density and. sound. speed: are. found from pu=wy.οἳany.," Using that atthe midplane $dw_0/dz(0)=0$, we can derive from equations (5-7) a single equation for the normalized pseudo-enthalpy The normalized density and sound speed are found from $\rho_0=w_0^s,~c_s^2=w_0$."263 Equation (9) shows that. even though the disc is in Weplerian rotation (1... selí-gravity in the radial direction can be neglected). it must be included in determining the vertical structure.," Equation (9) shows that even though the disc is in Keplerian rotation (i.e., self-gravity in the radial direction can be neglected), it must be included in determining the vertical structure."264 We integrate equation (9). starting at 2=O with aw(0)= 1. until i. monotonically decreasing with z. reaches zero at some finite height/edge z=hf. which is therefore determined as a result of the integration process.," We integrate equation (9), starting at $z=0$ with $w_0(0)=1$ , until $w_0$, monotonically decreasing with $z$, reaches zero at some finite height/edge $z=h$, which is therefore determined as a result of the integration process."265 At this edge. the density. ancl sound speed also vanish. pol)=Q0.c;(h)0 (see also GLB and RPL).," At this edge, the density and sound speed also vanish, $\rho_0(h)=0, c_s(h)=0$ (see also GLB and RPL)."266 Vhe height and entire. vertical structure of a polvtropic disc are therefore uniquely. specified: solely by Q and 5. which are free parameters in equation (9).," The height and entire vertical structure of a polytropic disc are therefore uniquely specified solely by $Q$ and $s$, which are free parameters in equation (9)."267 Figure 1 illustrates the sub- αμα superaciabatic equilibrium: vertical structures obtained from equation (9) for various €9., Figure 1 illustrates the sub- and superadiabatic equilibrium vertical structures obtained from equation (9) for various $Q$.268 For a fixed s. the disc height Ph decreases with decreasing Q.," For a fixed $s$, the disc height $h$ decreases with decreasing $Q$."269 Phe sound speed is a decreasing function of z that does not permit the existence of two-dimensional modes in threc-dimoensional models of polvtropic dises as opposed. to isothermal ones (7.LP.IXDP)..," The sound speed is a decreasing function of $z$ that does not permit the existence of two-dimensional modes in three-dimensional models of polytropic discs as opposed to isothermal ones \citep[][LP,270KP]{LPS90}."271 We also see that the equilibrium structures for sub- and superadiabatie cases look similar except that they have. respectively. everywhere positive and negative Ng that diverges at the surface because the sound speed. vanishes there.," We also see that the equilibrium structures for sub- and superadiabatic cases look similar except that they have, respectively, everywhere positive and negative $N_0^2$ that diverges at the surface because the sound speed vanishes there."272 We consider here small axisvmumetric (ὃν=ϐὐ) perturbations of the form up.picxerpliot|Hor) about the equilibrium states found above. where w and & are the frequency. and the racial wavenumber. respectively.," We consider here small axisymmetric $\partial/\partial y=0$ ) perturbations of the form ${\bf u'}, \rho', p', \psi' \propto273exp(-i\omega t+ikx)$ about the equilibrium states found above, where $\omega$ and $k$ are the frequency and the radial wavenumber, respectively."274 Without a loss of generality. we assume throughout that & is non-negative. &zO0.," Without a loss of generality, we assume throughout that $k$ is non-negative, $k\geq 0$."275" After switching to non-dimensional variables: we can derive [rom equations (1-4) the following set of equations governing the linear dynamics of axisvmmoetric perturbations we now make the changes: fe uL.wpfoe'wi'ca,and.. eliminate d)., ""nu.∕∕⋅pfrom :equations (10).pe (11). C13). we arrive at the following set of equations for the three basic quantities a.p.c (hencelorth. primes will be omitted) where the non-dimensional epievelic frequency A ds eiven by ho-οq)= 1."," After switching to non-dimensional variables: we can derive from equations (1-4) the following set of equations governing the linear dynamics of axisymmetric perturbations If we now make the changes: $iu'_z\rightarrow u'_z,~\omega276p'/\rho_0\rightarrow p',~\omega\psi'\rightarrow \psi'$ and eliminate $u'_x,~u'_y,~\rho'$ from equations (10), (11), (13), we arrive at the following set of equations for the three basic quantities $u'_z,~p',~\psi'$ (henceforth primes will be omitted) where the non-dimensional epicyclic frequency $\kappa$ is given by $\kappa^2=2(2-q)=1$ ."277 Notice that the density perturbationson the right hand side of the linearized Poisson's equation (18) consist of two physically cillerent parts., Notice that the density perturbationson the right hand side of the linearized Poisson's equation (18) consist of two physically different parts.278 The density perturbations duc to compressibility.," The density perturbations due to compressibility,"279The inethod described above provides a quantitative way of answeriug tlie questious such as: l. how the RV uncertatuty is correlated. with different levels of residual of telluric liue removal: 2. what the contribution of RV uncertainty due to tellurie Contamination is in the final RV error budget in each different observational baudpass.,"The method described above provides a quantitative way of answering the questions such as: 1, how the RV uncertainty is correlated with different levels of residual of telluric line removal; 2, what the contribution of RV uncertainty due to telluric contamination is in the final RV error budget in each different observational bandpass."280 RV calibration sources are used to track the drift that is uot caused by the stellar reflex motion due O all Unseen companion., RV calibration sources are used to track the drift that is not caused by the stellar reflex motion due to an unseen companion.281 A emission lamp or a gas absorption cell is usually used for sicl purpose., A emission lamp or a gas absorption cell is usually used for such purpose.282" We calculate the RV uncertainties bought by tje. Calibration sources themselves based o1 thei"" spectral properties.", We calculate the RV uncertainties brought by the calibration sources themselves based on their spectral properties.283" The RV calibration sources iu ¢ης‘ent observational baudpasses are clin""usse in $932.3..", The RV calibration sources in different observational bandpasses are discussed in \ref{sec:RVcal}.284 For gas absorption cells. we assune a contiLULL1 level of 30.000 ADU (wit1i the vpical liear rauge) on a CCD with a 16-bit dynamite ‘ange. Wwlich corresponds to à S/N of 125 ΙΓie gal is at 6 electron/ADU.," For gas absorption cells, we assume a continuum level of 30,000 ADU (within the typical linear range) on a CCD with a 16-bit dynamic range, which corresponds to a S/N of 425 if the gain is at 6 electron/ADU."285 For a emissiot klp. we assune that the strongest line in specla region has a peak flux of 30.000 ADU.," For a emission lamp, we assume that the strongest line in the spectral region has a peak flux of 30,000 ADU."286 Note that I pixels J)er 'esolutiou elemen is nssull th'oughout te paper., Note that 4 pixels per resolution element is assumed throughout the paper.287 Fig., Fig.288 2 shows the BV calibralol lice‘talies as a function of oervatlo baiepass at ¢ferent spectral resolutions., \ref{fig:Un_Cal_Res} shows the RV calibration uncertainties as a function of observational bandpass at different spectral resolutions.289" Note the ""mlere aσσ ‘rently two successlul calilati sources in V od. i.e.. a Th-Ar lamp (asterisk) a Lociue cell (square)."," Note that there are currently two successful calibration sources in $V$ band, i.e., a Th-Ar lamp (asterisk) and an Iodine cell (square)."290 'Therefo'e. both are Sidered aud plotted for V. baud in Fig. 2..," Therefore, both are considered and plotted for $V$ band in Fig. \ref{fig:Un_Cal_Res}."291 The “esls shown in Fig0, The results shown in Fig.292 9 are also suiinarized i e 2.., \ref{fig:Un_Cal_Res} are also summarized in Table \ref{tab:RV_cal}.293 Gas absorption cells usually offer higher calibraion precision thau emission latips because (leuser lines distribution and on-average higher S/N. However. this conclusion depends ou the ibration methods. it is usually the case for Nou-Comnon Path alle| Bracketing method while it ot always true in Superliposing scheme. which will be discussed ater iu this section.," Gas absorption cells usually offer higher calibration precision than emission lamps because of denser lines distribution and on-average higher S/N. However, this conclusion depends on the calibration methods, it is usually the case for Non-Common Path and Bracketing method while it is not always true in Superimposing scheme, which will be discussed later in this section."294 The optimal observational bandpass for precision RV measurements depends ou the cuality ol a stellar spectrum (Q factor). photon flux (S/N). RV calibration uncertainty. the seveguy of telluric liue contaiinatio1 ancl other actors.," The optimal observational bandpass for precision RV measurements depends on the quality of a stellar spectrum (Q factor), photon flux (S/N), RV calibration uncertainty, the severity of telluric line contamination and other factors."295 We will cousider different situations in the folOWing discussion., We will consider different situations in the following discussion.296 MὉ assne a S/N (per pixel) of 100 at the center o- Y baud (i.e.. A—1020 11m) al R=60.000. the S/N in otler observaticoial baudpass varies with stellar spectral energy clistriuton. (SED) zud spectra resolttion accordiielv.," We assume a S/N (per pixel) of 100 at the center of $Y$ band (i.e., $\lambda$ =1020 nm) at $\rm{R}$ =60,000, the S/N in other observational bandpass varies with stellar spectral energy distribution (SED) and spectral resolution accordingly."297 The S/N reported in tlis paper is at the center «of exich observatioual bandpass (see Table 1) uuless otherwise specified., The S/N reported in this paper is at the center of each observational bandpass (see Table \ref{tab:SpecBand}) ) unless otherwise specified.298 We will investigate the o(tiilal observatioual bandpass fo ‘precision Doppler nieasuremeuts given tle same exposure time. the sane telescope aperture aud the same instrunent throughput (incepenceut of wavelength).," We will investigate the optimal observational bandpass for precision Doppler measurements given the same exposure time, the same telescope aperture and the same instrument throughput (independent of wavelength)."299range goes from ~0.1 ddex to ~2 ddex in the unstable modes or 0.5 ddex to Sdex in the stable modes.,"range goes from $\sim0.1$ dex to $\sim2$ dex in the unstable modes or $0.5$ dex to $5\,$ dex in the stable modes."300 Changing the disk mass 7MaMoy. we also obtain a numper of interesting trends.," Changing the disk mass $M_{d}/M_{\rm BH}$, we also obtain a number of interesting trends."301 For the chosen 1) and )-ὐ. unstable modes first appear at Ady/Mii~OQ.> the criterion depends somewdat on these quantities. but in general we find it agrees more or |ess with our WKB instability crierion in Equation 27..," For the chosen $\eta$ and $\beta$, unstable modes first appear at $M_{d}/M_{\rm BH}\sim0.1$; the criterion depends somewhat on these quantities, but in general we find it agrees more or less with our WKB instability criterion in Equation \ref{eqn:instab.criterion}."302 At smaler MyfMg. there are only stable modes — these persist at arbitrar small M;/Myj and can still drive quite significant eccentricities and inflow rates. and at sufficiently small AZ;/Mp their properties can be well-approximated by the derivations in ?..," At smaller $M_{d}/M_{\rm BH}$, there are only stable modes – these persist at arbitrarily small $M_{d}/M_{\rm BH}$ and can still drive quite significant eccentricities and inflow rates, and at sufficiently small $M_{d}/M_{\rm BH}$ their properties can be well-approximated by the derivations in \citet{tremaine:slow.keplerian.modes}."303" Once instability arises. there is only a weak dependence of the growth rate and O, on Ma/Mgn. however (it is largely determined by © at the radius where M, reaches this threshold mass)."," Once instability arises, there is only a weak dependence of the growth rate and $\Omega_{p}$ on $M_{d}/M_{\rm BH}$, however (it is largely determined by $\Omega$ at the radius where $M_{d}$ reaches this threshold mass)."304 Inflow rates increase approximately in proportion to the disk mass., Inflow rates increase approximately in proportion to the disk mass.305 Figures +--8 illustrate some of the eigenvectors (normal modes) for a range of eigenvalues w. for representative choices of 1) and 7.," Figures \ref{fig:m1.1}- \ref{fig:m1.5} illustrate some of the eigenvectors (normal modes) for a range of eigenvalues $\omega$, for representative choices of $\eta$ and $\beta$."306 We focus on the global modes: there are of course a wide spectrum of local modes available on large scales of the self-gravitating disk., We focus on the global modes; there are of course a wide spectrum of local modes available on large scales of the self-gravitating disk.307" In each Figure. we plot the mode amplitude [1]. as well as Rec,/X)=Jetexpfé &drj. which shows the winding and corregations ofthe modes."," In each Figure, we plot the mode amplitude $|a(R)|$, as well as ${\rm Re}(\Sigma_{a}/\Sigma) = |a(R)|\,\exp{\{i\,\int^{r}k\,dr \}}$ , which shows the winding and corregations ofthe modes."308"f The surface density perturbations generically experience sharp gradients and reflect. off the OLR (Rew)2O5. r~ aa few) although in a some cases the V,0 earlier. at COR (a typical factor ~3 smaller radius)."," The surface density perturbations generically experience sharp gradients and reflect off the OLR $(\omega)=\Omega+\kappa$, $r\sim$ a few), although in a some cases the $\Sigma_{a}\rightarrow0$ earlier, at COR (a typical factor $\sim3$ smaller radius)."309" We also plot the vector radial perturbation. defined for simplicity here as just ΑιΑΝ (R,/R| is equivalent to the standard scalar eccentricity in the nearly-Keplerian regime: also in this regime [R,/R|zz|v,/V.| where the velocity perturbation ΛΙ)."," We also plot the vector radial perturbation, defined for simplicity here as just $R_{a}/R$ $|R_{a}/R|$ is equivalent to the standard scalar eccentricity in the nearly-Keplerian regime; also in this regime $|R_{a}/R| \approx |v_{a}/V_{c}|$ where the velocity perturbation $v_{1,\,R} = dR_{1}/dt$ )."310 This clearly reflects the X perturbation., This clearly reflects the $\Sigma$ perturbation.311" We also show the magnitude of the radial perturbation. |Ri|/R (defined above) along with the magnitude of its dimensionless derivative. ΑιfdΑΙ. and the same for the azimuthal perturbation Ó,."," We also show the magnitude of the radial perturbation, $|R_{1}|/R$ (defined above) along with the magnitude of its dimensionless derivative, $|d\,R_{1}/d\,R|$, and the same for the azimuthal perturbation $\phi_{1}$."312 If these quantities exceed unity. there are orbit crossings. therefore shocks and gas dissipation.," If these quantities exceed unity, there are orbit crossings, therefore shocks and gas dissipation."313 Note that orbit crossings can occur. in principle. even if these quantities do not exceed unity - this is only an approximate guideline.," Note that orbit crossings can occur, in principle, even if these quantities do not exceed unity - this is only an approximate guideline."314 In fact. ?/ show that in a disk with finite gas sound speed ο. there can be gas collisions and shocks. even where there are no orbit crossings.," In fact, \citet{hopkins:inflow.analytics} show that in a disk with finite gas sound speed $c_{s}$, there can be gas collisions and shocks, even where there are no orbit crossings."315 The requirement for dissipative encounters is that gas streams moving in the potential of the mode be compressed by the torques from the collisionless component at à velocity greater than ο., The requirement for dissipative encounters is that gas streams moving in the potential of the mode be compressed by the torques from the collisionless component at a velocity greater than $c_{s}$.316 This condition can be written lef] *| Fbposδν | where QO=ομπα.," This condition can be written ( | + | 1 where $Q=c_{s}\,\kappa/\pi\,G\,\Sigma$."317" This depends on the gas sound speed cy. 80 is not determined in the collisionless models here. but if we assume the gas in these disks has c,σε. then we can determine £."," This depends on the gas sound speed $c_{s}$, so is not determined in the collisionless models here, but if we assume the gas in these disks has $c_{s}\sim \sigma_{z}$, then we can determine $\xi$."318" The results are plotted: at small radii especially. £2| is common — for disks with finite c,c- in their gas. shocks will be common (owing to the large V. radial motions of the eccentric modes) at small radii. even when formal orbit erossings are rare."," The results are plotted; at small radii especially, $\xi\gg1$ is common – for disks with finite $c_{s}\sim \sigma_{z}$ in their gas, shocks will be common (owing to the large $\sim V_{c}$ radial motions of the eccentric modes) at small radii, even when formal orbit crossings are rare."319 Finally we show the induced inflow/outflow rates. using the scaling in Equation 43. to determine the gas inflow response to the stellar-BH potential.," Finally we show the induced inflow/outflow rates, using the scaling in Equation \ref{eqn:inflow} to determine the gas inflow response to the stellar+BH potential."320 Because of our choice of units. these inflow rates are in units of. fa.Mii(GMenRy* where eas=MaaΜη is the gas mass fraction in the disk.," Because of our choice of units, these inflow rates are in units of $f_{\rm gas}\,M_{\rm BH}\,(G\,M_{\rm BH}/R_{0}^{3})^{1/2}$, where $f_{\rm gas}=M_{\rm gas}/M_{\ast}$ is the gas mass fraction in the disk."321 The inflow rates can be quite large for the systems of interest — given typical numbers. a rate of ~107 in these plots corresponds to —0.1—LAL:vr! accretion rates onto a supermassive BH. or ~107M.vr! onto a star.," The inflow rates can be quite large for the systems of interest – given typical numbers, a rate of $\sim10^{-4}$ in these plots corresponds to $\sim0.1-1\,M_{\sun}\,yr^{-1}$ accretion rates onto a supermassive BH, or $\sim10^{-5}\,M_{\sun}\,yr^{-1}$ onto a star."322 Now. consider specifically Figures «οι which illustrate modes with different frequencies and radial wavenumbers. for a fixed disk system.," Now, consider specifically Figures \ref{fig:m1.1}- \ref{fig:m1.2}, which illustrate modes with different frequencies and radial wavenumbers, for a fixed disk system."323 We see several of the behaviors discussed in S:: the modes are global in dynamic range. but can have sizeable ΙΚΑ] and a large number of nodes.," We see several of the behaviors discussed in \ref{sec:sims}: the modes are global in dynamic range, but can have sizeable $|kR|$ and a large number of nodes."324 Since the slopes here are steeper than or equal to 7)—1/2. the modes can exist down to r=0.," Since the slopes here are steeper than or equal to $\eta=1/2$, the modes can exist down to $r\rightarrow0$."325 Modes with smaller pattern speed extend to larger radii (the OLR moves out) and can sustain their amplitude over a larger dynamic range. while modes with Reto)=>| are not supported at moderate to large radii.," Modes with smaller pattern speed extend to larger radii (the OLR moves out) and can sustain their amplitude over a larger dynamic range, while modes with $(\omega)\gg1$ are not supported at moderate to large radii."326 Modes with large negative pattern speed are not seen: but those with moderate pattern speed are present are are among the most long-wavelength modes., Modes with large negative pattern speed are not seen; but those with moderate pattern speed are present are are among the most long-wavelength modes.327 This behavior is similar to that of the e-modes in?) — however. that work concluded that when the disk mass is negligible compared to the BH mass. such modes cannot be supported in an isolated BH+disk system: here. we find that moderate disk-to-BH mass ratios allow for their existence.," This behavior is similar to that of the $g$ -modes in \citet{tremaine:slow.keplerian.modes} – however, that work concluded that when the disk mass is negligible compared to the BH mass, such modes cannot be supported in an isolated BH+disk system; here, we find that moderate disk-to-BH mass ratios allow for their existence."328 The induced velocity perturbation and eccentricities are large. and reflect the mode density structure.," The induced velocity perturbation and eccentricities are large, and reflect the mode density structure."329 Where present. orbit crossings tend to occur between the COR and OLR (8~Ro). and at the smallest radii.," Where present, orbit crossings tend to occur between the COR and OLR $R\sim R_{0}$ ), and at the smallest radii."330 However. one is rarely in the strong orbit-crossing regime — there seems to almost be a maximum Λι/dR|~L.," However, one is rarely in the strong orbit-crossing regime – there seems to almost be a maximum $|d R_{1}/d R|\sim1$."331" This is easy to understand from the WKB analysis: recall. we showed that in the nearly-Keplerian.low disk mass limit. Iv,ZV.]zJal/|AR|."," This is easy to understand from the WKB analysis: recall, we showed that in the nearly-Keplerian,low disk mass limit, $|v_{r}/V_{c}|\approx |a|/|kR|$."332 Since we are nearly Keplerian. it is trivial to show that correspondingly [Ri/R|z|v;/V.|].," Since we are nearly Keplerian, it is trivial to show that correspondingly $|R_{1}/R| \approx |v_{r}/V_{c}|$."333 And in the WKB limit. didR=ik. so Ri/dR|zx|a].," And in the WKB limit, $d/dR=i\,k$, so $|d R_{1}/d R| \approx |a|$."334 Since [αἱ<| always. we do not expect to see dramatic orbit crossings.," Since $|a|<1$ always, we do not expect to see dramatic orbit crossings."335 However. the criteria for shocks. from ?.. is satistied over a wide range of radii with ον1.," However, the criteria for shocks, from \citet{hopkins:inflow.analytics}, is satisfied over a wide range of radii with $\xi\gg 1$."336" This occurs because the perturbation velocities are a fixed fraction |a|£|KR| of V... and so diverge at small radii — thus even without formal orbit erossings. gas is being compressed in the mode at velocities “>c, at small radii. generating shocks and dissipation."," This occurs because the perturbation velocities are a fixed fraction $\sim|a|/|kR|$ of $V_{c}$, and so diverge at small radii – thus even without formal orbit crossings, gas is being compressed in the mode at velocities $\gg c_{s}$ at small radii, generating shocks and dissipation."337 This. correspondingly. allows for the inflow rates calculated (wherever£ |).," This, correspondingly, allows for the inflow rates calculated (wherever $\xi\gtrsim1$ )."338 The inflow rates drop towards Ro>0. as seen in hydrodynamic simulations (see Figures 5 112 in ο).," The inflow rates drop towards $R\rightarrow0$, as seen in hydrodynamic simulations (see Figures 5 12 in \citealt{hopkins:zoom.sims}) )."339" But given the choice of units here. they are still quite large at radii 107—Ro. where for the appropriate choice of ©, and 5j. they often asymptote to approximately constant MCR)."," But given the choice of units here, they are still quite large at radii $\sim 10^{-3}-10^{-2}\,R_{0}$, where for the appropriate choice of $\Omega_{p}$ and $\eta$, they often asymptote to approximately constant $\dot{M}(R)$."340 Recall again the units used: if the value in Figure 4+ is zr then the implied Eddington ratio of the BH is Af/AMyayzm892rifauGy/10M;2(Ro10pcY7. or SORifogsGe/10M.;Y!A(of10?pe7.," Recall again the units used: if the value in Figure \ref{fig:m1.1} is $\tilde{m}$, then the implied Eddington ratio of the BH is $\dot{M}/\dot{M}_{\rm Edd} \approx 341892\,\tilde{m}\,f_{\rm gas}\,(M_{\rm BH}/10^{8}\,\msun)^{1/2}\,(R_{0}/10\,{\rm pc})^{-3/2}$, or $508\,\tilde{m}\,f_{\rm gas}\,(M_{\rm BH}/10^{8}\,\msun)^{-1/4}\,342(\Sigma_{0}/10^{5}\,\msun\,{\rm pc^{-2}})^{3/4}$."343 So the implied accretion rates at these radii are about Eddington.Y for amode of near-maximal strength.," So the implied accretion rates at these radii are about Eddington, for amode of near-maximal strength."344 This is important. since these are the radii where we expect the viscous disk to take over inside such a radius. the ratio of the disk to BH mass is as low as ~—107. so Q becomes extremely large and we expect star formation (and thus the roleof the collisionless component) to be inefficient.," This is important, since these are the radii where we expect the viscous disk to take over – inside such a radius, the ratio of the disk to BH mass is as low as $\sim10^{-5}$, so $Q$ becomes extremely large and we expect star formation (and thus the roleof the collisionless component) to be inefficient."345 For a circum-stellar disk. these radii approach the stellar radius itself.," For a circum-stellar disk, these radii approach the stellar radius itself."346 In Figure 6.. we consider how the modes depend on the disk mass profile slope ἡ.," In Figure \ref{fig:m1.3}, we consider how the modes depend on the disk mass profile slope $\eta$ ."347 When the slope is shallow. the modes are confined to larger radii: at ;j~0.5—1.0 mode amplitudes propagate," When the slope is shallow, the modes are confined to larger radii; at $\eta\sim0.5-1.0$ mode amplitudes propagate"348The results show unequivocally that the thickness of (he tachocline increases with increasing latitude. making the overall shape of the latitude more complex — while (he outer boundary is prolate. the inner boundary is close to spherical or perhaps even a little oblate.,"The results show unequivocally that the thickness of the tachocline increases with increasing latitude, making the overall shape of the latitude more complex — while the outer boundary is prolate, the inner boundary is close to spherical or perhaps even a little oblate."349 This appears to be consistent with the [act that the base of the convection zone is almost spherical., This appears to be consistent with the fact that the base of the convection zone is almost spherical.350 The jump across the tachocline is the only parameter (that shows a significant change with solar activity., The jump across the tachocline is the only parameter that shows a significant change with solar activity.351 Other parameters also appear to show some change with time. however the tachocline properties obtained. with GONG data aud those wilh ALDI do not always show consistent behavior.," Other parameters also appear to show some change with time, however the tachocline properties obtained with GONG data and those with MDI do not always show consistent behavior."352 If the oscillatory temporal variations of tachocline properties are confirmed. it would imply (hat the solar zonal flow. (vhich is the temporally varvine component of solar rotation) penetrates to the base of the convection zone.," If the oscillatory temporal variations of tachocline properties are confirmed, it would imply that the solar zonal flow (which is the temporally varying component of solar rotation) penetrates to the base of the convection zone."353 This work utilizes data obtained by the Global Oscillation Network Group (GONG) project. managed by the National Solar Observatory. which is operated by AURA. Inc. under a cooperalive agreement wilh the National Science Foundation.," This work utilizes data obtained by the Global Oscillation Network Group (GONG) project, managed by the National Solar Observatory, which is operated by AURA, Inc. under a cooperative agreement with the National Science Foundation."354 The data were acquired bv instruments operated by the Bie Bear Solar Observatory. High. Altitude. Observatory. Learmonth Solar Observatory. Udaipur Solar Observatory. Instituto de Astrolisico de Canarias. and Cerro Tololo Inter-American Observatory.," The data were acquired by instruments operated by the Big Bear Solar Observatory, High Altitude Observatory, Learmonth Solar Observatory, Udaipur Solar Observatory, Instituto de Astrofisico de Canarias, and Cerro Tololo Inter-American Observatory."355 This work also utilizes data from the Solar Oscillations Iuivestigation/ Michelson Doppler Lnager (SOL/AIDI) on the Solar aud Heliospheric Observatory (SOHO)., This work also utilizes data from the Solar Oscillations Investigation/ Michelson Doppler Imager (SOI/MDI) on the Solar and Heliospheric Observatory (SOHO).356 SOIIO is a project of international cooperation between ESA and NASA., SOHO is a project of international cooperation between ESA and NASA.357 SD acknowledges support [rom NSF grant ATM 0348827 and NASA erant NNXIO0AEGOC., SB acknowledges support from NSF grant ATM 0348837 and NASA grant NXX10AE60G.358Maguetic fields are thought to be present ina variety of astroplivsical objects. including stars. planets. accretion disces. galaxies and the interstellar aud intergalactie media.,"Magnetic fields are thought to be present in a variety of astrophysical objects, including stars, planets, accretion discs, galaxies and the interstellar and intergalactic media."359 Iu some cases the, In some cases the360ol magnetic null points in the corona above.,of magnetic null points in the corona above.361 As a consequence we find that the density of magnetic null points in a potential field extrapolation is about ?Mam7 over any patch of quiet Sun. varving by roughly. LOW from. dav to day.," As a consequence we find that the density of magnetic null points in a potential field extrapolation is about $N_n(1.5\,{\rm Mm})=3.1\times 10^{-3}\,{\rm Mm}^{-2}$ over any patch of quiet Sun, varying by roughly $10\%$ from day to day."362 This value is just more than twice the number of nulls found by Régegnier. Parnell and. Haynes (2008) at heights greater (han 1.5 Mm. using IHinode data of much higher resolution.," This value is just more than twice the number of nulls found by Réggnier, Parnell and Haynes (2008) at heights greater than 1.5 Mm, using Hinode data of much higher resolution."363 The discrepancy. could possibly arise from the much greater [lux imbalance over that. particular maegnetogram., The discrepancy could possibly arise from the much greater flux imbalance over that particular magnetogram.364 The column we find corresponds (o 2 nulls above everv 5 hexagonal. supergranules (lagenaar.SchiijverandTitle1997) ," The column we find corresponds to 2 nulls above every 5 hexagonal, 14-Mm-diameter supergranules \citep{Hagenaar1997} ."365The potential magnetic field extrapolated from a photospheric magnetogram tends to become spatially smoother at increasing heights., The potential magnetic field extrapolated from a photospheric magnetogram tends to become spatially smoother at increasing heights.366 This is a general property of harmonic functions ancl their gradients., This is a general property of harmonic functions and their gradients.367 One consequence is that the density of null points in such a field decreases with height and most of the null points are lound close to the surface., One consequence is that the density of null points in such a field decreases with height and most of the null points are found close to the surface.368 Of the nul points above z=1.5 Mm roughly 75% are found within the next 3.0 Mm., Of the null points above $z=1.5$ Mm roughly $75\%$ are found within the next 3.0 Mm.369" We find the spectra estimate of the null point density in the generic quiet Sun to be p,(2)e0.04/(z+d)3, where d1.4Mm."," We find the spectral estimate of the null point density in the generic quiet Sun to be $\rho_n(z)\simeq0.04/(z+d)^{-3}$, where $d\simeq1.4\,{\rm Mm}$."370 This simple fiuetional form follows from the approximately exponentia nature of the photospheric spectrum., This simple functional form follows from the approximately exponential nature of the photospheric spectrum.371 The densitv al verv low heights. sav z<l1Man. is dictated by very. small horizonta structure in the photospheric field.," The density at very low heights, say $z<1\,{\rm Mm}$, is dictated by very small horizontal structure in the photospheric field."372 This structure is the most challenging to observe. and its observation is subject to the most instrumental distortion.," This structure is the most challenging to observe, and its observation is subject to the most instrumental distortion."373 Moreover. (his lowest atmospheric laver. the chromosphere. has the greatest plasma pressure aud mass density and is least likely to salis[v the conditions which would render a magnetic field potential. or even force free.," Moreover, this lowest atmospheric layer, the chromosphere, has the greatest plasma pressure and mass density and is least likely to satisfy the conditions which would render a magnetic field potential, or even force free."374 For these reasons we choose to locus our investigation on null points above 2=1.5 Mm.," For these reasons we choose to focus our investigation on null points above $z=1.5\,{\rm Mm}$ ."375 This nominal height has nothing to do with the empirical depth. 4. characterizing the exponential slope of the photospheric spectra.," This nominal height has nothing to do with the empirical depth, $d$, characterizing the exponential slope of the photospheric spectra."376 Rather. it arose from our experience wilh different instrumentation (MDI low-resolutionversus high-resolution) aud clifferent methods of accommodating instrumental effects such as the MTE.," Rather, it arose from our experience with different instrumentation (MDI low-resolution high-resolution) and different methods of accommodating instrumental effects such as the MTF."377 We lound that the null point densitv. px(z). varied less above z=1.5Mm due to these instrumental factors. so we deemed it to be more accurately measured there.," We found that the null point density, $\rho_N(z)$, varied less above $z=1.5\,{\rm Mm}$ due to these instrumental factors, so we deemed it to be more accurately measured there."378 The density aud distribution of null points in the corona is predicted somewhat reliably. alihough not perfectly. by spectral estimate of Longcope. Brown and Priest (2003. LDPO3)).," The density and distribution of null points in the corona is predicted somewhat reliably, although not perfectly, by spectral estimate of Longcope, Brown and Priest (2003, )."379 Alagnetic null points can be found directly. and (hus with more accuracy. in a potential field extrapolated) from a photospheric magnetogram.," Magnetic null points can be found directly, and thus with more accuracy, in a potential field extrapolated from a photospheric magnetogram."380 We used (his technique to test the spectral estimate. and found it predicted the shape of the density. px(z). reasonably well.," We used this technique to test the spectral estimate, and found it predicted the shape of the density, $\rho_N(z)$, reasonably well."381 The spectral estimate of the total column was. however. too low by a factor of two to three above one Mm.," The spectral estimate of the total column was, however, too low by a factor of two to three above one Mm."382 If the spectral estimate for everv maegnetogran is low bv (he same factor. then the actual null density in the quiet Sunwould be greater than (he value we report.," If the spectral estimate for every magnetogram is low by the same factor, then the actual null density in the quiet Sunwould be greater than the value we report."383for all seven observations but with one more degree of freedom. Model SRI outperforms Model SRC by Ay?>3 in only 3 observations: MCG+8-11-1]. Mrk 110 and HE 1143-1800.,"for all seven observations but with one more degree of freedom, Model SRI outperforms Model SRC by $\dc > 3$ in only 3 observations: MCG+8-11-11, Mrk 110 and HE 1143-1800."384 This suggests that strong relativistic effects are the dominant factor in producing a good fit in the 4 other observations well-fit by Models SRC and SRI., This suggests that strong relativistic effects are the dominant factor in producing a good fit in the 4 other observations well-fit by Models SRC and SRI.385 This is in agreement with the low disc ionisation parameters of€<100 erg em  across the seven observations., This is in agreement with the low disc ionisation parameters of $\xi < 100$ erg cm $^{-1}$ across the seven observations.386 Model SRI is also superior to Model ION for 5/7 observations., Model SRI is also superior to Model ION for 5/7 observations.387 The exceptions are Mrk 6 and NGC 7213. with the former marginally preferring Model ION over Model SRI.," The exceptions are Mrk 6 and NGC 7213, with the former marginally preferring Model ION over Model SRI."388 As with Model SRC. a steep emissivity index of g¢ 6.9 is preferred in 5/7 observations apart from Mrk 6 and NGC S5S06¢1). where it pegged at q=3.," As with Model SRC, a steep emissivity index of $q>$ 6.9 is preferred in 5/7 observations apart from Mrk 6 and NGC 5506(1), where it pegged at $q= 3$."389 Likewise. the dise inclinations found with Model SRI are very close to hose given by Model SRC.," Likewise, the disc inclinations found with Model SRI are very close to those given by Model SRC."390" They are higjer than /=58 for 5/7 of the well-tit observations. although ΝTrk 6 and NGC 5506@¢1) have lower inclinations. consistent with he 18 ""relativistie-line"" observations classitied by NO7."," They are higher than $i = \textrm{58}\de$ for 5/7 of the well-fit observations, although Mrk 6 and NGC 5506(1) have lower inclinations, consistent with the 18 “relativistic-line"" observations classified by N07."391 Unlike Model SRC. the upper error on the inclination for NGC 7469¢1) αιIES not extend to the mocel limit but it is still the highest of all he narrow observations.," Unlike Model SRC, the upper error on the inclination for NGC 7469(1) does not extend to the model limit but it is still the highest of all the narrow observations."392 Another difference with Model SRC is that the REFLIONX reflection strengths of the 7 well-fit observations span a smaller range of 0.7<A«5.0. although in most cases. this is still stronger than expected in the standard model.," Another difference with Model SRC is that the REFLIONX reflection strengths of the 7 well-fit observations span a smaller range of $\textrm{0.7} < R < \textrm{5.0}$, although in most cases, this is still stronger than expected in the standard model."393 The reflection strengths derived from Model SRI. which includes both strong relativistic effects and dise ionisation. can be compared to those of the 18 NO7 observations with a relativistically broadened iron line.," The reflection strengths derived from Model SRI, which includes both strong relativistic effects and disc ionisation, can be compared to those of the 18 N07 observations with a relativistically broadened iron line."394 Model SRI is used as it generally gave the best fit to most of the observations and all L1 narrow observations are considered., Model SRI is used as it generally gave the best fit to most of the observations and all 11 narrow observations are considered.395 Using the maximum likelihood method of Maccacaroetal. (L988). he narrow-line observations have a mean reflection strength of (2?=1.634 FE0.45 with an intrinsic spread of a;= 1.50+0.32.," Using the maximum likelihood method of \citet{ma88}, the narrow-line observations have a mean reflection strength of $\langle R \rangle=1.63\pm$ 0.45 with an intrinsic spread of $\sigma_{R}= 1.50 \pm$ 0.32."396 Tus is ~2 times higher than the relativistic-line observations. who showed an average (47)= O.7S+0.13 with an intrinsic spread of op= 0.20+0.12.," This is $\sim 2$ times higher than the relativistic-line observations, who showed an average $\langle R \rangle=0.78\pm$ 0.13 with an intrinsic spread of $\sigma_{R}= 0.20 \pm$ 0.12."397 Thus. on the face of it (and somewha paradoxically). the observations with no prominent," Thus, on the face of it (and somewhat paradoxically), the observations with no prominent"398emissions (2).. LUD emissions (2).. Compton cllect. and Memsstrahlung (?)..,"emissions \cite[][]{GP98}, HD emissions \cite[][]{HDcoolingfct}, Compton effect, and Bremsstrahlung \cite[][]{Black1981}."399" The timesteppingD is limited. by the cooling5 time. and by the electron recombination time. where £ and n, ave the energy and the electron number fraction of cach particle. and. £ and D, the corresponding time variations."," The timestepping is limited by the cooling time, and by the electron recombination time, where $E$ and $n_e$ are the energy and the electron number fraction of each particle, and $\dot E$ and $\dot n_e$ the corresponding time variations."400 For accuracy reasons in the abundance determinations. the chemical subeveles are done over 1/10 of miun(tete) fasdescribedbye.g.72??7?)..," For accuracy reasons in the abundance determinations, the chemical subcycles are done over 1/10 of $\rm min(t_{cool}, t_e)$ \cite[as described by e.g.][]{Anninos1997,Abel_et_al1997,Yoshida2003,Maio2007}."401" Phe additional constrain given by ἐν is useful mostly when n, changes very steeply. like behind the shock fronts. or at ~101Ix. below which hydrogen recombines very ellicientlv and above which hydrogen gets ionized very fast."," The additional constrain given by $t_e$ is useful mostly when $n_e$ changes very steeply, like behind the shock fronts, or at $\sim40210^4\,\rm K$, below which hydrogen recombines very efficiently and above which hydrogen gets ionized very fast."403 Further details can be found in ? and references therein., Further details can be found in \cite{Maio2007} and references therein.404 In order to test the implementation we perform. numerical simulations under dillerent conditions., In order to test the implementation we perform numerical simulations under different conditions.405 First. we numerically solve an expanding ionized sphere problem (Sect. ?7))," First, we numerically solve an expanding ionized sphere problem (Sect. \ref{Sect:ss}) )"406 by fully including both the WP and. chemistry treatments., by fully including both the RT and chemistry treatments.407 Then we show the cosmic evolution of the different chemical species. coupled with the radiative gas emissions (Sect. ?22)).," Then we show the cosmic evolution of the different chemical species, coupled with the radiative gas emissions (Sect. \ref{Sect:abundances}) )."408 Finally. we will perform cosmological simulations of carly structure formation (Sect. ??))," Finally, we will perform cosmological simulations of early structure formation (Sect. \ref{Sect:cosmo}) )"409 to check the cllects of radiative feedback on gas cooling and collapse., to check the effects of radiative feedback on gas cooling and collapse.410 For all simulations we use a set. of 284. frequencies. covering the range from 0.7 eV to LOO eV. The density of frequeney bins around the peaks of the photoionization and photodissociation cross-sections is increased. - Le. there are more frequency. bins in the spectral regions of interest.," For all simulations we use a set of 284 frequencies, covering the range from $0.7$ eV to $100$ eV. The density of frequency bins around the peaks of the photoionization and photodissociation cross-sections is increased - i.e. there are more frequency bins in the spectral regions of interest."411 In this wav we can ensure that photons are both traced. and absorbed properly and no spectrum-averaging mistakes are mace., In this way we can ensure that photons are both traced and absorbed properly and no spectrum-averaging mistakes are made.412 The expansion of an ionization [ront in a static. homogeneous and isothermal eas is the only problem in radiation hyedrocynamics that has a known analytical solution ancl is therefore the most widely usec test for ICE codes (e.g.??)..," The expansion of an ionization front in a static, homogeneous and isothermal gas is the only problem in radiation hydrodynamics that has a known analytical solution and is therefore the most widely used test for RT codes \cite[e.g.][]{Iliev2006,Iliev2009}."413 For such a set-up. the ionized bubble around the ionizing source reaches a final steady racius. called. the Strommeren radius. where absorptions ancl recombinations are balanced along the line of sight.," For such a set-up, the ionized bubble around the ionizing source reaches a final steady radius, called the Strömmgren radius, where absorptions and recombinations are balanced along the line of sight."414 For an H-onlv gas. the Str6mimeren radius is analytically given by with IN. the luminosity of the source in. photons per second: ay the case-B recombination cocllicicnt: and oy the hverogen number cdensitv.," For an H-only gas, the Strömmgren radius is analytically given by = , with $\dot{N}_\gamma$ – the luminosity of the source in photons per second; $\alpha_{\rm B}$ – the case-B recombination coefficient; and $n_{\rm H}$ – the hydrogen number density."415 “Phe case-B recombination coellicicnt assumes the so called on-the-spol approximation. where photons from recombinations to lower energv levels are. immediately. absorbed in the vicinity. of their emission. (e.g.2)...," The case-B recombination coefficient assumes the so called 'on-the-spot' approximation, where photons from recombinations to lower energy levels are immediately absorbed in the vicinity of their emission \cite[e.g.][]{Spitzer1978}."416" Lo we approximate the ionization front (L-front) as infinitely thin. Le. it features a cliscontinuity in the ionization fraction. the temporal expansion of the Strómmgren radius can be solved analytically in closed form. with the [οί radius ry, given by"," If we approximate the ionization front (I-front) as infinitely thin, i.e. it features a discontinuity in the ionization fraction, the temporal expansion of the Strömmgren radius can be solved analytically in closed form, with the I-front radius $r_{\rm I}$ given by"417In total. approximately 50 observations (0.5 per cent) were removed manually from the data set.,"In total, approximately 50 observations (0.5 per cent) were removed manually from the data set."418 The observed sources are presented in Table |. which. for each source. lists the date of the first and last observation. the total number of observations and the number of nights on. which the source was observed.," The observed sources are presented in Table \ref{tab:data} which, for each source, lists the date of the first and last observation, the total number of observations and the number of nights on which the source was observed."419 The full set of results are available electronically. with a subset presented in Table 2— and the lighteurves for the sources with data from more than one night (filtering out 19 sources) are presented in reftig:light-curves..," The full set of results are available electronically, with a subset presented in Table \ref{tab:tseries} and the lightcurves for the sources with data from more than one night (filtering out 19 sources) are presented in \\ref{fig:light-curves}."420 This paper presents the second data release of SCUBA pointing data for flat-speetrum radio sources., This paper presents the second data release of SCUBA pointing data for flat-spectrum radio sources.421 In total we have now catalogued fflux density measurements for ssources atpum., In total we have now catalogued flux density measurements for sources at.422.. Some of these sources have very sparsely sampled dati but our observations provide perhaps the only measurements of these objects at submillimetre wavelengths., Some of these sources have very sparsely sampled data but our observations provide perhaps the only measurements of these objects at submillimetre wavelengths.423 Other sources have well-sampled light curves that ean be used as part of multifrequency studies., Other sources have well-sampled light curves that can be used as part of multifrequency studies.424 We have shown that with care. the data can be calibrated in an automated manner to an accuracy of <10 per cent.," We have shown that with care, the data can be calibrated in an automated manner to an accuracy of $<10$ per cent."425 Furthermore. the development and retinement of the pipeline process means that it is a relatively simple task to extract and calibrate all these data and make them available to the scientific community.," Furthermore, the development and refinement of the pipeline process means that it is a relatively simple task to extract and calibrate all these data and make them available to the scientific community."426of other parameters such as effective temperature. surface eravily and ISA] absorption.,"of other parameters such as effective temperature, surface gravity and ISM absorption."427 The test model including S. for example. introduced an absorption edge near 43 wwith little effect on the emergent flix at longer wavelengths: careful adjustment. of the S abundance could aid in a better prediction of the observed drop in flix between 40. and 45A.," The test model including S, for example, introduced an absorption edge near 43 with little effect on the emergent flux at longer wavelengths; careful adjustment of the S abundance could aid in a better prediction of the observed drop in flux between 40 and 45."428 Further progress in this direction would demand some additional constraints on the abundances of these other metals in order to limit (he available parameter space to tractible proportions., Further progress in this direction would demand some additional constraints on the abundances of these other metals in order to limit the available parameter space to tractible proportions.429 We have shown that the LETG+IRC-S spectrum of iin the 25-90 rranee can be qualitatively modelled by photospheric emission from an atmosphere containing Ile. C. O and Ne in expected amounts. with the addition of Fe at a level consistent with the current observational upper limit.," We have shown that the LETG+HRC-S spectrum of in the 25-90 range can be qualitatively modelled by photospheric emission from an atmosphere containing He, C, O and Ne in expected amounts, with the addition of Fe at a level consistent with the current observational upper limit."430 With these quite plausible models. there is no requirement in (he data to resort to more exotic solutions such as a coronal model.," With these quite plausible models, there is no requirement in the data to resort to more exotic solutions such as a coronal model."431 The quality of the current short LETGS exposure does not allow us to rule out a significant amount of coronal enission will a hieh degree of confidence. though (he best fit model based onpurely coronal emission is statistically unacceptable with a reduced 4?=2.1.," The quality of the current short LETGS exposure does not allow us to rule out a significant amount of coronal emission with a high degree of confidence, though the best fit model based on coronal emission is statistically unacceptable with a reduced $\chi^2=2.1$."432 We can. however. completely discount a coronal interpretation of the ROSAT and spectra on energetic grounds.," We can, however, completely discount a coronal interpretation of the ROSAT and spectra on energetic grounds."433" A coronal plasma model at a temperature of 3x10? K absorbed by an ISM column of [Ng7107"" 7 and normalised to the observed ROSAT spectrum has a total luminosity 2-3 orders of magnitudegreafer than than the star itself.", A coronal plasma model at a temperature of $3\times 10^5$ K absorbed by an ISM column of $N_H\sim 10^{20}$ $^{-2}$ and normalised to the observed ROSAT spectrum has a total luminosity 2-3 orders of magnitude than than the star itself.434 This is qualitatively illustrated in Figure 2.. where the coronal model is shown normalised relative to the photospheric models to the approximate level recquired {ο explain the observed. 20-80 XA-rav ας.," This is qualitatively illustrated in Figure \ref{f:fluxes}, where the coronal model is shown normalised relative to the photospheric models to the approximate level required to explain the observed 20-80 X-ray flux."435 Despite the ability of photospheric models to explain the LETGS spectrum of aad (he energetic impossibili of a coronal explanation. there are (wo additional puzzles regarding the spectrum of this object at both shorter and longer wavelengths that cannot be," Despite the ability of photospheric models to explain the LETGS spectrum of and the energetic impossibility of a coronal explanation, there are two additional puzzles regarding the spectrum of this object at both shorter and longer wavelengths that cannot be"436wide component respectively).,wide component respectively).437 The energy distribution of the two-component jet can be parameterized as: The two components of the jet encounter the ISM and generate forward shock and reverse shock respectively., The energy distribution of the two-component jet can be parameterized as: The two components of the jet encounter the ISM and generate forward shock and reverse shock respectively.438 The observed afterglow emission Is the superposition of the two component., The observed afterglow emission is the superposition of the two component.439 Due to a higher kinetic energy. the contribution by the narrow component to the afterglow emission should dominate at the early time.," Due to a higher kinetic energy, the contribution by the narrow component to the afterglow emission should dominate at the early time."440 As the bulk Lorentz factor 24; of the narrow component decreases. the light curves breaks to a steeper one once ry<1/0y.," As the bulk Lorentz factor $\gamma_N$ of the narrow component decreases, the light curves breaks to a steeper one once $\gamma_N < 1/\theta_N$."441 After the break. the light curve of the narrow component declines much faster than that of the wide one. and the contribution by the wide component could dominate at late times.," After the break, the light curve of the narrow component declines much faster than that of the wide one, and the contribution by the wide component could dominate at late times."442 For the case of GRB 090902B. we can attribute the early optical emission around 50005 to the forward shock emission of the narrow component after the jet break. since the optical emission decays very fast.," For the case of GRB 090902B, we can attribute the early optical emission around 5000s to the forward shock emission of the narrow component after the jet break, since the optical emission decays very fast."443 The extended high-energy emission detected by LAT can be attributed to the afterglow emission of the narrow component before the jet break and the late radio. optical and X-ray emission can be attributed to the afterglow emission of the wide component.," The extended high-energy emission detected by LAT can be attributed to the afterglow emission of the narrow component before the jet break and the late radio, optical and X-ray emission can be attributed to the afterglow emission of the wide component."444" Considering the inverse Compton loss of electrons. the synchrotron flux density at frequency 7 after the jet break is (Rhoads 1999: Sari. Piran Halpern 1999) The jet break of the narrow component should occur after the last LAT detection (around 1000 s) and before the first ROTSE optical at about 5000 s. Assuming a jet break time at. e.g. Ti,dataTC~ 4000s. the broadband data of GRB 090902B imply By comparing the above flux data with the theory prediction of the two-component jet model. we get the constraints this set of equations. we obtain For the above parameter values. we find that (Wang et al."," Considering the inverse Compton loss of electrons, the synchrotron flux density at frequency $\nu$ after the jet break is (Rhoads 1999; Sari, Piran Halpern 1999) The jet break of the narrow component should occur after the last LAT detection (around 1000 s) and before the first ROTSE optical data at about 5000 s. Assuming a jet break time at, e.g. $T_{{\rm Br}eak}^{N}\sim 4000$ s, the broadband data of GRB 090902B imply By comparing the above flux data with the theory prediction of the two-component jet model, we get the constraints Solving this set of equations, we obtain For the above parameter values, we find that $Y(\rm 100 MeV)\ll 1$ (Wang et al."445 2010)., 2010).446 Figures 1-4 show the fit result of the LAT. R band. X- and radio data of GRB 090902B. respectively. and the fitting parameters are given in Table |.," Figures 1-4 show the fit result of the LAT, R band, X-ray and radio data of GRB 090902B, respectively, and the fitting parameters are given in Table 1."447 In the LAT energy band (Fig., In the LAT energy band (Fig.448 1). we plot the forward shock emission for three different values of the initial. Lorentz factor. Le. Ξ 3000. 1800 and 1300 respectively.," 1), we plot the forward shock emission for three different values of the initial Lorentz factor, i.e. $\eta=3000$ , 1800 and 1300 respectively."449In the case of 1)=3000. the shell crossing time Tuo.=Yoo25s is larger than. the shell deceleration time 744. so the reverse shock belongs,"In the case of $\eta=3000$, the shell crossing time $T_{\rm450cross}=T_{90}=25 {\rm s}$ is larger than the shell deceleration time $T_{\rm dec}$, so the reverse shock belongs"451for each spacecraft.,for each spacecraft.452 The top plot shows a large discrepancy between the 171 aand 195 oobservations. with the 195 ddata showing a large decrease with time while the 171 ddata shows no strong variation.," The top plot shows a large discrepancy between the 171 and 195 observations, with the 195 data showing a large decrease with time while the 171 data shows no strong variation."453 The FWHM does follow a linearly increasing trend with distance for both passbands. but the resulting variation in PA-averaged BD integrated intensity is inconclusive in each case.," The FWHM does follow a linearly increasing trend with distance for both passbands, but the resulting variation in PA-averaged BD integrated intensity is inconclusive in each case."454 In both cases the 195 =ata appears flat with distance (albeit with some stronger point-to-point variation). while the 171 =ata shows a generally increasing trend.," In both cases the 195 data appears flat with distance (albeit with some stronger point-to-point variation), while the 171 data shows a generally increasing trend."455" The rate of change of I, with distance ddcZ,;)/dr) 1s given in Table 1..", The rate of change of $I_{tot}$ with distance $I_{tot}$ )/dr) is given in Table \ref{tbl:events_characteristics}.456 These measurements show that more analysis is required to understand the morphology of the pulse., These measurements show that more analysis is required to understand the morphology of the pulse.457" The higher cadence observations available from should allow the variation | peak intensity and PA-averaged integrated intensity with ""Sistance to be determined with a nuch higher degree of accuracy than possible usingSTEREO.", The higher cadence observations available from should allow the variation in peak intensity and PA-averaged integrated intensity with distance to be determined with a much higher degree of accuracy than possible using.458. The intensity profile technique outlined in. Section 2 is extremely effective at identifying the CBF pulse in observations. with the associated errors much lower than those achieved with previous techniques.," The intensity profile technique outlined in Section \ref{sect:observations} is extremely effective at identifying the CBF pulse in observations, with the associated errors much lower than those achieved with previous techniques."459 Once the sector into which the pulse propagates has been identified. the technique automatically returns the centroid and FWHM of the fitted Gaussian as well as the integrated pulse intensity averaged over position angle at any given image time.," Once the sector into which the pulse propagates has been identified, the technique automatically returns the centroid and FWHM of the fitted Gaussian as well as the integrated pulse intensity averaged over position angle at any given image time."460 The technique also produces accurate and reproducible estimates of the pulse characteristics. making these results more robust.," The technique also produces accurate and reproducible estimates of the pulse characteristics, making these results more robust."461 The findings from the event of 2007 May 19 are discussed in detail in Section 4.1 with several other CBF events summarized in Section 4.2.. while all of the results are presented in Table 1..," The findings from the event of 2007 May 19 are discussed in detail in Section \ref{subsect:may19} with several other CBF events summarized in Section \ref{subsect:other_events}, while all of the results are presented in Table \ref{tbl:events_characteristics}."462 The event of 2007 May 19 displays kinematies consistent with those of a decelerating pulse. with an initial velocity that is towards the upper end of previous estimates.," The event of 2007 May 19 displays kinematics consistent with those of a decelerating pulse, with an initial velocity that is towards the upper end of previous estimates."463 The acceleration term was observed to be negative within the ]-sigma error range. with the similar results from both spacecraft suggesting that these are the true kinematies of the pulse.," The acceleration term was observed to be negative within the 1-sigma error range, with the similar results from both spacecraft suggesting that these are the true kinematics of the pulse."464 The pulse was observed to display clear spatial and temporal broadening during propagation. indicating that the CBF is dispersive.," The pulse was observed to display clear spatial and temporal broadening during propagation, indicating that the CBF is dispersive."465 As a result. the variation with distance of the integrated intensity of the pulse averaged across position angle rather than the peak intensity of the pulse was examined to try and understand the physical nature of the pulse.," As a result, the variation with distance of the integrated intensity of the pulse averaged across position angle rather than the peak intensity of the pulse was examined to try and understand the physical nature of the pulse."466 A decrease in the peak amplitude of a dispersive pulse does not, A decrease in the peak amplitude of a dispersive pulse does not467in section 2.3..,in section \ref{sec:o}.468 Note that in DOVSA. the outflow contained two sources: o(/)=ον]ουν(1) where Oy(1) is a global outflow powered by stellar explosious (galactic winds) ancl ogy(1) correspouds to stellar supernova ejecta that are Πασά directly out of the structures.," Note that in DOVSA, the outflow contained two sources: $o(t)=o_\mathrm{w}(t)+o_\mathrm{SN}(t)$ where $o_\mathrm{w}(t)$ is a global outflow powered by stellar explosions (galactic winds) and $o_\mathrm{SN}(t)$ corresponds to stellar supernova ejecta that are flushed directly out of the structures."469 Since it was shown in DOVSA that the second term las a very stall effect on the results. we have neglected it in this work (iu DOVSA’s notation. this is equivalent to setting a=0).," Since it was shown in DOVSA that the second term has a very small effect on the results, we have neglected it in this work (in DOVSA's notation, this is equivalent to setting $\alpha=0$ )."470 As seen in DOVSA. the term αμ} which stands for the process of structure formation can have a strong impact ou the high redshift evolution. inteusity of the star formation process. ionizing flux. aud the eurichiment of the IGM. as it governs the size of the reservoir of barvous available [or star formation.," As seen in DOVSA, the term $a_\mathrm{b}(t)$ which stands for the process of structure formation can have a strong impact on the high redshift evolution, intensity of the star formation process, ionizing flux, and the enrichment of the IGM, as it governs the size of the reservoir of baryons available for star formation."471 In DOVSA. although this term was estimated in an oversimplilied way. we assumed ouly that structure formation ellicieucy decays exponentially.," In DOVSA, although this term was estimated in an oversimplified way, we assumed only that structure formation efficiency decays exponentially."472 This first attempt allowed us to point out the key role of this term iu the generalized) chemical evolution model we have implementect., This first attempt allowed us to point out the key role of this term in the generalized chemical evolution model we have implemented.473 Here. we unprove the mocel with a more realistic description of structure formation.," Here, we improve the model with a more realistic description of structure formation."474 We adopt the framework of the hierarchical scenario where small structures are formed first., We adopt the framework of the hierarchical scenario where small structures are formed first.475 At redshift z. the comoving density of dark matter halos in the mass range [M.AL+dA] is fpsCM.z)dM. with where pp is the comoving dark matter deusity.," At redshift $z$, the comoving density of dark matter halos in the mass range $[M,M+dM]$ is $f_\mathrm{PS}(M,z)dM$, with where $\rho_\mathrm{DM}$ is the comoving dark matter density."476 The distribution function of halos fps(M.2) is computed using the method described in ? using a code provided by A. Jenkins.," The distribution function of halos $f_\mathrm{PS}(M,z)$ is computed using the method described in \citet{jenkins:01} using a code provided by A. Jenkins."477 It follows the standard theory (2).. including the moclilication of ? auc assumes a primordial power spectrum witha power-law index 1= and the fitting formula to the exact trausfer Cuuction for non-baryonie cold dark matter given by 2..," It follows the standard theory \citep{press:74}, including the modification of \citet{sheth:99} and assumes a primordial power spectrum with a power-law index $n=1$ and the fitting formula to the exact transfer function for non-baryonic cold dark matter given by \citet{bond:84}."478" We adopt a rms amplitude oy=0.9 for mass cleusity [Iuctuations in a sphere of radius 8/+Νίρο, We assume that the baryon distribution traces the dark matter distribution without any bias so that the deusity of baryous is just. proportional to the density of dark matter by a factor Op/(£2,—O5).", We adopt a rms amplitude $\sigma_{8}=0.9$ for mass density fluctuations in a sphere of radius $8\ h^{-1}\ \mathrm{Mpc}$ We assume that the baryon distribution traces the dark matter distribution without any bias so that the density of baryons is just proportional to the density of dark matter by a factor $\Omega_{b}/\left(\Omega_{m}-\Omega_{b}\right)$.479" We take a baryonie density Qj,=0.011 (?)..", We take a baryonic density $\Omega_\mathrm{b}=0.044$ \citep{spergel:03}. .480 We paraimetrize the [act that stars cau form only in structures which are suitably deuse by defining the μι mass Admin of a dark matter halo of the collapsed structures where star formation occurs., We parametrize the fact that stars can form only in structures which are suitably dense by defining the minimum mass $M_\mathrm{min}$ of a dark matter halo of the collapsed structures where star formation occurs.481 This mass could be related iu principle with the critical temperature at which the cooling processes become efficient enough to allow star formation., This mass could be related in principle with the critical temperature at which the cooling processes become efficient enough to allow star formation.482 In fact. this critical temperature. aud heuce the minimum mass Amin. should evolve with redshift z as the cooling processes of the Lot eas in structures depeud strongly on the Chemical composition and ionizing state of the gas.," In fact, this critical temperature, and hence the minimum mass $M_\mathrm{min}$, should evolve with redshift $z$ as the cooling processes of the hot gas in structures depend strongly on the chemical composition and ionizing state of the gas."483" It is however beyoud the scope of this study to iuclude such a detailed analysis so we prefer to keep Mii, coustaut aud to consider it as a [ree parameter of the inodel.", It is however beyond the scope of this study to include such a detailed analysis so we prefer to keep $M_\mathrm{min}$ constant and to consider it as a free parameter of the model.484 The fraction of baryonsat recdshitt z which are in such structures is then, The fraction of baryonsat redshift $z$ which are in such structures is then485the scatter. in the reverberation-based. sample is. slightly larger than that for the dvnamicallvy-based. sample.,the scatter in the reverberation-based sample is slightly larger than that for the dynamically-based sample.486 Lt is apparent already. from this figure that there is no strong correlation between Adpy0 scatter and nuclear luminosity within each sample., It is apparent already from this figure that there is no strong correlation between $\Mbh-\sigma$ scatter and nuclear luminosity within each sample.487" In order to investigate the dependence of the scatter on nuclear luminosity quantitatively, we show in Figure 2 re scatter versus the nuclear luminosity (top panel) and 1ο average scatter in bins of the nuclear luminosity level (bottom panel)."," In order to investigate the dependence of the scatter on nuclear luminosity quantitatively, we show in Figure 2 the scatter versus the nuclear luminosity (top panel) and the average scatter in bins of the nuclear luminosity level (bottom panel)."488 To keep track of the standard. deviation of the scatter at cach nuclei luminosity bin. we plot the gaandard deviation in each bin as vertical cash error bars.," To keep track of the standard deviation of the scatter at each nuclei luminosity bin, we plot the standard deviation in each bin as vertical dash error bars."489 We choose bins so that the number of galaxies per bin is comparable. in order to minimize Poisson noise.," We choose bins so that the number of galaxies per bin is comparable, in order to minimize Poisson noise."490 Specifically. 1e number of galaxies in cach bin are 13. 13. 12. 9. 8.," Specifically, the number of galaxies in each bin are 13, 13, 12, 9, 8."491 Notice that we do not mix the dynamically-basec and reverberation-basecl samples., Notice that we do not mix the dynamically-based and reverberation-based samples.492 The scatter and the standard deviation remain approximately constant as the nuclear luminosity increases., The scatter and the standard deviation remain approximately constant as the nuclear luminosity increases.493 This is the basie result of this article., This is the basic result of this article.494 ‘This result can be seen another way by considering the timescales that govern the growth of the BIL mass ancl the dynamical time., This result can be seen another way by considering the timescales that govern the growth of the BH mass and the dynamical time.495 We define the 111 growth timescale as: where c is the radiative ellicieney. which we take to be 10!⋅(te)L.↼⊔⊳is the. Exddington luminosity.," We define the BH growth timescale as: where $\epsilon$ is the radiative efficiency, which we take to be 0.1, $L_{Edd} = 3.5\times10^4 (\frac{\Mbh}{M_{\odot}}) L_{\odot}$ is the Eddington luminosity."496Di. ⋠⋠ The dynamical time is defined. via: where A. is the elective radius of the galaxy., The dynamical time is defined via: where $R_e$ is the effective radius of the galaxy.497 Because we are interested in the two timescales when the DLL is accreting rapidly. we set an arbitrary threshold. (410 Ενω) and select. galaxies. with nuclear bolometric luminosity higher than this value.," Because we are interested in the two timescales when the BH is accreting rapidly, we set an arbitrary threshold $4\times10^{-3}L_{Edd}$ ) and select galaxies with nuclear bolometric luminosity higher than this value."498 Our result is independent of this threshold., Our result is independent of this threshold.499 This leaves us with 3 dvnamically-based. measurements. and all the reverberation-based measurements.," This leaves us with 3 dynamically-based measurements, and all the reverberation-based measurements."500 Then. to calculate. μμ. we obtain the collective radii of these galaxies from the literature (????)..," Then, to calculate $t_{dyn}$, we obtain the effective radii of these galaxies from the literature \citep{Sani, Bentz, Lauer, Marconi}."501 For the galaxies with no measured cllective radii in the literature (NII94. UCGC3789. Mrk 202 and. N4253). we use 1 galaxy radius calculated as the following.," For the galaxies with no measured effective radii in the literature (N1194, UGC3789, Mrk 202 and N4253), we use the galaxy radius calculated as the following."502 We estimate rw radii of the galaxy by multiplving the angular radii by the angular-size distances., We estimate the radii of the galaxy by multiplying the angular radii by the angular-size distances.503 We obtain the angular radii from the 2ALASS isophotal measurements with reference level of the radii set at 2POWαπmagnitudearesec, We obtain the angular radii from the 2MASS isophotal measurements with reference level of the radii set at $20~\rm K-band~magnitude~arcsec^{-2}$.504" The angular-size distance is calculated assuming //)=75kms‘Alpe DOO,=027. Q4=0.73 as the four ealaxies are all z>0.01 galaxies."," The angular-size distance is calculated assuming $H_0 = 73 \rm~km~s^{-1}Mpc^{-1}$ , $\Omega_m = 0.27$, $\Omega_\Lambda = 0.73$ as the four galaxies are all $z>0.01$ galaxies."505 The redshift of the galaxies are obtained from NED. which compiled multiple consistent redshift measurements for cach galaxy.," The redshift of the galaxies are obtained from NED, which compiled multiple consistent redshift measurements for each galaxy."506" In Figure 3 we plot the ratio of face to μμ, as a function of the nuclear luminosity in units of the Eddington luminosity.", In Figure 3 we plot the ratio of $t_{acc}$ to $t_{dyn}$ as a function of the nuclear luminosity in units of the Eddington luminosity.507 We fit a straight line and find the slope of the line is 0.94 and the ratio approaches unity when the nuclear luminosity approaches the LEclelington limit., We fit a straight line and find the slope of the line is $-0.94$ and the ratio approaches unity when the nuclear luminosity approaches the Eddington limit.508 As discussed in, As discussed in509" CTegiiarketal.2001]]. 3, (Peebles1989).. (Frischetal.20023."," \citep{teg04}] $^{-1}$ \citep{pee89}, \citep{fri02}."510".. σα] region in parameter space favouring a low value of Q,,=0.22£0.02 for the density parameter.", small region in parameter space favouring a low value of $\Omega_m=0.22\pm 0.02$ for the density parameter.511 On cluster scales. recoustruction of the aiplitude of the first-approach Πα velocities provides a deteruinuation of the mass of the clusters at radii bevoud the vintalized region: radii ereater than those explored by X-ray or lensing studies.," On cluster scales, reconstruction of the amplitude of the first-approach infall velocities provides a determination of the mass of the clusters at radii beyond the virialized region; radii greater than those explored by X-ray or lensing studies."512 We show that the hieh amplitude observed in the infall region requires an assiguiuent of ML=500A./L.. to the Virgo Cluster (where the huuinosities are in the D baud)., We show that the high amplitude observed in the infall region requires an assignment of $M/L=500 M_{\odot}/L_{\odot}$ to the Virgo Cluster (where the luminosities are in the B band).513 The catalog of galaxies. is a aueinentation of the Nearby Galaxies Catalog (Tully1987)..now iucludiug 3300 galaxies within 3.000 lan," The catalog of galaxies, is a augmentation of the Nearby Galaxies Catalog \citep{tul87},now including 3300 galaxies within 3,000 km $^{-1}$."514 This depth is more han twice the distance of the dominant componcut. he Vireo Cluster. and the completion to this depth iu he current catalog conrpares favorably with other allsky surveysοὐ 2MASS(Jarrett 20001.," This depth is more than twice the distance of the dominant component, the Virgo Cluster, and the completion to this depth in the current catalog compares favorably with other all-sky surveys, 2MASS \citep{jar04}] ]."515 The catalog ius the following properties. (, The catalog has the following properties. (5161) All entries are given a detailed group and filament assignment (or non-assieunment if isolated). (,i) All entries are given a detailed group and filament assignment (or non-assignment if isolated). (5173) The catalog is supplemented wean all-sky complete sample of ταν selected. clusters (IKocevslkietal.2001) in the shell 3.0008.000 kins ! ο provide a description of poteutial influences ou very aree scales. (,"ii) The catalog is supplemented by an all-sky complete sample of X-ray selected clusters \citep{koc04} in the shell 3,000–8,000 km $^{-1}$ to provide a description of potential influences on very large scales. ("518id) “Fake galaxies are added at low Galactic latitudes to avoid an uuderdeusitv iu the zone of obscuration due to lost information. (,iii) `Fake' galaxies are added at low Galactic latitudes to avoid an underdensity in the zone of obscuration due to lost information. (519iv) Correction is made for the loss of lieht with clistance caused by an apparent maenitude cutoff in the coustruction of the catalog.,iv) Correction is made for the loss of light with distance caused by an apparent magnitude cutoff in the construction of the catalog.520 The second observational comipouent is au exteuded catalogs of galaxy distances., The second observational component is an extended catalog of galaxy distances.521 Information frou four techniques has been integrated: he Cepheid variable (Freediananetal.2001).. Tip of the Red Ciaut. Brauch (Iuracheutsev2003:Leeetal.1993).. Surface Brightucss Fluctuation(Tourv&Schucider1988:ονotal. 20013.. and LuminosityLinewidth (Tully&Fisher1977:methods.," Information from four techniques has been integrated: the Cepheid variable \citep{fre01}, Tip of the Red Giant Branch \citep{kar03,lee93}, Surface Brightness Fluctuation\citep{ton88,ton01}, and Luminosity–Linewidth \citep{tul77,tul00} methods."522 In all. there ave over 1100 galaxies with distance measures within the," In all, there are over 1400 galaxies with distance measures within the"523(CLOS. 0. 20.3. and -0.6 + 0.15).,"(+0.3, 0, -0.3 and -0.6 $\pm$ 0.15)."524 The distribution of survev stars from the same sample is also shown (dotted lino)., The distribution of survey stars from the same sample is also shown (dotted line).525 The distributions are normalized to the total star nuniber in cach plot., The distributions are normalized to the total star number in each plot.526 The comparison between the conrplete sample and the survey one suggests that uo stroug bias is iutroduced by the selective addition of lower main sequence objects to the magnitude complete survey siuuple., The comparison between the complete sample and the survey one suggests that no strong bias is introduced by the selective addition of lower main sequence objects to the magnitude complete survey sample.527 The metallicity suuple is not complete. but its size (more than 1500 stars) males the information frou it worth discussing.," The metallicity sample is not complete, but its size (more than 1500 stars) makes the information from it worth discussing."528 Tn the case of the |0.3 sample. of the sample stars has values ο τς {Olas|: for the sample with == -0.6. such a perceutage is3856: for == (aud -0.3. we have and 6356. respectively.," In the case of the +0.3 sample, of the sample stars has values of $\vert U \vert$ $\leq$ 40 km $\rm s^{-1}$; for the sample with = -0.6, such a percentage is; for = 0 and -0.3, we have and , respectively."529 For the V. component. values coniprised jetween |LO and -30 kinst amount to and .. from |0.3 to -0.6. samplesrespectively.," For the $V$ component, values comprised between +10 and -30 km $\rm s^{-1}$ amount to, and , from +0.3 to -0.6, respectively."530" These features suggest that the with [0.3.. 0.0 aud -0.3 share a common Κάποιατις distribution. peaked at [7 and V about zero: in the case of the V. component. all three samples show a tail towards negative values,"," These features suggest that the samples with = +0.3, 0.0 and -0.3 share a common kinematic distribution, peaked at $U$ and $V$ about zero; in the case of the $V$ component, all three samples show a tail towards negative values."531 Stars with == -0.6 apparcutly belong to a population with a less marked rotation ou the ealactic plane., Stars with = -0.6 apparently belong to a population with a less marked rotation on the galactic plane.532 Perhaps this reflects a composition difference between the disk (thin and thick) component and the (local) inner halo., Perhaps this reflects a composition difference between the disk (thin and thick) component and the (local) inner halo.533 The distribution of the vertical component TT supports the previous findings: the three more ietal rich samples exhibit distributions peaked at TV — (0. while the == -0.6 sample shows a iild concentration about zero.," The distribution of the vertical component $W$ supports the previous findings: the three more metal rich samples exhibit distributions peaked at $W$ = 0, while the = -0.6 sample shows a mild concentration about zero."534 Iu considering [J] < 20 kin s1 we have percentages:and with ) to -0.6j. respectively.," In percentages: considering $\vert W \vert$ $<$ 20 km $\rm s^{-1}$ we have, and with from +0.3 to -0.6, respectively."535 tail towards uceative V. velocities. can be intepreted iu the usual scheme as due to the thick disk. prescuting a lag or dift from the fattened. lighly rotational velocity thin disk (Stróuuuberg 1925. Cüliiore Reid 1985. Cülhuore Wyse 1985. Wvse Cüliiore 1956).," The tail towards negative $V$ velocities can be intepreted in the usual scheme as due to the thick disk, presenting a lag or drift from the flattened, highly rotational velocity thin disk (Strömmberg 1925, Gilmore Reid 1983, Gilmore Wyse 1985, Wyse Gilmore 1986)."536 We obtained an estimate of the eccentricity of our velocity and metallicity sample acopting the Eeecu. Sandage aud Lyuden-Bell (ELS) ealactic potential (Eeeengs et al.," We obtained an estimate of the eccentricity of our velocity and metallicity sample adopting the Eggen, Sandage and Lynden-Bell (ELS) galactic potential (Eggen et al."537 1962). which considers the C aud Wo componcuts onlv aud therefore computes the eccentricity of the orbit projected outo the ealactic plane. assuming the independence of the motion on this plane from the perpendicular one.," 1962), which considers the $U$ and $V$ components only and therefore computes the eccentricity of the orbit projected onto the galactic plane, assuming the independence of the motion on this plane from the perpendicular one."538 This approxination othe ealactic potential has been used by many authors beside Egeen et al. (, This approximation of the galactic potential has been used by many authors beside Eggen et al. (539e.e.. Carney ett al 1990. Chiba Yoshii 1908).,"e.g., Carney et al 1990, Chiba Yoshii 1998)."540 It has been demonstrate that the use of this poteutial overestimates the eccentricits (Yoshii Saio 1979)., It has been demonstrated that the use of this potential overestimates the eccentricity (Yoshii Saio 1979).541 We adapted the ELS potential to the update values of the distance of the Sun from the ealactic center P. aud of the circular velocity Vpag at the Sum position. usine the values of 8.5 kpc aud 220 kin s1. PeESpecively (sere Lyucen-Bell 1986).," We adapted the ELS potential to the updated values of the distance of the Sun from the galactic center $R_\odot$ and of the circular velocity $V_{\rm LSR}$ at the Sun position, using the values of 8.5 kpc and 220 km $\rm s^{-1}$, respectively (Kerr Lynden-Bell 1986)."542 We checked that a change in these parameters of the order of their errors (4 }) does not influence substautiallv the results: the variations rarely reach = 00.01 aud the square root of their quadratic mean «O03., We checked that a change in these parameters of the order of their errors $\pm$ ) does not influence substantially the results: the variations rarely reach $\pm$ 0.04 and the square root of their quadratic mean is $<$ 0.03.543 Iu Fig., In Fig.544 10 the beliasiour of the eccentricity is showu as function of IV. for the four values of cconsidered above.," 10 the behaviour of the eccentricity is shown as function of $W$, for the four values of considered above."545 When ==0. theoljects have eccentricities x O2: for ii3 i percentage becomes.. and for == (6. (for == (0.3. the percentage is 86 4).," When = 0, of the objects have eccentricities $\leq$ 0.2; for = -0.3 the percentage becomes, and for = -0.6, (for = +0.3, the percentage is 86 )."546 Comparing this behaviour with the one in Fie. ," Comparing this behaviour with the one in Fig. \ref{fig10},"547oue finds again that ohjects with == -0.6 (+ 0.15) have a motion in the Galaxy largely uot confined on the galactic plauc., one finds again that objects with = -0.6 $\pm$ 0.15) have a motion in the Galaxy largely not confined on the galactic plane.548 The ecceutricitics of the saluple with -0.3 being similar to the oues relative to == 0). the change at = -0.6 appears rather sudden.," The eccentricities of the sample with = -0.3 being similar to the ones relative to = 0, the change at = -0.6 appears rather sudden."549 Some kinematical features of the localpopulation have been ideutified., Some kinematical features of the localpopulation have been identified.550 The first row in Table 3 gives the values of the space velocity components for which very voune, The first row in Table 3 gives the values of the space velocity components for which very young551"paraueters (e.g. configuration. imstrunents, acquisition tine).","parameters (e.g. configuration, instruments, acquisition time)."552 Even with the most cficicut DOP. the precision of the bootstrap methods is limited by the πα. of observations. often in O(1//0). ," Even with the most efficient DGP, the precision of the bootstrap methods is limited by the number of observations, often in $\mathcal{O}(1/\sqrt{n})$ "553cach part.,each part.554 The two power spectra. presented in Figure 1. show strong differences not onlv iu unplitude. but also in frequency.," The two power spectra, presented in Figure 4, show strong differences not only in amplitude, but also in frequency."555 The first interpretation of such differeuces is siuplv that the data set is not long enough to “stabilize” the Fourier trausform., The first interpretation of such differences is simply that the data set is not long enough to “stabilize” the Fourier transform.556 Iu other words. the light curve is uot completely resolved.," In other words, the light curve is not completely resolved."557 The reliability of this hivpothesis is iucreased by the fact that our best multisiuusoidal fi of the eutire data set (see next section and Table 2) eives good results also when applied ouly to the first or the second half of data (Figure 1)., The reliability of this hypothesis is increased by the fact that our best multisinusoidal fit of the entire data set (see next section and Table 2) gives good results also when applied only to the first or the second half of data (Figure 4).558 If the DET apparen iustabilitv is actually due ο the insufficient coverage. nios of the analyses reported iu sectious 3.2. [1l aud L2. aud based on the assiuuption hat the DET of 2232 Lis no time dependenut on time scales shorter than our run. will need further confirmation from a new longer observational canpaleu.," If the DFT apparent instability is actually due to the insufficient coverage, most of the analyses reported in sections 3.2, 4.1 and 4.2, and based on the assumption that the DFT of 2324 is not time dependent on time scales shorter than our run, will need further confirmation from a new longer observational campaign."559 On the other haud. if the DET time instability was real. we would need a different explanation for such peculiar behaviour.," On the other hand, if the DFT time instability was real, we would need a different explanation for such peculiar behaviour."560 An alternative hvpothesis of a fast damped oscillator has been considered aud is reported iu Section 5., An alternative hypothesis of a fast damped oscillator has been considered and is reported in Section 5.561 Looking at Figure 2 aud 3. it is iuuediatelv evideut that deteriuuiug the active frequencies from he power spectu of 22321 will be iore difficult than in most other CAV Vir stars for several reasons: the power is concentrated in only 3 crowded regions: the amplitudes are very low: the low frequencies imply that the frequency and the period spacing expected may have about same values.," Looking at Figure 2 and 3, it is immediately evident that determining the active frequencies from the power spectrum of 2324 will be more difficult than in most other GW Vir stars for several reasons: the power is concentrated in only 3 crowded regions; the amplitudes are very low; the low frequencies imply that the frequency and the period spacing expected may have about same values."562 The high frequeney region does not help much because it seclus o be constituted only bv. linear combinatious of the low-frequency peaks., The high frequency region does not help much because it seems to be constituted only by linear combinations of the low-frequency peaks.563 Moreover we know that the frequencies are not completely resolved. aud therefore we certainly have errors both iu frequency aud in amplitude., Moreover we know that the frequencies are not completely resolved and therefore we certainly have errors both in frequency and in amplitude.564 To distinguish the real frequencies present in the 22321 data from the artifacts dutroduced bv the spectral window. we proceeded as follows.," To distinguish the real frequencies present in the 2324 data from the artifacts introduced by the spectral window, we proceeded as follows."565" First we selected the highest peak iu cach of the three ""active regions” near 390. 170 aud 950 plz."," First we selected the highest peak in each of the three “active regions” near 390, 470 and 950 $\mu$ Hz."566 The separation of the three active regions guarantees that the aliases of cach frequency have almost zero influence iu the other two regions., The separation of the three active regions guarantees that the aliases of each frequency have almost zero influence in the other two regions.567 Second we applied a least-squares iiultisimnsoidal fit to the data to determine accurate anuplitudes aud, Second we applied a least-squares multisinusoidal fit to the data to determine accurate amplitudes and568The infraredD. spectral energy. distributions (SEDs) of. cireunistellar transitional disks reveal the preseuce of au optically thin tuner region and an optically thick outer disk.,The infrared spectral energy distributions (SEDs) of circumstellar transitional disks reveal the presence of an optically thin inner region and an optically thick outer disk.569⋅ Several. mechanisms: relevant to the overall evolution: of Dlcirctuustellar disks.: aud in⋅ particular. to the short-lived. yhase when they dissipate.structures have been proposed to explainaud he so-called opacityprimary holes ofinotivation trausitionof disks:this elautwork. ↙ : or ≻↕⋪⋯↸∖≯∪↥⋅⊔⋪↧↑↕∪∐∙∩⊾↥⋅⋪↧↕∐∩⊾↥⋅∪↖↖↽↑∐∙≻∐∪↑∪↸∖↖⇁⋪↧≻∪↥⋅⋪↧↑↕∪∐∙⋪⋯≼↧D |apors ‘ idal trumeation im close binaries.," Several mechanisms relevant to the overall evolution of circumstellar disks, and in particular to the short-lived phase when they dissipate, have been proposed to explain the so-called opacity holes of transition disks: giant planet formation, grain growth, photoevaporation, and tidal truncation in close binaries."570 See Willams Cicza. 2011 ↽↽⋡for a recent review.," See Williams Cieza, 2011 for a recent review."571⋅ The↴ processes responsible⋅ for⋟ he oeiuner holes of transition disks can tentatively be distinguished when disk asses. accretion rates. and uultiplicity information are availableC(Najita et al.," The processes responsible for the inner holes of transition disks can tentatively be distinguished when disk masses, accretion rates, and multiplicity information are available (Najita et al."572 2007: Cieza 2008)., 2007; Cieza 2008).573 Followiug this approach. ieza et al. (," Following this approach, Cieza et al. ("574"2010. icreafter Paper ID) presented the initial results of an ongoing. project. to characterize. a large set of"" transitionp disk caudida: dn nearby Vstar-forminee Probing the structure of disks that are suspected to be formune planets is the most promisine approach to understaud the conditious im which planets are οσα,","2010, hereafter Paper I) presented the initial results of an ongoing project to characterize a large set of transition disk candidates in nearby star-forming Probing the structure of disks that are suspected to be forming planets is the most promising approach to understand the conditions in which planets are formed."575 The best indication for ongoing formation in disks is the detection of tidal gaps (e.g. pePiéttu et al., The best indication for ongoing planet formation in disks is the detection of tidal gaps (e.g. Piéttu et al.576 2006) corresponding to a ring with sienificaut decrease im the surface deusitv (or the whole inner disk if it was depleted by acerction. eg. Varneiérre et al 2006).," 2006) corresponding to a ring with significant decrease in the surface density (or the whole inner disk if it was depleted by accretion, e.g. Varneiérre et al 2006)."577" A spectacular confirmation bas arrived with the receut detection of the first potential substellar object within the gap of the transitional disk To Chamalooutis (Huélkuno et al,", A spectacular confirmation has arrived with the recent detection of the first potential substellar object within the gap of the transitional disk T Chamaleontis (Huéllamo et al.578 2011)., 2011).579 Inner holes and gaps have already. been observed at (subjmillimeter wavelengths iu a handful of objects bright enough for resolving disk structure (Piéttu et al., Inner holes and gaps have already been observed at (sub)millimeter wavelengths in a handful of objects bright enough for resolving disk structure (Piéttu et al.580 2006: Thighes et al., 2006; Hughes et al.581 2007. 2009: Brown et al.," 2007, 2009; Brown et al."582 2008. 2009: Andrews et al.," 2008, 2009; Andrews et al."583 2009. 2010a. 2011. Isclla et al 2010a. Comprehensive studies of similar transition disks are necessary to increase− the enmipiricala constraints: on their: investigate4.⋅↴ their diversity.," 2009, 2010a, 2011, Isella et al 2010a, Comprehensive studies of similar transition disks are necessary to increase the empirical constraints on their structures and investigate their diversity."584UM This. ds the where⋅⋅: we⋅ apply∙ a. ∙∙ ∙ ⋅⋅⋅ ↴⋅⋅⋅ ⋅ candidates: in ∙↽∙Ophiuchus preseuted in⋅ Paper I aud derive⋅ the best fitting physical characteristics for their known SEDs," This is the primary motivation of this work, where we apply a parametric description to the 4 planet-forming disks candidates in Ophiuchus presented in Paper I and derive the best fitting physical characteristics for their known SEDs."585" Tu Paper L the observed SEDs were characterized by tWex, paranueters.NEINbove asae introduced⋅ua by- Ciezadens. etN al.. ("," In Paper I, the observed SEDs were characterized by two parameters, as introduced by Cieza et al. ("586"2007):BFAT the longest wavelength at which the observed fux is dominated bv the stellar photosphere. Arunog. aud the of slopethe TR excess; os, Computed between Aruot aud 21422. The former parameter correlates with the size of the inner hole. aud the latter with the sharpuess ofthe edge of the hole. ie. a large increase in the dust density over a θα] range in radii is indicatedby a positive oa.","2007): the longest wavelength at which the observed flux is dominated by the stellar photosphere, $\lambda_{\rm turn-off}$, and the slope of the IR excess, $\alpha_{\rm excess}$, computed between $\lambda_{\rm turn-off}$ and 24 $\mu$ m. The former parameter correlates with the size of the inner hole, and the latter with the sharpness of the edge of the hole, i.e., a large increase in the dust density over a small range in radii is indicated by a positive $\alpha_{\rm excess}$."587 Accreting disks with sharp inner holes that sec to lack stellar compauious {οσοι frou adaptive optics niagiug) standas the most promising candidates for ongoing (giant) planet formation.," Accreting disks with sharp inner holes that seem to lack stellar companions (e.g., from adaptive optics imaging) stand as the most promising candidates for ongoing (giant) planet formation."588 There were D cases fulfilling these criteria in Paper I fom a sample of 26 of Spifzer-selected transitional disks 20: the Ophinchns molecular cloud (7~125 pe. Loud ct al.," There were 4 cases fulfilling these criteria in Paper I from a sample of 26 of -selected transitional disks in the Ophiuchus molecular cloud $d\sim 125$ pc, Loinard et al."589 2008)., 2008).590 Their basic properties are listed in Table 1, Their basic properties are listed in Table \ref{properties}.591 The mass accretion rates for our targets. interred from the Πα emission. Tne widths(Natta et al.," The mass accretion rates for our targets, inferred from the $\alpha$ emission line widths (Natta et al."592 2001). range from 1.3410 19 to «10 5 NL. vi.," 2004), range from $\times$ $^{-10}$ to $\times$ $^{-8}$ $_\odot/$ yr."593of this procedure is a list of synthetic stars wilh the same characteristics of real stars and containing a given Traction of binaries (δι).,of this procedure is a list of synthetic stars with the same characteristics of real stars and containing a given fraction of binaries $\xi_{\rm in}$ ).594 To be precise. the M$s of the resulting artificial CAIDs are narrower (han the observed ones. because the formal photometric errors of the artificial star catalogue svstematically underestimate the true observational uncertainties.," To be precise, the MSs of the resulting artificial CMDs are narrower than the observed ones, because the formal photometric errors of the artificial star catalogue systematically underestimate the true observational uncertainties."595 This is apparent in Figure 8.. where. for the magnitude range 19</«19.5. the histogram corresponds to the distribution of theobserved color differences (V—J) with respect to the AISRL. the solid line is the best-fitting Gaussian of the blue-sicle of this distribution (grav histogram: the red-side has been ignored because it also includes (he contribution of binaries and blends). and the dashed line is a Gaussian will a dispersion obtained by adopting the formal photometric error of the artifidal star catalogue.," This is apparent in Figure \ref{photerr}, where, for the magnitude range $19<I<19.5$, the histogram corresponds to the distribution of theobserved color differences $\Delta(V-I)$ with respect to the MSRL, the solid line is the best-fitting Gaussian of the blue-side of this distribution (gray histogram; the red-side has been ignored because it also includes the contribution of binaries and blends), and the dashed line is a Gaussian with a dispersion obtained by adopting the formal photometric error of the artificial star catalogue."596 In order to correct for this bias and adopt realistic values of (he photometric uncertainty. we increased the formal errors σι and oy thus to reproduce the observed error distribution as a function of magnitude.," In order to correct for this bias and adopt realistic values of the photometric uncertainty, we increased the formal errors $\sigma_I$ and $\sigma_V$ thus to reproduce the observed error distribution as a function of magnitude."597 As a check. we verified that the width of the resulting color distribution with respect to the MSRL well matches the observed one.," As a check, we verified that the width of the resulting color distribution with respect to the MSRL well matches the observed one."598 An example of the svuthetie CMD thus obtained. compared to the observed one is shown in Fig. 9..," An example of the synthetic CMD thus obtained, compared to the observed one is shown in Fig. \ref{simu}."599" From the simulated catalogue we then computed the ratio rjj,=Aο.λα belween the number of svnthetic stars belonging to the ""binary population"" defined in Sect. ??.."," From the simulated catalogue we then computed the ratio $r_{sim}=N_{bin}^{\rm600 sim}/N_{\rm MS}^{\rm sim}$ between the number of synthetic stars belonging to the “binary population” defined in Sect. \ref{fmin},"601 and that of the svnthetic “AIS population”., and that of the synthetic “MS population”.602" The same was done for the observed data-sets. thus obtaining rj,=ΑρηVee."," The same was done for the observed data-sets, thus obtaining $r_{obs}=N_{bin}^{\rm obs}/N_{\rm603 MS}^{\rm obs}$."604 For every value of μμ. [rom 0.5% to 25% with steps of 0.5%. the entire procedure was repeated. LOO times.," For every value of $\xi_{\rm in}$, from $0.5\%$ to $25\%$ with steps of $0.5\%$, the entire procedure was repeated 100 times."605" Then. the penalty [function αμ) was computed as the summation of (au—Fass) Dor i=1.100. and the associated probability P(£,) was derived."," Then, the penalty function $\chi^2(\xi_{\rm in})$ was computed as the summation of $(r_{sim, i} -r_{obs})^2$ for $i=1,100$, and the associated probability $P(\xi_{\rm in})$ was derived."606" To illustrate (his. Figure 10. shows the distribution of 2 as a function of the adopted values of &,. ranging [rom to105."," To illustrate this, Figure \ref{prob} shows the distribution of $P$ as a function of the adopted values of $\xi_{\rm607 in}$, ranging from to."608.. The mean of the best-litting Gaussian gives the global binary fraction (6ο) ancl its dispersion has been adopted as the error., The mean of the best-fitting Gaussian gives the global binary fraction $\xi_{TOT}$ ) and its dispersion has been adopted as the error.609 The values of &poy obtained in the various radial and magnitude ranges are reported in Table 3.., The values of $\xi_{TOT}$ obtained in the various radial and magnitude ranges are reported in Table \ref{tab:fglob}.610 The global binary traction shows the same radial behavior observed [or &i). varving from ~14% or ~LOY in the cluster core (for the ancl the magnitude ranges. respectively). down to ~1.55 in the outskirts (for both).," The global binary fraction shows the same radial behavior observed for $\xi_{min}$, varying from $\sim 14\%$ or $\sim 10\%$ in the cluster core (for the and the magnitude ranges, respectively), down to $\sim6111.5\%$ in the outskirts (for both)."612 As belore we find a dependence of the binary fraction on ihe magnitude., As before we find a dependence of the binary fraction on the magnitude.613 This could be an effect of mass segregation. since the average binary mass in thebright. ancl ranges is M. 1.1.0.8.0.5M... respectively.," This could be an effect of mass segregation, since the average binary mass in the, and ranges is $M\sim 1.1, 0.8, 0.5614M_\odot$ , respectively."615" However it could also depend on the assumed mass-ratio distribution and the estimate of blended sources, and future studies will be required to resolve this."," However it could also depend on the assumed mass-ratio distribution and the estimate of blended sources, and future studies will be required to resolve this."616using uniformi erids. the Lhuger the radius. Fry. of the sinulated sphere. the poorer is our ability to resolve ry. and hence to distinguish nunerically between singular (uustable) aud nonsineular (stable) cores;,"using uniform grids, the larger the radius, $R/r_{0}$, of the simulated sphere, the poorer is our ability to resolve $r_{0}$, and hence to distinguish numerically between singular (unstable) and nonsingular (stable) cores."617 For this reason. we are unable to obtain stable equilibria for cores with Πέ2LS (ne. ZO9M. for our standard truucation pressure aud ceutral tempcrature). as these cores behave essentially. iudistinguishablv from singular cores (even at the higher resolution of 255? cells).," For this reason, we are unable to obtain stable equilibria for cores with $R/r_{0} \gtrsim 4.5 $ (i.e. $ \gtrsim 9618M_{\odot}$ for our standard truncation pressure and central temperature), as these cores behave essentially indistinguishably from singular cores (even at the higher resolution of $255^{3}$ cells)."619 Our study of nonsingular cores ds therefore coufned to those with truncation radii Réryx:3.26 (corresponding to masses <5AL.). for which good initial equilibria can be obtained and ry can be properly resolved over 30 cells or more.," Our study of nonsingular cores is therefore confined to those with truncation radii $R/r_{0} \leq 3.26$ (corresponding to masses $\le 5 M_{\odot}$ ), for which good initial equilibria can be obtained and $r_{0}$ can be properly resolved over 30 cells or more."620 To initiate collapse of the nonsineular logatrope. we mcereased the density throughout the core by 54% above equilibria values.," To initiate collapse of the nonsingular logatrope, we increased the density throughout the core by $5\%$ above equilibrium values."621 Establishing aud maintaining the unstable equilibrium of the singular logatrope is considerably wore difficult., 	Establishing and maintaining the unstable equilibrium of the singular logatrope is considerably more difficult.622 As expected. almost any small perturbation. including those inherent iu the inteeration alegorithius. is sufiicicut to cause it to collapse.," As expected, almost any small perturbation, including those inherent in the integration algorithms, is sufficient to cause it to collapse."623 Our staudarcd procedure for the siugular collapses was to set thei up in the best umuerical equilibrimu we could achieve. aud then initiate the collapse inarelatively controlled manner by increasing the density of the central cell by a few percent (the results are Insensitive to the exact value of the density enhancement).," Our standard procedure for the singular collapses was to set them up in the best numerical equilibrium we could achieve, and then initiate the collapse in a relatively controlled manner by increasing the density of the central cell by a few percent (the results are insensitive to the exact value of the density enhancement)."624 Cüven a value for A. the mass of a logatropic spliere is wholly determined by its radius. 7. central temperature. T.. aud truncation pressure. PA.," 	Given a value for $A$, the mass of a logatropic sphere is wholly determined by its radius, $R$, central temperature, $T_{c}$ , and truncation pressure, $P_{s}$."625 Iu all of our simulations. we used sd=0.2 in the logatropie EOS.," In all of our simulations, we used $A =6260.2$ in the logatropic EOS."627 We take as our “standard” ceutral temperature and truucation pressure the values (CE... Py) = (10S. 1.3.10p ? KK. chosen to be cousisteut with those used by Shu(1977) aud MP97.," We take as our “standard” central temperature and truncation pressure the values $T_{c}$, $P_{s}$ ) = (10 K, $1.3 \times 10^5 k_{B}$ $^{-3}$ K), chosen to be consistent with those used by \citet{Shu77} and MP97."628 These plysical conditious are typical of those found in reeious of relatively isolated star formation., These physical conditions are typical of those found in regions of relatively isolated star formation.629 For example. by fitting a Dounor-Ebert sphere to the density structure of the isolated dark cloud Barnard 6s. Alves.Lada.&Lada(20013. derived a surface pressure of 1.8«Lp K and a temperature of 16 Ix. We cuiphasize that the TZ; and £P used herein are represcutative of conditious iu regions of star formation. where the surface pressures can be one or two orders of magnitude larger (see 87)).," For example, by fitting a Bonnor-Ebert sphere to the density structure of the isolated dark cloud Barnard 68, \citet{Alves}630 derived a surface pressure of $1.8 \times 10^{5} k_{B}$ $^{-3}$ K and a temperature of 16 K. 	We emphasize that the $T_{c}$ and $P_{s}$ used herein are representative of conditions in regions of star formation, where the surface pressures can be one or two orders of magnitude larger (see \ref{sec:disc}) )."631 In order to facilitate the extrapolation of our results to different LP. and7). values. we have inchided dimeusiouless versious of the primary results.," In order to facilitate the extrapolation of our results to different $P_{s}$ and$T_{c}$ values, we have included dimensionless versions of the primary results."632 We have simulated the collapse of nonsiugular logatropes truncated at radü Réfry=1.31.2.21. an 3.26.," 	We have simulated the collapse of nonsingular logatropes truncated at radii $R/r_{0} = 1.34, 2.21,$ and 3.26."633" Subject to our standard T; aud [δι these models have πάθος of 1. 2.5. and 5 and scale radi of ry=0.0071.0.065. and 0.060 pe. respectively,"," Subject to our standard $T_{c}$ and $P_{s}$, these models have masses of 1, 2.5, and 5 $_{\odot}$ and scale radii of $r_{0} = 0.071, 0.065,$ and 0.060 pc, respectively."634 The higher densities iu more massive cores lead to ereater optica depths. and lence the need to account for radiative effects.," The higher densities in more massive cores lead to greater optical depths, and hence the need to account for radiative effects."635 ILlowever. as our goal is to study the purely dynuaniica aspects of gravitational collapse when radiation pressure is not vet dominant. our models do not include radiative effects.," However, as our goal is to study the purely dynamical aspects of gravitational collapse when radiation pressure is not yet dominant, our models do not include radiative effects."636 Future sinulatious of the collapse of higher mass cores will have to account for such radiative effects., Future simulations of the collapse of higher mass cores will have to account for such radiative effects.637 The singular logatrope cousidered horeiu is the pure pxort case of equation (7)). correspouding to C=V2 aud ny=6.67«10+. in the terminology of MP97.," 	The singular logatrope considered herein is the pure $\rho \propto638r^{-1}$ case of equation \ref{eq:sing}) ), corresponding to $C = \sqrt{2}$ and $m_{0} = 6.67 \times 10^{-4}$, in the terminology of MP97."639 By iuposiug a truncation radius and our standard plyvsical conditions ou the singular logatrope. we scale it such that its total mass is 1 M.," By imposing a truncation radius and our standard physical conditions on the singular logatrope, we scale it such that its total mass is 1 $_{\odot}$."640 Tn this paper. we often represent plivsical quantities (density and intall speed) as a function of radius witlin a core.," 	In this paper, we often represent physical quantities (density and infall speed) as a function of radius within a core."641 To convert between a given quantity represented on a 3-D Cartesian erid and the same quantity expressed as a function of radius alone. we simply binned the data ou the Cartesian eid into spherical shells. cach onc pixel thick and centred ou the core’s ceutre.," To convert between a given quantity represented on a 3-D Cartesian grid and the same quantity expressed as a function of radius alone, we simply binned the data on the Cartesian grid into spherical shells, each one pixel thick and centred on the core's centre."642 We then averaged the given quantity over cach shell to plot the quantity as a function of radius alone., We then averaged the given quantity over each shell to plot the quantity as a function of radius alone.643 Iu this section we describe the results of simulations of the collapse of singular logatropes., 	In this section we describe the results of simulations of the collapse of singular logatropes.644 Our objectives iu siuulatiue the siugular collapse are (a) to eusure that our method for simulating a collapse iun 3-D accurately reproduces the selfsimular solutiou of MP97 and (b) to investigate the accretionhistorv of a sineular collapse iu which the available mass reservoir is finite., Our objectives in simulating the singular collapse are (a) to ensure that our method for simulating a collapse in 3-D accurately reproduces the self-similar solution of MP97 and (b) to investigate the accretionhistory of a singular collapse in which the available mass reservoir is finite.645 Figure 5 shows the tine evolution of the radial infall speed for a singular collapse (scaled such that the total mass of the core is 1. ML)., 	Figure \ref{fig:singvel} shows the time evolution of the radial infall speed for a singular collapse (scaled such that the total mass of the core is 1 $_{\odot}$ ).646 The solid lines in the figure are the analytic solutions of MP97 for the SES collapse., The solid lines in the figure are the analytic solutions of MP97 for the SLS collapse.647 Each one represeuts the infall speed of the gas as a function of radius at a eiven instant., Each one represents the infall speed of the gas as a function of radius at a given instant.648 Iu general. the core collapses iu the expected iuside-out manner described by MP97.," 	In general, the core collapses in the expected inside-out manner described by MP97."649 Due to the initial density chhancement applied to the ceutral cell. the core is initially slightly out of hydrostatie balance auc begins to collapse slowly at all radii.," Due to the initial density enhancement applied to the central cell, the core is initially slightly out of hydrostatic balance and begins to collapse slowly at all radii."650 This effect can be seen in the figure as the low-speed deviations of the simulation data frou je analytic curves. just past the expansion wave front at each time iuterval shown.," This effect can be seen in the figure as the low-speed deviations of the simulation data from the analytic curves, just past the expansion wave front at each time interval shown."651 At early times the expansion wave. which should be spherical. is poorly resolved on 16 rectangular grid. so we do uot expect good agreement j)otween smaiulatiou aud theory.," At early times the expansion wave, which should be spherical, is poorly resolved on the rectangular grid, so we do not expect good agreement between simulation and theory."652 By 0.5 fe. the expausion wave ds easily visible over the simall iuwud motion of ie whole core.," By 0.5 $\bar{t}_{\rm ff}$, the expansion wave is easily visible over the small inward motion of the whole core."653 By 1.0 fe. the simulation shows good agreement with the theory.," By 1.0 $\bar{t}_{\rm ff}$, the simulation shows good agreement with the theory."654 The density of the collapsing core. shown in Figure 6.. also shows good agreement with jo analytics of AIP97.," The density of the collapsing core, shown in Figure \ref{fig:singden}, , also shows good agreement with the analytics of MP97."655 Ouce the expansion wave leaves the core. we cau no onecr follow its behaviour. but we can coutiuue to track ie motions of material iuside the core.," 	Once the expansion wave leaves the core, we can no longer follow its behaviour, but we can continue to track the motions of material inside the core."656 As the 2.5 £g line oei Figure 5 indicates. the collapsing material within the runcation radius coutinues to closelv follow the analytic xedietious of MP97.," As the 2.5 $\bar{t}_{\rm ff}$ line in Figure \ref{fig:singvel} indicates, the collapsing material within the truncation radius continues to closely follow the analytic predictions of MP97."657 Equation (10)) tells us that the mass of the central object at ¢=0 iu a collapsing SES should increase as f., 	Equation \ref{eq:mdotvst}) ) tells us that the mass of the central object at $r=0$ in a collapsing SLS should increase as $t^{4}$.658 We can measure an approximately similar quautitv in our siuulatious by recording the accretion history. Mjcc(f). of the sink cell.," We can measure an approximately similar quantity in our simulations by recording the accretion history, $M_{\rm acc}(t)$ , of the sink cell."659 Figure 7. shows a plot of the accretion history of the 1 M...sineular core., Figure \ref{fig:sinkacc} shows a plot of the accretion history of the 1 $_{\odot}$singular core.660 Also shown is a three- fit to MaColt|C4)! . where the fitted piriuneters are the C.," Also shown is a three-parameter fit to $M_{\rm acc} = C_{0}(t+C_{1})^{4} +C_{2}$ , where the fitted parameters are the $C_{i}$ ."661 Here. Cy is a scaling factor plaving the same role as theconstant (AP.1zG)V? in equation (10)).," Here, $C_{0}$ is a scaling factor playing the same role as theconstant $(AP_{c}4 \pi G)^{3/2}$ in equation \ref{eq:mdotvst}))."662 The constant Cy accounts for the fact, The constant $C_{1}$ accounts for the fact663is larger than (?) Stellar black holes have a minimum mass =2M.. which is an upper limit for a neutron star mass for most proposed equations of state of nuclear matter.,"is larger than \citep{psaltis07}664 Stellar black holes have a minimum mass $\ga 2\ \Msun$, which is an upper limit for a neutron star mass for most proposed equations of state of nuclear matter."665 We can set an upper bound on the time-averaged value of f by requiring that the black hole has increased its mass at most by a factor of i=10 over its age. Taso.," We can set an upper bound on the time-averaged value of $f_E$ by requiring that the black hole has increased its mass at most by a factor of $n \la 10$ over its age, $\tau_{\rm age}$."666 This leads to As a result. the black hole could have accreted only at a fraction of a pereent of the Eddington rate over its lifetime.," This leads to As a result, the black hole could have accreted only at a fraction of a percent of the Eddington rate over its lifetime."667 An alternative interpretation is that the black hole could have acereted at the Eddington rate but only for a fraction £z of its lifetime., An alternative interpretation is that the black hole could have accreted at the Eddington rate but only for a fraction $f_E$ of its lifetime.668 In any case. if the observed black hole mass has been gained over time. the condition of equation (5)) must also be satisfied at some earlier time when the mass was lower.," In any case, if the observed black hole mass has been gained over time, the condition of equation \ref{eq:acc}) ) must also be satisfied at some earlier time when the mass was lower."669" In our example the initial mass was Mop,/ and hence aceretion dominates evaporation at all times if the current mass ts higher than The more mass a black hole gained by accretion the stricter is this limit.", In our example the initial mass was $M_{\rm obs}/n$ and hence accretion dominates evaporation at all times if the current mass is higher than The more mass a black hole gained by accretion the stricter is this limit.670 Figure | shows the limit for a black hole that doubled its mass over its lifetime (7= 2)., Figure \ref{fig:l} shows the limit for a black hole that doubled its mass over its lifetime $n=2$ ).671 This limit comes within a factor of 2 in mass M or size L obtained for RZ2109., This limit comes within a factor of 2 in mass $M$ or size $L$ obtained for RZ2109.672 Although interestingly close. this limit indicates that steady aceretion of matter could not have significantly hampered the evaporation of the black hole.," Although interestingly close, this limit indicates that steady accretion of matter could not have significantly hampered the evaporation of the black hole."673 Consider now the case in which the mass of the black hole has grown after it merged with other stars in the cluster., Consider now the case in which the mass of the black hole has grown after it merged with other stars in the cluster.674 The increase in mass by a factor of 7 requires a time-averaged rate of Mii9MrE-1/7).," The increase in mass by a factor of $n$ requires a time-averaged rate of $\dot{M}_{\rm675coll} = M \tau_{\rm age}^{-1} (1-1/n)$."676 This rate dominates the evaporation rate for This equation is essentially the same as equation (7)). except for a factor (1—1)? instead of (Inv)!?.," This rate dominates the evaporation rate for This equation is essentially the same as equation \ref{eq:macc}) ), except for a factor $(n-1)^{1/3}$ instead of $(\ln{n})^{1/3}$."677 As in the case of accretion. the strictest constraint on the mass occurs at the initial epoch when the black hole mass ts the smallest.," As in the case of accretion, the strictest constraint on the mass occurs at the initial epoch when the black hole mass is the smallest."678" Therefore. collisions can be important only in the same mass range as steady accretion,"," Therefore, collisions can be important only in the same mass range as steady accretion."679 The constraint on L scales with the mass of the black hole in RZ2109., The constraint on $L$ scales with the mass of the black hole in RZ2109.680 How reliable is our estimate of its mass of 10M..?, How reliable is our estimate of its mass of $10\ \Msun$?681 The strong eemission from RZ2109 strengthens the case for a stellar mass black hole in the cluster in three key ways., The strong emission from RZ2109 strengthens the case for a stellar mass black hole in the cluster in three key ways.682 First. it dramatically reduces the already low probability that the variable X-ray source in the cluster is a background active galactic nucleus superposed on the globular cluster in the galaxy. by providing strong evidence that there 1s an unusual feature at the same redshift as the cluster.," First, it dramatically reduces the already low probability that the variable X-ray source in the cluster is a background active galactic nucleus superposed on the globular cluster in the galaxy, by providing strong evidence that there is an unusual feature at the same redshift as the cluster."683 Second. the llines provide evidence against an alternative possibility that the source is an intermediate mass black hole accreting well below its Eddington limit.," Second, the lines provide evidence against an alternative possibility that the source is an intermediate mass black hole accreting well below its Eddington limit."684 The luminosity of the line is about 1.4«10 erg s! (2)... while the velocity width of the line is about 2000 km s7!.," The luminosity of the line is about $1.4 \times 10^{37}$ erg $^{-1}$ \citep{zepf_etal08}, while the velocity width of the line is about 2000 km $^{-1}$."685" This combination cannot be produced by virial motions around a black hole of less than about 10M., without invoking a density of oxygen atoms exceeding the critical density for the line (2).. and even at 10*M... considerable fine tuning is needed to have the full volume of the ""virial region"" at exactly the critical density of the lines."," This combination cannot be produced by virial motions around a black hole of less than about $10^4 \ \Msun$ without invoking a density of oxygen atoms exceeding the critical density for the line \citep{zepf_etal08}, and even at $10^4 \ \Msun$, considerable fine tuning is needed to have the full volume of the ""virial region"" at exactly the critical density of the lines."686 The most likely situation. then. is that the emission line’s large velocity width comes from a strongwind.," The most likely situation, then, is that the emission line's large velocity width comes from a strongwind."687 While energetically important disk winds have been suggested from sources accreting at low fractions of the Eddington limit ?).. only at very high fractions of Ly are winds expected with the mass loss rates needed to produce the observed eemission (e.g..?.andreferencestherein)..," While energetically important disk winds have been suggested from sources accreting at low fractions of the Eddington limit \citep[e.g.,][]{blandford_begelman99}, only at very high fractions of $L_E$ are winds expected with the mass loss rates needed to produce the observed emission \citep[e.g.,][and references688therein]{proga07}."689 Therefore. the strength and breadth of the lline indicates that the aceretor is an object of stellar mass accreting at or slightly above its Eddington luminosity.," Therefore, the strength and breadth of the line indicates that the accretor is an object of stellar mass accreting at or slightly above its Eddington luminosity."690 Third. the bright eemission presents a strong case that the source is not a neutron star accreting well above its Eddington luminosity.," Third, the bright emission presents a strong case that the source is not a neutron star accreting well above its Eddington luminosity."691 In? it was shown that. without beaming. an unphysically high accretion rate would be required to allow for this system to be a super-Eddington neutron star accretor.," In \citet{maccarone_etal07} it was shown that, without beaming, an unphysically high accretion rate would be required to allow for this system to be a super-Eddington neutron star accretor."692 However. geometric beaming has been suggested as a way to produce the high luminosities seen in some ultraluminous X-ray sources without invoking unphysically high mass. transfer rates and without invoking black hole masses in excess of ~20M. (e.g..?)..," However, geometric beaming has been suggested as a way to produce the high luminosities seen in some ultraluminous X-ray sources without invoking unphysically high mass transfer rates and without invoking black hole masses in excess of $\sim 20 \ \Msun$ \citep[e.g.,][]{king_etal01}."693 The observed eemission Is à new argument against significant beaming., The observed emission is a new argument against significant beaming.694 The eemission cannot come from a small enough region to be beamed geometrically. and hence must be unbeamed.," The emission cannot come from a small enough region to be beamed geometrically, and hence must be unbeamed."695 For the beaming factors of ~10. which would be needed to allow the accretor in RZ2109 to be a neutron star. one would first need to explain an intrinsic luminosity ratio {οLg~0.03. far below what is seen from active galactic nuclei (e.g..2)..," For the beaming factors of $\sim 10$, which would be needed to allow the accretor in RZ2109 to be a neutron star, one would first need to explain an intrinsic luminosity ratio $L_{\rm [O\,696III]}/L_{\rm bol} \sim 0.03$, far below what is seen from active galactic nuclei \citep[e.g.,][]{heckman_etal05}."697 Also. one would need to explain the lack of any globular clusters with strong. broad llines but no bright X-ray sources. given that a large number of globular clusters have been searched for emission lines. turning up no other cases of clusters with very broad lines but finding numerous narrow lines typically associated with planetary nebulae (e.g..2222).," Also, one would need to explain the lack of any globular clusters with strong, broad lines but no bright X-ray sources, given that a large number of globular clusters have been searched for emission lines, turning up no other cases of clusters with very broad lines but finding numerous narrow lines typically associated with planetary nebulae \citep[e.g.,][]{minniti_rejkuba02, brodie_etal05,698pierce_etal06, chomiuk_etal08}."699 Thus we conclude that the accretor in RZ2109 is à black hole of 5.3-20M..., Thus we conclude that the accretor in RZ2109 is a black hole of $5.3-20 \ \Msun$.700" These limits come from estimating the fraction of the Eddington luminosity that i5 contributed by the observed X-ray luminosity Lyz4«107? erg s7!. as follows: where j/, is the mean molecular weight per electron."," These limits come from estimating the fraction of the Eddington luminosity that is contributed by the observed X-ray luminosity $L_X \approx 4\times 10^{39}$ erg $^{-1}$, as follows: where $\mu_e$ is the mean molecular weight per electron."701" The lack of Balmer emission from the source indicates that the donor star is likely to be hydrogen poor. which gives ji,z 2."," The lack of Balmer emission from the source indicates that the donor star is likely to be hydrogen poor, which gives $\mu_e \approx 2$ ."702 Such a donor could be a white dwarf in a ~5 minute orbit. consistent with persistent emission.," Such a donor could be a white dwarf in a $\sim 5$ minute orbit, consistent with persistent emission."703 The lack of emission from any element heavier than oxygen is also a strong argument against the possibility of this system being a tidally-induced supernova (suggestedby ?).., The lack of emission from any element heavier than oxygen is also a strong argument against the possibility of this system being a tidally-induced supernova \citep[suggested by][]{rosswog_etal09}. .704 The lower bound on the mass can be estimated by looking at the degree to which black hole X-ray binaries inthe Galaxy, The lower bound on the mass can be estimated by looking at the degree to which black hole X-ray binaries inthe Galaxy705For long exposures in both bands. the terms including 2? can be neglected. ancl we obtain simply: being 3 the following: The parameter 2 has limit cases depending on qp.,"For long exposures in both bands, the terms including $R^2$ can be neglected and we obtain simply: being $\beta$ the following: The parameter $\beta$ has limit cases depending on $q_{\broadband}$."706 LW gy—0. the noise is dominated by the Poisson noise of the source flux: 1 quo. the equation is dominated by the Poisson noise of the skv background.," If $q_{\broadband} \to 0$, the noise is dominated by the Poisson noise of the source flux: If $q_{\broadband} \to \infty$, the equation is dominated by the Poisson noise of the sky background."707 This is the case lor faint objects in the images: We also make explicit the dependence on exposure (ime of the narrow-band combining Eq., This is the case for faint objects in the images: We also make explicit the dependence on exposure time of the narrow-band combining Eq.708 63 and Eq., \ref{eq:snr:explicit1} and Eq.709 65 to obtain: Equation 62. can be written: We trv to detect 5-0 over the mean objects with my = 22 and Qj = 1.8 (this represents a color excess of 0.6 magnitudes )., \ref{eq:snr:ratio} to obtain: Equation \ref{eq:optimal} can be written: We try to detect $\sigma$ over the mean objects with $m_{\narrowband}$ = 22 and $\mathcal{Q}_\mathrm{l}$ = 1.8 (this represents a color excess of 0.6 magnitudes ).710 Assuming a mean color of the objects without emission line of Qo=I. we immediately compute p—0.16.," Assuming a mean color of the objects without emission line of $\mathcal{Q_\mathrm{O}}=1$, we immediately compute $\rho=0.16$."711 With these fillers. the color of the skv background is Qu=0.23 and 5b=0.024.," With these filters, the color of the sky background is $\mathcal{Q}_\mathrm{S}=0.23$ and $b=0.024$."712 From the exposure time caleulator of the INT WFC.SIGNAL? we obtain that. for an object of mg = 22. with seeing of and a brightness of the skv background of 19.60 mag/arcs? (tvpical for a dark night). the SNR in the broad band is (he square root of Uae exposure time (times α — 0.1.," From the exposure time calculator of the INT WFC, we obtain that, for an object of $m_{\broadband}$ = 22, with seeing of and a brightness of the sky background of 19.60 $^2$ (typical for a dark night), the SNR in the broad band is the square root of the exposure time times $\alpha$ = 0.7."713to tailor these wings so as to deliver the observed rauge of IS VUV features.,to tailor these wings so as to deliver the observed range of IS VUV features.714 For this purpose. we set the additive constant in eq.," For this purpose, we set the additive constant in eq."715 2 to zero aud nmultiplv by a Caussian function of width 5. centered ou wy. and much wider than the logarithinic peak: Tere. wy iust be set equal to the same 7 or σ resonance frequency as in bulk eraplhite. ie. L3 or Ll eV. This is because the interlaver distance in eraphite (3.37 )) is inuch too large for a laver to notably perturb the resonance of its neighbours. as was recently confirmed bx DET calculations (see Miuinopoulos et al. (200 L)..," 2 to zero and multiply by a Gaussian function of width $\gamma$, centered on $\omega_{0}$, and much wider than the logarithmic peak: Here, $\omega_{0}$ must be set equal to the same $\pi$ or $\sigma$ resonance frequency as in bulk graphite, i.e. 4.3 or 14 eV. This is because the interlayer distance in graphite (3.37 ) is much too large for a layer to notably perturb the resonance of its neighbours, as was recently confirmed by DFT calculations (see Marinopoulos et al. \cite{mar}. ."716 We found that. if the σ resonance is omitted. the Exóllich feature associated with the 7 resonance is svstematically shifted well bevoud the observed 5.7 eV (L6 yan 1).," We found that, if the $\sigma$ resonance is omitted, the Fröllich feature associated with the $\pi$ resonance is systematically shifted well beyond the observed 5.7 eV (4.6 $\mu$ $^{-1}$ )."717" Thus. both +. and +, are uecessary and sufficient to deliver the desired feature at the right position with the right width."," Thus, both $\gamma_{\pi}$ and $\gamma_{\sigma}$ are necessary and sufficient to deliver the desired feature at the right position with the right width."718 J(w) becomes therefore a sunm of 2 similar terius., $J(\omega)$ becomes therefore a sum of 2 similar terms.719 Iu selecting the two 5 parameters for eraphenuc. we must keep iu mind the following: the width of the resonance of a PCG-like material made of bricks of stacked eraphene lavers uecessarily exceeds the width of a single eraplene resonance. because it is mereased both by stacking aud by mixing of es for Eο πας ELc as is shown below.," In selecting the two $\gamma$ parameters for graphene, we must keep in mind the following: the width of the resonance of a PG-like material made of bricks of stacked graphene layers necessarily exceeds the width of a single graphene resonance, because it is increased both by stacking and by mixing of $\epsilon$ 's for $E\parallel c$ and $E\perp c$, as is shown below."720 Thus. our scenario only applies if the width of the Frollich resonance of a single laver eraphene is found to be atmost as wide as the smallest observed IS feature width. namely ~0.7pam ," Thus, our scenario only applies if the width of the Fröllich resonance of a single layer graphene is found to be atmost as wide as the smallest observed IS feature width, namely $\sim0.7\, \mu$ $^{-1}$."721The proportionality factors. multipblius the z aud σ terms in eq.," The proportionality factors, multiplying the $\pi$ and $\sigma$ terms in eq."722 1 for e? are determined by application of the Sum Rule. related to the nunuber of electrons oer atom contributing to the π aud o resonances respectively (see Altarclli et al. (1972)..," 4 for $\epsilon_{2}$ are determined by application of the Sum Rule, related to the number of electrons per atom contributing to the $\pi$ and $\sigma$ resonances respectively (see Altarelli et al. \cite{as},"723 eq., eq.724 6)., 6).725 In this case. the rule is implemented by requiring that the ateaus of the function Xeowdi of wat ~T and ~1d eV respectively. be he same as for graphite as measured by Taft and Philipp (1965)..," In this case, the rule is implemented by requiring that the plateaus of the function $\Sigma \epsilon_{2}\omega\,{\rm{d}}\omega$ of $\omega$, at $\sim7$ and $\sim18$ eV respectively, be the same as for graphite as measured by Taft and Philipp \cite{tp}."726" With the above constraints in mind. we settled on the following expression or eraphene in the ELe polarization: where wis in ον (1 eV=0.805 µια 1). from 1 to 20 in steps of 0.01 eV. and A.—oT5uwa—d435.2.5.4.- I2123ugs—lls,=3."," With the above constraints in mind, we settled on the following expression for graphene in the $E\perp c$ polarization; where $\omega$ is in eV's (1 eV=0.805 $\mu$ $^{-1}$ ), from 1 to 20 in steps of 0.04 eV, and $A_{\pi}=-77, \omega_{0\pi}=4.3, \gamma_{\pi}=2.5, A_{\sigma}=-424.3, \omega_{0\sigma}=14, \gamma_{\sigma}=3$."727 This equation is plotted in Fie., This equation is plotted in Fig.728 LA. together with thecorrespouding curve for bulk eraphite as measured by Taft aud Philipp (1965).. for purposes of comparison.," 1A, together with thecorresponding curve for bulk graphite as measured by Taft and Philipp \cite{tp}, , for purposes of comparison."729 The real part of the diclectric function of eraphlieue. eq; was obtained by applviug," The real part of the dielectric function of graphene, $\epsilon_{1}$ was obtained by applying"730In this paper. we locus on non-Gaussianitv of local (vpe. where the amplitude of iis nieasured by a single parameter. cileplO90PhHRvD..42.39368..,"In this paper, we focus on non-Gaussianity of local type, where the amplitude of is measured by a single parameter, \\citep{1990PhRvD..42.3936S}."731 A common strategy for estimating co," A common strategy for estimating is to evaluate the bispectrum of the CMB \citep{2002ApJ...566...19K,732 2003ApJS..148..119K, 2007ApJS..170..377S, 2008PhRvL.100r1301Y,733 2009JCAP...09..006S}."734mbination of filtered CAIB maps reconstructing the primordial perturbations (???).. ," This is usually done indirectly via a cubic combination of filtered CMB maps reconstructing the primordial perturbations \citep{2005ApJ...634...14K, 2007ApJ...664..680Y,735 2008ApJ...678..578Y}."736This approach takes advantage of the specific signatures produced by primordialnon-Gaussianitv.. resulting in a computationally efficient algorithm.," This approach takes advantage of the specific signatures produced by primordial, resulting in a computationally efficient algorithm."737" A variant of (his estimator has been successfully applied to the 7-vear data release of the Wilkinson Microwave Anisotropy Probe (WMAD). resulting in 210<fx,74 al 95% confidence level (?).."," A variant of this estimator has been successfully applied to the 7-year data release of the Wilkinson Microwave Anisotropy Probe (WMAP), resulting in $-10 < f_{\NL} < 74$ at $95 \,738\%$ confidence level \citep{2010arXiv1001.4538K}."739 The bispecirum estimator used in previous analvses has been shown to be optimal. iil satisfies the Crameérr-Rao bound (?)..," The bispectrum estimator used in previous analyses has been shown to be optimal, it satisfies the Cramérr-Rao bound \citep{2005PhRvD..72d3003B}."740 However. this turns out to be (rue only in the limit ol vanishing cilep2007JCAD...03..019C..," However, this turns out to be true only in the limit of vanishing \\citep{2007JCAP...03..019C}."741 For a significant detection of[νι the estimator suffers [rom excess variance. a finding that has also been verified numerically (?)..," For a significant detection of, the estimator suffers from excess variance, a finding that has also been verified numerically \citep{2007PhRvD..76j5016L}."742 For (he simplified case of a flat skv approximation. neglected transfer Iunctions and instrumental noise. ?. showed that it should be possible to construct an improved version of the estimator (hat is equivalent to a [ull likelihood analvsis up to terms of the order O(1/Αν).," For the simplified case of a flat sky approximation, neglected transfer functions and instrumental noise, \cite{2007JCAP...03..019C} showed that it should be possible to construct an improved version of the estimator that is equivalent to a full likelihood analysis up to terms of the order $\mathcal{O}(1/\ln743N_{\mathrm{pix}})$."744 Bavesian methods for the analvsis of various aspects of CAIB data have been successfully developed in the past. e.g.. for an exact power specirum determination using Gibbs sampling to ," Bayesian methods for the analysis of various aspects of CMB data have been successfully developed in the past, e.g., for an exact power spectrum determination using Gibbs sampling \citep[e.g.][]{2004ApJ...609....1J, 2004PhRvD..70h3511W,745 2007ApJ...656..653L, 2009ApJ...697..258J}, to separate foreground contributions from the CMB anisotropies \citep[e.g.][]{1998MNRAS.300....1H, 2004MNRAS.351..515B,746 2006NewAR..50..861E, 2008ApJ...672L..87E, 2008ApJ...676...10E,747 2009ApJ...705.1607D}, or to probe for features \citep[e.g.][]{2001PhRvD..64f3512R, 2009arXiv0911.5399E,748 PhysRevD.80.105005, 2009MNRAS.397..837V}."749loreground contamination or instrumental effects., They offer a natural way to marginalize over uncertainties attributed to foreground contamination or instrumental effects.750 This is of particular importance for a reliable analvsis of weak signals and an advantage over Irequentist methods. where no such procedures exist.," This is of particular importance for a reliable analysis of weak signals and an advantage over frequentist methods, where no such procedures exist."751 Ilere. we advance (he exact scheme introduced in? to inler the level of {from realistic CMD data within a Bavesian approach.," Here, we advance the exact scheme introduced in \citet{2010A&A...513A..59E} to infer the level of from realistic CMB data within a Bayesian approach."752 We use simulated acid CCMD temperature maps to compare and contrast the conventional Irequentist (bispectirunm) estimator with the exact Bavesian approach., We use simulated and CMB temperature maps to compare and contrast the conventional frequentist (bispectrum) estimator with the exact Bayesian approach.753" We show that the latter method does not suffer from excess variance for non-zerofs,.. and can deal with partial skv coverage and anisotropic noise properties. a feature of particular importance for local"," We show that the latter method does not suffer from excess variance for non-zero, and can deal with partial sky coverage and anisotropic noise properties, a feature of particular importance for local"754Prep).,.755. Our estimates of the cloud structure (see Sect. 4.3)), Our estimates of the cloud structure (see Sect. \ref{sec.GMCinSB}) )756 depends on the averaged radiation field which might be different in both galaxies., depends on the averaged radiation field which might be different in both galaxies.757 The averaged radiation fields in both 2253 and 882 have been inferred [rom the fine structure lines and they are of 2x10! and 107. respectively. with large errors of a factor of 2 1996).," The averaged radiation fields in both 253 and 82 have been inferred from the fine structure lines and they are of $2\times10^4$ and $10^3$, respectively, with large errors of a factor of 2 \citep{Carral94,Lord96}."758. This would imply that the PDR envelope should be larger in the clouds of 2253 (han in 382., This would imply that the PDR envelope should be larger in the clouds of 253 than in 82.759 Since we do not aim to quantitatively model the particular abundances measured in 2253 but (o investigate the plivsical conditions that would give rise to the wealth of observed molecules in starburst. the value of Gy=5x10* used is a geometric mean value derived [rom the fine structure lines in both galaxies.," Since we do not aim to quantitatively model the particular abundances measured in 253 but to investigate the physical conditions that would give rise to the wealth of observed molecules in starburst, the value of $G_0=5\times10^3$ used is a geometric mean value derived from the fine structure lines in both galaxies."760 Given that our estimates of the Ay for the PDR are based on this geometric mean. the expected changes in ος Lor the two galaxies would be just a factor of 1.6.," Given that our estimates of the $A_{\rm v}$ for the PDR are based on this geometric mean, the expected changes in $A_{\rm v}$ for the two galaxies would be just a factor of 1.6."761 We have ran two different models: Model A is a standard time dependent. gas-phase PDR model where the initial composition is atomic: while Model B is computed using a coupled dense core-PDR model where (he diffuse material. iniüallv also purely atomic and gaseous. Collapses to reach a final density of LO?cm.," We have ran two different models: Model A is a standard time dependent gas-phase PDR model where the initial composition is atomic; while Model B is computed using a coupled dense core-PDR model where the diffuse material, initially also purely atomic and gaseous, collapses to reach a final density of $\rm 10^5\,cm^{-3}$."762 During the collapse the gas depletes on the grains forming ijev mantles whieh remain on the dust. until irradiation [rom a UV Ποια is switched on. evaporation occurs and the ἱνρίσα PDR chemistry takes place.," During the collapse the gas depletes on the grains forming icy mantles which remain on the dust until irradiation from a UV field is switched on, evaporation occurs and the typical PDR chemistry takes place."763 In both models the temperature is calculated sell-consistenilv al each depth and time step bv thermal balance., In both models the temperature is calculated self-consistently at each depth and time step by thermal balance.764 Fig., Fig.765 4 shows the predicted abundances ancl abundance ratios as a [unetion of visual extinction (ολ) for Model A (left panels) and B (right panels)., \ref{fig:PDRmod} shows the predicted abundances and abundance ratios as a function of visual extinction $A_{\rm v}$ ) for Model A (left panels) and B (right panels).766 UNCO and CIOL results are only shown for Model D in Fig. 4.., HNCO and $_3$ OH results are only shown for Model B in Fig. \ref{fig:PDRmod}.767 Observed abundancees of — and towards 2253 (shown as horizontal lines in the kev of Fig. 4)), Observed abundances of $^+$ and $^+$ towards 253 (shown as horizontal lines in the key of Fig. \ref{fig:PDRmod}) )768 are well reproduced by the models for very low extinction of dA.~1-2., are well reproduced by the models for very low extinction of $A_{\rm v}\sim1-2$.769 The HCO abundance observed is a factor 2—6 above the maximum predicted by the model D. It is important to take into account that while we assumed a, The HCO abundance observed is a factor $2-6$ above the maximum predicted by the model B. It is important to take into account that while we assumed a770Hatten.,flatten.771 We anticipate that in both cases the non-relativistic slopes do not depend on the viewing angle but only on the spectrum. Contrary to the temporal slopes in the relativistic regime (see also Fig. 6. 7).," We anticipate that in both cases the non-relativistic slopes do not depend on the viewing angle but only on the spectrum, contrary to the temporal slopes in the relativistic regime (see also Fig. \ref{fig:nse_lc}, , \ref{fig:se_lc}) )."772 lig., Fig.773 4 and Fig., \ref{fig:omcomlc} and Fig.774 5. also show that a SI jet has compared toa NSE jet and. these characteristics are even more evident for jets with a supersonic sidewavys expansion., \ref{fig:omcompo} also show that a SE jet has compared to a NSE jet and these characteristics are even more evident for jets with a supersonic sideways expansion.775 All these features (among others) are cliscussecl in more details in the following. comparing a NSE jet with a jet undergoing a sideways expansion given hy Eq. Ὁ..," All these features (among others) are discussed in more details in the following, comparing a NSE jet with a jet undergoing a sideways expansion given by Eq. \ref{se1}."776 For a jet evolution following Eq., For a jet evolution following Eq.777 11 we refer the reader to 803. where a more complete discussion is given.," \ref{eq:sejay} we refer the reader to S03, where a more complete discussion is given."778 The Ro band lighteurve for à NSE and for à SE homogeneous jet are shown in Fig., The R band lightcurve for a NSE and for a SE homogeneous jet are shown in Fig.779 6 and Fig., \ref{fig:nse_lc} and Fig.780 7. respectively., \ref{fig:se_lc} respectively.781 μον show interesting features. some of which have never been discussed before.," They show interesting features, some of which have never been discussed before."782 In the lower panels the temporal index a (defined as P)x C) ds plotted versus time., In the lower panels the temporal index $\alpha$ (defined as $F(t)\propto t^{\alpha}$ ) is plotted versus time.783 We call àj.02 and a; the pre-break. the post-break and the non-relativistic slope respectively.," We call $\alpha_1$ $\alpha_2$ and $\alpha_3$ the pre-break, the post-break and the non-relativistic slope respectively."784 The horizontal dot-dashed lines show the expected slopes from on-axis standard. calculations., The horizontal dot-dashed lines show the expected slopes from on-axis standard calculations.785 The standard? post-break slopes (central dot-dashed Lines in Fig., The “standard” post-break slopes (central dot-dashed lines in Fig.786 6 and Fig. 7..," \ref{fig:nse_lc} and Fig. \ref{fig:se_lc},"787" lower panels) are calculated considering the loss of the emitting area from a spherical blast. wave (1ου!3) to a conical one (1cos6;,4).", lower panels) are calculated considering the loss of the emitting area from a spherical blast wave $(1-\cos\Gamma^{-1})$ to a conical one $(1-\cos\theta_{jet})$.788 For the SE jet we also consider the more rapid. deceleration due to the increase of the shock front surface (Rhoads 1999: Sari. Piran Lalpern 1999).," For the SE jet we also consider the more rapid deceleration due to the increase of the shock front surface (Rhoads 1999; Sari, Piran Halpern 1999)."789 In. both cases the surface. brightness. is supposed to be the same across the surface of the jet at al times., In both cases the surface brightness is supposed to be the same across the surface of the jet at all times.790 For p>vw the expected breaks are Aes.=i fora NSE jet and Aa.=———1.125 for a SE onc., For $\nu>\nu_c$ the expected breaks are $\Delta \alpha_{nse}=\frac{3}{4}$ for a NSE jet and $\Delta\alpha_{se}=\frac{(p+2)}{4}=1.125$ for a SE one.791" ln fact we find that the flux after the break falls olf more rapidly than expected. ancl this elfeet is more eviden as the electron energy. distribution Αρx*"" becomes steeper."," In fact we find that the flux after the break falls off more rapidly than expected, and this effect is more evident as the electron energy distribution $N(\gamma)\propto\gamma^{-p}$ becomes steeper."792 This can be understood. by taking into accoun the clfect of LATS., This can be understood by taking into account the effect of EATS.793 When r/E«r6;4 the visible area can be schematizedas a bright ring with radius rfl ane," When $r/\Gamma<r\,\theta_{jet}$ the visible area can be schematizedas a bright ring with radius $r/\Gamma$ and"794L bar pressure level.,1 bar pressure level.795 Below that the interior is adiabatic., Below that the interior is adiabatic.796 For close-in) extrasolar giant plancts. the observed rausit radius occurs at L 6 orders of magnitude lower xessures than the onset of the adiabatic region. aud a xoper outer boundary condition has to be provided by a imnodol atmosphere.," For close-in extrasolar giant planets, the observed transit radius occurs at $-$ 6 orders of magnitude lower pressures than the onset of the adiabatic region, and a proper outer boundary condition has to be provided by a model atmosphere."797 Calculations for particular eiaut danuets predict the radiative/convective laver boundary deep in the atmosphere between LOO and 1000 bars (?).., Calculations for particular giant planets predict the radiative/convective layer boundary deep in the atmosphere between 100 and 1000 bars \citep{Showman+08}.798 The aean heliuun abundance should equal that of he protostellar cloud where the planet formed from., The mean helium abundance should equal that of the protostellar cloud where the planet formed from.799 Uowever. the atmospheres of Jupiter and Saturn are depleted iu Ποτά. compared to the solar value Y=12702:0.005 1. which motivates the introduction of a IIc-poor outer cuvelope aud a IHe-nich inner euvelopo.," However, the atmospheres of Jupiter and Saturn are depleted in helium compared to the solar value $Y=0.270\pm 0.005$ \citep{Bahcall+95}, which motivates the introduction of a He-poor outer envelope and a He-rich inner envelope."800 The metalliitv. Z in the atmospheres of the solar udanets is chhanced above the solar value Z.=(0.015 (2) as derived from abundance measurements of single species (C8: C. N. S. Ar. No).," The metallicity $Z$ in the atmospheres of the solar planets is enhanced above the solar value $Z_{\odot}=0.015$ \citep{Lodders03} as derived from abundance measurements of single species (e.g.; C, N, S, Ar, Xe)."801 Solar planets ire fast rotators. which gives rise to a eravitv field deformation as expressed by the eravitational ποιοτς Jy. 7). and Jg.," Solar planets are fast rotators, which gives rise to a gravity field deformation as expressed by the gravitational moments $J_2$, $J_4$, and $J_6$."802 Equivalent coustraints for extrasolar plaucts are tidal Love uiuubers ον., Equivalent constraints for extrasolar planets are tidal Love numbers $k_{2n}$.803 Parameters related to thermal or orbital evolutiou can give additional coustraints but are not addressed in this article., Parameters related to thermal or orbital evolution can give additional constraints but are not addressed in this article.804 For Jupiter aud Saturn. the simplest structure type that is consistent with the coustraints described above has three lavers: a core of rocks and/or ices. ae two envelopes that are convective. adiabatic. anc homogeucous. but differ inthe mass fraction of heli (Y) and metals CZ).," For Jupiter and Saturn, the simplest structure type that is consistent with the constraints described above has three layers: a core of rocks and/or ices, and two envelopes that are convective, adiabatic, and homogeneous, but differ inthe mass fraction of helium $(Y)$ and metals $(Z)$."805 We choose the metallicities Z and Zo! to adjust Jo and J)., We choose the metallicities $Z_1$ and $Z_2$ to adjust $_2$ and $J_4$.806 Often (e.g: ?2)) but no always (7). models that reproduce Jupiter's Jy aud J are found to reproduce also 4; within the obervationa error bar.," Often (e.g; \citealp{Gui99,Hori+08}) ) but not always \citep{Militzer+08}807 models that reproduce Jupiter's $J_2$ and $J_4$ are found to reproduce also $J_6$ within the obervational error bar."808 Physical reasons for a discontinuütv du Ile or metals can be phase transitions. IL/Ile phase separation. aud in particular for metals the process of plauct formation. but its location ids csscutially nuconstramed. and hence the transition pressure Py2 between the euvelopes a free parameter.," Physical reasons for a discontinuity in He or metals can be phase transitions, H/He phase separation, and in particular for metals the process of planet formation, but its location is essentially unconstrained, and hence the transition pressure $P_{1-2}$ between the envelopes a free parameter."809 Iu the absence of these particular plivesical processes. gaseous planets are likely to have a homogenous euvelope because of convection.," In the absence of these particular physical processes, gaseous planets are likely to have a homogenous envelope because of convection."810 If however convection is inhibited as suspected for Uranus (27) a series of double-diffusive lavers candevelop creating a large-scale compositional eracdieut.," If however convection is inhibited as suspected for Uranus \citep{Podolak+91}811 a series of double-diffusive layers candevelop creating a large-scale compositional gradient."812 Such complicated models are not considered here., Such complicated models are not considered here.813 At laver boundaries. pressure P and temperature T are required to trausit coutinouslh.," At layer boundaries, pressure $P$ and temperature $T$ are required to transit continously."814 The PTp xofile. where pis mass density. along the quasi-adiabat depends on the He abundances aud metallicities eliosen. and on the equations of state (EOS) of the uuderlviue uaterials allowed for.," The $P-T-\rho$ profile, where $\rho$ is mass density, along the quasi-adiabat depends on the He abundances and metallicities chosen, and on the equations of state (EOS) of the underlying materials allowed for."815 If the cuvelopes differ in Io mass yaction (34<15) or metallicity σι4Zo). then eutropyv and density transit discoutinously. so we call he internal PT profile quasi--adiabatie.," If the envelopes differ in He mass fraction $(Y_1<Y_2)$ or metallicity $(Z_1\not=Z_2)$, then entropy and density transit discontinously, so we call the internal $P-T$ profile -adiabatic."816 At a laver )oundary. a boundary laver can develop with chanec in temperature across or conductive heat trausport. causing a warmer interior at higher eutropy.," At a layer boundary, a boundary layer can develop with change in temperature across or conductive heat transport, causing a warmer interior at higher entropy."817 The effect of a boundary laver has been iucluded by ? for the mhonmogeneous evolution of Saturu: but not vet in structure calculations., The effect of a boundary layer has been included by \cite{ForHub03} for the inhomogeneous evolution of Saturn; but not yet in structure calculations.818 Since the gravity data probe the internal P/—p relation. the expected imfueuce of a warmer interior ou the structure would be a higher deep envelope metallicity.," Since the gravity data probe the internal $P-\rho$ relation, the expected influence of a warmer interior on the structure would be a higher deep envelope metallicity."819" It is convenicut to represent elenieuts heavier than Ile Gretals)) bv an equation of state of water (ο,2?) as also supported by planet formation theory (7).. aud to assume the core be made of rocks (e.g:777). or of water ice (0.8:?2).."," It is convenient to represent elements heavier than He ) by an equation of state of water \citep[e.g.;][]{ForHub03,SauGui04} as also supported by planet formation theory \citep{Helled+08}, , and to assume the core be made of rocks \citep[e.g.;][]{ForHub03,SauGui04,N-Jupiter+08} or of water ice \citep[e.g.;][]{SauGui04}."820 Jupiter-sized giant plauets are because they are predominantly composed of the light clemeuts IT and Ie., Jupiter-sized giant planets are because they are predominantly composed of the light elements H and He.821 For details of the EOS. see ον Ετος aud ?..," For details of the EOS, see \citet{SauGui04,N-Jupiter+08}, FN10, and \citet{Militzer+08}."822 Tn order to obtain core mass and metallicity we iuteerate the 1-diniensional equations of mass conservation dinαἱ=IxPpil). and of hivydrostatie equilibrium. along the quasiadiabat for eiven outer boundary conditions and abundances of helium aud metals.," In order to obtain core mass and metallicity we integrate the 1-dimensional equations of mass conservation, $dm/dl=4\pi l^2\rho(l)$, and of hydrostatic equilibrium, along the quasi-adiabat for given outer boundary conditions and abundances of helium and metals."823 The coordinate / paramctrizes surfaces of constant total potential C., The coordinate $l$ parametrizes surfaces of constant total potential $U$.824" Iu spherical οποίαν, ic. im the absence of rotation. / equals the radial coordinate r."," In spherical symmetry, i.e. in the absence of rotation, $l$ equals the radial coordinate $r$."825 The most often theory used to calculate the eravity field deformation according to shape deformation is the by ?.. but alternative theories can be applied as well (6.8: 7)..," The most often theory used to calculate the gravity field deformation according to shape deformation is the by \citet{ZT78}, , but alternative theories can be applied as well \citep[e.g.;][]{HubbBuch84}. ."826 The eravity field deformation ou or exterior to the surface (p(P=Έναν)z 0) cau be described bw multipole expansion iuto spherical harmonics. wherethe expansion cocfhücieuts are the eravitational moments," The gravity field deformation on or exterior to the surface $\rho(P=1\rm bar)\approx 0$ ) can be described by multipole expansion into spherical harmonics, wherethe expansion coefficients are the gravitational moments"827star formation rate per unit surface area on the molecular and total surface density (Fie. 3)).,star formation rate per unit surface area on the molecular and total surface density (Fig. \ref{fig:molbigiel}) ).828 The correlation between the star formation rate and the molecular gas surface density is linear with a molecular depletion timescale of ~1.5 Gyr for the ISALO5 star formation prescription aud ~2 Cor for the VBo3 star formation prescription., The correlation between the star formation rate and the molecular gas surface density is linear with a molecular depletion timescale of $\sim 1.5$ Gyr for the KM05 star formation prescription and $\sim 2$ Gyr for the VB03 star formation prescription.829 The correlation between the total eas surface density and the star formation rate is steep where is dominating (X<20 Mav P) and flattens for üesher eas surface deusities., The correlation between the total gas surface density and the star formation rate is steep where is dominating $\Sigma < 20$ $_{\odot}$ $^{-1}$ ) and flattens for higher gas surface densities.830 The VD03 moclel reproduces results bv Bigieletal.(2008) aud Lerovetal.(2008) who found (i) an average nolecular gas depletion timescale of 2 Cevr aud (11) a critical eas surface density of LL AL. ? for the change between eas predominantly im molecular rnm and eas predomunantly in atomic forni., The VB03 model reproduces results by \citet{Bigiel} and \citet{Leroy} who found (i) an average molecular gas depletion timescale of $2$ Gyr and (ii) a critical gas surface density of $14$ $_{\odot}$ $^{-2}$ for the change between gas predominantly in molecular form and gas predominantly in atomic form.831scale: The derived driving scale cheths are nionotonicallv increasing with increasing radius., The derived driving scale lengths are monotonically increasing with increasing radius.832 Typical values are 100-200 po in the ner ια of the optical disk., Typical values are $100$ $300$ pc in the inner half of the optical disk.833 At the optical radius he driving leugth scale is about 0-800. pe., At the optical radius the driving length scale is about $400$ $800$ pc.834 The radia increase and the large values at the optical radius are consistent with sizes ofIT shells observed in the Calaxy (Ies1981:A\IeChiue-Coifiithsetal. 2002).," The radial increase and the large values at the optical radius are consistent with sizes of shells observed in the Galaxy \citep{Heiles,McClure}."835.motions: Racial gas motious with velocity (rag can be estimated with the mass accretion rate AZ aud the gas surface density Mea. (scec.g.Pringle1981): The radial profiles of the radial velocity are presented in Figs., Radial gas motions with velocity $v_{\rm rad}$ can be estimated with the mass accretion rate $\dot{M}$ and the gas surface density $\Sigma_{\rm gas}$ \citep[see e.g.][]{Pringle}: The radial profiles of the radial velocity are presented in Figs.836 1 aud 2..," \ref{fig:radialprofilesKM05}837 and \ref{fig:radialprofilesVB03}."838 Typically. we find radial velocities sumaller than 2 |.," Typically, we find radial velocities smaller than $2$ $^{-1}$."839 This is consistent with the fiudiugs of Trachteruachetal.(2008) who found non-circular motions smaller than 5 log these galaxies., This is consistent with the findings of \citet{Trachternach} who found non-circular motions smaller than $5$ $^{-1}$ in these galaxies.840 Moreover. we observe a general increase of radial velocitics with decreasing ealactocentric radius.," Moreover, we observe a general increase of radial velocities with decreasing galactocentric radius."841" A stronglv increasing (Q in the outer disks of NGC 2976, NGC 1736. aud NCC 3627 due to a strongly decreasing gas surface density leads to steeply iucreasing radial velocities Grp to LO !) in these ealaxies."," A strongly increasing $Q$ in the outer disks of NGC 2976, NGC 4736, and NGC 3627 due to a strongly decreasing gas surface density leads to steeply increasing radial velocities (up to $10$ $^{-1}$ ) in these galaxies."842 This is again consisteut with the profiles of uou-circular motions derived by Trachternachetal.(2008)..estimates:, This is again consistent with the profiles of non-circular motions derived by \citet{Trachternach}.843 The free-fall time only depends on the cloud density ρα (Eq. 2))., The free-fall time only depends on the cloud density $\rho_{\rm cl}$ (Eq. \ref{eq:localff}) ).844 Typical deusities of eiut molecular clouds are between 100-1000. cm? (Solomonetal.1987:everet2009). leading to free fall times of 1.6-5.1 Myr.," Typical densities of giant molecular clouds are between $100$ $1000$ $^{-3}$ \citep{Solomon, Heyer} leading to free fall times of $1.6$ $5.1$ Myr."845 Tiuuburroetal.(2008) estimated ai characteristie timescale for star formation in the spiral axisof disk galaxies. eoiug from atomic lvdrogen (Ili) to dust-cushroucded massive stars.," \citet{Tamburro08} estimated a characteristic timescale for star formation in the spiral armsof disk galaxies, going from atomic hydrogen ) to dust-enshrouded massive stars."846 Their free fall time estimates vary between 1 and 6 Cir., Their free fall time estimates vary between $1$ and $6$ Gyr.847 The VBoO3 moclel vields the physical properties of the most massive selferavitating clouds at a given galactocentric radius via he local free-fall (t. ). turbulent (to).rub and molecule formation (to) timescales.," The VB03 model yields the physical properties of the most massive selfgravitating clouds at a given galactocentric radius via the local free-fall $t_{\rm ff}^{l}$ ), turbulent $t_{\rm turb}^{l}$ ), and molecule formation $t_{\rm mol}^{l}$ ) timescales."848 We recall that for sclfgravitating clouds ft=H4., We recall that for selfgravitating clouds $t_{\rm ff}^{l}=t_{\rm turb}^{l}$ .849 The radia profiles of the local free fall time or our sample galaxies are shown in Fies., The radial profiles of the local free fall time for our sample galaxies are shown in Figs.850 1 and 2.., \ref{fig:radialprofilesKM05} and \ref{fig:radialprofilesVB03}.851 They are calculated using Eq., They are calculated using Eq.852 2. aud Α10., \ref{eq:localff} and \ref{eq:phiv}.853", For the comparison with the free fallnuescales derived from observations we calculated he mean aud the standard deviation of the radial profiles within /.zxHRx2L."," For the comparison with the free falltimescales derived from observations we calculated the mean and the standard deviation of the radial profiles within $l_* \leq R \leq 2\,l_*$."854 Our free all timescales (Table3)) are iu good aerecient with those derived from observations except or those of NGC 2103. NGC 0925. (both. star ormnation prescriptions) aud NGC 7793 (VD03 star formation prescription).," Our free fall timescales (Table\ref{tab:galaxies1}) ) are in good agreement with those derived from observations except for those of NGC 2403, NGC 0925, (both star formation prescriptions) and NGC 7793 (VB03 star formation prescription)."855 By iiodifviug Eq., By modifying Eq.856" 1 o better match the observed metallicity profile: we the following parameters: NGC 7793: ὃ=1. obtainAf=0.06 Muse 5: NGC 2103: 6=|, A[A022 NGC Ρα..."," \ref{eq:alphacb} to better match the observed metallicity profile: we obtain the following parameters: NGC 7793: $\delta=1$, $\dot{M}$ =0.06 $_{\odot}$ $^{-1}$; NGC 2403: $\delta=4$, $\dot{M}$ =0.22 $_{\odot}$ $^{-1}$; NGC 0925: $\delta=9$ , $\dot{M}$ =0.31 $_{\odot}$ $^{-1}$."857 With these parameters the free fall timescales of these three galaxies are in good agreement with expectations., With these parameters the free fall timescales of these three galaxies are in good agreement with expectations.858 We note that in this case 5=0.33 for NGC 7793 aud NGC 2103., We note that in this case $\gamma=0.33$ for NGC 7793 and NGC 2403.859 Can these galaxies sustain their star formation rates by radial trausport of eas withinthe galactic disk?, Can these galaxies sustain their star formation rates by radial transport of gas withinthe galactic disk?860" To answer this question one las to compare he local star formation rate and the local viscous nuescale f,=V/v using Eq.", To answer this question one has to compare the local star formation rate and the local viscous timescale $t_{\nu}=R^{2}/\nu$ using Eq.861 ALL and À22. , \ref{eq:nu} and \ref{eq:nu1}. .862The local timescalecomparison is presented iu Figs., The local timescalecomparison is presented in Figs.863 l aud 2.., \ref{fig:radialprofilesKM05} and \ref{fig:radialprofilesVB03}. .864" The global comparison of the1ie2n Traction «f,/f.> caleulated over f,<RoxRos is shown in Fie. 5. ", The global comparison of themean fraction $<t_{\nu}/t_{*}>$ calculated over $l_{*} \leq R \leq R_{25}$ is shown in Fig. \ref{fig:sfrmdot}. .865The KM05 and VDB0US star ormnation prescriptions vield consistent results for lis fraction within the galactic disks., The KM05 and VB03 star formation prescriptions yield consistent results for this fraction within the galactic disks.866"summarised in reftable:re,,ass..",summarised in \\ref{table:re_mass}.867 We applied the same procedure to bby using our new parallax measurements and the information from the literature outlined in reftable:LB.., We applied the same procedure to by using our new parallax measurements and the information from the literature outlined in \\ref{table:LB}.868 Our mass estimate for the visual magnitude given by is consistent with the former results although we find that our calculations with the visual magnitude provided by is incompatible with our mass determination if we assume that the spectroscopically determined masses for aare correct., Our mass estimate for the visual magnitude given by is consistent with the former results although we find that our calculations with the visual magnitude provided by is incompatible with our mass determination if we assume that the spectroscopically determined masses for are correct.869" With the knowledge of the Μιωι for a given mass, the radius can be directly estimated at a given Τεῃ."," With the knowledge of the $M_{\rm bol}$ for a given mass, the radius can be directly estimated at a given $\Teff$."870 The radius estimates yield slightly different values when two core models are considered (see 6)., The radius estimates yield slightly different values when two core models are considered (see \ref{table:re_mass}) ).871" This is caused assuming the assumption for the hydrogen layer mass to be Mu/M.=107 in the CO cooling models versus the My/M,=10~° content in the ONe cooling models(?).", This is caused assuming the assumption for the hydrogen layer mass to be $M_{\rm H}/M_\ast=10^{-4}$ in the CO cooling models versus the $M_{\rm H}/M_\ast=10^{-6}$ content in the ONe cooling models.872. This produces different luminosities for a given effective temperature., This produces different luminosities for a given effective temperature.873 The assessment of the cooling ages of aand iis important to the understanding of the evolutionary history of the system., The assessment of the cooling ages of and is important to the understanding of the evolutionary history of the system.874 It was possible to evaluate the cooling ages of both objects with the mass estimates that we determined., It was possible to evaluate the cooling ages of both objects with the mass estimates that we determined.875" For our estimations, we used the grids of white dwarf cooling sequences for CO and ONe cores for their respective range of grid parameters; for masses above the available values, we extrapolated the age values in a way similar to that for the visual magnitudes (see reffig:extrapolation and 6))."," For our estimations, we used the grids of white dwarf cooling sequences for CO and ONe cores for their respective range of grid parameters; for masses above the available values, we extrapolated the age values in a way similar to that for the visual magnitudes (see \\ref{fig:extrapolation} and \ref{fig:age_extrapolation}) )."876" Surprisingly, the difference in the cooling age of the two binary components is smaller than formerly estimated."," Surprisingly, the difference in the cooling age of the two binary components is smaller than formerly estimated."877" For both assumed chemical compositions, the cooling age of the non-magnetic white dwarf lis within the error bars of the cooling age of the magnetic and very massive ((see reftable:re,,assand7))."," For both assumed chemical compositions, the cooling age of the non-magnetic white dwarf is within the error bars of the cooling age of the magnetic and very massive (see \\ref{table:re_mass} and \ref{table:lb_mass}) )."878Forthecaseo fanONecorewithane fectivetemperc ," For the case of an ONe core with an effective temperature as high as K, our conclusion is poorly constrained due to the extremely large uncertainties introduced by the extrapolation."879"Previous age estimates were unreliable because they inferred a cooling age of sshorter than that of9802,, simply based on its higher effective temperature."," Previous age estimates were unreliable because they inferred a cooling age of shorter than that of, simply based on its higher effective temperature."880" If we use the elementary theory of cooling by assuming for a fixed effective temperature of the white dwarf, the cooling age is a function of the mass and radius tooo)οςM/R?."," If we use the elementary theory of cooling by assuming for a fixed effective temperature of the white dwarf, the cooling age is a function of the mass and radius $t_{\rm cool}\propto M/R^2$."881 This means that the cooling age for low-mass white dwarfs («0.5 Mo) is simply proportional to mass M?P.," This means that the cooling age for low-mass white dwarfs $<0.5\,\Msolar$ ) is simply proportional to mass $M^{5/3}$."882" As the mass of the white dwarf approaches the Chandrasekhar limit the radius asymptotically approaches zero, which means that ages for a given effective temperature depend even more strongly on the mass."," As the mass of the white dwarf approaches the Chandrasekhar limit the radius asymptotically approaches zero, which means that ages for a given effective temperature depend even more strongly on the mass."883 The masses estimated here are quite close to the Chandrasekhar limit (21.30 Mo)) where post-Newtonian corrections should be considered for the stellar equilibrium(??).," The masses estimated here are quite close to the Chandrasekhar limit $\geq 1.30\,$ ) where post-Newtonian corrections should be considered for the stellar equilibrium."884". However, these corrections mostly affect the dynamical stability of the star, leading to collapse before reaching the Chandrasekhar limit, but induce only small corrections to mass-radius relationship."," However, these corrections mostly affect the dynamical stability of the star, leading to collapse before reaching the Chandrasekhar limit, but induce only small corrections to mass-radius relationship."885 This is because the estimated radii are three orders of magnitude larger than the Schwarzschild-radius: GM/c?Rwp~102., This is because the estimated radii are three orders of magnitude larger than the Schwarzschild-radius: $GM/c^2R_{WD}\sim10^{-3}$.886" Hence, we do not expect any effect on our mass determinations, as also noted by?.."," Hence, we do not expect any effect on our mass determinations, as also noted by."887 The projected distance of 210 AU between the two white dwarfs and their small relative proper motion suggest that they are companions and therefore share a common origin., The projected distance of 210 AU between the two white dwarfs and their small relative proper motion suggest that they are companions and therefore share a common origin.888 The ages of both objects should therefore be equal or comparable within, The ages of both objects should therefore be equal or comparable within889 Three sources are not included in Table 5.., Three sources are not included in Table \ref{table5}.890 The sources 31.16-0.20 and 41.58+0.04 do not have 1.2 mm or 870 jm flux densities. and in the absence of at least one of these two flux densities. SED fits are poorly constrained.," The sources 41.16–0.20 and 41.58+0.04 do not have 1.2 mm or 870 $\mu$ m flux densities, and in the absence of at least one of these two flux densities, SED fits are poorly constrained."891 In addition. a large number of models fit the data for source 40.94—0.04. and so meaningful parameters cannot be deduced by this method.," In addition, a large number of models fit the data for source 40.94–0.04, and so meaningful parameters cannot be deduced by this method."892 As noted in refindi and Table 3.. there are two possible infrared counterparts for 41.08—0.13 and 41.12-0.22.," As noted in \\ref{indi} and Table \ref{table3}, there are two possible infrared counterparts for 41.08–0.13 and 41.12–0.22."893" Hence. both possible SEDs have been modeled and the results indicated by suffixes ""A and B' in Table 5 and Figure 3.."," Hence, both possible SEDs have been modeled and the results indicated by suffixes `A' and `B' in Table \ref{table5} and Figure \ref{sedfits}."894 It is to be noted that uncertainties shown in Table 5 only take into account the y statistics of multiple models fitting the data. and do not show the systematic uncertainties from the underlying model assumptions.," It is to be noted that uncertainties shown in Table \ref{table5} only take into account the $\chi^2$ statistics of multiple models fitting the data, and do not show the systematic uncertainties from the underlying model assumptions."895 For example. model parameters such as stellar mass and age are derived from the luminosity and temperature of the star using evolutionary tracks (2)..," For example, model parameters such as stellar mass and age are derived from the luminosity and temperature of the star using evolutionary tracks \citep{robi08}."896 Consequently. uncertainties in. the. evolutionary tracks translate to uncertainties 1n the masses and ages.," Consequently, uncertainties in the evolutionary tracks translate to uncertainties in the masses and ages."897 These uncertainties have not been quantified and are not shown in Table 5.., These uncertainties have not been quantified and are not shown in Table \ref{table5}.898 Further. the envelope accretion rate shown in Table 5 is derived from the density profile measured from the SED through the assumption of a free-fall rotational collapse model (?)..," Further, the envelope accretion rate shown in Table \ref{table5} is derived from the density profile measured from the SED through the assumption of a free-fall rotational collapse model \citep{robi08}."899 Since the millimeter and submillimeter data (which primarily trace the envelope) have relatively poor angular resolution. source multiplicity potentially leads to estimation of the envelope accretion rates.," Since the millimeter and submillimeter data (which primarily trace the envelope) have relatively poor angular resolution, source multiplicity potentially leads to over-estimation of the envelope accretion rates."900 Keeping the caveats above in mind. Table 5. shows that the YSO models that fit the infrared and submillimeter data points are rapidly accreting massive stars.," Keeping the caveats above in mind, Table \ref{table5} shows that the YSO models that fit the infrared and submillimeter data points are rapidly accreting massive stars."901 The central stars have masses larger than ~8M«. and considering the rapid aceretion. the final mass of the central star is likely to be much higher.," The central stars have masses larger than $\sim 8~M_\odot$, and considering the rapid accretion, the final mass of the central star is likely to be much higher."902 In the case of the source 41.58+0.04. the upper limit at 1.2 mm corresponds to an isothermal mass of between 38 and 87 M... depending on the prescription of dust opacity assuming the dust temperature to be 30 K. which ts adequate to host a massive star (although the constraint is much tighter if one uses the Ic rather than 3c limit).," In the case of the source 41.58+0.04, the upper limit at 1.2 mm corresponds to an isothermal mass of between 38 and 87 $M_\odot$ depending on the prescription of dust opacity \citep[e.g.][]{osse94,hild83} assuming the dust temperature to be 30 K, which is adequate to host a massive star (although the constraint is much tighter if one uses the $1\sigma$ rather than $3\sigma$ limit)."903 The accretion rates and stellar temperatures in Table 5 give further confirmation of the results at centimeter wavelengths., The accretion rates and stellar temperatures in Table \ref{table5} give further confirmation of the results at centimeter wavelengths.904 The stellar temperatures are mostly too cool to form regions (which ts consistent with their young age and rapid accretion: e.g. ?))., The stellar temperatures are mostly too cool to form regions (which is consistent with their young age and rapid accretion; e.g. \citealt{hoso09}) ).905" Moreover. as pointed out by ?.. the “eritical aceretion rate"" required to confine the region to a volume close to the stellar surface is 1077 to 4x107°Ma vi! for stars of spectral type O5 (~60 M.) to BO (~17MJ) respectively."," Moreover, as pointed out by \citet{walm95}, the “critical accretion rate” required to confine the region to a volume close to the stellar surface is $10^{-4}$ to $4 \times 10^{-6}~M_\odot$ $^{-1}$ for stars of spectral type O5 $\sim 60~M_\odot$ ) to B0 $\sim 17~M_\odot)$ respectively."906 The aceretion rates deduced from the SED fitting are well above the critical accretion rate., The accretion rates deduced from the SED fitting are well above the critical accretion rate.907 This result is unlikely to change even accounting for source multiplicity. which is common in the context of massive star forming regions.," This result is unlikely to change even accounting for source multiplicity, which is common in the context of massive star forming regions."908 However. this calculation assumes that the accretion is spherical. which is not true in practice.," However, this calculation assumes that the accretion is spherical, which is not true in practice."909 This might explain why some of the sources are seen as ultracompact and hypercompact regions in spite of, This might explain why some of the sources are seen as ultracompact and hypercompact regions in spite of910The Horologimmu-BReticulum supercluster (IRS) is an extended region of high ealaxy density (27?73... covering —150 square degrees of sky. at a lean redshift of —20.000 |.,"The Horologium-Reticulum supercluster (HRS) is an extended region of high galaxy density \citep{sha35,luc83,ein03,fle05}, covering $\sim$ 150 square degrees of sky at a mean redshift of $\sim$ 20,000."911 The IRS also contaius more than 20 ealaxy clusters (?7)..," The HRS also contains more than 20 galaxy clusters \citep{ein97,ein02}. ."912 As discussed in 7? and 7. the TERS is the second largest mass concentration within ~300 Mpc. where it is onlv surpassed by the Shaplev supercluster (SSC).," As discussed in \citet{hud99} and \citet{ein01}, the HRS is the second largest mass concentration within $\sim$ 300 Mpc, where it is only surpassed by the Shapley supercluster (SSC)."913 While the SSC has been exteusivelv studied (222222).. the TRS remains relatively unexplored.," While the SSC has been extensively studied \citep{qui95,qui00,dri99,dri04,bar98,bar00}, the HRS remains relatively unexplored."914 Due to the potential iportauce of such a laree-scale structure in the prescnt-epoch wiiverse. we have emibarked ou a redshift survey to provide a colmprehensive mapping of the TIRS.," Due to the potential importance of such a large-scale structure in the present-epoch universe, we have embarked on a redshift survey to provide a comprehensive mapping of the HRS."915 Our initial results. which coutain 517 galaxy redshifts iu theinter-cluster veeious of the IRS. are reported iu 7.hereafterPaperL.," Our initial results, which contain 547 galaxy redshifts in the regions of the HRS, are reported in \citet[][hereafter Paper I]{fle05}."916 A kev result. from Paper I is that the distribution of inter-cluster galaxies is separated into two distinct redshift courponeuts., A key result from Paper I is that the distribution of inter-cluster galaxies is separated into two distinct redshift components.917 On the other haud. the published mean redshifts for 21 galaxy clusters in the IRS do not exhibit such a biauodal distribution.," On the other hand, the published mean redshifts for 21 galaxy clusters in the HRS do not exhibit such a bi-modal distribution."918 The differing results between the cluster and inter-cluster redshift distributions appear to coutradict the view that ealaxy clusters share the kinematics of the iuter-cluster galaxy distribution as a result of their location at intersecting filamcuts of galaxies (c.g. ανν," The differing results between the cluster and inter-cluster redshift distributions appear to contradict the view that galaxy clusters share the kinematics of the inter-cluster galaxy distribution as a result of their location at intersecting filaments of galaxies \citep[e.g.,][]{van93,bon96,col99,col05}."919 However. the mean redshift for many of these clusters is based on fewer than four galaxy redshifts per cluster. ie.. sparse information.," However, the mean redshift for many of these clusters is based on fewer than four galaxy redshifts per cluster, i.e., sparse information."920" To clarify the distribution of cluster redshifts iu the IIRS. we have obtzined new data for 12 clusters iu which the previously published data were sparse,"," To clarify the distribution of cluster redshifts in the HRS, we have obtained new data for 12 clusters in which the previously published data were sparse."921 The results of this program are reported below and. when combined with other previous redshift data. eive an iuproved asscssimeut of the distribution of cluster redshifts in the HRS.," The results of this program are reported below and, when combined with other previous redshift data, give an improved assessment of the distribution of cluster redshifts in the HRS."922" Throughout the paper. we adopt the following cosinological parameters: O,,=0.3. Qa=0.7, aud /Z,—70 1. which implies a spatial scale of 1.6 Mpe | (77 kpc Ly atthe ~20.000TU nuuean redshift peiof the IRS."," Throughout the paper, we adopt the following cosmological parameters: $\Omega _m = 0.3$, $\Omega _\Lambda = 0.7$, and $H_o = 70 $ $^{-1}$, which implies a spatial scale of 4.6 Mpc $^{-1}$ (77 kpc $^{-1}$ ) at the $\sim$ 20,000 mean redshift of the HRS."923 Lists of galaxy clusters iu the region of the TRS have been taken from two major studies., Lists of galaxy clusters in the region of the HRS have been taken from two major studies.924 The first is the Abell catalog (extension) (hereafter:ACOin?). while the second is the Automated Plate Measuring Machine cluster catalog (hereafterAPMCCin2?).," The first is the Abell catalog (extension) \citep[hereafter ACO in][]{aco89}, while the second is the Automated Plate Measuring Machine cluster catalog \citep[hereafter925APMCC in][]{dal94,dal97}."926 Since galaxy. clusters represent he largest (at least partlv) virialized structures. hey serve as massive siguposts for ideutifvine and stucving superclusters of galaxies;," Since galaxy clusters represent the largest (at least partly) virialized structures, they serve as massive signposts for identifying and studying superclusters of galaxies."927 Based on he ACO. ? ideutified 18 Πας clusters usine a conibination of partial redshift iuformation and vercolation algorithius.," Based on the ACO, \citet{zuc93} identified 18 HRS clusters using a combination of partial redshift information and percolation algorithms."928 While working with the same list of ACO clusters. ? identified 26 ucuubers of the IIRS.," While working with the same list of ACO clusters, \citet{ein94} identified 26 members of the HRS."929 InL. we used the 17 ACO clusters ocurring iu both studies to define the nean redshift of the IIRS (67= 19.900 13). and we adopted the PWHAL of the cluster redshift distribution as defining the IRS kincmatic core o lie between 17.000 and 22.500 (sce Figure L D).," In, we used the 17 ACO clusters ocurring in both studies to define the mean redshift of the HRS $\overline{cz} =$ 19,900 ), and we adopted the FWHM of the cluster redshift distribution as defining the HRS kinematic core to lie between 17,000 and 22,500 (see Figure 4, )."930" However. the mean redshifts are uncertain for 10 of the 17 ACO clusters because they are based on fewer than four galaxw redshifts cach (Nu,c— x D duT.hereafter SR99)."," However, the mean redshifts are uncertain for 10 of the 17 ACO clusters because they are based on fewer than four galaxy redshifts each \citep[``$N_{\rm{gx}}< < 4” in][hereafter ."931 Iu this paper we report new spectroscopic observatious together with previously unpublished redshifts. for 9 of these 10 clusters with the aim of determining a more accurate mean redshift and dispersion for cach cluster.," In this paper we report new spectroscopic observations, together with previously unpublished redshifts, for 9 of these 10 clusters with the aim of determining a more accurate mean redshift and dispersion for each cluster."932 Published data for the teuth cluster. AS109. have been reassessed. and additional spectra have been obtained for a further three clusters with sparse data in the literature.," Published data for the tenth cluster, A3109, have been reassessed, and additional spectra have been obtained for a further three clusters with sparse data in the literature."933 Fienre L shows the spatial locations of the thirteen clusters in this study as dotted circles., Figure \ref{f1} shows the spatial locations of the thirteen clusters in this study as dotted circles.934 A further 15 clusters with secure redshifts. based on 10 or more galaxies. are also displayed: those that fall within the kinematic cove of the TIRS are shown as solid-line open circles.," A further 15 clusters with secure redshifts, based on 10 or more galaxies, are also displayed; those that fall within the kinematic core of the HRS are shown as solid-line open circles."935 Clusters that fall outside the statistically-defined ο core day still. in fact. be members of the larger supercluster complex.," Clusters that fall outside the statistically-defined kinematic core may still, in fact, be members of the larger supercluster complex."936 Of the thirteen clusters in the curreut study. eleven are AC'O. BRichness 0 clusters and the remaining two are from the APMCC.," Of the thirteen clusters in the current study, eleven are ACO, Richness 0 clusters, and the remaining two are from the APMCC."937 Since the values of cluster richness. for the APMCC ire not assigned in the same wav as the ACO. comparative determinations were taken : from?2 forthe two APAICC2D clusters. aud they were found to be similar to ACO Richuess 0.," Since the values of cluster richness for the APMCC are not assigned in the same way as the ACO, comparative determinations were taken from \cite{ein01} forthe two APMCC clusters, and they were found to be similar to ACO Richness 0."938 Spectroscopic observations were conducted, Spectroscopic observations were conducted939of the 100 san band in the spectra presented here may be due to a difference in dust temperature.,of the 100 $\mu$ m band in the spectra presented here may be due to a difference in dust temperature.940 As well as broad emission bands. uuresolved. emission lines can be detected in the long-wavelength regions of the least noisy of our spectra. (e.g. WN Psc and AFGL 5319).," As well as broad emission bands, unresolved emission lines can be detected in the long-wavelength regions of the least noisy of our spectra, (e.g. WX Psc and AFGL 5379)."941 Most of these lines are pure rotational lines of water vapour., Most of these lines are pure rotational lines of water vapour.942 The 157.7-;an [C uf line is also visible iu most of our sources: this is the residual Galactic background |C enission after subtraction of the off-source spectra., The $\mu$ m [C ] line is also visible in most of our sources; this is the residual Galactic background [C ] emission after subtraction of the off-source spectrum.943 Iu the case of AFGL 5379. the |C uf line is sccminely in absorption: again. this is due to imperfect cancellation of the background emission.," In the case of AFGL 5379, the [C ] line is seemingly in absorption: again, this is due to imperfect cancellation of the background emission."944 Water ice is an important component of the solid-phase material in cool astronomical sources., Water ice is an important component of the solid-phase material in cool astronomical sources.945 Its spectrum shows bands at 3.1.) 6.0. 11-12. 13 and 62 peu. The jan stretching band is seen (always in absorption) iu the spectra of many highh-cunbedded voune stars (6.8. Whittet et al. 1988))," Its spectrum shows bands at 3.1, 6.0, 11-12, 43 and 62 $\mu$ m. The $\mu$ m stretching band is seen (always in absorption) in the spectra of many highly-embedded young stars (e.g. Whittet et al. \cite{whittet}) )"946 aud in some OIL/IR stars (c.e. Alever et αἱ. 1998))., and in some OH/IR stars (e.g. Meyer et al. \cite{meyer}) ).947 Its formation iun the circumstellar envelopes of OIL/IR stars has οσοι discussed in particular bv Jura Morris (1985))., Its formation in the circumstellar envelopes of OH/IR stars has been discussed in particular by Jura Morris \cite{jura}) ).948 Before he ISO 1uission. the far-IR ice bands had been observed iu emission i a simall uuniber of sources iuchludiug the OIL/IR stars OII26.5. OITI127.5 aud OII231.5| L2 (Omeout et al.," Before the ISO mission, the far-IR ice bands had been observed in emission in a small number of sources including the OH/IR stars OH26.5, OH127.8 and $+$ 4.2 (Omont et al."949 1990 aud references therein)., \cite{omont} and references therein).950 ISO spectra have shown the L3- aud 62-110 ice bands in enüssion in various objects (Barlow 1998)). such as the planetary nebulae /5678032 (Cohen ot al. 1999))," ISO spectra have shown the 43- and $\mu$ m ice bands in emission in various objects (Barlow \cite{barlow}) ), such as the planetary nebulae $-56^{\rm o} 8032$ (Cohen et al. \cite{cohen}) )"951 and NGC 6302 (Lim et al. 1999)).," and NGC 6302 (Lim et al. \cite{lim}) ),"952 he post Red Supereiant source AFCL 106 (Molster et al. 199929) , the post Red Supergiant source AFGL 4106 (Molster et al. \cite{molster}) )953auc Herbie Ac/Be stars (Waters Waelkeus 1998: Malfait et al. 1998.. 1999)).," and Herbig Ae/Be stars (Waters Waelkens \cite{wawa}; Malfait et al. \cite{malfait}, \cite{malf99}) ),"954" while the (3-;nu and has been detected in absorption toward the liehh-ubedded sources ΑΕΕ, 7009. and IRAS 19110)1015 (Dartois et al. 1998.."," while the $\mu$ m band has been detected in absorption toward the highly-embedded sources AFGL 7009 and IRAS 19110+1045 (Dartois et al. \cite{dartois},"955 Cox Rocltsema 1999))., Cox Roelfsema \cite{cox}) ).956 Both of 1ο far-IR bands can be bleuded with crystalline silicate wission. but exauuimnatiou of the shapes auc positions of 16 observed bands can distinguish between silicate aud ICO endsslon.," Both of the far-IR bands can be blended with crystalline silicate emission, but examination of the shapes and positions of the observed bands can distinguish between silicate and ice emission."957 The new ISO spectra have siguificanth better resolution and seusitivitv than the carler IKAO data., The new ISO spectra have significantly better resolution and sensitivity than the earlier KAO data.958 Fig., Fig.959 5 shows attempts to fit the 3090 pau region of our (coutinuunn-subtracted) spectra. using a spectral svuthesis routine kindly provided by Dr T. Lua (personal COMM.}.," \ref{icefig} shows attempts to fit the 30–90 $\mu$ m region of our (continuum-subtracted) spectra, using a spectral synthesis routine kindly provided by Dr T. Lim (personal comm.)."960 This routine takes absorption (or enmission) cficicucics for materials of interest. along with user-defined temperatures aud relative amounts. and produces the resulting spectrin for optically-thin enuüssion from the individual lnaterials. as well the total enudsson from all the materials (shown as the thin solid line in Fie. 5)).," This routine takes absorption (or emission) efficiencies for materials of interest, along with user-defined temperatures and relative amounts, and produces the resulting spectrum for optically-thin emission from the individual materials, as well the total emission from all the materials (shown as the thin solid line in Fig. \ref{icefig}) )."961 The materials used to fit the ΟΠΠ star spectra were forsterite. eustatite aud ervstalliue water ice: temperatures of order 50.100 Is were used for the fitting.," The materials used to fit the OH/IR star spectra were forsterite, enstatite and crystalline water ice; temperatures of order 50–100 K were used for the fitting."962 The detected ice features are listed in Table 3.., The detected ice features are listed in Table \ref{icetab}.963 Pyroxenes (such as eustatite: see dash-dotted line in Fig. 5)), Pyroxenes (such as enstatite; see dash-dotted line in Fig. \ref{icefig}) )964 also show strong [μαι features. therefore detection of a [3-411 baud in au observed spectrum is uot sufficient evidence to demonstrate the presence of ΠΟ ice.," also show strong $\mu$ m features, therefore detection of a $\mu$ m band in an observed spectrum is not sufficient evidence to demonstrate the presence of $_2$ O ice."965 ILowever. for temperatures 210 EK. the. L3-pan peak is at least as prominent as the 62-;24 peak. so objects which do not have a 13-420 feature are unlikely to coutai- much water ice (unless it is verv cold).," However, for temperatures $\ga$ 40 K, the $\mu$ m peak is at least as prominent as the $\mu$ m peak, so objects which do not have a $\mu$ m feature are unlikely to contain much water ice (unless it is very cold)."966 C'onverselv. if au object shows the 62-;an 'eature. TO ice is likely to be responsible for at least part of that objects 13-501 feature.," Conversely, if an object shows the $\mu$ m feature, $_2$ O ice is likely to be responsible for at least part of that object's $\mu$ m feature."967 We claim detections of crystalline water ice enuüission based ou the presence of the bands at [3 and 62 jau in OIII27.5. OII26.5 and AFCL 5379. confimuiug the tentative detections for the first two sources by Oinont et al. (1990)).," We claim detections of crystalline water ice emission based on the presence of the bands at 43 and 62 $\mu$ m in OH127.8, OH26.5 and AFGL 5379, confirming the tentative detections for the first two sources by Omont et al. \cite{omont}) )."968 OTT32.8 also shows a £40 feature (Fig. 1).," OH32.8 also shows a $\mu$ m feature (Fig. \ref{fir}) ),"969 but without observations of the 62-j feature. we caunot determine if ice enussiou is present.," but without observations of the $\mu$ m feature, we cannot determine if ice emission is present."970" CRL 2199 aud WX Pse both seem to show broad 50.70 yan features. but the shape of these features docs not resemble laboratory crystalline ice features. unlike the observed features of OI127.8. OII26.5 and CL5379,"," CRL 2199 and WX Psc both seem to show broad 50–70 $\mu$ m features, but the shape of these features does not resemble laboratory crystalline ice features, unlike the observed features of OH127.8, OH26.5 and GL5379."971 Iu particular. the ciissivity of ice has a niüninmun near 55 gan before reaching its peak at 62 jan (see dashed line in Fie. 5)).," In particular, the emissivity of ice has a minimum near 55 $\mu$ m before reaching its peak at 62 $\mu$ m (see dashed line in Fig. \ref{icefig}) )."972 This structure is present in the spectra ofthe latter three sources. while the CRE 2199 aud WX Psc features are more flat-topped. with strong enüssion at 55 pau and no real evidence of a peak at 62 µια. The attempt to fit the WX Psc spectra with ice emission (Fig. 5))," This structure is present in the spectra of the latter three sources, while the CRL 2199 and WX Psc features are more flat-topped, with strong emission at 55 $\mu$ m and no real evidence of a peak at 62 $\mu$ m. The attempt to fit the WX Psc spectrum with ice emission (Fig. \ref{icefig}) )"973 illustrates this point., illustrates this point.974" The ΟΠ 101.9 features are rather weak aud il-defiued: there may ne a weak 62-,n wand. but the 13-421 baud is replaced by a broader feature oeakiug near [7 pni. If the 5070 jan features in CRE 2199 and WX Psc are not water dec. what are they?"," The OH 104.9 features are rather weak and ill-defined; there may be a weak $\mu$ m band, but the $\mu$ m band is replaced by a broader feature peaking near 47 $\mu$ m. If the 50–70 $\mu$ m features in CRL 2199 and WX Psc are not water ice, what are they?"975 They aay simply 0 oedlustruinental artefacts: Fie., They may simply be instrumental artefacts: Fig.976 1 illustrates how the spectra are donmünated by the steep dowd slope of he SED. aud that spectral features around 60 µια are «ια. perturbatious ou this overall trend. (," \ref{fig1} illustrates how the spectra are dominated by the steep downward slope of the SED, and that spectral features around 60 $\mu$ m are small perturbations on this overall trend. ("977Clearly. this statement also holds for the features which we believe,"Clearly, this statement also holds for the features which we believe"978"Chevalier 1983): ere T. is the equivalent teniperature of the stellar notions (sco below). aud κMs) is he equivalent temperature 7,5;of theμη kineticEsx energv £x of the SNla’s ejecta. with ως=1075 ore for ono event (c.g.. ΜΕ ","Chevalier 1983): Here $T_{*}$ is the equivalent temperature of the stellar motions (see below), and $T_{ej}= 2\mu m_p E_{SN}/(3kM_{SN})$ is the equivalent temperature of the kinetic energy $E_{\rm SN}$ of the SNIa's ejecta, with $E_{\rm SN}= 10^{51}$ erg for one event (e.g., Larson 1974)."979Tj can be caleulated assuniug hat a factor f of ἕως is turned iuto heat: f<1. since radiative cucrey losses from expaudius supernova remnants may be nportaut. and values down to f=0.1 ave been adopted (Larson 197 Chevalier 1970): a value of f=(0.85 could be not too far1. off for the hot diluted ISM of ETCs (e.9.. Taug Wane 2005).," $T_{ej}$ can be calculated assuming that a factor $f$ of $E_{\rm SN}$ is turned into heat; $f<1$, since radiative energy losses from expanding supernova remnants may be important, and values down to $f=0.1$ have been adopted (Larson 1974, Chevalier 1974); a value of $f=0.85$ could be not too far off for the hot diluted ISM of ETGs (e.g., Tang Wang 2005)."980 In this wax. Tij=(GF/0.85)1.5& 10K. From approximating M~M. and using the estimates of Sect.," In this way, $T_{ej}= (f/0.85) 1.5\times 10^9$ K. From approximating $\dot M \simeq \dot M_*$, and using the estimates of Sect."981" 2? for May and AL (for a Ixroupa IME) at the prescut epoch. one obtains Τον~|(fF0.85)«10 k. The injection temperature Ti,; is thou the sui of two parts: one (Εςy) is independent of the position within the galaxwv where the eas is injected (e.e.. independent of radius in spherical svnuunetrv). and is also coustaut from galaxy to galaxy (for fixed. IAIF aud. age of the stellar population. aud ολίαν rate): for each ETC it can. though. evolve with time. if May aud AL. evolve ciffereutly with time (Ciotti et al."," \ref{loss} for $\dot M_{SN}$ and $\dot M_*$ (for a Kroupa IMF) at the present epoch, one obtains $T_{SN}\simeq 1.7(f/0.85)\times 10^7$ K. The injection temperature $T_{inj}$ is then the sum of two parts: one $T_{SN}$ ) is independent of the position within the galaxy where the gas is injected (e.g., independent of radius in spherical symmetry), and is also constant from galaxy to galaxy (for fixed IMF and age of the stellar population, and SNIa's rate); for each ETG it can, though, evolve with time, if $\dot M_{SN}$ and $\dot M_*$ evolve differently with time (Ciotti et al."982 1991)., 1991).983 The other part (Z4) is iustead basically independent of time. but has a radial cepeudence. and chauges with the galaxy structure. ie. with the total mass aud its distribution.," The other part $T_{star}$ ) is instead basically independent of time, but has a radial dependence, and changes with the galaxy structure, i.e., with the total mass and its distribution."984 An average Z4 ds obtained caleulatiug the sas iass-weighted temperature gained by the thermalization of the stellar raudonm motions. <T;>: where e(r) is the oue-dimensional velocity dispersiou of the stars.," An average $T_*$ is obtained calculating the gas mass-weighted temperature gained by the thermalization of the stellar random motions, $<T_*>$: where $\sigma (r)$ is the one-dimensional velocity dispersion of the stars."985 The inteeral term in Eq., The integral term in Eq.986" 2. is the same that eives the kinetic cucrev associated with the stellar random motious |Ej;,=L5fExi?p (eo?de]. and that euters the virial theorem for the stellar compoucut:Cr) the mass-aweighted temperature in Eq."," \ref{eq:tvir} is the same that gives the kinetic energy associated with the stellar random motions $E_{kin}=1.5 \int 4 \pi987r^2 \rho_*(r) \sigma^2 (r) \,dr $ ], and that enters the virial theorem for the stellar component; the mass-weighted temperature in Eq."988" 20 is then often called ""eas virial temperature”.", \ref{eq:tvir} is then often called “gas virial temperature”.989" Fora galaxy nass model made of stars aud dark matter. characterized bv AL, (AL... where Af, is the total dark mass. and ον With ry, and rss the scale radi of the two mass distributions. <T.7 cau be expressed using the ceutral velocity dispersion σ as «xTi,>=nn,c20(R.Dk (c.g. Ciotti Pellegrini 1992)."," For a galaxy mass model made of stars and dark matter, characterized by $ {\cal R}=M_h/M_*$ , where $M_h$ is the total dark mass, and $\beta=r_h/r_*$ , with $r_h$ and $r_*$ the scale radii of the two mass distributions, $<T_*>$ can be expressed using the central velocity dispersion $\sigma_c$ as $<T_*>=\mu m_p\, \sigma_c^2 \Omega ({\cal R},\beta)/k$ (e.g., Ciotti Pellegrini 1992)."990" The function © iucreases wuldly for lareer A aud for lower οὐ that is for a larger amount of eravitating mass or a higher mass concentration. but always O«1. since ofr) has in eoncral a negative radial eracdieut (ο, Sect."," The function $\Omega $ increases mildly for larger $\cal{R}$ and for lower $\beta$, that is for a larger amount of gravitating mass or a higher mass concentration, but always $\Omega <1$, since $\sigma (r) $ has in general a negative radial gradient (e.g., Sect."991 ο and Fie.," \ref{mass}992 and Fig."993 below)., \ref{f1} below).994" <T.> is then proportionalοι, to 62. and a siupli&edD. version of the virial tempcrature in Eq."," $<T_*>$ is then proportional to $\sigma_c^2$, and a simplified version of the virial temperature in Eq."995" 2 that is often used is T,=qunyó2/k: T of course overestimates the true <T.7.", \ref{eq:tvir} that is often used is $T_{\sigma}=\mu m_p\sigma_c^2/k$; $T_{\sigma}$ of course overestimates the true $<T_*>$.996 The imass-averaged injection temperature ijs finally eiven bv where in general the secouc term dominates. as is slow iu Sect.," The mass-averaged injection temperature is finally given by where in general the second term dominates, as is shown in Sect."997 77. below., \ref{disc} below.998 Iu case of mass losses flowing to the galactic ceuter. the gas can be heated due to infall iu the ealactic potential auc adiabatic compression: this process is sometimes referred to as veravitational heating.," In case of mass losses flowing to the galactic center, the gas can be heated due to infall in the galactic potential and adiabatic compression; this process is sometimes referred to as “gravitational heating”."999 The average change in eravitational cucrey per unit eas lass inflowing through the ealactic potential down to the ealactic center is for ealaxy mass distributions with a finite value of OofO) (see also Ciotti ct al., The average change in gravitational energy per unit gas mass inflowing through the galactic potential down to the galactic center is for galaxy mass distributions with a finite value of $\phi(0)$ (see also Ciotti et al.1000 1991)., 1991).1001 One can define a temperature equivalent to the enerev in Eq., One can define a temperature equivalent to the energy in Eq.1002" { απ Thi.vray>=Qn,BLN(3s."," \ref{eq:lgp}1003 as $<T_{\rm grav}^{+}>=2\mu m_p\,E_{\rm grav}^{+}/3k$ ."1004 As <To>. also <Tileray> is x02. aud imereases for largcr R aud smaller 3. which. for inflowing gas. can be understood as a larger gas heating bv compression during Πα for a larger dark matter amount or its higher concentration.," As $<T_*>$, also $<T_{\rm grav}^+> $ is $\propto \sigma_c^2$, and increases for larger ${\cal R}$ and smaller $\beta$, which, for inflowing gas, can be understood as a larger gas heating by compression during infall for a larger dark matter amount or its higher concentration."1005 Not all of EJ. can be available for heating. though.," Not all of $E_{\rm grav}^+$ can be available for heating, though."1006 Tt the inflow keeps quasi-livdrostatic. then. by the virial heorem. the cnerev radiated away is roughly onc-half of the change in the eravitational potential euerev. aud hat available for the heating of the eas is the remaining (he. ~OSE).," If the inflow keeps quasi-hydrostatic, then, by the virial theorem, the energy radiated away is roughly one-half of the change in the gravitational potential energy, and that available for the heating of the gas is the remaining (i.e., $\sim 0.5 E_{\rm grav}^+$ )."1007" Actually, the energy. available for reating will be mach less than this."," Actually, the energy available for heating will be much less than this."1008 Iuflows are caused by he radiative losses produced by the acctmlation of the stellar iiass return. that makes the cooling time lower hau the galactic age: in the ceutral regions. within a radius of ~1 kpc. the cooling time can be as short as X105 ve. even shorter than the iufall time (e.g.. Sarazin White 1988. Pellegrini 2011).," Inflows are caused by the radiative losses produced by the accumulation of the stellar mass return, that makes the cooling time lower than the galactic age; in the central regions, within a radius of $\sim 1$ kpc, the cooling time can be as short as $\lsim 10^8$ yr, even shorter than the infall time (e.g., Sarazin White 1988, Pellegrini 2011)."1009 Tn these conditions. the eas departs from a slow inflow. becomes very deuse aud supersonic close to the center. aud cools rapidly down to low temperatures. so that >0.52.ray is radiated away or goes into kinetic cnerey of coudensations (Sarazin Ashe 1989).," In these conditions, the gas departs from a slow inflow, becomes very dense and supersonic close to the center, and cools rapidly down to low temperatures, so that $> 0.5 E_{\rm grav}^+$ is radiated away or goes into kinetic energy of condensations (Sarazin Ashe 1989)."1010" Furthermore. there is the possibility that uot all the eas reaches hot the ealactic central region. if thermal iustabilities develop aud produce drop-outs frou. the flow: if gas cools aud condenses out of the flow at large radii. then EJ cau be inch lower than in the definition above. and heating due to iufall iu the eravitational potential is ""lost (Saraziu Ashe 1989)."," Furthermore, there is the possibility that not all the gas reaches hot the galactic central region, if thermal instabilities develop and produce drop-outs from the flow; if gas cools and condenses out of the flow at large radii, then $E_{\rm grav}^+$ can be much lower than in the definition above, and heating due to infall in the gravitational potential is “lost” (Sarazin Ashe 1989)."1011" Iu conclusion. without a precise -knowledge of how to compute EL Gchich depeuds ou the radius at which tlie injected eas drops below X-ray enüttiue temperatures). aud about what fraction of E), is radiated or goes iuto kinetic energy. of the coudensations. <Tj> remains a reference value: a iore direct use cau instead be mace of the analogous temperature for escape cTi> introduced in Sect."," In conclusion, without a precise knowledge of how to compute $E_{\rm1012 grav}^+$ (which depends on the radius at which the injected gas drops below X-ray emitting temperatures), and about what fraction of $E_{\rm1013 grav}^+$ is radiated or goes into kinetic energy of the condensations, $<T_{\rm grav}^{+}>$ remains a reference value; a more direct use can instead be made of the analogous temperature for escape $<T_{\rm1014 grav}^{-}>$ introduced in Sect."1015 ο) below., \ref{esc} below.1016 Due to the presence of a central MDITI in ETC. another potential source of heating for the σας could," Due to the presence of a central MBH in ETGs, another potential source of heating for the gas could"1017vhotometric distances. (adopting. for instance. distances rom Fernie et al.,"photometric distances (adopting, for instance, distances from Fernie et al."1018 1995) shows (Fig. 2)), 1995) shows (Fig. \ref{ebmv_dist}) )1019 that the observed Cepheicds are located in a sector., that the observed Cepheids are located in a sector.1020 All line of sight directions lave extinction (no point below the dashed line)., All line of sight directions have extinction (no point below the dashed line).1021 In slightly obscured directions (dashed line) one can see stars up to z5000. pc. while in very obscured regions (dotted line) the closest Cepheids are detected not farther than z1100 pe.," In slightly obscured directions (dashed line) one can see stars up to $\approx 5000$ pc, while in very obscured regions (dotted line) the closest Cepheids are detected not farther than $\approx 1100$ pc."1022 The slope £g.yifdistance is a measure of the density of the interstellar mecdium in a given direction., The slope $E_{(B-V)} / distance $ is a measure of the density of the interstellar medium in a given direction.1023 This density varies over a large range due to the patchiness of the galactic extinction. but. for a given line of sight. the extinction. and thus the color excess. is assumed to be proportional to the distance.," This density varies over a large range due to the patchiness of the galactic extinction, but, for a given line of sight, the extinction, and thus the color excess, is assumed to be proportional to the distance."1024 This figure is used to obtain the extinction for each Copheid., This figure is used to obtain the extinction for each Cepheid.1025 We draw at random the slope £g.\i/distanece over the range defined by the dashed and dotted lines (Fig. 2)), We draw at random the slope $E_{(B-V)} / distance $ over the range defined by the dashed and dotted lines (Fig. \ref{ebmv_dist}) ).1026 Using the true distance Léa we then deduce the true color excess Lgyy). and the true extinctions: with Z2 = 3.3 and Ry=43.," Using the true distance $1/\pi$ we then deduce the true color excess $E_{(B-V)}$, and the true extinctions: with $R_V$ = 3.3 and $R_B = 4.3$."1027 Now we calculate the parameters which would be observed., Now we calculate the parameters which would be observed.1028 First. the apparent 2 and V magnitudes are simply: where cep and ερ are two independent Ciaussian variables which reproduce measurement uncertainties (the intrinsic scatter of the PL relation is already. counted. in Ah and (A4g)).," First, the apparent $B$ and $V$ magnitudes are simply: where $\epsilon_V$ and $\epsilon_B$ are two independent Gaussian variables which reproduce measurement uncertainties (the intrinsic scatter of the PL relation is already counted in $\langle M_V \rangle $ and $\langle M_B \rangle $ )."1029" We adopted. for both: (ο=0.0 and m,=0.005.", We adopted for both: $\langle \epsilon \rangle = 0.0$ and $\sigma_{\epsilon} = 0.005$.1030" The parallax which would. be observed. is calculated from the true one and an associated a, obtained through the figure 11aa. This figure shows two populations: one below the dotted. line. the other about. the dotted. line."," The parallax which would be observed is calculated from the true one and an associated $\sigma_{\pi}$ obtained through the figure \ref{spi_v}a a. This figure shows two populations: one below the dotted line, the other about the dotted line."1031 First. we draw the membership to one of these families in the right. proportion.," First, we draw the membership to one of these families in the right proportion."1032" ""Then. from the linear. relationships of the corresponding family and the V magnitude already computed. we caleulate logez (i.e. 02)."," Then, from the linear relationships of the corresponding family and the $V$ magnitude already computed, we calculate $\log \sigma_{\pi}$ (i.e. $\sigma_{\pi}$ )."1033 Finally. the observed wis obtained by drawing one occurence in the Gaussian clistribution (x.0s). Concerning the observed color excess. it will simply be deduced from the relation: with (B0Yo deduced from the PC relation 9. as we did in section 2.," Finally, the observed $\pi$ is obtained by drawing one occurence in the Gaussian distribution $(\pi, \sigma_{\pi})$ Concerning the observed color excess, it will simply be deduced from the relation: with $\langle B \rangle _0 - \langle V \rangle _0$ deduced from the PC relation \ref{color} as we did in section 2."1034 We also need to determine the observed. value of the coellicient. Ay., We also need to determine the observed value of the coefficient $R_V$.1035 We draw its value according to a Caussian distribution centered on the chosen true value (3.3) with a dispersion of 0.05., We draw its value according to a Gaussian distribution centered on the chosen true value (3.3) with a dispersion of 0.05.1036 So. we suppose that the observed. value has no systematic shift with respect to the true value.," So, we suppose that the observed value has no systematic shift with respect to the true value."1037 Finally. in order to reproduce selection effects like the AMalmauist bias. (Alalmeuist 1920) we reject. the C'ephieids which could not be observed: according to their apparent magnitudes (i.c. their probability to be detected).," Finally, in order to reproduce selection effects like the Malmquist bias (Malmquist 1920) we reject the Cepheids which could not be observed according to their apparent magnitudes (i.e. their probability to be detected)."1038 We craw a random parameter £C0.1] and compute the quantity: Whenever ὁ<fy the star may be observed. by ΗΛο and we keep it in our sample. and in the other case it will be rejected.," We draw a random parameter $t \in [0, 1]$ and compute the quantity: Whenever $t \le t_0$ the star may be observed by HIPPARCOS and we keep it in our sample, and in the other case it will be rejected."1039" We assume a=1 and Vpn,3=12.5.", We assume $\alpha = 1$ and $\langle V_{lim} \rangle = 12.5$.1040 Moreover. whenever (05xL9. the Cepheicl would be too bright (unrealistic apparent magnitude) and then rejected.," Moreover, whenever $ \langle V \rangle \le 1.9$, the Cepheid would be too bright (unrealistic apparent magnitude) and then rejected."1041" The number of simulated Cepheids is then almost equal to the true one,", The number of simulated Cepheids is then almost equal to the true one.1042 In order to show that the simulated sample is comparable to the true HLIPPATRCOS one. we plot for one simulated sample the same figures (Fig.," In order to show that the simulated sample is comparable to the true HIPPARCOS one, we plot for one simulated sample the same figures (Fig."1043 5 to 13)) as those produced with the true HEPPATCOS sample., \ref{h_logp} to \ref{rho_v}) ) as those produced with the true HIPPARCOS sample.1044 Note that the liguresD [from the simulated. sample are made from a single5 drawing which is not necessarily an optimal representation of the true sample., Note that the figures from the simulated sample are made from a single drawing which is not necessarily an optimal representation of the true sample.1045 The result may depend on the particular sample we draw., The result may depend on the particular sample we draw.1046 La order to reduce the uncertainty due to this choice. we mace 1000 different random drawings (cach of them with about 240 Cepheids) and adopted the mean result.," In order to reduce the uncertainty due to this choice, we made 1000 different random drawings (each of them with about 240 Cepheids) and adopted the mean result."1047 We obtain the result shown in the table 2 (let us recall that the input zero- is pp= 1.30)., We obtain the result shown in the table 2 (let us recall that the input zero-point is $\rho_{V}=-1.30$ ).1048 The simulation clearly. confirms that the weighting in (σε/m;) is meaningless., The simulation clearly confirms that the weighting in $(\sigma_{\pi_{i}}/\pi_i)^{-2}$ is meaningless.1049" Again. it is confirmed that a cut in magnitude gives more stable results because the method of averaging 107"" to get p is better justified. with small"," Again, it is confirmed that a cut in magnitude gives more stable results because the method of averaging $10^{0.2 \rho}$ to get $\rho$ is better justified with small"1050Apart from measuring the non-potentialitv. SASSA also retains the sien of chirality ol the active region magnetic field. unlike other shear parameters such as MWSA.,"Apart from measuring the non-potentiality, SASSA also retains the sign of chirality of the active region magnetic field, unlike other shear parameters such as MWSA."1051 This property of sign seems {ο be crucial in obtaining the proper measure of global non-potentialitv. as will be explained later in the paper.," This property of sign seems to be crucial in obtaining the proper measure of global non-potentiality, as will be explained later in the paper."1052 The mean weighted shear angle was introduced by Wang(1992). to ceqantitativelv study (he changes in magnetic structure and (the build-up of the magnetic shear., The mean weighted shear angle was introduced by \cite{wang92} to quantitatively study the changes in magnetic structure and the build-up of the magnetic shear.1053" The mean weighted shear angle is given as where D, is the measured transverse field strength and @ is the clilference between the observed and potential azimuths.", The mean weighted shear angle is given as where $B_t$ is the measured transverse field strength and $\theta$ is the difference between the observed and potential azimuths.1054 The potential fields have been computed by (aking the longitudinal field as boundary., The potential fields have been computed by taking the longitudinal field as boundary.1055 The method used in computing the potential field is as per Sakurai(1989)., The method used in computing the potential field is as per \cite{saku89}.1056. The reason for calculating weiehted mean instead of a simple average of shear angle is that the MWSA fillers the weak field area., The reason for calculating weighted mean instead of a simple average of shear angle is that the MWSA filters the weak field area.1057 The stronger fields play more important role in determining the field structure and can be measured more accurately., The stronger fields play more important role in determining the field structure and can be measured more accurately.1058 We should note here that the MWSA will weight more on the high transverse field regions like penumbral fields. a fact that will be shown later in the paper to explain the relatively lower success of AIWSA as a flave intensity predictor.," We should note here that the MWSA will weight more on the high transverse field regions like penumbral fields, a fact that will be shown later in the paper to explain the relatively lower success of MWSA as a flare intensity predictor."1059 We have used the series of vector magnetograms of (vo eruptive ARs NOAA 10930 and, We have used the series of vector magnetograms of two eruptive ARs NOAA 10930 and1060reprocessed N-rav bursts.,reprocessed X-ray bursts.1061 To search for QPOs. we made 0.5-1096 Tz power spectra from the RNTE data.," To search for QPOs, we made 0.5-4096 Hz power spectra from the RXTE data."1062 We produced 2 8 Lealiv normalized power spectra (Lealivetal. 1983)) using the available data in the 2-20 keV energy. baud., We produced 2 s Leahy normalized power spectra \cite{leahy83}) ) using the available data in the 2-20 keV energy band.1063 For cach RATE orbit. the 2 s spectra were combined and we looked for QPOs in the combined spectra.," For each RXTE orbit, the 2 s spectra were combined and we looked for QPOs in the combined spectra."1064 For observation L. it is not possible to carry out this analysis because there are no high time resolution cata.," For observation 1, it is not possible to carry out this analysis because there are no high time resolution data."1065 We only detect QPOs during observation 3. which coufirms the result of Woman et al. (," We only detect QPOs during observation 3, which confirms the result of Homan et al. ("10661998).,1998).1067" A QPO at δι,1+2.7 Hz is detected during the first orbit of this observation anda QPO at LELLIm6.5 Iz is detected during the second orbit.", A QPO at $849.4\pm 2.7$ Hz is detected during the first orbit of this observation and a QPO at $1141.1\pm 6.5$ Hz is detected during the second orbit.1068 The errors given in tlus section are confidence., The errors given in this section are confidence.1069 QPOs are not detected for the other orbits., QPOs are not detected for the other orbits.1070 Fitting the power spectrum with a model consisting of a constaut plus a Lorentzian. we fine that the 819 Hz OPO has a width (FWIIM) 0o: 18.0dE19 Iz and a fractional rius amplitude of 7.E40.7 aud the 1111 Hz OPO has a width of 30.9313.1 Tz aud a fractional rms zuuplitude of 7.841.1," Fitting the power spectrum with a model consisting of a constant plus a Lorentzian, we find that the 849 Hz QPO has a width (FWHM) of $18.0\pm 4.9$ Hz and a fractional rms amplitude of $7.4\pm 0.7$, and the 1141 Hz QPO has a width of $30.9\pm 13.4$ Hz and a fractional rms amplitude of $7.8\pm 1.1$."1071 F-tests iucic:ue that both QPOs are detected at greater than confidence., F-tests indicate that both QPOs are detected at greater than confidence.1072 QPOs are observed during N-rav bursts frou several systems (Strolunaveret:. 1998))., QPOs are observed during X-ray bursts from several systems \cite{s98}) ).1073 We searched for. but do not detect. QPOs in the brighest two X-ray bursts.," We searched for, but do not detect, QPOs in the brightest two X-ray bursts."1074 With the detection of kKITz QPOs in NTE J2123058. this source joius a C»eroup of Ls other neutron star LAINDs with high frequeney QPOs (vanderKlis 1998)).," With the detection of kHz QPOs in XTE J2123–058, this source joins a group of 18 other neutron star LMXBs with high frequency QPOs \cite{v98}) )."1075" For several of these svsteuis; two hieli frequency QPOs ire observed simultaneously,"," For several of these systems, two high frequency QPOs are observed simultaneously."1076 According to the beat frequency model. the ΟΡΟ with the higher Yequeney corresponds to the Neplerian frequeucy at the inner edge of the accretion disk aud the QPO with he lower frequency corresponds to the beat frequeney between the I&eplerian frequency aud the spin requeney of the neutron star.," According to the beat frequency model, the QPO with the higher frequency corresponds to the Keplerian frequency at the inner edge of the accretion disk and the QPO with the lower frequency corresponds to the beat frequency between the Keplerian frequency and the spin frequency of the neutron star."1077 In this picture. the difference between the two QPO frequeucies is the spin requeney of the neutron star (Alparctal. 1982)).," In this picture, the difference between the two QPO frequencies is the spin frequency of the neutron star \cite{alpar82}) )."1078 This interpretation is supported by the fact that. iu several sources. the difference between the two QPO frequencies is approximately constant even though the OPO frequencies change (see e.g. Fordetal. 1997)).," This interpretation is supported by the fact that, in several sources, the difference between the two QPO frequencies is approximately constant even though the QPO frequencies change (see e.g. \cite{ford97}) )."1079 Tu addition to the detection of the 819 Tz OPO duriug he first RNTE orbit of oservation 3. there is mareinal evidence for à QPO at LLOL+15 Wz.," In addition to the detection of the 849 Hz QPO during the first RXTE orbit of observation 3, there is marginal evidence for a QPO at $1104\pm 15$ Hz."1080 The feature is sienificant at the confence level., The feature is significant at the confidence level.1081 The detection is siguificaut at the confidence level if we use ouly he last 2210 s of the first orbit data rather than the cutive 3211 5. The detection can be further proved o confidence if the L.6-20 keV enerev band is used rather than the 2-20 keV energy. band., The detection is significant at the confidence level if we use only the last 2240 s of the first orbit data rather than the entire 3344 s. The detection can be further improved to confidence if the 4.6-20 keV energy band is used rather than the 2-20 keV energy band.1082 This is consistent with the result « Toman ct al. (, This is consistent with the result of Homan et al. (10831999) that the OPO streneth increases with photon cucrey.,1999) that the QPO strength increases with photon energy.1084 Figu 05 shows the 16-20 keV power spectrum for the last 2210 s of the first orbit fitted with a model consisting of a coustant and two Lorentziuis., Figure 5 shows the 4.6-20 keV power spectrum for the last 2240 s of the first orbit fitted with a model consisting of a constant and two Lorentzians.1085 Both QPOs are detected at ereater than confidence., Both QPOs are detected at greater than confidence.1086" The OPO frequencies ave 817.1d:5.5 Tz aud 1102+13 Uz with fractional ruis amplitudes of 10.3+ aud 11.541.6 respectively,"," The QPO frequencies are $847.1\pm 5.5$ Hz and $1102\pm 13$ Hz with fractional rms amplitudes of $10.3\pm 1.4$ and $11.8\pm 1.6$, respectively."1087 According to the beat freqeucy model. the observed frequency. difference of 255E11 Uz iuplies a neutron star spin period of 3.92dE0.22 1s.," According to the beat frequency model, the observed frequency difference of $255\pm 14$ Hz implies a neutron star spin period of $3.92\pm 0.22$ ms."1088 However. we note that the validity of the sinipe beat frequency model is iu question because in some sources the difference between the two QPOs is uot constaut (vauderlisetal.1997:: Mendezetal. 1998)).," However, we note that the validity of the simple beat frequency model is in question because in some sources the difference between the two QPOs is not constant \cite{v97}; \cite{mendez98}) )."1089 In fact. Psaltis et al. (," In fact, Psaltis et al. ("10901998) suggest that the OPO separation is nof coustaut for anv source with two kIIz QPOs.,1998) suggest that the QPO separation is not constant for any source with two kHz QPOs.1091 For the first four RNTE observations. we produced 2.520 keV PCA euergy spectra using the processing," For the first four RXTE observations, we produced 2.5–20 keV PCA energy spectra using the processing"1092results. i.e.. the GRB formation rate increases quickly in the region of0€z<l| and keeps constant up to z10. which is inconsistent with the cosmic star formation rates (SFRs) inferred from UV. optical. and infrared observational data so far (Madauetal.1996:Lillyetal.1996:Barger2000:Stanway 2003).,"results, i.e., the GRB formation rate increases quickly in the region of $ 0 \leqslant z \leqslant 1$ and keeps constant up to $z \sim 10$, which is inconsistent with the cosmic star formation rates (SFRs) inferred from UV, optical, and infrared observational data so far \citep{b11,b12,b13,b14}."1093. The original concept of luminosity function comes from astrophysical objects such as stars and galaxies which are long-asting and quite stable in releasing their energy., The original concept of luminosity function comes from astrophysical objects such as stars and galaxies which are long-lasting and quite stable in releasing their energy.1094" For GRB-like ugh energy transients. the total isotropic-equivalent energy CE) released in the whole duration of one event can be reliably measured. and its function (1.e.. the number density of bursts yer £j, interval) likely provides an independent or even more representative clue on the underlying physics."," For GRB-like high energy transients, the total isotropic-equivalent energy $E_{\rm iso}$ ) released in the whole duration of one event can be reliably measured, and its function (i.e., the number density of bursts per $E_{\rm iso}$ interval) likely provides an independent or even more representative clue on the underlying physics."1095" That's why in his work we focus on the so-called “isotropic-equivalent-energy 'uncetion"" rather than the traditional luminosity function.", That's why in this work we focus on the so-called “isotropic-equivalent-energy function” rather than the traditional luminosity function.1096 This paper is arranged as follows., This paper is arranged as follows.1097 2 introduces our sample and data selection., 2 introduces our sample and data selection.1098 3 presents the statistical technique while 4 shows the results., 3 presents the statistical technique while 4 shows the results.1099" We adopt a robust. nonparametric statistical technique to derive the isotropic-equivalent-energy function and the cosmic formation rate of GRBs from a £i,—z sample."," We adopt a robust, nonparametric statistical technique to derive the isotropic-equivalent-energy function and the cosmic formation rate of GRBs from a $E_{\rm iso}-z$ sample."1100" For comparison. the results from a £i,—z GRB sample are also presented."," For comparison, the results from a $L_{\rm iso}-z$ GRB sample are also presented."1101 In $5. we discuss the implication of our results and compare the cosmic GRB formation rate with the observational cosmic star formation rate.," In 5, we discuss the implication of our results and compare the cosmic GRB formation rate with the observational cosmic star formation rate."1102" Throughout the paper. we use the standard A cold dark matter cosmology with the typical parameters O,,=0.27. Q4= 0.73. and h= 0.7."," Throughout the paper, we use the standard $\Lambda$ cold dark matter cosmology with the typical parameters $\Omega_{\rm m} =0.27$, $\Omega_{\Lambda} =0.73$ , and ${\rm h}=0.7$ ."1103 In this work. two sets of data are analyzed.," In this work, two sets of data are analyzed."1104 The Εως sample comes from Amatietal.(2008.2009... containing 95 long GRBs and X-Ray Flashes CXRF. i.e. particularly soft bursts).," The $E_{\rm iso}-z$ sample comes from \citet{b1,b2}, containing 95 long GRBs and X-Ray Flashes (XRF, i.e. particularly soft bursts)."1105 This sample is made up of two parts., This sample is made up of two parts.1106 The first part consists of 70 long GRBs from Amatietal.(2008) and their redshifts range from 0.033 to 6.3., The first part consists of 70 long GRBs from \citet{b1} and their redshifts range from 0.033 to 6.3.1107" The £i, values in this work are slightly different from those in Amatietal.(2008) because of the different cosmological parameters adopted in two works.", The $E_{\rm iso}$ values in this work are slightly different from those in \citet{b1} because of the different cosmological parameters adopted in two works.1108 The second part is from Amatiet without any modification., The second part is from \citet{b2} without any modification.1109 All the GRB spectra have been extrapolated and corrected to[1.10000] keV in the cosmological restframe.," All the GRB spectra have been extrapolated and corrected to[1,10000] keV in the cosmological restframe."1110" The Li,7z sample is from Wanderman&Piran(2010). ος represents the isotropic peak luminosity, and the time resolution is | s)."," The $L_{\rm iso}-z$ sample is from \citet{b15} $L_{\rm iso}$ represents the isotropic peak luminosity, and the time resolution is 1 $s$ )."1111 Due to the Suvi/BAT narrow energy band. only a small fraction of bursts have a well determined spectrum.," Due to the /BAT narrow energy band, only a small fraction of bursts have a well determined spectrum."1112" In order to obtain reasonable estimates of Li, for all bursts. WandermanPiran(2010) considered the characteristic Band function. i.e.. where the characteristic parameters (Es.a.6) taken as (511Κεν.—1.—2.25). respectively."," In order to obtain reasonable estimates of $L_{\rm iso}$ for all bursts, \citet{b15} considered the characteristic Band function, i.e., where the characteristic parameters $(E_{\rm peak},~\alpha,~\beta)$ taken as $(511~{\rm keV},~-1,~-2.25)$, respectively."1113 To account for the so-called k-correction. again all spectra have been extrapolated and corrected to [1.10000] keV in the cosmological restframe.," To account for the so-called k-correction, again all spectra have been extrapolated and corrected to [1,10000] keV in the cosmological restframe."1114 To test whether the above Band function applicable to all bursts. Wanderman&Pi-ran(2010). preformed Monte-Carlo simulation inorder to compare GRBs having simulated spectraal parameters with GRBs having measured spectral parameters.," To test whether the above Band function applicable to all bursts, \citet{b15} preformed Monte-Carlo simulation inorder to compare GRBs having simulated spectraal parameters with GRBs having measured spectral parameters."1115 The result of such a simulation demonstrates robustness of the Ljo sample adopted above., The result of such a simulation demonstrates robustness of the $L_{\rm iso}$ sample adopted above.1116" The E;,,—z sample sutters from various selection effects (Navaetal.2008:Luet 2011). among which the dominated one is the runcation due to the detection limit of the telescope. as seen in Fig."," The $E_{\rm iso}-z$ sample suffers from various selection effects \citep{N8,b35}, , among which the dominated one is the truncation due to the detection limit of the telescope, as seen in Fig."1117 |., 1.1118" If this bias not removed. the £j,—z correlation would be far Tom the intrinsic one."," If this bias not removed, the $E_{\rm iso}-z$ correlation would be far from the intrinsic one."1119 A nonparametric 7 statistical technique may be introduced to resolve this problem. which was first put forth by Lynden-Bell(1971). and further developed by Efron&Petrosian (1992).," A nonparametric $\tau$ statistical technique may be introduced to resolve this problem, which was first put forth by \citet{b16} and further developed by \citet{b17}."1120. Lloyd-Ronningetal.(2002). first applied this technique o GRBs with simulated redshifts and later Yonetokuetal. applied it to a larger GRB sample still with simulated redshifts put up to z~10., \citet{b7} first applied this technique to GRBs with simulated redshifts and later \citet{b9} applied it to a larger GRB sample still with simulated redshifts but up to $z\sim 10$.1121 In this work. we continue to use this technique. but for the first time to two GRB samples with observed/measured redshifts.," In this work, we continue to use this technique, but for the first time to two GRB samples with observed/measured redshifts."1122 In short. this nonparametrie 7 statistical technique uses awell-defined truncation criterion to estimate the correlation (f any) between the relevant variables and their underlying parent distributions.," In short, this nonparametric $\tau$ statistical technique uses awell-defined truncation criterion to estimate the correlation (if any) between the relevant variables and their underlying parent distributions."1123" The £i, and z are not independent.", The $E_{\rm iso}$ and $z$ are not independent.1124" Without loss of generality. the total isotropic-equivalent-energy function. can. be rewritten as Φις)=picidES/etcy)/etc) where ptz) is the GRB formation rate at z. ΦΕΒος). is the present-day (re. z— QO) isotropic-equivalent-energy function. and ος) counts for the cosmic evolution of Ενω, that said. £7.=Ej /g()."," Without loss of generality, the total isotropic-equivalent-energy function can be rewritten as $\Phi(E_{\rm iso},z)=\rho(z)\phi(E_{\rm iso}/g(z))/g(z)$, where $\rho(z)$ is the GRB formation rate at $z$, $\phi(E_{\rm iso}/g(z))$ is the present-day (i.e., $z=0$ ) isotropic-equivalent-energy function, and $g(z)$ counts for the cosmic evolution of $E_{\rm iso}$, that said, $E'_{\rm iso}=E_{\rm iso}/g(z)$ ."1125" Inthe following analysis. the evolution etc) will be removed from the £i, sample: after that one obtains the £7, distribution. then the cumulative function Εν and finally the GRB formation rate pz)."," In the following analysis, the evolution $g(z)$ will be removed from the $E_{\rm iso}$ sample; after that one obtains the $E'_{\rm iso}$ distribution, then the cumulative function $\psi(E'_{\rm iso})$, and finally the GRB formation rate $\rho(z)$."1126" Consider a set of observable £;,,; and zi. where / indexes the ith burst and in our case i runs from | to 95."," Consider a set of observable $E_{{\rm iso},i}$ and $z_{i}$ , where $i$ indexes the $i$ th burst and in our case $i$ runs from 1 to 95."1127 As shown in Fig., As shown in Fig.1128 1. for the ith sample of (5). Bia). we Consider an associated set of in which the number of samples in the J;set is N;.," 1, for the $i$ th sample of $z_{i}, E_{{\rm iso},i}$ ), we consider an associated set of in which the number of samples in the $J_{i}$set is $N_{i}$ ."1129" The ziji, is the redshift of thecrossing point between two lines of £=£,,,; and the fluence limit corresponding to its “isotropic-equivalent-energy” limit."," The $z_{i,\rm lim}$ is the redshift of thecrossing point between two lines of $E=E_{{\rm iso},i}$ and the fluence limit corresponding to its “isotropic-equivalent-energy"" limit."1130" If z; and £.,; are independentto each other. one would expect thenumber of the followingsample to be uniformly distributed between | and Aj."," If $z_{i}$ and $E_{{\rm iso},i}$ are independentto each other, one would expect thenumber of the followingsample to be uniformly distributed between 1 and $N_{i}$ ."1131" To estimate the correlation degree between E,jv and z. one may introduce the test"," To estimate the correlation degree between $E_{\rm iso}$ and $z$ , one may introduce the test"1132observed in L.5daysandpossibl ysdaysa flerihestartofthe August 10930ulburstbyil LOO6. 1997. 1998). and3daysa flerthestartofiheNovembe sedleofthedurationofthespiralshocks,"observed in $1.5$ days and possibly 8 days after the start of the August 1993 outburst by Steeghs (1996, 1997, 1998), and 3 days after the start of the November 1996 outburst by Harlaftis (1999); the spectra taken 8 days after the start of the August 1993 outburst only hint at the presence of the spiral shocks."1133iso flheorderofdaysinst," The data presented in this paper fit in nicely between the previous observations and have the extra advantage that, for the first time, were taken for two consecutive nights during an outburst."1134oadaytleb diesi bHisG6ad , We see that the spiral structure is strong both nights and with little alteration which indicates that the time-scale of the duration of the spiral shocks is of the order of days instead of hours.1135"ymentioned. thedatapresentedinthispaper were akend, lHivedsbructluresthatareprobabl ypresentithroughoullheentircoulbuirst digobgh wddad avdavs oybilelpcllstodoopyphordb coud redurationo | "," As already mentioned, the data presented in this paper were taken 5 and 6 days after the outburst had started, indicating that the spiral shocks are long-lived structures that are probably present throughout the entire outburst although we cannot be certain until spectroscopy for the entire duration of an outburst is obtained."1136Fig., Fig.1137 4 compares maps of different emission lines(11:3.. aand A4472X)) ancl also displays the data (top panels) and fits (lower panels).," 4 compares maps of different emission lines, and ) and also displays the data (top panels) and fits (lower panels)."1138 To construct. these. maps (and those of Fig. 3)), To construct these maps (and those of Fig. \ref{res:heiidopp}) )1139 the eclipse data have been removed as the behaviour during eclipse is not included in the model., the eclipse data have been removed as the behaviour during eclipse is not included in the model.1140 The spiral structure is strongest in whereas both aand [Teature very strong emission from the companion star., The spiral structure is strongest in whereas both and feature very strong emission from the companion star.1141 The image is distinethy cillerent in structure with the upper shock stronger than the lower., The image is distinctly different in structure with the upper shock stronger than the lower.1142 This may be associated with its weakness: for instance in computing this map we had to simultaneously. caleulate one for the nearby ∐⊲↓⊔∢, This may be associated with its weakness; for instance in computing this map we had to simultaneously calculate one for the nearby line.1143⋅⊳↾∐↕⋖⋅⊔↓≻≻⋖⊾↓⋅⊳∖↕⋯∼↳⊲↓⊔⇂↓↕∢⊾∐∢⊾↥∕∖≟≟⊤⇉⇀∖ nunaps shows a more complex structure than that of the other lines., The upper shock in the maps shows a more complex structure than that of the other lines.1144. pn:Fhis structure is. seen in. maps from⋅ both nights.. which suggests that it is real.," This structure is seen in maps from both nights, which suggests that it is real."1145 As forLL. the brightest region on the upper shock is shifted in azimuth with respect. toA4686AL.," As for, the brightest region on the upper shock is shifted in azimuth with respect to."1146 There are substantial Dares in the emission lines. e.g. in aand aat orbital phase 71.3 during the first night.," There are substantial flares in the emission lines, e.g. in and at orbital phase $\sim$ 1.3 during the first night."1147 We have labelled some of the flares in the trailed spectra qoaisetd, We have labelled some of the flares in the trailed spectra (top panels) of and in Fig. \ref{res:alldopp}.1148 a blake spectra (ic. a few minutes). are clear in both lines and occur in both the blue- and red-shifted sides of the lines.," The flare events, which last for one or two spectra (i.e. a few minutes), are clear in both lines and occur in both the blue- and red-shifted sides of the lines."1149 Flares A and D occur at high racial velocities in the bluc-shifted component., Flares A and B occur at high radial velocities in the blue-shifted component.1150 Label € is associated with a flare that took place in the red-shifted component of the lines., Label C is associated with a flare that took place in the red-shifted component of the lines.1151 The continuum ancl emission line Πάνος for the two nights are plotted: versus orbital phase in Fig. 5.., The continuum and emission line fluxes for the two nights are plotted versus orbital phase in Fig. \ref{res:alllc}.1152 Orbital phases have been calculated using Wolf. et. al, Orbital phases have been calculated using Wolf et al.1153s (1993). linear ephemoeris: The shape of the continuum eclipses is similar to that ∩⇂∐⋖⊾∐∕∖≟↻↖∖↻⇀∖ wμαrereas the shape of the eclipses for the other lines is quite. different.,'s (1993) linear ephemeris: The shape of the continuum eclipses is similar to that of whereas the shape of the eclipses for the other lines is quite different.1154D. ..They are more asymmetric. and show a slope shallower than that of aand the continuum during both ingress and egress., They are more asymmetric and show a slope shallower than that of and the continuum during both ingress and egress.1155 The eclipse of the emission. lines is shifted. to earlier-than-expected phases: the continuum is too. but to a lesser extent.," The eclipse of the emission lines is shifted to earlier-than-expected phases; the continuum is too, but to a lesser extent."1156 The shift in phase is different lor different Lines being the largest displacement that of wwhich we singled out earlier for its asvnunetry., The shift in phase is different for different lines being the largest displacement that of which we singled out earlier for its asymmetry.1157 The phases of mid-eclipse measured at. half eclipse depth are listed in ‘Table 2. during eclipse., The phases of mid-eclipse measured at half eclipse depth are listed in Table \ref{res:ecdisp} during eclipse.1158 Another feature of these light curves is the variability observed between eclipses with a, Another feature of these light curves is the variability observed between eclipses with a1159The results from. SPIERare compared. with those of (2). PEPE (2).. andCRASIL (7) in figures 18 to 16..,"The results from are compared with those of \citep{2006NewA...11..374M}, \citep{2005MNRAS.362.1413R}, and \citep{ 2003MNRAS.345..379M} in figures \ref{T4x1surf} to \ref{T4T3surf}."1160 General features of the ionization field including the extent and shape of the ionization front. the shadows from dense clumps. and the shape of the neutral island near the center of the slice. are similar in all codes.," General features of the ionization field including the extent and shape of the ionization front, the shadows from dense clumps, and the shape of the neutral island near the center of the slice, are similar in all codes."1161 Although ancl share the most similarities. including the sampling of high energy photons. we see some slight dillerences in the peak ionization and temperature values they produce in the central part of the highly ionized region.," Although and share the most similarities, including the sampling of high energy photons, we see some slight differences in the peak ionization and temperature values they produce in the central part of the highly ionized region."1162 We have presented. the cosmological SPLE ravtracing cocle and cliseussecl the results of several radiative transfer problems by wav of validation., We have presented the cosmological SPH raytracing code and discussed the results of several radiative transfer problems by way of validation.1163 emplovs a Monte Carlo approach to rav tracing applied directly to. the SPILL particle distribution native to a large fraction of current astrophysical and cosmological hvdrodynamic simulations., employs a Monte Carlo approach to ray tracing applied directly to the SPH particle distribution native to a large fraction of current astrophysical and cosmological hydrodynamic simulations.1164 The column density sums at the heart of the radiative transfer calculation. are carried out using the SPI kernels so that no regridding of the data is necessary. maintaining the adaptive Lagrangian nature that makes SPILL attractive in the first. place.," The column density sums at the heart of the radiative transfer calculation are carried out using the SPH kernels so that no regridding of the data is necessary, maintaining the adaptive Lagrangian nature that makes SPH attractive in the first place."1165 The statistical nature of the Monte. Carlo method: makes the inclusion of arbitrary source spectra ancl emission. profiles very straightforward., The statistical nature of the Monte Carlo method makes the inclusion of arbitrary source spectra and emission profiles very straightforward.1166 The simplicity of its implementation also allows the future addition of more complicated. physics as well as parallelization., The simplicity of its implementation also allows the future addition of more complicated physics as well as parallelization.1167 Llowever. a large number of ravs must be traced to get a fair representation of the auncerlsing probability cistribution functions being sampled and to maintain angular resolution.," However, a large number of rays must be traced to get a fair representation of the underlying probability distribution functions being sampled and to maintain angular resolution."1168 This translates to the numerical problem of finding the intersection of numerous ravs and spheres as quickly as possible., This translates to the numerical problem of finding the intersection of numerous rays and spheres as quickly as possible.1169 In order to do this we have applied a variant of the neighbor search techniques using oct-trees and a fast box-ray intersection test adapted from computer graphics. resulting in an ellicient. adaptive rav tracing code applicable to current astronomical hydro simulations.," In order to do this we have applied a variant of the neighbor search techniques using oct-trees and a fast box-ray intersection test adapted from computer graphics, resulting in an efficient adaptive ray tracing code applicable to current astronomical hydro simulations."1170 There are. in general. no analytic solutions to the types of radiative transfer problems that occur with sources embedded: in. 3D. density fields.," There are, in general, no analytic solutions to the types of radiative transfer problems that occur with sources embedded in 3D density fields."1171 Pherclore we. validated using the tests chosen by the Raciative Transfer Comparison Project., Therefore we validated using the tests chosen by the Radiative Transfer Comparison Project.1172 There is good agreement of results with codes that treat the same level of physics., There is good agreement of results with codes that treat the same level of physics.1173" We present the source code for on à companionwebsite"". together with a users guide and. some example input snapshot files."," We present the source code for on a companion, together with a users guide and some example input snapshot files."1174 An early. version of this IE approach was used to study the structure of neutral hydrogen in the Universe at the time of reionization in ?).., An early version of this RT approach was used to study the structure of neutral hydrogen in the Universe at the time of reionization in \cite{2007arXiv0709.2362C}.1175 This project is. supported by the National Science Foundation. NSE AST-0205978 and by NASA ATP erant NNGOG6-GIISSC. We thank Intel for their generous donation of processors used in this work.," This project is supported by the National Science Foundation, NSF AST-0205978 and by NASA ATP grant NNG 06-GH88G. We thank Intel for their generous donation of processors used in this work."1176 The rates below make use of thefollowing notation.," The rates below make use of thefollowing notation,"1177and model expectations. here we show that Alfvénnic reacceleration of secondary electrons and. positrons in. the ICM may generate relatively broad synchrotron profiles.,"and model expectations, here we show that Alfvénnic reacceleration of secondary electrons and positrons in the ICM may generate relatively broad synchrotron profiles."1178 If the reacceleration period is much longer than the reacceleration. timescale. the bulk of the secondary electrons. ancl positrons injected. above the momentum. pow which Coulomb losses outweight the acceleration ellicicney. is. essentially boosted around. a maximum momentum. pua. ab which acceleration is balanced by racliative losses.," If the reacceleration period is much longer than the reacceleration time–scale, the bulk of the secondary electrons and positrons injected above the momentum, $p_{_{_{_>}}}$, at which Coulomb losses outweight the acceleration efficiency, is essentially boosted around a maximum momentum, $p_{\rm max}$, at which acceleration is balanced by radiative losses."1179 From Figs., From Figs.1180 12 13 of Paper Lone finds that under the assumed. physical conditions the acceleration of the lower enerev electrons ancl positrons typically happens in the regime το227 while the acceleration of the higher energy leptons happens in the opposite regime., 12 13 of Paper I one finds that under the assumed physical conditions the acceleration of the lower energy electrons and positrons typically happens in the regime $\tau_s >> \tau_d$ while the acceleration of the higher energy leptons happens in the opposite regime.1181" Thus. assuming for simplicity a power law οποιον distribution of the relativistic protons IN,Αν >. from I5qs.(1)). (82) (51)). and (53)) one finds: where cle is the constant in I5q. 1.."," Thus, assuming for simplicity a power law energy distribution of the relativistic protons $N_p = K_p p^{-s}$ , from \ref{ion}) ), \ref{dpp}) ), \ref{wk_2}) ), and \ref{acctime_1}) ) one finds: where $A_C$ is the constant in Eq. \ref{ion},"1182 and while from IEqs.(2)). (8)). (49)). ancl (53)) one has: where cla is the constant in Eq. 2..," and while from \ref{syn+ic}) ), \ref{dpp}) ), \ref{wk_1}) ), and \ref{acctime_1}) ) one has: where $A_{\rm rad}$ is the constant in Eq. \ref{syn+ic},"1183" Bye=By.|Bo and The number density of the reaccelerated secondary electrons ancl positrons around: pas. Can be estimated. by the integral of the number density of secondary. particles injected with pzp, during the reacceleration stage."," $B_{\rm IC+}^2 = B_{\rm IC}^2 +B^2$ , and The number density of the reaccelerated secondary electrons and positrons around $p_{\rm max}$ can be estimated by the integral of the number density of secondary particles injected with $p > p_{_{_{>}}}$ during the reacceleration stage."1184 From I5qs.(38)) (neelecting for simplicity the contributions from the Ps and Ps terms) and (60)). one has : On the other hand. the number density of electrons with ppuax in the classical secondary model can be obtained [rom I5qs.(38)). (55)) and (62)): Thus the increase of the extension of the emitted svnchrotron profile (associated to electrons with p pumas) in the secondaryreacceleration model with respect to that in the classical secondary model can be directly estimated[rom the ratio: which. in the assumption that ὃντν nmi. roughly scales," From \ref{qepm_s}) ) (neglecting for simplicity the contributions from the ${\cal P}_2$ and ${\cal P}_3$ terms) and \ref{p>})), one has : On the other hand, the number density of electrons with $p \sim p_{\rm max}$ in the classical secondary model can be obtained from \ref{qepm_s}) ), \ref{sec_stat}) ) and \ref{pmax}) ): Thus the increase of the extension of the emitted synchrotron profile (associated to electrons with $p\sim p_{\rm max} {\rm c}$ ) in the secondary–reacceleration model with respect to that in the classical secondary model can be directly estimatedfrom the ratio: which, in the assumption that ${\cal E}_p \propto n_{\rm th}$ , roughly scales"1185Neutron stars contain matter in one of the densest forms found in the universe.,Neutron stars contain matter in one of the densest forms found in the universe.1186 Their central density ranges from a few time the density of normal nuclear matter to about one order of magnitude higher. depending on the star's nass and the equation of state (IOS).," Their central density ranges from a few time the density of normal nuclear matter to about one order of magnitude higher, depending on the star's mass and the equation of state (EOS)."1187 Neutron stars therefore provide us with a powerful tool for exploring the properties of such dense matter., Neutron stars therefore provide us with a powerful tool for exploring the properties of such dense matter.1188 In. the Last. decades. this tool was applied. to. among other topics. the determination of the EOS of dense. charge neutral. s;-equilibrated: matter by means of comparing the theoretical predicted: properties with observations of neutron stars.," In the last decades, this tool was applied to, among other topics, the determination of the EOS of dense, charge neutral, $\beta$ -equilibrated matter by means of comparing the theoretical predicted properties with observations of neutron stars."1189 Fhis was attempted bv studying. for example. the maximum stable star mass (vanIxerkwijketal..1995).. the minimum rotation period (Friedmanetab.1986:Weber&Clendenning.1992)... or the thermal behaviour (Lsuruta 1966 .. Schaab et al.," This was attempted by studying, for example, the maximum stable star mass \cite{Kerkwijk95a}, the minimum rotation period \cite{Friedman86a,Weber92a}, or the thermal behaviour (Tsuruta 1966 \nocite{Tsuruta66}, Schaab et al."1190 1996 . Page 1997 :: see Dalberg. Lichtenstadt Cook 1998 — for a recent review).," 1996 \nocite{Schaab95a}, Page 1997 \nocite{Page97a}; ; see Balberg, Lichtenstadt Cook 1998 \nocite{Balberg98a} for a recent review)."1191 Recenth. Strohmaver ct al.," Recently, Strohmayer et al."1192 (1996). and. Van der Ixlis et al., \shortcite{Strohmayer96a} and Van der Klis et al.1193 (1996) discovered with the Rossi X-ray Timing Explorer (INTI). kKilohertz quasi-periocic oscillations (QPOs) in the X-ray brightness of low-mass X-ray. binaries (LAINBs. see van der Whis 1997. for a recent review).," \shortcite{VanDerKlis96a} discovered with the Rossi X-ray Timing Explorer (RXTE) kilohertz quasi-periodic oscillations (QPOs) in the X-ray brightness of low-mass X-ray binaries (LMXBs, see van der Klis 1997 \nocite{VanDerKlis97a} for a recent review)."1194 In subsequent observations. three QPOs were often detected simultaneously in a given source.," In subsequent observations, three QPOs were often detected simultaneously in a given source."1195 “Lhe frequency separation ween. both QPOs is almost constant. although the requencies of the two QPOs themselves vary by. several vanced Hertz.," The frequency separation between both QPOs is almost constant, although the frequencies of the two QPOs themselves vary by several hundred Hertz."1196 Up to now. the only exceptions are the Atoll sources 11608-52 and 11735-44 and the Z-source Scorpius X-1 in which the frequeney separation varies with the luminosity by roughly +15 al.," Up to now, the only exceptions are the Atoll sources 1608-52 and 1735-44 and the Z-source Scorpius X-1 in which the frequency separation varies with the luminosity by roughly $\pm119715$ al."1198 (1998). found that the QPO dataof the other LAINBs, \shortcite{Psaltis98a} found that the QPO dataof the other LMXBs1199spectral type.,spectral type.1200 From astrometric and photometric observations of L dwarfs ?. give the mean effective temperature of an L8 dwarf as 1390K. although they caution that their derived values should be treated as schematic results only. and note that late L and early T dwarfs appear to occupy a fairly narrow temperature range from 1200«Tig<1550 K. The temperatures computed by ο for a small sample of late L and early T dwarfs are in agreement with these estimates.," From astrometric and photometric observations of L dwarfs \citet{vrba} give the mean effective temperature of an L8 dwarf as $1390$ K, although they caution that their derived values should be treated as schematic results only, and note that late L and early T dwarfs appear to occupy a fairly narrow temperature range from $1200 < T_{\rm eff} < 1550$ K. The temperatures computed by \citet{golimowski} for a small sample of late L and early T dwarfs are in agreement with these estimates."

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