ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 However. the 92 cin nuage in Fi," However, the 92 cm image in Fig."3e. 9 has a resolution of 15 arcsec or 71 kpe projected ou the aue of the sky., \ref{Fig. 9} has a resolution of 45 arcsec or 74 kpc projected on the plane of the sky.4 Gaps in the emission of this size would not be detected., Gaps in the emission of this size would not be detected.5 Taking a jetspeed of (Le (a tvpica spced. for conipact sviunietric objects on similar scales - Owsiauk Conway 1998: Tschager et al. 20001).," Taking a jetspeed of $0.1c$ (a typical speed for compact symmetric objects on similar scales - Owsianik Conway \cite{owsianik}; Tschager et al. \cite{tschager}) ),"6 anc asstmune that we acually see the jet and not the backflow ina thivlobe. we would not detect “off periods in jet activity asting less an 2<109 vears.," and assuming that we actually see the jet and not the backflow in a thin lobe, we would not detect 'off' periods in jet activity lasting less than $2\times 10^6$ years."7" This period is louger thau the pxhalle cheth of fje preseut ""ou period represeuted |wt je kpe ‘ontral component. 10!10"" vers."," This period is longer than the probable length of the present `on' period represented by the kpc central component, $10^4 - 10^5$ years."8 The ον]enucc| from je structure to the NW points more towSC jisocic rather than continuous activity., The evidence from the structure to the NW points more towards episodic rather than continuous activity.9" Iu the ceutral siloWISE, je jet ds raceable via a number of knots on 1sway roni the uucleus via component DI out to the WIluspot oei component A at a distance of ~1.2 kpc."," In the central kiloparsec, the jet is traceable via a number of knots on its way from the nucleus via component B1 out to the warmspot in component A at a distance of $\sim 1.2$ kpc."10 Iusufficieut sensitivitv παν nuit our ability to detect more of he jet on these su»ealactie scales., Insufficient sensitivity may limit our ability to detect more of the jet on these sub-galactic scales.11 Ou larger scales. tle cussion extends ~ 1.1pe in what appears to be a more relaxed jet than its well-collimated counterpart to the SE.," On larger scales, the emission extends $\sim 1.4$ Mpc in what appears to be a more relaxed jet than its well-collimated counterpart to the SE."12 In the 21 cum mage made by Barthel et al. (, In the 21 cm image made by Barthel et al. (131985) there is a pronünent featre in the NW structure which suggests that the enerev supply may have been variable.,1985) there is a prominent feature in the NW structure which suggests that the energy supply may have been variable.14 At 92 cii, At 92 cm (Fig.15 (Fig. 9 bottoiu) aud at 19 ci (Mack et al., \ref{Fig. 9} bottom) and at 49 cm (Mack et al.16 1997). there Is onissjon sout rand west of the main radio axis to the NW.," 1997), there is emission south and west of the main radio axis to the NW."17 The originOo of this emission is unclear., The origin of this emission is unclear.18 Double-double radio galaxies (Ixadser et al. 20003) , Double-double radio galaxies (Kaiser et al. \cite{kaiser}) )19appear o provide good evidence that activity in ACNs ca1i be recurrent., appear to provide good evidence that activity in AGNs can be recurrent.20 Prestmably these are objects in which the ou-off evceles are couparable., Presumably these are objects in which the `on-off' cycles are comparable.21" There may be a wide rage o duty cycles: auxmest ACNs: 30236 may be an exinuple of a sotree Which is occasionally ""off. perhaps due to fre jet channel collapsing or he flow being blocked x interaction wi ha cloud or a dicyp in supply of fucl to he ceutral black tole."," There may be a wide range of duty cycles amongst AGNs; 3C236 may be an example of a source which is occasionally `off', perhaps due to the jet channel collapsing or the flow being blocked by interaction with a cloud or a drop in supply of fuel to the central black hole."22 The central structure in 3C'236 may relect t1ο normal level of activity iu the nucleiIn., The central structure in 3C236 may reflect the normal level of activity in the nucleus.23 Mac set al. (1 995)), Mack et al. \cite{mack2}) )24 and Schoeninakers et al. (2000)), and Schoenmakers et al. \cite{schoenmakers}) )25 lave Osnuated tie age of 30236 from svuchrotron loss uodels aud spectral aging as ~105 vears., have estimated the age of 3C236 from synchrotron loss models and spectral aging as $\sim 10^8$ years.26 The latter authors also estimate the speed of advance of the western jet iuto the interealactic media as 0.1 c. This speed is at the lower Linu of what can be measured with VLBI Or conipact jets in the nucleus (eg., The latter authors also estimate the speed of advance of the western jet into the intergalactic medium as 0.1 c. This speed is at the lower limit of what can be measured with VLBI for compact jets in the nucleus (eg.27 Owsianils Comway L998.. Tschager et al. 2000)).," Owsianik Conway \cite{owsianik}, , Tschager et al. \cite{tschager}) )."28region representing the objects with an additional SB component.,region representing the objects with an additional SB component.29 The plain (dashed) line anc gravecd (black) region correspond to the COSMOS (ELAS) sample., The plain (dashed) line and grayed (black) region correspond to the COSMOS (ELAIS) sample.30 Again. the existence of such a component can be. in general. well constrained only in the presence. of data points longware A=24pm and this is valid for only and of COSMOS and LELAIS samples. respectively.," Again, the existence of such a component can be, in general, well constrained only in the presence of data points longward $\lambda=24$ and this is valid for only and of COSMOS and ELAIS samples, respectively."31 We will now attempt to put all the results from the various AGN samples together and construct a common description of their dust. properties., We will now attempt to put all the results from the various AGN samples together and construct a common description of their dust properties.32 “Lo this end. we will first. present a summary of the results of Paper 1. that will also be used in this combined study.," To this end, we will first present a summary of the results of Paper 1, that will also be used in this combined study."33 The Iow-z simple will be exelucded from this analysis. because of the unconfirmed (stellar vs. starburst) nature of the objects.," The $z$ sample will be excluded from this analysis, because of the unconfirmed (stellar vs. starburst) nature of the objects."34 They will be taken into account. however. when discussing the star formation. as the results on this issue seem to be more robust. and only," They will be taken into account, however, when discussing the star formation, as the results on this issue seem to be more robust, and only"35The first point to make from Fig.,The first point to make from Fig.36 2 is that simulated ULX continua seem perfectly capable of generating optical line ratios observed in transition-type objects and LINERs., \ref{fig:o3o1} is that simulated ULX continua seem perfectly capable of generating optical line ratios observed in transition-type objects and LINERs.37" The ULX ionizing continuum must include some FUV (~1- 10Ryd) in order to produce [Ο1]/Πα ratios in the correct range, but apart from this the simulated line ratios do not depend very strongly on the continuum shape."," The ULX ionizing continuum must include some FUV $\sim$ 1-10Ryd) in order to produce $[O_{I}]/H_{\alpha}$ ratios in the correct range, but apart from this the simulated line ratios do not depend very strongly on the continuum shape."38 The second point from Fig., The second point from Fig.39 2 is that ULX black hole mass can determine whether the optical line ratio is transition-like or LINER-like., \ref{fig:o3o1} is that ULX black hole mass can determine whether the optical line ratio is transition-like or LINER-like.40" For example, a blackbody temperature of 5x10°K, corresponds to emission from an accretion disk around a 10Mo black hole accreting near Eddington luminosity and generates a line ratio (middle point on solid curve) in the middle of the transition object region."," For example, a blackbody temperature of $5\times 10^{6}$ K, corresponds to emission from an accretion disk around a $\sim 10M_{\odot}$ black hole accreting near Eddington luminosity and generates a line ratio (middle point on solid curve) in the middle of the transition object region."41" By contrast, a blackbody temperature of 2x 10°K corresponds to an accretion disk around a 10?M5 black hole and generates a line ratio (rightmost point on solid curve) in the LINER region."," By contrast, a blackbody temperature of $2\times 10^{6}$ K corresponds to an accretion disk around a $\sim 10^{3}M_{\odot}$ black hole and generates a line ratio (rightmost point on solid curve) in the LINER region."42" From Fig. 2,,"," From Fig. \ref{fig:o3o1},"43" the ’radio quiet’ L2 and T2s have [O1]/Ha< 0.2, so if they are powered by ’soft-high’ state ULXs as we suggested in McKernanetal.(2010),, the black hole masses must be «10?M and some FUV continuum is required (possibly from star formation)."," the 'radio quiet' L2 and T2s have $[O_{I}]/H_{\alpha}<0.2$ , so if they are powered by 'soft-high' state ULXs as we suggested in \citet{b98}, the black hole masses must be $<10^{3}M_{\odot}$ and some FUV continuum is required (possibly from star formation)."44" We will carry out more detailed simulations in the future to understand the limits on optical line ratios for different values of log U, the absorbing column and different ionizing continua, nevertheless for the purposes of this Letter, ULXs can in principle generate optical line ratios observed in LINER and transition-type nuclei."," We will carry out more detailed simulations in the future to understand the limits on optical line ratios for different values of log U, the absorbing column and different ionizing continua, nevertheless for the purposes of this Letter, ULXs can in principle generate optical line ratios observed in LINER and transition-type nuclei."45 Recently Gonzalez-Martinetal.(2009) claimed that nuclear X-ray emission in LINERs could not be due to high mass XRBs since populations of young stars in these nuclei are generally ruled out., Recently \citet{b22} claimed that nuclear X-ray emission in LINERs could not be due to high mass XRBs since populations of young stars in these nuclei are generally ruled out.46" Of course, as discussed above, it is not necessary to have populations of young stars to account for X-ray observations of low luminosity galactic nuclei."," Of course, as discussed above, it is not necessary to have populations of young stars to account for X-ray observations of low luminosity galactic nuclei."47 Ptaketal.(2006) find that X-ray/optical flux ratios for optical counterparts to ULXs are generally consistent with LMXB in clusters., \citet{b17} find that X-ray/optical flux ratios for optical counterparts to ULXs are generally consistent with LMXB in clusters.48" Furthermore, in M31, the distribution of variable X-ray point sources in the innermost ~ 450pc may be consistent with an ageing population of low mass XRBs (Kaaret2002)."," Furthermore, in M31, the distribution of variable X-ray point sources in the innermost $\sim 450$ pc may be consistent with an ageing population of low mass XRBs \citep{b36}."49". Therefore, integrating over the contributions from low mass XRBs is perfectly capable of powering nuclear X-ray emission for Gyrs and potentially generating a LINER- or transition object-like appearance."," Therefore, integrating over the contributions from low mass XRBs is perfectly capable of powering nuclear X-ray emission for Gyrs and potentially generating a LINER-like or transition object-like appearance."50" Although low mass likeXRBs tend to be transient, they can actually dominate the XLF with reasonable choice of duty cycles (Piro&Bildsten2002)."," Although low mass XRBs tend to be transient, they can actually dominate the XLF with reasonable choice of duty cycles \citep{b38}."51". For example, a choice of outburst rate (O.R.)~10% during ~75% of the lifetime of XRBs is a reasonable estimate for the nucleus of Cen A (Piro&Bildsten 2002)."," For example, a choice of outburst rate $\sim 10\%$ during $\sim 75\%$ of the lifetime of XRBs is a reasonable estimate for the nucleus of Cen A \citep{b38}."52. Munoetal.(2005a) suggest O.R.~1% for an estimated population of ~10—10? binaries within « 1pc of SgrA* could account for XRT observations.," \citet{b83} suggest $\sim 1\%$ for an estimated population of $\sim 5310-10^{3}$ binaries within $<1$ pc of SgrA* could account for XRT observations."54 ULXs if unbeamed could have duty cycles as high as ~1096 (Kingetal. 2001).., ULXs if unbeamed could have duty cycles as high as $\sim 10\%$ \citep{b85}.55" We should expect (at least) several low mass XRBs in ~0.5—1"" X-ray observations of most galactic nuclei.", We should expect (at least) several low mass XRBs in $\sim 0.5-1''$ X-ray observations of most galactic nuclei.56" Nuclear ULXs, like that in M82 should occur with moderate levels of star formation in the nucleus, although ULXs are observed in early-type galaxies at a rate of a few per galaxy (e.g.Fabbiano&White2003)."," Nuclear ULXs, like that in M82 should occur with moderate levels of star formation in the nucleus, although ULXs are observed in early-type galaxies at a rate of a few per galaxy \citep[e.g.][]{b41}."57. Indeed the mass of the ULX in M82 suggests that it is cannibalizing its host cluster or has captured companions., Indeed the mass of the ULX in M82 suggests that it is cannibalizing its host cluster or has captured companions.58 Another possible inconsistency between LINER X-ray emission and ULX or XRB emission is the XLF of LINER nuclei (Gonzalez-Martinetal.2009)., Another possible inconsistency between LINER X-ray emission and ULX or XRB emission is the XLF of LINER nuclei \citep{b22}.59". However, the sample size (82) of Gonzalez-Martinetal. is limited (see (Kim&Fabbiano2004) for discussion of the dangers of this)."," However, the sample size (82) of \citet{b22} is limited (see \citep{b23} for discussion of the dangers of this)."60" Furthermore, their cumulative power-law indices (~—0.2, —0.8) before and after the power-law break are actually not that different from the power-law indices of XRBs at low luminosities (~—0.8) in (Kim&Fabbiano2004) or even from M31 (Kongetal. 2002), although these steepen at higher luminosities."," Furthermore, their cumulative power-law indices $\sim -0.2,-0.8$ ) before and after the power-law break are actually not that different from the power-law indices of XRBs at low luminosities $\sim -0.8$ ) in \citep{b23} or even from M31 \citep{b28}, although these steepen at higher luminosities."61 A much larger LINER sample is evidently required for a reliable understanding of the LINER XLF., A much larger LINER sample is evidently required for a reliable understanding of the LINER XLF.62" The UV band is important in our discussion, since emission from an accretion disk around supermassive black holes should peak in the UV band."," The UV band is important in our discussion, since emission from an accretion disk around supermassive black holes should peak in the UV band."63 Maozetal(2005) found evidence for UV variability in LINER 1s and LINER 2s., \citet{b29} found evidence for UV variability in LINER 1s and LINER 2s.64" However of the five LINER 2s in Maozetal(2005) without a compact radio core, none varied at >9596 confidence and three of the five radio-quiet LINER 2s (NGC 3486, NGC 4569 and NGC 5055 at 9,1 and 8Mpc distant respectively) were consistent with no UV variation whatsoever (Maozetal 2005).."," However of the five LINER 2s in \citet{b29} without a compact radio core, none varied at $>95\%$ confidence and three of the five radio-quiet LINER 2s (NGC 3486, NGC 4569 and NGC 5055 at 9,1 and 8Mpc distant respectively) were consistent with no UV variation whatsoever \citep{b29}."65 This suggests that hot stars rather than AGN are powering the UV emission in radio-quiet LINER 2s., This suggests that hot stars rather than AGN are powering the UV emission in radio-quiet LINER 2s.66 X-ray imaging of LINERs reveals that extended emission or complex clumpy emission is common in LINER 2 nuclei., X-ray imaging of LINERs reveals that extended emission or complex clumpy emission is common in LINER 2 nuclei.67" Extended emission can be explained in a nuclear ULX modelby several ULXs/XRBs in a nucleus, in a region of hot massive stars."," Extended emission can be explained in a nuclear ULX modelby several ULXs/XRBs in a nucleus, in a region of hot massive stars."68" In a small sample of L2 and T2 nuclei, around half showed clear evidence for extended emission"," In a small sample of L2 and T2 nuclei, around half showed clear evidence for extended emission"69Taam. White Lost) and (Alaldsishimiaetal.1982) have not been observed to varv systematically with the persistent fux. so we cannot predict bow observing bursts at low AZ du slow sources would affect our correlations.,"Taam, White 1984) and \citep{mak82}70 have not been observed to vary systematically with the persistent flux, so we cannot predict how observing bursts at low $\dot M$ in slow sources would affect our correlations."71 We have found that oscillations from the 6 fast burst oscillation sources are tightly connected to plotospheric radius expansion. whereas oscillations from the 23 slow sources are about equally likely to be found iu bursts both with aud without radius expansion.," We have found that oscillations from the 6 fast burst oscillation sources are tightly connected to photospheric radius expansion, whereas oscillations from the 3 slow sources are about equally likely to be found in bursts both with and without radius expansion."72 What drives this correlation remains to be determined: is it the burst properties themselves. the oscillation frequencies. or ποιο nuscen third parameter?," What drives this correlation remains to be determined: is it the burst properties themselves, the oscillation frequencies, or some unseen third parameter?"73" According to the beat frequency model of kz QPOs.the fact that zai&Amey for the ""low? sources whereas MigretC2AM for the fast? ones can be accounted for if one or two autipodal hot spots ou the surface of the rotating neutron star are visible to the observer (Miller et 11998)."," According to the beat frequency model of kHz QPOs,the fact that $\nu_{\rm burst}\simeq \Delta\nu_{\rm kHz}$ for the “slow” sources whereas $\nu_{\rm burst}\simeq742\Delta\nu_{\rm kHz}$ for the “fast” ones can be accounted for if one or two antipodal hot spots on the surface of the rotating neutron star are visible to the observer (Miller et 1998)."75 One possibility is that the distinction between ast aud slow oscillations is due to a difference iu the oricutation of the hot spots aud the observer with respect o the rotation axis of the star., One possibility is that the distinction between fast and slow oscillations is due to a difference in the orientation of the hot spots and the observer with respect to the rotation axis of the star.76 This secs unlikely., This seems unlikely.77 Radius expansion is observed with similar Likelihood from both ast aud slow sources. and therefore is uulikelv. to depend on our viewing anele.," Radius expansion is observed with similar likelihood from both fast and slow sources, and therefore is unlikely to depend on our viewing angle."78 We would not expect oscillations to © associated with radius expansion bursts oulv in the fast sources if viewing augle effects determine whether oue or wo spots are observed., We would not expect oscillations to be associated with radius expansion bursts only in the fast sources if viewing angle effects determine whether one or two spots are observed.79 Tt also does not appear that the strengths of the bursts determine the oscillation frequencies by iguiting either one or two hot spots., It also does not appear that the strengths of the bursts determine the oscillation frequencies by igniting either one or two hot spots.80 If this were the case. one would expect to detect slow oscillations during weal bursts without radius expausion fron the fast sources. aud fast oscillations during strong bursts from the slow sources.," If this were the case, one would expect to detect slow oscillations during weak bursts without radius expansion from the fast sources, and fast oscillations during strong bursts from the slow sources."81 Out of the 125 bursts we observed from sources ofoscillatious.. we find uno evidence for harmonic or half-Brequeucy signals with powers comparable to the signals at the frequencies in Table 1..," Out of the 125 bursts we observed from sources of, we find no evidence for harmonic or half-frequency signals with powers comparable to the signals at the frequencies in Table \ref{sum}."82 If the distinction between slow aud fast oscillators is equivalent to a division between slow and fast rotators. Man (ov some related quantity. eg. the effective surface eravity) could determine which bursts show oscillations.," If the distinction between slow and fast oscillators is equivalent to a division between slow and fast rotators, $\nu_{\rm spin}$ (or some related quantity, e.g., the effective surface gravity) could determine which bursts show oscillations."83 Uowever. that option is not free of complications. as the transition between the burst properties for sources that exhibit fast and slow oscillatious must be very sharp. since the two populations are uot at all well separated in frequency (see Table 1)).," However, that option is not free of complications, as the transition between the burst properties for sources that exhibit fast and slow oscillations must be very sharp, since the two populations are not at all well separated in frequency (see Table \ref{sum}) )."84 When comparing the observed distribution of 1/4: to a unlforu distribution of frequencies between 250650 Iz. a IKolinogorov-Suinrnov test (e.c. Eadie et 11971) cau exclude a uniform distribution at only the 1.36 (8I'4)) confidence level.," When comparing the observed distribution of $\nu_{\rm burst}$ to a uniform distribution of frequencies between 250–650 Hz, a Kolmogorov-Smirnov test (e.g., Eadie et 1971) can exclude a uniform distribution at only the $\sigma$ ) confidence level."85 It is interesting to uote that the recent report of a oossible ~[00 Tz burst oscillation from the 101 Iz musar SAN 3658 (n t Zaud et al., It is interesting to note that the recent report of a possible $\approx 400$ Hz burst oscillation from the 401 Hz pulsar SAX $-$ 3658 (in 't Zand et al.86" 2001) would nake the Migs, distribution even more consistent with a uuiforii distribution (excluded at ouly the 0.90 or confidence level). so the putative transition would have to © Correspondingly sharper."," 2001) would make the $\nu_{\rm burst}$ distribution even more consistent with a uniform distribution (excluded at only the $\sigma$ or confidence level), so the putative transition would have to be correspondingly sharper."87 We have listed a few additional propertics of these LAINBs in Table Ἐν., We have listed a few additional properties of these LMXBs in Table \ref{sum}.88 Neither the activity level nor the lone- average accretion rate <AP>. as determined from jicarlv 5 vears of data from the AAILSky Monitor (Levine ct al.," Neither the activity level nor the long-term average accretion rate $<\dot M>$, as determined from nearly 5 years of data from the All-Sky Monitor (Levine et al."89 1996). appears to © correlated with the frequencies of the burst oscillations.," 1996), appears to be correlated with the frequencies of the burst oscillations."90 Fast oscillations. are observed iu both ransicut and N-1)) aud persistent (c.e.. 53) sources. as well as from both low <AT> and hieh <M> sources.," Fast oscillations are observed in both transient and ) and persistent (e.g., ) sources, as well as from both low $<\dot M>$ and high $<\dot M>$ sources."91 Orbital periods are measured or ouly {| of the 9 sources. and range frou 0.81 to 19 tours.," Orbital periods are measured for only 4 of the 9 sources, and range from 0.81 to 19 hours."92 It is apparent that these burst oscillation sources are an inhomogeneous eroup. Which makes measurements of oscillations from other sources hiehllv desirable.," It is apparent that these burst oscillation sources are an inhomogeneous group, which makes measurements of oscillations from other sources highly desirable."93 We feel that the most likely explanation for the observed correlations is that the burst properties chanee differeutlv as a function of AL in fast and slow sources., We feel that the most likely explanation for the observed correlations is that the burst properties change differently as a function of $\dot M$ in fast and slow sources.94 AN-rayv burst theory predicts that radius expansion should occur ouly at low AM (Fujimoto. Tanawa. Mivaji 1981: Avasli Joss 1982).," X-ray burst theory predicts that radius expansion should occur only at low $\dot M$ (Fujimoto, Hanawa, Miyaji 1981; Ayasli Joss 1982)."95 This agrees with observations of the slow oscillator (Franco 2000: van Straaten et al., This agrees with observations of the slow oscillator (Franco 2000; van Straaten et al.96 2000). but does not appear to hold true for the fast oscillators citepiuiunü0.. (Atwakamietal.1980)... aud (vanderKlisetal.1990).," 2000), but does not appear to hold true for the fast oscillators \\citep{mun00}, \citep{mur80}, and \citep{vdk90}."97 Tf oscillatious ouly appear at high AT (as sugeested by Franco 2001). then they would indeed be associated with radius expansion in the fast sources. but not the slow sources.," If oscillations only appear at high $\dot M$ (as suggested by Franco 2001), then they would indeed be associated with radius expansion in the fast sources, but not the slow sources."98 Furthermore. Bildsten (2000) has sueeested that some mechanism acts d these latter sources. to coufine the accreted material such that the focal AL can decrease even as the elobal AL increases.," Furthermore, Bildsten (2000) has suggested that some mechanism acts in these latter sources to confine the accreted material such that the $\dot M$ can decrease even as the global $\dot M$ increases."99 If this is true. such coufinement is somehow related to the higher frequency of the fast burst oscillations.," If this is true, such confinement is somehow related to the higher frequency of the fast burst oscillations."100the spectral range is larger than the planet size so that the speckle pattern associated to the star can be reconstructed and eliminated using regions unaffected by the planet image.,the spectral range is larger than the planet size so that the speckle pattern associated to the star can be reconstructed and eliminated using regions unaffected by the planet image.101 Differently from the MDI described in the previous section. no assumption about the spectra of the companion objects is Spectral deconvolution should offer some advantage over the differential imaging approach. at least outside the BR. because it uses the companion spectrum as a whole.," Differently from the MDI described in the previous section, no assumption about the spectra of the companion objects is Spectral deconvolution should offer some advantage over the differential imaging approach, at least outside the BR, because it uses the companion spectrum as a whole."102 The value of the the SPHERE IFS BR ts around 0.20 aresee for the Y-J- and about 0.12 arcsec for the Y-H-mode., The value of the the SPHERE IFS BR is around 0.20 arcsec for the Y-J-mode and about 0.12 arcsec for the Y-H-mode.103 The procedure we followed is composed of four steps: In general. we assume that observations are done with the field fixed with respect to the IFU.," The procedure we followed is composed of four steps: In general, we assume that observations are done with the field fixed with respect to the IFU."104 In this case. the pupil rotates with time on an alt-az telescope. a typical value being 30° over a | hour exposure time.," In this case, the pupil rotates with time on an alt-az telescope, a typical value being $30^{\circ}$ over a 1 hour exposure time."105 In thisframework?.. angular differential imaging (ADI) can be applied to reduce the speckle noise further.," In this, angular differential imaging (ADI) can be applied to reduce the speckle noise further."106 Various codes have been written to perform ADI on real images (see Maroisetal. 2006))., Various codes have been written to perform ADI on real images (see \citealt{Ma06a}) ).107" Here. we considered a variant of this method that we defined as azimuthal filtering Cazimuthal"". meaning along ares at à constant radius)."," Here, we considered a variant of this method that we defined as azimuthal filtering (”azimuthal”, meaning along arcs at a constant radius)."108 This procedure is composed of the following steps: While this procedure does not completely eliminate the impact of static speckles. it also works well for quasi-static speckles. which are speckles having a lifetime longer than field rotation but shorter than the total exposure time.," This procedure is composed of the following steps: While this procedure does not completely eliminate the impact of static speckles, it also works well for quasi-static speckles, which are speckles having a lifetime longer than field rotation but shorter than the total exposure time."109 In this section. we review the most important. results obtained from our simulations., In this section we review the most important results obtained from our simulations.110 As said in previous sections. We eXpect a significant improvement in the contrast using the MDI method compared to a simple S-SDI. when exploiting all of the many monochromatic images provided by an IPS.," As said in previous sections, we expect a significant improvement in the contrast using the MDI method compared to a simple S-SDI, when exploiting all of the many monochromatic images provided by an IFS."111 In particular we expect that the contrast scales with the square root of the number of independent single differences that we can realize when using the whole spectrum., In particular we expect that the contrast scales with the square root of the number of independent single differences that we can realize when using the whole spectrum.112 Α΄ further, A further113which was part of a entirely different object at each of a series of earlier redshifts.,which was part of a entirely different object at each of a series of earlier redshifts.114" We refer to this fraction as the “accreted fraction” and we then estimate the distribution of accreted fraction for the halos in each of our four mass ranges and for accretion since redshifts of 0.5, 1, 2 and 3."," We refer to this fraction as the “accreted fraction” and we then estimate the distribution of accreted fraction for the halos in each of our four mass ranges and for accretion since redshifts of 0.5, 1, 2 and 3."115 For the purposes of this calculation we define the “core” of each z0 halo to consist of the 100 most bound particles in its main subhalo., For the purposes of this calculation we define the “core” of each $z=0$ halo to consist of the 100 most bound particles in its main subhalo.116 Each particle is considered to be part of a disjoint object at some earlier redshift (and thus part of the accreted fraction) if at that time it was more than 100h~'kpce (physical) from the centre of the largest progenitor of the core (defined by calculating the mutual gravitational potential of all 100 core particles and picking the particle with the lowest value)., Each particle is considered to be part of a disjoint object at some earlier redshift (and thus part of the accreted fraction) if at that time it was more than $100h^{-1}$ kpc (physical) from the centre of the largest progenitor of the core (defined by calculating the mutual gravitational potential of all 100 core particles and picking the particle with the lowest value).117 The results of this exercise are shown in Fig. 5.., The results of this exercise are shown in Fig. \ref{fig:fig5}.118 Each panel refers to one of our ranges of halo mass and contains, Each panel refers to one of our ranges of halo mass and contains119Whilst observations of powerful. racto-loud Active Galactic Nuelei (AGN) were an early. probe of the distant. Universe summary). starburst galaxies are three or more orders of magnitudes. less luminous at racio wavelengths and hence dillieult to observe at large distances.,"Whilst observations of powerful, radio-loud Active Galactic Nuclei (AGN) were an early probe of the distant Universe , starburst galaxies are three or more orders of magnitudes less luminous at radio wavelengths and hence difficult to observe at large distances."120 However the deepest. radio surveys at GCOLIZz now reach an rms below 10μονete)., However the deepest radio surveys at GHz now reach an rms below $10\uJy$.121 These deep radio observations reveal a (very well characterised) up-turn in the [Euclidean normalised sources counts below mmy above that predicted from the extrapolation of the AGN counts measured at brighter [ux densities., These deep radio observations reveal a (very well characterised) up-turn in the Euclidean normalised sources counts below mJy above that predicted from the extrapolation of the AGN counts measured at brighter flux densities.122 This up-turn has been attributed to the emergence of a star forming galaxy (SECO population. requiring strong evolution of the SEC radio luminosity function.2007).. although some authors argue that there is a significant. contribution due to relatively weak," This up-turn has been attributed to the emergence of a star forming galaxy (SFG) population, requiring strong evolution of the SFG radio luminosity function, although some authors argue that there is a significant contribution due to relatively weak"123Supermassive black holes have been couvincinely detected in the centers of some nearby galaxies (οποιον Richstone 1995).,Supermassive black holes have been convincingly detected in the centers of some nearby galaxies (Kormendy Richstone 1995).124 I&ormieudy: Gebhardt (2001. hereafter IKCG2001) eave a comprehleusive review of receut black hole discoveries made with theTelescope IST).," Kormendy Gebhardt (2001, hereafter KG2001) gave a comprehensive review of recent black hole discoveries made with the (HST)."125 A tight correlation between black hole mass auc bulge velocity dispersion is confirmed., A tight correlation between black hole mass and bulge velocity dispersion is confirmed.126 They noticed that black hole mass correlates with the luminosity of “pseudobulges” in disk ogalaxies. elliptical galaxies aud the bulges of disk. ealaxies. but is independent of the Iuuiuositv of galaxy disks.," They noticed that black hole mass correlates with the luminosity of “pseudobulges” in disk galaxies, elliptical galaxies and the bulges of disk galaxies, but is independent of the luminosity of galaxy disks."127 The correlation stronglv suggests a causal connection between t1e formation aud evolution of the black hole and the bulge but the nature of this connection τομας uuknowl., The correlation strongly suggests a causal connection between the formation and evolution of the black hole and the bulge but the nature of this connection remains unknown.128 It is interesting to check whether this correlation still applies to both larger aud simaller spherical systems., It is interesting to check whether this correlation still applies to both larger and smaller spherical systems.129 We may even speculate whether the correlation extends to systems with dispersion as ow as that of elobular clusters. since the elobular clusters are also sclferavitating splerical svsteus simular to galactic bulges.," We may even speculate whether the correlation extends to systems with dispersion as low as that of globular clusters, since the globular clusters are also self-gravitating spherical systems similar to galactic bulges."130 Using the AIpy 0 correlation. a crude estimate for the possible black hole mass in elolnlar clusters can be obtained.," Using the $_{BH}$ – $\sigma$ correlation, a crude estimate for the possible black hole mass in globular clusters can be obtained."131" For a typical massive globular cluster having a dispersion of the order of 10 l a black hole mass of about «10? NINE, is expected."," For a typical massive globular cluster having a dispersion of the order of 10 $^{-1}$, a black hole mass of about $\times\,10^3$ $_\odot$ is expected."132 In certain galaxies. the 1ack hole directly reveals itself through its associated accretion aud activity.," In certain galaxies, the black hole directly reveals itself through its associated accretion and activity."133 Such activity can hardly happen in elobulay clusters due to shortage of eas., Such activity can hardly happen in globular clusters due to shortage of gas.134 However. receut. N-ray. observations of several starburst galaxies (6.9. M82. NGC 1038/39) reveal the existence of iutermiediate-niass black hole im starburst regions which are related to the formation of elolar clusters (INiuucet et al.," However, recent X-ray observations of several starburst galaxies (e.g. M82, NGC 4038/39) reveal the existence of intermediate-mass black hole in starburst regions which are related to the formation of globular clusters (Kaaret et al."135 2001: Matsiunioto et al., 2001; Matsumoto et al.136 2001: Fabbiano. Zezas. Murray. 2001).," 2001; Fabbiano, Zezas, Murray 2001)."137 The preseuce of a black hole iu à globular cluster affects the stellar deusity profile aud the central stellar ΠΕ, The presence of a black hole in a globular cluster affects the stellar density profile and the central stellar dynamics.138 With tιο dynamical detection sensitivity currently available. black hole mass as low as 1000 AL. can hardly be ideuti&ied (wan der Marel 2001).," With the dynamical detection sensitivity currently available, black hole mass as low as 1000 $_\odot$ can hardly be identified (van der Marel 2001)."139 So far. the ouly example was presented by Ceblardt et al. (," So far, the only example was presented by Gebhardt et al. ("1402000) for MI5 wich Ίαν possibly host a black hole of the order of 10° ML...,2000) for M15 which may possibly host a black hole of the order of $^3$ $_\odot$.141rates in the universe (Per Fall 1995).,rates in the universe (Pei Fall 1995).142 LW the observed metallicities in QSO absorption systems are common. then their interpretation as galactic disks implies that substantial evolution has taken place since z~3.," If the observed metallicities in QSO absorption systems are common, then their interpretation as galactic disks implies that substantial evolution has taken place since $z\sim 3$."143 Lf the quantity of dust on cosmic scales also follows such a trend. then one niv expect the ellects of obscuration to high redshift to be reduced relative to non-evolving predictions.," If the quantity of dust on cosmic scales also follows such a trend, then one may expect the effects of obscuration to high redshift to be reduced relative to non-evolving predictions."144 In this paper. we continue to model the effects. of intervening galactic dust on the background. universe at optical wavelengths using a more generalised model where the dust. content evolves.," In this paper, we continue to model the effects of intervening galactic dust on the background universe at optical wavelengths using a more generalised model where the dust content evolves."145 We explore the effects of our predictions on quasar number counts in the optical and their implication for quasar evolution., We explore the effects of our predictions on quasar number counts in the optical and their implication for quasar evolution.146 This paper is organised as follows: The next section briellv describes the generalised model and. assumptions., This paper is organised as follows: The next section briefly describes the generalised model and assumptions.147 Section 3. describes the model parameters and their values assumed in our calculations.," Section \ref{mprev}148 describes the model parameters and their values assumed in our calculations."149 Mocdel results are presented and analysed in Section 4.., Model results are presented and analysed in Section \ref{rests}.150 Implications on quasar statistics and evolution are discussed in Section 5.., Implications on quasar statistics and evolution are discussed in Section \ref{QSOev}.151 Other implications are discussed in Section G6 and. all results are summarised in Section 7.., Other implications are discussed in Section \ref{evmodd} and all results are summarised in Section \ref{concfour}.152 Unless otherwise stated. all caleulations assume a Friedmann cosmology with qa=0.5. and Hubble parameter hoy=1 where Ly=50bs5kmsAlpe," Unless otherwise stated, all calculations assume a Friedmann cosmology with $q_{0}=0.5$, and Hubble parameter $h_{50}=1$ where $H_{0}=50h_{50}\, \rm km\,s^{-1}\,Mpc^{-1}$."153 We caleulate the probability distribution in total dust optical depth from model ealaxics along any random line-ol-sight as a function of redshift by following the method oesented in Masci Webster (1995)., We calculate the probability distribution in total dust optical depth from model galaxies along any random line-of-sight as a function of redshift by following the method presented in Masci Webster (1995).154 his was based on a method introduced by Wright (1986) which did not include any ellects of evolution with redshift., This was based on a method introduced by Wright (1986) which did not include any effects of evolution with redshift.155 Llere we &eneralise his model by considering the possibility. of evolution. in he dust. properties of galaxies., Here we generalise this model by considering the possibility of evolution in the dust properties of galaxies.156 In the discussion below zux unless otherwise indicated. by a subscript. we celine 7 to » the total optical depth encountered by emitted. photons and measured. in an (cllectively a À= 4400A)).," In the discussion below and unless otherwise indicated by a subscript, we define $\tau$ to be the total optical depth encountered by emitted photons and measured in an (effectively at $\lambda=4400$ )."157 We assume the following properties for individua absorbing galaxies., We assume the following properties for individual absorbing galaxies.158 Following previous studies (eg., Following previous studies (eg.159 Wrieh 1986. Leister Ostriker LOSS). we model galaxies as randomly. tilte exponential disks. where the optical depth through a [ace-on disk decreases exponentially with distance r from the center: ry ds à characteristic radius and. 7o( the value of τ through the center of the galaxy (r=0).," Wright 1986, Heisler Ostriker 1988), we model galaxies as randomly tilted exponential disks, where the optical depth through a face-on disk decreases exponentially with distance $r$ from the center: $r_{0}$ is a characteristic radius and $\tau_{0}(z)$, the value of $\tau$ through the center of the galaxy $(r=0)$."160 The redshift dependence o£ 7) is due to the increase in absorber rest fraume frequeney with redshift., The redshift dependence of $\tau_{0}$ is due to the increase in absorber rest frame frequency with redshift.161 Since we wish to model the observed. B-band. optical depth to 286. we require an extinction law £(A)=rfTg that extends to wavelengths. of ~630..," Since we wish to model the observed $B$ -band optical depth to $z\simlt6$, we require an extinction law $\xi(\lambda)\equiv\tau_{\lambda}/\tau_{B}$ that extends to wavelengths of $\sim630$."162. We use the analytical fit for €(A) as derived by Pei (1992) for cilfuse galactic dust in the range 500ASAS25m. The optical depth in an observers frame through an absorber at redshift z (Tu(2) in equation 1)) can be written: where 7g is the D-band optical depth through the center of an individual galactic absorber., We use the analytical fit for $\xi(\lambda)$ as derived by Pei (1992) for diffuse galactic dust in the range $500{\rm\AA}\simlt\lambda\simlt25\mu$ m. The optical depth in an observer's frame through an absorber at redshift $z$ $\tau_{0}(z)$ in equation \ref{expr}) ) can be written: where $\tau_{B}$ is the $B$ -band optical depth through the center of an individual galactic absorber.163 Equation (2)) must be mocified if the dust content in cach galaxy is assumed to evolve with cosmic time., Equation \ref{tz}) ) must be modified if the dust content in each galaxy is assumed to evolve with cosmic time.164 The optical depth seen through the center of a single absorber at some redshift. τος). will depend on the quantity of dust. formed roni past stellar processes.," The optical depth seen through the center of a single absorber at some redshift, $\tau_{0}(z)$, will depend on the quantity of dust formed from past stellar processes."165 Por simplicity. we assume all galaxies form simultaneously. maintain a constant space clensity. and increase in dust content at a rate that is uniform hroughout.," For simplicity, we assume all galaxies form simultaneously, maintain a constant space density, and increase in dust content at a rate that is uniform throughout."166 We also assume no evolution in the dust. law £(A) with redshift., We also assume no evolution in the dust law $\xi(\lambda)$ with redshift.167 Even though a lower mean metallicity at ugh redshift may suggest a dillerent wavelength dependence or the dust law. there is no evidence from local observations of the dilfuse ISM to support this view (eg.," Even though a lower mean metallicity at high redshift may suggest a different wavelength dependence for the dust law, there is no evidence from local observations of the diffuse ISM to support this view (eg."168 Whittet 1992)., Whittet 1992).169 We parameterise evolution in dust content by following simulations of the formation of heavy metals in the cold dark matter scenario. of. galaxy formation. by Blain Longair (1993a. 1993b).," We parameterise evolution in dust content by following simulations of the formation of heavy metals in the cold dark matter scenario of galaxy formation by Blain Longair (1993a, 1993b)."170 These authors assume that galaxies orm bv the coalescence of gaseous. protocloucs through ucrarchical clustering as prescribed. by Press Schechter (1974)., These authors assume that galaxies form by the coalescence of gaseous protoclouds through hierarchical clustering as prescribed by Press Schechter (1974).171 A fixed fraction of the mass involved in each merger event is converted. into stars. leading to the formation of wavy metals and. dust.," A fixed fraction of the mass involved in each merger event is converted into stars, leading to the formation of heavy metals and dust."172 Lt was assumed that the energy iberateck through stellar. radiation. was absorbed by dus and. re-raciated into the far-infrared., It was assumed that the energy liberated through stellar radiation was absorbed by dust and re-radiated into the far-infrared.173 “Phey found that such radiation can contribute substantially to the far-inlrarec vackerounc intensity from which they use to constrain a model for the formation of heavy metals as a function of cosmic time., They found that such radiation can contribute substantially to the far-infrared background intensity from which they use to constrain a model for the formation of heavy metals as a function of cosmic time.174 Their models show that the comoving density of heavy metals created by some redshift z. given that star formation commenced at some epoch ssp follows the form We assume that a fixed. fraction of heavy metals condense into dust. grains so that the comoving density in dust. Qu(2). follows a similar dependence as equation (3)).," Their models show that the comoving density of heavy metals created by some redshift $z$, given that star formation commenced at some epoch $z_{SF}$ follows the form We assume that a fixed fraction of heavy metals condense into dust grains so that the comoving density in dust, $\Omega_{d}(z)$, follows a similar dependence as equation \ref{omegaZ}) )."175" The density in dust relative to the present.closure density in my exponential disks per unit comoving volume is given by where p,=BUG/SxC and M, is the dust mass in a single exponential disk.", The density in dust relative to the presentclosure density in $n_{0}$ exponential disks per unit comoving volume is given by where $\rho_{c}=3H_{0}^{2}/8\pi G$ and $M_{d}$ is the dust mass in a single exponential disk.176 This mass can be estimated. using 150.17-24 from Spitzer (1978) where the total density in dust. fa ds related to the extinction ely along a path length £ in kpe by," This mass can be estimated using Eq.7-24 from Spitzer (1978) where the total density in dust, $\rho_{d}$ , is related to the extinction $A_{V}$ along a path length $L$ in kpc by"177above. this requires the IIT disk to be inhereutly elougate with an axis ratio of at least 2:1.,"above, this requires the HI disk to be inherently elongated with an axis ratio of at least 2:1."178 Such a highly nou circular disk would be very uuusual., Such a highly non circular disk would be very unusual.179" Further. the imucr regions of the ealaxy (νο, the distance at which the rotation curve of Carignanctal.(1990) ooeaks) will complete one rotation in ~ NO Ann. while the rotation period at the edge of the disk is ~ 1 Cor."," Further, the inner regions of the galaxy (i.e. the distance at which the rotation curve of \cite{carignan90} peaks) will complete one rotation in $\sim$ 80 Myr, while the rotation period at the edge of the disk is $\sim$ 1 Gyr."180 Houce. his differeutial rotation will wine up any clongation in the| disk on a timescale that is short compared to the age of he galaxy.," Hence, this differential rotation will wind up any elongation in the disk on a timescale that is short compared to the age of the galaxy."181 Alternatively. as first proposed by. Loetal.(1993).. the observed velocity field of GRS could also be the result of radial mo 1 the eas Le expansion or contraction.," 	 Alternatively, as first proposed by \cite{lo93}, the observed velocity field of GR8 could also be the result of radial motions in the gas i.e expansion or contraction."182 Since t the inclination of tje galaxy ΕΕ it is ot possible to distinguish between nsvard and outware motions.," Since the sign of the inclination of the galaxy is unknown, it is not possible to distinguish between inward and outward radial motions."183 Large scale bulk radial gas flows. al ifficult to understaxl in the context of normal spiral galaxies. could nonetheless be plausible iu siuall ea ike (115.," Large scale bulk radial gas flows, although difficult to understand in the context of normal spiral galaxies, could nonetheless be plausible in small galaxies like GR8."184 Iu models of dwart ealaxy formation a lon. enerev iyectce into the ISAL from stellar wiids and supernova explosions could daive significant expansive motions m the gasο," In models of dwarf galaxy formation and evolution, energy injected into the ISM from stellar winds and supernova explosions could drive significant expansive motions in the gas."185 Iu fact. in such inodels. « axies below a critical halo circular velocity of ~ LOO lare expected to lose a sjeuificaut fraction of their ISM. from the first burst of star formation (e.g. Dekel&Silk(1986).. 2)).," In fact, in such models, dwarf galaxies below a critical halo circular velocity of $\sim$ 100 are expected to lose a significant fraction of their ISM from the first burst of star formation (e.g. \cite{dekel86}, \cite{efstathiau00}) )."186 Expulsion of the ISM because of the energy input frou superiovae is also postulated as a possible mechlauisui for produci dwarf elliptical galaxies from eas rich progenitors (6.8B. Aliralda-Exscude Rees 1997)., Expulsion of the ISM because of the energy input from supernovae is also postulated as a possible mechanism for producing dwarf elliptical galaxies from gas rich progenitors (e.g. Miralda-Escude Rees 1997).187 Observatiounallv. outflows of ionized material have been seen iu star bursting (wart ealaxies (e.gB. Alay al.," Observationally, outflows of ionized material have been seen in star bursting dwarf galaxies (e.g. Marlowe et al."188 1995)., 1995).189" Of course. these models deal with the expulsion of hot superuovae heated eas, where as. in tUs instance we are dealing with cold neutral gas."," Of course, these models deal with the expulsion of hot supernovae heated gas, where as, in this instance we are dealing with cold neutral gas."190" For sufficiently small galaxies however. inodoel calculations (Ferrara Tolstoy 2000) suggest that the ISM could be “blown away"" ie. that he züuubieut medi could be swept oit bv the hot expanding superuovae superbubbles."," For sufficiently small galaxies however, model calculations (Ferrara Tolstoy 2000) suggest that the ISM could be “blown away” i.e. that the ambient medium could be swept out by the hot expanding supernovae superbubbles."191" This coutrast to the situation iu slightly larger galaxies where there is mstead a ""blow ot ie. the supernovae heated hot eas nerces the πι disk material aud escapes iuto the iutergalactic nediuu.", This is in contrast to the situation in slightly larger galaxies where there is instead a “blow out” i.e. the supernovae heated hot gas pierces the ambient disk material and escapes into the intergalactic medium.192 Althougho a situation where the entire ISM is expaudiug outwards has not vet been observed. expansio1i of the neutral ISAL on simaller scales has beci observed in a muuber of starbursting cwarf galaxies.," Although a situation where the entire ISM is expanding outwards has not yet been observed, expansion of the neutral ISM on smaller scales has been observed in a number of starbursting dwarf galaxies."193 81ch expawine III supershells have been secu in. for exame. Holubere II (Puche et al.," Such expanding HI supershells have been seen in, for example, Holmberg II (Puche et al."194 1992). IC 2571 (Walter Brinks 1999) aud Hohluberg I (Ott et al.," 1992), IC 2574 (Walter Brinks 1999) and Holmberg I (Ott et al."195 2001)., 2001).196 One should note lOWOCVOT. that while the observational evidence for expanding shells in the ISAL of these galaxies is reasoably eood. the mechanism by which these shells have heen created is less well established.," One should note however, that while the observational evidence for expanding shells in the ISM of these galaxies is reasonably good, the mechanism by which these shells have been created is less well established."197 Stewart&Walter(2000) find that the eiut supershell iu IC 2!f lis probably driven by energv input from supernovac. while Rhodeetal.(1999).. despite deep optical imaging. do uot find the star clusters that would be expected to be present iu this scenario. at the centers of the IIT holes iu Wolubere IT Tn light of the above discussion. aud the ougoing star formation in CRS. if mav be reasonable to assume that there are large scale racial flows in the galaxy.," \cite{stewart00} find that the giant supershell in IC 2574 is probably driven by energy input from supernovae, while \cite{rhode99}, despite deep optical imaging, do not find the star clusters that would be expected to be present in this scenario, at the centers of the HI holes in Holmberg II 	In light of the above discussion, and the ongoing star formation in GR8, it may be reasonable to assume that there are large scale radial flows in the galaxy."198 If we make this assumption. then the line of sight velocity Vj. is related to the circular velocity Vi; aud the racial velocity Vi by the relation where Vau is the svsteiie velocity. / is the iuclinatiou anele. and o is the azinnthal angle in the plane of the ealaxy (ο=0 along he receding half of the kiueimatical niajor axis)," If we make this assumption, then the line of sight velocity $V_{\rm los}$ is related to the circular velocity $V_{\rm rot}$ and the radial velocity $V_{\rm exp}$ by the relation where $V_{\rm sys}$ is the systemic velocity, $i$ is the inclination angle, and $\phi$ is the azimuthal angle in the plane of the galaxy $\phi = 0$ along the receding half of the kinematical major axis)."199 The sin such aodel is oue iu which there is no rotation., The simplest such model is one in which there is no rotation.200 [, Fig. \ref{fig:model}[ [201C] shows such a model for CGRea.,C] shows such a model for GR8.202" Iu this model ‘huation angle of the disk is taken to be 20"" aud the posiion angle 350"".", In this model the inclination angle of the disk is taken to be $20^o$ and the position angle $350^o$.203 These values were chosen to mate served velocity field. aud are in good agreemen he values expected from the cllipse fitting to the outer III contours (see Sect. 3.1:," These values were chosen to match the observed velocity field, and are in good agreement with the values expected from the ellipse fitting to the outer HI contours (see Sect. \ref{ssec:HI_dis};"204 note hat in the case of radial motion. the velocity eracdieut is mmasxinuun along the morpiological minor axis aud nof he morphological major axis).," note that in the case of radial motion, the velocity gradient is maximum along the morphological minor axis and not the morphological major axis)."205 The expansion is taken o be centered ou the kinematical center obtained from he velocity field. and not the morphological ceuter.," The expansion is taken to be centered on the kinematical center obtained from the velocity field, and not the morphological center."206 Since radial notions are probably driven by energy from star ornation. if is uot necessary for the expansion ceuter to )o comcideut with the geometric ceuter oftle ITI disk.," Since radial motions are probably driven by energy from star formation, it is not necessary for the expansion center to be coincident with the geometric center of the HI disk."207" The expansion Vi, Is assiuned to be aziuithally sviuuuctric. and its variation with ealacto-ceutric distance is as shown iu Fig. S|["," The expansion $V_{\rm exp}$ is assumed to be azimuthally symmetric, and its variation with galacto-centric distance is as shown in Fig. \ref{fig:model}[ ["208F|.,F].209 The rise in the expansion velocity till the radius R1 produces the parallel isovelocity contours iu the central regions of the galaxy. the fall after RL produces he closed οςtours.," The rise in the expansion velocity till the radius R1 produces the parallel isovelocity contours in the central regions of the galaxy, the fall after R1 produces the closed contours."210 The rise in the expansion curve. frou. radius R2 ouwards. produces the kinks seen im the eastern and western edges of the velocity feld.," The rise in the expansion curve, from radius R2 onwards, produces the kinks seen in the eastern and western edges of the velocity field."211 This particular onu of expansion was chosen because it provides a eood natch to the observed velocity field., This particular form of expansion was chosen because it provides a good match to the observed velocity field.212 While it is possible hat detailed eas dynamic modeling might be able to reproduce this curve. we have uot attempted any such uodeliug in this paper.," While it is possible that detailed gas dynamic modeling might be able to reproduce this curve, we have not attempted any such modeling in this paper."213 While a pure expansion model does produce the closed. coutours aloug the morphological münor axis. it does not produce the uetres iu the velocity field noted iu Sect. 3.2.," 	While a pure expansion model does produce the closed contours along the morphological minor axis, it does not produce the asymmetries in the velocity field noted in Sect. \ref{ssec:HI_Kin}."214 next qmost natural model to trv is lence one in which here is also some rotation., The next most natural model to try is hence one in which there is also some rotation.215" A velocity field with the sane Vag, as before. but with non zero Vi is shown in Fig. ΒΙ"," A velocity field with the same $V_{\rm exp}$ as before, but with non zero $V_{\rm rot}$ is shown in Fig. \ref{fig:model}[ ["216ΟΙ.,D].217 The rotation curve has been axstuned to be near: it rises fo a iuaxinnuu of 6 tat the edge of he ealaxy., The rotation curve has been assumed to be linear; it rises to a maximum of 6 at the edge of the galaxy.218 A linearly rising rotation curve was chosen because this form of rotation curve is typical of dwart galaxies., A linearly rising rotation curve was chosen because this form of rotation curve is typical of dwarf galaxies.219 Other types of rotation curves. Le. a coustant rotation curve. a Brandt and an exponential curve Gehiüch are seldom observed for dwarf ealaxies) were also tried.," Other types of rotation curves, i.e. a constant rotation curve, a Brandt and an exponential curve (which are seldom observed for dwarf galaxies) were also tried."220 While a constant rotation curve eives a poor fit to the data. Drandt and exponeutial curves do not provide a better fit to the observed velocity," While a constant rotation curve gives a poor fit to the data, Brandt and exponential curves do not provide a better fit to the observed velocity"221The chromospheric aud coronal activity of coo cava stars like the Sun is thought to arise from the interaction of stellar maguctic fields with differential rotation ane convection.,The chromospheric and coronal activity of cool dwarf stars like the Sun is thought to arise from the interaction of stellar magnetic fields with differential rotation and convection.222 Since significant convection zones make their appearance along the main sequence in late spectral class A. the inch debated turnon of such activity shoul occur at about the same spectral type. althoueh the precise dependence is uot well known.," Since significant convection zones make their appearance along the main sequence in late spectral class A, the much debated turn–on of such activity should occur at about the same spectral type, although the precise dependence is not well known."223 Ou the other hai sjenificautf radiatively driven winds (the imstabilities of which are thought to be responsible for the XNταν emission in O and carly Dtype stars) are not present bevolk spectral tvpe ~ Bl., On the other hand significant radiatively driven winds (the instabilities of which are thought to be responsible for the X–ray emission in O– and early B–type stars) are not present beyond spectral type $\sim$ B4.224 Thus in the BSAS spectral range a lack ofX.ταν emission is theoretically “expected”., Thus in the B5–A5 spectral range a lack of X–ray emission is theoretically “expected”.225 In spite of the observational efforts. no conclusive evideuce of Xrav cluission from BSAD type stars has been found: in fact in most of the observed cases the emission is thought to cole not from the carly type star itself. but from a cooler colupalion or from a uearby star (Schutt νήμα 1993: Caené Caillault 1991: Stauffer ot al.," In spite of the observational efforts, no conclusive evidence of X--ray emission from B5–A5 type stars has been found; in fact in most of the observed cases the emission is thought to come not from the early type star itself, but from a cooler companion or from a nearby star (Schmitt Kürrster 1993; Gagné Caillault 1994; Stauffer et al."226 1991: Stern et al., 1994; Stern et al.227 1995)., 1995).228 Few interesting cases have been found bx Schiuitt et al. (, Few interesting cases have been found by Schmitt et al. (2291993) and Derghóffer Schinitt (1991). which detected N-rav emission from both compoucuts iu sone Visual binaries formed by a BSAS primary star and a cooler compawion.,"1993) and Berghöffer Schmitt (1994), which detected X-ray emission from both components in some visual binaries formed by a B5–A5 primary star and a cooler companion."230 Stimgeut upper limits have been determuned for the Xray cussion of some well studied Atype stars; down to a huuinosity of Ly~3.5«107 | for the prototypical Atype star Vega (Sclunitt 1997).," Stringent upper limits have been determined for the X--ray emission of some well studied A–type stars, down to a luminosity of $L_{X} \sim 3.5 \times 10^{25}$ $^{-1}$ for the prototypical A–type star Vega (Schmitt 1997)."231 This secs to indicate that the coronae surrounding these stars (f may exist at all) iuust be very differcut from those surrounding cooler stars., This seems to indicate that the coronae surrounding these stars (if may exist at all) must be very different from those surrounding cooler stars.232 They do uot have massive winds. ucither have deep chough convective zoue for an effective dyuame activity.," They do not have massive winds, neither have deep enough convective zone for an effective dynamo activity."233 However. in all the cases reported above. onlv siuall suuples of late Bo carly Aotype stars were used.," However, in all the cases reported above, only small samples of late B– early A–type stars were used."234 Recently. Simon et al. (," Recently, Simon et al. ("2351995) tried to overcome this problenà bv using pointed ROSAT PSPC observations to study the Nταν properties of a sample of 71 Atype stars.,1995) tried to overcome this problem by using pointed ROSAT PSPC observations to study the X–ray properties of a sample of 74 A–type stars.236 They detected Norav cussion in 9 late A and 10 carly Atype stars., They detected X–ray emission in 9 late A– and 10 early A--type stars.237 Of the latter. 5 were confirmed double aud 5 were not known to be double but further optical study are necessary in order to determine if they are really single stars.," Of the latter, 5 were confirmed double and 5 were not known to be double but further optical study are necessary in order to determine if they are really single stars."238 Ou the other haud convincing evidence of chromospheric and Xrav cussion has been detected iu stars as early as spectral type AT (Schinitt et al., On the other hand convincing evidence of chromospheric and X–ray emission has been detected in stars as early as spectral type A7 (Schmitt et al.239 1985: Simon Landsman 19901)., 1985; Simon Landsman 1991).240 Recently Simou Landsman (1997) reported the detection of claomospheric emission iu IIST/GIRS spectra of the Al star 7° Exi that secus to be the hottest main sequence star known to have a chromosphere and thus an outer convection zone., Recently Simon Landsman (1997) reported the detection of chromospheric emission in HST/GHRS spectra of the A4 star $\tau^{3}$ Eri that seems to be the hottest main sequence star known to have a chromosphere and thus an outer convection zone.241 Activity indicators in ATF5 type stars seem to be independent ou rotation. while the coronal Nrav cussion. as measured relatively το chromospleric cussion. ids deficient 1 colmpared with latertype stars (Pallavicini et al.," Activity indicators in A7–F5 type stars seem to be independent on rotation, while the coronal X–ray emission, as measured relatively to chromospheric emission, is deficient if compared with later–type stars (Pallavicini et al."242 1981: Scehuutt et al., 1981; Schmitt et al.243 1985: Sinon Landsman 1991)., 1985; Simon Landsman 1991).244 The, The245"given the model parameters fy. e. (M,/L)g and dlogM/L)/dz which we abbreviate as £.","given the model parameters $f_*$ , $c$ , $(M_*/L)_0$ and $d\log(M/L)/dz$ which we abbreviate as $\bfxi$."246 Combining the (wo terms. we have the probability of the model filling the data D; for galaxy 7 In addition to the measurement errors listed in Table L.. we should also consider sources of svsteniatic errors.," Combining the two terms, we have the probability of the model fitting the data $D_i$ for galaxy $i$ In addition to the measurement errors listed in Table \ref{tab:tab1}, we should also consider sources of systematic errors."247" The essence of the method is to compare the mass inside (he Einstein ving M(«R,) toa virial mass estimate from the velocity dispersion o2/2/G.", The essence of the method is to compare the mass inside the Einstein ring $M(<R_e)$ to a virial mass estimate from the velocity dispersion ${\sigma}_v^2R/G$.248 We can identify five sources of svstematic errors., We can identify five sources of systematic errors.249 First. while there is little uncertainty in Mp. some of the mass may be projected surface density from either a parent group halo to which the lens belongs. or [rom another along the line of sight.," First, while there is little uncertainty in $M_E$, some of the mass may be projected surface density from either a parent group halo to which the lens belongs, or from another along the line of sight."250" The extra density. &=X/X,. in dimensionless units. modifies (he mass inside the Einstein radius by weREM... so we can think of its effects as a svstematic error in interpreting o, of e,=6,/2."," The extra density, $\kappa=\Sigma/\Sigma_c$ in dimensionless units, modifies the mass inside the Einstein radius by $\pi\kappa R_E^2 \Sigma_c$, so we can think of its effects as a systematic error in interpreting $\sigma_v$ of $\rm e_\sigma=\sigma_{\kappa}/2$."251" The Full probability distribution ol & is skewed to positive values (e.g. Takada&Ilamana 2003)). bul we will ignore this problem and assume 6,20.05 since the positive tail of the distribution is associated with detectable objects (galaxies and clusters)."," The full probability distribution of $\kappa$ is skewed to positive values (e.g. \citealt{th03}) ), but we will ignore this problem and assume $\sigma_{\kappa}\backsimeq 0.05$ since the positive tail of the distribution is associated with detectable objects (galaxies and clusters)."252 This svstematic error also affects. estimates of the mass-to-light ratios., This systematic error also affects estimates of the mass-to-light ratios.253 Second. there are 1—10 uncertainties in the galaxy effective radius measurements which contribute uncertainties of 0.5% to 5% to our interpretation of the velocity dispersion.," Second, there are $1-10\%$ uncertainties in the galaxy effective radius measurements which contribute uncertainties of $0.5\%$ to $5\%$ to our interpretation of the velocity dispersion."254 Third. the measured velocity dispersion is a Gaussian fit to the specirum. which is not identical to the rms velocity appearing in the Jeans equation (e.g. Dinnev&Tremaine 1957)).," Third, the measured velocity dispersion is a Gaussian fit to the spectrum, which is not identical to the rms velocity appearing in the Jeans equation (e.g. \citealt{bs87}) )."255 The difference can be estimated from the (vpical Gaussian-Hermite coefficients |;|=0.02 (Bender.Saglia&GerhardL994) as a fractional error in σι ol order νο=0.05 in (he velocity dispersion (e.g. vanderMarel.Dokkum 2003))., The difference can be estimated from the typical Gaussian-Hermite coefficients $|h_4|\backsimeq0.02$ \citep{bsg94} as a fractional error in $\sigma_v$ of order $\sqrt{6}|h_4|\backsimeq0.05$ in the velocity dispersion (e.g. \citealt{vf03}) ).256 Fourth. non-sphericitv. (somewhat to our surprise) leads (o negligible svstematic errors provided we use the intermediate scale length (the geometric mean of the semi-major and minor axes). al least in the limit of the tensor virial theorem.," Fourth, non-sphericity, (somewhat to our surprise) leads to negligible systematic errors provided we use the intermediate scale length (the geometric mean of the semi-major and minor axes), at least in the limit of the tensor virial theorem."257 It leads (ο large errors if any other scale length is used., It leads to large errors if any other scale length is used.258 Barnabe&Koopmans(2007) have taken the first steps towards removing these (wo dynamical problems. although they ave restricted to oblate Gwo-integral models which may not be appropriate for massive elliptical galaxies.," \citet{Barnabe07} have taken the first steps towards removing these two dynamical problems, although they are restricted to oblate two-integral models which may not be appropriate for massive elliptical galaxies."259 Finally. calibration errors in the velocity dispersions contribute Iractional errors of order 0.03 (see Dernardi 2003a)).," Finally, calibration errors in the velocity dispersions contribute fractional errors of order 0.03 (see \citealt{bernardi03a}) )."260 Combining all these contributions in quadrature. which corresponds (ο assuming a Gaussian model for each svstematic error. we estimate that the (wpical systematic uncertainty to interpreting the velocity dispersions is approximately 8% with the exact value depending on the uncertainties in (he effective radius.," Combining all these contributions in quadrature, which corresponds to assuming a Gaussian model for each systematic error, we estimate that the typical systematic uncertainty to interpreting the velocity dispersions is approximately $8\%$ with the exact value depending on the uncertainties in the effective radius."261 Our statistical methods are chosen so that we can understandthe homogeneityof the lens galaxies in either (heir evolution or their cdvnamical properties and estimate (heir average properties in the presence of inhomogeneities., Our statistical methods are chosen so that we can understandthe homogeneityof the lens galaxies in either their evolution or their dynamical properties and estimate their average properties in the presence of inhomogeneities.262 We will analvze (he results using two Davesian, We will analyze the results using two Bayesian263Ever since the discovery that only a small minority of selected quasars are also luminous radio sources (e.g. LocHy107 !sr 4). many studies have attempted to isolate the physical mechanism underlying this so-called) quasar radio-loudness dichotomy.,"Ever since the discovery that only a small minority of optically-selected quasars are also luminous radio sources (e.g. $L_{\rm{5GHz}}>10^{24}$ $^{-1}$ $^{-1}$ ), many studies have attempted to isolate the physical mechanism underlying this so-called quasar radio-loudness dichotomy."264 Although previous studies found a clear bimodality in the radio luminosities of optically-selected quasars (eg., Although previous studies found a clear bimodality in the radio luminosities of optically-selected quasars (eg.265 Kellermann et al., Kellermann et al.266 1989: Miller. Peacock Mead 1990). more recently the very existence of the radio-loudness dichotomy has been questioned (Lacy et al.," 1989; Miller, Peacock Mead 1990), more recently the very existence of the radio-loudness dichotomy has been questioned (Lacy et al."267 2001: Cirasuolo et al., 2001; Cirasuolo et al.268 2003: although see Ivezié et al., 2003; although see Ivezić et al.269 2002 for an alternative viewpoint)., 2002 for an alternative viewpoint).270 The principal reason. behind this renewed interest in the radio properties of optically selected quasars is the ability to combine the large SDSS and 2dF optical quasar samples with wide-area radio surveys such as the Faint Images of the Radio Sky at Twenty-cm (FIRST) and the NRAO VLA Sky Survey (NVSS)., The principal reason behind this renewed interest in the radio properties of optically selected quasars is the ability to combine the large SDSS and 2dF optical quasar samples with wide-area radio surveys such as the Faint Images of the Radio Sky at Twenty-cm (FIRST) and the NRAO VLA Sky Survey (NVSS).271 The FIRST survey (Becker. White Helfand 1995) in particular has identified large numbers of so-called radio-intermediate quasars which have largely tilled-in the apparent gap in radio luminosities between the RLQ and RQO populations teg.," The FIRST survey (Becker, White Helfand 1995) in particular has identified large numbers of so-called radio-intermediate quasars which have largely filled-in the apparent gap in radio luminosities between the RLQ and RQQ populations (eg."272 Lacy et al., Lacy et al.273 2001)., 2001).274 Consequently. the distribution of optically-selected quasars on the optical-radio luminosity plane is undoubtedly more continuous than was previously thought.," Consequently, the distribution of optically-selected quasars on the optical-radio luminosity plane is undoubtedly more continuous than was previously thought."275 Irrespective of this. the fundamental question of what causes luminous quasars with seemingly identical optical properties to differ in their radio luminosities by several orders of magnitude remains unanswered.," Irrespective of this, the fundamental question of what causes luminous quasars with seemingly identical optical properties to differ in their radio luminosities by several orders of magnitude remains unanswered."276 Recent progress has been made in largely eliminating two parameters which were originally suspected of influencing the radio-loudness dichotomy: host-galaxy morphology and cluster environment., Recent progress has been made in largely eliminating two parameters which were originally suspected of influencing the radio-loudness dichotomy; host-galaxy morphology and cluster environment.277 Thanks largely to the Hubble Space Telescope (HST). quasar host-galaxy morphologies have now been investigated out to intermediate redshifts. 0.1.<20.5 teg.," Thanks largely to the Hubble Space Telescope (HST), quasar host-galaxy morphologies have now been investigated out to intermediate redshifts, $0.1<z<0.5$ (eg."278 Dunlop et al., Dunlop et al.279 2003: Schade et al 2000: MeLure et al., 2003; Schade et al 2000; McLure et al.280 1999: Disney et al., 1999; Disney et al.281 1996)., 1996).282 Drawing together the results of these studies. it is clear that the hosts of optically luminous quasars (Le. Mj< 24) are bulge-dominated. spheroidal galaxies irrespective of radio luminosity (Dunlop et al.," Drawing together the results of these studies, it is clear that the hosts of optically luminous quasars (i.e. $M_{R}<-24$ ) are bulge-dominated, spheroidal galaxies irrespective of radio luminosity (Dunlop et al."283 2003: Schade et al., 2003; Schade et al.284 2000)., 2000).285 In the light of the discovery of the correlation between black-hole and bulge mass (Magorrian et al., In the light of the discovery of the correlation between black-hole and bulge mass (Magorrian et al.286 1998: Gebhardt et al., 1998; Gebhardt et al.287 2000: Ferrarese Merritt 2000). this result is perhaps not surprising.," 2000; Ferrarese Merritt 2000), this result is perhaps not surprising."288 However. it should also be remembered that in the optical the hosts of RLQs are consistently found to be 0.5 magnitudes brighter than their RQQ counterparts (eg.," However, it should also be remembered that in the optical the hosts of RLQs are consistently found to be $\simeq 0.5$ magnitudes brighter than their RQQ counterparts (eg."289 Dunlop et, Dunlop et2901 Introduction Open svstems tvpicallygive rise toresonances. Aresonance Is along-living quasi- stationarystate.,"on an analogy with Thouless' arguments concerning the sensitivity of eigenstates to the boundary conditions in Hermitian localization theory \cite{Thouless,gang4}."291 which eventually decavs into thecontimuum. Physically. it maybe thought infinity.of asaparticle.," Indeed, the coupling of the disordered system to the external world plays in our case a role similar to changing the boundary conditions in Thouless' picture."292" initiallytrapped inside (hesvstem. which eventually escapes to One common approach to studying resonances isbased onthe analytic properties ofthe scattering matrix 5(£) poles labelpoles E,bk, (10! 5(£) thenon-physical sheet|1."," Namely, the width of a typical resonance in the insulating regime should be exponentially small, $\Gamma_{typ}\sim \exp -L/\xi(E)$ $L$ being the size of the system), whereas in the metallic regime the typical width is $\Gamma_{typ}\sim {\cal D}/L^2$, namely, the inverse Thouless time scale ${\cal D}$ is the diffusion coefficient in the disordered metal)."293 2].. In alternative = 5b on an equivalent approach.," Thus, $\Gamma_{typ}$, measured in units of level spacing $\Delta$, is analogous to the Thouless conductance."294 whichweshall follow here.onesolves, This picture was already pursued numerically in \cite{Kot3}.295 theSchrodeinger equation subjected to the boundary, The continuum limit of the disordered chain was studied in \cite{mumbai}.296 condition of purely outgoing wave," For simplicity, a chain opened only at one end was studied."297 ejectedfrom the svstem. renders the problem non-IHermitian. The Sehiróddinger equation will this boundary condition leads ," The spectral determinant for the problem was derived, and the averaged DOR was expressed in terms of a certain integral over the solution of a certain singular two-dimensional Fokker-Planck equation. ("298"tocomplexeigenvalues €,which correspond Lo resonances[1.2].. Fora recentlucid",That Fokker-Planck equation determined the probability distribution of the logarithmic derivative of the outgoing wave at the open end of the chain.)299 discussionofresonances in quantunsvstems. with," The present work was motivated in part by \cite{ks1,ks2}."300 particular emphasis onthelatter approach. see3.4].. The outgoing-wave approach leads. inanatural way.to non-Hermitian effective 5. hamiltonians0]. whose c," In particular, an analytical approach was developed in \cite{ks2} for studying resonances, which is based on counting poles of the resolvent of the non-Hermitian tight-binding effective hamiltonian of the open chain."301omplex eigenvaluesare the resonances ofthe studied system 6. Such effective hamiltonians arevery use," In the case of a semi-infinite disordered chain, coupled to a semi-infinite perfect lead, these authors have derived an exact integral representation for the DOR, valid for arbitrary disorder and chain-lead coupling strength."302ful forstudying resonances in scattering theory.including scattering inchaotic anddisordered svstenms[0. 0. 0. 0. 0].. There are many," In the limit of weak chain-lead coupling (in which resonances are typically narrow) they were able to rigorously derive a universal scaling formula for the DOR, valid for any degree of disorder and everywhere inside the unperturbed energy band of the closed chain."303 examplesof resonancesin atom, The $1/\Gamma$ behavior of the DOR follows from that formula.304ic andnuclear plivsies. Recently. {herehasbeen considerable interestin resonances whicharise, In this paper we shall review and explain how to construct energy dependent non-hermitian hamiltonians for studying resonance statistics in open systems.305 in chaotic anddisordered systems. See [0] fora recent review. One ofthe main goals inthese studies," While many (but by no means all) of the results presented in this paper are known, we believe our presentation offers a somewhat fresh look at these issues."306 is computationof the distribution P(D) of resonance widths. There is ampleamount ofworkon computing (D) in one-dimensional disordered ," Upon elimination of the leads, one can reformulate the problem in terms of an effective non-hermitian hamiltonian, which depends only on the degrees of freedom of the disordered system."307chains[0. 0. 0. 0.0].. Numerical resultspresented in someof these works indicate(hat P(DP)DP  ina large rangeof values of E.where theexp," In this effective description, the outgoing-wave boundary condition in the original system is translated into a local non-hermitian, energy dependent boundary condition at the contact points (or more generally, contact regions) of the system and the leads."308onent 5 isveryclos, This paper is organized as follows.309"eto 1. A moregeneral quantitythan P(D)is the! density of labeldor » oly Πιό,).(2) ptr.y)—[; δα’~~ Re€,,m", In Section 2 we discuss resonances in a generic quantum system coupled to the external world by a single one-dimensional lead ( a single channel lead).310 It the averaged inthe complex plane contains is widely believedthat [0. DOR0., We derive a general expression for the DOR in terms of an appropriate diagonal matrix element of the resolvent of the original closed system.3110].. This ? based information aboutthe Anderson," From this expression, we derive an integral representation for the averaged DOR of the disordered system."312" transition 0. expectationis avoid forumias.wedo notuse resonance widthD,in(2?) Minargmueutorder to"," In Section 3 we specialize to the case of an open one dimensional disordered chain, derive the corresponding effective hamiltonian, and obtain its continuum limit."313" cluttering ofourT,,/2. the as anP7Ilearned ofthisHp.but aremimentratherabout the expected. scalingbehavior+ of.", The resulting continuum effective non-hermitian hamiltonian differs from the hermitian one of the closed system by a complex energy dependent boundary condition.314 the DOR- fromD.η Shapiro..," The structure revealed in this way is quite generic,"315"In Figure 14 we again plot e against Τομ, but this time adding three F stars for which mode identifications are ambiguous: Procyon, 449933 and 1181420.","In Figure \ref{fig14} we again plot $\epsilon$ against $T_\mathrm{eff}$, but this time adding three F stars for which mode identifications are ambiguous: Procyon, 49933 and 181420."316" For 449933, as previously mentioned, Scenario B is now considered to be correct, and indeed this is the identification that falls along the observed ε-Τεῃ trend."," For 49933, as previously mentioned, Scenario B is now considered to be correct, and indeed this is the identification that falls along the observed $\epsilon$ $T_\mathrm{eff}$ trend."317" Scenario 1 is the preferred identification in 1181420, and again this matches the trend."," Scenario 1 is the preferred identification in 181420, and again this matches the trend."318 Unfortunately the situation in Procyon is not completely clear., Unfortunately the situation in Procyon is not completely clear.319 The trend with which we hope to identify the correct e is still loosely defined due to the scarcity of F stars for which we have measured ε unambiguously., The trend with which we hope to identify the correct $\epsilon$ is still loosely defined due to the scarcity of F stars for which we have measured $\epsilon$ unambiguously.320 Scenario B appears to lie towards the top of any range we could expect for e for a star of its effective temperature., Scenario B appears to lie towards the top of any range we could expect for $\epsilon$ for a star of its effective temperature.321" On the other hand, Scenario A appears to be at the minimum."," On the other hand, Scenario A appears to be at the minimum."322" Expecting a correction for near-surface effects, we are inclined to believe Scenario B is more likely, but we cannot rule out the alternative."," Expecting a correction for near-surface effects, we are inclined to believe Scenario B is more likely, but we cannot rule out the alternative."323" We anticipate that a measurement of e in many stars observed byKepler could help clearly define the observationalF ε-Τοῃ relation, clarifying the correct mode identification in Procyon."," We anticipate that a measurement of $\epsilon$ in many F stars observed by could help clearly define the observational $\epsilon$ $T_\mathrm{eff}$ relation, clarifying the correct mode identification in Procyon."324"2001) as well as for the SZ, produced. bx the hot X- οπλο eas.",2004) as well as for the $_{th}$ produced by the hot X-ray emitting gas.325 According to these results. the spectral distortion of the CMD spectrin induced by a population of electron with momentum distribution f(y} cau be written as Ty is the CAIB temperature aud σ in terms of the pressure Z7. contributed by the specific electron ," According to these results, the spectral distortion of the CMB spectrum induced by a population of electron with momentum distribution $f_e(p)$ can be written as where $T_0$ is the CMB temperature and in terms of the pressure $P_{e}$ contributed by the specific electron population."326The spectral function gor). with ο τω. canbo popmtation.written as in terms of the photon redistribution function. (5) and of /j60)=2(kpοa?(e1)," The spectral function $\tilde{g}(x)$, with $x \equiv h \nu / k_{\rm B} T_0$ , can be written as in terms of the photon redistribution function $P(s)$ and of $i_0(x) = 2 (k_{\rm B}327T_0)^3 / (h c)^2 \cdot x^3/(e^x -1)$."328 Were 7= is the optical depth of the electrous with umber deusityns n. and £e;=c[Pdl=fyΡΟης is the average energy of the electronic plasina.," Here $\tau = \int d \ell n_e$ is the optical depth of the electrons with number density $n_e$ , and $ \langle \epsilon \rangle \equiv \frac{\sigma_{\rm T}}{\tau}\int P_{\rm e}329d\ell330 = \int_0^\infty dp f_{\rm e}(p) \frac{1}{3} p v(p) m_{\rm e} c331$ is the average energy of the electronic plasma."332" The photon redistribution fiction Ps)fdpGPosp) with s=Inv py, in terms of the CAIB photon frequency increase factor m/v. de)ouds on the electron moment distribution f.(p). where the momentum p is normalized to mec."," The photon redistribution function $P(s)= \int dp f_{\rm e}(p) P_{\rm s}(s;p)$ with $s =333\ln(\nu'/\nu)$ , in terms of the CMB photon frequency increase factor $\nu' / \nu$, depends on the electron momentum distribution $f_{\rm e}(p)$, where the momentum $p$ is normalized to $m_e c$."334" The CAB temperature change produced by the SZE is finally eiven by ""A", The CMB temperature change produced by the SZE is finally given by =.335"TnT TyThe specific SZpa; aud. SZ), effects for the various electronic components in the cluster are computed following the approach previously described.", The specific $_{DM}$ and $_{th}$ effects for the various electronic components in the cluster are computed following the approach previously described.336 The calculation of the secondary. clectron spectrum frou VA aunihilation iu ealaxv clusters has Όσοι already presented in de ailsby Colafrancesco Mole (2001) aud Colafrancesco ett al. (, The calculation of the secondary electron spectrum from $\chi \chi$ annihilation in galaxy clusters has been already presented in details by Colafrancesco Mele (2001) and Colafrancesco et al. (3372006). aud here we will ouly recall the relevant steo necessary for the preseut We assu. for simplicity. a spherical DAL halo model for cach DAL clump of the cluster as indicated bv the lensing maps derived by Clowe et al. (,"2006), and here we will only recall the relevant steps necessary for the present We assume, for simplicity, a spherical DM halo model for each DM clump of the cluster , as indicated by the lensing maps derived by Clowe et al. ("3382006). with DAL density profile given bv gor)soe(bpou)?5ο ΝΕ oeSrry.,"2006), with DM density profile given by $ g(x) = x^{-\eta} (1+ x)^{\eta - \xi}$, with $x \equiv r/r_s$."339" Values 4=1 ancl &£=3 reproduce theNΝΑΤΟ. Frenk White (1997) density The neutralino umber density profiles n,(E.r)= of the two DM chuups havebeen calculated followiug the approach described in Colatrancesco et al. ("," Values $\eta = 1$ and $\xi = 3$ reproduce the Navarro, Frenk White (1997) density The neutralino number density profiles $n_{\chi}(E,r) = n_{\chi,0}(E) g(r)$ of the two DM clumps have been calculated following the approach described in Colafrancesco et al. ("340"2006) with à NFW DAL density profile aud the following structure parameters: Ay,=LOMAL. Ru,=197 Moc aud ον.=Rey""wea.fre5.66 (for the larger East DM chuup) AM,=6.25 Πρι=0781 Mpe aud Corp=7.46 (for the ""bullet West DM The X annihilation rate in the DM clumps ds R=ny(rico. where iGUg is the yy anniiation Cross section averaged over a thermal velocity distribution at. freeze-out temperature.","2006) with a NFW DM density profile and the following structure parameters: $M_{vir}=34110^{15} M_{\odot}$, $R_{vir} = 1.97$ Mpc and $c_{vir}= R_{vir}/r_s = 5.66$ (for the larger East DM clump); $M_{vir} = 6.25 \cdot 10^{13} M_{\odot}$, $R_{vir} = 0.784$ Mpc and $c_{vir}= 7.56$ (for the ”bullet” West DM The $\chi$ annihilation rate in the DM clumps is $ R = n_{\chi}(r) \langle \sigma v342\rangle_0 ~,$ where $\langle \sigma v \rangle_0$ is the $\chi \chi$ annihilation cross section averaged over a thermal velocity distribution at freeze-out temperature."343 The range of ueutralino lnasses and pair annihilation cross sections dji the inost eeneral supersvnuuetric DM setup is extremely wide (see discussion in Colafrancesco e al., The range of neutralino masses and pair annihilation cross sections in the most general supersymmetric DM setup is extremely wide (see discussion in Colafrancesco et al.344 2006.lols 2007).," 2006, 2007)."345 We consider here. specifically. the neuralino iioc worked out in Colatrancesco ot al. (," We consider here, specifically, the neutralino models worked out in Colafrancesco et al. ("346"2006) with AL,=20.LO and SI GeV aud with their specific vales of (a0). The electron source unctions Q.GE.r)xUATEDr) for the specific neutralino model considered here have been derived in Colafraucesco et al. (","2006) with $M_{\chi}= 20, 40$ and $81$ GeV and with their specific values of $\langle347\sigma v \rangle_0$ The electron source functions $Q_{\rm e}(E,r) \propto \langle\sigma v\rangle_0348n^2_{\chi}(E,r)$ for the specific neutralino model considered here have been derived in Colafrancesco et al. ("3492006) and the time evolution of the elecron spectrun is eiven bv the equatiou GE.r)biE) | = QUE.r).(5 where spatial diffusion can be safelv neglected iu cluster-size DM. chumps (Colafraucesco et al.,"2006) and the time evolution of the electron spectrum is given by the equation - (E,r) ] = (E,r), where spatial diffusion can be safely neglected in cluster-size DM clumps (Colafrancesco et al."350 2006)., 2006).351" The fiction eives the euergv loss per unit time at enecrev EL where ng, is the mean nuuber density of thermal clectrous iu cmὃν +=)ο and We~(25. cm0.0251. 09,cG3. Dou,cm151. all in units of Di10!GeVs1,"," The function gives the energy loss per unit time at energy $E$ where $n_{th}$ is the mean number density of thermal electrons in $\rm{cm}^{-3}$, $\gamma \equiv E/m_e c^2$ and $b_{IC}^0352\simeq 0.25$, $b_{syn}^0 \simeq 0.0254$, $b_{Coul}^0 \simeq 6.13$, $b_{brem}^0 \simeq3531.51$, all in units of $10^{-16}\; \rm{GeV}\, \rm{s}^{-1}$."354 The equilibriun spectrum n.(L.46) obtained solving eq.(5)) allows to calculate the SZpa; effect.," The equilibrium spectrum $n_e(E,r)$ obtained solving \ref{eq.diffusion}) ) allows to calculate the $_{DM}$ effect."355 Εἶσ shows the CAMB temperature change. AT evaluated at the centers of the two DM clumps for differcu values of ALY., \ref{fig.sz_dm} shows the CMB temperature change $\Delta T$ evaluated at the centers of the two DM clumps for different values of $M_{\chi}$.356" The SZpay signals are overcome by the SZ, signals a low Gv&200 GITZ) aud hieh ἐνZ230 GITz) frequencies. while they dominate in the frequency range where the zero of SZg, is found. Le. at zz223 GIIz for the Eas chunp and at Ézc219 CGIIz for the West chup."," The $_{DM}$ signals are overcome by the $_{th}$ signals at low $\nu \simlt 200$ GHz) and high $\nu \simgt 230$ GHz) frequencies, while they dominate in the frequency range where the zero of $_{th}$ is found, i.e. at $\nu \approx 223$ GHz for the East clump and at $\nu \approx 219$ GHz for the West clump."357" A such frequencies the SM temperature decrement takes values &21.1.10.63 a μῖν(East cmp) and values xNl.L2.Ol nd ο) for A,=s20.10.5]GeV. respectively."," At such frequencies the $_{DM}$ temperature decrement takes values $\approx -21.1, -10.6, -0.3$ $\mu$ K (East clump) and values $\approx -8.4, -4.2, -0.1$ $\mu$ K (West clump) for $M_{\chi} = 20, 40, 81$GeV, respectively."358" TheSZ, from the two ταν chuups of the clusteris also computed from the general approach delineated in eqs.(1-l).", The$_{th}$ from the two X-ray clumps of the clusteris also computed from the general approach delineated in eqs.(1-4).359 Following Markeviteh et al. rites(, Following Markevitch et al. (3602002. 2001) aud Tucker etal. (,"2002, 2004) and Tucker etal. ("3611998). we use the assuniptiou that the IC eas distribution cau be described by isothermal spheres fitted by a .+profile.,"1998), we use the simplifying assumption that the IC gas distribution can be described by isothermal spheres fitted by a $\beta$ -profile."362" For the East N-ray chunp we adopt AZ,=Ll keV (Alarkevitch et al.", For the East X-ray clump we adopt $kT_e = 14$ keV (Markevitch et al.363as a single extended particle (Yangctal.901101.,as a single extended particle \citep{2010arXiv1011.0176Y}.364 This allows us to describe mereiug objects in the statistical mechanical theory., This allows us to describe merging objects in the statistical mechanical theory.365 These properties mean that we can represent many clusters of galaxies απ eroups of imostly virialized subclusters., These properties mean that we can represent many clusters of galaxies as groups of mostly virialized subclusters.366 The shapes of such clusters are thus given by the positions of their subclusters which reduces the many-body problem of describing all the salaxies iu a cluster to a few-body problem that describes how subchisters interact with cach other., The shapes of such clusters are thus given by the positions of their subclusters which reduces the many-body problem of describing all the galaxies in a cluster to a few-body problem that describes how subclusters interact with each other.367 Based on the probability that a cell is not completely bound aud virialized as discussed in the previous section. we expect that most cells will usually contain fewer than about LO of these subchisters. depending on the value of 5b.," Based on the probability that a cell is not completely bound and virialized as discussed in the previous section, we expect that most cells will usually contain fewer than about 10 of these subclusters, depending on the value of $b$."368 Some cells. however. can be dominated by a single virialized cluster.," Some cells, however, can be dominated by a single virialized cluster."369 Subclusters can be described bw the positions of their individual galaxies with respect to the subclusters center-of-mass and the positions of these ceuters-of-mass., Subclusters can be described by the positions of their individual galaxies with respect to the subcluster's center-of-mass and the positions of these centers-of-mass.370 To illustrate this. we use an example of a cluster composed of two subclusters.," To illustrate this, we use an example of a cluster composed of two subclusters."371 The total potential energy of such a cluster is given bv the stm of the internal potential energies of its subclusters and their mutual potential energies such that where the superscripts indicate particles frou different subclusters., The total potential energy of such a cluster is given by the sum of the internal potential energies of its subclusters and their mutual potential energies such that where the superscripts indicate particles from different subclusters.372 The first two terms are the internal potential energies of the subchisters. which are inaccessible to the rest of the cuscmble if these subclusters are virialized.," The first two terms are the internal potential energies of the subclusters, which are inaccessible to the rest of the ensemble if these subclusters are virialized."373 The last teria represcuts the potential energw between the subchisters., The last term represents the potential energy between the subclusters.374 We can write this term as where £C?D isH the separationB between the ceuters-of-.mass of cach subcluster.," We can write this term as where $r^{(1,2)}$ is the separation between the centers-of-mass of each subcluster."375 The detailed iuternal structure of the subclusters modifiestheir interaction potential., The detailed internal structure of the subclusters modifiestheir interaction potential.376 This modification is where AL) and AZC5 ave the masses of. subelusters ] and 2 respectively, This modification is where $M^{(1)}$ and $M^{(2)}$ are the masses of subclusters 1 and 2 respectively.377 Then the potential betwoeeu subclusters is where jpP2?) deseribes the modification to the point-lass potential bv a pair of extended structures.," Then the potential between subclusters is where $\kappa(r^{(1,2)})$ describes the modification to the point-mass potential by a pair of extended structures."378 This modification term enters as a coefficient. το ο) (Almadetal.2002:Yang2011) aud if iip0) is close to unity its effect will be sniall.," This modification term enters as a coefficient to $\beta$ \citep{2002ApJ...571..576A,2010arXiv1011.0176Y} and if $\kappa(r^{(1,2)})$ is close to unity its effect will be small."379 We can write the positions of galaxies as the vector siu of the position of their subcluster's ceuter-ofanass and their position within the subcluster: where x!) is the eeuter-ofanass of subceluster 1 and xU is the position of particle / with respect to the center-ofmass of subcluster 1., We can write the positions of galaxies as the vector sum of the position of their subcluster's center-of-mass and their position within the subcluster: where $\mathbf{x}^{(1)}$ is the center-of-mass of subcluster 1 and $\tilde{\mathbf{x}}_i^{(1)}$ is the position of particle $i$ with respect to the center-of-mass of subcluster 1.380 With this notation. the modification terii iu equation has the limits Iu the limit⋅⋅ where [x;-(2):«pO the modification term is 1.," With this notation, the modification term in equation has the limits In the limit where $|\tilde{\mathbf{x}}_i^{(1)} - \tilde{\mathbf{x}}_j^{(2)}| \ll r^{(1,2)}$ the modification term is 1."381 This meansxl that we can approximate subclusters that are widely separated as point masses when computing their iuteraction potential., This means that we can approximate subclusters that are widely separated as point masses when computing their interaction potential.382" For subclusters that are touching.- &(p)Dm0,5 because |~(1)JXi~(2) is on average the radius of a subcluster."," For subclusters that are touching, $\kappa(r^{(1,2)}) \approx 0.5$ because $|\tilde{\mathbf{x}}_i^{(1)}-\tilde{\mathbf{x}}_j^{(2)}|$ is on average the radius of a subcluster."383 Subclusters that are closer to each other may have a sanaller value of &(:AL.2) j. but such pairs may be mereine. in which case we can treat such pairs as single subclusters with a different iuterual structure (Yangctal.2011).," Subclusters that are closer to each other may have a smaller value of $\kappa(r^{(1,2)})$ , but such pairs may be merging, in which case we can treat such pairs as single subclusters with a different internal structure \citep{2010arXiv1011.0176Y}."384 This means that the many-body problem of studving all the ealaxies in a cluster is reduced to the few-body problem of studyiug the positions and velocities of the subclusters iu the cluster., This means that the many-body problem of studying all the galaxies in a cluster is reduced to the few-body problem of studying the positions and velocities of the subclusters in the cluster.385 This makes the problem considerably easier. since there are fewer “particles” to deal with.," This makes the problem considerably easier, since there are fewer “particles” to deal with."386 Because clusters with more than 10 particles are likely to be vintalized. we cousider the case where cells have less than 10 subclusters.," Because clusters with more than 10 particles are likely to be virialized, we consider the case where cells have less than 10 subclusters."387 These cells have a uon-neelieible probabilitv of having a positive specific heat., These cells have a non-negligible probability of having a positive specific heat.388 Although subclusters may have different masses aud different iuternal structures. there are analyses that take iuto account these more general cases.," Although subclusters may have different masses and different internal structures, there are analyses that take into account these more general cases."389 The analysis for particles of different internal structure is described iu Yaneetal.(2011)... aud as suggested by equation enters as a coefficient to 2.," The analysis for particles of different internal structure is described in \citet{2010arXiv1011.0176Y}, and as suggested by equation enters as a coefficient to $\beta$ ."390 The analysis for multiple masses is cousiderably more complicated (Alanaetal. 2006a).. so to simplify it we make the reasonable approximation that “particles” lave the same mass.," The analysis for multiple masses is considerably more complicated \citep{2006IJMPD..15.1267A}, so to simplify it we make the reasonable approximation that “particles” have the same mass."391 Iu Appendix A owe show that the masses of individual particles are typically within an order of maguitude of cach other., In Appendix \ref{app-mmass} we show that the masses of individual particles are typically within an order of magnitude of each other.392 The detailed configuration of a cellis directly related to its energy., The detailed configuration of a cell is directly related to its energy.393" We consider its potential aud kinetic energies separately, aud relate them to W and 2."," We consider its potential and kinetic energies separately, and relate them to $W_*$ and $T_*$ ."394 We work with the instautancous values of the energies since these quantities are well-defined andcau bedeteriuined iu principle bv taking a snapshot of a cluster at a given, We work with the instantaneous values of the energies since these quantities are well-defined andcan bedetermined in principle by taking a snapshot of a cluster at a given395No narrow spectral features are apparent.,No narrow spectral features are apparent.396 The absorption “feature” near 2 keV is likely to be an instrumental artifact(81)., The absorption “feature” near 2 keV is likely to be an instrumental artifact.397. The 2-0 upper limit on the [lux of a persistent 0.2-keV FWIIM emission line in (he 57 keV range ⋈∙is 10photonsem>s.|. corresponding. to an equivalent. width. at 6.5. keVT of. less (han 150 eV; narrower lines with similar equivalent widths would have been readily apparent in the data.," The $\sigma$ upper limit on the flux of a persistent 0.2-keV FWHM emission line in the 5–7 keV range \\citealt{si00}) ) is $10^{-5}\mbox{ photons cm}^{-2}\mbox{ s}^{-1}$, corresponding to an equivalent width at 6.5 keV of less than 150 eV; narrower lines with similar equivalent widths would have been readily apparent in the data."398 We attempted to extract time-averaged spectral information from the cddata as well., We attempted to extract time-averaged spectral information from the data as well.399 However. with the faintness of the source (which we estimate [rom our lits at σος for three active PCUS of the PPCA). the high background (100 !)) — some of which is likely due to unresolved sources near the Galactic plane ancl the non-imaging nature of the PCA. we have been unable so far to obtain meaningful results.," However, with the faintness of the source (which we estimate from our fits at 2 for three active PCUs of the PCA), the high background $\approx$ 100 ) – some of which is likely due to unresolved sources near the Galactic plane – and the non-imaging nature of the PCA, we have been unable so far to obtain meaningful results."400 To perform a phase-resolved spectral analvsis we divided the eevenis into six phase bins. according to the best fit period for each observation.," To perform a phase-resolved spectral analysis we divided the events into six phase bins, according to the best fit period for each observation."401 We constructed a spectrum for each spectral bin independently., We constructed a spectrum for each spectral bin independently.402" With the reduced counts of the phase-binned speclra we were unable to discriminate between multicomponent spectral models and fit a PL only. fixing Ny, to the best-fit value for the PL-onlx fits to the phase-averaged. cata set (2.75x107?em7: see Table 1))."," With the reduced counts of the phase-binned spectra we were unable to discriminate between multicomponent spectral models and fit a PL only, fixing $N_{H}$ to the best-fit value for the PL-only fits to the phase-averaged data set $2.75\times 10^{22}\mbox{403cm}^{-2}$; see Table \ref{tab:spec}) )."404 Whether or not this model is accurate. the fits illustrate (he gross variations in spectral shape (hardness) with phase exhibited by (the source.," Whether or not this model is accurate, the fits illustrate the gross variations in spectral shape (hardness) with phase exhibited by the source."405 We see inFigue 4 (hat there are moderate variations across the phase. with the beginning of the evele harder than the end. and with an additional soltening at pulseanaxinunm.," We see in Figure \ref{fig:ps} that there are moderate variations across the phase, with the beginning of the cycle harder than the end, and with an additional softening at pulse-maximum."406 The shape remains similar over the two observations., The shape remains similar over the two observations.407 As mentioned previously. we were not able to make a direct comparison with the sspectral results due to unresolved background emission in the cddata that corrupted the absolute flux levels.," As mentioned previously, we were not able to make a direct comparison with the spectral results due to unresolved background emission in the data that corrupted the absolute flux levels."408 ILowever. we were able to compare the fluxes for pulse ON-OFF.," However, we were able to compare the fluxes for pulse $-$ OFF."409 Specilicallv. we extracted spectral datasets for the 1/3 of the phase around the maxinum (ON) ancl the minimum (OFF) of the pulse for both aand {for the second epoch of (overlapping) observations.," Specifically, we extracted spectral datasets for the $1/3$ of the phase around the maximum (ON) and the minimum (OFF) of the pulse for both and for the second epoch of (overlapping) observations."410 Our goal was to use the (svo datasets in combination to make an independent test of the reasonabilitv of the PL+BB fits., Our goal was to use the two datasets in combination to make an independent test of the reasonability of the PL+BB fits.411"This can be verified from the data in Table 1 rere we compare the activity indices. logHis aud logtfx/fy). in the chromospheric activity aud. rvevs. respectively. for the for rsars 1 conunon to these rvevs,","This can be verified from the data in Table \ref{einstein} where we compare the activity indices, $\log R'_{\rm HK}$ and $\log(f_{\rm X}/f_{\rm V})$, in the chromospheric activity and surveys, respectively, for the four stars in common to these surveys."412 The bulk of the active stars. according to the distributionDoa: fuuctiou:a4 \(logSP!fer:|. hasao dog4.PinsJorPOI~r1.50. which from the values im Tabe would correspond to logfx/fv)xm3.9 or lower.," The bulk of the active stars, according to the distribution function $\chi(\log R'_{\rm HK})$, has $\left\langle\log R'_{\rm HK}\right413 \rangle\approx -4.50$, which from the values in Table \ref{einstein} would correspond to $\log(f_{\rm X}/f_{\rm V})\approx -3.9$ or lower."414 TMs. our Fig.," Thus, our Fig."415 does not ταle out the conclusions by Mox:i( et al. (19963)., \ref{m1active} does not rule out the conclusions by Morale et al. \cite{morale}) ).416" Note that our most active stars. that wou ive Ίοςἐνδν)τι2.8 if we extrapolate the relation for he stars from Table 1.. have daryzz(.07 in good agreeneat with Fiewure 3 bx Morale et al.. We can see that a ogfx/fy)=3.0. the CG aud Is cawarts still preseut siniar om, dudices."," Note that our most active stars, that would have $\log(f_{\rm X}/f_{\rm V})\approx 417 -2.8$ if we extrapolate the relation for the stars from Table \ref{einstein}, have $\delta m_1\approx 0.07$ in good agreement with Figure 3 by Morale et al.. We can see that at $\log(f_{\rm X}/f_{\rm V})\approx -3.0$, the G and K dwarfs still present similar $\delta m_1$ indices."418 Frou the considerations above. we can couchide that. oulv for the most active dwar. the cooler stars will preseut larger A compared to he €i dwarfs.," From the considerations above, we can conclude that, only for the most active dwarfs, the cooler stars will present larger $\Delta$ compared to the G dwarfs."419 From the fuuctio1 \(logA). these τον active stars comprise arouud ofthe active stars wie are clealing with (that is. O.05eNor stars). so that their influence on the metallicity distrition will be negligible. aud our hypothesis for equal c and A is fairly reasonable.," From the function $\chi(\log R'_{\rm HK})$, these very active stars comprise around of the active stars we are dealing with (that is, $0.05cN_{\rm tot}$ stars), so that their influence on the metallicity distribution will be negligible, and our hypothesis for equal $c$ and $\bar\Delta$ is fairly reasonable."420 Iu he last few vears. several works have investigated the observational aspects of the CG cavarf problem (Wyse Culmore 1995:: Rocha-Pinto Maciel 1996.. 19972:: Flvnu Morell 1997)).," In the last few years, several works have investigated the observational aspects of the G dwarf problem (Wyse Gilmore \cite{wyse}; Rocha-Pinto Maciel \cite{RPM96}, \cite{RPM97a}; Flynn Morell \cite{flynn}) )."421" All these works have folowed the steps delineated by Paecl Patchett (1975)) fex the selection of a unbiased metallicity distribution of loue-lved ciwarfs. * choosing stars in a volume Πίος, sauple aud τιsine photometric metallicities."," All these works have followed the steps delineated by Pagel Patchett \cite{pagel}) ) for the selection of a unbiased metallicity distribution of long-lived dwarfs, by choosing stars in a volume limited sample and using photometric metallicities."422 The receut paper by Favata et al. (1997 )), The recent paper by Favata et al. \cite{favata1}) )423 also analyzes he iuetallicity distribution of the solar icielibourhliood., also analyzes the metallicity distribution of the solar neighbourhood.424 The najor novelty of this work is that the authors nace the first attempt to systematically study the ocal metallicity disributiou by usine specrToscopic netallicities., The major novelty of this work is that the authors made the first attempt to systematically study the local metallicity distribution by using spectroscopic metallicities.425 Iu fact. the first local specrToscopic net:itv distribution was made by Rana Basu (1990)).," In fact, the first local spectroscopic metallicity distribution was made by Rana Basu \cite{ranabasu}) )."426 Ilowever. their selection criteria WLC not ap]ypriate to define a unbiased sample. axd thei LCT.101v database was largely. heterogeneous.," However, their selection criteria were not approppriate to define a unbiased sample, and their metallicity database was largely heterogeneous."427 Receitly. SOIC papers have also ταςe use of a specrToscopic netalliciv distributioi from the data of Edvarcdsso1 et al. (1993)).," Recently, some papers have also made use of a spectroscopic metallicity distribution from the data of Edvardsson et al. \cite{Edv}) )."428 Tlowever. this distribution camot be taken as representative either. as Edvardsson ct al.," However, this distribution cannot be taken as representative either, as Edvardsson et al."429 have selected heir stars m order to rave nearly equal iuuboers of t10111 in pre-determined metallicity IS., have selected their stars in order to have nearly equal numbers of them in pre-determined metallicity bins.430 The results by Favata et al. (1997)), The results by Favata et al. \cite{favata1}) )431 are quite peculiar: stars hotter than 5100 I& present motalicities spaninue the whole rauge of [Fe/TI| vaues expeced for the disk. whereas amongst the cooler objecta. no stars show ο<0.140 dex.," are quite peculiar: stars hotter than 5100 K present metallicities spanning the whole range of [Fe/H] values expected for the disk, whereas amongst the cooler objects, no stars show ${\rm [Fe/H]} < -0.40$ dex."432" Their sample comprises 91 stars. 65 of which are cousiered as € ¢warts and 26 are I& απάτες, their separation beige made a 5100 K."," Their sample comprises 91 stars, 65 of which are considered as G dwarfs and 26 are K dwarfs, their separation being made at 5100 K."433In a recent paper Chevalier and Li (1999) pointed out that some of the GRB afterglow light-curves are best modeled when the density of the circum-burst medium is taken to fall off as r7 (this is referred to as the model).,In a recent paper Chevalier and Li (1999) pointed out that some of the GRB afterglow light-curves are best modeled when the density of the circum-burst medium is taken to fall off as $r^{-2}$ (this is referred to as the ).434 These afterglows show no evidence for a jet. re. their light-curves follow a power-law decline without any break.," These afterglows show no evidence for a jet, i.e. their light-curves follow a power-law decline without any break."435 This is puzzling since collimated outflows are expected in the collapsar model for GRBs (MacFadyen. Woosley Heger 2000).," This is puzzling since collimated outflows are expected in the collapsar model for GRBs (MacFadyen, Woosley Heger 2000)."436 We offer a possible explanation for this puzzle by showing that the light-curve resulting from the interaction of a jet with a pre-ejected wind falls off as a power-law whose index changes very slowly with time., We offer a possible explanation for this puzzle by showing that the light-curve resulting from the interaction of a jet with a pre-ejected wind falls off as a power-law whose index changes very slowly with time.437 We carry out a detailed modeling of the multi-wavelength afterglow flux data for GRB 990510. which provides the best evidence for a jet propagation in a untform density medium (Harrison et al.," We carry out a detailed modeling of the multi-wavelength afterglow flux data for GRB 990510, which provides the best evidence for a jet propagation in a uniform density medium (Harrison et al."438" 1999, Stanek et al."," 1999, Stanek et al."439 1999). to show that effects associated with a finite jet opening-angle are insufficient to explain the observed rapid steepening ofthe light-curve.," 1999), to show that effects associated with a finite jet opening-angle are insufficient to explain the observed rapid steepening ofthe light-curve."440 In refdynamies we calculate the propagation of a jet ina stratified medium and in refsynchrotron we describe the calculation of the synchrotron emission and afterglow light-curve., In \\ref{dynamics} we calculate the propagation of a jet ina stratified medium and in \\ref{synchrotron} we describe the calculation of the synchrotron emission and afterglow light-curve.441" The dynamical evolution of Jets and its synchrotron emission have been previously investigated by à number of people. e.g. Rhoads (1999), Panaitescu (1999), Sart. Piran Halpern (1999). Moderski. Sikora. Bulik (2000). Huang et al. ("," The dynamical evolution of jets and its synchrotron emission have been previously investigated by a number of people, e.g. Rhoads (1999), Panaitescu (1999), Sari, Piran Halpern (1999), Moderski, Sikora, Bulik (2000), Huang et al. ("4422000).,2000).443" The evolution of the Lorentz factor (DL) can be calculated from the following set of equations where Ó is the half-opening angle of the jet. My. and Cy are the initial mass and Lorentz factor ofthe ejecta. AZ, is the swept-up mass. p(r)=<tr? is the density of the circum-stellar medium. and f=c/c, is the ratio of the speed of light to that of the jet sideways expansion: f Is a parameter of order unity whose effect can be absorbed in Dy. and which has little effect on the light-curve."," The evolution of the Lorentz factor $\Gamma$ ) can be calculated from the following set of equations where $\theta$ is the half-opening angle of the jet, $M_0$, and $\Gamma_0$ are the initial mass and Lorentz factor ofthe ejecta, $M_1$ is the swept-up mass, $\rho(r)=A r^{-s}$ is the density of the circum-stellar medium, and $f=c/c_s$ is the ratio of the speed of light to that of the jet sideways expansion; $f$ is a parameter of order unity whose effect can be absorbed in $\Gamma_0$, and which has little effect on the light-curve."444 O is the angle between the velocity vector at the jet edge and the jet axis (in the lab frame) and is determined by the modification of particle trajectory due to the sideways expansion., $\Theta$ is the angle between the velocity vector at the jet edge and the jet axis (in the lab frame) and is determined by the modification of particle trajectory due to the sideways expansion.445 The last equation above expresses the conservation of energy and it applies to an adiabatie shock when the heating of the original baryonic material of rest mass AJy by the reverse shock is ignored., The last equation above expresses the conservation of energy and it applies to an adiabatic shock when the heating of the original baryonic material of rest mass $M_0$ by the reverse shock is ignored.446" The above equations can be combined and rewritten in the following non-dimensional form which is applicable for relativistic as well as non-relativistic jet dynamics Where Ξ/ Rau. yy,= U/Ty. yo= 0/04. and"," The above equations can be combined and rewritten in the following non-dimensional form which is applicable for relativistic as well as non-relativistic jet dynamics where $x = r/R_{da}$ , $y_1 = \Gamma/\Gamma_0$ , $y_2 = \theta/\theta_0$ , and"447match all stars in each chip. regardless of the filter. in order to find an accurate coordinate transformation between the frames.,"match all stars in each chip, regardless of the filter, in order to find an accurate coordinate transformation between the frames."448 The matched solutions were then fed to MONTAGE? in order to build a stacked image of each chip., The matched solutions were then fed to MONTAGE2 in order to build a stacked image of each chip.449 In this way we could eliminate all the cosmic rays and obtain an image of the stars with the highest signal-to-noise ratio., In this way we could eliminate all the cosmic rays and obtain an image of the stars with the highest signal-to-noise ratio.450 We ran the DAOPHOT/FIND routine and the PSF-fitting on the stackec image in order to obtain a deep master star list., We ran the DAOPHOT/FIND routine and the PSF-fitting on the stacked image in order to obtain a deep master star list.451 The master list was then used as input for ALLFRAME (Stetson1994).. which simultaneously determines the brightness for stars 11 all frames while enforcing one set of centroids and one transformation between all images.," The master list was then used as input for ALLFRAME \citep{ste94}, which simultaneously determines the brightness for stars in all frames while enforcing one set of centroids and one transformation between all images."452 Finally. all the magnitudes for each star were normalized to a reference frame and averaged together. and the photometric error was derived as the standard deviation of the repeated measures.," Finally, all the magnitudes for each star were normalized to a reference frame and averaged together, and the photometric error was derived as the standard deviation of the repeated measures."453 We note here that the presence of saturated stars iu these deep images is the major source of artefacts causing spurious detections. especially in the core regions where most of the red giant stars are located.," We note here that the presence of saturated stars in these deep images is the major source of artefacts causing spurious detections, especially in the core regions where most of the red giant stars are located."454 In order to clea our catalogues from false detections. we used a statistical approach similar to the one proposed by Cooletal.(1996). that employs the sharpness (5/7) parameter provided as a output by ALLFRAME as the source quality diagnostic.," In order to clean our catalogues from false detections, we used a statistical approach similar to the one proposed by \cite{co96}, that employs the sharpness $sh$ ) parameter provided as an output by ALLFRAME as the source quality diagnostic."455 By plotting s/f as a function of the magnitude we founc that spurious objects. detected around the haloes and along diffraction spikes of saturated stars. have sharpness values that differ from the ones representative of bona-fide stars. which typically have —0.15<sf«0.15.," By plotting $sh$ as a function of the magnitude we found that spurious objects, detected around the haloes and along diffraction spikes of saturated stars, have sharpness values that differ from the ones representative of bona-fide stars, which typically have $-0.15 < sh < 0.15$."456 In Figure 2. we show that the effectiveness goodness of the selection in sharpness (left panel) in identifying false detections is confirmed by the fact that the objects with large sharpness values have also larger photometric errors (right panel)., In Figure \ref{sharp} we show that the effectiveness goodness of the selection in sharpness (left panel) in identifying false detections is confirmed by the fact that the objects with large sharpness values have also larger photometric errors (right panel).457 We finally transformed the instrumental F606W (V) and F814W (I) magnitudes to the VEGAMAG system following the prescriptions of Siriannietal.(2005) and Holtzmanetal.(1995) for the ACS and WFPC2 samples. respectively.," We finally transformed the instrumental F606W (V) and F814W (I) magnitudes to the VEGAMAG system following the prescriptions of \cite{si05} and \cite{ho95} for the ACS and WFPC2 samples, respectively."458 The relative star coordinates of both samples were transformed to the absolute right ascension and declination values (J2000) using the wide field catalogue published by Pollardetal.(2005) as secondary astrometric standard catalogue., The relative star coordinates of both samples were transformed to the absolute right ascension and declination values (J2000) using the wide field catalogue published by \cite{pol05} as secondary astrometric standard catalogue.459 In Figure we show the color-magnitude diagram (CMD) of the entire 9.data set., In Figure \ref{cmd} we show the color–magnitude diagram (CMD) of the entire data set.460 The WFPC?2 final catalogue (left panel) contains 4995 objects., The WFPC2 final catalogue (left panel) contains 4995 objects.461 The same data set have already been reduced by DeMarchi&Paresce(1996) and later by Piotto&Zoccali (1999).," The same data set have already been reduced by \cite{dem96}462 and later by \cite{pio99}."463. By comparing our photometry with the CMD of the latter (see their Figure 1). no differences are evident.," By comparing our photometry with the CMD of the latter (see their Figure 1), no differences are evident."464 The consistency of the two photometric analyses 18 further confirmed by a direct comparison of their published lummosity function (LF: see Table 4) and the one calculatec in this work for the WF2 chip (see Section 3. for a detailec discussion)., The consistency of the two photometric analyses is further confirmed by a direct comparison of their published luminosity function (LF; see Table 4) and the one calculated in this work for the WF2 chip (see Section \ref{lumin} for a detailed discussion).465 Due to the long exposure time of the WFPC2 images. the stars at the turn-off (TO) level in this data set are saturated.," Due to the long exposure time of the WFPC2 images, the stars at the turn-off (TO) level in this data set are saturated."466 Ii order to obtain a CMD in the WFPC? area with a I magnitude range comparable with that of the ACS data set. we decidec to complement our observations with a V. vs. (V—7) grounc based catalogue from Rosenbergetal.(2000)http://www.," In order to obtain a CMD in the WFPC2 area with a I magnitude range comparable with that of the ACS data set, we decided to complement our observations with a $V$ vs. $(V-I)$ ground based catalogue from \cite{ros00}."467astro.unipd.it/globulars/.. This data set was obtained using the 1.0mm Jacobus Kapteyn Telescope (JKT) at La Palma (Canary Island)., This data set was obtained using the $1.0$ m Jacobus Kapteyn Telescope (JKT) at La Palma (Canary Island).468 We transformed the standard Johnson V./ magnitudes of the JKT catalogue to the WFPC2? VEGAMAG system adopting color term as derived by comparison of all the non-saturated stars in the WFPC2 chips that were also measured in the ground-based images.," We transformed the standard Johnson $V, I$ magnitudes of the JKT catalogue to the WFPC2 VEGAMAG system adopting color term as derived by comparison of all the non-saturated stars in the WFPC2 chips that were also measured in the ground-based images."469 No color term is necessary for the 7 band., No color term is necessary for the $I$ band.470 The uncertainties in the V. zero points and in the (V—7) color transformations are of the order of 0.007 mag., The uncertainties in the $V$ zero points and in the $(V-I)$ color transformations are of the order of $0.007$ mag.471 Due to the extremely low crowding conditions of the area covered by the WFPC2 and to the relative proximity of M110 (Ruy=44 kkpe: Harris 1996). the completeness of the ground based catalogue in this area is expected to be very high.," Due to the extremely low crowding conditions of the area covered by the WFPC2 and to the relative proximity of 10 $R_{\rm sun}=4.4$ kpc; Harris 1996), the completeness of the ground based catalogue in this area is expected to be very high."472 By comparing the observed LFs from the WFPC2 and JKT data in the same area. we found a good agreement in the magnitude range 19<7«20 (corresponding to the mass range of approximately 0.6M..<M<0.7M..).," By comparing the observed LFs from the WFPC2 and JKT data in the same area, we found a good agreement in the magnitude range $19 < I < 20$ (corresponding to the mass range of approximately $0.6M_{\odot}<M<0.7M_{\odot}$ )."473 We therefore decided to use the JKT catalogue for stars with 7<20 and the WFPC2 catalogue at fainter magnitudes., We therefore decided to use the JKT catalogue for stars with $I < 20$ and the WFPC2 catalogue at fainter magnitudes.474 In the right panel of Figure 9 we show the CMD as derived from the photometric reduction of the ACS data set., In the right panel of Figure \ref{cmd} we show the CMD as derived from the photometric reduction of the ACS data set.475 The final catalogue contains 56812 objects., The final catalogue contains 56812 objects.476 The MS of the cluster is clearly visible and well sampled well above the TO that occurs at [ο17.5., The MS of the cluster is clearly visible and well sampled well above the TO that occurs at $\sim17.5$.477 A population of candidate blue stragglers departing from the TO along a bright extension of the MS is also recognizable., A population of candidate blue stragglers departing from the TO along a bright extension of the MS is also recognizable.478 For /<16 saturation starts to occur. thus making the photometry of brighter stars unreliable.," For $I< 16$ saturation starts to occur, thus making the photometry of brighter stars unreliable."479 According to Piotto&Zoceali(1990)... due to the Galactic latitude of 110 (5=23). the contamination from foreground/background stars is small and should not effect the LF.," According to \cite{pio99}, due to the Galactic latitude of 10 $b=23^{\circ}$ ), the contamination from foreground/background stars is small and should not effect the LF."480 On the other hand Pollardetal.(2005).. using wide field imaging of evolved stellar populations. claim that field contamination. mainly from the Galactic disk. should be taken into account.," On the other hand \cite{pol05}, using wide field imaging of evolved stellar populations, claim that field contamination, mainly from the Galactic disk, should be taken into account."481 Since no direct measurement of the field contamination in our magnitude range is possible. we used a statistical approach.," Since no direct measurement of the field contamination in our magnitude range is possible, we used a statistical approach."482 A catalogue of stars using the Galactic model from Robinetal.(2003) covering an area of | square degree around the cluster center wasused’., A catalogue of stars using the Galactic model from \cite{rob03} covering an area of 1 square degree around the cluster center was.483. After scaling for the ACS and WFPC2 FOV. we found a contamination of 425 and 159 stars in our magnitude range respectively for each sample.," After scaling for the ACS and WFPC2 FOV, we found a contamination of 425 and 159 stars in our magnitude range respectively for each sample."484 This means that. even in the worst case of the WFPC? sample. where the number of sources ts small. field contamination would be of the order of ~3%. and thus can be neglected.," This means that, even in the worst case of the WFPC2 sample, where the number of sources is small, field contamination would be of the order of $\sim 3\,\%$, and thus can be neglected."485 The MS mean ridge lines for the two data sets (open circles in Figure 9)) were computed by using a 2nd order polynomial to fit the locus of MS stars. after rejecting those farther than 20 from the best fit line. where c 1s the combined photometric uncertainty in V and 7.," The MS mean ridge lines for the two data sets (open circles in Figure \ref{cmd}) ) were computed by using a ${\rm nd}$ order polynomial to fit the locus of MS stars, after rejecting those farther than $2\,\sigma$ from the best fit line, where $\sigma$ is the combined photometric uncertainty in $V$ and $I$."486 Following De Marchi Pulone (2007: hereafter DPO7). we applied this same o—-clipping approach to identify the bona-fide stars to be used in computing the LF and MF of the cluster and. in order to increase the statistics. we decided to accept as bona-fide stars all those within 2.50 of the ridge line of best fit.," Following De Marchi Pulone (2007; hereafter DP07), we applied this same $\sigma-$ clipping approach to identify the bona-fide stars to be used in computing the LF and MF of the cluster and, in order to increase the statistics, we decided to accept as bona-fide stars all those within $2.5\,\sigma$ of the ridge line of best fit."487 The catalogue obtained after this procedure. containing 464407 and 43390 stars respectively in the ACS and WFPC? field. will be used hereafter to derive the LF and MF.," The catalogue obtained after this procedure, containing 407 and 390 stars respectively in the ACS and WFPC2 field, will be used hereafter to derive the LF and MF."488 We mark as shaded regions in the CMDs of Figure 9. the limits below which the photometric completeness. as detailed in 22.3. falls below calculation.," We mark as shaded regions in the CMDs of Figure \ref{cmd} the limits below which the photometric completeness, as detailed in 2.3, falls below calculation."489 The MS ridge line that we derived in this way agrees very well with the models of Baraffe et al. (, The MS ridge line that we derived in this way agrees very well with the models of Baraffe et al. (4901997).,1997).491 The level of, The level of4927. noted a correlation between the spectra of galaxies and the dominance of their central. bulge component.,\citet{Morgan1957} noted a correlation between the spectra of galaxies and the dominance of their central bulge component.493 ? elt that a shortcoming of the Hubble classification scheme was that it was not a strong indicator of spectral class., \citet{Morgan1958} felt that a shortcoming of the Hubble classification scheme was that it was not a strong indicator of spectral class.494 In order to rectily this. ? devised a galaxy classification svsten owed upon the central light concentration compared to its overall light. distribution.," In order to rectify this, \citet{Morgan1958} devised a galaxy classification system based upon the central light concentration compared to its overall light distribution."495 This concentration classification scheme involved analysing the Dux of galaxies to determine he degree of concentration of the central component., This concentration classification scheme involved analysing the flux of galaxies to determine the degree of concentration of the central component.496 The »urpose of this scheme was to study the colour-concentration correlation in an attempt to identify ealactic evolutionary states., The purpose of this scheme was to study the colour-concentration correlation in an attempt to identify galactic evolutionary states.497 Due to the concentration parameter's direct relation with spectral class and type of stellar population. the concentration parameter was also found to be indicative of Formation history and properties. such as velocity dispersion. ealaxy size. luminosity. and (more recently) central black hole mass (?)..," Due to the concentration parameter's direct relation with spectral class and type of stellar population, the concentration parameter was also found to be indicative of formation history and properties, such as velocity dispersion, galaxy size, luminosity, and (more recently) central black hole mass \citep{Graham2001}."498 Extending Morgans pioneering work. ?— proposed a new statistical measure of asymmetry. in conjunction with a revised. paranetrisation of Morgans concentration index.," Extending Morgan's pioneering work, \citet{Conselice2000b} proposed a new statistical measure of asymmetry, in conjunction with a revised parametrisation of Morgan's concentration index."499 ‘This classification svstem was based on the desire to classify galaxies quantitatively at a range of redshifts., This classification system was based on the desire to classify galaxies quantitatively at a range of redshifts.500 Asvnimetry was defined by rotating à galaxy 180. about a central axis and finding the absolute sum of the normalised residuals.," Asymmetry was defined by rotating a galaxy $\degrees$, about a central axis and finding the absolute sum of the normalised residuals."501 This method measures the high frequency structure within each galaxy. whilst also considering the symmetry.," This method measures the high frequency structure within each galaxy, whilst also considering the symmetry."502 The measure of asvmametrey focuses primarily on morphological shape. and has a strong correlation with colour. congruent with Morgan's concentration parameter.," The measure of asymmetry focuses primarily on morphological shape, and has a strong correlation with colour, congruent with Morgan's concentration parameter."503 Xs such. this property has a correlation with both star formation and merger history.," As such, this property has a correlation with both star formation and merger history."504 7. introduced. one additional. morphological measure sensitive to high spatial frequency clumpiness., \citet{Conselice2003} introduced one additional morphological measure sensitive to high spatial frequency clumpiness.505 “Phis parameter is defined by comparing a galaxy to a smoothed image of itself., This parameter is defined by comparing a galaxy to a smoothed image of itself.506 In doing so. the clumpiness parameter quantifies galaxy morphology in a manner which rellects star forming regions and evolutionary history.," In doing so, the clumpiness parameter quantifies galaxy morphology in a manner which reflects star forming regions and evolutionary history."507 This parameter distinguishes between varying types of galaxies ancl thus. partially. resembles Llubble’s classification svstem.," This parameter distinguishes between varying types of galaxies and thus, partially, resembles Hubble's classification system."508 Llowever. the clumpiness parameter quantifies galaxy morphology with respect to intrinsic characteristics and not morphology alone.," However, the clumpiness parameter quantifies galaxy morphology with respect to intrinsic characteristics and not morphology alone."509 7? combined the high spatial frequeney ebumpiness parameter with both the asymmetry. index and the concentration index to complete what is now called the CAS classification svstem., \citet{Conselice2003} combined the high spatial frequency clumpiness parameter with both the asymmetry index and the concentration index to complete what is now called the CAS classification system.510 Underlving the CAS system's empirical nature lies the fundamental physics which governs its individual €. X. and S. components.," Underlying the CAS system's empirical nature lies the fundamental physics which governs its individual C, A, and S, components."511 The CAS system hishlights the intrinsic nature of galaxies by considering their light distributions and spectral class., The CAS system highlights the intrinsic nature of galaxies by considering their light distributions and spectral class.512 The observable properties of galaxies are a function of their merger histories. masses and environments. cach of whieh are rellected in the CAS svstem.," The observable properties of galaxies are a function of their merger histories, masses and environments, each of which are reflected in the CAS system."513 His fitting to apply this new classification. method to the theoretically oedieted: properties. of galaxies. and use it as à gauge o determine where our current understanding of galaxy ormation and evolution is correct and where it is deficient., It is fitting to apply this new classification method to the theoretically predicted properties of galaxies and use it as a gauge to determine where our current understanding of galaxy formation and evolution is correct and where it is deficient.514 Galaxy simulations are an integral tool that can help interpolate between known stages of formation history. and hus further our understanding of galaxy. evolution.," Galaxy simulations are an integral tool that can help interpolate between known stages of formation history, and thus further our understanding of galaxy evolution."515 Within the observational community. the CAS svstem is become one of the most wiclely-usecl measures of galaxy morphology (??)..," Within the observational community, the CAS system has become one of the most widely-used measures of galaxy morphology \citep{Hern2008, Bertone2009}."516 Since the completion of the combined CAS svstem. it has been applied: to numerous ealaxies including the 113 galaxies observed by 2..," Since the completion of the combined CAS system, it has been applied to numerous galaxies including the 113 galaxies observed by \citet{Frei1996}. ."517 However. it has not vet been applied systematically to hieh-resolution computational galaxy simulations as a method of comparison between observations ancl simulations.," However, it has not yet been applied systematically to high-resolution computational galaxy simulations as a method of comparison between observations and simulations."518 In. this work. we clevclop a software package patterned on the ? and ? CAS system. calibrated on an optimised training set. and. applied to high resolution galaxy simulations.," In this work, we develop a software package patterned on the \citet{Conselice2000b} and \citet{Conselice2003} CAS system, calibrated on an optimised training set, and applied to high resolution galaxy simulations."519 We show that the simulated galaxies exhibit both similarities ane differences to real galaxies. and highlight the intrinsic physical process that are responsible for the differences.," We show that the simulated galaxies exhibit both similarities and differences to real galaxies, and highlight the intrinsic physical process that are responsible for the differences."520 Ins refSimSamp we describe our simulated. galaxy samples., In \\ref{SimSamp} we describe our simulated galaxy samples.521 In τοςAS owe discuss the three structural parameters of the CAS system. Concentration (C). symmetry. CX)and Clumpiness (5).," In \\ref{CAS} we discuss the three structural parameters of the CAS system, Concentration (C), Asymmetry (A)and Clumpiness (S)."522 We then compare the simulations with the empirical ? sample of galaxies in refC'omparison.., We then compare the simulations with the empirical \citet{Frei1996} sample of galaxies in \\ref{Comparison}.523 The results are discussed in refDiscuss and conclusions drawn in re[Concl.., The results are discussed in \\ref{Discuss} and conclusions drawn in \\ref{Concl}.524 ‘To compare with the morphological parameters. inferred from observed galaxies. we used three samples of simulated galaxies.," To compare with the morphological parameters inferred from observed galaxies, we used three samples of simulated galaxies."525 Each sample was generated using the gravitational N-Bodyv | smoothecl particle hiycrodyvnamies (SPLL) code (2).., Each sample was generated using the gravitational N-Body + smoothed particle hydrodynamics (SPH) code \citep{Wadsley2004}.526" We brielly outline the simulations here. but refer the reader to the detailed. descriptions found in ?.. for what will henceforth. be called the “UW sample. ?.. for the “Dwarf sample”. and ? for the “ALUGS (MeMaster Unbiased Galaxy Simulations) sample""."," We briefly outline the simulations here, but refer the reader to the detailed descriptions found in \citet{Brooks2009}, for what will henceforth be called the “UW sample”, \citet{Governato2010}, for the “Dwarf sample”, and \citet{Stinson2010} for the “MUGS (McMaster Unbiased Galaxy Simulations) sample”."527" ltegardless of the aforementioned ""sample! from which a specific simulation was crawn. each individual 7zoomeostyle"" simulation was run within a WALAP-8 ACDAL cosmological framework (7). and consisted. of a central high resolution region (centred on the target halo) embedded: within a lower resolution Cosmological volume."," Regardless of the aforementioned `sample' from which a specific simulation was drawn, each individual “zoom-style” simulation was run within a WMAP-3 $\Lambda$ CDM cosmological framework \citep{Spergel2007} and consisted of a central high resolution region (centred on the target halo) embedded within a lower resolution cosmological volume."528 Star formation and supernova feedback was computed using the recipes outlinedby νι with the primary dilference between the three samples," Star formation and supernova feedback was computed using the recipes outlinedby \citet{Stinson2006}, , with the primary difference between the three samples"529The results of the (wo models (thin and thick shell cases) ave shown in Figures 1. and 2.. and summarized in Table 2..,"The results of the two models (thin and thick shell cases) are shown in Figures \ref{fig:rad}~ and \ref{fig:opt}, and summarized in Table \ref{tab:ij}."530 We find that both models provide an equally adequate fit (with Vu71 per degree of freedom). but Ty is not well constrained. Pj~60—5x10* (Figure 3)).," We find that both models provide an equally adequate fit (with $\chi^2_{\rm min}\approx 1$ per degree of freedom), but $\Gamma_0$ is not well constrained, $\Gamma_0\sim 60-5\times 10^3$ (Figure \ref{fig:cont}) )."531 More importantly. both models require collimated ejecta with /;zz0.95 dav (hereafter. Jet).," More importantly, both models require collimated ejecta with $t_j\approx 0.95$ day (hereafter, Jet)."532" Models with a significantly wider collimation angle have x5,~LO per degree οἱ freedom. primarily because (μον underestimate (he flux in the X-ray band by a factor of about 20. and cannot explain the radio and optical emission simultaneously."," Models with a significantly wider collimation angle have $\chi^2_{\rm min}\sim 10$ per degree of freedom, primarily because they underestimate the flux in the X-ray band by a factor of about $20$, and cannot explain the radio and optical emission simultaneously."533 At the same time. the Jet models underestimate the radio flux at /Z15 davs by about do on dav 16.3. and about 2.50 on day 32.," At the same time, the Jet models underestimate the radio flux at $t\gtrsim 15$ days by about $4\sigma$ on day 16.3, and about $2.5\sigma$ on day 32."534 This is due to an apparent brightening of the radio⋅ emission⋅⋅ on this ⋅⋅timescale., This is due to an apparent brightening of the radio emission on this timescale.535" Since⋅ in⋅ the radio⋅ band P,xmj.1/2 one possible. explanation. for the brightening is that the forward shock encounters a density enhancement: a density increase by a factor of ten is required."," Since in the radio band $F_\nu\propto n_0^{1/2}$, one possible explanation for the brightening is that the forward shock encounters a density enhancement; a density increase by a factor of ten is required."536 The flux in the optical bands would remain lareely unallected since Voy.<7. (see Table 2)). in which case the fIuxis independent of density.," The flux in the optical bands would remain largely unaffected since $\nu_{\rm opt}<\nu_c$ (see Table \ref{tab:ij}) ), in which case the fluxis independent of density."537" Using the parameters of the forward shock emission we caleulate Ezz2x10°! ere. e,£Ol eg&0.5. and nyzz107 7 using equations 4.13.4.16 of Sari&Esin(2001)."," Using the parameters of the forward shock emission we calculate $E\approx 2\times 10^{51}$ erg, $\epsilon_e\approx 0.1$, $\epsilon_B\approx 0.5$, and $n_0\approx 10^{-2}$ $^{-3}$ using equations 4.13–4.16 of \citet{se01}."538 The opening angle of the jet is 0;zz0.1 (Frailefaf2001)., The opening angle of the jet is $\theta_j\approx 0.1$ \citep{fks+01}.539". Using this value we lind a beanming corrected 5-rav emergy. £L23.7x10?""50 erg (Priceefal.2002).. twpical for loue- GRBs (Frailεἰal. 2001).. and a beaming corrected kinetic energv. EyzzLO! erg. lower than the tvpical inferred. values of 10?"" to 3x107! erg (Panaiteseu&Kumar2002)."," Using this value we find a beaming corrected $\gamma$ -ray emergy, $E_\gamma\approx 3.7\times54010^{50}$ erg \citep{pkb+02}, typical for long-duration GRBs \citep{fks+01}, , and a beaming corrected kinetic energy, $E_K\approx54110^{49}$ erg, lower than the typical inferred values of $10^{50}$ to $3\times 10^{51}$ erg \citep{pk02}."542" In the previous section we did not consider the optical emission at /Z10 days since it has a distinct spectrum. Fx4797, compared to Fyx4.PPE! for the early alterglow data."," In the previous section we did not consider the optical emission at $t\gtrsim 10$ days since it has a distinct spectrum, $F_\nu\propto \beta^{-3.9\pm 0.1}$, compared to $F_\nu\propto543\beta^{-1.15\pm 0.07}$ for the early afterglow data."544 Moreover. the predicted brightness of the afterglow at late time is lower by a lactor of about 3—5in the and { bands compared to the flix measured with LIST (Figure 2)).," Moreover, the predicted brightness of the afterglow at late time is lower by a factor of about $3-5$ in the $R$ and $I$ bands compared to the flux measured with HST (Figure \ref{fig:opt}) )."545 These two observations indicate that the late-time emission comes Iron a separate component., These two observations indicate that the late-time emission comes from a separate component.546 Priceefal.(2002) interpreted this emission as coming from a supernova that occured at about the same time as the burst., \citet{pkb+02} interpreted this emission as coming from a supernova that occured at about the same time as the burst.547 However. (μον note that the significance of this conclusion depends sensitivelv on the time of the jet break.," However, they note that the significance of this conclusion depends sensitively on the time of the jet break."548 Dased solely on the optical data. these authors were unable to significantly constrain /;.," Based solely on the optical data, these authors were unable to significantly constrain $t_j$ ."549 However. our combined radio. optical. and X-ray model with/;%0.95 dav indicates that the SN interpretation is secure.," However, our combined radio, optical, and X-ray model with$t_j\approx 0.95$ day indicates that the SN interpretation is secure."550 We euin further confidence about this interpretation by comparing the Iate-tinme emission, We gain further confidence about this interpretation by comparing the late-time emission551predict.,predict.552 Saturated conduction is usually defined as heat conduction where electrons carry (heir own thermal energy al their thermal speed., Saturated conduction is usually defined as heat conduction where electrons carry their own thermal energy at their thermal speed.553 The rationale for (his is that at faster flow speeds (relative to the ions). a Buneman instability would develop. generating Langmuir waves that would inhibit the heat flow.," The rationale for this is that at faster flow speeds (relative to the ions), a Buneman instability would develop, generating Langmuir waves that would inhibit the heat flow."554 Applied to the case above. the saturated heat {lx would be ~3.5x10? eres 7s !.," Applied to the case above, the saturated heat flux would be $\sim 3.5\times 10^5$ ergs $^{-2}$ $^{-1}$."555 In our situation the heat conducting electrons navy. also excite lower-hybrid waves with a similar threshold diit velocity., In our situation the heat conducting electrons may also excite lower-hybrid waves with a similar threshold drift velocity.556 In fact we should expect the limiting flux to be lower than this simple estimate. as indeed it is. because in our case not only heat conducting electrons but also ions generate the lower-hvbrid turbulence.," In fact we should expect the limiting flux to be lower than this simple estimate, as indeed it is, because in our case not only heat conducting electrons but also ions generate the lower-hybrid turbulence."557 Any electron heating mechanism invoked to explain the observed charge state distributions in the fast solar wind must require an anomalous thermal conductivitv to avoid the deposited heat from being conducted back to the coronal hole. which would contliet with the SUMER temperature ciagnostics of Wilhelmetal.(1998) and Davidetal.(1998).," Any electron heating mechanism invoked to explain the observed charge state distributions in the fast solar wind must require an anomalous thermal conductivity to avoid the deposited heat from being conducted back to the coronal hole, which would conflict with the SUMER temperature diagnostics of \citet{wilhelm98} and \citet{david98}."558. We consider that the heating and anomalous thermal conductivity provided simultaneously. by. lower-hiybrid waves (o be a desirable aspect of the model. in that one mechanism provides both features.," We consider that the heating and anomalous thermal conductivity provided simultaneously by lower-hybrid waves to be a desirable aspect of the model, in that one mechanism provides both features."559 In (his paper we have argued that a small amount of the energy deposited in ions between 1.5 and 2 R.. should eventually find its wav to the electrons via an instability that generates lower hybrid waves., In this paper we have argued that a small amount of the energy deposited in ions between 1.5 and 2 $R_{\sun}$ should eventually find its way to the electrons via an instability that generates lower hybrid waves.560 No attempt has been made to address the ion evelotron heating problem. other than to show that the densitv gradients we require are similar {ο those postulated by Markovskii(2001) to generate electrostatic ion cvcelotron waves [from a global resonant. MIID mode.," No attempt has been made to address the ion cyclotron heating problem, other than to show that the density gradients we require are similar to those postulated by \citet{markovskii01} to generate electrostatic ion cyclotron waves from a global resonant MHD mode."561 As such. our line of reasoning is complementary (o that in a recent paper by Cranmer (2003).," As such, our line of reasoning is complementary to that in a recent paper by \citet{cranmer03}."562. In addressing the larger problem of ion exclotron heating. these authors speculate that low frequency Alfvénn waves can Landau damp on electrons.," In addressing the larger problem of ion cyclotron heating, these authors speculate that low frequency Alfvénn waves can Landau damp on electrons."563 This parallel heating should produce electron beaming and discrete phase-space holes which max heat ions via stochastic processes., This parallel heating should produce electron beaming and discrete phase-space holes which may heat ions via stochastic processes.564 Thus (he ion heating derives [rom (he electron energization (bv low lrequeney Allvénn waves). rather than the electron heating deriving from the ion heating as in the picture presented here.," Thus the ion heating derives from the electron energization (by low frequency Alfvénn waves), rather than the electron heating deriving from the ion heating as in the picture presented here."565 While a imber of quantitative issues remain unresolved (atomic data. thermal conduction). we believe that an explanation for the observed fast wind elemental charge states in terms of lower hybrid wave electron heating is certainly. plausible. and should be considered. along with other possibilities already discussed in the literature (e.gVocks&Mann2003).," While a number of quantitative issues remain unresolved (atomic data, thermal conduction), we believe that an explanation for the observed fast wind elemental charge states in terms of lower hybrid wave electron heating is certainly plausible, and should be considered along with other possibilities already discussed in the literature \citep[e.g][]{vocks03}."566.. More accurale numerical models would allow us to exploit this interpretation and allow more rigorous investigation of densitv inhomogeneities in the [ast solar wind. with important consequences for the generation of ion evelotron waves throughout the extended corona.," More accurate numerical models would allow us to exploit this interpretation and allow more rigorous investigation of density inhomogeneities in the fast solar wind, with important consequences for the generation of ion cyclotron waves throughout the extended corona."567 As, As568Alelotte 66 holds a really special position in our work.,Melotte 66 holds a really special position in our work.569 Whether it should be included in (his case or not is still not certain., Whether it should be included in this case or not is still not certain.570 Dased on the photoelectric and photographic photometry in [αννοι (1976). the BSSs in Melotte 66 were selected in the cluster central region of 7 arcmin.," Based on the photoelectric and photographic photometry in Hawarden (1976), the BSSs in Melotte 66 were selected in the cluster central region of 7 arcmin."571 However. the BSSs ISED plotted as dotted line in Figure 10 is not at all bluer (han the conventional SSP spectrum. therefore (he B-V color of the cluster is not modified (shown in Table 2). even though it has (he largest Nja οἱ forty-six among all the sample clusters.," However, the BSSs ISED plotted as dotted line in Figure 10 is not at all bluer than the conventional SSP spectrum, therefore the B-V color of the cluster is not modified (shown in Table 2), even though it has the largest $_{BS}$ of forty-six among all the sample clusters."572 Furthermore. we find that forty DS5s of the cluster have rather red spectra instead of blue ones compared. with the turnolf.," Furthermore, we find that forty BSSs of the cluster have rather red spectra instead of blue ones compared with the turnoff."573 The remaining six blue-spectrum BSSs are all located in Ring I of 3 arcmün (Ilwwarden 1976)., The remaining six blue-spectrum BSSs are all located in Ring I of 3 arcmin (Hawarden 1976).574 In. Figure 11. solid circles are the BSSs.," In Figure 11, solid circles are the blue-spectrum BSSs."575 The solid rectangles ave red-spectirum BSSs which should be better classified as vellow stragglers., The solid rectangles are red-spectrum BSSs which should be better classified as 'yellow stragglers'.576 This complicated situation can be partially attributed to Che significant metallicity dispersion in and around the turnoff region of the cluster (Twarog 1995). apart [rom the membership ancl observational uncertainty issues.," This complicated situation can be partially attributed to the significant metallicity dispersion in and around the turnoff region of the cluster (Twarog Anthony-Twarog 1995), apart from the membership and observational uncertainty issues."577 As one of the most studied old open clusters. NGC 138 has been the subject of numerous studies in many aspects. certainly including5 its BSS population.," As one of the most studied old open clusters, NGC 188 has been the subject of numerous studies in many aspects, certainly including its BSS population."578 All the twenty BSSs in AL95 were selected from Ring5 I and II in the finding5 chart of Sancdage SC(1962). with membership probabilities p > (Dinescu οἱ al.," All the twenty BSSs in AL95 were selected from Ring I and II in the finding chart of Sandage (1962), with membership probabilities p $\geq$ (Dinescu et al."579 1996)., 1996).580 This BSS number almost doubles the number ol eleven from an earlier work of Eggen Sandage (1969)., This BSS number almost doubles the number of eleven from an earlier work of Eggen Sandage (1969).581 AI the BSSs show obvious high central concentration., All the BSSs show obvious high central concentration.582 In the work of Dinescu et al. (, In the work of Dinescu et al. (5831996). nine out of eleven of the BSSs in Eggen Sanclage (1969) were confirmed as cluster members with high probabilities. while the other two (D and L102 in Sandage 1962) were excluded due to their proper motion membership probabilities.,"1996), nine out of eleven of the BSSs in Eggen Sandage (1969) were confirmed as cluster members with high probabilities, while the other two (D and I-102 in Sandage 1962) were excluded due to their proper motion membership probabilities."584 Dinescu (et al., Dinescu (et al.585" 1996) selected eleven probable BSSs with P, > and D, > (D, ds proper motion membership probability. and D,, is (he combined probabilities of both proper motion and spatial distribution). which include five of Eggen Sandage (1969) while adding six new BSSs."," 1996) selected eleven probable BSSs with $P_{\mu}$ $\ge$ and $P_{\mu,r}$ $\ge$ $P_{\mu,r}$ is proper motion membership probability, and $P_{\mu,r}$ is the combined probabilities of both proper motion and spatial distribution), which include five of Eggen Sandage (1969) while adding six new BSSs."586 Among the six new BSSs. four ave out of Bing-ILI and the other two are in Bine-II of Sandage (1962).," Among the six new BSSs, four are out of Ring-III and the other two are in Ring-II of Sandage (1962)."587 Although being the latest observation of the cluster. Dinescus BSS catalog does not show central concentration significantly higher than RGBs. therefore the original AL95 catalog is still adopted in our work.," Although being the latest observation of the cluster, Dinescu's BSS catalog does not show central concentration significantly higher than RGBs, therefore the original AL95 catalog is still adopted in our work."588 The BSS population in this cluster has been followed intensively in the past., The BSS population in this cluster has been followed intensively in the past.589 Although a few of DS5s are subject to dispute on their membership probabilities. the overall BSs," Although a few of BSSs are subject to dispute on their membership probabilities, the overall BSS"590is AX=3.9L40.73Α.,is $\Delta\lambda=3.94\pm0.73$.591. Fitting the IL) line of the LRD. we did not get a eood fit. due to the lack of spectral resolution aud the low woad to narrow flux ratio.," Fitting the $\beta$ line of the LRD, we did not get a good fit, due to the lack of spectral resolution and the low broad to narrow flux ratio."592 We could uot fit the bluer Balmer lines because of their low S/N ratios., We could not fit the bluer Balmer lines because of their low S/N ratios.593 We did fit he Ho line in the new data., We did fit the $\alpha$ line in the new data.594 Although we do not obtain a eood fit (AZ= L9) because of the complicated line profile tthe two lines lie ou the red aud blue wing of he Πα line). we [Nri]find that there is a broad component with a width of 19A.. while the width of the nebular component is 2.7À.," Although we do not obtain a good fit $\chi^2_{\nu}=4.9$ ) because of the complicated line profile the two ] lines lie on the red and blue wing of the $\alpha$ line), we find that there is a broad component with a width of 19, while the width of the nebular component is 2.7."595. The [Nit] lines are narrow. with a vpical width of 3A.. quantitatively supporting that the orbidden. nebular lines do not have broad componcuts.," The ] lines are narrow, with a typical width of 3, quantitatively supporting that the forbidden, nebular lines do not have broad components."596 Our new. higlh-resolutiou spectra show narrow nebular lues and broad compouenuts in theHenr. IL. aud Ia lines.," Our new, high-resolution spectra show narrow nebular lines and broad components in the, $\beta$, and $\alpha$ lines."597 Our previous. modoerate-resolutiou spectra show a broad component iu the line.," Our previous, moderate-resolution spectra show a broad component in the line."598 There is no broad component in the nebular lines iu either the new or old spectra., There is no broad component in the [O ] nebular lines in either the new or old spectra.599 There[O is still no sign of anv absorption lines in the new spectra., There is still no sign of any absorption lines in the new spectra.600 The broad components of bothTell aud IL have widths ~750 kms. consistent with production in the accretion disk. aud are roughly Cassia. instead of having P-Cweni profiles that would imdicate origin iu a wind.," The broad components of both and $\beta$ have widths $\sim$ 750 km/s, consistent with production in the accretion disk, and are roughly Gaussian, instead of having P-Cygni profiles that would indicate origin in a wind."601" Following Porter(2010).. woe estimate the size of the line-enüttius region. Ay. by assumdüus the lue-cinitting eas is in dKeplerian orbits around a conipaet object. thus Ry,<GAI/0."," Following \citet{porter}, we estimate the size of the line-emitting region, $R_{le}$, by assuming the line-emitting gas is in Keplerian orbits around a compact object, thus $R_{le} \le GM/v^2$."602 We find Ry<2.35vun) AU. which for a mass of 10. AD. would eive an upper limit of 3.1 Rw.," We find $R_{le}<2.35 \left( \frac{M_{\rm{BH}}}{1500\, \rm{M}_{\odot}} \right)$ AU, which for a mass of 10 $_{\odot}$ would give an upper limit of 3.4 $_{\odot}$."603 This is cousistent with oriein of the broad Bine in the accretion disk., This is consistent with origin of the broad line in the accretion disk.604 The broad line componcuts are shifted relative to th narrow compoucuts., The broad line components are shifted relative to the narrow components.605 In the new data. the shifts are simall compared to the line width. |56+17 |au/s for and =33420 kms for IL.," In the new data, the shifts are small compared to the line width, $+56 \pm 17$ km/s for and $-33 \pm 20$ km/s for $\beta$."606 These shifts are consistent oulv at the 30 level. which might indicate a difference in the spatial origin of the lines.," These shifts are consistent only at the $3\sigma$ level, which might indicate a difference in the spatial origin of the lines."607 Wowever. this is still consistent with production of both lines within the dis- since random motions within the disk and variatiou between the cussion regions could produce shifts that are siunall compared to the line widths. as observed.," However, this is still consistent with production of both lines within the disk since random motions within the disk and variation between the emission regions could produce shifts that are small compared to the line widths, as observed."608 The ceutral wavelength of theTei broad. component shifts markedly between the odld aud uew data. AA=3.914073 AorAc =252+IF kms. This shift is a substantial fraction of the line width.," The central wavelength of the broad component shifts markedly between the odld and new data, $\Delta\lambda=3.94\pm0.73$ $\,$ or $\Delta v = 252 \pm 47 $ km/s. This shift is a substantial fraction of the line width."609 The shift could be due to random motion within the disk. differing viewing gcomectrics (Robertsotal.2010).. or orbital motion of disk (aud the compact object).," The shift could be due to random motion within the disk, differing viewing geometries \citep{rob10}, or orbital motion of disk (and the compact object)."610 If the shifts in the broad component of the liue are due to orbital motion. then this would provide a mcans to deteriuue the orbital period and would also provide a lueasurenmient of the nass fiction for the secondary star.," If the shifts in the broad component of the line are due to orbital motion, then this would provide a means to determine the orbital period and would also provide a measurement of the mass function for the secondary star."611 Thus. a program of niionitoriug NGC 5los N-1 with hieh-resolutiou optical spectroscopic observations will be Huportant iu extending our understanding of the plysical nature of this svsteni.," Thus, a program of monitoring NGC 5408 X-1 with high-resolution optical spectroscopic observations will be important in extending our understanding of the physical nature of this system."612 Iu this section. we make some speculations based on interpretation of the shift in the broad component of the line as due to orbital motion.," In this section, we make some speculations based on interpretation of the shift in the broad component of the line as due to orbital motion."613 One can express the mass function aud the compact object mass. A). dn ternis of the orbital period. P. the velocity excursion. A. aud the companion mass. AL. as where /is the inclination angle aud G is the gravitational constant.," One can express the mass function and the compact object mass, $M_x$, in terms of the orbital period, $P$, the velocity excursion, $K_{x}$, and the companion mass, $M_{c}$ as where $i$ is the inclination angle and $G$ is the gravitational constant."614" From the shift of the line quoted above. we constraiu the scuu-ampltucde of the radial velocity iy,>Δον=126421 lan/s. Thus. if the maxinnun nass of the companion aud the orbital period are kuown. ren Eq."," From the shift of the line quoted above, we constrain the semi-amplitude of the radial velocity $K_x \ge \Delta v/2 = 126 \pm 24$ km/s. Thus, if the maximum mass of the companion and the orbital period are known, then Eq."615 2 leads to an upper bound onthe mass of the conrpact object., 2 leads to an upper bound onthe mass of the compact object.616 The binary svstem has a visual magnitude ey=22.2 lat eives an upper luit ou the absolute magnitude of i6 colupanion of Vo=6.2 at a distance of L5 Alpe INarachentseyetal. 2002)., The binary system has a visual magnitude $v_0=22.2$ that gives an upper limit on the absolute magnitude of the companion of $V_0=-6.2$ at a distance of 4.8 Mpc \citep{dist}. .617. Unfortunatelv. this places ittle restriction on the companionmass as even O3V y.ars.With masses of 120. AL... ave allowed.," Unfortunately, this places little restriction on the companionmass as even O3V stars,with masses of 120 $M_{\odot}$ , are allowed."618 However. very," However, very"619histogram clearly slows the coarse iutensitv binning.,histogram clearly shows the coarse intensity binning.620 Without dithering. the image breaks up iuto discrete “bands” of coustaut mutensitv which takes it more difficult to detect faint atures in the nuage.," Without dithering, the image breaks up into discrete “bands” of constant intensity which makes it more difficult to detect faint features in the image."621 This effect is shown in Figure 3.Pa (using aln even nire coarselv quantized Ga = 04 inage to chhance the effect). where the majority of the background pixels all have the same (nediuu erav) intensity value.," This effect is shown in Figure 3, (using an even more coarsely quantized q = 0.5 image to enhance the effect), where the majority of the background pixels all have the same (medium gray) intensity value."622 Iu this first experiment. we exanune how the uncertainties of the photometric aud astrometric nieasurenients of individual stars depend oi the q quantization factor.," In this first experiment, we examine how the uncertainties of the photometric and astrometric measurements of individual stars depend on the q quantization factor."623 To measure this effect. we computed the 5audard Deviation of the magnitude and position errors (ie. the value computed by SExtracOr Wiis he known iuput naenitude or position value) for 6250. «inulaed star Huages at each 0.5. inagnitude lncreiment.," To measure this effect, we computed the Standard Deviation of the magnitude and position errors (i.e., the value computed by SExtractor minus the known input magnitude or position value) for 6250 simulated star images at each 0.5 magnitude increment."624 Figure { shows how the naenitude uncertainties decrease as the brieltuess of the star diucreases (towards the right)., Figure 4 shows how the magnitude uncertainties decrease as the brightness of the star increases (towards the right).625 The ower. thicker line in the figure was derived from the original. uuquautized nuages and shows tha the statisical unecrtainty ou the magnitudes decreases from o=0.23 for the faintest detectable sars (width m = 20). to σ=0.015 for stars tha are 2 maeuitudes brighter.," The lower, thicker line in the figure was derived from the original, unquantized images and shows that the statistical uncertainty on the magnitudes decreases from $\sigma = 0.23$ for the faintest detectable stars (with m = 20), to $\sigma = 0.018$ for stars that are 3 magnitudes brighter."626 The line has a slope close to 1.0 (iu log - log coordinates) as expected in the limiting case where the noise is dominate by the sky. aud hence the sienal-o-nolse ratio of the measurement increases in direct proportion to the signal.," The line has a slope close to 1.0 (in log - log coordinates) as expected in the limiting case where the noise is dominated by the sky, and hence the signal-to-noise ratio of the measurement increases in direct proportion to the signal."627 The other 3 lines in Figure. Lowere derived from the same nuages after they were firs quautize and compressed with successively coarser q values of L.0. 0.5. and 0.25. when also applviung the subtractive ditherus option.," The other 3 lines in Figure 4 were derived from the same images after they were first quantized and compressed with successively coarser q values of 1.0, 0.5, and 0.25, when also applying the subtractive dithering option."628 The verical displacement of these lines shows that the measurement errors are systematically larecr in the quantized images as conpared to he iieasureimeuts m the origina nuage., The vertical displacement of these lines shows that the measurement errors are systematically larger in the quantized images as compared to the measurements in the original image.629 This increase is relatively simall for qo l. but increases rapidly for coarser quantization values.," This increase is relatively small for q $\geq$ 1, but increases rapidly for coarser quantization values."630 Figure 5 shows a similar plot of he Standard Deviation of the stellar ceutroid measurements. iu units of pixels. as a function of the magnitude of the star aud the q quantization factor.," Figure 5 shows a similar plot of the Standard Deviation of the stellar centroid measurements, in units of pixels, as a function of the magnitude of the star and the q quantization factor."631 In the original unuquautized images. the positional uncertainty decreases from σ=0.21 pixels for jo n = 20 stars. to σ=0035 pixels for 1ο stars that are 3H magnitudes brighter.," In the original unquantized images, the positional uncertainty decreases from $\sigma = 0.24$ pixels for the m = 20 stars, to $\sigma = 0.035$ pixels for the stars that are 3 magnitudes brighter."632 The )ositional nieasureukut uncertainties are larger iu je quantized mage by about the same factor as 10 increase in the magnituο uncertainties shown oeu Figure 1., The positional measurement uncertainties are larger in the quantized image by about the same factor as the increase in the magnitude uncertainties shown in Figure 4.633 Tn order to better quantity the effects shown iu jese 2 figures. Table 1 sunnuarizes how the noise aud the measurement uncertaimlos Inerease as the inages are quantized more coarsely.," In order to better quantify the effects shown in these 2 figures, Table 1 summarizes how the noise and the measurement uncertainties increase as the images are quantized more coarsely."634 The measured )ereentage merease in the VAD noise level in the quantized mages is eiven in column 2 aud agrees exactly with the prediced value. from equation 10.., The measured percentage increase in the MAD noise level in the quantized images is given in column 2 and agrees exactly with the predicted value from equation \ref{eq:fractionalnoise}.635" More strikingly. the maenitude and position uncertainties for the fainest stars also increase by about the same factor as the toisc, as shown in columns 3 and."," More strikingly, the magnitude and position uncertainties for the faintest stars also increase by about the same factor as the noise, as shown in columns 3 and 4."636" This ueans that equation 10 also provides a good esnuate of how much the neasurement unucert:ünties of the faintest objects iu an image. which are lianited by the backerouud roise, will increase when the image is quautized."," This means that equation \ref{eq:fractionalnoise} also provides a good estimate of how much the measurement uncertainties of the faintest objects in an image, which are limited by the background noise, will increase when the image is quantized."637 Finally. σοι 5 aud 6 in Table 1 give the corresponding increase i measurenmoeu uncertainties Or stars that are 5 magnitudes. or a factor of LOO. brighter than the image cetection threshold.," Finally, columns 5 and 6 in Table 1 give the corresponding increase in measurement uncertainties for stars that are 5 magnitudes, or a factor of 100, brighter than the image detection threshold."638 As expected. these bvieghter objects are relatively ess affected by quantization because he iuhereut DPoissonuiui noise iu the brighter pixels is larger hau the spacing hetween the quantized levels.," As expected, these brighter objects are relatively less affected by quantization because the inherent Poissonian noise in the brighter pixels is larger than the spacing between the quantized levels."639 Also. the small formal statistical errors on the naguitudes and posiious of the brighter stars (which are less than (LOOL of a naguitude or pixel. respectively. iu this Case] are often iusiguificant compared to the svstematic errors in the absolute calibration of the measurements.," Also, the small formal statistical errors on the magnitudes and positions of the brighter stars (which are less than 0.001 of a magnitude or pixel, respectively, in this case) are often insignificant compared to the systematic errors in the absolute calibration of the measurements."640 For comparison. Figures 6 aud 7 show that if the quantized pixels are not direred then he measurement orYOYs are larecr lan in the dithered case shown previously in Figures { and 5.," For comparison, Figures 6 and 7 show that if the quantized pixels are not dithered then the measurement errors are larger than in the dithered case shown previously in Figures 4 and 5."641 It is strikine tha while dithering provides a uodest increase πι he accuracy of the ceutroid neasurenieuts. it ereatly iniproves the magnitude neasurements.," It is striking that while dithering provides a modest increase in the accuracy of the centroid measurements, it greatly improves the magnitude measurements."642 Futwer juvestigation has shown hat the larecr nuvgnitude errors are almost entirely caused by a craluatic increase iu the errors in the SExtractor ]vackeround estimate around each star if the quaiitized mage is not dithered., Further investigation has shown that the larger magnitude errors are almost entirely caused by a dramatic increase in the errors in the SExtractor background estimate around each star if the quantized image is not dithered.643 SExtractor asstucs hat the best estimate of the true backeround level is given by the peak in the histogram of the pixcJ values (1.60. the mode) aud," SExtractor assumes that the best estimate of the true background level is given by the peak in the histogram of the pixel values (i.e., the mode) and"644colponcuts. and = 70.100 IK aud (Πο) 2 for the wing material near IRAS LA. Low amass star forming site suggested to be a binary svsteni separated by ~ 0.37 (Colicuetal.LOSL)..,"components, and = 70–100 K and ) = for the wing material near IRAS 4A. 		 Low mass star forming site suggested to be a binary system separated by $\sim$ $\arcsec$ \citep{Cohen84}."645 Single Gaussian cussion profiles were detected im both transitions with a central velocity typical of the region at ~ σιsi. Mori, Single Gaussian emission profiles were detected in both transitions with a central velocity typical of the region at $\sim$ 6.4.646arty-Schievenetal.(1995) used aud2oy.. 218 GIIZ) aud CS observations to derive a kinetic teniperature of ~ LO Iv and a spatial deusity ofcnr.," \citet{MS95} used and, 218 GHz) and CS observations to derive a kinetic temperature of $\sim$ 40 K and a spatial density of."647.. Robertset.al.(2002) and Roberts&Millar(2007) examined transition ratios of several species. ποιοπιο the (150 Giz) and (72 GIIz) trausitious ofToCO.. aud quote a bolometric teniperature of 97 I& for the region.," \citet{Rob02} and \citet{RM07} examined transition ratios of several species, including the (150 GHz) and (72 GHz) transitions of, and quote a bolometric temperature of 97 K for the region."648 Because the transitions emploved by Moriarty-Schieveuetal(1995) are biased toward temperatures < 50 Iv and the LVC prediction of our observed transition ratio supports a higher kinetic temperature. we have assumed 100 I for our analysis while also testing temperatures of LO and 150 Is. Additional measurements lave been conducted for L1551 for the transition bv Aravaetal.(2006)...," Because the transitions employed by \citet{MS95} are biased toward temperatures $\leq$ 50 K and the LVG prediction of our observed transition ratio supports a higher kinetic temperature, we have assumed 100 K for our analysis while also testing temperatures of 40 and 150 K. Additional measurements have been conducted for L1551 for the transition by \citet{Ara06}. ."649 The spatial deusitv of IBS 5 las Όσοι estimated: usine several methods., The spatial density of IRS 5 has been estimated using several methods.650 Butueretal.(1991) fouud an average volue deusitv of within au aneular radius of 1378 by modeling Eu-ufrared eiission. while Fulleretal.(1995). estimate usus OO emission.," \citet{But91} found an average volume density of within an angular radius of $\farcs$ 8 by modeling far-infrared emission, while \citet{Ful95} estimate using O emission."651 M«larty-Schievenetal.(1995). derived the significantly higher deusity of using transition ratios of the CS moleciule., \citet{MS95} derived the significantly higher density of using transition ratios of the CS molecule.652 The best-studied region of massive star formation to date (see review by Cenzel&Stutzikd 1989)) aud extremely bright iun ai plethora of chemical species (brigbtuess temperatures from Orion-KL are 2 5« that of anv other source in our studv)., The best-studied region of massive star formation to date (see review by \citealt{GS89}) ) and extremely bright in a plethora of chemical species (brightness temperatures from Orion-KL are $>$ $\times$ that of any other source in our study).653 This is the ouly source in our sanuple for which previous observations of the transition of have been made (Wilsonetal.1980:Myers.&BustonBastienetal. 1985).," This is the only source in our sample for which previous observations of the transition of have been made \citep{Wil80,MB80,Bas85}."654". Outflows. shocks. aud. turbulence arising from) newly formed stars in the region lave led to a complex velocity structure comprised of several distinct conponents (Blakeetal.1987).. at least three of which are captured iu our observations: the hot core ~ 6]anο, Ar> 10st. ~ 300 KR). compact ridge o8si. Apo Lhe. ~ 135 K) and extended ridge ~ 9103. Aw ~ Elaus. ~ 135 KR). cach with spatial density 2((I15)) > (Mauguuetal.1993:Mig&Wootten1993)."," Outflows, shocks, and turbulence arising from newly formed stars in the region have led to a complex velocity structure comprised of several distinct components \citep{Blake87}, at least three of which are captured in our observations: the hot core $\sim$ 6, $\Delta\nu >$ 10, $\sim$ 300 K), compact ridge $\sim$ 8, $\Delta\nu$ $\sim$ 4, $\sim$ 135 K), and extended ridge $\sim$ 9–10, $\Delta\nu$ $\sim$ 4, $\sim$ 135 K), each with spatial density ) $\gtrsim$ \citep{Man93,MW93}."655. Ow J= lLspectrum exhibits an anomalously intense velocity component at ~ 10.31... which also appears as a much smaller coutribution iu the J=3 trausition.," Our $J=4$ spectrum exhibits an anomalously intense velocity component at $\sim$ 10.3, which also appears as a much smaller contribution in the $J=3$ transition."656 A feature at this velocity exists LO” north of our observed position (αποσπάetal.19903... leading us fo suspect a pointing error.," A feature at this velocity exists $\arcsec$ north of our observed position \citep{Man90}, leading us to suspect a pointing error."657 Poiuting was checked prior to observing. aud the Oriou-KL sceau was followed bv observations of OMC-2 IRS Land NGC 2021.," Pointing was checked prior to observing, and the Orion-KL scan was followed by observations of OMC-2 IRS 4 and NGC 2024."658 If a pointing error is to be blamed. it should manifest itself in the subsequent observations of OMC-2 IRS 1 and NGC 2021. but we could find no evidence for this.," If a pointing error is to be blamed, it should manifest itself in the subsequent observations of OMC-2 IRS 4 and NGC 2024, but we could find no evidence for this."659 The possibilities of an unidentified line or rest frequeucy error were also ruled out., The possibilities of an unidentified line or rest frequency error were also ruled out.660 This spectrum is the average of ouly two Guutually consistent) scans conducted cing a single run., This spectrum is the average of only two (mutually consistent) scans conducted during a single run.661 We suggest that this cussion arises from the extended ridge. which is typically observed around ~ 9st. but occasionally as high as 10st.," We suggest that this emission arises from the extended ridge, which is typically observed around $\sim$ 9, but occasionally as high as 10."662. This interpretation.- and the physical parameters derived frou it. should be applied cautiously for the reasons explained above.," This interpretation, and the physical parameters derived from it, should be applied cautiously for the reasons explained above."663 Because of the disparity between the relative iuteusitv of the 10.3 feature in cach trausition. oulv the transition ratio for the hot core component could be fit by the LVG model. aud the extraordinarily biel iutensities precluded the determination of useful density limits for the other components through the procedure described ii refLTE..," Because of the disparity between the relative intensity of the 10.3 feature in each transition, only the transition ratio for the hot core component could be fit by the LVG model, and the extraordinarily high intensities precluded the determination of useful density limits for the other components through the procedure described in \\ref{LTE}. ."664 Broad SiO enmissiou coupled with relatively weak and CIT;OOITemission iudicates the presence ofau cherectic outflow in its earliest phase. sugeestiug that," 		 Broad SiO emission coupled with relatively weak and OHemission indicates the presence ofan energetic outflow in its earliest phase, suggesting that"665"A natural first step in explaining the observed emission line properties is to investigate whether the line ratios can be explained by photoionization from a single dominant star, an approach adopted qualitatively by Peimbertetal.(1975).","A natural first step in explaining the observed emission line properties is to investigate whether the line ratios can be explained by photoionization from a single dominant star, an approach adopted qualitatively by \citet{pei75}."666. We will follow their discussion except that we shall use the spectral types summarized in Goudis(1982) and use the Q(H) values from the recent study by Heapetal.(2006)., We will follow their discussion except that we shall use the spectral types summarized in \citet{gou} and use the Q(H) values from the recent study by \citet{srh06}.667". There are many candidate ionizing stars within Barnard's Loop and its extension into theBubble,, the brightest six in the LyC are the brightest Trapezium O6 V star with an expected LyC luminosity of 6 x 1045 photons1, the cooler (spectral type O9.5 II) 6 OOri with an expected LyC luminosity of 5.6x1045 photon ως OOri (O9.5 Ib) at 5.6x1045 photon ,, and z Ori (spectral type O9 IIT) at 6.6x1055 photons~!, plus aand σ Ori (both 09.5 V and 1.5x1045 photon s~'))."," There are many candidate ionizing stars within Barnard's Loop and its extension into the, the brightest six in the LyC are the brightest Trapezium O6 V star with an expected LyC luminosity of 6 x $^{48}$ photons, the cooler (spectral type O9.5 II) $\delta$ Ori with an expected LyC luminosity of $5.6\times 10^{48}$ photon, $\zeta$ Ori (O9.5 Ib) at $5.6\times 10^{48}$ photon , and $\iota$ Ori (spectral type O9 III) at $6.6\times 10^{48}$ photon, plus and $\sigma$ Ori (both 09.5 V and $1.5\times 10^{48}$ photon )."668 It is unclear if e OOri belongs in this list., It is unclear if $\epsilon$ Ori belongs in this list.669 With a spectral type of BO Ia it is cooler than the stars studied by Heapetal.(2006)., With a spectral type of B0 Ia it is cooler than the stars studied by \citet{srh06}.670. Vaccaetal.(1996) did include one star (HD 37128) of this spectral type in their study and found it to be be 6000 K cooler than an O9.5 Ia spectral type star (HD 30614) and would therefore have a much lower LyC luminosity., \citet{vacca} did include one star (HD 37128) of this spectral type in their study and found it to be be 6000 K cooler than an O9.5 Ia spectral type star (HD 30614) and would therefore have a much lower LyC luminosity.671" Since ¢ OOri has a spectral type of O9.5 Ib, we conclude that e OOri's LyC luminosity is much lower than 5.6x1035 photon aand we will not include it in our tally."," Since $\zeta$ Ori has a spectral type of O9.5 Ib, we conclude that $\epsilon$ Ori's LyC luminosity is much lower than $5.6\times 10^{48}$ photon and we will not include it in our tally."672 The location of these stars are shown in Figure 1., The location of these stars are shown in Figure 1.673" Although there are many additional stars of later spectral type and less luminous stars are distributed throughout the inner Orion constellation, their contribution to photoionization ofBarnard's Loop must be minimal."," Although there are many additional stars of later spectral type and less luminous stars are distributed throughout the inner Orion constellation, their contribution to photoionization ofBarnard's Loop must be minimal."674 For a summaryof the properties of these stars see Table 1.1.IV of Goudis (1982)., For a summaryof the properties of these stars see Table 1.1.IV of \citet{gou}. .675can be calculated.,can be calculated.676 Although the RV semi-amplitude K and the period P are determined by the RV curve. Mig. Mi and sin?{ remain free parameters.," Although the RV semi-amplitude $K$ and the period $P$ are determined by the RV curve, $M_{\rm sdB}$, $M_{\rm comp}$ and $\sin^3i$ remain free parameters."677 Nevertheless. the masses can be constrained by assuming tidal synchronisation (see also Napiwotzki et al. 200100.," Nevertheless, the masses can be constrained by assuming tidal synchronisation (see also Napiwotzki et al. \cite{napiwotzki5}) )."678 Combining the orbital parameters with an estimate of the sdB mass and with the determination of its vjsin/ and surface gravity. allows the mass of the invisible companion to be constrained.," Combining the orbital parameters with an estimate of the sdB mass and with the determination of its $v_{\rm rot}\sin{i}$ and surface gravity, allows the mass of the invisible companion to be constrained."679 The mass of the sdB primary is taken from the population synthesis models (Han et al. 2002.. 2003))," The mass of the sdB primary is taken from the population synthesis models (Han et al. \cite{han1}, , \cite{han2}) )"680" that predict a mass range of My 00.37 — MM... for sdBs in binaries. which experienced a common envelope ejection,"," that predict a mass range of $M_{\rm sdB}$ 0.37 – $_{\rm \odot}$ for sdBs in binaries, which experienced a common envelope ejection."681 The mass distribution shows a sharp peak at a mass of about 0.47M. (see Fig.," The mass distribution shows a sharp peak at a mass of about $0.47\,{\rm M_{\odot}}$ (see Fig."682 22 of Han et al. 2003)), 22 of Han et al. \cite{han2}) )683 ranging from 0.43 to MM..., ranging from 0.43 to $_{\rm \odot}$.684 This theoretical mass distribution is consistent with analyses of close binary systems (e.g. Geter et al. 2007)), This theoretical mass distribution is consistent with analyses of close binary systems (e.g. Geier et al. \cite{geier1}) )685 as well as asteroseismic analyses of pulsating sdBs (see Charpinet et al., as well as asteroseismic analyses of pulsating sdBs (see Charpinet et al.686 2008 and references therein)., \cite{charpinet} and references therein).687 If the rotational period of the sdB primary is synchronised the rotational velocity v=2gRap/P can be calculated., If the rotational period of the sdB primary is synchronised the rotational velocity $v_{\rm rot}= 2 \pi R_{\rm sdB}/P$ can be calculated.688 The radius of the primary is given by the mass radius relation R=JMagG/g., The radius of the primary is given by the mass radius relation $R = \sqrt{M_{\rm sdB}G/g}$.689" The measurement of the projected rotational velocity vj,sin/ therefore allows us to constrain the inclination angle i."," The measurement of the projected rotational velocity $v_{\rm rot}\,\sin\,i$ therefore allows us to constrain the inclination angle $i$."690 For the most likely sdB mass μμ=0.47M.« the mass function can be solved. and both the inclination angle and the companion mass can be derived.," For the most likely sdB mass $M_{\rm sdB}=0.47\,{\rm M_{\odot}}$ the mass function can be solved, and both the inclination angle and the companion mass can be derived."691 The errors are caleulated by chosing the most extreme values for the input parameters within their respective error limits., The errors are calculated by chosing the most extreme values for the input parameters within their respective error limits.692 In order to account for the theoretical uncertainity in sdB mass. we adopted the predicted mass range for the sdB (0.43—0.47 M.) and calculated the lower limit for the companion mass under the assumption that μμ=0.43M...," In order to account for the theoretical uncertainity in sdB mass, we adopted the predicted mass range for the sdB $0.43-0.47\,{\rm M_{\odot}}$ ) and calculated the lower limit for the companion mass under the assumption that $M_{\rm sdB}=0.43\,{\rm M_{\odot}}$."693 The error budget is dominated by the uncertainties in the vj;sin; and logg measurements., The error budget is dominated by the uncertainties in the $v_{\rm rot}\sin{i}$ and $\log{g}$ measurements.694 The mass function provides a lower limit to the mass of the invisible companion of 0.35M...," The mass function provides a lower limit to the mass of the invisible companion of $0.35\,{\rm M_{\odot}}$."695 In the case of a white dwarf primary it 1s impossible to hide the contribution of a main sequence star even of the lowest mass in optical/NIR spectra since these are mtrinsically faint., In the case of a white dwarf primary it is impossible to hide the contribution of a main sequence star even of the lowest mass in optical/NIR spectra since these are intrinsically faint.696 This is not the case for sdB stars., This is not the case for sdB stars.697 A main sequence companion with a mass lower than 0.45M.« can not be excluded because its luminosity would be too low to be detectable in the spectra (Lisker et al. 2005)).," A main sequence companion with a mass lower than $0.45\,{\rm M_{\odot}}$ can not be excluded because its luminosity would be too low to be detectable in the spectra (Lisker et al. \cite{lisker}) )."698 This is the reason why the companions’ nature still remains unknown for most of the 280 sdB systems in the catalogue of Ritter Kolb (2009))., This is the reason why the companions' nature still remains unknown for most of the $\approx$ 80 sdB systems in the catalogue of Ritter Kolb \cite{ritter}) ).699 Additional information is needed., Additional information is needed.700 No spectral features of a cool main sequence star are present in the optical spectra of 6687., No spectral features of a cool main sequence star are present in the optical spectra of 687.701 Furthermore. Farthi et al. (2005))," Furthermore, Farihi et al. \cite{farihi}) )"702 included 6687 in a near-infrared imaging survey to search for low-luminosity companions to white dwarfs and found no evidence for an infrared excess which could be caused by à cool main sequence companion., included 687 in a near-infrared imaging survey to search for low-luminosity companions to white dwarfs and found no evidence for an infrared excess which could be caused by a cool main sequence companion.703 As the lower limit for the mass of 6687's companion derived from the mass function. is lower than 0.45M... additional information is needed to clarify its nature.," As the lower limit for the mass of 687's companion derived from the mass function is lower than $0.45\,{\rm M_{\odot}}$, additional information is needed to clarify its nature."704 We made use of the gravity and projected rotational velocity to constrain the mass to 0.71703:M...," We made use of the gravity and projected rotational velocity to constrain the mass to $0.71_{-0.21}^{+0.22}\,{\rm M_{\odot}}$."705 The companion therefore can not be ἃ main sequence star but has to be a white dwarf., The companion therefore can not be a main sequence star but has to be a white dwarf.706" Taking into account the possible mass range it is very likely to be of C/O composition,", Taking into account the possible mass range it is very likely to be of C/O composition.707 Its mass exceeds that of an average white dwarf., Its mass exceeds that of an average white dwarf.708 6687 isonly the fourth sdB star. for which the white dwarf nature of the companion could be shown unamibiguously.," 687 isonly the fourth sdB star, for which the white dwarf nature of the companion could be shown unamibiguously."709 The others have been discovered by analysing ellipsoidal light variations 11930+2752. 00101+039) or eclipses 00422-5421]. Orosz Wade 1999)) 1," The others have been discovered by analysing ellipsoidal light variations $+$ 2752, $+$ 039) or eclipses $+$ 5421, Orosz Wade \cite{orosz}) )."7101930-2752 and PG00101-039 have been confirmed with the method used here (Geier et al. 2007. 2008).," $+$ 2752 and $+$ 039 have been confirmed with the method used here (Geier et al. \cite{geier1,geier2}) )."711 The derived companion mass was caleulated. under the assumption of orbital synchronisation., The derived companion mass was calculated under the assumption of orbital synchronisation.712 Since. theoretical synchronisation timescales. for hot stars with radiative envelopes are not consistent (Zahn 1977:; Tassoul Tassoul 1992)). empirical evidence for orbital sychronisation in sdB binaries is needed.," Since theoretical synchronisation timescales for hot stars with radiative envelopes are not consistent (Zahn \cite{zahn}; Tassoul Tassoul \cite{tassoul}) ), empirical evidence for orbital sychronisation in sdB binaries is needed."713 Geier et al. (2008)), Geier et al. \cite{geier2}) )714 found such evidence by detecting a variation in the lighteurve of the sdB+WD binary 00101+039. which could be identified as ellipsoidal deformation of the sdB. Since the orbital period of 001014039 ts 0.57 d. sdB binaries with shorter periods like 6687 are very likely synchronised as well.," found such evidence by detecting a variation in the lightcurve of the sdB+WD binary $+$ 039, which could be identified as ellipsoidal deformation of the sdB. Since the orbital period of $+$ 039 is $0.57\,{\rm d}$ , sdB binaries with shorter periods like 687 are very likely synchronised as well."715 Recently van Grootel et al. (2008)), Recently van Grootel et al. \cite{vangrootel}) )716 performed an asteroseismic analysis of the pulsating sdB binary Feige48 and for the first time proved orbital sychronisation in this way., performed an asteroseismic analysis of the pulsating sdB binary Feige48 and for the first time proved orbital sychronisation in this way.717 The orbital period of Feige 48 (0.36 d) is very similar tothe one of 6687.," The orbital period of Feige 48 $0.36\,{\rm d}$ ) is very similar tothe one of 687."718 Furthermore. the atmospheric parameters of 6687 (Tay=24300 K. logg= 5.32) indicate that it has already evolved away," Furthermore, the atmospheric parameters of 687 $T_{\rm eff}=24\,300\,{\rm K}$ , $\log{g}=5.32$ ) indicate that it has already evolved away"719 is the number of photometric objects in sample i.,where $N^{\rm phot}_i$ is the number of photometric objects in sample $i$.720 This wherecircumventsNphet the issue of which photometric objects to cross-correlate against a set of spectroscopic objects in a chosen bin of redshift., This circumvents the issue of which photometric objects to cross-correlate against a set of spectroscopic objects in a chosen bin of redshift.721 Clearly photometric samples which peak at very different redshifts from the spectroscopic sample are significantly down-weighted in the sum., Clearly photometric samples which peak at very different redshifts from the spectroscopic sample are significantly down-weighted in the sum.722" Note that our method also down-weights both objects with unusual colours that might have multi-peaked PDFs and objects with poorly constrained photometry, such as near survey limits, where the PDF might be very broad."," Note that our method also down-weights both objects with unusual colours that might have multi-peaked PDFs and objects with poorly constrained photometry, such as near survey limits, where the PDF might be very broad."723 Since the binning is so far arbitrary we can consider the limit where each slice in Eq. (6)), Since the binning is so far arbitrary we can consider the limit where each slice in Eq. \ref{eqn:wpvarweight}) )724" represents a single photometric object, i.e. NP**—1 for each i."," represents a single photometric object, i.e. $N_i^{\rm phot}=1$ for each $i$."725 In this case photometric objects that have some overlap with the spectroscopic bin of interest are included in the sum and photometric objects with zero overlap have zero weight., In this case photometric objects that have some overlap with the spectroscopic bin of interest are included in the sum and photometric objects with zero overlap have zero weight.726" Treating the photometric objects individually, rather than in an ensemble, removes the need for any arbitrary binning and effectively reduces the extension of the ensemble PDF along the line-of-sight and should thus significantly improve the clustering signal-to-noise."," Treating the photometric objects individually, rather than in an ensemble, removes the need for any arbitrary binning and effectively reduces the extension of the ensemble PDF along the line-of-sight and should thus significantly improve the clustering signal-to-noise."727 Because the weights in Eq. (6)), Because the weights in Eq. \ref{eqn:wpvarweight}) )728" are o;?=NP?f? a rough determination of how much this new estimator will improve the signal-to-noise of a w, estimate over existing methods, which only consider objects that have a peak photometric redshift in the bin of interest iswhere the { subscripts represent our new optimal estimator for a slice containing N?""°t photometric objects and the n represents the number of photometric objects with a PDF peak in the spectroscopic bin of interest."," are $\sigma_i^{-2} = N_i^{\rm phot} f_i^2$ a rough determination of how much this new estimator will improve the signal-to-noise of a $w_p$ estimate over existing methods, which only consider objects that have a peak photometric redshift in the bin of interest iswhere the $i$ subscripts represent our new optimal estimator for a slice containing $N^{\rm phot}$ photometric objects and the $n$ represents the number of photometric objects with a PDF peak in the spectroscopic bin of interest."729 The f; are the comoving fractional photometric redshift overlaps for objects in slice i and (f(x.)) is the same for the ensemble of photometric objects with a peak photometric redshift in the spectroscopic bin of interest.," The $f_i$ are the comoving fractional photometric redshift overlaps for objects in slice $i$ and $\langle730f(\chi_\star)\rangle$ is the same for the ensemble of photometric objects with a peak photometric redshift in the spectroscopic bin of interest."731" This is illustrated in Figure 2,, in which the upper panel plots the ensemble of the (n= 110410) PDFs with 1.8<Zpeak2.2."," This is illustrated in Figure \ref{fig:chibin}, , in which the upper panel plots the ensemble of the $n=110410$ ) PDFs with $1.8 < z_{\rm peak} < 2.2$."732 This ensemble has an (f(x.))=1.26x1073hMpc overlap with the true range 1.8«z2.2., This ensemble has an $\langle f(\chi_\star)\rangle=1.26\times10^{-3}\invMpch$ overlap with the true range $1.8 < z < 2.2$.733 The lower panels plot! three individual (i.e. phot—NPhet 1) PDFs and their overlaps with 1.8<z<2.2., The lower panels plot three individual (i.e. $N_1^{\rm phot}=N_2^{\rm phot}=N_3^{\rm phot}=1$ ) PDFs and their overlaps with $1.8 < z < 2.2$.734" In§ refsec:qsoresults,, we illustrate the degree to which our optimal estimator can improve clustering estimates for a “typical” analysis, using a sample of spectroscopic and photometric QSOs."," In \\ref{sec:qsoresults}, we illustrate the degree to which our optimal estimator can improve clustering estimates for a “typical” analysis, using a sample of spectroscopic and photometric QSOs."735" QSOs may be particularly well suited to our estimator as they are rare enough that their clustering is dominated by Poisson noise (e.g., see Figure 4)) out to reasonably large scales and f(x) is quite broad."," QSOs may be particularly well suited to our estimator as they are rare enough that their clustering is dominated by Poisson noise (e.g., see Figure \ref{fig:bootstrap}) ) out to reasonably large scales and $f(\chi)$ is quite broad."736" We note, though, that our optimal estimator should improve the signal-to-noise for any photometric clustering analysis."," We note, though, that our optimal estimator should improve the signal-to-noise for any photometric clustering analysis."737The exact methodology we use in practice is as follows.,The exact methodology we use in practice is as follows.738" Eq (6)) can be rewritten as where and we have used w,=wo/ fi.", Eq \ref{eqn:wpvarweight}) ) can be rewritten as where and we have used $w_p=w_\theta/f_i$ .739" Now, consider substituting Eq. (1)),"," Now, consider substituting Eq. \ref{eq:wtheta_DDDR}) ),"740" thetypical DD/DR estimator for w(), into Eq. (8))"," thetypical $DD/DR$ estimator for $w(\theta)$ , into Eq. \ref{eqn:cweight}) )"741" where the the transverse separation, R, is evaluated using the"," where the the transverse separation, $R$ , is evaluated using the"742(K=5.58mmag) and BD-0333826 (K=6.70mmag).,mag) and 3826 mag).743" We used the temperature reddening from ? to convert to L’, and scaled the magnitude with respect to the relative flux observed on both calibrator and science star: 992933 is 1.09+0.03 times brighter than 992945, and 33826 is 1.11+0.05 times brighter than 1141569."," We used the temperature reddening from \citet{2000asqu.book..143T} to convert to L', and scaled the magnitude with respect to the relative flux observed on both calibrator and science star: 92933 is $1.09\pm 0.03$ times brighter than 92945, and 3826 is $1.11\pm0.05$ times brighter than 141569."744" As a result, we estimated the L' magnitude of 992945 to be 5.58mmag and 1141569 to be mmag."," As a result, we estimated the L' magnitude of 92945 to be mag and 141569 to be mag."745" We checked that these values are roughly compatible with the magnitude derived solely by using the isochrones for pre-main sequence stars (?) giving 5.6 and 6.3mmag, respectively."," We checked that these values are roughly compatible with the magnitude derived solely by using the isochrones for pre-main sequence stars \citep{2000A&A...358..593S} giving 5.6 and mag, respectively."746" Scaling the brightness to derive the absolute magnitude at lO0ppc (assuming distances stated in Sect. 4.1)),"," Scaling the brightness to derive the absolute magnitude at pc (assuming distances stated in Sect. \ref{targets}) ),"747" we obtained My, mmag 992945) and Mjy,;—1.76 mmag 1141569).", we obtained $_{\rm L'}$ mag 92945) and $_{\rm L'}$ mag 141569).748" Thus, the 56 upper limits correspond to a nondetection of up to a absolute magnitude of Μι,= 10.4mmag for 992945 and My;= 7.6mmag_ for 1141569."," Thus, the $5\,\sigma$ upper limits correspond to a nondetection of up to a absolute magnitude of $M_{\rm L'}=10.4$ mag for 92945 and $M_{\rm L'}=7.6$ mag for 141569."749" To convert our detection limits to planetary masses limits, we usedDUSTY evolutionary models (?) convolved with the NaCo filters."," To convert our detection limits to planetary masses limits, we used evolutionary models \citep{2000ApJ...542..464C} convolved with the NaCo filters."750" Towards 992945, the models put a limit on the mass of a companion to 18 aat a separation of (A/D)."," Towards 92945, the models put a limit on the mass of a companion to 18 at a separation of $\lambda/D$ )."751" Towards 1141569, the models limit the mass of a companion to 22 aatau.."," Towards 141569, the models limit the mass of a companion to 22 at."752" We have shown that aperture masking gives detection limits of the order of AL/mag—6, with an inner working angle close to A/2D. These results confirm previous detection limits obtained by the same aperture masking technique on the Keck telescope (??) In terms of scientific impact, this observational domain is important because it corresponds to a few astronomical units at a hundred parsec, the distance where the closest formation regions are."," We have shown that aperture masking gives detection limits of the order of $\Delta~{\rm L'\,mag}=6$, with an inner working angle close to $\lambda$ /2D. These results confirm previous detection limits obtained by the same aperture masking technique on the Keck telescope \citep{2011ApJ...731....8K,2011ApJ...730L..21H} In terms of scientific impact, this observational domain is important because it corresponds to a few astronomical units at a hundred parsec, the distance where the closest formation regions are."753 The scientific importance of this parameter space is highlighted by T Cha b detected by the same technique (?).., The scientific importance of this parameter space is highlighted by T Cha b detected by the same technique \citep{2011A&A...528L...7H}.754 Simulations of the older debris disk tend to show that a magnitude or two in dynamic range is still needed to observe disk shaping planets., Simulations of the older debris disk tend to show that a magnitude or two in dynamic range is still needed to observe disk shaping planets.755" Considering 1141569, for example, ? show that the disk geometry could be best modeled by a flyby star and a planet of a few Jupiter masses."," Considering 141569, for example, \citet{2009A&A...493..661R} show that the disk geometry could be best modeled by a flyby star and a planet of a few Jupiter masses."756" For these kinds of objects, a detection limit of two Jupiter masses would require a precision on the closure phases of 0.01 degree, something only possible if we understand how to precisely account for the systematics errors."," For these kinds of objects, a detection limit of two Jupiter masses would require a precision on the closure phases of 0.01 degree, something only possible if we understand how to precisely account for the systematics errors."757 'This paper has to be considere along with other direct detection techniques., This paper has to be considere along with other direct detection techniques.758 In the case of ? ? ," In the case of \citet{2007ApJS..173..143B}759 \citet{2007ApJ...670.1367L} "760during Cycles 16 aud 21. ice. iu a gap of about 5 ceveles. may be relaed to a 555 vear cvele im solar activity (Yoshimura&Kambry1993:Javaraiah2008).,"during Cycles 16 and 21, i.e., in a gap of about 5 cycles, may be related to a 55 year cycle in solar activity \citep{yk93,jj08}."761. The value (it is oulv 0.08) of the cocfhicient of he correlation between the sunspot activity (amplitude of the evele) aud the slope is found to be negligible., The value (it is only 0.08) of the coefficient of the correlation between the sunspot activity (amplitude of the cycle) and the slope is found to be negligible.762 During the 90-vear cycle (Cleissbere cevcle) im the sunspot activity there are many relatively stall time-scale strong fiations. whereas there are no such fluctuations during the 90-vear cycle in the slope.," During the 90-year cycle (Gleissberg cycle) in the sunspot activity there are many relatively small time-scale strong fluctuations, whereas there are no such fluctuations during the 90-year cycle in the slope."763 However. there is a close agreement in the epochs of the maxima and the miniunua of these eveles of the slope and the cycle amplitude (the phase shift between these is not clear iu Fig. [)).," However, there is a close agreement in the epochs of the maxima and the minima of these cycles of the slope and the cycle amplitude (the phase shift between these is not clear in Fig. \ref{fig4}) )."764" This may suggest the existence of a relationship between the long-term, variations iu the slope aud tje sunspot activity.", This may suggest the existence of a relationship between the long-term variations in the slope and the sunspot activity.765 Fi, Fig.766"e.o 6 shows the variations in the slope ai the correlation coeffcieut determiued from the data im year MTIs 1187G. στη, 22017."," \ref{fig6} shows the variations in the slope and the correlation coefficient determined from the data in 3-year MTIs 1876, 1877, ...., 2011."767 In order to check the solar ceveles tren* Il these parameters. iu this figure we lave also shown the variationiu the iuteruational suuspot umber smootlie by taking 3-vear ruuniug average.," In order to check the solar cycles trends in these parameters, in this figure we have also shown the variation in the international sunspot number smoothed by taking 3-year running average."768 Onlv a few of these values ofthe slopes shown in this figure are statistically insiemificaut., Only a few of these values of the slopes shown in this figure are statistically insignificant.769" That is. in mauv intervals the values of κ are found to be insignificant at level. ancl the Student's “ft tests supgeest that the significant levels of the correspouding values of the correlation coefficieu are also good (Note: the big jump of the correlation cocfiicicnt from the interval 1977 to 1978 (the high values frou, LOTS onward) could be just an artifac of the multiplication of the area values of the SOON data with 1.1. in order to have a coniuuous and homogencous data for the whole period 22011 (cf."," That is, in many intervals the values of $\chi^2$ are found to be insignificant at level, and the Student's `t' tests suggest that the significant levels of the corresponding values of the correlation coefficient are also good (Note: the big jump of the correlation coefficient from the interval 1977 to 1978 (the high values from 1978 onward) could be just an artifact of the multiplication of the area values of the SOON data with 1.4, in order to have a continuous and homogeneous data for the whole period 2011 (cf.,"770 Sec;, Sec.771 2)., 2).772 As can be seen Fie. 6((, As can be seen Fig. \ref{fig6}( (773a) the values of the slopes are cousiderably low near the declining ends of s1alb eveles (12. 16 and 23). particularly in the eu of Cycle 23 the slope is s1uallest im the last abou 100 vears (which iuav be related to the παπααν low and prolonged recent activity mininimn).,"a) the values of the slopes are considerably low near the declining ends of small cycles (12, 16 and 23), particularly in the end of Cycle 23 the slope is smallest in the last about 100 years (which may be related to the unusually low and prolonged recent activity minimum)."774 The loue-terii (90-vear evele) variation seen in the evcle-to-evcle variation (Fig. [)), The long-term (90-year cycle) variation seen in the cycle-to-cycle variation (Fig. \ref{fig4}) )775 cau also be secu in Fie. σ, can also be seen in Fig. \ref{fig6}( (776α).,a).777 We have used the 3-AITIs for the sake of better statistics. but the aforementioned patterus is also seen in the vearly data (figure is not shown here). iu spite of the laree uucertaimties in the vearly values.," We have used the 3-MTIs for the sake of better statistics, but the aforementioned patterns is also seen in the yearly data (figure is not shown here), in spite of the large uncertainties in the yearly values."778 Fie., Fig.779 7 shows the plots of the mean slope values iu S-METTISies the data shown in Fig. 6((," \ref{fig7} shows the plots of the mean slope values in 3-MTIs–i.e., the data shown in Fig. \ref{fig6}( ("780a) versus the vear of the solar cvcles. 221 (data are available ouly for four vears of Cycle 11 aud ouly for 3 vears of Cycle 21).,"a)–versus the year of the solar cycles, 24 (data are available only for four years of Cycle 11 and only for 3 years of Cycle 24)."781 As can be seen in this figure. the pattern of the mean variation of the slope (the closed circle-solid curve) suggestsCoco a shelt increasing treud duniug the rising phases and a slight decreasing trend during the decay phases of a majority of the solar evcles.," As can be seen in this figure, the pattern of the mean variation of the slope (the closed circle-solid curve) suggests a slight increasing trend during the rising phases and a slight decreasing trend during the decay phases of a majority of the solar cycles."782 However. the overall spread in the data points is vorv lare particularly in the beeimuines aud the eudiues of the evcles.," However, the overall spread in the data points is very large, particularly in the beginnings and the endings of the cycles."783 That is. the variations during the different solar evcles highly differ from the mean pattern. mdicatiug the z ll-vear periodicity is very woeak/abseut iu the slope.," That is, the variations during the different solar cycles highly differ from the mean pattern, indicating the $\approx$ 11-year periodicity is very weak/absent in the slope."784" Overall we find that the relationship |Dy1,4| and AA, yds reasonably consistent and reliable even im the cases of the relatively siiall samples."," Overall we find that the relationship $|D_{\rm n-1, n}|$ and $A_{\rm n-1}$ is reasonably consistent and reliable even in the cases of the relatively small samples."785 It may be worth to note here that the average size of the spot eroups considerably varies duriug a cycle., It may be worth to note here that the average size of the spot groups considerably varies during a cycle.786 It also differs frou evcle-to-cvcle., It also differs from cycle-to-cycle.787 Therefore. the temporal variation im the slope of the Huear relationship may be mainly due to the dependence of the decay rate on the size/litetime of the spot groups.," Therefore, the temporal variation in the slope of the linear relationship may be mainly due to the dependence of the decay rate on the size/lifetime of the spot groups."788 We repeated all the above caleulatious for erowth rate., We repeated all the above calculations for growth rate.789" The correlation between the erowth rate. Gy,4,4. the corresponding μα. is found to be low. r= 0.39. for the whole period data (wilL 60087 points)."," The correlation between the growth rate, $G_{\rm n-1, n}$, and the corresponding $A_{\rm n-1}$ is found to be low, $r= 0.39$ , for the whole period data (with 60087 points)."790 But it is stil found to be statistically siguificaut from the above used al the significance tests Gt should be noted that the values of n is different for the growth al clecay rates)., But it is still found to be statistically significant from the above used all the significance tests (it should be noted that the values of n is different for the growth and decay rates).791 However. the correlation deermincd from the data of an individual evele is found to be still samall and statistically insignificant.," However, the correlation determined from the data of an individual cycle is found to be still small and statistically insignificant."792" Thus. the relationship between Gy,44, and ly4 is considerably inconsistent."," Thus, the relationship between $G_{\rm n-1, n}$ and $A_{\rm n-1}$ is considerably inconsistent."793 ence. it is not shown here.," Hence, it is not shown here."794 There is also a considerable spread in Figs., There is also a considerable spread in Figs.795 3 and I., 3 and 4.796" Therefore. eventhe relatiouship between 124,4, aud 21,1 found above. is ouly sugeestive rather than compelling."," Therefore, even the relationship between $|D_{\rm n-1, n|}$ and $A_{\rm n-1}$ found above, is only suggestive rather than compelling."797 We analysed a large and reliable suuspot eroup data and found that the total amounts of growth and decay of spot eroups whose life times =2 davs in a eiven time iuterval (sav one-vear) well correlate to the zinouut of activity in the same interval., We analysed a large and reliable sunspot group data and found that the total amounts of growth and decay of spot groups whose life times $\ge 2$ days in a given time interval (say one-year) well correlate to the amount of activity in the same interval.798 We have also found that there exist a reasonably good correlation, We have also found that there exist a reasonably good correlation799a reference DPH together with à group of nearly co-aligned DPHs. having ROLL angles within | aremin of the reference one. as well as pointing offsets (in R.A. and Dec.) within 7 aremin of the reference one.,"a reference DPH together with a group of nearly co-aligned DPHs, having ROLL angles within 1 arcmin of the reference one, as well as pointing offsets (in R.A. and Dec.) within 7 arcmin of the reference one."800 Then. each of the selected DPH rows was summed to the reference one. obtaining stacked DPH pairs. each being characterized by a “pointing offset” ranging from 0 to 7 arcmin.," Then, each of the selected DPH rows was summed to the reference one, obtaining stacked DPH pairs, each being characterized by a “pointing offset” ranging from 0 to 7 arcmin."801 For each of such stacked pairs. we performed a spectral analysis and we extracted the Crab flux. to be compared with the one obtained from the reference DPH.," For each of such stacked pairs, we performed a spectral analysis and we extracted the Crab flux, to be compared with the one obtained from the reference DPH."802 Details on the handling of different attitude files for the construction and analysis of a pair are given in Appendix AppendixB:.., Details on the handling of different attitude files for the construction and analysis of a pair are given in Appendix \ref{Aspect}.803 The resulting flux-losses with respect to the reference DPH. as a function of the offset. for different coded fractions. are given in Table 5..," The resulting flux-losses with respect to the reference DPH, as a function of the offset, for different coded fractions, are given in Table \ref{table_offset}."804 Although our investigation is far from complete. results suggest that significant flux losses (> 550)) may occur. especially for target position at low coded fractions. when stacking different DPHs with a pointing offset larger than 2 arcmin.," Although our investigation is far from complete, results suggest that significant flux losses $>$ ) may occur, especially for target position at low coded fractions, when stacking different DPHs with a pointing offset larger than 2 arcmin."805 Thus. we decided conservatively to stack DPHs only if their pointings are within 1.5 aremin.," Thus, we decided conservatively to stack DPHs only if their pointings are within 1.5 arcmin."806 Having assessed the overall correctness and reliability of our procedure on the bright Crab. we will proceed with the study of the microquasar GRO J1655-40. à source definitely fainter than the Crab and one known to be strongly variable. both in flux and in spectral shape.," Having assessed the overall correctness and reliability of our procedure on the bright Crab, we will proceed with the study of the microquasar GRO J1655-40, a source definitely fainter than the Crab and one known to be strongly variable, both in flux and in spectral shape."807 GRO J1655-40 had a large outburst in 2005., GRO J1655-40 had a large outburst in 2005.808 Such an event started in the middle of February (it was discovered on February 17.99 during Galactic bulge seans with the RXTE/PCA instrument (?))) and lasted for more than 9 months., Such an event started in the middle of February (it was discovered on February 17.99 during Galactic bulge scans with the RXTE/PCA instrument \citep{Markwardt_2005_GRO}) ) and lasted for more than 9 months.809 In what follows we shall take advantage of a very large database serendipitously collected by the BAT instrument during the whole outburst event as well as of the systematic monitoring performed by the RXTE satellite., In what follows we shall take advantage of a very large database serendipitously collected by the BAT instrument during the whole outburst event as well as of the systematic monitoring performed by the RXTE satellite.810 This will allow us to compare our BAT results with quasi-simultaneous results obtained with the well calibrated instruments on-board RXTE., This will allow us to compare our BAT results with quasi-simultaneous results obtained with the well calibrated instruments on-board RXTE.811 Such a cross-check will yield a very robust assessment of the capabilities of our analysis method as well as of the potentialities of BAT as a monitor for a (relatively) bright. strongly variable source.," Such a cross-check will yield a very robust assessment of the capabilities of our analysis method as well as of the potentialities of BAT as a monitor for a (relatively) bright, strongly variable source."812 All BAT observations covering the field of GRO J1655-40. collected between 2005/01/22 and 2005/11/11. were retrieved.," All BAT observations covering the field of GRO J1655-40, collected between 2005/01/22 and 2005/11/11, were retrieved."813 The complete dataset includes 796 observations. for a total of 8724 DPHs. corresponding to ~2.6 Ms observing time.," The complete dataset includes 796 observations, for a total of 8724 DPHs, corresponding to $\sim$ 2.6 Ms observing time."814 All the data analysis was performed by our automatic pipeline., All the data analysis was performed by our automatic pipeline.815 As a first step. good data are selected. according to the prescription deseribed in Appendix Α.Ι...," As a first step, good data are selected, according to the prescription described in Appendix \ref{Preliminary_data_selection_and_preparation}."816 A total of 2080 (~24%)) DPHs were discarded after data screening., A total of 2080 $\sim$ ) DPHs were discarded after data screening.817 Such a percentage is compatible with that found for the Crab dataset in section ??.., Such a percentage is compatible with that found for the Crab dataset in section \ref{Crab_results}.818 Nest. well-aligned. contiguous DPHs are combined up to a maximum integration time of | hour.," Next, well-aligned, contiguous DPHs are combined up to a maximum integration time of 1 hour."819 As a result. we obtained 1650 merged DPHs.," As a result, we obtained 1650 merged DPHs."820 Then. from each data block. a spectrum is extracted with the mask-weighting technique. and the appropriate response matrix is produced.," Then, from each data block, a spectrum is extracted with the mask-weighting technique, and the appropriate response matrix is produced."821 An automatic spectral analysis is then carried. out in XSPEC., An automatic spectral analysis is then carried out in XSPEC.822 After evaluating the source signal-to-noise. spectra with no signal (S/N=O)were discarded.," After evaluating the source signal-to-noise, spectra with no signal (S/N=0)were discarded."823This resulted in the rejection of 378 spectra (~ of the total).,This resulted in the rejection of 378 spectra $\sim$ of the total).824 Low S/N spectra (with source detection below ~Ia level) are used to set ar upper limit to the source flux., Low S/N spectra (with source detection below $\sim4\sigma$ level) are used to set an upper limit to the source flux.825 Contiguous. low-S/N spectra are summed. as well as their response matrices. in an attempt to increase the statistics. and the spectral analysis repeated on such combined spectra.," Contiguous, low-S/N spectra are summed, as well as their response matrices, in an attempt to increase the statistics, and the spectral analysis repeated on such combined spectra."826 High-S/N spectra are used for a complete spectral fit using a power law model., High-S/N spectra are used for a complete spectral fit using a power law model.827 A detailed description of the data analysis pipeline is giver in Appendix AppendixA:., A detailed description of the data analysis pipeline is given in Appendix \ref{Crab_pipeline}.828. The complete pipeline used for our study of GRO J1655-40 consists of steps 1. 2. 4. and 5 described there.," The complete pipeline used for our study of GRO J1655-40 consists of steps 1, 2, 4, and 5 described there."829 RXTE monitored the whole outburst of GRO J1655-40 since its discovery (?)., RXTE monitored the whole outburst of GRO J1655-40 since its discovery \citep{Markwardt_2005_GRO}.830 The dataset is composed of 490 observations. performed between 2005-02-26 and 2005-11-11.," The dataset is composed of 490 observations, performed between 2005-02-26 and 2005-11-11."831 Each observation has a typical integration time of ~ 1.5 ks. for a total observing time of ~664 ks.," Each observation has a typical integration time of $\sim$ 1.5 ks, for a total observing time of $\sim$ 664 ks."832 Spectral data extracted from the complete dataset have been kindly made available to the community by the MIT group .. Spectra for both source and background as well as response, Spectral data extracted from the complete dataset have been kindly made available to the community by the MIT group Spectra for both source and background as well as response833There is currently a growing interest in the acceleration of non-thermal particles at highly relativistic shocks.,There is currently a growing interest in the acceleration of non–thermal particles at highly relativistic shocks.834 There are three classes of velativistic sources: bevoud the well-established extra-Galactic (Blazars) aud Galactic (superluminal) sources. both of which exhibit superluninal notions. it is uow also well-established that Gamuna Ray Bursts (GRBs) display highly relativistic expausious. with Lorentz [actors well in excess of 100.," There are three classes of relativistic sources: beyond the well–established extra–Galactic (Blazars) and Galactic (superluminal) sources, both of which exhibit superluminal motions, it is now also well-established that Gamma Ray Bursts (GRBs) display highly relativistic expansions, with Lorentz factors well in excess of $100$."835 Other classes of relativistic sources may include Soft Gamuna Ray Repeaters (SCRs). whose recurrent explosions are largely super—Edclinetou. aud special SNe similar to SN 1998bw. which displayed marginally Newtouiau expausion 1) when optical emission lines became detectable. about a mouth after the explosion.," Other classes of relativistic sources may include Soft Gamma Ray Repeaters (SGRs), whose recurrent explosions are largely super–Eddington, and special SNe similar to SN 1998bw, which displayed marginally Newtonian expansion $\approx 6\times 10^4\; km\; s^{-1}$ ) when optical emission lines became detectable, about a month after the explosion."836 With the ciscovery of GRBs’ alterglows. it has now become feasible to derive the euergy spectral iudex & of electrous accelerated. at the forward shock. as a function of the varying (decreasing) shock Lorentz factor 5. provided simultaneous wide-band spectral coverage is available.," With the discovery of GRBs' afterglows, it has now become feasible to derive the energy spectral index $k$ of electrons accelerated at the forward shock, as a function of the varying (decreasing) shock Lorentz factor $\gamma$, provided simultaneous wide–band spectral coverage is available."837 With the launch of the USA/Italy/Uls mission SWIFT. these data will become available for a statistically significant uumber of bursts. testing directly inodels for particle acceleration at relativistic shocks.," With the launch of the USA/Italy/UK mission SWIFT, these data will become available for a statistically significant number of bursts, testing directly models for particle acceleration at relativistic shocks."838 Furthermore. since GRBs must also clearly accelerate protous. the same tides A& may cletermine the spectrum of ultra high euerey cosmic rays observed at Earth.," Furthermore, since GRBs must also clearly accelerate protons, the same index $k$ may determine the spectrum of ultra high energy cosmic rays observed at Earth."839 However. util recently. both the lack of astrophysical motivation aud the difficulty inherent in treating highly anisotropic distribution fuucetions have stiffened research on this topic.," However, until recently, both the lack of astrophysical motivation and the difficulty inherent in treating highly anisotropic distribution functions have stiffened research on this topic."840 Early, Early841class have been discovered receutlv (see Matt 1997. for a review].,class have been discovered recently (see Matt \cite{matt_b} for a review).842 As anticipated above. Sy2s in carly spectroscopic studies were mostly selected. frou former allsky Xταν surveys. henee these studies were generally biased for Xorav bright objects.," As anticipated above, Sy2s in early spectroscopic studies were mostly selected from former all–sky X–ray surveys, hence these studies were generally biased for X–ray bright objects."843 Very ikelv. this selectiou criterion resulted iu a bias in favor of low Nyy Sv2s.," Very likely, this selection criterion resulted in a bias in favor of low $_H$ Sy2s."844" Later on. hard Xray spectroscopic studies (nostlv bv means of ASC'A) probed fainter samples of ACNS (οιο, Turner et al. 1997a))."," Later on, hard X–ray spectroscopic studies (mostly by means of ASCA) probed fainter samples of AGNs (e.g. Turner et al. \cite{turner_a}) )."845 IIowever. many of he Sy2s observed by ASCA were selected amongst sources known to show broad liepA in polarized Light (Awaki ct al. 1997)).," However, many of the Sy2s observed by ASCA were selected amongst sources known to show broad lines in polarized light (Awaki et al. \cite{awaki}) )."846 This selection criterion nüehlt introduce a bias for low Ny as well., This selection criterion might introduce a bias for low $_H$ as well.847 ITeisler et al. (19973) , Heisler et al. \cite{heisler}) )848showed that the detectability of polarized broad lines is related to the obscuration of the nuclear reeglon., showed that the detectability of polarized broad lines is related to the obscuration of the nuclear region.849 Smunrizius. former Nrav spectroscopic surveys were seriously biased against heavily obscured Syv2s aud. therefore. they are not suitable to study the real distribution of the absorbing column deusities Nyy. The knowledge of the distribution of Ny iu Sv2s is Huportant to understand the nature of their obscuring medium. Which has implications for the unified model.," Summarizing, former X–ray spectroscopic surveys were seriously biased against heavily obscured Sy2s and, therefore, they are not suitable to study the real distribution of the absorbing column densities $_H$ The knowledge of the distribution of $_H$ in Sy2s is important to understand the nature of their obscuring medium, which has implications for the unified model."850 Also. the distribution of Nyy is relevaut to the svuthesis of the Xrav background.," Also, the distribution of $_H$ is relevant to the synthesis of the X–ray background."851 Indeed. obscured ACNs are thought to contribute to most of the high energy (> 2 keV) extragalactic backeround (Comastri et al. 1995..," Indeed, obscured AGNs are thought to contribute to most of the high energy $>$ 2 keV) extragalactic background (Comastri et al. \cite{comastri},"852 Madau et al. 1005)., Madau et al. \cite{madau}) ).853 We have undertaken a program of observations with BeppoSAX. the ItalianDutch Xray satellite. aimed at studving the hard X.rav properties of weak Sy2s aud at assessing the vreal” distribution of their absorbing coluun densities.," We have undertaken a program of observations with BeppoSAX, the Italian–Dutch X–ray satellite, aimed at studying the hard X–ray properties of weak Sy2s and at assessing the “real” distribution of their absorbing column densities."854 As described in the next section. BeppoSAN is au excellent ool to pursue this goal. since it combines high seusitivitv (required. to observe weak ACNs) aud a wide spectral coverage (0.1.300 keV. required to identify aud discutanele various spectral componcuts).," As described in the next section, BeppoSAX is an excellent tool to pursue this goal, since it combines high sensitivity (required to observe weak AGNs) and a wide spectral coverage (0.1–300 keV, required to identify and disentangle various spectral components)."855 Sv2s suitable for this study were drawn out of Maioliuo Ricke’s (1995)) sample., Sy2s suitable for this study were drawn out of Maiolino Rieke's \cite{maiolino_a}) ) sample.856 This sample is extracted from the Revised Shapleyv-Aines (RSA) catalog of galaxies (that is limited to uaeuitude Br<13.2. Saudage Tanuuaun LOST)). and Sevfert ealaxies are selected according to their optica lines.," This sample is extracted from the Revised Shapley-Ames (RSA) catalog of galaxies (that is limited to magnitude $B_T < 13.2$, Sandage Tammann \cite{sandage}) ), and Seyfert galaxies are selected according to their optical lines."857 As discussed in Maiolino Ricke. this sample is much less biased than others. both iu terms of huninosity of the Sevtert nuclei aud in terms of properties of their hos ealaxies.," As discussed in Maiolino Rieke, this sample is much less biased than others, both in terms of luminosity of the Seyfert nuclei and in terms of properties of their host galaxies."858 Out of the 51 Sy2s in the Maioliuo Ricke sample 22 have already been observed by. ASCA., Out of the 54 Sy2s in the Maiolino Rieke sample 22 have already been observed by ASCA.859 We selected 8 of the remaining 32 Sv2s. based on their (arrow} line flux: fo naxiuze the chauces of detection we chose the sources showing the highest |OITI| flux.," We selected 8 of the remaining 32 Sy2s, based on their (narrow) line flux: to maximize the chances of detection we chose the sources showing the highest [OIII] flux."860 Maiolino Ricke also show that. although the [OITI] Ine is e1uitfted on scales much larger than the putative oc-eale torus. the [OITI] is not a completely isotropic indicator of the nuclear huuünositw. for the host ealaxy disk might obscure wart of the NLR.," Maiolino Rieke also show that, although the [OIII] line is emitted on scales much larger than the putative pc-scale torus, the [OIII] is not a completely isotropic indicator of the nuclear luminosity, for the host galaxy disk might obscure part of the NLR."861 Iowever. once the ΟΠΗ flix is corrected for the extinction. deduced from he Baluer decrement. it should provide an indication of he nuclear activity that is independent of the pc-scale obscuration due to the torus.," However, once the [OIII] flux is corrected for the extinction deduced from the Balmer decrement, it should provide an indication of the nuclear activity that is independent of the pc-scale obscuration due to the torus."862 As a consequence. although our [OTH)|-based selection criterion might introduce a bias in our sauple forinfrinsicallg |uninous sources. it avoids biases against liehly obscured Sy2 uuclei. thus overcoming limitations of former survevs.," As a consequence, although our [OIII]-based selection criterion might introduce a bias in our sample for luminous sources, it avoids biases against highly obscured Sy2 nuclei, thus overcoming limitations of former surveys."863 Preliminary results of this survey were published iu Salvati et al. (1997... 10051).," Preliminary results of this survey were published in Salvati et al. \cite{salvati}, \cite{salvati2}) )."864 In this paper we report aud discuss results of BeppoSAN observations for all of the 8 Seyfert 2s in our [OTT] selected sample., In this paper we report and discuss results of BeppoSAX observations for all of the 8 Seyfert 2s in our [OIII] selected sample.865 A more thorough statistical analysis. obtained by mereine our BeppoSAX data with data in the literature. is preseuted iu Bassani et al. (," A more thorough statistical analysis, obtained by merging our BeppoSAX data with data in the literature, is presented in Bassani et al. ("866in prep.).,in prep.).867 A description of the BeppoSAN observatory is eiveu πι Boclla et al (1997a))., A description of the BeppoSAX observatory is given in Boella et al. \cite{boella_a}) ).868 The pavload iustruineuts include four coaligned narrow field iustrunents: a Low Encrev Concentrator Spectrometer (LECS. Parmar ct al. 1997).," The payload instruments include four co–aligned narrow field instruments: a Low Energy Concentrator Spectrometer (LECS, Parmar et al. \cite{parmar}) ),"869 three Medium Eucrex Concentrator Spectrometers (MECS. Boclla ot al. 199753).," three Medium Energy Concentrator Spectrometers (MECS, Boella et al. \cite{boella_b}) ),"870" a Teh Pressure Cas Scintillation Proportional Counter (ΠΡΟ, Alanzo et al 1997))"," a High Pressure Gas Scintillation Proportional Counter (HPGSPC, Manzo et al. \cite{manzo}) )"871 and ai Phoswich Detector System (PDS. Froutera ct al 1997) ," and a Phoswich Detector System (PDS, Frontera et al. \cite{frontera}) )."872Both LECS aud MECS spectrometers have naiagiue capabilities (angular resolution ~ 1.2 arcnun. FWOAD and cover the 0.110 keV and 1.510 keV spectral bands. respecively (in the overlapping spectral region the MECS are three times more scusitive thau LECS).," Both LECS and MECS spectrometers have imaging capabilities (angular resolution $\sim$ 1.2 arcmin, FWHM) and cover the 0.1–10 keV and 1.5–10 keV spectral bands, respectively (in the overlapping spectral region the MECS are three times more sensitive than LECS)."873 Their euergv resolution is about at 6 keV. IIPGSPC and PDS operate iu the 1120 keV aud 15300 keV spectral bands. respectively.," Their energy resolution is about at 6 keV. HPGSPC and PDS operate in the 4–120 keV and 15–300 keV spectral bands, respectively."874 Iu the overlapping region the PDS is more sensitive (bv a factor of 1.8). while the WPGSPC has superior energy resolution.," In the overlapping region the PDS is more sensitive (by a factor of 4–8), while the HPGSPC has superior energy resolution."875 Table 1 lists the sources observed iu our program so far. along with the onsource total integration time and net count rate (1.0. background subtracted) for each iustruinent.," Table \ref{tab_obs} lists the sources observed in our program so far, along with the on–source total integration time and net count rate (i.e. background subtracted) for each instrument."876 One of the MECS units stopped working iu May 1997. as a consequeuce ALCC-05-L8-002 was observed with two MECS units ouly.," One of the MECS units stopped working in May 1997, as a consequence MCG-05-18-002 was observed with two MECS units only."877 For all sources. but NGC 5613. LECS and NECS spectra were extracted from an aperture of δ aud Ll’ in radius. since these apertures were found to optimize the signaltonoise ratios for these faint sources.," For all sources, but NGC 5643, LECS and MECS spectra were extracted from an aperture of $'$ and $'$ in radius, since these apertures were found to optimize the signal–to–noise ratios for these faint sources."878 For NGC 5613 we chose au extraction radius of 1. since outside of this radius the observed fiw is affected by the emission of a nearby galaxy cluster (see Sect. L1)).," For NGC 5643 we chose an extraction radius of $'$, since outside of this radius the observed flux is affected by the emission of a nearby galaxy cluster (see Sect.\ref{results}) )."879 Another exception is NGC 1386. where we used for the LECS the same extraction aperture used for the MECS (i0. 0 iu radiux)," Another exception is NGC 1386, where we used for the LECS the same extraction aperture used for the MECS (i.e. $'$ in radius)"880The study of stellay populations of non-resolved svstcuis has greatly relied the models derived from evolutionlE populations svuthesisou technique.,The study of stellar populations of non-resolved systems has greatly relied on the models derived from evolutionary populations synthesis technique.881 This approach is based on the spectrophometric properties of stars at. ideally. all evolutionary phases and takes iuto acconnt all phenomena that argely affect the evolution of a star (e.g. duass-loss).," This approach is based on the spectrophometric properties of stars at, ideally, all evolutionary phases and takes into account all phenomena that largely affect the evolution of a star (e.g., mass-loss)."882 Over the wears. ever since the technique was first ∖⊳−implemented∖∖∖ (Tinsley↴⋅↴∖⇁↽≺⋅∖∖↽∢↼⊲≻1968.1972). a Mwide variety of nmodels based‘l ou differcutnveut uieredieutsBout ilave ;been constructed iand used .in the study of vounge2 and old. stellar populations.," Over the years, ever since the technique was first implemented \citep{tinsley68,tinsley72}, a wide variety of models based on different ingredients have been constructed and used in the study of young and old stellar populations."883"2005).. Not surprisingly. most of the work done up to date has vastly focused in the optical spectrophotomoetrie properties of stellar svsteius. aud until relatively recently it has expanded {ο other wavelengths (as far as the detailed analysis of spectral features ix concerned). and. ir sone cases. jucluded the effects of an interstellar medium (Silvactal,1908:Pauuzzoetal. 2005)."," Not surprisingly, most of the work done up to date has vastly focused in the optical spectrophotometric properties of stellar systems, and until relatively recently it has expanded to other wavelengths (as far as the detailed analysis of spectral features is concerned), and, in some cases, included the effects of an interstellar medium \citep{silva98,panuzzo05}."884" At ultraviolet (UV) waveleneths. usnally divided into two segments, the fa-UV. (2002000 Aj) and the imid-UV (20003200 A3). the natural systems to look at are those whose underlying populations copiouslv eiut aud have their enüssion maxima du ⋅D . . _ ↴∖↴⋅↖↽↴"," At ultraviolet (UV) wavelengths, usually divided into two segments, the far-UV (1200–2000 ) and the mid-UV (2000–3200 ), the natural systems to look at are those whose underlying populations copiously emit and have their emission maxima in that window, i.e. star-forming systems."885"∖↴↑↸∖⋯↴∖↴⋜⋯∖↸∖⊼⊓⋅↸∖⋯↸∖↕⋅↖↽↕∐∏⋯↥⋅⋜⋯↕↕⊔⊔⋜⋯⋅↖↽⋜↧↴∖↴⊓⋅≺∏≻↕⋅↖↽↴∖↴↕↸⊳⋜↧↕ contexts (see.οι,Duzzoni2002).. if was eventually realized that also old aud intermediate age populations. which will be the main subject in this paper. deserve attention bv their own right."," While these systems are extremely important in many astrophysical contexts \citep[see, e.g.,][]{buz02}, it was eventually realized that also old and intermediate age populations, which will be the main subject in this paper, deserve attention by their own right."886 As au cxample we cin mention the countless studies motivated by the anexpected finding of a prominent far-UV flux excess iu the bulge of Andromeda (Code1969)., As an example we can mention the countless studies motivated by the unexpected finding of a prominent far-UV flux excess in the bulge of Andromeda \citep{code69}.887. Aside of this ‘ar-UV fux excess. the mid-UWV still remains vastly quexylored. iu spite of the early suggestions that this wavelength region cau help iu lifting the so-called age-netallicity degeneracy (AMID) that plagues the optical spectrophotometzic⋅ properties⋅ of evolved populations. and that preveuts the uuivocalR determinationR: of: these xuiueters (Worthev-:1991:Dormanetal.⊀∙2003).," Aside of this far-UV flux excess, the mid-UV still remains vastly unexplored, in spite of the early suggestions that this wavelength region can help in lifting the so-called age-metallicity degeneracy (AMD) that plagues the optical spectrophotometric properties of evolved populations and that prevents the univocal determination of these parameters \citep{worthey94,dorman03}."888 Discutangling the effects of age and chemical compositioul is particularly imiportaut when attempting to evaluate he characteristics of distant red objects for which. hrough optical observations only feasible with the current seneration of large telescopes. we can only access the rest-frame mid-UV flux," Disentangling the effects of age and chemical composition is particularly important when attempting to evaluate the characteristics of distant red objects for which, through optical observations only feasible with the current generation of large telescopes, we can only access the rest-frame mid-UV flux \citep[e.g.,][]{dunlop96}. ."889these two lauits. we can find the reκ depeudeuce of the parameters via the requiremeut (Lujxps,"these two limits, we can find the redshift dependence of the parameters via the requirement $\avg{L n} \propto \csfr$."890" The vedshift historv of cosuic-star formation is well-known (IIoxiuchietal.2009).. aud we encode this in the diinensouless ""shape function Sz) (0)."," The redshift history of cosmic-star formation is well-known \citep{horiuchi}, and we encode this in the dimensionless “shape” function S(z) (0) ."891 Wο then have L.GO/L.()= 5S(:)inu the case of pure hinunosity evolution. aud (2)fr.(0)=5(:) in the case of pure density evolution.," We then have $\tracer_*(z)/\tracer_*(0) = S(z)$ in the case of pure luminosity evolution, and $n_*(z)/n_*(0) = S(z)$ in the case of pure density evolution."892 At a given redshift. 0) ," At a given redshift, eq. \ref{eq:mavg}) )"893gives the scaling (Mj=GUηρεxCMascnifS(:i)., gives the scaling $\avg{\mgas} = \avg{\mgas \psi n}/\csfr \propto \avg{\mgas \psi n}/S(z)$ .894" For our luminosity function and Keunicutt-Scliuidt melation we fud ""a local --value of (Mai.9=68s10?A.- ", For our luminosity function and Kennicutt-Schmidt relation we find a local value of $\avg{\mgas}_{z=0} =6.8 \times 10^{9} \ \msol$.895At ο we have CMconjx(112)SEAD). alc OUSx(L112)8£262).," At other redshifts we have $\avg{\mgas \psi n} \propto (1+z)^{-\beta} \tracer_*(z)^\omega S(z)$, and so $\avg{\mgas} \propto (1+z)^{-\beta} \tracer_*(z)^\omega$."896 Thus for the pire inuinositv case L.XS(2). we find that the gas mass stronely evolves as Lea.)WwOL[τσι9. in response o the stronely changing SER.," Thus for the pure luminosity case $\tracer_* \propto S(z)$, we find that the gas mass strongly evolves as $\avg{\mgas} \propto (1+z)^{-\beta} S(z)^\omega$, in response to the strongly changing SFR."897 Consequeuthy. the factor of 1t )rise nmi cosmic star-formation at +~| implics a net HHennma-rav Duiudnositv merease of a factor 230.," Consequently, the factor of $10$ rise in cosmic star-formation at $z \simeq 1$ implies a net gamma-ray luminosity increase of a factor $\simeq 30$."898" Ou the other haud. iu the pure density evolution case. galaxy SERs are coustaut. L(2)=const. so that the mean gas luas8 GMthe,(11:) actually With redshift. while colmoving uunber2 of star-forudus ealaxics Πιοοσακος. but the net enhancement at high redshift is SETHer than in the pure lhuninosity evolution case."," On the other hand, in the pure density evolution case, galaxy SFRs are constant, $\tracer_*(z) = const$, so that the mean gas mass $\avg{\mgas} \propto (1+z)^{-\beta}$ actually with redshift, while the comoving number of star-forming galaxies increases, but the net enhancement at high redshift is smaller than in the pure luminosity evolution case."899 This kev difference leads to the factor ~1 between the ECB predictions for the pure censity aud pure luuinosity evolution cases seen in Figure 1., This key difference leads to the factor $\sim 4$ between the EGB predictions for the pure density and pure luminosity evolution cases seen in Figure 1.900 Our full numerical calenlation uses a Milly Way pionic source spectzni Whoseshape is derived frou Ποιο.&Eubliu (2001)... calibrated to observations by normalizing the 2100 MeV photon enuüssion por hydrogen atom to the result at iuteriuediate Caletie latitudes (Abdoetal.20095)...," Our full numerical calculation uses a Milky Way pionic source spectrum whose is derived from \citet{pfrommer}, , calibrated to observations by normalizing the $> 100$ MeV photon emission per hydrogen atom to the result at intermediate Galactic latitudes \citep{FermiMW09}."901 The coziuic SER is from ITorxiucliietal.(2009).., The cosmic SFR is from \citet{horiuchi}.902 For theMilkv Way SER. used to normalize the cosmic-ray flux/SER ratio. we use the recent estimate of Robitaille&Whitney(2010) (UMw=LAL./vr. a factor of 3 lower than earlier work).," For the Milky Way SFR, used to normalize the cosmic-ray flux/SFR ratio, we use the recent estimate of \citet{robitaille} $\psi_{\rm MW} = 1 {M_\odot/\rm yr}$, a factor of 3 lower than earlier work)."903 Figure 1 shows our results for fhe normal galaxy contribution to the ECD., Figure 1 shows our results for the normal galaxy contribution to the EGB.904 We pkt predictions for the Iuuitiug cases of pure ήπιοsity aud of pure density evolutiou., We plot predictions for the limiting cases of pure luminosity and of pure density evolution.905" The uucertaiulos 111 the model inputs. Slmed in quadrature. propagate into the displaved ene baud that applies fo each curve. which we estimate to 2be a factor of 1000, resulting from uncertainties of: iu pionic enüissivitv (Abdoetal.20095)... in t16 normalization of the Galactic star-formation rate (Rovitaille&Whitney2010).. 1i the cosmic star-Orlation rates (IIoxinchietal.20Oy. aud in he huninosity scaling in eq. (2))."," The uncertainties in the model inputs, summed in quadrature, propagate into the displayed error band that applies to each curve, which we estimate to be a factor of $10^{\pm 0.3}$, resulting from uncertainties of: in pionic emissivity \citep{FermiMW09}, in the normalization of the Galactic star-formation rate \citep{robitaille}, in the cosmic star-formation rates \citep{horiuchi}, and in the luminosity scaling in eq. \ref{eq:mavg}) )."906 The true svsteinatic TLCvtadntv would also reflect the icealizations dn our nocel Giniversal cosmic-ray spectra and confinement)., The true systematic uncertainty would also reflect the idealizations in our model (universal cosmic-ray spectra and confinement).907 These errors are hard to estimate but iu any case ΠΠ] hat the uncertainty ranee in Figure Lis a lower bound otje error budget., These errors are hard to estimate but in any case imply that the uncertainty range in Figure 1 is a lower bound to the error budget.908 Within errors. our predictions for both Παπάας mocels all at or below the level of the data. where the data ποσα to support the pure Iuninositv evolution case that explains uecarly the cutire signal.," Within errors, our predictions for both limiting models fall at or below the level of the data, where the data seem to support the pure luminosity evolution case that explains nearly the entire signal."909 Comparing ceutral values. this model gives z50% of theFermi EGD <10 GeV. Thus. unresolved normal galaxies make a substantial aud likely doniuaut contribution to the observed EGD. without overpredicting the signal.," Comparing central values, this model gives $\approx 50\%$ of the EGB $\la 10$ GeV. Thus, unresolved normal galaxies make a substantial and likely dominant contribution to the observed EGB, without overpredicting the signal."910 Eveu the pure density evolution case accounts for a minima of of the EGB around 0.3 GeV: this provides alower liuüt to the normalealaxy signal., Even the pure density evolution case accounts for a minimum of of the EGB around 0.3 GeV; this provides a limit to the normal-galaxy signal.911 Thus. anvother EGB sources (Stecker&Salamou1996:Dennuer2007:Abdoctal.2010d:Faucher-Cagnere&Loeb2010) ust contribute no more than the remaining SO of the data.," Thus, any EGB sources \citep{ss96,dermer07,fermicounts,mspulsars}912 must contribute no more than the remaining $80\%$ of the data."913 Tudeed. the LAT teamupper lanit to the blazar ECB contribution shown in Figure 1 is comparable to our lower limit (Abdoetal.2010d).," Indeed, the LAT team limit to the blazar EGB contribution shown in Figure 1 is comparable to our limit \citep{fermicounts}."914. The spectral shapes of the two limiting cases are very similar: the peak in E772/dE lies at ~0.3 GeV because the bulk of the signal comes from 2~1., The spectral shapes of the two limiting cases are very similar: the peak in $\eobs^2 dI/d\eobs$ lies at $\sim 0.3$ GeV because the bulk of the signal comes from $z \sim 1$.915 These models predict that the EGB turus over for Ezx GeV. a testable prediction of our model.," These models predict that the EGB turns over for $\eobs \la 0.3$ GeV, a testable prediction of our model."916 For hadronic cluission. the ligh-cnerey spectral iudex is the same as the underlving proton spectral iudex. here s-padSer=2.75: this is somewhat steeper than theFermi sinele-power-law fit δω]2.11£0.05.," For hadronic emission, the high-energy spectral index is the same as the underlying proton spectral index, here $s_{\gamma,\rm had} = s_{\rm cr} = 2.75$ ; this is somewhat steeper than the single-power-law fit $s_{\rm obs} = 2.41 \pm 0.05$."917 Consequently. our predictions at high energies (210 CGoV) fall below the data.," Consequently, our predictions at high energies $\ga 10$ GeV) fall below the data."918 If normal galaxies had a of cosmic-rav spectral indices. the resulting ECB spectu would steepeu at high energies where the hardest sources would dominate. developing afa Tudeed. theFeri EGB data suggests a slight flattening of slope arouud E>10 GeV. which might lint at such a transition.," If normal galaxies had a of cosmic-ray spectral indices, the resulting EGB spectrum would steepen at high energies where the hardest sources would dominate, developing a. Indeed, the EGB data suggests a slight flattening of slope around $E \ga 10$ GeV, which might hint at such a transition."919" A ealaxy with characteristic lhuumositv L. has £°¢>100MeV)=1.1«107s1,", A galaxy with characteristic luminosity $\tracer_*$ has $L_\gamma^*(>100 {\rm MeV}) = 1.4 \times 10^{43} \ {\rm s^{-1}}$.920" Such objects have flux F if they lie at distances kr;=(Leο---Alpe(10on2sΤΕΙ 3, ThosFerm? "," Such objects have flux $F$ if they lie at distances $r_* = (L_\gamma^*/4\pi F)^{1/2} = 92111 \, {\rm \ Mpc} \ ({10^{-9} \ \rm cm^{-2} \ s^{-1}}/F)^{1/2}$ ."922should eventually resolve NGE) bir? nn(0)3 =51ESV?(19) normal galaxies. cousisteut with 23 detectious to date (theLMC.SAIC.andperhapsM31:Abdoetal.20106:al. 2010)..," Thus should eventually resolve N(>F) r_*^3 n_*(0)/3 = 5 normal galaxies, consistent with 2–3 detections to date \citep[the LMC, SMC, and perhaps M31;][]{fermi-LMC,fermi-SMC,923fermi-M31}."924 Our results do not account for starburst galaxies. nor for inverse-C'oniptou emission from any star-forming ealaxies: these nist contribute to the star-forming EGB. aud could have lid spectra dominating =10 GeV. We have also neglected gamma-ray attenuation by extragalactic background light (importantatEz30GeV:e.g.YoSteckeretal.2006.andreferences therein).," Our results do not account for starburst galaxies, nor for inverse-Compton emission from any star-forming galaxies; these must contribute to the star-forming EGB, and could have hard spectra dominating $\ga 10$ GeV. We have also neglected gamma-ray attenuation by extragalactic background light \citep[important at $E \ga 30$ GeV; e.g.,][and references therein]{sms}."925 We will address these issues in future work., We will address these issues in future work.926 The amplitude and configuration of magnetic fields ina ealaxy have an additional effect on the scaling of cosimic-rav flux with SER., The amplitude and configuration of magnetic fields in a galaxy have an additional effect on the scaling of cosmic-ray flux with SFR.927 Coufirmation that normal galaxies colmprise the bulk of the Fermi signal would constitute a uniqueprobe of the evolution of these magnetic fields between the redshift of peak star formation aud todas., Confirmation that normal galaxies comprise the bulk of the Fermi signal would constitute a uniqueprobe of the evolution of these magnetic fields between the redshift of peak star formation and today.928 Because of their ubiquity. normalgalaxies produce the sinallestauisotropies in the ECB. far less than blazirsor other| proposed sources.," Because of their ubiquity, normalgalaxies produce the smallestanisotropies in the EGB, far less than blazarsor other proposed sources."929 Thus. by studyiug the observed ECGD anisotropy as a function of energy. it may be possible to diseutaugle the spectrum aud. amplitude," Thus, by studying the observed EGB anisotropy as a function of energy, it may be possible to disentangle the spectrum and amplitude"930where II:gr and CO:gr represent 11 and CO on the grains.,where $:gr$ and $:gr$ represent H and CO on the grains.931 The exceptions are and where we follow ?. in assuming that these ions form No rather than NII and ND when thev Ireezeout., The exceptions are and where we follow \citet{roberts04} in assuming that these ions form $_2$ rather than NH and ND when they freezeout.932 All species are assumed to [reezeout. except lor Ile which has a very low binding energy aud is therefore easily thermally clesorbed even αἱ very low temperatures.," All species are assumed to freezeout, except for He which has a very low binding energy and is therefore easily thermally desorbed even at very low temperatures."933 Any that hits a exgrain is neutralized and returned immediately to the egas., Any $^+$ that hits a grain is neutralized and returned immediately to the gas.934 We include thermal desorption and desorption due (o cosmic rav heating of grains., We include thermal desorption and desorption due to cosmic ray heating of grains.935 Cosmic rav heating is able to maintain a low level of some volatile molecules such as CO and Ns in the cold midplane of our models., Cosmic ray heating is able to maintain a low level of some volatile molecules such as CO and $_2$ in the cold midplane of our models.936" These molecules can destroy ions such as IL, and its deuterated isotopes. aud produce ions such as | and in the midplane aud (thereby affect the ionization level in this region."," These molecules can destroy ions such as $_3^+$ and its deuterated isotopes, and produce ions such as $^+$ and $^+$ in the midplane and thereby affect the ionization level in this region."937 We have therefore run models without cosmic ray heating to determine how the inclusion of this process will alfect molecular abundances ancl the ionization level in cold regions of the disk., We have therefore run models without cosmic ray heating to determine how the inclusion of this process will affect molecular abundances and the ionization level in cold regions of the disk.938 The rates for cosmic rav heating are taken from ?.. using updated binding energies for some species. notably. CO. [or which we use the value determined by 2..," The rates for cosmic ray heating are taken from \citet{hh93}, using updated binding energies for some species, notably CO, for which we use the value determined by \citet{oberg05}."939 Table 7 gives the binding energies (775) used in our models., Table \ref{tab:be} gives the binding energies $E_D$ ) used in our models.940" Thermal desorption rates are calculated. [rom where 7,, is the grain temperature. and 7j is the frequency of oscillation between the absorbate and the surface given bv where n, is the surface density of sites ( 1.5 x LO’ 7) and m is the mass of the accreting species."," Thermal desorption rates are calculated from where $T_{gr}$ is the grain temperature, and $\nu_0$ is the frequency of oscillation between the absorbate and the surface given by where $n_s$ is the surface density of sites $\sim$ 1.5 $\times$ $^{15}$ $^{-2}$ ) and $m$ is the mass of the accreting species."941 ? recently observed a high column density of IDO in the disk around DM Tan., \citet{cec05} recently observed a high column density of HDO in the disk around DM Tau.942 They found NOIDO) ~ 1.6 x LOM ? in the outer disk. where the clensityv is ~ LO° * and the temperature is < 25 Ix. The emission comes from above the midplane and corresponds to a relatively high fractional abundance of ~ 3 x 7.," They found N(HDO) $\sim$ 1.6 $\times$ $^{13}$ $^{-2}$ in the outer disk, where the density is $\sim$ $^6$ $^{-3}$ and the temperature is $<$ 25 K. The emission comes from above the midplane and corresponds to a relatively high fractional abundance of $\sim$ 3 $\times$ $^{-9}$."943 At these densities and temperatures. water is expected to be completely removed Irom the gas by accretion onto erains. where it will remain in the absence of a nonthermal desorption process.," At these densities and temperatures, water is expected to be completely removed from the gas by accretion onto grains, where it will remain in the absence of a non–thermal desorption process."944 Cosmic rav heating is not efficient enough to remove such a strongly bound molecule as water., Cosmic ray heating is not efficient enough to remove such a strongly bound molecule as water.945 7? suggested that photodesorption. arising from the action of the interstellar farUV. field could be efficient enough to retain water vapor in the eas phase in the cold outer disk. and so account for the," \citet{dom05} suggested that photodesorption, arising from the action of the interstellar far–UV field could be efficient enough to retain water vapor in the gas phase in the cold outer disk, and so account for the"946over near 2)2—1.2 and obtains a similar shallow slope (dashed line in Figure 2).,over near $\beta \approx -1.2$ and obtains a similar shallow slope (dashed line in Figure 2).947 For LBCs in our sample with jm1.2. the clumpy model predicts larger values of IRN than the IRA-.> relation of MIIC'99.," For LBGs in our sample with $\beta > -1.2$, the clumpy model predicts larger values of IRX than the $\beta$ relation of MHC99."948 ILwius defined the UV reddenius relation expected for the dust models. we again use the same technique to predict the N-vav huuinosities of the LBC sample.," Having defined the UV reddening relation expected for the dust models, we again use the same technique to predict the X-ray luminosities of the LBG sample."949 The homogeneous model slehthy πάς predicts the mean N-ray luminosity (L1<10H Creswoe 1) compared to the observed value.," The homogeneous model slightly under predicts the mean X-ray luminosity $1.1 \times 10^{41}\,$ $\,$ $^{-1}$ ) compared to the observed value."950 Within strict error τς Guoclel and observed) the homogeneous model agrees with the observation., Within strict error limits (model and observed) the homogeneous model agrees with the observation.951 The chuupy model slightly over predicts it (LT«10H Cres Ly but the observed mean is well within he lo eror.," The clumpy model slightly over predicts it $4.7 \times 10^{41}\,$ $\,$ $^{-1}$ ), but the observed mean is well within the $1\sigma$ error."952 The histogram in Panel C (Panel D) of Figure 3 represeuts the homogeneous (cluupy) model., The histogram in Panel C (Panel D) of Figure 3 represents the homogeneous (clumpy) model.953 To within the uncertainties iu our technique. we are unable o differentiate between the empiicallv derived relation of MIIC99 aud either of the SMC-dust/shell geometry nodels.," To within the uncertainties in our technique, we are unable to differentiate between the empirically derived relation of MHC99 and either of the SMC-dust/shell geometry models."954 Witt Cordon claim that the clumpy model reproduces he effective starburst attenuation curve of Calzetti (1997: Calzetti et al., Witt Gordon claim that the clumpy model reproduces the effective starburst attenuation curve of Calzetti (1997; Calzetti et al.955 2000)., 2000).956 We have calculated the UV reddening relation for the Calzetti attenuation curve (dotted line of Figure 2) using the same method aud find it very similar to the elunipy model over the narrow range of j| measured for the LBGs., We have calculated the UV reddening relation for the Calzetti attenuation curve (dotted line of Figure 2) using the same method and find it very similar to the clumpy model over the narrow range of $\beta$ measured for the LBGs.957 When we use the Calzetti effective attenuation to predict N-rav cussion. we fud the mean luuinosity L5s10H cress ly Gs essentially the same as that from the ‘hunpy model aud also in agreement with the observed value (Figure 3: Panel E).," When we use the Calzetti effective attenuation to predict X-ray emission, we find the mean luminosity $4.5 \times 10^{41}\,$ $\,$ $^{-1}$ ) is essentially the same as that from the clumpy model and also in agreement with the observed value (Figure 3: Panel E)."958 We should note the effect our choice of intrinsic starburst imodel has ou the computed UV reddening relations., We should note the effect our choice of intrinsic starburst model has on the computed UV reddening relations.959 Choosing a higher metallicity (16. Z..) stellar population will produce a redder iutrinsic (unextincted) spectral slope CAJj~ 0.1)but would have little effect on IRN values for 3>2., Choosing a higher metallicity (i.e. $Z_{\odot}$ ) stellar population will produce a redder intrinsic (unextincted) spectral slope $\Delta\beta_0 \sim 0.1$ ) but would have little effect on IRX values for $\beta > -2$.960 Differences in either burst age or the IME upper mass lint will effect both ου aud IRN in the seuse that older bursts or smaller upper mass πες will redden y aud lower IRN., Differences in either burst age or the IMF upper mass limit will effect both $\beta_0$ and IRX in the sense that older bursts or smaller upper mass limits will redden $\beta_0$ and lower IRX.961 This would then result ina sanaller predicted N-rav flux for the LBC sample., This would then result in a smaller predicted X-ray flux for the LBG sample.962 We can use the machinery we have developed to test the extreme lypothesis that LBCs suffer no £u-UV extinction., We can use the machinery we have developed to test the extreme hypothesis that LBGs suffer no far-UV extinction.963 [f the LBC sample is actively forming stars and harbors little or uo dust. we can reasonably assuue that the far-UV flux is unattenuated auc dominates the bolometrie bhDuiuositv.," If the LBG sample is actively forming stars and harbors little or no dust, we can reasonably assume that the far-UV flux is unattenuated and dominates the bolometric luminosity."964 The reddened UV colors mist then be interpreted ax a simple effect of burst age., The reddened UV colors must then be interpreted as a simple effect of burst age.965 Although continuous star formation modes could not casily account for the rauge of J measured in the LBG sauple. imstantaneous burst modes with ages betwoeeou 302fna100 Mr can naturally redden enoush to explain the observed UV properties (Leitherer et al.," Although continuous star formation modes could not easily account for the range of $\beta$ measured in the LBG sample, instantaneous burst modes with ages between $30 > t_{\rm burst} > 100$ Myr can naturally redden enough to explain the observed UV properties (Leitherer et al."966 1999)., 1999).967 ILlowever. uuder this scenario. the mean ταν luuinosity is uuder predicted by. a factor of 6 (L6«10/9 eres. 1).," However, under this scenario, the mean X-ray luminosity is under predicted by a factor of 6 $4.6 \times96810^{40}\,$ $\,$ $^{-1}$ )."969 Given the large observational aud model uucertaiuties the difference is ~26 (Figure 3: Paucl FE)., Given the large observational and model uncertainties the difference is $\sim2\sigma$ (Figure 3: Panel F).970 Evidence is beginning to emerge that 28 keV Χανς are a good star formation rate indicator (Ranalli ct al., Evidence is beginning to emerge that 2–8 keV X-rays are a good star formation rate indicator (Ranalli et al.971 2002)., 2002).972 Iu local starbursts. the 28 keV N-rav enission is believed to be produced. primarily bv hiehauass N-rav binaries (IDNEND: Persic Rephacli 2002).," In local starbursts, the 2–8 keV X-ray emission is believed to be produced primarily by high-mass X-ray binaries (HMXB; Persic Rephaeli 2002)."973 This suggests that the Brandt et al. (, This suggests that the Brandt et al. (9742001) stacking technique applied to the IIDE-N LBC sample may be detecting binary stars at ~~3.,2001) stacking technique applied to the HDF-N LBG sample may be detecting binary stars at $z \sim 3$.975" Low luminosity AGN aud the class of ultraluninous N-rav sources (ULNs or INOs: Colbert AMiushotzisy ""ur which may be the beamed emission frou IINNDs (ie. Roberts et al."," Low luminosity AGN and the class of ultraluminous X-ray sources (ULXs or IXOs; Colbert Mushotzky 1999), which may be the beamed emission from HMXBs (i.e., Roberts et al."976 2002) or a new class of intermediate mass (107 10! AL.) black holes. may also contribute to the 2S keV flux.," 2002) or a new class of intermediate mass $10^2$ $10^4$ $_{\odot}$ ) black holes, may also contribute to the 2–8 keV flux."977 Furthermore. 28 keV. N-vavs suffer little intrinsic absorption and can escape regions where the far-UY tracers ofstar formation may be heavily extincted by a dusty interstellar mediuu.," Furthermore, 2–8 keV X-rays suffer little intrinsic absorption and can escape regions where the far-UV tracers of star formation may be heavily extincted by a dusty interstellar medium."978 For these reasons. the 28 keV N-rav huninosity strongly correlates with the bolometric huninosity of star fornüng galaxies.," For these reasons, the 2–8 keV X-ray luminosity strongly correlates with the bolometric luminosity of star forming galaxies."979 This mcaus that 28 keV A-vavs can serve as a proxy for the far-IR thermal dust emission at hiel-:., This means that 2–8 keV X-rays can serve as a proxy for the far-IR thermal dust emission at $z$.980 We have derived the bolometric to 28 keV Nav correlation for a local souple of normal and starburst ealaxies and have used it. iu combination with several UV reddening schemes. to predict the mean 28 keV ταν lununesity for a sample of 21 spectroscopically confirmed high redshift Lyiman-break galaxies.," We have derived the bolometric to 2–8 keV X-ray correlation for a local sample of normal and starburst galaxies and have used it, in combination with several UV reddening schemes, to predict the mean 2–8 keV X-ray luminosity for a sample of 24 spectroscopically confirmed high redshift Lyman-break galaxies."981 Tis simple analysis demonstrates that LBCs can not have far-IR to &u-UV flux ratios similar to those found for nearby ULICs. nor are they likely to he unatteuuated by dust.," This simple analysis demonstrates that LBGs can not have far-IR to far-UV flux ratios similar to those found for nearby ULIGs, nor are they likely to be unattenuated by dust."982 Of the extinction methods considered. we find that the starburst reddening relation of MIIC99 is the most accurate predictor of the mean X-rav Duuinositv for the sample.," Of the extinction methods considered, we find that the $\beta$ starburst reddening relation of MHC99 is the most accurate predictor of the mean X-ray luminosity for the sample."983 The very similar reddening relations derived frou Witt Cordon (2000) extinction models of low metallicity dust in a shell ecometiv aud the Calzetti et al. (, The very similar reddening relations derived from Witt Gordon (2000) extinction models of low metallicity dust in a shell geometry and the Calzetti et al. (9842000) effective starburst attenuation curve are also consistent with the observed X-ray enission.,2000) effective starburst attenuation curve are also consistent with the observed X-ray emission.985 These results provide additional evidence that LDCis can be considered as scaled-up local starbursts., These results provide additional evidence that LBGs can be considered as scaled-up local starbursts.986 Equally iuportanut. it sugeests that Πο may be a reasonable tool for estimating the UV extinction of high redshift LDCs.," Equally important, it suggests that $\beta$ may be a reasonable tool for estimating the UV extinction of high redshift LBGs."987 If this is the case. all 21 LBCs iu this sample have «που<3.1 Mae with a mean Qaedian) of 1.1 (1.5) Mag iurplviug a mean dadust correction factor of ~I.," If this is the case, all 24 LBGs in this sample have $A_{1600} < 3.1$ Mag with a mean (median) of 1.4 (1.5) Mag implying a mean dust correction factor of $\sim4$."988 This moderate level of UV. extinction is consistent with the results of Papovich et al. (, This moderate level of UV extinction is consistent with the results of Papovich et al. (9892001) who find typical ccorrection factors of 3Ll from an analysis of the UV-optical spectral energv distributions for a sample of 33 IIDF-N LBGs which includes 23 from our sample.,2001) who find typical correction factors of 3–4.4 from an analysis of the UV-optical spectral energy distributions for a sample of 33 HDF-N LBGs which includes 23 from our sample.990 Similar UV extinctions are also deduced for larecr LBG samples by Steidel et al. (, Similar UV extinctions are also deduced for larger LBG samples by Steidel et al. (9911999) and MIICO99.,1999) and MHC99.992 Our results are the first to use low extinction X-rav enüssion to test aud confini these clans., Our results are the first to use low extinction X-ray emission to test and confirm these claims.993 Although it is tempting to use the results developed here to predict the N-rav fluxes of individual LDCs. we caution the reader that our results are statistical.," Although it is tempting to use the results developed here to predict the X-ray fluxes of individual LBGs, we caution the reader that our results are statistical."994 The accuracy of the estimated N-vav cuussion for any suele LBC in this sample is only ~0.18 dex., The accuracy of the estimated X-ray emission for any single LBG in this sample is only $\sim0.48$ dex.995 With this iu nüud. it is interesting to note that when the UV reddening relations of MIIC99. Witt Cordon (clampy model}. aud Calzetti are applied. to this technique. more than of the 2ὃ keV flux originates from the half of the sample (12) with," With this in mind, it is interesting to note that when the UV reddening relations of MHC99, Witt Gordon (clumpy model), and Calzetti are applied to this technique, more than of the 2–8 keV flux originates from the half of the sample (12) with"996bancs 4.5-6.0 keV. and 3.0-4.5 keV and the Lard colour (LIC) as the ratio of count rates in energy. bands 9.7-16.0. keV and 6.0-9.7 keV. Average Crab colours obtained are ος = 1.986+0.002 and LIC = 0.5992+ 0.0007.,bands 4.5-6.0 keV and 3.0-4.5 keV and the Hard colour (HC) as the ratio of count rates in energy bands 9.7-16.0 keV and 6.0-9.7 keV. Average Crab colours obtained are SC = $1.986 \pm 0.002 $ and HC = $0.5992 \pm 0.0007$ .997 Figure 2. is the CD obtained by plotting normalised Aql X-1 HC versus SC., Figure \ref{fig:cd} is the CD obtained by plotting normalised Aql X-1 HC versus SC.998 All ποιακο. αι N-1 colours having error greater than of the observed. colour were ignored., All normalised Aql X-1 colours having error greater than of the observed colour were ignored.999 This amounted in rejecting 1H out of 307 points of the CD., This amounted in rejecting 14 out of 307 points of the CD.1000 From Figure 2. we conclude that during the second. third and fourth observations. Aql N-1 was in the ELS (compareFigure2. of his paper with Figure 2 We will refer to these three observations as ELL. E12. ELS respectively.," From Figure \ref{fig:cd} we conclude that during the second, third and fourth observations, Aql X-1 was in the EIS \citep[compare Figure \ref{fig:cd} of this paper with Figure 2 We will refer to these three observations as EI1, EI2, EI3 respectively."1001 I is noted that E12 observation ias the best statistics in the ELS and also EI2 is brighter han ELI indicating irregular decline in the lishteurve (Table 1)., It is noted that EI2 observation has the best statistics in the EIS and also EI2 is brighter than EI1 indicating irregular decline in the lightcurve (Table \ref{tab:table1}) ).1002 There are no simultaneous PCA observations during the irst observation to ascertain the spectral state of he source., There are no simultaneous PCA observations during the first observation to ascertain the spectral state of the source.1003 Hence we use a cdillerent method to find the normatisecl Aql Χο ancl HC during this observation., Hence we use a different method to find the normalised Aql X-1 SC and HC during this observation.1004 The best fit spectral model that can reproduce the observed spectrum is used to simulate a PCA spectrum., The best fit spectral model that can reproduce the observed spectrum is used to simulate a PCA spectrum.1005 The command of NSPISC package is used for this simulation., The command of XSPEC package is used for this simulation.1006 Average count rates in the four energy. bands required. to calculate the SC and LIC are obtained by this simulated PCA spectrum., Average count rates in the four energy bands required to calculate the SC and HC are obtained by this simulated PCA spectrum.1007 Aql N-1 8C and LIC thus obtained are normalised by the average Crab SC and LC respectively., Aql X-1 SC and HC thus obtained are normalised by the average Crab SC and HC respectively.1008 In figure 2 the point marked by an open plus sign with error bars represents this normalised Aql N-1 5€ and HC., In figure \ref{fig:cd} the point marked by an open plus sign with error bars represents this normalised Aql X-1 SC and HC.1009 Thus we conclude that during the first observation. Aql X-1 was in the DS.," Thus we conclude that during the first observation, Aql X-1 was in the BS."1010 Leneclorth this observation. will be referred. to as the DS observation., Henceforth this observation will be referred to as the BS observation.1011 The PCA spectra. from. simultaneous observations (Table 1)) ave used for comparison with the spectra., The PCA spectra from simultaneous observations (Table \ref{tab:table1}) ) are used for comparison with the spectra.1012 We have used the Std2 spectra and response files provided in the standard. products., We have used the Std2 spectra and response files provided in the standard products.1013 Energy. channels were appropriately regrouped before the final spectral fitting., Energy channels were appropriately regrouped before the final spectral fitting.1014 Lor cach front-illuminated NIS detector. (XISO and X183) we extracted the source spectra using a 260 arc-sec circular extraction region centered on the source., For each front-illuminated XIS detector (XIS0 and XIS3) we extracted the source spectra using a 260 arc-sec circular extraction region centered on the source.1015 The energy. scale is reprocessed using the task., The energy scale is reprocessed using the task.1016 Dackground spectra are extracted using appropriate circular regions outside the source region., Background spectra are extracted using appropriate circular regions outside the source region.1017 C'orresponding response files are. generated using the and tools., Corresponding response files are generated using the and tools.1018 The spectra from respective ALSO and. NIS3 detectors are then added together using the tool., The spectra from respective XIS0 and XIS3 detectors are then added together using the tool.1019 During high count rates. as is the case for the BS observation. there is a possibility of pile-up in the AIS detectors.," During high count rates, as is the case for the BS observation, there is a possibility of pile-up in the XIS detectors."1020 To check [or pile-up we extracted the source spectrum. from an annular region with inner radius of 40 arc-sec and an outer radius of 260 arc-sec., To check for pile-up we extracted the source spectrum from an annular region with inner radius of 40 arc-sec and an outer radius of 260 arc-sec.1021 Corresponding response files were also generated., Corresponding response files were also generated.1022 Figure 3. shows the ratio of NISO background subtracted spectrum. extracted. [rom the full circular region. ancl from the annular region., Figure \ref{fig:compare-xis0} shows the ratio of XIS0 background subtracted spectrum extracted from the full circular region and from the annular region.1023 The constant ratio indicates that both these spectra are similar and cilfer only in the observed. count. rates., The constant ratio indicates that both these spectra are similar and differ only in the observed count rates.1024 Similar result is seen for NIS3 detector also., Similar result is seen for XIS3 detector also.1025 This confirms that the Bs observation is not allected by. pile-up., This confirms that the BS observation is not affected by pile-up.1026 The data processing version used for the LIND cleaned products is 2.1.6.15., The data processing version used for the HXD cleaned products is 2.1.6.15.1027 Hence the PIN spectra are extracted using the cleaned event files Following the standard analysis threads on the The PIN non-X-rav background. is extracted. [rom the observation specificmodel provided by the instrument team., Hence the PIN spectra are extracted using the cleaned event files following the standard analysis threads on the The PIN non-X-ray background is extracted from the observation specificmodel provided by the instrument team.1028 (Batveinetal.2009)., \citep{bat09} \citep{ver09}.1029 (Verasetal.2009).. 2009).. (saneetal.2009).. (Dollinger," \citep{bar07a} \citep{lau09,mou09}, \citep{kan08,kan09a}, \citep{kan09b}."1030 (Niedzielskietal.2009).. Kennedy&Keuyou2008).," \citep{dol09} \citep{nie09}. \citep{ida05,ken08}."1031. planets orbiting elauts stars tend to lave larec transit probabilities due to the size of the lost stars (Assetetal. 2009)., planets orbiting giants stars tend to have large transit probabilities due to the size of the host stars \citep{ass09}.1032. Cüant stars present significant challenges. however. to those who intend to monitor those stars for the purpose of detecting cxoplanetary transits.," Giant stars present significant challenges, however, to those who intend to monitor those stars for the purpose of detecting exoplanetary transits."1033 A good exaniple is the planet orbiting ID 122130 (Sctiawanctal.200 1).. for which the combination of the 22.9 2. host star (daSilvaetal.2006). and the high ecceutricitv of the planetary orbit lead to a transit probability of ~32," A good example is the planet orbiting HD 122430 \citep{set04}, for which the combination of the 22.9 $R_\sun$ host star \citep{das06} and the high eccentricity of the planetary orbit lead to a transit probability of $\sim 32$."1034 ILowever. assmunme a Jupiter radius for the planet requires the wnambignous detection of a 1.9«10D transit depth.," However, assuming a Jupiter radius for the planet requires the unambiguous detection of a $1.9 \times 10^{-5}$ transit depth."1035 Additionally. the uncertiiuty in the orbital paralcters of the planet means that a laree fransit window will need to be continuously monitored (aneetal. 2009)..," Additionally, the uncertainty in the orbital parameters of the planet means that a large transit window will need to be continuously monitored \citep{kan09b}."1036 Finally. a photometric survey of giaut stars bv Πανetal.(2000). found that almost half of their salple exhibited low-level plotometric variability that would further complicate transit detection.," Finally, a photometric survey of giant stars by \citet{hen00} found that almost half of their sample exhibited low-level photometric variability that would further complicate transit detection."1037 The planet orbiting iota Draconis (hereafter + Dra} presents a particularly iuterestiug case., The planet orbiting iota Draconis (hereafter $\iota$ Dra) presents a particularly interesting case.1038 The host star is a 2 eiaut. is very bright (V.= 3.29). and is frequently referred to by its other common aliases of ΠΟ 137759 and HIP 75158.," The host star is a K2 giant, is very bright $V = 3.29$ ), and is frequently referred to by its other common aliases of HD 137759 and HIP 75458."1039 A thorough spectral analysis of this star was mndertaken by Sadakaueetal.(2005).. who fouud a uictallicity of =0.12.," A thorough spectral analysis of this star was undertaken by \citet{sad05}, who found a metallicity of [Fe/H] $= 0.12$."1040 The planetary companion was discovered by |Fe/II]Frinketal.(2002).. and the orbit was further refined by Zechinelsteretal.(2008). whose radial velocity data revealed a linear trend over tine.," The planetary companion was discovered by \citet{fri02}, and the orbit was further refined by \citet{zec08}, whose radial velocity data revealed a linear trend over time."1041 Tn addition to the lavee stellar radius. the planetary orbit is hiellv eccentric and the argument of periastrou (w~ 907) cusures that the periastron passage occurs approximately in the obscrver-star plane perpendicular to the line-ofsieht.," In addition to the large stellar radius, the planetary orbit is highly eccentric and the argument of periastron $\omega \sim 90\degr$ ) ensures that the periastron passage occurs approximately in the observer-star plane perpendicular to the line-of-sight."1042 Tere we present new radial velocity data for + Dra b and an analysis of the photometric stability of the host star., Here we present new radial velocity data for $\iota$ Dra b and an analysis of the photometric stability of the host star.1043 These data are used to provide a well-coustrained transit ephemeris for the next LO vears and an assessienut of the feasibility of detecting a transit for the planetary colupanion., These data are used to provide a well-constrained transit ephemeris for the next 10 years and an assessment of the feasibility of detecting a transit for the planetary companion.1044 This analysis and discussionmay be used as a nbodol for how to consider the transit detection potential for cach of the planets orbiting eiaut stars., This analysis and discussionmay be used as a model for how to consider the transit detection potential for each of the planets orbiting giant stars.1045to our AM-band data. since the reduction in sensitivity over L' (— 3mmag) is much greater than can be compensated for by the red colour of the quasar nucleus (L'Al=0.76 for a power law a=13: Neugebauer et 11987).,"to our $M$ -band data, since the reduction in sensitivity over $L'$ $\sim 3$ mag) is much greater than can be compensated for by the red colour of the quasar nucleus $L'-M=0.76$ for a power law $\alpha=1.3$; Neugebauer et 1987)."1046 We are therefore convinced. that we have not made any spurious detection. and that we have not failed to detect any sources which are in reality brighter than our quoted limits.," We are therefore convinced that we have not made any spurious detection, and that we have not failed to detect any sources which are in reality brighter than our quoted limits."1047 Ifthe standard interpretation of our nuclear sources as dust-obscured quasars is correct. they should have the colours of a quasar. modified by some amount of foreground reddening.," If the standard interpretation of our nuclear sources as dust-obscured quasars is correct, they should have the colours of a quasar, modified by some amount of foreground reddening."1048 We therefore perform linear regression. accounting for upper limits in the manner of Isobe. Feigelson Nelson (1986). on the data of Section 3...," We therefore perform linear regression, accounting for upper limits in the manner of Isobe, Feigelson Nelson (1986), on the data of Section \ref{sec:nuclei}."1049 “Phis analwsis produces. values for the intrinsic luminosity ancl extinction of cach nuclear source., This analysis produces values for the intrinsic luminosity and extinction of each nuclear source.1050 We adopt our own parametrization of the near-infrared. interstellar extinction. law. obtained by fitting a second-order polynomial to the data of Ricke Lebolsky (1985).," We adopt our own parametrization of the near-infrared interstellar extinction law, obtained by fitting a second-order polynomial to the data of Rieke Lebofsky (1985)."1051 This parametrization. by virtue of ignoring the optical data. provides a rather better fit to the longest. wavelengths than do those of llowarth (1983) ane Cardelli. Clavton Mathis (1989).," This parametrization, by virtue of ignoring the optical data, provides a rather better fit to the longest wavelengths than do those of Howarth (1983) and Cardelli, Clayton Mathis (1989)."1052 The intrinsic quasar spectrum is assumed to be that of an a=1.3 power law (Neugebauer et 11059)., The intrinsic quasar spectrum is assumed to be that of an $\alpha = 1.3$ power law (Neugebauer et 1987).1053 Table 5. lists the extinctions and intrinsic luminosities we derive for the obscured quasars in the five radio galaxies with detected nuclear sources., Table \ref{tab:exts} lists the extinctions and intrinsic luminosities we derive for the obscured quasars in the five radio galaxies with detected nuclear sources.1054 These data are presented graphically in Fig. 12.., These data are presented graphically in Fig. \ref{fig:irspec}.1055 For 3€ 223 and 3€ 234. where the nucleus was detected: at all four wavelengths. we also. performed regression. with the spectral index as an additional free," For 3C 223 and 3C 234, where the nucleus was detected at all four wavelengths, we also performed regression with the spectral index as an additional free"1056"The resulting spectrum shows the detection of many lines due to methane in Triton's atmosphere, particularly at 2320-2330 nm (Fig.","The resulting spectrum shows the detection of many lines due to methane in Triton's atmosphere, particularly at 2320-2330 nm (Fig."1057 1)., 1).1058 This is the first observation of gaseous methane since its discovery by Voyager (Herbert and Sandel 1991)., This is the first observation of gaseous methane since its discovery by Voyager (Herbert and Sandel 1991).1059" As for our study of Pluto's CH4, we constructed a direct line-by-line atmospheric model of Triton, integrated over angles and including solar lines reflected off Triton's surface as well as the telluric transmission (see details in Lellouch et al."," As for our study of Pluto's $_4$, we constructed a direct line-by-line atmospheric model of Triton, integrated over angles and including solar lines reflected off Triton's surface as well as the telluric transmission (see details in Lellouch et al."1060 2009)., 2009).1061" The spectrum was first modelled by assuming a single-temperature layer, with Triton's atmospheric methane mean temperature (T) and column density (a) as free parameters."," The spectrum was first modelled by assuming a single-temperature layer, with Triton's atmospheric methane mean temperature (T) and column density (a) as free parameters."1062 We inferred T-50*7? K and a = 0.08+0.03 cm-am (Fig., We inferred $^{+20}_{-15}$ K and a = $\pm$ 0.03 cm-am (Fig.1063 2 on-line)., 2 on-line).1064 The same analysis for Pluto had given T-90*75 Kanda- 0.757333 cm-am., The same analysis for Pluto had given $^{+25}_{-18}$ K and a = $^{+0.55}_{-0.30}$ cm-am.1065" This confirms that Pluto’s atmosphere is warmer than Triton’s, as a result of its higher methane abundance."," This confirms that Pluto's atmosphere is warmer than Triton's, as a result of its higher methane abundance."1066 The error bars on the inferred mean methane temperature are such that it is not possible to constrain the methane vertical distribution., The error bars on the inferred mean methane temperature are such that it is not possible to constrain the methane vertical distribution.1067" Instead, we used the Voyager-determined thermal structure (temperature vs altitude, Krasnopolsky et al.,"," Instead, we used the Voyager-determined thermal structure (temperature vs altitude, Krasnopolsky et al.,"1068" 1993) and methane vertical profile (Herbert and Sandel 1991, ingress UV occultation profile)."," 1993) and methane vertical profile (Herbert and Sandel 1991, ingress UV occultation profile)."1069 The latter shows a decrease of the, The latter shows a decrease of the1070and is included in the recorded spectra.,and is included in the recorded spectra.1071" For this reason, contamination by emission lines originating in the often bright, extended nebulae surrounding WR stars is often a concern."," For this reason, contamination by emission lines originating in the often bright, extended nebulae surrounding WR stars is often a concern."1072" SCORE’ss small 1”x2” slit excludes most of this nebular emission, leading in some cases to significant differences between spectra of the same variable WR star observed with both ISO and "," s small $1\arcsec\times2\arcsec$ slit excludes most of this nebular emission, leading in some cases to significant differences between spectra of the same non-variable WR star observed with both ISO and (cf."1073"WR146 in ? vs. ?,, as described in §44.2 of the ((cf."," WR146 in \citet{Willis1997} vs. \citetalias{2001AJ....121.2115S}, as described in 4.2 of the latter)."1074" While we know of no cases in which neon or other latter).abundances computed using ISO data were affected by this type of contamination, the sspectra of fainter WR stars used here should be relatively less affected by nebular emission."," While we know of no cases in which neon or other abundances computed using ISO data were affected by this type of contamination, the spectra of fainter WR stars used here should be relatively less affected by nebular emission."1075" For a uniform, spherical, but clumped wind with terminal velocity vo; and constant volume filling fraction ó (0€6 1), as depicted in Fig. 2,,"," For a uniform, spherical, but clumped wind with terminal velocity $v_{\infty}$ and constant volume filling fraction $\delta$ $0\le\delta\le1$ ), as depicted in Fig. \ref{fig:windmodel}, ,"1076" the mass loss rate can be written: where µ is the mean atomic mass per ion, and n is the number density of the ionized gas."," the mass loss rate can be written: where $\mu$ is the mean atomic mass per ion, and $n$ is the number density of the ionized gas."1077" Defining the standard A=TanMHMUoc, the density can be expressed as: The dominant radiative output of the wind at mid-infrared and longer wavelengths is free-free emission (?).."," Defining the standard $\mathcal{A}\equiv \frac{\dot{M}}{4\pi\mu1078 m_Hv_{\infty}}$, the density can be expressed as: The dominant radiative output of the wind at mid-infrared and longer wavelengths is free-free emission \citep{Wright1975}."1079" The free-free optical depth along a particular line of sight through the clumped wind to the observer is where the reduced free-free opacity K(v,T)Kpp/MMe, Ye is the number of electrons per ion, and we have made use of the 1/r? density profile of Eq. 2.."," The free-free optical depth along a particular line of sight through the clumped wind to the observer is where the reduced free-free opacity $\mathcal{K}(\nu,T)=\kappa_{ff}/nn_e$ , $\gamma_e$ is the number of electrons per ion, and we have made use of the $1/r^2$ density profile of Eq. \ref{eq:2}."1080" Assuming a constant, thermal source function, and integrating over cylinders of constant impact parameter b thus constant free-free optical depth), we recover ?""s (andinfrared/radio free-free flux expression, modified to include the effects of clumping via the fill factor ó: where D is the distance to the star, g, is the frequency dependent free-free Gaunt factor, and Z is the rms average charge per ion."," Assuming a constant, thermal source function, and integrating over cylinders of constant impact parameter $b$ (and thus constant free-free optical depth), we recover \citeauthor{Wright1975}' 's infrared/radio free-free flux expression, modified to include the effects of clumping via the fill factor $\delta$: where $D$ is the distance to the star, $g_\nu$ is the frequency dependent free-free Gaunt factor, and $Z$ is the rms average charge per ion."1081 Most WR. mass loss rate estimates are derived from radio measurements of the free-free emission using Eq. 4.., Most WR mass loss rate estimates are derived from radio measurements of the free-free emission using Eq. \ref{eq:4}.1082" Given the same assumptions of atomic parameters of the wind (Z, µ. Ye), it is apparent that, in the absence of information about the clumping fill factor 6, therate, Mss=Μ/νὸ, is derived."," Given the same assumptions of atomic parameters of the wind $Z$, $\mu$, $\gamma_e$ ), it is apparent that, in the absence of information about the clumping fill factor $\delta$, the, $\dot{M}_{scl}\equiv\dot{M}/\sqrt{\delta}$, is derived."1083" For fine structure lines arising from ions with ground states consisting of only two energy levels, the fractional abundance of the ion by number,jnj, can be calculated straightforwardly from the observed line flux by neglecting all other transitions."," For fine structure lines arising from ions with ground states consisting of only two energy levels, the fractional abundance of the ion by number, can be calculated straightforwardly from the observed line flux by neglecting all other transitions."1084" Following ?,, the flux due to a given line transitioncan be written: where Αμ is the Einstein emission coefficient for the line in question, and m, is the density of the ions populating the upper level of the transition."," Following \citet{Barlow1988}, the flux due to a given line transitioncan be written: where $A_{ul}$ is the Einstein emission coefficient for the line in question, and $n_u$ is the density of the ions populating the upper level of the transition."1085Z used here (lromHaeusel&Zdunik1990a) is roughly the average charge of the uuclei actually present.,$Z$ used here \citep[from][]{haensel90b} is roughly the average charge of the nuclei actually present.1086 A self-consistent calculation of the crust composition. aud the resultine phase diagraiu. is required to couclusively determine if laver cake melting actually occurs.," A self-consistent calculation of the crust composition, and the resulting phase diagram, is required to conclusively determine if layer cake melting actually occurs."1087 There are three inain couclusious presented in this work., There are three main conclusions presented in this work.1088 First. for neutron stars accreting ‘apidly enough for the accreted hydrogen aud helium to burn stably. most of the leat released iu he crust [lows into the core.," First, for neutron stars accreting rapidly enough for the accreted hydrogen and helium to burn stably, most of the heat released in the crust flows into the core."1089 As a result. the thermal prolile in the inner crust is nearly inclepeudenut ol the temperature at the top of the crust.," As a result, the thermal profile in the inner crust is nearly independent of the temperature at the top of the crust."1090 Secoud. if the crust lattice is very impure. there is a uaximnur in temperature at deusities greater than neutron drip. where the heating occurs.," Second, if the crust lattice is very impure, there is a maximum in temperature at densities greater than neutron drip, where the heating occurs."1091 The peak eniperature in the crust in tliis case is set by the ability of the crust to carry tlie generated nuclear uminosity iuward [rom the reaction shell aud is relatively iuseusitive to the core temperature., The peak temperature in the crust in this case is set by the ability of the crust to carry the generated nuclear luminosity inward from the reaction shell and is relatively insensitive to the core temperature.1092 Third. heating the inner crusi to temperatures zz8x105IN might melt. t1le Crust ---in thin layers where electron captures have reduced the lonic charge.," Third, heating the inner crust to temperatures $\approx 8\ee{8}\K$ might melt the crust in thin layers where electron captures have reduced the ionic charge."1093 There are several consequences of these results., There are several consequences of these results.1094 Because a fluid layer ¢oes not support shear stress. the strain inthe crust must vanish in these melt lavers.," Because a fluid layer does not support shear stress, the strain in the crust must vanish in these melt layers."1095 This will limit tje quadrupole that ean ye induced by thermal perturbatious to the electron capture rate (Bildsten1998) if these captures occur above the melt laver., This will limit the quadrupole that can be induced by thermal perturbations to the electron capture rate \citep{bildsten98:gravity-wave} if these captures occur above the melt layer.1096 Iu addition. the fluid layers can. clissipate roatioual energy. eitler hrough. hydrodsuamical or maguetolydrodyuamical processes. aud thus οςjntribute to balauciug he accretion torque acting on the stellar surface.," In addition, the fluid layers can dissipate rotational energy, either through hydrodynamical or magnetohydrodynamical processes, and thus contribute to balancing the accretion torque acting on the stellar surface."1097 The electrical conductiviy Of an accreted crust is reduced. both because of erust heating (Urpin&Ceppert1995:GeppertUrpin1991) aud yecause of crust impurities (Brown&Bildsten1995).," The electrical conductivity of an accreted crust is reduced, both because of crust heating \citep{urpin95,geppert94} and because of crust impurities \citep{brown98a}."1098. LP the crust is as impwe as considered here. he timescale for Olunic decay over a pressure scalelieight is much less (by a factor of 100) than the low timescale. for much of the crust.," If the crust is as impure as considered here, the timescale for Ohmic decay over a pressure scaleheight is much less (by a factor of 100) than the flow timescale, for much of the crust."1099 As a result. the inward advection of magnetic [flux (Ixonar is reduced in importance.," As a result, the inward advection of magnetic flux \citep{konar97} is reduced in importance."1100 Thermomaguetic ellects. such as current clrift (Ceppert&Urpin19901) aud the battery ellect (e.g..Blandford.Applegate.&Heruquist.1982).. will be comparatively more important. however. because of the greater thermal gradieut.," Thermomagnetic effects, such as current drift \citep{geppert94} and the battery effect \citep*[e.g.,][]{blandford83}, will be comparatively more important, however, because of the greater thermal gradient."1101 In recent vears. attention has been giveu to other. more efficient. cooling mechanisms.," In recent years, attention has been given to other, more efficient, cooling mechanisms."1102 The direct. Urea process cau operate if the proton fraction is [n]ϱ‘eater than 0.115 (Lattimer or if hyvperous are present (Prakashetal. 1992).., The direct Urca process can operate if the proton fraction is greater than 0.148 \citep{lattimer91} or if hyperons are present \citep{prakash92:_rapid_delta}. .1103 Other exotic mechanisms may be possible. includiug pion condensates (οσαetal.1991).. kaon condensates (Brownetal.1988).. or quark uatter (Iwamoto1952)..," Other exotic mechanisms may be possible, including pion condensates \citep{umeda94}, kaon condensates \citep{brown88:_stran}, or quark matter \citep{iwamoto82:_neutr}."1104 The exotic mechauisius have the same temperature dependeuce as the direct. Urea (x. 7?) but are weaker., The exotic mechanisms have the same temperature dependence as the direct Urca $\propto T^6$ ) but are weaker.1105" Although none of the hydrostatic st""uctures cousidered iu his paper has an interior proton fraction large enough to activate the direct Urea. some form of enhanced cooling could operate."," Although none of the hydrostatic structures considered in this paper has an interior proton fraction large enough to activate the direct Urca, some form of enhanced cooling could operate."1106 However. tlie crust temperature would still femmain high 1.2)) if he crust were very impure.," However, the crust temperature would still remain high \ref{sec:Simple-expr-crust}) ) if the crust were very impure."1107 Direct observational couseqtences ofthe core 1eutriuo emissivityv are, Direct observational consequences ofthe core neutrino emissivity are1108our conclusions.,our conclusions.1109 Firstly. we have seen that the presence of a high mass galaxy within a region if size /? does not uniquely specify the value of the overdensity 9.," Firstly, we have seen that the presence of a high mass galaxy within a region if size $R$ does not uniquely specify the value of the overdensity $\delta$."1110 Rather we obtain a probability density (which is Gaussian in shape) and work with the value where this probability is maximum., Rather we obtain a probability density (which is Gaussian in shape) and work with the value where this probability is maximum.1111 In reality. however. the actua value of ὁ could be different and this may possibly affect the predicted luminosity function.," In reality, however, the actual value of $\delta$ could be different and this may possibly affect the predicted luminosity function."1112 Note that the luminosity function a the brighter end is almost independent of the details of reionization history. and this. in principle. can be used for constraining the value of 9.," Note that the luminosity function at the brighter end is almost independent of the details of reionization history, and this, in principle, can be used for constraining the value of $\delta$."1113 The effect of feedback can then be studied using the faint enc of the luminosity function., The effect of feedback can then be studied using the faint end of the luminosity function.1114 The radiative feedback prescription used in this paper is based on a Jeans mass calculation (2).., The radiative feedback prescription used in this paper is based on a Jeans mass calculation \citep{2005MNRAS.361..577C}.1115 However. alternate prescriptions for feedback exist in literature. e.g. ?. and hence the shape of the luminosity function at faint ends as predicted by our mode may not be robust.," However, alternate prescriptions for feedback exist in literature, e.g., \citet{2000ApJ...542..535G} and hence the shape of the luminosity function at faint ends as predicted by our model may not be robust."1116" Interestingly. the presence of a ""knee"" in the luminosity function can be used to estimate the value of the halo mass below which star formation can be suppressed (which in turn can indicate the temperature) while the shape of the function below this knee should indicate the nature of feedback."," Interestingly, the presence of a “knee” in the luminosity function can be used to estimate the value of the halo mass below which star formation can be suppressed (which in turn can indicate the temperature) while the shape of the function below this knee should indicate the nature of feedback."1117 This study can also be complemented with proposed for studying feedback using other observations. e.g.. 21 em observation (2) and CMBR (?)..," This study can also be complemented with proposed for studying feedback using other observations, e.g., 21 cm observation \citep{2008MNRAS.384.1525S} and CMBR \citep{2008MNRAS.385..404B}."1118 Finally. we have neglected the presence of other sources of reionization. e.g.. metal-free stars. minihaloes. and so on.," Finally, we have neglected the presence of other sources of reionization, e.g., metal-free stars, minihaloes, and so on."1119 It is expected that these sources would be too faint to affect the luminosity function in the ranges we are considering., It is expected that these sources would be too faint to affect the luminosity function in the ranges we are considering.1120 However. these sources may affect the thermal history of the medium. e.g. the metal-free stars would produce higher temperatures because of harder spectra.," However, these sources may affect the thermal history of the medium, e.g, the metal-free stars would produce higher temperatures because of harder spectra."1121 In such cases. it is most likely that feedback would oceur at magnitude brighter than what we have indicated and hence would possibly be easier to detect.," In such cases, it is most likely that feedback would occur at magnitude brighter than what we have indicated and hence would possibly be easier to detect."1122 GK acknowledges useful discussion with Prof. Jasjeet S. Bagla., GK acknowledges useful discussion with Prof. Jasjeet S. Bagla.1123 Computational work for this study was carried out at the cluster computing facility in the Harish-Chandra Research Institute (http://cluster.hrires.in/index.html)., Computational work for this study was carried out at the cluster computing facility in the Harish-Chandra Research Institute (http://cluster.hri.res.in/index.html).1124 We would also like to thank the referee for suggestions that improved this paper's quality., We would also like to thank the referee for suggestions that improved this paper's quality.1125 As expressed in Equation (5)). the number density of ionizing shotons produced per unit time is related to the SFR density. which in turn depends on the SFR in each halo. given by Equation (4800). and the number density of haloes of a certain age. given by Equation (1)) for average regions. and by Equation (159) for overdense regions.," As expressed in Equation \ref{nnu}) ), the number density of ionizing photons produced per unit time is related to the SFR density, which in turn depends on the SFR in each halo, given by Equation \ref{global_sfr}) ), and the number density of haloes of a certain age, given by Equation \ref{nmzzc}) ) for average regions, and by Equation \ref{nmzzc_biased}) ) for overdense regions."1126 We derive Equation (15)) in this appendix., We derive Equation \ref{nmzzc_biased}) ) in this appendix.1127" We denote the number density at redshift + of haloes formed between redshifts z, and z.|dz. with mass between À/ and A|dM. by NM.2.z,2)Md'z,.."," We denote the number density at redshift $z$ of haloes formed between redshifts $z_c$ and $z_c+dz_c$, with mass between $M$ and $M+dM$, by $N(M,z,z_c)dMdz_c$."1128" This quantity is related to(1) the ormation rate at redshift ο, of haloes with mass between AJ and Al|dAl. denoted by NowM.2JdAL. and (2) the probability of their survival at redshift z. denoted by pouy(2.2)."," This quantity is related to (1) the formation rate at redshift $z_c$ of haloes with mass between $M$ and $M+dM$, denoted by $\dot N_\mathrm{form}(M,z_c)dM$, and (2) the probability of their survival at redshift $z$ , denoted by $p_\mathrm{surv}(z,z_c)$."1129 We calculate hese two quantities using a technique given by ?.. applied to an overdense region with overdensity ὁ and size 2.," We calculate these two quantities using a technique given by \citet{1994PASJ...46..427S}, applied to an overdense region with overdensity $\delta$ and size $R$ ."1130 Recall that in extended Press-Schechter theory (2).. the mass 'uncetion of dark matter haloes is detined as the comoving number density of haloes with mass between Af and AZ|dA.," Recall that in extended Press-Schechter theory \citep{1991ApJ...379..440B}, the mass function of dark matter haloes is defined as the comoving number density of haloes with mass between $M$ and $M+dM$ ."1131" At redshift 2. this quantity is given by where p,, is the average matter density. and. as before. V(Al.z)=6,DI2)mCAL)]."," At redshift $z$, this quantity is given by where $\bar\rho_m$ is the average matter density, and, as before, $\nu(M,z)\equiv\delta_c/[D(z)\sigma(M)]$."1132 The critical overdensity of collapse of a halo is denoted by 0... (2) is the growth function of density perturbations. and (A7) is the rms value of density perturbations at the comoving scale corresponding to mass A.," The critical overdensity of collapse of a halo is denoted by $\delta_c$, $D(z)$ is the growth function of density perturbations, and $\sigma(M)$ is the rms value of density perturbations at the comoving scale corresponding to mass $M$."1133 In a region with overdensity ὁ and linear size /?. the mass function is enhanced.," In a region with overdensity $\delta$ and linear size $R$, the mass function is enhanced."1134 This enhancement can be calculated using the excursion set formalism (?).., This enhancement can be calculated using the excursion set formalism \citep{1991ApJ...379..440B}.1135 The resulting mass function is again given by Equation (I9)). except that now the quantity v(A/.z) is defined as where op is the rms value of density perturbations at comoving scale 77.," The resulting mass function is again given by Equation \ref{ps-mf}) ), except that now the quantity $\nu(M,z)$ is defined as where $\sigma_R$ is the rms value of density perturbations at comoving scale $R$."1136 Closely following 2.. we can write where Nios(AZ.z)dM is the destruction rate at redshift = of haloes of mass between Al and dA. (," Closely following \citet{1994PASJ...46..427S}, we can write where $\dot N_\mathrm{dest}(M,z)dM$ is the destruction rate at redshift $z$ of haloes of mass between $M$ and $dM$. ("1137The halo formation rate is detined as the number density of haloes formed per unit time from mergers of lower mass haloes.,The halo formation rate is defined as the number density of haloes formed per unit time from mergers of lower mass haloes.1138 Similarly the halo destruction rate is detined as the number density of haloes destroyed per unit time due to mergers with other haloes.), Similarly the halo destruction rate is defined as the number density of haloes destroyed per unit time due to mergers with other haloes.)1139 Here. an overdot denotes the time derivative.," Here, an overdot denotes the time derivative."1140 We can write the destruction rate as and the formation rate as where QUM.AL.2) is the probability that a halo of mass Al merges with another halo to result in a halo of mass Al’ per unit time. and (QV.ΛΙ.2) that an halo of mass AJ forming at redshift + has a progenitor of mass Al’.," We can write the destruction rate as and the formation rate as where $\tilde Q(M,M^\prime,z)$ is the probability that a halo of mass $M$ merges with another halo to result in a halo of mass $M^\prime$ per unit time, and $Q(M^\prime,M,z)$ that an halo of mass $M$ forming at redshift $z$ has a progenitor of mass $M^\prime$."1141 The threshold mass Aui is introduced at this stage to avoid divergence., The threshold mass $M_\mathrm{min}$ is introduced at this stage to avoid divergence.1142 This gives We now assume that ó has no characteristic mass scale so that OCAL2)=AL“oz).," This gives We now assume that $\phi$ has no characteristic mass scale so that $\phi(M,z)=M^\alpha\tilde\phi(z)$."1143 This gives But since the left hand side of Equation (263) is a function of time alone(through theredshift). the right hand sideof this equation also has to be independent of mass.," This gives But since the left hand side of Equation \ref{phi1}) ) is a function of time alone(through theredshift), the right hand sideof this equation also has to be independent of mass."1144" In particular. we can then set AZ=Ai, in this equation. giving us Now. in the case of the overdense region that we are considering here. we have"," In particular, we can then set $M=M_\mathrm{min}$ in this equation, giving us Now, in the case of the overdense region that we are considering here, we have"1145L4tkms! ffor maser sources. compared to 1.1] ffor other sources). indicating that the high density gas surrounding the protostellar cores traced by ammonia emission is dynamically linked to the collisional processes associated with the maser emission.,"1.4 for maser sources, compared to 1.1 for other sources), indicating that the high density gas surrounding the protostellar cores traced by ammonia emission is dynamically linked to the collisional processes associated with the maser emission."1146 In this section we will compare the derived ammonia and dust properties to identify correlations and anti-correlations in the data and to check for inconsistencies between the different tracers., In this section we will compare the derived ammonia and dust properties to identify correlations and anti-correlations in the data and to check for inconsistencies between the different tracers.1147 In Section 2.3. we derived the kinetic temperatures and NH; column densities which are the most readily available quantities we have at hand to compare with quantities derived from the dust emission., In Section \ref{sec:parameters} we derived the kinetic temperatures and $_3$ column densities which are the most readily available quantities we have at hand to compare with quantities derived from the dust emission.1148 In the next section we will describe how the dust temperatures were determined and estimate the H» column densities., In the next section we will describe how the dust temperatures were determined and estimate the $_2$ column densities.1149 In an earlier paper (?)) we presented observations of submillimetre emission which tracing the distribution of warm «dust., In an earlier paper \citealt{Morgan2008}) ) we presented observations of submillimetre emission which tracing the distribution of warm dust.1150 Spectral energy distributions (SEDs) were determined by fitting grevbody functions to the measured submillimetre fluxes and mid- and far-infrared fluxes., Spectral energy distributions (SEDs) were determined by fitting greybody functions to the measured submillimetre fluxes and mid- and far-infrared fluxes.1151 Fits were presented for all sources for which good quality data was available., Fits were presented for all sources for which good quality data was available.1152" The H» column density associated with each SFO object detected by ? may be calculated using where S, is the 850 fflux density. © is the solid angle associated with the aperture used to observe each core in 2.. j( = 2.3 is the mean molecular weight. mj is the mass of a hydrogen atom. αι. is the dust opacity per unit mass at 850 (0.02 cm? g |. following 21) and BG) is the Planck function. evaluated at dust temperature 7,4."," The $_2$ column density associated with each SFO object detected by \citet{Morgan2008} may be calculated using where $S_{\nu}$ is the 850 flux density, $\Omega$ is the solid angle associated with the aperture used to observe each core in \citet{Morgan2008}, $\mu$ = 2.3 is the mean molecular weight, $\mathrm{m_H}$ is the mass of a hydrogen atom, $\kappa_{\nu}$ is the dust opacity per unit mass at 850 (0.02 $^2$ $^{-1}$ following \citet{Morgan2008}) ) and $\mathrm{B}_{\nu}(T_\mathrm{d})$ is the Planck function, evaluated at dust temperature $T_\mathrm{d}$."1153 Resulting values of H» column density are presented in the tinal column of Table ??.., Resulting values of $_{2}$ column density are presented in the final column of Table \ref{tbl:Detections}.1154 In Fig., In Fig.1155 3 we present two scatter plots comparing the temperatures (upper panel) and column densities (lower panel) derived from the two tracers of ammonia and submillimetre emission., \ref{fig:Temp_Graph} we present two scatter plots comparing the temperatures (upper panel) and column densities (lower panel) derived from the two tracers of ammonia and submillimetre emission.1156 We show the linear-square fit to the data as a solid line., We show the linear-square fit to the data as a solid line.1157 Additionally. in the temperature plot. we include a dashed line indicating the position of the data if both temperatures were equal.," Additionally, in the temperature plot, we include a dashed line indicating the position of the data if both temperatures were equal."1158 There is quite a lot of scatter in the distributions seen in both plots., There is quite a lot of scatter in the distributions seen in both plots.1159 However. there is a general correlation between the kinetic and dust temperatures and the H» and NH; column densities.," However, there is a general correlation between the kinetic and dust temperatures and the $_2$ and $_3$ column densities."1160 The dust temperatures are generally slightly higher than the observed kinetic temperatures., The dust temperatures are generally slightly higher than the observed kinetic temperatures.1161 The ratio of dust temperature to ranges from 0.9 to [.6 with a mean of 1.2. this slightly higher dust temperature may be attributed to the fact that submillimetre emission 1s associated with a wide range of densities. covering the star-forming core itself as well as the warm envelope surrounding ye core Cand the interface between the two).," The ratio of dust temperature to ranges from 0.9 to 1.6 with a mean of 1.2, this slightly higher dust temperature may be attributed to the fact that submillimetre emission is associated with a wide range of densities, covering the star-forming core itself as well as the warm envelope surrounding the core (and the interface between the two)."1162 As ammonia emission requires a critical density of*.. it is likely to trace the inner. more dense regions of the protostellar core.," As ammonia emission requires a critical density of, it is likely to trace the inner, more dense regions of the protostellar core."1163 It should be noted yat the dust temperatures were derived using fluxes from the IRAS with a significantly larger beam than the present observations., It should be noted that the dust temperatures were derived using fluxes from the IRAS with a significantly larger beam than the present observations.1164 These observations are therefore likely to incorporate more of the yotter dust at the edges of the BRCs., These observations are therefore likely to incorporate more of the hotter dust at the edges of the BRCs.1165 We therefore conclude that the Wo tracers are probing material at similar temperatures (difference between median averages is «3 K). though the submillimetre observations may incorporate some additional material associated with the warm protostellar envelopes and cloud rims.," We therefore conclude that the two tracers are probing material at similar temperatures (difference between median averages is $<$ 3 K), though the submillimetre observations may incorporate some additional material associated with the warm protostellar envelopes and cloud rims."1166 Although there is some correlation seen in the comparison jxot of the H» and NH; column densities the scatter is significant., Although there is some correlation seen in the comparison plot of the $_2$ and $_3$ column densities the scatter is significant.1167 The fractional abundance of mmay be found through simple comparison of the derived H and ccolumn densities?., The fractional abundance of may be found through simple comparison of the derived $_2$ and column .1168". Looking at individual sources we find the Tactional abundances range from a few times "" to a few times 5.", Looking at individual sources we find the fractional abundances range from a few times $^{-9}$ to a few times $^{-8}$.1169 The mean fractional abundance of to Hs is 2.6 x 7. this is the value used in Fig.," The mean fractional abundance of to $_2$ is 2.6 $\times$ $^{-8}$, this is the value used in Fig."1170 3. to illustrate a line of constant fractional abundance., \ref{fig:Temp_Graph} to illustrate a line of constant fractional abundance.1171 The scatter in the plot of vs. H» column density reflects the variation of fractional abundance from source to source., The scatter in the plot of vs. $_2$ column density reflects the variation of fractional abundance from source to source.1172 Overall. the determined values of fractional abundance are typical across a wide range of protostellar environments. from low-mass. starless cores (2? and low to intermediate mass dense cores (??).. to complex. PDR-associated regions (2). and high-mass star forming regions (2?," Overall, the determined values of fractional abundance are typical across a wide range of protostellar environments, from low-mass starless cores \citep{Tafalla2006,Crapsi2007} and low to intermediate mass dense cores \citep{Hotzel2001,Friesen2009}, to complex, PDR-associated regions \citep{Larsson2003} and high-mass star forming regions \citep{Kuiper1995,Pillai2006}."1173 The fractional abundances found here reflect a more general trend in the properties of ammonia in star forming regions., The fractional abundances found here reflect a more general trend in the properties of ammonia in star forming regions.1174 The physical properties of our sources. as determined from our ammonia observations. are typical in most star forming environments. with only very hot cores showing any significant variation. in. column density or temperature (c.f. 229).," The physical properties of our sources, as determined from our ammonia observations, are typical in most star forming environments, with only very hot cores showing any significant variation in column density or temperature (c.f. \citealt{Longmore2007,Pillai2007}) )."1175 The implication of our analysis is that ammonia.once excited beyond its critical threshold. is insensitive to environmental circumstances.i.e. resistant to depletion in cold. dense cores and likely shielded from photoionisation in high-radiation environments.," The implication of our analysis is that ammonia,once excited beyond its critical threshold, is insensitive to environmental circumstances,i.e. resistant to depletion in cold, dense cores and likely shielded from photoionisation in high-radiation environments."1176Our target5 selection sampled a diverse range.5 of stellar parameters. such as evolution. surface chemistry. metallicity and luminosity.,"Our target selection sampled a diverse range of stellar parameters, such as evolution, surface chemistry, metallicity and luminosity."1177 Phough our sample is bv no means unbiased (see below). we obtain a much more representative sample of a globular clusters dust. production than previous studies. Lebzelteretal.(2006).," Though our sample is by no means unbiased (see below), we obtain a much more representative sample of a globular cluster's dust production than previous studies. \citet{LPH+06},"1178.. the closest similar study. focussed on the higher-metallicity Γον 0.7) cluster 47 Tuc and observed. stars. chosen for their luminosity ancl pulsation niodes. resulting in their more homogeneous sample.," the closest similar study, focussed on the higher-metallicity $\sim$ –0.7) cluster 47 Tuc and observed stars chosen for their luminosity and pulsation modes, resulting in their more homogeneous sample."1179 Prom our diverse sample. we arrive at some significant conclusions: (1) Dust. production in the cluster is limited. to a small number of highlv-evolved. objects.," From our diverse sample, we arrive at some significant conclusions: (1) Dust production in the cluster is limited to a small number of highly-evolved objects."1180 Several of our 14 targets have no dust emission. corroborating our recent finding that dust production first. occurs. in. stars. above 1000 L. and becomes ubiquitous at ~2000 L. (MyVLD: Joverοἱal.2009:: McDonaldctal. 201Ib:: MeDonaldetal. 2011a)).," Several of our 14 targets have no dust emission, corroborating our recent finding that dust production first occurs in stars above 1000 $_\odot$ and becomes ubiquitous at $\sim$ 2000 $_\odot$ (MvLD; \citealt{BMvL+09}; \citealt{MBvL+11}; \citealt{MBvLZ11}) )."1181 Stellar temperature would appear to be the main [actor influencing whether dust is produced or not: with the exception of the post-AGB star VI. dust-producing stars all have temperatures of Ix. while dustless stars are all 23950 Ix. However. an <3950intentional selection bias was introduced. to favour cooler targets that may. have been recdelened by dust. (," Stellar temperature would appear to be the main factor influencing whether dust is produced or not: with the exception of the post-AGB star V1, dust-producing stars all have temperatures of $\lesssim$ 3950 K, while dustless stars are all $\gtrsim$ 3950 K. However, an intentional selection bias was introduced to favour cooler targets that may have been reddened by dust. ("11822) Despite being lew in number. the metal-rich population appears to produce most of the dust.,"2) Despite being few in number, the metal-rich population appears to produce most of the dust."1183 Assuming V42 is metal-rich. the post-AGB star VI (LIELD 32029) is the only dust-producing star with a metallicity below Fe/LI] = 145. whereas only of cluster stars have Fe/L] > 1.45 (Johnson&Pilachowski2010).," Assuming V42 is metal-rich, the post-AGB star V1 (LEID 32029) is the only dust-producing star with a metallicity below [Fe/H] = –1.45, whereas only of cluster stars have [Fe/H] $>$ –1.45 \citep{JP10}."1184. It may be that the metal-poor population possesses a sulliciently high gas-to-dust ratio that dust is not important in their winds., It may be that the metal-poor population possesses a sufficiently high gas-to-dust ratio that dust is not important in their winds.1185 We note that the aforementioned temperature selection bias also juases us towards metal-rich stars. which are cooler at a eiven Luminosity. (," We note that the aforementioned temperature selection bias also biases us towards metal-rich stars, which are cooler at a given luminosity. ("11863) The dominant form of dust produced in the cluster is ikely to be metallic iron. followed by silicates.,"3) The dominant form of dust produced in the cluster is likely to be metallic iron, followed by silicates."1187 Only the two most metal-rich stars have visible silicate emission features. compared to five other (still comparatively metal-rich) stars hat produce solely metallic iron.," Only the two most metal-rich stars have visible silicate emission features, compared to five other (still comparatively metal-rich) stars that produce solely metallic iron."1188 The availability of iron to »oduce such opacity is discussed in Section 4.5.., The availability of iron to produce such opacity is discussed in Section \ref{ImplySect}.1189 As we will discuss in the next section. the inaccuracies in determining mass-loss rates with absolute accuracy means hat we can neither determine the true composition of the dust. produced: within the cluster. nor the clusters. dust-»oduction rate.," As we will discuss in the next section, the inaccuracies in determining mass-loss rates with absolute accuracy means that we can neither determine the true composition of the dust produced within the cluster, nor the cluster's dust-production rate."1190 We note. however. that the mass-Ioss rates or individual stars in Table 3.λ have increased by a factor of 7-6 from those listed in MvLD.," We note, however, that the mass-loss rates for individual stars in Table \ref{DustyTable} have increased by a factor of $\sim$ 6 from those listed in MvLD."1191 Ehe summed dust production rate of these stars is approximately that listed in MyvLD. winciplv due to the determination of V42 as metal-rich.," The summed dust production rate of these stars is approximately $\times$ that listed in MvLD, principly due to the determination of V42 as metal-rich."1192 We remind the reader that we have not necessarily observed. all he clusters clusty stars in this work., We remind the reader that we have not necessarily observed all the cluster's dusty stars in this work.1193 refAlBolkcliPie shows w Cen’s stars in context with other globular cluster giants., \\ref{MBolFeHFig} shows $\omega$ Cen's stars in context with other globular cluster giants.1194 Metal-poor. 1.2) stars appear to only produce iron dust. with silicates becoming more prevalent with increasing metallicity.," Metal-poor $\lesssim$ –1.2) stars appear to only produce iron dust, with silicates becoming more prevalent with increasing metallicity."1195 Crystalline silicates appear confined to stars with lower luminosities and there is a lack of luminous metal-poor stars., Crystalline silicates appear confined to stars with lower luminosities and there is a lack of luminous metal-poor stars.1196 The low terminal velocities implied by our mocelling are typically lower than the thermal speed. of small molecules and the turbulent velocity in the wind. and much. lower than the pulsation amplitude and. escape velocity of the stars Clable 3)).," The low terminal velocities implied by our modelling are typically lower than the thermal speed of small molecules and the turbulent velocity in the wind, and much lower than the pulsation amplitude and escape velocity of the stars (Table \ref{DustyTable}) )."1197 This problem has been well-noted in other elobular clusters (MeDonaldetal.2009:DoverοἱAMeDonaldetal.2010. 2011a).," This problem has been well-noted in other globular clusters \citep{MvLD+09,BMvL+09,MSZ+10,MBvLZ11}."1198. As gravity is not Cully modelled inDUSTY. it is not clear whether such outllows can be sustained.," As gravity is not fully modelled in, it is not clear whether such outflows can be sustained."1199 This implies that raciation pressure on dust is probably not the dominant method of accelerating dust from the star. therefore the wind. velocity (and. by implication. the mass-loss rate) may be higher than we model.," This implies that radiation pressure on dust is probably not the dominant method of accelerating dust from the star, therefore the wind velocity (and by implication, the mass-loss rate) may be higher than we model."1200 Despite this. observations of low-metallicity stars (Marshall2004) have so far followed the same velocityluminositymetallicity relation we use here (eq. (3)):," Despite this, observations of low-metallicity stars \citep{MvLM+04} have so far followed the same velocity--luminosity--metallicity relation we use here (Eq. \ref{VEqun}) );"

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