ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 Phe stars are impeded rom virialising due to the changing potential. and the gas accretion.," The stars are impeded from virialising due to the changing potential, and the gas accretion."3 Therefore the gas and stellar velocities are locally correlated such that the relative gas velocity is small., Therefore the gas and stellar velocities are locally correlated such that the relative gas velocity is small.4 This results in a large Roy such that Roy2μμ and therefore the smaller {ζω is the appropriate accretion radius.," This results in a large $\Rbh$ such that $\Rbh > 5\Rroche$ and therefore the smaller $\Rroche$ is the appropriate accretion radius."6 1n contrast. once the stars dominate the gravitational potential. which occurs first in the core of the cluster due to the higher accretion rates there and the sinking of the more massive stars. the stars virialise ancl their velocities relative to the gas become large.," In contrast, once the stars dominate the gravitational potential, which occurs first in the core of the cluster due to the higher accretion rates there and the sinking of the more massive stars, the stars virialise and their velocities relative to the gas become large."7 When this occurs the Bondi Lovie radius becomes much smaller due to the large gas velocities such that Rey< hip., When this occurs the Bondi Hoyle radius becomes much smaller due to the large gas velocities such that $ \Rbh < \Rroche$ .8 Atthis point. the Dondi- radius is a better description of the accretion radius (Bonnell 2000).," Atthis point, the Bondi-Hoyle radius is a better description of the accretion radius (Bonnell 2000)."9P- DP.|yl?sign(p}) ,P - P_c ).1013) Mean field theories normally give a=0.3 =1/2.5 =1. and 6=3. as we shall see.," Mean field theories normally give $\alpha = 0$ , $\beta = 1/2$, $\gamma = 1$, and $\delta = 3$, as we shall see."11 Typical fIuids are measured to havea «1. ο.]1/3. 1.2&5«1.3. and 4«9<5.," Typical fluids are measured to have $\alpha \ll 1$, $\beta \approx 1/3$, $1.2 < \gamma < 1.3$, and $4 < \delta < 5$."12 For experimental measurements and results see [21] and references therein., For experimental measurements and results see \cite{fluidexpts} and references therein.13 The 3D Ising model has a=Q.11. 9=0.325. 5=1.24. and 9=4.815.," The 3D Ising model has $\alpha = 0.11$, $\beta = 0.325$, $\gamma = 1.24$, and $\delta = 4.815$."14 A good general reference is |[22].., A good general reference is \cite{Zinnbook}.15 We will now proceed to parameterize the equation of state near the chiral critical point of QCD at increasing levels of sophistication., We will now proceed to parameterize the equation of state near the chiral critical point of QCD at increasing levels of sophistication.16 As mentioned earlier. (here are certain properties near a critical point that are identical for all theories within (he same universality class.," As mentioned earlier, there are certain properties near a critical point that are identical for all theories within the same universality class."17 Away [rom the critical point the equation of state depends on Che details of the degrees of Ireedom and the interactions among them., Away from the critical point the equation of state depends on the details of the degrees of freedom and the interactions among them.18 To proceed we will first briefly review eeneric descriptions that arise Irom most if not all mean fields theories., To proceed we will first briefly review generic descriptions that arise from most if not all mean fields theories.19 The results will be used to motivate a more sophisticated parameterization relevant for QCD., The results will be used to motivate a more sophisticated parameterization relevant for QCD.20 Dv mean field theories it is meant that although interactions are included. correlations among the particles are not.," By mean field theories it is meant that although interactions are included, correlations among the particles are not."21 This usually results in thermodynamic variables scaling as rational powers of η and /., This usually results in thermodynamic variables scaling as rational powers of $\eta$ and $t$ .22 This can be represented by expanding f in a Taxvlor series im a about 1—0., This can be represented by expanding $f$ in a Taylor series in $\eta$ about $\eta = 0$.23" : — [ion"" QU The 2coefficient fanctions (0) themselves may be expanded in a Tavlor series about /=0 and (μονall have energy. dimension 4.", f = f_k(t) ^k The coefficient functions $f_k(t)$ themselves may be expanded in a Taylor series about $t=0$ and theyall have energy dimension 4.24 The resulting pressure is , The resulting pressure is P = P_k(t) ^k P_k = (t) + (k-1)f_k(t) .25EPIC cameras: PN. MOSI. and MOS2.,"EPIC cameras: PN, MOS1, and MOS2."26 These fits were carried out over the 2.510keV baud exchiding the Felka reeion (b7.5 keV)., These fits were carried out over the $2.5-10\kev$ band excluding the $\alpha$ region $5-7.5\kev$ ).27 All the fits resulted in acceptable 47: however. the best-fit values of equivalent hivdrogeu column (Ny) were mel higher (Ny~1.7107cm7 for the PN data of December 2001) than the Calactic coli of δις10?9cin2. (Elvis.Wilkes.&Lockinan1989).," All the fits resulted in acceptable $\chi^2$; however, the best-fit values of equivalent hydrogen column $\nh$ ) were much higher $\nh \sim 1.7\times10^{22}{\rm~cm^{-2}}$ for the PN data of December 2001) than the Galactic column of $8.82\times10^{20}{\rm~cm^{-2}}$ \citep{EWL89}."28 Setting the Nyy parameter to the Calactic value resulted in unacceptable fits for all the data sets thus implying reavy obscuration.," Setting the $\nh$ parameter to the Galactic value resulted in unacceptable fits for all the data sets, thus implying heavy obscuration."29 The excess absorption column was hen determined by introducing au additional absorption component at the source redshift aud by refitting the vower-law model to individual data sets., The excess absorption column was then determined by introducing an additional absorption component at the source redshift and by refitting the power-law model to individual data sets.30" Table 1 lists he best-fit parameters: excessNg. the photon index Ex. and the fit-statistic \2,,,."," Table \ref{tab1} lists the best-fit parameters: excess, the photon index $\Gamma_X$, and the fit-statistic $\chi^2_{min}$."31 All the errors quoted. lere aud low. are at the 90% confidence level.," All the errors quoted, here and below, are at the $90\%$ confidence level."32 Also listed iu Table 1 are the observed dux in the ιοLOkeV. baud and the absorption corrected (1ntriusic) flux in the same wand., Also listed in Table \ref{tab1} are the observed flux in the $2.5-10\kev$ band and the absorption corrected (intrinsic) flux in the same band.33 As can be secu in Table L.. the best-fit pariuneters Nyand Py. derived from the data obtained simultancously with different iustruuieuts. are consistent within the errors.," As can be seen in Table \ref{tab1}, the best-fit parameters and $\Gamma_X$, derived from the data obtained simultaneously with different instruments, are consistent within the errors."34 However. the observed flux is {ος to differ by ~20% between EPIC PN aud MOS cameras.," However, the observed flux is found to differ by $\sim 20\%$ between EPIC PN and MOS cameras."35 This discrepancy is not unusual for X-ray instruments in their carly phase of calibration., This discrepancy is not unusual for X-ray instruments in their early phase of calibration.36 Iu order to further constrain the spectral shape. the absorbed power-kuv model was fitted to the PN and MOS spectra jointly.," In order to further constrain the spectral shape, the absorbed power-law model was fitted to the PN and MOS spectra jointly."37 The relative uormalizatious for the different iustrunients were kept free allowing for the sunall difference in the calibrated absolute flux. aud any differences in the fraction of encircled counts contained mn he PN aud MOS extraction cells.," The relative normalizations for the different instruments were kept free allowing for the small difference in the calibrated absolute flux, and any differences in the fraction of encircled counts contained in the PN and MOS extraction cells."38 The results of these fits are alsolisted in Table 1.., The results of these fits are alsolisted in Table \ref{tab1}.39 There are small variations in the vest-fit spectral paraiueters between the two observations: ANy=επιΕ2.7)«1022αν7: ATy=0.130.06: Afing=τν1Perescn7., There are small variations in the best-fit spectral parameters between the two observations: $\Delta\nh = (4.4\pm2.7)\times10^{21}{\rm~cm^{-2}}$; $\Delta\Gamma_X=0.13\pm0.06$; $\Delta f_{int}=7\times10^{-12}\funit$.40 The source became jurder and faimter in Dec. 2001., The source became harder and fainter in Dec. 2001.41 To deteriuue the average contimmiun shape. we fitted he absorbed and red-shifted power-law model to the time averaged PN data obtained by combining the two PN data sets frou the two observations.," To determine the average continuum shape, we fitted the absorbed and red-shifted power-law model to the time averaged PN data obtained by combining the two PN data sets from the two observations."42 The time averaged plioton index is Dy=1.6940.03 aud the observed fiux in the 2510keV baud is 7«10“erestem7., The time averaged photon index is $\Gamma_X = 1.69\pm0.03$ and the observed flux in the $2.5-10\kev$ band is $7\times10^{-11}\funit$.43 Fiewre 2 shows the ratio of the PN spectrum extracted frou the December 2001 observation to the best-fit power law derived bvusing the data iu the 2.5—5keV aud 7.5—10keV. bands as describediu the preceding section (see Table 133., Figure \ref{f2} shows the ratio of the PN spectrum extracted from the December 2001 observation to the best-fit power law derived by using the data in the $2.5-5\kev$ and $7.5-10\kev$ bands as described in the preceding section (see Table \ref{tab1}) ).44 This plot clearly reveals a broad eiissiou feature in the 57keV baud and peaking at ~6.1keV., This plot clearly reveals a broad emission feature in the $5-7\kev$ band and peaking at $\sim6.4\kev$.45 This feature is conuuon among Sevfert galaxies aud is attributed to the fiuorescence cussion from the ion Ix- shellαν(c.g.Nandraetal.1997).," This feature is common among Seyfert galaxies and is attributed to the fluorescence emission from the iron K-shell \citep[e.g.,][]{Nandraetal97}."46. The Εονα emission of AIC»2:-16x appears to be nearly svuuuetric in its red andl blue wings and ds clearly different in shape from the red-shifted aud. asviunietrie Felva profiles generally observed from Sevtert 1 salaxies., The $\alpha$ emission of MCG-5-23-16 appears to be nearly symmetric in its red and blue wings and is clearly different in shape from the red-shifted and asymmetric $\alpha$ profiles generally observed from Seyfert 1 galaxies.47 Fig., Fig.48 2 also suggests the likely preseuce of au mon I-edee at ~7.1keV., 2 also suggests the likely presence of an iron K-edge at $\sim7.1\kev$.49 To measure the streneth aud shape of the Fel&o. emission. we paralcterize the observed profile im teris of simple Gaussian models.," To measure the strength and shape of the $\alpha$ emission, we parameterize the observed profile in terms of simple Gaussian models."50 For this analysis. the co-added PN data were used. as the PN has the largest effective area alone he three EPIC cameras.," For this analysis, the co-added PN data were used, as the PN has the largest effective area among the three EPIC cameras."51 Heuce the derived parameters characterize the time averaged Εονα profile., Hence the derived parameters characterize the time averaged $\alpha$ profile.52 Initially. a uurow unresolved Caussian (6=(0.01keV) was used or the Felxa cussion aud the absorbed and red-shifted vower-law model was used for the continu as described in section 23.1. (Table 1).," Initially, a narrow unresolved Gaussian $\sigma=0.01\kev$ ) was used for the $\alpha$ emission and the absorbed and red-shifted power-law model was used for the continuum as described in section \ref{continuum} (Table \ref{tab1}) )."53" This model resulted iu a poor fit with 42,, of 262 for 235 dof.", This model resulted in a poor fit with $\chi^2_{min}$ of 262 for 235 dof.54 The ratio of the data to he best-fit narrow Caussian model is plotted in Figure (second. panel from the top) which shows a dip at ~G.|keV. and excess counts on the red and blue sides of he dip., The ratio of the data to the best-fit narrow Gaussian model is plotted in Figure \ref{f3} (second panel from the top) which shows a dip at $\sim6.4\kev$ and excess counts on the red and blue sides of the dip.55 This suggests a stroug core at 6.1keV and xoad wings ou both sides of the core., This suggests a strong core at $\sim6.4\kev$ and broad wings on both sides of the core.56 Varving the width of the Gaussian improved the fit significantly (A47=19 or l additional parameter)., Varying the width of the Gaussian improved the fit significantly $\Delta \chi^2 = 49$ for 1 additional parameter).57 This sugeests that the line nav be broad., This suggests that the line may be broad.58 Addition of a narrow Caussiuu component (o=0.01keV) at ~6.1keV improves the fit significantly (A?=26.3 for two additional parameters)., Addition of a narrow Gaussian component $\sigma=0.01\kev$ ) at $\sim6.4\kev$ improves the fit significantly $\Delta \chi^2 = 26.3$ for two additional parameters).59 The best-fit parameters describing the observed Fel&a profile are isted in Table 2.., The best-fit parameters describing the observed $\alpha$ profile are listed in Table \ref{tab2}.60 The peak cuereies of both the narrow and broad components are consistent with neutral iron., The peak energies of both the narrow and broad components are consistent with neutral iron.61 The full width at half masini (EWIIMD of the broad conrponeut is —12000kms, The full width at half maximum (FWHM) of the broad component is $\sim 42000\kms$.62" Addition of an absorption edee at 7.1keV results in mareinal inproveimoeut inthe fit (NA?=2,7 for one additional parameter) at a significance level of ~93% based on an F-test (Bevineton1969).", Addition of an absorption edge at $7.1\kev$ results in marginal improvement inthe fit $\Delta \chi^2 = 2.7$ for one additional parameter) at a significance level of $\sim 93\%$ based on an F-test \citep{Bevington69}.63. The an of the broad ion Ίνα line observed frou AICC-5-23-16à is too large to be |in regions other than the accretion disk aroundcheckedpreme supermassive black hole (SMBII)., The width of the broad iron $\alpha$ line observed from MCG-5-23-16 is too large to be produced in regions other than the accretion disk around a super-massive black hole (SMBH).64 Therefore we whether the observed profile is consistent with a relativistic disk-lue model (Fabianctal.1989)., Therefore we checked whether the observed profile is consistent with a relativistic disk-line model \citep{Fabianetal89}.65. This model assunies a Sclawarzsclild econmetrv and the disk enuissivitv is a power-law function of disk radius r ie. Xr., This model assumes a Schwarzschild geometry and the disk emissivity is a power-law function of disk radius r i.e. $\propto r^{q}$.66" We fixed the iuner disk radius at Gr, aud the outer disk radius at 5007. where =GALe"," We fixed the inner disk radius at $6r_g$ and the outer disk radius at $500r_g$, where $r_g = GM/c^2$."67 First we fitted the disk-liue model withoutry a narrow Gaussian component., First we fitted the disk-line model without a narrow Gaussian component.68 The coutiuuuu was the absorbed power-law model as before., The continuum was the absorbed power-law model as before.69 The free paramecters were the disk inclination angle (7) between our line of sight aud the disk normal. the disk cuussivity q. aud the normalization of the disk line.," The free parameters were the disk inclination angle $i$ ) between our line of sight and the disk normal, the disk emissivity $q$, and the normalization of the disk line."70" This fit resulted in au acceptable fit statistic (AA,=229.8 for 236 dof).", This fit resulted in an acceptable fit statistic $\chi^2_{min} = 229.8$ for 236 dof).71 The ratio of the data and the best-fit model is plotted im Figure (top panel)., The ratio of the data and the best-fit model is plotted in Figure (top panel).72 The dip seen at 6.IkeV is due to the characteristic shape of the line profile from a face-on disk — muncly a strong core and a red wing., The dip seen at $\sim6.4\kev$ is due to the characteristic shape of the line profile from a face-on disk – namely a strong core and a red wing.73 The disk inchnation angle was found to be in the range 07l., The disk inclination angle was found to be in the range $0^\circ-11^\circ$.74 This is physically Incousistent with a Sevfert 1.9 ealaxy according to the 199:y.andard unification scheme of Sevfert galaxies (Autonucci ., This is physically inconsistent with a Seyfert 1.9 galaxy according to the standard unification scheme of Seyfert galaxies \citep{Antonucci93}.75 Iu view of the fact that the observed Εονα profile can be described by a combination of narrow ancl broma Gaussian aud narrow component is expected due to reflection from acold matter away from the disk. we addec a narrow Caussian component to our cdisk-line model.," In view of the fact that the observed $\alpha$ profile can be described by a combination of narrow and broad Gaussian and a narrow component is expected due to reflection from cold matter away from the disk, we added a narrow Gaussian component to our disk-line model."76 The chorey of the narrow componcut was fixed at 6.1 keV., The energy of the narrow component was fixed at $6.4\kev$ .77 This fit resulted in significant iniprovenient over that witlou a narrow conpoueut (A47=32.1 for oue additiona paralcter)., This fit resulted in significant improvement over that without a narrow component $\Delta\chi^2 = 32.4$ for one additional parameter).78 This is an nuprovenient at a siguificauce leve of > 99.994., This is an improvement at a significance level of $>99.99\%$ .79 The ratio of the data to the best-fit model is shown in Figure P (secoud paucl from the top)., The ratio of the data to the best-fit model is shown in Figure \ref{f4} (second panel from the top).80 The best- inclination angle now is /=16.313 audM , The best-fit inclination angle now is $i=46.3_{-3.8}^{+3.4}$ .81The equivalent width of the disk-line is 12054eV the liue euergv, The equivalent width of the disk-line is $129_{-23}^{+31}\ev$ and the line energy82and the pressure. instead. both continue to increase and they reach their maximum well later.,"and the pressure, instead, both continue to increase and they reach their maximum well later."83 We note that the shorter the heat pulse. the longer ts the delay between the beginning of the temperature decay and the density maximum.," We note that the shorter the heat pulse, the longer is the delay between the beginning of the temperature decay and the density maximum."84 For the longest-lasting heat pulse. the density and pressure values are very close to the asymptotic equilibrium values. estimated from loop scaling laws (Rosner et al.," For the longest-lasting heat pulse, the density and pressure values are very close to the asymptotic equilibrium values, estimated from loop scaling laws (Rosner et al."85 1978)., 1978).86 We have checked that the evolution is self-similar for a longer loop L=1010 em at the same temperature. with the evolutiontimes scaling as το," We have checked that the evolution is self-similar for a longer loop $L87= 10^{10}$ cm at the same temperature, with the evolutiontimes scaling as $\tau_s$."88 In the density-temperature diagram (Fig. 4)).," In the density-temperature diagram (Fig. \ref{fig:mod_nt}) ),"89 the flare evolution for the different heat pulse durations is well in agreement with that sketched in Fig. 2.., the flare evolution for the different heat pulse durations is well in agreement with that sketched in Fig. \ref{fig:nt_diag_eq}.90 For short-lasting pulses. phase IV starts as soon as the path crosses the QSS curve.," For short-lasting pulses, phase IV starts as soon as the path crosses the QSS curve."91" For fie,=3r, phase II ends and the decay (phase IV) starts both very close to the QSS curve. while phase III is practically absent (Jakimiec et al."," For $t_{heat}92\approx 3 \tau_s$, phase II ends and the decay (phase IV) starts both very close to the QSS curve, while phase III is practically absent (Jakimiec et al."93 1992)., 1992).94 We now derive simple diagnostic tools for the analysis of the rise and decay phase of a flare. taking advantage of detailed numerical modeling.," We now derive simple diagnostic tools for the analysis of the rise and decay phase of a flare, taking advantage of detailed numerical modeling."95 We first observe that the maximum possible duration of the rise phase ts the time taken by the loop to reach equilibrium conditions under the action of a constant (flare) heating., We first observe that the maximum possible duration of the rise phase is the time taken by the loop to reach equilibrium conditions under the action of a constant (flare) heating.96 The simulation results in Fig., The simulation results in Fig.97 3. show that the time taken by the plasma to reach equilibrium conditions is much longer than the sound crossing time (Eq.[2]]. which rules the very initial plasma evaporation.," \ref{fig:mod_evol} show that the time taken by the plasma to reach equilibrium conditions is much longer than the sound crossing time \ref{eq:tsound}] ]), which rules the very initial plasma evaporation."98 This is also clear in Fig. 5..," This is also clear in Fig. \ref{fig:mod_lin},"99 which shows the evolution of the pressure at the loop apex in a linear scale: after ¢=50 s. the rate of pressure enhancement becomes more gentle.," which shows the evolution of the pressure at the loop apex in a linear scale: after $t = 50$ s, the rate of pressure enhancement becomes more gentle."100 As mentioned in Sec. 2.1..," As mentioned in Sec. \ref{sec:fl_ev}, ,"101 in this phase the dynamics become much less important and, in this phase the dynamics become much less important and102and somewhat less significant for OBS2 (3.5 0).,and somewhat less significant for OBS2 (3.5 $\sigma$ ).103 In both cases. the derived cutoff energy turned out to be much lower (~4 keV. see Table 2)) than that measured previously when the source was In outburst (—13 keV).," In both cases, the derived cutoff energy turned out to be much lower $\sim$ 4 keV, see Table \ref{tab:xtefit}) ) than that measured previously when the source was in outburst $\sim$ 13 keV)."104 Such a low value for the cutoff energy might not be unlikely for an X-ray pulsar (see Sect. 5))., Such a low value for the cutoff energy might not be unlikely for an X-ray pulsar (see Sect. \ref{sec:discussion}) ).105 In the ease of OBSI. when an additional spectral component to that of the CUTOFFPL appears to be clearly significant. we also tried to investigate the applicability of other spectral models.," In the case of OBS1, when an additional spectral component to that of the CUTOFFPL appears to be clearly significant, we also tried to investigate the applicability of other spectral models."106 We again fixed the cutoff energy of the CUTOFFPL component at 13 keV and tried first a phenomenological model including an additional black-body component (BB) at lower energies (<2 keV)., We again fixed the cutoff energy of the CUTOFFPL component at 13 keV and tried first a phenomenological model including an additional black-body component (BB) at lower energies $<$ 2 keV).107 We found that both a BB with kT~I- keV and a small emitting area (few hundreds m?) and a much colder (KT-—0.1-0.3 keV) BB with an emitting radius of ~100 km could reproduce the spectrum reasonably well., We found that both a BB with $\sim$ 1-2 keV and a small emitting area (few hundreds $^2$ ) and a much colder $\sim$ 0.1-0.3 keV) BB with an emitting radius of $\sim$ 100 km could reproduce the spectrum reasonably well.108 The interpretation of both of these models for the soft X-ray excess faces difficulties: à BB emitting area of about one hurdred km radius would be much larger than the NS. while a small emitting spot on the star surface might also be unlikely 1n the case of a low-Iuminosity wind-accretilο NS (see Sect. 5)).," The interpretation of both of these models for the soft X-ray excess faces difficulties: a BB emitting area of about one hundred km radius would be much larger than the NS, while a small emitting spot on the star surface might also be unlikely in the case of a low-luminosity wind-accreting NS (see Sect. \ref{sec:discussion}) )."109 We therefore tried to fit the spectrum of OBSI using models that provide to alternative physical interpretations., We therefore tried to fit the spectrum of OBS1 using models that provide to alternative physical interpretations.110 We adopted first a model comprising a CUTOFFPL and à MKL component. and then tried à second model in which we included the effect of partial covering in XSPEC) on the CUTOFFPL component.," We adopted first a model comprising a CUTOFFPL and a MKL component, and then tried a second model in which we included the effect of partial covering in ) on the CUTOFFPL component."111 We note that these two models were suggested to fit the quiescent sspectra of the SFXTs JJ1845-0433 (Zurita-Heras&Wal-ter.2009) and (Tomsicketal..2009)., We note that these two models were suggested to fit the quiescent spectra of the SFXTs J1845-0433 \citep{zurita09b} and \citep{tomsick09}.112. In these cases. the authors suggested that the MKL component might represent the contribution due to the shocks in the stellar wind around the NS. whereas the partial covering may be caused by the obscuration of the NS by clumps in this wind.," In these cases, the authors suggested that the MKL component might represent the contribution due to the shocks in the stellar wind around the NS, whereas the partial covering may be caused by the obscuration of the NS by clumps in this wind."113 Finally. we also attempted to fit the spectrum of OBSI by using the COMPTT and the BMC models. as suggested by Sidolietal.(2009) and Sidolietal.(2009b).," Finally, we also attempted to fit the spectrum of OBS1 by using the COMPTT and the BMC models, as suggested by \citet{sidoli09} and \citet{sidoli09b}."114. These two models provided à good fit to the data. but in the case of the BMC we found that most of the model parameters were only poorly determined in the fit. and thus we do not discuss this model further in the case of The results of the fits obtained with all the other models discussed in this section are reported in Table 2..," These two models provided a good fit to the data, but in the case of the BMC we found that most of the model parameters were only poorly determined in the fit, and thus we do not discuss this model further in the case of The results of the fits obtained with all the other models discussed in this section are reported in Table \ref{tab:xtefit}."115 We checked that a fit to the spectrum of OBS? with all these models would give results comparable to those obtained for OBS1., We checked that a fit to the spectrum of OBS2 with all these models would give results comparable to those obtained for OBS1.116" All the spectral models reported in Table 2. provided reasonable values of the fit parameters and very similar X2,,; (note that all the models have the same number of free parameters).", All the spectral models reported in Table \ref{tab:xtefit} provided reasonable values of the fit parameters and very similar $\chi^2_{red}$ (note that all the models have the same number of free parameters).117" In the best case. we obtained 7, /d.o.f.20.98/173. and thus the significance of the improvement of these fits. with respect to that obtained with a simple absorbed CUTOFFPL model and the energy cutoff fixed at 13 keV. was of 5.6 c."," In the best case, we obtained $\chi^2_{red}$ /d.o.f.=0.98/173, and thus the significance of the improvement of these fits, with respect to that obtained with a simple absorbed CUTOFFPL model and the energy cutoff fixed at 13 keV, was of 5.6 $\sigma$."118 As an example. we show in Fig.," As an example, we show in Fig."119 9 the unfolded spectrum of OBSI obtained by using à MKL component to fit the low-energy excess., \ref{fig:xtesp1unfolded} the unfolded spectrum of OBS1 obtained by using a MKL component to fit the low-energy excess.120 The interpretation of these results is discussed in Sect. 5.., The interpretation of these results is discussed in Sect. \ref{sec:discussion}.121 We also performed a Fourier analysis of the lightcurves of OBSI and OBS2. in search of coherent pulsations. by using the method deseribed in Israel&Stella(1996).," We also performed a Fourier analysis of the lightcurves of OBS1 and OBS2, in search of coherent pulsations, by using the method described in \citet{israel96}."122. No significant (above 35 level) signal was detected in either observation., No significant (above $\sigma$ level) signal was detected in either observation.123 The corresponding 3o c.l., The corresponding $\sigma$ c.l.124 upper limits to the pulsed fraction (defined as the semi-amplitude of the sinusoid divided by the, upper limits to the pulsed fraction (defined as the semi-amplitude of the sinusoid divided by the125The size of the dusty structure detected by MIDI by the baseline closer to the equatorial plane 1: Table 1)) is approximately 33 mas (Fig. 5)).,The size of the dusty structure detected by MIDI by the baseline closer to the equatorial plane 1; Table \ref{table-log}) ) is approximately 33 mas (Fig. \ref{fig:gauss}) ).126 Extrapolating to a projected baseline at (equatorial plane) we would expect a minimum size of 41 mas., Extrapolating to a projected baseline at (equatorial plane) we would expect a minimum size of 41 mas.127 From that we presume that the central cavity must be smaller than this size., From that we presume that the central cavity must be smaller than this size.128 Our modelling has showed that a diameter of approximately 3042 AU (or ~25 mas) fits the inner portion of the disk (Table 3))., Our modelling has showed that a diameter of approximately $\pm$ 2 AU (or $\sim$ 25 mas) fits the inner portion of the disk (Table \ref{tab:param}) ).129 We did not find a better fit to the MIDI data than the one presented here by increasing the disk’s inner rim., We did not find a better fit to the MIDI data than the one presented here by increasing the disk's inner rim.130" We have used a relation for dust sublimation radius (Ru, in AU) by ?:: where L is the stellar luminosity and Των is the dust sublimation temperature.", We have used a relation for dust sublimation radius $R_{\rm sub}$ in AU) by \citet{2001Natur.409.1012T}: : where $L$ is the stellar luminosity and $T_{\rm sub}$ is the dust sublimation temperature.131 For a star of 2500 Lc (Table 5)) it is suggested that the inner rim of the disk must reside at a distance larger thar 4 AU but within the limits defined by the MIDI observations., For a star of 2500 $_{\sun}$ (Table \ref{tab:sublim}) ) it is suggested that the inner rim of the disk must reside at a distance larger than 4 AU but within the limits defined by the MIDI observations.132 An 100 Li heating source. such as the accretion disk in the case of M2-9. does not fit the observational data: neither did the 553 Le suggested by ?..," An 100 $_{\sun}$ heating source, such as the accretion disk in the case of M2-9, does not fit the observational data; neither did the 553 $_{\sun}$ suggested by \citet{1997A&A...319..267S}."133 We estimated orbital periods for the binary by using the observations of 18 years from ?.., We estimated orbital periods for the binary by using the observations of 18 years from \citet{2000AJ....119.1339D}.134 From those. it can be seen that the lighthouse beam covered less than of the perimeter of the lobes within that time scale.," From those, it can be seen that the lighthouse beam covered less than of the perimeter of the lobes within that time scale."135 We found that the period ranges from 90 to 120 years., We found that the period ranges from 90 to 120 years.136 A binary system should reside within the structure detected by MIDI., A binary system should reside within the structure detected by MIDI.137 By applying simple Keplerian physics (assuming circular orbits). we have used several mass for the binary components to estimate the corresponding orbital diameters. for periods of 90 and 120 years. in physical units and converted them to angular sizes for a distance of 1.25 kpe (Table 6)).," By applying simple Keplerian physics (assuming circular orbits), we have used several mass for the binary components to estimate the corresponding orbital diameters, for periods of 90 and 120 years, in physical units and converted them to angular sizes for a distance of 1.25 kpc (Table \ref{tab:binsep}) )."138 As seen in Table 6 orbital diameters that fit within the extrapolated angular size of41 mas range from 42-52 AU., As seen in Table \ref{tab:binsep} orbital diameters that fit within the extrapolated angular size of 41 mas range from 42–52 AU.139 This is larger than our best fit model. where the size of the disk’s inner cavity is 30 AU.," This is larger than our best fit model, where the size of the disk's inner cavity is 30 AU."140 We should draw attention though to the fact that the disks inner rim is centered at the heating source. which in turn ts not positioned on the binary's centre-of-mass.," We should draw attention though to the fact that the disk's inner rim is centered at the heating source, which in turn is not positioned on the binary's centre-of-mass."141 The model in use cannot reproduce a partially illuminated disk or a disk with an off-centre illuminating source., The model in use cannot reproduce a partially illuminated disk or a disk with an off-centre illuminating source.142 Thus. we believe that the compantor is truncating the disk. since its heating capabilities are minimal.," Thus, we believe that the companion is truncating the disk, since its heating capabilities are minimal."143 We can only surmise that high-angular resolution radio observations could establish the astrometric position of the companion (WD/accretion disk)., We can only surmise that high-angular resolution radio observations could establish the astrometric position of the companion (WD/accretion disk).144 The obtained NACO images are fully dominated by the central source and lack dynamical range in its close vicinity (Fig. 1))., The obtained NACO images are fully dominated by the central source and lack dynamical range in its close vicinity (Fig. \ref{fig:hst-naco}) ).145" At ~3” from the core ? found that the CO emission is coming from a large ring. whose center seemed offset by 0.50.3"". from the compact radio source («0.1andunre-solvedat1.3em. ?).."," At $\sim$ from the core \citet{1997A&A...324..624Z} found that the CO emission is coming from a large ring, whose center seemed offset by $\pm$ from the compact radio source \citep[$<0.1$\arcsec~and unresolved at 1.3~cm,][]{1983IAUS..103...69B}."146 More recent Plateau de Bure data (Castro- et al..," More recent Plateau de Bure data (Castro-Carrizo et al.,"147 in preparation) with angular resolution confirm the presence of an offset. and detect additional CO emission coming from regions at a distance of «1. from the center.," in preparation) with angular resolution confirm the presence of an offset, and detect additional CO emission coming from regions at a distance of $\sim$ from the center."148" Molecular hydrogen spectroscopy has vielded two different velocity components at distances x0.5"" latitudinally from the central illuminating source: 10.9kms! (blue-shifted) and 1237kms! (red-shifted)."," Molecular hydrogen spectroscopy has yielded two different velocity components at distances $\lesssim$ latitudinally from the central illuminating source: $\rm km\,s^{-1}$ (blue-shifted) and $\rm km\,s^{-1}$ (red-shifted)."149 This points to a Hs» disk-like structure (?).., This points to a $_{2}$ disk-like structure \citep{2005AJ....130..853S}.150 Spiral structures (as expected in a symbiotic type system) can be formed by binary interactions during the ejection of the primary's CO envelope (?).. yet this is not clear at this point for the case of M2-9.," Spiral structures (as expected in a symbiotic type system) can be formed by binary interactions during the ejection of the primary's CO envelope \citep{2008ApJ...675L.101E}, yet this is not clear at this point for the case of M2-9."151 If there are spirals. they are seen at a high inclination (pole-on).," If there are spirals, they are seen at a high inclination (pole-on)."152 Our source is edge-on., Our source is edge-on.153 The differential phases of the disk detected by VLTI are small. lying within a range of +10°.. 1e. well below some strong signature from dusty rings reported in the literature (22)..," The differential phases of the disk detected by VLTI are small, lying within a range of $\pm$, i.e. well below some strong signature from dusty rings reported in the literature \citep{2007A&A...474L..45D, 2008A&A...490..173O}."154 These two bipolar nebulae are spectroscopic twins and both exhibit complex gaseous shell structures., These two bipolar nebulae are spectroscopic twins and both exhibit complex gaseous shell structures.155 Both are extended at similar sizes., Both are extended at similar sizes.156 Their main parts. including the lobes. are and at length and ~15” at width. for M2-9 and Mz3 respectively.," Their main parts, including the lobes, are and at length and $\sim$ at width, for M2-9 and Mz3 respectively."157 The ansae of M2-9 are apart. while the farther regions of Mz3 are at about130”.," The ansae of M2-9 are apart, while the farther regions of Mz3 are at about."158 Distances to both objects are not well determined and the estimates given stand forthe best fits to the observational data: M2-9 at I.2kpe. Mz3 at I.4kpc.," Distances to both objects are not well determined and the estimates given stand forthe best fits to the observational data: M2-9 at 1.2kpc, Mz3 at 1.4kpc."159 Indirect evidence for binarity in the case of M2-9 are the lighthouse knots in the nebula and, Indirect evidence for binarity in the case of M2-9 are the lighthouse knots in the nebula and160configuration observation: where iis the integration time scale.,configuration observation: where $\tau$ is the integration time scale.161" For 7visibility (or image) subtraction, the peak flux lost from time smearing is similar to the flux residual in the differenced data given by Equation 2.."," For visibility (or image) subtraction, the peak flux lost from time smearing is similar to the flux residual in the differenced data given by Equation \ref{bgerr}."162 This error will contribute to the mean bispectrum in proportion to the fraction of all triples that contain the long baseline., This error will contribute to the mean bispectrum in proportion to the fraction of all triples that contain the long baseline.163" A single antenna is part of (ng—1)(n,2)/2 ttriples, so errors for a long baseline are suppressed by the fraction of triples with that baseline, or a factor of 3/n,."," A single antenna is part of $(n_a-1) \, (n_a-2)/2$ triples, so errors for a long baseline are suppressed by the fraction of triples with that baseline, or a factor of $3/n_a$."164 Table 1 gives the longest time scale for which the bispectrum technique can be used on several radio interferometers., Table \ref{sub} gives the longest time scale for which the bispectrum technique can be used on several radio interferometers.165 The time scale shows when the systematic errors introduced by background subtraction biases the mean bispectrum more than its thermal noise (1e)., The time scale shows when the systematic errors introduced by background subtraction biases the mean bispectrum more than its thermal noise $\sigma$ ).166 This shows that most interferometers are suitable for using the bispectrum technique to search for transients as long as 1 second., This shows that most interferometers are suitable for using the bispectrum technique to search for transients as long as 1 second.167 The VLBA is so extended that the fringe rate can only be subtracted on millisecond timescales?., The VLBA is so extended that the fringe rate can only be subtracted on millisecond time.168. The bispectrum also contains information about the spatial distribution of emission., The bispectrum also contains information about the spatial distribution of emission.169" For a point source with large s, the standard deviation of complex bispectra is op=V3s?Q?, where Q iis the noise per baseline (Kulkarni1989).."," For a point source with large $s$, the standard deviation of complex bispectra is $\sigma_B=\sqrt{3} \, s^2 \, Q^3$, where $Q$ is the noise per baseline \citep{1989AJ.....98.1112K}."170" Note that the standard deviation of bispectra subject to correlated noise, as opposed to the standard deviation of the mean bispectrum in time."," Note that the standard deviation of bispectra subject to correlated noise, as opposed to the standard deviation of the mean bispectrum in time."171" In contrast with a celestial source, interference is often in the near-field or subject to multipath propagation, which produces a random triple phase and a larger variance between bispectra."," In contrast with a celestial source, interference is often in the near-field or subject to multipath propagation, which produces a random triple phase and a larger variance between bispectra."172 Another way to think about this is that terrestrial interference can look like a spatially-extended transient., Another way to think about this is that terrestrial interference can look like a spatially-extended transient.173" The variance between bispectra provides a simple way to quantify whether a transient is point-like, as expected."," The variance between bispectra provides a simple way to quantify whether a transient is point-like, as expected."174" To use the bispectrum for transient detection, we assume that the real part of the mean of all bispectra is related to the brightness of a single source in the field of view."," To use the bispectrum for transient detection, we assume that the real part of the mean of all bispectra is related to the brightness of a single source in the field of view."175" To use the bispectrum to detect and localize pulses, we propose the following algorithm: Figure ὃ shows how the bispectrum and coherent beamforming techniques detect pulses in PoCo data toward B0329+54."," To use the bispectrum to detect and localize pulses, we propose the following algorithm: Figure \ref{snr} shows how the bispectrum and coherent beamforming techniques detect pulses in PoCo data toward B0329+54."176" For both techniques, the plot shows the apparent pulse SNR when the pulsar is at the phase center, away from the phase center, and at the phase center but uncalibrated."," For both techniques, the plot shows the apparent pulse SNR when the pulsar is at the phase center, away from the phase center, and at the phase center but uncalibrated."177 The beamforming technique only detects the pulse when it is at the phase center and data are calibrated., The beamforming technique only detects the pulse when it is at the phase center and data are calibrated.178 The bispectrum detects the pulse regardless of its location or the phase calibration., The bispectrum detects the pulse regardless of its location or the phase calibration.179 The apparent SNR of the bispectrum and coherent beamforming techniques for data including several pulses are shown in Figure 4.., The apparent SNR of the bispectrum and coherent beamforming techniques for data including several pulses are shown in Figure \ref{snrobs}.180 The top panel in Figure 4 shows that the PoCo pulse SNR distribution measured with beamforming and the bispectrum follow the relation of Rogersetal.(1995) well., The top panel in Figure \ref{snrobs} shows that the PoCo pulse SNR distribution measured with beamforming and the bispectrum follow the relation of \citet{1995AJ....109.1391R} well.181" Since there are only nine baselines and five triples in this analysis, the pulses shown here have relatively high s."," Since there are only nine baselines and five triples in this analysis, the pulses shown here have relatively high $s$."182" The brightest pulse in this data has s~3, corresponding to a brightness of about 50 Jy."," The brightest pulse in this data has $s\sim3$, corresponding to a brightness of about 50 Jy."183 A similar search with a larger array would have a much slower rise in SNRpisp rrelative to SNR., A similar search with a larger array would have a much slower rise in $\rm{SNR}_{bisp}$ relative to $\rm{SNR}_{bfc}$.184 Figure 5 shows how the bispectrum can distinguish between a celestial point transient and terrestrial interference., Figure \ref{rfi} shows how the bispectrum can distinguish between a celestial point transient and terrestrial interference.185 The top panel shows a typical dynamic spectrum for a VLA observation of the Crab pulsar with 12 millisecond integrations., The top panel shows a typical dynamic spectrum for a VLA observation of the Crab pulsar with 12 millisecond integrations.186" As is well known from single-dish observing, interference is bright enough to be detected even after dedispersion."," As is well known from single-dish observing, interference is bright enough to be detected even after dedispersion."187 The bottom panel, The bottom panel188the recent version of the stellar spectral synthesis program MOOCG (Sneden 1973).,the recent version of the stellar spectral synthesis program MOOG (Sneden 1973).189 As inputs. we used the NextGen model atmospheres (Ilauschildt et 11999) and the CO linelist of Goorvilch (1994).," As inputs, we used the NextGen model atmospheres (Hauschildt et 1999) and the CO linelist of Goorvitch (1994)."190 The ability to fit the CO spectrum in this wavelength region was verified on a spectrum of the IN5 dwarf Gl Cve A. which was obtained with the same instrumental setup as the spectrum of V836 Tan.," The ability to fit the CO spectrum in this wavelength region was verified on a spectrum of the K5 dwarf 61 Cyg A, which was obtained with the same instrumental setup as the spectrum of V836 Tau."191 For our adopted stellar parameters for 61 Cve A (T=4400 Ix. logg= 4.5) ancl near-solar metallicities. we obtain an excellent fit to the spectrum.," For our adopted stellar parameters for 61 Cyg A $T=4400$ K, $\log g = 4.5$ ) and near-solar metallicities, we obtain an excellent fit to the spectrum."192 In contrast. with the atmospheric models of INurucz (1993). it is not possible to match the relative strengths of the weak and strong CO lines.," In contrast, with the atmospheric models of Kurucz (1993), it is not possible to match the relative strengths of the weak and strong CO lines."193 We selected an atmosphere model (hat is appropriate for the stellar photospheric temperature (Teg=4000 KIN) and gravity (logy= 4.0) (hat are implied by the stellar effective temperature and Iuminositv of V336 Tau measured by White Hillenbrand (2004)., We selected an atmosphere model that is appropriate for the stellar photospheric temperature $T_{\rm eff}= 4000$ K) and gravity $\log g = 4.0$ ) that are implied by the stellar effective temperature and luminosity of V836 Tau measured by White Hillenbrand (2004).194 We adopted a solar metalliityv. as appropriate for (he Taurus star forming region (Padgett 1996: Santos et 220083).," We adopted a solar metallicity, as appropriate for the Taurus star forming region (Padgett 1996; Santos et 2008)."195 A comparison of the svnthetie stellar spectrum and the observed spectrum of V836 Tau shows that much of the structure in the continuum is due to absorption features in (he stellar photosphere Ll aud 2. top panels).," A comparison of the synthetic stellar spectrum and the observed spectrum of V836 Tau shows that much of the structure in the continuum is due to absorption features in the stellar photosphere 1 and 2, top panels)."196 Stellar photospheric features are expected to be detectable in high signal-to-noise spectra given (he weak near-infrared excess of V836 Tau., Stellar photospheric features are expected to be detectable in high signal-to-noise spectra given the weak near-infrared excess of V836 Tau.197 The heliocentric radial velocity of 13.5kms.|! (which corresponds to a topocentrie velocity of vy.=35.5kms !) and the stellar rotational velocity of esinc12.1kms| measured by White Lillenbrane (2004) are in agreement with (he stellar photospheric leatures identified in (he observed spectrum., The heliocentric radial velocity of $18.5 \kms$ (which corresponds to a topocentric velocity of $v_{\rm obs}=35.5 \kms$ ) and the stellar rotational velocity of $v\sin i \simeq 12.1 \kms$ measured by White Hillenbrand (2004) are in agreement with the stellar photospheric features identified in the observed spectrum.198 These parameters. combined with a continuum veiling of riz3 (where rps is the ratio of the excess flux to the stellar photospheric [τις at 4.7jmi). provides a reasonably good fit to the observed spectrum.," These parameters, combined with a continuum veiling of $r_{4.7}=2$ (where $r_{4.7}$ is the ratio of the excess flux to the stellar photospheric flux at $4.7\micron$ ), provides a reasonably good fit to the observed spectrum."199 The depth of the CO absorption in the veiled stellar photospheric spectrum shows that some of the central absorption in the observed CO enission profile arises fom CO absorption in tlie stellar photosphere., The depth of the CO absorption in the veiled stellar photospheric spectrum shows that some of the central absorption in the observed CO emission profile arises from CO absorption in the stellar photosphere.200 The measured veiling has (wo sources of uncertaintv., The measured veiling has two sources of uncertainty.201 The low signal-to-noise of the spectrumintroduces uncertainty in the location of the continuum. contributing an unucertaintiv of 40.3 to the veiling measurement.," The low signal-to-noise of the spectrum introduces uncertainty in the location of the continuum, contributing an uncertainty of $\pm 0.3$ to the veiling measurement."202 The uncertainty in the stellar effective temperature zx200IXIX) and logy (20.3) o£ V836 Tau (see 82.3) contributes an additional uncertainty of -0.16 to the veiling., The uncertainty in the stellar effective temperature $\pm 200$ K) and $\log g$ $\pm 0.3$ ) of V836 Tau (see 3.3) contributes an additional uncertainty of $\pm 0.16$ to the veiling.203 Figure 3 shows the dereddened SED of V836 Tan., Figure 3 shows the dereddened SED of V836 Tau.204 We constructed the SED from the UDVRI photometry of Kenvon Hartmann (1995). 11ο. 111ν thixes from 2MASS. and theSpilzer IRAC and. MIPS photometry reported by Padgett et ((2006).," We constructed the SED from the $UBVRI$ photometry of Kenyon Hartmann (1995), the $JHK$ fluxes from 2MASS, and the IRAC and MIPS photometry reported by Padgett et (2006)."205 The fluxes were dereddened: using the reddening law of Mathis (1990) assuming sl).=1.1 as in Furlan et ((2006)., The fluxes were dereddened using the reddening law of Mathis (1990) assuming $A_V=1.1$ as in Furlan et (2006).206 A Basel stellar atmosphere v2.2 (corrected: Lejeune 2002) with Toy=4060 ΝΑ and logg=4.0 provides a good fit to the dereddened optical colors of the star., A Basel stellar atmosphere v2.2 (corrected; Lejeune 2002) with $T_{\rm eff} = 4060$ K and $\log g = 4.0$ provides a good fit to the dereddened optical colors of the star.207 The stellar, The stellar208Newton Telescope (ENT) on 1998 November 12 and 13.,Newton Telescope (INT) on 1998 November 12 and 13.209 The camera consists of a mosaic of four x [kk Loral CCD detectors. providing a pixel projection of 0.33 aud covering au effective area of 1012 arciuuin? in cach exposure.," The camera consists of a mosaic of four $\times$ k Loral CCD detectors, providing a pixel projection of 0.33 and covering an effective area of 1012 $^2$ in each exposure."210 We observed four differeut fields with tiny overlapping between onus polutiugs. coveriug a total area of 1.12 deg?.," We observed four different fields with tiny overlapping between neighboring pointings, covering a total area of 1.12 $^2$."211ucight The ceutral coordinates of these poiutiugs are indicated i Table 1, The central coordinates of these pointings are indicated in Table \ref{tab1}.212 A representation of the sivey can be seen in Figure 1.., A representation of the survey can be seen in Figure \ref{fig1}.213 We performed three individual exposures of ss in cach poiutiug. resulting in a total exposure time of 1 hour iu cach field aud filter.," We performed three individual exposures of s in each pointing, resulting in a total exposure time of 1 hour in each field and filter."214 Raw funes were reduced within the environment. using the package.," Raw frames were reduced within the environment, using the package."215 huages were bias subtracted. trimuned aud flat-field corrected.," Images were bias subtracted, trimmed and flat-field corrected."216" We suitably conibined our own lone exposure scientific images to obtain ΠατΠοια»,", We suitably combined our own long exposure scientific images to obtain flat-fields.217 These flat images. usually called superflats. are very useful for correcting fineiue patterus uot present in sky or dome flats.," These flat images, usually called superflats, are very useful for correcting fringing patterns not present in sky or dome flats."218 The photometric analysis was performed using routines withinDAOPHOT. which include the selection of (extendedobjects with stella: PSF using the task photeineobjects were mostly avoided) aud aperture aud PSE try.," The photometric analysis was performed using routines within, which include the selection of objects with stellar PSF using the task (extended objects were mostly avoided) and aperture and PSF photometry."219 The average secing ou both nights varied from 1.0 to 1.2 arcsec., The average seeing on both nights varied from 1.0 to 1.2 arcsec.220 Nights were not photometric aud instruuenutal maenitudes were ransformed iuto the real magnitudes iu the Cousins { system using observations of common stars obtained with he same instruucutation on a photometric night ou 2003 January 8., Nights were not photometric and instrumental magnitudes were transformed into the real magnitudes in the Cousins $I$ system using observations of common stars obtained with the same instrumentation on a photometric night on 2003 January 8.221 This night was calibrated using photometric standard stars from Landolt (Laudolt1992).. observed hroughout the night aud in cach of the four detectors.," This night was calibrated using photometric standard stars from Landolt \citep{landolt92}, observed throughout the night and in each of the four detectors."222 We found a difference in the zero points of the detectors. and hence. we calibrated cach of them iucdependecutly.," We found a difference in the zero points of the detectors, and hence, we calibrated each of them independently."223" Basically. the detector 1 (the one iu the ceuter) has systematically a zero point ~ linmae füuter. while he rest of them are simular within πας,"," Basically, the detector 4 (the one in the center) has systematically a zero point $\sim$ mag fainter, while the rest of them are similar within mag."224 The calibration of these data in BAIZO was done assumiug hat the sensitivity of all the detectors were similar and lis explains why the Z-baud photometivy of some of the objects preseuted hereis different from that preseuted iu DNIZO and ZapateroOsorioetal.(2000)., The calibration of these data in BMZO was done assuming that the sensitivity of all the detectors were similar and this explains why the $I$ -band photometry of some of the objects presented here is different from that presented in BMZO and \cite{osorio00}.225. Tustrmmcutal uaenitudes of Z filter were pseudo-transtormed iuto apparent magnitudes asstuine that the distribution of he uuuber of stars per iuterval of magnitude J/—Z is similar that of the Pleiades cluster (ZapateroOso-rioetal.1999) aud has a mnaxiauuni around 7/—Z~ l1nunuag.," Instrumental magnitudes of $Z$ filter were pseudo-transformed into apparent magnitudes assuming that the distribution of the number of stars per interval of magnitude $I-Z$ is similar to that of the Pleiades cluster \citep{osorio99b} and has a maximum around $I-Z226\sim$ mag."227 The absolute calibration of this filter is not strictly necessarv for the selection of our caudidates. since this task is carried out in relative terms: for a given I-band maeuitude. candidates must have £ Z colors redder than field sources aud overlap aud extrapolate he expected plotometric sequence of the cluster defines ' kuowu members.," The absolute calibration of this filter is not strictly necessary for the selection of our candidates, since this task is carried out in relative terms: for a given $I$ -band magnitude, candidates must have $I-Z$ colors redder than field sources and overlap and extrapolate the expected photometric sequence of the cluster defined by known members."228 We always refer to the calibratec I baud toestimate masses for our objects., We always refer to the calibrated $I$ band toestimate masses for our objects.229" The survey completeness magnitudes are f=22.0. Z=21.5 πας) iux he limiting maenitudes are J=23.8. Z-22.0 πας,"," The survey completeness magnitudes are $I$ =22.0, $Z$ mag and the limiting magnitudes are $I$ =23.8, $Z$ mag."230 We adopted as the completeness magnitude the value at which the histogram of detections as a function of uaenitude reaches a maxi (~ 10-6 detection). ac as liiting magnitude the value at which histogram are detected (~ 3-0 detection limit).," We adopted as the completeness magnitude the value at which the histogram of detections as a function of magnitude reaches a maximum $\sim$ $\sigma$ detection), and as limiting magnitude the value at which histogram are detected $\sim$ $\sigma$ detection limit)."231 Table 2 contains the optical photometry and coordinates of selected.both. objects (sec section ??))., Table \ref{tab2} contains the optical photometry and coordinates of selected objects (see section \ref{sec3}) ).232 The error bars account for the instrmucutal magnitude errors and the wncertaintics in the photometric calibrations. which απο typically Linmae.," The error bars account for both the instrumental magnitude errors and the uncertainties in the photometric calibrations, which are typically mag."233 Astrometry was derived from the UKIDSS Calactic Cluster. Survey (GSC) catalogue for those objects prescut in the Data Release 6 (a correlation radius of 5 arcsec were used to cross-latch the list of targets)., Astrometry was derived from the UKIDSS Galactic Cluster Survey (GSC) catalogue for those objects present in the Data Release 6 (a correlation radius of 5 arcsec were used to cross-match the list of targets).234 The astrometry of fainter candidates not detected iu URKIDSS was obtained frou the plate solution of cach detector derived using the UIKIDSS astrometry of bright objects i common and the routine., The astrometry of fainter candidates not detected in UKIDSS was obtained from the plate solution of each detector derived using the UKIDSS astrometry of bright objects in common and the routine.235 Typical root-meau-square of 0.1 arcsec were found in the astrometric solution for differcut detectors., Typical root-mean-square of 0.1–0.4 arcsec were found in the astrometric solution for different detectors.236 We obtained /-hand photometry with the CAIN infrared camera ou the Telescopio Carlos Sanchez (TCS) at Observatorio del Teide. ou 1998 15. 1999 January 23. 21. February 21. AugustSeptember ned22. 23. 21. Novoeiber 26. 27. December 28. 29. aud 2000 27. and February 11. 12. and with the MAGIC οσὲ mounted on the 2.2 im telescope at the Calar Alto Observatory on 1998 December SO," We obtained $J$ -band photometry with the CAIN infrared camera on the Telescopio Carlos Sánnchez (TCS) at Observatorio del Teide, on 1998 September 18, 1999 January 23, 24, February 24, August 22, 23, 24, November 26, 27, December 28, 29, and 2000 January 27, and February 11, 12, and with the MAGIC instrument mounted on the 2.2 m telescope at the Calar Alto Observatory on 1998 December 6."237S The CAIN camera consists of a 2564256 pixel NIC infrared array. providing a pixel projection of 1.00 arcsec and covering a total area of L3 arcmin? iu cach exposure.," The CAIN camera consists of a $\times$ 256 pixel NICMOS3 infrared array, providing a pixel projection of 1.00 arcsec and covering a total area of $\times$ 4.3 $^2$ in each exposure."238 The MACIC instrmucut has also a «256 pixel NICAIOS3 infrared array. providing a pixel projection of 0.6 Larescc and covering au area of 42.7 arcinin?.," The MAGIC instrument has also a $\times$ 256 pixel NICMOS3 infrared array, providing a pixel projection of 0.64 arcsec and covering an area of $\times$ 2.7 $^2$."239 Exposure times ranged from 60 to 1000ss (CAIN) and from 105 to 900S5 (ATACIC)., Exposure times ranged from 60 to s (CAIN) and from 405 to s (MAGIC).240 Average sccing varied frou 1.5 to LO arcsec during the TCS observations aud from 1.0 to 2.0 aresec during theCalw Alto run., Average seeing varied from 1.5 to 4.0 arcsec during the TCS observations and from 1.0 to 2.0 arcsec during the Calar Alto run.241 We also obtained -7-baud photometry for the complete areca of the BZOR survey on the 3.5 1m Cala Alto telescope iu 1998 October. using the Oueea-Prime instrmucut. which was cross-imatched with our optical photometry.," We also obtained $J$ -band photometry for the complete area of the BZOR survey on the 3.5 m Calar Alto telescope in 1998 October, using the Omega-Prime instrument, which was cross-matched with our optical photometry."242 See ZapateroOsorioctal.(2000). and DMZO for more details about these J-baud data., See \cite{osorio00} and BMZO for more details about these $J$ -band data.243 The raw CAIN and MAGIC data were processed within the IRAF cuviromment. iucludiug sky subtraction and flat field correction.," The raw CAIN and MAGIC data were processed within the IRAF environment, including sky subtraction and flat field correction."244 Final individual images were properly aligued aud combined., Final individual images were properly aligned and combined.245 Aperture photometry was performed using routines., Aperture photometry was performed using routines.246 LIustrunueutal magnitudes were transformed into apparent magnitudes in the UKIRT. system using several photometric feld standards obtained for cach might (intetal.1998)., Instrumental magnitudes were transformed into apparent magnitudes in the UKIRT system using several photometric field standards obtained for each night \citep{hunt98}.247. For some of our objects observed. in non-photomoetric condidtious. the CAIN photometry was calibrated using the 2MASS photometry ofobjects iu common iu the same field of view.," For some of our objects observed in non-photometric condidtions, the CAIN photometry was calibrated using the 2MASS photometry of objects in common in the same field of view."248" For a few iniiobjects for which the CAIN photometry has large wacers (0.2 numae) or there are no available data. we have adopted the photometry frou, UKIDSS (described below)."," For a few objects for which the CAIN photometry has large uncertainties $>$ mag) or there are no available data, we have adopted the photometry from UKIDSS (described below)."249 All the available -/- data for our candidates are provided in Table 2.., All the available $J$ -band data for our candidates are provided in Table \ref{tab2}. .250 Error bars account for the instrmucutal maeuitude errors and the uncertainties in the photometric calibrations. which are typically 121nag for the CAIN and MACIC data and uunae for Omeega-Prime.," Error bars account for the instrumental magnitude errors and the uncertainties in the photometric calibrations, which are typically mag for the CAIN and MAGIC data and mag for Omega-Prime."251simulations.,simulations.252 Under these conditions. with high S/N. this region could also be used in the modelling.," Under these conditions, with high S/N, this region could also be used in the modelling."253 For our spectrum. due to the low S/N. we consider only the simple (optimistic) case that the ionised region is completely transparent. tgp«I.," For our spectrum, due to the low S/N, we consider only the simple (optimistic) case that the ionised region is completely transparent, $\tau_{GP}\ll 1$."254 We assume a uniform prior on each parameter except for the column density., We assume a uniform prior on each parameter except for the column density.255 Since GRBs are most likely to occur in regions with significant neutral hydrogen. we apply a prior which scales linearly with column density.," Since GRBs are most likely to occur in regions with significant neutral hydrogen, we apply a prior which scales linearly with column density."256 We find best-fit parameters of log(Nyj/cm7)= 19.60. Nap=0.06. cightu=6.733.," We find best-fit parameters of $\log{(\nhi/\mathrm{cm^{-2}})}=19.60$ , $\xhi=0.06$, $z_{\mathrm{IGM, u}}=6.733$."257 To determine the uncertainties in each of these parameters we use a Markov Chain Monte Carlo (MCMC) algorithm and sample the posterior probability distribution., To determine the uncertainties in each of these parameters we use a Markov Chain Monte Carlo (MCMC) algorithm and sample the posterior probability distribution.258 The result is presented in Fig. 3.," The result is presented in Fig. $\ref{F:grb080913_xhi_prob}$,"259 which shows the posterior probability distribution of the [GM neutral fraction having marginalised over all other parameters., which shows the posterior probability distribution of the IGM neutral fraction having marginalised over all other parameters.260 We find vy)<0.73 with a probability of 90%., We find $\xhi<0.73$ with a probability of $90\%$.261 Our analysis also. provides constraints on the size of the ionised region around the GRB host., Our analysis also provides constraints on the size of the ionised region around the GRB host.262 In Fig., In Fig.263" 4. we plot the marginalized posterior probability contours 1n vy -"" space produced from our fits."," $\ref{F:grb080913_contour_r_xhi}$ , we plot the marginalized posterior probability contours in $\xhi$ $r$ space produced from our fits."264 Here we see that an iontsed region which has a size smaller than ~2 proper Mpe is favoured.," Here we see that an ionised region which has a size smaller than $\sim2\,$ proper Mpc is favoured."265 The regions in parameter space where r is negative correspond to situations where the DLA material is accelerated towards us due to either the GRB event or its progenitor., The regions in parameter space where r is negative correspond to situations where the DLA material is accelerated towards us due to either the GRB event or its progenitor.266 If we ignore these regions. we find that r<1.3 proper Mpe with a probability of 90%. which suggests that a large tontsed region Is not present around the host galaxy.," If we ignore these regions, we find that $r<1.3$ proper Mpc with a probability of $90\%$, which suggests that a large ionised region is not present around the host galaxy."267 This value ts. however. still consistent with external sources of tonising flux being present.," This value is, however, still consistent with external sources of ionising flux being present."268 For comparison ? found that the ionised regions around LAEs have a typical size of 0.8 proper Mpe.," For comparison \cite{Haiman:2002} found that the ionised regions around LAEs have a typical size of $0.8\,$ proper Mpc."269 New optical spectroscopic observations of GRB 080913 have been presented and analysed., New optical spectroscopic observations of GRB 080913 have been presented and analysed.270 The detection. of SII+Sill absorption (0.12604m) at 2.9c provides a redshift of the DLA host galaxy of z;=6.733., The detection of SII+SiII absorption $0.1260\mu$ m) at $2.9\sigma$ provides a redshift of the DLA host galaxy of $z=6.733$.271 Employing a joint DLA+IGM model to fit the observed continuum break. we find an upper limit to the neutral fraction of the IGM vy)<0.73 at a probability of 90%.," Employing a joint $+$ IGM model to fit the observed continuum break, we find an upper limit to the neutral fraction of the IGM $\xhi<0.73$ at a probability of $90\%$."272 However this result rests on the assumption that the ronised region surrounding the host galaxy is transparent to Lye., However this result rests on the assumption that the ionised region surrounding the host galaxy is transparent to $\alpha$.273 Any analysis of a GRB spectrum needs to include the radius of the tontsed region as a free parameter. and to consider the question of the neutral fraction withinthis zone.," Any analysis of a GRB spectrum needs to include the radius of the ionised region as a free parameter, and to consider the question of the neutral fraction withinthis zone."274 Furthermore the scatterin measurements of vy] between different sources at similar redshifts 1s predicted to be substantial (??)..," Furthermore the scatterin measurements of $\xhi$ between different sources at similar redshifts is predicted to be substantial \citep{McQuinn_etal:2008,Mesinger_Furlanetto:2008},"275"where agi, is given by Eq. (27)).",where $\alpha_{\mathrm{min}}$ is given by Eq. \ref{eq:theta_min}) ).276 In this section we solve this integral explicitly and provide analytical expressions for Ap(0)., In this section we solve this integral explicitly and provide analytical expressions for $A_D(\theta)$.277" For a source at infinity with 0«o9, itis more convenient to use Eq. 28))"," For a source at infinity with $\theta < \alpha_0$, it is more convenient to use Eq. \ref{eq:Aeff_fin_infty}) )"278 with τα)=1 which can be immediately solved Recalling Eq. (14)), with $r_{\lambda}(\alpha) = 1$ which can be immediately solved Recalling Eq. \ref{eq:Ae_inf_on}) )279" for the on-axis area A..(0), we obtain which is exactly Eq. (1))"," for the on-axis area $A_{\infty}(0)$, we obtain which is exactly Eq. \ref{eq:SC_formula}) )"280" found by Van Speybroeck and Chase (1972)), after approximating zt~3."," found by Van Speybroeck and Chase \cite{VanSpeybroeck}) ), after approximating $\pi \simeq 3$."281" For off-axis angles larger than ao, Eq. (32))"," For off-axis angles larger than $\alpha_0$ , Eq. \ref{eq:Ageom_SC3}) )"282 is no longer valid., is no longer valid.283" An extension of the curve Δω(θ)for 6>αρ can be obtained from Eq. (30)),"," An extension of the curve $A_{\infty}(\theta)$for $\theta > \alpha_0$ can be obtained from Eq. \ref{eq:Ageom_SC1}) ),"284" after setting the integrand to 0 when cos9>αρ/θ, according to Eq. (27))."," after setting the integrand to 0 when $\cos\varphi > \alpha_0/\theta$, according to Eq. \ref{eq:theta_min}) )."285" The result is a non-linear function of the 0/a ratio, which is identicalI to ⊏≜Eq. (32))"," The result is a non-linear function of the $\theta/\alpha_0$ ratio, which is identical to Eq. \ref{eq:Ageom_SC3}) )"286 for 0= ap; this is 2jcorrect because the geometrical vignetting must be a continuous function of 0., for $\theta = \alpha_0$ ; this is correct because the geometrical vignetting must be a continuous function of $\theta$.287" We note that, for sufficiently large 0, Eq. (33))"," We note that, for sufficiently large $\theta$, Eq. \ref{eq:Ageom_SC4}) )"288 can be approximated well by A.o(0)a'o/(x0).," can be approximated well by $A_{\infty}(0)\,\alpha_0/(\pi\theta)$."289 A complete vignetting curve for 6=0 is shown in Fig., A complete vignetting curve for $\delta = 0$ is shown in Fig.290 6 (solid line)., \ref{fig:geom_vignetting} (solid line).291 The predicted deviation from linearity is verified in Sect., The predicted deviation from linearity is verified in Sect.292 5 by means ofan accurate ray-tracing routine., \ref{Comp} by means ofan accurate ray-tracing routine.293" We now consider the variation in the geometric area, for a sourceat a finite distance (6> 0)."," We now consider the variation in the geometric area, for a sourceat a finite distance $\delta >0$ )."294" In this case, the integration dependson whether 6«αρ/2 or not."," In this case, the integration dependson whether $\delta<\alpha_0/2$ or not."295 We consider firstly the case 6« αρ/2., We consider firstly the case $\delta<\alpha_0/2$ .296 We then assume initially 0«6., We then assume initially $\theta < \delta$.297" With these conditions, 0coso<6a— for all o, therefore Eq. (27))"," With these conditions, $\theta\cos\varphi < \delta < \alpha_0-\delta$ for all $\varphi$, therefore Eq. \ref{eq:theta_min}) )"298 becomes Substituting this expression into Eq. (29)), becomes Substituting this expression into Eq. \ref{eq:Ageom_fin_off}) )299" and solving, we derive the area that is, Ap(9)=Ap(0) (see Eq. (17)))."," and solving, we derive the area that is, $A_{D}(\theta)= A_{D}(0)$ (see Eq. \ref{eq:case1}) ))."300" In other words, the mirror geometric area is constant as far as 0«6ao/2."," In other words, the mirror geometric area is constant as far as $\theta<\delta<\alpha_0/2$."301" This is often observed in optics calibrations at on-ground facilities (see, e.g., Gondoin et al. 1998b))."," This is often observed in optics calibrations at on-ground facilities (see, e.g., Gondoin et al. \cite{Gondoin2}) )."302 We now increase 0 beyond 6., We now increase $\theta$ beyond $\delta$.303" Since 6<ag— by hypothesis, we can consider the case 6<0«ay—óao*ó."," Since $\delta < \alpha_0-\delta$ by hypothesis, we can consider the case $\delta <\theta< \alpha_0-\delta < \alpha_0+\delta$."304 We are therefore allowed to write Eq. (29)), We are therefore allowed to write Eq. \ref{eq:Ageom_fin_off}) )305 as where the integrands are always positive., as where the integrands are always positive.306" This yields We note that for ó—0, Eq. (37))"," This yields We note that for $\delta \rightarrow 0$, Eq. \ref{eq:Ageom_D5}) )"307" reduces to Eq. (32)),"," reduces to Eq. \ref{eq:Ageom_SC3}) ),"308" and for 0—6 to Eq. (35)),"," and for $\theta \rightarrow \delta$ to Eq. \ref{eq:Ageom_D3}) ),"309 as expected.,as expected.310 We now suppose ag—6<0«ao+6., We now suppose $\alpha_0-\delta <\theta< \alpha_0+\delta$.311" In this case, the integration returns some more terms This equation, as expected, returns the same result as Eq. (37))"," In this case, the integration returns some more terms This equation, as expected, returns the same result as Eq. \ref{eq:Ageom_D5}) )"312" at 0=a—6, and is valid for off-axis angles in the interval [αρ—ó,oo+6]."," at $\theta=\alpha_0-\delta$, and is valid for off-axis angles in the interval $[\alpha_0-\delta, \alpha_0+\delta]$."313" Therefore, for 6—0 it reduces to Eq. (32))"," Therefore, for $\delta \rightarrow 0$ it reduces to Eq. \ref{eq:Ageom_SC3}) )"314 and (33)) for the single point 0=ao., and \ref{eq:Ageom_SC4}) ) for the single point $\theta = \alpha_0$.315" Now, consider thecase 6>αρ/2, unlike we have hitherto assumed, but still that 6«αρ."," Now, consider thecase $\delta > \alpha_0/2$, unlike we have hitherto assumed, but still that $\delta <\alpha_0$."316" This time αρ—6<6: the condition 0<6 is insufficient for avoiding negative values of Qmin in Eq. (34)),"," This time $\alpha_0-\delta <\delta$: the condition $\theta<\delta$ is insufficient for avoiding negative values of $\alpha_{\mathrm{min}}$ in Eq. \ref{eq:Ageom_D1}) ),"317 therefore Eq. (35)), therefore Eq. \ref{eq:Ageom_D3}) )318 is valid only if 0«a—6., is valid only if $\theta<\alpha_0-\delta$.319" Beyond this limit and up to 0=6, Eq. (37))"," Beyond this limit and up to $\theta = \delta$, Eq. \ref{eq:Ageom_D5}) )"320" should be replaced by which, unexpectedly, isan function| of 0 inthe interval ag—6«0< 6."," should be replaced by which, unexpectedly, isan function of $\theta$ inthe interval $\alpha_0-\delta<\theta<\delta$ ."321" When 6<06+ ag, the geometric area again follows Eq. (38)),"," When $\delta <\theta <\delta+\alpha_0$ , the geometric area again follows Eq. \ref{eq:Ageom_D6}) ),"322 which for 6>αρ/2 exhibits a at such a maximum is not present if 6< ag/2., which for $\delta >\alpha_0/2$ exhibits a at such a maximum is not present if $\delta < \alpha_0/2$ .323" In a similar fashion, one can easily compute the total geometric vignetting for 0>αρ+ 6, evenif the resulting expression would be too long to report here, and it is also"," In a similar fashion, one can easily compute the total geometric vignetting for $\theta>\alpha_0+\delta$ , evenif the resulting expression would be too long to report here, and it is also"324"Xj,.",$\coh{X}{pq}$.325" In the traditional view of radio interferometry. Xj, is a measurement of the coherency function X(u4.v.ww) at point Ipg.VpgWpy GNI X being a 2x complex matrix rather than the traditional scalar complex function)."," In the traditional view of radio interferometry, $\coh{X}{pq}$ is a measurement of the coherency function $\coh{X}{}(u,v,w)$ at point $u_{pq},v_{pq},w_{pq}$ (with $\coh{X}{}$ being a $2\times2$ complex matrix rather than the traditional scalar complex function)."326 For the purposes of these papers. let us adopt an operational definition of as being the visibility that would be measured by a corruption-free interferometer.," For the purposes of these papers, let us adopt an operational definition of as being the visibility that would be measured by a corruption-free interferometer."327 For a point source. the coherency is given by Eq. (11).," For a point source, the coherency is given by Eq. \ref{eq:me-point-source}) )."328" A real-world interferometer will have some “corrupting” effects in the signal path. m addition to the nominal phase delay K,."," A real-world interferometer will have some “corrupting” effects in the signal path, in addition to the nominal phase delay $K_p$."329" Since the latter is scalar and thus commutes with everything. we can move it to the beginning of the Jones chain. and write the total Jones J,, of Eq. (8))"," Since the latter is scalar and thus commutes with everything, we can move it to the beginning of the Jones chain, and write the total Jones $\jones{J}{p}$ of Eq. \ref{eq:me0}) )"330" as where G,, represents all the other (corrupting) effects.", as where $\jones{G}{p}$ represents all the other (corrupting) effects.331 We can then formulate the RIME for a single corrupted point source as: where Xpy 18 the source coherency. as defined above.," We can then formulate the RIME for a single corrupted point source as: where $\coh{X}{pq}$ is the source coherency, as defined above."332 Let us now consider a sky composed of N point sources., Let us now consider a sky composed of $N$ point sources.333" The contributions of each source to the measured visibility matrix V, add up linearly.", The contributions of each source to the measured visibility matrix $\coh{V}{pq}$ add up linearly.334" The signal propagation path is different for each source s and antenna p. but each path can be described by its own Jones matrix J,,,."," The signal propagation path is different for each source $s$ and antenna $p$, but each path can be described by its own Jones matrix $\jones{J}{sp}$."335" Equation (8)) then becomes: Remember that each J,, is a product of a (generally non-commuting) chain. corresponding to the physical order of effects along the signal path: where effects represented by the right side of the chain GJ pi) occur ""at the source"". and effects on the left side of the chain (J ,,...) ""at the antenna""."," Equation \ref{eq:me0}) ) then becomes: Remember that each $\jones{J}{sp}$ is a product of a (generally non-commuting) , corresponding to the physical order of effects along the signal path: where effects represented by the right side of the chain $...\jones{J}{sp1}$ ) occur “at the source”, and effects on the left side of the chain $\jones{J}{spn}...$ ) “at the antenna”."336 Somewhere along the chain is the phase term Λο. but since (being a scalar matrix) it commutes with everything. we are free to move it to any position in the product.," Somewhere along the chain is the phase term $K_{sp}$, but since (being a scalar matrix) it commutes with everything, we are free to move it to any position in the product."337 Some elements in the chain may be the same for all sources., Some elements in the chain may be the same for all sources.338 This tends to be true for effects at the antenna end of the signal path. such as electronic gain.," This tends to be true for effects at the antenna end of the signal path, such as electronic gain."339" Let us then collapse the chain into a product of three Jones matrices: G, is the source-independent ""antenna"" (left) side of the Jones chain. i.e. the product of the terms beginning with Jyyy. up to and not including the leftmost source-dependent term (if the entire chain is source-dependent. G, is simply unity). E, is the source-dependent remainder of the chain. and Ky,is the phase term."," Let us then collapse the chain into a product of three Jones matrices: $\jones{G}{p}$ is the source-independent “antenna” (left) side of the Jones chain, i.e. the product of the terms beginning with $\jones{J}{spn}$, up to and not including the leftmost source-dependent term (if the entire chain is source-dependent, $\jones{G}{p}$ is simply unity), $\jones{E}{sp}$ is the source-dependent remainder of the chain, and $K_{sp}$is the phase term."340 We can then recast Eq. (14)), We can then recast Eq. \ref{eq:me-nps-j}) )341" as follows: Or. using the source coherency of Eq. (11)): G, describes "," as follows: Or, using the source coherency of Eq. \ref{eq:me-point-source}) ):"342"thedirection-independent effects (DIES). or the terms. and Ey, the etfects (DDEs). or the terms."," $\jones{G}{p}$ describes the effects (DIEs), or the terms, and $\jones{E}{sp}$ the effects (DDEs), or the terms."343 In principle. the sum in Eq. (16))," In principle, the sum in Eq. \ref{eq:me-nps-ge}) )"344 should be taken over all sufficiently sources in the sky. but in practice our FoV is limited by the voltage beam pattern of each antenna. or by the horizon. in the case of an all-sky instrument such as the Low Frequency Array (LOFAR).," should be taken over all sufficiently sources in the sky, but in practice our FoV is limited by the voltage beam pattern of each antenna, or by the horizon, in the case of an all-sky instrument such as the Low Frequency Array (LOFAR)."345" In RIME terms. beam gain ts just another Jones term in the chain. ensuring £,,,—0 for sources outside the beam."," In RIME terms, beam gain is just another Jones term in the chain, ensuring $\jones{E}{sp}\to 0$ for sources outside the beam."346 If the observed field has little to none spatially extended emission. this form of the RIME is already powerful enough to allow for calibration of DDEs. as I shall show in Paper IH (?)..," If the observed field has little to none spatially extended emission, this form of the RIME is already powerful enough to allow for calibration of DDEs, as I shall show in Paper III \citep{RRIME3}."347 In the more general case. the sky Is not a sum of discrete sources. but rather a continuous brightness distribution Bio). where c is a (unit) direction vector.," In the more general case, the sky is not a sum of discrete sources, but rather a continuous brightness distribution $\coh{B}{}(\vec\sigma)$, where $\vec\sigma$ is a (unit) direction vector."348" For each antenna p. we then have a Jones term J,(o). describing the signal path for direction σ."," For each antenna $p$, we then have a Jones term $\jones{J}{p}(\vec\sigma)$, describing the signal path for direction $\vec\sigma$."349 To get the total visibility as measured by an interferometer. we must integrate Eq. (8)) ," To get the total visibility as measured by an interferometer, we must integrate Eq. \ref{eq:me0}) )"350over all possible directions. Le. over a unit sphere: This spherical integral is not very tractable. so we perform a sine projection of the sphere onto the plane (/.11) tangential at the field Note that this analysis is fully analogous to that of ?.Sect.3.1.. with only the integrand being somewhat different.,"over all possible directions, i.e. over a unit sphere: This spherical integral is not very tractable, so we perform a sine projection of the sphere onto the plane $(l,m)$ tangential at the field Note that this analysis is fully analogous to that of \citet[Sect.~3.1]{tms}, with only the integrand being somewhat different."351 The integral then becomes: [Tm going to use / and (/.i) interchangeably from now on.," The integral then becomes: I'm going to use $\vec l$ and $(l,m)$ interchangeably from now on."352 By analogy with Eq. (15).," By analogy with Eq. \ref{eq:me-nps-gek}) ),"353" we now decompose J,,(/) into a direction-independent part G. a direction-dependent part £. and the phase term K: Substitutingthis into the integral. and commuting the K terms around. we get This equation is one form of a general full-sky RIME."," we now decompose $\jones{J}{p}(\vec l)$ into a direction-independent part $\jones{G}{}$, a direction-dependent part $\jones{\bar E}{}$, and the phase term $K$: Substitutingthis into the integral, and commuting the $K$ terms around, we get This equation is one form of a general full-sky RIME."354" It is in fact a type of three-dimensional Fourier transform: the term in the exponent. wy),(2— D). is what prevents us from treating it as the much simpler 2D transform."," It is in fact a type of three-dimensional Fourier transform; the term in the exponent, $w_{pq}(n-1)$ , is what prevents us from treating it as the much simpler 2D transform."355" Since wy,=wy— Wy. We can decompose the non-coplanarity term into per-antenna terms W,,=weLeFAVslit D."," Since $w_{pq}=w_p-w_q$ , we can decompose the non-coplanarity term into per-antenna terms $W_p=\frac{1}{\sqrt{n}} \mathrm{e}^{-2\pi i w_p (n-1)}$ ."356 These can, These can357the local LFs. largely due to the fact that the local LFs are calculated for the total galaxy light (ΑΝΕΠΟΣ} rather than the magnitude of the AGN alone.,"the local LFs, largely due to the fact that the local LFs are calculated for the total galaxy light (AGN+host) rather than the magnitude of the AGN alone."358 Nonetheless. many of the AGN candidates detected in our survey may be truly fainter than those of 11B92.," Nonetheless, many of the AGN candidates detected in our survey may be truly fainter than those of HB92."359 Dased on the spectroscopic selection criterion emploved by H1B92. most of our sources would not be detected as AGN (see Section 6) in the IID92 survey.," Based on the spectroscopic selection criterion employed by HB92, most of our sources would not be detected as AGN (see Section 6) in the HB92 survey."360 Therefore. we assume (hat the AGN component in our galaxies do nol comprise as much of the total galaxy. lieht as the I1D92 sources and are likely to be intrinsically fainter.," Therefore, we assume that the AGN component in our galaxies do not comprise as much of the total galaxy light as the HB92 sources and are likely to be intrinsically fainter."361 The UIIOI LF covers the same integrated galaxy magnitude range as IID92 but shows an overall higher clensitv for local Sevferts., The UH01 LF covers the same integrated galaxy magnitude range as HB92 but shows an overall higher density for local Seyferts.362 Ulvestad IIo explain that (his is due to the fact that their LF includes inirinsicallv. fainter sevlert nuclei than does the ILD92 sample., Ulvestad Ho explain that this is due to the fact that their LF includes intrinsically fainter seyfert nuclei than does the HB92 sample.363 For the Sevlert 1 galaxies. Ilo Pene (2001) decompose the nuclei fom the host galaxies in both local samples ancl confirm this assertion. finding a median nuclear magnitude of 5—-14.6 lor UIIOL versus -17.4 for the IIDB92 Sevfert 1 galaxies.," For the Seyfert 1 galaxies, Ho Peng (2001) decompose the nuclei from the host galaxies in both local samples and confirm this assertion, finding a median nuclear magnitude of $_B$ =-14.6 for UH01 versus -17.4 for the HB92 Seyfert 1 galaxies."364 From their study. we also lind that the nuclear magnitudes of the local sevIerts in bot samples can be extremely [unt when compared to the total galaxy. magnitude. in some cases up to 10 magnitudes fainter.," From their study, we also find that the nuclear magnitudes of the local seyferts in both samples can be extremely faint when compared to the total galaxy magnitude, in some cases up to 10 magnitudes fainter."365" ""Therefore. an LF consisting of nuclear magnitudes for local Sevferts would be a much better comparison to our IDF AGN candidates."," Therefore, an LF consisting of nuclear magnitudes for local Seyferts would be a much better comparison to our HDF AGN candidates."366 since (his is not currently. available. an alternative is (o produce the LF of our sources using (he total integrated galaxy magnitude rather (han the nuclear magnitude alone (dashed LF).," Since this is not currently available, an alternative is to produce the LF of our sources using the total integrated galaxy magnitude rather than the nuclear magnitude alone (dashed LF)."367 The integrated galaxy magnitudes for our variable sources cover the same range as the faint end of the local Sevlert LFs but have a number density 10x greater than the local Sevlert density of UIIOL1., The integrated galaxy magnitudes for our variable sources cover the same range as the faint end of the local Seyfert LFs but have a number density $\times$ greater than the local Seyfert density of UH01.368 If the AGN in these two samples cover a similar magnitude range. {his is evidence for a significant increase in number density from z=0 to ~0.7.," If the AGN in these two samples cover a similar magnitude range, this is evidence for a significant increase in number density from z=0 to $\sim$ 0.7."369 The magnitudes for the UIIOI ACN determined in Ilo Peng (2001) for the Sevfert 1 population cover the range -0z Mg> z-22 mag with most lving within -12z:M 5-20., The magnitudes for the UH01 AGN determined in Ho Peng (2001) for the Seyfert 1 population cover the range $\gea$ $_B$$\gea$ -22 mag with most lying within $\gea$ $_B$$\gea$ -20.370 Our nuclear aperture LF (open circles in Figure 9) extends from -1H4.57;M 57-19., Our nuclear aperture LF (open circles in Figure 9) extends from $\gea$ $_B$$\gea$ -19.371 In the most extreme case. based on ihe over and underestimates of the true AGN magnitudes discussed previously. the variable AGN in our survey could cover the magnitude range 27 Mp -12.5z;-20.," In the most extreme case, based on the over and underestimates of the true AGN magnitudes discussed previously, the variable AGN in our survey could cover the magnitude range $\gea$ $_B$$\gea$ -20."372 This magnitude range is consistent with that estimated for the UIIOI sample., This magnitude range is consistent with that estimated for the UH01 sample.373 It is therefore unlikely Chat (he increase in number density between the UIIOI LF and our LE is due to the inclusion of instrinsically fainter AGN as appears to be the case for the difference between the UIIOT and I1D92 LFs., It is therefore unlikely that the increase in number density between the UH01 LF and our LF is due to the inclusion of instrinsically fainter AGN as appears to be the case for the difference between the UH01 and HB92 LFs.374 Finally. we note that the LF for the variable nuclei continues to rise at faint magnitudes. indicating that number counts have not begun to (urn over al magnitudes even as [aint as Mpyc-15.," Finally, we note that the LF for the variable nuclei continues to rise at faint magnitudes, indicating that number counts have not begun to turn over at magnitudes even as faint as $_B$$\sim$ -15."375 The ellects of incompleteness in our survey due to AGN light dilution would cause us (o be less complete at the faint end ancl corrections in this sense would likely increase rather than decrease our faintest LF bin., The effects of incompleteness in our survey due to AGN light dilution would cause us to be less complete at the faint end and corrections in this sense would likely increase rather than decrease our faintest LF bin.376 Most local AGN LFs. such as those shown in Figure," Most local AGN LFs, such as those shown in Figure"377lincreases with the interaction strength as indicated by our correlation analvsis.,increases with the interaction strength as indicated by our correlation analysis.378 Svstematic differences in FIR color are also appreciable., Systematic differences in FIR color are also appreciable.379 The depletion time is Z10? vr foralf interaction classes (including isolated objects) in the BIRG sample., The depletion time is $\simlt 10^9$ yr for interaction classes (including isolated objects) in the BIRG sample.380" In the CS objects. zj,~LO!"" vr. comparable to the Hubble time."," In the CS objects, $\tau_{H_2} \sim 10^{10}$ yr, comparable to the Hubble time."381" There is a monotonic trend from isolatecl ealaxies {ο nergers. in terms of increasing SFR and decreasing 7,,,. but it is noteworthy that iis 100 statistically different in the various interaction classes."," There is a monotonic trend from isolated galaxies to mergers, in terms of increasing SFR and decreasing $\tau_{H_2}$, but it is noteworthy that is not statistically different in the various interaction classes."382 Isolated objects from the control sample. ancl isolated objects Grom the DIRG sample. wave inipressively different.," Isolated objects from the control sample, and isolated objects from the BIRG sample, have impressively different."383Lig. This apparent contradiction needs an explanation., This apparent contradiction needs an explanation.384 There are only 3 isolated DIRGs., There are only 3 isolated BIRGs.385 NGC 5937. NGC 7083. and NGC 5936 did not show a companion arger (han 5 Ixpc on the D5S-II within 250 Ixpce.," NGC 5937, NGC 7083, and NGC 5936 did not show a companion larger than 5 Kpc on the DSS-II within 250 Kpc."386 However. all of these galaxies present »eculiarities. (," However, all of these galaxies present peculiarities. ("3871) NGC 5937 has a distorted morphologv.5. and it mav have a loop of 5eas which could be a signature of interaction. (,"1) NGC 5937 has a distorted morphology, and it may have a loop of gas which could be a signature of interaction. ("3882) NGC 7033 is à barred Se galaxy that hosts a LINER.,2) NGC 7083 is a barred Sc galaxy that hosts a LINER.389 It looksooks perturbedpeος becaubecause of[ an off-centeredIItered |loop. (, It looks perturbed because of an off-centered loop. (3903) NGC 5936 ]has a hiehlv.highly distortecdistorted morphology. which may be indicative of recent interaction.,"3) NGC 5936 has a highly distorted morphology, which may be indicative of recent interaction."391 These galaxies may have been disturbed by the presence of a small companion disrupted or projected over the main galaxy., These galaxies may have been disturbed by the presence of a small companion disrupted or projected over the main galaxy.392 ]solated. CS galaxies do not show distortions or peculiarities that could make (hem special objects in terms of morphology or interaction., Isolated CS galaxies do not show distortions or peculiarities that could make them special objects in terms of morphology or interaction.393 The percentage of companion galaxies within 305 aand the distributions of observed and phvsieal companions show an highlyS. significant5 excess for the DIRGs., The percentage of companion galaxies within $3D_S$ and the distributions of observed and physical companions show an highly significant excess for the BIRGs.394 The difference between BIRGs and CS galaxies is especially striking if large companions with Dez20 Inpe are considered (the DIRG 5ealaxies have 3+ limes more companions within zz 140 IXpe: stronely interacting svstenis in the CS may be & κ)., The difference between BIRGs and CS galaxies is especially striking if large companions with $D_C \simgt 20$ Kpc are considered (the BIRG galaxies have 3–4 times more companions within $\approx$ 140 Kpc; strongly interacting systems in the CS may be $\simlt$ ).395 Our results also indicate a direct relationship between interaction and enhancement of I emission., Our results also indicate a direct relationship between interaction and enhancement of IR emission.396 We have considered a very large range inLian. ~LOS?—1077?LL... which is unprecedented and probably sufficient to overcome (he bias introduced by random projection of separation.," We have considered a very large range in, $ \sim39710^{8.5} - 10^{12.5}$, which is unprecedented and probably sufficient to overcome the bias introduced by random projection of separation."398 This may explain why. wilh some notable exceptions (e. g. Sanders&Mirabel(1996) and references (herein). several previous analyses did not found any convincing correlation between dp aand aamong interacting galaxies.," This may explain why, with some notable exceptions (e. g. \citet{sm96} and references therein), several previous analyses did not found any convincing correlation between $d_P$ and among interacting galaxies."399 Our result extends (o a lower rranee and quantifies results (hat were known qualitatively for LIBGs and ULIBRGs (1999)))., Our result extends to a lower range and quantifies results that were known qualitatively for LIRGs and ULIRGs \citet{ssi99}) ).400and E. Piconcelli for partially reducing the data.,and E. Piconcelli for partially reducing the data.401" We also thauk AL Cüerlisshi for help with models. M. Eracleous aud R. Siuubruua for sending us their und ‘data, D. Iuris for letting us know of his results prior to publication. Ix. Leighlv. €. Malaguti. C. Palunibo aud J. Poutanen for valuable discussions. and the auouvimous referee for insightful comamueuts."," We also thank M. Gierlińsski for help with models, M. Eracleous and R. Sambruna for sending us their and data, D. Harris for letting us know of his results prior to publication, K. Leighly, G. Malaguti, G. Palumbo and J. Poutanen for valuable discussions, and the anonymous referee for insightful comments."402lo center-pulse ancl center-pulse to off-pulse transitions.,to center-pulse and center-pulse to off-pulse transitions.403 This mirrors (he fact that emission comes only from a narrow cone about (the line of sight of half opening angle 0zzL/T.," This mirrors the fact that emission comes only from a narrow cone about the line of sight of half opening angle $\theta \approx 1 /404\Gamma$."405 For given values of D and £. (he particle spectral index p affects only (he average degree of polarization degree but not the light curve nor the polarization angle.," For given values of $\Gamma$ and $\xi$, the particle spectral index $p$ affects only the average degree of polarization degree but not the light curve nor the polarization angle."406 For example. taking T=10 and €=60° .a spectral index of p=2 leads to an average polarization of II=19.2% whereas for p—3 it leads to IT=30.8%.," For example, taking $\Gamma=10$ and $\xi=60\degr$, a spectral index of $p=2$ leads to an average polarization of $\tilde{\Pi}=19.2\%$ whereas for $p=3$ it leads to $\tilde{\Pi}=30.8\%$."407 In the striped wind model. the high energy. (infra-red to gaammnma-ray) emission of pulsars arises [rom outside the light evlinder. in accordance with the early suggestions of and Shklovsky(1970).," In the striped wind model, the high energy (infra-red to gamma-ray) emission of pulsars arises from outside the light cylinder, in accordance with the early suggestions of \citet{pacinirees70} and \citet{shklovsky70}."408. It provides an alternative to the more intensivelv studied polar cap. outer gap and two-pole caustic models.," It provides an alternative to the more intensively studied polar cap, outer gap and two-pole caustic models."409 All models contain essentially arbitrary assumptions concerning the configuration of the emission region and the distribution function of the emitting particles. rendering it difficult to distinguish between them on the basis ol observations.," All models contain essentially arbitrary assumptions concerning the configuration of the emission region and the distribution function of the emitting particles, rendering it difficult to distinguish between them on the basis of observations."410 [lowever. the geometry of the magnetic field. which is the crucial factor determining the polarization properties. is constrained in (he striped model to be close to that of (he analvtic asvimptolic solution presented by Bogovaloy(1999).," However, the geometry of the magnetic field, which is the crucial factor determining the polarization properties, is constrained in the striped model to be close to that of the analytic asymptotic solution presented by \cite{bogovalov99}."411. We have therefore presented. detailed computations of the polarization properties of the pulses expected in (his scenario., We have therefore presented detailed computations of the polarization properties of the pulses expected in this scenario.412 These possess the characteristic properly. unique amongst currently discussed models. (hat the electric vector of the off-pulse emission is aligned with the projection of (he pulsar's rotation axis on the plane of the skv.," These possess the characteristic property, unique amongst currently discussed models, that the electric vector of the off-pulse emission is aligned with the projection of the pulsar's rotation axis on the plane of the sky."413 This is in striking agreement wilh recent observations of the Crab pulsar., This is in striking agreement with recent observations of the Crab pulsar.414 In addition the striped wind scenario naturally incorporates features of the phase-dependent properties of the polarization angle. degree of polarization and intensity that are also seen in the data.," In addition the striped wind scenario naturally incorporates features of the phase-dependent properties of the polarization angle, degree of polarization and intensity that are also seen in the data."415 This unclerlines the need to develop the model further. in order to confront. hieh-enerev observations of the Crab and other pulsars.," This underlines the need to develop the model further, in order to confront high-energy observations of the Crab and other pulsars."416 In particular. (ae manner in which magnetic energy is released into particles in the current sheet remains poorly understood ancl the link between the asvinplolic magnetic lield structure and (he pulsar magnetosphere is obscure.," In particular, the manner in which magnetic energy is released into particles in the current sheet remains poorly understood and the link between the asymptotic magnetic field structure and the pulsar magnetosphere is obscure."417 We thank Gottlried Ixanbach lor providing us with the OPTIMA data and for helpful discussions., We thank Gottfried Kanbach for providing us with the OPTIMA data and for helpful discussions.418 This work was supported by a grant from the G.LE.. (the German-Israeli Foundation for Scientific Research aud Development.," This work was supported by a grant from the G.I.F., the German-Israeli Foundation for Scientific Research and Development."419approximated by a 6000Ix black body for wavelengths below about Lom.,approximated by a 6000K black body for wavelengths below about 1cm.420 Longwarel of about lem the spectrum deviates from a blackbody aud becomes dependent on the solar cvele., Longward of about 1cm the spectrum deviates from a blackbody and becomes dependent on the solar cycle.421 For the active Sun il rises to a secondary peak at around lin. Therefore. a relative mininuumn exists just shortward of lem.," For the active Sun it rises to a secondary peak at around 1m. Therefore, a relative minimum exists just shortward of 1cm."422 However. even al num the diffraction limited size of an antenna (of realistic size) will be large compared to the size of the solar disk.," However, even at 1mm the diffraction limited size of an antenna (of realistic size) will be large compared to the size of the solar disk."423 At 550 AU the sun subtends about 3.5 while a 10nr antenna has a beam size of (FWEZ) about 50°., At 550 AU the sun subtends about 3.5” while a 10m antenna has a beam size of (FWFZ) about 50”.424 Ilence. unless the source to be observed is strong. observations in the mam-wave range will have to be differential in wavelength space and have to require that the source has a different spectrum than the Sun.," Hence, unless the source to be observed is strong, observations in the mm-wave range will have to be differential in wavelength space and have to require that the source has a different spectrum than the Sun."425 This observing strategy iniposes severe requirements on the stability ol the detector svstem. such that a reliable subtraction of the solar [ιν can be achieved.," This observing strategy imposes severe requirements on the stability of the detector system, such that a reliable subtraction of the solar flux can be achieved."426 Coronogralic observations can be envisioned al short (I. visual) wavelength observations. however. in the IR ancl optical. emission and/or scattering Irom the Zodiacal dust will present a challenge for such observations.," Coronografic observations can be envisioned at short (IR, visual) wavelength observations, however, in the IR and optical, emission and/or scattering from the Zodiacal dust will present a challenge for such observations."427 Further study is required to quantilv these effects., Further study is required to quantify these effects.428 As noted above. in order (o guarantee propagation of the radiation through the solar atmosphere. observations have to be restricted to frequencies above (he plasma frequency at a eiven inipact parameter as well as above those where (he refraction cancels (he gravitational convergence.," As noted above, in order to guarantee propagation of the radiation through the solar atmosphere, observations have to be restricted to frequencies above the plasma frequency at a given impact parameter as well as above those where the refraction cancels the gravitational convergence."429 If we want to minimize the distance from the Sun required (his forces us to consider onlv lrequencies well above about. 100 GIIz (3 mm)., If we want to minimize the distance from the Sun required this forces us to consider only frequencies well above about 100 GHz (3 mm).430" Both the magnification and the plate scale of a ""Solar Gravilational Telescope’ (SGT) - ie. the tangential offset in (he image plane corresponding (o a given angular offset in the source - are very. large.", Both the magnification and the plate scale of a “Solar Gravitational Telescope” (SGT) - i.e. the tangential offset in the image plane corresponding to a given angular offset in the source - are very large.431 Since it is not possible. due to e.g. propulsion consideration to expect a solar gravitational lens mission (o be able to perform much controlled tangential motion. the observational program has to be restricted to those that can be accomplished utilizing the trajectory given by the initial ejection from the inner solar svstem.," Since it is not possible, due to e.g. propulsion consideration to expect a solar gravitational lens mission to be able to perform much controlled tangential motion, the observational program has to be restricted to those that can be accomplished utilizing the trajectory given by the initial ejection from the inner solar system."432 This will first place verv high requirements on (he absolute navigation of the mission aud in consequence the trajectory., This will first place very high requirements on the absolute navigation of the mission and in consequence the trajectory.433 Second. the source selection for a SGT is limited to sources that are small (because it takes a long time to transverse a source). but with interesting smaller-scale (οἱ (he order of the beam) variations which can be explored with one dimensional mapping.," Second, the source selection for a SGT is limited to sources that are small (because it takes a long time to transverse a source), but with interesting smaller-scale (of the order of the beam) variations which can be explored with one dimensional mapping."434 The source selection further has to be made prior to launch and hence survev-like observations are out of consideration., The source selection further has to be made prior to launch and hence survey-like observations are out of consideration.435 À likelv observing scenario is thus to allow the tangential component of the trajectory velocity. to sweep (he space craft across the image of the source under study eathering a one dimensional map as illustrated in Figure 10.., A likely observing scenario is thus to allow the tangential component of the trajectory velocity to sweep the space craft across the image of the source under study gathering a one dimensional map as illustrated in Figure \ref{fig:concept}.436 It is questionable whether any source can be found that both. can be successfully observed with a SGT and. cannot be," It is questionable whether any source can be found that both, can be successfully observed with a SGT and, cannot be"437 This steepening can be modelled theoretically using the analytic expressions for the beam convolution from Benschetal..., This steepening can be modelled theoretically using the analytic expressions for the beam convolution from \citeauthor{Bensch}.438 In fact. the A-variance spectrum computed from the o Oph map with full weights can be fitted by a single power-law structure with a=0.68 (see Fig. 7)).," In fact, the $\Delta$ -variance spectrum computed from the $\rho$ Oph map with full weights can be fitted by a single power-law structure with $\alpha=0.68$ (see Fig. \ref{fig_ophdelta}) )."439 The fitted exponent of 0.68 falls into the range measured in molecular line observations of molecular elouds covering exponents between 0.5 and 1.3 (Benschetal..2001:Elmegreen&Scalo.2004:Fal-garoneetal.. 2004).," The fitted exponent of 0.68 falls into the range measured in molecular line observations of molecular clouds covering exponents between 0.5 and 1.3 \citep{Bensch, Elmegreen, Falgarone04}."440. In contrast. the two lower curves cannot be fitted in the same way.," In contrast, the two lower curves cannot be fitted in the same way."441 These spectra would lead to the conclusion of a surplus of small-scale structure relative to a power-law sealing relation., These spectra would lead to the conclusion of a surplus of small-scale structure relative to a power-law scaling relation.442 Such a relative surplus of structure on small scales 1s hard to explain Thus we conclude from the sealing behaviour that the full weighting of intensity maps by their inverse noise RMS results in the most reliable A-variance spectra., Such a relative surplus of structure on small scales is hard to explain Thus we conclude from the scaling behaviour that the full weighting of intensity maps by their inverse noise RMS results in the most reliable $\Delta$ -variance spectra.443 With this weighting the A-variance analysis 1s able to distinguish insignificant small-scale structure. dominating the lowest contour in Fig. 4..," With this weighting the $\Delta$ -variance analysis is able to distinguish insignificant small-scale structure, dominating the lowest contour in Fig. \ref{fig_ophmap},"444 from significant structures which are intuitively better presented by the contours chosen m the original plot by Motteetal..., from significant structures which are intuitively better presented by the contours chosen in the original plot by \citeauthor{Motte}.445 The increase of the absolute value of the A-variance at large lags when using the weighting function is explained by the relative increase of the contribution of the bright cores in the map when virtually reducing the map size by weighting the outer parts by lower significance values., The increase of the absolute value of the $\Delta$ -variance at large lags when using the weighting function is explained by the relative increase of the contribution of the bright cores in the map when virtually reducing the map size by weighting the outer parts by lower significance values.446 To get a feeling for the reliability of the different points in the A-variance spectrum we plot in Fig., To get a feeling for the reliability of the different points in the $\Delta$ -variance spectrum we plot in Fig.447 7. the A-variance spectrum including the error bars.," \ref{fig_ophdelta}448 the $\Delta$ -variance spectrum including the error bars."449 The error bars arise from the statistical uncertainty of the measurement of the average variance in a filtered map (Bensch et al., The error bars arise from the statistical uncertainty of the measurement of the average variance in a filtered map (Bensch et al.450 2001)., 2001).451 Due to the lower number of statistically independent points in maps convolved with a larger filter. the A-variance Is most uncertain at the largest lags.," Due to the lower number of statistically independent points in maps convolved with a larger filter, the $\Delta$ -variance is most uncertain at the largest lags."452 In spite of the large error bars. the general scaling behaviour can be accurately traced.," In spite of the large error bars, the general scaling behaviour can be accurately traced."453 The solid line shows the, The solid line shows the454and e=c is the ambient velocity.,and $v=\sigma$ is the ambient velocity.455" Using the virial theorem. 4xGp~(o/RY. one finds TcRefCausuuo)e100 Myr. where we have assumed AL~2m. adopted a cluster radius of Hoclpc. umposed Heggies Law (ty,0). and dropped Iactors of order unity."," Using the virial theorem, $4\pi G\rho \sim (\sigma/R)^2$, one finds $T\sim R^2/(a_{\rm break}\sigma)\sim 100\,$ Myr, where we have assumed $M\sim 2m$, adopted a cluster radius of $R\sim 1\,\pc$, imposed Heggie's Law $v_\orb\sim \sigma$ ), and dropped factors of order unity."456 Since open clusters generally dissolve on timescales (hat are one or several (mes (his binary-disruption timescale. it is plausible that the binary distribution does not have time to fully reach its asvinplolic state.," Since open clusters generally dissolve on timescales that are one or several times this binary-disruption timescale, it is plausible that the binary distribution does not have time to fully reach its asymptotic state."457 The explanation just given makes an important prediction., The explanation just given makes an important prediction.458 The binding energy of a binary scales £j~M4M»S/e. where M4 ancl As are the component masses.," The binding energy of a binary scales $E_b\sim M_1 M_2/a$, where $M_1$ and $M_2$ are the component masses."459 TheLipparcos primaries in the Lépine&Donegiorno(2006) study are virtually all solau-tvpe stars. Le.. Aly~AL...," The primaries in the \citet{lepine06} study are virtually all solar-type stars, i.e., $M_1\sim M_\odot$."460 This means (hat for secondaries of different masses. the break point scales as (weak~Ale.," This means that for secondaries of different masses, the break point scales as $a_{\rm break}\sim M_2$."461 Il is plausible (ο assume that the secondaries wilh «peak are initially drawn randomly [rom the field population., It is plausible to assume that the secondaries with $a\sim a_{\rm break}$ are initially drawn randomly from the field population.462 Then we would predict (hat alter the binaries diffuse to larger a. the ratio of secondaries to field stars of the same mass would [all by a factor aj. or in other words as οι," Then we would predict that after the binaries diffuse to larger $a$, the ratio of secondaries to field stars of the same mass would fall by a factor $a_{\rm break}^\alpha$, or in other words as $M_2^\alpha$."463 Figure 9 of Lépine&Bongiorno(2006) shows the Irequeney of observed secoucaries compared to what would be expected based on a distribution normalized al 4<AZ8. Le. stars of mass Ma=OSM...," Figure 9 of \citet{lepine06} shows the frequency of observed secondaries compared to what would be expected based on a distribution normalized at $4<M_V<8$, i.e., stars of mass $M_2=0.8\,M_\odot$."464 The foregoing argument would predict that al A)=12 GM»~0.25M. ). the observed secondaries should be deficient by a [actor ~(0.25/0.8)b70.15.," The foregoing argument would predict that at $M_V=12$ $M_2\sim 0.25\,M_\odot$ ), the observed secondaries should be deficient by a factor $\sim (0.25/0.8)^{1.67}\sim 0.15$."465 The actual deficiency is about 0.5.κ which is significantly less cramatic.," The actual deficiency is about 0.5, which is significantly less dramatic."466 Nevertheless. this figure does show the expected overall trend.," Nevertheless, this figure does show the expected overall trend."467 One possible explanation for the discrepancy is that the timescale lor disruption of the binaries with smaller secondaries at their break point is considerably longer simply. because (heir orbils present smaller cross sections., One possible explanation for the discrepancy is that the timescale for disruption of the binaries with smaller secondaries at their break point is considerably longer simply because their orbits present smaller cross sections.468" Since (he binary disruption timescales at ""typical masses are already of order the cluster-disruption timescale. (hiis increase in binary-disruption timescale could substantially mitigate the accelerated disruption relative to the naive scaling we lave eiven."," Since the binary disruption timescales at “typical” masses are already of order the cluster-disruption timescale, this increase in binary-disruption timescale could substantially mitigate the accelerated disruption relative to the naive scaling we have given."469 The same argument predicts that the Chanamé&Gould(2004). sample should have a smaller ως than the Lépine&Dongiorno(2006) sample because each of the latter is euaranteed to have aLipparcos (ie.. roughly solar mass) component. aid so to have a systematically higher binding energy.," The same argument predicts that the \citet{chaname04} sample should have a smaller $a_{\rm break}$ than the \citet{lepine06} sample because each of the latter is guaranteed to have a (i.e., roughly solar mass) component, and so to have a systematically higher binding energy."470" We attempt a first test of our hvpothesis by dividing the sample shown in Lépine into three subsamples. with Vy 8.8<My,12. and M,>12."," We attempt a first test of our hypothesis by dividing the sample shown in \citet{lepine06} into three subsamples, with $M_V<8$, $8\leq M_V<12$, and $M_V\geq 12$."471 See Figure 1.., See Figure \ref{fig:f1}.472 Our prediction would be that (he fainter stars should plateau at smaller r_., Our prediction would be that the fainter stars should plateau at smaller $r_\perp$.473" If (here is anv trend il would appear to go in the opposite direction. although these subcdivided dala are quite noisy and could still be subject to selection effects i£ the faintest stars are more difficult to detect al ~20""/ separations that Lépine&Bongiorno(2006) believe."," If there is any trend it would appear to go in the opposite direction, although these subdivided data are quite noisy and could still be subject to selection effects if the faintest stars are more difficult to detect at $\sim 20''$ separations that \citet{lepine06} believe."474 An important implication of this argumente is that the break in the binary. separation, An important implication of this argument is that the break in the binary separation475"The orbits of sub halos around their host can be characterised (Lacey&Cole1993) by the dimensionless parameter », where rc(E) and Ίε(Ε) are the radius and specific angular momentum of a circular orbit with energy E.",The orbits of sub halos around their host can be characterised \cite{Lacey93} by the dimensionless parameter = )^2 where $r_c(E)$ and $j_c(E)$ are the radius and specific angular momentum of a circular orbit with energy $E$.476" For a potential with a flat rotation curve; where the circular velocity at all radii is vc, &((r) $((r.) -- left((—) ."," For a potential with a flat rotation curve; where the circular velocity at all radii is $v_{\rm c}$, (r) = ) + ) ."477" Hence, for a subhalo at position, r with velocity v, the radius of a circular orbit with the same energy is: — - "," Hence, for a subhalo at position, ${\bf r}$ with velocity ${\bf v}$, the radius of a circular orbit with the same energy is: ) = - ]."478"The orbital parameters are found by simply applying equations (A1)) to (??)) to the position and velocity vectors of each satellite halo (after moving to a frame where these vectors are both for the host halo): c − i) The model assigns each satellite a value for this parameter, O, drawn at random from the log-normal distribution that it was found to follow in simulations by Tormen(1997):: 928107] , with c=0.26."," The orbital parameters are found by simply applying equations \ref{ThetaOrbit}) ) to \ref{r_c}) ) to the position and velocity vectors of each satellite halo (after moving to a frame where these vectors are both for the host halo): = - 1 ] The model assigns each satellite a value for this parameter, $\Theta$, drawn at random from the log-normal distribution that it was found to follow in simulations by \scite{Tormen97}: ] , with $\sigma=0.26$."479" The sample of orbit parameters produced by this random assignment is shown in Fig. ??,,"," The sample of orbit parameters produced by this random assignment is shown in Fig. \ref{orbits},"480 together with the actual values from the Brookset simulation., together with the actual values from the \scite{Brooks09} simulation.481 'The fraction ofthe halo free-fall time that it takes for the satellite to merge through dynamical friction is assumed to be proportional to Θ: κκ., The fraction ofthe halo free-fall time that it takes for the satellite to merge through dynamical friction is assumed to be proportional to $\Theta$: =.482 This is based on the standard Chandrasekhar formula for the dynamical friction and appears originally in Lacey&C, This is based on the standard Chandrasekhar formula for the dynamical friction and appears originally in \scite{Lacey93}.483"ole (1993). p, is the mean density at the virial προας (determined by the cosmology, not the specific halo’s properties)."," $\rho_{\rm v}$ is the mean density at the virial radius (determined by the cosmology, not the specific halo's properties)."484 The distribution of angles at which sub structures enter their host halo has been studied by Benson(2005) for the VLS and VIRGO simulations and and found to have a repeatable distribution., The distribution of angles at which sub structures enter their host halo has been studied by \scite{Benson05} for the VLS and VIRGO simulations and and found to have a repeatable distribution.485" This distribution can be applied in the model to generate an alternative set of orbital parameters, O, which are shown in Fig."," This distribution can be applied in the model to generate an alternative set of orbital parameters, $\Theta$, which are shown in Fig."486" ?? alongside the standard assumption of the log-normal distribution, and the results fromGASOLINE."," \ref{orbits} alongside the standard assumption of the log-normal distribution, and the results from."487 Merger times predicted by (??)) have been compared by Jiangetal.(2008) with the results of GADGET2 simulations (Springel2005)., Merger times predicted by \ref{t_mrg}) ) have been compared by \scite{Jiang08} with the results of GADGET2 simulations \cite{Springel05}.488". The agreement found was of the order of a factor of two, which is deemed acceptable for the continued use of this formula inGALFORM."," The agreement found was of the order of a factor of two, which is deemed acceptable for the continued use of this formula in."489" However, since (?7)) was found to consistently underestimate the simulated merger time, the improved fitting formula proposed byJiangetal.(2008) may well be adopted in future."," However, since \ref{t_mrg}) ) was found to consistently underestimate the simulated merger time, the improved fitting formula proposed \scite{Jiang08} may well be adopted in future."490" Unfortunately, due to the very different definition of merging adopted by the halo finder used here refMergerTree)), a meaningful comparison of the respective times in the two realisation has not been possible."," Unfortunately, due to the very different definition of merging adopted by the halo finder used here \\ref{MergerTree}) ), a meaningful comparison of the respective times in the two realisation has not been possible."491 The stellar disk radii that appear in Fig., The stellar disk radii that appear in Fig.492 ?? are generated from analysis of the distribution of stars in the simulation., \ref{Radii} are generated from analysis of the distribution of stars in the simulation.493 Fig., Fig.494" compares the distribution of stellar mass from the simulation with the analytic formsassumed by GALFORM, both for disk stars and for the mass of stars in the bulge, assumed to be (21))distributed such that the projected MaceyFr"," \ref{stars} compares the distribution of stellar mass from the simulation with the analytic formsassumed by , both for disk stars \ref{RadialProfile})) and for the mass of stars in the bulge, assumed to be distributed such that the projected surface density profile is given by:"495Non-radial. pulsations. (NRPs). are commonly found.. in. isolated white cdwarfs (WDs) of DA type. so called ZZ Ceti stars.,"Non-radial pulsations (NRPs) are commonly found in isolated white dwarfs (WDs) of DA type, so called ZZ Ceti stars."496" Phese stars have hyclrogen-rich atmospheres. and oulsationsj occur, as the WD cools""n ancl passed. throughnM a phase of pulsational instability. detected mainly as g-mocdes (7))."," These stars have hydrogen-rich atmospheres, and pulsations occur as the WD cools and passed through a phase of pulsational instability, detected mainly as g-modes \citealt{2006AJ....132..831G}) )."497 DuringIn the last decennium. similar signals.Ind ogenerally interpreted:. as non-racial. .WD pulsations.. have also. been detected in ⊀⋅⊀faint cataclysmic. variables. (CVs).," During the last decennium, similar signals, generally interpreted as non-radial WD pulsations, have also been detected in faint cataclysmic variables (CVs)."498""" A CV ""mis a close binary system where a late-type main-sequence star looses mass to a primary white ναί", A CV is a close binary system where a late-type main-sequence star looses mass to a primary white dwarf.499 Phe first CY proposed. to harbour a pulsating white dwarf was GW Librae., The first CV proposed to harbour a pulsating white dwarf was GW Librae.500 2? found rapid. periodic. and non-conimensurate signalsN in its light° Curve. suggesting non-racial pulsations of the underlving white cwarf.," \cite{1998IAUS..185..321W} found rapid, periodic, and non-commensurate signals in its light curve, suggesting non-radial pulsations of the underlying white dwarf."501 In most. CVs. the accretion energy. tends to dominate the Iuminosity. and the white chwarl itself. shining with. Ady~ 19 13. MEis seldom seen.," In most CVs, the accretion energy tends to dominate the luminosity, and the white dwarf itself, shining with $M_{V} \sim$ 10 – 13, is seldom seen."502" However. for⋅ some of⋅ the most intrinsically faint CVs. spectroscopy. ancl time-series photometry can reveal signatures of the underlying white ναί, such as broad. absorption features in the spectrum. sharp eclipses. ancl sometimes non-radial pulsations in the light curve."," However, for some of the most intrinsically faint CVs, spectroscopy and time-series photometry can reveal signatures of the underlying white dwarf, such as broad absorption features in the spectrum, sharp eclipses, and sometimes non-radial pulsations in the light curve."503 These signals have now been detected in about a dozen CVs. all quiescent svstems of low Iuminositv.," These signals have now been detected in about a dozen CVs, all quiescent systems of low luminosity."504 Here. we call these svstemsstars. after the first discovery.," Here, we call these systems, after the first discovery."505 and 2? present recent reviews of this group of stars., \cite{2010ApJ...710...64S} and \cite{2009JPhCS.172a2069M} present recent reviews of this group of stars.506 Acereting WDs are different. from. isolated: ones. since, Accreting WDs are different from isolated ones since507"In precstellar cores, cold outer protostellar envelopes and protoplanetary disk midplanes, most molecules, except for H», are frozen out on dust grains, forming ice mantles.","In pre-stellar cores, cold outer protostellar envelopes and protoplanetary disk midplanes, most molecules, except for $_2$, are frozen out on dust grains, forming ice mantles."508" The main ice component in most lines of sight is H»O, followed by CO and CO», with a typical abundance of (0.5—1.5)710+ for H5O ice with respect to Hs around solar-type protostars 0(?).."," The main ice component in most lines of sight is $_2$ O, followed by CO and $_2$, with a typical abundance of $(0.5 - 1.5) \times 10^{-4}$ for $_2$ O ice with respect to $_2$ around solar-type protostars \citep{Vandishoeck_06}."509 Infrared. observations of pre-stellar cores show that most CO» ice and some of the CO ice is mixed with H2O (?)., Infrared observations of pre-stellar cores show that most $_2$ ice and some of the CO ice is mixed with $_2$ O \citep{Knez_05}.510 The remaining CO and CO» are found in separate ice layers., The remaining CO and $_2$ are found in separate ice layers.511" Based on these observations, ΠΟ and CO» are thought to form simultaneously on the grain surface during the carlv stage of cloud formation."," Based on these observations, $_2$ O and $_2$ are thought to form simultaneously on the grain surface during the early stage of cloud formation."512" When the cloud becomes denser, gas phase CO freezes out on top of the water-rich ice, resulting in a lavered ice mantle, as described in 2.."," When the cloud becomes denser, gas phase CO freezes out on top of the water-rich ice, resulting in a bi-layered ice mantle, as described in \cite{Pontoppidan_08}."513" Once the pre- core starts collapsing into a protostar, it heats its environment, including the icy grains."," 	 Once the pre-stellar core starts collapsing into a protostar, it heats its environment, including the icy grains."514" This results in the desorption of the CO-rict layer into the [e]σας phase, in structural changes in the water-rich ice layer, and eventually in the desorption of the water-rich layer (?).."," This results in the desorption of the CO-rich layer into the gas phase, in structural changes in the water-rich ice layer, and eventually in the desorption of the water-rich layer \citep{Pontoppidan_08}."515 Such an ice desorption scheme provides most of the gas phase reactants for the chemistry taking place at later stages in these warm regions (?)., Such an ice desorption scheme provides most of the gas phase reactants for the chemistry taking place at later stages in these warm regions \citep{Doty_04}.516 It is therefore crucial to understand ice mixture desorption and to effectively. implement it in astrochemical networks., It is therefore crucial to understand ice mixture desorption and to effectively implement it in astrochemical networks.517 The aim of this study is to provide a laboratorv basis for this process and to demonstrate how it can be modeled both in the laboratory and in space., The aim of this study is to provide a laboratory basis for this process and to demonstrate how it can be modeled both in the laboratory and in space.518" Laboratory experiments have provided most of the current. knowledge about ice thermal desorption, including desorption energies for most pure simple "," 	 	Laboratory experiments have provided most of the current knowledge about ice thermal desorption, including desorption energies for most pure simple ices \citep{Sandford_88,Sandford_90, Fraser_01, Collings_04, Oberg_05, Brown_07, Brown_10}."519"Desorption from ice mixtures differs from pure ice desorption because of different binding energics between the mixture components (c.g., the CO binding energy increases from 830 K in pure ice to 1180K in H»O-dominated ice mixtures (?))) and because of trapping of volatile species in the H»O hvdrogerbonding ices (?).."," Desorption from ice mixtures differs from pure ice desorption because of different binding energies between the mixture components (e.g., the CO binding energy increases from 830 K in pure ice to $1180\, \rm K$ in $_2$ O-dominated ice mixtures \citep{Collings_03_b}) ) and because of trapping of volatile species in the $_2$ O hydrogen-bonding ices \citep{Collings_04}. ."520" Volatile components therefore desorb from H»O-rich ice mixtures at a minimum of two different temperatures, corresponding to the desorption of the species from the surface of the H2O ice and from molecules trapped inside the bulk of the H2O ice, which only start desorbing at the onset of H»O desorption."," Volatile components therefore desorb from $_2$ O-rich ice mixtures at a minimum of two different temperatures, corresponding to the desorption of the species from the surface of the $_2$ O ice and from molecules trapped inside the bulk of the $_2$ O ice, which only start desorbing at the onset of $_2$ O desorption."521" Additional desorption is sometimes observed at the temperature for pure volatile ice desorption and during ice re-structuring,e.g.,, at the H»O phase change from amorphous to crystalline (2).."," Additional desorption is sometimes observed at the temperature for pure volatile ice desorption and during ice re-structuring, at the $_2$ O phase change from amorphous to crystalline \citep{Viti_04}."522" This Π.Ο restructuring occurs at ~140 K in the laboratory (for astrophysical timescales the re-structuring temperature and desorptior temperature decrease), which is close to the onset of H2O desorption (?).."," This $_2$ O restructuring occurs at $\sim$ 140 K in the laboratory (for astrophysical timescales the re-structuring temperature and desorption temperature decrease), which is close to the onset of $_2$ O desorption \citep{Collings_04}."523" Of the different ice mixture desorptior features, the entrapment of volatile species in H2O ice is astrochemically the most important to quantify."," 	 	Of the different ice mixture desorption features, the entrapment of volatile species in $_2$ O ice is astrochemically the most important to quantify."524 The trapping of CO in a water ice results in a factor ο five increase in the effective desorption temperature., The trapping of CO in a water ice results in a factor of five increase in the effective desorption temperature.525" Ir a recent cloud core collapse model, this corresponds to trapped CO desorbing at 30 AU from the protostar compared to pure CO ice desorbing at 3000 AU."," In a recent cloud core collapse model, this corresponds to trapped CO desorbing at 30 AU from the protostar compared to pure CO ice desorbing at 3000 AU."526" The case is less dramatic, but still significant, for CO», which desorbs at ~300 AU when pure, and at 30 AU if trapped in H2O ice (??)."," The case is less dramatic, but still significant, for $_2$, which desorbs at $\sim$ 300 AU when pure, and at 30 AU if trapped in $_2$ O ice \citep{Aikawa_08, Visser_09}."527 Efficient ice trapping may therefore allow some volatiles to stav frozen on the dust grains during accretion of envelope material onto the forming protoplanetary disk (?).., Efficient ice trapping may therefore allow some volatiles to stay frozen on the dust grains during accretion of envelope material onto the forming protoplanetary disk \citep{Visser_09}.528 There are onlv a few models that have incorporated the effects of ice mixture desorption., There are only a few models that have incorporated the effects of ice mixture desorption.529 ? investigated the desorption of 16 astrophysically relevant species from H»O:X 20:1 ice mixtures., \cite{Collings_04} investigated the desorption of 16 astrophysically relevant species from $_2$ O:X 20:1 ice mixtures.530" ? and ? used the results of ? to split up the abundance of volatiles μαςin up to four different flavors, with different desorption temperatures."," \cite{Viti_04} and \cite{Visser_09} used the results of \cite{Collings_04} to split up the abundance of volatiles in up to four different flavors, with different desorption temperatures."531" These correspond to the fraction of cach meice desorbingat the pure ice desorption temperature, from a H2O surface, during H2O ice restructuring and with Π.Ο, respectively."," These correspond to the fraction of each ice desorbingat the pure ice desorption temperature, from a $_2$ O surface, during $_2$ O ice restructuring and with $_2$ O, respectively."532 This approach has provided information on the potential importance of ice trapping for the chemical, This approach has provided information on the potential importance of ice trapping for the chemical533Figure 3. shows the mass outflow parameter as a function of the BLE spin parameter.,Figure \ref{fig:qjets} shows the mass outflow parameter as a function of the BH spin parameter.534 For e;=0.95. the mass outflow into the jets is only about S per cent of the available mass inllow through the disc inside the ergosphere.," For $a_* = 0.95$, the mass outflow into the jets is only about 8 per cent of the available mass inflow through the disc inside the ergosphere."535" Instead. for a spin parameter near the maximal one (e,~1). the mass outIlow increases to about OS per cent of the available mass inflow."," Instead, for a spin parameter near the maximal one $a_* \sim 1$ ), the mass outflow increases to about 98 per cent of the available mass inflow."536 This means that in the case of near maxima spin. the DII almost stops being fed by accreting matter.," This means that in the case of near maximal spin, the BH almost stops being fed by accreting matter."537 Suppose the inner cise would have been extende bevond the stationary limit surface., Suppose the inner disc would have been extended beyond the stationary limit surface.538 In this case. the clise particles can form the jets (disc 0) if and only i£ the BL spin parameter were e;0.755 (plot not shown).," In this case, the disc particles can form the jets $q_{\mathrm{jets}} > 0$ ) if and only if the BH spin parameter were $a_* > 0.755$ (plot not shown)."539 We mention that the results presented in this section are valid for our choice of p=0., We mention that the results presented in this section are valid for our choice of $p = 0$.540 This. of course. need no be a necessary condition for jet launching. since we have examined the mass outflow parameter for just one value of p. that which makes Xe constant for any radius of the disc inside the DII ergosphere ancl dj; dependent only on the DII spin parameter. but it is certainly. sullicient.," This, of course, need not be a necessary condition for jet launching, since we have examined the mass outflow parameter for just one value of $p$, that which makes $\Sigma \bar{v}^{\hat{r}}$ constant for any radius of the disc inside the BH ergosphere and $q_{\mathrm{jets}}$ dependent only on the BH spin parameter, but it is certainly sufficient."541 The DII rotation causes an outflow of particles from the disc. where the energy (and angular momentum) carried by the escape particles is taken from the accretion disc.," The BH rotation causes an outflow of particles from the disc, where the energy (and angular momentum) carried by the escape particles is taken from the accretion disc."542 The escape particles then slide along the open magnetic field lines. being accelerated by magnetic forces (see Section 5)).," The escape particles then slide along the open magnetic field lines, being accelerated by magnetic forces (see Section \ref{sec:jetspower}) )."543 lo describe the structure o£. the. disc. inside the BIL ergosphere. we use the angular momentum: and. energy conservation laws derivec Lby ? and include both the BlI-disc magnetic connection anc| the jet formation.," To describe the structure of the disc inside the BH ergosphere, we use the angular momentum and energy conservation laws derived by \citet{pt} and include both the BH-disc magnetic connection and the jet formation."544 When deriving he conservation laws. ? clo not make any assumption about the type of stress-energyv. present (eg... magnetic ields. viscous stresses. ete). ," When deriving the conservation laws, \citet{pt} do not make any assumption about the type of stress-energy present (e.g., magnetic fields, viscous stresses, etc.). ["545The calculations. performe o» ? are valid even if the cise is highly. dynamical. bu can also be applied: to steady-state ancl cuasi-steacky-state discs. in which case the mass accretion rate is constan hroughout the disc.],"The calculations performed by \citet{pt} are valid even if the disc is highly dynamical, but can also be applied to steady-state and quasi-steady-state discs, in which case the mass accretion rate is constant throughout the disc.]"546 Here. we consider that the removal of he angular momentum of the disc inside the ergosphere can »e produced by the external jet torque and that the externa orques acting on the disc inside the ergosphere (i.e. Bl-clise magnetic torque and jet torque) dominate over the interna viscous torque of the dise (2)..," Here, we consider that the removal of the angular momentum of the disc inside the ergosphere can be produced by the external jet torque and that the external torques acting on the disc inside the ergosphere (i.e., BH-disc magnetic torque and jet torque) dominate over the internal viscous torque of the disc \citep{blandford01}."547 In this case. we can write the angular momentunm conservation. as where on the left-hand. side. the first. termi describes the angular momentum carried by the accreting mass of the disc inside the DII ergosphere. and the second. term. describes the angular momentum transferred. from. the BII to the disc inside the ergosphere.," In this case, we can write the angular momentum conservation as where on the left-hand side, the first term describes the angular momentum carried by the accreting mass of the disc inside the BH ergosphere, and the second term describes the angular momentum transferred from the BH to the disc inside the ergosphere."548 Ehe term on the right describes the angular momentum carried away by. the jets., The term on the right describes the angular momentum carried away by the jets.549 L* is the specific angular momentum of a gas particle orbiting in the accretion disc. J is the total flux of energy (of particle and electromagnetic origin) carried away by jets ancl Lf is the lus of angulare momentum transferred from the DII to the disc inside the ergosphere.," $L^{\dagger}$ is the specific angular momentum of a gas particle orbiting in the accretion disc, $J$ is the total flux of energy (of particle and electromagnetic origin) carried away by jets and $H$ is the flux of angular momentum transferred from the BH to the disc inside the ergosphere."550 £f is defined through the magnetic torque produced by the BLE on both surfaces of the accretion disc Tup (?) where the limits of integration are two radii of the accretion disc with rp«rs., $H$ is defined through the magnetic torque produced by the BH on both surfaces of the accretion disc $T_{\mathrm{HD}}$ \citep{li02} where the limits of integration are two radii of the accretion disc with $r_1 < r_2$.551 Similar to the angular momentum conservation law. we can write the energy. conservation law as where on the left hancl-sicle. the first term describes the rate of the energy How through the disc inside the DII ergosphere. and the second term is the rate at which the magnetic torque per unit area of the dise does work. ZupOp (here O5 is the Ixeplerian angular velocity of the gas particles in the disc).," Similar to the angular momentum conservation law, we can write the energy conservation law as where on the left hand-side, the first term describes the rate of the energy flow through the disc inside the BH ergosphere, and the second term is the rate at which the magnetic torque per unit area of the disc does work, $T_{\mathrm{HD}}\Omega_{\mathrm{D}}$ (here $\Omega_{\mathrm{D}}$ is the Keplerian angular velocity of the gas particles in the disc)."552 The third term describes the energy How along the jets., The third term describes the energy flow along the jets.553 £7 is the specific energy of a gas particle having mass yr ancl orbiting in the same clirection as the DII rotation (?):: The Dux of angular momentum transferred from the DII to the disc inside the ergosphere by magnetic connection has the following expression (?):: where Wp is the Dux of the poloidal magnetic field lines which thread the surface of the disc inside the DII creosphere and Oy is the BL angular velocity., $E^{\dagger}$ is the specific energy of a gas particle having mass $\mu$ and orbiting in the same direction as the BH rotation \citep{bardeenPT}: The flux of angular momentum transferred from the BH to the disc inside the ergosphere by magnetic connection has the following expression \citep{li02}: where $\Psi_{\mathrm{D}}$ is the flux of the poloidal magnetic field lines which thread the surface of the disc inside the BH ergosphere and $\Omega_{\mathrm{H}}$ is the BH angular velocity.554 The derivation. of Eq. (1431) , The derivation of Eq. \ref{eq:li}) )555is based on the supposition that the accretion disc consists of highly conducting ionised gas., is based on the supposition that the accretion disc consists of a highly conducting ionised gas.556 This implies that (1) the accretiona disc resistance is neglected in coniparison with the DII surface resistance anc (ii) the magnetic field ines are frozen in the accretion disc. being transported. by he disc gas and rotating with Q5.," This implies that (i) the accretion disc resistance is neglected in comparison with the BH surface resistance and (ii) the magnetic field lines are frozen in the accretion disc, being transported by the disc gas and rotating with $\Omega_{\mathrm{D}}$ ."557 On the other hand. the angular velocity of the magnetic field lines threading the rorizon is Og. due to the elfect of the fraume-drageing at the DII horizon.," On the other hand, the angular velocity of the magnetic field lines threading the horizon is $\Omega_{\mathrm{H}}$, due to the effect of the frame-dragging at the BH horizon."558" For e,>0.35 and r2ru. 8gcOp. so that he DIL transfers encrey (and angular momentum) to the disc."," For $a_* > 0.35$ and $r\geq r_{\mathrm{ms}}$, $\Omega_{\mathrm{H}} > \Omega_{\mathrm{D}}$, so that the BH transfers energy (and angular momentum) to the disc."559 For a;«0.35. Og«Op. and this time the accretion disc transfers energy (and angular momentum) to the DIL," For $a_* < 0.35$, $\Omega_{\mathrm{H}} < \Omega_{\mathrm{D}}$, and this time the accretion disc transfers energy (and angular momentum) to the BH."560" For a,=0.35. Oy=Op: this condition implies that there is no energy (nor angular momentum) transfer between the DII and the accretion disc by magnetic connection."," For $a_* = 0.35$, $\Omega_{\mathrm{H}} = \Omega_{\mathrm{D}}$; this condition implies that there is no energy (nor angular momentum) transfer between the BH and the accretion disc by magnetic connection."561 We are now in the position to calculate the launching power of the jets with the help of the conservation laws previously derived., We are now in the position to calculate the launching power of the jets with the help of the conservation laws previously derived.562 First. we define the launching power of both jets as Integrating the equation of theenergy. conservation law (Eq.1 12))," First, we define the launching power of both jets as Integrating the equation of theenergy conservation law (Eq. \ref{eq:energy}) )"563 over the disc inside the BLE creosphere.SOs} we find the," over the disc inside the BH ergosphere, we find the"56410* s (for the long-duration GRBs).,$10^3$ s (for the long-duration GRBs).565 This diversity presumably reflects a dispersion in the progenitors and central engine properties., This diversity presumably reflects a dispersion in the progenitors and central engine properties.566 Perhaps the most impressive leature of GRBs are (heir brilliant luminosities ancl isotropic energy releases approaching (he rest mass of a neutron star. E.~10?! erg (INulkarniεἰal.1999:Andersen2000).," Perhaps the most impressive feature of GRBs are their brilliant luminosities and isotropic energy releases approaching the rest mass of a neutron star, $E_{\gamma,\rm iso}\sim 10^{54}\,$ erg \citep{kdo+99,ahp+00}."567. The quantity of energy imparted to the relativistic ejecta. Z4. and the quality parameterized bv the bulk Lorentz factor. P. are the two fundamental properties of GRB explosions.," The quantity of energy imparted to the relativistic ejecta, $E_{\rm568rel}$, and the quality parameterized by the bulk Lorentz factor, $\Gamma$, are the two fundamental properties of GRB explosions."569 In parüceular. extremely. hieh energies push the boundaries of current. progenitor and engine models. while low energies could point to a population of sources that is intermediate between GRBs and core-collapse supernovae.," In particular, extremely high energies push the boundaries of current progenitor and engine models, while low energies could point to a population of sources that is intermediate between GRBs and core-collapse supernovae."570" The (rue enerev release depends sensitively on the eeometry of the ejecta,", The true energy release depends sensitively on the geometry of the ejecta.571 1 GRB explosions are conical (as opposed to spherical) then (he (rue energy release is significantly below that inferred. by assuming isotropy., If GRB explosions are conical (as opposed to spherical) then the true energy release is significantly below that inferred by assuming isotropy.572 Starling with 9970508 (Waxman.Kulkarni&Frail1993:Rhoads1999) there has been growing observational evidence for collimatec outflows. coming mainly [rom achromatic breaks in the allerglow lightcurves.," Starting with 970508 \citep{wkf98,rho99}573 there has been growing observational evidence for collimated outflows, coming mainly from achromatic breaks in the afterglow lightcurves."574" In the conventional interpretation. the epoch at which the alterelow lehtcurves steepen (""break"") corresponds to the time at which P decreases below 6;!Fodhe inverse opening angle of the collimated outflow or ""jet (Ihoads1999)."," In the conventional interpretation, the epoch at which the afterglow lightcurves steepen (“break”) corresponds to the time at which $\Gamma$ decreases below $\theta_j^{-1}$, the inverse opening angle of the collimated outflow or “jet” \citep{rho99}."575. The break happens for (wo reasons: an edee effect. and lateral spreading of the jet which results in a significant increase of the swepl up mass.," The break happens for two reasons: an edge effect, and lateral spreading of the jet which results in a significant increase of the swept up mass."576 Many alterglows have /;~1—few davs. which are best measured [rom optical/near-IR. lishteurves (e.g. Harrison.efaf1999:INulkarni 1999)). while wider opening angles are easily measured [rom radio lighteurves (e.g. Frail1998:Dergerefaf 2001)).," Many afterglows have $t_j 577\sim 1-{\rm few}$ days, which are best measured from optical/near-IR lightcurves (e.g. \citealt{hbf+99,kdo+99,sgk+99}) ), while wider opening angles are easily measured from radio lightcurves (e.g. \citealt{wkf98,bdf+01}) )."578" Recently. Frailefaf.(2001) interred 8; for fifteen GRB alterglows rom measurements of /; and found the surprisingresult that Ly44, is strongly. correlated. with the beaming actor. f, ‘here. f,=||—cos(@;)| is the beaming fraction and E.i, is the 5-rav energy release inferred by: assuming isotropy."," Recently, \citet{fks+01} inferred $\theta_j$ for fifteen GRB afterglows from measurements of $t_j$ and found the surprisingresult that $E_{\gamma,\rm iso}$ is strongly correlated with the beaming factor, $f_b^{-1}$ ; here, $f_b\equiv[1-{\rm cos}(\theta_j)]$ is the beaming fraction and $E_{\gamma,\rm iso}$ is the $\gamma$ -ray energy release inferred by assuming isotropy."579" In effect. the true 5-rav energy release. B=fyE,i is approximately the same [or all the GRBs in their sample. with a value of about 5x10°? erg (assuming a constant circumburst density. 7)=0.1 *)."," In effect, the true $\gamma$ -ray energy release, $E_\gamma=f_bE_{\gamma,{\rm iso}}$ is approximately the same for all the GRBs in their sample, with a value of about $5\times 10^{50}$ erg (assuming a constant circumburst density, $n_0=0.1$ $^{-3}$ )."580" In the same vein. broad-band nodeling of several GRD alterglows indicates that the twpical blastwave kinetic energy in the adiabatic afterglow phase is E~5xLO"" erg. with a spread of about 1.5 orders of nagnitude (Panaitescu&Ixumar2002)."," In the same vein, broad-band modeling of several GRB afterglows indicates that the typical blastwave kinetic energy in the adiabatic afterglow phase is $E_b\sim 5\times58110^{50}$ erg, with a spread of about 1.5 orders of magnitude \citep{pk02}."582. Llowever. the general lack of hieh quality alterglow data severely limits the application of the broad-band modeling method.," However, the general lack of high quality afterglow data severely limits the application of the broad-band modeling method."583" separately, Kumar(2000) and Freedman&Waxman(2001) noted that the afterglow fhix at frequencies above the svnchrotron cooling Irequency. 7. isproportional to εαν. where e, is the fraction of the shock energy carried by electrons and dl,/dQ is the energy"," Separately, \citet{kum00} and \citet{fw01} noted that the afterglow flux at frequencies above the synchrotron cooling frequency, $\nu_c$ , isproportional to $\epsilon_e dE_b/d\Omega$, where $\epsilon_e$ is the fraction of the shock energy carried by electrons and $dE_b/584d\Omega$ is the energy"585have used the CTIO [-11 to obtain optical spectra of teu HID regions located in five of these dwarf irregular galaxies.,have used the CTIO 4-m to obtain optical spectra of ten HII regions located in five of these dwarf irregular galaxies.586 These spectra are used to measure chemical abuudances. which are compared to the HII region chemical abundances available for Local Group cls.," These spectra are used to measure chemical abundances, which are compared to the HII region chemical abundances available for Local Group dIs."587 Spectra were taken with the cassegrain R-C spectrograph (f/7.8) on the ςΓΙΟ [2n telescope ou the evening of 6 September 1997 and the first |alt ol T September 1997., Spectra were taken with the cassegrain R-C spectrograph $f$ /7.8) on the CTIO 4-m telescope on the evening of 6 September 1997 and the first half of 7 September 1997.588 High uunklity aud preciPitation prevented observations ou tlie secoud hidf oC7 September 1997 and 8 September 1907., High humidity and precipitation prevented observations on the second half of 7 September 1997 and 8 September 1997.589" Weised the Blue Air Sclunidt camera with a Loral tiiuned Bl, x Ls format CCD wih 15 qi pixels as the detector.", We used the Blue Air Schmidt camera with a Loral thinned 3K $\times$ 1K format CCD with 15 $\mu$ pixels as the detector.590 A 527 line min.! erating (IKPQGL3) 'esulted in a dispersion scale of |LOLA | and a spatial scale of pixel.|., A 527 line $^{-1}$ grating (KPGL3) resulted in a dispersion scale of 1.91 $^{-1}$ and a spatial scale of $^{-1}$.591 A àví( WG360: 3600 A) blocking fiter was usecl to suppress second order contamination iu the red., A uv (WG360; 3600 ) blocking filter was used to suppress second order contamination in the red.592 Useful data were collected over t1e wavelenetli range of 3600 — 7100A., Useful data were collected over the wavelength range of 3600 – 7100.593 Observations were obtained with a wwide slit observing at low air mass and near the parallactic angle in order to avoid problems of differential atmospheric refraction FFiippeuko 1982)., Observations were obtained with a wide slit observing at low air mass and near the parallactic angle in order to avoid problems of differential atmospheric refraction Filippenko 1982).594 The projected slit leugth is slightly larger than3., The projected slit length is slightly larger than.595 Bias frames. come flats. twilight sky lats. and He-Ne-Ar comparison exposures were taken at the beginniug aud eud of the nights.," Bias frames, dome flats, twilight sky flats, and He-Ne-Ar comparison exposures were taken at the beginning and end of the nights."596 Ou he first night. three staucard stars from the list of Oke (1990) were observed (2 x LTT 9191. 2 κ Feige 110. Cil58-100).," On the first night, three standard stars from the list of Oke (1990) were observed (2 $\times$ LTT 9491, 2 $\times$ Feige 110, G158-100)."597 LTT 9191 aud Feige 110 were observed on the second night., LTT 9491 and Feige 110 were observed on the second night.598" The stauda(d stars were oerved with a slit width of 6"" in order to avoid auy effects of cifferential atimosphieric refraction.", The standard stars were observed with a slit width of $^{\prime\prime}$ in order to avoid any effects of differential atmospheric refraction.599 Observations of a total of teu HII regious iu five clilerent galaxies were obtained as follows: 2 x 1800s observatious were made of E317-G17 #55 L10 (see paper 1) at au average airmass of 1.2 with an E-W slit position angle. 3+) x 1800s observaticos were made of E3[5-C9. 3233 (paper 1) at an average alirmass of 1.1 witl an E-W sli| position aigle. Εκ 1200s observatious were made of E171-G06 #22 (as numbered by liller 1996 at au average airmass of 1. [£iwith au E-W slit position augle. [o 1800s observations were mace of E173-C21 23 #11 (paper 1) at an average alrmass of 1.02 with an E-W slit position angle. aix 3 x 1800s«Pbservatious were mace of NGC 625 #55. #99. #118. aud 2] (paper 1) at all averaee aitmass of 1.06 with a position auele of —987.," Observations of a total of ten HII regions in five different galaxies were obtained as follows: 2 $\times$ 1800s observations were made of E347-G17 5 10 (see paper 1) at an average airmass of 1.2 with an E-W slit position angle, 3 $\times$ 1800s observations were made of E348-G09 3 (paper 1) at an average airmass of 1.1 with an E-W slit position angle, 4 $\times$ 1200s observations were made of E471-G06 2 (as numbered by Miller 1996) at an average airmass of 1.4 with an E-W slit position angle, 4 $\times$ 1800s observations were made of E473-G24 2 4 (paper 1) at an average airmass of 1.02 with an E-W slit position angle, and 3 $\times$ 1800s observations were made of NGC 625 5, 9, 18, and 21 (paper 1) at an average airmass of 1.06 with a position angle of $-$."600 Standard reduction procedu'es were folowed usiug the programs available within the ssvslelnn., Standard reduction procedures were followed using the programs available within the system.601 The staudard star observations from the two niglts were reduced iudepeucdently aud compare., The standard star observations from the two nights were reduced independently and compared.602 wasn—(u/IL)?and wy=kv the dynamical and byAlfvénn frequencies. respectively.,"by $\omega_{\rm dyn} \equiv (g/H)^{1/2}$and $\omega_{\rm A} \equiv \bb{k} \bcdot \bb{v}_{\rm A}$ the dynamical and Alfvénn frequencies, respectively."603" The inverse time-scales ΤιἘνμυ)”DE ... 7l=DDi(k-by. and n=οληes,2r» characterize. respectively. the diffusion of heat. and momentum field lines."," The inverse time-scales $\tci\equiv \kappa (\bb{k} \bcdot \hat{\bb{b}})^2(\gamma-1)/\gamma$ , $\tdi\equiv D604(\bb{k} \bcdot \hat{\bb{b}})^2$, and $\tvi\equiv 3 k_\parallel^2 v_{\rm th}^2/2\nu$ characterize, respectively, the diffusion of heat, particles, and momentum along magnetic field lines."605" We also define particles.two quantities which alongappear magneticnaturally when thermal and composition gradients are considered NT""(Ti).. ""m )("," We also define two quantities which appear naturally when thermal and composition gradients are considered ^2, ^2 )."60610) We are concerned with modes for which heat conduction is slow compared to the dynamical timescale and thus sae0» , We are concerned with modes for which heat conduction is slow compared to the dynamical timescale and thus $\omega_{\rm dyn} \gg \tci$.607"Because the timescales associated with viscous 7 which are to those involved in diffusion. are processes.longer than the comparableconduction timescales by an order of magnitude (Kunz2011).. we also have 7,1>noloom s "," Because the timescales associated with viscous processes, which are comparable to those involved in diffusion, are longer than the conduction timescales by an order of magnitude \citep{2011MNRAS.417..602K}, we also have $\tci > \tvi \sim \tdi$ ."608We further focus our attention on modes for which magnetic tension is unimportant. ie. kL«P7. and thus the Alfvénn frequency issmall compared to other inverse timescales.," We further focus our attention on modes for which magnetic tension is unimportant, i.e., $k_\parallel H\ll \beta^{1/2}$, and thus the Alfvénn frequency issmall compared to other inverse timescales."609 Since the plasma .} ranges from 107 from the centers of cool core clusters to 10! in the outskirts of the ICM (Carilli&Taylor2002).. there is a reasonable range of wavenumbers for which a local is sensible.," Since the plasma $\beta$ ranges from $10^2$ from the centers of cool core clusters to $10^4$ in the outskirts of the ICM \citep{2002ARA&A..40..319C}, there is a reasonable range of wavenumbers for which a local analysis is sensible."610 We can thus summarize the regime in which analysiswe are interested according to Co, We can thus summarize the regime in which we are interested according to >.611wa For a homogeneous the modes these conditions the plasma.overstable g-modes satisfyingstudied in Balbus&Re," For a homogeneous plasma, the modes satisfying these conditions encompass the overstable $g$ -modes studied in \citet{2010ApJ...720L..97B}."612ynoldsencompass(2010).. The set of (27))-(38)) allows us to address the behavior of these. as Equationswell as other new modes. in the of a in the mean molecular presenceand account non-vanishingself-consistently gradientfor the diffusion of tons along weightmagnetic field lines.," The set of Equations \ref{deltav}) \ref{d_rho_T_mu_eq0}) ) allows us to address the behavior of these, as well as other new modes, in the presence of a non-vanishing gradient in the mean molecular weight and account self-consistently for the diffusion of ions along magnetic field lines."613 Let us first consider the case in which there is no ion diffusion., Let us first consider the case in which there is no ion diffusion.614 Setting D=ν0 the relation corresponding to Equations (27)) to (37))dispersion faetorizes and possesses as non-trivial solutions two Alfvénn waves. with στtrey. and the roots of the polynomial |ai)=O0.. with coefficients where the approximate expressions for the coefficients follow from the general considerations outlined above.," Setting $D=\nu=0$ the dispersion relation corresponding to Equations \ref{deltav}) ) to \ref{deltamu}) ) factorizes and possesses as non-trivial solutions two Alfvénn waves, with $\sigma = \pm615i\omega_{\rm A}$ , and the roots of the polynomial +a_3=0, with coefficients a_1 =, a_2 = N^2, a_3 = ^2 - ) ^2, where the approximate expressions for the coefficients follow from the general considerations outlined above."616 The Routh-Hurwitz stability criteria that predict real— for the roots of the— cubic exclusively (42)) are: negativeeq20.03parts0. and aya03>0.," The Routh–Hurwitz stability criteria that predict exclusively negative real parts for the roots of the cubic Equation \ref{pol_a}) ) are: $a_1>0,617a_3>0,$ and $a_1a_2-a_3>0$."618 The first Equationcondition ts trivially satisfied while the other two imply Nr? « 0..(16) N? NT νετ) respectively.," The first condition is trivially satisfied while the other two imply ^2 < 0 N^2 ^2 > 0, respectively."619 To leading order. two of the solutions. of Equation. (42)) are given. by oztia1|(sαπο) 2410. 1.9. which correspond to gravity modes.," To leading order, two of the solutions of Equation \ref{pol_a}) ) are given by $\sigma\approx\pm i a_2^{1/2}+(a_3-a_1a_2)/2a_2$ , i.e., - (1 + ) , which correspond to gravity modes."620 In the absence of a gradient in the mean molecular weight. thesereduce to the," In the absence of a gradient in the mean molecular weight, thesereduce to the"621decreased relative to the original population.,decreased relative to the original population.622 Fherefore. the number decrease of the short period systems in Fig.," Therefore, the number decrease of the short period systems in Fig."623 6b also supports the prediction of period. decrease in the binary evolution., 6b also supports the prediction of period decrease in the binary evolution.624 By comparing the period histograms of the G. SG. and AIS systems between the ALG: and the field stars. Fig.," By comparing the period histograms of the G, SG, and MS systems between the MG and the field stars, Fig."625 7 also oesents evidence of decreasing orbital periods during the παν evolution., 7 also presents evidence of decreasing orbital periods during the binary evolution.626 It is noticeable that the histogram of €i systems for the field stars shows a sharp peak at 20 (/og?= 1.3) days., It is noticeable that the histogram of G systems for the field stars shows a sharp peak at 20 $logP=1.3$ ) days.627 There is a sharper decrease towards the shorter »eriods., There is a sharper decrease towards the shorter periods.628 Such a sharp decrease is not visible in the voung population (€i systems of MG)., Such a sharp decrease is not visible in the young population (G systems of MG).629 This sharp decrease could e caused by the missing svstems which are no longer on the ist: clue to evolution they became contact or semi contact systems., This sharp decrease could be caused by the missing systems which are no longer on the list; due to evolution they became contact or semi contact systems.630 The shifting of the peak of the normal distribution owards the shorter periods as an evidence of the orbital »eriod. decrease is clearly visible in the comparison ofthe €; eroups: perhaps among the SC., The shifting of the peak of the normal distribution towards the shorter periods as an evidence of the orbital period decrease is clearly visible in the comparison of the G groups; perhaps among the SG.631 Nevertheless. the opposite. hat is. the peak of the distribution of feld (AIS) svstems appears to be at longer periods with respect to the peak of the AIG (MS) systems.," Nevertheless, the opposite, that is, the peak of the distribution of f,eld (MS) systems appears to be at longer periods with respect to the peak of the MG (MS) systems."632 However. considering the [act hat evolving into contact. or semi-contact. configuration is most likely among the short period. MS systems rather than C svstenms. therefore it could. be normal to see the peak moving towards the longer periods in the statistics of the MS systems.," However, considering the fact that evolving into contact, or semi-contact configuration is most likely among the short period MS systems rather than G systems, therefore it could be normal to see the peak moving towards the longer periods in the statistics of the MS systems."633 The MS systems causing a peak at around the one day period in the MC. group must have evolved to contact or semi contact configurations so that the number of such systems appears to be less in the field stars., The MS systems causing a peak at around the one day period in the MG group must have evolved to contact or semi contact configurations so that the number of such systems appears to be less in the field stars.634 Therefore. the peak appears to have moved towards the longer periods for [eld (AIS) binaries.," Therefore, the peak appears to have moved towards the longer periods for field (MS) binaries."635 One may ask why the peak of field (CMS). binaries indicates a shorter period than the peak of field (Cr) binaries if evolution to contact configuration is cllective for up to 10 davs. which is indicated by the histogram of the field. (64) binaries.," One may ask why the peak of field (MS) binaries indicates a shorter period than the peak of field (G) binaries if evolution to contact configuration is effective for up to 10 days, which is indicated by the histogram of the field (G) binaries."636 Here. we must remember that neither the younger (MG) nor the older. (field) group are very homogeneous.," Here, we must remember that neither the younger (MG) nor the older (field) group are very homogeneous."637 There could. be older binaries among the possible MC members. so they are called: possible. and there could. be many voung binaries among the field stars.," There could be older binaries among the possible MG members, so they are called possible, and there could be many young binaries among the field stars."638 Phe kinematical criteria only select. possible MG members., The kinematical criteria only select possible MG members.639 IH is possible that unscelected stars could be voung systems but not satisfy the AIG criteria., It is possible that unselected stars could be young systems but not satisfy the MG criteria.640 This complication. however. is not to such a degree that despite this heterogeneous nature. the period shortening effect of the binary evolution is perceptible on our histograms.," This complication, however, is not to such a degree that despite this heterogeneous nature, the period shortening effect of the binary evolution is perceptible on our histograms."641 It is a challenge for future studies to select the older svstems from the possible MCG moenmboers and select the vounger svstems from the field stars for a better comparison of the vounger and the older groups of binaries., It is a challenge for future studies to select the older systems from the possible MG members and select the younger systems from the field stars for a better comparison of the younger and the older groups of binaries.642 Orbital periods decreasing with age are confirmed. by the kinematical data., Orbital periods decreasing with age are confirmed by the kinematical data.643 The older population (field. stars) has been divided. into three period. ranges (Table 5) and the space velocity dispersions ancl kinematical ages were calculated. for the short (Fog?< OLS). intermediate (0.8.«log?x 1.7) and the long period (1.7«fog?< 3.0) systems.," The older population (field stars) has been divided into three period ranges (Table 5) and the space velocity dispersions and kinematical ages were calculated for the short $logP\leq0.8$ ), intermediate $0.8<logP\leq1.7$ ) and the long period $1.7<logP\leq3.0$ ) systems."644 The increase of the dispersions. implving older ages. towards the shorter. periods appears to support. the," The increase of the dispersions, implying older ages, towards the shorter periods appears to support the"645unable to detect iinibalo clouds with a x: 10 kpc dianeter due to beam dilution.,unable to detect minihalo clouds with a $\le$ 10 kpc diameter due to beam dilution.646 The GBT data were reduced in the standard nanucr using the GDTIDL aud data reduction packages., The GBT data were reduced in the standard manner using the GBTIDL and data reduction packages.647 Iun order to match our velocity resolution o the expected Lnewidths of clouds iu he eroup. spectra were simoothed to a chauncl spacing of 21.1 kz. correspondiug to a velocity resolution of 5.2 lan |.," In order to match our velocity resolution to the expected linewidths of clouds in the group, spectra were smoothed to a channel spacing of 24.4 kHz, corresponding to a velocity resolution of 5.2 km $^{-1}$."648 A reference spectrum or each of the observation sessions was mace using an observation of au enüssion-free region. usually from the edees of the maps.," A reference spectrum for each of the observation sessions was made using an observation of an emission-free region, usually from the edges of the maps."649 The reference spectruni was then used to perform a (sigual-reference}/refereuce calibration of cach pixel., The reference spectrum was then used to perform a (signal-reference)/reference calibration of each pixel.650 The calibrated spectra were scaled by the systems temperature. corrected for atmospheric opacity and GBT efficiency.," The calibrated spectra were scaled by the system temperature, corrected for atmospheric opacity and GBT efficiency."651 We adopted the GBT efficiency equation (1) from Laneston&Turner(2007) with a zenith atinospheric opacity 7 = 0.009., We adopted the GBT efficiency equation (1) from \citet{lang07} with a zenith atmospheric opacity $\tau_{0}$ = 0.009.652 Velocities are in the kincmatic LSR velocity frame., Velocities are in the kinematic LSR velocity frame.653 The frequency ranec observed was relatively free of REI. with less than of all spectra adversely affected.," The frequency range observed was relatively free of RFI, with less than of all spectra adversely affected."654 The spectra exhibiting RFI were identified by tabulating the RAIS noise level iu channels free of neutral hydrogen ΟΙΒΙΟΙ., The spectra exhibiting RFI were identified by tabulating the RMS noise level in channels free of neutral hydrogen emission.655 Spectra that showed Ligh values of RAIS noise across Imany channels were flageed aud. removed., Spectra that showed high values of RMS noise across many channels were flagged and removed.656 Observations were eridded using the AIPS task SDIMC. which also averages polarizations.," Observations were gridded using the AIPS task SDIMG, which also averages polarizations."657 After wuplitude calibration and exidding. a lst-order polynomial was fit to hue-free regions of the spectra aud subtracted from the eridded spectra using the AIPS task IMLIN.," After amplitude calibration and gridding, a 1st-order polynomial was fit to line-free regions of the spectra and subtracted from the gridded spectra using the AIPS task IMLIN."658 Only the channels in the velocity range -10 to -NOO lau &5 were used for the ft., Only the channels in the velocity range -400 to -800 km $^{-1}$ were used for the fit.659 This siuple baseline fit was extrapolated to the »oxitive velocity range. where ealaxies anake a baseline fit unreliable.," This simple baseline fit was extrapolated to the positive velocity range, where galaxies make a baseline fit unreliable."660" This vascline velocity range for the fit vielded a flat vascline for areas free of stroug contiuuun radio sources, Which is true of the majority of the region."," This baseline velocity range for the fit yielded a flat baseline for areas free of strong continuum radio sources, which is true of the majority of the region."661 The effective angular resolution. determined from naps of 3€286. is 9157+0.," The effective angular resolution, determined from maps of 3C286, is $\pm$."66205/.. To convert to units of flux density. we observed the calibration source 3C286. whose flux deusitv is 1157 + 0.91 Jv at 1.H8 CGUIz (Ottetal.199D.," To convert to units of flux density, we observed the calibration source 3C286, whose flux density is 14.57 $\pm$ 0.94 Jy at 1.418 GHz \citep{ott94}."663. The calibration roni Ik to Jw was derived by mapping 3C286 iu he same wav that the maps were produced., The calibration from K to Jy was derived by mapping 3C286 in the same way that the maps were produced.664 After all correctious for the GBT efficieucy aud the napping process. the scale factor from EK/Douu o Jv/Demu nuages is 13 4.0.08.," After all corrections for the GBT efficiency and the mapping process, the scale factor from K/Beam to Jy/Beam images is 0.43 $\pm$ 0.03."665 Due to the vatclavork nature of the observations. the RAIS LOISC varies considerably across the datacubo. ranging between 6-30 iuJv/beani," Due to the patchwork nature of the observations, the RMS noise varies considerably across the datacube, ranging between 6-30 mJy/beam."666 The average RAIS noise in the final data cube is 20 11Jv per 21.1 sz channel., The average RMS noise in the final data cube is 20 mJy per 24.4 kHz channel.667 Figure 3 shows the map sensitivity as a function of position., Figure \ref{RMSfig} shows the map sensitivity as a function of position.668 The iustrmucutal yavalucters are sunmnmnarizediu Table 2. aud Table BU eives a sunmuarv of the observations.," The instrumental parameters are summarized in Table 2, and Table 3 gives a summary of the observations."669 The spectral line images are availableon-linc?., The spectral line images are available.670. Iu order to detect either clouds associated with dark matter nünihalos. or cold accretion. a larec-area map is required.," In order to detect either clouds associated with dark matter minihalos, or cold accretion, a large-area map is required."671 clouds in dark matter munihalos are predicted to be found at distances of up to 1 Alpe from a iajor halo (Blitzctal.1999)., clouds in dark matter minihalos are predicted to be found at distances of up to 1 Mpc from a major halo \citep{blitz99}.672. Cold accretion clouds aid iuteractiou-eenerated clouds are expected to be contained within a ~ 60 kpe radius around large ealaxies (Chynowcethetal.2008:eres&IIeru-quist 2009).," Cold accretion clouds and interaction-generated clouds are expected to be contained within a $\sim$ 60 kpc radius around large galaxies \citep{chy08, Dusan:2009}."673.. Our map lias a projected size of 150 spe « 12 Alpe. which is adequate to detect all hree phenomena.," Our map has a projected size of 480 kpc $\times$ 1.2 Mpc, which is adequate to detect all three phenomena."674" Spectral maps were made in the velocity range overlapped by all observations. from -890 to 1320 au ο,"," Spectral maps were made in the velocity range overlapped by all observations, from -890 to 1320 km $^{-1}$."675 Spectra naps were visually inspected or possible new clouds., Spectral maps were visually inspected for possible new clouds.676 We required a cloud candidate to v0 Visible im oat least two chaunels. herefore the lowes velocity width that could be detected was LO ans 3.," We required a cloud candidate to be visible in at least two channels, therefore the lowest velocity width that could be detected was 10 km $^{-1}$."677 For each candidate. a ot of inteusitv versus velocity was also produced and checked.," For each candidate, a plot of intensity versus velocity was also produced and checked."678 At the locations of strong continui radio sources. the linear spectral bascline fit was occasionally poor.," At the locations of strong continuum radio sources, the linear spectral baseline fit was occasionally poor."679 Iun these cases. the spectra would show a broad slope. > 100 lan | wile. either increasing or cecreasing with frequency.," In these cases, the spectra would show a broad slope, $>$ 400 km $^{-1}$ wide, either increasing or decreasing with frequency."680 Candidates in the regious with poor spectral baseline were also discarded., Candidates in the regions with poor spectral baseline were also discarded.681 Ouly 26 of the more than 10.000 CBT beams covering the map showed spectra with poor spectral baselines.," Only 26 of the more than 10,000 GBT beams covering the map showed spectra with poor spectral baselines."682classifications are nuclei of tidally disrupted uncleated dwarf cllipticals (dE.Ns).,"classifications are nuclei of tidally disrupted nucleated dwarf ellipticals (dE,Ns)."683 NAunenieal simulatious by Bassino et al. (199 D) , Numerical simulations by Bassino et al. \cite{bass}) )684reveal that such nuclei ean survive he dissolution in the eravitational feld even curing he eutie lifetime of the nuiverse and would appear as Dhunünous elobular cluster-like objects, reveal that such nuclei can survive the dissolution in the gravitational field even during the entire lifetime of the universe and would appear as luminous globular cluster-like objects.685 The nuclear uaguitudes of all Virgo dE.Ns (Diugeeli Cameroun 1991)). for example. fall indeed in the magnitude surface xiehtness sequence defined by the elobular clusters (0.9. Bineecli 1991)).," The nuclear magnitudes of all Virgo dE,Ns (Binggeli Cameron \cite{bing91}) ), for example, fall indeed in the magnitude – surface brightness sequence defined by the globular clusters (e.g. Binggeli \cite{bing94}) )."686" At the distance of the Fornasx cluster. hese objects would hardly be resolved and can only be ""ucovered by spectroscopic observations."," At the distance of the Fornax cluster, these objects would hardly be resolved and can only be uncovered by spectroscopic observations."687 Iu the first oper (πλου. ot al. 1998..," In the first paper (Hilker et al. \cite{hilk},"688 hereafter Paper D a ealaxy catalog with photometric properties and surface briehtuess profiles for galaxies iu sclectec fields of the central Fornax cluster has been preseuted., hereafter Paper I) a galaxy catalog with photometric properties and surface brightness profiles for galaxies in selected fields of the central Fornax cluster has been presented.689 Au excess population of galaxies near NCC 1399. the ceutral ealaxy of the cluster. has con found as conmparec o the other Fornax fields aud o absolute backerounm fields.," An excess population of galaxies near NGC 1399, the central galaxy of the cluster, has been found as compared to the other Fornax fields and to absolute background fields."690 The photometric analysis iis shown that most of he excess galaxies have sizes and surface brightuesses which are more typical for background spirals are ellipticals than for dwart ellipticals., The photometric analysis has shown that most of the excess galaxies have sizes and surface brightnesses which are more typical for background spirals and ellipticals than for dwarf ellipticals.691 However. as diseussec vefore. plotometric properties alone are not sufficicut to distinguish between background galaxies and high surface xiehtuess dwarf galaxies in the Fornax cluster.," However, as discussed before, photometric properties alone are not sufficient to distinguish between background galaxies and high surface brightness dwarf galaxies in the Fornax cluster."692 This paper oeseuts redshift determinations of a bright sub-suuple of our plhotometiie catalog (Paper I) to investigate the ature of the mentioned excess galaxies;, This paper presents redshift determinations of a bright sub-sample of our photometric catalog (Paper I) to investigate the nature of the mentioned excess galaxies.693 Furthermore. liue iudices for the objects that have been identified as Foruax. nembers were measured.," Furthermore, line indices for the objects that have been identified as Fornax members were measured."694 Tn the following the expression ‘racial velocity” has οσο used for the measurement of ez imsteac of redshift. (jns aware of the fact that the true radial velocity or high - ifers from οἱ depending on the applied cosmological ποσο].," In the following the expression `radial velocity' has been used for the measurement of $cz$ instead of redshift, being aware of the fact that the true radial velocity for high $z$ differs from $cz$ depending on the applied cosmological model."695 Previous radial velocity measurements of galaxies iu he Fornax cluster brighter than Br=15.5 mag were xeseuted dy Jones Jones (1980)). Lauberts (1982)) aud Richter Sadler (1985)).," Previous radial velocity measurements of galaxies in the Fornax cluster brighter than $B_T = 15.5$ mag were presented by Jones Jones \cite{jone}) ), Lauberts \cite{laub}) ) and Richter Sadler \cite{rich}) )."696 They are compiled iu the Fornax Cluster Catalog (FCC) by Ferguson (1989))., They are compiled in the Fornax Cluster Catalog (FCC) by Ferguson \cite{ferg89}) ).697 Except for he eiut galaxies. there are only two ealaxies that overlap with our sample: NGC 1396 and FCC 222. two bright dE.Ns.," Except for the giant galaxies, there are only two galaxies that overlap with our sample: NGC 1396 and FCC 222, two bright dE,Ns."698 Ποια Mould (1991)) took spectra of 10 dE.Ns in the Fornax cluster: one of hese is in common with our salple.," Held Mould \cite{held}) ) took spectra of 10 dE,Ns in the Fornax cluster; one of these is in common with our sample."699 Sect., Sect.700 2.3. and d eive a detailed description of the observations. data reduction. aud velocity determination.," 2, 3, and 4 give a detailed description of the observations, data reduction, and velocity determination."701 The resulting radial velocities and the analysis of individual objects are presented iu Sect., The resulting radial velocities and the analysis of individual objects are presented in Sect.702 5., 5.703 The main results are sunimnuiuilzed in Sect., The main results are summarized in Sect.704 6., 6.705 The observations have been performed with the 2.51 DuPout telescope at the Las Campanas Observatory. Chile. during the niehts of 79 December. 1996.," The observations have been performed with the 2.5m DuPont telescope at the Las Campanas Observatory, Chile, during the nights of 7–9 December, 1996."706 The iiulti-fiber spectrograph from Shectinman (1989)) has been used., The multi-fiber spectrograph from Shectman \cite{shec}) ) has been used.707 The fiele of view is 1.5« degree., The field of view is $1.5\times1.5$ degree.708 The aperture size of each fiber is 2 arcsec dn diameter on the sky., The aperture size of each fiber is 2 arcsec in diameter on the sky.709 The fibers Were connected with a Boller Chiveus spectrograph coupled to a 2DFrutti detector (2DE)., The fibers were connected with a Boller Chivens spectrograph coupled to a 2DFrutti detector (2DF).710 With a blaze anele of 9°15’ we eot a spectral range of 2500Α-6800AÀ., With a blaze angle of $9^\circ45\arcmin$ we got a spectral range of -.711. The spectra are projected to a 1520105 pixel area. with a dispersion of ~ 23 À-  aud a final resolution of =A.," The spectra are projected to a $1520\times1024$ pixel area, with a dispersion of $\simeq$ 2–3 $\cdot$ $^{-1}$ and a final resolution of $\simeq$."712 From our catalog 125 galaxies brighter than V.=20.0 mae were selected., From our catalog 125 galaxies brighter than $V = 20.0$ mag were selected.713 Accurate positions have been obtained by using reference stars from the Caude Star Catalog., Accurate positions have been obtained by using reference stars from the Guide Star Catalog.714 Astrometric solutions vielded positions with accuracics better than 073., Astrometric solutions yielded positions with accuracies better than $0\farcs3$.715 In addition. three bright dE.Ns have been included from the FCC (Ferguson 1989)). uamely ECC," In addition, three bright dE,Ns have been included from the FCC (Ferguson \cite{ferg89}) ), namely FCC"716model (Chiang Goldreich 1997) they. adopted.,model (Chiang Goldreich 1997) they adopted.717 Inoue. Oka. Nakamoto (2009) showed that (he three laver approach is necessary to obtzin an accurate midplane temperature.," Inoue, Oka, Nakamoto (2009) showed that the three layer approach is necessary to obtain an accurate midplane temperature."718 Figures 8. and 9 show the midplane temperature and the surface density. profiles by our caleulation and by Giraud Lin (2007)., Figures \ref{temperature_Garaud_Lin} and \ref{surface_density_Garaud_Lin} show the midplane temperature and the surface density profiles by our calculation and by Garaud Lin (2007).719 These figures clearly show that the midplane temperatures by both models agree well in (he inner opticallv-thick region. whereas our result is lower than that by Garand Lin (2007) in the outer optically-thin region.," These figures clearly show that the midplane temperatures by both models agree well in the inner optically-thick region, whereas our result is lower than that by Garaud Lin (2007) in the outer optically-thin region."720 similarly. the surface density distributions in both models agree in the inner region. whereas there is a dillerence in the outer region.," Similarly, the surface density distributions in both models agree in the inner region, whereas there is a difference in the outer region."721 We conclude (hat if we are concerned wilh detailecl evolution of the snow line in the opticallv-thin phases in which planet formation may proceed. we need to numerically calculate the temperature. (," We conclude that if we are concerned with detailed evolution of the snow line in the optically-thin phases in which planet formation may proceed, we need to numerically calculate the temperature. ("7221 we are concerned with opticallv-thick phases or qualitative features of the snow line evolution in entire phases. semi-analviical calculations are sullicient.),"If we are concerned with optically-thick phases or qualitative features of the snow line evolution in entire phases, semi-analytical calculations are sufficient.)"723 In the early phase in which the snow line mierates inward. the main heating source al (he midplane around the snow line is the viscous dissipation (Fig. 2)).," In the early phase in which the snow line migrates inward, the main heating source at the midplane around the snow line is the viscous dissipation (Fig. \ref{temperature_profile8_0}) )."724 So. the temperature is determined bv the viscous heating and the radiative cooling.," So, the temperature is determined by the viscous heating and the radiative cooling."725" The diffusive radiative enerev (ransfer gives the midplane temperature. Z,. as (e.g... Nakamoto Nakagawa 1994). where 7, is (he optical depth for the midplane ancl o is (he Stefan-Bollzimann constant."," The diffusive radiative energy transfer gives the midplane temperature, $T_{c}$, as (e.g., Nakamoto Nakagawa 1994), where $\tau_{c}$ is the optical depth for the midplane and $\sigma$ is the Stefan-Boltzmann constant."726 substituting 7.=&X/2 (& is the Rosseland mean opacity of the disk medium) and noticing, Substituting $\tau_{c} =\kappa \Sigma/2$ $\kappa$ is the Rosseland mean opacity of the disk medium) and noticing727Over the past decade it has become clear that the supermassive black holes (Bilis) founc at the centres of virtually all galaxies with spheroidal components. have masses that are coupled to the properties of their. host ealaxies (Alagorrianctal.1998:Ferrarese&Alerritt2000: 2007)..,"Over the past decade it has become clear that the supermassive black holes (BHs) found at the centres of virtually all galaxies with spheroidal components, have masses that are coupled to the properties of their host galaxies \citep{magg98,ferr00,trem02,hari04,hopk07b}."728 Adcditionallv. there exists evidence that BIL masses are coupled to the properties of the dark matter haloes in which they reside (Eerrarese2002:Booth&Schave2010).," Additionally, there exists evidence that BH masses are coupled to the properties of the dark matter haloes in which they reside \citep{ferr02,boot10}."729 Further correlations between quasar activity. (c.g.Bovle&Verlevich1998) and the evolution of the cosmic star formation rate (c.g.Macauetal.1900) provide evidence that there exists a link between galactic star formation and accretion onto a central AGN.," Further correlations between quasar activity \citep[e.g.][]{boyl98}730 and the evolution of the cosmic star formation rate \citep[e.g.][]{mada96} provide evidence that there exists a link between galactic star formation and accretion onto a central AGN."731 It has long been recognised that thegrowth. of DlIIs is likely selt-regulated. (Silk&Rees1998). and that these tight correlations indicate that the growth of DlIIs is tightly. intertwined with the physical processes that. drive. galaxy formation., It has long been recognised that thegrowth of BHs is likely self-regulated \citep{silk98} and that these tight correlations indicate that the growth of BHs is tightly intertwined with the physical processes that drive galaxy formation.732 Llowever. despite a wide varicty of theoretical ancl observational studies. the origin of these relations is still debated.," However, despite a wide variety of theoretical and observational studies, the origin of these relations is still debated."733 The study of the evolution of the BL scaling relations therefore represents a crucial aspect of the galaxy formation process that may provide us with additional ebues regarding the physical processes that οἶνο rise to the DII scaling relations., The study of the evolution of the BH scaling relations therefore represents a crucial aspect of the galaxy formation process that may provide us with additional clues regarding the physical processes that give rise to the BH scaling relations.734 Addressing these questions observationally is challenging., Addressing these questions observationally is challenging.735 Due to their extremely high. luminosities. right quasars provide a promising route to measuring DII masses at high redshift through the widths of low-ionization ines that are associated with the broad-line region close o the DII and using the assumption of virial equilibrium (c.g.Vestergaard2002).," Due to their extremely high luminosities, bright quasars provide a promising route to measuring BH masses at high redshift through the widths of low-ionization lines that are associated with the broad-line region close to the BH and using the assumption of virial equilibrium \citep[e.g.][]{vest02}."736. It has. however. been claimed that his procedure systematically: uncerestimates BLL masses (Jarvis&AleLure2002).," It has, however, been claimed that this procedure systematically underestimates BH masses \citep{jarv02}."737. Measuring. galaxy masses lor hese objects is very dillieult. as the DII. outshines the ealaxy bv a Large [actor (seee.g.thediscussionin.Merlonietal. 2010)., Measuring galaxy masses for these objects is very difficult as the BH outshines the galaxy by a large factor \citep[see e.g.\ the discussion in ][]{merl09}.738. Since AGN surveys are biased: towards more massive black holes. selection cllects also need to be taken into account (e.g.Shen&Welly2009:Bennertetal. 2010).. which can make it οΠο to distinguish between evolution," Since AGN surveys are biased towards more massive black holes, selection effects also need to be taken into account \citep[e.g.][]{shen09,benn10}, , which can make it difficult to distinguish between evolution"739"WIMP annihilation produces energy at a rate per unit volume where 17, is the WIMP number density. m, is the WIMP mass. and p, is the WIMP energy density.","WIMP annihilation produces energy at a rate per unit volume where $n_\chi$ is the WIMP number density, $_\chi$ is the WIMP mass, and $\rho_\chi$ is the WIMP energy density."740" The final annihilation products typically are electrons, photons, and neutrinos."," The final annihilation products typically are electrons, photons, and neutrinos."741" The neutrinos escape the star, while the other annihilation products are trapped in the dark star, thermalize with the star. and heat it up."," The neutrinos escape the star, while the other annihilation products are trapped in the dark star, thermalize with the star, and heat it up."742 The luminosity from the DM heating ts where {ο is the fraction of the annihilation energy deposited in the star (not lost to neutrinos) and dV is the volume clement., The luminosity from the DM heating is where $f_Q$ is the fraction of the annihilation energy deposited in the star (not lost to neutrinos) and $dV$ is the volume element.743" The DM heating rate in Dark Stars scales as the square of the WIMP density times the annihilation cross section, as can be seen from Eq.(1))."," The DM heating rate in Dark Stars scales as the square of the WIMP density times the annihilation cross section, as can be seen from \ref{eq:Q}) )."744" The WIMP density inside the star adjusts in response to changes in the star’s baryonic mass profile, since the gravitational potential well of the star is determined by the baryons. ("," The WIMP density inside the star adjusts in response to changes in the star's baryonic mass profile, since the gravitational potential well of the star is determined by the baryons. ("745The DM profile responds to changes in the gravitational potential due to the conservation of adiabatic invariants.),The DM profile responds to changes in the gravitational potential due to the conservation of adiabatic invariants.)746" In this paper. we investigate the dependence of Dark Star properties on these two quantities: (1) the annihilation cross section and (1) the density of the halo within which the star forms, as characterized by the concentration parameter."," In this paper, we investigate the dependence of Dark Star properties on these two quantities: (i) the annihilation cross section and (ii) the density of the halo within which the star forms, as characterized by the concentration parameter."747 For a short list of papers by various other authors that have continued the work of ? and explored the repercussions of DM heating in the first stars sce 22222??? ," For a short list of papers by various other authors that have continued the work of \citet{DS2} and explored the repercussions of DM heating in the first stars see \citet{Iocco2008,DMfs3, DMfs1, DMfs2, DMfs4, Gondolo2010, Ripamonti:2010ab, Sivertsson2010}. ."748Their potential observability has been discussed in ???..," Their potential observability has been discussed in \citet{SMDS, Zackrisson2010, Zackrisson2010b}."749 The possibility that DM annihilation might have effects on. stars was actually considered in the ‘80s by various authors such as ???..," The possibility that DM annihilation might have effects on stars was actually considered in the $`80s$ by various authors such as \citet{krauss, bouquet, salatisi}."750 More recently the effect on today’s stars has been re-examined under the assumption that DM is made of WIMPs (????) or within the hypothesis of inelastic dark matter (?)..," More recently the effect on today's stars has been re-examined under the assumption that DM is made of WIMPs \citep{moskalenko, scott1, bertone, scott2} or within the hypothesis of inelastic dark matter \citep{Hooper2010}."751 Recent measurements of cosmic ray positrons and electrons in the GeV-TeV range couldhave significant implications on our understanding of dark matter (DM)., Recent measurements of cosmic ray positrons and electrons in the GeV-TeV range couldhave significant implications on our understanding of dark matter (DM).752" The PAMELA collaboration reported ae flux excess in the cosmic energy spectrum from 10 to 100 GeV, reinforcing what was previously observed up to an energy of 50 GeV bythe HEAT experiment (?).."," The PAMELA collaboration \citep{PAMELA, Adriani2010} reported a $e^{+}$ flux excess in the cosmic energy spectrum from $10$ to $100$ GeV, reinforcing what was previously observed up to an energy of $50$ GeV bythe HEAT experiment \citep{HEAT}. ."753 The, The754Understanding star formation and the origin of the Sellar initial ass function GAIF) remains a major Cidleuge in astrophysics.,Understanding star formation and the origin of the stellar initial mass function (IMF) remains a major challenge in astrophysics.755 Various observations have sugeested a strong sinibuitv between the IME and t1ο lnass function of eravitationally bound structures i molecular οouds. identified as the prestellacore massas function. (CME).?. the first: one beine Qoshifted downwards compared to the second oue by à ucarly iiass-independent factor of about 2-3~ (Motte et al.," Various observations have suggested a strong similarity between the IMF and the mass function of gravitationally bound structures in molecular clouds, identified as the prestellar mass function (CMF), the first one being shifted downwards compared to the second one by a nearly mass-independent factor of about 2-3 (Motte et al."756. 1998.UC Testi| SareeutSare 1993.008. .Johnstone: ct al.," 1998, Testi Sargent 1998, Johnstone et al."757. 2000. 2001. ;André et al.," 2000, 2001, André et al."758 2007. Alvéss et al.," 2007, Alvéss et al."759 2007. Nutter Ward-Thoupsou 2007. Simpson et al.," 2007, Nutter Ward-Thompson 2007, Simpson et al."760 2008. Enoch et al.," 2008, Enoch et al."761 2008. Aucdié et al.," 2008, André et al."762 E2009. 42010).," 2009, 2010)."763 Thesed obscrvatious: sugeestUN that the IME is: essentially deteruined by the xoperties of the turbulent selt-exavitatiug eas in the parcxt iiolecular cloud. which leads to tie core fornation.," These observations suggest that the IMF is essentially determined by the properties of the turbulent self-gravitating gas in the parent molecular cloud, which leads to the core formation."764" Then. magneticallv«riven. outflows are probabY orosposible for the subsequeut ποο between thο core mass and the stellar Lllass, Yiclding the aforcmetioned ~ 30-50% cffiicicucy .chaviour characteristic of the €""NIE. to IME evolution (Matzuer AlcI&ee 2000)."," Then, magnetically-driven outflows are probably responsible for the subsequent mass-loss between the core mass and the stellar mass, yielding the aforementioned $\sim 30$ $50\%$ efficiency factor characteristic of the CMF to IMF evolution (Matzner McKee 2000)."765 An anaIvtical theory for the formation aud the mass distributioi of unbound overdeuse ΟΠΗΣ. and eravitationallv Ὡςnud cores directly inherited from the elobal physical xoperties of the molecular cloud has receutlv been fornalized by HIeuuebelle Chabricr (2008. COs: 2009. TIC’09) aud has received some support from numerical sia:ous of compressible turbulence ainied at exploring this jsste (Scluuidt et al.," An analytical theory for the formation and the mass distribution of unbound overdense ""clumps"" and gravitationally bound ""cores"" directly inherited from the global physical properties of the molecular cloud has recently been formalized by Hennebelle Chabrier (2008, HC08; 2009, HC09) and has received some support from numerical simulations of compressible turbulence aimed at exploring this issue (Schmidt et al."766 2010)., 2010).767" Alternatively, some authors (Date Bonnell 2005 and references therein) have sugeestedOO that the CALF is esseutiallv determined by the various environmental conditious iu the star' fornune region (nearbs 7onüasslve stars. colpectitive accretion between prestellar cores. diniu:al nu|eractions....). Le.: bs ili various: processes converting sas into stars"," Alternatively, some authors (Bate Bonnell 2005 and references therein) have suggested that the CMF is essentially determined by the various environmental conditions in the star forming region (nearby massive stars, competitive accretion between prestellar cores, dynamical interactions,...), i.e. by the various processes converting gas into stars."768 Accordingly.| these authors argue“oOH that» thereway islu no correlation*woods1 betweenοwatas theB CALF' aud as als possible∙ link. between these Wo distributheIMF. wi: inevitably he Anded ont ; hCSC variousTALIOUS juseenvironmentalYOH factorασ," Accordingly, these authors argue that there is no correlation between the CMF and the IMF, as any possible link between these two distributions will inevitably be wiped out by these various environmental factors."769"τον, ἐuotherQer notablωτοιο difference between these two scenarios of star formation is the reason for the uuversal behaviour of 1ο IME and he near Vvoinvariance of the location of the peak of the CALF/IME ii various star foriumeg regions.", Another notable difference between these two scenarios of star formation is the reason for the universal behaviour of the IMF and the nearly invariance of the location of the peak of the CMF/IMF in various star forming regions.770 Tn the first scenario. this universa property arises fron je universal oliiof⋅ the∖ tur⋅ actornleut spectrum. which tends to orm clouds with similar (Larsou-like)ies... while he peak invariance arises frou the simular )ut opposite dependence of the Jeans mass aud Mach inber upon," In the first scenario, this universal property arises from the universal behaviour of the turbulent spectrum, which tends to form clouds with similar (Larson-like), while the peak invariance arises from the similar but opposite dependence of the Jeans mass and Mach number upon"771 Tn the first scenario. this universa property arises fron je universal oliiof⋅ the∖ tur⋅ actornleut spectrum. which tends to orm clouds with similar (Larsou-like)ies... while he peak invariance arises frou the simular )ut opposite dependence of the Jeans mass aud Mach inber uponu," In the first scenario, this universal property arises from the universal behaviour of the turbulent spectrum, which tends to form clouds with similar (Larson-like), while the peak invariance arises from the similar but opposite dependence of the Jeans mass and Mach number upon"772adopted in subsequent analysis in 833.,adopted in subsequent analysis in 3.773" By using tlie best-fit CLFs for extrapolation. we estimate the number of MSPs in each cluster with Lyica,>0.5 mJy kpc?."," By using the best-fit CLFs for extrapolation, we estimate the number of MSPs in each cluster with $L_{\rm 1.4 GHz}>0.5$ mJy $^{2}$."774 Almost all the MSPs in GCs considered in this study have their racio luminosities above this threshold level., Almost all the MSPs in GCs considered in this study have their radio luminosities above this threshold level.775 Since the errors of both g and Ny are considered in (he extrapolation. the uncertainties of (hese estimates are larger than (hat ol No.," Since the errors of both $q$ and $N_{0}$ are considered in the extrapolation, the uncertainties of these estimates are larger than that of $N_{0}$."776 These population estimates are also given in Table 2.., These population estimates are also given in Table \ref{gc_lf_par}.777 For those clusters which have been searched deep enough that the sensitivity is close to this threshokl. e... 47 Tuc. the population esGimates based on the CLFs are close to the observed number of uncovered MSPs.," For those clusters which have been searched deep enough that the sensitivity is close to this threshold, e.g., 47 Tuc, the population estimates based on the CLFs are close to the observed number of uncovered MSPs."778 On the other hand. for those clusters where pulsation searches have not vet reached (his sensitivity level. our results provide predictions for their MSP populations when searches towards these clusters become sufficiently deep.," On the other hand, for those clusters where pulsation searches have not yet reached this sensitivity level, our results provide predictions for their MSP populations when searches towards these clusters become sufficiently deep."779 Apart from estimating the CLFs for these individual GCs. we have also constructed the Iuninositw function by combining all the cluster MISPs (i.e. 16 pulsars in total) used in this studs.," Apart from estimating the CLFs for these individual GCs, we have also constructed the luminosity function by combining all the cluster MSPs (i.e. 76 pulsars in total) used in this study."780 The combined CLES of the selected cluster MSP population ave displaved in Figure L.., The combined CLFs of the selected cluster MSP population are displayed in Figure \ref{gal_gc_clf}.781 In the combined distribution. we have observed (here is a Curn-off for the pseucdo-Inminosities smaller than ~1.5 mJy kpe?.," In the combined distribution, we have observed there is a turn-off for the pseudo-luminosities smaller than $\sim1.5$ mJy $^{2}$."782 Ilessels et al. (, Hessels et al. (7832007) have also observed the same behaviour in an independent analysis.,2007) have also observed the same behaviour in an independent analysis.784 In order to compare our result will Hessels et al. (, In order to compare our result with Hessels et al. (785"2007). we followed )eir procedure and usecl a mininnun Iuninositv cut-off of L4,4cu;=1.5 mJy Κρο for the filling procedure.","2007), we followed their procedure and used a minimum luminosity cut-off of $L_{\rm 1.4~GHz}=1.5$ mJy $^{2}$ for the fitting procedure."786 The results of this analysis are summarized in Table 3.., The results of this analysis are summarized in Table \ref{gal_gc_clf_par}.787 The logarithmic slope inferred [rom (his collective sample is ο=—0.83£0.05. which is consistent with the value deduced by Hessels et al. (," The logarithmic slope inferred from this collective sample is $q=-0.83\pm0.05$, which is consistent with the value deduced by Hessels et al. ("7882007) (1.6. 4=—0.71 £0.03) within lo error.,2007) (i.e. $q=-0.77\pm0.03$ ) within $1\sigma$ error.789 llessels et al. (, Hessels et al. (7902007) have further compared the huninositw distribution of the MSP population in GCs with those of other pulsar populations.,2007) have further compared the luminosity distribution of the MSP population in GCs with those of other pulsar populations.791 They suggested that the distribution of cluster MSPs is marginally consistent with that of the MSPs in the Galactic field reported bv Corde Chernoll (1997) and Lyne et al. (, They suggested that the distribution of cluster MSPs is marginally consistent with that of the MSPs in the Galactic field reported by Corde Chernoff (1997) and Lyne et al. (7921995).,1998).793 However. the samples adopted in these investigations contain not more (han 22 pulsars.," However, the samples adopted in these investigations contain not more than 22 pulsars."794 This relative small sample size may introduce bias in (he analvsis and inlerence., This relative small sample size may introduce bias in the analysis and inference.795 Thanks to the extensive pulsar searches in the recent vears. the whole pulsar population has been significantly increased.," Thanks to the extensive pulsar searches in the recent years, the whole pulsar population has been significantly increased."796 Iessels et al. (, Hessels et al. (7972007) have also compared (heir results wilh a more updated pulsar sample reported by Lorimer οἱ al. (,2007) have also compared their results with a more updated pulsar sample reported by Lorimer et al. (7982006) which used 1008 pulsars in (their study.,2006) which used 1008 pulsars in their study.799 Lorimer et al. (, Lorimer et al. (8002006) have found a distribution of dlogN~—Q.8dlogL for their sample. which is very similar to that inferred from (he cluster population as reported by Iessels et al. (,"2006) have found a distribution of $d\log N\sim -0.8d\log L$ for their sample, which is very similar to that inferred from the cluster population as reported by Hessels et al. ("8012007) and this paper.,2007) and this paper.802 Nevertheless. (he sample used bv Lorimer οἱ al. (," Nevertheless, the sample used by Lorimer et al. ("8032006) consist of non-recveled canonical pulsars.,2006) consist of non-recycled canonical pulsars.804 It is more instructive (o compare the CLF of the cluster MSP population aud the ISPs in the Galactic field. both of which have undergone (he recvcling processes in binary. svsteuis.," It is more instructive to compare the CLF of the cluster MSP population and the MSPs in the Galactic field, both of which have undergone the recycling processes in binary systems."805 Therefore. we construct the huninosity [function for the MSP population in the Galactic field with all the available," Therefore, we construct the luminosity function for the MSP population in the Galactic field with all the available"806and 0.03<byxO07hApe+.,"and $0.03 \leq k_0 \leq 0.07\,h\,\,{\mathrm Mpc^{-1}}$."807" ""Fo illustrate this case. we show in table L (second line) a particular example: h—d45.O4—0.3.p=L3.ky=0.03Alpe ((Qy Ls chosen to obtain the preferred value ρα=28.10."". and p iis as low as possible. in order to maximize small scales anisotropies)."," To illustrate this case, we show in table I (second line) a particular example: $h=0.5,\ \Omega_{\Lambda}=0.3,\ p=1.3,\ 808k_0=0.03 \,h\,\,{\mathrm Mpc^{-1}}$ $\Omega_{\Lambda}$ is chosen to obtain the preferred value $A_{peak}=28\times 10^{-6}$, and $p$ is as low as possible, in order to maximize small scales anisotropies)."809 We also give anexample of the case A=0. p=2.1. though it is excluded by CAT.," We also give anexample of the case $\Lambda=0$, $p=2.1$, though it is excluded by CAT."810 Phe corresponding power spectra are plotted in Fig. 3..," The corresponding power spectra are plotted in Fig. \ref{figPK},"811 the CALB anisotropics in bie. 4.., the CMB anisotropies in Fig. \ref{figCMB}.812 This type of model could. be easily. discriminated: by he forthcoming improvements of redshift surveys and CMD observations., This type of model could be easily discriminated by the forthcoming improvements of redshift surveys and CMB observations.813 The former might state about the little well oreclictecl in the (4) aaround &2(0.1.0.2).Alpe1," The former might state about the little well predicted in the $P(k)$ around $k\simeq (0.1-0.2) \,h\,\,{\mathrm Mpc^{-1}}$."814 The atter will soon inclicate: This mocel is very unlikely to be degenerate with some other one (for instance. other cosmological parameters plus tilted spectrum) from the point of view ofCALB anisotropies. because it predicts à. tremencously high ratio between multipoles at scales /~200 aand /~600 (recall that. in contrast with tilted.»«1. or with double inflationary niocdels. small scales are lowered however intermediate scales are preserved).," The latter will soon indicate: This model is very unlikely to be degenerate with some other one (for instance, other cosmological parameters plus tilted spectrum) from the point of view of CMB anisotropies, because it predicts a tremendously high ratio between multipoles at scales $l\sim200$ and $l\sim600$ (recall that, in contrast with tilted, $n<1$, or with double inflationary models, small scales are lowered however intermediate scales are preserved)."815 A similar analysis can be performed. for higher fh vvalues., A similar analysis can be performed for higher $h$ values.816 Since increasing /7 Howers the €CMD naiultipoles. p iis more restricted. now by the constraints on small scales anisotropies.," Since increasing $h$ lowers the CMB multipoles, $p$ is more restricted now by the constraints on small scales anisotropies."817 At 0.6. possible models have 0.4<Oyx 0.6. 1.pX15 aand 0.03<Aux0.075Alpe*.," At $h$ =0.6, possible models have $0.4 \leq \Omega_{\Lambda} \leq 0.6$ , $1 \leq p \leq 1.5$ and $0.03 \leq k_0 \leq 0.07\,h\,\,{\mathrm Mpc^{-1}}$."818" ""The first peak reaches lower values as well: 2610""Xous27.]0 "".", The first peak reaches lower values as well: $26 \times 10^{-6} \leq A_{peak} \leq 27\times 10^{-6}$ .819" When h=0.7. we find 0.5<OXOyQT.1«Xp<l4.0.08<kyO07hMpe and furthermore 24510-υ-.Ἡἳ""."," When $h=0.7$, we find $0.5 \leq \Omega_{\Lambda} \leq 0.7,~1\leq p \leq 1.4,~8200.03 \leq k_0 \leq 0.07~h~{\rm Mpc}^{-1}$ and furthermore $24.5\times 10^{-6} \leq A_{peak} \leq 26\times 10^{-6}$."821 The resulting allowed region in the (. O4) plane is plotted in Fig. 2..," The resulting allowed region in the $h$ , $\Omega_\Lambda$ ) plane is plotted in Fig. \ref{figWINDOW}."822 For a few successfull examples. we give the results of the tests in Table 1. Again. we first consider the case —0.5.," For a few successfull examples, we give the results of the tests in Table I. Again, we first consider the case $h=0.5$."823 When 0.45< FT. one can find some (p.Au) iin good agreement with ax. Vo aanel v," When $0.45\leq\Omega_{\Lambda}\leq0.7$ , one can find some $(p,k_0)$ in good agreement with $\sigma_8$, $V_{50}$ and $\chi^2$."824 For instance. when ον=0.6. the allowed region is ὑπὸXopo1 aand 0.003—kux0.045Ape+. In the [as subsection. it was found that for p> l.the most compelling constraint was on ax.," For instance, when $\Omega_{\Lambda}=0.6$, the allowed region is $0.75 \leq p \leq 1$ and $0.003 \leq k_0 \leq 0.04\,h\,\,{\mathrm Mpc^{-1}}$ In the last subsection, it was found that for $p>1$, the most compelling constraint was on $\sigma_8$."825 Now the three tests play an importan xwt in the definition of the allowed region., Now the three tests play an important part in the definition of the allowed region.826 Indeed. the above mentioned sharp maximum appears in Z(&). preceeded a arger scales by a depression at ye1.2 ((the inverted bump of the case p> 1).," Indeed, the above mentioned sharp maximum appears in $P(k)$, preceeded at larger scales by a depression at $y\approx 1.2$ (the inverted bump of the case $p>1$ )."827 As à result. the power spectrum. L(A) thas no pronounced second maximum at the place where i exists for p=1. namely &c0.05οthAlpe1.," As a result, the power spectrum $P(k)$ has no pronounced second maximum at the place where it exists for $p=1$, namely $k\simeq 0.05~\Omega^{-1}h~{\rm Mpc}^{-1}$."828 Note tha his depression would become very pronounced in the case p-<ld. dts position in this limit being given by y=V/2.5p (Starobinsky. 1992).," Note that this depression would become very pronounced in the case $p\ll1$, its position in this limit being given by $y=\sqrt{2.5 p}$ (Starobinsky, 1992)."829 When fy0.015Alpe|. the bulk velocity. is sometimes too small due to this. little depression.," When $k_0>0.015\,h\,\,{\mathrm Mpc^{-1}}$, the bulk velocity is sometimes too small due to this little depression."830 On the contrary. when fy«0.015Alpe*. the maximum often generates excessive bulk velocities.," On the contrary, when $k_0<0.015\,h\,\,{\mathrm Mpc^{-1}}$, the maximum often generates excessive bulk velocities."831 As expected. the CAIB anisotropies are aniplifiec by both the comological constant ancl the primordial spectrum step.," As expected, the CMB anisotropies are amplified by both the comological constant and the primordial spectrum step."832 The basic picture is that the C's are enhanced by a [actor p. [for /2250/aolac1200054.," The basic picture is that the $C_l$ 's are enhanced by a factor $p^2$ for $l>2 k_0/a_0 H_0\simeq12\,000k_0$."833 When do=0.010.02Alpe1 . the first⋅ peak is. enhanced. by the maximum. of the primordial spectrum. so its location and maximum value are highly dependent on all parameters. including Au aand p ((in contrast with the case p«1). The secondary »vks are Cgiven by an almost [lat regiono of the primordial spectrum. so they depend on all parameters. Ay exceptect.," When $k_0=0.01-0.02\,h\,\,{\mathrm Mpc^{-1}}$ , the first peak is enhanced by the maximum of the primordial spectrum, so its location and maximum value are highly dependent on all parameters, including $k_0$ and $p$ (in contrast with the case $p<1$ ).The secondary peaks are given by an almost flat region of the primordial spectrum, so they depend on all parameters, $k_0$ excepted."834" As in the previous subsection. we can use the last CAT point to reduce the allowed. window. confidently excluding any C; curve that would not pass cl)=2110"" (the lo vvalue) in the range 550</120."," As in the previous subsection, we can use the last CAT point to reduce the allowed window, confidently excluding any $C_l$ curve that would not pass $A_l=21\times 10^{-6}$ (the $-1\sigma$ value) in the range $550<l<720$."835 This rules out many low p vvalues for a given 4., This rules out many low $p$ values for a given $\Omega_{\Lambda}$.836 In fact models with O4-0.5 ddo not survive., In fact models with $\Omega_{\Lambda}>0.5$ do not survive.837 At O4=0.5 wwe find the allowed window: 0.85<px1. 0.003<by«0.04Alpe5.," At $\Omega_{\Lambda}=0.5$ we find the allowed window: $0.85 \leq p \leq 1$, $0.003<k_0<0.04\,h\,\,{\mathrm Mpc^{-1}}$."838 Similarily. when h=0.6. successfull models can be found or 0.55<Oy0.65. extending the validity range of the scale invariant model," Similarily, when $h=0.6$, successfull models can be found for $0.55\leq\Omega_{\Lambda}\leq0.65$, extending the validity range of the scale invariant model."839 At O4=0.65 tthe allowed window is LSO«p0.85. 0.003<byx0.045Alpe|.," At $\Omega_{\Lambda}=0.65$ the allowed window is $0.80<p<0.85$, $0.003 \leq k_0 \leq 0.04\,h\,\,{\mathrm Mpc^{-1}}$."840 Finally. when b=0.7. 065<OXx0.75 is allowed.," Finally, when $h=0.7$, $0.65\leq\Omega_{\Lambda}\leq0.75$ is allowed."841 At O4=0.72 wwe ind OO«pO85. (LOO3<ky0.045Alpe1.," At $\Omega_{\Lambda}=0.72$ we find $0.80<p<0.85$, $0.003 \leq k_0 \leq 0.04\,h\,\,{\mathrm Mpc^{-1}}$."842 These results are also summarized in Fig. 2.., These results are also summarized in Fig. \ref{figWINDOW}. .843 Table Ll contains a ew examples. aid for one of them the power spectrum and CABanisotropies are illustrated in Fig.," Table I contains a few examples, and for one of them the power spectrum and CMBanisotropies are illustrated in Fig."844 3. and Fig. 4.., \ref{figPK} and Fig. \ref{figCMB}.845 At first sight. the case p«1 iis not interesting since it does not extend very much the allowed region for. (0: OX): good results are obtained for cosmological paranictcrs that are not in conllict with the scale invariant model.," .At first sight, the case $p<1$ is not interesting since it does not extend very much the allowed region for $h$ , $\Omega_{\Lambda}$ ): good results are obtained for cosmological parameters that are not in conflict with the scale invariant model."846 The interest of thep«I ssteplike spectrum lies in the prediction of specific features. namely:," The interest of the $p<1$ steplike spectrum lies in the prediction of specific features, namely:"847"spectral indices, 8s and 6p.","spectral indices, $\beta_{\rm848S}$ and $\beta_{\rm D}$."849" After adding the above foreground maps (smoothed with a 9.16-degree beam at Nsgide=128 and degraded to Λίιας--ι6) to the CMB-plus-noise map, we mask the simulated sky by theWMAP P06 mask (f.i,=73%) (Pageetal.2007)."," After adding the above foreground maps (smoothed with a 9.16-degree beam at $N_{\rm side}=128$ and degraded to $N_{\rm side=16}$ ) to the CMB-plus-noise map, we mask the simulated sky by the P06 mask $f_{sky}=73\%$ \citep{page/etal:2007}."850". The norm of the pixel vector, is 2259x2, where 2259 is the number of pixels [Q,U],outside the P06 mask."," The norm of the pixel vector, $Q$ $U$ ], is $2259\times 2$, where 2259 is the number of pixels outside the P06 mask."851" In order to mask the covariance matrix, we use the techniquedescribed in Appendix D of Pageetal.(2007):: we compute an inverse of 6144x matrix and reduce it to 4518x matrix using Equation (D7) of Pageetal. (2007).. ("," In order to mask the covariance matrix, we use the techniquedescribed in Appendix D of \citet{page/etal:2007}: we compute an inverse of $6144\times 6144$ matrix and reduce it to $4518\times 4518$ matrix using Equation (D7) of \citet{page/etal:2007}. ("852Note that there is a typo in this equation: D should be replaced by D.),Note that there is a typo in this equation: $D$ should be replaced by $D^{-1}$ .)853" In Figure 6, we show the B-mode power spectra measured from the PSM (Neide= 128) at 100 GHz outside the P06 mask."," In Figure \ref{fig:clfg}, we show the $B$ -mode power spectra measured from the PSM $N_{\rm side}=128$ ) at 100 GHz outside the P06 mask."854" The total foreground power spectrum has [(|+1)CPP/(2z)=107!pK? at 1<10, which is 250 and 2500 times larger than the primordial B- spectra with r—0.01 and 0.001, respectively."," The total foreground power spectrum has $l(l+1)C_l^{BB}/(2\pi)\approx85510^{-1}~\mu{\rm K}^2$ at $l\lesssim 10$, which is 250 and 2500 times larger than the primordial $B$ -mode spectra with $r=0.01$ and 0.001, respectively."856" The problem seems formidable; however, as we show below, the simple cleaning method can reduce the foreground-induced bias in r to Ar&0.002(«0.001) with the P06(extended) mask."," The problem seems formidable; however, as we show below, the simple cleaning method can reduce the foreground-induced bias in $r$ to $\Delta r\approx8570.002(<0.001)$ with the P06(extended) mask."858" Before we use our full likelihood function given by Equation (9)), let us first try a simpler version and show that it actually fails."," Before we use our full likelihood function given by Equation \ref{eq:fulllike}) ), let us first try a simpler version and show that it actually fails."859" For the moment (only within this we fix the amplitude of the scalar E modes, ie., subsection),s=1, and consider cleaning dust using a map at 240 GHz. "," For the moment (only within this subsection), we fix the amplitude of the scalar $E$ modes, i.e., $s=1$, and consider cleaning dust using a map at 240 GHz. ("860will not be discussed in this subsection.),Synchrotron will not be discussed in this subsection.)861" Our(Synchrotron model is thus As we described at the end of Section 3,, we ignore noise at 240 GHz."," Our model is thus As we described at the end of Section \ref{sec:method}, we ignore noise at 240 GHz."862" We then fit the 240 GHz map to the 100 GHz map: Minimizing x?=[Q',U']TC!U'] with respect to Qp gives the following least-square solution: As the polarization signal is dominated by scalar E modes, we can set r=0 when computing the covariance matrix C in this equation. ("," We then fit the 240 GHz map to the 100 GHz map: Minimizing $\chi^2 = [Q',U']^T{\bm C}^{-1}[Q',U']$ with respect to $\alpha_{\rm D}$ gives the following least-square solution: As the polarization signal is dominated by scalar $E$ modes, we can set $r=0$ when computing the covariance matrix ${\bm C}$ in this equation. ("863"In practice, we used T'input.)","In practice, we used $r_{\rm input}$ .)"864" Finally, we maximize the likelihood given in Equation (9)) with respect to r, with s=1 and ap given by the above least-square solution."," Finally, we maximize the likelihood given in Equation \ref{eq:fulllike}) ) with respect to $r$, with $s=1$ and $\alpha_{\rm D}$ given by the above least-square solution."865 The left panel of Figure 7 shows the values of r and αρ obtained from many random realizations of noise and CMB skies. (, The left panel of Figure \ref{fig:r-alpha} shows the values of $r$ and $\alpha_{\rm D}$ obtained from many random realizations of noise and CMB skies. (866The input tensor-to-scalar ratio is rinput= 0.003.),The input tensor-to-scalar ratio is $r_{\rm input}=0.003$ .)867" There is a clear correlation betweenr and ap, indicating a failure of this algorithm."," There is a clear correlation between$r$ and $\alpha_{\rm D}$, indicating a failure of this algorithm."868 This correlation is caused by a chance correlation between foreground and the dominant scalar E modes (Chiangetal.2008;Ef- 2009).," This correlation is caused by a chance correlation between foreground and the dominant scalar $E$ modes \citep{chiang/naselsky/coles:2008,efstathiou/gratton/paci:2009}."869. The correlation disappears when we set CP”=0., The correlation disappears when we set $C_l^{EE}=0$.870 This result motivates our treating the amplitude of scalar modes as a nuisance parameter., This result motivates our treating the amplitude of scalar modes as a nuisance parameter.871 The right panel of Figure 7 shows the results when s is treated as a nuisance parameter and marginalized over., The right panel of Figure \ref{fig:r-alpha} shows the results when $s$ is treated as a nuisance parameter and marginalized over.872" For this, we have maximized the likelihood given by Equation by varying r, s, and ap simultaneously."," For this, we have maximized the likelihood given by Equation \ref{eq:fulllike}) ) by varying $r$, $s$ , and $\alpha_{\rm D}$ simultaneously."873 'The correlation (9))between r and op has disappeared., The correlation between $r$ and $\alpha_{\rm D}$ has disappeared.874 How well was dust cleaned?,	 How well was dust cleaned?875 We have repeated this one- foreground cleaning test for various values of input from 0.001 to 0.1., We have repeated this one-component foreground cleaning test for various values of $r_{\rm input}$ from 0.001 to 0.1.876" The results are shown in Table 1:: in all cases, the method recovers r successfully."," The results are shown in Table \ref{tab:dustcleaning}: : in all cases, the method recovers $r$ successfully."877 We are now ready to include synchrotron., We are now ready to include synchrotron.878 Our model is, Our model is879Chinese records which states it lasted until the niuth Iunar month. namely 22 October through 19 November.,"Chinese records which states it lasted until the ninth lunar month, namely 22 October through 19 November."880 Of course the description of util’ the ninth 1ioutli could mean that its visibility was only up to the 9th mouth and uot cliring it., Of course the description of `until' the ninth month could mean that its visibility was only up to the 9th month and not during it.881 Stephenson&Creen(2002) interpret the duration of the guest star until the Chinese 9th lunar mouth (22 October 19 November) as meaning the star remained visible iuto the the ninth mouth., \citet{SG02} interpret the duration of the guest star `until' the Chinese 9th lunar month (22 October – 19 November) as meaning the star remained visible into the the ninth month.882 However. on October 22 it would have set just some 15 minutes after sunset aud to be visible uudoer these circumstances the star would lave required a relatively bright object. thereby. tuplving a brilliant object mouths earlier at maxi light.," However, on October 22 it would have set just some 15 minutes after sunset and to be visible under these circumstances the star would have required a relatively bright object, thereby implying a brilliant object months earlier at maximum light."883 Iu an attempt to resolve this dilemma. Stepleuson aud Green propose a recording error of one mouth regarding the objects disappearance (the sth instead of the 9th mouth). allowing the object to set well after sunset ina dark sky.," In an attempt to resolve this dilemma, Stephenson and Green propose a recording error of one month regarding the object's disappearance (the 8th instead of the 9th month), allowing the object to set well after sunset in a dark sky."884 Cousicering the visibility of Scorpius’ asterisiuWer in late September and carly October 393 x allowing for atmospheric extinction. Clark&Stephenu-son(1977) estimate a inaxinuuni apparent magnitude around 0 imag or perhaps a bit brighter. noting that hac the star been much brighter than this the Chinese likely would have included a coment onu its brightuess.," Considering the visibility of Scorpius' asterism in late September and early October 393 and allowing for atmospheric extinction, \citet{CS77} estimate a maximum apparent magnitude around $0$ mag or perhaps a bit brighter, noting that had the star been much brighter than this the Chinese likely would have included a comment on its brightness."885 Iu Table 5.. we list the expected biightuesses cigh mouths (dav 210) after παπα Πο for several different. (οον subtypes assunidug a distance and sly equal to that of RN J1713.7-3916.," In Table \ref{tab:lc}, we list the expected brightnesses eight months (day 240) after maximum light for several different CCSN subtypes assuming a distance and $A_{\rm V}$ equal to that of RX J1713.7-3946."886 The table shows tha in all cases the supernovalG would have been brighter than 0 Sco (i = 1.87). the brightest star iu the tail of Scorpius.," The table shows that in all cases the supernova1G would have been brighter than $\theta$ Sco $m_{\rm v}$ = 1.87), the brightest star in the tail of Scorpius."887 Thus. if RN. J17123.7-3916 is à. CCSN and was the guest star seen in 393. then its expected brightucss between 0 and [1.5 mag would make it possible for i to stav visible a little longer but perhaps not past the uniddle of October as the Chinese reported.," Thus, if RX J1713.7-3946 is a CCSN and was the guest star seen in 393, then its expected brightness between 0 and +1.5 mag would make it possible for it to stay visible a little longer but perhaps not past the middle of October as the Chinese reported."888 A nore serious problem with this scenario is that there is no mention ofthe star being recovered carly in 391 AD when it would have again become visible from behind the Sun., A more serious problem with this scenario is that there is no mention of the star being recovered early in 394 AD when it would have again become visible from behind the Sun.889 Caven average huuinositv decline. times commonly seen for core-collapse supernovae. a RN J1713.7-3916 supernova should have becu casily visible to observers with an apparent brightuess between Ist and 3rd mas. comparable to the stars in Scorpiuss tail (sec Table 5)).," Given average luminosity decline times commonly seen for core-collapse supernovae, a RX J1713.7-3946 supernova should have been easily visible to observers with an apparent brightness between 1st and 3rd mag, comparable to the stars in Scorpius's tail (see Table \ref{tab:lc}) )."890 Although the very brief Chinese record should not be interpreted as complete. it is unusual that there were no further reports of its contiuued presence. especially since reports of other guest stars returmine from behind the Suu exist. such as SN 185.," Although the very brief Chinese record should not be interpreted as complete, it is unusual that there were no further reports of its continued presence, especially since reports of other guest stars returning from behind the Sun exist, such as SN 185."891 Uowever. in light of the considerable spread im the decline rates of SN Type Ih.c events. the possibility exists that the supernova faded below widespread notice when it came from around the Sun three months later.," However, in light of the considerable spread in the decline rates of SN Type Ib,c events, the possibility exists that the supernova faded below widespread notice when it came from around the Sun three months later."892 Some subhuninous eveuts exhibit a steepemime of their licht curve at times bevoud 120 davs. diminishing iu visual brightuess fairly rapidly.," Some subluminous events exhibit a steepening of their light curve at times beyond 120 days, diminishing in visual brightness fairly rapidly."893 For iustance. had à RX J1712.7-3916 supernova followed the light curves of the SN 2005cs or SN 20091ad (Pastorelloetal.2009:Fraser2011) ). it would have faded 2 5 mae one vear past maxi. and hence possibly would have been nissed.," For instance, had a RX J1713.7-3946 supernova followed the light curves of the SN 2005cs or SN 2009md \citealt{Pastorello2009,Fraser2011}) ), it would have faded $>$ 5 mag one year past maximum, and hence possibly would have been missed."894 Iu closing. we note that if SN 393 had instead becu a Type Ia event aud unrelated to the CCSN reimnaut RN J1713.7-39 sinülar brightuess issues at late times would apply.," In closing, we note that if SN 393 had instead been a Type Ia event and unrelated to the CCSN remnant RX J1713.7-3946, similar brightness issues at late times would apply."895 That16. is. at dav 210 a Type Ia guest star would appear & 6 magnitudes füuter than at masini light (Leibundgutetal.1991).," That is, at day 240 a Type Ia guest star would appear $\simeq$ 6 magnitudes fainter than at maximum light \citep{Lei91}."896.. À peak brightucss of 0 niae estimated by Stephenson&Green(2002) would mean the guest star would approach the naked eve visibility liit of 6th mae some mouths after παΙΙΙ., A peak brightness of 0 mag estimated by \citet{SG02} would mean the guest star would approach the naked eye visibility limit of 6th mag some months after maximum.897 This would make the star even more difficult to view im carly October 393 since it would be less than 5 degrees above the western horizon at the eud of twilight aud thus subject to significant atmospheric attenuation., This would make the star even more difficult to view in early October 393 since it would be less than 5 degrees above the western horizon at the end of twilight and thus subject to significant atmospheric attenuation.898 Relevant to the apparent brightness of the SN. 393 euest star. there is an European text written around 398 AD by the Roman poet Claudian describing a bright star about which he said was plainly visible even iu midday a few veis earlier.," Relevant to the apparent brightness of the SN 393 guest star, there is an European text written around 398 AD by the Roman poet Claudian describing a bright star about which he said was plainly visible even in midday a few years earlier."899 Claucian viewed this star as an omen of Tlonorius being made emperor in thereby iuiplviug that it occurred around 393 AD., Claudian viewed this star as an omen of Honorius being made emperor in thereby implying that it occurred around 393 AD.900 The possibility of a connection between the brigl: star described in the Claudian poeni aud the Chinese euest star of 393 AD has been mace by several authors including Drever(1913). Stothers(1977). Barret(1978).. Clark&Stephenson(1982).. Clark(1981).. aud TGuusev(2006).," The possibility of a connection between the bright star described in the Claudian poem and the Chinese guest star of 393 AD has been made by several authors including \cite{Dreyer1913}, \citet{Stothers77}, \citet{Barrett78}, \citet{CS82}, \citet{Clark84}, and \citet{Ramsey2006}."901. Towever. uo mention of this reference is found in the most recent astronomical reviews of ancieu euest star observations iucludiug discussions directly regarding the suspected SN of 393 (Clark&Steplen-2002:Green&Steplieuson2003:Wang 2006).," However, no mention of this reference is found in the most recent astronomical reviews of ancient guest star observations including discussions directly regarding the suspected SN of 393 \citep{CS75,CS77,Wang97,SG02,GS03,Wang06}."902. Tuterestinely. this Roman record has loug been kuown. eoing back some L10 vears to the time of Tycho Bralic.," Interestingly, this Roman record has long been known, going back some 440 years to the time of Tycho Brahe."903 A vear after he sighted his supernova of 1572. Tycho learned about the Claudian text through a letter from Paul IIlüuzel. a longtime friend aud then mavor of Augsbure. to the hnuuaulist Ilerouvinous Wolf in which Ibuuzel mentions the Claudian text about a bright new star in the ska. auch like the 1572 star (Brahe1602).," A year after he sighted his supernova of 1572, Tycho learned about the Claudian text through a letter from Paul Hainzel, a longtime friend and then mayor of Augsburg, to the humanist Hieronymous Wolf in which Hainzel mentions the Claudian text about a bright new star in the sky, much like the 1572 star \citep{Tycho1602}."904.. Tycho never reached a definitive conclusion about the meaning of the Claudiau pocin. i... whether it was a description of a comet. a daytime sightine of Venus. or something else. but it was obvious. he concluded. that new stars like the oue le saw iu 1572 sometimes appear in the heavens (Drever1913).," Tycho never reached a definitive conclusion about the meaning of the Claudian poem, i.e., whether it was a description of a comet, a daytime sighting of Venus, or something else, but it was obvious, he concluded, that new stars like the one he saw in 1572 sometimes appear in the heavens \citep{Dreyer1913}."905. The relevant passages about the new star appear in Claudian’s The Fourth Coustlship of Honorius., The relevant passages about the new star appear in Claudian's `The Fourth Consulship of Honorius'.906 Since to our knowledge this text has never been preseuted in the astronomical literature. we reproduce it here.," Since to our knowledge this text has never been presented in the astronomical literature, we reproduce it here."907 According to the Enelish translation of the Latin by (1922).. the pertinent passages read:," According to the English translation of the Latin by \citet{Platnauer22}, , the pertinent passages read:"908that au increase of 10 to 100 times in the total power of CGRCs would lead to values of Pty~1 for these sources.,that an increase of 10 to 100 times in the total power of GRGs would lead to values of $P_{CN} \sim 1$ for these sources.909 Note that a two order of nagnuitude increase in the total power of GRGs would also be consistent with the size diagram im Fie. 11.., Note that a two order of magnitude increase in the total power of GRGs would also be consistent with the power-size diagram in Fig. \ref{pd}.910 We finally note hat apparent correlations of the core radio power with the source redshift aud Luear size are eutirelv due to biases introduced iu the sample selection through the Zux deusitv and the aneular size hlnuüts. and to the correlation between the total aud the core radio power (Paper Dj.," We finally note that apparent correlations of the core radio power with the source redshift and linear size are entirely due to biases introduced in the sample selection through the flux density and the angular size limits, and to the correlation between the total and the core radio power (Paper I)."911 This bias arises from the need for larger sources to have more flux deusitv to exceed the nina surface brightuess iuit of the NVSS., This bias arises from the need for larger sources to have more flux density to exceed the minimum surface brightness limit of the NVSS.912 As au example. we show in Fig.," As an example, we show in Fig."913 9 the core power as a functiou of the source linear size. which could be interpreted as sources being intrinsically larger due to an unusually üegher core power (Copal-Ixxislina et al. 19893).," \ref{D_Pc5}914 the core power as a function of the source linear size, which could be interpreted as sources being intrinsically larger due to an unusually higher core power (Gopal-Krishna et al. \cite{gopal1}) )."915 However. 16 dashed line represeuts how the limits iu flux density aneular size translate iuto this plot. taking also iuto account the total power vs core power correlation nentioned above.," However, the dashed line represents how the limits in flux density and angular size translate into this plot, taking also into account the total power vs core power correlation mentioned above."916 We note that it is fully consistent with i6 observed trend. so that it is possible to conclude iat the source size is unrelated to the core power. m aerectuent with studies on CRCs (Issvara-Clhaudra Saikia 1999)).," We note that it is fully consistent with the observed trend, so that it is possible to conclude that the source size is unrelated to the core power, in agreement with studies on GRGs (Ishwara-Chandra Saikia \cite{ishwara}) )."917 It could also be argued tha the core powcr vs source size is a pliysically mieaniugful correlation. aud that from the biases introduced through the selection criteria we could derive the total vs core power correlation.," It could also be argued that the core power vs source size is a physically meaningful correlation, and that from the biases introduced through the selection criteria we could derive the total vs core power correlation."918 To isolate the problem iu our sample is not easy since we have both. flux density and angular size lits in our sample definition. but we note that biases miduced correlations depend stronglv on the adopted sclection criteria.," To isolate the problem in our sample is not easy since we have both, flux density and angular size limits in our sample definition, but we note that biases induced correlations depend strongly on the adopted selection criteria."919 Towever. consistent correlations of the total vs core power have been obtained with well defined complete samples incliding compact aud giant radio sources as well as quasars and radio galaxies (sce e.g. Cdovannini et al. 1958.. 2001:," However, consistent correlations of the total vs core power have been obtained with well defined complete samples including compact and giant radio sources as well as quasars and radio galaxies (see e.g. Giovannini et al. \cite{giov88}, \cite{giov01};"920 de Ruiter et al. 1990))., de Ruiter et al. \cite{deruiter}) ).921 Oue of the aims of this work was to select a sample of radio ealaxies with their jets orieutec near the plane of the sky or a subsequent study of the parsee scale properties of hese jets., One of the aims of this work was to select a sample of radio galaxies with their jets oriented near the plane of the sky for a subsequent study of the parsec scale properties of these jets.922 Although reliable limits to the oricutation of the ucimbers of our sample with respect to the observer camot ο derived from current data. two lines of arguuenutation avor the idea that these sources have moderately large aueles of oricutation.," Although reliable limits to the orientation of the members of our sample with respect to the observer cannot be derived from current data, two lines of argumentation favor the idea that these sources have moderately large angles of orientation."923 First. statistics of radio quasars: we find in our sample 3 objects out of 16 with FR II radio structure which are classified as quasars (Paper IT).," First, statistics of radio quasars: we find in our sample 3 objects out of 46 with FR II radio structure which are classified as quasars (Paper II)."924 If we consider that the probability of fiudiug an object with a certain anele 0 to the line of sight is P(0)~sind. we can estimate the expected πάρα” of quasars in a raudondlv oriented sample if quasars are assumed to have orieutatio- angles below 38° (Urry. Padovani 1995)).," If we consider that the probability of finding an object with a certain angle $\theta$ to the line of sight is $P(\theta) \sim \sin\theta$, we can estimate the expected number of quasars in a randomly oriented sample if quasars are assumed to have orientation angles below $38^{\circ}$ (Urry Padovani \cite{urry}) )."925 This number is 10 for a sample of 16 FR II radio galaxies. more than three times larger than found im our sample. whic[um nieaus that most objects must have orientation angles well above 387.," This number is $\sim 10$ for a sample of 46 FR II radio galaxies, more than three times larger than found in our sample, which means that most objects must have orientation angles well above $38^{\circ}$."926 And second. source iutrinsic linear sizes: with a dnean projected linear size of 1.02 Alpe in our sample. oricutation angles below 207 can. with a high degree of confidence. be discarded for most objects in order not to have iutriusicallv too large radio galaxies. which are not observed in other samples.," And second, source intrinsic linear sizes: with a mean projected linear size of 1.02 Mpc in our sample, orientation angles below $20^{\circ}$ can, with a high degree of confidence, be discarded for most objects in order not to have intrinsically too large radio galaxies, which are not observed in other samples."927 Ilowever. we have found (Section 2.3)) that the correlation between the core power and the total radio power is consistent with that derived by Ciüovanuimi et al. (20013) ," However, we have found (Section \ref{pcore}) ) that the correlation between the core power and the total radio power is consistent with that derived by Giovannini et al. \cite{giov01}) )"928for a sample of raucomly oricuted radio galaxies., for a sample of randomly oriented radio galaxies.929rate of its companion.,rate of its companion.930 For this paper. I use the values of q determined by ? and thevalues of O bv ?.. even though these two results use different methods of calculating turbulence.," For this paper, I use the values of $q$ determined by \citet{althaus98} and thevalues of $\Theta$ by \citet{paquette86}, even though these two results use different methods of calculating turbulence."931 This method has been shown to produce the accretion rate for the DAZ G29-38 reasonably well in light of independent estimations of the accretion rate (??)..," This method has been shown to produce the accretion rate for the DAZ G29-38 reasonably well in light of independent estimations of the accretion rate \citep{graham90,debes02}."932" Additionally for WD 10494-103 and WD 12104-464. their T,jj ave higher than those calculated by either method. so I use the values from the highest effective temperatures calculated."," Additionally for WD 1049+103 and WD 1210+464, their $_{eff}$ are higher than those calculated by either method, so I use the values from the highest effective temperatures calculated."933 Inferring the mass loss rate of the companion requires a mechanism for accretion., Inferring the mass loss rate of the companion requires a mechanism for accretion.934" For simpliditv and without knowledge of the exact mechanism lor creating a stellar wind. I assume (he M cwarl companion expels a spherically svimnetric [low at the escape speed from (he surface of the M να],"," For simplicity and without knowledge of the exact mechanism for creating a stellar wind, I assume the M dwarf companion expels a spherically symmetric flow at the escape speed from the surface of the M dwarf."935 I assume that the white dwarl accretes material through a Doncdi-IIovle acceretion flow determined by where G is the gravitational constant. p is the density of material surrounding the WD. and v is the relative velocity to the WD at which the gas is passing. which I take to be V[2Olid+Vorb3 (?)..," I assume that the white dwarf accretes material through a Bondi-Hoyle accretion flow determined by where $G$ is the gravitational constant, $\rho$ is the density of material surrounding the WD, and $v$ is the relative velocity to the WD at which the gas is passing, which I take to be $\sqrt{v_{wind}^2+v_{orb}^2}$ \citep{boni}."936 The escape speed from a low mass star is 600 km/s. assuming that ALLEBo1.," The escape speed from a low mass star is $\sim$ 600 km/s, assuming that $M/R\sim1$."937 Wis possible that the widely separated binaries have a higher mass (han (he close binaries., It is possible that the widely separated binaries have a higher mass than the close binaries.938" The mass-radius relation is roughly true for most low mass stars as can be seen in Table 1. (butseeο),", The mass-radius relation is roughly true for most low mass stars as can be seen in Table \ref{tab:closeorb} \citep[but see][]{lopez05}.939 However. WD 0419-487s radius is roughly twice as large as would be expected.," However, WD 0419-487's radius is roughly twice as large as would be expected."940 This could be related to the possiblitity of its red dwarf undergoing mass (ransler with the white dwarl. or the fact that it is most likely tically locked and is a fast rotator.," This could be related to the possiblitity of its red dwarf undergoing mass transfer with the white dwarf, or the fact that it is most likely tidally locked and is a fast rotator."941 In anv case. (he assumption of 600 kim/s lor an escape speed for the widely separated binaries Im studying is probably sale. since they should be similar to field red dwarf.," In any case, the assumption of 600 km/s for an escape speed for the widely separated binaries I'm studying is probably safe, since they should be similar to field red dwarfs."942 Using the escape speed at the radius of the companion max not be strictly (rue., Using the escape speed at the radius of the companion may not be strictly true.943 For exanple. one could model isothermal or polviropic winds from (he M clwarls assuming some heating mechanism.," For example, one could model isothermal or polytropic winds from the M dwarfs assuming some heating mechanism."944 This is hiehlv model dependent ancl requires information about the M cwarf companions (hat is not easily determined by (he observations al hand., This is highly model dependent and requires information about the M dwarf companions that is not easily determined by the observations at hand.945 Presumably the main source of heating for (he companions is comparable to that for the solar wind. where coronal heating provides the bulk of energy lor the acceleration of the wind.," Presumably the main source of heating for the companions is comparable to that for the solar wind, where coronal heating provides the bulk of energy for the acceleration of the wind."946 Uncertainties in e are discussed further in Section 4.., Uncertainties in $v$ are discussed further in Section \ref{s3}.947 Adcditionallv. Dondi-Ilovle accretion may not. accurately describe these svstems.," Additionally, Bondi-Hoyle accretion may not accurately describe these systems."948 Many astrophysical objects show departures [rom the simple Bondi-Hovle picture. such as isolated neulron stars accreting from the ISM (2). and super massive black holes (?)..," Many astrophysical objects show departures from the simple Bondi-Hoyle picture, such as isolated neutron stars accreting from the ISM \citep{perna03} and super massive black holes \citep{dimatteo01}. ."949 In these cases. there are departures [rom (he simple plane parallel geometry of the Boucli-Llovle case due," In these cases, there are departures from the simple plane parallel geometry of the Bondi-Hoyle case due"950mass solar nebula) model for the gas and dust discs around a voung star. both the initial dust and σας discs are eravilalionally stable and the only force available for the early stage of planet formation is electrostatic sticking.,"mass solar nebula) model for the gas and dust discs around a young star, both the initial dust and gas discs are gravitationally stable and the only force available for the early proto-planetesimal stage of planet formation is electrostatic sticking."951 For planets to form. the dust must therefore grow [rom electrostatic forces until gravity can play. a significant role.," For planets to form, the dust must therefore grow from electrostatic forces until gravity can play a significant role."952 The basic model for how such a state could can arise was put forth by Goldreich and Ward (Goldreich&Ward(1973).. hereafter GW).," The basic model for how such a state could can arise was put forth by Goldreich and Ward \citet{GW73}, hereafter GW)."953 In their proposed route to planet formation. dust grains initially collide and stick.," In their proposed route to planet formation, dust grains initially collide and stick."954 The growing grain mass eventually reduces the clust's thermal velocity dispersion and therefore. (he scale height of the dust. disc.," The growing grain mass eventually reduces the dust's thermal velocity dispersion and therefore, the scale height of the dust disc."955 Eventually the grains settle into the discs mid-plane until the critical density at which this dust disc becomes gravitationally unstable is reached and the formation of kilometer sized planetesimals is facilitated., Eventually the grains settle into the disc's mid-plane until the critical density at which this dust disc becomes gravitationally unstable is reached and the formation of kilometer sized planetesimals is facilitated.956 Subsequent accretion of surrounding σας would then complete the core-accretion model for giant planet formation., Subsequent accretion of surrounding gas would then complete the core-accretion model for giant planet formation.957 Recent observations of Colkw Tau/4 (D'Alessioetal.2005) seem to imply that massive planets must be able to form within ~10° vr. which is the tightest constraint to date on the total available time for anv planet formation mechanism.," Recent observations of CoKu Tau/4 \citep{d'Alessio05} seem to imply that massive planets must be able to form within $\sim 10^6$ yr, which is the tightest constraint to date on the total available time for any planet formation mechanism."958 In the absence of turbulence in the gas disc. the GW model is very efficient. ancl the {ime scale to egrow egrains to the size al which enoughex settlinge occurs lor exgravitational instability to occur is a small fraction of 109 vears.," In the absence of turbulence in the gas disc, the GW model is very efficient and the time scale to grow grains to the size at which enough settling occurs for gravitational instability to occur is a small fraction of $10^6$ years."959 However. Weidenschilling (Weidenschilling argued that turbulence can catastrophically prevent the required early erowtl pliase bv sting up the dust disc. thereby. delaving or preventing the subsequent gravitational instabilitv.," However, Weidenschilling \citep{Weidenschilling80} argued that turbulence can catastrophically prevent the required early growth phase by stirring up the dust disc, thereby delaying or preventing the subsequent gravitational instability."960 Because of prevalent sources of disc turbulence (such as cdust-gas shear. Cuzzi (1993).. Champnevetal.(1995). and AIR instability Balbus&Hawley (1991))) a turbulent dise is likely (he norm rather than the exception aud the GW theory mist be revisited.," Because of prevalent sources of disc turbulence (such as dust-gas shear, \citet{Cuzzi93}, \citet{Champney95} and MRI instability \citet{Balbus91}) ) a turbulent disc is likely the norm rather than the exception and the GW theory must be revisited."961 Ironically. even turbulence driven from the dust settling itself (Ishitsu& 2003).. might prematurely quench the GW process.," Ironically, even turbulence driven from the dust settling itself \citep{Ishitsu03}, might prematurely quench the GW process."962 The potential show-stopping ellect of turbulence has led to a substantial body. of work incorporating additional physics. such as anti-cvelonic vortices. that can accelerate the agglomeration of dust. grains should the early GW phase fail.," The potential show-stopping effect of turbulence has led to a substantial body of work incorporating additional physics, such as anti-cyclonic vortices, that can accelerate the agglomeration of dust grains should the early GW phase fail."963 But even if extra processes are present ancl helpful. the need for such processes has remained unclear.," But even if extra processes are present and helpful, the need for such processes has remained unclear."964 Despite the conceptual concerns induced by turbulence. its actual effect on planet growth has not been conclusively calculated.," Despite the conceptual concerns induced by turbulence, its actual effect on planet growth has not been conclusively calculated."965 Regardless of the details ol the turbulence. there will exist à dust grain size for which the effects of the turbulence on the dust are sullicientIlv weak that the GW process can proceed to instability.," Regardless of the details of the turbulence, there will exist a dust grain size for which the effects of the turbulence on the dust are sufficiently weak that the GW process can proceed to instability."966 The question therefore is whether the presence of turbulence catastrophically slows or even stops grain erowth before that size can be reached., The question therefore is whether the presence of turbulence catastrophically slows or even stops grain growth before that size can be reached.967 We attempt to answer that question., We attempt to answer that question.968 The effect of turbulence on dust growth is two-fold., The effect of turbulence on dust growth is two-fold.969 On the one hand it can increase the dust's collisional velocities (and so the collisional rate) which is a positive effect [or, On the one hand it can increase the dust's collisional velocities (and so the collisional rate) which is a positive effect for970angular momentum gain.,angular momentum gain.971 Simulations show that the largest decrease of angular momentum occurs integrating up the original dise size (in this case LOO AU). for smaller or larger raclii (he loss is less marked.," Simulations show that the largest decrease of angular momentum occurs integrating up the original disc size (in this case 100 AU), for smaller or larger radii the loss is less marked."972 Therefore in this paper the change of angular momentum100.4 will be taken as the figure of merit: the change in the entire disc will only be used when comparing to previous work., Therefore in this paper the change of angular momentum will be taken as the figure of merit; the change in the entire disc will only be used when comparing to previous work.973 The encounter parameters mass aid periastron significantly change (he part of the disc which is affect most in terms of angular momentum change., The encounter parameters mass and periastron significantly change the part of the disc which is affect most in terms of angular momentum change.974 A higher mass or closer periastron ol the secondary results in effecting regions further inside the disc., A higher mass or closer periastron of the secondary results in effecting regions further inside the disc.975 By contrast. altering the velocity changes the amount rather than the location of angular momentum transfer. (see Fig. 2)).," By contrast, altering the velocity changes the amount rather than the location of angular momentum transfer, (see Fig. \ref{fig:depend1}) )."976 The temporal development of (he angular momentum curing the encounter can be seen in Fig 3 - a) shows this for the angular momentum contained within the original 100AU sized dise and b) includes all particles still bound to the central star., The temporal development of the angular momentum during the encounter can be seen in Fig \ref{fig:ang_temp} - a) shows this for the angular momentum contained within the original 100AU sized disc and b) includes all particles still bound to the central star.977 For the latter the angular momentum initiallv increases due to the particles accelerated out of the disc ancl (then drops when (hese particles become unbound., For the latter the angular momentum initially increases due to the particles accelerated out of the disc and then drops when these particles become unbound.978 Turning now to Fig 3. a) it can be seen that the angular momentum within the original dise radius decreases. reaches à minimum and therealter settles at a nearly constant value somewhat lower than the initial angular momentum.," Turning now to Fig \ref{fig:ang_temp} a) it can be seen that the angular momentum within the original disc radius decreases, reaches a minimum and thereafter settles at a nearly constant value somewhat lower than the initial angular momentum."979 It is this difference between the angular monientunm before and after the encounter which will now be considered in more detail., It is this difference between the angular momentum before and after the encounter which will now be considered in more detail.980 First the simulation results are compared with the analvtical result of Ostriker developed for distant parabolic encountersOstriker(1994)., First the simulation results are compared with the analytical result of Ostriker developed for distant parabolic \cite{ostriker:apj94}.981. This result is complex and requires numerical integration. so that only values for the ease mq = ma = 1 M. aad img—0.5M. with a surface mass distribution x.! are available lor comparison.," This result is complex and requires numerical integration, so that only values for the case $m_1$ = $m_2$ = 1 $M_\sun$ and $m_d=0.5 M_\sun $ with a surface mass distribution $\sim r^{-1}$ are available for comparison."982 If we use such a mass distribution in a simulation it is usually unstable for such a high disc mass. and the steady state solution tends io differ significantly from the distribution used in the analvtical ealeulation.," If we use such a mass distribution in a simulation it is usually unstable for such a high disc mass, and the steady state solution tends to differ significantly from the distribution used in the analytical calculation."983 Therefore. we use a lower disc mass and balance it out with a higher central mass.," Therefore, we use a lower disc mass and balance it out with a higher central mass."984 For distant encounters the actual path of the secondary is not much. altered. by the extended mass around. the primary., For distant encounters the actual path of the secondary is not much altered by the extended mass around the primary.985 In addition. Ostriker presented the angular momentum change averaged over all possible encounter angles between (he disc and the perturber path.," In addition, Ostriker presented the angular momentum change averaged over all possible encounter angles between the disc and the perturber path."986 Here the Ostriker results, Here the Ostriker results987The error on each bisector point is propagated on the bisector measures 1n a standard fashion by adding quadratically the errors of the bisector points used in the computation of the measure.,The error on each bisector point is propagated on the bisector measures in a standard fashion by adding quadratically the errors of the bisector points used in the computation of the measure.988 Here we will discuss spectrum-to-spectrum variations of CCF bisectors. and their effects on the computation of mean bisectors and bisector measures.," Here we will discuss spectrum-to-spectrum variations of CCF bisectors, and their effects on the computation of mean bisectors and bisector measures."989 The RV for each spectrum has been calculated by the HARPS DRS by a Gaussian fit to the CCF profile., The RV for each spectrum has been calculated by the HARPS DRS by a Gaussian fit to the CCF profile.990" This RV has been subtracted from the individual CCF bisector,", This RV has been subtracted from the individual CCF bisector.991 As a result. spectrum-to-spectrum variations in the CCF bisector are mainly caused by (1) SNR differences due to differences in exposure time and variations in the conditions of the Earth’s atmosphere. (2) instrumental effects. e.g. temperature drift. (3) errors coming from. the reduction procedure. (4) variations in the stellar atmosphere due to magnetic activity. stellar oscillations. granulation. and any other variable velocity fields.," As a result, spectrum-to-spectrum variations in the CCF bisector are mainly caused by (1) SNR differences due to differences in exposure time and variations in the conditions of the Earth's atmosphere, (2) instrumental effects, e.g. temperature drift, (3) errors coming from the reduction procedure, (4) variations in the stellar atmosphere due to magnetic activity, stellar oscillations, granulation, and any other variable velocity fields."992 Note that orbiting planets do ot leave a signature on the CCF bisectors., Note that orbiting planets do not leave a signature on the CCF bisectors.993 In order to illustrate to what degree the bisectors are stable. we show the individual bisectors of obtained during more than 10 hours of asteroseismological observations in the night of21 April 2005 as well as their mean (Fig. 3)).," In order to illustrate to what degree the bisectors are stable, we show the individual bisectors of obtained during more than 10 hours of asteroseismological observations in the night of 21 April 2005 as well as their mean (Fig. \ref{fig:alfCenAmeanbis}) )."994 The SNR of the mean bisector is moderate (~875) compared to that for other stars in Table 1.. all of which were observed for durations less than the total obervation time allocated for in one night.," The SNR of the mean bisector is moderate $\sim$ 875) compared to that for other stars in Table \ref{tab:obs}, all of which were observed for durations less than the total obervation time allocated for in one night."995 To illustrate the long term consistency. 21 CCF bisectors of obtained in 21 different nights in the period 26 December 2003 — | September 2009 is shown in Fig. 4..," To illustrate the long term consistency, 21 CCF bisectors of obtained in 21 different nights in the period 26 December 2003 — 1 September 2009 is shown in Fig. \ref{fig:HD21693meanbis}."996 Fig., Fig.997 and 4 show that the IP is very stable. both short term and long term.," \ref{fig:alfCenAmeanbis} and \ref{fig:HD21693meanbis} show that the IP is very stable, both short term and long term."998 An interesting spectrum-to-spectrum variation was observed for Eri... which is a well-known active star (??)..," An interesting spectrum-to-spectrum variation was observed for , which is a well-known active star \citep{croll+2006,graybaliunas1995}."999 The star was observed on two nights. on 25 January 2007 and 2 February 2007.," The star was observed on two nights, on 25 January 2007 and 2 February 2007."1000 Five spectra were obtained on each of the nights., Five spectra were obtained on each of the nights.1001 The change in individual CCF bisectors from one night to another is remarkable (Fig. 5)).," The change in individual CCF bisectors from one night to another is remarkable (Fig. \ref{fig:epsEri}) ),"1002 and illustrates both intra-night short term. variation and longer term variations due to magnetic activity., and illustrates both intra-night short term variation and longer term variations due to magnetic activity.1003 In such cases. we used a mean CCF bisector obtained às an average of the bisectors observed in one night during which the shape is the most stable.," In such cases, we used a mean CCF bisector obtained as an average of the bisectors observed in one night during which the shape is the most stable."1004 A systematic change of CCF bisector shape with surface gravity and with effective temperature is expected., A systematic change of CCF bisector shape with surface gravity and with effective temperature is expected.1005 This was demonstrated by ? for classical single line bisector shapes over the HR diagram., This was demonstrated by \citet{gray2005} for classical single line bisector shapes over the HR diagram.1006 In Sec., In Sec.1007 3. we present the equivalent for the HARPS CCF bisectors., \ref{results} we present the equivalent for the HARPS CCF bisectors.1008 However. in order to quantify the variations. à measure that can numerically represent the bisector shape is required. ?..," However, in order to quantify the variations, a measure that can numerically represent the bisector shape is required. \citet{gray2005},"1009 made use of the height of the blue-most point of a single line bisector as an empirical indicator of the luminosity of a star., made use of the height of the blue-most point of a single line bisector as an empirical indicator of the luminosity of a star.1010 However. CCF bisectors have shapes considerably different than those of single lines.," However, CCF bisectors have shapes considerably different than those of single lines."1011" The famous ""C"" shape of the bisector of the neutral iron line at 6253 in cool stars’s spectra is physically attributed to granulation."," The famous “C"" shape of the bisector of the neutral iron line at $\lambda$ 6253 in cool stars's spectra is physically attributed to granulation."1012" Because granulation ts depth dependent. the shape of the ""C. and hence its blue-most point. changes from one star to another depending on how transparent the atmosphere is to granulation."," Because granulation is depth dependent, the shape of the “C"", and hence its blue-most point, changes from one star to another depending on how transparent the atmosphere is to granulation."1013 Therefore. such a measure referring tothe height of that point would," Therefore, such a measure referring tothe height of that point would"1014positional error.,positional error.1015 No further analysis of this source was published so its true classification remains unknown., No further analysis of this source was published so its true classification remains unknown.1016" Within the X-ray positional error, we find that an optical and nIR source is detected in all filters reffig.4fields;; best seeing was ~0.95"" iin nIR filters and iin optical filters)."," Within the X-ray positional error, we find that an optical and nIR source is detected in all filters \\ref{fig.4fields}; best seeing was $\sim 0.95$ in nIR filters and in optical filters)."1017" From examination of our second epoch nIR images we derive a position of RA, Dec = 16:37:02.66 —49:51:40.0 (+0.16”)), consistent with 2MASS object J16370267—4951401, noted by Starlingetal.(2008)."," From examination of our second epoch nIR images we derive a position of RA, Dec = 16:37:02.66 $-$ 49:51:40.0 $\pm 0.16$ ), consistent with 2MASS object $-$ 4951401, noted by \cite{Starling2008ATel.1704}."1018. We find no variability (<0.05 magnitudes) of the counterpart between the two epochs so present only the average values reftable:mags))., We find no variability $\lesssim0.05$ magnitudes) of the counterpart between the two epochs so present only the average values \\ref{table:mags}) ).1019" We note that the observed magnitudes in J, H and K; are consistent with the cataloged 2MASS values; this is not surprising, given that the observations were obtained after the X-ray outburst had faded."," We note that the observed magnitudes in $J$, $H$ and $K_s$ are consistent with the cataloged 2MASS values; this is not surprising, given that the observations were obtained after the X-ray outburst had faded."1020 Furthermore we note that this source is also tabulated in the ccatalog (G335.4256-01.7828)., Furthermore we note that this source is also tabulated in the catalog (G335.4256-01.7828).1021" reffig.xte1637sE Dshowsthespectralshapeo fthecounterpartof, includingtheGLIM ddata."," \\ref{fig.xte1637_SED} shows the spectral shape of the counterpart of, including the data."1022"Alsoplottedarethe f luxescorrected f oraGalacticextinctioninthzstdondosiow(fheltbebadacgland 928)dgh (Ax~0.8, Ay~7.1; Cardellietal. 1989)), though this should be considered as an upper limit."," Also plotted are the fluxes corrected for a Galactic extinction in that direction \citep{schlegel1998:ApJ500} of $A_K \sim 0.8$, $A_V \sim 7.1$; \citealt{cardelli1989:ApJ345}) ), though this should be considered as an upper limit."1023" Though we are unable to find a single model — for any value of Galactic extinction — that fits both the NTT and ddata, we find that the NTT data alone can be fit by black body radiation at a temperature of KK and corresponding extinctions of 0.4«Egy<2.0."," Though we are unable to find a single model – for any value of Galactic extinction – that fits both the NTT and data, we find that the NTT data alone can be fit by black body radiation at a temperature of K and corresponding extinctions of $0.4 < E_{B-V} < 2.0$."1024" However, when extended to the ddata, this model underestimates the flux at those wavelengths."," However, when extended to the data, this model underestimates the flux at those wavelengths."1025" In fact, the ddata itself implies a power law (Ενc v) of spectral index 1.0«<1.7 for the same range of extinctions as implied by the black body fit to the NTT data."," In fact, the data itself implies a power law $F_{\nu} \propto \nu^{\alpha}$ ) of spectral index $1.0 < \alpha < 1.7$ for the same range of extinctions as implied by the black body fit to the NTT data."1026 A power law of similar slope is not a good fit to the NTT data alone or the NTT and ddata combined (y?>> 1)., A power law of similar slope is not a good fit to the NTT data alone or the NTT and data combined $\chi_{\nu}^{2} >> 1$ ).1027" This implies that there is excess emission at the Spitzer--IRAC wavelengths (see section ??)), either due to intrinsic IR excess or an excess at the time of the oobservations which, as catalog magnitudes, were not simultaneous with the NTT observations."," This implies that there is excess emission at the -IRAC wavelengths (see section \ref{section:conclusions}) ), either due to intrinsic IR excess or an excess at the time of the observations which, as catalog magnitudes, were not simultaneous with the NTT observations."1028NGC 5506 hosts a nearby (z20.006) AGN. rather bright in hard X-rays.,"NGC 5506 hosts a nearby (z=0.006) AGN, rather bright in hard X-rays."1029 It has been generally classified as a NELG., It has been generally classified as a NELG.1030 Recently ? observed the source in the near-IR and discovered an heavily reddened (Av ~5) Narrow Line Seyfert 1 nucleus., Recently \citet{nag02} observed the source in the near–IR and discovered an heavily reddened $_V\sim$ 5) Narrow Line Seyfert 1 nucleus.1031 The source. being very bright. was observed by all X-ray satellites. starting with Uu.," The source, being very bright, was observed by all X–ray satellites, starting with $Uhuru$."1032" In recent times. it was observed by Einstein (2).. EXOSAT (?) and Ginga (2): the latter fittec the spectrum with à power law absorbed by neutral matter with column density of 3—4x1077 em"". plus a soft excess."," In recent times, it was observed by $Einstein$ \citep{mac82}, $EXOSAT$ \citep{pounds89} and $Ginga$ \citep{bmy93}; the latter fitted the spectrum with a power law absorbed by neutral matter with column density of $3-4\times10^{22}$ $^{-2}$, plus a soft excess."1033 Furthermore. thedata showed a reflection component and ai iron Ka line (?)..," Furthermore, thedata showed a reflection component and an iron $\alpha$ line \citep{bmy93}."1034 Later on. ROSAT HRI images suggested that the soft emission is extended and coincident with the radio emission (?)..," Later on, $ROSAT$ HRI images suggested that the soft emission is extended and coincident with the radio emission \citep{colbert98}."1035 Results from ASCA (?).. BeppoSAX (?) and an RXTE variability analysis (?). pointed out the complexity of the iron line profile. which was finally resolved by Newton in at least two components. the narrower at 6.4 keV being likely associated with the reflection component. arising from a neutral Compton-thick material (2)..," Results from $ASCA$ \citep{wang99}, BeppoSAX \citep{per02} and an $RXTE$ variability analysis \citep{lamer00} pointed out the complexity of the iron line profile, which was finally resolved by $Newton$ in at least two components, the narrower at 6.4 keV being likely associated with the reflection component, arising from a neutral Compton-thick material \citep{Matt01}."1036 The origin. of the bluer and broader component is less clear. but may be associated to the soft excess (see Sect. 3.2.4)).," The origin of the bluer and broader component is less clear, but may be associated to the soft excess (see Sect. \ref{softpar}) )."1037 Finally. the source is variable on short time scales. but no long term trend has been found yet (e.g.?)..," Finally, the source is variable on short time scales, but no long term trend has been found yet \citep[e.g.][]{papa02}."1038 In this paper we present results from two XMM-Newton observations (the first one simultaneous with à BeppoSAX observation. see 2)) and a Chandra/HETG observation.," In this paper we present results from two $Newton$ observations (the first one simultaneous with a BeppoSAX observation, see \citealt{Matt01}) ) and a $Chandra$ /HETG observation."1039 We have also reanalysed past BeppoSAX and ASCA observations (see Table 1))., We have also reanalysed past BeppoSAX and ASCA observations (see Table \ref{log}) ).1040 All these observations will allow us to check and refine the interpretation proposed by ? and ?.. in which the nucleus is surrounded by at least two reflecting regions. one Compton-thick and neutral and the other one Compton- and highly ionized. and obscured by a Compton-thin cold absorber.," All these observations will allow us to check and refine the interpretation proposed by \citet{Matt01} and \citet{bm02}, in which the nucleus is surrounded by at least two reflecting regions, one Compton–thick and neutral and the other one Compton--thin and highly ionized, and obscured by a Compton–thin cold absorber."1041 We will assume Ho=75 km/s/Mpe throughout the paper., We will assume $_0=75$ km/s/Mpc throughout the paper.1042 NGC 5506 was observed twice by XMM-Newton. on February 2001 and on January 2002 (Table 1)).," NGC 5506 was observed twice by $Newton$, on February 2001 and on January 2002 (Table \ref{log}) )."1043 We defer the reader to ? for details on the first observation and the related data reduction., We defer the reader to \citet{Matt01} for details on the first observation and the related data reduction.1044 Both observations were performed with the imaging CCD cameras. the EPIC-MOS (?) and the EPIC-pn (?) operating in Large Window mode and the Medium filter.," Both observations were performed with the imaging CCD cameras, the EPIC-MOS \citep{turner01} and the EPIC-pn \citep{struder01} operating in Large Window mode and the Medium filter."1045 X-ray events corresponding to pattern 0 were used for the pn and for the MOS., X-ray events corresponding to pattern 0 were used for the pn and 0-12 for the MOS.1046 We will not deal with the RGS spectra in this paper. because of the too poor statistics.," We will not deal with the RGS spectra in this paper, because of the too poor statistics."1047 Data were reduced with SAS 5.3.0. including the first observation which was reprocessed.," Data were reduced with SAS 5.3.0, including the first observation which was reprocessed."1048 As an effect of the new adopted response matrix. we found a slightly different normalization factor between PDS and pn. 1.15. instead of 1.215 used by ?..," As an effect of the new adopted response matrix, we found a slightly different normalization factor between PDS and pn, 1.15, instead of 1.215 used by \citet{Matt01}."1049" EPIC-pn spectra (0.5-10 keV) and lightcurves were extracted from a radius of 30"".", EPIC-pn spectra (0.5-10 keV) and lightcurves were extracted from a radius of $40\arcsec$ .1050" An extraction region of 45"" radii was instead adopted for the EPIC MOSI and MOS? spectra (0.3-10 keV).", An extraction region of $45\arcsec$ radii was instead adopted for the EPIC MOS1 and MOS2 spectra (0.3-10 keV).1051 Both observations are affected by negligible pileup (less than in the pn)., Both observations are affected by negligible pileup (less than in the pn).1052 Spectra were analysed with 1.1.0., Spectra were analysed with 11.1.0.1053Establishing the cluser nature of a stellar overdesity requires inectine criteria stenunius from two different perspectives. one reated to. the spatial distribtion of the stars. and the other to the colourauaguiude diaeran (CAID) morshology.,"Establishing the cluster nature of a stellar overdensity requires meeting criteria stemming from two different perspectives, one related to the spatial distribution of the stars, and the other to the colour-magnitude diagram (CMD) morphology."1054 Iu short. a star clusvs overdesity should be spatially exteudec and prese ita CNID norpholoey sigificautlv different from that of the ποια sars.," In short, a star cluster's overdensity should be spatially extended and present a CMD morphology significantly different from that of the field stars."1055 Otherwise. it may simply be a statisical fluctuation of the fiek or a low-absorption wiudow. a SO0-called asterisun.," Otherwise, it may simply be a statistical fluctuation of the field or a low-absorption window, a so-called asterism."1056 Usually. a star clusters overdeusity disributes racially frou its ceutre followiie an analvtical profile. πιch as the siueleauass. isothermal spheres of Nine(962) aud Nine (1966).. the modified isothermal sphere of Wilso1(1975|. or the power-law with a core of Elson.Fall&Freeman (1987).," Usually, a star cluster's overdensity distributes radially from its centre following an analytical profile, such as the single-mass, isothermal spheres of \citet{King1962} and \citet{King1966}, the modified isothermal sphere of \citet{Wilson75}, or the power-law with a core of \citet{EFF87}."1057. However. this expectation docs not necessarily apdv tfo clusters in all scales.," However, this expectation does not necessarily apply to clusters in all scales."1058" Faint and/or poorV-20ULated star clusters nav have a stellar radial density DEfile (RDP) that does not folow any analytical profile (ee,oO Donatto&Bica 20085).", Faint and/or poorly-populated star clusters may have a stellar radial density profile (RDP) that does not follow any analytical profile (e.g. \citealt{FSR20}) ).1059 lustead. the very poorV-20nated ones may have an RDP characterised esseutialv a central overdeusiv togetjer with sienificaut nolse Otwards. typical featires of an asteri (e.g. Fig.," Instead, the very poorly-populated ones may have an RDP characterised essentially by a central overdensity together with significant noise outwards, typical features of an asterism (e.g. Fig."1060 9 of Bonato&Bica2008b ))., 9 of \citealt{FSR20}) ).1061 Iu these cases. only the CND norptology may provile clues o the overdensity natur5," In these cases, only the CMD morphology may provide clues to the overdensity nature."1062" With respect to he photometric properties. fhe Calaclc opel clusterμα (OC's) λαστ d lot in CXD 11ΟΥ)tology. such as the presence of evolutionary setences ranging frou a ~ LAD: to a few Cor (c.g, Douatto&Dica20100. DBonatto&Bica20106 )). lucluine here the very voung embedded (n gas aud dust) clusers (ECs). which have CAIDs dominated by pre-main seteace (PAIS) stars (e.g. Ortolanictal. 2008))."," With respect to the photometric properties, the Galactic open clusters (OCs) vary a lot in CMD morphology, such as the presence of evolutionary sequences ranging from a $\sim1$ Myr to a few Gyr (e.g. \citealt{OvrlTeut}; \citealt{Rup15}) ), including here the very young embedded (in gas and dust) clusters (ECs), which have CMDs dominated by pre-main sequence (PMS) stars (e.g. \citealt{Orto08}) )."1063 These cluscrs can also present significant differences in terms of observable stellar magnitude ranges. the amount of stellar fore/backeround contamination. as well as foreground and internal differential reddening (especially the ECs).," These clusters can also present significant differences in terms of observable stellar magnitude ranges, the amount of stellar fore/background contamination, as well as foreground and internal differential reddening (especially the ECs)."1064 All these asους should be taken iuto account when identifving and ¢characterising a star cluster., All these aspects should be taken into account when identifying and characterising a star cluster.1065" Several aqyproaches have been employed. to cope with these πωlos. adapted o the available photometric range. but usually iu the optical or near inyared (e.g. Douatto&Bica20105: Moiteiro.,Dias&Cactano 20101: Alessi.Moitiilk»>&Dias2 WO9O:: Subrinuuia11.Carraro&Janes 2010))."," Several approaches have been employed to cope with these difficulties, adapted to the available photometric range, but usually in the optical or near infrared (e.g. \citealt{OvrlTeut}; \citealt{Monteiro10}; \citealt{Alessi03}; ; \citealt{Subra10}) )."1066 For lustance. dt Is colon to fiud works based on oxtrac CAIDs withott applviug field star decontamination (e.g. Ortolauietal.2005)). proper inotiou-filtcring {e.g. Diasctal.2006)) or. CMD field clecoutamunatio1 fee. Donato&Bica 201053).," For instance, it is common to find works based on extracted CMDs without applying field star decontamination (e.g. \citealt{Orto05}) ), proper motion-filtering (e.g. \citealt{Dias06}) ) or, CMD field decontamination (e.g. \citealt{OvrlTeut}) )."1067" IDstork‘ally. optical cluster parincters were the lua1 source of Information. but in recent vears the ucar-infrared. usiug nrostly the wniforu2MASS!., las become a dnnajor data inmit. especially for reddened clusters,"," Historically, optical cluster parameters were the main source of information, but in recent years the near-infrared, using mostly the uniform, has become a major data input, especially for reddened clusters."1068 Our eroup. nn particidar. has heen οuploviug 2\TASS CAIDs and RDPs buit with statistical field decontamination aud ΟΕe filters (Bonatto&Bica2007 ).," Our group, in particular, has been employing 2MASS CMDs and RDPs built with statistical field decontamination and colour-magnitude filters \citealt{BB07}) )."1069 We have studied clusters in different evohltionary stages. suce EC ornation iu couplexes (Sauriu.Bica&Bonatto 20103) otLely eveutua dissolution (e.g. Dica.Bouatto&Dutra 2008: Bonatto&Dica 2009b:: Bonatto&Bica 2010a)).," We have studied clusters in different evolutionary stages, since EC formation in complexes \citealt{Sh2-132}) ) to their eventual dissolution (e.g. \citealt{Bochum1}; \citealt{Pi5}; \citealt{vdB92}) )."1070 The respective photometric and structural parameters. wave been shown to constrain the study of particular argets.," The respective photometric and structural parameters, have been shown to constrain the study of particular targets."1071 Different targets. im general. require analyses with articular approaches. until getting a clear picture of their wture.," Different targets, in general, require analyses with particular approaches, until getting a clear picture of their nature."1072 However. when the targets are poorly-populated. which applies to most Calactie OCs aud ECs. the star cluster characterisation would further require:(7) a cluster mative determination for the first time by meaus of derivationof fundamental and structural parameters. aud two or more studies ou the same object to allow for 2ΠΟΤΟ Coluparisous aud consisteney checks.," However, when the targets are poorly-populated, which applies to most Galactic OCs and ECs, the star cluster characterisation would further require: a cluster nature determination for the first time by means of derivationof fundamental and structural parameters, and two or more studies on the same object to allow for parameter comparisons and consistency checks."1073" feo,<typ. TiaκοΤΠ. Πο IT|eΣΠ5. H|I>IIo«|. T—200K. u~LOtemi)m IT» 10710?NL... IT» iX zol ina Πο II» Πο {ο Πο "," $t_{\rm cool} < t_{\rm H}$ $T_{\rm vir} <107410^4$ ${\rm H_{2}}$ ${\rm H + e^{-} \rightarrow H^{-} + \gamma}$ ${\rm H^{-} + H \rightarrow H_{2} + e^{-}}$ ${\rm T1075\sim 200~{\rm K}\,}$ ${\rm n \sim 10^{4} \, {\rm cm}^{-3}}$ ${\rm H_2}$ $10^{2}-10^{3} \, {\rm M_\odot}$ ${\rm H_2}$ $\gsim 1$ ${\rm H_2}$ ${\rm H_2}$ $\Htwo$ $H_{2}$ ${\rm H_2}$ "1076emplate fitting that simultaneously. provides a photometric redshift estimate for the quasar candidates.,template fitting that simultaneously provides a photometric redshift estimate for the quasar candidates.1077 Phe point source emplate library comprises quasar ancl stellar. templates anc the observed. SED of cach object is compared. to the one computed by convolving cach template with the filters ransmissions (for further details sec Hatziminaoglouοἱal.2000 and 2002)., The point source template library comprises quasar and stellar templates and the observed SED of each object is compared to the one computed by convolving each template with the filters transmissions (for further details see \citealt{hatzi00} and 2002).1078 is expected to give higher confirmation rates (ie. number of real quasars over then number of quasar candidates) at low and. intermediate redshifts. but its ellicieney greatly. depends on the photometric system used and can not be applied as such when other filters are used., is expected to give higher confirmation rates (i.e. number of real quasars over then number of quasar candidates) at low and intermediate redshifts but its efficiency greatly depends on the photometric system used and can not be applied as such when other filters are used.1079AL2 is subject to higher contamination from: sources other than quasars (e.g. stars) but is expected to have a much better efficiency at high redshift anc can be used for any filter combination., is subject to higher contamination from sources other than quasars (e.g. stars) but is expected to have a much better efficiency at high redshift and can be used for any filter combination.1080 In order to improve the results. we also make use of the It information available for the 15 sources keeping in münd that the combination of all hese techniques will be applied in the near future in the ramework of SWIRL.," In order to improve the results, we also make use of the IR information available for the 15 sources keeping in mind that the combination of all these techniques will be applied in the near future in the framework of SWIRE."1081 AX first test is made using the more reliable SDSS shotometry (Section 4.1)) but an attempt of selecting candidates based on the WES photometry will also. be resented. (Section 4.2))., A first test is made using the more reliable SDSS photometry (Section \ref{sdsscand}) ) but an attempt of selecting candidates based on the WFS photometry will also be presented (Section \ref{wfscand}) ).1082 Our test sample consists of 21 spectroscopically confirmed: quasars with available SDSS photometry and 25 with WES photometry. which include all 21 from SDSS (see Table 1)).," Our test sample consists of 21 spectroscopically confirmed quasars with available SDSS photometry and 25 with WFS photometry, which include all 21 from SDSS (see Table \ref{tabconfquasars}) )."1083 Finc-tuning the method or WES data is very important as large part of the SWIRL ields have been observed by the WES., Fine-tuning the method for WFS data is very important as large part of the SWIRE fields have been observed by the WFS.1084 A sample1 of S2. 15 ELALS sources identified as point sources from their optical photometry (SDSS σοι = 6) with ραπ magnitudes brighter that 22.6 has been selected (rom the SDSS photometric catalogue., A sample of 82 15 ELAIS sources identified as point sources from their optical photometry (SDSS TYPE = 6) with $r$ -band magnitudes brighter that 22.6 has been selected from the SDSS photometric catalogue.1085 “Phe optical magnitude cut has been imposed in order to avoid spurious detections and. large photomoetric OLPOES., The optical magnitude cut has been imposed in order to avoid spurious detections and large photometric errors.1086 The 15 information can be used in order to impose IR. conditions in the selection of quasar candidates., The 15 information can be used in order to impose IR conditions in the selection of quasar candidates.1087 Stars. galaxies. and AGN all have different: optical to. mic-LR slopes. with stars typically having larger optical than mid-IR) fluxes (Gonzalez-Solaresetal.2004)..Furthermore. according to mocels of galaxies in the LR (Itowan-lItobinson 2001).. quasar mid-Ilt fluxes are some 10 to 100 times larger than their optical ones.," Stars, galaxies, and AGN all have different optical to mid-IR slopes, with stars typically having larger optical than mid-IR fluxes \citep{gonzalez04}.Furthermore, according to models of galaxies in the IR \citep{rowan01}, quasar mid-IR fluxes are some 10 to 100 times larger than their optical ones."1088 Taking this into account. one can impose additional constraints on the selection criteria requiring a mid-Ilt to optical [lux ratio of at least. LO [or quasar candidates (hereafter condition C4).," Taking this into account, one can impose additional constraints on the selection criteria requiring a mid-IR to optical flux ratio of at least 10 for quasar candidates (hereafter condition )."1089 This condition allows the removal of three quasar candidates selected: by Al? that have mid-It to optical Uuxes those of stars., This condition allows the removal of three quasar candidates selected by $M2$ that have mid-IR to optical fluxes those of stars.1090 Fig., Fig.1091 5 illustrates the positions of the dillerent objects types and the regions where quasars and quasar candidates selected by the two methods Lic., \ref{log15rmag} illustrates the positions of the different objects types and the regions where quasars and quasar candidates selected by the two methods lie.1092 In order to distinguish between quasars and. galaxies. one can make a combined use of optical and optical/lh colours taking advantage of the Lact that quasars up to a redshift of ~3 are typically blucr than galaxies (Conzalez-Solaresetal. 2004).," In order to distinguish between quasars and galaxies, one can make a combined use of optical and optical/IR colours taking advantage of the fact that quasars up to a redshift of $\sim 3$ are typically bluer than galaxies \citep{gonzalez04}."1093. Furthermore. of all spectroscopically confirmed. quasars in the DRI quasar catalogue (Schneideretal.2008) have r7<0.52 (hereafter C2).," Furthermore, of all spectroscopically confirmed quasars in the DR1 quasar catalogue \citep{schneider04} have $r-i < 0.52$ (hereafter )."1094 Fig., Fig.1095 6 shows the distribution of stars (lower mid-LIlt to optical Luxes). galaxies ancl quasers (bluer than galaxies in general).," \ref{iroptcolour} shows the distribution of stars (lower mid-IR to optical fluxes), galaxies and quasars (bluer than galaxies in general)."1096 Marked in red are the spectroscopically confirmed quasars (left panel) and the candidates selected by methocks and A2 (middle ancl right panels. respectively).," Marked in red are the spectroscopically confirmed quasars (left panel) and the candidates selected by methods and (middle and right panels, respectively)."1097 As can be seen. all spectroscopically confirmed quasars form a clump bluewards of ry7~0.52.," As can be seen, all spectroscopically confirmed quasars form a clump bluewards of $r-i \sim 0.52$."1098 In this particular case.C2 does not improve the results of any of the methods but will be used further on.," In this particular case, does not improve the results of any of the methods but will be used further on."1099 If Nis the number of quasar candidates. stemaming from the identification technique. IN; 1 number of real quasars among the candidates. and AY the number of expected (based. on models) or. known. (based. on complete observations) quasars. anc can be defined as Ny fo and Ny Δι respectively (Llatziminaoglou," If $N_c$ is the number of quasar candidates stemming from the identification technique, $N_f$ the number of real quasars among the candidates, and $N_e$ the number of expected (based on models) or known (based on complete observations) quasars, and can be defined as ${N_f}$ ${N_e}$ and ${N_f}$ ${N_c}$, respectively \citep{hatzi00}."1100ctal.2000).. Table 2. compares the two quantities vieldecd by the two methods., Table \ref{tabcand} compares the two quantities yielded by the two methods.1101 Both methods eivethe same completeness but the colour-colour selection favours the confirmation rate., Both methods givethe same completeness but the colour-colour selection favours the confirmation rate.1102Note. however. that the values given here for confirmation rate are ης. A,"Note, however, that the values given here for confirmation rate are A"11033 caption). we have found that a comparison between these model predictions and observations at low and intermediate 2 shows that the best match is obtained for models with a rapidly declining Type Ia rate 1.1) cousistent with the constraints on s from chemical evolution.,"3 caption), we have found that a comparison between these model predictions and observations at low and intermediate $z$ shows that the best match is obtained for models with a rapidly declining Type Ia rate ) consistent with the constraints on $s$ from chemical evolution."1104 Iu figure 1 we have plotted the predicted SNIa/II rates in SNu., In figure 4 we have plotted the predicted SNIa/II rates in SNu.1105 As can be seen. the SNIa rate is nearly constant.," As can be seen, the SNIa rate is nearly constant."1106 This is expected since both the Rsνα per, This is expected since both the $R_{SNIa}$ per1107keV luminosities 10% of the Exldington limit: the 0.310 keV luminosity of XBo 144 exceeds 0.20 Lg for all known neutron stars (2.1 M. or less).,keV luminosities $\la$ of the Eddington limit; the 0.3–10 keV luminosity of XBo 144 exceeds 0.20 $L_{\rm Edd}$ for all known neutron stars (2.1 $_{\odot}$ or less).1108 Estimating the 0.01.1000 keV luminosity of Χο 144 is not às simple as extrapolating the power law to 1000 keV. Low state spectra are thought to be caused by unsaturated inverse Compton scattering of cool photons on hot electrons ina corona. resulting in a power law for energies lower than he electron temperature. and a Wien spectrum for higher energies (2)..," Estimating the 0.01–1000 keV luminosity of XBo 144 is not as simple as extrapolating the power law to 1000 keV. Low state spectra are thought to be caused by unsaturated inverse Compton scattering of cool photons on hot electrons in a corona, resulting in a power law for energies lower than the electron temperature, and a Wien spectrum for higher energies \citep{sun80}."1109 Phe coronae in black hole X-ray binaries tend o have temperatures of 100.300 keV. (2): hence we cannot determine the corona temperature with 0.3.10 keV. data., The coronae in black hole X-ray binaries tend to have temperatures of $\sim$ 100–300 keV \citep{mr03}; hence we cannot determine the corona temperature with 0.3–10 keV data.1110 We obtained lower limit estimates to the 0.011000. keV uminosity of Χο 144 bv measuring the [ux of a power law with L—1.48 for energy ranges 0.3.100 keV and and 0.3300 keV. We therefore expect the 0.01.1000 keV luminosity of XDo 144 to be at least ~37 times higher than the observed A310 keV luminosity. Le. 20.61.4. Ley for a neutron star with mass 2.1. AZ..," We obtained lower limit estimates to the 0.01–1000 keV luminosity of XBo 144 by measuring the flux of a power law with $\Gamma$ =1.48 for energy ranges 0.3–100 keV and and 0.3–300 keV. We therefore expect the 0.01–1000 keV luminosity of XBo 144 to be at least $\sim$ 3–7 times higher than the observed 0.3–10 keV luminosity, i.e. $>$ 0.6–1.4 $L_{\rm Edd}$ for a neutron star with mass 2.1 $M_{\odot}$."1111 Hence. we propose NBo 144 as à candidate GC black hole LAINB.," Hence, we propose XBo 144 as a candidate GC black hole LMXB."1112 Without the strong time-variability. observed in XBo 45. it is possible that Χο 144 is simply an active galactic nucleus (AGN). since. D 1.4 for tvpical AGN.," Without the strong time-variability observed in XBo 45, it is possible that XBo 144 is simply an active galactic nucleus (AGN), since $\Gamma$ $\sim$ 1.4 for typical AGN."1113 Hence. associating the X-ray source with a GC is strong evidence that it is an X-rav binary.," Hence, associating the X-ray source with a GC is strong evidence that it is an X-ray binary."1114 We therefore calculated the probability of an AGN coinciding with a GC within the observed. field of view., We therefore calculated the probability of an AGN coinciding with a GC within the observed field of view.1115" We emploved the X-ray luminosity funetions (XLES) for AGN devised. by ον,", We employed the X-ray luminosity functions (XLFs) for AGN devised by \citet{mor03}.1116 They. ereated AGN XLEs in 12 keV. and 210 keV bands: therefore we calculated. the absorbed. 12 and 210 keV Uusxes of XBo 144 (1.08.10 4% and 5.69.10 1% erg ? fL. respectively).," They created AGN XLFs in 1–2 keV and 2–10 keV bands; therefore we calculated the absorbed 1–2 and 2–10 keV fluxes of XBo 144 $\times$ $^{-13}$ and $\times$ $^{-13}$ erg $^{-2}$ $^{-1}$, respectively)."1117 From the NLEsS of Moretti et al. (, From the XLFs of Moretti et al. (11182003). we expeet 3.80.9. * AGN per square aresee to exhibit 12 keV fluxes as bright as XBo 144. and only St5. 7 ACN per square aresec to exhibit 210 keV Ηχος as bright as NDBo 144.,"2003), we expect $\pm$ $\times$ $^{-7}$ AGN per square arcsec to exhibit 1–2 keV fluxes as bright as XBo 144, and only $\pm$ $\times$ $^{-8}$ AGN per square arcsec to exhibit 2–10 keV fluxes as bright as XBo 144."1119 ? found the Chandra position of Νο 144 to be 2.2” from the G:C position., \citet{K02} found the Chandra position of XBo 144 to be $''$ from the GC position.1120" There are 20 GCs within the field of view of the NATALNewton observation we are interested in: hence. the probability for a chance coincidence between a GC and an AGN as bright as Bo 144 in the 210 keV band within 2.2"" is 2441.5. 7."," There are 20 GCs within the field of view of the XMM-Newton observation we are interested in; hence, the probability for a chance coincidence between a GC and an AGN as bright as Bo 144 in the 2–10 keV band within $''$ is $\pm$ $\times$ $^{-5}$."1121 The 0.310 keV Lighteurve of Χο 144 is consistent with a low state LMXD. but also is consistent with being constant.," The 0.3–10 keV lightcurve of XBo 144 is consistent with a low state LMXB, but also is consistent with being constant."1122 We note that XDBo 144 is ~5 times fainter than XDo 45. and may be more severely limited. by low photon counts.," We note that XBo 144 is $\sim$ 5 times fainter than XBo 45, and may be more severely limited by low photon counts."1123 There is a remarkable similarity between the two systems: they exhibit very similar emission spectra. they are both associated. with GCs. and both appear to have been persistenthy bright over the 730 vear period of observation.," There is a remarkable similarity between the two systems: they exhibit very similar emission spectra, they are both associated with GCs, and both appear to have been persistently bright over the $\sim$ 30 year period of observation."1124 We infer that Χο 144 and. XBo 45 are the same class of object: black hole LAINDs. Likely produced by tidal capture of a main sequence star.," We infer that XBo 144 and XBo 45 are the same class of object: black hole LMXBs, likely produced by tidal capture of a main sequence star."1125 We now consider the influence of metallicity on the xobabilitv of finding black hole LAINBs in. GC's., We now consider the influence of metallicity on the probability of finding black hole LMXBs in GCs.1126 ? discovered. a novel mechanism to promote tidal capture a ugher metallicities. in addition to the previously suspectec correlation between metallicity ancl initial mass. function (AIF).," \citet{bel95} discovered a novel mechanism to promote tidal capture at higher metallicities, in addition to the previously suspected correlation between metallicity and initial mass function (IMF)."1127 They assume that for a fixed. cluster density. the rate of tidal capture depends on the mass and. radius of he capturing star.," They assume that for a fixed cluster density, the rate of tidal capture depends on the mass and radius of the capturing star."1128 They find that higher metallicity stars jwe larger masses and radii: therefore. they expect the tida capture rate to increase with metallicity.," They find that higher metallicity stars have larger masses and radii; therefore, they expect the tidal capture rate to increase with metallicity."1129 Furthermore. a metal-rich star will more easily fill its Roche lobe.," Furthermore, a metal-rich star will more easily fill its Roche lobe."1130 Vhev conclude that this οσοι alone could. explain the observec ratio between frequencies of X-ray sources in metal-rich ane metal-poor clusters. although there is no reason to exclude the elfects of metallicity on the IME.," They conclude that this effect alone could explain the observed ratio between frequencies of X-ray sources in metal-rich and metal-poor clusters, although there is no reason to exclude the effects of metallicity on the IMF."1131 7 have produced the most comprehensive survey of metallicities of M31. GCs vet made., \citet{fan08} have produced the most comprehensive survey of metallicities of M31 GCs yet made.1132 They combine spectroscopically-derived metallicities for 295 GCs and GC candidates with colour-derived metallicities for 209 GCs and candidates., They combine spectroscopically-derived metallicities for 295 GCs and GC candidates with colour-derived metallicities for 209 GCs and candidates.1133 ? found à mean. Fe/l] οἱ 1.2940.03 for the, \citet{fan08} found a mean [Fe/H] of $-$ $\pm$ 0.03 for the1134The expected umber is 220R4C,"The expected number is $2\pi \nbar R\,dR$."1135" Treating the iutegral as à Riemann sum in which the bins are so sinall as to contain O or 1 observed pair leads to the conclusion that ο.» GUI) where the sums are over the objects in spectroscopic subsample aud the Πασπα subsample. respectively, Nop is the umnber of spectroscopic objects. and jj is the transverse separation of the ]dh"" spectroscopic object to the A imaging object."," Treating the integral as a Riemann sum in which the bins are so small as to contain 0 or 1 observed pair leads to the conclusion that = ) where the sums are over the objects in spectroscopic subsample and the imaging subsample, respectively, $N_{sp}$ is the number of spectroscopic objects, and $R_{jk}$ is the transverse separation of the $j^{th}$ spectroscopic object to the $k^{th}$ imaging object."1136 An Προτα! point is that we can now treat cach spectroscopic object separately. vieldiue the following nolsv measure of the overdensity around object j: Py j)(," An important point is that we can now treat each spectroscopic object separately, yielding the following noisy measure of the overdensity around object $j$: _j = )."113712) Note how simple this formula is: one counts the imaging objects. weighting by GR). and divides by the expectedumber of objects in the real-space window (Woy).," Note how simple this formula is: one counts the imaging objects, weighting by $G(R)$, and divides by the expectednumber of objects in the real-space window $V\phi_0$ )."1138 We can recover the average density around any subset of the spectroscopic sample simply by averaging the selected Aj., We can recover the average density around any subset of the spectroscopic sample simply by averaging the selected $\Delta_j$.1139 It is interesting to conirpare equation (??)) to a more conventional backerouud-subtraction method iu which one suns all of the objects in an angular aperture aud subtracts an appropriately scaled value of the areal density averaged over the entire survey., It is interesting to compare equation \ref{eq:Deltaj}) ) to a more conventional background-subtraction method in which one sums all of the objects in an angular aperture and subtracts an appropriately scaled value of the areal density averaged over the entire survey.1140 This would correspond to a G function that was coustaut and positive for R less than the aperture aud then constant aud negative for all greater R., This would correspond to a $G$ function that was constant and positive for $R$ less than the aperture and then constant and negative for all greater $R$.1141 The ditfereuce is that this background subtraction would eive an estimate for the deusity in a cvlindrical region. iu which the axis of the evliuder lies along the line of sight aud is much longer than the radius of the cvlinder.," The difference is that this background subtraction would give an estimate for the density in a cylindrical region, in which the axis of the cylinder lies along the line of sight and is much longer than the radius of the cylinder."1142 The resulting density would sample the correlation function £i at a wide ranee of radii., The resulting density would sample the correlation function $\xiis$ at a wide range of radii.1143 The formula eiven here creates a compact region in all three dimoeusious., The formula given here creates a compact region in all three dimensions.1144 Some workers (c.g..Gaidos1997:Valottoctal.1997). have used anlar regious for the determination of the background.," Some workers \citep[e.g.,][]{Gai97,Val97} have used annular regions for the determination of the background."1145 This tzuucates the evliudrical region in some fashion. but the detailed effects were not assessed.," This truncates the cylindrical region in some fashion, but the detailed effects were not assessed."1146" For a useful aud illustrative example.we will treat the case in which the window is assuued to be a Gaussian: Wr)-=expt249,42r7/2a7)."," For a useful and illustrative example,we will treat the case in which the window is assumed to be a Gaussian $W(r) = \exp(-r^2/2a^2)$."1147" The: volume of+ the window: is: V-—(απ)ο3/22 σα, ", The volume of the window is $V=(2\pi)^{3/2}a^3$ .1148Then: F(R) = L.1).., Then F(R) = _0^R = .1149 Then CUR} —, Then G(R) =1150constitutive plivsies lor dense helium. including a better calculation of the ionization equilibrium and of the Ile ff and Ravleigh scattering absorptions (lelesiasοἱal.|2002:Kowalski&Saumon2004:Kowalskietal.2005. 2006).,"constitutive physics for dense helium, including a better calculation of the ionization equilibrium and of the $^-$ ff and Rayleigh scattering absorptions \citep{irs02,KS04,KSM05,KMS06}."1151.. A detailed description of these models will be the subject of a future publication., A detailed description of these models will be the subject of a future publication.1152 Qualitativelv. (he correlations in dense fluid He reduces the contribution of Raleigh scattering by à factor of ~10 (Iglesiasοἱal.2002) and the strong interactions in the fluid increase the ionization fraction (aud hence. the Lf opacity) by 2-3 orders of magnitude (Ixowalskietal.2005. 2006)..," Qualitatively, the correlations in dense fluid He reduces the contribution of Raleigh scattering by a factor of $\sim 10$ \citep{irs02} and the strong interactions in the fluid increase the ionization fraction (and hence, the $^-$ ff opacity) by 2-3 orders of magnitude \citep{KSM05,KMS06}. ."1153 The combination of these effects make If 1e only important source of opacity in these models., The combination of these effects make $^-$ ff the only important source of opacity in these models.1154 On the other hand. because of a lower ionization Traction and the higher Ravleigh scattering opacity in a dilute gas. the pure 116 model spectra of Bergeronetal.(1995a) ave affected by both opacities (see their Fig.," On the other hand, because of a lower ionization fraction and the higher Rayleigh scattering opacity in a dilute gas, the pure He model spectra of \citet{bsw95} are affected by both opacities (see their Fig."1155 13)., 13).1156 since [fis a nearly grav opacityv. our pure Le atmosphere models are essentially grav and (he emereent [αν is close to that. of a black body.," Since $^-$ ff is a nearly gray opacity, our pure He atmosphere models are essentially gray and the emergent flux is close to that of a black body."1157 The colors of this pure He sequence are shown in Fie., The colors of this pure He sequence are shown in Fig.1158 4 along with those of black bodies., 4 along with those of black bodies.1159 Compared to the Bergeronetal.(1995a) pure 119 sequence. to our pure IL sequence. aud to the observed sequence of vervcool WDs. this new pure Ile sequence is much redder for ToyS4500 Ix. As the ionization fraction is sullicientlv large for the Wf opacity to dominate. the colors of our new Ie sequence are insensitive (o modest pollution by metals since increasing the fraction of free electrons will onlv increase (he ff opacity without anv effect on the emergent spectrum.," Compared to the \citet{bsw95} pure He sequence, to our pure H sequence, and to the observed sequence of verycool WDs, this new pure He sequence is much redder for $\teff\wig< 4500\,$ K. As the ionization fraction is sufficiently large for the $^-$ ff opacity to dominate, the colors of our new He sequence are insensitive to modest pollution by metals since increasing the fraction of free electrons will only increase the $^-$ ff opacity without any effect on the emergent spectrum."1160 On the basis of the location of the pure II and pure Ie model sequences in the color-color diagrams (Fig., On the basis of the location of the pure H and pure He model sequences in the color-color diagrams (Fig.1161 4) ancl the excellent fit we obtain for WD2054—050 with a pure hydrogen model. it appears that the atmospheric composition of the coolest DC stars needs to be revisited.," 4) and the excellent fit we obtain for $-$ 050 with a pure hydrogen model, it appears that the atmospheric composition of the coolest DC stars needs to be revisited."1162 The existence of an unidentified absorption mechanism i cool hydrogen white dwarls abmospheres was reported a decade ago (Bergeronetal.1997)., The existence of an unidentified absorption mechanism in cool hydrogen white dwarfs atmospheres was reported a decade ago \citep{BRL97}.1163. The interpretation of this missing Opacity as the pseudo-continuum absorption from hydrogen atoms has been recently shown to be incorrect. (IXowalski2006b)., The interpretation of this missing opacity as the pseudo-continuum absorption from hydrogen atoms has been recently shown to be incorrect \citep{Kowalski06b}.1164. On the other hand. the red wing of the Lva line opacity [roi hydrogen could provide the required absorption (Wolffetal.2002).," On the other hand, the red wing of the $\rm Ly \, \alpha$ line opacity from hydrogen could provide the required absorption \citep{Wolff02}."1165. We present a new calculation of the exireme pressure-broadening of the Lvo line by both I and Il.," We present a new calculation of the extreme pressure-broadening of the $\rm Ly \,1166\alpha$ line by both $\rm H$ and $\rm H_2$."1167 When included in our new pure hydrogen a(mosphere models. we obtained an excellent agreement wilh the UV/optical/near-IH8R spectral energy distribution (SED) of the cool DA white dwarf DPM 4729 and we successfully fitted the D through Ix spectral energy distributions of stars with hvdrogen-rich atmospheres. as determined bv Dergeron andBergeronetal. (2001)..," When included in our new pure hydrogen atmosphere models, we obtained an excellent agreement with the UV/optical/near-IR spectral energy distribution (SED) of the cool DA white dwarf BPM 4729 and we successfully fitted the B through K spectral energy distributions of stars with hydrogen-rich atmospheres, as determined by \citet{BRL97} and\citet{BLR01}. ."1168 The inclusion of broadening bv collisions with Hs is essential to reproduce the SED of very cool hydrogen white clwarls., The inclusion of broadening by collisions with $_2$ is essential to reproduce the SED of very cool hydrogen white dwarfs.1169comparable luminosity and a very long pulse period (2? = 5560 8). and in the X-ray pulsar (P? = 358.6 s) SAX J2103.54-4545 (2). ,"comparable luminosity and a very long pulse period $P$ = 5560 s), and in the X–ray pulsar $P$ = 358.6 s) SAX J2103.5+4545 \citep{Inam+04}. ."1170In Fig., In Fig.1171 7 we report the best-fit radius and temperature for these sources. together with lines showing four different levels of the blackbody luminosity.," \ref{BBparameters} we report the best–fit radius and temperature for these sources, together with lines showing four different levels of the blackbody luminosity."1172" In the case of circles) and 4U 03524309 squares). we report two set of values. since both sources were observed by aand aat two different luminosity levels (Lx~10?! and ~1075 erg +, respectively): in the case of tthe low and high luminosity were observed by aand respectively. while for 4U 03524309 it was the opposite."," In the case of ) and 4U 0352+309 ), we report two set of values, since both sources were observed by and at two different luminosity levels $L_{\rm X} \sim 10^{34}$ and $\sim 10^{35}$ erg $^{-1}$, respectively): in the case of the low and high luminosity were observed by and respectively, while for 4U 0352+309 it was the opposite."1173 We report various measurements also for 4U 2206454 (crosses). corresponding to different observations.," We report various measurements also for 4U 2206+54 ), corresponding to different observations."1174 The figure shows that the results obtained for aare in full agreement with those obtained by various observations of the previous sources. since their spectral parameters are clustered in a narrow range of values. re. Τον~ I-15 keV and Py~ 100 m. We emphasize that. in all these cases. the estimated total source X-ray luminosity is ~JU eres +. with a 20-40 contribution of the blackbody component.," The figure shows that the results obtained for are in full agreement with those obtained by various observations of the previous sources, since their spectral parameters are clustered in a narrow range of values, i.e. $kT_{\rm BB} \sim$ 1–1.5 keV and $R_{\rm BB} \sim$ 100 m. We emphasize that, in all these cases, the estimated total source X–ray luminosity is $\sim 10^{34}$ erg $^{-1}$, with a 20–40 contribution of the blackbody component."1175 For the persistent Be pulsars aand 4U 03524309. spectral values outside the previous range (points 2 and 4) were obtained by the oobservation of 4U 03524309 and the oobservation of J1037.5-5647.. when the sources were detected at a higher luminosity level (Lx.~10°? erg 4): however. we note that comparable blackbody parameters were obtained also for SAX J2103.54+4545. which is characterized by a comparable luminosity.," For the persistent Be pulsars and 4U 0352+309, spectral values outside the previous range (points 2 and 4) were obtained by the observation of 4U 0352+309 and the observation of , when the sources were detected at a higher luminosity level $L_{\rm X} \sim 10^{35}$ erg $^{-1}$ ); however, we note that comparable blackbody parameters were obtained also for SAX J2103.5+4545, which is characterized by a comparable luminosity."1176 On the other hand. in most cases the non-Be binary pulsar 4U 2206+54 shows a different behavior also when observed at a comparable Iuminosity level: AiIpp«1keV and Rpp> 500 m (points 8 to 11).," On the other hand, in most cases the non–Be binary pulsar 4U 2206+54 shows a different behavior also when observed at a comparable luminosity level: $kT_{\rm BB} <$ 1 keV and $R_{\rm BB} >$ 500 m (points 8 to 11)."1177 Finally. we note that the sspectrum of iis characterized by the hardest component among the previous sources. since it has a photon-index D 2 0.5. while T>Linallthe other sources.," Finally, we note that the spectrum of is characterized by the hardest component among the previous sources, since it has a photon–index $\Gamma$ = 0.5, while $\Gamma \ge 1$ in all the other sources."1178 An X-ray excess has been observed also in several other XBPs (see?forareview) but. contrary to the previous sources. in their case the fit of this excess with a thermal emission model provided low temperatures (&T.« 0.5 keV) and large emitting regions > 100 km): for this reason. this feature is usually described as a excess.," An X–ray excess has been observed also in several other XBPs \citep[see][ for a review]{LaPalombaraMereghetti2006} but, contrary to the previous sources, in their case the fit of this excess with a thermal emission model provided low temperatures $kT <$ 0.5 keV) and large emitting regions $>$ 100 km); for this reason, this feature is usually described as a excess."1179 In Fig., In Fig.1180 8 we report the luminosity and pulse period of the XBPs with a detected thermal excess., \ref{luminosity_period} we report the luminosity and pulse period of the XBPs with a detected thermal excess.1181" They are divided in two well distinet groups: the sources in the first group are characterized by high luminosity (Lx=10°"" eres. +) and short pulse period < 100 s). and in most cases they are in close binary systems with an accretion disk: those in the second group have low luminosities (Lx.<1079 erg 1 and long pulse periods > 100 s). since they have wide orbits and are wind fed systems."," They are divided in two well distinct groups: the sources in the first group are characterized by high luminosity $L_{\rm X}\ge10^{37}$ erg $^{-1}$ ) and short pulse period $<$ 100 s), and in most cases they are in close binary systems with an accretion disk; those in the second group have low luminosities $L_{\rm X}\le10^{36}$ erg $^{-1}$ ) and long pulse periods $>$ 100 s), since they have wide orbits and are wind fed systems."1182 Among the sources of the second group of XBPs. the six pulsars discussed above (reported as and circle)) are the ones that have. at the same time. the lowest luminosities and the longest periods with the only exception of SAX J2103.5+4545. which has the highest luminosity of this group of sources.," Among the sources of the second group of XBPs, the six pulsars discussed above (reported as and ) are the ones that have, at the same time, the lowest luminosities and the longest periods with the only exception of SAX J2103.5+4545, which has the highest luminosity of this group of sources."1183 They are characterized by a component with a high temperature and a small emission radius. while the others show a thermal excess with low temperature (AT« 0.5 keV) and largeemission area ~ a few hundred km).," They are characterized by a component with a high temperature and a small emission radius, while the others show a thermal excess with low temperature $kT <$ 0.5 keV) and largeemission area $\sim$ a few hundred km)."1184 The spectral component separates these low-luminosity and long-period sourcesfrom all the, The spectral component separates these low–luminosity and long–period sourcesfrom all the1185brightest object isnof necessarily the optical counterpart of theROSAT source.,brightest object is necessarily the optical counterpart of the source.1186 The brightest sources 52.1. 62.1 and 65.1 (the first ΠΡΟ being the source nuniber and the decimal the source label) in Fig.," The brightest sources 52.1, 62.1 and 65.1 (the first number being the source number and the decimal the source label) in Fig."1187 6 are at least one magnitude brighter han the uext füuter object within the fiudiug circle (see Table D)., \ref{ps:charts} are at least one magnitude brighter than the next fainter object within the finding circle (see Table \ref{tab:shapepars}) ).1188 Object 63.1 has about the same maenitude as object 63.2., Object 63.1 has about the same magnitude as object 63.2.1189 Therefore no clear preference can be given just from considering the Lbaud fiux., Therefore no clear preference can be given just from considering the I-band flux.1190 The PSF-shape xuwanmeters of these [objects agree with those fouud for stars (soe Fie. 7))., The PSF-shape parameters of these 4 objects agree with those found for stars (see Fig. \ref{ps:shapepars}) ).1191 The CL classification of SExtractor outs all [ sources iu the poiut-source regune., The CL classification of SExtractor puts all 4 sources in the point-source regime.1192 Yet. the optical Ποιος are prone to niüs-classification since not every brightest object is most ceutral within the finding circle.," Yet, the optical findings are prone to mis-classification since not every brightest object is most central within the finding circle."1193 Although they are not the briehtest. the sources 62.5 and 63.2 are the most likely candidate optical counterparts Guterine from their most central position only).," Although they are not the brightest, the sources 62.5 and 63.2 are the most likely candidate optical counterparts (infering from their most central position only)."1194 These were classified as slightly extended aud slightly elliptical. respectively.," These were classified as slightly extended and slightly elliptical, respectively."1195 As can be seen from Fig., As can be seen from Fig.1196 6 there are 2 fiudiug charts (i.c. charts 62 and 65) from the edge of the CCD image., \ref{ps:charts} there are 2 finding charts (i.e. charts 62 and 65) from the edge of the CCD image.1197 Thus. we cannot exclude Irighter objects within the area rot covered bv the exposure.," Thus, we cannot exclude brighter objects within the area not covered by the exposure."1198 Chart 59 is too crowded o give a reliable identification onlv ou the basis of aux photometric PSF-shape parameter., Chart 59 is too crowded to give a reliable identification only on the basis of any photometric PSF-shape parameter.1199 However. we note that he center of theROSAT eror circle coincides with the ealaxy’s center.," However, we note that the center of the error circle coincides with the galaxy's center."1200 Thus. it is very likely that theROSAT source Is connected with a N-ray source which is located rear the ceuter of the galaxy.," Thus, it is very likely that the source is connected with a X-ray source which is located near the center of the galaxy."

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