ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 For the three microquasars GRO J1655-40. XTE J1550-564 and GRS 1915+105 measurements of their masses have been made but there is so far no way to determine the angular momenta. so the test is necessarily restricted to their masses.," For the three microquasars GRO J1655-40, XTE J1550-564 and GRS 1915+105 measurements of their masses have been made but there is so far no way to determine the angular momenta, so the test is necessarily restricted to their masses."3 Masses are usually derived from the determination of the orbit parameters in case of a binary., Masses are usually derived from the determination of the orbit parameters in case of a binary.4 This holds for the three microquasars but also for the blaek hole AA* in the Galactic Center which 15 orbited by the S2 (SO-2) star (Schéddel et al..," This holds for the three microquasars but also for the black hole A* in the Galactic Center which is orbited by the S2 (S0-2) star (Schöddel et al.,"5 2002. Ghez et al..," 2002, Ghez et al.,"6 2003)., 2003).7 Gezel et al. (, Genzel et al. (82003) have reported a QPO period of min observed in two new-infrared flares.,2003) have reported a QPO period of min observed in two near-infrared flares.9 Aschenbach et al. (, Aschenbach et al. (1020041) have claimed additionally quasi-periods around s. s. s and s. with the s period being consistent with the NIR period.,"2004) have claimed additionally quasi-periods around s, s, s and s, with the s period being consistent with the NIR period."11 This set of quasi-periods was found in the power density spectra of one X-ray flare observed withChandra (Baganoff et al..," This set of quasi-periods was found in the power density spectra of one X-ray flare observed with (Baganoff et al.,"12 2001) and a second X-ray flare with (Porquet et al..," 2001) and a second X-ray flare with (Porquet et al.,"13 2003)., 2003).14 Interesting in this context is that the frequencies corresponding to the latter three quasi-periods are close to a 3:2:1 ratio., Interesting in this context is that the frequencies corresponding to the latter three quasi-periods are close to a 3:2:1 ratio.15 Enforeing such a ratio sequence in a best fit. it turns out that such a ratio is consistent with the measurements.," Enforcing such a ratio sequence in a best fit, it turns out that such a ratio is consistent with the measurements."16 Accordingly. | include the Galactic Center black hole in this test and predict the mass of AA*.," Accordingly, I include the Galactic Center black hole in this test and predict the mass of A*."17 The frequencies in question are 450 and 300 Hz (Strohmayer 2001a. Remillard et al.," The frequencies in question are 450 and 300 Hz (Strohmayer 2001a, Remillard et al."18 1999) with Oq- Ξ 450 Hz., 1999) with $\Omega\sb{V}$ = 450 Hz.19 According to Equation 5. the predicted black hole mass is Ap;=6.760.13..., According to Equation \ref{eq:5} the predicted black hole mass is $M\sb{BH} = 6.76 \pm 0.1 M\sb{\odot}$ .20 The relative uncertainty of the mass ts the same as that of the HFQPO measurements of z1.5%.., The relative uncertainty of the mass is the same as that of the HFQPO measurements of $\approx$.21 Dynamical mass measurements have been reported by Orosz Bailyn (1997) with A/5;;=7.02d0.22M.. and more recently by Greene et al. (, Dynamical mass measurements have been reported by Orosz Bailyn (1997) with $M\sb{BH} = 7.02\pm 0.22 M\sb{\odot}$ and more recently by Greene et al. (222001) who obtained a mass range of pj;=5.8.G:8M,2001) who obtained a mass range of $M\sb{BH} = 5.8 - 6.8 M\sb{\odot}$.23 The agreement between model prediction and observation is quite satisfactory., The agreement between model prediction and observation is quite satisfactory.24 Frequencies of 276 and 184 Hz (Remillard et al..," Frequencies of 276 and 184 Hz (Remillard et al.,"25 2002) have been measured., 2002) have been measured.26 With Οι: = 276 Hz Equation 5 predicts a black hole mass of Ap;=11.010.2ÀA7..., With $\Omega\sb{V}$ = 276 Hz Equation \ref{eq:5} predicts a black hole mass of $M\sb{BH} = 11.04 \pm 0.2 M\sb{\odot}$.27 The relative uncertainty of the mass is again due to the accuracy of the HFQPO measurements of z2%.., The relative uncertainty of the mass is again due to the accuracy of the HFQPO measurements of $\approx$.28 I»Dynamical mass measurements have been reported by Orosz et al. (, Dynamical mass measurements have been reported by Orosz et al. (292002a) with a +10 mass range of Mpj=S.I.11.6A/.. which is nicely matched by the predicted mass.,"2002a) with a $\pm$ $\sigma$ mass range of $M\sb{BH} = 8.4 - 11.6 M\sb{\odot}$, which is nicely matched by the predicted mass."30 The relevant 3:2 pair at 168 and 113 Hz has only recently been found (Remillard et al..," The relevant 3:2 pair at 168 and 113 Hz has only recently been found (Remillard et al.,"31 2003. McClintock Remillard. 2004).," 2003, McClintock Remillard, 2004)."32 With Ου: = 168 Hz Equation 5. predicts a black hole mass of lpj;=18.13+0.363..., With $\Omega\sb{V}$ = 168 Hz Equation \ref{eq:5} predicts a black hole mass of $M\sb{BH} = 18.13 \pm 0.36 M\sb{\odot}$.33" The relative uncertainty of the mass is due the accuracy of the HFQPO measurements of z2%,..", The relative uncertainty of the mass is due the accuracy of the HFQPO measurements of $\approx$.34 Dynamical mass measurements have been reported by Greiner at al. (, Dynamical mass measurements have been reported by Greiner at al. (35"2001) with Afpy,,=110czLOAL.. and Harlaftis Greiner (2004) with 3p;=τιοτε11M...",2001) with $M\sb{BH} = 14.0 \pm 4.0 M\sb{\odot}$ and Harlaftis Greiner (2004) with $M\sb{BH} = 14.0 \pm 4.4 M\sb{\odot}$.36 Also in this case the predicted mass matches the dyamically mass within the «1o range. but the measurements of this source illustrate nicely the potential uncertainty in cynamical mass measurements.," Also in this case the predicted mass matches the dynamically mass within the $\pm$ $\sigma$ range, but the measurements of this source illustrate nicely the potential uncertainty in dynamical mass measurements."37 Harlaftis Greiner (2004) point out that the biggest uncertainty is related to the inclinatico of the orbit. which for GRS 19154105 is taken from the iclination of the associated jet assuming that the Jet axis ts orthogonal to the orbital plane of the binary.," Harlaftis Greiner (2004) point out that the biggest uncertainty is related to the inclination of the orbit, which for GRS 1915+105 is taken from the inclination of the associated jet assuming that the jet axis is orthogonal to the orbital plane of the binary."38 If. for instance. the 1nclination angle is changed from the adopted to the estimated black hole mass is Mp;=16.945.0M. (Harlaftis Greiner. 2004).," If, for instance, the inclination angle is changed from the adopted $\sp{\deg}$ to $\sp{\deg}$ the estimated black hole mass is $M\sb{BH} = 16.9 \pm 5.9 M\sb{\odot}$ (Harlaftis Greiner, 2004)."39 Actually. Kaiser et al. (," Actually, Kaiser et al. ("402004) suggest that the inclination angle is putting the best estimate for the dynamical black hole mass at 17.8 A... which is within the 316 measurement,"2004) suggest that the inclination angle is $\sp{\deg}$ putting the best estimate for the dynamical black hole mass at 17.8 $M\sb{\odot}$ , which is within the $\pm$ $\sigma$ measurement"41The alternative technique we use to analyse the stellar populations of 3357 is to cross-correlate the galaxy spectrum with each SSP spectrum from the Vazdekisetal.(2010) model library.,The alternative technique we use to analyse the stellar populations of 357 is to cross-correlate the galaxy spectrum with each SSP spectrum from the \citet{2010MNRAS.404.1639V} model library.42" For this purpose the model spectra are previously prepared to match the spectral range, velocity dispersion, and spectral resolution of the data."," For this purpose the model spectra are previously prepared to match the spectral range, velocity dispersion, and spectral resolution of the data."43" Moreover, the galaxy and model spectra are rebinned logarithmically and normalized to remove the continua."," Moreover, the galaxy and model spectra are rebinned logarithmically and normalized to remove the continua."44" In order to optimize the cross-correlation method for disentangling different stellar populations, it is necessary to adequately filter the spectra and multiply them by a cosine-bell-like function (Tonry&Davis1979).."," In order to optimize the cross-correlation method for disentangling different stellar populations, it is necessary to adequately filter the spectra and multiply them by a cosine-bell-like function \citep{1979AJ.....84.1511T}."45" The importance of choosing a suitable filter lies in the possibility of getting rid of the noise in the spectrum; this purpose can be achieved by simply removing the largest wavenumbers, where the information about the shortest wavelength ranges is included."," The importance of choosing a suitable filter lies in the possibility of getting rid of the noise in the spectrum; this purpose can be achieved by simply removing the largest wavenumbers, where the information about the shortest wavelength ranges is included."46" Therefore, the limit is imposed by the resolution of the data."," Therefore, the limit is imposed by the resolution of the data."47" On the other hand, shorter wavenumbers contain information about wider spectral ranges, so possible residuals of the continuum removal due to errors in the flux calibration might also be filtered."," On the other hand, shorter wavenumbers contain information about wider spectral ranges, so possible residuals of the continuum removal due to errors in the flux calibration might also be filtered."48" The drawback of this procedure is that it implies a power loss of the final cross-correlation function, specially when filtering short wavenumbers where most of the signal is included."," The drawback of this procedure is that it implies a power loss of the final cross-correlation function, specially when filtering short wavenumbers where most of the signal is included."49" Apart from the filtering, it might be required to mask some regions in the original spectra, as is usually done in the full-spectrum fitting technique in the wavelength space."," Apart from the filtering, it might be required to mask some regions in the original spectra, as is usually done in the full-spectrum fitting technique in the wavelength space."50 We tested different masks trying to avoid those features that are not well reproduced by the models due to mismatched abundance ratios: the CN in the blue spectral range and the Mg and Hf features in the red spectral range., We tested different masks trying to avoid those features that are not well reproduced by the models due to mismatched abundance ratios: the CN in the blue spectral range and the Mg and $\beta$ features in the red spectral range.51" Again, these features contain most of the signal of the power spectrum so the choice of the masks has to be done very carefully in order to not lose most of the information."," Again, these features contain most of the signal of the power spectrum so the choice of the masks has to be done very carefully in order to not lose most of the information."52" Finally, the peak height obtained for each correlation function is plotted against the model age and metallicity."," Finally, the peak height obtained for each correlation function is plotted against the model age and metallicity."53 Since the cross-correlation profile reaches a higher value when object and template are more similar (getting a, Since the cross-correlation profile reaches a higher value when object and template are more similar (getting a54model so that the 230GIIz flux is 3.4Jv.,model so that the $230\GHz$ flux is $3.4\Jy$.55 The model can also fal by cooling too rapillv to be consistent wilh our neglect of cooling in the dynamical model., The model can also fail by cooling too rapidly to be consistent with our neglect of cooling in the dynamical model.56 The Tables list a radiative efficiency 72μοιMc. where Lpoy is the bolometric Iuminositv. (1ntegrated over solid angle). and for comparison a thin disk efficiency. at the same ἄν.," The Tables list a radiative efficiency $\eta \equiv L_{\rm BOL}/\mdot c^2$, where $L_{\rm BOL}$ is the bolometric luminosity (integrated over solid angle), and for comparison a thin disk efficiency at the same $a_*$ ."57" ranges between 5.4x10! for a,—0.5.Ti/T.=10 to 0.18 [or a,=0.98.75/7.1 (the thin disk efficiency for (he latter is 0.25)."," $\eta$ ranges between $5.4 \times 10^{-4}$ for $a_* = 0.5, \Trat = 10$ to $0.18$ for $a_* = 0.98, \Trat = 1$ (the thin disk efficiency for the latter is $0.25$ )."58" Only in the e,=0.98. T/T.=1 model is the radiative efficiency. sufficiently high that cooling is likely to have a significant. effect on the GRMIID model."," Only in the $a_* = 0.98$, $\Trat = 1$ model is the radiative efficiency sufficiently high that cooling is likely to have a significant effect on the GRMHD model."59 We will consider models with cooling in a [uture publication., We will consider models with cooling in a future publication.60 Very [ew of the time averaged SEDs based on a single-temperature (7)/7.=1) models produce the correct o.," Very few of the time averaged SEDs based on a single-temperature $\Trat61= 1$ ) models produce the correct $\alpha$."62 The exception is edge-on lori (/=85dee) around [ast spinning black holes (model E and E)., The exception is edge-on tori $i=85\deg$ ) around fast spinning black holes (model E and F).63 These models are ruled out. however. because they overproduce NIR and X-ray (lus.," These models are ruled out, however, because they overproduce NIR and X-ray flux."64" For T;/T.=3 only the model with e,=0.94 seen al /=85dee agrees with the data.", For $\Trat=3$ only the model with $a_* = 0.94$ seen at $i=85\deg$ agrees with the data.65 This is the best-bet model discussed im ??.., This is the best-bet model discussed in \ref{sec:4.1}.66" For 7=85deg. models with spins below a,=0.94 (A. D and C) are ruled out by the inconsistent spectral slope. and models with hieher spins (E and F). allhoueh consistent with the observed a. overproduce the quiescent NIR and X-ray emission."," For $i=85\deg$, models with spins below $a_* = 0.94$ (A, B and C) are ruled out by the inconsistent spectral slope, and models with higher spins (E and F), although consistent with the observed $\alpha$, overproduce the quiescent NIR and X-ray emission."67 All models with 7;/7.=3 observed al 7=5deg and 45cdeg are ruled out by the inconsistent a., All models with $\Trat=3$ observed at $i=5\deg$ and $45\deg$ are ruled out by the inconsistent $\alpha$.68 For 7/7.=10. we find that all models with 7=85deg are ruled out by both a and violation of NIB. and X-ray. limits.," For $\Trat=10$, we find that all models with $i=85\deg$ are ruled out by both $\alpha$ and violation of NIR and X-ray limits."69 For lower inclination angles (7=5deg.45 clea) a few models (E and F with /=5deg. and A. D. C. and D at ¢=15 clee) reproduce the observed a.," For lower inclination angles $i=5\deg,45\deg$ ) a few models (E and F with $i =705\deg$, and A, B, C, and D at $i = 45\deg$ ) reproduce the observed $\alpha$."71 These models are consistent with N-ravs and NIB. limitations., These models are consistent with X-rays and NIR limitations.72 Models E andF for 7=45deg are ruled oul by NIR ancl X-ray. limitations whereas models A. D. C and D for 7=5deg produce a which is too small.," Models E andF for $i=45\deg$ are ruled out by NIR and X-ray limitations whereas models A, B, C and D for $i=5\deg$ produce $\alpha$ which is too small."73 What is the physical origin of (hese constraints?, What is the physical origin of these constraints?74" The dependence on e, arises lareely because as a, increases (he inner edge of the clisk the ISCO — reaches deeper into the gravitational potential of the black hole. where the temperature and magnetic field strength are higher."," The dependence on $a_*$ arises largely because as $a_*$ increases the inner edge of the disk — the ISCO – reaches deeper into the gravitational potential of the black hole, where the temperature and magnetic field strength are higher."75" In the disk mid-plaue. the temperature is a fraction of the virial temperature and scales with radius 0,xl/r. Dxαν. "," In the disk mid-plane, the temperature is a fraction of the virial temperature and scales with radius $\Theta_e \propto 1/r$. $B \propto 1/r$,"76while the density. ~r. below the pressure maximunm.," while the density $\sim77r$, below the pressure maximum."78 Holding all else constant (which we do not: we hold the 230Gllz flix constant) this implies a higher peak [requency for svuchrotron emission. a constant Thomson depth (in our modelsthe Thomson depth at the ISCO is roughly constant. since the path length 1/~rgo but the density 7 rico). aud a larger energy boost per scattering 1z 1607. as can be seen in comparing models with different," Holding all else constant (which we do not: we hold the $230\GHz$ flux constant) this implies a higher peak frequency for synchrotron emission, a constant Thomson depth (in our modelsthe Thomson depth at the ISCO is roughly constant, since the path length $1/\sim \risco$ but the density $\sim \risco$ ), and a larger energy boost per scattering $A \approx 16 \Theta_e^2$ , as can be seen in comparing models with different"79The spin composition of the proton in terms of its fundamental quark and eluon degrees of freedom is a central focus of proton structure.,The spin composition of the proton in terms of its fundamental quark and gluon degrees of freedom is a central focus of proton structure.80 Whether the quark orbital angular momentum is zero or not is one of the kev points to solve this problem., Whether the quark orbital angular momentum is zero or not is one of the key points to solve this problem.81 The importance of quark orbital angular momentum. whieh one might have taken to vanish in the ground state. has been evident since the work of Sehgal |1]..," The importance of quark orbital angular momentum, which one might have taken to vanish in the ground state, has been evident since the work of Sehgal \cite{seh74}."82 The orbital angular momentum structure of the proton is, The orbital angular momentum structure of the proton is83Ιω A μοντί2NLN],$\rho_{\rm local}$ and $N_{\rm HDF-N}^{(m<28.8)}$.84 Results are plotted in− Fig.− 5.. ," Results are plotted in Fig. \ref{mod_halo}, ,"85"where pi and Nieτί38,8]< are shown as unctons of ALfpsony. the absolute magnitude of the halo population objects."," where $\rho_{\rm local}$ and $N_{\rm HDF-N}^{(m<28.8)}$ are shown as functions of $M_{\rm F606W}$, the absolute magnitude of the halo population objects."86 Tmiis figure implies (he existence of a large number of halo objects that should be present . ∐⊔∐↲∐↻∊↕∐⋯≸≟≼↲⋟, This figure implies the existence of a large number of halo objects that should be present in the HDF images.87∖⊽⋅⋋≼≻↥↩⊔⋯↴↥↼∖↓↓↻↓⇄⋋↕⋟∖⇁↖≺↽↔↴↕⋅≼↲≀↧↴∩↲↕⋅⊔↥≀↧↴∐↴∿↴−≻↱≻∪↕∐≀↧↴↥≺∢≀↕⊔∖⊽≼↲⋟∖⊽⋅⊺∐↕⋟∖⊽↕⋅≼↲⋟∖⇁∏∐↕⋟∖⊽∐∪↥., Note that $N_{\rm HDF-N}^{(m<28.8)}$ is greater than $\sim$ 250 in all cases.88 ⋅ - zmNN2pe . . :⋅ ⋅ compatible with the ILDE-N observations. where no obvious stars are present. except [or a ew 200h magnitude ones. (INawaler.1996:Floin.Gould.&Baheall1996).," This result is not compatible with the HDF-N observations, where no obvious stars are present, except for a few 20th magnitude ones, \citep{K96,F96}."89". In conclusion. the observed excess in SBF-measured af, cannot be produced by objects belonging to the Milkv. Wax halo."," In conclusion, the observed excess in SBF-measured $\sigma_{\rm BG}^{2}$ cannot be produced by objects belonging to the Milky Way halo."90 Otherwise a large number of resolved objects from this halo population would show up in the IIDE-N images. which is not tlie case.," Otherwise a large number of resolved objects from this halo population would show up in the HDF-N images, which is not the case."91 If the observed σ]ς; excess cannot be produced by Milky Way halo objects. the only possibility is (hab it is caused by [aint galaxies.," If the observed $\sigma_{BG}^{2}$ excess cannot be produced by Milky Way halo objects, the only possibility is that it is caused by faint galaxies."92" The large excess obtained in (he στ, with respect to the n(m)-estimated o7,; would imply an increase in the slope of n(m) al some magnitude fainter than my=28.8.", The large excess obtained in the SBF-measured $\sigma_{BG}^{2}$ with respect to the $n(m)$ -estimated $\sigma_{BG}^{2}$ would imply an increase in the slope of $n(m)$ at some magnitude fainter than $m_c=28.8$.93" This slope can be computed by fitting the n(n)-estimated 07,; to our SBF-measured σ]ς; and taking the slope as a [ree parameter.", This slope can be computed by fitting the $n(m)$ -estimated $\sigma_{BG}^{2}$ to our SBF-measured $\sigma_{BG}^{2}$ and taking the slope as a free parameter.94" If it is assumed that the slope change occurs αἱ m,=28.8 for all filters. the resulting slopes for the [ainter range are 5?=0.60. 0.44. ancl 0.54 for Bysy. Ving. ancl {κι respectively."," If it is assumed that the slope change occurs at $m_c = 28.8$ for all filters, the resulting slopes for the fainter range are $\gamma=0.60$, $0.44$, and $0.54$ for $B_{450}$, $V_{606}$, and $I_{814}$, respectively."95" These slopes would be valid up to σου=34.4. Ving=31.9. ancl fy)=32.5 al least since the contribution of fainter magnitudes to o7; becomes smaller than the uncertainties in the SBF-measured 67,; results."," These slopes would be valid up to $B_{450}=34.4$, $V_{606}=31.9$, and $I_{814}=32.5$ at least since the contribution of fainter magnitudes to $\sigma_{BG}^{2}$ becomes smaller than the uncertainties in the SBF-measured $\sigma_{BG}^{2}$ results."96 Hf the slope change were to occur at a magnitude fainter than 28.8. it would result in a steeper vr).," If the slope change were to occur at a magnitude fainter than 28.8, it would result in a steeper $n(m)$."97 In anv case. such bie changes in the slope of n(m) seem unrealistic.," In any case, such big changes in the slope of $n(m)$ seem unrealistic."98 In our opinion. this possibility should be rejected.," In our opinion, this possibility should be rejected."99 As a consequence. it must be concluded that the Williamsetal.(1996) data are incomplete.," As a consequence, it must be concluded that the \citet{W96} data are incomplete."100" Asstuning that the Metealleοἱal.(2001). differential number counts are correct. the SDF-measured o5, results listed in Table 7 and the n(m)-estimated oj; values obtained using the Metcalfeetal.(2001). data. listed in Table 3.. can be compared."," Assuming that the \citet{Met01} differential number counts are correct, the SBF-measured $\sigma_{\rm BG}^2$ results listed in Table \ref{t-results-bg} and the $n(m)$ -estimated $\sigma_{\rm BG}^2$ values obtained using the \citet{Met01} data, listed in Table \ref{t-sigma}, can be compared."101 It can be seen that the SBF-measured and n(m)-estimated σος coincide withinthe error bars for the FSl4W filter. and is very similar for the FASOW filter.," It can be seen that the SBF-measured and $n(m)$ -estimated $\sigma_{\rm BG}^2$ coincide withinthe error bars for the F814W filter, and is very similar for the F450W filter."102 Only in the filter F606W some differences arise., Only in the filter F606W some differences arise.103 This implies that extrapolation of the Metcalfe n(n) bunction to magnitudes fainter than 28.8 accounts almost entirely for the measured, This implies that extrapolation of the \citet{Met01} $n(m)$ function to magnitudes fainter than 28.8 accounts almost entirely for the measured104ealaxiesnupliceatious.andgalaxyIufact.if Dark Matter (DAD aunibhilatious in the halo of clusters have crucial astrophysical DM.,"}\tikzmark{mainBodyEnd0}105\date{Received 16 October 2006 / Accepted 25 January 2007 }106 107\authorrunning {S. Colafrancesco et al.}108 109\titlerunning {SZ effect from 1ES0657-556 cluster}110 111\abstract112 % contex\tikzmark{mainBodyStart1}xt\tikzmark{mainBodyEnd1} \tikzmark{mainBodyStart2}heading\tikzmark{mainBodyEnd2} \tikzmark{mainBodyStart3}(optional)\tikzmark{mainBodyEnd3}113 %{} leave it empty if necessary114 {}\tikzmark{mainBodyStart4}}\tikzmark{mainBodyEnd4}115 % aims heading (mandatory)116 {The cluster \es is an ideal astrophysical laboratory to study the117 distribution and the nature of Dark Matter because this last component is spatially118 separated from the intracluster gas.119 We show that microwave observations can provide crucial probes of Dark Matter in this120 system.}\tikzmark{mainBodyStart5}}\tikzmark{mainBodyEnd5}121 % methods heading (mandatory)122 {We calculate the expected SZ effect from Dark Matter annihilation in the main mass123 concentrations of the cluster 1ES0657-556, and we estimate the sources of contamination,124 confusion and bias to asses its significance.}\tikzmark{mainBodyStart6}}\tikzmark{mainBodyEnd6}125 % results heading (mandatory)126 {We find that SZ observations at $\nu \approx 223$ GHz can resolve both spatially and127 spectrally the SZ$_{DM}$ signal and isolate it from the other SZ signals,128 and mainly from the thermal SZ effect which is null at $ \nu \sim 220-223$ GHz129 for the case of \es. We conclude that SZ observations with $\simlt$ arcmin resolution130 and $\simlt \mu$K sensitivity of \es are crucial, and maybe unique, to find direct131 astrophysical probes of the existence and of the nature of Dark Matter,132 or to set strong experimental limits.}\tikzmark{mainBodyStart7}}\tikzmark{mainBodyEnd7}133 % conclusions heading (optional), leave it empty if necessary134 {}\tikzmark{mainBodyStart8}} Dark Matter (DM) annihilations in the halo of galaxies and galaxy clusters have crucial astrophysical implications."135 is constituted by weakly interacting inassive particles (for which the leaciug candidate is the liehtest supersviuinetrie particle. plausibly the ucutralino X). their annihilation produces secondary particles (e.g. neutral aud charged pious. secondary electrons and protons. neutrinos) that eive rise to various astrophysical signals.," In fact, if DM is constituted by weakly interacting massive particles (for which the leading candidate is the lightest supersymmetric particle, plausibly the neutralino $\chi$ ), their annihilation produces secondary particles (e.g., neutral and charged pions, secondary electrons and protons, neutrinos) that give rise to various astrophysical signals."136 These are. amoung others. observable fluxes of positrous. antiprotous. eamunua raves. neutrinos. as well as signals due to secondary clectrous which COVOT the whole eau.," These are, among others, observable fluxes of positrons, antiprotons, gamma rays, neutrinos, as well as signals due to secondary electrons which cover the whole e.m."137" spect (sec, e.g.. Colafrancesco ct al."," spectrum (see, e.g., Colafrancesco et al."138 2006 for details): svuchrotron radio cussion (in the iutra-cluster maeuctic field). brenisstrahnluus cussion Gf there ds co-spatial iutra-cluster eas). inverse Compton cussion due to the upescatteriue of CAIB photous aud lence a specific SZ effect (as first noticed aud derived by Colafraucesco 20080.," 2006 for details): synchrotron radio emission (in the intra-cluster magnetic field), bremsstrahlung emission (if there is co-spatial intra-cluster gas), inverse Compton emission due to the up-scattering of CMB photons and hence a specific SZ effect (as first noticed and derived by Colafrancesco 2004)."139 The spatial and spectral intensity of the astrophysical siguals coming frou xy annihlilation is expected. however. to be confused or even overcome bv other astrophysical sicnals originating from the intracluster (IC) eas aud/or from). the relativistic plasmas present iu the cluster atinospheres. especially when all these componcuts are co-spatially distributed with he DM componeut.," The spatial and spectral intensity of the astrophysical signals coming from $\chi \chi$ annihilation is expected, however, to be confused or even overcome by other astrophysical signals originating from the intracluster (IC) gas and/or from the relativistic plasmas present in the cluster atmospheres, especially when all these components are co-spatially distributed with the DM component."140 This situation occurs in nost galaxw clusters (see ciscussion by Colatrancesco et al., This situation occurs in most galaxy clusters (see discussion by Colafrancesco et al.141 2006 or the case of An ideal system to detect DALI auuihilation siguals would. therefore. be a clhuster with a clear spatial separation between the various matter components.," 2006 for the case of An ideal system to detect DM annihilation signals would, therefore, be a cluster with a clear spatial separation between the various matter components."142 This is. indeed. the case of the cluster 1ES0657-556 where the spatial distribution of DAL is clearly offset παν," This is, indeed, the case of the cluster 1ES0657-556 where the spatial distribution of DM is clearly offset w.r.t."143 that of the IC eas (Clowe et al., that of the IC gas (Clowe et al.144 2006)., 2006).145 The two barvonic clumps of hot eas cuit A-ravs by (thermal) broenisstrahluug. as Observer by Chaudra (AMarkevitch et al.," The two baryonic clumps of hot gas emit X-rays by (thermal) bremsstrahlung, as observed by Chandra (Markevitch et al."146 2002. 2001).," 2002, 2004)."147 The shock observed in the westeruanost region of the cluster (Markevitch et al., The shock observed in the western-most region of the cluster (Markevitch et al.148 2002) wieght be the site of high euergv chussion from particles accelerated at the shock., 2002) might be the site of high energy emission from particles accelerated at the shock.149 Ward X-rav elussion from the direction of 1ES0657-556 has been mareiually detected by Rossi-XTE (Petrosian et al., Hard X-ray emission from the direction of 1ES0657-556 has been marginally detected by Rossi-XTE (Petrosian et al.150 2006) but its augular resolution is uot sufficient to eive iv information on the spatial distribution of this cussion., 2006) but its angular resolution is not sufficient to give any information on the spatial distribution of this emission.151 No eanmua-rav Cluission has been detected from this svsteus with EGRET., No gamma-ray emission has been detected from this system with EGRET.152 The extended radio halo associated to this cluster (Liane ¢ al., The extended radio halo associated to this cluster (Liang et al.153 2000) has a surface brightuess slieltly clongated along the direction of the two X-ray chumps. but without clear signatures ofradio-briehtuess euliancemeuts at the DM. chunp locations.," 2000) has a surface brightness slightly elongated along the direction of the two X-ray clumps, but without clear signatures of radio-brightness enhancements at the DM clump locations."154 Finally. the SZ maps of 1ES0657-556 obtained with ACBAR (with ~L5 arciniu FEWIIM resolution. Gomez et al.," Finally, the SZ maps of 1ES0657-556 obtained with ACBAR (with $\sim 4.5$ arcmin FWHM resolution, Gomez et al."155 2003) are quite smooth iid regular wi1 no evidence of chhancement at both X-rav and/or DM clump locations., 2003) are quite smooth and regular with no evidence of enhancement at both X-ray and/or DM clump locations.156 Iu this Letter. we will compute the specific feature of the SZ effect. (horefator SZE) produced by DM annihilation. SZpy. iu the cluster aud we will show that it is possible to detect such SZpay signal with a specific observational strategy.," In this Letter, we will compute the specific feature of the SZ effect (herefater SZE) produced by DM annihilation, $_{\rm DM}$, in the cluster and we will show that it is possible to detect such $_{\rm DM}$ signal with a specific observational strategy."157" The relevaut physical quautities are calculated using 77,= Tülans + banda flat. ACDAL (Q,,=0.3.04 0.7) cosmological model."," The relevant physical quantities are calculated using $H_0 = 70$ km $^{-1}$ $^{-1}$ and a flat, $\Lambda$ CDM $\Omega_{\rm m} = 0.3, \Omega_{\Lambda}=0.7$ ) cosmological model."158" The various SZ signals expected from the subsvsteuis of the cluster are: 1) the SZpa, effect. which is expected to be located at the two DM chips: ii) the thermal SZ effect (SZin) which is expected to be located at the two N-rav chuups."," The various SZ signals expected from the subsystems of the cluster are: i) the $_{\rm DM}$ effect, which is expected to be located at the two DM clumps; ii) the thermal SZ effect $_{\rm th}$ ) which is expected to be located at the two X-ray clumps."159 We will compute in the following these two sources of SZE aud we will also discuss the possible sources of coutamunation. bias aud confusion.," We will compute in the following these two sources of SZE and we will also discuss the possible sources of contamination, bias and confusion."160 The seueral expression for the SZE which is valid in the Thotsou Πιτ for a eeneric electron population in the relativistic hit aud includes also the effects of unultiple scatteriues and the combination with other electron population iu the cluster atmospheres hay. been derived by Colafraucesco et al. (, The general expression for the SZE which is valid in the Thomson limit for a generic electron population in the relativistic limit and includes also the effects of multiple scatterings and the combination with other electron population in the cluster atmospheres has been derived by Colafrancesco et al. (1612003).,2003).162 This approac[um is the one that will be used for the derivation of the SZpyy effect induce by the secondary electrons produced by \ αλαπο (see the original derivation by Colafraucesco, This approach is the one that will be used for the derivation of the $_{\rm DM}$ effect induced by the secondary electrons produced by $\chi \chi$ annihilation (see the original derivation by Colafrancesco163between different planet masses when comparing actual measurements to evolution nary models.,between different planet masses when comparing actual measurements to evolution nary models.164" We see two major effects: (i) the photometric performance clearly depends on wavelength, and (ii) there are two different regimes depending on the position compared to the AO control radius."," We see two major effects: (i) the photometric performance clearly depends on wavelength, and (ii) there are two different regimes depending on the position compared to the AO control radius."165" The first effect is directly related to the chromaticity of the PSF: in speckle-limited regime the noise attenuation is almost constant with angular separation compared to the coronagraphic profile, and the level of the coronagraphic profile linearly depends on wavelength."," The first effect is directly related to the chromaticity of the PSF: in speckle-limited regime the noise attenuation is almost constant with angular separation compared to the coronagraphic profile, and the level of the coronagraphic profile linearly depends on wavelength."166 The second effect is related to the AO correction inside the control radius., The second effect is related to the AO correction inside the control radius.167" Inside that region we see a stabilization of the performance: 0.2 mag photometric precision can be reached up to contrast of 10 to 11 mag (10* to 4x 10*) from to the AO control radius, which extends from in Y band to in K band."," Inside that region we see a stabilization of the performance: 0.2 mag photometric precision can be reached up to contrast of 10 to 11 mag $10^{-4}$ to $4 \times 10^{-4}$ ) from to the AO control radius, which extends from in Y band to in K band."168" Outside of the AO control radius, the photometric performance increases almost linearly with angular separation at all wavelengths to reach contrast values of 14 to 15 mag (2.5x10 to 10 9) around2."," Outside of the AO control radius, the photometric performance increases almost linearly with angular separation at all wavelengths to reach contrast values of 14 to 15 mag $2.5 \times 10^{-6}$ to $10^{-6}$ ) around."169"0"".. These numbers are given in the context? of our simulated test case, but the general effects should be similar for any data obtained with high contrast coronagraphic imagers."," These numbers are given in the context of our simulated test case, but the general effects should be similar for any data obtained with high contrast coronagraphic imagers."170" Similarly to the noise level, using the SDI+ADI data analysis method improves the photometric accuracy."," Similarly to the noise level, using the SDI+ADI data analysis method improves the photometric accuracy."171" However, using SDI+ADI will only provide an estimation of the differential flux of the planet between the 2 filters, contrary to ADI which provides an absolute measurement."," However, using SDI+ADI will only provide an estimation of the differential flux of the planet between the 2 filters, contrary to ADI which provides an absolute measurement."172" To preserve the planet differential flux, the amplitude correction factor usually applied for SDI in the subtraction is taken equal to a fixed value of 1."," To preserve the planet differential flux, the amplitude correction factor usually applied for SDI in the subtraction is taken equal to a fixed value of 1."173" The photometric error estimated with SDI+ADI follows the same variations as for ADI, but at higher contrast values."," The photometric error estimated with SDI+ADI follows the same variations as for ADI, but at higher contrast values."174" Figure 2,, right, illustrates the photometric performance as a function of wavelength and angular separation in SDIJ-ADI."," Figure \ref{fig:flux_error_summary}, right, illustrates the photometric performance as a function of wavelength and angular separation in SDI+ADI."175" The trends are similar to ADI alone, but the chromatic effect is less significant because the PSF chromaticity has been mitigated by the SDI part of the analysis."," The trends are similar to ADI alone, but the chromatic effect is less significant because the PSF chromaticity has been mitigated by the SDI part of the analysis."176" Compared to ADI alone, the contrast values at which a 0.2 mag photometric error is reached are 1.5 to 2.5 mag higher."," Compared to ADI alone, the contrast values at which a 0.2 mag photometric error is reached are 1.5 to 2.5 mag higher."177" At shorter wavelengths, in Y2Y3 filters, performances at separations larger than decrease."," At shorter wavelengths, in Y2Y3 filters, performances at separations larger than decrease."178" This effect is related to the size of the aperture for photometry which is very small in Y band (4 pixels in diameter), and to the field rotation which has strong effect on encircled energy at separations larger thana in Y band."," This effect is related to the size of the aperture for photometry which is very small in Y band (4 pixels in diameter), and to the field rotation which has a strong effect on encircled energy at separations larger than in Y band."179 Considering shorter exposures for individual images where the field rotation is negligible would decrease the photometric errors in that particular case., Considering shorter exposures for individual images where the field rotation is negligible would decrease the photometric errors in that particular case.180 We hereafter combine the photometric accuracy obtained in ADI and SDI+ADI to define empirical photometric error curves for each filter pair as a function of contrast., We hereafter combine the photometric accuracy obtained in ADI and SDI+ADI to define empirical photometric error curves for each filter pair as a function of contrast.181" The photometric error curves as a function of contrast at each angular separation have been fitted with the empirically defined function: where phote is the photometric error, c the contrast and (p1,p2,pa) the fitted parameters."," The photometric error curves as a function of contrast at each angular separation have been fitted with the empirically defined function: where $\mathrm{phot_{err}}$ is the photometric error, $c$ the contrast and $(p_1, p_2, p_3)$ the fitted parameters."182 This function approaches the measured points with a precision of ~1%.., This function approaches the measured points with a precision of $\sim$.183 The fitting has been performed for ADI and SDI+ADI., The fitting has been performed for ADI and SDI+ADI.184" To take into account the scattering of the error with the planet position in the images, different cases have been considered at each separation, corresponding to the 3 different simulated planet positions: a standard case with an average photometric error, an optimal case corresponding to the lowest estimation of the error and a pessimistic case corresponding to the upper estimation of the error."," To take into account the scattering of the error with the planet position in the images, different cases have been considered at each separation, corresponding to the 3 different simulated planet positions: a standard case with an average photometric error, an optimal case corresponding to the lowest estimation of the error and a pessimistic case corresponding to the upper estimation of the error."185 These empirical photometric errors are plotted in Fig., These empirical photometric errors are plotted in Fig.186 3 for the 4 simulated filter pairs., \ref{fig:error_curves_phot_all} for the 4 simulated filter pairs.187 The amplitude of the error bars is defined by the optimal and pessimistic error curves described above., The amplitude of the error bars is defined by the optimal and pessimistic error curves described above.188" We assume that the photometric error in ADI is the same in the two filters of a pair, which is legitimate given the amplitude of the error bars."," We assume that the photometric error in ADI is the same in the two filters of a pair, which is legitimate given the amplitude of the error bars."189 These empirical error curves lie in the same range as the expected photometric accuracy of other data analysis methods developed within the SPHERE consortium by ? and ?.., These empirical error curves lie in the same range as the expected photometric accuracy of other data analysis methods developed within the SPHERE consortium by \citet{mugnier2008} and \citet{smith2009}.190 Table 3 gives for each filter pair and each angular separation the contrast value at which the photometric error in ADI becomes lower than the differential photometric error in SDI+ADI., Table \ref{tab:methods_limits} gives for each filter pair and each angular separation the contrast value at which the photometric error in ADI becomes lower than the differential photometric error in SDI+ADI.191 These values give the contrast at which it becomes more interesting in terms of photometric error to obtain a differential flux estimation., These values give the contrast at which it becomes more interesting in terms of photometric error to obtain a differential flux estimation.192" As explained in Sect. 4.4,,"," As explained in Sect. \ref{sec:photometric_accuracy_sdi_adi},"193 aperture photometry in Y band is extremely sensitive to errors introduced by the position of the aperture or the field rotation because the aperture is very small., aperture photometry in Y band is extremely sensitive to errors introduced by the position of the aperture or the field rotation because the aperture is very small.194 This is why in Y2Y3 pair at there is no contrast limit between ADI and SDI+ADI: for that particular case the flux estimation error is slightly better in ADI than SDI+ADI., This is why in Y2Y3 pair at there is no contrast limit between ADI and SDI+ADI: for that particular case the flux estimation error is slightly better in ADI than SDI+ADI.195" In this section we evaluate characterization capabilities of IRDIS in imaging mode, ie. how well the physical parameters and of the planets can be estimated from photometric measurements in different spectral bands."," In this section we evaluate characterization capabilities of IRDIS in imaging mode, i.e. how well the physical parameters and of the planets can be estimated from photometric measurements in different spectral bands."196" To estimate the characterization capabilities of IRDIS, we performed a new simulation using as input the ὅ-σ detection limits obtained from Sect."," To estimate the characterization capabilities of IRDIS, we performed a new simulation using as input the $\sigma$ detection limits obtained from Sect."197 4.1 and the empirical error curves obtained in Sect. 4.5.., \ref{sec:noise_level} and the empirical error curves obtained in Sect. \ref{sec:empirical_photometric_accuracy}.198 The goal of the simulation was to test the efficiency of all filter pair sequences for characterization, The goal of the simulation was to test the efficiency of all filter pair sequences for characterization199frequency shift was affected.,frequency shift was affected.200 This resulted in an estimated stray-light temperature of ~35 K which corresponds to ~4 pW of parasitic power per pixel at 150 GHz., This resulted in an estimated stray-light temperature of $\sim 35$ K which corresponds to $\sim 4$ pW of parasitic power per pixel at 150 GHz.201 The unwanted radiation has thus been reduced by more than a factor of two compared with the first generation NIKA and is now comparable to the best sky conditions at Pico Veleta., The unwanted radiation has thus been reduced by more than a factor of two compared with the first generation NIKA and is now comparable to the best sky conditions at Pico Veleta.202 The dual-band NIKA run took place in October 2010., The dual-band NIKA run took place in October 2010.203 The instrument was installed in the receiver cabin of the IRAM 30-meter telescope at Pico Veleta. Spain. and operated remotely from the control room.," The instrument was installed in the receiver cabin of the IRAM 30-meter telescope at Pico Veleta, Spain, and operated remotely from the control room."204 The cool-down of the instrument was also performed remotely. taking approximately 18 hours to reach the operating temperature of 70 mK. Astronomical data from the two arrays are reduced with dedicated software.," The cool-down of the instrument was also performed remotely, taking approximately 18 hours to reach the operating temperature of 70 mK. Astronomical data from the two arrays are reduced off-line with dedicated software."205 The raw data (/.Q) are converted to complex phase angle using the closest previous KID calibration., The raw data $I$ $Q$ ) are converted to complex phase angle using the closest previous KID calibration.206 Then a conversion to an equivalent frequency shift is done with the same calibration using the derivative of the frequency with the complex phase at the zero phase. as described in4.," Then a conversion to an equivalent frequency shift is done with the same calibration using the derivative of the frequency with the complex phase at the zero phase, as described in."207. Data are thus internally converted to frequencies which are assumed to be linear with the absorbed photon counts. as in equation(2).," Data are thus internally converted to frequencies which are assumed to be linear with the absorbed photon counts, as in equation."208. After opacity correction. and using Mars as the primary calibrator. we obtain that the overall median gain is of 14 mJy/beam/Hz and 9 mJy/beam/Hz for the I.4 and 2 mm (220 GHz and 150 GHz) channels. with a 30% dispersion.," After opacity correction, and using Mars as the primary calibrator, we obtain that the overall median gain is of 14 mJy/beam/Hz and 9 mJy/beam/Hz for the 1.4 and 2 mm (220 GHz and 150 GHz) channels, with a $30\%$ dispersion."209 The focal plane geometry of each array ts measured by using scanning maps of planets (see 7))., The focal plane geometry of each array is measured by using scanning maps of planets (see ).210 The fitted focal plane geometry is found by matching the pixel position in the array as measured on the wafer to the measured position on planets. by optimizing a simple set of parameters: a center. a tilt angle and a sealing expressed in areseconds/mm.," The fitted focal plane geometry is found by matching the pixel position in the array as measured on the wafer to the measured position on planets, by optimizing a simple set of parameters: a center, a tilt angle and a scaling expressed in arcseconds/mm."211 Most detectors are within less than 2 arcseconds of their expected position., Most detectors are within less than 2 arcseconds of their expected position.212 The beam width is also found from planet measurements., The beam width is also found from planet measurements.213 Typically the FWHM is 12.4 and 16.7 areseconds for the two arrays (1.4 and 2 mm respectively. see figure 8) with a dispersion of | aresecond.," Typically the FWHM is 12.4 and 16.7 arcseconds for the two arrays (1.4 and 2 mm respectively, see figure 8) with a dispersion of 1 arcsecond."214 This is close to the diffraction limit for the 2 mm array., This is close to the diffraction limit for the 2 mm array.215 Pixelisation, Pixelisation216magnetar flares can point to the location where a long GRB (the time it takes for B—[0' G fields toY.,magnetar flares can point to the location where a long GRB (the time it takes for $B\sim 10^{16}$ G fields to.217. Here. I show that the GRB afterglow emission should be still detectable in the radio when the superflare takes place.," Here, I show that the GRB afterglow emission should be still detectable in the radio when the superflare takes place."218 GRB afterglows can be followed in the radio wavelengths for years after the burst., GRB afterglows can be followed in the radio wavelengths for years after the burst.219 GRB 030329 is an intrinsically typical long GRB that took place particularly nearby at z=0.1685 tor luminosity distance of dg;=800 Mpe for standard cosmology: Greiner et al., GRB 030329 is an intrinsically typical long GRB that took place particularly nearby at $z=0.1685$ (or luminosity distance of $d_L=800$ Mpc for standard cosmology; Greiner et al.220 2003)., 2003).221 Its radio afterglow remains fairly bright (at the mJy level) years after the burst and the blastwave is resolved (e.g. Berger et al., Its radio afterglow remains fairly bright (at the mJy level) years after the burst and the blastwave is resolved (e.g. Berger et al.222 2003: Tavlor et al., 2003; Taylor et al.223 2004: Resmi et al., 2004; Resmi et al.224 2005: Frail et al., 2005; Frail et al.225 2005: Pihlstrómm et al., 2005; Pihlströmm et al.226 2007: van der Horst et al., 2007; van der Horst et al.227 2008)., 2008).228 Because of the slow decline in flux. the afterglow is expected to be observable over the next decade in the GHz range and beresolved ~7 years after the burst (Pihlstrómm et al.," Because of the slow decline in flux, the afterglow is expected to be observable over the next decade in the $GHz$ range and be $\sim$ 7 years after the burst (Pihlströmm et al."229 2007)., 2007).230 With the Low Frequency Array (LOFAR) the afterglow of GRB 030329 can be detected for several decades (van der Horst et al., With the Low Frequency Array ) the afterglow of GRB 030329 can be detected for several decades (van der Horst et al.231 2008)., 2008).232 The afterglow emission of a GRB similar to that of 030329 located at a distance d;~250 Mpe will be ~10 times more bright and with the radio image a factor of ~2.6 larger., The afterglow emission of a GRB similar to that of 030329 located at a distance $d_L\sim 250$ Mpc will be $\sim 10$ times more bright and with the radio image a factor of $\sim 2.6$ larger.233 Such an afterglow emission can be detected and resolved for hundred cor hundreds) of years after the burst., Such an afterglow emission can be detected and resolved for hundred (or hundreds) of years after the burst.234 Two-dimensional relativistic hydrodynamical simulations (Zhang and MacFadyen 2009) indicate that the GRB blast reaches a distance of ~3 peat ~100 years which corresponds to a source of angular size of ~2.7 mas (for a corresponding angular distance of ας~224 Mpc) and flux density of ~0.1 mJy (at ~ IGHz) allowing for the morphological study of the blastwave with high-sensitivity Very Long Baseline Interferometry (VLBI) observations similar to those reported in Pihlstrómm et al. (, Two-dimensional relativistic hydrodynamical simulations (Zhang and MacFadyen 2009) indicate that the GRB blast reaches a distance of $\sim 3$ pc at $\sim 100$ years which corresponds to a source of angular size of $\sim 2.7$ mas (for a corresponding angular distance of $d_A\sim 224$ Mpc) and flux density of $\sim$ 0.1 mJy (at $\sim 1$ GHz) allowing for the morphological study of the blastwave with high-sensitivity Very Long Baseline Interferometry (VLBI) observations similar to those reported in Pihlströmm et al. (2352007).,2007).236 According to the same simulations. the decelerating GRB blastwave is morphologically very different from a supernova remnant for the first ~200 years allowing for the distinction between the two types of explosions.," According to the same simulations, the decelerating GRB blastwave is morphologically very different from a supernova remnant for the first $\sim 200$ years allowing for the distinction between the two types of explosions."237 For radio follow-ups to be possible. a good enough localization of the superflare is needed.," For radio follow-ups to be possible, a good enough localization of the superflare is needed."238 Such localization can be provided with the Burst Alert Telescope (BAYT) detector onSW/FT., Such localization can be provided with the Burst Alert Telescope ) detector on.239 The rate at whichSWIFT detects GRBs is ~ 1/3 of that ofBATSE mainly because of its smaller field of view., The rate at which detects GRBs is $\sim$ 1/3 of that of mainly because of its smaller field of view.240 I. thus. estimate that detects Ry/3-.. superflares per year.," I, thus, estimate that detects ${\dot R}_{\rm sf}/3\sim 1fL_{49}^{3/2}$ superflares per year."241 detection rate of flares is a factor of «2.5 higher but the Glast Burst Monitor (GBAT) lacks the localization needed for a radio follow-up., detection rate of flares is a factor of $\sim$ 2.5 higher but the Glast Burst Monitor ) lacks the localization needed for a radio follow-up.242 The pulsating tail that is expected to follow the superflare may. in some cases. be powerful enough to be observed withXA hundreds of seconds after the event.," The pulsating tail that is expected to follow the superflare may, in some cases, be powerful enough to be observed with hundreds of seconds after the event."243 Although the pulsating tails that follow bright SGR flares of Galactic magnetars for ~200— 400s have Lay107 ergs/s (Mereghetti 2008). the strong magnetic field of the GRB magnetar can confine ~100 times more energy in the magnetosphere of the neutron star resulting in far brighter ray tails.," Although the pulsating tails that follow bright SGR flares of Galactic magnetars for $\sim 200-400$ s have $L_{\rm tail}\sim 10^{42}$ ergs/s (Mereghetti 2008), the strong magnetic field of the GRB magnetar can confine $\sim 100$ times more energy in the magnetosphere of the neutron star resulting in far brighter X-ray tails."244 It is furthermore possible that the superflare has a strong enough “afterglow” of its own that allows for X-ray (tor longer wavelength) detection and accurate localization shortly after the burst (Eichler 2002)., It is furthermore possible that the superflare has a strong enough “afterglow” of its own that allows for X-ray (or longer wavelength) detection and accurate localization shortly after the burst (Eichler 2002).245 If GRB-magnetars exist. their magnetic field should decay on a time-scale of a few hundred years possibly producing SGR-like flares with peak luminosities of .0 ergs/s. A few of these flares per year should have been detected by BATSE out to d;~250 Mpe classified as short-duration GRBs.," If GRB-magnetars exist, their magnetic field should decay on a time-scale of a few hundred years possibly producing SGR-like flares with peak luminosities of $\sim 10^{49}$ ergs/s. A few of these flares per year should have been detected by BATSE out to $d_L\sim 250$ Mpc classified as short-duration GRBs."246 Such superflares can be detected withSWIFT at a rate of about one per year., Such superflares can be detected with at a rate of about one per year.247 The host galaxy of the flare should be typical of those of long-duration GRBs., The host galaxy of the flare should be typical of those of long-duration GRBs.248 High sensitivity radio observations at the location of the flare can resolve a~ [00-year-old blastwave result of the interaction of the GRB jets with the circumburst medium., High sensitivity radio observations at the location of the flare can resolve a $\sim 100$ -year-old blastwave result of the interaction of the GRB jets with the circumburst medium.249 This detection can prove that GRBs are connected to the birth of magnetars., This detection can prove that GRBs are connected to the birth of magnetars.250 I thank Brian Metzger and Dmitri Uzdensky for stimulating discussions during the preparation of the manuscript., I thank Brian Metzger and Dmitri Uzdensky for stimulating discussions during the preparation of the manuscript.251 I acknowledge support from the Lyman Spitzer. Jr. Fellowship awarded by the Department of Astrophysical Sciences at Princeton University.," I acknowledge support from the Lyman Spitzer, Jr. Fellowship awarded by the Department of Astrophysical Sciences at Princeton University."252"(Tor our fiducial choices),",(for our fiducial choices).253" At the small apertures we will consider. the diffraction limit is larger than the seeing. so it is possible to make (he PSF much smaller (han a pixel. ρω<06,."," At the small apertures we will consider, the diffraction limit is larger than the seeing, so it is possible to make the PSF much smaller than a pixel, $\theta_{\rm PSF}\ll \theta_p$."254 This would have the advantage of reducing sky. noise and is a useful approach when it is possible to always center the telescope at the same fiekl position as is the case lor “point and stare” experiments., This would have the advantage of reducing sky noise and is a useful approach when it is possible to always center the telescope at the same field position as is the case for “point and stare” experiments.255 Hlowever. for an all-sky survey. which eveles through maux fields. such precision repeat pointing is extremely difficult.," However, for an all-sky survey, which cycles through many fields, such precision repeat pointing is extremely difficult."256 Without it. precision photometry is impossible unless (he sub-pixel response of the CCD is mapped out in detail.," Without it, precision photometry is impossible unless the sub-pixel response of the CCD is mapped out in detail."257 We therefore adopt a Nyquist-sampled PSF. for which the sky noise is approximately that falling on da~13 pixels.," We therefore adopt a Nyquist-sampled PSF, for which the sky noise is approximately that falling on $4\pi\sim 13$ pixels."258 Our overall consideration for telescope design must (ake into account three factors., Our overall consideration for telescope design must take into account three factors.259 First. we with to maximize observing elliciency Ey.," First, we with to maximize observing efficiency ${\cal E}_S$."260 Second. we wish to achieve the highest possible signal-to-noise ratio.," Second, we wish to achieve the highest possible signal-to-noise ratio."261 Third. we must avoil anv distortion problems with the optics.," Third, we must avoid any distortion problems with the optics."262 There are four effects through which aperture size can impact these factors., There are four effects through which aperture size can impact these factors.263 Two of these effects. observing ellicieney ancl scintillation noise. will drive us to larger telescopes. while (he other {wo elfects. sky noise and focal plane distortion. will drive us to smaller telescopes.," Two of these effects, observing efficiency and scintillation noise, will drive us to larger telescopes, while the other two effects, sky noise and focal plane distortion, will drive us to smaller telescopes."264 As we show below. for the observing parameters we have specified an aperture of 5 cm ensures a manageable (uid unique) balance between (he various effects.," As we show below, for the observing parameters we have specified an aperture of 5 cm ensures a manageable (and unique) balance between the various effects."265 Assuming Nyquist sampling. at most half the light from a point source [alls within one pixel.," Assuming Nyquist sampling, at most half the light from a point source falls within one pixel."266 We can directly. calculate the ratio of time lost to readout Zi44 to the time spent exposing Lox). where WW. is the well depth of the detector pixels. and Wi = 10?e 1 a fiducial well depth.," We can directly calculate the ratio of time lost to readout $T_{\rm read}$ to the time spent exposing $T_{\rm exp}$, where $W$ is the well depth of the detector pixels, and $W_{0}$ = $10^{5}{\rm e}^{-}$ is a fiducial well depth."267" Note that the factor 10.I which arises [rom the need to avoid saturation of the brightest stas (where Vi,=Vinay— AV). has been broken up into two terms to permit easy comparisons of equation (14)) with equations (16)) ancl (18)) below."," Note that the factor $10^{-0.4(V_{\rm min}-10)}$, which arises from the need to avoid saturation of the brightest stars (where $V_{\rm min} = V_{\rm max} - \Delta V$ ), has been broken up into two terms to permit easy comparisons of equation \ref{equtexp}) ) with equations \ref{equscint2}) ) and \ref{equskynoise}) ) below."268 In order to maximize the efficiency. Ey. the fractionof observing time devoted to readout should be minimized. aud therefore. according to equation (14)). so should the aperture size.," In order to maximize the efficiency ${\cal E}_{S}$, the fractionof observing time devoted to readout should be minimized, and therefore, according to equation \ref{equtexp}) ), so should the aperture size."269 The telescope will operate reasonably efficiently so long as TiaS Tu., The telescope will operate reasonably efficiently so long as $T_{\rm read} \la T_{\rm exp}$ .270of po.,of $\rho_0$.271 In comparing mocdel results we therefore note that a change of po may also imply a change in eo., In comparing model results we therefore note that a change of $\rho_0$ may also imply a change in $a_0$.272 Finally. the slope of the power-law energy distribution of the relativistic electrons strongly inlluences the slope of the observed racio spectrum.," Finally, the slope of the power-law energy distribution of the relativistic electrons strongly influences the slope of the observed radio spectrum."273 We adjust the value of 6 in the range 2 to 2.5 as discussed in the next sub-section., We adjust the value of $\delta$ in the range 2 to 2.5 as discussed in the next sub-section.274 For cach individual lobe we use the lobe length and aspect ratio as well as the luminosity densities measured at two frequencies in the fitting process., For each individual lobe we use the lobe length and aspect ratio as well as the luminosity densities measured at two frequencies in the fitting process.275 Table 4. summarises the model inputs derived from our observations., Table \ref{obpara} summarises the model inputs derived from our observations.276 To determine the model. parameters po. €. / and. ἐς. we randomly choose a large number of combinations of these four parameters and calculate the prediction of the mocel for the lobe length. L and the luminosity densities £7. at two observing frequencies.," To determine the model parameters $\rho_0$, $Q$, $t$ and $t_{\rm s}$, we randomly choose a large number of combinations of these four parameters and calculate the prediction of the model for the lobe length $L$ and the luminosity densities $P_{\nu}$ at two observing frequencies."277 A given parameter combination is deemed to be consistent with the observations. if the mocel results are all within of the observed. values of £L and the two values of P.," A given parameter combination is deemed to be consistent with the observations, if the model results are all within of the observed values of $L$ and the two values of $P_{\nu}$ ."278 Each lobe is fitted individually and the results for the source age / and the jet power Q are shown in the top panel of Fig., Each lobe is fitted individually and the results for the source age $t$ and the jet power $Q$ are shown in the top panel of Fig.279 4 where we have set à=2 for all obes., \ref{model} where we have set $\delta =2$ for all lobes.280 It is re-assuring that for most. possible jet. powers the obe age rellects the lobe size with the outer lobes the oldest and the inner lobes the voungest., It is re-assuring that for most possible jet powers the lobe age reflects the lobe size with the outer lobes the oldest and the inner lobes the youngest.281 We would expect that the jets inflating cach pair of lobes. outer. middle and. inner. jwe the same jet power and age on both sides of the AGN.," We would expect that the jets inflating each pair of lobes, outer, middle and inner, have the same jet power and age on both sides of the AGN."282 llence we expect the patches in Fig., Hence we expect the patches in Fig.283 4. (top) for a given »ur to show at least some overlap., \ref{model} (top) for a given pair to show at least some overlap.284 While this is the case or the inner and outer lobe pair. the middle pair shows no overlap at. all.," While this is the case for the inner and outer lobe pair, the middle pair shows no overlap at all."285 Also. the area in the Q-/ plane allowed. for xh lobes of the outer pair is only small.," Also, the area in the $Q$ $t$ plane allowed for both lobes of the outer pair is only small."286 This may be a result. of a wrong for slope of the initial power- energy spectrum of choicethe relativisticthe electrons. ὃν for some ofthe lobes.," This may be a result of a wrong choice for the slope of the initial power-law energy spectrum of the relativistic electrons, $\delta$, for some of the lobes."287 The radio spectra of the middle lobes are steep compared to the spectra of most of the other lobes and may imply a steeper initial energy spectrum., The radio spectra of the middle lobes are steep compared to the spectra of most of the other lobes and may imply a steeper initial energy spectrum.288 In the interests of exploring the parameter space. in the middle panel of Fig.," In the interests of exploring the parameter space, in the middle panel of Fig."289 we show the result of changing 6 to 2.5 for the middle lobes., \ref{model} we show the result of changing $\delta$ to 2.5 for the middle lobes.290 We also change 9 to for the northern. outer lobe and to 2.5 for the southern. 2.2inner lobe.," We also change $\delta$ to 2.2 for the northern, outer lobe and to 2.5 for the southern, inner lobe."291 Both of these also show at least.slightly steeper radio spectra., Both of these also show at leastslightly steeper radio spectra.292 This demonstrates the ellect of changing ὁ on the model results., This demonstrates the effect of changing $\delta$ on the model results.293Ranges and steps for all seven basic parameters of the grid of synthetic spectra are given in. Table 2.,Ranges and steps for all seven basic parameters of the grid of synthetic spectra are given in Table 2.294 We adopt à common convention of quoting metallicity and enhancement of a—elements in logarithmic units with respect to the solar values., We adopt a common convention of quoting metallicity and enhancement of $\alpha$ --elements in logarithmic units with respect to the solar values.295 The gravity is 1n logarithmic οσς units., The gravity is in logarithmic cgs units.296 Details of all calculated parameter combinations are given i Figures 1—3., Details of all calculated parameter combinations are given in Figures 1–3.297 Spectra are placed in gravity-temperature planes. with metallicity coded by a symbol type.," Spectra are placed in gravity–temperature planes, with metallicity coded by a symbol type."298 Figure 1 covers the most numerous spectra. tthe ones with no a-enhancement and with microturbulent velocity of 2 km s!.," Figure 1 covers the most numerous spectra, the ones with no $\alpha$ –enhancement and with microturbulent velocity of 2 km $^{-1}$."299 The computed spectra cover the whole gravity-temperature plane except for hot low-gravity models which are not radiatively stable., The computed spectra cover the whole gravity–temperature plane except for hot low-gravity models which are not radiatively stable.300 Low-temperature spectra (Tay<5000 K) were computed for a sparser set of metallicities due to large requirements of computing time., Low–temperature spectra $T_\mathrm{eff} < 5000$ K) were computed for a sparser set of metallicities due to large requirements of computing time.301 These spectra will be added online when completed., These spectra will be added online when completed.302 Fig., Fig.303 2 corresponds to a-enhanced cases and Fig., 2 corresponds to $\alpha$ –enhanced cases and Fig.304 3 to those with a different value of microturbulent velocity., 3 to those with a different value of microturbulent velocity.305 Note that each of the symbols actually corresponds to HL (Fey<7000 K) or 14 (£y77000 K) spectra with different values of rotational velocity (see Table 1) and to three different resolving powers., Note that each of the symbols actually corresponds to 11 $T_\mathrm{eff} < 7000$ K) or 14 $T_\mathrm{eff} \ge 7000$ K) spectra with different values of rotational velocity (see Table 1) and to three different resolving powers.306 All spectra are available as ascii files grouped into different directories according to their resolving power and temperature., All spectra are available as ascii files grouped into different directories according to their resolving power and temperature.307 The filenames are in a standard format identified in Table 3., The filenames are in a standard format identified in Table 3.308 So corresponds to a flux calibrated spectrum between 7650 and 8750 Á.. with Vio=10 km s!. 4/A4=20000. [M/H]=-0.5. 5250 K. logg= 4.5.€= 2km «τὶς and no a—enhancement.," So corresponds to a flux calibrated spectrum between 7650 and 8750 , with $V_\mathrm{rot} = 10 $ km $^{-1}$, $\lambda / \Delta \lambda = 20\,000$, $[\mathrm{M} / \mathrm{H} ] = -0.5$, $T_\mathrm{eff} = 5250$ K, $\log g = 4.5$, $\xi = 2$ km $^{-1}$, and no $\alpha$ –enhancement."309 The calculated grid is by far too large to present all of its properties here. so we explore only sample cross-sections across the grid.," The calculated grid is by far too large to present all of its properties here, so we explore only sample cross-sections across the grid."310 Figure 4+ 1s a greyscale presentation of the spectra which were normalized to enhance line visibility., Figure 4 is a greyscale presentation of the spectra which were normalized to enhance line visibility.311 Each panel shows variation along one parameter axis. starting from a spectrum of a non-rotating KO V type star.," Each panel shows variation along one parameter axis, starting from a spectrum of a non-rotating K0 V type star."312 Note that all spectra were calculated in a wider wavelength domain. but only the 8400-8750 range is plotted for clarity.," Note that all spectra were calculated in a wider wavelength domain, but only the 8400–8750 range is plotted for clarity."313 The temperature panel of Fig., The temperature panel of Fig.314 4 clearly shows the importance of sharp Ca II lines for any radial velocity study., 4 clearly shows the importance of sharp Ca II lines for any radial velocity study.315 The panel is a textbook example of the expected behaviour of the Paschen lines and metallic lines., The panel is a textbook example of the expected behaviour of the Paschen lines and metallic lines.316 The metallicity panel illustrates that the Ca II lines remain strong even at the lowest metallicities and the gravity panel shows their presence in all luminosity classes., The metallicity panel illustrates that the Ca II lines remain strong even at the lowest metallicities and the gravity panel shows their presence in all luminosity classes.317 The rotational velocity and resolving power panels show how the lines get smeared at high rotational velocities or if observing at low resolving powers., The rotational velocity and resolving power panels show how the lines get smeared at high rotational velocities or if observing at low resolving powers.318 The steps in the calculated grid are relatively small. but the coverage Is not continuous.," The steps in the calculated grid are relatively small, but the coverage is not continuous."319 As an example. the step in temperature is 250 K (for Tyx10000 K).," As an example, the step in temperature is 250 K (for $T_\mathrm{eff} \le 10\,000$ K)."320 This is larger than the baselined accuracy of temperature determination for both GAIA and RAVE surveys., This is larger than the baselined accuracy of temperature determination for both GAIA and RAVE surveys.321 So the grid will have to be interpolated to smaller steps., So the grid will have to be interpolated to smaller steps.322 Figure 5 illustrates the errors introduced by a simple linear interpolation., Figure 5 illustrates the errors introduced by a simple linear interpolation.323 At a certain grid point ¢ with the parameter values p; we compare the true synthetic spectrum S(p;) with the spectrum $ obtained from a linear combination of spectra at neighbouring grid. points: So=fiASQ+SIG)., At a certain grid point $i$ with the parameter values $p_i$ we compare the true synthetic spectrum $S(p_i)$ with the spectrum $S'$ obtained from a linear combination of spectra at neighbouring grid points: $S' = f_{i-1} S(p_{i-1}) + f_{i+1} S(p_{i+1})$.324" The weights f, and fi, are optimized so that [Spa—§’Fda is minimal.", The weights $f_{i-1}$ and $f_{i+1}$ are optimized so that $\int [S(p_i) - S']^2 d\lambda$ is minimal.325 The difference between the interpolated values of parameters p’ and the true ones p; can then be expressed in units of a grid step: Figure 5 shows that linear interpolation is accurate to =10 oof the grid step., The difference between the interpolated values of parameters $p'$ and the true ones $p_i$ can then be expressed in units of a grid step: Figure 5 shows that linear interpolation is accurate to $\simlt 10$ of the grid step.326 Note that this is the worst case scenario. corresponding to a reconstruction of the spectrum at the middle of the grid interval.," Note that this is the worst case scenario, corresponding to a reconstruction of the spectrum at the middle of the grid interval."327 Linear interpolation would be more accurate for spectra lying closer to one of the grid points., Linear interpolation would be more accurate for spectra lying closer to one of the grid points.328 The results could be improved further by employing non-linear interpolation schemes., The results could be improved further by employing non-linear interpolation schemes.329 One may conclude that linear interpolation itself does not introduce errors exceeding 25 K in temperature (for Typ<10000 K). 0.05 dex in [M/H] or logg and | km s! in V4.," One may conclude that linear interpolation itself does not introduce errors exceeding 25 K in temperature (for $T_\mathrm{eff} < 10\,000$ K), 0.05 dex in $[\mathrm{M}/\mathrm{H}]$ or $\log g$ and 1 km $^{-1}$ in $V_\mathrm{rot}$."330 Note that other errors are more important: degeneracy of parameter values fitting spectra with a limited signal to noise ratio complicates their determination (Bailer-Jones 2003. see also Fig.," Note that other errors are more important: degeneracy of parameter values fitting spectra with a limited signal to noise ratio complicates their determination (Bailer-Jones 2003, see also Fig."331 | in Zwitter 2002)., 1 in Zwitter 2002).332 Also. spectra of real starsdo not correspond exactly to the synthetic spectra due to their peculiarities eemission lines. varied abundances of individual elements. non-LTE effects. and atmospheric structure).," Also, spectra of real starsdo not correspond exactly to the synthetic spectra due to their peculiarities emission lines, varied abundances of individual elements, non-LTE effects, and non-static atmospheric structure)."333"prominent for intermediate harmonics, we nonetheless follow the recommendation of ? to flag this mode as suspect.","prominent for intermediate harmonics, we nonetheless follow the recommendation of \citet{Gilliland} to flag this mode as suspect."334" The quasi-regularity of the small (6v,9) and large frequency separations (Av,o and Av?) is evident from Figs.", The quasi-regularity of the small $\delta\nu_{n0}$ ) and large frequency separations $\Delta\nu_{n0}$ and $\Delta\nu_{n2}$ ) is evident from Figs.335 [7] and [8]., \ref{Mulder_echelle} and \ref{Scully_echelle}.336" Notice that if these stars were to strictly obey the asymptotic relation in Eq. [I],"," Notice that if these stars were to strictly obey the asymptotic relation in Eq. \ref{asymptotic},"337 they would then exhibit vertical ridges in the écchelle diagram provided use of the correct Av., they would then exhibit vertical ridges in the écchelle diagram provided use of the correct $\Delta\nu$.338" The small separation óv,o is, however, more clearly distinguished in the case of KIC 10920273, which might be an indication of smaller mode linewidths in this cooler star (see Sect."," The small separation $\delta\nu_{n0}$ is, however, more clearly distinguished in the case of KIC 10920273, which might be an indication of smaller mode linewidths in this cooler star (see Sect."339 ?? fora discussion on mode linewidths)., \ref{WH} for a discussion on mode linewidths).340" A striking feature in both écchelle diagrams is the jagged appearance of the /=1 ridge, a trademark of the presence of avoided crossings and an indicator of the evolved nature of these stars."," A striking feature in both écchelle diagrams is the jagged appearance of the $l\!=\!1$ ridge, a trademark of the presence of avoided crossings and an indicator of the evolved nature of these stars."341" These same features have also been seen in the cases of ground-based observations of 7 Boo (?),, 6 Hyi (?) and possibly Procyon (?), as well as in the cases of the target HD 49385 (?),, and KASC survey targets KIC 11026764 (?),, KIC 11395018 and KIC 11234888 (?).."," These same features have also been seen in the cases of ground-based observations of $\eta$ Boo \citep{Kjeldsen03}, $\beta$ Hyi \citep{Bedding07} and possibly Procyon \citep{Procyon}, as well as in the cases of the target HD 49385 \citep{HD49385}, and KASC survey targets KIC 11026764 \citep{Gemma}, KIC 11395018 and KIC 11234888 \citep{FurryMathur}."342" Figure D] displays a so-called p-g diagram as introduced by ?,, where the frequencies of the avoided crossings (i.e., the frequencies of the pure g modes in the core cavity) for a number of stars are plotted against the large separation of the p modes."," Figure \ref{pg} displays a so-called p-g diagram as introduced by \citet{Bedding_pg}, where the frequencies of the avoided crossings (i.e., the frequencies of the pure g modes in the core cavity) for a number of stars are plotted against the large separation of the p modes."343" Much of the diagnostic potential of mixed modes can be captured in this way, since their overall pattern is determined by the mode bumping at each avoided crossing, which in turn is determined by the g modes trapped in the core."," Much of the diagnostic potential of mixed modes can be captured in this way, since their overall pattern is determined by the mode bumping at each avoided crossing, which in turn is determined by the g modes trapped in the core."344 This diagram could prove to be an instructive way to display results of many stars and to allow for a first comparison with theoretical models., This diagram could prove to be an instructive way to display results of many stars and to allow for a first comparison with theoretical models.345" We also report here the possible presence of a/=2 mixed mode in the power spectrum of KIC 10920273 (at 873.10 μΗΖ) that should, however, be confirmed by stellar models."," We also report here the possible presence of a $l\!=\!2$ mixed mode in the power spectrum of KIC 10920273 (at $873.10\:{\rm{\mu Hz}}$ ) that should, however, be confirmed by stellar models."346 Detection of /=3 modes with photometric observations is made very difficult due to geometric cancellation effects., Detection of $l\!=\!3$ modes with photometric observations is made very difficult due to geometric cancellation effects.347 Solar-like oscillations with /23 from photometry have nonetheless been reported for a set of low-luminosity red giants by ?.., Solar-like oscillations with $l\!=\!3$ from photometry have nonetheless been reported for a set of low-luminosity red giants by \citet{Bedding_rg}.348 ? have also reported the presence of /23 modes for the target HD 49385., \citet{HD49385} have also reported the presence of $l\!=\!3$ modes for the target HD 49385.349" We should bear in mind that, except for ORK and SYD, all the remaining fitters used deterministicmodels in their frequency-domain representations of the data that only contained modes of degree up to /=2, meaning that a statistical assessment of the presence or not of /=3 modes could not be done."," We should bear in mind that, except for ORK and SYD, all the remaining fitters used deterministicmodels in their frequency-domain representations of the data that only contained modes of degree up to $l\!=\!2$, meaning that a statistical assessment of the presence or not of $l\!=\!3$ modes could not be done."350" ORK and SYD, which were the only fitters that did not make any prior assumptions about the degree of the modes, have not reported the detection of modes that could be interpreted as /=3 modes."," ORK and SYD, which were the only fitters that did not make any prior assumptions about the degree of the modes, have not reported the detection of modes that could be interpreted as $l\!=\!3$ modes."351" A thorough discussion of the mode linewidths, heights, and amplitudes goes beyond the scope of this work."," A thorough discussion of the mode linewidths, heights, and amplitudes goes beyond the scope of this work."352" However, there are some aspects we would like to mention here."," However, there are some aspects we would like to mention here."353 The intrinsic frequency resolution of the spectra (x0.05 uHz) makes it possible to resolve the modes., The intrinsic frequency resolution of the spectra $\approx\!0.05\:{\rm{\mu Hz}}$ ) makes it possible to resolve the modes.354 This condition is obeyed provided the observation length T>2Tmode (?).., This condition is obeyed provided the observation length $T\!\gg\!2\tau_{\rm{mode}}$ \citep{Chaplin03}.355" Figure displays, for each star, the linewidths of the radial modes ποreturned by the respective (see also Tables and [8))."," Figure \ref{widths} displays, for each star, the linewidths of the radial modes returned by the respective (see also Tables \ref{Freq_Mulder2} and \ref{Freq_Scully2}) )."356 The radial modes considered are those belonging to the set.., The radial modes considered are those belonging to the .357" Notice the near-constancy with frequency of the mode linewidths in the case of KIC 10920273, whereas for KIC 10273246 the linewidths increase steadily,"," Notice the near-constancy with frequency of the mode linewidths in the case of KIC 10920273, whereas for KIC 10273246 the linewidths increase steadily,"358Before producing our final cluster catalog. we need to define a criferiun to identify1 clusters by associating Huctuations detected in different inagnitude bius.,"Before producing our final cluster catalog, we need to define a criterium to identify clusters by associating fluctuations detected in different magnitude bins."359 The criteri will consists of à maxima projected distauce vetween the centers of fluctuations to be associated aud of a minimi uunber of coincident fluctuations required or a positive detection. [Ng," The criterium will consists of a maximum projected distance between the centers of fluctuations to be associated and of a minimum number of coincident fluctuations required for a positive detection, $N_{min}$."360 In fact. because of the statistical noise of the oreeround/backeround galaxy distribution. the ceuters of the 8ctuations produced by a cluster in different magnitude bins will be sliehtlv different.," In fact, because of the statistical noise of the foreground/background galaxy distribution, the centers of the fluctuations produced by a cluster in different magnitude bins will be slightly different."361 As far as the umber of coincident fluctuations produced by a cluster is concerned. it will depeud on the cluster distance. richness and luuinosity fiction.," As far as the number of coincident fluctuations produced by a cluster is concerned, it will depend on the cluster distance, richness and luminosity function."362 Clearly the choice of the criterium has to be mace having in wind the goal of the detection algoritlin and the characteristics of the galaxy catalog., Clearly the choice of the criterium has to be made having in mind the goal of the detection algorithm and the characteristics of the galaxy catalog.363 Tn order to define the criterium of association for our test application. we peform extended tests both ou he PDCS field aud ou simulations of Poissonian fields with embedded: simulated clusters.," In order to define the criterium of association for our test application, we peform extended tests both on the PDCS field and on simulations of Poissonian fields with embedded simulated clusters."364 Our simulated fields lave the sale eeneral properties of the PDCS ποια., Our simulated fields have the same general properties of the PDCS field.365 Tn particular. we run the VGCF on LOO catalogs cach containing LS simulated clusters (a umuboer similar to the iunber of clusters in the PDCS field) eiibedded within a Poissonian galaxy field.," In particular, we run the VGCF on 100 catalogs each containing 18 simulated clusters (a number similar to the number of clusters in the PDCS field) embedded within a Poissonian galaxy field."366 Clusters are smniulate« as in the xevious subsection., Clusters are simulated as in the previous subsection.367 All simmlated catalogs coutaiu 25132 ealaxies. ie. the same number of PDCS galaxies.," All simulated catalogs contain 25432 galaxies, i.e. the same number of PDCS galaxies."368 As a result of our tests. we conskler coincident wo fluctuations with centers separated on the skv by a projected. distance dyxODRy. Ro). where Ry and Ro are the radi of the two fluctuations.," As a result of our tests, we consider coincident two fluctuations with centers separated on the sky by a projected distance $d_{12} \leq3690.3\,min(R_1,R_2)$ , where $R_1$ and $R_2$ are the radii of the two fluctuations."370 A ighter criteri would break the sequence of fluctuations corresponding to a real cluster. a looser criterimu would incorrectly associate fluctuations produced by adjacenut clusters/fluctuations to the same cluster.," A tighter criterium would break the sequence of fluctuations corresponding to a real cluster, a looser criterium would incorrectly associate fluctuations produced by adjacent clusters/fluctuations to the same cluster."371 We now set the nünmuuu nmuuber of fluctuations. Minin required. for the detection. of a cluster.," We now set the minimum number of fluctuations, $N_{min}$, required for the detection of a cluster."372 In Fig., In Fig.373 G we plot the average nuuniber of spurious fluctuations ni-ideuti&ed as clusters as a function of μι, 6 we plot the average number of spurious fluctuations mis-identified as clusters as a function of $N_{min}$.374 The uuuber of spurious clusters drops dramatically as κρεμ increases from 1 to 5., The number of spurious clusters drops dramatically as $N_{min}$ increases from 1 to 5.375" For N,,;,—5 here are ou average 1.5 spurious clusters per field.", For $N_{min} = 5$ there are on average 1.5 spurious clusters per field.376 This απ. decreases slowly as ορ ducreases further., This number decreases slowly as $N_{min}$ increases further.377" This result indicates that N,,;,=5 is aa good choice to keep the number of Poisson fluctuations low while still being scusitive to poor or distant clusters."," This result indicates that $N_{min} =3785$ is a a good choice to keep the number of Poisson fluctuations low while still being sensitive to poor or distant clusters."379 In Fig., In Fig.380" 7 we show the variation with N,,;, of the detection efficiency of simulated clusters at redshifts z=0.3 (panel a). 0.5 (pancl b). aud 0.8 (panel ο)."," 7 we show the variation with $N_{min}$ of the detection efficiency of simulated clusters at redshifts z=0.3 (panel ), 0.5 (panel ), and 0.8 (panel )."381 At each redshift the different curves correspond to riclinesses ranging from Np=10 to Ngσυ., At each redshift the different curves correspond to richnesses ranging from $N_R=10$ to $N_{R}=60$.382 Clearly the fraction of detected clusters decreases as Vy) Increases., Clearly the fraction of detected clusters decreases as $N_{min}$ increases.383 We note that the curve in Fig., We note that the curve in Fig.384 6 corresponds to au evaluation of the False Positive Rate (FPR). ic. the probability of detecting as a cluster a random fluctuation of the galaxy distribution.," 6 corresponds to an evaluation of the False Positive Rate (FPR), i.e. the probability of detecting as a cluster a random fluctuation of the galaxy distribution."385" For [N,,;,,=5. our FPR is very low."," For $N_{min}=5$, our FPR is very low."386 By comparison. P96 eive. 1.2 spurious detections per square deerce with peak signal ereatcr than 3o.," By comparison, P96 give 4.2 spurious detections per square degree with peak signal greater than $3\sigma$."387 The curves in Fig., The curves in Fig.388 7 correspond to a measure of the False Negative Rate (CENR)., 7 correspond to a measure of the False Negative Rate (FNR).389" We present here the results of the run of the VOCE ou he V, catalog of the PDCS field at a=13 26"" and à = 20"" 52 (12000).", We present here the results of the run of the VGCF on the $V_4$ catalog of the PDCS field at $\alpha = 13^{h}$ $^{m}$ and $\delta$ = $29^{o}$ 52' (J2000).390 As diseussed in the previous section. we run the VOCE in bins two magnitude wide. “sliding” with Kl magnitude steps within the magnitude rauge 18.00<VQox23.8.," As discussed in the previous section, we run the VGCF in bins two magnitude wide, “sliding” with 0.1 magnitude steps within the magnitude range $18.00 \leq V_{4} < 23.8$ ."391 In total we run the VOCF in 39 magnitude ius ancl identify as clusters at least five fluctuations that. according to our criteria. are anenlarly coicideut (sec xevious subsection).," In total we run the VGCF in 39 magnitude bins and identify as clusters at least five fluctuations that, according to our criterium, are angularly coincident (see previous subsection)."392 Ou a Sun ULTRASpare 30 workstation. the time required to run the whole procedure is about LO minutes.," On a Sun ULTRASparc 30 workstation, the time required to run the whole procedure is about 40 minutes."393 Our output cluster list consists of 37 objects., Our output cluster list consists of 37 objects.394 We characterize each cluster with the properties of the fluctuation with the lighest signal-to-noise ratio as estiniatec w the ratio of the numuber of cluster galaxies to the square root of the number of background galaxies expected within the cluster area., We characterize each cluster with the properties of the fluctuation with the highest signal-to-noise ratio as estimated by the ratio of the number of cluster galaxies to the square root of the number of background galaxies expected within the cluster area.395 Iu Table 1. for each cluster we list: 1) ideutification munhber. 2) J2000 right ascension aud 3) J2000 declination. 1) radius. 5) the cluster signal-to-noise ratio. 6) the estimated umber of cluster ealaxies aud 7) the uuuber of expected backeromn ealaxies. 8) the central maguitude of the bin where we detect the cluster with the highest sigual-to-nolse ratio. 9) he cross-identification with the PDCS catalog.," In Table 1, for each cluster we list: 1) identification number, 2) J2000 right ascension and 3) J2000 declination, 4) radius, 5) the cluster signal-to-noise ratio, 6) the estimated number of cluster galaxies and 7) the number of expected background galaxies, 8) the central magnitude of the bin where we detect the cluster with the highest signal-to-noise ratio, 9) the cross-identification with the PDCS catalog."396 Iu Fig., In Fig.397 δ we plot circles on the sky corresponding to our clusters (solid lines)., 8 we plot circles on the sky corresponding to our clusters (solid lines).398" We label oux clusters with a ""V7 followed by their order umuuber in Table 1.", We label our clusters with a “V” followed by their order number in Table 1.399 In Fie., In Fig.400 9. we eive a evaphic sumuuary of all the fluctuations of cach cluster.," 9, we give a graphic summary of all the fluctuations of each cluster."401 The abscissa is the order umber of the uaenitude bin of the fluctuation and each cluster is represeuted. by a row of circles parallel to the magnitude bin axis., The abscissa is the order number of the magnitude bin of the fluctuation and each cluster is represented by a row of circles parallel to the magnitude bin axis.402 The radii of the circles are scaled with the signal-to-noise ratio of the detection., The radii of the circles are scaled with the signal-to-noise ratio of the detection.403 We renuud rere that we fit a circle to a fluctuation after its detection. aud that the oulv use of the circle is to provide a convenieut wav to catalog the cluster with a ceuter and a radius.," We remind here that we fit a circle to a fluctuation after its detection, and that the only use of the circle is to provide a convenient way to catalog the cluster with a center and a radius."404 The richest aud more reliable clusters exhibit. in Fie.," The richest and more reliable clusters exhibit, in Fig."405 9. a sequence of fluctuations.," 9, a sequence of fluctuations."406 The signal-to-noise ratio of these fluctuations regularly increases up to a maxiumni and then decreases., The signal-to-noise ratio of these fluctuations regularly increases up to a maximum and then decreases.407 Several fainter clusters show the same behavior. although at a generally lower S/N level.," Several fainter clusters show the same behavior, although at a generally lower S/N level."408 Clearly. the position of he fluctuations along the magnitude axisis related to the cluster distance.," Clearly, the position of the fluctuations along the magnitude axisis related to the cluster distance."409 Some clusters. for example VF aud V12. displav substantial gaps along the sequence.," Some clusters, for example V7 and V12, display substantial gaps along the sequence."410 The suspicion is, The suspicion is411he remnant lifetime eenerally iucreases with the density and the flow velocity of the surrouncdiug nedium.,the remnant lifetime generally increases with the density and the flow velocity of the surrounding medium.412 The üighest value found iu our simulations. Mf=77Mvr. is obtained when a=10°cu Sand e=5000kims!.," The highest value found in our simulations, $Mt = 77 \Msol \yr$, is obtained when $n = 10^{6} \pcm3$ and $v = 5000 \kmps$."413 A supernova rate of L/vr would then imply a mass or the clouds enüttiug the IIILs of up to ~soXl... This is easily compatible with the lower cud of DELR πάσα estimates in the literature(c.e... Peterson 1997)). althoueh our model (and most others} would ο severely challenged to explain uch more extreme estimates of the uass of BELR eas (see Balelwin 2003. aac references herein).," A supernova rate of 1/yr would then imply a mass for the clouds emitting the HILs of up to $\sim 80 \Msol$, This is easily compatible with the lower end of BELR mass estimates in the literature, Peterson \cite{P1997}) ), although our model (and most others) would be severely challenged to explain much more extreme estimates of the mass of BELR gas (see Baldwin \cite{B2003} and references therein)."414" We note that it is currently uuclear row this mass 1s partitioned between the TIL aud LIL eas in these higher estimates,", We note that it is currently unclear how this mass is partitioned between the HIL and LIL gas in these higher estimates.415 Iu earlier work it was shown that for typical QSO paraucters the power going into supernova renimauts is comparable to that of the QSO wind. but is 11ncli less than he bolometric QSO luminosity (Perry Dyson 1985).," In earlier work it was shown that for typical QSO parameters the power going into supernova remnants is comparable to that of the QSO wind, but is much less than the bolometric QSO luminosity (Perry Dyson \cite{PD1985}) )."416 However. it is more difficult to estimate whether emission roni the SN would be visible above the QSO in a specific wavebaud.," However, it is more difficult to estimate whether emission from the SN would be visible above the QSO in a specific waveband."417 The typical J-baud magnitude for a QSO at a redshift +~ lods c91δ19% whereas the J1II baud naenitude for a type Ia SN is ~21 at comparable :.," The typical J-band magnitude for a QSO at a redshift $z \sim 1$ is $\sim 18-19$, whereas the J+H band magnitude for a type Ia SN is $\sim 24$ at comparable $z$."418 Ou his basis. individual SN will no be disceruible. but clearly his conclusion depends on the luminosity of the QSO. as well as other variables such as the oricutation of the SN with respect o the molecular torus. and the ambieut density of the surroundings(e.g... if the SNR expands iuto a nearby noleculu cloud then its luninosity could be senuificautlv increased).," On this basis, individual SN will not be discernible, but clearly this conclusion depends on the luminosity of the QSO, as well as other variables such as the orientation of the SN with respect to the molecular torus, and the ambient density of the surroundings, if the SNR expands into a nearby molecular cloud then its luminosity could be significantly increased)."419 Detailed uunuerical modelling will be required to determine the likelihood of this possibility., Detailed numerical modelling will be required to determine the likelihood of this possibility.420 One of the most interesting questions concerning ACGNs is the connection between nuclear aud starburst activity., One of the most interesting questions concerning AGNs is the connection between nuclear and starburst activity.421 Miwed stayburst-ACUN. SOMYCOS ay c, Mixed starburst-AGN sources may be422and with indices a=0.2*27 and 8=1.4707.,and with indices $\alpha = 0.2^{+0.2}_{-0.1}$ and $\beta = 1.4^{+0.3}_{-0.6}$.423" The broken power law fit is very good, giving X?=0.63 for 4 d.o.f."," The broken power law fit is very good, giving $\chi^2 = 0.63$ for 4 d.o.f."424 This result agrees with previous studies (e.g.Daigneetal.Piran 2007)..," This result agrees with previous studies \citep[e.g.][]{Daigne(2006),Guetta(2007)}."425" The cannot be fitted with a single power law, since such fit give high y?, rejecting such a model with high significance (98%))."," The cannot be fitted with a single power law, since such fit give high $\chi^2$, rejecting such a model with high significance )."426 This contradict the results of Pélangeonetal.(2008) who studied the HETE-2 GRBs and found a consistency with a single power lawfunction., This contradict the results of \cite{Pelangeon(2008)} who studied the HETE-2 GRBs and found a consistency with a single power law.427". The rate is described as well by a broken power law for 14- z, with a break at 2=3.1702 and indices of ny=2.1702 and πο=—1.4771."," The rate is described as well by a broken power law for $1+z$ , with a break at $z = 3.1^{+0.6}_{-0.8}$ and indices of $n_1 = 2.1^{+0.5}_{-0.6}$ and $n_2 = -1.4^{+2.4}_{-1.0}$."428" The local event rate is ppc1.3*52[Gpc ?yr-!], in agreement with previous studies e.g. Schmidt (1999)[[po~ 1.5] (see however Schmidt (2001b)[[po~ 0.15)]); Guettaetal.(2005)[[po 0.5]; GuettaandDellaValle (2007)[[po 1.1]; Liangetal. (2007)[[oo~ 1.1]; al. 2008)[[po.Z 0.5]."," The local event rate is $\rho_0 \simeq 1.3^{+0.6}_{-0.7} [Gpc^{-3}yr^{-1}]$ , in agreement with previous studies e.g. \cite{Schmidt(1999)}[ $\rho_0 \simeq 1.5$ ] (see however \cite{Schmidt(2001b)}[ $\rho_0 \simeq 0.15$ )]); \cite{Guetta(2005)}[ $\rho_0 \simeq 0.5$ ]; \cite{GuettaDV(2007)}[ $\rho_0 \simeq 1.1$ ]; \cite{Liang(2007)}[ $\rho_0 \simeq 1.1$ ]; \cite{Pelangeon(2008)}[ $\rho_0 \gtrsim 0.5$ ]."429" The main factors determining thelow redshift (current) event rateare the overall GRB rate normalization, the low-redshift slope, the low end of the"," The main factors determining thelow redshift (current) event rateare the overall GRB rate normalization, the low-redshift slope, the low end of the"430tomogram is then at the right phase to correspond. to emission from either the secondary star or the bright spot where the stream hits the cise (or a mixture of these: the hase uncertainty prohibits a secure distinction between the »ossibilities).,tomogram is then at the right phase to correspond to emission from either the secondary star or the bright spot where the stream hits the disc (or a mixture of these; the phase uncertainty prohibits a secure distinction between the possibilities).431 Weaker emission is then seen looping leftsvarcds owards the higher-velocity feature. and. could be emission rom the overllowing stream.," Weaker emission is then seen looping leftwards towards the higher-velocity feature, and could be emission from the overflowing stream."432 We don't have sullicient information (masses and inclination) to interpret the velocities in. the tomogram directly. but we can perform a plausibility check.," We don't have sufficient information (masses and inclination) to interpret the velocities in the tomogram directly, but we can perform a plausibility check."433 The high-velocity. wings in eclipsing SW Sex stars extend. to velocities of 14001600 iin stars such as SW Sex itself (Dhillon. Marsh JJones 1997) and V1315 λα (Llellier 1996): the equivalent component in eextends to 1300 in data with a comparable signal-to-noise ratio.," The high-velocity wings in eclipsing SW Sex stars extend to velocities of 1400–1600 in stars such as SW Sex itself (Dhillon, Marsh Jones 1997) and V1315 Aql (Hellier 1996); the equivalent component in extends to 1300 in data with a comparable signal-to-noise ratio."434 These velocities match if hhas an inclination of60.. or a sin/ of O.S7.," These velocities match if has an inclination of, or a $\sin i$ of 0.87."435 Further. adopting à white-dwarl mass of 0.7 aancd a red-cdwarl mass of 0.1 iimplies that the red. cwarf has an orbital velocity of 4405. that the Lagrangian point orbits at 290|. and that the outer edge of the dise (assuming it is located at the tidal limit) orbits at. 650 (μου Warner 1995. chapter 2. for the relevant formulae).," Further, adopting a white-dwarf mass of 0.7 and a red-dwarf mass of 0.1 implies that the red dwarf has an orbital velocity of 440, that the Lagrangian point orbits at 290, and that the outer edge of the disc (assuming it is located at the tidal limit) orbits at 650 (see Warner 1995, chapter 2, for the relevant formulae)."436 These values compare with the observed S-wave amplitude of 350L|. or 400 wwith the above sini.," These values compare with the observed S-wave amplitude of 350, or 400 with the above $\sin i$."437 Thus the S-wave is compatible with arising [rom the secondary or the carly part of the stream. but less compatible with arising [rom the streamdisc impact (unless the inclination or the white-clwarl mass are lower than adopted. above).," Thus the S-wave is compatible with arising from the secondary or the early part of the stream, but less compatible with arising from the stream–disc impact (unless the inclination or the white-dwarf mass are lower than adopted above)."438 Thus. overall. the line profiles are consistent with the stream-overllow idea. in that both the lower-velocity S-wave and the lino wings have compatible velocities.," Thus, overall, the line profiles are consistent with the stream-overflow idea, in that both the lower-velocity S-wave and the line wings have compatible velocities."439 A crucial observation for models of iis that the A-ray lighteurve. varies only with the 2147-5 spin period. and not with the orbital evcle nor the orbital sidebancs of the spin period. (Llellier 11998).," A crucial observation for models of is that the X-ray lightcurve varies only with the 2147-s spin period, and not with the orbital cycle nor the orbital sidebands of the spin period (Hellier 1998)."440 This implies that the accreting material loses knowlecdee of orbital phase before attaching to field. lines., This implies that the accreting material loses knowledge of orbital phase before attaching to field lines.441 ‘This. in turn. suggests that. if the stream-overllow mocel is correct. the overflowing stream does not travel far enough o encounter the magnetosphere. but. instead. re-inipacts he disc further out.," This, in turn, suggests that, if the stream-overflow model is correct, the overflowing stream does not travel far enough to encounter the magnetosphere, but instead re-impacts the disc further out."442 This contrasts with suggestions [or other IPs. for instance FO Aqr. where the interaction of he overllowing stream with the magnetopshere was invoked specifically to explain an X-ray beat pulse (οπου 1993: Bearcmore 1998).," This contrasts with suggestions for other IPs, for instance FO Aqr, where the interaction of the overflowing stream with the magnetopshere was invoked specifically to explain an X-ray beat pulse (Hellier 1993; Beardmore 1998)."443 Two caveats should. be mace., Two caveats should be made.444 First. the overllow müsght be intermittent. and might not have been occurring during the X-ray observations.," First, the overflow might be intermittent, and might not have been occurring during the X-ray observations."445 Indeed. the X-ray beat pulse in FO Aqr is variable and sometimes absent.," Indeed, the X-ray beat pulse in FO Aqr is variable and sometimes absent."446 Secondly. we should consider whether the 2147-5 period is misidentified. ancl is actually the beat Q)) period.," Secondly, we should consider whether the 2147-s period is misidentified, and is actually the beat ) period."447 This. though. would imply a spin period of 1509 s. and no such periodicity has ever been seen inCen: and further. other observed »riodicities. such as the IS60-5. modulation. would. then lave no natural identification.," This, though, would imply a spin period of 1509 s, and no such periodicity has ever been seen in; and further, other observed periodicities, such as the 1860-s modulation, would then have no natural identification."448 ‘There is. however. a significant beat-cvele modulation in he line V/1t ratios (Section 2).," There is, however, a significant beat-cycle modulation in the line V/R ratios (Section 2)."449 Phis can be explained in the standard way for optical beat periods. namely irradiation of structure fixed in the binary [rame (secondary or streani) w the spin-pulsed X-ray beam.," This can be explained in the standard way for optical beat periods, namely irradiation of structure fixed in the binary frame (secondary or stream) by the spin-pulsed X-ray beam."450 However. the period of the observed: modulation. differs from. the expected value. by LT per cent.," However, the period of the observed modulation differs from the expected value by 0.7 per cent."451 Over the 2-d span of the observations this amounts to a shift of 0.85 evcles., Over the 2-d span of the observations this amounts to a shift of 0.35 cycles.452 | possible explanation is that over the 2-cl interval the N-rav. beam switched from illuminating (preclominanth:) the secondary. to illuminating (predominantly) the structure formed where the overflowing stream re-impacts the disc.," A possible explanation is that over the 2-d interval the X-ray beam switched from illuminating (predominantly) the secondary, to illuminating (predominantly) the structure formed where the overflowing stream re-impacts the disc."453 As can be seen from the tomogram. these two regions are separated by 0.35 in orbital phase.," As can be seen from the tomogram, these two regions are separated by 0.35 in orbital phase."454 Hf correct. this again suggeests that the overllow is intermittent. occuring only some of the timo.," If correct, this again sugggests that the overflow is intermittent, occuring only some of the time."455 One puzzle for the above model is the observation of the 1860-5. photometric modulation. identified with O0)) whenw lis not seen.," One puzzle for the above model is the observation of the 1860-s photometric modulation, identified with ), when is not seen."456 Reprocessing of N-ravs would. likely result. in an optical moclulation. as is observed in many LPs. but not 3).," Reprocessing of X-rays would likely result in an optical modulation, as is observed in many IPs, but not )."457 One plausible explanation. that the illuminating X-ray beam is double-pealked. resulting in reprocessing at Q)). is contradicted by the fact that the observed. X-ray pulse is nearly sinusoical (Llellier 11998).," One plausible explanation, that the illuminating X-ray beam is double-peaked, resulting in reprocessing at ), is contradicted by the fact that the observed X-ray pulse is nearly sinusoidal (Hellier 1998)."458 hus. this explanation only works if the X-ray pulse is beamed such that it is double-peaked in the orbital plane but sinusoidal from our line of sight. which is unlikely.," Thus, this explanation only works if the X-ray pulse is beamed such that it is double-peaked in the orbital plane but sinusoidal from our line of sight, which is unlikely."459 Lavine considered a mocel for bbased on the conventional partial disc. we now consider the alternative discless model based on a diamagnetie Dow.," Having considered a model for based on the conventional partial disc, we now consider the alternative discless model based on a diamagnetic flow."460 This model was proposed by Ixing (1993) and Wynn Whine (1995). see also Wynn (2001).," This model was proposed by King (1993) and Wynn King (1995), see also Wynn (2001)."461 Ht treats the accretion How as à set of diamagnetie blobs. and represents these by the particles in a hyvdrodynamical code. with the addition of a magnetic drag term which acts like the tension of the magnetic field lines.," It treats the accretion flow as a set of diamagnetic blobs, and represents these by the particles in a hydrodynamical code, with the addition of a magnetic drag term which acts like the tension of the magnetic field lines."462 Εις term is proportional to the rate at which particles cross field lines. giving an acceleration where ο and v; are the velocities of the material and field and the symbol L indicates the component perpendicular to the field lines.," This term is proportional to the rate at which particles cross field lines, giving an acceleration where $\mbold{v}$ and $\mbold{v}_{\rm f}$ are the velocities of the material and field and the symbol $\perp$ indicates the component perpendicular to the field lines."463 Phe parameter & is dependent on factors such as the the local field strength. blob density and Alfvénn," The parameter $k$ is dependent on factors such as the the local field strength, blob density and Alfvénn"464the times of maxima of the 11-21 variation to obtain au ephemeris wherein both linear aud quadratic terms are sienificaut.,the times of maxima of the 11-m variation to obtain an ephemeris wherein both linear and quadratic terms are significant.465 To our knowledge. this is the most precise ephemeris in the literature at this time.," To our knowledge, this is the most precise ephemeris in the literature at this time."466 We detect the periodicity in the ASN liebt curve with Ligh significance: see Fig., We detect the periodicity in the ASM light curve with high significance; see Fig.467 12. and. Tabο 3., \ref{fig:pds1820} and Table \ref{tbl:detect}.468" The period we obtain. P=685.01192+O.00007 s. is an average over the curatiui of the ASAT [250.0005data set aud1] effectively a»plies near the miud-time of this interval. Ίνοι, near MJD 52620."," The period we obtain, $P = 685.01092 \pm 0.00007\,[\pm 0.00054]$ s, is an average over the duration of the ASM data set and effectively applies near the mid-time of this interval, i.e., near MJD 52620."469 We Call COpare our])oriod iueasureimentwiti the period of D—685.01126 s predicted for this epoch |w the Chou&(αποΊαν(2001), We can compare our period measurementwith the period of $P = 685.01126$ s predicted for this epoch by the \citet{chougrn01} ephemeris.470 οΣπ. iat the s1ualler ο the wo uncertaiuties in the ASM perio that are given in Table 30 is applicable. then the ASA period is about | standard deviations below the prediction of the Chou&Caindlay(2001). ephemeris.," If we assume that the smaller of the two uncertainties in the ASM period that are given in Table \ref{tbl:detect} is applicable, then the ASM period is about 4 standard deviations below the prediction of the \citet{chougrn01}471 ephemeris."472 This sugeests that the cocfiicicut of the quadratic term in that ephemeris should be more negative., This suggests that the coefficient of the quadratic term in that ephemeris should be more negative.473 However. we have not undertaken a proper joint analvsis of all of the timing results and so this conclusion iust be regarded as tentative.," However, we have not undertaken a proper joint analysis of all of the timing results and so this conclusion must be regarded as tentative."474 The orbital periods of a umber of IININDs are listed iu Table 3.., The orbital periods of a number of HMXBs are listed in Table \ref{tbl:detect}.475 Iu contrast with the results on LAINBs. Table 3 shows that the majority of the most significant detections of these svstenis were made in the 5-12 keV energy baud.," In contrast with the results on LMXBs, Table \ref{tbl:detect} shows that the majority of the most significant detections of these systems were made in the 5-12 keV energy band."476 This is in accordance with expectations based on the observation that πας of the accreting compact objects in IIMXNDs are X-ray pulsars that teud to have relatively hard X-ray spectra., This is in accordance with expectations based on the observation that many of the accreting compact objects in HMXBs are X-ray pulsars that tend to have relatively hard X-ray spectra.4770535426 is a De/N-rav pulsar that can be rather bright in N-ravs duriug trausicut outbursts., is a Be/X-ray pulsar that can be rather bright in X-rays during transient outbursts.478 The carly observations are reviewed by Fingerctal.(1996)., The early observations are reviewed by \citet{fwh96}.479. Pulse timing analyses of observations obtained with the BATSE instrument were used to determine that the orbital period is P?=110.3250.3 davs (Fineeretal.1996.andreferences therein). , Pulse timing analyses of observations obtained with the BATSE instrument were used to determine that the orbital period is $P = 110.3 \pm 0.3$ days \citep[and references therein]{fwh96}. .480A portion of an ASAI power density spectrun is shown iu Figure 1L., A portion of an ASM power density spectrum is shown in Figure \ref{fig:pdsj1008}. .481 This figure, This figure482photoevaporated by the ionising background. and/or ejected from haloes due to supernovae feedback.,"photoevaporated by the ionising background, and/or ejected from haloes due to supernovae feedback."483" At 2=3. the mass-scale of 107LO""fINS corresponds to a circular velocity of 1015kms'. or a virial temperat slightly below 10!K."," At $z=3$, the mass-scale of $10^8 - 10^{8.5}\himsun$ corresponds to a circular velocity of $10-15\kms$, or a virial temperature slightly below $10^4\,{\rm K}$."484 Note that this is a smaller mass-scale ure.than was suggested by Quinn.Ixatz.&Efstathiou(1996). and Thoul&Weinberg (1996).. who argued that haloes with circular velocities less than 40kms+ are unlikely to harbour DLAs.," Note that this is a smaller mass-scale than was suggested by \citet{Qui96} and \citet{Tho96}, who argued that haloes with circular velocities less than $40\kms$ are unlikely to harbour DLAs."485 We will discuss this point further in Section 7.., We will discuss this point further in Section \ref{section:discussion}.486 1n Figure 4.. we show DLA cross-sections as a function of total halo mass for >=1 and z— 0. and the parameters of the fitted. power-laws are summarised in Table 4...," In Figure \ref{area_lowz.eps}, we show DLA cross-sections as a function of total halo mass for $z=1$ and $z=0$ , and the parameters of the fitted power-laws are summarised in Table \ref{table:lowzfit}."487 A similar trend in the slope as a function of resolution exists at 2=1 as we saw ab 2=3., A similar trend in the slope as a function of resolution exists at $z=1$ as we saw at $z=3$.488 Le is clearthat the slope cannot. be determined. reliably for G4 and G5 at 2=0 (and possibly at 2= 1) clue to limited resolution. as is evident [rom the ‘stripes’ seen at low cross-sections in the bottom two panels of Figure 4..," It is clearthat the slope cannot be determined reliably for G4 and G5 at $z=0$ (and possibly at $z=1$ ) due to limited resolution, as is evident from the `stripes' seen at low cross-sections in the bottom two panels of Figure \ref{area_lowz.eps}."489 Dark matter haloes with masses below the resolution limit ofa simulation cannot be resolved., Dark matter haloes with masses below the resolution limit of a simulation cannot be resolved.490 This is a serious problem. when one tries to compute the number density of DLAs based on a cosmological simulation that does not resolve all small mass haloes that may host a DLA., This is a serious problem when one tries to compute the number density of DLAs based on a cosmological simulation that does not resolve all small mass haloes that may host a DLA.491 Note in particular that the number density of dark matter haloes is known to increase strongly towards lower masses., Note in particular that the number density of dark matter haloes is known to increase strongly towards lower masses.492 Even a small incompleteness at low masses will hence prevent a reliable estimate of the DLA abundance if only a simple number count of DLAs found in a cosmological simulation is used., Even a small incompleteness at low masses will hence prevent a reliable estimate of the DLA abundance if only a simple number count of DLAs found in a cosmological simulation is used.493 Vo overcome this limitation. Gardneretal.(1997a.b.2001) convolved a theoretical Gt to the dark matter halo mass function with the measured relationship between DLA cross-section and halo mass.," To overcome this limitation, \citet{Gar97a,Gar97b,Gar01}494 convolved a theoretical fit to the dark matter halo mass function with the measured relationship between DLA cross-section and halo mass."495 In this way. they were able to correct for incompleteness in the resolved halo abundance of the simulations.," In this way, they were able to correct for incompleteness in the resolved halo abundance of the simulations."496 The cumulative abundance (or equivalently the rate of incidence) of DLAs per unit redshift as a function of halo mass in this approach can be expressed as πο. -- ο eppattMA where aayCM.2) ix the dark matter halo. mass function (for whieh we usethe Sheth&Lormen(1999) porameterisation). and dr/dz=ο(ς) with H(z)=οί)=HyQuL2)|OY for a flat universe.," The cumulative abundance (or equivalently the rate of incidence) of DLAs per unit redshift as a function of halo mass in this approach can be expressed as (>M, z) = (M',z) M', where $n_{\rm dm}(M,z)$ is the dark matter halo mass function (for which we usethe \citet{She99} parameterisation), and ${\rm d}r/{\rm497d}z = c/H(z)$ with $H(z)=H_0 E(z) = H_0\sqrt{\Om(1+z)^3+\Ol}$ for a flat universe."498 1n order to carry out this integral. the power-law fits obtained in Section + can be used to represent pLGM.z) which give the mean relation between the halo mass and the DLA cross-section.," In order to carry out this integral, the power-law fits obtained in Section \ref{section:cross} can be used to represent $\sdla(M,z)$ which give the mean relation between the halo mass and the DLA cross-section."499 Note that the dependence on the Llubble constant disappears on the right-hancl-sicle of equation (8) because dr£dz scales as h1. while naycd depends on h. and epa scales as h7 in the simulation.," Note that the dependence on the Hubble constant disappears on the right-hand-side of equation (8) because ${\rm d}r/{\rm d}z$ scales as $\hinv$, while $n_{\rm dm}{\rm d}M$ depends on $h^3$, and $\sdla$ scales as $h^{-2}$ in the simulation."500 1n Figure 5.. we show the cumulative abundance of DLAs per unit redshift at >=3 as a function of total halo mass.," In Figure \ref{cum_z3.eps}, we show the cumulative abundance of DLAs per unit redshift at $z=3$ as a function of total halo mass."501 The horizontal shaded region in the left panel indicates the observed DLA abundance of Pérouxetal.(2001)., The horizontal shaded region in the left panel indicates the observed DLA abundance of \citet{Per01}.502. We note that the data-set analysed by Pérouxetal.(2001). inelucles that of Storrie-Lombardi&Wolfe (2000)... and a similar value for the DLA abundance was also reported by Storric-(2000).. It is encouraging that the DLA abundances found in our simulations agree well with the observed range.," We note that the data-set analysed by \citet{Per01} includes that of \citet{Sto00}, , and a similar value for the DLA abundance was also reported by \citet{Sto00}.. It is encouraging that the DLA abundances found in our simulations agree well with the observed range."503The precisev onieasured frequencies of solar oscillations provile us with a unique tool to probe the solar interior with sutiicicnt accuracy.,The precisely measured frequencies of solar oscillations provide us with a unique tool to probe the solar interior with sufficient accuracy.504 These frequencies are primarily deteruiued x the dynamical quantities like sound speed. (Lens voor the adiabatie index of the solar material aud a primary inversion of the observed frequencies vields the sound. speec and deusitv profiles inside the Sun (Cough 1985: Cough Isosovichey 1990: Cough Thompson 1991: Dzicnubowski et al. 1991:," These frequencies are primarily determined by the dynamical quantities like sound speed, density or the adiabatic index of the solar material and a primary inversion of the observed frequencies yields the sound speed and density profiles inside the Sun (Gough \cite{dog85}; Gough Kosovichev \cite{dog90}; Gough Thompson \cite{dog91}; Dziembowski et al. \cite{dz94};"505 Autia Basu 199la: Basu et al. 1996:, Antia Basu \cite{ab94a}; Basu et al. \cite{b96};506 Ciough et al. 19963)., Gough et al. \cite{dog96}) ).507 Ou the other hand. in order to incr the temperature and chemical composition profiles acditional assumptions regarding the input plysics are recwired (Shibahashi 1993:: Autia Chitre 1995: Shibahashi Takata 1996: Ikosovichev 1996)).," On the other hand, in order to infer the temperature and chemical composition profiles additional assumptions regarding the input physics are required (Shibahashi \cite{shi93}; ; Antia Chitre \cite{ac95}; Shibahashi Takata \cite{st96}; Kosovichev \cite{kos96}) )."508 Thus. the equons of thermal equilibrium euable us to determine the teuperature aud bydrogen abundance profiles in the solar interior provided the opacities. equation of state auk nuclear energy. generation rates are prescribed.," Thus, the equations of thermal equilibrium enable us to determine the temperature and hydrogen abundance profiles in the solar interior provided the opacities, equation of state and nuclear energy generation rates are prescribed."509 Although he primary mversious can vield the sound speed to an accuracy of. the opacities aud nuclear reactioji ates are hardly known to comparable acctirmaev aud COlLISCGIieutlv. more systematic errors are introduced in tjese secondary mversous for teniperature and chemical composition.," Although the primary inversions can yield the sound speed to an accuracy of, the opacities and nuclear reaction rates are hardly known to comparable accuracy and consequently, more systematic errors are introduced in these secondary inversions for temperature and chemical composition."510 There aro 2a 1uber of approaches adopted for secondary Versions., There are a number of approaches adopted for secondary inversions.511 Ikosovichev (1996)) has eumploved the equations of theαπλα] equilibrium to express the lauges in primary variables (p.D4) iu terms of those oel secoidarv variabless (YZ) aud obtained equations connecting the freque1ο cifferences to variatiows in] vbunidaice profiles.," Kosovichev \cite{kos96}) ) has employed the equations of thermal equilibrium to express the changes in primary variables $\rho,\Gamma_1$ ) in terms of those in secondary variables $Y,Z$ ) and obtained equations connecting the frequency differences to variations in abundance profiles."512 It should be noted that modifications oei Z profile mainly affect the opacities iu the solar oeterior while the equation of state and nuclear energy ecnoration rates are aflected to a much lesser extent., It should be noted that modifications in $Z$ profile mainly affect the opacities in the solar interior while the equation of state and nuclear energy generation rates are affected to a much lesser extent.513 Such a procedure is essentially equivalent to fiudiug the Y profile aloie with the unecessary opacity modifications., Such a procedure is essentially equivalent to finding the $Y$ profile along with the necessary opacity modifications.514 Shibahashi aud Takata (1996.. hereinafter ST96) adopt je standard opacities and nuclear reactiou rates o obtain re feniperaure anc chenical abuudauce profies usus 16 inverted sound speed xofile.," Shibahashi and Takata \cite{st96}, hereinafter ST96) adopt the standard opacities and nuclear reaction rates to obtain the temperature and chemical abundance profiles using the inverted sound speed profile."515 Antia aucL Chitre (19€)5.. 1996)) set out to estimate ιο central eniperature of the Sun.," Antia and Chitre \cite{ac95}, \cite{ac96}) ) set out to estimate the central temperature of the Sun."516 Thev adoated the oeweyed souid speed aux density profiles to oltain the enperature CZ) and οτι abundance (Y) profiles iu ie solar core. but the main difference was that opacity aud melear reaction rates were not directly «3uploved or tus purpose.," They adopted the inverted sound speed and density profiles to obtain the temperature $T$ ) and helium abundance $Y$ ) profiles in the solar core, but the main difference was that opacity and nuclear reaction rates were not directly employed for this purpose."517 Tustead. the T aud Y profiles were obtained by minimizing the varialon I opacities from the Stauard values.," Instead, the $T$ and $Y$ profiles were obtained by minimizing the variation in opacities from the standard values."518 The main reasou for allowing variations in theoretically deteriuuedquatity like opacity rather, The main reason for allowing variations in theoretically determinedquantity like opacity rather519"(2001).. Mane Tor an old population has variations with metallicity ~2x that of Mj,gc. an effect confirmed in (he empirical investigation of Pielrzviskietal.(2010).. who looked at the RC of 15 nearby galaxies observed with LST.",", $M_{V,RC}$ for an old population has variations with metallicity $\sim$ $\times$ that of $M_{I,RC}$, an effect confirmed in the empirical investigation of \citet{2010AJ....140.1038P}, who looked at the RC of 15 nearby galaxies observed with HST."520 Moreover. any residual differenGal reddening will be ~2x as significant in V.," Moreover, any residual differential reddening will be $\sim$ $\times$ as significant in $V$."521 These (wo effects render the bulge RC non-horizontal in V. [further complicating the fitting routine.," These two effects render the bulge RC non-horizontal in $V$, further complicating the fitting routine."522 There is a difference between (his parameter and that predominantly used in the literature., There is a difference between this parameter and that predominantly used in the literature.523" We computed AJ#CS"" whereas most results present AWPU72.", We computed ${\Delta}I^{RGBB}_{RC}$ whereas most results present ${\Delta}V^{RGBB}_{ZAHB}$.524 However. these two values should be very nearly equal as the two largest biases are not large ancl go in opposing directions.," However, these two values should be very nearly equal as the two largest biases are not large and go in opposing directions."525 Firstly. AWM? should be a little larger than ALCS because the RC will be a little bluer than the RG stars. the bias is expected [rom stellar theory. but is consistent with negligible in our data.," Firstly, ${\Delta}V^{RGBB}_{RC}$ should be a little larger than ${\Delta}I^{RGBB}_{RC}$ because the RC will be a little bluer than the RG stars, the bias is expected from stellar theory but is consistent with negligible in our data."526" Conversely. AV}(7% will be a little smaller than AVE?"" as the ZAIB is the dimmest phase of horizontal branch evolution. however in our analvsis of elobular cluster data we find that this effect can be no more than 70.05 mag."," Conversely, ${\Delta}V^{RGBB}_{ZAHB}$ will be a little smaller than ${\Delta}V^{RGBB}_{RC}$ as the ZAHB is the dimmest phase of horizontal branch evolution, however in our analysis of globular cluster data we find that this effect can be no more than $\sim$ 0.05 mag."527" We thus adopt (he approximation A[8655R¢_=""ROBLESAZ.", We thus adopt the approximation ${\Delta}I^{RGBB}_{RC} = {\Delta}V^{RGBB}_{ZAHB}$.528" It is reassuring that the Galactic bulge has the faintest RGBB relative to its horizontal branch as it is the mostmetal-rich RGBB detected thus far,", It is reassuring that the Galactic bulge has the faintest RGBB relative to its horizontal branch as it is the mostmetal-rich RGBB detected thus far.529 Galactic elobular clusters do not typically reach metallicities as high as |M/ILI] 0.0. and those that do have substantial differential reddening (Ortolanietal.2001) or multiple stellar populations 2009).. effects that render the RGBB harcler to detect.," Galactic globular clusters do not typically reach metallicities as high as [M/H] $\approx 0.0$, and those that do have substantial differential reddening \citep{2001A&A...376..878O} or multiple stellar populations \citep{2009Natur.462..483F}, effects that render the RGBB harder to detect."530 This expansion of the parameter space al the metal rich end follows recent. complementary detections of the RGBB in vounger and moremetal-poor svstenms. those of the nearby cwarl galaxies.," This expansion of the parameter space at the metal rich end follows recent, complementary detections of the RGBB in younger and moremetal-poor systems, those of the nearby dwarf galaxies."531 There have been detections of the RGDD toward the Sculptor dwarl spheroidal galaxy (Majewskietal.1999).. Ursa Minor (Bellazzinietal.2002).. Sagittarius (Monacoetal.2002).. and Sextans (Leeetal.2003).. and M32 (Monachesietal. 2011).. Mon," There have been detections of the RGBB toward the Sculptor dwarf spheroidal galaxy \citep{1999ApJ...520L..33M}, Ursa Minor \citep{2002AJ....124.3222B}, Sagittarius \citep{2002ApJ...578L..47M}, and Sextans \citep{2003AJ....126.2840L}, and M32 \citep{2011ApJ...727...55M}. ."532ellietal.(2010) recently reported on the detection of the RGBB toward Cetus. 101010. LGS 3 and Tucana.," \citet{2010ApJ...718..707M} recently reported on the detection of the RGBB toward Cetus, IC1613, LGS 3 and Tucana."533 The observed relation between AVore and [M/IT] is shown in Figure 3.. with the Zinn&West(1984). metallicity scale asstuned for the Galactic globular clusters and w C'en.," The observed relation between ${\Delta}V^{RGBB}_{ZAHB}$ and [M/H] is shown in Figure \ref{Fig:BumpEmpiricalHistory}, with the \citet{1984ApJS...55...45Z} metallicity scale assumed for the Galactic globular clusters and $\omega$ $Cen$."534 We estimate [M/II] via the conversion function suggested by Salarisetal. (1993): and an [a /Fe]=+04 for the Galactic globular clusters ance Cen. and [a /Fe]=+0.25 for the Galactic bulge ancl M32.," We estimate [M/H] via the conversion function suggested by \citet{1993ApJ...414..580S}: : and an $\alpha$ $=+0.4$ for the Galactic globular clusters and$\omega$ $Cen$ , and $\alpha$ $=+0.25$ for the Galactic bulge and M32."535 , 536emission as well.,emission as well.537 This suggests two possible results for the method's application to real data., This suggests two possible results for the method's application to real data.538 First. if there are few or no soft sources just slightly harder than the canonical SSSs. the procedure will select only SSSs.," First, if there are few or no soft sources just slightly harder than the canonical SSSs, the procedure will select only SSSs."539 Second. if there is a supply of somewhat harder sources. we will select them as well.," Second, if there is a supply of somewhat harder sources, we will select them as well."540 We have now had opportunities to apply the selection criteria to the 4+ galaxies studied in the companion paper Kong 2003). to M104 eet al.," We have now had opportunities to apply the selection criteria to the $4$ galaxies studied in the companion paper Kong 2003), to M104 et al."541 2003a). M31 eet al.," 2003a), M31 et al."542 2003b). and roughly one dozen additional. galaxies eet al.," 2003b), and roughly one dozen additional galaxies et al."543 2003c)., 2003c).544 We have found that most galaxies have significant populations of both SSSs and. sources with somewhat harder spectra (e.g.. ΚΑΤ«250 eV).," We have found that most galaxies have significant populations of both SSSs and sources with somewhat harder spectra (e.g., $k\, T < 250$ eV)."545 We refer to the latter as quasisoft sources (QSSs)., We refer to the latter as quasisoft sources (QSSs).546 Our selection procedure distinguishes between SSSs and QSSs according to which step in the algorithm identifies the source as being very soft., Our selection procedure distinguishes between SSSs and QSSs according to which step in the algorithm identifies the source as being very soft.547 In the galaxies we have studied. spectral fits for the brightest SSS and QSS candidates have verified that the algorithmic classification works.," In the galaxies we have studied, spectral fits for the brightest SSS and QSS candidates have verified that the algorithmic classification works."548 To simplify the terminology. we will sometimes use the term “very soft source” (VSS) to refer to both SSSs and QSSs.," To simplify the terminology, we will sometimes use the term “very soft source"" (VSS) to refer to both SSSs and QSSs."549 The physical significance of this new class is not yet understood. but there are likely to be several physical models corresponding to QSSs.," The physical significance of this new class is not yet understood, but there are likely to be several physical models corresponding to QSSs."550 First. hot SSSs located behind large gas columns will have photons in the medium energy band. M (1.122 keV). but may have few photons in the soft band. S (0.1—1.1 keV).," First, hot SSSs located behind large gas columns will have photons in the medium energy band, $M$ $1.1-2$ keV), but may have few photons in the soft band, $S$ $0.1-1.1$ keV)."551 For such sources. the hardness ratios typically used to identify SSSs will have values not normally associated with SSSs. even though their intrinsic characteristics clearly place them in the SSS category.," For such sources, the hardness ratios typically used to identify SSSs will have values not normally associated with SSSs, even though their intrinsic characteristics clearly place them in the SSS category."552 Second if the detector has poorer than anticipated sensitivity to soft photons. soft sources can appear to be harder than they actually are.," Second if the detector has poorer than anticipated sensitivity to soft photons, soft sources can appear to be harder than they actually are."553 Thus. some QSSs are likely to have the same physical characteristics as some other sources identified as SSSs.," Thus, some QSSs are likely to have the same physical characteristics as some other sources identified as SSSs."554 Finally. some QSSs are likely to be genuinely harder than SSSs. so hard that white dwarf models can be ruled out.," Finally, some QSSs are likely to be genuinely harder than SSSs, so hard that white dwarf models can be ruled out."555 As we will discuss in 82. intermediate mass black hole models may be appropriate for such systems. but neutron star or stellar mass black hole models should also be considered.," As we will discuss in 2, intermediate mass black hole models may be appropriate for such systems, but neutron star or stellar mass black hole models should also be considered."556 Below we list some of the questions we hope to answer with studies that compare VSS populations in different galaxies. (, Below we list some of the questions we hope to answer with studies that compare VSS populations in different galaxies. (5571) What are typical galactic populations of SSSs and QSSs?,1) What are typical galactic populations of SSSs and QSSs?558 Irrespective of their fundamental natures. the answer to this question will allow us to estimate the influence of soft X-ray sources as Ionizers of the ISM. (," Irrespective of their fundamental natures, the answer to this question will allow us to estimate the influence of soft X-ray sources as ionizers of the ISM. ("5592) Are any spiral galaxy parameters related to the relative sizes of SSS and QSS populations?,2) Are any spiral galaxy parameters related to the relative sizes of SSS and QSS populations?560 Answering this question can provide insight into the age of the populations that spawn very soft sources. and hence might help to illuminate their nature.," Answering this question can provide insight into the age of the populations that spawn very soft sources, and hence might help to illuminate their nature."561 Rappaport (1994) suggested that for spiral galaxies. the size of the SSS population might scale with blue luminosity. but this has not been tested. (," Rappaport (1994) suggested that for spiral galaxies, the size of the SSS population might scale with blue luminosity, but this has not been tested. ("5623) Do elliptical galaxies house large SSS/QSS populations?,3) Do elliptical galaxies house large SSS/QSS populations?563 Although it has been suggested that the diffuse soft emission in ellipticals may be due to SSSs (see. e.g.. Fabbiano. Kim. Trinchiert 1994). we still know very little about SSSs in ellipticals.," Although it has been suggested that the diffuse soft emission in ellipticals may be due to SSSs (see, e.g., Fabbiano, Kim, Trinchieri 1994), we still know very little about SSSs in ellipticals."564 If accreting WDs form the largest segment of SSS populations. and if a significant fraction of the donor stars have masses small enough to be typical of the stars found in elliptical galaxies. then we may expect SSSs to be important parts of the X-ray source population in ellipticals. (," If accreting WDs form the largest segment of SSS populations, and if a significant fraction of the donor stars have masses small enough to be typical of the stars found in elliptical galaxies, then we may expect SSSs to be important parts of the X-ray source population in ellipticals. ("5654) Within spiral galaxies. what are the relative populations of SSSs/QSSs in the galaxy bulges and disks? (,"4) Within spiral galaxies, what are the relative populations of SSSs/QSSs in the galaxy bulges and disks? ("5665) Do galaxies with massive central black holes have more SSSs or QSSs located within | kpe of the nucleus than comparable galaxies without massive central black holes?,5) Do galaxies with massive central black holes have more SSSs or QSSs located within 1 kpc of the nucleus than comparable galaxies without massive central black holes?567 It has been suggested that some SSSs within the central kpc of galaxies which harbor massive black holes may actually be the stripped cores of stars that have been tidally disrupted eet al., It has been suggested that some SSSs within the central kpc of galaxies which harbor massive black holes may actually be the stripped cores of stars that have been tidally disrupted et al.568 2001)., 2001).569 Verification of this hypothesis by studying individual SSSs will be difficult. so statistical studies of SSS populations in a large number of galaxies may provide the best tests. (," Verification of this hypothesis by studying individual SSSs will be difficult, so statistical studies of SSS populations in a large number of galaxies may provide the best tests. ("5706) For all galaxies. are the positions of QSSs and SSSs correlated to the positions of other objects. such as HII regions. planetary nebulae. supernova remnants. or globular clusters?,"6) For all galaxies, are the positions of QSSs and SSSs correlated to the positions of other objects, such as HII regions, planetary nebulae, supernova remnants, or globular clusters?"571 The distances to most external galaxies are too large to allow for convincing optical identifications., The distances to most external galaxies are too large to allow for convincing optical identifications.572 It is nevertheless useful to identify the types of populations which tend to be associated with VSSs., It is nevertheless useful to identify the types of populations which tend to be associated with VSSs.573 This can provide clues to their fundamental natures. (, This can provide clues to their fundamental natures. (5747) Are SSSs significant contributors to the rates of Type la SNe?,7) Are SSSs significant contributors to the rates of Type Ia SNe?575 The answer to this question can. be achieved. by combining information about typical total galactic populations with studies of the viability of the accreting WD models., The answer to this question can be achieved by combining information about typical total galactic populations with studies of the viability of the accreting WD models.576 Previous studies of SSSs in external galaxies have used a variety of selection criteria., Previous studies of SSSs in external galaxies have used a variety of selection criteria.577" In NGC 4697, e.g.. Sarazin. Irwin. Bregman (2001) identified 3 SSSs by requiring that HRI=(M—S)/(M+S)=-1 and HR2=(H—S)/(H+S)=—1. where S. M. and H represent the numbers of counts in the bands 0.3—| keV. 1-2 keV. and 2—IO keV. In their studies of the colors of X-ray sources. Prestwich et (2002). used the same criteria, which are satisfied by only a handful of the sources they analyzed. drawn from both MIOI and M83."," In NGC 4697, e.g., Sarazin, Irwin, Bregman (2001) identified $3$ SSSs by requiring that ${\tilde {HR1}}=(\tilde M-\tilde S)/(\tilde M+\tilde S) = -1$ and ${\tilde {HR2}}=(\tilde H-\tilde S)/(\tilde H+\tilde S) = -1,$ where $\tilde S,$ $\tilde M,$ and $\tilde H$ represent the numbers of counts in the bands $0.3-1$ keV, $1-2$ keV, and $2-10$ keV, In their studies of the colors of X-ray sources, Prestwich et (2002), used the same criteria, which are satisfied by only a handful of the sources they analyzed, drawn from both M101 and M83."578 Less restrictive criteria were used by Swartz et (2002) to identify SSSs in M81., Less restrictive criteria were used by Swartz et (2002) to identify SSSs in M81.579 The criteria HRI<—0.5. HR2——0.5 selected 12 M8] X-ray sources. 2 of which were eliminated because they are identified with foreground stars. while one is identified with a supernova remnant (SNR).," The criteria ${\tilde {HR1}} < -0.5,$ ${\tilde {HR2}} < -0.5$ selected $12$ M81 X-ray sources, $2$ of which were eliminated because they are identified with foreground stars, while one is identified with a supernova remnant (SNR)."580 Pence et (2002a) identified 10 SSSs in MIOI. but did not specify the selection criteria.," Pence et (2002a) identified $10$ SSSs in M101, but did not specify the selection criteria."581 The possible physical interpretation of the sources seemed to play a role. as one of the galaxy’s softest sources was not counted among the SSSs. perhaps because tt appears to be too luminous to be a nuclear-burning WD (Pence et 2002b).," The possible physical interpretation of the sources seemed to play a role, as one of the galaxy's softest sources was not counted among the SSSs, perhaps because it appears to be too luminous to be a nuclear-burning WD (Pence et 2002b)."582" Kong et (2002a) took another approach. requiring (HR240gsx—]and (HRI <0.) CHRI0,4 <—0.8])."," Kong et (2002a) took another approach, requiring $({\tilde {HR2}} + \sigma_{{\tilde {HR2}}} \leq -1$ $[{\tilde {HR1}} < 0,$ ] ${\tilde {HR1}} + \sigma_{{\tilde {HR1}}} \leq -0.8]$ )."583 Fourteen sources in the central 17«17! of M31 satisfied these conditions. of which 2 were apparently identified with SNRs (Kong et al.," Fourteen sources in the central $17' \times 17'$ of M31 satisfied these conditions, of which $2$ were apparently identified with SNRs (Kong et al."584 2002b) and 3 with possible foreground stars., 2002b) and $3$ with possible foreground stars.585 These latter criteria were developed in parallel with a study, These latter criteria were developed in parallel with a study586the models.,the models.587 The DFs of the best models for FS373 and FS76 are presented in Figs., The DFs of the best models for FS373 and FS76 are presented in Figs.588 12. and 13.. respectively.," \ref{mod373} and \ref{mod76}, respectively."589 We plot the DF in the equatorial plane in turning-point space., We plot the DF in the equatorial plane in turning-point space.590" Each orbit in this plane is labeled uniquely by its pericenter distance Aa; and apocenter distance Ray, if. A4; 18 given the same sign as L..", Each orbit in this plane is labeled uniquely by its pericenter distance $R_{\rm peri}$ and apocenter distance $R_{\rm apo}$ if $R_{\rm peri}$ is given the same sign as $L_z$.591 Circular orbits lie on two straight lines with Rayo=ER., Circular orbits lie on two straight lines with $R_{\rm apo} = \pm R_{\rm peri}$.592 Radial orbits lie on the vertical line with Ανν=0., Radial orbits lie on the vertical line with $R_{\rm peri}=0$.593 In both galaxy models. an excess phase-space density of stars on near-circular orbits. forming the KDC. is clearly visible.," In both galaxy models, an excess phase-space density of stars on near-circular orbits, forming the KDC, is clearly visible."594 Moreover. the KDC is obviously disjunct from the central nucleus or density cusp.," Moreover, the KDC is obviously disjunct from the central nucleus or density cusp."595 Since the KDCs form a distinct subcomponent within their host galaxies. the stars that make up a KDC can be singled out of the DF and be studied separately (especially in the case of FS373. it was very clear which basis functions in the expansion of the DF formed the KDC).," Since the KDCs form a distinct subcomponent within their host galaxies, the stars that make up a KDC can be singled out of the DF and be studied separately (especially in the case of FS373, it was very clear which basis functions in the expansion of the DF formed the KDC)."596 In order to roughly estimate the stellar mass of the KDC. we assumed a stellar mass-to-light ratio of Μην=2—AMLp. which agrees with the observed colors and line-strengths.," In order to roughly estimate the stellar mass of the KDC, we assumed a stellar mass-to-light ratio of $M/L_B = 2-4 M_\odot/L_{B,\odot}$, which agrees with the observed colors and line-strengths."597 Thus. we find Μίκης=173x107M. for both galaxies or a few percent at most of the total mass.," Thus, we find $M_{\rm598KDC} \approx 1-5 \times 10^7 M_\odot$ for both galaxies or a few percent at most of the total mass."599 The adopted M/Ly is both typical fora 10 Gyr old. metal-poor (21 «[Fe/H]« —-0.5) stellar population (which would agree with dEs being primordial stellar systems) and for a 5 Gyr old. more metal-rich (-0.5. «|Fe/H]« 0.0) stellar population (which would agree with dEs being harassed late-type spirals that experienced a starburst) (Worthey (1994))).," The adopted $M/L_B$ is both typical for a 10 Gyr old, metal-poor $-1<$ $<-0.5$ ) stellar population (which would agree with dEs being primordial stellar systems) and for a 5 Gyr old, more metal-rich $-0.5<$ $<0.0$ ) stellar population (which would agree with dEs being harassed late-type spirals that experienced a starburst) \cite{wo94}) )."600 The key question is whether KDCs in dwarf elliptical galaxies are produced the same way as in massive ellipticals., The key question is whether KDCs in dwarf elliptical galaxies are produced the same way as in massive ellipticals.601 We explore two possible avenues to KDC formation in. dEs., We explore two possible avenues to KDC formation in dEs.602 The first is the merger hypothesis. as in. giant. ellipticals: the second is the harassment scenario. which posits that. gravitational interactions play an important role in the evolution of dEs.," The first is the merger hypothesis, as in giant ellipticals; the second is the harassment scenario, which posits that gravitational interactions play an important role in the evolution of dEs."603 The analytical arguments given below are strictly speaking only valid for anddistant encounters., The analytical arguments given below are strictly speaking only valid for and encounters.604" An encounter between to galaxies. with nasses M, and M». qualifies as if. at closest approach. the change in the potential energy of the pair is much smaller than the initial orbital kinetic energy."," An encounter between to galaxies, with masses $M_1$ and $M_2$, qualifies as if, at closest approach, the change in the potential energy of the pair is much smaller than the initial orbital kinetic energy."605 In afast encounter. the relative velocity of the galaxies is much larger than the internal stellar velocities.," In a encounter, the relative velocity of the galaxies is much larger than the internal stellar velocities."606 This translates into the following constraints on the impact parameter 5 and the internal velocity dispersion cn: with V4.4 the relative velocity of the interacting galaxies., This translates into the following constraints on the impact parameter $b$ and the internal velocity dispersion $\sigma_{\rm int}$: with $V_{\rm rel}$ the relative velocity of the interacting galaxies.607 For Ms9κΙΟΥM. a typical dE mass. and Mj=Mpc<<M. we find 6>250—500 pe for Vig=c300—400 km/s. Also. cp>Oi.," For $M_2 \approx 5 \times 10^9 M_\odot$, a typical dE mass, and $M_1 =608M_{\rm KDC} << M$, we find $b > 250 - 500$ pc for $V_{\rm rel} =609\sigma_{\rm gal} = 300 - 400$ km/s. Also, $\sigma_{\rm gal} >610\sigma_{\rm int}$."611 Hence. any non-penetrating encounter between a dE and a much smaller dwarf galaxy classifies as a fast and distant encounter (even if we take the dwarf galaxy to be originally 10 times more massive than Mypc. the minimum impact parameter would change by only 10%)).," Hence, any non-penetrating encounter between a dE and a much smaller dwarf galaxy classifies as a fast and distant encounter (even if we take the dwarf galaxy to be originally 10 times more massive than $M_{\rm KDC}$, the minimum impact parameter would change by only )."612" In the case of a giant elliptical with M»=5κ10!'M. and M,=Ma<<M». the condition for a fast flyby becomes b>25—50 kpe. again rather unsensitive to Maji."," In the case of a giant elliptical with $M_2613\approx 5 \times 10^{11} M_\odot$ and $M_1 = M_{\rm dE} << M_2$, the condition for a fast flyby becomes $b > 25 - 50$ kpc, again rather unsensitive to $M_{\rm dE}$."614 In a group or cluster environment. galaxies keep respectable distances of a few tens of kpe (Mooreefaf.(1996))).," In a group or cluster environment, galaxies keep respectable distances of a few tens of kpc \cite{mkldo}) )."615 With this in mind. we can discuss possible mechanism of producing KDCs in dEs.," With this in mind, we can discuss possible mechanism of producing KDCs in dEs."616 While the merger origin of KDCs in bright ellipticals is well accepted. anumber of facts argue against the merger hypothesis in the case of dEs.," While the merger origin of KDCs in bright ellipticals is well accepted, a number of facts argue against the merger hypothesis in the case of dEs."617" The change of the forward velocity of a galaxy with mass M, induced by a fast. distant hyperbolic encounter with a galaxy with mass M» with a relative velocity V4 is given by (Sparke&Gallagher(2000).. Binney&Tremaine (1987)))."," The change of the forward velocity of a galaxy with mass $M_1$ induced by a fast, distant hyperbolic encounter with a galaxy with mass $M_2$ with a relative velocity $V_{\rm rel}$ is given by \cite{sg},, \cite{bt}) )."618. The closer and the slower the encounter. the more orbital energy is converted into internal (stellar) kinetic energy.," The closer and the slower the encounter, the more orbital energy is converted into internal (stellar) kinetic energy."619 For an encounter between a typical M;=5xIOM. dE anda Mj=5x10’M. dwarf galaxy with a relative velocity V4=c300 km/s. AV) is very small (e.g. AV)~35 km/s for a collision with 6=1 kpe).," For an encounter between a typical $M_2 =5 \times 10^9620M_\odot$ dE and a $M_1 =5 \times 10^7 M_\odot$ dwarf galaxy with a relative velocity $V_{\rm rel} = \sigma_{\rm gal} = 300$ km/s, $\Delta621V_{||}$ is very small (e.g. $\Delta V_{||} \sim 35$ km/s for a collision with $b=1$ kpc)."622" In the case of an encounter between a M»=5x10!'M, elliptical and a M;=5x10°M.. dE. on the other hand. the velocity change is substantial: AV)~Vier. even for impact parameters of a few tens of kiloparsecs."," In the case of an encounter between a $M_2=5 \times 10^{11} M_\odot$ elliptical and a $M_1=5 \times 10^9623M_\odot$ dE, on the other hand, the velocity change is substantial: $\Delta V_{||} \sim V_{\rm rel}$, even for impact parameters of a few tens of kiloparsecs."624 This suggests that a dE. in a group or cluster environment. has virtually no chance of slowing down and capturing another (smaller) dwarf galaxy. contrary to a more massive elliptical galaxy.," This suggests that a dE, in a group or cluster environment, has virtually no chance of slowing down and capturing another (smaller) dwarf galaxy, contrary to a more massive elliptical galaxy."625 Hence. once the galaxy group or cluster is 1n place. the chance of forming a KDC in a dE by à merger is exceedingly small.," Hence, once the galaxy group or cluster is in place, the chance of forming a KDC in a dE by a merger is exceedingly small."626 Also. it is unclear how the merger scenario can explain the complex velocity profile of FS373. particularly the velocity changing sign around a radius of 12”=2.4 kpe.," Also, it is unclear how the merger scenario can explain the complex velocity profile of FS373, particularly the velocity changing sign around a radius of $12'' = 2.4$ kpc."627 Alternatively. the merger could have taken place the group or cluster virialized. in an environment where relative velocities were smaller than the present values.," Alternatively, the merger could have taken place the group or cluster virialized, in an environment where relative velocities were smaller than the present values."628 The low galaxy density in such an environment argues against this idea., The low galaxy density in such an environment argues against this idea.629 Also. it remains to be seen. e.g. using high-resolution N- simulations. whether à KDC formed this way can survive the dE’s falling into à group or cluster and the subsequent gravitational interactions with giant group or cluster members.," Also, it remains to be seen, e.g. using high-resolution $N$ -body simulations, whether a KDC formed this way can survive the dE's falling into a group or cluster and the subsequent gravitational interactions with giant group or cluster members."630 A plausible alternative is the spin-up of a dE's halo by fly-by encounters with other galaxies., A plausible alternative is the spin-up of a dE's halo by fly-by encounters with other galaxies.631" The impulse approximation and the tensor virial theorem yield the following expression for the maximum amount of angular momentum that can be transfered to a galaxy with mass M, during an encounter with a galaxy with mass M»:with qi the axis ratio and{τι a component of the inertial tensor (S", The impulse approximation and the tensor virial theorem yield the following expression for the maximum amount of angular momentum that can be transfered to a galaxy with mass $M_1$ during an encounter with a galaxy with mass $M_2$ :with $q_1$ the axis ratio and$I_{11}$ a component of the inertial tensor \cite{ssk}) ).632omSunder&Kochhar (1990))). Using AJ.~ to roughly estimate Άγιοι the maximum possible," Using $\Delta J \sim M_1 R_{\rm e,1} \Delta633v_{\rm rot}$ to roughly estimate $\Delta v_{\rm rot}$ , the maximum possible"634data on the Sn rates and star formation rates to infer the relative role played by type Ia and II Sn (SnIa and SnII hereafter).,data on the Sn rates and star formation rates to infer the relative role played by type Ia and II Sn (SnIa and SnII hereafter).635 A different approach was pursued by other authors. which considered. gas-dynamical mechanisms that at relatively low redshift are responsible for redistributing previously produced metals.," A different approach was pursued by other authors, which considered gas–dynamical mechanisms that at relatively low redshift are responsible for redistributing previously produced metals."636 For instance. ? suggested that clumps of low-entropy highly enriched gas may sink in the central cluster regions. thereby leading to an increase of the observed emission—weighted metallicity.," For instance, \cite{2008arXiv0802.0975C} suggested that clumps of low–entropy highly enriched gas may sink in the central cluster regions, thereby leading to an increase of the observed emission–weighted metallicity."637 For instance. ram—pressure stripping of the interstellar medium (SM) of merging galaxies has been suggested as a mechanism o pollute at relatively low redshift a metal-poor ICM with highly enriched gas (e.g.2.andreferencestherein). while causing a morphological transformation of cluster galaxies (e.g.22).," For instance, ram–pressure stripping of the interstellar medium (ISM) of merging galaxies has been suggested as a mechanism to pollute at relatively low redshift a metal–poor ICM with highly enriched gas \citep[e.g.,][and references638therein]{2006A&A...452..795D}, while causing a morphological transformation of cluster galaxies \citep[e.g.,][]{2007MNRAS.tmpL..43C,2007MNRAS.380.1399R}."639 Although possible evidences of ram-pressure stripping of cluster galaxies have been detected (e.z..?) the question remains as to whether this mechanism dominates the evolution of the ICM enrichment.," Although possible evidences of ram–pressure stripping of cluster galaxies have been detected \citep[e.g.,][]{2007ApJ...659L.115C} the question remains as to whether this mechanism dominates the evolution of the ICM enrichment."640 Indeed. since ram pressure is expected to be more efficient in high-temperature clusters. one expects an increasing trend of metallicity with ICM temperature (e.g.2y..," Indeed, since ram pressure is expected to be more efficient in high–temperature clusters, one expects an increasing trend of metallicity with ICM temperature \citep[e.g.,][]{1997ApJ...488...35R}."641 If any. observations suggest that hotter systems have a relatively lower metallicity (e.g..2).. thus suggesting that ram-pressure stripping is not the dominant process in enriching the ICM.," If any, observations suggest that hotter systems have a relatively lower metallicity \citep[e.g.,][]{2005ApJ...620..680B}, thus suggesting that ram–pressure stripping is not the dominant process in enriching the ICM."642 It is clear that understanding the history of the ICM enrichment in cosmological context. during the cluster hierarchical build up. requires describing in detail the gasdynamics related to the merging processes. while including a self-consistent treatment of star formation and chemical evolution.," It is clear that understanding the history of the ICM enrichment in cosmological context, during the cluster hierarchical build up, requires describing in detail the gasdynamics related to the merging processes, while including a self–consistent treatment of star formation and chemical evolution."643 In this context. cosmological hydrodynamical simulations offer a unique means to capture in full detail the complexity of these processes (e.g. 2222. see ?.. for a recent review).," In this context, cosmological hydrodynamical simulations offer a unique means to capture in full detail the complexity of these processes (e.g., \citealt{2003MNRAS.339.1117V,2004MNRAS.349L..19T,2006MNRAS.371..548R,2007MNRAS.382.1050T}, see \citealt{2008arXiv0801.1062B}, for a recent review)."644 In their mos advanced versions. chemo-dynamical simulation codes treat the production of different metal species. released by different stellar populations by resorting to detailed stellar yields. also accounting for the dependent stellar lifetimes.," In their most advanced versions, chemo–dynamical simulation codes treat the production of different metal species, released by different stellar populations by resorting to detailed stellar yields, also accounting for the mass--dependent stellar lifetimes."645 In this paper we will present results on the ICM metal abundance from cosmological simulations of galaxy clusters. using the chemo-dynamical version of the ccode (??1. which has been recently presented by ? (TO7 hereafter).," In this paper we will present results on the ICM metal abundance from cosmological simulations of galaxy clusters, using the chemo–dynamical version of the code \citep{SP01.1,2005MNRAS.364.1105S}, which has been recently presented by \cite{2007MNRAS.382.1050T} (T07 hereafter)."646 We will compare the simulations with observational— results on the Iron abundance profiles.Zi... of nearby clusters. on the evolution of the ICM metallicity and on the SnIa rates.," We will compare the simulations with observational results on the Iron abundance profiles, of nearby clusters, on the evolution of the ICM metallicity and on the SnIa rates."647 This comparison will be performed with the aim of shading light on the relative role played by star formation. feedback processes and gus dynamics in determining the cosmic history of metal enrichment.," This comparison will be performed with the aim of shading light on the relative role played by star formation, feedback processes and gas dynamics in determining the cosmic history of metal enrichment."648 The plan of the paper is as follows., The plan of the paper is as follows.649 In Section 2 we review our implementation of chemical evolution in the ccode and present the main characteristics of the cluster simulations., In Section 2 we review our implementation of chemical evolution in the code and present the main characteristics of the cluster simulations.650 Section 3 will be devoted to the comparison between simulation results and observations., Section 3 will be devoted to the comparison between simulation results and observations.651 After comparing the profiles of the Iron abundance. we will concentrate on the evolution of the ICM metallicity.," After comparing the profiles of the Iron abundance, we will concentrate on the evolution of the ICM metallicity."652 We will then compare observations and simulation predictions on the rate of SnIu., We will then compare observations and simulation predictions on the rate of SnIa.653 We will draw our conclusions in Section 4., We will draw our conclusions in Section 4.654 All values of Tron abundance that we will quote in the following are scaled to the solar abundance value by ?.., All values of Iron abundance that we will quote in the following are scaled to the solar abundance value by \cite{1998SSRv...85..161G}.655" In this letter we present a set of simulations of four massive isolated clusters. which have been identified in a Dark-Matter only simulation having a box size 47941Mpe (2)... performed for a flat ACDM cosmological model with €,=0.3. Pius=0.7. c4=0.9 and O,=0.04."," In this letter we present a set of simulations of four massive isolated clusters, which have been identified in a Dark–Matter only simulation having a box size $479 \hm$ \citep{2001MNRAS.328..669Y}, performed for a flat $\Lambda$ CDM cosmological model with $\Omega_m =6560.3$, $h_{100} =0.7$ , $\sigma_8 = 0.9$ and $\Omega_b = 0.04$."657 The four extracted Lagrangian regions. centred on these clusters with virial in the range Alas—1.022.3 107ΑΙ. have been resimulated using the Zoomed Initial Condition (ZIC) technique by ?.. which allows one to increase force and mass resolution in the regions of interest.," The four extracted Lagrangian regions, centred on these clusters with virial in the range $M_{\rm658 vir}=$ $\,\times 10^{15} \msun$, have been resimulated using the Zoomed Initial Condition (ZIC) technique by \cite{TO97.2}, which allows one to increase force and mass resolution in the regions of interest."659" The high-resolution DM particles have mass mpi;=1.1810°PhAL... and the barionie particles have been added with a mass my,=L7105b.FAL. inorderto reproduce the assumec cosmic barionic fraction."," The high–resolution DM particles have mass $m_{DM}=1.13\times 10^9 \msun$ , and the barionic particles have been added with a mass $m_{gas}=1.7\times 10^8 \msun$ in order to reproduce the assumed cosmic barionic fraction."660 The basic characteristics of the simulated clusters are summarized in Table I.., The basic characteristics of the simulated clusters are summarized in Table \ref{tab:simul}. .661 The simulations are performed using the hydrodynamica Tree-SPH code (9). with the implementation of chemical enrichment by TO7., The simulations are performed using the hydrodynamical Tree-SPH code \citep{2005MNRAS.364.1105S} with the implementation of chemical enrichment by T07.662 The Plummer-equivalent softening length for gravitational force is set to ο=5htkpe in physica units from ο=2 to >=(0. while at higher redshifts is ο=15htkpe in comoving units.," The Plummer–equivalent softening length for gravitational force is set to $\epsilon = 5 \hk$ in physical units from $z=2$ to $z=0$, while at higher redshifts is $\epsilon = 15 \hk$ in comoving units."663 The simulations include heating from a uniform time-dependent UV background (2). anc metallicity-dependent radiative cooling based on the tables by for an optically thin plasma., The simulations include heating from a uniform time-dependent UV background \citep{1996ApJ...461...20H} and metallicity–dependent radiative cooling based on the tables by \cite{1993ApJS...88..253S} for an optically thin plasma.664 The process of star formation (SF hereafter) is described by the sub-resolution multiphase model by ?.. for which the density threshold for the onset of SF is set to ny=O1lem ," The process of star formation (SF hereafter) is described by the sub–resolution multiphase model by \cite{2003MNRAS.339..289S}, for which the density threshold for the onset of SF is set to $n_H=0.1\,$ $^{-3}$."665 While the relevant features of the chemical evolution model are described here below. we address the reader to TO7 for a more detailed description.," While the relevant features of the chemical evolution model are described here below, we address the reader to T07 for a more detailed description."666 Metals are produced by SnII. SnIa and intermediate and low-mass stars (ILMS hereafter). with only SnIa and SnII providing energy feedback.," Metals are produced by SnII, SnIa and intermediate and low–mass stars (ILMS hereafter), with only SnIa and SnII providing energy feedback."667 We assume SnII to arise from stars having mass above SA/.., We assume SnII to arise from stars having mass above $8M_\odot$.668" As for the SnIa. we assume their progenitors to be binary systems. whose total mass lies in the range (3-16,U.."," As for the SnIa, we assume their progenitors to be binary systems, whose total mass lies in the range $M_\odot$."669 Metals and energy are released by stars of different mass by properly accounting for mass—dependent lifetimes., Metals and energy are released by stars of different mass by properly accounting for mass–dependent lifetimes.670 In this work we assume the lifetime function proposed by ?.., In this work we assume the lifetime function proposed by \cite{1993ApJ...416...26Pb}.671 We adopt the metallicity-dependent stellar yields by 3 for SnIIL. the yields by ? for the ILMS and by ? for SnIa.," We adopt the metallicity–dependent stellar yields by \cite{1995ApJS..101..181W} for SnII, the yields by \cite{1997A&AS..123..305V} for the ILMS and by \cite{2003NuPhA.718..139T} for SnIa."672 The version of the code used for the simulations presented here allowed us to follow H. He. C. N. ο. Mz. Si and Fe.," The version of the code used for the simulations presented here allowed us to follow H, He, C, N, O, Mg, Si and Fe."673 Once produced by a star particle. metals are then spread to the surrounding gas particles by using the B-spline kerne with weights comouted over 64 neighbours and taken to be proportional to the volume of each particle.," Once produced by a star particle, metals are then spread to the surrounding gas particles by using the B-spline kernel with weights computed over 64 neighbours and taken to be proportional to the volume of each particle."674 TO7 verified with detailed tests that the final results on the pattern of chemical enrichment are ratyer insensitive to tle Weighting scheme (kernel shape andnumber of neighbours) used to spread metals., T07 verified with detailed tests that the final results on the pattern of chemical enrichment are rather insensitive to the weighting scheme (kernel shape andnumber of neighbours) used to spread metals.675 Our simulations include the kinetic feedback model implemented by ?» ., Our simulations include the kinetic feedback model implemented by \cite{2003MNRAS.339..289S}. .676 According to tus scheme. SnII explosions trigger galactic winds. whose mass upload rate is assumed to be proportional to the star formation rae. Aly=WAL.," According to this scheme, SnII explosions trigger galactic winds, whose mass upload rate is assumed to be proportional to the star formation rate, $\dot{M}_W =\eta677\dot{M}_{\star}$."678 Therefore. fixing the parameter 7) and the wind velocity ey; amounts to fix the total energy carried by the winds.," Therefore, fixing the parameter $\eta$ and the wind velocity $v_W$ amounts to fix the total energy carried by the winds."679 Our choice of 7—3 and my=500kms1 corresponds to assume.for the initial mass function (IMF) by ?.. with SnIIreleasing 10'1 ergs each. nearly unity efficiency in powering galactic outflows.," Our choice of $\eta=3$ and $v_W = 500\vel$ corresponds to assume,for the initial mass function (IMF) by \cite{1955ApJ...121..161S}, , with SnIIreleasing $10^{51}$ ergs each, nearly unity efficiency in powering galactic outflows."680 In our comparison with observational data. we will first explore the effect of changing the IMF.," In our comparison with observational data, we will first explore the effect of changing the IMF."681 We use the IMF by 9? and, We use the IMF by \cite{1955ApJ...121..161S} and682in Fig. 105. ,"in Fig. \ref{fig:m_hi_optsize}) ),"683although with a larger scatter., although with a larger scatter.684 A linear fit with a slope and intercept of 1.744-0.2? and 6.93-0.18. respectively is shown as a solid line.," A linear fit with a slope and intercept of $\pm$ 0.22 and $\pm$ 0.18, respectively is shown as a solid line."685 The larger scatter in the relation between Mu and the optical diameter. also seen in sample of brighter dwarfs (e.g. Swaters (1999))). is probably indicative of a looser coupling between the gas and star formation in dwarfs. compared to that in spiral galaxies.," The larger scatter in the relation between ${\rm{_{HI}}}$ and the optical diameter, also seen in sample of brighter dwarfs (e.g. \cite{swater99}) ), is probably indicative of a looser coupling between the gas and star formation in dwarfs, compared to that in spiral galaxies."686 Figure 11. shows the HI mass to light ratio for the FIGGS sample plotted asa function of the HI extent. Dui/Dy...," Figure \ref{fig:mtol_size} shows the HI mass to light ratio for the FIGGS sample plotted asa function of the HI extent, ${\rm{_{HI}/D_{Ho}}}$."687 A trend of an increase in the My)/Lis with an increase in the HI extent of the galaxies is clearly seen., A trend of an increase in the ${\rm{_{HI}/L_B}}$ with an increase in the HI extent of the galaxies is clearly seen.688 The best fit to the FIGGS sample shown as a solid line gives van Zee et al.(1995) from a HI mapping of a sample of low luminosity galaxies also found an evidence of an extended HI extent for high Mui/Ly galaxies., The best fit to the FIGGS sample shown as a solid line gives van Zee et al.(1995) from a HI mapping of a sample of low luminosity galaxies also found an evidence of an extended HI extent for high ${\rm{_{HI}/L_B}}$ galaxies.689 Figure 12. shows Myij/Li for the FIGGS sample as a function of My., Figure \ref{fig:mtol_lb} shows ${\rm{_{HI}/L_B}}$ for the FIGGS sample as a function of ${\rm{_B}}$ .690 The same quantity for several other spiral and, The same quantity for several other spiral and691infinitesimally thin. relativistic self-gravitating disces with internal pressure.,"infinitesimally thin, relativistic self-gravitating discs with internal pressure."692 The pressure is given by a polytropic equation of state., The pressure is given by a polytropic equation of state.693 The. polvtropic exponent +=3 was used. since in this case there exists an cxact solution in the ανομία limit.," The polytropic exponent $\gamma=3$ was used, since in this case there exists an exact solution in the Newtonian limit."694 This special choice corresponds to three-dimensional bodies of constant densities as well (see LEunter 1972)., This special choice corresponds to three-dimensional bodies of constant densities as well (see Hunter 1972).695 Thus. we may make a comparison of the results ounce here for Hat disces with those of rotating. homogeneous relativistic stars.," Thus, we may make a comparison of the results found here for flat discs with those of rotating, homogeneous relativistic stars."696 As Butterworth Ipser (1976) showed. sequences of homogeneous. rotating relativistic stars usually. erminate at the mass-shee limit.," As Butterworth Ipser (1976) showed, sequences of homogeneous, rotating relativistic stars usually terminate at the mass-shed limit."697 Close to the Newtonian case however. they were not able to follow the sequences o this limit.," Close to the Newtonian case however, they were not able to follow the sequences to this limit."698 We suggest that. as weaker relativistic disces Xfurcate into a ring. weaker relativistic stars of constant clensity bifurcate into a toroid structure as well. ancl do not end at the mass-shed limit.," We suggest that, as weaker relativistic discs bifurcate into a ring, weaker relativistic stars of constant density bifurcate into a toroid structure as well, and do not end at the mass-shed limit."699 In the Newtonian limit. the structure of these constant density toroids were calculated by Eriguchi Sugimoto (1981).," In the Newtonian limit, the structure of these constant density toroids were calculated by Eriguchi Sugimoto (1981)."700 The pressure-less disces possess ergo-regions. where the drageing of inertial frames would force observers to rotate.," The pressure-less discs possess ergo-regions, where the dragging of inertial frames would force observers to rotate."701 These first appear at a single point within the disc at =[4l and reach the edge of the disc at z=1.89 (Meine IxIeinwacchter 1993)., These first appear at a single point within the disc at $z\subscr{e}=1.41$ and reach the edge of the disc at $z=1.89$ (Meinel Kleinwäcchter 1993).702 Phev also occur in rotating stars (Butterworth Lpser 1976)., They also occur in rotating stars (Butterworth Ipser 1976).703 For disces with internal oressure however. we found. no indication of the existence of ergo-regions.," For discs with internal pressure however, we found no indication of the existence of ergo-regions."704 It is to be expected. that there exists a continuous transition from the zero-pressure A=Q0 case o disces with non-vanishing pressure (A. small)., It is to be expected that there exists a continuous transition from the zero-pressure $K=0$ case to discs with non-vanishing pressure $K$ small).705 However. his connection could not be demonstrated numerically. as disc sequences end either at the mass-shecl limit or bifurcate into rings before reaching the pressure-less limit.," However, this connection could not be demonstrated numerically, as disc sequences end either at the mass-shed limit or bifurcate into rings before reaching the pressure-less limit."706 One might speculate. perhaps. that such a connection can be achieved by a disc which consists of two parts: a pressure supported central region (0«p py). surrounded. by a dust. disc (pympx pa).," One might speculate, perhaps, that such a connection can be achieved by a disc which consists of two parts: a pressure supported central region $0 < \rho < \rho\subscr{p}$ ), surrounded by a dust disc $\rho\subscr{p} < \rho < \rho\subscr{d}$ )."707" Phe dust cise would refer to pj,=0. and the disc sequences to py=pa."," The dust disc would refer to $\rho\subscr{p}=0$, and the disc sequences to $\rho\subscr{p}=\rho\subscr{d}$."708 In some rotating relativistic stars. there are sequences of supra-massive stars (Cook. Shapiro “Teukolsky 1992). which are so massive that they exceed the rest mass of a non-rotating star. and can only exist for non-zero rotation.," In some rotating relativistic stars, there are sequences of supra-massive stars (Cook, Shapiro Teukolsky 1992), which are so massive that they exceed the rest mass of a non-rotating star, and can only exist for non-zero rotation."709 In the case of Dat. relativistic discs with non-zero internal pressure. we did not find any supra-massive disc sequences.," In the case of flat relativistic discs with non-zero internal pressure, we did not find any supra-massive disc sequences."710 Possibly. these negative results are a result of the particular equation of state where in the strong relativistic limit the mass ds always concentrated in the centre of the disc. as shown in Fig.," Possibly, these negative results are a result of the particular equation of state where in the strong relativistic limit the mass is always concentrated in the centre of the disc, as shown in Fig."711 4 for the non-rotating case., 4 for the non-rotating case.712 Other relations between pressure and surface density. in particular a smaller ὃν could. also possibly leac το supra-niassivo sequences or ergo-reglons.," Other relations between pressure and surface density, in particular a smaller $\gamma$, could also possibly lead to supra-massive sequences or ergo-regions."713 The numerical method. developed here is. sullicientLy general to be applied to the study of cifferentially rotating discs. and can casily be extended. to. threc-cdimensional rotating stars as well.," The numerical method developed here is sufficiently general to be applied to the study of differentially rotating discs, and can easily be extended to three-dimensional rotating stars as well."714 This may be the subject of a future further investigation., This may be the subject of a future further investigation.715 A stability analysis of the computed equilibrium. configurations lies bevonc the scope of the present papor., A stability analysis of the computed equilibrium configurations lies beyond the scope of the present paper.716 Useful discussions with Drs it. Aleinel and. T. Wolf are eratefullys acknowledged., Useful discussions with Drs R. Meinel and T. Wolf are gratefully acknowledged.717including RR Lyrae stars. TRGB. and Cepheids.,"including RR Lyrae stars, TRGB, and Cepheids."718 Insofar as all these methods start from a common. fundamental Local Group distance seale that has been carefully assembled by a combination of many standard candles. the ~£0.2- mag variances noted above are reflective of the small discrepancies that can emerge from the different methods in ways that are often still hard to pinpoint and that are not even consistent from one galaxy to another.," Insofar as all these methods start from a common, fundamental Local Group distance scale that has been carefully assembled by a combination of many standard candles, the $\sim \pm0.2-$ mag variances noted above are reflective of the small discrepancies that can emerge from the different methods in ways that are often still hard to pinpoint and that are not even consistent from one galaxy to another."719 For a more extensive discussion on another system (NGC 5128) where several stellar candles can be accurately compared. see Harris et al. (2010)).," For a more extensive discussion on another system (NGC 5128) where several stellar candles can be accurately compared, see Harris et al. \cite{har10}) )."720 Another direct. though somewhat less precise. comparison method of interest is the linear size distribution of globular clusters (GCs). which has been developed by Jordánn et ((2005)) into a standard-ruler technique.," Another direct, though somewhat less precise, comparison method of interest is the linear size distribution of globular clusters (GCs), which has been developed by Jordánn et \cite{jor05}) ) into a standard-ruler technique."721 The key quantity is the peak of the GC half-light radius distribution. normalized to host galaxy size and calibrated via the Milky Way GCs.," The key quantity is the peak of the GC half-light radius distribution, normalized to host galaxy size and calibrated via the Milky Way GCs."722 Using the Jordann et al., Using the Jordánn et al.723 data for M87 and their calibration. we obtain d=(16.442.3) Mpe or Ga—M);=31.07+0.30.," data for M87 and their calibration, we obtain $d = (16.4 \pm7242.3)$ Mpc or $(m-M)_0 = 31.07 \pm 0.30$."725" Combining the four methods listed above (TRGB. PNLF. GC sizes. SBF/Cepheids). we obtain a weighted average distance modulus (n—M),31.08+0.06 for M87. or d(16.4+0.5) Mpe."," Combining the four methods listed above (TRGB, PNLF, GC sizes, SBF/Cepheids), we obtain a weighted average distance modulus $\langle m-M \rangle_0 = 31.08726\pm 0.06$ for M87, or $d = (16.4 \pm 0.5)$ Mpc."727 A more precise TRGB distance especially could be obtained very straightforwardly with halo-star photometry in a less crowded region. and would in our view be the most effective way to calibrate the distance to this important galaxy.," A more precise TRGB distance especially could be obtained very straightforwardly with halo-star photometry in a less crowded region, and would in our view be the most effective way to calibrate the distance to this important galaxy."728 To test the internal errors and completeness of the photometry we ran two separate artificial-star procedures., To test the internal errors and completeness of the photometry we ran two separate artificial-star procedures.729 Inthe first series. stars were added to a representative 1500κ 500-px region of the image in the lower left corner (similar to the region shown in Figure 1).," Inthe first series, stars were added to a representative $1500 \times 500-$ px region of the image in the lower left corner (similar to the region shown in Figure 1)."730 These added stars were distributed evenly in color and magnitude over the ranges 0.5«(V—7)5.0 and 27.0«I« 29.6. as shown in Figure 7..," These added stars were distributed evenly in color and magnitude over the ranges $0.5 < (V-I) < 5.0$ and $27.0 < I < 29.6$ , as shown in Figure \ref{cmd_fake}."731 These intervals deliberately covered a larger range in both color and magnitude than in our observed CMD (Figure 3))., These intervals deliberately covered a larger range in both color and magnitude than in our observed CMD (Figure \ref{cmd4}) ).732 The same measurement sequence as done on the original frames was then carried out. with a two-pass sequence off," The same measurement sequence as done on the original frames was then carried out, with a two-pass sequence of."733ind/phot/allstar.. Figure 7. shows the results for inserted stars that were actually recovered in the photometry. including both their input magnitudes and colors (center panel) and their actually measured values (right panel).," Figure \ref{cmd_fake} shows the results for inserted stars that were actually recovered in the photometry, including both their input magnitudes and colors (center panel) and their actually measured values (right panel)."734 Of the total of 10000 added stars. just 1917 of these were successfully found and measured in both colors. and a high fraction of these lie in the upper left (bright. blue) part of the CMD.," Of the total of 10000 added stars, just 1917 of these were successfully found and measured in both colors, and a high fraction of these lie in the upper left (bright, blue) part of the CMD."735 The completeness of detection fniCrecovered)/n(input) as a function of magnitude is shown in Figure 8:: the completeness levels are reached at FOOOW=29.00 and F814W=28.15.," The completeness of detection $f =736n(recovered)/n(input)$ as a function of magnitude is shown in Figure \ref{completeness}; the completeness levels are reached at $F606W = 29.00$ and $F814W = 28.15$."737" To be classified as ""recovered"" a star must be detected in both images.", To be classified as “recovered” a star must be detected in both images.738 Note that at very faint levels (below the point) the formal values of f tend to decrease rather slowly. a result of the very high degree of crowding.," Note that at very faint levels (below the point) the formal values of $f$ tend to decrease rather slowly, a result of the very high degree of crowding."739 Figure 7 (particularly the difference between the second and third panels) clearly indicates that internal random uncertainties are large at all levels of the CMD., Figure \ref{cmd_fake} (particularly the difference between the second and third panels) clearly indicates that internal random uncertainties are large at all levels of the CMD.740 Figure 9 displays the differences between the measured and input magnitudes more completely., Figure \ref{random} displays the differences between the measured and input magnitudes more completely.741 For Jz28.0. one magnitude below the RGB tip. completeness of detection becomes low and the systematic errors increase. such that most stars are measured too bright.," For $I \gtrsim 28.0$, one magnitude below the RGB tip, completeness of detection becomes low and the systematic errors increase, such that most stars are measured too bright."742 We do not consider this faint region further., We do not consider this faint region further.743 The measured are on average slightly too blue independent of magnitude. by (ACV—7))=—0.22 mag.," The measured are on average slightly too blue independent of magnitude, by $\langle \Delta (V-I)744\rangle = -0.22$ mag."745 Over the top magnitude of the RGB (727— 28) the internal random scatter of the magnitudes and colors (rms) is 7=£0.36 mag in F814W. £0.53 mag in F606W. and £0.40 mag in (F606W— F814W).," Over the top magnitude of the RGB $I = 27 - 28$ ) the internal random scatter of the magnitudes and colors (rms) is $\sigma =746\pm0.36$ mag in $F814W$, $\pm0.53$ mag in $F606W$, and $\pm 0.40$ mag in $(F606W-F814W)$ ."747 The artificially even distribution of input stars in Figure 7 overpopulates the brightest part of the luminosity function compared with the real CMD.," The artificially even distribution of input stars in Figure \ref{cmd_fake}748 overpopulates the brightest part of the luminosity function compared with the real CMD."749 A second run of artificial-star, A second run of artificial-star750large (7)..,large \citep{1998T}.751" The parazuueters of this model are Neptune's ""Uóutial (defined below) senuüauajor axis. ecceutricitv and inclination. the planets migration rate. and the timescales for Neptune eccentricity and inclination damping."," The parameters of this model are Neptune's “initial"" (defined below) semi-major axis, eccentricity and inclination, the planet's migration rate, and the timescales for Neptune's eccentricity and inclination damping."752 In this model. we include the effects of only oue plauet (Neptune). an approach we justify briefly in Section 3.3. and more thoroughly in ?..," In this model, we include the effects of only one planet (Neptune), an approach we justify briefly in Section \ref{subsec:justnep} and more thoroughly in \citet{2012D}."753 We define Noptuue's orbital evolution using the following parameters: ere we consider what range of parameters we should explore for Neptunes migration direction. distance. aud timescale: Direct computational modeling of the effect of planctesimals on Neptune’s orbit would be colputationally expensive. so iusteac we apply fictitious forces (Appendix) to evolve Neptune’s soimianajor axis ay. eccentricity ον. and inclination xw. with anv specified functional form.," We define Neptune's orbital evolution using the following parameters: Here we consider what range of parameters we should explore for Neptune's migration direction, distance, and timescale: Direct computational modeling of the effect of planetesimals on Neptune's orbit would be computationally expensive, so instead we apply fictitious forces (Appendix) to evolve Neptune's semi-major axis $a_N$, eccentricity $e_N$, and inclination $i_N$, with any specified functional form."754 Following ?— and ?.. we use the functional forms: where ey is the initial senuiuajor axis of Neptune. d; = 30 AU is the final semi-major axis. and 7. 7;. aud Τι ave the eccentricity damping timescale. inclination damping timescale. aud migration timescale respectively.," Following \citet{1993M} and \citet{2008L}, we use the functional forms: where $a_0$ is the initial semi-major axis of Neptune, $a_f$ = 30 AU is the final semi-major axis, and $\tau_e$, $\tau_i$, and $\tau_a$ are the eccentricity damping timescale, inclination damping timescale, and migration timescale respectively."755 Oi results do not depeud ou the specific form of Equ (1))., Our results do not depend on the specific form of Eqn \ref{eqn:forms}) ).756" As we will demonstrate in Section L.. sometimes the instantaneous rate of change of the variables 5.ipds "" most relevant. while m other cases the total(4, evolution,matters most."," As we will demonstrate in Section \ref{sec:results}, sometimes the instantaneous rate of change of the variables $\frac{\dot{a}}{a}, \frac{\dot{e}}{e}, \frac{\dot{i}}{i}$ ) is most relevant, while in other cases the total evolutionmatters most."757 We have verified these statements wit1 integratious (not shown) using an alternative mieratio1 fori 46«x;= constaut., We have verified these statements with integrations (not shown) using an alternative migration form $\frac{\dot{a}}{a} \varpropto \frac{\dot{e}}{e} \varpropto \frac{\dot{i}}{i} \equiv {\rm constant}$ .758 We model an initially unexcited disk of planctesimals that becomes todaws cold classical population., We model an initially unexcited disk of planetesimals that becomes today's cold classical population.759 Iu Section 3.1... we present the observational coustraiuts ou the excitation of this population.," In Section \ref{sec:obs}, we present the observational constraints on the excitation of this population."760 Iu Section 3.2.. we present an analytical model for the evolution of this planetesimal disk uuder the influence of Neptune. which we use to predict and interpret the results of umnucrical simulations.," In Section \ref{subsec:sec}, we present an analytical model for the evolution of this planetesimal disk under the influence of Neptune, which we use to predict and interpret the results of numerical simulations."761 Iu Section 3.3.. we justify directly modeling ouly Neptune instead of all four giant plaucts.," In Section \ref{subsec:justnep}, we justify directly modeling only Neptune instead of all four giant planets."762" The cold classicals are a class of dyviiuuicallv ""cold? objects on low-ceceutricity. low-inclination orbits. with positions starting at 12.5 AU. the reeion interior to which 15is unstable. aud falling off quickly bevoud 15 AU (?).."," The cold classicals are a class of dynamically “cold"" objects on low-eccentricity, low-inclination orbits, with positions starting at 42.5 AU, the region interior to which is unstable, and falling off quickly beyond 45 AU \citep{2009K}."763 We assune that todav's cold classical IKRBOs are remnant plauctesimals that formed sins and we use theseternis interchangeably.," We assume that today's cold classical KBOs are remnant planetesimals that formed , and we use theseterms interchangeably."764 Stroug constraints cau be placed, Strong constraints can be placed765The observable part. of debris disks are small (: lumn) clusty or icy grains. collisionally produce [rom larger. undetectable parent bodies.,"The observable part of debris disks are small $\leq 1\,$ mm) dusty or icy grains, collisionally produced from larger, undetectable parent bodies."766 In addition to the gravitational »ull of the star. these grains are also alfected by several orces such as stellar radiation pressure. Povnting-Robertson (DIU) drag and the possible gravitational inlluence of large »odies in the neighborhood.," In addition to the gravitational pull of the star, these grains are also affected by several forces such as stellar radiation pressure, Poynting-Robertson (PR) drag and the possible gravitational influence of large bodies in the neighborhood."767 As has been shown in numerous numerical studies. the combined. effect of hese different orces can lead to complex spatial structures in resolved disks. (c.g.ναι2008).," As has been shown in numerous numerical studies, the combined effect of these different forces can lead to complex spatial structures in resolved disks \citep[e.g.][]{wyatt08}."768. A less investigated: additional orce that could. have an influence on grain dynamics is he crag due to particles [rom the surrounding interstellar medium (1981)., A less investigated additional force that could have an influence on grain dynamics is the drag due to particles from the surrounding interstellar medium (ISM).769 Phe elfect of ISM has first been addressed w Artvmowicz&Clampin(1997).. who studied the level of disk erosion. due to sandblasting by ISAT dust. @rains.," The effect of ISM has first been addressed by \citet{arty97}, who studied the level of disk erosion due to sandblasting by ISM dust grains."770 They coneluded that. at least around: massive stars. this ellect was negligible because small LSAT grains felt a strong repulsive radiation force.," They concluded that, at least around massive stars, this effect was negligible because small ISM grains felt a strong repulsive radiation force."771 More recentlv.Scherer. (2000).. Debesetal.(2009)... Manessctal. (2009)... Belvaey&Ralikov(2010) and Pastor(2011)| considered. instead the οσοι of ISAL on disk grains.," More \citet{scherer}, , \citet{debes09}, \citet{manes09}, \citet{bera} and \citet{pasto} considered instead the effect of ISM on disk grains."772 Vhis Πακ of neutral atoms acts indeed similarly to the solar wind or radiation pressure from a physical point of view but. being monocdirectional. can significantly perturb the trajectories of the grains. ancl potentially induce asvnimetric structures in the disk.," This flux of neutral atoms acts indeed similarly to the solar wind or radiation pressure from a physical point of view but, being monodirectional, can significantly perturb the trajectories of the grains, and potentially induce asymmetric structures in the disk."773 In particular Manessctal.(2009). ancl Debesetal.(2009) sugeest that the ISM. Bux. can explain the unusual morphology of some debris disks like HD61005 anc 1132997., In particular \citet{manes09} and \citet{debes09} suggest that the ISM flux can explain the unusual morphology of some debris disks like HD61005 and HD32997.774 In their model Debesetal.(2009). consider dus particles close to the blow-out size for the star and compute the trajectories of perturbed grains over a timescale of 5000 ves., In their model \citet{debes09} consider dust particles close to the blow-out size for the star and compute the trajectories of perturbed grains over a timescale of 5000 yrs.775 The majority of their grains are strongly perturbed ane enc up quickly on hyperbolic orbits., The majority of their grains are strongly perturbed and end up quickly on hyperbolic orbits.776 A similar scenario is outlined by Manessetal.(2009) where they concentrate on small grains (0.1 pam) whose lifetime before ejection is of the order of afew 10°? vears., A similar scenario is outlined by \citet{manes09} where they concentrate on small grains (0.1 $\mu$ m) whose lifetime before ejection is of the order of afew $10^3$ years.777 The morphology changes they, The morphology changes they778"to LO ke utιο MECS 1.55 to 10 keV: the IIPCGSPC 7 to 65 keV axd the PDS 13 to 200 keV. To ensure that he fittius statisic D (A7) was unbiased across the eutire cnerey range. data were rebinuned to a width of of the ""ull width at ial :anaxinun cherev resolution function of ecli lustrewt and also under the condition that each iu contaiue ΠΕ of 20 counts.","to 10 keV; the MECS 1.85 to 10 keV; the HPGSPC 7 to 65 keV and the PDS 13 to 200 keV. To ensure that the fitting statistic $\chi^2$ ) was unbiased across the entire energy range, data were rebinnned to a width of of the full width at half maximum energy resolution function of each instrument and also under the condition that each bin contained a minimum of 20 counts."779 It is known from iuter-lustreit spectral calibrations that there can be simall position ¢lepeudeut normalization differences between he lustreits., It is known from inter-instrument spectral calibrations that there can be small position dependent normalization differences between the instruments.780 Therefore. these factors were included as free multiplicative parameters during multiple NFI spectral fittine.," Therefore, these factors were included as free multiplicative parameters during multiple NFI spectral fitting."781 Fie., Fig.782 ls rows low aud high cucerey light curves measired by the MECS (1.310.0 keV) aud the PDS (€3200) NV) after background subtraction., 1 shows low and high energy light curves measured by the MECS (1.3–10.0 keV) and the PDS (13–200 keV) after background subtraction.783 The time resolulon dis [00 s. The sotrco intensity is clearly variable with a doubliug of the fiux occuring on the time scale of adjacent biis., The time resolution is 400 s. The source intensity is clearly variable with a doubling of the flux occurring on the time scale of adjacent bins.784 The fastest observed fluctuation in the MECS is on a time scale of —10 s. consistent with the ASCA resul of Kubo e al. (," The fastest observed fluctuation in the MECS is on a time scale of $\sim$ 10 s, consistent with the ASCA result of Kubo et al. ("7851998).,1998).786 In the PDS. the fastes observable variatioLis of the order of  10 s. This time πεale implies an upper iuit on the size of the cussion region of a few. « 10H. cx.," In the PDS, the fastest observable variation is of the order of $\sim$ 40 s. This time scale implies an upper limit on the size of the emission region of a few $\times$ $^{11}$ cm."787 Next a search for periodic variations was carried out., Next a search for periodic variations was carried out.788 On short time scales (fντα ! 0.5 Iz). a powcr density curve reveals à l/f tvpo distribution. |mt no clear periodicities (see Fie.," On short time scales $f \sim$ $^{-4}$ –0.5 Hz), a power density curve reveals a ${1/f}$ –type distribution, but no clear periodicities (see Fig."789 2)., 2).790 At ΠΙΟ longer periocls. a period search reveals weak chhancements at 35 aud 115 nius.," At much longer periods, a period search reveals weak enhancements at 35 and 145 mins."791 We estimate hat for narrow QPO/periodicities iu the 0.01 lz &>» 0.1 Tz range. we could detect a zuuplitude moclation at the 3o level.," We estimate that for narrow QPO/periodicities in the 0.01 Hz to 0.1 Hz range, we could detect a amplitude modulation at the $\sigma$ level."792" Iu order to studv the loug-terii X-ray vaability of ~ Cas, we have also analyzed R-NTE All Sky Monitor (ASN) data which has coutinuously observed the source from 1996 February. 20 to 1998 Deceuber. 31."," In order to study the long-term X-ray variability of $\gamma$ –Cas, we have also analyzed R-XTE All Sky Monitor (ASM) data which has continuously observed the source from 1996 February, 20 to 1998 December, 31."793 We have searched for periods in the range 30?500 days using the Lomb-Scarele periodoeram. using oth the individual dwell aud i-dav averages data.," We have searched for periods in the range 30–500 days using the Lomb-Scargle periodogram, using both the individual dwell and 1-day averages data."794 No cals wdhoa lig[um sjeuilficance (e... >99%)) were ford in the individual dwel data. although one peak at a periocL of —20 davs was of mareinal significance (a the e»t) level).," No peaks with a high significance (i.e., $>$ ) were found in the individual dwell data, although one peak at a period of $\sim$ 200 days was of marginal significance (at the $\sim$ level)."795" As a check. «un dts reality, we replace the R-XTE ASA measurements with data drawn from <Vv Gassa cüstribution ceitered on zero With ao of 1 (i.e. 10 signal)."," As a check on its reality, we replaced the R-XTE ASM measurements with data drawn from a Gaussian distribution centered on zero with a $\sigma$ of 1 (i.e. no signal)."796 We note that he peak still existed (albei with a lucu lower significance). implying that it is probably caused by a windowing cifect and therefore does not reflect a true period in the N-vay flux of y Cas.," We note that the peak still existed (albeit with a much lower significance), implying that it is probably caused by a windowing effect and therefore does not reflect a true period in the X-ray flux of $\gamma$ –Cas."797 Analysis of the l-dav averaged data vielded. sinilu results. i.c.. no sieuificaut periodicities.," Analysis of the 1-day averaged data yielded similar results, i.e., no significant periodicities."798 We estunate that for periods aroun 100 davs. we would have detected a periodic modulation at the confidence level.," We estimate that for periods around 100 days, we would have detected a periodic modulation at the confidence level."799 Siuple models (ie. power-laws. bremsstrahlung. ete.)," Simple models (i.e., power-laws, bremsstrahlung, etc.)"800 eave poor fits to the data., gave poor fits to the data.801 For example. a1. absorbed power-law gives a X of GAL for 203 degrees of freedom (dof).," For example, an absorbed power-law gives a $\chi ^2$ of 684 for 203 degrees of freedom (dof)."802 The addition of au ion line at 0.03 keV iuproves the fit sienificautly (\?/dof=505/2WO). but is still unacceptable at energies above I) keV. Based ou previous ROSAT aud ASC'A measuremeits CIaberl 1995: Ίνπνο ct al.," The addition of an iron line at $\pm$ 0.03 keV improves the fit significantly $\chi ^2$ /dof=505/200), but is still unacceptable at energies above 10 keV. Based on previous ROSAT and ASCA measurements (Haberl 1995; Kubo et al."803 1998). we nest investigated opically thin thermal plasina models with both the eniperature aud elemental abundance as free parameters.," 1998), we next investigated optically thin thermal plasma models with both the temperature and elemental abundance as free parameters."804 The results are listed in Table 1., The results are listed in Table 1.805 A best-fit MEIAL model. based. iu," A best-fit MEKAL model, based in"806the disc illuiunatiou is not taken iuto account.,the disc illumination is not taken into account.807 Whereas ina nonirradiated disc small amplitude outbursts appear when the heating frout cannot bring the whole disc iuto a hot state. here the disc never returus to quiescence iu its inner parts. so the cooling wave is reflected into a heating wave when it ects close to the stable hot inner part of the disc.," Whereas in a non–irradiated disc small amplitude outbursts appear when the heating front cannot bring the whole disc into a hot state, here the disc never returns to quiescence in its inner parts, so the cooling wave is reflected into a heating wave when it gets close to the stable hot inner part of the disc."808 The amplitude of these reflares grows as a consequence of the culanced mass transfer durius asin. until the disc mass has grown up to a point where a self-sustained long outburst is possible.," The amplitude of these reflares grows as a consequence of the enhanced mass transfer during maximum, until the disc mass has grown up to a point where a self-sustained long outburst is possible."809 The refiaves properties also depend on the ratio μονρα2 the smaller this ratio. the more important he veflares (see Menou et al.," The reflares properties also depend on the ratio $\alpha_{\rm hot}/\alpha_{\rm810cold}$: the smaller this ratio, the more important the reflares (see Menou et al."811 1999. for a discussion of lis effect in the context of XN-rav tranusicuts)., \cite{mhln99} for a discussion of this effect in the context of X-ray transients).812 This is simply due to the fact hat. the lower this ratio. the larger MNaas after the passage of a cooling frout. Mayas boiug he maximum surface deusitv on the cold stable brauch: in the limiting case μοι=65444 there are no outbursts (Sinals 198 1)). but a heating/coolne wave that propagates jack and forth.," This is simply due to the fact that, the lower this ratio, the larger $\Sigma / \Sigma_{\rm max}$ after the passage of a cooling front, $\Sigma_{\rm max}$ being the maximum surface density on the cold stable branch; in the limiting case $\alpha_{\rm hot} = \alpha_{\rm cold}$ there are no outbursts (Smak \cite{s84}) ), but a heating/cooling wave that propagates back and forth."813 Fie., Fig.814 5 shows the effect of chaugiug oc o a παω: (by a factor 2) value.," \ref{fig:alpha} shows the effect of changing $\alpha_{\rm815cold}$ to a smaller (by a factor 2) value."816 Successive reflares no ouecr reach the outer edge of the disc. aud their amplitude herefore decreases from one imini-outbirst to the uext onc.," Successive reflares no longer reach the outer edge of the disc, and their amplitude therefore decreases from one mini-outburst to the next one."817 This accounts for the presence of flat top outbursts which were absent in Fie., This accounts for the presence of flat top outbursts which were absent in Fig.818" Lob. The lightcurves are similar or all mass transfer rates. showing the pattern of Fie 5 with longer recurrence times for smaller AÁ4,."," \ref{fig:mdot}b b. The lightcurves are similar for all mass transfer rates, showing the pattern of Fig \ref{fig:alpha}819 with longer recurrence times for smaller $\dot{M}_{\rm tr}$."820 The oulv exception is for 7«Lot! gs +t awhich is close to stability. and for which the main outbursts are of he outsicde-in type.," The only exception is for $7 \times 10^{16}$ g $^{-1}$, which is close to stability, and for which the main outbursts are of the outside-in type."821 Since small discs favour large reflares. it is not surprisiug that when oue considers discs with average rou1059 cni. and one takes api = 0.02 and Ayor = 0.2. one obtains a combination of the lighteurves shown in the two previous sections: Fig 6 is a good example of this.," Since small discs favour large reflares, it is not surprising that when one considers discs with average $r_{\rm out} = 1.3 \times 10^{10}$ cm, and one takes $\alpha_{\rm cold}$ = 0.02 and $\alpha_{\rm hot}$ = 0.2, one obtains a combination of the lightcurves shown in the two previous sections; Fig \ref{fig:rout} is a good example of this."822 It is worth notius that such a light curve is reniuisceut of that ofCue.. even though the timescales are not quite the same.," It is worth noting that such a light curve is reminiscent of that of, even though the timescales are not quite the same."823 We do obtain the right pattern for the reflares. but we do not reproduce the very loug superoutburst of (100 days). that would require 5 to be very close to unitv. caning that the linear approximation in Eq.," We do obtain the right pattern for the reflares, but we do not reproduce the very long superoutburst of (100 days), that would require $\gamma$ to be very close to unity, meaning that the linear approximation in Eq."824 l ds invalid., \ref{eq:ill_sec} is invalid.825 ForSee.. one already. had to assmue a relatively large value of + (0.87) in order to reproduce the observed 25 days duration: since the outburst duration varies as l/log(2) (Wameury et al. 1997)).," For, one already had to assume a relatively large value of $\gamma$ (0.87) in order to reproduce the observed 25 days duration; since the outburst duration varies as $1/\log(\gamma)$ (Hameury et al. \cite{hlh97}) ),"826 we would need y=0.97 to obtain 100 davs., we would need $\gamma = 0.97$ to obtain 100 days.827 Another differeuce with EG Cue is the amplitude of the 10ànjoutbursts: the observed ones have approximately the same amplitude. whereas we ect two identical nmuünioutbursts. the others being of decreasing amplitude.," Another difference with EG Cnc is the amplitude of the minioutbursts: the observed ones have approximately the same amplitude, whereas we get two identical minioutbursts, the others being of decreasing amplitude."828 We have not been able to reproduce this behaviour with our parameterization: a possible solution is to introduce a time dependeut temperature of the white dwarf., We have not been able to reproduce this behaviour with our parameterization; a possible solution is to introduce a time dependent temperature of the white dwarf.829 This is expected. because the superoutburst asted lone enough to heat up the surface of the white dwarf that will then cool.," This is expected, because the superoutburst lasted long enough to heat up the surface of the white dwarf that will then cool."830" If the rebrightcnmes of ire dudeed due to illumination effects. his iuiplies that à5,44 cannot be πια] as we do not obtain reflares when ecg Is significantly less than 0.0! Osaki et al. (1997))"," If the rebrightenings of are indeed due to illumination effects, this implies that $\alpha_{\rm cold}$ cannot be small as we do not obtain reflares when $\alpha_{\rm cold}$ is significantly less than 0.01; Osaki et al. \cite{ost97}) )"831 reached the same conclusion. but on different grounds: they assuued that Aeold Was increased to 0.1 caving the superoutburst. renamed hieh for 2 months. aud then decreased back to sunall values (0.001). and had therefore to set αμα to be an explicit fiction of time.," reached the same conclusion, but on different grounds; they assumed that $\alpha_{\rm cold}$ was increased to 0.1 during the superoutburst, remained high for 2 months, and then decreased back to small values (0.001), and had therefore to set $\alpha_{\rm cold}$ to be an explicit function of time."832Aloute Carlo analyses suggest a marginal significauce of ~99% for this possible periodicity. though the low wuplitude aud siguificauce. aud the brief evcle-count of the 3.51 observations. demand additional data to verity.,"Monte Carlo analyses suggest a marginal significance of $\sim99\%$ for this possible periodicity, though the low amplitude and significance, and the brief cycle-count of the 3.5m observations, demand additional data to verify."833 For SDSS JO092613621. both the l-hour timespan March sequence with 10 sec exposures (aud 60) sec time-resolution). and the longer 2-hour timespan April sequence with 20 sec exposures (and [0 κας time-resolution) reveal a strongly detected 28.3140.01 1uinute modulation. with striking eclipses (Figure 2).," For SDSS J0926+3624, both the 1-hour timespan March sequence with 40 sec exposures (and 60 sec time-resolution), and the longer 2-hour timespan April sequence with 20 sec exposures (and 40 sec time-resolution) reveal a strongly detected $\pm$ 0.01 minute modulation, with striking eclipses (Figure 3)."834 From our Apri data. we estimate eclipse ceuters at IJD(TT)=2153173.725393(3)|E« 0.01966(1).," From our April data, we estimate eclipse centers at ${\rm HJD(TT)} = 2453473.725393(3) + E\times0.01966(1)$ ."835 The eclipses are sharp and deep. with mid-eclipse depth of (at least) about Linagnitude.," The eclipses are sharp and deep, with mid-eclipse depth of (at least) about 1 magnitude."836", A Caussian fit to the sharp portion of the eclipse duration vields a fullwidth at half iiiuinimua of about LO seconds and. for example. a ~1.3 münute duratiou full width at of the niuiuinua eclipse depth."," A Gaussian fit to the sharp portion of the eclipse duration yields a full-width at half minimum of about 40 seconds and, for example, a $\sim1.3$ minute duration full width at of the minimum eclipse depth."837 As our ιοτοσοΊο is oulv of order LO sec. the eclipses could be even sharper/deeper.," As our time-resolution is only of order 40 sec, the eclipses could be even sharper/deeper."838 Application of Lonib-Scarele analysis confirms this (obvious) period with very high confidence (e... 299.9% xienificant in the April data).," Application of Lomb-Scargle analysis confirms this (obvious) period with very high confidence (e.g., $>99.9\%$ significant in the April data)."839 The lightcurve also shows additional reproducible structure that is seen in both March and April 2005 3.511 data: for example. there is a plateau just following the eclipse. aud. note the low-amplitude relative depression near phase 0.6.," The lightcurve also shows additional reproducible structure that is seen in both March and April 2005 3.5m data; for example, there is a plateau just following the eclipse, and note the low-amplitude relative depression near phase 0.6."840 As fay as we are aware. SDSS 10056|3621 is the first example of an eclipsing eiAM. CVn.," As far as we are aware, SDSS J0926+3624 is the first example of an eclipsing AM CVn."841 Our visual spectroscopic search vielded Ll new AND CVu candidates frou recent SDSS. spectroscopic plates covering about 2100 dee?. while the subsequent aleorithimic search recovered 3° AMD ονα candidates (two of the new candidates discussed herein. as wel as the Roelofs et al.," Our visual spectroscopic search yielded 4 new AM CVn candidates from recent SDSS spectroscopic plates covering about 2400 $^2$, while the subsequent algorithmic search recovered 3 AM CVn candidates (two of the new candidates discussed herein, as well as the Roelofs et al."842 200L object. SDSS J1210-0159) frou plates cucompassing about 1700 dee?.," 2004 object, SDSS J1240-0159) from plates encompassing about 4700 $^2$."843 We are not aware of any examples in the SDSS spectral database of strong cluissiou-line AM. CVni binaries obviously άσσος by either visual or algorithmic searches., We are not aware of any examples in the SDSS spectral database of strong emission-line AM CVn binaries obviously missed by either visual or algorithmic searches.844 On the other haud. the overlap-uunibers are too siiall to be considere definitive.," On the other hand, the overlap-numbers are too small to be considered definitive."845 Accounting for the 250 plates covered both in the visual and aleorithimic searches. the combines curent SDSS) spectroscopic vield is 5 (emissiou-lue) AM CVn candidates from a region caucompassing about 5900 dee? of sy.," Accounting for the 250 plates covered both in the visual and algorithmic searches, the combined current SDSS spectroscopic yield is 5 (emission-line) AM CVn candidates from a region encompassing about 5900 $^2$ of sky."846" We thus estimate that spectroscopically similar AAT CV systems might be expected to be found frou, the SDSS spectral database at a rough surface deusity of order 1 every 1200 dee.", We thus estimate that spectroscopically similar AM CVn systems might be expected to be found from the SDSS spectral database at a rough surface density of order 1 every 1200 $^2$.847 Estimates of the actual surface density of SDSS AND ογι binaries (even just those with heliuu in cussion) are complicated in that the AMD CVu candidates found thus far with SDSS were chosen for spectroscopy by: 4) several different target, Estimates of the actual surface density of SDSS AM CVn binaries (even just those with helium in emission) are complicated in that the AM CVn candidates found thus far with SDSS were chosen for spectroscopy by: (i) several different target848 | (secAcrtsrecentreviews).. (e.g.Micheletal.2008).. (Gillilandetal.2010:Chaplin2011)..," $^{-1}$ \citep[see][for recent reviews]{Aerts08, Bedding11b}. \citep[e.g.][]{Michel08}. \citep{Gilliland10, Chaplin11a}."849 1. /.1986): Tere. Av ds the so-called large separation between modes of the same / aud consecutive à. while ὃν is the small separation between nodes of different 7. aud € js a climensionless offset.," $n$ $l$: Here, $\Delta\nu$ is the so-called large separation between modes of the same $l$ and consecutive $n$ , while $\delta\nu_{0l}$ is the small separation between modes of different $l$, and $\epsilon$ is a dimensionless offset."850 To a good approximation. Av is proportional to the square root of the mean density of the star (Ulrich1986). aud iu Section ?? we juvestigate the validity of this approximation.," To a good approximation, $\Delta\nu$ is proportional to the square root of the mean density of the star \citep{Ulrich86} and in Section \ref{scale} we investigate the validity of this approximation."851 The s«1uall separations. Ongj. are scusitive to the structure of the core and hence to the age of the star. at least on the main sequence.," The small separations, $\delta\nu_{0l}$, are sensitive to the structure of the core and hence to the age of the star, at least on the main sequence."852 These somewhat orthogonal dependencies leads to their use iu the so-called C-D diagram. in which the large aud small separations are plotted against each other (Christenscu-Dalseaarcd 1981).," These somewhat orthogonal dependencies leads to their use in the so-called C-D diagram, in which the large and small separations are plotted against each other \citep{C-D84}."853. Calculating the C-D diagram is one of the main ais of this paper., Calculating the C-D diagram is one of the main aims of this paper.854 Previous studies of the C-D diagram aud its variations have determined the expected evolution of stars with varving dass and metallheitv (Ulrich1986:Gough1987:Cliaisteuscu-Dalseaard 1988). and assessed the feasibility of applviug the diagram to real data (Monteroetal. 2009).," Previous studies of the C-D diagram and its variations have determined the expected evolution of stars with varying mass and metallicity \citep{Ulrich86,Gough87,C-D88}, and assessed the feasibility of applying the diagram to real data \citep{Monteiro02,OtiFloranes05,Mazumdar05,Gai09}."855. However. none of these studies followed the evolution bevoud the end of the main sequence.," However, none of these studies followed the evolution beyond the end of the main sequence."856 Recently. Moutalbanetal.(2010) computed the theoretical spectrum of solu-like oscillations in red-giaut stars. findine that the simall separation νο depends alinost linearly on Ar. in aerecment with the red-egiaut results fromKepler (Beddingetal.2010a:Tuber2010).," Recently, \citet{Montalban10} computed the theoretical spectrum of solar-like oscillations in red-giant stars, finding that the small separation $\delta\nu_{02}$ depends almost linearly on $\Delta\nu$, in agreement with the red-giant results from \citep{Bedding10c, Huber10}."857. Tn Section ?? we bridee the gap. exteudiug the C-D diagram bevoud main-sequencestars to the subeiauts and uptowards the tip of the red-eiaut brauch.," In Section \ref{CD} we bridge the gap, extending the C-D diagram beyond main-sequencestars to the subgiants and uptowards the tip of the red-giant branch."858 Acomplication with the C-D diagram for subeiauts and red-eiaut stars arises four mode bumping., Acomplication with the C-D diagram for subgiants and red-giant stars arises from mode bumping.859 As stars, As stars860 Here. we discuss this issue in terms of the grain size distribution.," Here, we discuss this issue in terms of the grain size distribution."861 The contribution from grains in a logarithmic size range Bano. Ine| dine] to the extinction can be written as essi= Qx(a)n(a)a dine. where ένα). is the extinction cross section normalized to the geometrical cross section Gra7).," The contribution from grains in a logarithmic size range $\ln a$ , $\ln a +\mathrm{d}\ln a$ ] to the extinction can be written as $\mathrm{d}\kappa_\mathrm{ext}\equiv862\pi a^2Q_\lambda (a)n(a)a\,\mathrm{d}\ln a$ , where $Q_\lambda (a)$ is the extinction cross section normalized to the geometrical cross section $\pi a^2$ )."863" If the size distribution is approximated by a power-law (nxe.""over a certain size range. cles/dinexa? να)."," If the size distribution is approximated by a power-law $n\propto a^{-p}$ ) over a certain size range, $\mathrm{d}\kappa_\mathrm{ext}/\mathrm{d}\ln a\propto864a^{3-p}Q_\lambda(a)$ ."865" Since Q\(a)~1 for 2x«aA and (Qu(a)xa for σπα À te.g.Bohren&Hutf-man 1983). we obtain csi/dlnexa?"" for σπαZoA and disdinaxat"" for 2za«A."," Since $Q_\lambda (a)\sim 1$ for $2\pi a\ga\lambda$ and $Q_\lambda (a)\propto a$ for $2\pi a\ll\lambda$ \citep[e.g.][]{bohren83}, we obtain $\mathrm{d}\kappa_\mathrm{ext}/\mathrm{d}\ln a\propto a^{3-p}$ for $2\pi a\ga\lambda$ and $\mathrm{d}\kappa_\mathrm{ext}/\mathrm{d}\ln a\propto a^{4-p}$ for $2\pi a\ll\lambda$."866 Thus. if p«3. the largest grains have the largest contribution to the extinction.," Thus, if $p<3$, the largest grains have the largest contribution to the extinction."867 In order for small grains to have significant contribution to the extinction. pz3 should be satistied.," In order for small grains to have significant contribution to the extinction, $p\geq 3$ should be satisfied."868 If 3.«p4. the largest contribution to the extinction comes from the grains with 27a~A.," If $3<p<4$, the largest contribution to the extinction comes from the grains with $2\pi a\sim\lambda$."869 In other words. the UV (A~0.2 jum) extinction curve is steepened significantly if grains with e0.03μπι are produced and p3 is satisfied around this grain size.," In other words, the UV $\lambda\sim 0.2~\micron$ ) extinction curve is steepened significantly if grains with $a\sim 0.03~\micron$ are produced and $p\ga 3$ is satisfied around this grain size."870" From reftis:size,0.1 4.. weobserecthatalargenumberofqrainswilhagnderestimate are produced and the slope around this grain radius is p<3 for the solar metallicity cases."," From \\ref{fig:size_n0.1}- \ref{fig:size_n10}, we observe that a large number of grains with $a\sim 0.03~\micron$ are produced and the slope around this grain radius is $p\ga 3$ for the solar metallicity cases."871" Indeed. the UV slope of extinction curve is steepened for the solar metallicity cases as shown in reftig:ext,, ge.."," Indeed, the UV slope of extinction curve is steepened for the solar metallicity cases as shown in \\ref{fig:ext_age}."872 In this paper. the shattered fragments are distributed with a size distribution with exponent a;=3.3 (Section ?2)). Jonesal. (1996)..," In this paper, the shattered fragments are distributed with a size distribution with exponent $\alpha_\mathrm{f}=3.3$ (Section \ref{subsec:shatter}) ). \citet{jones96}, ,"873" from a discussion on the cratering flow. argue that the value of o, slightly larger than 3 is robust."," from a discussion on the cratering flow, argue that the value of $\alpha_\mathrm{f}$ slightly larger than 3 is robust."874 Even if ay=2.5 is assumed as an extreme case. the difference in the extinction curve is less than at A=0.1pum and smaller at longer wavelengths (see the Appendix ?? for details).," Even if $\alpha_\mathrm{f}=2.5$ is assumed as an extreme case, the difference in the extinction curve is less than at $\lambda =0.1~\micron$ and smaller at longer wavelengths (see the Appendix \ref{app:alpha2.5} for details)."875 From the results above. the presence of small grains in starburst environments is generally predicted. although SNe II tend to eject large grains because ofSNRs.," From the results above, the presence of small grains in starburst environments is generally predicted, although SNe II tend to eject large grains because of."876 For example. BCDs tor H galaxies) in the nearby Universe host large ionized region and the age of the current star formation episode is a few Myr-20 Myr (e.g.Hirashita&Hunt2004:Takeuchial. 2005).," For example, BCDs (or H galaxies) in the nearby Universe host large ionized region and the age of the current star formation episode is a few Myr–20 Myr \citep[e.g.][]{hirashita04,takeuchi05}."877. These ages are just in the range where shattering could modify the grain size distribution and extinction curve. although we should take into account the low metallicity in BCDs.," These ages are just in the range where shattering could modify the grain size distribution and extinction curve, although we should take into account the low metallicity in BCDs."878 Some BCDs show an excess of near-infrared emission (e.g.Hunt.Vanzi.&Thuan 2001). which can be attributed by the emission from transiently heated very small grains CAannestad&Kenyon1979:Sellgren1984:Draine&And," Some BCDs show an excess of near-infrared emission \citep[e.g.][]{hunt01}, which can be attributed by the emission from transiently heated very small grains \citep{aannestad79,sellgren84,draine85}."879erson 1985).. Gallianoetal.(2005) have carried out a comprehensive analysis of the SEDs of dust and stars in some dwarf galaxies (dwarf irregular galaxies and BCDs). and have shown that the grain size is biased to small grains with ~ afew nm.," \citet{galliano05} have carried out a comprehensive analysis of the SEDs of dust and stars in some dwarf galaxies (dwarf irregular galaxies and BCDs), and have shown that the grain size is biased to small grains with $\sim$ a few nm."880 Since their sample galaxies have metallicities larger than 1/10 Z.;. shattering in WIM can work as a production source of nm-sized grains on time-scales of a few Myr and thus can be considered as an origin of small grains in these galaxies.," Since their sample galaxies have metallicities larger than 1/10 $_{\sun}$, shattering in WIM can work as a production source of nm-sized grains on time-scales of a few Myr and thus can be considered as an origin of small grains in these galaxies."881 It is natural to expect that a similar condition tturbulence in WIM sustained more than a few Myr) is generally realized in starburst galaxies., It is natural to expect that a similar condition turbulence in WIM sustained more than a few Myr) is generally realized in starburst galaxies.882 Although it is hard to compare the extinction curve with the observed wavelength dependence of the dust attenuation because of the effects of radiative transfer (Calzetti 2005).. shattering may be crucial to reproduce the reddening in starburst galaxies.," Although it is hard to compare the extinction curve with the observed wavelength dependence of the dust attenuation because of the effects of radiative transfer \citep{calzetti01,inoue05}, shattering may be crucial to reproduce the reddening in starburst galaxies."883 Therefore. shattering should be considered as a source of small grains. which contribute to the reddening.," Therefore, shattering should be considered as a source of small grains, which contribute to the reddening."884 Efficient shattering also occurs in the ISM by the passage of SN shocks., Efficient shattering also occurs in the ISM by the passage of SN shocks.885 Jonesetal.(1996). show that a large fraction of large grains with e0.1pum is redistributed into smaller grains by a single passage of shock with a velocity of ~100 km +., \citet{jones96} show that a large fraction of large grains with $a>0.1~\micron$ is redistributed into smaller grains by a single passage of shock with a velocity of $\sim 100$ km $^{-1}$.886 and are subject to more collisions with dust., and are subject to more collisions with dust.887 Jonesetal.(1996). consider the MRN distribution as the initial grain size distribution. which enhances the shattering efficiency compared with our case. because of the enhanced collision with the abundant small grains.," \citet{jones96}888 consider the MRN distribution as the initial grain size distribution, which enhances the shattering efficiency compared with our case, because of the enhanced collision with the abundant small grains."889 Below. we estimate the time-scale on which shattering in SN shocks destroys large grains based on Jonesetal.(1996).. although the time-scale obtained might be an distributio," Below, we estimate the time-scale on which shattering in SN shocks destroys large grains based on \citet{jones96}, although the time-scale obtained might be an underestimate."890"n, The time-scale on which shattering in SN shocks effectively destroys large grains can basically estimated by a similar way to McKee(1989).", The time-scale on which shattering in SN shocks effectively destroys large grains can basically estimated by a similar way to \citet{mckee89}.891. A single SN can sweep Aly~107AL. of gas Mac2/2~fen with a shock velocity ος~LOO km 1 and energy given to gas by a SN y~1073 erg)., A single SN can sweep $M_\mathrm{sw}\sim 10^4~\Msun$ of gas $M_\mathrm{sw}v_\mathrm{s}^2/2\sim E_\mathrm{SN}$ with a shock velocity $v_\mathrm{s}\sim 100$ km $^{-1}$ and energy given to gas by a SN $E_\mathrm{SN}\sim 10^{51}$ erg).892 Then. the gas muss swept by SN shocks with eZ100 km + per unit time can be estimated as AZ.7. where > is the SN rate.," Then, the gas mass swept by SN shocks with $v_\mathrm{s}\ga 100$ km $^{-1}$ per unit time can be estimated as $M_\mathrm{sw}\gamma$, where $\gamma$ is the SN rate."893 Thus. the on which the entire gas mass Ad. is affected by shattering by SN shocks is estimated as Taw~AM(Mas).," Thus, the time-scale on which the entire gas mass $M_\mathrm{g}$ is affected by shattering by SN shocks is estimated as $\tau_\mathrm{sw}\sim M_\mathrm{g}/894(M_\mathrm{sw}\gamma)$."895 Since +fer~10.7M. for a Salpeter initial mass function/ (Salpeter1955) (c is the star formation rate). the above time-scale is estimated. as Teol0FAL.c.," Since $\gamma/\psi\sim 10^{-2}\Msun^{-1}$ for a Salpeter initial mass function \citep{salpeter55}896 $\psi$ is the star formation rate), the above time-scale is estimated as $\tau_\mathrm{sw}\sim 10^{-2}M_\mathrm{g}/\psi$."897 This estimate indicates that the shattering scale by SN shocks is about 0.01 times the gas consumption time- by star formation., This estimate indicates that the shattering time-scale by SN shocks is about 0.01 times the gas consumption time-scale by star formation.898 In starburst environments. Ad.ευ107— 10° yr may be reasonable (Youngetal.1986)... and shattering in SN shocks occurs in 1-10 Myr. which is comparable to the time-scale investigated in this paper.," In starburst environments, $M_\mathrm{g}/\psi\sim 10^8$ $10^9$ yr may be reasonable \citep{young86}, and shattering in SN shocks occurs in 1–10 Myr, which is comparable to the time-scale investigated in this paper."899 Therefore. both shattering in turbulence and that in SN shocks can affect the grain size distribution.," Therefore, both shattering in turbulence and that in SN shocks can affect the grain size distribution."900 A detailed calculation of shattering in SN shocks of grains produced by SNe IL is required before we judge which of these two shattering mechanisms 1s dominated., A detailed calculation of shattering in SN shocks of grains produced by SNe II is required before we judge which of these two shattering mechanisms is dominated.901 It might be also useful to discuss our results in terms of the extinction curves of the Large and Small Magellanic Cloud (LMC and SMC). both of which have developed H regions such as 30 Doradus.," It might be also useful to discuss our results in terms of the extinction curves of the Large and Small Magellanic Cloud (LMC and SMC), both of which have developed H regions such as 30 Doradus."902 Indeed. Bernardetal.(2008) indicate that the 70 jum excess around 30 Doradus can be explained by an enhancement of the abundance of very small grains possibly by the destruction of large grains.," Indeed, \citet{bernard08} indicate that the 70 $\micron$ excess around 30 Doradus can be explained by an enhancement of the abundance of very small grains possibly by the destruction of large grains."903 Botetal.(2004). find this excess in the SMC., \citet{bot04} find this excess in the SMC.904 Paradisetal.(2009). show that the very small grain abundance is really enhanced around 30 Doradus by using an SED model of dust emission., \citet{paradis09} show that the very small grain abundance is really enhanced around 30 Doradus by using an SED model of dust emission.905 However. the extinction curves in these galaxies are much steeperthan our results Glfelyc2.9 and 3.2 at A— for the LMC and the SMC. respectively: Pei 19923).," However, the extinction curves in these galaxies are much steeperthan our results $A_\lambda /A_V\simeq 2.9$ and 3.2 at $\lambda\simeq 0.2~\micron$ for the LMC and the SMC, respectively; \citealt{pei92}) )."906 Since those galaxies have less intensestar formation than BCDs. it is hard to extract the starbursting components where shattering of large grains should be working as investigated in this paper.," Since those galaxies have less intensestar formation than BCDs, it is hard to extract the starbursting components where shattering of large grains should be working as investigated in this paper."907 The steep extinction curves of the LMC and the SMC indicate that we should consider not only the dust production/shattering in star-forming regions but also some other mechanisms which act as efficient production sources of small grains., The steep extinction curves of the LMC and the SMC indicate that we should consider not only the dust production/shattering in star-forming regions but also some other mechanisms which act as efficient production sources of small grains.908 For example. shattering in," For example, shattering in"9092010).,.910.. As flix is being redistributed owing to the granular evolution. the bundles are dispersed and the spatial smearing of more isolated loop-like structures reduces the linear polarization signal to values below the noise level.," As flux is being redistributed owing to the granular evolution, the bundles are dispersed and the spatial smearing of more isolated loop-like structures reduces the linear polarization signal to values below the noise level."911 Based on Sunrise/IMaX data and using an automated detection method. we obtained statistical properties of 4536 features with significant linear polarization signal.," Based on Sunrise/IMaX data and using an automated detection method, we obtained statistical properties of 4536 features with significant linear polarization signal."912 Their iletimes are consistent with examples given previously in the literature., Their lifetimes are consistent with examples given previously in the literature.913 However. the iletime distribution indicates no characteristic value. in contrast (o. previous studies (Ishikawaetal.2008:Ishikawa&Tsuneta2009:Jin2009).," However, the lifetime distribution indicates no characteristic value, in contrast to previous studies \citep{Ishikawa:etal:2008,Ishikawa:Tsuneta:2009,Jin:etal:2009}."914. The detected. features iive no characteristic size either., The detected features have no characteristic size either.915 Around 97% of them are smaller than 1 arcesec?. which is (he value previously (taken as (he mean size of HIF (shikawa&Tsuneta2009).," Around $97$ of them are smaller than $\sim$ 1 $^2$, which is the value previously taken as the mean size of HIF \citep{Ishikawa:Tsuneta:2009}."916. We lind (hat their rate of occurrence is 1-2 orders of magnitude higher (han reported earlier (Litesetal.1996:Ishikawa&Tsuneta2009;MartínezGonzálezDellotRaibio2009).," We find that their rate of occurrence is 1-2 orders of magnitude higher than reported earlier \citep{Lites:etal:1996,Ishikawa:Tsuneta:2009,Marian:Luis:2009}."917. We attribute Chis discrepancy (o selection effects., We attribute this discrepancy to selection effects.918" If we take only the biggest features (sizes >0.55 arcsec?). only 45 of the detected features remain and the rate of occurrence decreases to ~4-10? | 7, which is in closer agreement with the references cited above."," If we take only the biggest features (sizes $>0.88$ $^2$ ), only $\sim$ of the detected features remain and the rate of occurrence decreases to $\sim4\cdot10^{-5}$ $^{-1}$ $^{-2}$, which is in closer agreement with the references cited above."919 Longer-lived HIF tend to be lareer and display a higher mean linear polarization signals., Longer-lived HIF tend to be larger and display a higher mean linear polarization signals.920 The HIF appear preferentially al (he eranule boundaries. with most of them being caught by downllows at some point in their evolution.," The HIF appear preferentially at the granule boundaries, with most of them being caught by downflows at some point in their evolution."921 We showed that ~16% of the features we detected are completely embedded in upflows and ~8% are entirely embedded in downllows., We showed that $\sim$ of the features we detected are completely embedded in upflows and $\sim$ are entirely embedded in downflows.922 The latter are very. small in size (as illustrated by the two examples discussed in greater detail)., The latter are very small in size (as illustrated by the two examples discussed in greater detail).923 Although their origin is still uncertain it is clear that they do not fit into (he scenario of magnetic [Iux emergence as their plvsical cause., Although their origin is still uncertain it is clear that they do not fit into the scenario of magnetic flux emergence as their physical cause.924"comes from the ""C destruction via the CN cycle, and the oxygen content O remains about constant.","comes from the $^{12}$ C destruction via the CN cycle, and the oxygen content $O$ remains about constant."925" Thus, one has dC=-$dN since N globally results from the addition of two protons to !7C, This gives the slope always in mass fractions."," Thus, one has ${\rm d}C= -\frac{6}{7} {\rm d}N $ since $^{14}$ N globally results from the addition of two protons to $^{12}$ C, This gives the slope always in mass fractions."926" With ratios N/C and N/O of 0.31 and 0.11, respectively, we get This ratio is evidently greater than 1, since as N starts growing, C decreases, while O does not vary much."," With ratios $N/C$ and $N/O$ of 0.31 and 0.11, respectively, we get This ratio is evidently greater than 1, since as $N$ starts growing, $C$ decreases, while $O$ does not vary much."927 The relation turns slightly upward as N/C is increasing owing to the term in brackets in Eq. (2))., The relation turns slightly upward as $N/C$ is increasing owing to the term in brackets in Eq. \ref{slope}) ).928" However, at some advanced stage in evolution, corresponding to WN stars not shown here, the curve will saturate and turn down slightly (Maeder2009,p. 699),, since the CN cycle is then at equilibrium, while !6O is still turned to '4N. Dilution mixes a fraction f of N++AN enriched and C depleted materials with a fraction (1—f) of the original N and C."," However, at some advanced stage in evolution, corresponding to WN stars not shown here, the curve will saturate and turn down slightly \citep[p.~699]{maeder09}, , since the CN cycle is then at equilibrium, while $^{16}$ O is still turned to $^{14}$ N. Dilution mixes a fraction $f$ of $N$ $\Delta N$ enriched and C depleted materials with a fraction $(1-f)$ of the original $N$ and $C$."929" Under the same assumptions as above, it is easy to show that, to the first order, the slope for the relative enrichments in the N/C vs. N/O plot behaves the same way as in Eq. (2))"," Under the same assumptions as above, it is easy to show that, to the first order, the slope for the relative enrichments in the $N/C$ vs. $N/O$ plot behaves the same way as in Eq. \ref{slope}) )"930 independently of f., independently of $f$.931" The value of f, however, determines the amplitudes of the departures from the cosmic ratios."," The value of $f$, however, determines the amplitudes of the departures from the cosmic ratios."932" Our models with rotational mixing (Meynet Maeder 2003, MM03; Ekstrómm et al."," Our models with rotational mixing (Meynet Maeder 2003, MM03; Ekströmm et al."933" 2008, E08) or with rotation and magnetic fields (MMOS), as illustrated e.g. in Fig. 1,,"," 2008, E08) or with rotation and magnetic fields (MM05), as illustrated e.g. in Fig. \ref{litsummary},"934" have an initial slope EI 944, which is in excellent agreement with Eq. (3))."," have an initial slope $\frac{{\rm d}(N/C)}{{\rm935d}(N/O)}$ $\approx$ 4, which is in excellent agreement with Eq. \ref{sl4}) )."936" The amplitude f of the mixing depends on the various model assumptions, in particular on the treatment of the shear mixing with or without horizontal turbulence."," The amplitude $f$ of the mixing depends on the various model assumptions, in particular on the treatment of the shear mixing with or without horizontal turbulence."937" The models without horizontal turbulence (Meynet&Maeder2000,MMO0) predict more mixing than models that account for it (MM03)."," The models without horizontal turbulence \citep[MM00]{mema00}938 predict more mixing than models that account for it (MM03)."939 Models that include both rotation and magnetic field predict a still larger mixing (ΜΜΟΣ)., Models that include both rotation and magnetic field predict a still larger mixing (MM05).940" Let us now consider the behaviour of the helium surface content Y, vs. N/O (as illustrated later).", Let us now consider the behaviour of the helium surface content $Y_{\mathrm{s}}$ vs. $N/O$ (as illustrated later).941" Strictly and only at the very beginning of the CN burning, and under the assumption of an initially constant oxygen, we get dY, = 2dN, since when 4 units of mass of helium are made, 14 units of mass of nitrogen are produced."," Strictly and only at the very beginning of the CN burning, and under the assumption of an initially constant oxygen, we get ${\rm d}Y_{\mathrm{s}}$ $=$ $\frac{2}{7}{\rm d}N$, since when 4 units of mass of helium are made, 14 units of mass of nitrogen are produced."942" The slope is i.e., it 7is essentially flat initially."," The slope is i.e., it is essentially flat initially."943" Later in the evolution, both N and O change simultaneously, and one has to rely on numerical models."," Later in the evolution, both N and O change simultaneously, and one has to rely on numerical models."944" The resulting slope in the models can vary; e.g., a steeper slope is inferred for the Μο model of both MMO3 and models byMMO0 than for the Μο models of MMO03 and MMOS."," The resulting slope in the models can vary; e.g., a steeper slope is inferred for the $M_{\odot}$ model of both MM03 and models byMM00 than for the $M_{\odot}$ models of MM03 and MM05."945 This depends on whether the matter that arrives at the surface comes from inner regions that are at both, This depends on whether the matter that arrives at the surface comes from inner regions that are at both946data revealed that the source is a pulsar withs.,data revealed that the source is a pulsar with.947. The spectral fit provided a value of Ny=3.2x10? cm? (2)., The spectral fit provided a value of $N_{H} = 3.2 \times 10^{22}$ $^{-2}$ \citep{bamba03}.948". A fast outburst observed by INTEGRAL was attributed by ? to this A Chandra observation of the field revealed the counterpart to be 2MASS 18410043-0535465, a reddened star with weak Ha in emission (?), suggesting it was a Be star. ?,,"," A fast outburst observed by INTEGRAL was attributed by \citet{halgot04} to this A Chandra observation of the field revealed the counterpart to be 2MASS 18410043-0535465, a reddened star with weak $\alpha$ in emission \citep{halpern04}, suggesting it was a Be star. \citet{negue06},"949" from optical spectroscopy, proposed the star is instead a luminous BO-1 type, although with some uncertainty, classifying the system as an Figure 4 shows the K, spectrum we obtained, with identified spectral features marked."," from optical spectroscopy, proposed the star is instead a luminous B0-1 type, although with some uncertainty, classifying the system as an Figure \ref{fig:AXJ1841} shows the $K_{s}$ spectrum we obtained, with identified spectral features marked."950" The spectrum shows He1205581 eemission, accompanied by a spurious feature, possibly due to poor telluric component removal; we observe absorption atHer21 1126, a weak Nm (Cur) 211155 eemission; moreover, there is moderately strong Bry absorption."," The spectrum shows 581 emission, accompanied by a spurious feature, possibly due to poor telluric component removal; we observe absorption at 126, a weak ) 155 emission; moreover, there is moderately strong $\gamma$ absorption."951" The side features of the Bry absorption profile are probably due to poor telluric correction, but they do not prevent us from measuring the equivalent The observed transitions are typical of an early supergiant, and by comparison with the atlases from ??,, we can conclude that the star is of B1 Ib type."," The side features of the $\gamma$ absorption profile are probably due to poor telluric correction, but they do not prevent us from measuring the equivalent The observed transitions are typical of an early supergiant, and by comparison with the atlases from \citet{hanson96,hanson05}, we can conclude that the star is of B1 Ib type."952" Together with X-ray properties, this NIR spectral classification allows us to confirm the nature of the system as an SEXT."," Together with X-ray properties, this NIR spectral classification allows us to confirm the nature of the system as an SFXT."953" The wind-accreting system 4U 1907409 (?) is a known HMXB consisting of a neutron star in an eccentric (e = 0.28) 8.3753 dayorbit around its companion, which has been optically identified as a highly reddened star (?).."," The wind-accreting system 4U 1907+09 \citep{giacc71} is a known HMXB consisting of a neutron star in an eccentric $e$ = 0.28) 8.3753 dayorbit around its companion, which has been optically identified as a highly reddened star \citep{schwa80}."954 The spectral classification of the counterpart to 4U 1907+09 has been matter of debate., The spectral classification of the counterpart to 4U 1907+09 has been matter of debate.955 The presence of X-ray flaring seen twice per neutron star orbit (?) had led some authors (e.g.???) to the hypothesis of a Be star companion.," The presence of X-ray flaring seen twice per neutron star orbit \citep{mar80} had led some authors \citep[e.g.][]{maki84,copa87,Iye86} to the hypothesis of a Be star companion."956" However, this classification would require a distance of <1.5 kpc, which is in contradiction to the significant interstellar extinction measured in optical observations by ?,, who also classified the counterpart as a B supergiant."," However, this classification would require a distance of $<$ 1.5 kpc, which is in contradiction to the significant interstellar extinction measured in optical observations by \citet{vanker89}, who also classified the counterpart as a B supergiant."957" Using interstellar atomic lines of Na I and K I, set a lower limit of 5 kpc for the distance and proposed that the stellar companion is instead a O8-O9 Ia supergiant with an effective temperature of 305500 K, a radius of 26 Ro, a luminosity of 5x10? Lo, and a mass loss rate of 7x10-° Mo ντ,"," Using interstellar atomic lines of Na I and K I, \citet{cox05} set a lower limit of 5 kpc for the distance and proposed that the stellar companion is instead a O8-O9 Ia supergiant with an effective temperature of 500 K, a radius of 26 $R_{\sun}$, a luminosity of $5 \times 10^5$ $_{\sun}$, and a mass loss rate of $7 \times 10^{-6}$ $_{\sun}$ $^{-1}$."958" Similarly to other accreting neutron stars, the X-ray continuum of 4U 1907+09 can be described by a power-law spectrum with an exponential turnover at 13 keV. The spectrum is modified by strong photoelectric absorption with a column density Ny=1.5—5.7x10? cm""? (e.g.?).."," Similarly to other accreting neutron stars, the X-ray continuum of 4U 1907+09 can be described by a power-law spectrum with an exponential turnover at 13 keV. The spectrum is modified by strong photoelectric absorption with a column density $N_{H} = 1.5 - 5.7 \times 10^{22}$ $^{-2}$ \citep[e.g.][]{copa87}."959" We show for the first time an infrared spectrum of the source, which permits us to confirm the spectral classification as estimated from optical data."," We show for the first time an infrared spectrum of the source, which permits us to confirm the spectral classification as estimated from optical data."960" Figure 5 presents the K, spectrum we obtained, with identified spectral features marked."," Figure \ref{fig:4U1907} presents the $K_{s}$ spectrum we obtained, with identified spectral features marked."961" The spectrum shows absorption both at 205580 aand at 1126A,, a weak N ΠΙ (or C III) emission line at 211155 aand strong Bry absorption (EW « 4 A)), the typical features of an early supergiant."," The spectrum shows absorption both at 580 and at 126, a weak N III (or C III) emission line at 155 and strong $\gamma$ absorption (EW $<$ 4 ), the typical features of an early supergiant."962 The presence of1 5580 in absorption strongly constrains the spectral type to a late O star., The presence of 580 in absorption strongly constrains the spectral type to a late O star.963" By comparison with the atlases from ??,, we conclude that the star isan O9.5 Iab."," By comparison with the atlases from \citet{hanson96,hanson05}, we conclude that the star isan O9.5 Iab."964 We thus confirm and refine the previous spectral classification., We thus confirm and refine the previous spectral classification.965 The INTEGRAL discovery of this source was reported by ?.., The INTEGRAL discovery of this source was reported by \citet{hann03}. .966 Observations with the Rossi X-Ray Timing Explorer (RXTE), Observations with the Rossi X-Ray Timing Explorer (RXTE)967We also find a small number of opticallv-faint. very low redshift. compact objects which fall outside the genera trend in the by> plane.,"We also find a small number of optically-faint, very low redshift, compact objects which fall outside the general trend in the $b_{\rm J}-z$ plane."968 The X-ray luminositics of these sources range from 4107 cerg/s to 1107 cores suggesting that they are either. very luminous starbursts or AGN., The X-ray luminosities of these sources range from $4\times 10^{41}$ erg/s to $1\times 10^{43}$ erg/s suggesting that they are either very luminous starbursts or AGN.969 However. in all but one case. the 6dEGS optica spectra does not provide any evidence of AGN or starburs activity.," However, in all but one case, the 6dFGS optical spectra does not provide any evidence of AGN or starburst activity."970 Further observational follow up is needed to confirm the physical properties of these sources., Further observational follow up is needed to confirm the physical properties of these sources.971 Vhere are 918. (27%) RASS6dEGS. sources. detecte in either the llz NRAO VLA Sky Survey (NVSS) or the MMlIz Sydney. University Molonglo Sky Survey (SUMSS)., There are 918 $\%$ ) RASS–6dFGS sources detected in either the GHz NRAO VLA Sky Survey (NVSS) or the MHz Sydney University Molonglo Sky Survey (SUMSS).972 The fraction of sources with radio counterparts changes with redshift. and at z21 nearly all the RASS6dECGS sources have radio detections.," The fraction of sources with radio counterparts changes with redshift, and at $z>1$ nearly all the RASS–6dFGS sources have radio detections."973 These sources are strong radio sources with a median [lux density. of 1151muns whereas the median [lux censity for the ful sample is mmy., These sources are strong radio sources with a median flux density of mJy whereas the median flux density for the full sample is mJy.974 We attribute this to the presence of a radio jet which Doppler boosts the radio emission., We attribute this to the presence of a radio jet which Doppler boosts the radio emission.975 The ray [lux of these sources is also boosted by a jet componen and thus at large redshifts selecting bright N-rav. sources preferentially selects radio-oud ACGN., The X-ray flux of these sources is also boosted by a jet component and thus at large redshifts selecting bright X-ray sources preferentially selects radio-loud AGN.976 The RASSGdb€GS catalogue. when reduced. to jus those sources with radio detections. can be used as the southern counterpart to the RBSCNVSS catalogue and as such ollers a large sample of BL-Lac anc blazar sources.," The RASS–6dFGS catalogue, when reduced to just those sources with radio detections, can be used as the southern counterpart to the RBSC–NVSS catalogue and as such offers a large sample of BL-Lac and blazar sources."977 Other. properties. of RASSος sources. in. particular the high-frequeney. radio properties. will be examined. in forthcoming papers.," Other properties of RASS–6dFGS sources, in particular the high-frequency radio properties, will be examined in forthcoming papers."978 This will enable further. studies: of BL-Lac objects and a more extensive. analysis of the multiwavelength properties (X-ray - optical - radio)., This will enable further studies of BL-Lac objects and a more extensive analysis of the multiwavelength properties (X-ray - optical - radio).979 Future work also includes observational follow-up of the small number of optically faint. very low redshift sources identified in this paper.," Future work also includes observational follow-up of the small number of optically faint, very low redshift sources identified in this paper."980 2 , \ref{wrongredshiftstab} 981"is calculated by where dy, is the luminosity distance and S, the fluence in the1/(1+z) keV to 10/(1+z) MeV frame.",is calculated by where $d_L$ is the luminosity distance and $S_\gamma$ the fluence in the$1/(1+z)$ keV to $10/(1+z)$ MeV frame.982" We determine S, using the energy flux provided by the best-fit spectral parameters and multiplying it with the total time interval over which the fit was performed.", We determine $S_\gamma$ using the energy flux provided by the best-fit spectral parameters and multiplying it with the total time interval over which the fit was performed.983" Since we performed the fit for time intervals where the count rate exceeded a S/N ratio of 3.5, it happened that some time intervals of some bursts were not included in the fit (e.g. phases of quiescence where the count rate dropped back to the background level)."," Since we performed the fit for time intervals where the count rate exceeded a S/N ratio of 3.5, it happened that some time intervals of some bursts were not included in the fit (e.g. phases of quiescence where the count rate dropped back to the background level)."984 These time intervals were not used to calculate the fluence., These time intervals were not used to calculate the fluence.985" The S, distribution is shown in Fig.5..", The $S_\gamma$ distribution is shown in \ref{fig:flugbm}.986 The median value of the fluence distribution is 1.6x10? erg cm? and the mean value is 5.9x10? erg cm?., The median value of the fluence distribution is $1.6\times10^{-5}$ erg $^{-2}$ and the mean value is $5.9\times10^{-5}$ erg $^{-2}$.987 A log-normal fit to the data peaks at 2.2x102 erg cm?., A log-normal fit to the data peaks at $2.2\times10^{-5}$ erg $^{-2}$.988 The distribution is shown in Fig.6.., The distribution is shown in \ref{fig:histeiso}. .989" The distribution for the long bursts has a median and mean value of 1.2x erg and 1.4x10? erg, respectively."," The distribution for the long bursts has a median and mean value of $1.2\times10^{53}$ erg and $1.4\times10^{53}$ erg, respectively."990" Short bursts, on the other hand, have significantly lower values of 2.9x10?! erg and 4.0x10?! erg, respectively."," Short bursts, on the other hand, have significantly lower values of $2.9\times10^{51}$ erg and $4.0\times10^{51}$ erg, respectively."991 A log-normal fit to the long bursts reveals a central value of 105?! erg., A log-normal fit to the long bursts reveals a central value of $10^{53.1}$ erg.992 Because our sample is dominated by long GRBs a log-normal fit to the whole distribution results in an essentially unchanged peak value (1053 erg)., Because our sample is dominated by long GRBs a log-normal fit to the whole distribution results in an essentially unchanged peak value $10^{53}$ erg).993 ? first showed that there is a tight correlation between and (the isotropic equivalent bolometric energy determined in the energy range between 1 keV to 10 MeV)., \citet{amati02} first showed that there is a tight correlation between and (the isotropic equivalent bolometric energy determined in the energy range between 1 keV to 10 MeV).994" This relation is now known as the ""Amati relation"".", This relation is now known as the “Amati relation”.995 In Fig.7 we show the Amati relation for the 30 GBM GRBs with measured andΕικο., In \ref{fig:amati} we show the Amati relation for the 30 GBM GRBs with measured and.996. While there is an evident correlation between these two quantities (Spearman's rank correlation of p=0.74 with a chance probability of 1.7x 107?) the extrinsic scatter of the long GRBs is larger by a factor of ~2 in log-space compared to ?.., While there is an evident correlation between these two quantities (Spearman's rank correlation of $\rho= 0.74$ with a chance probability of $1.7\times10^{-5}$ ) the extrinsic scatter of the long GRBs is larger by a factor of $\sim 2$ in $\log$ -space compared to \citet{amati10}.997" Also, the best fit to our data is shifted to slightly larger Values."," Also, the best fit to our data is shifted to slightly larger values."998 The best fit power-law index to the long GRBs of our sample is 0.52+0.06 which is in agreement with the indices obtained by e.g. ???..," The best fit power-law index to the long GRBs of our sample is $0.52\pm0.06$ which is in agreement with the indices obtained by e.g. \citet{amati10, ghina09, ghirlanda10}."999" As has been shown by other authors in the past (seee.g.???) short bursts do not follow the relation, being situated well outside the 2 o scatter around the best-fit."," As has been shown by other authors in the past \citep[see e.g.][]{amati08, ghina09, amati10} short bursts do not follow the relation, being situated well outside the 2 $\sigma$ scatter around the best-fit."1000" This is true also for the power-law fit derived here (see Fig.7)) except for GRB 100816A. However, as already stated above this burst may actually fall in an intermediate or hybrid class of short GRBs with extended emission (seee.g. ??).."," This is true also for the power-law fit derived here (see \ref{fig:amati}) ) except for GRB 100816A. However, as already stated above this burst may actually fall in an intermediate or hybrid class of short GRBs with extended emission \citep[see e.g.][]{norris06, zhang09}. ."1001" ? found a tight correlation between the rest frame peak energy in the vF, spectrum and the 1-s peak luminosity (119) in GRBs (so called Yonetoku relation).", \citet{yonetoku04} found a tight correlation between the rest frame peak energy in the $\nu \rm{F}_{\nu}$ spectrum and the 1-s peak luminosity $(L_p)$ in GRBs (so called Yonetoku relation).1002 The peak luminosity is calculatedwith, The peak luminosity is calculatedwith1003sources with radio detections and those without.,sources with radio detections and those without.1004 What is immecdiately obvious in these plots is that at high recshilts virtually all of the sources fall into the radio sample and in [act ave quite strong radiosources!., What is immediately obvious in these plots is that at high redshifts virtually all of the sources fall into the radio sample and in fact are quite strong radio.1005. Phe median Dux density for sources with z lis H151mnis while the median Hux density for the entire RASS6dECGS radio sample is mum., The median flux density for sources with $z>1$ is mJy while the median flux density for the entire RASS–6dFGS radio sample is mJy.1006v. This suggests that the more distant sources are Doppler boosted due to the presence of a radio jet. pointed towards our line of sight., This suggests that the more distant sources are Doppler boosted due to the presence of a radio jet pointed towards our line of sight.1007 As such. the X-ray. emission (or some fraction of it) is also being boosted by a jet component and hence we only detect bright X-ray sources that are raclio-loud at high redshifts.," As such, the X-ray emission (or some fraction of it) is also being boosted by a jet component and hence we only detect bright X-ray sources that are radio-loud at high redshifts."1008 This is in agreement with ? who founcl that radio-loud QSOs have a higher average X-ray luminosity., This is in agreement with \citet{1987ApJ...313..596W} who found that radio-loud QSOs have a higher average X-ray luminosity.1009 The fraction of sources with radio detections changes with redshift. as shown in Figure 11.," The fraction of sources with radio detections changes with redshift, as shown in Figure \ref{radiodetz}."1010 Vhere is a high detection. rate at. low redshift where we detect a large fraction of low luminosity. radio-quiet. AGN in addition to the racio-Ioud sources.," There is a high detection rate at low redshift where we detect a large fraction of low luminosity, radio-quiet AGN in addition to the radio-loud sources."1011 This drops olf quite rapidly as these racio-quict sources fall below the detection limit of the radio surveys. leaving only the radio-Ioud AGN in the sample.," This drops off quite rapidly as these radio-quiet sources fall below the detection limit of the radio surveys, leaving only the radio-loud AGN in the sample."1012The initial condition for the magnetic field in this case is a two-dimensional potential field which is independent of the ν- (see Figs. 2..3.,"The initial condition for the magnetic field in this case is a two-dimensional potential field which is independent of the $x$ -coordinate (see Figs. \ref{fig:coords},"1013 for the coordinate system) and falls off exponentially with height v., \ref{fig:emergeschematic} for the coordinate system) and falls off exponentially with height $y$.1014 It is generated by the vector potential where ;Ur is the width of the arcades and οἱ is the scale height of B=, It is generated by the vector potential where $\lambda\pi$ is the width of the arcades and $\lambda$ is the scale height of $B=\abs{\vec{B}}$.1015" By is the field strength at the intersection of the lower boundaryπι +=5, with the central axis (vy).", $B_\bnd$ is the field strength at the intersection of the lower boundary $r=\rb$ with the central axis $y$ ).1016 To avoid numerical problems at thelateral boundaries. we limit the number of ares to 4. setting A=B=0 for [5]>Zurand for |]>2;Ur.," To avoid numerical problems at thelateral boundaries, we limit the number of arcs to 4, setting $\vec{A}=\vec{B}=0$ for $\abs{z} > 2\lambda\pi$and for $\abs{x} >10172\lambda\pi$."1018 The magnetic field is embedded in aspherically stratified atmosphere with p«ση and po77. held in hydrostatic equilibrium by the staticgravitational field ᾧo+7! of a point mass at the coordinate origin.," The magnetic field is embedded in aspherically stratified atmosphere with $p1019\propto r^{-4}$ and $\rho \propto r^{-3}$, held in hydrostatic equilibrium by the staticgravitational field $\Phi \propto r^{-1}$ of a point mass at the coordinate origin."1020" Temperature and sound speed vary às Toxr and e,&777, respectively."," Temperature and sound speed vary as $T \propto r^{-1}$ and $\cs \propto r^{-1/2}$, respectively."1021" In the outer. unmagnetized region ([x[.]z|> 2,Ur). we compensated for the absence of magnetic pressure by increasing the gas pressure."," In the outer, unmagnetized region $\abs{x},\abs{z} > 2\lambda\pi$ ), we compensated for the absence of magnetic pressure by increasing the gas pressure."1022 To maintain hydrostatic equilibrium. the density is also increased correspondingly.," To maintain hydrostatic equilibrium, the density is also increased correspondingly."1023" At the lower(r2 ry) boundary we maintain. through ""ghost cells” outside of the computational domain. an azimuthal velocity field i=Vee, corresponding to rigid rotation: v—ViNSR/Ry for R€Ry and 0 elsewhere."," At the lower$r=\rb$ ) boundary we maintain, through “ghost cells” outside of the computational domain, an azimuthal velocity field $\vec{v}=v_\varphi1024\evarphi$ corresponding to rigid rotation: $v_\varphi = \vphimax R/\Rb$ for $R1025\le \Rb$ and 0 elsewhere."1026 All quantities except for B are fixed at their initial values in the ghost cells: B is extrapolated from the interior of the domain., All quantities except for $\vec{B}$ are fixed at their initial values in the ghost cells; $\vec{B}$ is extrapolated from the interior of the domain.1027 At the sides (0 and 6) and top (upper r) of the domain.we use open boundary conditions which allow for an almost force-free outflow of material and cause no evident artifacts in the form of reflections.," At the sides $\theta$ and $\phi$ ) and top (upper $r$ ) of the domain,we use open boundary conditions which allow for an almost force-free outflow of material and cause no evident artifacts in the form of reflections."1028" A 18 chosen such that in the x=0 plane B, is positive for ||<Rp and negative for Ry«[:]<285. 1.8. arcades which start at |z|Αι from the r=ην surface have their second footpoint outside the rotating region."," $\lambda$ is chosen such that in the $x=0$ plane $B_y$ is positive for $\abs{z}1029< \Rb$ and negative for $\Rb < \abs{z} < 2\Rb$, i.e. arcades which start at $\abs{z} < \Rb$ from the $r=\rb$ surface have their second footpoint outside the rotating region."1030 This is achieved by choosing the length scale of the arcade as 4|22Rj/7., This is achieved by choosing the length scale of the arcade as $\lambda = 2\Rb / \pi$.1031 In this case. the initial condition is again an equilibrium stratification with p«r7. p«r? and «77.," In this case, the initial condition is again an equilibrium stratification with $p \propto r^{-4}$, $\rho \propto r^{-3}$ and $\Phi \propto r^{-1}$."1032 However. unlike in setup D. the atmosphere is completely unmagnetized.," However, unlike in setup D, the atmosphere is completely unmagnetized."1033 The magnetic field enters the domain through the lower boundary r=n the conditions of which are determined through ghost cells at r€ry.," The magnetic field enters the domain through the lower boundary $r=\rb$, the conditions of which are determined through ghost cells at $r<\rb$."1034" There. we impose a transverse magnetic field By (= B.) with constant amplitude B, and a polarity that alternates with =(ycos4 in step sizes of 2R,. the diameter of the rotating surface (described below)."," There, we impose a transverse magnetic field $B_\theta$ $\approx B_z$ ) with constant amplitude $B_\bnd$ and a polarity that alternates with $z=\rb \cos\theta$ in step sizes of $2\Rb$, the diameter of the rotating surface (described below)."1035" Where the polarity of By changes. the solenoidality of the magnetic field is maintained by an appropriate B,."," Where the polarity of $B_\theta$ changes, the solenoidality of the magnetic field is maintained by an appropriate $B_r$."1036 The field lines thus have the shape sketched in Fig. 3.., The field lines thus have the shape sketched in Fig. \ref{fig:emergeschematic}.1037 An approximate equilibrium is maintained through lowering the gas pressure by the value of the magnetic pressure. as far as this ts possible (p must not be negative).," An approximate equilibrium is maintained through lowering the gas pressure by the value of the magnetic pressure, as far as this is possible $p$ must not be negative)."1038 For this to work. Bp=Sxpp/B; must be greater than one. which limits the possible field strengths to By<1 in our system of units (described below).," For this to work, $\betab \coloneqq 8\pi p_\bnd / B_\bnd^2$ must be greater than one, which limits the possible field strengths to $B_\bnd < 1$ in our system of units (described below)."1039 To model the emergence of magnetic fields into the atmosphere we impose the radial velocity field in the ghostcells of the lower boundary., To model the emergence of magnetic fields into the atmosphere we impose the radial velocity field in the ghostcells of the lower boundary.1040" The injection velocity is too small to form a jet by itself: the maximum amounts to 41% of the escape velocity at the boundary. gas with this speed gets theoretically as far as r=1.27, without acceleration other than gravity."," The injection velocity is too small to form a jet by itself: the maximum amounts to $41\%$ of the escape velocity at the boundary, gas with this speed gets theoretically as far as $r \approx10411.2 \rb$ without acceleration other than gravity."1042 In addition to the radial velocity field. we maintain an azimuthal velocity field v.οR (rigid rotation) within R< Ry.," In addition to the radial velocity field, we maintain an azimuthal velocity field $v_\varphi \propto R$ (rigid rotation) within $R\le\Rb$ ."1043 The shape of the emerging magnetic field is sketched in Fig., The shape of the emerging magnetic field is sketched in Fig.1044 laa. For the other boundaries. we use the same outflow conditions as in the model described in the preceding section.," \ref{fig:emergecases}a a. For the other boundaries, we use the same outflow conditions as in the model described in the preceding section."1045 Two variations of the above-described setup have also been studied. correspondi£ to the cases (b) and (c) deseribed in Sect. 2..," Two variations of the above-described setup have also been studied, corresponding to the cases (b) and (c) described in Sect. \ref{sec:models}."1046" In the first. the positions where B, changes its polarity. and with it the radial velocity field that injects the magnetic field. are shifted by Ry in —z direction."," In the first, the positions where $B_\theta$ changes its polarity, and with it the radial velocity field that injects the magnetic field, are shifted by $R_\bnd$ in $-z$ direction."1047 Thus. both footpoints of an individual field loop rotate with the same angular velocity.," Thus, both footpoints of an individual field loop rotate with the same angular velocity."1048" In the second case (c). the magnetic field and vertical velocity in the lower boundary are changed such that only a small. confined arcade in 0.2«R/R,0.8 with awidth of 0.2R, emerges. and the azimuthal velocity field has a Keplerian profile with v...=v""VO.IRS/R for 0.1<R/Ry1."," In the second case (c), the magnetic field and vertical velocity in the lower boundary are changed such that only a small, confined arcade in $0.2 < R/R_\bnd < 0.8$ with awidth of $0.2\Rb$ emerges, and the azimuthal velocity field has a Keplerian profile with $v_\varphi = \vphimax1049\sqrt{0.1\Rb/R}$ for $0.1 \le R/R_\bnd \le 1$."1050" The inner edge (R= 0.2R,) of the arcade rotates twice as fast as the outer edge (R= 0.8A,). the difference in rotation velocity iseVB."," The inner edge $R=0.2\Rb$ ) of the arcade rotates twice as fast as the outer edge $R=0.8\Rb$ ), the difference in rotation velocity is $\vphimax/\sqrt{8}$."1051" The models described above contain the following 6 parameters. not all of which are independent: ry. Rp. pp. py. By and v""."," The models described above contain the following 6 parameters, not all of which are independent: $r_\bnd$ , $\Rb$ , $\rho_\bnd$ , $p_\bnd$ , $B_\bnd$ and $\vphimax$ ."1052 We eliminate the dependences by taking /;= 28s. Po=py and po=py as units of length. density and pressure. and expressing all physical quantities in terms of these. see Table 1..," We eliminate the dependences by taking $l_0 \equiv 2\Rb$ $\rho_01053\equiv \rho_\bnd$ and $p_0 \equiv p_\bnd$ as units of length, density and pressure, and expressing all physical quantities in terms of these, see Table \ref{tab:units}. ."1054 The remaining3 parameters can then be expressed as dimensionless numbers., The remaining3 parameters can then be expressed as dimensionless numbers.1055 The first of these is /o/ry. which is à measure for the curvature of the rotating surface.," The first of these is $l_0/r_\bnd$ , which is a measure for the curvature of the rotating surface."1056 In all, In all1057While a general solution to the initial value problem is not kuown. we use the particular solution obtained as follows: To solve the momentum constraints (33)) aud (31)) set. p.pefea=ea Oto leave padwpaw0 which may be satisfied by requizing pay=ec.,"While a general solution to the initial value problem is not known, we use the particular solution obtained as follows: To solve the momentum constraints \ref{ber-Hu}) ) and \ref{ber-hv}) ) set $p_x = p_z = \varphi,_a = \omega,_a = 0$ to leave $p_\Lambda \, \Lambda,_a -\, p_\Lambda,_a = 0$ which may be satisfied by requiring $p_\Lambda = c \,e^\Lambda$."1058" For sufficiently large ο, the Hamiltonian constraint nav be solved alecbraically for either p or r."," For sufficiently large $c$, the Hamiltonian constraint may be solved algebraically for either $p$ or $r$."1059 Iu general. this leaves as free data the four functions «c. 2. A. and either r or p.," In general, this leaves as free data the four functions $x$, $z$, $\Lambda$, and either $r$ or $p$."1060 Since there are four free functions at cach spatial point. we expect generic behavior.," Since there are four free functions at each spatial point, we expect generic behavior."1061 As a first case. we cousider polarized τς} models obtained by setting This condition is preserved umumerically as well as analytically.," As a first case, we consider polarized $U(1)$ models obtained by setting This condition is preserved numerically as well as analytically."1062 It has becu conjectured [11]. that polarized ((1) models are ΑΥΤΟ., It has been conjectured \cite{ber-bm2} that polarized $U(1)$ models are AVTD.1063 This is reasonable because the Mixiuaster poteutial-ike teri, This is reasonable because the Mixmaster potential-like term1064 This is reasonable because the Mixiuaster poteutial-ike terii, This is reasonable because the Mixmaster potential-like term1065In Fig.,In Fig.1066 1. we present the LSD Stokes J and V obtained for ten orbital phases of 66 Eri., \ref{LSD} we present the LSD Stokes $I$ and $V$ obtained for ten orbital phases of 66 Eri.1067 The longitudinal magnetic field was determined from the first moment of theLSD Stokes V profile (?).., The longitudinal magnetic field was determined from the first moment of theLSD Stokes $V$ profile \citep{Kochukhov:2010}.1068 Due to the contribution of blends the continuum level of raw LSD Stokes 7 profiles is slightly offset from unity., Due to the contribution of blends the continuum level of raw LSD Stokes $I$ profiles is slightly offset from unity.1069 We use a constant factor to correct the continuum level., We use a constant factor to correct the continuum level.1070 This factor is applied to the LSD V and null profiles., This factor is applied to the LSD $V$ and null profiles.1071 Such a correction changes the value of the longitudinal magnetic field and its error by 2-3 G. For nine LSD V profiles we could measure the longitudinal field for each component separately., Such a correction changes the value of the longitudinal magnetic field and its error by 2–3 G. For nine LSD $V$ profiles we could measure the longitudinal field for each component separately.1072 At the phase 0.827 (see Fig. 1)), At the phase 0.827 (see Fig. \ref{LSD}) )1073 we have measured both components as a single star., we have measured both components as a single star.1074 The results of the longitudinal magnetic field measurements are presented in Table 1.., The results of the longitudinal magnetic field measurements are presented in Table \ref{tab1}.1075" Its columns contain the following information: the heliocentric Julian date of observation, the signal-to-noise ratio of the original spectra measured around 5200A,, the signal-to-noise ratio of the LSD V profiles, an orbital phase, determined from the binary solution discussed below."," Its columns contain the following information: the heliocentric Julian date of observation, the signal-to-noise ratio of the original spectra measured around 5200, the signal-to-noise ratio of the LSD $V$ profiles, an orbital phase, determined from the binary solution discussed below."1076" The next three columns represent measurements for the HgMn star (component A) as follows: the mean longitudinal magnetic field inferred from the LSD Stokes V, the longitudinal field inferred from the null profile, and a False Alarm Probability (FAP, see below)."," The next three columns represent measurements for the HgMn star (component A) as follows: the mean longitudinal magnetic field inferred from the LSD Stokes $V$, the longitudinal field inferred from the null profile, and a False Alarm Probability (FAP, see below)."1077" The last three columns give the same information for the component B. The errors of the magnetic field measurements were obtained by the standard error propagation, using the uncertainties of the LSD V profiles."," The last three columns give the same information for the component B. The errors of the magnetic field measurements were obtained by the standard error propagation, using the uncertainties of the LSD $V$ profiles."1078 The mean error of longitudinal field measurements is ~14 G for the HgMn component and ~20 G for the secondary., The mean error of longitudinal field measurements is $\sim$ 14 G for the HgMn component and $\sim$ 20 G for the secondary.1079 For the HgMn star the longitudinal field value reaches the confidence level of 2c only at the orbital phase 0.193., For the HgMn star the longitudinal field value reaches the confidence level of $\sigma$ only at the orbital phase 0.193.1080 For the secondary star the measurements of magnetic field do not exceed —1.5c level for most of the orbital phases., For the secondary star the measurements of magnetic field do not exceed $\sim$ $\sigma$ level for most of the orbital phases.1081" Thus, none of the individual mmeasurements indicate the presence of magnetic field in 66 Eri."," Thus, none of the individual measurements indicate the presence of magnetic field in 66 Eri."1082 Our magnetic field measurements for both components with their respective error bars are presented in Fig., Our magnetic field measurements for both components with their respective error bars are presented in Fig.1083 2 as a function of orbital phase., \ref{Bz_phase} as a function of orbital phase.1084" The actual values of the longitudinal field measurements do not exceed the level of 30, so the periodic-like fluctuation of magnetic field measurements in both components are fully attributed to errors."," The actual values of the longitudinal field measurements do not exceed the level of $\sigma$, so the periodic-like fluctuation of magnetic field measurements in both components are fully attributed to errors."1085" Assuming a dipolar configuration of the magnetic field we made an assessment of the upper limit of its strength, which would be consistent with the entire set of mmeasurements."," Assuming a dipolar configuration of the magnetic field we made an assessment of the upper limit of its strength, which would be consistent with the entire set of measurements."1086" Using a relation between the longitudinal field and parameters of an oblique dipole (?),, we estimated the strength of dipolar magnetic field to be 60—70 G with an uncertainty of 50—70 G for both stars."," Using a relation between the longitudinal field and parameters of an oblique dipole \citep{Leroy:1994}, we estimated the strength of dipolar magnetic field to be 60–70 G with an uncertainty of 50–70 G for both stars."1087" However, based on the reduced x? statistics, the dipolar fit has no advantage over the null hypothesis."," However, based on the reduced $\chi^{2}$ statistics, the dipolar fit has no advantage over the null hypothesis."1088" At the same time, much more complex magnetic fields can exist in the atmospheres of both stars."," At the same time, much more complex magnetic fields can exist in the atmospheres of both stars."1089" To investigate possible presence of such complex magnetic structures, which might yield negligible(B,),, we employed the FAP analysis of LSD profiles."," To investigate possible presence of such complex magnetic structures, which might yield negligible, we employed the FAP analysis of LSD profiles."1090" FAP is a y? statistical estimate, which assesses if the Observed structure in the Stokes V line profile is produced by a random noise."," FAP is a $\chi^2$ statistical estimate, which assesses if the observed structure in the Stokes $V$ line profile is produced by a random noise."1091" Following the definition by ?,, these numbers"," Following the definition by \citet{Donati:1997}, , these numbers"1092reflection of the primary continuum from a photoionized gas or thermal emission from diffuse gas (MEKAL)). which was found to give good fits in a sample of Compton-thin Seyfert 2s observed by BeppoSAX (?)..,"reflection of the primary continuum from a photoionized gas or thermal emission from diffuse gas ), which was found to give good fits in a sample of Compton–thin Seyfert 2s observed by BeppoSAX \citep{risa02}."1093 The first one is parametrized (when self absorption effects are neglected) by a power law with the spectral index linked to that of the primary continuum responsible for the photoionization of the gas itself., The first one is parametrized (when self absorption effects are neglected) by a power law with the spectral index linked to that of the primary continuum responsible for the photoionization of the gas itself.1094 We further allowed for absorption by an intervening column density of neutral gas., We further allowed for absorption by an intervening column density of neutral gas.1095 The best fits for the two models are presented in Table 4:: even if marginally better from a statistical point of view. the fits have metal abundances unphysically low.," The best fits for the two models are presented in Table \ref{softfit}: even if marginally better from a statistical point of view, the fits have metal abundances unphysically low."1096 This means that the resulting spectrum lacks emission lines and is virtually indistinguishable from the already rejected bremsstrahlung interpretation., This means that the resulting spectrum lacks emission lines and is virtually indistinguishable from the already rejected bremsstrahlung interpretation.1097 Reflection from photoionized gas remains then the only tenable model., Reflection from photoionized gas remains then the only tenable model.1098" The observed intervening absorption is «2x107! em"". in excess of the Galactic one. and is possibly due to the host galaxy. which is seen almost edge-on."," The observed intervening absorption is $\simeq2\times 10^{21}$ $^{-2}$, in excess of the Galactic one, and is possibly due to the host galaxy, which is seen almost edge–on."1099 As expected from an origin from diffuse gas. the flux of this component is remarkably constant between the two XMM observations (see Table 4)). while the flux of the primary component almost doubles (see Sect. 2)).," As expected from an origin from diffuse gas, the flux of this component is remarkably constant between the two XMM observations (see Table \ref{softfit}) ), while the flux of the primary component almost doubles (see Sect. \ref{data}) )."1100 Therefore. the ratio," Therefore, the ratio"1101however. for 7)=0 the discrete spectrum disappears. together with the eigenfunctions.,"however, for $\eta=0$ the discrete spectrum disappears, together with the eigenfunctions."1102 Indeed. (his singularity in the induction operator lies al the heart of fast dynamo t(lieory (see.[orexample.Childress&Gilbert1995).," Indeed, this singularity in the induction operator lies at the heart of fast dynamo theory \citep[see, for example,][]{CG95}."1103. By contrast. the linear operator for the stability problem has a discrete spectrum of unstable modes and associated eisenfunctions. leading to an unambiguous determination of the electromotive lorce.," By contrast, the linear operator for the stability problem has a discrete spectrum of unstable modes and associated eigenfunctions, leading to an unambiguous determination of the electromotive force."1104" In this section we consider the emf resulting from the instability of a unidirectional mean magnetic field of the form: B=DBo(124-6z/d)e,. with non-zero values of the viscosity and magnetic diffusivitv."," In this section we consider the emf resulting from the instability of a unidirectional mean magnetic field of the form $\bfbarB=B_{0}(1+\zeta z/d)\mathbf{e}_{x}$, with non-zero values of the viscosity and magnetic diffusivity."1105" The instability evolves according to equations (16)) (22)) (with D,= 0). and the mean emf is calculated via horizontal averaging. given by (23)) (25)). and ihe weighting procedure (26))."," The instability evolves according to equations \ref{eq:u_pert}) \ref{eq:rho_pert}) ) (with $\Bbar_y =0$ ), and the mean emf is calculated via horizontal averaging, given by \ref{eq:Ex}) \ref{eq:Ez}) ), and the weighting procedure \ref{eq:weighted_emf}) )."1106 Figure 1. shows the three components of € plotted as functions of z. for a test case al colatitude 9=75°. representing the region in which most magnetic activity is observed on the solar surface.," Figure \ref{fig:emfs} shows the three components of $\bfcalE$ plotted as functions of $z$, for a test case at colatitude $\theta = 75^{\circ}$, representing the region in which most magnetic activity is observed on the solar surface."1107 For this parameter set. (he modes with largest growth rates have wave numbers (&./)=(0.70367.14.812) (with complex erowth rate s=0.082626— 0.0618231) for &>0. and (&./)=(—0.70334.14.312) (with s=0.082602+ 0.067830/) lor κ«0.," For this parameter set, the modes with largest growth rates have wave numbers $(k,l)=(0.70367,14.812)$ (with complex growth rate $s=0.082626-0.067823i$ ) for $k>0$, and $(k,l)=(-0.70334,14.812)$ (with $s=0.082602+0.067830i$ ) for $k<0$."1108 The ells in the figure are calculated rom the mode with largest growth rate: when there is a unique mode of maximum growth rate. as here. the differences between (he weighted aud unweighted emls are small.," The emfs in the figure are calculated from the mode with largest growth rate; when there is a unique mode of maximum growth rate, as here, the differences between the weighted and unweighted emfs are small."1109 It is of interest to note that the y-component of the emf pperpendicular to the imposed magnetic field) has the largest magnitude., It is of interest to note that the $y$ -component of the emf perpendicular to the imposed magnetic field) has the largest magnitude.1110 The calculations in indicate that in the absence of viscosity and magnetic diffusivitv. the ratio," The calculations in \\ref{sec:ideal} indicate that in the absence of viscosity and magnetic diffusivity, the ratio"1111distribution (Ratcliffeetal.1998).,distribution \citep{ratcliffe_IV_1998}.1112. Then we have probability density (9) of random variable & as follows 1n case of Gaussian distribution of velocities we have The convolution of c with e vields the distribution of pair numbers as a function of H., Then we have probability density $\Phi(\delta)$ of random variable $\delta$ as follows In case of Gaussian distribution of velocities we have The convolution of $\psi$ with $\Phi$ yields the distribution of pair numbers as a function of $\Pi$.1113 We used this to fit the observed. pair numbers in dilferent bins with the projected separation σ«Ly=2 Alpe alter randomized. background subtraction., We used this to fit the observed pair numbers in different bins with the projected separation $\sigma<L_{0}=2$ Mpc after randomized background subtraction.1114 The randomized. background. is caleulatecl as described in Sec. ??.., The randomized background is calculated as described in Sec. \ref{sec:2.7}.1115 Because the number of pairs is not large. there is a considerable variation of results for cilferent binnings. so we do not consider the numerical estimates as very reliable.," Because the number of pairs is not large, there is a considerable variation of results for different binnings, so we do not consider the numerical estimates as very reliable."1116" Llowever.we may argue that the model dependence on 5, and 5 parameters is rather insignificant."," However,we may argue that the model dependence on $\gamma_1$ and $\eta$ parameters is rather insignificant."1117" For illustration. we present the results. CLable 4) of fitting the pair numbers (alter randomized. background: subtraction) on account. of (11)) and (CIable 5) on account. of (12)) for two cdillerent binnings having minimal jackknife clispersion estiniates [or (63/7—(ut f23b7, "," For illustration, we present the results (Table 4) of fitting the pair numbers (after randomized background subtraction) on account of \ref{eq:zh3}) ) and (Table 5) on account of \ref{gauss}) ) for two different binnings having minimal jackknife dispersion estimates for $\langle v^2\rangle^{1/2}=\langle w^2/2\rangle^{1/2}$ ."1118Alnning | involves numbers. of pairs with line-of-sight. separations £7 from [five intervals 2.11]. 11.30]. 20.29]. 39.38]. 38.47] (Alpe).," Binning 1 involves numbers of pairs with line-of-sight separations $Pi$ from five intervals $[2,11]$ , $[11,20]$, $[20,29]$, $[29,38]$ , $[38,47]$ (Mpc)."1119 Binning 2 deals with separations from three intervals 2.17]. 17.32]. 32.41] (Alpe)," Binning 2 deals with separations from three intervals $[2,17]$, $[17,32]$, $[32,47]$ (Mpc)."1120 The bar charts in Fiο., The bar charts in Fig.1121 16 and 17 we show corresponding numbers after the average backgrounc subtraction., \ref{fig_vel_eg1} and \ref{fig_vel_eg2} we show corresponding numbers after the average background subtraction.1122 Here we prefer to avoid separations less than 2 Alpe., Here we prefer to avoid separations less than 2 Mpc.1123 Also for illustration in Fig., Also for illustration in Fig.1124" 10 and 17 we presen re results of fitting for 5,=1.85 and dillerent. values of η.", \ref{fig_vel_eg1} and \ref{fig_vel_eg2} we present the results of fitting for $\gamma_1=1.85$ and different values of $\eta$.1125" As one can see [rom the results. the values of (ο215 do no 4vary considerably under rather cilferent. (even unrealistic) 'hoices of unknown parameters gj. 5,4: the variations are of 16 order of the jackknife dispersion estimate."," As one can see from the results, the values of $\langle v^2\rangle^{1/2}$ do not vary considerably under rather different (even unrealistic) choices of unknown parameters $\eta$, $\gamma_1$: the variations are of the order of the jackknife dispersion estimate."1126" In fact the values £02517 in Tables 5.66 do not represen real quasar velocity. dispersion. but a superposition of two components: ieο=ory,|5iA where τοσο ETEds the true velocity dispersion anc Όρων is due to the redshif measurement errors."," In fact the values $\langle v^2\rangle^{1/2}$ in Tables 6 do not represent real quasar velocity dispersion, but a superposition of two components: $\langle v^2\rangle = v_{err}^2 + \langle \bar{v}^2\rangle$, where $\langle\bar{v}^2\rangle^{1/2}$ is the true velocity dispersion and $v_{err}$ is due to the redshift measurement errors."1127 The last value corresponds to intrinsic emission lines shifts in quasars pointed out by Croometal. (2005).. as it is an estimation [rom emission-line or cross-correlation technique of redshift measurement caused by the impossibilitv of precise determination of the line centre due to its large width.," The last value corresponds to intrinsic emission lines shifts in quasars pointed out by \citet{croom_2005}, as it is an estimation from emission-line or cross-correlation technique of redshift measurement caused by the impossibility of precise determination of the line centre due to its large width."1128 For detailed investigation of this elfec see lDuchardsetal.(2002):Shenct(2007).," For detailed investigation of this effect see \citet{richards_2002,shen_2007}."1129. The redshifi measurement errors from the SDSS data base forour sample is A>=0.0019. which corresponds to 644ez/(1|2)230 kms. In this case we would obtain too large value of n2," The redshift measurement errors from the SDSS data base forour sample is $\Delta z=0.0019 $, which corresponds to $v _{err}\sim c\Delta z/(1+\bar{z})=230$ km/s. In this case we would obtain too large value of $\langle\bar{v}^2\rangle$."1130 Once work on the first version of the text had. been finished. the paper by Llewett&Wild(2010) was appeare with the error estimate ey.=600 km/s for SDSS data.," Once work on the first version of the text had been finished, the paper by \citet{hewett_10} was appeared with the error estimate $v_{err}=600$ km/s for SDSS data."1131 In this. case z-errors dominate. in. i£e7ο IMPΗΕ, In this case $z$ -errors dominate in ${\langle v^2\rangle}^{1/2}$.1132 we take the results from Table 5. which vield smaller jackknife dispersion estimate Lor (i2i1/2 than the residual. upper estimate of (73072«(6907GOOFA==340 km/s seems to he more adequate.," If we take the results from Table 5, which yield smaller jackknife dispersion estimate for $\langle{v}^2\rangle^{1/2}$, than the residual upper estimate of $\langle\bar{v}^2\rangle^{1/2}\le (690^2-600^2)^{1/2}=340$ km/s seems to be more adequate."1133 The values of the pairwise velocity dispersion. (7j=2073 corresponding to ‘Lables 5 are comparable with hat mentioned in previous studies of quasar clustering., The values of the pairwise velocity dispersion $\langle w^2\rangle= 2 \langle v^2\rangle$ corresponding to Tables 5 are comparable with that mentioned in previous studies of quasar clustering.1134 Outramοἱal.(2001) used the value 400 km/s obtained from he Llubble Volume Simulations: daAngelaetal.(2005) ixed the value SOO km/s and found that this value gives an adequate result for s«10 5.+ Alpe region ancl noted that it is dominated by the rms pairwise redshift error 600 kni/s: he same value SOO kis was used by daAnecla and the close value 600 km/s was used by Croom (2005)., \citet{outram_2001} used the value 400 km/s obtained from the Hubble Volume Simulations; \citet{daAngela_2005} fixed the value 800 km/s and found that this value gives an adequate result for $s<10$ $h^{-1}$ Mpc region and noted that it is dominated by the rms pairwise redshift error $600$ km/s; the same value 800 km/s was used by \citet{daAngela_2008} and the close value 690 km/s was used by \citet{croom_2005}.1135. Phe last value was chosen as a mean one of the range 630-750 kms: this is a quadrature superposition of (i) the real pairwise velocity dispersion recaleulatecl with redshift estimated [rom the galaxies. pairwise velocity dispersion 500 kms (Llawkinsetal. 2003).. (1) redshift’ measurement errorobtained. [rom repeat observations. ancl (iii) velocityerror due to intrinsic emission lines shifts in QSOs (Richards 2002)..," The last value was chosen as a mean one of the range 630-750 km/s; this is a quadrature superposition of (i) the real pairwise velocity dispersion recalculated with redshift estimated from the galaxies pairwise velocity dispersion 500 km/s \citep{hawkins_2003}, (ii) redshift measurement errorobtained from repeat observations, and (iii) velocityerror due to intrinsic emission lines shifts in QSOs \citep{richards_2002}. ."1136 Only Mountrichasetal.(2009). treating the velocity dispersion as a free parameter estimated.its value [or a sample of quasars and. luminous red. galaxies (LIC) as 620 km/s and 727 km/s (two values are the result. of, Only \citet{Mountrichas_2009} treating the velocity dispersion as a free parameter estimatedits value for a sample of quasars and luminous red galaxies (LRG) as 620 km/s and 727 km/s (two values are the result of1137Recurrent novae (RNe) are ordinary novae (binary svstems with mass accreting onto a white dwarl until (hermonuclear runaway is triggered) for which the recurrence time scale is between a decade and a century. such that more than one eruption has been observed 1964: Bode Evans 2008: Evans οἱ al.,"Recurrent novae (RNe) are ordinary novae (binary systems with mass accreting onto a white dwarf until thermonuclear runaway is triggered) for which the recurrence time scale is between a decade and a century, such that more than one eruption has been observed (Payne-Gaposchkin 1964; Bode Evans 2008; Evans et al."1138 2008)., 2008).1139 To have the last recurrence time scale. the novae must have the white dwarl near the Chandrasekhar mass and have a high accretion rate.," To have the fast recurrence time scale, the novae must have the white dwarf near the Chandrasekhar mass and have a high accretion rate."1140 These properties. at lace value. imply that the white dwarf will soon exceed the Chandrasekhar mass and become a Type Ia supernova. and thus RNe are one of (he premier candidates for the progenitor class of these supernovae.," These properties, at face value, imply that the white dwarf will soon exceed the Chandrasekhar mass and become a Type Ia supernova, and thus RNe are one of the premier candidates for the progenitor class of these supernovae."1141 RNe t(vpically have relatively fast eruptions. high ejection velocities. aud small eruption ampliticdes when compared to ordinary novae.," RNe typically have relatively fast eruptions, high ejection velocities, and small eruption amplitudes when compared to ordinary novae."1142 Only ten RNe are known with certainty in our Milkv. Way (Schaefer 2010)., Only ten RNe are known with certainty in our Milky Way (Schaefer 2010).1143 U Scorpii (U Sco) previously erupted in March 1999 with a peak al V=7.5 mag (Schaeler 2010)., U Scorpii (U Sco) previously erupted in March 1999 with a peak at V=7.5 mag (Schaefer 2010).1144 In quiescence. it has Vzz17.6 and has deep/ofal eclipses taking it down to V—18.9 mag (Schaefer 2010) with an orbital period of 1.23 days (Schaeler 1990; Schaeler Ringwald 1995).," In quiescence, it has $\approx$ 17.6 and has deep eclipses taking it down to V=18.9 mag (Schaefer 2010) with an orbital period of 1.23 days (Schaefer 1990; Schaefer Ringwald 1995)."1145 U Sco is the lastest of all known novae. fading by three magnitudes from peak in just 2.6 davs. while its rise from minimum to peak is 6-12 hours (Schaefer 2010).," U Sco is the fastest of all known novae, fading by three magnitudes from peak in just 2.6 days, while its rise from minimum to peak is 6-12 hours (Schaefer 2010)."1146 No light echo was detected to deep limits alter the 1987 eruption (Schaefer 1983)., No light echo was detected to deep limits after the 1987 eruption (Schaefer 1988).1147 U Seo has now had ten known eruptions. in (he vears 1863. 1906. 1917. 1936. 1945. 1969. 1979. 1957. 1999 (Schaefer 2010). and now 2010 as we report in this paper.," U Sco has now had ten known eruptions, in the years 1863, 1906, 1917, 1936, 1945, 1969, 1979, 1987, 1999 (Schaefer 2010), and now 2010 as we report in this paper."1148 With the discovery of the 1917. 1945. and 1969 eruptions (Schaeler 2001: 2004). it has become apparent that U Sco has outbursts at intervals of 10+2 vears since 1900.," With the discovery of the 1917, 1945, and 1969 eruptions (Schaefer 2001; 2004), it has become apparent that U Sco has outbursts at intervals of $10\pm2$ years since 1900."1149 The exceptions to Chis are the two intervals of 19 and 24 vears. which are easily interpreted as being double intervals. with eruptions around 1927 and 1957 having been missed. (," The exceptions to this are the two intervals of 19 and 24 years, which are easily interpreted as being double intervals, with eruptions around 1927 and 1957 having been missed. ("1150U Sco is 3οἳ from the Sun every 28 November. so a significant [raction of its very [ast eruptions must be missed.),"U Sco is $3.6\degr$ from the Sun every 28 November, so a significant fraction of its very fast eruptions must be missed.)"1151 With Chis. it became apparent that the next eruption of U Seo should occur in (hie vear 2009--2.," With this, it became apparent that the next eruption of U Sco should occur in the year $2009\pm2$."1152 Schaefer (2005) made a better prediction. on the physical basis that (he time," Schaefer (2005) made a better prediction, on the physical basis that the time"1153as in the Milky Way.,as in the Milky Way.1154 The model is described in Matteucci et al. (, The model is described in Matteucci et al. (11551998) where we address the reader for more details.,1998) where we address the reader for more details.1156" The star formation rate is given by: Le, normalized to the 1Utial total volume deusitv.", The star formation rate is given by: i.e. normalized to the initial total volume density.1157 c(t) 1s asstuued to drop to 0 at the ouset of the ealactic wind., $\psi(t)$ is assumed to drop to 0 at the onset of the galactic wind.1158 The quantity vis expressed in units of Cry| and represents the efficiency of star ornation. namely the iuverse of the time scale of star formation.," The quantity $\nu$ is expressed in units of $\rm Gyr^{-1}$ and represents the efficiency of star formation, namely the inverse of the time scale of star formation."1159 The star formation is ASSI to stop after t16 development of a galactic wine OCCULToο before than | Gar. from the begiuuiug of star formatic1. for all the ealaxies listed above.," The star formation is assumed to stop after the development of a galactic wind occurring before than 1 Gyr, from the beginning of star formation, for all the galaxies listed above."1160 Thereore. the star fornation rate iM these galaxies can be cojsdderec as a strong burst whic1i does not last more tha jid Cs a idis sjorter da more nassive svstenas.," Therefore, the star formation rate in these galaxies can be considered as a strong burst which does not last more than 1 Gyr and is shorter in more massive systems."1161" This is obtaiucc by assuwine that the star formation efficiency dICLCASCS with eaactic mass tlis producing au "" inverse wind OFfect. as ¢escribed in Matteucci (1991). where the ealactic wind occtis before i more massive than iu less massive ¢5lipticaS."," This is obtained by assuming that the star formation efficiency increases with galactic mass thus producing an “ inverse wind” effect, as described in Matteucci (1994), where the galactic wind occurs before in more massive than in less massive ellipticals."1162 As a consequence of this. the star formation )eriod is onuecr m smaller svsteis thus allowing the SNe Ta to subsautially pollute the ISAL," As a consequence of this, the star formation period is longer in smaller systems thus allowing the SNe Ia to substantially pollute the ISM."1163 This effect can explain 1ο observed increase of the [a/Fe] ratio with galactic nass (AVGxthev et al., This effect can explain the observed increase of the $\alpha$ /Fe] ratio with galactic mass (Worthey et al.1164 1992: Matteucci 1991). which is rot obtaired in oa classic wind scenario. where the more nassive objects formi stars for a longer time (Larson. 1971).," 1992; Matteucci 1994), which is not obtained in a classic wind scenario, where the more massive objects form stars for a longer time (Larson, 1974)."1165 The galactic wind develops as à consequence of the enerev transfer froii SNe into the ISM., The galactic wind develops as a consequence of the energy transfer from SNe into the ISM.1166" In fact. when the hermal enerevOo, of the Ooeas becomes IlarecrOo than the bindingC» cnerev of the eas. the wind starts (Arimoto Yoshii. 1987: Matteucci Tornambe 1987: Matteucci 1992. 199 Dipi loc al."," In fact, when the thermal energy of the gas becomes larger than the binding energy of the gas, the wind starts (Arimoto Yoshii, 1987; Matteucci Tornambe' 1987; Matteucci 1992, 1994; Pipino et al."1167 2002)., 2002).1168 In order to compute tlic|] udine enerev of the e:Us solic asstuuptions have to be uade about he ealactic potential wel., In order to compute the binding energy of the gas some assumptions have to be made about the galactic potential well.1169 In particular. it is ussted that a1 cliplcas possess heavy hit diffuse dark 11aatter halos: : ratio heween the haf-lish radius aud t1ο radius of li dark luatter core {ηνμονRdar το. aud a ratio dar tohWUnOUs mass of ]0 are assunied.," In particular, it is assumed that all ellipticals possess heavy but diffuse dark matter halos; a ratio between the half-light radius and the radius of the dark matter core $R_{luminous}/R_{dark}$ =0.10 and a ratio dark to luminous mass of 10 are assumed."1170 The D aud I& Iuniuosities for the ellipticals of differeut lle9SCR are colmputed by means of the spectro-photomoetric inodel o| Jimenez et al. (, The B and K luminosities for the ellipticals of different masses are computed by means of the spectro-photometric model of Jimenez et al. (11711999) and are usxl to compute the SN Ta vate iun SM aud the nova rate per unit of Ly. respectively.,"1999) and are used to compute the SN Ia rate in SNu and the nova rate per unit of $L_K$, respectively."1172 The mai cliffereices between the inodel for the Galaxy. and the modcl for an elliptical οalaxy couceru the different SER. which is much strougcr in the carliest stages. and then is set o zero after the ealacic Wind in the case of ellipticals.," The main differences between the model for the Galaxy, and the model for an elliptical galaxy concern the different SFR, which is much stronger in the earliest stages, and then is set to zero after the galactic wind in the case of ellipticals."1173" It is worth notius that «ealactic winds in the case of elliptica enlaxies seen necessary to explain their lack of gas aud tιο Chemica παςit of the ICM. wherCas he Galactic model does not take iuto account the occurrence of a stroug πια, maiilv. because of the strong eyavitatknal potential well associated witji our Galaxy. aud the xeseuce of the gas in the Galactic clik."," It is worth noting that galactic winds in the case of elliptical galaxies seem necessary to explain their lack of gas and the chemical enrichment of the ICM, whereas the Galactic model does not take into account the occurrence of a strong wind, mainly because of the strong gravitational potential well associated with our Galaxy, and the presence of the gas in the Galactic disk."1174 We adopt two differeut initia mass functions (IAIFs): the Salpeter Grpapr1.35 ) one aud the Arimoto Yoshii (OST) ΕΕ 0.95) One., We adopt two different initial mass functions (IMFs): the Salpeter $x_{IMF}=1.35$ ) one and the Arimoto Yoshii (1987) $x_{IMF}=0.95$ ) one.1175 Iu tevet. successful models of chemical evolution of ellipticals have shown," In fact, successful models of chemical evolution of ellipticals have shown"1176Figue 2 shows the Eddington cnhaucement factor for variable inclination. of slabs (upper panels) and for changing density contrast of vertical slabs (lower panels).,Figure 2 shows the Eddington enhancement factor for variable inclination of slabs (upper panels) and for changing density contrast of vertical slabs (lower panels).1177 Iu all cases. the Thomsou depth of the Ligh density slabs Tj ls constant but the optical depth across low density regions mereases from values7z« οτι >1 from left to right (see caption of Fie.," In all cases, the Thomson depth of the high density slabs $\tau_{h}$ is constant but the optical depth across low density regions increases from values$\tau_{l}<1$ to $\tau_{l}>1$ from left to right (see caption of Fig."1178 2 for more details)., 2 for more details).1179 As expected. the Eddington factor increases as the slabs rotate toward. the vertical direction because the atinosphere effectively becomes more porous (see upper panels}.," As expected, the Eddington factor increases as the slabs rotate toward the vertical direction because the atmosphere effectively becomes more porous (see upper panels)."1180 When the slabs are vertical. the flux cnhancemenut factor increases as the density contrast σι becomes larger for constant mean density.," When the slabs are vertical, the flux enhancement factor increases as the density contrast $\sigma_{h}/\sigma_{l}$ becomes larger for constant mean density."1181 This is due to the fact that the vohune filling factor of the high-density eas decreases while that of the low-density eas increases. but the respective masses of the two density phases remain the same.," This is due to the fact that the volume filling factor of the high-density gas decreases while that of the low-density gas increases, but the respective masses of the two density phases remain the same."1182" Therefore. the mean. voluueaveielted. flux is where fe is the volume filius factor of the dense gas and Fy aud F), are the fluxes propagating through tenuous and dense regions. respectively."," Therefore, the mean, volume-weighted, flux is where $f_{v}$ is the volume filling factor of the dense gas and $F_{l}$ and $F_{h}$ are the fluxes propagating through tenuous and dense regions, respectively."1183" As the density coutrast lnereases and ff, decreases. radiation tends to flow primarily through the low deusity channels aud. therefore. tore flux is necessary to exert the same total force as in the homogeneous case because radiation iuteracts less efficicutly with teuuous eas."," As the density contrast increases and $f_{v}$ decreases, radiation tends to “flow” primarily through the low density channels and, therefore, more flux is necessary to exert the same total force as in the homogeneous case because radiation interacts less efficiently with tenuous gas."1184 Quautitatively. iu the diffusion nuit. we have (Shaviv1998) When most volume is in the low-density phase but most mass is in the ligh-deusity phase (ie. fe>0 or €n/Q> O) then |zfopy/pi it fe9ppp.," Quantitatively, in the diffusion limit, we have \citep{sh98}1185 When most volume is in the low-density phase but most mass is in the high-density phase (i.e., $f_{v}\rightarrow 0$ or $\xi_{h}/\xi_{l}\rightarrow 0$ ), then $l\approx f_{v}\rho_{h}/\rho_{l}$ if $f_{v}\gg\rho_{l}/\rho_{h}$."1186 This qualitatively explains why 7 decreases with 7= lat constant density contrast 05/0; (cf, This qualitatively explains why $l$ decreases with $\tau_{l}\ge 1$ at constant density contrast $\sigma_{h}/\sigma_{l}$ (cf.1187 third aud fourth columns on Fie., third and fourth columns on Fig.1188 2)., 2).1189 At small optical depth τι. equation (23) would lead to very inaccurate answers.," At small optical depth $\tau_{l}$, equation (23) would lead to very inaccurate answers."1190" For example. equation (23) predicts |~23 for vertical slabs with 75=(kl aud e,/o;=100. compared to the actual value 7—5 aud our analytic result —L from eq. ("," For example, equation (23) predicts $l\sim 23$ for vertical slabs with $\tau_{l}=0.1$ and $\sigma_{h}/\sigma_{l}=100$, compared to the actual value $l\sim 5$ and our analytic result $\sim 4$ from eq. ("119121) (cf,21) (cf.1192 lower left panel), lower left panel).1193" This discrepancy is due larecly to ueelect of the amisotropy of the radiation feld. whereas our approach eives much more accurate results even in such au extreme case,"," This discrepancy is due largely to neglect of the anisotropy of the radiation field, whereas our approach gives much more accurate results even in such an extreme case."1194 Moreover. note that the “anisotropy term” in our expression for the flux cuhancement factor. which ix proportional to (No)?=(ojσι)”. vanishes for large Thomson depths aud thus equatious (21) aud (15) reduce to equation (23) iu the diffusion limit.," Moreover, note that the “anisotropy term” in our expression for the flux enhancement factor, which is proportional to $(\Delta\sigma)^{2}1195=(\sigma_{h}-\sigma_{l})^{2}$, vanishes for large Thomson depths and thus equations (21) and (15) reduce to equation (23) in the diffusion limit."1196" We also considered ""unulti-streaua approximation schemes in order to account for the radiatiou anisotropy. but found the ""iutensitv moment” approach developed here to be in significantly better agreement with Monte Carlo simulations."," We also considered “multi-stream” approximation schemes in order to account for the radiation anisotropy, but found the “intensity moment” approach developed here to be in significantly better agreement with Monte Carlo simulations."1197 We have considered radiative transfer deep within extremely inhomogeneous atinospheres. and lave demonstrated that. under such conditions. radiation viscosifv — Le. the off-diagonal clemeuts of the radiation stress tensor — plays an maportaut role.," We have considered radiative transfer deep within extremely inhomogeneous atmospheres, and have demonstrated that, under such conditions, radiation viscosity – i.e., the off-diagonal elements of the radiation stress tensor – plays an important role."1198 Our approach is sienificautly more accurate than approaches based on the diffusion οςation aud iulti-trezu approximation., Our approach is significantly more accurate than approaches based on the diffusion equation and multi-stream approximation.1199 The technique develyped here cau be applied to the noulinear evohtion of radiation-driven dustabilifies iun accretion clisks., The technique developed here can be applied to the nonlinear evolution of radiation-driven instabilities in accretion disks.1200" Iu parictlar. it can be used to study the dynamical coupine of iater and radiation iu order to determune the characteristic leneth scales and density contrasts arising frou ""photoilu ibble instability."," In particular, it can be used to study the dynamical coupling of matter and radiation in order to determine the characteristic length scales and density contrasts arising from “photon bubble” instability."

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