ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 In this toy model we consider a very simple scenario., In this toy model we consider a very simple scenario.3 We consider AN number of spherical. non-overlapping and randomly placed ionized bubbles in a uniform H I medium in the coeval cube.," We consider $N$ number of spherical, non-overlapping and randomly placed ionized bubbles in a uniform H I medium in the coeval cube."4 The spherically averaged 3D power spectrum for such a scenario can be written as ου” where |;=iz4 and WAR?) is the spherical top hat window function defined as Now Pap(h)=aanMP for eLfRus. where Fax IS the radius of the biggest bubble in the cube since ΤΕ(11)s| for rox].," The spherically averaged 3D power spectrum for such a scenario can be written as V_i^2 W^2(kR_i) where $V_i=\frac{4}{3} \pi R_i^3$ and $W(kR)$ is the spherical top hat window function defined as (kR)] Now $P_{\rm{3D}}(k)=\sum_{i=1}^N V_i^2$ for $k<1/R_{\rm{max}}$, where $R_{\rm{max}}$ is the radius of the biggest bubble in the cube since $ W(x) \approx 1$ for $x<1$."5 For the coeval eube we assume that all bubbles are of the same size V... therefore the power spectrum can simply be written as. NV.," For the coeval cube we assume that all bubbles are of the same size $V_o$, therefore the power spectrum can simply be written as, }(k)=N V_o^2."6‘ Because of the evolution effect in the light cone cube. bubbles at the back side will appear smaller and bubbles at the front side will appear bigger and in addition their shapes could be somewhat elongated along the LOS (seeFigure|ofMajumdaretal.," Because of the evolution effect in the light cone cube, bubbles at the back side will appear smaller and bubbles at the front side will appear bigger and in addition their shapes could be somewhat elongated along the LOS \citep[see Figure 1 of][]{majumdar10}."72010) To make our calculations simpler we assume the bubbles in the light cone cube are spherical but have different sizes V;|AV)., To make our calculations simpler we assume the bubbles in the light cone cube are spherical but have different sizes $V_o+\Delta V_i$.8 As we saw in the simulation results. the global ionization fraction for light cone cubes is almost the same as in the coeval cube at the central redshift. so we assume Y.AV;=0.," As we saw in the simulation results, the global ionization fraction for light cone cubes is almost the same as in the coeval cube at the central redshift, so we assume $\sum_{i=1}^N \Delta V_i=0$."9 The spherically averaged 3D power spectrum for the light cone cube at larger scales is then given as. The above equation explains two major features we see in the simulation.," The spherically averaged 3D power spectrum for the light cone cube at larger scales is then given as, The above equation explains two major features we see in the simulation."10 First it explains why the light cone effect is relatively small., First it explains why the light cone effect is relatively small.11 We see that the effect cancels out in the linear order., We see that the effect cancels out in the linear order.12" Only the 2nd order term Σο,AVS survives the averaging and affects the light cone power spectrum.", Only the 2nd order term $\sum_{i=1}^N\Delta V_i^2$ survives the averaging and affects the light cone power spectrum.13" So in this sense the light cone effect is a ""2nd order in the averaged power spectrum,", So in this sense the light cone effect is a `2nd order effect' in the spherically averaged power spectrum.14 Second. becauseeffect»»scales is always sphericallypositive the power is always enhanced at larger 12MMwhich is exactly what we see in the simulation.," Second, because$\sum_{i=1}^N\Delta V_i^2$ is always positive the power is always enhanced at larger scales which is exactly what we see in the simulation."15 When the bubble sizes are not identical in the coeval, When the bubble sizes are not identical in the coeval16 =tly H=iytlhy (25; and lo < h<Tinarty (26: 2 andb=fy in (22))(this willbea goodapproximation forlarger ir:see Figure 3)) gilu/2) ο... - gio2)(1 2/EH )),In this section we will briefly show that the quantum interest inequalities \ref{x_max_ie}) ) and \ref{q_int4}) ) and hence all the results from the previous section also apply to the massive scalar field in 4 dimensional Minkowski spacetime.17" where wehave used (25)) fy).fy Usingfy(25))to (27)) wecan findthe range of z:0positive<2 X fae=(Umar— 1/2. When r=tine, (and theexact inequality. (22))givese> —1). 2= tyra,— 1."," Fewster and Eveson \cite{fe_flat} obtained the following expression for $\rom$ in $4D$ Minkowski spacetime for a scalar field of mass $m$ : where $A$ is a positive constant, $\widehat{g^{1/2}}(s)$ is the Fourier transform of $g^{1/2}(t)$, and one integrates over the spectrum of field modes (i.e. $\omega_k=\sqrt{|k|^2+m^2}$, $\vec{k}$ is the 3-momentum of a mode with frequency $\omega_k$ )."18"With these definitions(23))becomes (alter some simplification) it large z,,,, » D dad I 3(5X5 —cU/;—4 :- €,>um 1) m | 1 (30) Figure5)). separation increases."," If $\rom(m)$ denotes the minimum negative energy bound for a field of mass $m$ with sampling function $g(t)$, then where $\robm(m)$ is the minimum bound with a sampling function $\bar{g}(t)=g(t/x)/x$ (the Fourier transform of the scaling relation is $\widehat{\bar{g}^{1/2}}(s)=\sqrt{x} \widehat{g^{1/2}}(sx)$ )."19«quite clearly of quantum exampleerowswill eive (almost linearly)accurate lower pulse quantum Bul onlya noteif caution:choiceof(his function an overe," But notice from \ref{fe_rom}) ) that $\rom(mx) \ge \rom(m)$ for $x\ge 1$ (due to the $m$ dependance in the integrand and lower limit of the second integral), hence Thus a massive scalar field will have tighter constraints on allowed negative energies than a massless field (compare \ref{scale}) )), and all the inequalities derived in the previous section remain valid for a massive field. ("20stimate boundthe “real”on ,"In 2D Minkowski space \ref{m_scale}) ) holds with $x^4$ replaced by $x^2$, but one cannot conclude that \ref{m_scale2}) ) is valid $\forall x$ .)"21"the interestforgiven distributionourof negativesampling Recall doesnthattthe “real” tye,nme μον Dist satisIv function inequality (e."," The scaling argument used to prove quantum interest for scalar fields might readily be applied to other quantum fields, such as the Electromagnetic (EM) field or Dirac field, and possibly to certain curved spacetimes or Minkowski space with boundary conditions as in the Casimir effect."22g.(15))(9))for withanychoicelarge») of will samplingnotgive function. stringentFor example.lowera sharpl, Ford and Roman found a quantum inequality for EM fields in 4D Minkowski space using a Lorentzian sampling function \cite{fr_em}: This expression certainly indicates that a scaling relation like \ref{scale}) ) holds for EM fields.23ybounds peaked(Pmind. samplingand consequently (15))will," The only complicationto obtaining definitive results in this case is that the Lorentzian sampling function does not have compact support, so one cannot rule out the possibility"24 Despite being invoked to power a variety of energetic astrophysical phenomena. the detailed structure and dynamics of black hole accretion flows remain a central problem in astrophysics.," Despite being invoked to power a variety of energetic astrophysical phenomena, the detailed structure and dynamics of black hole accretion flows remain a central problem in astrophysics."25 Moreover. using electromagnetic observations to probe the structure and dynamies of the black hole spacetimes requires a substantial understanding of the physical processes that determine the fate of the accreting matter.," Moreover, using electromagnetic observations to probe the structure and dynamics of the black hole spacetimes requires a substantial understanding of the physical processes that determine the fate of the accreting matter."26 Only recently has it become possible to probe this physics via large-scale computational simulations., Only recently has it become possible to probe this physics via large-scale computational simulations.27 Nevertheless. ab initio calculations are beyond our present capability. requiring numerous simplifying. and 1n some cases unphysical. assumptions.," Nevertheless, ab initio calculations are beyond our present capability, requiring numerous simplifying, and in some cases unphysical, assumptions."28 This is evidenced the number of models to explain the various propertiesby of accreting black hole profferedcandidates., This is evidenced by the number of models proffered to explain the various properties of accreting black hole candidates.29 In turn. this efforts to use electromagnetic observations to ambiguityprobe the complicatesstructure and dynamics of the the black hole.," In turn, this ambiguity complicates efforts to use electromagnetic observations to probe the structure and dynamics of the spacetime surrounding the black hole."30 By spacetimevirtue of its surroundingproximity. the supermassive black hole at the center of the Milky Way. associated with the bright radio point source Sagittarius A* (Ser A*). provides an unparalleled opportunity to study black hole accretion in detail.," By virtue of its proximity, the supermassive black hole at the center of the Milky Way, associated with the bright radio point source Sagittarius A* (Sgr A*), provides an unparalleled opportunity to study black hole accretion in detail."31 For this reason. Ser A* may serve as an exemplar of the larger class of supermassive black holes specifically. and of black holes in general.," For this reason, Sgr A* may serve as an exemplar of the larger class of supermassive black holes specifically, and of black holes in general."32 Presently. the best estimates of the mass and distance of Ser A* come from the observations of orbiting stars.," Presently, the best estimates of the mass and distance of Sgr A* come from the observations of orbiting stars."33 These have yielded M=4.3+0.5«109M... and D=8.3t0.4 kpe. respectively. where both include the uncertainties (???)..," These have yielded $M=4.3\pm0.5\times10^6\,\Ms$ and $D=8.3\pm0.4\,\kpc$ , respectively, where both include the uncertainties \citep{Ghez_etal:08,Gill_etal:09a,Gill_etal:09b}."34 The mass is necessarily confined to within the periapse of nearby stars. giving a maximum radius of roughly 10°AU~3«100GM/c. ruling out many extended objects.," The mass is necessarily confined to within the periapse of nearby stars, giving a maximum radius of roughly $10^2\,\AU\simeq3\times10^3GM/c^2$, ruling out many extended objects."35 These represent the best mass measurement for any known black hole to date., These represent the best mass measurement for any known black hole to date.36 In addition to the dynamical observations. a wealth of spectral and polarization data exists for Ser A*.," In addition to the dynamical observations, a wealth of spectral and polarization data exists for Sgr A*."37 From these it is apparent that Ser A* is unlike many active galactic nuclei. being vastly underluminous. emitting a bolometric luminosity of roughly 10ere. approximately 107? of Eddington.," From these it is apparent that Sgr A* is unlike many active galactic nuclei, being vastly underluminous, emitting a bolometric luminosity of roughly $10^{36}\,\erg$, approximately $10^{-9}$ of Eddington."38 This is especially small in light of the considerable amount of gas within the black hole's sphere of influence. presumably available for aceretion (22)...," This is especially small in light of the considerable amount of gas within the black hole's sphere of influence, presumably available for accretion \citep{Loeb-Waxm:07,Cuad-Naya-Mart:07}."39 As a result it is widely accepted that Ser A*'s accretion flow is qualitatively different from those in its active analogs. though perhaps indicative of the roughly of black holes that are presently not in an active phase.," As a result it is widely accepted that Sgr A*'s accretion flow is qualitatively different from those in its active analogs, though perhaps indicative of the roughly of black holes that are presently not in an active phase."40 Nevertheless. the existing spectral and polarization data has a canonical set of components all models for Ser A* producedinclude: populations of thermal and nonthermal electrons. nearly equipartition magnetic fields.," Nevertheless, the existing spectral and polarization data has produced a canonical set of components all models for Sgr A* include: populations of thermal and nonthermal electrons, nearly equipartition magnetic fields."41 Less certain is the structure of the emission region., Less certain is the structure of the emission region.42 This is evidenced by the variety of models that have been proposed (e.g..222???)," This is evidenced by the variety of models that have been proposed \citep[e.g.,][]{Nara_etal:98,Blan-Bege:99,Falc-Mark:00,Yuan-Mark-Falc:02,Yuan-Quat-Nara:03,Loeb-Waxm:07}."43" Despite being able to reproduce the observed features of Ser A*, these differ dramatically in the morphology of the emitting region."," Despite being able to reproduce the observed features of Sgr A*, these differ dramatically in the morphology of the emitting region."44 As a consequence. many of the theoretical ambiguities can be immediately addressed by direct probes of the spatial distribution of the emitting plasma surrounding the central supermassive black hole.," As a consequence, many of the theoretical ambiguities can be immediately addressed by direct probes of the spatial distribution of the emitting plasma surrounding the central supermassive black hole."45 The spectrum of Ser A* peaks near millimeter wavelengths. implying a transition from optically thick to. optically thin emission.," The spectrum of Sgr A* peaks near millimeter wavelengths, implying a transition from optically thick to optically thin emission."46 The location of this emission is currently debated. however the presence of short-timescale variability at millimeter. near-infrared and X-ray wavelengths implies that optically thin emission ts dominated by contributions arising," The location of this emission is currently debated, however the presence of short-timescale variability at millimeter, near-infrared and X-ray wavelengths implies that optically thin emission is dominated by contributions arising"47"oof our data and lower our detection threshold, we repeat the approach of L09 and calculate a weighted average of all LSD profiles obtained in each observing run.","of our data and lower our detection threshold, we repeat the approach of L09 and calculate a weighted average of all LSD profiles obtained in each observing run."48" We therefore end up with 4 distinct averaged Stokes V profiles, plus grand average obtained by averaging all LSD profiles collected in 2008 and 2009 (Fig. 1,,"," We therefore end up with 4 distinct averaged Stokes V profiles, plus grand average obtained by averaging all LSD profiles collected in 2008 and 2009 (Fig. \ref{fig:stokesv},"49 upper frame)., upper frame).50" All averaged profiles show a polarized signal located around the central radial velocity of the intensity profile (about -13.7 s!)), although the signal detection is ambiguous for the two observing runs suffering from the highest noise levels."," All averaged profiles show a polarized signal located around the central radial velocity of the intensity profile (about -13.7 ), although the signal detection is ambiguous for the two observing runs suffering from the highest noise levels."51" Using a ttest similar to the one proposed by LO9, the false-alarm probability of a detection is equal to 3x107""! in July 2008, 3x in June 2009, 7x10? in September 2009, 107! in October 2009 and 10:15 in the grand average."," Using a test similar to the one proposed by L09, the false-alarm probability of a detection is equal to $3\times 10^{-11}$ in July 2008, $3\times 10^{-1}$ in June 2009, $7\times 10^{-3}$ in September 2009, $10^{-1}$ in October 2009 and $10^{-15}$ in the grand average."52" Compared to the first averaged profile obtained in 2008, no statistically significant difference is observed in the signatures obtained during the 2009 observing runs."," Compared to the first averaged profile obtained in 2008, no statistically significant difference is observed in the signatures obtained during the 2009 observing runs."53" We emphasize that a similar signature is obtained using either NARVAL or ESPaDOnS data, and with or without inserting the Atmospheric Dispersion Corrector (ADC) in the beam prior to the polarimeter (observations from 2008 were taken without the ADC)."," We emphasize that a similar signature is obtained using either NARVAL or ESPaDOnS data, and with or without inserting the Atmospheric Dispersion Corrector (ADC) in the beam prior to the polarimeter (observations from 2008 were taken without the ADC)."54" The grand average LSD profile, obtained by grouping all available profiles together, has a noise level of 1.6x10-61. and displays a polarized signal antisymmetric about the line centre, with a peak-to-peak amplitude of 1.8x107."," The grand average LSD profile, obtained by grouping all available profiles together, has a noise level of $1.6\times 10^{-6}I_c$ and displays a polarized signal antisymmetric about the line centre, with a peak-to-peak amplitude of $1.8\times 10^{-5}I_c$."55" The full velocity width of the signature is about 20 s!(or 10 velocity bins), showing that it is comfortably resolved by our instrumental setup."," The full velocity width of the signature is about 20 (or 10 velocity bins), showing that it is comfortably resolved by our instrumental setup."56" By using another combination of the four sub-exposures constituting the Stokes V spectrum, it is possible to calculate a ""null"" line profile which should contain no stellar polarized signal and from which many spurious instrumental signatures can be diagnosed."," By using another combination of the four sub-exposures constituting the Stokes V spectrum, it is possible to calculate a ""null"" line profile which should contain no stellar polarized signal and from which many spurious instrumental signatures can be diagnosed."57" Similarly to L09, we do not detect any significant spurious signature when running this control calculation (Fig. 1,,"," Similarly to L09, we do not detect any significant spurious signature when running this control calculation (Fig. \ref{fig:stokesv},"58 lower panel) suggesting that most instrumental effects are kept below a limit of about 10767.," lower panel), suggesting that most instrumental effects are kept below a limit of about $10^{-6}I_c$."59" Any significant spurious signature generated by a variability in the shape of Stokes I profiles (for instance, owing to the presence of stellar pulsations) can be ruled out by this test, since (a) its associated signal should show up in the control profile as well and (b) the line variability is unlikely to be confined to the line-center only, contrary to the observed Stokes V signal."," Any significant spurious signature generated by a variability in the shape of Stokes I profiles (for instance, owing to the presence of stellar pulsations) can be ruled out by this test, since (a) its associated signal should show up in the control profile as well and (b) the line variability is unlikely to be confined to the line-center only, contrary to the observed Stokes V signal."60" A detailed investigation of Stokes I variability, based on the same observing material, is presented by Bóhhm et al."," A detailed investigation of Stokes I variability, based on the same observing material, is presented by Böhhm et al."61 2010 (in prep)., 2010 (in prep).62The dispersion in the A. band magnitudes along the fy: diagram. has been used as an indicator of the evolution of the stellar population in powerful galaxies2004).,The dispersion in the $K-$ band magnitudes along the $K-z$ diagram has been used as an indicator of the evolution of the stellar population in powerful galaxies.63.. We caleulated the dispersion of the measured A band magnitudes from the line of best fit (Paper D) and compared this value in redshift bins., We calculated the dispersion of the measured $K-$ band magnitudes from the line of best fit (Paper I) and compared this value in redshift bins.64 Galaxies in each unit of redshift (rom z=O L1 uptoz—3 4 had standard deviations of 1.1. 1.0. 0.7 and 0.5 respectively.," Galaxies in each unit of redshift from $z=0$ –1 up to $z=3$ –4 had standard deviations of 1.1, 1.0, 0.7 and 0.8 respectively."65 Ehe standard deviation for z«2 was 1.0. decreasing to 0.7 for z>2.," The standard deviation for $z<2$ was 1.0, decreasing to 0.7 for $z>2$."66 found. an increase in the dispersion of A band magnitude for z2 galaxies and usecl this to support their model that ο2 is the epoch of galaxy formation., found an increase in the dispersion of $K-$ band magnitude for $z>2$ galaxies and used this to support their model that $z>2$ is the epoch of galaxy formation.67 Our results do not. support. this miocdel. but instead we see a slight. decrease in dispersion. at. higher redshifts. which is more consistent with the observations of(2001).," Our results do not support this model, but instead we see a slight decrease in dispersion at higher redshifts, which is more consistent with the observations of."68. We need to caution that if there is a significant contribution to the Av band magnitude from non-stellar emission. (scattered. or transmitted. ACN light. emission. lines) then the assumption that the dispersion in the A—z plot is indicative of the stellar evolution is compromised.," We need to caution that if there is a significant contribution to the $K-$ band magnitude from non-stellar emission (scattered or transmitted AGN light, emission lines), then the assumption that the dispersion in the $K-z$ plot is indicative of the stellar evolution is compromised."69 While redshifts have not. been measured. for. our complete sample. the low scatter around the fyz relation seems at least consistent with a mocel in which the epoch of formation of ellipticals may be at a similar high redshift (2;c d) with passive evolution since then.," While redshifts have not been measured for our complete sample, the low scatter around the $K-z$ relation seems at least consistent with a model in which the epoch of formation of ellipticals may be at a similar high redshift $z>4$ ), with passive evolution since then."70 tz >1. the SUAISSNVSS sources also appear slightly fainter than the 3€. 6€ ancl TC radio galaxies.," At $z>1$, the SUMSS–NVSS sources also appear slightly fainter than the 3C, 6C and 7C radio galaxies."71 H£ the. A band Light is indeed. dominated by stars. this can be interpreted. as a lower average mass in the range 104 1027 MAL.2004)..," If the $K-$ band light is indeed dominated by stars, this can be interpreted as a lower average mass in the range $^{11}$ $^{12}$ $_{\odot}$."72. This would be consistent with the lower radio luminosities ofthe SUAISSNVSS sources implving less massive central black holes in their host ealaxies., This would be consistent with the lower radio luminosities ofthe SUMSS–NVSS sources implying less massive central black holes in their host galaxies.73 In Paper Lowe used the A2 relation to predict. the mecian redshift of our sample to be 1.75., In Paper I we used the $K-z$ relation to predict the median redshift of our sample to be 1.75.74 Ehe distribution of measurecl redshifts forour sample is shown in Fig. 5..," The distribution of measured redshifts forour sample is shown in Fig. \ref{K-z},"75 with a median z of 1.2., with a median $z$ of 1.2.76" Lo the galaxies listed as ""undetected! in ‘Table 2. are not detected because they are at high recdshift (at least z2 1.75). then this would shift the median z up to 1.5."," If the galaxies listed as `undetected' in Table \ref{spectroscopyjournal}77 are not detected because they are at high redshift (at least $z>1.75$ ), then this would shift the median $z$ up to 1.5."78 There also remains a further 23 sources for which the redshift is vet to be determined: 15 of the 23 are faint chough GNS7]2 18.3) to lie at 2>1.75. therefore increasing the median z to at least 1.75.," There also remains a further 23 sources for which the redshift is yet to be determined; 15 of the 23 are faint enough $K[8\arcsec]>18.3$ ) to lie at $z>1.75$, therefore increasing the median $z$ to at least 1.75."79 Pherefore we anticipate that the mecian redshift will be close to that predicted when we have spectroscopic redshifts for the complete sample., Therefore we anticipate that the median redshift will be close to that predicted when we have spectroscopic redshifts for the complete sample.80 The redshift clistribution from the A2 relation included: at. [east three galaxies with z 4., The redshift distribution from the $K-z$ relation included at least three galaxies with $z>4$ .81 Follow-up spectroscopy has vet to find any galaxies with z2 4., Follow-up spectroscopy has yet to find any galaxies with $z>4$ .82"where the flare region"" has source functionJ"" ον. optical"" depth τν. and subtends solid. angle Q=z72gfdp ","where the flare region has source function $J_\nu$, optical depth $\tau_\nu$, and subtends solid angle $\Omega = \pi R^2/d^2$ "83influence of a possible second dvnaimo in the shallower sub-surface lavers.,influence of a possible second dynamo in the shallower sub-surface layers.84 The unclear trend obtained in this analvsis neitlier supports nor rules out the arguments made by (2010)., The unclear trend obtained in this analysis neither supports nor rules out the arguments made by \citet{bison10}.85. We emphasize that (his analvsis has been made possible with (he access {ο continuous high-precision oscillation data for more than a solar cycle. in particular during the prolonged unusually low activity period.," We emphasize that this analysis has been made possible with the access to continuous high-precision oscillation data for more than a solar cycle, in particular during the prolonged unusually low activity period."86 These results are important to understand the origin of the modification of oscillation frequencies which have been known to vary with the phase of activity. evele for last two decades. but. whose detailed physical mechanism still remains an open question.," These results are important to understand the origin of the modification of oscillation frequencies which have been known to vary with the phase of activity cycle for last two decades, but whose detailed physical mechanism still remains an open question."87 We thank the anonuvmous releree for useful comments., We thank the anonymous referee for useful comments.88 We also thank John Leibacher for many discussions and critically reading the manuscript., We also thank John Leibacher for many discussions and critically reading the manuscript.89 This paper utilizes data obtained bv the GONG program. managed by the National Solar Observatory. which is operated by AURA. Inc. under a cooperative agreement with the National Science Foundation.," This paper utilizes data obtained by the GONG program, managed by the National Solar Observatory, which is operated by AURA, Inc. under a cooperative agreement with the National Science Foundation."90 The data were acquired by instruments operated bv the Big Bear Solar Observatory. High Altitude Observatory. Learmonth Solar Observatory. Udaipur Solar Observatory. Instituto de Astroffssica de Canarias. and Cerro Tololo Interamerican Observatory.," The data were acquired by instruments operated by the Big Bear Solar Observatory, High Altitude Observatory, Learmonth Solar Observatory, Udaipur Solar Observatory, Instituto de Astrofíssica de Canarias, and Cerro Tololo Interamerican Observatory."91 This work has been partially supported by NASA Grant NNG-08EIS4I to National Solar Observatory., This work has been partially supported by NASA Grant NNG-08EI54I to National Solar Observatory.92The calculation of angular size aud luminosity distances then follows Wright (2006).,The calculation of angular size and luminosity distances then follows Wright (2006).93 Note that the biuned distance moduli were not used for the aualysis., Note that the binned distance moduli were not used for the analysis.94 Thus the Hubble coustauts usecl when producing the binned data tables are irrelevant in the aualysis., Thus the Hubble constants used when producing the binned data tables are irrelevant in the analysis.95" But both the supernovae aud the GRBs have au associated ""nuisauce parameter. Myy aud Mery. which are adjusted to vive the best modified X? at every position in the [Qaj.Qjuwi parameter space."," But both the supernovae and the GRBs have an associated “nuisance” parameter, ${\cal M}_{SN}$ and ${\cal96M}_{GRB}$, which are adjusted to give the best modified $\chi^2$ at every position in the $\{\Omega_M, \Omega_k, w, w^\prime\}$ parameter space."97" Thus (Qn, = Ium + »log(D (2:0 πο... The loriH inη 2 Eq(7)) isη used twice.. once forH the supernovae givingη. Vy> aud ouce forH the GRBs giviugfei[n] 2XVZ;ug."," Thus _M, _k, w, ) = _i _i) _c(z) = + 5 (D_L(z; _M, _k, w, )) The form in \ref{eq:HD}) ) is used twice, once for the supernovae giving $\chi^2_{SN}$ and once for the GRBs giving $\chi^2_{GRB}$."98 1Contours of. the sum of. these two terms are shown in. Figurexs 5.., Contours of the sum of these two terms are shown in Figure \ref{fig:Wm-Wv-both-CC-15Jan07}.99"- The acousticH scale quantitiesna (4 aud 0,35 give. a contributionH to the overall 47> of"" o ου...∕∣ Ute where n is the function from Eq(2.1)) with the trausitiou from quadratic to linear behavior set . » Dok2. ⋜↕↕∙⋝√⊼∶∙∕↸↜↽∣⊲⋝∶↽∣⊲−↥∩↕⋅↴∣⊢∖∙⋝⋅∩↕⋅↻↴↽∣⊲↴≓∪∩↕∐≺↵↕⋅∖∖↽↓↜∖≺↲⋅, ⋅"," The acoustic scale quantities $\ell_a$ and $R_{0.35}$ give a contribution to the overall $\chi^2$ of _M, _k, w, ) = _M, _k, w, _a)) + _M, _k, w, where $\hat{f}$ is the function from \ref{eq:modchi}) ) with the transition from quadratic to linear behavior set at $3 \sigma$: $\hat{f}(x) = x^2$ for$|x| < 3$ , or $6|x|-9$ otherwise."100 Contours1 of 05V7 are shown in. Figurei. -5.., Contours of $\chi^2_a$ are shown in Figure \ref{fig:Wm-Wv-both-CC-15Jan07}.101 Normally the data on T= Qai. He and 35/7 can be combined to give a prior on Q5.," Normally the data on $\Gamma = \Omega_M h$ , $H_\circ$ and $\Omega_M h^2$ can be combined to give a prior on $\Omega_M$."102" There is an overdetermiued set of equations with variables £24; aud {11 un = | uti least squares solution of these equations gives ος =67.3d:3.7kan/sec/Mpe and Qa, ", There is an overdetermined set of equations with variables $\Omega_M$ and $h$: ) ) = ) The least squares solution of these equations gives $H_\circ = 67.3 \pm 3.7$ km/sec/Mpc and $\Omega_M = 0.296 \pm 0.029$ .103Contours showingthis priorare the vertical lines in Figure 5.., Contoursshowing thisprior are the vertical lines in Figure \ref{fig:Wm-Wv-both-CC-15Jan07}. .104"where Απο 3}=2. which is appropriate for astronomical silicates. we find that the slope of the SED is equal to 4j, for the short waveleneth part of the Ravleigh-Jeaus tail of theSED aud 1oy, for the long wavelength regime. where Qui(Ao)=L1 for the particles contributing the most to the emission.","where Assuming $\beta=2$, which is appropriate for astronomical silicates, we find that the slope of the SED is equal to $-\eta_a$ for the short wavelength part of the Rayleigh-Jeans tail of theSED and $1-\eta_a$ for the long wavelength regime, where $Q_{\rm abs}(\lambda,a)=1$ for the particles contributing the most to the emission."105 Similar results have been fouud by Wratt&Dent(2002)., Similar results have been found by \cite{wyatt02}.106.. This behavior explains why the slope of the flux density iu the long waveleugth regime is not dependent on the optical properties of the eraius. as QuiA.)=1 for all exain types at these wavelengths that effectively contribute to it.," This behavior explains why the slope of the flux density in the long wavelength regime is not dependent on the optical properties of the grains, as $Q_{\rm abs}(\lambda,a)=1$ for all grain types at these wavelengths that effectively contribute to it."107" Our models viekll a quasi steady-state distribution slope of i,2:3.65. meaning that the Ravleigh-Jeaus tail eud of the SEDs should be proportional to as long as the particles are in collisional quasi state."," Our models yield a quasi steady-state distribution slope of $\eta_a\approx3.65$, meaning that the Rayleigh-Jeans tail end of the SEDs should be proportional to as long as the particles are in collisional quasi steady-state."108 To compare the computed spectra of quasi steady-state collisional disks to data. we assembled the available data for debris disks with far-IR and sibinillimeter observations.," To compare the computed spectra of quasi steady-state collisional disks to data, we assembled the available data for debris disks with far-IR and submillimeter observations."109 As a result of our analysis in 85. where we deternuned the wavelength ranee that is east scusitive to paranueters. we use only data at wavelengths larger than 250jan.," As a result of our analysis in \ref{sec:synthetic}, where we determined the wavelength range that is least sensitive to parameters, we use only data at wavelengths larger than $250~\micron$."110 To fit a power-aw to the Ravleigh-Jeaus τοσο of the SEDs. we weed a. limi of three data poiuts above our wavelength cut-off.," To fit a power-law to the Rayleigh-Jeans regime of the SEDs, we need a minimum of three data points above our wavelength cut-off."111 We found a total of ouly nine sources hat fulfill these requirements., We found a total of only nine sources that fulfill these requirements.112 We present the far-IR/subiullhineter fluxes for these sources in3., We present the far-IR/submillimeter fluxes for these sources in.113. Occasionally. published subiuilimeter measurements do rot account for systematic errors.," Occasionally, published submillimeter measurements do not account for systematic errors."114 In these cases. we applied a total of error to all ground based measurements at 350 aie 150pon and for all Uerschel data ancl iieasureimenuts above 850yan.," In these cases, we applied a total of error to all ground based measurements at 350 and $450~\micron$ and for all Herschel data and measurements above $850~\micron$."115 We also made sure that the data include all the fiux from cach source aud applied. au aperture correction estimate otherwise., We also made sure that the data included all the flux from each source and applied an aperture correction estimate otherwise.116 All corrections are Listec as notes iu. Table 3.., All corrections are listed as notes in Table \ref{tab:data}.117 We perform individual power-law fits to the data of each source as well as a fit to all sources sinultiuieouslv with a common Ravleigh-Jeaus slope., We perform individual power-law fits to the data of each source as well as a fit to all sources simultaneously with a common Rayleigh-Jeans slope.118 In Figure L1.. we present the photosphere subtracted excess enmissious for cach source in the left panels aud plot the best-fit law spectrum of the form. obtained from individual fits.," In Figure \ref{fig:stars}, we present the photosphere subtracted excess emissions for each source in the left panels and plot the best-fit power-law spectrum of the form obtained from individual fits."119 We show iu the right panels of Figure 11. the error contours of the slope and normalization of the power-law at the 1. 2. and 3o levels.," We show in the right panels of Figure \ref{fig:stars} the error contours of the slope and normalization of the power-law at the 1, 2, and $3\sigma$ levels."120" The plots also indicate the A24,/d.o.f. (the iiniuu of the reduced 47) of cach fit.", The plots also indicate the $\chi^2_{\rm min}/{\rm d.o.f.}$ (the minimum of the reduced $\chi^2$ ) of each fit.121 The solid red line represeuts the Ravleigh-Jeanus slope calculated from the Dohnauvi(1969). analytic solution. the ereen baud represcuts the best slope elven by our reference model calculation Gucliding errors from variations m the slope of the strength curve. sec Figure 7)). aud the blue baud vields our global fit solution of The global fit aud our reference model agree witlin the errors of the prediction.," The solid red line represents the Rayleigh-Jeans slope calculated from the \cite{dohnanyi69} analytic solution, the green band represents the best slope given by our reference model calculation (including errors from variations in the slope of the strength curve, see Figure \ref{fig:errs}) ), and the blue band yields our global fit solution of The global fit and our reference model agree within the errors of the prediction."122" Iu this paper. we uxed our nuuerical model introduced in Paper I to follow the evolution of a distribution of outiele masses,"," In this paper, we used our numerical model introduced in Paper I to follow the evolution of a distribution of particle masses."123 Our umunuerical model has been built O ensure mass conservation and that the resulting distribution of particles is not artificially offset due to Munerical errors. as the inteeratious of the model span over LO orders of magnitude m mass.," Our numerical model has been built to ensure mass conservation and that the resulting distribution of particles is not artificially offset due to numerical errors, as the integrations of the model span over 40 orders of magnitude in mass."124 In 82.1. of this vapor. we demonstrate that lower precision integrationus can lead to shallower particle distributions.," In \ref{sec:var} of this paper, we demonstrate that lower precision integrations can lead to shallower particle distributions."125 We varied all twelve collisional. all six system. anc all wee nunierieal variables of our model and examined ie. effects of these variations on the evolution of je particle mass distribution.," We varied all twelve collisional, all six system, and all three numerical variables of our model and examined the effects of these variations on the evolution of the particle mass distribution."126 The quasi steady-state yarticle distribution of the collisional svsteni is extremely robust against variations in its variables. with the y.ronecst effects οὐαπο from chauges to the tensile streneth curve (IHolsappleetal.2002:Benz&Asphang1999).," The quasi steady-state particle distribution of the collisional system is extremely robust against variations in its variables, with the strongest effects occurring from changes to the tensile strength curve \citep{holsapple02,benz99}."127. Even these variations have mill effects on the slope of the particle mass distribution. modifving it only between the values of 1.51 and 1.91 (3.52 aud 3.82 in size space. respectively).," Even these variations have mild effects on the slope of the particle mass distribution, modifying it only between the values of 1.84 and 1.94 (3.52 and 3.82 in size space, respectively)."128 We find the dust mass distribution of our reference inodel to be 1.88 (3.65 im size space)., We find the dust mass distribution of our reference model to be $1.88$ (3.65 in size space).129 We find that waves occur when the collisional velocities are high or when particle streneths are low at the mass distribution cut-off. where the radiation force blowout dominates the cyvuamics.," We find that waves occur when the collisional velocities are high or when particle strengths are low at the mass distribution cut-off, where the radiation force blowout dominates the dynamics."130 Nonetheless. in §??.. we show that a simple power-law amass (size) distribution is au appropriate approximation even for exteuded disks witli components only outside of 10 - 15AU for solar- and 50 - 60AU for early-type stars.," Nonetheless, in \ref{sec:approx}, we show that a simple power-law mass (size) distribution is an appropriate approximation even for extended disks with components only outside of 10 - $15~{\rm AU}$ for solar- and 50 - $60~{\rm AU}$ for early-type stars."131" The Ravleigh-Jeaus tail of the debris disk SEDs is dominated bv the mediun sized particles. whose mass distribution is less affected by possible wavy structures,"," The Rayleigh-Jeans tail of the debris disk SEDs is dominated by the medium sized particles, whose mass distribution is less affected by possible wavy structures."132 We derive a simple formula that gives the slope of the nieasured fux deusitv in the Ravleigh-Jeaus part of the SEDs as This nuplies that the mass distribution slope itself could. in principle. be measured from long-waveleneth observations.," We derive a simple formula that gives the slope of the measured flux density in the Rayleigh-Jeans part of the SEDs as This implies that the mass distribution slope itself could, in principle, be measured from long-wavelength observations."133 We assemble a list of niue debris disks that have been measured at the far-IR. submillimeter. and iillimeter wavelengths aud examine the Ravleigh-Jeanus slope of their cussions.," We assemble a list of nine debris disks that have been measured at the far-IR, submillimeter, and millimeter wavelengths and examine the Rayleigh-Jeans slope of their emissions."134 Our predictions of a slope of ]—2.65£0.05 aerces well with the observations. which have a elobal slope fit of/=2.58 £0.06.," Our predictions of a slope of $l = 2.65 \pm 0.05$ agrees well with the observations, which have a global slope fit of $l=2.58\pm0.06$ ."135 Support for this work was provided by NASA through Contract Number 1255091 issued bv JPL/Caltech., Support for this work was provided by NASA through Contract Number 1255094 issued by JPL/Caltech.136 We thank Viktor Zubko aud Rarl Misselt for providing the uunnercal code to calculate the optical properties of larec eralus., We thank Viktor Zubko and Karl Misselt for providing the numerical code to calculate the optical properties of large grains.137(2009).. with the Coronagraphic Low-Order Wavefront Scusor (CLOWFS). a scheme using tle licht occulted by a modified focal plane mask as an accurate pointing tracker.,", with the Coronagraphic Low-Order Wavefront Sensor (CLOWFS), a scheme using the light occulted by a modified focal plane mask as an accurate pointing tracker."138 The idea of using the light otherwise lost in the coronagraphic focal plane for tracking is rot a novelty., The idea of using the light otherwise lost in the coronagraphic focal plane for tracking is not a novelty.139 It was for instance successfully implemented on the LYOT project (Dighyctal. 2006).., It was for instance successfully implemented on the LYOT project \citep{2006ApJ...650..484D}.140 The calibration uuit of CPT also uses the ight occulted by the focal plaue mask to measure ow order aberrations. after re-dinagiug the pupi ij a Shack ILhutmann type wavefrout sensor (Wallaceetal.2010): pointing performance with lis scheme reaches 2 mas for typical expecte observing⋅↜ conditions.," The calibration unit of GPI also uses the light occulted by the focal plane mask to measure low order aberrations, after re-imaging the pupil in a Shack Hartmann type wavefront sensor \citep{2010SPIE.7736E.179W}: pointing performance with this scheme reaches 2 mas for typical expected observing conditions."141⋅⋅ Maximum. sensitivity.∙∙∙ to pointing∙∙ crrors ds. reached when the light from opposite edges of he pupil is allowed to interfere. which naturally lappens in the focal plane.," Maximum sensitivity to pointing errors is reached when the light from opposite edges of the pupil is allowed to interfere, which naturally happens in the focal plane."142 In this respect. while robust to a wide range of errors. eosa Shack-HartinauData appear ↙⊓∙optimal to‘ measure pointine: vecause it splits the pupil iuto sub-pupils. this capability is lost. resulting iu lesser performance han a focal-plane based svavefrout seusime scheme (Civon2005)..," In this respect, while robust to a wide range of errors, a Shack-Hartman doesn't appear optimal to measure pointing: because it splits the pupil into sub-pupils, this capability is lost, resulting in lesser performance than a focal-plane based wavefront sensing scheme \citep{2005ApJ...629..592G}."143" The originality of the CLOWFS desigu resides in its dualzoue focal pluie mask. designed to suppress a strong offset∙ to the signal.∙ carrving. mostt of oftthe ]power lutbut no information.""∙⋠↙≯∙: : ina ⊀≚≼↧⋜⋯⊓↖⇁↸∖∪↻↑↕↸⊳↴∖↴↕⋟⊱⇪↥⋅↸∖↸⊳∪∐↴"," The originality of the CLOWFS design resides in its dual-zone focal plane mask, designed to suppress a strong offset to the signal, carrying most of the power but no information, in a manner reminiscent of strioscopy."144∖↴⊓⋅⋯⊳⊓≺⊔∐⋜↧↴∖↴⋝↸∖↸∖∐manner ⋅⋅ ↴ ‘ offsesot t!us thejerwise otherwiseotlmipereepti ⋅⋅causeserceptiblede (Warderchangesdl due to sinall poiutiug errors into a macroscopic chauge of the CLOWFS image., The suppression of this offset turns the otherwise imperceptible changes due to small pointing errors into a macroscopic change of the CLOWFS image.145 Using this scheme. CGuvonetal.(2009) were able to stabilize tip-tilt at the level of LO2A/D in a closed-loop system for A=633 nm. in a laboratory experiucut.," Using this scheme, \citet{2009ApJ...693...75G} were able to stabilize tip-tilt at the level of $10^{-3} \lambda/D$ in a closed-loop system for $\lambda=633$ nm, in a laboratory experiment."146 The nup of CLOWES SCEXAQ eurmeutexhibits pointing ementaresidualsJon <0.2 mas. withon a 50 Iz frame rate.," The current implementation of CLOWFS on SCExAO exhibits pointing residuals $<$ 0.2 mas, with a 50 Hz frame rate."147 level of performace is quitevery dm this work that additional remarkable.using theCLOWES be achieved in post-processing. aud nuplementatious of an iurproved subtraction of coronagraplic our scheme fo low-order aberrations in a long coronagrap," While this level of performance is quite remarkable, we demonstrate in this work that additional calibration can be achieved in post-processing, and lead to an improved subtraction of coronagraphic leaks due to low-order aberrations in a long exposure."148hie imaging. the SCEXAO systems as a testbed. is highly demonstrate a 10 times improvement of non-conuuon detection limit over a classical calibration ix however angular separation of a few A/D. the c," Using the SCExAO system as a testbed, we experimentally demonstrate a 40 times improvement of the detection limit over a classical calibration procedure at angular separation of a few $\lambda/D$."149oronagraphic is organized as follows: inSection 2.. the1 we introduce how to use CLOWES for post processing of coronagraphic iuages.," This paper is organized as follows: in Section \ref{sec:method}, we introduce how to use CLOWFS for post processing of coronagraphic images."150 Iu Section ?7?.. we describe the inplemenutation of the concept ou the SCEXxAO experiment of the Subaru telescope. aud we present our results iu Section ??..," In Section \ref{sec:exp}, we describe the implementation of the concept on the SCExAO experiment of the Subaru telescope, and we present our results in Section \ref{Sec:results}."151 In Section ??.. we summarise our results aud discuss possible updates fo the presented CLOWPS configuration.," In Section \ref{sec:discussion}, we summarise our results and discuss possible updates to the presented CLOWFS configuration."152" A hieh. performance. ""PSF calibration. procedure such as LOCT (Lattemierectal.2007)... is based on a direct analysis of the science data alone."," A high performance PSF calibration procedure such as LOCI \citep{2007ApJ...660..770L}, is based on a direct analysis of the science data alone."153 Yet near the edge of the coronagraplic mask. if is inpossible..: from:: such data ouly. to distinguishDa. between the signal3o of: an actual faintAE companionF and the oue of a systematic tip-tilt excursion off the coronagraphic mask at a eiven azimuth. that would be for imstance due to a vibration.," Yet near the edge of the coronagraphic mask, it is impossible, from such data only, to distinguish between the signal of an actual faint companion and the one of a systematic tip-tilt excursion off the coronagraphic mask at a given azimuth, that would be for instance due to a vibration."154 acquired with: Το. ΝΕ⋅during a⋅↙ lone doesu't exposure on the science camera can however be used to discriminate the two situations. in post-processing.," Data acquired with CLOWFS during a long exposure on the science camera can however be used to discriminate the two situations, in post-processing."155 The scheme proposed iu this paper is a form of adaptive optics PSF recoustruction. which uses nieasurenieuts acquired in a wavefrout seusor to estimate the long-exposure PSF in the science camera (Veranetal.1997:Ceudron2006).. : ↥⋅↸∖⋯∐∐↴∖↴↸⊳↸∖∐↑∪↕↴∖↴⊓⋅↕∪↴∖↴," The scheme proposed in this paper is a form of adaptive optics PSF reconstruction, which uses measurements acquired in a wavefront sensor to estimate the long-exposure PSF in the science camera \citep{1997JOSAA..14.3057V, 2006A&A...457..359G}."156↸⊳≺∏≻⋅↖↽∙↽∕∏∐∖↴∖↴↿∏∏∐⋅↸∖↴∖∷∖↴↕∪∐∪↕↑↕∐↴∖↴↽∙ ⊲ ⋅ nuplemented ou several adaptive optics svstenuis &Chelli2000:Jolissaintctoeal.2010)...wen and relies ou the fact that the wavefront scusor. by mncasuring residual wavefrout errors at a fixed spatial samplue. can be used to estimate the inner part of the PSF iu the science camera.," Adaptive Optics PSF reconstruction has been implemented on several adaptive optics systems \citep{2000A&AS..142..119H,2010SPIE.7736E..48J}, and relies on the fact that the wavefront sensor, by measuring residual wavefront errors at a fixed spatial sampling, can be used to estimate the inner part of the PSF in the science camera."157 This estimation can be done at the wavefrout sensing sampling speed (typically 100 Tz to 1XITz). aud ix then averaged for the duration of the Iu---," This estimation can be done at the wavefront sensing sampling speed (typically 100 Hz to 1kHz), and is then averaged for the duration of the science exposure."158 this⋅↴ paper. woedy reconstruct While sciencethisexposure. imuer part of the corouagraphic PSF we deimoustrate telemetry.," In this paper, we reconstruct the very inner part of the coronagraphic PSF using CLOWFS telemetry."159" Conipared to previous calibration can adaptive optics PSF recoustruction. lead to is better suited to high contrast leaks due as it uses a seusor which exposure, Using scusitive to low order aberrations and free we experimentally path errors."," Compared to previous implementations of adaptive optics PSF reconstruction, our scheme is better suited to high contrast coronagraphic imaging, as it uses a sensor which is highly sensitive to low order aberrations and free of non-common path errors."160 Our PSF reconstruction of the limited to the verv inner part of procedure at PSF. and is most effective in This paper A/D wide area iuuuediatelv around the," Our PSF reconstruction is however limited to the very inner part of the coronagraphic PSF, and is most effective in the 1 $\lambda$ /D wide area immediately around the"161aceretion disc and it becomes enutraiued.,accretion disc and it becomes entrained.162 Let us cousider a quautitative estimate: we consider a case where the juvenile planet has collapsed rapidly to fori a relativeM7 dense body., Let us consider a quantitative estimate: we consider a case where the juvenile planet has collapsed rapidly to form a relatively dense body.163 We asstje that the juvenile planet has density pp510*kem and nxves throeh an aceretion dise iu a rouguly cireularH orbitH at radiusH 4?=4107>ii.," We assume that the juvenile planet has density $\rho_{\rm p}\approx 10^3\,{\rm kg\,m}^{-3}$ and moves through an accretion disc in a roughly circular orbit at radius $R\approx 10^{12}\,{\rm m}$."164 The densityH ofH gas iH1 the protostellar disc is qui uuce‘ain and it omust be highly. variable: we assume that tle eas οy in the accretion disc : this 'aclius is pycAv©10Pkem (this is a representative ligure. COLlslsteut with the «ala used Wilkiusi1.Mehlilig&Uski (2008))).," The density of gas in the protostellar disc is quite uncertain and it must be highly variable; we assume that the gas density in the accretion disc at this radius is $\rho_{\rm g}\approx 10^{-6}\,{\rm kg\,m}^{-3}$ (this is a representative figure, consistent with the data used by \citet{Wil+08}) )."165" Finally. we assume the juvenile plael has mass i1,=107""MoC0 (apprimately 10"" solar inasses). correspoudiug to a linear cdineunsion acAv10i."," Finally, we assume the juvenile planet has mass $M_{\rm p}=10^{27}\,{\rm kg}$ (approximately $10^{-3}$ solar masses), corresponding to a linear dimension $a\approx 10^8\,{\rm m}$."166 I he orbit lies wit e disc. with each orbit he juvenile planet therefore ylaces a lass Of gas approximately equa 440423107kg.," If the orbit lies within the disc, with each orbit the juvenile planet therefore displaces a mass of gas approximately equal to $10^{23}\,{\rm kg}$."167 This estimate indicates that it will be enined by te accretion dise over 101 orbi. that is within a period of approximately LO?vr.," This estimate indicates that it will be entrained by the accretion disc over $10^4$ orbits, that is within a period of approximately $10^5\,{\rm yr}$."168 LE tel elite of the protostellar accretiou disc yproximately T=10°vr i ihis case we conclude tha the juveule planet would reach a lealy circular aid equatorial orbit. alter rualkiug a very large umber of eccentric orbits.," If the lifetime of the protostellar accretion disc is approximately $T=10^6\,{\rm yr}$, in this case we conclude that the juvenile planet would reach a nearly circular and equatorial orbit, after making a very large number of eccentric orbits."169 The values of he mass of tl ejvelile plauet aud the deusiy ol gas 1 the accretion dise cotd vary by orders of iagnitude., The values of the mass of the juvenile planet and the density of gas in the accretion disc could vary by orders of magnitude.170 La OLe extreme. where the juvenie planet has not vet collapsed to a ugh deusity and roves through al acc'etiou disc with higher density than was assuimed above. iS uotion may be eiined to the dise wihiu the period of a few orbits.," In one extreme, where the juvenile planet has not yet collapsed to a high density and moves through an accretion disc with higher density than was assumed above, its motion may be entrained to the disc within the period of a few orbits."171 For a the situation described N the estimate a)ove. a juvenile plalet may make a large nulaber of orbits before becomi[n]0 entrained to the «isc.," For a the situation described by the estimate above, a juvenile planet may make a large number of orbits before becoming entrained to the disc."172 In other cases. wl he deusity of gas iu he clise is low or when the juveuie jxlane has au inclijec orbit. (which speids little time passing throwel the accretion disc). it night 101 be entr:üued by the disc at al.," In other cases, where the density of gas in the disc is low or when the juvenile planet has an inclined orbit (which spends little time passing through the accretion disc), it might not be entrained by the disc at all."173 The mocel therefore pre‘ts that some planetary systenis woulc eud up with planets in icliied. auk ec'ceutric orbits. wule others would have all plane ILL rotelily circular aud equaorial o‘bits.," The model therefore predicts that some planetary systems would end up with planets in inclined and eccentric orbits, while others would have all planets in roughly circular and equatorial orbits."174 li line with tlie arguluelis presened above. the current ist of extrasolar plauets coutal iiy exagles which have highly eccertrie orbits. as well as exalljles wih near circular orbits (Butler.Wright&MNareyοίJOG).," In line with the arguments presented above, the current list of extrasolar planets contains many examples which have highly eccentric orbits, as well as examples with near circular orbits \citep{But+06}."175" Most. discussions of the lute""acion of platets with gaseous λα{ου n tre accretion disc have focused on tjelr gravitational ineraction: the planet caines a gravitational clisturbance of the disc. t11 the resuling gravitatioial fied frou the clise can catse the planet to spira in 1996)."," Most discussions of the interaction of planets with gaseous matter in the accretion disc have focused on their gravitational interaction: the planet causes a gravitational disturbance of the disc, and the resulting gravitational field from the disc can cause the planet to spiral in \citep{Lin+96}."176. This mocle is ap»ropriate when the plane moves In an approximately circular ‘bit. at nearly the same velocity as tle gas in the circumstella lise.," This model is appropriate when the planet moves in an approximately circular orbit, at nearly the same velocity as the gas in the circumstellar disc."177 How'ever our mocel allows for panets to be created in eccentric orbis aud non-equatorial orljs. so that their orjts will involve largee velocities relative to the egas in he accretion disc.," However our model allows for planets to be created in eccentric orbits and non-equatorial orbits, so that their orbits will involve large velocities relative to the gas in the accretion disc."178 In our model clilferent plvsical processes t'e relevant., In our model different physical processes are relevant.179 We have shown above that direct rnomentum trausfer is important. wlereas the larger relative velocity is expected to reduce the effectiveness of the ο‘avitational interaction discussed by Liu.Bodeuheimer&Richardson(1996).," We have shown above that direct momentum transfer is important, whereas the larger relative velocity is expected to reduce the effectiveness of the gravitational interaction discussed by \cite{Lin+96}."180. L3planets The gravitational collapse of the juvenile planets proceeds uutil it is balauced by the effects ol pressure aud centrifugal forces., 4.3 The gravitational collapse of the juvenile planets proceeds until it is balanced by the effects of pressure and centrifugal forces.181 The latter are expected to determiue that the iuitial state of a, The latter are expected to determine that the initial state of a182Llowever. the pulse broadening because of the interstellar scattering as predicted. from C&bLbL model. (87M ms). appears to be over-estimated by a Large factor. given. the narrow widths of bright pulses (about 20 ms or narrower) and the width of pulse components in the average pulse-profile.,"However, the pulse broadening because of the interstellar scattering as predicted from L model $87^{+50}_{-35}$ ms), appears to be over-estimated by a large factor, given the narrow widths of bright pulses (about 20 ms or narrower) and the width of pulse components in the average pulse-profile."183 Follow-up observations at. higher frequencies. (100. to 300 Mllz) and with better sensitivity would be useful in improving DAL estimate. and for confirming the most likely association of the bright pulses with the pulsar.," Follow-up observations at higher frequencies (100 to 300 MHz) and with better sensitivity would be useful in improving DM estimate, and for confirming the most likely association of the bright pulses with the pulsar."184 Lo confirmed. the comparison between the pulse profiles in the two extreme parts of the electromagnetic spectrum. and. the location of bright. single pulses would. provide further insight. into emission in the form of giant pulses (e.g.Llankins2003:Ixnightetal.2006) or radiation spikes etal. 1997).," If confirmed, the comparison between the pulse profiles in the two extreme parts of the electromagnetic spectrum, and the location of bright single pulses would provide further insight into emission in the form of giant pulses \citep[e.g.][]{Hankins03,Knight06} or radiation spikes \citep[e.g.][]{Ables97}."185. In this paper. we have presented. results of our two kinds of searches (at 34.5 MIaIzZ) for radio pulses in the direction of the LAT pulsar J1732-3131. ancl report in detail an intriguing detection of periodic pulsed signal at DAL of about 15.44 pcjcc.," In this paper, we have presented results of our two kinds of searches (at 34.5 MHz) for radio pulses in the direction of the LAT pulsar J1732-3131, and report in detail an intriguing detection of periodic pulsed signal at DM of about $15.44$ pc/cc."186 The possible reasons for its non-detection. in our other observing sessions and at higher frequencies. and related. implications are ciscussed.," The possible reasons for its non-detection, in our other observing sessions and at higher frequencies, and related implications are discussed."187 The DM based distance estimate. using Cordes Lazio electron. density model. matches well with earlier. estimates. based. on 5-rav emission elliciency.," The DM based distance estimate, using Cordes Lazio electron density model, matches well with earlier estimates based on $\gamma$ -ray emission efficiency."188 These results also demonstrate the potential ancl the importance of such searches/surveys at low radio frequencies., These results also demonstrate the potential and the importance of such searches/surveys at low radio frequencies.189 We hope our estimate of DM along with the other results will help follow-ups at suitable higher frequencies., We hope our estimate of DM along with the other results will help follow-ups at suitable higher frequencies.190 We thank our referee. Fernando Camilo. for his comments and sugeestions which have helped in improving our manuscript.," We thank our referee, Fernando Camilo, for his comments and suggestions which have helped in improving our manuscript."191 The CGauribidanur radio telescope is jointly operated by the Raman Research Institute and the Indian Institute of Astrophysies., The Gauribidanur radio telescope is jointly operated by the Raman Research Institute and the Indian Institute of Astrophysics.192 We gratefully acknowledge the support from the observatory stall, We gratefully acknowledge the support from the observatory staff.193 YAL is thankful to Larsha Raichur. Nishant Singh and Wasim Raja for useful discussions and ΠΠ on the manuscript.," YM is thankful to Harsha Raichur, Nishant Singh and Wasim Raja for useful discussions and comments on the manuscript."194Another interestine feature in relfig:pd. is the tiny bt clearly observable scatter Dor the very first dip at he low-/ eud.,Another interesting feature in \\ref{fig:pd} is the tiny but clearly observable scatter for the very first dip at the $l$ end.195 This scatter corresponds to extrerle power spectrum variations that reside on the surace of the confidence set and have an up-ttri at low / values., This scatter corresponds to extreme power spectrum variations that reside on the surface of the confidence set and have an up-turn at low $l$ values.196 Iu the ACDM cosmology. such àp-turn at the low-/ endl is primarily the result of the integrated Sachs-Wolle (ISW) effect. aud is seeLinall parametric ACDM fits in reffig:fitsl aud LL.," In the $\Lambda$ CDM cosmology, such up-turn at the $l$ end is primarily the result of the integrated Sachs-Wolfe (ISW) effect, and is seen in all parametric $\Lambda$ CDM fits in \\ref{fig:fits1} and \ref{fig:fits2}."197 It would therefore be interesting to see what coul be said about the low-/ up-turu (aid thereby about the ISW effect) based ou the nonparametric coufideuce sel., It would therefore be interesting to see what could be said about the $l$ up-turn (and thereby about the ISW effect) based on the nonparametric confidence set.198 Notice that our nonpartnetrie fits. which are at the center of their 'espective confidence sets. CLO ιοί show a low-/ up-(ur.," Notice that our nonparametric fits, which are at the center of their respective confidence sets, do not show a $l$ up-turn."199 However. the 7-year parametric ACDM fit. e.g.. does show a clear lp-turn at the low-/ encL," However, the 7-year parametric $\Lambda$ CDM fit, e.g., does show a clear up-turn at the $l$ end."200 This parametric [it is at a distance correspoicing to coiUiclence level of about (zz0.120: see Table Lit‘oOn our 7-year holparametric full-Lfreecor lnionotone fit., This parametric fit is at a distance corresponding to confidence level of about $\approx 0.12\sigma$; see Table \ref{tab:lambda}) ) from our 7-year nonparametric full-freedom monotone fit.201 This means hat the confidence set for tle T-vear nonparaljetric fit contains specra witl al wed up-turn at vost as far away as the 7-vear parametric fit., This means that the confidence set for the 7-year nonparametric fit contains spectra with a $l$ up-turn at most as far away as the 7-year parametric fit.202 We therefore conclude conservaively that the low-/ ρα as a feature of the CMB angular power spectrin cannot be ruled ottal any coulideuce evel in excess of about Actually. there are indications iu our resuis (not shown) that such up-urned variations of he spectrum may be much closer to the center ol the coulideuce set for the 7-vear full-freeclous uonotone fit: this needs further investigation.," We therefore conclude conservatively that the $l$ up-turn as a feature of the CMB angular power spectrum cannot be ruled out at any confidence level in excess of about Actually, there are indications in our results (not shown) that such up-turned variations of the spectrum may be much closer to the center of the confidence set for the 7-year full-freedom monotone fit; this needs further investigation."203 Iu this paper. we have presetec a comparative noiparametric analysis of the WMAP Ἱ-. 3-. 2-. aud 7-vear data reeases for the CMB augular )Ower spectrum. Using a nonparanetric fuuctiou estimation methocdoloe€v (??)..," In this paper, we have presented a comparative nonparametric analysis of the WMAP 1-, 3-, 5-, and 7-year data releases for the CMB angular power spectrum, using a nonparametric function estimation methodology \citep{GMN+2004,BSM+2007}."204 In the context of this uethodology. we have also presented. our owl numerical forumatiou for mininizatiou of he iuverse-nolse-weighted risk fiuction subject to monotonicity coumnstraluis. ald a prescription for obaiming monotone uouparaimetric fits that are closer to cosinologic| expectatious on smoothjess.," In the context of this methodology, we have also presented our own numerical formulation for minimization of the inverse-noise-weighted risk function subject to monotonicity constraints, and a prescription for obtaining monotone nonparametric fits that are closer to cosmological expectations on smoothness."205 For all data realizatious. we have presented results pertaining to tl ollowü& questions: (a) how wel is the angular power spectrum determined by thedata alone. (b) Iv well is the ACDMI mocel supported by a mocdel-iu«cepeudent. nonparametric. data-driven analysis. au (c) wlal are the realistic uncertainties on peak/dip locations aud heights.," For all data realizations, we have presented results pertaining to the following questions: (a) how well is the angular power spectrum determined by the data alone, (b) how well is the $\Lambda$ CDM model supported by a model-independent, nonparametric, data-driven analysis, and (c) what are the realistic uncertainties on peak/dip locations and heights."206 The motivation for the anaysis preseuted here was to explore what coud be iulerrecd about the CAMB aigular power spectrum in a mocdel-indepeudent. data-driven manner.," The motivation for the analysis presented here was to explore what could be inferred about the CMB angular power spectrum in a model-independent, data-driven manner."207 Ou te other haud. the basi€ physics of the CMB is quite well established.," On the other hand, the basic physics of the CMB is quite well established."208 It would therefore be useul to connect a nonparametric/modelindependent analysis such as ours with the known physics of the CMB, It would therefore be useful to connect a nonparametric/model-independent analysis such as ours with the known physics of the CMB209Below we derive the formulas given by equation (20) in the main text.,Below we derive the formulas given by equation (20) in the main text.210 To begin with. we apply the induction method to the well-known Schott formula Performing term-by-term cillerentiation of the series and finding the first- and second-order derivatives. one can obtain Above we have taken into account the Bessel equation. AY(ο)|Jo(s)fsμίαyi)=o.," To begin with, we apply the induction method to the well-known Schott formula Performing term-by-term differentiation of the series and finding the first- and second-order derivatives, one can obtain Above we have taken into account the Bessel equation, $J_\nu^{\prime\prime}(z)+J_\nu^\prime (z)/z+J_\nu211(1-\nu^2/z^2)=0$."212 Using equations CX1))-CX2)) vields Then making use of the integral (Ciradshtevn&Itvzhik1980) ," Using equations \ref{a1}) \ref{a2}) ) yields Then making use of the integral \citep{gr}213 "214attempted to identify the possible cause of contamination. but were unable to associate the extra component with any metal line from either of the other 2 DLAs.,"attempted to identify the possible cause of contamination, but were unable to associate the extra component with any metal line from either of the other 2 DLAs."215 To show that the etfect of the blending is probably negligible. we assume that the fractional distribution of gas is the same for Co as for the other metals and that therefore the N.(Co)=12.94 represents of the total. implving a total V(Co) = 13.08. almost exactly what is determined from the original fit.," To show that the effect of the blending is probably negligible, we assume that the fractional distribution of gas is the same for Co as for the other metals and that therefore the $N_r$ (Co)=12.94 represents of the total, implying a total $N$ (Co) = 13.08, almost exactly what is determined from the original fit."216 There is no Co LE A2012 absorption visible in the combined UVES|LIERES spectrum of Q1223|17. see Figure 2.," There is no Co II $\lambda$ 2012 absorption visible in the combined UVES+HIRES spectrum of Q1223+17, see Figure 2."217 To place an upper limit on the Αςο LE) value and in turn the Co/TIe ratio. we integrated the apparent column over à small region covering the Co IL A2012 transition.," To place an upper limit on the $N$ (Co II) value and in turn the Co/Fe ratio, we integrated the apparent column over a small region covering the Co II $\lambda$ 2012 transition."218 For high S/N data iin the limit that In(lο) or). this is equivalent to deriving the equivalent width over the same velocity range and then calculating the column density assuming the linear curve of growth.," For high S/N data in the limit that $\ln (1-x) \approx x$ ), this is equivalent to deriving the equivalent width over the same velocity range and then calculating the column density assuming the linear curve of growth."219 Although the stronger metal line transitions span over 200 Fe HE 1608). to place the tightest constraints on the Co/le ratio we integrated. [rom —20 km/s to. |20 km/s which covers the strongest Fe Ll feature in the velocity profile.," Although the stronger metal line transitions span over 200 Fe II 1608), to place the tightest constraints on the Co/Fe ratio we integrated from $-20$ km/s to $+20$ km/s which covers the strongest Fe II feature in the velocity profile."220 Restricting our analysis to this velocity range. we lind IN (Co H)« 12.63. N (Fe W=15.05 and Co/Ee] <10.18 where the limits are at the 30 level.," Restricting our analysis to this velocity range, we find $N$ (Co $ < 12.63$ , $N$ (Fe $ = 15.05$ and [Co/Fe] $< +0.18$ where the limits are at the $3 \sigma$ level."221 lt is usually assumed in DLA abundance studies that the column densities of the singly ionized metal species are a good approximation to the total column density. of this clement. based. on observations and theoretical mocleling (e.g. Viegas 1995).," It is usually assumed in DLA abundance studies that the column densities of the singly ionized metal species are a good approximation to the total column density of this element, based on observations and theoretical modeling (e.g. Viegas 1995)."222 However. there has been some suggestion (1lowk and Sembach 1999: Izotov et al.," However, there has been some suggestion (Howk and Sembach 1999; Izotov et al."223 2000) that ionization corrections may in fact be important when deriving DLA abundances., 2000) that ionization corrections may in fact be important when deriving DLA abundances.224 Although there is some temptation to invoke ionization corrections to explain a few unusual abundance trends in DLAs. the preclietions of these models are often not borne out by observations (Pettini et al.," Although there is some temptation to invoke ionization corrections to explain a few unusual abundance trends in DLAs, the predictions of these models are often not borne out by observations (Pettini et al."225 2000: Lattanzio et al 2001)., 2000; Lattanzio et al 2001).226 In addition. Levshakoy et al. (," In addition, Levshakov et al. ("2272000) have recently shown that the physical conditions adopted: by these models are unrealistic when compared. with those observed. in local. DLA analogs.,2000) have recently shown that the physical conditions adopted by these models are unrealistic when compared with those observed in local DLA analogs.228 Here. we are. specifically concerned with the relative abundances of Co and Fe.," Here, we are specifically concerned with the relative abundances of Co and Fe."229 Even in the unlikely event that some correction is relevant to the absolute abundances as suggested by Izotov et. al. (, Even in the unlikely event that some correction is relevant to the absolute abundances as suggested by Izotov et al. (2302000). the first and. second. ionization stages of cobalt. ancl iron have very similar potentials (e.g. 7.88 eV and 7.90 eV. for Co Land Fe D so that it is highlv unlikely that an ionization correction is required when converting N(Co LE) and N(Ee LL) to Co/Fe].,"2000), the first and second ionization stages of cobalt and iron have very similar potentials (e.g. 7.88 eV and 7.90 eV for Co I and Fe I) so that it is highly unlikely that an ionization correction is required when converting N(Co II) and N(Fe II) to [Co/Fe]."231 Phe same is true for nickel. since the ionization potential for Ni Lis 7.64 eV. The presence of dust in DLAs and its tenceney to remove a fraction of the total metals from the gas phase has now been well documented (c.g. Pettini et al.," The same is true for nickel, since the ionization potential for Ni I is 7.64 eV. The presence of dust in DLAs and its tendency to remove a fraction of the total metals from the gas phase has now been well documented (e.g. Pettini et al."232 1994: Pettini et al., 1994; Pettini et al.233 1997)., 1997).234 Phis renders the task of determining the true abundances in these systems somewhat uncertain. although several attempts have been made. to recover intrinsic abundances by correcting for. Calactic depletion patterns (Vlaclilo 1998: Savaglio 2000).," This renders the task of determining the true abundances in these systems somewhat uncertain, although several attempts have been made to recover intrinsic abundances by correcting for Galactic depletion patterns (Vladilo 1998; Savaglio 2000)."235 In the case of Co. some of the more interesting Galactic (stellar) abundance patterns are seen not in absolute (e.g. Co/L]) measurements. but in the values of relative abundances Like οο] and Co/Cr].," In the case of Co, some of the more interesting Galactic (stellar) abundance patterns are seen not in absolute (e.g. [Co/H]) measurements, but in the values of relative abundances like [Co/Fe] and [Co/Cr]."236 Phe important consideration is therefore the depletion [ractions of these elements. which can be determined. from local interstellar observations.," The important consideration is therefore the depletion fractions of these elements, which can be determined from local interstellar observations."237 From Savage and Sembach (1996) and Mullman et al. (, From Savage and Sembach (1996) and Mullman et al. (2381998b) we can see that Co. Cr. Ni and ke are all depleted: to a very. similar. level.,"1998b) we can see that Co, Cr, Ni and Fe are all depleted to a very similar level."239 In addition. at relatively low levels of depletion. as is the case For 199. the small cilferences between the dust correction required. for these elements. becomes negligible (Pettini et al.," In addition, at relatively low levels of depletion, as is the case for $-$ 199, the small differences between the dust correction required for these elements becomes negligible (Pettini et al."240 2000)., 2000).241" '""herefore. we assume that we can salely investigate relative abundance ratios such as Co/Fe] without the need for either corrections for dust or ionization."," Therefore, we assume that we can safely investigate relative abundance ratios such as [Co/Fe] without the need for either corrections for dust or ionization."242 In ‘Table 4. we list the abundances of the iron peak elements (Lo. Ni. Cr. Zn. Co) measured for the two DLAs analysed herein and two other systenis found. in the literature for which useful Co/1] upper limits can be determined.," In Table 4, we list the abundances of the iron peak elements (Fe, Ni, Cr, Zn, Co) measured for the two DLAs analysed herein and two other systems found in the literature for which useful [Co/H] upper limits can be determined."243 The cobalt abundances measured in the four DLAs will be compared in Section 5.2 with those for stars spanning a range of Galactic populations anc metallicitics (Snecden Gratton 1991: MeWilliam Rich 1994: MeWilliam et al., The cobalt abundances measured in the four DLAs will be compared in Section 5.2 with those for stars spanning a range of Galactic populations and metallicities (Sneden Gratton 1991; McWilliam Rich 1994; McWilliam et al.244 1995: να. Norris. Beers 1996: Prochaska et al.," 1995; Ryan, Norris, Beers 1996; Prochaska et al."245 2000)., 2000).246 The stellar measurements use solely Co | lines., The stellar measurements use solely Co I lines.247 All stellar measurements utilised laboratory gf. values from Cardon et al. (, All stellar measurements utilised laboratory $gf$ values from Cardon et al. (2481982). with the exception.of Sneden,"1982), with the exceptionof Sneden"249reduce the poluizatiou of the light.,reduce the polarization of the light.250 The authors have ocalized scattering «pot which is probably associated with the optically thin polar regious., The authors have localized scattering 'spot' which is probably associated with the optically thin polar regions.251 Similar effect in xolurization behavior would be produced by a jet eiiergiusg orpendieular to the disk plane., Similar effect in polarization behavior would be produced by a jet emerging perpendicular to the disk plane.252 It is obvious that Piirola et ((2005) polarimetric studv of W Ser emerged to he model similar to > Lyr as proposed by Tarimanec et ((1996) from an interferometric study; and supported wv spectrypolariuectric investigation bv IHoffinan ct ({1998).," It is obvious that Piirola et (2005) polarimetric study of W Ser emerged to the model similar to $\beta$ Lyr as proposed by Harmanec et (1996) from an interferometric study, and supported by spectropolarimetric investigation by Hoffman et (1998)."253 Ον disk image reconstrucion 1s based on a model that includes only an accretion disk aud probably suffers from the absence of additional structures. in particular stream of the matter from cool companion in direction of more Inassive coniponent and/or its. already. formed accretion disk.," Our disk image reconstruction is based on a model that includes only an accretion disk and probably suffers from the absence of additional structures, in particular stream of the matter from cool companion in direction of more massive component and/or its, already, formed accretion disk."254 But pseudophotosphnere of this optically thick. disk. which las completely hidden tot componcut of the binary system has undertaken its role iu the cussion of radiation., But pseudophotosphere of this optically thick disk which has completely hidden hot component of the binary system has undertaken its role in the emission of radiation.255 Systematic photoclectric photometry of the loue-period eclipsing binary W Cru in 7-color Geneva system has been carried out at the Swiss Telescope at La Silla roni 19slL1989 and is. for the first time. preseuted iu his paper.," Systematic photoelectric photometry of the long-period eclipsing binary W Cru in 7-color Geneva system has been carried out at the Swiss Telescope at La Silla from 1984-1989 and is, for the first time, presented in this paper."256 Several cycles of this aliost 200 davs loug period binary system lave been covered., Several cycles of this almost 200 days long period binary system have been covered.257 Signatures of the still preseut activity iu this svsteni are obvious: maxima of the liebt curves are unequal. asviuuetry is present in the eclipse branches. laups/bumps are present in the elt curve aud migrate from cvele-to-cyele. the width of the eclipses are varving.," Signatures of the still present activity in this system are obvious: maxima of the light curves are unequal, asymmetry is present in the eclipse branches, humps/bumps are present in the light curve and migrate from cycle-to-cycle, the width of the eclipses are varying."258 Previous researchli ou this binary is corroborated: modeling of the light curve with an accretion disk model has revealed ecometrically aud optically thick accretion disk iu which a more massive and presumably hotter colponcut of iid-D type is completely hidden., Previous research on this binary is corroborated: modeling of the light curve with an accretion disk model has revealed geometrically and optically thick accretion disk in which a more massive and presumably hotter component of mid-B type is completely hidden.259 We have used 3D eclipse-lmapping techuique to reconstruct an accretion disk image., We have used 3D eclipse-mapping technique to reconstruct an accretion disk image.260 Since the binary is viewed almost edee-on our map revealed au nmuiage of acerction disk rim oulv., Since the binary is viewed almost edge-on our map revealed an image of accretion disk rim only.261 Its ποιο. brightucss distribution reveals rather chuupy structure., Its nonuniform brightness distribution reveals rather clumpy structure.262 We shortly discussed recoustructed disk mage with hvdrodvuauuical siuulatious of the matter flow im senu detached binaries which have shown that à uuuber of features and structures night be formed in such processes., We shortly discussed reconstructed disk image with hydrodynamical simulations of the matter flow in semi detached binaries which have shown that a number of features and structures might be formed in such processes.263the observation. and. subtracted it to give zero counts in eclipse.,"the observation, and subtracted it to give zero counts in eclipse."264 The 20 lighteurves are presented in Fig., The 20 lightcurves are presented in Fig.265 1., 1.266 Note that in reality the gaps between the observations (1 d) are large compared to the length of each observation 15 min). but they are highly contracted to display the whole dataset in one plot.," Note that in reality the gaps between the observations 1 d) are large compared to the length of each observation 15 min), but they are highly contracted to display the whole dataset in one plot."267 The most striking aspect of Fie., The most striking aspect of Fig.268 1 is that while the mean count rate increases during the outburst. the amplitude of the spin pulse increases from a quiescent level of 5030 per cent (so low that it is hard to see amonest the IHickering) to SO90 per cent.," 1 is that while the mean count rate increases during the outburst, the amplitude of the spin pulse increases from a quiescent level of 20–30 per cent (so low that it is hard to see amongst the flickering) to 80–90 per cent."269 Furthermore the increase in pulse amplitude occurs à clay before the average count rate rises., Furthermore the increase in pulse amplitude occurs a day before the average count rate rises.270 This is illustrated in Fig., This is illustrated in Fig.271 2. which shows the mean count rate and »ulse amplitude. plotted. this time. on a continuous time axis.," 2, which shows the mean count rate and pulse amplitude, plotted, this time, on a continuous time axis."272 Fig., Fig.273 3 compares the pulse profiles at all stages through he outburst., 3 compares the pulse profiles at all stages through the outburst.274 The quiescent pulse (the average of all. 14 observations before and after the outburst) is shown at the rottom ane top of the plot., The quiescent pulse (the average of all 14 observations before and after the outburst) is shown at the bottom and top of the plot.275 Ht has a low zumplitude and is clouble-peakec (as it was in the observations reported ον IWamata IxIxovama 1993)., It has a low amplitude and is double-peaked (as it was in the observations reported by Kamata Koyama 1993).276 The 6 outburst observations (observations 4 to 9 in Fig., The 6 outburst observations (observations 4 to 9 in Fig.277 2) follow in order from the bottom upwards., 2) follow in order from the bottom upwards.278 In outburst the profile becomes single peaked. and at the peak of the outburst it is nearly sinusoidal.," In outburst the profile becomes single peaked, and at the peak of the outburst it is nearly sinusoidal."279 However. both on the rise and fall (observations 5 and 9) the profile is [lat topped.," However, both on the rise and fall (observations 5 and 9) the profile is flat topped."280 The mean quiescent ancl outburst pulse profiles are shown together with the 615/25 hhardness ratios in Fig., The mean quiescent and outburst pulse profiles are shown together with the 6–15/2–5 hardness ratios in Fig.281 4., 4.282 The hardness ratio increases markedly in the outburst. from 1L.7 to 72323.," The hardness ratio increases markedly in the outburst, from 1.7 to 3."283 Further. during outburst. the hardness ratio varies with spin phase. being greater at [ux maximum.," Further, during outburst, the hardness ratio varies with spin phase, being greater at flux maximum."284 The quiescent spectrum is adequately fit by an absorbed 30 bbremsstrahlung. although the adequacy derives. Iargelv from the limited spectral resolution of and the low number of counts from such short observations.," The quiescent spectrum is adequately fit by an absorbed 30 bremsstrahlung, although the adequacy derives largely from the limited spectral resolution of and the low number of counts from such short observations."285 As a check we extracted from the archive the 40 ks observation of AY Avi performed on 1995 August 7., As a check we extracted from the archive the 40 ks observation of XY Ari performed on 1995 August 7.286 The spectral resolution of is much better but the low count rate of 0.158 limits the usefulness of the data., The spectral resolution of is much better but the low count rate of 0.158 limits the usefulness of the data.287 The 0.510. SSIS and GIS spectra are again well fitted. by. a bremsstrahlung with a (fixed) temperature of 30. aand an absorption column of LHW atom7., The 0.5–10 SIS and GIS spectra are again well fitted by a bremsstrahlung with a (fixed) temperature of 30 and an absorption column of H atom.288. With the addition of an iron line at 6.6keV. this model gives .— 10.," With the addition of an iron line at 6.6, this model gives = 1.0."289 The spectra during outburst show greatly. increased absorption. explaining the increased hardness ratio (Fig.," The spectra during outburst show greatly increased absorption, explaining the increased hardness ratio (Fig."290 5)., 5).291 ‘To investigate this we fitted the spectra. from all 20 observations with the same absorbed 30. bbremsstrahlung model. allowing the column and the normalisation of the bremsstrahlung to optimise for cach observation inciviclually.," To investigate this we fitted the spectra from all 20 observations with the same absorbed 30 bremsstrahlung model, allowing the column and the normalisation of the bremsstrahlung to optimise for each observation individually."292 The resulting parameters are plotted in the lower panels of Fig., The resulting parameters are plotted in the lower panels of Fig.293 2., 2.294 While this mocel fits the quiescent data adequately οσα LO). it was a poorer Lit to the outburst spectra = 1.5).," While this model fits the quiescent data adequately = 1.0), it was a poorer fit to the outburst spectra = 1.8)."295 Unfortunately. the low spectral resolution of means that fitting more complex models to the outburst," Unfortunately, the low spectral resolution of means that fitting more complex models to the outburst"296We can compare our results with the magnetic fields measured on the other maser species i the circiunustellar envelope.,We can compare our results with the magnetic fields measured on the other maser species in the circumstellar envelope.297 As remarked before there lave been several observations to determine the maenetic fields in the SiO mmaser regions (e.g. Darvainis ct al., As remarked before there have been several observations to determine the magnetic fields in the SiO maser regions (e.g. Barvainis et al.298 1987. Ieiiball Diuuoud 1997).," 1987, Kemball Diamond 1997)."299 Assundug that the circular polarization observed on these sources ds caused by Zee splitting. fields between 50 and LOO € have heen inferred.," Assuming that the circular polarization observed on these sources is caused by Zeeman splitting, fields between $50$ and $100$ G have been inferred."300 This had already been predicted earlier from. observations of the Zeeman splitting in ΟΠ masers. which indicated fields of 12 mG in Mira stars and up to zz10 mC in supereiants (Reid et al.," This had already been predicted earlier from observations of the Zeeman splitting in OH masers, which indicated fields of $1-2$ mG in Mira stars and up to $\approx 10$ mG in supergiants (Reid et al."301 1979. Claussen Fix 1982).," 1979, Claussen Fix 1982)."302 Various other observatious of ΟΠ iiasers have since then confirmed these Πάσης fields., Various other observations of OH masers have since then confirmed these milliGauss fields.303 The high field streugths ou the SiO mascrs however. remain the topic of debate.," The high field strengths on the SiO masers however, remain the topic of debate."304 It has been shown that fields of not more than zz30 11€. can cause the high circular polarization observed: as described in the nou-Zeenuui effect above., It has been shown that fields of not more than $\approx 30$ mG can cause the high circular polarization observed; as described in the non-Zeeman effect above.305 Also. Elitzur (1996) argues that the maguetic fields inferred on both the SiO aud the OIL maser could be lower by a factor of 8 — 10.," Also, Elitzur (1996) argues that the magnetic fields inferred on both the SiO and the OH maser could be lower by a factor of $8$ – $10$."306 Additionally. fields of teus to huudreds of Cuss iu the SiO maser region would indicate fields of the order of 10° G on the surface of the star.," Additionally, fields of tens to hundreds of Gauss in the SiO maser region would indicate fields of the order of $10^3$ G on the surface of the star."307 It was argued. that such fields could not be produced by ACB stars (Soker Tarpaz. 1992).," It was argued that such fields could not be produced by AGB stars (Soker Harpaz, 1992)."308 The Heh magnetic fields were determined Vv oassunidnes he field streneth varies with distance from he star by the relation Boxe., The high magnetic fields were determined by assuming the field strength varies with distance from the star by the relation $B \propto r^{\alpha}$.309 The expouent à depends ou the structure of the magnetic field iu the circtuustellay envelope., The exponent $\alpha$ depends on the structure of the magnetic field in the circumstellar envelope.310 A solar-type maguctic field has a=2. while or a dipole medium a=3.," A solar-type magnetic field has $\alpha = -2$, while for a dipole medium $\alpha = -3$."311 For a comparison between the different iiaser species. he results from this paper are shown in Fie. 15..," For a comparison between the different maser species, the results from this paper are shown in Fig. \ref{rb},"312 combined with results obtained on our sample of stars for the other uasers, combined with results obtained on our sample of stars for the other masers.313 The figure displays the magnetic field streugth as, The figure displays the magnetic field strength as314⋅ ↽ ⋅ ⋅∣∣⋡∣∣↨ ∖∖⊽↕⊔↥≀↧↪∖⊽≀↧↴∐↓↕≻↥≼↲∖↽≀↧↴↕⋅↕≀↧↴∐≺∢≼↲∪↓⊔↓⊓≜≟∖⇁∶∪⋅−≻∪∣∣,with a sample variance of $\sigma_{\log{V}} = 0.20^{+0.04}_{-0.04}$.315∡∣∣↓⋅ DER thanks Don Lamb for useful discussions and very gratefully acknowledges support from NSF's MRI. CAREER. PREST. and REU programs. NASA's APRA. Swift GI and IDEAS programs. and especially Leonard Goodman and Henry Cox.," DER thanks Don Lamb for useful discussions and very gratefully acknowledges support from NSF's MRI, CAREER, PREST, and REU programs, NASA's APRA, Swift GI and IDEAS programs, and especially Leonard Goodman and Henry Cox."316respectively.,respectively.317 The morphological analvsis of galaxies al redshilts 0.3 is limited from ground based images., The morphological analysis of galaxies at redshifts $\sim 0.3$ is limited from ground based images.318 In fact. at the distances of the three CGs. (he spatial scales are 4.53. 5.21. and 5.05 kpe + for MC4629. MCT7697. and. MC13069respectively!.," In fact, at the distances of the three CGs, the spatial scales are 4.53, 5.21, and 5.05 kpc $^{-1}$ for MC4629, MC7697, and MC13069."319. Nevertheless. none of the CG candidates shows conspicuous sigus of interactions and/or major distortions.," Nevertheless, none of the CG candidates shows conspicuous signs of interactions and/or major distortions."320 None of the galaxies shows evidence of significant star formation or AGN activity., None of the galaxies shows evidence of significant star formation or AGN activity.321 Onlv in the case of the galaxies MC7697-3 ancl AIC7697-5 (this object was not included as menmber of the CG in MC09: however we look a spectra that allow to determine a redshift concordant with being a member of the CG. see below) tiny lines of [OLL](A3727) wwere detected.," Only in the case of the galaxies MC7697-3 and MC7697-5 (this object was not included as member of the CG in MC09; however we took a spectra that allow to determine a redshift concordant with being a member of the CG, see below) tiny lines of $[OII](\lambda3727)$ were detected."322 So. the morphological aud spectroscopic analysis of the galaxies in the three CGs. shows that all the members are old ellipticals.," So, the morphological and spectroscopic analysis of the galaxies in the three CGs, shows that all the members are old ellipticals."323 The absence of galaxies with emission lines contrasts with what is found in Iiekson CGs., The absence of galaxies with emission lines contrasts with what is found in Hickson CGs.324 In fact. several authors (e.g.. Martinez οἱ 22010 and reference therein) have studied samples [rom IHickson CGs and found that of all the galaxies have emission lines.," In fact, several authors (e.g., Martinez et 2010 and reference therein) have studied samples from Hickson CGs and found that of all the galaxies have emission lines."325 About one quarter and one third ol such emission is due to AGN and star formation activity respectively., About one quarter and one third of such emission is due to AGN and star formation activity respectively.326 The criteria imposed to select the CG candidates by ALCO9 are basically the same as those adopted for Lickson's sample., The criteria imposed to select the CG candidates by MC09 are basically the same as those adopted for Hickson's sample.327 However. owing to the fact that the sample of galaxies used by MC09 is limited to those objects with r«21 mag. the criteria of isolation as defined in that paper can be only applied for those candidates as MC4629 in which the brightest ealaxv has r<18 mag.," However, owing to the fact that the sample of galaxies used by MC09 is limited to those objects with $r<21$ mag, the criteria of isolation as defined in that paper can be only applied for those candidates as MC4629 in which the brightest galaxy has $r<18$ mag."328 We have checked (hat extending the sample of galaxies considered in the SDSS photometric survey up (o r=22 mag. neither MC7697 nor MC13069 strictly follow the isolation criteria.," We have checked that extending the sample of galaxies considered in the SDSS photometric survey up to $r=22$ mag, neither MC7697 nor MC13069 strictly follow the isolation criteria."329 In the case of MC769T there is a galaxy about 2 mags fainter, In the case of MC7697 there is a galaxy about 2 mags fainter330spectrophotometry with the VLT instrument FORS2 in HIT-MS mode and detect four pulsations above the c threshold.,spectrophotometry with the VLT instrument FORS2 in HIT-MS mode and detect four pulsations above the $\sigma$ threshold.331 The S/N of the data was sufficient to extract high-quality monochromatic amplitudes and phases only for the dominant pulsation. noisier results being obtained for the remaining periodicities.," The S/N of the data was sufficient to extract high-quality monochromatic amplitudes and phases only for the dominant pulsation, noisier results being obtained for the remaining periodicities."332 Using full model atmosphere codes appropriate for the atmospheric parameters of our target and also incorporating non-adiabatic effects. we computed accurate theoretical amplitudes and phases for comparison to the observations.," Using full model atmosphere codes appropriate for the atmospheric parameters of our target and also incorporating non-adiabatic effects, we computed accurate theoretical amplitudes and phases for comparison to the observations."333 From the fits achieved to the observed amplitudes alone we determined the dominant pulsatior to be a radial mode., From the fits achieved to the observed amplitudes alone we determined the dominant pulsation to be a radial mode.334 This conclusion was found to be consistent with the monochromatic phase shifts observed under the assumption of a very reasonable radial velocity variation of 11 km/s. For two lower amplitude periodicities the data were found to be of sufficient quality to exclude higher degree modes with {> 3., This conclusion was found to be consistent with the monochromatic phase shifts observed under the assumption of a very reasonable radial velocity variation of 11 km/s. For two lower amplitude periodicities the data were found to be of sufficient quality to exclude higher degree modes with $\ell\geq$ 3.335 To our knowledge. this is the first time that mode identification has been attempted for an EC 14026 star using monochromatic amplitudes.," To our knowledge, this is the first time that mode identification has been attempted for an EC 14026 star using monochromatic amplitudes."336 The fact that we were able to identify the main periodicity as a radial mode is therefore quite encouraging for future studies. particularly considering the relative faintness of our target.," The fact that we were able to identify the main periodicity as a radial mode is therefore quite encouraging for future studies, particularly considering the relative faintness of our target."337 Moreover. the excellent match between theoretical predictions and the observations in the continuum confirms the basic validity of our approach and our models. although the discrepancies in the line cores indicate that there 1s still room for improvement. especially with respect to the chemical composition assumed in. the model atmosphere calculations.," Moreover, the excellent match between theoretical predictions and the observations in the continuum confirms the basic validity of our approach and our models, although the discrepancies in the line cores indicate that there is still room for improvement, especially with respect to the chemical composition assumed in the model atmosphere calculations."338 Unfortunately. sdB stars are all chemically peculiar and contain heavy elements in varying abundances. implying that for a perfect match each target would first have to be submitted to a detailed abundance analysis and then analysed using a specially computed grid of model atmospheres.," Unfortunately, sdB stars are all chemically peculiar and contain heavy elements in varying abundances, implying that for a perfect match each target would first have to be submitted to a detailed abundance analysis and then analysed using a specially computed grid of model atmospheres."339 This is extremely time consuming both on the observational and the computational front. and not necessary for the practical application presented here. given that we have proved mode identification to be possible on the basis of the continuum behaviour alone.," This is extremely time consuming both on the observational and the computational front, and not necessary for the practical application presented here, given that we have proved mode identification to be possible on the basis of the continuum behaviour alone."340 It is quite striking that in the few cases where observational mode identification has been possible for rapidly pulsating subdwarf B stars. the dominant mode of pulsation was always found to be a radial mode (for Balloon 090100001 from ?.. KPD 21094-4401 from ?.. HS 220142610 from Silvotti et al.," It is quite striking that in the few cases where observational mode identification has been possible for rapidly pulsating subdwarf B stars, the dominant mode of pulsation was always found to be a radial mode (for Balloon 090100001 from \citealt{charp2008}, KPD 2109+4401 from \citealt{randall2005}, HS 2201+2610 from Silvotti et al."341 2010. submitted. and now for EC 20338-1925).," 2010, submitted, and now for EC 20338-1925)."342 Of course. this cannot automatically be assumed to hold true for all the highest amplitude frequencies detected in EC 14026 stars. but it does seem reasonable to deduce that mode visibility across the disk of the star is a very important factor influencing the observed amplitude.," Of course, this cannot automatically be assumed to hold true for all the highest amplitude frequencies detected in EC 14026 stars, but it does seem reasonable to deduce that mode visibility across the disk of the star is a very important factor influencing the observed amplitude."343" Asteroseismological solutions assigning high-degree modes to the strongest frequencies observed can in all likelyhood be disregarded from the outset. as has occasionally been done in the past to distinguish between several possible “optimal models"" (e.g.?)."," Asteroseismological solutions assigning high-degree modes to the strongest frequencies observed can in all likelyhood be disregarded from the outset, as has occasionally been done in the past to distinguish between several possible “optimal models” \citep[e.g.][]{randall2009}."344 This approach allows unambiguous model solutions to be found on the basis of fewer observed periods than if all observed frequencies are allowed to take on degree indices of (=0.1.2. and 4. and can therefore save valuable observing time.," This approach allows unambiguous model solutions to be found on the basis of fewer observed periods than if all observed frequencies are allowed to take on degree indices of $\ell$ =0,1,2, and 4, and can therefore save valuable observing time."345 One puzzling implication of our identification of the 146.9- periodicity as a radial mode is that this frequency cannot then contain closely spaced components due to a rotationally split multiplet., One puzzling implication of our identification of the 146.9-s periodicity as a radial mode is that this frequency cannot then contain closely spaced components due to a rotationally split multiplet.346 Consequently. it is difficult to explain the strong amplitude variations observed over several years (see Fig.," Consequently, it is difficult to explain the strong amplitude variations observed over several years (see Fig."347 3) in terms of the beating of unresolved frequencies., 3) in terms of the beating of unresolved frequencies.348 Given that the photometry data obtained by Dave Kilkenny have time baselines of several days. the two independent harmonic frequencies would have to be spaced less than ~ 2 μΗΖ apart in order to not be resolved.," Given that the photometry data obtained by Dave Kilkenny have time baselines of several days, the two independent harmonic frequencies would have to be spaced less than $\sim$ 2 $\mu$ Hz apart in order to not be resolved."349 Additionally. the strong amplitude variations observed can be produced only if the two pulsations have comparable amplitudes. effectively implying two very closely spaced modes with degree indices (= 0 and/or 1.," Additionally, the strong amplitude variations observed can be produced only if the two pulsations have comparable amplitudes, effectively implying two very closely spaced modes with degree indices $\ell$ = 0 and/or 1."350 From our stellar models we know that the required proximity in frequency is impossible for modes of the same degree index. and extremely unlikely for the combination of £/= 0 and £21 (see.e.g.?)..," From our stellar models we know that the required proximity in frequency is impossible for modes of the same degree index, and extremely unlikely for the combination of $\ell=$ 0 and $\ell=$ 1 \citep[see, e.g.][]{charp2000}."351 This is particularly true for a target with as high à surface gravity as EC 20338-1925. since the period density predicted is lower than for a more typical. less compact EC 14026 star.," This is particularly true for a target with as high a surface gravity as EC $-$ 1925, since the period density predicted is lower than for a more typical, less compact EC 14026 star."352 Therefore. we believe there is a high probability that the observed amplitude variations for the main mode are intrinsic to the star.," Therefore, we believe there is a high probability that the observed amplitude variations for the main mode are intrinsic to the star."353 In conclusion. we have shown that the monochromatic amplitude and phase variations can be effectively used for mode identification in rapidly pulsating subdwarf B stars.," In conclusion, we have shown that the monochromatic amplitude and phase variations can be effectively used for mode identification in rapidly pulsating subdwarf B stars."354 The most critical factor ts the quality of the observational data. as the S/N level attained limits the discriminative power especially between modes of low degree indices with £x 2.," The most critical factor is the quality of the observational data, as the S/N level attained limits the discriminative power especially between modes of low degree indices with $\ell\leq$ 2."355 Even though we were allocated observing time using a highly suitable instrument mounted on one of the world’s largest telescopes we were able to unambiguously identify the degree index for only the dominant. rather high amplitude mode.," Even though we were allocated observing time using a highly suitable instrument mounted on one of the world's largest telescopes we were able to unambiguously identify the degree index for only the dominant, rather high amplitude mode."356 On the other hand. EC 20338-1925 is relatively faint. and there are several brighter targets available.," On the other hand, EC $-$ 1925 is relatively faint, and there are several brighter targets available."357 Aoreover. our observing run was affected by severe technical problems. due to which we lost a quarter of our allocated time completely. and did not obtain enough red data to constructively include it in our analysis.," Moreover, our observing run was affected by severe technical problems, due to which we lost a quarter of our allocated time completely, and did not obtain enough red data to constructively include it in our analysis."358 Therefore it seems likely that better results could be obtained in future similar studies., Therefore it seems likely that better results could be obtained in future similar studies.359 It is not straightforwarc to objectively assess the relative merits of the different techniques currently in use for mode identification in subdwarf B stars. and opinions on this will vary.," It is not straightforward to objectively assess the relative merits of the different techniques currently in use for mode identification in subdwarf B stars, and opinions on this will vary."360 We believe that for the time being the exploitation. of the pulsational amplitude's signature on ( as a function of wavelength is the most promising method. and it is so far the only one to have yielded unambiguous determinations of the degree index /.," We believe that for the time being the exploitation of the pulsational amplitude's signature on $\ell$ as a function of wavelength is the most promising method, and it is so far the only one to have yielded unambiguous determinations of the degree index $\ell$."361 Given that the work presented here constitutes the first study employing monochromatic rather than broadband amplitudes. it is too early to say which of these two closely related techniques is more efficient.," Given that the work presented here constitutes the first study employing monochromatic rather than broadband amplitudes, it is too early to say which of these two closely related techniques is more efficient."362 One drawback of the amplitude-wavelength approach to mode identification 1s that medium-sized or large telescopes coupled with specialised instruments are needed in order to obtain rapid time-series data of sufficient quality., One drawback of the amplitude-wavelength approach to mode identification is that medium-sized or large telescopes coupled with specialised instruments are needed in order to obtain rapid time-series data of sufficient quality.363 However. this is equally true for the study of line-profile variations. where the low S/N achievable even with the world’s largest telescopes," However, this is equally true for the study of line-profile variations, where the low S/N achievable even with the world's largest telescopes"364l1.,$4$.365 The fiducial biases and dispersions are the same for all coniponeut Caussiaus., The fiducial biases and dispersions are the same for all component Gaussians.366 So the fiducial P(zu4]:)the is ideutical ta all cases. but with higher Vy. re is more freedom for deviations from the fiducial.," So the fiducial $P(z_{\rm367 ph}|z)$ is identical in all cases, but with higher $N_g$, there is more freedom for deviations from the fiducial."368 The second. third. and fourth Gaussian componcuts are cach fixed to have one-fourth the total normalization of the distribution.," The second, third, and fourth Gaussian components are each fixed to have one-fourth the total normalization of the distribution."369 At fixed dark energv degradation. the required size of the calibration suuple (ορού). increases with the uunuber of Caussiaus and reaches an asvuiptotic m when zL photo-," At fixed dark energy degradation, the required size of the calibration sample $N_{\rm spect}$ ) increases with the number of Gaussians and reaches an asymptotic value when $N_g \approx 4$."370"zWhen dark energy degradation is 1.5. rationthe NV.=L AV, model requires 2:5 times the calil salple of the Ny= Lanodel."," When dark energy degradation is 1.5, the $N_{\rm g} = 4$ photo-z model requires $\approx5$ times the calibration sample of the $N_{\rm g} = 1$ model."371 Another view is that the dark-cucrev uncertainties will be underestimated if oue fits a sinele-Caussian model to photo-z distributions that actually require more freedom., Another view is that the dark-energy uncertainties will be underestimated if one fits a single-Gaussian model to photo-z distributions that actually require more freedom.372 For example. assuine we obtain 1«104 spectra. as required to keep dark energy degradation under 1.5 for a sinegle-Gaussian ploto-z iode.," For example, assume we obtain $4 \times 10^4$ spectra, as required to keep dark energy degradation under 1.5 for a single-Gaussian photo-z model."373 Bud. however that the dark energy degradation for INMy=Ll rises above 2.0.," We find, however that the dark energy degradation for $N_g=4$ rises above 2.0."374 So relaxing the Gaussian assmuption for photo-z'* inflates the cosmological uncertainties by zz35%, So relaxing the Gaussian assumption for photo-z's inflates the cosmological uncertainties by $\approx35\%$.375" We also note from the left panel of Figure 2. that the ark eueres ation has a characteristic dependence On Naso: for onroughMauZ the dark cucrey parameter q3TOr scales Voas ""i:HNuus"," We also note from the left panel of Figure \ref{fig:fid1234G} that the dark energy degradation has a characteristic dependence on $N_{\rm spect}$; for $N_{\rm spect}\gtrsim10^3$, the dark energy parameter error scales roughly as $N_{\rm spect}^{1/4}$."376 When the dark energy ceradation reaches zx at Nau.beconie=La? 109. the eains from additional spectra weaker and a eeradation of unitv is approached only very slowly.," When the dark energy degradation reaches $\approx1.2$, at $N_{\rm spect}=10^5$ $10^6$, the gains from additional spectra become weaker and a degradation of unity is approached only very slowly."377" As we vary we change the location of this ""hkuec in the curve. Vy.but not the scaling for Noyce below the kuec."," As we vary $N_g$, we change the location of this “knee” in the curve, but not the scaling for $N_{\rm spect}$ below the knee."378 This scaling is not scusitive to either the fiducial photo-Ζ inodels or survey specs., This scaling is not sensitive to either the fiducial photo-z models or survey specs.379" For example. as shown iu the right panel of Figure 2.. for a model with 6.=0.0301|2). the scaling is NI12οT photozfor a SNAP-like with faL000 dee.,i100 galaxies 7. andva=0.22. the scaling is also NIpect as shown in the right panel of Figure 2.."," For example, as shown in the right panel of Figure \ref{fig:fid1234G}, for a photo-z model with $\sigma_z = 0.03 (1+z)$, the scaling is $N_{\rm spect}^{1/5}$; for a SNAP-like with $f_{\rm sky} = 4000$ $^2$, $\bar n^{A}=100$ galaxies $^{-2}$, and $\gamma_{\rm int}=0.22$, the scaling is also $N_{\rm spect}^{1/5}$ as shown in the right panel of Figure \ref{fig:fid1234G}."380 The desired spectroscopic survey size Miu Will i general depend on the width aud shape of the fiducial photo-z distribution. uot just Ny.," The desired spectroscopic survey size $N_{\rm spect}$ will in general depend on the width and shape of the fiducial photo-z distribution, not just $N_g$."381 We next ivestigate the dependence on the detailed shape of the fiducial distribution., We next investigate the dependence on the detailed shape of the fiducial distribution.382 The left panel of reffie:Nspect2G shows dark cucreydegradation versus Nopeer for several Vy=2 anodeIs. all haviπιο fiducial rns width 0.05(1|a but with different fiducial biases and dispersions for the two compoucuts.," The left panel of \\ref{fig:Nspect2G} shows dark energy degradation versus $N_{\rm spect}$ for several $N_g=2$ models, all having fiducial rms width $0.05(1+z)$, but with different fiducial biases and dispersions for the two components."383" In detail. our study includes fiducial photo-z distributions in which: the conrponeut Caussiaus have the same biases but different 0. values (""200 0. diff"" model): the same o; values but different biases (72€ zbias diff”): the same biases aud σ. values but with normalizatious a ) to 1 ratio (""2€ DU aud LO models iuo which the fiducial μας aud 0..,; are randonly assigned while i1nziutaiuiug fixed ruis yhoto-z error δι seed xxx models)."," In detail, our study includes fiducial photo-z distributions in which: the component Gaussians have the same biases but different $\sigma_z$ values (“2G $\sigma_z$ diff” model); the same $\sigma_z$ values but different biases (“2G zbias diff”); the same biases and $\sigma_z$ values but with normalizations at a 3 to 1 ratio (“2G 3:1”); and 10 models in which the fiducial $z_{\rm {bias;j}}$ and $\sigma_{z;j}$ are randomly assigned while maintaining fixed rms photo-z error (“2G seed xxx” models)."384 The INuu requiremeuts span a rather large range., The $N_{\rm spect}$ requirements span a rather large range.385 For example. nodeat 5 dark euergvdegradation. most of the ohoto-z 8 νομος requirement is within a factor of lof that of the sinele-Gaussian model.," For example, at $50\%$ dark energy degradation, most of the photo-z models' $N_{\rm spect}$ requirement is within a factor of 4 of that of the single-Gaussian model."386 But some of the nodels require LO times more Noyeer., But some of the models require $40$ times more $N_{\rm spect}$.387 Threc- aud Gaussian ploto-z models exhibit simular behaviors., Three- and four-Gaussian photo-z models exhibit similar behaviors.388 To unclerstand the wide rauge of N4 requirements or differeut ploto-z models. we perform the following est.," To understand the wide range of $N_{\rm spect}$ requirements for different photo-z models, we perform the following test."389 We fix the underlving galaxy. redshift 0(:) aud do iot use any iuiforiatiou from Canssian(tpn)., We fix the underlying galaxy redshift ${n(z)}$ and do not use any information from ${n(z_{\rm ph})}$.390 The resulting Nuu requirements for the double- photo-z models are shown in the middle panel of χοπο, The resulting $N_{\rm spect}$ requirements for the double-Gaussian photo-z models are shown in the middle panel of \\ref{fig:Nspect2G}.391 At fixed dark energy. degradation.the range of μου. requienients is ercatly MN," At fixed dark energy degradation,the range of $N_{\rm spect}$ requirements is greatly reduced."392 For example. at 50% dark cucrey deeradation. the Apect requirement is within a factor of 2 of that of the . model.," For example, at $50\%$ dark energy degradation, the $N_{\rm spect}$ requirement is within a factor of 2 of that of the single-Gaussian model."393 We find similar reduction of the rauge of IN. requirements in the case of three- aud four-Gaussian models., We find similar reduction of the range of $N_{\rm spect}$ requirements in the case of three- and four-Gaussian models.394 The test shows that the reason for the wide range of Noyceme requirements for different. ploto-z nodels is that nition constrains the underlying galaxy redshift distiil ph)aud the photo-z parameters much setter in some of the photo-z models than others., The test shows that the reason for the wide range of $N_{\rm spect}$ requirements for different photo-z models is that $n(z_{\rm ph})$ constrains the underlying galaxy redshift distribution and the photo-z parameters much better in some of the photo-z models than others.395 It is the redshift knowledge. rather than weak-leusing information itxelf. that is sensitive to the details of the photo-z xobabilitv distribution.," It is the redshift knowledge, rather than weak-lensing information itself, that is sensitive to the details of the photo-z probability distribution."396 Oue possible cause of the poor sensitivity iu some ioto-z anodels is) the rapid variation of photo-z aranmeters in redshift., One possible cause of the poor sensitivity in some photo-z models is the rapid variation of photo-z parameters in redshift.397 The melt panel of shows the result of reducing the degree of rapid variation of the ploto-z parameters., The right panel of \\ref{fig:Nspect2G} shows the result of reducing the degree of rapid variation of the photo-z parameters.398 The rauge of IN Is reduced to within a factor of bof that of the sinele-Gaussiansoe model as shown im right panel of Nspect2G.., The range of $N_{\rm spect}$ is reduced to within a factor of 4 of that of the single-Gaussian model as shown in right panel of \\ref{fig:Nspect2G}. .399" In detail. we demand that the fiducial photo-z parameter ip, aud σ. values to be proportional to 1l|: within cach of the three redshift intervals"," In detail, we demand that the fiducial photo-z parameter $z_{\rm bias}$ and $\sigma_z$ values to be proportional to $1+z$ within each of the three redshift intervals"400angular momentun to cross the black hole horizon promptly.,angular momentum to cross the black hole horizon promptly.401 This creates a temporary disk of debris material around the DII. whose accretion over times long compared to a dynamic lime can power a GRB jet. (," This creates a temporary disk of debris material around the BH, whose accretion over times long compared to a dynamic time can power a GRB jet. ("4023) The black hole. right after it forms. is initially deformed. and in a vine-down phase radiates away the enerev associated with these delormations as gravitational waves. until it settles into a Kerr geometry.,"3) The black hole, right after it forms, is initially deformed, and in a ring-down phase radiates away the energy associated with these deformations as gravitational waves, until it settles into a Kerr geometry."403 Collapsars. i.e. massive stellar collapses leading to à GRLB. require a hieh core rotation rate. which may be easier (ο achieve if the star is in a binary. svstem. although this is not necessary (e.g. Wooslev. 2001).," Collapsars, i.e. massive stellar collapses leading to a GRB, require a high core rotation rate, which may be easier to achieve if the star is in a binary system, although this is not necessary (e.g. Woosley, 2001)."404 The high rotation rate is required (o form a centriligally supported disk around a central. possibly spinning black hole. to power a GRD jet.," The high rotation rate is required to form a centrifugally supported disk around a central, possibly spinning black hole, to power a GRB jet."405 A hieh rotation rate. however. max be conducive to the development of bar or Iragmentation instabiliües in the collapsing core or/and in the massive disk around the central object (Nakamura Fukuegita 1939: Bonnell Pringle 1995: van Putten 2001. 2002: Davies et al.," A high rotation rate, however, may be conducive to the development of bar or fragmentation instabilities in the collapsing core or/and in the massive disk around the central object (Nakamura Fukugita 1989; Bonnell Pringle 1995; van Putten 2001, 2002; Davies et al."406 2002: Fiver. Holz Unehes 2002).," 2002; Fryer, Holz Hughes 2002)."407 The asvnunetrically infalling matter also perturbs the black hole's geometry. which leads to rig-down gravitational radiation.," The asymmetrically infalling matter also perturbs the black hole's geometry, which leads to rig-down gravitational radiation."408 The gravitational wave enussion [rom collapsars can thus in principle be estimated in a similar way (ο what is done in binaries during the in-spiral. merger and rine-down phases. alühough with considerably ]argere uncertainties.," The gravitational wave emission from collapsars can thus in principle be estimated in a similar way to what is done in binaries during the in-spiral, merger and ring-down phases, although with considerably larger uncertainties."409 In-spiraling compact binaries can be described as two point particles will masses n4 and mo. whose orbital parameters evolve secularly due to gravitational radiation.," In-spiraling compact binaries can be described as two point particles with masses $m_1$ and $m_2$, whose orbital parameters evolve secularly due to gravitational radiation."410 The radiation carries away orbital binding energv. which leads (o a faster orbiting and more compact svstem.," The radiation carries away orbital binding energy, which leads to a faster orbiting and more compact system."411 Though the amplitude of the gravitational wave ilsell h(/) increases as the system evolves. the frequency f/. also rapiclly increases.," Though the amplitude of the gravitational wave itself $h(t)$ increases as the system evolves, the frequency $f$ also rapidly increases."412 As the result. the energv spectrum is a decreasing function of f (e.g.. Misner. Thorne Wheeler 1973). where M=(nye)!PCy+e)I? is the chirp mass.," As the result, the energy spectrum is a decreasing function of $f$ (e.g., Misner, Thorne Wheeler 1973), where $\mathcal{M}=(m_1m_2)^{3/5}(m_1+m_2)^{-1/5}$ is the chirp mass."413 The characteristic gravitational wave aniplitude is defined with the Fourier translorm of h(/) as ο)=ΠΡΩΙ. and equal to ~VN where N=[2(df/dt)! is the number of eveles radiated while the frequency changes by an amount of order [.," The characteristic gravitational wave amplitude is defined with the Fourier transform of $h(t)$ as $h_c(f)=f|\tilde{h}(f)|$, and equal to $\sim \sqrt{N} h$ where $N=f^2(df/dt)^{-1}$ is the number of cycles radiated while the frequency changes by an amount of order $f$."414 The characteristic amplitude at a detector at a distance dis eiven by a function of the energy spectrum., The characteristic amplitude at a detector at a distance $d$ is given by a function of the energy spectrum.415The form of the pseudo phase-space density. profile of simulated haloes. recovered. by the present model. coincides with that predicted by Bertschinger’s (1985) model for collisionless spherically svmametric. self-similar. svstems evolving by PA.,"The form of the pseudo phase-space density profile of simulated haloes, recovered by the present model, coincides with that predicted by Bertschinger's (1985) model for collisionless spherically symmetric, self-similar, systems evolving by PA."416 Phis implies that the ultimate reason for such a coincidence cannot be neither the shape (spherically svnimetric vs. triaxial) of the system nor the form (power-aw vs. non-power-Iaw) of the density profile., This implies that the ultimate reason for such a coincidence cannot be neither the shape (spherically symmetric vs. triaxial) of the system nor the form (power-law vs. non-power-law) of the density profile.417 Phe only more fundamental aspect in the formation of virialised objects grown by PA directly or indirectly. included in both models is the way the coarse-grained phase space density increases via phase mixing (entropy generation) when the system loses energy. via shell-crossing and contracts., The only more fundamental aspect in the formation of virialised objects grown by PA directly or indirectly included in both models is the way the coarse-grained phase space density increases via phase mixing (entropy generation) when the system loses energy via shell-crossing and contracts.418 ortschingers mocel is cvnamical and can properly follow the cllects of shell-crossing. while the SVMS model is steacy aud focuses on th1C οςuilibrium state resulting from that process.," Bertschinger's model is dynamical and can properly follow the effects of shell-crossing, while the SVMS model is steady and focuses on the equilibrium state resulting from that process."419 However. the inside-out growth condition the SVMS mode relies on clirectly follows from the ack of apocentre-crossing during virialisation. a condition that is also fulfilled by Dertschir19er mocel.," However, the inside-out growth condition the SVMS model relies on directly follows from the lack of apocentre-crossing during virialisation, a condition that is also fulfilled by Bertschinger's model."420 Thus. despite the cisinct approach. the ellects of shell-crossing are siniarly accounted for in the two mocoels.," Thus, despite the distinct approach, the effects of shell-crossing are similarly accounted for in the two models."421 Certainly. tre power-law form of the pseudo phase-space density. profile oreclictecl by Jertschinecr’s model is tightly related to the sell-similarity assumption. while the present nioclel makes no such an assumption.," Certainly, the power-law form of the pseudo phase-space density profile predicted by Bertschinger's model is tightly related to the self-similarity assumption, while the present model makes no such an assumption."422 However. PA ds always close to self-similar.," However, PA is always close to self-similar."423 It is driven by gravitation. a scale-[ree force. and the iniial conitions are also very apoximately. scale-[ree: the initial niass distribution is esseniallv uniform (with essentialv the critical density) and the velociy Ποιά corresponds to the scale-Dre unperturxd Llu»ble-tow form.," It is driven by gravitation, a scale-free force, and the initial conditions are also very approximately scale-free: the initial mass distribution is essentially uniform (with essentially the critical density) and the velocity field corresponds to the scale-free unperturbed Hubble-flow form."424 Thus. the solution «X the esent model at small z shoul| not be very far [rom self-similar. «νο for he elfec‘ts of the increasing departure from the Einstein-ce Sitter universe owing lot 16 specific density profile of the seec .," Thus, the solution of the present model at small $z$ should not be very far from self-similar, except for the effects of the increasing departure from the Einstein-de Sitter universe owing to the specific density profile of the seed."425l1n ls sense. the oedieted profiles should not © [far roni power-laws. particularly t1e pseudo phase-space density profile tha apCALs LO IC SO itle sensitive to the details of the seed.," In this sense, the predicted profiles should not be far from power-laws, particularly the pseudo phase-space density profile that appears to be so little sensitive to the details of the seed."426 nother fundamental assumΣο of Bertschinger's model is the racial inkul of the SYSLOnmi. while the SVMS model takes into accoun that the collapse aud viriajsation is actuallytall non-racial.," Another fundamental assumption of Bertschinger's model is the radial infall of the system, while the SVMS model takes into account that the collapse and virialisation is actually non-radial."427 |lowewver. i “the tangenti] velocities develop at the expense of the iniial raclial velocities witrout altering the otal velocity dispCrsion. as assumed in ecuation (74)). the velocity dispersion hat emoerges as a consequence of shell-crossing shoud )0 The same in sphericaIv svmmetriC às in triaxial svstenis.," However, if the tangential velocities develop at the expense of the initial radial velocities without altering the total velocity dispersion, as assumed in equation \ref{00th}) ), the velocity dispersion that emerges as a consequence of shell-crossing should be the same in spherically symmetric as in triaxial systems."428 The sitijtion is therefore as folows., The situation is therefore as follows.429 The power-law form. with index equa to -1.875. of the pseuco phase-space density »olile: founL bv Bertselinger is the| direct. consequence o “the shell-crossing produced. in self-similar radial PA.," The power-law form, with index equal to -1.875, of the pseudo phase-space density profile found by Bertschinger is the direct consequence of the shell-crossing produced in self-similar radial PA."430 Phus. the CONCitions that: iVP.self-similar and ii)modificd. ac‘cording to t1e condition (74)). by the appearance of tangential velocities in non-radial PA. should guarantee that he evolution of he couse-erained phase-space density found in Bertschinger’s model is kept essentially. unaltered in the ecncral (non-striclty self-similar ancl non-radial) case of PA.," Thus, the conditions that: i) and ii), according to the condition \ref{00th}) ), by the appearance of tangential velocities in non-radial PA, should guarantee that the evolution of the coarse-grained phase-space density found in Bertschinger's model is kept essentially unaltered in the general (non-striclty self-similar and non-radial) case of PA."431 This would explain why the present model recovers the pseudo phase-space density proile à la Bertschinger in agreement with the results of numerical simulations., This would explain why the present model recovers the pseudo phase-space density profile à la Bertschinger in agreement with the results of numerical simulations.432 Note that such a pseuclo ohase-space density. profile does not necessarily implies that the density. profile must. also be roughly proportional to +25 as [oui by Bertschinger., Note that such a pseudo phase-space density profile does not necessarily implies that the density profile must also be roughly proportional to $r^{-2.25}$ as found by Bertschinger.433 This would be the case if PA were strictly. self-similar. so to end up with a power-law density »olile. :ux. more importantly. racial.," This would be the case if PA were strictly self-similar, so to end up with a power-law density profile, and, more importantly, radial."434" As stated by Bertschinger(1985) when comenting on his densitv profile poxr2 ""Seli-sinilar relaxation is not compete as it proceeds along one direction onlv] and. thus heuristically should not [cad Qa cdlensity orofi cas dlat as poxr72 as predicted by Lynden-Bell(1967). in the case of complete 3D relaxation]."," As stated by \citet{Ber85} when comenting on his density profile $\rho\propto435r^{-2.25}$: “Self-similar relaxation is not complete [as it proceeds along one direction only] and thus heuristically should not lead to a density profile as flat as $\rho \propto r^{-2}$ [as predicted by \citet{LB67} in the case of complete 3D relaxation]."436 Ht is uncerain o what extent the addition of anguar momentum (i.e. non-radial orbits) will c1ange this result.....," It is uncertain to what extent the addition of angular momentum (i.e. non-radial orbits) will change this result,...”."437 In other words. if PA is non-racial. tian the power index of the density profile is expected to change. in agreement with the results of SVMS. clesjte he fact that the pseudo-phase space! density. profile. driven by the evolution of the phase-space density during virialisation in he absence of apocentre-crossing. srould be kept roughly unaltered as à consecuence of condition (74)).," In other words, if PA is non-radial, than the power index of the density profile is expected to change, in agreement with the results of SVMS, despite the fact that the pseudo-phase space density profile, driven by the evolution of the phase-space density during virialisation in the absence of apocentre-crossing, should be kept roughly unaltered as a consequence of condition \ref{00th}) )."438 Astuenioned. a kev point in he present model. arising from tje particidar wav shell-crossing proceeds in accreting virialised haoes. is their inside-out growth.," As mentioned, a key point in the present model, arising from the particular way shell-crossing proceeds in accreting virialised haloes, is their inside-out growth."439 Bertschingers model is insead. base lon he selt-similar evolution of such svstenis and does not care about the implicaions this has on the growth of the steady object., Bertschinger's model is instead based on the self-similar evolution of such systems and does not care about the implications this has on the growth of the steady object.440 But. if our explanation of the pseudo phase-space density. profile is correct. the two models shoul| essentiaIv coincide (except for the svmmoetrv and the strict selssimilarity condition). meaning that Bertschinger’s solution s10ulc alse» approximately satisfy the insicle-out growth condition.," But, if our explanation of the power-law-like pseudo phase-space density profile is correct, the two models should essentially coincide (except for the symmetry and the strict self-similarity condition), meaning that Bertschinger's solution should also approximately satisfy the inside-out growth condition."441 This is indeed the case., This is indeed the case.442 As stated by Bertschinger. as a consequence of shel-Crossing. particle orbits rapidly become approximately periodic. that is. the mass inside them stabilises and the inner svstem ¢oes not change anymore.," As stated by Bertschinger, as a consequence of shell-crossing, particle orbits rapidly become approximately periodic, that is, the mass inside them stabilises and the inner system does not change anymore."443 In oher words. the system develops a steady core ancl grows from the inside-out as new shells virialise.," In other words, the system develops a steady core and grows from the inside-out as new shells virialise."444 Of course. such a behaviotu can only beapprorimatedy satisfied in Bertschinger’s model.," Of course, such a behaviour can only be satisfied in Bertschinger's model."445 As a consequence of self-similaritv. steaciness can only be strictv achieved in the orradii: particle orbits can never become exactly periodic. they can only tend to become πο (see )otschinger's Fig.," As a consequence of self-similarity, steadiness can only be strictly achieved in the or; particle orbits can never become exactly periodic, they can only tend to become so (see Betschinger's Fig."446 9 at the base of his comment regarding the inside-out &rowth)., 9 at the base of his comment regarding the inside-out growth).447 To obtain a Lully steacv solution. the self-similarity assumption must be replaced by the inside-out. erowth condition as in the present moclel.," To obtain a fully steady solution, the self-similarity assumption must be replaced by the inside-out growth condition as in the present model."448 As has long been known. there is in radial PA a one-to-one correspondence between the density. profiles of virialised objects and their seeds (Bertschinger1985:DelPopoloetal.2000).," As has long been known, there is in radial PA a one-to-one correspondence between the density profiles of virialised objects and their seeds \citep{Ber85,DPea00}."449. The reason for this is that in radial PA. there is no phase-mixing," The reason for this is that in radial PA, there is no phase-mixing"450solar mass stars.,solar mass stars.451 Phe mass transfer rate through a steady state disc is given by Mx9X (Pringle1981).. where the viscosity is parametrised with the a prescription so that where ος ," The mass transfer rate through a steady state disc is given by $\dot M \propto \nu \Sigma$ \citep{pringle81}, where the viscosity is parametrised with the $\alpha$ prescription so that \citep{shakura73} where $\Omega=\sqrt{GM_{\rm p}/r}$."452"and £4, are the viscosities in the circumstellar ancl circumplanctary clises respectively. and o4 and αρ similarly refer the à values in the disces."," It then follows that where $\nu_{\rm s}$ and $\nu_{\rm p}$ are the viscosities in the circumstellar and circumplanetary discs respectively, and $\alpha_{\rm s}$ and $\alpha_{\rm p}$ similarly refer the $\alpha$ values in the discs."453 Consider a solar mass star and a Jupiter mass planet. ες10.7. and circumstellar and cireumplanetary disc aspect ratios of 0.04 and. 0.3 respectively. as discussed. above.," Consider a solar mass star and a Jupiter mass planet, $\mu=10^{-3}$, and circumstellar and circumplanetary disc aspect ratios of $0.04$ and 0.3 respectively, as discussed above."454" For r=0.2rg and equal a values (a.=αγ) in the above equation. the ratio of the surface densities is S/S,0.25."," For $r= 0.2 r_{\rm H}$ and equal $\alpha$ values $\alpha_{\rm s} = \alpha_{\rm p}$ ) in the above equation, the ratio of the surface densities is $\Sigma_{\rm s}/\Sigma_{\rm p} \sim 0.25$."455 So the eireumplanetary disc surface density is somewhat higher that the local circumstellar disc density., So the circumplanetary disc surface density is somewhat higher that the local circumstellar disc density.456 Cireumstellar clises could. under some circumstances contain dead: zones. regions where the disc ionization is too low for the magneto-rotational instability to operate as a source of turbulence (Ciammie 1996).," Circumstellar discs could under some circumstances contain dead zones, regions where the disc ionization is too low for the magneto-rotational instability to operate as a source of turbulence (Gammie 1996)."457 Dead. zones operate where the temperature is sullicientIy low that thermal ionization is weak (less than about 10 degrees) and where the surface densities are high enough that external sources of ionization such as cosmic ravs do not penetrate far below the disc surface., Dead zones operate where the temperature is sufficiently low that thermal ionization is weak (less than about $10^3$ degrees) and where the surface densities are high enough that external sources of ionization such as cosmic rays do not penetrate far below the disc surface.458 For expected conditions in a circumstellar disc. dead zones may extend from a few tenths of an AU to several AU. in some cases bevond Jupiter's orbital radius (e.g.Terquem2008).," For expected conditions in a circumstellar disc, dead zones may extend from a few tenths of an AU to several AU, in some cases beyond Jupiter's orbital radius \citep[e.g.][]{terquem08}."459. Phe model here suggests that the conditions for dead zone formation within a cireumplanetary disc are perhaps more favorable than in the nearby circumstellar disc gas., The model here suggests that the conditions for dead zone formation within a circumplanetary disc are perhaps more favorable than in the nearby circumstellar disc gas.460 The reason is that the circumstellar dise surface densities are higher than in the nearby circumstellar dise gas. while the temperatures are low enough to avoid sullicient ionisation in much of the cireumplanetary. disc.," The reason is that the circumstellar disc surface densities are higher than in the nearby circumstellar disc gas, while the temperatures are low enough to avoid sufficient ionisation in much of the circumplanetary disc."461" A cdillerence in the properties of turbulence in the two disces violates our assumption of a,=oy.", A difference in the properties of turbulence in the two discs violates our assumption of $\alpha_{\rm s} = \alpha_{\rm p}$.462 But. it does so in à way that may further enforce the importance of dead zones in the circumplanetary disc.," But, it does so in a way that may further enforce the importance of dead zones in the circumplanetary disc."463" That is. αςαμ would be expected to increase. leading to a decrease in X,/X. We do not pursue the possibility of dead zones further in our disc models described later and assume a simple viscous disc."," That is, $\alpha_{\rm s} / \alpha_{\rm p}$ would be expected to increase, leading to a decrease in $\Sigma_{\rm464 s}/\Sigma_{\rm p}.$ We do not pursue the possibility of dead zones further in our disc models described later and assume a simple viscous disc."465 Phe viscous timescale in the clise is where 2 is the orbital period of the planet., The viscous timescale in the disc is where $P$ is the orbital period of the planet.466 So we expect that such dises should. be viscouslv relaxed. for Jupiter and Saturn., So we expect that such discs should be viscously relaxed for Jupiter and Saturn.467 This result has the implication that the viscous disc How can be regarded to be in a steady state., This result has the implication that the viscous disc flow can be regarded to be in a steady state.468" A crude estimate of the steady state luminosity ratio of the circumplanctary to circumstellar discs in à svstem with a Jupiter mass planet is where £, anc A. are the planet ancl star radii. respectively."," A crude estimate of the steady state luminosity ratio of the circumplanetary to circumstellar discs in a system with a Jupiter mass planet is where $R_{\rm p}$ and $R_{\rm s}$ are the planet and star radii, respectively."469" For M,—1.10M.AL,~000111. and e,~0.1. we estimate L/L. to be of order a few percent."," For $\dot{M}_{\rm p} \sim 1-10 \dot{M}_{\rm s}, M_{\rm470 p} \sim 0.001 M_{\rm s},$ and $R_{\rm p} \sim 0.1 R_{\rm s}$, we estimate $L_{\rm p}/ L_{\rm s}$ to be of order a few percent."471 We see that circumplanctary cliscs are not very bright., We see that circumplanetary discs are not very bright.472 We discuss this further in Section &.., We discuss this further in Section \ref{concs}.473 In this section we consider ballistic particle orbits in a planct-star system in order to find their nonlveplerian angular velocity and where the orbits begin to cross., In this section we consider ballistic particle orbits in a planet-star system in order to find their nonKeplerian angular velocity and where the orbits begin to cross.474" As à simple two-dimensional disc model. we consider ballistic particles orbiting a planet of mass M, in the corotating frame of the star-planct system with a star of mass M.."," As a simple two-dimensional disc model, we consider ballistic particles orbiting a planet of mass $M_{\rm p}$ in the corotating frame of the star-planet system with a star of mass $M_{\rm s}$."475 “Phe particles lie in the star-planet orbit plane., The particles lie in the star-planet orbit plane.476 For such à model to represent a low pressure (cold) steady state [uid disc. each orbit must be periodic in the corotating frame and be nonintersecting. either with itself or neighboring orbits. in order that the velocity be single-valued in space.," For such a model to represent a low pressure (cold) steady state fluid disc, each orbit must be periodic in the corotating frame and be nonintersecting, either with itself or neighboring orbits, in order that the velocity be single-valued in space."477 In addition. the orbit must be stable.," In addition, the orbit must be stable."478" The equation of motion of a ballistic particle at position * for potential ó in the corotating frame is where £2, is the angular velocity of the planet.", The equation of motion of a ballistic particle at position $\bm{r}$ for potential $\phi$ in the corotating frame is where $\bm{\Omega}_{\rm p}$ is the angular velocity of the planet.479 The potential due to the rotation of the frame and the gravity of the planet and the star is given by, The potential due to the rotation of the frame and the gravity of the planet and the star is given by480an uncertainty of <15% on the depth of the survey.,an uncertainty of $<$ on the depth of the survey.481 The spectra of maguetars are eeucrallv. described as the stun of a blackbody componcut with a temperature of 15.00 keV auc a soft power-law tail with ploton iudex Dz3 (e...Woods&Thompson2006).," The spectra of magnetars are generally described as the sum of a blackbody component with a temperature of $kT$$\approx$ 0.6 keV and a soft power-law tail with photon index $\Gamma$$\approx$ 3 \citep[e.g.,][]{wt06}."482. The overall spectrum can be roughly approximated as à 52 power law. so we take that as our fiducial spectrim.," The overall spectrum can be roughly approximated as a $\Gamma$ =2 power law, so we take that as our fiducial spectrum."483 Choosing instead a softer P=3 power law results in values of D that are up to smaller (depeudiug upon the absorption through the line of sight: see below). while choosing a harder &T—0.6 keV blackbody increases D by up toC," Choosing instead a softer $\Gamma$ =3 power law results in values of $D$ that are up to smaller (depending upon the absorption through the line of sight; see below), while choosing a harder $kT$ =0.6 keV blackbody increases $D$ by up to."484oe We estimated the absorption as a function of distance along differcut Lues of sight using models for Calactic optical aud infrared extinction., We estimated the absorption as a function of distance along different lines of sight using models for Galactic optical and infrared extinction.485 For most of the Galactic plane. we luearly interpolated visual extinction values Glo) from the model of Drinunelctal. (2003).. aud converted them to Jv band extinction values using the relation Ayfy=0.11 (Rieke&Lehotsky 19903.," For most of the Galactic plane, we linearly interpolated visual extinction values $A_V$ ) from the model of \citet{dri03}, , and converted them to $K$ band extinction values using the relation $A_K/A_V = 0.11$ \citep{rl85,mat90}."486". Tlowever. within the central oof the Calasy the mocel extinction from Drinuuel(2003) was significantly lower than that observed (e.8..Launhardtetal. 2002).. so instead we interpolated value:μα of the A, band extinction from the table in Marshalletal. (2006)."," However, within the central of the Galaxy the model extinction from \citet{dri03} was significantly lower than that observed \citep[e.g.,][]{lzm02}, , so instead we interpolated values of the $K_s$ band extinction from the table in \citet{mar06}."487". We then converted the A baud extinction Gegnorine the differcuce in Ay and sio) into a cohuunu density using Ay=1.6«1074, cu? (Ricke&Lebotsky1985:PredelilSclinitt 1995)."," We then converted the $K$ band extinction (ignoring the difference in $A_K$ and $A_{K_s}$ ) into a column density using $N_{\rm H} = 1.6\times10^{23}488A_K$ $^2$ \citep{rl85,ps95}."489. Absorption through the Galactic plane can reduce the flux observed from a source by up to a factor of 30 compared to the value without absorption., Absorption through the Galactic plane can reduce the flux observed from a source by up to a factor of 30 compared to the value without absorption.490 We tested cdiffercut values for Niu/Ag: in the range (1.22.1)&10°? em? (representingvaluesfrom.e.g...Class1999:Tan&Draine 2001).. and found that the uncertainty in D introduced by our choice of absorption model is &15% The depth of our survey depends strongly upon the assuued hunuinositv aud the fractional root-miean-squared aus) amplitude of the pulsations (yy) for which we are searching.," We tested different values for $N_{\rm H}/A_K$ in the range $(1.2-2.1)\times10^{22}$ $^2$ \citep[representing values from, e.g.,][]{glass99,td04}, and found that the uncertainty in $D$ introduced by our choice of absorption model is $\approx$ The depth of our survey depends strongly upon the assumed luminosity and the fractional root-mean-squared (rms) amplitude of the pulsations $A_{\rm rms}$ ) for which we are searching."491 The rims amplitude cuters consideration because it determines Cg: where Pi. is the intrinsic power of a detectable sienal. the factor of 1.13 is an average correction that accounts for the fact that signals will often fall between independent Fourier bius. aud the sine terii takes into account the attenuation of the power of a signal as its frequency ν approaches the Nyquist value (Vaughanetal. 1991).," The rms amplitude enters consideration because it determines $C_{\rm lim}$: where $P_{\rm sig}$ is the intrinsic power of a detectable signal, the factor of 1.13 is an average correction that accounts for the fact that signals will often fall between independent Fourier bins, and the ${\rm sinc}$ term takes into account the attenuation of the power of a signal as its frequency $\nu$ approaches the Nyquist value $\nu_{\rm Nyq}$ \citep{vau94}."492". The iutriusic power Py. detectablezx, ina search ust be determined using the distribution of noise powers. as described in Vaughanctal.(1991)."," The intrinsic power $P_{\rm sig}$ detectable in a search must be determined using the distribution of noise powers, as described in \citet{vau94}."493. For a search threshold of Pay a.=32.8. the expected value confidence) is Pyje=31.8. and the power detectable in of trials is {όλως18.0.," For a search threshold of $P_{\rm meas}$ =32.8, the expected value confidence) is $P_{\rm sig}$ =31.8, and the power detectable in of trials is $P_{\rm sig}$ =48.0."494 In the following we will use the confidence level. Pye=18.0.," In the following we will use the confidence level, $P_{\rm sig}$ =48.0."495" The value of D computed for Pye =3BLS js SLO larger than the value for 2,15.0,", The value of $D$ computed for $P_{\rm sig}$ =31.8 is $\approx$ larger than the value for $P_{\rm sig}$ =48.0.496 For our depth calculation. we use two extremes as exanrples.," For our depth calculation, we use two extremes as examples."497 The first is an casily-detectable magnetar., The first is an easily-detectable magnetar.498" As our model for this. we use a faint pulsar with a hieh pulse fraction. such as CNOU JIG1710.2155216 in Westerlund 1 (Manoetal.2006).. which hada luuinosity of Ex=3«LO? ((0.510. keV) aud a full-iuodulated: sinusoidal pulse profile with ;14,,:20.71."," As our model for this, we use a faint pulsar with a high pulse fraction, such as CXOU J164710.2–455216 in Westerlund 1 \citep{mun06}, which had a luminosity of $L_{\rm X}$ $3\times10^{33}$ (0.5–10 keV) and a fully-modulated sinusoidal pulse profile with $A_{\rm499rms}$ =0.71."500 Pulsatious like this could be detected in of trials with as few as z120 photons., Pulsations like this could be detected in of trials with as few as $\approx$ 120 photons.501 The depth probed by any given observation scales as Ly− ⋜⋯≼↧∐∐↸∖⋜∐⋅↕⋅↖⇁↖↖⇁↕↑∐⊀↨⋯↓∖∙↴∖↴∪↑∐↸∖↸∖⋜↧↴∖↴↕⋅↖↽⊣∐∖↑↸∖↸⊳↑⋜∏⋝↕↸∖↸∖⊼⋜⋯∏≻↕↸∖ ↕↴∖↴↸∖≺∏∏↖⇁⋜↧↕↸∖∐↑↑∪⋜↧↴⋝↥⋅↕∶↴⋁∐↑⋯⋜↧∶↴∙⊾∐↸∖↑⋜∐⋅∐↘↽↸∖≋≼∶↕⊰↕∩∩⋯⊔∙ ↖↖⇁↕↑∐⊉⇀↸∶↕∩⋮⋝⊽↴↸∖↥⋅∶↴∙∷∖↴⊥ ⊓∩∙⋅↱⊐↕∩↨↘↽↸∖∖⊽⋝⋜∐∐↧⋜↧↴∖↴↕↕⋯↴∖↴∪↕≼↧⋜↧⋯↕↴∖↴↸∖↻↥⋅∪∐↕↸∖↖↖⇁↕↑∐ ⊸⇂⋯↓∖∶∩∙⊔⋖∐↿∐⋅↕↸∖⋅↖↽," The depth probed by any given observation scales as $L_{\rm X}^{1/2}$ and linearly with $A_{\rm502rms}$, so the easily-detectable example is equivalent to a bright magnetar like SGR 1900+14, with $L_{\rm X}$ $10^{35}$ (0.5–10 keV) and a sinusoidal pulse profile with $A_{\rm rms}$ =0.12 \citep{hur99}."503↸∖↑⋜↧↕⋅↕∩∩≝⊔∙∙↕∐↑∐↸∖↑∪↻↻⋜⋯↸∖↕∪↕≯ Figure 6.. we plot the depth at which each observation would have been seusitive as a function of exposure time for our casily-detectable example.," In the top panel of Figure \ref{fig:depths}, we plot the depth at which each observation would have been sensitive as a function of exposure time for our easily-detectable example."504 Only of the oobservations and of the oobservatious probe the entire depth of the Calactic plane to a distance of 21 Ipc from Earth., Only of the observations and of the observations probe the entire depth of the Galactic plane to a distance of 24 kpc from Earth.505" The other extreme is a barely-detectable pulsar. with a low luminosity Lx23 «107 aand a sinall pulse fraction «μμ, το."," The other extreme is a barely-detectable pulsar, with a low luminosity $L_{\rm X}$ $3\times10^{33}$ and a small pulse fraction $A_{\rm506rms}$ =0.15."507 This example is chosen to have been just detectable iu observations comparable to those of NTE J1810197 iu quiescence. for which Ey=2 «10°? (0.510. keV). and from which pulsations were not detected to a Bit of Aq (Cotthelfal. 2001)..," This example is chosen to have been just detectable in observations comparable to those of XTE J1810–197 in quiescence, for which $L_{\rm X}$ $2\times10^{33}$ (0.5–10 keV), and from which pulsations were not detected to a limit of $A_{\rm rms}$$<$ \citep{got04}. ."508 A source with Ay).=0.15 would require 2800et photous to be ideutified in of trials., A source with $A_{\rm rms}$ =0.15 would require 2800 photons to be identified in of trials.509 Consequently. a search sensitive to our barelv-doetectable pulsar would cover a factor of z5 less depth than a search for casily-detectable maguetars like the one πι Westerluud 1.," Consequently, a search sensitive to our barely-detectable pulsar would cover a factor of $\approx$ 5 less depth than a search for easily-detectable magnetars like the one in Westerlund 1."510 We displav the depth of a survey for a barely-detectable maguetar m the bottom paucl of Figure 6.., We display the depth of a survey for a barely-detectable magnetar in the bottom panel of Figure \ref{fig:depths}.511 None of the archival observations would probe the cutire Galaxy when searchiug for our barehlv-detectable pulsar., None of the archival observations would probe the entire Galaxy when searching for our barely-detectable pulsar.512 Iun order to estimate the nuuber of maguetars in the Calaxy and their birth rates. we need to know the fraction of the Calaxy that we have iieaninefullv surveved for maguetars.," In order to estimate the number of magnetars in the Galaxy and their birth rates, we need to know the fraction of the Galaxy that we have meaningfully surveyed for magnetars."513 Magnuetars have lnassive progenitors: neutron stars form fom stars within inital niasses >A citepliegü3.. aud there is evidence that magnuetars form from 230 stars (Cacnusleretal.2005:FigerMuno 2006).," Magnetars have massive progenitors: neutron stars form from stars within inital masses $>$ \\citep{heg03}, and there is evidence that magnetars form from $>$ 30 stars \citep{gae05,fig05,mun06}."514". The lifetimes of maguctars are thought to be ~10t vr (louveliotouctal.1999:Cacuslerot1999)... so even if some magnuetzrs receive kicks of 1000 lan s+, they will be found within —10 pc of their birth place."," The lifetimes of magnetars are thought to be $\sim$$10^4$ yr \citep{kou99,ggv99}, so even if some magnetars receive kicks of $\sim$ 1000 km $^{-1}$, they will be found within $\sim$ 10 pc of their birth place."515" Most iuassive stars are concentrated im the Calaxws spiral arms. so we have calculated the fraction of the stellar mmass iu the spiral arias that our obscrvatious have covered,"," Most massive stars are concentrated in the Galaxy's spiral arms, so we have calculated the fraction of the stellar mass in the spiral arms that our observations have covered."516" We usethe model for the stellar mass in the spiral avis from Wainscoatetal.(1992)..The locations of the arms are defined as a logarithiic spiral: where Ris the radial distance from the Galactic ceuter. Mis the azimuthal anele in raciaus (with J=0 along the lue connecting the Earth to the Calactic center. aud O<O<m for sm <0). Pg, is the racial distance at which the aris start.Qu isthe angle at which the aris start. and o is the winding constant."," We usethe model for the stellar mass in the spiral arms from \citet{wain92}.The locations of the arms are defined as a logarithmic spiral: where $R$ is the radial distance from the Galactic center, $\theta$ is the azimuthal angle in radians (with $\theta$ =0 along the line connecting the Earth to the Galactic center, and $\le$$\theta$$<$$\pi$ for $\sin l$$\le$ 0), $R_{\min}$ is the radial distance at which the arms start,$\theta_{\rm min}$ isthe angle at which the arms start, and $\alpha$ is the winding constant."517 We define four main, We define four main518most striking. and concern the red galaxy population. and the morphological types of galaxies.,"most striking, and concern the red galaxy population, and the morphological types of galaxies."519" In WINGS clusters. none of the characteristics of the colour-magnitude red sequence (slope. scatter. luminous-to-faint ratio. blue fraction, morphological mix on the red sequence) depend on global eluster properties connected with eluster mass. such as cluster velocity dispersion and X-ray luminosity."," In WINGS clusters, none of the characteristics of the colour-magnitude red sequence (slope, scatter, luminous-to-faint ratio, blue fraction, morphological mix on the red sequence) depend on global cluster properties connected with cluster mass, such as cluster velocity dispersion and X-ray luminosity."520 In contrast.af! of these characteristics vary systematically with the local galaxy density (Valentinuzzietal.2011).," In contrast, of these characteristics vary systematically with the local galaxy density \citep{valentinuzzi11}."521 Also in WINGS. we have shown that the fractions of spiral. SO and elliptical galaxies do not vary systematically with cluster velocity dispersion and X-ray luminosity (Poggianti et al 2009). while a strong morphology-density relation is present in WINGS as in any other sample (Fasano et al.," Also in WINGS, we have shown that the fractions of spiral, S0 and elliptical galaxies do not vary systematically with cluster velocity dispersion and X-ray luminosity (Poggianti et al 2009), while a strong morphology-density relation is present in WINGS as in any other sample (Fasano et al."522 in prep.)., in prep.).523" In addition. Baloghetal.(2004)... analysing the colour distribution of bright (M,< I8) galaxies in the local Universe (οκ 0.08)."," In addition, \cite{balogh04}, analysing the colour distribution of bright $M_r\leq 18$ ) galaxies in the local Universe $z < 0.08$ )."524 found that the red fraction of galaxies is a strong function of local density. increasing from 10G—90 of the population in the lowest density environments to ~70% at the highest densities. while within the virialized regions of clusters it shows no significant dependence on cluster velocity dispersion.," found that the red fraction of galaxies is a strong function of local density, increasing from $\sim 10\%- 30\%$ of the population in the lowest density environments to $\sim 70\%$ at the highest densities, while within the virialized regions of clusters it shows no significant dependence on cluster velocity dispersion."525 Also Martínez.Coenda.&Muriel(2008). found that bright galaxy properties do not clearly depend on cluster mass for clusters more massive than AYLOM.. while they correlate with clustercentric distance.," Also \cite{mart08} found that bright galaxy properties do not clearly depend on cluster mass for clusters more massive than $M\sim 10^{14}M_{\odot}$, while they correlate with clustercentric distance."526 Our results on global and local environments now allow and require a comparison with theoretical expectations. to understand whether simulations predict a mass segregation with environment. both considering the initial and evolved halo mass and the local density and how they predict the evolution with redshift as a function of the environment.," Our results on global and local environments now allow and require a comparison with theoretical expectations, to understand whether simulations predict a mass segregation with environment, both considering the initial and evolved halo mass and the local density and how they predict the evolution with redshift as a function of the environment."527 In this paper. we have tried to quantify the importance of the local density in shaping the stellar galaxy mass function of galaxies located in different environments both at low and intermediate redshifts taking directly into account also the cluster environment.," In this paper, we have tried to quantify the importance of the local density in shaping the stellar galaxy mass function of galaxies located in different environments both at low and intermediate redshifts taking directly into account also the cluster environment."528 Our main conclusion is that at all redshifts and in all environment local density plays a significant role in driving the mass distribution., Our main conclusion is that at all redshifts and in all environment local density plays a significant role in driving the mass distribution.529 In the general field at low-z. local density influences the stellar mass distribution both at low and high masses.," In the general field at low-z, local density influences the stellar mass distribution both at low and high masses."530" In the field at high- the dependence exists at high masses. while our mass limit ""oes not allow us to inspect low masses."," In the field at high-z, the dependence exists at high masses, while our mass limit does not allow us to inspect low masses."531 On the other hand. in clusters. the biggest differences are always confined at low masses.," On the other hand, in clusters, the biggest differences are always confined at low masses."532" If we perform a higher mass cut (log/M.10.1 for WINGS and logM,/M.10.4 in EDISCS).M. every difference in slope disappears."," If we perform a higher mass cut $ \log M_{\ast}/M_{\odot}>10.1$ for WINGS and $ \log M_{\ast}/M_{\odot}>10.4$ in EDisCS), every difference in slope disappears."533 We have found that not only the shape of the mass function depends on local density. but also the highest mass reached in euch density bin: very massive galaxies (having excluded the cluster BCGs) seem to be located only in the highest density bin while they are absent at lower densities (the so-called mass segregation).," We have found that not only the shape of the mass function depends on local density, but also the highest mass reached in each density bin: very massive galaxies (having excluded the cluster BCGs) seem to be located only in the highest density bin while they are absent at lower densities (the so-called mass segregation)."534 Comparing our results with those present in Calvi et al. (, Comparing our results with those present in Calvi et al. (535QUIIb in preparation) and Vuleanietal.(201Ib). for the global environment. we conclude that local environment plays a much more visible role than global environment in shaping the stellar galaxy mass distribution.,"2011b in preparation) and \cite{global} for the global environment, we conclude that local environment plays a much more visible role than global environment in shaping the stellar galaxy mass distribution."536 We thank the referee for useful comments., We thank the referee for useful comments.537 We would like to thank the whole WINGS team for stimulating discussions., We would like to thank the whole WINGS team for stimulating discussions.538 We also would like to thanks Alfonso Aragónn-Salamanca and Gabriella De Lucia whose suggestions helped us to improve the paper., We also would like to thanks Alfonso Aragónn-Salamanca and Gabriella De Lucia whose suggestions helped us to improve the paper.539 BV and BMP acknowledge financial support from ASI contract I/016/07/0 and ASLINAF I/009/10/0., BV and BMP acknowledge financial support from ASI contract I/016/07/0 and ASI-INAF I/009/10/0.540 BV also acknowledges financial support from the Fondazione Ing., BV also acknowledges financial support from the Fondazione Ing.541 Aldo Gini., Aldo Gini.542(deuterium) burnius to the total huninesitv.,(deuterium) burning to the total luminosity.543 For the most massive objects. this ratio reaches fairly large values (well over )).," For the most massive objects, this ratio reaches fairly large values (well over )."544 Tlowever. the main sequence is where this ratio is esseutially (60. where Ikelvin-Uehuholtz contraction has ceased). aud so it is clear that uoue of these models goes through a deuteriuni main sequence stage.," However, the main sequence is where this ratio is essentially (i.e., where Kelvin-Helmholtz contraction has ceased), and so it is clear that none of these models goes through a deuterium main sequence stage."545 The bottom right xuel shows the evolution of the fraction of the initial deuterium Gu this case. gp—ὃν10. 7) that has mined.," The bottom right panel shows the evolution of the fraction of the initial deuterium (in this case, $y_{\rm D,i}=2\times 10^{-5}$ ) that has burned."546 Hieher mass objects burn a larger fraction of their initial deuterimm. and do so faster than ower nass objects," Higher mass objects burn a larger fraction of their initial deuterium, and do so faster than lower mass objects."547 Regardless of mass. very little deuterun burus after a few hundred million. veurs.," Regardless of mass, very little deuterium burns after a few hundred million years."548 Note. in comparing the top row to the bottom row. hat the 15-A£; and 20-M; inodels. which fuse the ercatest amount of deuterimun (among the models displaved). cool and shriuk very quickly after the deuterunm-buruius plase.," Note, in comparing the top row to the bottom row, that the $M_J$ and $M_J$ models, which fuse the greatest amount of deuterium (among the models displayed), cool and shrink very quickly after the deuterium-burning phase."549 Iun Fie. 2..," In Fig. \ref{fig:frac_burnedt},"550 we examine the deuteriunu-buruiug evolutionary profiles of 13-M objects from a variety of models., we examine the deuterium-burning evolutionary profiles of $M_J$ objects from a variety of models.551 Each row shows ;analogous plots to the bottom row of Fie. l..," Each row shows analogous plots to the bottom row of Fig. \ref{fig:diagnosticsB2},"552 ouly instead of cdiffercut curves represcuting different amass objects. they represent differeut model properties.," only instead of different curves representing different mass objects, they represent different model properties."553 The left coliuun shows the evolution of the ratio of nuclear power to total huninositv. aud the right coluun shows the fraction of the initial deuterium that burns.," The left column shows the evolution of the ratio of nuclear power to total luminosity, and the right column shows the fraction of the initial deuterium that burns."554 The three rows show. from top to bottom. moclels IIe22IIe32. (vurviug helm fraction). models D1DI (varving initial deuteriuui fraction). aud models ZO21.0 (varviug mctallicity through its influence ou atmospheric opacity).," The three rows show, from top to bottom, models He22–He32 (varying helium fraction), models D1--D4 (varying initial deuterium fraction), and models Z0–Z1.0 (varying metallicity through its influence on atmospheric opacity)."555 Each row also shows models IIe25 @vhlich is also D2) and Z1.0. for comparison to “fiducial” models.," Each row also shows models He25 (which is also D2) and Z1.0, for comparison to “fiducial” models."556 First. if is important to note the difference of the radiative boundary condition.," First, it is important to note the difference of the radiative boundary condition."557 The Zsequence io0dels have higher opacity. which leads to slower cooling. than the other models Gvlich have the ? boundary condition).," The Z-sequence models have higher opacity, which leads to slower cooling, than the other models (which have the \citealt{burrows_et_al1997} boundary condition)."558 As a result. models Z1.0 and TWe25/D2. which are otherwise identical. have markedly differeut evolutionary trajectories.," As a result, models Z1.0 and He25/D2, which are otherwise identical, have markedly different evolutionary trajectories."559 The former reaches a peak nuclear-to-total power ratio of zmNOU.. while the latter reaches oulv +50%..," The former reaches a peak nuclear-to-total power ratio of $\approx$, while the latter reaches only $\approx$."560 Furthermore. the former eventually burus of its initial deuterimm. while the latter burus only of its.," Furthermore, the former eventually burns of its initial deuterium, while the latter burns only of its."561 In fact. of the Z-sequence imnodels; model ZO.3 (with «.— solar οσοτα] abundance) mere nearly approximates the II1e25/D2 evolution than does Z1.0.," In fact, of the Z-sequence models, model Z0.3 (with $\times$ solar elemental abundance) more nearly approximates the He25/D2 evolution than does Z1.0."562 With its slower cooling. model Z1.0 has a moderate uuclear-burnius to total huniuositv ratio until later times: the ratio shown in the left coluuu stavs above πι] S Cv.," With its slower cooling, model Z1.0 has a moderate nuclear-burning to total luminosity ratio until later times; the ratio shown in the left column stays above until $\sim$ 5 Gyr."563 More generally. within each row of Fig. 2..," More generally, within each row of Fig. \ref{fig:frac_burnedt},"564 the expected trends hold., the expected trends hold.565 The top row shows that more heliuniich models buru a greater fraction of their initial deuteriuni which is uusurprisng because these are the mocels with fewer electrons to support the mass via degeneracy pressure: thus. these models have denser. hotter cores.," The top row shows that more helium-rich models burn a greater fraction of their initial deuterium, which is unsurprising because these are the models with fewer electrons to support the mass via degeneracy pressure; thus, these models have denser, hotter cores."566 The middle row shows that models with higher initial deuteriua coutent burn a ereater fraction of their initial deuterium., The middle row shows that models with higher initial deuterium content burn a greater fraction of their initial deuterium.567" This is a ""Cnewhat subtle poiut.", This is a somewhat subtle point.568 The deuteru-burning rate is roughly linear in gp. suggesting that. other thines being equal. the fractional depletion. of deuteriua with time should be coustaut irrespective of initial deuterim abundance.," The deuterium-burning rate is roughly linear in $y_D$, suggesting that, other things being equal, the fractional depletion of deuterium with time should be constant irrespective of initial deuterium abundance."569 Iowever. other things are not equal," However, other things are not equal."570 Iu particular. the central temperature of more deuteriunirich models is maintained at a higher value for a lonecr period of time.," In particular, the central temperature of more deuterium-rich models is maintained at a higher value for a longer period of time."571 As a result. the integrated fractional amount of deuteriuna burned is ereater for these models.," As a result, the integrated fractional amount of deuterium burned is greater for these models."572 The bottom row shows that more metal-rich models burn a greater fraction of their initial ceuterivim. which stands to reason because their higher opacities produce a blanket effect. allowing them to maintain higher core teiiperatures for a longer time.," The bottom row shows that more metal-rich models burn a greater fraction of their initial deuterium, which stands to reason because their higher opacities produce a blanket effect, allowing them to maintain higher core temperatures for a longer time."573 We now quantity the deuterimm-buruing lass lit. and its dependence on the various model paralucters we have varied.," We now quantify the deuterium-burning mass limit, and its dependence on the various model parameters we have varied."574 Figure 3. displavs the siue basic information in two different wavs., Figure \ref{fig:edges} displays the same basic information in two different ways.575 Iu the left colum. the fraction of the initial deuterim that combusts within LO Gyr is plotted versus object mass.," In the left column, the fraction of the initial deuterium that combusts within 10 Gyr is plotted versus object mass."576 Horizontal dashed lines are plotted at50%... aud 90%.. illustrating various (arbitrary) deuterimu-burniues cut-offs.," Horizontal dashed lines are plotted at, and , illustrating various (arbitrary) deuterium-burning cut-offs."577 The right column plots the deuterimm-burning mass edge for each of these three criteria (i.c.. the mass at the intersection of cach curve in the left column with the corresponding dashed line) as a function of the three tunable model parameters: Y. gp. aud Z.," The right column plots the deuterium-burning mass edge for each of these three criteria (i.e., the mass at the intersection of each curve in the left column with the corresponding dashed line) as a function of the three tunable model parameters: $Y$, $y_{\rm D,i}$ , and $Z$."578 From top to bottom. the rows show the same respective model sets as in Fie. 2..," From top to bottom, the rows show the same respective model sets as in Fig. \ref{fig:frac_burnedt}."579 As in Fie. 2.. ," As in Fig. \ref{fig:frac_burnedt}, ,"580models IIe25/D2 aud Z1.0 are shown in all three panels of the left column., models He25/D2 and Z1.0 are shown in all three panels of the left column.581 The last three cohuuus of Table 1 contain the sale imuformation as the rieht cobhuunu of Fig. 3..," The last three columns of Table \ref{ta:models} contain the same information as the right column of Fig. \ref{fig:edges},"582 and also include data for the sequence of models (ΤουT3)., and also include data for the sequence of models (T0.3–T3).583 Note that the solarimetallicity model (TL) and the fiducial ? model (IIc25/D2) are quite similar to one another., Note that the solar-metallicity model (T1) and the fiducial \citet{burrows_et_al1997} model (He25/D2) are quite similar to one another.584 There are four main lessons fromthe datain Fie., There are four main lessons fromthe datain Fig.585 9 aud Table 1::, \ref{fig:edges} and Table \ref{ta:models}: :586components is progressively smaller than a cooling flow model as the temperature decreases.,components is progressively smaller than a cooling flow model as the temperature decreases.587 The lack of detections of cool gas in other clusters using RGS observations could be due to their relatively short exposures. which are typically only 30-40 ks (2)..," The lack of detections of cool gas in other clusters using RGS observations could be due to their relatively short exposures, which are typically only 30–40 ks \citep{Peterson03}."588 The large range in temperature in this cluster may be connected to the lack of disruption in its core., The large range in temperature in this cluster may be connected to the lack of disruption in its core.589 The high enrichment of the central parts of the cluster indicates it has been stable for 8 Gyr or more (2).., The high enrichment of the central parts of the cluster indicates it has been stable for 8 Gyr or more \citep{SandersEnrich06}. .590 Fig., Fig.591 10 and Fig., \ref{fig:norms} and Fig.592 12. show that a full simple cooling flow. where gas is cooling by radiative cooling at a constant rate. is not operating in this cluster.," \ref{fig:mdott} show that a full simple cooling flow, where gas is cooling by radiative cooling at a constant rate, is not operating in this cluster."593 However there are some possible reasons why the amount of cold gasmay be underestimated:, However there are some possible reasons why the amount of cold gasmay be underestimated:594Below we present simple estimations of electron acceleration by shocks.,Below we present simple estimations of electron acceleration by shocks.595" The injection spectrum of electrons accelerated in shocks is power-law. QUE.)xE,7. and the maximum energy of accelerated electrons can be estimated from a kinetic equation describing their spectrum at the shock (Berezinskiietal.1990)... E,702,/D3. where ry010 em/s is the velocity of shock front. D is the diffusion coefficient at the shock front and the energy. losses of electrons (synchrotron and IC) ave: dI,/d!=—3E?."," The injection spectrum of electrons accelerated in shocks is power-law, $Q(E_e)\propto596E_e^{-2}$, and the maximum energy of accelerated electrons can be estimated from a kinetic equation describing their spectrum at the shock \citep{ber90}, $E_{max}\simeq {v_{sh}^2}/{D\beta}$ , where $v_{sh}\sim 10^8$ cm/s is the velocity of shock front, $D$ is the diffusion coefficient at the shock front and the energy losses of electrons (synchrotron and IC) are: $dE_e/dt=-\beta E_e^2$."597" Recall d is a function of the magnetic and background radiation energy densities. ΟΡ”... where oy is Thompson cross section and ie=iw,+wy is the combined energy density of background photons wy, and the magnetic energy. density wy respectively."," Recall $\beta$ is a function of the magnetic and background radiation energy densities, $\beta \sim w\sigma_Tc/(m_ec^2)^2$, where $\sigma_T$ is Thompson cross section and $w=w_{ph}+w_B$ is the combined energy density of background photons $w_{ph}$ and the magnetic energy density $w_B$ respectively."598 It is difficult to estimate the diffusion coefficient near the shock., It is difficult to estimate the diffusion coefficient near the shock.599 For qualitative estimation. we can use the Bohm diffusion (~rp (je). where rj is the Larmor radius of electrons.," For qualitative estimation, we can use the Bohm diffusion $\sim r_L(E_e)$ c), where $r_L$ is the Larmor radius of electrons."600" Using the (vpical values of these parameters. we obtain E,,,~1TeV-vD1/2.zie1ο45. where ος is theshock velocity in units of 106m/s. B.5 is the magnetic field in the shock in units of 10.°G and wy is the energy density in units of Perg ιν."," Using the typical values of these parameters, we obtain $E_{max}\sim6011~TeV~v_8B_{-5}^{1/2}w_{-12}^{-1/2}$, where $v_8$ is theshock velocity in units of $10^8$ cm/s, $B_{-5}$ is the magnetic field in the shock in units of $10^{-5}$ G and $w_{-12}$ is the energy density in units of $^{-12}$ $^3$."602 The spectrum of electrons in (he bubble is modilied by processes of energy losses ancl escape., The spectrum of electrons in the bubble is modified by processes of energy losses and escape.603" It can be derived [rom the kinetic equation where dE/di=3E?+Vu(z)E describes the inverse Compton. svnchrotron and acliabalic (because of wind velocity variations) energy losses. Tis the time of particle escape from the bubble. and QUE)=NE?0(E,,,,—E) describes particles injection spectrum in the bubble."," It can be derived from the kinetic equation where $dE/dt=\beta E^2+\nabla u(z)E$ describes the inverse Compton, synchrotron and adiabatic (because of wind velocity variations) energy losses, $T$ is the time of particle escape from the bubble, and $Q(E)=KE^{-2}\theta(E_{max}-E)$ describes particles injection spectrum in the bubble."604 As one can see. in general case the spectrum of electrons in the bubble cannot be described by a single power-law as assumed by Suetal.(2010).," As one can see, in general case the spectrum of electrons in the bubble cannot be described by a single power-law as assumed by \citet{meng}."605". The spectrum of electrons has a break at the energy. £,~1/21. where T is the characteristic time of either particle escape [rom the bubble or of the acliabatic losses. e.g. lor Vu=a (he break position folows from 7 1/a."," The spectrum of electrons has a break at the energy $E_b\sim 1/\beta606T$ where $T$ is the characteristic time of either particle escape from the bubble or of the adiabatic losses, e.g. for $\nabla u=\alpha$ the break position follows from $T\sim 1/\alpha$ ."607 By solving equation 3. we can see (hat the electron spectrum cannol," By solving equation 3, we can see that the electron spectrum cannot"608Nevertheless. this Model Bois not satisfactory.,"Nevertheless, this Model B is not satisfactory."609 Tn effect. a cavity with zp=0.7 requies a cavity of size rp~2 Gpc. which is more than half the path-leneth to the highest-: quasar in the sample (ie. 3.75 Cpe for τω=3.6).," In effect, a cavity with $\zP = 0.7$ requires a cavity of size $\rP610\sim 2$ Gpc, which is more than half the path-length to the $z$ quasar in the sample (i.e. 3.75 Gpc for $z_Q=3.6$ )."611 Ποσο most linc-of-sights would cross many overlapping cavities (henee condition. is not satisfied) and such a situation not properly clescribed bw eq. (2))., Hence most line-of-sights would cross many overlapping cavities (hence condition is not satisfied) and such a situation not properly described by eq. \ref{eq:nhb}) ).612 Conditione (consistency with other reliable information. see §2.3.2)) is not respected either.," Condition (`consistency with other reliable information', see \ref{sec:cond}) ) is not respected either."613 Fist. the cumulative volue of quasar influence on eexceeeds of the total volume sampled.," First, the cumulative volume of quasar influence on exceeeds of the total volume sampled."614 Secoud. the exponent of (112). 5δν is mach too steep if we were to compare our Model D to model-predictions of the evolution of the WITA," Second, the exponent of $(1+z)$, $\gamma = -3.0$, is much too steep if we were to compare our Model B to model-predictions of the evolution of the WHIM."615L For instance. most models iu Davéetal.(2001) are characterized by redshift-averaged values of + inthe range Lito 1.5.," For instance, most models in \citet{davea} are characterized by redshift-averaged values of $\gamma$ in the range $-1.1$ to $-1.5$."616 Tn order to ensure a plivsically 1006 meaninetil ddistribution. we replaced the (+) power-law dependence on redshift by an exponential fit to the WHIM Model D2 of Davéctal.(2001).. the description of which lies iu the ποτάτον of eq. (3)).," In order to ensure a physically more meaningful distribution, we replaced the $\gamma$ ) power-law dependence on redshift by an exponential fit to the WHIM Model D2 of \citet{davea}, the description of which lies in the numerator of eq. \ref{eq:nhc}) )."617 Replacing the previous best fit distribution with ~=3 bw a distribution that matches the behavior of the WIITME with redshift better [lay using cither eq. (3)), Replacing the previous best fit distribution with $\gamma =-3$ by a distribution that matches the behavior of the WHIM with redshift better [by using either eq. \ref{eq:nhc}) )618 or 5&1.2 and eq. (2))], or $\gamma \simeq -1.2$ and eq. \ref{eq:nhb}) )]619 conies af a price. however.," comes at a price, however."620 Iu effect. such distributions alwavs result m a smooth rise in fransnüsson towards the short wavelength extremity of the SED. bevond 500À.," In effect, such distributions always result in a smooth rise in transmission towards the short wavelength extremity of the SED, beyond 500."621. Interestingly. the more recent composite spectrum from Τσ prescuts such a rise in the far UV as displaved in Fie. 2..," Interestingly, the more recent composite spectrum from TZ02 presents such a rise in the far UV as displayed in Fig. \ref{fig2}."622 TZ02 have questioned the reality of this vise., TZ02 have questioned the reality of this rise.623 The latter mieht be caused by a tendency of high redshift quasars to have a harder ISED., The latter might be caused by a tendency of high redshift quasars to have a harder ISED.624 Nonetheless. because the TZ02 work contaius more objects than the ZN97. and because this feature is seen iu both radio-loud as well as racdio-quict quasars. we will take their results at face values aud compare their radio-quiet composite SED with models which used eq. (3)).," Nonetheless, because the TZ02 work contains more objects than the ZK97, and because this feature is seen in both radio-loud as well as radio-quiet quasars, we will take their results at face values and compare their radio-quiet composite SED with models which used eq. \ref{eq:nhc}) )."625 The thick solid hue in Fie., The thick solid line in Fig.626 2. represents our Model €. which is characterized by a signifieautlv sinaller tp=0.3.," \ref{fig2} represents our Model C, which is characterized by a significantly smaller $\zP = 0.3$."627 Although the fit is imperfect. it inatelies the overall treuds present in the TZ02 composite spectrum.," Although the fit is imperfect, it matches the overall trends present in the TZ02 composite spectrum."628The adopted intrinsic SED used here is somewhat harder. corresponding to an iudex of 0.72 (which is the value interred by TZ02).,"The adopted intrinsic SED used here is somewhat harder, corresponding to an index of $-0.72$ (which is the value inferred by TZ02)."629" For Model ο, with zp=0.3 we fud that rp=800 Mpc."," For Model C, with $\zP = 0.3$ we find that $\rP = 800$ Mpc."630 A single cavity occupies therefore of the total volume sampled., A single cavity occupies therefore of the total volume sampled.631" Using the kuown huninosity function of bright QSOs πιο, a quasar deusity of order £=3«107Mpe° (Dovle2001)]]. the correspouding to this value of ls too lavee by a factor ~650 and conditionc is therefore not fulfilled on the eround of the known density of QSOs."," Using the known luminosity function of bright QSOs [i.e. a quasar density of order $\xi = 3 \times 10^{-7} \, {\rm Mpc}^{-3}$ \citep{Boyle}] ], the corresponding to this value of is too large by a factor $\sim 650$ and condition is therefore not fulfilled on the ground of the known density of QSOs."632 With this caveat ii iind. we proceed to study the behavior of the absorption of our putative intergalactic conrponeut at waveleusths shorter than provided bv IIST-FOS.," With this caveat in mind, we proceed to study the behavior of the absorption of our putative intergalactic component at wavelengths shorter than provided by HST-FOS."633 This will allow us to calibrate a new method to detect the WIIINE aud. indirectly. to determine to what extent conditionbis satisfied in Model €. The derivation of the composite SED of Model C required using eq. (3))," This will allow us to calibrate a new method to detect the WHIM and, indirectly, to determine to what extent condition is satisfied in Model C. The derivation of the composite SED of Model C required using eq. \ref{eq:nhc}) )"634 aud calculating the rausluission fiction at evenly spaced redshift values., and calculating the transmission function at evenly spaced redshift values.635 We now turn to the particularities of these ΠΠ curves., We now turn to the particularities of these transmission curves.636 Two such trausuission curves are presented in Fig., Two such transmission curves are presented in Fig.637 3. for illustrative. purposes or quasars of redshifts 2.76 and 0.33., \ref{fig3} for illustrative purposes for quasars of redshifts 2.76 and 0.33.638 Clearly. the uain opacity source is the line.," Clearly, the main opacity source is the line."639 The contribution of photoclectrie absorption o the total opacity is relatively stall as illustrated in the Figure while the contribution of higher series lines can be appreciated by the reduced size of the jumps that are visible iu the trausiissiou curves., The contribution of photoelectric absorption to the total opacity is relatively small as illustrated in the Figure while the contribution of higher series lines can be appreciated by the reduced size of the jumps that are visible in the transmission curves.640 The main result to eurphasize is that a discontinuity appears to the blue of )) (that is bevoud the UV linüt of the IIST- detector) in all the calculated transimission curves. not only when assiuniuse the parameters of Model €. but in all the ddistributious that satisfied condition « Ceood fit’. see 82.:3.2)).," The main result to emphasize is that a discontinuity appears to the blue of ) (that is beyond the UV limit of the HST-FOS detector) in all the calculated transmission curves, not only when assuming the parameters of Model C, but in all the distributions that satisfied condition (`good fit', see \ref{sec:cond}) )."641 By comparing the transmission curves im Fie., By comparing the transmission curves in Fig.642 3 with those resulting from fforest absorbers. ai clear difference clacrecs.," \ref{fig3} with those resulting from forest absorbers, a clear difference emerges."643needs the different numbers to be estimated to be of roughly the same order of magnitude.,needs the different numbers to be estimated to be of roughly the same order of magnitude.644" For this reason we estimate for some parameters D, which for bin 5 is defined as where £5 is the first multipole in bin b.", For this reason we estimate for some parameters $D_b$ which for bin $b$ is defined as where $\ell_b$ is the first multipole in bin $b$.645" Since the C, are coupled. one can not use all multipoles in the data vector. the covariance matrix would in this case become singular."," Since the $\tilde C_\ell$ are coupled, one can not use all multipoles in the data vector, the covariance matrix would in this case become singular."646 One has to choose a number NY of multipoles £; for which one finds d;., One has to choose a number $N^\mathrm{in}$ of multipoles $\ell_i$ for which one finds $d_i$.647 low many multipoles to use depends on how tight the CS are coupled which depends on the width iu of the kernel (Fig. 5))," How many multipoles to use depends on how tight the $\tilde648C_\ell$ are coupled which depends on the width $\Delta\ell_\mathrm{kern}$ of the kernel (Fig. \ref{fig:fwhmrel}) )"649 or the width 2; of the correlation matrix., or the width $\Delta\ell_\mathrm{cor}$ of the correlation matrix.650 Phe width of the correlation matrix(normalised with the psuedo power spectrum) varies with window size in the same wav as the width of the kernel varies with window size., The width of the correlation matrix(normalised with the psuedo power spectrum) varies with window size in the same way as the width of the kernel varies with window size.651 In fact for the top-hat window these two widths are the same and for the Gaussian window we found that Ato.&LARA., In fact for the top-hat window these two widths are the same and for the Gaussian window we found that $\Delta\ell_\mathrm{cor}\approx1.42\Delta\ell_\mathrm{kern}$.652 The optimal number of IN to use seems to be ANCUS&3/2μον «λέων., The optimal number of $N^\mathrm{in}$ to use seems to be $N^\mathrm{in}\approx3/2\ \ell_\mathrm{max}/\Delta\ell_\mathrm{kern}$ .653 To use a lower INT increases the error bars on the estimates and a higher A does not improve the estimates., To use a lower $N^\mathrm{in}$ increases the error bars on the estimates and a higher $N^\mathrm{in}$ does not improve the estimates.654 One can at most fit for as many C's as the number of ο (NV)duy one has used in the analvsis., One can at most fit for as many $C_\ell$ s as the number of $\tilde C_\ell$ $N^\mathrm{in}$ ) one has used in the analysis.655 So one needs to find th: pe . . ⋜↧⊔⊔⊔↓∣⋊⋅↓⋅⇀∖⋯≞⇀∖⋯∪⇂∣⋡↓⊔∖⇁⋜↧↓⋯⊾⊳∖∐∕↾⇂↓⋅∪⊔↓∖∖⋎↓⊔≼∼↓↕∪⊔∢⊾≼↛⋜⋃⊔⇍∪⊔⊳∖⇂↓⋅⋯⇍∣↿↓↥⋖⊾⇂⊔∐⊳∖↓∡∙∖⇁↓≻∪∖∖⊽⋖⋅↓⋅⊳∖↓≻∢⋅≼⇍⇂↓⋅⊔⊔↓↙⊽∣⋡ ⋅ ↓⊔⇀∖↓≻↓≻∢⊾↓⊔⇂⊲∟∖↿∖∣⊲⇀⊲∩⋜⋯∠⇂↿∖↓⊲↸∣∩∖∖⋎∢⋅⇂⋅∪⊔⊔∠⊓↓↕⋜∐↿↓∐⋅⇂⋅⊔∐≼⇍⋖⋟↓⋅↓⋅⋖⊾↓⋜↧⇂↕∢≱↓↕⊔↓⋜⊔↓⋰∟∖≼⇍⋜⋯∣⋈⋅∖∖⊽↓⋰↓∏∢⊾⊔⋜↧⊳∖ where AS is the noise correlation matrix which has tobe precomputecl for a specific noise model (analytically or by, So one needs to find a number $N^\mathrm{bin}\le N^\mathrm{in}$ of bin values $D_b$ from which one can construct the full sky power spectrum $C_\ell$ In Appendix \ref{app:cor}) ) and \ref{app:noise}) ) we found that the full correlation matrix can be written as where $M_{ij}^\mathrm{N}$ is the noise correlation matrix which has tobe precomputed for a specific noise model (analytically or by656The binary fraction of massive stars is not well constrained. but studies of young open clusters indicate that it can easily reach (e.g.?)..,"The binary fraction of massive stars is not well constrained, but studies of young open clusters indicate that it can easily reach \citep[e.g.][]{san08}."657 The effects of binarity on stellar evolution depend not only on the properties of the components. but also on the mass ratio. the separation. the eccentricity.," The effects of binarity on stellar evolution depend not only on the properties of the components, but also on the mass ratio, the separation, the eccentricity."658 Consequently. their study is complex. requiring the exploration of a large parameter space (?)..," Consequently, their study is complex, requiring the exploration of a large parameter space \citep{dem11}."659 In the case of young systems with large separations. the components of the binary evolve independently. following single-star evolution (2)..," In the case of young systems with large separations, the components of the binary evolve independently, following single-star evolution \citep{pav05}."660 In evolved binary systems. the evolutionary scheme is completely different.," In evolved binary systems, the evolutionary scheme is completely different."661 If Roche lobe overflow happens. the surface chemistry and rotational rate of the components are deeply affected.," If Roche lobe overflow happens, the surface chemistry and rotational rate of the components are deeply affected."662 In particular. the mass gainer Is expected to show large nitrogen surface abundance enhancements (?)..," In particular, the mass gainer is expected to show large nitrogen surface abundance enhancements \citep{langer08}."663 In order to better understand the physics of binary systems and to test the predictions of theoretical models. it is thus important to quantitatively analyze the properties of massive binary systems with well-constrained orbital parameters.," In order to better understand the physics of binary systems and to test the predictions of theoretical models, it is thus important to quantitatively analyze the properties of massive binary systems with well-constrained orbital parameters."664 LZCCep 2209481) Is a double-lined spectroscopic binary system composed of a primary component with a spectral type 88.5III and an O99.5V secondary (?).., Cep 209481) is a double-lined spectroscopic binary system composed of a primary component with a spectral type 8.5III and an 9.5V secondary \citep{con71}.665 The projected rotational velocities were reported to be close to l55 and 105 by ?.., The projected rotational velocities were reported to be close to 155 and 105 by \citet{howarth91}.666 The period of the system was found to be 3.070508 d by ?.. and was confirmed by ? and ?..," The period of the system was found to be 3.070508 d by \citet{rao72}, and was confirmed by \citet{howarth91} and \citet{harries98}."667 The eccentricity estimated by ? 1s about 0.031., The eccentricity estimated by \citet{howarth91} is about 0.031.668 Although small. this is significant enough to not be neglected.," Although small, this is significant enough to not be neglected."669 Indeed. according to ?.. the null hypothesis of a circular orbit can be rejected with a significance level of about 0.05.," Indeed, according to \citet{luc71}, the null hypothesis of a circular orbit can be rejected with a significance level of about 0.05."670 However ? determined an orbital eccentricity close to zero in their orbital solution (e=0.017+ 0.084)., However \citet{harries98} determined an orbital eccentricity close to zero in their orbital solution $e = 0.017\pm0.084$ ).671 It thus appears that the cireularization of the system is not clearly established., It thus appears that the circularization of the system is not clearly established.672 From the photometric point of view. CCep is not an eclipsing system but ellipsoidal variations are clearly visible in the light curve.," From the photometric point of view, Cep is not an eclipsing system but ellipsoidal variations are clearly visible in the light curve."673 The photometric analysis indicates that this binary is an evolved system (?) with à secondary component that fills up its Roche lobe., The photometric analysis indicates that this binary is an evolved system \citep{hill76} with a secondary component that fills up its Roche lobe.674 Hence. the system is most likely in a configuration of post case A mass transfer Le.. a system where the mass transfer happened while both components are still in à hydrogen-burning core phase (?).. LZ," Hence, the system is most likely in a configuration of post case A mass transfer i.e., a system where the mass transfer happened while both components are still in a hydrogen-burning core phase \citep{howarth91}."675CCep is thus a target of choice for the study of the effects of binary interactions and their impacts on massive star evolution., Cep is thus a target of choice for the study of the effects of binary interactions and their impacts on massive star evolution.676 The present paper is organized as follows., The present paper is organized as follows.677 Sect., Sect.678 2 presents the journal of observations and the data-reduction technique., \ref{s_obs} presents the journal of observations and the data-reduction technique.679 Then. we devote the Sect.," Then, we devote the Sect."680 3 to the determination of the orbital solution and the spectroscopic classification., \ref{s_orb} to the determination of the orbital solution and the spectroscopic classification.681 Using the radial velocities obtained from the orbital solution. we apply a disentangling programme to separate the individual spectrum of both components.," Using the radial velocities obtained from the orbital solution, we apply a disentangling programme to separate the individual spectrum of both components."682 In Sect. 4..," In Sect. \ref{s_spec},"683 we apply the CMFGEN atmosphere code on the separated spectra to determine the main stellar and wind parameters as well as the surface abundances of each star., we apply the CMFGEN atmosphere code on the separated spectra to determine the main stellar and wind parameters as well as the surface abundances of each star.684 These parameters provide us with information about the stars’ evolutionary status., These parameters provide us with information about the stars' evolutionary status.685 The last step in our investigation is reported in Sect., The last step in our investigation is reported in Sect.686 5. and consists in the analysis of the Hipparcos light curve., \ref{s_light} and consists in the analysis of the Hipparcos light curve.687 It provides the system inclination and consequently the real masses of the stars., It provides the system inclination and consequently the real masses of the stars.688 All the parameters and results determined in the present paper are discussed in Sect. 6.., All the parameters and results determined in the present paper are discussed in Sect. \ref{s_disc}.689 Finally. we present the conclusions in Sect. 7.. LZ," Finally, we present the conclusions in Sect. \ref{s_conc}."690CCep was observed with the spectropolarimeter NARVAL mounted on the Téllescope Bernard Lyot (TBL) located at the Pic du Midi observatory in the french Pyrenees., Cep was observed with the spectropolarimeter NARVAL mounted on the Téllescope Bernard Lyot (TBL) located at the Pic du Midi observatory in the french Pyrenees.691 Table 1. gives the journal of observations., Table \ref{tab_obs} gives the journal of observations.692 A total of ten spectra over a period, A total of ten spectra over a period693may lie a factor of a few lower).,may lie a factor of a few lower).694 We- now use Model C as a test case. since. it⋅⋅ is the most physical at haud under the assumption that the 500 wise iu the composite ISED of TZ02 is real aud that the break is entirely due to intergalactic . ⋜∏⋝↴∖↴∪↥⋅," We now use Model C as a test case, since it is the most physical at hand under the assumption that the 500 rise in the composite ISED of TZ02 is real and that the break is entirely due to intergalactic absorption."695↻⊓∪∐∙⊟≻↥⋅⋜⋯⋅↖⇁≺∣∏⋜↧↴∖↴⋜∐⋅−∙≺↘≻∩∙⋅↱⊐∙∪∐↸∖∏∐≼↧↴∖↴ ⋅ Taco quiteED siguificaut.," For any quasar $z_Q > 0.5$, one finds that is quite significant."696 .Typically. του- 2;0.25Fig.as secu otc Fie.," Typically, $\tauv \ga 0.25$ as seen in \ref{fig4}."697 I£ thatmuch absorption were preseut. it . would therefore⋅⋅⋝⋡ be a striking ⋅feature in≽⇁⇁ the £u-UVTZ02 spectra [provided the quasar could be observed Dlueward of 1200 )].," If that much absorption were present, it would therefore be a striking feature in the far-UV spectra [provided the quasar could be observed blueward of 1200 )]."698" It turus however, that the observations of (Avis,the quasar TS1513out.|5921 by (Bowen.Tripp.&Joeukius2001.το=(0.807) with STIS aud ΠΕΣΟ1312 by (Ixrissctal.2001.το=2.885) with FUSE. show no indication at all of a discontinuity at the expected level of 74469=0.27 and 0.28. respectively. in the 1160 irregion. as compared to the extrapolation from the 1270 iregion."," It turns out, however, that the observations of the quasar HS1543+5921 by \citep[][$z_Q=0.807$]{bowen} with STIS and HE2347–4342 by \citep[][$z_Q=2.885$]{kriss} with FUSE, show no indication at all of a discontinuity at the expected level of $\tauv699=0.27$ and 0.28, respectively, in the 1160 region, as compared to the extrapolation from the 1270 region."700 We consider that a discontiuuitv as simall as Troy=0.05. if present in the two spectra. would have been apparent.," We consider that a discontinuity as small as $\tauv = 0.05$, if present in the two spectra, would have been apparent."701 We conclude. that intergalactic absorption cannot bethe main cause of the observed steepeniug iu the composite SED., We conclude that intergalactic absorption cannot be the main cause of the observed steepening in the composite SED.702 Model € fails uot only because of the observed abseuce of a discontinuity in the far-UWV but also because it is Inconsisteut with the known deusity of quasars (condition c)., Model C fails not only because of the observed absence of a discontinuity in the far-UV but also because it is inconsistent with the known density of quasars (condition ).703 No other ddistribution could be found that would solve alll three conditious., No other distribution could be found that would solve alll three conditions.704 Our study therefore coufirmis that the change of slope near 1100 nüuust be in origin intrinsic to quasars. as proposedby ZI97 aud TZü2.," Our study therefore confirms that the change of slope near 1100 must be in origin intrinsic to quasars, as proposed by ZK97 and TZ02."705 This general conclusion is not dependeut on the particular distribution adopted. since in all the distributions we have explored (which satisfied condition a). wwas always >0.2 when τω>().5.," This general conclusion is not dependent on the particular distribution adopted, since in all the distributions we have explored (which satisfied condition ), was always $\ge 0.2$ when $z_Q > 0.5$."706" ILwius. recognized. that most of. the break is. lutrinsic∙∙∙↖ to quasars, we now turn to the problem. of determing how muuch fiux discontinuity near 1160 (ce. Tyy6y)}} can be expected if we assmme the ddeusitv predicted by WHT models aud a fiducial teniperature of 1077. KIX. For this purpose. ↖↖⇁↸∖⋪∥↧∪≻↑⋪⋯↕∐⊓⋅↕∐↴∖↴↕↸⊳≋⊏↕≻∙↖↖⇁↕∐↸⊳∐⋪↧∐⋅↸∖⋪∥↧↖⇁↕↕⊔⊳∪↥⋅≻∪↥⋅⋪↧↑↸∖↴∖↴ acopre RM por: he iutrinsic £u-UV steepening."," Having recognized that most of the break is intrinsic to quasars, we now turn to the problem of determining how much flux discontinuity near 1160 (i.e. ) can be expected if we assume the density predicted by WHIM models and a fiducial temperature of $10^{5.3}$ K. For this purpose, we adopt an intrinsic SED, which already incorporates the intrinsic far-UV steepening."707 It consists of a xokenu power-law. which has the same index of 0.72 in the near-UV as in Fig. 2. ," It consists of a broken power-law, which has the same index of $-0.72$ in the near-UV as in Fig. \ref{fig2}, ,"708but that sharply turus over at 1200 ∖⋅⋅↕∐↑∪⋪↧↴∖↴↑↸∖↸∖↸∖⋅⋅≼↸∖↼↽∪⋟↽∙⋅↱↼⋅| per Indes of 1.57 in thi fa↸∖∶⋅≓ - Lrepresented by the short-loug dashedος line iu that 5..," but that sharply turns over at 1200 ) into a steeper index of $-1.57$ in the far-UV, as represented by the short-long dashed line in Fig. \ref{fig5}."709∎ These two| iudices correspond∎ to: the values lis|in characterizing the radio-quiet quasar composite of while the⋅⋅⋅ turu-over waveleneth is° within. the range of values eucouutered by TZ02 (z 1300 A))., These two indices correspond to the values characterizing the radio-quiet quasar composite of TZ02 while the turn-over wavelength is within the range of values encountered by TZ02 $\approx $ 1200--1300 ).710 Adopting eq. (3)), Adopting eq. \ref{eq:nhc}) )711 aud the above broken law. we first deteriuiue which values of aan bbest reproduce the observed composite SED.," and the above broken power-law, we first determine which values of and best reproduce the observed composite SED."712 The result is Model D. plotted as the solid line iu Fig. 5..," The result is Model D, plotted as the solid line in Fig. \ref{fig5}."713 The same 3=1.5 is used as for Model € aud ccould now be set to the sialb value of 0.08 without producing auv significant ou the blue side of the quasar ecnissiou line., The same $\beta=1.5$ is used as for Model C and could now be set to the small value of 0.08 without producing any significant on the blue side of the quasar emission line.714" Model D succeeds rather well in fitting the TZ02 composite,", Model D succeeds rather well in fitting the TZ02 composite.715 It docs not coustitute. however. a uuique solution because of the uncertainties regarding the intrinsic SED.," It does not constitute, however, a unique solution because of the uncertainties regarding the intrinsic SED."716 If for instance. we shifted the break fom 1200. to 1100A. the assed ISED would Πο higher above the coniposite of TZ02 aud a higher deusity WIIIM would therefore be required: for the model to overlap the data.," If for instance, we shifted the break from 1200 to 1100, the assumed ISED would lie higher above the composite of TZ02 and a higher density WHIM would therefore be required for the model to overlap the data."717 With a predicted value of ans stnall as 0.05 (see Table 1)). Model D is characterized by aiunuch smaller discoutinuity than Models AoC. μην because the assumed ISED is much closer to the observed composite of," With a predicted value of as small as $0.05$ (see Table \ref{tbl_1}) ), Model D is characterized by amuch smaller discontinuity than Models A–C, simply because the assumed ISED is much closer to the observed composite of"718shock generated by a propeller effect. or the shock frou a pulsar wind at lower accretion rates. could also provide an explanation for the hard power law N-rav cuissiou (see Campana Stella 2000).,"shock generated by a propeller effect, or the shock from a pulsar wind at lower accretion rates, could also provide an explanation for the hard power law X-ray emission (see Campana Stella 2000)."719 The transition to a propeller effect in the expected Iuiiuositv range (Ly~1076 eres S ‘Ty quay have been observed in Aql N-1 (Zhaug et 11998. Campana et al.," The transition to a propeller effect in the expected luminosity range $L_X\sim10^{36}$ ergs $^{-1}$ ) may have been observed in Aql X-1 (Zhang et 1998, Campana et al."720 1998: but cf., 1998b; but cf.721 Maccaroune Coppi 2002. and Chandler Rutledge 2000) and 1U 0115|63 (Campana ct 22001).," Maccarone Coppi 2002, and Chandler Rutledge 2000) and 4U 0115+63 (Campana et 2001)."722 A pulsar wind is thought to eject matter falling from the Roche-lobe overflowing secoudary in the millisecond pulsar PSR J1710-5310 in NGC 6397 (Burderi et 22002)., A pulsar wind is thought to eject matter falling from the Roche-lobe overflowing secondary in the millisecond pulsar PSR J1740-5340 in NGC 6397 (Burderi et 2002).723 The advent of a pulsar wind may sweep away the entire accretion disk due to the radial dependencies of the pulsar radiation pressure and the disk pressure (Durderi et 22002)., The advent of a pulsar wind may sweep away the entire accretion disk due to the radial dependencies of the pulsar radiation pressure and the disk pressure (Burderi et 2002).724 However. this assumes a standard Shakura-Suuvaev disk structure throughout the eutire disk.," However, this assumes a standard Shakura-Sunyaev disk structure throughout the entire disk."725 Due to dynamical eucouuters in elobular clusters (cf., Due to dynamical encounters in globular clusters (cf.726 Catudlay et al., Grindlay et al.727 2002). if may be possible to evele between pulsar emission aud accretion regimes.," 2002), it may be possible to cycle between pulsar emission and accretion regimes."728 We note a possible correlation between the existence of a strong power law component and recent (sugeestiug frequent?), We note a possible correlation between the existence of a strong power law component and recent (suggesting frequent?)729 outbursts., outbursts.730 Con N-1. Aglh N-1. CXL in NGC GLLO (int Zaud ct 22001). INS 1731-260. (Wijnands et al," Cen X-4, Aql X-1, CX1 in NGC 6440 (in't Zand et 2001), KS 1731-260 (Wijnands et al."731 2001). and IU 2129)LF (Nowak et al," 2001), and 4U 2129+47 (Nowak et al."732 2002) cach have stroug PL components aud recorded (recent) outbursts. while X5 aud N7. U21 iu NGC 6397 (Caiudlay et 22001b). and CNOU 132619.7-172910.5 in x Cen (Rutledee et 220022) have exhibited evidence of neither (although the limuts ou the 6397 and w Cen sources PL components are currently weak).," 2002) each have strong PL components and recorded (recent) outbursts, while X5 and X7, U24 in NGC 6397 (Grindlay et 2001b), and CXOU 132619.7-472910.8 in $\omega$ Cen (Rutledge et 2002a) have exhibited evidence of neither (although the limits on the 6397 and $\omega$ Cen sources' PL components are currently weak)."733 This may indicate a difference in the mode or level of accretion activity between the two eroups., This may indicate a difference in the mode or level of accretion activity between the two groups.734 The N-rav sources NS and N7 are thermally radiatiug ueutron stars with bydrogen atiiosplieres. probably heated bv transient accretion.," The X-ray sources X5 and X7 are thermally radiating neutron stars with hydrogen atmospheres, probably heated by transient accretion."735 X5 shows eclipses. which allow piraueters of the binary svstem to be inferred.," X5 shows eclipses, which allow parameters of the binary system to be inferred."736 Both X5 and X7 are wellfit bv the bydrogen atinosphere model spectra of Cutmusicke et al. (, Both X5 and X7 are well-fit by the hydrogen atmosphere model spectra of Gännsicke et al. (7372002) aud Lloyd ct al. (,2002) and Lloyd et al. (738"2002). absorbed by a column of gas with the known cluster metallicity aud displaviug a possible absorption feature near 0.61 keV tentatively identified with au OV οσο,","2002), absorbed by a column of gas with the known cluster metallicity and displaying a possible absorption feature near 0.64 keV tentatively identified with an OV edge."739 The feature may instead be intrinsic to the neutron star atmosphere. i which case it is most likely identified with the 0.87 keV (vest-frame) complex. of oxveen aud. metal lines in a subsolarancetallicity neutrou star atmosphere.," The feature may instead be intrinsic to the neutron star atmosphere, in which case it is most likely identified with the 0.87 keV (rest-frame) complex of oxygen and metal lines in a subsolar-metallicity neutron star atmosphere."740 A hard power-law componcut to the spectra. such as has )eni observed. iu other qLMAXDs. is extremely weak or ionexistent in XD aud X7.," A hard power-law component to the spectra, such as has been observed in other qLMXBs, is extremely weak or nonexistent in X5 and X7."741 The woell-kuoxwn distance to £7 Tucanae allows modeling of the neutron star atmospheres ο cOnstrain a space dm mass and radius for each. if the atmospheres are purely lvdrogen.," The well-known distance to 47 Tucanae allows modeling of the neutron star atmospheres to constrain a space in mass and radius for each, if the atmospheres are purely hydrogen."742 Fits using the ISIS xleup model aud hydrogen atimosphere fits require X7 to © 1nore massive than 1.5 for the range of radi 9-16 kan. while the constraints on X5 are cousisteut with a iass of 1.1 for a wide range of radi.," Fits using the ISIS pileup model and hydrogen atmosphere fits require X7 to be more massive than 1.8 for the range of radii 9-16 km, while the constraints on X5 are consistent with a mass of 1.4 for a wide range of radii."743 ILowever. if the majority of 1ο N-rav luminosity is derived from low-level accretion. ien appreciable amounts of metals would remain in the jieutron star afmospheres.," However, if the majority of the X-ray luminosity is derived from low-level accretion, then appreciable amounts of metals would remain in the neutron star atmospheres."744 In addition to producing the eature near 0.61 keV. the metals would alter the overall shape of the spectrum «Πο closer to a blackbody. yossibly allowing both X5 and N7 to ft a canonical NS nass and radius.," In addition to producing the feature near 0.64 keV, the metals would alter the overall shape of the spectrum slightly closer to a blackbody, possibly allowing both X5 and X7 to fit a canonical NS mass and radius."745 If accretion is not continuing. a lieh mass Or NT is unavoidable.," If accretion is not continuing, a high mass for X7 is unavoidable."746 A series of observatious (~300 ksec total) iu October 2002 withChandra. using the back-ilhuninated ACIS-S chips for greater scusitivitv below 1 keV. will give us more data with which to constraiu tle mass and radius. and mode of cussion. of these neutron stars.," A series of observations $\sim$ 300 ksec total) in October 2002 with, using the back-illuminated ACIS-S chips for greater sensitivity below 4 keV, will give us more data with which to constrain the mass and radius, and mode of emission, of these neutron stars."747 We will be particularly interested iu looking for intrinsic variability. and coufriiuins or refuting the possible edge feature.," We will be particularly interested in looking for intrinsic variability, and confirming or refuting the possible edge feature."748 The eclipsing behavior of X5 also allows the possibility of using tfo ieasure the radial velocity. of the secoucary. constraining the mass of X5.," The eclipsing behavior of X5 also allows the possibility of using to measure the radial velocity of the secondary, constraining the mass of X5."749 UCutortunately optical spectroscopy of NT is bevond the reach ofS7.. due to crowding (Edinouds et 22002).," Unfortunately optical spectroscopy of X7 is beyond the reach of, due to crowding (Edmonds et 2002)."750 These demonstrations of fits with hydrogen atinosphere models show that the project of constraining the neutron star equation of state through spectral fitting holds particular interest for these two svstenis., These demonstrations of fits with hydrogen atmosphere models show that the project of constraining the neutron star equation of state through spectral fitting holds particular interest for these two systems.751 This work was supported in part by. eerants COO-LO9SA and CO2-3059A. οΠ. thanks. M. Nowak. J. E. AicClintock. J. Ravinoud. J. MeDosvell. F. Walter. P. Ioudvratko. and J. Lattimer for helpful discussions.," This work was supported in part by grants GO0-1098A and GO2-3059A. C.H. thanks M. Nowak, J. E. McClintock, J. Raymond, J. McDowell, F. Walter, P. Kondratko, and J. Lattimer for helpful discussions."752 CLT. also thanks M. C. Miller. for EOS relations. the anonymous referee for helpful suggestions. D. Cauusicke and Ik. Arnaud for assistance with NSPEC implementation of NS models. aud especially J. Houck for assistance with ISIS.," C.H. also thanks M. C. Miller for EOS relations, the anonymous referee for helpful suggestions, B. Gännsicke and K. Arnaud for assistance with XSPEC implementation of NS models, and especially J. Houck for assistance with ISIS."753 We thauk the AACTS team at Poeun State aud the CXC team at the CLA for advice ou data analysis., We thank the ACIS team at Penn State and the CXC team at the CfA for advice on data analysis.754 Since X5 and NF possess soft spectra. cut off below 1 keV bw the falling detector response aud neutral hwdroseu absorption. their raw spectra can be modeled to zeroth order as eaussians with peaks at energv ~1l keV and widths of ση03 keV. from a simple fit to the pulse height data.," Since X5 and X7 possess soft spectra, cut off below 1 keV by the falling detector response and neutral hydrogen absorption, their raw spectra can be modeled to zeroth order as gaussians with peaks at energy $\sim1$ keV and widths of $\sigma\sim0.3$ keV from a simple fit to the pulse height data."755 Thus. the pileup willproduce a secondary peak at ~2 keV with 0 ~(hl keV. coutaining and for NS aud X7 respectively of the total received flux. neelecting erade mieration. (," Thus, the pileup willproduce a secondary peak at $\sim2$ keV with $\sigma$ $\sim0.4$ keV, containing and for X5 and X7 respectively of the total received flux, neglecting grade migration. ("756Grade migration occurs when the charge clouds from two plotous are recorded at the same time in adjacent pixels. aud the pattern of charge is assigned au iuferior erade. leading to the discarding of the eveut: see Davis 2001).,"Grade migration occurs when the charge clouds from two photons are recorded at the same time in adjacent pixels, and the pattern of charge is assigned an inferior grade, leading to the discarding of the event; see Davis 2001)."757 This secondary peak was misinterpreted iu GITEOT (where pileup was ignored) as a high energy tail., This secondary peak was misinterpreted in GHE01 (where pileup was ignored) as a high energy tail.758 We added a gaussian componoeut to model the pilewp compouent of the spectra. allowed the parameters to vary freely. and discovered that the best-fitting eaussian conrponent eave a inedia cucrev of :3 or 2.25 keV for NS and NT. 020.38 keV. for both. aud a total flux fraction (considering5 that the effective area at 1.1 and 2.2 keV differs by a factor of 3/5) of and . respectively.," We added a gaussian component to model the pileup component of the spectra, allowed the parameters to vary freely, and discovered that the best-fitting gaussian component gave a median energy of 2.23 or 2.25 keV for X5 and X7, $\sigma$ =0.38 keV for both, and a total flux fraction (considering that the effective area at 1.1 and 2.2 keV differs by a factor of 3/5) of and , respectively."759 The, The760ihe most huminous blazars (LSPs) 2009).,the most luminous blazars (LSPs) .761. This is also similar to the AICcase and implies that the peak in Che spectral energy distribution of the svnehrotron component occurs close to the self-absorption freeuency., This is also similar to the MIC-case and implies that the peak in the spectral energy distribution of the synchrotron component occurs close to the self-absorption frequency.762 The main difference between (he (wo scenarios concerns (he value of e;/eg., The main difference between the two scenarios concerns the value of $\epsilon_{\rm e}/\epsilon_{\rm B}$.763 Single scattering models are usually consistent with rough equipartition between the energy densities in electrons and magnetic field (1.e.. e;~ei). while multiple scattering models require e;3»ἐμ (cf," Single scattering models are usually consistent with rough equipartition between the energy densities in electrons and magnetic field (i.e., $\epsilon_{\rm e} \sim \epsilon_{\rm B}$ ), while multiple scattering models require $\epsilon_{\rm e} \gg \epsilon_{\rm B}$ (cf."764 eq. 13]., eq. \ref{eq:1.14}] ]).765" Furthermore. the smooth power-law X-ray spectra in LSPs indicate 7,ο>lin AUCπιοςθ]ς in order for this radiation to be produced by the lowest οποιον electrons (cf."," Furthermore, the smooth power-law X-ray spectra in LSPs indicate $\tau_{\rm o} \gtrsim 1$ in MIC-models in order for this radiation to be produced by the lowest energy electrons (cf."766 eq. [8]])., eq. \ref{eq:1.9}] ]).767 The distinct minimum in the spectral energv. distribution occurring al the transition between the svnchrotron and inverse Compton components. which is particularly pronounced in LSPs. is not consistent with a strictly homogeneous one-zone MIC-model.," The distinct minimum in the spectral energy distribution occurring at the transition between the synchrotron and inverse Compton components, which is particularly pronounced in LSPs, is not consistent with a strictly homogeneous one-zone MIC-model."768" The low value of mi, Heeclecl to produce the observed smooth power-law in the X-ray regine would also fill in (his minimum by inverse Compton scattering of (he svnchrotron component1996).", The low value of $\gamma_{\rm min}$ needed to produce the observed smooth power-law in the X-ray regime would also fill in this minimum by inverse Compton scattering of the synchrotron component.769. However. anv one-zone svnchrotron/Compton model have problems accounüng for some of the main characteristics of LSP: for example. although correlated lime variations are sometimes seen between the optical and the gamma frequency ranges. (his is not generally the case.," However, any one-zone synchrotron/Compton model have problems accounting for some of the main characteristics of LSP; for example, although correlated time variations are sometimes seen between the optical and the gamma frequency ranges, this is not generally the case."770 The similar value of the magnetic field D in single and multiple scattering scenarios have (wo implications: (4) The deduced location of the emission site should be roughly (he same. (, The similar value of the magnetic field $B$ in single and multiple scattering scenarios have two implications: (i) The deduced location of the emission site should be roughly the same. (771ii) In LSPs most of the radiation is emitted bv cooling electrons.,ii) In LSPs most of the radiation is emitted by cooling electrons.772" Hence. the much larger value of the energy density of electrons in a MIC-model as compared (o a single scattering model necessitates a correspondingly smaller emission volume. ie. 5,«HR. where His the size ol the available emission region."," Hence, the much larger value of the energy density of electrons in a MIC-model as compared to a single scattering model necessitates a correspondingly smaller emission volume, i.e., $r_{\rm o} \ll R$, where $R$ is the size of the available emission region."773 This suggests a possible extension of (he one-zone MIC model (hat can account for the minimum in the spectral energy distribution., This suggests a possible extension of the one-zone MIC model that can account for the minimum in the spectral energy distribution.774 For simplicity. assume (hat the values of B as well as ως are the same throughout the emission region. including (he smaller injection region.," For simplicity, assume that the values of $B$ as well as $v_{\rm esc}$ are the same throughout the emission region, including the smaller injection region."775" The uniform injection of relativistic electrons inside r, implies that the fraction of electrons with 5>5,.. which escapes and fills the whole emission region /2. is proportional to their cooling time."," The uniform injection of relativistic electrons inside $r_{\rm o}$ implies that the fraction of electrons with $\gamma > \gamma_{\rm c}$, which escapes and fills the whole emission region $R$, is proportional to their cooling time."776 The contributions to the optically thin svnchrotron {lux is determined by (the average time spent by an electron in the (wo regions., The contributions to the optically thin synchrotron flux is determined by the average time spent by an electron in the two regions.777" With no additional cooling outside the injection region. the shape of the sviiclirotron spectrum emitted by (he escaping electrons is. therefore. similar to that inside r,. while the flux is a factor 2/r, laveer."," With no additional cooling outside the injection region, the shape of the synchrotron spectrum emitted by the escaping electrons is, therefore, similar to that inside $r_{\rm o}$, while the flux is a factor $R/r_{\rm o}$ larger."778" Although cooling on the inverse Compton component is less efficient by. a factor Rr, outside as compared to imside the injection region. cooling may steepen (he svnchrotron spectrum [rom the escaping electrons al hisher frequencies."," Although cooling on the inverse Compton component is less efficient by a factor $R/r_{\rm o}$ outside as compared to inside the injection region, cooling may steepen the synchrotron spectrum from the escaping electrons at higher frequencies."779 A further contribution could come from svnehirotron cooling., A further contribution could come from synchrotron cooling.780 Hence. the smaller injection," Hence, the smaller injection"781"Under the extreme temperatures and densities of the solar core, the plasma is fully ionized.","Under the extreme temperatures and densities of the solar core, the plasma is fully ionized."782 The free electrons and ions interact via the Coulomb potential, The free electrons and ions interact via the Coulomb potential783eray-age ds rich in both temperature. deusitv. aud velocity structure.,"gray-age is rich in both temperature, density, and velocity structure."784 Studving this structure via IIT 2lem absorption lines will offer important clues to the evolution of the ICAL at the very ouset of galaxy formation., Studying this structure via HI 21cm absorption lines will offer important clues to the evolution of the IGM at the very onset of galaxy formation.785 Plans for future large radio telescopes involve building an aperture svuthesis array with roughly a square slometer of collecting area. naicly a “square kilometer array’ ).," Plans for future large radio telescopes involve building an aperture synthesis array with roughly a square kilometer of collecting area, namely a 'square kilometer array' )."786 The detailed design and specifications or such au array are currently Όσιο considered., The detailed design and specifications for such an array are currently being considered.787 Iu he analvsis below we assunie an effective area of 5«10* in? at 200 MITz. two orthogonal polarizations. and a svsteni temperature of 250 [| (100 I from he receiver and 150 EK from diffuse Ctalactie sjon)]).," In the analysis below we assume an effective area of $5\times10^5$ $^2$ at 200 MHz, two orthogonal polarizations, and a system temperature of 250 K (100 K from the receiver and 150 K from diffuse Galactic )."788 We also make the simplifying assuuption hat the ratio of effective area to svsteni teniperature remains roughly coustaut down to 100 MITz. as could arise in the case of a low frequency array composed of dipole autcunas. and hence that the sensitivity is constant across the frequency range of interest (100 MIIz to 200 NITZ).," We also make the simplifying assumption that the ratio of effective area to system temperature remains roughly constant down to 100 MHz, as could arise in the case of a low frequency array composed of dipole antennas, and hence that the sensitivity is constant across the frequency range of interest (100 MHz to 200 MHz)."789 We adopt a long. but not unreasonable. iutegration time of 10 davs (210 hours).," We adopt a long, but not unreasonable, integration time of 10 days (240 hours)."790 These parameters lead to au expected ruis noise level of 31gJy ii a 1 kIIz spectral channel., These parameters lead to an expected rms noise level of $\mu$ Jy in a 1 kHz spectral channel.791 Tn section 3.3 we assume thermal (ie., In section 3.3 we assume thermal (ie.792 Gaussian) noise lanited spectra., Gaussian) noise limited spectra.793 A Gaussian noise ecuerator based on algorithius iu the AIPS software aud using the staudard FORTRAN random nuuber generator is used. nonualized to an riis level of Lady.," A Gaussian noise generator based on algorithms in the AIPS software and using the standard FORTRAN random number generator is used, normalized to an rms level of $\mu$ Jy."794 We asstune that the correlator will provide at least 10! spectral chanuels over a 10 Az band. iuplving a channel width of 1 kHz = 2 kins |.," We assume that the correlator will provide at least $^4$ spectral channels over a 10 MHz band, implying a channel width of 1 kHz = 2 km $^{-1}$."795 We also asstuue that the spectral bandpass deteruuation will be at least as good as current telescopes. aud prestunably considerably better.," We also assume that the spectral bandpass determination will be at least as good as current telescopes, and presumably considerably better."796 Current telescopes such as the VLA aud the WSRT can attain spectral dyuamic ranges of up to 10! over 10's of MIITz of radio spectrun with proper attention to bandpass calibration (Dwarakanath. Carilli. Coss 2002).," Current telescopes such as the VLA and the WSRT can attain spectral dynamic ranges of up to $^4$ over 10's of MHz of radio spectrum with proper attention to bandpass calibration (Dwarakanath, Carilli, Goss 2002)."797 This dynamic range is adequate to detect the z1% absorption sienals discussed. below., This dynamic range is adequate to detect the $\ge 1\%$ absorption signals discussed below.798 Screening and excision of terrestrial iuterfereuce is also critical to these observations., Screening and excision of terrestrial interference is also critical to these observations.799 Much work is being doue in this area in preparation for future large area radio telescopes (Fisher 2001)., Much work is being done in this area in preparation for future large area radio telescopes (Fisher 2001).800 We assume that effective. techniques. will be available for RFI uutigation to the required levels., We assume that effective techniques will be available for RFI mitigation to the required levels.801 The parameters adopted above are withiu the scope of what is being cousidered for the SEA., The parameters adopted above are within the scope of what is being considered for the SKA.802 Indeed. analyses of scientific issues such as those presented herein are fuudamenutal to defining the requirements for future large area radio telescopes.," Indeed, analyses of scientific issues such as those presented herein are fundamental to defining the requirements for future large area radio telescopes."803 An interesting point to keep im mind is that at the low frequencies considered herein. the major cost for an SILA is not likely to be collecting area.," An interesting point to keep in mind is that at the low frequencies considered herein, the major cost for an SKA is not likely to be collecting area."804" Hence. one nught consider building an even larger telescope. thereby pushing to even faimter sources,"," Hence, one might consider building an even larger telescope, thereby pushing to even fainter sources."805 The sources being considered correspond to powerful radio galaxies for which the enüssiou mechanism is 1on-theriual (νοοτο) raciation from a relativistic asina of electrous aud maenuetic fields., The sources being considered correspond to powerful radio galaxies for which the emission mechanism is non-thermal (synchrotron) radiation from a relativistic plasma of electrons and magnetic fields.806 Iu most such sources the spectruni can be described well by a vower-law over the frequency range of interest (0.6 Cz to 3 GIIz in the rest frame)., In most such sources the spectrum can be described well by a power-law over the frequency range of interest (0.6 GHz to 3 GHz in the rest frame).807 At the worst he spectra are slowly curving (in log space) over jucdreds of MIIz (de Breuck ct al., At the worst the spectra are slowly curving (in log space) over hundreds of MHz (de Breuck et al.808 2000)., 2000).809 Iu the analysis below we adopt the spectrum of he powerful radio galaxy Cvenus A. Cyvguus. A was included in the initial deteriunation of the absolute celestial radio flux density scale by Baars et al. (, In the analysis below we adopt the spectrum of the powerful radio galaxy Cygnus A. Cygnus A was included in the initial determination of the absolute celestial radio flux density scale by Baars et al. (8101977). aud has accurate absolute flux deusity measurements at many frequencies over the fequency range ofiuterest.,"1977), and has accurate absolute flux density measurements at many frequencies over the frequency range of interest."811 Fieure { shows the spectrum of Cyeuns A from 50 AIIIZz to 5000 MIITz., Figure 4 shows the spectrum of Cygnus A from 500 MHz to 5000 MHz.812 The solid line corresponds te a first order polvuonmdal fit to the data iu the log plane. corresponding to a power-law of idex 1.054 0.03.," The solid line corresponds to a first order polynomial fit to the data in the log plane, corresponding to a power-law of index $-1.05\pm0.03$ ."813 The dashed line correspoucds to a second. order polvuomdal, The dashed line corresponds to a second order polynomial.814 We use this second order polvuonmial iu the aualvsis below., We use this second order polynomial in the analysis below.815 Figure 5 shows a simulated spectrum at 1 kIIz resolution of a 2=10 radio source with a flux density of 20 wy at au observing frequency of 120 ATTz (Syoy}., Figure 5 shows a simulated spectrum at 1 kHz resolution of a $z = 10$ radio source with a flux density of 20 mJy at an observing frequency of 120 MHz $_{120}$ ).816 The implied luminosity deusitv at a rest frame frequency of 151 MITIz is then {οι=2.5<107 ore, The implied luminosity density at a rest frame frequency of 151 MHz is then $P_{151} = 2.5\times10^{35}$ erg817emission is resolved at the 0.5-1 AU scale 2009).,emission is resolved at the 0.5-1 AU scale .818. While I1D69330 is (oo faint [or observations with the nulling mode of the Neck Interferometer (xt) at 10 jan2009).. we did obtain visibility meastrements on Wis 85 nm baseline in the A band on 2006 Nov 11.," While HD69830 is too faint for observations with the nulling mode of the Keck Interferometer (KI) at 10 $\mu$ m, we did obtain visibility measurements on KI's 85 m baseline in the $K$ band on 2006 Nov 11."819 Three integrations were made in the medium resolution mocde (IX  200)., Three integrations were made in the medium resolution mode (R $\sim$ 200).820 ILD63146 and IILD71155 were used as calibrators. chosen to match the (areel near-intrarecl brightness and spatial location. ancl the wide-band and spectroscopic observations were processed with the standard settings. including a correction [or flux Although IID71155 has a mid-infrared excess2005).. its spectral energy distribution shows no evidence for a near-inlrared. excess and the uncertainty in its stellar size is not the dominant term in the final uncertainty [or the measured visibilitw of ILD 69830.," HD68146 and HD71155 were used as calibrators, chosen to match the target near-infrared brightness and spatial location, and the wide-band and spectroscopic observations were processed with the standard settings, including a correction for flux Although HD71155 has a mid-infrared excess, its spectral energy distribution shows no evidence for a near-infrared excess and the uncertainty in its stellar size is not the dominant term in the final uncertainty for the measured visibility of HD 69830."821 The calibrated average visibility squared for IID69830 is 1.01 +4 0.05., The calibrated average visibility squared for HD69830 is 1.01 $\pm$ 0.05.822 For a stellar raclius of 0.57 d: 0.04 BR... the visibility squared for the stellar photosphere at ἐν band should be 0.97 d: 0.01.," For a stellar radius of 0.87 $\pm$ 0.04 $_{\odot}$, the visibility squared for the stellar photosphere at $K$ band should be 0.97 $\pm$ 0.01."823 Thus our measurements are consistent wilh a completely unresolved source and no excess flux., Thus our measurements are consistent with a completely unresolved source and no excess flux.824 The 1 σ uncertainty on incoherent ddistributed) flux within the 50 mas EWIIM beam (0.63 AU) is of the stellar Παν., The 1 $\sigma$ uncertainty on incoherent distributed) flux within the 50 mas FWHM beam (0.63 AU) is of the stellar flux.825 Observations in the L band were taken at IXI on 26 Feb 2010., Observations in the $L$ band were taken at KI on 26 Feb 2010.826 The same calibrators were used as for the Jv band observations and 5 calibrated scans on ILD69330 were obtained., The same calibrators were used as for the $K$ band observations and 5 calibrated scans on HD69830 were obtained.827 The data were processed as lor A band. except that no flux bias was applied.," The data were processed as for $K$ band, except that no flux bias was applied."828 The central wavelength is 3.91 jn and (he source was unresolved with an average visibility squared of 0.97 + 0.05., The central wavelength is 3.91 $\micron$ and the source was unresolved with an average visibility squared of 0.97 $\pm$ 0.05.829 The 1 σ uncertainty on incoherent [lux within the 90 mas EWIIM (1.18 AU) is of the stellar f[Iux., The 1 $\sigma$ uncertainty on incoherent flux within the 90 mas FWHM (1.13 AU) is of the stellar flux.830 , 	 831 ↴∖↴↸∖∐⋜∐⋅↴⋝⋜∐⋅∙∏↴∖↴↕∐∶↴∙⊾⋜↧∐⋜↧↕⋅↖↽⊓↸⊳⋜↧↕≼⊲⋀∖∐,"stellar bar, using analytical CMC and DM halo."832⊲⋜⋯≼↧↕≻⋀∖⊔↕⋜↧↕∪∙∐∪↖↖↽↸∖↖↽↸∖↥⋅∙ ↑∐∖↕⋜↧↑↑↸∖↥⋅⋯⋯⊳↸∖↴∖∷∖↴∐⋜↧↴∖↴↴⋝↸∖↸∖∐↕⋟∪∏∐≼⇂∐∪↑↕∐∏⋯↥⋅↑⋜⋯↑↴⋝∙↖⇁ Bereutzen et al. (," However, the latter process has been found not important by Berentzen et al. ("8332007) following a detailed analysis of the angular momentum transter in live poteutials of the CAC and. DM. halo.,2007) following a detailed analysis of the angular momentum transfer in live potentials of the CMC and DM halo.834 Moreover. Berenutzen ct al. (," Moreover, Berentzen et al. ("8351998. 2007)x have used selt£-cousisteutlv exowing CAICs in the easeous/stellar disks to demonstrate that the secular bar erowtli is strongly affected.,"1998, 2007) have used self-consistently growing CMCs in the gaseous/stellar disks to demonstrate that the secular bar growth is strongly affected."836 The set of nuucerical mocels ijidvzed here is in fact the most controlled. experiment performed so far to test the influence of eas fraction aud its resolution on the bar evolution., The set of numerical models analyzed here is in fact the most controlled experiment performed so far to test the influence of gas fraction and its resolution on the bar evolution.837 Fig., Fig.838" 10a slows the dependence of the bar streusthenius after the first buckliug. Avo, on finalMeses with all other parameters characterizing the stellar disk aud the DM halo being fixed."," 10a shows the dependence of the bar strengthening after the first buckling, $\Delta$ on final, with all other parameters characterizing the stellar disk and the DM halo being fixed."839 Oue model. has Όσοι onütted. as its CALC secular evolution is COSS.unusually flat and falls out ofthe sequence with e;440.016.," One model, G8S1, has been omitted, as its CMC secular evolution is unusually flat and falls out of the sequence with $=0.016$."8407FAL is the sinele defining variable which coutrols Adan... all three —5equences are expected to merece iuto a sinele sequence in Fig.," If is the single defining variable which controls $\Delta$, all three -sequences are expected to merge into a single sequence in Fig."841 10a., 10a.842 What is actually observed is that the three sequenes οκ a verv sinudlar behavior cach curve is flat for the 8eas-poor models. experieuces an abrupt drop. aid flattens out.," What is actually observed is that the three sequences exhibit a very similar behavior — each curve is flat for the gas-poor models, experiences an abrupt drop, and flattens out."843 However. the curves co uot coincide completely as would be expected if were thewrtgie auderlving parameter.," However, the curves do not coincide completely as would be expected if were the underlying parameter."844 Iu fact. in some cases the points corresponding to the same but differeut have a substantial vertical dispersion in Ado.," In fact, in some cases the points corresponding to the same but different have a substantial vertical dispersion in $\Delta$."845 Hence. the issue remains inconclusive.," Hence, the issue remains inconclusive."846 In coutrast. we show the final value normalized by the disk mass at t=0 a5 a fuuction of (Fig.," In contrast, we show the final value normalized by the disk mass at $t=0$ as a function of (Fig."847 10b)., 10b).848 This fractional value is indeed unique for the three sequences. as all three curves have nearly imierged.," This fractional value is indeed unique for the three sequences, as all three curves have nearly merged."849 We now tum to a plausible correlation between the buckling amplitude aud the bar strenethenine., We now turn to a plausible correlation between the buckling amplitude and the bar strengthening.850 The vertical buckling (c.¢.. Toomre 1966: Combes et al.," The vertical buckling (e.g., Toomre 1966; Combes et al."851 1990: Raha et al., 1990; Raha et al.852 1991) is a recurrent iustabilitv (Martiuez-Valpuesta et al., 1991) is a recurrent instability (Martinez-Valpuesta et al.853 2006) that was recentlv analyzed by Berentzen et al. (, 2006) that was recently analyzed by Berentzen et al. (8542007) in the preseuce of eas (soe also Bereutzen ct al,2007) in the presence of gas (see also Berentzen et al.855 1998)., 1998).856 The gas conrponeut. it has been concluded. leads to a milder istabilitv.," The gas component, it has been concluded, leads to a milder instability."857" Tere we have attempted to relate the buckling amplitude. ly... to the change iu the bar amplitude. οι, in the dynamical and secular plascs of evolution (Fig."," Here we have attempted to relate the buckling amplitude, $A_{\rm 1,z}$, to the change in the bar amplitude, $\Delta $, in the dynamical and secular phases of evolution (Fig."858 11)., 11).859 Iu both phases we observe a clear correlation between and οι., In both phases we observe a clear correlation between and $\Delta $.860 Stronger bar instability leads to a stronger buckling. aud imdeed. increasing maakes the bar aud buckling stabilities nulder (Figs.," Stronger bar instability leads to a stronger buckling, and indeed, increasing makes the bar and buckling instabilities milder (Figs."861 Lla: see also Fig., 11a; see also Fig.862 9a)., 9a).863 Ou the other laud. «τοσο buckling goes iu tandem with the bar secular erowth (Fig.," On the other hand, stronger buckling goes in tandem with the bar secular growth (Fig."864 lib)., 11b).865 This trend shows saturation for the strongest bars., This trend shows saturation for the strongest bars.866 Higher resolution sequences with e;44:— O.016endü.bbehaceinacergsimilarfashion. whilethelowestresolutic durin," Higher resolution sequences with $= 0.016$ and 0.5 behave in a very similar fashion, while the lowest resolution sequence stands out of this correlation."867g the buckling aud fiud a clear match between the higher resolutiou sequences. while the lower resolution models behave ciffereutly.," We have also checked the value of the drop in during the buckling and find a clear match between the higher resolution sequences, while the lower resolution models behave differently."868 The physical exteut of the bar depends on its ability to capture additional orbits., The physical extent of the bar depends on its ability to capture additional orbits.869 While iu principle this capture can proceed at all radii. the fertile region lies hetween the bars end aud its CR radius. where various famulics of orbits can be easily. destabilized.," While in principle this capture can proceed at all radii, the fertile region lies between the bar's end and its CR radius, where various families of orbits can be easily destabilized."870 Theretere. the bar erowtl due to the orbit capture should eo in tandem with the augulu momentumffc because the ucar-CR orbits will have à larger nonmenutun-to-energy. J/E. ratio than the bar orbits.," Therefere, the bar growth due to the orbit capture should go in tandem with the angular momentum because the near-CR orbits will have a larger momentum-to-energy, J/E, ratio than the bar orbits."871" In Paper L we have shown. and this is coufirmed here. that the influx of angular momentum across the CR and into the bar is able to maintain Jq4,7const."," In Paper I, we have shown, and this is confirmed here, that the influx of angular momentum across the CR and into the bar is able to maintain $\sim $ const."872 m time. as long the CR radius lies within the disk. but in the presence of the easonly.," in time, as long the CR radius lies within the disk, but in the presence of the gas."873 This happeus despite that the CR remains within the disk at all times and for all easvich models (Fig., This happens despite that the CR remains within the disk at all times and for all gas-rich models (Fig.874 D., 4).875 Iu other words. in gas-rich models the J influx across the CR cannot compensate for its loss within the CR.," In other words, in gas-rich models the $J$ influx across the CR cannot compensate for its loss within the CR."876 The amplitude is expected to be related to the ability of the bar to capture additional orbits iu the bar, The amplitude is expected to be related to the ability of the bar to capture additional orbits in the bar877One of the most recent alternative measurements of gravity and temperature of HZ 43A were given by ? based on FUSE observations of the Lyman series lines.,One of the most recent alternative measurements of gravity and temperature of HZ 43A were given by \citet{barstow2003} based on FUSE observations of the Lyman series lines.878 They obtain values of Tey=50380x320 K and loge (mss) =5.97+0.03.," They obtain values of $T_{\mathrm{eff}}=50\,380\pm 320$ K and $\log g$ $^{-2}$ ) $=5.97\pm 0.03$."879 These values are not consistent with our model 1 or model 2 (Fig. 3)).," These values are not consistent with our model 1 or model 2 (Fig. \ref{fig:ellips}) ),"880 but they are closer to model 2., but they are closer to model 2.881 The uncertainties given. by ? correspond to the scatter between the parameters derived from the individual fits of the only three FUSE spectra that were available. hence the nominal uncertainty may be quite uncertain by itself.," The uncertainties given by \citet{barstow2003} correspond to the scatter between the parameters derived from the individual fits of the only three FUSE spectra that were available, hence the nominal uncertainty may be quite uncertain by itself."882 We also note that the differences between our best fit model and the model by ? are less than | of the continuum level in the Lyman series line cores. hence rather sensitive to uncertainties m scattered light contributions or background subtraction.," We also note that the differences between our best fit model and the model by \citet{barstow2003} are less than 1 of the continuum level in the Lyman series line cores, hence rather sensitive to uncertainties in scattered light contributions or background subtraction."883 Also. for model | the allowed range for the gravitational redshift is relatively high. given that the best value is 30+10 to," Also, for model 1 the allowed range for the gravitational redshift is relatively high, given that the best value is $30\pm 10$ to"884bv luminosity ancl (wpe effects. rather than the influence of redshift evolution.,"by luminosity and type effects, rather than the influence of redshift evolution."885 In the top panel of Figure 4.. we show the evolution of the mean cumulative overdensity ol photometric galaxies in the environments of Type I quasar. Type 1 AGN and Type II AGN samples.," In the top panel of Figure \ref{scale_spectargs_z}, we show the evolution of the mean cumulative overdensity of photometric galaxies in the environments of Type I quasar, Type I AGN and Type II AGN samples."886 Ht is important to recall (hat we have placed the random points at the same redshift as the spectroscopic targets. and that we have imposed 62 cuts on the photometric galaxies (as described in Section ??)) in order to minimize the effect of redshift evolution in the photometric galaxy sample.," It is important to recall that we have placed the random points at the same redshift as the spectroscopic targets, and that we have imposed $\delta z$ cuts on the photometric galaxies (as described in Section \ref{techniquesection}) ) in order to minimize the effect of redshift evolution in the photometric galaxy sample."887 Therefore we can compare objects in different redshift bins., Therefore we can compare objects in different redshift bins.888 Figure 4. demonstrates (hat higher redshilt Type I quasars are in environments 1.24 (imes more overdense (han the lower redshift quasars on scales <500fo)kpe. while at larger scales. (here appears to be littile-to-10 redshift evolution.," Figure \ref{scale_spectargs_z} demonstrates that higher redshift Type I quasars are in environments 1.24 times more overdense than the lower redshift quasars on scales $\lesssim500\kpchseventy$, while at larger scales, there appears to be little-to-no redshift evolution."889 However. there is scale-dependent redshift evolution evident on scales <1.0htApe for the Type H AGN. shown in the lowest panel.," However, there is scale-dependent redshift evolution evident on scales $\lesssim1.0\Mpchseventy$ for the Type II AGN, shown in the lowest panel."890 The Type | AGN begin to exhibit noticeable redshift evolution at scales <300ho)kpe. where the environments of lower redshift Type I AGN are 1.26 times less dense than those ol the higher redshift Type I AGN.," The Type I AGN begin to exhibit noticeable redshift evolution at scales $\lesssim300\kpchseventy$, where the environments of lower redshift Type I AGN are 1.26 times less dense than those of the higher redshift Type I AGN."891 We see therefore that there is some evidence for a change in local environment as a [function of redshift. all else being held constant.," We see therefore that there is some evidence for a change in local environment as a function of redshift, all else being held constant."892 HLowever. we have not vel taken AGN luminosity into account.," However, we have not yet taken AGN luminosity into account."893 Even in the same redshift range. selection effects due to the samples may come into play. which we investigate in Sections ?? and ??..," Even in the same redshift range, selection effects due to the magnitude-limited samples may come into play, which we investigate in Sections \ref{lumsubsec} and \ref{allsubsec}."894 In Figuree 5.. we identily three redshift rangese where there is overlap between our AGN samples ancl explore whether differences in (vpe are reflected in the relative overdensity.," In Figure \ref{scale_spectargs_type}, we identify three redshift ranges where there is overlap between our AGN samples and explore whether differences in type are reflected in the relative overdensity."895 The lop panel shows the overdensity as a function of scale for both twpes of hieher-luninosity AGN (ie. quasars) in the range 0.3<2< 0.6. and for both types of lower-liminosity AGN in (wo redshift ranges. 0.11z<0.15 and 0.15<z0.33.," The top panel shows the overdensity as a function of scale for both types of higher-luminosity AGN (i.e. quasars) in the range $0.3 \leqslant z \leqslant 0.6$ , and for both types of lower-luminosity AGN in two redshift ranges, $0.11 \leqslant z \leqslant 0.15$ and $0.15 < z \leqslant 0.33$."896 The dividing redshilt value of zc0.15 is chosen to roughly equalize the number of lower-Iuminositv AGN in each redshilt range., The dividing redshift value of $z=0.15$ is chosen to roughly equalize the number of lower-luminosity AGN in each redshift range.897 The lower three panels show the ratio of Type IHE environment overdensitv to Tvpe I environment overdensity in the three redshift ranges., The lower three panels show the ratio of Type II environment overdensity to Type I environment overdensity in the three redshift ranges.898 Again. we are able to compare objects in different. redshift ranges because we have imposed ὃς cuts on the photometric galaxies around both the spectroscopic targets and (he random positions to which they are compared (see Section ??)) in order to account for anv redshiftevolution in (he photometric galaxy sample ancl (to minimize projection effects.," Again, we are able to compare objects in different redshift ranges because we have imposed $\delta z$ cuts on the photometric galaxies around both the spectroscopic targets and the random positions to which they are compared (see Section \ref{techniquesection}) ) in order to account for any redshiftevolution in the photometric galaxy sample and to minimize projection effects."899anticorrelation becomes somewhat steeper. but the difference overall is not particularly marked.,"anticorrelation becomes somewhat steeper, but the difference overall is not particularly marked."900 This is so because. even though the absolute number of objects as a function of Lj has changed radically. the fraction of absorbed sources depends solely on the mix of values of Myj; contributing to each bin of lummosity.," This is so because, even though the absolute number of objects as a function of $L_{b}$ has changed radically, the fraction of absorbed sources depends solely on the mix of values of $M_{BH}$ contributing to each bin of luminosity."901 In particular. for instance. in the highest lumonosity bin the change ts almost imperceptible because. despite the greatest change (decrease) in the absolute number of objects. theinterval of My; values contributing to it have remained almost unchanged.," In particular, for instance, in the highest lumonosity bin the change is almost imperceptible because, despite the greatest change (decrease) in the absolute number of objects, theinterval of $M_{BH}$ values contributing to it have remained almost unchanged."902" To proceed to a comparison with the results obtained in the hard X-rays. we need to turn from L, to L,."," To proceed to a comparison with the results obtained in the hard X-rays, we need to turn from $L_{b}$ to $L_{x}$."903 The bolometric correction used comes from Marconi et al. (, The bolometric correction used comes from Marconi et al. (9042004) and ts not linear.,2004) and is not linear.905 We thereforerecalculated Eq. (7)), We thereforerecalculated Eq. \ref{formulafabs}) )906 after converting Ly into {νι, after converting $L_{b}$ into $L_{x}$.907 In the right panel of Fig., In the right panel of Fig.908 7. the expectation for the two options on g Is compared with the results obtained by LF2005 around z 2 0.35.," \ref{Abs_z035}909 the expectation for the two options on $q$ is compared with the results obtained by LF2005 around $z$ = 0.35."910" The two data points. with Poissonian error bars. represent the objects in their samples within the interval z 2 0.2-0.5. while the solid line represents the outcome at z20.35 of their ""global"" fit of the intrinsic distribution after correcting for selection effects."," The two data points, with Poissonian error bars, represent the objects in their samples within the interval $z$ = 0.2-0.5, while the solid line represents the outcome at $z$ =0.35 of their “global” fit of the intrinsic distribution after correcting for selection effects."911" It must be noted that the ""global"" fit given by LF2005 (dotted lines in their figure 11) also includes Compton-thick AGN with 1077<Nj10>. so we recalculated their best-fit relation to take only the contribution of the Compton-thin AG into The difference between the data points and the line illustrates the relevance of the various selection effects that LF2005 take into account As it can be seen. our model predicts a decrease in the absorbed AGN fraction with increasing X-ray luminosity. but the slope of the predicted anticorrelation is not as steep as in LF2005."," It must be noted that the “global” fit given by LF2005 (dotted lines in their figure 11) also includes Compton-thick AGN with $^{24}<N_{H}<10^{25}$, so we recalculated their best-fit relation to take only the contribution of the Compton-thin AGN into The difference between the data points and the line illustrates the relevance of the various selection effects that LF2005 take into account As it can be seen, our model predicts a decrease in the absorbed AGN fraction with increasing X-ray luminosity, but the slope of the predicted anticorrelation is not as steep as in LF2005."912 We next move up to z-0.7. the highest redshift where the NT2007 findings do apply.," We next move up to $z$ =0.7, the highest redshift where the NT2007 findings do apply."913" The results on fj, (Eq. 7)»."," The results on $f_{abs}$ (Eq. \ref{formulafabs}) ),"914 keeping g — constant. are shown in the left panel of Fig. 8..," keeping $q$ = constant, are shown in the left panel of Fig. \ref{Abs_z07},"915 as a function of Lj. for Ly> 10?ergs7!. where the completeness is ensured. and in the right panel of Fig. 8.. ," as a function of $L_{b}$ , for $L_{b}\geq$ $^{45.4} erg s^{-1}$, where the completeness is ensured, and in the right panel of Fig. \ref{Abs_z07}, ,"916"as a function of L,.", as a function of $L_{x}$ .917" Notably the values of fj4,, are almost identical to those calculated at 220.35 for the same assumption on q.", Notably the values of $f_{abs}$ are almost identical to those calculated at $z$ =0.35 for the same assumption on $q$.918 Despite the significant differences in ρω) at the two redshifts. the parameters into play conjure to give essentially the same quantitative outcome: not surprisingly in the highest bin of Ly. which remains dominated by the highest masses.," Despite the significant differences in $\lambda_{peak}(M_{BH})$ at the two redshifts, the parameters into play conjure to give essentially the same quantitative outcome: not surprisingly in the highest bin of $L_x$, which remains dominated by the highest masses."919 Even if. at this particular redshift. the global best fit at z=0.7 from LF2005 (solid line) appears to be ui reasonably good agreement with our prediction. the fundamental point is that the z-dependence of the (Mg) distribution does not in itself introduce any increasing trend in fipy. at least between z=0.35 and z=0.7.," Even if, at this particular redshift, the global best fit at z=0.7 from LF2005 (solid line) appears to be in reasonably good agreement with our prediction, the fundamental point is that the z-dependence of the $\lambda(M_{BH})$ distribution does not in itself introduce any increasing trend in $f_{abs}$, at least between z=0.35 and z=0.7."920 This conclusion ts strengthened by the fact that a possible dependence of q on Mj. reflecting changes in the shape of ΕΜΜ) above 10 M. is likely to be less steep at 220.7 than assumed at z20.35. for demonstrative purpose. in the previous section. and would therefore make no significant difference for the We now move to the local Universe.," This conclusion is strengthened by the fact that a possible dependence of $q$ on $M_{BH}$, reflecting changes in the shape of $F^*(M_{BH})$ above $^7$ $M_{\odot}$, is likely to be less steep at $z$ =0.7 than assumed at $z$ =0.35, for demonstrative purpose, in the previous section, and would therefore make no significant difference for the We now move to the local Universe."921 We used the information extracted from H2004. as described in Sect.," We used the information extracted from H2004, as described in Sect."922 2 and summarised in Table 1.., 2 and summarised in Table \ref{tabHeckman}. .923 Figure 9.. left panel. shows the results on. f;p(Ls) obtained in two ways. one directlyfrom the curvesinFig.," Figure \ref{Heckmanz01}, , left panel, shows the results on $f_{abs}(L_{b})$ obtained in two ways, one directlyfrom the curvesinFig."924 3 of H2004. the other from their Lorentzian representation.," 3 of H2004, the other from their Lorentzian representation."925" The latter allowed us to go beyond logL,246."," The latter allowed us to go beyond $L_{b}$ =46,"926Now (that we were confident with our radial velocity results. we made a [ist pass αἱ identifving our program targets as either SAIC members or foreground stars.,"Now that we were confident with our radial velocity results, we made a first pass at identifying our program targets as either SMC members or foreground stars."927 As Figure 4 shows. a first eut al classifving (he stars was relatively simple.," As Figure \ref{fig:radVelRplot} shows, a first cut at classifying the stars was relatively simple."928 Just as we had hoped. the plot of radial velocity (Lhe r parameter is clearly bimodal with one grouping; of stars centered around the SMC's radial velocity (158 km 1) and another grouping of stars centered around O0 km +. the radial velocity of the Milky Wav in the direction of the SMC.," Just as we had hoped, the plot of radial velocity the $r$ parameter is clearly bimodal with one grouping of stars centered around the SMC's radial velocity (158 km $^{-1}$ ) and another grouping of stars centered around 0 km $^{-1}$, the radial velocity of the Milky Way in the direction of the SMC."929 In general. the olfseis ave large enough to accommocdate velocity dispersion in each galaxy. and still remain Clearly separated.," In general, the offsets are large enough to accommodate velocity dispersion in each galaxy and still remain clearly separated."930 Bul. what about the small number of stars (730) in the middle?," But, what about the small number of stars $\sim$ 30) in the middle?"931 For stars with intermediate radial velocities in Figure 4.. we used a luminosity sensitive line. OL AT774. to determine membership.," For stars with intermediate radial velocities in Figure \ref{fig:radVelRplot}, we used a luminosity sensitive line, OI $\lambda$ 7774, to determine membership."932 According to Osmer (1972). Ol ATTT4 is strong in F supereiants as compared (ο its strength in dwarls due to non-LTE effects ancl as a result. of spheroidicitv (Przvbilla οἱ 22000). at least at. Galactic metallicities.," According to Osmer (1972), OI $\lambda$ 7774 is strong in F supergiants as compared to its strength in dwarfs due to non-LTE effects and as a result of spheroidicity (Przybilla et 2000), at least at Galactic metallicities."933" So. the ""questionable"" stars wilh measurable amounts of OL ATT14 should be supergiants. while the stars that contained very little OI AT774 should be foreground stars."," So, the “questionable"" stars with measurable amounts of OI $\lambda$ 7774 should be supergiants, while the stars that contained very little OI $\lambda$ 7774 should be foreground stars."934 However. (his luminosity dependence hasn't vel been tested al SAIC metallicities or lor the cooler (G-(vpe) superegiants.," However, this luminosity dependence hasn't yet been tested at SMC metallicities or for the cooler (G-type) supergiants."935 50. before applving this rule. we first needed to check these two points using the stars clearly separated as a test of the method.," So, before applying this rule, we first needed to check these two points using the stars clearly separated as a test of the method."936 We did (ais bv determining the effective temperature ancl luminosity [or every observed star using the relations described below in Section 4.1.. and measure (he equivalent width of the ΟΙ AT774 line.," We did this by determining the effective temperature and luminosity for every observed star using the relations described below in Section \ref{makeHRD}, and measure the equivalent width of the OI $\lambda$ 7774 line."937 We assume (hat stars wilh very. large racial velocities are SAIC supergiants and those with low velocities are foreground dwarts., We assume that stars with very large radial velocities are SMC supergiants and those with low velocities are foreground dwarfs.938 The resulis of measuring (he equivalent widths of the OL ATTT4 lines are shown in Table 2.., The results of measuring the equivalent widths of the OI $\lambda$ 7774 lines are shown in Table \ref{tab:derived}.939 While we knew that ΟΙ ATTTd is strong in F supergiants (Osmer 1972). we didui know its behavior for G-(vpe supereiants.," While we knew that OI $\lambda$ 7774 is strong in F supergiants (Osmer 1972), we didn't know its behavior for G-type supergiants."940 We first needed to determine if there is a lemperature cut-off for the luminosity dependence., We first needed to determine if there is a temperature cut-off for the luminosity dependence.941 Indeed. after examining our results. we determined that the relationship is only significant in hotter stars. specifically our category l stars with logZig23.72 (25200 IX) at SAIC metallicities (2=0.22. ).," Indeed, after examining our results, we determined that the relationship is only significant in hotter stars, specifically our category 1 stars with $\log T_{\rm eff} > 3.72$ $ > $ 5200 K) at SMC metallicities $z = 0.2z_\odot$ )."942 So. almost all of our category 1 supergiants with logTug>3.72 had a measurable amount (> 0.2A)) of ΟΙ ATTi4 while almost all of ow stus with logTay<3.72 didit.," So, almost all of our category 1 supergiants with $\log T_{\rm eff} > 3.72$ had a measurable amount $ > 0.2$ ) of OI $\lambda$ 7774 while almost all of our stars with $\log T_{\rm eff} \leq 3.72$ didn't."943 This lower temperature limit of 5200 Ix falls near the bottom of our identified vellow supergiant temperature range of 4800 to 1500 Ix (Drout et 22009)., This lower temperature limit of 5200 K falls near the bottom of our identified yellow supergiant temperature range of 4800 to 7500 K (Drout et 2009).944 While this huminosity dependence appears to hold (rue for most G supergiants. it mav not hold true for the coolest of them.," While this luminosity dependence appears to hold true for most G supergiants, it may not hold true for the coolest of them."945 For (he category 1 stus with higher temperatures. we confirmed that we could use the OI AT774 line as a method of determining membership aud for those that we couldn't use the OI AT174 line. we assiened," For the category 1 stars with higher temperatures, we confirmed that we could use the OI $\lambda$ 7774 line as a method of determining membership and for those that we couldn't use the OI $\lambda$ 7774 line, we assigned"946the importance of the background subtraction. but also the need to obtain accurate spectral data (Sclunelz 2002. Martens et al.,"the importance of the background subtraction, but also the need to obtain accurate spectral data (Schmelz 2002, Martens et al."947 2002. Asclwwanden 2002. Schinelz et al.," 2002, Aschwanden 2002, Schmelz et al."948 2003)., 2003).949 Similar results but different couclusions are reached by Laudi Laucini (2001). aud Laudi Feldiuau (2001) who analyze a loop observed with SoIIO aud. finding it nearly isothermal. consider this evidence as real aud invoke a non-coustant cross-section to explain it.," Similar results but different conclusions are reached by Landi Landini (2004), and Landi Feldman (2004) who analyze a loop observed with SoHO and, finding it nearly isothermal, consider this evidence as real and invoke a non-constant cross-section to explain it."950 Frou their analysis of SOTO/CDS data compared to other simular analyses mace by other authors. Schiuelz et al. (," From their analysis of SoHO/CDS data compared to other similar analyses made by other authors, Schmelz et al. ("9512005) xopose that there may be two different classes of loops. iuulti-thermal aud isothermal. while Asclyvauden Nightineale (2005) analyze the thinnest loop structures detected with TRACE aud find that a few are isothermal along the Lue of sight and may therefore be elementary loop compoucuts.,"2005) propose that there may be two different classes of loops, multi-thermal and isothermal, while Aschwanden Nightingale (2005) analyze the thinnest loop structures detected with TRACE and find that a few are isothermal along the line of sight and may therefore be elementary loop components."952 Another puzzling issue. certainly linked to the loop isothermal appearance. is the loop overdensity.," Another puzzling issue, certainly linked to the loop isothermal appearance, is the loop overdensity."953 In order to explain both these pieces of evidence. several autlors claim that the loop cannot be at equilibrium and it must be filamented and coolme from a hotter state. probably continuously subject to heating episodes (uauoflares. Warren et al.," In order to explain both these pieces of evidence, several authors claim that the loop cannot be at equilibrium and it must be filamented and cooling from a hotter state, probably continuously subject to heating episodes (nanoflares, Warren et al."954 2002. Warren ct al.," 2002, Warren et al."955 2003. Careill Πιοτής 2001).," 2003, Cargill Klimchuk 2004)."956 The presence of nanoflares nmüeht explain the oeseuce of Coronal loops. stable although heated at the ootpoluts and with a peaked distribution of enmüssion neasure. as observed m active stars (Testa et al.," The presence of nanoflares might explain the presence of coronal loops, stable although heated at the footpoints and with a peaked distribution of emission measure, as observed in active stars (Testa et al."957 200, 2004).958 Ad anticoincidence between hot aud cooler loops has Όσοι ound from the comparison of simuitancous Yohkol aud TRACE data (Nagata et al., An anticoincidence between hot and cooler loops has been found from the comparison of simultaneous Yohkoh and TRACE data (Nagata et al.959 2003. Schinieder et al.," 2003, Schmieder et al."960 2001). who. however. find tha the DEM of loops have a 11oderate mut finite width.," 2004), who, however, find that the DEM of loops have a moderate but finite width."961 Time-dependent imodeling of one coronal loop observed with TRACE pointed out that the detailed description of the evolution of this loop requires a heating ocated at intermediate position between the apex and he footpoiuts. probably initially hieh and then slowly decaying (Reale et al.," Time-dependent modeling of one coronal loop observed with TRACE pointed out that the detailed description of the evolution of this loop requires a heating located at intermediate position between the apex and the footpoints, probably initially high and then slowly decaying (Reale et al."962 2000)., 2000).963 The current debate in the interpretation of coronal oop observations points out the presence of intrinsic nuitatious in the information that one can derive frou oeseut-day data., The current debate in the interpretation of coronal loop observations points out the presence of intrinsic limitations in the information that one can derive from present-day data.964 Tere. we take the analysis of a miulti-wavelength observation of a time-evolving coronal loop as a euide to study how deep one can go in the diagnostics and characterization of the loop. and puts the basis for further aualvsis through detailed forward modeling which we leave for a future work.," Here, we take the analysis of a multi-wavelength observation of a time-evolving coronal loop as a guide to study how deep one can go in the diagnostics and characterization of the loop, and puts the basis for further analysis through detailed forward modeling which we leave for a future work."965 To this purpose we have searched for the observation of a loop in particularly good conditions for analysis: a simple aud well-defined svsteun. ax isolated as possible. imaged in more than one TRACE filter baud. in several SoIIO/CDS spectral lines aud with Yohkoh/SXT. and for a fiue period of more than one hour.," To this purpose we have searched for the observation of a loop in particularly good conditions for analysis: a simple and well-defined system, as isolated as possible, imaged in more than one TRACE filter band, in several SoHO/CDS spectral lines and with Yohkoh/SXT, and for a time period of more than one hour."966 Its eventual disappearance allows us to use the last nuageso as point-to-point background to be subtracted., Its eventual disappearance allows us to use the last images as point-to-point background to be subtracted.967 We try to use the coherence of the structure. its evolution and the spectral data to extract the muaxiumui possible information from the data.," We try to use the coherence of the structure, its evolution and the spectral data to extract the maximum possible information from the data."968 The selection of the loop observation. its description aud the inethods of the data analysis are illustrated in Section 2.. the results of the analysis are shown iu Section 3. aud they are discussed in Section [: we draw our conclusion in Section 5..," The selection of the loop observation, its description and the methods of the data analysis are illustrated in Section \ref{sec:data}, the results of the analysis are shown in Section \ref{sec:res} and they are discussed in Section \ref{sec:disc}; we draw our conclusion in Section \ref{sec:concl}."969 From the list of SolIO campaigus available at the Web ste/cei-bin/eui.. we have selected the campaign. with ID umuber 5170. namedStudy.," From the list of SoHO campaigns available at the Web site, we have selected the campaign, with ID number 5170, named."970 The Observation date is 13 Mav 1998 and the coordinator is Robert Walsh., The Observation date is 13 May 1998 and the coordinator is Robert Walsh.971 The campaign includes data from TRACE. SoIIO/CDS and Yolikol/SXNT.," The campaign includes data from TRACE, SoHO/CDS and Yohkoh/SXT."972 TRACE data consist of a 3.5 hours iue-sequenuce of 10211021 full resolution images in al lice filters (171À.. 195Α.. 281 Aj).," TRACE data consist of a 3.5 hours time-sequence of $\times$ 1024 full resolution images in all three filters (171, 195, 284 )."973 Yohkob/SXT data consist of a time-sequence of half-xesolution (5 pixel size) Wlbdisk images mostly m a single filter. with a goo ime overlap with the time period of the TRACE data.," Yohkoh/SXT data consist of a time-sequence of half-resolution (5"" pixel size) full-disk images mostly in a single filter, with a good time overlap with the time period of the TRACE data."974 SoIlIO/CDS data include several rasters but ouly two of hem with eoo spectral resolution aud a relevant ficl« of view (see Section 2.5))., SoHO/CDS data include several rasters but only two of them with good spectral resolution and a relevant field of view (see Section \ref{sec:cdsdata}) ).975 The first raster overlaps the TRACE observation., The first raster overlaps the TRACE observation.976 Fie., Fig.977 1 shows the time coverage of cach piece of observation relevant for the present analysis., \ref{fig:times} shows the time coverage of each piece of observation relevant for the present analysis.978 The TRACE frames span from 6:30 UT to 10 UT with wo sigmificant eaps of about 20 min around 7:15 UT anc 8:50 UT. which divide the TRACE data into τος nain warts.," The TRACE frames span from 6:30 UT to 10 UT with two significant gaps of about 20 min around 7:15 UT and 8:50 UT, which divide the TRACE data into three main parts."979 Most of the loop evolution is included im the first wo TRACE seeiieuts., Most of the loop evolution is included in the first two TRACE segments.980 These are well covered by the SNT ata (until 8:50 UT)., These are well covered by the SXT data (until 8:50 UT).981 The first CDS raster occurs curing he second TRACE segieut., The first CDS raster occurs during the second TRACE segment.982 The second (onger) raster is aken after the end of the TRACE data., The second (longer) raster is taken after the end of the TRACE data.983 For completeness. oe1 order to report on the loop evolution at times before 16 calnpaiegn. we have partially aualvzed TRACE data in ιο 171 and 195 filter bauds (about 50 additional inaeges iu each filter) taken between 0:15 UT and 6:20 UT and one Yolikoh/SNT nage taken at 5:26 UT.," For completeness, in order to report on the loop evolution at times before the campaign, we have partially analyzed TRACE data in the 171 and 195 filter bands (about 50 additional images in each filter) taken between 0:18 UT and 6:20 UT and one Yohkoh/SXT image taken at 5:26 UT."984 The loop has been selected on the TRACE images., The loop has been selected on the TRACE images.985 It appears as an cutive loop in several 171 filter images. and it is clearly visible also im the 195 baud.," It appears as an entire loop in several 171 filter images, and it is clearly visible also in the 195 band."986 A mostly visible loop is well suitable to provide complete coustraiuts on diagnostics and models., A mostly visible loop is well suitable to provide complete constraints on diagnostics and models.987 May loops are faint around their apex. simply because of the stratification due to eravitv.," Many loops are faint around their apex, simply because of the stratification due to gravity."988 The loop is bright. 1.0. observed with good count statistics aud with a high contrast over the background.," The loop is bright, i.e. observed with good count statistics and with a high contrast over the background."989 We have searched for à loop as far as possible free frou other structures intersecting the line of sight. which nuelt be difficult to disentangle from the analyzed loop.," We have searched for a loop as far as possible free from other structures intersecting the line of sight, which might be difficult to disentangle from the analyzed loop."990 ≓≻∖∖⊽⋜⊔⋅⇂⋅∢⊾⇂↓↕↓≻↿↕≼⇍⋜↧↓≻⋜↧⊳∖⋜↧↓⋅⊔↓∢⊾⋜⋯⋅↓≻↓⋅∢⊾⊳∖⊳∖⊔↓⋅⋖⋅−⊳∖⊔↓≻↓≻⋖≱↓⋅↿⋯⇂∪∣⋡≯↕⋯∙↥≱∖⋡ characterized by very low rotation velocities compare o their velocity dispersions (fast-rotating dis do exis ub they are rares see De Rijeke (2001))).,"Dwarf ellipticals as a rule are pressure-supported objects, characterized by very low rotation velocities compared to their velocity dispersions (fast-rotating dEs do exist but they are rare, see De Rijcke \cite{der}) )."991 There is currently a number of models in vogue that. attemp o explain this apparent lack of rotation as a resul of significant mass-loss., There is currently a number of models in vogue that attempt to explain this apparent lack of rotation as a result of significant mass-loss.992 According to the “wind-nioclel”. oposed by Dekel Silk (1986).. dls form from average-amplitude density ποιαος.," According to the “wind-model”, proposed by Dekel Silk \cite{ds}, dEs form from average-amplitude density fluctuations."993 Most. if not all. of the ESA is subsequently blown away after it has been heated. to velocities that exceed the ealaxy's escape velocity by the first. burst. of supernova explosions.," Most, if not all, of the ISM is subsequently blown away after it has been heated to velocities that exceed the galaxy's escape velocity by the first burst of supernova explosions."994 This dramatic mass-loss causes a more anisotropic. orbital. structure ancl makes je galaxy pull up., This dramatic mass-loss causes a more anisotropic orbital structure and makes the galaxy puff up.995 A more sophisticated version of this scenario can be found in Mori (L997) who cliscuss je c. ↥∢⋅⊔↓∢⊔⇂∙∖⇁⊔⋜⋯↓⊔⇍⋜↧⇂⋖⋅∖⇁∪↓⋯↓∪⊔∪⇂⋜↧↓∪⊔∆∪⋅∠⇂∖∖⊽⋜⊔⋅⇂⋏∙≟⋜↧↓⋜∟∖∙∖⇁⊳., A more sophisticated version of this scenario can be found in Mori \cite{more} who discuss the chemodynamical evolution of a $10^{10}M_\odot$ dwarf galaxy.996 ⋅ ⊏ The first supernovae expell a supersonic outllow of gas rom the center of the galaxy., The first supernovae expell a supersonic outflow of gas from the center of the galaxy.997 Stars form in this expanding shell and subsequent supernova explosions further accelerate 1e expansion of the shell and enrich it with metals., Stars form in this expanding shell and subsequent supernova explosions further accelerate the expansion of the shell and enrich it with metals.998 This model explains the outward reddening of cles as a metallicity ellect ancl reflects in the characteristic exponential surface-xightness profile., This model explains the outward reddening of dEs as a metallicity effect and reflects in the characteristic exponential surface-brightness profile.999 Other scenarios take into account the fact that cles are ouncl predominantly in high-density environments such as eroups and clusters., Other scenarios take into account the fact that dEs are found predominantly in high-density environments such as groups and clusters.1000 Mori Burkert (2000) argue that rame-pressure stripping is able to completely remove the gas ⋅rom a dl⊲ less massive. than 105AZ. withinqs a few⋅ 107↴ vears.," Mori Burkert \cite{mor} argue that ram-pressure stripping is able to completely remove the gas from a dE less massive than $10^91001M_\odot$ within a few $10^8$ years."1002"the radioactive heating rate of all the relevant isotopes synthesized in the CC-SN explosion and is given by: where X;, Τι, €j,4 and represent the mass fraction, lifetime, energy per unit €;,-+mass and unit time released by the decay of the i-th isotope in the form of 4-rays and positrons, respectively, and the factor f; accounts for the fact that the y-rays are not totally trapped in the envelope (fordetails,seeBalbergetal.2000,andreferences therein)..","the radioactive heating rate of all the relevant isotopes synthesized in the CC-SN explosion and is given by: where $X_i$ , $\tau_i$ , $\varepsilon_{i,\gamma}$ and $\varepsilon_{i,e^{+}}$ represent the mass fraction, lifetime, energy per unit mass and unit time released by the decay of the $i$ -th isotope in the form of $\gamma$ -rays and positrons, respectively, and the factor $f_i$ accounts for the fact that the $\gamma$ -rays are not totally trapped in the envelope \citep[for details, see][and references therein]{balberg00}."1003 The relevant radioactive nuclei considered in the present investigation and the values of their characteristic parameters are reported in Table 1.. The?6Co, The relevant radioactive nuclei considered in the present investigation and the values of their characteristic parameters are reported in Table \ref{tab:features}.1004" abundance is evaluated considering that the isotope is involved into the nuclear decay chain — —56je, so its mass as a function of the time t is determined from: where we assume that the initial abundance of?9Co is equal to zero and that 1/(1—Tsewi/Tseco)&1."," The abundance is evaluated considering that the isotope is involved into the nuclear decay chain $\rightarrow$ $\rightarrow$, so its mass as a function of the time $t$ is determined from: where we assume that the initial abundance of is equal to zero and that $1/(1-\tau_{\mathrm{^{56}{Ni}}}/\tau_{\mathrm{^{56}{Co}}}) \simeq 1$."1005" In order to test the dependability of the new version of the code, a few simulations have been performed with both the new and old version."," In order to test the dependability of the new version of the code, a few simulations have been performed with both the new and old version."1006" The evolution starts from the same set of initial conditions reported in sect. 2.3,,"," The evolution starts from the same set of initial conditions reported in sect. \ref{sec:code:IniCond},"1007 except for the radial distribution of that is assumed to be uniform., except for the radial distribution of that is assumed to be uniform.1008" We varied several input parameters of points, location of the inner boundary, mass of the (numberejecta, initial radius and to check the stability and accuracy of the code."," We varied several input parameters (number of points, location of the inner boundary, mass of the ejecta, initial radius and energy) to check the stability and accuracy of the code."1009" In the energy)outer expanding part of the flow (which comprises most of the mass, in practice all the envelope mass apart from the innermost ~107? the fractional difference between the values of the variablesΜς))) computed with the new and old version of the code is 10-2096 (e.g., Figures 1 and 2;; see also Pumo,Zampieri&Turatto"," In the outer expanding part of the flow (which comprises most of the mass, in practice all the envelope mass apart from the innermost $\sim 10^{-3}$ ) the fractional difference between the values of the variables computed with the new and old version of the code is $\lesssim$ (e.g., Figures \ref{fig:tvrho} and \ref{fig:w01}; see also \citealt*{pumo09a}) )."1010 The only exception is the profile of the radiative flux 2010)).that differs by <50%., The only exception is the profile of the radiative flux that differs by $\lesssim 50$.1011". Indeed, the radiative flux depends sensitively on the numerical treatment."," Indeed, the radiative flux depends sensitively on the numerical treatment."1012 The improved stability of the new version makes the profile computed by the new code more reliable., The improved stability of the new version makes the profile computed by the new code more reliable.1013" A significant difference (< 40%)) is present also in the innermost ~107? of the envelope (below logR~12.7), where the flow starts to fall back onto the remnant."," A significant difference $\lesssim 40$ ) is present also in the innermost $\sim 10^{-3}$ of the envelope (below $\log R \sim 12.7$ ), where the flow starts to fall back onto the remnant."1014" This is most likely linked to the delicate balance between the pressure gradients and the gravitational force, that determines the location of the accretion radius γα (seeBalbergetal.2000,fordetails).."," This is most likely linked to the delicate balance between the pressure gradients and the gravitational force, that determines the location of the accretion radius $r_a$ \citep[see][for details]{balberg00}."1015" Even a slight difference in the calculation of the gas and radiation pressures may cause a sign reversal in the velocity of the marginally bound gas shells (containing €10-+Mo ,)) located near to Τα, that start then to fall back onto the remnantinstead ofgoing outwards."," Even a slight difference in the calculation of the gas and radiation pressures may cause a sign reversal in the velocity of the marginally bound gas shells (containing $\lesssim 10^{-4}$ ) located near to $r_a$, that start then to fall back onto the remnantinstead ofgoing outwards."1016" While the simulations with the old version often develop numerical instabilities, those evolved with the new version show to be stable."," While the simulations with the old version often develop numerical instabilities, those evolved with the new version show to be stable."1017 Several models were, Several models were1018the phase defined as ο)=0(/)/2x in HITT does not suffer the above-mentioned problems.,the phase defined as $\phi(t)=\theta(t)/2\pi$ in HHT does not suffer the above-mentioned problems.1019 Figure G shows the folded lisht curve of SAIC X-1. and the phase zero epoch is defined bv (he first data point in the light curve (MJD 50.134).," Figure \ref{fold_lc} shows the folded light curve of SMC X-1, and the phase zero epoch is defined by the first data point in the light curve (MJD 50,134)."1020 The folded light curve shown in Figure 6 seems mostly in agreement with (he results of Trowbridgeetal.(2007)., The folded light curve shown in Figure \ref{fold_lc} seems mostly in agreement with the results of \citet{Trowbridge2007}.1021. The major distinction between this superorbital modulation profile and that obtained from previous studies is a clear low state wilh a negligible X-ray Εαν lasting for ~0.3 evcle., The major distinction between this superorbital modulation profile and that obtained from previous studies is a clear low state with a negligible X-ray flux lasting for $\sim 0.3$ cycle.1022 Moreover. the asvinmetric features of the superorbital profile can also be obtained in the folded light curve.," Moreover, the asymmetric features of the superorbital profile can also be obtained in the folded light curve."1023 In order to describe the asvannmnetric profile. the low state count rate was defined as the mean count rate during phase ~0.2 to ~0.55 and the hieh state count rate was considered by averaging the count rate between phase ~0.75 to o1.0.," In order to describe the asymmetric profile, the low state count rate was defined as the mean count rate during phase $\sim 0.2$ to $\sim 0.55$ and the high state count rate was considered by averaging the count rate between phase $\sim 0.75$ to $\sim 1.0$."1024 Thus. the rising and falling time scale can be estimated by caleulating the time scale between and of amplitude.," Thus, the rising and falling time scale can be estimated by calculating the time scale between and of amplitude."1025 By this definition. the rising time scale is ~0.14 evele (from phase 0.05 to 0.19). which is shorter than the Falling Gime scale of ~0.19 cvcle (fom phase 0.54 to 0.13).," By this definition, the rising time scale is $\sim0.14$ cycle (from phase 0.05 to 0.19), which is shorter than the falling time scale of $\sim0.19$ cycle (from phase 0.54 to 0.73)."1026 The ASM light curve can further be divided into three channels., The ASM light curve can further be divided into three channels.1027 The spectral hardness provides crude information about the emission mechanisms during superorbital modulation., The spectral hardness provides crude information about the emission mechanisms during superorbital modulation.1028 The ASAI hardness ratio was defined as ch3/(chl+eh2). since ch3 and chi+ch? have similar photon count rates during the high state.," The ASM hardness ratio was defined as $ch3/(ch1+ch2)$, since $ch3$ and $ch1+ch2$ have similar photon count rates during the high state."1029 Only the data wilh a signal to noise ratio (SNR) greater than 5 were chosen and folded according to the superorbital phase defined in TWIT., Only the data with a signal to noise ratio (SNR) greater than 5 were chosen and folded according to the superorbital phase defined in HHT.1030 During the entire observation time span. (here are no data points wilh SNRs greater than 5 between phase 0.73 and 1.05.," During the entire observation time span, there are no data points with SNRs greater than 5 between phase 0.73 and 1.05."1031 Therefore. no reliable hardness ratio in the low state was obtained.," Therefore, no reliable hardness ratio in the low state was obtained."1032 The folded hardness ratio is shown in Figure 7.., The folded hardness ratio is shown in Figure \ref{fold_hr}.1033 It is easily observed. that the hardness ratios in the high state (from phase 0.19 to 0.54) are relatively stable., It is easily observed that the hardness ratios in the high state (from phase 0.19 to 0.54) are relatively stable.1034 In the transition state (phase 0.050.19. and 0.540.73). the hardness ratios do not appear to significantly deviate from (he mean value as compared with that in the high state although," In the transition state (phase 0.05–0.19, and 0.54–0.73), the hardness ratios do not appear to significantly deviate from the mean value as compared with that in the high state although"1035For a physical interpretation of the iucompressive sliwaves in the stratified shearing sleet. we repeat the analysis of section 3.3 [or the solution given in the previous section.,"For a physical interpretation of the incompressive shwaves in the stratified shearing sheet, we repeat the analysis of section 3.3 for the solution given in the previous section."1036 For a complete description of the energy. in this case. however. we must include the potential euergy of a Πα element displaced in the radial direction.," For a complete description of the energy in this case, however, we must include the potential energy of a fluid element displaced in the radial direction."1037" Following Miles(1961).. an expression for the energy in the Boussinesq approximation is obtaiued by πας equation (??2)) multiplied by de, aud equation (?7)) multiplied by 9c."," Following \cite{jwm61}, an expression for the energy in the Boussinesq approximation is obtained by summing equation \ref{LIN2}) ) multiplied by $\delta v_x$ and equation\ref{LIN3}) ) multiplied by $\delta v_y$ ."1038 Replacing 9X/Xj by £;/Ls via equation (??)) results in the following expression for the energy evolution: ∖∖↽∐≺↵↥⋅≺↵↙↘∣⋅−∶↙↘∣⋅⊽⊺∣↲↱↙↘∣⋅≳−↙⋅↽⋡∏↕≺↵↕⊔⋅≺↵≺↵↕↩⊔∐⊳∖⋯↩≺↽↓⋯↕⋃∩∐⋖↜∙↗∙↗⊔∢∙⋜↕∐∣⋈↵∐⇂≺↲∐⊔," Replacing $\delta \Sigma/\Sigma_0$ by $\xi_x/L_S$ via equation \ref{SOX}) ) results in the following expression for the energy evolution: _0 v^2 + _0 N_x^2 _x^2 ) = _0 v_x v_y, where $\delta v^2 = \delta v_x^2 + \delta v_y^2$."1039∐≺↵≼⇂⋜↕⊳∖↕∐≺↵↕⊆⋯≺↵⋃∢∙≺↵∐≺↵↕⋅∑≟⊽∖⇁⋅-05-0v ⋅ ⋅ ∣∙∙ ⋅⋅⋅ ⋅ ↥↽≻∩↕≺↵⋯↕⋜↕↥≺↵∐≺↵↓⋅∑≟⊽∖⇁⋜↕∐≺∐≹≺↵⊽∖⊽∐∩∐⊳∖⊳∖⋃⋅↩⊳∖⊳∖⋜↕⊳∖⊳∖∩∢∙↥⋜↕↕↩≼⇂∖∖↽∐∐⋜⋯↥∐≼∐∖⊽↥≼⇂⋯↕↥⊳∖∐∖∖↽⋜↕∖⇁≺↵⋅⋃∐≺↵⋯⋜↕⊽," The three terms in equation \ref{ENERGY}) ) can be identified as the kinetic energy, potential energy and Reynolds stress associated with an individual shwave."1040∖⊽↕⋅≺↵⋯∐↥⊽∖⇁∖⊽≺↵↕⋅∐∎⊽∖⇁ that the vortical⋅ shwaves (see] equations⋅ ∣∙∙ (??))-(??)))Oe in] the unstratified⋅⋅ shearing⋅ sheet (V7NES=0) satisfy equation (??)). ⋅ ⋅ ⋅ ⋅ ∣∙, One may readily verify that the vortical shwaves (see equations \ref{IVX}) \ref{IS}) )) in the unstratified shearing sheet $N_x^2 = 0$ ) satisfy equation \ref{ENERGY}) ).1041∙ ⋅ ⋅ ⋅⋅ ⊺∐≺↵⊔∑∸∐∐⋜↕∐≺⇂⊳∖∐⇂≺↵∩↥≺↵≺↽↓⋯↕↕∩↥↸↜∙↗∙↗⊔∢∙⋜↕∐∣≻≺↲↕⋅≺↲∖∖↽⊔⊓≺↵∐≓⊤↙↘∣⋅⊽⊺∣⋜↕∐≼⇂∐∐∐∖⇁∐⇂⋯↕↥⋃⋅⋜⋃∐∐∑≟⊳∖∐∖∖↽⋜↕∖⇁≺↵⊳∖ ⋜⋮∣∔↙∖∕∖≼⊔⋜⋃⋅≺↵↕⇂≺↵↕⋅≺↵↥∎∩↕⋅↩⋜↕⊳∖⊳∖≺⋈∙↥⋜⋯↵≺⇂∖∖↽∎∐⋜↕∐≺↵∑≟⋜↕∏∖⊽≺↵⋜↕∐∑≟⋃↥⋜⋃⋅∐↕∩⋯≺↵∐⊓∐∐∐⇂∟∖⋅∐∎↕∐≺↵≺↵," The right hand side of equation \ref{ENERGY}) ) can be rewritten $-\tilde{\tau}1042\delta v_x^2$ and individual trailing shwaves $\tilde{\tau} > 0$ ) are therefore associated with a negative angular momentum flux."1043∐≺↲↥⋅∑≟⊽∖⇁∖∖↽≺↵↕⋅≺↵↥↽≻∩⊳∖∐↥∖⊽≺↵ ≺⇂≺↵∐∐∐≺↵↕∐↥⊳∖∖∖↽⋯∐≼⊔⋅≺↵≺↽↓⋃∐⋅≺↵↕∐⋜↕↕↥∐⇂∎∖⇁↥⋔⋯↥⊳∖∐∖∖↽⋜↕∖⇁≺↵⊳∖⋜, If the energy were positive definite this would require that individual shwaves always decay.1044↕↥∖∖↽⋜↕⊽∖⊽⊳∖≺⇂≺↲∢∙⋜↕⊽∖⇁⋅⊟⋯∖∖↽∐≺↵∐∖⋮−⋟∕∖∕∪↸∫∐↥∕∖∕⋯↕∐≺↵ ↥↽≻∩↕↩⋯↥⋜↕↥≺↵∐≺↵⋅∑≟⊽∖⇁⋜↕⊳∖⊳∖∩∢∙↥⋜↕↕≺↵≺⇂∖∖↽∐∐⋜↕↕⊳∖↥↽≻↥⋜↕∢∙≺↵⋯↩∐↕↥⊳∖∐≺↵∑≟⋜↕∏∖⇁≺↵⋅⊳∖∩↕∐≺↵≺↵∐≺↵↕⋅∑∸⊽∖⊽≿↴∕⋅∢∙⋜↕∐∣⋈↵∐≺↵∑≟⋜↕∏∖⊽≺↵⋜↕∐≺⇂ ⋜↕∐≺↵∑≟⋜↕∏∖⊽≺↵⋜↕∐∑≟⇂∐⋜⋃⋅∐↕∩∐↕≺↵∐⊓," But when $N_x^2 < 0$ ${\rm Ri} < 0$ ) the potential energy associated with a displacement is negative, so the energy $E_k$ can be negative and a negative angular momentum flux is not enough to halt shwave growth."1045"⊔∐∐∟∖∎⊳∖∐∩↕≺↵∐∩⋃∑∸∐↕∩∐⋜↕∐⊳∖∐∖∖↽⋜↕∖⊽≺↵∑≟↕⋅∩∖∖↽↕∐⋅ ⋃⇂⊔⋅∐≺↵⊸∖⊳∖↕≺↵↥↽≻↥⊳∖↕∩∖∖↽∏↕↩↕∐↩∢∙∩∐⊳∖↕⋜↕∐↕⊳∖∩↥∎∐∐↩∑≟↕⋅⋜↕∏∩∐∁↴↓⋜↕∐≼⇂∁↴⊇↥∐↕≺↵⊔∐⊳∖∩⊓∐≺↵↕∐∐↥⋜↕⊔⋅⋯∐⋜↕↥ ∖⊽≺↵↥∩∢∙∐⊽∖⇁⋜↕∐≼⇂≺∐⊳∖↥↽≻↥⋜↕∢∙≺↵⋯≺↵∐↕∩⊓∐≺↲⊳∖∐≺↵⋜∐⋅↕∐∑≟∖∖↽⋜↕∖⊽≺↵⋅↙↘⋅∣⋅⊽⋮∣∣∣⋜↕∐≺⇂⋚⊽⋮∣∣∣∶ οιασ -- C2: y= where το=μην. Oty, is the hypergeometric function given by equation (??)) with Cy=1 and Cs= 0. and the other functions are similarly defined."," Our next step is to write the constants of integration $C_1$ and $C_2$ in terms of the initial radial velocity and displacement of the shearing wave, $\delta v_{x0}$ and $\xi_{x0}$: C_1 =, C_2 = where $\tilde{\tau}_0 = k_{x0}/k_y$, $\delta v_{x1}$ is the hypergeometric function given by equation \ref{SOLVX}) ) with $C_1 1046= 1$ and $C_2 = 0$ , and the other functions are similarly defined."1047" These expressions cau be simplified by noticing that the denominator of Cy aud C» is theWronskian of the dilIerential equation for £,:7 ", These expressions can be simplified by noticing that the denominator of $C_1$ and $C_2$ is theWronskian of the differential equation for $\xi_x$ 1048"broadening but rather to “morphological broadening"": in slitless spectroscopy spectral features are effectively images of the galaxy in that particular wavelength.",broadening but rather to “morphological broadening”: in slitless spectroscopy spectral features are effectively images of the galaxy in that particular wavelength.1049 This will be discussed further in refdise.sec.., This will be discussed further in \\ref{disc.sec}.1050 The galaxies with weak Ha emission have strong stellar absorption features typical. of intermediate age stellar populations., The galaxies with weak $\alpha$ emission have strong stellar absorption features typical of intermediate age stellar populations.1051 This is demonstrated in refstack.plot.. which compares the averaged rest-frame spectra of galaxies with strong and weak Ho.," This is demonstrated in \\ref{stack.plot}, which compares the averaged rest-frame spectra of galaxies with strong and weak $\alpha$."1052" The stellar absorption features Mg,. DD. and several TiO bands are clearly detected in the stacked spectrum of the weak Ha galaxies — for the first time at these redshifts."," The stellar absorption features $_b$, D, and several TiO bands are clearly detected in the stacked spectrum of the weak $\alpha$ galaxies – for the first time at these redshifts."1053 The colored lines in refstack.plot are stellar population synthesis models of (2010) with metallicity 2200.22. and different ages.," The colored lines in \\ref{stack.plot}1054 are stellar population synthesis models of (2010) with metallicity 0.22 and different ages."1055 The best-fitting age for the galaxies with low star formation is 2 GGyr: models with ages of up to GGyr also provide good fits., The best-fitting age for the galaxies with low star formation is $2$ Gyr; models with ages of up to Gyr also provide good fits.1056 We note that this is an average and that the galaxies probably have a range of ages., We note that this is an average and that the galaxies probably have a range of ages.1057 As can be seen in refnmbs.plot the galaxies with strongHa emission are slightly bluer (by ~0.3 mmag in Ü—V ) than the galaxies with weak Ha.," As can be seen in \\ref{nmbs.plot}1058 the galaxies with strong$\alpha$ emission are slightly bluer (by $\approx 0.3$ mag in $U-V$ ) than the galaxies with weak $\alpha$."1059 The fact that the color difference ts relatively small is because the star-forming galaxies have more dust: gaxies with <0 — hhaveameanbestfit(Ay)20.5+0.1 whereas galaxies with >10 hhavetAv) =1.02:0.32 (see also. e.g.. Labbé 2005:Papovich 2006: 2011).," The fact that the color difference is relatively small is because the star-forming galaxies have more dust: gaxies with $<10$ have a mean best-fit $\langle A_V\rangle1060= 0.5 \pm 0.1$ whereas galaxies with $>10$ have $\langle A_V\rangle = 1.0 \pm 0.2$ (see also, e.g., 2005; 2006; 2011)."1061 Besides the number of objects with strong Ho emission. a striking aspect of refsample.plot is that the morphologies of the galaxies correlate with the Ha line strength.," Besides the number of objects with strong $\alpha$ emission, a striking aspect of \\ref{sample.plot}1062 is that the morphologies of the galaxies correlate with the $\alpha$ line strength."1063" Massive |<z«1.5 galaxies with the highest star formation rates tend to be “grand design"" spiral galaxies. whereas those with no detected Hoa emission tend to be early-type galaxies."," Massive $1<z<1.5$ galaxies with the highest star formation rates tend to be “grand design” spiral galaxies, whereas those with no detected $\alpha$ emission tend to be early-type galaxies."1064 This result ts qualitatively similar to trends at z—20. although massive galaxies with >10 aarerareinthenearbyU niverse(sees .33).," This result is qualitatively similar to trends at $z=0$, although massive galaxies with $>10$ are rare in the nearby Universe (see 3)."1065 We quantify this correlation between galaxy structure and star formation rate in the top panel of refewn.plot.. which shows the relation between aand (1968) index.," We quantify this correlation between galaxy structure and star formation rate in the top panel of \\ref{ewn.plot}, which shows the relation between and (1968) index."1066 The Sersic index is a quantitative measure of galaxy structure. and is a proxy for the bulge-to-disk ratio: galaxies dominated by disks have zn—1 and galaxies dominated by bulges have 5~4.," The Sersic index is a quantitative measure of galaxy structure, and is a proxy for the bulge-to-disk ratio: galaxies dominated by disks have $n\sim 1$ and galaxies dominated by bulges have $n\sim 4$."1067 Splitting the galaxies in two equal bins. the median Sersic index of the 17 galaxies with 12 iis2.2. whereasitist.2 forthe \7 galaxies withEW «12 AA.," Splitting the galaxies in two equal bins, the median Sersic index of the 17 galaxies with $>12$ is 2.2, whereas it is 4.2 for the 17 galaxies with $<12$."1068.AccordingtotheMann -W hitnevtestthisdif ferenceissignificantatthe: Weinferthatstar formationinmassivegalaxiesat V«z«l.Stvpicallytakesplo dominated(spiralgalaxies., According to the Mann-Whitney test this difference is significant at the $>99$ We infer that star formation in massive galaxies at $1<z<1.5$ typically takes place in disk-dominated (spiral) galaxies.1069"T hisresultisconsistentwithrecentsuggestionst. Forminggalaxiesatz»lare""scaled versionsofnearbvgalaxieste.g.. Elbazet 2011)."," This result is consistent with recent suggestions that many star-forming galaxies at $z>1$ are ``scaled-up'' versions of nearby galaxies (e.g., 2011)."1070" The bottom panel of refewn.plot shows the relation between aand the inferred velocity dispersions of the4,,, galaxies. which are derived. from their stellar. masses. effective. radii. and Sersic indices followingBezanson (2011)."," The bottom panel of \\ref{ewn.plot} shows the relation between and the inferred velocity dispersions of the galaxies, which are derived from their stellar masses, effective radii, and Sersic indices following (2011)."1071 The inferred dispersions are a measure of the compactness of the stellar components of galaxies as they are proportional to vMre (with a Sersic-dependent correction factor)., The inferred dispersions are a measure of the compactness of the stellar components of galaxies as they are proportional to $\sqrt{M/r_e}$ (with a Sersic-dependent correction factor).1072 Again. there is a clear relation between these quantities: the median inferred dispersion of the half of the sample with the strongest Ha is kkm/s whereas it is kknys for the galaxies with the 174732weakest Ha.," Again, there is a clear relation between these quantities: the median inferred dispersion of the half of the sample with the strongest $\alpha$ is $174^{+30}_{-25}$ km/s whereas it is $299^{+51}_{-43}$ km/s for the galaxies with the weakest $\alpha$."1073 The relation 29011between aand dispersion has much smaller scatter than the relations of wwith effective radius and mass separately., The relation between and dispersion has much smaller scatter than the relations of with effective radius and mass separately.1074 The trend in refewn.plot is qualitatively consistent with the relation between estimated specific star formation rate (SSFR) and inferred dispersion found by (2008).," The trend in \\ref{ewn.plot}1075 is qualitatively consistent with the relation between estimated specific star formation rate (SSFR) and inferred dispersion found by (2008)."1076 Figure + showcases the large variety of galaxies., Figure \ref{ewn.plot} showcases the large variety of galaxies.1077" The range inEWu,, aamong massive galaxies with detected Ho is a factor of 12. and it is obviously even largerwhen undetected galaxies are taken into account (see refstack.plot))."," The range in among massive galaxies with $\alpha$ is a factor of 12, and it is obviously even largerwhen undetected galaxies are taken into account (see \\ref{stack.plot}) )."1078" The structure and morphologies of galaxies also show a large range. going from large spiral galaxies with hightto compact early-type galaxies with low EWy,,.."," The structure and morphologies of galaxies also show a large range, going from large spiral galaxies with highto compact early-type galaxies with low ."1079 The Sersic, The Sersic1080GRB photons in the literature.,GRB photons in the literature.1081 We will not repeat the full derivation here., We will not repeat the full derivation here.1082 Instead we refer th[e reader toGuettaetal(2004) and we only present here the major features relevant to this paper.," Instead we refer the reader to\citet{2004APh....20..429G}1083 and we only present here the major features relevant to this paper."1084" Protons accelerated in internal shocks interact with GRB photons via the process: and Because the photon-proton interaction has to create a A resonance, given a photon energy there is a minimum proton energy for which Eqs.3 and 4 can take place."," Protons accelerated in internal shocks interact with GRB photons via the process: and Because the photon-proton interaction has to create a $\Delta$ resonance, given a photon energy there is a minimum proton energy for which \ref{eqn:pgamma} and \ref{eqn:pi0} can take place."1085 In Earth's reference frame: Correspondingly the neutrinos resulting from Eq.3 have a minimum energy: where <ry.81/5 1s the fraction of the energy transferred to the charged pion from the initial proton energy and the factor of 1/4 arises because on average each one of the four final leptons in Eq.3 has the same energy., In Earth's reference frame: Correspondingly the neutrinos resulting from \ref{eqn:pgamma} have a minimum energy: where $<x_{p \rightarrow \pi^+}> \approx 1/5$ is the fraction of the energy transferred to the charged pion from the initial proton energy and the factor of 1/4 arises because on average each one of the four final leptons in \ref{eqn:pgamma} has the same energy.1086" It is customary to approximate the Band function fit to the average photon spectra as a broken power law (which we label approximation A)): Supposing that protons have a power law spectrum (LN,ο.E, 7. the neutrino spectrum traces Eq.7:: where a,=—53,— 3,9,=—a.—3 and the neutrino break energy e"" istaken from the minimum energy in Eq.6::"," It is customary to approximate the Band function fit to the average photon spectra as a broken power law (which we label approximation ): Supposing that protons have a power law spectrum $dN_p/dE_p \sim E_p^{-2}$ , the neutrino spectrum traces \ref{eqn:bandapprox}: where $\alpha_\nu = -\beta_\gamma -3$, $\beta_\nu = -\alpha_\gamma -3$ and the neutrino break energy $\epsilon^{\mathrm b}_\nu$ istaken from the minimum energy in \ref{eqn:nuphotoncorr}: :"1087evidence for bIuer optical-LR colours than expected for non-evolving or passively evolving elliptical galaxies (c.g. Lilly Longair 1984).,evidence for bluer optical-IR colours than expected for non-evolving or passively evolving elliptical galaxies (e.g. Lilly Longair 1984).1088 Initiallv. the UV. excess was interpreted in terms of bursts of star formation. possibly linked. to the evolution of the host. galaxies.," Initially, the UV excess was interpreted in terms of bursts of star formation, possibly linked to the evolution of the host galaxies."1089 This interpretation is attractive in the light of morphological studies which show evidence for recent mergers in a large fraction of powerful radio galaxies at low recdshilts (leckman ct al., This interpretation is attractive in the light of morphological studies which show evidence for recent mergers in a large fraction of powerful radio galaxies at low redshifts (Heckman et al.1090 1986): and mereer-ineduceck star formation has been suggested as a possible triggering mechanism (Smith Lleckman 1989)., 1986); and merger-induced star formation has been suggested as a possible triggering mechanism (Smith Heckman 1989).1091 llowever. given the degree. of nuclear and. extranuclear activity likelv to. be present in most. powerful radio ealaxies. some caution is required. in ceclucing starburst properties purely on the basis of broad-band. photometric measurements.," However, given the degree of nuclear and extranuclear activity likely to be present in most powerful radio galaxies, some caution is required in deducing starburst properties purely on the basis of broad-band photometric measurements."1092 Recognising the potential ACN contribution. an alternative explanation for the UV excess was stimulate w the development of the anisotropy-based unified schemes in the late 1980s (e.g. Barthel 1989).," Recognising the potential AGN contribution, an alternative explanation for the UV excess was stimulated by the development of the anisotropy-based unified schemes in the late 1980's (e.g. Barthel 1989)."1093 In the frame of such schemes the UM. excesses can be explained. in terms of ight scattered. from broad. radiation cones of the hidden quasar nuclei Clacdhunter et al., In the frame of such schemes the UV excesses can be explained in terms of light scattered from broad radiation cones of the hidden quasar nuclei (Tadhunter et al.1094 1988. Fabian 1989).," 1988, Fabian 1989)."1095 Lark polarimetric attempts to test this model proved. successtu in the sense that they showed the high. degrees of linear »olarization. characteristic of anisotropic scattering in. the UV continua of several high. redshift radio galaxies (c.g. ‘Tadhunter et al., Early polarimetric attempts to test this model proved successful in the sense that they showed the high degrees of linear polarization characteristic of anisotropic scattering in the UV continua of several high redshift radio galaxies (e.g. Tadhunter et al.1096 1992. Cimatti et al.," 1992, Cimatti et al."1097 1993. Vernet et al.," 1993, Vernet et al."1098 2001)., 2001).1099 However. while these observations demonstrate tha scattered quasar light is an important. component of the UW continuum in sources. they clo not establish he significance of the scattered. component in the genera »opulation of powerful radio galaxies.," However, while these observations demonstrate that scattered quasar light is an important component of the UV continuum in sources, they do not establish the significance of the scattered component in the general population of powerful radio galaxies."1100 Because polarimetric observations of faint objects are dillieult. previous studies iwe tended to be biased towards the brightest. mos spectacular objects in à given redshift’ range.," Because polarimetric observations of faint objects are difficult, previous studies have tended to be biased towards the brightest, most spectacular objects in a given redshift range."1101 There are also redshift-depenclent biases which arise. because optica (mostly. V-band) observations sample the rest-frame UV in the high redshift. objects with minimal dilution bv he old stellar populations of the host galaxies bu sample the rest-frame optical in the low redshift objects with substantial dilution bv the old. stellar populations., There are also redshift-dependent biases which arise because optical (mostly V-band) observations sample the rest-frame UV in the high redshift objects — with minimal dilution by the old stellar populations of the host galaxies — but sample the rest-frame optical in the low redshift objects --- with substantial dilution by the old stellar populations.1102 The importance of this observational selection cllect is emphasised by multiwavelength polarimetric observations of individual sources which show a sharp decline in the measured polarization between. the UV. and the optical (Tachunter ct al., The importance of this observational selection effect is emphasised by multi-wavelength polarimetric observations of individual sources which show a sharp decline in the measured polarization between the UV and the optical (Tadhunter et al.1103 1996. Oele ct al.," 1996, Ogle et al."1104 1997. Tran ct al.," 1997, Tran et al."1105 1998)., 1998).1106 1n addition to the scattered. component. detailed observations over the last decade have revealed the presence of two further activity-relatecl components. which can contribute to the UV. excess.," In addition to the scattered component, detailed observations over the last decade have revealed the presence of two further activity-related components which can contribute to the UV excess."1107 These. are: the nebular continuum emitted by the extended. emission line nebulae (Dickson et al., These are: the nebular continuum emitted by the extended emission line nebulae (Dickson et al.1108 1995): and. direct. AGN light. emitted. by weak. or partially extinguished. quasars in the nuclei of the ealaxies (Shaw et al.," 1995); and direct AGN light emitted by weak, or partially extinguished, quasars in the nuclei of the galaxies (Shaw et al."1109 1995)., 1995).1110 Phe nebular continuum is likely to be particularly significant in regions where the emission lines have large equivalent. widths. including the extended emission line nebulae around: powerful radio galaxies.," The nebular continuum is likely to be particularly significant in regions where the emission lines have large equivalent widths, including the extended emission line nebulae around powerful radio galaxies."1111 In contrast. the direct ACN component will only be important in the nuclear regions of the sources.," In contrast, the direct AGN component will only be important in the nuclear regions of the sources."1112 AMlost recentlv. events have turned full circle. with je spectroscopic detection. of voung stellar populations in at least some powerful radio galaxies (c.g. Facdhbunter et al.," Most recently, events have turned full circle with the spectroscopic detection of young stellar populations in at least some powerful radio galaxies (e.g. Tadhunter et al."1113 1996. Alelnick ct al.," 1996, Melnick et al."1114 LOOT)., 1997).1115 The detection. of this component is consistent with the carly interpretation of the UV excess in terms of starbursts associated with the evolution of the host galaxies (Lilly Longair 1984)., The detection of this component is consistent with the early interpretation of the UV excess in terms of starbursts associated with the evolution of the host galaxies (Lilly Longair 1984).1116 ‘nfortunately. apart. [rom cases in which it dominates 16 optical continuum (c.g. Miller: 1951). the starburst component is notoriously οσο το detect at optical wavelengths.," Unfortunately, apart from cases in which it dominates the optical continuum (e.g. Miller 1981), the starburst component is notoriously difficult to detect at optical wavelengths."1117 Hs presence can be masked by the light of the old stellar populations in the bulges of the host. galaxies. by the various activitv-related continuum components noted above. and by emission lines which can contaminate the absorption features characteristic of voung stars.," Its presence can be masked by the light of the old stellar populations in the bulges of the host galaxies, by the various activity-related continuum components noted above, and by emission lines which can contaminate the absorption features characteristic of young stars."1118 “This ds illustrated by the case of 3€321 which shows polarimetric evidence for a significant scattered. quasar component. but also shows evidence for a starburst component in the form of a Balmer break and Balmer absorption features CEachbunter et al.," This is illustrated by the case of 3C321 which shows polarimetric evidence for a significant scattered quasar component, but also shows evidence for a starburst component in the form of a Balmer break and Balmer absorption features (Tadhunter et al."1119 1996. Robinson et al.," 1996, Robinson et al."1120 2000)., 2000).1121 It is notable that. the starburst component in 3€321 only came to light through detailed modelling of the optical/UV. continuum using a combination of spectrophotometry anc spectropolarimetry measurements., It is notable that the starburst component in 3C321 only came to light through detailed modelling of the optical/UV continuum using a combination of spectrophotometry and spectropolarimetry measurements.1122 Given the complex circum-nuclear environments. of powerful radio galaxies revealed by recent LIST imaging studies (e.g. Jackson. Tadhunter Sparks 1998). it is no surprising that no single mechanism is responsible for the UV excess.," Given the complex circum-nuclear environments of powerful radio galaxies revealed by recent HST imaging studies (e.g. Jackson, Tadhunter Sparks 1998), it is not surprising that no single mechanism is responsible for the UV excess."1123 Observations of individual sources demonstrate the presence of at least four UV-emitting components tha can contribute to the UN. excess: scattered GN. light. direct AGN light. nebular continuum. and the light of voung stellar populations.," Observations of individual sources demonstrate the presence of at least four UV-emitting components that can contribute to the UV excess: scattered AGN light, direct AGN light, nebular continuum, and the light of young stellar populations."1124 However. the relative importance of these components. ancl particularlv the importance of any starburst component. is not clear from the previously published. data.," However, the relative importance of these components, and particularly the importance of any starburst component, is not clear from the previously published data."1125 In this paper we attempt to remedy this situation by combining spectroscopic ancl polarimetric observations to quantify the contributions of the various UV-cmitting components in a complete. optically unbiased sample of powerful δν radio galaxies at intermediate redshifts (0.15«z< 0.7).," In this paper we attempt to remedy this situation by combining spectroscopic and polarimetric observations to quantify the contributions of the various UV-emitting components in a complete, optically unbiased sample of powerful 2Jy radio galaxies at intermediate redshifts $0.15 < z < 0.7$ )."1126 We also consider the link between the optical/UV. signs of star formation activity and the far-llt continuum excess., We also consider the link between the optical/UV signs of star formation activity and the far-IR continuum excess.1127 La à companion paper we report a similar study of a lower redshift sample of 3€ radio galaxies (z«0.2: Wills et al., In a companion paper we report a similar study of a lower redshift sample of 3C radio galaxies $z < 0.2$: Wills et al.1128 2002)., 2002).1129" Throughout this paper we assume a Hubble constant of Hy—50 km | "" ancl a deceleration. parameter of qu=O.", Throughout this paper we assume a Hubble constant of $H_0 = 50$ km $^{-1}$ $^{-1}$ and a deceleration parameter of $q_0 = 0$.1130 The objects included in this study comprise radio galaxies selected from the Tadhunter et al.(1993) complete sample of 2Jv radio sources with redshifts z«0.7 and. declinations, The objects included in this study comprise radio galaxies selected from the Tadhunter et al.(1993) complete sample of 2Jy radio sources with redshifts $z < 0.7$ and declinations1131With the three-dimensional GG and GI power spectra and the redshift distributions p(y)=p()/y'(2) at hand. one can calculate the tomographic power spectra according to (1) and (3).,"With the three-dimensional GG and GI power spectra and the redshift distributions $p^{(i)}(\chi) = p^{(i)}(z) / \chi'(z)$ at hand, one can calculate the tomographic power spectra according to ) and )."1132 For the further analysis we divide the angular frequency into N; =200logarithmic bins between / =10and , For the further analysis we divide the angular frequency range into $N_\ell=200$ logarithmic bins between $\ell=10$ and $\ell=20000$.11334o 3zu the performance of the boosting technique into = 20 number. we define the median with respect to angular  P4 the ratio of GI over GG signal. V i can be replaced by any tomography power spectrum opr PP(£) the transformed power spectra Π.Ι (0.," To condense the performance of the boosting technique into a single number, we define the median with respect to angular frequency of the ratio of GI over GG signal, where $X$ can be replaced by any tomography power spectrum $P^{(ij)}(\ell)$ or the transformed power spectra $\Pi^{(i)}(\ell)$."1134" Notethat this ""—— quantity not available from a real survey because we are not ox E separate the GG and GI signals. but only extract their 100 F the data."," Note that this quantity is not available from a real survey because we are not able to separate the GG and GI signals, but only extract their sum from the data."1135 We have chosen the median in (26) since we find that the mean is not a robust measure for two reasons., We have chosen the median in ) since we find that the mean is not a robust measure for two reasons.1136 First. 0r -— GG signal is suppressed by several orders of magnitude. = 7 numerical noise stemming from the οςthe power e 1L spectra can become important. leadirunphysical dips in / / the residual power spectrum.," First, if the GG signal is suppressed by several orders of magnitude, numerical noise stemming from the computation of the power spectra can become important, leading to unphysical dips in the residual power spectrum."1137 Second. the residual GG signal may have sign changes close to which οι becomes very large. thus dominating the mean.," Second, the residual GG signal may have sign changes close to which $r_{\rm GI}$ becomes very large, thus dominating the mean."1138 Both effects would mimic a stronger boosting than ts actually observed., Both effects would mimic a stronger boosting than is actually observed.1139 In Fig.3 we show rq). together with the diagnostic Z as defined in (23). as a function of c. for one z; per survey model.," In $\,$ we show $r_{\rm GI}$, together with the diagnostic $\zeta$ as defined in ), as a function of $\sigma_z$ for one $z_i$ per survey model."1140 Overall we find that small values of Z indeed indicate regimes of σ- in which the GI signal is well boosted., Overall we find that small values of $\zeta$ indeed indicate regimes of $\sigma_z$ in which the GI signal is well boosted.1141 It is important to note that the absolute value of Z is meaningless due to the arbitrariness in the overall amplitude of€U7(y)., It is important to note that the absolute value of $\zeta$ is meaningless due to the arbitrariness in the overall amplitude of $G^{(i)}(\chi)$.1142 When G) is no longer well sampled for small c-. Z features a clear increase.," When $G^{(i)}(\chi)$ is no longer well sampled for small $\sigma_z$, $\zeta$ features a clear increase."1143" Sometimes secondary minima in Z can be observed. see the centre panel of 3. which 15 caused by the sampling points being consecutively placed at the extrema of B""(y)."," Sometimes secondary minima in $\zeta$ can be observed, see the centre panel of $\,$, which is caused by the sampling points being consecutively placed at the extrema of $B^{(i)}(\chi)$."1144 Thereby. although only sparsely sampled. the discrete form (22) captures the main characteristics of B'(y) and hence can well represent G?(p). yielding à small value of Z.," Thereby, although only sparsely sampled, the discrete form ) captures the main characteristics of $B^{(i)}(\chi)$ and hence can well represent $G^{(i)}(\chi)$, yielding a small value of $\zeta$."1145 In the top panel of rq) for both surveys S and PI is given.," In the top panel of $\,$ $r_{\rm GI}$ for both surveys S and P1 is given."1146 Since the binning scheme is identical for both surveys. £ is the same.," Since the binning scheme is identical for both surveys, $\zeta$ is the same."1147" This example demonstrates that οι depends considerably on the details of the actual signals. in this case a change from cy,=0 to cy= 0.03."," This example demonstrates that $r_{\rm GI}$ depends considerably on the details of the actual signals, in this case a change from $\sigma_{\rm ph} = 0$ to $\sigma_{\rm ph} = 0.03$ ."1148 The diagnostic Z does not trace the boosting of the actual signals and can consequently not be exploited to find the maximum οι., The diagnostic $\zeta$ does not trace the boosting of the actual signals and can consequently not be exploited to find the maximum $r_{\rm GI}$ .1149 However. for both surveys Z identifies the regime of small c- in. which the boosting performs worse and which thus should be avoided.," However, for both surveys $\zeta$ identifies the regime of small $\sigma_z$ in which the boosting performs worse and which thus should be avoided."1150" In the case cy,=0.05 the sampling in redshift becomes fully insufficient for small o.", In the case $\sigma_{\rm ph} = 0.05$ the sampling in redshift becomes fully insufficient for small $\sigma_z$.1151 Accordingly. Z rises sharply. and the GG signal starts to dominate again.," Accordingly, $\zeta$ rises sharply, and the GG signal starts to dominate again."1152" The optimal width of G""'(y) can be chosen freely in the interval where Z is stable and small.", The optimal width of $G^{(i)}(\chi)$ can be chosen freely in the interval where $\zeta$ is stable and small.1153 If there is a clear minimum. we place cry there: otherwise we setop Coἃ small value in the," If there is a clear minimum, we place $\sigma_{\rm opt}$ there; otherwise we set$\sigma_{\rm opt}$ toa small value in the"1154" IL 60637. USA, "," } IL 60637, USA. }"1155"80002-1149. USA, "," 86002-1149, USA. }"1156The SDSS consists of two surveys. one photometric and one spectroscopic.," The SDSS consists of two surveys, one photometric and one spectroscopic."1157 To complete a digital survey over a huge fraction of the sky within a finite amount of time. it is necessary to conduct wide-field imaging and multi-object spectroscopy.," To complete a digital survey over a large fraction of the sky within a finite amount of time, it is necessary to conduct wide-field imaging and multi-object spectroscopy."1158 To meet this need. a wide-field telescope. oedmaging camera aud iulti-fibre spectrograplis were desigued aud built specifically for this purpose.," To meet this need, a wide-field telescope, imaging camera and multi-fibre spectrographs were designed and built specifically for this purpose."1159 The alt-az telescope uses a modified Ritchey-Chiétticu design [|2].. with a primary aperture of 2.511 aud a focal ratio of f/5 to produce a flat field of with a plate scale of 16.51 aresec/nuu.," The alt-az telescope uses a modified Ritchey-Chréttien design \cite{wmgk}, with a primary aperture of 2.5m and a focal ratio of f/5 to produce a flat field of with a plate scale of 16.51 arcsec/mm."1160" It is situated at Apache Point Observatory. near Sunspot. New Mexico. at a height of 2.50012. The telescope is housed iu an enclosure which τοῖς off for observing. aud is cucased in a co-otatiug baffle which protects it from wind disturbances and straw ποτ,"," It is situated at Apache Point Observatory, near Sunspot, New Mexico, at a height of 2,800m. The telescope is housed in an enclosure which rolls off for observing, and is encased in a co-rotating baffle which protects it from wind disturbances and stray light."1161 This unique design allows the telescope to remain free of doimoc-iuduced seeimg., This unique design allows the telescope to remain free of dome-induced seeing.1162 First-light images aud recent photographs of the site and telescope can be found athttp://www., First-light images and recent photographs of the site and telescope can be found at.1163sdss.org/. Technical details about the survey can be obtained οι//www.astro.princeton., Technical details about the survey can be obtained from.1164edu/BBOOK/. The photometric tiaging survey will produce a database of roughly ealaxics aud 1075 stellar objects; with accurate (< 0.10 arcsec) astrometry. 5-colour," The photometric imaging survey will produce a database of roughly $^8$ galaxies and $^8$ stellar objects, with accurate $\leq$ 0.10 arcsec) astrometry, 5-colour"1165The statistics of an X-ray source in the field are not governed by Πως.,The statistics of an X-ray source in the field are not governed by $P_{back}$.1166 If we can identify X-ray source i and optical source k with probability Mj. then we should drop that source from the calculation of the background probability.," If we can identify X-ray source $i$ and optical source $k$ with probability $M_{ik}$, then we should drop that source from the calculation of the background probability."1167 The calculation. will (briefly) appear to be very complex because we must include all possible discrete identifications and then select between them., The calculation will (briefly) appear to be very complex because we must include all possible discrete identifications and then select between them.1168 The method we now outline is based on ?.., The method we now outline is based on \citet{pre97}.1169 While the initial results for the probabilities are very similar to those found by ?. or ?.. our approach has greater formal clarity and lends itself to some useful extensions.," While the initial results for the probabilities are very similar to those found by \citet{der76} or \citet{ben83}, our approach has greater formal clarity and lends itself to some useful extensions."1170 We include all possible identifications by introducing a binary vector v for the case in which optical source & (kK=1... is identified with X-ray source 7. where 7j 1s the. fetal number of possible identificationsi in the field around the X-ray source.," We include all possible identifications by introducing a binary vector $\vec{v}^{ik}$ for the case in which optical source $k$ $k=1 \cdots n_i$ ) is identified with X-ray source $i$, where $n_i$ is the total number of possible identifications in the field around the X-ray source."1171 Each vector is a binary code whose entries are v=0 for azK and v=1 for o-κ (ie. the true identification)., Each vector is a binary code whose entries are $v^{ik}_\alpha=0$ for $\alpha\ne k$ and $v^{ik}_\alpha = 1$ for $\alpha=k$ (i.e. the true identification).1172 We allow for the possibility that none of the optical sources are the identification by adding the extra vector i? all of whose entries are zero., We allow for the possibility that none of the optical sources are the identification by adding the extra vector $\vec{v}^{i0}$ all of whose entries are zero.1173 We also introduce a probability f for an X-ray source possessing an optical identification., We also introduce a probability $f$ for an X-ray source possessing an optical identification.1174 The objective of the calculation ts to determine the probabilities of the different possible identifications P()=P; and the mean completeness f., The objective of the calculation is to determine the probabilities of the different possible identifications $P(\vec{v}^{ik})=P_{ik}$ and the mean completeness $f$.1175 Since our possible identifications are exhaustive. the total probability isi simply the sum over all the mutually exclusive possibilities: This may look overly complex. but the structure of the identification vectors v allows us to simplify it to The leading term of |—f is the case of no identification (&2 0). and the sum covers the possibility of identifying X-ray source / with each of the &=1---7; optical sources.," Since our possible identifications are exhaustive, the total probability is simply the sum over all the mutually exclusive possibilities: This may look overly complex, but the structure of the identification vectors $\vec{v}^{ik}$ allows us to simplify it to The leading term of $1-f$ is the case of no identification $k=0$ ), and the sum covers the possibility of identifying X-ray source $i$ with each of the $k=1\cdots n_i$ optical sources."1176 Thus. the relative likelihoods of the identifications are determined by the ratios of the likelihoods that an optical source is comeident with the X-ray source compared to the likelihood that it is just there by chance.," Thus, the relative likelihoods of the identifications are determined by the ratios of the likelihoods that an optical source is coincident with the X-ray source compared to the likelihood that it is just there by chance."1177 Since we intend to use a fixed background model we can simply drop the ως term as it will have no effect on the subsequent results., Since we intend to use a fixed background model we can simply drop the $P_{back}$ term as it will have no effect on the subsequent results.1178 It should be retained if the model of the background is going to be optimized as part of the later calculations., It should be retained if the model of the background is going to be optimized as part of the later calculations.1179 The simplest model of the probability of optical source & being associated with X-ray source / is a Gaussian model incorporating the distance of the optical source given the X-ray positional error. where rj 15 the distance of the optical source from the X-ray source and σε is the uncertainty in the relative position. which can be modeled by The first term. σι. models any remaining systematic astrometry problems that do not depend on the X-ray flux.," The simplest model of the probability of optical source $k$ being associated with X-ray source $i$ is a Gaussian model incorporating the distance of the optical source given the X-ray positional error, where $r_{ik}$ is the distance of the optical source from the X-ray source and $\sigma_k$ is the uncertainty in the relative position, which can be modeled by The first term, $\sigma_{a}$, models any remaining systematic astrometry problems that do not depend on the X-ray flux."1180 The second term models the position- and flux-dependent PPSF. with oo giving the width at the pointing center (d;2 0) and geoo describing the quadratic growth of the PSF width off the axis.," The second term models the position- and flux-dependent PSF, with $\sigma_0$ giving the width at the pointing center $d_k=0$ ) and $\sigma_{600}$ describing the quadratic growth of the PSF width off the axis."1181 The accuracy with which an X-ray source is centroided improves as the number of counts increases., The accuracy with which an X-ray source is centroided improves as the number of counts increases.1182 We therefore scale with the number of X-ray counts Cy., We therefore scale with the number of X-ray counts $C_k$.1183" We will refer to this as the ""PSF model""", We will refer to this as the “PSF model”.1184 The derivation for multiple ID possibilities is more elaborate and we used Cartesian rather than polar coordinates. but our basic expressions are identical to those of ?..," The derivation for multiple ID possibilities is more elaborate and we used Cartesian rather than polar coordinates, but our basic expressions are identical to those of \citet{ben83}. ."1185 The probabilities always depend on the ratio Mj/Bj. which ought to be dimensionless.," The probabilities always depend on the ratio $M_{ik}/B_k$, which ought to be dimensionless."1186 If we use the number counts as a function of magnitude B; (units mag”! deg) and the probability for the source position in Eqn., If we use the number counts as a function of magnitude $B_k$ (units $^{-1}$ $^{-2}$ ) and the probability for the source position in Eqn.1187 A8 (units deg). then the ratio is not in some senses dimensionless.," \ref{eqn:match0} (units $^{-2}$ ), then the ratio is not in some senses dimensionless."1188 This does not matter if we force all sources to have optical IDs (f» 1). but the probability of finding no ID for a given source and the posterior probability distribution Ptf|D) are affected by this problem.," This does not matter if we force all sources to have optical IDs $f\rightarrow 1$ ), but the probability of finding no ID for a given source and the posterior probability distribution $P(f|D)$ are affected by this problem."1189 We could include the probability that an X-ray source of a given flux has a given optical magnitude. but this adds more parameters than we presently want toexplore.," We could include the probability that an X-ray source of a given flux has a given optical magnitude, but this adds more parameters than we presently want toexplore."1190 Instead we use, Instead we use1191Here Band B' denote barvons and P stands for hadron () or antikaon (A) phase.,Here $B$ and $B'$ denote baryons and P stands for hadron $h$ ) or antikaon $K$ ) phase.1192 Further nucleons do not couple with strange strange mesons Le. gov=0., Further nucleons do not couple with strange strange mesons i.e. $g_{\sigma^* N} = g_{\phi N} = 0$.1193 Similarly. A hvperons do not couple with p meson ie. g;4=0.," Similarly, $\Lambda$ hyperons do not couple with $\rho$ meson i.e. $g_{\rho \Lambda} = 0$."1194 The results for other as in the antikaon condensed phase are given below. where. and In the second term in Eq.(27) and (28). +ve sien corresponds (ο neutrons and -ve is for protons.," The results for other $\alpha$ s in the antikaon condensed phase are given below, where, and In the second term in Eq.(27) and (28), +ve sign corresponds to neutrons and -ve is for protons."1195 With the given αι we can now calculate relaxation time lor the non-leptonic process in hadron as well as antikaon condensed phases.," With the given $\alpha_{ij}$, we can now calculate relaxation time for the non-leptonic process in hadron as well as antikaon condensed phases."1196 As soon as we know the relaxation lime. we can caleulate the bulk viscosity coefficient in each phase.," As soon as we know the relaxation time, we can calculate the bulk viscosity coefficient in each phase."1197 , 1198bias-subtracted and flat-fielded with the ESO FORS pipeline.,bias-subtracted and flat-fielded with the ESO FORS pipeline.1199 Point spread function (PSF) fitting photometry was carried out with the DAOPHOT II. ALLSTAR and ALLFRAME packages using a constant model PSF across the field. which experience showed to yield the best results.," Point spread function (PSF) fitting photometry was carried out with the DAOPHOT II, ALLSTAR and ALLFRAME packages using a constant model PSF across the field, which experience showed to yield the best results."1200 The photometric calibration was done using stars i common with photometry from the literature: we used the V. T catalogue published by for NGC 1851: the B. V catalogue by supplementec by | magnitudes (Dalessandro. private communication) for NGC 6388; and the V. I catalogue by for 47 Tue (NGC 104).," The photometric calibration was done using stars in common with photometry from the literature: we used the V, I catalogue published by for NGC 1851; the B, V catalogue by supplemented by I magnitudes (Dalessandro, private communication) for NGC 6388; and the V, I catalogue by for 47 Tuc (NGC 104)."

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