ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 Bespouse and aucillary response fles were produced for the spectra and. the ight curves were corrected usine ae SAS taskviclecorr., Response and ancillary response files were produced for the spectra and the light curves were corrected using the SAS task.3. The spectra were erouped at 20 couits ox biu to provide suffiicicut statistics for \? fitlue and analysed using NSPEC v12.6.0q (Arnaud19fI6)., The spectra were grouped at 20 counts per bin to provide sufficient statistics for $\chi^2$ fitting and analysed using XSPEC v12.6.0q \citep{arn96}.4. Data below 0.2 keV aud above ? keV (where tje statistics are very poor) were ignored for t16 spectral fitting., Data below 0.2 keV and above 7 keV (where the statistics are very poor) were ignored for the spectral fitting.5 Sticleetal.(2011) fitted spectra extracted fro heir 2008 oobservation wih three models: absorbed disk blackbody plus power law. absorbed disk blackbody. audasorbed brequsstralline models.," \citet{sti11} fitted spectra extracted from their 2008 observation with three models: absorbed disk blackbody plus power law, absorbed disk blackbody, and absorbed bremsstrahlung models."6 They fouxd that he disk backbody plus power law model was hne best fitting model obtaining ?/dof = lTl/1l15. altlrough they also clan formally accepable fits 1sing the two other models (vith κ fdof= 27T and 209/117 for the simpe disk blackbody aid breinisstraliluns models. respeccfively).," They found that the disk blackbody plus power law model was the best fitting model obtaining $\chi^2$ /dof = 174/145, although they also claim formally acceptable fits using the two other models (with $\chi^2$ /dof = 270/147 and 209/147 for the simple disk blackbody and bremsstrahlung models, respectively)."7 We fitter the spectra we extracted. frou the 2008 oobservation with the same models aud olaimed simular resuts for the disk blackbody plus powcr aw and the sine isk bladishoddy τιodels. although we aret ethat due to tlje high «nualitv of the data he fit with tie siniple disk blacshacky uodel is unaccepabο with a κ ος = 812/711.," We fitted the spectra we extracted from the 2008 observation with the same models and obtained similar results for the disk blackbody plus power law and the simple disk blackbody models, although we argue that due to the high quality of the data the fit with the simple disk blackbody model is unacceptable with a $\chi^2$ /dof = 812/714."8 We therefore ο] report the resiIts of the» clisk. dlackbody jus )OWOY aw ft uπι Table m, We therefore only report the results of the disk blackbody plus power law fit in Table \ref{bhxrb}.9 contrast. our fit with he absorbed »yenisstrathine noctel obtained a Πιο better ft (A?lof = TOL/TLL see Table 2)) with a sigificautlv lower enrperature of kT = 0.98 + 0.02 keV. thai the sT = 1.91 dFE (.07 keV obtaired w Sticleetal. (2011)..," In contrast, our fit with the absorbed bremsstrahlung model obtained a much better fit $\chi^2$ /dof = 764/714, see Table \ref{specpar}) ) with a significantly lower temperature of kT = 0.98 $\pm$ 0.02 keV than the kT = 1.91 $\pm$ 0.07 keV obtained by \citet{sti11}. ."10 The cause of the difkvonces betwee our fittine aud that reported bv Sticleetal.(2011) is unclear., The cause of the differences between our fitting and that reported by \citet{sti11} is unclear.11 We also fitted he spectra with a more physical model represeiting ΠΕΟΕ an accreting black hole. i.c. ali absorbed disk blackbody plus thermal Couptonisation niodel (compTT iu NSPEC). with t16 input soft photon (Wien) temperature fixed to the disk blackbody temperature.," We also fitted the spectra with a more physical model representing emission from an accreting black hole, i.e. an absorbed disk blackbody plus thermal Comptonisation model (compTT in XSPEC), with the input soft photon (Wien) temperature fixed to the disk blackbody temperature."12 Again. we obtaired an acceptable fit with \?/dof = 716/7)L (see Table 1)).," Again, we obtained an acceptable fit with $\chi^2$ /dof = 746/711 (see Table \ref{bhxrb}) )."13 Iu addition to the nodel fsre pored by al.(2011).. we atteupted o fit the 2008 sspectra with power law. blackbody (tic BBODYRAD model in NSPEC). aud ticrmial dasna (the1956:Ixaastra1992:Liedalloetal.1995) 111Ωίcls.," In addition to the model fits reported by \citet{sti11}, we attempted to fit the 2008 spectra with power law, blackbody (the BBODYRAD model in XSPEC), and thermal plasma \citep[the MEKAL model in XSPEC;][]{mew85,mew86,kaa92,lie95} models."14 Iu each case phooclectric absorption was accounted for using the phabs couponent iu NSPEC aud the Wihus abundances (Wilms.Allen.&[οταν 2000)., In each case photoelectric absorption was accounted for using the phabs component in XSPEC and the Wilms abundances \citep{wil00}.15". Neither he simple power law model nor blackbody modeog. woVIder an acceptable fit. with \7/dof = 120!IÉ'""119 ax 1165/719. respectively. auc significa residuals appearing below 2 keV. Adding a low teur)oratire blackbody component to the power aw inode improved the fit sienificautly (A7 4ος = δ16/712). although with a very steep power law photou index (see Table 2))"," Neither the simple power law model nor blackbody models provided an acceptable fit, with $\chi^2$ /dof = 1205/719 and 1165/719, respectively, and significant residuals appearing below 2 keV. Adding a low temperature blackbody component to the power law model improved the fit significantly $\chi^2$ /dof = 806/712), although with a very steep power law photon index (see Table \ref{specpar}) )."16 The addition of a SCCOLLC blackbody component to the simple absorbe blackbody model. prodiced a better fit (C ‘cdot = 152/712) aud completely sinoothed out the low energy residuals (see Table 2) |., The addition of a second blackbody component to the simple absorbed blackbody model produced a better fit $\chi^2$ /dof = 752/712) and completely smoothed out the low energy residuals (see Table \ref{specpar}) ).17 Attempts to fit the spectra with an absorbe AIERAL model with t1ο abundance parameter frozen at Solar values did not provide au acceptable fit (A? /dof = 11527/719)., Attempts to fit the spectra with an absorbed MEKAL model with the abundance parameter frozen at Solar values did not provide an acceptable fit $\chi^2$ /dof = 11527/719).18 Allowing the abuudauce to vary freely improved tje fit significantly (A? /dof = 769/718). however the abuidauce value fell to zero ndicating that no sieuificai line endssiou Is present and therefore the 1Clel is cousisteut with the πιο xyenisstraliune continu uodel.," Allowing the abundance to vary freely improved the fit significantly $\chi^2$ /dof = 769/718), however the abundance value fell to zero indicating that no significant line emission is present and therefore the model is consistent with the underlying bremsstrahlung continuum model."19 Iu snnudnarv. we oMtined acceptable fits with the double dlackbody. blackbody plus ΝΟΥ law. disk blackboc ypDS rower law. disk dackbody plus thernal Cyuponisatiou. anc xenisstraliluue models bi tax abe to rule out the simple blackbody. simde power law. aud thermal Ιωη) (with ποσο elemental abundances) uocdoels.," In summary, we obtained acceptable fits with the double blackbody, blackbody plus power law, disk blackbody plus power law, disk blackbody plus thermal Comptonisation, and bremsstrahlung models but are able to rule out the simple blackbody, simple power law, and thermal plasma (with non-zero elemental abundances) models."20 The best fits were obtained with the disk blackbody plus thermal Comptonisation aud he double blackbody models. which areshown iu Figures l and 2..," The best fits were obtained with the disk blackbody plus thermal Comptonisation and the double blackbody models, which areshown in Figures \ref{dbbplmod} and \ref{specbb}. ."21vertical disk structure (see?)..,vertical disk structure \citep[see][]{Dullemond01}.22" The disk is in hydrostatic equilibrium between the gas pressure and the stellar gravity, which leads to a flared geometry with the opening angle increasing with the distance from the central star."," The disk is in hydrostatic equilibrium between the gas pressure and the stellar gravity, which leads to a flared geometry with the opening angle increasing with the distance from the central star."23 The dust opacity is calculated by assuming an interstellar grain composition (?) and particle size distribution between a minimum and a maximuma value GQmin and Gmax according to n(a)οςα-ᾱ., The dust opacity is calculated by assuming an interstellar grain composition \citep{Pollack94} and a particle size distribution between a minimum and a maximum value $a_{min}$ and $a_{max}$ according to $n(a) \propto a^{-q}$.24 We fix 0.05 um and vary ἅπιαι and q to reproduce the spectral index α of the millimeter disk emission., We fix $a_{min} = 0.05$ $\mu$ m and vary $a_{max}$ and $q$ to reproduce the spectral index $\alpha$ of the millimeter disk emission.25 For sake of simplicity we assume that the dust opacity is constant throughout the disk (althoughsee, For sake of simplicity we assume that the dust opacity is constant throughout the disk \citep[although see][]{Birnstiel10b}.26" The radial distribution of the circumstellar?).. material follows the similarity solution for the disk surface density of a viscous keplerian disk (?) expressed by where the characteristic radius Τε, y, and the surface(1) density normalization X are free parameters of the model, as well as the disk inclination and position angle."," The radial distribution of the circumstellar material follows the similarity solution for the disk surface density of a viscous keplerian disk \citep{Lynden74} expressed by where the characteristic radius $r_t$, $\gamma$, and the surface density normalization $\Sigma_t$ are free parameters of the model, as well as the disk inclination and position angle."27" From the derived dust density, temperature, and opacity we calculate the disk SED and synthetic disk images in the dust continuum at 0.87 mm and 3.3 mm using the radiative transfer solution discussed in ?.."," From the derived dust density, temperature, and opacity we calculate the disk SED and synthetic disk images in the dust continuum at 0.87 mm and 3.3 mm using the radiative transfer solution discussed in \citet{Dullemond01}."28" The synthetic disk images are then Fourier transformed and sampled at the appropriate positions on the (u,v) plane corresponding to our CARMA and SMA observations."," The synthetic disk images are then Fourier transformed and sampled at the appropriate positions on the (u,v) plane corresponding to our CARMA and SMA observations."29intensity the following equation is used: where ¢ is the speed of light and fy is the Doltzmann constant.,intensity the following equation is used: where $c$ is the speed of light and $k_B$ is the Boltzmann constant.30" As the PPDR code models the PDR as a semi-infinite slab and the visual extinction. A, in the slab is related to both the number density as well as the metallicitv. a fixed A, will correspond to different physical distances. L. for different values of the density. ancl metallicity."," As the PDR code models the PDR as a semi-infinite slab and the visual extinction, $A_v$ in the slab is related to both the number density as well as the metallicity, a fixed $A_v$ will correspond to different physical distances, $L$, for different values of the density and metallicity."31" In order to derive values lor the relative temperatures (hat are comparable and independent of the size of the emitting region. we also divide (he relative velocity integrated antenna (temperatures by the distance in parsec corresponding to the A, at which the temperature is calculated. L4,."," In order to derive values for the relative temperatures that are comparable and independent of the size of the emitting region, we also divide the relative velocity integrated antenna temperatures by the distance in parsec corresponding to the $A_v$ at which the temperature is calculated, $L_{A_v}$."32 This distauce will obviously be much larger for low density and low metallicity svstems for a fixed du, This distance will obviously be much larger for low density and low metallicity systems for a fixed $A_v$.33" Our figures therefore represent the relative velocity integrated antenna temperatures [or the different ""CO transitions per unit parsec except in Figure 14 where we plot the relative velocity. integrated temperatures as a function of 4,", Our figures therefore represent the relative velocity integrated antenna temperatures for the different $^{12}$ CO transitions per unit parsec except in Figure \ref{fig:IMF2} where we plot the relative velocity integrated temperatures as a function of $A_v$.34 Note that the imunbers calculated using Eq 2 are important only in terms of observing trends., Note that the numbers calculated using Eq \ref{eq:TA} are important only in terms of observing trends.35 In order to match the absolute values of the theoretical velocity integrated antenna temperature to those [rom observations. one has to consider several other factors.," In order to match the absolute values of the theoretical velocity integrated antenna temperature to those from observations, one has to consider several other factors."36 Firstly. all models in BOO assume a turbulent velocity of 1.5 km ! typical for a giant molecular cloud in the Galaxy.," Firstly, all models in B09 assume a turbulent velocity of 1.5 km $^{-1}$ typical for a giant molecular cloud in the Galaxy."37 In reality. observed lines of CO in exiragalactie sources tvpically have widths οἱ several LOO km ! due to contributions [rom several PDR regions within the galaxy and the temperature has (o be scaled accordingly.," In reality, observed lines of CO in extragalactic sources typically have widths of several 100 km $^{-1}$ due to contributions from several PDR regions within the galaxy and the temperature has to be scaled accordingly."38 Secondly. we need (to account for a surface filling [actor which takes into account the size of the source as well as the telescope beam.," Secondly, we need to account for a surface filling factor which takes into account the size of the source as well as the telescope beam."39 Finally. all observational results will be affected by factors such as the atinospherie conditions ancl the telescope efficiency.," Finally, all observational results will be affected by factors such as the atmospheric conditions and the telescope efficiency."40 One wav of comparing our tlieoretical predictions to observations however. is to consider line ratios rather (han the intensities aud brightness teniperatures of individual lines.," One way of comparing our theoretical predictions to observations however, is to consider line ratios rather than the intensities and brightness temperatures of individual lines."41 Assuming the emission from both lines comes from the same clouds. the various factors discussed above should cancel oul when computing the ratio of either the intensiv or the integrated temperature.," Assuming the emission from both lines comes from the same clouds, the various factors discussed above should cancel out when computing the ratio of either the intensity or the integrated temperature."42 We therefore compare our theoretical predictions to observed line ratios in § 3.6.., We therefore compare our theoretical predictions to observed line ratios in $\S$ \ref{sec:obs}.43 In the following sections. we list in all cases our relative integrated temperatures per unit distance.," In the following sections, we list in all cases our relative integrated temperatures per unit distance."44 We emphasise that (he results presented here are only useful in terms of observing tvends and should not be compared to absolute values obtained through observation as thev do noi take into account the factors already stated above., We emphasise that the results presented here are only useful in terms of observing trends and should not be compared to absolute values obtained through observation as they do not take into account the factors already stated above.45Tot subcdwarf D stars (sdBs) ave core helium-burning stars with hydrogen envelopes too {hin to sustain hydrogen shell burning and have masses of about 0.47M... (Ueber2009).,"Hot subdwarf B stars (sdBs) are core helium-burning stars with hydrogen envelopes too thin to sustain hydrogen shell burning and have masses of about $0.47\,M_{\rm \odot}$ \citep{heber09}."46. The large fraction of close binaries about half of the known sdB stars are members of short-period (P. S 10 days) binaries (Maxtedοἱal.2001:Napiwotzkiet2004a) can be explained by binary evolution models.," The large fraction of close binaries – about half of the known sdB stars are members of short-period (P $\lesssim$ 10 days) binaries \citep{maxted01,napiwotzki04a} – can be explained by binary evolution models."47 The required extraordinarily large mass loss in the red giant phase is triggered by the formation of a common envelope. which is finally ejected.," The required extraordinarily large mass loss in the red giant phase is triggered by the formation of a common envelope, which is finally ejected."48 Binary population svnthesis models (lanetal.2002.2003) are successful in matching the observed properties of known svstems qualitatively.," Binary population synthesis models \citep{han02,han03} are successful in matching the observed properties of known systems qualitatively."49 The existence of apparently single sdB stars poses another problem., The existence of apparently single sdB stars poses another problem.50 However. even in (liis case binary evolution comes to (he rescue. because such stars may form from the merger of two helium white cwarls (Webbink1984) or from the engulfment and possible destruction of a substellar object (Soker1998:Nelemans&Tauris1993).," However, even in this case binary evolution comes to the rescue, because such stars may form from the merger of two helium white dwarfs \citep{webbink84,ibentutukov84} or from the engulfment and possible destruction of a substellar object \citep{soker98,nelemans98}."51. The existence of eclipsing sdB+clAl binaries of IWVir (vpe with very short. orbital periods (0.1—0.26 d) aud. very low companion masses between 0.1M. and 0.2AL. (e.g.For shows that stars close to the nuclear burning limit of," The existence of eclipsing sdB+dM binaries of Vir type with very short orbital periods $0.1-0.26\,{\rm d}$ ) and very low companion masses between $0.1\,M_{\rm \odot}$ and $0.2\,M_{\rm \odot}$ \citep[e.g.][]{for10, oestensen10} shows that stars close to the nuclear burning limit of"52explanation).,explanation).53 Conversely. a majority of the active asteroids lie in regions of the r vs. H plane where many processes are potentially important.," Conversely, a majority of the active asteroids lie in regions of the $r$ vs. $R$ plane where many processes are potentially important."54 For example. in 238P. sublimation. electrostatic ejection. rotational instability. radiation pressure and impact process are all potentially active.," For example, in 238P, sublimation, electrostatic ejection, rotational instability, radiation pressure and impact process are all potentially active."55 Only through detailed physical investigation is il possible to discriminate between these possibilities (in favor of sublimation. in the case of 238P. based principally on (he repetition of (he observed mass-Ioss).," Only through detailed physical investigation is it possible to discriminate between these possibilities (in favor of sublimation, in the case of 238P, based principally on the repetition of the observed mass-loss)."56 For many active asteroids. the physical observations needed to discriminate amongst mechanisms do not exist.," For many active asteroids, the physical observations needed to discriminate amongst mechanisms do not exist."57 Collisions are implicated in active asteroids both directly. as in (he case of (596) Scheila and. perhaps. P/2010 A2. and indirectly as a trigger for activity (for example. (o expose buried ice). as in 133P and 205). Here. we brielly examine (the expected rate of collision between asteroids.," Collisions are implicated in active asteroids both directly, as in the case of (596) Scheila and, perhaps, P/2010 A2, and indirectly as a trigger for activity (for example, to expose buried ice), as in 133P and 238P. Here, we briefly examine the expected rate of collision between asteroids."58 The tvpical collision probability per unit area in the asteroid belt is P.— 3x10 P 7 Lo with variations by a [actor of several reflecting a collisional environment that varies wilh location in the belt (Bottke et al.," The typical collision probability per unit area in the asteroid belt is $P_c \sim$ $\times$ $^{-18}$ $^{-2}$ $^{-1}$, with variations by a factor of several reflecting a collisional environment that varies with location in the belt (Bottke et al."59 1994)., 1994).60 The interval between impacts onto an asteroid of radius r is where N(7ry) is the number of inpactors larger than ry., The interval between impacts onto an asteroid of radius $r$ is where $N( \ge r_p)$ is the number of impactors larger than $r_p$.61 Estimates of the size distribution of the asteroids are many and varied. with significant uncertainties resulting from (he unmeasured albedos of most asteroids. as well as [rom severe observational bias effects (Jedicke et al.," Estimates of the size distribution of the asteroids are many and varied, with significant uncertainties resulting from the unmeasured albedos of most asteroids, as well as from severe observational bias effects (Jedicke et al."62 2002)., 2002).63 The uncertainties are particularly acute for sub-kilometer asteroids because such objects are faint ancl remain largely unobserved., The uncertainties are particularly acute for sub-kilometer asteroids because such objects are faint and remain largely unobserved.64 For radii r> 1 km. the best-fitting differential power law index is about -2. albeit with significant. size-dependent deviations from this value.," For radii $r >$ 1 km, the best-fitting differential power law index is about -2, albeit with significant, size-dependent deviations from this value."65 For radii krx 1 km. perhaps the best constraints on the distribution come from the impact crater size distribution on asteroid Gaspra.," For radii $r \le$ 1 km, perhaps the best constraints on the distribution come from the impact crater size distribution on asteroid Gaspra."66 There. craters from 0.4 km (ο 1.5 km in diameter (caused by projectiles perhaps 10 to 20 (mes smaller) are distributed as a power-law wilh a dilferential size index -3.7+0.5 (Belton οἱ al.," There, craters from 0.4 km to 1.5 km in diameter (caused by projectiles perhaps 10 to 20 times smaller) are distributed as a power-law with a differential size index $\pm$ 0.5 (Belton et al."67 1992: note that Chapman et al. (, 1992; note that Chapman et al. (681996) report thal craters on Gaspra lollow an even sleeper distribution. with differential power law index -4.32:0.3).,"1996) report that craters on Gaspra follow an even steeper distribution, with differential power law index $\pm$ 0.3)."69 We assime that the total main-belt population is ~1.4x 10° asteroids with diameters 21 km., We assume that the total main-belt population is $\sim$ $\times$ $^{6}$ asteroids with diameters $>$ 1 km.70" Combining these results and integrating over the size distribution we take the number of projectiles with radius >ry, as", Combining these results and integrating over the size distribution we take the number of projectiles with radius $\ge r_p$ as71To determine the local cooling rate. we assume that each annulus of the disk racdiates as a black body so that where 7. is the temperature at the surface of the disk aud σ is the Stefan-Bolizimann constant.,"To determine the local cooling rate, we assume that each annulus of the disk radiates as a black body so that where $T_{\rm e}$ is the temperature at the surface of the disk and $\sigma$ is the Stefan-Boltzmann constant."72 The kinematic turbulent viscosity in the magnetic laver is taken to be where the sound speed is en=yRTy/pn with temperature in the magnetic laver Tj., The kinematic turbulent viscosity in the magnetic layer is taken to be where the sound speed is $c_{\rm m}=\sqrt{{\cal R} T_{\rm m}/\mu} $ with temperature in the magnetic layer $T_{\rm m}$.73 The disk is sell-gravitating if the Toomre parameter (Q<Qu. where and the sound speed at the disk mid-plane is given by c;=yRT./p. where we approximate (he temperature of the sell-gravitating region that extends to (he disk mid-plane as ~7;.," The disk is self-gravitating if the Toomre parameter $Q<Q_{\rm crit}$, where and the sound speed at the disk mid-plane is given by $c_{\rm74 g}=\sqrt{ {\cal R}T_{\rm c}/\mu},$ where we approximate the temperature of the self-gravitating region that extends to the disk mid-plane as $\simeq T_{\rm c}$."75 The elective kinematic viscosity [rom the turbulence induced by the sell-gravitational instability is approximated by for Q«Qe anc zero otherwise (Lin&Pringle1937.1990).," The effective kinematic viscosity from the turbulence induced by the self-gravitational instability is approximated by for $Q<Q_{\rm crit}$ and zero otherwise \citep{lin87,lin90}."76. The milplane disk temperature for an optically thick disk in thermal equilibrium is obtained by consilering the energv balance in a lavered model above the disk mid-plane., The mid-plane disk temperature for an optically thick disk in thermal equilibrium is obtained by considering the energy balance in a layered model above the disk mid-plane.77" One laver contains the surface density X,,/2.", One layer contains the surface density $\Sigma_{\rm m}/2$.78" The other laver contains the complementary surface density X,/2.", The other layer contains the complementary surface density $\Sigma_{\rm g}/2$.79 The results are that and, The results are that and The optical depth to the magnetic region is80Iu this subsection we investigate how well this coild be doue in practice.,In this subsection we investigate how well this could be done in practice.81" In the next subsection. we will include information on all galaxies iu the cluster rather tha1 just splitting the ealaxy population iuto ""ceutra ealaxy and other”."," In the next subsection, we will include information on all galaxies in the cluster rather than just splitting the galaxy population into “central galaxy” and “other”."82 With the difference in eravitational redshift commatccd from the simulation. we male an estimate of mannm ver of clusters needed for a detection.," With the difference in gravitational redshift computed from the simulation, we make an estimate of the number of clusters needed for a detection."83 We try two cases. ralonlv selecting either Ngai=50 galaxies per cluser or Nya oue tenth of the nuuber of dark matter paricles. so that Nou=Moetuster{tStotthFAL...," We try two cases, randomly selecting either $N_{gal}=50$ galaxies per cluster or $N_{gal}$ = one tenth of the number of dark matter particles, so that $N_{gal}=M_{cluster}/7\times 10^{11} \msun$."84 We assunie hat the noise from the difference iu position aud velocities coutributes iucepenudoeutly., We assume that the noise from the difference in position and velocities contributes independently.85" Iucludiug the measurement uicertaiutyv A, we have where andl Aud the error on the mean is given by We lave split the clusters in the simiulatiou iuto bius by mass and CV here is the nuuber of clusters in the simulation ina particular biu."," Including the measurement uncertainty $\Delta_{meas.}$, we have where and And the error on the mean is given by We have split the clusters in the simulation into bins by mass, and $N_{c}$ here is the number of clusters in the simulation in a particular bin."86 For each biu we compute the παπαον of clusters CV) actually needed for a detection of the C»eravitational redshift. with a Ooeiven statistical significance.," For each bin we compute the number of clusters $N_{0}$ ) actually needed for a detection of the gravitational redshift, with a given statistical significance."87"Oo For example. for clusters in the mass bin centered on —υυIM 03001s+ and Av,~7kinsl"," For example, for clusters in the mass bin centered on $\sim 8 \times8810^{14} \msun$, $\sigma \sim 300 \kms$ and $\Delta v_{g} \sim7 89\kms$."90 With —10! clusters we expect our error bar to be ~JSlaus5o which is a ~26 detection of exavitational redshift.," With $\sim10^4$ clusters we expect our error bar to be $\sim3 \kms$, which is a $\sim 2 \sigma$ detection of gravitational redshift."91 We iueht expect that the uumber of clusters should decrease for high τιass because the eravitational redshift is proportional to the cluster velocity dispersion., We might expect that the number of clusters should decrease for high mass because the gravitational redshift is proportional to the cluster velocity dispersion.92 However. kx these clusters. tre error bars also increase because the dispersion iu velocity difference between central galaxy id others is ecttiic larger.," However, for these clusters, the error bars also increase because the dispersion in velocity difference between central galaxy and others is getting larger."93 Figure 7 shows how iuinuv ‘lusters we need to detect the eravitational redshift at the σ and lo levels as a function of cluster mass., Figure \ref{fig:nc_2bin} shows how many clusters we need to detect the gravitational redshift at the $\sigma$ and $\sigma$ levels as a function of cluster mass.94" We choose 16 nieasuremenut uncertainty ο be 30 kms. 100 kii/s and 10 lans as best. typical aud worst cases (ο,ο,, Stoueltou al."," We choose the measurement uncertainty to be 30 km/s, 100 km/s and 300 km/s as best, typical and worst cases (e.g., Stoughton et al."95 2002)., 2002).96 Civen relatively siiall measurement uncertaiuty. je nuiber of clusters need decreases at first aud then avs roughly the same (~104 clusters for A44= | lau/s) after M2ΤονtAL...," Given relatively small measurement uncertainty, the number of clusters needed decreases at first and then stays roughly the same $\sim10^4$ clusters for $\Delta_{meas.} =$ 30 km/s) after $M \simgt 10^{14}\msun$."97" Since we use average Vanes. it does not make nuuc1 difference whether we use D) galaxies por cluster or a ΠΠΡΟ proportional to the οster lass,"," Since we use average values, it does not make much difference whether we use 50 galaxies per cluster or a number proportional to the cluster mass."98 Iu order to understand the behaviour seen Fig 7.. we can ask what should happen if the redshift noise on the central ooOalaxy frou peculiar velocities and position cüfferences were proportional to the cluster velocity dispersion (Cassuimiug we are averaging over a fixed munhber of galaxies in cach Cluster).," In order to understand the behaviour seen Fig \ref{fig:nc_2bin}, we can ask what should happen if the redshift noise on the central galaxy from peculiar velocities and position differences were proportional to the cluster velocity dispersion (assuming we are averaging over a fixed number of galaxies in each cluster)."99 As the eravitational redshift is proportional to cluster velocity dispersion also (Figure 5)). then the ummber of clusters for a detection of a given significance should be constant.," As the gravitational redshift is proportional to cluster velocity dispersion also (Figure \ref{fig:dvtot}) ), then the number of clusters for a detection of a given significance should be constant."100 This is approximately what is secu for clusters of nass AL ereater than ~LottLIAL..., This is approximately what is seen for clusters of mass $M$ greater than $\sim 10^{14}\msun$.101" For smaller clusters. he noise from the disXacement of the ceutral galaxy (the IIubble velocity component. Ag,«Ho) is becoming a ron neelieible fraction of the total noise. and its effect neans that more clusCrs nius be averaged over."," For smaller clusters, the noise from the displacement of the central galaxy (the Hubble velocity component, $\Delta y_{c.m.}\times H_{0}$ ) is becoming a non negligible fraction of the total noise, and its effect means that more clusters must be averaged over."102 Note that. as neutioned alowe. onlv the mass-averaged eravitational redshift has beeji used here aud it has not con taken into accouit that f16 eravitational redshift las a gradual radial depencence.," Note that, as mentioned above, only the mass-averaged gravitational redshift has been used here and it has not been taken into account that the gravitational redshift has a gradual radial dependence."103 \ore information is therefore available which col i priiciple aid a detection., More information is therefore available which could in principle aid a detection.104 We discuss this in the following sbsection., We discuss this in the following subsection.105 We now calculate the profie of gravitational redshifts averaged over may clusters., We now calculate the profile of gravitational redshifts averaged over many clusters.106 As in the previous section. we take the ceutral galaxy to ]x© our zero point.," As in the previous section, we take the central galaxy to be our zero point."107 The other ealaxies in tfje cluster are bimed as a function of their nupact paraueter from this ealaxy {ήAG?|Az. where yg is the line of sight) Iu each bin. aud for all clusters. we have ΗΤΟ: the gravitational redshift difference between the galaxy aud he ceutral cluster galaxy.," The other galaxies in the cluster are binned as a function of their impact parameter from this galaxy $r = \sqrt{\Delta x^{2} +108\Delta z^{2}}$, where $y$ is the line of sight) In each bin, and for all clusters, we have summed the gravitational redshift difference between the galaxy and the central cluster galaxy."109" We then divide by the nuuber of galaxies iu each biu (as mentioned previously the ""galaxies which are not the central one are actually paricles)", We then divide by the number of galaxies in each bin (as mentioned previously the “galaxies” which are not the central one are actually particles).110 Figure 5 shows the resulting gravitational redshift profile for clusters within different mass ranges as a function of the impact xwalnueter r., Figure \ref{fig:dvg} shows the resulting gravitational redshift profile for clusters within different mass ranges as a function of the impact parameter $r$.111 All of the clusters in the simulation have been used. ancl i should be noted that cach mass bin does not an have equal uuuber of clusters contributing to it.," All of the clusters in the simulation have been used, and it should be noted that each mass bin does not an have equal number of clusters contributing to it."112 Also. at large radii within each mass range. oulv the more massive clusers contribute. because the smaller clusters do not have aiv galaxies out that far.," Also, at large radii, within each mass range, only the more massive clusters contribute, because the smaller clusters do not have any galaxies out that far."113 As expected. gravitational redshifts increase for laree mass clusters.," As expected, gravitational redshifts increase for large mass clusters."114 This result is consistent with that of Cappi (1995) who used analytic profiles. in tha the fiction decreases smoothly with a masinuun at the center.," This result is consistent with that of Cappi (1995) who used analytic profiles, in that the function decreases smoothly with a maximum at the center."115(2004).. where two possible discretisations of the wavelength derivative are combined in a Crank-Nicholson-like scheme.,", where two possible discretisations of the wavelength derivative are combined in a Crank-Nicholson-like scheme."116 Since we allow for arbitrary velocity fields. the formal solution must allow for an arbitrary sense of wavelength derivative that is. the upwind direction may correspond either to longer or shorter wavelengths.," Since we allow for arbitrary velocity fields, the formal solution must allow for an arbitrary sense of wavelength derivative that is, the upwind direction may correspond either to longer or shorter wavelengths."117 To insure the stability of the discretisation. local upwind schemes are introduced (Baron&Hauschildt2004) depending on the coupling term a).," To insure the stability of the discretisation, local upwind schemes are introduced \citep{petereddienms3} depending on the coupling term $a_\lambda$."118" We assume a sorted wavelength grid jj,«2)Apa. and the wavelength dependence is represented by the wavelength index."," We assume a sorted wavelength grid $\lambda_{l-1} < \lambda_l < \lambda_{l+1}$, and the wavelength dependence is represented by the wavelength index."119" The wavelength derivative can then be written as: where the p? are Apadefined as: It should be noted that the p? Yrdependug not only on wavelength but also on spatial position sincethe sign of the coupling term «, may change along the characteristic.", The wavelength derivative can then be written as: where the $p_l^\bullet$ are defined as: It should be noted that the $p_l^\bullet$ depend not only on wavelength but also on spatial position sincethe sign of the coupling term $a_\lambda$ may change along the characteristic.120 For mixing parameters of £€[0.1] for the two different discretisations. the equation of radiative transfer then reads: To solve Eq.," For mixing parameters of $\xi \in [0,1]$ for the two different discretisations, the equation of radiative transfer then reads: To solve Eq."121 4 for monotonic velocity fields. it is customary to define a generalised opacity: This p)in general. however. often fails because the generalised opacity in Eq.," \ref{eq:eqrt2} for monotonic velocity fields, it is customary to define a generalised opacity: This approach in general, however, often fails because the generalised opacity in Eq."122" 5 may become negative if: (Note that the p, coefficient always has the same sign as cj).", \ref{eq:chihat} may become negative if: (Note that the $p_l^|$ coefficient always has the same sign as $a_l$ ).123 For strong wavelength couplings — as for instance m shock flows — the condition 6 is easily fulfilled., For strong wavelength couplings — as for instance in shock flows — the condition \ref{eq:chihatineq} is easily fulfilled.124 To avoid negative optical depths along the characteristics. the generalised opacity must be defined differently.," To avoid negative optical depths along the characteristics, the generalised opacity must be defined differently."125" In the €=| case. negative opacities could be eliminated by adopting a fine wavelength sampling anywhere apart from at the boundaries where the p, vanish."," In the $\xi = 1$ case, negative opacities could be eliminated by adopting a fine wavelength sampling anywhere apart from at the boundaries where the $p_l^|$ vanish."126 In principle. one could consider a method of correcting the formal solution at these points. but the corrections must then also be applicable to the explicit construction of the A-operator.," In principle, one could consider a method of correcting the formal solution at these points, but the corrections must then also be applicable to the explicit construction of the $\Lambda$ -operator."127 A positive generalised opacity is assured by the following definition: which only incorporates the physical opacity and a purely positive contribution from the velocity field., A positive generalised opacity is assured by the following definition: which only incorporates the physical opacity and a purely positive contribution from the velocity field.128 The remaining term 4a;/; must then be incorporated into the formal solution of the equation of radiative transfer., The remaining term $4 a_l I_l$ must then be incorporated into the formal solution of the equation of radiative transfer.129 This term then has the same effect as if 1t was included in the opacity definition., This term then has the same effect as if it was included in the opacity definition.130 For positive a). the contribution to the formal solution is negative and therefore decreases the intensity along the ray 1n à way similar to an increase in opacity provides.," For positive $a_l$, the contribution to the formal solution is negative and therefore decreases the intensity along the ray in a way similar to an increase in opacity provides."131 For negative a. the contribution is positive which behaves like a negative opacity.," For negative $a_l$, the contribution is positive which behaves like a negative opacity."132 This new solution indeed provides identical results to the previous discretisation method (see Sect. 3))., This new solution indeed provides identical results to the previous discretisation method (see Sect. \ref{sec:03}) ).133 After integrating Eq., After integrating Eq.134" 4 along a photon path from path length s, to s». the formal solution between two spatial points on a characteristic can then be written in terms of optical depth. since the optical depth τι along the characteristic relates to the path length by means of dr;=£d."," \ref{eq:eqrt2} along a photon path from path length $s_1$ to $s_2$, the formal solution between two spatial points on a characteristic can then be written in terms of optical depth, since the optical depth $\tau_\lambda$ along the characteristic relates to the path length by means of $\mathrm{d} \tau_l = \hat{\chi}_l135\mathrm{d} s$."136 where r;=T/(5;) and In a discrete atmosphere model. the integrals in Eq.," where $\tau_i = \tau_l (s_i)$ and In a discrete atmosphere model, the integrals in Eq."137 8 can be evaluated by means of piecewise linear- or parabolic interpolation of the auxiliary source functions: where the coefficients o. B. and y are deseribed in Olson(1987) and Hauschildt(1992)..," \ref{eq:frmsl} can be evaluated by means of piecewise linear- or parabolic interpolation of the auxiliary source functions: where the coefficients $\alpha$, $\beta$, and $\gamma$ are described in \cite{frmsol2} and \cite{peter1992JQSRT}."138 Note that the contribution from the explicit wavelength derivative has been only linearly interpolated. whereas the implicit part can also be parabolically interpolated.," Note that the contribution from the explicit wavelength derivative has been only linearly interpolated, whereas the implicit part can also be parabolically interpolated."139 The construction of the matrix equation for the formal solution as well as the analytic construction scheme for a A operator described in Baron&Hauschildt(2004) can be used without modification in the new formal solution., The construction of the matrix equation for the formal solution as well as the analytic construction scheme for a $\Lambda$ operator described in \cite{petereddienms3} can be used without modification in the new formal solution.140 These steps will therefore not be repeated here., These steps will therefore not be repeated here.141 To compare the new solution with other solutions. we used a simplified test setup (see also Hauschildt&Baron(2004) and Knopetal. (2007))).," To compare the new solution with other solutions, we used a simplified test setup (see also \cite{petereddie2004} and \cite{grline}) )."142 The opacity consists of a grey continuum and a single atomic line., The opacity consists of a grey continuum and a single atomic line.143" The continuum opacity y, IS grey and varies with the radial structure according to y,X177."," The continuum opacity $\chi_\kappa$ is grey and varies with the radial structure according to $\chi_\kappa \propto144r^{-2}$."145" The expression y,=&+, includes absorption x, as well as scattering «7,. which are related by a thermalisation parameter e.=&,/y,."," The expression $\chi_\kappa=\kappa_\kappa +\sigma_\kappa$ includes absorption $\kappa_\kappa$ as well as scattering $\sigma_\kappa$, which are related by a thermalisation parameter $\epsilon_\kappa = \kappa_\kappa/\chi_\kappa$."146" The corresponding opacities Aigo.Tine and thermalisation eg, are used for the — assumed to be Gaussian shaped — spectral line of the two-level-atom. where its strength is parameterised relative to the continuum opacity R=Viine/¥«-"," The corresponding opacities $\kappa_{\mathrm{line}}, 147\sigma_{\mathrm{line}}$, and thermalisation $\epsilon_{\mathrm{line}}$ are used for the — assumed to be Gaussian shaped — spectral line of the two-level-atom, where its strength is parameterised relative to the continuum opacity $R=\chi_{\mathrm{line}}/\chi_\kappa$."148" The atmosphere has an extension of rij«r< 101. where ry,=IO0Uem."," The atmosphere has an extension of $r_{\mathrm{min}} < r < 101\, $ , where $r_{\mathrm{min}}149 = 10^{13} \mathrm{cm}$."150 A radial optical-depth scale is mapped onto the radial grid with the continuum opacity and ranges from 107°<r 107., A radial optical-depth scale is mapped onto the radial grid with the continuum opacity and ranges from $10^{-6} < \tau < 10^{4}$ .151 To include wavelength couplings in the atmosphere. a velocity field is imposed on the radial structure.," To include wavelength couplings in the atmosphere, a velocity field is imposed on the radial structure."152 At first. we checked that. for an absent velocity field. the old and new formal solutions provide identical results.," At first, we checked that, for an absent velocity field, the old and new formal solutions provide identical results."153 Then we used monotonic velocity fields. in order to compare the," Then we used monotonic velocity fields, in order to compare the"154I turn to consider the possibility that the jets penetrate the small mass at r<107km. and are shocked at a larger radius pr>107kan.,"I turn to consider the possibility that the jets penetrate the small mass at $r \la 10^3 \km$, and are shocked at a larger radius $r > 10^3 \km$."155 Whokhlov et al. (, Khokhlov et al. (1561999) and Couch et al. (,1999) and Couch et al. (157"2009). for example. injected jets al 2,=3800km from the center.","2009), for example, injected jets at $R_{\rm in}=3800 \km$ from the center."158" I take a mass of O.OLAL. to be shocked at a radius of ke;3000km. and the two bubbles to occupy most of the volume inside ry. V.o1079cm""."," I take a mass of $\sim 0.01 M_\odot$ to be shocked at a radius of $r_s \simeq 3000 \km$, and the two bubbles to occupy most of the volume inside $r_s$, $V \simeq 10^{26} \cm^3$."159 In such a large volume the radiation energy aT!V. in the post shock region must be considered., In such a large volume the radiation energy $a T^4 V$ in the post shock region must be considered.160" The temperature of the post-shock gas is Using this expression for the temperature in equation (2)). scaling with the kinetic energy of the [ast jets E;=(1/2)Mpe]. and using the distance of the shock r;c(0.251)"", I find that the total energy. carried by neutrinos in a time Af in this volume is Equation (4)) shows that for neutrino loses to be neeligible. (he narrow fast jets should be shocked at a distance of r,23000km."," The temperature of the post-shock gas is Using this expression for the temperature in equation \ref{eq:cool2}) ), scaling with the kinetic energy of the fast jets $E_f=(1/2)M_f v_f^2$, and using the distance of the shock $r_s \simeq (0.25V)^{1/3}$, I find that the total energy carried by neutrinos in a time $\Delta t$ in this volume is Equation \ref{eq:cool3}) ) shows that for neutrino loses to be negligible, the narrow fast jets should be shocked at a distance of $r_s \ga 3000 \km$."161 The formation of jets as used by Khokhlov et al. (, The formation of jets as used by Khokhlov et al. (1621999) and Couch et al. (,1999) and Couch et al. (1632009) can be explained by this mechanism.,2009) can be explained by this mechanism.164In the initial model used by Couch et al. (,In the initial (pre-explosion) model used by Couch et al. (1652009) the mass inside 3800kin is ~1.6...,2009) the mass inside $3800 \km$ is $\sim 1.6 M_\odot$.166 This is (he mass assumed to collapse and form the core that forms the NS. and is not treated by Couch et al. (," This is the mass assumed to collapse and form the core that forms the NS, and is not treated by Couch et al. ("1672009).,2009).168 The collapse time of this region is ~1 s., The collapse time of this region is $\sim 1 \s$ .169 Let the [ast jets [rom the inner disk zone have a mass outflow rate in both directions of My. a velocity vy. and let the (wo jets cover a solid angle of 429 (on both sides of the disk together).," Let the fast jets from the inner disk zone have a mass outflow rate in both directions of $\dot M_f$, a velocity $v_f$, and let the two jets cover a solid angle of $4 \pi \delta$ (on both sides of the disk together)."170 The density of the outflow at raclius r is The jetsencounter (he surrounding gas residing within a distance r; and having a typical densitv ps., The density of the outflow at radius $r$ is The jetsencounter the surrounding gas residing within a distance $r_s$ and having a typical density $\rho_s$.171 The head of each jet proceeds at à speed 0; given bv the balance Ássuming supersonic.motion. this. equality. reads piv;>=pple— c5). which. can be solved [orH vy ," The head of each jet proceeds at a speed $v_h$ given by the balance Assuming supersonicmotion this equality reads $\rho_s v_h^2 = \rho_f (v_f-v_h)^2$ , which can be solved for $v_h$ "172"we describe below, and optimized on these values (i.e., we required that Cloudy models produce them).","we describe below, and optimized on these values (i.e., we required that Cloudy models produce them)."173 We choose as the transition on which we optimize because it is located in a relatively “clean” spectral region where there are few blends., We choose as the transition on which we optimize because it is located in a relatively “clean” spectral region where there are few blends.174" This allows us to determine its column density, Doppler parameter, and coverage fraction via Voigt profile fiting."," This allows us to determine its column density, Doppler parameter, and coverage fraction via Voigt profile fitting."175" The code AUTOVP (Dave,Hernquist&Weinberg1997) is used to derive an initial solution, and then MINFIT is used to determine the minimum number of components that produce an adequate fit."," The code AUTOVP \citep{dav97} is used to derive an initial solution, and then MINFIT is used to determine the minimum number of components that produce an adequate fit."176" The goal of the modeling exercise is to reproduce the observed absorption profiles for all other ions three physical Z/Zo, byionization adjustingparameter, U, and hydrogen parameters:number metallicity,density, ny."," The goal of the modeling exercise is to reproduce the observed absorption profiles for all other ions by adjusting three physical parameters: metallicity, $Z/Z_\odot$ , ionization parameter, $U$, and hydrogen number density, $n_{\rm H}$."177 The approach of the MINFIT code is to first “overfit” the system using many Voigt components and then to reject components that do not improve the fits at a confidence level above 95%., The approach of the MINFIT code is to first “overfit” the system using many Voigt components and then to reject components that do not improve the fits at a confidence level above $95\%$.178" This fitting has been used extensively in studies of interveningII techniquesystems (e.g., Ding et al."," This fitting technique has been used extensively in studies of intervening systems (e.g., Ding et al."179" 2003; Ding, Charlton Churchill 2005; Lynch, Charlton Kim 2006))."," 2003; Ding, Charlton Churchill 2005; Lynch, Charlton Kim \nocite{din03,din05,lyn06}) )."180 Table 2 liststhe resulting fitting parameters., Table \ref{tab-nvfit} liststhe resulting fitting parameters.181 It is, It is182each cluster is larger than 6.,each cluster is larger than 6.183 These requirements elininate lost artifacts due to bright and CCD defects that do not exhibit a clear spatial PSF-like patteru., These requirements eliminate most artifacts due to bright and CCD defects that do not exhibit a clear spatial PSF-like pattern.184 We finally keep 717 super-pixel light curves., We finally keep 747 super-pixel light curves.185 The sensitivity of these thresholds is illustrated in Fie. 1.., The sensitivity of these thresholds is illustrated in Fig. \ref{fig:eff}.186 Among the 717 selected variations.⋅⋅ two have been countedtwice. leaviug. 115 independent light curves.," Among the 747 selected variations, two have been counted, leaving 745 independent light curves."187 We select 237 light curves for which there is at least one bad pixel (saturated or set at zero) within a «21 window ceutred on the selected. pixel for at least one epoch aud at least one colour., We select 237 light curves for which there is at least one bad pixel (saturated or set at zero) within a $\times$ 21 window centred on the selected pixel for at least one epoch and at least one colour.188 A careful visual inspection of these helt curves shows 121 eeuune variable stars 116 artifacts. subsequently removed.," A careful visual inspection of these light curves shows 121 genuine variable stars 116 artifacts, subsequently removed."189 Figure 2. shows that the removed light curves are mainly couceutrated close to the edges. whereas the distribution of the kept light curves (z1none the 237) is more unitorm.," Figure \ref{fig:cleand} shows that the removed light curves are mainly concentrated close to the edges, whereas the distribution of the kept light curves (among the 237) is more uniform."190 We finally cud with a catalogue of 631 variable stars., We finally end with a catalogue of 631 variable stars.191 Whereas the pixel method of analysis is able to detect variable stars bevoud the crowding dut. it does not nieasure photometry total flux — of these objects. that can be bleuded or even uuresolved on part of the liebt curves.," Whereas the pixel method of analysis is able to detect variable stars beyond the crowding limit, it does not measure photometry – total flux – of these objects, that can be blended or even unresolved on part of the light curves."192 Obtaining their photometry would eive a first indication of the type of the variable stars., Obtaining their photometry would give a first indication of the type of the variable stars.193 Hence in this section. We associate a magnitude aud colour to cach fiux niecasurenment.," Hence in this section, we associate a magnitude and colour to each flux measurement."194 As discussed in Paper Π. the flux of the super-pixel is composed of the fraction of the flux of the star plus he background Cou sky aud undoetected stars).," As discussed in Paper II, the flux of the super-pixel is composed of the fraction of the flux of the star plus the background (from sky and undetected stars)."195 For our sample of variable stars. we can presume that here is a star within the correspondiug super-pixel aud hat its flux siguificautlv contributes to this super-pixcl. at least at the imaxiuuin of the variation.," For our sample of variable stars, we can presume that there is a star within the corresponding super-pixel and that its flux significantly contributes to this super-pixel, at least at the maximum of the variation."196 Because of he crowding couditions. standard background estimates (circular anulus for example. see Stetson (1987))) fail aud cannot be used m an automatic wav.," Because of the crowding conditions, standard background estimates (circular annulus for example, see Stetson \nocite{Stetson:1987}) ) fail and cannot be used in an automatic way."197 Deuce. we choose to oerform a pseudo-aperture photometry as follows.," Hence, we choose to perform a pseudo-aperture photometry as follows."198 For au iuage taken in the middle of the period of observation (JD2Lis678.3) and with an average seeing. we use the PSF fitting procedure of DAOPPIIOT (Stetson. o measure the fluxes of the resolved stars. and the backgrouud below them.," For an image taken in the middle of the period of observation (JD2448678.3) and with an average seeing, we use the PSF fitting procedure of PHOT (Stetson, \nocite{Stetson:1987} to measure the fluxes of the resolved stars, and the background below them."199 This thus gives a local estimate of the backeround that is the less affected by the crowding of the field., This thus gives a local estimate of the background that is the less affected by the crowding of the field.200 Then for cach selected super-pixel we look for the detected star that is closest., Then for each selected super-pixel we look for the detected star that is closest.201 The backeround estimate Hassociated with this star is supposed to be the same as the one preseut below the variable star (and is even ideutical if the variable stars are resolved on this reference frame)., The background estimate associated with this star is supposed to be the same as the one present below the variable star (and is even identical if the variable stars are resolved on this reference frame).202 This backerouud is subtracted from the super-pixel fux., This background is subtracted from the super-pixel flux.203 This fiux is then corrected for the seciug fraction and, This flux is then corrected for the seeing fraction and204hat the difference in bolometric magnitude is 0.15.,that the difference in bolometric magnitude is 0.15.205 loLASS0920+35 is also a close binary whose spectral type is L6.5 (Reid 1999).," 2MASS0920+35 is also a close binary whose spectral type is L6.5 \citep{rei01a,kir99}."206.. Weak methane absorption features are seen atAH aud fy bauds 2001)., Weak methane absorption features are seen at$H$ and $K$ bands \citep{nak01}.207. The magnitude cdiffereuce at J is O.L1 and Beid et al., The magnitude difference at $I$ is 0.44 and Reid et al.208 estimate tliat he difference in bolometric magnitude is 0.15., estimate that the difference in bolometric magnitude is 0.15.209 The parallax of this object is not known aud we use his object only for the discussion of its spectrum., The parallax of this object is not known and we use this object only for the discussion of its spectrum.210 We examine our spectra which cover a represeutative sample of L aud T types in some detail., We examine our spectra which cover a representative sample of L and T types in some detail.211 ]t turus out that some of the prominent spectral features remain unkleutified aud the interpretation ol the identified features is by no means clear yet., It turns out that some of the prominent spectral features remain unidentified and the interpretation of the identified features is by no means clear yet.212 In this sectiou. we apply the predicted spectral line inteusities based ou the UCMIs discussed in a separate paper 2001) as a gukle to interpret the observed spectra.," In this section, we apply the predicted spectral line intensities based on the UCMs discussed in a separate paper \citep{tsu03}213 as a guide to interpret the observed spectra."214" The spectra of eight objects in the A-baind region are shown ou the log/,, scale in Fig.l.", The spectra of eight objects in the $K$ -band region are shown on the $\log f_\nu$ scale in Fig.1.215 The prominent features are CO first overtone bands at 2.3 yan in L dwarfs aud can be traced up to T2 or T3.5 dwarls in our sample., The prominent features are CO first overtone bands at 2.3 $\mu$ m in L dwarfs and can be traced up to T2 or T3.5 dwarfs in our sample.216 The methane bands at 2.2 jan are quite strong in T dwarfs. and a question is if they are already seen in late L clwarls.," The methane bands at 2.2 $\mu$ m are quite strong in T dwarfs, and a question is if they are already seen in late L dwarfs."217 A very weak bancheac feature may be seen al 2.2 gon in the L6.5 dwarf 2MASSO920+35 as already noted previously (Nakajima. 2001)., A very weak bandhead feature may be seen at 2.2 $\mu$ m in the L6.5 dwarf 2MASS0920+35 as already noted previously \citep{nak01}.218. The spectrum of another L6.5 dwarf 2MÀSS1711-22 is a bit noisy and it is difficult to identify the methane 2.2 pan bands., The spectrum of another L6.5 dwarf 2MASS1711+22 is a bit noisy and it is difficult to identify the methane 2.2 $\mu$ m bands.219 In LS dwarf 281A8815234-30. the presence of the methane 2.2 sam bands was previously suggestedMOD by MeLeanetal.(2001).," In L8 dwarf 2MASS1523+30, the presence of the methane 2.2 $\mu$ m bands was previously suggested by \citet{mcl01}."220. The S/N ratio of our spectrum of 2MLASS1523+30 may be somewhat better than that of MeLean et αἱ., The S/N ratio of our spectrum of 2MASS1523+30 may be somewhat better than that of McLean et al.221" aud the methane 2,2 yan bauds cau be clearly seen in Fig.l.", and the methane 2.2 $\mu$ m bands can be clearly seen in Fig.1.222 Thus. the methane 2.2 sam bands cau be deemed as detected at Ls.," Thus, the methane 2.2 $\mu$ m bands can be deemed as detected at L8."223 This better S/N ratio is probably due to the lower spectral resolution and higher throughput of CISCO ou Subaru than NIRSPEC on eck., This better S/N ratio is probably due to the lower spectral resolution and higher throughput of CISCO on Subaru than NIRSPEC on Keck.224 Iu the H-baud region. absorption features are clearly seen at 1.58. 1.59. 1.61. and. 1.625 sam in L3 aud LS cdwarls as shown by the filled triangles in Fig.," In the $H$ -band region, absorption features are clearly seen at 1.58, 1.59, 1.61, and 1.625 $\mu$ m in L3 and L5 dwarfs as shown by the filled triangles in Fig."225 2., 2.226 Of these features. those at 1.58. 1.613. and 1.627 san were noted in L dwarls by Reidetal...(2001b).," Of these features, those at 1.58, 1.613, and 1.627 $\mu$ m were noted in L dwarfs by \citet{rei01b}."227. Ou the other haud. the features at 1.583. 1.591. and 1.625 pan were identilied as due to the FeH E!HIE-AHI system in the spectra oL sunspot as well as of M - L dwarls by Wallace&Hinkle (2001).. who also remarked that the," On the other hand, the features at 1.583, 1.591, and 1.625 $\mu$ m were identified as due to the FeH $E^4\Pi - A^4\Pi$ system in the spectra of sunspot as well as of M - L dwarfs by \citet{wal01}, , who also remarked that the"228"the volume filling factor. C. of (he gas: 7=nC, (equation 15 of ?)).","the volume filling factor, $C_\nu$, of the gas: $\overline{n}=n C_\nu$ (equation 15 of \citealt{2005A&A...431..111B}) )."229 The volume filling [actor of the gas cannot be directly. measured and is οπΠιοα to estimate (?).. , The volume filling factor of the gas cannot be directly measured and is difficult to estimate \citep{2007MNRAS.379.1359M}. .230"Therefore we use C,=1 [or simplicity.", Therefore we use $C_\nu=1$ for simplicity.231 We make a substitution to eliminate 77 using Eq. (1))., We make a substitution to eliminate $R^2$ using Eq. \ref{simple}) ).232 Q is the solid angle subtended by the outflow., $\Omega$ is the solid angle subtended by the outflow.233 Assuming a spherical outflow where Q=tx. Eq. (2))," Assuming a spherical outflow where $\Omega=4\pi$, Eq. \ref{outflow}) )"234 provides an upper limit on the mass outflow rate., provides an upper limit on the mass outflow rate.235 A summary of these caleulations is shown in Table 5..., A summary of these calculations is shown in Table \ref{outflowtbl}.236 As a check. .NR/R=0.037 for (n=10 7): the constraint that AR/R<1 is met (see diseussion in ?— around equation 22).," As a check, $\Delta R / R = 0.037$ for $(n=10^4$ $^{-3})$; the constraint that $\Delta R / R \leq 1$ is met (see discussion in \citealt{2005A&A...431..111B} around equation 22)."237 The dependence on n is AR/B-0031(0/105ae By)7)1/2F7., The dependence on $n$ is $\Delta R / R = 0.037(n/10^4$ $^{-3})^{-1/2}$.238 The kinetic luminosity. Lj associated with a spherical mass outflow rate of Αμα αἱ velocity e is The value of £j can tell us how significant an outflow is in terms of energy.," The kinetic luminosity, $L_{\rm k}$ associated with a spherical mass outflow rate of $\dot M_{\rm wind}$ at velocity $v$ is The value of $L_{\rm k}$ can tell us how significant an outflow is in terms of energy."239 For the —360 km ! wind. the kinetic luminosity is 8.6xLOM eres !..," For the $-360$ km $^{-1}$ wind, the kinetic luminosity is $8.6\times 10^{40}$ erg $^{-1}$."240 This power is only a small fraction L/L.~0.005 of the X-ray huninosity of the source., This power is only a small fraction $L_{\rm k}/L_{\rm x}\sim 0.005$ of the X-ray luminosity of the source.241 We can also estimate the rate of accretion onto the black hole with The bolometric huminositw. Lj. can be approximated from (he 2 10 keV. luminosity applving the bolometric correction of ?..," We can also estimate the rate of accretion onto the black hole with The bolometric luminosity, $L_{\rm bol}$, can be approximated from the $2$ $10$ keV luminosity applying the bolometric correction of \citet{2004MNRAS.351..169M}."242 For a Sevfert galaxy with a huninosity like the bolometric correction to the 2 10 keV luminosity is about 10. πο we estimate that Αμ=2-2x1031 gs +=0.035AL. +.," For a Seyfert galaxy with a luminosity like 18325-5926, the bolometric correction to the $2$ $10$ keV luminosity is about $10$, so we estimate that $\dot M_{\rm accretion}=2.2\times 10^{24}$ g $^{-1}=0.035 M_\odot$ $^{-1}$."243 The rate of outflow due to the wind is about 2 orders of magnitude greater than the accretion rate. if we assume the filling factor. C5. is close to unity.," The rate of outflow due to the wind is about $2$ orders of magnitude greater than the accretion rate, if we assume the filling factor, $C_\nu$, is close to unity."244 Even if the filling factor is as small as 0.01. the mass outflow rate is comparable to the accretion rate.," Even if the filling factor is as small as $0.01$, the mass outflow rate is comparable to the accretion rate."245 Namely. one might conclude (hat a significant aanount of (he mass appears to be leaving the 118325-5926 ealactie nuclei compared to the matter being captured bv the accretion disk. although these two flows may result. [rom different mechanisms and have clifferent mass reservoirs since the distance of the outflow Irom the source. £2. is found to be large (1.35.(0/10! ο)E? pe).," Namely, one might conclude that a significant amount of the mass appears to be leaving the 18325-5926 galactic nuclei compared to the matter being captured by the accretion disk, although these two flows may result from different mechanisms and have different mass reservoirs since the distance of the outflow from the source, $R$ , is found to be large $1.35\,\,\,(n/10^4$ $^{-3})^{-1/2}$ pc)."246 The Eddington huninositv of the source is erg I. where A/ is the mass of the object in solar mass units. [or which we use a value of ~10*M... (2.104)..," The Eddington luminosity of the source is $L_{\rm edd}=1.25\times10^{38} (M/M_\odot)247=1.25\times10^{45}$ erg $^{-1}$, where $M$ is the mass of the object in solar mass units, for which we use a value of $\sim 10^7 M_\odot$ \citep[][I04]{2005Ap&SS.300...67L}."248" Then. the ratio L,/Log is equal to 0.16. meaning that isonly at a small fraction of its Eddington luminosity."," Then, the ratio $L_{\rm x} / L_{\rm edd}$ is equal to $0.16$, meaning that 18325-5926 isonly at a small fraction of its Eddington luminosity."249 Since the warm absorber has a slenilicantly higher opacity than a totally ionized gas. a wind may be racliatively driven even if the source is only al a small fraction of its Eddington huninosity (see. for example. the steacly-state. raciatively driven modelby 2)).," Since the warm absorber has a significantly higher opacity than a totally ionized gas, a wind may be radiatively driven even if the source is only at a small fraction of its Eddington luminosity (see, for example, the steady-state, radiatively driven modelby \citealt{1995MNRAS.273.1167R}) )."250models.,models.251 For example. the proposed double pulsar would link the radio emission (o a 77 min.," For example, the proposed double pulsar would link the radio emission to a 77 min."252 orbital period., orbital period.253 In this model. coherent radio emission is triggered by the shock formed through the interaction of the wind of the more enigmatic pulsar with the magnetosphere of the companion pulsar.," In this model, coherent radio emission is triggered by the shock formed through the interaction of the wind of the more enigmatic pulsar with the magnetosphere of the companion pulsar."254 On the other hand. in analogy to the Psi 1259-63 svstem which consists of a pulsar and. Be star companion. it is also possible that the magnetosphere of (he companion is not constant. and therefore that the radio bursts are not always triggered every orbit.," On the other hand, in analogy to the PSR B1259-63 system which consists of a pulsar and Be star companion, it is also possible that the magnetosphere of the companion is not constant, and therefore that the radio bursts are not always triggered every orbit."255 Indeed. (he much fainter detection from rreported in (his could be evidence of variable conditions in (hie environment around a companion star.," Indeed, the much fainter detection from reported in this could be evidence of variable conditions in the environment around a companion star."256 Sinularly. (he precessing radio pulsar and transient white dwarf pulsar models would also require one or more types of nulling elfects to explain the occurrence of isolated bursts in the short term. as well as the low duty evele in the long term.," Similarly, the precessing radio pulsar and transient white dwarf pulsar models would also require one or more types of nulling effects to explain the occurrence of isolated bursts in the short term, as well as the low duty cycle in the long term."257 A few radio pulsars are known to have a very laree nulling fraction., A few radio pulsars are known to have a very large nulling fraction.258 PSR DI9314-24 remains in an olf state for ~90% of the time. and it emits bursts quasi-periodically al ~40 per dav (Cordesοἱal.2004).," PSR B1931+24 remains in an off state for $\sim$ of the time, and it emits bursts quasi-periodically at $\sim$ 40 per day \citep{cordesetal04}."259. Such a high nulling fraction may be consistent with the measured duty evele estimated [orJ1745—3009., Such a high nulling fraction may be consistent with the measured duty cycle estimated for.260. The new. serendipitous detection reported in (his paper is derived from 330 MIIz GAIRT Galactic center observations obtained by (vo of us (5. Rov and ο. Bhatnagar) as part of an unrelated project anc not included in Ivanetal.(2006).," The new, serendipitous detection reported in this paper is derived from 330 MHz GMRT Galactic center observations obtained by two of us (S. Roy and S. Bhatnagar) as part of an unrelated project and not included in \cite{hlrrkn06}."261. One of the observations. from 2004 March 20-21. is pointed [from acid consists of eleven 10 min.," One of the observations, from 2004 March 20-21, is pointed from and consists of eleven 10 min."262 scans spread over six hours., scans spread over six hours.263 The observations were carried oul using the default observing mode with a bandwidth of 16 MIIz in each of the two available sidebands., The observations were carried out using the default observing mode with a bandwidth of 16 MHz in each of the two available sidebands.264 The sources D1322-096 and D1T14-25 were used as secondary. calibrators., The sources B1822-096 and B1714-25 were used as secondary calibrators.265" The GMBRT does not measure the svstem temperature (7.,,). and the increase in T.sys from the calibrator lield to the target source affects the source visibility amplitudes in the default observing mode (i.e.. the Automatic Level Control [ALC] in the svstem is turned on)."," The GMRT does not measure the system temperature $T_{sys}$ ), and the increase in $T_{sys}$ from the calibrator field to the target source affects the source visibility amplitudes in the default observing mode (i.e., the Automatic Level Control [ALC] in the system is turned on)."266 We emploved the following method to correct for the Τὸ variation., We employed the following method to correct for the $T_{sys}$ variation.267 As the svstem gain does not change with the ALC off. we observed 3C48 and DI322-096 once with the ALC olf and determined the flux density of D13822-096 to be 10.8 Jv using the known flix clensity of 3C48 from Baarsetal.(1977).," As the system gain does not change with the ALC off, we observed 3C48 and B1822-096 once with the ALC off and determined the flux density of B1822-096 to be 10.8 Jy using the known flux density of 3C48 from \cite{baarsetal77}."268. Also with the ALC off. we determined the ratio of the total power on (he target source to that of D1822-096 to be 1.8.," Also with the ALC off, we determined the ratio of the total power on the target source to that of B1822-096 to be 1.8."269 Since Chis ratio was quite similar, Since this ratio was quite similar270of the tangential point. close to1.,"of the tangential point, close to."271. From the mean radial velocity of Component 3. a kinematic distance of ~ 8 kpe is determined. indicating that Component 43 ts unrelated to.," From the mean radial velocity of Component 3, a kinematic distance of $\sim$ 8 kpc is determined, indicating that Component 3 is unrelated to."272. Very likely. Component 3 is associated with the complex of regions at a velocity of ~ +20 rreported by ?..," Very likely, Component 3 is associated with the complex of regions at a velocity of $\sim$ +20 reported by \citet{g00}."273 A direct comparison of Component | with the molecular cloud detected by (see Fig., A direct comparison of Component 1 with the molecular cloud detected by (see Fig.274 2u from that work). shows that the angular size of Component | is about a factor 3 - 4 greater than the latter.," 2u from that work), shows that the angular size of Component 1 is about a factor 3 - 4 greater than the latter."275 Clearly. only the densest part of the molecular cloud associated with (clump A) was detected in the CO observations of?.," Clearly, only the densest part of the molecular cloud associated with (clump A) was detected in the $^{13}$ CO observations of."276. From here onwards. the analysis," From here onwards, the analysis"277In the ideal ALLID case. the plasma is wound. up by the WH instability and the magnetic field experiences a similar winding force as a result of the frozen-in approximation (see Fie. 3..,"In the ideal MHD case, the plasma is wound up by the KH instability and the magnetic field experiences a similar winding force as a result of the frozen-in approximation (see Fig. \ref{nonideal_bfield_vectorplot},"278 upper panel)., upper panel).279 lt can clearly be seen that the magnetic field undergoes a very dillerent/ evolution when multilluid ellects are included. (see Fig. 3.," It can clearly be seen that the magnetic field undergoes a very different evolution when multifluid effects are included (see Fig. \ref{nonideal_bfield_vectorplot},"280 lower panel)., lower panel).281 The inclusion of ambipolar resistivity into the svstem allows for decoupling between the various fluids., The inclusion of ambipolar resistivity into the system allows for decoupling between the various fluids.282 This breaks the frozen-in approximation of ideal MILD., This breaks the frozen-in approximation of ideal MHD.283 As a result. the magnetic field is able to diffuse with respect to the bulk Iuid.," As a result, the magnetic field is able to diffuse with respect to the bulk fluid."284 This ambipolar ciffusion is the source of the altered magnetic feld configuration observed., This ambipolar diffusion is the source of the altered magnetic field configuration observed.285 The changes in the magnetic field development can be analvsed in à more quantitative manner using the plot in figure 4.., The changes in the magnetic field development can be analysed in a more quantitative manner using the plot in figure \ref{nonideal_perturbedB}.286 The thin line shows the amplification experienced bv the magnetic field through the wind-up it undergoes in the ideal MILD. case., The thin line shows the amplification experienced by the magnetic field through the wind-up it undergoes in the ideal MHD case.287 The thick line shows that this amplification is significantlv. reduced. in the presence of ambipolar dilfusion., The thick line shows that this amplification is significantly reduced in the presence of ambipolar diffusion.288 Similar results were observed in Paper Lin the ambipolar-dominatec simulation., Similar results were observed in Paper I in the ambipolar-dominated simulation.289 As this was not observed in the LHall-dominated simulations in Paper LI. we can deduce that this is solely as a result of the ambipolar resistivity.," As this was not observed in the Hall-dominated simulations in Paper I, we can deduce that this is solely as a result of the ambipolar resistivity."290 We know that the introduction of ambipolar resistivity has allowed for decoupling of the magnetic field from the neutral luid., We know that the introduction of ambipolar resistivity has allowed for decoupling of the magnetic field from the neutral fluid.291 We now examine the behaviour of the charged [uids hemselves., We now examine the behaviour of the charged fluids themselves.292 The exact behaviour of cach charged. Duid. can x understood by examining its density profile ancl velocity ield during the development of the instability., The exact behaviour of each charged fluid can be understood by examining its density profile and velocity field during the development of the instability.293 Phe state of each of the four Duids in the svstem has been plotted. in igure 5 at the time of saturation of the instability., The state of each of the four fluids in the system has been plotted in figure \ref{results_1KH_density_den5} at the time of saturation of the instability.294 lt can be seen that the mass density of the dust. grain ]uicl closely rellects that of the bulk [uic signifving a strong coupling between the two.," It can be seen that the mass density of the dust grain fluid closely reflects that of the bulk fluid, signifying a strong coupling between the two."295 This would be expected. due to its relatively low Hall parameter (see equation 36))., This would be expected due to its relatively low Hall parameter (see equation \ref{eqn:dust_hall}) ).296 On the other hand. the ion and electron Duids more closely reflect the configuration of the magnetic field. implving that they are still strongly coupled to the magnetic field. lines. as expected. by their high. Hall. parameter (equations 85 and 31)).," On the other hand, the ion and electron fluids more closely reflect the configuration of the magnetic field, implying that they are still strongly coupled to the magnetic field lines, as expected by their high Hall parameter (equations \ref{eqn:ion_hall} and \ref{eqn:electron_hall}) )."297 The decoupling of the ion and electron Iuids from the neutral uid is the source of the ambipolar cdilfusion in the system., The decoupling of the ion and electron fluids from the neutral fluid is the source of the ambipolar diffusion in the system.298 The magnetic field is tied to the neutral uid. only through the coupling of the charged Uuics with the neutrals. so à low collisional coupling between the charged Iuids and the neutrals allows for the magnetic field to dilfuse relative to the bulk Heil.," The magnetic field is tied to the neutral fluid only through the coupling of the charged fluids with the neutrals, so a low collisional coupling between the charged fluids and the neutrals allows for the magnetic field to diffuse relative to the bulk fluid."299 The various dynamics discussed above are confirmed in ligure 6.., The various dynamics discussed above are confirmed in figure \ref{nonideal_KEx4}.300 Phese plots of the transverse kinetic energy. [or each o£ the four I[uids clearly demonstrate the behaviour of cach., These plots of the transverse kinetic energy for each of the four fluids clearly demonstrate the behaviour of each.301 We can see that the bulk [uid undergoes Further winel-up in the muttifluicl MEID case than in the ideal ΑΗ) case (see the top panel of figure 6))., We can see that the bulk fluid undergoes further wind-up in the multifluid MHD case than in the ideal MHD case (see the top panel of figure \ref{nonideal_KEx4}) ).302 This is due to two distinct phenomena (see Paper E for more details)., This is due to two distinct phenomena (see Paper I for more details).303 In general. the system is prevented from as strong a wind-up as seen in the hydrodynamic case by the presence of a magnetic field.," In general, the system is prevented from as strong a wind-up as seen in the hydrodynamic case by the presence of a magnetic field."304 In multilluii MIID. there are two effects at work that limit the effectiveness of the magnetic field. in suppressing this wind-up.," In multifluid MHD, there are two effects at work that limit the effectiveness of the magnetic field in suppressing this wind-up."305 Firstly. the introduction of even a small amount of ambipolar dilfusion causes the magnetic field to experience a significant. reduction in its amplification.," Firstly, the introduction of even a small amount of ambipolar diffusion causes the magnetic field to experience a significant reduction in its amplification."306 The resulting weaker magnetic field. allows the bulk. [uid to undergo a stronger wind-up., The resulting weaker magnetic field allows the bulk fluid to undergo a stronger wind-up.307 Secondly. with higher levels of ambipolar diffusion being introduced. into the system. the bulk [uid becomes further decoupled from the magnetic field. further reducing its ellectiveness in opposing the wind-up.," Secondly, with higher levels of ambipolar diffusion being introduced into the system, the bulk fluid becomes further decoupled from the magnetic field, further reducing its effectiveness in opposing the wind-up."308 On the other hand both the electron. ancl ion. Εις experience a decoupling from the neutral Duid., On the other hand both the electron and ion fluids experience a decoupling from the neutral fluid.309 As they are still well tied to the magnetic field. and the magnetic field no longer winds up in a manner similar to the bulk ILuid. the," As they are still well tied to the magnetic field, and the magnetic field no longer winds up in a manner similar to the bulk fluid, the"310"is referred to as the ""restricted. sample’ and. allows us to explore the sensitivity. of our results to the presence of eroup or cluster members within the NIIS.",is referred to as the `restricted sample' and allows us to explore the sensitivity of our results to the presence of group or cluster members within the NHS.311 Figure 3. plots the local luminosity function for the subsaniples (ii) anc (ui).," Figure \ref{lf1}312 plots the local luminosity function for the subsamples (ii) and (iii)."313 For clarity we do not show the luminosity function for sample (1)., For clarity we do not show the luminosity function for sample (i).314 We find that the luminosity function for the restricted sample. very closely resembles that of the tota sample., We find that the luminosity function for the restricted sample very closely resembles that of the total sample.315 Llenceforth. we will be using the total saniple (ii) in our analysis.," Henceforth, we will be using the total sample (ii) in our analysis."316 Vhe luminosity function. derived. above contains al galaxy types Le. both carly and late., The luminosity function derived above contains all galaxy types i.e. both early and late.317 Next. we attemp o explore the luminosity function. for dillerent) galaxy vpes using the combined NIUS/CDE sample.," Next, we attempt to explore the luminosity function for different galaxy types using the combined NHS/CDF sample."318 Calaxies with absorption optical lines are classified as early. while systems with narrow cmission-lines or galaxies presenting »»h absorption and emission lines are grouped. into. the ale type category., Galaxies with absorption optical lines are classified as early while systems with narrow emission-lines or galaxies presenting both absorption and emission lines are grouped into the late type category.319 Lor svstenis without optical spectra we use the best-fit SED estimated. as a by-product of the xhotometrie redshift estimation for classification., For systems without optical spectra we use the best-fit SED estimated as a by-product of the photometric redshift estimation for classification.320 Phere are 27 and 19 [ate and carly twpe galaxies respectively., There are 27 and 19 late and early type galaxies respectively.321 The results are shown in Fig., The results are shown in Fig.322 4 and are compared. with the oediceted: star-forming X-ray galaxy luminosity function derived. by Georgantopoulos. Basilakos Plionis (1999).," \ref{lf2} and are compared with the predicted star-forming X-ray galaxy luminosity function derived by Georgantopoulos, Basilakos Plionis (1999)."323 This is estimated by convolving the optical star-forming uminositv function with the opticaltoX-ray luminosity. relation., This is estimated by convolving the optical star-forming luminosity function with the optical–to–X-ray luminosity relation.324 The optical luminosity function has been derived rom the Πο et al. (, The optical luminosity function has been derived from the Ho et al. (3251997) spectroscopic sample of galaxies whereas the opticalto.X-ray luminosity relation is taken rom the sample of Fabbiano et al. (,1997) spectroscopic sample of galaxies whereas the optical–to–X-ray luminosity relation is taken from the sample of Fabbiano et al. (3261992).,1992).327 We also plot. the N-rav. luminosity function. derived. by orman et al (, We also plot the X-ray luminosity function derived by Norman et al. (3282004) by convolving the ‘warm’ LAS uminositv function. (Takeuchi et al.,2004) by convolving the 'warm' IRAS luminosity function (Takeuchi et al.329 2003) with the luminosity relation for star-forming ealaxies (Ranalli et al., 2003) with the luminosity relation for star-forming galaxies (Ranalli et al.330 2003)., 2003).331 In Table 4 we summarise the best-fit parameters for the slope and the break luminosity as well as the normalization derived from the maximum likelihood method., In Table \ref{lf} we summarise the best-fit parameters for the slope and the break luminosity as well as the normalization derived from the maximum likelihood method.332 In the same table we give the X-ray emissivity. (Luminosity per Alpe?) as well as the fractional contribution to the 0.5-8 keV. X-ray background., In the same table we give the X-ray emissivity (luminosity per $\rm Mpc^3$ ) as well as the fractional contribution to the 0.5-8 keV X-ray background.333 The integrated galaxy X-ray [lux is given by We integrate all luminosities fron 107eres1 to infinity up to to à maximum recdshift of =2.," The integrated galaxy X-ray flux is given by We integrate all luminosities from $10^{38}\rm \, erg \, s^{-1}$ to infinity up to to a maximum redshift of $z=2$."334 We have assumed an energy. spectral index of Vy=OT (eig. Zezas. CGeorgantopoulos Ware 1998).," We have assumed an energy spectral index of $\alpha_x=0.7$ (e.g. Zezas, Georgantopoulos Ward 1998)."335 “Phe X-ray background intensity in the O.5-SkkeV bane is taken from Gendreau et al. (, The X-ray background intensity in the keV band is taken from Gendreau et al. (3361995).,1995).337 Phe X-ray Εαν sensitively depends on the assumed form of galaxy evolution., The X-ray flux sensitively depends on the assumed form of galaxy evolution.338 Hopkins (2004) combined the luminosity function information at many. wavelengths. from radio to XN-ravs and concluded that the luminosity. censity evolves as (1)2)? with p=3.3 for z<1. while for higher redshifts it appears to remain constant.," Hopkins (2004) combined the luminosity function information at many wavelengths, from radio to X-rays and concluded that the luminosity density evolves as $(1 + z)^{p}$ with $p=3.3$ for $z<1$, while for higher redshifts it appears to remain constant."339 Norman et al. (, Norman et al. (3402004) find a luminosity evolution consistent with p=2.7 at X-ray wavelengths up to their maximum redshift of z1. close to the value derived by Llopkins (2004).,"2004) find a luminosity evolution consistent with p=2.7 at X-ray wavelengths up to their maximum redshift of $z\approx1$ , close to the value derived by Hopkins (2004)."341 In ‘Table 4.. we eive the contribution to the X-ray background (Z/£x58) Lor both evolution indices.," In Table \ref{lf}, we give the contribution to the X-ray background $I/I_{XRB}$ ) for both evolution indices."342" Phe errors for both j, and {ένας are estimated in the same manner as the uncertainties in ó,.", The errors for both $j_x$ and $I/I_{XRB}$ are estimated in the same manner as the uncertainties in $\phi_\star$.343" We use a total of 70 fields overlapping with he SDSS-DR2 to compile a sample of 28 X-ray. selected ""normal galaxies with z<0.22.", We use a total of 70 fields overlapping with the SDSS-DR2 to compile a sample of 28 X-ray selected `normal' galaxies with $z<0.22$.344" These systems have X-ravtooptical Hux ratios (logfi/f.)κ 2). luminositios (Ly<10eres ty, X-ray. colours and optical spectroscopic sroperties (available for most of our sources) all suggesting X-ray emission dominated by stellar processes (hot gas and X-ray binaries) rather than accretion on a supermassive slack hole."," These systems have X-ray--to--optical flux ratios $\log345(f_x / f_o) < -2$ ), luminosities $\rm L_X < 10^{42} erg \,346s^{-1}$ ), X-ray colours and optical spectroscopic properties (available for most of our sources) all suggesting X-ray emission dominated by stellar processes (hot gas and X-ray binaries) rather than accretion on a supermassive black hole."347 Using this carefully selected sample we construct he local (2S 0.2) X-ray luminosity function of ‘normal’ galaxies., Using this carefully selected sample we construct the local $z \la 0.2$ ) X-ray luminosity function of `normal' galaxies.348 Our survey nicely complements the deeper surveys in the coverage of the Lyz plane xobing lower redshifts and higher luminosities.," Our survey nicely complements the deeper surveys in the coverage of the $L_X -349z$ plane probing lower redshifts and higher luminosities."350" We combine he two samples. exploiting the depth of and the wide areal coverage of the NIIS. to provide a ""normal galaxy sample totaling 46 svstemis at 0.22."," We combine the two samples, exploiting the depth of and the wide areal coverage of the NHS, to provide a `normal' galaxy sample totaling 46 systems at $z<0.22$."351 We attempt to assess the clliciency of the logfif.)< criterion in selecting the most luminous normal galaxies., We attempt to assess the efficiency of the $\log(f_x/f_o)<-2$ criterion in selecting the most luminous normal galaxies.352 We use the star-forming galaxy sample compiled by Zezas (2001) which comprisesROSAL PSPC observations of systems Classified on the basis of high quality nuclear spectra from Llo οἱ al. (, We use the star-forming galaxy sample compiled by Zezas (2001) which comprises PSPC observations of systems classified on the basis of high quality nuclear spectra from Ho el al. (3531997).,1997).354 The above sample comprises 43 galaxies. cletected by PSPCcither as targets or," The above sample comprises 43 galaxies, detected by PSPCeither as targets or"355period.,period.356 In any case. the order of magnitude of such à period is compatible with an apparently motionless object on a timescale of a week.," In any case, the order of magnitude of such a period is compatible with an apparently motionless object on a timescale of a week."357 It is also possible to examine the data obtained before the outburst., It is also possible to examine the data obtained before the outburst.358 The best are those obtained with the ESO telescope on April 10. 1H and 12. 2003 (see ? for more details).," The best are those obtained with the ESO telescope on April 10, 11 and 12, 2003 (see \cite{rousselot:2005a} for more details)."359 We have coadded all these data (total integration time of 7.5 hours) and could not find any evidence of a satellite up to ij=26 (Fig. 10))., We have coadded all these data (total integration time of 7.5 hours) and could not find any evidence of a satellite up to $m_R\simeq 26$ (Fig. \ref{f:t360}) ).360 The apparent magnitude at the time of the observations corresponds to an absolute magnitude of 14.5. ie. to an upper diameter limit of 7 km (with a R geometric albedo of 0.04).," The apparent magnitude at the time of the observations corresponds to an absolute magnitude of 14.5, i.e. to an upper diameter limit of 7 km (with a R geometric albedo of 0.04)."361 Such an upper limit ts compatible with the one derived from the coma itself., Such an upper limit is compatible with the one derived from the coma itself.362 If the cometary activity presently observed 1s created by a satellite. two Issues remain unexplained: (1) what is the origin of the outburst (collision ?):," If the cometary activity presently observed is created by a satellite, two issues remain unexplained: (i) what is the origin of the outburst (collision ?);"363 and (11) why does it appear as a diffuse source ?, and (ii) why does it appear as a diffuse source ?364 Other investigators (?) have also pointed out the apparent random motion of this source on the timescale of several months. on the basis of their own observations.," Other investigators \citep{weissman:2006} have also pointed out the apparent random motion of this source on the timescale of several months, on the basis of their own observations."365 If such a random motion is confirmed it would exclude the satellite hypothesis., If such a random motion is confirmed it would exclude the satellite hypothesis.366 Finally. the more realistic explanation remains that Echeclus has ejected a fragment.," Finally, the more realistic explanation remains that Echeclus has ejected a fragment."367 The reason for this ejection remains unclear. and is still to be investigated in. more detail.," The reason for this ejection remains unclear, and is still to be investigated in more detail."368 This fragment has probably suffered a disintegration process., This fragment has probably suffered a disintegration process.369 The mechanism responsible for the outburst is probably not a simple impact that would have thrown off dust particules because it would not have lasted several months and some changes would have been apparent at the timescale of a week., The mechanism responsible for the outburst is probably not a simple impact that would have thrown off dust particules because it would not have lasted several months and some changes would have been apparent at the timescale of a week.370 As for other similar events observed at large heliocentric distances. à more complex process probably occured.," As for other similar events observed at large heliocentric distances, a more complex process probably occured."371 It can be either a activity or driven by an amorphous — crystalline phase transition for water ice., It can be either a CO-driven activity or driven by an amorphous $\rightarrow$ crystalline phase transition for water ice.372 The onset of activity was probably triggered by an unknown external phenomenon because it did not occur at the smallest heliocentric distance., The onset of activity was probably triggered by an unknown external phenomenon because it did not occur at the smallest heliocentric distance.373 It is also important to point out that the 2007 observations. which did not permit to detect any activity. were performed at a smaller heliocentric distance.," It is also important to point out that the 2007 observations, which did not permit to detect any activity, were performed at a smaller heliocentric distance."374 The Centaur (60558) Echeclus. renamed 174P/Echeclus after the discovery of an important cometary outburst. has been observed with FORS | at VLT.," The Centaur (60558) Echeclus, renamed 174P/Echeclus after the discovery of an important cometary outburst, has been observed with FORS 1 at VLT."375 The main conclusions of our observations are: ο The source of cometary activity appears distinct from Echeclus itself (about 8 arscec. corresponding to a projected distance of about 60.000-70.000 km). and stable at the timescale of a week.," The main conclusions of our observations are: $\bullet$ The source of cometary activity appears distinct from Echeclus itself (about 8 arscec, corresponding to a projected distance of about 60,000-70,000 km), and stable at the timescale of a week."376 e The brightness distribution of this source does not follow that of a cometary coma created by a point-like source (cometary nucleus)., $\bullet$ The brightness distribution of this source does not follow that of a cometary coma created by a point-like source (cometary nucleus).377 It look likes a diffusesource., It look likes a diffusesource.378 e , $\bullet$ 379"In order to use the algorithm we choose a set of scales which are powers of two: s=2"" and the first. scale always corresponds to the size of 1. pixel.",In order to use the algorithm we choose a set of scales which are powers of two: $s=2^r$ and the first scale always corresponds to the size of 1 pixel.380 The scale s in this kind of analysis may be considered as the resolution., The scale $s$ in this kind of analysis may be considered as the resolution.381 In other words. if we perform a calculation on a scale su. we expect the wavelet transform to be sensitive to structures with tvpical size of about sy and to be able to reveal them.," In other words, if we perform a calculation on a scale $s_0$, we expect the wavelet transform to be sensitive to structures with typical size of about $s_0$ and to be able to reveal them."382 The first step of the wavelet matrices computation is the evaluation of the coellicient e(0)., The first step of the wavelet matrices computation is the evaluation of the coefficient $c(0)$.383 This is defined as: On the other scales the coelficients e are given by: Since the function © satisfies: for />0. we can write: where fin)=l6έν. CI being the binomial coellicients.," This is defined as: On the other scales the coefficients $c$ are given by: Since the function $\phi$ satisfies: for $i \ge 0$, we can write: where $h(n)=\frac{1}{16} C^4_{2-n}$, $C^{m}_{n}$ being the binomial coefficients."384 Using to eqs.1. and 8 we can write the following expression for the wavelet coefficients on the various scales: The wavelet analysis associates to each pixel a real number. which represents the smoothed local density contrast at a given scale.," Using to \ref{eq1} and \ref{eq:atrous} we can write the following expression for the wavelet coefficients on the various scales: The wavelet analysis associates to each pixel a real number, which represents the smoothed local density contrast at a given scale."385 At the end of this part our result is à set of matrices of wavelet. cocllicients: One matrix. [or cach scale investigated., At the end of this part our result is a set of matrices of wavelet coefficients; one matrix for each scale investigated.386 Even if the histogram> of the wavelet coellicicnts may suggest the presence of substructure. revealed by asvmmetries between the positive and negative parts of the probability distributions (see e.g. figs.," Even if the histogram of the wavelet coefficients may suggest the presence of substructure, revealed by asymmetries between the positive and negative parts of the probability distributions (see e.g. figs."387 2-4 in GPAD). this kind of information is only visual and not easily quaatifiable and spatially localizable.," 2-4 in GPAB), this kind of information is only visual and not easily quantifiable and spatially localizable."388 The thresholding is made on the wavelet coellicient histogram., The thresholding is made on the wavelet coefficient histogram.389 Lor an ideal Uat background. the wavelet transform coefficients. should be equal ο zero.," For an ideal flat background, the wavelet transform coefficients should be equal to zero."390 “Phe existence of structures at a given. seale gives wavelet coefficient with large positive values., The existence of structures at a given scale gives wavelet coefficient with large positive values.391 Lt is however quite obvious that this is strictly true only in an ideal case: a random distribution may have non-zero cocllicicnts even if there are no structures. due to statistical Uuctuations.," It is however quite obvious that this is strictly true only in an ideal case: a random distribution may have non-zero coefficients even if there are no structures, due to statistical fluctuations."392 Moreover. the statistical behaviour of the wavelet coellicient is complex due to the correlation among nearby. In order to decide whether a structure detected on a given scale we need to fix a significance threshold.," Moreover, the statistical behaviour of the wavelet coefficient is complex due to the correlation among nearby In order to decide whether a structure detected on a given scale we need to fix a significance threshold."393 We choose it through a classical decision rule., We choose it through a classical decision rule.394 We calculate the wavelet coefficients. (768) for each scale of our analysis. for a random distribution in the same region of space of our data and on the same grid.," We calculate the wavelet coefficients $w_{ran}(s)$ for each scale of our analysis, for a random distribution in the same region of space of our data and on the same grid."395 Then we calculate the probability Pae(s)Sνα(51 and choose the value wiis(8) so that: Our threshold) on the scale. 5 is the value Wihres(S)., Then we calculate the probability $P[w(s) \le w_{ran}(s)]$ and choose the value $w_{thres}(s)$ so that: Our threshold on the scale $s$ is the value $\nu_{thres} = w_{thres}(s)$ .396 For example. a choice for the value of € of: ensures a 99.94 confidence level in the structure detection.," For example, a choice for the value of $\epsilon$ of: ensures a $99.9 \%$ confidence level in the structure detection."397 We have also explored. the consequences of an alternative choice for the treshold. ic. to fix it in terms of a eiven number of standard deviations from the variance. but the final results are insensitive to this choices.," We have also explored the consequences of an alternative choice for the treshold, i.e. to fix it in terms of a given number of standard deviations from the variance, but the final results are insensitive to this choices."398 The second step of our analvsis is the. determination of connected: pixels over a fixed. threshold.(segmenlalion. ltosenfeld (1969))). the numbering of the selected structures and their morphological analysis.," The second step of our analysis is the determination of connected pixels over a fixed threshold, Rosenfeld \shortcite{rose}) ), the numbering of the selected structures and their morphological analysis."399 The segmentation and numbering consists in the exam of the wavelet coellicients matrix: all the pixels associated with a wavelet cocllicicnt greater than the selected threshold are labelled with an integer number., The segmentation and numbering consists in the exam of the wavelet coefficients matrix; all the pixels associated with a wavelet coefficient greater than the selected threshold are labelled with an integer number.400 AL other pixel labels are set equal to zero., All other pixel labels are set equal to zero.401 Then. the same label is associated with all the pixels connected in a single structure. in a sequential way.," Then, the same label is associated with all the pixels connected in a single structure, in a sequential way."402 So. the first. structure individuated bears the label 1 and so on.," So, the first structure individuated bears the label '1' and so on."403 We also compute the volume and surface of each structure found., We also compute the volume and surface of each structure found.404 In order to perform a morphological analvsis we have to introduce a morphological parameter that quantifies the sphericity of the structures., In order to perform a morphological analysis we have to introduce a morphological parameter that quantifies the sphericity of the structures.405 We choose the parameter:, We choose the parameter:406"Deep observations of nearby galaxies have uncovered a wealth of faint streams, shells and other ςgrremgalaetistructuresác 2010).","Deep observations of nearby galaxies have uncovered a wealth of faint circumgalactic streams, shells and other structures \citep[e.g.][]{McConnachie09, MD10}."407". Such features are a natural occurrence in cold dark matter cosmogony, in which the dark haloes hosting (CDM)massive galaxies continually accrete and disrupt their smaller companions."," Such features are a natural occurrence in the cold dark matter (CDM) cosmogony, in which the dark haloes hosting massive galaxies continually accrete and disrupt their smaller companions."408 hereafterC10) have carried out ultra-high resolution simulations of this process using six N-body models of Milky Way-mass dark matter haloes from the Aquarius project et(Springelal.]2008]., \citet[][hereafter C10]{Cooper10} have carried out ultra-high resolution simulations of this process using six N-body models of Milky Way-mass dark matter haloes from the Aquarius project \citep{Springel08}.409". Using the semi-analytic model of galaxy formation to calculate the epoch and location of star formation in the simulation, C10 tagged dark matter particles in appropriate regions of phase-space to follow the dynamical evolution of stars stripped from the progenitors of these haloes."," Using the semi-analytic model of galaxy formation to calculate the epoch and location of star formation in the simulation, C10 tagged dark matter particles in appropriate regions of phase-space to follow the dynamical evolution of stars stripped from the progenitors of these haloes."410" In this way, they were able to model the build-up of galactic stellar haloes through the tidal disruption of satellite galaxies."," In this way, they were able to model the build-up of galactic stellar haloes through the tidal disruption of satellite galaxies."411" In this paper, we present a from one of the six simulations of C10 (Aq-F-2)."," In this paper, we present a from one of the six simulations of C10 (Aq-F-2)."412 The movie is a compelling illustration of the complexity and dynamism of structure formation inCDM., The movie is a compelling illustration of the complexity and dynamism of structure formation in.413". Because of this complexity, full cosmological modeling is essential — a conclusion emphasized by our movie."," Because of this complexity, full cosmological modeling is essential – a conclusion emphasized by our movie."414 The stellar halo of Aq-F-2 contains an extensive system of interleaved ‘shells’., The stellar halo of Aq-F-2 contains an extensive system of interleaved `shells'.415 Examples of stellar haloes with distinctive have been known for decades (ee(c.g.[ArpI066morphologyMalin& and their fainter seem to common in the Carten[1953)local universe (e.g.analogsMartinez-Delgado=aeetal.010] 2009).," Examples of stellar haloes with this distinctive morphology have been known for decades \citep[e.g.][]{Arp66,Malin83} and their fainter analogs seem to be common in the local universe \citep[e.g.][]{MD10,Tal09}."416" In this we present a new deep [Τα]panoramicetal] image of the diffuse light around one such galaxy, NGC 7600, showing"," In this paper we present a new deep panoramic image of the diffuse light around one such galaxy, NGC 7600, showing"417ccubes that were cleaned but did not have the ccomponents added to them.,cubes that were cleaned but did not have the components added to them.418" These integrated maps have not been corrected for primary-beam attenuation and for the ddata, no residual scaling has been applied."," These integrated maps have not been corrected for primary-beam attenuation and for the data, no residual scaling has been applied."419 The masking applied to the integrated maps hides the signature of the clean bowl seen in the channel maps of the ddata in Figures 4 to 6.., The masking applied to the integrated maps hides the signature of the clean bowl seen in the channel maps of the data in Figures \ref{fig:ngc2403-chanmaps} to \ref{fig:ic2574-chanmaps}.420" The residual integrated mmaps in Figures 7 to 9 do show a significant pedestal of uncleaned flux, while the rresidual maps have no such feature."," The residual integrated maps in Figures \ref{fig:ngc2403-msclean-mom0} to \ref{fig:ic2574-msclean-mom0} do show a significant pedestal of uncleaned flux, while the residual maps have no such feature."421" There is trace source emission in the rresidual integrated maps, but generally the residuals are much more 'noise-like'."," There is trace source emission in the residual integrated maps, but generally the residuals are much more `noise-like'."422" Despite being on the same flux scale, there is a definite visual difference between the aand ddata, most clearly seen where there is significant source flux (the darker regions) in Holmberg II and IC 2574."," Despite being on the same flux scale, there is a definite visual difference between the and data, most clearly seen where there is significant source flux (the darker regions) in Holmberg II and IC 2574."423 Conversely the low-level extended structure is more clearly seen in the iintegrated maps and extends out to the mask boundary., Conversely the low-level extended structure is more clearly seen in the integrated maps and extends out to the mask boundary.424" The peak flux for compact features is therefore higher in the iintegrated images, while the total flux of the underlying, extended structure is greater inM"," The peak flux for compact features is therefore higher in the integrated images, while the total flux of the underlying, extended structure is greater in."425"SCLEAN.. To the flux scales between the data-sets, contour lines of column density 1-10?! and 2-10?! cm""? have been plotted on the compare(residual scaled) aand ddata for each galaxy, shown in Figures 10,, 11 and 12.."," To compare the flux scales between the data-sets, contour lines of column density $1\cdot10^{21}$ and $2\cdot10^{21}$ $^{-2}$ have been plotted on the (residual scaled) and data for each galaxy, shown in Figures \ref{fig:ngc2403-fluxcomp}, \ref{fig:hol2-fluxcomp} and \ref{fig:ic2574-fluxcomp}."426" Again, this data has been masked and corrected for primary-beam attenuation."," Again, this data has been masked and corrected for primary-beam attenuation."427" The location of the contours match closely across the aand ddata, but they appear much smoother in the ddata."," The location of the contours match closely across the and data, but they appear much smoother in the data."428 The contours in the iimages for each galaxy appears to trace a much finer structure boundary., The contours in the images for each galaxy appears to trace a much finer structure boundary.429 This is likely due to the pedestal of leftover flux in classicalCLEAN., This is likely due to the pedestal of leftover flux in classical.430". The pedestal still has the dirty beam as its PSF, the more extended wings of this beam will wash out structure more severely than a Gaussian beam, and the low-level, small-scale structure will be lost in the image."," The pedestal still has the dirty beam as its PSF, the more extended wings of this beam will wash out structure more severely than a Gaussian beam, and the low-level, small-scale structure will be lost in the image."431" For low-level column densities the rresolution is thus worse than one would expect on the basis of the clean beam size, as we will show later."," For low-level column densities the resolution is thus worse than one would expect on the basis of the clean beam size, as we will show later."432" In tthere is no pedestal, and all fine-scale structure is imaged at the full resolution of the clean beam, enhancing the detailed structures in the disk."," In there is no pedestal, and all fine-scale structure is imaged at the full resolution of the clean beam, enhancing the detailed structures in the disk."433hhas brighteued.,has brightened.434 We interpret this diffuse feature as a liebt echo from the trausieut. which allows us to constraiu the peak lhunuinositv of the outburst.," We interpret this diffuse feature as a light echo from the transient, which allows us to constrain the peak luminosity of the outburst."435 Finally. we compare the enerectics of the X-ray aud radio outburst. iu order to understand how accretion proceeds m this remarkable example of a faint A-ray trausicut.," Finally, we compare the energetics of the X-ray and radio outburst, in order to understand how accretion proceeds in this remarkable example of a faint X-ray transient."436 The N&-rav Observatory has observed the iuner oof the Galaxy with the Advanced CCD Tmagine Spectrometer imaging array (ACTS-I:Weisskopfetal.2002) at least once a vear between 1999 aud 2001 (Table1:2005)., The X-ray Observatory has observed the inner of the Galaxy with the Advanced CCD Imaging Spectrometer imaging array \citep[ACIS-I;][]{wei02} at least once a year between 1999 and 2004 \citep[Table~\ref{tab:obs};.437" As mentioned in Munoetal.(2005)... a new trausieut source,200031... was identified 2799 south of dduring 99 ks of observatious on 2001 July 57 (Fie. 1))."," As mentioned in \citet{mun05}, a new transient source, was identified 9 south of during 99 ks of observations on 2004 July 5–7 (Fig. \ref{fig:img}) ),"438 and curing 5 ks of directors discretionary observations on 2001 Aneust 28., and during 5 ks of director's discretionary observations on 2004 August 28.439 We obtained another 5 ks observation of the field on 2005 February 27. which we report here for the first time.," We obtained another 5 ks observation of the field on 2005 February 27, which we report here for the first time."440 Each observation las been processed using the techniques described in Munoctal.(2003a)., Each observation has been processed using the techniques described in \citet{mun03a}.441. Iu. brict. for cach observation we corrected the pulse heights ofthe events for position-dependecut charge-trausfer incficicucy (Townsleyetal.20025)... excluded eveuts that dic not pass the standard ASCA erade filters and AN-aav center (CNC) eoocd-time filters. aud removed intervals during which the backeround rate flared to =30 above the mean level.," In brief, for each observation we corrected the pulse heights ofthe events for position-dependent charge-transfer inefficiency \citep{tow02b}, excluded events that did not pass the standard ASCA grade filters and X-ray center (CXC) good-time filters, and removed intervals during which the background rate flared to $\ge 3\sigma$ above the mean level."442 Finalv. we applied a correction to the absolute astrometry cft cach pointing using three Tycho sources detected stroely in cach oobservation (Daganoffctal.2003).," Finally, we applied a correction to the absolute astrometry of each pointing using three Tycho sources detected strongly in each observation \citep[][]{bag03}."443 We estimated combined accuracy of our astrometric frame and of the positions of the individual X-ray sources by comparing the offsets between 36 foreground X-ray sources that were located within oof citepiuunüJa and their counterparts from the 2\TASS catalog., We estimated combined accuracy of our astrometric frame and of the positions of the individual X-ray sources by comparing the offsets between 36 foreground X-ray sources that were located within of \\citep{mun03a} and their counterparts from the 2MASS catalog.444" The rms dispersion in the offsets was 07225,", The rms dispersion in the offsets was 25.445 We conclude that the positious of individual X-ray sources are accurate to 0733 with confidence., We conclude that the positions of individual X-ray sources are accurate to 3 with confidence.446 The image of the 20’ around Hs displaved im Figure 1., The image of the $\times$ around is displayed in Figure \ref{fig:img}.447 The location of ds a=2667 111680. d— 292000861 (0733: T2000).," The location of is $\alpha$ 41680, $\delta$ 00861 $\pm$ 3; J2000)."448 luspection of the fleure reveals that the appearauce of the trausieut was accompanied by a factor of two merease in the flux of the diffuse N-rav cussion ssouth of the trausicut., Inspection of the figure reveals that the appearance of the transient was accompanied by a factor of two increase in the flux of the diffuse X-ray emission south of the transient.449 The region is indicated by the white cllipse., The region is indicated by the white ellipse.450 In order to understand the uature of290031.. we analyzed the light curve and spectrum for Hin the 0.58.0 keV band using the acis_cextract routine frou the Tools for N-rav Analysis md CIAO version 3.0.2.," In order to understand the nature of, we analyzed the light curve and spectrum for in the 0.5–8.0 keV band using the extract routine from the Tools for X-ray Analysis and CIAO version 3.0.2."451 From cach observation. we first extracted events associated with the source from a circular region that cuclosed of the point spread function.," From each observation, we first extracted events associated with the source from a circular region that enclosed of the point spread function."452" The reeion lad a radius of z1""..", The region had a radius of $\approx$.453 Then we extracted background eveut lists for cach observation frou larger circular regions centered ou 290031.. excluding from the event list," Then we extracted background event lists for each observation from larger circular regions centered on , excluding from the event list"454models to the prediction the models eive for the mass loss rate.,models to the prediction the models give for the mass loss rate.455 For the standard evaporation model. we adopt the mass loss rate &26908.(Cp)?mInA. presented by (2001).. as thev explicilly give this rate constant for their solution.," For the standard evaporation model, we adopt the mass loss rate $k = 269 \xi_e (G \bar{\rho})^{1/2} m \ln \Lambda$, presented by \citet{FZ}, as they explicitly give this rate constant for their solution."456 Our simplification of ihe Daumgardt&Makino.(2003) model makes it difficult to test that model., Our simplification of the \citet{BM} model makes it difficult to test that model.457 We can derive the expected rate from (he Lamersοἱal.(2005). disruption Gime. which vields To ⋅ ," We can derive the expected rate from the \citet{Lamers} disruption time, which yields $k =458\frac{\bar{\rho}^{1/2}}{0.62 C_{env}} (10^4)^{0.62}$ ."459"compare (hese rates with our∙ best fit values.cc we have assumed a constant density lor all of our clusters based on the M87 mass profile Hom Vesperini etal.(2003).. calculated at our median galactocentric distance (2,=4.4kpc)."," To compare these rates with our best fit values, we have assumed a constant density for all of our clusters based on the M87 mass profile from \citet{Vesperini}, calculated at our median galactocentric distance $R_g = 4.4$ kpc)."460 For (he evaporation model. the best fitng mass loss rate is consistent with that expected from theoretical ealeulations.," For the evaporation model, the best fitting mass loss rate is consistent with that expected from theoretical calculations."461" We find that the fit of the Lamersetal.(2005) model to our AIST data requires a value of ων=720 in their notation. which is close to the value of C,=SLO they derive [roin the Daunmegardt&Makino(2003). disruption (ime."," We find that the fit of the \citet{Lamers} model to our M87 data requires a value of $C_{env} = 720$ in their notation, which is close to the value of $C_{env} = 810$ they derive from the \citet{BM} disruption time."462 Somewhat lower values of C4. which vields a faster disruption (ümescale. can be accommodated by using lower mass to light ratios to convert the eluster luminosities into masses.," Somewhat lower values of $C_{env}$, which yields a faster disruption timescale, can be accommodated by using lower mass to light ratios to convert the cluster luminosities into masses."463" ILowever. even including anv uncertainties in our mass (o light ratio. our data are clearly inconsistent. with some of the smallest values (C,~ 300) suggested by Lamersetal.(2005). based on their analvsis of voung cluster svstems."," However, even including any uncertainties in our mass to light ratio, our data are clearly inconsistent with some of the smallest values $C_{env} \sim464300$ ) suggested by \citet{Lamers} based on their analysis of young cluster systems."465 This shows (hat mass loss rates for two-body processes in fully relaxed old clusters can not be extrapolated from unrelaxed voung svstems., This shows that mass loss rates for two-body processes in fully relaxed old clusters can not be extrapolated from unrelaxed young systems.466 One further effect is that toward the end of a globular clusters lifetime. mass segregation has moved the lowest mass stars to the outer edges of the cluster.," One further effect is that toward the end of a globular cluster's lifetime, mass segregation has moved the lowest mass stars to the outer edges of the cluster."467 These low mass stars are then prelerenGally stripped Grom the cluster. as (hey ave less tightly bound.," These low mass stars are then preferentially stripped from the cluster, as they are less tightly bound."468 This tends to decrease the AZ/L ratio of the cluster at the end of its life. as these low mass stars contribute more mass to the cluster than light.," This tends to decrease the $M / L$ ratio of the cluster at the end of its life, as these low mass stars contribute more mass to the cluster than light."469 Since the globular cluster mass function is based on observations of the cluster lisht. using a constant M/L ratio [ον all clusters overestimates the mass of these faintest clusters.," Since the globular cluster mass function is based on observations of the cluster light, using a constant $M / L$ ratio for all clusters overestimates the mass of these faintest clusters."470 We may see evidence for (his effect. as our lowest mass bin falls below all of the model predictions.," We may see evidence for this effect, as our lowest mass bin falls below all of the model predictions."471 Anv correction for such a changing M/L ratio will serve to spread our lowest mass bin {ο even lower masses. which will tend (ο bring the result into agreement with the predictions of the evaporation moclel.," Any correction for such a changing $M / L$ ratio will serve to spread our lowest mass bin to even lower masses, which will tend to bring the result into agreement with the predictions of the evaporation model."472 Previous studies have probed bevond (he turnover of the elobular cluster luminosity function. vel none have reached the same depth as our new Duminosity [unction lor MS8T.," Previous studies have probed beyond the turnover of the globular cluster luminosity function, yet none have reached the same depth as our new luminosity function for M87."473 This new depth has allowed us to trace the effects of dvnamical evolution down to clusters that are in the last few Gyr of their lifetime. where the ellects of the mass loss are most severe.," This new depth has allowed us to trace the effects of dynamical evolution down to clusters that are in the last few Gyr of their lifetime, where the effects of the mass loss are most severe."474 The superior resolution offered by the data has also allowed us to establish that the, The superior resolution offered by the data has also allowed us to establish that the47524 color to be used as criterion to select AGN that dominateum the mid-IR emission.,24 $\micron$ color to be used as a criterion to select AGN that dominate the mid-IR emission.476"a Specifically, we exclude objects with log(fzo/fo4) « 0.22+0.7 (i.e., objects with enhanced 24 wm flux for a given 70 wm flux compared to the SEDs of star-forming galaxies), which removes 86 galaxies."," Specifically, we exclude objects with $_{70}$ $_{24}$ ) $<$ $0.2z +0.7$ (i.e., objects with enhanced 24 $\micron$ flux for a given 70 $\micron$ flux compared to the SEDs of star-forming galaxies), which removes 86 galaxies."477" Above 101??Lo,, the sample contains very few sources that do not harbor AGN or QSO."," Above $10^{12.5}$, the sample contains very few sources that do not harbor AGN or QSO."478 We limit our comparison sample to those with uncertainties in SED-fitted j0.35dextoavoidcomparingtoobjectswithuncertainluminosity., We limit our comparison sample to those with uncertainties in SED-fitted $<0.35$ dex to avoid comparing to objects with uncertain luminosity.479" Among the 1503 galaxies selected at 70 463 are detected at 160 um and their fluxes have been wm,included in"," Among the 1503 galaxies selected at 70 $\micron$, 463 are detected at 160 $\micron$ and their fluxes have been included in"480entire accretion phase.,entire accretion phase.481 The base pressure is independent of the temperature in the thiu-shell Init aud is Ε» ín_ t where AZ is the envelope mass," The base pressure is independent of the temperature in the thin-shell limit and is 	P_b = , where $M_{\rm env}$ is the envelope mass."482 This assumption will not be valid once the temperature rises during the thermonuclear runaway., This assumption will not be valid once the temperature rises during the thermonuclear runaway.483" For a 0.6Af. WD. fh~Rhen Ti,7.10°K."," For a $0.6 \ M_\odot$ WD, $h \simeq R$ when $T_b \simeq 7\E{8} \ {\rm K}$."484 We first estimate the Lbhuuimositv im the accreting laver following Nomoto(1982) and Towusley&Bild-«ten. (2001)., We first estimate the luminosity in the accreting layer following \cite{nom82} and \cite{tb04}.485.. When material accretes outo the WE surface. the gravitational energv. GAZZR. is released iux radiated by the spreading boundary laver (Piro&Bild-sten2001). and is not carried into the star. because the thermal timescale at the photosphere for hnuuinosities of order the accretion huuimositv is far shorter than the aceretion timescale.," When material accretes onto the WD surface, the gravitational energy, $GM/R$, is released and radiated by the spreading boundary layer \citep{pb04} and is not carried into the star, because the thermal timescale at the photosphere for luminosities of order the accretion luminosity is far shorter than the accretion timescale."486 Tustead. prior to the onset of unclear burning. the pre-iguition Wuuinosity exiting the deep accreting laver is produced by eutropy. released. as the material acctuuulates.," Instead, prior to the onset of nuclear burning, the pre-ignition luminosity exiting the deep accreting layer is produced by entropy released as the material accumulates."487 The eutropy equation viclds the compressional luminosity at the surface. = MpT4 dP. where s is the specific entropy. aud we have neglected the term: Gs ," The entropy equation yields the compressional luminosity at the surface, = T dP, where $s$ is the specific entropy, and we have neglected the term $ \left. \partial s / \partial t \right|_P$."488"The lower bound. 7"". is the depth at which the ορ.thermal time is equal to the time for which accretion has been on-going. so that the Iuninositv produced there las had time to make its way through the euvelope."," The lower bound, $P'$, is the depth at which the thermal time is equal to the time for which accretion has been on-going, so that the luminosity produced there has had time to make its way through the envelope."489" For illustration. we assmne Wramers’ opacity (6κpl 7/23. ideal eas (Px pf). and a constaut hnuuinositv above I"". so that DirxTio, "," For illustration, we assume Kramers' opacity $\kappa \propto \rho T^{-7/2}$ ), ideal gas $P \propto \rho T$ ), and a constant luminosity above $P'$ , so that $ P(r)^2 \propto T(r)^{17/2} $."490"An ideal gas has s= Kplu(T?/p)/pny,. which vields dsfdPτρμην."," An ideal gas has $ s = k_B \ln \lp T^{3/2} / \rho \rp / \mu m_p $ , which yields $ds/dP = -7k_B/17 \mu m_p P$."491" This gives — Ξ 0 ( ). where T"" is the temperature at P'. AL4 is the mass accretion rate in units of 10.5AL.yrft. and we have set p=0.6."," This gives = = 0.4 ( ), where $ T' $ is the temperature at $P'$, $ \dot{M}_{-8} $ is the mass accretion rate in units of $ 10^{-8} \ \smpy$, and we have set $\mu=0.6$."492 If the opacity is due to electron scattcring. the pre-factor becomes 3/2 iustead of 7/1. so the exact relation is only weakly depeudenut ou the form of raciative opacity.," If the opacity is due to electron scattering, the pre-factor becomes $ 3/2 $ instead of $7/4$, so the exact relation is only weakly dependent on the form of radiative opacity."493" The thermal time at Poisfu,—epMALLoom: where ep=ορμὴν is the specific heat at coustaut pressure for an ideal gas. AL. is the mass du the laver above P. aud we use a ouc-zoue approximation. OL/OM~Loa/M' (e.g.Paczvuski1983)."," The thermal time at $P'$ is$t_{\rm therm}' \equiv c_P T' M'_{\rm env} / L_{\rm comp}$, where $c_P = 5 k_B / 2 \mu m_p$ is the specific heat at constant pressure for an ideal gas, $M'_{\rm env}$ is the mass in the layer above $P'$, and we use a one-zone approximation, $ \partial L / \partial M \sim L_{\rm comp}/M' $ \citep[e.g.,][]{pac83}."494. The time to acerete an envelope mass Mag Is face—AtayM., The time to accrete an envelope mass $M_{\rm env}$ is $t_{\rm acc} \equiv M_{\rm env} / \dot{M}$.495 To find the depth frou: which Iuniuositv is able to /escape daring accretion. we set the two timescales equal aud use equation (2)). viclding Po~Py: ie. most of the Iuminositv in the envelope comes frou only the euvelope itself. and so we neglect the compressional hunuinositv from the core (see the appeudix of Townsley&Dildsteu200L for further discussion of the core’s role).," To find the depth from which luminosity is able to escape during accretion, we set the two timescales equal and use equation \ref{eq:thinshell}) ), yielding $P' \simeq P_b$; i.e., most of the luminosity in the envelope comes from only the envelope itself, and so we neglect the compressional luminosity from the core (see the appendix of \citealt{tb04} for further discussion of the core's role)."496" Thus. the colupressional luminosity is given by equation (5)). with T’=T,,."," Thus, the compressional luminosity is given by equation \ref{eq:complum}) ), with $T'=T_b$ ."497" Using the radiative diffusion equation with Irmunuers opacity. H—K ""uon (phy where sgcNN1077 cur5 ! from. fitting⋅⋅ to OPAL. opacities (Telesias&Rogers1993.1996)— for solar composition around 7—10' K aud p=10"" οcm” we derive the temperature at the base of the accreting laver as a function of pp. T,= L373/11. where py=ppflO ο cm7."," Using the radiative diffusion equation with Kramers' opacity, = _0 ( where $\kappa_0 \simeq 10^{22}$ $^2$ $^{-1}$ from fitting to OPAL opacities \citep{ir93,ir96} for solar composition around $T=10^7$ K and $\rho=10^3$ g$^{-3}$, we derive the temperature at the base of the accreting layer as a function of $\rho_b$, 	T_b	= 1.37, where $ \rho_3 = \rho_b / 10^3 $ g $^{-3}$."498 We have assumed solar metallicity. but thisresult is ucarly independentof composition.," We have assumed solar metallicity, but thisresult is nearly independentof composition."499 The bottom of the laver follows the rajectorv given by equation (7)) uutil uuclear burniug )conies coniparable to compressional heating. i.c.. when Lan. Leo Where Lyne d8 the dhuuinosty xoduced. by nuclear burning.," The bottom of the layer follows the trajectory given by equation \ref{eq:traj}) ) until nuclear burning becomescomparable to compressional heating, i.e., when $L_{\rm nuc} \sim L_{\rm comp}$ , where $L_{\rm nuc}$ is the luminosity produced by nuclear burning."500" For highaccretion rates >10°ALvyο, Teburnine occurs via CNO reactions when base conditions reach Tj~2«10"" K and pucxMP ecuὉ (ignoring ""He burniug)."," For highaccretion rates $\geq 10^{-9} \ \smpy$, H-burning occurs via CNO reactions when base conditions reach $T_b \simeq 2\E{7}$ K and $\rho_b \simeq 10^3$ g $^{-3}$ (ignoring $^3$ He-burning)."501 If the accreting material las near-solar isotopic ratios. the most relevaut isotope is LC. since proton captires onto. EN. are slower than onto 1C. and ο does uot participate in the CNO evele at these temperatures.," If the accreting material has near-solar isotopic ratios, the most relevant isotope is $^{12}$ C, since proton captures onto $^{14}$ N are slower than onto $^{12}$ C, and $^{16}$ O does not participate in the CNO cycle at these temperatures."502" Moreover. p| reactions are προτα! at 7,2«10* I& because the lifetime of a proton with respect to sclfburuing is z10 times ouger than with respect to coustumption by °C nuclei."," Moreover, $p+p$ reactions are unimportant at $T_b \simeq 2\E{7}$ K because the lifetime of a proton with respect to self-burning is $\simeq 10$ times longer than with respect to consumption by $^{12}$ C nuclei."503 Thus. proton captures onto. !1?C will be the first non-weheible reaction.," Thus, proton captures onto $^{12}$ C will be the first non-negligible reaction."504 These are quickly followed by the decay of PN (with a half-life of του=603 s) and xotou captures onto DC (z[ timesmore rapid than onto ?C). so that we approximate the first nuclear reactions of interest as the conversion of °C to 1!N at he C proton capture rate.," These are quickly followed by the $\beta$ -decay of $^{13}$ N (with a half-life of $\tau_{1/2}=603$ s) and proton captures onto $^{13}$ C $\simeq 4$ timesmore rapid than onto $^{12}$ C), so that we approximate the first nuclear reactions of interest as the conversion of $^{12}$ C to $^{14}$ N at the $^{12}$ C proton capture rate."505"This reaction chain releases aspocific cuore XqoEq,=seslottNyo/l0 Pyeree ll ",This reaction chain releases a specific energy $ X_{12} E_{12} = 8.8\E{14} (X_{12}/10^{-3})$ erg $^{-1}$ .506Linear stability analysis (Fujimotoctal.1051) shows hat nuclear burniug is unstable iua coustaut-pressure hin shell if , Linear stability analysis \citep{fhm81} shows that nuclear burning is unstable ina constant-pressure thin shell if .507|IP - , |_P > .508"| IPs OY meμαςD€coolVeool: Where €yye is the nuclear οποιον generation rate. the one-zoue approximation to the cooling rate is έωω L/Atay. aud \= Olue/OluT|,."," |_P , or $ \epsilon_{\rm nuc} \chi_{\rm nuc} > \epsilon_{\rm cool} \chi_{\rm cool} $, where $ \epsilon_{\rm nuc}$ is the nuclear energy generation rate, the one-zone approximation to the cooling rate is $ \epsilon_{\rm cool} \sim L/M_{\rm env} $ , and $ \chi \equiv \left. \partial \ln \epsilon / \partial \ln T \right|_P $ ."509 For Kramers” opacity aud ideal gas. \eool= 17/2.," For Kramers' opacity and ideal gas, $ \chi_{\rm cool} = 17/2 $ ."510 The cooling rate is rewritten as, The cooling rate is rewritten as511For the static case of the coexistence of two gas phases. namely. clouds embedded in a HIM. the mass transfer according to heat conduction can be calculated analytically (CM77).,"For the static case of the coexistence of two gas phases, namely, clouds embedded in a HIM, the mass transfer according to heat conduction can be calculated analytically (CM77)."512 We have chosen plasma conditions that would require evaporation of cloud material and therefore mass loss from the cloud from analytical considerationsly., We have chosen plasma conditions that would require evaporation of cloud material and therefore mass loss from the cloud from analytical considerationsly.513 Under the dynamical action of a relative motion between the gas phases the conditions change with respect to the static case in two ways: Dynamical instabilities can change the shape of the cloud and ean increase its surface., Under the dynamical action of a relative motion between the gas phases the conditions change with respect to the static case in two ways: Dynamical instabilities can change the shape of the cloud and can increase its surface.514 In contrast to the analytical results. the state of the hot ISM remains constant because of its replenishment by the fixed streaming conditions and therefore cannot react to the evaporation and condensation process and by this e.g. self-regulate the mass transfer to find an equilibrium (see e.g. Kópppen et al.," In contrast to the analytical results, the state of the hot ISM remains constant because of its replenishment by the fixed streaming conditions and therefore cannot react to the evaporation and condensation process and by this e.g. self-regulate the mass transfer to find an equilibrium (see e.g. Köpppen et al."515 1998)., 1998).516 Large and massive clouds survive longer in the hot plasma flow with heat conduction than without., Large and massive clouds survive longer in the hot plasma flow with heat conduction than without.517 Because of electro invasion through the surface. a transition zone forms at the edge of the cloud where density and velocity gradients are lowered.," Because of electron invasion through the surface, a transition zone forms at the edge of the cloud where density and velocity gradients are lowered."518 A state can be reached where the KH instability 1$ suppressec and the formerly unstable cloud becomes stabilized., A state can be reached where the KH instability is suppressed and the formerly unstable cloud becomes stabilized.519 This cai be shown analytically and numerically reproduced (model U)., This can be shown analytically and numerically reproduced (model U).520 Since the evaporation rate is much less than the one predictec by CM77 these facts lead to a cloud mass at the end of the calculation that is even slightly higher (7%)) than in the case without heat conduction., Since the evaporation rate is much less than the one predicted by \cite{cm77} these facts lead to a cloud mass at the end of the calculation that is even slightly higher ) than in the case without heat conduction.521 Although the maximum cloud mass implied here is much lower than those of HVC complexes moving through the galactic halo with masses of a few 109 ; such as Complex C (Wakker et al. 1988)), Although the maximum cloud mass implied here is much lower than those of HVC complexes moving through the galactic halo with masses of a few $10^6$ $_{\sun}$ such as Complex C (Wakker et al. \cite{w88}) )522" or compact HVCs located in. the intergalactic medium (Braun&Burton 1999)), only clumpy substructures seem to decouple from complexes and approach the galactic disk and experience on their path through the halo interaction with the hot gas that leads to the observed head-tail structures (Briinsetal. 2000))."," or compact HVCs located in the intergalactic medium \cite{bb99}) ), only clumpy substructures seem to decouple from complexes and approach the galactic disk and experience on their path through the halo interaction with the hot gas that leads to the observed head-tail structures \cite{br00}) )."523 Their masses. on the other hand. range from a few umpteen solar masses to a few 10' M.. like recently found compact HVCs in the inner galaxy (Stiletal.2006)).," Their masses, on the other hand, range from a few umpteen solar masses to a few $^4$ $_{\sun}$, like recently found compact HVCs in the inner galaxy \cite{st06}) )."524 Nevertheless. calculations with even higher masses are in preparation but it can be expected that the tendency to stabilize the cloud and to reduce the ablation of material from the cloud will continue.," Nevertheless, calculations with even higher masses are in preparation but it can be expected that the tendency to stabilize the cloud and to reduce the ablation of material from the cloud will continue."525 Heat conduction is therefore a physical process that enhances the dynamical stabilization and has to be taken into account in the consideration of the survival of HVCs., Heat conduction is therefore a physical process that enhances the dynamical stabilization and has to be taken into account in the consideration of the survival of HVCs.526 For the PCCs. heat conduction offers a mechanism to incorporate metal-rich hot gas that becomes homogeneously mixed.," For the PCCs, heat conduction offers a mechanism to incorporate metal-rich hot gas that becomes homogeneously mixed."527 Even with a low accretion fraction of only a hot gas metal content of solar and above. which is reasonable ffrom X-ray determinations of the halo gas around giant ellipticals (Matsushitaetal. 2003)). would lead to almost 1/100 Z:.," Even with a low accretion fraction of only a hot gas metal content of solar and above, which is reasonable from X-ray determinations of the halo gas around giant ellipticals \cite{ma03}) ), would lead to almost 1/100 $_{\sun}$."528 Globular clusters formed from PCCs and enriched by this accretion nechanism caused by heat conduction must be expected to show a large range of metallicities., Globular clusters formed from PCCs and enriched by this accretion mechanism caused by heat conduction must be expected to show a large range of metallicities.529 When star formation sets 1n. all protostars are formed from molecular clouds with nearly equal metallicity.," When star formation sets in, all protostars are formed from molecular clouds with nearly equal metallicity."530 The absence of a significant spread in [Fe/H] in. most globular clusters (Freeman Norris 1981:: Fahlmann et al. 1985:;, The absence of a significant spread in [Fe/H] in most globular clusters (Freeman Norris \cite{fn81}; Fahlmann et al. \cite{frv85};531 Norris 1988)) is an indication that the stars have formed out of well mixed metal-enriched substrates that could have been polluted by an external source (Murray Lin 1990))., Norris \cite{n88}) ) is an indication that the stars have formed out of well mixed metal-enriched substrates that could have been polluted by an external source (Murray Lin \cite{ml90}) ).532 This mechanism provides an alternative. explanation to the. self-enrichment scenario of globular clusters (Brownetal.1991.. 1995)).," This mechanism provides an alternative explanation to the self-enrichment scenario of globular clusters \cite{br91}, \cite{br95}) )."533 When looking at smaller clouds one has to distinguish between a homogeneous (model K) and a clearly centrally peaked density. distribution (model E)., When looking at smaller clouds one has to distinguish between a homogeneous (model K) and a clearly centrally peaked density distribution (model E).534 In the latter case the gravitational potential is strong enough to stabilize the clouc against large-scale perturbations triggered by the dynamical action of the streaming ISM., In the latter case the gravitational potential is strong enough to stabilize the cloud against large-scale perturbations triggered by the dynamical action of the streaming ISM.535 The influence of the HIM is limited to an additional heat input due to heat conduction and small-scale mixing especially in regions near the vortex in the slipstream of the cloud., The influence of the HIM is limited to an additional heat input due to heat conduction and small-scale mixing especially in regions near the vortex in the slipstream of the cloud.536 Because of the high density in the core regions. the additional heat input is nearly compensatec," Because of the high density in the core regions, the additional heat input is nearly compensated"537out imdicate considerable evolution iu the SFR for. «1 although there is disagreement on the amount of evolution required.,out indicate considerable evolution in the SFR for $z<1$ although there is disagreement on the amount of evolution required.538 A complementary method has beeu to probe the far-infrared cussion of galaxies (LOjam«A300421) where dust-processed UV is re-cimitted thermally., A complementary method has been to probe the far-infrared emission of galaxies $10\micron<\lambda<300\micron$ ) where dust-processed UV is re-emitted thermally.539 At high redshifts this must be followed iuto the sub-nuni radio waveleugths., At high redshifts this must be followed into the sub-mm radio wavelengths.540 The cussion has been used to coustrain SER at low-redshift (Rowan-Robinsonetal.1997). and at high redshift (IDughesetal.1998) but this approach suffers roni both wncertainty in the dust modcling aud a lack of spectroscopic redshifts.," The emission has been used to constrain SFR at low-redshift \citep{rowan97} and at high redshift \citep{hughes98}541 but this approach suffers from both uncertainty in the dust modeling and a lack of spectroscopic redshifts."542 The latter issue ds addressed w fitting the spectral energy. distributions (SED) with a series of templates in order to photometrically estimate he redshifts. however there are huge degeucracics between he photometric redshift) cstimate and the assumed cluperature of the dust SED (Blainetal.2002).," The latter issue is addressed by fitting the spectral energy distributions (SED) with a series of templates in order to photometrically estimate the redshifts, however there are huge degeneracies between the photometric redshift estimate and the assumed temperature of the dust SED \citep{blain02}."543. All these approaches involve estimating a bDuninosity. either continui or lue. per galaxy and then multipling * the space density iu order to cive a hDnuninositv » colmoving volume.," All these approaches involve estimating a luminosity, either continuum or line, per galaxy and then multiplying by the space density in order to give a luminosity per comoving volume."544 At this point the scale factor. SER/Iumiuositv. which is where the main uucertainties arise. allows trausformation to SER per uuit volume.," At this point the scale factor, SFR/luminosity, which is where the main uncertainties arise, allows transformation to SFR per unit volume."545" The jieht budget CL VEdune ds aseful quantity because it allows the steματ οwission histxv of the Universe to be decoupled. iu aseie. from it «ανασα. historv cchauges in f1C Lluber of couποσα objects by processes such as galaxy forlation aud ealaxy-galaxy ΠΟΤΟ},"," The light budget per volume is a useful quantity because it allows the stellar emission history of the Universe to be decoupled, in a sense, from its dynamical history changes in the number of counted objects by processes such as galaxy formation and galaxy-galaxy merging)."546 This use of nusity density is a«ου method. iu which an obscyved uununositw censitv at a eiven redshift is converted toa SER deusitv at the same redshift.," This use of luminosity density is a method, in which an observed luminosity density at a given redshift is converted to a SFR density at the same redshift."547 Au alternative approach is that of fossil cosmology where the past history of the Universe is determined frou its current contents;, An alternative approach is that of fossil cosmology where the past history of the Universe is determined from its current contents.548 This can be done bv examining the resolved stellar populations in the Local Croup (Wopkinsetal.2001) or in eusenibles of galaxies. for example iu carly type galaxies (e.c. Bernardietal.(2002):Eisensteinetal.x (2002)3).," This can be done by examining the resolved stellar populations in the Local Group \citep{HIC01} or in ensembles of galaxies, for example in early type galaxies (e.g. \cite{Bernard02,eisenstein02}) )."549 Our approach is to look at the enscuible ofall ealaxies: the ‘Cosmic Optical Spectra of the local Universe., Our approach is to look at the ensemble of galaxies; the `Cosmic Optical Spectrum' of the local Universe.550 This represents the buuinositv-scaled spectra sununed over all galaxies., This represents the luminosity-scaled spectra summed over all galaxies.551 The cosmic spectruni cau be hought of as the total cmission from all the objects iu a representative volume of the Objects contribute to the cosmüc spectruni according to their uninositv., The cosmic spectrum can be thought of as the total emission from all the objects in a representative volume of the Objects contribute to the cosmic spectrum according to their luminosity.552 As in the case for an individual galaxy. this spectrum contains a huuinositv-woeiehted nux of features Your both old aud young aud we cau fit models of star-formation historv to it.," As in the case for an individual galaxy, this spectrum contains a luminosity-weighted mix of features from both old and young and we can fit models of star-formation history to it."553 In particular because the cosnie spectrum represents an average. it will represent he cud point of the average ΕΠ.," In particular because the cosmic spectrum represents an average, it will represent the end point of the average SFH."554 Thus we can fit much simpler models to the cosmic spectrmu than are required or the spectra of individual galaxies. since we expect the SFI history of the Universe. as a whole.," Thus we can fit much simpler models to the cosmic spectrum than are required for the spectra of individual galaxies, since we expect the SFH history of the Universe, as a whole."555 to vary simoothiy with time., to vary smoothly with time.556 This euseiible approach was applied by Baldryetal. (2002. hereafter DG02) to the cosmic spectrum (uicanine the optical spectrum per unit volume) of 0000 ealaxics in the 2dF Galaxy Redshift Survey (2dFCRS.Collessetal.2001) and derived coustraints ou allowable star-formation histories (SEII) which agreed well with results derived from direct ligh redshift mieasureiieuts via hunuinositv deusities.," This ensemble approach was applied by \citeauthor{BAL02} (2002, hereafter BG02) to the cosmic spectrum (meaning the optical spectrum per unit volume) of 000 galaxies in the 2dF Galaxy Redshift Survey \citep[2dFGRS,][]{GRS01} and derived constraints on allowable star-formation histories (SFH) which agreed well with results derived from direct high redshift measurements via luminosity densities."557 The Sloan Digital Sky Survey (SDSS.Yorketal.2000) provides many advantages over the 2dFCRS for this tvpe of analysis: it is of higher spectral resolution. (though we are not vet able to exploit this iu this paper) aud will beabout four tunes lareer upon completion.," The Sloan Digital Sky Survey \citep[SDSS,][]{SDSS} provides many advantages over the 2dFGRS for this type of analysis: it is of higher spectral resolution (though we are not yet able to exploit this in this paper) and will beabout four times larger upon completion."558 The spectral wavelength coverage is lareer (3600A<<A<συν for 2dFCRS aud 3800A<A9200A for SDSS)., The spectral wavelength coverage is larger $3600\rm\AA<\lambda<8000\AA$ for 2dFGRS and $3800\rm\AA<\lambda<9200\AA$ for SDSS).559 The photometric calibration is uch better as cach SDSS unilti-fber observation contains numerous παπαατα stars and can be individually calibrated. whereas for the 2dFGRS a mean calibration was applied to all the survey spectra.," The photometric calibration is much better as each SDSS multi-fiber observation contains numerous standard stars and can be individually calibrated, whereas for the 2dFGRS a mean calibration was applied to all the survey spectra."560 The excellent spectrophotometry is borne out bv the good agreement between svuthetic colors computed from the spectra aud actual colors which agree. in average spectra to «2% (Tremonti 2002. private columunication).," The excellent spectrophotometry is borne out by the good agreement between synthetic colors computed from the spectra and actual colors which agree, in average spectra to $<\pm 5$ (Tremonti 2002, private communication)."561 Also theaccurate five-color photometry allows comparisons of photometric coustraints with color constramts., Also theaccurate five-color photometry allows comparisons of photometric constraints with color constraints.562 In particular SDSS is selected im the à band (A=6200+GOOA)). whereas 24EQGRBS is selected in (A=1600+ 700A}).," In particular SDSS is selected in the $r$ band $\lambda = 6200\pm600$ ), whereas 2dFGRS is selected in $\lambda = 4600\pm 700$ )."563 Thus oιο would expect SDSS to be more biased toward old massive galaxies aud 2dFCRS to be biased toward vouug. star-forming galaxies.," Thus one would expect SDSS to be more biased toward old massive galaxies and 2dFGRS to be biased toward young, star-forming galaxies."564" The conrparison between the wo alows us to investigate the ""uncertainties in the determination of the SEIT.", The comparison between the two allows us to investigate the uncertainties in the determination of the SFH.565 Tn this paper we compite the| cosmic spectrum for the SDSS local volume. we nake :v direct comparison with that derived from 20FGBS by DGO2. aud we derive new coustraints on star-foriuation bLüstorv models from the SDSS spectrum.," In this paper we compute the cosmic spectrum for the SDSS local volume, we make a direct comparison with that derived from 2dFGRS by BG02, and we derive new constraints on star-formation history models from the SDSS spectrum."566 The plan of this paper is as follows., The plan of this paper is as follows.567 Iu Section 2. we describe the SDSS data aud our methods for combining the spectra to form cosmic spectra., In Section \ref{sec:data} we describe the SDSS data and our methods for combining the spectra to form cosmic spectra.568 Iu Section 3 we describe our iiodeliug aud fitting procedure and the outcome of the comparison of best fitting SEIT« between the SDSS aud 2dFCRS survevs., In Section \ref{sec:results} we describe our modeling and fitting procedure and the outcome of the comparison of best fitting SFHs between the SDSS and 2dFGRS surveys.569 We also test the consistency. of models of SEIT which form a lot of stars at 521., We also test the consistency of models of SFH which form a lot of stars at $z>1$.570 Iu Section 1. we generate an absolute cosmic spectrum which we show iu plivsical units., In Section \ref{sec:phys} we generate an absolute cosmic spectrum which we show in physical units.571 We usethis to estimate enissiou-liue Iuninositv densities aud the current SER density., We usethis to estimate emission-line luminosity densities and the current SFR density.572 Finally we give our sunny aud conclusions (Section 5))., Finally we give our summary and conclusions (Section \ref{sec:summary}) ).573" Throughout this paper we take My=Tülknis|Mpe1 Qj,—0.3 and O4,—0.7 for our cosinological quantities. and where appropriate. define h=ZIy/1001aus|Mpe.|."," Throughout this paper we take $H_0 = 70 \,{\rm km\,s^{-1}\,Mpc^{-1}}$, $\Omega_{m_0}=0.3$ and $\Omega_{\Lambda_0}=0.7$ for our cosmological quantities, and where appropriate, define $h = H_0 / 100\,{\rm574 km\,s^{-1}\,Mpc^{-1}}$."575 The Sloan Digital SkySurvey is a digital CCD survev iu 5 optical bands which intends to cover up to 0000 deg., The Sloan Digital SkySurvey is a digital CCD survey in 5 optical bands which intends to cover up to 000 $^2$.576 Au overview is eiven by Yorketal (2000)., An overview is given by \cite{SDSS}. .577. The Huaging camera is described by Camuetal.(1998).. the ügréz photometric system and calibration by Fukugita (1996).. Luptonetal. (1999).. Ποσοetal.(2001) and Sinithetal. (2002)...," The imaging camera is described by \cite{SDSSGunn}, the $ugriz$ photometric system and calibration by \cite{SDSSFuk}, , \cite{SDSSasinh}, , \cite{SDSSHogg} and \cite{SDSSSmith}. ."578 A laree fraction of SDSS data is currently available to the eutire astrouomical counumnumnnuitv (Stoughtonctal. 2002)., A large fraction of SDSS data is currently available to the entire astronomical community \citep{SDSSedr}. .579. The coordinate svstem isdefined to a precision of better than 0.1 arcsec (Pieretal. 2002).., The coordinate system isdefined to a precision of better than 0.1 arcsec \citep{SDSSAstrom}. .580In 1998 and 1999 two groups collecting far supernovae data presented evidence for an acceleration of the expansion of the universe. and consequently for a non-zero cosmological constant. based on the Hubble diagram of the SN Ia supernovae (Riessetal. 1998:; Perlmutteretal. 1999)).,"In 1998 and 1999 two groups collecting far supernovae data presented evidence for an acceleration of the expansion of the universe, and consequently for a non-zero cosmological constant, based on the Hubble diagram of the SN Ia supernovae \cite{Riess98}; ; \cite{Perlmutter}) )."581 Since these times published supernovae datasets have continuously increased and strengthened the case for an acceleration. of the expansion of the universe., Since these times published supernovae datasets have continuously increased and strengthened the case for an acceleration of the expansion of the universe.582 This has been corroborated by others data sets. (Friemanetal.2008:; Blanchard 2010))., This has been corroborated by others data sets \cite{FTH08}; \cite{Blanchard10}) ).583. Although. the cosmological constant is entirely consistent. with the detected acceleration. the addition of this term to the theory of general relativity has no known direct motivation.," Although the cosmological constant is entirely consistent with the detected acceleration, the addition of this term to the theory of general relativity has no known direct motivation."584 However. the cosmological constant can also be interpreted as arising from the vacuum contribution to the energy-momentum tensor.," However, the cosmological constant can also be interpreted as arising from the vacuum contribution to the energy-momentum tensor."585 Indeed. the contributions of the quantum fluctuations of all the fields filling the universe. provide a non-zero density to the vacuum and a negative pressure acting exactly as a cosmological constant.," Indeed, the contributions of the quantum fluctuations of all the fields filling the universe provide a non-zero density to the vacuum and a negative pressure acting exactly as a cosmological constant."586 However. such anticipated contribution from quantum fluctuations is many orders of magnitude larger than the presently observed value.," However, such anticipated contribution from quantum fluctuations is many orders of magnitude larger than the presently observed value."587 The low level of the energy scale of the cosmological constant Is therefore a mystery., The low level of the energy scale of the cosmological constant is therefore a mystery.588 Facing such a difficulty in understanding this discrepancy. one can consider the existence of some unknown mechanism that cancels the contribution from vacuum energy. and look for other physical components in the Universe that can produce an acceleration of the expansion.," Facing such a difficulty in understanding this discrepancy, one can consider the existence of some unknown mechanism that cancels the contribution from vacuum energy, and look for other physical components in the Universe that can produce an acceleration of the expansion."589" Motivated by these considerations. Ratra&Peebles(1988) showed that the presence of a dynamical scalar field. not exactly at rest (otherwise. it would behave exactly as a cosmological constant) can actually generate an accelerated expansion,"," Motivated by these considerations, \cite{RP88} showed that the presence of a dynamical scalar field, not exactly at rest (otherwise, it would behave exactly as a cosmological constant) can actually generate an accelerated expansion."590 This scenario. known as the quintessence paradigm. has received a lot of attention in recent years after the discovery of the acceleration.," This scenario, known as the quintessence paradigm, has received a lot of attention in recent years after the discovery of the acceleration."591 Other options have been proposed for its origin., Other options have been proposed for its origin.592 An attractive idea is the possibility that acceleration appears as a non-linear contribution from inhomogeneities (Buchert2008))., An attractive idea is the possibility that acceleration appears as a non-linear contribution from inhomogeneities \cite{Buchert2008}) ).593" However. no convineing arguments have been proposed to show that the actual contribution from these non-linearities can be brought to an observable level much above the naive expectation <7 107, nor that there is reason why this contribution could have a significant apparent ""negative pressure"" to actually produce an acceleration."," However, no convincing arguments have been proposed to show that the actual contribution from these non-linearities can be brought to an observable level much above the naive expectation $<h^2>\sim 10^{-10}$ , nor that there is reason why this contribution could have a significant apparent “negative pressure” to actually produce an acceleration."594 Another more radical option i$ to modify the equations of the general relativity (Cognolaetal.2006))., Another more radical option is to modify the equations of the general relativity \cite{Cognola}) ).595 However. adding new “exotic” components to the universe to obtain the acceleration is the most simple solution. and quintessence is natural in this context: in such models dark energy occurs from the late domination of some scalar field o.," However, adding new “exotic” components to the universe to obtain the acceleration is the most simple solution, and quintessence is natural in this context: in such models dark energy occurs from the late domination of some scalar field $\phi$."596 The canonical Lagrangian of such a scalar field is given by with X being the kinetic energy of the field and V(@) the potential., The canonical Lagrangian of such a scalar field is given by with $X$ being the kinetic energy of the field and $V(\phi)$ the potential.597 The equation governing the evolution of this homogeneous field in an expanding universe Is The stress-energy tensor has a form identical to that of an ideal fluid with pressure and density given by the two relations where x stands for à: ," The equation governing the evolution of this homogeneous field in an expanding universe is The stress-energy tensor has a form identical to that of an ideal fluid with pressure and density given by the two relations where $_{,X}$ stands for $\displaystyle \frac{\partial} {\partial X}$."598For a field which is spatially homogeneous the parameter w is defined from the equation of state which remainsgreater than -1. while the sound velocity," For a field which is spatially homogeneous the parameter $w$ is defined from the equation of state which remainsgreater than -1, while the sound velocity"599stronely magnetic.,strongly magnetic.600 In the Holberg.Oswalt&Sion(2002) sample 21 of the 109 local white dwarfs are magnetic. 19X ρου cent.," In the \citet{holberg2002} sample 21 of the 109 local white dwarfs are magnetic, $19\pm 4\,$ per cent."601 The latter is arguably close to volume- because all lie within 20 pe according to best distance estimates.," The latter is arguably close to volume-limited because all lie within $20\,$ pc according to best distance estimates."602 This distinction has been discussed. by Liebertetal.(2005). and by Wawkactal.(2007)., This distinction has been discussed by \citet{liebert2005} and by \citet{kawka2007}.603.. Both groups argue that the likely true frequeney of strong magnetism: in LIPAIWDs approaches or exceeds 10 per cent.," Both groups argue that the likely true frequency of strong magnetism in HFMWDs approaches or exceeds $10\,$ per cent."604 Llowever. given hat the SDSS is magnitude limited. we can conservatively estimate that we should. expect about 20. pre-magnetic cataclysmic variables in the sample of the 1.258 stars so ar observed but none have been found.," However, given that the SDSS is magnitude limited, we can conservatively estimate that we should expect about $25$ pre-magnetic cataclysmic variables in the sample of the $1{,}253$ stars so far observed but none have been found."605 AX svstematie elfect. that might have gone some wav owards explaining this discrepancy is the evidence that magnetic white clwarls tend to be more massive ancl hence ess luminous than nonmagnetic white cdwarfs., A systematic effect that might have gone some way towards explaining this discrepancy is the evidence that magnetic white dwarfs tend to be more massive and hence less luminous than nonmagnetic white dwarfs.606 Lichert(JOSS) first sumnmarised the evidence that several nearby magnetic white dwarfs with trigonometric parallaxes have relatively small racii ancl anomalously high. masses and. lie xdow the sequence of most white dwarfs in an Ht Diagraun., \citet{liebert1988} first summarised the evidence that several nearby magnetic white dwarfs with trigonometric parallaxes have relatively small radii and anomalously high masses and lie below the sequence of most white dwarfs in an HR Diagram.607 These objects include the well known 707 S247. C 227-35. € 240-72 and €D 229.," These objects include the well known $70^\circ$ 8247, G 227-35, G 240-72 and GD 229."608 Since then many more magnetic white chwarfs have been shown to be massive., Since then many more magnetic white dwarfs have been shown to be massive.609 However there is also evidence that many of them have more ordinary masses near 0.6AZ. or less.," However there is also evidence that many of them have more ordinary masses near $0.6\,M_{\odot}$ or less."610 The presence of a very strong Ποιά generally prevents any direct measurement of the mass through logg so that the mass estimates for magnetic white thwarts have been possible for only a small subset. of the known objects., The presence of a very strong field generally prevents any direct measurement of the mass through $\log g$ so that the mass estimates for magnetic white dwarfs have been possible for only a small subset of the known objects.611 Three methods have been used to estimate masses [ου suitable magnetic white chwarts., Three methods have been used to estimate masses for suitable magnetic white dwarfs.612 First. i£ the field strength is of order 15 MG or less. standard broadening theory applied to cach Zeeman component. vields an approximate surface eravity (πουexamplesinBergeron.Legectt&Ruiz2001).," First, if the field strength is of order $15\,$ MG or less, standard broadening theory applied to each Zeeman component yields an approximate surface gravity \citep[see examples613in][]{bergeron2001}."614. Secondly the measurement of a good-quality trigonomoetric parallax is a Κον way to measure the racius and Luminosity. of the magnetic star in comparison with the nonmagnetic white dwarfs., Secondly the measurement of a good-quality trigonometric parallax is a key way to measure the radius and luminosity of the magnetic star in comparison with the nonmagnetic white dwarfs.615 A third method has been applied to binary systems with a nonmagnetic DA paired with a magnetic white chvarl., A third method has been applied to binary systems with a nonmagnetic DA paired with a magnetic white dwarf.616 Phe spectrum of the magnetic component must be subtracted out if the binary is spatially unresolved., The spectrum of the magnetic component must be subtracted out if the binary is spatially unresolved.617 The fitting of the Balmer lines of the nonmagnetic object. to determine logg sets the distance to the svstem and allows comparison of the radii between the two components., The fitting of the Balmer lines of the nonmagnetic object to determine $\log g$ sets the distance to the system and allows comparison of the radii between the two components.618 Thus the mass estimates from these methods are not as accurate as those obtained for nonmagnetic objects with log g., Thus the mass estimates from these methods are not as accurate as those obtained for nonmagnetic objects with $\log g$ .619 The distribution of measured masses of HEMWDs (Ixzwvkaotal.2007) is shown in Fig., The distribution of measured masses of HFMWDs \citep{kawka2007} is shown in Fig.620 1 ancl compared with normal DA white cdwarfs in the SDSS sample (Ixepleretal. 2007)., \ref{mass} and compared with normal DA white dwarfs in the SDSS sample \citep{kepler2007}.621. The mean mass of the LIFAIWDs is 0.78Al. if we include the rather low mass helium white cwarls and O.S2AZ. if we exclude these stars.," The mean mass of the HFMWDs is $0.78\,M_{\odot}$ if we include the rather low mass helium white dwarfs and $0.82\,M_{\odot}$ if we exclude these stars."622 The mean mass is somewhat higher than the mean mass of 0.58AZ. of all white warfs and the radii are therefore typically smaller. than those of nonmagnetic white dwarls.," The mean mass is somewhat higher than the mean mass of $0.58\,M_{\odot}$ of all white dwarfs and the radii are therefore typically smaller than those of nonmagnetic white dwarfs."623 However the caleulations ol Silvestriet.al.(2007) show that a much larger mass iference ts required to explain the absence of any magnetic pre-CVs in terms of such a selection ellect., However the calculations of \citet{silvestri2007} show that a much larger mass difference is required to explain the absence of any magnetic pre-CVs in terms of such a selection effect.624 In addition the istribution of masses of HEPMWDs is broad so still includes a substantial fraction of low-mass stars., In addition the distribution of masses of HFMWDs is broad so still includes a substantial fraction of low-mass stars.625 There exists a small number of observed high field. MCVs hat have accretion rates much lower than expected for a semi-detached svstem (Webbink&Wickramasinghe2005)., There exists a small number of observed high field MCVs that have accretion rates much lower than expected for a semi-detached system \citep{webbink2005}.626. Thev are thought to be sulliciently close that the magnetic 1ο of the white dwarl can capture a weak stellar wind rom the companion., They are thought to be sufficiently close that the magnetic field of the white dwarf can capture a weak stellar wind from the companion.627 Phev have periods ranging from 1.3 o 4.39hr and magnetic fields from 42 to 65 MG. or so (Schmidtctal.2005.2007).," They have periods ranging from $1.3$ to $4.39\,$ hr and magnetic fields from $42$ to $65\,$ MG or so \citep{schmidt2005,schmidt2007}."628.. MI have low temperatures. 7.500<Digfy«13.000 and so have not recently emerged rom a common envelope.," All have low temperatures, $7{,}500629< T_{\rm eff}/{\rm K} < 13{,}000$ and so have not recently emerged from a common envelope."630 We propose that these. and systems like them. have emerged from the common envelope as very close pairs but must still wait for gravitational radiation to bring them close enough for Roche lobe overllow.," We propose that these, and systems like them, have emerged from the common envelope as very close pairs but must still wait for gravitational radiation to bring them close enough for Roche lobe overflow."631 Phev are the magnetic analogues of the normal pre-cataclysmic variables like W471 Tau with a period of ο. αν (Warner1995).," They are the magnetic analogues of the normal pre-cataclysmic variables like V471 Tau with a period of $6.9\,$ hr \citep{warner1995}."632. Phe narrow field range in which the LARPs have been found is a selection clleet related to the use of evelotron harmonics in their discovery in the SDSS sample., The narrow field range in which the LARPs have been found is a selection effect related to the use of cyclotron harmonics in their discovery in the SDSS sample.633 We expect that LARPs with magnetic fields over the entire intermediate polar to AM Ller range exist. and will be found in the future., We expect that LARPs with magnetic fields over the entire intermediate polar to AM Her range exist and will be found in the future.634 1n addition to the MCVs there are seven binary svstenis in which one star has a high magnetic field. [listed by Ixawkaetal.(2007) in their appendix., In addition to the MCVs there are seven binary systems in which one star has a high magnetic field listed by \citet{kawka2007} in their appendix.635 Four of these have been examined in more detail., Four of these have been examined in more detail.636 EUVE JO0317855 is thought to jwe evolved. from a triple svstem in which two of the stars merged to form the HEMWD (Ferrarioetal.1997)., EUVE J0317–855 is thought to have evolved from a triple system in which two of the stars merged to form the HFMWD \citep{ferrario97}.637.. G6246 shows evidence that it has emerged. [rom a Cl phase (Bergeron.Ruiz&Leggett1993). as two very. close white chvarts. one of which is highly magnetic and of very low mass. 25AL...," G62--46 shows evidence that it has emerged from a CE phase \citep{bergeron1993} as two very close white dwarfs, one of which is highly magnetic and of very low mass, $0.25\,M_\odot$."638 Similarly EUV 1439|75 is a close system that ws probably emerged. from a CL phase (Vennes.Ferrario&Wickramasinghe1909). às two close and massive white chvarts. one of which is highly magnetic.," Similarly EUVE 1439+75 is a close system that has probably emerged from a CE phase \citep{vennes1999} as two close and massive white dwarfs, one of which is highly magnetic."639 C141.2 (Bergeron.tug&LeeeettLOOT) has a mass of 0.26£0.12M. and so could only have formed in binary interaction.," G141–2 \citep{bergeron1997} has a mass of $0.26\pm 0.12\,M_\odot$ and so could only have formed in binary interaction."640 Thus there is no evidence that any ofthese HIEMWDs with degenerate companions must have formed without binary interactions., Thus there is no evidence that any of these HFMWDs with degenerate companions must have formed without binary interactions.641 Because the white dwarls in cataclysmic variables must have once been the cores of giants their binary orbits must have shrunk substantially from at least several hundred: solar radii. to accommocdate a giant. to only a few. so that the του. chwarl companions to the white cwarks now fill their Roche lobes.," Because the white dwarfs in cataclysmic variables must have once been the cores of giants their binary orbits must have shrunk substantially from at least several hundred solar radii, to accommodate a giant, to only a few, so that the red dwarf companions to the white dwarfs now fill their Roche lobes."642 The process leading to this is not understood at all well but is encapsulated in the common envelope (CI) evolution described by Paczváski(1976)., The process leading to this is not understood at all well but is encapsulated in the common envelope (CE) evolution described by \citet{paczynski1976}.643. When a giant star fills its Roche lobe. unstable mass transfer can lead a state in which the giant envelope surrounds the two dense cores. its own degenerate core and its companion.," When a giant star fills its Roche lobe, unstable mass transfer can lead a state in which the giant envelope surrounds the two dense cores, its own degenerate core and its companion."644 This companion is most likely an unevolved lower-mass main-sequence star but might itsell be already. a white dwarf., This companion is most likely an unevolved lower-mass main-sequence star but might itself be already a white dwarf.645 These two cores are then supposed tospiral together inside the CL while energy, These two cores are then supposed tospiral together inside the CE while energy646"and average the density fields (quantiles .r;. denoting either my) or 7j) where parameter averages are computed by summing over grid cells (j). subject to various ""cuts. on the IGM overdensity and gas temperature and. weighted by factors. wy). In the second calculation. we compare the local recombination rate to the global average recombination rate. averaged over density and temperature in cells. where again: Gr) denotes a weighted: average and ajj,G3)(D)⋉− is the case-D radiative−− recombination− rate coefficient [or hydrogen. as tabulated by Osterbrock & Ferland (2006).","and average the density fields (quantities $x_i$, denoting either $n_{\rm HII}$ or $n_{\rm HII}^2$ ) where parameter averages are computed by summing over grid cells $j$ ), subject to various “cuts” on the IGM overdensity and gas temperature and weighted by factors, $w_j$, In the second calculation, we compare the local recombination rate to the global average recombination rate, averaged over density and temperature in cells, where again $\langle x \rangle$ denotes a weighted average and $\alpha_H^{(B)} (T)$ is the case-B radiative recombination rate coefficient for hydrogen, as tabulated by Osterbrock & Ferland (2006)."647" We refer to this as the ""recombination rate"" (RR) method."," We refer to this as the “recombination rate"" (RR) method."648 Because the purpose of the clumping factor is to correct for an enhanced recombination rate. we believe Chi lo be a more appropriate representation.," Because the purpose of the clumping factor is to correct for an enhanced recombination rate, we believe $C_{\rm RR}$ to be a more appropriate representation."649 The recombinations (hat are important to removing ionizing photons occur in (he filamentary structure of the IGM. and the clumping factor should only be caleulated im these structures.," The recombinations that are important to removing ionizing photons occur in the filamentary structure of the IGM, and the clumping factor should only be calculated in these structures."650 To assess the critical SFR. necessary to maintain an ionizecl medium. we focus on grid cells Chat are significantly ionized.," To assess the critical SFR necessary to maintain an ionized medium, we focus on grid cells that are significantly ionized."651 Because a negligible amount of recombination occurs in cells containing mostly neulral gas. these cells should not contribute to the chunpineg factor.," Because a negligible amount of recombination occurs in cells containing mostly neutral gas, these cells should not contribute to the clumping factor."652" If. we do not exclude neutral gas. the clamping factor is extremely high (Cy,~ 100) belore the jionizing background is turned on."," If we do not exclude neutral gas, the clumping factor is extremely high $C_H \sim 100$ ) before the ionizing background is turned on."653 We find large density gradients between the neutral gas (iniformily distributed over the simulation) sud the ionized gas., We find large density gradients between the neutral gas (uniformly distributed over the simulation) and the ionized gas.654 Because the clumping [actor is a measure of ihe inhomogeneity of the medium. a large clensity gradient. vields a large value of Cy.," Because the clumping factor is a measure of the inhomogeneity of the medium, a large density gradient yields a large value of $C_H$."655 If low-density voids are included in the calculation. the larger clensityv gradient. leads (o an overestimate of the clumping.," If low-density voids are included in the calculation, the larger density gradient leads to an overestimate of the clumping."656 By setting both upper ancl lower density thresholds. we can exclude collapsed halos and low-density voids from our calculations.," By setting both upper and lower density thresholds, we can exclude collapsed halos and low-density voids from our calculations."657 Previous studies (Miralda-Escudé 2000: Miralda-IEscudéetal. 2003: Pawliketal. 2009) acldressecl these issues by setting a density threshold that excludes collapsed halos. but they did not set a lower limit to exclude voids from (heir calculations.," Previous studies (Miralda-Escudé 2000; Miralda-Escudé 2003; Pawlik 2009) addressed these issues by setting a density threshold that excludes collapsed halos, but they did not set a lower limit to exclude voids from their calculations."658" To explore these effects in a filamentary IGM. we make various cuts of our data in barvon overdensity (A,=pi/ fy) and in temperature. metallicity, and hydrogen ionization traction (4x=nm Ημ)."," To explore these effects in a filamentary IGM, we make various cuts of our data in baryon overdensity $\Delta_b \equiv \rho_b/\bar{\rho}_b$ ) and in temperature, metallicity, and hydrogen ionization fraction $x \equiv n_{\rm HII}/n_H$ )."659" In our stanclarelformulation. we include only those cells that meet the following criteria: |<A,100. 300IK«T10 Kk. Z«10*Z.. andr>0.05."," In our standardformulation, we include only those cells that meet the following criteria: $1 < \Delta_b < 100$, $300~{\rm K} < T < 10^5$ K, $Z < 10^{-6}\, Z_\odot$, and $x > 0.05$."660" We believe this ""data cut” adequately represents unenriched IGM line on an adiabat (see Figure 19 of Smith etal. 2011)."," We believe this “data cut"" adequately represents unenriched IGM lying on an adiabat (see Figure 19 of Smith 2011)."661 We, We662field could be observed.,field could be observed.663 The scenario presented here is speculative in nature since the information about the interior can onlv be obtained through indirect measurements. e.g. frequencies of solar oscillations.," The scenario presented here is speculative in nature since the information about the interior can only be obtained through indirect measurements, e.g. frequencies of solar oscillations."664 The continuing elforts to measure hieh-precision oscillation data for a complete 2?-vear magnetic cvcle may unveil the influence of a relic field on the variation of oscillation frequencies., The continuing efforts to measure high-precision oscillation data for a complete 22-year magnetic cycle may unveil the influence of a relic field on the variation of oscillation frequencies.665 Usine uninterrupted and uniform acoustic mode oscillation frequencies from GONG. we investigated (he variation of Irequency shifts during the last (wo solar activity. minina.," Using uninterrupted and uniform acoustic mode oscillation frequencies from GONG, we investigated the variation of frequency shifts during the last two solar activity minima."666 Although the perturbations of near-surface lavers generated by the changes at the tachocline are mainlv responsible for the changes in frequencies. the observations during (the extended minimun) suggest that there might be some elfect [rom (he lavers as deep as the core.," Although the perturbations of near-surface layers generated by the changes at the tachocline are mainly responsible for the changes in frequencies, the observations during the extended minimum suggest that there might be some effect from the layers as deep as the core."667 Our analvsis provides evidence for a double minima in oscillation Irequencies during the current prolonged low activity phase., Our analysis provides evidence for a double minima in oscillation frequencies during the current prolonged low activity phase.668" It also supports previous results obtained with GOLF and GONG data for low- and intermediate degree modes respectively, where different epochs of minimum were reported on the basis of angular degree (Salabertοἱal.Tripathyοἱal. 2010).."," It also supports previous results obtained with GOLF and GONG data for low- and intermediate degree modes respectively, where different epochs of minimum were reported on the basis of angular degree \citep{david09,sct10b}."669 In other words. the minima seen in oscillation lrequencies vary. will the depth of turning point radius of the modes.," In other words, the minima seen in oscillation frequencies vary with the depth of turning point radius of the modes."670 The waves reaching the inner of the interior exhibit a minimum one vear earlier than that [rom the outermost which is in agreement with the surface-activity minmum., The waves reaching the inner of the interior exhibit a minimum one year earlier than that from the outermost which is in agreement with the surface-activity minmum.671 Although there is considerable evidence for the variation of oscillation frequencies in phase with the surface activity. (he analysis presented in (his paper hints towards a possible role of relic magnetic fields in changing the oscillation Irequencies which was addressed by Gough&Thompson(1990).," Although there is considerable evidence for the variation of oscillation frequencies in phase with the surface activity, the analysis presented in this paper hints towards a possible role of relic magnetic fields in changing the oscillation frequencies which was addressed by \citet{mjt}."672. We also searched. for a quasi-biennial signal in the GONG frequencies in order the explore the, We also searched for a quasi-biennial signal in the GONG frequencies in order the explore the673In Fig. 12..,"In Fig. \ref{fig5},"674 the relation between amount of rotational support ancl isophotal shape is examined., the relation between amount of rotational support and isophotal shape is examined.675 We plot anisotropy parameter against the By cocllicient of our sample galaxies. and the values of bright. cllipticals by Joenderetαἱ.(1994). [or comparison.," We plot anisotropy parameter against the $\overline{B_{4}}$ coefficient of our sample galaxies, and the values of bright ellipticals by \cite{bender94} for comparison."676 There exists a relation such that galaxies with discy isophotes tend to be more rotationally supported than boxy galaxies., There exists a relation such that galaxies with discy isophotes tend to be more rotationally supported than boxy galaxies.677 The relation is independent of galaxys luminosity (e.g.. Benderetal. 19949).," The relation is independent of galaxy's luminosity (e.g., \citealt{bender94}) )."678 We find that almost SO percent of the low-luminosity galaxies have clisev-shapecl isophotes or in other terms an excess of lieht along the galaxy’s major and/or minor axis., We find that almost 80 percent of the low-luminosity galaxies have discy-shaped isophotes or in other terms an excess of light along the galaxy's major and/or minor axis.679 The remaining objects have boxy isophotes. for which the excess of light lies along a line at 45° with respect to the galaxys axes.," The remaining objects have boxy isophotes, for which the excess of light lies along a line at $^{\circ}$ with respect to the galaxy's axes."680Luninous Blue Variables (Conti 198D) ave massive stars undergoing a brief. but important stage of evolution.,"Luminous Blue Variables (Conti 1984) are massive stars undergoing a brief, but important stage of evolution."681 During this period they suffer severe mass loss with vvalues of up to 10.1A.xy.+., During this period they suffer severe mass loss with values of up to $10^{-4} \msunyr$.682 LBVs are characterized by typical variations iu the order of AV of 1 to 2 magnitudes., LBVs are characterized by typical variations in the order of $\Delta V$ of 1 to 2 magnitudes.683 Nevertheless. the total bolometric Iuuinositv of the star L. seems to be about constant.," Nevertheless, the total bolometric luminosity of the star $L_*$ seems to be about constant."684 The reason for the tvpical LBV variations is still uuknown., The reason for the typical LBV variations is still unknown.685 For reviews see Nota Lamers (1997)., For reviews see Nota Lamers (1997).686 Leitherer et al. (, Leitherer et al. (6871989) and de I&oter et al. (,1989) and de Koter et al. (6881996) lave shown that it must be the actual racius of the star that increases during these typical variations.,1996) have shown that it must be the actual radius of the star that increases during these typical variations.689 Therefore. Tig decreases during the variatious. if L. is about constant.," Therefore, $\teff$ decreases during the variations, if $L_*$ is about constant."690 Iu this paper. we have calculated the mass-Ioss behaviour for normal OD supereiauts as a function ofTiag.," In this paper, we have calculated the mass-loss behaviour for normal OB supergiants as a function of."691. Despite many differences between OB supereiauts and LBVs. we can retrieve valuable information about the behaviour of dduring a typical LBV variation by investigating the Dhehaviour of normal OB supergiauts. since both types of stars ave located in the same part of the IIRD.," Despite many differences between OB supergiants and LBVs, we can retrieve valuable information about the behaviour of during a typical LBV variation by investigating the behaviour of normal OB supergiants, since both types of stars are located in the same part of the HRD."692 Our calculations can be used as a tool to understand the mass loss changes of au LBV in terms of changes in dauiug such a typical variation (see also Leitherer ct al., Our calculations can be used as a tool to understand the mass loss changes of an LBV in terms of changes in during such a typical variation (see also Leitherer et al.693 19501., 1989).694 Observations of LBVs show that for some LBVs that nuuderego typical variations lis miereasing fron) visual müniuun to maxinmuu. while for others it is the other wav around: is decreasing.," Observations of LBVs show that for some LBVs that undergo typical variations is increasing from visual minimum to maximum, while for others it is the other way around: is decreasing."695 This “unpredictable” behaviour of dduiug au LBV variation is nof a complete surprise. if one considers our. vvalues as a fiction of ζω.," This “unpredictable” behaviour of during an LBV variation is not a complete surprise, if one considers our values as a function of $\teff$."696 We have found that iu the τασος f= do 00030 000 and — 20 00012 500K.. ddecreases for a decreasingDiyg.. whereas in the interval between = 30-000 20000K.. Wucreases for a decreasingτομ.," We have found that in the ranges = 40 000-30 000 and = 20 000-12 500, decreases for a decreasing, whereas in the interval between = 30 000-20 000, increases for a decreasing."697 This shows that whether one expects an increasing or decreasing dduiug an LBV variation depeuds on the specific rauge πι, This shows that whether one expects an increasing or decreasing during an LBV variation depends on the specific range in698Weak C»eravitational lensingC» of backeround galaxies by foreground. large-scale structures. the so-called cosiic shear. is one of the best tools to probe the uature of the iain components of the Universe. such as dark matter and dark energy.,"Weak gravitational lensing of background galaxies by foreground large-scale structures, the so-called cosmic shear, is one of the best tools to probe the nature of the main components of the Universe, such as dark matter and dark energy."699 Thus. weak lensing has the highest potential to. conustraiu the properties of dark energev among other cosmological observations. if the systematic errors are well kept under control (7).," Thus, weak lensing has the highest potential to constrain the properties of dark energy among other cosmological observations, if the systematic errors are well kept under control \citep{Albrecht2006}."700 To address questions about the nature of dark energy and ie properties of eravitv on cosmological scales; various surveys are plauned. such as the πηρα Suprimc-Cam Weak Leusiug Survey (2)Aiudex.hitial.. he Dark Eucgv Survey(DES). the Large Synoptic Survey Telescope (LSST?.. Euclid (?) aud the Wide-Field Iufrared Survey Telescope(WFIRST)*.," To address questions about the nature of dark energy and the properties of gravity on cosmological scales, various surveys are planned, such as the Hyper Suprime-Cam Weak Lensing Survey \citep{Miyazaki2006}, the Dark Energy Survey, the Large Synoptic Survey Telescope , Euclid \citep{Refregier2010}, and the Wide-Field Infrared Survey Telescope."701. To exploit the full potential of future weak-leusiug survers. it will be important to analyze data with adequate statistical iieasures and tools;," To exploit the full potential of future weak-lensing surveys, it will be important to analyze data with adequate statistical measures and tools."702 Particularly. one necds to properly take into account the correlations of the observables between different angular scales aud redshifts. be. them covariance matrices (2777)..," Particularly, one needs to properly take into account the correlations of the observables between different angular scales and redshifts, i.e., their covariance matrices \citep{Cooray2001b,Takada2009,Sato2009,Sato2011a}."703 Furthermore. oue has to use an appropriate likelihood fuuctiou with eiveu mareinal distributions (?7)..," Furthermore, one has to use an appropriate likelihood function with given marginal distributions \citep{Sato2010,Sato2011}."704 Since most of the useful cosmological iuforiination contained in the cosuuc shear signal is associated with μα]. angular scales that are affected by nonlinear clustering. we also need to iuclude these nonlinear effects to accurately model the weak-leusing statistics (??)..," Since most of the useful cosmological information contained in the cosmic shear signal is associated with small angular scales that are affected by nonlinear clustering, we also need to include these nonlinear effects to accurately model the weak-lensing statistics \citep{Takada2004,Sato2009}."705 Most researchers use fitting formmlas based on uunucerical sinulatious or phenomenological approaches but it would be useful to obtain analytical methods that are more directly related. to the cosmiological parameters and primordial fluctuations., Most researchers use fitting formulas based on numerical simulations or phenomenological approaches but it would be useful to obtain analytical methods that are more directly related to the cosmological parameters and primordial fluctuations.706 Tn this paper. we exiuuine the performance of the theoretical modeling of the 3D matter density distribution proposed bv 77.. which is based on a combination of perturbation theories and halo models.," In this paper, we examine the performance of the theoretical modeling of the 3D matter density distribution proposed by \citet{Valageas2011d,Valageas2011e}, which is based on a combination of perturbation theories and halo models."707 We focus on the convergence power spectrum and bispectrum. which are basic statistical measurements mm weak leusimg studies (see.?.forarecentmethodofleusingpowerspec-truniimneasurenient)..," We focus on the convergence power spectrum and bispectrum, which are basic statistical measurements in weak lensing studies \citep[see,][for a recent method of lensing power spectrum708measurement]{Hikage2011}."709 As compared with simple fitting foruuulas or direct numerical smiulations. a siguificaut advantage of our approach is that we can evaluate and conipare differeut contributions that can be measured iu weak-lensing survevs.," As compared with simple fitting formulas or direct numerical simulations, a significant advantage of our approach is that we can evaluate and compare different contributions that can be measured in weak-lensing surveys."710 Since different contributions suffer frou different theoretical uncertainties. this is useful to estimate the accuracy that can be aimed at In weak-lensing statistics. as a function of scales.," Since different contributions suffer from different theoretical uncertainties, this is useful to estimate the accuracy that can be aimed at in weak-lensing statistics, as a function of scales."711 Furthermore. we find tha our model provides better agrecment with numerical smaulatious than other existent models.," Furthermore, we find that our model provides better agreement with numerical simulations than other existent models."712 This paper is organized as follows., This paper is organized as follows.713 Iu Sect., In Sect.714 2 we first present our model for the 3D matter density power spectrmm aud bispectrum., \ref{Analytic} we first present our model for the 3D matter density power spectrum and bispectrum.715 Next. we recall how this vields the weak lensing convergence power spectruni and bispectimm through the Boru approximation.," Next, we recall how this yields the weak lensing convergence power spectrum and bispectrum through the Born approximation."716 We describe our numerical snmlations aud he data analysis i] Sect. 3., We describe our numerical simulations and the data analysis in Sect. \ref{Numerical}.717 Then. we present detailed conrparisons between the simulation results. previous models. and our theoretical predictions. for the convergence power spectrin in Sect. L.," Then, we present detailed comparisons between the simulation results, previous models, and our theoretical predictions, for the convergence power spectrum in Sect. \ref{Convergence-power-spectrum},"718 and for the convergence bispectiua iu Sect. 5.," and for the convergence bispectrum in Sect. \ref{Convergence-bispectrum},"719 considering the cases of both equilateral and more general isosceles configurations., considering the cases of both equilateral and more general isosceles configurations.720 We study the relative importance of the different contrbutious to the power spectrum and bispectiumi in Sect. 6.. aridus," We study the relative importance of the different contributions to the power spectrum and bispectrum in Sect. \ref{contributions},"721" from ""]-halo. ""2-halo'. or ""halo terius."," arising from “1-halo”, “2-halo”, or “3-halo” terms."722 Finally. we check the robustuess of our mocel as we vary the cosmological parameters in Sect.," Finally, we check the robustness of our model as we vary the cosmological parameters in Sect."7237. and we conclude in Sect. 8..,\ref{Cosmology} and we conclude in Sect. \ref{Conclusion}. .724"line shows the model MIANI2 from ? plus an extinction of A,= I5mmag. which allows to reproduce the Ix-band flux and the colour simultaneously.","line shows the model MRN12 from \citet{1993ApJ...414..773K} plus an extinction of $A_V = 15$ mag, which allows to reproduce the K-band flux and the colour simultaneously."725 This analysis confirms wt the object is mostly seen in scattered light through an edge-on disk., This analysis confirms that the object is mostly seen in scattered light through an edge-on disk.726 In summary. the information from. photometry and spectroscopy indicates that AB anc € are both low-mass stars.," In summary, the information from photometry and spectroscopy indicates that AB and C are both low-mass stars."727 Since the mass of AB is likely to be higher than the mass of C and AB is located closer to the core of the nebula. AB is probably the most relevant center of infall in the IRASO4325 svstem.," Since the mass of AB is likely to be higher than the mass of C and AB is located closer to the core of the nebula, AB is probably the most relevant center of infall in the IRAS04325 system."728 lt been speculated that AB might be a binary (hence the name)., It has been speculated that AB might be a binary (hence the name).729neum Based on the LIST images. ? argue that there is à structure. possibly indicating two sources or possibly indicating a dark absorption lane running roughly cast-west across the object.," Based on the HST images, \citet{1999AJ....118.1784H} argue that 'there is a double structure, possibly indicating two sources or possibly indicating a dark absorption lane running roughly east-west across the object.'"730 In the LIST images the separation between the (vo components is in the range of 0722 roughly in north-south direction. corresponding to 30 AAU.," In the HST images the separation between the two components is in the range of 2 roughly in north-south direction, corresponding to $\sim 30$ AU."731" The ""dark lane’ would indicate an absorption feature in front. of the object. possibly a disk with diameter of a few tens AU"," The 'dark lane' would indicate an absorption feature in front of the object, possibly a disk with diameter of a few tens AU."732 Dased on our K-band iniage. we test for the presence of a second source in AB by constructing a model PSE from the three well-detectecl fick stars outside LRASOL325.," Based on our K-band image, we test for the presence of a second source in AB by constructing a model PSF from the three well-detected field stars outside IRAS04325."733 All sources in the image are fit with this model PSE. using withinIRAP.," All sources in the image are fit with this model PSF, using withinIRAF."734 The 4? of the fit is <2 for all field stars. 3.2 for object €. and 12.0 for object--AB.," The $\chi^2$ of the fit is $<2$ for all field stars, 3.2 for object C, and 12.0 for objectAB."735 The contour plot of the residuals (Eig. 7)), The contour plot of the residuals (Fig. \ref{f2}) )736 after ing one PSE does not show any evidence for a second. point source. and fitting two PSEs instead of one does not improve the fit.," after subtracting one PSF does not show any evidence for a second point source, and fitting two PSFs instead of one does not improve the fit."737 The high V ds most Likely caused by the strongly uneven background and not by a stellar companion., The high $\chi^2$ is most likely caused by the strongly uneven background and not by a stellar companion.738 Thus. we prefer to interpret the double structure seen in the LST image as an indication for a disk seen at high inclination that bisects the image of the star. rather than the presence of a resolved: companion.," Thus, we prefer to interpret the double structure seen in the HST image as an indication for a disk seen at high inclination that bisects the image of the star, rather than the presence of a resolved companion."739 This finding is supported. by the combined information from photometry and spectroscopy: for a binary we would expect a mismatch (i.e. a later spectral type than expected from photometry)., This finding is supported by the combined information from photometry and spectroscopy; for a binary we would expect a mismatch (i.e. a later spectral type than expected from photometry).740 The orientation of the ‘lane’ is roughly perpendicular to the outflow emanating from AB (Sect. 4))., The orientation of the 'lane' is roughly perpendicular to the outflow emanating from AB (Sect. \ref{s4}) ).741 In the submim continuum image both AB and € are spatially resolved., In the submm continuum image both AB and C are spatially resolved.742 The spatial structure ds. studied: after discarcüng the data [rom baselines shorter than mum. which cllectively removes the structures larger than a few aresec.," The spatial structure is studied after discarding the data from baselines shorter than m, which effectively removes the structures larger than a few arcsec."743 We used the task in the Miriad package to fit the visibilities of the sources., We used the task in the Miriad package to fit the visibilities of the sources.744 Various combinations of point sources ancl gaussian sources were tried for both objects., Various combinations of point sources and gaussian sources were tried for both objects.745 The northern source C is well matched by an elliptical gaussian with axes of 1722 and 0722 and a position angle of ~50 ddeg (Fig. ) , The northern source C is well matched by an elliptical gaussian with axes of 2 and 2 and a position angle of $\sim 50$ deg (Fig. \ref{f9}) ).746Note that the position angle of the beam is SEto NW. perpendicular to the orientation of the source.," Note that the position angle of the beam is SE to NW, i.e. perpendicular to the orientation of the source."747 “Phe parameters of the gaussian have large uncertainties. but it is sale to conclude that the position anele is consistent with the orientation of the disk. as inferred. from the HIST. images (PA30dog. ," The parameters of the gaussian have large uncertainties, but it is safe to conclude that the position angle is consistent with the orientation of the disk, as inferred from the HST images \citep[PA 30\,deg,][]{1999AJ....118.1784H}. ."748The same LIST images also constrain the radius of the disk to 0722 (~ AAW). which is not resolved by the SALA.," The same HST images also constrain the radius of the disk to 2 $\sim 30$ AU), which is not resolved by the SMA."749 The elongated structure seen in the subnim data might be caused by a cold outer disk or by an elongated. cireumstellar envelope with a diameter of ~1.2” 150-300AAU.," The elongated structure seen in the submm data might be caused by a cold outer disk or by an elongated circumstellar envelope with a diameter of $\sim 1-2""$, i.e. AU."750 This size matches well with the constraint [rom the SED mocleling (Sect. 5.2))., This size matches well with the constraint from the SED modeling (Sect. \ref{s52}) ).751 The southern AB source contains a compact component that is well matched by a point source. Likely caused bv a small-scale disk.," The southern AB source contains a compact component that is well matched by a point source, likely caused by a small-scale disk."752 Lo addition there is a contribution of spatially extended: emission. mostly oriented. in E-W direction over an area of 3-5," In addition there is a contribution of spatially extended emission, mostly oriented in E-W direction over an area of 3-5""."753 Based on the PSE fit discussed in Sect., Based on the PSF fit discussed in Sect.754 3.4. the relative positions of AB and € were determined with an accuracy in the range of (1 pixel)., \ref{s34} the relative positions of AB and C were determined with an accuracy in the range of 1 (1 pixel).755 The distance between the two sources measured from the peak position of the model PSE is 87332., The distance between the two sources measured from the peak position of the model PSF is 32.756 Simply measuring the MN of the emission peaks also gives a consistent clistance of fr, Simply measuring the positions of the emission peaks also gives a consistent distance of 3.757omFrom the coordinates eiven by ?.. based on images November 1997. we infer a distance between AB and C of 87223.," From the coordinates given by \citet{1999AJ....118.1784H}, based on images from November 1997, we infer a distance between AB and C of 23."758 Within the errorbar both measurements are The position angles [from the available near-inlrared images agree well: We measure 351.8ddeg (E of N). while the literature values are 351.4 (2). ancl ddeg (7).. all with uncertainties of 1 ddeg.," Within the errorbar both measurements are The position angles from the available near-infrared images agree well: We measure deg (E of N), while the literature values are 351.4 \citep{2008AJ....135.2496C} and deg \citep{1999AJ....118.1784H}, all with uncertainties of $\la 1$ deg."759 These measurements constrain the relative proper motion between AB and Coto c Ommasyver t, These measurements constrain the relative proper motion between AB and C to $<9$ $^{-1}$.760o For comparison. the average proper motion of νους stars within 5ddeg o£ LRASO4325 is vvr.+ (22). with a standard deviation of +.," For comparison, the average proper motion of young stars within deg of IRAS04325 is $^{-1}$ \citep{2005A&A...438..769D,2009ApJ...703..399L}, with a standard deviation of $^{-1}$."761 While the constraints on the proper motion for AB and do not prove that he object is a physically bound. system. they do confirm common membership in the Taurus association.," While the constraints on the proper motion for AB and C do not prove that the object is a physically bound system, they do confirm common membership in the Taurus association."762 The angular distance between AB and correspond ο à separation of AU. anc a relative movement 15 AAU over vvr. which results in an upper velocity limit of  between AB and € ‘This does not rule out the possibility that € has been much closer to AB in the past: With a velocity of tit would have taken only 107 vvr or C to move to its current position from a starting point close to AB.," The angular distance between AB and C correspond to a separation of AU and a relative movement $\la 15$ AU over yr, which results in an upper velocity limit of $^{-1}$ between AB and C. This does not rule out the possibility that C has been much closer to AB in the past: With a velocity of $^{-1}$ it would have taken only $10^3$ yr for C to move to its current position from a starting point close to AB."763 I is thus conceivable that € has been ejected by a close cvnamical encounter with AB in the early evolution of the system., It is thus conceivable that C has been ejected by a close dynamical encounter with AB in the early evolution of the system.764 The LUCAS. source is located. within the small dark cloud L1535. a part of the BIS cloud complex in Taurus.," The IRAS source is located within the small dark cloud L1535, a part of the B18 cloud complex in Taurus."765 The few Ποια stars visible in both H- and Ix-band have JfAv colours of image. corresponding to extinetions of mmag. which indicates substantial amounts of gas and dust along the line-of-ight.," The few field stars visible in both H- and K-band have $H-K$ colours of mag, corresponding to extinctions of mag, which indicates substantial amounts of gas and dust along the line-of-sight."766" The near- ancl mid-infrared images M 11,A804325 show a bright elongated emission nebula(???).. In nebulo"," The near- and mid-infrared images of IRAS04325 show a bright elongated emission nebula \citep{1994ApJS...94..615H,1999AJ....118.1784H,2007AJ....133.1528C}. ."767sityour images in the JIN bands the dimensions of this are about 10. 207. corresponding to 1500.3000 AAU. with a position angle (PA) of ~15.—20 ddeg.," In our images in the JHK bands the dimensions of this nebulosity are about $10"" \times 20""$ , corresponding to $1500 \times 3000$ AU, with a position angle (PA) of $\sim 15-20$ deg."768 The nebula isdivided in two, The nebula isdivided in two769from the coupling cfficicucy between the fiber aud the waveguides aud the propagation losses.,from the coupling efficiency between the fiber and the waveguides and the propagation losses.770 Table 1 stmuarizes estimation of losses coming frou different origins., Table \ref{tab:loss} summarizes estimation of losses coming from different origins.771 The propagation losses aud the coupling omes have been measured with a straight waveguide nanufactured iu the same couditious., The propagation losses and the coupling losses have been measured with a straight waveguide manufactured in the same conditions.772 The Fresnel losses rave been theoretically estimated to , The Fresnel losses have been theoretically estimated to $\%$.773Auv function causes additional losses which cannot be evaluated separately but have been estimated to LU%., Any function causes additional losses which cannot be evaluated separately but have been estimated to $\%$.774 One should rotice that the reverse Y-juuction acts as oulv one of he two outputs of an optical beamsplitter (see paper li, One should notice that the reverse Y-junction acts as only one of the two outputs of an optical beamsplitter (see paper I).775 Therefore 50% of the light is radiated outside the waveguide., Therefore $\%$ of the light is radiated outside the waveguide.776 The first two columns of Table 1. show that our nueasurenients are consistent with the theoretical performances computed from the different optical losses reported iu the Table., The first two columns of Table \ref{tab:loss} show that our measurements are consistent with the theoretical performances computed from the different optical losses reported in the Table.777 Last colmun of Table P. gives au order of inaguitude of expected improvement in the future., Last column of Table \ref{tab:loss} gives an order of magnitude of expected improvement in the future.778 The main progress concerns the beam combination function., The main progress concerns the beam combination function.779 We should be able to retrieve the secoud half of the combined plotous thanks to new conbiation schemes like N-couplers. niultiaxial beam combiners or multimode interferometric (AIA) imiultiplexers (see paper D) at the cost of a slight chromaticity of the function.," We should be able to retrieve the second half of the combined photons thanks to new combination schemes like X-couplers, multiaxial beam combiners or multimode interferometric (MMI) multiplexers (see paper I) at the cost of a slight chromaticity of the function."780 Some componcuts including these new functions are being manufactured and will be soon tested., Some components including these new functions are being manufactured and will be soon tested.781 The ultimate optical throughput would be aroundTO-SO%.. twice more than our current results.," The ultimate optical throughput would be around, twice more than our current results."782 We have obtaimed first ligh-coutrast wlhite-lelt iuterferoerauus with an offthe-shelves inteerated optics conrponeut used as a two aperture beam combiner., We have obtained first high-contrast white-light interferograms with an off-the-shelves integrated optics component used as a two aperture beam combiner.783H TheJj lieh. aud stable contrasts as well as the high. optical: throughput validate our approach for combining stella beans. by meaus of integrated optics presented in paper T. This preliminary analysis requires further haracterizatious: and lmprovemeuts., The high and stable contrasts as well as the high optical throughput validate our approach for combining stellar beams by means of integrated optics presented in paper I. This preliminary analysis requires further characterizations and improvements.784: The importance: ofd . ≼∐↴∖↴↻↸∖↥⋅↴∖↴↕∪∐∙↴⋝∐⋅↸∖↕↥⋅↕∐∶↴∙↸∖∐↸⊳↸⊳↸∖⋜⋯≼↧∪↑∐↸∖↥⋅↻↕∐∖∐∪⋯↸∖∐⋜↧⋃↑∐↸∖ ↴∎⋝↸∖↥⋅↴∖↴⋜⋯≼⊔∐↑∐↸∖↸⊳∪∐∏⋯∐↸∖," The importance of dispersion, ce and other phenomena in the fibers and in the components have to be fully understood."785∐↑↴∖↴∐⋜↧↖↽↸∖↑∪↴⋝↸∖↕⋟∏∐⋅↖⇁∏∐≼∐∖↥⋅↴∖↴↑∪∪≺↧∙ For this: purpose. two-wav beau combiners: optimized⋅∙ ]or astronomy are under characterization. (spectroscopic. and polariuetric. ineasurements for] iustance). diu. order o carefully. coutrol their. optical. properties.," For this purpose, two-way beam combiners optimized for astronomy are under characterization (spectroscopic and polarimetric measurements for instance) in order to carefully control their optical properties."786. A complete optical⋅⋅ and⋅ interferometric⋅ propcrtics 2001.κ ΟΙbination” optics. component will. be preseutedGl in a Naanber- of ↽(IHaguenauer: et al.19993., A complete description of optical and interferometric properties of integrated optics component will be presented in a forthcoming paper \citep{Hag99}.787".The:optical Detectedf photonsπρ] imaintain⋅⋅ polarization to⋅ avoid⋅⋅ specific Experimental""m throughputfibers aud have optimized lengths to— | avoid ο.", The optical fibers should maintain polarization to avoid specific contrast losses and have optimized lengths to avoid chromatic dispersion.788 This: experimentalqi. precaution. is. : S ecisive to achieve image reconstruction (Delage1998)., This experimental precaution is decisive to achieve image reconstruction \citep{Del98}.789. Our research program is based on the studv of new integrated optics technologies for long baseline -interferometry in the imufrared. and. the desigu of beams conibiuers for multiple (see paper D.," Our research program is based on the study of new integrated optics technologies for long baseline interferometry in the infrared, and, the design of beam combiners for multiple (see paper I)."790 Some specifie beam combiners will then be eventually used in a scienti&c iustrmucutal prototype on astronomical oeiterferometers., Some specific beam combiners will then be eventually used in a scientific instrumental prototype on astronomical interferometers.791 Preliminary tests on the GI2T/Reeain oeiterterometer (Mourardetal.1998) will be carried out with the Integrated Optics Near-infrared Iuterferoimoctric Camera (IONIC) prototype (Bergeretal.1995]., Preliminary tests on the GI2T/Regain interferometer \citep{Mou98} will be carried out with the Integrated Optics Near-infrared Interferometric Camera (IONIC) prototype \citep{Ber98}.792 We would like to αλα] thauk LLe Coarer for his precious support ii nistrunent control., We would like to warmly thank Le Coarer for his precious support in instrument control.793 We thauk the referee. SShaklau. for a careful reading of ow paper and for suggestious which helped to improve its content.," We thank the referee, Shaklan, for a careful reading of our paper and for suggestions which helped to improve its content."794 The work was partially fuudedbx PNIIRA / INSU. CNRS / Ultimattech and DOA / DRET (Contract 971091).," The work was partially funded by PNHRA / INSU, CNRS / tech and DGA / DRET (Contract 971091)."795 The iutegrated optics components have been mauufactured aud fiber-couuected by the GeeO company., The integrated optics components have been manufactured and fiber-connected by the GeeO company.796From the projected lisht curve 5/N we can estimate how well the SNe Ia distances can be determined.,From the projected light curve S/N we can estimate how well the SNe Ia distances can be determined.797" The SNAP filter set consists of nine filters evenly spaced in logÀ where the effective wavelength of filter n is A,=(1.16)""x4400À wwith n€[0....3]."," The SNAP filter set consists of nine filters evenly spaced in $\log{\lambda}$ where the effective wavelength of filter $n$ is $\lambda_n=(1.16)^n\times4400$ with $n\in\{0,\dots 8\}$."798 This spacing. somewhat liner than that of the Johnson-Cousins set. bounds B to V-band Ix-correction uncertainties to less than 0.02 mag (Davisetal.2006).," This spacing, somewhat finer than that of the Johnson-Cousins set, bounds $B$ to $V$ -band K-correction uncertainties to less than 0.02 mag \citep{davis06}."799. The supernova-frame B-band shifts out of the penultimate »=7 filler at 2= 1.5., The supernova-frame $B$ -band shifts out of the penultimate $n=7$ filter at $z \gtrsim 1.8$ .800 The low, The low801follow a power-law both in tux and spectral shape in optical wavelengths.,follow a power-law both in flux and spectral shape in optical wavelengths.802 It should be noted that the later transient had an observed rising phase of optical emission (e.g. Calama et al., It should be noted that the later transient had an observed rising phase of optical emission (e.g. Galama et al.803 1997)., 1997).804" Although individual cases may vary. in calculating the expected signal as a function of wavelength and time. we adopt the functional form of the Ilux as: where £5, properly normalises the spectrum at fy. the ime at which the decay begins."," Although individual cases may vary, in calculating the expected signal as a function of wavelength and time, we adopt the functional form of the flux as: where $F_{t_0}$ properly normalises the spectrum at $t_0$, the time at which the decay begins."805 Wijers. Rees. Mésszárros (1997) lind that the afterglow adequately fits the carly light curve with 6=OS and 3;=1.2 for GRB 970228.," Wijers, Rees, Mésszárros (1997) find that the afterglow adequately fits the early light curve with $\delta = 0.8$ and $\beta = -1.2$ for GRB 970228."806 Our oeliminary fits to the data from GIUD 970508 indicate that ὃcOS and 3cLO., Our preliminary fits to the data from GRB 970508 indicate that $\delta \simeq 0.8$ and $\beta \simeq -1.0$.807 HÉ the afterglow is observed. as a Target of Opportunity fois<3 weeks after the burst (c.g. CCLau)&22.7 lor GRB 970508). a redshift could. be obtained in less than 10 LIST orbits (sce fig. ," If the afterglow is observed as a Target of Opportunity $t_{\rm obs}808\ale 3$ weeks after the burst (e.g. $U(t_{\rm obs}) \simeq 22.7$ for GRB 970508), a redshift could be obtained in less than 10 HST orbits (see fig. ["8092]) using the either FUY or NUV. ALAALA detectors.,2]) using the either FUV or NUV MAMA detectors.810 UnlessS57 is able to observe the afterglow of a GRB while it is still bright (C.< 20). detection of damped Lyman à absorption at low redshift (2< 1.5) will require a very larec integration time on STIS.," Unless is able to observe the afterglow of a GRB while it is still bright $U \ale 20$ ), detection of damped Lyman $\alpha$ absorption at low redshift $z \ale 1.5$ ) will require a very large integration time on STIS."811 However. a significant detection of a Lyman limit requires far less S/N per unit wavelength and thus improves the chance of determining a redshift of €iltDs from fewer orbits.," However, a significant detection of a Lyman limit requires far less S/N per unit wavelength and thus improves the chance of determining a redshift of GRBs from fewer orbits."812 Although the Lyman break occurs at shorter wavelengths (A<91201:|2) Aj) than the Lyman «a forest (Ac—1216(1| 2)A)) where the detectors are less sensitive. the distinct. eut-olf of this spectral feature is unambiguous ancl does not require good spectral resolution. making this i0 most elfective and clearcut wav to limit the redshift of faint sources.," Although the Lyman break occurs at shorter wavelengths $\lambda \le 912 (1 +813z)$ ) than the Lyman $\alpha$ forest $\lambda \simeq 1216814(1+z)$ ) where the detectors are less sensitive, the distinct cut-off of this spectral feature is unambiguous and does not require good spectral resolution, making this the most effective and clearcut way to limit the redshift of faint sources."815 Figure. (2)) shows the expected integration time required to achieve à 8/N—3 in a 100 bbin as a function of C. magnitude of the afterglow and redshift of the Lyman limit source for both the CCD and ALAALA detector onhttp://www., Figure \ref{fig:int}) ) shows the expected integration time required to achieve a S/N=3 in a 100 bin as a function of $U$ magnitude of the afterglow and redshift of the Lyman limit source for both the CCD and MAMA detector on.816gtsci.edu/.. As seen in the figure. if the afterglow is observed while it is still reasonably bright (Cz 21). detection of a redshift 2m0.3 would require less than 1 HIST orbit.," As seen in the figure, if the afterglow is observed while it is still reasonably bright $U \ale 21$ ), detection of a redshift $z \age 0.3$ would require less than 1 HST orbit."817 Figure (3)) shows a simulated spectrum of an afterelow obtained with ALAAMIA with ~1.5 LST orbits (5400. sec) where the source is a magnitude @=21.0 ancl the spectral shape is &=1 (eq., Figure \ref{fig:mama}) ) shows a simulated spectrum of an afterglow obtained with MAMA with $\sim 1.5$ HST orbits (5400 sec) where the source is a magnitude $U = 21.0$ and the spectral shape is $\delta=1$ (eq.818 1)., 1).819 We have removed the contribution of the source to the observed spectrum for wavelengths Ax ecorresponding to a Lyman limit at a maxinium redshift of, We have removed the contribution of the source to the observed spectrum for wavelengths $\lambda \le 2098$ corresponding to a Lyman limit at a maximum redshift of820"the Eddington rate, as indicated by the continuous lines (becoming probably radiatively inefficient).","the Eddington rate, as indicated by the continuous lines (becoming probably radiatively inefficient)."821" Thus, for most of the time this AGN would be optically dim, exhibiting only very few, brief luminous episodes."," Thus, for most of the time this AGN would be optically dim, exhibiting only very few, brief luminous episodes."822" In contrast, the BH kicked in the plane of the galaxy initially grows more as it encounters a larger supply of material on its orbit through the gas-rich galactic disc."," In contrast, the BH kicked in the plane of the galaxy initially grows more as it encounters a larger supply of material on its orbit through the gas-rich galactic disc."823" Consequently, its bolometric luminosity is up to an order of magnitude higher than that of the BH which never leaves the centre."," Consequently, its bolometric luminosity is up to an order of magnitude higher than that of the BH which never leaves the centre."824" Once the BH orbit circularises in a ring of low density material formed by feedback, its accretion is even more sub-Eddington than that of the BH which stays in the galactic centre."," Once the BH orbit circularises in a ring of low density material formed by feedback, its accretion is even more sub-Eddington than that of the BH which stays in the galactic centre."825 Note however that the AGN bolometric luminosity obtained in this case should be an upper limit for several reasons., Note however that the AGN bolometric luminosity obtained in this case should be an upper limit for several reasons.826" First, it is probably not very common that the BH is gravitationally recoiled exactly within the disc, as assumed here, given that at present there is no evidence for a correlation between the spin orientations of the BH and of the host galaxy."," First, it is probably not very common that the BH is gravitationally recoiled exactly within the disc, as assumed here, given that at present there is no evidence for a correlation between the spin orientations of the BH and of the host galaxy."827" Second, during a galaxy merging event, which is a much more realistic setting for the occurrence of a gravitationally recoiled BH, the largest amount of gas available for accretion will be in central regions, meaning that a kicked BH will be biased towards accreting less gas (see Section ??))."," Second, during a galaxy merging event, which is a much more realistic setting for the occurrence of a gravitationally recoiled BH, the largest amount of gas available for accretion will be in central regions, meaning that a kicked BH will be biased towards accreting less gas (see Section \ref{merging}) )."828" Finally, the BH accretion rate estimated from equation (1)) should be considered as an upper limit if the gas surrounding the BH is not multiphase, and the BH feedback is not strong enough to self-regulate the BH growth."," Finally, the BH accretion rate estimated from equation \ref{Bondi_eq}) ) should be considered as an upper limit if the gas surrounding the BH is not multiphase, and the BH feedback is not strong enough to self-regulate the BH growth."829" While for a stationary BH in the centre of the host galaxy this is unlikely to occur, for a recoiled BH the actual accretion rate may well be lower if it leaves the dense multiphase medium."," While for a stationary BH in the centre of the host galaxy this is unlikely to occur, for a recoiled BH the actual accretion rate may well be lower if it leaves the dense multiphase medium."830 We explore this issue in detail in Appendix A.., We explore this issue in detail in Appendix \ref{appen}.831" Nonetheless, our findings suggest that the recoiled AGN could have accretion rates up to a few percent of the Eddington rate on timescales of a few 10’ yrs, if their orbits are approximately contained within the gas-rich galactic disc."," Nonetheless, our findings suggest that the recoiled AGN could have accretion rates up to a few percent of the Eddington rate on timescales of a few $10^7$ yrs, if their orbits are approximately contained within the gas-rich galactic disc."832" Gravitational recoil of the BH perpendicular to the galactic disc significantly suppresses BH accretion, but it does not truncate it all together."," Gravitational recoil of the BH perpendicular to the galactic disc significantly suppresses BH accretion, but it does not truncate it all together."833" As the BH orbit decays towards the centre, the accretion rate increases as the BH experiences more and more passages through the disc."," As the BH orbit decays towards the centre, the accretion rate increases as the BH experiences more and more passages through the disc."834" Eventually, once back in the centre the accretion rate is very similar to the case of the stationary BH, and the difference between the final masses is not very large, i.e. 10'h!."," Eventually, once back in the centre the accretion rate is very similar to the case of the stationary BH, and the difference between the final masses is not very large, i.e. $\sim 10^7 \,h^{-1}{\rm M}_\odot\,$."835" This is, however, very likely a lower limit to the mass differenceMs between a recoiled and a stationary BH, given the quiescent nature of the host galaxy."," This is, however, very likely a lower limit to the mass difference between a recoiled and a stationary BH, given the quiescent nature of the host galaxy."836" In a more realistic scenario, where the progenitor BHs merge during a merger of two galaxies, a large amount of gas will be funnelled towards the central regions."," In a more realistic scenario, where the progenitor BHs merge during a merger of two galaxies, a large amount of gas will be funnelled towards the central regions."837" This gas will form a copious reservoir for BH accretion and it will thus make a much bigger difference for BH growth whether the remnant BH stays in the centre or is gravitationally recoiled, as we discuss in Section ??.."," This gas will form a copious reservoir for BH accretion and it will thus make a much bigger difference for BH growth whether the remnant BH stays in the centre or is gravitationally recoiled, as we discuss in Section \ref{merging}."838" In the bottom panel of Figure 6, we show the total SFR of the simulated galaxy, where the blue line denotes the simulation result without a BH, for comparison."," In the bottom panel of Figure \ref{mbh_iso}, we show the total SFR of the simulated galaxy, where the blue line denotes the simulation result without a BH, for comparison."839 The feedback from the stationary BH reduces the SFR of the host galaxy in the central regions during the simulated time, The feedback from the stationary BH reduces the SFR of the host galaxy in the central regions during the simulated time840Cas A. It is found that the 6 em power spectrum is also a broken power law with the same power law index and the break at the same angular seale as in the 20 em power spectrum.,Cas A. It is found that the 6 cm power spectrum is also a broken power law with the same power law index and the break at the same angular scale as in the 20 cm power spectrum.841 The VLA 6 cm power spectra obtained from observation with different array configurations and two different IFs are plotted in Figure GE)., The VLA 6 cm power spectra obtained from observation with different array configurations and two different IFs are plotted in Figure \ref{fig:4}) ).842 This shows that the steeper power law at the long baseline range is in fact extended upto 100 KA ες2.5 aresec)., This shows that the steeper power law at the long baseline range is in fact extended upto $100$ $\lambda$ $\sim 2.5$ arcsec).843 The four panels in Figure (50) show the power spectra with lo errorbars derived using the data from four different VLA array configuration and two IFs., The four panels in Figure \ref{fig:5}) ) show the power spectra with $\pm 1 \sigma$ errorbars derived using the data from four different VLA array configuration and two IFs.844 Clearlv. for Cas A also. the power spectra derived from 20 em and 6 em data with different array configurations and different TFs are in good agreement.," Clearly, for Cas A also, the power spectra derived from 20 cm and 6 cm data with different array configurations and different IFs are in good agreement."845 The power law index of the steeper part of the Cas A angular power spectrum is completely consistent. within the measurement errorbars. with the power law index of the Crab Nebula power spectra.," The power law index of the steeper part of the Cas A angular power spectrum is completely consistent, within the measurement errorbars, with the power law index of the Crab Nebula power spectra."846 The break in the Cas A power spectrum and the change of the power law index at small baseline range (or large angular scale) is very interesting., The break in the Cas A power spectrum and the change of the power law index at small baseline range (or large angular scale) is very interesting.847 We have veritied analytically that the shell type geometry of Cas A will affect the power spectrum significantly only at very small € by convolving it with a window function which is the Fourier transform of the two dimensional projection of this optically thin shell., We have verified analytically that the shell type geometry of Cas A will affect the power spectrum significantly only at very small $U$ by convolving it with a window function which is the Fourier transform of the two dimensional projection of this optically thin shell.848 The same is also true for the optically un spherical geometry of the Crab Nebula., The same is also true for the optically thin spherical geometry of the Crab Nebula.849 For the long baseline range around L0 KA. the effect will be negligible and can not explain ye sharp break and the signiticant change of power law index by 1.," For the long baseline range around $10$ $\lambda$, the effect will be negligible and can not explain the sharp break and the significant change of power law index by $\sim 1$."850 Tt appears that a plausible explanation is a transition from iree dimensional at small scales (£7710 KA) to two dimensional urbulence at large scales (£7<LO ΚΑ)., It appears that a plausible explanation is a transition from three dimensional at small scales $U > 10$ $\lambda$ ) to two dimensional turbulence at large scales $U < 10$ $\lambda$ ).851 The shell thickness sets je angular scale of the transition., The shell thickness sets the angular scale of the transition.852 On length scales smaller than ye shell thickness. the shell can have modes of perturbation in all three independent directions.," On length scales smaller than the shell thickness, the shell can have modes of perturbation in all three independent directions."853 But on length scales larger than ye shell thickness. there will be no modes perpendicular to the Palhell thiekness.," But on length scales larger than the shell thickness, there will be no modes perpendicular to the shell thickness."854 This makes the turbulence to change from a three dimensional to effectively a two dimensional in nature and hence ye power law index changes by 1., This makes the turbulence to change from a three dimensional to effectively a two dimensional in nature and hence the power law index changes by $1$.855 This change in slope may yossibly be related to the fact that the slope of the velocity power spectrum changes from 11/2 to. 5/3 in going from 3D to 2D or incompressible. Kolmogorov turbulence (Kolmogorov1941).," This change in slope may possibly be related to the fact that the slope of the velocity power spectrum changes from $-11/3$ to $-8/3$ in going from 3D to 2D for incompressible, Kolmogorov turbulence \citep{ko41}."856 The density power spectrum is predicted to follows the velocity »ower spectrum in the Goldreich&Sridhar(1995). model of MHD urbulence., The density power spectrum is predicted to follows the velocity power spectrum in the \citet{gs95} model of MHD turbulence.857 The observation. that the angular scale of this break matches approximately with the shell thickness. is indicative of the consistency ofthis picture.," The observation, that the angular scale of this break matches approximately with the shell thickness, is indicative of the consistency of this picture."858 A similar difference of e| in the power aw index has also been observed and interpreted as a transition rom three dimensional turbulence to two dimensional turbulence in the power spectrum of H1 21 em emission intensity fluctuations of the Large Magellanic Cloud (Elmegreenetal.2001). and the galaxy NGC 628 (Duttaetal.2008).., A similar difference of $\approx 1$ in the power law index has also been observed and interpreted as a transition from three dimensional turbulence to two dimensional turbulence in the power spectrum of H 21 cm emission intensity fluctuations of the Large Magellanic Cloud \citep{el01} and the galaxy NGC 628 \citep{dp08}.859 The scale-free nature of the power spectra over a wide range of scales and a very similar value of the power law index for power spectra of two very different type of supernova remnants suggests the universality of the physical process responsible for the observed intensity fluctuation., The scale-free nature of the power spectra over a wide range of scales and a very similar value of the power law index for power spectra of two very different type of supernova remnants suggests the universality of the physical process responsible for the observed intensity fluctuation.860 We propose that the fluctuation is most probably due to the turbulence in the svnchrotron emitting plasma that gives rise to the power law power spectrum., We propose that the fluctuation is most probably due to the turbulence in the synchrotron emitting plasma that gives rise to the power law power spectrum.861 The interaction of the propagating shock with the turbulent interstellar medium is known to enhance the turbulence in the postshock region and causes the spatial variation of emission in supernova remnants (Balsaraetal.2001)., The interaction of the propagating shock with the turbulent interstellar medium is known to enhance the turbulence in the postshock region and causes the spatial variation of emission in supernova remnants \citep{ba01}.862".. We investigate here whether the observed power spectrum 24)x.&.7. or equivalently the energy spectrum (fh)=LDPOSxfk17, is consistent with our present understanding of astrophysical turbulence."," We investigate here whether the observed power spectrum $P(k) \propto k^{-3.2}$, or equivalently the energy spectrum $E(k) = k^2 P(k) \propto k^{-1.2}$, is consistent with our present understanding of astrophysical turbulence."863 The observed intensity fluctuation. power spectra is related to the density and magnetic field power spectra which. in turn. are found. from numerical simulations. to closely follow the velocity fluctuation power spectra.," The observed intensity fluctuation power spectra is related to the density and magnetic field power spectra which, in turn, are found, from numerical simulations, to closely follow the velocity fluctuation power spectra."864 For incompressible and nonmagnetized turbulence Kolmogorov theory suggests an isotropic power law velocity fluctuation energy spectrum (Kk)oxf&7? where k is the magnitude of the wave vector (Kolmogorov1941)., For incompressible and nonmagnetized turbulence Kolmogorov theory suggests an isotropic power law velocity fluctuation energy spectrum $E_v(k)\propto k^{-5/3}$ where $k$ is the magnitude of the wave vector \citep{ko41}.865 Irosnikov(1964) and Kraichna(1965). gave a model of magnetic incompressible turbulence UK theory) that predicts. even in the presence of magnetic field. isotropic power law energy spectra L(A)oxfk42 for both velocity and magnetic feld.," \citet{ir64} and \citet{kr65} gave a model of magnetic incompressible turbulence (IK theory) that predicts, even in the presence of magnetic field, isotropic power law energy spectra $E(k) 866\propto k^{-3/2}$ for both velocity and magnetic field."867" Without any assumption of isotropic energy distribution. Goldreich&Sridhar(1995). proposed a model of incompressible magnetohydrodynamic turbulence that predicts a Kolmogorov-like energy spectra Ac(ki)xAy75 where hk, ds the component of the wave vector perpendicular to the local magnetic field direction."," Without any assumption of isotropic energy distribution, \citet{gs95} proposed a model of incompressible magnetohydrodynamic turbulence that predicts a Kolmogorov-like energy spectra $E_v(k_\perp) \propto k_\perp^{-5/3}$ where $k_\perp$ is the component of the wave vector perpendicular to the local magnetic field direction."868 It also predicts an anisotropy condition &|xn? where /| is the component of the wave vector parallel to the local magnetic tield direction.," It also predicts an anisotropy condition $k_\parallel \propto 869k_\perp^{2/3}$ where $k_\parallel$ is the component of the wave vector parallel to the local magnetic field direction."870 But. even if there is anisotropy in the system of reference defined by the local magnetic field. it is worth keeping in mind tha there will only be moderate anisotropy in the observer's reference.," But, even if there is anisotropy in the system of reference defined by the local magnetic field, it is worth keeping in mind that there will only be moderate anisotropy in the observer's reference."871 For compressible magnetohydrodynamics turbulence. there is. unfortunately. no widely-accepted theory and much of the presen understanding has come from numerical results.," For compressible magnetohydrodynamics turbulence, there is, unfortunately, no widely-accepted theory and much of the present understanding has come from numerical results."872 Recent numerica simulation indicates that. for compressible magnetohydrodynamic turbulence. both the velocity and magnetic field energy spectra and anisotropy in Alfvén modes and slow modes are as predicted by (Goldreich&Sridhar1995).," Recent numerical simulation indicates that, for compressible magnetohydrodynamic turbulence, both the velocity and magnetic field energy spectra and anisotropy in $\acute{e}$ n modes and slow modes are as predicted by \citep{gs95}."873. But the energy spectra for fas modes are isotropic and the scaling is as predicted in IK theory (Cho&Lazarian2002b)., But the energy spectra for fast modes are isotropic and the scaling is as predicted in IK theory \citep{cl02}.874. It is also found that. at least in case of incompressible magnetic turbulence. viscous damping on scales larger than the magnetic diffusion scale can make the magnetic energy spectrum signiticantly less steep.," It is also found that, at least in case of incompressible magnetic turbulence, viscous damping on scales larger than the magnetic diffusion scale can make the magnetic energy spectrum significantly less steep."875" Choetal.(2002) reports magnetic energy spectrum £,(4)x& implying rich structure of magnetic field on small scales.", \citet{ch02} reports magnetic energy spectrum $E_b(k) \propto k^{-1}$ implying rich structure of magnetic field on small scales.876 The synchrotron emissivity ἐςxn.|BL4|2U? where n. is, The synchrotron emissivity $i_s \propto n_e|B_\perp|^{(p+1)/2}$ where $n_e$ is877evolution of a disk svsem from high redshift to the present clay.,evolution of a disk system from high redshift to the present day.878 The kinematical estimate of the disk mass allows us to derive the mass-to-ight ratios for our disk svstems as a function of luminosity and colour., The kinematical estimate of the disk mass allows us to derive the mass-to-light ratios for our disk systems as a function of luminosity and colour.879 In Fig., In Fig.880 3 we compare the disk mass ane colour as a function of mass-to-light ratio compared to the relaion in local spirals (Shankarctal. 2006)., 3 we compare the disk mass and colour as a function of mass-to-light ratio compared to the relation in local spirals \citep{Shankar06}.881. In order to compare directly with local relations. we consider a simple passive evolution model for the luminosity. evolution.," In order to compare directly with local relations, we consider a simple passive evolution model for the luminosity evolution."882 For a single stellar. population the zero-point of the local relation is cleereaed by a factor /og(13.776) which accounts for the passive evolution of a stellar population from z=l1 to ς=0., For a single stellar population the zero-point of the local relation is decreaed by a factor $log (13.7/6)$ which accounts for the passive evolution of a stellar population from $z=1$ to $z=0$.883 As Fig., As Fig.884 3 shows the mass-to-light ratios as a function of galaxv (D. Y) colour are in broad. agreement with predictions of a single stellar population which is 1C/gyr old (Bruzual&Charlot 2003).. although clearly photometry at other wavelengths (such as rest-frame Ix-band) would allow a more detailed decomposition of the stellar popultations in these galxies.," 3 shows the mass-to-light ratios as a function of galaxy $B-V$ ) colour are in broad agreement with predictions of a single stellar population which is $\sim1Gyr$ old \citep{Bruzual03}, although clearly photometry at other wavelengths (such as rest-frame K-band) would allow a more detailed decomposition of the stellar popultations in these galxies."885 Figure 2 shows that at a radius corresponding to Vip he high redshift &alaxies are significantly denser than comparably luminous local cisk-galaxies: the average offset is about 0.6 dex in {ουκp) >., Figure 2 shows that at a radius corresponding to $V_{opt}$ the high redshift galaxies are significantly denser than comparably luminous local disk-galaxies: the average offset is about 0.6 dex in $log(<\rho)>$ .886 Although we can not exclude hat dynamical processes occur between z=1 and 2=0 o reduce the dark-matter density in the luminous regions. his offset is naturally explained if the halos embedding hese disk galaxies formed at earlier times than the halos around similarly massive >=0 spirals.," Although we can not exclude that dynamical processes occur between $z=1$ and $z=0$ to reduce the dark-matter density in the luminous regions, this offset is naturally explained if the halos embedding these disk galaxies formed at earlier times than the halos around similarly massive $z=0$ spirals."887 In this framework we estimate the ratio between the virialization redshift of the ocal galaxies and and that of the galaxies in our sample., In this framework we estimate the ratio between the virialization redshift of the local galaxies and and that of the galaxies in our sample.888" Since p.x.AtaJO|n)? where p, and τε are average density and. recdshift at. virialization anc A, is known. for ty—d. =lO. which corresponds tof.=6Gyr."," Since $\rho_v\propto~\Delta(z_v) (1+z_v)^3$ where $\rho_v$ and $z_v$ are average density and redshift at virialization and $\Delta_v$ is known, for $z_{0}=1$, $z_{v}=1.7$, which corresponds to $t_v=6 \ Gyr$."889 Assuming that our sample is a [air representation of disk galaxies at 21 and that these are approximately coeval. from the comxwison of their structural properties with those of 2=0 spirals. the following simple picture enierges: α present clay spiral. with a given circular velocity. half-lisht. racius and tic angular pmionmentunm per unit niass. at redshift 1 had similar values for these quantities. but a smaller stellar mass: <ων)νο).co 0.3.," Assuming that our sample is a fair representation of disk galaxies at $z\sim 1$ and that these are approximately coeval, from the comparison of their structural properties with those of $z=0$ spirals, the following simple picture emerges: a present day spiral, with a given circular velocity, half-light radius and the angular momentum per unit mass, at redshift $1$ had similar values for these quantities, but a smaller stellar mass: $<M_\star (t_{obs})/ M_\star (t_0)> \simeq 0.3$ ."890 This induces a scale for twe average SER in the past S Civr: ~UOT5MS(10)(ConsfolVALΠΟ(LOMyr.," This induces a scale for the average SFR in the past 8 Gyr: $ \sim ~8910.75 M_\star (t_{0}) /(t_{obs}-t_{0}) \sim \ 1 (M_\star(t_0)/ (10^{10}892M_\odot) M_\odot/yr$."893 With these disks having an average age of LCCyrAL./ at >=] we can also derive an “early times” average SER MO.25AL(aGOCur)~BALGo)(OMAL.fyr which points towards a declining SER. history.," With these disks having an average age of Gyr at $z=1$ we can also derive an ""early times"" average SFR $ \sim ~ 0.25894M_\star (t_{0}) / (1 Gyr) \sim 3 (M_\star(t_0)/ (10^{10} M_\odot)895M_\odot/yr$ which points towards a declining SFR history."896 The marked inerease of the Luminosity per unit stellar mass in objects at high redshifts with respect to their local counterparts has the simplest explanation in a passive evolution of the starforming disks., The marked increase of the luminosity per unit stellar mass in objects at high redshifts with respect to their local counterparts has the simplest explanation in a passive evolution of the starforming disks.897 Obviously. this simple picture requires us to assume that the high redshift svstenis are the direct counter-parts of similar rotation speed spirals at low redshift.," Obviously, this simple picture requires us to assume that the high redshift systems are the direct counter-parts of similar rotation speed spirals at low redshift."898 In this study. we have investigated the detailed: properties of four disk galaxies at z=1.," In this study, we have investigated the detailed properties of four disk galaxies at $z=1$."899 These galaxies were observed at high spatial resolution thanks to the boost in angular size provided by gravitational lensing by foreground massive galaxy clusters and allow a much more detailed comparison with local populations than usually possible for galaxies at these early times., These galaxies were observed at high spatial resolution thanks to the boost in angular size provided by gravitational lensing by foreground massive galaxy clusters and allow a much more detailed comparison with local populations than usually possible for galaxies at these early times.900 Modelling the one-dimensional rotation curves with those of Persieetal.(L996) we derive best fit parameters for the total dvnamical mass. the core radius. the effective core density and the angular momentum. per unit mass.," Modelling the one-dimensional rotation curves with those of \citet{Persic96} we derive best fit parameters for the total dynamical mass, the core radius, the effective core density and the angular momentum per unit mass."901 The best fit model rotation curves to the data show that the amplitude ancl profileof the stellar disk componentcan not unambiguously reproduce the rise in the rotation curve withouta dark matter component., The best fit model rotation curves to the data show that the amplitude and profileof the stellar disk componentcan not unambiguously reproduce the rise in the rotation curve withouta dark matter component.902 Comparing the average, Comparing the average903plate.,plate.904 We can also define an cllcctive SB. where the constant € depends on the exact definition of he ellective SB.," We can also define an effective SB, where the constant C depends on the exact definition of the effective SB."905 It can also be useful to define an elfective radius.re. which is the radius containing half the light. of he galaxy.," It can also be useful to define an effective radius,$r_{\rm e}$, which is the radius containing half the light of the galaxy."906 This is related to the scale size by ο=L678ro or a circularlv-svmmetric image with an exponential light oolfile.," This is related to the scale size by $r_{\rm e} =9071.678 r_{0}$ for a circularly-symmetric image with an exponential light profile."908 For the SD at 7. the constant is €=1.822. and or the mean SD within p. € —1.124.," For the SB at $r_{\rm e}$, the constant is $C=1.822$, and for the mean SB within $r_{\rm e}$, $C =9091.124$."910" Also the average SB within the isophotal area (for the APAL scans of UST blue ates this isophote is zz25 by mag 7)E can be written as where sla, and Zi; are the corresponding isophotal size and. brightness. derived. directly from eq.(9))."," Also the average SB within the isophotal area (for the APM scans of UKST blue plates this isophote is $\approx 25$ $_{J}$ mag $^{-2}$ ) can be written as where $A_{\rm iso}$ and $I_{\rm iso}$ are the corresponding isophotal size and brightness, derived directly from \ref{eq_pr}) )."911 Xcdditionallv. one can also calculate the ‘total AVAL magnitude from Zia. for circular images.," Additionally, one can also calculate the `total APM magnitude' from $I_{\rm tot}$, for circular images."912 This is related to the conventional total magnitude of the image. which is given by where Z is the magnitude zero-point.," This is related to the conventional total magnitude of the image, which is given by where $Z$ is the magnitude zero-point."913 The relationship between these three SB measures can be seen in Figure 2.., The relationship between these three SB measures can be seen in Figure \ref{fig_u0ue}.914" In this Figure. we fix the value of rj to illustrate the dependencies between these SB paranicters. giving ry à vàue of 2.15 aresο, chosen to be fairly tvpical of the APM sample."," In this Figure, we fix the value of $r_{0}$ to illustrate the dependencies between these SB parameters, giving $r_0$ a value of 2.15 arcsec, chosen to be fairly typical of the APM sample."915" Thougi the ciflerent SB measures are all clerivec from the sani| seb of (po. ro) data. we see in Figure 2aa that some eaaxies can show much larger dillerences between jas, and either po or fee than other galaxies."," Though the different SB measures are all derived from the same set of $p_{0}$, $r_{0}$ ) data, we see in Figure \ref{fig_u0ue}a a that some galaxies can show much larger differences between $\mu_{\rm916iso}$ and either $\mu_{0}$ or $\mu_{\rm e}$ than other galaxies."917 Figure 2bb presents the isophotal magnitude. labelleck mi. as à function of the total magnitude for the same value of ro.," Figure \ref{fig_u0ue}b b presents the isophotal magnitude, labelled $m_{\rm iso}$, as a function of the total magnitude for the same value of $r_0$."918 This is shown for both the stancare magnitude and for the APAL magnituce parameters. of equations (4)) and (19))., This is shown for both the standard magnitude and for the APM magnitude parameters of equations \ref{eq_miso}) ) and \ref{eq_mtot2}) ).919" mi;, can be significantly fainter than moa. at both high and low SB."," $m_{\rm iso}$ can be significantly fainter than $m_{\rm tot}$ , at both high and low SB."920 At high SD (bright total magnitude). the Dux Za is lost because of the emulsion saturation: at low SB (faint total magnitude) the Dux Zia is missed. because of the isophotal limit.," At high SB (bright total magnitude), the flux $I_{\rm sat}$ is lost because of the emulsion saturation; at low SB (faint total magnitude) the flux $I_{\rm921field}$ is missed because of the isophotal limit."922 This also provides a rough estimate of how much jo will be underestimated if these two parts of missing Hux are not accounted. for., This also provides a rough estimate of how much $\mu_{0}$ will be underestimated if these two parts of missing flux are not accounted for.923 The clleet of saturation and isophotal threshold. on the magnitude is shown explicitly in Figure 8((a)., The effect of saturation and isophotal threshold on the magnitude is shown explicitly in Figure \ref{fig dm}( (a).924 As mentioned in Section. 3.1.. bright galaxies may be saturated over a large fraction of the image.," As mentioned in Section \ref{sec_apm}, bright galaxies may be saturated over a large fraction of the image."925 This can be seen quantitatively in Figure 3((b). which shows the ratio of isophotal radius. Fs. nd saturation radius. ray. to the scale length. ry as a function of total magnitucle.," This can be seen quantitatively in Figure \ref{fig dm}( (b), which shows the ratio of isophotal radius, $r_{\rm iso}$, and saturation radius, $r_{\rm sat}$, to the scale length, $r_0$ as a function of total magnitude."926 As described above. this approach only provides a rough measurement of the SB of galaxies.," As described above, this approach only provides a rough measurement of the SB of galaxies."927 Lt does not use the real profile of different types of galaxies. which may be different from an exponential disk.," It does not use the real profile of different types of galaxies, which may be different from an exponential disk."928 Lt also neglects any internal structures. such as arms. bars or a central bulge.," It also neglects any internal structures, such as arms, bars or a central bulge."929 Also. although we have rejected images that are most likely to be merged pairs. the automated image classification is not perfect. and there is a residual contamination of about of merged images. whose profiles will not be well represented by our simple mocel.," Also, although we have rejected images that are most likely to be merged pairs, the automated image classification is not perfect, and there is a residual contamination of about of merged images, whose profiles will not be well represented by our simple model."930 Although for anw individual ealaxy our SB measurcment is unlikely to be very accurate. it is helpful to constrain the shape of any given. profile anc it does allow us to make general comparisons of galaxy SB within the whole sample.," Although for any individual galaxy our SB measurement is unlikely to be very accurate, it is helpful to constrain the shape of any given profile and it does allow us to make general comparisons of galaxy SB within the whole sample."931 Theoretically. this approach is suitable for any other profile which is specified by only two parameters. such as a Gaussian profile. or ant? law prolile. Without any other cllective observational constraints on the profile shape an exponential profile is the most reasonable choice since it is à good representation for a majority of galaxies.," Theoretically, this approach is suitable for any other profile which is specified by only two parameters, such as a Gaussian profile, or an $r^{1/4}$ law profile, Without any other effective observational constraints on the profile shape an exponential profile is the most reasonable choice since it is a good representation for a majority of galaxies."932 As discussed. in Section 5.2... we lind that a7 as defined in eq.(7)) is not very effective in distinguishing between cillerent profiles.," As discussed in Section \ref{sec_profiles}, we find that $\sigma^{2}$ as defined in \ref{eq_sig2}) ) is not very effective in distinguishing between different profiles."933 Actelitionally. the exponential profile has been apopular choice in earlier work. so it allows us to compare with other results.," Additionally, the exponential profile has been apopular choice in earlier work, so it allows us to compare with other results."934 So. in this," So, in this"935while in none of them a detailed. determination of the detectability by INTEECILAL was performed.,while in none of them a detailed determination of the detectability by INTEGRAL was performed.936 Phe aim of this paper is to accurately. compute the evolution of the 5-ràv spectra for a complete set of models. covering all the theories already mentioned. and to determine which spectral features could provide interesting information about SNlIa.," The aim of this paper is to accurately compute the evolution of the $\gamma$ -ray spectra for a complete set of models, covering all the theories already mentioned, and to determine which spectral features could provide interesting information about SNIa."937 A Monte-Carlo 5-ray transfer code has been developed to compute the 5-rav emission for all the explosion mocels., A Monte-Carlo $\gamma$ -ray transfer code has been developed to compute the $\gamma$ -ray emission for all the explosion models.938 Afterwards. the spectra have been convolved with the expected instrumenta response for LBES (Lei1995) and SPE (Jeanetal.1995). on-board of INTEGRAL to obtain the observational properties.," Afterwards, the spectra have been convolved with the expected instrumental response for IBIS \cite{Le95} and SPI \cite{Pj95} on-board of INTEGRAL to obtain the observational properties."939 A set of quantities that characterize the detectable spectra properties including line and continuum. intensities. aun line shapes have been determined., A set of quantities that characterize the detectable spectral properties including line and continuum intensities and line shapes have been determined.940 We have also compute which are the detectability limits of these properties anc investigated when. any given model could. be rejected: or identified. if à SNla is observed.," We have also computed which are the detectability limits of these properties and investigated when, any given model could be rejected or identified if a SNIa is observed."941 Although the radioactive decav of freshly svathesized nuclei is the main source of 5- emission for SNla. it is not the unique one.," Although the radioactive decay of freshly synthesized nuclei is the main source of $\gamma$ -ray emission for SNIa, it is not the unique one."942 We have also investigated the emission produced by the nuclear excitation due to the interaction between the fast ejecta and. the circumstellar medium. as would happen in the case of the explosion of a type la supernova in a svmbiotic binary. or in a ISM cloud.," We have also investigated the emission produced by the nuclear excitation due to the interaction between the fast ejecta and the circumstellar medium, as would happen in the case of the explosion of a type Ia supernova in a symbiotic binary, or in a ISM cloud."943 Although. this mechanism is much weaker it has the advantage that it operates on longer time-scales (up to 1000s of vears)," Although, this mechanism is much weaker it has the advantage that it operates on longer time-scales (up to 1000's of years)."944 In order to compute the 5-rav spectra of the dillerent models we have developed: a code for the treatment of the s-ray transfer. as described by Pozdnvyakov ct al. (," In order to compute the $\gamma$ -ray spectra of the different models we have developed a code for the treatment of the $\gamma$ -ray transfer, as described by Pozdnyakov et al. ("9451983) and Ambwani et al. (,1983) and Ambwani et al. (9461955),1988).947 Lt is based on the Monte-Carlo method technique. which allows the treatment of the comptonization process without approximations.," It is based on the Monte-Carlo method technique, which allows the treatment of the comptonization process without approximations."948 With the code we can simulate the 5-rav. spectra emitted by a SNla with arbitrary composition. velocity ancl density profiles.," With the code we can simulate the $\gamma$ -ray spectra emitted by a SNIa with arbitrary composition, velocity and density profiles."949LE Although many radioactive chains are included in the code only the following ones are important in the case of type Ia SNe: Three dillerent sources of opacity have been taken into account: Compton scattering. photo-electrie absorption and pair production.," Although many radioactive chains are included in the code only the following ones are important in the case of type Ia SNe: Three different sources of opacity have been taken into account: Compton scattering, photo-electric absorption and $^+$ $^-$ pair production."950 Phe cross section for Compton scattering is given by the habitual Wlein-Nishina expression. while absorption and pair production cross sections were taken from the compilation of experimentally evaluated data maintained by the Brookhaven National Laboratory Three sources of 5. photons are considered besides nuclear decay: direct emission of two photons (511 keV) by electron. positron annihilation. indirect emission of two or three photons by positronium annihilation (Ore&Powell 1949).. and emission of Duorescence photons (not relevant in the present work since they are low energy. photons E < 10 keV).," The cross section for Compton scattering is given by the habitual Klein-Nishina expression, while absorption and pair production cross sections were taken from the compilation of experimentally evaluated data maintained by the Brookhaven National Laboratory Three sources of $\gamma$ photons are considered besides nuclear decay: direct emission of two photons (511 keV) by electron positron annihilation, indirect emission of two or three photons by positronium annihilation \cite{Or49}, and emission of fluorescence photons (not relevant in the present work since they are low energy photons E $<$ 10 keV)."951 Simulations have been carried out to obtain both he evolution of the intensity of the strongest lines in the orm of light curves and the detailed spectra at given times., Simulations have been carried out to obtain both the evolution of the intensity of the strongest lines in the form of light curves and the detailed spectra at given times.952 The properties of the ejecta for the different models iwe been kindly provided by IZ. Bravo who obtainec hem from accurate simulations of SNla explosions., The properties of the ejecta for the different models have been kindly provided by E. Bravo who obtained them from accurate simulations of SNIa explosions.953 Al he calculations were performed. following the evolution of he system through the accretion phase and starting with a Qs partially cooled. white dwarf with a composition (No =0.51. No=049).," All the calculations were performed following the evolution of the system through the accretion phase and starting with a 0.8 partially cooled white dwarf with a composition $_{C}$ =0.51, $_{O}$ =0.49)."954 The general procedure follower in the simulations is fully described. in Bravo οἱ al. (, The general procedure followed in the simulations is fully described in Bravo et al. (9551996) with the exception of the sub-Chancdrasekhar moce (hereafterSUB) were a particularly accurate simulation of we accretion phase was carried. out by José (José 1996) with a hvdrodynamical code.,"1996) with the exception of the sub-Chandrasekhar model (hereafter,SUB) were a particularly accurate simulation of the accretion phase was carried out by José (José 1996) with a hydrodynamical code."956 VPhis calculation is. up to ate. the most consistent simulation of a sub-Chancrasekhar supernova in 1D. TFhree other models have been considered: DEF. DEL and DET. representing dellagration. delayed etonation and detonation. supernovae. respectively.," This calculation is, up to date, the most consistent simulation of a sub-Chandrasekhar supernova in 1D. Three other models have been considered: DEF, DEL and DET, representing deflagration, delayed detonation and detonation supernovae, respectively."957 The etails of the parameterizations adopted in the propagation X the burning front for DEF. DEL. and. DET models are uso described in Bravo et al.," The details of the parameterizations adopted in the propagation of the burning front for DEF, DEL, and DET models are also described in Bravo et al."958 1996., 1996.959 Phe main properties of rese models at the beginning of the homologous expansion phase are summarized in Table 1 and Figure 1.., The main properties of these models at the beginning of the homologous expansion phase are summarized in Table \ref{Tab1} and Figure \ref{fig}.960" Phe values in the table correspond to the ""Ni and "" Ni contain. mass of C | O. velocity of the shell with m= I and total kinetic energy."," The values in the table correspond to the $^{56}$ Ni and $^{57}$ Ni contain, mass of C + O, velocity of the shell with m= 1 and total kinetic energy."961" The basic properties of our models (particularly. the ejected ""NI mass and kinetic energy) are compatible within uncertainities with those found in the literature (see for example mocels edtgr (Woosley&Weaverl086). DIEI and DLETI (ülIolich&WKhoklov1996).. N21 (Ixhokhloy.1991).. Model 7 (Wooslev&Weaver 1994)))."," The basic properties of our models (particularly, the ejected $^{56}$ Ni mass and kinetic energy) are compatible within uncertainities with those found in the literature (see for example models cdtg7 \cite{Wo86} DF1 and DET1 \cite{Ho96}, N21 \cite{Kh91}, Model 7 \cite{Wo94}) )."962 'T'he evolution of the 5-rav. emission of these mocels is shown by the instantaneous spectra appearing in Figure 2 and by the light. curves of the strongest lines (Figure 3))., The evolution of the $\gamma$ -ray emission of these models is shown by the instantaneous spectra appearing in Figure \ref{fig1} and by the light curves of the strongest lines (Figure \ref{fig2}) ).963 As expected from the models considered here the main properties of these spectra and light curves are compatible with those found in the literature for similar scenarios (see results for WT (BurrowsandThe1990). and DEF (Llollichetal. 1994): WDD2 (Ixumagai&Nomoto1995). and N21 (Llollichetal.1994): DIZEL1(LIOllichetal. 1994): Model 2 (Woosley&Timmes 1996)))., As expected from the models considered here the main properties of these spectra and light curves are compatible with those found in the literature for similar scenarios (see results for W7 \cite{Bu90} and DEF \cite{Ho94}; WDD2 \cite{Ku95} and N21 \cite{Ho94}; \cite{Ho94}; Model 2 \cite{Wo96}) ).964 However. not all the properties are comparable since in some of these works either the continuum properties or the line profiles are not described.," However, not all the properties are comparable since in some of these works either the continuum properties or the line profiles are not described."965 Twenty days. after the explosion. the DELE model only shows a continuum component while the DEL. DET and SUB already. display strong lines due to their higher expansion rates.," Twenty days after the explosion, the DEF model only shows a continuum component while the DEL, DET and SUB already display strong lines due to their higher expansion rates."966" Lines are particularly intense lor DET and SUD models since they contain ""Ni and ""Co in he outermost shells.", Lines are particularly intense for DET and SUB models since they contain $^{56}$ Ni and $^{56}$ Co in the outermost shells.967 Phe cllicieney of comptonization to xocduce continuum at low energies is limited in all models w the competing photo-clectric absorption which imposes a cutoll below 40 100 keV. The energv of the cutoll is determined by the chemical composition of the external avers where most of the emergent continuum is formed at his epoch., The efficiency of comptonization to produce continuum at low energies is limited in all models by the competing photo-electric absorption which imposes a cutoff below 40 – 100 keV. The energy of the cutoff is determined by the chemical composition of the external layers where most of the emergent continuum is formed at this epoch.968 In DEP and SUB models. comptonization mainly," In DEF and SUB models, comptonization mainly"969(UVOT) observations took place intermittently between 03:58 UT and 12:10 UT. with a total ou-source exposure time of SO36 s. Very Large observations were conducted at a frequency of 8.16 GITz in the standard coutiuuuau mode with 2«50 MIIz coutiguous bands.,"(UVOT) observations took place intermittently between 03:58 UT and 12:10 UT, with a total on-source exposure time of 8036 s. Very Large observations were conducted at a frequency of 8.46 GHz in the standard continuum mode with $2\times 50$ MHz contiguous bands."970 Scans of 295 s ou source were interleaved with 50 s scans on the phase calibrator J1515|236., Scans of 295 s on source were interleaved with 50 s scans on the phase calibrator J1513+236.971 The flux deusitv scale was determined using the extragalactic source Lis (JO127|331)., The flux density scale was determined using the extragalactic source 48 (J0137+331).972 The data were reduced auc analyzed using the Astronomical Tage Processing Svstem (AIPS)., The data were reduced and analyzed using the Astronomical Image Processing System (AIPS).973 The visibility. data were inspected for quality. aud leisy points were removed.," The visibility data were inspected for quality, and noisy points were removed."974 To search for source variability. we constructed Πο curves using the following method.," To search for source variability, we constructed light curves using the following method."975 We removed all the bright feld sources using the AIPS/IMACGR routine to CLEAN the region around cach source. and the AIPS/UVSUD routine to subtract the resulting source models frou the visibility data.," We removed all the bright field sources using the AIPS/IMAGR routine to CLEAN the region around each source, and the AIPS/UVSUB routine to subtract the resulting source models from the visibility data."976 We then plotted the real part of the complex visibilities at the position of aas a function of time using the AIPS/DFTPL routine., We then plotted the real part of the complex visibilities at the position of as a function of time using the AIPS/DFTPL routine.977 The subtraction of field sources is required since their sidelobes aud the change in the shape of the svuthesized bean during the observation result in flux variations over the map that may contanunate real variability or generate false variabilitv., The subtraction of field sources is required since their sidelobes and the change in the shape of the synthesized beam during the observation result in flux variations over the map that may contaminate real variability or generate false variability.978 The resulting light curves are shown iu Figures 1 and 2.., The resulting light curves are shown in Figures \ref{fig:all} and \ref{fig:flares}.979" The observations were made with the οὐ (backsicdealhuninated chip). with ooffset. from the on-axis focal poit by 15""."," The observations were made with the Chandra/ACIS-S3 (backside-illuminated chip), with offset from the on-axis focal point by $15''$."980 À total of 20.76 ks were obtained., A total of 29.76 ks were obtained.981" Data were analyzed using CIAO version 3.3. aud counts were extracted in a 1"" radius civcle centered ou the source position."," Data were analyzed using CIAO version 3.3, and counts were extracted in a $1''$ radius circle centered on the source position."982 We find a total of 8 counts in the 0.2.2 keV range. and 2 additional counts with ADx10 keV. Backeround counts were extracted from annuli ceutered. ou the source position. exchiding other point sources detected in the observation.," We find a total of 8 counts in the $0.2-2$ keV range, and 2 additional counts with $kT\approx 10$ keV. Background counts were extracted from annuli centered on the source position, excluding other point sources detected in the observation."983" We find that 2 backeround counts are expected within the source extraction aperture. likely correspouding to the two photons with &Tx10 keV. The source comnts exhibit a narrow energy range with RD)=930+250 eV. corresponding to a typical plasina temperature of LL«107 EK. Usine this temperature with a Ravinoud-Suuth plasima model we find an energy conversion factor of Lcount=δεν100D ere 2 t (0.2...2 keV),"," We find that 2 background counts are expected within the source extraction aperture, likely corresponding to the two photons with $kT\approx 10$ keV. The source counts exhibit a narrow energy range with $\langle984kT\rangle=930\pm 250$ eV, corresponding to a typical plasma temperature of $1.1\times 10^7$ K. Using this temperature with a Raymond-Smith plasma model we find an energy conversion factor of $1\,{\rm count}=3.4\times 10^{-12}$ erg $^{-2}$ $^{-1}$ $0.2-2$ keV)."985" Thus. the observed count rate of 2.69«10.! s| translates toa flux of 8.3410.16 eee 7s 1(02.2 keV). or a flux deusitv of 1.1 uJv at AD=1 keV. At the distance of tthe correspouding hiuiuositv is Lyzc12«107 ere 1 or a ratio of Ly/Ly4z10.H9,"," Thus, the observed count rate of $2.69\times 10^{-4}$ $^{-1}$ translates to a flux of $9.3\times 10^{-16}$ erg $^{-2}$ $^{-1}$ $0.2-2$ keV), or a flux density of $1.4$ nJy at $kT=1$ keV. At the distance of the corresponding luminosity is $L_X\approx9861.2\times 10^{25}$ erg $^{-1}$, or a ratio of $L_X/L_{\rm bol}\approx98710^{-4.9}$."988 This detection is at the sale level as the quiescent enuisson from the ALS dwarf 110 (Flemingetal.2003).. the faintest N-rav οιτας ]ate-M cawart to date.," This detection is at the same level as the quiescent emission from the M8 dwarf 10 \citep{fgg03}, the faintest X-ray emitting late-M dwarf to date."989 We nest find that of the 8 detected plotous | arrive as pairs with separations of 217 aud 31 s (Figure 1))., We next find that of the 8 detected photons 4 arrive as pairs with separations of 217 and 31 s (Figure \ref{fig:all}) ).990 The chance probabilities of such short time separations in a 29.76 ks observation are 1.7«105 and 341«&10. respectively.," The chance probabilities of such short time separations in a 29.76 ks observation are $1.7\times 10^{-3}$ and $3.4\times 10^{-5}$ , respectively."991 It is thus possible that the second pair constitutes a flare., It is thus possible that the second pair constitutes a flare.992 If true. the flare hunünositv is Ados10?! ere 2s oor Ly/Lygcm10.77. the lowest DIuniuositv flare detected from any late-M. chwart to dato.," If true, the flare luminosity is $3.1\times 10^{24}$ erg $^{-2}$ $^{-1}$, or $L_X/L_{\rm bol}\approx 10^{-5.5}$, the lowest luminosity flare detected from any late-M dwarf to date."993" The quiesceut component would be correspoudinely lower. Ly/Lic10.729,"," The quiescent component would be correspondingly lower, $L_X/L_{\rm bol}\approx 10^{-5.0}$."994 As we show below. the putative N-rav flare mav coincide with the peak of the broadest radio flare.," As we show below, the putative X-ray flare may coincide with the peak of the broadest radio flare."995 We the Gemini Multi-Object Spectrograph— (GMOS: Tooketal.2001)) mounted on the Ciomimi-Northl Saa telescope with the D600 erating set at a ceutral wavelength of 5250A.. auc with a 1 slit.," We the Gemini Multi-Object Spectrograph (GMOS; \citealt{hja+04}) ) mounted on the Gemini-North 8-m telescope with the B600 grating set at a central wavelength of 5250, and with a $1''$ slit."996 A series of cighty 300-89 exposures were obtained with a readout time of 18 s providins 91% cficiency., A series of eighty 300-s exposures were obtained with a readout time of $18$ s providing $94\%$ efficiency.997 The individual exposures were reduced using the package iu IRAF (for bias subtraction and flat-fielding). aud rectification and sky subtraction were performed using the method and software described iu Welson(2003).," The individual exposures were reduced using the package in IRAF (for bias subtraction and flat-fielding), and rectification and sky subtraction were performed using the method and software described in \citet{kel03}."998. Wavelength calibration was performed using CuAr arc lamps and air-to-vacumna corrections were applied., Wavelength calibration was performed using CuAr arc lamps and air-to-vacuum corrections were applied.999 The spectrum covers JSI0/—66850 aat a resolution of about 5À., The spectrum covers $3840-6680$ at a resolution of about 5.1000. To measure the equivalent widths of the Πα aud. 1.) enission lines we use continua reeious centered on 6551 and 6572A. and on Is5l and Ls70À.. respectively.," To measure the equivalent widths of the $\alpha$ and $\beta$ emission lines we use continuum regions centered on 6551 and 6572, and on 4854 and 4870, respectively."1001 Sample spectra in the low and high Balmer euiussion state are shown in Figure 3.., Sample spectra in the low and high Balmer emission state are shown in Figure \ref{fig:optical}.1002 The Ta lisht curve exhibits a clear sinusoidal behavior (Figure 1))., The $\alpha$ light curve exhibits a clear sinusoidal behavior (Figure \ref{fig:all}) ).1003 The data were obtained with the /UVOT in the UVWIT filter CÀagz2510 Aj). as a series of 6 images with exposure times ranging from 560 to 1630 s (Figure 1)).," The data were obtained with the /UVOT in the UVW1 filter $\lambda_{\rm eff}\approx 2510$ ), as a series of 6 images with exposure times ranging from 560 to 1630 s (Figure \ref{fig:all}) )."1004 No source is detected at the position of Hu anv of the individual exposures. or iu the combined inage with a total exposure time of 8036 s. We performed photometry on the combined exposure usine a circular aperture matched to the PSF of the UVWH filter (21. and found a 36 limit of FA(UVWI)<2.1«10D ore 7s LA tora Veen maenitude of ini(UNVW1)>23.0 mae.," No source is detected at the position of in any of the individual exposures, or in the combined image with a total exposure time of 8036 s. We performed photometry on the combined exposure using a circular aperture matched to the PSF of the UVW1 filter $2.2''$ ), and found a $3\sigma$ limit of $F_\lambda({\rm UVW1})<2.4\times 10^{-18}$ erg $^{-2}$ $^{-1}$ $^{-1}$, or a Vega magnitude of $m({\rm1005UVW1})>23.0$ mag."1006 This limit correspouds to a ratio of UV to bolometric Iuuinositv of ALA/Li«10.D°°., This limit corresponds to a ratio of UV to bolometric luminosity of $\lambda L_\lambda/L_{\rm bol}<10^{-3.2}$.1007 We observed aacross a wide wavelength range that traces activity in various lavers of the outer atmosphere., We observed across a wide wavelength range that traces activity in various layers of the outer atmosphere.1008 The radio emission traces particle acceleration by magnetic processes. and corresponds το gvrosvuchrotron radiation or coherent radiation (electron cyclotron απο or plasma. enissiou).," The radio emission traces particle acceleration by magnetic processes, and corresponds to gyrosynchrotron radiation or coherent radiation (electron cyclotron maser or plasma emission)."1009 The Balmer cussion lines are thought to be collisionally excited iu the chromosphere. aud the N-ray thermal Cluission arises iu the corona.," The Balmer emission lines are thought to be collisionally excited in the chromosphere, and the X-ray thermal emission arises in the corona."1010illustrative model fit. we assuned == LLOON. eravity = 10508 7. abundances of oue half solar. alkali line wine cutoff parameters defined in BAIS of 0.2 (Na TD) and 0.5 (I5 D. and an intermediate deerec of rainout for the alkalis (BAIS).,"illustrative model fit, we assumed = 1100 K, gravity = $10^5$ cm $^{-2}$, abundances of one half solar, alkali line wing cutoff parameters defined in BMS of 0.2 (Na I) and 0.5 (K I), and an intermediate degree of rainout for the alkalis (BMS)."1011 The SDSS 1621 daa WCve smoothed with a Dboxcar function. which. among other thiues. lulied he depth of the Cs lines relative to the model. but are of simular streneth.," The SDSS 1624 data were smoothed with a boxcar function, which, among other things, muted the depth of the Cs lines relative to the model, but are of similar strength."1012 No strong Lila sorption is predicted., No strong Li I absorption is predicted.1013 To obain a reasonable fit. it is not clear to us tha a diist conrponeut or additional source ored opacity is required.," To obtain a reasonable fit, it is not clear to us that a dust component or additional source of red opacity is required."1014 Tsuji's need for additional red opacity may be explanale by (1) nuderestimation of the alkali wing opacity due to he asstuuption of a Lorentzian. aud (2) the E-baud broad band flux was plotted at the wrong mcan wavelcneth (see BAIS).," Tsuji's need for additional red opacity may be explainable by (1) underestimation of the alkali wing opacity due to the assumption of a Lorentzian, and (2) the I-band broad band flux was plotted at the wrong mean wavelength (see BMS)."1015 Although he presence of dust iu he atmosphere certalily cannot be precluded. the alkalis appear to be the domimaut cause of the unique shape of the red eneres* distributinl.," Although the presence of dust in the atmosphere certainly cannot be precluded, the alkalis appear to be the dominant cause of the unique shape of the red energy distribution."1016 The detecion of flux to the blue boundary of the spectitlu also has consequences., The detection of flux to the blue boundary of the spectrum also has consequences.1017 In paricula. a Rayleigh scatteris dust opacity. as sugeested by Pavleuko et al (2000). wotld have more than double the opacity at tthan atSLOOA.," In particular, a Rayleigh scattering dust opacity, as suggested by Pavlenko et al (2000), would have more than double the opacity at than at."1018. Finally. the observed narrowness of the feature (relative to our inodols at the Gl 229B temperature near 950 I) aud the preseuce of strong cesi features together argue that the effective teniperature of SDSS 1621 is above that of Cliese 229B (BAIS). in concurrence with Nakajima et al. (," Finally, the observed narrowness of the feature (relative to our models at the Gl 229B temperature near 950 K) and the presence of strong cesium features together argue that the effective temperature of SDSS 1624 is above that of Gliese 229B (BMS), in concurrence with Nakajima et al. ("10192000).,2000).1020 We emphasize that no concerted attempt was made to find a vigorous fit. that other combinations of parameters are still viable. and that. given the SNR of the data at the shorter waveleugths. there are indeed parameter degeueracies.," We emphasize that no concerted attempt was made to find a rigorous fit, that other combinations of parameters are still viable, and that, given the SNR of the data at the shorter wavelengths, there are indeed parameter degeneracies."1021 This research is supported bv a NASA JPL eraut (961040NSE) permitting us to undertake a core science project on very low inass objects discovered in the 2MASS survev., This research is supported by a NASA JPL grant (961040NSF) permitting us to undertake a core science project on very low mass objects discovered in the $2MASS$ survey.1022 AB ackuowledecs support from NASA erauts NACH5S-7199 and NAG5-7073., AB acknowledges support from NASA grants NAG5-7499 and NAG5-7073.1023 The amodel curve was computed based upon a temperature/pressure profile econerated by M. Alarley (private communication) aud the models in Burrows et al. (, The model curve was computed based upon a temperature/pressure profile generated by M. Marley (private communication) and the models in Burrows et al. (10241997).,1997).1025 We wish to acknowledge helpful sugeestionsOO from zu auonviuious referee., We wish to acknowledge helpful suggestions from an anonymous referee.1026sinulations.,simulations.1027 We found a zero average correlation aud the RAIS of the correlations normalized by the error bars (calculated with Eq. 7)), We found a zero average correlation and the RMS of the correlations normalized by the error bars (calculated with Eq. \ref{err_a}) )1028 appears to be 1.1., appears to be 1.1.1029 This shows that the covariance matrices of the CMD aud the data and therefore our error bars are correctly estimated. confirming the significance of the correlation cocfiicicuts we obtain.," This shows that the covariance matrices of the CMB and the data and therefore our error bars are correctly estimated, confirming the significance of the correlation coefficients we obtain."1030" We do. rowever. find the following poiuts iuteresting: As seen previously (deOliveira-Costaetab.1997). the correlation between the Q-band and the 1007102. enission is stronecr than the correlation between the E,-baud and the Ἰθθμιι ciission."," We do, however, find the following points interesting: As seen previously \cite{doc_saskatoon} the correlation between the Q-band and the $100\mu\mathrm{m}$ emission is stronger than the correlation between the $_a$ -band and the $100\mu\mathrm{m}$ emission."1031 If the correlation we found is to be believed. the ratio of the RATS of the 10041n template times the fitted correlation cocthicicut to the nuplied sky RMS is 0.38. Gu the Q-band).," If the correlation we found is to be believed, the ratio of the RMS of the $100\mu\mathrm{m}$ template times the fitted correlation coefficient to the implied sky RMS is $0.38$ (in the Q-band)."1032 This result duclicates hat roughly 11€ of the power seen ou the sky by ACME/SP9L Q-baud could be due to Calactic enission., This result indicates that roughly $14\%$ of the power seen on the sky by ACME/SP94 Q-band could be due to Galactic emission.1033 The C; could eo down bv LL% aud the amplitude bv 38%., The $C_\ell$ could go down by $14\%$ and the amplitude by $38\%$.1034" This however does not apply to the Ix,,-baud.", This however does not apply to the $_a$ -band.1035" This result is in qualitative agreement with (Coumndersenetal..1995) and (Cangaetal.1997).. both of which fouud different spectral iudices for the Ix,- aud Q-baud data. though again. with low statistical significance."," This result is in qualitative agreement with \cite{gundersen95} and \cite{kmg_acme}, both of which found different spectral indices for the $_a$ - and Q-band data, though again, with low statistical significance."1036 We have also done the above analysis using as a template not the raw d00;a12 data but rather the, We have also done the above analysis using as a template not the raw $100\mu\mathrm{m}$ data but rather the1037"most notable difference is that for the latter case there seem to be fewer sources which confound the classifier,i.e.,, with P;~0.5.","most notable difference is that for the latter case there seem to be fewer sources which confound the classifier, with $\ps \simeq 0.5$."1038" Table 6.1 lists the fraction of sources for which the classifier gives 0.4<P,0.6.", Table \ref{table:singVSjoint} lists the fraction of sources for which the classifier gives $0.4 \leq \ps \leq 0.6$.1039" Compared to the single-band model, there is a decrease of at least 25percent in this number for the combined model."," Compared to the single-band model, there is a decrease of at least $25 \unit{per cent}$ in this number for the combined model."1040" While a reduction in the classifier-confounding region is not always desirable, here this decrease translates the fact that the classifier will be at a loss only when the data from different bands are contradictory, or when a source's type is unclear in all the bands in which it was detected."," While a reduction in the classifier-confounding region is not always desirable, here this decrease translates the fact that the classifier will be at a loss only when the data from different bands are contradictory, or when a source's type is unclear in all the bands in which it was detected."1041" shows the distribution of the posterior star class probabilities over Y-—H H—K space. Wesepu HLAisht. —colourspace,", shows the distribution of the posterior star class probabilities over $\ymh$ $\hmk$ space.1042 Eventhoughthemodelhasnotbeendesignedtooptimisedlüstherearetwoclearlydistinctpopulations.," Even though the model has not been designed to optimise class separation in colour--colour space, there are two clearly distinct populations."1043"F' vale UE and H—K~0.8, as expected. ("," Furthermore, sources with low star probabilities have $\ymh \simeq 1.5$ and $\hmk \simeq 0.8$, as expected. ("1044"left) shows the posterior stellar probabilities in the cy Yplane(thechoiceof bhandisunimportant, astheJ, HandKbandplot ste \di","left) shows the posterior stellar probabilities in the $\stat_Y$ $Y$ plane (the choice of band is unimportant, as the $J$, $H$ and $K$ band plots are similar)."1045"tticdkbenthatd inparticr or cy25, the Bayesian classifier gives very definite classifications(i.e.,, values close to either 0 or 1)."," It is clear that for the overwhelming majority of objects, in particular those with either $Y \la 18$ or $\stat_Y \ga 5$, the Bayesian classifier gives very definite classifications, values close to either 0 or 1)."1046" Unsurprisingly, the region where the classifier is most often confounded is where the star and galaxy loci merge."," Unsurprisingly, the region where the classifier is most often confounded is where the star and galaxy loci merge."1047" Indeed, as the two loci overlap completely at the faint end, there is very little information regarding object class to be extracted from the measured vvalues, and the prior knowledge drives the classification."," Indeed, as the two loci overlap completely at the faint end, there is very little information regarding object class to be extracted from the measured values, and the prior knowledge drives the classification."1048 One of the main aims of our classifier is to make the fullest possible use of whatever morphology statistic is available — the UKIDSS sstatistic in the case considered here — and in particular for sources where it has been measured in multiple bands., One of the main aims of our classifier is to make the fullest possible use of whatever morphology statistic is available – the UKIDSS statistic in the case considered here – and in particular for sources where it has been measured in multiple bands.1049" Several heuristic methods are used to combine multiple measurements in the WSA, including simple averaging and a plausible — but again heuristic — contingency table for sources where the mmeasurements in different bands imply contradictory classifications."," Several heuristic methods are used to combine multiple measurements in the WSA, including simple averaging and a plausible – but again heuristic – contingency table for sources where the measurements in different bands imply contradictory classifications."1050" Our Bayesian method has the potential to propagate all the information contained in the individual c values correctly, albeit at the cost of introducing an explicit — and complicated — model."," Our Bayesian method has the potential to propagate all the information contained in the individual $\stat$ values correctly, albeit at the cost of introducing an explicit – and complicated – model."1051 'The UKIDSS pipeline posterior star probabilities can be compared to that from our model 12))., The UKIDSS pipeline posterior star probabilities can be compared to that from our model ).1052" Both classifiers yield similar posterior star probabilities for sources which aiia or have large urthermare, Bestel With, faint, spurTX with small "," Both classifiers yield similar posterior star probabilities for sources which are fairly bright and/or have large values, but deal differently with faint sources with small values."1053"Apart from slight shift to the left at the faint end, the UKIDSS pipelinea classifier can be seen to consist essentially of a vertical cut on the vvalue."," Apart from a slight shift to the left at the faint end, the UKIDSS pipeline classifier can be seen to consist essentially of a vertical cut on the value."1054" The classifier-confounding region(i.e.,, where the classifier outputs probabilities near 0.5) is fairly small, and, crucially, does not widen at the faint end."," The classifier-confounding region, where the classifier outputs probabilities near $0.5$ ) is fairly small, and, crucially, does not widen at the faint end."1055" Our classifier, however, through the input of prior knowledge, is not limited éhidwlnseifieh«lontogndijareégiwfob;ects, is larger, ¢akingorparticularly at the faint end."," Our classifier, however, through the input of prior knowledge, is not limited to taking a vertical cut and the classifier-confounding region is larger, particularly at the faint end."1056" Indeed, near the detection limit, the vvalues carry almost no information concerning object type, as stars and galaxies have similar values at those fluxes."," Indeed, near the detection limit, the values carry almost no information concerning object type, as stars and galaxies have similar values at those fluxes."1057 It thus makes very little sense to base a classification on that information., It thus makes very little sense to base a classification on that information.1058 Using prior knowledge is vital for such faint sources., Using prior knowledge is vital for such faint sources.1059 Our classifier allows a continuous transition from vvalue based classification to prior knowledge based classification., Our classifier allows a continuous transition from value based classification to prior knowledge based classification.1060" The resulting broader classifier-confounding region is not a drawback: if an object has P;~ 0.5, it means that, given the observed data, it is impossible to tell whether that source is a star or a galaxy."," The resulting broader classifier-confounding region is not a drawback: if an object has $\ps\simeq0.5$ , it means that, given the observed data, it is impossible to tell whether that source is a star or a galaxy."1061 Artificially coercing, Artificially coercing1062"region m Z, Sy, plane that is consistent wit1 helioseisiüic aud linünositv constraints.",region in $Z_c$ $S_{11}$ plane that is consistent with helioseismic and luminosity constraints.1063" It cau be seen that ο)rent best estinates for Z, and 544 (Bahcall. Basu Pinsouneault 19 98)) are ouly nareinally cosistent with helioseisnüc coistradufs a1 xobaijv need to be increased slightly."," It can be seen that current best estimates for $Z_c$ and $S_{11}$ (Bahcall, Basu Pinsonneault \cite{bp98}) ) are only marginally consistent with helioseismic constraints and probably need to be increased slightly."1064" This figure al«) shows the Ini son the values of Z, obtained x Fukugita Tata (1998 )) as well as the range of 51 as Inferrec TOlü Various heoreticalcalculations so far (Dalicall Pinsonneault 1995: Turcναüézze Lopes 199233).", This figure also shows the limits on the values of $Z_c$ obtained by Fukugita Hata \cite{fuk98}) ) as well as the range of $S_{11}$ as inferred from various theoreticalcalculations so far (Bahcall Pinsonneault \cite{bp95}; Turck-Chiézze Lopes\cite{tc93}) ).1065 One5 herefore. expects that the vaues of Z. and Sy should fal withiu the region with vertic:d shading in Fig.," One therefore, expects that the values of $Z_c$ and $S_{11}$ should fall within the region with vertical shading in Fig."1066 9, 2.1067 The neutri10 fluxes 1n seismic iodoels with the correct παλπιο (for the value of S44 Correspoline to the5 central line in Fig., The neutrino fluxes in seismic models with the correct luminosity (for the value of $S_{11}$ corresponding to the central line in Fig.1068" 2] as d function of Z, ire shown in Fie.", 2) as a function of $Z_c$ are shown in Fig.1069 3., 3.1070" It can be SCCLL that the neutrino flux nu ""la detector ls ever as ow as the observed value. while the “B Leute flux aud the neutrino fiux nu TOC] are within observed liwuts. although for dixjoiut values of Z.."," It can be seen that the neutrino flux in $^{71}$ Ga detector is never as low as the observed value, while the $^8$ B neutrino flux and the neutrino flux in $^{37}$ Cl are within observed limits, although for disjoint values of $Z_c$."1071" TMIS, a variaion of Z, values does not vield neutriuo fluxes tha are siuultaueouslv cousisteut with anv two ο| the thyce solar neutrino experiments."," Thus, a variation of $Z_c$ values does not yield neutrino fluxes that are simultaneously consistent with any two of the three solar neutrino experiments."1072" Siuilur couchisions were reached frou, more seucral considerations bv Tata. Dhudiiui Laugacker (1991)). Ieeger Roberson (1996)). Baheall (01996). Castellaui et al. (1997))."," Similar conclusions were reached from more general considerations by Hata, Bludman Langacker \cite{hat94}) ), Heeger Robertson \cite{hee96}) ), Bahcall \cite{bah96}) ), Castellani et al. \cite{cas97}) ),"1073 Aiia Chitre (1997))., Antia Chitre \cite{ac97}) ).1074 Tt is clear that Z profile is t10 nuüajor solree of uncertainty in helioseisunic constraint ou the pp nuclear reaction CYOss-sectio1, It is clear that $Z$ profile is the major source of uncertainty in helioseismic constraint on the pp nuclear reaction cross-section.1075 We. therefore. explore he possibility. of determining the Z profile i1 adclition fc| the T..X. profiles musing the ecnations of thermal equilibrii. along with the sound speed. density ane. pressure prefiles.," We, therefore, explore the possibility of determining the $Z$ profile in addition to the $T,X$ profiles using the equations of thermal equilibrium, along with the sound speed, density and pressure profiles."1076" This would require a ceteriunationu o| [wo of the three unkuowus T.X.Z. wih the two cousraints obtaiied foun primary Inversion. παλιο], p(T.p..X.Z) and e(T.p..X. Z)."," This would require a determination of two of the three unknowns $T,X,Z$ , with the two constraints obtained from primary inversions, namely, $p(T,\rho,X,Z)$ and $c(T,\rho,X,Z)$ ."1077 We can thus write Since p is known incdependeuth. we ignore the variation iu p andconsider ouly T..X. Z.," We can thus write Since $\rho$ is known independently, we ignore the variation in $\rho$ andconsider only $T,X,Z$ ."1078 Now for a fully ionized, Now for a fully ionized1079A and B parameter sets fit three of the darker line of sight observations to within a factor of 3 or better.,A and B parameter sets fit three of the darker line of sight observations to within a factor of 3 or better.1080 The N[CO(g)] vs. NIHs(g)] data appear in Figure 3 as either. circles or inverted triangles for upper limits., The $N$ [CO(g)] vs. $N$ $_{2}$ (g)] data appear in Figure \ref{fig-3CO} as either circles or inverted triangles for upper limits.1081 The data. which are more numerous than those plotted against Ay and tend to contain lower CO(g) columns from diffuse and translucent cloud data. are fit best by model 2-A. The B-models tend to be somewhat worse than the A-models.," The data, which are more numerous than those plotted against $A_{\rm V}$ and tend to contain lower CO(g) columns from diffuse and translucent cloud data, are fit best by model 2-A. The B-models tend to be somewhat worse than the A-models."1082 Although the density. gas temperature. and size of thepost-shock objects for the lower H» columns may not correspond with these parameters for actual observed clouds. the CO(g) columns we calculate are dependent mainly on the visual extinction. so observation and theory are in reasonable agreement anyway.," Although the density, gas temperature, and size of thepost-shock objects for the lower $_{2}$ columns may not correspond with these parameters for actual observed clouds, the CO(g) columns we calculate are dependent mainly on the visual extinction, so observation and theory are in reasonable agreement anyway."1083 In addition. the caleulated CO(g) columns agree well with steady-state values for gas-phase models. if not quite as well as in Figure 2..," In addition, the calculated CO(g) columns agree well with steady-state values for gas-phase models, if not quite as well as in Figure \ref{fig-2NH}."1084 Our predicted columr densities for ices as functions of edge-to-center visual extinction can be compared with at least some infrared observational data along quiescent lines of sight in Taurus in our low visual extinction regime., Our predicted column densities for ices as functions of edge-to-center visual extinction can be compared with at least some infrared observational data along quiescent lines of sight in Taurus in our low visual extinction regime.1085 Shown in Figure 2.. the limited data available in the extinction range up to 3.3 come from Whittetetal.(2007);Murakawa(2000):Teixeira&Emerson (1999).. and references therein.," Shown in Figure \ref{fig-2NH}, the limited data available in the extinction range up to 3.3 come from \citet{dougco207, Murakawa00, Teixeira99}, , and references therein."1086 Some of these data are merely upper limits. while for CH4(s) and CH;OH(s). there are to the best of our knowledge not even upper limits in this range.," Some of these data are merely upper limits, while for $_{4}$ (s) and $_{3}$ OH(s), there are to the best of our knowledge not even upper limits in this range."1087 The question arises as to whether observations at our relatively low extinction range belong to small cores or whether the material being sampled is simply the diffuse background., The question arises as to whether observations at our relatively low extinction range belong to small cores or whether the material being sampled is simply the diffuse background.1088 That at least some of the Taurus observations at low extinction pertain to small cores has been shown by Whittetet 2004).. who concluded that the lines of sight to HD 29647 and HD 283809 sample dense gas with extinctions of Ay=1.82 and 2.85 (see their Figure | in the 2004 paper).," That at least some of the Taurus observations at low extinction pertain to small cores has been shown by \citet{Whittet01, Whittet04}, who concluded that the lines of sight to HD 29647 and HD 283809 sample dense gas with extinctions of $A_V = 1.82$ and 2.85 (see their Figure 1 in the 2004 paper)."1089 If representative of expanding objects as treated by our shock model. the size of the object with lower extinctior. in the absence of self-gravity. would be in the range 0.05 pe (Model 4) to 0.5 pe (Model 3) (see Table 1)).," If representative of expanding objects as treated by our shock model, the size of the object with lower extinction, in the absence of self-gravity, would be in the range 0.05 pc (Model 4) to 0.5 pc (Model 3) (see Table \ref{tbl-shockmods}) )."1090 The vertical line or lines 1 panels (b)-(d) are empirically determined threshold extinetions. Αι. and their uncertainty ranges for the Taurus dark clc»ud (the panel for CO(s) only shows the lower limit of this ra1ge).," The vertical line or lines in panels (b)-(d) are empirically determined threshold extinctions, $A_{\rm th}$, and their uncertainty ranges for the Taurus dark cloud (the panel for CO(s) only shows the lower limit of this range)."1091 The center lines represent the lowest Ay values above which the specific ices are detectable in a cloud and are obtained by empirical fits to column density vs. visual extiction for a wide range of dark quiescent lines of sight in Taurus towards background stars at larger visual extinction (Whittetetal.2007)., The center lines represent the lowest $A_V$ values above which the specific ices are detectable in a cloud and are obtained by empirical fits to column density vs. visual extinction for a wide range of dark quiescent lines of sight in Taurus towards background stars at larger visual extinction \citep{dougco207}.1092. The specific edge-to-center thresholds for Taurus are Ay=1.6+0.05 for H»:O(s). 3.4+0.8 for CO(s). and 2.15+0.5 mag for CO:(s).," The specific edge-to-center thresholds for Taurus are $A_{\rm th}=1.6 \pm 0.05$ for $_2$ O(s), $3.4 \pm 0.8$ for CO(s), and $2.15 \pm 0.5$ mag for $_2$ (s)."1093 These threshold values can be regarded as conservative compared with some of the equivocal data at lower extinetion from other groups (Teixeira&Emerson1999;Murakawaetal. 2000).. which might represent the diffuse background.," These threshold values can be regarded as conservative compared with some of the equivocal data at lower extinction from other groups \citep{Teixeira99, Murakawa00}, which might represent the diffuse background."1094 The thresholds are thought to roughly correspond with the accumulation of the equivalent of a few monolayers of a surface species. in a sudden onset above the threshold extinction.," The thresholds are thought to roughly correspond with the accumulation of the equivalent of a few monolayers of a surface species, in a sudden onset above the threshold extinction."1095 To help interpret these thresholds. we have also plotted minimum detectable columns for the major ices. which are shown as horizontal lines.," To help interpret these thresholds, we have also plotted minimum detectable columns for the major ices, which are shown as horizontal lines."1096 The estimates are made by substituting a minimal discernible optical depth of 720.01 (Whittet. private communication) into equation (5.5) of Whittet(2003).," The estimates are made by substituting a minimal discernible optical depth of $\tau=0.01$ (Whittet, private communication) into equation (5.5) of \citet{dustbook03}."1097. At the time when AyxAy). the horizontal lines in panels (b) and (d) represent the equivalent column density of about one or two monolayers of H»O(s) and CO:(s). while the line in panel (c) is closer to five layers of CO(s).," At the time when $A_V \approx A_{\rm th}$, the horizontal lines in panels (b) and (d) represent the equivalent column density of about one or two monolayers of $_2$ O(s) and $_2$ (s), while the line in panel (c) is closer to five layers of CO(s)."1098 The observations of N[H»O(s)] appear in Figure 2((b)., The observations of $N$ $_2$ O(s)] appear in Figure \ref{fig-2NH}( (b).1099 The Murakawa et al., The Murakawa et al.1100 detections were reported as optical depths. r. and we note that several of these values are less than the observational uncertainty of ór=£0.05 reported.," detections were reported as optical depths, $\tau$, and we note that several of these values are less than the observational uncertainty of $\delta \tau=\pm 0.05$ reported."1101 If we instead count these points as upper limits. as shown in the plot. the data below Whittet's threshold range are only limits. while firm detections appear at greater Ay than the threshold.," If we instead count these points as upper limits, as shown in the plot, the data below Whittet's threshold range are only limits, while firm detections appear at greater $A_{\rm V}$ than the threshold."1102 Below the threshold. the models results lie below these “limits.”," Below the threshold, the models results lie below these “limits.”"1103 Above the threshold. the spread of data points and upper limits falls within the range of our model results. although it is difficult to determine which models are best.," Above the threshold, the spread of data points and upper limits falls within the range of our model results, although it is difficult to determine which models are best."1104 Regarding the threshold itself. our calculated columns do not show a real threshold. but rise gradually and reach the empirical threshold. around the minimum detectable column (the horizontal line).," Regarding the threshold itself, our calculated columns do not show a real threshold, but rise gradually and reach the empirical threshold around the minimum detectable column (the horizontal line)."1105 À proper interpretation may be that there 1s not really a threshold. so much as a drop below detectability masquerading as one.," A proper interpretation may be that there is not really a threshold, so much as a drop below detectability masquerading as one."1106 Towards the highest extinction. plotted. the assorted model results tend to converge to a narrow range of values 3-10 * larger than the observed columns.," Towards the highest extinction plotted, the assorted model results tend to converge to a narrow range of values 3-10 $\times$ larger than the observed columns."1107 In some sense this is due to the chemistry readily hydrogenating oxygen atoms on grain surfaces., In some sense this is due to the chemistry readily hydrogenating oxygen atoms on grain surfaces.1108 At cold temperatures it is difficult to stop this process., At cold temperatures it is difficult to stop this process.1109 The difference between model and observations could be related to our assumed oxygen atom abundance being too high. perhaps through the presence of another reservoir of oxygen (see.e.g.Whittetetal.2007).," The difference between model and observations could be related to our assumed oxygen atom abundance being too high, perhaps through the presence of another reservoir of oxygen \citep[see, e.g.][]{dougco207}."1110 For the other major ices. CO(s) and CO:(s). there are only upper limits in the extinction range Ay through = 3. except for one detection of 009) toward Tamura 2 (Whittetetal.1989. 2007)..," For the other major ices, CO(s) and $_{2}$ (s), there are only upper limits in the extinction range $A_{\rm V}$ through $ \approx 3$ , except for one detection of $_{2}$ (s) toward Tamura 2 \citep{Whittet89, dougco207}. ."1111 The observational N[CO(s)] upper limits are not very constrainmg except perhaps at the highest visual extinction plotted where two upper limits are in better agreement with shock models 1 and 3., The observational $N$ [CO(s)] upper limits are not very constraining except perhaps at the highest visual extinction plotted where two upper limits are in better agreement with shock models 1 and 3.1112 For the case of CO2(s). the B parameter models are required to bring the column density to near-detectable abundances.," For the case of $_2$ (s), the B parameter models are required to bring the column density to near-detectable abundances."1113 The one firmly detected observational data point is fit best by models 4-B and 2-B. Figure 2. shows very sharp thresholds for the onset of column densities of CO(s) and CO:s(s). but only for the latter are the calculated thresholds even in rough agreement with the empirical range of Whittetetal. (2007)..," The one firmly detected observational data point is fit best by models 4-B and 2-B. Figure \ref{fig-2NH} shows very sharp thresholds for the onset of column densities of CO(s) and $_{2}$ (s), but only for the latter are the calculated thresholds even in rough agreement with the empirical range of \citet{dougco207}. ."1114 ForCO(s). we reach the minimum detectable column at visual extinction much smaller than the empirical threshold. which needs to be checked by data at lowerextinction. where there are currently only high upper limits to the CO(s) column.," ForCO(s), we reach the minimum detectable column at visual extinction much smaller than the empirical threshold, which needs to be checked by data at lowerextinction, where there are currently only high upper limits to the CO(s) column."1115 It should benoted that. in the absence of photodesorption. minimum detectable," It should benoted that, in the absence of photodesorption, minimum detectable"1116 Inthe past 10 wears or so. there has been mounting evidence that massive galaxies host supermassive black holes in their centres. and that the mass of the black hole correlates with other galaxy properties. particularly Luminosity. stellar mass (or bulec luminosity ancl stellar mass in the case of disc galaxies) and central velocity dispersion therein).,"In the past 10 years or so, there has been mounting evidence that massive galaxies host supermassive black holes in their centres, and that the mass of the black hole correlates with other galaxy properties, particularly luminosity, stellar mass (or bulge luminosity and stellar mass in the case of disc galaxies) and central velocity dispersion ."1117 Such relations are being discussed and. revised. with several important details being disclosed (222272777). and a consensus emerges that they reveal a connected growth. of black holes and their host. galaxies or bulges. e.g. via mechanisms of feedback 272).," Such relations are being discussed and revised, with several important details being disclosed , and a consensus emerges that they reveal a connected growth of black holes and their host galaxies or bulges, e.g. via mechanisms of feedback ."1118 With growing evidence that galaxy. bulges are not a single. homogeneous class. but in fact comprise classical bulges and pseudo-bulges. with dillerent formation histories D.. a new ingredient is added: to this investigation.," With growing evidence that galaxy bulges are not a single, homogeneous class, but in fact comprise classical bulges and pseudo-bulges, with different formation histories , a new ingredient is added to this investigation."1119 Do black holes in. elliptical galaxies. classical bulges ancl pseuclo-bulges follow similar relations between their masses and host ealaxy/bulge mass or velocity dispersion?," Do black holes in elliptical galaxies, classical bulges and pseudo-bulges follow similar relations between their masses and host galaxy/bulge mass or velocity dispersion?"1120 suggests that the relation between black hole mass Apg ancl velocity dispersion e is dilferent for classical bulges (including there elliptical galaxies) aud pseudo-bulges., suggests that the relation between black hole mass $M_{\rm{BH}}$ and velocity dispersion $\sigma$ is different for classical bulges (including there elliptical galaxies) and pseudo-bulges.1121 ‘To address this issue. one would. ideally. have secure. direct. measurements of AZig for a statistically significant sample of galaxies. which is currently. not available.," To address this issue, one would ideally have secure, direct measurements of $M_{\rm{BH}}$ for a statistically significant sample of galaxies, which is currently not available."1122 In this Paper. we approach the question by using measurements of the stellar mass in elliptical galaxies and bulges. obtained in Paper L for a sample of nearly 1000 svstems from the Sloan Digital Sky Survey (SDSS).," In this Paper, we approach the question by using measurements of the stellar mass in elliptical galaxies and bulges, obtained in Paper I, for a sample of nearly 1000 systems from the Sloan Digital Sky Survey (SDSS)."1123 We combine these results with 7 measurements fron SDSS. and investigate how the stellar mass of the bulge relates to e in ellipticals. classical bulges and. pseudo-bulges.," We combine these results with $\sigma$ measurements from SDSS, and investigate how the stellar mass of the bulge relates to $\sigma$ in ellipticals, classical bulges and pseudo-bulges."1124 By assuming that we can infer Alou [rom bulge stellar masses using a single relation. we indirectly assess the Adpyoo relation for these systems.," By assuming that we can infer $M_{\rm{BH}}$ from bulge stellar masses using a single relation, we indirectly assess the $M_{\rm{BH}}-\sigma$ relation for these systems."1125 1n the next section. we briclly recall how the bulge stellar mass measurements were done. as well as how ellipticals. classical bulges anc pseudo-bulges were defined. and. address our use of SDSS σ measurements.," In the next section, we briefly recall how the bulge stellar mass measurements were done, as well as how ellipticals, classical bulges and pseudo-bulges were defined, and address our use of SDSS $\sigma$ measurements."1126 In Sect. 3..," In Sect. \ref{sec:results},"1127 we show the results. which are discussed in Sect. 4..," we show the results, which are discussed in Sect. \ref{sec:dis}."1128 In Paper Lowe have performed careful ancl detailed. image fitting of the galaxies in the sample in the g. à and ὁ bands. including up to three components in the models. namely," In Paper I, we have performed careful and detailed image fitting of the galaxies in the sample in the $g$, $r$ and $i$ bands, including up to three components in the models, namely"1129Since and first. demonstrated. using observations of type la supernovac (Να). that the expansion. history of the Universe is accelerating at late times. improved SNla studies have continuously corroborated these results ).,"Since and first demonstrated, using observations of type Ia supernovae (SNIa), that the expansion history of the Universe is accelerating at late times, improved SNIa studies have continuously corroborated these results ."1130. At the Senec time. measurenents ol anisotropies in the cosmic microwave background. (CM) with the Wilkinson Microwave Anisotropy Probe and other CALB experiments have tightly constrained other key cosmological parameters.," At the same time, measurements of anisotropies in the cosmic microwave background (CMB) with the Wilkinson Microwave Anisotropy Probe and other CMB experiments have tightly constrained other key cosmological parameters."1131 AX varicty of other. cosmological cata sets have also been used to independently measure cosmic acceleration., A variety of other cosmological data sets have also been used to independently measure cosmic acceleration.1132 Measurements of the gas mass fraction ealaxy clusters. having earlier shown that the mean matter density of the Universe is. low. o=Flit0.257). have cürectlv confirmed the elects of cosmic acceleration. at comparable significance to that seen in SNIa data," Measurements of the gas mass fraction $f_{\rm gas}$ ) in galaxy clusters, having earlier shown that the mean matter density of the Universe is low, $\Omega_{\rm m}\sim 0.25$, have directly confirmed the effects of cosmic acceleration, at comparable significance to that seen in SNIa data"1133"However, their transient nature makes it likely that they are binary systems in the SMC.","However, their transient nature makes it likely that they are binary systems in the SMC."1134" One of these candidate sources (IGR J00523—7217) was detected by combining data over a ~10 day period in June 2009 and is spatially consistent with SXP327 SXP4.78, known Be/X-ray binaries in the SMC."," One of these candidate sources (IGR $-$ 7217) was detected by combining data over a $\sim10$ day period in June 2009 and is spatially consistent with SXP327 SXP4.78, known Be/X-ray binaries in the SMC."1135" The region of the SMC in which this potential new source was seen was monitored weekly by RXTE, but pulsations were not detected from either of those sources."," The region of the SMC in which this potential new source was seen was monitored weekly by RXTE, but pulsations were not detected from either of those sources."1136 The SMC is turning out to be an exciting nest of X-ray binary pulsars., The SMC is turning out to be an exciting nest of X-ray binary pulsars.1137 It is possible to estimate the number of systems one would expect based upon the relative masses of our galaxy and the SMC., It is possible to estimate the number of systems one would expect based upon the relative masses of our galaxy and the SMC.1138" This mass ratio is approx 50, so with 64 known or suspected systems in our galaxy we would only expect 1 or 2 systems in the SMC."," This mass ratio is approx 50, so with 64 known or suspected systems in our galaxy we would only expect 1 or 2 systems in the SMC."1139" However, Maeder, Grebel Mermilliod (1999) have shown that the fraction of Be stars to stars is 0.39 in the SMC compared with 0.16 in our galaxy."," However, Maeder, Grebel Mermilliod (1999) have shown that the fraction of Be stars to B stars is 0.39 in the SMC compared with 0.16 in our galaxy."1140 BSo this raises the expected number of Be/X-ray systems to approx 3 for the SMC - but we now know of more than 50 such systems in SMC!, So this raises the expected number of Be/X-ray systems to approx 3 for the SMC - but we now know of more than »50 such systems in SMC!1141" Many of these detections have come from XTE, Chandra XMM X-ray observations over the last couple of years (Galache et al."," Many of these detections have come from XTE, Chandra XMM X-ray observations over the last couple of years (Galache et al."1142" 2008, McGowan et al."," 2008, McGowan et al."1143" 2008, Haberl, Eger Pietsch 2008)."," 2008, Haberl, Eger Pietsch 2008)."1144" This large number suggests a dramatic phase of star birth in the past, probably associated with the most recent closest approach between the SMC and the LMC some 0.2 Gyrs ago (Gardiner Noguchi 1996)."," This large number suggests a dramatic phase of star birth in the past, probably associated with the most recent closest approach between the SMC and the LMC some 0.2 Gyrs ago (Gardiner Noguchi 1996)."1145" Even more extreme, the very recent work of Naze et al (2003) in just one 20 x 20 arcmin Chandra field identified more than 20 probable Be/X-ray binary systems."," Even more extreme, the very recent work of Naze et al (2003) in just one 20 x 20 arcmin Chandra field identified more than 20 probable Be/X-ray binary systems."1146" Multiplying these numbers up by the 2 x 2 degree size of the SMC, and allowing for ~10% X-ray duty cycles, suggests the final number of Be/X-ray binaries could be well in excess of 1,000!"," Multiplying these numbers up by the »2 x 2 degree size of the SMC, and allowing for $\sim$ X-ray duty cycles, suggests the final number of Be/X-ray binaries could be well in excess of 1,000!"1147" These observations of the SMC are not only providing a great sample of HMXBs for study, but are also providing direct insights into the history of our neighbouring galaxy."," These observations of the SMC are not only providing a great sample of HMXBs for study, but are also providing direct insights into the history of our neighbouring galaxy."1148" Since the positional accuracy of Chandra XMM is a few arcsec, or less, optical counterpart have been located for many of these potential XRB systems."," Since the positional accuracy of Chandra XMM is a few arcsec, or less, optical counterpart have been located for many of these potential XRB systems."1149 The reason for the large number of HMXBs in the SMC probably lies in the history of the Magellanic Clouds., The reason for the large number of HMXBs in the SMC probably lies in the history of the Magellanic Clouds.1150 Detailed H1 mapping by Stavely-Smith et al (1997) and Putman et al (1998) has shown a strong bridge of material between the Magellanic Clouds and between them and our own galaxy., Detailed H1 mapping by Stavely-Smith et al (1997) and Putman et al (1998) has shown a strong bridge of material between the Magellanic Clouds and between them and our own galaxy.1151" Furthermore, Stavely-Smith et al have demonstrated the existence of a large number of supernova remnants of a similar age (~5 Myr), strongly suggesting enhanced starbirth has taken place as a result of tidal interactions between these component systems."," Furthermore, Stavely-Smith et al have demonstrated the existence of a large number of supernova remnants of a similar age $\sim$ 5 Myr), strongly suggesting enhanced starbirth has taken place as a result of tidal interactions between these component systems."1152 It seems very likely that the previous closest approach of the SMC to the LMC ~100 Myrs ago may have triggered the birth of many new massive stars which have given rise to the current population of HMXBs., It seems very likely that the previous closest approach of the SMC to the LMC $\sim$ 100 Myrs ago may have triggered the birth of many new massive stars which have given rise to the current population of HMXBs.1153" In fact, other authors (eg Popov et al 1998) claim that the presence of large numbers of HMXBs may be the best indication of starburst activity in a system."," In fact, other authors (eg Popov et al 1998) claim that the presence of large numbers of HMXBs may be the best indication of starburst activity in a system."1154" If the explanation of tidal interactions producing lots of starbirth is correct, it is very likely that there are many more systems waiting to be discovered in the SMC than the 60-100 known at this time."," If the explanation of tidal interactions producing lots of starbirth is correct, it is very likely that there are many more systems waiting to be discovered in the SMC than the 60-100 known at this time."1155" In total, INTEGRAL detected seven sources in the SMC - four of which were previously unknown systems."," In total, INTEGRAL detected seven sources in the SMC - four of which were previously unknown systems."1156 Combining this with the population of the five new sources detected in the Magellanic Bridge makes this a very productive survey of the SMC region., Combining this with the population of the five new sources detected in the Magellanic Bridge makes this a very productive survey of the SMC region.1157 Comments on specific SMC sources are: The large number of sources seen by INTEGRAL is, Comments on specific SMC sources are: The large number of sources seen by INTEGRAL is1158"and NIT, have been observed in this cloud.",and $_3$ have been observed in this cloud.1159 However. from the abundance ratio of the two species. we can speculate the Lup4 C2 is vounger than Lup4 Cl.," However, from the abundance ratio of the two species, we can speculate the Lup4 C2 is younger than Lup4 C1."1160 We can compare our classification with the results of the Spitzer survey carried out in the c2d Legacy Program (Chapmanetal.2007:: Merinetal.2008. .)., We can compare our classification with the results of the Spitzer survey carried out in the c2d Legacy Program \citealt{chapman07}; \citealt{merin08} ).1161 As commonly known the Spitzer surveys. covering the 3.160 spectral range. are efficient in discovering aud classilving YSOs in the Class I. HE and HI evolutionary stage.," As commonly known the Spitzer surveys, covering the 3–160 spectral range, are efficient in discovering and classifying YSOs in the Class I, II and III evolutionary stage."1162 On the contrary. the sources that are in a previous evolutionary stage are not detected in (he Spitzer survevs since the SED of these vounger sources peaks al longer wavelengths then the Spitzer bands.," On the contrary, the sources that are in a previous evolutionary stage are not detected in the Spitzer surveys since the SED of these younger sources peaks at longer wavelengths then the Spitzer bands."1163 Our evolutionary classification of the dense cores identified in the Mopra maps is supported bv the analvsis of (he Spitzer survey., Our evolutionary classification of the dense cores identified in the Mopra maps is supported by the analysis of the Spitzer survey.1164 Indeed only (wo of our millimetre cores are also detected by Spitzer ie. Lupl C4. which is associated with source 10 and classified as Flat by (the same source was previously classified as Class I bv Chapmanetal. (2007))) and Lup3 C3 which is associated with source 87 by Merinetal.(2008). ancl classified as Class L. Ht is worth noting that looking at the WCyN/Noll column density ratio. Lupl C4 and Lup3 C'S seem to be two of the most evolved sources of our sample.," Indeed only two of our millimetre cores are also detected by Spitzer i.e. Lup1 C4, which is associated with source 10 and classified as Flat by \citet{merin08} (the same source was previously classified as Class I by \citet{chapman07}) ) and Lup3 C3 which is associated with source 87 by \citet{merin08} and classified as Class I. It is worth noting that looking at the $_3$ column density ratio, Lup1 C4 and Lup3 C3 seem to be two of the most evolved sources of our sample."1165 Another comparison can be made with the ICO and 1.2 mm maps of Lupus 3 by Tachiharaetal.(2007)., Another comparison can be made with the $^{13}$ $^+$ and 1.2 mm maps of Lupus 3 by \cite{tachihara07}.1166. By means of a SED analvsis. core Lup3 C3 has been classified by Tachiharaetal.(2007) as a Class 0 object while cores Lup3 C2. C4 and C5 have been classified as pre-stellar cores.," By means of a SED analysis, core Lup3 C3 has been classified by \cite{tachihara07} as a Class 0 object while cores Lup3 C2, C4 and C5 have been classified as pre-stellar cores."1167" These classifications agree wilh our data since Lup3 C3 is the most prominent core in NIL, and Lup3 C5 is (he most prominent core in ICN: Lup3 C2 and Lup3 C4 seem to be at an intermediate stage between the former (vo since thev are bright in NIL; and but also weakly emit in.", These classifications agree with our data since Lup3 C3 is the most prominent core in $_3$ and Lup3 C5 is the most prominent core in $_3$ N; Lup3 C2 and Lup3 C4 seem to be at an intermediate stage between the former two since they are bright in $_3$ and but also weakly emit in.1168. Our study shows (hat Lupus 1 is the cloud richest in millimetre dense cores. most of those likely being protostellar cores.," Our study shows that Lupus 1 is the cloud richest in millimetre dense cores, most of those likely being protostellar cores."1169 On the other hand. the Spitzer surveys have shown that Lupus 3 is richer in YSOs with respect to Lupus 1 and 4: indeed 69. 12 and 12 YSOs have been detected in Lupus 3. 1 and 4 respectively (Merinetal.2008).," On the other hand, the Spitzer surveys have shown that Lupus 3 is richer in YSOs with respect to Lupus 1 and 4; indeed 69, 13 and 12 YSOs have been detected in Lupus 3, 1 and 4 respectively \citep{merin08}."1170. The ratio between YSOs candidates. i.e. Class 1. HH and HII objects detected by Spitzer aud (he millimetre dense cores i.e. prestellar and voung protostellar cores detected in our maps is 13.3. 6.0 and 1.6 in Lupus 3. 4 and 1 respectively.," The ratio between YSOs candidates, i.e. Class I, II and III objects detected by Spitzer and the millimetre dense cores i.e. prestellar and young protostellar cores detected in our maps is 13.8, 6.0 and 1.6 in Lupus 3, 4 and 1 respectively."1171 All these evidences point towards a picture where in Lupus, All these evidences point towards a picture where in Lupus1172decreases eraduallv as the flax decreases. which is oue of he major factors in the slow turnover of the ciunulative distribution function.,"decreases gradually as the flux decreases, which is one of the major factors in the slow turnover of the cumulative distribution function."1173 For this reason. we oulv use data within the range FasoFy<Foy5 to obtain a fit o the cumulative flux distribution.," For this reason, we only use data within the range $F_{\rm 8, max} < F_81174< F_{8, N=5}$ to obtain a fit to the cumulative flux distribution."1175 We take FXως=6. aud assuue that all sources with fluxes above lis lait ive been resolved by EGRET.," We take $F_{\rm 8, max} = 6$, and assume that all sources with fluxes above this limit have been resolved by EGRET."1176 We define £uv5 to  the flux for which. iu each sample. 5 objects with Huxes higher tha or cqual to it have heen resolved.," We define $F_{8, N=5}$ to be the flux for which, in each sample, 5 objects with fluxes higher than or equal to it have been resolved."1177 The vost-fit values of C αιid & for cach sample are shown iu Table L.., The best-fit values of $C$ and $\kappa$ for each sample are shown in Table \ref{sometable}. .1178 As we can see in ((2)) as well as from the xuinueter values m T:ible 1.. the slopes of the cumulative Hux distribution iu the regime where most objects are expected to have beuu resolved by EGRET are fully consistent with each other.," As we can see in \ref{lognlogs}) ) as well as from the parameter values in Table \ref{sometable}, the slopes of the cumulative flux distribution in the regime where most objects are expected to have been resolved by EGRET are fully consistent with each other."1179 This in turn implies that he data are cousistewt with the bypothesis that most ucnibers of all sailes have been drawn from a single »opulation of extragaactic emitters., This in turn implies that the data are consistent with the hypothesis that most members of all samples have been drawn from a single population of extragalactic emitters.1180 Ilowever. we note that the flux distribution slope. close to 72.5 in all cases. is steeper han the slope tha would be expected fro na single-Iuninosity population of sources with a unuiforu distribution iu a flat cosmology Gvhich is equal to 5D. DDermer 2007). aud is also steeper than the slope of the flux distribution of he coufideutlv ideutified blazar population.," However, we note that the flux distribution slope, close to $\sim$ 2.5 in all cases, is steeper than the slope that would be expected from a single-luminosity population of sources with a uniform distribution in a flat cosmology (which is equal to $1.5$, Dermer 2007), and is also steeper than the slope of the flux distribution of the confidently identified blazar population."1181" This result nav reflect the cosuxlogical distribution and evolution xoperties of the poplation of extragalactic unidenutifie sources,", This result may reflect the cosmological distribution and evolution properties of the population of extragalactic unidentified sources.1182 However. it may also originate iu a selection effect in the identification of eamuna-ray sources: the yositional identification of brighter ποιάος ds ndore Yequent as more pliotous are detecte froin these sources which allows for a more accurate pinpointing of their ocation.," However, it may also originate in a selection effect in the identification of gamma-ray sources: the positional identification of brighter sources is more frequent as more photons are detected from these sources which allows for a more accurate pinpointing of their location."1183 Iu addition. inultiwaveleneth campaigus for he identification of gamma-ray sources naturally tarec he brightest objects first.," In addition, multiwavelength campaigns for the identification of gamma-ray sources naturally target the brightest objects first."1184 For these reasons. the hieh-flux end of the flux «listribution may be preferentially depleted. which would lead to an appareut steepenuiug of he distribution of tlic| sources that remain unideutified.," For these reasons, the high-flux end of the flux distribution may be preferentially depleted, which would lead to an apparent steepening of the distribution of the sources that remain unidentified."1185 Finally. the steepness of the slope could be au effect of viewing a distribution with real curvature in à very σημα] dynamical range in fux.," Finally, the steepness of the slope could be an effect of viewing a distribution with real curvature in a very small dynamical range in flux."1186 A smuple example quautifviug such a possible effect is the following: if we were to treat all sources in Sample 1 and all couficlently ideutifie dazars which are located outside our exclusion mask as asinele population. then the cumulative fux distribution vower-law fit in the flux range 6<FyFay5 wouk lave a slope &=1.63+£0.03. wach closer to 1.5.," A simple example quantifying such a possible effect is the following: if we were to treat all sources in Sample 1 and all confidently identified blazars which are located outside our exclusion mask as a single population, then the cumulative flux distribution power-law fit in the flux range $6 <F_8 < F_{8, N=5}$ would have a slope $\kappa =11871.63 \pm 0.03$, much closer to $1.5$."1188 Finally. we should add a cautionary note on fits to he cumulative. ratler “than differential. flux cistribution uction. such as the one presented here.," Finally, we should add a cautionary note on fits to the cumulative, rather than differential, flux distribution function, such as the one presented here."1189 Qur fits »irpostfullv do not account for uncertainties in cach biu since. from a statistic:d point of view. such uucertainties are almost orfectlv correlated (each bin contains the sale data as dts adjacent ones plus/minus one data point).," Our fits purposfully do not account for uncertainties in each bin since, from a statistical point of view, such uncertainties are almost perfectly correlated (each bin contains the same data as its adjacent ones plus/minus one data point)."1190 Ou he other loui. the poor dynamical rauge in flux ane the depeudeice of uncertainties of thedifferential Hux function on the size of the biu make constructing and fttiis the differential flux. fiction problematic as well.," On the other hand, the poor dynamical range in flux and the dependence of uncertainties of the flux function on the size of the bin make constructing and fitting the differential flux function problematic as well."1191 For these reasons. if is inportaut to uot over-interpret these results. which should be viewed as broad. order-ofmaeüitude assessinenuts of the behavior of the flux distribution. rather than robust statistical evaluations and strict c'Onstraiuts.," For these reasons, it is important to not over-interpret these results, which should be viewed as broad, order-of-magnitude assessments of the behavior of the flux distribution, rather than robust statistical evaluations and strict constraints."1192 The secoud imuportaut observational iuput in our calculation is the distribution of spectral iudices of unideuti&ed objects pta)., The second important observational input in our calculation is the distribution of spectral indices of unidentified objects $p(\alpha)$.1193" In the lait that the spectral index of sources is incependeut of source redshift aud ""uumositv. the spectral iudex distribution uniquely determines the spectral shape of the collective emission roni the unresolved population."," In the limit that the spectral index of sources is independent of source redshift and luminosity, the spectral index distribution uniquely determines the spectral shape of the collective emission from the unresolved population."1194 The spectral shape of he unresolved cussion provides. in turi. an additional ool to assess the possibility that unidentified sources constitute a dominant contribution to the ECRB hrough between the observed aud tle oedieted spectra of diffuse extragalactic emission.," The spectral shape of the unresolved emission provides, in turn, an additional tool to assess the possibility that unidentified sources constitute a dominant contribution to the EGRB through between the observed and the predicted spectra of diffuse extragalactic emission."1195 Tn our analysis we adopt the assumption that the spectral index distribution of unresolved unidentified sources is the same as that of the resolved unidentified sources., In our analysis we adopt the assumption that the spectral index distribution of unresolved unidentified sources is the same as that of the resolved unidentified sources.1196 The latter can be deduced. frou 1icasurenmenuts of the spectral iudex a for sources in each oue of our sunuples. following the method presented im Veuters Pavlidou (2007).," The latter can be deduced from measurements of the spectral index $\alpha$ for sources in each one of our samples, following the method presented in Venters Pavlidou (2007)."1197 The details of this calculation. properly accounting for measurement uncertainties iu individual spectral iudices of resolved sources. are presented iu Appendix A..," The details of this calculation, properly accounting for measurement uncertainties in individual spectral indices of resolved sources, are presented in Appendix \ref{spindex}."1198 As is inunecdiately obyious from ((6)). the shape aud the overall normalization fy of the cumulative cluission from unresolved. unidentified sources are decoupled wnder our assuniptiouns.," As is immediately obvious from \ref{contr}) ), the shape and the overall normalization $I_0$ of the cumulative emission from unresolved unidentified sources are decoupled under our assumptions."1199" The shape of the spectrin depends on the spectral iudex distribution. while the normalization. given a fit to the flux distribution. depends ouly ou Fi, (the value of the flux where the extrapolated power Luv breaks)."," The shape of the spectrum depends on the spectral index distribution, while the normalization, given a fit to the flux distribution, depends only on $F_{\rm 8,min}$ (the value of the flux where the extrapolated power law breaks)."1200 Asstuning that. close to the ECRET flux limit. the flux distribution docs not evolve drastically. au extrapolati of the measured flux function to lower fluxes can be considered represeutative of its behavior in the low-flux reenuc.," Assuming that, close to the EGRET flux limit, the flux distribution does not evolve drastically, an extrapolation of the measured flux function to lower fluxes can be considered representative of its behavior in the low-flux regime."

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