source,target
 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.
. 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}.
. 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.
 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."
 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)."
 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."
 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}.
 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}. ."
 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.
 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."
 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}) )."
 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."
 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}.
". 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}) )."
 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}) ).
 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).
 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."
 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."
 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}. ."
vertical disk structure (see?)..,vertical disk structure \citep[see][]{Dullemond01}.
" 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."
 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 $n(a) \propto a^{-q}$.
 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.
 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}.
" 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."
" 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}."
" 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."
intensity 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.
" 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."
" 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, $L_{A_v}$."
 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 $A_v$.
" 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 $A_v$.
 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.
 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."
 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."
 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."
 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."
 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."
 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."
 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."
 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}.
 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."
 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.
Tot 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}."
. 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."
 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."
 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."
 The existence of apparently single sdB stars poses another problem., The existence of apparently single sdB stars poses another problem.
 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}."
. 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"
explanation).,explanation).
 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."
 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."
 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)."
 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."
 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."
 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."
 1994)., 1994).
 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 $r_p$.
 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."
 2002)., 2002).
 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.
 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."
 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."
 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."
 1992: note that Chapman et al. (, 1992; note that Chapman et al. (
1996) 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)."
 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.
" 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 $\ge r_p$ as
To 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."
 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 $T_{\rm m}$.
 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 $c_{\rm
 g}=\sqrt{ {\cal R}T_{\rm c}/\mu},$ where we approximate the temperature of the self-gravitating region that extends to the disk mid-plane as $\simeq T_{\rm c}$."
 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}."
. 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.
" One laver contains the surface density X,,/2.", One layer contains the surface density $\Sigma_{\rm m}/2$.
" The other laver contains the complementary surface density X,/2.", The other layer contains the complementary surface density $\Sigma_{\rm g}/2$.
 The results are that and, The results are that and The optical depth to the magnetic region is
Iu 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.
" 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”."
 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."
 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 $N_{gal}=M_{cluster}/7\times 10^{11} \msun$."
 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.
" 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."
 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."
"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 $\sim 8 \times
10^{14} \msun$, $\sigma \sim 300 \kms$ and $\Delta v_{g} \sim7 
\kms$."
 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."
 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.
 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."
 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.
" 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."
 2002)., 2002).
 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 $M \simgt 10^{14}\msun$."
" 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."
 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)."
 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."
 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 $\sim 10^{14}\msun$.
" 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."
 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."
 \ore information is therefore available which col i priiciple aid a detection., More information is therefore available which could in principle aid a detection.
 We discuss this in the following sbsection., We discuss this in the following subsection.
 We now calculate the profie of gravitational redshifts averaged over may clusters., We now calculate the profile of gravitational redshifts averaged over many clusters.
 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."
 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 $r = \sqrt{\Delta x^{2} +
\Delta z^{2}}$, 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."
" 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).
 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 $r$.
 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."
 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."
 As expected. gravitational redshifts increase for laree mass clusters.," As expected, gravitational redshifts increase for large mass clusters."
 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."
(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."
 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."
 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 $a_\lambda$."
" 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."
" 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.
 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."
 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."
" 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 $a_l$ ).
 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.
 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."
" 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."
 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."
 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.
 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.
 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.
 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."
 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."
 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}) ).
 After integrating Eq., After integrating Eq.
" 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 $\mathrm{d} \tau_l = \hat{\chi}_l
\mathrm{d} s$."
 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."
 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}."
 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."
 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.
 These steps will therefore not be repeated here., These steps will therefore not be repeated here.
 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}) )."
 The opacity consists of a grey continuum and a single atomic line., The opacity consists of a grey continuum and a single atomic line.
" 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 $\chi_\kappa \propto
r^{-2}$."
" 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 $\epsilon_\kappa = \kappa_\kappa/\chi_\kappa$."
" 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 $\kappa_{\mathrm{line}}, 
\sigma_{\mathrm{line}}$, 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 $R=\chi_{\mathrm{line}}/\chi_\kappa$."
" The atmosphere has an extension of rij«r< 101. where ry,=IO0Uem."," The atmosphere has an extension of $r_{\mathrm{min}} < r < 101\, $ , where $r_{\mathrm{min}}
 = 10^{13} \mathrm{cm}$."
 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 $10^{-6} < \tau < 10^{4}$ .
 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."
 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."
 Then we used monotonic velocity fields. in order to compare the," Then we used monotonic velocity fields, in order to compare the"
I 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 $r > 10^3 \km$."
 Whokhlov et al. (, Khokhlov et al. (
1999) and Couch et al. (,1999) and Couch et al. (
"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."
" 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 $r_s$, $V \simeq 10^{26} \cm^3$."
 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.
" 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 $r_s \ga 3000 \km$."
 The formation of jets as used by Khokhlov et al. (, The formation of jets as used by Khokhlov et al. (
1999) and Couch et al. (,1999) and Couch et al. (
2009) can be explained by this mechanism.,2009) can be explained by this mechanism.
In the initial model used by Couch et al. (,In the initial (pre-explosion) model used by Couch et al. (
2009) the mass inside 3800kin is ~1.6...,2009) the mass inside $3800 \km$ is $\sim 1.6 M_\odot$.
 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. ("
2009).,2009).
 The collapse time of this region is ~1 s., The collapse time of this region is $\sim 1 \s$ .
 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)."
 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 $\rho_s$.
 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 $v_h$ "
"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)."
 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.
" 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."
" 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."
" 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, $n_{\rm H}$."
 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 $95\%$.
" 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."
" 2003; Ding, Charlton Churchill 2005; Lynch, Charlton Kim 2006))."," 2003; Ding, Charlton Churchill 2005; Lynch, Charlton Kim \nocite{din03,din05,lyn06}) )."
 Table 2 liststhe resulting fitting parameters., Table \ref{tab-nvfit} liststhe resulting fitting parameters.
 It is, It is
each cluster is larger than 6.,each cluster is larger than 6.
 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.
 We finally keep 717 super-pixel light curves., We finally keep 747 super-pixel light curves.
 The sensitivity of these thresholds is illustrated in Fie. 1.., The sensitivity of these thresholds is illustrated in Fig. \ref{fig:eff}.
 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."
 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.
 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."
 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."
 We finally cud with a catalogue of 631 variable stars., We finally end with a catalogue of 631 variable stars.
 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."
 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.
 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."
 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)."
 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."
 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."
 Deuce. we choose to oerform a pseudo-aperture photometry as follows.," Hence, we choose to perform a pseudo-aperture photometry as follows."
 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."
 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.
 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.
 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).
 This backerouud is subtracted from the super-pixel fux., This background is subtracted from the super-pixel flux.
 This fiux is then corrected for the seciug fraction and, This flux is then corrected for the seeing fraction and
hat the difference in bolometric magnitude is 0.15.,that the difference in bolometric magnitude is 0.15.
 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}."
.. Weak methane absorption features are seen atAH aud fy bauds 2001)., Weak methane absorption features are seen at$H$ and $K$ bands \citep{nak01}.
. The magnitude cdiffereuce at J is O.L1 and Beid et al., The magnitude difference at $I$ is 0.44 and Reid et al.
 estimate tliat he difference in bolometric magnitude is 0.15., estimate that the difference in bolometric magnitude is 0.15.
 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.
 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.
 ]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.
 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}
 as a guide to interpret the observed spectra."
" 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.
 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.
 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."
 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}.
. 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.
 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}."
. 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.
" 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.
 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."
 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.
 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."
 2., 2.
 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}."
. 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"
"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}) )."
 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}. .
"Therefore we use C,=1 [or simplicity.", Therefore we use $C_\nu=1$ for simplicity.
 We make a substitution to eliminate 77 using Eq. (1))., We make a substitution to eliminate $R^2$ using Eq. \ref{simple}) ).
 Q is the solid angle subtended by the outflow., $\Omega$ is the solid angle subtended by the outflow.
 Assuming a spherical outflow where Q=tx. Eq. (2))," Assuming a spherical outflow where $\Omega=4\pi$, Eq. \ref{outflow}) )"
 provides an upper limit on the mass outflow rate., provides an upper limit on the mass outflow rate.
 A summary of these caleulations is shown in Table 5..., A summary of these calculations is shown in Table \ref{outflowtbl}.
 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)."
 The dependence on n is AR/B-0031(0/105ae By)7)1/2F7., The dependence on $n$ is $\Delta R / R = 0.037(n/10^4$ $^{-3})^{-1/2}$.
 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."
 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 $^{-1}$."
 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.
 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}."
 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 $^{-1}=0.035 M_\odot$ $^{-1}$."
 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."
 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."
 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)."
 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 $L_{\rm edd}=1.25\times10^{38} (M/M_\odot)
=1.25\times10^{45}$ 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}."
" 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."
 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}) )."
models.,models.
 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."
 orbital period., orbital period.
 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."
 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."
 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."
 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."
 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.
 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}."
. 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.
. 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}."
. 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."
 scans spread over six hours., scans spread over six hours.
 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.
 The sources D1322-096 and D1T14-25 were used as secondary. calibrators., The sources B1822-096 and B1714-25 were used as secondary calibrators.
" 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)."
 We emploved the following method to correct for the Τὸ variation., We employed the following method to correct for the $T_{sys}$ variation.
 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}."
. 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."
 Since Chis ratio was quite similar, Since this ratio was quite similar
of the tangential point. close to1.,"of the tangential point, close to."
. 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."
. 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}."
 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.
 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."
 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."
. From here onwards. the analysis," From here onwards, the analysis"
In 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},"
 upper panel)., upper panel).
 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},"
 lower panel)., lower panel).
 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.
 This breaks the frozen-in approximation of ideal MILD., This breaks the frozen-in approximation of ideal MHD.
 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."
 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.
 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}.
 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.
 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.
 Similar results were observed in Paper Lin the ambipolar-dominatec simulation., Similar results were observed in Paper I in the ambipolar-dominated simulation.
 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."
 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.
 We now examine the behaviour of the charged [uids hemselves., We now examine the behaviour of the charged fluids themselves.
 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.
 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.
 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."
 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}) ).
 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}) )."
 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.
 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."
 The various dynamics discussed above are confirmed in ligure 6.., The various dynamics discussed above are confirmed in figure \ref{nonideal_KEx4}.
 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.
 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}) ).
 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).
 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."
 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."
 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."
 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.
 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."
 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.
 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"
"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.
 Figure 3. plots the local luminosity function for the subsaniples (ii) anc (ui).," Figure \ref{lf1}
 plots the local luminosity function for the subsamples (ii) and (iii)."
 For clarity we do not show the luminosity function for sample (1)., For clarity we do not show the luminosity function for sample (i).
 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.
 Llenceforth. we will be using the total saniple (ii) in our analysis.," Henceforth, we will be using the total sample (ii) in our analysis."
 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.
 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."
 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.
 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.
 Phere are 27 and 19 [ate and carly twpe galaxies respectively., There are 27 and 19 late and early type galaxies respectively.
 The results are shown in Fig., The results are shown in Fig.
 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)."
 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.
 The optical luminosity function has been derived rom the Πο et al. (, The optical luminosity function has been derived from the Ho et al. (
1997) 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. (
1992).,1992).
 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. (
2004) by convolving the ‘warm’ LAS uminositv function. (Takeuchi et al.,2004) by convolving the 'warm' IRAS luminosity function (Takeuchi et al.
 2003) with the luminosity relation for star-forming ealaxies (Ranalli et al., 2003) with the luminosity relation for star-forming galaxies (Ranalli et al.
 2003)., 2003).
 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.
 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.
 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 $z=2$."
 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)."
 “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. (
1995).,1995).
 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.
 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."
 Norman et al. (, Norman et al. (
2004) 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)."
 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."
" 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 $\phi_\star$.
" 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 $z<0.22$.
" 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 $\log
(f_x / f_o) < -2$ ), luminosities $\rm L_X < 10^{42} erg \,
s^{-1}$ ), 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."
 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.
 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 $L_X -
z$ plane probing lower redshifts and higher luminosities."
" 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 $z<0.22$."
 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.
 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. (
1997).,1997).
 The above sample comprises 43 galaxies. cletected by PSPCcither as targets or," The above sample comprises 43 galaxies, detected by PSPCeither as targets or"
period.,period.
 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."
 It is also possible to examine the data obtained before the outburst., It is also possible to examine the data obtained before the outburst.
 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)."
 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}) ).
 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)."
 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.
 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 ?);"
 and (11) why does it appear as a diffuse source ?, and (ii) why does it appear as a diffuse source ?
 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."
 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.
 Finally. the more realistic explanation remains that Echeclus has ejected a fragment.," Finally, the more realistic explanation remains that Echeclus has ejected a fragment."
 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."
 This fragment has probably suffered a disintegration process., This fragment has probably suffered a disintegration process.
 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.
 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."
 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.
 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.
 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."
 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."
 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."
 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).
 It look likes a diffusesource., It look likes a diffusesource.
 e , $\bullet$ 
"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.
 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.
 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."
 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 $c(0)$.
 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."
 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."
 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.
 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."
 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."
 The thresholding is made on the wavelet coellicient histogram., The thresholding is made on the wavelet coefficient histogram.
 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."
 “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.
 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."
 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."
 We choose it through a classical decision rule., We choose it through a classical decision rule.
 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."
 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 $\nu_{thres} = w_{thres}(s)$ .
 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."
 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."
 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."
 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.
 AL other pixel labels are set equal to zero., All other pixel labels are set equal to zero.
 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."
 So. the first. structure individuated bears the label 1 and so on.," So, the first structure individuated bears the label '1' and so on."
 We also compute the volume and surface of each structure found., We also compute the volume and surface of each structure found.
 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.
 We choose the parameter:, We choose the parameter:
"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}."
". 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."
 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}.
". 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."
" 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."
" 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)."
 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.
". 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."
 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'.
 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}."
" 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"
ccubes 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.
" 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."
 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}.
" 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."
" 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'."
" 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."
 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.
" 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."
"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}."
" Again, this data has been masked and corrected for primary-beam attenuation."," Again, this data has been masked and corrected for primary-beam attenuation."
" 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."
 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.
 This is likely due to the pedestal of leftover flux in classicalCLEAN., This is likely due to the pedestal of leftover flux in classical.
". 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."
" 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."
" 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."
hhas brighteued.,has brightened.
 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."
 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."
 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};.
" 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}) ),"
 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.
 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."
 Each observation las been processed using the techniques described in Munoctal.(2003a)., Each observation has been processed using the techniques described in \citet{mun03a}.
. 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."
 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}."
 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.
" The rms dispersion in the offsets was 07225,", The rms dispersion in the offsets was 25.
 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.
 The image of the 20’ around Hs displaved im Figure 1., The image of the $\times$ around is displayed in Figure \ref{fig:img}.
 The location of ds a=2667 111680. d— 292000861 (0733: T2000).," The location of is $\alpha$ 41680, $\delta$ 00861 $\pm$ 3; J2000)."
 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.
 The region is indicated by the white cllipse., The region is indicated by the white ellipse.
 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."
 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."
" The reeion lad a radius of z1""..", The region had a radius of $\approx$.
 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"
models to the prediction the models eive for the mass loss rate.,models to the prediction the models give for the mass loss rate.
 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."
 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.
 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 $k =
\frac{\bar{\rho}^{1/2}}{0.62 C_{env}} (10^4)^{0.62}$ ."
"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)."
 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."
" 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."
 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."
" 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 $C_{env} \sim
300$ ) suggested by \citet{Lamers} based on their analysis of young cluster systems."
 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.
 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."
 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."
 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."
 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."
 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."
 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."
 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."
 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."
 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 the
24 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.
"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."
" 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."
 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.
" 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"
entire accretion phase.,entire accretion phase.
 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."
 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.
" For a 0.6Af. WD. fh~Rhen Ti,7.10°K."," For a $0.6 \ M_\odot$ WD, $h \simeq R$ when $T_b \simeq 7\E{8} \ {\rm K}$."
 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}.
.. 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."
 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."
 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$."
"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."
" 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} $."
"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 $ds/dP = -7k_B/17 \mu m_p P$."
" 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 $\mu=0.6$."
 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."
" 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}."
. The time to acerete an envelope mass Mag Is face—AtayM., The time to accrete an envelope mass $M_{\rm env}$ is $t_{\rm acc} \equiv M_{\rm env} / \dot{M}$.
 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)."
" Thus. the colupressional luminosity is given by equation (5)). with T’=T,,."," Thus, the compressional luminosity is given by equation \ref{eq:complum}) ), with $T'=T_b$ ."
" 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 $^{-3}$."
 We have assumed solar metallicity. but thisresult is ucarly independentof composition.," We have assumed solar metallicity, but thisresult is nearly independentof composition."
 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."
" 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)."
 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."
" 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."
 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."
 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."
"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 $^{-1}$ .
Linear 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 .
|IP - , |_P > .
"| 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 $ ."
 For Kramers” opacity aud ideal gas. \eool= 17/2.," For Kramers' opacity and ideal gas, $ \chi_{\rm cool} = 17/2 $ ."
 The cooling rate is rewritten as, The cooling rate is rewritten as
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).,"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)."
 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.
 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.
 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."
 1998)., 1998).
 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.
 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."
 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.
 This cai be shown analytically and numerically reproduced (model U)., This can be shown analytically and numerically reproduced (model U).
 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.
 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}) )
" 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}) )."
 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}) )."
 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."
 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.
 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."
 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 $_{\sun}$."
 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.
 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."
 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};
 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}) ).
 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}) )."
 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).
 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.
 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.
 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"
out 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.
 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.
 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.
 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}
 but this approach suffers from both uncertainty in the dust modeling and a lack of spectroscopic redshifts."
 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}."
. 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."
 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."
" 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)."
 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."
 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.
 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}) )."
 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.
 This represents the buuinositv-scaled spectra sununed over all galaxies., This represents the luminosity-scaled spectra summed over all galaxies.
 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.
 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."
 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."
 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."
 to vary simoothiy with time., to vary smoothly with time.
 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."
 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."
 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).
 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."
 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)."
 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.
 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 $\lambda = 4600\pm 700$ )."
 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."
" 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.
 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."
 The plan of this paper is as follows., The plan of this paper is as follows.
 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.
 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.
 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 $z>1$.
 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.
 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.
 Finally we give our sunny aud conclusions (Section 5))., Finally we give our summary and conclusions (Section \ref{sec:summary}) ).
" 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 $h = H_0 / 100\,{\rm
 km\,s^{-1}\,Mpc^{-1}}$."
 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 $^2$.
 Au overview is eiven by Yorketal (2000)., An overview is given by \cite{SDSS}. .
. 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}. ."
 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}. .
. 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}. .
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 (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}) )."
 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.
 This has been corroborated by others data sets. (Friemanetal.2008:; Blanchard 2010))., This has been corroborated by others data sets \cite{FTH08}; \cite{Blanchard10}) ).
. 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."
 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."
 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."
 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."
 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.
 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."
" 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."
 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."
 Other options have been proposed for its origin., Other options have been proposed for its origin.
 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}) ).
" 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."
 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}) ).
 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 $\phi$."
 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.
 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 $\displaystyle \frac{\partial} {\partial X}$."
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," 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"
stronely magnetic.,strongly magnetic.
 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."
 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."
 This distinction has been discussed. by Liebertetal.(2005). and by Wawkactal.(2007)., This distinction has been discussed by \citet{liebert2005} and by \citet{kawka2007}.
.. 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."
 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."
 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.
 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.
 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."
 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.
 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."
 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.
 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.
 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 examples
in][]{bergeron2001}."
. 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.
 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.
 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.
 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.
 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 $\log g$ .
 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.
 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}.
. 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."
 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."
 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.
 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.
 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}.
. 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.
 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}."
.. MI have low temperatures. 7.500<Digfy«13.000 and so have not recently emerged rom a common envelope.," All have low temperatures, $7{,}500
< T_{\rm eff}/{\rm K} < 13{,}000$ and so have not recently emerged from a common envelope."
 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."
 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}."
. 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.
 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.
 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.
 Four of these have been examined in more detail., Four of these have been examined in more detail.
 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}.
.. 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, $0.25\,M_\odot$."
 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."
 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."
 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.
 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."
 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}.
. 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."
 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.
 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 energy
"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)."
" We refer to this as the ""recombination rate"" (RR) method."," We refer to this as the “recombination rate"" (RR) method."
 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."
 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."
 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."
 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."
" 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."
 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.
 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 $C_H$."
 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."
 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."
 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."
" 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 $x \equiv n_{\rm HII}/n_H$ )."
" 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 $x > 0.05$."
" 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)."
 We, We
field could be observed.,field could be observed.
 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."
 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.
 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."
 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."
 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.
" 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}."
 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."
 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.
 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}."
. 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 the
In Fig. 12..,"In Fig. \ref{fig5},"
 the relation between amount of rotational support ancl isophotal shape is examined., the relation between amount of rotational support and isophotal shape is examined.
 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."
 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.
 The relation is independent of galaxys luminosity (e.g.. Benderetal. 19949).," The relation is independent of galaxy's luminosity (e.g., \citealt{bender94}) )."
 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.
 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."
Luninous 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."
 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 $10^{-4} \msunyr$.
 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.
 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."
 The reason for the tvpical LBV variations is still uuknown., The reason for the typical LBV variations is still unknown.
 For reviews see Nota Lamers (1997)., For reviews see Nota Lamers (1997).
 Leitherer et al. (, Leitherer et al. (
1989) and de I&oter et al. (,1989) and de Koter et al. (
1996) 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.
 Therefore. Tig decreases during the variatious. if L. is about constant.," Therefore, $\teff$ decreases during the variations, if $L_*$ is about constant."
 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."
. 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."
 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.
 19501., 1989).
 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."
 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 $\teff$."
 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."
 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 in
Weak 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."
 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}."
 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."
. 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."
 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}."
 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}."
 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}."
 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.
 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."
 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 spectrum
measurement]{Hikage2011}."
 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."
 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."
 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."
 This paper is organized as follows., This paper is organized as follows.
 Iu Sect., In Sect.
 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.
 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."
 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}.
 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},"
 and for the convergence bispectiua iu Sect. 5.," and for the convergence bispectrum in Sect. \ref{Convergence-bispectrum},"
 considering the cases of both equilateral and more general isosceles configurations., considering the cases of both equilateral and more general isosceles configurations.
 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},"
" from ""]-halo. ""2-halo'. or ""halo terius."," arising from “1-halo”, “2-halo”, or “3-halo” terms."
 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."
7. and we conclude in Sect. 8..,\ref{Cosmology} and we conclude in Sect. \ref{Conclusion}. .
"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."
 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.
 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."
 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."
 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).
neum 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.'"
 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."
" 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."
 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."
 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."
 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."
 The contour plot of the residuals (Eig. 7)), The contour plot of the residuals (Fig. \ref{f2}) )
 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."
 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.
 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."
 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).
 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}) ).
 In the submim continuum image both AB and € are spatially resolved., In the submm continuum image both AB and C are spatially resolved.
 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."
 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.
 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.
 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}) ).
Note 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."
 “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}. ."
The 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."
 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."
 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}) ).
 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."
 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""."
 Based on the PSE fit discussed in Sect., Based on the PSF fit discussed in Sect.
 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).
 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.
 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.
omFrom 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."
 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."
 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 $<9$ $^{-1}$.
o 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 $^{-1}$."
 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."
 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."
 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.
 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."
 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."
" 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}. ."
sityour 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."
 The nebula isdivided in two, The nebula isdivided in two
from 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.
 Table 1 stmuarizes estimation of losses coming frou different origins., Table \ref{tab:loss} summarizes estimation of losses coming from different origins.
 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.
 The Fresnel losses rave been theoretically estimated to , The Fresnel losses have been theoretically estimated to $\%$.
Auv 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 $\%$.
 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).
 Therefore 50% of the light is radiated outside the waveguide., Therefore $\%$ of the light is radiated outside the waveguide.
 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.
 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.
 The main progress concerns the beam combination function., The main progress concerns the beam combination function.
 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."
 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.
 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."
 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.
H 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.
: The importance: ofd . ≼∐↴∖↴↻↸∖↥⋅↴∖↴↕∪∐∙↴⋝∐⋅↸∖↕↥⋅↕∐∶↴∙↸∖∐↸⊳↸⊳↸∖⋜⋯≼↧∪↑∐↸∖↥⋅↻↕∐∖∐∪⋯↸∖∐⋜↧⋃↑∐↸∖ ↴∎⋝↸∖↥⋅↴∖↴⋜⋯≼⊔∐↑∐↸∖↸⊳∪∐∏⋯∐↸∖," The importance of dispersion, ce and other phenomena in the fibers and in the components have to be fully understood."
∐↑↴∖↴∐⋜↧↖↽↸∖↑∪↴⋝↸∖↕⋟∏∐⋅↖⇁∏∐≼∐∖↥⋅↴∖↴↑∪∪≺↧∙ 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."
. 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}.
".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.
 This: experimentalqi. precaution. is. : S ecisive to achieve image reconstruction (Delage1998)., This experimental precaution is decisive to achieve image reconstruction \citep{Del98}.
. 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)."
 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.
 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}.
 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.
 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."
 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)."
 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.
From 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.
" 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 $n\in\{0,\dots 8\}$."
 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}."
. 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 $z \gtrsim 1.8$ .
 The low, The low
follow 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.
 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.
 1997)., 1997).
" 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."
 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."
 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 $\beta \simeq -1.0$.
 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 $t_{\rm obs}
\ale 3$ 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. ["
2]) using the either FUY or NUV. ALAALA detectors.,2]) using the either FUV or NUV MAMA detectors.
 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."
 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."
 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 $\lambda \le 912 (1 +
z)$ ) than the Lyman $\alpha$ forest $\lambda \simeq 1216
(1+z)$ ) 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."
 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.
gtsci.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."
 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.
 1)., 1).
 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 of
"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)."
" 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."
" 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."
" 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."
" 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."
 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.
" 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."
" 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}) )."
" 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."
" 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."
 We explore this issue in detail in Appendix A.., We explore this issue in detail in Appendix \ref{appen}.
" 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."
" 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."
" 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."
" 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. $\sim 10^7 \,h^{-1}{\rm M}_\odot\,$."
" 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."
" 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."
" 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}."
" 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."
 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 time
Cas 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.
 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}) ).
 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).
 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.
 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."
 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."
 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.
 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.
 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.
 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 $\sim 1$."
 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 $U < 10$ $\lambda$ ).
 The shell thickness sets je angular scale of the transition., The shell thickness sets the angular scale of the transition.
 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."
 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."
 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 $1$.
 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}."
 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.
 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."
 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}.
 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.
 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.
 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}.
".. 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."
 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."
 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}.
 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 $E(k) 
\propto k^{-3/2}$ for both velocity and magnetic field."
" 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."
 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 $k_\parallel \propto 
k_\perp^{2/3}$ where $k_\parallel$ is the component of the wave vector parallel to the local magnetic field direction."
 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."
 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."
 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}."
. 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}.
. 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."
" 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.
 The synchrotron emissivity ἐςxn.|BL4|2U? where n. is, The synchrotron emissivity $i_s \propto n_e|B_\perp|^{(p+1)/2}$ where $n_e$ is
evolution of a disk svsem from high redshift to the present clay.,evolution of a disk system from high redshift to the present day.
 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.
 In Fig., In Fig.
 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}.
. 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."
 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 $z=0$.
 As Fig., As Fig.
 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."
 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 $log(<\rho)>$ .
 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."
 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.
" 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 $t_v=6 \ Gyr$."
 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: $<M_\star (t_{obs})/ M_\star (t_0)> \simeq 0.3$ ."
 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 ~
0.75 M_\star (t_{0}) /(t_{obs}-t_{0}) \sim \ 1 (M_\star(t_0)/ (10^{10}
M_\odot) M_\odot/yr$."
 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 ~ 0.25
M_\star (t_{0}) / (1 Gyr) \sim 3 (M_\star(t_0)/ (10^{10} M_\odot)
M_\odot/yr$ which points towards a declining SFR history."
 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.
 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."
 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 $z=1$."
 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.
 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."
 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.
 Comparing the average, Comparing the average
plate.,plate.
 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."
 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."
 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 $r_{\rm e} =
1.678 r_{0}$ for a circularly-symmetric image with an exponential light profile."
 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 $r_{\rm e}$, $C =
1.124$."
" 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}) )."
 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."
 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."
 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}.
" 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."
" 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 $\mu_{\rm
iso}$ and either $\mu_{0}$ or $\mu_{\rm e}$ than other galaxies."
 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 $r_0$."
 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}) ).
" 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."
 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 $I_{\rm
field}$ is missed because of the isophotal limit."
 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.
 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).
 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."
 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."
 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."
 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."
 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."
 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."
 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."
 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."
 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."
 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."
 So. in this," So, in this"
while 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.
 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."
 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.
 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."
 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.
 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."
 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."
 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."
 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)."
 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. ("
1983) and Ambwani et al. (,1983) and Ambwani et al. (
1955),1988).
 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."
 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."
LE 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."
 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)."
 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.
 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.
 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)."
 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. (
1996) 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."
 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."
 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."
 1996., 1996.
 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}.
" 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."
" 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}) )."
 '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}) ).
 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}) ).
 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."
 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."
" 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.
 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.
 In DEP and SUB models. comptonization mainly," In DEF and SUB models, comptonization mainly"
(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."
 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.
 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).
 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).
 The visibility. data were inspected for quality. aud leisy points were removed.," The visibility data were inspected for quality, and noisy points were removed."
 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."
 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."
 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.
 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.
 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}.
" 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 $15''$."
 À total of 20.76 ks were obtained., A total of 29.76 ks were obtained.
" 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."
 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."
" 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 $\langle
kT\rangle=930\pm 250$ 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)."
" 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 $L_X\approx
1.2\times 10^{25}$ erg $^{-1}$, or a ratio of $L_X/L_{\rm bol}\approx
10^{-4.9}$."
 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."
 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}) ).
 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."
 It is thus possible that the second pair constitutes a flare., It is thus possible that the second pair constitutes a flare.
 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."
" The quiesceut component would be correspoudinely lower. Ly/Lic10.729,"," The quiescent component would be correspondingly lower, $L_X/L_{\rm bol}\approx 10^{-5.0}$."
 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."
 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."
 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.
 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}."
. 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.
 The spectrum covers JSI0/—66850 aat a resolution of about 5À., The spectrum covers $3840-6680$ at a resolution of about 5.
. 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."
 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}.
 The Ta lisht curve exhibits a clear sinusoidal behavior (Figure 1))., The $\alpha$ light curve exhibits a clear sinusoidal behavior (Figure \ref{fig:all}) ).
 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}) )."
 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 $m({\rm
UVW1})>23.0$ mag."
 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 $\lambda L_\lambda/L_{\rm bol}<10^{-3.2}$.
 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.
 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)."
 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."
illustrative 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)."
 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."
 No strong Lila sorption is predicted., No strong Li I absorption is predicted.
 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."
 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)."
 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."
 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.
 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."
. 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. ("
2000).,2000).
 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."
 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.
 AB ackuowledecs support from NASA erauts NACH5S-7199 and NAG5-7073., AB acknowledges support from NASA grants NAG5-7499 and NAG5-7073.
 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. (
1997).,1997).
 We wish to acknowledge helpful sugeestionsOO from zu auonviuious referee., We wish to acknowledge helpful suggestions from an anonymous referee.
sinulations.,simulations.
 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}) )
 appears to be 1.1., appears to be 1.1.
 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."
" 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."
 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)."
 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.
 The C; could eo down bv LL% aud the amplitude bv 38%., The $C_\ell$ could go down by $14\%$ and the amplitude by $38\%$.
" This however does not apply to the Ix,,-baud.", This however does not apply to the $_a$ -band.
" 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."
 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 the
"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 $\ps \simeq 0.5$."
" 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 $0.4 \leq \ps \leq 0.6$.
" 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."
" 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."
" 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.
 Eventhoughthemodelhasnotbeendesignedtooptimisedlüstherearetwoclearlydistinctpopulations.," Even though the model has not been designed to optimise class separation in colour--colour space, there are two clearly distinct populations."
"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. ("
"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)."
"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)."
" 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."
" 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."
 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.
" 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."
" 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."
 '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 ).
" 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."
"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."
" 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."
" 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."
" 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."
 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.
 Using prior knowledge is vital for such faint sources., Using prior knowledge is vital for such faint sources.
 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.
" 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."
 Artificially coercing, Artificially coercing
"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.
" 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."
" 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}) ).
 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."
 9, 2.
 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.
" 2] as d function of Z, ire shown in Fie.", 2) as a function of $Z_c$ are shown in Fig.
 3., 3.
" 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 $Z_c$."
" 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."
" 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}) ),"
 Aiia Chitre (1997))., Antia Chitre \cite{ac97}) ).
 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.
 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."
" 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 $c(T,\rho,X,Z)$ ."
 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 $T,X,Z$ ."
 Now for a fully ionized, Now for a fully ionized
A 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.
 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.
 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."
 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."
 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}."
 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.
 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."
 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."
 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.
 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)."
 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}) )."
 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)."
 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}.
. 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)."
 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."
 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."
 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."
 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}."
. 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)."
 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).
 The Murakawa et al., The Murakawa et al.
 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."
 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."
 Below the threshold. the models results lie below these “limits.”," Below the threshold, the models results lie below these “limits.”"
 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."
 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)."
 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."
 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."
 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.
 At cold temperatures it is difficult to stop this process., At cold temperatures it is difficult to stop this process.
 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}."
 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}. ."
 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.
 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."
 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}. ."
 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."
 It should benoted that. in the absence of photodesorption. minimum detectable," It should benoted that, in the absence of photodesorption, minimum detectable"
 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 ."
 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 ."
 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."
 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?"
 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.
 ‘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."
 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)."
 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."
 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."
 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."
 In Sect. 3..," In Sect. \ref{sec:results},"
 we show the results. which are discussed in Sect. 4..," we show the results, which are discussed in Sect. \ref{sec:dis}."
 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"
Since 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 ."
. 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."
 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.
 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"
"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."
" 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."
" 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."
 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.
 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.
" 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."
" 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."
 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!
" 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."
" 2008, McGowan et al."," 2008, McGowan et al."
" 2008, Haberl, Eger Pietsch 2008)."," 2008, Haberl, Eger Pietsch 2008)."
" 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)."
" 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."
" 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!"
" 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."
" 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."
 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.
 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.
" 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."
 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.
" 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."
" 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."
" 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."
 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.
 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 is
"and NIT, have been observed in this cloud.",and $_3$ have been observed in this cloud.
 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."
 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} ).
 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."
 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."
 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.
 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."
 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}.
. 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."
" 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.
. 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."
 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}."
. 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."
 All these evidences point towards a picture where in Lupus, All these evidences point towards a picture where in Lupus
decreases 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."
 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 $F_{\rm 8, max} < F_8
< F_{8, N=5}$ to obtain a fit to the cumulative flux distribution."
 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."
 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."
 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}. .
 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."
 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.
 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."
" 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.
 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."
 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."
 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."
 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."
 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 $\kappa =
1.63 \pm 0.03$, much closer to $1.5$."
 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."
 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)."
 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."
 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."
 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 $p(\alpha)$.
" 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."
 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."
 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.
 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)."
 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}."
 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."
" 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)."
 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."
 This assumption is less likely to hold as the luniting flux to which we are coxtrapolating becomes lower: the ffux distribution eveutuallv exhibit a break due to cosmological effects and/or lnuninositv evolution., This assumption is less likely to hold as the limiting flux to which we are extrapolating becomes lower: the flux distribution eventually exhibit a break due to cosmological effects and/or luminosity evolution.
 The question is how far in the low-flux regime our extrapolation must continue before we get a significant contribution of unresolved unideutified sources to the eanuns-rav background., The question is how far in the low-flux regime our extrapolation must continue before we get a significant contribution of unresolved unidentified sources to the gamma-ray background.
" H the answer is ""not very far”. then our extrapolation may indeed be reasonable over such a small ranee. aud unresolved. unidentified sources are likevo nike up a cousiderable fraction of the ECGRD."," If the answer is “not very far”, then our extrapolation may indeed be reasonable over such a small range, and unresolved, unidentified sources are likely make up a considerable fraction of the EGRB."
 On the other haud. if we need to extrapolate he flux distribution down to fluxes very low compared to the resolve. flux range. then it is quite uulikelv fvat our oxtrapolation is valid throughout the flux reeime in which we use it.," On the other hand, if we need to extrapolate the flux distribution down to fluxes very low compared to the resolved flux range, then it is quite unlikely that our extrapolation is valid throughout the flux regime in which we use it."
 In such a case it is doubtful that the actual fluxdistribution of the unresolved τςeutified, In such a case it is doubtful that the actual fluxdistribution of the unresolved unidentified
Whether massive stars (D and O-(ype) form via an accretion process similar to that for low-mass stars (Osorioetal. 10009: MeIxee&Tan2003)) or instead. via collisions with lower-mass stars (Bonnelletal.1998) is currently under debate.,Whether massive stars (B and O-type) form via an accretion process similar to that for low-mass stars \citealt{Osorio99}; ; \citealt{McKee03}) ) or instead via collisions with lower-mass stars \citep{Bonnell98} is currently under debate.
 Highly collimated radio jets (Rodríguez1997: Anelacaοἱal. 1993)) and Herbig-IHaro (LIT) flows are frequently observed towards voung low-mass stars., Highly collimated radio jets \citealt{Rodriguez97}; \citealt{Anglada98}) ) and Herbig-Haro (HH) flows \citep{Reipurth02} are frequently observed towards young low-mass stars.
 It is now widely accepted Chat jets are intümatelv linked to (hie accretion process and the formation of both bipolar molecular oulllows ancl LL flows (seereviewbyBeipurth&Bally2001).," It is now widely accepted that jets are intimately linked to the accretion process and the formation of both bipolar molecular outflows and HH flows \citep[see review
by][]{Reipurth01}."
. The role of collimated jets in massive stars (M > 8 AL.) is less certain., The role of collimated jets in massive stars (M $>$ 8 $_{\odot}$ ) is less certain.
 In this higher mass regime observations of jets are difficult. primarily because of the greater distances involved ancl because the evolutionary lime scales of such jets are expected to be much shorter.," In this higher mass regime observations of jets are difficult, primarily because of the greater distances involved and because the evolutionary time scales of such jets are expected to be much shorter."
 Garayetal.(2003) recently reported the discovery. of a triple radio continuum source associated with IIRLAS 16547-4247. a voung stellar object with a bolometric liminosity of 6.2x104L... equivalent to that of a single O8 ZAMS star.," \citet{Garay03} recently reported the discovery of a triple radio continuum source associated with IRAS $-$ 4247, a young stellar object with a bolometric luminosity of $6.2 \times 10^4$, equivalent to that of a single O8 ZAMS star."
 The three radio components are aligned in a southeast-norlhwest direction with the outer components (lobes) svmuuetrically separated Irom the central source by an angular distance of ~20 arcsec., The three radio components are aligned in a southeast-northwest direction with the outer components (lobes) symmetrically separated from the central source by an angular distance of $\sim$ 20 arcsec.
 The triple system is centred on the position of the IILÀS source and is within a 1.2-mm dust continuum emission core whose properües are similar to other massive star-forming cores (e.g. 20023)., The triple system is centred on the position of the IRAS source and is within a 1.2-mm dust continuum emission core whose properties are similar to other massive star-forming cores (e.g. \citealt{Garay02}) ).
 The spectral indices between 1.4 and 5.6 GIlz are 0.49 for the central source and —0.61 and —0.33 for the (wo outer components., The spectral indices between 1.4 and 8.6 GHz are 0.49 for the central source and $-0.61$ and $-0.33$ for the two outer components.
 This is consistent with the central source being a thermal jet ancl the (wo outer components being non-thermal emission arising from the working surfaces of the jet as it interacts with the surrounding ambient medium., This is consistent with the central source being a thermal jet and the two outer components being non-thermal emission arising from the working surfaces of the jet as it interacts with the surrounding ambient medium.
 This is (he first reported case of a radio jet associated with a voung O-tvpe star., This is the first reported case of a radio jet associated with a young O-type star.
 We have performed a series of infrared observations towards IRAS 16547-4247 to confirm (he existence of a collimated flow. and to investigate the nature of the powering source., We have performed a series of infrared observations towards IRAS $-$ 4247 to confirm the existence of a collimated flow and to investigate the nature of the powering source.
 Near-intrarecl images were obtained at the European Southern Observatory in Paranal. Chile. using the ISAAC! short wave camera (Cubyetal.2000). mounted on the ANTU telescope of the Very Large Telescope (VLT).," Near-infrared images were obtained at the European Southern Observatory in Paranal, Chile, using the ISAAC short wave camera \citep{Cuby00} mounted on the ANTU telescope of the Very Large Telescope (VLT)."
 The short wave camera is equipped wilh a 1024x pixel Rockwell LAWALLHeg:Cd:Te array with a pixel scale of 0”..148 pixel /," The short wave camera is equipped with a $1024 \times 1024$ $^2$ Rockwell HAWAIIHg:Cd:Te array with a pixel scale of .148 $^{-1}$ ,"
 The short wave camera is equipped wilh a 1024x pixel Rockwell LAWALLHeg:Cd:Te array with a pixel scale of 0”..148 pixel /.," The short wave camera is equipped with a $1024 \times 1024$ $^2$ Rockwell HAWAIIHg:Cd:Te array with a pixel scale of .148 $^{-1}$ ,"
| aud linear fluctuation amplitude ou spheres of radius + Πο og=0.9.,"$^{-1}$ and linear fluctuation amplitude on spheres of radius $^{-1}$ Mpc, $\sigma_8=0.9$."
" Of these parameters. the uucertaintv in the value of a, has most impact on the model results;"," Of these parameters, the uncertainty in the value of $\sigma_8$ has most impact on the model results."
 While several studies support a value of σς~0.9 (e... Baconetal. (2002).. IToekstraetal.(2002) [gravitational leusiug]: Eke.Cole&Frenk(1996)... etal.(2002). [cluster abundance}: Spergeletal.(2003) [cosmic nücrowave background. (CMD)]: Sieverset.al. [Suuyaev-Zeldovich effect]). other recent analyses have sugeested lower values. gg~0.7 (ego Peacock(2003) [large scale structive: AMelehiorietal.(2002) [CAID]: Jarvisetal.(2003) [gravitational lensing}: Allenetal. (2003).. Snithetal.(2003) [cluster abundauce[).," While several studies support a value of $\sigma_8 \sim 0.9$ (e.g., \citet{bacon02}, , \citet{hoekstra02} [gravitational lensing]; \citet{eke96}, \citet{vianna02} [cluster abundance]; \citet{spergel03} [cosmic microwave background (CMB)]; \citet{contaldi02} [Sunyaev-Zeldovich effect]), other recent analyses have suggested lower values, $\sigma_8
\sim 0.7$ (e.g., \citet{peacock02} [large scale structure]; \citet{melchiori02} [CMB]; \citet{jarvis02} [gravitational lensing]; \citet{allen02}, , \citet{smith03} [cluster abundance])."
 A discussion of recent results may be found in Waneetal. (2003)., A discussion of recent results may be found in \citet{wang03}.
. Except where specified. we show models based ο- σς=0.9: however. (as we shall see) taking the lower value. σς=07. considerably eases the energy budget audor reduces the conduction cfiicicncy required to match the ealaxv luminosity function.," Except where specified, we show models based on $\sigma_8=0.9$; however, (as we shall see) taking the lower value, $\sigma_8=0.7$, considerably eases the energy budget and/or reduces the conduction efficiency required to match the galaxy luminosity function."
 Throughout. we use the halo lnass function derived frou N-body simulations by Jenkinsetal.(2001) histories... instead of the Press-Schechter mass function used by etal. (2000).," Throughout, we use the halo mass function derived from N-body simulations by \citet{jenkins01} , instead of the Press-Schechter mass function used by \citet{cole00}."
. We compare our model with recent determünations of he [-band bnuuimositv function assumine a I[xeunicutt stellar initial mass function (I&eunicutt1983)., We compare our model with recent determinations of the K-band luminosity function assuming a Kennicutt stellar initial mass function \citep{ken83}.
. Iu order to acilitate comparison between models. we have kept the IMFE fixed. and assumed a neglieible fraction of brown dwarfstars?.," In order to facilitate comparison between models, we have kept the IMF fixed, and assumed a negligible fraction of brown dwarf."
. We choose the K-baud in order to minimize he sensitivity of our results to recent star formation and o dust obscuration., We choose the K-band in order to minimize the sensitivity of our results to recent star formation and to dust obscuration.
 The model of Coleetal.(2000) iucludes a detailed and fully self-consisteut caleulatio- of dust extinction which is used in this work., The model of \citet{cole00} includes a detailed and fully self-consistent calculation of dust extinction which is used in this work.
 We fiud. jiowever. that dust-obscuration has a neglieible effect ou our results for the EIK-boaud Inuuimositv fuuctiou (typically shifting the bright eud faintwiuds bv less than one tent[um of a maeuitude.)," We find, however, that dust-obscuration has a negligible effect on our results for the K-band luminosity function (typically shifting the bright end faintwards by less than one tenth of a magnitude.)"
" For the observational coniparison. we use he local Γάιος Iuuinositv fuuctious neasured by Coleetal.(2001) aud Iochaneketal.(2001). (both based ou he 2ATASS survey) aud the local (2<0.1). lminesity ""uetiou derived from the much deeper ERK-band survey of IIuaugetal.(2002)."," For the observational comparison, we use the local K-band luminosity functions measured by \citet{cole2mass} and \citet{koch01} (both based on the 2MASS survey) and the local $z<0.1$ ) luminosity function derived from the much deeper K-band survey of \citet{huang02}."
. The analysis bv IHuaug ct al., The analysis by Huang et al.
 sugecsts a faint-eud slope (ag=1.37£0.10). steeper han the values found bv Cole et al (ag=193) aud * ochaueck et al.," suggests a faint-end slope $\alpha_{\rm
K}=-1.37\pm0.10$ ), steeper than the values found by Cole et al $\alpha_{\rm K}=-0.93$ ) and by Kochaneck et al."
 (og=1.09).," $\alpha_{\rm
K}=-1.09$ )."
 These latter two are also in good agreenient with the faint cud slope of the g-band buuiuositv function measured by Blanton et al., These latter two are also in good agreement with the faint end slope of the z-band luminosity function measured by Blanton et al.
" (a,= 1.05) from the SDSS survey.", $\alpha_{\rm z}=-1.08$ ) from the SDSS survey.
" The z-baud data should also be little affected by residual star formation aud dust extinction. but have a deeper surface brigltucss Πιτ,"," The z-band data should also be little affected by residual star formation and dust extinction, but have a deeper surface brightness limit."
 These discrepancies indicate that there remain siguificaut systematic uncertainties mn current measurements of the faint eud of the E-baud bhuuimositv function. perhaps due to liminosity frou low-surtace brightness regions of ealaxies being niüssed as recently sugeested by Audreou (2002)..," These discrepancies indicate that there remain significant systematic uncertainties in current measurements of the faint end of the K-band luminosity function, perhaps due to luminosity from low-surface brightness regions of galaxies being missed as recently suggested by \citet{andreon}."
 Tn Fig., In Fig.
" 1 we show the simplest possible model of the ""nnuimositv function which we call Model 1 (shown as the dashed line).", \ref{fig:models_123} we show the simplest possible model of the luminosity function which we call Model 1 (shown as the dashed line).
 In this model. the mass function of dark natter halos (Jeukiusetal.2001) has been converted iuto a huninosity function simply by assiuniiug a fixed mass-to-ight ratio CA/Ly=WAL. Ey.) chosen so as to match he kuee of the observed luuinositv function.," In this model, the mass function of dark matter halos \citep{jenkins01} has been converted into a luminosity function simply by assuming a fixed mass-to-light ratio $M/L_{\rm K} = 11 M_\odot/L_{\rm
K,\odot}$ ), chosen so as to match the knee of the observed luminosity function."
 As is well shown. this produces a Iuninositv function which is much steeper at the faint eud than is observed. and also fails to cut off at bright maguitudes (the halo mass function docs possess a cut-off. but it occurs at much higher mass aud ower abundance than shown iu the plot).," As is well known, this produces a luminosity function which is much steeper at the faint end than is observed, and also fails to cut off at bright magnitudes (the halo mass function does possess a cut-off, but it occurs at much higher mass and lower abundance than shown in the plot)."
 White&Rees(1978) argued that the difference between he halo mass and the galaxy. luminosity functions is due o the dependence of the eas cooling time on halo mass aud ο feedback processes., \citet{wr} argued that the difference between the halo mass and the galaxy luminosity functions is due to the dependence of the gas cooling time on halo mass and to feedback processes.
 We use the semi-aualvtic nocel to follow eas cooling and star formation iu a niereiug vicrarchy of dark matter halos in the ACDAL cosmology., We use the semi-analytic model to follow gas cooling and star formation in a merging hierarchy of dark matter halos in the $\Lambda$ CDM cosmology.
 In order to illustrate the simplest possible model first. we do rotinclude photoionization suppression. feedback. galaxy ucreiug or conduction.," In order to illustrate the simplest possible model first, we do notinclude photoionization suppression, feedback, galaxy merging or conduction."
 The result is Model 2 (shown as a dotted line in Fig. 1))., The result is Model 2 (shown as a dotted line in Fig. \ref{fig:models_123}) ).
" It clearly displays the ""overcooliugxoblenmi: gas has cooled iuto the smallest halos resolved in the caleulatiou. producing an overabundance of faint"," It clearly displays the “overcoolingproblem”: gas has cooled into the smallest halos resolved in the calculation, producing an overabundance of faint"
From preliminary analvsis. a classification of Bl Vo was adopted for the secondary (sce Section 4.4)) and its angular diameter was assumed to be 0.342E0.04 mamas aa radius of GARI. with a 12 per cent uncertainty at the distance obtained from the dynamical parallax).,"From preliminary analysis, a classification of B1 V was adopted for the secondary (see Section \ref{sig_sec}) ) and its angular diameter was assumed to be $0.34\pm0.04$ mas a radius of $_{\sun}$ – with a 12 per cent uncertainty – at the distance obtained from the dynamical parallax)."
" Phe three parameters 6,. 6» and 3 are coupled and hence a change in one will allect the other two without significantly. changing the orbital parameters."," The three parameters $\theta_1$, $\theta_2$ and $\beta$ are coupled and hence a change in one will affect the other two without significantly changing the orbital parameters."
 The best-fitting values of the model parameters are eiven in Table 4. ancl four nights data are shown in Fig., The best-fitting values of the model parameters are given in Table \ref{tab:sig_Sco_final} and four nights data are shown in Fig.
 2 with the predieted V? model overlaid as the solid curve., \ref{fig:sig_Sco_example} with the predicted $V^2$ model overlaid as the solid curve.
 The projected orbit on the plane of the sky is shown in Fig 3.., The projected orbit on the plane of the sky is shown in Fig \ref{fig:sig_Sco_orbit}.
 The reduced x? of the fit was 3.58. implying that the measurement errors are underestimated by a factor of 1.89.," The reduced $\chi^2$ of the fit was 3.58, implying that the measurement errors are underestimated by a factor of 1.89."
 Two possible effects were investigated., Two possible effects were investigated.
 Firstly. the secing conditions during some observations were poor and then only the brightest calibrator could be used. resulting in data of lower quality than on other nights.," Firstly, the seeing conditions during some observations were poor and then only the brightest calibrator could be used, resulting in data of lower quality than on other nights."
 While à non-linear seeing correction (Ireland.2006) was applied to all data as part of the data reduction. there could. be some residual atmospheric effects.," While a non-linear seeing correction \citep{Ireland06} was applied to all data as part of the data reduction, there could be some residual atmospheric effects."
 Secondly. the primary star. being of 3 Cophei pulsator type. varies in diameter. temperature and apparent brightness.," Secondly, the primary star, being of $\beta$ Cephei pulsator type, varies in diameter, temperature and apparent brightness."
 These properties will also allect the results of fitting equation (6)) to the data and contribute to the somewhat laree value of reduced 47.2 and non-Gaussian parameter uncertainty distributions (discussed further below)., These properties will also affect the results of fitting equation \ref{eq:sig_Sco_V2}) ) to the data and contribute to the somewhat large value of reduced $\chi^2$ and non-Gaussian parameter uncertainty distributions (discussed further below).
 However the quality. ane resolution of the SUSL data combined. with the uncertainty in the literature values does not justify a more complicated. model that includes the intrinsic variability., However the quality and resolution of the SUSI data combined with the uncertainty in the literature values does not justify a more complicated model that includes the intrinsic variability.
 Furthermore. the number and time base of V? measures is sullicient to average oul any effects. from the intrinsic variability of the primary.," Furthermore, the number and time base of $V^2$ measures is sufficient to average out any effects from the intrinsic variability of the primary."
 Lencee. the angular diameter of the primary. along with the component brightness ratio. are treated as mean values by equation (6)).," Hence, the angular diameter of the primary, along with the component brightness ratio, are treated as mean values by equation \ref{eq:sig_Sco_V2}) )."
 The three different uncertainty estimation techniques (described in. Section. 3.2)). produced: distributions. of each [free model parameter similar in appearance anc approximately centred on the best-fitting values., The three different uncertainty estimation techniques (described in Section \ref{fit_err}) ) produced distributions of each free model parameter similar in appearance and approximately centred on the best-fitting values.
 Phe Monte Carlo and bootstrap methods were set to each generate 107 svnthetie data sets while the ALCALC simulations completec 10' iterations., The Monte Carlo and bootstrap methods were set to each generate $10^3$ synthetic data sets while the MCMC simulations completed $10^7$ iterations.
 The shape of the likelihood. functions. of he semi-major axis. eccentricitv. inclination. uniform disc angular diameters and the brightness ratio were Caussian in appearance.," The shape of the likelihood functions of the semi-major axis, eccentricity, inclination, uniform disc angular diameters and the brightness ratio were Gaussian in appearance."
 The Probability Density Functions produce o» the ALCAIC simulation for the remaining (free) moce xwameters were slightly non-Gaussian. most. likely clue o the intrinsic. pulsations of the primary.," The Probability Density Functions produced by the MCMC simulation for the remaining (free) model parameters were slightly non-Gaussian, most likely due to the intrinsic pulsations of the primary."
 Even though some model parameters produced: (weakly) non-Caussian distributions. the uncertainty values quoted in Table 4 are he standard deviations.," Even though some model parameters produced (weakly) non-Gaussian distributions, the uncertainty values quoted in Table \ref{tab:sig_Sco_final} are the standard deviations."
 As the MCMZC simulation includes he uncertainties in the tertiary incoherent [ux and angular cliameter of the secondary. the values it produced form the xis of the final parameter uncertainties given in Table 4 cause we believe they are the most realistic estimates of xwameter uncertainties for our data set.," As the MCMC simulation includes the uncertainties in the tertiary incoherent flux and angular diameter of the secondary, the values it produced form the basis of the final parameter uncertainties given in Table \ref{tab:sig_Sco_final} because we believe they are the most realistic estimates of parameter uncertainties for our data set."
 The orbital parameters found by the analyses. of Mathiasetal.(1991) and Pieulski(1992).. together with he final values determined from the SUSI data. are given in ‘Table 4..," The orbital parameters found by the analyses of \citet{Mathias91} and \citet{Pigulski92}, together with the final values determined from the SUSI data, are given in Table \ref{tab:sig_Sco_final}."
 Phe values for the period and time of periastron massage are all in excellent. agreement., The values for the period and time of periastron passage are all in excellent agreement.
 There is some disagreement among the two remaining orbital. parameters when considering the quoted. uncertainties., There is some disagreement among the two remaining orbital parameters when considering the quoted uncertainties.
 Llowever. all values are consistent at the two standard. deviation level.," However, all values are consistent at the two standard deviation level."
 Vhe analvsis of Mathias.ctal.(1991) is. considered to be the most up-to-date. due to the detection of the secondary spectral lines and the inclusion. of the most recent (published) data., The analysis of \citet{Mathias91} is considered to be the most up-to-date due to the detection of the secondary spectral lines and the inclusion of the most recent (published) data.
 Pherefore. comparing only the SUSI and the Mathiasetal.(1991). results all parameters are consistent at the Ll standard deviation level.," Therefore, comparing only the SUSI and the \citet{Mathias91} results all parameters are consistent at the 1.1 standard deviation level."
 Alathiasetal.(1991). contains the only published semi-amplitudes of both the primary and secondary components., \citet{Mathias91} contains the only published semi-amplitudes of both the primary and secondary components.
 The small ciscrepaney between the SUSL and Mathiasctal.(1991) eccentricity and loneituce of periastron passage may allect the estimation of those physical parameters obtained bv the combination of interferometric ancl spectroscopic results., The small discrepancy between the SUSI and \citet{Mathias91} eccentricity and longitude of periastron passage may affect the estimation of those physical parameters obtained by the combination of interferometric and spectroscopic results.
 We note. however. that the inclination is close to and consequently. the uncertainty in sin? will dominate the error budget (see for example Section 4.1)).," We note, however, that the inclination is close to and consequently, the uncertainty in $\sin i$ will dominate the error budget (see for example Section \ref{sig_dis}) )."
 The caleulation of the dynamical parallax. requires the semi-major axis of the relative orbit in both linear units AAW) and angular units.," The calculation of the dynamical parallax, requires the semi-major axis of the relative orbit in both linear units AU) and angular units."
 Using the, Using the
S0 models predict lower lifetimes. (he relative durations predicted by the 53 models do a better job at matching our observed results.,"S0 models predict lower lifetimes, the relative durations predicted by the S3 models do a better job at matching our observed results."
 So. even though the moclel’s relative curations are mostly correct. the (me spent in the vellow supergiant stage is off bv a [actor of ten for both the SO and 53 models.," So, even though the model's relative durations are mostly correct, the time spent in the yellow supergiant stage is off by a factor of ten for both the S0 and S3 models."
 This last test relies on our knowledge of the number of unevolvecl massive SAIC stars., This last test relies on our knowledge of the number of unevolved massive SMC stars.
 While (he numbers are good approximations. thev should be taken as lower limits due to the effects of crowding (Massey. 2003).," While the numbers are good approximations, they should be taken as lower limits due to the effects of crowding (Massey 2003)."
 Still. we estimate that they are probably good to a factor οἱ a lew.," Still, we estimate that they are probably good to a factor of a few."
 Thus. while our current prediction is that the moclels are off bv a factor of ten. the actual error is probably somewhat lower due to uncertainties in the number of unevolved SAIC stars.," Thus, while our current prediction is that the models are off by a factor of ten, the actual error is probably somewhat lower due to uncertainties in the number of unevolved SMC stars."
 After selecting 677 potential SAIC supergiants. we observed 498.," After selecting 677 potential SMC supergiants, we observed 498."
 We identify L76 stars as candidate SAIC vellow supergiants aud 16 stars as possible SAIC vellow superegiants while the rest are categorized as foreground stars., We identify 176 stars as candidate SMC yellow supergiants and 16 stars as possible SMC yellow supergiants while the rest are categorized as foreground stars.
 Our literature search confirmed that we identified nearly all of the SMC vellow supergiants down to 12..., Our literature search confirmed that we identified nearly all of the SMC yellow supergiants down to $12M_\odot$.
 Additionally. the Besancoon models suggest a Milkv. Way halo contamination of less than of our 176 SAIC supergiants.," Additionally, the Besançoon models suggest a Milky Way halo contamination of less than of our 176 SMC supergiants."
 We also note that. as shown in Figure 7.. the median radial velocity of our category 1 SAIC supergiants doesn't «quite fall on the line denoting the published svstemic racial velocity of the SMC (158 km +) (Richter et 11987).," We also note that, as shown in Figure \ref{fig:radVelRplotMem}, the median radial velocity of our category 1 SMC supergiants doesn't quite fall on the line denoting the published systemic radial velocity of the SMC (158 km $^{-1}$ ) (Richter et 1987)."
 Instead. our caleulated median is 166.0 km ! with a spread. (standard deviation) of 24.3 km |.," Instead, our calculated median is 166.0 km $^{-1}$ with a spread (standard deviation) of 24.3 km $^{-1}$."
 Evans IHowarth (2008) founcl similar radial velocity. results when studying the kinematics of massive stars in the SAIC., Evans Howarth (2008) found similar radial velocity results when studying the kinematics of massive stars in the SMC.
 They found the average radial velocity of F and G (vpe stars to be 160.8 + 0.5 kan Fl where o= 35.1 km 1| and the average radial velocity of all O.D.A.F and G tvpe stars in their sample to be 172.0 & 0.2 where o= 33.6 km |.," They found the average radial velocity of F and G type stars to be 160.8 $\pm$ 0.5 km $^{-1}$ where $\sigma =$ 35.1 km $^{-1}$ and the average radial velocity of all O,B,A,F and G type stars in their sample to be 172.0 $\pm$ 0.2 where $\sigma =$ 33.6 km $^{-1}$."
 The large sigmas of both studies reflect the true range of the SMC's radial velocity due to the complicated kinematics of the SAIC! as revealed by the HI maps of Stanimirovié et ((2004)., The large sigmas of both studies reflect the true range of the SMC's radial velocity due to the complicated kinematics of the SMC as revealed by the HI maps of Stanimirović et (2004).
 We also placed the supergiants on (he IRD and compared our results to the Geneva evolutionary tracks., We also placed the supergiants on the HRD and compared our results to the Geneva evolutionary tracks.
 In terms of the stars’ locations relative to the tracks. we found good agreement.," In terms of the stars' locations relative to the tracks, we found good agreement."
 In terms of the relative number of different mass stars. we found that the ratio for 15 20M. stars (o 1 19141. stars agreed almost perfectly.," In terms of the relative number of different mass stars, we found that the ratio for 15 – $M_\odot$ stars to 12 – $M_\odot$ stars agreed almost perfectly."
 However for stars greater than 204.. this comparison quickly begins (o fail.," However for stars greater than $M_\odot$, this comparison quickly begins to fail."
" It is interesting to mention here that the apparent lack of vellow superegiants in (he upper WIRD occurs at the position where the ""vellow evolutionary void"" defined by Nieuwenhuijzen and de Jager (1995) happens to be."," It is interesting to mention here that the apparent lack of yellow supergiants in the upper HRD occurs at the position where the “yellow evolutionary void"" defined by Nieuwenhuijzen and de Jager (1995) happens to be."
C2 is fainter in ammonia.,C2 is fainter in ammonia.
 The coordinates and the sizes of the cores. as well as the kinetic temperature. are given in Table 2. and the column densities in Table 6..," The coordinates and the sizes of the cores, as well as the kinetic temperature, are given in Table \ref{coord} and the column densities in Table \ref{column}."
 From a first look at the line maps (Figs. 4..," From a first look at the line maps (Figs. \ref{lup1},"
" 7 and 8)) it is evident that the relative intensity of the lines of the three speciesHCSN.. NIL; anced changes significantly. between the various cores: cores (hat are brighter in Gore [nter or undetected in NIL, and and vice versa."," \ref{lup3} and \ref{lup4}) ) it is evident that the relative intensity of the lines of the three species, $_3$ and changes significantly between the various cores: cores that are brighter in are fainter or undetected in $_3$ and and vice versa."
" Although previousstudies suggested that the abundance ratio of NIL, over can be considered as à chemical clock since 1t is higher towards starless cores (han towards protostellar cores (Casellietal.2002a:: Aikawaetal. 2005: Busquetοἱal. 2010: Friesenetal. 2010)). our maps show a strong anticorrelation between on one side and and NIL, on the other side."," Although previousstudies suggested that the abundance ratio of $_3$ over can be considered as a chemical clock since it is higher towards starless cores than towards protostellar cores \citealt{caselli02a}; \citealt{aikawa05}; \citealt{busquet10}; \citealt{friesen10}) ), our maps show a strong anticorrelation between on one side and and $_3$ on the other side."
 This behavior can be quantified bv considering the ratio between the column densities (hat max reflect (he ratio of the chemical abunelances of the species if all lines are emitted by (he same region., This behavior can be quantified by considering the ratio between the column densities that may reflect the ratio of the chemical abundances of the species if all lines are emitted by the same region.
 Therelore. we calculated the ratio HCN/NSIE. (Column 6/Column 5 of Table 6)) and the ratio ΠΟ δα (Columm 7/Column 8 of Table 6)). considering column densities derived [rom lines observed. with similar angular resolution.," Therefore, we calculated the ratio $_3$ (Column 6/Column 5 of Table \ref{column}) ) and the ratio $_3$ $_3$ (Column 7/Column 8 of Table \ref{column}) ), considering column densities derived from lines observed with similar angular resolution."
 We found indeed. that the two ratios change by about one order of magnitude between cores (see Table 7)).," We found indeed, that the two ratios change by about one order of magnitude between cores (see Table \ref{column_ratio}) )."
 In particular. (he HCSN/NSIE. ratio ranges from lio 10 and the Πο Να ratio ranges[rom 0.3 {ο 3.," In particular, the $_3$ ratio ranges from 1 to 10 and the $_3$ $_3$ ratio rangesfrom 0.3 to 3."
 Even if the errors associated to the ratios are high. the observed trend is certainly sienilicaml for the ΠΟ ratio while il is less so for the Νο ratio.," Even if the errors associated to the ratios are high, the observed trend is certainly significant for the $_3$ ratio while it is less so for the $_3$ $_3$ ratio."
 ILowever. we point out that there are 4 cores that emit in 1ICSN. and not in NIL. and 3 cores (hat emit in NIL. and not in HCSN clearly indicating a change in the chemical abundance ratio of the (wo species.," However, we point out that there are 4 cores that emit in $_3$ N, and not in $_3$ , and 3 cores that emit in $_3$ , and not in $_3$ N clearly indicating a change in the chemical abundance ratio of the two species."
"leads. in the test-particle regime. to the well known power-law spectrum of accelerated parücles f(p)xpa"". with a—3r/(r2—1) where r is (he compression factor at the shock.","leads, in the test-particle regime, to the well known power-law spectrum of accelerated particles $f(p)\propto p^{-\alpha}$, with $\alpha=3r/(r-1)$ where $r$ is the compression factor at the shock."
 The power law extends to infinitely large momenta., The power law extends to infinitely large momenta.
 Since for ordinary non-relativistic easeous shocks r«4 (namely a>4). (he total energy in the form of accelerated particles remains finite.," Since for ordinary non-relativistic gaseous shocks $r<4$ (namely $\alpha>4$ ), the total energy in the form of accelerated particles remains finite."
 This solution is found by imposing as boundary condition al upstream infinity (Cr— —o) that f(—2€)=0 and ο(ο)ιτ=0., This solution is found by imposing as boundary condition at upstream infinity $x=-\infty$ ) that $f(-\infty)=0$ and $\partial f(-\infty)/\partial x=0$.
" Ifthe boundary condition [Cr=rj)0 is used. instead. at some finite distance rj«0 upstream. the solution of the transport equation is easily calculated to be where In the case of Bolin diffusion. D(p)=Do(p/in,e) and one obtains: where p,=Lvy|uymyc/Dy."," If the boundary condition $f(x=x_0)=0$ is used, instead, at some finite distance $x_0<0$ upstream, the solution of the transport equation is easily calculated to be where In the case of Bohm diffusion, $D(p)=D_0 (p/m_p c)$ and one obtains: where $p_{*}=|x_0| u_1 m_p c/D_0$."
" Now one can show that for p< py. folp)x(p/p""9. with r=uq/us. the standard result."," Now one can show that for $p\ll p_*$ , $f_0(p)\propto (p/p_*)^{-3r/(r-1)}$, with $r=u_1/u_2$, the standard result."
" However. for pEp,. fot(p)xexpIl-z."," However, for $p\gg p_*$, $f_0(p)\propto\exp\left[-\frac{3r}{r-1}\frac{p}{p_*}\right]$."
 The quantiiv paa=Petr—1)/2r plavs (he role of maxinum momentum of the accelerated particles., The quantity $p_{max}=p_*(r-1)/3r$ plays the role of maximum momentum of the accelerated particles.
 This simple example shows how a maxinum momentum can be obtained in a stationary approach only by imposing the boundary condition at a finite boundary., This simple example shows how a maximum momentum can be obtained in a stationary approach only by imposing the boundary condition at a finite boundary.
" Physically (his corresponds to particles. escape. as shown by the fact that the flux of particles al =ry is The fact that óGrg.p)<0 shows that the f[Iux of particles is directed Cowares upstream infinity,"," Physically this corresponds to particles' escape, as shown by the fact that the flux of particles at $x=x_0$ is The fact that $\phi(x_0,p)<0$ shows that the flux of particles is directed towards upstream infinity."
" Moreover. the escape flux as a function of momentum. (ση,p). is negligible lor all p with the exception of a narrow region around p,,,: Only particles with momentum close lo p,,4, can escape (he svstem towards upstream infinitv."," Moreover, the escape flux as a function of momentum, $\phi(x_0,p)$, is negligible for all $p$ with the exception of a narrow region around $p_{max}$: only particles with momentum close to $p_{max}$ can escape the system towards upstream infinity."
 The escape flux as a function of momentum is plotted in Fig., The escape flux as a function of momentum is plotted in Fig.
 d. for two values of the compression factor. r=4 (solid line) and r=7 (dashed line).," \ref{fig:escapeflux} for two values of the compression factor, $r=4$ (solid line) and $r=7$ (dashed line)."
 The normalizations are arbitrary. since the calculations are carried out in the context of test particle theory.," The normalizations are arbitrary, since the calculations are carried out in the context of test particle theory."
The latter value of r cannot be realized al purely,The latter value of $r$ cannot be realized at purely
which. interestingly. coincides with the result (3.2)) that we have obtained [or the zero-guide field case.,"which, interestingly, coincides with the result \ref{eq-EIC-theta}) ) that we have obtained for the zero-guide field case."
" The main reason for this clearly lies in the [act that. apart [rom its temperature dependence. (he EIC radiative cooling rate (3.2)) scales wilh the compression ratio lin the same wav (linearly) as the ohmic heating rate Qui,Qu."," The main reason for this clearly lies in the fact that, apart from its temperature dependence, the EIC radiative cooling rate \ref{eq-Q_rad-EIC-cyclo}) ) scales with the compression ratio $A$ in the same way (linearly) as the ohmic heating rate $Q_{\rm ohm} \sim A\, Q_0$."
 Therefore. the 1 factors on both sides of the heating/cooling balance cancel out and (he resulting temperature (urns out to be independent of the plasma compression ratio (which is controlled by D. ).," Therefore, the $A$ factors on both sides of the heating/cooling balance cancel out and the resulting temperature turns out to be independent of the plasma compression ratio (which is controlled by $B_z$ )."
 In the case of evclotron cooling. the situation is very similar. we just need (to replace Ü in the expression for the radiative cooling rate bv the magnetic energy density. /8z.," In the case of cyclotron cooling, the situation is very similar, we just need to replace $U$ in the expression for the radiative cooling rate by the magnetic energy density, $U\simeq U_{\rm mag} \simeq B_{z0}^2/8\pi$ ."
" From equation (5)) we then immediately get: which differs from the corresponding zero-guide-field expression only bya factor of D/DZ,."," From equation \ref{eq-heat-cool-guide-strong}) ) we then immediately get: _e. which differs from the corresponding zero-guide-field expression only bya factor of $B_0^2/B_{z,0}^2$."
" Recall that. as we discussed in 3.2.. in the D.=0 case the condition that the electrons inside the reconnection laver are non-relativistic (8,< 1) coincides with the condition (because of the pressure balance and the 7;=T; assumption)."," Recall that, as we discussed in \ref{subsec-EIC-Cyclotron}, in the $B_z=0$ case the condition that the electrons inside the reconnection layer are non-relativistic $\theta_e \ll 1$ ) coincides with the condition $\Omega_{ce}<\omega_{pe}$ (because of the pressure balance and the $T_e=T_i$ assumption)."
 Then. the cvclotron photons cannot propagate effectively through the laver ancl this is why we chose to neglect the evelotvon cooling process for that (relativistic zero-guide field) case.," Then, the cyclotron photons cannot propagate effectively through the layer and this is why we chose to neglect the cyclotron cooling process for that (relativistic zero-guide field) case."
 We would like to note. however. that in the case of a strong guide field. the restrictions due to the model assumptions appear to be not as severe: in particular. there exist a parameter regime where cvclotron cooling can be «uite effective.," We would like to note, however, that in the case of a strong guide field, the restrictions due to the model assumptions appear to be not as severe; in particular, there exist a parameter regime where cyclotron cooling can be quite effective."
 This is possible because now the electron temperature is no longer determined from the pressure balance and can in [act be quite low., This is possible because now the electron temperature is no longer determined from the pressure balance and can in fact be quite low.
" Then. the electron cvclotvon frequency. Q,,. can be higher than «y provided that D,cdmΠρ,ο”."," Then, the electron cyclotron frequency $\Omega_{ce}$ can be higher than $\omega_{pe}$ provided that $B_{z0}^2 > 4\pi \, n_0 m_e c^2$."
 We (hus see that a more powerful soft radiation field or a stronger magnetic guide field lead to a more efficient inverse-C'ómpton or evelotron cooling. respectively. which results in a lower plasma temperature.," We thus see that a more powerful soft radiation field or a stronger magnetic guide field lead to a more efficient inverse-Compton or cyclotron cooling, respectively, which results in a lower plasma temperature."
 This. in turn. makes (he reconnection process go faster because of the T*? dependence of the Spitzer resistivity on the temperature.," This, in turn, makes the reconnection process go faster because of the $T^{-3/2}$ dependence of the Spitzer resistivity on the temperature."
" In. particular. [rom equation (75)). we get (ir, pul- where. once again.. (=MUdE DZ/8z."," In particular, from equation \ref{eq-rec_rate-guide}) ), we get _T , where, once again, $U = U_{\rm rad} + B_{z0}^2/8\pi$ ."
"Whether mass loss from the nucleus ts by sublimation or by ablation. the total energy needed to vaporize the whole nucleus is &4,=M,£ while the energy needed to stop it is Gg,3 M,vz/2.","Whether mass loss from the nucleus is by sublimation or by ablation, the total energy needed to vaporize the whole nucleus is ${\cal E}_{vap}=M_o{\cal L}$ while the energy needed to stop it is ${\cal E}_{kin}\approx M_ov_\odot^2/2$ ."
" The ratio is tiny. €,,,/655*2L/v7,=4x1074 for the solar escape speed with G.M.R« the gravitational constant. solar mass. and solar radius respectively."," The ratio is tiny, ${\cal E}_{vap}/{\cal E}_{kin} \approx 2{\cal L}/v_\odot^2= 4\times 10^{-5}\tilde{\cal L}$ for the solar escape speed with $G,M_\odot,R_\odot$ the gravitational constant, solar mass, and solar radius respectively."
 Thus total vaporization can occur well before the nucleus decelerates significantly. though ram pressure can result in explosive destruction dominating.," Thus total vaporization can occur well before the nucleus decelerates significantly, though ram pressure can result in explosive destruction dominating."
" Equivalently. to conserve momentum in slowing down. the nucleus must encounter an atmospheric mass comparable to M,."," Equivalently, to conserve momentum in slowing down, the nucleus must encounter an atmospheric mass comparable to $M_o$."
 In doing so it absorbs far more energy than needed to vaporize it., In doing so it absorbs far more energy than needed to vaporize it.
" The mass per unit area (g ΟΠ} of a comet nucleus is X,xMa)=MIO?108M,109)(pop? & cm while that of the sun's atmosphere even down to the photosphere is only X4=| g em.", The mass per unit area (g $^{-2}$ ) of a comet nucleus is $\Sigma_c\approx M_o/a^2=M_o^{1/3}\rho^{2/3}=10^4(M_o/10^{12})^{1/3}(\tilde{\rho})^{2/3}$ g $^{-2}$ while that of the sun's atmosphere even down to the photosphere is only $\Sigma_\odot \approx 1$ g $^{-2}$ .
 Consequently. unless they explode. increasing the deceleration. only objects of <10? ¢ or so would be much decelerated by the mass of the sun's atmosphere down to the photosphere though. in practice. they would be vaporized earlier by sublimation and/or ablation.," Consequently, unless they explode, increasing the deceleration, only objects of $<10^3$ g or so would be much decelerated by the mass of the sun's atmosphere down to the photosphere though, in practice, they would be vaporized earlier by sublimation and/or ablation."
 Note also that. at infall speed v. in the frame of the nucleus a solar atmospheric proton has kinetic energy ~ 2 keV which is enough to knock off about 4000 water molecules. or about 10° times Its ow! mass.," Note also that, at infall speed $v_\odot$, in the frame of the nucleus a solar atmospheric proton has kinetic energy $\sim$ 2 keV which is enough to knock off about 4000 water molecules, or about $10^5$ times its own mass."
 This situation of initial ablative mass loss without significant deceleration is paralleled by the dynamics in planetary atmospheres of meteors - e.g. McKinley (1961). Kaiser (1962) - and at least of the initial (high altitude) stages of comet-planet impacts - e.g. Shoemaker Levy 9 with Jupiter - cf.," This situation of initial ablative mass loss without significant deceleration is paralleled by the dynamics in planetary atmospheres of meteors - e.g. McKinley (1961), Kaiser (1962) - and at least of the initial (high altitude) stages of comet-planet impacts - e.g. Shoemaker Levy 9 with Jupiter - cf."
 Section 6., Section 6.
 In the sublimation regime the radiation has negligible effect on the nucleus speed. even though it delivers a large amount of energy.," In the sublimation regime the radiation has negligible effect on the nucleus speed, even though it delivers a large amount of energy."
" Specifically the ratio of the radiation pressure force F,44 to the gravitational is (ignoring the correction factor 1.0-2.0 forS albedo) =""n«πρΙ.", Specifically the ratio of the radiation pressure force $F_{rad}$ to the gravitational is (ignoring the correction factor 1.0-2.0 for albedo) $ \frac{F_{rad}}{F_{grav}}\preceq \frac{{10^{-4}}}{a(cm)\tilde{\rho}}$.
 The radiation pressure Εως2 dyne/emr is also tiny compared to the nucleus strength P. so causes no direct explosion effect., The radiation pressure $F_{rad}/c \simeq 2$ $^2$ is also tiny compared to the nucleus strength $P_c$ so causes no direct explosion effect.
 It is also straightforward to show that. during perihelion passage. the rocket effect of mass loss leaving the nucleus anisotropically has negligible effect on v during vaporization.," It is also straightforward to show that, during perihelion passage, the rocket effect of mass loss leaving the nucleus anisotropically has negligible effect on $v$ during vaporization."
 This is because the very high nucleus p value implies very low mass loss speed « and hence momentum flux., This is because the very high nucleus $\rho$ value implies very low mass loss speed $u$ and hence momentum flux.
 Consequently. the velocity of the nucleus during its vaporization is well approximated by that of a gravitational parabolic orbit. viz..," Consequently, the velocity of the nucleus during its vaporization is well approximated by that of a gravitational parabolic orbit, viz.,"
 in orbital plane polar coordinate (0. 6) and for perthelion distance q While. throughout the total vaporization lifetime of the nucleus. its velocity 1s well deseribed by Eqns. (4)).," in orbital plane polar coordinate $r,\theta$ ) and for perihelion distance $q$ While, throughout the total vaporization lifetime of the nucleus, its velocity is well described by Eqns. \ref{veloccomps}) ),"
 this ts not true of the material it loses., this is not true of the material it loses.
 Small particles leaving the nucleus do not obey Eqns. (4)).," Small particles leaving the nucleus do not obey Eqns. \ref{veloccomps}) ),"
 non-gravitational accelerations on them being very important., non-gravitational accelerations on them being very important.
" These include F,,; on sub-micron particles and atmospheric drag on atoms and tons.", These include $F_{rad}$ on sub-micron particles and atmospheric drag on atoms and ions.
" The Coulomb collisional stopping column density for à proton of speed vax618 km sec""! (~2 keV) in a hydrogen plasma is around N,=10° em- (Emslie 1978).", The Coulomb collisional stopping column density for a proton of speed $v_\odot\approx 618$ km $^{-1}$ $\sim 2$ keV) in a hydrogen plasma is around ${\cal N}_s=10^{15}$ $^{-2}$ (Emslie 1978).
 Thus the stopping distance at number density #7 1s diem)=Νx107/n. i.e. just | km in the corona and 0.1 mm in the photosphere.," Thus the stopping distance at number density $n$ is $d ({\rm cm}) \approx {\cal N}/n\approx 10^{15}/n$, i.e. just 1 km in the corona and 0.1 mm in the photosphere."
 So ablated dust and tons stop abruptly and form an exploding wake as they blend with and heat the atmosphere. creating large local enhancements of heavy element abundances.," So ablated dust and ions stop abruptly and form an exploding wake as they blend with and heat the atmosphere, creating large local enhancements of heavy element abundances."
" Very near the sun. the timescale for sublimation of the whole mass is ru=Mo£jazs4x105MI27 s, where 7.= ere/em-/s is theT bolometric photospheric energy flux and Mis=M,/10' e. The corresponding distance scale is roughly d,=Varo*3.RSXMISSESÉ cm as first seen directly by Schrijver at al. ("," Very near the sun, the timescale for sublimation of the whole mass is $\tau_{sub}\succeq M_o{\cal L}/a_o^2{\cal F}_\odot \approx 4\times 10^3M_{12}^{1/3}\tilde{\rho}^{2/3}\tilde{{\cal L}}$ s, where ${\cal F}_\odot =6\times 10^{10}$ $^2$ /s is the bolometric photospheric energy flux and $M_{12}=M_o/10^{12}$ g. The corresponding distance scale is roughly $d_{sub}\approx v_\odot\tau_{sub}\approx 3.5R_\odot\times M_{12}^{1/3}\tilde{\rho}^{2/3}\tilde{{\cal L}}$ cm as first seen directly by Schrijver at al. ("
2011).,2011).
" Total sublimation occurs in a close perihelion passage roughly for d,xR.. which is the case for masses M,<3x101/52£? e or about I0!!g for 0.5.£= 1."," Total sublimation occurs in a close perihelion passage roughly for $d_{sub}\preceq R_\odot$ which is the case for masses $M_o\preceq 3\times 10^{10}/ \tilde{\rho}^2\tilde{{\cal L}}^3$ g or about $10^{11}$ g for $\tilde{\rho}= 0.5,\tilde{{\cal L}}=1$ ."
" This shows the majority of close sun-grazers 1.01R.) to have M,<10""! & as they never re-emerge.", This shows the majority of close sun-grazers $q\succeq1.01R_\odot$ ) to have $M_o \preceq 10^{11}$ g as they never re-emerge.
 The problems of comet. asteroid. and even large meteoroid npact with planetary atmospheres closely parallel those of a solar impact. though the parameter regimes are rather different. and there is no planetary equivalent of insolation.," The problems of comet, asteroid, and even large meteoroid impact with planetary atmospheres closely parallel those of a solar impact, though the parameter regimes are rather different, and there is no planetary equivalent of insolation."
 Unlike the solar case. planetary impacts have been addressed in detail. early work including that of Revelle (1979) and others.," Unlike the solar case, planetary impacts have been addressed in detail, early work including that of Revelle (1979) and others."
 Progress was greatly accelerated in anticipation. and in the aftermath. of the collisions of fragments of Comet Shoemaker-Levy 9 with Jupiter in July 1994.," Progress was greatly accelerated in anticipation, and in the aftermath, of the collisions of fragments of Comet Shoemaker-Levy 9 with Jupiter in July 1994."
 Many authors (e.g. Chyba et al 1993. Chevalier and Sarazin 1994. Zahnle and MacLow 1994) developed semr-analytic and numerical models to predict what should be expected of these impacts.," Many authors (e.g. Chyba et al 1993, Chevalier and Sarazin 1994, Zahnle and MacLow 1994) developed semi-analytic and numerical models to predict what should be expected of these impacts."
 Others. notably MacLow and Zahnle (1994). Field and Ferrara (1995) and Carlson et al. (," Others, notably MacLow and Zahnle (1994), Field and Ferrara (1995) and Carlson et al. ("
1905. 1997). developed models further by drawing on actual event data.,"1995, 1997), developed models further by drawing on actual event data."
 In particular the Carlson etal. (, In particular the Carlson etal. (
"1995, 1997) “heuristic model combined data analysis. numerical simulations. and observational inputs.","1995, 1997) 'heuristic model' combined data analysis, numerical simulations, and observational inputs."
" They identified and addressed both the ""bolide initial phase’ (which we have called the detonation or airburst) and the subsequent ‘fireball’ exploding out anc up from the nucleus and its", They identified and addressed both the 'bolide initial phase' (which we have called the detonation or airburst) and the subsequent 'fireball' exploding out and up from the nucleus and its
We developed a custom data reduction routine to extract the highest precision photometry possible.,We developed a custom data reduction routine to extract the highest precision photometry possible.
 We first applied a third order linearity correction to the data using cocfficieuts in the SQUD users manual. aud then divided these data bv a normalized flat field) iuage.," We first applied a third order linearity correction to the data using coefficients in the SQIID user's manual, and then divided these data by a normalized flat field image."
 Skv subtraction and dark correction of our sejence Mages was achieved by subtracting mauuediatelv adjacent dither frames from cach other., Sky subtraction and dark correction of our science images was achieved by subtracting immediately adjacent dither frames from each other.
 Dudividual pixels 716.000 ADUs (the linearity limit) or < -500 ADUs were next flageed as bad or war pixels. and corrected using the IRAF routineΠ," Individual pixels $>$ 16,000 ADUs (the linearity limit) or $<$ -500 ADUs were next flagged as bad or warm pixels, and corrected using the IRAF routine."
"ρ, Next. low-level array artifacts; such as column baudius aud less frequently observed row banding. were characterized by sapling this structure iu star-free reeious of the array aud removed via custom IDL routines."," Next, low-level array artifacts, such as column banding and less frequently observed row banding, were characterized by sampling this structure in star-free regions of the array and removed via custom IDL routines."
 To obtain photometry for our SOIID data. we first identified the centroid position of cach star in our FOVs using SExtractor (Bertin&Árnouts1996).. and a custom reference profile which udmicked the extended douut-«hape of our sources;," To obtain photometry for our SQIID data, we first identified the centroid position of each star in our FOVs using SExtractor \citep{ber96}, and a custom reference profile which mimicked the extended donut-shape of our sources."
 Next. we ran these stellar positions through IRAF’s routine to extract aperture photometry. using a target aperture of radius 20 pixels (EV Lac and YZ CAG) to 21 pixels (AD Leo) anda 1 pixel wide backerouud sky aunulus starting at a radius of 30 pixels from cach centroid position.," Next, we ran these stellar positions through IRAF's routine to extract aperture photometry, using a target aperture of radius 20 pixels (EV Lac and YZ CMi) to 24 pixels (AD Leo) and a 4 pixel wide background sky annulus starting at a radius of 30 pixels from each centroid position."
 We then extracted ditfereutial photometry for our science targets using the brightest. and often only. comparison star with the SQUD ΕΟΝ. as sununarized in Table 2..," We then extracted differential photometry for our science targets using the brightest, and often only, comparison star with the SQIID FOV, as summarized in Table \ref{comp}."
 Previous IR iiouitoriug programs dedicated to observing AL dwarfs for transits (ATEarth: Ίσαctal. 2011)) or high precision observations of brown dwarts to characterize photospheric condensates (Bailer-Jones&[μαι2003) have described how variations iu relative hunidityv can affect IR. differential photometry., Previous IR monitoring programs dedicated to observing M dwarfs for transits (MEarth; \citealt{irw11}) ) or high precision observations of brown dwarfs to characterize photospheric condensates \citep{bai03} have described how variations in relative humidity can affect IR differential photometry.
 We found we were able to remove most of the siall auplitude. lone time-scale photometric trends in our data likely attributable to these effects by simply fitting a linear function to each dither positiou's light curve individually.," We found we were able to remove most of the small amplitude, long time-scale photometric trends in our data likely attributable to these effects by simply fitting a linear function to each dither position's light curve individually."
 Finally. cach dither position was normalized to a uniform scale and combined to vield the highest time cadence cüffereutial photometry from our observations.," Finally, each dither position was normalized to a uniform scale and combined to yield the highest time cadence differential photometry from our observations."
 Table 3. sunuuarizes the relative photometric stability we were able to obtain for every target aud filter. both across an cutire nieht auc across l-hour wiudows. quantified as the observed standard deviation.," Table \ref{flaresum} summarizes the relative photometric stability we were able to obtain for every target and filter, both across an entire night and across 1-hour windows, quantified as the observed standard deviation."
 The IR stability we achieved for AD Leo. 9.7-12.6 1illiauags over a full wight and 8.10.5 mulli-maes over a 1 hour window. was systematically larger than that achieved for our other targets due to the lower fux of the brightest comparison star iu its fiocld of view.," The IR stability we achieved for AD Leo, 9.7-12.6 milli-mags over a full night and 8.4-10.5 milli-mags over a 1 hour window, was systematically larger than that achieved for our other targets due to the lower flux of the brightest comparison star in its field of view."
 The best IR photometric stability we achieved was au impressive 5.1-6.0 iillianaes over a full night aud 3.8-3.9 mulli-mags over a 1 hour window for our 2011 February 13 monitoring of YZ CAG., The best IR photometric stability we achieved was an impressive 5.1-6.0 milli-mags over a full night and 3.8-3.9 milli-mags over a 1 hour window for our 2011 February 13 monitoring of YZ CMi.
 Figure l shows a represeutative απαπο differential photometric light curve obtained for the star AD Leo ou 2011 February 13., Figure \ref{adleoall} shows a representative multi-filter differential photometric light curve obtained for the star AD Leo on 2011 February 13.
 Note that photon statistics-based error bars are plotted in all panels of Figure 1.. aud for all figures in this paper. but these error bars are ecucrally smaller than the size of the data points.," Note that photon statistics-based error bars are plotted in all panels of Figure \ref{adleoall}, and for all figures in this paper, but these error bars are generally smaller than the size of the data points."
 Before characterizing the behavior of stellar flares in our IR data. we first identified these events im our siuultaneouslv obtained optical photometry.," Before characterizing the behavior of stellar flares in our IR data, we first identified these events in our simultaneously obtained optical photometry."
 We used the IDL-based. flare finding software described i Hilton(2011) and Hiltonctal.(2011)., We used the IDL-based flare finding software described in \citet{hi11a} and \citet{hil11}.
. Flares are identified as a single epoch which is 35-0 brighter than the standard deviation of the local mean. followed by three epochs which are 2-0 above the local mean.," Flares are identified as a single epoch which is $\sigma$ brighter than the standard deviation of the local mean, followed by three epochs which are $\sigma$ above the local mean."
 Each flare identified was also double-checked by eve to confirm the eveut was robust., Each flare identified was also double-checked by eye to confirm the event was robust.
 The total umber of flares detected iu cach bandpass using this flare finding algoritlian is shown iu Table 3: a total of 20 flares were detected im our C--banud data., The total number of flares detected in each bandpass using this flare finding algorithm is shown in Table \ref{flaresum}; a total of 20 flares were detected in our -band data.
 For the larger optical flare eveuts observed. additional flare properties such as the peak magnitude culancemeut and total fare duration are compiled in Table L.," For the larger optical flare events observed, additional flare properties such as the peak magnitude enhancement and total flare duration are compiled in Table \ref{flarenergy}."
 Flare equivalent duratious. defined as the amount of time cach star would need to spend at a quiescent level to produce the same total cherey as during cach flare (Gershbere1972).. were deteriuined via our flare findiug software by inteeration under cach lieht curve.," Flare equivalent durations, defined as the amount of time each star would need to spend at a quiescent level to produce the same total energy as during each flare \citep{ger72}, were determined via our flare finding software by integration under each light curve."
" We adopted the quiesccut Iuninosities for AD Leo (1.59 x 10°"" eres 1). EV Lac (6.63 x 1075 eres s1). aud YZ CAG (1.57 x 1075 eres 5) computed by Tilton(2011) aud Wiltonetal.(2011).. aud based ou data in Reidetal.(1995)."," We adopted the quiescent luminosities for AD Leo (1.59 x $^{29}$ ergs $^{-1}$ ), EV Lac (6.63 x $^{28}$ ergs $^{-1}$ ), and YZ CMi (4.57 x $^{28}$ ergs $^{-1}$ ) computed by \citet{hi11a} and \citet{hil11}, and based on data in \citet{rei95}."
. We then multiplied the quiesceut huuinosifies bv the equivaleut duratiou of cach event. to extract flare energies (Table £0).," We then multiplied the quiescent luminosities by the equivalent duration of each event, to extract flare energies (Table \ref{flarenergy}) )."
 As the focus of this paper is on characterizing the properties of stellar fares in the IR. we focus our attention on the four largest U-band flares we observed on AD Leo (event 411). YZ CAG (events #22 433). and EV Lac (event ELI). as listed iu Table { aud illustrated in Figure 2..," As the focus of this paper is on characterizing the properties of stellar flares in the IR, we focus our attention on the four largest U-band flares we observed on AD Leo (event 1), YZ CMi (events 2 3), and EV Lac (event 4), as listed in Table \ref{flarenergy} and illustrated in Figure \ref{adleozoom}."
 Our flares exhibited band euereies ranging fro LS x LO’ (event Φε.) toÜC-— 1 κ 1072 (event #11) ores., Our flares exhibited -band energies ranging from $\sim$ 7.8 x $^{30}$ (event 4) to $\sim$ 1.3 x $^{32}$ (event 1) ergs.
 Flare eveuts #11-3 are considered strong (Lacyetal.1976) although they are less cnerectic than the very rare ~ 10°! cre megaflare Nowalskietal.(2010) observed on YZ CAG., Flare events 1-3 are considered strong \citep{lac76} although they are less energetic than the very rare $\sim$ $^{34}$ erg megaflare \citet{kow10} observed on YZ CMi.
 For cach of our targets. Lacyetal.(L976) presented fare frequency. distributions which follow power laws. except at the lowest aud highest energv regimes.," For each of our targets, \citet{lac76} presented flare frequency distributions which follow power laws, except at the lowest and highest energy regimes."
 Hilton(2011) and Wiltonetal.(2011) expanded upon this earlier work. prescuting fare frequency distributions for a wider range of M dwarfs.," \citet{hi11a} and \citet{hil11} expanded upon this earlier work, presenting flare frequency distributions for a wider range of M dwarfs."
 After correcting for detection efficicucy. Tilton(2011) was able to demonstrate that flare frequency distributions follow power law distributions even dowu to low cnereies.," After correcting for detection efficiency, \citet{hi11a} was able to demonstrate that flare frequency distributions follow power law distributions even down to low energies."
 We use the flare frequency distributions presented in Tilton(2011) and Wiltonetal.(2011) for this paper., We use the flare frequency distributions presented in \citet{hi11a} and \citet{hil11} for this paper.
 Note that since the flare energies we computed in Table |. used the same quiescent stellar huuinosities cluploved to construct the Tilton et al flare frequency distributions. any future refinements of these quiescenut huninosities will not iuflueuce the flare rates we hereafter cite.," Note that since the flare energies we computed in Table \ref{flarenergy} used the same quiescent stellar luminosities employed to construct the Hilton et al flare frequency distributions, any future refinements of these quiescent luminosities will not influence the flare rates we hereafter cite."
 We determine that a flare having equal or greater Ü-—band euerev to our event #11. on AD Leo. would occur less than once per 15 hours.," We determine that a flare having equal or greater -band energy to our event 1, on AD Leo, would occur less than once per 18 hours."
 For YZ CAL. we fined that a flare having equal or greater Ü-banud energy for events 22-3 would occur less than once per LO hours. aud the EV Lac flare frequency. distribution indicates that a flare having equal or greater ÜC-band euergy to our event #11 would occur less than once per 7 hours.," For YZ CMi, we find that a flare having equal or greater -band energy for events 2-3 would occur less than once per 10 hours, and the EV Lac flare frequency distribution indicates that a flare having equal or greater -band energy to our event 4 would occur less than once per 7 hours."
 We utilized the same flare finding algorithm described, We utilized the same flare finding algorithm described
enerev. hence a more tight constraint on the maxima cherey can be obtained from the following equation: where D ds the diffusion coofücient aud pu.c«1019 «nm the size of the acceleration region.,"energy, hence a more tight constraint on the maximum energy can be obtained from the following equation: where $D$ is the diffusion coefficient and $r_{\rm lobe}\approx
1.1\times10^{16}$ cm the size of the acceleration region."
 This assunption is supported by the fact that particles lose all their energv before they diffuse out of the emuüttiug reelon (1.6. Tecoline“< Tau) (see Fig. 2))., This assumption is supported by the fact that particles lose all their energy before they diffuse out of the emitting region (i.e. $\tau_{\rm cooling} < \tau_{\rm diff}$ ) (see Fig. \ref{losses}) ).
" Working ou the Doluu Inuit we cau set D=Dp—ως, with rs the evro-radius."," Working on the Bohm limit we can set $D=D_{\rm B}=r_{\rm g} c/3$, with $r_{\rm
g}$ the gyro-radius."
 In such a case we get the maxima euereies shown in Table 3.. which are more than one order of maeguitude lower than in the previous calculation.," In such a case we get the maximum energies shown in Table \ref{diffusion}, which are more than one order of magnitude lower than in the previous calculation."
 The leptou particle distribution iu the emitting region cau be calculated. as a first order approximation. adopting a one-zone model. in which particles. ounce injected following a power-law enerev distribution. evolve suffering mainly svuchrotron aud relativistic Dreunisstrahluus losses.," The lepton particle distribution in the emitting region can be calculated, as a first order approximation, adopting a one-zone model, in which particles, once injected following a power-law energy distribution, evolve suffering mainly synchrotron and relativistic Bremsstrahlung losses."
 Iu such a context. the spectiiun of the particles is deteruined by the following transport equation (c.g. Khaneulvan et al.," In such a context, the spectrum of the particles is determined by the following transport equation (e.g. Khangulyan et al."
 2007): where Q(f.>) is the function for the particle injection. which takes place during the lifetime of the source (nig). estimated in z100 wre3&109 & (see Caray et al.," 2007): where $Q(t,\gamma)$ is the function for the particle injection, which takes place during the lifetime of the source $\tau_{\rm life}$ ), estimated in $\ga
100$ $\approx 3\times 10^9$ s (see Garay et al."
 2003)., 2003).
 Here. fis the time. aud 5 is the lepton Loreutz factor.," Here, $t$ is the time, and $\gamma$ is the lepton Lorentz factor."
 Acinittedly. the age of the source is not well constrained. although it could madly be siguificautlv vounecr than ~100 vr. the nnnmuiunjet crossing finie. suce the shock has been probably active for most of this period while the shocked material was being to its preseut location.," Admittedly, the age of the source is not well constrained, although it could hardly be significantly younger than $\sim 100$ yr, the minimum jet crossing time, since the shock has been probably active for most of this period while the shocked material was being to its present location."
 Concerning Tac. at this stage we take 1 as being the shortest diffusion timescale. ic. that corresponding to the maxima energy particles.," Concerning $\tau_{\rm
esc}$, at this stage we take it as being the shortest diffusion timescale, i.e. that corresponding to the maximum energy particles."
 The time-derivative 5 is a function accounting for all the energv losses affecting leptons. ie. basically svuchrotron and relativistic Droimisstraliluug.," The time-derivative $\dot{\gamma}$ is a function accounting for all the energy losses affecting leptons, i.e. basically synchrotron and relativistic Bremsstrahlung."
 The solutiou of Eq. (11)), The solution of Eq. \ref{solution0}) )
 Is: where The time depeudeuce comes through Eq. (15))., is: where The time dependence comes through Eq. \ref{tt}) ).
 For snall ἐν >SStoe: for larger fo 5<< rcp.," For small $t$, $\gamma\la \gamma_{\rm eff}$; for larger $t$, $\gamma\ll\gamma_{\rm eff}$ ."
 Sünco jog can be arbitrarily lege. for >! in Eq. (11))," Since $\gamma_{\rm eff}$ can be arbitrarily large, for $\gamma'$ in Eq. \ref{solution0}) )"
 above the maxima Lorentz factor Q will be zero., above the maximum Lorentz factor $Q$ will be zero.
 Iu addition. if 7. beiug shorter than Tooling. becomes laveer thau Τις. the final particle spectrum will be affected by particle escapo.," In addition, if $\tau$, being shorter than $\tau_{\rm cooling}$, becomes larger than $\tau_{\rm esc}$, the final particle spectrum will be affected by particle escape."
 The computed particle euergy distributions of primary and secondary leptons are shown in Fig. 3., The computed particle energy distributions of primary and secondary leptons are shown in Fig. \ref{evol}.
 As seen iu the figure. for injection timescales rijLO? smg. the particle distribution »(f.5) has already reaches the steady rogue. as expected from the fact that Τον~10? s. Moreover. the final particle euergv distribution is nof affected bv τις Owhich is actually a lower haut for the timescale of diffusion particle escape). suce Zac2Tesoliue (sce Fig. 2)).," As seen in the figure, for injection timescales $\tau_{\rm{inj}}\sim 10^9$ $< \tau_{\rm life}$, the particle distribution $n\left(t,\gamma\right)$ has already reached the steady regime, as expected from the fact that $\tau_{\rm
cooling}\sim 10^9$ s. Moreover, the final particle energy distribution is not affected by $\tau_{\rm esc}$ (which is actually a lower limit for the timescale of diffusion particle escape), since $\tau_{\rm esc}\ga \tau_{\rm cooling}$ (see Fig. \ref{losses}) ),"
 i.e. particles will raciate inside the ciittine reelonu., i.e. particles will radiate inside the emitting region.
 Regarding protons. their diffusion timescales and source lifetime are oue enough to let them radiate alimos all their cucreyv iu the rot spot.," Regarding protons, their diffusion timescales and source lifetime are long enough to let them radiate almost all their energy in the hot spot."
 Moreover. the energy loss timescale is ouly slehthy depeudent on energy.," Moreover, the energy loss timescale is only slightly dependent on energy."
" This iuplies that proton energv distribution. in the contex of our scenario. keeps almost the same spectral shape as that of the iujecte one. andreaches. as it ds the case for leptons. the steady τοσο, without suffering significan iurpact from cscape losses."," This implies that proton energy distribution, in the context of our scenario, keeps almost the same spectral shape as that of the injected one, andreaches, as it is the case for leptons, the steady regime, without suffering significant impact from escape losses."
"asstuue the euüittiug region to be au optically thin sphere instead of a gaussian (Pearson 1995)) imm which case the diameter is less than 1.5 times the photosphere diameter. and it therefore has an extent above the photosphere of less than 0.5 F2,.","assume the emitting region to be an optically thin sphere instead of a gaussian \cite{Pearson}) ) in which case the diameter is less than 1.8 times the photosphere diameter, and it therefore has an extent above the photosphere of less than 0.8 $R_\star$."
 The relatively large signal-to-noise ratio for YZ CAG and 16 phase referencing to a calibrator with good («0.5 mas) vositional accuracy in the radio frame (Jolustouetal. 1995) alowed us to deteriuue a precise position for this sar., The relatively large signal-to-noise ratio for YZ CMi and the phase referencing to a calibrator with good $<$ 0.5 mas) positional accuracy in the radio frame \cite{Johnston} 1995) allowed us to determine a precise position for this star.
 This position was compared with the position given w the Hipparcos catalogue (ESA 1997)., This position was compared with the position given by the Hipparcos catalogue (ESA 1997).
 Correcting for oper notion aix parallax. we found a cliscrepaucy of 19 unas dno aud 30.1 mas in 6. hus a total deviation [36.9 las.," Correcting for proper motion and parallax, we found a discrepancy of 20.9 mas in $\alpha$ and 30.4 mas in $\delta$, thus a total deviation of 36.9 mas."
 The xoper motion of the star is given in 1e Tipxwcos catalogue as 3119 2.6 mas/vr iu à. aud HOS #175 mas/vr in 9.," The proper motion of the star is given in the Hipparcos catalogue as -344.9 $\pm$ 2.6 mas/yr in $\alpha$, and -450.8 $\pm$ 1.75 mas/yr in $\delta$."
 Considering the time interval )etween the two measurements of 6 veis. the differeuce Ίσσαid thus witin the accuracy of the proper motion error bars.," Considering the time interval between the two measurements of 6 years, the difference is 2 $\sigma$ and thus within the accuracy of the proper motion error bars."
 Combining the VLBA aud IHippircos positions (courtesy of F. Árenou). an improved proper motion of 318.6 £0.6 mas/vr ina. and -116.6 £0.3 mas/vr in à can be derived.," Combining the VLBA and Hipparcos positions (courtesy of F. Arenou), an improved proper motion of -348.6 $\pm$ 0.6 mas/yr in $\alpha$, and -446.6 $\pm$ 0.3 mas/yr in $\delta$ can be derived."
 The position of AD Leo obtained with the VLBA was compared with those available im the Cliese and Tycho catalogues., The position of AD Leo obtained with the VLBA was compared with those available in the Gliese and Tycho catalogues.
" The latter showed a deviation with the VLBA position of 176.3 mas and 100.0 mas in a aud 4, respectively,"," The latter showed a deviation with the VLBA position of 176.3 mas and 100.0 mas in $\alpha$ and $\delta$, respectively."
 They are within one standard deviation of the Tycho catalogue accuracy., They are within one standard deviation of the Tycho catalogue accuracy.
 VLBA observatiois have spatially resolved YZ CAG aud he data could be fitted with a circular gaussian of a FWIIP of 0.98 +02 as., VLBA observations have spatially resolved YZ CMi and the data could be fitted with a circular gaussian of a FWHP of 0.98 $\pm$ 0.2 mas.
 The radio corona extent Is Έττ«1010ERN<LO? σι above the photosphere (tle shospheric radius is assumed to be 2.6« 101901. Pettersen 1980).," The radio corona extent is $1.77\times 10^{10} \pm8.8\times 10^{9}$ cm above the photosphere (the phospheric radius is assumed to be $2.6\times 10^{10}$ cm, \cite{Pettersen} 1980)."
 For AD Leo. which is closer aud has a larecr shotosphere. but was observed at a iiuchli weaker flux level. he corona was not resolved and we set a robust upper," For AD Leo, which is closer and has a larger photosphere, but was observed at a much weaker flux level, the corona was not resolved and we set a robust upper"
these spacetimes.,these spacetimes.
 We also 1se a third integral of motion related to the nori of the photon. iu order to monitor the accuracy of the caleulations., We also use a third integral of motion related to the norm of the photon 4-momenta in order to monitor the accuracy of the calculations.
 In the first paper of tliis series. we focus on an application relaed to the line spectra of accreting black holes with spacetimes that violate the no-hair theorem.," In the first paper of this series, we focus on an application related to the line spectra of accreting black holes with spacetimes that violate the no-hair theorem."
 Iu 822. we describe the uetric of Clampecdakis Babak (2006) in some detail αμα. in 833. we outline the uumerical algorilun.," In 2, we describe the metric of Glampedakis Babak (2006) in some detail and, in 3, we outline the numerical algorithm."
 Finally. in Sli. we present some illustrative results for different astroplivsical settings while comparing the results of our algorithm with other calculatious for Ixerr black holes.," Finally, in 4, we present some illustrative results for different astrophysical settings while comparing the results of our algorithm with other calculations for Kerr black holes."
 We describe the external spacetime of a spinning compact object with au arbitrary euadrupole moment using the metric of Glampedakis Babak (2006)., We describe the external spacetime of a spinning compact object with an arbitrary quadrupole moment using the metric of Glampedakis Babak (2006).
 This inetric arises by addiug to the Ixerr solution a coutributiou that has au arbitrary quadrupole moment aud is by itself a solution to the vacuum Einstein field ecquations (Hartle Thorne 1968)., This metric arises by adding to the Kerr solution a contribution that has an arbitrary quadrupole moment and is by itself a solution to the vacuum Einstein field equations (Hartle Thorne 1968).
 The metric is specified tuiiquely by three parameters: the mass A of the compact object. the spina. and the deviation e of its quadrupole moment from tlie Ixerr value.," The metric is specified uniquely by three parameters: the mass $M$ of the compact object, the spin $a$ , and the deviation $\epsilon$ of its quadrupole moment from the Kerr value."
 Setting e=0 makes the metric equal to the Ixerr solution. which is appropriate for a black hole of arbitrary spin.," Setting $\epsilon=0$ makes the metric equal to the Kerr solution, which is appropriate for a black hole of arbitrary spin."
 Ou the other hand. when «/MS0.1. all moments of the spacetime that are higher than the quadrupoe are negligible aud the metric becomes appropriate for neutron stars that are spinuine mocerately but not close to thelr mass shedding limit (Hartle Thorne 1968).," On the other hand, when $a/M\lesssim 0.4$, all moments of the spacetime that are higher than the quadrupole are negligible and the metric becomes appropriate for neutron stars that are spinning moderately but not close to their mass shedding limit (Hartle Thorne 1968)."
" Following Clampedakis Babak (2006). we write the metric in Bover-Lindquist. coordinates Here gy),lx is the err metric with the line element In this relation. aud The quadrupole correction isegliveu. in coutravariant form. by"," Following Glampedakis Babak (2006), we write the metric in Boyer-Lindquist coordinates as Here $g_{\mu\nu}^{\rm K}$ is the Kerr metric with the line element In this relation, and The quadrupole correction isgiven, in contravariant form, by"
Iu these formulae. Jandνα(AL(Ne is⋅ the Fermi⊲⋅ constant. are elements in⋅ the WeClyM matrix.. aud232/81.,"In these formulae, and, is the Fermi constant, are elements in the CKM matrix, and."
. The functious.(Gr).Gr).. and Gr).. which. represeut the loop integral[n] contributious to the Jamplitude. aregiventy [13]..," The functions, and , which represent the loop integral contributions to the amplitude, are given in \cite{Barger:1989fj}."
 The constraints ou aud )frombb JaredisplayedinFig. l., The constraints on and from are displayed in Fig. \ref{fig:bsgammaGraph}.
.Eachceurvetlhereinrepreseulsthecalueof BR(bssv) for a given choice of mye as a function of tan’., Each curve therein represents the value of $\mathrm{BR}(b\rightarrow s\gamma)$ for a given choice of $m_{H^\pm}$ as a function of $\tan\beta$.
 Note that lor the case under consideration here. in which GeV. the experimental coustraints are satisfied as long as tan=2.," Note that for the case under consideration here, in which $m_{H^\pm}>500\mbox{~GeV}$ , the experimental constraints are satisfied as long as $\tan\beta\gtrsim 2$."
 Constraints on and tau; can also be obtained [rom limits on the observed imixiug in the ruesonic and systems., Constraints on and $\tan\beta$ can also be obtained from limits on the observed mixing in the mesonic and systems.
 The diagramunatie contributions to uixiug are shown in Fig. 5..," The diagrammatic contributions to mixing are shown in Fig. \ref{fig:MesonBoxDiagram},"
 and these contributions translate iuto shift in the mass-splittiug between aud, and these contributions translate into shift in the mass-splitting between and
"The short-lived radioisotope (SLRI) ""Fe appears to have been synthesized in a Type 1l supernova (Alostelaoui. Lugmair. Hoppe 2005: Tachibana et al.","The short-lived radioisotope (SLRI) $^{60}$ Fe appears to have been synthesized in a Type II supernova (Mostefaoui, Lugmair, Hoppe 2005; Tachibana et al."
 2006) and injected into the presolar cloud (Boss οἱ al., 2006) and injected into the presolar cloud (Boss et al.
 2008. 2010; Boss Weiser 2010) from the same massive star that is likely to be the source of the bulk of the solar nebula’s 7° AI (Limonei Chielli 2006: sSahijpal Soni 2006).," 2008, 2010; Boss Keiser 2010) from the same massive star that is likely to be the source of the bulk of the solar nebula's $^{26}$ Al (Limongi Chieffi 2006; Sahijpal Soni 2006)."
 Given (the injection of SLBRIs into the presolar cloud by fingers (Boss et al., Given the injection of SLRIs into the presolar cloud by Rayleigh-Taylor fingers (Boss et al.
 2008. 2010: Boss Ixeiser 2010). it might be expected that the SLHIs would be initially highly spatially ancl temporally heterogeneous in their distribution in the solar nebula.," 2008, 2010; Boss Keiser 2010), it might be expected that the SLRIs would be initially highly spatially and temporally heterogeneous in their distribution in the solar nebula."
" However. the nearly identical Fe and Ni isotopic compositions of iron meteorites. chondrites. and the Earth require that the injected ""Fe must have been mixed to less than heterogeneity in the solar nebula (Dauphas et al."," However, the nearly identical Fe and Ni isotopic compositions of iron meteorites, chondrites, and the Earth require that the injected $^{60}$ Fe must have been mixed to less than heterogeneity in the solar nebula (Dauphas et al."
 2008)., 2008).
 A similar constraint arises [rom the need to preserve the use of 7 AI as an accurate nebular chronometer (e.g.. Thrane. Dizzauro. Baker 2006). while simultaneouslv allowing for the spread of stable oxygen Isotope ratios (Lyons Young 2005: Lee. Dergin. Lyons 2008).," A similar constraint arises from the need to preserve the use of $^{26}$ Al as an accurate nebular chronometer (e.g., Thrane, Bizzarro, Baker 2006), while simultaneously allowing for the spread of stable oxygen isotope ratios (Lyons Young 2005; Lee, Bergin, Lyons 2008)."
 Three-dimensional hvedrodsnamical models of the evolution of a marginally gravitationally unstable (MGU) solar nebula have shown that mixing of initially highly heterogeneous distributions of SLRIs can indeed reduce the level of heterogeneity to ~ or lower in less than 1000 vrs (Boss 2004a. 2006. 2007. 2003).," Three-dimensional hydrodynamical models of the evolution of a marginally gravitationally unstable (MGU) solar nebula have shown that mixing of initially highly heterogeneous distributions of SLRIs can indeed reduce the level of heterogeneity to $\sim$ or lower in less than 1000 yrs (Boss 2004a, 2006, 2007, 2008)."
 The discovery of refractory. grains among the particles collected from Comet 81P/Wild 2 by the Stardust spacecraft. (Brownlee οἱ al., The discovery of refractory grains among the particles collected from Comet 81P/Wild 2 by the Stardust spacecraft (Brownlee et al.
 2006: Simon et al., 2006; Simon et al.
 2008: Nakamura οἱ al., 2008; Nakamura et al.
 2008) provided the first ground truth for large-scale transport of materials formed in hieh temperature regions close to the protosun outward to the comet-Forming reeions of the solar nebula., 2008) provided the first ground truth for large-scale transport of materials formed in high temperature regions close to the protosun outward to the comet-forming regions of the solar nebula.
 One refractory. particle found. by. Starclust. Coki. has an age  1.7 Myr vounger (Matzel et al.," One refractory particle found by Stardust, Coki, has an age $\sim$ 1.7 Myr younger (Matzel et al."
 2010) than that of caleium. aluminum-rich inclusions (CAIs). implving that outward racial transport continied for millions of vears after CAI formation.," 2010) than that of calcium, aluminum-rich inclusions (CAIs), implying that outward radial transport continued for millions of years after CAI formation."
 Measurements of the iron sulfide content of particles [rom Wild 2 imply that over half of the comets mass derived from the inner solar nebula (Westphal et al., Measurements of the iron sulfide content of particles from Wild 2 imply that over half of the comet's mass derived from the inner solar nebula (Westphal et al.
 2009)., 2009).
 Similar hydrogen. nitrogen. ancl oxygen isotopic anomalies occur in both primitive meteorites and in cometary dust particles. inplving that meteorites and comets both formed [rom (he same basic mixture of disk material (Busemann et al.," Similar hydrogen, nitrogen, and oxygen isotopic anomalies occur in both primitive meteorites and in cometary dust particles, implying that meteorites and comets both formed from the same basic mixture of disk material (Busemann et al."
 2009: Aléoon et al., 2009; Aléoon et al.
 2009)., 2009).
 Observations of disks around voung stars often find evidence for ervstalline silicate grains αἱ distances ranging [rom inside 3 AU to bevond 5 AU. in both the disk's midplane and its surface lavers (e.g.. Alerinn et al.," Observations of disks around young stars often find evidence for crystalline silicate grains at distances ranging from inside 3 AU to beyond 5 AU, in both the disk's midplane and its surface layers (e.g., Merínn et al."
 2007)., 2007).
 Only the most massive AGB stars produce significant quantities of crystalline grains (Speck et al., Only the most massive AGB stars produce significant quantities of crystalline grains (Speck et al.
 2008): grains in the interstellar medium are primarily amorphous., 2008); grains in the interstellar medium are primarily amorphous.
 Crvstalline silicate erains could have been produced (through thermal annealing of amorphous grains (e.g.. Sargent οἱ al.," Crystalline silicate grains could have been produced through thermal annealing of amorphous grains (e.g., Sargent et al."
 2009a.b) by the hot disk temperatures," 2009a,b) by the hot disk temperatures"
is) represents a three-geometry.,$|s\rangle$ represents a three-geometry.
 A three-geometry is an equivalence class of three-metrics under diffeomorphisms., A three-geometry is an equivalence class of three-metrics under diffeomorphisms.
 The geometry represented by |) is quantized. in (he sense that it is formed by regions and surfaces having quantized values of volume and area.," The geometry represented by $|s\rangle$ is quantized, in the sense that it is formed by regions and surfaces having quantized values of volume and area."
" Intuitively. each node of s represents a ""chunk"" of space. whose (quantized) volume is determined by the inter(sviner associated to the node."," Intuitively, each node of $s$ represents a “chunk” of space, whose (quantized) volume is determined by the intertwiner associated to the node."
 Two of such ehunks of space are adjacent il there is a link between (he corresponding nodes., Two of such chunks of space are adjacent if there is a link between the corresponding nodes.
 The (quantized) area of the surface that separates (hem is determined by the representation j associated (o this link. according to the now well known relation [6] where fi.C.5 are the reduced Planck constant. the Newton constant and the hnunmirzi parameter (the dimensionless [ree parameter in the theory).," The (quantized) area of the surface that separates them is determined by the representation $j$ associated to this link, according to the now well known relation \cite{carlolee}
 where $\hbar, G, \gamma$ are the reduced Planck constant, the Newton constant and the Immirzi parameter (the dimensionless free parameter in the theory)."
 This interpretation of the states |s) follows from the study of the area and volume operator on the IHilbert space of the non-diffeomorphism invariant states., This interpretation of the states $|s\rangle$ follows from the study of the area and volume operator on the Hilbert space of the non-diffeomorphism invariant states.
 Notice that the states |s) are not gauge invariant either. and do not represent physical gauge invariant notions.," Notice that the states $|s\rangle$ are not gauge invariant either, and do not represent physical gauge invariant notions."
 The same is true for the corresponding classical notion of three-geometry: a three-geometry is determined by an ADM surface. which is a non-gauge-invariant notion in general relativitv.," The same is true for the corresponding classical notion of three-geometry: a three-geometry is determined by an ADM surface, which is a non-gauge-invariant notion in general relativity."
 The dvnamics of the theory is given by the Hamiltonian constraint /7(7). which we assume here to be a svimetric operator.," The dynamics of the theory is given by the Hamiltonian constraint $H(x)$, which we assume here to be a symmetric operator."
" The space of (he solutions of this constraint is the physical Hilbert space of the theory. 77,4.", The space of the solutions of this constraint is the physical Hilbert space of the theory $H_{ph}$.
" Instead of using the Iomiltonian constraint. we can work with the linear operator PosLapp—Hy, that projects on the Wernel of Πα]. ("," Instead of using the Hamiltonian constraint, we can work with the linear operator $P: H_{diff} \to H_{ph}$ that projects on the Kernel of $H(x)$. ("
A suitable extension of Πρ bo its generalized states or any other of the many techniques developed for this purpose should be used in order to take care of the technical complications in defining the Iilbert eigenspace corresponding to an eigenvalue in the continuum spectrum.),A suitable extension of $H_{diff}$ to its generalized states –or any other of the many techniques developed for this purpose– should be used in order to take care of the technical complications in defining the Hilbert eigenspace corresponding to an eigenvalue in the continuum spectrum.)
 For more details on this operator. and. in particular. a more precise definition as a three-dilfeomorphism invariant object. see [10]..," For more details on this operator, and, in particular, a more precise definition as a three-diffeomorphism invariant object, see \cite{CarloMike}."
" Iistead of worrving about the explicit construction of P. we assume here that the operator P:Mapp—I, is given. and we consider the quantity We claim that (his is a well«defined fully eauge invariant equantitv. which represents a physical observable in quantum gravity. aid has a precise and well-understood physical interpretation."," Instead of worrying about the explicit construction of $P$, we assume here that the operator $P: H_{diff} \to H_{ph}$ is given, and we consider the quantity We claim that this is a well-defined fully gauge invariant quantity, which represents a physical observable in quantum gravity and has a precise and well-understood physical interpretation."
It ji been recognized since the beeimuine of ταν astrononuiv that the flux of accreting N-rav binarles demonstrates strong aperiodic variability (seee.g.Rappa-)OY.Doxsey.&Zamuen1971:Odaetal.,"It has been recognized since the beginning of X-ray astronomy that the flux of accreting X-ray binaries demonstrates strong aperiodic variability \cite[see
e.g.][]{rappaport71,oda74}."
1971) ον Almost nunediatelv after the discovery. the roise in the ταν ight curves ο accreting binaries (like eg.DEN CreTO N-1) was ος)aimed as a SULverposition of randomly occuring X-ray CLUISSI1O1 flashes shots) of simular diraion (the shot noise nocel. Terrel 1972)).," Almost immediately after the discovery, the noise in the X-ray light curves of accreting binaries (like e.g. Cyg X-1) was explained as a superposition of randomly occurring X-ray emission flashes (shots) of similar duration (the shot noise model, \citealt{terrell72}) )."
 This provided au explanation to he sha© of t »ower deusitv spectra (PDS. the Fourier ranstorm of t1e autocorrelation function of the liehteurve of a source) o ‘different ταν sources.," This provided an explanation to the shape of the power density spectra (PDS, the Fourier transform of the autocorrelation function of the lightcurve of a source) of different X-ray sources."
 However. the accumulation of more data posed serious questiois totus xuwadieui.," However, the accumulation of more data posed serious questions to this paradigm."
 Iu particular. it was very lard o explain a huge range of the N-rav variability time scales observed da some sources (seee.g.Cliurazov.Cülfanov.&Revuivtsey2001) and the linear correlation betwee- je variability amplitude aud the average flux of source:μα Uttley&AlcWardy20013.," In particular, it was very hard to explain a huge range of the X-ray variability time scales observed in some sources \cite[see
e.g.][]{churazov01} and the linear correlation between the variability amplitude and the average flux of sources \citep{uttley01}."
. Indeed. to explain observed aree variability amplitude. the individual flashes/shots iu 1e shot noise model should be very powerful.," Indeed, to explain observed large variability amplitude, the individual flashes/shots in the shot noise model should be very powerful."
 Therefore rese flashes μις coue from the iunenriuost region of 1ο accretioi flow. where most of the eunergv is released.," Therefore these flashes must come from the innermost region of the accretion flow, where most of the energy is released."
 The characteristic time scales in this region are wvorv VAiort muillisecouds ¢Di eus of milliseconds for stellag-10asμα conrpact objects., The characteristic time scales in this region are very short – milliseconds or tens of milliseconds for stellar-mass compact objects.
 However. very ofen. e.g. in the soft/hie[um state of accreting biuaries. the observed power spectra ave a power law sipe exteudi1ο down to frequeucies as low as 1TE109 Tz. ie. 5-7 orders of mmaenitude ouecr tine scales fiu all time scales charactcistic for he region of the main ΟΠΟΥ release (seeClawvov.Cal-nov.&Revuivtsev2001:CulfanovArefiev2105 ).," However, very often, e.g. in the soft/high state of accreting binaries, the observed power spectra have a power law shape extending down to frequencies as low as $10^{-5}-10^{-6}$ Hz, i.e. 5-7 orders of magnitude longer time scales than all time scales characteristic for the region of the main energy release \cite[see][]{churazov01,gilfanov05}."
". Α νον promisiis anodel for the aperioclc Nouv variability of accreting sources Is the “perurbatiou oxopasation"" λος (Lvubirski1997:ChuraZOV.Cal2001:Arévalo&Utlev 2006)."," A very promising model for the aperiodic X-ray variability of accreting sources is the ""perturbation propagation"" model \citep{lyubarskii97,churazov01,kotov01,arevalo06}."
. In this model. the X-rav flux variability is caused by the variations of the lustantaneous value of the mass accretion rae in the ΠΙΟ accretion flow.," In this model, the X-ray flux variability is caused by the variations of the instantaneous value of the mass accretion rate in the inner accretion flow."
 Iu tiwh. the viriatious of the mass accretion rate are due to he perturbations introduced to the accretion flow by the stochastic variations of the disk viscous stresses.," In turn, the variations of the mass accretion rate are due to the perturbations introduced to the accretion flow by the stochastic variations of the disk viscous stresses."
 In this ταιodel the observed variability is a multiplicative superposiion of perturbations introduced at different radii., In this model the observed variability is a multiplicative superposition of perturbations introduced at different radii.
 Asstuing that the fractional amplitudes of the mass accretion rate perturbations are tlC Sade at all raclii. the PDS of the cmereinge lightcurve will ιαπαν appear as a xcfsinular power-law with slope l..1.5 up to the maxiual frequeucies that can be eecnerated in the disk. (Lyubirskii1997).," Assuming that the fractional amplitudes of the mass accretion rate perturbations are the same at all radii, the PDS of the emerging lightcurve will naturally appear as a self-similar power-law with slope $-1...-1.5$ up to the maximal frequencies that can be generated in the disk \citep{lyubarskii97}."
. Direct hagucto wadrodyvuamic simulations of accretion flows (see.g.Dran-rose.Ivolik.&Stone2000) provide further swyport to lis semi-phenomenological model.," Direct magneto hydrodynamic simulations of accretion flows \cite[se e.g.][]{brandenburg95,balbus99,hirose06} provide further support to this semi-phenomenological model."
 Ta paricular. these snlations show that perturbations in the iustauntaucous nass accretion rate gener:uted at any eiven radius of the disk have characteristic fiue scale proportional to the ocal dynamical time.," In particular, these simulations show that perturbations in the instantaneous mass accretion rate generated at any given radius of the disk have characteristic time scale proportional to the local dynamical time."
 This model of the ajveriodic N-rav flux. variahiitv nupics that the presence of the accretion disk edges. Ixth outer aud iuuer. should be reflected in the noise proper105 oftie X-ray elt curve.," This model of the aperiodic X-ray flux variability implies that the presence of the accretion disk edges, both outer and inner, should be reflected in the noise properties of the X-ray light curve."
 Signatures of outer edges of accretion disks were found bv Cülfaunov&Arefiev.(2005) in the low frequency parts of the noise power spectra of low mass XN-rav binaries.," Signatures of outer edges of accretion disks were found by \cite{gilfanov05}
 in the low frequency parts of the noise power spectra of low mass X-ray binaries."
 Accretion disks avouud conrpact stars m X-ray binaries should also have inner edges. which should imanites itself in the power spectnuu of their X-ray light curves.," Accretion disks around compact stars in X-ray binaries should also have inner edges, which should manifest itself in the power spectrum of their X-ray light curves."
 Specifically. a definite break is expected to be preseu iu the PDS at the characeristic frequency of variability generated at the inner e«ee of the disk.," Specifically, a definite break is expected to be present in the PDS at the characteristic frequency of variability generated at the inner edge of the disk."
 At frequencies below this break the powor spoectrun is expeced to produced in the accretion ¢isk anc have a self-similar slo about -1.0...-1.5 (Lyubarskii1997:Clhiurazov.Cafauov.al. 2006).. while at higher requeucies the characer oft flow changes and the PDS slope may be different.," At frequencies below this break the power spectrum is expected to be produced in the accretion disk and have a self-similar slope about -1.0...-1.5 \citep{lyubarskii97,churazov01,gilfanov05,revnivtsev06}, while at higher frequencies the character of the flow changes and the PDS slope may be different."
 Iu accreting X-ray pulsars and intermediate polars the central compact object (a neutron star or a white dwarf) has a strongC» maeneticOo field which cau disrupt he, In accreting X-ray pulsars and intermediate polars the central compact object (a neutron star or a white dwarf) has a strong magnetic field which can disrupt the
For the gas. I adopt the distribution given bv Olling Merrifield (2001 their Table D1).,"For the gas, I adopt the distribution given by Olling Merrifield (2001 — their Table D1)."
 L include both the molecular and atomic gas components. treating (hem as being in a neelieibly (hin disk.," I include both the molecular and atomic gas components, treating them as being in a negligibly thin disk."
 I do not include the ionized gas component for consisteney. with the treatment of other galaxies., I do not include the ionized gas component for consistency with the treatment of other galaxies.
 Moreover. this is a very small [raction of the total with an estimated surface density (1.4ML.pe 7) that is only available at the solar radius.," Moreover, this is a very small fraction of the total with an estimated surface density $1.4\;\surfdens$ ) that is only available at the solar radius."
 Olling Merrifield (2001) give the surface densities scaled bv Ay., Olling Merrifield (2001) give the surface densities scaled by $R_0$.
 For consistency with the munodel I fix these imunbers (o fy=8 kpc., For consistency with the model I fix these numbers to $R_0 = 8$ kpc.
 The surface densities of Is ancl eegas are corrected upwards by a factor of 1.4 to account for the associated mass in helium and metals., The surface densities of $_2$ and gas are corrected upwards by a factor of 1.4 to account for the associated mass in helium and metals.
 For these assumptions. the gas distribution integrates to a total mass OM...," For these assumptions, the gas distribution integrates to a total mass $\mass_{gas} = 1.18 \times 10^{10}\;\Msun$ ."
 This is slightly more gas mass than inferred by Flvnn ((2006) from clifferent data. whose total sums to just under 10710αι.," This is slightly more gas mass than inferred by Flynn (2006) from different data, whose total sums to just under $10^{10}\;\Msun$."
 This seems like an adecquate level of agreement considering (he diversity of published opinions., This seems like an adequate level of agreement considering the diversity of published opinions.
 The gas is usually neglected in mass models of (he Milky Way as il is a (race component compared to the stars aud dark matter halo., The gas is usually neglected in mass models of the Milky Way as it is a trace component compared to the stars and dark matter halo.
 ILowever. (he gas is not negligible in MOND.," However, the gas is not negligible in MOND."
 The models considered here have gas mass fractions in the range fy=ωςτν0.190.01 (Table 1))., The models considered here have gas mass fractions in the range $f_g = \mass_{gas}/\mass_{b} = 0.19 \pm 0.01$ (Table \ref{MW_mods}) ).
 This is an important component of the total gravitating mass in (he absence of dark matter., This is an important component of the total gravitating mass in the absence of dark matter.
 Effects of the detailed distribution of the gas are rellected in the total rotation οΝΟ., Effects of the detailed distribution of the gas are reflected in the total rotation curve.
 Given the \lilky Way mass distribution. MOND predicts the rotation curve.," Given the Milky Way mass distribution, MOND predicts the rotation curve."
" Unlike the case will external galaxies. (he mass-to-light ratio is not a fit parameter,"," Unlike the case with external galaxies, the mass-to-light ratio is not a fit parameter."
 The mnmocdel plus the gas distribution of Olling Merrifield (1999) specilv the mass., The model plus the gas distribution of Olling Merrifield (1999) specify the mass.
 The only choices to be made are (he scale length and the interpolation function., The only choices to be made are the scale length and the interpolation function.
 Figs. 2.. 3..," Figs. \ref{MW_panelA}, \ref{MW_panelB},"
 and Ε show the results for increasing choices of scale length., and \ref{MW_panelC} show the results for increasing choices of scale length.
 In each case. four interpolation functions are illustrated: vy aud 7s (these are practically indistinguishable from the simple and standard interpolation functions) and for comparison the functions 7 and δι newly suggested by Milgrom Sanders (2007).," In each case, four interpolation functions are illustrated: $\hat \nu_1$ and $\hat \nu_2$ (these are practically indistinguishable from the simple and standard interpolation functions) and for comparison the functions $\tilde \nu_1$ and $\bar \nu_1$ newly suggested by Milgrom Sanders (2007)."
 MOND produces a realistic rotation curve given a mass distribution. especially for the shorter scale lengths preferred. by the CODE data.," MOND produces a realistic rotation curve given a mass distribution, especially for the shorter scale lengths preferred by the COBE data."
(NRAQO) (Hornsteinetal.2007:Marrone2008:Yusel-Zaceh2008)..,"(NRAO) \citep{hornstein07,marrone08,zadeh08}."
 The, The
closed orbit for m=2 will only then obtain at the centre of a homogeneous core.,closed orbit for $m=2$ will only then obtain at the centre of a homogeneous core.
 Both of these conditions are represented by à vanishingly small number of orbits and therefore there are no resonant contributions bv internally orbiting point masses for harmonics with /«3., Both of these conditions are represented by a vanishingly small number of orbits and therefore there are no resonant contributions by internally orbiting point masses for harmonics with $l<3$.
 We consider three classes of initial profiles: Wing models (1966) with concentrations e between 0.67 and 1.5. Plummer models (e.g. Binney “Tremaine 1987). and. models of the form: Solution of the evolution equation requires repetitive integration of the distribution function to derive the density. mass and potential profiles.," We consider three classes of initial profiles: King models (1966) with concentrations $c$ between 0.67 and 1.5, Plummer models (e.g. Binney Tremaine 1987), and models of the form: Solution of the evolution equation requires repetitive integration of the distribution function to derive the density, mass and potential profiles."
 For this reason. the dynamic range of cuspy models present considerable numerical challenge. anc are not considered here. unfortunately.," For this reason, the dynamic range of cuspy models present considerable numerical challenge and are not considered here, unfortunately."
 Llowever. the instantaneous Ductuation spectrum in models with and without cores exhibit strong enhancement: due of=] modes (sce Weinberg 1998): this suggests that qualitative behavior here will be similar as well since he underlving physical process is the same.," However, the instantaneous fluctuation spectrum in models with and without cores exhibit strong enhancement due to $l=1$ modes (see Weinberg 1998); this suggests that qualitative behavior here will be similar as well since the underlying physical process is the same."
 The mocel described. in equation (1)) has most of the features. of »opular cusp but gets around numerical difficulties of divergent. distribution phase-space distribution functions or carefully chosen values of small but non-vanishing values ob c., The model described in equation \ref{eq:NFWlike}) ) has most of the features of popular cusp but gets around numerical difficulties of divergent distribution phase-space distribution functions for carefully chosen values of small but non-vanishing values of $\epsilon$.
 Ht remains a possibility that an initial cusp may effect he sense of the evolution of the inner power law., It remains a possibility that an initial cusp may effect the sense of the evolution of the inner power law.
 We will extend the development to study this case in detail in a later xiper., We will extend the development to study this case in detail in a later paper.
 Here. we locus on the rapid approach to a self-similar orm ouside of the core.," Here, we focus on the rapid approach to a self-similar form ouside of the core."
 We consider three specific noise sources: (1) transient noise due to blobs moving on rectilinear trajectory (shrapnel model): (2) transient noise due to substructure on decaving halo orbits due to dynamical friction. (CCsatellite model): and (3) quasi-periodic noise due to blobs orbiting within the halo (black hole model)., We consider three specific noise sources: (1) transient noise due to blobs moving on rectilinear trajectory (`shrapnel' model); (2) transient noise due to substructure on decaying halo orbits due to dynamical friction (`satellite' model); and (3) quasi-periodic noise due to blobs orbiting within the halo (`black hole' model).
 The derivation. of moments for the evolution equation can be found in £44 of Paper 1., The derivation of moments for the evolution equation can be found in 4 of Paper 1.
 Por all noise sources. the amplitude for a single event is proportional to the square of the mass in the perturbation since the net change in| conserved quantities is second order.," For all noise sources, the amplitude for a single event is proportional to the square of the mass in the perturbation since the net change in conserved quantities is second order."
 From the form of the collisional 3oltzmann equation. the evolutionary time scale is inversely proportional to amplitude of the collision term.," From the form of the collisional Boltzmann equation, the evolutionary time scale is inversely proportional to amplitude of the collision term."
 This allows easy scaling of the results derived here for cach noise source cleseribecl below., This allows easy scaling of the results derived here for each noise source described below.
 We will set some fiducial parameters [or results quoted in refsec:results ancl give the scaling formula for the amplitudes so that the time scales can be casily derived: for other scenarios., We will set some fiducial parameters for results quoted in \\ref{sec:results} and give the scaling formula for the amplitudes so that the time scales can be easily derived for other scenarios.
 For the shrapnel model. the overall amplitude for the process is also proportional to the bombarcment rate.," For the shrapnel model, the overall amplitude for the process is also proportional to the bombardment rate."
 We assume that the tux of shrapnel is uniform. so that the distribution impact parameters ὁ is proportional to b., We assume that the flux of shrapnel is uniform so that the distribution impact parameters $b$ is proportional to $b$.
 Soon after formation. one expects encounters to be more numerous so we adopt a fiducial rate of LO encounters per gieavear inside of 50 kpe. each with a mass of 0.003. halo masses.," Soon after formation, one expects encounters to be more numerous so we adopt a fiducial rate of 10 encounters per gigayear inside of 50 kpc, each with a mass of 0.003 halo masses."
 Scaling to our Galaxy. our fiducial shrapnel has of the LMC mass.," Scaling to our Galaxy, our fiducial shrapnel has of the LMC mass."
 The trajectories have constant velocity chosen to be V2 times the peak halo circular. velocity., The trajectories have constant velocity chosen to be $\sqrt{2}$ times the peak halo circular velocity.
 However. the results are nearly unchanged if the incoming 7elocity is increased or decreased. by a factor of two and so —Us is Dot à sensitive assumption.," However, the results are nearly unchanged if the incoming velocity is increased or decreased by a factor of two and so this is not a sensitive assumption."
 For the satellite model. we assume a halo's worth of satellites of a given mass assimilating within | Civr.," For the satellite model, we assume a halo's worth of satellites of a given mass assimilating within 1 Gyr."
 Because 1e amplitude is proportional to the square of the satellite to halo mass ratio but the number of satellites is proportional to the inverse of this ratio. the overall amplitudes. scales as the satellite to halo mass ratio.," Because the amplitude is proportional to the square of the satellite to halo mass ratio but the number of satellites is proportional to the inverse of this ratio, the overall amplitudes scales as the satellite to halo mass ratio."
 This scaling is roughly consistent with the substructure distribution described. by Aloore et al. (, This scaling is roughly consistent with the substructure distribution described by Moore et al. (
1999).,1999).
 For smaller numbers of satellite per halo. the overall amplitude can be multiplied by the desire [actor which lengthens the time scale proportionately.," For smaller numbers of satellite per halo, the overall amplitude can be multiplied by the desired factor which lengthens the time scale proportionately."
 The noise spectrum results from following the orbital clecay of a satellite of given mass ratio by direct integration of the equations of motion of an initially circular orbit at à radius enclosing of the halo mass., The noise spectrum results from following the orbital decay of a satellite of given mass ratio by direct integration of the equations of motion of an initially circular orbit at a radius enclosing of the halo mass.
" The drag force is compute using Chandrasekhar's formula with In,.X=SN: this value oovides a good match to substructure simulation Clormen et al.", The drag force is computed using Chandrasekhar's formula with $\ln\Lambda=8$; this value provides a good match to substructure simulation (Tormen et al.
 1998)., 1998).
 Although the power spectrum is computer or the full orbital decay of the satellite. the amplitude is diminished by the fraction of satellites with orbits that can tully decay in one gigavear.," Although the power spectrum is computed for the full orbital decay of the satellite, the amplitude is diminished by the fraction of satellites with orbits that can fully decay in one gigayear."
 Mass loss from the satellite is not included., Mass loss from the satellite is not included.
 In the case of the black hole model. the amplitude of he noise also is proportional to the square of the perturber mass for a single perturber.," In the case of the black hole model, the amplitude of the noise also is proportional to the square of the perturber mass for a single perturber."
 However. the amplitude is also »oportional to number of perturbers.," However, the amplitude is also proportional to number of perturbers."
 For a fixed fraction in Xack holes. the number is then inversely proportional to the jack hole mass.," For a fixed fraction in black holes, the number is then inversely proportional to the black hole mass."
 Altogether. then. the amplitude is directly woportional to the perturber mass and the fraction of the ido represented by the perturber mass.," Altogether, then, the amplitude is directly proportional to the perturber mass and the fraction of the halo represented by the perturber mass."
" For our fiducial example. we assume a halo fully populated by 10"". mass black holes (Lacey Ostriker 1985)."," For our fiducial example, we assume a halo fully populated by $10^6$ solar-mass black holes (Lacey Ostriker 1985)."
 The scaling and fiducial parameters for all of these cases is summarized in Table 1.., The scaling and fiducial parameters for all of these cases is summarized in Table \ref{tab:scale}.
 The evolution equation. a Boltzmann equation. with a bokker-Planek-type collision term. is derived in Paper 1.," The evolution equation, a Boltzmann equation with a Fokker-Planck-type collision term, is derived in Paper 1."
 Yo simplify the numerical solution. the full equation 1s isotropized by averaging over angular momentum to leave an equation for the phase-space distribution function in energy L and time { (see Appencix and Paper 1).," To simplify the numerical solution, the full equation is isotropized by averaging over angular momentum to leave an equation for the phase-space distribution function in energy $E$ and time $t$ (see Appendix \\ref{sec:FP} and Paper 1)."
 The Fokker-Planck equation is solved on a grid as described in Appendix, The Fokker-Planck equation is solved on a grid as described in Appendix
One of the important steps in our study was to describe the orbital motion of Phoche by fitting the curves of t temporal variations of the orbital elements ον¢.AM and Ly with polvnomia functions.,"One of the important steps in our study was to describe the orbital motion of Phoebe by fitting the curves of the temporal variations of the orbital elements $a, e, M$ and $L_{s}$ with polynomial functions."
 As shown in 2.. the periodic variations of the semüauajor axis around its nean value with a relative amplitude of the order of 10! are clearly due to the pertirbiug effects of other celestial bodies like the Sun.," As shown in \ref{fig3new}, the periodic variations of the semi-major axis around its mean value with a relative amplitude of the order of $10^{-3}$ are clearly due to the perturbing effects of other celestial bodies like the Sun."
" The Orvital motion is far from being a keperui ono. as shown by the large polvuonmdal expressious of C.M. and £,. aud bv the large sinusoidal amplitudes characterizing re residuals after substraction of these yolvnouuals."," The orbital motion is far from being a keplerian one, as shown by the large polynomial expressions of $e, M$ and $L_{s}$, and by the large sinusoidal amplitudes characterizing the residuals after substraction of these polynomials."
 Ayplvine the theoritical franeworlk already used by Wainoshita (1977) for he Earth. the precession and the nuation motion of Phoebe are cdeterinined οι analvticalyo and from nunierical iuceration of the equations of motion.," Applying the theoritical framework already used by Kinoshita (1977) for the Earth, the precession and the nutation motion of Phoebe are determined both analytically and from numerical integration of the equations of motion."
" We found that the precessiou-mitation 110ion of Pwehbe nudereoing tje gravitational yerturbation of Satur Lis quite simular to that the Earth ""undergone he eravitational effect of bot1i the Moou aud he Sun.", We found that the precession-nutation motion of Phoebe undergoing the gravitational perturbation of Saturn is quite similar to that the Earth undergoing the gravitational effect of both the Moon and the Sun.
 Tlis our valie for the precession of Phoebe. that Is fo sav 558065 ον. is very close to the correspoxdiug value for t1C Earth (50817/cv) and the nutatkna in ongitude aud in oblicuity of Phoebe with peak to peal variatious of 267 and S are of the same order of apitude as the nutaion of the Earth (respectively. 367 andLS” o) to peak).," Thus our value for the precession of Phoebe, that is to say 5580"".65 cy, is very close to the corresponding value for the Earth (5081""/cy) and the nutation in longitude and in obliquity of Phoebe with peak to peak variations of $26""$ and $8""$ are of the same order of amplitude as the nutation of the Earth (respectively 36"" and 18"" peak to peak)."
 Aloreover Phoehe j)bliquitv. (237.95) Is rougeilv the same as the Earth's one (23 V3)., Moreover Phoebe obliquity $23^\circ.95$ ) is roughly the same as the Earth's one $23^\circ.43$ ).
 Notice tlat he plysical cissviunetrv (large value of the dvuamical Hattenimg and of the triaxialitv) aud the Iarge eccentric of Proebe which direclty iuerease the amplitude of he recession. and the nutation is compensated by dts slow revolution axd ast rotation., Notice that the physical dissymmetry (large value of the dynamical flattening and of the triaxiality) and the large eccentricity of Phoebe which direclty increase the amplitude of the precession and the nutation is compensated by its slow revolution and fast rotation.
 Iu C'ottereau and Souchay (2009). woe have Lom»nistratec hat the ejffects of the ]uege traxialitv of Venus o- its nutation are of the sale order of enitude thai the effects of the dynamical flattening.," In Cottereau and Souchay (2009), we have demonstrated that the effects of the large triaxiality of Venus on its nutation are of the same order of magnitude than the effects of the dynamical flattening."
 ον contrast. he effects of the large triaxialiv of Phoebe on its nutakl are coli»onusated by dts ast rotation id. decrease he amplitude which become ucelieilde 'onmpared to he dvnanucal flatteniug.," By contrast, the effects of the large triaxiality of Phoebe on its nutation are compensated by its fast rotation and decrease the amplitude which become negligible compared to the dynamical flattening."
 We also investigated the possibility O construct jalvtical ables of Phoebe mutation. as was done for the Earth.," We also investigated the possibility to construct analytical tables of Phoebe nutation, as was done for the Earth."
 As Phoebe has a large eccentricity. tje analvtical developeits at the 3th oxler given by Ninoshita (1977) for the Earth are not valid.," As Phoebe has a large eccentricity, the analytical developments at the 3th order given by Kinoshita (1977) for the Earth are not valid."
 We lust carry out the developeits up fo 6th order to reach a relative 101 accuracy., We must carry out the developments up to 6th order to reach a relative $10^{-4}$ accuracy.
 Thus athough the ampliude of the uutation motion is close to the Earth one. we demoustrated that the analytical model used by Winoshita for he Earth does uot describe the nutatiou mioion of a disturbed body like Phoebe with the same accuracy.," Thus although the amplitude of the nutation motion is close to the Earth one, we demonstrated that the analytical model used by Kinoshita for the Earth does not describe the nutation motion of a disturbed body like Phoebe with the same accuracy."
 This analytical model does not take mto account the large portirhing effects of the celestial |)xdies on the orvt of the satellite., This analytical model does not take into account the large perturbing effects of the celestial bodies on the orbit of the satellite.
 To deseribe the mutation motion of Phoebe a FFT approach is better than a pure analytical iitegration done with linear expressions for e.AM aud Ly ass rown aud 15..," To describe the nutation motion of Phoebe a FFT approach is better than a pure analytical integration done with linear expressions for $e, M$ and $L_S$ as shown \ref{fig12} and \ref{fig13}."
 The FFT analvsis is better fitter| to describe the periodic variations cliaracteriziis the uuation signals of Phoebe., The FFT analysis is better fitted to describe the periodic variations characterizing the nutation signals of Phoebe.
 These periodic variaicls aro ave:raged cling the calculation of the precession wlüch «ecroases the discrepancies between the two mocels., These periodic variations are averaged during the calculation of the precession which decreases the discrepancies between the two models.
" To conclude we ie shown that the anavtical model set] w Kinoshita (1977) gives a BOLE first approximalon of hne precession-uutaion of Phoebe but urther anavtical developments ire reecded to reacit 1C Saue accuracy than or the terrestrial panets,", To conclude we have shown that the analytical model set by Kinoshita (1977) gives a good first approximation of the precession-nutation of Phoebe but further analytical developments are needed to reach the same accuracy than for the terrestrial planets.
 We think tha this work. can be starting polit for Aurther studies such as the elaboratiou of another very wrecise analytical uodel of the rotation of Phoeye by aking into acco effects ignored in this ]oper. as the direct effects of the Sun. of Titan iud of Saturn dvuauical Hattening.," We think that this work can be starting point for further studies such as the elaboration of another very precise analytical model of the rotation of Phoebe by taking into account effects ignored in this paper, as the direct effects of the Sun, of Titan and of Saturn dynamical flattening."
 Such a nodel is required to develop the long enu ephemerides of Phoeobe's rotation. which should require lone teri orbital ephemerides. not still available.," Such a model is required to develop the long term ephemerides of Phoebe's rotation, which should require long term orbital ephemerides, not still available."
indicate the existence of differential rotation in many stars.,indicate the existence of differential rotation in many stars.
 Among the stellar population of F. G and Ix stars. solar-like positive pole-lo-equator differential rotation. as well as antisolar pattern in which the equator rotates slower (han the pole. are observed.," Among the stellar population of F, G and K stars, solar-like positive pole-to-equator differential rotation, as well as antisolar pattern in which the equator rotates slower than the pole, are observed."
 For example. nmultiwavelength studies of GO-G5V stars by Messina&Guinan(2003).. and Zeeman- imaging by Jeffers&Donati(2009) have revealed (he existence of solar-like (positive) ancl antisolar (negative) pole-to-equator differential rotation.," For example, multiwavelength studies of G0-G5V stars by \citet{mg2003}, and Zeeman-Doppler imaging by \citet{jd2009} have revealed the existence of solar-like (positive) and antisolar (negative) pole-to-equator differential rotation."
 For the spot-dominated late (wpe stus. inversions of light curves for images of dark starspots on the surface reveal the dillerential rotation pattern of Ix-stars: so [ar all of ihem were found to have solar-like profiles (Rottenbacherοἱal2011).," For the spot-dominated late type stars, inversions of light curves for images of dark starspots on the surface reveal the differential rotation pattern of K-stars; so far all of them were found to have solar-like profiles \citep{rhvh2011}."
.. Antisolar differential rotation has been found among F and G stars. but occurs much less frequently than differential rotation.," Antisolar differential rotation has been found among F and G stars, but occurs much less frequently than solar-like differential rotation."
 Furthermore. the amplitude of antisolar differential rotation in those stars are also found to be smaller than solar type pole-to-equator differential rotation.," Furthermore, the amplitude of antisolar differential rotation in those stars are also found to be smaller than solar type pole-to-equator differential rotation."
 Theoretical modeling has enabled us to understand how (he solar-like positive differential rotation is formed in (he solar and in stellar convection zones (Gilman 2005).," Theoretical modeling has enabled us to understand how the solar-like positive pole-to-equator differential rotation is formed in the solar and in stellar convection zones \citep{gm1986,rempel2005}."
. Stars will deeper convection zones are likely to have broader differential rotations with latitude (Gilman1979)., Stars with deeper convection zones are likely to have broader differential rotations with latitude \citep{gilman1979}.
. Except for anomalously weak rotators. such stars are likely (to have equatorial acceleration like the Sun does.," Except for anomalously weak rotators, such stars are likely to have equatorial acceleration like the Sun does."
 On the other hand. stars with shallow convection zones. like F stars. may not have broad clifferential rotation. but rather a much more structured pattern.," On the other hand, stars with shallow convection zones, like F stars, may not have broad differential rotation, but rather a much more structured pattern."
 Even if thev rotate much faster than the Sun. if the turnover time in their shallow convection zone is short enough. thev could have antisolar differential rotations.," Even if they rotate much faster than the Sun, if the turnover time in their shallow convection zone is short enough, they could have antisolar differential rotations."
 llvdrodynamie and magnetohyvdrodvuamic instability of solar-like differential rotation in stars has also been explored (Ixnobloch&Spruit)1982:Urpin.ShalvbkovSpruit.1996:Spruit1999.2002:Braithwaite 90060).," Hydrodynamic and magnetohydrodynamic instability of solar-like differential rotation in stars has also been explored \citep{ks1982,uss1996, spruit1999, spruit2002, braithwaite2006}."
.. But (to our knowledge for the case of antisolar differential rotation neither detailed theory of formation nor the stability analyses have been carried oul vet., But to our knowledge for the case of antisolar differential rotation neither detailed theory of formation nor the stability analyses have been carried out yet.
 The aim of (his paper is (o analvze the instability of antisolar differential rotation in order to answer the following «questions. (, The aim of this paper is to analyze the instability of antisolar differential rotation in order to answer the following questions. (
1) Why have only about a dozen antisolar stars been found? (,i) Why have only about a dozen antisolar stars been found? (
1) Is antisolar differential rotation more unstable than Che solar-like pattern. ancl could Chat be the reason? (,"ii) Is antisolar differential rotation more unstable than the solar-like pattern, and could that be the reason? ("
ii) What is the limiting amplitude of a negative pole-to-ecquator differential rotation that can be stable? (,iii) What is the limiting amplitude of a negative pole-to-equator differential rotation that can be stable? (
iv) Why has no antisolar IX-star been found vet?,iv) Why has no antisolar K-star been found yet?
 The observations of stellar rotation are made at the surface of a star. and we do not know (he differential rotation pattern in their tachoclines.," The observations of stellar rotation are made at the surface of a star, and we do not know the differential rotation pattern in their tachoclines."
 Using (he analogy that the Sun5 positive pole-to-equator surface latitudinal differential rotation persists down to the tachocline. we assume (hat the stellar tachoclines reflect the same sign of the pole-to-equator Iatitudinal," Using the analogy that the Sun's positive pole-to-equator surface latitudinal differential rotation persists down to the tachocline, we assume that the stellar tachoclines reflect the same sign of the pole-to-equator latitudinal"
It is possible to transfer [users treatiment from Fourier to configuration space (Πατοι1992).. iu which x is the distance separation along the LOS aud σ is the perpendicular separation.,"It is possible to transfer Kaiser's treatment from Fourier to configuration space \citep{1992ApJ...385L...5H}, in which $\pi$ is the distance separation along the LOS and $\sigma$ is the perpendicular separation."
 The absolute distance of separation is indicated by 5=v6?|z2. p=zs is the cosine of the angle between the separation vector aud the LOS.," The absolute distance of separation is indicated by $s=\sqrt{\sigma^2+\pi^2}$, $\mu=\pi/s$ is the cosine of the angle between the separation vector and the LOS."
 The imultipoles of £(o.x) are eiven in terms of the real space correlation function £(re): andl If the real space correlation function ή) is computed from linear theory. these equatious describe the typical squashing of the correlation function along the LOS of the Naiser effect.," The multipoles of $\hat{\xi}(\sigma, \pi)$ are given in terms of the real space correlation function $\xi(r)$: and If the real space correlation function $\xi(r)$ is computed from linear theory, these equations describe the typical squashing of the correlation function along the LOS of the Kaiser effect."
 The imultipoles of £(o.3) can be extracted through the projectious Tamilton(1992) showed that the noriialized quadrupole. defined as can be used to estimate the .} parameter. since the Isaiscr result. valid in linear theory and laree scales. brings to the constant ratio All these equations mimic the Fourier description. iu particular iu both cases the normalized quadrupole on the large scales described by linear theory is a coustaut plateau.," The multipoles of $\xi(\sigma,\pi)$ can be extracted through the projections \cite{1992ApJ...385L...5H} showed that the normalized quadrupole, defined as can be used to estimate the $\beta$ parameter, since the Kaiser result, valid in linear theory and large scales, brings to the constant ratio All these equations mimic the Fourier description, in particular in both cases the normalized quadrupole on the large scales described by linear theory is a constant plateau."
 The imltipole correlation functions are related to the corresponding power spectra by fiaFL des PO(23) here fj mdicates the spherical Bessel function of the ith order and the following ideutities preseuted in provide useful conuectious. that will prove helpful also later ou. jathsy Pau jythesy Data," The multipole correlation functions are related to the corresponding power spectra by _l(s)=i^l j_l(ks) P_l(k), here $j_l$ indicates the spherical Bessel function of the $l$ th order and the following identities presented in provide useful connections, that will prove helpful also later on, j_2(ks) P_0(k) j_4(ks) P_0(k)."
 On verv πα scales the raucom motions of the ealaxies will produce the FOCt phenomenon: an elongation of the correlation function mostly on the LOS direction., On very small scales the random motions of the galaxies will produce the FOG phenomenon: an elongation of the correlation function mostly on the LOS direction.
 The FOC effect cam be muiuicked by a convolution of the correlation function £(0.$5) with the distribution fiction either of random pairwise velocities to eive (Peebles150}: where the peculiar velocities are expressed i comoviug coordinates.," The FOG effect can be mimicked by a convolution of the correlation function $\hat{\xi}(\sigma, \pi)$ with the distribution function either of random pairwise velocities to give \citep{1980lssu.book.....P}: where the peculiar velocities are expressed in comoving coordinates."
 The convolution device is usually defined as the streaming model., The convolution device is usually defined as the streaming model.
" The random motious of particles belonging to a virialized syste depeud ou how the galaxies are selected and have been represented in the literature by au exponcutial form. ora Cassian form where e, is the pairwise peculiar velocity dispersion."," The random motions of particles belonging to a virialized system depend on how the galaxies are selected and have been represented in the literature by an exponential form, or a Gaussian form where $\sigma_{v}$ is the pairwise peculiar velocity dispersion."
 The exponeutial and Gaussian forms have proved to be eood fits of the observed data and simulations (sce.foretal.2012:Chuang&Wane 2011).," The exponential and Gaussian forms have proved to be good fits of the observed data and simulations \citep[see, for example,][]{1996MNRAS.280L..19P,1998ASSL..231..185H,2001Natur.410..169P,2008Natur.451..541G,2009MNRAS.393.1183C,2011MNRAS.415.2876B,2012MNRAS.423.3430B,2012arXiv1203.1002M,2011arXiv1102.2251C}."
 Iu this work our ain concern is on relatively large scales aud our results do not depend much on the choice of the distribution function., In this work our main concern is on relatively large scales and our results do not depend much on the choice of the distribution function.
 An important addition to the applicability of the above couvolutiou las been offered by Percival&White (2009)..., An important addition to the applicability of the above convolution has been offered by \cite{2009MNRAS.393..297P}.
" They showed that the convolution with 0, asa free parameter could be useful to describe scales niportaut for the transition to linear scales.", They showed that the convolution with $\sigma_v$ as a free parameter could be useful to describe scales important for the transition to linear scales.
 As we mentioned in the Introduction. at πια. cnough scales non lnearifies aud galaxy bias will start to spoil the simplicity of the model.," As we mentioned in the Introduction, at small enough scales non linearities and galaxy bias will start to spoil the simplicity of the model."
 How sinall these limut scales have to be depends also on the bias of the set of galaxies uuder study., How small these limit scales have to be depends also on the bias of the set of galaxies under study.
 Corrviug over the convolution to Fourier space. oue simply ects an additional factor to the IWaiscr formmlation. and what we clefine as the observed power spectrum looks like Chetty 223pPii ;," Carrying over the convolution to Fourier space, one simply gets an additional factor to the Kaiser formulation, and what we define as the observed power spectrum looks like _k)= P(k) _v _k),"
Alliance under NSF Cooperative Agreement ASCOT-10300. PACT Subaward 766.,"Alliance under NSF Cooperative Agreement ASC97-40300, PACI Subaward 766."
 Computer time was provided by NCSA and the Pittsburgh Supercomputing Center., Computer time was provided by NCSA and the Pittsburgh Supercomputing Center.
The source is a well-known low mass N-rav binary (hereafter LAINB) secu almost edec-on with au inclination angle of /~857 (7)..,The source is a well-known low mass X-ray binary (hereafter LMXB) seen almost edge-on with an inclination angle of $i \sim 85^\circ$ \citep{Hellier_89}.
 The observed average unabsorbed fiux of the source iu the 0.1.100 keV energy range is 1.5.10 ores 7s 1 (7)., The observed average unabsorbed flux of the source in the $0.1-100$ keV energy range is $\sim 1.5 \times 10^{-9}$ ergs $^{-2}$ $^{-1}$ \citep{Iaria_01}.
 This corresponds o an unabsorbed huuinostyv of ~1.2«1079 eres 1 adopting a distance of 2.5 kpe (2).," This corresponds to an unabsorbed luminosity of $\sim 1.2 \times 10^{36}$ ergs $^{-1}$, adopting a distance of 2.5 kpc \citep{Mason_82}."
". However. it has been jioted (2). that the mean ratio of the N-ray. over optical undnositv. Ly/L,,,. for is about 20. while 1e average value for LAINBs is about 500 (23.."," However, it has been noted \citep{Parmar_00} that the mean ratio of the X-ray over optical luminosity, $L_X / L_{opt}$, for is about 20, while the average value for LMXBs is about 500 \citep{vanParadijs_94}."
 This would oeuply an unobscured X-ray Iuniuositv as biel as 3«10mμη cres/s for the assumed distance of 2.5 kpe., This would imply an unobscured X-ray luminosity as high as $3 \times 10^{37}$ ergs/s for the assumed distance of 2.5 kpc.
 The apparent ow Iuninositv of the source has therefore to be ascribed to 1e high inclination of the svstem with respect to the line of sight., The apparent low luminosity of the source has therefore to be ascribed to the high inclination of the system with respect to the line of sight.
 Indeed. the ight curve of shows both dips aud eclipses of the Nay. source by the companion star.," Indeed, the light curve of shows both dips and eclipses of the X-ray source by the companion star."
 The partial nature of the eclipse indicates that the A-rav cluitting region is exteuded aud that the observe N-ravs are scattered dn oan accretion disk corona (ADC. 2y).," The partial nature of the eclipse indicates that the X-ray emitting region is extended and that the observed X-rays are scattered in an accretion disk corona (ADC, \citet{White_81}) )."
 The N-vav light curve shows clear sigus of orbita nodulation with a binary orbital period of 5.57 hi. This X-rav nodulation is probably caused by the obscuration of he ADC by the thick riu of au accretion disk., The X-ray light curve shows clear signs of orbital modulation with a binary orbital period of $5.57$ h. This X-ray modulation is probably caused by the obscuration of the ADC by the thick rim of an accretion disk.
 The orbita 21ος has been measured frou eclipse timing to iucrease eraduallv (2).., The orbital period has been measured from eclipse timing to increase gradually \citep{Hellier_90}.
 7. eave the best ephemeris of this source vefore this work., \citet{Parmar_00} gave the best ephemeris of this source before this work.
" In particeulu they found a significau oositive orbital period derivative of P4,=Ll.75«10 s/s. ? reported ou the discovery of 0.59 ταν pulsations in this source iu au RNTE observation performed in 1998.", In particular they found a significant positive orbital period derivative of $\dot P_{\rm orb} = 1.78 \times 10^{-10}$ s/s. \citet{Jonker_01} reported on the discovery of 0.59 s X-ray pulsations in this source in an RXTE observation performed in 1998.
 The timing analysis of the pulse arrival times indicates a circular orbit with an eccentricity e<0.03 cL), The timing analysis of the pulse arrival times indicates a circular orbit with an eccentricity $e < 0.03$ c.l.)
 aud an asin/ for the neutron star of 1.006(5) It-x. inplviug a mnass function of (2.0340.03)«10.2AZ...," and an $a \sin i$ for the neutron star of 1.006(5) lt-s, implying a mass function of $(2.03 \pm 0.03) \times 10^{-2}\; 
M_\odot$."
" The conrparisonu between the pulse period measured by RATE in 1996 aud L998 also indicates tha the neutron star m this svsten is spinning up at a rate of P—((2.85Eοντα12 κος, ? oeuferred a bolometric N-vav Inniinositv of about (2Ls10 eres/s asstmuing a magnetic field of (1.5)«1013 lanmss."," The comparison between the pulse period measured by RXTE in 1996 and 1998 also indicates that the neutron star in this system is spinning up at a rate of $\dot P = (-2.85 \pm 0.04) \times 10^{-12}$ s/s. \citet{Jonker_01} inferred a bolometric X-ray luminosity of about $(2-4) \times 10^{37}$ ergs/s assuming a magnetic field of $(1-5) \times 
10^{12}$ Gauss."
" From. spectroscopic measurements of the radial velocity curve ofthe companion. ? derived a lower limit to the mass of the neutron star aud to that of the companion PAar of 0.97d:0.21 and 0.53+0.05AL... respectively (1 a. oecluding uncertaiutics in the inclination). and au accurate estimate of the svsteni inclination angle, /—827.5."," From spectroscopic measurements of the radial velocity curve of the companion, \citet{Jonker_03} derived a lower limit to the mass of the neutron star and to that of the companion star of $0.97 \pm 0.24$ and $0.33 \pm 0.05\; M_\odot$, respectively (1 $\sigma$, including uncertainties in the inclination), and an accurate estimate of the system inclination angle, $i= 82^\circ.5$."
 Iu this paper we report ou the analvsis of N-rav observatious of performed from 1996 to 2008 by RATE. Newton. and Chaudra with the aim to derive eclipse arrival times auk to improve the orbital cphemeris.," In this paper we report on the analysis of X-ray observations of performed from 1996 to 2008 by RXTE, , and Chandra with the aim to derive eclipse arrival times and to improve the orbital ephemeris."
 We confirm with higher precision and over a muuch larger time span (about 31 vears) the ephemeris found by ?.., We confirm with higher precision and over a much larger time span (about 31 years) the ephemeris found by \citet{Parmar_00}.
 In particular we find that the orbital period derivative has remained coustant during the last 30 vears., In particular we find that the orbital period derivative has remained constant during the last 30 years.
 Finally we discuss the implications of a high aud positive value of the orbital period derivative on the mass transfer rate and secular evolution of this source., Finally we discuss the implications of a high and positive value of the orbital period derivative on the mass transfer rate and secular evolution of this source.
 We analysed all available X-ray observations of performed over the period from 1996 to 2008., We analysed all available X-ray observations of performed over the period from 1996 to 2008.
 Tn particular we used observations from the PCA ou board RATE performed in 1996 (P10115). 1998 (P30060). 2001 50015). 2002 (P?0036). 2002-2003 (PT0037). one observation from performed in 2001 (Obs ID: 0111230101. and 0111230201). and two Chandra observations performed in 2000 (Obs ID: 671) aud in 2008 (Obs ID: 9076 and 9858). respectively.," In particular we used observations from the PCA on board RXTE performed in 1996 (P10115), 1998 (P30060), 2001 (P50048), 2002 (P70036), 2002-2003 (P70037), one observation from performed in 2001 (Obs ID: 0111230101 and 0111230201), and two Chandra observations performed in 2000 (Obs ID: 671) and in 2008 (Obs ID: 9076 and 9858), respectively."
" The arrival tines of all eveuts were referred to the solar svsteii barveeuter. using as the best estimate for the source coordinates those derived from the 2008 Chandra observations (RA: Ls 25 16.51. DEC: -37 06 18.5. nucertaziutv: 0.67),"," The arrival times of all events were referred to the solar system barycenter, using as the best estimate for the source coordinates those derived from the 2008 Chandra observations (RA: 18 25 46.81, DEC: -37 06 18.5, uncertainty: $0.6''$ )."
 The typical eclipse duration is around 2.2 ks. which corresponds to 104 of the binary orbital period.," The typical eclipse duration is around 2.2 ks, which corresponds to $10\%$ of the binary orbital period."
 Tn order to muprove the statistics for the measure of the eclipse epochs aud to havethe possibility of fitting a complete, In order to improve the statistics for the measure of the eclipse epochs and to havethe possibility of fitting a complete
from further ümüng observations of PSR D09194-06.,from further timing observations of PSR B0919+06.
 The observations in the nearest vears allow us to find out whether there is a relationship between different phenomena observed in (his pulsar. such as a large elitch and a sequence of the slow elitches.," The observations in the nearest 5--10 years allow us to find out whether there is a relationship between different phenomena observed in this pulsar, such as a large glitch and a sequence of the slow glitches."
 Whether a large elitch has put a stop to a process of generation of slow elitelies or (is process continues to work alter a large glitch in the same moce., Whether a large glitch has put a stop to a process of generation of slow glitches or this process continues to work after a large glitch in the same mode.
 I should like to thank R. D. Dagkesamansky for useful discussion aud comments. the staff of the PRAO for their aid in earrving out the manv-vear observations of this pulsar on ihe LPÀ antenna.," I should like to thank R. D. Dagkesamansky for useful discussion and comments, the staff of the PRAO for their aid in carrying out the many-year observations of this pulsar on the LPA antenna."
 This work was supported by the European Commission 6th. Framework Program. Square Kilometre Array Design Studies (SIXADS project. contract no.," This work was supported by the European Commission 6th Framework Program, Square Kilometre Array Design Studies (SKADS project, contract no."
 011933) and the Russian Foundation for Basic Research (grant.LS 00-02-00413)., 011938) and the Russian Foundation for Basic Research (grant 09-02-00473).
We thank R. Ixennieutt ancl A. Dressler for helpful discussions about the nature of C.,We thank R. Kennicutt and A. Dressler for helpful discussions about the nature of $G^*$.
 JSB thanks the PParecles and the oof Barcelona as hosts., JSB thanks the Paredes and the of Barcelona as hosts.
 He also acknowledges Irwitfil conversations with IHIorth. WWatson. FFvubo during his stav at the Dark Cosmology. Centre in Copenhagen.," He also acknowledges fruitful conversations with Horth, Watson, Fynbo during his stay at the Dark Cosmology Centre in Copenhagen."
 We thank the referee for a careful reacing and thoughtfal comments on the submitted manuscript., We thank the referee for a careful reading and thoughtful comments on the submitted manuscript.
 The Peters Automated Infrared Imaging Telescope (PAIRITEL) is operated by (the Smithsonian. Astrophysical Observatory (SAQ) and was made possible by a grant [rom the Harvard. University Milton Fund. the camera loan from ihe University of Virginia. and the continued support of the SAO and UC Berkeley.," The Peters Automated Infrared Imaging Telescope (PAIRITEL) is operated by the Smithsonian Astrophysical Observatory (SAO) and was made possible by a grant from the Harvard University Milton Fund, the camera loan from the University of Virginia, and the continued support of the SAO and UC Berkeley."
 The PAIRITEL project and DP are further supported by NASA/Swilt Guest Investigator Grant NNGOGGII50G. We thank SSkrutskie for his continued support of the PAIRITEL project., The PAIRITEL project and DP are further supported by NASA/Swift Guest Investigator Grant NNG06GH50G. We thank Skrutskie for his continued support of the PAIRITEL project.
 Some of the data presented herein were obtained at the IxXIxeck Observatory. which is operated as a scientific partnership among the California Institute of Technology. the University of California. and NASA: the Observatory was made possible bv the generous financial support of the Wieck Foundation.," Some of the data presented herein were obtained at the Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and NASA; the Observatory was made possible by the generous financial support of the Keck Foundation."
 We wish (o extend special (hanks to (hose of Hawaiian ancestry on whose sacred mountain we are privileged to be guests., We wish to extend special thanks to those of Hawaiian ancestry on whose sacred mountain we are privileged to be guests.
where D;-—0.318(1 2)7 is the magnetic field strength equivalent to the inverse-C'ompton. microwave background raciation: D and Dc are expressed in units of nT. while my is in Cillz.,"where $B_{\rm iC}$ $z$ $^{2}$ is the magnetic field strength equivalent to the inverse-Compton microwave background radiation; $B$ and $B_{\rm iC}$ are expressed in units of nT, while $\nu_{\rm br}$ is in GHz."
 1n order to determine a value of oj. we first fitted the CL (continuous injection: Pacholezvk 1970) and JP (Jalle Perola 1973) models of radiative losses to the Dux densities of the outer lobes. and. found that the uncertainties of the fitted oj; values are large.," In order to determine a value of $\alpha_{\rm inj}$, we first fitted the CI (continuous injection; Pacholczyk 1970) and JP (Jaffe Perola 1973) models of radiative losses to the flux densities of the outer lobes, and found that the uncertainties of the fitted $\alpha_{\rm inj}$ values are large."
 Also there is no evidence for significantly different values of this parameter in the opposite lobes., Also there is no evidence for significantly different values of this parameter in the opposite lobes.
" The typical sizes of hotspots are S10 kpe (c.g. Jevakumar Saikia 2000 and references therein) which at the redshift, of 0.249 for this source corresponds to an angular size of ~3 aresec.", The typical sizes of hotspots are $\lapp$ 10 kpc (e.g. Jeyakumar Saikia 2000 and references therein) which at the redshift of 0.249 for this source corresponds to an angular size of $\sim$ 3 arcsec.
 This is similar to our GAIRY full- image at 1287. MllIz which shows no significant iotspots in either of the outer lobes., This is similar to our GMRT full-resolution image at 1287 MHz which shows no significant hotspots in either of the outer lobes.
 We have therefore oeferred to use the JP rather than the Cb model for the outer lobes., We have therefore preferred to use the JP rather than the CI model for the outer lobes.
 Also the JP model gives an overall better fit to he spectra of the dilferent. strips discussed. below., Also the JP model gives an overall better fit to the spectra of the different strips discussed below.
 The fit of the model to the Dux. densities of both the outer lobes ogether (column 9 in Table 3) is shown in Fig., The fit of the model to the flux densities of both the outer lobes together (column 9 in Table 3) is shown in Fig.
 Sa., 8a.
 This fit is used to estimate the value of ej; for the ageing analvsis of the outer structure of the source., This fit is used to estimate the value of $\alpha_{\rm inj}$ for the ageing analysis of the outer structure of the source.
 The corresponding fit. oit. with the Cl model applied to the fux densities of the inner double. is shown in Fig.," The corresponding fit, but with the CI model applied to the flux densities of the inner double, is shown in Fig."
 Sb., 8b.
 It is worth noting that roth the fitted values of oi; are similar ~0.6., It is worth noting that both the fitted values of $\alpha_{\rm inj}$ are similar $\sim0.6$.
 Next. the total-intensity maps at the frequencies of 240. 334. 605. 1287 and 4860 MlIIz were convolved to à common angular resolution of 15.2 arcesec.," Next, the total-intensity maps at the frequencies of 240, 334, 605, 1287 and 4860 MHz were convolved to a common angular resolution of 15.2 arcsec."
 Each lobe was then split into a number of strips. separated: approximately by. the resolution clement along the axis of the source. and the spectrum of each strip determined from 235 to 4860 MIL.," Each lobe was then split into a number of strips, separated approximately by the resolution element along the axis of the source, and the spectrum of each strip determined from 235 to 4860 MHz."
 Using the SYNAGE software (Alureia 1996) we searched for the best fit applying the JP model to the spectra in the six strips covering the outer. northern lobe and the other eight covering the outer. southern lobe.," Using the SYNAGE software (Murgia 1996) we searched for the best fit applying the JP model to the spectra in the six strips covering the outer, northern lobe and the other eight covering the outer, southern lobe."
" Although the resulting values of oi; for dillerent strips show significant variations. the best fits with the same injection spectrum are achieved [or e3,270.568."," Although the resulting values of $\alpha_{\rm inj}$ for different strips show significant variations, the best fits with the same injection spectrum are achieved for $\alpha_{\rm inj}$ =0.568."
 The results for a few tvpical strips are shown in Fig., The results for a few typical strips are shown in Fig.
 9., 9.
 In cases where the Dux density of a particular strip at 235 MlIZ appeared discrepant. from the overall fit. we attempted to determinethe values of ma with and without the cliserepant point ancl found no significant dillerence.," In cases where the flux density of a particular strip at 235 MHz appeared discrepant from the overall fit, we attempted to determinethe values of $\nu_{\rm br}$ with and without the discrepant point and found no significant difference."
 Phe values of ty including the lo errors for the northern ancl southern lobes are listed in Table 5., The values of $\nu_{\rm br}$ including the $\sigma$ errors for the northern and southern lobes are listed in Table 5.
 ‘To determine the age of the particles in. particular strips we have to estimate the magnetic Ποια. strength. in the corresponding strips., To determine the age of the particles in particular strips we have to estimate the magnetic field strength in the corresponding strips.
 Phe values of the equipartition energy density and the corresponding. magnetic field. Bey. are calculated) using the revised formula given. by Beck Krause (2005).," The values of the equipartition energy density and the corresponding magnetic field, $_{\rm eq}$ , are calculated using the revised formula given by Beck Krause (2005)."
 This formula (their equation (ALS)) accounts for a ratio Ko between the number densities of protons and electrons in the energy range where radiation losses are small., This formula (their equation (A18)) accounts for a ratio $_{0}$ between the number densities of protons and electrons in the energy range where radiation losses are small.
" Assuming Ko-70 implied by their equation (7) for àz o;,4,20.568. we obtain the revised magnetic Ποιά. strength. 2.4. which depends on the low-frequency spectral index à in the observed svnchrotron spectrum."," Assuming $_{0}$ =70 implied by their equation (7) for $\alpha\approx \alpha_{\rm inj}$ =0.568, we obtain the revised magnetic field strength, $B_{\rm eq}$, which depends on the low-frequency spectral index $\alpha$ in the observed synchrotron spectrum."
 The revised. Ποια. caleulatecl assuming a filling factor of unity. Qing 0.568. the Dux densities at 334 MIIz and a rectangular xxx for each strip are listed in Table 5 which is arranged as follows.," The revised field, calculated assuming a filling factor of unity, $\alpha_{\rm inj}$ =0.568, the flux densities at 334 MHz and a rectangular box for each strip are listed in Table 5 which is arranged as follows."
 Column 1:identification of the strip: column 2: he projected. distance of the strip-centre from. the radio core: column 3: the break frequency in Cllz: column 4: the reduced. x value of the fit: column 5: the revised magnetic ield in nΕν column 6: the resulting svnchrotron age of the xwticles in the given strip., Column 1:identification of the strip; column 2: the projected distance of the strip-centre from the radio core; column 3: the break frequency in GHz; column 4: the reduced $\chi^{2}$ value of the fit; column 5: the revised magnetic field in nT; column 6: the resulting synchrotron age of the particles in the given strip.
 These latter values as a function of distance are plotted in Fig., These latter values as a function of distance are plotted in Fig.
 10., 10.
 We have repeated. the calculations using the classical equipartition magnetic field (c.g. Miley. 1980) and have also plotted the variation of age with distance using these fields., We have repeated the calculations using the classical equipartition magnetic field (e.g. Miley 1980) and have also plotted the variation of age with distance using these fields.
 Within the uncertainties here is no significant dilference between the age estimates using the revised and classical equipartition magnetic fields., Within the uncertainties there is no significant difference between the age estimates using the revised and classical equipartition magnetic fields.
 As expected the svnchrotron age for both the outer obes inereases with distance from the edges of the lobes., As expected the synchrotron age for both the outer lobes increases with distance from the edges of the lobes.
 The maximum ages for the northern ancl southern lobes are ~47 and 58 Myr respectively., The maximum ages for the northern and southern lobes are $\sim$ 47 and 58 Myr respectively.
 Phe northern lobe has a higher surface brightness along most of its length. is closer to the nucleus and hence its vounger spectral age may. be due to a combination of reacceleration of particles and better confinement.," The northern lobe has a higher surface brightness along most of its length, is closer to the nucleus and hence its younger spectral age may be due to a combination of reacceleration of particles and better confinement."
 A weighted least-squares fit to the ages vields a mean separation velocity of the head from the radio-emitting plasma of 0.036€ for both the northern and southern lobes., A weighted least-squares fit to the ages yields a mean separation velocity of the head from the radio-emitting plasma of 0.036c for both the northern and southern lobes.
 Llowever. these separation velocities are referred to a region of the last acceleration of emitting particles (shock atthe end. of the lobe) which advances from the origin of. the jets. i.e. the radio core. with an advance speed. (qve.," However, these separation velocities are referred to a region of the last acceleration of emitting particles (shock atthe end of the lobe) which advances from the origin of the jets, i.e. the radio core, with an advance speed, $v_{\rm adv}$ ."
 HE the backXACRILONVIDas a SDOCO| Lolο' ey Cup. ANCL bouCnpσσaly. μις tblon απ averagee," If the backflowhas a speed of $v_{\rm bf}$ , and $v_{\rm bf}\approx v_{\rm adv}$ , then an average"
We adopt the following method for the eigenvalue selection.,We adopt the following method for the eigenvalue selection.
" Assuming that the first p eigenvalues surviving the cut are almost clean from noise, after having found the best-fit 8 and o,, the corresponding x? will have effectively p—2 degrees of freedom, in the presence of a noise close to Gaussian."," Assuming that the first $p$ eigenvalues surviving the cut are almost clean from noise, after having found the best-fit $\beta$ and $\sigma_v$ , the corresponding $\chi^2$ will have effectively $p-2$ degrees of freedom, in the presence of a noise close to Gaussian."
 Hence we choose to place the cut where X2-2 can no longer be accepted as a null hypothesis., Hence we choose to place the cut where $\chi^2_{p-2}$ can no longer be accepted as a null hypothesis.
" In practical terms, we summed the X2-2 for each of the Nun=30 realizations to form a total XN(p-2) statistic."," In practical terms, we summed the $\chi^2_{p-2}$ for each of the $N_{\mathrm{run}}=30$ realizations to form a total $\chi^2_{N_{\mathrm{run}}(p-2)}$ statistic."
" Then we considered the variable ,|2X(p-2)? that is empirically known to approximately follow a Gaussian with mean /2Nrun(p—2)—1 and unit variance if Nrun(p—2) is greater than 30, as it is practically always the case in our computations."," Then we considered the variable $\sqrt{2 \chi^2_{N_{\mathrm{run}}(p-2)}}$, that is empirically known to approximately follow a Gaussian with mean $\sqrt{2 N_{\mathrm{run}}(p-2)-1}$ and unit variance if $N_{\mathrm{run}}(p-2)$ is greater than 30, as it is practically always the case in our computations."
 We verified that a stable criterion of rejection is when the statistical significance of the test of the correctness of the null hypothesis was smaller than 5%., We verified that a stable criterion of rejection is when the statistical significance of the test of the correctness of the null hypothesis was smaller than $5\%$.
 To decide over borderline cases we added a Kolmogorov-Smirnov test with the same rejection barrier of 5%., To decide over borderline cases we added a Kolmogorov–Smirnov test with the same rejection barrier of $5\%$.
 Rejection was conservatively enacted even if only one of the two tests was passed., Rejection was conservatively enacted even if only one of the two tests was passed.
" We found that the two tests gave very similar results and that the estimated £, found by averaging over the Λι=30 best-fit values obtained by minimizing ((57)) for each simulation realization, and its error, Equationfound from the standard deviation of the best fits, were very stable for eigenvalues neighboring the cut."," We found that the two tests gave very similar results and that the estimated $\beta$, found by averaging over the $N_{\mathrm{run}}=30$ best-fit values obtained by minimizing \ref{eq:chisq}) ) for each simulation realization, and its error, found from the standard deviation of the best fits, were very stable for eigenvalues neighboring the cut."
" Concerning the range of separation distances used in the analysis, we fixed the maximum radius to smax= 80h-!Mpc, as with our box volume no statistical improvements were evident for larger separations."," Concerning the range of separation distances used in the analysis, we fixed the maximum radius to $s_{\mathrm{max}}=80\,h^{-1}\mathrm{Mpc}$ , as with our box volume no statistical improvements were evident for larger separations."
" Instead, we varied the minimal separation, that should crucially indicate to us where systematics due to non linearity are important."," Instead, we varied the minimal separation, that should crucially indicate to us where systematics due to non linearity are important."
 The best-fit maximum likelihood values of theparameters constitute marginalizedsamples., The best-fit maximum likelihood values of theparameters constitute marginalizedsamples.
" As shown in reffig:datapoints,, we found that for a minimum separation such that smin>30h-!Mpc the retrieved B was compatible at lo with the fiducial input value 084—0.85 with a marginalized statistical error of 5%."," As shown in \\ref{fig:datapoints}, we found that for a minimum separation such that $s_{\mathrm{min}}>30\,h^{-1}\mathrm{Mpc}$ the retrieved $\beta$ was compatible at $1\sigma$ with the fiducial input value $\beta^{\mathrm{fid}}=0.85$ with a marginalized statistical error of $5\%$ ."
" While for separations such that smin>35h7'Mpe, even the errors on the mean were consistent with 014,"," While for separations such that $s_{\mathrm{min}}>35\,h^{-1}\mathrm{Mpc}$, even the errors on the mean were consistent with $\beta^{\mathrm{fid}}$."
 At Smin=35h7'Mpc we found that the marginalized statistical error on 9 is 6%.," At $s_{\mathrm{min}}=35\,h^{-1}\mathrm{Mpc}$ we found that the marginalized statistical error on $\beta$ is $6\%$."
" We conclude that for dark matter boxes of volume V,=1(hGpc), we obtain reliable results for Sin>30!Mpc, since the statistical errors are large enough to provide for possible systematic ones."," We conclude that for dark matter boxes of volume $V_s=1\,\left( h^{-1}\,\mathrm{Gpc} \right)^3$, we obtain reliable results for $s_{\mathrm{min}}>30\,h^{-1}\mathrm{Mpc}$, since the statistical errors are large enough to provide for possible systematic ones."
" While for sq,>35h-!Mpc we do not see evidence for bias and we could imagine to apply our method to larger volumes with smaller statistical uncertainties."," While for $s_{\mathrm{min}}>35\,h^{-1}\mathrm{Mpc}$ we do not see evidence for bias and we could imagine to apply our method to larger volumes with smaller statistical uncertainties."
" In order to theoretically estimate the magnitude of the error on the parameter £8 given a galaxy survey configuration, we employ the Fisher matrix formalism applied to Fourier space."," In order to theoretically estimate the magnitude of the error on the parameter $\beta$ given a galaxy survey configuration, we employ the Fisher matrix formalism applied to Fourier space."
 This technique allows us to propagate the uncertainties on measured quantities into an uncertainty on f., This technique allows us to propagate the uncertainties on measured quantities into an uncertainty on $\beta$.
" We pursue the following schema: we interpret the difference D as a function depending on the monopole and quadrupole projections of the observed power spectrum, as in we compute the errors on those projections; we ((40));propagate those errors on D; finally we transfer the uncertainties on the 6 and συ parameters."," We pursue the following schema: we interpret the difference $\mathcal{D}$ as a function depending on the monopole and quadrupole projections of the observed power spectrum, as in \ref{eq:defDk}) ); we compute the errors on those projections; we propagate those errors on $\mathcal{D}$; finally we transfer the uncertainties on the $\beta$ and $\sigma_v$ parameters."
" This calculation is based on the model of Equation(29)), linear theory convolved with a velocity dispersion."," This calculation is based on the model of \ref{eq:modelPW}) ), linear theory convolved with a velocity dispersion."
 We choose the same cosmology used in the simulations., We choose the same cosmology used in the simulations.
" 'The variance of the measurement error on the observed power spectrum (Feldmanetal.1994) is ο ο where k is a specific wavenumber πμat the center of the interval Ak, V; is the survey geometric volume, and 7 is the mean number density of the tracer."," The variance of the measurement error on the observed power spectrum \citep{1994ApJ...426...23F} is _k) ]^2, where $k$ is a specific wavenumber at the center of the interval $\Delta k$, $V_s$ is the survey geometric volume, and $\overline{n}$ is the mean number density of the tracer."
" We can then buildthe covariance matrix for the multipoles of the observed power spectrum (Yamamoto 2003):: dui, APSμι) τμ Po)."," We can then buildthe covariance matrix for the multipoles of the observed power spectrum \citep{2006PASJ...58...93Y,2003ApJ...595..577Y}: : _k _k) ]^2 _k) _k)."
" Itis possible now to calculate the diagonal covariance matrix for the difference operator D of ((40)): (k) 'The needed partial apederivatives0 are APSP*(k)=—ha(B,.0 »)(62)", Itis possible now to calculate the diagonal covariance matrix for the difference operator $\mathcal{D}$ of \ref{eq:defDk}) ): (k) The needed partial derivatives are _v k)
possible effect of red noise on our analvsis by modeling instrument noise as correlated with a power spectrum ecp(—owr). where 7 is the noise coherence time.,"possible effect of red noise on our analysis by modeling instrument noise as correlated with a power spectrum $exp(-\omega \tau)$, where $\tau$ is the noise coherence time."
" Uncorrelated. (white"") noise values (0; at (mes /; are replaced by ""red noise values r; where and the sum is overaff observations. whether thev are of a given star. or not."," Uncorrelated (“white”) noise values $w_i$ at times $t_i$ are replaced by “red” noise values $r_i$ where and the sum is over observations, whether they are of a given star, or not."
 In calculating reddened instrumental noise. we use the actual epochs of the observations /;.," In calculating reddened instrumental noise, we use the actual epochs of the observations $t_i$."
 [Errors are (hen re-normalized (to keep the variance (he same., Errors are then re-normalized to keep the variance the same.
 The coherence time of WIRES instrument noiseis not known but we assume 7=20 d. Figure 9bb shows that the impact on our resulis is very small., The coherence time of HIRES instrument noiseis not known but we assume $\tau = 20$ d. Figure \ref{fig.tests}b b shows that the impact on our results is very small.
 Inferences about densities and a mass-racdius relationship depend sensilively on Aeplers estimates of planet radii. which are uncertain.," Inferences about densities and a mass-radius relationship depend sensitively on 's estimates of planet radii, which are uncertain."
 To investigate the effect of random errors. we added gaussian-cistributed errors with RAIS to theKepler radii.," To investigate the effect of random errors, we added gaussian-distributed errors with RMS to the radii."
 This modification broadens the locus of acceptable parameter values and shifts the best-fit models to slightly lower a and slightly higher jitter. but otherwise does not significantly impact our results (Figure 9cc).," This modification broadens the locus of acceptable parameter values and shifts the best-fit models to slightly lower $\alpha$ and slightly higher jitter, but otherwise does not significantly impact our results (Figure \ref{fig.tests}c c)."
 The astvoseismicallv-determined radii of manyKepler soliu-tvpe stars are systematically larger (a median of 20%)) than KIC. estimates 2011)., The astroseismically-determined radii of many solar-type stars are systematically larger (a median of ) than KIC estimates \citep{Verner2011}.
. If this were also the case for the late Ix and early M stars in our sample. the planets they. host would be larger by (he same amount. and hence less dense.," If this were also the case for the late K and early M stars in our sample, the planets they host would be larger by the same amount, and hence less dense."
 If (he effect is uniform. the inferred frequency of planets. which depends mostly on detectability. transit depth and hence the ratio of radii. is largely unchanged.," If the effect is uniform, the inferred frequency of planets, which depends mostly on detectability, transit depth and hence the ratio of radii, is largely unchanged."
 We investigated (his scenario by increasing the radii of all stars and planets by (Figure 9dd)., We investigated this scenario by increasing the radii of all stars and planets by (Figure \ref{fig.tests}d d).
 Larger planet radii and lower densities shift the locus of permissable a aud oy to only slightly lower values., Larger planet radii and lower densities shift the locus of permissable $\alpha$ and $\sigma_0$ to only slightly lower values.
 On the other hand. Muirheadetal.(2011). point ont that a stellar evolution model predicts consistently simalfer radii lor planet-hosüng M cdwarls compared to KIC estimates.," On the other hand, \citet{Muirhead2011} point out that a stellar evolution model predicts consistently radii for planet-hosting M dwarfs compared to KIC estimates."
LDG candidates are extremely difficult uuless they are bright aud have strong eenission lines. in which case spectroscopy could still be costly (Starketal.2010:Ono2011:Vanzella2011).,"LBG candidates are extremely difficult unless they are bright and have strong emission lines, in which case spectroscopy could still be costly \citep{sta10,ono11,van11}."
. Unfortunatelv most of the known LBC caudidates at +>6 are iu the Dubble Ultra Deep Field (IUDF) due to the abundance of the high-quality deep data. aud thus thev are very faint.," Unfortunately most of the known LBG candidates at $z>6$ are in the Hubble Ultra Deep Field (HUDF) due to the abundance of the high-quality deep data, and thus they are very faint."
 Even the Z79T WEC3 carly release science data (Windhorstetal.2011) cover only LO50 arcuuin? aud bright candidates are rare., Even the $HST$ WFC3 early release science data \citep{win11} cover only 40–50 $^2$ and bright candidates are rare.
 With a ereat depth over an effective area of ~8TG arci. the Subaru Deep Field (SDF:Iwashikawaetal.2001) provides a uuique field to search for relatively bright LDCis.," With a great depth over an effective area of $\sim876$ $^2$, the Subaru Deep Field \citep[SDF;][]{kas04} provides a unique field to search for relatively bright LBGs."
 The SDF project has been very successful in searching for high-redshift galaxies., The SDF project has been very successful in searching for high-redshift galaxies.
 Taking advantage of an Sau telescope and a prime-focus camera with a larec field-ofview (FOV. 31« 27). SDF has an impressive depth (27.5~28.5 AB nae) iu five broad bands BYRi’ over a survey area of one FOV.," Taking advantage of an 8-m telescope and a prime-focus camera with a large field-of-view (FOV, $34'\times27'$ ), SDF has an impressive depth $27.5\sim28.5$ AB mag) in five broad bands $BVRi'z'$ over a survey area of one FOV."
 Especially noteworthy +!is the deep observations with three narrow-baud filters. NBS16. ND921. aud ND973. corresponding to the detection of LAEs at 2~5.7. 6.5. and 7. respectively.," Especially noteworthy is the deep observations with three narrow-band filters, NB816, NB921, and NB973, corresponding to the detection of LAEs at $z\sim5.7$, 6.5, and 7, respectively."
 So far SDF has spectroscopically identified ~100 LAEs at i~5.7 Shimasakuetal.2006) and 2~6.5 (e.g.al.2006. 2011).. aud a few LAEs at z~7 (Iveetal.2006:Otaetal. 2010).," So far SDF has spectroscopically identified $\sim100$ LAEs at $z\sim5.7$ \citep[e.g.][]{shi06} and $z\sim6.5$ \citep[e.g.][]{kas06,kas11}, and a few LAEs at $z\sim7$ \citep{iye06,ota10}."
. SDF has also found a suuple of brigh LBC candidates at 2>6 (Shimasakuetal.2005) up to >>7 (Ouchietal.2009)., SDF has also found a sample of bright LBG candidates at $z>6$ \citep{shi05} up to $z>7$ \citep{ouc09}.
. Five ποιο LAEs from a lis of /-dropout objects (or LBC candidates) have already been spectroscopically confirmed at 6<2«6.1 (Nagaoetal.20041.2005. 2007).," Five strong LAEs from a list of $i'$ -dropout objects (or LBG candidates) have already been spectroscopically confirmed at $6<z<6.4$ \citep{nag04,nag05,nag07}."
. Note that the difference between LAEs aud LBCs is somewhat arbitrary aud there is no clear separation line between them. so we simply call the ealaxies found by the narrow-band technique as LAEs and those found by the dropout teclhuique as LBCs.," Note that the difference between LAEs and LBGs is somewhat arbitrary and there is no clear separation line between them, so we simply call the galaxies found by the narrow-band technique as LAEs and those found by the dropout technique as LBGs."
 A LBCis also a LAE if it is identified to have a strong eenission line., A LBGis also a LAE if it is identified to have a strong emission line.
 Tn this paper we present our decp spectroscopic observations of 276 LBC candidates in SDF using a new. ultra deep z/-band mnaaee (29 hour integration) for target selection.," In this paper we present our deep spectroscopic observations of $z>6$ LBG candidates in SDF using a new, ultra deep $z'$ -band image (29 hour integration) for target selection."
 This nuage allows us to select candidates down to :/=27 mae. roughly one mag deeper than the LBCs found by Nagaoetal.(2001.2005. 2007).," This image allows us to select candidates down to $z'=27$ mag, roughly one mag deeper than the LBGs found by \citet{nag04,nag05,nag07}."
. The structure of the paper is as follows., The structure of the paper is as follows.
 Section 2 briefly describes our selection criteria and follow-up observations of galaxy candidates., Section 2 briefly describes our selection criteria and follow-up observations of galaxy candidates.
 Section 3 presents the results of our spectroscopic observatious., Section 3 presents the results of our spectroscopic observations.
 We derive the UV-coutinmun aud LLFs iu Section 1. and sununarize the paper iu Section 5.," We derive the UV-continuum and LFs in Section 4, and summarize the paper in Section 5."
" Throughout the paper weuse a A-dominated flat cosmology with Ty=το lau s+ |. ,,= 0.3. aud O4—0.7."," Throughout the paper weuse a $\Lambda$ -dominated flat cosmology with $_0=70$ km $^{-1}$ $^{-1}$, $\Omega_{m}=0.3$ , and $\Omega_{\Lambda}=0.7$."
 All mmenitudes are on an AB svstem (Oke& 1983)., All magnitudes are on an AB system \citep{oke83}.
. We selected 2>6 galaxy candidates using the SDF broad-hand images., We selected $z>6$ galaxy candidates using the SDF broad-band images.
 The SDF public data have a depth ofB=28.15. VW= 27.11. R= 27.80.77=27.18. NBO21= 26.51. and z/=26.62 (30 detection for point sources). covering au effective area of ~S76 arcinin?.," The SDF public data have a depth of $B=28.45$, $V=27.74$ $R=27.80$ , $i'=27.43$, $\rm NB921=26.54$ , and $z'=26.62$ $3\sigma$ detection for point sources), covering an effective area of $\sim876$ $^2$."
 Nagaoetal.(2001.2005.2007) have used the public data to find brieht LBGs down to z/—26.1.," \citet{nag04,nag05,nag07} have used the public data to find bright LBGs down to $z'\sim26.1$."
 Receutlv the SDF team has obtained a much deeper + baud image with a total integration time of ~29 hours aud a depth of ~27.5 mae (Pozuauskietal.2007:Richmoud2009).," Recently the SDF team has obtained a much deeper $z'$ -band image with a total integration time of $\sim29$ hours and a depth of $\sim27.5$ mag \citep{poz07,ric09}."
. Our candidate selection was based ou this deep z baud tae together with the public data in the other four bluer broad bands., Our candidate selection was based on this deep $z'$ -band image together with the public data in the other four bluer broad bands.
 We used the traditional dropout technique. ic. our candidates are baud dropout objects.," We used the traditional dropout technique, i.e., our candidates are $i'$ -band dropout objects."
 The basic criteria are The color cut is more stringent than οτς>1.5 used by Nagaoetal.(2004.2005.2007).," The basic criteria are The color cut is more stringent than $i'-z'>1.5$ used by \citet{nag04,nag05,nag07}."
.. This is to reduce the wmmber of contaminants scattered into the selection region due to large /-baud photometric errors., This is to reduce the number of contaminants scattered into the selection region due to large $i'$ -band photometric errors.
 To remove foreground contaminants. we required that the candidates are not detected (<<20) in three broad bands BVAR.," To remove foreground contaminants, we required that the candidates are not detected $<2\sigma$ ) in three broad bands $BVR$ ."
 We also rejected possible 2~6.56 LAE candidates which are relatively bright in the NB921 baud with respect to their z-band plotometry(:’ΡΟΣΙ<1). since these candidates were being targeted iu another progranmi (Nashikwwactal.2011).," We also rejected possible $z\sim6.56$ LAE candidates which are relatively bright in the NB921 band with respect to their $z$ -band $z'-{\rm NB921}<1$ ), since these candidates were being targeted in another program \citep{kas11}."
. We obtained L99 dropouts in the whole SDF field., We obtained 499 $i'$ -dropouts in the whole SDF field.
 We them visually inspected each candidate. aud removed those with any possible detections in auv of the BYR bands aud those that were likely spurious detections (6.8. blended with bright stars).," We then visually inspected each candidate, and removed those with any possible detections in any of the $BVR$ bands and those that were likely spurious detections (e.g. blended with bright stars)."
 The /-baud image is deep enouehi in most cases of our selection., The $i'$ -band image is deep enough in most cases of our selection.
 In the extreme case of :/=27 iu which the color cut deteriuines 7>28.7. we visually inspected the candidates aud simply required that the candidates should uot be detected im the ας Gu addition to the BYR bauds).," In the extreme case of $z'=27$ in which the color cut determines $i'>28.7$, we visually inspected the candidates and simply required that the candidates should not be detected in the $i'$ -band (in addition to the $BVR$ bands)."
 We generated an //228.7 yolut source (alinost all known :=>6 SDF ealaxics are yolut sources in SDF mages) and put it iu a nunuber of blank regious of the /-band image., We generated an $i'=28.7$ point source (almost all known $z\ge6$ SDF galaxies are point sources in SDF images) and put it in a number of blank regions of the $i'$ -band image.
 We cut out these reeions aud mixed them with other blank regious that do rot have the simulated point source., We cut out these regions and mixed them with other blank regions that do not have the simulated point source.
 As a result. more han of the reeious with the //=28.7 source were visually identified. so our visual iuspection is reliable iu lis case.," As a result, more than of the regions with the $i'=28.7$ source were visually identified, so our visual inspection is reliable in this case."
 Finally. 196 promising candidates survived for our follow-up spectroscopy.," Finally, 196 promising candidates survived for our follow-up spectroscopy."
 The follow-up spectroscopic observations were cared out with DEIMOS (Faberetal.2003) ou the Weel Il telescope on 2528 April 2009., The follow-up spectroscopic observations were carried out with DEIMOS \citep{fab03} on the Keck II telescope on 25–28 April 2009.
" The typical sccine was 1"".", The typical seeing was $1\arcsec$.
 A total of 79 galaxy candidates frou the above were covered by six masks. but oulv 73 of them were observed due to slit conflict.," A total of 79 galaxy candidates from the above were covered by six masks, but only 73 of them were observed due to slit conflict."
" There were roughly 100 slitlets per mask: most ofthe slitlets were assigned to the targets of Ikashikwvaetal.(2011) aud various secondary targets,", There were roughly 100 slitlets per mask; most of the slitlets were assigned to the targets of \citet{kas11} and various secondary targets.
 Wo used the 830 lines + erating with the order blocking filter OG550., We used the 830 lines $^{-1}$ grating with the order blocking filter OG550.
 The wavelengthcoverageis roughly from 6000 to 10.000 A.," The wavelengthcoverageis roughly from 6000 to 10,000 ."
. Witha 1 slit width. the resolving power was  3600.," With a $1\arcsec$ slit width, the resolving power was $\sim3600$ ."
 The total integration time perniask was 3 hours.broken into individual exposures of 20 or 30 min.," The total integration time permask was $\sim3$ hours,broken into individual exposures of 20 or 30 min."
 We alsoobserved a spectrophotometric standard star DD|28401211 in lone-slit mode with the sale erating and order blocking filter., We alsoobserved a spectrophotometric standard star BD+28d4211 in long-slit mode with the same grating and order blocking filter.
 The data were reduced with the DEEP2 DEIMOS data pipeline based ou the IDL package”., The data were reduced with the DEEP2 DEIMOS data pipeline based on the IDL .
.. The DEIMOS flexure colupensation svsteni (FCS) failed iu the begiunius of, The DEIMOS flexure compensation system (FCS) failed in the beginning of
mode (sequence C).,mode ('sequence C').
 Sequence D can thus not be associated with higher harmonics. which have periods (sequences A and B)," Sequence D can thus not be associated with higher harmonics, which have periods ('sequences A' and 'B')."
 A possible relation between Wood's sequence D and the Roche limit in binary systems (via ellipsoidal variations or dust obscuration events) was originally proposed by ? and ?.. and more recently again by 2.. ? and ?..," A possible relation between Wood's sequence D and the Roche limit in binary systems (via ellipsoidal variations or dust obscuration events) was originally proposed by \citet{Wood-1999} and \citet{Wood-2000}, and more recently again by \citet{Soszynski-2004b}, \citet{Derekas-2006}
 and \citet{Soszynski-2007}."
 Fig., Fig.
 7 is à variant of Fig., \ref{Fig:MbolP} is a variant of Fig.
 + that makes it easy to compare our data with the period — luminosity diagram of LPVs in the LMC (??)..," \ref{Fig:radius} that makes it easy to compare our data with the period – luminosity diagram of LPVs in the LMC \citep{Wood-1999,Wood-2000}."
 The ordinate axis of Fig., The ordinate axis of Fig.
 7 corresponds to the A magnitude that our M giants would have if they were at the distance of the LMC. re. ΓΕΛΙΟ=My|15.50. where the ? LMC distance modulus has been adopted.," \ref{Fig:MbolP} corresponds to the $K$ magnitude that our M giants would have if they were at the distance of the LMC, i.e., $K
({\rm LMC}) = M_K + 18.50$, where the \citet{McNamara-2007} LMC distance modulus has been adopted."
 It is quite interesting to notice that Wood's sequence D does match the upper envelope of the region occupied by the galactic binary M giants., It is quite interesting to notice that Wood's sequence D does match the upper envelope of the region occupied by the galactic binary M giants.
 Our finding of a clear relationship between Wood's D sequence and the Roche limit in binary systems involving M giants supports the similar suggestion made by ? and ?.., Our finding of a clear relationship between Wood's D sequence and the Roche limit in binary systems involving M giants supports the similar suggestion made by \citet{Soszynski-2004b} and \citet{Soszynski-2007}.
 A striking difference between K and M giants apparent on Fig., A striking difference between K and M giants apparent on Fig.
 | is thegiants., \ref{Fig:elogP_M} is the.
 The short-period circular systems observed among K giants result from tidal effects which circularise the orbit when the giant star is close to filling its Roche lobe (e.g..?).," The short-period circular systems observed among K giants result from tidal effects which circularise the orbit when the giant star is close to filling its Roche lobe \citep[e.g., ][]{North-92}."
 The difference between K and M giants Is surprising. since both stellar families involve stars with deep convective envelopes which should react similarly to tidal effects.," The difference between K and M giants is surprising, since both stellar families involve stars with deep convective envelopes which should react similarly to tidal effects."
 M giants. however. have shorter lifetimes than K giants. because the former suffer from à much more severe wind mass loss. and this difference offers perhaps a clue to account for the differences observed at short periods in their (c.logP) diagrams.," M giants, however, have shorter lifetimes than K giants, because the former suffer from a much more severe wind mass loss, and this difference offers perhaps a clue to account for the differences observed at short periods in their $(e - \log P)$ diagrams."
 Tidal forces may not have enough time to efficiently operate in the case of M giants., Tidal forces may not have enough time to efficiently operate in the case of M giants.
 Indeed. the many circular systems observed among post-AGB stars seem to be the circular population missing among the M giants.," Indeed, the many circular systems observed among post-AGB stars seem to be the circular population missing among the M giants."
 This hints at mass loss and tidal effects operating on similar time scales: shortly after the system has been circularised. the envelope is lost and the primary star no longer looks as an M giant but rather as a post-AGB star.," This hints at mass loss and tidal effects operating on similar time scales: shortly after the system has been circularised, the envelope is lost and the primary star no longer looks as an M giant but rather as a post-AGB star."
 The very existence of a system like SS Lep does lend support to the above suggestion., The very existence of a system like SS Lep does lend support to the above suggestion.
 In Fig., In Fig.
 8 investigating a possible correlation between dust excess and position of the binary M giants in the (c.logP) diagram. SS Lep. having a large A|12| excess. appears as the big circle along the tidal boundary.," \ref{Fig:elogP_K12} investigating a possible correlation between dust excess and position of the binary M giants in the $(e - \log P)$ diagram, SS Lep, having a large $K - [12]$ excess, appears as the big circle along the tidal boundary."
 Similarly. it is interesting to note that circular orbits are common among red symbiotics as well. albeit with somewhat longer periods.," Similarly, it is interesting to note that circular orbits are common among red symbiotics as well, albeit with somewhat longer periods."
" The implications of this result actually depend on whether the red symbiotics are pre-mass-transfer systems δι, with a main-sequence companion) or post-mass-transfer"," The implications of this result actually depend on whether the red symbiotics are pre-mass-transfer systems (i.e., with a main-sequence companion) or post-mass-transfer"
occur in long streams and spheroidal clouds. aud are found in large complexes aud as stall isolated clouds.,"occur in long streams and spheroidal clouds, and are found in large complexes and as small isolated clouds."
 The neutral hydrogen IIVCs cover nearly of the sky (Wakker&vanWoerden1997:Lockmanetal. 2002).," The neutral hydrogen HVCs cover nearly of the sky \citep{wvw97, loc02}."
. In contrast. the ionized clouds cover as much as of the sky (Shulletal. 2009).," In contrast, the ionized clouds cover as much as of the sky \citep{shull09}."
. In total. these clouds make up as much as of the total IIT mass of the Milky Wav (Walder&vanWoerden1997).," In total, these clouds make up as much as of the total HI mass of the Milky Way \citep{wvw97}."
. Possible analogs o the Milkv Way clouds have been found around nearby galaxies iucludiug M31 (Thilkeretal.2001)... M33. (Crossietal.2008).. and others (vauderΠιτ&Sancisi1988:Milleretal.2009:Tess 2009).," Possible analogs to the Milky Way clouds have been found around nearby galaxies including M31 \citep{thilker04}, M33 \citep{grossi08}, and others \citep{vdH88, miller09, hess09}."
. The best-studied external TT cloud svsteni in an isolated ealaxy is that of AIBL., The best-studied external HI cloud system in an isolated galaxy is that of M31.
 Around the galaxy. Westimeicretal.(2008) found a population of III clouds with oxoperties consistent with those of Milkv Way VCs.," Around the galaxy, \citet{west08} found a population of HI clouds with properties consistent with those of Milky Way HVCs."
 The N33] clouds have typical TIT masses of 10 AL... and the svstem extends 50 kpe from he AL31 disk.," The M31 clouds have typical HI masses of $^5$ $_{\odot}$, and the system extends 50 kpc from the M31 disk."
 There are severa propose theories for the source of III clouds., There are several proposed theories for the source of HI clouds.
 Droadlv. they consist of wo classes: those that invoke a galactic plane origin and rely on secular dynamics to remove he eas from the disk. and hose thatinvoke an extraplanar origin aud tie the dynamics to aree scale structure.," Broadly, they consist of two classes: those that invoke a galactic plane origin and rely on secular dynamics to remove the gas from the disk, and those thatinvoke an extraplanar origin and tie the dynamics to large scale structure."
 Table 1 lists the expected xoperties of II clouds in cach case. which we describe below.," Table \ref{millertable} lists the expected properties of HI clouds in each case, which we describe below."
 Note that the properties of cold-accretion ogenerate clouds are not wellconstrained by current simulations. particularly in terius of their velocities ancl sizes.," Note that the properties of cold-accretion generated clouds are not well-constrained by current simulations, particularly in terms of their velocities and sizes."
 Iu a galactic fountain. gas is blown out of the disk by a supernova outburst. after which it cools. condenses and rains back outo the disk (Shapiro&Field1976:Bregman 1980).," In a galactic fountain, gas is blown out of the disk by a supernova outburst, after which it cools, condenses and rains back onto the disk \citep{shap76, bre80}."
. The galactic fountain model for ος is supported by the existence of a hot (109 IK) ealactic corona with a scale Leight of a few kpc. detected iu x-rays around galaxies (e.9.. Stricklandetal. (2001))).," The galactic fountain model for HVCs is supported by the existence of a hot $^{6}$ K) galactic corona with a scale height of a few kpc, detected in x-rays around galaxies (e.g., \citet{strick04}) )."
 This corona is supplied width gas bv supernovae explosions frou he disk. and radiative cooling causes the formation of III louds through thermal instabilities (Shapiro&Field1976:Breeman 1980).," This corona is supplied with gas by supernovae explosions from the disk, and radiative cooling causes the formation of HI clouds through thermal instabilities \citep{shap76, bre80}."
 Although ealactic fountains iuost certainly exist af some level iu all star-forming galaxies. not all observed TII clouds are produced this way (Frateruali&Binneyx 2006).," Although galactic fountains most certainly exist at some level in all star-forming galaxies, not all observed HI clouds are produced this way \citep{frat06}."
. Iu particular. the galactic fountain model fails to explai1i III clouds furtier than a few kpc roni the disk of a galaxy. bevoud the extent of he hot galactic corona.," In particular, the galactic fountain model fails to explain HI clouds further than a few kpc from the disk of a galaxy, beyond the extent of the hot galactic corona."
 Our observations are not sensitive to galactic fountain-egencrated IIT clouds. as we are Πίος by both angular resolution aud nass sensitivity.," Our observations are not sensitive to galactic fountain-generated HI clouds, as we are limited by both angular resolution and mass sensitivity."
 Galaxy interactions may egencrate TT clouds hrough tidal stripping (Putinanctal.2003:Clhyuowethetal.2008:Sancisi 2008).," Galaxy interactions may generate HI clouds through tidal stripping \citep{put03, chy08, san08}."
. Tn the Milky Way. the Magellanic Stream is a wine example of this phenomenonhere gas was stripped out of a satellite galaxy durius a minor nerecr.," In the Milky Way, the Magellanic Stream is a prime example of this phenomenon–here gas was stripped out of a satellite galaxy during a minor merger."
 Another possiblesource of IIE clouds far yon galaxy disks is leftover fragnieuts of tidal ails., Another possiblesource of HI clouds far from galaxy disks is leftover fragments of tidal tails.
" HI clouds may be tracers of a population of 10*ΛΙ, dark matter halos (svavtsovetal.200 1).", HI clouds may be tracers of a population of $10^7-10^{10} M_\odot$ dark matter halos \citep{kra04}.
. Cosmological simulations based upou the accepter paradigm of ACDM (Cold Dark Matter) cosmology. such as the Via Lactea IE simulation of Diciuaudetal.(2005)... consistently predict a liel deerce of dark matter substructure.," Cosmological simulations based upon the accepted paradigm of $\Lambda$ CDM (Cold Dark Matter) cosmology, such as the Via Lactea II simulation of \citet{die08}, consistently predict a high degree of dark matter substructure."
 This aspect of simulations is not welbiuatehed to observations ≯∪↥⋅↕∐↴∖↴↑⋜∐⊔⊳↸∖∙↑∐↸∖ Allkv Wav is observed to lavo a actor of at least [ fewer satellites (in he form of dwarf Oogalaxies) than predicted. bv siauulations. despite sophisticated treatinent of xuwvonic heatius. cooling. aud feedback im low nass halos (Simon&Coha2007).," This aspect of simulations is not well-matched to observations--for instance, the Milky Way is observed to have a factor of at least 4 fewer satellites (in the form of dwarf galaxies) than predicted by simulations, despite sophisticated treatment of baryonic heating, cooling, and feedback in low mass halos \citep{sim07}."
. One possible solution to this “missing satellites problemi could e TIT clouds. if such objects are tracers of dark uatter halos.," One possible solution to this “missing satellites problem"" could be HI clouds, if such objects are tracers of dark matter halos."
 However. there are still not enough clouds observed to supply the predicted number of satellites. and the clouds that ire observed do not have the expected spatia or kinematic distribution of dark matter halos (Chnyuoweth 2011).," However, there are still not enough clouds observed to supply the predicted number of satellites, and the clouds that are observed do not have the expected spatial or kinematic distribution of dark matter halos \citep{chy09,chy11}."
. Nunnerical siauulatious show that eas iav arrive to galaxies via accretion along dark matter fibuneuts (Nervesetal.2005)., Numerical simulations show that gas may arrive to galaxies via accretion along dark matter filaments \citep{keres05}.
".. Gas accretion along fibuneuts appears to happen in two niodes. a ""hot? CE ~ 10° K) and a ceold CP < 107 KO) node."," Gas accretion along filaments appears to happen in two modes, a “hot"" (T $\sim$ $^6$ K) and a “cold"" (T $<$ $^5$ K) mode."
 The cold iode of accretion. where gas ds not shock heated to the halo virial temperature as it falls in. is of primary relevance to III studies. since some cold-anode accretion gas nw appear as III (Ixeres&Teruquis 2009)..," The cold mode of accretion, where gas is not shock heated to the halo virial temperature as it falls in, is of primary relevance to HI studies, since some cold-mode accretion gas may appear as HI \citep{keres09}. ."
 TID clouds could be a result of iustabilitios iu a hot halo that causes the eas to cool iu clumps aud fall toward the ealactic midplane (Maller&Bullock2001: 2009)..," HI clouds could be a result of instabilities in a hot halo that causes the gas to cool in clumps and fall toward the galactic midplane \citep{mal04,keres09}. ."
 Tu this case. HIE clouds," In this case, HI clouds"
nature of the emission [from the two 22-CGllIz components leads us to conclude that the 22-CGllIz components are the stellar winds associated with the two stellar components imaged with the HIST by Niemela et al. (,nature of the emission from the two 22-GHz components leads us to conclude that the 22-GHz components are the stellar winds associated with the two stellar components imaged with the HST by Niemela et al. (
1988).,1988).
 This is the first time that the stellar wind of the companion in a WR binary has been spatially resolved., This is the first time that the stellar wind of the companion in a WR binary has been spatially resolved.
 In Paper Lowe concluded that ος was the thermal emission from the Westar wind., In Paper I we concluded that $_5$ was the thermal emission from the WR-star wind.
 Laceecd. if we take the mean Εαν value for ος from our two epochs of AUERLIN observations. the spectral index between 22 and 5 Cllz for he southern component ijs |0.82+0.1. consistent with hose observed in the stellar winds of other WC-tvpe WR stars (e.g. Williams 1996).," Indeed, if we take the mean flux value for $_5$ from our two epochs of MERLIN observations, the spectral index between 22 and 5 GHz for the southern component is $+0.82\pm0.14$, consistent with those observed in the stellar winds of other WC-type WR stars (e.g. Williams 1996)."
" We estimate the diameter of S5 to ο.190 mas from the diameter of the Soo. since angular size xpUU ""TN fora~OS."," We estimate the diameter of $_5$ to be $\sim190$ mas from the diameter of the $_{22}$, since angular size $\propto\nu^{-0.6}$ for $\alpha\sim0.8$."
 This Wsis approximately. four⋅ times. larger iun that given in Paper EL. However. we feel the diameter oesented here is a more reliable estimate.," This is approximately four times larger than that given in Paper I. However, we feel the diameter presented here is a more reliable estimate."
 Aclelitionally. in Paper I we identified Nz as non-thermal emission [rom a wind-wind collision region.," Additionally, in Paper 1 we identified $_5$ as non-thermal emission from a wind-wind collision region."
 HE we overlay the 22-CGllIz and 5-Cillz data assuming two southern components originate in the WI star wind (see Figure 4) we can see that the relative separation of the components supports such a model. where the wind-collision region must fall between the two stars.," If we overlay the 22-GHz and 5-GHz data assuming two southern components originate in the WR star wind (see Figure 4) we can see that the relative separation of the components supports such a model, where the wind-collision region must fall between the two stars."
" For a steady state. smooth. fully ionized stellar wind having a radial. r7 3.ion density. clistribution.. the free-LfreeB racio.(ux 5, is related to the stellar-wind density ic. Mv by where v is the frequency in Lz. d is the distance in kpc. Al is the mass-loss rate in M. vt. ο the terminal velocity of the wind in km s.|: &. Z. pp and go, are respectively. the number of electrons per ion. the mean charge per ion. the mean atomic weight and the Gaunt [ree-[ree factor. a function of electron. temperature and. frequency."," For a steady state, smooth, fully ionized stellar wind having a radial $r^{-2}$ ion density distribution, the free-free radioflux $S_\nu$ is related to the stellar-wind density i.e. $\dot M/v$ by where $\nu$ is the frequency in Hz, $d$ is the distance in kpc, $\dot M$ is the mass-loss rate in $_\odot$ $^{-1}$, $v$ the terminal velocity of the wind in km $^{-1}$; $\gamma$, $Z$, $\mu$ and $g_{\nu,T_e}$ are respectively, the number of electrons per ion, the mean charge per ion, the mean atomic weight and the Gaunt free-free factor, a function of electron temperature and frequency."
 Lt follows [rom (1)) that ‘Thus. the measurement of radio emission from the two stellar wind components in the WIUIIJ6 system. leads to he density ratio of the two winds.," It follows from \ref{eqn:swf}) ) that Thus, the measurement of radio emission from the two stellar wind components in the 146 system leads to the density ratio of the two winds."
 Lo the stellar winds are clumped rather than smooth. we can allow for this by replacing Al in the above with GMVfF). where f is the wind illine factor. assumed to be constant over the radio-emitting region.," If the stellar winds are clumped rather than smooth, we can allow for this by replacing ${\dot M}$ in the above with $({\dot M}/\surd f)$, where $f$ is the wind filling factor, assumed to be constant over the radio-emitting region."
 In the case of the collision of two spherical winds at erminal velocity. the contact discontinuity between the two winds intersects the line of centres between the stars at the »oint of momentum balance.," In the case of the collision of two spherical winds at terminal velocity, the contact discontinuity between the two winds intersects the line of centres between the stars at the point of momentum balance."
 LE the projected: separation of the WIt and. OB star is Dcos;. and that of the OB companion from the non-thermal region is ropcos. we can hen write where 5 is the ratio of W1t and. OB-companion wind momenta. CArogCUew.," If the projected separation of the WR and OB star is $D \cos i$, and that of the OB companion from the non-thermal region is $r_{\rm OB}\cos i$, we can then write where $\eta$ is the ratio of WR and OB-companion wind momenta, $(\dot M v)_{\rm OB}/(\dot M v)_{\rm WR}$."
 The wind-collision ecometry and equation 3 would also be allected by clumping. but this is bevond the scope of the present study.," The wind-collision geometry and equation \ref{eqn:rdr} would also be affected by clumping, but this is beyond the scope of the present study."
 ὃν defining the ratio of the OB star ancl Westar wind densities. (MMop(AlDn. as € then Ixnowing Alyanc eywg we can now uniquely determine Mog and cop that satisfy simultaneously both € and y," By defining the ratio of the OB star and WR-star wind densities, $(\dot M / v)_{\rm OB}/ (\dot M /v)_{\rm WR}$, as $\xi$, then Knowing $\dot M_{\rm WR}$ and $v_{\rm WR}$ we can now uniquely determine $\dot M_{\rm OB}$ and $v_{\rm OB}$ that satisfy simultaneously both $\xi$ and $\eta$."
 An attractive property of these ratios is that they are independent of distance. tvpically a very uncertain parameter for WR stars and. particularly for 1110.," An attractive property of these ratios is that they are independent of distance, typically a very uncertain parameter for WR stars and particularly for 146."
 For the OB companion we will assume that hydrogen ancl helium. are. respectively. singly ancl doubly ionizect. leading to values ο=L1.Z=1.15. pe=1.34 (Lamers Leitherer 1993) and Z;~101 EK. Taking the values o[ 5=L15.ZL2. s=529. T;=5000 Ix from Willis et. al. (," For the OB companion we will assume that hydrogen and helium are, respectively, singly and doubly ionized, leading to values $\gamma=1.1$,$Z=1.15$, $\mu=1.34$ (Lamers Leitherer 1993) and $T_e\sim10^4$ K. Taking the values of $\gamma=1.15, Z=1.2$, $\mu=5.29$, $T_e=8\,000$ K from Willis et al. ("
1997) for the WR star. and that the I[uxes olf No» and Ss» are those of the OD star and the WC star respectively. implies that €=0.36+0.19.,"1997) for the WR star, and that the fluxes of $_{22}$ and $_{22}$ are those of the OB star and the WC star respectively, implies that $\xi=0.36\pm0.19$."
 From Table 2. D is 16248 mas and rog is 40d:9 mas. so equation 3. gives 7—0.11£0.03.," From Table 2, $D$ is $162\pm8$ mas and $r_{OB}$ is $40\pm9$ mas, so equation \ref{eqn:rdr} gives $\eta=0.11\pm0.03$."
 Phus. the ratios of mass-loss rates and wind velocities are 0.20£0.06 and 0.56+0.17 respectively.," Thus, the ratios of mass-loss rates and wind velocities are $0.20\pm0.06$ and $0.56\pm0.17$ respectively."
 The largest uncertainty in these ratios arises [rom £., The largest uncertainty in these ratios arises from $\xi$.
 Though this requires knowledge of the relative metallicity and ionization structure within the two winds. the values of Z and ~ are closely the same ancl cllectively cancel.," Though this requires knowledge of the relative metallicity and ionization structure within the two winds, the values of $Z$ and $\gamma$ are closely the same and effectively cancel."
 On the other hand. the mean molecular weights of the two winds are quite cillerent and contributes a factor 2 to the ratio.," On the other hand, the mean molecular weights of the two winds are quite different and contributes a factor $\sim 2$ to the ratio."
 The relative uncertainty in the observed Duxes provides the bulk of the uncertainty in £., The relative uncertainty in the observed fluxes provides the bulk of the uncertainty in $\xi$.
 From the cecduced velocity ratio and the terminal wind velocity measured for the WC6 star (2900 km +. Benens Williams 1994). we derive a terminal velocity of the OB wind of 1600£480 km ντ.," From the deduced velocity ratio and the terminal wind velocity measured for the WC6 star $2900 $ km $^{-1}$, Eenens Williams 1994), we derive a terminal velocity of the OB wind of $1600\pm480$ km $^{-1}$."
 This is consistent. with those determined. for late O-tvpe stars of any Iuminosity class (Prinja. Barlow Llowarth 1990).," This is consistent with those determined for late O-type stars of any luminosity class (Prinja, Barlow Howarth 1990)."
 Lowever. the deduced: ratio (Q.19) of niws-loss rates implies a very high mass-loss rate for the OB star. irrespective of the distance to 1140.," However, the deduced ratio (0.19) of mass-loss rates implies a very high mass-loss rate for the OB star, irrespective of the distance to 146."
" For example. if the WCG star has a miass-loss rate comparable to the average rate derived. from radio or from. ""Standard Model analyses of optical emission lines (4.10.7 M. yf. Willis 1999). that of the OD star would be 2810Ὁ Moy ἂν "," For example, if the WC6 star has a mass-loss rate comparable to the average rate derived from radio or from “Standard Model” analyses of optical emission lines $4\times10^{-5}$ $_\odot$ $^{-1}$, Willis 1999), that of the OB star would be $\simeq 8\times10^{-6}$ $_\odot $ $^{-1}$ ."
This is comparable to that determined. for. the Osf supergiant 1151804 (Biegine. Abbott Churchwell 1989. Crowther Bohannan 1997) ancl almost 50. greater than the mass-loss rates typical of main-sequence OS stars (~17-10 5M. Lo Howarth Prinja 1989).," This is comparable to that determined for the O8f supergiant 151804 (Bieging, Abbott Churchwell 1989, Crowther Bohannan 1997) and almost $50\times$ greater than the mass-loss rates typical of main-sequence O8 stars $\sim 1.7 \times 10^{-7}$ $_\odot$ $^{-1}$ Howarth Prinja 1989)."
 ‘Phis result still holds if the true mass-loss rates of WIR stars are lower than the value cited owing to clumping since it is really the, This result still holds if the true mass-loss rates of WR stars are lower than the value cited owing to clumping since it is really the
The evolution of cluster galaxies and their star-formation rates have been studied using several different approaches in the last few decades.,The evolution of cluster galaxies and their star-formation rates have been studied using several different approaches in the last few decades.
 Optical surveys have shown clear correlations between galaxy colours and local galaxy density or cluster-centric radius (222)).," Optical surveys have shown clear correlations between galaxy colours and local galaxy density or cluster-centric radius \citealt{Dressler80, Dressler97, Kodama01}) )."
 Spectroscopic observations have consistently identitied rends in the star-formation activity of cluster galaxies. both as a function of cluster-centric distance (e.g. 2: 2 and references qerein) and at different redshifts { ," Spectroscopic observations have consistently identified trends in the star-formation activity of cluster galaxies, both as a function of cluster-centric distance (e.g. \citealt*{Verdugo08}; \citealt{Braglia09} and references therein) and at different redshifts \citep{Poggianti06, Poggianti09}. ."
Variation of the star-ormation rate (SFR) and correlation with the local environment 145 also been investigated at different mass scales. from groups o large superclusters (2).. and also in relation to local large-scale Hlamentary structures (2:: 2)).," Variation of the star-formation rate (SFR) and correlation with the local environment has also been investigated at different mass scales, from groups \citep{Wilman08} to large superclusters \citep{Porter07}, and also in relation to local large-scale filamentary structures \citealt{Braglia07}; \citealt{Porter08}) )."
 Observations with/RAS and provided a way to investigate ye nature. of dust and to correlate the SFRs of cluster galaxies with their dust content. albeit mostly covering the spectral regions dominated by warm (240 K) dust.," Observations with and provided a way to investigate the nature of dust and to correlate the SFRs of cluster galaxies with their dust content, albeit mostly covering the spectral regions dominated by warm $> 40$ K) dust."
 While part of these studies was aimed at detecting diffuse emission from warm intracluster dust (e.g. 2: 2z 2z 29. several results were also obtained with observations of individual cluster members in several clusters.," While part of these studies was aimed at detecting diffuse emission from warm intracluster dust (e.g. \citealt{Stickel98}; \citealt{Stickel02}; \citealt{Montier05}; \citealt{Giard08}) ), several results were also obtained with observations of individual cluster members in several clusters."
 ? used combined/RAS. IRAM and JCMT observations to detect CO line emission from molecular gas in the central galaxies of a sample of 16 cooling core galaxies.," \citet{Edge01} used combined, IRAM and JCMT observations to detect CO line emission from molecular gas in the central galaxies of a sample of 16 cooling core galaxies."
 Tuffs et al. (, Tuffs et al. (
2002) and Popescu et al. (,2002) and Popescu et al. (
002a: 2002b) observed alarge sample of galaxies in Virgo. finding a dependence in the dust content of galaxies with Hubble type.,"2002a; 2002b) observed alarge sample of galaxies in Virgo, finding a dependence in the dust content of galaxies with Hubble type."
 ?.found that dust luminosity and mass depend on galaxy geometry and shape as well as stellar mass., \citet{Pierini03} found that dust luminosity and mass depend on galaxy geometry and shape as well as stellar mass.
 Several recent 24 observations with Spizer-MIPS have detected dusty star-forming galaxies in intermediate- to high-z clusters.," Several recent $24\,$ observations with -MIPS have detected dusty star-forming galaxies in intermediate- to $z$ clusters."
 ? find an increase of the total SFR in clusters with increasing redshift fromSpitzer observations. although with large scatter.," \citet{Geach06} find an increase of the total SFR in clusters with increasing redshift from observations, although with large scatter."
 ? investigate the IR properties and the mid-IR luminosity function of cluster galaxies in a higher redshift cluster at 2= 0.83. confirming the presence of evolution in the star-formation rate of cluster galaxies.," \citet{Bai07} investigate the IR properties and the mid-IR luminosity function of cluster galaxies in a higher redshift cluster at $z = $ 0.83, confirming the presence of evolution in the star-formation rate of cluster galaxies."
 ? identify consistent overdensities of 24.um sources along two filaments between the clusters Abell 1770 and Abell 1763 (2= 0.23) with respect to the surrounding field.," \citet{Fadda08} identify consistent overdensities of $24\,$ sources along two filaments between the clusters Abell 1770 and Abell 1763 $z = $ 0.23) with respect to the surrounding field."
 Similar to ?.. 2?) confirm an excess of Εμ. sources in the cluster Abell 1758 at 2= 0.28.," Similar to \citet{Bai07}, \citet{Haines09a} confirm an excess of $24\,$ sources in the cluster Abell 1758 at $z = $ 0.28."
 2? also compare the 24pm luminous members of a cluster. a supergroup and the field. concluding that the mid-IR inferred SFR is higher in the intermediate environment of the groups than in the field. while it is globally lower in the cluster.," \citet{Tran09} also compare the $24\,$ luminous members of a cluster, a supergroup and the field, concluding that the mid-IR inferred SFR is higher in the intermediate environment of the groups than in the field, while it is globally lower in the cluster."
 Local dependence of the density of sources in clusters is investigated in the LoCuSS survey by ?.. who find a global decrease of star-forming systems with decreasing cluster-centric radius.," Local dependence of the density of sources in clusters is investigated in the LoCuSS survey by \citet{Haines09b}, who find a global decrease of star-forming systems with decreasing cluster-centric radius."
 Recently. ? have used the AZTEC camera to observe a field centred on the cluster MSO451.6—0305 at >=0.54. identifying two luminous infrared galaxies (LIRG) with a combined SER of 100L," Recently, \citet{Wardlow10} have used the AzTEC camera to observe a field centred on the cluster MS0451.6–0305 at $z = 0.54$, identifying two luminous infrared galaxies (LIRG) with a combined SFR of 100."
2 They suggest that. if these are indeed cluster members. they can be examples of a population. of galaxies undergoing transformation to the red sequence through interaction with the cluster environment.," They suggest that, if these are indeed cluster members, they can be examples of a population of galaxies undergoing transformation to the red sequence through interaction with the cluster environment."
 All the studies presented have investigated the star-formation activity of cluster galaxies either in the mid-IR or at millimetre wavelengths., All the studies presented have investigated the star-formation activity of cluster galaxies either in the mid-IR or at millimetre wavelengths.
 However. a complete characterization of the output of star-formation requires coverage of the spectral region. where the peak of the far-IR emission is expected to lie.," However, a complete characterization of the output of star-formation requires coverage of the spectral region, where the peak of the far-IR emission is expected to lie."
 The Balloon-borne Large Aperture Submillimeter Telescope (BLAST: 2: 2) is a pathtfinder experiment to Herschel/SPIRE. and ws provided the first maps of selected areas of the sky at 250. 350. andmicron.," The Balloon-borne Large Aperture Submillimeter Telescope (BLAST: \citealt{Pascale08}; \citealt{Devlin09}) ) is a pathfinder experiment to /SPIRE, and has provided the first maps of selected areas of the sky at 250, 350, and."
. These wavelengths were mainly chosen to constrain the yeak of the FIR emission from galaxies at redshifts >—1., These wavelengths were mainly chosen to constrain the peak of the FIR emission from galaxies at redshifts $z \gtrsim 1$.
 Several studies carried out by the BLAST collaboration on extragalactic fields. either on individual sources (2:: 2:: 2)). using stacking (2:: 2:: 2: ?n. or other statistical analyses (2:: 2)). have been performed on blank-field maps.," Several studies carried out by the BLAST collaboration on extragalactic fields, either on individual sources \citealt{Dye09}; \citealt{Dunlop09}; \citealt{Ivison10}) ), using stacking \citealt{Devlin09}; ; \citealt{Marsden09}; \citealt{Pascale09}; \citealt{Ivison10}) ), or other statistical analyses \citealt{Patanchon09}; \citealt{Viero09}) ), have been performed on blank-field maps."
 A few other studies (2:: 2) have been conducted on known targets., A few other studies \citealt{Rex09}; \citealt{Wiebe09}) ) have been conducted on known targets.
 In particular. Rex et al.," In particular, Rex et al."
 have provided the first sub-mm maps of the “Bullet” cluster (25). investigating the nature of a bright sub-mm source identified as a counterpart of a lensed > star-forming galaxy.," have provided the first sub-mm maps of the `Bullet' cluster \citealt{Tucker98}) ), investigating the nature of a bright sub-mm source identified as a counterpart of a lensed $z$ star-forming galaxy."
 However. no direct investigation of sub-mm emission from cluster members has been conducted so far.," However, no direct investigation of sub-mm emission from cluster members has been conducted so far."
 We present here 250. 350. and 500 observations. of a field centred on the nearby cluster Abell 3112— (2= 0.075: A3|I2 hereafter) carried out by BLAST. and the results. of a combined analysis of the optical and sub-mm properties of a spectroscopic sample of its cluster members.," We present here 250, 350, and 500 observations of a field centred on the nearby cluster Abell 3112 $z = $ 0.075; A3112 hereafter) carried out by BLAST, and the results of a combined analysis of the optical and sub-mm properties of a spectroscopic sample of its cluster members."
 These results demonstrate that observation of cluster galaxies at sub-mm wavelengths can provide insight into the star-formation activity in clusters and help understanding galaxy evolution within these overdense environments., These results demonstrate that observation of cluster galaxies at sub-mm wavelengths can provide insight into the star-formation activity in clusters and help understanding galaxy evolution within these overdense environments.
 This paper is organized as follows., This paper is organized as follows.
 Section 2. introduces the BLAST observations of A312 and the ancillary optical and IR data used for our study., Section \ref{obsdata} introduces the BLAST observations of A3112 and the ancillary optical and near-IR data used for our study.
 Section 3. shows the results from stacking analyses of cluster member catalogues and the properties of sub-mm bright cluster members., Section \ref{results} shows the results from stacking analyses of cluster member catalogues and the properties of sub-mm bright cluster members.
 These results are discussed in Section 4 and summarized in Section 5.., These results are discussed in Section \ref{discuss} and summarized in Section \ref{summ}.
" Throughout the paper. we use a standard ACDM cosmology. where Q4;=0.3. Q420,7 and h=Hu/100kms+Alpe1- 0T."," Throughout the paper, we use a standard $\Lambda$ CDM cosmology, where $\Omega_\rmn{M} = 0.3$, $\Omega_{\Lambda} = 0.7$ and $h \equiv H_0/100~\rmn{km}~\rmn{s}^{-1}~\rmn{Mpc}^{-1} = 0.7$ ."
 The BLAST stratospheric telescope has a 1.8-m primary mirror and three broad-band bolometer arrays that observe the sky simultaneously at 250. 350. andmicron.," The BLAST stratospheric telescope has a 1.8-m primary mirror and three broad-band bolometer arrays that observe the sky simultaneously at 250, 350, and."
. This array system is effectively a prototype of the SPIRE instrument onboard the satellite., This array system is effectively a prototype of the SPIRE instrument onboard the satellite.
 The instrument beams are nearly diffraction-limited and are approximately described as Gaussians with full width at half maximum (FWHM) of 36. 42. and 60 aresee at 250. 350. andmicron. respectively.," The instrument beams are nearly diffraction-limited and are approximately described as Gaussians with full width at half maximum (FWHM) of 36, 42, and 60 arcsec at 250, 350, and, respectively."
 For an extended description of the instrument. data analysis. and calibration procedures. see ?:: ?..," For an extended description of the instrument, data analysis, and calibration procedures, see \citet{Pascale08}; \citet{Truch09}."
 A large fraction of the successful BLAST observational campaign of 2006 (BLASTO6) from McMurdo Station. Antarctica. was dedicated to completing deep and wide blank-field extragalactic surveys (cf.," A large fraction of the successful BLAST observational campaign of 2006 (BLAST06) from McMurdo Station, Antarctica, was dedicated to completing deep and wide blank-field extragalactic surveys (cf."
 Section 19)., Section \ref{intro}) ).
 Smaller fields centred on the positions of well-known targets were also observed (e.g. 2: 2»)., Smaller fields centred on the positions of well-known targets were also observed (e.g. \citealt{Rex09}; \citealt{Wiebe09}) ).
 Among those was a [I deg? field centred on the nearby cluster A3|I2 at >= 0.075., Among those was a 1.1 $\rmn{deg}^2$ field centred on the nearby cluster A3112 at $z = 0.075$ .
 This target was observed for a total time of 4.2 hr., This target was observed for a total time of 4.2 hr.
 The BLAST time-stream data were reduced using a common pipeline to identify spikes. correct detector time drift and calibrate data (2: 2)).," The BLAST time-stream data were reduced using a common pipeline to identify spikes, correct detector time drift and calibrate data \citealt{Pascale08}; ; \citealt{Truch09}) )."
 Maps were generated using the SANEPIC software. which uses a maximum-likelihood algorithm to estimate. the optimal solution for the map.as well as producing an associated noise map (?)).," Maps were generated using the SANEPIC software, which uses a maximum-likelihood algorithm to estimate the optimal solution for the map,as well as producing an associated noise map\citealt{Patanchon08}) )."
 Absolute calibration is based on observations of, Absolute calibration is based on observations of
"0,4.",$\sigma_y$.
 We find that the caleulated ry is only weakly dependent on the y used. ancl is only alfected at the level.," We find that the calculated $r_{0}$ is only weakly dependent on the $\bar y$ used, and is only affected at the level."
 We interpret our results with the aid of a cosmological Nbody simulation populated with CLALEOLUM semi-analvtic galaxies (Colectal.2000). at different out—puts corresponding to cillerent redshifts. z=0.1. and 3.," We interpret our results with the aid of a cosmological N–body simulation populated with GALFORM semi-analytic galaxies \citep{cole} at different outputs corresponding to different redshifts, $z=0,1$, and $3$."
 TEhis simulation was kindly. provided by the Durham group., This simulation was kindly provided by the Durham group.
" The cosmological model corresponds to matter and cosmological constant density parameters QO.,,,=0.25. O4—0.75. a power spectrum tilt»=0.95. an amplitude of Dluctuations. of a=OS. and a Ilubble constant of //;=100 f kms *. where f=0.7."," The cosmological model corresponds to matter and cosmological constant density parameters $\Omega_m=0.25$, $\Omega_{\Lambda}=0.75$, a power spectrum tilt $n=0.95$, an amplitude of fluctuations of $\sigma_8=0.8$, and a Hubble constant of $H_{0}=100$ $h$ $^{-1}$ $^{-1}$, where $h=0.7$."
 The total number of particles is 10502. the mass resolution is 5.05.1 TAL:. and the number of dark matter haloes with masses greater than Al=IJ07h !M.; ranges from ~400.000 at z=3 to 2.200.000 at z0.," The total number of particles is $1080^3$, the mass resolution is $5.05\times10^{10}$ $^{-1}$ $_{\sun}$, and the number of dark matter haloes with masses greater than $M=10^{12}$ $^{-1}$ $_{\sun}$ ranges from $\sim400,000$ at $z=3$ to $\sim2,200,000$ at $z=0$."
 The number of GALFORAL galaxies ranges [rom ~20.000.000 to 120.000.000 at z=3 and >=0 respectively.," The number of GALFORM galaxies ranges from $\sim20,000,000$ to $120,000,000$ at $z=3$ and $z=0$ respectively."
 We now briclly explain the procedure by which galaxies are assigned their properties in the Semi-analvtie code., We now briefly explain the procedure by which galaxies are assigned their properties in the Semi-analytic code.
 GALEOLDM is run for cach halo in the numerical simulation. where galaxies are assigned to a randomly selected: dark matter halo particle.," GALFORM is run for each halo in the numerical simulation, where galaxies are assigned to a randomly selected dark matter halo particle."
 Phe cdillerent. galaxy properties. such as magnitudes in dillerent. bands. including the A band. depend on the dark matter halo merger tree.," The different galaxy properties such as magnitudes in different bands, including the $K$ –band, depend on the dark matter halo merger tree."
 This merger tree is gencrated via Monte-Carlo modelling based on the extended: Press-Schechter theory. and the evolution of the galaxy population in the halo is followed. through time and dilferent processes are. considered. in this evolution. including gas cooling. quiescent star formation and star formation bursts. mergers. galactic winds and super winds. metal enrichment. extinction by dust.," This merger tree is generated via Monte-Carlo modelling based on the extended Press-Schechter theory, and the evolution of the galaxy population in the halo is followed through time and different processes are considered in this evolution, including gas cooling, quiescent star formation and star formation bursts, mergers, galactic winds and super winds, metal enrichment, extinction by dust."
 For full details on the modelling the reader is referred to Colectal.(2000)., For full details on the modelling the reader is referred to \citet{cole}.
 We calculate. the crosscorrelation function using the simulation haloes with masses above a lower mass limit as centres. ancl as tracers. the GALPORAL semi-analytic galaxies.," We calculate the cross–correlation function using the simulation haloes with masses above a lower mass limit as centres, and as tracers, the GALFORM semi-analytic galaxies."
 By comparing these measurements to the results from the crosscorrelation between USS and normal galaxies. we make the implicit assumption that USS galaxies reside at the centres of dark-matter haloes.," By comparing these measurements to the results from the cross–correlation between USS and normal galaxies, we make the implicit assumption that USS galaxies reside at the centres of dark-matter haloes."
 This comparison will make it possible to infer the mass of the structures associated to the USShosts., This comparison will make it possible to infer the mass of the structures associated to the USShosts.
 ligue 1 shows the resulting real-space cross-correlation functions betweenhaloes and semi-analvtic— galaxies at 2=1 (top panel) for cillerent halo masses., Figure \ref{nel} shows the resulting real-space cross-correlation functions betweenhaloes and semi-analytic galaxies at $z=1$ (top panel) for different halo masses.
 The shaded: area corresponds. to the power law [it for the real-space correlation function inferred. from the crosscorrelation function for USS radio sources with spectroscopic redshifts in the range 0.6Z5281.5 (See Figure 2)., The shaded area corresponds to the power law fit for the real-space correlation function inferred from the cross--correlation function for USS radio sources with spectroscopic redshifts in the range $0.6 \lesssim z \lesssim 1.5$ (See Figure 2).
 In the middle panel of this figure. we compare the values of USSgalaxy cross-correlation length. as a function of halo mass for three different redshift outputs from the numerical simulations: as can be seen. the observed. values are consistent with cluster masses within As=Lobe?the fh+ NL at redshift z—1. indicating that our USS sample resides in massive clusters.," In the middle panel of this figure, we compare the values of USS–galaxy cross-correlation length as a function of halo mass for three different redshift outputs from the numerical simulations; as can be seen, the observed values are consistent with cluster masses within $M=10^{13.4-14.2}$ $h^{-1}$ $_{\sun}$ at redshift z=1, indicating that our USS sample resides in massive clusters."
 La order to check whether our observational estimate of ry is allected by systematic jases. we caleulate the projected correlation function in the numerical simulation and recover the real-space correlation οποία using I5q. 4..," In order to check whether our observational estimate of $r_0$ is affected by systematic biases, we calculate the projected correlation function in the numerical simulation and recover the real-space correlation length using Eq. \ref{lil},"
 setting £2=1: we consider the same range of separations available in the real data., setting $B=1$; we consider the same range of separations available in the real data.
 The results or 2=1 are shown in filled circles in the micelle panel., The results for $z=1$ are shown in filled circles in the middle panel.
 As can be seen. our conclusions on the mass of USS host raloes changes only slightly to AZ=10557te 53 ALS. although we note that for lower ancl higher halo masses.he value of ro recovered from projected: correlations is dnderestiniatecl ancl overestimated. respectively.," As can be seen, our conclusions on the mass of USS host haloes changes only slightly to $M=10^{13.2-13.8}$ $h^{-1}$ $_{\sun}$, although we note that for lower and higher halo masses,the value of $r_0$ recovered from projected correlations is underestimated and overestimated, respectively."
" This test oovides a useful check of our observational results which were derived. from relatively small projected. scales (r,Z1 Alpe).", This test provides a useful check of our observational results which were derived from relatively small projected scales $r_p \lesssim$ 1 Mpc).
 Our findings in the simulations indicate that reliable ry values are obtained. using the power law approximation applied to projected. correlations for ry1h+ Alpe when he true correlation. length is lesser than ~15h1 Alpe corresponding to host halo mass AZ< 10 M., Our findings in the simulations indicate that reliable $r_0$ values are obtained using the power law approximation applied to projected correlations for $r_p <1 h^{-1}$ Mpc when the true correlation length is lesser than $\sim 15 h^{-1}$ Mpc corresponding to host halo mass $M\lesssim$ $^{14}$ $_{\sun}$.
 A further indication of the mass of USS galaxy. host jdoes comes from the lower panel of this figure. where the ines correspond to the projected. cross-correlation function measured. in the CLALEOBRM simulation for cillerent masses (Lligh to low masses from top to bottom lines at og(o/h ‘\Ipe)= 0.3).," A further indication of the mass of USS galaxy host haloes comes from the lower panel of this figure, where the lines correspond to the projected cross-correlation function measured in the GALFORM simulation for different masses (High to low masses from top to bottom lines at $\log_{10}(\sigma/$ $^{-1}$ $)=-0.3$ )."
" Bla) is calculated directly using. where we have used πω=SO h *\Ipe. and the normalisation. Norm.. is set so that Z(o) and wl) coincide at log,4(0/h. *Mpe)= l."," $\Xi(\sigma)$ is calculated directly using, where we have used $\pi_{max}=80$ $^{-1}$ Mpc, and the normalisation, ${\rm Norm.}$ , is set so that $\Xi(\sigma)$ and $\omega(\sigma)$ coincide at $\log_{10}(\sigma/$ $^{-1}$ $)=-1$ ."
 The grav area shows the measurecl values of (c) from the USS sample: as can be seen the measured. projected. correlation function is in best agreement for AJ~ loth TAL., The gray area shows the measured values of $\omega(\sigma)$ from the USS sample; as can be seen the measured projected correlation function is in best agreement for $M\sim10^{13.85}$ $^{-1}$ $_{\sun}$ .
they are embedded into positive polarity open magnetic fields from the coronal hole.,they are embedded into positive polarity open magnetic fields from the coronal hole.
 This type of magnetic field configuration make it very unlikely that there was a direct magnetic connectivity between these two active regions., This type of magnetic field configuration make it very unlikely that there was a direct magnetic connectivity between these two active regions.
" The topology is much simpler than other cases near solar maximum, where Roussevetal.(2007) found connectivity between as many as three active regions via multiple null points and quasi-separatrix layers."," The topology is much simpler than other cases near solar maximum, where \citet{Roussev:2007} found connectivity between as many as three active regions via multiple null points and quasi-separatrix layers."
 There is one null point above the negative polarity part of AR 10798 separating the 3 flux systems as illustrated, There is one null point above the negative polarity part of AR 10798 separating the 3 flux systems as illustrated
Our improved dvnamical model for Cvg X-1 enables other studies of (his kev binary.,Our improved dynamical model for Cyg X-1 enables other studies of this key black-hole binary.
 Using our precise measurement of the distance (Reid et al., Using our precise measurement of the distance (Reid et al.
 2011). we are now able to compute the stellar Iuminositv. as a function of the assumed temperature. which allows one to place the star on a IL-R. diagram with some confidence.," 2011), we are now able to compute the stellar luminosity as a function of the assumed temperature, which allows one to place the star on a H-R diagram with some confidence."
 We have also provided precise values of the component masses. (he eccentricity. and the degree of nonsvnchronous rotation. quantities which max be used to test binary evolutionary models (such a study will be presented elsewhere).," We have also provided precise values of the component masses, the eccentricity, and the degree of nonsynchronous rotation, quantities which may be used to test binary evolutionary models (such a study will be presented elsewhere)."
 Finally. with our accurate values for Che distance. the black hole mass. and (he orbital inclination angle. one can model X-ray spectra of the source in order to measure the spin of the black hole primary.," Finally, with our accurate values for the distance, the black hole mass, and the orbital inclination angle, one can model X-ray spectra of the source in order to measure the spin of the black hole primary."
 In our third paper in (his series. Gou οἱ ((2011). we show that Cvg X-1 is à near-extreme Ixerr black hole.," In our third paper in this series, Gou et (2011), we show that Cyg X-1 is a near-extreme Kerr black hole."
 We thank Catherine Brocksopp lor sending us the optical light curves., We thank Catherine Brocksopp for sending us the optical light curves.
 The work of JEM was supported in part by NASA grant NNXILADOSG. This research has made use of NASA's Astrophysics Data Svstem., The work of JEM was supported in part by NASA grant NNX11AD08G. This research has made use of NASA's Astrophysics Data System.
the nucleon. generalized parton distributions. quark (ransversitv. óq(c.Q7) and double {ransverse spin asvmnmetries elyy. single spin asvinmetries (SSA) AA and QCD mechanisms. In this opening lecture. for lack of time. we will have to make a strong selection. but eiven (he high densitv of the scientific program. it will certainly allow to cover all missing important subjects.,"the nucleon, generalized parton distributions, quark transversity $\delta q(x,Q^2)$ and double transverse spin asymmetries $A_{TT}$, single spin asymmetries (SSA) $A_N$ and QCD mechanisms, In this opening lecture, for lack of time, we will have to make a strong selection, but given the high density of the scientific program, it will certainly allow to cover all missing important subjects."
simulation fall below the detection threshold of many current survevs.,simulation fall below the detection threshold of many current surveys.
 The Lyra escape fraction correlates with a number of physical properties of the galaxy. such as mass. SER aud netallicity.," The $\lya$ escape fraction correlates with a number of physical properties of the galaxy, such as mass, SFR and metallicity."
" We find a ""viewiug-auegle scatter” in which the photon escape depends strongly ou the galaxy morphology and oricutation. such that the Ίνα photous escape iu a preferred direction normal to he gas disk iu disk ealaxies. but randomly iu compact or nreenlar galaxies."," We find a “viewing-angle scatter” in which the photon escape depends strongly on the galaxy morphology and orientation, such that the $\lya$ photons escape in a preferred direction normal to the gas disk in disk galaxies, but randomly in compact or irregular galaxies."
 \Lor¢over. the EWs of LAEs increases with redshift. from teis of Anestroms at redshift 2~0 hundreds of Anesτοις at 2~NO.," Moreover, the EWs of LAEs increases with redshift, from tens of Angstroms at redshift $z \sim 0$ to hundreds of Angstroms at $z \sim 8.5$."
" Furthermore. we find that high-redshift LAEs show Lye line profiles characteristic of gas 1iflow. ancl that the Lye emission w excitation cooling iucreases with redshift. accounting ~50% of the total at 26,"," Furthermore, we find that high-redshift LAEs show $\lya$ line profiles characteristic of gas inflow, and that the $\lya$ emission by excitation cooling increases with redshift, accounting $\sim 50 ~\%$ of the total at $z \gtrsim 6$."
 Our results sugecst hat galaxies at high redshift form hrough accretion of cold gas. which accounts for the he high EWs. the bluc-shifted. line profiles. and the dominant contributioi from excitation cooling iu Lva enüssion.," Our results suggest that galaxies at high redshift form through accretion of cold gas, which accounts for the the high EWs, the blue-shifted line profiles, and the dominant contribution from excitation cooling in $\lya$ emission."
" Moreover. some of the observed LAEs at :—ς2.6 ⋅⋅with Li,↽⋅≻∶↘107.Bores ay evolve into⋅ present-day L galaxies such as the Milky3 Way."," Moreover, some of the observed LAEs at $z \sim 2-6$ with $\La \sim 10^{42-43}~\ergs$ may evolve into present-day $L^{*}$ galaxies such as the Milky Way."
 We thank Carlos Freuk for kiudlv providing us the Aquila initial condition for the cosmological simulation., We thank Carlos Frenk for kindly providing us the Aquila initial condition for the cosmological simulation.
 We thank Mark Dijkstra. Clande-Audré Faucher-Cauenerre. Erie Gawiser. Lars Heruquist. and Avi Loch for stimulating discussions and helpful conuueuts. as well as the referee for an insightful report which has helped improve the imaunuscrpt.," We thank Mark Dijkstra, Claude-André Faucher-Gigu{\`e}rre, Eric Gawiser, Lars Hernquist, and Avi Loeb for stimulating discussions and helpful comments, as well as the referee for an insightful report which has helped improve the mannuscript."
 Support frou NSF grants AST-096569L AST-LO09867 (to YL). AST-0s07075 (to TA). aud AST-Os807TS85 (to CG RC) is gratefully. acknowledged.," Support from NSF grants AST-0965694 AST-1009867 (to YL), AST-0807075 (to TA), and AST-0807885 (to CG RC) is gratefully acknowledged."
 YL thanks the Tustitute for Theory aud Computation ITC) at ITarviurd University where the project was started for wari. hospitality., YL thanks the Institute for Theory and Computation (ITC) at Harvard University where the project was started for warm hospitality.
 We acknowledge the Research Computing and Cyberinfrastructure uiuit of Iuformation Technology Services at The Penusvlvania State University for providing computational resources and services. that have contributed to the research results reported iu this paper (URL: http://rccdts.psu.edu)., We acknowledge the Research Computing and Cyberinfrastructure unit of Information Technology Services at The Pennsylvania State University for providing computational resources and services that have contributed to the research results reported in this paper (URL: http://rcc.its.psu.edu).
 The Institute for Cravitation and the Cosmos is supported by the Eberly College of Science and the Office of the Senior Vice President for Research at the Peuusylviuia State University., The Institute for Gravitation and the Cosmos is supported by the Eberly College of Science and the Office of the Senior Vice President for Research at the Pennsylvania State University.
appears to have reached its physical limits (in the number of trausistors on a chip).,appears to have reached its physical limits (in the number of transistors on a chip).
 The nauo- convergence currently occurring suggests.MOD however. that the growth: will coutinue. or. following Ixurzweil (2001) accelerate.," The nano-bio-cyber convergence currently occurring suggests, however, that the growth will continue, or, following Kurzweil (2001) accelerate."
 The uature of the changes are still in the realin of science fiction: Stapeltou (1930) foresaw the [ate of the “last men”. after which (evolutionarily) luunans became a new race: ]t appears that we huimaus. like the Ixrell (MIGM 1956). will be (or indeed are) increasingly interconnected with au electro-mechanical system of almost unimaginable power.," The nature of the changes are still in the realm of science fiction; Stapelton (1930) foresaw the fate of the ""last men"", after which (evolutionarily) humans became a new race: It appears that we humans, like the Krell (MGM 1956), will be (or indeed are) increasingly interconnected with an electro-mechanical system of almost unimaginable power."
 Already we communicate uear telepathically with almost anyone on the planet. at almost any. time. via cell phone: already our Memories are tremendously augmented by interuet search eugines.," Already we communicate near telepathically with almost anyone on the planet, at almost any time, via cell phone; already our memories are tremendously augmented by internet search engines."
 While we cannot know exactly w the future will bring. we can intuit some things couceruing the elements of our new euvironnmuent. based onu past treuds.," While we cannot know exactly what the future will bring, we can intuit some things concerning the elements of our new environment, based on past trends."
 The elements we construct. will be extraordinarily complex: each with a imultitude of design decisious., The elements we construct will be extraordinarily complex; each with a multitude of design decisions.
 This is uulike the exact sciences. where there is a siugle correct description of a plivsical reality: it is more like architecture. there is uo single exactly correct bridge or building design.," This is unlike the exact sciences, where there is a single correct description of a physical reality; it is more like architecture, there is no single exactly correct bridge or building design."
 Certainly there are architectural elements which persist. such as a key stone in building arches.," Certainly there are architectural elements which persist, such as a key stone in building arches."
 Perhaps the closest analog to the information entity we are now coustructing. (the super-brain?)," Perhaps the closest analog to the information entity we are now constructing, (the super-brain?)"
 is a city., is a city.
 Cities are constructed by the long term aud large scale combined ellorts of people., Cities are constructed by the long term and large scale combined efforts of people.
 Cities are not explicitly desigued. but they grow as a result of numerous mostly independent: efforts.," Cities are not explicitly designed, but they grow as a result of numerous mostly independent efforts."
 Even without explicit desigu cities normally have a uumber of design elements in Common. such as neighborhoods. or sidewalk cafes (Alexander. et al 1977).," Even without explicit design cities normally have a number of design elements in common, such as neighborhoods, or sidewalk cafes (Alexander, et al 1977)."
 Major elements in all cities are places to get thines., Major elements in all cities are places to get things.
 These are often the eid. poiuts of complex, These are often the end points of complex
material component.,material component.
" The effective mass absorption coefficient of material component i of the aggregate is defined as where f; is the volume fraction of the total aggregate composed of materialcomponent i, p; is the material density of this component, and the summation over j now only involves the dipoles composed of material i."," The effective mass absorption coefficient of material component $i$ of the aggregate is defined as where $f_i$ is the volume fraction of the total aggregate composed of materialcomponent $i$, $\rho_i$ is the material density of this component, and the summation over $j$ now only involves the dipoles composed of material $i$."
" When there are Nmat different materials that make up the aggregate, the total mass absorption coefficient is simply given by Aggregates in astronomical environments form by coagulation of small grains."," When there are $N_\mathrm{mat}$ different materials that make up the aggregate, the total mass absorption coefficient is simply given by Aggregates in astronomical environments form by coagulation of small grains."
 The structures that form in this way can have various shapes and degrees of compactness depending on the environmental conditions., The structures that form in this way can have various shapes and degrees of compactness depending on the environmental conditions.
" On the one hand, fluffy aggregates might form under conditions where aggregates of approximately equal sizes coagulate to form larger structures (Kempfetal}[[999)."," On the one hand, fluffy aggregates might form under conditions where aggregates of approximately equal sizes coagulate to form larger structures \citep{kempf99}."
". On the other hand, very compact structures might form when single monomers are added to a larger aggregate [I984)."," On the other hand, very compact structures might form when single monomers are added to a larger aggregate \citep{Ball84}."
. As shown by (2006a) the compactness of the aggregate has a large impact on its spectral appearance., As shown by \citet{2006A&A...445.1005M} the compactness of the aggregate has a large impact on its spectral appearance.
" For very fluffy aggregates the spectral structure typical for their constituents is visible, whereas for very compact aggregates the spectral structure of the total aggregate dominates."," For very fluffy aggregates the spectral structure typical for their constituents is visible, whereas for very compact aggregates the spectral structure of the total aggregate dominates."
 We construct the aggregates by adding single particles to a growing aggregate., We construct the aggregates by adding single particles to a growing aggregate.
 We start out with a single particle and shoot a second particle with a random impact parameter at the particle till it hits the particle and sticks., We start out with a single particle and shoot a second particle with a random impact parameter at the particle till it hits the particle and sticks.
 The resulting cluster is randomly rotated and a new particle is shot at the aggregate in the same way., The resulting cluster is randomly rotated and a new particle is shot at the aggregate in the same way.
 In this way we produce moderately fluffy aggregates., In this way we produce moderately fluffy aggregates.
" In order to construct aggregates of irregularly shaped particles we shoot Gaussian Random Field (GRF) particles at each other 2003; [2005)., thus constructing an aggregate of these very irregularly shaped particles."," In order to construct aggregates of irregularly shaped particles we shoot Gaussian Random Field (GRF) particles at each other \citep{2003JQSRT..78..319G, 2005Icar..173...16S}, thus constructing an aggregate of these very irregularly shaped particles."
 We then locate a dipole with CDE polarizability at the center of mass of each GRF particle., We then locate a dipole with CDE polarizability at the center of mass of each GRF particle.
 We consider inhomogeneous aggregates., We consider inhomogeneous aggregates.
 We take of the constituents of the aggregate to be composed of amorphous carbon and to be composed of silicate., We take of the constituents of the aggregate to be composed of amorphous carbon and to be composed of silicate.
 Of the silicate a fraction is crystalline while the rest is amorphous., Of the silicate a fraction is crystalline while the rest is amorphous.
" Crystalline silicates display a very pronounced spectral structure, and part of our study is to see how this spectral structure is displayed for various fractions of crystalline silicates."," Crystalline silicates display a very pronounced spectral structure, and part of our study is to see how this spectral structure is displayed for various fractions of crystalline silicates."
 The polarizabilities are computed using Eq. (6)), The polarizabilities are computed using Eq. \ref{eq:CDE}) )
 with laboratory measurements for the refractive index as a function of wavelength., with laboratory measurements for the refractive index as a function of wavelength.
 For the amorphous carbon we used measurements by ([993).., For the amorphous carbon we used measurements by \citet{1993A&A...279..577P}.
 Forsterite and enstatite are crystalline materials that have a refractive index different for the electric field oriented along the different crystallographic axis., Forsterite and enstatite are crystalline materials that have a refractive index different for the electric field oriented along the different crystallographic axis.
 We take this into account in the computations coupling the dipoles., We take this into account in the computations coupling the dipoles.
" The refractiveΠάρο etindexal, data was taken from Servoin&Piriou and for the forsterite and the enstatite (1973)respectively.", The refractive index data was taken from \citet{Servoin} and \citet{1998A&A...339..904J} for the forsterite and the enstatite respectively.
 For the polarizability of the amorphous silicate constituents we take a mixture of various amorphous silicates according to the composition derived for the interstellar amorphous silicates by (2007).. , For the polarizability of the amorphous silicate constituents we take a mixture of various amorphous silicates according to the composition derived for the interstellar amorphous silicates by \citet{2007A&A...462..667M}. .
This mixture is given in table [I] and represents an average amorphous silicate composition of Mg1.36Feo.13Na0.05Alo.95S1O3.5o., This mixture is given in table \ref{tab:Materials} and represents an average amorphous silicate composition of $_{1.36}$ $_{0.13}$ $_{0.05}$ $_{0.05}$ $_{3.59}$ .
with emissivity varyingIn accordinge to (LeTas),with emissivity varying according to $(T/T_{\rm max})^\alpha$.
 “Exchanging the two single-temperature MEKALS for à caused a verv large (—8SOO) increase in suggesting that emissivity in the accretion column does not have a law clependence on temperature.," Exchanging the two single-temperature s for a caused a very large 800) increase in, suggesting that emissivity in the accretion column does not have a power-law dependence on temperature."
 We present spin-folded. light-curves and a softness ratio in Fie. 5.., We present spin-folded light-curves and a softness ratio in Fig. \ref{fig:spin}.
" In previously reported data (Mason 1997). the soft N-ravs show a dip at. phase 0. à broad. maximum centred on phase 0.2 and a ""shoulder around phases 0.4.0.5."," In previously reported data (Mason 1997), the soft X-rays show a dip at phase 0, a broad maximum centred on phase 0.2 and a `shoulder' around phases 0.4–0.5."
" The harder X-rays show the dip and also a ""spike! coincident with the soft shoulder.", The harder X-rays show the dip and also a `spike' coincident with the soft shoulder.
 Our data are similar. except that the A-ray dip is shallower.," Our data are similar, except that the X-ray dip is shallower."
 “Phis was most prominent in data (from 1993: Mason. 1997). less so in. data (from 1996: de Martino 22004). and still less prominentAX. in our clelata (from 2002).," This was most prominent in data (from 1993; Mason 1997), less so in data (from 1996; de Martino 2004), and still less prominent in our data (from 2002)."
 To investigate these spectral changes we applicc two models to. four phase regions (the dip. the spike. and phases 0.204 and 0.60.9). testing whether the changes are reproduced. by variations in absorption. moce normalisation. or both.," To investigate these spectral changes we applied two models to four phase regions (the dip, the spike, and phases 0.2–0.4 and 0.6–0.9), testing whether the changes are reproduced by variations in absorption, model normalisation, or both."
 “Phe first model was that developec in Section 4. in which the temperatures and normalisations can vary with respec to onc-another.," The first model was that developed in Section 4, in which the temperatures and normalisations can vary with respect to one-another."
 The second model was the stratified column model ofCropper ((1999). which uses multiple ΕΝΑΝ with temperatures ancl relative normalisations cdeterminec by the physics of an aceretion column.," The second model was the stratified column model of Cropper (1999), which uses multiple s with temperatures and relative normalisations determined by the physics of an accretion column."
 30th models gave adequate fits i£. both their normalisations and the absorption are allowed to vary on the spin cvele., Both models gave adequate fits if both their normalisations and the absorption are allowed to vary on the spin cycle.
 An example fit is given in Table 3.., An example fit is given in Table \ref{tab:pres}.
 Neither mocel gave an acceptable fit if only the absorption was allowed to change (with ANE ΦΕΒ) when this was attempted. compared to a fit where all parameters can vary).," Neither model gave an acceptable fit if only the absorption was allowed to change (with $\Delta\chisq$ 40 when this was attempted, compared to a fit where all parameters can vary)."
 We then tried. instead. forcing the absorption to remain constant across the spin cvcle., We then tried instead forcing the absorption to remain constant across the spin cycle.
 The stratified column model did not give an acceptable fit in this case. however the greater freedom of the unconstrained nimiocdel did allow acceptable fits ppoorer by no more than 20) except during the dip.," The stratified column model did not give an acceptable fit in this case, however the greater freedom of the unconstrained model did allow acceptable fits poorer by no more than 20) except during the dip."
 I£ we accept that the relative nnormalisations must be constrained as in the stratified column model. this implies that the absorption must. be allowed to vary between phase regions.," If we accept that the relative normalisations must be constrained as in the stratified column model, this implies that the absorption must be allowed to vary between phase regions."
 Potter ((1997) and Mason (1997) developed a model for PQ Gem based on optical photometry. polarimetry and X-ray observations.," Potter (1997) and Mason (1997) developed a model for PQ Gem based on optical photometry, polarimetry and X-ray observations."
 In this model the accreting field lines at the upper magnetic pole lie in our line of sight at phase zero. obscuring our view of the X-ray emitting accretion footprints and causing the X-ray dip.," In this model the accreting field lines at the upper magnetic pole lie in our line of sight at phase zero, obscuring our view of the X-ray emitting accretion footprints and causing the X-ray dip."
 Lowever. to explain asvninictrics in the lighteurve. the accretion needs to be predominantly along field lines preceding the pole: thus the magnetic pole itself is not on the white-dwarl moeridian until phase 0.1.," However, to explain asymmetries in the lightcurve, the accretion needs to be predominantly along field lines preceding the pole; thus the magnetic pole itself is not on the white-dwarf meridian until phase 0.1."
 ὃν phase 0.1 the curtains are moving out of our line of sight. so the X-ray and UV Lux start to rise (Fig. 6)).," By phase 0.1 the curtains are moving out of our line of sight, so the X-ray and UV flux start to rise (Fig. \ref{fig:schem}) )."
 ὃν phase 0.2 the aceretion curtains have moved on. giving us a relatively unobscured: view of the heated white-cdwarl surface near the accretion column.," By phase 0.2 the accretion curtains have moved on, giving us a relatively unobscured view of the heated white-dwarf surface near the accretion column."
 This results in soft-N-rav maximum., This results in soft-X-ray maximum.
 While the soft. X-ray emission comes from the heated white-dwarl surface. the Z-band flux comes from cevclotron emission in the accretion columns above the surface.," While the soft X-ray emission comes from the heated white-dwarf surface, the $I$ -band flux comes from cyclotron emission in the accretion columns above the surface."
 We see maximum. Z-band flux when the magnetic poles are across our line of sight. ancl we can see emission from both poles simultaneously pphase 0.4. see Fig," We see maximum $I$ -band flux when the magnetic poles are across our line of sight, and we can see emission from both poles simultaneously phase 0.4, see Figs."
 s.5 and 6))., \ref{fig:spin} and \ref{fig:schem}) ).
 Z-band minima occur when the magnetic axis points towards us ancl we see only one pole., $I$ -band minima occur when the magnetic axis points towards us and we see only one pole.
 In Section 5 we concluded that the absorption varies over the spin cevcle., In Section 5 we concluded that the absorption varies over the spin cycle.
 This can be explained by the accretion curtain model. in which opacity along the line of sight is highest when the curtain points towards us (phase 0 in Fig 6) and lowest half a evele later (phase 0.5). producing a sinusoicdal variation in the softness ratio (sec. e.g.. Hellier. Cropper AIMason 199]. and the modelling by Ixim Beucrmann 1995).," This can be explained by the accretion curtain model, in which opacity along the line of sight is highest when the curtain points towards us (phase 0 in Fig 6) and lowest half a cycle later (phase 0.5), producing a sinusoidal variation in the softness ratio (see, e.g., Hellier, Cropper Mason 1991, and the modelling by Kim Beuermann 1995)."
 The overall softness variation in Fig., The overall softness variation in Fig.
 5. has the correct phasing to be explained. as above. however there is à reduction in softness during phases 0.50.8. giving apparent maxima at phases 0.45 and 0.85.," \ref{fig:spin} has the correct phasing to be explained as above, however there is a reduction in softness during phases 0.5–0.8, giving apparent maxima at phases 0.45 and 0.85."
 We suggest that this could arise if the base of the upper accretion column has passed over the white-cbwarf limb (see Fig. 6)), We suggest that this could arise if the base of the upper accretion column has passed over the white-dwarf limb (see Fig. \ref{fig:schem}) )
 such that we don't see the softest emission [ron the cooler regions near the base of the column., such that we don't see the softest emission from the cooler regions near the base of the column.
 To complete the explanation we would also need an asvmametey between the upper and. lower poles so that the base of the lower pole did not appear ancl produce an opposite elfect: alternatively. if there were considerable," To complete the explanation we would also need an asymmetry between the upper and lower poles so that the base of the lower pole did not appear and produce an opposite effect; alternatively, if there were considerable"
that there is only one positive fixed point with with Note that. in this case. This solution. represents à. state. of. fully develope: turbulent. convection. which is statistically steady auk homogeneous.,"that there is only one positive fixed point with with Note that, in this case, This solution represents a state of fully developed turbulent convection, which is statistically steady and homogeneous."
" The solution. exists. in the statistically. axisvmmetric subspace in which. {νε=6, and Rey=Hy.y.""L, ) and is stable with respec to perturbations transverse to this subspace."," The solution exists in the statistically axisymmetric subspace in which $\bar R_{xx}=\bar R_{yy}$ and $\bar
R_{xy}=\bar R_{xz}=\bar R_{yz}=\bar F_x=\bar F_y=0$ , and is stable with respect to perturbations transverse to this subspace."
 It has the desired: properties that. the vertical motion is dominan (Re.>Ree=HB). while the heat Dux is purely vertica and directed: down the temperature eradient.," It has the desired properties that the vertical motion is dominant $(\bar
R_{zz}>\bar R_{xx}=\bar R_{yy})$, while the heat flux is purely vertical and directed down the temperature gradient."
 Moreover. numerical integrations suggest that. where it exists. this state is stable anc universally attracting.," Moreover, numerical integrations suggest that, where it exists, this state is stable and universally attracting."
 Defining the Nusselt numer Nu as the ratio of the total to the conducted heat (lux. ‘This scaling recovers the “ultimate turbulence” regime. where the turbulent. transport properties are independent of microscopic cillusivities (Spiegel 1971).," Defining the Nusselt number Nu as the ratio of the total to the conducted heat flux, we have, in the limit Ra $\gg$ Pr, This scaling recovers the “ultimate turbulence” regime, where the turbulent transport properties are independent of microscopic diffusivities (Spiegel 1971)."
 Defining the turbulent Reynolds number Re as Re = Ld?1/2p. we have again reproducing the standard sealing for the ultimate regime of convection.," Defining the turbulent Reynolds number Re as Re = $L \bar R^{1/2}/\nu$, we have again reproducing the standard scaling for the ultimate regime of convection."
 Numerical simulations of ΗΛ convection were Lirst performed by Borue Orzag (1997)., Numerical simulations of HRB convection were first performed by Borue Orzag (1997).
 More recently. Foschi Lohse (2003) and Calzavarini ct al. (," More recently, Toschi Lohse (2003) and Calzavarini et al. ("
"2005) performed a range of LatticeBoltzmann simulations in a cubic geometry. for various values of the Bavleigh and Prandtl numbers. and report on the first evidence for scalings consistent with the ""ultimate regime” of convection. namely Nux(BaPr)!? and Bex(Ba/Pr)*7.","2005) performed a range of Lattice–Boltzmann simulations in a cubic geometry, for various values of the Rayleigh and Prandtl numbers, and report on the first evidence for scalings consistent with the “ultimate regime” of convection, namely ${\rm Nu} \propto ({\rm Ra Pr})^{1/2}$ and ${\rm Re} \propto \left({\rm Ra }/{\rm Pr} \right)^{1/2} $."
 llowever. it is now recognized that the dynamics of URB convection are more subtle than previously thought.," However, it is now recognized that the dynamics of HRB convection are more subtle than previously thought."
 As discussed by Calzavarini et al. (, As discussed by Calzavarini et al. (
"2006). simulations a unit aspect ratio show huge Iluctuations in the instantaneous usselt and Revnolels numbers arising from the intermitten or quasi-periodic (depending on Ita) exponential growth of so-called ""elevator modes.","2006), simulations at unit aspect ratio show huge fluctuations in the instantaneous Nusselt and Reynolds numbers arising from the intermittent or quasi-periodic (depending on Ra) exponential growth of so-called “elevator modes”."
 These modes are thus name oeause they. are independent. of z. and have the peculiar operty of being exact nonlinear and exponentially growing solutions of the governing equations (49)).," These modes are thus named because they are independent of $z$, and have the peculiar property of being exact nonlinear and exponentially growing solutions of the governing equations \ref{eq:HRBorig}) )."
 The mos unstable mode has a horizontal wavelength equal to. the arger horizontal dimension of the box., The most unstable mode has a horizontal wavelength equal to the larger horizontal dimension of the box.
 Hence. the aspec ratio of the svstem directly. inlluences. the macroscopic solution.," Hence, the aspect ratio of the system directly influences the macroscopic solution."
 This phenomenon has a close parallel in shearing-box studies of the magnetorotational instability., This phenomenon has a close parallel in shearing-box studies of the magnetorotational instability.
 In that case. orcing by a constant velocity graclicnt plavs the role of the constant temperature gradient. while perturbations to the xkeround. fields are also assumed to be triply periodic.," In that case, forcing by a constant velocity gradient plays the role of the constant temperature gradient, while perturbations to the background fields are also assumed to be triply periodic."
 This svstem is unstable to equivalent “channel modes? exact nonlinear. ancl exponentially growing solutions of he equations and. associated periodic boundary. conditions (Goodman Xu. 1994).," This system is unstable to equivalent “channel modes”, exact nonlinear and exponentially growing solutions of the equations and associated periodic boundary conditions (Goodman Xu, 1994)."
 In this case. it is known that he channel modes are themselves subject. to. secondary shearing instabilities which limit their growths.," In this case, it is known that the channel modes are themselves subject to secondary shearing instabilities which limit their growths."
 However. the existence ancl growth rates of garearing instabilities depend sensitively on aspect ratio: they are strongly inhibited. in systems where the streamwise direction is smaller than the cross-stream directions.," However, the existence and growth rates of shearing instabilities depend sensitively on aspect ratio: they are strongly inhibited in systems where the streamwise direction is smaller than the cross-stream directions."
 As a result. svstems with roughly. cubic ecometry are dominated by the channel modes and are found to have very strongly fluctuating large-scale transport properties. but for larger aspect ratio the fluctuations are much smaller and the channel modes are inhibited (Dodo et al.," As a result, systems with roughly cubic geometry are dominated by the channel modes and are found to have very strongly fluctuating large-scale transport properties, but for larger aspect ratio the fluctuations are much smaller and the channel modes are inhibited (Bodo et al."
 2008)., 2008).
 For these reasons. we performed a series of HIR simulations of various aspect ratios. in order to determine whether the same phenomenon occurs. and to provide a better. point of comparison for the closure. moclel.," For these reasons, we performed a series of HRB simulations of various aspect ratios, in order to determine whether the same phenomenon occurs, and to provide a better point of comparison for the closure model."
 Appendix € provides a brief description of the numerical algorithm: used. and the resultsare summarized in Fig. S..," Appendix C provides a brief description of the numerical algorithm used, and the resultsare summarized in Fig. \ref{fig:HRBRaNu}."
" We studied. 5 cases. with £L,=L, and L,/L. =1/2. 2/3. 9/10. 1/1 and 4/3."," We studied 5 cases, with $L_x = L_y$ and $L_x/L_z=$ 1/2, 2/3, 9/10, 1/1 and 4/3."
 In the last case. the elevator modes continue growing unallected by perturbations until the code fails. which seems to corroborate the premise that the secondary instabilities are inhibited. in wicler-than-tall boxes.," In the last case, the elevator modes continue growing unaffected by perturbations until the code fails, which seems to corroborate the premise that the secondary instabilities are inhibited in wider-than-tall boxes."
 For E«1. the measured Nusselt number eventually converges to a meaningful average and is found to scale as predicted by the closure model. namely proportional to (Pr Ia)717.," For $\Gamma < 1$, the measured Nusselt number eventually converges to a meaningful average and is found to scale as predicted by the closure model, namely proportional to (Pr $^{1/2} \Gamma^2$."
" A good fit with the model predictions is found by selecting L—9L,=Lfs.", A good fit with the model predictions is found by selecting $L = \delta L_x = L_x/\sqrt{\pi}$.
" For the purpose of illustration. a snapshot of the temperature field for our largest Itavleigh number. Ra25.r10"" (with Pr = 1) and aspect ratio 1/2 is shown in Figure 9.."," For the purpose of illustration, a snapshot of the temperature field for our largest Rayleigh number, ${\rm Ra} = 5 \times 10^6$ (with Pr = 1) and aspect ratio 1/2 is shown in Figure \ref{fig:HRBeyecandy}. ."
 We now consider the effect of rotation on IRB convection.," We now consider the effect of rotation on HRB convection,"
which cau be simplified as Therefore. only three inclices are tucepenclent in Eqs. (9))—(12)).,"which can be simplified as Therefore, only three indices are independent in Eqs. \ref{eq:iva}) \ref{eq:iTa}) )."
" IE we consider 7,. i. aud 5M to be independent. other indices can then be expressed as Eqs. (13 (17 )"," If we consider $i_L$ , $i_t$, and ${i_M}$ to be independent, other indices can then be expressed as Eqs. \ref{eq:ivb}) \ref{eq:iE}) )"
 show that the scaling relation of the pLVSical quantities cau be directly iuferrec from their αἱ1neusious based on the vaste units of mass. leneth. aud time.," show that the scaling relation of the physical quantities can be directly inferred from their dimensions based on the basic units of mass, length, and time."
 Dludeed. there Is nO coustraint on the cioice of 7p. 4. Or vay [rom the governing equations (1)-(3) ol this simgle case (see also Ryutoveal.1999 where sich a property of the equations is callec| Euler similarity).," Indeed there is no constraint on the choice of $i_L$, $i_t$, or $i_M$ from the governing equations (1)–(3) for this simple case (see also \citealt{Ryutov99} where such a property of the equations is called Euler similarity)."
 But £p is restrictec| by dg and i; throwh the equation of state., But $i_T$ is restricted by $i_L$ and $i_t$ through the equation of state.
" This coustrali ds elven )ecatlse I, is fixed (to a iiinber with nou-vanishine dimension hard-wired in a specilic simulation). which reduces one degree of freedom for the scaling of the pressure. density. and teiiperature."," This constraint is given because $R_\mu$ is fixed (to a number with non-vanishing dimension hard-wired in a specific simulation), which reduces one degree of freedom for the scaling of the pressure, density, and temperature."
 [n other words. althowh we have four basic units for tle ideal gas livelrocdsnamies (1.9. lass. leugt1. time. aud temperature). we are only able to freely change 11ree o them when scalii&[rom oue Case 10 another. i.e.. jay ancl two other itdices [‘om the pool o dd. aud iy.," In other words, although we have four basic units for the ideal gas hydrodynamics (i.e., mass, length, time, and temperature), we are only able to freely change three of them when scalingfrom one case to another, i.e., $i_M$ and two other indices from the pool of $i_L$, $i_t$, and $i_T$."
 A special class of the scalajlity is the selfsimilar soution., A special class of the scalability is the self-similar solution.
 In this case. clearly ouly one solution is needed.," In this case, clearly only one solution is needed."
 However. such a soltion. if exists. tay 100 be easily expressed iu an analytic form aud may be applicable ον asyiiptotically (e.g... when the elfect of the initial concitiou becomes neelieible).," However, such a solution, if exists, may not be easily expressed in an analytic form and may be applicable only asymptotically (e.g., when the effect of the initial condition becomes negligible)."
 In general. «ye may resort to a simulation to reach the solution.," In general, one may resort to a simulation to reach the solution."
 Thus it can be studied as part of the scalability prodei considered here., Thus it can be studied as part of the scalability problem considered here.
 If Eqs. (, If Eqs. (
1)-(3) have source teris. more coustralnts may then be placed ou the scaling relation.,"1)–(3) have source terms, more constraints may then be placed on the scaling relation."
 Forexample. the inclusion of the thermal conduction term. qd= (ΤΙΝT]. at the r-bes in equation (3) requires," Forexample, the inclusion of the thermal conduction term, $q=\nabla\cdot[\kappa(T)\nabla T]$ , at the r.h.s in equation (3) requires"
Black hole X-ray transients in outhurst are now well-known for exhibiting astrophysical jets. which produce svnehrotron emission. at. radio and higher frequencies. (Fender 2006 and. references therein).,"Black hole X-ray transients in outburst are now well-known for exhibiting astrophysical jets, which produce synchrotron emission at radio and higher frequencies (Fender 2006 and references therein)."
 Typical lightcurves show an initial phase during which the radio source has the flat spectrum. associated with a compact jet., Typical lightcurves show an initial phase during which the radio source has the flat spectrum associated with a compact jet.
 Later during the outburst. depending on the A-rayv spectral behaviour. the radio emission may be quenched or there may be a sequence of one or more optically thin ejection events. when the radio ightcurve rises and falls with each ejection (e.g. Brocksopp et al.," Later during the outburst, depending on the X-ray spectral behaviour, the radio emission may be quenched or there may be a sequence of one or more optically thin ejection events, when the radio lightcurve rises and falls with each ejection (e.g. Brocksopp et al."
 2002)., 2002).
 Finally there is typically an additional phase associated with a flat-spectrum. compact jet at the end of he outburst.," Finally there is typically an additional phase associated with a flat-spectrum, compact jet at the end of the outburst."
 Each of these phases of the radio lighteurve is connected. to the underlving X-ray. spectral state: in xwticular the behaviour of the radio source appears to be inked with the power-law component of the X-ray emission (Fender 2006 and references therein)., Each of these phases of the radio lightcurve is connected to the underlying X-ray spectral state; in particular the behaviour of the radio source appears to be linked with the power-law component of the X-ray emission (Fender 2006 and references therein).
 Only a few Galactic X-ray transients have been detected with a significant level of linear polarisation (LP)., Only a few Galactic X-ray transients have been detected with a significant level of linear polarisation (LP).
 “Phe irst was Cyg N-3. detected at during a bright racio outburst soon after discovery of the radio. counterpart (Ciregory et al.," The first was Cyg X-3, detected at during a bright radio outburst soon after discovery of the radio counterpart (Gregory et al."
 1972)., 1972).
 The level of polarisation increased as he flux decayed. suggesting the evolution of a svnchrotron source [rom optically thick to thin.," The level of polarisation increased as the flux decayed, suggesting the evolution of a synchrotron source from optically thick to thin."
 Seaquist ct al. (, Seaquist et al. (
1974) later detected the source with ~14% polarisation.,1974) later detected the source with $\sim14$ polarisation.
 88433 was discovered a few vears later and found to have a radio source with polarisation (Hjellming Johnston 1981)., SS433 was discovered a few years later and found to have a radio source with polarisation (Hjellming Johnston 1981).
 Alore recently. CRS 1915)105. was detected at LP whenwl ththe emission was dominated|ted by ththe approachingcoaching component as opposed to the stationary core (Rocrigeucz et al.," More recently, GRS 1915+105 was detected at LP when the emission was dominated by the approaching component as opposed to the stationary core (Rodrígguez et al."
 1995)., 1995).
 Further observations by Fender et al. (, Further observations by Fender et al. (
1999) detected. higher. variable levels of linear. polarisation (LP: 14%)) and highly variable position angle. again in the approaching component and not in the core.,"1999) detected higher, variable levels of linear polarisation (LP; ) and highly variable position angle, again in the approaching component and not in the core."
 Lt was sugeested. that the variability may be. due to increasing randomisation of the magnetic field within the ejecta., It was suggested that the variability may be due to increasing randomisation of the magnetic field within the ejecta.
" Additional observations ofGAS 1915|105 revealed a ""linear polarisation rotator event when the position angle of the electric vector rotated smoothly. by 50° at both 4.80 and 8.64 Gllz (Fender ct al."," Additional observations of GRS 1915+105 revealed a “linear polarisation rotator event”, when the position angle of the electric vector rotated smoothly by $50^{\circ}$ at both 4.80 and 8.64 GHz (Fender et al."
 2002)., 2002).
 With no frequency dependence. this event seemed: to. indicate rotation of the jet/ficle structure or progressive forniaion of a shock in the outllow.," With no frequency dependence, this event seemed to indicate rotation of the jet/field structure or progressive formation of a shock in the outflow."
 The highest fractional LP detected in GRS 1915|105 was ~24 CMiller-Jones et al., The highest fractional LP detected in GRS 1915+105 was $\sim24\%$ (Miller-Jones et al.
 200ut)., 2005).
 Ljellming ct al. (, Hjellming et al. (
1999) cleected linearly polarised racio emission from the recurrent truisient AU 47 during its 1998 outburst.,1999) detected linearly polarised radio emission from the recurrent transient 4U $-$ 47 during its 1998 outburst.
 This source weis found to be and. polarised. at 4.80 and 8.64 GLΖ respectively. at the peak of the radio outburst.," This source was found to be and polarised, at 4.80 and 8.64 GHz respectively, at the peak of the radio outburst."
 Finally €RO 40 also exhibited strong linear polarisation (up 0o 11)5 Hannikainen et al., Finally GRO $-$ 40 also exhibited strong linear polarisation (up to $\sim 11$; Hannikainen et al.
 2000) during its 1994 outburst., 2000) during its 1994 outburst.
 The LP lighteurve showed, The LP lightcurve showed
The binary GRS 19154105 is a member of the group called microquasars.,The binary GRS 1915+105 is a member of the group called microquasars.
 It is a stellar size analogue of quasars. containing an accreting black hole ancl ejecting two jets αἱ relativistic speeds (Mirabel Rodriguez 1998).," It is a stellar size analogue of quasars, containing an accreting black hole and ejecting two jets at relativistic speeds (Mirabel Rodriguez 1998)."
 A number of groups have attempted to lind (the basic properties of the svstem: Morgan. Remillard Greiner (1997) and. Greiner. Morgan Remillard (1993) used the RNTE data to constrain the mass of the black hole," A number of groups have attempted to find the basic properties of the system: Morgan, Remillard Greiner (1997) and Greiner, Morgan Remillard (1998) used the RXTE data to constrain the mass of the black hole"
context of the dust emission from galaxies that are members of the Virgo cluster by Popescu ct (2002).,context of the dust emission from galaxies that are members of the Virgo cluster by Popescu et (2002).
 A fourth. physically motivated. and vet still adequately constrained model was desceribed by Dale et ((2001). who assumed a power-law distribution of dust. masses as a function of temperature. in which the mass of dust heated to a temperature between Y and T|d. is given. by m)xT0.," A fourth, physically motivated, and yet still adequately constrained model was described by Dale et (2001), who assumed a power-law distribution of dust masses as a function of temperature, in which the mass of dust heated to a temperature between $T$ and $T + {\rm d}T$, is given by $m(T) \propto T^{-\gamma}$."
" Ehe spectral contribution to the SED from cach temperature Component is /D, and so the composite SED is given by the integral"," The spectral contribution to the SED from each temperature component is $\nu^\beta B_\nu$, and so the composite SED is given by the integral"
than 2 percent are detected. when observed. for the second time).,than 2 percent are detected when observed for the second time).
 Furthermore. many of the candidate stars are O-rich (LIS types 2n3n. tthe 9.7-micron silicate [eature is present. in either emission or absorption).," Furthermore, many of the candidate stars are O-rich (LRS types 2n–3n, the 9.7-micron silicate feature is present in either emission or absorption)."
 Lewis (1992a) and Lewis Engels (1993) demonstrated that of LRS tvpe 2n.3n sources with colours suggestive of CS dust shells have no OLI or HO masers., Lewis (1992a) and Lewis Engels (1993) demonstrated that of LRS type 2n–3n sources with colours suggestive of CS dust shells have no OH or $_2$ O masers.
 lt has been suggested (Lewis 1992b) that the natural explanation for the “OLL/LR. colour mimics” is that they are systems with a degenerate companion — afocad source of UV which disrupts the CS shell and prevents the masing action. tthat the colour mimics are closely related to symbiotic Miras.," It has been suggested (Lewis 1992b) that the natural explanation for the “OH/IR colour mimics” is that they are systems with a degenerate companion – a source of UV which disrupts the CS shell and prevents the masing action, that the colour mimics are closely related to symbiotic Miras."
 According to the conventional picture of the svmbiotic Alivas (which are. probably represented exclusively by. the Dusty)-type sub-class of svmibiotic stars). a hot. degenerate star ionizes the Mira wind giving rise to a forest of emission ines in the optical/UV. (together with the normal far-LR dust emission. ancl semi-regular pulsations expected. from he cooler star).," According to the conventional picture of the symbiotic Miras (which are probably represented exclusively by the D(usty)-type sub-class of symbiotic stars), a hot, degenerate star ionizes the Mira wind giving rise to a forest of emission lines in the optical/UV (together with the normal far-IR dust emission and semi-regular pulsations expected from the cooler star)."
 The hot companion exhibits unusually slow nova-like outbursts RRR Fel). possibly the consequence of shell ashes resulting from accretion from the Mira. wind (sce Αλλοι Wright 1988).," The hot companion exhibits unusually slow nova-like outbursts RR Tel), possibly the consequence of shell flashes resulting from accretion from the Mira wind (see Allen Wright 1988)."
 The svmbiotic Miras are less numerous han the S(tellar)-type sub-class which contain a first-ascent red. giant whose stellar atmosphere is the dominan contributor to the observed. Li emission., The symbiotic Miras are less numerous than the S(tellar)-type sub-class which contain a first-ascent red giant whose stellar atmosphere is the dominant contributor to the observed IR emission.
 The known svmbiotic Miras appear to be generally devoid of maser emission. according to a number of recen searches. and the hypothesis is that the hot. companion is responsible for either the dissociation. of the relevan molecules or for disruption of the maser emission mechanism NNorris et 11984).," The known symbiotic Miras appear to be generally devoid of maser emission, according to a number of recent searches, and the hypothesis is that the hot companion is responsible for either the dissociation of the relevant molecules or for disruption of the maser emission mechanism Norris et 1984)."
 In. support. of. this. picture. Lewis. Hajian Terzian (1992) searched the Internationa Ultraviolet Explorer (LUI) data archive for a small. colour- sample of stars without Oll or 11Ο masers (many. in fact. were bona fide svmibiotic stars) and found that mos exhibited a strong. UM. continuum.," In support of this picture, Lewis, Hajian Terzian (1992) searched the International Ultraviolet Explorer (IUE) data archive for a small, colour-selected sample of stars without OH or $_2$ O masers (many, in fact, were bona fide symbiotic stars) and found that most exhibited a strong UV continuum."
 Thus it is reasonable to suspect that the absence. of maser emission. may be associated with the presence of a hot companion., Thus it is reasonable to suspect that the absence of maser emission may be associated with the presence of a hot companion.
 Phenomenologically. symbiotic Aliras cluster in the zone where field. Miras transform into ΟΠΥΕ stars (Schild 1989).," Phenomenologically, symbiotic Miras cluster in the zone where field Miras transform into OH/IR stars (Schild 1989)."
 The correspondingly high mass-loss rate of D-type svmbiotic Miras is generally thought to lead to stronger optical/UV. line emission than is seen from the S-types., The correspondingly high mass-loss rate of D-type symbiotic Miras is generally thought to lead to stronger optical/UV line emission than is seen from the S-types.
" ""This οσοι enhances a svinbiotic Miras chance of discovery in objective prism. surveys.", This effect enhances a symbiotic Mira's chance of discovery in objective prism surveys.
 However. it dis possible that these svmbioties spend many vears prior to outburst in hibernation (resembling solitary Miras in most respects) as the hidden companion accretes slowly from the Miras wind.," However, it is possible that these symbiotics spend many years prior to outburst in hibernation (resembling solitary Miras in most respects) as the hidden companion accretes slowly from the Mira's wind."
 In this case the hot companion and associated emission lines would be totally obscured optically by the dusty CS shell of the Mira., In this case the hot companion and associated emission lines would be totally obscured optically by the dusty CS shell of the Mira.
 Schild (1989) has suggested that the obscuration of the hot component by the dusty CS shell produces a selection against the detection. of svmbiotic binaries with Mira or OLL/LR stars cool components and may therefore be responsible for their paucity., Schild (1989) has suggested that the obscuration of the hot component by the dusty CS shell produces a selection against the detection of symbiotic binaries with Mira or OH/IR stars cool components and may therefore be responsible for their paucity.
 The suggestion by Lewis (1992h) is that the hot companion may never-the-less be ellective in destroving any maser action. even though it is not optically visible.," The suggestion by Lewis (1992b) is that the hot companion may never-the-less be effective in destroying any maser action, even though it is not optically visible."
 Recently. Lewis et ((in preparation) obtained new IUIZ data for an unbiased sample of colour mimics (our sample — see later) they failed. to detect. UV continuum) enüssion. presumably because of obscuration by CS dust.," Recently, Lewis et (in preparation) obtained new IUE data for an unbiased sample of colour mimics (our sample – see later) they failed to detect UV continuum emission, presumably because of obscuration by CS dust."
 Lewis suggests with resignation that “D-type svmbiotic stars can be identified among sources with thick. opadque dust. shells by a persistent absence of appropriate Disers.," Lewis suggests with resignation that `D-type symbiotic stars can be identified among sources with thick, opaque dust shells by a persistent absence of appropriate masers.'"
 Thus these colour-mimics have implications for a proper understanding of the evolution of ΟΙΗν stars and. [or he behaviour of svmbiotic binaries., Thus these colour-mimics have implications for a proper understanding of the evolution of OH/IR stars and for the behaviour of symbiotic binaries.
 To properly test. the wpothesis of Lewis (ancl thereby address some of the questions posed. above) it is necessary to somehow probe hrough the CS dust shells of ΟΙΗν colour mimics., To properly test the hypothesis of Lewis (and thereby address some of the questions posed above) it is necessary to somehow probe through the CS dust shells of OH/IR colour mimics.
 llere. we describe a search. for free-free. continuum at em wavelengths from gas ionized by the hot. stellar component.," Here, we describe a search for free-free continuum at cm wavelengths from gas ionized by the hot, stellar component."
 tacdio continuum radiation should easily escape from within a CS cust shell., Radio continuum radiation should easily escape from within a CS dust shell.
 Observations of radio continuum emission have long en exploited to acquire knowledge of of processes. in svmbioties Sseacquist ‘Taylor 1990) and it is worth noting that all of he svmbiotic Aliras accessible from the VLA have been detected at ccm., Observations of radio continuum emission have long been exploited to acquire knowledge of of processes in symbiotics Seaquist Taylor 1990) and it is worth noting that all of the symbiotic Miras accessible from the VLA have been detected at cm.
 Our method of determining whether the degenerate companions truly exist is therefore to compare he continuum flux densities of the OLL/LR. colour. mimics with continuum measurements of svmbiotic stars from the northern- and southern-sky surveys by Seaquist. Ixrogulec and Tavlor (1993. hereafter SIVT93) and Ivison Seaquist (in preparation).," Our method of determining whether the degenerate companions truly exist is therefore to compare the continuum flux densities of the OH/IR colour mimics with continuum measurements of symbiotic stars from the northern- and southern-sky surveys by Seaquist, Krogulec and Taylor (1993, hereafter SKT93) and Ivison Seaquist (in preparation)."
 In what follows we describe our continuum measurements of 15PSC OLL/LR colour minies (massive. oxvgen-rich. LIUS types 2n.3n) using the Very Large Array (VLA).," In what follows we describe our continuum measurements of 15 OH/IR colour mimics (massive, oxygen-rich, LRS types 2n–3n) using the Very Large Array (VLA)."
 Observations of 15 ΟΙΗν colour mimics at cem. were carried out during 1993 September 03.04 using the VLA in a hvbrid of the € and D configurations with the northern arm of the array longer than the eastern and western aris., Observations of 15 OH/IR colour mimics at cm were carried out during 1993 September 03–04 using the VLA in a hybrid of the C and D configurations with the northern arm of the array longer than the eastern and western arms.
 The total bandwidth for our observations was MMLIEIz. centred at CGIlz οσα)," The total bandwidth for our observations was MHz, centred at GHz cm)."
 Two separate Le pairs were emploved. cach containing right ancl left circular polarizations. thus four measurements were recorded at. 15-s intervals for cach antenna.," Two separate IF pairs were employed, each containing right and left circular polarizations, thus four measurements were recorded at 15-s intervals for each antenna."
 Later. during mapping. the four measurements were averaged for each time interval.," Later, during mapping, the four measurements were averaged for each time interval."
 Phe ΕΑΝΝΕ of the svnthesized. beam. (averaged: between: major and minor axes) was about 7 aresec., The FWHM of the synthesized beam (averaged between major and minor axes) was about 7 arcsec.
 The observing procedure was standard in most respects., The observing procedure was standard in most respects.
 To relieve these problems and concerns. we introduce a supplementary function into the A-variance analysis which is used to weight the data points in the spatial map according to their significance.," To relieve these problems and concerns, we introduce a supplementary function into the $\Delta$ -variance analysis which is used to weight the data points in the spatial map according to their significance."
 This helps to derive correct contributions of data points with a different signal-to-noise ratio to the structure information on a particular spatial scale and it allows us to calculate the A-variance in. Fourier space and thus to make use of the numerical advantages of the fast Fourier transform algorithm., This helps to derive correct contributions of data points with a different signal-to-noise ratio to the structure information on a particular spatial scale and it allows us to calculate the $\Delta$ -variance in Fourier space and thus to make use of the numerical advantages of the fast Fourier transform algorithm.
 After revising the fundamental properties of the A-variance and defining appropriate images to test the method in Sect., After revising the fundamental properties of the $\Delta$ -variance and defining appropriate images to test the method in Sect.
 2. we introduce the concepts of the improved A-variance including a weighting function in Sect.," 2, we introduce the concepts of the improved $\Delta$ -variance including a weighting function in Sect."
 3 and optimise it with respect to the wavelet filter function in Sect., 3 and optimise it with respect to the wavelet filter function in Sect.
 4. where we also verify its performance by extensively testing 1t against the test structures.," 4, where we also verify its performance by extensively testing it against the test structures."
 summarises our findings providing recommendations for the optimum method and£o wavelet to use., summarises our findings providing recommendations for the optimum method and wavelet to use.
 In a second paper. we test the capability of the new method applying it to simulations of interstellar turbulence and observed molecular line maps exploiting. the improved sensitivity to derive general properties of interstellar turbulence.," In a second paper, we test the capability of the new method applying it to simulations of interstellar turbulence and observed molecular line maps exploiting the improved sensitivity to derive general properties of interstellar turbulence."
 The A-variance analysis was comprehensively introduced by Stutzkietal.(1998) and Benschetal.(2001)., The $\Delta$ -variance analysis was comprehensively introduced by \citet{Stutzki} and \citet{Bensch}.
. Here. we only repeat those equations which are essential to understand the extensions proposed in Sects.," Here, we only repeat those equations which are essential to understand the extensions proposed in Sects."
 3 and 4.., \ref{sect_edge} and \ref{sect_filter}.
 Although the A- can be used in principle for an arbitrary number of dimensions we restrict ourselves to the two-dimensional case. i.e. the analysis of maps or images.," Although the $\Delta$ -variance can be used in principle for an arbitrary number of dimensions we restrict ourselves to the two-dimensional case, i.e. the analysis of maps or images."
 The A-variance measures the amount of structure on a given scale / in a map f(r) by filtering the map with a spherically symmetric down-up-down function of size / (French-hat filter) and computing the variance of the thus filtered map., The $\Delta$ -variance measures the amount of structure on a given scale $l$ in a map $f(\vec{r})$ by filtering the map with a spherically symmetric down-up-down function of size $l$ (French-hat filter) and computing the variance of the thus filtered map.
" It is given by where. (imthe average (Quy)is taken over the area of the map. the symbol s stands for a convolution. and (2, describes the French-hat function defined as Thus the filter consists of a positive core and a negative annulus where the width of the annulus agrees with the diameter of the core and!.."," It is given by where, the average is taken over the area of the map, the symbol $*$ stands for a convolution, and $\bigodot_l$ describes the French-hat function defined as Thus the filter consists of a positive core and a negative annulus where the width of the annulus agrees with the diameter of the core and."
 In a more general picture one can consider the filter function as a wavelet composed of a negative and a positive part both normalised to integral values of unity so that the overall filter has a vanishing integral., In a more general picture one can consider the filter function as a wavelet composed of a negative and a positive part both normalised to integral values of unity so that the overall filter has a vanishing integral.
 Using an arbitrary diameter ratio between the annulus and the core v we can write The “traditional” A-variance filter is reproduced for a diameter ratio v23., Using an arbitrary diameter ratio between the annulus and the core $v$ we can write The “traditional” $\Delta$ -variance filter is reproduced for a diameter ratio $v=3$.
 We come back to discussing the choice of v in Sect., We come back to discussing the choice of $v$ in Sect.
 4., 4.
 Because the average distance between two points in the core and the annulus of the filter is close to the length / (see Sect. 4.2)).," Because the average distance between two points in the core and the annulus of the filter is close to the length $l$ (see Sect. \ref{sect_effectivelength}) ),"
 the convolved map only retains variations on that scale whereas variations on smaller and larger scales are suppressed., the convolved map only retains variations on that scale whereas variations on smaller and larger scales are suppressed.
 The A-variance as the variance of the convolved map thus measures the amount of structural variation on the scale /., The $\Delta$ -variance as the variance of the convolved map thus measures the amount of structural variation on the scale $l$.
 Plotting the A-variance as a function of the filter size | then provides a spectrum showing the relative amount of structure in a given map as a function of the structure size., Plotting the $\Delta$ -variance as a function of the filter size $l$ then provides a spectrum showing the relative amount of structure in a given map as a function of the structure size.
 The filter convolution and computation of the A-variance can be easily performed in Fourier space where they are reduced to a simple multiplication and integration., The filter convolution and computation of the $\Delta$ -variance can be easily performed in Fourier space where they are reduced to a simple multiplication and integration.
 This directly relates the A-variance to the power spectrum., This directly relates the $\Delta$ -variance to the power spectrum.
" If P(|K|) 1s the radially averaged power spectrum of the structure f(r). the A- Is given by where (2, is the Fourier transform of the filter function with the size / and k denotes the spatial frequency or wavenumber."," If $P(|\vec{k}|)$ is the radially averaged power spectrum of the structure $f(\vec{r})$, the $\Delta$ -variance is given by where $\tilde{\bigodot}_l$ is the Fourier transform of the filter function with the size $l$ and $\vec{k}$ denotes the spatial frequency or wavenumber."
 If the power spectrum is given by a power law. Pikpο|K[*. the A-variance also follows a power law σιxd with a=€—2 within the exponential range 0€Z«6 (Stutzkietal..1998) I.," If the power spectrum is given by a power law, $P(|\vec{k}|)\propto
|\vec{k}|^{-\zeta}$, the $\Delta$ -variance also follows a power law $\sigma_\Delta^2 \propto l^\alpha$ with $\alpha={\zeta-2}$ within the exponential range $0\le \zeta < 6$ \citep{Stutzki} ."
.. Thus. the A-variance shows in principle only information that is also contained in the power spectrum.," Thus, the $\Delta$ -variance shows in principle only information that is also contained in the power spectrum."
 The main advantage of the A-variance method compared to the direct computation of the power spectrum results from the smooth filter shape which provides à very robust way for an angular average. insensitivity to singular variations. and independence of gridding and finite map size effects.," The main advantage of the $\Delta$ -variance method compared to the direct computation of the power spectrum results from the smooth filter shape which provides a very robust way for an angular average, insensitivity to singular variations, and independence of gridding and finite map size effects."
 It provides a good separation of different effects based on their characteristic scale. e.g. à clear distinction between observational noise. structure blurring by the finite telescope beam. and the internal scaling of the astrophysical source.," It provides a good separation of different effects based on their characteristic scale, e.g. a clear distinction between observational noise, structure blurring by the finite telescope beam, and the internal scaling of the astrophysical source."
 À detailed computation of the influence of finite map sizes and telescope blurring was provided by Benschetal.(2001 ).., A detailed computation of the influence of finite map sizes and telescope blurring was provided by \citet{Bensch}. .
where q is the electron charge. ancl applying conservation laws for angular momentum and kinetic energy (rec and v? constant) vields where L is the angular momentum of the charge. £ the kinetic energy. and esind=ο relates (he total velocity to (he component perpendicular to the field line.,"where $q$ is the electron charge, and applying conservation laws for angular momentum and kinetic energy ${r_G} v_\perp$ and ${v^2}$ constant) yields where $L$ is the angular momentum of the charge, $E$ the kinetic energy, and $v\sin{\theta} = v_\perp$ relates the total velocity to the component perpendicular to the field line."
 The pitch anele. 98. is the angle between the field line and the velocity. vector.," The pitch angle, $\theta$, is the angle between the field line and the velocity vector."
 As the charge enters a region ol increasing D. such as a magnetic compression. the pitch angle evolves according to where 02 is the increase in field strength. ancl 04 is the pitch. angle at field strength D98D.," As the charge enters a region of increasing $B$, such as a magnetic compression, the pitch angle evolves according to where $\delta B$ is the increase in field strength and ${\theta_1}$ is the pitch angle at field strength $B+\delta B$."
 When sinf4=1. the charge cannot penetrate further into the compression. and reflects.," When $\sin{\theta_1} = 1$, the charge cannot penetrate further into the compression, and reflects."
 This process. known as magnetic mirroring. is commonly used to confine laboratory plasmas (Dendy1990).," This process, known as magnetic mirroring, is commonly used to confine laboratory plasmas \citep{Dendy}."
. It follows immediatelv (hat mirroring will not occur al a given compression unless the initial pitch angle satisfies Fermi (1949. 1954) showed that moving magnetic mirrors. in particular molecular clouds. can accelerate charees.," It follows immediately that mirroring will not occur at a given compression unless the initial pitch angle satisfies Fermi (1949, 1954) showed that moving magnetic mirrors, in particular molecular clouds, can accelerate charges."
 In the clouds frame of reference (primed). mirroring results in only a change in the sign of E the component of the initial velocity of the charge parallel to the Ποια line in the compressions rest frame.," In the cloud's frame of reference (primed), mirroring results in only a change in the sign of $v^{\prime}_\parallel$, the component of the initial velocity of the charge parallel to the field line in the compression's rest frame."
 Let us work for the moment in the limit where the compression speed and the particle speed are both «e., Let us work for the moment in the limit where the compression speed and the particle speed are both $ \ll c$.
 Transforming to the lab frame. dey=cz26. where ος is the dift velocity of the cloud.," Transforming to the lab frame, $\delta v_\parallel = \pm 2v_c$, where $v_c$ is the drift velocity of the cloud."
 The positive (negative) sign is [or head-on (catch-up) reflections between the charge and cloud., The positive (negative) sign is for head-on (catch-up) reflections between the charge and cloud.
 Catch-up reflections are defined as (hose where the components of the compression and charge velocities parallel to the field line have (he same sign., Catch-up reflections are defined as those where the components of the compression and charge velocities parallel to the field line have the same sign.
 Head on reflections are those where (he parallel components have opposite siens., Head on reflections are those where the parallel components have opposite signs.
 The net change in energy from a reflection is given by, The net change in energy from a reflection is given by
Figure 4. shows our continuum map ofPINS1330-211..,Figure \ref{fig:pkse-contin} shows our continuum map of.
 The two point sources (NE and, The two point sources (NE and
 10P ~10! 10?—106 and Nested Sampling techniques2009)., $10^{13}$ $\sim 10^{15}$ $\sim 10^5 - 10^6$ and Nested Sampling techniques.
.. addressed for the fist time fully relativistic long-term (2008)numerical evolutions of three equal-mass BHs and found that the merger dynamics is very distinct from binaries., addressed for the fist time fully relativistic long-term numerical evolutions of three equal-mass BHs and found that the merger dynamics is very distinct from binaries.
" In particular, the trajectories were intricate and led to singular waveforms, as e.g. their figure 4 shows, in which we can see two mergers."," In particular, the trajectories were intricate and led to singular waveforms, as e.g. their figure 4 shows, in which we can see two mergers."
 Recently there has been an effort in calculating in detail the waveforms of systems of three and four BHs interacting in full GR., Recently there has been an effort in calculating in detail the waveforms of systems of three and four BHs interacting in full GR.
 have developed a knowledgeable scheme to study the (2010)waveforms of such configurations and find intricate templates for the waves., have developed a knowledgeable scheme to study the waveforms of such configurations and find intricate templates for the waves.
" Also, have addressed the problem of critical BH separations (2010)for the formation of a common apparent horizon."," Also, have addressed the problem of critical BH separations for the formation of a common apparent horizon."
 The authors study in detail the aligned equal mass cases for up to 5 BHs., The authors study in detail the aligned equal mass cases for up to 5 BHs.
" If we increase the number of BHs involved in the GW, the number of to increases enormously."," If we increase the number of BHs involved in the GW, the number of templates to develop increases enormously."
" Putting it in Neil Cornish’ templateswords, “The developsensitive dependence on initial conditions will send the template count through the roof”."," Putting it in Neil Cornish' words, “The sensitive dependence on initial conditions will send the template count through the roof”."
 It is consequently important to understand the limits imposed the systems which harbour these sources of GWs., It is consequently important to understand the limits imposed by the physical systems which harbour these sources of GWs.
 byTherefore we physicaladdress the question of the existence of a system with more than two BHs in a relativistic regime., Therefore we address the question of the existence of a system with more than two BHs in a relativistic regime.
 In section [] we calculate the probability of having a relativistic three-body encounter in a dense stellar cluster with three BHs initially unbound.," In section \ref{sec.two_bhs}
 we calculate the probability of having a relativistic three-body encounter in a dense stellar cluster with three BHs initially unbound."
 In section B| we estimate the possibility that an already formed binary of two BHs interacts relativistically with a third BH., In section \ref{sec.bin_bh} we estimate the possibility that an already formed binary of two BHs interacts relativistically with a third BH.
 In section] we summarise our results and give the conclusions., In section \ref{sec.discussion} we summarise our results and give the conclusions.
 Rough estimtes will be sufficient to show how unlikely triple relativistic encounters are., Rough estimtes will be sufficient to show how unlikely triple relativistic encounters are.
" Therefore, for simplicity, we assume that all BHs in a given stellar system have the same mass, m."," Therefore, for simplicity, we assume that all BHs in a given stellar system have the same mass, $m$."
 Let us assumethat we have two of them fly, Let us assumethat we have two of them fly
Since the discovery of a dipole in the CMD (77)τν it has been identified as the Doppler signature of our motion relative to the CAIB vest frame.,"Since the discovery of a dipole in the CMB \citep{lubin:83,fixs:83} it has been identified as the Doppler signature of our motion relative to the CMB rest frame."
 Strong evidence in favor of this interpretation las been provided∙ bv the observation. of à ∙∙∙similar dipolei oaiu the| surtacesurface brigbriehtuesssss of radio galaxies in the same‘ direction (?).., Strong evidence in favor of this interpretation has been provided by the observation of a similar dipole in the surface brightness of radio galaxies in the same direction \citep{bw:02}.
 7. make‘ the distinction between velocity vendipoles caused by our motion aud dipoles which measure the distribujon of clusteringgalaxies.," \citeauthor{bw:02}
 make the distinction between velocity dipoles caused by our motion and clustering dipoles which measure the distribution of galaxies."
 Attempts to measure the clustering dipole of local galaxies iu the 1980s (7777) from only the fluxes and positions of ealaxics led to results that were within 2307 from the CXMB velocity dipole.," Attempts to measure the clustering dipole of local galaxies in the 1980s \citep{md:86,ywrr:86,lahav:87,vs:87} from only the fluxes and positions of galaxies led to results that were within $30\arcdeg$ from the CMB velocity dipole."
 The inclusion of redshift information led to a controversy over out to which distance⋅ the clustering ⋅⋝⋅dipole converges ⋝⋅⋅⋅⋅⋅(????7)..," The inclusion of redshift information led to a controversy over out to which distance the clustering dipole converges \citep{sd:88,llb:89,rowan:90,pv:91,svz:91}."
 Through the 1990s progressively larger redshift surveys were used in au effort to determune where ⋅ ⋅ ⋅ ↑∐↸∖↸⊳↕∏↴∖↴↑↸∖↥⋅∐↕∶↴∙⊾≼∐↻∪↕↸∖↸⊳∪∐↖⇁↸∖↥⋅∶↴∙⊾↸∖↴∖↴⋜⋯≼↧↑∪∐⊔↻↥⋅∪↖⇁↸∖↑↕∐∖ calenlation of cosmological parameters (1772)..," Through the 1990s progressively larger redshift surveys were used in an effort to determine where the clustering dipole converges and to improve the calculation of cosmological parameters \citep{stra:92,huds:93,schm:99,rowan:00}."
 These improvements included determining the shot noise in the sample. optimizing the window fuuctiou for smoothing aud estimating the coutribution of nonlinear effects to the velocity dipole (?)..," These improvements included determining the shot noise in the sample, optimizing the window function for smoothing and estimating the contribution of nonlinear effects to the velocity dipole \citep{stra:92}."
 These efforts have receuthy determined that the ↸⊳↕∏↴∖↴↑↸∖↥⋅↕∐∶↴⋁≼∐↻∪↕↸∖↸⊳∪∐↖↽↸∖↥⋅∶↴∙⊾↸∖↴∖↴⋜↧↕⋅↱⊐∩⊇∩∩∕∣↓⋀∖↕↻↸⊳ (22)," These efforts have recently determined that the clustering dipole converges at $150 - 200 h^{-1}$ Mpc \citep{schm:99,rowan:00}."
 OMASS irs(2) is. the frst⋅ near-intravedDog (TITER.- passhands} all-sky survey., 2MASS \citep{skrut:97} is the first near-infrared $JHK_s$ passbands) all-sky survey.
 .2MASS- has an effective⋅⋅ ⋅ . ∐⊔⋜↕∶↴∙⊾↸∖↥⋅↸∖↴∖↴∪↕∏⊓∪∐∪↕↓⋜∐⋅↸⊳↴∖↴↸∖↸⊳∪↕≼↧⋜⋯≼↧↓∩∩∖∩⊾↥⋅↸∖⋜↧↑↸∖↥⋅ . ↽ o υπ ---- IRAS.," 2MASS has an effective image resolution of 1 arcsecond and $100\times$ greater sensitivity than the far-infrared all-sky survey, IRAS."
 Most passbands tend to be seusitive to star formation rate. while the A passbaud is most sensitive to stellar mass (2).. which probably makes the A-baund a better tracer of total mass.," Most passbands tend to be sensitive to star formation rate, while the $K_s$ passband is most sensitive to stellar mass \citep{bd:00}, which probably makes the $K_s$ -band a better tracer of total mass."
 Therefore. 2\TASS offers a unique opportunity for calculating a flux-weighted clustering dipole.," Therefore, 2MASS offers a unique opportunity for calculating a flux-weighted clustering dipole."
 The median depth of the survey is 2=0.073. or 220h+ Alpe (2)... a distance past where the ] ‘ ≺∐≻∪↕↸∖∐↧↴∖↴↴⋝↸∖↸∖↕↴∖↴∐∪↖↖⇁∐∪↸," The median depth of the survey is $z=0.073$, or $220 h^{-1}$ Mpc \citep{bell:03}, a distance past where the dipole has been shown to converge."
⊳∪∐↖↽↸∖↥⋅∩⊾↸∖∙⊟∩⊾↿∐⋅↸∖↕↴∖↴∐∪↖↖↽↴∖↴o e the distance distribution for a maenitude-limited sample of 2ATASS ealaxies as determined from, Figure \ref{fig:select} shows the distance distribution for a magnitude-limited sample of 2MASS galaxies as determined from
0.5 and X; — 1 teem 7.,0.5 and $\Sigma_l$ = 1–4 g $^{-2}$.
" The planetesimals have m, = 107! e: the oligarchs have my=107? e. comparable to the isolation mass for this grid."," The planetesimals have $m_s$ = $10^{24}$ g; the oligarchs have $m_l = 10^{26}$ g, comparable to the isolation mass for this grid."
 The Hill parameter increases from py=0.04 (lower panel) to py = 0.07 (nildle panel) to py = 0.13 (upper panel)., The Hill parameter increases from $p_H = 0.04$ (lower panel) to $p_H$ = 0.07 (middle panel) to $p_H$ = 0.13 (upper panel).
 In each frame. the colored. tracks indicate the eccentricities of oligarchs in the grid.," In each frame, the colored tracks indicate the eccentricities of oligarchs in the grid."
 Along the track of a single oligarch. the color changes when two oligarchs merge.," Along the track of a single oligarch, the color changes when two oligarchs merge."
 Although a single color does not track ihe motion of an individual oligarch throughout the evolution. the ensemble of curves tracks ihe merger history of the final set of oligarchs.," Although a single color does not track the motion of an individual oligarch throughout the evolution, the ensemble of curves tracks the merger history of the final set of oligarchs."
 Tracking backwards in time along connected curves vields the evolution of one of the oligarchs that remains at the end of the calculation., Tracking backwards in time along connected curves yields the evolution of one of the oligarchs that remains at the end of the calculation.
 The legends list X; and the initial and final number of oligarchs (Figure 2)., The legends list $\Sigma_l$ and the initial and final number of oligarchs (Figure 2).
 The eccentricity evolution is sensitive (ο the initial mass in the swarm., The eccentricity evolution is sensitive to the initial mass in the swarm.
" For Xj— 1 ο em the oligarchs have a tvpical separation of 1520 Ay, ancl do not have significant interactions."," For $\Sigma_l$ = 1 g $^{-2}$, the oligarchs have a typical separation of 15–20 $R_H$ and do not have significant interactions."
 As the oligarchs stir up the planetesimals. dynamical frietion maintains a constant ratio eer~ nim)? ~ 0.1.," As the oligarchs stir up the planetesimals, dynamical friction maintains a constant ratio $e_s/e_l \sim$ $(m_l/m_s)^{1/2}$ $\sim$ 0.1."
 Although the orbits of the oligarchs become more and more eccentric. the growth of e; is slow (Figure 1. lower panel).," Although the orbits of the oligarchs become more and more eccentric, the growth of $e_l$ is slow (Figure 1, lower panel)."
 It takes  1 Myr to reach €;~ 0.01 and another 89 Myr to reach e;~ 0.02., It takes $\sim$ 1 Myr to reach $e_l \sim$ 0.01 and another 8–9 Myr to reach $e_l \sim$ 0.02.
 After ~ 100 Myr. when e~ 0.04. the orbits heein (o overlap.," After $\sim$ 100 Myr, when $e \sim$ 0.04, the orbits begin to overlap."
" As X, increases. orbital interactions occur on shorter timescales (Figure 1. middle and upper panels)."," As $\Sigma_l$ increases, orbital interactions occur on shorter timescales (Figure 1, middle and upper panels)."
" For X, = 2 g 2. the initial separation of the oligarchs is ~ 1012 Ry."," For $\Sigma_l$ = 2 g $^{-2}$, the initial separation of the oligarchs is $\sim$ 10–12 $R_H$."
 It takes only 5x107 vr for the typical eccentricity to reach €~ 0.01. when the mininium separation between oligarchs is only ~ 8 Ry.," It takes only $5 \times 10^4$ yr for the typical eccentricity to reach $e \sim$ 0.01, when the minimum separation between oligarchs is only $\sim$ 8 $R_H$."
 At ~LO? vr. €~ 0.02 and orbits overlap.," At $\sim 10^5$ yr, $e \sim$ 0.02 and orbits overlap."
 Two oligarchs merge al c2x10? vr: two more merge al ~ I Myr., Two oligarchs merge at $\sim 2 \times 10^5$ yr; two more merge at $\sim$ 1 Myr.
 When we stop the caleulation at 1 Myr. (wo oligarchs remain in eccentricorbits. οZ 0.025 and are likely to merge with other oligarchs.," When we stop the calculation at 1 Myr, two oligarchs remain in eccentricorbits, $e \gtrsim$ 0.025 and are likely to merge with other oligarchs."
 For Xj {σοι 7. orbits begin to overlap in ~10! vr.," For $\Sigma_l$ = 4 g $^{-2}$, orbits begin to overlap in $\sim 10^4$ yr."
 After a single merger at ~LO! vr. orbits continue to grow more eccentric.," After a single merger at $\sim 10^4$ yr, orbits continue to grow more eccentric."
 At 5x10! vr. all orbits overlap and the merger rate accelerates.," At $5 \times 10^4$ yr, all orbits overlap and the merger rate accelerates."
 There are two additional mergers al ~10? vr. another two bv 3x10? vr. and three more by ~ 1. Myr.," There are two additional mergers at $\sim 10^5$ yr, another two by $3 \times 10^5$ yr, and three more by $\sim$ 1 Myr."
 At 1 Myr. all of the remaining oligarchs have eccentric. overlapping orbits and many are likely to merge over the next lew Avr.," At 1 Myr, all of the remaining oligarchs have eccentric, overlapping orbits and many are likely to merge over the next few Myr."
 Figure 2 illustrates the chaotic behavior of the semimajor axis in these test cases., Figure 2 illustrates the chaotic behavior of the semimajor axis in these test cases.
 For ο the oligarchs have a constant semimajor axis for almost 100 Myr.," For $\Sigma_l$ = 1 g $^{-2}$, the oligarchs have a constant semimajor axis for almost 100 Myr."
 When the total mass is a [actor of two larger (Ej = 2 g 7). the semimajor axes are constant [or ~ LO? vr.," When the total mass is a factor of two larger $\Sigma_l$ = 2 g $^{-2}$ ), the semimajor axes are constant for $\sim$ $10^5$ yr."
 Once the orbits start to overlap. several oligarchs show considerable excursions in semimajor axis of 0.1. AU or more. e to of the grid.," Once the orbits start to overlap, several oligarchs show considerable excursions in semimajor axis of 0.1 AU or more, $\sim$ to of the grid."
 Two of these oligarchs merge with other oligarchs., Two of these oligarchs merge with other oligarchs.
 For V; = 4 g 7. the orbits are very chaotic. with larger radial excursions and many mergers.," For $\Sigma_l$ = 4 g $^{-2}$ , the orbits are very chaotic, with larger radial excursions and many mergers."
the Dirac-Milne universe.,the Dirac-Milne universe.
 However. this present belief 1s based on a QCD calculation. whereas the situation of the primordial universe is more complicated. including. additional light leptons (electrons. positrons. neutrinos. and antineutrinos).," However, this present belief is based on a QCD calculation, whereas the situation of the primordial universe is more complicated, including additional light leptons (electrons, positrons, neutrinos, and antineutrinos)."
 In addition. present calculations use light quark masses for the u and d quarks that are significantly higher than. the actual masses of these quarks.," In addition, present calculations use light quark masses for the u and d quarks that are significantly higher than the actual masses of these quarks."
 Therefore. the observation of laree matter-antimatter domains would be an extremely useful indication that. in contrast to present expectations. there is a sharp transition allowing the survival of significant regions of antimatter at the QCD transition.," Therefore, the observation of large matter-antimatter domains would be an extremely useful indication that, in contrast to present expectations, there is a sharp transition allowing the survival of significant regions of antimatter at the QCD transition."
 It should also be noted that some authors are clearly considering the possibility that baryogenesis occurs at the QCD transition or at a O( 100 MeV) temperature (see for example ? for a review)., It should also be noted that some authors are clearly considering the possibility that baryogenesis occurs at the QCD transition or at a $O$ (100 MeV) temperature (see for example \citet{Dolgov92} for a review).
 Acoustic waves then propagate in the plasma as long as matter and antimatter are in contact. until the gravitational decoupling. estimated in the previous section ασ=3x107.," Acoustic waves then propagate in the plasma as long as matter and antimatter are in contact, until the gravitational decoupling, estimated in the previous section at $z_{end} \approx 3\times 10^{4}$."
 With these values. the comoving sound horizon is found to be," With these values, the comoving sound horizon is found to be."
 The expression of the angular position of the first acoustic peak then follows It can be shown that the redshift of the last scattering surface in the Dirac-Milne universe is a few percent lower than in the standard cosmology. here again due to the late decoupling of the radiative processes leading to recombination.," The expression of the angular position of the first acoustic peak then follows It can be shown that the redshift of the last scattering surface in the Dirac-Milne universe is a few percent lower than in the standard cosmology, here again due to the late decoupling of the radiative processes leading to recombination."
" We found that 5,~1040.", We found that $z_*\sim 1040$.
" Calculating the multipole of the acoustic scale using expression (30)). we obtain £,~160."," Calculating the multipole of the acoustic scale using expression \ref{acoustic}) ), we obtain $\ell_a\sim 160$."
" The standard value of this quantity is £,~300 (2)...", The standard value of this quantity is $\ell_a\sim 300$ \citep{WMAP1}. .
 Instead of a discrepancy of a factor =169. there is an almost exact compensation between the lareer geometrical term. induced by the oper geometry of the Dirac-Milne universe. and the larger sound horizon. caused by the slow evolution of the expansion rate before recombination.," Instead of a discrepancy of a factor $\approx 169$, there is an almost exact compensation between the larger geometrical term, induced by the open geometry of the Dirac-Milne universe, and the larger sound horizon, caused by the slow evolution of the expansion rate before recombination."
 Taking into account the numerous approximations in the model. this remarkable coincidence is quite unexpected and represents a fascinating motivation to study the Dirac-Milne universe in more detail.," Taking into account the numerous approximations in the model, this remarkable coincidence is quite unexpected and represents a fascinating motivation to study the Dirac-Milne universe in more detail."
 However. the sound horizon seale is also imprinted in the large-scale structure power spectrum under the form of small oscillations (2) called baryonic acoustic oscillations (BAOs).," However, the sound horizon scale is also imprinted in the large-scale structure power spectrum under the form of small oscillations \citep{Eisenstein98} called baryonic acoustic oscillations (BAOs)."
 These oscillations are expected. at least in a first approximation. on the same scale as the sound horizon.," These oscillations are expected, at least in a first approximation, on the same scale as the sound horizon."
 As discussed above. the sound horizon is much larger in the Dirac-Milne universe than in the standard cosmology.," As discussed above, the sound horizon is much larger in the Dirac-Milne universe than in the standard cosmology."
 Admitting that there are BAOs in the Dirac-Milne universe. they should be expected on a scale much larger than that of the standard cosmology.," Admitting that there are BAOs in the Dirac-Milne universe, they should be expected on a scale much larger than that of the standard cosmology."
 The claimed detection of these BAOs on the expected scale (within the standard cosmology) of (?).. presently detected at the ~30 level. if confirmed by ongoing experiments. would therefore provide a strong constraint on the Dirac-Milne universe.," The claimed detection of these BAOs on the expected scale (within the standard cosmology) of \citep{Eisenstein05}, presently detected at the $\sim 3 \sigma$ level, if confirmed by ongoing experiments, would therefore provide a strong constraint on the Dirac-Milne universe."
 Since. the standard ACDM model is in. good agreement with observations but rather poorly theoretically motivated. we have studied here an alternative cosmological model. the Dirac-Milne universe.," Since the standard $\Lambda$ CDM model is in good agreement with observations but rather poorly theoretically motivated, we have studied here an alternative cosmological model, the Dirac-Milne universe."
 Inspired by the work of Dirac. Kerr. and Carter. this model restores the symmetry between matter and antimatter.," Inspired by the work of Dirac, Kerr, and Carter, this model restores the symmetry between matter and antimatter."
 Relying on the symmetries of the Kerr-Newman solutions in. general relativity. it makes the hypothesis that particles and antiparticles behave similarly to quasiparticles such as electrons and holes in a semiconductor. and that antimatter has a negative active gravitational mass.," Relying on the symmetries of the Kerr-Newman solutions in general relativity, it makes the hypothesis that particles and antiparticles behave similarly to quasiparticles such as electrons and holes in a semiconductor, and that antimatter has a negative active gravitational mass."
 A fundamental characteristic of this Universe is the linear evolution of its scale factor. which solves in an elegant way ¥-Botltthe problems of the horizon and the age of the universe.," A fundamental characteristic of this Universe is the linear evolution of its scale factor, which solves in an elegant way both the problems of the horizon and the age of the universe."
 For primordial nucleosynthesis. we have found that the Dirac-Milne universe is able to produce He at an adequate level. while producing “Li nuclei in proportions admittedly a factor three higher than the observed values but with a smaller disagreement between observations and. predictions than the standard cosmology.," For primordial nucleosynthesis, we have found that the Dirac-Milne universe is able to produce $^4$ He at an adequate level, while producing $^7$ Li nuclei in proportions admittedly a factor three higher than the observed values but with a smaller disagreement between observations and predictions than the standard cosmology."
 We have also shown that surface annihilations at the frontiers of matter and antimatter naturally lead to the production of D nuclei. in amounts. that are proportional to the inverse of the characteristic size of the emulsion.," We have also shown that surface annihilations at the frontiers of matter and antimatter naturally lead to the production of D nuclei, in amounts that are proportional to the inverse of the characteristic size of the emulsion."
 The main focus of this study has been the production of D. although the assumption that the emulsion has a fixed characteristic size is clearly an approximation.," The main focus of this study has been the production of D, although the assumption that the emulsion has a fixed characteristic size is clearly an approximation."
 Relaxing this assumption will allow the possibility of the total annihilation of small patches of antimatter inside larger regions of matter., Relaxing this assumption will allow the possibility of the total annihilation of small patches of antimatter inside larger regions of matter.
 This might lead toa net production of D by nucleodisruption. which has a higher D/*He (?)..," This might lead toa net production of D by nucleodisruption, which has a higher $^3$ \citep{Balestra88},"
confidence in the flix averages in those nights.,confidence in the flux averages in those nights.
 In the first hour after impact. the [OI] flux rises by about a factor of 3. and then slowly declines after peak [ας in (he aperture was reached 45 minutes alter impact.," In the first hour after impact, the [OI] flux rises by about a factor of 3, and then slowly declines after peak flux in the aperture was reached 45 minutes after impact."
 The decline in flux is slower than that of CN flux and of blue broad-band continu» flux., The decline in flux is slower than that of CN flux and of blue broad-band continuum flux.
 In the night following the impact [OI] flux in the photometry aperture is down to less than half of the peak flux. but still appears somewhat elevated above the level seen before impact. even though tliis statement is uncertain due to the poor signal-to-noise of the data.," In the night following the impact [OI] flux in the photometry aperture is down to less than half of the peak flux, but still appears somewhat elevated above the level seen before impact, even though this statement is uncertain due to the poor signal-to-noise of the data."
 Three ancl four nights after the impact. the [OL] flux in the aperture is indistinguishable from that before the impact.," Three and four nights after the impact, the [OI] flux in the aperture is indistinguishable from that before the impact."
 Spatially. the [OL] flux expands in unison with the continuum. and much slower than the CN flux.," Spatially, the [OI] flux expands in unison with the continuum, and much slower than the CN flux."
 CN is probably a daughter species of a vet unidentified parent molecule. whereas ΟΕ is both a daughter anc a granddaughter of HsO anc can also be produced from other parents.," CN is probably a daughter species of a yet unidentified parent molecule, whereas [OI] is both a daughter and a granddaughter of $_2$ O and can also be produced from other parents."
 Dissociation of HaO (and other parent molecules) produces OI in its excited state of short lifetime and the [OI] emission therefore traces the presence of the parent. closely., Dissociation of $_2$ O (and other parent molecules) produces OI in its excited state of short lifetime and the [OI] emission therefore traces the presence of the parent closely.
 Additionally. the impact released a great. deal of large sO ice particles which had a slower outflow velocity than the gas and subsequently fragmented. with some producing [OI].," Additionally, the impact released a great deal of large $_2$ O ice particles which had a slower outflow velocity than the gas and subsequently fragmented, with some producing [OI]."
 This more complicated combined production and close link to the presence of [LO ice and gas can account for the different scale lengths of [OI] when compared with CN and for the different temporal evolution of the [OI] flux., This more complicated combined production and close link to the presence of $_2$ O ice and gas can account for the different scale lengths of [OI] when compared with CN and for the different temporal evolution of the [OI] flux.
 Overall. the spectrophotomeltry of comet Tempel 1 both before and after the impact indicates a red color of the scattered light. similar to that found in most comets.," Overall, the spectrophotometry of comet Tempel 1 both before and after the impact indicates a red color of the scattered light, similar to that found in most comets."
 In the, In the
plane for all bursts.,plane for all bursts.
 This could well explain why almost all outliers to Amati relation have redshifts z«0.2., This could well explain why almost all outliers to Amati relation have redshifts $z<0.2$.
" The Amati relation is created by apparently low dispersion, highly correlated bivariate distribution of GRBs in the plane."," The Amati relation is created by apparently low dispersion, highly correlated bivariate distribution of GRBs in the plane."
 The low dispersion effect is itself created by the detection and selection effects on the faint and low energy edges., The low dispersion effect is itself created by the detection and selection effects on the faint and low energy edges.
" To show this more clearly, we derive the linear fits in the observer and rest frames to the sample of G08 bursts by excluding outliers in both planes as labeled in Figure (except XRF 050416A which is not an outlier in either of [9]the planes and was labeled for another reason to be discussed below), for which we find, The variance between Όροι and Epint in both the observer and rest frames, as shown in the plots of Figure[9] has about the same scatter — 0.23 dex and 0.21 dex — with a slightly higher correlation coefficient being found in the rest frame of the bursts: Τκ.ους=0.59+0.05,7.50 TKrest=0.65+0.04,80 respectively."," To show this more clearly, we derive the linear fits in the observer and rest frames to the sample of G08 bursts by excluding outliers in both planes as labeled in Figure \ref{AG08} (except XRF 050416A which is not an outlier in either of the planes and was labeled for another reason to be discussed below), for which we find, The variance between $\sbol$ and $\epi$ in both the observer and rest frames, as shown in the plots of Figure \ref{AG08} has about the same scatter – 0.23 dex and 0.21 dex – with a slightly higher correlation coefficient being found in the rest frame of the bursts: $\tau_{K,obs}=0.59\pm 0.05, 7.5\sigma$ $\tau_{K,rest}=0.65\pm 0.04, 8\sigma$ respectively."
" This slight improvement, however, is statistically marginal, undermining a potential physical origin to the Amati relation."," This slight improvement, however, is statistically marginal, undermining a potential physical origin to the Amati relation."
" According to F-test, there is only lo (p= 0.285) weak evidence of a significant difference between the variances of the observer and rest frame Amati relations."," According to F-test, there is only $1\sigma$ $p=0.285$ ) weak evidence of a significant difference between the variances of the observer and rest frame Amati relations."
 In order to show how redshifting of the parameters on, In order to show how redshifting of the parameters on
line parameters given in Table 1..,line parameters given in Table \ref{linepara}.
 We detect a continuum level of 12.8 bbeam™! at GGHz., We detect a continuum level of 12.8 $^{-1}$ at GHz.
" Our GGHz spectrum shows two absorption features, one centered at the systemic velocity of M82 corresponding to the lline, and a second stronger feature blue-shifted by ~1.8 GGHz with respect to the systemic velocity."," Our GHz spectrum shows two absorption features, one centered at the systemic velocity of M82 corresponding to the line, and a second stronger feature blue-shifted by $\sim1.8$ GHz with respect to the systemic velocity."
" We identify the shifted absorption feature as (vies=1115.186 GGHz, Mürrtz citemuertz98))."," We identify the blue-shifted absorption feature as $\nu_{\rm rest}=1115.186$ GHz, Mürrtz \\cite{muertz98}) )."
 Both absorption line profiles are identical within the uncertainties (see Fig. 2))., Both absorption line profiles are identical within the uncertainties (see Fig. \ref{absprofiles}) ).
 The absorption profile is approximated reasonably well by a single Gaussian (see Table 1 for the line parameters)., The absorption profile is approximated reasonably well by a single Gaussian (see Table \ref{linepara} for the line parameters).
" The continuum level detected at GGHz is 78 bbeam""!.", The continuum level detected at GHz is 78 $^{-1}$.
 The lline at GGHz is detected in emission., The line at GHz is detected in emission.
 Its line profile differs from both the eemission profile and the aabsorption profiles., Its line profile differs from both the emission profile and the absorption profiles.
" It shows emission between νιοκ=500 ((similar to the velocity range covered by CO at the same spatial resolution, see below) and is almost flat-topped for velocities between 100 andkms."," It shows emission between $_{\rm LSR}=50-500$ (similar to the velocity range covered by CO at the same spatial resolution, see below) and is almost flat-topped for velocities between 100 and."
. Thus the spectrum does not indicate absorption (or absence of emission) at the systemic velocity., Thus the spectrum does not indicate absorption (or absence of emission) at the systemic velocity.
" The spectrum can be decomposed into two Gaussian profiles, with parameters given in Table 1.."," The spectrum can be decomposed into two Gaussian profiles, with parameters given in Table \ref{linepara}."
" The continuum flux detected at GHz is 61 bbeam""!.", The continuum flux detected at GHz is 61 $^{-1}$.
" Given the large body of high spatial resolution observations of molecular gas tracers published for M82, the line profile of the water lines can be compared to other data to learn more about the location and extent of the water emitting/absorbing regions in the disk."," Given the large body of high spatial resolution observations of molecular gas tracers published for M82, the line profile of the water lines can be compared to other data to learn more about the location and extent of the water emitting/absorbing regions in the disk."
 We here compare the water line profiles to the high spatial resolution (3.5) ddata cube obtained by Walter ((2002)); 1200 (CO thereafter) is the best-studied tracer of the molecular gas in M82., We here compare the water line profiles to the high spatial resolution $3.5''$ ) data cube obtained by Walter \cite{walter02}) ); $^{12}$ CO (CO thereafter) is the best-studied tracer of the molecular gas in M82.
 We first compare the CO spectra in beams synthesized to the same spatial resolutions as the HIFI beams., We first compare the CO spectra in beams synthesized to the same spatial resolutions as the HIFI beams.
" From the comparison of the aabsorption spectrum to CO, it is apparent that the absorption is not only detected in the pronounced absorption feature close to the systemic velocity, but also at velocities in the wings of the CO profile (Fig."," From the comparison of the absorption spectrum to CO, it is apparent that the absorption is not only detected in the pronounced absorption feature close to the systemic velocity, but also at velocities in the wings of the CO profile (Fig."
 1 bottom)., \ref{lines} bottom).
" It is therefore tempting to speculate that the lack of absorption at certain velocities has a geometrical origin, i.e., that gas at these velocities is located behind the continuum."," It is therefore tempting to speculate that the lack of absorption at certain velocities has a geometrical origin, i.e., that gas at these velocities is located behind the continuum."
" This is also supported by the shape of the lline emission profile, which shows that water is abundant in the gas phase of M82 at all velocities where CO (i.e. molecular gas) is present."," This is also supported by the shape of the line emission profile, which shows that water is abundant in the gas phase of M82 at all velocities where CO (i.e. molecular gas) is present."
 The very good correspondence of the aabsorption profile near the systemic velocity suggests that the ionised water traces the same gas as is detected in the water absorption., The very good correspondence of the absorption profile near the systemic velocity suggests that the ionised water traces the same gas as is detected in the water absorption.
" A closer inspection of the pprofile shows, however, a lack of absorption in the red wing of the line profile (see Fig.2))."," A closer inspection of the profile shows, however, a lack of absorption in the red wing of the line profile (see \ref{absprofiles}) )."
 The blue wing is only partly covered by our spectrum and shows emission at the very blue edge., The blue wing is only partly covered by our spectrum and shows emission at the very blue edge.
" This could come from calibration uncertainties at the edge of the IF-band, but it is unclear whether this feature is an artifact or is real."," This could come from calibration uncertainties at the edge of the IF-band, but it is unclear whether this feature is an artifact or is real."
 Our finding that the lline is observed in absorption while the lline is detected in emission can be used to obtain an estimate of the excitation temperatures of both lines., Our finding that the line is observed in absorption while the line is detected in emission can be used to obtain an estimate of the excitation temperatures of both lines.
" We used the dust model by Siebenmorgen Krüggel (2007)) to estimate a background temperature of KK and 20KK at and GGHz, respectively."," We used the dust model by Siebenmorgen Krüggel \cite{siebenmorgen07}) ) to estimate a background temperature of K and K at and GHz, respectively."
" This implies Te,« 20KK for aand Tex>18 KK for ((or Tex«19 KK if both lines are close to LTE).", This implies $_{\rm ex} < 20$ K for and $_{\rm ex} > 18$ K for (or $_{\rm ex}\approx 19$ K if both lines are close to LTE).
" Given the complexity of the water energy level diagram and the various level population channels (collisional or radiative), detailed models will be required for investigating the underlying excitation mechanisms."," Given the complexity of the water energy level diagram and the various level population channels (collisional or radiative), detailed models will be required for investigating the underlying excitation mechanisms."
" Owing to the much larger beam size of the oobservations, a comparison to the other water lines is not straightforward."," Owing to the much larger beam size of the observations, a comparison to the other water lines is not straightforward."
" In comparison to CO, however, it is apparent that the emission arises exclusively from velocities in the line wings of the CO spectrum."," In comparison to CO, however, it is apparent that the emission arises exclusively from velocities in the line wings of the CO spectrum."
" These velocities mainly correspond to emission in the southwestern and northeastern molecular lobes that are located within the 41"" beam (see Fig.3 for the CO", These velocities mainly correspond to emission in the southwestern and northeastern molecular lobes that are located within the $41''$ beam (see \ref{co-profilematch} for the CO
fitted with simple power-laws.,fitted with simple power-laws.
" In fact, the spectra can be fitted accurately by the standard FRII model for parameters avoiding much spectral ageing, if we assume that m>2."," In fact, the spectra can be fitted accurately by the standard FRII model for parameters avoiding much spectral ageing, if we assume that $m>2$."
" For example, we obtain an excellent fit, x?=0.38, for the spectrum of the north outer lobe by setting m—2.5."," For example, we obtain an excellent fit, $\chi^2 = 0.38$, for the spectrum of the north outer lobe by setting $m=2.5$."
 The problem with this solution is the very young age predicted by the model of t= 6MMyr., The problem with this solution is the very young age predicted by the model of $t=6$ Myr.
 The outer lobes would have to expand with an average velocity of almost 0.4cc and this requires an extremely high jet power in excess of 1040 WW. It is therefore unlikely that such a solution accurately describes the outer lobes of 118344-620., The outer lobes would have to expand with an average velocity of almost c and this requires an extremely high jet power in excess of $10^{40}$ W. It is therefore unlikely that such a solution accurately describes the outer lobes of 1834+620.
 The model with £8=1.5 and k=0 requires a density distribution in the source environment consistent with the range of properties in the ? galaxy group sample., The model with $\beta =1.5$ and $k=0$ requires a density distribution in the source environment consistent with the range of properties in the \citet{jph07} galaxy group sample.
" In contrast to the situation for 11450--333, there is no need to increase k in order to allow for denser, more realistic source environments."," In contrast to the situation for 1450+333, there is no need to increase $k$ in order to allow for denser, more realistic source environments."
 The source density required for the model with k=10 is about two times higher than the upper end of the range of the sample of ?.., The source density required for the model with $k=10$ is about two times higher than the upper end of the range of the sample of \citet{jph07}.
" Much higher values for k, comparable to the k—100 for 114504-333, would again result in unacceptably high jet powers and densities for the source environment."," Much higher values for $k$, comparable to the $k=100$ for 1450+333, would again result in unacceptably high jet powers and densities for the source environment."
 These results strongly suggest that k is not very large in the outer lobes of 118344-620., These results strongly suggest that $k$ is not very large in the outer lobes of 1834+620.
" Figs. 12,,"," Figs. \ref{1834powerdensity},"
 19 and 14 show the confidence contours on the model parameters for the assumed error on the flux measurements., \ref{1834powertime} and \ref{1834powerfield} show the confidence contours on the model parameters for the assumed error on the flux measurements.
" Again, the smaller errors argued for above would decrease the range of the confidence contours further."," Again, the smaller errors argued for above would decrease the range of the confidence contours further."
" These plots are analogous to Figs. 7, 8"," These plots are analogous to Figs. \ref{1450powerdensity}, ,"
 and 9 for B11450--333., \ref{1450powertime} and \ref{1450powerfield} for 1450+333.
 The model parameters are constrained to a similar degree for 118344-620., The model parameters are constrained to a similar degree for 1834+620.
" However, in Fig."," However, in Fig."
 19 the contours for the two outer lobes do not overlap., \ref{1834powertime} the contours for the two outer lobes do not overlap.
" We would expect that the plotted parameters, the jet power and the source age, should be the same for both lobes on either side of the source."," We would expect that the plotted parameters, the jet power and the source age, should be the same for both lobes on either side of the source."
 While this discrepancy is certainlyvisible in, While this discrepancy is certainlyvisible in
mixing in both cases) in 3.1 and 3.2 respectively. and discuss the uncertainties on the thermohaline diffusivity in 3.,"mixing in both cases) in 3.1 and 3.2 respectively, and discuss the uncertainties on the thermohaline diffusivity in 3.3."
 3.4 1s devoted to the case of stars in the mass range M.. , 3.4 is devoted to the case of stars in the mass range 1.5-2.2 $_{\odot}$.
Then in 3.5 we shortly discuss the predictions for intermediate-mass stars., Then in 3.5 we shortly discuss the predictions for intermediate-mass stars.
 Figure | presents the evolutionary track in the Hertzsprung- diagram (HRD) of the 1.25 M. model computed with thermohaline mixing only (no rotation)., Figure \ref{fig:hrd1p25} presents the evolutionary track in the Hertzsprung-Russell diagram (HRD) of the 1.25 $_{\odot}$ model computed with thermohaline mixing only (no rotation).
 Several points are selected along the track in order to discuss the evolution of some relevant stellar properties., Several points are selected along the track in order to discuss the evolution of some relevant stellar properties.
 A;25 corresponds to the turnoff. when the hydrogen mass fraction in the stellar core is below 1077.," $_{1.25}$ corresponds to the turnoff, when the hydrogen mass fraction in the stellar core is below $10^{-8}$."
" ss is chosen at intermediate luminosity between the bump (which minimum and maximum luminosities. Lymig and Lyimay. are also shown) and the moment when the thermohaline zone ""contacts"" the convective envelope (see below)."," $_{1.25}$ is chosen at intermediate luminosity between the bump (which minimum and maximum luminosities, $_{\rm b, min}$ and $_{\rm b, max}$, are also shown) and the moment when the thermohaline zone “contacts"" the convective envelope (see below)."
" ος stands at the “contact” luminosity Lei, where surface abundances start changing due to thermohaline mixing."," $_{1.25}$ stands at the “contact"" luminosity $_{\rm c, th}$ where surface abundances start changing due to thermohaline mixing."
" D;»s and E,»s are close to and at the tip of the RGB (then the mass of the helium core is 0.428 and 0.486 M. respectively. for a total stellar mass of 1.14 and 1.03 )."," $_{1.25}$ and $_{1.25}$ are close to and at the tip of the RGB (then the mass of the helium core is 0.428 and 0.486 $_{\odot}$ respectively, for a total stellar mass of 1.14 and 1.03 $_{\odot}$ )."
 Figure 2. depicts the chemical structure of a 1.25 M. star at the end of central hydrogen-burning (point Àj»s: top left panel for the present case without rotation-induced mixing)., Figure \ref{fig:profil_1.25_diffrot_Tof} depicts the chemical structure of a 1.25 $_{\odot}$ star at the end of central hydrogen-burning (point $_{1.25}$; top left panel for the present case without rotation-induced mixing).
 The most fragile elements lithium. beryllium. and boron. which burn at relatively low-temperatures and are preserved only in the most external stellar layers. are hot shown here.," The most fragile elements lithium, beryllium, and boron, which burn at relatively low-temperatures and are preserved only in the most external stellar layers, are not shown here."
" On the pre-main sequence. pristine deuterium is converted to *He. while on the main sequence H-burning through the pp-chains builds up a *He peak at M,/M. ~0.65."," On the pre-main sequence, pristine deuterium is converted to $^3$ He, while on the main sequence H-burning through the pp-chains builds up a $^3$ He peak at $_{\rm r}$ $_* \sim$ 0.65."
" Deeper inside the star the ""C peak results from the competition between the LC(p.y) NO)|v) ?C and y) PC(p.N. reactions.", Deeper inside the star the $^{13}$ C peak results from the competition between the $^{12}$ $\gamma)^{13}$ $\beta +\nu)^{13}$ C and $^{13}$ $\gamma)^{14}$ N reactions.
 7C and ΙΟ are partially converted into N which abundance profile presents a double plateau., $^{12}$ C and $^{16}$ O are partially converted into $^{14}$ N which abundance profile presents a double plateau.
 ON-cycling results in ‘SO depletion and in the building up of a !’O peak., ON-cycling results in $^{18}$ O depletion and in the building up of a $^{17}$ O peak.
 In the very central regions. Να is produced through proton capture by  Ne.," In the very central regions, $^{23}$ Na is produced through proton capture by $^{22}$ Ne."
 When the star moves towards the RGB its convective envelope deepens and engulfes most of the regions that have been nuclearly processed (IDUP)., When the star moves towards the RGB its convective envelope deepens and engulfes most of the regions that have been nuclearly processed (1DUP).
 In Fig., In Fig.
 2 the maximum depth reached by the convective envelope 15 indicated by the vertical arrow., \ref{fig:profil_1.25_diffrot_Tof} the maximum depth reached by the convective envelope is indicated by the vertical arrow.
 The so-called first dredge-up results in severe changes in the surface chemical properties of the star (see Fig. 6)), The so-called first dredge-up results in severe changes in the surface chemical properties of the star (see Fig. \ref{fig:surfaceabundances1p25}) )
" since surface material is diluted with matter enriched in “He. PC. and ""N. but depleted in ""C and. O. In the standard models the surface abundances are not predicted to change anymore after the end of the first dredge-up until the"," since surface material is diluted with matter enriched in $^3$ He, $^{13}$ C, and $^{14}$ N, but depleted in $^{12}$ C and $^{18}$ O. In the standard models the surface abundances are not predicted to change anymore after the end of the first dredge-up until the"
the theory of close binary evolution (c.g.. Webbinkeal.1987)).,"the theory of close binary evolution (e.g., \cite{web87}) )."
 Χαν recentlv. Hachisu Kato (19995) have chicidated the reason why its companion has a heliun-rich envelope aud. at the same time. why the white dwarf Is πο lnassive as the Claucdrasclhar mass limit.," Very recently, Hachisu Kato (1999b) have elucidated the reason why its companion has a helium-rich envelope and, at the same time, why the white dwarf is so massive as the Chandrasekhar mass limit."
 Iu IHachisu I&ato's (1999b) U Sco scenario. they star your a progenitor binary svsteniofo 7SAL. and ~2M. stars with the iuitial separation of 500R...," In Hachisu Kato's (1999b) U Sco scenario, they start from a progenitor binary system of $\sim 7-8 M_\odot$ and $\sim 2 M_\odot$ stars with the initial separation of $\sim 500 ~R_\odot$."
 The primary compoucut lias first evolved to fill its Roche lobe wheu the welimm core erows to~1.1.L.6AL..., The primary component has first evolved to fill its Roche lobe when the helium core grows to $\sim 1.4-1.6 M_\odot$.
 The binary uudergoes a common euvelope evolution and shrinks to the separation of LOR. between the naked heliuu core aud the ~241. uadn-sequence star., The binary undergoes a common envelope evolution and shrinks to the separation of $\sim 10 R_\odot$ between the naked helium core and the $\sim 2 M_\odot$ main-sequence star.
 The helm core evolves to fill its Roche lobe aud stably trausters almost pure helium onto he secondary. because of the mass ratio Αλ<0.79., The helium core evolves to fill its Roche lobe and stably transfers almost pure helium onto the secondary because of the mass ratio $M_1/M_2 \lesssim 0.79$.
 As a result. the secoudary becomes a lelinmerich star.," As a result, the secondary becomes a helium-rich star."
 After the helium cuvelope of the primary is exhausted. he primary becomes a carbou-oxveen (C|O) white dwarf of 0.9LOAM. and the secondary erows iu nass fo —2.5M..," After the helium envelope of the primary is exhausted, the primary becomes a carbon-oxygen (C+O) white dwarf of $0.9-1.0 M_\odot$ and the secondary grows in mass to $\sim 2.5 M_\odot$."
 When the secondary slightly evolves to fil its Roche lobe. it transfers helimmevich matter onto the ο white dwarf on a thermal time scale.," When the secondary slightly evolves to fill its Roche lobe, it transfers helium-rich matter onto the C+O white dwarf on a thermal time scale."
" The white dwart burus hydrogen atop the surface at a critical rate of AL,S20610ΕΣ + for heliumrich matter aud blows excess matter iu winds."," The white dwarf burns hydrogen atop the surface at a critical rate of $\dot M_{\rm cr} \sim 2.0 \times 10^{-6} 
(M_{\rm WD}/M_\odot - 0.40) ~M_\odot$ $^{-1}$ for helium-rich matter and blows excess matter in winds."
 Tle white dwarf uow grows to near the Claucrasekhar mass limi and the mass transfer rate decreases to a few to several times 10AL. vrb , The white dwarf now grows to near the Chandrasekhar mass limit and the mass transfer rate decreases to a few to several times $10^{-7} M_\odot$ $^{-1}$.
These pictures seenus to be very consistent with the present distinct observational aspects of U Sco., These pictures seems to be very consistent with the present distinct observational aspects of U Sco.
 To σπα the recirent novae secur to be a critical system χο.for SN la explosion.," To summarize, the recurrent novae seem to be a critical system for SN Ia explosion."
 Recurrent novae are morphologically divided iuto three eroups: cdwuf colupanion. slightly evolved main-sequence conanion. and red-eiant companion (c.e.. Schaefer& BRiugwald 1995)).," Recurrent novae are morphologically divided into three groups; dwarf companion, slightly evolved main-sequence companion, and red-giant companion (e.g., \cite{sch95}) )."
" T CoB (Po,=228 d) aud RS Oph (Poy,=160 d) belong to the last eroup of red-giaut companion.", T CrB $P_{\rm orb}= 228$ d) and RS Oph $P_{\rm orb}= 460$ d) belong to the last group of red-giant companion.
 U Sco (Pon=1.23 d: Schacter&Rinewald 1995)) and V391 CrA (Pan=0.758 d: Schaefer 1990)) beloug to the middle eroup of the slightly evolved main-sequence colupanions., U Sco $P_{\rm orb}= 1.23$ d; \cite{sch95}) ) and V394 CrA $P_{\rm orb}= 0.758$ d; \cite{sch90}) ) belong to the middle group of the slightly evolved main-sequence companions.
 Two of the three suberoups of the recurrent novae correspond to our progenitors (WD|MS/WDRG systems)., Two of the three subgroups of the recurrent novae correspond to our progenitors (WD+MS/WD+RG systems).
 This close relation between the recurrent uovae and our progenitors stronelv support our scenario of SN Ia progenitors., This close relation between the recurrent novae and our progenitors strongly support our scenario of SN Ia progenitors.
 Based ou the population svuthesis analysis. Yuugelsou Livio (1998) claimed that alinost no realization frequency is derived for the original ITIKN96's WD|RC model.," Based on the population synthesis analysis, Yungelson Livio (1998) claimed that almost no realization frequency is derived for the original HKN96's WD+RG model."
 First. we bricfly explain their analvsis why the original model by II&N96 does not produce enough. Πα of SNe Ta. Second. we point out that very wide binaries with the initial separation ofa;z1500Rk... which were not included πι Yuneclson Livio’s (1998) analvsis. ire essentiallv iuportant iu our SN Ia modeling.," First, we briefly explain their analysis why the original model by HKN96 does not produce enough number of SNe Ia. Second, we point out that very wide binaries with the initial separation of $a_i \gtrsim 1500 ~R_\odot$, which were not included in Yungelson Livio's (1998) analysis, are essentially important in our SN Ia modeling."
 A inore massive conrpouent Guass of AL) of a binary first evolves to a red-giaut (ACD stage) iud fills its inner critical Roche lobe.," A more massive component (mass of $M_{1,i}$ ) of a binary first evolves to a red-giant (AGB stage) and fills its inner critical Roche lobe."
" After a common cuvelope plasc. the more Inassive component leaves a ο WD and the separation of the binary decreases by a factor of where ας is the efficiency factor of common cuvclope evolutions. e, (a;) the final (initial) separation. aud AM» he mass of the secondary."," After a common envelope phase, the more massive component leaves a C+O WD and the separation of the binary decreases by a factor of where $\alpha_{\rm CE}$ is the efficiency factor of common envelope evolutions, $a_f$ $a_i$ ) the final (initial) separation, and $M_2$ the mass of the secondary."
 Adopting a standard value of AcE=1.weobtaiega; 1/10.1/50 tor Mw~1M. aud A~|ALL. because a ~1A. WD desceuds roni a niain-xsequencee star of Mj;~78M. (c9. Weidemann1986: Yuneclsonetal.19953).," Adopting a standard value of $\alpha_{\rm CE}=1$, we obtain $a_f/a_i \sim 1/40 - 1/50$ for $M_{\rm WD} \sim 1 ~M_\odot$ and $M_2 \sim 1 ~M_\odot$, because a $\sim 1 ~M_\odot$ WD descends from a main-sequence star of $M_{1,i} \sim 7-8 ~M_\odot$ (e.g., \cite{wei86}; \cite{yun95}) )."
 Yuugclson Livio (1998) asstuned that the separation of interacting Xuaries is e;<1500KR..., Yungelson Livio (1998) assumed that the separation of interacting binaries is $a_i \lesssim 1500 ~R_\odot$.
 Then. the most wide Muarics has the separation of o;x;30LOR. atter the colulmon envelope evolution.," Then, the most wide binaries has the separation of $a_f \lesssim 30-40 ~R_\odot$ after the common envelope evolution."
 Its orbital period is Py<20 d for Awp.y~1M. aud AfRey~1AL...," Its orbital period is $P_0 \lesssim 20$ d for $M_{\rm WD,0} \sim 1 ~M_\odot$ and $M_{\rm RG,0} \sim 1 ~M_\odot$."
 There is no SN Ta region of the WD|RC systems for Pyx20 d as seen from Figure All..., There is no SN Ia region of the WD+RG systems for $P_0 \lesssim 20$ d as seen from Figure \ref{zams10}.
 Thus. they concluded that we caunot expect auv SN Ta explosions from the right SN Ia region (WD|RG svstein) of Figure ALL..," Thus, they concluded that we cannot expect any SN Ia explosions from the right SN Ia region (WD+RG system) of Figure \ref{zams10}."
" If the WDIRC evolution starts ouly from an initial condition of Py<20 d aud νουLAL... however. the present states of T CrB or RS Oph caunuot be reached because of low mass transfor rates of |M,|<1<10TAL, Lb (see also Figs."," If the WD+RG evolution starts only from an initial condition of $P_0 \lesssim 20$ d and $M_{\rm WD,0} \sim 1 M_\odot$, however, the present states of T CrB or RS Oph cannot be reached because of low mass transfer rates of $|\dot M_{\rm t}| \lesssim 1 \times 10^{-7} M_\odot$ $^{-1}$ (see also Figs."
 A11 and A12})., \ref{zams10} and \ref{ztotreg100}) ).
 Thus. the existence of recurrent novae T. CrD and RS Oph secus to be against the above Yuuselson Livio’s conjecture.," Thus, the existence of recurrent novae T CrB and RS Oph seems to be against the above Yungelson Livio's conjecture."
 The reason why T CrB or RS Oph are failed to be reproduced iu Yuugelson Livios modeling is due to their assmuption of a;<1500FE., The reason why T CrB or RS Oph are failed to be reproduced in Yungelson Livio's modeling is due to their assumption of $a_i \lesssim 1500 ~R_\odot$.
 In what follows. we show that such wide WDIRC binaries as Py)—100L000 d are born from initially very wide binaries with a;—150010000£...," In what follows, we show that such wide WD+RG binaries as $P_0 \sim 100-1000$ d are born from initially very wide binaries with $a_i \sim 1500-40000 ~R_\odot$."
 A star with the zero-age main-sequeuce mass of SAL. ends up its life by ejecting its envelope in a wind of relatively slow velocities (6~10 kis Ly)," A star with the zero-age main-sequence mass of $M_{1,i} \lesssim 8 ~M_\odot$ ends up its life by ejecting its envelope in a wind of relatively slow velocities $v \sim 10-40$ km $^{-1}$ )."
 These wind velocity is as low as the orbital velocity of binaries with the separation of a4;~L500)10000... for M4;~7M. aud Mo;~1AL...," These wind velocity is as low as the orbital velocity of binaries with the separation of $a_i \sim 1500-40000 ~R_\odot$ for $M_{1,i} \sim 7 ~M_\odot$ and $M_{2,i} \sim 1 ~M_\odot$."
 When the wiud velocity is as low as the orbital velocity. the nuinerical factor (4. in equation (11)) lucreases to uailv because outflowing iuatter can ect anenlar uonientuni from the binary motion by torque during its journey (see Appendix A}.," When the wind velocity is as low as the orbital velocity, the numerical factor $\ell_{\rm w}$ in equation \ref{specific_angular_momentum_wind}) ) increases to mainly because outflowing matter can get angular momentum from the binary motion by torque during its journey (see Appendix A)."
 Here. e is the radial component of the wind velocity near the immer critical Roche lobe aud he laniting case of fy=L7 for e=0 was obtained wo Nari (1975) and Narid Sugimoto (1976) for a est particle simulation ejecting fom the outer Lagrangian yoiluts and Sawada. Hachisu. Matsuda (1981) for a 2- (equatorial plane) hydrodvunamical simulation blowing a very slow wind from the primary surface which fills the inner critical Roche lobe.," Here, $v$ is the radial component of the wind velocity near the inner critical Roche lobe and the limiting case of $\ell_{\rm w}=1.7$ for $v=0$ was obtained by Nariai (1975) and Nariai Sugimoto (1976) for a test particle simulation ejecting from the outer Lagrangian points and Sawada, Hachisu, Matsuda (1984) for a 2-D (equatorial plane) hydrodynamical simulation blowing a very slow wind from the primary surface which fills the inner critical Roche lobe."
 Combining the two expressions. we obtain which is a good approximation to fy iu the reeion of the wind velocity from zero to infinity.," Combining the two expressions, we obtain which is a good approximation to $\ell_{\rm w}$ in the region of the wind velocity from zero to infinity."
 Switehliug frou, Switching from
"in the range observable with are present: NGC 6811 (9.5 < Vgg < 12.0), NGC 6819 (13.5 « κο< 14.3) and NGC 6791 (13.7 « Vgg «17.5).","in the range observable with are present: NGC 6811 (9.5 $<$ $_{\rm RG}$ $<$ 12.0), NGC 6819 (13.5 $<$ $_{\rm RG}$$<$ 14.3) and NGC 6791 (13.7 $<$ $_{\rm RG}$ $<$ 17.5)."
 NGC 6811 has an age of 0.7 x 0.1 Gyr (?) and contains only a handful of red giants., NGC 6811 has an age of 0.7 $\pm$ 0.1 Gyr \citep{glushkova1999} and contains only a handful of red giants.
" The older clusters NGC 6819 and NGC 6791 with ages of about 2.5 and 10 Gyr, respectively, have a considerable population of red-giant stars."," The older clusters NGC 6819 and NGC 6791 with ages of about 2.5 and 10 Gyr, respectively, have a considerable population of red-giant stars."
 The fourth and youngest cluster NGC 6866 has an age of about 0.56 Gyr (?) and no red giants have been observed in this cluster., The fourth and youngest cluster NGC 6866 has an age of about 0.56 Gyr \citep{frolov2010} and no red giants have been observed in this cluster.
" NGC 6791 is one of the oldest, most massive and most metal- open clusters known (???),, and contains a population of hot blue stars (??) and white dwarfs extending to the end of the cooling sequence (???).."," NGC 6791 is one of the oldest, most massive and most metal-rich open clusters known \citep{origlia2006,carretta2007,anthony2007}, and contains a population of hot blue stars \citep{liebert1994,landsman1998} and white dwarfs extending to the end of the cooling sequence \citep{bedin2005,bedin2008,kalirai2007}."
 For these reasons NGC 6791 has been studied extensively., For these reasons NGC 6791 has been studied extensively.
" Nevertheless, little agreement concerning its basic parameters has been reached."," Nevertheless, little agreement concerning its basic parameters has been reached."
" Normally, a colour-magnitude diagram is used to derive the age of the cluster."," Normally, a colour-magnitude diagram is used to derive the age of the cluster."
 The non-negligible reddening increases the uncertainty of the age for NGC 6791., The non-negligible reddening increases the uncertainty of the age for NGC 6791.
" Therefore, other probes have been used, such as eclipsing binary systems (seee.g.,22) and the white dwarf cooling sequence (???).."," Therefore, other probes have been used, such as eclipsing binary systems \citep[see e.g.,][]{grundahl2008,brogaard2011} and the white dwarf cooling sequence \citep{bedin2005,bedin2008,kalirai2007}."
" The ages proposed for NGC 6791 range from 7 to 12 Gyr (seee.g.,??),, which is longer than the dynamical relaxation time, i.e., the time in which individual stars exchange energies and thier velocity distribution approaches a Maxwellian equilibrium."," The ages proposed for NGC 6791 range from 7 to 12 Gyr \citep[see e.g.,][]{basu2011,grundahl2008}, which is longer than the dynamical relaxation time, i.e., the time in which individual stars exchange energies and thier velocity distribution approaches a Maxwellian equilibrium."
" Thus, NGC 6791 is dynamically relaxed (?).."," Thus, NGC 6791 is dynamically relaxed \citep{durgapal2001}."
" In addition, there are four independent studies available to determine the metallicity of this cluster."," In addition, there are four independent studies available to determine the metallicity of this cluster."
" They found [Fe/H] = +0.39 + 0.05 (?,high-resolutionspectroscopy), [Fe/H] = 40.35 + 0.02 (?,high-resolutionspectroscopy). [Fe/H] = +0.45 + 0.04 (?,multi-colourphotometry) and [Fe/H] = +0.29 + 0.03 (random) + 0.07 (systematic) (?,spectroscopy).."," They found [Fe/H] = +0.39 $\pm$ 0.05 \citep[][high-resolution spectroscopy]{carraro2006}, [Fe/H] = +0.35 $\pm$ 0.02 \citep[][high-resolution spectroscopy]{origlia2006}, [Fe/H] = +0.45 $\pm$ 0.04 \citep[][multi-colour photometry]{anthony2007} and [Fe/H] = +0.29 $\pm$ 0.03 (random) $\pm$ 0.07 (systematic) \citep[][spectroscopy]{brogaard2011}."
" As pointed out by ?,, comparing these values is complicated as different subsets of stars are observed in each study."," As pointed out by \citet{carretta2007}, , comparing these values is complicated as different subsets of stars are observed in each study."
" It seems likely that the differences are mainly caused by differences in the adopted reddening, ie., either E(B—V) = 0.09 (? or E(B-V) = 0.15 (anaverageoflitera-turedeterminations, ?).."," It seems likely that the differences are mainly caused by differences in the adopted reddening, i.e., either $E(B-V)$ = 0.09 \citep{stetson2003} or $E(B-V)$ = 0.15 \citep[an average of literature determinations,][]{carretta2007}."
 These reddening values are used to derive atmospheric stellar parameters from photometry., These reddening values are used to derive atmospheric stellar parameters from photometry.
 The resulting different atmospheric stellar parameters are used in the different spectroscopic metallicity studies., The resulting different atmospheric stellar parameters are used in the different spectroscopic metallicity studies.
" NGC 6819 is a very rich open cluster with roughly solar metallicity of [Fe/H] = +0.09 + 0.03 (?), an age of about 2.5 Gyr (??) and reddening E(B—V) = 0.15."," NGC 6819 is a very rich open cluster with roughly solar metallicity of [Fe/H] = +0.09 $\pm$ 0.03 \citep{bragaglia2001}, an age of about 2.5 Gyr \citep{kalirai2001,kalirai2004} and reddening $E(B-V)$ = 0.15."
" There is reasonable agreement on the metallicity, reddening and age of this cluster and therefore NGC 6819 has been used to study other phenomena, such as the initial-final mass relation using the population of white dwarfs present in this cluster (e.g.?).."," There is reasonable agreement on the metallicity, reddening and age of this cluster and therefore NGC 6819 has been used to study other phenomena, such as the initial-final mass relation using the population of white dwarfs present in this cluster \citep[e.g.][]{kalirai2008}."
" There is also clear evidence for mass segregation in NGC 6819, i.e., the giants and upper main-sequence stars are concentrated in the inner regions, whereas the lower main-sequence stars distribute almost uniformly throughout the cluster."," There is also clear evidence for mass segregation in NGC 6819, i.e., the giants and upper main-sequence stars are concentrated in the inner regions, whereas the lower main-sequence stars distribute almost uniformly throughout the cluster."
 This results from the fact that the age of NGC 6819 is about 10 times larger than its dynamical relaxation time (?).., This results from the fact that the age of NGC 6819 is about 10 times larger than its dynamical relaxation time \citep{kang2002}.
" NGC 6811 is a young, sparse, not particularly well studied cluster."," NGC 6811 is a young, sparse, not particularly well studied cluster."
 Studies on this cluster tended to focus on membership or variability of stars and no direct metallicity studies are available., Studies on this cluster tended to focus on membership or variability of stars and no direct metallicity studies are available.
 Solar metallicity has been used as an initial guess., Solar metallicity has been used as an initial guess.
" In the present study we compare asteroseismic global parameters Vmax (the frequency of maximum oscillation power) and Av (the large frequency spacing between modes of the same degree and consecutive order) of solar-like oscillations in red-giant stars in the three open clusters NGC 6791, NGC 6819 and NGC 6811, and of field giants, all observed withKepler."," In the present study we compare asteroseismic global parameters $\nu_{\rm max}$ (the frequency of maximum oscillation power) and $\Delta \nu$ (the large frequency spacing between modes of the same degree and consecutive order) of solar-like oscillations in red-giant stars in the three open clusters NGC 6791, NGC 6819 and NGC 6811, and of field giants, all observed with."
". In this paper, we subsequently derive stellar parameters, such as mass and radius, from the asteroseismic parameters and investigate the influence of evolution and metallicity on the observed red-giant populations."," In this paper, we subsequently derive stellar parameters, such as mass and radius, from the asteroseismic parameters and investigate the influence of evolution and metallicity on the observed red-giant populations."
 The data of the cluster stars are also being used to investigate mass loss along the red-giant branch (Miglio et al., The data of the cluster stars are also being used to investigate mass loss along the red-giant branch (Miglio et al.
" in preparation), the ages of the clusters (?) andcluster membership (?).."," in preparation), the ages of the clusters \citep{basu2011} andcluster membership \citep{stello2011}."
 The latter will be an extension of the study of NGC 6819 recently presented by ?.., The latter will be an extension of the study of NGC 6819 recently presented by \citet{stello2010}.
 To select the stars in NGC 6819 we used the radial velocity study by ?.., To select the stars in NGC 6819 we used the radial velocity study by \citet{hole2009}. .
" It gives membership probabilities for all stars in thecluster vicinity down to V= 15.0, which includes all stars targeted in this paper."," It gives membership probabilities for all stars in thecluster vicinity down to $V=15.0$ , which includes all stars targeted in this paper."
 All stars with high membership probability (Pry> 80%) were chosen., All stars with high membership probability $P_{\mathrm{RV}}>80\%$ ) were chosen.
 With this purely kinematic criterion we avoid any biases in our selection, With this purely kinematic criterion we avoid any biases in our selection
be significantly less (han this upper limit.,be significantly less than this upper limit.
 Thus the detection of Ila emission lines with hieh equivalent width is consistent wilh the range of ages determined [rom SED modelling of theclusters!., Thus the detection of $\alpha$ emission lines with high equivalent width is consistent with the range of ages determined from SED modelling of the.
. Finally we note that the NICMOS upper limits rule out ages older than 11 Myr wilh reddenings similar (0 or lower (han (hose presented in Table 3. or ages <7 Myr with higher reddening values Chan the models in Table 3.," Finally we note that the NICMOS upper limits rule out ages older than $\sim$ 11 Myr with reddenings similar to or lower than those presented in Table 3, or ages $<$ 7 Myr with higher reddening values than the models in Table 3."
 The masses of the SSC detected in PINS13454-12 (10°<M10* M.) are comparable with those of the most massive clusters detected in the Milky Wax (e.g. Omega Centauri). in merger systems such as the ULIRG Arp220 (7). and The Antennae (?).. and in some other interacting svstems (?)..," The masses of the SSC detected in PKS1345+12 $10^6 < M_{ssc} <
10^7$ $_{\odot}$ ) are comparable with those of the most massive clusters detected in the Milky Way (e.g. Omega Centauri), in merger systems such as the ULIRG Arp220 \citep{Wilson06} and The Antennae \citep{Fall05}, , and in some other interacting systems \citep{deGrijs}."
 Given the diffieuliv of detecting individual SSC at the relatively high redshift of PINS13452-12. itis not surprising that the clusters we have detected are relatively voung and massive.," Given the difficulty of detecting individual SSC at the relatively high redshift of PKS1345+12, it is not surprising that the clusters we have detected are relatively young and massive."
" Certainly, our imaging observations do not rule out the presence of a more numerous cluster population in the halo of PINS13454+12. comprising SSC that are older and/or less massive (han C1. C2 and C4."," Certainly, our imaging observations do not rule out the presence of a more numerous cluster population in the halo of PKS1345+12, comprising SSC that are older and/or less massive than C1, C2 and C4."
 Figure 3 shows the slit positions and the apertures used for the spectroscopic analvsis., Figure 3 shows the slit positions and the apertures used for the spectroscopic analysis.
 The sale routine as described above was used (to create simple stellar population templates of different age and reddening., The same routine as described above was used to create simple stellar population templates of different age and reddening.
 BReddened model spectra were created using E(D-V) values from 0.0 to 1.6 and (he parametrized ealactic extinction law of ?.., Reddened model spectra were created using E(B-V) values from 0.0 to 1.6 and the parametrized galactic extinction law of \cite{Seaton79}.
 Each extracted spectrum was modelled using a combination of a voung and an okl stellar population (see ?)): we used a 12.5Gvr model for the old stellar population (OSP). adding YSP ranging in age from 0.001Gyr to GGyr (we will refer to this component as voung component).," Each extracted spectrum was modelled using a combination of a young and an old stellar population (see \cite{Tadhunter05}) ): we used a 12.5Gyr model for the old stellar population (OSP), adding YSP ranging in age from 0.001Gyr to 6Gyr (we will refer to this component as young component)."
 For each spectroscopic aperture the continuum flux was measured in several wavelength bins (50) chosen to be as evenly distributed in wavelength as possible. and to avoid strong; emission lines- and. atinospherie. absorptionH leatures.," For each spectroscopic aperture the continuum flux was measured in several wavelength bins $\sim$ 50) chosen to be as evenly distributed in wavelength as possible, and to avoid strong emission lines and atmospheric absorption features."
. We- then fitted. these data usingB aminimum- X> , We then fitted these data using aminimum $\chi^2$ 
cTr.,$\frac{c^2\Lambda_-}{3}r$.
 Since A is negative the induced. force is. directed towards the centre. just as the gravitational The above expression leads to the condition for the critical radius. ]t turns. out that this radius is about rayστ«10! AU.," Since $\Lambda_-$ is negative the induced force is directed towards the centre, just as the gravitational The above expression leads to the condition for the critical radius, It turns out that this radius is about $r_{crit}\approx 4.5 \times 10^4~\mathrm{AU}$ ."
" At this distance from the Sun the inlluence of the vacuum cannot be neglected. anvmore. or. in other words. it is not. possible to use perturbation theory. because the ""perturbation"" is neither small nor time limited on a small interval."," At this distance from the Sun the influence of the vacuum cannot be neglected anymore, or, in other words, it is not possible to use perturbation theory because the ""perturbation"" is neither small nor time limited on a small interval."
 By comparison. the general. cosmological constant with an upper limit of 101Tm> would lead to a critical racius of about 8 light Obviously ᾱ- distance. of the order of. the critical radius is too large to expect a direct inlluence on planetary orbits.," By comparison, the general cosmological constant with an upper limit of $10^{-47}~\mathrm{m^{-2}}$ would lead to a critical radius of about 8 light Obviously a distance of the order of the critical radius is too large to expect a direct influence on planetary orbits."
 But if one takes the Oort cloud. into account with an extent of about 1 light. vear. it should be possible to see deviations from pure Ixeplerian expectations.," But if one takes the Oort cloud into account with an extent of about 1 light year, it should be possible to see deviations from pure Keplerian expectations."
 hspacebmmsSince the critical radii of the three gravitational modifications that are investigated in this paper. are very large. they are not able to explain phenomena like the Pioncer-anomaly.," Since the critical radii of the three gravitational modifications that are investigated in this paper, are very large, they are not able to explain phenomena like the Pioneer-anomaly."
 In order to investigate the impact of the three modifications of gravity derived. above we use an orbit-integrator based on an embedded. πασοκτα method. of 4th order., In order to investigate the impact of the three modifications of gravity derived above we use an orbit-integrator based on an embedded Runge-Kutta method of 4th order.
 The energy and angular momentum turns out to be à conserved quantity for all Since the distances that were considered here are of the order the distance to the Oort cloud (zz107 AU). the whole problem reduced. to a two-body problem: The central mass and the orbiting hspace*5mmWWe considered. eleven cases with initial conditions that would cause clear circular orbits. -with initial distances in a range between 500050000 AU- in à pure Ixeplerian. potential and. two cases that correspond. tolipses?.," The energy and angular momentum turns out to be a conserved quantity for all Since the distances that were considered here are of the order the distance to the Oort cloud $\approx 10^{4}$ AU), the whole problem reduced to a two-body problem: The central mass and the orbiting We considered eleven cases with initial conditions that would cause clear circular orbits, -with initial distances in a range between $5000-~50000~\mathrm{AU}$ - in a pure Keplerian potential and two cases that correspond to."
. The integration times were chosen cillercnthy (see Fig., The integration times were chosen differently (see Fig.
 2-7) ina range between 4.9 and 17.5MYr. Lt should. be noted. here that curing the investigation of these three modifications every inlluence of external fields. like the Galactic tical field. has been neglected.," 2 - 7) in a range between $4.9$ and $17.5~\mathrm{MYr}$ It should be noted here that during the investigation of these three modifications every influence of external fields, like the Galactic tidal field, has been neglected."
 So only the gravitational force and the additional forces have been considered., So only the gravitational force and the additional forces have been considered.
 Fig., Fig.
 2-7 show the results of the orbit-integration for all three modifications., 2-7 show the results of the orbit-integration for all three modifications.
 Phe solid line marks the circular orbit in a pure central-zmass lxeplerian case and the dashed line denotes the orbit. under the respective gravitational nioclification., The solid line marks the circular orbit in a pure central-mass Keplerian case and the dashed line denotes the orbit under the respective gravitational modification.
 As one can see all three modilications cause strong deviations from. pure Weplerian orbits around. the central mass., As one can see all three modifications cause strong deviations from pure Keplerian orbits around the central mass.
 Circular orbits become elliptical ones that in addition experience an aphelion-migration. a so called: rosette-orbit.," Circular orbits become elliptical ones that in addition experience an aphelion-migration, a so called rosette-orbit."
 This qualitative behaviour occurs in all cases., This qualitative behaviour occurs in all cases.
 The differences lic in parameters like the value of the aphelion-mieration and the eccentricity for one turn., The differences lie in parameters like the value of the aphelion-migration and the eccentricity for one turn.
 The results of the investigation of these parameters are presented in the Dext In order to compare the impact of Dark-Matter.. MOND," The results of the investigation of these parameters are presented in the next In order to compare the impact of Dark-Matter, MOND"
 effectstrongest(Dressler The morphology segregation 1980; Whitemore Gilmore.,"}\tikzmark{mainBodyEnd1}

 \offprints{A. Boselli}


 \institute{Laboratoire d'Astrophysique de Marseille, UMR 6110 CNRS, 38 rue F. Joliot-Curie, F-13388 Marseille France\\
 \email{Alessandro.Bosellioamp.fr}
	 \and
	 Universita degli Studi di Milano-Bicocca, Piazza delle Scienze 3,
	 20126 Milano, Italy
	 \email{Giuseppe.Gavazzimib.infn.it}
 %\thanks{}
 \tikzmark{mainBodyStart2}}\tikzmark{mainBodyEnd2}

 \date{}


% \abstract{}{}{}{}{} 
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 \abstract
 % context heading (optional)
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 {Pre-processing within small groups has been proposed to explain 
 sev\tikzmark{mainBodyStart3}veral\tikzmark{mainBodyEnd3} \tikzmark{mainBodyStart4}of\tikzmark{mainBodyEnd4} \tikzmark{mainBodyStart5}the\tikzmark{mainBodyEnd5} \tikzmark{mainBodyStart6}properties\tikzmark{mainBodyEnd6} \tikzmark{mainBodyStart7}of\tikzmark{mainBodyEnd7} \tikzmark{mainBodyStart8}galaxies\tikzmark{mainBodyEnd8} \tikzmark{mainBodyStart9}inhabiting\tikzmark{mainBodyEnd9} \tikzmark{mainBodyStart10}rich\tikzmark{mainBodyEnd10} \tikzmark{mainBodyStart11}clusters.}\tikzmark{mainBodyEnd11} 
 % aims heading (mandatory)
 {The aim of the present work is to see whether pre-processing is acting in the nearby universe, where the structures that are merging to form 
 rich clusters are rather large and massive.}\tikzmark{mainBodyStart12}}\tikzmark{mainBodyEnd12}
 % methods heading (mandatory)
 {We study the HI gas properties of a large sample of late-type galaxies belonging to the Coma I cloud, an association of 
 objects close to the Virgo cluster.}\tikzmark{mainBodyStart13}}\tikzmark{mainBodyEnd13}
 % results heading (mandatory)
 {Contrary to what previously claimed, late-type galaxies in the Coma I cloud are not deficient in HI gas ($HI-def$=0.06$\pm$0.44).}\tikzmark{mainBodyStart14}} }\tikzmark{mainBodyEnd2}

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% \abstract{}{}{}{}{} 
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 \abstract
 % context heading (optional)
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 {Pre-processing within small groups has been proposed to explain 
 sev\tikzmark{mainBodyStart3}veral\tikzmark{mainBodyEnd3} \tikzmark{mainBodyStart4}of\tikzmark{mainBodyEnd4} \tikzmark{mainBodyStart5}the\tikzmark{mainBodyEnd5} \tikzmark{mainBodyStart6}properties\tikzmark{mainBodyEnd6} \tikzmark{mainBodyStart7}of\tikzmark{mainBodyEnd7} \tikzmark{mainBodyStart8}galaxies\tikzmark{mainBodyEnd8} \tikzmark{mainBodyStart9}inhabiting\tikzmark{mainBodyEnd9} \tikzmark{mainBodyStart10}rich\tikzmark{mainBodyEnd10} \tikzmark{mainBodyStart11}clusters.}\tikzmark{mainBodyEnd11} 
 % aims heading (mandatory)
 {The aim of the present work is to see whether pre-processing is acting in the nearby universe, where the structures that are merging to form 
 rich clusters are rather large and massive.}\tikzmark{mainBodyStart12}}\tikzmark{mainBodyEnd12}
 % methods heading (mandatory)
 {We study the HI gas properties of a large sample of late-type galaxies belonging to the Coma I cloud, an association of 
 objects close to the Virgo cluster.}\tikzmark{mainBodyStart13}}\tikzmark{mainBodyEnd13}
 % results heading (mandatory)
 {Contrary to what previously claimed, late-type galaxies in the Coma I cloud are not deficient in HI gas ($HI-def$=0.06$\pm$0.44).}\tikzmark{mainBodyStart14}}\tikzmark{mainBodyEnd14}
 % conclusions heading (optional), leave it empty if necessary 
 {If the Coma I cloud is representative of infalling groups in nearby clusters, 
 this result suggests that, in the local universe, the evolution of late-type galaxies belonging to loose structures with 
 high velocity dispersions ($\geq$ 300 km s$^{-1}$)
 associated to rich clusters such as Virgo is not significantly perturbed by pre-processing. }\tikzmark{mainBodyStart15}} The morphology segregation effect (Dressler 1980; Whitemore Gilmore."
 1991) 1 the evidence that the environment played a major role in shaping galaxy evolution., 1991) is the strongest evidence that the environment played a major role in shaping galaxy evolution.
 Recent surveys such as SDSS (Gomez et al., Recent surveys such as SDSS (Gomez et al.
 2003) and 2dF (Lewis et al., 2003) and 2dF (Lewis et al.
 2002). which allowed to continuously trace galaxy properties from the highest density regions in the core of rich clusters down to the field. have shown that the star formation activity already decreases at the periphery of clusters. probably because the interactions responsible for removal of gas. the principal feeder of star formation (e.g. Boselli et al.," 2002), which allowed to continuously trace galaxy properties from the highest density regions in the core of rich clusters down to the field, have shown that the star formation activity already decreases at the periphery of clusters, probably because the interactions responsible for removal of gas, the principal feeder of star formation (e.g. Boselli et al."
 2001). were already in place in the infalling groups prior to the formation of rich clusters.," 2001), were already in place in the infalling groups prior to the formation of rich clusters."
 These results are consistent. with our own studies of the gas and star formation properties of galaxies in nearby clusters (Gavazzi et al., These results are consistent with our own studies of the gas and star formation properties of galaxies in nearby clusters (Gavazzi et al.
 2002; 2005; 2006a: 2006b: 2008)., 2002; 2005; 2006a; 2006b; 2008).
 Although in some cases the presence of hot gas might trigger galaxy interactions with the intergalactic medium. the low velocity dispersion of small groups (x 200 km s!) suggests that. gravitational interactions are probably at the origin of the pre-processing of galaxies even before they enter rich clusters (Dressler Probably efficient at high redshift. when clusters were under formation (Gnedin 2003). pre-processing is less evident in the nearby universe (Boselli Gavazzi 2006). where clusters are rather accreting large structures characterized by high velocity dispersions (Donnelly et al.," Although in some cases the presence of hot gas might trigger galaxy interactions with the intergalactic medium, the low velocity dispersion of small groups $\leq$ 200 km $^{-1}$ ) suggests that gravitational interactions are probably at the origin of the pre-processing of galaxies even before they enter rich clusters (Dressler Probably efficient at high redshift, when clusters were under formation (Gnedin 2003), pre-processing is less evident in the nearby universe (Boselli Gavazzi 2006), where clusters are rather accreting large structures characterized by high velocity dispersions (Donnelly et al."
 2001: Ferrari et al., 2001; Ferrari et al.
 2003: Cortese et al., 2003; Cortese et al.
 2004) or single galaxies. making gravitational interactions rather rare.," 2004) or single galaxies, making gravitational interactions rather rare."
 For instance the velocity dispersion of the M and W clouds in the Virgo cluster are relatively high. of the order of 450-650 km s! (Gavazzi et al.," For instance the velocity dispersion of the M and W clouds in the Virgo cluster are relatively high, of the order of 450-650 km $^{-1}$ (Gavazzi et al."
" 1999), thus almost comparable to that of an already formed cluster."," 1999), thus almost comparable to that of an already formed cluster."
 The only exception found in the local universe tis the blue infalling group in A1367 (Sakai et al., The only exception found in the local universe is the blue infalling group in A1367 (Sakai et al.
 2002: Gavazzi et al., 2002; Gavazzi et al.
 2003a; Cortese et al., 2003a; Cortese et al.
 2006). a compact group of galaxies with a velocity dispersion of only 150 km s! infalling into the cluster A1367.," 2006), a compact group of galaxies with a velocity dispersion of only 150 km $^{-1}$ infalling into the cluster A1367."
 Here pre-processing is efficiently perturbing the galaxies morphology and star formation activity. creating long tails of ionized The study of the Virgo cluster. the nearest rich cluster of galaxies. and 1ts surroundings. however. revealed the presence of satellite clouds with HI-deficient objects witnessing an ongoing interaction. thus making these clouds of particular interest for studying pre-processing in the nearby universe.," Here pre-processing is efficiently perturbing the galaxies morphology and star formation activity, creating long tails of ionized The study of the Virgo cluster, the nearest rich cluster of galaxies, and its surroundings, however, revealed the presence of satellite clouds with HI-deficient objects witnessing an ongoing interaction, thus making these clouds of particular interest for studying pre-processing in the nearby universe."
 Being loosely anchored to the galaxy potential. the HI component can be easily removed during any kind of interaction. and ts thus an ideal tracer of ongoing perturbations (Boselli Gavazzi 2006).," Being loosely anchored to the galaxy potential, the HI component can be easily removed during any kind of interaction, and is thus an ideal tracer of ongoing perturbations (Boselli Gavazzi 2006)."
 Among these. the Coma I cloud. a loose aggregation of galaxies in the projected direction of the Coma/ÀA1367 supercluster located at ~ 5 Mpe from M87 (see sect.," Among these, the Coma I cloud, a loose aggregation of galaxies in the projected direction of the Coma/A1367 supercluster located at $\sim$ 5 Mpc from M87 (see sect."
 4 and 5). is the most promising since previous studies have shown that this loose cloud is composed of HI-deficient galaxies (Garcia-Barreto et al.," 4 and 5), is the most promising since previous studies have shown that this loose cloud is composed of HI-deficient galaxies (Garcia-Barreto et al."
 1994)., 1994).
 The availability of new HI data more than doubled the sample of Garcia-Barreto et al. (, The availability of new HI data more than doubled the sample of Garcia-Barreto et al. (
1994). suggesting us to reanalyze the HI gas properties of the Coma I cloud galaxies in the framework of pre-processing in the nearby universe.,"1994), suggesting us to reanalyze the HI gas properties of the Coma I cloud galaxies in the framework of pre-processing in the nearby universe."
 The Coma I cloud has been defined by Gregory Thompson (1977) as the cloud of nearby galaxies (< 20 Mpc) in the foreground of the Coma/A1367 supercluster., The Coma I cloud has been defined by Gregory Thompson (1977) as the cloud of nearby galaxies $\le$ 20 Mpc) in the foreground of the Coma/A1367 supercluster.
" The analysis presented in this work is thus based on a sample composed of all galaxies extracted from NED in the sky region 11/30” < R.A.(2000) <13""30"" 20"" < dee < 34 with a recessional velocity € 2000 km s7!.", The analysis presented in this work is thus based on a sample composed of all galaxies extracted from NED in the sky region $^h$ $^m$ $<$ R.A.(2000) $<$ $^h$ $^m$; $^o$ $<$ dec $<$ $^o$ with a recessional velocity $\leq$ 2000 km $^{-1}$.
 Excluding misclassified HII regions associated to bright galaxies. the resulting sample is composed of 161 galaxies.," Excluding misclassified HII regions associated to bright galaxies, the resulting sample is composed of 161 galaxies."
 Since no limits on the magnitude or diameter of the selected galaxies are applied. the selected sample ts not complete in any sense.," Since no limits on the magnitude or diameter of the selected galaxies are applied, the selected sample is not complete in any sense."
 The set of data necessary for the following analysis. restricted to those galaxies with available HI data (72 objects). are listed in Table |.," The set of data necessary for the following analysis, restricted to those galaxies with available HI data (72 objects), are listed in Table 1."
 This includes morphological type. optical and near IR magnitudes. optical diameters and HI flux and line width measurements.," This includes morphological type, optical and near IR magnitudes, optical diameters and HI flux and line width measurements."
 Coordinates and morphological type have been taken from NED. in its updated version including," Coordinates and morphological type have been taken from NED, in its updated version including"
cdenamical tme scale al radius of about 84 fy.,dynamical time scale at radius of about 84 $R_S$.
 The peak is broad because the torus increases in size with time. in particular the (torus radius increases.," The peak is broad because the torus increases in size with time, in particular the torus radius increases."
 We computed additional models [or 5=L.01 with higher resolution in @ direction (400 ancl 800 points in 0 angle)., We computed additional models for $\gamma=1.01$ with higher resolution in $\theta$ direction (400 and 800 points in $\theta$ angle).
 We found that oscillations appear to be independent of the eric resolution., We found that oscillations appear to be independent of the grid resolution.
 For >1.01. the flow behaves in a similar wavs as that in run G. However. there is an additional complexity due to high gas pressure and müxing.," For $\gamma>1.01$, the flow behaves in a similar ways as that in run G. However, there is an additional complexity due to high gas pressure and mixing."
 For 5>1.01. the flow is less gravitationally bound than in run. G and the torus is not as much confined by the supersonic inflow.," For $\gamma>1.01$, the flow is less gravitationally bound than in run G and the torus is not as much confined by the supersonic inflow."
 Therefore. in runs with higher gas pressure the flow is subsonic in a relatively big region where mixing between low- and high-/ occurs.," Therefore, in runs with higher gas pressure the flow is subsonic in a relatively big region where mixing between low- and $l$ occurs."
 Because of the shock amplified asvnuuelry the mixing leads to large scale asymmetry. (compare run G and IL in Fig. 16))., Because of the shock amplified asymmetry the mixing leads to large scale asymmetry (compare run G and H in Fig. \ref{fig:4}) ).
" As we mentioned above. [or ?=4/3 and =1.2. we also observe occasional bursts in the M, evolution (see e.g. Fig. 1))."," As we mentioned above, for $\gamma=4/3$ and $\gamma=1.2$, we also observe occasional bursts in the $\MDOT_a$ evolution (see e.g. Fig. \ref{fig:1a}) )."
 The mass accretion rate can significantly increase. because of mixing of the high- and low-/ gas at large radii.," The mass accretion rate can significantly increase, because of mixing of the high- and $l$ gas at large radii."
 The flaring behavior of the mass accretion rate in models for ο=4/3 and 5=1.2 is caused by the torus movement in the 'z direction., The flaring behavior of the mass accretion rate in models for $\gamma=4/3$ and $\gamma=1.2$ is caused by the torus movement in the `z' direction.
 Fig., Fig.
 10. (panels corresponding to 2 —1.2 case) captured a situation when the torus moved toward the southern hemisphere and partially blocked an inflow of low-/ gas in the polar funnel., \ref{fig:3c} (panels corresponding to $\gamma$ =1.2 case) captured a situation when the torus moved toward the southern hemisphere and partially blocked an inflow of $l$ gas in the polar funnel.
 Then this low-/ gas is pushed toward equator., Then this $l$ gas is pushed toward equator.
 When the torus later swings toward the northern hemisphere. a channel for the low-/ widens one sees a flare in the mass accretion rate curve.," When the torus later swings toward the northern hemisphere, a channel for the $l$ widens one sees a flare in the mass accretion rate curve."
 The reason we do not observe strong flares for y=1.01 is that there is no mixing of gas with high- and low-/ at larger clistances., The reason we do not observe strong flares for $\gamma=1.01$ is that there is no mixing of gas with high- and $l$ at larger distances.
 We find that the flow oscillates in the *z direction. and is asymmetric with respect to the equatorial plane., We find that the flow oscillates in the `z' direction and is asymmetric with respect to the equatorial plane.
 Instabilities in the accretion disks were studied by many authors., Instabilities in the accretion disks were studied by many authors.
 Pulsational instabilitw of quasi-acliabatic and quasi-inviseid accretion disks. was examined by in manv studies (e.g.. Kato 1973 Muchotrzeb-Czerny. 1936: Ἱναίο et al.," Pulsational instability of quasi-adiabatic and quasi-inviscid accretion disks, was examined by in many studies (e.g., Kato 1978 Muchotrzeb-Czerny 1986; Kato et al."
 1988: Okuda et al., 1988; Okuda et al.
 1993)., 1993).
 Ixato et al. (, Kato et al. (
1978) found that the condition lor pulsation instability depend on how viscosity changes during pulsation.,1978) found that the condition for pulsation instability depend on how viscosity changes during pulsation.
 In our simulation only artificial viscosity is introduced. which is small.," In our simulation only artificial viscosity is introduced, which is small."
 Nevertheless (his viscous proves (o be important., Nevertheless this viscous proves to be important.
 1n summary. we find that the asvimmetry of the flow is initially induced by the numerical effects. but the propagation and amplification of (he asvnunetry stronely depends on the physical conditions in the accretion flow.," In summary, we find that the asymmetry of the flow is initially induced by the numerical effects, but the propagation and amplification of the asymmetry strongly depends on the physical conditions in the accretion flow."
 In the cases where the eas pressure is reduced because of low 5 the asymmetry is stronger., In the cases where the gas pressure is reduced because of low $\gamma$ the asymmetry is stronger.
 For higher 5. (he gas pressure is larger and (he information about Che perturbation propagates faster.," For higher $\gamma$, the gas pressure is larger and the information about the perturbation propagates faster."
 The gas pressure works against effects of shocks ancl (ries to restore (he svimmetiry., The gas pressure works against effects of shocks and tries to restore the symmetry.
 We explore effects of gas pressure {ο confirm its role in maintaining sviunetrv in the flow., We explore effects of gas pressure to confirm its role in maintaining symmetry in the flow.
 To (his end. we performed additional simulations lor the same parameters as run J. bul with higher ὃς corresponding to models," To this end, we performed additional simulations for the same parameters as run J, but with higher $c_{\infty}$ corresponding to models"
about. of the time (down from for three Neptune-mass. planets).,about of the time (down from for three Neptune-mass planets).
" However. thev also found that only of svstems of three 3 Mj,up planets settled into a configuration with ο«l.l."," However, they also found that only of systems of three 3 $_{\textrm{Jup}}$ planets settled into a configuration with $\beta/\beta_{crit} < 1.1$."
 Therefore we expect that these (wo parameters will be (he hardest to reproduce via scattering., Therefore we expect that these two parameters will be the hardest to reproduce via scattering.
 As we see below. this expectation is borne out by our modeling.," As we see below, this expectation is borne out by our modeling."
 In our study. a successful model conserved energy. adequately (1 part in 103). removed ihe extra planet. and the remaining planets all had orbits with a<10 AU.," In our study, a successful model conserved energy adequately (1 part in $10^4$ ), removed the extra planet, and the remaining planets all had orbits with $a < 10$ AU."
 2072 trials met (hese requirements (1416 collisions and 656 ejections)., 2072 trials met these requirements (1416 collisions and 656 ejections).
 We ran each of these final configurations lor an additional 10° vears (again validating the simulation via energy conservalion) {ο assess secular behavior for comparison with the svstem presented in Table 9, We ran each of these final two-planet configurations for an additional $10^5$ years (again validating the simulation via energy conservation) to assess secular behavior for comparison with the system presented in Table 2.
 In Fig., In Fig.
" ὁ we show the outcome of one such (rial in which a hvpothetical planet was ejected,", \ref{fig:example} we show the outcome of one such trial in which a hypothetical planet was ejected.
 The format of this ligure is (he same as Fie. 1.., The format of this figure is the same as Fig. \ref{fig:secular}. .
 The behavior is qualitatively similar as in Fig. 1..," The behavior is qualitatively similar as in Fig. \ref{fig:secular},"
 including anti-aligned libration of the apses. the magnitudes of (hie eccentricities and the inclinations. ancl (he short period oscillation superposed on the longer oscillation.," including anti-aligned libration of the apses, the magnitudes of the eccentricities and the inclinations, and the short period oscillation superposed on the longer oscillation."
 The mutual inclination for this case is even larger (han the observed svstem., The mutual inclination for this case is even larger than the observed system.
 This svstems 3 Is 1.06. slightly lower than the observed svstem.," This system's $\beta/\beta_{crit}$ is 1.06, slightly lower than the observed system."
 This simulation. which is one of the closest matches to the observed svstem. shows that the ejection of a single additional planet could have produced the svstem.," This simulation, which is one of the closest matches to the observed system, shows that the ejection of a single additional planet could have produced the system."
 Figure 3. is but one outcome., Figure \ref{fig:example} is but one outcome.
 We next explore (he statistics of this suite of simulations and consider the other orbital elements and clvuamiical properties., We next explore the statistics of this suite of simulations and consider the other orbital elements and dynamical properties.
 We divide the outcomes into two cases: Ejections and Collisions., We divide the outcomes into two cases: Ejections and Collisions.
 These two phenomena could produce significantly different outcomes., These two phenomena could produce significantly different outcomes.
 For example. collisions tend (o occur near periastron of one planet ancl apoastron of the other. and we might expect the merged body (ο have a lower eccentricity than either of the progenitors.," For example, collisions tend to occur near periastron of one planet and apoastron of the other, and we might expect the merged body to have a lower eccentricity than either of the progenitors."
 We show (he cumulative distributions of the properties listed in Table 2 in Fig. 4.., We show the cumulative distributions of the properties listed in Table 2 in Fig. \ref{fig:single}.
 Comparing the values of orbital elements al a given lime is not ideal. but as it has been done many limes (see Ford 2001: Ford Rasio 2008: Juric Tremaine 2008: Chatterjee 2003: Raymond 2010). we do so here as well.," Comparing the values of orbital elements at a given time is not ideal, but as it has been done many times (see Ford 2001; Ford Rasio 2008; Juric Tremaine 2008; Chatterjee 2008; Raymond 2010), we do so here as well."
 In Figs., In Figs.
 daac. we show the values of e. 7. anc V. atthe end of the initial 10? vear integration.," \ref{fig:single}a a–c, we show the values of $e$, $i$, and $\Psi$ atthe end of the initial $10^5$ year integration."
" In panels dh we show the ranges of ;/"""""", 77"" "" and wee’)"," In panels d–h we show the ranges of $i^{min}$, $i^{max}$, $\Psi^{min}$ and $\Psi^{max}$."
" We find that. of successful models produced. a svstem wilh V""z30°. consistent with Rasmond (2010)."," We find that of successful models produced a system with $\Psi^{max} > 30^\circ$, consistent with Raymond (2010)."
 Note that ejections produce V**>30° about of the time.," Note that ejections produce $\Psi^{max} >
30^\circ$ about of the time."
 In Fig., In Fig.
 Aii we show the e distribution. which is bimodal with one peak near 0.1 and another near 107.," \ref{fig:single}i i we show the $\epsilon$ distribution, which is bimodal with one peak near 0.1 and another near $10^{-3}$."
" The observed value of 0.17 is not an unusual value. anc we find that svslens with this e value can have appropriate values of €EET and e"", "," The observed value of 0.17 is not an unusual value, and we find that systems with this $\epsilon$ value can have appropriate values of $e^{min}$ and $e^{max}$ ."
We note that the significant [raction of svstems near (the apsidalseparatrix contracdicts the results of Barnes, We note that the significant fraction of systems near the apsidalseparatrix contradicts the results of Barnes
"> 1.2 nuu and nor the HO. production. both of which contribute at least as nmch mass. each seperately as doeshis ""secondary iucleus.","$\ge$ 0.2 mm and nor the $_2$ O production, both of which contribute at least as much mass, each seperately as doeshis “secondary nucleus”."
 The historie outbursts. as discussed by Whipple (1986)). show several sinularitics to the present one. sueecstine that they happened the same way. but in 2 steps.," The historic outbursts, as discussed by Whipple \cite{whi}) ), show several similarities to the present one, suggesting that they happened the same way, but in 2 steps."
 After all. comet 17 P/IIohues is a comet like may others whose appearance is determined by sublimation of cometary ices.," After all, comet 17 P/Holmes is a comet like many others whose appearance is determined by sublimation of cometary ices."
" What makes it peculiar is that it had a big dust cover aud hat it seldom comes close enough to the Sun to afford a ereat cisplay of activity,", What makes it peculiar is that it had a big dust cover and that it seldom comes close enough to the Sun to afford a great display of activity.
 Dust covers of cometary nuclei are standard (see model of Torauvi et al. 198 1)), Dust covers of cometary nuclei are standard (see model of Horanyi et al. \cite{hor}) )
 and do rot judicate a splitting comet., and do not indicate a splitting comet.
 We think that the delaved sublimation. as explained above. ix a viable alternative o the theory of splitting or sudden fragmentation of he cometary nucleus.," We think that the delayed sublimation, as explained above, is a viable alternative to the theory of splitting or sudden fragmentation of the cometary nucleus."
 We are erateful to Dr. J. Boissicr (IRAM) for conununicatiug he 90 (πε results to us prior to publication., We are grateful to Dr. J. Boissier (IRAM) for communicating the 90 GHz results to us prior to publication.
 We thank he director of IRAM. Dr. P. Cox. for erautine special observing tine aud the staff on Pico Voleta. Spain. for heir support of the observing program.," We thank the director of IRAM, Dr. P. Cox, for granting special observing time and the staff on Pico Veleta, Spain, for their support of the observing program."
GOF for answering our inquiries in such a timely manner.,GOF for answering our inquiries in such a timely manner.
 JCL janks the Isaac Newton Trust. the Overseas Research Studentship 0ogramme (ORS) and the Cambridge Commonwealth Trust for support.," JCL thanks the Isaac Newton Trust, the Overseas Research Studentship programme (ORS) and the Cambridge Commonwealth Trust for support."
 ACF thanks the Royal Society for support., ACF thanks the Royal Society for support.
 KI and WNB ink. PPARC and NASA grant NAGS-6852 for support respectively., KI and WNB thank PPARC and NASA grant NAG5-6852 for support respectively.
 CSR thanks the National Science Foundation for support under grant AST9529175. and NASA for support under ye Long Term Space Astrophysics grant NASA-NAG-6337.," CSR thanks the National Science Foundation for support under grant AST9529175, and NASA for support under the Long Term Space Astrophysics grant NASA-NAG-6337."
 CSR also acknowledges support from Hubble Fellowship grant HF-O1113.01-98A awarded by the Space Telescope Institute. which is Operated by the Association of Universities for Research in Astronomy. Ine.. for NASA under contract 55-26555.," CSR also acknowledges support from Hubble Fellowship grant HF-01113.01-98A awarded by the Space Telescope Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA under contract 5-26555."
a with 8 fixed to 0.1.,$\alpha$ with $\beta$ fixed to 0.1.
" A value near zero means that the DEM distribution is very peaked (near single-temperature), and a value significantly larger than zero means that there is a significant contribution of low-temperature gas."," A value near zero means that the DEM distribution is very peaked (near single-temperature), and a value significantly larger than zero means that there is a significant contribution of low-temperature gas."
" Surprisingly, there is a small region in the cluster with a large value for o, which is located just to the North-Western side of the central galaxy."," Surprisingly, there is a small region in the cluster with a large value for $\alpha$, which is located just to the North-Western side of the central galaxy."
 This region is indicated with an arrow in Fig. 6.., This region is indicated with an arrow in Fig. \ref{fig:wdem-alphamap}.
" The maximum value for @ is 1.06+0.09, while the values in the immediate surroundings are typically 0.3."," The maximum value for $\alpha$ is $\pm$ 0.09, while the values in the immediate surroundings are typically 0.3."
 The large value suggests a large contribution of a cool component., The large value suggests a large contribution of a cool component.
 These bins that have an unusually high « value are associated with a very interesting multi-temperature region., These bins that have an unusually high $\alpha$ value are associated with a very interesting multi-temperature region.
" Therefore, we extract a spectrum from a circular region centered on the bin with the high @ value."," Therefore, we extract a spectrum from a circular region centered on the bin with the high $\alpha$ value."
 The resulting spectra for EPIC MOS and pn are shown in Fig. 7.., The resulting spectra for EPIC MOS and pn are shown in Fig. \ref{fig:spectrum}.
" The radius of the extraction region is 15"".", The radius of the extraction region is $^{\prime\prime}$.
" We attempt to put constraints on the DEM distribution by fitting six empirical DEM distributions to the spectrum, which we explain in Section 3.."," We attempt to put constraints on the DEM distribution by fitting six empirical DEM distributions to the spectrum, which we explain in Section \ref{sec:models}."
 The results of the fits are listed in Table 3.., The results of the fits are listed in Table \ref{tab:multit}.
" Although there are some variations, the best-fit C-statistic values for the multi-temperature fits are very similar."," Although there are some variations, the best-fit C-statistic values for the multi-temperature fits are very similar."
" The iron abundances that we derive from the multi-temperature models are typically around 1.25 solar, except for the logarithmic Gaussian DEM model, which gives a lower iron abundance of 1.14+0.02."," The iron abundances that we derive from the multi-temperature models are typically around 1.25 solar, except for the logarithmic Gaussian DEM model, which gives a lower iron abundance of $\pm$ 0.02."
" In general, the derived mean temperatures and iron abundances are almost the same regardless of the used multi-temperature model."," In general, the derived mean temperatures and iron abundances are almost the same regardless of the used multi-temperature model."
" However, this does not hold for a single-temperature model."," However, this does not hold for a single-temperature model."
 A single-temperature fit to this region results in an unacceptable C-stat value of 2795 / 942 d.o.f., A single-temperature fit to this region results in an unacceptable C-stat value of 2795 / 942 d.o.f.
 The temperature and iron abundance values are unrealistically low compared to the multi-temperature results., The temperature and iron abundance values are unrealistically low compared to the multi-temperature results.
" Therefore, we ignore this model in the discussion about the temperature structure of this region."," Therefore, we ignore this model in the discussion about the temperature structure of this region."
 The multi-temperature distributions that we fit are best compared by plotting them., The multi-temperature distributions that we fit are best compared by plotting them.
" In Fig. 8,,"," In Fig. \ref{fig:dem},"
 we plot the DEM distributions and normalisations of five multi-temperature models., we plot the DEM distributions and normalisations of five multi-temperature models.
" In this plot, the emission measures are normalised using the bin width to be able to compare them directly."," In this plot, the emission measures are normalised using the bin width to be able to compare them directly."
" Since the best-fit models have similar C-statistic values, the exact shape of the DEM distribution is uncertain."," Since the best-fit models have similar C-statistic values, the exact shape of the DEM distribution is uncertain."
" However, they all show a similar trend."," However, they all show a similar trend."
" The peak temperature of the distribution is found around temperatures of 2 and 3 keV. Above 3 keV, the contribution of high temperatures drops rapidly."," The peak temperature of the distribution is found around temperatures of 2 and 3 keV. Above 3 keV, the contribution of high temperatures drops rapidly."
" Below 2 keV all models show a significant contribution of cool gas even down to 0.5 keV. Interestingly, the four-temperature models show an emission measure distribution that is comparable to the Gaussian DEM models."," Below 2 keV all models show a significant contribution of cool gas even down to 0.5 keV. Interestingly, the four-temperature models show an emission measure distribution that is comparable to the Gaussian DEM models."
" Using the 4-temperature model with the fixed temperatures, we estimate the volume-filling fractions of the temperature components if we assume that the gas is in pressure equilibrium."," Using the 4-temperature model with the fixed temperatures, we estimate the volume-filling fractions of the temperature components if we assume that the gas is in pressure equilibrium."
" For component i of n temperature components,"," For component $i$ of $n$ temperature components,"
"If the data quality were not so high. we would iof lave been able to distinguish so many details of the lieht curve and to address them one by one. and we would have limited our analysis, for instance. o an overall application of f enrpirical lov (Eq. (3). (3)). CD) ","If the data quality were not so high, we would not have been able to distinguish so many details of the light curve and to address them one by one, and we would have limited our analysis, for instance, to an overall application of the empirical scaling law (Eq. \ref{eq:lreale}) ), \ref{eq:fzeta}) ), \ref{eq:t7}) ))"
approxiniaweine the decay to a scaliugsinele decay., approximating the decay to a single decay.
" We would have obtained a decay time z;;,L3 ss. ↴aad slope∖⋅ ∖≓↴⋅⊀in the n-T undiagram Qi;5cE0.5."," We would have obtained a decay time $\tau_{sin} \sim 4.3$ ks, and a slope in the n-T diagram $\zeta_{sin}
\sim 0.5$."
 With: logDons)zT7.1 (Fig.ie. 2 2)).," With $\log (T_{obs}) \approx 7.4$ (Fig. \ref{fig:datnt}) ),"
 we owwould Laveave obtaineained Lox=113- je. larecr than the best value derived with detailed wdrodvuamuc modclng.," we would have obtained $L_9 \approx 13$, i.e. larger than the best value derived with detailed hydrodynamic modeling."
 The agreeimieut between the two approaches is relatively good. also considering that the slope Gein is close to the lower μπιτ of the applicability of onmuula (3)). ancl therefore it is better to take Lo as al upper linüt.," The agreement between the two approaches is relatively good, also considering that the slope $\zeta_{sin}$ is close to the lower limit of the applicability of formula \ref{eq:fzeta}) ), and therefore it is better to take $L_9$ as an upper limit."
 The lidrodyaiauic evolution of the plasiua coufiued inside a sinele loop of total leugth 2.«1079 cu (loop A} is able to explain the initial phases of the flare., The hydrodynamic evolution of the plasma confined inside a single loop of total length $2 \times 10^{10}$ cm (loop A) is able to explain the initial phases of the flare.
" The later phases, ai in particular the second peak. iustead require he ignition of a secoud loop system."," The later phases, and in particular the second peak, instead require the ignition of a second loop system."
 The modeling teIx us that a secoud longer loop triggeredao simultaucouslv to oop A can fit the secoud peak.but not the slow monotonic cluperature decay after the flare inaxiuimu.," The modeling tells us that a second longer loop triggered simultaneously to loop A can fit the second peak, but not the slow monotonic temperature decay after the flare maximum."
 To fit both. it is necessary to assume a residual cdecaving heating iu he coronal section of loop A. and an arcade of ~5 loops identical to loop A triggeredao ~LO ain later.," To fit both, it is necessary to assume a residual decaying heating in the coronal section of loop A, and an arcade of $\sim 5$ loops identical to loop A triggered $\sim 40$ min later."
 We come up therefore witha flare iuvolviie a Μπο of almost identical loops. a single one first. aud ararcade later.," We come up therefore with a flare involving a system of almost identical loops, a single one first, and an arcade later."
 We have also realized that there is at least oue solar event which prescuts several awoeies with this scenario: the so-called Bastille Day flare (Li July 2000)., We have also realized that there is at least one solar event which presents several analogies with this scenario: the so-called Bastille Day flare (14 July 2000).
 This is quite an intense solar flare (GOES class N5.7) whose light curve in the ALI2 filter passhaud of the Soft N-vayv Telescope οhoard the satellite» Yolikoli shows a clear bun after the main⋅ maximum⋅ (see Fie.3 MNi1 Asclavanden Alexander οX013., This is quite an intense solar flare (GOES class X5.7) whose light curve in the Al.12 filter passband of the Soft X-ray Telescope onboard the satellite Yohkoh shows a clear bump after the main maximum (see Fig.3 in Aschwanden Alexander 2001).
 The same figure clearv shows also that the bun is associated with the spectacular ignition of a long arcade. also deected by the TRACE telescope.," The same figure clearly shows also that the bump is associated with the spectacular ignition of a long arcade, also detected by the TRACE telescope."
 All his may Sugeest a certain similarity of the loop morphology of this event with that ou Proxima Centauri., All this may suggest a certain similarity of the loop morphology of this event with that on Proxima Centauri.
 Also the iniug of the lel curve phases is not tremendously differeut: the bump ο ‘the solar flare occurs about GOO s after he peak. the secoud maxiumu of the Prxiua Centauri flare occurs 3000 μαter the first onc.," Also the timing of the light curve phases is not tremendously different: the bump of the solar flare occurs about 600 s after the peak, the second maximum of the Proxima Centauri flare occurs 3000 s after the first one."
 The cliffereut delay may |© linked to the scale size of the Oops. the solar arcade loops are a factor ~| shorter tha1i the predicted stellar loops., The different delay may be linked to the scale size of the loops: the solar arcade loops are a factor $\sim 4$ shorter than the predicted stellar loops.
 We sketch a possible scenario of the flaring loop system ou Proxima Centauri scalec to the resolved scenario of the solar Bastille Dav flare in Fie. 5., We sketch a possible scenario of the flaring loop system on Proxima Centauri scaled to the resolved scenario of the solar Bastille Day flare in Fig. \ref{fig:photo}.
" The halfleneth of boh loop A and loop D is found to be of the same order as he estimated radius of Proxima Centami {L/R,1)."," The half-length of both loop A and loop B is found to be of the same order as the estimated radius of Proxima Centauri $L/R_\star \approx
1$ )."
 This length is neither very far (1.1 times) from the zmleneth estimated for the fare observed with (Reale et al., This length is neither very far (1.4 times) from the length estimated for the flare observed with (Reale et al.
 1988). nor very large in absolute value (the radius of Proxima Centam is indeed a small," 1988), nor very large in absolute value (the radius of Proxima Centauri is indeed a small"
constraints from studies of the 2D correlation function (see Chuang&Wang (2011).,constraints from studies of the 2D correlation function (see \cite{Chuang:2011fy}) ).
 We find that [/7(0.35). D1(0.35)] from the spherically-averaged correlation function provide much weaker constraints than the 2D correlation function: this is as expected since. spherically-averaging reduces the amount of information extractable from data.," We find that $\{H(0.35)$, $D_A(0.35)\}$ from the spherically-averaged correlation function provide much weaker constraints than the 2D correlation function; this is as expected since spherically-averaging reduces the amount of information extractable from data."
 The correlation function analysis is expected to be a more robust way to extract the BAO signals than the power spectrum analysis. because one can easily get rid of the systematic uncertainties such as the redshift distortion. the galaxy bias. and the non-linear effect by cutting off the small seale range (Sanchez.Baugh.andAngulo 2008)..," The correlation function analysis is expected to be a more robust way to extract the BAO signals than the power spectrum analysis, because one can easily get rid of the systematic uncertainties such as the redshift distortion, the galaxy bias, and the non-linear effect by cutting off the small scale range \citep{Sanchez:2008iw}."
 The power of the correlation function analysis is limited at present by the available data., The power of the correlation function analysis is limited at present by the available data.
 The correlation funeiton that we have measured from the SDSS DR7 data has a high tail (larger than expected correlations) at large scales 6s 120) (see Fig. 2))., The correlation funciton that we have measured from the SDSS DR7 data has a high tail (larger than expected correlations) at large scales $s>120$ ) (see Fig. \ref{fig:kazin_my}) ).
" Whether this high tail is simply due to the sample variance or some other systematic issue. e.g.. extinction correction. will only become clear as more ambitious galaxy survey data become available in the future (e.g.. fromBOSS"".. or y)."," Whether this high tail is simply due to the sample variance or some other systematic issue, e.g., extinction correction, will only become clear as more ambitious galaxy survey data become available in the future (e.g., from, or )."
 We would like to thank Michael Blanton. Daniel Eisenstein. Alex Kim. Antony Lewis. Ariel Sanchez. and Martin White for useful comments.," We would like to thank Michael Blanton, Daniel Eisenstein, Alex Kim, Antony Lewis, Ariel Sanchez, and Martin White for useful comments."
 We are grateful to the LasDamas project for making their mock catalogs publicly available., We are grateful to the LasDamas project for making their mock catalogs publicly available.
 The computing for this project was performed at the OU Supercomputing Center for Education and Research (OSCER) at the University of Oklahoma (OU)., The computing for this project was performed at the OU Supercomputing Center for Education and Research (OSCER) at the University of Oklahoma (OU).
 OSCER Director Henry eeman and HPC Application Software Specialist Joshua Alexander provided invaluable technical support., OSCER Director Henry Neeman and HPC Application Software Specialist Joshua Alexander provided invaluable technical support.
 This work was supported in part by DOE grant DE-FG02-04ER41305., This work was supported in part by DOE grant DE-FG02-04ER41305.
provides randomly scattered light to the corrector. reproducing the flux from a uniforii sky.,"provides randomly scattered light to the corrector, reproducing the flux from a uniform sky."
 Such a iiethod Is necessary to accurately flat field our images. as Wild (1997) poiuts out that over a one deeree scale. no part of the sky is really fat.," Such a method is necessary to accurately flat field our images, as Wild (1997) points out that over a one degree scale, no part of the sky is really flat."
 Additionally. this fact is attested to by the many BATC images our survey las obtained.," Additionally, this fact is attested to by the many BATC images our survey has obtained."
 We note. however. that it is oulv with ΗΧΟΥΣ or inermediate-baud filters that this diffuser ou a Sclianiclt telescope cau produce reliable flat fields.," We note, however, that it is only with narrow or intermediate-band filters that this diffuser on a Schmidt telescope can produce reliable flat fields."
 Otherwise. he dome flat field cau introduce second-order color terus to broad baud observations that nius be renmovec using direct sky inages (Fanetal.1996)).," Otherwise, the dome flat field can introduce second-order color terms to broad band observations that must be removed using direct sky images \cite{Fan96}) )."
 We ake twelve dome flats cach daw each wih exposure ines of 150 seconds.," We take twelve dome flats each day, each with exposure times of 150 seconds."
 This leusth of exposure reduces the effect of the finite time for shutter opening aud cosing. resulting iu a spurious eradicut of less than (cf.," This length of exposure reduces the effect of the finite time for shutter opening and closing, resulting in a spurious gradient of less than (cf."
 Sec., Sec.
 3.3)., 3.3).
 All twelve dome flats iione day are combined as the final flat field to correct the Biuues ostained ou the same nieht., All twelve dome flats in one day are combined as the final flat field to correct the frames obtained on the same night.
 The total count of combined come flat is about 810.000 clectrous per pixel. far higher than that of «kv background (about 2.000 electrous per pixel) ina single exposure frame.," The total count of combined dome flat is about 840,000 electrons per pixel, far higher than that of sky background (about 2,000 electrons per pixel) in a single exposure frame."
 Air mass correctious have to be done for our images on a pixel-by-pixel basis; as there exists close to ad eracdient in air niass correction over one square deeree. even at an altitude of 60 degrees.," Air mass corrections have to be done for our images on a pixel-by-pixel basis, as there exists close to a gradient in air mass correction over one square degree, even at an altitude of 60 degrees."
 To take inte account the different sets of data (gain differences. dithering. secius differences. ete).," To take into account the different sets of data (gain differences, dithering, seeing differences, etc.),"
 we combine these nuages in two steps., we combine these images in two steps.
 First we separate t1ο inuage frames mto Ll groups., First we separate the image frames into 11 groups.
 Each eroup includes the frunes observed in the same state of iustrunieit system and simular observation conditious (e.g... sinuülar seeine).," Each group includes the frames observed in the same state of instrument system and similar observation conditions (e.g., similar seeing)."
 On average. the observations for a en«1 night are in the same group.," On average, the observations for a given night are in the same group."
 The availability of hundreds well-defined point sources (both stars aud «istant galaxies) in these frames aided the combination of ] frames toa common system., The availability of hundreds of well-defined point sources (both stars and distant galaxies) in these frames aided the combination of all frames to a common system.
 This combination accounts for both dithered frames as well as for slight rtations in the CCD chip from vear-to-vear., This combination accounts for both dithered frames as well as for slight rotations in the CCD chip from year-to-year.
 To eet all combined images to the same effective seeing radius of 2.3 pixels CI). some of the combined nuages8 were convolved with CGaussiau fuuctious to acd small Hadditional values of seeiug.," To get all combined images to the same effective seeing radius of 2.3 pixels $4""$ ), some of the combined images were convolved with Gaussian functions to add small additional values of seeing."
 Three signa rejection was used to remove cosmiüc-ravs. hot-poiuts. bad. pixels xd Sclunidt telescope-related ehost-iuages.," Three sigma rejection was used to remove cosmic-rays, hot-points, bad pixels and Schmidt telescope-related ghost-images."
 The final nuage shown in Figure 1is the result of mereie the 1l combined frames. a total of 12.79 hours of observation.," The final image shown in Figure 1 is the result of merging the 11 combined frames, a total of 42.79 hours of observation."
" Photometric calibration was provided bv the five nights that were photometric (Alar. Ll. 1995. λίαν, 6. 1995. Jan. 6. 1997. Jan. 17. 1997. aud Apr. 16. 1997)."," Photometric calibration was provided by the five nights that were photometric (Mar. 4, 1995, Mar. 6, 1995, Jan. 6, 1997, Jan. 17, 1997, and Apr. 16, 1997)."
 Following the now-staudard BATC photometric calibration (cf. Zhouetal.2001:: Yanetal. 200033.," Following the now-standard BATC photometric calibration (cf. \cite{Zhou01}; \cite{Yan00}) ),"
 four Oke Cun (1983) standard stars (IID 19115. IID 51957. BD 26°2606 aud L708) axe used as BATC calibration stars.," four Oke Gunn (1983) standard stars (HD 19445, HD 84937, BD $^{\rm \circ}$ 2606 and $^{\rm \circ}$ 4708) are used as BATC calibration stars."
 The calibrations of five uiehts agree quite well. viclding a zero point accuracy of 0.02 mae as determined from 18 bright stars over," The calibrations of five nights agree quite well, yielding a zero point accuracy of 0.02 mag as determined from 48 bright stars over"
"10 candidates have questionable membership (0.4—D,<0.8). and there is no proper motion information on another five of our candidates.","10 candidates have questionable membership $0.4 <
P_{\mu} < 0.8$ ), and there is no proper motion information on another five of our candidates."
 Since the field of Cotéetal.(2002). extended bevond our observed field. we used their photometry (to identilv 5 additional candidates (although three of these appear to be fiekl stars).," Since the field of \citet{cot02} extended beyond our observed field, we used their photometry to identify 5 additional candidates (although three of these appear to be field stars)."
 Several of the stars in our list [all close enough to the subgiant branch (hat there is a substantial probability Chat they. are detached binary svstenis these stars are identified in (he table. ancl were noted by SMC'T as an apparent sequence of stars parallel to the subgiant branch.," Several of the stars in our list fall close enough to the subgiant branch that there is a substantial probability that they are detached binary systems — these stars are identified in the table, and were noted by SMCT as an apparent sequence of stars parallel to the subgiant branch."
 Dorrisova οἱ al. (, Borrisova et al. (
1997) and Siegeletal.(2001) each identified seven BSS candidates.,1997) and \citet{sie01} each identified seven BSS candidates.
 llowever. our smaller measurement errors for stars near the cluster (urnoll allow us to identifv candidates (hat are closer to the main-sequence turnoff in the CMD. ancl our better image resolution allowed us to locate BSS candidates closer to the cluster core.," However, our smaller measurement errors for stars near the cluster turnoff allow us to identify candidates that are closer to the main-sequence turnoff in the CMD, and our better image resolution allowed us to locate BSS candidates closer to the cluster core."
 One of the BSS candidates (BSS 4: SMCTT ID 428) that was originally identified by Borissova et al. (, One of the BSS candidates (BSS 4; SMCT ID 428) that was originally identified by Borissova et al. (
1997) is not included here because it clearly falls within the cluster main-sequence tunolf band in our photometry and has a low membership probability (2?=0.23).,1997) is not included here because it clearly falls within the cluster main-sequence turnoff band in our photometry and has a low membership probability $P = 0.23$ ).
 The following subsections will provide analysis of our BSS population aud comparison of Palomar 195 population with other clusters., The following subsections will provide analysis of our BSS population and comparison of Palomar 13's population with other clusters.
 The brightest strageler (ID 2) deserves some comment., The brightest straggler (ID 2) deserves some comment.
 From proper motions. the star has a moderate probability of membership. but Blechaetal.(2004) mace (wo radial velocity measurements for the star (25.85 and 25.67 km !) placing it (uite near the cluster mean (24.12:0.5 kan 1).," From proper motions, the star has a moderate probability of membership, but \citet{blech} made two radial velocity measurements for the star (25.85 and 25.67 km $^{-1}$ ) placing it quite near the cluster mean $24.1 \pm 0.5$ km $^{-1}$ )."
 Given that it is the brightest blue straggler in the cluster. its red color is surprising.," Given that it is the brightest blue straggler in the cluster, its red color is surprising."
 A blend of a bluer blue strageler with a faint red giant can probably be ruled out since (he stars &—V color is consistent with colors using other filter combinations., A blend of a bluer blue straggler with a faint red giant can probably be ruled out since the star's $U-V$ color is consistent with colors using other filter combinations.
 Models of stellar collisions (e.g. Sills Bailvn 1999) generally predict that (he most massive blue stragglers will tend to be among the bluest. primarily as a result of the relationship between effeclive temperature and mass for main sequence stars.," Models of stellar collisions (e.g. Sills Bailyn 1999) generally predict that the most massive blue stragglers will tend to be among the bluest, primarily as a result of the relationship between effective temperature and mass for main sequence stars."
 Spectroscopic measurement of the stars surface eravitv might help verily whether it is an evolved blue straggler or not., Spectroscopic measurement of the star's surface gravity might help verify whether it is an evolved blue straggler or not.
 At the risk of overanalvzing this relatively small population of stragelers. we note a couple of features of the CMD cdistiibution.," At the risk of overanalyzing this relatively small population of stragglers, we note a couple of features of the CMD distribution."
 The color distribution for the seven brightest BSS shows no tendency lor the stragelers to cluster toward the zero-age main sequence., The color distribution for the seven brightest BSS shows no tendency for the stragglers to cluster toward the zero-age main sequence.
 In fact. these strageglers are spread almost evenly from near (he zero-age main sequence {ο the (urnoll color.," In fact, these stragglers are spread almost evenly from near the zero-age main sequence to the turnoff color."
 This twpe of color distribution is seen in many other clusters. ancl is not predicted by models of stellar collisions (e.g.. Sills Bailvn 1999).," This type of color distribution is seen in many other clusters, and is not predicted by models of stellar collisions (e.g., Sills Bailyn 1999)."
 In addition. there is a gap ol over 0.5 mag between the bright blue stragglers and the 17 straggler candidates fainter than the subgiant branch.," In addition, there is a gap of over 0.5 mag between the bright blue stragglers and the 17 straggler candidates fainter than the subgiant branch."
One star (AIBM 124-5) with a rather significant peak (FAP = 0.02) is not included in our list of positive detections because its period is 0.505 davs.,One star (MBM 12A-5) with a rather significant peak (FAP = 0.02) is not included in our list of positive detections because its period is 0.505 days.
 Lf (his star is truly periodic with that period it would be impossible for us to discern it with confidence based on the current observations., If this star is truly periodic with that period it would be impossible for us to discern it with confidence based on the current observations.
 The reason is that they were not [requent enough during any parücular night to clearly distinguish such a putative evele Irom an harmonie of the typical sampling interval of 1 day., The reason is that they were not frequent enough during any particular night to clearly distinguish such a putative cycle from an harmonic of the typical sampling interval of 1 day.
 Future observations with a higher cadence may reveal whether this star is. in fact. a evelic variable with a period near 0.5 d. Another possibly periodic siar (MDMI2A-2). with FAP = 0.07. is noted in the table and discussed further in the next secon.," Future observations with a higher cadence may reveal whether this star is, in fact, a cyclic variable with a period near 0.5 d. Another possibly periodic star (MBM12A-2), with FAP = 0.07, is noted in the table and discussed further in the next section."
 Tt may be noted that all of the stars identified as periodic have more than one significant peak in their periodograms., It may be noted that all of the stars identified as periodic have more than one significant peak in their periodograms.
 The reason is quite simple: nightly observations from a single longitude introduce a sampling frequency of about one day into the data., The reason is quite simple: nightly observations from a single longitude introduce a sampling frequency of about one day into the data.
 When a (rulv periodic star is observed. the actual period “beats” with the sampling interval to creale an alias or “beat” period.," When a truly periodic star is observed, the actual period “beats"" with the sampling interval to create an alias or “beat"" period."
 One can easily see that there are complementary peaks in (he power spectra of all of these stars which are separated in [frequency space by 1 + 1/P where P is the true period., One can easily see that there are complementary peaks in the power spectra of all of these stars which are separated in frequency space by 1 $\pm$ 1/P where P is the true period.
 Identifving which is the true period and which is the beat period is not always easy. but (here is little ambiguity for the four stars in (his sample.," Identifying which is the true period and which is the beat period is not always easy, but there is little ambiguity for the four stars in this sample."
 In three cases. one of the peaks is significantly higher ancl the light curve phased with that period significantly less scattered than the other.," In three cases, one of the peaks is significantly higher and the light curve phased with that period significantly less scattered than the other."
 In the case of MDMI2AÀ-4 (there are two peaks of nearly equal heieht but the light curve phased with a period of 2.603 cays looks better than (the one phased al 0.722 davs., In the case of MBM12A-4 there are two peaks of nearly equal height but the light curve phased with a period of 2.603 days looks better than the one phased at 0.722 days.
 Of course. it is possible (hat variations in light curve shape during an observing season could cause us (ο mistake the beat. period for the iue period but in samples where (his can be tested (e.g. the ONC) it happens less than of the Gime. and usually with less well-defined light curves than are seen here 2000).," Of course, it is possible that variations in light curve shape during an observing season could cause us to mistake the beat period for the true period but in samples where this can be tested (e.g. the ONC) it happens less than of the time, and usually with less well-defined light curves than are seen here \citep{h00}."
. We conclude that the periods of (hese four stars are known wilh reasonable confidence. allhougl v sin i measurements might be helpful in confirming them.," We conclude that the periods of these four stars are known with reasonable confidence, although v sin i measurements might be helpful in confirming them."
were used.,were used.
" After removing the cosmic rays, profile fitting photometry was done using the DAOPHOT and ALLSTAR packages."," After removing the cosmic rays, profile fitting photometry was done using the DAOPHOT and ALLSTAR packages."
 The observed R-band frame is shown in Fig.2.. The lightcurves of the Hg flux and the continuum at 5100 wwere obtained using the final inter-calibrated spectra., The observed R-band frame is shown in Fig.\ref{fig:image}. The lightcurves of the $_\beta$ flux and the continuum at 5100 were obtained using the final inter-calibrated spectra.
 The continuum flux in the rest-frame of the galaxy at was obtained using the mean flux within the observed band from 5172 to, The continuum flux in the rest-frame of the galaxy at was obtained using the mean flux within the observed band from 5172 to
 The continuum flux in the rest-frame of the galaxy at was obtained using the mean flux within the observed band from 5172 to , The continuum flux in the rest-frame of the galaxy at was obtained using the mean flux within the observed band from 5172 to
 The continuum flux in the rest-frame of the galaxy at was obtained using the mean flux within the observed band from 5172 to A, The continuum flux in the rest-frame of the galaxy at was obtained using the mean flux within the observed band from 5172 to
 The continuum flux in the rest-frame of the galaxy at was obtained using the mean flux within the observed band from 5172 to AA, The continuum flux in the rest-frame of the galaxy at was obtained using the mean flux within the observed band from 5172 to
 The continuum flux in the rest-frame of the galaxy at was obtained using the mean flux within the observed band from 5172 to AA., The continuum flux in the rest-frame of the galaxy at was obtained using the mean flux within the observed band from 5172 to
 The continuum flux in the rest-frame of the galaxy at was obtained using the mean flux within the observed band from 5172 to AA.., The continuum flux in the rest-frame of the galaxy at was obtained using the mean flux within the observed band from 5172 to
the loop unich more slowly: reaching a deusity above 1011 em? in the corona.,"the loop much more slowly, reaching a density above $10^{11}$ $^{-3}$ in the corona."
 The loop svstem D. undergoes a simular evolution. but sienificautly less dynamic: he nuinuuni temperature is about 20 ME. the coronal deusitv :ut its mnaxinuuni is one order of magnitude less twan in loop A. and the maxinuun velocity oue half that of loop. A. T1C inodeliis hiehliehts the presence of very hot plasina compoucuts. wihi wice the temperature value than the one oltained from simple data fitting.," The loop system B undergoes a similar evolution, but significantly less dynamic; the maximum temperature is about 20 MK, the coronal density at its maximum is one order of magnitude less than in loop A, and the maximum velocity one half that of loop A. The modeling highlights the presence of very hot plasma components, with twice the temperature value than the one obtained from simple data fitting."
 This is furtler apparent from the total distribution of the CLUISSIOli lueoasure vorsts teniperature. EAT). obtaiied by sununumne the contribuions of loop A aud arcade D. show1 iin Fig. 11..," This is further apparent from the total distribution of the emission measure versus temperature, EM(T), obtained by summing the contributions of loop A and arcade B, shown in Fig. \ref{fig:emt}."
 The distributions are averaged over tine intervals correspouding to the OCS of the istinitions Obtained from data anavss. shown iu Figs.," The distributions are averaged over time intervals corresponding to the ones of the distributions obtained from data analysis, shown in Figs."
 8 aud 9 of Papcr II Gutervals A O D)., 8 and 9 of Paper II (intervals A to D).
 The EM(CT) istinitions of Fig., The EM(T) distributions of Fig.
 LL share elobal similarities with those crived from the «afa. ln particuar to hose of Fig.," \ref{fig:emt} share global similarities with those derived from the data, in particular to those of Fig."
 5 in Paper IT: a dominant hot comonent (230 Ms) in oeπαντα. A. a bronder and cooler cistribuion in interval D. al OVOL COCder distribution wih a long cool tail iu oeterval C. the ap])'rance of a sienificaut cool (~10* IX) componeit iuiiterval D. The atter Ομ relates to he ignition of the loop arcade D. The differences )etsveen the cistributious derived from the νάνοςlvmanic modeling aud tjose derived frou t data are 1O surprising because he iuteeral8 iuversk techniques usc| to derive the distributions in Paper aro iUb-posed.," 8 in Paper II: a dominant hot component $\ga 30$ MK) in interval A, a broader and cooler distribution in interval B, an even cooler distribution with a long cool tail in interval C, the appearance of a significant cool $\sim
10^7$ K) component in interval D. The latter cool component relates to the ignition of the loop arcade B. The differences between the distributions derived from the hydrodynamic modeling and those derived from the data are not surprising because the integral inversion techniques used to derive the distributions in Paper II are ill-posed."
 Iu spite of this. he comparison wi lydvodvuaimic modchug clearly provides a kev for t1ο iuterpretatioi of the main features of the distributions obtained from the data.," In spite of this, the comparison with hydrodynamic modeling clearly provides a key for the interpretation of the main features of the distributions obtained from the data."
 The agreement of the hydrodywunic modeling resuts to the ¢ata is further confirmed by the foca-plaue EPIC- spectra SVthesized from the model of Fie., The agreement of the hydrodynamic modeling results to the data is further confirmed by the focal-plane EPIC-PN spectra synthesized from the model of Fig.
 7 for intervals A to D. compared to t1C 0served οres (Fie. 12)).," \ref{fig:best} for intervals A to D, compared to the observed ones (Fig. \ref{fig:spec}) )."
 The ecreral trends are well xxxlDuced. dw the mode spectra: discre»ucles nally coucern the intensity of sole Lue erows. Inostly relatec o differences of meta abundances. wlich we assu11ο X Z=0.5 for all clemeuts in the model spectra.," The general trends are well reproduced by the model spectra; discrepancies mainly concern the intensity of some line groups, mostly related to differences of metal abundances, which we assume to be Z=0.5 for all elements in the model spectra."
 The eood aSroeonien in the hare section of the svectra is a furt101) proof of the presence of sienificant hot uoasmia components., The good agreement in the hard section of the spectra is a further proof of the presence of significant hot plasma components.
 There are no deusitv-seusitive Ile-like triplets iu the RCS baud for very high tenmiperature pasus. all therefore it is ¢lifficult to «laenose the predicted. density values of the hottest flariis plasiua.," There are no density-sensitive He-like triplets in the RGS band for very high temperature plasma, and therefore it is difficult to diagnose the predicted density values of the hottest flaring plasma."
 Available deusitv diagnostics for this flare comes frou line ratios of O VII and Ne IX eroups obtained with the RGS (Payer D., Available density diagnostics for this flare comes from line ratios of O VII and Ne IX groups obtained with the RGS (Paper I).
 The line analysis provides density values ~[«103 3 with a large error bar for O VIL and betwee1 1013 and .24yal10/72 357. for£ Ne- IN. -0iin a time: interval: around the flare peak.," The line analysis provides density values $\approx 4 \times 10^{11}$ $^{-3}$ with a large error bar for O VII, and between $10^{11}$ and $2 \times 10^{12}$ $^{-3}$, for Ne IX, in a time interval around the flare peak."
 In approximately the same time interval. the loop model yields. an average deusitv: of] zκ2«+1012 5m and zLOY? * at the temperatures of 2 aud £M. of uaxinumn formation of the respective ious.," In approximately the same time interval, the loop model yields an average density of $\approx 2 \times 10^{12}$ $^{-3}$, and $\approx 10^{12}$ $^{-3}$ at the temperatures of 2 and 4 MK of maximum formation of the respective ions."
 For the Ne IX. he average density obtained frou he model is compatible o the aree interval allowed by the cata. although the Ne IX derived deusities are lighly uncertain due to severe ine blending (Paper IT).," For the Ne IX, the average density obtained from the model is compatible to the large interval allowed by the data, although the Ne IX derived densities are highly uncertain due to severe line blending (Paper II)."
 The vaues obtained from the nodeling at 2 MIN. are quite higrer than those derived roni the analvsis of the ο VIE line., The values obtained from the modeling at 2 MK are quite higher than those derived from the analysis of the O VII line.
 This may be motivated as folows: the ο VII lines are intensely emitted both roni the flaring plasimua and frou the remaimine quiet corona., This may be motivated as follows: the O VII lines are intensely emitted both from the flaring plasma and from the remaining quiet corona.
 What we detect is therefore the sum of the two coutrlmtious. and the density an average of the 2 MEK," What we detect is therefore the sum of the two contributions, and the density an average of the 2 MK"
thank Nevin Bundy for generously sharing lis Iy-baud photometry aud Cliaisty Tremouti for making her measurements available.,thank Kevin Bundy for generously sharing his K-band photometry and Christy Tremonti for making her measurements available.
 We are erateful to Stephane Arnout and Olivier bert for making their photo-z code available for use in estimating galaxy stellar mass aud are thankful to Olivicr Hbert and C.J. Ma for help in installing and implementing Le Phare., We are grateful to Stephane Arnout and Olivier Ilbert for making their photo-z code available for use in estimating galaxy stellar mass and are thankful to Olivier Ilbert and C.J. Ma for help in installing and implementing Le Phare.
 Finally. we would like to thank Charlie Conroy. Christy Tremouti. Ixistiau Fiulator. Len Cowie. David Rupke. Dave Saucers. Cliali Iobavashi. Ezequiel Treister aud TC (the plaver) aud Josh Barnes for useful discussion.," Finally, we would like to thank Charlie Conroy, Christy Tremonti, Kristian Finlator, Len Cowie, David Rupke, Dave Sanders, Chiaki Kobayashi, Ezequiel Treister and TC (the player) and Josh Barnes for useful discussion."
 We acknowledee the cultural significance Mana Wea has for the HEvidian conmamnuitv and with all due respect sav mahalo for its use in this work., We acknowledge the cultural significance Mauna Kea has for the Hawaiian community and with all due respect say mahalo for its use in this work.
 Conventionally. when spectra are not flux calibrated. as is the case in most spectroscopic redshift surveys. equivalent widths are utilized in determining the cussion line ratios used for inferring metallicity (7.hereafterIDP03)..," Conventionally, when spectra are not flux calibrated, as is the case in most spectroscopic redshift surveys, equivalent widths are utilized in determining the emission line ratios used for inferring metallicity \citep[hereafter KP03]{Kobulnicky2003b}."
 The essential feature of equivalent widths is the normalization of the liue cuission to the uuderlviug continua., The essential feature of equivalent widths is the normalization of the line emission to the underlying continuum.
" Tere we will discuss the algorithm developed to deteriinue line ratios in a self-cousistant ΠΙΑΤΟ,", Here we will discuss the algorithm developed to determine line ratios in a self-consistant manner.
 We define FOr) as the flux vector of our spectra with ας being the rest-frame wavelength vector corresponding to cach resolution clement., We define $F(x)$ as the flux vector of our spectra with $x$ being the rest-frame wavelength vector corresponding to each resolution element.
" We mask out £50, of our rest-frame Lue center wavelengths (frou NIST?)) and fit a elobal continui.", We mask out $\pm 5 \sigma_{v}$ of our rest-frame line center wavelengths (from ) and fit a global continuum.
 Tere we takeσι to be a velocity dispersion of 150 ή»., Here we take$\sigma_{v}$ to be a velocity dispersion of $150$ $km/s$.
 We model the global continu as where Z;(Ce) are model stellar spectra obtained from ?., We model the global continuum as where $T_{i}(x)$ are model stellar spectra obtained from \citet{Bruzual2003}.
 We perform a bounded value non-linear least square fit usus the set of routines (7) iu IDL to obtain c; aud pj with the coustraiut that €;0., We perform a bounded value non-linear least square fit using the set of routines \citep{Markwardt2009} in IDL to obtain $c_{i}$ and $p_{j}$ with the constraint that $c_{i}\geq0$.
 We obtain a contimmun-normalized flux. such that and fit a three parameter gaussian. «Lye to all emission lines.," We obtain a continuum-normalized flux, such that and fit a three parameter gaussian, $A_{N} e^{- \frac{(x-x_{N})^2}{2 \sigma_{N}}}$ to all emission lines."
 Ay. and oy are the eau. line center aud siena of the gaussian aud are used as initial estimates for fits to the local flux.," $A_{N}, x_{N}$ and $\sigma_{N}$ are the gain, line center and sigma of the gaussian and are used as initial estimates for fits to the local flux."
 In all our fits to the DEEP? cata. we derive the errors on our paraueters by propagating the measurement uucertaimties in the spectrun.," In all our fits to the DEEP2 data, we derive the errors on our parameters by propagating the measurement uncertainties in the spectrum."
 We define £60) as the local flux for each liue., We define $L(x)$ as the local flux for each line.
 £(c0)=FOr) in the range evMoy«orory|250y aud zero clsewhere., $L(x) = F(x)$ in the range $x_{N}-25 \sigma_{N} < x < x_{N}+25 \sigma_{N}$ and zero elsewhere.
"We perform a botnded value nou-Imear least scuare Gt to the local flux Lor) with a two component model roe). such that r(e)=ptc)gle) where is à linear fit that models the uuderlviug coutiuuuna auk is a eaussian that models the emission line. where e5..0,5 aud σι are defined as the ean. center aud sigma of the eaussian fit to Lor) respectively,","We perform a bounded value non-linear least square fit to the local flux $L(x)$ with a two component model $r(x)$ , such that $r(x) = p(x) + g(x)$ where is a linear fit that models the underlying continuum and is a gaussian that models the emission line, where $a_{L}, x_{oL}$ and $\sigma_{L}$ are defined as the gain, center and sigma of the gaussian fit to $L(x)$ respectively."
 We note that in the case of 11.0. due to possible uuderlviug stellaz absorption. we fit contiuuuu between L775 Ιδ15.11 aud. 1905 1915.4. It should be noted that σ in equation 1 does not have a," We note that in the case of $H\beta$ , due to possible underlying stellar absorption, we fit continuum between $4775-4815\AA$ and $4905 - 4945\AA$ It should be noted that $\sigma$ in equation \ref{eq:gauss} does not have a"
"9M. WC star, modelling the binary orbit and components simultaneously and considering the age of the best fitting initial secondary mass with and without enhanced mixing.","$9M_{\odot}$ WC star, modelling the binary orbit and components simultaneously and considering the age of the best fitting initial secondary mass with and without enhanced mixing."
 We find that the age must be older than 3.5 Myrs and by combining different ages we estimate that it is 5.5+1 Myrs., We find that the age must be older than 3.5 Myrs and by combining different ages we estimate that it is $5.5\pm1$ Myrs.
 The 2 Myrs difference is because Northetal.(2007) used single-star non-rotating isochrones to determine a lower limit for the secondary star age., The 2 Myrs difference is because \citet{north07} used single-star non-rotating isochrones to determine a lower limit for the secondary star age.
 T'his work demonstrates the necessity for publicly available grids of binary star models to be created., This work demonstrates the necessity for publicly available grids of binary star models to be created.
 The use of single-star models can give misleading results that lead to incorrect conclusions., The use of single-star models can give misleading results that lead to incorrect conclusions.
 Our age estimate is in better agreement with ages derived for the surrounding lower-mass stars from(2009)., Our age estimate is in better agreement with ages derived for the surrounding lower-mass stars from.
. It suggests that all the stars in the Vela OB2 association formed at a similar time., It suggests that all the stars in the Vela OB2 association formed at a similar time.
 The older age estimate may also help explain the non-detection of 1.8 MeV photon emission from 4? Velorum., The older age estimate may also help explain the non-detection of 1.8 MeV photon emission from $\gamma^2$ Velorum.
 This emission is due to the radioactive decay of ?? A1 formed during core hydrogen burning by proton capture on ??Mg., This emission is due to the radioactive decay of $^{26}$ Al formed during core hydrogen burning by proton capture on $^{25}$ Mg.
 ?6 Al has a half-life of 0.75 Myrs and ? Velorum is predicted by Mowlavi&Meynet(2006) to have detectable emission., $^{26}$ Al has a half-life of 0.75 Myrs and $\gamma^2$ Velorum is predicted by \citet{al26} to have detectable emission.
 Currently no such emission has been detected., Currently no such emission has been detected.
 We suggest there are two factors reducing the amount of ??Al below the detectable abundance., We suggest there are two factors reducing the amount of $^{26}Al$ below the detectable abundance.
 First in our models of 5? Velorum we find the time difference between the end of core hydrogen burning and our age estimate is 0.85 Myrs thus less than half of ?9ΑΙ created remains., First in our models of $\gamma^2$ Velorum we find the time difference between the end of core hydrogen burning and our age estimate is 0.85 Myrs thus less than half of $^{26}Al$ created remains.
 Second the lower initial mass of the WR star may mean less 7°Al is created during the main-sequence as predicted for the 60M star by Mowlavi&Meynet (2006)., Second the lower initial mass of the WR star may mean less $^{26}$ Al is created during the main-sequence as predicted for the $60M_{\odot}$ star by \citet{al26}.
. The fact that the binary is still eccentric does not rule out a binary mass-transfer event., The fact that the binary is still eccentric does not rule out a binary mass-transfer event.
 Our binary models indicate that some post main-sequence (Case B) mass-transfer events occur so rapidly that the tides formed in the mostly radiative envelope are unable to circularise the orbit., Our binary models indicate that some post main-sequence (Case B) mass-transfer events occur so rapidly that the tides formed in the mostly radiative envelope are unable to circularise the orbit.
" On the other hand, WR binaries with periods below 30 days experiences Case A mass-transfer on the main-sequence and the tides do have time to circularise the orbit."," On the other hand, WR binaries with periods below 30 days experiences Case A mass-transfer on the main-sequence and the tides do have time to circularise the orbit."
" This places a limit on the circularization timescale of tides in radiative envelopes to a few thousand years, the time required for the hydrogen envelope to be removed in a mass-transfer event."," This places a limit on the circularization timescale of tides in radiative envelopes to a few thousand years, the time required for the hydrogen envelope to be removed in a mass-transfer event."
 Our major remaining uncertainty is the evolution of the secondary., Our major remaining uncertainty is the evolution of the secondary.
 We find that it is possible to explain its current evolutionary state if initially it was a 31.5M star with a rotation rate of zz200kms!.," We find that it is possible to explain its current evolutionary state if initially it was a $31.5M_{\odot}$ star with a rotation rate of $\approx 200{\rm km \, s^{-1}}$."
 Less massive stars that accrete a large amount of mass never match the radius and luminosity of the secondary when the primary star is a WC star of 9Mo., Less massive stars that accrete a large amount of mass never match the radius and luminosity of the secondary when the primary star is a WC star of $9M_{\odot}$.
 Future study of this system may provide more clues to the effect of rotational mixing and of mass-transfer on the secondary stars in binary systems., Future study of this system may provide more clues to the effect of rotational mixing and of mass-transfer on the secondary stars in binary systems.
into ils eruption.,into its eruption.
 At a height of 4R... the LE showed an acceleration value of over 200ms>.," At a height of $4\Rsun$, the LE showed an acceleration value of over $200\mpss$."
 We have analvsed six CMESs from the coronagraphs CORI and COR2. and the associated EPs in three of the cases from EUVI on board the identical AA and D spacecraft.," We have analysed six CMEs from the coronagraphs COR1 and COR2, and the associated EPs in three of the cases from EUVI on board the identical A and B spacecraft."
 We identified and tracked a feature in the LE of all the CAIEs in both CORI and COLDB2. and in (he associated prominences. wherever applicable.," We identified and tracked a feature in the LE of all the CMEs in both COR1 and COR2, and in the associated prominences, wherever applicable."
 While most of the earlier studies on CME acceleration were carried oul using projected measurements. we have used a stereoscopic reconstruction technique (Joshi&Srivastava2011). to obtain the true coordinates. ancl hence the true speed and acceleration of the feature.," While most of the earlier studies on CME acceleration were carried out using projected measurements, we have used a stereoscopic reconstruction technique \citep{Joshi.Srivastava2011} to obtain the true coordinates, and hence the true speed and acceleration of the feature."
 On fitting a polvnomial ΠΟΙΟ to the true heieht. the speed and acceleration of the CAIEs as a function of time and true height were determined.," On fitting a polynomial function to the true height, the speed and acceleration of the CMEs as a function of time and true height were determined."
 The results of the kinematie study of EPs and the CME LEs are shown in Figures 7- 12.., The results of the kinematic study of EPs and the CME LEs are shown in Figures \ref{F:res16nov}- \ref{F:res01aug}.
 We summarise the results obtained from the reconstruction in Table 1.., We summarise the results obtained from the reconstruction in Table \ref{T:summa}.
 It is believed that most of the CME acceleration (vpically occurs in the lower corona., It is believed that most of the CME acceleration typically occurs in the lower corona.
 Chen&να(2003) have found the height of maximum acceleration of CME to be 2—3H. from a study of several CMS. Vrsnak(2001). have considered Chis height to be ΕΠ...," \citet{Chen.Krall2003} have found the height of maximum acceleration of CME to be $2-3\Rsun$ from a study of several CMEs, \citet{Vrsnak2001a} have considered this height to be $4\Rsun$."
 However. from our reconstructed results (Figures 7- 12)). we observe that in all the cases studied here. the peak of main phase of acceleration lies below the true height of 2Rh...," However, from our reconstructed results (Figures \ref{F:res16nov}- \ref{F:res01aug}) ), we observe that in all the cases studied here, the peak of main phase of acceleration lies below the true height of $2\Rsun$."
 This indicates (hat most of theCME cdiynamies occurs closer to the Sun than previously believed. as shown by Chenetal.(2006). [rom a comparison of observations ancl models.," This indicates that most of theCME dynamics occurs closer to the Sun than previously believed, as shown by \citet{Chen.etal2006} from a comparison of observations and models."
 Earlier studies (Zhaugetal.2001:Chen&Ixrall2003).. have observed. CATES in all the three SolIO/LASCO coronagraphs which together cover a range trom 1.1—32 R..," Earlier studies \citep{Zhang.etal2001,Chen.Krall2003}, have observed CMEs in all the three SoHO/LASCO coronagraphs which together cover a range from $1.1-32\Rsun$ ."
 In, In
departure from sinusoidalitv of its companion (confirming he reality of the harmonic) are shown in Fig. 19..,departure from sinusoidality of its companion (confirming the reality of the harmonic) are shown in Fig. \ref{avprof}.
 Clearly he 31.16 s signal is caused. by interaction with the ΟΡΟ signal — but is not due to amplitude modulation otherwise here would. be two sidebands of equal. amplitude., Clearly the 31.16 s signal is caused by interaction with the QPO signal – but is not due to amplitude modulation otherwise there would be two sidebands of equal amplitude.
 The elfect is similar to the orbital sideband in. intermeciate »olars (e.g. Warner 1986). where the lower frequency signal arises from reprocessing of a rotating beam (from the wimarv) periodically illuminating the secondary or bright spot region. which makes 7OQDPO sideband an appropriate description.," The effect is similar to the orbital sideband in intermediate polars (e.g. Warner 1986), where the lower frequency signal arises from reprocessing of a rotating beam (from the primary) periodically illuminating the secondary or bright spot region, which makes “QPO sideband” an appropriate description."
" In Paper HL we suggest that the QPO sideband arises [rom a progeracely rotating ""wall in the inner disc.", In Paper II we suggest that the QPO sideband arises from a progradely rotating `wall' in the inner disc.
 These signals are only clearly present in the first. part of the light curve., These signals are only clearly present in the first part of the light curve.
 From an ΟC analysis we find that at this time the DNOs show only relatively small jumps in period or phase. which is what allows the Fourier transform process to detect the signals easily.," From an O–C analysis we find that at this time the DNOs show only relatively small jumps in period or phase, which is what allows the Fourier transform process to detect the signals easily."
 It is possible that in the remainder of this run. and in other similar runs. the QPO sideband and/or its harmonic may be physically present. but do not stay still long enough to be captured by our analysis techniques.," It is possible that in the remainder of this run, and in other similar runs, the QPO sideband and/or its harmonic may be physically present, but do not stay still long enough to be captured by our analysis techniques."
 In the earlier studies by WB and. RW examples were eiven of the amplitudes of the DNOs being modulated. at the QPO period., In the earlier studies by WB and RW examples were given of the amplitudes of the DNOs being modulated at the QPO period.
 We have found several further examples of this. though it is rare to find both oscillations of sullicient," We have found several further examples of this, though it is rare to find both oscillations of sufficient"
energy of gas. we take into account the presence of a dark matter halo.,"energy of gas, we take into account the presence of a dark matter halo."
 The assumed prescriptions are the same as in our previous models (e.g. Pipino Matteucei 2004)., The assumed prescriptions are the same as in our previous models (e.g. Pipino Matteucci 2004).
 The yields used in this paper are as follows: We adopt the dust model of Caluraetal.(2008) —which uses the formalism developed by Dwek(1998)., The yields used in this paper are as follows: We adopt the  dust model of \cite{calura08dust}  which uses the formalism developed by \cite{dwek98}.
. Let us define Χο) as the abundance by massof the element / at the time t in the dust and since G(r) is the ISM fraction at the time r. the quantity Gus;=Xeus7GI) represents the normalized mass of the element / at the time fin the dust.,"  Let us define $X_{dust,i}(t)$ as the abundance by massof the element $i$ at the time $t$ in the dust and since $G(t)$ is the ISM fraction at the time $t$, the quantity $G_{dust,i}=X_{dust,i}\cdot G(t)$ represents the normalized mass of the element $i$ at the time $t$ in the dust."
 The time evolution of Cqs; 18 therefore computed as: where 4=8M..," The time evolution of $G_{dust,i}$ is therefore computed as: where $M_w=8M_{\odot}$."
 Here recall the general features of the model as well as the maur assumptions., Here recall the general features of the model as well as the main assumptions.
 Only the main refractory elements. C. O. Mg. Si. S. Ca. Fe. are depleted into dust. and we assume that stars car produce two different types of grains: 1) silicate dust. composed of O. Mg. Si. S. Ca and Fe. and 11) carbon dust. composed of C. As suggested by Dwek(1998).. we consider that the dust producers are low and intermediate mass stars. SNIa anc SNII.," Only the main refractory elements, C, O, Mg, Si, S, Ca, Fe, are depleted into dust, and we assume that stars can produce two different types of grains: i) silicate dust, composed of O, Mg, Si, S, Ca and Fe, and ii) carbon dust, composed of C.  As  suggested by \cite{dwek98}, we consider that the dust producers are  low and intermediate mass stars,  SNIa and  SNII."
" The condensation efficiencies o?M om and on, for low and intermediate mass stars. SNIa and SNIL. respectively. are as follows."," The condensation efficiencies $\delta_i^{SW}$, $\delta_i^{Ia}$ and $\delta_i^{II}$ for low and intermediate mass stars, SNIa and SNII, respectively, are as follows."
" with 52.""=1 for all the other elements.", with $\delta^{SW}_{C}=1$ for all the other elements.
 ∖∖⇁≣⋔⇂≀∣⋅⇂↴⊜⋯∶↔⊺⋔⊜∏⋯⋋⋋⋂↑↴⋔⊜∣⊖∣⊜⋯⊜∏⊓∏⋅≏↧↾∪⋯≣∁∏⋯⋋⋋," with $\delta^{SW}_{i}=1$ for Mg, Si,S, Ca, Fe and"
where we used ,where we used ) = 1.
"Tere we introduced the scaled mass function of dar matter halos. that is. we write the halo mass fuuction as (-Q M). where dy, is the linear deusitv threshold that defines these halos. given by Eq.(1)) aud e(M)=6,4."," Here we introduced the scaled mass function of dark matter halos, that is, we write the halo mass function as n(M) M = ) , where $\deltaLs$ is the linear density threshold that defines these halos, given by \ref{qr-F}) ), and $\sigma(M)=\sigma_q$."
 The well-kuow constraints (299) aud (27)) follow from the requirement that all he mass is accounted for bv the mass function of halos Gvhateverthe choice of δρ... which leads to Eq.(29)). so that the density field ou large scales (bevoud the size of these halos} can he written iun terius ofthe halo mass fuucion. ax in the usual halo model (?) (the so-called “two-halo tern”).," The well-know constraints \ref{fnu-norm}) ) and \ref{b-fnu}) ) follow from the requirement that all the mass is accounted for by the mass function of halos (whateverthe choice of $\deltaLs$ ), which leads to \ref{fnu-norm}) ), so that the density field on large scales (beyond the size of these halos) can be written in terms of the halo mass function, as in the usual halo model \citep{Cooray2002} (the so-called “two-halo term”)."
 Then. requiring that oue recovers the dark matter two-point correlation function leads to the coustraimt (27]). provided the bias can be factorized as (25)) (otherwise the coustraint involves a bidiimieusionalES. integral. over 5b(Mq.P M»o]).," Then, requiring that one recovers the dark matter two-point correlation function leads to the constraint \ref{b-fnu}) ), provided the bias can be factorized as \ref{b-fact}) ) (otherwise the constraint involves a bidimensional integral over $b^2(M_1,M_2)$ )."
 We do not claim here that the halo bias has a nonzero asvinptote at low mass., We do not claim here that the halo bias has a nonzero asymptote at low mass.
 Iu fact. the asvuptotic behavior of the low-mass ail of the bias (and of the mass function itself) is largely unknown. but umnerical simulations show hat the depeudeuce ou dass flattens below vo~ and seenis roughly constant down to vi~ 0.3.," In fact, the asymptotic behavior of the low-mass tail of the bias (and of the mass function itself) is largely unknown, but numerical simulations show that the dependence on mass flattens below $\nu \sim 1$ and seems roughly constant down to $\nu \sim 0.3$ ."
 Then. he prescription (26)) is intended to describe both this ychavior (since frou expression (21)) we can sec tha b.(AL)>0 for AL»0. or more preciscly when Ty> x) and the constraint (27)).," Then, the prescription \ref{bM-def}) ) is intended to describe both this behavior (since from expression \ref{b2-def}) ) we can see that $b_{\rm r.e.}(M) \rightarrow 0$ for $M\rightarrow 0$, or more precisely when $\sigma_q \rightarrow \infty$ ) and the constraint \ref{b-fnu}) )."
 Indeed. if the asvuptotic wchavior (2 )) provides a good description for r we can expect the coustraint (27)) to provide a good estimate for the (almost constant) value of ΟΛΠ) in the reenner«ol.," Indeed, if the asymptotic behavior \ref{b2-def}) ) provides a good description for $\nu > 1$ we can expect the constraint \ref{b-fnu}) ) to provide a good estimate for the (almost constant) value of $b(M)$ in the regime$\nu < 1$."
 Moreover. it is always useful to nake sure normalizatiou constraints such as (27)) are satisfied by the models.," Moreover, it is always useful to make sure normalization constraints such as \ref{b-fnu}) ) are satisfied by the models."
 DIudeed. this eusures that the models are selfconsistent aud that absurd results will not be produced by the violation of basic internal constraints.," Indeed, this ensures that the models are self-consistent and that absurd results will not be produced by the violation of basic internal constraints."
 Another advantage of this simple prescription is that our model (26)) of the halo bias has specitic free parameter. apart from those already contained in the halo nias function (especially its low-mass tail).," Another advantage of this simple prescription is that our model \ref{bM-def}) ) of the halo bias has specific free parameter, apart from those already contained in the halo mass function (especially its low-mass tail)."
 This is whi we prefer to keep a simple constant στι by. instead of introducing for instance higher-order polvuomials (over v or M) that would require some fitting over nunerical siuulations.," This is why we prefer to keep a simple constant term $b_0$, instead of introducing for instance higher-order polynomials (over $\nu$ or $M$ ) that would require some fitting over numerical simulations."
 This provides a ereater flexibility to the model which can be used for a variety of cosinologies.," This provides a greater flexibility to the model, which can be used for a variety of cosmologies."
 Finally. for ummerical computations we use the mass dpa σαι iu 7. 0.502 Το... which has Όσοι shown to agree with nunerica siniulations (for halos defined by Ó=200).," Finally, for numerical computations we use the mass function given in \citet{Valageas2009d}, ) = 0.502 + (0.62 ], which has been shown to agree with numerical simulations (for halos defined by $\deltas=200$ )."
" The oncntial falloff. ο7/2, where v is defined by Eqs.(30)) and (1)) is consistent with the exponential term of Eq.(5))."," The exponential falloff, $e^{-\nu^2/2}$, where $\nu$ is defined by \ref{fnu-def}) ) and \ref{qr-F}) ), is consistent with the exponential term of \ref{xiL-s}) )."
" Indeed. both the l-poiut distribution (io. the uass function) aud the 2-poiut distribution (1.6. the halo correlation or bias) are obtained in the arge-niass iui] youn spherical overdcusitics 07. in the linear deusity field. with àp.=FH6.) and 6,=200."," Indeed, both the 1-point distribution (i.e. the mass function) and the 2-point distribution (i.e. the halo correlation or bias) are obtained in the large-mass limit from spherical overdensities $\deltaLs$ in the linear density field, with $\deltaLs=\cF^{-1}(\deltas)$ and $\deltas=200$."
 Note also that the rorlnalization of the mass function (31)) is not a free λαοΤο since it is set by the coustraimt (29))., Note also that the normalization of the mass function \ref{fnu-fit}) ) is not a free parameter since it is set by the constraint \ref{fnu-norm}) ).
 This is why we prefer touse the mass function (31)). so that the uodel is fully selt£-cousisteut aux large-nass tails do not involve free parameters.," This is why we prefer touse the mass function \ref{fnu-fit}) ), so that the model is fully self-consistent and large-mass tails do not involve free parameters."
 Tn particular. following ?.. applying the pealk-vackeround split argument to Eq.(31)) gives b~ὃνa. in the rare-event and laree-distance Bhits.," In particular, following \citet{Cole1989}, , applying the peak-background split argument to \ref{fnu-fit}) ) gives $b \sim \deltaLs/\sigma_q^2$, in the rare-event and large-distance limits."
" This agrees with the asvinptotic behavior of Eq.(21)). except that Eq.(21)) also vields the svefactor o,46s)συοί). which is different from unity."," This agrees with the asymptotic behavior of \ref{b2-def}) ), except that \ref{b2-def}) ) also yields the prefactor $\sigma_{q,q}(s)/\sigma_{0,0}(x)$, which is different from unity."
 This expresses the facts that 1) contributions to the correlation of objects of size q are damped for high waveumnubers &>Liq. and dj halo notions are nonzero al correlated. sxut.," This expresses the facts that i) contributions to the correlation of objects of size $q$ are damped for high wavenumbers, $k \gg 1/q$, and ii) halo motions are nonzero and correlated, $s\neq x$."
 Of course. these two effects are neglected by the peak-backeround split arguineut.," Of course, these two effects are neglected by the peak-background split argument."
 We now compare the model defined by Eqxs.(22)). (21)). (26)). and (28)). with results from uuuenrcal sinulatious.," We now compare the model defined by \ref{s-x-M}) ), \ref{b2-def}) ), \ref{bM-def}) ), and \ref{b0-def}) ), with results from numerical simulations."
 We first consider in Fie., We first consider in Fig.
 1 the depeudeuce on halo nass AL of the large-scale bias. for halos defined. by the noulinear density contrast ὃ-=200 (whence dp.& 1.59) at distance «2505. ΙΕ," \ref{figbiasM_D200} the dependence on halo mass $M$ of the large-scale bias, for halos defined by the nonlinear density contrast $\deltas=200$ (whence $\deltaLs\simeq 1.59$ ) at distance $x=50 h^{-1}$ Mpc."
 We show our results at redshifts 2=0.1.25. and 2.5.," We show our results at redshifts $z=0, 1.25$, and $2.5$."
 We can see that we obtain a goodl agreement with the uunerical simmlations of ?.., We can see that we obtain a good agreement with the numerical simulations of \citet{Tinker2010}.
 This was expected at high masses. where the aremucuts based on he clustering of rare overdeusities iu the lear Cassia density Seld apply (as introduced by? aud implemented iu a sliehtly modified variant here).," This was expected at high masses, where the arguments based on the clustering of rare overdensities in the linear Gaussian density field apply (as introduced by \citet{Kaiser1984} and implemented in a slightly modified variant here)."
 Au improvement over xevious models of this kind (27). is the good agrecimeut at low mass. which is obtained through the constant term dyiu Eq.(26)). associated with the normalization of the wo bias through Eq.(28)).," An improvement over previous models of this kind \citep{Kaiser1984,Valageas2009d} is the good agreement at low mass, which is obtained through the constant term $b_0$in \ref{bM-def}) ), associated with the normalization of the halo bias through \ref{b0-def}) )."
 Thus. it appears that this constraint is sufficientto obtain a good description of he halo bias over the whole rauge e(M)< 10.," Thus, it appears that this constraint is sufficientto obtain a good description of the halo bias over the whole range $\sigma(M)<10$ ."
 Indeed. as explained iuSect. 2.3.. ," Indeed, as explained inSect. \ref{Normalization}, ,"
since the model is reasonably Successful at large mass. 0< 1l. the iutegral coustraiut (27)) euxures that the value of the bias over the range 1< 10. which contaims the other half of the total matter," since the model is reasonably successful at large mass, $\sigma<1$ , the integral constraint \ref{b-fnu}) ) ensures that the value of the bias over the range $1<\sigma<10$ , which contains the other half of the total matter"
We used XSPEC v.11.3 (Arnaud 1996) for all of the spectral analysis reported in this work.,We used XSPEC v.11.3 (Arnaud 1996) for all of the spectral analysis reported in this work.
" All errors stated were found using the ""error"" and ""steppar commands in XSPEC. and correspond to the lo level of confidence."," All errors stated were found using the “error” and “steppar” commands in XSPEC, and correspond to the $\sigma$ level of confidence."
 The energy of all spectral lines 1s reported in the source frame. unless otherwise noted.," The energy of all spectral lines is reported in the source frame, unless otherwise noted."
 All of the spectral models described below were modified by an interstellar absorption column density set to 3«10em- (Dickey Lockman 1990) via the “phabs” model., All of the spectral models described below were modified by an interstellar absorption column density set to $3\times 10^{20}~{\rm cm}^{-2}$ (Dickey Lockman 1990) via the “phabs” model.
 In all fits. we tied the parameters for all four cameras together but allowed a constant factor to float between the HXD and XIS detectors to account for absolute flux offsets.," In all fits, we tied the parameters for all four cameras together but allowed a constant factor to float between the HXD and XIS detectors to account for absolute flux offsets."
 Our fit model (see below) gives a value of 1.16 for the normalizing constant. consistent with current calibrations (see. e.g.. Memo 2008-06).," Our best-fit model (see below) gives a value of 1.16 for the normalizing constant, consistent with current calibrations (see, e.g., Memo 2008-06)."
 We first fit the data with a power-law between 2-3 keV and 7-10 keV. The data/model ratio resulting from this initial fit is shown in Figure |., We first fit the data with a power-law between 2–3 keV and 7–10 keV. The data/model ratio resulting from this initial fit is shown in Figure 1.
 This exercise revealed several characteristic spectral features., This exercise revealed several characteristic spectral features.
 Below 2 keV. there is a soft flux excess that has sometimes been modeled using a KT20.2 keV blackbody or disk blackbody.," Below 2 keV, there is a soft flux excess that has sometimes been modeled using a $=0.2$ keV blackbody or disk blackbody."
 Where required. we fit this component with a disk blackbody in the models described below. but we caution that this is a fiducial model to account for the flux. not strong evidence of such a hot disk (see Crummy et 22006 for a more physical treatment of the soft excess).," Where required, we fit this component with a disk blackbody in the models described below, but we caution that this is a fiducial model to account for the flux, not strong evidence of such a hot disk (see Crummy et 2006 for a more physical treatment of the soft excess)."
 Above 9 keV. there is à Weak excess above the power-law. particularly in the HXD data.," Above 9 keV, there is a weak excess above the power-law, particularly in the HXD data."
 This excess is consistent with à Compton-backscattering hump due to disk reflection of the incident hard X-ray flux., This excess is consistent with a Compton-backscattering hump due to disk reflection of the incident hard X-ray flux.
 The putative hard flux excess is consistent with the presence of Fe K emission lines. which also arise through reflection.," The putative hard flux excess is consistent with the presence of Fe K emission lines, which also arise through reflection."
 The most prominent emission line is narrow and has a measured energy of 6.10 keV. or 6.40 keV in the frame of Fairall 9.," The most prominent emission line is narrow and has a measured energy of 6.10 keV, or 6.40 keV in the frame of Fairall 9."
 Narrow Fe Ko lines are common in the X-ray spectra of AGN. and may result from illumination of the “torus” (Nandra 2006).," Narrow Fe $\alpha$ lines are common in the X-ray spectra of AGN, and may result from illumination of the “torus” (Nandra 2006)."
 In all models discussed below. we fit this line with a simple Gaussian function of zero width. since the line is not resolved.," In all models discussed below, we fit this line with a simple Gaussian function of zero width, since the line is not resolved."
 For consistency. we also fit an Fe line at the proper energy. and with its flux constrained to be 0.16 times that of the Ka line (Molendi. Bianchi. Matt 2003).," For consistency, we also fit an Fe $\beta$ line at the proper energy, and with its flux constrained to be 0.16 times that of the $\alpha$ line (Molendi, Bianchi, Matt 2003)."
 After these narrow lines are fit. a broad asymmetric line ts revealed. consistent with reflection from the inner accretion disk (see Figure 3).," After these narrow lines are fit, a broad asymmetric line is revealed, consistent with reflection from the inner accretion disk (see Figure 3)."
 As simple models are easily reproducible. we adopted a simple disk blackbody plus power-law model in order to measure a flux.," As simple models are easily reproducible, we adopted a simple disk blackbody plus power-law model in order to measure a flux."
 We measure a 0.5-10.0 keV flux of 107!ergem s. and a 0.5-30.0 keV flux of 5.9(2)<107!ereem s.," We measure a 0.5–10.0 keV flux of $4.0(1) \times 10^{-11}~ {\rm erg}~{\rm
cm}^{-2}~{\rm s}^{-1}$ , and a 0.5–30.0 keV flux of $5.9(2) \times
10^{-11}~ {\rm erg}~{\rm cm}^{-2}~{\rm s}^{-1}$ ."
 The latter flux corresponds to an X- luminosity of 2.6(1)«107ergs7'.," The latter flux corresponds to an X-ray luminosity of $2.6(1)\times 10^{44}~ {\rm
erg}~{\rm s}^{-1}$."
 With the bolometric correction found by Marconi Hunt (2003). this corresponds to an Eddington fraction of approximately 0.13.," With the bolometric correction found by Marconi Hunt (2003), this corresponds to an Eddington fraction of approximately 0.13."
 With evidence for disk reflection both in the Fe K band and in hard X-rays. we proceeded to fit the spectrum with common reflection models.," With evidence for disk reflection both in the Fe K band and in hard X-rays, we proceeded to fit the spectrum with common reflection models."
 The reflection models were convolved with à relativistic line function to account for the relativistic Doppler and gravitational red-shifts expected near to the black hole (Brenneman Reynolds 2006)., The reflection models were convolved with a relativistic line function to account for the relativistic Doppler and gravitational red-shifts expected near to the black hole (Brenneman Reynolds 2006).
 With the assumption that the accretion disk is truncated at the ISCO (consistent with the high Eddington fraction of Fatrall 9: also see Miller et 22006). the degree to which the line and reflection spectrum are skewed can be used to constrain the spin of the black hole in Fairall 9.," With the assumption that the accretion disk is truncated at the ISCO (consistent with the high Eddington fraction of Fairall 9; also see Miller et 2006), the degree to which the line and reflection spectrum are skewed can be used to constrain the spin of the black hole in Fairall 9."
 These fits are discussed in detail in the following section., These fits are discussed in detail in the following section.
 The “pexrav” model describes the reflection of αἱ exponentially cut-off power-law spectrum from a neutral disk (Magdziarz Zdziarski 1995)., The “pexrav” model describes the reflection of an exponentially cut-off power-law spectrum from a neutral disk (Magdziarz Zdziarski 1995).
" As noted above. we blurrec this spectrum using the ""kerrconv"" model."," As noted above, we blurred this spectrum using the “kerrconv” model."
" Pexrav does not include an emission line. so our spectral model also includec the ""kerrdisk"" line model."," Pexrav does not include an emission line, so our spectral model also included the “kerrdisk” line model."
 Parameters common to the line anc convolution blurring function were linked for self-consistency., Parameters common to the line and convolution blurring function were linked for self-consistency.
 A fiducial disk blackbody component (“diskbb”) was includec in the model to account for the soft excess seen in Figure |., A fiducial disk blackbody component (“diskbb”) was included in the model to account for the soft excess seen in Figure 1.
 Pexrav requires the metal abundance in solar units anc the iron abundance relative to. the metal abundance. as fit parameters.," Pexrav requires the metal abundance in solar units and the iron abundance relative to the metal abundance, as fit parameters."
 In the absence of observational constraints on elemental abundances in Fairall 9. we fixed the metal abundance to 1.0 and ran the fit three separate times with an tron abundance of 0.5. 1.0. and 2.0 which gave 4 values of 6575.3. 6553.7. 6626.3 (respectively) for 5970 degrees of freedom.," In the absence of observational constraints on elemental abundances in Fairall 9, we fixed the metal abundance to 1.0 and ran the fit three separate times with an iron abundance of 0.5, 1.0, and 2.0 which gave $\chi^2$ values of 6575.3, 6553.7, 6626.3 (respectively) for 5970 degrees of freedom."
Y.-F.J thanks Chien Peng for help in using GALFIT and Miujiu Wim for helpful discussions on fitting the inages.,Y.-F.J thanks Chien Peng for help in using GALFIT and Minjin Kim for helpful discussions on fitting the images.
 We also thank the anonvaiuous referee for valuable conuunents to improve the iuanuscript., We also thank the anonymous referee for valuable comments to improve the manuscript.
 This work was supported bv the Carnegie Institution for Scieuce aud by NASA eraut HST-GO-11130.00. from the Space Telescope Scieuce Tustitute. which is operated by AURA. Iuc.. under NASA contract NÀAS5-26555.," This work was supported by the Carnegie Institution for Science and by NASA grant HST-GO-11130.01 from the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS5-26555."
While the analviic estimates allow us to wnelerstand the scaling of the power- thev are not appropriate for describing (he inverse Compton component ancl internal 5-rav absorption processes as (hese (wo depend on the details of the svnchrotron photon enerev specirum.,"While the analytic estimates allow us to understand the scaling of the power-requirements, they are not appropriate for describing the inverse Compton component and internal $\gamma$ -ray absorption processes as these two depend on the details of the synchrotron photon energy spectrum."
 The following numerical estimates use electron energv spectra dN/ds iusteacd of a mono-energelic electron. distribution., The following numerical estimates use electron energy spectra $dN_{\rm e}/d\gamma$ instead of a mono-energetic electron distribution.
 We use energv spectra that resemble broken power laws over small dvnamic ranges with a ratio of the maximum io minimum Lorentz [actor of 100., We use energy spectra that resemble broken power laws over small dynamic ranges with a ratio of the maximum to minimum Lorentz factor of $\sim100$.
 The svnchrotron power emitted by the leptons at frequency v per frequency interval div is computed using the standard equation 1979): where the first integral runs over the electron Lorentz [actors and the second averages over (he pitch angle distribution., The synchrotron power emitted by the leptons at frequency $\nu$ per frequency interval $\nu$ is computed using the standard equation \citep{Rybicki1986}: where the first integral runs over the electron Lorentz factors and the second averages over the pitch angle distribution.
 Here and in (he following we use the constant ο= to normalize the integrals over the pitch angle distribution.," Here and in the following we use the constant $c_1\,\equiv$ $(1-\cos{\theta_{\rm max}})^{-1}$ to normalize the integrals over the pitch angle distribution."
 The function Fr) equals rfUxW2(€)Mead£- with. WF-5 the modifiedlp Bessel function. of: 5/2. order. and rv= v/5.," The function $F(x)$ equals $x\int_x^{\infty}~K\frac{5}{2}(\xi)~d\xi$ with $K\frac{5}{2}$ the modified Bessel function of $5/2$ order, and $x\,=$ $\nu\,/\,\nu_{\rm c}$."
 The emitted inverse Compton power is approximately given bv Ilere we use θα. θµ in rough approximation.," The emitted inverse Compton power is approximately given by Here we use $\theta'_{\rm max}\,=\,\theta_{\rm max}$ in rough approximation."
 The last term in the integrand is the enerev (hat a photon eains in a scattering., The last term in the integrand is the energy that a photon gains in a scattering.
 The other terms give the scattering rate that depends on the angle between the electron and photon velocity vectors and on (he density of svuchrotvon photons Πε., The other terms give the scattering rate that depends on the angle between the electron and photon velocity vectors and on the density of synchrotron photons $n_{\rm s}$.
 The Ixlein-Nishina cross section is {ο good approximation where op is the Thomson cross section., The Klein-Nishina cross section is to good approximation where $\sigma_{\rm T}$ is the Thomson cross section.
 The value y is the photon energy in the electron rest [raane in units of the electron rest mass Following Dermer&Schlickeiser (1993).. we use the approximation," The value $y$ is the photon energy in the electron rest frame in units of the electron rest mass Following \citet{Dermer1993}, , we use the approximation"
name. SWP image number of the specific observation. date. and exposure leneth.,"name, SWP image number of the specific observation, date, and exposure length."
 All were obtained through the large aperture ofZUE with the exception of SWP21720 as indicated in the table., All were obtained through the large aperture of with the exception of SWP21720 as indicated in the table.
 We pursued three avenues in modeling the observations with synthetic spectra: an accretion disk model alone. a single white dwarf photosphere. or a combination of the two.," We pursued three avenues in modeling the observations with synthetic spectra: an accretion disk model alone, a single white dwarf photosphere, or a combination of the two."
 For the accretion disks. we adopted models from. Wade παρουν (1998).," For the accretion disks, we adopted models from Wade Hubeny (1998)."
 UsingIUEFIT. a A7 minimization routine. the model disk was scaled and fit to the spectrum.," Using, a $\chi^{2}$ minimization routine, the model disk was scaled and fit to the spectrum."
" The fitting scale factor can then be shown to be related to the white ανα distance in pc though d=100/""VIE where Sis (he scale [actor given by theZUEPFIT routine.d is the svslenm distance in pc. and the factor of LOO arises from the fact that the theoretical disk [Iuxes are normalized (o a distance of 100 pc."," The fitting scale factor can then be shown to be related to the white dwarf distance in pc though $d=100/\sqrt{(S)}$ where is the scale factor given by the routine, is the system distance in pc, and the factor of 100 arises from the fact that the theoretical disk fluxes are normalized to a distance of 100 pc."
 Using this approach we have (wo parameters in determining the goodness of a fit: a minimum X? and a scale-[actor distance to compare with the parallax distance., Using this approach we have two parameters in determining the goodness of a fit: a minimum $\chi^{2}$ and a scale-factor distance to compare with the parallax distance.
 For single photospheres. we used the codesZLUSTY (IIubenyv 1983) in conjunction wilhNSPEC withROTTING (IIubenyv Lanz 1995) to generate svnthetic photosphere spectra convolved with theZUE instrumental profile.," For single photospheres, we used the codes (Hubeny 1988) in conjunction with with (Hubeny Lanz 1995) to generate synthetic photosphere spectra convolved with the instrumental profile."
 We generated a new grid of solar abundance models. covering a range of temperatures from 15.000 - 50.000 Ix in increments of 1000 Ix with log(g) ranging Irom 7.0 to 8.6 in increments of 0.2.," We generated a new grid of solar abundance models, covering a range of temperatures from 15,000 - 50,000 K in increments of 1000 K with $\log(g)$ ranging from 7.0 to 8.6 in increments of 0.2."
 This erid of models was then applied to the observations usingZUEFTIT., This grid of models was then applied to the observations using.
 The scale [actor5 for the photosphere fits is related (ο the radius of the white dwarf given by Rig=(i)VIEDIS. where i. is the radius of the Sun (6.96xLOM em).d is the known svstem distance in pe. and the factor of 1000 arises from the fact that the theoretical photosphere [Iuxes are normalized to a," The scale factor for the photosphere fits is related to the radius of the white dwarf given by $R_{wd}=(\frac{d}{1000})\sqrt{(S)}R_{\sun}$, where $R_{\sun}$ is the radius of the Sun $6.96\times 10^{10}$ cm), is the known system distance in pc, and the factor of 1000 arises from the fact that the theoretical photosphere fluxes are normalized to a"
the power asvuuuetry extends to much smaller scales than previously thought. aud by Eriksenetal.(2007)).. who quantified the large-scale power asvuuuetry in the 3-vear WAIAP data using an optimal Bayesian framework.,"the power asymmetry extends to much smaller scales than previously thought, and by \citet{eriksen:2007b}, who quantified the large-scale power asymmetry in the 3-year WMAP data using an optimal Bayesian framework."
 A separate. but possibly plysically related. Hine of work was recently presented by Crocnchoom&ILxik-sen(2009).. who considered the specific model for violation of Lorenz invariance in the carly universe. proposed by Ackermanetal.(2007).," A separate, but possibly physically related, line of work was recently presented by \citet{groeneboom:2009}, who considered the specific model for violation of Lorenz invariance in the early universe, proposed by \citet{ackerman:2007}."
. This model involves CXMB correlations with a quadrupolar distribution on the ska. aud is thus orthogonal to the current dipolar model.," This model involves CMB correlations with a quadrupolar distribution on the sky, and is thus orthogonal to the current dipolar model."
 Surprisingly. when analyzing the S-vear WALAP data. Croenebooni&Eviksen(2009) found supportive evidence for this model at the 3.80 significance level. when cousidering augular scales up to (x00.," Surprisingly, when analyzing the 5-year WMAP data, \citet{groeneboom:2009} found supportive evidence for this model at the $3.8\sigma$ significance level, when considering angular scales up to $\ell \le 400$."
 Thus. asstunine that the WALAP observations are free of unknown systematics. there appears to be increasing evidence for both dipolar and quadrupolar structure iu the CMD power distribution. at all augular scales.," Thus, assuming that the WMAP observations are free of unknown systematics, there appears to be increasing evidence for both dipolar and quadrupolar structure in the CMB power distribution, at all angular scales."
 Iu this paper. we repeat the Bavesian analysis of Eriksenctal.(2007)).. but double the angulaxy resolution of the data.," In this paper, we repeat the Bayesian analysis of \citet{eriksen:2007b}, but double the angular resolution of the data."
 Nevertheless. we are still limited to relatively low aneulay resolutions. since the method inhereutly relies on brute-force evaluation of a pixelbased likelihood. aud therefore scales as OLN?ux)," Nevertheless, we are still limited to relatively low angular resolutions, since the method inherently relies on brute-force evaluation of a pixel-based likelihood, and therefore scales as $\mathcal{O}(N_{\textrm{pix}}^3)$."
" Yet. simply by speucding more computer resources we are able to increase the pixel resolution from ας=16 to 32 and decrease the degradation sinoothing scale from 9"" to 1.57 FWIIN"," Yet, simply by spending more computer resources we are able to increase the pixel resolution from $N_{\textrm{side}}=16$ to 32 and decrease the degradation smoothing scale from $9^{\circ}$ to $4.5^{\circ}$ FWHM."
L This provides additional support for multipoles between (&[0 and SO., This provides additional support for multipoles between $\ell \approx 40$ and 80.
 While not sufficicut to provide a full ancl direct comparison with the results of Tausenetal. (2008).. it is a significant improvement over the results presented by Eriksenetal.(2007)).," While not sufficient to provide a full and direct comparison with the results of \citet{hansen:2008}, it is a significant improvement over the results presented by \citet{eriksen:2007b}."
. The Bayesian analysis framework used iu this paper are very simular to that enmploved by Exikseuoetal. (2007b)., The Bayesian analysis framework used in this paper are very similar to that employed by \citet{eriksen:2007b}.
. We therefore ouly give a brief overview of its main features here. aud refer the reader interested in the full details to the original paper aud refereuces therein.," We therefore only give a brief overview of its main features here, and refer the reader interested in the full details to the original paper and references therein."
 The starting point for our analysis is the phenomenological CAIB signal ος. first proposed by Cordonetal.(2005).. Tere dto) denotes the observed data in direction n». 5η}. is an intrinsicallv isotropic aud Coussian random field with power spectrum Cy). fla) is an auxiliary modulating field. aud n(») denotes instrumental noise.," The starting point for our analysis is the phenomenological CMB signal model first proposed by \citet{gordon:2005}, Here $\mathbf{d}(\hat{n})$ denotes the observed data in direction $\hat{n}$, $\mathbf{s}(\hat{n})$ is an intrinsically isotropic and Gaussian random field with power spectrum $C_{\ell}$, $f(\hat{n})$ is an auxiliary modulating field, and $\mathbf{n}(\hat{n})$ denotes instrumental noise."
 Obvioush. if f=0. one recovers the standard isotropic model.," Obviously, if $f = 0$, one recovers the standard isotropic model."
 Iowever. we are interested m a possible hemispherical asvuuuetry. and we therefore paraietrize the modulation field in terms of a dipole with a free amplitude A and a preferred direction p. The modulated. signal compoucut is thus an anisotropic. but still Caussian. random field. with covariance niatrix where We now introduce oue new feature compared to the analysis of Eviksenetal.(2007b).. for two reasons.," However, we are interested in a possible hemispherical asymmetry, and we therefore parametrize the modulation field in terms of a dipole with a free amplitude $A$ and a preferred direction $\hat{p}$, The modulated signal component is thus an anisotropic, but still Gaussian, random field, with covariance matrix where We now introduce one new feature compared to the analysis of \citet{eriksen:2007b}, for two reasons."
 First. we are interested iu studvius the behaviour of he modulation field as a function of (range. aud herefore want a imechanig to restrict the impact of he modulation parameters m harmonie space.," First, we are interested in studying the behaviour of the modulation field as a function of $\ell$ -range, and therefore want a mechanism to restrict the impact of the modulation parameters in harmonic space."
" Secoud. we also want to minumuze the iupact of the arbitrary reeularization noise (sce Section 3)) on the modulation xuwaneters at hieh Cs. Therefore. we split the signal covariance matrix uto two parts. one modulated low-f wt aud one isotropic high-f part. where only unultipoles between 2zi(«μμ are included in S,,,,:. and ouly imultipoles at (2fod are iucluded in Si... ("," Second, we also want to minimize the impact of the arbitrary regularization noise (see Section \ref{sec:data}) ) on the modulation parameters at high $\ell$ 's. Therefore, we split the signal covariance matrix into two parts, one modulated $\ell$ part and one isotropic $\ell$ part, where only multipoles between $2\le \ell < \ell_{\textrm{mod}}$ are included in $\mathbf{S}_{\textrm{mod}}$, and only multipoles at $\ell
\ge \ell_{\textrm{mod}}$ are included in $\mathbf{S}_{\textrm{iso}}$. ("
Note that we are uot proposing a physical mechanisin for generating the modulation field in this paper. but only attempt to characterize its properties.,"Note that we are not proposing a physical mechanism for generating the modulation field in this paper, but only attempt to characterize its properties."
 This split may or may uot be plysically wellanotivated. but it does serve a useful purpose in the present paper as it allows us to study the scale dependence of the inodulation field in a controlled lusnuer.)," This split may or may not be physically well-motivated, but it does serve a useful purpose in the present paper as it allows us to study the scale dependence of the modulation field in a controlled manner.)"
 Iucludius iustrumieutal noise and possible foreground contamination. the full data covariance matrix reacρα The noise aud foreground covariance matrices depend ou the dataprocessing. aud will be described in ereater detail in &3..," Including instrumental noise and possible foreground contamination, the full data covariance matrix reads The noise and foreground covariance matrices depend on the dataprocessing, and will be described in greater detail in \ref{sec:data}."
 We also have to paraimetrize the power spectimi for the underlying isotropic component. Cy.," We also have to parametrize the power spectrum for the underlying isotropic component, $C_{\ell}$."
 Following Eriksenctal.(2007)... we choose a simple two-paramctcr model with a free amplitude q aud tilt » for this purpose. Tere (y is a pivot iiultipole aud οσα isa fiducial model. in the following chosen to be the best-fit ACTDAL power law spectra of Komatsuetal.(2009).," Following \citet{eriksen:2007b}, we choose a simple two-parameter model with a free amplitude $q$ and tilt $n$ for this purpose, Here $\ell_0$ is a pivot multipole and $C_{\ell}^{\textrm{fid}}$ is a fiducial model, in the following chosen to be the best-fit $\Lambda$ CDM power law spectrum of \citet{komatsu:2009}."
. Since both the signal and noise are assumed to be Gaussian. the loe-likchhood now reads up to an relevant coustaut. with C=CGl.p.q.n).," Since both the signal and noise are assumed to be Gaussian, the log-likelihood now reads up to an irrelevant constant, with $\mathbf{C}=\mathbf{C}(A, \hat{p},
q, n)$."
" The posterior distribution for our model is eiven by Bayes’ theorem. Πωο Piq.n.A.ΠΠ is a prior. and P(d|H) is a normalization| factor often called the ""Davesiau evidence”."," The posterior distribution for our model is given by Bayes' theorem, Here $P(q, n, A, \hat{p}|H)$ is a prior, and $P(\mathbf{d|H})$ is a normalization factor often called the “Bayesian evidence”."
" Note that we now have included. au explicit reference to the hypothesis (or model). 11. in all factors. as we will iu the following compare two different hypotheses, namely ""ITE: The universe is isotropic C1 0) versus ""II2: The universe is anisotropic CAz 0)"," Note that we now have included an explicit reference to the hypothesis (or model), $H$ , in all factors, as we will in the following compare two different hypotheses, namely “H1: The universe is isotropic $A=0$ )” versus “H2: The universe is anisotropic $A\ne0$ )”."
diagram.,diagram.
" The representing object types in the regions are; A: Red carbon stars, B: OH/IR stars and some YSOs, C: M-type giants, supergiants and S-type stars, as well as bluer carbon stars in blue part, and PMS stars in red part, D: Be stars, M- giants, and S-type stars, E: PMS stars, PNe, and PAGB stars, F: PNe and PAGB stars."," The representing object types in the regions are; A: Red carbon stars, B: OH/IR stars and some YSOs, C: M-type giants, supergiants and S-type stars, as well as bluer carbon stars in blue part, and PMS stars in red part, D: Be stars, M-type giants, and S-type stars, E: PMS stars, PNe, and PAGB stars, F: PNe and PAGB stars."
" Objects in regions A and B are most likely to be carbon stars and OH/IR stars, respectively, while PNe, post-AGB stars and YSOs tend to spread over the diagram, and it is difficult to identify these types of stars only with these infrared colors."," Objects in regions A and B are most likely to be carbon stars and OH/IR stars, respectively, while PNe, post-AGB stars and YSOs tend to spread over the diagram, and it is difficult to identify these types of stars only with these infrared colors."
 Region D is mixed up with Be stars and red giants (M-type giants/supergiants and S-type stars)., Region D is mixed up with Be stars and red giants (M-type giants/supergiants and S-type stars).
" However, these two populations can be easily separated by seeing their optical color, such as (B— V) (see Figure 4))."," However, these two populations can be easily separated by seeing their optical color, such as $B-V$ ) (see Figure \ref{VS9W-BV}) )."
 A comparison of the two panels of Figure 6 indicates that there are many infrared stars without object-type classifications., A comparison of the two panels of Figure \ref{S9WL18W-JL18W} indicates that there are many infrared stars without object-type classifications.
" Some objects fall into regions A and B, and they are likely to be extremely red carbon stars and OH/IR stars, respectively."," Some objects fall into regions A and B, and they are likely to be extremely red carbon stars and OH/IR stars, respectively."
" To explore these unidentified objects, we are now conducting follow-up observations, using the AKARI during post-helium mission, which take 2.5 — 5 jum spectra with redder than A/AA~100forselectedsources in |b]>30° (P.L: S. Oyabu) and also for selected fsow/fk.sources in |b]<30° (PL: D. Ishihara), where fggw is S9W flux in fk,is2MASS'sK;-bandfluxin Jy and b is the galactic latitude, respectively."," To explore these unidentified objects, we are now conducting follow-up observations, using the AKARI during post-helium mission, which take 2.5 – 5 $\mu$ m spectra with $\lambda / \Delta\lambda \sim 100$ for selected sources redder than $f_{\textrm{S9W}} / f_{\textrm{K$ in $| b | > 30^\circ$ (P.I.: S. Oyabu) and also for selected sources in $| b | < 30^\circ$ (P.I.: D. Ishihara), where $f_{\textrm{S9W}}$ is $S9W$ flux in Jy, $f_{\textrm{K$ is 2MASS's $K_s$ -band flux in Jy and $b$ is the galactic latitude, respectively."
" In Table 5,, we summarize the number"," In Table \ref{table:nsource}, , we summarize the number"
the large number of force evaluations for standard. higher-order compositional svinplectic nethods and the lack of individual ümestepping svinplectic Runge-Ixutta-Nystrómm algoritlinis. jas led researchers to seek alternative wavs to reduce dissipation. uusing time-reversible integration (??)..,"the large number of force evaluations for standard higher-order compositional symplectic methods and the lack of individual timestepping symplectic Runge-Kutta-Nyströmm algorithms, has led researchers to seek alternative ways to reduce dissipation, using time-reversible integration \citep{Makino1996,PretoTremaine1999}."
 These techniques treat the svanptonis of non-syinplecticity. (linear growth in various errors) without treating the cause (non-conservation of the svimplectic form)., These techniques treat the symptoms of non-symplecticity (linear growth in various errors) without treating the cause (non-conservation of the symplectic form).
 Our aleorithim addresses the cause. ancl we see corresponding improvements in svinplecticily ancl nomentiunm conservation for equivalent energv error to relative standard algoritlinis.," Our algorithm addresses the cause, and we see corresponding improvements in symplecticity and momentum conservation for equivalent energy error to relative standard algorithms."
 In this paper we present a fourth-order integrator requiring only (wo force evaluations per timestep. which is fifth-order in svanplecticity.," In this paper we present a fourth-order integrator requiring only two force evaluations per timestep, which is fifth-order in symplecticity."
 Each additional force evaluation improves the svinplecticily by two powers of the timestep., Each additional force evaluation improves the symplecticity by two powers of the timestep.
 We generalize the integrator to individual limestleps and analvze (he breakdown of syaplecticity when adaptive aud individual timesteps are used., We generalize the integrator to individual timesteps and analyze the breakdown of symplecticity when adaptive and individual timesteps are used.
 We show that svuipleclicily is effectively restored when block power of two timesteps are use., We show that symplecticity is effectively restored when block power of two timesteps are used.
 The algorithm is based on a discrete approximation to the action of a system. described in Section 2..," The algorithm is based on a discrete approximation to the action of a system, described in Section \ref{VariationalIntegrators}."
 The algorithin contains a non-linear equation whose solution must be approximated: we compare two approximation methods in Section 3.., The algorithm contains a non-linear equation whose solution must be approximated; we compare two approximation methods in Section \ref{IterationPrescriptions}.
 Adaptive. individual. and combined block Umesteps are discussed in Sections 4.. 5.. amd G respectively.," Adaptive, individual, and combined block timesteps are discussed in Sections \ref{AdaptiveTimesteps}, \ref{IndividualTimeSteps}, and \ref{Implementation} respectively."
 Numerical tests. are presented in Section 7.., Numerical tests are presented in Section \ref{SimulationResults}.
 Conclusions are given in Section ὃν., Conclusions are given in Section \ref{Conclusions}.
 Varialional integrators are based on applving Lamiil(on’s principle of stationary action to discrete approximations to the action lor a physical svstem., Variational integrators are based on applying Hamilton's principle of stationary action to discrete approximations to the action for a physical system.
 ? is an excellent introduction lo variational integrators in an engineering context: ? provides a much more mathematical discussion. including proofs of the essential properties of variational integrators and many exaniples of particular integration rules.," \citet{Lew2004}
 is an excellent introduction to variational integrators in an engineering context; \citet{Marsden2001} provides a much more mathematical discussion, including proofs of the essential properties of variational integrators and many examples of particular integration rules."
 This section is a brief introduction (o. variational integrators., This section is a brief introduction to variational integrators.
 Here ancl (hroughout we suppress vector indices on variables (juxtaposition of variables thus denotes multiplication in the one-dimensional case and (he usual dot-product in (he multidimensional case)., Here and throughout we suppress vector indices on variables (juxtaposition of variables thus denotes multiplication in the one-dimensional case and the usual dot-product in the multidimensional case).
 We denote the derivative of the function / by Df: we denote the partial derivative on the ith argument of the funetion g by jg (awgument labels begin at Q0)., We denote the derivative of the function $f$ by $Df$; we denote the partial derivative on the $i$ th argument of the function $g$ by $\partial_i g$ (argument labels begin at 0).
 The fundamental theorem of variational integration (?.Theorem2.3.1) states that if," The fundamental theorem of variational integration \citep[Theorem
2.3.1]{Marsden2001} states that if"
a doublet.,a doublet.
 The 2*8 level is metastable and cannot radiate to ground or be racliatively excited [rom (he singlet (1S) ground state., The $^3$ S level is metastable and cannot radiate to ground or be radiatively excited from the singlet (1S) ground state.
 The n=? levels can be populated Irom below by collisional excitation (collision energies 720 eV [or the 278 level) or [rom above by radiative decay such as would occur following recombination of Πο II., The n=2 levels can be populated from below by collisional excitation (collision energies $>$ 20 eV for the $^3$ S level) or from above by radiative decay such as would occur following recombination of He II.
 Ionization of Ie I to lle II requires either collisions or photons of energv 724 eV: the latter seems unlikely in view of the lack of ultraviolet radiation in the line-lorming regions of RCB and Πας stars., Ionization of He I to He II requires either collisions or photons of energy $>$ 24 eV; the latter seems unlikely in view of the lack of ultraviolet radiation in the line-forming regions of RCB and HdC stars.
 Collisions with sullicient enerev could be present in shocks or where the eas in the wind is being accelerated by dust grains., Collisions with sufficient energy could be present in shocks or where the gas in the wind is being accelerated by dust grains.
 Clavtonοἱal.(2003) have shown that most. i£ not all. RCD stars possess strong winds.," \citet{cla03} have shown that most, if not all, RCB stars possess strong winds."
 On the other hand. the existence of winds in HdC stars has not been stringently tested.," On the other hand, the existence of winds in HdC stars has not been stringently tested."
 All that is known is that the dust elouds responsible for the huge light variations in RCD stars. which first form and then dissipate. are not present in HdC stus.," All that is known is that the dust clouds responsible for the huge light variations in RCB stars, which first form and then dissipate, are not present in HdC stars."
 In RCD stars the He I absorption lines are usually broad. ancl blueshifted (Clavtonetal.2003).. implving hot expanding gas with velocities of several hundred kins !. [ar greater than the escape velocities.," In RCB stars the He I absorption lines are usually broad and blueshifted \citep{cla03}, implying hot expanding gas with velocities of several hundred km $^{-1}$, far greater than the escape velocities."
 From optical spectroscopy Raoetal.(2006) have shown that in R CYD itself the wind starts in the photosphere and is heated and accelerated as it moves outwa., From optical spectroscopy \citet{rao06} have shown that in R CrB itself the wind starts in the photosphere and is heated and accelerated as it moves outward.
 The winds observed in the RCB stars are strongly correlated with dust formation episodes that produce laree declines in visible brightness (Clavtonetal.2003.andinpreparation).., The winds observed in the RCB stars are strongly correlated with dust formation episodes that produce large declines in visible brightness \citep[][and in preparation]{cla03}.
 During such an episode the IIe I absorption is sometimes accompanied by a red-shifted P Cveni emission feature., During such an episode the He I absorption is sometimes accompanied by a red-shifted P Cygni emission feature.
 However. the wind line weakens or disappears within a few davs or weeks of the ends of the decline and the return of the star to maximum light (Clavton et al..," However, the wind line weakens or disappears within a few days or weeks of the ends of the decline and the return of the star to maximum light (Clayton et al.,"
 in preparation)., in preparation).
 Because the He 10830 ]line can reveal and characterize the winds in carbon-rich stars. we have used the Gemini south telescope to obtain high resolution spectra in the vicinity of (his line in the five known," Because the He 10830 line can reveal and characterize the winds in carbon-rich stars, we have used the Gemini South telescope to obtain high resolution spectra in the vicinity of this line in the five known"
the extent of the clearing will be greater than this because of the extended chaotic zone.,the extent of the clearing will be greater than this because of the extended chaotic zone.
" Hence, if the disc particles have low eccentricities, the mass estimated by will be correct, and the planet mass will be around 10 Jovian masses."," Hence, if the disc particles have low eccentricities, the mass estimated by will be correct, and the planet mass will be around $10$ Jovian masses."
" However, if the disc particles’ eccentricities are higher than ~0.02, the same clearing will be achieved with a smaller planet mass."," However, if the disc particles' eccentricities are higher than $\sim0.02$, the same clearing will be achieved with a smaller planet mass."
 We quantify this effect in Figure 5.., We quantify this effect in Figure \ref{fig:HR8799}.
" This compares the shape and extent of the clearing due to planets of 2, 4, 6, 8 and 10 Jovian masses, under the assumptions that particles are removed only in the classical chaotic zone (dotted lines) or also in the extended chaotic zone (solid line)."," This compares the shape and extent of the clearing due to planets of 2, 4, 6, 8 and 10 Jovian masses, under the assumptions that particles are removed only in the classical chaotic zone (dotted lines) or also in the extended chaotic zone (solid line)."
" In each case, particle eccentricities were distributed uniformly between 0 and 0.1."," In each case, particle eccentricities were distributed uniformly between $0$ and $0.1$."
 We also show as vertical dotted lines the location of the edge for particles on circular orbits., We also show as vertical dotted lines the location of the edge for particles on circular orbits.
" We see that the profiles for 8 and 10 Jovian mass planets under the Wisdom prescription (whose medians straddle AAU) are similar to the profiles for the 4 and 8 Jovian mass planets, respectively, under the extended zone prescription."," We see that the profiles for 8 and 10 Jovian mass planets under the Wisdom prescription (whose medians straddle AU) are similar to the profiles for the 4 and 8 Jovian mass planets, respectively, under the extended zone prescription."
" Hence, the planet masses required to achieve a given clearing may be less than predicted by the Wisdom criterion by as much as50%."," Hence, the planet masses required to achieve a given clearing may be less than predicted by the Wisdom criterion by as much as."
". Thus, if the edge of the outer disc is located at AAU, and the particles in the disc have eccentricities of order 0.1, then the mass of planet b would be in the range 4—8 Jovian masses, rather than the 8-10 Jovian masses that it would be if the particles’ eccentricities were below 0.02."," Thus, if the edge of the outer disc is located at AU, and the particles in the disc have eccentricities of order $0.1$, then the mass of planet b would be in the range 4–8 Jovian masses, rather than the 8–10 Jovian masses that it would be if the particles' eccentricities were below $0.02$."
" For now it is not possible to make such firm conclusions, since observations have yet to resolve the inner edge of the disc, and its 90AU location inferred from SED modelling is degenerate with the assumptions made about the particle properties."," For now it is not possible to make such firm conclusions, since observations have yet to resolve the inner edge of the disc, and its 90AU location inferred from SED modelling is degenerate with the assumptions made about the particle properties."
" Nevertheless, the inner edge will likely be resolved by future observations, and this will help to reduce the uncertainty in the planet mass."," Nevertheless, the inner edge will likely be resolved by future observations, and this will help to reduce the uncertainty in the planet mass."
" For example, some authors,?,, claim a lower mass for planet b of 6-7 Jovian masses, and this is consistent with the planet truncating a disc of planetesimals, whose eccentricities range up to 0.1, at AAU, if the edge indeed be located there."," For example, some authors, claim a lower mass for planet b of 6–7 Jovian masses, and this is consistent with the planet truncating a disc of planetesimals, whose eccentricities range up to $0.1$, at AU, if the edge indeed be located there."
" The eccentricities of the disc particles may have been excited to such an extent by the growth of large planetesimals in the disc(?),, secular perturbations from the planets, if one or more is eccentric(?),, or sweeping by mean motion or secular resonances during past evolution of the system(??)."," The eccentricities of the disc particles may have been excited to such an extent by the growth of large planetesimals in the disc, secular perturbations from the planets, if one or more is eccentric, or sweeping by mean motion or secular resonances during past evolution of the system."
". Finally, we note that our main conclusion — that the mass of planet b estimated from the extent of the chaotic zone will depend on the eccentricities of the disc particles — does not depend on the actual location of the disc edge."," Finally, we note that our main conclusion – that the mass of planet b estimated from the extent of the chaotic zone will depend on the eccentricities of the disc particles – does not depend on the actual location of the disc edge."
" If the disc prove to be at a greater radius, the mass estimated for a disc of eccentric particles will still be greater than that estimated for particles on circular orbits, although each will be greater than its corresponding mass estimated for a disc edge at AAU."," If the disc prove to be at a greater radius, the mass estimated for a disc of eccentric particles will still be greater than that estimated for particles on circular orbits, although each will be greater than its corresponding mass estimated for a disc edge at AU."
 There are also important implications for the evolution of planetary systems when a star loses mass during post-Main Sequence evolution., There are also important implications for the evolution of planetary systems when a star loses mass during post-Main Sequence evolution.
 When stars lose mass on the Asymptotic Giant Branch the planet:star mass ratios increase and previously stable systems can be destabilised(??)., When stars lose mass on the Asymptotic Giant Branch the planet:star mass ratios increase and previously stable systems can be destabilised.
". Stars typically lose mass at relatively modest rates, and under these conditions orbits expand adiabatically and the ratios of semi-major axes are unchanged(?)."," Stars typically lose mass at relatively modest rates, and under these conditions orbits expand adiabatically and the ratios of semi-major axes are unchanged."
". However, since the planet:star mass ratio increases as the star loses mass, quantities which depend on this ratio, such as the Hill's radius and the widths of resonances and the chaotic zone, will change too."," However, since the planet:star mass ratio increases as the star loses mass, quantities which depend on this ratio, such as the Hill's radius and the widths of resonances and the chaotic zone, will change too."
" The chaotic zone expands, and after mass loss particles which were previously on stable orbits may find themselves in the chaotic zone."," The chaotic zone expands, and after mass loss particles which were previously on stable orbits may find themselves in the chaotic zone."
" The presence of this reservoir of newly unstable material may explain the existence of metal pollution in the atmospheres of White Dwarfs(?),, as well as hot discs orbiting some White Dwarfs(?),, as bodies are scattered onto highly eccentric orbits and tidally disrupted(??)."," The presence of this reservoir of newly unstable material may explain the existence of metal pollution in the atmospheres of White Dwarfs, as well as hot discs orbiting some White Dwarfs, as bodies are scattered onto highly eccentric orbits and tidally disrupted."
". estimated the amount of destabilised material simply by expanding the u?/* zone according to the new, lower, stellar mass."," estimated the amount of destabilised material simply by expanding the $\mu^{2/7}$ zone according to the new, lower, stellar mass."
" While this will correctly describe the new chaotic zone at low eccentricity, seemingly vulnerable particles with higher eccentricity may escape being engulfed by the new chaotic zone."," While this will correctly describe the new chaotic zone at low eccentricity, seemingly vulnerable particles with higher eccentricity may escape being engulfed by the new chaotic zone."
 This is because the lower boundary of the extended chaotic zone increases as ji increases., This is because the lower boundary of the extended chaotic zone increases as $\mu$ increases.
" However, a further complication may counteract this: showed that if mass loss rates are relatively rapid then particles’ orbits do not expand adiabatically and they may acquire some eccentricity."," However, a further complication may counteract this: showed that if mass loss rates are relatively rapid then particles' orbits do not expand adiabatically and they may acquire some eccentricity."
 This could push seemingly safe bodies into the extended chaotic zone., This could push seemingly safe bodies into the extended chaotic zone.
" Since the eccentricities required to enter the extended chaotic zone are relatively modest, this could be an important mechanism for destabilising bodies."," Since the eccentricities required to enter the extended chaotic zone are relatively modest, this could be an important mechanism for destabilising bodies."
 AJM is grateful for the support of an STFC studentship., AJM is grateful for the support of an STFC studentship.
 We are indebted to Amy Bonsor for comments on the manuscript., We are indebted to Amy Bonsor for comments on the manuscript.
 We should like to thank the anonymous referee for suggesting improvements to the paper., We should like to thank the anonymous referee for suggesting improvements to the paper.
Szucard radiation driven wiud nocels (CATS. Abbott 1982. Pauldrach et al.,"Standard radiation driven wind models (CAK, Abbott 1982, Pauldrach et al."
 1991) treat the momentum eqation lu a cor-halo approach (1) αςlopting the single-line approximation (2)., 1994) treat the momentum equation in a core-halo approach (1) adopting the single-line approximation (2).
 Various degrees of sophisticatiol cali be applied to determine the occupation imbers., Various degrees of sophistication can be applied to determine the occupation numbers.
 The studies of Pauldrach ot al. (, The studies of Pauldrach et al. (
1991) aud Taresch ot. al. (,1994) and Taresch et al. (
1997) represent the current state-of-the-art. ic. they trea all relevant ious explicitly iu noun-LTE (3) aid solve the equation of motion selt-consisteutlv (1).,"1997) represent the current state-of-the-art, i.e. they treat all relevant ions explicitly in non-LTE (3) and solve the equation of motion self-consistently (4)."
 Paudrach et al. (, Pauldrach et al. (
"1991) also use a unified method for the caleulatiou of the occupation nunubers but a ""core-haloapproach is appied with respect to f1e line force.","1994) also use a unified method for the calculation of the occupation numbers, but a “core-halo”approach is applied with respect to the line force."
 Additiorally. as line overlap is ueelected in the method used by Pauldrach e al. (," Additionally, as line overlap is neglected in the method used by Pauldrach et al. ("
1991). these models can overestimate the line feECC as unattoimated plhotospleric fux is offered o cach line. which consequently may TOCuce efficicucey umubers larger than wits,"1994), these models can overestimate the line force as unattenuated photospheric flux is offered to each line, which consequently may produce efficiency numbers larger than unity."
 Puls {1987) found tlat for winds of reatively low deusitv (sav ogS1/2) )tthe iiclusion of multi-liue. effects leacs to a reduction of wixl moinentunimodel due to ckscattering axd blocking of photou sin the lower par of the wiid., Puls (1987) found that for winds of relatively low density (say $\eta \la 1/2$ ) the inclusion of multi-line effects leads to a reduction of wind momentum due to backscattering and blocking of photons in the lower part of the wind.
 For wiuds of relatively vigh density (say i)Z 1). such as the deuse winds Q: Wolt-Ravet stars. the situation is likev to be reversed.," For winds of relatively high density (say $\eta \ga 1$ ), such as the dense winds of Wolf-Rayet stars, the situation is likely to be reversed."
 Tere Επ trauster froll all ontcleed diffuse field is expected ο dominate over the ctfect o| the ateuuation of flux iu the lavers just above the piotospliere., Here momentum transfer from an extended diffuse field is expected to dominate over the effect of the attenuation of flux in the layers just above the photosphere.
 This could resi]t in more mass loss coirparec to the standard radiation driven wind theory (Abbot Lucv 1985. Smeniain 1991).," This could result in more mass loss compared to the standard radiation driven wind theory (Abbott Lucy 1985, Springmann 1994)."
 Wolt-Ravet aud Of/WN stars profit from a lavered ionization structire. which increases: the nunbero ‘lines that can be used or the driving aud thus lucreaslis the nias loss (Liev Abbott 1993. de Noter et al.," Wolf-Rayet and Of/WN stars profit from a layered ionization structure, which increases the number of lines that can be used for the driving and thus increasing the mass loss (Lucy Abbott 1993, de Koter et al."
 L997)., 1997).
 Qur method differs iu aliuos all aspects from that of Pauldrach e al. (, Our method differs in almost all aspects from that of Pauldrach et al. (
199D.,1994).
 Iu οιr method. plotosphere aud wiud are reated in a unified manner (1) aud we properly take iulti-scatteriugs mo account with a Monte Carlo techuique (2).," In our method, photosphere and wind are treated in a unified manner (1) and we properly take multi-scatterings into account with a Monte Carlo technique (2)."
 Ou the other haud. we derive the level populatiois of the mon-group clements using (a sophisticated version of) the nebular approximation (3).," On the other hand, we derive the level populations of the iron-group elements using (a sophisticated version of) the nebular approximation (3)."
" Finally, we derive the mass loss from a global energv argument (1)."," Finally, we derive the mass loss from a global energy argument (4)."
 This distinct difference of approach imuplies that a comparison beween both methods is dificult., This distinct difference of approach implies that a comparison between both methods is difficult.
 Still. we will acdress some of the differcuces in approach by focusing on a star with parameters representative for the Ol(f)-«tar ¢ Puppis. which has been studied. iu detail bv Abbott Lucy (1985). Puls (19857). Paukrach et al. (," Still, we will address some of the differences in approach by focusing on a star with parameters representative for the O4I(f)-star $\zeta$ Puppis, which has been studied in detail by Abbott Lucy (1985), Puls (1987), Pauldrach et al. ("
1991) aud Puls et al. (,1994) and Puls et al. (
1996).,1996).
 We caji test the difference between single scattering and unItie scattering by allowing photous to interact with a lii6 only once., We can test the difference between single scattering and multiple scattering by allowing photons to interact with a line only once.
 Fig., Fig.
 6 show a conmparison between t1e sinele- aud multiple scattering case for three representativo wind models at == 10.001! I. The model parameers are eiven in Table 3.," \ref{f_msplot} show a comparison between the single- and multiple scattering case for three representative wind models at = 40,000 K. The model parameters are given in Table 3."
" For the often studied wind of the ο supergiaut ¢ Puppis. which has a massloss rate of 3=5.9.LoPAL,wo (Puls et al."," For the often studied wind of the O supergiant $\zeta$ Puppis, which has a mass-loss rate of $\dot{M}^{\rm obs} = 5.9 \times 10^{-6} \msunyr$ (Puls et al."
 1996). the observe efficiency uuuber is about ηzz0.6. sugeestinggs that thereal efficiency of multiple vs. sinele scattering is a factor of about four for ¢ Puppis (sec Fie. 6)).," 1996), the observed efficiency number is about $\eta \simeq 0.6$, suggesting that the efficiency of multiple vs. single scattering is a factor of about four for $\zeta$ Puppis (see Fig. \ref{f_msplot}) )."
 This is close to the findings of Abbott Lucy (1985) who found au increase iu by a factor of 3.3 for the wind of ¢ Puppis if uultipe scattering was taken mto account im a Moute Carlo simulation., This is close to the findings of Abbott Lucy (1985) who found an increase in $\dot{M}$ by a factor of 3.3 for the wind of $\zeta$ Puppis if multiple scattering was taken into account in a Monte Carlo simulation.
 Note from the figure that at low wind densities. the sinele- aud multiple scatering approach converge.n as one would expect.," Note from the figure that at low wind densities, the single- and multiple scattering approach converge, as one would expect."
 For typical O-stars. which have 4X0.5. he mass loss will increase by up to a factor otwo when uultiple scattering is properly included.," For typical O-stars, which have $\eta \la 0.5$, the mass loss will increase by up to a factor of two when multiple scattering is properly included."
 The Wolt-Ravet stars. located at the extreme high wind deusity side. aud which in some cases have observed efficiency numbers of actors 10 or even higher. wav benefit by factors of up to ~ DU.," The Wolf-Rayet stars, located at the extreme high wind density side, and which in some cases have observed efficiency numbers of factors 10 or even higher, may benefit by factors of up to $\sim$ 50."
 The reason why Puls (1987) fouud a reduced nass oss for ¢ Puppis when comparing the sinegle-lue approach with the multiline approach is because the sinele-line approach (which is the same as the sinele scattering xocess) overestimates the line force at the base of the wind. where the mass loss is fixed.," The reason why Puls (1987) found a reduced mass loss for $\zeta$ Puppis when comparing the single-line approach with the multi-line approach is because the single-line approach (which is the same as the single scattering process) overestimates the line force at the base of the wind, where the mass loss is fixed."
 However. a sinuilar relative behaviour isnot found when we compare the xedieted. sinele-line mass loss AT5.]«10SALsr| of Pauldrach et al. (," However, a similar relative behaviour is found when we compare the predicted single-line mass loss $\mdot\ = 5.1 \times 10^{-6} \msunyr$ of Pauldrach et al. ("
1991) with the value of Mo—86«LOSALvy| derived from our fitting formula based on uultiple scattering nodels.,1994) with the value of $\mdot\ = 8.6 \times 10^{-6} \msunyr$ derived from our fitting formula based on multiple scattering models.
 It is not ]xsible to exactly Mupoint the cause «M this difference. 12 ti is likely to © related to differences im our multi-lHi jiofro‘catiuent axd hat of Puls (1957).," It is not possible to exactly pinpoint the cause of this difference, but it is likely to be related to differences in our multi-line treatment and that of Puls (1987)."
 Contrary to Puls (aud also coutrary o Abbott Lucy 1985). we do not adoot he core-halo approximation.," Contrary to Puls (and also contrary to Abbott Lucy 1985), we do not adopt the core-halo approximation."
" The ormnation region o hesrong dri""m ines extends from the photosphere out to the base of he wind.", The formation region of the strong driving lines extends from the photosphere out to the base of the wind.
 If oue asstmes an input photosphericOS spectantni representative of the emergeut ultraviolet spectrum as i a core-halo approach. oue may overestimate the blocki18o in the subsonic wind regime which rezIts in a lower mass loss.," If one assumes an input photospheric spectrum representative of the emergent ultraviolet spectrum as in a core-halo approach, one may overestimate the blocking in the subsonic wind regime which results in a lower mass loss."
Observations of starlight polarization have revealed that some interstellar cust. &rains are non-spherical and aligned.,Observations of starlight polarization have revealed that some interstellar dust grains are non-spherical and aligned.
 The degree. of alignment. and hence the polarization. depends on both aligning processes (c.g.. radiative torques and paramagnetic dissipation) ancl cdisaligning processes (c.g.. random torques arising from collisions with gas atoms).," The degree of alignment, and hence the polarization, depends on both aligning processes (e.g., radiative torques and paramagnetic dissipation) and disaligning processes (e.g., random torques arising from collisions with gas atoms)."
 See Whittet (2004) for a review of polarization observations and Lazarian (2003). Roberee (2004). and Lazarian (2007) or reviews of alignment theory.," See Whittet (2004) for a review of polarization observations and Lazarian (2003), Roberge (2004), and Lazarian (2007) for reviews of alignment theory."
 ]tecently. Weingartner (2006. hereafter WOG) proposed an alternative cdisalignment mechanism lor a grain that las à dime-varving electric dipole moment p and. drifts across the interstellar magnetic field.," Recently, Weingartner (2006, hereafter W06) proposed an alternative disalignment mechanism for a grain that has a time-varying electric dipole moment $\bmath{p}$ and drifts across the interstellar magnetic field."
 Phe poteney of this mechanism is sensitive to the magnitude anc time-scale of luctuations in p., The potency of this mechanism is sensitive to the magnitude and time-scale of fluctuations in $\bmath{p}$.
 WO06 considered highly. simplified: models or the IEuctuating electric dipole moment., W06 considered highly simplified models for the fluctuating electric dipole moment.
 Here. we examine his process and the implications for disalignment in greater detail.," Here, we examine this process and the implications for disalignment in greater detail."
 We will consider relatively luge (size 70.1 ja) silicate grains. since the 9.7 and 20s features. exhibit xolarization (c.@.. Martin Whittet 1990: Smith et al.," We will consider relatively large (size $\ga 0.1 \ \micron$ ) silicate grains, since the $9.7$ and $20 \micron$ features exhibit polarization (e.g., Martin Whittet 1990; Smith et al."
 2000: Wright et al., 2000; Wright et al.
 2002) and the wavelength dependence of the observed polarization implies that relatively small grains are not efficient. polarizers (kim Martin. 1995)., 2002) and the wavelength dependence of the observed polarization implies that relatively small grains are not efficient polarizers (Kim Martin 1995).
" In δι, we review the main elements of disalignment associated with ILuctuations in p."," In \ref{sec:summary}, we review the main elements of disalignment associated with fluctuations in $\bmath{p}$."
 Next. we introduce models for the transport of charge to and within silicate grains (83)).," Next, we introduce models for the transport of charge to and within silicate grains \ref{sec:models}) )."
 We describe simulations of the fluctuating dipole moment ancl associated cisalignment in $4 and. present results in and conclusions in €6.., We describe simulations of the fluctuating dipole moment and associated disalignment in \ref{sec:simulations} and present results in \ref{sec:results} and conclusions in \ref{sec:conclusion}.
 When a gas atom collides with a grain. it imparts an angular impulse to the erain.," When a gas atom collides with a grain, it imparts an angular impulse to the grain."
 Lino other mechanisms excite rotation. then the energy in. rotation. about any axis 20.is Zn.docu where Ay is Doltzmann's constant ancl μμ is the gas temperature.," If no other mechanisms excite rotation, then the energy in rotation about any axis is $\sim \frac{1}{2} k_{\mathrm{B}} T_{\mathrm{gas}}$, where $k_{\mathrm{B}}$ is Boltzmann's constant and $T_{\mathrm{gas}}$ is the gas temperature."
" Such motion is called ""thermal rotation’.", Such motion is called `thermal rotation'.
 The thermal rotation rate for a sphere with radius e is given by where p is the density of the grain material., The thermal rotation rate for a sphere with radius $a$ is given by where $\rho$ is the density of the grain material.
 In general. grains are subjected to additional torques that may drive them to suprathermal rotation. with angular speed wur (Purcell 1975. 1979: Draine Lazarian 1998).," In general, grains are subjected to additional torques that may drive them to suprathermal rotation, with angular speed $\omega > \omega_{T}$ (Purcell 1975, 1979; Draine Lazarian 1998)."
 For thermally rotating erains. the random collisional impulses constitute an important disalignment mechanism.," For thermally rotating grains, the random collisional impulses constitute an important disalignment mechanism."
 A spinning grain with non-zero electric charge acquires a magnetic dipole moment ye|w (Martin. 1971)., A spinning grain with non-zero electric charge acquires a magnetic dipole moment $\bmu \parallel \bomega$ (Martin 1971).
 Dolginov, Dolginov
data was gridded into 49 positions with a spacing of10”. 3),data was gridded into 49 positions with a spacing of. )
 was observed at the IRAS source position., was observed at the IRAS source position.
 All observations were carriecl out with low-noise SIS waveguide receivers and a 1000 channel. 50 MIIz wide acousto-optical spectrometer.," All observations were carried out with low-noise SIS waveguide receivers and a 1000 channel, 50 MHz wide acousto-optical spectrometer."
 The main beam efficiency al 345 Gllz is ~0.65., The main beam efficiency at 345 GHz is $\sim 0.65$.
 Calibration of observations was done by the chopper wheel technique., Calibration of observations was done by the chopper wheel technique.
 SEO 4 is a bright rimmed cloud with a tvpe D morphology on the edge of the ILLI region 5185 (5 Cas) (SFO)., SFO 4 is a bright rimmed cloud with a type B morphology on the edge of the HII region S185 $\gamma$ Cas) (SFO).
 IRAS source 00560+6037 is embedded within SFO 4., IRAS source 00560+6037 is embedded within SFO 4.
 This IRAS source has been classified by SFO as having Πλ colors consistent with hot cirrus sources. and nol a forming or newly formed star (SFO).," This IRAS source has been classified by SFO as having IRAS colors consistent with hot cirrus sources, and not a forming or newly formed star (SFO)."
 ILowever according to the criteria of SFO 4 fits the IRAS color profile of an embedded star forming region., However according to the criteria of \citet{chs} SFO 4 fits the IRAS color profile of an embedded star forming region.
 SFO 4 is nearby (190 pc). and has no known associated outflows or HII objects.," SFO 4 is nearby (190 pc), and has no known associated outflows or HH objects."
 Figure 3aa shows the spectra of our observations towards the IRAS source in SFO 4., Figure \ref{sfoiv_xiii_profiles}a a shows the spectra of our observations towards the IRAS source in SFO 4.
 Although 0) was not detected. our observations limit the integrated intensity of that Uüransition to less that 0.037 IX kam |.," Although ) was not detected, our observations limit the integrated intensity of that transition to less that 0.037 K km $^{-1}$."
 Based on this limit. and the integrated intensity measurement of 0). and an assumed C/MC abundance ratio of G4 we derive an upper limil to the column density of ito be 2xLOM 7.," Based on this limit, and the integrated intensity measurement of ), and an assumed $^{13}$ C abundance ratio of 64 we derive an upper limit to the column density of to be $2\times
10^{13}$ $^{-2}$."
 The line profiles appear fairly gaussian. in all the observed transitions. with nearly identical centroid velocities.," The line profiles appear fairly gaussian, in all the observed transitions, with nearly identical centroid velocities."
" None of the isotopic lines of either CO or were cletected,", None of the isotopic lines of either CO or were detected.
 Figure 4 shows the aad CO integrated intensity maps., Figure \ref{sfoiv_itty} shows the and CO integrated intensity maps.
 Neither the CO 0) map. nor the mnmaps show much structure.," Neither the CO ) map, nor the maps show much structure."
 In the CO 0) map and the 0) map the cloud core surrounding the embedded IRAS source is visible. but no eas (races (he ionization lront or the elephant trunk morphology seen in the D55 image in Figure 2..," In the CO ) map and the ) map the cloud core surrounding the embedded IRAS source is visible, but no gas traces the ionization front or the elephant trunk morphology seen in the DSS image in Figure \ref{sfo_dss}."
 The 2) map shows only one point whose integrated intensity is above 1.0 IKs... (he three sigma threshold for the map.," The ) map shows only one point whose integrated intensity is above 1.0 K, the three sigma threshold for the map."
 This source is unusually weak compared to the other, This source is unusually weak compared to the other
empirical WEPC2 PSEs is that they have infinite signal-to-noise. and can be produced to match the (Gr.9g) coordinates of each radio galaxy on the WES chip.,"empirical WFPC2 PSFs is that they have infinite signal-to-noise, and can be produced to match the $(x,y)$ coordinates of each radio galaxy on the WF3 chip."
" Although the mocel PSEsS produced. by TinyTim do not reproduce the large-scale halo of scattered. light of the empirical WEPC2 PSE at pacti ↔⋅of ryc∕∕1.5"". this. was not considered. to be a serious. problem for the current analysis because the Luminosity of the any nuclear point sources were anticipated to be only a small fraction of the host-ealaxy luminosity."," Although the model PSFs produced by TinyTim do not reproduce the large-scale halo of scattered light of the empirical WFPC2 PSF at radii of $r>1.5''$, this was not considered to be a serious problem for the current analysis because the luminosity of the any nuclear point sources were anticipated to be only a small fraction of the host-galaxy luminosity."
 “This iasstunption proved to be justified. with the vast majority of the radio galaxies proving to possess a negligible nuclear point-source Component (the median nuclear:host (Hux ratio for the ZP5 sample is 0.03)," This assumption proved to be justified, with the vast majority of the radio galaxies proving to possess a negligible nuclear point-source component (the median nuclear:host flux ratio for the ZP5 sample is $0.03$ )."
 In order to match the final reduced radio-galaxy images as accurately as possible. model PSEs were produced. at the two dithered positions of each raclio-galaxy observation separately.," In order to match the final reduced radio-galaxy images as accurately as possible, model PSFs were produced at the two dithered positions of each radio-galaxy observation separately."
 The two model PSEs were then processed. by the routine in an identical fashion to the racio-galaxy images to produce the final model PSE used during the modelling process., The two model PSFs were then processed by the routine in an identical fashion to the radio-galaxy images to produce the final model PSF used during the modelling process.
 1n this section the results of the two-dimensional moclelline of the host galaxies of the ZP5 sample are presented. and, In this section the results of the two-dimensional modelling of the host galaxies of the ZP5 sample are presented and
origin of the frequency plane [zo]. with the phase 8 defined as tand=SCO/Y(cz).,"origin of the frequency plane $|z_0|$, with the phase $\theta$ defined as $\tan\theta = \Im(z)/\Re(z)$."
 The closure phase is defined as the phase of the triple product (or bispectrum) of the complex visibilities on three baselines. which form a closed loop joining three stations A. B. and C. If the projection of the baseline AB ts (44.v). that for BC is (4.v2). and thus (1+ae.)v2) for AC. the closure phase is: The projected baselines and stations are those of the observations.," The closure phase is defined as the phase of the triple product (or bispectrum) of the complex visibilities on three baselines, which form a closed loop joining three stations A, B, and C. If the projection of the baseline AB is $\left(u_1,v_1\right)$, that for BC is $\left(u_2,v_2\right)$, and thus $\left(u_1+u_2,v_1+v_2\right)$ for AC, the closure phase is: The projected baselines and stations are those of the observations."
 Following the method explained in Paper Ll. we computed visibility curves and closure phases for 36 different rotation angles with a step of 5° from all the available intensity maps (x3.5 years of stellar time). giving a total of +2000 synthetic visibilities and +2000 synthetic closure phases per filter.," Following the method explained in Paper I, we computed visibility curves and closure phases for 36 different rotation angles with a step of $^\circ$ from all the available intensity maps $\approx$ 3.5 years of stellar time), giving a total of $\approx$ 2000 synthetic visibilities and $\approx$ 2000 synthetic closure phases per filter."
 We begin by comparing with the 16400 ddata because this filter is centered where the H! continuous opacity minimum oecurs., We begin by comparing with the 16400 data because this filter is centered where the $^{-1}$ continuous opacity minimum occurs.
 Consequently. the continuum-forming region is more visible and the granulation pattern is characterized by large scale granules of about 400—500 ΑΛ. (=60% of the stellar radius) evolving on a timescale of years (Fig.," Consequently, the continuum-forming region is more visible and the granulation pattern is characterized by large scale granules of about 400–500 $R_{\odot}$ $\approx$ $\%$ of the stellar radius) evolving on a timescale of years (Fig."
 4+ in Paper D)., 4 in Paper I).
 On the top of these cells. there are short-lived (a few months to one year) small-scale (about 50—100 R.) structures.," On the top of these cells, there are short-lived (a few months to one year) small-scale (about 50--100 $_{\odot}$ ) structures."
 The resulting granulation pattern causes significant fluctuations of the visibility curves and the signal to be expected in the second. third and fourth lobes deviates greatly from that predicted by uniform disk (UD) and limb-darkened disk (LD) models (Fig.," The resulting granulation pattern causes significant fluctuations of the visibility curves and the signal to be expected in the second, third and fourth lobes deviates greatly from that predicted by uniform disk (UD) and limb-darkened disk (LD) models (Fig."
 11 in Paper D., 11 in Paper I).
 Also the closure phases show large departures from OQ and +27. the values which would indicate a point-symmetric brightness distribution.," Also the closure phases show large departures from 0 and $\pm\pi$, the values which would indicate a point-symmetric brightness distribution."
 Within the large number of computed visibilities and closure phases for this filter. we found that some match the observation data very well (Fig. 2)).," Within the large number of computed visibilities and closure phases for this filter, we found that some match the observation data very well (Fig. \ref{comparison_1a}) )."
" We selected the best-fitting snapshot minimizing the function: where V; is the observed visibility amplitude data with its corresponding error cy. My, is the synthetic visibility amplitude at the same spatial frequency. óc, 1s the observed closure phase with corresponding error c, . and My, the synthetic closure phase for the observed UV coordinates."," We selected the best-fitting snapshot minimizing the function: where $V_i$ is the observed visibility amplitude data with its corresponding error $\sigma_{V_{i}}$, $M_{V_{i}}$ is the synthetic visibility amplitude at the same spatial frequency, $\phi_{C_{i}}$ is the observed closure phase with corresponding error $\sigma_{\phi_{C_{i}}}$ , and $M_{\phi_{C_{i}}}$ the synthetic closure phase for the observed UV coordinates."
 The best matching visibilities and closure phases correspond to a particular snapshot and rotation angle., The best matching visibilities and closure phases correspond to a particular snapshot and rotation angle.
 In Fig., In Fig.
 3. the simulation has been scaled to an apparent diameter of «45.1 mas in order to fit the data points in. the first lobe. corresponding to a distance of 172.1 pe for the simulated star.," \ref{comparison_1b} the simulation has been scaled to an apparent diameter of $\sim$ 45.1 mas in order to fit the data points in the first lobe, corresponding to a distance of 172.1 pc for the simulated star."
 The angular diameter is slightly larger than the limb-darkened diameter of 44.2840.15 mas found by ?.., The angular diameter is slightly larger than the limb-darkened diameter of $\pm$ 0.15 mas found by \cite{2009A&A...508..923H}.
 Our distance i8 also in agreement with ?.. who reported a distance of 197+45 pe.," Our distance is also in agreement with \cite{2008AJ....135.1430H}, who reported a distance of $197\pm45$ pc."
 Using Harper et al., Using Harper et al.
's distance and an effective temperature of 3650 K (?).. the radius is R=890+200... neglecting any uncertainty in Tyr.,"'s distance and an effective temperature of 3650 K \citep{2005ApJ...628..973L}, the radius is $R=890\pm200 R_\odot$, neglecting any uncertainty in $T_{\rm eff}$."
 On the other hand. using Harper et al.," On the other hand, using Harper et al."
 2008 distance and the apparent diameter of 45 mas (?).. the radius is R=950+200R..," 2008 distance and the apparent diameter of 45 mas \citep{2004A&A...418..675P}, the radius is $R=950\pm200 R_\odot$."
 All these results match evolutionary tracks by ?. for an initial mass of between 15 and 25 M.," All these results match evolutionary tracks by \cite{2003A&A...404..975M}
 for an initial mass of between 15 and 25 $M_\odot$."
 The radius (R=832K... see Section ??)) and the effective temperature (J.=3490 K) of our 3D simulation are smaller because the simulations start with an initial model that has a guessed radius. a certain envelope mass. a certain potential profile. and a preseribed luminosity.," The radius $R\approx832 R_\odot$, see Section \ref{paramSect}) ) and the effective temperature $T_{\rm eff}\approx3490$ K) of our 3D simulation are smaller because the simulations start with an initial model that has a guessed radius, a certain envelope mass, a certain potential profile, and a prescribed luminosity."
 However. during the run the internal structure relaxes so something not to far away from the initial guess (otherwise the numerical grid is inappropriate).," However, during the run the internal structure relaxes so something not to far away from the initial guess (otherwise the numerical grid is inappropriate)."
 The average final radius is determined once the simulation is finished., The average final radius is determined once the simulation is finished.
 Therefore. since the radius (and the effective temperature) cannot be tuned. the model is placed at some distance in order to provide the angular diameter that best matches the observations.," Therefore, since the radius (and the effective temperature) cannot be tuned, the model is placed at some distance in order to provide the angular diameter that best matches the observations."
 Finally. within. the error bars our model radius agrees with all other data derived using the distance determined by ?..," Finally, within the error bars our model radius agrees with all other data derived using the distance determined by \cite{2008AJ....135.1430H}."
 Our RHD simulation provides a better fit than uniform disk and limb-darkened models used by ? in all lobes of the visibility function., Our RHD simulation provides a better fit than uniform disk and limb-darkened models used by \citeauthor{2009A&A...508..923H} in all lobes of the visibility function.
 The departure from circular symmetry is more evident at high spatial frequencies (e.g.. the fourth lobe) where the visibility predicted from the parametric model is lower than the observed data.," The departure from circular symmetry is more evident at high spatial frequencies (e.g., the fourth lobe) where the visibility predicted from the parametric model is lower than the observed data."
 The small-scale convection-related surface structures are the cause of this departure anc can only be explained by RHD simulations that are permeatec with irregular convection-related structures of different size., The small-scale convection-related surface structures are the cause of this departure and can only be explained by RHD simulations that are permeated with irregular convection-related structures of different size.
 Also the closure phases display a good agreement with the simulation indicating that a possible solution to the distributior of the inhomogeneities on the surface of Betelgeuse is the intensity map of Fig., Also the closure phases display a good agreement with the simulation indicating that a possible solution to the distribution of the inhomogeneities on the surface of Betelgeuse is the intensity map of Fig.
 3 (though the reconstructed images found by ? are more probable)., \ref{comparison_1b} (though the reconstructed images found by \citet{2009A&A...508..923H} are more probable).
 This ts the first robust confirmation of the physical origi of surface granulation for Betelgeuse. following on from the detection in the K band (Paper D.," This is the first robust confirmation of the physical origin of surface granulation for Betelgeuse, following on from the detection in the K band (Paper I)."
 Recently. ? Were able to reconstruct two images of Betelgeuse. using the data presented in this work. with two different image reconstruction algorithms.," Recently, \cite{2009A&A...508..923H} were able to reconstruct two images of Betelgeuse, using the data presented in this work, with two different image reconstruction algorithms."
 The image reconstructed with WISARD (??) Is displdyda in Fig.," The image reconstructed with WISARD \citep{2009M, 2005JOSAA..22.2348M} is displayed in Fig."
 4. (left)., \ref{images_1} (left).
 Both reconstructed images in ? paper have two spots of unequal brightness located at roughly the same positions near the center of the stellar disk., Both reconstructed images in \citeauthor{2009A&A...508..923H} paper have two spots of unequal brightness located at roughly the same positions near the center of the stellar disk.
 One of these spots is half the stellar radius in size., One of these spots is half the stellar radius in size.
 Fig., Fig.
 4 shows à comparison of the reconstructed image to our best fitting snapshot of Fig. 3.., \ref{images_1} shows a comparison of the reconstructed image to our best fitting snapshot of Fig. \ref{comparison_1b}.
 Fainter structures are visible in the synthetic image (right panel) while the reconstructed image (left panel) is dominated by two bright spots., Fainter structures are visible in the synthetic image (right panel) while the reconstructed image (left panel) is dominated by two bright spots.
 Moreover. the bigger spot visible in the reconstructed image is not present in our synthetic image. whereas there is good agreement in term of location with the smaller spot located close to the center.," Moreover, the bigger spot visible in the reconstructed image is not present in our synthetic image, whereas there is good agreement in term of location with the smaller spot located close to the center."
 However. itis possible that the synthetic map does not match exactly the location of the spots because it cannot perfectly reproduce the closure phase data.," However, itis possible that the synthetic map does not match exactly the location of the spots because it cannot perfectly reproduce the closure phase data."
Hot subdwarfs are generally classtied into three types by their spectra.,Hot subdwarfs are generally classfied into three types by their spectra.
 These are subdwarf Β (sdB. with a surface effective temperature.Το. in à range from 20.000 to 40.000K. with H-Balmer absorption lines wider than in normal Β. stars). subdwarf O (sdO. Tay ranging from 40.000K to 80.000K with strong He absorption lines). and subdwarf OB (sdOB. a transition between O and B. Moehler et al.," These are subdwarf B (sdB, with a surface effective temperature,$T_{\rm eff}$, in a range from 20,000 to 40,000K, with H-Balmer absorption lines wider than in normal B stars), subdwarf O (sdO, $T_{\rm eff}$ ranging from 40,000K to 80,000K with strong He absorption lines), and subdwarf OB (sdOB, a transition between O and B, Moehler et al."
 1990; Heber 2009)., 1990; Heber 2009).
 These objects are located below the upper main sequence on the Hertzsprung-Russell diagram(HRD) and are also known as extreme horizontal branch (EHB) stars from the view of their evolutionary stages: Le.. they are believed to be core He-burning objects with extremely thin hydrogen envelopes (< 0.02 M...," These objects are located below the upper main sequence on the Hertzsprung-Russell diagram(HRD) and are also known as extreme horizontal branch (EHB) stars from the view of their evolutionary stages; i.e., they are believed to be core He-burning objects with extremely thin hydrogen envelopes $<$ 0.02 $M_\odot$ )."
 Hot subdwarfs are an important population in. several respects., Hot subdwarfs are an important population in several respects.
 For example. pulsating sdB stars are standard candles in distance determination (Kilkenny et al.," For example, pulsating sdB stars are standard candles in distance determination (Kilkenny et al."
 1999)., 1999).
 Likewise. close binaries composed of an sdB star and a massive white dwarf (WD) are qualified as supernova Ia progenitors (Maxted et al.," Likewise, close binaries composed of an sdB star and a massive white dwarf (WD) are qualified as supernova Ia progenitors (Maxted et al."
 2000)., 2000).
 Moreover. hot subdwarfs are an important source of far-UV light in the galaxy. anc they are successfully used to explain the UV-upturn in elliptical galaxies (Kilkenny et al.," Moreover, hot subdwarfs are an important source of far-UV light in the galaxy, and they are successfully used to explain the UV-upturn in elliptical galaxies (Kilkenny et al."
 1997; Han et al., 1997; Han et al.
 2007)., 2007).
 Several scenarios have beer proposed to explain the formation of these objects. re. strong mass loss for a star on the red giant branch (Dorman et al.," Several scenarios have been proposed to explain the formation of these objects, i.e. strong mass loss for a star on the red giant branch (Dorman et al."
 1993. D'Cruz et al.," 1993, D'Cruz et al."
 1996). mass transfer in close binary systems (Mengel et al.," 1996), mass transfer in close binary systems (Mengel et al."
 1976). and the coalescence of two heltum white dwarfs (He-WDs) (ben 1990. Webbink 1984).," 1976), and the coalescence of two helium white dwarfs (He-WDs) (Iben 1990, Webbink 1984)."
 Recent radial velocity (RV) surveys reveal that two thirds of all sdB stars reside in close binaries (Maxted et al., Recent radial velocity (RV) surveys reveal that two thirds of all sdB stars reside in close binaries (Maxted et al.
 2001)., 2001).
 Han et al. (, Han et al. (
2002. 2003) propose a binary model for the formation of hot subdwarf stars. in which three channels (stable Roche lobe overflow (RLOF). common envelope (CE) ejection. and merging of two He-WDs) are included. (,"2002, 2003) propose a binary model for the formation of hot subdwarf stars, in which three channels (stable Roche lobe overflow (RLOF), common envelope (CE) ejection, and merging of two He-WDs) are included. ("
For details see Han et al.,For details see Han et al.
 2002. 2003.)," 2002, 2003.)"
 This binary model successfully explained most of the observational characteristics of hot subdwarfs. and is now widely used in the study of hot subdwarf stars. e.g. OToole. Heber Benjamin. 2004.," This binary model successfully explained most of the observational characteristics of hot subdwarfs, and is now widely used in the study of hot subdwarf stars, e.g. O'Toole, Heber Benjamin, 2004."
 Mass is à fundamental parameter of stars. but it is very uncertain for most hot subdwarfs. which are to be around 0.5 M. (Heber 1986. Satfer et al.," Mass is a fundamental parameter of stars, but it is very uncertain for most hot subdwarfs, which are to be around 0.5 $M_\odot$ (Heber 1986, Saffer et al."
 1994)., 1994).
 Sometimes we need a more precise mass to study these objects further., Sometimes we need a more precise mass to study these objects further.
 In recent years. more than 2300 objects have been included in à hand hot subdwarf database (Ostensen 2004). among these more than 200 hot subdwarfs have been studied in detail for atmospheric parameters (e.g. Saffer et al.," In recent years, more than 2300 objects have been included in a hand hot subdwarf database stensen 2004), among these more than 200 hot subdwarfs have been studied in detail for atmospheric parameters (e.g. Saffer et al."
 1994: Maxted et al., 1994; Maxted et al.
 2001: Edelmann et al., 2001; Edelmann et al.
 2003. Lisker et al.," 2003, Lisker et al."
 2005. Stroeer et al.," 2005, Stroeer et al."
 2007)., 2007).
 However. only a few hot subdwarfs have well-defined masses from asteroseismology. e.g. PG 0014-067 (Brassard et al.," However, only a few hot subdwarfs have well-defined masses from asteroseismology, e.g. PG 0014+067 (Brassard et al."
 2001). PG 12194534 (Charpinet et al.," 2001), PG 1219+534 (Charpinet et al."
 2005a). PG 3254101(Charpinet et al.," 2005a), PG 1325+101(Charpinet et al."
 2006). and Feige 48 (Charpinet et al.," 2006), and Feige 48 (Charpinet et al."
 2005b)., 2005b).
 In addition. Wood Saffer (1999) show an sdB star HW Vir (PG 1241-082). which is in a double-lined eclipsing binary. to be 0.48+0.09M... from dynamical methods.," In addition, Wood Saffer (1999) show an sdB star HW Vir (PG 1241-082), which is in a double-lined eclipsing binary, to be $0.48 \pm 0.09 M_\odot$ from dynamical methods."
 For other hot subdwarfs. which are not pulsating stars or are in binary systems without detailed light or radial-velocity curves. masses are derived from theoretical evolutionary tracks (Dorman et al.," For other hot subdwarfs, which are not pulsating stars or are in binary systems without detailed light or radial-velocity curves, masses are derived from theoretical evolutionary tracks (Dorman et al."
 1993). e.g.. choosing the track closest to the data point on the Zr—log(g) diagram. where Το and g are effective temperature and surface gravity. respectively.," 1993), e.g., choosing the track closest to the data point on the $T_{\rm eff}- \rm
 log(\it g)$ diagram, where $T_{\rm eff}$ and $g$ are effective temperature and surface gravity, respectively."
 The commonly used evolution library of hot subdwarfs is that of Dorman et al. (, The commonly used evolution library of hot subdwarfs is that of Dorman et al. (
1993). with masses from 0.4 to 0.5 Ms.,"1993), with masses from 0.4 to 0.5 $M_\odot$."
 However. Han et al.(2002. 2003) show that the masses of hot subdwarfs can be in a much wider range: te.. from 0.3 M.. to more than 0.7 M...," However, Han et al.(2002, 2003) show that the masses of hot subdwarfs can be in a much wider range; i.e., from 0.3 $M_\odot$ to more than 0.7 $M_\odot$."
 Thus. it is necessary to extend the evolution library of hot subdwarfs or find a simple method of estimating the masses of hot subdwarfs.," Thus, it is necessary to extend the evolution library of hot subdwarfs or find a simple method of estimating the masses of hot subdwarfs."
 In this letter. we carry out full evolutionary calculations for hot subdwarfs and obtain an approach to determining the masses of hot subdwarfs.," In this letter, we carry out full evolutionary calculations for hot subdwarfs and obtain an approach to determining the masses of hot subdwarfs."
 Using this approach. we study the masses and mass distributions of observed hot subdwarfs.," Using this approach, we study the masses and mass distributions of observed hot subdwarfs."
 The stellar evolution code used was originally developed by Eggleton (1971. 1972. 1973).," The stellar evolution code used was originally developed by Eggleton (1971, 1972, 1973)."
 The code has been updated with the latest input physics over the past three decades as described by Han. Podsiadlowski Eggleton (1994. hereafter HPE) and by Pols et al. (," The code has been updated with the latest input physics over the past three decades as described by Han, Podsiadlowski Eggleton (1994, hereafter HPE) and by Pols et al. ("
1995. 1998).,"1995, 1998)."
" We set the ratio of mixing length to local pressure scale height. a=//H,. to 2.0 and the convective overshooting parameter. doy. to 0.12 (Pols et al."," We set the ratio of mixing length to local pressure scale height, $\alpha = l/H_{\rm p}$, to 2.0 and the convective overshooting parameter, $\delta_{\rm OV}$ to 0.12 (Pols et al."
 1997; Schroder et al., 1997; $\ddot{o}$ der et al.
 1997)., 1997).
 The opacity tables for various metallicities are, The opacity tables for various metallicities are
"For the cold flow gas at 10* K and 10? K, the dotted lines where the cooling times equal the age of the universe are outside of the plotting range, so the minimum allowed value of n, is where R~ Ryiriqtt about 8x1077 cm? for the 10? K gas and even smaller for the 104 K gas.","For the cold flow gas at $10^4$ K and $10^5$ K, the dotted lines where the cooling times equal the age of the universe are outside of the plotting range, so the minimum allowed value of $n_e$ is where $R \sim R_{virial}$ : about $8 \times 10^{-7}$ $^{-3}$ for the $10^5$ K gas and even smaller for the $10^4$ K gas."
" For the cooling hot halo gas at 109 K, the condition that the cooling time be less than the age of the universe forces ne to be larger than about 2x107? cm?."," For the cooling hot halo gas at $10^6$ K, the condition that the cooling time be less than the age of the universe forces $n_e$ to be larger than about $2 \times 10^{-5}$ $^{-3}$."
 These calculations don’t put strong constraints on the density of the halo gas since the cooling times are so rapid for a large range of temperatures and densities., These calculations don't put strong constraints on the density of the halo gas since the cooling times are so rapid for a large range of temperatures and densities.
" How the gas gets into the galaxies themselves will involve a more complete treatment including the effects of self-sheilding, which is beyond the scope of this paper."," How the gas gets into the galaxies themselves will involve a more complete treatment including the effects of self-sheilding, which is beyond the scope of this paper."
" The rate inferred from our open box model provides an dpcex+/dtestimate for the average rate at which the baryonic fuel is required to make its way to a galactic disk in order to sustain the observed star formation, which largely occurs in the disk."," The rate $d\mrext/dt$ inferred from our open box model provides an estimate for the average rate at which the baryonic fuel is required to make its way to a galactic disk in order to sustain the observed star formation, which largely occurs in the disk."
 A comparison of this rate with the mean rate of baryon accretion at the virial radius of the host dark matter halo will provide an estimate for the efficiency of converting the cosmological infalling baryons into stars., A comparison of this rate with the mean rate of baryon accretion at the virial radius of the host dark matter halo will provide an estimate for the efficiency of converting the cosmological infalling baryons into stars.
 Many cooling and feedback processes obviously affect the fate of baryons after their infall onto the halo and whether they will reach the disk., Many cooling and feedback processes obviously affect the fate of baryons after their infall onto the halo and whether they will reach the disk.
" In fact, much of the current research in galaxy formation modeling is aimed at understanding this transition."," In fact, much of the current research in galaxy formation modeling is aimed at understanding this transition."
" Our goal here is to estimate an overall ratio, as a function of redshift, of the baryon accretion rates at the virial radius and at the disk scale."," Our goal here is to estimate an overall ratio, as a function of redshift, of the baryon accretion rates at the virial radius and at the disk scale."
" We begin with the dark matter accretion rate from McBrideetal.(2009) and Fakhouri,Ma&Boylan- which quantified the mass accretion histories of all dark matter halos with masses above ~10109 Mo in the two Millennium simulations of a ACDM universe (Springeletal.2005;Boylan-Kolch"," We begin with the dark matter accretion rate from \cite{McBride09} and \cite{FMBK10}, which quantified the mass accretion histories of all dark matter halos with masses above $\sim 10^{10} $ $_\odot $ in the two Millennium simulations of a $\Lambda$ CDM universe \citep{Springel05,BK09}."
"in An approximate function is provided for the average mass accretion rate as a function of redshift and halo mass (Fakhouri,Ma&Boylan-Kolchin2010):: where =(25.3,1.65) for the median rate and (46.1,(6,7) 1.11) for the mean rate, O,, and Qa are the present-day density parameters in matter and the cosmological constant, and €),+Qa is assumed to be unity (as in the Millennium "," An approximate function is provided for the average mass accretion rate as a function of redshift and halo mass \citep{FMBK10}: where $(\beta,\gamma)=(25.3, 1.65)$ for the median rate and (46.1, 1.11) for the mean rate, $\Omega_m$ and $\Omega_\Lambda$ are the present-day density parameters in matter and the cosmological constant, and $\Omega_m +
\Omega_\Lambda$ is assumed to be unity (as in the Millennium simulation)."
The mean rate is ~50% higher than thesimulation). median rate due to the long tail of halos with high accretion rates in the distribution., The mean rate is $\sim 50$ higher than the median rate due to the long tail of halos with high accretion rates in the distribution.
 This M represents the average rate at which the mass in dark matter is being accreted through the virial radius of a halo., This $\dot{M}$ represents the average rate at which the mass in dark matter is being accreted through the virial radius of a halo.
" The mass growth comes in two forms in cosmological simulations: via mergers with other resolved halos (Fakhouri&Ma2009a),, and via ""diffuse"" accretion of non-halo material that is a combination of unresolved halos and unbound dark matter particles (Fakhouri&Ma2009b)."," The mass growth comes in two forms in cosmological simulations: via mergers with other resolved halos \citep{FM09a}, and via ""diffuse"" accretion of non-halo material that is a combination of unresolved halos and unbound dark matter particles \citep{FM09b}."
". We convert M above into a mean accretion rate for the baryons, My, by assuming a cosmic baryon-to-dark matter ratio of fy=QO,/Q,,1/6."," We convert $\dot{M}$ above into a mean accretion rate for the baryons, $\dot{M}_b$, by assuming a cosmic baryon-to-dark matter ratio of $f_b=
\Omega_b/\Omega_m = 1/6$."
 The result should provide a reasonable approximation for the mean rate of baryon mass that is entering the virial radius via mergers plus accretion of intergalactic gas., The result should provide a reasonable approximation for the mean rate of baryon mass that is entering the virial radius via mergers plus accretion of intergalactic gas.
" These infalling baryons are presumably in a mixture of forms: warm-hot ionized hydrogen gas of 10? to 10""K, “cold” flows of ~ 10*K (still ionized) gas, andL, H22, and stars brought in from merging galaxies."," These infalling baryons are presumably in a mixture of forms: warm-hot ionized hydrogen gas of $10^5$ to $10^7$ K, “cold” flows of $\sim 10^4$ K (still ionized) gas, and, 2, and stars brought in from merging galaxies."
" As discussed earlier, the majority of these baryons must be in the form of ggas."," As discussed earlier, the majority of these baryons must be in the form of gas."
" To compare My, with the rate of external gas inflow, Dext (8 refopenbox)), needed to account for the evolution of the observed star formation rates, we define where M is the mass of the dark matter halo under consideration, M is calculated using Eq. a"," To compare $\dot{M}_b$ with the rate of external gas inflow, $\dot{\rho}_{ext}$ \\ref{openbox}) ), needed to account for the evolution of the observed star formation rates, we define where $M$ is the mass of the dark matter halo under consideration, $\dot{M}$ is calculated using Eq. \ref{rate}) ),"
"nd dn/dM is the (comoving) number density of dark (9)),matter halos with mass in the range of M and M4- dM.", and $dn/dM$ is the (comoving) number density of dark matter halos with mass in the range of $M$ and $M+dM$ .
 The parameter o represents thefraction of accreting baryons the virial that must beconverted into stars in (atour open box radius)models., The parameter $\alpha$ represents thefraction of accreting baryons (at the virial radius) that must beconverted into stars in our open box models.
 The value of a can be estimated by combining the allowed range of ἆρενι/αί from Fig., The value of $\alpha$ can be estimated by combining the allowed range of $d\mrext/dt$ from Fig.
 5 with the halo abundance dn/dM from the Millenniumsimulation (Springeletal. 2005)., \ref{OBfig} with the halo abundance $dn/dM$ from the Millenniumsimulation \citep{Springel05}. .
". Taking fj=1/6 and M=1013 Mo, we find the predicted a to be ~70—100% at z= 3,"," Taking $f_b = 1/6$ and $M =
10^{12}$ $_{\odot}$ , we find the predicted $\alpha$ to be $\sim 70-100$ at $z\ga 3$ ,"
(NED).,(NED).
 For a detailed description of this data-set. we refer the reader to Tavloretal.(2005).. aud refereuces therein.," For a detailed description of this data-set, we refer the reader to \citet{taylor05}, and references therein."
" The effective exposure times inC...D...WV. and απο 1200. G00. 150. and ssec. respectively,"," The effective exposure times in, and are 1200, 600, 480, and sec, respectively."
 The native resolution aud pixel scale are ~ 133 (FWITAD) aud Q'337 !., The native resolution and pixel scale are $\sim$ 3 (FWHM) and 37 $^{-1}$.
 Those images are registered. convolved and resampled to match the orientation. PSF. aud pixel scale of the NUV image.," These images are registered, convolved and resampled to match the orientation, PSF, and pixel scale of the NUV image."
 The Spizer//IRAC ppipeliuc-product iniiges were obtained from the viaLeopard., The /IRAC pipeline-product images were obtained from the via.
. For cach filter. the mosaiced iuage was created with an effective exposure time of ssec.," For each filter, the mosaiced image was created with an effective exposure time of sec."
 The native pixel scale is 1722 |. and the effective resolution (FWIIM) ranges frou —2/22 at Πο ~2733 atnmn.," The native pixel scale is 2 $^{-1}$, and the effective resolution (FWHM) ranges from $\sim$ 2 at to $\sim$ 3 at."
 Like for the VATT images. we match the oricutations. PSF. aud pixel scale of the TRAC images to those of the NUV image.," Like for the VATT images, we match the orientations, PSF, and pixel scale of the IRAC images to those of the NUV image."
 Iu Paper L we estimated the visual dust extinction ii 7)) measured over cach 175541755 c 12.12ppc pixel iu 009580 as follows.," In Paper I, we estimated the visual dust extinction in ) measured over each $\times$ 5 $\simeq$ $\times$ $^2$ pixel in 0959 as follows."
 From histograms of the observed visual to füux ratio (fi/ fou) 1 cach pixel we estimate the intrinsic extinction-frec flux ratios στ) for two eroups of pixels: pixels appareutly dominated by the helt from voungcr and pixels apparently dominated by the lelt from older stellar populations.," From histograms of the observed visual to flux ratio $f_V$ $f_{\hbox{\scriptsize 3.6\mum}}$ ) in each pixel, we estimate the intrinsic extinction-free flux ratios ) for two groups of pixels: pixels apparently dominated by the light from younger and pixels apparently dominated by the light from older stellar populations."
 These are separable based ou their distribution pattern in a pCAID of the observed jy versus (U - mumy)jcolor., These are separable based on their distribution pattern in a pCMD of the observed $\mu_V$ versus $U$ $-$ ) color.
" SincethemidIBR36 fflucisassumedtobemininallyaf foetedbythedust. andhence πώ” MOEXKELSEIS οσα.Faiioctal,2001:Willneret2001). Hu each pixel can be inferred from the differcuce between the Gon) aud extinction-frec (i.e. Frou ποs fojuors) V-band fuxes"," Since the mid-IR flux is assumed to be minimally affected by the dust, and hence usually treated as extinction-free \citep[e.g.,][]{fazio04, willner04}, in each pixel can be inferred from the difference between the $f_{V,\rm obs}$ ) and extinction-free (i.e., $f_{V,\rm 0}$ $\beta_{V,\rm 0} \times f_{\rm 3.6\mu m,obs}$ ) -band fluxes."
 For further details of the method. we refer the reader to Paper I. The extinctions in other bandpasses NUN aud FUV. and opticalC...Bo and bands) are then scaled from musing the adopted LMC2 supershell extinction curve of Cordonetal. (2003)..," For further details of the method, we refer the reader to Paper I. The extinctions in other bandpasses NUV and FUV, and optical, and bands) are then scaled from using the adopted LMC2 supershell extinction curve of \citet{gordon03}. ."
 Iu1.. the extinction map of thus xoduced. darker eravscales correspond to higher 00959.values ofAy-.," In, the extinction map of 0959 thus produced, darker grayscales correspond to higher values of."
. The eravscales saturate for > ((iucicated by the white vertical line in the color bar) to chhance the visibility of the lower vvalues in the ealaxy. and πο differ from that of Figure 10(4)) iv Paper L The maxiuum extinction measured in this ealaxy. averaged over a pixcl. Is Atma 200.," The grayscales saturate for $\geq$ (indicated by the white vertical line in the color bar) to enhance the visibility of the lower values in the galaxy, and so differ from that of Figure ) in Paper I. The maximum extinction measured in this galaxy, averaged over a pixel, is $A_{V,\rm
max}$ $\simeq$."
8 To visually (qualitatively) investigate the effect of our pixel-based extinction correction on an image of 00059. we first construct. two color composites of the galaxy. composed of the //TRAC (red channel). the eround-based ((ereen channel). aud the FUV (blue channel) images.," To visually (qualitatively) investigate the effect of our pixel-based extinction correction on an image of 0959, we first construct two color composites of the galaxy, composed of the /IRAC (red channel), the ground-based (green channel), and the FUV (blue channel) images."
 Figures 2((60)) aud 2((0)) show the color composites aud extiuctiou correction., Figures \ref{colimg}( ) and \ref{colimg}( ) show the color composites and extinction correction.
 The image resolutions are matched to that of the NUV nuage., The image resolutions are matched to that of the NUV image.
 For easy. comparison. both nuages were created using the color stretch. aud with the TRAC ccoutours over-plotted.," For easy comparison, both images were created using the color stretch, and with the IRAC contours over-plotted."
 Iu 2((«)). there are several regions in the galaxy thatappear mich redder than other parts of the galaxy.," In ), there are several regions in the galaxy thatappear much redder than other parts of the galaxy."
lt is well established that most ~1 Myr-old stars are surrounded by relatively massive,It is well established that most $\sim$ 1 Myr-old stars are surrounded by relatively massive
questionable although worth mentioning.,questionable although worth mentioning.
 The ionized material at the center of the cigar-like feature being very tenuous (or simply non-existent: see above). all. points filline the diagram are found along the external bright rims.," The ionized material at the center of the cigar-like feature being very tenuous (or simply non-existent; see above), all points filling the diagram are found along the external bright rims."
 Panel (d) reveals that the “SNRs” area of shock-dominated material is highly favored. in agreement with the prediction of shock development proposed by the theory.," Panel (d) reveals that the “SNRs” area of shock-dominated material is highly favored, in agreement with the prediction of shock development proposed by the theory."
 The particular shape of the elongated. structure presented in Panel (c) could be casily mistaken for jets attributed to Lerbig-Llaro (LIII) objects., The particular shape of the elongated structure presented in Panel (c) could be easily mistaken for jets attributed to Herbig-Haro (HH) objects.
 Llowever. Figure of Frew&Parker(2010). indicates the peculiar low intensities of the Ν vesiseiilfimesim LL Lobjects," However, Figure of \citet{Fre2010} indicates the peculiar low intensities of the $[$ $]$ lines in HH objects."
 Thisleudstonposilion. for LLL Lobject si vs. logislessuHiHe diagram.. clearly above the “SNRs”↴⇁↼↼ area.," This leads to a position, for HH objects in the $_{10}\left[\frac{\textnormal{I}(\textnormal{H}\alpha)}{\textnormal{I}([\textnormal{S}\,\textsc{ii}])}\right]$ vs. $_{10}\left[\frac{\textnormal{I}(\textnormal{H}\alpha)}{\textnormal{I}([\textnormal{N}\,\textsc{ii}])}\right]$ diagram, clearly above the “SNRs” area."
 This said. the ciagram of Panel (d) most likely confirms that the cigar-like feature is not part of an LILLE object. in 11505.," This said, the diagram of Panel (d) most likely confirms that the cigar-like feature is not part of an HH object in 1805."
 Rather. the clephant-trunk nature. suggested here. appears very plausible.," Rather, the elephant-trunk nature, suggested here, appears very plausible."
 The use of the imaging Fourier transform spectrometer SpLIOMM allowed us to obtain series of emission-line profiles of the optical gas in the brightest. central portions of the Galactic 11505 ," The use of the imaging Fourier transform spectrometer SpIOMM allowed us to obtain series of emission-line profiles of the optical gas in the brightest, central portions of the Galactic 1805 region."
The bandwidth: used. at data acquisition allowed. the τηESISumultaneousobservations. of⋅ the A6563.⋅⋅⋅ A. ↽ ," The bandwidth used at data acquisition allowed the simultaneousobservations of the $\lambda$ 6563 $\mbox{\AA}$ , $[$ "
The distributions of the photon index. flux and TS [ον dillerent energy ranges are shown in ligure 2.,"The distributions of the photon index, flux and TS for different energy ranges are shown in figure 2."
 They. are compatible with Gaussian distributions., They are compatible with Gaussian distributions.
 In the 13 and 3300 GGeV. the mean fluxes are 4.30 and 0.364 (in the unit of [LO! pph em7s ΕΠ]. their relative errors are The errors estimated here are similar to that found in the fourth paragraph.," In the 1–3 and 3–300 GeV, the mean fluxes are 4.30 and 0.364 (in the unit of $10^{-11}$ ph $^{-2}$ $^{-1}$ ]), their relative errors are The errors estimated here are similar to that found in the fourth paragraph."
 Comparing the input parameters. we find that the svstematic errors occur. especially for the flux in the 3GGeV energy range.," Comparing the input parameters, we find that the systematic errors occur, especially for the flux in the GeV energy range."
 Thev could be caused by that diffuse background source can not be described by a single power-law spectrum., They could be caused by that diffuse background source can not be described by a single power-law spectrum.
 Because the MC method can obtain the svstematic errors. we use this method to correct our results as follows: in the 13 and GGeV. the fhixes are 3.48+£0.36 ancl 0.380-E0.080 in unit of [10!! pph em7? !]). and the photon indexes are 3.0940.23 and 2.614 0.26 respectively. while the contribution to the EGB is (10.5zc1.1) V.naller than the result — ‘(he soft spectrum in GGeV is caused by the spectral broken of some sources. the photon index would not be extrapolated to lower energy range.," Because the MC method can obtain the systematic errors, we use this method to correct our results as follows: in the 1–3 and GeV, the fluxes are $\pm$ 0.36 and $\pm$ 0.080 (in unit of $10^{-11}$ ph $^{-2}$ $^{-1}$ ]), and the photon indexes are $\pm$ 0.23 and $\pm$ 0.26 respectively, while the contribution to the EGB is $\pm$ smaller than the result If the soft spectrum in GeV is caused by the spectral broken of some sources, the photon index would not be extrapolated to lower energy range."
 However. as long as the spectrum of stacked source is not harder than the EGB. the contribution to the EGD in GGeV will be larger than that in GGeV. Our result is compatible with the result because other point sources could contribute to the EGD.," However, as long as the spectrum of stacked source is not harder than the EGB, the contribution to the EGB in GeV will be larger than that in GeV. Our result is compatible with the result because other point sources could contribute to the EGB."
 In this letter. we introduce a new method of images stacking to directly study the contribution of undetected point sources to the EGB.," In this letter, we introduce a new method of images stacking to directly study the contribution of undetected point sources to the EGB."
 Our method is more direct than the nethods used by many authors., Our method is more direct than the methods used by many authors.
 Those methods involve the >-rav luminosity of undetectecd sources which is estimated through the properties of a few detected sources., Those methods involve the $\gamma$ -ray luminosity of undetected sources which is estimated through the properties of a few detected sources.
 They. include nany uncertainties and lead (he result to be questionable validity., They include many uncertainties and lead the result to be questionable validity.
 Applying our method. we find that the undetected sources in AT20G* can contribute (10.52c1.1) ," Applying our method, we find that the undetected sources in AT20G can contribute $\pm$ "
the width of the resonance as roughly estimated by equation (6)).,the width of the resonance as roughly estimated by equation \ref{dares}) ).
 To have crossed the 10:9 resonance. the satellite orbits must have expanded by —[(oa2/041)0—((t2/e1)109]F400km.," To have crossed the 10:9 resonance, the satellite orbits must have expanded by $\sim$$[(a_2/a_1)_0 - (a_2/a_1)_{10:9}]\,r \sim 400\km$."
 Since (his distance exceeds the radial width of the e ring (Arz60km). which we take to be the maximum length by which the ring-satellite svstem has expanded during its lifetime (but see also the last paragraph of this section). we conclude that the moons could not have crossed anv first-order resonance in the past.," Since this distance exceeds the radial width of the $\epsilon$ ring $\Delta r \approx 60 \km$ ), which we take to be the maximum length by which the ring-satellite system has expanded during its lifetime (but see also the last paragraph of this section), we conclude that the moons could not have crossed any first-order resonance in the past."
 This conclusion is consistent with Ophelia. the more massive of (he pair. currently possessing the greater orbital eccentricity of the two: repeated resonance crossines would predict the opposite to be true.," This conclusion is consistent with Ophelia, the more massive of the pair, currently possessing the greater orbital eccentricity of the two; repeated resonance crossings would predict the opposite to be true."
 In our view. Ophelia's aberrantly large eccentricity is primordial.," In our view, Ophelia's aberrantly large eccentricity is primordial."
 What about [uture crossines?, What about future crossings?
 The ratio of (ασαυ sits closest to. but does not overlap with. the 9:8 resonance: (a25/a4)os=1.08169+105.," The ratio of $(a_2/a_1)_0$ sits closest to, but does not overlap with, the 9:8 resonance: $(a_2/a_1)_{9:8} = 1.08169 \pm 10^{-6}$."
 The satellite orbits must diverge by another oese(raftaJor−≼⋝∩⊋∕∕∕∩↓∣⋟∣∣↴ ∣⋮↴∿↴≡↽⊰≤∐↘↽∐↓∣↽≻≼↲↓∪↕⋅≼↲↕⋅≼↲⋟∖⊽∪∐≀↧↴∐≺∢≼↲≼↲∐≺∢∪∏∐∥↲↕⋅⋅− ↴∏∐↲≼↲∏↲∐↥∖∖↽↕∐∣↽≻≼↲↥∪∐≸≟↕∐⊔∐↲∖∖⊽≀↧↴∐↕∐≸≟∶⊔∐↲∐∐∐↲∪↓⋟≼↲∐≺∢∪∏∐∩↲↕⋅∐≼↲⋟∖⊽≺↘⋝∕∩∶⋉∶≺↘⋝∩≝↘⋮⋉∕∕∕↙∎⇃↓↴∿↴ ∃⋗⋖−⊁∩↓⋡∖↽↕⋅↕∐⊔∐↲↓⋟∏⊓∐⋅≼↲⋅⋮⋡⋡↧⋝⋟∖⊽↕↕↥≸↽↔↴↕⋅≼↲↥≀↧↴∐∪↕↥⋟∖⊽≼⇂≼↲∏∏↲≺⇂∣↽≻⋡∖↽↻≼↲↕⋅∐↓∪⊔⋅⇀∖↕≀↧↴∐↥∪∏⋅≀↧↴⋅≪↽∖↽⇀∖↕⋯⋅↕⋅≀↧∶∖↽⊔≤∍⋖↽∖⋟∣⋖↽∖⋚∶ see their Appenclix B). we estimate the perturbation eccentricity alter resonance crossing {ο be on the order of 6x101 (= eqq as defined bv Dermott οἱ al.," The satellite orbits must diverge by another $\delta a_{9:8} \sim [(a_2/a_1)_{9:8} - (a_2/a_1)_0] \, r \sim 39 \km$ before resonance The event will be long in the waiting; the time of encounter lies $\delta t_{9:8} = \delta a_{9:8} / \dot{a}_1 \sim 2 \times 10^4\yr$ in the Using relations derived by Dermott, Malhotra, Murray (1988; see their Appendix B), we estimate the perturbation eccentricity after resonance crossing to be on the order of $6 \times 10^{-4}$ (= $e_{\rm crit}$ as defined by Dermott et al."
 1988)., 1988).
 This will be a minor perturbation for Ophelia but will be relatively significant lor Cordelia., This will be a minor perturbation for Ophelia but will be relatively significant for Cordelia.
 What about the e ring’s direct. ellects on satellite eccentricities?, What about the $\epsilon$ ring's direct effects on satellite eccentricities?
 Both first-order Corques and first-order Lindblad torques operate simultaneously in (he e ring system. resulting in eccentricity damping on a tünmescale (hat is 22 x greater than (hat. given by equation (11)) (GS; Goldreich Tremaine 1980).," Both first-order co-rotation torques and first-order Lindblad torques operate simultaneously in the $\epsilon$ ring system, resulting in eccentricity damping on a timescale that is 22 $\times$ greater than that given by equation \ref{mineedot}) ) (GS; Goldreich Tremaine 1980)."
 We estimate an exponential decay time [or the satellite eccentricity of ~3.6xLO’vr. much longer than either 0/54 or the likely age of the We note in passing (hat our expressions imply (hat (he e ring is a voung creation of the solar svstem.," We estimate an exponential decay time for the satellite eccentricity of $\sim$$3.6 \times 10^7\yr$, much longer than either $\delta t_{9:8}$ or the likely age of the We note in passing that our expressions imply that the $\epsilon$ ring is a young creation of the solar system."
" For the ring width to grow from Ar/2 to its current width of Ar would require of order oly,c0gr/Ong~3Xx10!vr."," For the ring width to grow from $\Delta r/2$ to its current width of $\Delta r$ would require of order $\delta t_{\Delta r} \sim \delta t_{9:8} \Delta r / \delta a_{9:8}
\sim 3 \times 10^4\yr$."
" Uf the viscous flux of angular momentunm across (he rine midlne were higher in (he past. we expect ον, to approximate well (he age of the ring."," If the viscous flux of angular momentum across the ring midline were higher in the past, we expect $\delta t_{\Delta r}$ to approximate well the age of the ring."
 Even if the viscous flux were (o remain constant at all stages of ring evolutionas might be expected if MvxX/r were conserved. where we have assumed (hat the rings vertical optical," Even if the viscous flux were to remain constant at all stages of ring evolution—as might be expected if $\Sigma \nu \propto \Sigma / \tau$ were conserved, where we have assumed that the ring's vertical optical"
D'Autona aud. Mazzitelli 1997)). aud the accretion rates have been scaled to these values. when necessary.,"D'Antona and Mazzitelli \cite{DM97}) ), and the accretion rates have been scaled to these values, when necessary."
 Note that we have plotted upper limits for oonlv for objects frou this paper., Note that we have plotted upper limits for only for objects from this paper.
 Both aand hhave large uncertainties. discussed ia detail. among others. by Muzerolle et al. (2003))," Both and have large uncertainties, discussed in detail, among others, by Muzerolle et al. \cite{Mea03}) )"
 and in this paper., and in this paper.
 There are. however. some clear treuds.," There are, however, some clear trends."
 First of all. Fig.," First of all, Fig."
 8 confirms. over a large range of masses. the treud already found by other authors (Muzerolle et al. 2003::," \ref{acc} confirms, over a large range of masses, the trend already found by other authors (Muzerolle et al. \cite{Mea03};"
 Rebull et al. 20003) , Rebull et al. \cite{Rea00}) )
of decreasing ffor decreasingAL., of decreasing for decreasing.
".. Tf for example. we compare the meclia ffor M,iU.1A, tto that in the mass interval 10.5AL... we find values of —31029 and ~105/yr.. respectively (ucelecting pper hits to YQ"," If, for example, we compare the median for $<$ 0.1 to that in the mass interval 1–0.3, we find values of $\sim 3\times 10^{-10}$ and $\sim 10^{-8}$, respectively (neglecting upper limits to )."
 Tt is unlikely that this ποια is caused by sensitivity limits., It is unlikely that this trend is caused by sensitivity limits.
" Although. as we will discuss in the following section. in many VLMOSs the accretion rate is close to the model seusitivitv. this is uot the case of TTS (see, e.g.àY Muzerolle et al. 2003))."," Although, as we will discuss in the following section, in many VLMOs the accretion rate is close to the model sensitivity, this is not the case of TTS (see, e.g., Muzerolle et al. \cite{Mea03}) ),"
 so that the correlation we find ueelecting upper limits is probably somewhat shallower than the true onc., so that the correlation we find neglecting upper limits is probably somewhat shallower than the true one.
 A second effect is clearly shown in Fig. 8..," A second effect is clearly shown in Fig. \ref{acc},"
 namely that the acerction rate. for the same mass of the ceutral object. is higher in vounger regions.," namely that the accretion rate, for the same mass of the central object, is higher in younger regions."
 The bbrown dwarfs have accretion rates of roughly 10.ο το19Af.fwr.s unore than an order of magnitude larger than most objects of similar mass in Taurus. Chamacleon aud IC 318.," The brown dwarfs have accretion rates of roughly $10^{-9}$ $10^{-10}$, more than an order of magnitude larger than most objects of similar mass in Taurus, Chamaeleon and IC 348."
 An age dependence of lis known in TTS TONSe Calvet ct al. 20003).," An age dependence of is known in TTS (e.g., Calvet et al. \cite{CHS00}) ),"
 and is sugeested for VELMOs iby the fact that the fraction of objectswith narrow pprofiles (non-accretors) is larger in older star forming reeions (Javawardana et al. 2002.. 2003b)).," and is suggested for VLMOs by the fact that the fraction of objectswith narrow profiles (non-accretors) is larger in older star forming regions (Jayawardana et al. \cite{Jay02}, \cite{Jay03b}) )."
 Our results confirm this trend: only (1: ont of 10) of the objects in our Cha I sample are accretiug: if we include also the Cónunez aud Pers (2001) VLMOs. then the fraction becomes (5 out of 18 objects}.," Our results confirm this trend: only (1 out of 10) of the objects in our Cha I sample are accreting; if we include also the Gómmez and Persi \cite{GP01}) ) VLMOs, then the fraction becomes (5 out of 18 objects)."
 The dependence of oon age makes it hard to determine the exact relationship of vvs. ffromi saauples where objects iu regions of very different age are collecte together. as in Fig. 8..," The dependence of on age makes it hard to determine the exact relationship of vs. from samples where objects in regions of very different age are collected together, as in Fig. \ref{acc}."
 For example. the BBD) population selected by Natta ct al. (2002))," For example, the BD population selected by Natta et al. \cite{Nea02}) )"
 is particularly voune. aud it would be interesting to compare their accretion rates to equally voung TTS inOph.. rather than to TTS in Taurus.," is particularly young, and it would be interesting to compare their accretion rates to equally young TTS in, rather than to TTS in Taurus."
 Also. there are a few VLMOs in Taurus. Cha I aud IC318 with very laree accretion rates. comparable or even higher than those of the VVLAIOs.," Also, there are a few VLMOs in Taurus, Cha I and IC348 with very large accretion rates, comparable or even higher than those of the VLMOs."
 Some of these estimates need to be coufirmed. and the possibility of having detected a flare ruled out.," Some of these estimates need to be confirmed, and the possibility of having detected a flare ruled out."
 Still. one wouclers if they could )o niuchi vounger than the average population of the star-forming region to which they helone.," Still, one wonders if they could be much younger than the average population of the star-forming region to which they belong."
 Tn spite of the large uncertainties that affect iudividual objects. these preliminary results show that it is now possible. with the advent of Sau class telescopes that eive access to the VLAIOs population. to quantify the dependence of OOL Nass and age. overcomune. due to the large range of tthat one can explore. the uncertamties of individual nieasurenaents.," In spite of the large uncertainties that affect individual objects, these preliminary results show that it is now possible, with the advent of 8-m class telescopes that give access to the VLMOs population, to quantify the dependence of on mass and age, overcoming, due to the large range of that one can explore, the uncertainties of individual measurements."
 For this oue needs Luger aud more homogeneous samples of stars (not only VLALOs but also TTS) iu a variety of star-forming regions., For this one needs larger and more homogeneous samples of stars (not only VLMOs but also TTS) in a variety of star-forming regions.
 Classical TTS show a clear correlation between accretion and the presence ofa circumstellar disk., Classical TTS show a clear correlation between accretion and the presence of a circumstellar disk.
 Disks are detected around a umber of VLAIOs.which show mid-infrared fluxes well iun excess of the plotospheric ones (¢.e.. Comeroun et al. 1998.. ," Disks are detected around a number of VLMOs,which show mid-infrared fluxes well in excess of the photospheric ones (e.g., Comerónn et al. \cite{Cea98}, ,"
Persi et al. 2000..," Persi et al. \cite{Pea00},"
 Douteimps oet, Bontemps et
based on a Bayesian maximum likelihood approach where the model consists of a periodic step function with period p. and m bins (labelled Toto j) of equal. duration. p/m (which can readily be generalised to unequal curation bins if necessary).,"based on a Bayesian maximum likelihood approach where the model consists of a periodic step function with period $p$, and $m$ bins (labelled $1$ to $j$ ) of equal duration $p/m$ (which can readily be generalised to unequal duration bins if necessary)."
" IZach. model is characterised by p. m. the epoch c which is equal to the time fat the start of the first bin) and the individual bin levels οτε,"," Each model is characterised by $p$, $m$, the epoch $e$ (which is equal to the time $t$ at the start of the first bin) and the individual bin levels $r_j$."
 Such a model is illustrated in Fig. L.., Such a model is illustrated in Fig. \ref{fig:glmod}.
 Phe repartition of the data points into the m bins is defined by: where j; is the number of the bin into which the 4 data point falls and int(r) is the largest integer less than or equal tour., The repartition of the data points into the $m$ bins is defined by: where $j_i$ is the number of the bin into which the $i^{\mathrm{th}}$ data point falls and $\mathrm{int}(x)$ is the largest integer less than or equal to $x$.
 For à given m. p and c. the contributions [rom all possible values for the individual bin levels rj are analytically integrated over.," For a given $m$, $p$ and $e$, the contributions from all possible values for the individual bin levels $r_j$ are analytically integrated over."
 Individual likelihoods are then computed. at each point in the (m.p.e) parameter space.," Individual likelihoods are then computed at each point in the $(m,p,e)$ parameter space."
 v marginalising over cach parameter in turn. one obtains a global posterior probability. for the entire family of periodic models.," By marginalising over each parameter in turn, one obtains a global posterior probability for the entire family of periodic models."
 Marginalising over a parameter @ consists of multiplving the (multi-dimensional) likelihood. function bv the (assumed) prior probability. distribution (Bayesian prior) for 8. then integrating over all values of 0.," Marginalising over a parameter $\theta$ consists of multiplying the (multi-dimensional) likelihood function by the (assumed) prior probability distribution (Bayesian prior) for $\theta$, then integrating over all values of $\theta$."
 This global posterior. probability can then be divided. bv. the equivalent probabilities for a constant and/or aperioclic model to give an odds ratio. which is greater than 1 if there is significant evidence for periodicity.," This global posterior probability can then be divided by the equivalent probabilities for a constant and/or aperiodic model to give an odds ratio, which is greater than $1$ if there is significant evidence for periodicity."
 H£ this is the case. à posterior probability. distribution for cach parameter 8 can be computed by marginalising the likelihood. function over all the other parameters.," If this is the case, a posterior probability distribution for each parameter $\theta$ can be computed by marginalising the likelihood function over all the other parameters."
 The best value of 8 is that which gives rise to the maximum in the 1-D posterior probability distribution for 6., The best value of $\theta$ is that which gives rise to the maximum in the 1-D posterior probability distribution for $\theta$.
 The interested reader is referred to 2 G99 for more details., The interested reader is referred to GL92 G99 for more details.
 We discuss in the next section how this approach can be modified. without loss of generality. to obviate the need for marginalising out. the m variables rj. corresponding to the values of cach model bin.," We discuss in the next section how this approach can be modified, without loss of generality, to obviate the need for marginalising out the $m$ variables $r_j$, corresponding to the values of each model bin."
 This in turn leads to a very simple transit. detection algorithm: for the special case of two discrete levels. of unequal duration. applicable to most eeneric transit. searches.," This in turn leads to a very simple transit detection algorithm for the special case of two discrete levels, of unequal duration, applicable to most generic transit searches."
 ὃν directlv maximising the likelihood. or in this case nüninising X7. for any generalised step-Dunction. model. it is straightforward to show that whatever the number and relative duration of the bins. the optimal value for the bin levels rj can be determined. directly. from the cata given the other model parameters p. m and e.," By directly maximising the likelihood, or in this case minimising $\chi^2$, for any generalised step-function model, it is straightforward to show that whatever the number and relative duration of the bins, the optimal value for the bin levels $r_j$ can be determined directly from the data given the other model parameters $p$, $m$ and $e$ ."
 IH we refer to the contribution [rom bin j to the overall X7 as we and define J as the ensemble of indices falling into bin j. we have: The value à; of the model level rj that mininises V5M is then simply given by the standard inverse variance-weighted mean of the data inside bin j. since by setting NSÜrj to zero we have: hence: Substituting into Iq. (5)).," If we refer to the contribution from bin $j$ to the overall $\chi^2$ as $\chi^2_j$, and define $J$ as the ensemble of indices falling into bin $j$, we have: The value $\widetilde{r_j}$ of the model level $r_j$ that minimises $\chi^2_j$ is then simply given by the standard inverse variance-weighted mean of the data inside bin $j$, since by setting $\partial \chi^2_j / \partial r_j$ to zero we have: hence: Substituting into Eq. \ref{eq:chi2j1}) ),"
 v now becomes: where 47κ denotes the minimised∢⋠⋠ value of⋅ yj.2 E, $\chi^2_j$ now becomes: where $\widetilde{\chi^2_j}$ denotes the minimised value of $\chi^2_j$.
HThe contribution from each of the m bins can be simplified. by expanding I5q. (8)):, The contribution from each of the $m$ bins can be simplified by expanding Eq. \ref{eq:chi2j2}) ):
 From I5q. (7)), From Eq. \ref{eq:dmj}) )
 we have: PESPhe overall minimised. 472 over all bins. is. thus: The first term in Eq. (13)), we have: so that: The overall minimised $\chi^2$ over all bins is thus: The first term in Eq. \ref{eq:chi2tot}) )
 is entirely. independent of the model. and hence stays constant. so that only the second term needs to be calculated foreach set of trial parameters.," is entirely independent of the model, and hence stays constant, so that only the second term needs to be calculated foreach set of trial parameters."
 The Gregory-Loredo method makes no assumptions about, The Gregory-Loredo method makes no assumptions about
"and W20 samples. respectively,","and K20 samples, respectively."
 At fainter inasuitudoes (Rapc 25). the BPZ method eives smaller scatter than the conventional \? minimization technique with uo priors.," At fainter magnitudes $R_{AB} > 25$ ), the BPZ method gives smaller scatter than the conventional $\chi^2$ minimization technique with no priors."
 The BPZ results are presented iu Figure 1., The BPZ results are presented in Figure 1.
 The agreeineut between the photometric aud spectroscopic redshifts is excellent. with median offset (A)—0.01.," The agreement between the photometric and spectroscopic redshifts is excellent, with median offset $\langle \Delta \rangle = -0.01$."
 There is uo substantial trend in (A> with redshift. except perhaps for a slight tendency for the photometric redshifts to be underestimated at z21.3.," There is no substantial trend in $\langle \Delta \rangle$ with redshift, except perhaps for a slight tendency for the photometric redshifts to be underestimated at $z > 1.3$."
 The values are all based ou a total of 133 ealaxies in I20 (270) and FORS2 (163). with the object at 2=2.8 excluded (see. 1.25).," The values are all based on a total of 433 galaxies in K20 (270) and FORS2 (163), with the object at $z=2.8$ excluded (see 4.2b)."
 For redshifts estimated with Bayesian priors. we find that the fraction of catastrophic outliers. jj. ranges from 0.02 to 0.10. depending on the subsample cousidered.," For redshifts estimated with Bayesian priors, we find that the fraction of catastrophic outliers, $\eta$, ranges from 0.024 to 0.10, depending on the subsample considered."
" As describedL in tez (2000). the value of the ODDS paramcter is a reasonable iudicator of the reliability of the plotometric redshift. galaxies with larger ODDS values have a smaller rate of outliers,"," As described in tez (2000), the value of the ODDS parameter is a reasonable indicator of the reliability of the photometric redshift, galaxies with larger ODDS values have a smaller rate of outliers."
 We lave measured o(A) using only galaxies with [A|<02 (ie. excluding the outlicrs). and find 0.019 (FORS2) and 0.016 (IS20) from the DPZ method.," We have measured $\sigma (\Delta)$ using only galaxies with $|\Delta | < 0.2$ (i.e., excluding the outliers), and find 0.049 (FORS2) and 0.046 (K20) from the BPZ method."
 The outlierclippedries is simular when using the conveutional \? method without priors. but the failure rate. jg. from this method is much larger.," The outlier–clipped is similar when using the conventional $\chi^2$ method without priors, but the failure rate, $\eta$, from this method is much larger."
 We have estimated redshifts using different colmbinations of the available photometric data in CDF-S. aud find no significant differcuces in the 6(AÀ) values.," We have estimated redshifts using different combinations of the available photometric data in CDF-S, and find no significant differences in the $\sigma (\Delta)$ values."
 Iu particular. we have compared the performance with and without using the ACS photometry. aud found uo significant differcuce in the overall result.," In particular, we have compared the performance with and without using the ACS photometry, and found no significant difference in the overall result."
 The deep ACS photometry. however. may well be important at fainter magnitudes. bevoud the μπιτς of the spectroscopic sample.," The deep ACS photometry, however, may well be important at fainter magnitudes, beyond the limits of the spectroscopic sample."
 of the FORS2 galaxies. and of the N20 galaxies. are undetected (< 30) in the relatively shallow WFIU or U' mages.," of the FORS2 galaxies, and of the K20 galaxies, are undetected $< 3\sigma$ ) in the relatively shallow WFI$U$ or $U'$ images."
 However. we fiud no significant difference in A values for galaxies with aud without C/U' detections down to the spectroscopic magnitude luit (crosses i Figure 1).," However, we find no significant difference in $\Delta$ values for galaxies with and without $U/U'$ detections down to the spectroscopic magnitude limit (crosses in Figure 1)."
 We have also estimated plotometric redshifts using the WEI and SOFT data alone. which cover a wider CDFS area. Óucludius areas not imaged by ACS.," We have also estimated photometric redshifts using the WFI and SOFI data alone, which cover a wider CDF–S area, including areas not imaged by ACS."
 We measure GUA)—01 (for ap< 25)., We measure $\sigma (\Delta) = 0.11$ (for $R_{AB} < 25$ ).
" Figure 2 plots the redshift errors A versus calaxy magnitudes in the R and A, bauds.", Figure 2 plots the redshift errors $\Delta$ versus galaxy magnitudes in the $R$ and $K_s$ bands.
" There is no strong trend in 6A) with magnitude. except at the faintest A, band limits. A,z22.5."," There is no strong trend in $\sigma(\Delta)$ with magnitude, except at the faintest $K_s$ --band limits, $K_s \gtrsim 22.5$."
" The outlier fraction j increases from 0.03 (A, 20) to 0.05 (20<AY« 22) to O11 (22«NK, 21).", The outlier fraction $\eta$ increases from 0.03 $K_s < 20$ ) to 0.05 $20 < K_s < 22$ ) to 0.11 $22 < K_s < 24$ ).
" The photometric redshifts are also. on average. slightly unuderestinated for A,>22."," The photometric redshifts are also, on average, slightly underestimated for $K_s > 22$."
" At these faint magnitudes. πας of the galaxies are only poorly detected. if at all. iu the widefeld (but relatively shallow) SOFI JIT, images. causing au increase in redshift errors."," At these faint magnitudes, many of the galaxies are only poorly detected, if at all, in the wide–field (but relatively shallow) SOFI $JHK_s$ images, causing an increase in redshift errors."
 Results from Table 1 indicate that the photometric redshift) performance is correlated with the ODDS piuuueter. aud is better for higher ODDS values (ODDS > 0.99).," Results from Table 1 indicate that the photometric redshift performance is correlated with the ODDS parameter, and is better for higher ODDS values (ODDS $>$ 0.99)."
 It is important to remember that the galaxies in the spectroscopic sample are relatively bright compared to the large majority of objects in the GOODS fields., It is important to remember that the galaxies in the spectroscopic sample are relatively bright compared to the large majority of objects in the GOODS fields.
 The ODDS parameter. perhaps combined with other indicators. (c.@.. the nuniber of passbauds in which the ealaxv is significantly detected: availability of C-baud and near-IR data: the width of the redshift probability distribution). offers a useful metric for the likely reliability of photometric redshifts at maguitudes fainter than the Iuuit of our spectroscopic test sample.," The ODDS parameter, perhaps combined with other indicators, (e.g., the number of passbands in which the galaxy is significantly detected; availability of $U$ -band and near-IR data; the width of the redshift probability distribution), offers a useful metric for the likely reliability of photometric redshifts at magnitudes fainter than the limit of our spectroscopic test sample."
 One of the main aims of the GOODS project is to identify aud study different populations of galaxies. such as EROs and ACNs.," One of the main aims of the GOODS project is to identify and study different populations of galaxies, such as EROs and AGNs."
 Iu tlis section we carry out au analysis of the reliability of photometric redshifts to these objects. , In this section we carry out an analysis of the reliability of photometric redshifts to these objects. —
The GOODS ERO sample is selected. to have (RoWap>3.35 and is complete to A4p<22 mae., The GOODS ERO sample is selected to have $(R-K)_{AB} > 3.35$ and is complete to $K_{AB} < 22$ mag.
 A total of 66 EROs have spectroscopic redshifts iu the combined FORS2 (36) aud EK20 (30) samples., A total of 66 EROs have spectroscopic redshifts in the combined FORS2 (36) and K20 (30) samples.
 Figure 3a compares the photometric and spectroscopic redshifts for EROs., Figure 3a compares the photometric and spectroscopic redshifts for EROs.
 There is an excellent agreecineut. with G(A)=0.051. and is equally good for objects classified as absorption and cussion line systems.," There is an excellent agreement, with $\sigma (\Delta) = 0.051$, and is equally good for objects classified as absorption and emission line systems."
 Furthermore. we find a very small fraction of outliers (4=3%).," Furthermore, we find a very small fraction of outliers $\eta =3\%$ )."
 This performance is significautlybetter than that for the ealaxy sample as a whole., This performance is significantly than that for the galaxy sample as a whole.
 This may not be surprising: m eoncral. red galaxies have strouger features in their broad baud spectral αισον distributions (breaks. curvature) than do blue ones.," This may not be surprising: in general, red galaxies have stronger features in their broad band spectral energy distributions (breaks, curvature) than do blue ones."
 However. it is a τον helpful result. because EROs are amoung the most dificult galaxies for spectroscopic observations.," However, it is a very helpful result, because EROs are among the most difficult galaxies for spectroscopic observations."
 The ERO population is kuown to consist of high redshift (2~ 1) ellipticals and dusty starbursts (Cimatti ct al 2002c)., The ERO population is known to consist of high redshift $z\sim 1$ ) ellipticals and dusty starbursts (Cimatti et al 2002c).
 Tlowever. the starburst ealaxy templates frou Iiuuev et al (1996) that are used for photometric redshift estimation are uot significantly reddened. aud certainly do not match the colors of EROs.," However, the starburst galaxy templates from Kinney et al (1996) that are used for photometric redshift estimation are not significantly reddened, and certainly do not match the colors of EROs."
 Photometric redshifts for the majority of the EROs. therefore. are derived from the elliptical ealaxy spectral template. regardless of the true nature of the ealaxics.," Photometric redshifts for the majority of the EROs, therefore, are derived from the elliptical galaxy spectral template, regardless of the true nature of the galaxies."
 Moustakas et ((2003) fiud that —10:4 of the GOODS EROs are morphologically carlytype galaxies: the rest are either disk galaxies or regular svstenis., Moustakas et (2003) find that $\sim 40\%$ of the GOODS EROs are morphologically early–type galaxies; the rest are either disk galaxies or irregular systems.
 However. they also find that the broad baud SEDs of the EROs in differeut morphological subclasses are virtually iudistinguishable.," However, they also find that the broad band SEDs of the EROs in different morphological subclasses are virtually indistinguishable."
 Thus. we expect comparably eood photometric redshift estimates for most EROs. regardless of their intrinsic nature. ," Thus, we expect comparably good photometric redshift estimates for most EROs, regardless of their intrinsic nature. —"
158 galaxies in the spectroscopic N20 (31) and FORS2 (17) samples have N-vav detection (Alexander et al 2003)., 48 galaxies in the spectroscopic K20 (31) and FORS2 (17) samples have X-ray detection (Alexander et al 2003).
 Figure 3b compares photometric and spectroscopic redshifts for these N-ray sources., Figure 3b compares photometric and spectroscopic redshifts for these X-ray sources.
 The scatter. excluding the object at 2.8. which is confirmed to be a QSO. is ofA)=0.101. with an oulicr fraction of ;j=0.11.," The scatter, excluding the object at $z=2.8$, which is confirmed to be a QSO, is $\sigma (\Delta) = 0.104$, with an oulier fraction of $\eta = 0.11$."
 Excluding the five outliers reduces the scatter to a(A)=0.012., Excluding the five outliers reduces the scatter to $\sigma (\Delta) = 0.042$.
 The majority of the N-ray sources at higher redshifts here are ACNs although some are likely to be X-ray starbursts., The majority of the X-ray sources at higher redshifts here are AGNs although some are likely to be X-ray starbursts.
 Six of these sources are spectroscopically confirmed as ACGNs (crosses in Figure 3b)., Six of these sources are spectroscopically confirmed as AGNs (crosses in Figure 3b).
 The scatter aud the outlier fraction for the N-rayv sources (Le. ACUNS). is similar to that for normal galaxies in Fieure 1.," The scatter and the outlier fraction for the X-ray sources (i.e. AGNs), is similar to that for normal galaxies in Figure 1."
 We tried using an independent set of observed ACN SEDs as templates. but did not significantly: improve c(A).," We tried using an independent set of observed AGN SEDs as templates, but did not significantly improve $\sigma(\Delta)$ ."
 Using the conventional 47 method without priors increases o(A) value to 0.13., Using the conventional $\chi^2$ method without priors increases $\sigma (\Delta)$ value to 0.43.
 Combining iuultisvaveband ground-based and ACS photometric data (with up to 18 photometric passbauds per object). we have estimated photometric redshüfts for," Combining multi-waveband ground-based and ACS photometric data (with up to 18 photometric passbands per object), we have estimated photometric redshifts for"
"tensor M;(x.x"")=(Bji(x)Bj(x') is frequently used for which this translational invariances to For homogeneous and isotropic magnetic turbulence the translationally invariant magnetic correlation tensor can be written as with the longitudinal. normal and helical spectra denoted by MG). Myr) and Λη) respectively.","tensor $M_{ij}(\fe{x},\fe{x}')=\langle B_{i}(\fe{x})B_{j}(\fe{x}')\rangle$ is frequently used for which this translational invariance leads to 			For homogeneous and isotropic magnetic turbulence the translationally invariant magnetic correlation tensor can be written as 			with the longitudinal, normal and helical spectra denoted by $M_{L}(r)$ , $M_{N}(r)$ and $M_{H}(r)$ respectively."
 The solenoidal condition V-B=0 enables connection of the two non-helical spectra by My)=thexΜΟΥ)., The solenoidal condition $\nabla\cdot\fe{B}=0$ enables the connection of the two non-helical spectra by $M_{N}(r)=\frac{1}{2r}\frac{d}{dr}\big(r^2M_{L}(r)\big)$.
 By applying a Fourier transformation. we obtain: In this case. the condition V-B.=0 was used directly in the form k;M¥;;(k)=0 to reduce the degrees of freedom to the normal and the helical spectra.," 			By applying a Fourier transformation, we obtain: 			In this case, the condition $\nabla\cdot\fe{B}=0$ was used directly in the form $k_{i}\hat{M}_{ij}(\fe{k})=0$ to reduce the degrees of freedom to the normal and the helical spectra."
 These two functions are specified in terms of their real space counterparts as Some interesting properties are: The magnetic correlation tensor is closely related to the energy spectrum of the magnetic field., These two functions are specified in terms of their real space counterparts as 			Some interesting properties are: 			The magnetic correlation tensor is closely related to the energy spectrum of the magnetic field.
 The field’s mean energy density can be expressed as follows In this case. we have used M;(&)=2My and ep(k) denotes the 1D-energy density of B.," The field's mean energy density can be expressed as follows 			In this case, we have used $M_{ii}(k)= 2 M_{N}$ and $\epsilon_{B}(k)$ denotes the 1D-energy density of $\fe{B}$ ."
 From this we derive which is used in the following to replace My(k) by the more commonly applied magnetic energy spectrum., 			From this we derive 			which is used in the following to replace $M_{N}(k)$ by the more commonly applied magnetic energy spectrum.
" Analogously to (14)). we can relate the helical part of the spectrum A(k) to the mean j-B and deduce a ID-helical energy density ει): We can read off the 1D-heltcal energy density €,(4) which also can be used to substitute F(K): Nevertheless. in our calculations we want to relate to the helicity spectrum Rik) rather then to the current helicity spectrum ΕΙ) since it is the helicity B-A that usually is the subject of magnetohydrodynamies and dynamo theory."," 			 			Analogously to \ref{al:dens}) ), we can relate the helical part of the spectrum $\hat{H}(k)$ to the mean $\fe{j} \cdot \fe{B}$ and deduce a 1D-helical energy density $\epsilon_{H}(k)$: 			We can read off the 1D-helical energy density $\epsilon_{H}(k)$ which also can be used to substitute $H(k)$: 			 			Nevertheless, in our calculations we want to relate to the helicity spectrum $\hat{R}(k)$ rather then to the current helicity spectrum $\hat{H}(k)$ since it is the helicity $\fe{B} \cdot \fe{A}$ that usually is the subject of magnetohydrodynamics and dynamo theory."
 for isotropic. turbulent fields the current helicity and the magnetic helicity B-A are closely connected.," 			 			Fortunately, for isotropic, turbulent fields the current helicity and the magnetic helicity $\fe{B} \cdot \fe{A}$ are closely connected."
 Since the current helicity (VxB)-B has the same mathematical structure as the helicity (VΧΑ):A. we can perform exactly the same derivation as in (16)) to show that the mean helicity relates to the helicity spectrum RUD) of the correlation tensor for the vector potential in the same way as the mean current helicity relates to the current helicity spectrum of the magnetic correlation. tensor.," Since the current helicity $(\nabla \times \fe{B}) \cdot \fe{B}$ has the same mathematical structure as the helicity $(\nabla \times \fe{A}) \cdot \fe{A}$, we can perform exactly the same derivation as in \ref{curhel}) ) to show that the mean helicity relates to the helicity spectrum $\hat{R}(k)$ of the correlation tensor for the vector potential in the same way as the mean current helicity relates to the current helicity spectrum of the magnetic correlation tensor."
 We can construct the correlation. tensor (A(GOA(x')) for the magnetic vector potential A similar to the magnetic correlation. tensor., 			We can construct the correlation tensor $\langle \fe{A}(\fe{x})\fe{A}^*(\fe{x}') \rangle$ for the magnetic vector potential $\fe{A}$ similar to the magnetic correlation tensor.
 If we assume translational invariance for the statistics and apply the Lorenz gauge condition V-A=0 to the vector potential. all deductions made for the magnetic correlation tensor will also hold for the correlation tensor of the vector potential.," If we assume translational invariance for the statistics and apply the Lorenz gauge condition $\nabla\cdot\fe{A}=0$ to the vector potential, all deductions made for the magnetic correlation tensor will also hold for the correlation tensor of the vector potential."
 In Fourier space it will have the form: From here we can start by rewriting the magnetic correlation tensor in terms of thecorrelation tensor for the vector potential: If wenow perfom a Fourier transformation on both sides and furthermore apply the condition for translational invariance (6)) we get: Thus. we find Using," In Fourier space it will have the form: 			From here we can start by rewriting the magnetic correlation tensor in terms of thecorrelation tensor for the vector potential: 			If wenow perfom a Fourier transformation on both sides and furthermore apply the condition for translational invariance \ref{transcon}) ) we get: 			Thus, we find 			Using"
PROS software package.,PROS software package.
 X-ray contours overlaid onto the It-band optical image are shown in Figure 1., X-ray contours overlaid onto the R-band optical image are shown in Figure 1.
 “Pwo fainter point objects about 4 ancl 10 aresec away from RA 1334.2|3759 are seen on the overlay., Two fainter point objects about 4 and 10 arcsec away from RX J1334.2+3759 are seen on the overlay.
 Ehe Ro magnitudes of these objects are ~22.3 (nearest: hereafter.object A) and ~22.9 (object D) estimated from the It band image ancl known t magnitude of RX J1334.2|3759., The R magnitudes of these objects are $\sim22.3$ (nearest; hereafterobject A) and $\sim22.9$ (object B) estimated from the R band image and known R magnitude of RX J1334.2+3759.
 Object. D is unlikely to » the optical counterpart of the X-ray source because of its distance from the X-ray peak., Object B is unlikely to be the optical counterpart of the X-ray source because of its distance from the X-ray peak.
 On the other hand. object A is unresolved and could contribute the X-ray intensity.," On the other hand, object A is unresolved and could contribute the X-ray intensity."
 In order o investigate the amount of X-ray emission from the object A. we caleulate the ratio of soft. X-ray to I-band Huss... or 22 OSOs including RA J1334.2|3759. al.which are within a circle of radius 15 arcmin (Dewangan 2001).," In order to investigate the amount of X-ray emission from the object A, we calculate the ratio of soft X-ray to R-band $\frac{f_{X}}{f_{R}}$, for 22 QSOs including RX J1334.2+3759, which are within a circle of radius 15 arcmin (Dewangan 2001)."
 The Εις ratios were calculated using the relation where my is the R-banc magnitude., The flux ratios were calculated using the relation where $m_{R}$ is the R-band magnitude.
 The soft. X-ray Iluxes of all the QSOs have been derived from the ROSAT PSPC observation of 1991 listed in Table 2 (Dewangan 2001)., The soft X-ray fluxes of all the QSOs have been derived from the $ROSAT$ PSPC observation of 1991 listed in Table 2 (Dewangan 2001).
 Phe ratio. A for the QSOs ranges [rom 0.003 to 0.040 with a mean value of 0.014+0.010.," The ratio, $\frac{f_{X}}{f_{R}}$, for the QSOs ranges from 0.003 to 0.040 with a mean value of $0.014\pm0.010$."
 A we assume the object A to be the counterpart ofthe X-ray source. then the ratlo is estimated to be ~0.20 for A. A comparison of this X)ratio with that obtained for the QSOs shows that A for the object A is much higher than that for the QSOs.," If we assume the object A to be the counterpart of the X-ray source, then the ratio $\frac{f_{X}}{f_{R}}$ ) is estimated to be $\sim0.20$ for A. A comparison of this ratio with that obtained for the QSOs shows that $\frac{f_{X}}{f_{R}}$ for the object A is much higher than that for the QSOs."
 Llowever. or RX J1334.2|3759 is 0.017 which is similar to that of ~other QSOs.," However, $\frac{f_{X}}{f_{R}}$ for RX J1334.2+3759 is 0.017 which is similar to that of other QSOs."
 LE the objec AX ds also similar to 16 QSOs. the contribution of this source to the total X-ray emission is expected to be ~7," If the object A is also similar to the QSOs, the contribution of this source to the total X-ray emission is expected to be $\sim7\%$."
 The total source. counts for RX 1334.2|3759 were obtained from the unsmoothecl PSPC images using a circle ol radius of 1.G centered on the peak position. and after subtracting the background. estimated. from five nearby . . . . µη ⋅ ≼⇍↓↓⋅≼∼⊔↓⋜⊔⋅↓⋅⋖⋅⋏∙≟↓∪⊔⊳∖∖∖⊽↓∣↓↕↿↓↕⋖⋅↓↓⋅≼∼∢⊾⊔⇂↓⋅∢⋅⊳∖∿⋀⋅∪⋜↧∖∖⊽⋜↧∙∖⇁⇂↓⋅∪⊔↓↿↓↥⋖⊾ source.," The total source counts for RX J1334.2+3759 were obtained from the unsmoothed PSPC images using a circle of radius of $1.6\arcmin$ centered on the peak position, and after subtracting the background estimated from five nearby circular regions with their centres $\sim7.0\arcmin$ away from the source."
" This was done using the select program in. the I""FOOLS (version 5.0) software package.", This was done using the $xselect$ program in the FTOOLS (version 5.0) software package.
" The LURE count rate for RN 1334.2|3759 was extracted. [rom a circle o£ radius 25"" centered on the peak position. after subtracting the background. estimated from an annulus of width 1.5’ with the same centre anc with an inner circle radius of 2"," The HRI count rate for RX J1334.2+3759 was extracted from a circle of radius $25\arcsec$ centered on the peak position, after subtracting the background estimated from an annulus of width $1.5\arcmin$ with the same centre and with an inner circle radius of $2\arcmin$."
 The count rates thus estimated are given in Table 2, The count rates thus estimated are given in Table 2.
 In order to investigate the time variability of soft. X-ray emission from RN J1334.2|3759. we have extracted. the light curves [rom the ΟΣΕ PSPC observations.," In order to investigate the time variability of soft X-ray emission from RX J1334.2+3759, we have extracted the light curves from the $ROSAT$ PSPC observations."
" The ligh curves for the source and. the background: were extractec using the ""xselect package in the PSPC energy. band. of 0.12.4 keV containing all the N-rav. photons falling within ""good time intervals”."," The light curves for the source and the background were extracted using the `xselect' package in the PSPC energy band of 0.1–2.4 keV containing all the X-ray photons falling within “good time intervals""."
 The time bin sizes are 500 s so tha on an average cach bin has 10 counts., The time bin sizes are 500 s so that on an average each bin has $\sim10$ counts.
 The source regions and the background regions were the same as describe above., The source regions and the background regions were the same as described above.
 I was found that the background was highly variable during the observation of 1993. June 19., It was found that the background was highly variable during the observation of 1993 June 19.
 Vherefore. the ieht curve of RN JI884.2|3759 obtained [from the 1993 observation is not suitable for variability stuclies.," Therefore, the light curve of RX J1334.2+3759 obtained from the 1993 observation is not suitable for variability studies."
 During he observation of 19901 June 23. the backeround was reasonably constant.," During the observation of 1991 June 23, the background was reasonably constant."
 A constant count rate [it to the xwkeround light curve gives the best-fit minimum. value of A7=73.54 for 75 degrees of freedom., A constant count rate fit to the background light curve gives the best-fit minimum value of $\chi^{2}=73.54$ for 75 degrees of freedom.
 The backegroun subtractions were carried out after appropriately scaling the xckeround light curve to have the same area as the source extraction area., The background subtractions were carried out after appropriately scaling the background light curve to have the same area as the source extraction area.
 The background subtracted light. curve of UN J1334.2|3759 and the background light curve are shown in Figure 2., The background subtracted light curve of RX J1334.2+3759 and the background light curve are shown in Figure 2.
 X remarkable variability in the soft. X-ray [lux rom RN J1334.2|3759can be seen in Fig., A remarkable variability in the soft X-ray flux from RX J1334.2+3759can be seen in Fig.
 2, 2.
 A constan count rate fit to the light curve of RX 1334.2|3759. gives minimum. value of X7 of 154.6 for 75 degrees of [reedom., A constant count rate fit to the light curve of RX J1334.2+3759 gives minimum value of $\chi^{2}$ of $154.6$ for $75$ degrees of freedom.
 X- emission from RX 1334.2|3759 changedby a factor of ~2 on time scales of 20)0040000 s., X-ray emission from RX J1334.2+3759 changedby a factor of $\sim2$ on time scales of $20000-40000{\rm ~s}$ .
 Variability on shorter time scales is also observed. on several occasions. notably at the beginning of the observation. alter ~200000 s. and after ~240000s.," Variability on shorter time scales is also observed on several occasions notably at the beginning of the observation, after $\sim200000{\rm~s}$ , and after $\sim240000{\rm~s}$ ."
 The most significant and extreme, The most significant and extreme
66110 is a. elobular cluster near the center of the Galaxy. at a distance of kkpce and reddeued by E(BWV)=L0 (Ortolani et 11991).,"6440 is a globular cluster near the center of the Galaxy, at a distance of kpc and reddened by $E(B-V)=1.0$ (Ortolani et 1994)."
 A bright Noa source was detected near this cluster with OSO-7 aud with UITURU from 1971 December 17 to 1972 Jaunary 2] (Markert et 11975. Forman et 11976).," A bright X-ray source was detected near this cluster with OSO-7 and with UHURU from 1971 December 17 to 1972 January 21 (Markert et 1975, Forman et 1976)."
 UIIURU observations obtained before 1971 Oct 23 aud after 1972 Alar 1 did not detect the source (Forman et 11976)., UHURU observations obtained before 1971 Oct 23 and after 1972 Mar 1 did not detect the source (Forman et 1976).
 During the outburst the trausicnt X-rav source had a virtually coustant Iuuinositv of about 3«LOeres+. iu the kkeV baud.," During the outburst the transient X-ray source had a virtually constant luminosity of about $3\times 10^{37}\ergs$, in the keV band."
 Before aud after the outburst the flux was less thaw oof this. (, Before and after the outburst the flux was less than of this. (
We use the conversion of UIIURU ctss1! to flux given by Bradt AMeClintocl: 1983: and the absorption cobluunu Vy6.9«T0?enn.2 determined by im t Zand et 11999.),We use the conversion of UHURU $\cts$ to flux given by Bradt McClintock 1983; and the absorption column $N_H=6.9\times10^{21}\cmsq$ determined by in 't Zand et 1999.)
 A dim source was detected iu the core of 66110 with the Einstein satellite. aud again with ROSAT. at a luninositv of ~LOores+t. in the kkeV band (Mertz CCwindlay 1983: Johuston et 11995): after conversion to the kkeV band. this correspouds to ας10! of the outburst flux.," A dim source was detected in the core of 6440 with the Einstein satellite, and again with ROSAT, at a luminosity of $\sim10^{33}\ergs$, in the keV band (Hertz Grindlay 1983; Johnston et 1995); after conversion to the keV band, this corresponds to $\ltap 10^{-4}$ of the outburst flux."
 Ou 1998 Aueust 22 a bright trausieut source appeared again in 66110. observed with BeppoSAX.," On 1998 August 22 a bright transient source appeared again in 6440, observed with BeppoSAX."
 The position coincides with the globular cluster within the accuracy of WU., The position coincides with the globular cluster within the accuracy of $'$.
" This time the outburst lasted rather shorter: the source had a Iuninositv of 6.0«10°%erest on Ang 22, 3.6\10°%eres ton Ang 26. aud <10Serest ou sep 1. in the kkeV. baud (n t Zand et 11999. also see rofxeur))."," This time the outburst lasted rather shorter: the source had a luminosity of $6.0\times 10^{36}\ergs$ on Aug 22, $3.6\times 10^{36}\ergs$ on Aug 26, and $< 10^{36}\ergs$ on Sep 1, in the keV band (in 't Zand et 1999, also see \\ref{xcur}) )."
 Like persistcut xieht N-rav sources. ransicuts occur more often in globular clusters per uut of stellar ass than iu the ealactic disk.," Like persistent bright X-ray sources, transients occur more often in globular clusters per unit of stellar mass than in the galactic disk."
 To nuuderstaud this overabundance one would like to study these sources at optical aud ultraviolet waveleugths., To understand this overabundance one would like to study these sources at optical and ultraviolet wavelengths.
 So far. uo trausieut N-ray source in a elobular cluster has been optically identified.," So far, no transient X-ray source in a globular cluster has been optically identified."
 Such identification is difficult because the relatively large error circle of the X-ray position contaius a lavee umber of stars., Such identification is difficult because the relatively large error circle of the X-ray position contains a large number of stars.
 We therefore obtained a ROSAT IIRI observation as soon as possible after the detection of he transient with DeppoSAX. in the hope of improving he Nav position.," We therefore obtained a ROSAT HRI observation as soon as possible after the detection of the transient with BeppoSAX, in the hope of improving the X-ray position."
 The optical brightuess of soft N-rav rausicuts is known to vary in fanden with the N-ray muinosity (for a review. see CChen et 11997).," The optical brightness of soft X-ray transients is known to vary in tandem with the X-ray luminosity (for a review, see Chen et 1997)."
 We therefore obtained optical images of 66110. to ook for objects that vary in tandem with the N-ray fux. in the hope of ideutifvine the optical counterpart of the ransicut.," We therefore obtained optical images of 6440 to look for objects that vary in tandem with the X-ray flux, in the hope of identifying the optical counterpart of the transient."
 Iu 22 we describe the results of the new ROSAT IRI observation. auc also analyse archival ROSAT data of 66110.," In 2 we describe the results of the new ROSAT HRI observation, and also analyse archival ROSAT data of 6440."
 Tn 33 we describe the optical, In 3 we describe the optical
a [ew percent longer than the orbital periods (Warner 1995). so à Pay  1.50 h is expected.,"a few percent longer than the orbital periods (Warner 1995), so a $P_{orb}$ $\sim$ 1.50 h is expected."
 No spectroscopic or photometric periods in quiescence have hitherto been obtained., No spectroscopic or photometric periods in quiescence have hitherto been obtained.
 We observed “PY Cry at minimum light in the hope of detecting an orbital modulation., We observed TV Crv at minimum light in the hope of detecting an orbital modulation.
 Our observations are isted in Table 1., Our observations are listed in Table 1.
 Having found a clear orbital modulation on the first night. we observed on the second. night for just sullicient time to include another orbital hump.," Having found a clear orbital modulation on the first night, we observed on the second night for just sufficient time to include another orbital hump."
 Phe double 1uniped. profile of the light curve puts a great deal of power into the first harmonic. which has three aliases in the ET: we use these to find three possibilities for the fundamental »eriod: 1.414. 1.4361 and 1.512 h. In addition. there are three aliases at the fundamental itself. at 1.506. 1.617 and. 1.747 i. Knowing the superhumyp period. enables: unambiguous selection of δν = 1.509 h from this suite.," The double humped profile of the light curve puts a great deal of power into the first harmonic, which has three aliases in the FT; we use these to find three possibilities for the fundamental period: 1.414, 1.461 and 1.512 h. In addition, there are three aliases at the fundamental itself, at 1.506, 1.617 and 1.747 h. Knowing the superhump period enables unambiguous selection of $P_{orb}$ = 1.509 h from this suite."
 Phe ephemoeris or times of maxima is given by In Fig., The ephemeris for times of maxima is given by In Fig.
 S we show the mean light curve. co-adcded. at the orbital period.," \ref{lctvcrv} we show the mean light curve, co-added at the orbital period."
 The range of the orbital modulation is 0.2 mag., The range of the orbital modulation is 0.2 mag.
" The superhump excess (2a,Porn) D, = 0.034. and the beat period. £7, = (dDa) += 1.9 d. These values are similar to those of other SU UMa stars with orbital periods near 1.5 h (Warner 1995)."," The superhump excess $P_{sh} - P_{orb}$ $P_{orb}$ = 0.034, and the beat period $P_b$ = $P_{orb}^{-1} - P_{sh}^{-1}$ $^{-1}$ = 1.9 d. These values are similar to those of other SU UMa stars with orbital periods near 1.5 h (Warner 1995)."
 Nova Coronae Austrinac was discovered on objective prism plates in June 1967 and was very poorly observed., Nova Coronae Austrinae was discovered on objective prism plates in June 1967 and was very poorly observed.
 Downes et al. (, Downes et al. (
2001) give a magnitude of 17.6 at quiescence. measured on aJ plate.,"2001) give a magnitude of 17.6 at quiescence, measured on a J plate."
 No observations of V655 CrA at quiescence have previously been reported: our photometric runs are listed in ‘Table 1., No observations of V655 CrA at quiescence have previously been reported; our photometric runs are listed in Table 1.
 A CCD frame of the vicinity of W655 Cra is illustrated in Fig. 9:, A CCD frame of the vicinity of V655 CrA is illustrated in Fig. \ref{fcv655cra};
 this shows that the nova remnant. is a member of a close triplet of stars., this shows that the nova remnant is a member of a close triplet of stars.
 The star that we have found to be variable is marked., The star that we have found to be variable is marked.
 The light curves of V655 CrX are displaved in Fig. 10.., The light curves of V655 CrA are displayed in Fig. \ref{lcv655cra}.
 ‘There are large variations around a mean magnitude of 17.6., There are large variations around a mean magnitude of 17.6.
 Although there are clearly preferred. time scales associated with the variations. we find nothing in the bls indicative of repetitive modulations | às we added more data. the EE changed in character and in the positions of the principal peaks.," Although there are clearly preferred time scales associated with the variations, we find nothing in the FTs indicative of repetitive modulations – as we added more data, the FT changed in character and in the positions of the principal peaks."
 CP Cru was Nova Crucis 1996. discovered. by Liller at V. = 9.2 (Liller 1996) and observed at V — 19.48 in March," CP Cru was Nova Crucis 1996, discovered by Liller at V = 9.2 (Liller 1996) and observed at V = 19.48 in March"
The reason for this behaviour is that. for the higher terms. the Edgeworth expansion assigns high weights to the tails of the distribution.,"The reason for this behaviour is that, for the higher terms, the Edgeworth expansion assigns high weights to the tails of the distribution."
 Since the distribution we are analysing is in fact far from Gaussian. especially 1n the tails. the fit to the peak correspondingly gets worse. and often even multiple peaks appear.," Since the distribution we are analysing is in fact far from Gaussian, especially in the tails, the fit to the peak correspondingly gets worse, and often even multiple peaks appear."
 This ts similar to the effect noticed by ? forthe example of y distributions., This is similar to the effect noticed by \cite{Blinnikov1998} for the example of $\chi^2$ distributions.
 Also. the regions of negative probability density are generic features of the Edgeworth expansion when applied to strongly non-Gaussian distributions.," Also, the regions of negative probability density are generic features of the Edgeworth expansion when applied to strongly non-Gaussian distributions."
 Still. if we truncate the Edgeworth expansion after a wisely chosen number of terms. it will provide a good approximation to the true probability distribution.," Still, if we truncate the Edgeworth expansion after a wisely chosen number of terms, it will provide a good approximation to the true probability distribution."
 Since Eq. (86)), Since Eq. \ref{eq:edgeworth}) )
" is an asymptotic series expansion. it generally does not converge, but we do have a method at hand to find the optimal number of. terms and to control the error we make."," is an asymptotic series expansion, it generally does not converge, but we do have a method at hand to find the optimal number of terms and to control the error we make."
 If we truncate the sum over n in Eq. (86)), If we truncate the sum over $n$ in Eq. \ref{eq:edgeworth}) )
 after N terms. the last term retained willalso give the order of the difference between the full p(é jand this partial sum expansion.," after $N$ terms, the last term retained will also give the order of the difference between the full $p(\xi)$ and this partial sum expansion."
 Therefore we can. in practice. simply truncate the expansion at the term with minimal contribution (measured at the peak of the distribution. at a certain point of evaluation. or integrated over a domain in £ we are interested in).," Therefore we can, in practice, simply truncate the expansion at the term with minimal contribution (measured at the peak of the distribution, at a certain point of evaluation, or integrated over a domain in $\xi$ we are interested in)."
 For both cases illustrated in Fig. 4..," For both cases illustrated in Fig. \ref{fig:pxi_edge},"
 this eriterion gives N= as the optimal order of expansion., this criterion gives $N=3$ as the optimal order of expansion.
 Also for other parameters x/L and Lop. such a third-order Edgeworth expansion seems to be a safe choice to get a substantial improvement as opposed to a simple Gaussian likelihood.," Also for other parameters $x/L$ and $L \, \sigma_P$, such a third-order Edgeworth expansion seems to be a safe choice to get a substantial improvement as opposed to a simple Gaussian likelihood."
 In all of the above calculations. we assumed one-dimensional random fields.," In all of the above calculations, we assumed one-dimensional random fields."
 However. we can easily generalise all results to higher dimensions.," However, we can easily generalise all results to higher dimensions."
" If we go to Ng dimensions. with lag parameters""vM LLX2(vy...⋅YA,,,). then the allowed⋅⇁ Fourier""ar modes are all with integer 7."," If we go to $N_{\mathrm{dim}}$ dimensions, with lag parameters $\vec{x} = (x_1, \dots, x_{N_{\mathrm{dim}}})$, then the allowed Fourier modes are all with integer $n_i$."
" Still. all the modes are independent and each has a Gaussian probability distribution with its dispersion given by c,=PURD/L."," Still, all the modes are independent and each has a Gaussian probability distribution with its dispersion given by $\sigma_{\vec{n}}=P(|\vec{k}_{\vec{n}}|)/L^N_{\mathrm{dim}}$."
 The derivation of p(£) stays exactly the same as presented in Sect. 2.1.., The derivation of $p(\xi)$ stays exactly the same as presented in Sect. \ref{sec:univar_derivation}.
 Where necessary. we can renumber all modes 77 with a single integer 7 by an arbitrary scheme and retain the old notations with scalar indices.," Where necessary, we can renumber all modes $\vec{n}$ with a single integer $n$ by an arbitrary scheme and retain the old notations with scalar indices."
 Then. Eq. (22))," Then, Eq. \ref{eq:univar_derivation_pxifinal}) )"
 still holds. with only two important changes.," still holds, with only two important changes."
 First. the sums now go over many more modes. namely all possible vectors of integers 7=(neeΗΝ) with p;€E.," First, the sums now go over many more modes, namely all possible vectors of integers $\vec{n} = (n_1, \dots, n_{N_{\mathrm{dim}}})$ with $n_i \in \mathbb{N}$ ."
 If. in a numerical implementation. we want to cover a box in &- space with N grid points in each direction. we therefore end up with N= modes.," If, in a numerical implementation, we want to cover a box in $k$ -space with $N$ grid points in each direction, we therefore end up with $N^{N_{\mathrm{dim}}}$ modes."
 Besides the increased computational cost. this also leads to frequent occurrences of multiple poles.," Besides the increased computational cost, this also leads to frequent occurrences of multiple poles."
 This 15 the case especially for ¥=0. since then the C; depend on μή only.," This is the case especially for $\vec{x} = \vec{0}$, since then the $C_{\vec{n}}$ depend on $|\vec{n}|$ only."
 Therefore. the gereralised result of appendix AppendixA: gets naturally important in higher dimensions.," Therefore, the generalised result of appendix \ref{sec:multipoles} gets naturally important in higher dimensions."
" However. 1n. real application scerarios. where accuracy is limited by external factors anyway. it is always possible to avoid multiple poles by slightly changirg the C, factors. e.g. by adding a small Number e in the cosine. Doing this removes the multiple poles while only slightly changing the results with respect to using the unmodified C, and the full multi-pole formula. Eq. (A3))."," However, in real application scenarios, where accuracy is limited by external factors anyway, it is always possible to avoid multiple poles by slightly changing the $C_{\vec{n}}$ factors, e.g. by adding a small number $\epsilon$ in the cosine, Doing this removes the multiple poles while only slightly changing the results with respect to using the unmodified $C_n$ and the full multi-pole formula, Eq. \ref{eq:univar_derivation_pximultipole}) )."
" As a second effect. the factors C,, now depend on the angle between separation. vector ¥ and mode vector >Κι; However. a Gaussian random field is completely determined by its power spectrum. and when we assume à. P(k,;) which depends on the absolute values of the &, only. such a field should be statistically isotropic."," As a second effect, the factors $C_n$ now depend on the angle between separation vector $\vec{x}$ and mode vector $\vec{k}_{\vec{n}}$: However, a Gaussian random field is completely determined by its power spectrum, and when we assume a $P(\vec{k}_{\vec{n}})$ which depends on the absolute values of the $\vec{k}_{\vec{n}}$ only, such a field should be statistically isotropic."
 Any anisotropies seen in. our results must be a consequence ofN using. a finite.HEN cubic field instead of an infinite field.," Any anisotropies seen in our results must be a consequence of using a finite, cubic field instead of an infinite field."
 So weexpect that all anisotropies vanish as soon as most of the power comes from scales much smaller than the field size., So weexpect that all anisotropies vanish as soon as most of the power comes from scales much smaller than the field size.
 For power spectra, For power spectra
around the jet axis. to produce three cylinders of radius 11 Kpe and length 20 Κρο.,"around the jet axis, to produce three cylinders of radius 11 kpc and length 20 kpc."
 Gas densities in each cylinder are taken to be the average density at the mean radius of the region. as determined in paper I. We take the abundance of this region to be1.3Z... based on the mean value found for the regions along the jet.," Gas densities in each cylinder are taken to be the average density at the mean radius of the region, as determined in paper I. We take the abundance of this region to be, based on the mean value found for the regions along the jet."
 The abundances measured from the rectangular regions around the je suggest a background level of.. but the clumpiness of the abundance distribution on these scales makes this uncertain.," The abundances measured from the rectangular regions around the jet suggest a background level of, but the clumpiness of the abundance distribution on these scales makes this uncertain."
 To ge a more reliable measure of the general level of enrichment in the central part of the cluster. we extracted a spectrum from a circular region of radius ~ (5-65 kpe) centred just south of the radio core. with the region of he jets excluded.," To get a more reliable measure of the general level of enrichment in the central part of the cluster, we extracted a spectrum from a circular region of radius $\sim$ $\sim$ 65 kpc) centred just south of the radio core, with the region of the jets excluded."
 This encloses the whole high abundance part of he cluster core. and while there is spatial variation in metallicity. it should provide a reasonable average enrichment level.," This encloses the whole high abundance part of the cluster core, and while there is spatial variation in metallicity, it should provide a reasonable average enrichment level."
 The best fitting abundance for this region is 0.86AL... suggesting that a background abundance of 1s acceptable.," The best fitting abundance for this region is $^{+0.09}_{-0.08}$, suggesting that a background abundance of is acceptable."
 This then suggests an excess iron mass of ~L4.10AZ.., This then suggests an excess iron mass of $\sim1.4\times10^6$.
. Beyond the central region the mean abundance falls o 0.6Z.., Beyond the central region the mean abundance falls to $\sim$.
. From the. gas mass profile of OSOS. we estimate he total gas mass within 65 kpe to be 101A7..," From the gas mass profile of OS05, we estimate the total gas mass within 65 kpc to be $\times10^{10}$."
. For an excess abundance of.. this suggests that the volume has been enriched by an additional 2.4.10 oof iron.," For an excess abundance of, this suggests that the volume has been enriched by an additional $\times10^{7}$ of iron."
 NGC 6051 is the most massive galaxy in AWM 4+ by a Significant margin. and given its central position it is likely to be the source of a large fraction of the enrichment.," NGC 6051 is the most massive galaxy in AWM 4 by a significant margin, and given its central position it is likely to be the source of a large fraction of the enrichment."
 If the super-solar abundances are associated with material entrained by the radio jets. the gas now seen along the jets must have been enriched in the galaxy core.," If the super-solar abundances are associated with material entrained by the radio jets, the gas now seen along the jets must have been enriched in the galaxy core."
 Using the regions described above. we can estimate that ifthe enriched material was originally all in the central ~10 kpe of the galaxy. ~45¢ of the metals originally formed in this central region have been transported out along the Jets.," Using the regions described above, we can estimate that if the enriched material was originally all in the central $\sim$ 10 kpc of the galaxy, $\sim$ of the metals originally formed in this central region have been transported out along the jets."
 We can assume that the emission observed from the region of the jets represents a mix of gas. both highly enriched uplifted material and the lower metallicity gas which occupied the whole region.," We can assume that the emission observed from the region of the jets represents a mix of gas, both highly enriched uplifted material and the lower metallicity gas which occupied the whole region."
 The two phases may be physically mixed or separate. but the measured abundance represents an average of the two.," The two phases may be physically mixed or separate, but the measured abundance represents an average of the two."
 The mass of enriched gas which must be uplifted and the energy required to do so will depend on the level of enrichment and on the abundance of the gas it mixes with., The mass of enriched gas which must be uplifted and the energy required to do so will depend on the level of enrichment and on the abundance of the gas it mixes with.
 If the core were very highly enriched. even a small amount of gas transported outward would produce the abundances we observe. when mixed with the less enriched gas at that radius.," If the core were very highly enriched, even a small amount of gas transported outward would produce the abundances we observe, when mixed with the less enriched gas at that radius."
" We can detine the mass of gas which must be transported to be: where pV)= nmij,,—1.19.1041. iis the mass of gas in the jets outside the core. Ζω is the abundance now observed in the jets. Z,,;,; 18 the abundance in the jets prior to mixing with more enriched material from the core. and Zeic) is the abundance of that highly enriched material."," We can define the mass of gas which must be transported to be: where $\rho V=m_{gas}$ $\times10^9$ is the mass of gas in the jets outside the core, $Z_{obs}$ is the abundance now observed in the jets, $Z_{prior}$ is the abundance in the jets prior to mixing with more enriched material from the core, and $Z_{enrich}$ is the abundance of that highly enriched material."
" If we assume that the jets expanded into material with abundance Z,,;,,20.9Z.. as for the surrounding gas. we can estimate Ζω by assuming that the excess metals now observed in the jets were once in the core."," If we assume that the jets expanded into material with abundance $Z_{prior}$, as for the surrounding gas, we can estimate $Z_{enrich}$ by assuming that the excess metals now observed in the jets were once in the core."
 This suggests that the uplifted enriched material had an abundance Zevrich=l., This suggests that the uplifted enriched material had an abundance $Z_{enrich}$.
"OZ... In this ease miu ,20.57.yas.", In this case $m_{trans.}$ $\times m_{gas}$.
 The energy required to uplift the gas from the core is simply the change in gravitational potential energy as the gas is lifted from the core to the mean radius A. /£—CAL(RRMansfI where A~20 kpe. MiteB) S4.1077 iis the total mass within this radius (from. OSO5). and C is the gravitational constant.," The energy required to uplift the gas from the core is simply the change in gravitational potential energy as the gas is lifted from the core to the mean radius $R$, $E=GM_{tot}(<R)m_{trans.}/R$ where $R\sim20$ kpc, $M_{tot}(<R)$ $\times10^{12}$ is the total mass within this radius (from OS05), and $G$ is the gravitational constant."
 For Εναν το.mys. this gives ££.—4.5«10° ergy.," For $m_{trans.}$ $\times m_{gas}$, this gives $E=4.5\times10^{57}$ erg."
 The maximum energy which could be required QU=7.9.1075 erg) corresponds to the case where the gas uplifted has Zire=Zo. in which case all the gus currently in the jets has been uplifted. displacing that which was there prior to the outburst.," The maximum energy which could be required $E=7.9\times10^{57}$ erg) corresponds to the case where the gas uplifted has $Z_{enrich}=Z_{obs}$, in which case all the gas currently in the jets has been uplifted, displacing that which was there prior to the outburst."
 Less energy will be required if higher enrichment levels are assumed in the core: taking the 90 per cent., Less energy will be required if higher enrichment levels are assumed in the core; taking the 90 per cent.
" upper bound on the current abundance there 9) and again assuming the excess metals in the jets originated .in the core. its abundance would have been —1.9Z... giving mios,0 m4, and uplift energy --3.2.10°"" erg."," upper bound on the current abundance there ) and again assuming the excess metals in the jets originated in the core, its abundance would have been $\sim$, giving $m_{trans.}=$ $\times m_{gas}$ and uplift energy $E=3.2\times10^{57}$ erg."
 In any case. the energy required to uplift the enriched material is a significant fraction ofthe expected mechanical power output of the jets. which we estimate to be 9.4...107 erg. where ó is the filling factor of the lobes (see paper Ij," In any case, the energy required to uplift the enriched material is a significant fraction of the expected mechanical power output of the jets, which we estimate to be $\times10^{58}\phi$ erg, where $\phi$ is the filling factor of the lobes (see paper I)."
 Our best estimate of filling factor. for the western lobe where a cavity is detected. is 020.21. and the 3¢ upper limit on the mean tilling factor of the two lobes is ©«0.6.," Our best estimate of filling factor, for the western lobe where a cavity is detected, is $\phi$ =0.21, and the $\sigma$ upper limit on the mean filling factor of the two lobes is $\phi<$ 0.6."
 This suggests that 7-20 ver cent., This suggests that $>$ 20 per cent.
 of the mechanical energy of the jets could be required to oroduce the observed uplift., of the mechanical energy of the jets could be required to produce the observed uplift.
 Further limits on the level of enrichment of uplifted material can be estimated based on surface brightness., Further limits on the level of enrichment of uplifted material can be estimated based on surface brightness.
 If we assume that he pressure of the uplifted material decreases as the gas rises. maintaining pressure equilibrium with its surroundings. we can consider two extreme cases: either the pressure decrease is achieved hrough density decrease (expansion) or through temperature decrease.," If we assume that the pressure of the uplifted material decreases as the gas rises, maintaining pressure equilibrium with its surroundings, we can consider two extreme cases; either the pressure decrease is achieved through density decrease (expansion) or through temperature decrease."
 For each case. we can estimate the expected surface brightness increase for a given abundance and mass of uplifted gas Cuso and Mpa).," For each case, we can estimate the expected surface brightness increase for a given abundance and mass of uplifted gas $Z_{enrich}$ and $m_{trans}$ )."
 As discussed in paper IL there is some apparent increase in surface brightness along the jets. but these features are not statistically significant.," As discussed in paper I, there is some apparent increase in surface brightness along the jets, but these features are not statistically significant."
 Determining a “background” level of surface brightness is also difficult. since the mild offset between the position of NGC 6051 and the X-ray centroid of the ICM means that surface brightness north of the jets is systematically brighter than to the south. and there is some evidence of additiona structures north of the jet.," Determining a `background' level of surface brightness is also difficult, since the mild offset between the position of NGC 6051 and the X–ray centroid of the ICM means that surface brightness north of the jets is systematically brighter than to the south, and there is some evidence of additional structures north of the jet."
 We determine the 0.7-3 keV surface brightness in a number of segments of an elliptical annulus chosen to match the mean ellipticity of the diffuse emission. corrected using a [1.05 keV. monoenergetic exposure map.," We determine the 0.7-3 keV surface brightness in a number of segments of an elliptical annulus chosen to match the mean ellipticity of the diffuse emission, corrected using a 1.05 keV monoenergetic exposure map."
 As expected. surface brightness declines from north to south across each jet by a factor larger than the statistical uncertainty. and there is significan bin-to—bin variation around the annulus. beyond that expected for a smooth distribution.," As expected, surface brightness declines from north to south across each jet by a factor larger than the statistical uncertainty, and there is significant bin–to–bin variation around the annulus, beyond that expected for a smooth distribution."
 For excess surface brightness to be detectec in the jets. it would have to exceed that of the brighter neighbouring bin by a significant margin.," For excess surface brightness to be detected in the jets, it would have to exceed that of the brighter neighbouring bin by a significant margin."
 We define this as an increase of three times the mean variation between bins across the jets., We define this as an increase of three times the mean variation between bins across the jets.
 On this basis. we can consider two possible scenarios. depending on whether the uplifted material expands adiabatically or isothermally as it rises.," On this basis, we can consider two possible scenarios, depending on whether the uplifted material expands adiabatically or isothermally as it rises."
 The first case would occur if conduction between the material and its surroundings is strongly suppressed. he latter if conduction were highly efficient.," The first case would occur if conduction between the material and its surroundings is strongly suppressed, the latter if conduction were highly efficient."
 For adiabatic expansion. we ean determine the expected change in temperature or a monatomic ideal gas using the relation T2 Τι (P»/P4)ss where T and P are temperate and pressure before (61) and after (2) expansion. and the adiabatic index ~=5/3.," For adiabatic expansion, we can determine the expected change in temperature for a monatomic ideal gas using the relation $_2$ $_1$ $_2$ $_1$ $^{(\gamma-1)/\gamma}$, where T and P are temperate and pressure before (1) and after (2) expansion, and the adiabatic index $\gamma$ =5/3."
 The known change in oressure then allows us to calculate the expected change in density., The known change in pressure then allows us to calculate the expected change in density.
 We find that the uplifted material would still be both cooler and denser than the surrounding gas. and therefore significantly more uminous than the surrounding ICM with even aabundance.," We find that the uplifted material would still be both cooler and denser than the surrounding gas, and therefore significantly more luminous than the surrounding ICM with even abundance."
 The surface brightness limit for the west jet rules out his scenario., The surface brightness limit for the west jet rules out this scenario.
 For the east jet. the upper limit on surface brightness," For the east jet, the upper limit on surface brightness"
determined by comparing the positions of emission lines in the median sky spectra of each observation to their positions in sky spectra averaged over all observations.,determined by comparing the positions of emission lines in the median sky spectra of each observation to their positions in sky spectra averaged over all observations.
 The magnitude of the offset varied between and (0 to 0.3 kmss.4)., The magnitude of the offset varied between and (0 to 0.3 $^{-1}$ ).
 Finally. target spectra were sky subtracted. averaged and corrected for telluric absorption.," Finally, target spectra were sky subtracted, averaged and corrected for telluric absorption."
 To allow for variations in fibre efficiency. the proportion of the median sky spectrum subtracted from each target spectrum was tuned to minimise the peak amplitude of the cross-correlation function between the sky-subtracted target spectrum and the median sky spectrum.," To allow for variations in fibre efficiency, the proportion of the median sky spectrum subtracted from each target spectrum was tuned to minimise the peak amplitude of the cross-correlation function between the sky-subtracted target spectrum and the median sky spectrum."
 Additionally. the sky subtracted spectrum was masked over the width of the mayor sky emission lines.," Additionally, the sky subtracted spectrum was masked over the width of the major sky emission lines."
 The two exposures recorded within each observation block were averaged if they differed by less than 2e otherwise the lower of the two local values was taken (to deal with cosmie rays)., The two exposures recorded within each observation block were averaged if they differed by less than $2\sigma$ otherwise the lower of the two local values was taken (to deal with cosmic rays).
 Spectra from each configuration were corrected for telluric absorption over the wavelength to using templates derived from the co-temporal UVES spectra of bright blue stars. which were broadened to mimic the spectral resolution of Giraffe.," Spectra from each configuration were corrected for telluric absorption over the wavelength to using templates derived from the co-temporal UVES spectra of bright blue stars, which were broadened to mimic the spectral resolution of Giraffe."
 The broadened spectra showed only minor effects of telluric absorption for A2S440A.. so no telluric compensation was made in this wavelength range.," The broadened spectra showed only minor effects of telluric absorption for $\lambda > 8440$, so no telluric compensation was made in this wavelength range."
 To determine radial velocities (RV) and projected equatorial velocities (er sins). the spectra of target stars were rebinned onto a logarithmic scale and convolved with template spectra of standard stars over the wavelength range to8530À.. deliberately avoiding the chromospherically contaminated CaT lines and masking out mayor sky emission features.," To determine radial velocities (RV) and projected equatorial velocities $v\sin i$ ), the spectra of target stars were rebinned onto a logarithmic scale and convolved with template spectra of standard stars over the wavelength range to, deliberately avoiding the chromospherically contaminated CaT lines and masking out major sky emission features."
 Templates of type K4.5V (AD 209100) and ΜΟΝ (HD 34055) from the UVES atlas (Bagnulo et al., Templates of type K4.5V (HD 209100) and M6V (HD 34055) from the UVES atlas (Bagnulo et al.
 2003) were used. encompassing the full range of target spectral types.," 2003) were used, encompassing the full range of target spectral types."
 These were broadened using a Gaussian kernel to match the resolution of the Giraffe spectra., These were broadened using a Gaussian kernel to match the resolution of the Giraffe spectra.
 A Gaussian profile. was fitted to the peak in the cross-correlation function over a width of EO.Sc.," A Gaussian profile, was fitted to the peak in the cross-correlation function over a width of $\pm0.8 \sigma$."
 The offset of this profile gave the relative RV of the target star and its width. σ. gave a measure of rotational broadening that we used to estimate esin7.," The offset of this profile gave the relative RV of the target star and its width, $\sigma$, gave a measure of rotational broadening that we used to estimate $v \sin i$."
" For spectra with a SNR >5, there was usually a clearly defined. single peak in the cross-correlation function that could be fitted with a Gaussian profile to determine a unique RV and esin7."," For spectra with a SNR $\geq 5$, there was usually a clearly defined, single peak in the cross-correlation function that could be fitted with a Gaussian profile to determine a unique RV and $v \sin i$."
 For spectra with average SNR «5. the cross-correlation peak was often sufficiently distorted by random noise that we considered the results unreliable and these targets were rejected from our sample at this stage.," For spectra with average SNR $< 5$, the cross-correlation peak was often sufficiently distorted by random noise that we considered the results unreliable and these targets were rejected from our sample at this stage."
 RVs were heliocentrically corrected to an arbitary zeropoint for each standard., RVs were heliocentrically corrected to an arbitary zeropoint for each standard.
 Values of esin? were determined from the measured widths using calibration curves derived by broadening standard star spectra to simulate a series of known rotation velocities., Values of $v\sin i$ were determined from the measured widths using calibration curves derived by broadening standard star spectra to simulate a series of known rotation velocities.
 This was done in two stages., This was done in two stages.
 The standards were first broadened with a Gaussian to match the cross-correlation function widths to the average width. A. obtained for 40 slow-rotating targets (with period. 1?5 days) as these were expected to have negligible broadening compared with the spectral resolution.," The standards were first broadened with a Gaussian to match the cross-correlation function widths to the average width, $K$, obtained for 40 slow-rotating targets (with period, $P > 5$ days), as these were expected to have negligible broadening compared with the spectral resolution."
" This gave ""zero velocity” widths of A.=19.14+0.64 and A=17.664048 + for the K4.5 and M6 standards respectively."," This gave “zero velocity” widths of $K=19.14\pm
0.64$ $^{-1}$ and $K=17.66 \pm 0.48$ $^{-1}$ for the K4.5 and M6 standards respectively."
 These broadened spectra were then convolved with rotational broadening kernels for esin; values between ϐ and ss, These broadened spectra were then convolved with rotational broadening kernels for $v \sin i$ values between 0 and $^{-1}$.
 A linear limb darkening coefticient of 0.6 was used (Claret. Diaz-Cordoves Gimenez 1995). but the results are insensitive to this parameter.," A linear limb darkening coefficient of 0.6 was used (Claret, Diaz-Cordoves Gimenez 1995), but the results are insensitive to this parameter."
 Originally it was intended to interpolate between esin/ values found from the two templates. using colour as a proxy for spectral type.," Originally it was intended to interpolate between $v \sin i$ values found from the two templates, using colour as a proxy for spectral type."
 However. we found that the two esin values did not differ significantly. either on average or as a function of colour. so we took their average to minimise any uncertainty.," However, we found that the two $v \sin i$ values did not differ significantly, either on average or as a function of colour, so we took their average to minimise any uncertainty."
 Uncertainties in the RV and esin/ measurements were determined by comparing repeated measurements made on a subset of the targets., Uncertainties in the RV and $v \sin i$ measurements were determined by comparing repeated measurements made on a subset of the targets.
 The functional form of the uncertainty in RV and width was found by analysing the uncertainty produced. by convolving artificially broadened standards with dummy spectra. generated by injecting random noise of a Gaussian distribution at increasing levelsof SNR into the standard spectra.," The functional form of the uncertainty in RV and width was found by analysing the uncertainty produced by convolving artificially broadened standards with dummy spectra, generated by injecting random noise of a Gaussian distribution at increasing levelsof SNR into the standard spectra."
This indicated an uncertainty of the form for both RV and the width VV of the eross-correlation function. where οἱ. D and C' are empirically derived constants.,"This indicated an uncertainty of the form for both RV and the width $W$ of the cross-correlation function, where $A$, $B$ and $C$ are empirically derived constants."
 The constants ;1 and £3 which characterise the effects of noise in the measured spectra were found by comparing RVs and widths measured for 60 targets (44 with measured periods) in the repeated runs with the same configuration (see Table |)., The constants $A$ and $B$ which characterise the effects of noise in the measured spectra were found by comparing RVs and widths measured for 60 targets (44 with measured periods) in the repeated runs with the same configuration (see Table 1).
 The constant C' which represents additional uncertainties due to changes in fibre allocation and night-to-night calibration variations was estimated by comparing results from spectra for 16 targets recorded on different days with different fibre allocations., The constant $C$ which represents additional uncertainties due to changes in fibre allocation and night-to-night calibration variations was estimated by comparing results from spectra for 16 targets recorded on different days with different fibre allocations.
" The empirically derived uncertainties in RV and cross-correaltion width were The uncertainty in esin? was then determined from its relationship with 11 and the ""zero velocity width"" A for a particular standard.", The empirically derived uncertainties in RV and cross-correaltion width were The uncertainty in $v\sin i$ was then determined from its relationship with $W$ and the “zero velocity width” $K$ for a particular standard.
 where a is a scaling constant., where $\alpha$ is a scaling constant.
 Hence the uncertainty in sin is Spectra with 5 were obtained for 239 stars with known periods., Hence the uncertainty in $v\sin i$ is Spectra with $\geq$ 5 were obtained for 239 stars with known periods.
 One of these (N2516-3-8-1301) showed a clear double peak in the cross correlation and is almost certainly a double-lined spectroscopic binary., One of these (N2516-3-8-1301) showed a clear double peak in the cross correlation and is almost certainly a double-lined spectroscopic binary.
 The other (N2316-1-2-369) shows a more noisy cross-correlation and is a possible binary system., The other (N2516-1-2-369) shows a more noisy cross-correlation and is a possible binary system.
 The measured RV and esin? for the remaining 237 targets are given in Table I., The measured RV and $v\sin i$ for the remaining 237 targets are given in Table 1.
 V and / photometry was initially taken from Irwin et al. (, $V$ and $I$ photometry was initially taken from Irwin et al. (
2007). but we corrected their photometric values to put them onto the better calibrated photometric scale of Jeffries et al. (,"2007), but we corrected their photometric values to put them onto the better calibrated photometric scale of Jeffries et al. ("
2001). using a set of stars common to both papers.,"2001), using a set of stars common to both papers."
 The corrections added to the Irwin et al., The corrections added to the Irwin et al.
 values were AJ—0.0800.00767 and ACY £). A," values were $\Delta I =
0.080-0.0076\,I$ and $\Delta (V-I) = 0.300-0.153\,(V-I)$ ."
 magnitudes are from the Two- All-Sky Survey (2MASS) catalogue (Cutri et al., $K$ magnitudes are from the Two-micron All-Sky Survey (2MASS) catalogue (Cutri et al.
 2003). transformed to the CIT system using {νο=fveariss|0.024 (Carpenter 2001).," 2003), transformed to the CIT system using $K_{CIT} = K_{2MASS} + 0.024$ (Carpenter 2001)."
PSR B1612-03(Shabanova.Lyne&Urama2001).,PSR B1642-03\citep{slu01}.
. However. solid pulsars are suggestive because of the difficulties of explaining this feature iu the the conventional models of fluid neutron stars.," However, solid pulsars are suggestive because of the difficulties of explaining this feature in the the conventional models of fluid neutron stars."
" The precession should be damped down soou due to various dissipation Xocesses (e... the vertex pinning. the surface-rubbing of Ekman laver innediatelv beneath the crust), aud solid. quark star model for pulsar-like stars is thenproposed (Xu2003c).. Receutly. Levin&D'Àugelo(2001) studied. the imaenuetolvdrodyiuanüc coupling between the crust and the core of a rotating ueutron star. aud found that the precession of PSR D1s28-11 should decay over a buuana lifetime."," The precession should be damped down soon due to various dissipation processes (e.g., the vertex pinning, the surface-rubbing of Ekman layer immediately beneath the crust), and solid quark star model for pulsar-like stars is thenproposed \citep{xu03c}.. Recently, \cite{ld04} studied the magnetohydrodynamic coupling between the crust and the core of a rotating neutron star, and found that the precession of PSR B1828-11 should decay over a human lifetime."
 This well-defined MITD dissipation should certainly be inportaut in order to test the stellar models., This well-defined MHD dissipation should certainly be important in order to test the stellar models.
" A solid quark star is just a rigid body. no damping occurs, and the solid pulsar model may survive the observational tests ifthe free precession keeps the sale over several tens of vears."," A solid quark star is just a rigid body, no damping occurs, and the solid pulsar model may survive the observational tests if the free precession keeps the same over several tens of years."
 We nav expect a precession Without damping even hundreds of vears. or we nieht- be lucky A neutron star can not be in a solic state.," We may expect a precession without damping even hundreds of years, or we might be lucky A neutron star can not be in a solid state."
 The unclear liquid model is successful experinoenutally. the original version ofwhich is the unclear eas inodel.," The nuclear liquid model is successful experimentally, the original version ofwhich is the nuclear Fermi-gas model."
 Nucleous cau be regarded as Ferai-eas due to the Pauli exclusive in the model., Nucleons can be regarded as Fermi-gas due to the Pauli exclusive in the model.
 A ereat part of neutron star matter has deusitv to be approximately the nuclear saturation density. and at least this part is in a fluid state.," A great part of neutron star matter has density to be approximately the nuclear saturation density, and at least this part is in a fluid state."
 Iu this sense. a quark star is identified if one convinces that a pulsar is m a solic state.," In this sense, a quark star is identified if one convinces that a pulsar is in a solid state."
 2., 2.
 A quark star (or quark matter) is called to be strange if it has straugeness., A quark star (or quark matter) is called to be strange if it has strangeness.
 Certainly itis not recessary that quark matter is strange (Cea2003:Shovkovy.Hauauske&Ππαπο 2003).. but it isconjectured that the presence of strangeness might ο cherectically favorable (Bodiner1971:Witten 1981).," Certainly itis not necessary that quark matter is strange \citep{cea03,shh03}, but it isconjectured that the presence of strangeness might be energetically favorable \citep{bodm71,wit84}."
.Phenomenological calculation shows that he conjecture isvery likely to be true(Farhi&Jaffe198 1L)., Phenomenological calculation shows that the conjecture isvery likely to be true\citep{fj84}.
. For quark matter in low temperature. T. mt Lhieh barvou density. ο. there exists a between color supercouductivity aud solidification. just like the case of laboratory low- physics.," For quark matter in low temperature, $T$, but high baryon density, $n_{\rm b}$, there exists a between color superconductivity and solidification, just like the case of laboratory low-temperature physics."
 Normal matter should besolidified as long as the interaction energy between ucighboring iousis at ~10? (Dubin&1999)., Normal matter should besolidified as long as the interaction energy between neighboring ionsis at $\sim 10^2$ \citep{dn99}.
. /) Aév3inkT>To Gin / T Z my. (Clendenning2000).. a-decay. a-clusters) ," $l$ $\lambda\sim
h/\sqrt{3mkT}>l$ $m$ $l$ $T$ $T$ $n_{\rm b}$ \citep{glen00}, $\alpha$ $\alpha$ "
A huge extracsolay pluiet survey has been underway suce 1991. at the Observatory of Haute-Proveuce with the liel-precision. fber-fed echelle spectrograph (Darauuectal. 1996)) motte on the ccm telescope.,"A large extra-solar planet survey has been underway since 1994 at the Observatory of Haute-Provence with the high-precision, fiber-fed echelle spectrograph \cite{Baranne96}) ) mounted on the cm telescope."
 The search for extra-soklu planets is carried out bv seekiug chanecs in the radial velocity of cach star produced bv gravitational interaction with orbiting planets., The search for extra-solar planets is carried out by seeking changes in the radial velocity of each star produced by gravitational interaction with orbiting planets.
 In 1995 this program lead to the first detection of an extrasolar planet orbiting a Sunu-like star (Mayor&Queloz 1995))., In 1995 this program lead to the first detection of an extrasolar planet orbiting a Sun-like star \cite{MayorQueloz95}) ).
 Our survey. coutains 321 dwart stars brighter than V. — 7.65. iucludiung ΠΟ 166135 (Quelozetal. L99Sb)).," Our survey contains 324 G dwarf stars brighter than $V$ = 7.65, including HD 166435 \cite{Quelozetal98b}) )."
 The star ΠΟ 166135 isa GO dwart with V)0.633., The star HD 166435 is a G0 dwarf with $-$ $=0.633$.
 From its distance of ppc and its apparcut magnitude my=6085. we find an absolute magnitude Ae=L8.," From its distance of pc and its apparent magnitude $m_V=6.85$, we find an absolute magnitude $M_V=4.8$."
 If the mmetallicity is roughly solav. ΠΟ 166135° location in the IER diagraun suggestsOO a WUL-SCGUCLICe age o a few bilion vears.," If the metallicity is roughly solar, HD 166435's location in the H-R diagram suggests a main-sequence age of a few billion years."
" Iuterestinely the star was detecte in the ROSAT all-xkv. survey as an extreme ultraviolet (EUV) source. but no other evidence of activity was fou w Mulliss&Bopp(1991). in their analysis of the IL, and Call((8512À)) lines."," Interestingly, the star was detected in the ROSAT all-sky survey as an extreme ultraviolet (EUV) source, but no other evidence of activity was found by \cite{Mulliss94} in their analysis of the $_\alpha$ and ) lines."
 Burleighetal.L997 found. a iut of emüssion in the ((1519À)) Bue but doetectec 10 other obvious spectral ciissiou features., \cite{Burleigh97} found a hint of emission in the ) line but detected no other obvious spectral emission features.
 When we selected ΠΟ 166135 for ELODIE observatious. woe hac 10 real indication that IID 166135 uieht be voung ax active.," When we selected HD 166435 for ELODIE observations, we had no real indication that HD 166435 might be young and active."
 A possible coincidence with another EUV source rad been mentioned (Burleighetal. 1997)) as a possible explanation for the EUV ROSAT deteclon., A possible coincidence with another EUV source had been mentioned \cite{Burleigh97}) ) as a possible explanation for the EUV ROSAT detection.
 After only a few vacdal-velocity iueasureieuts of IID 166135. it became apparent that the star exhibited low-anuplitude. racdial-velocity variations with a period of about | davs.," After only a few radial-velocity measurements of HD 166435, it became apparent that the star exhibited low-amplitude, radial-velocity variations with a period of about 4 days."
 Further moasuremeuts in the following mouths confirmed our initial fiudiug. leading us to believe that TD 166135 may have a planetary companion in a close orbit.," Further measurements in the following months confirmed our initial finding, leading us to believe that HD 166435 may have a planetary companion in a close orbit."
 Subsequently we began a campaigi of high-precision plotometric observations with an automatic photoelectric telescope (APT) at Fairborn Observatory in Arizona to search for plauctary transits and iade tentative planus το announce the new janet at the Protostars and Planets IV conference (Alannines.Boss.&Russell (2000))).," Subsequently, we began a campaign of high-precision photometric observations with an automatic photoelectric telescope (APT) at Fairborn Observatory in Arizona to search for planetary transits and made tentative plans to announce the new planet at the Protostars and Planets IV conference \cite{manetal00}) )."
" To OUL surprise. jowever, we found the star to be photoποσαν variable with the same period as the radial-vekcity variations."," To our surprise, however, we found the star to be photometrically variable with the same period as the radial-velocity variations."
 Iu lis article we describe these data. aloic with additional IIT IT and Wh incasuremicuts acquire at Mount Wilson Observatory. and discuss the most likely explanation for he observed variations in all three data sets.," In this article we describe these data, along with additional II H and K measurements acquired at Mount Wilson Observatory, and discuss the most likely explanation for the observed variations in all three data sets."
 We obtained 70 spectra with from L997 May. to 1999 September., We obtained 70 spectra with from 1997 May to 1999 September.
 These spectra have vpical signal-to-noise ratios of TO150 (at 5O00A)) per resolution clement and a resolution (A/AA) of about 12.000.," These spectra have typical signal-to-noise ratios of 70–150 (at ) per resolution element and a resolution $\lambda/\Delta\lambda$ ) of about 42,000."
 The data reduction was carried out ou-Iine during ie observatious bv the automatic reduction software (see Baranneetal.1996 for details)., The data reduction was carried out on-line during the observations by the automatic reduction software (see \cite{Baranne96} for details).
 All the spectra were acquired iu he high-precision mode. which xovides a simultaneous thorimm reference spectrum.," All the spectra were acquired in the high-precision mode, which provides a simultaneous thorium reference spectrum."
 The zero-poin wavelength calibration has au intrinsic oeistrunieutal precision of, The zero-point wavelength calibration has an intrinsic instrumental precision of.
 To examine certain key spectral features. we co-added the 70 individual spectra to obtain a composite spectrum with a verv lich signal-to-noise ratio of about 1000.," To examine certain key spectral features, we co-added the 70 individual spectra to obtain a composite spectrum with a very high signal-to-noise ratio of about 1000."
 Since the individual spectra were sampled at shelthy different velocities relative to the star due to the earth's orbital motion. the composite spectrum also las a better quality than the individual spectra.," Since the individual spectra were sampled at slightly different velocities relative to the star due to the earth's orbital motion, the composite spectrum also has a better quality than the individual spectra."
 Two kev spectral features m the composite spectrum are shown in 11., Two key spectral features in the composite spectrum are shown in 1.
 The Call II spectral reeion shows an οσο reversal in the core of the absorption line. sugeesting strong chromospheric activity.," The II H spectral region shows an emission reversal in the core of the absorption line, suggesting strong chromospheric activity."
 The broader CallI plhotospheric, The broader II photospheric
ouly ciffereice between the two is the setup of the initial concitious: the supersonie «‘ase starts [rom the 1-D solujon. siliar to what is presented in TaiOmeetal.(2009b).. whereas the σισοιic Case starts ron te final oput of a 1-D sunulatiou. which inclues the evolution of the meclitt ii1a more 'ealistic context of galaxy. evoution (Àodel VE: Tangοἱal.2009a)).,"only difference between the two is the setup of the initial conditions: the supersonic case starts from the 1-D solution, similar to what is presented in \citet{Tang09b}, whereas the subsonic case starts from the final output of a 1-D simulation, which includes the evolution of the circum-galactic medium in a more realistic context of galaxy evolution (Model VE; \citealt{Tang09a}) )."
 By compari1g resIts [rom 1e two cases. we inteud to illustrate t1e clepencleice of the tron ejeca evolutionT oi the [n]elobal outíOW speed.," By comparing results from the two cases, we intend to illustrate the dependence of the iron ejecta evolution on the global outflow speed."
 Both tle gas lass alid ie mechanical energy injecLOLS ale assuned to folow the same simooh distribution as the stars. wich is a Heruquist. profile (Heruquist1990) nitl the characteristic raclits of ry.," Both the gas mass and the mechanical energy injections are assumed to follow the same smooth distribution as the stars, which is a Hernquist profile \citep{Hernquist1990} with the characteristic radius of $r_b$."
 The tjcertaint]es lu the tass aud energy 1jection rates are a [ac[9]of 2. depeuciug Ol s»ecific empirical calibratios. potential mass-loacing from cool gas. etc. (," The uncertainties in the mass and energy injection rates are a factor of $\sim 2$, depending on specific empirical calibrations, potential mass-loading from cool gas, etc. ("
e.g.. 20006:Tangοἱal.2009a auc references therein).,"e.g., \citealt{David06,Tang09a} and references therein)."
 Our €hoseu energy rate is οἱ the lower side of the unce‘tainty range. whereas the lass rate is ou the hieler side.," Our chosen energy rate is on the lower side of the uncertainty range, whereas the mass rate is on the higher side."
 These choices 'esult in οἱ average a lower gas teiiperature. a greater soft X-ray emissivity. aud a lower iron abuncdatce. which are more close to what are directly. infer'ed fromm X-ray. observatious.," These choices result in on average a lower gas temperature, a greater soft X-ray emissivity, and a lower iron abundance, which are more close to what are directly inferred from X-ray observations."
 The 1-D models also assume au iποπ mixiug between the ejecta aud stellar mass injection and hence a uniform irou abuxlance of 2.7 solar., The 1-D models also assume an instantaneous mixing between the ejecta and stellar mass injection and hence a uniform iron abundance of 2.7 solar.
 We |ave Iguored auy [eedback from the supermassive black hole expected o be present a he center of a spheroid., We have ignored any feedback from the supermassive black hole expected to be present at the center of a spheroid.
" This feedback. likely occurring in bursts with certain p'eferential clirectious (e.g.. in form of jets). cau occasionally result iu significant disturbances in global hot gas dis""butions. as reflected by the asynetric X-ray morphologies observed in some elliptical galaxies (Diehl&Statler2008)."," This feedback, likely occurring in bursts with certain preferential directions (e.g., in form of jets), can occasionally result in significant disturbances in global hot gas distributions, as reflected by the asymmetric X-ray morphologies observed in some elliptical galaxies \citep{die08}."
. But. averaged over the time. Ia SNe are eiereetically more importau or a low- or iutermecdiate-nnass spjeroid with LyX10HL. (Davidelal.2006).," But, averaged over the time, Ia SNe are energetically more important for a low- or intermediate-mass spheroid with $L_K \lesssim 10^{11}L_{\odot K}$ \citep{David06}."
. The simulatious are perormed with FLASH (Fryxeletal.2000).. au Eulerian astrophysicaljl νά‘odynatnics code with the adaptive mesh refinement CAMB) capability.," The simulations are performed with FLASH \citep{Fryxell00}, an Eulerian astrophysical hydrodynamics code with the adaptive mesh refinement (AMR) capability."
 The 3-D simulaed box. 128 kpe ona side. is centerec on the spheroid aud has the so-called outLow (sometimes callCL boundary coucditio1," The 3-D simulated box, 128 kpc on a side, is centered on the spheroid and has the so-called outflow (sometimes called zero-gradient) boundary condition."
 As in Tangetal.(2009b).. only one octaut of the box is sinuulated at ful resolution. (down to about 1 pe). while the resolution is degraded by a [actor of four in the ‘est of the grid. except for regious where SNRs seeds have just been embedded.," As in \citet{Tang09b}, only one octant of the box is simulated at full resolution (down to about 4 pc), while the resolution is degraded by a factor of four in the rest of the grid, except for regions where SNRs seeds have just been embedded."
 The ci[Terence intie. resolution between the regious of the same simulation allows us to check the resolution, The difference in the resolution between the regions of the same simulation allows us to check the resolution
Table | gives the photometry and best estimates found for some of the early-type systems m CIO939-4713 which have observed counterparts in Dressler Gunn (1992) and give a good fit (4< 1.0).,Table 1 gives the photometry and best estimates found for some of the early-type systems in Cl0939+4713 which have observed counterparts in Dressler Gunn (1992) and give a good fit $\chi^2 < 1.0$ ).
 The mass fraction in young stars varies widely among galaxies., The mass fraction in young stars varies widely among galaxies.
 In order to show the range in fy and fi allowed. we show in figure 2 the contours at 75 and (thick line) confidence levels for some of these galaxies.," In order to show the range in $t_Y$ and $f_M$ allowed, we show in figure 2 the contours at 75 and (thick line) confidence levels for some of these galaxies."
 The crosses give the position of the minima., The crosses give the position of the minima.
 The elongated contours are a consequence of the age-mass degeneracy mentioned above., The elongated contours are a consequence of the age-mass degeneracy mentioned above.
 However. one can see from the figure that for some of these galaxies. a significant fraction in young stars is needed in order to explain their colors.," However, one can see from the figure that for some of these galaxies, a significant fraction in young stars is needed in order to explain their colors."
 In order to gauge the contribution from young stars to the photometry of the system. we define the fractional contribution of the young stellar component to the lummosity of the galaxy.," In order to gauge the contribution from young stars to the photometry of the system, we define the fractional contribution of the young stellar component to the luminosity of the galaxy."
 Using the V. band as reference: where £v=Yyv/Yoy is the ratio of the mass-to-light ratios between the young and the old components in the reference band.," Using the $V$ band as reference: where $\xi_V = \Upsilon_{Y,V}/\Upsilon_{O,V}$ is the ratio of the mass-to-light ratios between the young and the old components in the reference band."
 From an observational point of view it is worth relating fi to the fractional age change (Az) between the oldest burst (fo: zp= 3) and the V band luminosity-weighted age (5) after adding the younger burst (fj) whose mass fraction is given by far The top left panel of figure 2 shows three contours at An=(25.50.75% }. and the bottom left panel shows similar contours ," From an observational point of view it is worth relating $f_V$ to the fractional age change $\Delta\tau_V$ ) between the oldest burst $t_O$; $z_F=3$ ) and the $V$ band luminosity-weighted age $t_V$ ) after adding the younger burst $t_Y$ ) whose mass fraction is given by $f_M$: The top left panel of figure 2 shows three contours at $\Delta\tau_V = \{ 25, 50, 75\%\}$ , and the bottom left panel shows similar contours for $f_V$."
3truein +0.2truein For some of the galaxies. the most probable SFH corresponds to a fractional age reduction (with respect to the old population) above with respect to a single burst at zj;23. even though these galaxies will display at z2O a similar CM relation as the one found in Coma.," 3truein +0.2truein For some of the galaxies, the most probable SFH corresponds to a fractional age reduction (with respect to the old population) above with respect to a single burst at $z_F=3$, even though these galaxies will display at $z=0$ a similar CM relation as the one found in Coma."
 The bottom right panel overlays three contours corresponding to equivalent widths of H./ of 3. 5. and ((thick). showing that a combined NUV-optical photometry along with a spectroscopic measurement of Balmer indices will greatly reduce the age-mass degeneracy.," The bottom right panel overlays three contours corresponding to equivalent widths of $H\beta$ of 3, 5, and (thick), showing that a combined NUV-optical photometry along with a spectroscopic measurement of Balmer indices will greatly reduce the age-mass degeneracy."
 This paper represents a first attempt atquantifying the fraction in. young stars in early-type cluster galaxies., This paper represents a first attempt at the fraction in young stars in early-type cluster galaxies.
 From a spectrophotometric point of view. these galaxies commonly feature a population of very old stars. without any traces of recent star formation.," From a spectrophotometric point of view, these galaxies commonly feature a population of very old stars, without any traces of recent star formation."
 However. from a dynamical point of view. early-type systems must form from succesive merging stages.," However, from a dynamical point of view, early-type systems must form from succesive merging stages."
 The observation of these mergers locally display an active process of star formation. but progenitors with very little cold gas will undergo mergers which will not trigger star formation (Van Dokkum et al.," The observation of these mergers locally display an active process of star formation, but progenitors with very little cold gas will undergo mergers which will not trigger star formation (Van Dokkum et al."
 1999)., 1999).
 So far. observations of elliptical galaxies in the NUV spectral range were confined to the search of very old helium core-burning stars as a way of estimating very old ages in stellar populations.," So far, observations of elliptical galaxies in the NUV spectral range were confined to the search of very old helium core-burning stars as a way of estimating very old ages in stellar populations."
 However. the existence of early-type systems with a clear E+A spectral feature show that galaxies with this morphological type may have a more interesting star formation history.," However, the existence of early-type systems with a clear E+A spectral feature show that galaxies with this morphological type may have a more interesting star formation history."
 We focus on the NUV spectral range around rest frame where young stars overwhelm any contribution from older stellar populations., We focus on the NUV spectral range around rest frame where young stars overwhelm any contribution from older stellar populations.
 Observations of spectral indices have found arather large age spread in field and group early-type systems (Trager et al., Observations of spectral indices have found a rather large age spread in field and group early-type systems (Trager et al.
 2000)., 2000).
 However. their analysis — based on simple stellar populations — cannot quantify a young-to-old mass fraction.," However, their analysis — based on simple stellar populations — cannot quantify a young-to-old mass fraction."
 A comparison between NUV and optical colors allows us to quantify this stellar mass fraction. although with large error bars.," A comparison between NUV and optical colors allows us to quantify this stellar mass fraction, although with large error bars."
 Figure 3 gives the age and mass fraction of young stars (left) in early-type galaxies in cluster 0100204713., Figure 3 gives the age and mass fraction of young stars ) in early-type galaxies in cluster Cl0939+4713.
 Notwithstanding the large error bars. there is a significant trend towards younger ages and mass fractions in fainter galaxies. with a large fractional age difference with respect to a monolithic star formation history at high redshift which can," Notwithstanding the large error bars, there is a significant trend towards younger ages and mass fractions in fainter galaxies, with a large fractional age difference with respect to a monolithic star formation history at high redshift which can"
(Parmarctal.1985) Warner1995)]. Kaine2006)).,"\citep{parmar85} \citep{wade85}. \citep{white95}. \citealt{warner95}) \citealt{king06}) \citep{vanparadijs96,king97}."
 ting(2006) ~quu1077ke ~1.3&107!ke., \cite{king06} $\sim10^{22}~\mbox{kg}$ $\sim1.3\times10^{21}~\mbox{kg}$ \citep{king98}.
 757«ocN27 , $75^{\circ}<i<82^{\circ}$ 
Grandi et ((1997) mentioned the possibility that the unusual line parameters were caused by that asstuption not beime valid.,Grandi et (1997) mentioned the possibility that the unusual line parameters were caused by that assumption not being valid.
" Iudeecd. Wozuniak et ((1998. hereafter W9s) found that if the ‘data (with au updated calibration of 1997) were fittedin the |10 keV rauge assuninug the preseuce of Compton reflection with a reflector solid augle of O between 0 aud 27. the parameters of the ine became much more plivysically plausible. with he best-fit values of Wi,260 110 eV. the peal enerev. Egg,26.1 keV. aud oj,&0.32 keV and 20 keV assuming ο=0 and 27. respectively."," Indeed, Woźnniak et (1998, hereafter W98) found that if the data (with an updated calibration of 1997) were fitted in the 4–10 keV range assuming the presence of Compton reflection with a reflector solid angle of $\Omega$ between 0 and $2\pi$, the parameters of the line became much more physically plausible, with the best-fit values of $\wfe\approx 60$ –110 eV, the peak energy, $\efe
\approx 6.4$ keV, and $\sfe\simeq 0.32$ keV and 0.20 keV assuming $\Omega=0$ and $2\pi$, respectively."
" The line in the data was again claimed to be very strong aud ποσα. by. Sambruna. Exracleous Mushotzkw (1999). who obtained Wh,=510» eV and ox=USODHT keV. virtually identical with the values of Grandi et (C1997)."," The line in the data was again claimed to be very strong and broad by Sambruna, Eracleous Mushotzky (1999), who obtained $\wfe=510_{- 90}^{+70}$ eV and $\sfe=0.89^{+0.17}_{- 0.15}$ keV, virtually identical with the values of Grandi et (1997)."
 This issue has recently been resolved thanks to results of andBeppoSaX., This issue has recently been resolved thanks to results of and.
". Evacleous. οαπλα Mushotzky (2000. hereafter E0Q) have found the line in the ‘data (€1 keV) to be weak with the paramecters consistent with those of WS. namely Hg,=90139 eV aud ej,<L2 keV. Similarly. Grandi (2000. hereafter GO0) have found Wi,=6050 eV aud on,=O.27'032 keV iu a preliminary analvsis of the data."," Eracleous, Sambruna Mushotzky (2000, hereafter E00) have found the line in the data $\geq 4$ keV) to be weak with the parameters consistent with those of W98, namely $\wfe=90^{+30}_{- 20}$ eV and $\sfe<1.2$ keV. Similarly, Grandi (2000, hereafter G00) have found $\wfe=60^{+80}_{- 40}$ eV and $\sfe=0.27_{-0.27}^{+0.40}$ keV in a preliminary analysis of the data."
 Since did uot observe 3€ 120. the actual strength of Coniptou reflection had been uukuown until the results of EQOQ aud GOO. who found Q/27= and 0.7|ar respectively.," Since did not observe 3C 120, the actual strength of Compton reflection had been unknown until the results of E00 and G00, who found $\Omega/2\pi=0.4^{+0.4}_{- 0.1}$ and $0.7^{+0.4}_{-0.4}$, respectively."
 These values of the TERREsolid augle are compatible (George Fabian 1901: Zavvi Czerny 1991) with the presence of a modest Fe Ίνα line with the parameters of W98. E00 aud CO.," These values of the solid angle are compatible (George Fabian 1991; Żyycki Czerny 1994) with the presence of a modest Fe $\alpha$ line with the parameters of W98, E00 and G00."
 Tere. we preseut a comprehensive analysis of the observation of 3C 120 hyPeppoSAX.. which combines the broad-baud lard X-ray. coverage of 'owidth a ligh cnerev resolution and an energv range in soft N-ravs comparable to that ofASCA.," Here, we present a comprehensive analysis of the observation of 3C 120 by, which combines the broad-band hard X-ray coverage of with a high energy resolution and an energy range in soft X-rays comparable to that of."
. We address the issues of the parameters of the line and the continua. their variability. raciative processes and ecometry of the source. and the relationship of 3€ 120 to other BLRGs as well as Sevterts.," We address the issues of the parameters of the line and the continuum, their variability, radiative processes and geometry of the source, and the relationship of 3C 120 to other BLRGs as well as Seyferts."
 The observation log is given in Table 1.., The observation log is given in Table \ref{t:log}.
 Data from cach instrmucut have been reduced following the standard procedures (Fiore. Cainazzi ας 1999. hereafter F99).," Data from each instrument have been reduced following the standard procedures (Fiore, Guainazzi Grandi 1999, hereafter F99)."
 Spectra of LECS aud AIECS (2 units) detectors were extracted using a radius of G and lL’. respectively.," Spectra of LECS and MECS (2 units) detectors were extracted using a radius of $6'$ and $4'$, respectively."
 The backeround spectra were taken from the blank sky fields in the position of the source with the same extraction reeglons., The background spectra were taken from the blank sky fields in the position of the source with the same extraction regions.
 We bin the LECS aud. MECS spectral files proportionally to the iustrmucutal resolution (F99)., We bin the LECS and MECS spectral files proportionally to the instrumental resolution (F99).
 After rebinuing. there is always more than 20 counts per channel. as required for the validity of \? fitting.," After rebinning, there is always more than 20 counts per channel, as required for the validity of $\chi^2$ fitting."
 The LECS data are analyzed in tlie 0.3L keV cnerev range (chaunels 2180)., The LECS data are analyzed in the 0.3–4 keV energy range (channels 24–80).
 The lower limit is above the standard value of 0.15 keV (F99) because the source was stronely dominated by the backeround below 0.3 keV. The energy range of 1.310 keV (channels 31111) is used for the MECS data., The lower limit is above the standard value of 0.15 keV (F99) because the source was strongly dominated by the background below 0.3 keV. The energy range of 1.3–10 keV (channels 34–114) is used for the MECS data.
 We allow a free normalization of the LECS spectrmm with respect to the MECS one (E99)., We allow a free normalization of the LECS spectrum with respect to the MECS one (F99).
 We use the variable rise-time. PDS προςαπ., We use the variable rise-time PDS spectrum.
 This choice is im aerecmentC» with F99. who reconunend this method for weak sources with count rates <0.5 1 + and the statistical uncertainty of the photon index. E. of ATz0.1. and with spectra simular to that of the Crab.," This choice is in agreement with F99, who recommend this method for weak sources with count rates $\la 0.5$ –1 $^{-1}$ and the statistical uncertainty of the photon index, $\Gamma$, of $\Delta \Gamma\ga 0.1$, and with spectra similar to that of the Crab."
" ludeed. D~2.140.1. in the PDS data. very simular to the Crab spectrum. aud the 13.110 keV count rate is 0.728 7,"," Indeed, $\Gamma\simeq 2.1 \pm 0.1$ in the PDS data, very similar to the Crab spectrum, and the 13–110 keV count rate is 0.72 $^{-1}$."
 After using the logaritlinic rebinming in LS chanucls (F99). photons are detected up to chaunel 15. and hereafter we use channels 215.," After using the logarithmic rebinning in 18 channels (F99), photons are detected up to channel 15, and hereafter we use channels 2–15."
 When the variable auc fixed. rise-time spectra are fitted by the same model. the normalization of the former is about 0.95 of the latter.," When the variable and fixed rise-time spectra are fitted by the same model, the normalization of the former is about 0.95 of the latter."
 The same value is obtained bv directly dividing the two spectra in the 15100 keV energy range., The same value is obtained by directly dividing the two spectra in the 15–100 keV energy range.
 Lf the lowest clhamnels (1315 keV) are also iucluded. the ratio becomes slightly lower (0.93).," If the lowest channels (13–15 keV) are also included, the ratio becomes slightly lower (0.93)."
 From this aud recouunendations of F99. we derive the allowed relative normalization of the PDS spectrin with respect to the NECS one of 0.77," From this and recommendations of F99, we derive the allowed relative normalization of the PDS spectrum with respect to the MECS one of 0.77--0.85."
dominate cuuission and absorption at É2νι,dominate emission and absorption at $\nu>\nu_i$.
" Shock acceleration is expected to generate a power-law cucrey distribution of clectrous. di.fdr,x5,7 at 5>5;"," Shock acceleration is expected to generate a power-law energy distribution of electrons, $dn_e/d\gamma_e\propto\gamma_e^{-2}$ at $\gamma_e>\gamma_i$."
" For this euergv distribution. the volume averaged ΠΙΟ density. of electrons with Loreutz factor 5,2+; ds ne[t-GoMtal(si/5)τιfet?"," For this energy distribution, the volume averaged number density of electrons with Lorentz factor $\gamma_\nu>\gamma_i$ is $n_e[t_c(\gamma_\nu)/t_d](\gamma_i/\gamma_\nu)=n_e[t_c(\gamma_\nu)/t_d](\nu_i/\nu)^{1/2}$."
 Using the sale argument leading to eq. (1)), Using the same argument leading to eq. \ref{eq:absorp_nu}) )
" we find. for 14,2i. The fat electron euerev distribution. 52dn.fd5,x 29. eenerates equal amounts of synchrotron energy in logarithuic photon eucrev intervals. Fy,xb) for v>νι Qvhen 12 νι)."," we find, for $\nu_a>\nu_i$, The flat electron energy distribution, $\gamma_e^2dn_e/d\gamma_e\propto\gamma_e^0$ , generates equal amounts of synchrotron energy in logarithmic photon energy intervals, $\nu F_\nu\propto\nu^0$ for $\nu>\nu_a$ (when $\nu_a>\nu_i$ )."
" We therefore obtain for v«rj, a (time inteerated) spectrin given by pgjPF,xEggImR163...pe 6 "," We therefore obtain for $\nu<\nu_{ia}$ a (time integrated) spectrum given by $\nu F_\nu\propto E_{\rm
fluc}y^{-1}|_{\nu_a=\nu}\propto R^{-4/3}|_{\nu_a=\nu}\propto\nu^{7/6}$ ."
Combining the above results. the observed flux at Vig Is givou by Several conuuenuts should be made here.," Combining the above results, the observed flux at $\nu<\nu_{ia}$ is given by Several comments should be made here."
 The fiux ratio eiven by eq. (8)), The flux ratio given by eq. \ref{eq:F_ratio}) )
 holds only ou average., holds only on average.
 The observed flux ratios in individual CRB eveuts may differ sisuificauflv. since for a small nuuber of shells (and collisions) large variations iu the late residual collisions should be expected.," The observed flux ratios in individual GRB events may differ significantly, since for a small number of shells (and collisions) large variations in the late residual collisions should be expected."
" It should also be noticed that we have assumed epocE. while initial conditions with Cp,2D maw lead to more cficient 5-rav production at sinall radi. in which case ΕΕ should be sinaller by a factor of a few than the ratio given in eq. (8))."," It should also be noticed that we have assumed $\sigma_{\Gamma,0}<\Gamma$, while initial conditions with $\sigma_{\Gamma,0}>\Gamma$ may lead to more efficient $\gamma$ -ray production at small radii, in which case $F_\nu/F_{\nu_\gamma}$ should be smaller by a factor of a few than the ratio given in eq. \ref{eq:F_ratio}) )."
 We have shown that late residual collisions. that occur af radi auch larger than those where 2-rav producing collisions take place. may naturally accounut for the observed strong optical emüssion accompanying the prompt CRB.," We have shown that late residual collisions, that occur at radii much larger than those where $\gamma$ -ray producing collisions take place, may naturally account for the observed strong optical emission accompanying the prompt GRB."
 Tuternal collisions at 11all radii reduce the variance of colliding shell velocities., Internal collisions at small radii reduce the variance of colliding shell velocities.
 As a result. the enerev available for radiation at laree radii aud the characteristic frequency of radiated photons decrease with radius.," As a result, the energy available for radiation at large radii and the characteristic frequency of radiated photons decrease with radius."
 We find that one may expect optical to +- chevey ratio ~LO| with laree burst-to-burst scatter (sce fig. 1..," We find that one may expect optical to $\gamma$ -ray energy ratio $\sim10^{-4}$, with large burst-to-burst scatter (see fig. \ref{fig},"
 eq., eq.
 & aud discussion at the eud of 3.2)., \ref{eq:F_ratio} and discussion at the end of \ref{sec:rad}) ).
" This is consistent with the results of Yostetal.§(2007).. who find that during the prompt emission of GRBs the spectral indices between the optical aud the 5-xav. bands are in the range of 0<Apo.«XU. corresponding to F,/F.~I10 and implying that the optical eluission is only a small fraction. ~10°10°. of the total emitted energy."," This is consistent with the results of \cite{Yost07}, who find that during the prompt emission of GRBs the spectral indices between the optical and the $\gamma$ -ray bands are in the range of $0<\beta_{{\rm op}-\gamma}<0.5$, corresponding to $F_{\nu_{\rm
op}}/F_{\nu_\gamma}\sim1-10^3$ and implying that the optical emission is only a small fraction, $\sim10^{-6}-10^{-3}$, of the total emitted energy."
 Although the optical eniüission is produced at LÓlurge radi where svuchrotron soelfabsorptiou is avoided. the expected time delay between 5-ray aud optical emission. ~OL 8 (see eg. 3).," Although the optical emission is produced at large radii, where synchrotron self-absorption is avoided, the expected time delay between $\gamma$ -ray and optical emission, $\sim0.1$ s (see eq. \ref{eq:delay time}) ),"
 is shorter than the characteristic temporal resolution of the optical observations. which is a few seconds (e.g.Tang&Zhang2006).," is shorter than the characteristic temporal resolution of the optical observations, which is a few seconds \citep[e.g.][]{TZ06}."
. Thus. optical aud -rav enuission nav appear to be sinmltaucous.," Thus, optical and $\gamma$ -ray emission may appear to be simultaneous."
" However. better temporal resolution may allow one to detect a systematic tine delay between the two wave ας,"," However, better temporal resolution may allow one to detect a systematic time delay between the two wave bands."
 Iu addition. oue would expect larger observed variability timescales at louger wavelengths. fau~Tdclay:," In addition, one would expect larger observed variability timescales at longer wavelengths, $t_{\rm var, op}\sim\tau_{\rm delay}$."
 Wei(2007) has suggested that optical cussion nav be eenerated by strong iuterial shocks at radii R/e>10° «s. driven by shells emitted with a large time delay. 10 s. following those producie the ndn οταν cussion (seealsoFanetal.2005).," \citet{Wei07} has suggested that optical emission may be generated by strong internal shocks at radii $R/c>10^6$ s, driven by shells emitted with a large time delay, $\sim10$ s, following those producing the main $\gamma$ -ray emission \citep[see
also][]{Fan05}."
. Our imodel is quite. different., Our model is quite different.
 We show that optical enuüssiou is naturally expected to arise. without postulating the existence of delaved shells. by residual collisions at Rée~LO! s. in which the characteristic cuutted photon frequency is low. fi~1 eV. due to the reduction of the Lorentz factor variance iithe flow (rather than by the lavee radius 2/e>108 «).," We show that optical emission is naturally expected to arise, without postulating the existence of delayed shells, by residual collisions at $R/c\sim10^4$ s, in which the characteristic emitted photon frequency is low, $h\nu\sim1$ eV, due to the reduction of the Lorentz factor variance in the flow (rather than by the large radius $R/c>10^6$ s)."
 YMoreover. we have shown that the optical Iuninositv can be estimated from the burst 5-ray. properties. and that it ds consistent with the observations.," Moreover, we have shown that the optical luminosity can be estimated from the burst $\gamma$ -ray properties, and that it is consistent with the observations."
 The energv released in residual collisious of the relativistic outflow is large., The energy released in residual collisions of the relativistic outflow is large.
 Iu fact. it would overproduce the optical e1uission if all the energy is released in the optical baud.," In fact, it would overproduce the optical emission if all the energy is released in the optical band."
 Tn the models discussed here. only a suiall fraction of the cnerey. 107. is released as svuchrotron radiation. since electrons accelerated im residual collisious cool mainly by IC scattering of the prompt GRD ο ταν».," In the models discussed here, only a small fraction of the energy, $\sim10^{-2}$, is released as synchrotron radiation, since electrons accelerated in residual collisions cool mainly by IC scattering of the prompt GRB $\gamma$ -rays."
" This has some inuportaut implications to observations at lieh euergy. 2100 MeV. Such observations are expected to be useful iu determining the bulk Loreutz factor of GRD outflows aud the size of the enuüttiug region by detecting the hieh euergv cutoff due to 55 absorption (οιο,,Baring2000:Litlwick&Sari2001:Lietal.2003)."," This has some important implications to observations at high energy, $> 100$ MeV. Such observations are expected to be useful in determining the bulk Lorentz factor of GRB outflows and the size of the emitting region by detecting the high energy cutoff due to $\gamma\gamma$ absorption \citep[e.g.,][]{Baring00,Lithwick01,LZ03}."
.. The identification of this cutoff may be complicated iu the the presence of strong hieh cucrey cussion frou residual collisions. that take place at laree radii where the 5*5 optical depth is reduced.," The identification of this cutoff may be complicated in the the presence of strong high energy emission from residual collisions, that take place at large radii where the $\gamma\gamma$ optical depth is reduced."
 A conuuent is iu place here regarding some recent constraints on the size of the GRB emission region. which were inferred from the carly X-ray steep decay.," A comment is in place here regarding some recent constraints on the size of the GRB emission region, which were inferred from the early X-ray steep decay."
 Asstumine that the steep decay arises frou cussionby plasma ling away from our line of sight. large radi were interred. Baaο26sLM cur for faga.21078 and @;S0.3 (Lazzati&Degehuanu2006:Lyutikov2006:Iwunmaretal. 2007).," Assuming that the steep decay arises from emission by plasma lying away from our line of sight, large radii were inferred, $R_{\rm em}>2t_{\rm decay}c/\theta_j^2\ga6\times10^{13}$ cm for $t_{\rm
decay}\ga10^2$ s and $\theta_j\la0.3$ \citep{Lazz06,Lyutikov06,Kumar07}."
. Such radi are larecr than typically predicted im internal shock models., Such radii are larger than typically predicted in internal shock models.
 It should he realized. however. that if the off-the-lince-ofsieht emission explanation is adopted. the emission chairing this phase should peak below the N-xav band. aud should therefore arise In a region different than that where 5-rays are produced.," It should be realized, however, that if the off-the-line-of-sight emission explanation is adopted, the emission during this phase should peak below the X-ray band, and should therefore arise in a region different than that where $\gamma$ -rays are produced."
 This is due to the fact that the flat N-ray spectrin (FL x») seen in GRD spectra would imply light curve decay xf7 (eoKuuuarwm X00)... muuch shallower than observed (e.g...Tagliaterrietal. 2005).," This is due to the fact that the flat X-ray spectrum $F_\nu\propto \nu^{0}$ ) seen in GRB spectra would imply a light curve decay $\propto t^{-2}$ \citep[e.g.,][]{Kumar00}, much shallower than observed \citep[e.g.,][]{Tagli05}."
. In fact. the spectra cing the steep decay are soft. suggesting that indeed the energy peak is below the Nerav band.," In fact, the spectra during the steep decay are soft, suggesting that indeed the energy peak is below the X-ray band."
 Thus. if the steep decay is due to offthe-lne-ofsight emission. it should originate from a reeion Wine at a larger radius thin that where 5-rays are produced. producing emission that peaks below the A-rav band.," Thus, if the steep decay is due to off-the-line-of-sight emission, it should originate from a region lying at a larger radius than that where $\gamma$ -rays are produced, producing emission that peaks below the X-ray band."
 Such cussion may be produced. e.g. bv residual collisions.," Such emission may be produced, e.g, by residual collisions."
 This research was supported iu part bv ISF and Minerva erauts., This research was supported in part by ISF and Minerva grants.
Tuteractions between a gaseous disk aud embedded proto-planetary cores could be decisive to understand the distribution of senmüanuajor axis. eccentricities aud masses of extra-solar eiut planets (Perryman 2000. Schueider 2001).,"Interactions between a gaseous disk and embedded proto-planetary cores could be decisive to understand the distribution of semi-major axis, eccentricities and masses of extra-solar giant planets (Perryman 2000, Schneider 2004)."
 Exchanges of augular momentum can eficicutly operate through the excitation of spiral density waves at the sites of Lindblad resonances. leading to inward uueration of solid bodies (Coldreich Tremaine 1979 1980. Ward 1997).," Exchanges of angular momentum can efficiently operate through the excitation of spiral density waves at the sites of Lindblad resonances, leading to inward migration of solid bodies (Goldreich Tremaine 1979 1980, Ward 1997)."
 For planets with mass less than about a Jovian mass. the interaction between the disk aud the planct is mostly linear (tvpe-I uuegration). iu coutrast with the non-linear προ migration where massive planet:J4. open a gap.," For planets with mass less than about a Jovian mass, the interaction between the disk and the planet is mostly linear (type-I migration), in contrast with the non-linear type-II migration where massive planets open a gap."
 In any case. the drift time-scale is mich shorter than the time required for the completion of a (ciant) planet.," In any case, the drift time-scale is much shorter than the time required for the completion of a (giant) planet."
 Several works have receutly focused on niens to slow down or stop nüeration., Several works have recently focused on means to slow down or stop migration.
 The presence of a toroidal magnetic field (Terquem 2003). tri-cimensional effects (Tanaka. Takeuchi Ward 2002) or corotation torques (DDAneclo. Wenning Klev 2002) could act in this wav.," The presence of a toroidal magnetic field (Terquem 2003), tri-dimensional effects (Tanaka, Takeuchi Ward 2002) or corotation torques (D'Angelo, Henning Kley 2002) could act in this way."
 From uunerical smmlatious. Nelson Benz (2003a b) have shown that disk selt-eravitv cau noticeably affect the drift velocity (even for low mass disks).," From numerical simulations, Nelson Benz (2003a b) have shown that disk self-gravity can noticeably affect the drift velocity (even for low mass disks)."
 They sugeested that even verv weak changes of the rotation curve induced by disk gravitv significautflv miodifiv he location of Lindblad resonances. aud subsequently he total differentiali torque.," They suggested that even very weak changes of the rotation curve induced by disk gravity significantly modifiy the location of Lindblad resonances, and subsequently the total differential torque."
 Their conclusions are jiowever stronely resolutiou-depeudent., Their conclusions are however strongly resolution-dependent.
 Iu this short cobmullication. we clarify the infiuence of disk eravity on type-I nueration by a semi-analvtical approach.," In this short communication, we clarify the influence of disk gravity on type-I migration by a semi-analytical approach."
 Iu yarticular. we determine analytically for the first time the ocation of Lindblad resonances modified by disk gravity. and compute the correspoudiug eravitational torques.," In particular, we determine analytically for the first time the location of Lindblad resonances modified by disk gravity, and compute the corresponding gravitational torques."
 Analytical techniques ecnerally provide reliable diaguostic ools and powerful predictions as they implicitely correspond to an infinite nunerical resolution., Analytical techniques generally provide reliable diagnostic tools and powerful predictions as they implicitely correspond to an infinite numerical resolution.
 Iu Sect. 2..," In Sect. \ref{sec:location},"
 we derive and discuss a general expression or the location of Lindblad resonances as functions of the disk surface deusity profile. orbit of the planet. relative disk mass aud edges.," we derive and discuss a general expression for the location of Lindblad resonances as functions of the disk surface density profile, orbit of the planet, relative disk mass and edges."
 In Sect. 3..," In Sect. \ref{sec:influence},"
 we successfully check this expression in the simple case of radially homogeuous disks., we successfully check this expression in the simple case of radially homogenous disks.
 The effect of the disk mass on Lindblad torques is then analyzed., The effect of the disk mass on Lindblad torques is then analyzed.
 Finally. we cousider the case of disks with power-law surface deusitv profiles.," Finally, we consider the case of disks with power-law surface density profiles."
 We conclude iu Sect. l.., We conclude in Sect. \ref{sec:conc}.
 A planet embedded in a gaseous disk exerts eravitational orques at sites of Lindblad resonances., A planet embedded in a gaseous disk exerts gravitational torques at sites of Lindblad resonances.
 For low mass )xdies. the disk response to the perturbing point mass xteutial cau be considered as linear. so that torques can explicitly be determined (Coldreich Tremaine 1979. Artvinowicz 1993).," For low mass bodies, the disk response to the perturbing point mass potential can be considered as linear, so that torques can explicitly be determined (Goldreich Tremaine 1979, Artymowicz 1993)."
" The nominal positious RpGi) of he inner (ILRs) and outer (OLRs) Liudblad resouauces associated with the m-th order Fourier pattern are found roni the equation D(fij)=0 with where # is the epievelie frequeney defined by. 4?=107.| 2PROGQ/AR. OQ is the Suid angular velocity aud Q, ps the aneular velocity of the planet."," The nominal positions $\rn(m)$ of the inner (ILRs) and outer (OLRs) Lindblad resonances associated with the $m$ -th order Fourier pattern are found from the equation $D(\rn)=0$ with where $\kappa$ is the epicyclic frequency defined by $\kappa^2=4\Omega^2+2R\Omega d\Omega/dR$ , $\Omega$ is the fluid angular velocity and $\op$ is the angular velocity of the planet."
 Generally. Rudin) differs frou the effective locatious of Lindblad POSOLALLCCS(hereafter R.} where the Waves become evanescent.," Generally, $\rn(m)$ differs from the effective locations of Lindblad resonances(hereafter $\re$ ) where the waves become evanescent."
 Effective resonances are found from the equation D.(R.)= Owith (Artvinowicz 1993. Ward 1997) where ος ds the sound speed.," Effective resonances are found from the equation $D_*(\re)=0$ with (Artymowicz 1993, Ward 1997) where $\cs$ is the sound speed."
 If the disk aspect ratio ITfr— ads a constant. we then have e=ΟΠ. aud so where e=1d stands for the ILRs. e=11 is for the OLRs. aud f=Yl| 2a.," If the disk aspect ratio $H/r \equiv \eta$ is a constant, we then have $\cs = \ok \eta R$, and so where $\epsilon=-1$ stands for the ILRs, $\epsilon=+1$ is for the OLRs, and $f=\sqrt{1+m^2\eta^2}$ ."
 This expression shows that nuoninal and effective resonances coincide oulv for low (n values., This expression shows that nominal and effective resonances coincide only for low $m$ values.
photoionized emission: indeed a model including emission from a collisionally ionized gas is unable to produce an acceptable fit to the spectrum.,photoionized emission; indeed a model including emission from a collisionally ionized gas is unable to produce an acceptable fit to the spectrum.
 The enussion from the IHe-like triplets oftextsevil..lexiscix.. and appear lo be resolved into their respective forbidden and intercombination lines.," The emission from the He-like triplets of, and appear to be resolved into their respective forbidden and intercombination lines."
 Indeed all of the IHe-like lines are well modeled in (his manner. e.g. lor example. as cliscussed in Sections 3 and 4. while the line energies are in agreement with the expected rest.[rame energies of the forbidden and intercombination transitions.," Indeed all of the He-like lines are well modeled in this manner, e.g. for example, as discussed in Sections 3 and 4, while the line energies are in agreement with the expected rest–frame energies of the forbidden and intercombination transitions."
 The fact that significant intercombination enmission is detected suggests the density of the plasma is high., The fact that significant intercombination emission is detected suggests the density of the plasma is high.
 Indeed the ratio /2 of the forbidden to intercombination emission is close to. Ro—1 (see Section 3.2.2)., Indeed the ratio $R$ of the forbidden to intercombination emission is close to $R\sim1$ (see Section 3.2.2).
 This sets a lower-limit on the density of the He-like emitting gas of ? (see Porquet&Duban2000.. Figure 8).," This sets a lower-limit on the density of the He-like emitting gas of $n_{\rm e}>10^{10}$ $^{-3}$ (see \citealt{porquet00}, Figure 8)."
 Thus an upperlimit of the radial distance to the emitter [rom central X-ray source can be estimated [rom the definition of the ionization parameter of the emitting gas. Le. R?= μπα. Ile," Thus an upper–limit of the radial distance to the emitter from central X-ray source can be estimated from the definition of the ionization parameter of the emitting gas, i.e. $R^{2} = L_{\rm ion} / \xi n_{\rm e}$ ."
"re Li, is the ionizing luminosity from 1—1000 Rdberg. which from the bestfit continuum parameters in 33. gives Li,=3xl0! + for 4445."," Here $L_{\rm ion}$ is the ionizing luminosity from $1-1000$ Rydberg, which from the best–fit continuum parameters in 3, gives $L_{\rm ion} = 3\times 10^{44}$ $^{-1}$ for 445."
" The ionization parameter of the He-like emitting gas is log£=L8eergcemss |. as measured [rom (he emission model (Section 4.1. Table 3). while n,>10 oοE as describedabove."," The ionization parameter of the He-like emitting gas is $\log \xi=1.8$ $^{-1}$, as measured from the emission model (Section 4.1, Table 3), while $n_{\rm e}>10^{10}$ $^{-3}$ as describedabove."
 Thus the radial distance to the emitter derived from this method is R«2xLOM eem (or <0.01 ppc)., Thus the radial distance to the emitter derived from this method is $R<2\times 10^{16}$ cm (or $<0.01$ pc).
" For an estimated black hole mass of 4445 of Mpue»2x105 citepbettoni03. marchesini04.. (his corresponds (o a radius of 10007""e "," For an estimated black hole mass of 445 of $M_{\rm BH} \sim 2\times10^{8}$ \\citep{bettoni03, marchesini04}, this corresponds to a radius of $\sim1000 R_{\rm g}$."
Alternatively the location of the emitting gas can be estimated from the measured line widths of the emission., Alternatively the location of the emitting gas can be estimated from the measured line widths of the emission.
 The best fit width of the three strongest emission lines (namely [and i and Lyman-a) is epyyμοι=2600ue +(section 3.2.3)., The best fit width of the three strongest emission lines (namely f and i and $\alpha$ ) is $v_{FWHM}=2600^{+1000}_{-600}$ $^{-1}$(section 3.2.3).
 Thus assuming Weplerian motion. R~GALBLL /(7. where here we define the velocity width as e=∙≽↓∖↓∟∖↓ Xe.," Thus assuming Keplerian motion, $R \sim GM_{\rm BH} / v^{2}$ , where here we define the velocity width as $v=\frac{\sqrt{3}}{2} v_{\rm FWHM}$ ."
 Thus by, Thus by
lis a voung nearby supernova remnant (SNIU recently discovered. (Aschenbach1998:Lyvucinetal.1905) near the southeastern perimeter of the well known old Vela SNR.,"is a young nearby supernova remnant (SNR) recently discovered \citep{aschenbach98,iyudin.et.al98} near the southeastern perimeter of the well known old Vela SNR."
 thas generated much interest since the distance and age could be as lowas 200pc and TOOwr respectively. and hus it could have been generated by the nearest supernova explosion in recent human history.," has generated much interest since the distance and age could be as lowas $200~{\rm pc}$ and $700~{\rm
yr}$ respectively and thus it could have been generated by the nearest supernova explosion in recent human history."
 The SNR was discovered. in. Rosat hard. N-rav. data (shown as contours in 1)) and at these energies iw a shell-like morphology., The SNR was discovered in Rosat hard X-ray data (shown as contours in \ref{esorass}) ) and at these energies has a shell-like morphology.
 Fhere is no obvious optical counterpart to the main body of the SNR but Hedmanetal.(2000) showed that a fragment of X-ray emission (labelled D/D' by Aschenbachctal. 1995)) coincides. closely with a bright optical nebula. ROW 37.," There is no obvious optical counterpart to the main body of the SNR but \citet{redman.et.al00} showed that a fragment of X-ray emission (labelled D/D' by \citealt{aschenbach.et.al95}) ) coincides closely with a bright optical nebula, RCW 37."
 Phe X-ray [ragmoent. is ocated just bevond the main circular body of the remnant and is clearly visible in hard X-ray images., The X-ray fragment is located just beyond the main circular body of the remnant and is clearly visible in hard X-ray images.
 Phe main X-ray shell is not complete and there is a break in the emission in a direction coincident with that of the X-ray. fragment and with ROW 37 (see 1))., The main X-ray shell is not complete and there is a break in the emission in a direction coincident with that of the X-ray fragment and with RCW 37 (see \ref{esorass}) ).
 Reclmanetal.(2000). suggested hat ROW 37 is physically associated with aand represents a venting of hot gas from the interior of the remnant to bevond the roughly circular shell as delimited in he X-ray., \citet{redman.et.al00} suggested that RCW 37 is physically associated with and represents a venting of hot gas from the interior of the remnant to beyond the roughly circular shell as delimited in the X-ray.
 ROW 37 (NGC 2736) was discovered in the 15405 by Sir John Llerschel anc is a bright optical nebula known o amateur astronomers as the Peneil Nebula 2))., RCW 37 (NGC 2736) was discovered in the 1840s by Sir John Herschel and is a bright optical nebula known to amateur astronomers as the Pencil Nebula \ref{eso}) ).
 The unusual. intricate morphology of the nebula ancl its arge size ancl brightness make it surprising that there have xen few studies of this object.," The unusual, intricate morphology of the nebula and its large size and brightness make it surprising that there have been few studies of this object."
 Its apparent. location at he clust-obseurecl eastern. side of the six degree. diameter old. Vela SNR. away from the photogenic western filaments may be one reason.," Its apparent location at the dust-obscured eastern side of the six degree diameter old Vela SNR, away from the photogenic western filaments may be one reason."
 Blairetal.(1995). used the Ultraviolet Spectrometer on the Vovager 2 spacecraft to investigate O emission from ROW 37 and inferred that shock speeds of, \citet{blair.et.al95} used the Ultraviolet Spectrometer on the Voyager 2 spacecraft to investigate O emission from RCW 37 and inferred that shock speeds of
ANT sources appear in both.,387 sources appear in both.
 The 222 sources that appear in the RBSCNVSS comparison sample but not in the RASSσσ catalogue are the candidate galaxy clusters which were removed. in our selection. process., The 222 sources that appear in the RBSC–NVSS comparison sample but not in the RASS--6dFGS catalogue are the candidate galaxy clusters which were removed in our selection process.
 94 of these sources were observed as part of the entire 6dI Galaxy Survey ane as a result optical spectra of these are available from the GdGS website. but are not included in this catalogue.," 94 of these sources were observed as part of the entire 6dF Galaxy Survey and as a result optical spectra of these are available from the 6dFGS website, but are not included in this catalogue."
" Phese sources are discussed in Section Έντο,", These sources are discussed in Section \ref{clusters}.
 There are 569. (59.5%) sources that appear in the RASSGdECS comparison catalogue. but were not. found in the RBSCNVSS sample.," There are 569 $\%$ ) sources that appear in the RASS–6dFGS comparison catalogue, but were not found in the RBSC–NVSS sample."
" The main reason [for this (accounting for 96%) is that these objects do not have racio counterparts above 5,4=2.5 mmJy. the NVSS Ilux limit."," The main reason for this (accounting for $\%$ ) is that these objects do not have radio counterparts above $S_{1.4}=2.5$ mJy, the NVSS flux limit."
 Figures 12. and 13. show that although the RASSσσ and RBSCNVSS samples were selected in slightly cilferent wavs. the redshift ancl magnitude clistributions are reasonably similar. with the only significant dillerence being the number of objects in the LASS6dEXCS sample.," Figures \ref{allzhist} and \ref{allbmaghist} show that although the RASS--6dFGS and RBSC–NVSS samples were selected in slightly different ways, the redshift and magnitude distributions are reasonably similar, with the only significant difference being the number of objects in the RASS–6dFGS sample."
 As only οτιA οἱ our sample are detected in the radio. it highlights how many potential AGN are missed in a radio selected: sample.," As only $27 \%$ of our sample are detected in the radio, it highlights how many potential AGN are missed in a radio selected sample."
 The RASS6dECGS radio sample (when tailored to the selection criteria described. above) can be viewed. as the southern counterpart to the λοςNVSS catalogue., The RASS–6dFGS radio sample (when tailored to the selection criteria described above) can be viewed as the southern counterpart to the RBSC–NVSS catalogue.
 Figure 14. shows that the distribution of flux density at 1 GGlIZz is very similar for these two samples., Figure \ref{radiodist} shows that the distribution of flux density at $\sim$ GHz is very similar for these two samples.
 In this figure. the observed Lux densities in cach catalogue were firstly binned in log Lux and then normalised by the total number of sources of cach sample.," In this figure, the observed flux densities in each catalogue were firstly binned in log flux and then normalised by the total number of sources of each sample."
 Looking at the fraction of sources in cach bin allows us to compare these saniples more accurately., Looking at the fraction of sources in each bin allows us to compare these samples more accurately.
 The slight excess of RBSCNVSS sources in the lower bins is due to the mareinally fainter Dux limit of the NVSS mmy) as opposed to the SUMSS catalogue (6mm.Jv)., The slight excess of RBSC–NVSS sources in the lower bins is due to the marginally fainter flux limit of the NVSS mJy) as opposed to the SUMSS catalogue mJy).
 Ixolmogorov-Smirnoy tests. comparing the optical magnitude and redshift cüstributions of the RBSCNVSS sample and the RASSGabGS radio sample show. with 99% significance. that we can reject the null hypothesis that they are drawn from the same population.," Kolmogorov-Smirnov tests comparing the optical magnitude and redshift distributions of the RBSC–NVSS sample and the RASS–6dFGS radio sample show, with $\%$ significance, that we can reject the null hypothesis that they are drawn from the same population."
 However. reducing the RASS6dECGS sample to only those sources with an X-rav count rate above 0.1 cts/s and repeating the Ίντο tests reveals that we can no longer reject this null hypothesis (the probability. of rejection is 83.3%).," However, reducing the RASS–6dFGS sample to only those sources with an X-ray count rate above 0.1 cts/s and repeating the K-S tests reveals that we can no longer reject this null hypothesis (the probability of rejection is $\%$ )."
} Phe optical magnitucle distributions remain dillerent at the 99% significance level due to slightly. larger fraction of optically bright objects in the RASSθα catalogue., The optical magnitude distributions remain different at the $\%$ significance level due to slightly larger fraction of optically bright objects in the RASS–6dFGS catalogue.
 A number of RASS sources were removed from the 6dECS target list under the assumption that they were cluster galaxies., A number of RASS sources were removed from the 6dFGS target list under the assumption that they were cluster galaxies.
" ""This makes it unclear if the X-rav emission originates from an AGN or from the intracluster medium.", This makes it unclear if the X-ray emission originates from an AGN or from the intracluster medium.
 Comparisons with the οςNVSS catalogue revealed 222 sources that were excluded: due to this selection criteria. but a number were observed. as part. of the 6dl Galaxy Survey. the majority as part of the primary 2LASS selected survey.," Comparisons with the RBSC–NVSS catalogue revealed 222 sources that were excluded due to this selection criteria, but a number were observed as part of the 6dF Galaxy Survey, the majority as part of the primary 2MASS selected survey."
 Of the 94 sources with optical spectra. SI have reliable redshifts.," Of the 94 sources with optical spectra, 81 have reliable redshifts."
 These were visually inspected. to check if a large number of AGN were excluded in the selection process., These were visually inspected to check if a large number of AGN were excluded in the selection process.
 Table 6 details this inspection process., Table \ref{clusterspectratab} details this inspection process.
 As expected. the majority (0784) are absorption line objects. typical of a passivo galaxy. with the optical spectrum showing no," As expected, the majority $\%$ ) are absorption line objects, typical of a passive galaxy, with the optical spectrum showing no"
For most of our sample stars as well as for a laree fraction of RY ‘Tau stars and PAGD stars we Lined Ca/Fe] and Ε/Γο) much lower than those expected even for thin disc stars.,For most of our sample stars as well as for a large fraction of RV Tau stars and PAGB stars we find [Ca/Fe] and [Ti/Fe] much lower than those expected even for thin disc stars.
 Although Fe abundance can be estimated with better precision using lines. for Ca. the abundance is estimated using lines hence Non-LTIS corrections for supergiants need to be investigated. (," Although Fe abundance can be estimated with better precision using lines, for Ca, the abundance is estimated using lines hence Non-LTE corrections for supergiants need to be investigated. ("
Lor dwarls and subeiants | O.1dex is estimated but could be larger for lower gravity PAGD stars).,for dwarfs and subgiants $+$ 0.1dex is estimated but could be larger for lower gravity PAGB stars).
 Although this Non-LTI2 correction for supergaint eravities are not available. it is comforting to note that there is no perceptible dillerence between Ca/Fe] for a sample ofgiants used by Takeda. Sato and Murata (2008) and those ofchwarls and subgiants (Benshy 2005. Reddy et al.," Although this Non-LTE correction for supergaint gravities are not available, it is comforting to note that there is no perceptible difference between [Ca/Fe] for a sample of giants used by Takeda, Sato and Murata (2008) and those of dwarfs and subgiants (Bensby 2005, Reddy et al."
 2006)., 2006).
 Hence we do not expect very large reduction in. Ca/Fe] caused by Non-ΕΓΙΟ etfect. (a likely Non-LVE correction would be in. | 0.1 ο 0.2 dex range)., Hence we do not expect very large reduction in [Ca/Fe] caused by Non-LTE effect (a likely Non-LTE correction would be in $+$ 0.1 to 0.2 dex range).
 Mild to severe. reduction in. Ca/Fc] can be caused ov the fact that the Te: for Ca and Fe are 1517Ix and 1334 respectively. hence Ca is relatively more susceptible o depletion via condensation onto the grains.," Mild to severe reduction in [Ca/Fe] can be caused by the fact that the $_{C}$ for Ca and Fe are 1517K and 1334 respectively, hence Ca is relatively more susceptible to depletion via condensation onto the grains."
 To understand Ca/Fe] variations seen in PACGDs and AW ‘Lau stars a plot of Ca/Ee] as function of temperature could be instructive notwithstanding the fact that some of he heavily depleted objects do not have Ca measurements and. Non-LTI correction could. result. in at least | O.1elex vertical shift to all data points., To understand [Ca/Fe] variations seen in PAGBs and RV Tau stars a plot of [Ca/Fe] as function of temperature could be instructive notwithstanding the fact that some of the heavily depleted objects do not have Ca measurements and Non-LTE correction could result in at least $+$ 0.1dex vertical shift to all data points.
 The Figure 5. shows thick disc Ca/Fe] value of | 0.21 by dotted horizontal linc., The Figure \ref{loci5} shows thick disc [Ca/Fe] value of $+$ 0.21 by dotted horizontal line.
 The post-ACD stars with s-process enhancement generally have Ca/be] > 0., The post-AGB stars with s-process enhancement generally have [Ca/Fe] $>$ 0.
 For these objects. a elements including Ca/LFe are consistently positive.," For these objects, $\alpha$ elements including [Ca/Fe] are consistently positive."
 A few PAGB stars with very milc or no s-process enrichment also show Ca/Fe] of [0.1 to 0.0., A few PAGB stars with very mild or no s-process enrichment also show [Ca/Fe] of +0.1 to 0.0.
 RV “Tauris such as V453 Oph showing mild. s-process enhancement also show similar Ca/Fe]. values., RV Tauris such as V453 Oph showing mild s-process enhancement also show similar [Ca/Fe] values.
 Deplete PAGBs and RY ‘Tauris understandably show negative Ca/Ee]., Depleted PAGBs and RV Tauris understandably show negative [Ca/Fe].
 IW Car and Η Lyr are well known doepletec objects with very small scatter in their Te: vs. N/M] plots., IW Car and HP Lyr are well known depleted objects with very small scatter in their $_{C}$ vs [X/H] plots.
 jut even those objects with no established indication. of dust-gas separation have small negative Ca/Fe] in excess of what can be ascribed to Non-LTI ellects., But even those objects with no established indication of dust-gas separation have small negative [Ca/Fe] in excess of what can be ascribed to Non-LTE effects.
 A large fraction of them have temperatures lower than 50001. hence the signature of depletion may be mullled for them.," A large fraction of them have temperatures lower than 5000K, hence the signature of depletion may be muffled for them."
 From the study of extended samples of PAGB stars -- has become obvious that they exhibit απ enormous chemical variety., From the study of extended samples of PAGB stars it has become obvious that they exhibit an enormous chemical variety.
 However. hardcore. PAGB stars showing the predicted: outcome of the third. clredgc-up (increased C/O ratio anc s-process enhancements) make a much smaller [fraction of known PAGB stars.," However, hardcore PAGB stars showing the predicted outcome of the third dredge-up (increased C/O ratio and s-process enhancements) make a much smaller fraction of known PAGB stars."
 We have compiled the abundance data for PAGB stars ancl present. them in three tables., We have compiled the abundance data for PAGB stars and present them in three tables.
 We have tabulated separately the PAGB stars showing very clistinet s-process enhancement. (s/Fe] z 0.5 dex). those showing very. distinct. depletion of condensable elements (Depletion Index (DI) 1.0) and those exhibiting neither distinct s-process enhancement nor depletion in an attempt to statistically infer the inlluence of factors such as binaritv. HU fluxes.," We have tabulated separately the PAGB stars showing very distinct s-process enhancement ([s/Fe] $>$ 0.5 dex), those showing very distinct depletion of condensable elements (Depletion Index (DI) $>$ 1.0) and those exhibiting neither distinct s-process enhancement nor depletion in an attempt to statistically infer the influence of factors such as binarity, IR fluxes."
 Our compilation of data for PAGB stars with significant s-process enhancements is presented in Table 9., Our compilation of data for PAGB stars with significant s-process enhancements is presented in Table 9.
 X. few stars have more than one analysis., A few stars have more than one analysis.
 Most. analyses employ resolution around 40.000.," Most analyses employ resolution around 40,000."
 More recent analyses emplov more accurate oscillator strengths., More recent analyses employ more accurate oscillator strengths.
 Lt should. be noted. that a majority of them belong to thick disc population with Fe/L] inrange O.3to ON dex., It should be noted that a majority of them belong to thick disc population with [Fe/H] in range $-$ 0.3 to $-$ 0.8 dex.
 Early discoveries of this class with large s/Fe] led to phrase “have” meaning members with κο) in range 11.5 10 | 2.3 and “have not” with s/Fe] ~ 0.," Early discoveries of this class with large [s/Fe] led to phrase ""have"" meaning members with [s/Fe] in range $+$ 1.5 to $+$ 2.3 and ""have not"" with [s/Fe] $\sim$ 0."
 llowever. recent studies (including the present work) have found the objects with moderate: s-process enhancements and. C/O πο exceeding one.," However, recent studies (including the present work) have found the objects with moderate s-process enhancements and C/O not exceeding one."
 Heavilv enriched. objects. seem to favour a temperature range of GOOOK to 7500Ix. They. all have a/c] in similar to rose Of thick disc stars., Heavily enriched objects seem to favour a temperature range of 6000K to 7500K. They all have $\alpha$ /Fe] in similar to those of thick disc stars.
 A Large fraction of them show 2158 feature., A large fraction of them show $\mu$ feature.
 The SED generally contains well resolved llt component of strength comparable το photospheric component., The SED generally contains well resolved IR component of strength comparable to photospheric component.
 Three objects from Table 9 LIGAS. OS143-4406. IRAS 22223]4327 and IRAS 2310416147. have nebulae of SOLE class (generally. of 2 aresee size) detected. by Sidcelmial et al. (," Three objects from Table 9 IRAS 08143-4406, IRAS 22223+4327 and IRAS 23104+6147 have nebulae of SOLE class (generally of 2 arcsec size) detected by Sióddmiak et al. ("
2008).,2008).
 Another interesting feature of this class of s-process enhanced. PACGD stars is that very few of them are known binaries., Another interesting feature of this class of s-process enhanced PAGB stars is that very few of them are known binaries.
 They appear to represent. single star evolution of moderately metal-poor thick disce stars., They appear to represent single star evolution of moderately metal-poor thick disc stars.
at the high end of its luminosity range.,at the high end of its luminosity range.
 Their photometry falls (after correction for reddening) close to the regression lines derived from the present work., Their photometry falls (after correction for reddening) close to the regression lines derived from the present work.
 The infrared. increase thes observed was attributed to a previously noted increase in its optical-UV. radiation. providing early evidence for the dust reverberation moclel.," The infrared increase they observed was attributed to a previously noted increase in its optical-UV radiation, providing early evidence for the dust reverberation model."
 The slope of the regression in the A. vs L diagram may have changed with time in the sense that the £ [lux is continuing to decrease even though the A tux has bottomed out., The slope of the regression in the $K$ vs $L$ diagram may have changed with time in the sense that the $L$ flux is continuing to decrease even though the $K$ flux has bottomed out.
 This may be a rellection of a very long-term decrease in the £ flux. arising from relatively distant dust. following a protracted decline in UV activity since the time of the Lebolsky Ricke work.," This may be a reflection of a very long-term decrease in the $L$ flux, arising from relatively distant dust, following a protracted decline in UV activity since the time of the Lebofsky Rieke work."
 See also 22902. \ICC-2-58-22 and 77469 below.," See also 2992, MCG-2-58-22 and 7469 below."
 This Sevfert. 2 galaxy has shown very Little activity., This Seyfert 2 galaxy has shown very little activity.
 The colours of its variable components are considerably. redder than average. suggesting strong nuclear reddening.," The colours of its variable components are considerably redder than average, suggesting strong nuclear reddening."
 “There appears to be a delay of about 100d between J ancl L., There appears to be a delay of about 100d between $J$ and $L$.
 The data on Fairall 9 vield the best argument so far for the cust reverberation model., The data on Fairall 9 yield the best argument so far for the dust reverberation model.
 The delay of  400 d found by Clavel. Wanmisteker Glass (1989) between the IUIZ continuum and the L- xuxd light curve remains the strongest evidence for the dust reverberation model.," The delay of $\sim$ 400 d found by Clavel, Wamsteker Glass (1989) between the IUE continuum and the $L$ -band light curve remains the strongest evidence for the dust reverberation model."
 Monitoring has continued at SAAQ in he C band and a delay is still seen in the infrared response., Monitoring has continued at SAAO in the $U$ band and a delay is still seen in the infrared response.
 The SAAO C data are shown in Fig 1., The SAAO $U$ data are shown in Fig 1.
 Variations seen in he new ( data are found to precede those at £ by. τά., Variations seen in the new $U$ data are found to precede those at $L$ by 470d.
 The lag between J and £ for the entire data set is found to re 310d., The lag between $J$ and $L$ for the entire data set is found to be 370d.
" Fie 5 shows the Uux-lux plots for F9. together with he ""activity. parameter. cl."," Fig 5 shows the flux-flux plots for F9, together with the `activity parameter', $A$."
" In the J vs df diagram. the »oint. corresponding to the level of activity the lowest (ux comes closer to the ""ordinary. galaxy! line than in the other wo diagrams."," In the $J$ vs $H$ diagram, the point corresponding to the level of activity the lowest flux comes closer to the `ordinary galaxy' line than in the other two diagrams."
 We now assume that the point of intersection of the two lines. (14..) = (1842. 13.542). represents pure ealaxy and an activity of ;1 = 0.," We now assume that the point of intersection of the two lines, $(H,J)$ = $\pm$ 2, $\pm$ 2), represents pure galaxy and an activity of $A$ = 0."
 The minimum observed activity. as a proportion of the maximum. is then f=0.114 0.03.," The minimum observed activity, as a proportion of the maximum, is then $A = 0.11 \pm 0.03$ ."
 Using the minimum and maximum levels of cl. we can estimate the points on the ff vs AN diagram where <4 would be zero. namely at CA.1) = (22.18). with correlated uncertainties of about £2 mJv in each coordinate.," Using the minimum and maximum levels of $A$, we can estimate the points on the $H$ vs $K$ diagram where $A$ would be zero, namely at $(K,H)$ = (22,18), with correlated uncertainties of about $\pm$ 2 mJy in each coordinate."
 Lis clear that in Fairall 9. as well as many other galaxies. this point does not coincide with the intersection of the regression line and the ordinary galaxy line.," It is clear that in Fairall 9, as well as many other galaxies, this point does not coincide with the intersection of the regression line and the ordinary galaxy line."
" Instead. the position of the point at (22.18) can be regarded as the sum of an ""ordinary galaxy’ component of (16.18) and an underlying constan component with fg  0 (see next paragraph) and fy = 6X2 mJs."," Instead, the position of the point at (22,18) can be regarded as the sum of an `ordinary galaxy' component of (16,18) and an underlying constant component with $F_H$ $\sim$ 0 (see next paragraph) and $F_K$ = $\pm$ 2 mJy."
 Similarly. for the A. vs L diagram. the position of he point corresponding to cf = O. namely (L.AN) = (50.24) can be regarded. as the sum of an ordinary galaxy component of (9.16) with an underlving constant componen of (41.8).," Similarly, for the $K$ vs $L$ diagram, the position of the point corresponding to $A$ = 0, namely $(L,K)$ = (50,24) can be regarded as the sum of an ordinary galaxy component of (9,16) with an underlying constant component of (41,8)."
 Fhis corresponds to a dyL colour of 2.42. or a Xackbody temperature of 850Ix. Ehe ffA colour for this emperature of blackbocly is 2.4. which would imply an Lf lus only about of the A Lux. or about 1.4 mJy.," This corresponds to a $K-L$ colour of 2.42, or a blackbody temperature of $\sim$ 850K. The $H-K$ colour for this temperature of blackbody is 2.4, which would imply an $H$ flux only about of the $K$ flux, or about 1.4 mJy."
 ‘This is sullicicntly close to the estimated [ux of 0 to be acceptable., This is sufficiently close to the estimated flux of 0 to be acceptable.
 Barvainis (1992) mace a detailed reverberation model of Fairall 9. based. on the cata presented by Glass (1986) and Clavel. Warnsteker Class (1989).," Barvainis (1992) made a detailed reverberation model of Fairall 9, based on the data presented by Glass (1986) and Clavel, Wamsteker Glass (1989)."
 Ht should be noted that information from a well-sampled IUIS UV light curve. contemporary with the infrared. data. was available for this ealaxy.," It should be noted that information from a well-sampled IUE UV light curve, contemporary with the infrared data, was available for this galaxy."
 From 22 of Glass (1986) he took the underlying galaxy contribution in a 12 arcsec diameter aperture to be 14. 19. 17 and 9 mJy at JEANL respectively.," From 2 of Glass (1986) he took the underlying galaxy contribution in a 12 arcsec diameter aperture to be 14, 19, 17 and 9 mJy at $JHKL$ respectively."
 These figures are close to the 13.5. 18. 16 and 9 mJy used in the work just described.," These figures are close to the 13.5, 18, 16 and 9 mJy used in the work just described."
 From fits of his dust model. Barvainis concluded that there must be a ‘fourth component! of Dux that. is constant with time.," From fits of his dust model, Barvainis concluded that there must be a `fourth component' of flux that is constant with time."
 Le found for this (ux the JAL values, He found for this flux the $JHKL$ values
"Now, we have to remove the weak-lensing term from the x function, because no weak-lensing data points are available at the high resolution required in the core.","Now, we have to remove the weak-lensing term from the $\chi^2$ function, because no weak-lensing data points are available at the high resolution required in the core."
" The strong-lensing data points, however, are available at high resolution, because the critical points can be determined very accurately."," The strong-lensing data points, however, are available at high resolution, because the critical points can be determined very accurately."
" Yet, the weak-lensing reconstruction enters even at this resolution level through the regularisation term."," Yet, the weak-lensing reconstruction enters even at this resolution level through the regularisation term."
" Thus, the result is based on the weak-lensing constraints."," Thus, the result is based on the weak-lensing constraints."
" We finish the reconstruction by inserting the high-resolution cluster-core result into the result obtained at a coarser resolution, which consists of the complete cluster field."," We finish the reconstruction by inserting the high-resolution cluster-core result into the result obtained at a coarser resolution, which consists of the complete cluster field."
 Due to the regularisation function the strong-lensing result fits nicely into the weak-lensing results since we do not allow that the two different reconstructions differ significantly at pixels where no strong-lensing constraints are available., Due to the regularisation function the strong-lensing result fits nicely into the weak-lensing results since we do not allow that the two different reconstructions differ significantly at pixels where no strong-lensing constraints are available.
 This is also the last major change in our method compared to ?.., This is also the last major change in our method compared to \citet{Cacciato2006}.
 The use of the regularisation function as a tool to match results on different scales improves the quality of our reconstructions significantly., The use of the regularisation function as a tool to match results on different scales improves the quality of our reconstructions significantly.
 We first repeat the tests also carried out in ?.., We first repeat the tests also carried out in \citet{Cacciato2006}.
 We take simulated clusters from the N-body simulations described in ? and compute maps of their reduced shear and their critical curves., We take simulated clusters from the $N$ -body simulations described in \citet{Bartelmann1998} and compute maps of their reduced shear and their critical curves.
" Based on this information, we try to reconstruct the known potential of the simulated cluster."," Based on this information, we try to reconstruct the known potential of the simulated cluster."
" Since this is an idealised lensing scenario which does not include a realistic background-galaxy distribution or image analysis, it is sufficient to compare the convergence map obtained by the reconstruction with the real convergence map of the simulated cluster."," Since this is an idealised lensing scenario which does not include a realistic background-galaxy distribution or image analysis, it is sufficient to compare the convergence map obtained by the reconstruction with the real convergence map of the simulated cluster."
 The results confirm the reliability of our method and are shown in Figs., The results confirm the reliability of our method and are shown in Figs.
 and [B]., \ref{syntheticrec} and \ref{profile}.
" In particular, Fig."," In particular, Fig."
 [8] shows how significantly the results are improved when the strong-lensing constraints on a refined grid are added., \ref{profile} shows how significantly the results are improved when the strong-lensing constraints on a refined grid are added.
 Otherwise the central density peak is underestimated by almost20%., Otherwise the central density peak is underestimated by almost.
". Next, we use the method detailed in ? to simulate an observation of another cluster field."," Next, we use the method detailed in \citet{Meneghetti2008} to simulate an observation of another cluster field."
" The target of this simulated observation is the galaxy cluster g72, described in several previous papers (???).."," The target of this simulated observation is the galaxy cluster g72, described in several previous papers \citep{Dolag2005,Puchwein2005,Meneghetti2007a}."
 This cluster was simulated with different physics., This cluster was simulated with different physics.
 For thepresent work we have used a pure dark matter simulation., For thepresent work we have used a pure dark matter simulation.
 The cluster is at redshift z.=0.297 and has a main halo mass of Moo=6.7x10'4Mo/h., The cluster is at redshift $z_{\text{c}}=0.297$ and has a main halo mass of $M_{200}=6.7\times10^{14}M_{\odot}/h$.
 It is in the process of merging with a massive substructure of mass My)~3X104Mo/h., It is in the process of merging with a massive substructure of mass $M_{200}\sim3\times10^{14}M_{\odot}/h$.
 In the projection chosen for this simulation the subclump is located at ~150kpc/h north of the main clump., In the projection chosen for this simulation the subclump is located at $\sim 150~\text{kpc}/h$ north of the main clump.
 A second massive substructure is present at a distance of ~2.5Mpc/h from the cluster centre., A second massive substructure is present at a distance of $\sim2.5~\text{Mpc}/h$ from the cluster centre.
 The projected density of the cluster is shown in Fig. [IO]., The projected density of the cluster is shown in Fig. \ref{simulation_rec}.
" We mimic a 2500""x SUBARU observation of this cluster and of the sky behind it in the R-band assuming an exposure time of 6000s and an isotropic, Gaussian PSF of 0.6"" FWHM."," We mimic a $2500^{\prime\prime}\times2500^{\prime\prime}$ SUBARU observation of this cluster and of the sky behind it in the R-band assuming an exposure time of 6000s and an isotropic, Gaussian PSF of $0.6^{\prime\prime}$ FWHM."
" The distortion field, which is used to lens the background galaxies, is calculated from the cluster mass distribution following the method described in ?.."," The distortion field, which is used to lens the background galaxies, is calculated from the cluster mass distribution following the method described in \citet{Meneghetti2007a}."
" The background galaxies have realistic morphologies, being drawn from shapelet decompositions of real galaxies taken from the Hubble-Ultra-Deep Field (HUDF)."," The background galaxies have realistic morphologies, being drawn from shapelet decompositions of real galaxies taken from the Hubble-Ultra-Deep Field (HUDF)."
 Their luminosity and redshift distributions also reflect those of the HUDF (?).., Their luminosity and redshift distributions also reflect those of the HUDF \citep{Coe2006}.
 The weak lensing analysis of the field was carried out by E. Bellagamba (Univ., The weak lensing analysis of the field was carried out by F. Bellagamba (Univ.
 of Bologna) using an advanced KSB method (?)., of Bologna) using an advanced KSB method \citep{Kaiser1995}. .
 It returned an ellipticity catalogue of 39788 background sources., It returned an ellipticity catalogue of 39788 background sources.
 For the strong lensing analysis we followed two different approaches., For the strong lensing analysis we followed two different approaches.
" First, we used the"," First, we used the"
For the axially symmetric problem. it is convenient to introduce the impact parameter 5 relative to the point mass. which remains constant in the null approximation for the photon moving along the axis z.,"For the axially symmetric problem, it is convenient to introduce the impact parameter $b$ relative to the point mass, which remains constant in the null approximation for the photon moving along the axis $z$."
 The plasma has a sphericallvy-svmmoetric distribution around the point mass. with the concentration W=IN(r).," The plasma has a spherically-symmetric distribution around the point mass, with the concentration $N = N(r)$."
 In the axially νοric situation the position of the photon is characterized. by b and z. and the absolute value of the racius-veetor is r=vid[ος—be|28.," In the axially symmetric situation the position of the photon is characterized by $b$ and $z$, and the absolute value of the radius-vector is $r =
\sqrt{x_1^2+x_2^2+z^2}= \sqrt{b^2+z^2}$."
" We have the following expression for the dellection angle in the plane perpendicular to direction of the unperturbed photon trajectory: that à, <0corresponds to bending of the light trajectory towards the eravitation center. and a, c0 corresponds to the opposite deflection."," We have the following expression for the deflection angle in the plane perpendicular to direction of the unperturbed photon trajectory: Note that $\hat{\alpha}_b < 0$ corresponds to bending of the light trajectory towards the gravitation center, and $\hat{\alpha}_b > 0$ corresponds to the opposite deflection."
" In our previous paper (DBisnovatvi-lxogan&""Fsupko2009) we have considered a weakly inhomogeneous plasma with Αμ=Ny|Niort).const.NpκNy."," In our previous paper \citep{BK&Ts2009} we have considered a weakly inhomogeneous plasma with $N(x^\alpha) =
N_0 + N_1(x^\alpha), \; \; N_0 = {\rm const}, \; \; N_1\ll N_0$."
 llere we assume that the deflection angle is small. but we do not assume that Ny is much smaller than No. so the representation of INGre) as a sum is not required.," Here we assume that the deflection angle is small, but we do not assume that $N_1$ is much smaller than $N_0$, so the representation of $N(x^\alpha)$ as a sum is not required."
 Let us calculate the deflection angle for a photon moving in the inhomogeneous plasma. in the Schwarzschild metric of the point mass M. with In the weak field approximation this metric is written as (Landau&Lifshitz1993) where ds; is a Mat part of the metric ds;=cdi?2|di?|(de?sin?6d ).," Let us calculate the deflection angle for a photon moving in the inhomogeneous plasma, in the Schwarzschild metric of the point mass $M$, with In the weak field approximation this metric is written as \citep{LL2}
 where $ds_0^2$ is a flat part of the metric $ds_0^2 =-c^2
dt^2+dr^2+r^2(d \theta^2 + \sin^2 \theta \, d\varphi^2)$ ."
" The components fj, are written in the Cartesian frame as (Landau&Lifshitz1993) llere $, is a unit. vector in the direction of theracdius- ra= Grypore.ry). the components of which are equal to directional cosines. the angle6 is the polar angle between J3-vector rr. and oz-axis. and 3Cosvb?| 22."," The components $h_{ik}$ are written in the Cartesian frame as \citep{LL2}
 Here $s_\alpha$ is a unit vector in the direction of theradius-vector $r_\alpha = (x_1,x_2,x_3)$ , the components of which are equal to directional cosines, the angle$\theta$ is the polar angle between 3-vector $r^\alpha$ $r_\alpha$, and $z$ -axis, and $s_3=\cos \theta = z/r = z/\sqrt{b^2+z^2}$ ."
 Using formula (30)) we obtain: ‘To demonstrate the physical meaning of dillerent terms in (34)). we write this expression under condition Loon=E1.," Using formula \ref{angle}) ) we obtain: To demonstrate the physical meaning of different terms in \ref{angle-inhom}) ), we write this expression under condition $1-n
= \omega_e^2/\omega^2 \ll 1$ ."
 Carrying out the expansion of terms with the plasma frequency. we obtain: ‘The first term is a vacuum gravitational dellection.," Carrying out the expansion of terms with the plasma frequency, we obtain: The first term is a vacuum gravitational deflection."
 The second term is an additive correction to the eravitational dellection. due to the presence of the plasma.," The second term is an additive correction to the gravitational deflection, due to the presence of the plasma."
 This term is esent in the dellection angle both in the inhomogeneous and in the homogeneous plasma. and depends on the photon requenev.," This term is present in the deflection angle both in the inhomogeneous and in the homogeneous plasma, and depends on the photon frequency."
 The third termi is a non-relativistic dellection due to the plasma inhomogeneity (the retraction)., The third term is a non-relativistic deflection due to the plasma inhomogeneity (the refraction).
 This erm depends on the frequency. but it is absent if the Xdasma is homogeneous.," This term depends on the frequency, but it is absent if the plasma is homogeneous."
 The forth term is a small acdclitive correction to the third term., The forth term is a small additive correction to the third term.
 I£ we use the approximation Lon=wifau«1. and neglect small second. and. the orth terms. we obtain a separate input of the two elfects: he vacuum gravitational dellection. and the refraction dellection in the inhomogeneous plasma.," If we use the approximation $1-n =
\omega_e^2/\omega^2 \ll 1$, and neglect small second and the forth terms, we obtain a separate input of the two effects: the vacuum gravitational deflection, and the refraction deflection in the inhomogeneous plasma."
" Calculation of the refraction dellection for a power-law concentration was given in our previous work (Disnovatvi-Ixogan&""Tsupko2009).. see also Bliokh&Minakov (1989).. \lublemanetal.(1970).. Thompsonetal. (1994).. Lightmanetal. (1979).."," Calculation of the refraction deflection for a power-law concentration was given in our previous work \citep{BK&Ts2009}, see also \citet{B-Minakov}, , \citet{Muhl1970}, \citet{Thompson}, \citet{zadachnik}."
. Note that the refraction in the inhomogeneous plasma with ΑΟNolRyry! where No = const. fy) = const. h = const z0. leads to the refraction deflection angle αν. which is opposite to the gravitational dellection (Bliokh&Minakov1989:Disnovatv," Note that the refraction in the inhomogeneous plasma with $N(r) = N_0 (R_0/r)^h$ , where $N_0$ = const, $R_0$ = const, $h$ = const $\neq 0$, leads to the refraction deflection angle $\alpha_r$, which is opposite to the gravitational deflection \citep{B-Minakov, BK&Ts2009}."
"i-Ixogan&""Tsupko 2009).. For awXa we have: For the arbitrary n one needs to use the expression (34)) which is valid in a general case.", For $\omega \gg \omega_e$ we have: For the arbitrary $n$ one needs to use the expression \ref{angle-inhom}) ) which is valid in a general case.
 The main approximation used here. is the smallness of the dellection angle. what can be satisfied even if the concentration IN changes significantIv. or i£ the refraction index » is not close to the unity.," The main approximation used here, is the smallness of the deflection angle, what can be satisfied even if the concentration $N$ changes significantly, or if the refraction index $n$ is not close to the unity."
 The most interesting result following [rom our calculation is that even in the case of the homogeneous plasma the photon deflection angle differs from the vacuum. case. and depends on the plasma and. photon frequency.," The most interesting result following from our calculation is that even in the case of the homogeneous plasma the photon deflection angle differs from the vacuum case, and depends on the plasma and photon frequency."
" Indeed. for a, = const we obtain from (34)) ""This formula is valid only forao. because the waves with cw<sy do not propagate in the plasma (Cinzb"," Indeed, for $\omega_e $ = const we obtain from \ref{angle-inhom})) This formula is valid only for $\omega > \omega_e$, because the waves with $\omega< \omega_e$ do not propagate in the plasma \citep{Ginzb}. ."
"urg 1970).. Llere à,« 0.", Here $\hat{\alpha}_b < 0$ .
 This means that the light rav is bent, This means that the light ray is bent
at 6 keV. The Phoswich Detector System (PDS: 12-300 keV) observed V464] Ser simultaneously with the LECS and MECS.,at 6 keV. The Phoswich Detector System (PDS; 12–300 keV) observed V4641 Sgr simultaneously with the LECS and MECS.
 The statistical quality of the high energy spectrum obtained ts relatively poor. and does not allow for tighter constraints on the continuum.," The statistical quality of the high energy spectrum obtained is relatively poor, and does not allow for tighter constraints on the continuum."
" In particular. reflection models — which describe a geometry in which the Fe Ko emission line and a ""Compton hump” result from the irradiation of the disk — are not better-constrained by considering the PDS spectrum."," In particular, reflection models — which describe a geometry in which the Fe $\alpha$ emission line and a “Compton hump” result from the irradiation of the disk — are not better-constrained by considering the PDS spectrum."
 Our analysis is therefore limited to the time-averaged NFI spectra., Our analysis is therefore limited to the time-averaged NFI spectra.
 All aspects of the source and background spectral extraction. instrument response function generation. and filtering are exactly the same as reported 1n in t Zand et al. (," All aspects of the source and background spectral extraction, instrument response function generation, and filtering are exactly the same as reported in in 't Zand et al. ("
2000).,2000).
 We considered the LECS spectrum between 0.4 and 4.0 keV. the MECS spectrum between 2.0 and 10.0 keV (again. similar to in t Zand et al.," We considered the LECS spectrum between 0.4 and 4.0 keV, the MECS spectrum between 2.0 and 10.0 keV (again, similar to in 't Zand et al."
 2000)., 2000).
 The spectra were fit using XSPEC version 11.1 (Arnaud 1996)., The spectra were fit using XSPEC version 11.1 (Arnaud 1996).
 All errors reported 1n this work are confidence errors., All errors reported in this work are confidence errors.
 The LECS and MECS spectra were fit jointly., The LECS and MECS spectra were fit jointly.
 An overall normalizing constant was allowed to float between the spectra to account for differences in the instrumental flux calibration., An overall normalizing constant was allowed to float between the spectra to account for differences in the instrumental flux calibration.
 Preliminary. fits suggested that the absorbing column and the nature of the soft component could not be constrained independently., Preliminary fits suggested that the absorbing column and the nature of the soft component could not be constrained independently.
" We therefore fixed the equivalent neutral hydrogen column density at the weighted average measured along this line of sight by Dickey Lockman (1990): Nj,22.3«107!atomsem (assuming the ""phabs"" model in XSPEC).", We therefore fixed the equivalent neutral hydrogen column density at the weighted average measured along this line of sight by Dickey Lockman (1990): $N_{H}=2.3\times 10^{21}~{\rm atoms}~{\rm cm}^{-2}$ (assuming the “phabs” model in XSPEC).
" We attempted to describe the continuum spectra with a number of models. including the “bulk— motion Comptonization"" model (Shrader Titarchuk 1999), à model consisting of a multicolor disk black-body (MCD: Mitsuda et al."," We attempted to describe the continuum spectra with a number of models, including the “bulk motion Comptonization” model (Shrader Titarchuk 1999), a model consisting of a multicolor disk black-body (MCD; Mitsuda et al."
" 1984) and power-law components. and a model consisting of MCD and ""comptt"" (Titarehuk 1994) components (as per in ""t Zand et al."," 1984) and power-law components, and a model consisting of MCD and “comptt” (Titarchuk 1994) components (as per in 't Zand et al."
 2000)., 2000).
 None of these models gives an acceptable fit to the data. yielding V/»r=6.22.5.83.and5.96. respectively (7 is the number of degrees offreedom: »=76 for the first two models. v=74 for the last).," None of these models gives an acceptable fit to the data, yielding $\chi^{2}/\nu =~~6.22,~5.83,~{\rm and}~5.96$, respectively $\nu$ is the number of degrees offreedom; $\nu=76$ for the first two models, $\nu=74$ for the last)."
 These continuum models all fail to account for a strong emission feature in the Fe Ko line region., These continuum models all fail to account for a strong emission feature in the Fe $\alpha$ line region.
 In Figure |. the line profile is shown as a ratio of the spectrum to these continuum models.," In Figure 1, the line profile is shown as a ratio of the spectrum to these continuum models."
 Following Iwasawa et al. (, Following Iwasawa et al. (
1999). the ratio is formed by ignoring the 4—7 keV range when fitting the spectra.,"1999), the ratio is formed by ignoring the 4–7 keV range when fitting the spectra."
 It is apparent that the line may not be intrinsically narrow — the profile revealed in the data/model ratio is similar to those expected for a line produced by irradiation of the inner accretion disk around a black hole (Fabian et al., It is apparent that the line may not be intrinsically narrow — the profile revealed in the data/model ratio is similar to those expected for a line produced by irradiation of the inner accretion disk around a black hole (Fabian et al.
 1989. Laor 1991).," 1989, Laor 1991)."
 In a previous examination of this spectrum. in “t Zand et al. (," In a previous examination of this spectrum, in 't Zand et al. ("
2000) modeled the Fe Ko line region with two Gaussians (at 6.68 keV and 6.97 keV. as per Fe XXV and Fe XXVI) — each with zero widths — assuming that the intrinsic. width of each line is below the instrumental resolution.,"2000) modeled the Fe $\alpha$ line region with two Gaussians (at 6.68 keV and 6.97 keV, as per Fe XXV and Fe XXVI) --- each with zero widths — assuming that the intrinsic width of each line is below the instrumental resolution."
 The bottom panel in Figure | shows the data/model ratio obtained with this narrow line model: clearly. flux between 5.0-6.4 keV — perhaps associated with an intrinsically broad line — is not accounted for by this model.," The bottom panel in Figure 1 shows the data/model ratio obtained with this narrow line model; clearly, flux between 5.0–6.4 keV --- perhaps associated with an intrinsically broad line — is not accounted for by this model."
 Adopting the MCD plus power-law model for the continuum. we next investigated the nature of the Fe Ka line region in detail.," Adopting the MCD plus power-law model for the continuum, we next investigated the nature of the Fe $\alpha$ line region in detail."
 For a line model consisting of two zero-width Gaussians. v/v=1.721.(774).," For a line model consisting of two zero-width Gaussians, $\chi^{2}/\nu
= 1.721, (\nu = 74)$."
 However. for fits with the Laor line model. V/»=1.230.(»271).," However, for fits with the Laor line model, $\chi^{2}/\nu = 1.230, (\nu = 71)$."
 The improvement in the fit statistic is significant at the 4.5c level of confidence., The improvement in the fit statistic is significant at the $\sigma$ level of confidence.
 This continuum plus line model is our best-fit spectral model. and it is shown in Figure 2.," This continuum plus line model is our best-fit spectral model, and it is shown in Figure 2."
 The inclusion of a smeared Fe K edge (“smedge.” Ebisawa et al.," The inclusion of a smeared Fe K edge (“smedge,” Ebisawa et al."
 1994) does not improve the fit significantly., 1994) does not improve the fit significantly.
 When a smeared edge 15 included. the edge parameters are not well-constrained: Ευ=9.17 keV and T=]οB," When a smeared edge is included, the edge parameters are not well-constrained: $E_{edge} = 9.1^{+0.2}_{-1.1}$ keV and $\tau
= 1.6^{+2.7}_{-1.4}$."
 Allowing a standard narrow edge component to float in the Fe Ko region does not give an improvement in the fit statistic., Allowing a standard narrow edge component to float in the Fe $\alpha$ region does not give an improvement in the fit statistic.
 The Laor line energy was only permitted to vary within the range 6.40keV<Ej;6.97 (Fe [ - Fe XXVI., The Laor line energy was only permitted to vary within the range $6.40~{\rm keV} \leq {\rm E}_{Laor} \leq 6.97~{\rm keV}$ (Fe I – Fe XXVI).
" The best-fit energy is measured to be Ej,=6.407? keV. The line emitting region is relatively well constrained: Rj,=8HR, and Roy=30518Ry (Re= Με)."," The best-fit energy is measured to be ${\rm E}_{Laor} =
6.40^{+0.3}$ keV. The line emitting region is relatively well constrained: $R_{in} = 8^{+4}_{-3}~R_{g}$ and $ R_{out} =
30^{+40}_{-10}~R_{g}$ $R_{g} = G M_{BH} / c^{2}$ )."
" As is evident from the line profile shown in Figure |. the line equivalent width is very high: Wy,=87070"" eV (9.8*l5«10115ergs!. 04-10 keV)."," As is evident from the line profile shown in Figure 1, the line equivalent width is very high: $W_{K \alpha} = 870^{+100}_{-70}$ eV $9.8^{+1.2}_{-1.0}
\times 10^{-12}~{\rm erg}~{\rm s}^{-1}$, 0.4–10 keV)."
 The inclination is measured to be /243°+ 15°., The inclination is measured to be $i = 43^{\circ} \pm 15^{\circ}$ .
 This inclination ts lower than the optically-determined range: however. Orosz et al. (," This inclination is lower than the optically-determined range; however, Orosz et al. ("
2001) note that the inclination implied by the Jet is very,2001) note that the inclination implied by the jet is very
The electrons aud positrons in the halo will inverse-Compton scatter soft photons into the 5-rav band where they can be observed with. e.g.. the Fermi-LAT detector.,"The electrons and positrons in the halo will inverse-Compton scatter soft photons into the $\gamma$ -ray band where they can be observed with, e.g., the Fermi-LAT detector."
 The target photon field includes the microwave background. galactic infrared emission. ancl galactic optical emission. only the first of which is isotropic.," The target photon field includes the microwave background, galactic infrared emission, and galactic optical emission, only the first of which is isotropic."
 The latter (wo will be backscattered toward (he Galaxy. (hus somewhat increasing the scattering rate compared wilh the isotropic case.," The latter two will be backscattered toward the Galaxy, thus somewhat increasing the scattering rate compared with the isotropic case."
 The radiation field has been recently modeled out to 2=5 kpe (Porter&Strong2005)., The radiation field has been recently modeled out to $z=5$ kpc \citep{porter}.
. Surprisingly. the energy densitv of optical light is hieher in the halo than in the midplane on account of the thin-disk distribution of absorbers.," Surprisingly, the energy density of optical light is higher in the halo than in the midplane on account of the thin-disk distribution of absorbers."
 The differential cross section lor the up-scattering of isotropic photons of enerev € (o energv £L is given by (Blumenthal&Gould1970) where The 5-rav intensity observed Irom the Galactic pole is then computed using the differential density of electrons/positrons (Eq. 8))," The differential cross section for the up-scattering of isotropic photons of energy $\epsilon$ to energy $E_\gamma$ is given by \citep{bg70}
 where The $\gamma$ -ray intensity observed from the Galactic pole is then computed using the differential density of electrons/positrons (Eq. \ref{eq6}) )"
 ancl the differential densitv of soft. photons. n(e) (Porter&Strong2005)..," and the differential density of soft photons, $n(\epsilon)$ \citep{porter}."
 The resulting intensiv is shown in Figure 2.., The resulting intensity is shown in Figure \ref{fig1}.
 To be noted [rom the figure is that even al 30 GeV. where the emission arises [rom upscattering optical photons. the expected intensity is below of the preliminary estimate of the extragalactic isotropic background observed with Fermi (Ackermann2009).. in line with the findings of Ishiwataetal.(2009)..," To be noted from the figure is that even at 30 GeV, where the emission arises from upscattering optical photons, the expected intensity is below of the preliminary estimate of the extragalactic isotropic background observed with Fermi \citep{ackermann}, in line with the findings of \citet{ishiwata}."
 Diffuse galactic emission [rom cosmic-ray interaction has an intensity similar to that of the extragalactic isotropic backeround. ancl hence dark-matter decay is poorly constrained. by -rav emission in the Galaxy.," Diffuse galactic emission from cosmic-ray interaction has an intensity similar to that of the extragalactic isotropic background, and hence dark-matter decay is poorly constrained by $\gamma$ -ray emission in the Galaxy."
 Whereas no significant intensity above 1 GeV is expected to come [rom beyond a distance of 5 kpc. the limit to which we have integrated (he galactic emission. this is not true [ου the upscattering of nicrowave-background photons into the 100-MeV. band.," Whereas no significant intensity above 1 GeV is expected to come from beyond a distance of 5 kpc, the limit to which we have integrated the galactic emission, this is not true for the upscattering of microwave-background photons into the 100-MeV band."
 In fact. in the," In fact, in the"
fits the observed counts extremely well with the LIG/ULIC component accounting for the bumps in the L5pum counts at O.l-I1niJy. the rise towards fainter Hluxes in the 60tum dillerential counts. the excesses at 0pm 170tum and much ofthe SCUBA population brighter than 2mJy at S50tfum. At 170pum Matsuharaet al.,"fits the observed counts extremely well with the LIG/ULIG component accounting for the bumps in the $\umu$ m counts at 0.1-1mJy, the rise towards fainter fluxes in the $\umu$ m differential counts, the excesses at $\umu$ m $\umu$ m and much of the SCUBA population brighter than 2mJy at $\umu$ m. At $\umu$ m Matsuhara et al."
 (2000) concludedon the of basisthe 1TOLun /90pum colours of galaxies in their Lockman Hole field. hat the faint sources could not be cirrus dominated (normal ealaxies) but had to be starforming svstenis. consistent with the model prediction of a change in the dominant »opulation. from cirrus to star forming ULlICs at Εθν.," \shortcite{mat00} concluded on the basis of the $\umu$ $\umu$ m colours of galaxies in their Lockman Hole field, that the faint sources could not be cirrus dominated (normal galaxies) but had to be starforming systems, consistent with the model prediction of a change in the dominant population, from cirrus to star forming ULIGs at $\sim$ 400mJy."
 vote that there is still significant cliscrepaney between the 9Opun ESO source counts conducted. by the the Japanese eam (Alatsuhbara et al. (2000).," Note that there is still significant discrepancy between the $\umu$ m ISO source counts conducted by the the Japanese team (Matsuhara et al. \shortcite{mat00},"
.. Wawara et al. (2000))), Kawara et al. \shortcite{kawara00}) )
 and the ELAILS survey (Efstathiouetal.2000)., and the ELAIS survey \cite{esf003}.
. The mociel orediets a value conservatively between these 2 estimations., The model predicts a value conservatively between these 2 estimations.
 Figs. 9.. LO. 14.," Figs. \ref{nz15}, \ref{nz170},"
 show number redshift distributions for the new evolutionary model at 15. 170 S50tun respectively.," \ref{nz850} show number redshift distributions for the new evolutionary model at 15, 170 $\umu$ m respectively."
 The numerous ISO. surveys at. L5pun have a gencral consensus with a strong evolution of sources to 2.1., The numerous ISO surveys at $\umu$ m have a general consensus with a strong evolution of sources to $z \sim 1$.
 The corresponding redshift distribution peaking in the range z~O.7-1.0 (Elbazοἱal.1999b)., The corresponding redshift distribution peaking in the range $\sim$ 0.7-1.0 \cite{elbaz99b}.
. The N-z distributions in ligure 9 are broadly consistent with this strong evolution although due to the form of the evolution assumed. there is à double. peak in the distribution., The N-z distributions in figure \ref{nz15} are broadly consistent with this strong evolution although due to the form of the evolution assumed there is a double peak in the distribution.
 The lower redshift peak is due to the normal galaxies that dominate the source counts to zz1mJv., The lower redshift peak is due to the normal galaxies that dominate the source counts to $\approx$ 1mJy.
 As the N-z distribution probes to fainter Iluxes the contribution from the ULICG population (centred around z1) increases., As the N-z distribution probes to fainter fluxes the contribution from the ULIG population (centred around $\sim$ 1) increases.
 These models serve to show the cHleet of a strongly evolving population to ze1 on the source counts and moving the peak of the density evolution to lower redshift - or increasing the Gaussian width of the evolution would. produce a smoother N-z distribution cllectively merging the 2 peaks., These models serve to show the effect of a strongly evolving population to $\sim$ 1 on the source counts and moving the peak of the density evolution to lower redshift - or increasing the Gaussian width of the evolution would produce a smoother N-z distribution effectively merging the 2 peaks.
" At s50pum. the redshift of the detected: sources. is notoriously dillieult to measure unambiguously. the main problem being. the 2-3""(or more) positional2. uncertainty. in. the sub-mim observations. for⋅ a resolution. at SbOLun (Iluehes 2000)."," At $\umu$ m, the redshift of the detected sources is notoriously difficult to measure unambiguously, the main problem being the (or more) positional uncertainty in the sub-mm observations for a resolution at $\umu$ m \cite{hugh00}."
.Furthermore. there is often only a single," Furthermore, there is often only a single"
and faint clusters that are vet to be detected.,and faint clusters that are yet to be detected.
 Ougoing and prospective space-based. observations may further increase the number of known star clusters., Ongoing and prospective space-based observations may further increase the number of known star clusters.
 The most recent catalog cross-correlating all known objects of the LMC. SAIC. and the Magellanic Dridge reeion was published by Bicactal.(2008) (Bos).," The most recent catalog cross-correlating all known objects of the LMC, SMC, and the Magellanic Bridge region was published by \citet{bica08b} (B08)."
 However. the cluster sample still is higehlv incomplete as pointed out by the authors.," However, the cluster sample still is highly incomplete as pointed out by the authors."
 Ouly for a few clusters in BOs’s catalog. ages have been determined.," Only for a few clusters in B08's catalog, ages have been determined."
 For vouug SAIC clusters. Pietrzvuski&Udalski(1999). (PU99) used isochrone fitting on data from the Optical Gravitational Lensing Experiment (OGLEIIUdalskietal.1998a) to determine ages for 93 clusters.," For young SMC clusters, \citet{pietrzynski99} (PU99) used isochrone fitting on data from the Optical Gravitational Lensing Experiment \citep[OGLE II; ][]{udal98a} to determine ages for 93 clusters."
 Dieballctal.(2002) compiled ages for 306 binary cluster caudidates in the LMC from a varicty of literature sources ranging from multiwavelength iutegrated light studies to isochrone fitting to resolve clusters., \citet{Dieball02} compiled ages for 306 binary cluster candidates in the LMC from a variety of literature sources ranging from multiwavelength integrated light studies to isochrone fitting to resolve clusters.
 Rafelski&Zaritsky(2005) (RZ05) made use of integrated colors and derived ages for 200 clusters., \citet{rafelski05} (RZ05) made use of integrated colors and derived ages for 200 clusters.
 C06 determined ages of 161 associations and 311 star clusters based ou data from the OGLE using isochrone fitting., C06 determined ages of 164 associations and 311 star clusters based on data from the OGLE using isochrone fitting.
 Their sample is the largest available catalog with SAIC cluster ages., Their sample is the largest available catalog with SMC cluster ages.
 Ages for voung LMC clusters have been provided by C95 based on integrated colors (621 objects)Lr audby PUOO using isochrone fitting applied to OCII data (7600 clusters)., Ages for young LMC clusters have been provided by G95 based on integrated colors (624 objects) and by PU00 using isochrone fitting applied to OGLE-II data $\sim$ 600 clusters).
 Luniuosities have been published for 201 SMC star clusters by RZ05 measuriug iutegrated colors frou the Magellanic Clouds Photometric Survey (MCTPS)., Luminosities have been published for 204 SMC star clusters by RZ05 measuring integrated colors from the Magellanic Clouds Photometric Survey (MCPS).
 Dica621LMCορ) {396) published integrated photometry of star clusters that was based om observations carried out at the 0.6l-n telescope at CTIO in Chile and at the 2.15-n CASLEO telescope in Argentina., \citet{bica96} (B96) published integrated photometry of 624 LMC star clusters that was based on observations carried out at the 0.61-m telescope at CTIO in Chile and at the 2.15-m CASLEO telescope in Argentina.
 Iu the present study we merease the nmuuber of aee-dated voung LAIC anc SAIC star clusters and calculate V-band huminosities., In the present study we increase the number of age-dated young LMC and SMC star clusters and calculate V-band luminosities.
 We aim at improving the nuderstauding of the cluster age distribution of these two iregular galaxies aud preseut spatial distribution maps of the star clusters iu both galaxies., We aim at improving the understanding of the cluster age distribution of these two irregular galaxies and present spatial distribution maps of the star clusters in both galaxies.
 To achieve this goal. we make use of ground-based data of the Magellanic Clouds Photometric Surveys (AICPSs} (Zaritskyotal.2002. 200L).," To achieve this goal, we make use of ground-based data of the Magellanic Clouds Photometric Surveys (MCPSs) \citep{zar02,zar04}."
. In the next Section the observations aud data reduction are described., In the next Section the observations and data reduction are described.
 In 5 3. the distances. reddenings. and imetallicities of both the SMC and the LMC are giveu.," In $\S$ \ref{sec:metunddistmod} the distances, reddenings, and metallicities of both the SMC and the LMC are given."
 In 5 [. the clusters’ age distribution. spatial distribution. aud dissolution effects are discussed and in $8 5 the correlation between the cluster huninositics and age/radius is derived.," In $\S$ \ref{sec:agedist} the clusters' age distribution, spatial distribution, and dissolution effects are discussed and in $\S$ \ref{sec:youngies_lum} the correlation between the cluster luminosities and age/radius is derived."
 We iade use of three catalogs in order to select clusters and to obtain color-magnitude diagrams (CMDsx) of the voung SAIC aud. LMC star clusters (age «1 Cx)., We made use of three catalogs in order to select clusters and to obtain color-magnitude diagrams (CMDs) of the young SMC and LMC star clusters (age $<$ 1 Gyr).
 The first catalog was published bv DOS (seealso.Dica&Seluuitt1995:Bica&Dutra2000) aud includes cluster positions. angular sizes. aud object classes for 17.515 objects in the LAIC. SAIC. and Magellanic Bridge.," The first catalog was published by B08 \citep[see also ][]{bica95,bica00} and includes cluster positions, angular sizes, and object classes for 17,815 objects in the LMC, SMC, and Magellanic Bridge."
 This catalog combines and cross-ideutifics objects measured ou the ESO/SERC R and J Sky Survey Sclunidt filuis and other catalogs (e.g...Pietrzvuski&Udalski1999).," This catalog combines and cross-identifies objects measured on the ESO/SERC R and J Sky Survey Schmidt films and other catalogs \citep[e.g., ][]{pietrzynski99}."
 The other two catalogs are from the MCPS presented bv Zaritskyctal.(2002.2001). coutaidug U. D. V. and I point-source photometry of the central Ls dee? area of the SAIC) (5.156.057 stars) aud of the ceutral Gl deg? area of the LAC. (2.107.011 stars).," The other two catalogs are from the MCPS presented by \citet{zar02,zar04} containing U, B, V, and I point-source photometry of the central 18 $^2$ area of the SMC (5,156,057 stars) and of the central 64 $^2$ area of the LMC (24,107,014 stars)."
 The data were obtained using the Las Campaws lan Swope telescope in Chile., The data were obtained using the Las Campanas 1-m Swope telescope in Chile.
 The V frame was used as reference aud only stars detectec in both the Via id D frame were retained., The V frame was used as reference and only stars detected in both the V and B frame were retained.
 Du both catalogs. the linitine magnitude of the photometry is V—21 mac.," In both catalogs, the limiting magnitude of the photometry is $\sim$ 24 mag."
" The photometry is highly incomplete below U=21.5 mag, B=23.5 mae. V=23 mag. and I=22 mae."," The photometry is highly incomplete below U=21.5 mag, B=23.5 mag, V=23 mag, and I=22 mag."
 This means that it is dificult to derive ages of star clusters older than ~1 Car due to the limited photometric depth of the AICPS. which does not resolve niadn-sequence turnoff-poiuts« (AISTOs) of iuteiuediate-age aud older clusters.," This means that it is difficult to derive ages of star clusters older than $\sim$ 1 Gyr due to the limited photometric depth of the MCPS, which does not resolve main-sequence turnoff-points (MSTOs) of intermediate-age and older clusters."
 Each object iu DOS catalog is categorized by au object class;, Each object in B08's catalog is categorized by an object class.
 Obvious star clusters are indicated by a € and cuussionless associations bv au A. (, Obvious star clusters are indicated by a 'C' and emissionless associations by an 'A'. '
"CAT aud ""ACT iudicate intermediate classes between these two types for which a classification was not clear. ",CA' and 'AC' indicate intermediate classes between these two types for which a classification was not clear. '
NC refers to small II reeious with embedded star clusters. while “CN” are clusters that show traces of enüssion. ,"NC' refers to small HII regions with embedded star clusters, while 'CN' are clusters that show traces of emission. '"
DCN refers to clusters that are decoupled from nebulae.,DCN' refers to clusters that are decoupled from nebulae.
 For our study. ouly including a. €classification were κος (SAIC:ο. 765 «Mobjects: LMC: 1089 objects). because these objects are defined and. not too extended so that cluster stars can be distinguished from the surroundiug field stars.," For our study, only objects including a 'C'-classification were used (SMC: 765 objects; LMC: 4089 objects), because these objects are well defined and not too extended so that cluster stars can be distinguished from the surrounding field stars."
 Star clusters that have very siunall radii or that are very sparse could not be age-dated (see 8 L1))., Star clusters that have very small radii or that are very sparse could not be age-dated (see $\S$ \ref{sec:youngies_ages}) ).
 Our resulting catalogs contain ages of star clusters between 10 Myy and 1 Cr., Our resulting catalogs contain ages of star clusters between $\sim$ 10 Myr and 1 Gyr.
 Clusters whose appearauce in the CNIDs indicated au age older than 1 Cyr were discarded from the sample. because the MSTOs were uot resolved.," Clusters whose appearance in the CMDs indicated an age older than 1 Gyr were discarded from the sample, because the MSTOs were not resolved."
 Because we oulv age-dated objects includiug a € iu the Bos classification. our suuples coutain only objectsον witli a nuninuun age of LO Myr. since very voune jjects are usually classified as associations or nebulae aud thus were excluded from our suuple.," Because we only age-dated objects including a 'C' in the B08 classification, our samples contain only objects with a minimum age of 10 Myr, since very young objects are usually classified as associations or nebulae and thus were excluded from our sample."
 For many iutermediate-age and old SAIC and LALC clusters accurate ages have been determined elsewhere in the literature mostly based ou IST data (e.g...Mighelletal.1998:Olsen1995:Richctal.2000:Piattiet2001:Cdatt 2008a.b).," For many intermediate-age and old SMC and LMC clusters accurate ages have been determined elsewhere in the literature mostly based on HST data \citep[e.g., ][]{migh98,olsen98,rich00,pia01,glatt08a,glatt08b}."
. The latest low-resolution spectroscopic measurements of SAIC star clusters by Parisietal.(2009) showed that the vouug clusters with ages between ~ 0.9 aud 2 Cir have a spread im ietallicity of 0.53 dex., The latest low-resolution spectroscopic measurements of SMC star clusters by \citet{Parisi08} showed that the young clusters with ages between $\sim$ 0.9 and 2 Gyr have a spread in metallicity of 0.53 dex.
 The two voungest clusters in their sample. 1106 aud 1108. both with ages around 0.9 Car. have mean unctallicities of |Fe/II|2-0.88 aud -1.05. respectively.," The two youngest clusters in their sample, 106 and 108, both with ages around 0.9 Gyr, have mean metallicities of [Fe/H]=-0.88 and -1.05, respectively."
 Studies based on spectroscopy of six suporgiauts in the voung cluster 3330 (age~20-25 Myr: Caebel (1996))) rendered a ietallicity of = 0.69 dex (e.g...Ihll1999).. whereas Gonzalez[Fe/H]&Waller(1999). found. |Fe/TI] 0.91+0.02 from lieh-resolution sprectra of seven supereiauts in this cluster.," Studies based on spectroscopy of six supergiants in the young cluster 330 $\sim$ 20-25 Myr; \citet{grebel96}) ) rendered a metallicity of [Fe/H] = $-0.69 \pm 0.11$ dex \citep[e.g., ][]{hill99}, whereas \citet{Gonzalez99} found [Fe/H] = $-0.94\pm0.02$ from high-resolution sprectra of seven supergiants in this cluster."
 It has beeu suggested repeatedly that NCC 330 is more metal-poor than the surrounding fiek star population (ee.Grebel&Richtler1992:GonzalezWallerstein 1999).," It has been suggested repeatedly that NGC 330 is more metal-poor than the surrounding field star population \citep[e.g., ][]{Grebel92,Gonzalez99}."
. On the other haud. most fieldstar studics aeree on a value of |Fe/II|] 2.— 0.704:0.07 dex (e.g...Illetal. 1999)..," On the other hand, most fieldstar studies agree on a value of [Fe/H] = $-0.70 \pm 0.07$ dex \citep[e.g., ][]{Hill97,venn99}. ."
 This metallicitv. corresponds to an isochrone model of Z = 0.001. which we used for the age determination.," This metallicity corresponds to an isochrone model of Z = 0.004, which we used for the age determination."
 We do not cousider a possible metallicity spread here., We do not consider a possible metallicity spread here.
 A distance modulus of (1i1-M)= 15.90 mag, A distance modulus of (m-M) = 18.90 mag
 A distance modulus of (1i1-M)= 15.90 mage, A distance modulus of (m-M) = 18.90 mag
"On the contrary. when the ""DP(p.5) rate is reduced by a [actor of 100. dramatic changes in the expected vields occur.","On the contrary, when the $^{30}$ $\gamma$ ) rate is reduced by a factor of 100, dramatic changes in the expected yields occur."
" Now. ""P. ) competes favorably with proton captures. and an important enhancement of ""Si is obtained."," Now, $^{30}$ $\beta^+$ ) competes favorably with proton captures, and an important enhancement of $^{30}$ Si is obtained."
 In fact. the reduction of the proton capture rate halts significantly the svnthesis of elements above Si (bv à factor of ~ 10 with respect to the values found with the nominal rate).," In fact, the reduction of the proton capture rate halts significantly the synthesis of elements above Si (by a factor of $\sim$ 10 with respect to the values found with the nominal rate)."
 We have compared our results with the latest available results [rom hvdrodsnamie simulations of ONe novae by Starfield et al. (, We have compared our results with the latest available results from hydrodynamic simulations of ONe novae by Starrfield et al. (
2001): thev state that the switeh to an updated nuclear network (Iiadis οἱ al.,2001): they state that the switch to an updated nuclear network (Iliadis et al.
 2001) is accompanied by an important reduction of the abundances of nuclei above aluminum. in good agreement wilh the results found here.," 2001) is accompanied by an important reduction of the abundances of nuclei above aluminum, in good agreement with the results found here."
" However. our new computations show (hat reduction of the vields affect only nuclei above 78. In [act. a significant reduction of 78 results only when we adopt the low ""DP(p.5) test rate."," However, our new computations show that reduction of the yields affect only nuclei above $^{32}$ S. In fact, a significant reduction of $^{32}$ S results only when we adopt the low $^{30}$ $\gamma$ ) test rate."
" Hence. this discrepancy might be likely attributed to a different prescription for the adopted ""P(p.5) rate."," Hence, this discrepancy might be likely attributed to a different prescription for the adopted $^{30}$ $\gamma$ ) rate."
 In particular. the rate used by Starrfield οἱ al. (," In particular, the rate used by Starrfield et al. ("
2001) seems to be somewhat lower than (he nominal rate adopted in our paper. which stresses again (he crucial dependence of the SCa vields on this particular rate.,"2001) seems to be somewhat lower than the nominal rate adopted in our paper, which stresses again the crucial dependence of the S–Ca yields on this particular rate."
 Despite a detailed comparison with observations is out of the scope of this paper. because a larger number of nova models is required {ο properly explore (he wide parameter space. some conclusions can be outlined.," Despite a detailed comparison with observations is out of the scope of this paper, because a larger number of nova models is required to properly explore the wide parameter space, some conclusions can be outlined."
 In fact. spectroscopic abundance determinations show evidence for some overproduction of nuclei in the SiCa mass region in a number of classical novae. including silicon (Nova Aql 1932. Snijders et al.," In fact, spectroscopic abundance determinations show evidence for some overproduction of nuclei in the Si–Ca mass region in a number of classical novae, including silicon (Nova Aql 1982, Snijders et al."
 1937. Andrea οἱ al.," 1987, Andreä et al."
 1994; QU Vul 1984. Andrea et al.," 1994; QU Vul 1984, Andreä et al."
 1994). sulfur (Nova Aq 1932. Snijders et al.," 1994), sulfur (Nova Aql 1982, Snijders et al."
 1937. Anclrea et al.," 1987, Andreä et al."
 1994). chlorine (Nova GQ Mus 1983. Morisset Pequignot 1996). argon aud calcium (Nova GQ Aus 1983. Morisset Pequignot 1996: Nova V2214 Oph LO8s. Nova V977 Sco 1939 and Nova V443 Set 1989. Andrea οἱ al.," 1994), chlorine (Nova GQ Mus 1983, Morisset Pequignot 1996), argon and calcium (Nova GQ Mus 1983, Morisset Pequignot 1996; Nova V2214 Oph 1988, Nova V977 Sco 1989 and Nova V443 Sct 1989, Andreä et al."
 1994)., 1994).
 Indeed. models of explosions in 1.35 ONe white cwarls have an end-point lor nucleosynthesis below calcium. hence in agreement wilh observations.," Indeed, models of explosions in 1.35 ONe white dwarfs have an end-point for nucleosynthesis below calcium, hence in agreement with observations."
 This suggests that peak temperatures attained at (he burning shell during nova outbursts cannot be much larger than 3xLO” Ix. otherwise an rp-process would result. at such high temperatures. driving the nuclear path towards heavier species. not observed so far.," This suggests that peak temperatures attained at the burning shell during nova outbursts cannot be much larger than $3 \times 10^8$ K, otherwise an rp-process would result at such high temperatures, driving the nuclear path towards heavier species, not observed so far."
 Aloreover. as stated in the discussion of (he main nuclear paths. determination of chemical abundances in the Si-Ca mass region during nova outbursts is affected by uncertainties of nuclear physics origin.," Moreover, as stated in the discussion of the main nuclear paths, determination of chemical abundances in the Si-Ca mass region during nova outbursts is affected by uncertainties of nuclear physics origin."
 In particular. the uncertainty associated to δρ.) makes it difficult to determine realistic abundances above silicon. and (o clarify as well whether the path towards heavier species is halted or. on the contrary. i£ significant production of Si-Ca nuclei is still expected.," In particular, the uncertainty associated to $^{30}$ $\gamma$ ) makes it difficult to determine realistic abundances above silicon, and to clarify as well whether the path towards heavier species is halted or, on the contrary, if significant production of Si-Ca nuclei is still expected."
 A better determination of this crucial rate would be of significant importance for the studies of nova nucleosvuthesis (hat takes place in massive ONe white clwarls., A better determination of this crucial rate would be of significant importance for the studies of nova nucleosynthesis that takes place in massive ONe white dwarfs.
 The authors would like to thank an anonymous releree for his suggestions., The authors would like to thank an anonymous referee for his suggestions.
 This research has been partially supported by the CICYT-DP.N.LE. (ESP95-1348). bv the DGICYT," This research has been partially supported by the CICYT-P.N.I.E. (ESP98-1348), by the DGICYT"
evolutionary history of the secondary star.,evolutionary history of the secondary star.
 In summary. the evidence to date for magnetic activity in CV secondary stars amounts to using them as possible post-[acto explanations of extant observational data.," In summary, the evidence to date for magnetic activity in CV secondary stars amounts to using them as possible post-facto explanations of extant observational data."
 What is required is an observational test of a prediction based on the idea that the secondary stars have strong magnetic fields., What is required is an observational test of a prediction based on the idea that the secondary stars have strong magnetic fields.
 Slarspols are the kev (o the technique we present here., Starspots are the key to the technique we present here.
 Their presence can be deduced from rotational modulation of stellar brightness or more directly from Doppler imagine of the surfaces of rapidly rotating stars (e.g.Barnesetal. 2001)., Their presence can be deduced from rotational modulation of stellar brightness or more directly from Doppler imaging of the surfaces of rapidly rotating stars \citep[e.g.][]{bel}. .
. Donati(1997) have used Zeeman Doppler imaging to show that starspots do indeed coincide with regions of strong magnetic field. and starspots are now known to exist in both single cool stars and non-interacting binaries which have rotation periods from about 12 hours to a few weeks.," \citet{14} have used Zeeman Doppler imaging to show that starspots do indeed coincide with regions of strong magnetic field, and starspots are now known to exist in both single cool stars and non-interacting binaries which have rotation periods from about 12 hours to a few weeks."
 O'Nealetal.(1996). aid O'Nealetal.(1998) have developed a new wav to measure the spol area and temperature. which relies on a (vpical stuspot being approximately 1000 cooler than (he unspotted photosphere.," \citet{11} and \citet{20} have developed a new way to measure the spot area and temperature, which relies on a typical starspot being approximately 1000K cooler than the unspotted photosphere."
 The total spectrum from the star is then the mean [from (he spotted. and unspotted. areas., The total spectrum from the star is then the flux-weighted mean from the spotted and unspotted areas.
 In. particular. when one observes inagnelically active IX stus. molecular absorption features due to TiO are seen. which can onlv come Irom much cooler M-tvpe atmospheres.," In particular, when one observes magnetically active K stars, molecular absorption features due to TiO are seen, which can only come from much cooler M-type atmospheres."
 By modeling the total spectrum as the sum of template Ix-tvpe ancl M-(vpe stars. an estimate of the spot area ancl temperature is recovered. assuming that the star is uniformly covered by spots.," By modeling the total spectrum as the sum of template K-type and M-type stars, an estimate of the spot area and temperature is recovered, assuming that the star is uniformly covered by spots."
 In tliis letter we present the first results using a similar method for a CV secondary star., In this letter we present the first results using a similar method for a CV secondary star.
 Although the application of this technique to CVs is straüghtforward in principle. there are observational complications which make it difficult in practice.," Although the application of this technique to CVs is straightforward in principle, there are observational complications which make it difficult in practice."
 First. unlike (1996).. we cannot normalise (he spectra such (hat the continuum flux is unity. as (he presence of non-stellar components (e.g. the accretion disc) whose [αν varies wilh wavelength. would make the relative Iluxes in (he lines incorrect.," First, unlike \citet{11}, we cannot normalise the spectra such that the continuum flux is unity, as the presence of non-stellar components (e.g. the accretion disc) whose flux varies with wavelength, would make the relative fluxes in the lines incorrect."
 Thus we must flux our spectra. ensuring (hat the relative levels across the spectra are accurate to approximately one percent.," Thus we must flux our spectra, ensuring that the relative levels across the spectra are accurate to approximately one percent."
 It is well known that normal techniques can introduce problems at this level. ancl worse still the TiO bands are contaminated by absorption from (the Earth's atmosphere.," It is well known that normal techniques can introduce problems at this level, and worse still the TiO bands are contaminated by absorption from the Earth's atmosphere."
 ILowever. preserving (his {his information means that our fitting technique can utilize (he overall continuum shape of the template spectra. in addition to the strengths and widths of the absorption lines.," However, preserving this flux information means that our fitting technique can utilize the overall continuum shape of the template spectra, in addition to the strengths and widths of the absorption lines."
 For the latter information to be useful. verv high signal-to-noisespectra are required.," For the latter information to be useful, very high signal-to-noisespectra are required."
suggest that the absence of prograde and low inclination (~170?— 180°) retrograde irregular satellites in the region encompassed between 10.47x10° km and 14.96x10° km is a by-product of the sweeping effect of Phoebe.,suggest that the absence of prograde and low inclination $\sim 170^{\circ} - 180^{\circ}$ ) retrograde irregular satellites in the region encompassed between $10.47 \times 10^{6}$ km and $14.96 \times 10^{6}$ km is a by-product of the sweeping effect of Phoebe.
" It is less clear if the absence of retrograde satellites with lower inclinations (i.e. high velocities ejecta from Phoebe or other captured bodies) in the same radial region could be due to the same reason or if it is a primordial structure related to the capture We also found evidences of dynamical groupings among prograde and retrograde satellites, even if their interpretation in terms of families is not straightforward due to the effects of chaotic and resonant evolution."," It is less clear if the absence of retrograde satellites with lower inclinations (i.e. high velocities ejecta from Phoebe or other captured bodies) in the same radial region could be due to the same reason or if it is a primordial structure related to the capture We also found evidences of dynamical groupings among prograde and retrograde satellites, even if their interpretation in terms of families is not straightforward due to the effects of chaotic and resonant evolution."
" By applying the HCM algorithm and assuming a velocity cut—off of about 200 m/s, we retrieved two candidate families between the prograde and six between the retrograde satellites."," By applying the HCM algorithm and assuming a velocity cut--off of about $200$ m/s, we retrieved two candidate families between the prograde and six between the retrograde satellites."
 Some of these families merge in bigger clusters at higher but possibly still acceptable velocity cut-offs., Some of these families merge in bigger clusters at higher but possibly still acceptable velocity cut–offs.
 This might be an indication that the system suffered intense post—breakup collisional evolution which could have, This might be an indication that the system suffered intense post–breakup collisional evolution which could have
the Crab ancl Vela pulsars. may. have the jet configuration. which suggests (he existence of a disk surrounding the neutron star (Blackman&Perna2004.andreferencestherein)..,"the Crab and Vela pulsars, may have the jet configuration, which suggests the existence of a disk surrounding the neutron star \citep[][and references
therein]{bla04}."
 The strongest constraints on (hie presence of a disk is given by its optical ancl longer wavelength enussion., The strongest constraints on the presence of a disk is given by its optical and longer wavelength emission.
 Perna&Hernquist(2000) have examined (he reprocessing of beamed pulsar emission bv the debris disks., \citet{perna00} have examined the reprocessing of beamed pulsar emission by the debris disks.
 They found that. since the reradiated flux gives the dominant contribution at long wavelengths produced in the bulk of the disk. whereas the optical enission is generated in ils innermost part. the optical rather the longer wavelength emission would be highly suppressed. if (he inner edge of the disk were truncated at a radius larger (han je magnetospherie radius.," They found that, since the reradiated flux gives the dominant contribution at long wavelengths produced in the bulk of the disk, whereas the optical emission is generated in its innermost part, the optical rather the longer wavelength emission would be highly suppressed, if the inner edge of the disk were truncated at a radius larger than the magnetospheric radius."
 Most recently. Wang.Chakrabarty.&Ixaplan(2006). report the discovery of middnlrared emission from a cool disk around the isolated voung X-ray pulsar 4U 0142-61. presenting the first direct evidence for supernova [allback.," Most recently, \citet{wan06} report the discovery of mid-infrared emission from a cool disk around the isolated young X-ray pulsar 4U $+$ 61, presenting the first direct evidence for supernova fallback."
 In (he original picture of Sturrock(1971) and Michel&Dessler(1981). (he debris disk is magnetically coupled with the neutron star with no accretion., In the original picture of \citet{stu71} and \citet{mic81} the debris disk is magnetically coupled with the neutron star with no accretion.
" This may be true for cold disks with extvemely low viscosity,", This may be true for cold disks with extremely low viscosity.
 However. it is conventionally thought Chat the pulsar enussion will quenched if (he disk wind plasma penetrating into the light cvlinder.," However, it is conventionally thought that the pulsar emission will quenched if the disk wind plasma penetrating into the light cylinder."
 Most of the neutron stars with a surrounding disk should have experienced the accretor and propeller regimes (Illarionov&Sunvave1975)., Most of the neutron stars with a surrounding disk should have experienced the accretor and propeller regimes \citep{ill75}.
. The existence of a disk inside the lieht cvlinder may significantlv influence the pulsar radiation processes., The existence of a disk inside the light cylinder may significantly influence the pulsar radiation processes.
 Magnetocentrifugally driven outflows Irom the disks has been discussed by a number of authors during the propeller phase (e.g.Camenzind1990;Ixónigl1991:Lovelaceetal.1995;Agapitou&Ustvugovaetal. 2006).," Magnetocentrifugally driven outflows from the disks has been discussed by a number of authors during the propeller phase \citep[e.g.][]{cam90,kon91,lov95,aga00,ust06}."
.. The disk wind itself may also be strong enough to influence the structure of pulsar winds (Blackman&Perna2004)., The disk wind itself may also be strong enough to influence the structure of pulsar winds \citep{bla04}.
. It has already. been shown that the ~10? V potential difference across the magnetospheric gap and the outward-directed electric field required by the Ruderman-Sutherland model for (he generation of radio waves will be negated. if the number density of matter at the All&een surface is greater than ~7.2x10* | (Wang1983).. a condition satisfied by most neutron stars with a debris disk where there is significant wind or outflow from the disk.," It has already been shown that the $\sim 10^{12}$ V potential difference across the magnetospheric gap and the outward-directed electric field required by the Ruderman-Sutherland model for the generation of radio waves will be negated, if the number density of matter at the Alfv́een surface is greater than $\sim 7.2\times 10^7$ $^{-3}$ \citep{wan83}, a condition satisfied by most neutron stars with a debris disk where there is significant wind or outflow from the disk."
" The densitv of the outflow plasma. il similar (ο that in the disk. can be estimated to be where A/ is the mass inflow rate in the disk. // the half thickness. e, the radial velocity. /2 (he inner radius of (he disk. a (he viscosity parameter. and my the proton mass. respectively."," The density of the outflow plasma, if similar to that in the disk, can be estimated to be where $\dot{M}$ is the mass inflow rate in the disk, $H$ the half thickness, $v_{\rm r}$ the radial velocity, $R$ the inner radius of the disk, $\alpha$ the viscosity parameter, and $m_{\rm H}$ the proton mass, respectively."
 It can be much larger than the Goldreich-Julian density pe.) For (vpical values of the adopted parameters. if one assumes (hat the electron-positron pairs in (he gap are close to saturation.," It can be much larger than the Goldreich-Julian density $\rho_{\rm GJ}$ for typical values of the adopted parameters, if one assumes that the electron-positron pairs in the gap are close to saturation,"
jxrofiles for r>071 limited to only a few percent.,profiles for $r>0\asec1$ limited to only a few percent.
 This is consistent. with tlie expectatious frou the simulations aud tests quoted above. which show that WEPCI cecouvolutious are largely accurate into rzz071 (with the caveat noted in Laueretal.2005 that WEPC1 decouvolutious may be less accurate at this radius if a stroug nuclear point source is present).," This is consistent with the expectations from the simulations and tests quoted above, which show that WFPC1 deconvolutions are largely accurate into $r\approx0\asec1$ (with the caveat noted in \citealt{l05} that WFPC1 deconvolutions may be less accurate at this radius if a strong nuclear point source is present)."
 ACS/WFC has superior resolution or r«071. as evidenced by the systematically hieher central surface brightnesses recovered interior o this radius.," ACS/WFC has superior resolution for $r<0\asec1,$ as evidenced by the systematically higher central surface brightnesses recovered interior to this radius."
 Since Figure 10. shows nearly all of the 10 WEPCL overlapgalaxies!.. it demonsrates directly that the use of WEPCHI profiles iu the present sample is not a facor in the strouely different values clerivecl from the Nuker aud VCS models.," Since Figure \ref{fig:acsdecon} shows nearly all of the 10 WFPC1 overlap, it demonstrates directly that the use of WFPC1 profiles in the present sample is not a factor in the strongly different $\gamma'$ values derived from the Nuker and VCS models."
 The two galaxies selected for the WEDPC2/ACS comparisous are the most centrally compact galaxies observed with WEPC? in the overlap satuple. aud thus are the 1lost seusitive to dillerences iu resolution.," The two galaxies selected for the WFPC2/ACS comparisons are the most centrally compact galaxies observed with WFPC2 in the overlap sample, and thus are the most sensitive to differences in resolution."
 The WFPC? profiles show superix resolution to ACS/WEC for ruw«O71. which is expected. given the sharper WEPC2 PSF.," The WFPC2 profiles show superior resolution to ACS/WFC for $r<0\asec1,$ which is expected, given the sharper WFPC2 PSF."
 Again. however. noje of the differences between the VC'S results and ours depeuds ou the exquisite treatment of details near theAST diffraction limit. as we will show in the next section.," Again, however, none of the differences between the VCS results and ours depends on the exquisite treatment of details near the diffraction limit, as we will show in the next section."
 Tle VCS and present 5 values both come frou 1uodels of the galaxy intrinsic light distributions., The VCS and present $\gamma'$ values both come from models of the galaxy intrinsic light distributions.
" Understanding the dillerences between the 5 valtes shown in Figure 8 requires comparing the VCS and Niser intrinsic models to the decouvolvect 5uface brightness profiles. which are themselves a uou-pa""metric representatiou of the intrinsic light cistributions of the galaxies."," Understanding the differences between the $\gamma'$ values shown in Figure \ref{fig:gam_diff} requires comparing the VCS and Nuker intrinsic models to the deconvolved surface brightness profiles, which are themselves a non-parametric representation of the intrinsic light distributions of the galaxies."
 The concordance betwee ACS and WEPC2 or WEPCL decouvoved profiles further meaus that we can directly compal'e the VCS intrinsic »ofile models (the acopted representation of the prolilesprior to PSE convoltjot) to the deconvoved WEPC2 or WEPCl profiles. as well as comparing the Nuker mocels to decoiwolved ACS/WEC orofiles.," The concordance between ACS and WFPC2 or WFPC1 deconvolved profiles further means that we can directly compare the VCS intrinsic profile models (the adopted representation of the profiles to PSF convolution) to the deconvolved WFPC2 or WFPC1 profiles, as well as comparing the Nuker models to deconvolved ACS/WFC profiles."
 In practice. we cau select the camera that provides the highest spatial 'esolutioi Or a given galaxy. thus comparing both the Nuker aud VCS models to the best deconvolved prolile of the galaxy.," In practice, we can select the camera that provides the highest spatial resolution for a given galaxy, thus comparing both the Nuker and VCS models to the best deconvolved profile of the galaxy."
 Iu general. this meats using WEPC2 profiles as the first choice. with the AC'S as tie secoud choice (WEPCI profiles wil still be used for the two exceptions noted above).," In general, this means using WFPC2 profiles as the first choice, with the ACS as the second choice (WFPC1 profiles will still be used for the two exceptions noted above)."
 The disagreement of >! values shown iu Figure 5 can be traced to differences between the VCS aud Nuker profile inodels.," The disagreement of $\gamma'$ values shown in Figure \ref{fig:gam_diff}
 can be traced to differences between the VCS and Nuker profile models."
 We show this ou a galaxy by galaxy basis in Figures 11. to 13. by comparing the publishedΠίο VCS g-band uodels aud Nuker models to WEPC2. Ας. aud WEPCI deconvolved isophotal brightuesses.," We show this on a galaxy by galaxy basis in Figures \ref{fig:acscomp1} to \ref{fig:acscomp3}
 by comparing the published VCS -band models and Nuker models to WFPC2, ACS, and WFPC1 deconvolved isophotal brightnesses."
 The measured brightness values are preseuted twice., The measured brightness values are presented twice.
 The lower trace has tlie isophotal scale convertec to mean radii to accommodate the VCS models. which are normalized to the surface brightuess 1leastires at r>2” to account for the color offset," The lower trace has the isophotal scale converted to mean radii to accommodate the VCS models, which are normalized to the surface brightness measures at $r>2''$ to account for the color offset"
We also present and discuss €DV/ photometry of nine star clusters all located in the fourth Galactic quadrant except for one - Czernik 38-. which is located in the first quadrant (see Table |).,"We also present and discuss $UBVI$ photometry of nine star clusters all located in the fourth Galactic quadrant except for one - Czernik 38-, which is located in the first quadrant (see Table 1)."
 Most of them are nothing more than simple star cluster candidates. according to most public catalogs. and do not have any published data.," Most of them are nothing more than simple star cluster candidates, according to most public catalogs, and do not have any published data."
 Howvere. we expect that they are mostly young clusters based both on inspection of DSS maps and on the widely spread idea that clusters cannot survive fora long time in the inner Galactic disk.," Howvere, we expect that they are mostly young clusters based both on inspection of DSS maps and on the widely spread idea that clusters cannot survive for a long time in the inner Galactic disk."
" Apart from the obvious goal to establish their nature and derive their fundamental parameters. we aim to use them - when they are sufficiently young- as spiral arm tracers in the longitude range 200""</x:360""."," Apart from the obvious goal to establish their nature and derive their fundamental parameters, we aim to use them - when they are sufficiently young- as spiral arm tracers in the longitude range $290^{o} \leq l \leq 360^{o}$."
 In this MW sector. inside the solar ring. we expect the lines of sight of the clusters to first encounter the Carina-Sagittarius arm. and hopefully. also the Scutum-Crux arm. which is much closer to the Galactic Center. as well as the Perseus arm. which is much further away (Vazzquez et al.," In this MW sector, inside the solar ring, we expect the lines of sight of the clusters to first encounter the Carina-Sagittarius arm, and hopefully, also the Scutum-Crux arm, which is much closer to the Galactic Center, as well as the Perseus arm, which is much further away (Vázzquez et al."
 2005: Carraro Costa 2009: Baume et al., 2005; Carraro Costa 2009; Baume et al.
 The technique we used is based on the analysis of the color- and color-magnitude diagrams of groups of stars properly selected after having performed star counts and defined clusters’ reality and size (see Seleznev et al., The technique we used is based on the analysis of the color-color and color-magnitude diagrams of groups of stars properly selected after having performed star counts and defined clusters' reality and size (see Seleznev et al.
 2010 for As a consequence. the paper is organized as In Sect.," 2010 for As a consequence, the paper is organized as In Sect."
 2. we present information culled from literature on the objects under investigation. which demonstrate they have been almost completely overlooked in the past.," 2 we present information culled from literature on the objects under investigation, which demonstrate they have been almost completely overlooked in the past."
 Sect., Sect.
 3 presents the observations and basic data reduction. together with photometric calibration. completeness analysis and cross-correlation with 2MASS.," 3 presents the observations and basic data reduction, together with photometric calibration, completeness analysis and cross-correlation with 2MASS."
 The comparison with previous photometry - when available- are discussed in Sections 4., The comparison with previous photometry - when available- are discussed in Sections 4.
 Section 5 is devoted to star counts and the derivation of clusters’ size., Section 5 is devoted to star counts and the derivation of clusters' size.
 We then estimate the method to infer clusters” fundamental parameters in Sect., We then estimate the method to infer clusters' fundamental parameters in Sect.
 6., 6.
 Sect., Sect.
 7. finally. discusses the outcome of this analysis.," 7, finally, discusses the outcome of this analysis."
 The conclusions of this investigation. together with suggestions/recommendations for further studies. are provided in Sect.," The conclusions of this investigation, together with suggestions/recommendations for further studies, are provided in Sect."
 8., 8.
 Most clusters in the sample we investigated for this paper have not been studied so far. and only for one -Czernik 38- some prelimiary CCD data have been We present here a compilation of any previous study we could find in the literature to date. on a cluster-by-cluster This is the star cluster of the whole sample which received more attention in the past.," Most clusters in the sample we investigated for this paper have not been studied so far, and only for one -Czernik 38- some prelimiary CCD data have been We present here a compilation of any previous study we could find in the literature to date, on a cluster-by-cluster This is the star cluster of the whole sample which received more attention in the past."
 We selected this cluster also as a control object for our photometry. which we are going to compare in Sect.," We selected this cluster also as a control object for our photometry, which we are going to compare in Sect."
 4., 4.
 UBV photo-electrie photometry of about 200 stars have been presented by Claria et al. (, UBV photo-electric photometry of about 200 stars have been presented by Claria et al. (
1994). together with spectroscopy of I4 probable giant star members of the cluster.,"1994), together with spectroscopy of 14 probable giant star members of the cluster."
 These authors derived an age of 300 million years and place the cluster at a distance of 1300 pe. in agreement with previous findings by Becker (1960).," These authors derived an age of 300 million years and place the cluster at a distance of 1300 pc, in agreement with previous findings by Becker (1960)."
 They found that the cluster suffers from variable extinction. and obtain ECB-V)=0.36 from the turnoff. and 0.37 from giant stars.," They found that the cluster suffers from variable extinction, and obtain E(B-V)=0.36 from the turnoff, and 0.37 from giant stars."
 As for the metallicity. they found a large range of value. from +0.05 using DDO to -0.18 using Whasington photometric system.," As for the metallicity, they found a large range of value, from +0.05 using DDO to -0.18 using Whasington photometric system."
 A revision of the DDO calibration led Twarog et al (1997) to provide [Fe/H] ranging from -0.01 to 0.02. and E(B-V)=0.35.," A revision of the DDO calibration led Twarog et al (1997) to provide [Fe/H] ranging from -0.01 to 0.02, and E(B-V)=0.35."
 More recently. spectroscopic analysis by Santos et al. (," More recently, spectroscopic analysis by Santos et al. ("
2009) confirmed the range of metallicity found by Twarog et al. (,2009) confirmed the range of metallicity found by Twarog et al. (
1997). ruling out the results of the Washington photometry.,"1997), ruling out the results of the Washington photometry."
 Finally. Smiljanic et al (2009) derived [Fe/H]=0.12 from one giant. and reddening E(CB-V)20.33.," Finally, Smiljanic et al (2009) derived [Fe/H]=0.12 from one giant, and reddening E(B-V)=0.33."
 By adopting Shaller et al (1992) isochrones. they fit Claria et al (1994) photometry. getting an apparent distance modulus (m-M) =11.5. and an age of 400 million van den Berg Hagen (1975) describe NGC 4052 as a a medium richness. real cluster. mostly composed of blue stars. and possibly embedded in some nebulosity.," By adopting Shaller et al (1992) isochrones, they fit Claria et al (1994) photometry, getting an apparent distance modulus (m-M) =11.5, and an age of 400 million van den Berg Hagen (1975) describe NGC 4052 as a a medium richness, real cluster, mostly composed of blue stars, and possibly embedded in some nebulosity."
 The shallow study of Kharchenko et al. (, The shallow study of Kharchenko et al. (
2005) provides preliminary estimates of the cluster parameters based on photometry and astrometry of less than 20 stars brighter than V—12.,2005) provides preliminary estimates of the cluster parameters based on photometry and astrometry of less than 20 stars brighter than $\sim$ 12.
 They locate this 250 million years old cluster at 1200 pe from the Sun., They locate this 250 million years old cluster at 1200 pc from the Sun.
 No CCD studies of NGC 4052 have been conducted so No information is available for this cluster apart from its size. which is around 5 aremin according to Dias et al.," No CCD studies of NGC 4052 have been conducted so No information is available for this cluster apart from its size, which is around 5 arcmin according to Dias et al."
 No information is available for this cluster beyond the mere The only available study for this cluster is the photo-electric investigation by Ramin (1966) down to V —16. whicy places the cluster at an heliocentric distance of 1200 pe.," No information is available for this cluster beyond the mere The only available study for this cluster is the photo-electric investigation by Ramin (1966) down to V $\sim$ 16, whicj places the cluster at an heliocentric distance of 1200 pc."
 The age of 150 million is derived by Kharchenko et al. (, The age of 150 million is derived by Kharchenko et al. (
2005) from a subsample of stars brighter than —12.,2005) from a subsample of stars brighter than $\sim$ 12.
 Its young age is also recognized by the visual inspection of van den Berg Hagen van den Berg Hagen (1975) describe NGC 5715 as a medium richness. real cluster. mostly composed of blue stars.," Its young age is also recognized by the visual inspection of van den Berg Hagen van den Berg Hagen (1975) describe NGC 5715 as a medium richness, real cluster, mostly composed of blue stars."
 No optical study is available for NGC 5715. whose properties have been however investigated using 2MASS by Bonatto Bica (2007).," No optical study is available for NGC 5715, whose properties have been however investigated using 2MASS by Bonatto Bica (2007)."
 They report an age of 800 million years and a distance of 1.5 kpe from the van den Berg Hagen (1973) describe this cluster as a very poor ensemble of blue stars., They report an age of 800 million years and a distance of 1.5 kpc from the van den Berg Hagen (1975) describe this cluster as a very poor ensemble of blue stars.
 No data is available for it to Seggewiss (1968) provided some photographie photometry of NGC 6268 down to V — I4. and its analysis led to an helio-centric distance of 1200 pe.," No data is available for it to Seggewiss (1968) provided some photographic photometry of NGC 6268 down to V $\sim$ 14, and its analysis led to an helio-centric distance of 1200 pc."
 Later. van den Berg Hagen (1975) deseribed it as a very poor ensemble of blue stars.," Later, van den Berg Hagen (1975) described it as a very poor ensemble of blue stars."
 The shallower study by, The shallower study by
several recent studies have shown that complicated color distributions in globular cluster svslems (GCSs) are the norm rather than the exception (Gebhardt&Ixissler-Patig1999:Kundu&Whitmore2001:Larsenοἱal. 2001).,"Several recent studies have shown that complicated color distributions in globular cluster systems (GCSs) are the norm rather than the exception \citep{gk99,kw01,lar01}."
. In many cases. the GCS color distributions can be fairly well modeled as a superposition of two Gaussians with peaks al (V—)g20.95 and (V—7)y2LAS.," In many cases, the GCS color distributions can be fairly well modeled as a superposition of two Gaussians with peaks at $\vio\approx0.95$ and $\vio\approx1.18$."
" These colors correspond. to mean metallicities of [Z/Il]=—1.4 and IZ/M|=—0.6 (INissler-Patigetal.1998). if both populations are ""old. (they have similar ages (10.15 Gvrs) as those in the Milky Wavy."," These colors correspond to mean metallicities of $\zh=-1.4$ and $\zh=-0.6$ \citep{kis98} if both populations are “old”, they have similar ages (10–15 Gyrs) as those in the Milky Way."
 Although the color differences of globular clusters have generally been assumed to be mainlv a function of metallicity. it is clear Chat age differences between GC sub-populations will also affect their colors. making a vounger population appear bluer for a given metallicity.," Although the color differences of globular clusters have generally been assumed to be mainly a function of metallicity, it is clear that age differences between GC sub-populations will also affect their colors, making a younger population appear bluer for a given metallicity."
 There are a [few cases in which only a single. broad peak is observed in the optical GC color distribution. usually at blue or intermediate colors.," There are a few cases in which only a single, broad peak is observed in the optical GC color distribution, usually at blue or intermediate colors."
 While (hese svstems might simply lack a distinct metal-rich component. which would normally show up as the red peak. another interesting possibility is that the metal-rich. population is indeed. present but. has a significantly lower age than the metal-poor one. shifüng it to bluer colors and making the (wo populations appear as a single broad peak in optical colors.," While these systems might simply lack a distinct metal-rich component, which would normally show up as the red peak, another interesting possibility is that the metal-rich population is indeed present but has a significantly lower age than the metal-poor one, shifting it to bluer colors and making the two populations appear as a single broad peak in optical colors."
 Using optical photometry alone. this degeneracy between age and metallicity cannot easily be broken and alternative methods are needed to provide independent constraints on metallicitv or age (or both).," Using optical photometry alone, this degeneracy between age and metallicity cannot easily be broken and alternative methods are needed to provide independent constraints on metallicity or age (or both)."
 Combining optical and near-inlrared imagine of GCs in the ~3 Gyr old merger remnant NGC 1316. Goudlrooijetal.(2001) have recently demonstrated Chat an old. metal-poor," Combining optical and near-infrared imaging of GCs in the $\sim3$ Gyr old merger remnant NGC 1316, \citet{goud01} have recently demonstrated that an old, metal-poor"
compiled by Chen Tout (2007) from Iglesias Rogers (1996) and Alexander Ferguson (1994).,compiled by Chen Tout (2007) from Iglesias Rogers (1996) and Alexander Ferguson (1994).
" The initial hydrogen mass fraction, X, is obtained by, X=0.76— 3.0Z, where Z is the metallicity (Pols et al."," The initial hydrogen mass fraction, $X$, is obtained by, $X=0.76-3.0Z$ , where $Z$ is the metallicity (Pols et al."
 1998)., 1998).
" We constructed a series of zero-age extreme horizontal branch models (ZAEHB, i.e. helium begins stably burning in the core) of Pop I (Z=0.02) and carried out their evolutions in detail."," We constructed a series of zero-age extreme horizontal branch models (ZAEHB, i.e. helium begins stably burning in the core) of Pop I $Z$ =0.02) and carried out their evolutions in detail."
" The model grid contains a wide mass range; i.e., the core mass ranges from 0.33 to 1.4 Mo, and the envelope mass changes, by a step of about 0.005 Mo, from zero to the maximum envelope mass (see Fig.1)), beyond which the constructed object is not a hot subdwarf any more (i.e. Teg< 20,000K or log(g)« 4.5)."," The model grid contains a wide mass range; i.e., the core mass ranges from 0.33 to 1.4 $M_\odot$, and the envelope mass changes, by a step of about 0.005 $M_\odot$, from zero to the maximum envelope mass (see \ref{fig1}) ), beyond which the constructed object is not a hot subdwarf any more (i.e. $T_{\rm eff}<$ 20,000K or $\rm log(\it g)<$ 4.5)."
" As an example, we show the evolutionary tracks of hot subdwarfs with a core mass of 0.475 Μο in Fig.2."," As an example, we show the evolutionary tracks of hot subdwarfs with a core mass of 0.475 $M_\odot$ in Fig.2."
" The envelope masses, Meny, are 0.000, 0.001, 0.005, 0.010, and 0.015 Mo."," The envelope masses, $M_{\rm env}$, are 0.000, 0.001, 0.005, 0.010, and 0.015 $M_\odot$."
" TAEHB is the termination-age EHB, i.e., at the core helium exhaustion (Dorman et al."," TAEHB is the termination-age EHB, i.e., at the core helium exhaustion (Dorman et al."
 1993)., 1993).
 The region between ZAEHB and TAEHB is known as the main sequence., The region between ZAEHB and TAEHB is known as the main sequence.
 The age difference between two neighbouring crosses is 10 Myr., The age difference between two neighbouring crosses is 10 Myr.
" From the figure, we see that most of the observed sdB stars are located in the main sequence."," From the figure, we see that most of the observed sdB stars are located in the main sequence."
" However, we cannot confirm their core masses and their evolutionary stages yet, since a star with a different core mass in a different evolutionary stage is also likely in this region of the Τεῃ—log(g) diagram (see Sect.3)."," However, we cannot confirm their core masses and their evolutionary stages yet, since a star with a different core mass in a different evolutionary stage is also likely in this region of the $T_{\rm eff}-{\rm log}(g)$ diagram (see Sect.3)."
" For instance, an sdO star is possibly a main sequence star with a core mass higher than that of an sdB star, or in the stage of post main sequence of a sdB star."," For instance, an sdO star is possibly a main sequence star with a core mass higher than that of an sdB star, or in the stage of post main sequence of a sdB star."
" As we know, more than one evolutionary tracks pass through the same point on the Teg—log(g) diagram."," As we know, more than one evolutionary tracks pass through the same point on the $T_{\rm eff}- \rm log(g)$ diagram."
" Thus, we cannot figure out the most probable one from them just by comparing the evolutionary tracks."," Thus, we cannot figure out the most probable one from them just by comparing the evolutionary tracks."
" To solve this problem, we intend to find another approach to deriving the masses of hot subdwarfs."," To solve this problem, we intend to find another approach to deriving the masses of hot subdwarfs."
" Hot subdwarfs are core helium-burning stars with hydrogen envelopes that are too thin to sustain hydrogen burning; therefore, the luminosity of a hot subdwarf, L, depends upon the core mass, M., and the age, t."," Hot subdwarfs are core helium-burning stars with hydrogen envelopes that are too thin to sustain hydrogen burning; therefore, the luminosity of a hot subdwarf, $L$ , depends upon the core mass, $M_{\rm c}$, and the age, $t$."
" Meanwhile, we know that 1,νTi,RR.HMA, where R is the radius."," Meanwhile, we know that $L \sim T_{\rm eff}^4 \cdot R^2 \sim M_{\rm c} \cdot \frac{T_{\rm eff}^4}{g}$, where $R$ is the radius."
" Thus, we have a relation as f(M.,ft)~log(4), where Τεῃ and g are two fundamental parameters of hot subdwarfs“st from observations."," Thus, we have a relation as $f(M_{\rm c},t) \sim \log (\frac{T_{\rm eff}^4 }{g})$, where $T_{\rm eff}$ and $g$ are two fundamental parameters of hot subdwarfs from observations."
" Thus, we choose log(T.) as a basic. parameter for further study of the masses of these αιobjects."," Thus, we choose $\log (\frac{T_{\rm eff}^4}{g})$ as a basic parameter for further study of the masses of these objects."
" In general, stars evolves at different speeds in different evolutionary stages."," In general, stars evolves at different speeds in different evolutionary stages."
" If a star evolves slowly in a certain stage, it has more chance of being observed in this stage."," If a star evolves slowly in a certain stage, it has more chance of being observed in this stage."
 We may then find out the most probable mass via studying the change rate of log( as described in the following.," We may then find out the most probable mass via studying the change rate of $\log (\frac{T_{\rm eff}^4}{g})$, as described in the following."
" We divide log(τα) into small Zit),intervals of 0.1 from 10.0 to 16.0, and calculate the evolutionary time, dt, of each model in these intervals."," We divide $\log (\frac{T_{\rm eff}^4
 }{g})$ into small intervals of 0.1 from 10.0 to 16.0, and calculate the evolutionary time, $\delta t$, of each model in these intervals."
" Thus, for each interval of log(TA.5L), we may obtain a core mass, with which a hot subdwarf stays in it for the longest time amongst all the models (i.e. having the maximum value of 6f), and has the most chance of being observed."," Thus, for each interval of $\log (\frac{T_{\rm eff}^4}{g})$, we may obtain a core mass, with which a hot subdwarf stays in it for the longest time amongst all the models (i.e. having the maximum value of $\delta
 t$ ), and has the most chance of being observed."
" This core mass is then the most probable mass, M,, in the observations, and is assumed to be the real mass of the subdwarf !."," This core mass is then the most probable mass, $M_{\rm p}$, in the observations, and is assumed to be the real mass of the subdwarf ."
". We finally obtained a relation between M, and log( which is shown in Fig.3."," We finally obtained a relation between $M_{\rm p}$ and $\log
 (\frac{T_{\rm eff}^4}{g})$, which is shown in Fig.3."
" From this relation we may simply zr),know the mass of a hot subdwarf for given Te and g.", From this relation we may simply know the mass of a hot subdwarf for given $T_{\rm eff}$ and $g$.
" Using the M,-log( relation, we studied the masses of some observed hot subdwarfs,can) including 164 sdB stars and 46 sdO stars."," Using the $M_{\rm p}$ $\log (\frac{T_{\rm eff}^4}{g})$ relation, we studied the masses of some observed hot subdwarfs, including 164 sdB stars and 46 sdO stars."
" Some sdB stars are from the ESO supernova Iaprogenitor survey (SPY, Lisker et al."," Some sdB stars are from the ESO supernova Iaprogenitor survey (SPY, Lisker et al."
" 2005) and the other sdB stars are fromthe Hamburg quasar survey (HQS, Edelmann et 31.2003)."," 2005) and the other sdB stars are fromthe Hamburg quasar survey (HQS, Edelmann et al.2003)."
 The sdO stars come from SPY(Stroeer et al., The sdO stars come from SPY(Stroeer et al.
 2007)., 2007).
The extreme brightness and compact size of masers make them valuable probes of regions of high mass star formation.,The extreme brightness and compact size of masers make them valuable probes of regions of high mass star formation.
 However it is not clear how. or indeed if. the different types of maser... OH andCH3OH.. are related to each other towards typical high mass protostars.," However it is not clear how, or indeed if, the different types of maser, OH and, are related to each other towards typical high mass protostars."
 Studies of aand mmasers towards a number of sources have failed to find a coherent view of their relationship (e.g. Beuther et al 2002). however statistical studies of OH and mmasers suggest that their associations can tell us about the evolutionary sequence of star formation (e.g. Caswell 1997; Szymezak. Gerard 2004).," Studies of and masers towards a number of sources have failed to find a coherent view of their relationship (e.g. Beuther et al 2002), however statistical studies of OH and masers suggest that their associations can tell us about the evolutionary sequence of star formation (e.g. Caswell 1997; Szymczak, Gerard 2004)."
 While the presence of particular types of maser towards a source may trace the evolutionary stage of the source. many sources show emission from multiple types of masers.," While the presence of particular types of maser towards a source may trace the evolutionary stage of the source, many sources show emission from multiple types of masers."
 Since the different masers can require different excitation conditions. these multiple species can be used as high resolution probes of different components of the circumstellar environment.," Since the different masers can require different excitation conditions, these multiple species can be used as high resolution probes of different components of the circumstellar environment."
 Theoretical. models suggest that the spatial coincidence. of different maser transitions or maser species can be used to infer the properties of the emitting material., Theoretical models suggest that the spatial coincidence of different maser transitions or maser species can be used to infer the properties of the emitting material.
 For example. Cragg et al. (," For example, Cragg et al. ("
2002) found that gas phase molecular abundance is the key determinant of observable maser activity for both OH and mmolecules.,2002) found that gas phase molecular abundance is the key determinant of observable maser activity for both OH and molecules.
 Detailed modelling of high resolution observations towards particular sources can also. provide value insights on the structure of the circumstellar material., Detailed modelling of high resolution observations towards particular sources can also provide value insights on the structure of the circumstellar material.
 For example. models have shown that the complexity of observed magnetic field structure in W75N can be explained by the maser emission originating from different depths within the protostellar disk (Gray et al.," For example, models have shown that the complexity of observed magnetic field structure in W75N can be explained by the maser emission originating from different depths within the protostellar disk (Gray et al."
 2003)., 2003).
 With these possibilities in mind. we present here the results of a study of the.. OH and mmasers associated with the well studied high mass young source IRAS 2012644104.," With these possibilities in mind, we present here the results of a study of the, OH and masers associated with the well studied high mass young source IRAS $20126+4104$."
 This source is located in the Cygnus X region at an estimated distance of 1.7 kpe (Wilking et., This source is located in the Cygnus X region at an estimated distance of 1.7 kpc (Wilking et.
 al., al.
 1989)., 1989).
 It has a luminosity of 107 aand is perhaps the best studied example of massive protostar associated with a Keplerian disk and a jet/outflow system., It has a luminosity of $10^4$ and is perhaps the best studied example of massive protostar associated with a Keplerian disk and a jet/outflow system.
 The molecular outflow has been mapped by Cesaront et al. (, The molecular outflow has been mapped by Cesaroni et al. (
1997; C97) and observations at centimetre wavelengths have shown that the outflow is fed by a jet (Hofner et al.,1997; C97) and observations at centimetre wavelengths have shown that the outflow is fed by a jet (Hofner et al.
 1999)., 1999).
 On the other hand. CH;CN (5-4) observations (C97) have revealed a molecular disk almost perpendicular to the jet axis and rotating around the embedded young stellar object (YSO) at the origin of the outflow/jet.," On the other hand, $_3$ CN (5-4) observations (C97) have revealed a molecular disk almost perpendicular to the jet axis and rotating around the embedded young stellar object (YSO) at the origin of the outflow/jet."
 Subsequent observations in the CH3CN (12-11) (Cesaroni et al., Subsequent observations in the $_3$ CN (12-11) (Cesaroni et al.
 1999: C99) and NH3 (1.1) lines (Zhang et al.," 1999; C99) and NH3 (1,1) lines (Zhang et al."
 1998) have found evidence for Keplerian rotation. implying a central disk plus stellar mass of 24M.," 1998) have found evidence for Keplerian rotation, implying a central disk plus stellar mass of 24."
.. The source is associated with OH. aand mmasers.," The source is associated with OH, and masers."
 Two features of OH masers were detected in the 1665-MHz line by Cohen et al. (, Two features of OH masers were detected in the 1665-MHz line by Cohen et al. (
1988) and more recent unpublished VLA data (Cohen. priv.,"1988) and more recent unpublished VLA data (Cohen, priv."
 comm.)., comm.).
" Observations of the water masers using the VLA with angular resolution of 0.1"" identified three emission regions (Tofani et al.", Observations of the water masers using the VLA with angular resolution of $0.1''$ identified three emission regions (Tofani et al.
 1995)., 1995).
 Moscadelli et al. (, Moscadelli et al. (
2000: hereafter MCR) resolved two of these into 26 unresolved spots using the VLBA.,2000; hereafter MCR) resolved two of these into 26 unresolved spots using the VLBA.
 The velocity and spatial structure of these spots were well fitted by a model with the spots arising at the interface between a jet and the surrounding molecular gas., The velocity and spatial structure of these spots were well fitted by a model with the spots arising at the interface between a jet and the surrounding molecular gas.
 Maser emission from the 6.7-GHz line of hhas recently been observed by Minier et al. (, Maser emission from the 6.7-GHz line of has recently been observed by Minier et al. (
2001).,2001).
 Using the EVN. they found two maser clumps separated by 100 AU and 0.8” to the north of the central source. a region relatively remote from the central source and with no other known indication of activity related to star formation.," Using the EVN, they found two maser clumps separated by 100 AU and $0.8''$ to the north of the central source, a region relatively remote from the central source and with no other known indication of activity related to star formation."
 To determine how these three types of masers are related to the circumstellar disk and/or the jet and investigate the connection between them. we have observed IRAS 20126+4104 at high angular resolution using MERLIN.," To determine how these three types of masers are related to the circumstellar disk and/or the jet and investigate the connection between them, we have observed IRAS $20126+4104$ at high angular resolution using MERLIN."
 The details of the observations and reduction are given in Sec., The details of the observations and reduction are given in Sec.
 2 and the results presented in Sec., 2 and the results presented in Sec.
 3., 3.
 In Sec., In Sec.
 4 we discuss the interpretation while conclusions are drawn in Sec., 4 we discuss the interpretation while conclusions are drawn in Sec.
 5., 5.
Figure 1: The VSNET optical light. curve of the 2001 outburst of WZ See.,Figure 1: The VSNET optical light curve of the 2001 outburst of WZ Sge.
 The first 6 observations are marked by arrows., The first 6 observations are marked by arrows.
 The four different phases of WZ See have been marked for elaritv., The four different phases of WZ Sge have been marked for clarity.
 Figure 2: Modeling the heating aud cooling of WZ See., Figure 2: Modeling the heating and cooling of WZ Sge.
 The temperature (in Ixelvin) of the white dwarl is drawn as a function of time (in davs) since the start of the outburst (July 23. 2001) The solid line represents (he compressional heating modeling. for 1.2 solar mass white dwarf with an initial temperature of 14.500. accreting al arate of 9xLOCAL./vear for 52 davs.," The temperature (in Kelvin) of the white dwarf is drawn as a function of time (in days) since the start of the outburst (July 23, 2001) The solid line represents the compressional heating modeling, for 1.2 solar mass white dwarf with an initial temperature of 14,500K, accreting at a rate of $9 \times 10^{-9} M_{\sun}/$ year for 52 days."
" The stars. squares and plus signs denote the temperatures listed in Table 2 7). Tj aud T, respectively."," The stars, squares and plus signs denote the temperatures listed in Table 2 $T_a$ , $T_b$ and $T_c$ respectively."
 The (triangles are (he FUSE data points and the circles represent the temperature estimates using the flix values (see text)., The triangles are the FUSE data points and the circles represent the temperature estimates using the flux values (see text).
 Figure 3: Same as Figure 2. but here (the solid line represent a model with a mass accretion rate of 5x10.7M. /vear and an initial temperature of 15.000IX. (model 4 in Table 3).," Figure 3: Same as Figure 2, but here the solid line represent a model with a mass accretion rate of $5 \times 10^{-9} M_{\sun}/$ year and an initial temperature of 15,000K (model 4 in Table 3)."
 Figure 4: Same as Figures 2 and 3., Figure 4: Same as Figures 2 and 3.
 The solid line represents model 2 in Table3., The solid line represents model 2 in Table3.
distance J.-5.,distance $D_{z=0}$.
 Both distances have been normalised by the clusters present dav virial raclius A's., Both distances have been normalised by the cluster's present day virial radius $R_{\rm vir}$.
 Phere are four distinct. populations of satellites visible in this (the infalling population) ‘These satellites are falling in for the first (infalling sub-population) This population is made up of subhalos orbiting satellites. Le. (backsplash satellites) These satellites once passed through the virial radius of the respective host but have “rebound” to the outskirts of the galaxy (the bound population) This is the “normal” satellite population orbiting within the virial racius and bound to the Our data sets indicates that the maximum backsplash distance encountered is 2.5/2; which is larger than the," There are four distinct populations of satellites visible in this (the infalling population) These satellites are falling in for the first (infalling sub-population) This population is made up of subhalos orbiting satellites, i.e. (backsplash satellites) These satellites once passed through the virial radius of the respective host but have “rebound” to the outskirts of the galaxy (the bound population) This is the “normal” satellite population orbiting within the virial radius and bound to the Our data sets indicates that the maximum backsplash distance encountered is $\sim 2.5 R_{vir}$ which is larger than the"
astrometry to reflect the improved calibrator position.,astrometry to reflect the improved calibrator position.
 The archival L-band observations of SSA taken in 2000 used a pointing centre displaced by zz aaremin from the centre of the source., The archival L-band observations of 84 taken in 2000 used a pointing centre displaced by $\approx$ arcmin from the centre of the source.
 The C-band. data were usually taken in two adjacent -MlIz frequency channels. which were imaged together.," The C-band data were usually taken in two adjacent 50-MHz frequency channels, which were imaged together."
 The L-band channels were also imaged together in. /. order to derive spectral-index images.," The L-band channels were also imaged together in $I$, in order to derive spectral-index images."
 For all sources except 1326|39. they were also imaged indepencdentIy. primarily for analysis of linear polarization.," For all sources except 0326+39, they were also imaged independently, primarily for analysis of linear polarization."
 In order to avoid the well-known problems introduced »w the conventional algorithm for well-resolved. diffuse brightness distributions. Cotalintensity images at he higher resolutions were produced using the multi-scale algorithm as implemented in the package Or. lin one case. a maximunmr- algorithm.," In order to avoid the well-known problems introduced by the conventional algorithm for well-resolved, diffuse brightness distributions, total-intensity images at the higher resolutions were produced using the multi-scale algorithm as implemented in the package or, in one case, a maximum-entropy algorithm."
1991)mainDBodvyCitationEind1529]CI. Ehe standard. resolution was found to be adequate for the lowest-resolution £ images., The standard single-resolution was found to be adequate for the lowest-resolution $I$ images.
 Stokes Q and ( images were CLEANed using one or more resolutions (we found few cillerences between single and. multiple-resolution for. these images. which have little power on large spatial scales).," Stokes $Q$ and $U$ images were ed using one or more resolutions (we found few differences between single and multiple-resolution for these images, which have little power on large spatial scales)."
 All of the images were corrected for the elfects of the antenna primary beam., All of the images were corrected for the effects of the antenna primary beam.
 In general. the deep. 4.9-Cillz images have olf-source noise levels very close to those expected from thermal noise in the receivers alone.," In general, the deep 4.9-GHz images have off-source noise levels very close to those expected from thermal noise in the receivers alone."
 Phere are a few faint artefacts on the £ images., There are a few faint artefacts on the $I$ images.
 These are visible as concentric rings around the bright cores and. for 1193 at 1.35 ancl 1.6-aresec resolution. a quadrupolar pattern at the 2a level.," These are visible as concentric rings around the bright cores and, for 193 at 1.35 and 1.6-arcsec resolution, a quadrupolar pattern at the $2\sigma$ level."
 These are clue to errors in cross-calibration of the dillerent. array configurations. which were particularly troublesome due to the low declination of this source.," These are due to errors in cross-calibration of the different array configurations, which were particularly troublesome due to the low declination of this source."
 The » of the L-band images and for the €C-bandimage ο...ofm0326ddM|3N are shorter ancl confusion [rom sources outside view ds worse. so noise levels are correspondingly higher.," The integrations for all of the L-band images and for the C-band image of 0326+39 are shorter and confusion from sources outside the field of view is worse, so noise levels are correspondingly higher."
 Finally. we produced. improved. £ images from calibrated L- and X-band visibility datafor 2296(Laine using the multi-resolution algorithm.," Finally, we produced improved $I$ images from self-calibrated L- and X-band visibility datafor 296 using the multi-resolution algorithm."
 As a check on the amplitude calibration and imaging of the J images used in spectral-zindex analysis. we integrated the [lux densities using the verbTVSTAT.," As a check on the amplitude calibration and imaging of the $I$ images used in spectral-index analysis, we integrated the flux densities using the verb."
 We estimate that our errors are dominated by a residual scale. error of z24., We estimate that our errors are dominated by a residual scale error of $\approx$.
 All of the results are in excellent. agreement with single-dish measurements (Vable 3))., All of the results are in excellent agreement with single-dish measurements (Table \ref{tab:images}) ).
 ‘The configurations. resolutions. deconvolution algorithms and noise levels for the final images are listed in “Table 3.," The configurations, resolutions, deconvolution algorithms and noise levels for the final images are listed in Table \ref{tab:images}."
0 The noise levels were measured: before correction for the primary beam. and are appropriate for the centre of the field.," The noise levels were measured before correction for the primary beam, and are appropriate for the centre of the field."
 We also present MEBRLIN imaging in total intensity only for two of the sources., We also present MERLIN imaging in total intensity only for two of the sources.
 0206135 was observed for a total time of about 14 hours., 0206+35 was observed for a total time of about 14 hours.
 The array included the following telescopes: Dellord. Cambridge. Knockin. Wardle. Darnhall. AIk2. Lovell and TVablev.," The array included the following telescopes: Defford, Cambridge, Knockin, Wardle, Darnhall, Mk2, Lovell and Tabley."
 Phe observations were carried out at 1420 MlIz with a bandwidth of 15 Mllz. in cach of Left ight) circular. polarizations.," The observations were carried out at 1420 MHz with a bandwidth of 15 MHz, in each of left and right circular polarizations."
 Ehe nearby compact source MMQ2011365 was used as the phase calibrator and the llux-density scale was determined. using 2286elects., The nearby compact source 0201+365 was used as the phase calibrator and the flux-density scale was determined using 286.
 The data were edited. corrected. for elevation-depencdent ancl non-closing errors ancl [lux-calibrated: using the standard AIERLIN analysis programs.," The data were edited, corrected for elevation-dependent effects and non-closing errors and flux-calibrated using the standard MERLIN analysis programs."
 Imaging anc self-calibration were again performed using the package., Imaging and self-calibration were again performed using the package.
 Phe oll-source image rms after self-calibration was close to that expected [rom receiver noise alone., The off-source image rms after self-calibration was close to that expected from receiver noise alone.
 The MIZRLIN. observations of 0755|37 were described by(2000)., The MERLIN observations of 0755+37 were described by.
. The parameters of both MIZRLIN imagesare given in ‘Table 3.., The parameters of both MERLIN imagesare given in Table \ref{tab:images}. .
 Our conventions for Figs 1 12. and the descriptions in the text are as follows., Our conventions for Figs \ref{fig:ngc193all} – \ref{fig:0326_i_si18} and the descriptions in the text are as follows.
"of the spectral features are also strongly dependent on the choice of orbits, decorrelation parameters, and the nature of the model assumed for the baseline function.","of the spectral features are also strongly dependent on the choice of orbits, decorrelation parameters, and the nature of the model assumed for the baseline function."
" Given there is no physical reason to assume the baseline flux should follow a linear function of a particular set of optical state parameters, there is no reason to prefer one model over another."," Given there is no physical reason to assume the baseline flux should follow a linear function of a particular set of optical state parameters, there is no reason to prefer one model over another."
" We take this as evidence that the linear decorrelation model used is not a robust method to remove systematic effects from the light curves, and that the baseline function in the case of NICMOS grism data cannot reliably be given by a linear function of the optical state vectors from S08."," We take this as evidence that the linear decorrelation model used is not a robust method to remove systematic effects from the light curves, and that the baseline function in the case of NICMOS grism data cannot reliably be given by a linear function of the optical state vectors from S08."
 Fig., Fig.
" 28 shows a plot of the overall transmission spectrum of HD 189733, including the ACS optical data from Pontetal.(2008),, the NICMOS photometric measurements from Singetal.(2009),, and the reduction using only orbits 2 and 4 from this paper."," \ref{fig:HD189733_overall_trans_spec} shows a plot of the overall transmission spectrum of HD 189733, including the ACS optical data from \citet{Pont_2008}, the NICMOS photometric measurements from \citet{Sing_2009}, and the reduction using only orbits 2 and 4 from this paper."
" This shows that we can interpret the NICMOS transmission spectrum as consistent with the optical haze, if we adopt this reduction."," This shows that we can interpret the NICMOS transmission spectrum as consistent with the optical haze, if we adopt this reduction."
" We emphasise that our analysis does not rule out the presence of molecules in the NIR transmission spectrum of HD 189733, but merely shows that the detection of molecular species is highly dependent on the decorrelation method used."," We emphasise that our analysis does not rule out the presence of molecules in the NIR transmission spectrum of HD 189733, but merely shows that the detection of molecular species is highly dependent on the decorrelation method used."
" For GJ-436 we find an amplitude of about 0.07 absorption in the transmission spectrum, which is similar to that seen in P09; however, the overall levels are inconsistent."," For GJ-436 we find an amplitude of about 0.07 absorption in the transmission spectrum, which is similar to that seen in P09; however, the overall levels are inconsistent."
 We also find the transmission spectrum is inconsistent with the transit depth of the white light curve., We also find the transmission spectrum is inconsistent with the transit depth of the white light curve.
 The latter is much more robust given that the integrated white light curve suffers from fewer systemics., The latter is much more robust given that the integrated white light curve suffers from fewer systemics.
 The transmission spectrum is consistent with the white light curve when only decorrelating using the orbital phase parameters., The transmission spectrum is consistent with the white light curve when only decorrelating using the orbital phase parameters.
" This suggests that decorrelating with more parameters, particularly those with offsets in the parameter values, induces spurious offsets in the transmission spectrum."," This suggests that decorrelating with more parameters, particularly those with offsets in the parameter values, induces spurious offsets in the transmission spectrum."
" Generally, we conclude that it is unstable to decorrelate HST data using decorrelation parameters that contain offsets between each orbit, as these offsets in easily be transferred to spurious offsets in flux levels of the in-transit orbits."," Generally, we conclude that it is unstable to decorrelate HST data using decorrelation parameters that contain offsets between each orbit, as these offsets in easily be transferred to spurious offsets in flux levels of the in-transit orbits."
" The fact that we can produce a variable but unphysical transmission spectrum with the linear decorrelation model, suggests that we cannot extract useful spectral information below about 0.196 using NICMOS transmission spectroscopy, at least using current methods."," The fact that we can produce a variable but unphysical transmission spectrum with the linear decorrelation model, suggests that we cannot extract useful spectral information below about $0.1\%$ using NICMOS transmission spectroscopy, at least using current methods."
" For XO-1 we are unable to reproduce the results from T10, because the decorrelation parameters we measure require an extrapolation for the in-transit orbits to determine the baseline function, and introduce large offsets in the flux levels for different orbits."," For XO-1 we are unable to reproduce the results from T10, because the decorrelation parameters we measure require an extrapolation for the in-transit orbits to determine the baseline function, and introduce large offsets in the flux levels for different orbits."
 The best transmission spectrum that we can produce show uncertainties much larger than those reported in T10., The best transmission spectrum that we can produce show uncertainties much larger than those reported in T10.
" We do not have enough information to identify the source of the discrepancy, but we expect that their uncertainties are underestimated, in a similar way to HD 189733."," We do not have enough information to identify the source of the discrepancy, but we expect that their uncertainties are underestimated, in a similar way to HD 189733."
 This is all the more puzzling given that Burkeetal.(2010) also produce decorrelation parameters that would require extrapolation for the in-transit orbits., This is all the more puzzling given that \citet{Burke_2010} also produce decorrelation parameters that would require extrapolation for the in-transit orbits.
 We note the importance of reporting in detail the methods used to correct systematics when they dominate the error budget., We note the importance of reporting in detail the methods used to correct systematics when they dominate the error budget.
 Our re-analysis of all three datasets shows that the systematics in NICMOS transmission spectra cannot reliably be corrected for - at the level needed to detect, Our re-analysis of all three datasets shows that the systematics in NICMOS transmission spectra cannot reliably be corrected for - at the level needed to detect
"where the subscripts ""€q' aud “per!” reler. respectively. to variations in the backgrouud equilibrium fluid aud in the perturbed fluid element.","where the subscripts $eq$ ” and $pert$ ” refer, respectively, to variations in the background equilibrium fluid and in the perturbed fluid element."
 ID ΑΣ0. the fluid can support oscillations with buoyant restoring forces (gravity waves)aud characteristic frequency NV.," If $N^2>0,$ the fluid can support oscillations with buoyant restoring forces (gravity waves)and characteristic frequency $N$."
 Uf N72<0. the fluid is unstable to cojvective overtudl.," If $N^2<0$, the fluid is unstable to convective overturn."
 Take the entropy per baryo1 of the equilibrium fluid to je SCP). and its chemical composition to be parameterized by a set of variables 3;CP) (abundanee. per baryou. of particle species nu).," Take the entropy per baryon of the equilibrium fluid to be $S(P)$, and its chemical composition to be parameterized by a set of variables $Y_i(P)$ (abundance, per baryon, of particle species $i=1,2,..., n$ )."
 The pressure is used to mark the depth in the luid at which the variables are to be evaluated., The pressure is used to mark the depth in the fluid at which the variables are to be evaluated.
 Assije that the cisylaced fluid. element does neX change its internal variables 5$ aud [iu, Assume that the displaced fluid element does not change its internal variables $S$ and $\{Y_i\}_{i=1}^n$.
 The σοιdition for stabe stratification. IN?20. ca1 then be rewritten in the alternative forms or (Ledoux(1917):Epstein (1979))) where. in the usual thermocdyuamic notation. the variables iu tle subscripts are to be held constant. when taking the partial derivatives.," The condition for stable stratification, $N^2>0$, can then be rewritten in the alternative forms or \cite{Ledoux,Epstein}) ) where, in the usual thermodynamic notation, the variables in the subscripts are to be held constant when taking the partial derivatives."
 If the stun involving the composition gradieut cau be neglected (as usually tle case in non-degenerate stars such as the Sun aud other iunaiu-sequeuce or eiaut stars). the coucition reduces to the familiar Seliwarzschild coudition (Schwarzschild (1906))) ol decreasing eutropy per baryon with increasiug pressure.," If the sum involving the composition gradient can be neglected (as usually the case in non-degenerate stars such as the Sun and other main-sequence or giant stars), the condition reduces to the familiar Schwarzschild condition \cite{Schwarzschild}) ) of decreasing entropy per baryon with increasing pressure."
 Iu what follows. it is assumed that the {lid iszsentropic (Le. ο=Sy) constant throughout) and that in the unperturbed configuration the matter iscatalyzed. i.e.. the parameters [Y;(P.50)] are those correspoucing to full chemical (aud thermodyuamic) equilibrium at the local pressure.," In what follows, it is assumed that the fluid is (i.e., $S=S_0=$ constant throughout) and that in the unperturbed configuration the matter is, i.e., the parameters $\{Y_i(P,S_0)\}$ are those corresponding to full chemical (and thermodynamic) equilibrium at the local pressure."
 This equilibrium state is determined by minimizing the enthalpy per baryon. “(2.59.[Y;1) over all values of {¥5} allowed by conservation laws. Al given entropy per baryon 5g. the resulting functiou [40/7ου). defines a curve on the pressure-enthalpy. plane (see Fig.," This equilibrium state is determined by minimizing the enthalpy per baryon, $h(P,S_0,\{Y_i\})$ over all values of $\{Y_i\}$ allowed by conservation laws, At given entropy per baryon $S_0$, the resulting function $h_{eq}(P,S_0)$ defines a curve on the pressure-enthalpy plane (see Fig."
 1)., 1).
 Point { on the curve represents the initial (equilibrium) state of the fluid element to be perturbed., Point $I$ on the curve represents the initial (equilibrium) state of the fluid element to be perturbed.
 The perturbation. at constant S=η aud {{35}. takes the (hud to a dillerent pressure audΕΠ. therelore to a point the equilibrium curve.," The perturbation, at constant $S=S_0$ and $\{Y_i\}$, takes the fluid to a different pressure and, therefore to a point the equilibrium curve."
 The trajectory of the [Iuid element is tangent to the equilibrium curve at the point represeitine, The trajectory of the fluid element is tangent to the equilibrium curve at the point representing
 Cliaudraseshar(1913) &MeMilla12002) ilu Yexilvurt.&Erca12003).. ‘has (Dotti.Colpi.&Haard2(006).. 200L).. (Ogihara.," \citet{c43} \citep{pm02} \citep{dye03}. \citep{d06}, \citep{e04}, \citep{odi10}."
Duical&Kka22010).. V.> eV Rephaeli&Salpeer1980:Ost‘iker1999). (Dokuchaev19," $V^{-2}$ $V$ \citep{d64,rs71,rs80,o99}. \citep{d64},"
61).. er(1980) Lo Osriker(1999) Al. V , \citet{rs80} \citet{o99} $\Delta t$ $V$ 
stronger line 3.,stronger line 3.
 In the case of the 33.13 system and lines 13. 14 and 16 the situation is similar since the reduced cchanged from ~1.16 to ~L.17.," In the case of the 3.13 system and lines 13, 14 and 16 the situation is similar since the reduced changed from $\sim 1.16$ to $\sim 1.17$."
 ‘The simulations thus allowed us to distinguish for which lines an ADR may have a physical cause., The simulations thus allowed us to distinguish for which lines an ADR may have a physical cause.
 The choice of an upper limit for the significance of the WS statistic was somewhat arbitrary., The choice of an upper limit for the significance of the KS statistic was somewhat arbitrary.
 We chose iin an ellort not to discard too many lines. since few lines were available anyway.," We chose in an effort not to discard too many lines, since few lines were available anyway."
 However. the ccumulative distribution plots for lines 25 ancl 26 strongly indicate that a lower value might be appropriate since vvalues for fits of simulated lines with excess flux cid. not show a clear trend to be higher.," However, the cumulative distribution plots for lines 25 and 26 strongly indicate that a lower value might be appropriate since values for fits of simulated lines with excess flux did not show a clear trend to be higher."
 Since we were mainly interested in illustrating a technique. we formally accepted he level ancl used. these two lines in further analysis.," Since we were mainly interested in illustrating a technique, we formally accepted the level and used these two lines in further analysis."
 Lf this caveat is taken into account. suggests that a hreshold. column. densitv for an observable ADR. in this model is given by 1v)) 13.1 with bz10ον," If this caveat is taken into account, suggests that a threshold column density for an observable ADR in this model is given by ) $\approxgt 13.1$ with $b\approx 10$."
 This explains the failure to reproduce lines in group (iv) above since all of these lines (except. perhaps. for line 2. which. however. has large σι) are below this threshold.," This explains the failure to reproduce lines in group (iv) above since all of these lines (except, perhaps, for line 2, which, however, has large $\sigma_{{\rm log}N}$ ) are below this threshold."
are appropriate.,are appropriate.
 This potential decreases drastically with the separation of the two particles., This potential decreases drastically with the separation of the two particles.
 Therefore it can be truncated quite reasonably at a distance of = (2.5 — Do )., Therefore it can be truncated quite reasonably at a distance of = (2.5 - 3).
".TheCoulombpotential. ontheotherhand, decaysstowlvywithparticleseparation."," The Coulomb potential, on the other hand, decays slowly with particle separation."
Pearticlesatnichgreaterdistance rangei, Particles at much greater distances must be included in order to accurately compute the force on each particle.
nteractions( see," Ideally, the contribution of each of the infinite image particles should be included in the potential sums and the potential should never be truncated."
",forexample", Unfortunately this would take infinite computing time and is therefore impractical.
",Frenkel&Smit2002;Allen&Tildesley1987).."," Fortunately, more efficient techniques have been developed to compute long-range interactions \citep[see, for example,][]{Frenkel_text,
Allen_text}."
" In their simulations, Shaviv and Shaviv took advantage of the screening of the plasma to shorten the effective range of the potential."," In their simulations, Shaviv and Shaviv took advantage of the screening of the plasma to shorten the effective range of the potential."
 They assume that interactions between particles that are farther apart than a few Debye lengths will be screened by the surrounding plasma., They assume that interactions between particles that are farther apart than a few Debye lengths will be screened by the surrounding plasma.
 We have tested the truncation of the potential and determined that this assumption is appropriate for our simulation (Mussacketal.2007;Mussack2007)..," We have tested the truncation of the potential and determined that this assumption is appropriate for our simulation \citep{Mussack_2007, Mussack_thesis}."
" This enables us to truncate the interactions beyond a few Debye lengths, reducing the infinte-range potential to a manageable long-range potential."," This enables us to truncate the interactions beyond a few Debye lengths, reducing the infinte-range potential to a manageable long-range potential."
 When particles in a two-component plasma are closer than the thermal deBroglie wavelength the effects of quantum diffraction and symmetry become significant., When particles in a two-component plasma are closer than the thermal deBroglie wavelength the effects of quantum diffraction and symmetry become significant.
 The thermal deBroglic wavelengths for our systemare shown in Table .., The thermal deBroglie wavelengths for our systemare shown in Table \ref{table:deBroglie_wavelengths}.
" The average interparticle distance in our model is <r>=.203a,.", The average interparticle distance in our model is $<r>= .203 a_B$.
" Since A,K«r».à classical treatment is generally sufficient for the protons."," Since $\Lambda_{p} \ll \; <r>$, a classical treatment is generally sufficient for the protons."
" However, it will be common to have two electrons that are separated by a distance less than.. requiring quantum mechanical treatment."," However, it will be common to have two electrons that are separated by a distance less than, requiring quantum mechanical treatment."
" We therefore include the quantum approximations used by Shaviv&(1996)., i.c. the effective pair potentials derived for a hydrogen plasma by Barker(1971);Deutsch(1977);etal.(1978, 1979).."," We therefore include the quantum approximations used by \citet{Shaviv_1996}, i.e. the effective pair potentials derived for a hydrogen plasma by \citet{Barker_1971,Deutsch_1977,Deutsch_1978,
 Deutsch_1979}. ."
 Quantum diffraction effects are described by, Quantum diffraction effects are described by
experiencing collisional slowdown duc to interaction with he pre-explosiou cireustellar wind of the progenitor.,experiencing collisional slowdown due to interaction with the pre-explosion circumstellar wind of the progenitor.
 We calculate. the time evolution of the radius. bul- Loreutz factor and thermal euergv of the decelerating dlastwave.," We calculate the time evolution of the radius, bulk Lorentz factor and thermal energy of the decelerating blastwave."
 Our solution reduces to the ? solution. iu he ultra-relativistic. neeheible ejecta mass limit.," Our solution reduces to the \citet{1976PhFl...19.1130B}
 solution, in the ultra-relativistic, negligible ejecta mass limit."
 We alx quantify the density of accelerated. electrons. amplified naenetic fields and lence the radio svuchirotrou euissio- your the blastwave of a CEDEN.," We also quantify the density of accelerated electrons, amplified magnetic fields and hence the radio synchrotron emission from the blastwave of a CEDEX."
 Iu Section 2. wο outline the conditions that require ultra-high bulk Lorentz factors aud very low ejecta uasses du classical Lone GRBs., In Section \ref{golpo} we outline the conditions that require ultra-high bulk Lorentz factors and very low ejecta masses in classical Long GRBs.
 We argue why these constraints are reaxed in the case of mildly relativistic outflows detected in SN 2009bb like events. that have jio. detected. CRBs.," We argue why these constraints are relaxed in the case of mildly relativistic outflows detected in SN 2009bb like events, that have no detected GRBs."
 It provides the motivation for he analytic soluion derived here., It provides the motivation for the analytic solution derived here.
 In Section 3. we develop the analyic solution of a relativistic blast wave aunched by a CEDEN. for the collisional slowdown nodel described o» 72," In Section \ref{blast} we develop the analytic solution of a relativistic blast wave launched by a CEDEX, for the collisional slowdown model described by \citet{1999PhR...314..575P}."
 We use this solution to show hat the SN 2009jb blast wave is substantially Darvon oacded aud. realis in the nearly free expausion pliase hroughout the ~1 year of observations (Figure 1))., We use this solution to show that the SN 2009bb blast wave is substantially baryon loaded and remains in the nearly free expansion phase throughout the $\sim1$ year of observations (Figure \ref{R_t}) ).
 Iu section { we discuss the relativistic blast wave cucrectics., In section \ref{energy} we discuss the relativistic blast wave energetics.
 We quantify the amount of shock accelerated electrons and magnetic field amplification iu à CEDEN blast wave., We quantify the amount of shock accelerated electrons and magnetic field amplification in a CEDEX blast wave.
 Iu Section 5 woe use this information to model the radio spectrum and light curve of a CEDEX iu the nearly free expansion phase., In Section \ref{spectrum} we use this information to model the radio spectrum and light curve of a CEDEX in the nearly free expansion phase.
 In section 6 we provide expressions to deduce the blast wave parameters fou the observed radio spectrum., In section \ref{inversion} we provide expressions to deduce the blast wave parameters from the observed radio spectrum.
 We also compare our blastwave solution to other kuown solutions relevant for relativistic dlastwaves in the literature (Section 7))., We also compare our blastwave solution to other known solutions relevant for relativistic blastwaves in the literature (Section \ref{comp}) ).
 In section 5. we discuss the implications of barvon loading in determining he evolution aud observational signatures of a CEDEN.," In section \ref{polao}
 we discuss the implications of baryon loading in determining the evolution and observational signatures of a CEDEX."
 Iu the Appendix we provide the analytic expressions or the temporal evolution of the blast wave parameters (Section Aj)., In the Appendix we provide the analytic expressions for the temporal evolution of the blast wave parameters (Section \ref{exact}) ).
 We demonstrate that our solution reduces ο the ultra-relativistic ?. solution for a coustaut velocity wind. in the low mass. ultra-velativistic limit (Section Dj).," We demonstrate that our solution reduces to the ultra-relativistic \cite{1976PhFl...19.1130B} solution for a constant velocity wind, in the low mass, ultra-relativistic limit (Section \ref{ultra}) )."
" Iu Section € we provide ""stimfrv for he radio spectrum of à CEDEN with known initial blast wave parameters.", In Section \ref{radiotv} we provide “stir-fry for the radio spectrum of a CEDEX with known initial blast wave parameters.
 Ta Section D we invert the problem and provide handy expressions for estimating the initial xuanneters for a CEDEX from radio observations., In Section \ref{inversiontv} we invert the problem and provide handy expressions for estimating the initial parameters for a CEDEX from radio observations.
 Iu Section Ewe provide an expression to compute augular size of a CEDEN from iulti-band radio spectrum., In Section \ref{vlbi} we provide an expression to compute angular size of a CEDEX from multi-band radio spectrum.
 Using he radio spectra of SN 2009bb. we show that our xedieted angular size is consistent with the reported upper Πές (7). from VEDI. but should be resolvable oesentlv.," Using the radio spectrum of SN 2009bb, we show that our predicted angular size is consistent with the reported upper limits \citep{2010arXiv1006.2111B} from VLBI, but should be resolvable presently."
 Relativistic superuovae have. until receuth. been discovered only through their temporal auc spatial association with long duration GRBs.," Relativistic supernovae have, until recently, been discovered only through their temporal and spatial association with long duration GRBs."
 Au acceptable model for GRBs must Sud a wav to circuuvent the aud problems., An acceptable model for GRBs must find a way to circumvent the and problems.
 Theobserved rapid temporal variability in CRBs imply a very compact source., Theobserved rapid temporal variability in GRBs imply a very compact source.
 The compactness problemi pointed out bv ? and 7.. indicates that x-ray photons of sufficiently. lieh energies will produce clectrou-positrou pairs and will not be able to come out due to the resulting lich opacity.," The compactness problem pointed out by \citet{1975NYASA.262..164R} and \citet{1978Natur.271..525S}, indicates that $\gamma$ -ray photons of sufficiently high energies will produce electron-positron pairs and will not be able to come out due to the resulting high opacity."
 However. the observation of high energv photons from CRBs was recouciled with such theoretical constraints bv ? and ?.. allowing the high energy photons to come out from a relativistic explosion.," However, the observation of high energy photons from GRBs was reconciled with such theoretical constraints by \citet{1986ApJ...308L..47G} and \citet{1986ApJ...308L..43P}, , allowing the high energy photons to come out from a relativistic explosion."
 This requires initial bull Loreutz factors of the radiatiug shell. συZ10? (T).," This requires initial bulk Lorentz factors of the radiating shell, $\gamma_0\gtrsim10^2$ \citep{1999PhR...314..575P}."
 2 poiuted out that iu the presence of even siuall amounts of barvous orcontamdnation.. essenutiallv the cutive energy of the explosion ects locked up in the kinetic enerey of the barvous. leaving little enerev for the electromagnetic display.," \citet{1990ApJ...365L..55S}
 pointed out that in the presence of even small amounts of baryons or, essentially the entire energy of the explosion gets locked up in the kinetic energy of the baryons, leaving little energy for the electromagnetic display."
 This problem was solved bx ?. and independently by several authors (777?.. by considering the recouversion of the kinetic energy of the fireball iuto radiation. due to interaction with au external mediuni or via internal shocks.," This problem was solved by \citet{1992MNRAS.258P..41R}
 and independently by several authors \citep{1992ApJ...395L..83N,1994ApJ...430L..93R,1994ApJ...427..708P}, by considering the reconversion of the kinetic energy of the fireball into radiation, due to interaction with an external medium or via internal shocks."
 However the allowed initial iiass is still very πια] (ALz10.AZ.) as too ch barvouic mass will slow down the explosion aud it will no louger be relativistic (?)..," However the allowed initial mass is still very small $M\approx10^{-6}M_\odot$ ), as too much baryonic mass will slow down the explosion and it will no longer be relativistic \citep{1999PhR...314..575P}."
 Hence. observation of a short bright pulse of οταν photous iu GRBs require a very small amount of mass to be ejected with a very veh bulk Loreutz factor.," Hence, observation of a short bright pulse of $\gamma$ -ray photons in GRBs require a very small amount of mass to be ejected with a very high bulk Lorentz factor."
 The burst in the GRB itself results from the conversion of kinetic energy of ultra-velativistic particles or possibly he electromaguetic energv of a Povutiug fux to radiation in an optically thin region., The burst in the GRB itself results from the conversion of kinetic energy of ultra-relativistic particles or possibly the electromagnetic energy of a Poynting flux to radiation in an optically thin region.
 An iuner eugine is sclieved to accelerate the outflow to relativistic speeds. although the eugine iav remain hidden from direct observations.," An inner engine is believed to accelerate the outflow to relativistic speeds, although the engine may remain hidden from direct observations."
" The ""afterelow ou the other hiud results roni the slowing down of a relativistic shell on the external medium surrounding the progenitor star."," The “afterglow"" on the other hand results from the slowing down of a relativistic shell on the external medium surrounding the progenitor star."
 There can also be an additional coutribution to the afterglow roni the immer eugine that powers the GRB. since the cheine may contiuue to emit enerev for longer duration with a lower inteusitv and may produce the earlier part of the afterelow. sav the first dav or two in GRB 970228 and GRD 970508 (?7)..," There can also be an additional contribution to the afterglow from the inner engine that powers the GRB, since the engine may continue to emit energy for longer duration with a lower intensity and may produce the earlier part of the afterglow, say the first day or two in GRB 970228 and GRB 970508 \citep{1999PhR...314..575P,1998PhRvL..80.1580K}."
 Iu superuovae associated with GRBs. after a brief high enerev electromagnetic display. the relativistic ejecta continues to power a lone lived radio afterglow (?77)..," In supernovae associated with GRBs, after a brief high energy electromagnetic display, the relativistic ejecta continues to power a long lived radio afterglow \citep{1998Natur.395..663K,2004Natur.430..648S}."
 Since the cmergence of οταν photons. carly iu its evolution. constrains the initial relativistic ejecta lass to be very small aud the initial bulk Loreutz factor to be very large. the relativistic ejecta sweeps up nore circuuustellar material than its own rest mass bv the time the radio afterglow is detected.," Since the emergence of $\gamma$ -ray photons, early in its evolution, constrains the initial relativistic ejecta mass to be very small and the initial bulk Lorentz factor to be very large, the relativistic ejecta sweeps up more circumstellar material than its own rest mass by the time the radio afterglow is detected."
 The evolution of the radiative blastwave has beeu described by ?.., The evolution of the radiative blastwave has been described by \citet{1998ApJ...509..717C}.
 During the radio afterglow phase if radiative losses do not take away a sieuificaut fraction of the thermal cucrey. the blastwave mav be treated as adiabatic.," During the radio afterglow phase if radiative losses do not take away a significant fraction of the thermal energy, the blastwave may be treated as adiabatic."
 Under these couditious. the evolution of the blastwave is well described by the 7 solution if the blastwave remains ultra-relativistic or —bv the Sedov-Tavlor solution if the blastwawe has slowed down iuto the Newtonian regine.," Under these conditions, the evolution of the blastwave is well described by the \citet{1976PhFl...19.1130B} solution if the blastwave remains ultra-relativistic or by the Sedov-Taylor solution if the blastwave has slowed down into the Newtonian regime."
 The imteraction of GRBs with their circumstellar wind has been discussed by ?.., The interaction of GRBs with their circumstellar wind has been discussed by \citet{2000ApJ...536..195C}.
 The spectra aud light curves of GRB afterelows have been computed in the ultra-relativistic regie by and in the Newtonian reginae by ?.. ?, The spectra and light curves of GRB afterglows have been computed in the ultra-relativistic regime by \citet{1998ApJ...497L..17S} and in the Newtonian regime by \citet{2000ApJ...537..191F}. .
 have receutlydiscovered bright radio ciission. associated with the type Ibe SN 2009bb. requiring a," \citet{2010Natur.463..513S} have recentlydiscovered bright radio emission, associated with the type Ibc SN 2009bb, requiring a"
Measurements of the masses and radii of M-dwarfs are significantly discrepant from the predictions of evolutionary models (Ribas e al.,Measurements of the masses and radii of M-dwarfs are significantly discrepant from the predictions of evolutionary models (Ribas et al.
 2008)., 2008).
 Initial evidence for this comes from eclipsing binaries. where radii are 10—15 per cent higher at a given mass than predicted tLóppez-Morales 2007: Morales et al.," Initial evidence for this comes from eclipsing binaries, where radii are 10–15 per cent higher at a given mass than predicted (Lóppez-Morales 2007; Morales et al."
 2009)., 2009).
 It has been suggestec that the presence of dynamo-generated magnetic fields in wha are relatively fast rotating stars. can suppress convection. produce cool star spots and hence reduce the stellar effective temperature (D'Antona. Ventura Mazzitelli 2000: Mullan MacDonale 2001: Chabrier. Gallardo Baraffe 2007).," It has been suggested that the presence of dynamo-generated magnetic fields in what are relatively fast rotating stars, can suppress convection, produce cool star spots and hence reduce the stellar effective temperature (D'Antona, Ventura Mazzitelli 2000; Mullan MacDonald 2001; Chabrier, Gallardo Baraffe 2007)."
 Jackson. Jeffries Maxted (2009) measured the radii of single. rapidly rotating M-dwarfs in the young open cluster NGC 2516.," Jackson, Jeffries Maxted (2009) measured the radii of single, rapidly rotating M-dwarfs in the young open cluster NGC 2516."
 They found tha their radit. at a given luminosity. are also larger than predicted by evolutionary models.," They found that their radii, at a given luminosity, are also larger than predicted by evolutionary models."
 The discrepancy increases from a few per cen for early (MO) M-dwarfs. to some 50 per cent for mid-M dwarfs (M4).," The discrepancy increases from a few per cent for early (M0) M-dwarfs, to some 50 per cent for mid-M dwarfs $\simeq $ M4)."
 The same evolutionary models correctly predict the radii of magnetically inactive M-dwarfs. thus implicating rotationally induced magnetic activity as the source of the discrepancy.," The same evolutionary models correctly predict the radii of magnetically inactive M-dwarfs, thus implicating rotationally induced magnetic activity as the source of the discrepancy."
 Whilst this appears credible in qualitative terms. further data are required to correlate measurements of mass and radii with measurements of rotation. magnetic field strength and indicators of chromospheric and coronal activity.," Whilst this appears credible in qualitative terms, further data are required to correlate measurements of mass and radii with measurements of rotation, magnetic field strength and indicators of chromospheric and coronal activity."
 In low-mass F-. G- and K-type stars. the ratio of coronal X-ray to bolometric flux. Li/Li. or a variety of similarly defined chromospheric flux indicators. are used as proxies for magnetic activity.," In low-mass F-, G- and K-type stars, the ratio of coronal X-ray to bolometric flux, $L_{\rm x}/L_{\rm bol}$, or a variety of similarly defined chromospheric flux indicators, are used as proxies for magnetic activity."
 Magnetic flux and X-ray/chromospheric¢ activity both appear to depend primarily on rotation rate. but also on the convective turnover time. as expected from simply dynamo models (e.g. Mangeney Praderie 1984).," Magnetic flux and X-ray/chromospheric activity both appear to depend primarily on rotation rate, but also on the convective turnover time, as expected from simply dynamo models (e.g. Mangeney Praderie 1984)."
 Magnetic flux and magnetically induced emissions increase with rotation speed and with decreasing Rossby number — defined as the ratio of rotation period to convective turnover time (Vy;= τι).," Magnetic flux and magnetically induced emissions increase with rotation speed and with decreasing Rossby number – defined as the ratio of rotation period to convective turnover time $N_R =
P/\tau_c$ )."
 However. for Neo0.1. magnetic activity reaches a saturation plateau where," However, for $N_R < 0.1$, magnetic activity reaches a saturation plateau where"
of the ratio Prp/P4 is found in the range of 0<107. mt the probability is quite small.,"of the ratio $P_{\rm EB}/P_{\rm rnd}$ is found in the range of $\theta<10\farcm$, but the probability is quite small."
" Since they are not sienificaut. we cannot ideutify fake E-mode peaks usine he distance frou, Danode peaks."," Since they are not significant, we cannot identify fake E-mode peaks using the distance from B-mode peaks."
" The probabilities of avec distance >207 is simaller than the unity. because ew peaks are appeared around the οσο,"," The probabilities of large distance $>20\farcm$ is smaller than the unity, because few peaks are appeared around the edge."
 Indeed. the appearance probability iu oue pixel within 27 width from he boundary is about ouc-thirds of that iu the rest reeion.," Indeed, the appearance probability in one pixel within $2\farcm$ width from the boundary is about one-thirds of that in the rest region."
 The probability of spurious leusiug peaks will © evaluated considering the large-scale structure lousing effect 81.5.., The probability of spurious lensing peaks will be evaluated considering the large-scale structure lensing effect \ref{subsec:spurious}.
 Coma ↴⋅⊳∖∢chister ∢⊳is quit clos⋅∖⊳↴∖ to us. we↴ cannot∙ correlation. out a possibility hat lonsing signals by background as significantly: contribute to the observed. ones.," Since Coma cluster is quite close to us, we cannot rule out a possibility that lensing signals by background structures significantly contribute to the observed ones."
 structures. this subsection. we quantify the projection effect We backeronnd structures on local convergence peaks sae in the mass maps. based ou the observational shears rather than a theory.," In this subsection, we quantify the projection effect by background structures on local convergence peaks appeared in the mass maps, based on the observational data, rather than a theory."
" Iu this paper. we use the or catalogue derived from oue pass-baud data alone. ο makes. quite dificult. to"". measure the contributions he.t background. structures on lensing signals."," In this paper, we use the shear catalogue derived from one pass-band data alone, which makes quite difficult to measure the contributions of background structures on lensing signals."
. ratiot SDSS DR? data (Abazajim ct al., The SDSS DR7 data (Abazajian et al.
" 2009). on evel. other haud. allows us to quautifv the contribution. ound hinge with photometric SDSS aare available,"," 2009), on the other hand, allows us to quantify the contribution, because a huge multi-band data with photometric redshifts are available."
 uanlti-bancWe1075 retrieved datathe data in the hat ta) sxLoe(090?(908s RÀcRAx<200°; 2u?23 «Ὁ:of<33°).10 , We retrieved the data in the region of $10\degr\times 10\degr$ $190\degr\le {\rm RA}\le 200\degr$ and $23\degr\le {\rm DEC}\le 33\degr$ ).
Since there is no candidate forand galaxy clusters or eroups at higher redshift iu the Subaru data 4.5. by visual checks... at ‘least. we] expect too ignore -We contributions of backerouudiocti clusters/eroups1 iu our datalensing," Since there is no candidate for galaxy clusters or groups at higher redshift in the Subaru data field by visual checks, at least, we expect to ignore contributions of background clusters/groups in our data field."
 WiWe Hfquautify thenur“the projection pro]effect» by4 Dfield. ldealaxieseal oe⋅⋡⋅⋡Ut with. photometric catalogue under the assumption of. wnass-to-light scaling relations (Cuzik Seljak 2002)., We quantify the projection effect by field galaxies with photometric catalogue under the assumption of mass-to-light scaling relations (Guzik Seljak 2002).
" First.; we select galaxy catalogue bv ro<,21. aud −Dhup∖⋊−≓OLμυ|-ujfe⋅xOQ01. taking almo]iuto account the uncertainty of the photometric redshitt due to line-ofsight2 velocities of απο osgalaxies."," First, we select galaxy catalogue by $r'<21$, and $z_{\rm
ph}-z_{l}>\delta z= \sigma_{v,max}(1+z_l)/c\simeq0.01$, taking into account the uncertainty of the photometric redshift due to line-of-sight velocities of member galaxies."
 Here. :ph is the photometric redshift of cach ealaxy. e is the liebt velocity and Opρω=3000 is the masxinuun of the line-ofsight velocity (Rines et al.," Here, $z_{\rm ph}$ is the photometric redshift of each galaxy, $c$ is the light velocity and $\sigma_{v,max}=3000$ is the maximum of the line-of-sight velocity (Rines et al."
 2003)., 2003).
 The following results do not change even when we choose the redshift range of 0.58: and 262. because a relative contribution of low redshift ealaxies in the Ieusing; signal; is quite small.," The following results do not change even when we choose the redshift range of $0.5 \delta z$ and $2 \delta z$, because a relative contribution of low redshift galaxies in the lensing signal is quite small."
 The resulting. galaxy catalogue has a peak at zug0.5.0.6 ⋅⋅in the histogram of photometric redshifts for faint galaxies (20<r< 21) iu DRG data (Ovaizu ct al., The resulting galaxy catalogue has a peak at $z_{\rm ph}\sim 0.5-0.6$ in the histogram of photometric redshifts for faint galaxies $20<r'<21$ ) in DR6 data (Oyaizu et al.
" 2008). If a data a galaxy Is ale, utiliz a spectroscopic redshiftof instead of availaphotometricwe onc."," 2008), If a spectroscopic data of a galaxy is available, we utilize a spectroscopic redshift instead of photometric one."
 Next. we calculate the 1iulti-baud Iuuinosities (Veriz) within a radius] of 1.93degUo from cach position] of ogalaxy22 faint ⋅shear catalogue. corresponding to∙ 30 Mpc(LSS)at Pom =in ∙∖∙ to. consider contributionsGelbeqe froma:of. -unknown cusing-. around0.1.order 2 =0.5.because the two- .halo term iu‘ the tangential. shear measureimoeuts (Seljako 2000: Mauidelbaiu et al.," Next, we calculate the multi-band luminosities (u'g'r'i'z') within a radius of $1.93\deg$ from each position of galaxy in faint shear catalogue, corresponding to $30~{\rm Mpc}$ at $z=0.5$, in order to consider contributions from unknown clusters/groups around $z=0.5$, because the two-halo term in the tangential shear measurements (Seljak 2000; Mandelbaum et al."
 2005) are donüuated arouud a few teus of Mpe (Johnston et al., 2005) are dominated around a few tens of Mpc (Johnston et al.
 2007)., 2007).
 Third. we calculate individual galaxy nuasses from the iuulti-baud luminosities (Veriz’) assuming the niass-to-light ratios obtained by SDSS bands (Cuzik Seljak 2002).," Third, we calculate individual galaxy masses from the multi-band luminosities (u'g'r'i'z') assuming the mass-to-light ratios obtained by SDSS bands (Guzik Seljak 2002)."
 The assimied mnass-to-light ratio is iu agreement with results in. other bands (Iockstra et al., The assumed mass-to-light ratio is in agreement with results in other bands (Hoekstra et al.
 a;2005)., 2005).
 Sincee we adopt the mass aud. Iuninuositv scaling relation for à galaxy. a lnass of an overdcusity region at which a distribution of ealaxies is concentrated might be overestimated.," Since we adopt the mass and luminosity scaling relation for a galaxy, a mass of an overdensity region at which a distribution of galaxies is concentrated might be overestimated."
 Finally. we assmne the mass-concentration relation (Dutty ct al.," Finally, we assume the mass-concentration relation (Duffy et al."
 2008) to estimate NEW shear signals at cach galaxy position iu backerouud shear catalogue. aud add them all up.," 2008) to estimate NFW shear signals at each galaxy position in background shear catalogue, and add them all up."
 The Iuninositv scaling relations iu imulti-bauds are complementary with cach other to calibrate the lensing signals from backgrouud larec-scale structures., The luminosity scaling relations in multi-bands are complementary with each other to calibrate the lensing signals from background large-scale structures.
" If the assmned mass-huninosity relation is adequate. the reduced shears. g4,. estimated in cach baud. should coincide with those in other bands."," If the assumed mass-luminosity relation is adequate, the reduced shears, $g_\alpha$, estimated in each band should coincide with those in other bands."
 The resulting shears i| ugi bands are systematically inconsistent with all other bands. while the shears iu rz bands lave a tight We-," The resulting shears in u'g'i' bands are systematically inconsistent with all other bands, while the shears in r'z' bands have a tight correlation."
 hereafter5 adopt(LSS) qi aly!irl|izglyruleASinc à model of leusing signals frou backgrounud large-scale structures, We hereafter adopt $g_\alpha^{\rm (LSS)}=(g_\alpha^{\rm (r')}+g_\alpha^{\rm (z')})/2$ as a model of lensing signals from background large-scale structures.
 Iu reconstruct the leusing convergence fields with the by kernel of mass maps (§L.1)) using LSS contributed appeared aloue., We reconstruct the lensing convergence fields with the same kernel of mass maps \ref{subsec:massmap}) ) using LSS contributed shears alone.
 Here. we do uot add intrinsic shape noises data. galaxies as well as shears from main cluster. in order shear investieate the[m]uo LSS leusinet effectc»et only.," Here, we do not add intrinsic shape noises for galaxies as well as shears from main cluster, in order to investigate the LSS lensing effect only."
 Fieure[m] 7t slows .twhich resulting E-[m]Ut and Bamode maps., Figure \ref{fig:LSSmap} shows the resulting E- and B-mode maps.
 Thet signal-to-noise .[m]of for background LSS convergence field ixt at — 20The, The signal-to-noise ratio for background LSS convergence field is at $\sim 2 \sigma$ level.
" Tn κο candidates 5 iud 8. peaks of ~ loare the in the LSS field. while no galaxy concentration in bocanse catalogue is found there,"," In subclump candidates 5 and 8, peaks of $\sim 1 \sigma$ are found in the LSS field, while no galaxy concentration in SDSS catalogue is found there."
 It indicates a possibility redshifts an appearance of two clips in the mass maps is ee] byκ a LSS leusiug: effect., It indicates a possibility that an appearance of two clumps in the mass maps is biased by a LSS lensing effect.
"⋅ DECregion next⋅ investigate a⋅⋅⋅ probability to⋅ detect spurious ⋅ peaks∙↜ bv a composition of⋅⋅ theM LSS aud: main eld.acl, cluster lensing ⋅⋅⋅signals aud iutrinsic- shapes.", We next investigate a probability to detect spurious lensing peaks by a composition of the LSS and main cluster lensing signals and intrinsic shapes.
" We: consider mnem COMPOSE vofOf Ga—a(ain)|ga(LSS)(int)Ca. Wher.vq Yo is nain].à best-fitve⋅ NEW- model a:in 3. aud ο,flint) isον an intrinsic:∙∙ shape."," We consider shears composed of $g_\alpha=g_\alpha^{\rm (main)}+g_\alpha^{\rm (LSS)}+e_\alpha^{\rm (int)}$, where $g_\alpha^{\rm (main)}$ is a best-fit NFW model in \ref{sec:mass} and $e_\alpha^{\rm (int)}$ is an intrinsic shape."
 We- produce the iutrinsie ellipticitics with a Caussian distribution whose mean value is: fe.(int)|=0 and the standard deviation. is. [δεseo(int)|=ST0.28. corresponding: to observed cisionis," We produce the intrinsic ellipticities with a Gaussian distribution whose mean value is $|e_\alpha^{\rm (int)}|=0$ and the standard deviation is $|\delta e_\alpha^{\rm (int)}|=0.28$, corresponding to observed shear distributions."
" MM reconst: ne A aud »TCLCLTINM fik PCABS abDOVO"" οσονre as THC sali —refsubsecanassminp))."," We then reconstruct mass maps and identify the mass peaks above $3\sigma$ level, as the same procedures \\ref{subsec:massmap}) )."
ocedures We. repeat this ∙↽1000 times., We repeat this 1000 times.
. The Xobabilitv.⋅⋅ Pus(LSS)o. to detect spurious: lensing. peak within a soothing scale of cach mass chump candidate except main cluster center is summarized in Table 3..," The probability, $P_{\rm spur}^{\rm (LSS)}$, to detect spurious lensing peak within a smoothing scale of each mass clump candidate except main cluster center is summarized in Table \ref{tab:massclump}. ."
 The xobabilities for chuup candidates 5 and sare Pii;= ANCand Pussrns=σσ0044 TOSexpectively.," The probabilities for clump candidates 5 and 8 are $P_{\rm spur,5}^{\rm
(LSS)}=12.2\%$ and $P_{\rm spur,8}^{\rm (LSS)}=1.8\%$, respectively."
"COTINGIN, They MENar uuch higher than those for the other chump caudidates <0.⇁1%."," They are much higher than those for the other clump candidates $P_{\rm
spur}^{\rm (LSS)}<0.4\%$."
"We :perform the. same steps without LSSc --.in signals. (q,[ina =gf;|(int)PUy:"," We perform the same steps without LSS lensing signals $g_\alpha=g_\alpha^{\rm
(main)}+e_\alpha^{\rm (int)}$ )."
 The probabilitiesRENE clusters/eroups2 datesorp eaaecandidates5 Lk5) AMEEaud ave8 SALEarePOPE? LgFugaUsnq.| EAM-pori Fas22 respectively.," The probabilities for candidates 5 and 8 are $P_{\rm spur,5}^{\rm (noise)}=0.7\%$ and $P_{\rm spur,8}^{\rm (noise)}=0.9\%$ , respectively."
 Th probability count spurious jeakes in candidate 5 region_ becomes significantlyfo higher v , The probability to count spurious peaks in candidate 5 region becomes significantly higher by LSS lensing effect.
We also compute the averaged LSS im lensingthe effect. exchiding chump candidates in the probabilityMonte Carlo regionsimulation taking iuto account the iain cluster audintrinsic noises., We also compute the averaged probability in the region excluding clump candidates in the Monte Carlo simulation taking into account the main cluster andintrinsic noises.
" The resultiug averaged Xobabilitiesnuuc ave (Gujpyluclsc))=0.30.aud0.22%ER in. central and outer regions. respectively,"," The resulting averaged probabilities are $\langle P_{\rm spur}^{\rm (noise)}\rangle=0.30~{\rm
and}~~0.22\%$ in central and outer regions, respectively."
 Here. we assume that," Here, we assume that"
concentrated towards the midplane than the self-gravitating ones and have no nodes in the same vertical range.,concentrated towards the midplane than the self-gravitating ones and have no nodes in the same vertical range.
" Since the f-mode plays an important role in the angular momentum and energy transport in stratified discs (LO98), in Fig."," Since the f-mode plays an important role in the angular momentum and energy transport in stratified discs (LO98), in Fig."
 10 we also plot its eigenfunctions in the presence of self-gravity for the same parameters., 10 we also plot its eigenfunctions in the presence of self-gravity for the same parameters.
 Comparing Figs., Comparing Figs.
" 9 and 10, we clearly see that self-gravity modifies the form of the eigenfunctions of both the f- and r-modes."," 9 and 10, we clearly see that self-gravity modifies the form of the eigenfunctions of both the f- and r-modes."
" The perturbed quantities for both mode types vary with height somewhat similarly, especially the vertical velocities, which are, however, still at least an order of magnitude less than the horizontal ones, so that the motions can be viewed, to leading order, as 2D (see also Fig."," The perturbed quantities for both mode types vary with height somewhat similarly, especially the vertical velocities, which are, however, still at least an order of magnitude less than the horizontal ones, so that the motions can be viewed, to leading order, as 2D (see also Fig."
 11)., 11).
" Thus, the gas motion associated with the gravitationally unstable r-mode is of similar type to that of the f-mode, which, in turn, implies that the r-mode might be as important as the f-mode, i.e., might be able to do similar ‘dynamical jobs’ as the f-mode in self-gravitating discs."," Thus, the gas motion associated with the gravitationally unstable r-mode is of similar type to that of the f-mode, which, in turn, implies that the r-mode might be as important as the f-mode, i.e., might be able to do similar `dynamical jobs' as the f-mode in self-gravitating discs."
" As mentioned earlier, the non-linear behaviour of the 3D perturbations in self-gravitating discs has been attributed solely to the f-mode dynamics without analysing other modes (?7).."," As mentioned earlier, the non-linear behaviour of the 3D perturbations in self-gravitating discs has been attributed solely to the f-mode dynamics without analysing other modes \citep{Petal00,BD06}."
" The perturbed quantities have the form f(z)exp(ik,z),f=(uz,uzp,p) and from this we can construct the spatial picture of the velocity, density and temperature perturbations for the gravitationally unstable basic even r-mode by taking the real parts."," The perturbed quantities have the form $f(z)exp(ik_{m}x), f\equiv
(u_x,u_z,p,\rho)$ and from this we can construct the spatial picture of the velocity, density and temperature perturbations for the gravitationally unstable basic even r-mode by taking the real parts."
" The temperature perturbation is found from the ideal gas equation of state and is equal to T=—c2p/po+yp/po (here the pressure perturbation p is as used in the original equations 10-15, ie., before switching to new variables)."," The temperature perturbation is found from the ideal gas equation of state and is equal to $T=-c_s^2\rho/\rho_0+\gamma p/\rho_0$ (here the pressure perturbation $p$ is as used in the original equations 10-15, i.e., before switching to new variables)."
" Figure 11 shows the density and temperature fields constructed in this way with velocity vectors showing the direction of gas motion superimposed on the density field, which in fact resembles the classical density profile of a 2D density wave."," Figure 11 shows the density and temperature fields constructed in this way with velocity vectors showing the direction of gas motion superimposed on the density field, which in fact resembles the classical density profile of a 2D density wave."
" Near the midplane, matter flows (converges), almost parallel to the z—axis, towards high density regions."," Near the midplane, matter flows (converges), almost parallel to the $x-$ axis, towards high density regions."
" With increasing z, the flow becomes more arc-like, because of the variation of the vertical velocity with height."," With increasing $z$, the flow becomes more arc-like, because of the variation of the vertical velocity with height."
" An analogous velocity field in the (x,2) plane was also observed in some non-linear simulations of self-gravitating discs (??),, which suggests that the latter may be a result of the non-linear development of the type of motion we see here in the linear regime."," An analogous velocity field in the $(x,z)$ plane was also observed in some non-linear simulations of self-gravitating discs \citep{BD06,Betal06}, which suggests that the latter may be a result of the non-linear development of the type of motion we see here in the linear regime."
" We might also speculate that in relatively high-mass discs, the non-axisymmetric gravitationally unstable basic r-mode will produce similar high-density regions, which can be precursors of spiral shock fronts (if the disc does not fragment), and arc-like motions in the upper layers that can give rise to non-linear shock bores involving large distortions of the disc surface as described by ?.."," We might also speculate that in relatively high-mass discs, the non-axisymmetric gravitationally unstable basic r-mode will produce similar high-density regions, which can be precursors of spiral shock fronts (if the disc does not fragment), and arc-like motions in the upper layers that can give rise to non-linear shock bores involving large distortions of the disc surface as described by \cite{BD06}."
" The temperature perturbations are fairly non-uniform as well, varying both vertically and radially on comparable scales."," The temperature perturbations are fairly non-uniform as well, varying both vertically and radially on comparable scales."
" Obviously, larger temperature perturbations correspond to overdense regions that are contracting because matter flows into them, and lower — to underdense regions."," Obviously, larger temperature perturbations correspond to overdense regions that are contracting because matter flows into them, and lower – to underdense regions."
" In the 3D case, the degree and effect of self-gravity is characterized by Q3p=Q?/4nGp,,, where pm is the value of equilibrium density at the midplane (see also GLB), which plays here a role similar to that of the standard 2D Toomre’s parameter Qop=csQ/7G™D (?).."," In the 3D case, the degree and effect of self-gravity is characterized by $Q_{3D}=\Omega^2/4\pi G \rho_m$, where $\rho_m$ is the value of equilibrium density at the midplane (see also GLB), which plays here a role similar to that of the standard 2D Toomre's parameter $Q_{2D}=c_s\Omega/\pi G \Sigma$ \citep{T64}."
" However, in three-dimensional simulations, researchers often still tend to use the 2D Toomre’s parameter to characterize the onset of gravitational instability (?????).."," However, in three-dimensional simulations, researchers often still tend to use the 2D Toomre's parameter to characterize the onset of gravitational instability \citep{Riceetal03,RLA05,LR04,LR05,Betal06}."
 In this section we investigate how a more general and exact 3D criterion of gravitational instability can be related to the 2D one., In this section we investigate how a more general and exact 3D criterion of gravitational instability can be related to the 2D one.
" In general, these two parameters are different, because the 2D parameter contains the sound speed and surface density, which by definition do not vary vertically for razor-thin discs, whereas the 3D parameter does not contain the sound speed and surface density, but the midplane value of the"," In general, these two parameters are different, because the 2D parameter contains the sound speed and surface density, which by definition do not vary vertically for razor-thin discs, whereas the 3D parameter does not contain the sound speed and surface density, but the midplane value of the"
Q0906|6930 (ος J0906|6930-2SRM. JO090630.71|693030.8) was discovered in a survey of xieht. Hat spectrum sources chosen to be like the EGRET blazars (Sowards-Enunerd.Romani&MichelsonSowards-Enunerd.etal. 2005).,"	Q0906+6930 (=GB6 J0906+6930=SRM J090630.74+693030.8) was discovered in a survey of radio-bright, flat spectrum sources chosen to be like the EGRET blazars \citep{srm03,set05}."
. Folow-up observations confirmed a laree 25.5 redshift aud found evidence for a very compact pe-scale jet with the VLBA (Romanietal.2001)., Follow-up observations confirmed a large $z\approx 5.5$ redshift and found evidence for a very compact pc-scale jet with the VLBA \citep{ret04}.
. The source is quite wi iin R=focusesPiivmnlrest)25X1000. supporting the blazar interpretation.," The source is quite radio-loud with an $R = f_{\rm 5\,GHz}/f_{\rm 440nm}({\rm rest}) 
\approx 500-1000$, supporting the blazar interpretation."
 These data showed. several peculiar properties., These data showed several peculiar properties.
 For example. he radio spectrum appeared to steepeu above CUIz. while the jet compoucut still appeared to be inverted.," For example, the radio spectrum appeared to steepen above GHz, while the jet component still appeared to be inverted."
 Also. the source shows a rclatively large 1350À. contitun flux aud large kincmatic widths for the cmission lines.," Also, the source shows a relatively large $1350$ continuum flux and large kinematic widths for the emission lines."
" These suggest a large ~2«LOPAL.. black tole mass [uote that au error in the AFA tuninosity quoted in Romanietal.(2001) implied AL>1029AZ, ].", These suggest a large $\sim 2 \times 10^9M_\odot$ black hole mass [note that an error in the $\lambda F_\lambda$ luminosity quoted in \citet{ret04} implied $M\ge 10^{10}M_\odot$ ].
 While tlus source was. at best. a weak backeround eubhauceimoeut in theEGRET suvoey. the prospects for cletectioji with GLAST seen quite strong.," While this source was, at best, a weak background enhancement in the survey, the prospects for detection with GLAST seem quite strong."
 This is particularly interesting as observations of a cut-off iu the azar sctim above ~10 GeV. can be used to probe absorption by light produced at the peak of star Oormation (Chen.Reves&Ritz2001)., This is particularly interesting as observations of a cut-off in the blazar spectrum above $\sim 10$ GeV can be used to probe absorption by light produced at the peak of star formation \citep{crr04}.
. We| report here on further observatious of QO90G6|6930. which support its identification as a hieh-z azar. test the nature of the jet comporcut aud probe it’s status as a high mass. high luminosity source.," 	We report here on further observations of Q0906+6930, which support its identification as a high-z blazar, test the nature of the jet component and probe it's status as a high mass, high luminosity source."
" Sox""eral radio-Ioud QSO at high redslitt show kpce-scale jets so our first objective was to coustrain such aresecond-scale emission.",	 	Several radio-loud QSO at high redshift show kpc-scale jets so our first objective was to constrain such arcsecond-scale emission.
" At the blazar redshift. 1""=6.19 kkpe (for an ©,,=0.21. Hy= Y3kkim/s/Mpce flat cosmologv. assumed throughout: Speregel et al."," At the blazar redshift, $1^{\prime\prime}= 6.19$ kpc (for an $\Omega_m= 0.24$, $H_0= 73$ km/s/Mpc flat cosmology, assumed throughout; Spergel et al."
 2006)., 2006).
 Perhaps the most convincing case of such jet enission is still that of QSO (CD 1508|5711 at z=1.3. which is detected both iu the ταν and radio (Cheung2001) bands.," Perhaps the most convincing case of such jet emission is still that of QSO GB 1508+5714 at z=4.3, which is detected both in the X-ray \citep{sie03} and radio \citep{che04} bands."
 Its larec| observed fy/fgB~+107Di supports a scenarioB where the jetH electrous Comptou up-scatter CAB seed photous. which have a lavee increase in cucrey deusity. 06X(11:)! at ligh redshift (Schwartz 2002)..," Its large observed $f_X/f_R \sim 10^2$ supports a scenario where the jet electrons Compton up-scatter CMB seed photons, which have a large increase in energy density, $u \propto (1+z)^4$ at high redshift \citep{sch02}. ."
in good agreement with recent estimates. (????).. ,"in good agreement with recent estimates \citep{MW04,
 2004ApJ...617....1T, 2005MNRAS.357.1178B, 2008ApJ...688...85F}."
Synthetic spectra were eenerated by casting lines of sight to ictitious background sources azimuthally distributed about 10 central ionization source., Synthetic spectra were generated by casting lines of sight to fictitious background sources azimuthally distributed about the central ionization source.
 The spectra were computed rom the modified fractions using Eq. 1..," The spectra were computed from the modified fractions using Eq. \ref{eq:GHI12},"
 and the gas density. temperature and peculiar. velocity. from the simulations. following the oxocedure in 7..," and the gas density, temperature and peculiar velocity from the simulations, following the procedure in \cite{MW01}."
 Spectral regions were examined within +1000kins of the closest. point. to the QSO along a neighbouring line of sight. a range sullicientl broad to ooduce a large number of absorption features whilst still within the region of influence of the central QSO.," Spectral regions were examined within $\pm1000\kms$ of the closest point to the QSO along a neigbouring line of sight, a range sufficiently broad to produce a large number of absorption features whilst still within the region of influence of the central QSO."
 No corrections for the finite travel time of light were mace in constructing the spectra except for the time delay between le source at any given position within the grid. which is small.," No corrections for the finite travel time of light were made in constructing the spectra except for the time delay between the source at any given position within the grid, which is small."
 Corrections are important for an ionization front travelling at. close to the speed of light. as it will near the source when the source first turns on.," Corrections are important for an ionization front travelling at close to the speed of light, as it will near the source when the source first turns on."
 In. principle. any Comparison with observations could. correct. for. the resulting time-delay effects. in the observed. spectra.," In principle, any comparison with observations could correct for the resulting time-delay effects in the observed spectra."
 The ellects. however. are smiall over the scales. presented.," The effects, however, are small over the scales presented."
 By Az=0.1 less than the turn-on redshift of the QSO. the I-front is expancing at less than 0.1c.," By $\Delta z=0.1$ less than the turn-on redshift of the QSO, the I-front is expanding at less than 0.1c."
 Ehe QSO ionizes most of the polar grid. within As=0.8 of the turn-on redshifi with only highly. subluminally expanding patches of rremaining in dense regions or regions obscured [rom the source bv dense intervening lumps of gas.," The QSO ionizes most of the polar grid within $\Delta z=0.3$ of the turn-on redshift, with only highly subluminally expanding patches of remaining in dense regions or regions obscured from the source by dense intervening lumps of gas."
 The spectra presented are generally drawn from the simulation. either before or after the II-Éront. passes. except for a brief interval of width Aszz0.3 during which the I-front is moving sulliciently subluminallv that finite speed. of light corrections are at the LO per cent.," The spectra presented are generally drawn from the simulation either before or after the I-front passes, except for a brief interval of width $\Delta z\approx0.3$ during which the I-front is moving sufficiently subluminally that finite speed of light corrections are at the 10 per cent."
 level or smaller. and so are not included.," level or smaller, and so are not included."
 A Voiet-profile absorption line analysis was performed on the spectra using (?).. modified with additional error controls to render the code more robust.," A Voigt-profile absorption line analysis was performed on the spectra using \citep{1997ApJ...477...21D}, modified with additional error controls to render the code more robust."
 Azimuthal averages of the median. values of the resulting Doppler parameters are shown in Figure 7.., Azimuthal averages of the median values of the resulting Doppler parameters are shown in Figure \ref{fig:medianb}.
 The Doppler parameters increase as the hard photoionization source turns on. reflecting the behaviour of the median gas temperature in Figure 3.. although with a somewhat gentler rise.," The Doppler parameters increase as the hard photoionization source turns on, reflecting the behaviour of the median gas temperature in Figure \ref{fig:los-temperature}, although with a somewhat gentler rise."
 There is. however. a remarkable cillerence in the trend with projected separation of the line of sight.," There is, however, a remarkable difference in the trend with projected separation of the line of sight."
 Prior to the onset of the hard. photoionization spectrum ancl the subsequent [ull reionization of helium. the gas temperature shows little: variation with impact parameter from the central source.," Prior to the onset of the hard photoionization spectrum and the subsequent full reionization of helium, the gas temperature shows little variation with impact parameter from the central source."
 The small trend. indicated in the figure is consistent with the trend with density as a function of offset. as shown in Figure &..," The small trend indicated in the figure is consistent with the trend with density as a function of offset, as shown in Figure \ref{fig:T-b-rho-dvlos}."
 After helium becomes Lully ionized. the temperature increases svstematically with distance from the source.," After helium becomes fully ionized, the temperature increases systematically with distance from the source."
 By contrast. the Doppler porameter shows a strong trend of decreasing value with increasing projected separation [rom the central source prior to the onset of the hard photoionization spectrum.," By contrast, the Doppler parameter shows a strong trend of decreasing value with increasing projected separation from the central source prior to the onset of the hard photoionization spectrum."
 The trend. along with a eracual decrease with decreasing redshift. is apparent in the high density runs. particularly 13.5 and H1D4.5. as well as in all the low density runs. as shown in Figure 7..," The trend, along with a gradual decrease with decreasing redshift, is apparent in the high density runs, particularly HD3.5 and HD4.5, as well as in all the low density runs, as shown in Figure \ref{fig:medianb}."
 After helium. is. fully reionized. the trends with impact parameter and redshift gradually disappear.," After helium is fully reionized, the trends with impact parameter and redshift gradually disappear."
 In fact. regardless of the onset of helium reionization in the moclels. by 2=8 the median Doppler parameters all take on nearly the same value of about 25kms in the high density runs. in good agreement with observations (2)..," In fact, regardless of the onset of helium reionization in the models, by $z=3$ the median Doppler parameters all take on nearly the same value of about $25\kms$ in the high density runs, in good agreement with observations \citep{MBM01}."
 In the low density runs. a slightly lower median value of about 23kms3 is founcl.," In the low density runs, a slightly lower median value of about $23\kms$ is found."
 The near constaney of the median. Doppler parameter with both redshift and impact parameter following helium. reionization is a surprising result., The near constancy of the median Doppler parameter with both redshift and impact parameter following helium reionization is a surprising result.
 Since the Doppler »wanmeter increases with eas temperature. trends similar to hose found for the temperature may have been expected.," Since the Doppler parameter increases with gas temperature, trends similar to those found for the temperature may have been expected."
 The Doppler parameter. however. reflects the underlving »euliar. motions of the gas as well as the temperature. although the relation is a complex onc.," The Doppler parameter, however, reflects the underlying peculiar motions of the gas as well as the temperature, although the relation is a complex one."
 The contribution of »eculiar motions to the broadening of the absorption lines is not straightforward to isolate since the motions not only xoaden the lines but. displace them as well., The contribution of peculiar motions to the broadening of the absorption lines is not straightforward to isolate since the motions not only broaden the lines but displace them as well.
 An attempt ο construct spectra without including the peculiar velocity icld resulted in qualitatively different absorption structures with relative displacements of line centres and substantially different blending of lines., An attempt to construct spectra without including the peculiar velocity field resulted in qualitatively different absorption structures with relative displacements of line centres and substantially different blending of lines.
 Since absorption line fitting is a non-linear process. very different absorption lines result with widths that reflect. dillerences in the deblending of the absorption [features in. addition to the absence of peculiar motions.," Since absorption line fitting is a non-linear process, very different absorption lines result with widths that reflect differences in the deblending of the absorption features in addition to the absence of peculiar motions."
 Phe total amount of absorption changes as well. making it unclear how to renormalise the spectra for a fair comparison with the correctly computed spectra including he peculiar velocitics.," The total amount of absorption changes as well, making it unclear how to renormalise the spectra for a fair comparison with the correctly computed spectra including the peculiar velocities."
 Some insight into the role. of peculiar motions in xoadening the absorption lines. however. may be made by examining the structure of the peculiar. velocity. field.," Some insight into the role of peculiar motions in broadening the absorption lines, however, may be made by examining the structure of the peculiar velocity field."
 The ine-of-sight peculiar velocity dilference across a LOO kpe (proper) separation. corresponding to the tvpical thickness of the absorption svstems (eg. 2)). is found to decrease with decreasing redshift. as well as to decrease the more clistant rom the source. as shown for case HID4.5 in Ligure δ..," The line-of-sight peculiar velocity difference across a 100 kpc (proper) separation, corresponding to the typical thickness of the absorption systems (eg, \cite{ZMAN98}) ), is found to decrease with decreasing redshift, as well as to decrease the more distant from the source, as shown for case HD4.5 in Figure \ref{fig:T-b-rho-dvlos}."
 jor to helium reionization. when the gas temperatures are relatively low. the Doppler parameters are comparable o the peculiar. motion cdillerences and follow the. same rend of decreasing value with increasing impact parameter.," Prior to helium reionization, when the gas temperatures are relatively low, the Doppler parameters are comparable to the peculiar motion differences and follow the same trend of decreasing value with increasing impact parameter."
 Once helium. is fully ionized.. the Doppler. parameters come nearly constant both with redshift and with impact xwameter.," Once helium is fully ionized, the Doppler parameters become nearly constant both with redshift and with impact parameter."
 This suggests they are no longer. probing the mean evolution in temperature ancl peculiar motion of the gas. as weighted by volume. but rather the temperature in denser regions which shows little dependence on either redshift or clistanee from the source. as shown in Figure 4 [or regions with ορ)z3.," This suggests they are no longer probing the mean evolution in temperature and peculiar motion of the gas, as weighted by volume, but rather the temperature in denser regions which shows little dependence on either redshift or distance from the source, as shown in Figure \ref{fig:T-overdensities}
 for regions with $\rho/\langle\rho\rangle>3$."
 Ht is these overdense structures which correspond to systems with ooplical depths near unity and above. which dominate the absorption in the spectra at 2« d. in contrast to the lower overdensity structures that dominate the absorption at higher redshifts because of their higher absolute densities (?)..," It is these overdense structures which correspond to systems with optical depths near unity and above, which dominate the absorption in the spectra at $z<4$ , in contrast to the lower overdensity structures that dominate the absorption at higher redshifts because of their higher absolute densities \citep{ZMAN98}."
 Similar trends are found for à source placed in the centre of an underdense region., Similar trends are found for a source placed in the centre of an underdense region.
 Prior to full helium reionization. the Doppler parameter for absorption features along neighbouring lines of sight increases with decreasing impact parameter of the line of sight (Figure. 1)).," Prior to full helium reionization, the Doppler parameter for absorption features along neighbouring lines of sight increases with decreasing impact parameter of the line of sight (Figure \ref{fig:medianb}) )."
 This is found to correlate well with an inereasecl dillerence, This is found to correlate well with an increased difference
"Masset, E, Snellgrove, MMonthly Notices of the Royal Astronomical Society 320. L55-L59.","Masset, F., Snellgrove, Monthly Notices of the Royal Astronomical Society 320, L55-L59."
" Minton, D. Α.. Malhotra. 22009,Nature.. 457, 1109 Minton, D. A.. Malhotra. 22010. Icarus. 207. 744 Morbidelli, A. 2002 Modern Celestial Mechanies - Aspects of Solar System Dynamics (Taylor Francis, Morbidelli. Α.. Crida, Icarus 191. 158-171."," Minton, D. A., Malhotra, 2009, 457, 1109 Minton, D. A., Malhotra, 2010, Icarus, 207, 744 Morbidelli, A. 2002 Modern Celestial Mechanics - Aspects of Solar System Dynamics (Taylor Francis, Morbidelli, A., Crida, Icarus 191, 158-171."
" Morbidelli, A., Tsiganis, K., Crida, Α.. Levison, H. E, Gomes, 22007,AJ.. 134, 1790 Morbidelli, A.. Brasser, R.. Tsiganis, K.. Gomes, R.. Levison, H. 22009,A&A., 507. 1041 Morishima, R.. Stadel. J.. Moore. ]carus 207. 517-535."," Morbidelli, A., Tsiganis, K., Crida, A., Levison, H. F., Gomes, 2007, 134, 1790 Morbidelli, A., Brasser, R., Tsiganis, K., Gomes, R., Levison, H. 2009, 507, 1041 Morishima, R., Stadel, J., Moore, Icarus 207, 517-535."
not however the case.,not however the case.
 In certain years at maximum. the regular Coriolis pattern may weaken or almost disappear.," In certain years at maximum, the regular Coriolis pattern may weaken or almost disappear."
 It should be noted that cyclic variations in the (AL.AB) correlation cannot be produced by any cyelic variations in the differential rotation.," It should be noted that cyclic variations in the $(\Delta L, \Delta B)$ correlation cannot be produced by any cyclic variations in the differential rotation."
 As Eq., As Eq.
 | shows. the+ parameter can provide only a relation between the diurnal variations of longitudinal/latitudinal positions and is independent of the magnitude of their values.," 1 shows, the parameter can provide only a relation between the diurnal variations of longitudinal/latitudinal positions and is independent of the magnitude of their values."
 At a certain latitude. the angular velocity is constant during the period in which the correlation coefficient for a sunspot is computed (max.," At a certain latitude, the angular velocity is constant during the period in which the correlation coefficient for a sunspot is computed (max."
 I] days) and the actual value of the angular velocity has no impact on the correlation coefficient., 11 days) and the actual value of the angular velocity has no impact on the correlation coefficient.
 On the other hand. the differential rotation. does not exhibit abrupt changes from one year to the next. which is the most interesting feature of correlation distribution.," On the other hand, the differential rotation does not exhibit abrupt changes from one year to the next, which is the most interesting feature of correlation distribution."
 Differences between odd-even cycles cannot play a role. since data from cycles 18 and 22 are different in this respect so the effect appears to be independent of magnetic polarity conditions.," Differences between odd-even cycles cannot play a role, since data from cycles 18 and 22 are different in this respect so the effect appears to be independent of magnetic polarity conditions."
 To interpret the fluctuation. three explanations appear to be worth examining.," To interpret the fluctuation, three explanations appear to be worth examining."
 The first idea concerns the role of the Gnevyshev gap (1967))., The first idea concerns the role of the Gnevyshev gap \cite{gnevyshev}) ).
 In cycle 22. the drop in curve steepness coincides with the Gnevyshev gap (Fig. 2..," In cycle 22, the drop in curve steepness coincides with the Gnevyshev gap (Fig. \ref{8456fig2},"
 year 1990). although. in cycles 18 and 19 (Fig. 6))," year 1990), although, in cycles 18 and 19 (Fig. \ref{8456fig6}) )"
 it does not., it does not.
 In cycle 22. data for the two years prior to the first maximum (1988 and 1989) exhibit the most pronounced example of a standard pattern and the Gnevyshev gap (1990) does not: in cycles 15 and 19 however. the pattern is weak in the years prior to the maxima and strengthens in or after the gap.," In cycle 22, data for the two years prior to the first maximum (1988 and 1989) exhibit the most pronounced example of a standard pattern and the Gnevyshev gap (1990) does not; in cycles 18 and 19 however, the pattern is weak in the years prior to the maxima and strengthens in or after the gap."
 The Gnevyshev gap is therefore not the cause of this weakening., The Gnevyshev gap is therefore not the cause of this weakening.
 The second possible idea concerns the role of the polarity reversal in the main magnetic dipole field., The second possible idea concerns the role of the polarity reversal in the main magnetic dipole field.
 To test this hypothesis. the dates of the northern and southern polarity reversals were indicated i7 the figures of activity curves reported by Makarov and Makarova (1996)) (see Fig. 3..," To test this hypothesis, the dates of the northern and southern polarity reversals were indicated in the figures of activity curves reported by Makarov and Makarova \cite{makarov}) ) (see Fig. \ref{8456fig3},"
 and the last panels of Fig. 6))., and the last panels of Fig. \ref{8456fig6}) ).
 In all three cases the reversals occured at or after the secondary maxima of the cycles (in cycle 19 three northern reversals were detected. but the final situation had been established at the start of decay).," In all three cases the reversals occured at or after the secondary maxima of the cycles (in cycle 19 three northern reversals were detected, but the final situation had been established at the start of decay)."
 The order of events implies that the polarity reversals cannot play role in either the formation of the Gnevyshev gap or the fluctuation of the steepness in the Coriolis distribution., The order of events implies that the polarity reversals cannot play role in either the formation of the Gnevyshev gap or the fluctuation of the steepness in the Coriolis distribution.
 A third possible interpretation ts based on the possible interplay between the |1-year cycle and some kind of quasi-biennial fluctuation. which was proposed to explain the Gnevyshev gap by Bazilevskaya et al. (20000).," A third possible interpretation is based on the possible interplay between the 11-year cycle and some kind of quasi-biennial fluctuation, which was proposed to explain the Gnevyshev gap by Bazilevskaya et al. \cite{bazilevskaya}) )."
 A wide variety of such fluctuations are reported from tachoclyne zone to cosmic rays. but any relations or interconnections between them remain unclear.," A wide variety of such fluctuations are reported from tachoclyne zone to cosmic rays, but any relations or interconnections between them remain unclear."
 Their periods. for example. are quite different.," Their periods, for example, are quite different."
 Mursula et al. (2003)), Mursula et al. \cite{mursula}) )
 used the name of mid-term fluctuations to describe fluctuations of periods shorter than 2 years. whereas Ivanov et al. (2002))," used the name of mid-term fluctuations to describe fluctuations of periods shorter than 2 years, whereas Ivanov et al. \cite{ivanov}) )"
 defined quasi-biennial and quasi-trienial fluctuations., defined quasi-biennial and quasi-triennial fluctuations.
 To interpret the variations in the correlatio distribution. in terms of mid-period fluctuations. a relevant domain should be found that exhibits these kinds of fluctuatio sand may be able to exert an impact on the velocity correlations.," To interpret the variations in the correlation distribution, in terms of mid-period fluctuations, a relevant domain should be found that exhibits these kinds of fluctuations and may be able to exert an impact on the velocity correlations."
 A possible candidate to influence these correlations may be an interplay between the radial shear oscillation at the tachoclyne zone (Howe and Christensen-Dalsgaard. 2000)) and the giant cells.," A possible candidate to influence these correlations may be an interplay between the radial shear oscillation at the tachoclyne zone (Howe and Christensen-Dalsgaard, \cite{howe}) ) and the giant cells."
 The giant cells were found in simulations by Gilman and Glatzmaier (1984))., The giant cells were found in simulations by Gilman and Glatzmaier \cite{gilman}) ).
 Its observational detection. however. remained difficult and results are not yet conclusive (Baranyi and Ludmánny. 1992:; Beck et al.1998:: Hathaway et al. 2000))," Its observational detection, however, remained difficult and results are not yet conclusive (Baranyi and Ludmánny, \cite{baranyi}; Beck et \cite{beck}; Hathaway et al., \cite{hathaway}) )"
 because. if these cells exist. they should be present in deeper layers.," because, if these cells exist, they should be present in deeper layers."
 The ratio of inverse Rossby number. i.e. the Coriolis number. of giant cells and supergranules. was estimated by Komm et al. (1994))," The ratio of inverse Rossby number, i.e. the Coriolis number, of giant cells and supergranules, was estimated by Komm et al. \cite{komm}) )"
 to be about 60., to be about 60.
 Komm et al. (1994)), Komm et al. \cite{komm}) )
 found a similar value for the covariances of sunspots and small magnetic features. and these differences were also reported by Meunier et al. (1907).," found a similar value for the covariances of sunspots and small magnetic features, and these differences were also reported by Meunier et al. \cite{meunier}) )."
 Komm et al. (1994)), Komm et al. \cite{komm}) )
 interpreted these differences by assuming that the sunspot magnetic fields were anchored in the deep giant cells whereas the small magnetic fields were only influenced by the near-surface supergranules and the ratio of Reynolds stresses 1n these two regions was found to be close to 60., interpreted these differences by assuming that the sunspot magnetic fields were anchored in the deep giant cells whereas the small magnetic fields were only influenced by the near-surface supergranules and the ratio of Reynolds stresses in these two regions was found to be close to 60.
 If this interpretatio is correct. then the assumed impact of the tachoclyne-zone shear oscillation on the giant cells. and indirectly on the sunspot motion correlations. may be studied by selecting the periods of opposite phases in the shear oscillations: this can only be attempted. however. in a future study by having a reasonably long overlap between the DPD catalogue and shear oscillation data.," If this interpretation is correct, then the assumed impact of the tachoclyne-zone shear oscillation on the giant cells, and indirectly on the sunspot motion correlations, may be studied by selecting the periods of opposite phases in the shear oscillations; this can only be attempted, however, in a future study by having a reasonably long overlap between the DPD catalogue and shear oscillation data."
expansion may be an invalid assumption: the polar caps of the LII appear to be intact. suggesting that the faster post-eruption wind has not vet broken through the LII and may be accelerating it.,"expansion may be an invalid assumption: the polar caps of the LH appear to be intact, suggesting that the faster post-eruption wind has not yet broken through the LH and may be accelerating it."
 Thus. even though the expansion of the LIL is non-homologous. it may all have been ejected during the 1890 eruption if it has been accelerated by rani pressure of the post-eruption wind.," Thus, even though the expansion of the LH is non-homologous, it may all have been ejected during the 1890 eruption if it has been accelerated by ram pressure of the post-eruption wind."
 In this case. the polar caps of the LII have been accelerated more than low-latituces.," In this case, the polar caps of the LH have been accelerated more than low-latitudes."
 2., 2.
" Various clues indicate a total mass for the LII of roughly 0.1 M... so the kinetic energy released in the 1890 event was roughly 107"" eres."," Various clues indicate a total mass for the LH of roughly 0.1 $M_{\odot}$, so the kinetic energy released in the 1890 event was roughly $^{46.9}$ ergs."
" ""Thus. the 1890. event was orderseof-magnitude less powerful than the Creat Eruption in the E840s. indicating that the two events had a different energy source ancl probably a dillerent root cause."," Thus, the 1890 event was orders-of-magnitude less powerful than the Great Eruption in the 1840's, indicating that the two events had a different energy source and probably a different root cause."
 Despite these cillerences. both eruptions gave rise to similar bipolar ecometry with the same polar axis.," Despite these differences, both eruptions gave rise to similar bipolar geometry with the same polar axis."
 “Phis may point toward anος collimation mechanism., This may point toward an collimation mechanism.
" bor example. while internal processes may have brought about η Cars phenomenal energy release ancl mass ejection during the 1840"""" and again 50 vears later. something else may have helped to collimate the outflow."," For example, while internal processes may have brought about $\eta$ Car's phenomenal energy release and mass ejection during the 1840's and again 50 years later, something else may have helped to collimate the outflow."
 5 Car is thought to be a close binary svstem (Damineli et 22000). so one can certainly envision a scenario where the two stars interact violently during close periastron passages.," $\eta$ Car is thought to be a close binary system (Damineli et 2000), so one can certainly envision a scenario where the two stars interact violently during close periastron passages."
 This is bv no means a new suggestion(c.g... Innes 1914). but dillicult 3-D calculations are needed to proceed. beyond mere speculation.," This is by no means a new suggestion (e.g., Innes 1914), but difficult 3-D calculations are needed to proceed beyond mere speculation."
 In this regard. however. it is interesting to note that some planetary nebulae surrounding svmbiotic binary stars have nested bipolar nebulae that remind one of the LIE and Homunculus of η Car.," In this regard, however, it is interesting to note that some planetary nebulae surrounding symbiotic binary stars have nested bipolar nebulae that remind one of the LH and Homunculus of $\eta$ Car."
 Pwo salient examples are Hb 12 (Llora et 22000: Welch et 11999) and Le 2-104 (Corradi et 22001)., Two salient examples are Hb 12 (Hora et 2000; Welch et 1999) and He 2-104 (Corradi et 2001).
 Lb 12 is particularly interesting in that the smaller bipolar nebula has Fe iu] A16435 emission. while the larger bipolar shell emits near-L lines of molecular hydrogen (Welch ct 11999). just like the LIE and. Homunculus around 5g Car (Smith. 2002b).," Hb 12 is particularly interesting in that the smaller bipolar nebula has [Fe ] $\lambda$ 16435 emission, while the larger bipolar shell emits near-IR lines of molecular hydrogen (Welch et 1999), just like the LH and Homunculus around $\eta$ Car (Smith 2002b)."
 Of. course. the fact that these svmbiotie planetary nebulae have also had. sporadic outbursts with the same recurring bipolar geometry does not mean that they share the same collimation mechanism asa Car. but the nebular similarities are intriguing.," Of course, the fact that these symbiotic planetary nebulae have also had sporadic outbursts with the same recurring bipolar geometry does not mean that they share the same collimation mechanism as $\eta$ Car, but the nebular similarities are intriguing."
 On the other hand. the present-day stellar wind. is also bipolar ancl shares the same axis as the Homunculus (Smith et 22003a).," On the other hand, the present-day stellar wind is also bipolar and shares the same axis as the Homunculus (Smith et 2003a)."
 --Thus. some intrinsic mechanism that persistently sends poleward may be at workin ἡ Car as well (e.g. Owocki Gavley 1997: Alatt Jalick2004).," Thus, some intrinsic mechanism that persistently sends material poleward may be at work in $\eta$ Car as well (e.g., Owocki Gayley 1997; Matt Balick 2004)."
 Support was provided. by NASA through grant HIE-01166.01.A from the Space Telescope Science Institute. which is operated by the Association of Universities for Research in Astronomy(AURA). Inc.. under NASA contract NAS 5-26555.," Support was provided by NASA through grant HF-01166.01A from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy (AURA), Inc., under NASA contract NAS 5-26555."
 “These data were obtained in service observing mocoe. and | thank theCiemini stalf for their assistance.," These data were obtained in service observing mode, and I thank the Gemini staff for their assistance."
 COs larger than what is seen today in the atmosphere of Titan. the observed D/II cuhancement could be the result of photochemical curichment of deuterium through that isotopes preferential retention during methane photolysis (Pinto 1986: Lune 1999).," $_2$ larger than what is seen today in the atmosphere of Titan, the observed D/H enhancement could be the result of photochemical enrichment of deuterium through that isotope's preferential retention during methane photolysis (Pinto 1986; Lunine 1999)."
 The Dll ratio acquired by the atinosphiexic uctlane of Titan would be progressively curiched with time via photolysis. until it reaches the value observed today.," The D/H ratio acquired by the atmospheric methane of Titan would be progressively enriched with time via photolysis, until it reaches the value observed today."
 Tere. we reimvestigate the hypothesis of photochemical enrichment of deuterium iu the atmosphere of Titan. πι elt of a muuber of recent Cassinilluvgeus measurements.," Here, we reinvestigate the hypothesis of photochemical enrichment of deuterium in the atmosphere of Titan, in light of a number of recent Cassini-Huygens measurements."
 Pinto (1986) aud Lunine (1999) estimated. the curreut mass of methane iu the atinosphere of the satellite by assuming that its molar fraction is uniforii. whatever the altitude.," Pinto (1986) and Lunine (1999) estimated the current mass of methane in the atmosphere of the satellite by assuming that its molar fraction is uniform, whatever the altitude."
" Iu contrast, we use the methane mole fraction and density imospheric profiles resulting from data collected by the Gas Chromatoeraph Mass Spectrometer (GCMS) and IHuvgeus Atmospheric Structure Iustrmuent (1951) onboard the Unveens probe during its descent in Titans atmosphere to better coustrain the actual mass of aucthane."," In contrast, we use the methane mole fraction and density atmospheric profiles resulting from data collected by the Gas Chromatograph Mass Spectrometer (GCMS) and Huygens Atmospheric Structure Instrument (HASI) onboard the Huygens probe during its descent in Titan's atmosphere to better constrain the actual mass of methane."
" Cassini data also have provided new constraints on the vertical mixing in the atmosphere of Titan. leading Yelle (2008) to derive the existence of a CTL, escape flux which is about one third the photolytic destruction rate of CIT,."," Cassini data also have provided new constraints on the vertical mixing in the atmosphere of Titan, leading Yelle (2008) to derive the existence of a $_{4}$ escape flux which is about one third the photolytic destruction rate of $_4$."
" Were. we investigate the influence of this prodigious escape on the total fractionation between CIT;D aud CIT,."," Here, we investigate the influence of this prodigious escape on the total fractionation between $_3$ D and $_4$."
 Moreover. we utilize the most recent determination of D/II obtained by Dézzard (2007) from. Cassini/CIRS infrared spectra. which indicates values of L32hs10à substantially higher than those emploved by Lunine et (1999) (7.7542.25.10.?: Orton 1992).," Moreover, we utilize the most recent determination of D/H obtained by Bézzard (2007) from Cassini/CIRS infrared spectra, which indicates values of $1.32^{+0.15}_{-0.11} \times 10^{-4}$, substantially higher than those employed by Lunine et (1999) $7.75\pm 2.25 \times 10^{-5}$; Orton 1992)."
" Since the determination of Bézzard (2007) was obtained bv fitting simaultancously the rg bands of both CTD and I CIT;D aud the 7, baud of", Since the determination of Bézzard (2007) was obtained by fitting simultaneously the $\nu$$_6$ bands of both $^{13}$ $_3$ D and $^{12}$ $_3$ D and the $\nu$$_4$ band of
€= 505 km !. and Alogο=£0.5 dex. with respect to the best-lit parameters.,"$\rm \Delta \xi=\mp$ 0.5 km $^{-1}$ , and $\rm \Delta log~g=\pm$ 0.5 dex, with respect to the best-fit parameters."
 Fig., Fig.
 shows an example for star 733., \ref{param} shows an example for star 3.
 It is clearly seen (hat models with z0.2 dex abundance variations give remarkably different molecular line profiles., It is clearly seen that models with $\pm$ 0.2 dex abundance variations give remarkably different molecular line profiles.
 Temperature variations of £200 Ix and microturbulence variation of 40.5 km/s mainly affects (he OL lines. while gravity mainly allects the CO lines.," Temperature variations of $\pm$ 200 K and microturbulence variation of $\pm$ 0.5 km/s mainly affects the OH lines, while gravity mainly affects the CO lines."
 As a further check of the statistical significance of our best-fit solution. we also compute svnthetic spectra with Try=4200 I. Aloe@=zx0.5 dex and F0.5 km 1— and with corresponding simultaneous variations of the C and O abundances (on average. £0.2 dex) to reproduce the depth of the molecular features.," As a further check of the statistical significance of our best-fit solution, we also compute synthetic spectra with $\rm \Delta T_{eff}=\pm$ 200 K, $\rm \Delta log~g=\pm$ 0.5 dex and $\rm \Delta \xi=\mp$ 0.5 km $^{-1}$, and with corresponding simultaneous variations of the C and O abundances (on average, $\pm$ 0.2 dex) to reproduce the depth of the molecular features."
 As a figure of merit of the statistical test we adopt the difference between the model and (he observed spectrum (hereafter 9)., As a figure of merit of the statistical test we adopt the difference between the model and the observed spectrum (hereafter $\delta$ ).
 In order (o quantily svstematic discrepancies. (is parameter is more powerful than the classical A7 test. which is instead equally sensitive to andsystemalic errors (seealsoOrigliaetal.2003:&Rich2004).," In order to quantify systematic discrepancies, this parameter is more powerful than the classical $\chi ^2$ test, which is instead equally sensitive to and errors \citep[see also][]{ori03,ori04}."
". Our best fit solutions always show 299 probability to be representative of the observed spectra, while spectral fitting solutions with abundance variations of 40.2 dex. due to possible svstematic uncertainties of X200 IX in temperature. £0.5 dex in gravity or $0.5 km/s in microturbulence are statistical significant αἱ 1-26 level. only."," Our best fit solutions always show $>$ probability to be representative of the observed spectra, while spectral fitting solutions with abundance variations of $\pm$ 0.2 dex, due to possible systematic uncertainties of $\pm$ 200 K in temperature, $\pm$ 0.5 dex in gravity or $\mp$ 0.5 km/s in microturbulence are statistical significant at $\sigma$ level, only."
 Hence. as a conservative estimate of the svstematic error in the derived best-fit abundances. due to the residual uncertainty in the adopted stellar parameters. one can assunme a value of <+0.1 dex.," Hence, as a conservative estimate of the systematic error in the derived best-fit abundances, due to the residual uncertainty in the adopted stellar parameters, one can assume a value of $\le \pm 0.1$ dex."
 However. it must be noted that since the stellar features under consideration show a similar trend with variations in (he stellar parameters. althoush with different sensitivitlles.| abundances are less dependent on (he adopted. stellar parameters (ie. on the svstematic errors) and (heir values are well constrained clown to & -EO0.1 dex (see also Table 1)).," However, it must be noted that since the stellar features under consideration show a similar trend with variations in the stellar parameters, although with different sensitivities, abundances are less dependent on the adopted stellar parameters (i.e. on the systematic errors) and their values are well constrained down to $\approx \pm$ 0.1 dex (see also Table \ref{tab1}) )."
 Our derived iron abundance for NGC 6791 is in excellent agreement wilh the results of Peterson&Green(1998) and Carraroetal.(2006) and only slightly lower than the etal.(2006) ones., Our derived iron abundance for NGC 6791 is in excellent agreement with the results of \citet{pet98} and \citet{car06} and only slightly lower than the \citet{gra06} ones.
 All these works suggest about 0.2 dex higher iron abundances than those obtained bv Friel&Janes(1993):et.al.(2002) from low--resolution spectroscopy ([Fe/IJ=+0.19 dex and |Fe/1I]—--0.11 dex. respectively).," All these works suggest about 0.2 dex higher iron abundances than those obtained by \citet{fj93,friel02}
 from -resolution spectroscopy ([Fe/H]=+0.19 dex and [Fe/H]=+0.11 dex, respectively)."
 Hence. the high (2-3 times solar) metalliitv of NGC 6791. now confirmed by 4 independent survevs al mecdium-high resolution in the optical and in the IR. strongly supports a 5-9 Gyr age as derived [rom the Main sequenceTrrn-Off (Carraroοἱal.2006).," Hence, the high (2-3 times solar) metallicity of NGC 6791, now confirmed by 4 independent surveys at medium-high resolution in the optical and in the IR, strongly supports a 8-9 Gyr age as derived from the Main Sequence \citep{car06}."
. Our solar [a /Fe] abundance ratio is in good agreement with thefinding by [or O. Ca. Ti. while their Si and Mg abunclances are slightly higher.," Our solar $\alpha$ /Fe] abundance ratio is in good agreement with thefinding by \citet{pet98} for O, Ca, Ti, while their Si and Mg abundances are slightly higher."
 Our (CFe] abundance is a factor of 2 lower than the one by Peterson&Green(1998). but iΕ, Our [C/Fe] abundance is a factor of 2 lower than the one by \citet{pet98} but in
 Our (CFe] abundance is a factor of 2 lower than the one by Peterson&Green(1998). but iΕν, Our [C/Fe] abundance is a factor of 2 lower than the one by \citet{pet98} but in
observation are indicated by the size of the symbols.,observation are indicated by the size of the symbols.
" The small beam broadening by the comet, reported by Boissier et al. (2008))"," The small beam broadening by the comet, reported by Boissier et al. \cite{boi}) )"
 shows that the source is optically thin., shows that the source is optically thin.
" The two data sets are interpolated, suggesting a signal loss of 7 per day."," The two data sets are interpolated, suggesting a signal loss of 7 per day."
 The series of nuclear magnitudes m» shows a similar slope., The series of nuclear magnitudes $m_2$ shows a similar slope.
" In a separate paper, Altenhoff et al. (2008))"," In a separate paper, Altenhoff et al. \cite{alt1}) )"
" show that most cometary mm/radio light curves can be represented by the following equation: with A and r the geocentric and heliocentric distances in AU, respectively."," show that most cometary mm/radio light curves can be represented by the following equation: with $\Delta$ and $r$ the geocentric and heliocentric distances in AU, respectively."
" The constant S,ος 74.5 is derived from the last data points."," The constant $S_{\nu,0}$ = 74.5 is derived from the last data points."
 Thus the light curve is calculated and plotted in Fig., Thus the light curve is calculated and plotted in Fig.
 1., 1.
" It is obviously a reasonable fit for the time after day 33, when insolation and dust production (determining the intensity of the mm radiation) are apparently coming to equilibrium."," It is obviously a reasonable fit for the time after day 33, when insolation and dust production (determining the intensity of the mm radiation) are apparently coming to equilibrium."
" For the first 30 days, this radio light curve is the baseline for the burst."," For the first 30 days, this radio light curve is the baseline for the burst."
" As a further indicator of cometary activity, we use the nuclear magnitude, m», reported with the astrometric positions (Marsden 2007))."," As a further indicator of cometary activity, we use the nuclear magnitude, $m_2$ , reported with the astrometric positions (Marsden \cite{mar1}) )."
 These values with limited accuracy are averaged over three days (typically over 100 observations) to reduce the noise., These values with limited accuracy are averaged over three days (typically over 100 observations) to reduce the noise.
 These data also confirm increased nuclear activity in the first 30 days., These data also confirm increased nuclear activity in the first 30 days.
 Red circles show the H3O production rates measured with the Solar Wind ANisotropy (SWAN) experiment on the SOlar Heliospheric Observatory (SOHO) reported by Combi (2007))., Red circles show the $_2$ O production rates measured with the Solar Wind ANisotropy (SWAN) experiment on the SOlar Heliospheric Observatory (SOHO) reported by Combi \cite{com}) ).
" This system has a beam of about one degree, probing the water production of about 4 days."," This system has a beam of about one degree, probing the water production of about 4 days."
" 'This may be a crude guess, considering that we are using observing results obtained with very different resolutions."," This may be a crude guess, considering that we are using observing results obtained with very different resolutions."
" Even though we guess that, with the resulting smearing, the production rate might fit even better to our observed extended cometary activity."," Even though we guess that, with the resulting smearing, the production rate might fit even better to our observed extended cometary activity."
 Spectroscopic observations of HCN by Biver et al. (2008)), Spectroscopic observations of HCN by Biver et al. \cite{biv2}) )
" at Pico Veleta and at the Caltech Submillimeter Observatory (CSO), and by Drahus et al. (2007,,2008))"," at Pico Veleta and at the Caltech Submillimeter Observatory (CSO), and by Drahus et al. \cite{dra}, \cite{dra1}) )"
" with the Arizona Radio Observatory (ARO), are shown for comparison."," with the Arizona Radio Observatory (ARO), are shown for comparison."
 The data sets are consistent which each other and show a steeper decay than the cometary activity described before., The data sets are consistent which each other and show a steeper decay than the cometary activity described before.
" Optically, the scattered light by small dust particles is dominating the appearance of comets, even though the mass of these particles is low."," Optically, the scattered light by small dust particles is dominating the appearance of comets, even though the mass of these particles is low."
 Sekanina (1982)) has estimated the mass of 2 wm sized fine dust in comet 17P/Holmes (see Table 2) near its outbreak., Sekanina \cite{sek1}) ) has estimated the mass of $2~\mu$ m sized fine dust in comet 17P/Holmes (see Table 2) near its outbreak.
 The size of the scattering particles is too small to detect with radio or mm telescopes., The size of the scattering particles is too small to detect with radio or mm telescopes.
 This dust is responsible for the optical appearance seen at magnitude m4., This dust is responsible for the optical appearance seen at magnitude $m_1$.
 The particulate dust and the bulk of the molecular gas are almost invisible optically., The particulate dust and the bulk of the molecular gas are almost invisible optically.
" Radio and mm continuum observations measure the thermal emission of dust particles of size > of the observing wavelength, here > 0.2 mm."," Radio and mm continuum observations measure the thermal emission of dust particles of size $\ge$ of the observing wavelength, here $\ge$ 0.2 mm."
" Since the observed signal is proportional to the integrated particle cross sections, but the particle mass is proportional to its volume, the mass of big particles is underestimated, so observations at different wavelengths are needed for a more precise mass estimate.. We estimate the dust mass with the photometric diameter to be the size of a disk at the distance of the comet with its equilibrium temperature, radiating as black body, yielding the same flux density as the radio/mm halo."," Since the observed signal is proportional to the integrated particle cross sections, but the particle mass is proportional to its volume, the mass of big particles is underestimated, so observations at different wavelengths are needed for a more precise mass estimate.. We estimate the dust mass with the photometric diameter to be the size of a disk at the distance of the comet with its equilibrium temperature, radiating as black body, yielding the same flux density as the radio/mm halo."
" For cometary dust, we find that the black body condition (emissivity ~1) is fulfilled with a density of 1 g cm7? and a layer depth of 3 wavelengths (as confirmed by the rigorous halo evaluation for comets Hyakutake and Hale-Bopp (Altenhoff et al. 2000))."," For cometary dust, we find that the black body condition (emissivity $\approx$ 1) is fulfilled with a density of 1 g $^{-3}$ and a layer depth of 3 wavelengths (as confirmed by the rigorous halo evaluation for comets Hyakutake and Hale-Bopp (Altenhoff et al. \cite{alt2}) )."
 This allows calculation of the dust mass in the halo for any observed signal., This allows calculation of the dust mass in the halo for any observed signal.
" The average particle moves through the telescope's diffraction beam in about 60 hours, and the resulting dust production rate and the dust mass in the beam are listed in Table 2."," The average particle moves through the telescope's diffraction beam in about 60 hours, and the resulting dust production rate and the dust mass in the beam are listed in Table 2."
" The radio light curve, as defined above, can be extrapolated backwards over the whole apparition to calculate“hypothetical” signals and masses that would"," The radio light curve, as defined above, can be extrapolated backwards over the whole apparition to calculate“hypothetical” signals and masses that would"
ones.,ones.
 Some individuals of this subsample also. show. similar to the P Cygni-type ones. higher velocity absorptioαυ] through superimposed to à narrower component (best seen in. e.g... Q084243431. QI235-1453).," Some individuals of this subsample also show, similar to the P Cygni-type ones, higher velocity absorption through superimposed to a narrower component (best seen in, e.g., Q0842+3431, Q1235+1453)."
 The introduction of a significant rotation of the wind around the polar axis is requirecο to produce the broad asymmetric emission peaks observed 1S57 the line profile of seven out of the ten objects in ou sample (Q0019+0107. Q0145--416. Q0226-1024. Q032-3344. Q08424+3431. Q1235+1453. and Q1239+0995).," The introduction of a significant rotation of the wind around the polar axis is required to produce the broad asymmetric emission peaks observed in the line profile of seven out of the ten objects in our sample (Q0019+0107, Q0145+416, Q0226-1024, Q032-3344, Q0842+3431, Q1235+1453, and Q1239+0995)."
 The rotational speed generally needs to be quite higher than the polar terminal velocity (reaching up to 50 of2 po Vinay) and Is. approximatelyP. equal to the equatorial wind terminal velocity., The rotational speed generally needs to be quite higher than the polar terminal velocity (reaching up to $50$ of $\rm{v}_{max}^{po}$ ) and is approximately equal to the equatorial wind terminal velocity.
 For the P type profiles (Q1333+2840. QI413-1143 or even QOO4I-3023). it is also necessary to consider a rotation of the wind around the polar axis. although 1t must be smaller to properly account for the higher emission peak and the sharp transition between the emission and the absorption parts of the profiles.," For the P Cygni-type profiles (Q1333+2840, Q1413+1143 or even Q0041-4023), it is also necessary to consider a rotation of the wind around the polar axis, although it must be smaller to properly account for the higher emission peak and the sharp transition between the emission and the absorption parts of the profiles."
 In each case. the best fit was chosen by eye. once the model was qualitatively similar to the profile of the observed line.," In each case, the best fit was chosen by eye, once the model was qualitatively similar to the profile of the observed line."
 The simulation time needed to produce a single line profile in these optically thick winds prevents us from using à y type technique while searching for the best model., The simulation time needed to produce a single line profile in these optically thick winds prevents us from using a $\chi^2$ type technique while searching for the best model.
" However. this is not a main drawback since our main goal is to show that a simple wind model is able to approximately reproduce a variety of resonance line profiles observed in BAL QSOs,"," However, this is not a main drawback since our main goal is to show that a simple wind model is able to approximately reproduce a variety of resonance line profiles observed in BAL QSOs."
" Moreover. given the degeneracy between some of the model parameters (Ap, with /. vi with i. 8 with a. etc). as well as the difficulty in some cases of correctly evaluating vi"". or other model parameters. more than one best fit is generally possible."," Moreover, given the degeneracy between some of the model parameters $k_{pm}$ with $i$, $\rm{v}_{max}^{eq}$ with $i$, $\beta$ with $\alpha$ , etc), as well as the difficulty in some cases of correctly evaluating $\rm{v}_{max}^{po}$ or other model parameters, more than one best fit is generally possible."
 The absence of the two-component wind signatures defined above in the line profile of some objects led us to define a third subsample of line profiles., The absence of the two-component wind signatures defined above in the line profile of some objects led us to define a third subsample of line profiles.
 These line profiles can be fitted by a two-component wind (see upper panel of Fig. 5))., These line profiles can be fitted by a two-component wind (see upper panel of Fig. \ref{fite2}) ).
 However. some profiles (the prototype being Q0019+0107) do not show evidence of a polar absorption component at high velocities. suggesting that the polar outflow may not be present in these objects.," However, some profiles (the prototype being Q0019+0107) do not show evidence of a polar absorption component at high velocities, suggesting that the polar outflow may not be present in these objects."
 Several tests performed on such line profiles with MCRT showed that Q0019-0107-type line profiles can be produced in a single. rapidly rotating equatorial wind seen nearly edge-on (see lower left panel of Fig. 5)).," Several tests performed on such line profiles with MCRT showed that Q0019+0107-type line profiles can be produced in a single, rapidly rotating equatorial wind seen nearly edge-on (see lower left panel of Fig. \ref{fite2}) )."
 In the same vein. in the bottom right panel of Fig. 5..," In the same vein, in the bottom right panel of Fig. \ref{fite2},"
 we illustrate how the line profile of Q0041-4023 can be reproduced by a two-component wind seen nearly pole-on., we illustrate how the line profile of Q0041-4023 can be reproduced by a two-component wind seen nearly pole-on.
 This arises when a single deep absorption trough ts associated. with à quasi-symmetric emission profile., This arises when a single deep absorption trough is associated with a quasi-symmetric emission profile.
 Once again. given the uncertainties on the wind parametersbecause of the lack of clear signatures in the," Once again, given the uncertainties on the wind parametersbecause of the lack of clear signatures in the"
"(non-J band detection) stars, which include the stars in the CTTS region or not detected in the J band, are (12/34) and (13/26) for the SW and NE clusters, respectively.","$J$ band detection) stars, which include the stars in the CTTS region or not detected in the $J$ band, are (12/34) and (13/26) for the SW and NE clusters, respectively."
" The CTTS and infrared-excess (H—Ks> 1.5) sources are identified in Fig. 4,,"," The CTTS and infrared-excess $H-K_S > 1.5$ ) sources are identified in Fig. \ref{ysomark},"
" with red crosses and green boxes, respectively."," with red crosses and green boxes, respectively."
 Some very red objects located at outskirts of this molecular seem to be isolated star-forming sources., Some very red objects located at outskirts of this molecular seem to be isolated star-forming sources.
 The nature of these sources will be discussed in the second paper., The nature of these sources will be discussed in the second paper.
 We identified about 800 sources in total within the cloud boundary., We identified about 800 sources in total within the cloud boundary.
 It was expected that a significant number of background sources exist toward the target cloud in the observed bands., It was expected that a significant number of background sources exist toward the target cloud in the observed bands.
 It is an important but very difficult job to separate the member sources from the background., It is an important but very difficult job to separate the member sources from the background.
" Without proper motion data for the cluster, statistical subtraction is the only way to determine the member stars."," Without proper motion data for the cluster, statistical subtraction is the only way to determine the member stars."
" To subtract the background stars, we chose a region outside the molecular boundary, centered at a=0538""40.1* 6=+35°42'07.7”, as a reference field withno extinction."," To subtract the background stars, we chose a region outside the molecular boundary, centered at $\alpha=05^h38^m40.1^s$ $\delta=+35^{\circ}42' 07.7""$, as a reference field with extinction."
 The reference field was chosen in the area well outside the cloud boundary based on radio observations., The reference field was chosen in the area well outside the cloud boundary based on radio observations.
" By assuming that there exists thesame background stars in the target cloud (the S233IR cloud), we removed expected background sources statistically, following the procedure summarized by Joseetal.(2008):: select a star on the color-magnitude diagram (CMD) of the reference field, eliminate the star with same color and magnitude on the CMD of the target field within the observed uncertainties (A(H—K3)< 0.08 and AKs< 0.07)."," By assuming that there exists the background stars in the target cloud (the S233IR cloud), we removed expected background sources statistically, following the procedure summarized by \cite{jose08}: select a star on the color-magnitude diagram (CMD) of the reference field, eliminate the star with same color and magnitude on the CMD of the target field within the observed uncertainties $\Delta (H-K_S) \leq$ 0.08 and $\Delta K_S \leq$ 0.07)."
" By repeating this procedure for all sources in CMD, we subtract background sources in the target field."," By repeating this procedure for all sources in CMD, we subtract background sources in the target field."
 There were 254 sources cleaned in a 5' radius region., There were 254 sources cleaned in a $\arcmin$ radius region.
" This leads to a number of ~2 background sources in 30"" radius region.", This leads to a number of $\sim2$ background sources in $\arcsec$ radius region.
" In other words, and of the sources are associated with SW and NE cluster, respective."," In other words, and of the sources are associated with SW and NE cluster, respective."
 Fig., Fig.
" 5 shows the color-magnitude diagram (Kg vs. H— Kg) for the sources in the S233IR cloud, the reference field, and the background cleaned “member sources"", respectively."," \ref{cmd} shows the color-magnitude diagram $K_S$ vs. $H-K_S$ ) for the sources in the S233IR cloud, the reference field, and the background cleaned “member sources”, respectively."
 The red lines in the panels represent the age-averaged isochrone between 1.0 to 10.0 Myrs from (1994)., The red lines in the panels represent the age-averaged isochrone between 1.0 to 10.0 Myrs from \cite{dm94}.
". Although there should exist various uncertainties in this process, we think that this method is the most efficient way to determine the member sources at least within the observational uncertainties."," Although there should exist various uncertainties in this process, we think that this method is the most efficient way to determine the member sources at least within the observational uncertainties."
" Additionally, stars on the left side of the isochrone in Fig."," Additionally, stars on the left side of the isochrone in Fig."
 5 were removed as foreground stars., \ref{cmd} were removed as foreground stars.
" The final result, after the background elimination, is shown in the right panel of Fig. 5.."," The final result, after the background elimination, is shown in the right panel of Fig. \ref{cmd}."
" With these “member” sources, we made extinction correction for pre-main sequence stars (PMSs) and CTTSs with two different ways, respectively, using two diagrams (Fig."," With these “member” sources, we made extinction correction for pre-main sequence stars (PMSs) and CTTSs with two different ways, respectively, using two diagrams (Fig."
 3 and Fig. 5))., \ref{hr} and Fig. \ref{cmd}) ).
" Extinction corrections for PMSs were made by projecting them back to the mean isochrone along the reddening vector on Fig. 5,, (H—Kgobserved=Kg)'""**-0.063xAy,"," Extinction corrections for PMSs were made by projecting them back to the mean isochrone along the reddening vector on Fig. \ref{cmd}, , $(H-K_S)^{observed}=(H-K_S)^{true}+0.063 \times A_V$,"
 by assuming a normal reddening law (Rieke&Lebofsky1985)., by assuming a normal reddening law \citep{rl85}.
. The error of dereddened Kg magnitudes is expected <0.2 from the mean isochrone we used (Massietal.2006)., The error of dereddened $K_S$ magnitudes is expected $\leq 0.2$ from the mean isochrone we used \citep{massi06}.
. The extinction can be derived by comparing observed and intrinsic color of each star., The extinction can be derived by comparing observed and intrinsic color of each star.
" On the other hand, extinctions of the CTTSs (filled symbols in the figures) were corrected by projecting them back to the CTTS locus on Fig. 3.."," On the other hand, extinctions of the CTTSs (filled symbols in the figures) were corrected by projecting them back to the CTTS locus on Fig. \ref{hr}."
" The averaged visual extinction (Ay) were found to be 9.8+5.2 (the SW cluster, 36 stars), 28.9+10.4 (the NE cluster, 25 stars), and 13.0410.4 (“distributed stars"", 124 stars)."," The averaged visual extinction $A_V$ ) were found to be $\pm$ 5.2 (the SW cluster, 36 stars), $\pm$ 10.4 (the NE cluster, 25 stars), and $\pm$ 10.4 (“distributed stars”, 124 stars)."
" These extinction are larger than the previous values by a factor of about 1.3—2 (PCS), which result fromdeeper observations"," These extinction are larger than the previous values by a factor of about $1.3-2$ (PCS), which result fromdeeper observations"
"structure could be caused by orbital motion in a binary black hole system, coupled with the interaction of the plasma jet with the surrounding medium.","structure could be caused by orbital motion in a binary black hole system, coupled with the interaction of the plasma jet with the surrounding medium."
" Indeed, the binary black hole scenario could explain the periodicity observed in the radio light curves of BL Lacertae 2009b),, the discovery of a precessing jet nozzle with the VLBA 2003),, and possibly the parsec-to-kiloparsec jet misalignment 2010)."," Indeed, the binary black hole scenario could explain the periodicity observed in the radio light curves of BL Lacertae , the discovery of a precessing jet nozzle with the VLBA , and possibly the parsec-to-kiloparsec jet misalignment ."
". Moreover, the analysis of the BL Lacertae spectral evolution in 2000-2008 by favoured a picture where the optical and near-IR flux and colour variability can be explained by a variable viewing angle of the emitting region."," Moreover, the analysis of the BL Lacertae spectral evolution in 2000–2008 by favoured a picture where the optical and near-IR flux and colour variability can be explained by a variable viewing angle of the emitting region."
 These authors also suggested that a fractal helical structure may be at the origin of the different time scales of variability., These authors also suggested that a fractal helical structure may be at the origin of the different time scales of variability.
" The values of the angles ὅ=2° and y= 4.5—-S°, as well as the Lorentz factor I=7 adopted in the model fits for the low-energy component, agree very well with the corresponding values of(2010),, thus supporting the common interpretation."," The values of the angles $\zeta=2\degr$ and $\psi=4.5$ $5\degr$, as well as the Lorentz factor $\Gamma=7$ adopted in the model fits for the low-energy component, agree very well with the corresponding values of, thus supporting the common interpretation."
" The helix pitch angle ὅ=8? found for the high-energy component indicates that this inner jet helical region would be more twisted than the outer, lower-energy one."," The helix pitch angle $\zeta=8\degr$ found for the high-energy component indicates that this inner jet helical region would be more twisted than the outer, lower-energy one."
" In practice, our model results indicate a helical jet whose axis is bent between the X-ray and optical regions by about 2? (see the values of y in Table 4)) and that is more wrapped near the apex and then tends to relax with a decreasing pitch angle."," In practice, our model results indicate a helical jet whose axis is bent between the X-ray and optical regions by about $2\degr$ (see the values of $\psi$ in Table \ref{modelfit}) ) and that is more wrapped near the apex and then tends to relax with a decreasing pitch angle."
" The different orientations assumed by such a jet in 2008 and 1997 are sketched in refsketch,, where all the angles are strongly increased for clarity."," The different orientations assumed by such a jet in 2008 and 1997 are sketched in \\ref{sketch}, where all the angles are strongly increased for clarity."
" The thermal emission component that we added to the helical jet model is justified by the UV excess found in the OM data from XMM-Newton, and (though with less evidence) in the UVOT data from Swift."," The thermal emission component that we added to the helical jet model is justified by the UV excess found in the OM data from XMM-Newton, and (though with less evidence) in the UVOT data from Swift."
" As discussed in the present paper and in(2009), the amount of this excess strongly depends on both the Galactic extinction and instrument calibration, but it is not easy to cancel it out completely."," As discussed in the present paper and in, the amount of this excess strongly depends on both the Galactic extinction and instrument calibration, but it is not easy to cancel it out completely."
" In any case, showed that after twelve years from the first detection of the Ha broad emission line by and2000)mainBodyCitationEnd5426]cor96, the Ha line is still there, even more luminous than before."," In any case, showed that after twelve years from the first detection of the $\alpha$ broad emission line by and, the $\alpha$ line is still there, even more luminous than before."
 This suggests that a disc is also there to photoionise the broad line region., This suggests that a disc is also there to photoionise the broad line region.
" Photons coming from the disc or broad line region could then enter the jet, and be inverse-Compton scattered, giving rise to other high-energy emission components that are sometimes invoked to account for the SED properties of blazars."," Photons coming from the disc or broad line region could then enter the jet, and be inverse-Compton scattered, giving rise to other high-energy emission components that are sometimes invoked to account for the SED properties of blazars."
" In particular, the 1997 outburst state has previously been interpreted by in terms of three emission components: synchrotron, synchrotron self-Compton, and Comptonisation of the broad emission line flux."," In particular, the 1997 outburst state has previously been interpreted by in terms of three emission components: synchrotron, synchrotron self-Compton, and Comptonisation of the broad emission line flux."
 Similar results were obtained by and by(2002)., Similar results were obtained by and by.
". Our “geometrical” interpretation does not require these external-Compton emission components, which are not expected to contribute if the jet emission regions are parsecs away from the central black hole 2010b).."," Our “geometrical"" interpretation does not require these external-Compton emission components, which are not expected to contribute if the jet emission regions are parsecs away from the central black hole ."
 (radiusz425-850 SO» (radius<S150 SO» >2x10? C!*O H2CO ????;; ?)). 10 Μο. hypotheses for the formation process.," $\approx425$ $_2$ $\lesssim$ $_2$ $\gtrsim2\times10^9$ $^{17}$ $_2$ \citealt{1971Larson,
1974Kahn,1977Yorke, 1994Beech}; \citealt{2007Zinnecker}) $\sim$ $_{\sun}$ \citealt{1987Wolfire,1989Nakano, 1996Jijina, 2002Yorke,
2000Norberg, 2003McKee, 2005Krumholz}) hypotheses for the formation process."
" Perhaps the most important ones are: (1) large accretion rates (3 or 4 orders of magnitude greater than those observed in low- (2) competitive accretion between small protostars of the same cluster, that could result in eventual mergers and (3) accretion of ionized material, even after the (???7)),formation of a compact HII region generated by the protostar (?7))."," Perhaps the most important ones are: (1) large accretion rates (3 or 4 orders of magnitude greater than those observed in low-mass protostars) through circumstellar disks \citealt{1995Walmsley, 1996Jijina, 2003McKee,
2005Zhang,2007Banerjee}) ), (2) competitive accretion between small protostars of the same cluster, that could result in eventual mergers \citealt{1998Bonnell,2008Clarke,2011Moeckel,2011Baumgardt}) ), and (3) accretion of ionized material, even after the formation of a compact HII region generated by the protostar \citealt{2002Keto, 2006Keto}) )."
" In recent years, several works have provided evidence for the presence of collimated jets 80-81, ?;; Cep A, ?;; IRAS 23139, ?;; IRAS 16547, ?)), (HHmolecular outflows (see a summary in ??)), and flattened structures of dust and gas (some with rotation and some with infall signposts; e.g., Cep A, ?;; IRAS 20126, ?;; AFGL 2591, ?:; W51 North, ?;; IRAS 16547, ?;; W33A-MMI, ?)), surrounding high-mass protostars."," In recent years, several works have provided evidence for the presence of collimated jets (HH 80-81, \citealt{1993Marti}; Cep A, \citealt{2006Curiel}; IRAS 23139, \citealt{2006Trinidad}; IRAS 16547, \citealt{2008Rodriguez}) ), molecular outflows (see a summary in \citealt{2005Zhang,2007Arce}) ), and flattened structures of dust and gas (some with rotation and some with infall signposts; e.g., Cep A, \citealt{2005Patel}; IRAS 20126, \citealt{2005Cesaroni}; AFGL 2591, \citealt{2006VanderTak}; W51 North, \citealt{2008Zapata}; IRAS 16547, \citealt{2009Franco-Hernandez}; W33A-MM1, \citealt{2010GalvanMadrid}) ), surrounding high-mass protostars."
" The evidence leads to the interpretation that massive star formation is analogous to low-mass star formation, that is, via accretion from flatrotating disk, with a jet of ionized material, and awith an associated molecular outflow."," The evidence leads to the interpretation that massive star formation is analogous to low-mass star formation, that is, via accretion from a flatrotating disk, with a jet of ionized material, and with an associated molecular outflow."
" However, the physical characteristics of the possible"," However, the physical characteristics of the possible"
associated wilh dSph galaxies.,associated with dSph galaxies.
 Terzan 7 and Pal 12 are the only. elobular clusters known to lack the Na-O anticorrelation (hat is ubiquitous in Galactic globular clusters (Carreta οἱ al., Terzan 7 and Pal 12 are the only globular clusters known to lack the Na-O anticorrelation that is ubiquitous in Galactic globular clusters (Carreta et al.
 2010a)., 2010a).
 Using previous distance measures. LMIOb concluded that Terzan 7 was unlikely to be aligned by chance based on the clusters location. radial velocity aud distance.," Using previous distance measures, LM10b concluded that Terzan 7 was unlikely to be aligned by chance based on the cluster's location, radial velocity and distance."
 However. we decided to re-examine (he latter point in light of our new distance estimates.," However, we decided to re-examine the latter point in light of our new distance estimates."
 To determine the status of Terzan T. we re-ran the LM10a model and checked the status of all the Ser member clusters [or varying Ser distances.," To determine the status of Terzan 7, we re-ran the LM10a model and checked the status of all the Sgr member clusters for varying Sgr distances."
" If Ser is at a distance of 28 κρο, Arp 2. Terzan 7 and Terzan 8 all can be matched with individual test particles in the Ser simulation."," If Sgr is at a distance of 28 kpc, Arp 2, Terzan 7 and Terzan 8 all can be matched with individual test particles in the Sgr simulation."
 In the simulation. (he clusters have come unbound on the last pericenter (0.1 Gyr ago) and will move much further (70-110 degrees) downstream before the next pericenter.," In the simulation, the clusters have come unbound on the last pericenter (0.1 Gyr ago) and will move much further (70-110 degrees) downstream before the next pericenter."
 NI54. of course. is in the center of Ser in this simulation Increasing (he Ser distance to 30 kpe and placing M54 2 kpe in the foreground changes {his picture somewhat.," M54, of course, is in the center of Sgr in this simulation Increasing the Sgr distance to 30 kpc and placing M54 2 kpc in the foreground changes this picture somewhat."
 All four clusters match test particles within the Ser debris. but Terzan 7 requires a much more generous search tolerance.," All four clusters match test particles within the Sgr debris, but Terzan 7 requires a much more generous search tolerance."
 Using the D3 [rom LMIOb. we lind (hat Terzan 7's P3 value increases [rom 0.043 (0 0.12 (compared to «001 lor Terzan 5 and Arp 2).," Using the P3 from LM10b, we find that Terzan 7's P3 value increases from 0.043 to 0.12 (compared to .001 for Terzan 8 and Arp 2)."
 Given that ~6 such false-positives expected at the level P3 ~12%.. it seems possible that Terzan 7 could be a chance alignment.," Given that $\sim 6$ such false-positives expected at the level P3 $\sim 12$, it seems possible that Terzan 7 could be a chance alignment."
 Given this now more troubling statistic. measuring an absolute proper motion for Terzan 7 is criücal to allirmine its status as a menber of Ser.," Given this now more troubling statistic, measuring an absolute proper motion for Terzan 7 is critical to affirming its status as a member of Sgr."
 If Terzan 7 is indeed a member. the distance discrepancy hints that Terzan 7 has a different dynamical history than the other classical Ser member clusters.," If Terzan 7 is indeed a member, the distance discrepancy hints that Terzan 7 has a different dynamical history than the other classical Sgr member clusters."
 As for M54. the simulation with the cluster in front of the dSph indicates that M54 should sink to (he center of Ser via dvinamical friction in approximately 3 Gyr if the dSph has a cuspy core consistent wilh (the analvsis of DOS.," As for M54, the simulation with the cluster in front of the dSph indicates that M54 should sink to the center of Sgr via dynamical friction in approximately 3 Gyr if the dSph has a cuspy core consistent with the analysis of B08."
 This would seem to argue against the idea that M54 is 1-2 kpe in front of the dSph., This would seem to argue against the idea that M54 is 1-2 kpc in front of the dSph.
 However. if we assume a shallower density profile for Ser. M54 maa stall its descent near the core radius of ~2 kpe (M03).," However, if we assume a shallower density profile for Sgr, M54 may stall its descent near the core radius of $\sim 2$ kpc (M03)."
 Given (he similarity between this distance and our measured. M54-Sgr clistance (2 kpc) this may already have happened. although it would seem a remarkable coincidence that M54. has stalled precisely along our line of sight to," Given the similarity between this distance and our measured M54-Sgr distance (2 kpc) this may already have happened, although it would seem a remarkable coincidence that M54 has stalled precisely along our line of sight to"
Transitions appearing in Figures ].. 2.. and 43.. but not described above. provide limits for model constraints. either because they are not detected or because they thought to be affected by blends.,"Transitions appearing in Figures \ref{fig-q0130-sys}, , \ref{fig-q1009-sys},, and \ref{fig-q1700-sys}, but not described above, provide limits for model constraints, either because they are not detected or because they thought to be affected by blends."
 Our calculations were performed with version 07.02.01 of Cloudy. last described by Ferland(1998).," Our calculations were performed with version 07.02.01 of Cloudy, last described by \citet{fer98}."
. Our modeling assumes a series of plane-parallel slabs of gas (clouds) exposed to the ionizing continuum from the central engine., Our modeling assumes a series of plane-parallel slabs of gas (clouds) exposed to the ionizing continuum from the central engine.
 The gas within each absorbing cloud is assumed to have a uniform density. metallicity and abundance pattern.," The gas within each absorbing cloud is assumed to have a uniform density, metallicity and abundance pattern."
 In most cases. We assume a solar abundance pattern (Holweger2001).. so that for element /.A;/A;.. =Z/Z. where Aj=nj/11.," In most cases, we assume a solar abundance pattern \citep{hol01}, so that for element $i$, $A_i/A_{i,\odot}=Z/Z_\odot$ where $A_i=n_i/n_{\rm H}$."
 When an adequate fit cannot be achieved using the solar abundance pattern. we consider deviations.," When an adequate fit cannot be achieved using the solar abundance pattern, we consider deviations."
 The intensity of the tonizing continuum is parameterized by the ionization parameter. where ris the distance of the illuminated face of the cloud from the continuum source. εἰ Is the lowest energy required to phototonize the gas. Le.. €;=| Ry. and &» is the high energy cutoffof the SED.," The intensity of the ionizing continuum is parameterized by the ionization parameter, where $r$ is the distance of the illuminated face of the cloud from the continuum source, $\epsilon_1$ is the lowest energy required to photoionize the gas, i.e., $\epsilon_1=1$ Ry, and $\epsilon_2$ is the high energy cutoff of the SED."
 In our model. we take £x=7.354«10° Ry.," In our model, we take $\epsilon_2=7.354\times10^6$ Ry."
 Each of our models are specified by U and nj. which (given the quasar luminosity and spectral shape) corresponds to a given r.," Each of our models are specified by $U$ and $n_{\rm H}$, which (given the quasar luminosity and spectral shape) corresponds to a given $r$."
 We also assume that all the tons within a cloud have the same coverage fraction. and that the gas cloud is in a state of thermal equilibrium. so it is parameterized by asingle electron temperature. 7...," We also assume that all the ions within a cloud have the same coverage fraction, and that the gas cloud is in a state of thermal equilibrium, so it is parameterized by a single electron temperature, $T_e$."
 The assumption of the same coverage fraction for different lines is likely to be valid for those from ions with similar ionization states. particularly aand wwhich are the most important constraints for out models.," The assumption of the same coverage fraction for different lines is likely to be valid for those from ions with similar ionization states, particularly and which are the most important constraints for out models."
 aabsorption may also arise from additional regions. but in any case will provide a lower limit on metallicity.," absorption may also arise from additional regions, but in any case will provide a lower limit on metallicity."
 In our favored models. the clouds are optically thin to the incident continuum so that the incident SED does not change after the ionizing photons pass through an absorbing cloud.," In our favored models, the clouds are optically thin to the incident continuum so that the incident SED does not change after the ionizing photons pass through an absorbing cloud."
 We have measured the Doppler 5 parameters. column densities and coverage fractions of thedoublets. as," We have measured the Doppler $b$ parameters, column densities and coverage fractions of thedoublets, as"
al low temperatures the strong lines which are present display self absorption even if it is nol immediately apparent [rom (he line shape and at high temperatures there are lew lines to draw conclusive comparisons from. since they are not given in HITRAN.,"at low temperatures the strong lines which are present display self absorption even if it is not immediately apparent from the line shape and at high temperatures there are few lines to draw conclusive comparisons from, since they are not given in HITRAN."
" The overall maximum error of (he empirical lower state energies in the line list should therefore be taken asον, but we believe that the quality [actor gives a better indication of how accurate the empirical lower state energy is for each Ine."," The overall maximum error of the empirical lower state energies in the line list should therefore be taken as, but we believe that the quality factor gives a better indication of how accurate the empirical lower state energy is for each line."
 There are (wo approaches to obtaining an ammonia line list to model brown clwarl and exoplanet spectra: the first is experimental measurement consistent with the work presented here and (he second is an theoretical calculation., There are two approaches to obtaining an ammonia line list to model brown dwarf and exoplanet spectra: the first is experimental measurement consistent with the work presented here and the second is an theoretical calculation.
 These (wo methods each have their own strengths and weaknesses. but in general are complementary.," These two methods each have their own strengths and weaknesses, but in general are complementary."
 The experimental approach provides fewer lines but more accurate line positions. while the theoretical approach provides many more lines but with reduced line position accuracy.," The experimental approach provides fewer lines but more accurate line positions, while the theoretical approach provides many more lines but with reduced line position accuracy."
 Calculated line lists ave particularly useful for assigning quantum numbers to the measured lines. which can then be used to improve the calculations.," Calculated line lists are particularly useful for assigning quantum numbers to the measured lines, which can then be used to improve the calculations."
 Such line assignments of new Να data are currently underway and will be reported elsewhere (Zobovοἱal.2011)., Such line assignments of new $_{3}$ data are currently underway and will be reported elsewhere \citep{zobov11}.
. The line lists provided are given in (he format shown in Table 7 and can be obtained as electronic supplements wilh extra details and spectra provided upon request., The line lists provided are given in the format shown in Table \ref{tab7} and can be obtained as electronic supplements with extra details and spectra provided upon request.
 It is important to note that the line lists are temperature specific aud should only be used at the appropriate temperature., It is important to note that the line lists are temperature specific and should only be used at the appropriate temperature.
 If the intensities need to be scaled. then (he closest temperature line list should be chosen and (he empirical lower state energies can be used to adjust the lines intensities as needed (using Equation 3) to reach additional temperatures.," If the intensities need to be scaled, then the closest temperature line list should be chosen and the empirical lower state energies can be used to adjust the lines intensities as needed (using Equation 3) to reach additional temperatures."
 We are currently in the process of completing our NIL; measurements in (he 3 micron region and are set (o record new spectra in (he near infrared: a similar comprehensive study ol CIL; is also underway., We are currently in the process of completing our $_{3}$ measurements in the 3 micron region and are set to record new spectra in the near infrared; a similar comprehensive study of $_{4}$ is also underway.
worse.,worse.
 For the strongest. field. considered: we can see that he N-body satellite quickly develops a constant density core. the density of which decreases with time.," For the strongest field considered we can see that the N-body satellite quickly develops a constant density core, the density of which decreases with time."
 Our model does not reproduce this behaviour., Our model does not reproduce this behaviour.
 This may rellect the act that our model applies only first. order. perturbations o the particle orbits., This may reflect the fact that our model applies only first order perturbations to the particle orbits.
 As frida is increased. the orbits of xwticles which remain bound to the satellite become ever more perturbed due to the tidal force., As $f_{\rm tidal}$ is increased the orbits of particles which remain bound to the satellite become ever more perturbed due to the tidal force.
 A measure of this »erturbation can be constructed by averaging —NEZE (see eqn., A measure of this perturbation can be constructed by averaging $-\Delta E/E$ (see eqn.
 42. for the definition of Af) over all particles which remain bound. which measures the fractional change in xwticle orbital energies.," \ref{eq:deltaE} for the definition of $\Delta E$ ) over all particles which remain bound, which measures the fractional change in particle orbital energies."
 This quantity. after one iteration. is 0:06. 0.21 and 0.30 for fiii=5:8107. 5.8«107? and 5.85107 respectively.," This quantity, after one iteration, is 0.08, 0.21 and 0.30 for $f_{\rm tidal}=5.8\times 10^{-4}$, $5.8\times 10^{-3}$ and $5.8\times 10^{-2}$ respectively."
 Thus. for the strongest. field considered this factor is becoming quite large.," Thus, for the strongest field considered this factor is becoming quite large."
 Furthermore. [or an NEW potential. the gravitational potential varies only very slowly with radius at radii less than the scale radius.," Furthermore, for an NFW potential, the gravitational potential varies only very slowly with radius at radii less than the scale radius."
 Thus. a relatively small perturbation in the energies of particles at these radit can lead to a large perturbation in their apocentric distance.," Thus, a relatively small perturbation in the energies of particles at these radii can lead to a large perturbation in their apocentric distance."
 As a result. the second. order correction to the work done by the tidal field can be Large.," As a result, the second order correction to the work done by the tidal field can be large."
 We have presented. a model of ical mass loss from collisionless svstenis— with arbitrary phase space distributions., We have presented a model of tidal mass loss from collisionless systems with arbitrary phase space distributions.
 Our calculation has many acvantages over the classic model of tidal mass loss (in whieh the censity profile is truncated bevond a tidal radius determined through force valance arguments)., Our calculation has many advantages over the classic model of tidal mass loss (in which the density profile is truncated beyond a tidal radius determined through force balance arguments).
 In. particular. our calculation takes into account the orbital structure of the system. permitting he ellects of anisotropic orbits on the degree of mass loss o be investigated.," In particular, our calculation takes into account the orbital structure of the system, permitting the effects of anisotropic orbits on the degree of mass loss to be investigated."
 Furthermore. we are able to estimate he density. profile of the material remaining after mass loss mis occurred.," Furthermore, we are able to estimate the density profile of the material remaining after mass loss has occurred."
 A kev predietion from this model is that mass loss will » continuous even in a static fieldthe bound mass of the system shows no sign of converging to a fixed. value., A key prediction from this model is that mass loss will be continuous even in a static field—the bound mass of the system shows no sign of converging to a fixed value.
 This ychaviour is also seen in the N-body simulations which we jwe carried out., This behaviour is also seen in the N-body simulations which we have carried out.
 In particular. the N-hocky simulations show evidence for two distinct regimes of mass loss: an initial rapid ohase in whieh the mass declines exponentially with time ollowed by a slower phase during which the mass declines as à power-law in time.," In particular, the N-body simulations show evidence for two distinct regimes of mass loss: an initial rapid phase in which the mass declines exponentially with time followed by a slower phase during which the mass declines as a power-law in time."
 The rate of mass loss predicted. by Our model is comparable to that seen in he N-bodv simulations curing 1 initial. rapid mass loss phase. although we find that re parameter. fs (which scales the rate of mass loss in our model) must vary with the tidal field strength in order to match N-body results.," The rate of mass loss predicted by our model is comparable to that seen in the N-body simulations during the initial, rapid mass loss phase, although we find that the parameter $f_\tau$ (which scales the rate of mass loss in our model) must vary with the tidal field strength in order to match N-body results."
 We intend to explore and characterize lis svstematic variation of f- in a future paper., We intend to explore and characterize this systematic variation of $f_\tau$ in a future paper.
 This ΠΕ mass loss is à consequence of the [act that mass loss weakens the gravitational potential of the system rereby allowing particles to become unbound that could not jwe escaped from the original potential., This continuous mass loss is a consequence of the fact that mass loss weakens the gravitational potential of the system thereby allowing particles to become unbound that could not have escaped from the original potential.
 At larger times. while the N-body simulations transition to a slower mass oss regime our model continues to show a rapid. exponential mass loss.," At larger times, while the N-body simulations transition to a slower mass loss regime our model continues to show a rapid, exponential mass loss."
 Phe origin of the slow mass loss regime in the N- simulations and the failure of our model to reproduce his is not understood at present. but is the focus of ongoing study.," The origin of the slow mass loss regime in the N-body simulations and the failure of our model to reproduce this is not understood at present, but is the focus of ongoing study."
 Nevertheless. our model is able to describe the rate," Nevertheless, our model is able to describe the rate"
Dust halos. often seen arouud bright poiut-like N-ray objects. are formed by scattering of source X-ray photous on dust grains.,"Dust halos, often seen around bright point-like X-ray objects, are formed by scattering of source X-ray photons on dust grains."
 Here we will oulv discuss the case of dust optically thin with respect to the photon scattering. Tocazlo and consider only azimuthally symmetric halos (which ünplies that the dust. distribution across the liue of sight (LOS) is uniform within the interval of angles J at which we see the halo).," Here we will only discuss the case of dust optically thin with respect to the photon scattering, $\tau_{\rm scat}\lesssim 1$, and consider only azimuthally symmetric halos (which implies that the dust distribution across the line of sight (LOS) is uniform within the interval of angles $\theta$ at which we see the halo)."
 In this case the spectral halo intensity 7? ! ! 7) is given by the equation where PCE) is the point source spectral [lux cciἂν they fea (D—d)/D is the dimeusiouless distance [rom the X-ray source to the scatterer (DD aid d are the distauces from the observer to the source and the scatterer. respectively). 0;20f:r (for small angles) is the scattering augle. fGr) ?2)). ? ?.. ? ?..," In this case the spectral halo intensity $^{-2}$ $^{-1}$ $^{-1}$ $^{-2}$ ) is given by the equation where $F(E)$ is the point source spectral flux $^{-2}$ $^{-1}$ $^{-1}$ ), $x=(D-d)/D$ is the dimensionless distance from the X-ray source to the scatterer $D$ and $d$ are the distances from the observer to the source and the scatterer, respectively), $\theta_s\simeq \theta/x$ (for small angles) is the scattering angle, $f(x)$ \citealt{1991ApJ...376..490M}) \citet{2003ApJ...598.1026D}
 \citet{2001ApJ...548..296W}, \citet{2010A&A...520A..71B} \citet{1998ApJ...503..831S}."
Depolarization due to the Hanle effect can be used to retrieve information on solar magnetic fields (e.g. Trujillo Bueno 2001).,Depolarization due to the Hanle effect can be used to retrieve information on solar magnetic fields (e.g. Trujillo Bueno 2001).
 This magnetic depolarization is usually mixed with a collisional depolarization., This magnetic depolarization is usually mixed with a collisional depolarization.
 To quantitatively use the Hanle effect as a technique of investigation of solar magnetic fields. one needs to know the collisional rates.," To quantitatively use the Hanle effect as a technique of investigation of solar magnetic fields, one needs to know the collisional rates."
 In addition. one should include properly both the collisional depolarizing andtransfer rates in the line formation modeling.," In addition, one should include properly both the collisional depolarizing and rates in the line formation modeling."
 For instance. Derouich et al. (," For instance, Derouich et al. ("
2007) found that the effect of the collisions. in typical solar conditions of temperature and hydrogen density. is particularly important for the very important Ti 114536 line- a collisional depolarization of more than 25 is obtained.,"2007) found that the effect of the collisions, in typical solar conditions of temperature and hydrogen density, is particularly important for the very important Ti ${\lambda}4536$ line– a collisional depolarization of more than 25 is obtained."
 In fact. at a first glance. because the inverse lifetime of the upper level is larger than the value of the elastic depolarizing rate D. one might think (wrongly) that the effect of the collisions is negligible for the Ti 24536 line.," In fact, at a first glance, because the inverse lifetime of the upper level is larger than the value of the elastic depolarizing rate $D^2$, one might think (wrongly) that the effect of the collisions is negligible for the Ti ${\lambda}4536$ line."
 Collisional depolarization of this line is mainly due to which are generally neglected (see Eq., Collisional depolarization of this line is mainly due to which are generally neglected (see Eq.
 14 of Derouich et al., 14 of Derouich et al.
 2007)., 2007).
 Since their ionization potential is rather low. most Barium atoms are ionized throughout the low chromosphere (Tandbere-Hanssen Smythe 1970).," Since their ionization potential is rather low, most Barium atoms are ionized throughout the low chromosphere (Tandberg-Hanssen Smythe 1970)."
 The core of the Ba 4554 line is formed at about 800 km above the photosphere (e.g. Uitenbroek Bruls 1992)., The core of the Ba ${\lambda}4554$ line is formed at about 800 km above the photosphere (e.g. Uitenbroek Bruls 1992).
 The wings are formed in deeper layers of the photosphere., The wings are formed in deeper layers of the photosphere.
 Recently. à renewed interest in the measurement and the physical interpretation of the linear polarization of the Ba 24554 line have emerged (e.g. Malherbe et al..," Recently, a renewed interest in the measurement and the physical interpretation of the linear polarization of the Ba ${\lambda}4554$ line have emerged (e.g. Malherbe et al.,"
 2007; Belluzzi et al., 2007; Belluzzi et al.
 2007: Lopez Ariste et al., 2007; Lopez Ariste et al.
 2008)., 2008).
 It has been shown that during the formation of this line the hyperfine structure and the partial redistribution of the frequencies effects are very important., It has been shown that during the formation of this line the hyperfine structure and the partial redistribution of the frequencies effects are very important.
 In this work. we investigate fully the importance of isotropic collisions with neutral hydrogen in its modeling (Sects.," In this work, we investigate fully the importance of isotropic collisions with neutral hydrogen in its modeling (Sects."
 2 and 3)., 2 and 3).
 Sect., Sect.
 4 1s dedicated to the calculation of the impact of neglecting collisional etfects on the magnetic field determination., 4 is dedicated to the calculation of the impact of neglecting collisional effects on the magnetic field determination.
 Our concluding remarks are given in Sect., Our concluding remarks are given in Sect.
 5., 5.
"Damped Lyiman-a (DLA) absorption line svstenis observed iu the spectrum of quasars are associated with laree cobuun densities. CV(ILI);210°"" 3).",Damped $\alpha$ (DLA) absorption line systems observed in the spectrum of quasars are associated with large column densities $N$ $)>2\times 10^{20}$ $^{-2}$ ).
 Therefore. they are probably associaed with regions of the Universe where star formation OCCIULS (Pettini ct al.," Therefore, they are probably associated with regions of the Universe where star formation occurs (Pettini et al."
 1997)., 1997).
 It is still unclear whether the eas producing the absorption lines is located iu large. fast-rotatiug protogalactic discs (Wolfe et al.," It is still unclear whether the gas producing the absorption lines is located in large, fast-rotating protogalactic discs (Wolfe et al."
 1986. Prochaska Wolfe 1997). in iuteractiug building blobs (TWachuelt et al.," 1986, Prochaska Wolfe 1997), in interacting building blobs (Haehnelt et al."
 1998) or in deusitv fluctuations of galaxy haloes (Ledoux ct al., 1998) or in density fluctuations of galaxy haloes (Ledoux et al.
 1998)., 1998).
 Whatever the exact nature of DLA svsteius may boe. molecules (especially IT») are expected to be found inthose clouds.," Whatever the exact nature of DLA systems may be, molecules (especially $_2$ ) are expected to be found in those clouds."
 However. despite intensive searches (e.g. Black et al.," However, despite intensive searches (e.g. Black et al."
 19587. Ge Bechtold 1999. Petitjean et al.," 1987, Ge Bechtold 1999, Petitjean et al."
 2000) ouly four detectious of IT) have been reported to date., 2000) only four detections of $_2$ have been reported to date.
 Recently. a &fth case has been discovered. sereudipitousIv bv Levshakov et al. (," Recently, a fifth case has been discovered serendipitously by Levshakov et al. ("
2002) at τμ=3.025) toward 383.,2002) at $z_{\rm abs}=3.025$ toward $-$ 383.
 The most receut survey for molecular lvdrogen iu Ll EDSοLae DLA svstems. capitalizing on the unique capabilities of the UVES high-resolution spectrograp[um of the ESO Very Large. Telescope. las given stringent upper limits. in the range 1.2«10* 1.6«107. for the molecular fraction fo= 2N(IT/(2N(IT2) IN (ILiynonincofthesustems(Petitjeanctal," The most recent survey for molecular hydrogen in 11 $z_{\rm abs}>1.8$ DLA systems, capitalizing on the unique capabilities of the UVES high-resolution spectrograph of the ESO Very Large Telescope, has given stringent upper limits, in the range $1.2\times 10^{-7}$ – $1.6\times 10^{-5}$, for the molecular fraction $f=2N($ $_2)/(2N($ $_2)+N($ $))$ in nine of the systems (Petitjean et al."
 2000), 2000).
",T wopossiblt biel ⊇∙∶≩⊤↑∪↖↖↽⋜∐⋅≺↧≼⊽≥∩∩≺∖∖↓⊓⊔∩⋖↕⋟↸∖↑↕↑⋅↿≱↸∖⋜⊔↸∖↑⋜↧↕∙⊇∩∩↭⋜⋯≼↧ ⋜↧↑−∙⋤⋔∖∶∶≩∙∶≩∩∩↑∪↖↖↽⋜∐⋅≼↧≼⊽", Two possible detections have also been reported at $z_{\rm abs}=2.374$ toward $+$ 129 (Petitjean et al.
≥∩∩∣∩∩⊇⊓∶≩∏⇀↸∖↖⇁↴∖↴∐⋜∐↘↽∪↖⇁↸∖↑⋜↧∙ ⊇∪∩∩∏⋝⋜↧↴∖↴↸∖≺↧∙∐∪↖↖⇁↸∖↖↽↸∖↥⋅∙∪∐, 2000) and at $z_{\rm abs}=3.390$ toward $-$ 263 (Levshakov et al.
↑∐↸∖≼∐∖↑↸∖↸⊳↑↕∪∐∪↕⋟∪∐↕⋅↖↽↑↖↖↽∪↖↖⇁↸∖⋜↧↘↽ ↕⋟↸∖⋜↧↑⋃⋅↸∖↴∖↴↕∪↸⊳⋜↧↑↸∖≼⇂↕∐↑∪↑∐↸∖∫⇀⋅↖↽⊔⋜⋯⊣↿≯∪↥⋅↸∖↴∖↴↑∙↕⋟↸∖," 2000) based, however, on the detection of only two weak features located into the $\alpha$ forest."
↑↕↑⋅∣↾↸∖⋜⋯↸∖↑ al. (, Petitjean et al. (
2000) concluded that the nou-detection of molecular hydrogen m most of the DLA systems could be a direct consequeuce of hieh kinetic temperatures. T—3000 Tx. nuplving low fornation rates of IIo onto dust grains.,"2000) concluded that the non-detection of molecular hydrogen in most of the DLA systems could be a direct consequence of high kinetic temperatures, $T>3000$ K, implying low formation rates of $_2$ onto dust grains."
 Therefore. most «X the DLA systems probably arise in warm and diffuse neutral eas.," Therefore, most of the DLA systems probably arise in warm and diffuse neutral gas."
 Fig., Fig.
 5 of Petitjcan oet al. (, 5 of Petitjean et al. (
2000) also sugecsts that. even if the gas is worin. IL should invariably be detected with fx109.,"2000) also suggests that, even if the gas is warm, $_2$ should invariably be detected with $f\la 10^{-6}$."
 Such very low imnolecular fractious probably result from high uubieut UV fiux., Such very low molecular fractions probably result from high ambient UV flux.
" Tn this paper. we preseut new results obtained from VLT-UVES high resolution spectroscopy of a DLA syste at tap,=1.962 toward 366."," In this paper, we present new results obtained from VLT-UVES high resolution spectroscopy of a DLA system at $z_{\rm abs}=1.962$ toward $-$ 366."
 Details of the observations are given in Sect., Details of the observations are given in Sect.
 2., 2.
 The metal couteut. dust depletion patteru aud Ts molecular coutent of the vbsorber are discussed in. respectively. Sects.," The metal content, dust depletion pattern and $_2$ molecular content of the absorber are discussed in, respectively, Sects."
 3. land 5.," 3, 4 and 5."
 Ον results are finally sununarized and their implications discussed in Sect., Our results are finally summarized and their implications discussed in Sect.
 6., 6.
 The Ultraviolet aud Visible Echelle Spectrograph (UVES: see Dekker et al., The Ultraviolet and Visible Echelle Spectrograph (UVES; see Dekker et al.
 2000) motte: ou the ESO I&ueveu VLT-UT2 8.2 ui telescope on Cerro Paranal in Chile has becu used in the course of a survey to search for IT» absorption lines in a sample of DLA svsteus., 2000) mounted on the ESO Kueyen VLT-UT2 8.2 m telescope on Cerro Paranal in Chile has been used in the course of a survey to search for $_2$ absorption lines in a sample of DLA systems.
 Maas}μη ratio spectra of the aay=↽⋅17.6. AMiseagselutionMOS⊲∙∶⊅⋪−↣∪∩⋅≽⋅↗↽ 366 quasar were obtained on October 20-23. 2000.," High-resolution, high signal-to-noise ratio spectra of the $m_{\rm V}=17.6$, $z_{\rm em}=2.32$ $-$ 366 quasar were obtained on October 20-23, 2000."
 Standard settings were used in both blue and red arms with Dichroic #11 (central wavelengths: 3160 and 5800. A) and central waveleuetls were adjusted to 1370 iu the Blue (7500 in the Red) with Dichroic #22., Standard settings were used in both blue and red arms with Dichroic 1 (central wavelengths: 3460 and 5800 ) and central wavelengths were adjusted to 4370 in the Blue (7500 in the Red) with Dichroic 2.
 This way. full wavelcueth coverage was obtained from 3050 to 7112 aand from 7566 to 9396 aaccountiue for the gap between red-arm CCDs.," This way, full wavelength coverage was obtained from 3050 to 7412 and from 7566 to 9396 accounting for the gap between red-arm CCDs."
 The CCD, The CCD
ocated in dillerent orbits (72??7)).,"located in different orbits \citealt{1995ApJ...440..742H, 1995ApJ...446..741B,
1998ApJ...501L.189A, 2000ApJ...528..462H, 2006ApJ...640..901H}) )."
 Despite the significant heoretical progress achieved in this field. the details of this ransport mechanism have vet to be fully understood. and it is not clear if. MIU alone is able to account for the mass accretion and for the removal of excess angular momentunir (??7)).," Despite the significant theoretical progress achieved in this field, the details of this transport mechanism have yet to be fully understood, and it is not clear if MRI alone is able to account for the mass accretion and for the removal of excess angular momentum \citealt{2007MNRAS.376.1740K,
2007A&A...476.1113F, 2008A&A...487....1B}) )."
 Given the complexity of this mechanism ancl our »oor knowledge of its details. the ellicieney of angular momentum. transport within the disk is often modeled. in he literature by including a viscosity in the disk mocdulated via an analogue of the Shakura-Sunvacy a-parameter (2)) which can be expressed in terms of the Ductuating velocity and magnetic field (22?)).," Given the complexity of this mechanism and our poor knowledge of its details, the efficiency of angular momentum transport within the disk is often modeled in the literature by including a viscosity in the disk modulated via an analogue of the Shakura-Sunyaev $\alpha$ -parameter \citealt{1973A&A....24..337S}) ) which can be expressed in terms of the fluctuating velocity and magnetic field \citealt{2002ApJ...578..420R, Romanova2003ApJ, 2008MNRAS.386..673K}) )."
 On the other hand. observations in. the X-ray band have shown that pre-main-secquence stars are strong sources with X-rav luminosity 3-4 orders of magnitude greater than that of the present-day Sun (22)).," On the other hand, observations in the X-ray band have shown that pre-main-sequence stars are strong sources with X-ray luminosity 3-4 orders of magnitude greater than that of the present-day Sun \citealt{2005ApJS..160..353G, 2007A&A...468..379A}) )."
 Phe source. of this X-ray radiation is a plasma at 1100 Ally in the stellar outer atmospheres (coronae). heated. by magnetic activity analogous to the solar one but much stronger (7)).," The source of this X-ray radiation is a plasma at $1-100$ MK in the stellar outer atmospheres (coronae), heated by magnetic activity analogous to the solar one but much stronger \citealt{1999ARAA..37..363F}) )."
 X-ray Dares are violent manifestations of this magnetic activity ancl are triggered. by an impulsive energy. input rom coronal magnetic field., X-ray flares are violent manifestations of this magnetic activity and are triggered by an impulsive energy input from coronal magnetic field.
 X-ray observations in the [ast decades have shown that [lares in CIISs have amplitudes arecr than solar analogues and occur much more frequently (???7)).," X-ray observations in the last decades have shown that flares in CTTSs have amplitudes larger than solar analogues and occur much more frequently \citealt{2005ApJS..160..469F, 2005ApJS..160..353G, 2007A&A...468..379A,
2010ApJ...717...93A}) )."
 Examples of these Dares are those collected by the Chandra satellite in the Orion star-formation region (COUP enterprise: 2)., Examples of these flares are those collected by the Chandra satellite in the Orion star-formation region (COUP enterprise; \citealt{2005ApJS..160..469F}) ).
 Phe analysis of these [ares revealed that they lave peak temperatures often in excess of LOO MIX. are long-asting. and are confined in very long magnetic structures extending for several stellar radii which may connect the stars photosphere with the aceretion disk (structures that could be of the same kind as those which channel the plasma in the magnetospheric accretion).," The analysis of these flares revealed that they have peak temperatures often in excess of 100 MK, are long-lasting, and are confined in very long magnetic structures – extending for several stellar radii – which may connect the star's photosphere with the accretion disk (structures that could be of the same kind as those which channel the plasma in the magnetospheric accretion)."
 At the present time. it is unclear. where these [ares occur.," At the present time, it is unclear where these flares occur."
 The cillerential rotation of the disk together with the interaction of the disk with the magnetosphere may cause magnetic reconnection close to the disks surface. triggering arge-scale [ares there.," The differential rotation of the disk together with the interaction of the disk with the magnetosphere may cause magnetic reconnection close to the disk's surface, triggering large-scale flares there."
 In this case. the Dares may perturb he stability of the circumstellar disk causing. in particular. a strong local overpressure.," In this case, the flares may perturb the stability of the circumstellar disk causing, in particular, a strong local overpressure."
 The pressure gradient force might oe able to push disks matter out of the equatorial plane into funnel streams. thus providing a mechanism to drive mass accretion that οους from that. commonly invoked in he literature. based on the disk viscosity which determines he accumulation of disk matter and the increase of gas oressure close to the truncation radius (2)).," The pressure gradient force might be able to push disk's matter out of the equatorial plane into funnel streams, thus providing a mechanism to drive mass accretion that differs from that, commonly invoked in the literature, based on the disk viscosity which determines the accumulation of disk matter and the increase of gas pressure close to the truncation radius \citealt{2002ApJ...578..420R}) )."
 Bright [lares close to circumstellar disks may therefore have important implications for a number of issues such as the transfer of angular momentum and mass between the star and the disk. the powering of outllows. and the ionization of circumstellar disks thus influencing also the elliciencv of MIR (see. also τη. ," Bright flares close to circumstellar disks may therefore have important implications for a number of issues such as the transfer of angular momentum and mass between the star and the disk, the powering of outflows, and the ionization of circumstellar disks thus influencing also the efficiency of MRI (see also \citealt{2010ApJ...717...93A}) )."
In this paper. we investigate the elfects of a Hare on the stability of the circumstellar disk with a threc-cdimensional (3D) maenetohyverocdynamic (MEID) simulation.," In this paper, we investigate the effects of a flare on the stability of the circumstellar disk with a three-dimensional (3D) magnetohydrodynamic (MHD) simulation."
 We model he evolution of the star-disk plasma heated by a strong energev release (with intensity comparable to that of [ares vpically observed. in voung stars). close to a thick disk surrounding a rotating magnetized CTS.," We model the evolution of the star-disk plasma heated by a strong energy release (with intensity comparable to that of flares typically observed in young stars), close to a thick disk surrounding a rotating magnetized CTTS."
 The mocel akes into accountall kev physical processes. including the eravitational force. the viscosity of the disk. the magnetic-ield-oriented thermal conduction. the radiative losses from optically thin plasma. and the coronal heating.," The model takes into accountall key physical processes, including the gravitational force, the viscosity of the disk, the magnetic-field-oriented thermal conduction, the radiative losses from optically thin plasma, and the coronal heating."
 Ehe wealth of nonlinear physical processes governing the star-disk svstem and the evolution of the [lare made this a challenging task., The wealth of nonlinear physical processes governing the star-disk system and the evolution of the flare made this a challenging task.
 In Sect., In Sect.
 2. we describe the ΑΔΗ mocel and the numerical setup: in Sect.," \ref{sec2}
 we describe the MHD model and the numerical setup; in Sect."
 3. we deseribe the results: in Sect.," \ref{sec3}
 we describe the results; in Sect."
 4 we discuss the implications of our results and craw our conclusions., \ref{sec4} we discuss the implications of our results and draw our conclusions.
 Our mocel describes a laree Hare in a rotating magnetized star surrounded by a thick (quasi-Ixeplerian disk., Our model describes a large flare in a rotating magnetized star surrounded by a thick quasi-Keplerian disk.
 Phe flare occurs close to the inner portion of the disk. within the corotation radius (i.e. where a Weplerian orbit around. the star has the same angular velocity as the stars surface). where accretion streams are expected to originate (22)).," The flare occurs close to the inner portion of the disk, within the corotation radius (i.e. where a Keplerian orbit around the star has the same angular velocity as the star's surface), where accretion streams are expected to originate \citealt{2002ApJ...578..420R, 2008A&A...478..155B}) )."
 Phe magnetic field of the star is aligned clipole-like. with intensity Dc] ko at the stellar surface according to observations (?)).," The magnetic field of the star is aligned dipole-like, with intensity $B \approx 1$ kG at the stellar surface according to observations \citealt{1999ApJ...510L..41J}) )."
 The Iud is assumed to be fully ionized with a ratio of specilic heats ?—5/3., The fluid is assumed to be fully ionized with a ratio of specific heats $\gamma = 5/3$.
 The system ds described. by the time-dependent MILD equations in a 3D spherical coordinate. svstem (2.6.0). extended with gravitational force. viscosity of the. disk. thermal conduction. (including the ellects of heat [lux saturation). coronal heating (via a phenomenological term). ancl radiative losses from optically thin plasma.," The system is described by the time-dependent MHD equations in a 3D spherical coordinate system $(R,\theta,\phi)$, extended with gravitational force, viscosity of the disk, thermal conduction (including the effects of heat flux saturation), coronal heating (via a phenomenological term), and radiative losses from optically thin plasma."
 Γω our knowledge. this is the first numerical time-dependent. global simulation of the star-cisk system that takes into account simultaneously all key physical ingredients necessary to describe accurately the ellects of a Pare on the structure of the circumstellar disk.," To our knowledge, this is the first numerical time-dependent global simulation of the star-disk system that takes into account simultaneously all key physical ingredients necessary to describe accurately the effects of a flare on the structure of the circumstellar disk."
 The time-dependent. MIED equations written in non-dimensional conservative form are: where are the total pressure. and the total gas energv per unit mass (internal energy. c. kinetic energy. and magnetic energy) respectively. (is the time. p=sarang is the mass density. f=1.28 is the mean atomic mass (assuming metal abundances of 0.5 of the solar values: 2)). mg is the mass of the hydrogen atom. ng is the hydrogen number density. Wis the gas velocity. 7 is the viscous stress tensor. d=Vy is the gravity acceleration. vector. Py=CGAL.LH is the gravitational potential of a central star of mass AM. C ," The time-dependent MHD equations written in non-dimensional conservative form are: where are the total pressure, and the total gas energy per unit mass (internal energy, $\epsilon$, kinetic energy, and magnetic energy) respectively, $t$ is the time, $\rho = \mu m_H n_{\rm H}$ is the mass density, $\mu = 1.28$ is the mean atomic mass (assuming metal abundances of 0.5 of the solar values; \citealt{Anders1989GeCoA}) ), $m_H$ is the mass of the hydrogen atom, $n_{\rm H}$ is the hydrogen number density, $\vec{u}$ is the gas velocity, $\vec{\tau}$ is the viscous stress tensor, $\vec{g}=\nabla\Phi\rs{g}$ is the gravity acceleration vector, $\Phi\rs{g}=- GM_*/R$ is the gravitational potential of a central star of mass $M_*$ , $G$ "
 οταν (E. (Ey). (£4) 5-ravs (e.=E./LD) CF.) (dp(:)) Ly: Berecretal.2000:etal.2003)). 7... Ej ej (Panaitescu&Ixiunar2002:Berecr," $\gamma$ $E_\gamma$ $E_K$ $E_{\rm rel}$ $\gamma$ $\epsilon_\gamma\equiv E_\gamma/E_{\rm rel}$ $F_\gamma$ $d_L(z)$ $E_K$ \citealt{bsf+00,pk02,yhs+03}) $\nu_c$ $E_K$ $\epsilon_B$ \citep{kum00,fw01,bkf03}. \citep{pk02,bkf03},"
" r.. LyXἐκ e, (Z5)z2 E.. Ey. ~1PL (Frailetal.2001:2003b).."," $\nu_c$ $L_X\propto\epsilon_eE_K$ $\epsilon_e$ $T_{90}\gtrsim 2$ $E_\gamma$ $E_K$ $\sim 10^{51}$ \citep{fks+01,pk02,bkf03,bfk03,bkp+03}."
 (1079 (Soderb," $\sim 10^{50}$ \citep{skb+04,skn+06}."
erg 0;~57. ~LOS1072 (Burrowsetal.2006," $\theta_j\sim 5^\circ$ $\sim
10^{48}-10^{49}$ \citep{bpc+05,ffp+05,gso+05,bpp+06}, \citep{bgc+06,sbk+06}."
erg 0;~57. ~LOS1072 (Burrowsetal.2006," $\theta_j\sim 5^\circ$ $\sim
10^{48}-10^{49}$ \citep{bpc+05,ffp+05,gso+05,bpp+06}, \citep{bgc+06,sbk+06}.\"
erg 0;~57. ~LOS1072 (Burrowsetal.2006:," $\theta_j\sim 5^\circ$ $\sim
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erg 0;~57. ~LOS1072 (Burrowsetal.2006:N," $\theta_j\sim 5^\circ$ $\sim
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erg 0;~57. ~LOS1072 (Burrowsetal.2006:Na," $\theta_j\sim 5^\circ$ $\sim
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erg 0;~57. ~LOS1072 (Burrowsetal.2006:Nakar," $\theta_j\sim 5^\circ$ $\sim
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erg 0;~57. ~LOS1072 (Burrowsetal.2006:Nakar(2," $\theta_j\sim 5^\circ$ $\sim
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erg 0;~57. ~LOS1072 (Burrowsetal.2006:Nakar(20," $\theta_j\sim 5^\circ$ $\sim
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erg 0;~57. ~LOS1072 (Burrowsetal.2006:Nakar(2007)," $\theta_j\sim 5^\circ$ $\sim
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"calledN132D_3d_Olll_Hb.pdf,, the H8 emission as been plotted in red over the blue [O III] emission (shown alone in the map N132D_3d_Olll.pdf)), similarly to the data shown in Fig. 4--","called, the $\beta$ emission as been plotted in red over the blue [O III] emission (shown alone in the map ), similarly to the data shown in Fig. \ref{fig:above}-"
 Right., -Right.
" As for the Real 3D movie, it can be looked at using the stereo pairs viewing technique described above and in Vogt,Wagner&Do-pita(2010b)."," As for the Real 3D movie, it can be looked at using the stereo pairs viewing technique described above and in \cite{Vogt10b}."
. Note that the plotted data is identical to that contained in the interactive 3D map., Note that the plotted data is identical to that contained in the interactive 3D map.
" In its broad characteristics, N132D is a typical young SNR, with several high-velocity oxygen-rich filaments, excited by a reverse blast wave, while the forward shock wave is expanding into space, shocking the surrounding medium."," In its broad characteristics, N132D is a typical young SNR, with several high-velocity oxygen-rich filaments, excited by a reverse blast wave, while the forward shock wave is expanding into space, shocking the surrounding medium."
" The forward shock wave is nicely traced by strong X-ray emission of the shocked ISM, a feature which can be easily observed in the case of N132D. The reverse shock wave signature, in that of X-ray emission superposed to the oxygen-rich ejecta, has only been recently detected (Borkowski,Hendrick&Reynolds2007;Xiao&Chen 2008)."," The forward shock wave is nicely traced by strong X-ray emission of the shocked ISM, a feature which can be easily observed in the case of N132D. The reverse shock wave signature, in that of X-ray emission superposed to the oxygen-rich ejecta, has only been recently detected \citep[][]{Borkowski07,Xiao08}."
" The Ni-bubble scenario for this feature (Socratesetal2005;Wang2005), as suggested by Borkowski,Hendrick&Reynolds (2007),, appears rather unlikely."," The Ni-bubble scenario for this feature \citep[][]{Socrates05,Wang05}, as suggested by \cite{Borkowski07}, appears rather unlikely."
" This scenario might be responsible for initially shaping the O-rich ejecta into a ring, but not for the emission of X-rays 2500 years after the shock breakout."," This scenario might be responsible for initially shaping the O-rich ejecta into a ring, but not for the emission of X-rays 2500 years after the shock breakout."
 'The shape of the ejecta within N132D has been a puzzling question in the past studies of this remnant., The shape of the ejecta within N132D has been a puzzling question in the past studies of this remnant.
" From our 3D maps, it is now clear that the ejecta traces a distorted ring, as first suggested in the pioneering work of Lasker(1980)."," From our 3D maps, it is now clear that the ejecta traces a distorted ring, as first suggested in the pioneering work of \citet{Lasker80}."
" However, with the greater age of ~2500 years that we have inferred here, the ring is less inclined that Lasker initially thought, lying at ~20-30 degrees with respect to the line of sight."," However, with the greater age of $\sim 2500$ years that we have inferred here, the ring is less inclined that Lasker initially thought, lying at $\sim$ 20-30 degrees with respect to the line of sight."
" The ring appears rather distorted on the redshifted side, and is systematically blue-shifted by ~400 km s-! with respect to the LMC rest frame."," The ring appears rather distorted on the redshifted side, and is systematically blue-shifted by $\sim$ 400 km $^{-1}$ with respect to the LMC rest frame."
" This fact, already identified in previous studies, is most probably associated with an asymmetry during the explosion."," This fact, already identified in previous studies, is most probably associated with an asymmetry during the explosion."
 The ratio of the forward shock radius to the reverse shock radius is —3.20., The ratio of the forward shock radius to the reverse shock radius is $\sim 3.20$.
 This high value is a sign that N132D is in rather a late stage for a young SNR., This high value is a sign that N132D is in rather a late stage for a young SNR.
" The reverse shock must have already started accelerating towards the center, at which point the SNR will complete its transition to the Sedov phase (Reynolds 2008).."," The reverse shock must have already started accelerating towards the center, at which point the SNR will complete its transition to the Sedov phase \citep[][]{reynolds2008}."
" In this scenario, the shocked ejecta, moving at ballistic velocities since the explosion should be expanding at comparatively slower speed with respect to other younger SNR."," In this scenario, the shocked ejecta, moving at ballistic velocities since the explosion should be expanding at comparatively slower speed with respect to other younger SNR."
" Given the fact that the oxygen-rich ejecta form a (somewhat thick) ring, and since these ejecta are amongst the slowest of the helium burnt products of the exploding star, it is very tempting to propose that these represent a denser equatorial ring of ejecta from an initially rotating star."," Given the fact that the oxygen-rich ejecta form a (somewhat thick) ring, and since these ejecta are amongst the slowest of the helium burnt products of the exploding star, it is very tempting to propose that these represent a denser equatorial ring of ejecta from an initially rotating star."
" In this scenario the polar ejecta will have higher velocities, but lower column densities, and so will have interacted with more of the surrounding ISM, allowing the reverse shock to fully propagate through them."," In this scenario the polar ejecta will have higher velocities, but lower column densities, and so will have interacted with more of the surrounding ISM, allowing the reverse shock to fully propagate through them."
" It is interesting that the major axis of the outer X-ray shell associated with the blast wave also forms an ellipse with PA~45 deg.,"," It is interesting that the major axis of the outer X-ray shell associated with the blast wave also forms an ellipse with $PA\sim 45$ deg.,"
" and is more or less aligned with the major axis of the fast-moving ring of ejecta in the XY plane (in Fig. 6,,"," and is more or less aligned with the major axis of the fast-moving ring of ejecta in the XY plane (in Fig. \ref{fig:angle},"
 the X’Y’Z reference frame is rotated by 45 deg., the X'Y'Z reference frame is rotated by $45$ deg.
 around Z with respect to the XYZ reference frame.)., around Z with respect to the XYZ reference frame.).
" The outer shell may be either itself a ring-like structure, the dense mid-plane of an oblate ellipsoid or (less probably) it may represent a fattened (oblate) ellipsoid (or pumpkin shape)."," The outer shell may be either itself a ring-like structure, the dense mid-plane of an oblate ellipsoid or (less probably) it may represent a ßattened (oblate) ellipsoid (or pumpkin shape)."
" If interpreted as a ring, and assuming that, as for the oxygen-rich ejecta, this ring is circular, then we infer that it has an inclination to the line of sight of ~40 deg.,"," If interpreted as a ring, and assuming that, as for the oxygen-rich ejecta, this ring is circular, then we infer that it has an inclination to the line of sight of $\sim 40$ deg.,"
 as deduced from the length ratio of the primary to the secondary axis of the outer ellipsoid X-ray shell., as deduced from the length ratio of the primary to the secondary axis of the outer ellipsoid X-ray shell.
 This is sufficiently close in angle to the ~25 deg., This is sufficiently close in angle to the $\sim 25$ deg.
 inferred for the oxygen-rich ring to speculate that the outer X-ray ring may represent the remnants of a (possibly toroidal) ring nebula ejected during an earlier Wolf-Rayet phase of evolution of the SN progenitor., inferred for the oxygen-rich ring to speculate that the outer X-ray ring may represent the remnants of a (possibly toroidal) ring nebula ejected during an earlier Wolf-Rayet phase of evolution of the SN progenitor.
 This hypothesis is capable of a number of observational tests., This hypothesis is capable of a number of observational tests.
" First, if the optical outer shell represents material originally ejected from the central star, then we would expect it to be enhanced in the products of hydrogen-burning, notably helium and nitrogen."," First, if the optical outer shell represents material originally ejected from the central star, then we would expect it to be enhanced in the products of hydrogen-burning, notably helium and nitrogen."
" Blairetal.(2000) have obtained the optical spectra of one of the bright knot within the outer ring, and found its elements abundances to be similar to that of the ISM in the LMC."," \cite{Blair00} have obtained the optical spectra of one of the bright knot within the outer ring, and found its elements abundances to be similar to that of the ISM in the LMC."
 This analysis would need to be expanded to other locations on the outer rim by further spectrophotometric work in order to detect any helium or nitrogen enhancement., This analysis would need to be expanded to other locations on the outer rim by further spectrophotometric work in order to detect any helium or nitrogen enhancement.
" Second, we would expect the blast wave to have interacted with this ring already, and to have swept around it."," Second, we would expect the blast wave to have interacted with this ring already, and to have swept around it."
" Indeed, such appears to be the case, since the radiative small clumps of gas in both the NW and and SE of the remnant clearly lie inside outer X-ray bright shell (see for example Figure 5))."," Indeed, such appears to be the case, since the radiative small clumps of gas in both the NW and and SE of the remnant clearly lie inside outer X-ray bright shell (see for example Figure \ref{fig:xray}) )."
" Third, in this scenario, the polar direction will have mostly been swept clear of interstellar gas by the fast wind."," Third, in this scenario, the polar direction will have mostly been swept clear of interstellar gas by the fast wind."
" This will have the effect that, contrary to our supposition above that the reverse shock has propagated back to the center of the remnant in the polar direction, the development of the reverse shock"," This will have the effect that, contrary to our supposition above that the reverse shock has propagated back to the center of the remnant in the polar direction, the development of the reverse shock"
of the Universe is related. to the large-scale structure and ealaxy formation and is called [ate reionization.,of the Universe is related to the large-scale structure and galaxy formation and is called late reionization.
 The mocel ol the late reionization is not vet well-established and. needs further investigations., The model of the late reionization is not yet well-established and needs further investigations.
" The conventional view of the ionization is that cosmological hydrogen became neutral after recombination ab nes0DU"" and was reionized at some recdshift. zi. where 7. is the Thomson optical depth. Oj is the present barvonic density scaled to the critical density. 44, is the dark matter density. b.=Lo/100kms*Alpe is he Llubble constant. (1,2 is the helium mass fraction of matter."," The conventional view of the ionization is that cosmological hydrogen became neutral after recombination at $\zrec\simeq 10^3$ and was reionized at some redshift $\zreio$ , where $\tau_r$ is the Thomson optical depth, $\Ob$ is the present baryonic density scaled to the critical density, $\Odm$ is the dark matter density, $h=H_0/100 \kms \mpc$ is the Hubble constant, $\langle
Y_p\rangle$ is the helium mass fraction of matter."
 Recently Cen (2002). has. proposed the model of he late reionization with two epochs., Recently Cen \shortcite{cen} has proposed the model of the late reionization with two epochs.
" Firstly. hydrogen was reionizedMEN at redshiftun 277.TYeioniL15 by Population. LL stars and secondly at 2.3),i276⋅ by stars in: large galaxies."," Firstly, hydrogen was reionized at redshift $\zreio^{(1)}\simeq 15$ by Population III stars and secondly at $\zreio^{(2)}\simeq 6$ by stars in large galaxies."
: On the other 1and. we also diseuss another distinct feature of reionization nmociel. which is calledreionization.," On the other hand, we also discuss another distinct feature of reionization model, which is called."
 This shoot-up in the ionization fraction at z>100 can be induced by enerey injection into the cosmic plasma., This shoot-up in the ionization fraction at $z >100$ can be induced by energy injection into the cosmic plasma.
 These two-epoched: reionization models. which can be tested by the and future data (Cen2002).. would be significant for the interpretation of the polarization measurements.," These two-epoched reionization models, which can be tested by the and future data \cite{cen}, would be significant for the interpretation of the polarization measurements."
" The polarization of the CALB from the late reionization epoch (or epochs) is sensitive to the width of the period τμ when the ionization fraction wy. increases from the residual ionization Gr,~10 7) up to uw.~0.1.1 (SeljakanclZaldarriaga1996)."," The polarization of the CMB from the late reionization epoch (or epochs) is sensitive to the width of the period $\Delta \zreio$, when the ionization fraction $x_e$ increases from the residual ionization $x_e\sim 10^{-3}$ ) up to $x_e \sim 0.1-1$ \cite{cmbfast}."
. They can provide unique information about the physical processes induced by complicated ionization regimes., They can provide unique information about the physical processes induced by complicated ionization regimes.
 The aim of the paper is to discuss the distinct characters of these mocdels in the light of recent data and to predict the peculiarities in the polarization power spectrum induced from both the Cen model (2002). of the late reionization and the extra peak-like reionization. taking into account the properties and the sensitivities of the upcoming polarization measurements.," The aim of the paper is to discuss the distinct characters of these models in the light of recent data and to predict the peculiarities in the polarization power spectrum induced from both the Cen model \shortcite{cen} of the late reionization and the extra peak-like reionization, taking into account the properties and the sensitivities of the upcoming polarization measurements."
 The model of the retonization process. proposed. by Cen (2002) can be described. phenomenologically in terms of the injection of additional Lv-e photons via the approach bv Peebles. Seager and Llu (2000). Doroshkevich and Naselsky (2002).. Doroshkevich al.(2003)..," The model of the reionization process proposed by Cen \shortcite{cen}
 can be described phenomenologically in terms of the injection of additional $c$ photons via the approach by Peebles, Seager and Hu \shortcite{psh}, Doroshkevich and Naselsky \shortcite{dn}, Doroshkevich \shortcite{dnnn}."
" For the epochs of reionization the rate of tonizecl photon production nm; is defined as where £/(2) and mi(z) are the Hubble parameter and the mean barvonic density at respectively, 2;(2) ds the effectiveness of the Ly-e. photon production."," For the epochs of reionization the rate of ionized photon production $n_{i}$ is defined as where $H(z)$ and $\nb(z)$ are the Hubble parameter and the mean baryonic density at $z$, respectively, $\varepsilon_{i}(z)$ is the effectiveness of the $c$ photon production."
 As one can see from Lq.(??)) the dependence of 2;(2). parameter upon redshift z allows us to model any kind. of ionization regimes. including heavy particle decavs.," As one can see from \ref{eq:eq2}) ) the dependence of $\varepsilon_{i}(z)$ parameter upon redshift $z$ allows us to model any kind of ionization regimes, including heavy particle decays."
 TFhis parameter also includes uncertainties from the fraction of barvons that collapse and form stars. and the escape fractionfor ionizing photons.," This parameter also includes uncertainties from the fraction of baryons that collapse and form stars, and the escape fractionfor ionizing photons."
" For late reionization. the ionization fraction of matter, —ΠΠ can be obtained [rom the balance between the recombination and the ionization process where αγ}094.10P(T107A)77alem is the recombination coctlicient anc Z7 is the temperature of the plasma and m, is the mean value of the baryonic number density of matter."," For late reionization, the ionization fraction of matter $x_e=n_e/\overline{n}$ can be obtained from the balance between the recombination and the ionization process where $\alpha_{\rm rec}(T)\simeq 4\times 10^{-13} \left(T/10^4
K \right)^{-0.6} {\rm s}^{-1}{\rm cm}^{-3}$ is the recombination coefficient and $T$ is the temperature of the plasma and $\nb$ is the mean value of the baryonic number density of matter."
 In an equilibrium between the recombination and the ionization process the ionization [raction of the matter follows the well-known regime where 44(=ΠανQu.PoP11.Ov and ny10(ΩΣ/0.02)(1| zY., In an equilibrium between the recombination and the ionization process the ionization fraction of the matter follows the well-known regime where $H(z)=H_0\sqrt{\Om(1+z)^3+1-\Om}$ and $\nb \simeq 2 \times 10^{-7}(\Ob h^2/0.02)(1+z)^3$ .
 We would like to point out hat l|2q.(4)) can be used for any models of the late reionization. including the Cen model (2002). by choosing he corresponding dependence of the 2;(2) parameter on redshift.," We would like to point out that \ref{eq4}) ) can be used for any models of the late reionization, including the Cen model \shortcite{cen} by choosing the corresponding dependence of the $\varepsilon_{i}(z)$ parameter on redshift."
" This point is vital in our mocification of the and the packages.from which we can use the standard relation for matter temperature (2)c210(1|2/100)""Ix ancl all the temperature peculiarities of he reionization and clumping would be related with the σι) parameter through the mimic of ionization history."," This point is vital in our modification of the and the packages,from which we can use the standard relation for matter temperature $T(z)\simeq 270
\left(1+z/100 \right)^2 {\rm K}$ and all the temperature peculiarities of the reionization and clumping would be related with the $\varepsilon_{i}(z)$ parameter through the mimic of ionization history."
 For example. in the Cen model (2002). the function 7(/) has a ont. of. maximaη ueDias~(1.5.⋅15).107L at z~zutli and decreases slowly ats<CotaT down to op:LU)~10!7const at he redshift range 6«z12.," For example, in the Cen model \shortcite{cen} the function $T(t)$ has a point of maxima $T_{\rm max} \sim (1.3-1.5) \times 10^4$ at $z \sim \zreio^{(1)}$ and decreases slowly at $z < \zreio^{(1)}$ down to $T(t) \sim 10^4 \simeq {\rm const}$ at the redshift range $6< z <12$."
" Let us introduce some moclel of the 2;(2) parameter dependence over z as where συ δι and m are the free parameters. Ac,Trelon lio.is the width. of thefirst⋅ epoch of ⋅∢reionization. and Of(.r) is the step function."," Let us introduce some model of the $\varepsilon_{i}(z)$ parameter dependence over $z$ as where $\varepsilon_{0}$ $\varepsilon_{1}$ and $m$ are the free parameters, $\Delta z_1\ll \zreio^{(1)}$ is the width of thefirst epoch of reionization and $\Theta(x)$ is the step function."
 The first term of Eq.(5)) corresponds to peak-like reionization at 2 παν which decreases significantly⋠⋠⋅' at 2/29lololbii LG.," The first term of \ref{eq5.0}) ) corresponds to peak-like reionization at $z=\zreio$ , which decreases significantly at $z > \zreio^{(1)}$ ."
 The second term is. related to modelling the second. epoch of the retonization mocel discussed. by Cen (2002). which results in a monotonic increasing in ) function as a function of time.," The second term is related to modelling the second epoch of the reionization model discussed by Cen (2002), which results in a monotonic increasing in $\varepsilon_{i}(z)$ function as a function of time."
 From Iq.(5)) αἲ zozuli we obtain, From \ref{eq5.0}) ) at $z\simeq \zreio^{(1)}$ we obtain
 From Iq.(5)) αἲ zozuli we obtain., From \ref{eq5.0}) ) at $z\simeq \zreio^{(1)}$ we obtain
barycentric frequencies between 2006 March 17 and April 25.,barycentric frequencies between 2006 March 17 and April 25.
 The two 7 values differ by only 2.760 of the (much smaller) uncertainty of the phase-connected fit. and this agreement allows us to extend our record of 7 by 1 additional month.," The two $\dot \nu$ values differ by only $2.7\,\sigma$ of the (much smaller) uncertainty of the phase-connected fit, and this agreement allows us to extend our record of $\dot \nu$ by 1 additional month."
 The run of 77 measured over 9 months is shown in the top panel of Figure 4.., The run of $\dot \nu$ measured over 9 months is shown in the top panel of Figure \ref{fig:fdot}.
 The overall trend is one of increasing i (as could be inferred from the top panel of Fig. 3))," The overall trend is one of increasing $\dot
\nu$ (as could be inferred from the top panel of Fig. \ref{fig:res}) )"
 but the way in which this occurs is far from steady., but the way in which this occurs is far from steady.
 In the 3 months prior to mid 2006 July. 7 varied in a relatively steady and gradual fashion. from —3.3« I0ss7 to —3.0« 1077.," In the 3 months prior to mid 2006 July, $\dot \nu$ varied in a relatively steady and gradual fashion, from $-3.3\times10^{-13}$ $^{-2}$ to $-3.0\times10^{-13}$ $^{-2}$."
 Then. in late July. it changed to 22.7P«107 ss over a spanss of 15 days — the implied change in torque is -2«10? cem (using a stellar moment of inertia of 10? cem). which is larger than the torque powering three-quarters of all known ordinary pulsars!," Then, in late July, it changed to $-2.7\times10^{-13}$ $^{-2}$ over a span of 15 days — the implied change in torque is $-2\times10^{32}$ cm (using a stellar moment of inertia of $10^{45}$ $^2$ ), which is larger than the torque powering three-quarters of all known ordinary pulsars!"
 Regardless of the detailed mechanisms that produce radio pulses inJ1810—197.. it should perhaps not be surprising if other observational properties of the magnetar should have changed around this time.," Regardless of the detailed mechanisms that produce radio pulses in, it should perhaps not be surprising if other observational properties of the magnetar should have changed around this time."
 In fact. as the middle panel of Figure + shows. the peak flux density of hhas dramatically decreased since about that time.," In fact, as the middle panel of Figure \ref{fig:fdot} shows, the peak flux density of has dramatically decreased since about that time."
 Interestingly. while the period-averaged flux density has also decreased compared to its average value before mid July (bottom panel of Fig. 4)).," Interestingly, while the period-averaged flux density has also decreased compared to its average value before mid July (bottom panel of Fig. \ref{fig:fdot}) ),"
 until about 2006 October it did so by a smaller factor and continued to fluctuate greatly from day to day (when average flux densities are available from at least two ofNangay.. Parkes or VLA within a day of each other. they are consistent within expectations given the inherent variations).," until about 2006 October it did so by a smaller factor and continued to fluctuate greatly from day to day (when average flux densities are available from at least two of, Parkes or VLA within a day of each other, they are consistent within expectations given the inherent variations)."
 These two observations can be understood by inspection of the profiles shown in Figure [:: from late July to mid September (MJD~53994). the daily profiles of ttended to be composed of two (or more) significant peaks. each much broader than the one peak generally prominent before mid July (with. typical full-width at half-maximum zz0.04P. versus about half that value beforehand). and with greater pulse-shape variance than before.," These two observations can be understood by inspection of the profiles shown in Figure \ref{fig:profs_nancay}: from late July to mid September $\mbox{MJD} \sim 53994$ ), the daily profiles of tended to be composed of two (or more) significant peaks, each much broader than the one peak generally prominent before mid July (with typical full-width at half-maximum $\approx0.04P$, versus about half that value beforehand), and with greater pulse-shape variance than before."
 This may also explain why the ttiming residuals for each 1-month fit after mid 2006 July are about mms rms. twice as large as the typical corresponding value before then.," This may also explain why the timing residuals for each 1-month fit after mid 2006 July are about ms rms, twice as large as the typical corresponding value before then."
 Since 2006 October. the pprofiles appear to have varied less. and to be composed mainly of one broad peak (Fig. 1).," Since 2006 October, the profiles appear to have varied less, and to be composed mainly of one broad peak (Fig. \ref{fig:profs_nancay}) ),"
 although on some days the trailing peak is still recognizable (as it is more often in higher quality GBT data)., although on some days the trailing peak is still recognizable (as it is more often in higher quality GBT data).
 After another relatively large increase over the month of September. 7” has continued a steady increase at approximately the average rate for the 9-month span of our observations. 7.5«1079 ss per day.," After another relatively large increase over the month of September, $\dot \nu$ has continued a steady increase at approximately the average rate for the 9-month span of our observations, $7.5\times10^{-16}$ $^{-2}$ per day."
 On 2006 September 10-11 we observed ffor hhr with the GBT at GGHz. starting hhr after the beginning of the oobservation 22)).," On 2006 September 10–11 we observed for hr with the GBT at GHz, starting hr after the beginning of the observation \ref{sec:cxo}) )."
 We have used the contemporaneous TOAs thus obtained to measure the phase offset between the X-ray and radio pulses., We have used the contemporaneous TOAs thus obtained to measure the phase offset between the X-ray and radio pulses.
 The folded X-ray profile is shown in Figure 5.. with the first phase bin chosen to begin at midnight on September 11 (TDB).," The folded X-ray profile is shown in Figure \ref{fig:cxo}, with the first phase bin chosen to begin at midnight on September 11 (TDB)."
 After translating the TOAs for the first radio profile (see Fig. 5)), After translating the TOAs for the first radio profile (see Fig. \ref{fig:cxo}) )
 converted to infinite frequency to the solar system barycenter. a TEMPO fit yields a phase offset for the fiducial point of the radio profile (here its middle peak) of 0.16740.006 in the Figure.," converted to infinite frequency to the solar system barycenter, a TEMPO fit yields a phase offset for the fiducial point of the radio profile (here its middle peak) of $0.167\pm0.006$ in the Figure."
 The uncertainty includes a component due to the fit and a slightly smaller contribution from the uncertainty in the dispersion measure (DM) ofJ1810-197., The uncertainty includes a component due to the fit and a slightly smaller contribution from the uncertainty in the dispersion measure (DM) of.
. Within the larger uncertainty imposed by the rresolution (0.08P: see ??)) and the relatively small number of pulsed X-ray counts. the main component of the radio profile on this day arrives at the same time as the peak of the X-ray pulse (Fig. 5)).," Within the larger uncertainty imposed by the resolution $0.08P$; see \ref{sec:cxo}) ) and the relatively small number of pulsed X-ray counts, the main component of the radio profile on this day arrives at the same time as the peak of the X-ray pulse (Fig. \ref{fig:cxo}) )."
 Interestingly. the radio profile changed in both shape and flux during the oobservation — twice. within a span of 30mmin (Fig. 5)).," Interestingly, the radio profile changed in both shape and flux during the observation — twice, within a span of min (Fig. \ref{fig:cxo}) )."
 This does not modify the conclusion in the above paragraph. but helps answer a question concerning the radio flux and profile variations observed in.J1810-197:: they can occur suddenly (observed at a resolution of ~10 ss).," This does not modify the conclusion in the above paragraph, but helps answer a question concerning the radio flux and profile variations observed in: they can occur suddenly (observed at a resolution of $\sim 10$ s)."
" We have ""caught in the act at least nine such changes atNangay.. GBT and Parkes. all since mid2006 July."," We have “caught in the act” at least nine such changes at, GBT and Parkes, all since mid2006 July."
 As this corresponds to some 150 hours of observing time. we can estimate that such transitions occur on average every ~ I5hhr. at the present epoch.," As this corresponds to some 150 hours of observing time, we can estimate that such transitions occur on average every $\sim 15$ hr, at the present epoch."
 No X-ray bursts or significant changes in the ray flux or pulse shape were seen at the times of the radio transitions indicated in Figure 5.., No X-ray bursts or significant changes in the X-ray flux or pulse shape were seen at the times of the radio transitions indicated in Figure \ref{fig:cxo}. .
 The, The
al £986)).,al \cite{lebofsky86}) ).
 We have since observed Neptune and correction fuctors between the output of the photometer pipeline and the model of Neptune based on the work of Moreno (1995.. 2040)) have been established (sec Griffin et al. 2010)).," We have since observed Neptune and correction factors between the output of the photometer pipeline and the model of Neptune based on the work of Moreno \cite{moreno98}, \cite{moreno10}) ) have been established (see Griffin et al. \cite{griffin10}) )."
" We discuss the accuracy of the Moreno model further in Sect,", We discuss the accuracy of the Moreno model further in Sect.
 7. und the accuracy of the calibration constants in Sect., \ref{testing_models} and the accuracy of the calibration constants in Sect.
 40. of the present paper., \ref{conclusions} of the present paper.
" The calibration of the spectrometer follows «a different method compared to the photometer,", The calibration of the spectrometer follows a different method compared to the photometer.
 The signal that is measured by the spectrometer detectors is not a direct nieasitrenicnt of the [ως density integrated. over. the passband as iu the photometer but rather the Fourier component of the spectral content., The signal that is measured by the spectrometer detectors is not a direct measurement of the flux density integrated over the passband as in the photometer but rather the Fourier component of the spectral content.
 Therefore Ly., Therefore Eq.
 1 is not directly applicable but an analogous equation can be used to correct for any non-linearity between absorbed power and bolometer voltage before transforming into the frequency domain., \ref{equation1} is not directly applicable but an analogous equation can be used to correct for any non-linearity between absorbed power and bolometer voltage before transforming into the frequency domain.
 The parameters in this scheme are derived froin a model response of the bolometer and have different values depending on the bolometer bias that is set., The parameters in this scheme are derived from a model response of the bolometer and have different values depending on the bolometer bias that is set.
 Once a. linearised thneline in volts has been obtained the signal versus optical path difference is caleulated using the mechanisin position «nd further corrections for phase error are made (see Fulton et al. 2005))., Once a linearised timeline in volts has been obtained the signal versus optical path difference is calculated using the mechanism position and further corrections for phase error are made (see Fulton et al. \cite{fulton08}) ).
 The sore. telescope. SCALE und the tnstrianent self critssion arc aheays nicasured together and it is necessary to subtract a reference: interferogram taken on dark sky to. obtain the ος on its own.," The source, telescope, SCAL and the instrument self emission are always measured together and it is necessary to subtract a reference interferogram taken on dark sky to obtain the source on its own."
" This difference interferogram ds transformed into spectral space end finally converted to flue density using a relative spectral response function (ΠΕ),", This difference interferogram is transformed into spectral space and finally converted to flux density using a relative spectral response function (RSRF).
" The RSRF is derived by taking the intevferogram of an astronomical source with a well modelled continui. subtracting the reference interferogram. transforining this into spectral space and dividing by a model of the source speciem,"," The RSRF is derived by taking the interferogram of an astronomical source with a well modelled continuum, subtracting the reference interferogram, transforming this into spectral space and dividing by a model of the source spectrum."
 In the present pipeline we use the asteroid Vesta as the calibration source with a continiuian model provided by T. Mucller (Mueller and Layerros. 2002)).," In the present pipeline we use the asteroid Vesta as the calibration source with a continuum model provided by T. Mueller (Mueller and Lagerros, \cite{mueller02}) )."
" Interferograins taken on Vesta. Neptune and Üranus showed that. with the SCALE source off. the signal at the central peak docs not saturate, or at nost. only a few samples are saturated. once the detector bias is correctly set."," Interferograms taken on Vesta, Neptune and Uranus showed that, with the SCAL source off, the signal at the central peak does not saturate, or at most only a few samples are saturated, once the detector bias is correctly set."
 The fuct that we do not require SCALE to null the telescope cinission ds a consequence of the lower total emission from the telescope and straglight compared to the erpected values used in the initial desiyn of the SPIRE instrument., The fact that we do not require SCAL to null the telescope emission is a consequence of the lower total emission from the telescope and straylight compared to the expected values used in the initial design of the SPIRE instrument.
 Given this. and that using SCAL adds to the photon noise in the measurement. we have: decided not to HSE the SCAL SOUPCE dn routine observations.," Given this, and that using SCAL adds to the photon noise in the measurement, we have decided not to use the SCAL source in routine observations."
 An additional benefit of this made of operation ts that. with SCAL off it. and the rest of the instrument. are at a temperature between 4.50 and 5 I and the thermal eidssion from. these components is limited to frequencics only detectable in the SEW band.," An additional benefit of this mode of operation is that, with SCAL off it, and the rest of the instrument, are at a temperature between 4.5 and 5 K and the thermal emission from these components is limited to frequencies only detectable in the SLW band."
" The standard calibration for SPIRE spectra is bused on a point source,", The standard calibration for SPIRE spectra is based on a point source.
 An alternative calibration can be derived using the telescope which is appropriate for a source that entirely fills the detector field of view., An alternative calibration can be derived using the telescope which is appropriate for a source that entirely fills the detector field of view.
 A correction based on measurements of the spectrometer beam shape ts required to convert from one to the other (sec Sect. 7})., A correction based on measurements of the spectrometer beam shape is required to convert from one to the other (see Sect. \ref{testing_models}) ).
 Tt. should also be noted that instrument dependent spectral features in the passband of the spectrometer will change as a function of source crtent., It should also be noted that instrument dependent spectral features in the passband of the spectrometer will change as a function of source extent.
" To fest the CCCIπμ of the models used for both the spectrometer and photometer we have derived. the calibration using an alternative method. where we Hsc the telescope itself plus knowledge of the instrument throughput (sce Sect. Sj}, ", To test the accuracy of the models used for both the spectrometer and photometer we have derived the calibration using an alternative method where we use the telescope itself plus knowledge of the instrument throughput (see Sect. \ref{beam}) ).
"As discussed in Sect,", As discussed in Sect.
 2 the telescope is represented by a blackbody with a well known relative dependence between emdssivity and wavclength even df the «absolute overall eimissivitg may have an uncertainty up to (sec Fischer ct al. 2004))., \ref{initial} the telescope is represented by a blackbody with a well known relative dependence between emissivity and wavelength even if the absolute overall emissivity may have an uncertainty up to (see Fischer et al. \cite{fisher04}) ).
 We can therefore generate an RSRE from the measured telescope spectrin on dark sky and usc this to calibrate the spectra obtained on Vesti. Neptune und Uranus and compare to the models to check for self consistency.," We can therefore generate an RSRF from the measured telescope spectrum on dark sky and use this to calibrate the spectra obtained on Vesta, Neptune and Uranus and compare to the models to check for self consistency."
 The results together with contin models are shown in Fig. 3.., The results together with continuum models are shown in Fig. \ref{spectra}.
 The basic comparison is with the Neptune model of Moreno which shows an eccellent agreement across all wavelengths giving confidence tn both the relative and absolute love of the telescope emissivity., The basic comparison is with the Neptune model of Moreno which shows an excellent agreement across all wavelengths giving confidence in both the relative and absolute level of the telescope emissivity.
 The Uranits model shown ts also that of Moreno. but here we ας mereascd tre," The Uranus model shown is also that of Moreno, but here we have increased the"
(Smithetal.2002).. selected for distribution on the skv and range in color.,"\citep{smith02}, selected for distribution on the sky and range in color."
 The g.r.i.z. D51. ancl JILIN magnitudes vield 7 independent color measurements that are calibrated by zero-point offsets derived [rom cluster observations aud Sloan standard stars.," The $g,r,i,z$, D51, and J,H,K magnitudes yield 7 independent color measurements that are calibrated by zero-point offsets derived from cluster observations and Sloan standard stars."
" These 7 observables are used together with the r magnitude and the galactie latitude to derive 11 parameters. namely: effective temperature (T,j;). surlace gravity (οσο). metallicity (log( Z)). mass. radius. luminosity. bolometric correction. distance. interstellar ex(netion C1. and :d,:). and reddening(gj4)."," These 7 observables are used together with the $r$ magnitude and the galactic latitude to derive 11 parameters, namely: effective temperature $_{eff}$ ), surface gravity $\log(g)$ ), metallicity $\log(Z)$ ), mass, radius, luminosity, bolometric correction, distance, interstellar extinction $A_r$ and $A_V$ ), and reddening$E_{B-V}$ )."
 Functions relating (hese parameters (e.g. extinction laws (Cardelli.Clavton.&Mathis1989).. the radius dependence on mass aud surface eravitv. the luminosity dependence on effective temperature ancl radius. and the apparent magnitude dependence ou huninositv. the bolometric correction. interstellar extinction. and distance) reduce the number of unknowns from 11 to 5.," Functions relating these parameters (e.g. extinction laws \citep{cardelli}, the radius dependence on mass and surface gravity, the luminosity dependence on effective temperature and radius, and the apparent magnitude dependence on luminosity, the bolometric correction, interstellar extinction, and distance) reduce the number of unknowns from 11 to 5."
5 Stellar classilication requires choosing; among mocdel stellar atinosphlieres that best fit the observables., Stellar classification requires choosing among model stellar atmospheres that best fit the observables.
 The Castelli&Ixurucz(2004) models provide flux as a function of wavelength for temperatures ranging Irom 3500 to 50000 Ix. surface eravilies of 0 to 5.5 dex. and metallicities of —3.5 (to +0.5.," The \citet{kurucz} models provide flux as a function of wavelength for temperatures ranging from 3500 to 50000 K, surface gravities of 0 to 5.5 dex, and metallicities of $-3.5$ to $+0.5$."
 Fluxes are transformed to magnitudes by mulüplving by an estimate of the CCD response and filter transmission and integrating over wavelength., Fluxes are transformed to magnitudes by multiplying by an estimate of the CCD response and filter transmission and integrating over wavelength.
 The model colors (formed taking relevant magnitude differences) are calibrated to the eluster observations using a zero-point offset and a term linear in (g— r)., The model colors (formed taking relevant magnitude differences) are calibrated to the cluster observations using a zero-point offset and a term linear in $g-r$ ).
 The evolutionary (racks ol Girardietal.(2000) are used to constrain stellar luminosity (ancl. ultimately. radius and mass) given elfective temperature ancl surface gravity. (assuming solar metallicity).," The evolutionary tracks of \citet{girardi00} are used to constrain stellar luminosity (and, ultimately, radius and mass) given effective temperature and surface gravity (assuming solar metallicity)."
 The photometric data are minimally sufficient. for obtaining reliable surface gravity determinations., The photometric data are minimally sufficient for obtaining reliable surface gravity determinations.
 The parameter estimation is. therefore. carried oul using additional astrophysical information to form Bavesian priors.," The parameter estimation is, therefore, carried out using additional astrophysical information to form Bayesian priors."
 A star's physical parameters (given as the vector 7) are those which maximize (he posterior probability of obtaining the observed magnitudes and colors (given as the vector q)., A star's physical parameters (given as the vector $\vec{x}$ ) are those which maximize the posterior probability of obtaining the observed magnitudes and colors (given as the vector $\vec{q}$ ).
 The posterior probability. E P(r|q). is given," The posterior probability, $P(\vec{x}|\vec{q})$ , is given"
"The luminosity of the gas ejected by the wind in the annulus is dL=ied. where the outflow speed satisfies so in combination with (17)) we have Usine (14)). (15)). (16)). (13)) and (19)) in (13)) gives where r,=GAL/e*.","The luminosity of the gas ejected by the wind in the annulus is $dL = \frac{1}{2} {v}^2 |d\dot{M}|$, where the outflow speed satisfies so in combination with \ref{14}) ) we have Using \ref{17}) ), \ref{18}) ), \ref{19a}) ), \ref{14a}) ) and \ref{15}) ) in \ref{13a}) ) gives where $r_g=GM/c^2$."
" For a standard Shakura-Sunyaev. disc model (Shakura&Sunyaev1973) supplemented by our racially dependent accretion rate M=η) we have and Usine (21)) and (22)) in (20)). the time required to wander an angle @ racians is For stochastic wobble to be observable /,,(0) must at least be less than the age of a system Tage."," For a standard Shakura-Sunyaev disc model \citep{ss73} supplemented by our radially dependent accretion rate ${\dot M}={\dot M}_o(r/r_o)^s$ we have and Using \ref{20}) ) and \ref{21}) ) in \ref{19}) ), the time required to wander an angle $\theta$ radians is For stochastic wobble to be observable $t_{w}(\theta)$ must at least be less than the age of a system $\tau_{age}$."
 A further constraint. follows from the standard accretion paradigm in which accrelion supplies the energv for a turbulent viscositw which. together with the outflow. transport angular momentum ancl sustain the accretion.," A further constraint follows from the standard accretion paradigm in which accretion supplies the energy for a turbulent viscosity which, together with the outflow, transport angular momentum and sustain the accretion."
 As cliseussecl at the end of Sec.3. the turbulent viscosity is also a means of (transporting the angular momentum associated with tilt between annuli such that the tlt of inner annuli is compensated by the opposing tilt of outer annuli.," As discussed at the end of Sec.3, the turbulent viscosity is also a means of transporting the angular momentum associated with tilt between annuli such that the tilt of inner annuli is compensated by the opposing tilt of outer annuli."
" For stochastic wobble to produce a net mean Glt on an annulus at an inner radius. (he viscous time scale there 7,(r) should be short compared to the tilt (ine. so that the compensating angular momentum opposite to that associated with the tlt can be"," For stochastic wobble to produce a net mean tilt on an annulus at an inner radius, the viscous time scale there $\tau_\nu(r)$ should be short compared to the tilt time, so that the compensating angular momentum opposite to that associated with the tilt can be"
Figure 1. shows the evolution of the DM mass inside the star ancl its fine derivative.,Figure \ref{f4} shows the evolution of the DM mass inside the star and its time derivative.
 The left panel shows the total DM. mass inside the star. whereas the right pancl shows the ratio of the rate of DAL aunililation in mass to the rate of DM lass increase (within the star) owing to adiabatic contraction: Iu Figure L. we show the results for an additional uodel iu which the depletion of DM in the star is taken iuto account.," The left panel shows the total DM mass inside the star, whereas the right panel shows the ratio of the rate of DM annihilation in mass to the rate of DM mass increase (within the star) owing to adiabatic contraction: In Figure \ref{f4}, we show the results for an additional model in which the depletion of DM in the star is taken into account."
 Although this case uieht appear unrealistic. if is useful to see when DM depletion becomes substantial.," Although this case might appear unrealistic, it is useful to see when DM depletion becomes substantial."
" The solid line represents our ""base model while the dashed ie shows the result of the no-depletion case.", The solid line represents our “base model” while the dashed line shows the result of the no-depletion case.
 Up to AM~200.300ML... there is alinost. no differeuce between thetwo cases;," Up to $M \sim 200 - 300 \ \mathrm{M_{\odot}}$, there is almost no difference between thetwo cases."
 At AL>3003... rowever. DAL depletion becomes significant and hen the total DM mass actually starts decreasing.," At $M > 300 M_{\odot}$, however, DM depletion becomes significant and then the total DM mass actually starts decreasing."
 The evolution thereafter is iuterestiug., The evolution thereafter is interesting.
" The DM ""fuel inside the star runs short to sustain the star.", The DM “fuel” inside the star runs short to sustain the star.
 The star stops expaudius. the eas density lucreases niore efficientlv. aud then DM density also increases again.," The star stops expanding, the gas density increases more efficiently, and then DM density also increases again."
 Then DM aunibilation coustuues rapidly the DAI fuel inside the star., Then DM annihilation consumes rapidly the DM fuel inside the star.
 Finally. the DAL annihilation energv cannot sustain the star. marking the end of the dark star phase.," Finally, the DM annihilation energy cannot sustain the star, marking the end of the dark star phase."
 The star collapses aud will eventually reach the main-sequence pliase., The star collapses and will eventually reach the main-sequence phase.
 Figure Ὁ shows the radial profiles for various quantities of gas (left) and DAL (right) when the stellar mass is AZ=200 (solid lines). 800 (dashed lines} and LOOOAL. (dotted lines) respectively.," Figure \ref{f5} shows the radial profiles for various quantities of gas ) and DM ) when the stellar mass is $M = 200$ (solid lines), 800 (dashed lines) and $1000 \ \mathrm{M_{\odot}}$ (dotted lines) respectively."
 The horizoutal axis is the radial distance from the stellar center divided by the stellar radius., The horizontal axis is the radial distance from the stellar center divided by the stellar radius.
 The top paucls show the evolution of gas density aud DM deusitv., The top panels show the evolution of gas density and DM density.
 Between AL=200 to SOOAD... the star has an exteuded structure aud the ceutral deusitv docs not merease much.," Between $M=200$ to $800 \ \mathrm{M_{\odot}}$, the star has an extended structure and the central density does not increase much."
 The DAL deusitv iucreases by adiabatie contraction but actually decreases slightly at the immer most part owing to anuihilation., The DM density increases by adiabatic contraction but actually decreases slightly at the inner most part owing to annihilation.
 At the final contraction phase (AF=8OO to 1000 NT... both the gas density aud the DM deusity increase substautially.," At the final contraction phase $M=800$ to $1000 \ \mathrm{M_{\odot}}$ ), both the gas density and the DM density increase substantially."
 The aiddle panels show the evolution of enclosed mass of eas and DAI., The middle panels show the evolution of enclosed mass of gas and DM.
 Although the eax nis profile stavs roughly unchanged. the DM unass decreases dramatically during the final phase from M.=8OO to 1000ALL.," Although the gas mass profile stays roughly unchanged, the DM mass decreases dramatically during the final phase from $M=800$ to $1000 \ \mathrm{M_{\odot}}$."
 Note that the horizontal axis iu the plots shows a normalized radius ARR., Note that the horizontal axis in the plots shows a normalized radius $R/R_{*}$.
 The stellay radius A. itself changes sieuificautlv over the plotted rauge of evolutionary stages., The stellar radius $R_{*}$ itself changes significantly over the plotted range of evolutionary stages.
 Because the dark star phase euds with the runaway buruiugof DM inside of the star. the total amount ofDAE schen AZ=1000M. is alveacky very sinall.," Because the dark star phase ends with the runaway burning of DM inside of the star, the total amount of DM when $M=1000 \ \mathrm{M_{\odot}}$ is already very small."
 The bottom-left paucl shows the DM annihilation rate and the bottom-right pancl shows the total huninositv generated by the DAL annihilation within the radius., The bottom-left panel shows the DM annihilation rate and the bottom-right panel shows the total luminosity generated by the DM annihilation within the radius.
 These panels show the energy eoncrating efficiency from the DAL annihilation., These panels show the energy generating efficiency from the DM annihilation.
 Again. we see that the annihilation rate is low inside the star at the final stage AZ=1000AI. aud the euclosed DAL Duuinositv at the stellar surface (at loeyyRadius/R.= 0) is simaller thaw in the earlier phases.," Again, we see that the annihilation rate is low inside the star at the final stage $M=1000 \ \mathrm{M_{\odot}}$ and the enclosed DM luminosity at the stellar surface (at $\mathrm{log_{10} Radius/R_* = 0}$ ) is smaller than in the earlier phases."
 The stellar mass increases by eas accretion but the DM cucrey supply decreases: this causes the star to contract., The stellar mass increases by gas accretion but the DM energy supply decreases; this causes the star to contract.
 Figure 6 shows the evolution of some basic stellar quantities which characterize the dark star., Figure \ref{f6} shows the evolution of some basic stellar quantities which characterize the dark star.
 We compare the results of our base model (solid lines) with those of no-DM model (dashed lines) and of no-depletion model (dotted lines)., We compare the results of our base model (solid lines) with those of no-DM model (dashed lines) and of no-depletion model (dotted lines).
 Until the star grows to AM~200300AL... the base model and the uo-depletion model appear very simular. showing again that DAL depletion is negligible iu carly phases.," Until the star grows to $M \sim 200 - 300 \ \mathrm{M_{\odot}}$, the base model and the no-depletion model appear very similar, showing again that DM depletion is negligible in early phases."
 After the star grows to ~3003ML.. we see sinall but appreciable differences between the base model aud the no-depletion model.," After the star grows to $\sim 300 \mathrm{M_{\odot}}$, we see small but appreciable differences between the base model and the no-depletion model."
 Ax has been shown in Figure. L. DM is coustumed bx annililation inside the star whereas the supply by adiabatic contraction is slow owing to the siuall eas Inass accretion rate.," As has been shown in Figure \ref{f4}, DM is consumed by annihilation inside the star whereas the supply by adiabatic contraction is slow owing to the small gas mass accretion rate."
 As the star becomes more lnassive. if needs more DM to produce necessary enerev to sustain eravitational equilibrimm.," As the star becomes more massive, it needs more DM to produce necessary energy to sustain gravitational equilibrium."
 When the DAL supply becomes insufficient. this quasi-stable dark star phase cannot be sustained.," When the DM supply becomes insufficient, this quasi-stable dark star phase cannot be sustained."
 It occurs at AL~600ML. for the base model., It occurs at $M \sim 600 \ \mathrm{M_{\odot}}$ for the base model.
 The stellar properties. however. do not change iuunnediatelv until up to Af~900 AL...," The stellar properties, however, do not change immediately until up to $M \sim 900 \ \mathrm{M_{\odot}}$ ."
 At around ALc900AL... the DAL inside the star lurus out rapidly. the star begius to collapse. aud the Cutral teiiperature mereases rapidly.," At around $M \ge 900 \ \mathrm{M_{\odot}}$, the DM inside the star burns out rapidly, the star begins to collapse, and the central temperature increases rapidly."
 Finally the cπα temperature reaches 104Lo’ EK. the uuclear burning will soon start. and the star will eventually laud on the main-sequence.," Finally the central temperature reaches $10^7 - 10^8 \ \mathrm{K}$ , the nuclear burning will soon start, and the star will eventually land on the main-sequence."
 Table E. stumumarizes thebasic stellar properties at several characteristic phases., Table \ref{table1} summarizes thebasic stellar properties at several characteristic phases.
 Note that the, Note that the
its contribution to the total emission from the region is only about 10 per cent.,its contribution to the total emission from the region is only about 10 per cent.
 Since the spatial resolution of is 75 aresec (for the MOS cameras: Jansen 2001). our present result is fully consistent with the LCTure.," Since the spatial resolution of is $\sim$ 5 arcsec (for the MOS cameras; Jansen 2001), our present result is fully consistent with the picture."
" ""here is a further extended X-ray emission to the cast rom Ser A. which is distinct in both the soft anc hard mands."," There is a further extended X-ray emission to the east from Sgr $^*$, which is distinct in both the soft and hard bands."
" When we exclude the 20 aresec-radius region around Ser A. the centre of the dilfuse emission is found to be ocated at (17! 45"" 44°. 29° 0/3) in the J2000 coordinates."," When we exclude the 20 arcsec-radius region around Sgr $^*$, the centre of the diffuse emission is found to be located at $^{\rm
h}$ $^{\rm m}$ $^{\rm s}$, $-29\degr~0{\farcm}3$ ) in the J2000 coordinates."
 The c-folcling radius is 28 arcsec in the core in the 2.10 keV uid. although the enhancement in the surface brightness (with respect to the surrounding region) has a Lull extent closer to 7200 arcsec across.," The e-folding radius is 28 arcsec in the core in the 2–10 keV band, although the enhancement in the surface brightness (with respect to the surrounding region) has a full extent closer to $\sim$ 200 arcsec across."
 This clilluse feature is clearly elongated. along an axis roughly parallel to the Galactic jane., This diffuse feature is clearly elongated along an axis roughly parallel to the Galactic plane.
 As shown in Fig. Ll.," As shown in Fig. \ref{fig:img},"
 the X-rav emitting region is mostly confined within the radio shell ofLast. in full agreement with earlier. observations (Alaccaetal. 2002).," the X-ray emitting region is mostly confined within the radio shell of, in full agreement with earlier observations \cite{Maeda2002}."
. On the basis of this strong correlation between the extended: X-ray. emission and the radio shell structure. hereafter we refer to this bright dilluse X-ray source asLast.," On the basis of this strong correlation between the extended X-ray emission and the radio shell structure, hereafter we refer to this bright diffuse X-ray source as."
 Since the X-ray spectrum of shows clistinet emission lines (see Section 3.2)). we have mace line intensity images at 6.7-keV and 2.4-keV: the former represents the ha ine from helium-like iron (re) whereas the latter is from 1elium-like sulfur (S).," Since the X-ray spectrum of shows distinct emission lines (see Section \ref{sec:spec}) ), we have made line intensity images at 6.7-keV and 2.4-keV; the former represents the $\alpha$ line from helium-like iron (Fe) whereas the latter is from helium-like sulfur (S)."
 We mace three images corresponcing o energv bands 2.2 keV2.6 keV (2.4-koV-band). 4.0 6.0 keV. (continuum). and 6.55 keV6.85 keV (6.7-keV-iid).," We made three images corresponding to energy bands 2.2 keV–2.6 keV (2.4-keV-band), 4.0 keV--6.0 keV (continuum), and 6.55 keV–6.85 keV (6.7-keV-band)."
 From the measured continuum image. we estimated continuum images appropriate to the 6.7-keV ancl 2.4-keV rans. taking into account the detector energy response and the continuum shape averaged over the whole region.," From the measured continuum image, we estimated continuum images appropriate to the 6.7-keV and 2.4-keV bands, taking into account the detector energy response and the continuum shape averaged over the whole region."
 ‘These narrow-band continuum images were then subtracted o reasonable approximations to pure line images at 6.7-keV and 2.4-keV. (Fig., These narrow-band continuum images were then subtracted to reasonable approximations to pure line images at 6.7-keV and 2.4-keV (Fig.
 lee. d).," \ref{fig:img}c c, d)."
 Phe 6.7-keV line is clearly more concentrated in the core of than the continuum (Lig., The 6.7-keV line is clearly more concentrated in the core of than the continuum (Fig.
 lee)., \ref{fig:img}c c).
 This implies that the core of is more abundant in iron. or possibly higher in temperature. or à combination of these two ellects.," This implies that the core of is more abundant in iron, or possibly higher in temperature, or a combination of these two effects."
 In contrast. the 24-keV line peak is located on Ser A (Fig.," In contrast, the 2.4-keV line peak is located on Sgr $^*$ (Fig."
 ldd), \ref{fig:img}d d).
 These cllects are. investigated: quantitatively via. the spatially-resolved. spectral analysis described. in the [ater sections (Section 3.2.4))., These effects are investigated quantitatively via the spatially-resolved spectral analysis described in the later sections (Section \ref{sec:separate-reg-fit}) ).
 We note that three further bright. sources are. visible in Fig. l((, We note that three further bright sources are visible in Fig. \ref{fig:img}( (
a. b).,"a, b)."
 The hard source appears to be a. non-thermal X-ray filament (κου Sakano 2003a for details)., The hard source appears to be a non-thermal X-ray filament (see Sakano 2003a for details).
 The two soft sources. and RN 2904. have previously been detected. byROSAL (Precehl Trtimmper 1994: $Sidoli. Belloni Alercehetti 2001).," The two soft sources, and RX $-$ 2904, have previously been detected by (Predehl Trümmper 1994; Sidoli, Belloni Mereghetti 2001)."
 is presumably identical with a source CNOGC 285828 (Muno 2003)., is presumably identical with a source CXOGC $-$ 285828 (Muno 2003).
 We identify RN 2004 as a foreground star. GSC 06840. .," We identify RX $-$ 2904 as a foreground star, GSC $-$ ."
. As illustrated in Fig. , As illustrated in Fig. \ref{fig:img}( (
Πα.) we accumulated the source spectrum from a circular. cell of 1060 aresec-radius but excluding the regions within 24 and 16 arcsec-racdii of Ser A ancl285830. respectively.,"a,b), we accumulated the source spectrum from a circular cell of 100 arcsec-radius but excluding the regions within 24 and 16 arcsec-radii of Sgr $^*$ and, respectively."
 The choice of an appropriate background field is not a trivial task due to the elumpy nature of hot plasma. which pervades the whole region.," The choice of an appropriate background field is not a trivial task due to the clumpy nature of hot plasma, which pervades the whole region."
 Variations in absorption also add to the complexity of ie situation., Variations in absorption also add to the complexity of the situation.
 Llere. we chose a nearby background region at nearly the same galactic latitude as the source region (see Fig. 1)).," Here, we chose a nearby background region at nearly the same galactic latitude as the source region (see Fig. \ref{fig:img}) ),"
 so as to minimize systematic effects., so as to minimize systematic effects.
 In fact. the N-rav. hardness does not. vary strongly. along this axis (Sakano 9005). ane rw dillerence. of the X-ray. absorption between the source ancl backgroun regions is also minimized.," In fact, the X-ray hardness does not vary strongly along this axis (Sakano 2003b), and the difference of the X-ray absorption between the source and background regions is also minimized."
 Since is a very brieh source. the spectrum is not strongly allected by selection of the background. except. for the outer region. definec in Section 3.2.4.. as long as we choose the backgrotune from a relatively nearby region.," Since is a very bright source, the spectrum is not strongly affected by selection of the background, except for the outer region defined in Section \ref{sec:separate-reg-fit}, as long as we choose the background from a relatively nearby region."
 For example. the use of a cillerent background dataset gave rise to an overall [ux increased in of 5 per cent. whereas the derivec temperature changed by ~1O per cent or less.," For example, the use of a different background dataset gave rise to an overall flux increased in of 5 per cent, whereas the derived temperature changed by $\sim$ 10 per cent or less."
 Although the best-fitting values change slightly. depending on the backeround selection. the spectral structure never changes.," Although the best-fitting values change slightly depending on the background selection, the spectral structure never changes."
 We conclude that the spectral results presented below which ave derived on the basis of the background field identified in Fig. 1((, We conclude that the spectral results presented below which are derived on the basis of the background field identified in Fig. \ref{fig:img}( (
a) are reasonably robust.,a) are reasonably robust.
 Fie., Fig.
 2 shows the resultant pn spectra., \ref{fig:pn-fit} shows the resultant pn spectra.
 Several emission lines can be seen. implying that a significant fraction of the spectrum originates from hot thermal plasma.," Several emission lines can be seen, implying that a significant fraction of the spectrum originates from hot thermal plasma."
" Using the package we initially experimented with the simultaneous [fitting of the MOSI anc MOS2 spectra with a “phenomenological model"" consisting of a multi-temperature continuum plus many Caussian lines.", Using the package we initially experimented with the simultaneous fitting of the MOS1 and MOS2 spectra with a “phenomenological model” consisting of a multi-temperature continuum plus many Gaussian lines.
 The continuum comprised. three thermal bremsstrahlung components with temperatures initially set at 0.5. 1.0 and 4 keV. each absorbed by a separate column. density component.," The continuum comprised three thermal bremsstrahlung components with temperatures initially set at 0.5, 1.0 and 4 keV, each absorbed by a separate column density component."
 Llowever. in the event ib proved. necessary to reduce the number of free parameters. describing the continuum: this was achieved by fixing the temperature and column for the softest component at 0.5. keV. and 7o1077em> respectively and absorbing the two higher temperature Components with the same column density.," However, in the event it proved necessary to reduce the number of free parameters describing the continuum; this was achieved by fixing the temperature and column for the softest component at 0.5 keV and $7 \times 10^{22} \rm~cm^{-2}$ respectively and absorbing the two higher temperature components with the same column density."
 With continuum so defined. we were able to determinethe equivalent widths and centre energies for the set. of lines. although for most of the weak lines we fixed the centre," With continuum so defined, we were able to determinethe equivalent widths and centre energies for the set of lines, although for most of the weak lines we fixed the centre"
"Iu the third and fal experiment we performed tests on a set of real astronomical CCD images to confirma the previous results derived from svuthetic ππαρος,",In the third and final experiment we performed tests on a set of real astronomical CCD images to confirm the previous results derived from synthetic images.
 We used a sequence of 20 similar CCD images taken with the 2.5-1n Isaac Newton Telescope at La Pahua that show a random distribution of faint stars aud galaxies (Figure 11)., We used a sequence of 20 similar CCD images taken with the 2.5-m Isaac Newton Telescope at La Palma that show a random distribution of faint stars and galaxies (Figure 11).
 All the exposures were for G00 seconds through a V-baud filter with the same poiutius on the sky (12517.2672]/).," All the exposures were for 600 seconds through a V-band filter with the same pointing on the sky $12^h 51^m,
26^{\circ} 24'$ )."
 These images are publicly available through the virtual observatory portal at//portal-nvo., These images are publicly available through the virtual observatory portal at.
noao.edu. We performed 2 tests to measure the effects of quantization on these images., We performed 2 tests to measure the effects of quantization on these images.
 Iu the first test we coarsely quantized oue of the muiages using q = 1 (with subtractive dithering). bv compressing it with and then wncompressing it again withfunpack.," In the first test we coarsely quantized one of the images using q = 1 (with subtractive dithering), by compressing it with and then uncompressing it again with."
" As predicted by cquation Ον, achieved a compression ratio of about 10. which is equivalent to 3.2 bits per pixel in the compressed image,"," As predicted by equation \ref{eq:ratio3}, achieved a compression ratio of about 10, which is equivalent to 3.2 bits per pixel in the compressed image."
 Also as expected from equation 10.. the measured backeround noise level increased by. from σ = 22.79 in the original image to g = 23.73 in the quantized image.," Also as expected from equation \ref{eq:fractionalnoise}, the measured background noise level increased by, from $\sigma$ = 22.79 in the original image to $\sigma$ = 23.73 in the quantized image."
 We then compared the SExtractor magnitude mcasurements in the original nuage to those derived. from the quantized image., We then compared the SExtractor magnitude measurements in the original image to those derived from the quantized image.
 Since we do uot know the true magnitudes of the stars in this nuaee (unlike iu the experiments on the svuthetic stars}. we can only compare the measurements of the stars ini the 2 images. both of which lave ineasurement uncertainties," Since we do not know the true magnitudes of the stars in this image (unlike in the experiments on the synthetic stars), we can only compare the measurements of the stars in the 2 images, both of which have measurement uncertainties."
 The top panel of Figure 12 shows the difference between the 2 magnitude measurements for cach star as a πιοΊο. of the magnitude of the star. aud the widdle pancl shows the corresponding errors (tlhe magnitude difference divided bv the statistical error on that magnitude as calculated x SExtractorj.," The top panel of Figure 12 shows the difference between the 2 magnitude measurements for each star as a function of the magnitude of the star, and the middle panel shows the corresponding errors (the magnitude difference divided by the statistical error on that magnitude as calculated by SExtractor)."
 The larger poiuts iu these paucls show the 1ueali differeuce averaged over 0.5 nae bius. which demonstrate that there is no sienificant systematic bias between the 2 sets of maguitudes measurements.," The larger points in these panels show the mean difference averaged over 0.5 mag bins, which demonstrate that there is no significant systematic bias between the 2 sets of magnitudes measurements."
 The RMS value of all the relative errors in the middle panel is 310., The RMS value of all the relative errors in the middle panel is $0.34 \sigma$.
 This is sheltly lareer than the factor of V1/12=0.29 hat one would expect simply from he added quantization noise and nav be due to other residual sources of noise in the SExtractor calculations., This is slightly larger than the factor of $\sqrt{1/12} = 0.29$ that one would expect simply from the added quantization noise and may be due to other residual sources of noise in the SExtractor calculations.
 The fact that this is πιο less than he approximately lo dispersion that one would expect when comparing the magnitudes derived roni 2 identical CCD images of the same stars. confirms that quantizing the image with q = 1 has rot introduced statistically significant differences in the maguitude measurements.," The fact that this is much less than the approximately $ 1 \sigma$ dispersion that one would expect when comparing the magnitudes derived from 2 identical CCD images of the same stars, confirms that quantizing the image with q = 1 has not introduced statistically significant differences in the magnitude measurements."
 Finally. the lower panel plots the ratio of the magnitude errors iu the quantized aud original dmaees which shows that he statistical errors of the faiutest stars are ou average about ereater m the q = 1 quautized nage. as expected.," Finally, the lower panel plots the ratio of the magnitude errors in the quantized and original images which shows that the statistical errors of the faintest stars are on average about greater in the q = 1 quantized image, as expected."
 For the second test we created 2 new images w co-adding the 20 original CCD images aud by coadding the q = 1 quantized version of cach of he dmages and then repeated the same tests as described above., For the second test we created 2 new images by co-adding the 20 original CCD images and by coadding the q = 1 quantized version of each of the images and then repeated the same tests as described above.
 The results. shown in Fieure 13. are siuular to those iu Figure 12 except that the ‘faintest detected stars are now 2.5loge20=1.6 nag fainter. as a result of co-adcdiug the 20 images.," The results, shown in Figure 13, are similar to those in Figure 12 except that the faintest detected stars are now $2.5 \log{\sqrt{20}} = 1.6$ mag fainter, as a result of co-adding the 20 images."
 The RAIS value of the relative errors shown iu the uiddle pauel is 0.336 in this case. which again demonstrates that quantizing the images with q = 1 has not produced any significant photometric errors. even in objects that are fainter than the detection threshold iu a single nuage.," The RMS value of the relative errors shown in the middle panel is $0.33 \sigma$ in this case, which again demonstrates that quantizing the images with q = 1 has not produced any significant photometric errors, even in objects that are fainter than the detection threshold in a single image."
ealaxies. the BH-NS inerecrs will take place typically a few times closer to t1e host ealaxy thau the NS-NS imerecrs.,"galaxies, the BH-NS mergers will take place typically a few times closer to the host galaxy than the NS-NS mergers."
 However. there is still a long tail of the distribution. with a significant fracion extending to aree distances.," However, there is still a long tail of the distribution, with a significant fraction extending to large distances."
 We have shiwn that the disances from the host ealaxies where conmpact object biaries ineree decrease with increasing he mass of the binary., We have shown that the distances from the host galaxies where compact object binaries merge decrease with increasing the mass of the binary.
 The reasons for such a behavior are twofold., The reasons for such a behavior are twofold.
 First. he lifetimes of heavier Dinarics are sualer. because of the increased eravitational wave enerev loss.," First, the lifetimes of heavier binaries are smaller, because of the increased gravitational wave energy loss."
 Second. the wid hoof the kick velocity distribution ina supernova explosko ds probably sinaller when black holes are formed. wuch leads to smaller center of lass velocities.," Second, the width of the kick velocity distribution in a supernova explosion is probably smaller when black holes are formed, which leads to smaller center of mass velocities."
 We couchde that DII-NS binary merecrs are more likely progenitors of ganunuverav bursts than the NS-NS binaries., We conclude that BH-NS binary mergers are more likely progenitors of gamma-ray bursts than the NS-NS binaries.
 Their distribution closely follows that of the matter iu massive galaxies. aud also allows to explain the extreme cuerectics of some bursts.," Their distribution closely follows that of the matter in massive galaxies, and also allows to explain the extreme energetics of some bursts."
 However. this conclusion is so far based on a small sample of well observed CRB afterelows for long aud hard bursts.," However, this conclusion is so far based on a small sample of well observed GRB afterglows for long and hard bursts."
 “This work has been supported by the ABN erants 2P03D01616. and 2P03D00415 and also mace use of the NASA Astrophysics Data System.," This work has been supported by the KBN grants 2P03D01616, and 2P03D00415 and also made use of the NASA Astrophysics Data System."
"This template is reddened by the starburst extinction law from ?,, with a distribution in E(B—V).","This template is reddened by the starburst extinction law from \citet{calzetti00}, with a distribution in $E(B-V)$."
 This distribution we choose such that the UV-continuum slopes that we measure from the data are matched when we use our fiducial template as a base., This distribution we choose such that the UV-continuum slopes that we measure from the data are matched when we use our fiducial template as a base.
" To measure the UV-continuum slopes, we use a colour redward of 1600À rest-frame, i.e. the r—i colour for the u- and the i—z colour for the g-dropouts."," To measure the UV-continuum slopes, we use a colour redward of $\AA$ rest-frame, i.e. the $r-i$ colour for the $u$ -dropouts and the $i-z$ colour for the $g$ -dropouts."
 For the r- we can not perform a similar measurement because we do not have observations in a band redward of the z-band., For the $r$ -dropouts we can not perform a similar measurement because we do not have observations in a band redward of the $z$ -band.
 Therefore we will use the same distribution of dust as we find for the g-dropouts., Therefore we will use the same distribution of dust as we find for the $g$ -dropouts.
" For the u-dropouts we find that a uniform dust distribution with reddening between with 0.1«E(B—V) «0.4 gives a good fit to the data, see Fig. 3.."," For the $u$ -dropouts we find that a uniform dust distribution with reddening between with $<E(B-V)<$ 0.4 gives a good fit to the data, see Fig. \ref{fig:uvcontslopesu}."
" For the g-dropouts we measure a larger spread in UV-continuum slopes, and find a reasonable fit when using a uniform dust distribution with reddening between 0.0«E(B—V) «0.5."," For the $g$ -dropouts we measure a larger spread in UV-continuum slopes, and find a reasonable fit when using a uniform dust distribution with reddening between $<E(B-V)<$ 0.5."
" It should be noted that the age and amount of dust attenuation of the template are highly degenerate, so that different combinations of these parameters fit the UV-continuum slopes in the data."," It should be noted that the age and amount of dust attenuation of the template are highly degenerate, so that different combinations of these parameters fit the UV-continuum slopes in the data."
" It is especially important to correctly match the distribution of the UV-continuum slopes from the data with the model galaxies, since an increase (decrease) in the age of the galaxy model template has a similar effect on the LF as an increase (decrease) of the amount of dust."," It is especially important to correctly match the distribution of the UV-continuum slopes from the data with the model galaxies, since an increase (decrease) in the age of the galaxy model template has a similar effect on the LF as an increase (decrease) of the amount of dust."
 We will elaborate on this in Sect. 4.3.., We will elaborate on this in Sect. \ref{sec:robust}.
" If we measure the UV-continuum slopes in our data for different magnitude bins, we do not find a significant evolution."," If we measure the UV-continuum slopes in our data for different magnitude bins, we do not find a significant evolution."
 Therefore we will use a distribution of dust attenuation in our simulations that is independent of magnitude., Therefore we will use a distribution of dust attenuation in our simulations that is independent of magnitude.
 LBGs have typical half-light radii of rjj?~ 0.1”-0.3” and thus are unresolved by the CFHT and can be treated as point sources.," LBGs have typical half-light radii of $r_{1/2} \sim$ 0.1""-0.3"" \citep{giavalisco96} and thus are unresolved by the CFHT and can be treated as point sources."
" As the size of the PSF in the CFHT images is strongly position dependent, we have to adapt the injected sources accordingly."," As the size of the PSF in the CFHT images is strongly position dependent, we have to adapt the injected sources accordingly."
" We parametrize the PSF by a Moffat profile, in which 8 and Rp are the parameters that we adapt to adjust the shape and size of the profile respectively."," We parametrize the PSF by a Moffat profile, in which $\beta$ and $R_{0}$ are the parameters that we adapt to adjust the shape and size of the profile respectively."
 Jo represents the flux normalisation., $I_{0}$ represents the flux normalisation.
" In order to measure the PSF as a function of position for the different filters and fields, we first select several hundred stars based on their magnitudes and half-light radii, in each field and each filter."," In order to measure the PSF as a function of position for the different filters and fields, we first select several hundred stars based on their magnitudes and half-light radii, in each field and each filter."
" We measure the and flux radii of these stars, rso and roo, using SExtractor."," We measure the and flux radii of these stars, $\rm{r_{50}}$ and $\rm{r_{90}}$, using SExtractor."
" The ratio of these flux radii uniquely determines the Moffat-6 parameter, which, in combination with either one of the flux radii, gives the Moffat profile radius Ro for each star."," The ratio of these flux radii uniquely determines the $\beta$ parameter, which, in combination with either one of the flux radii, gives the Moffat profile radius $R_{0}$ for each star."
 We find that the Moffat-6 parameter is fairly constant over the fields and filters (854.0) and only Ro changes significantly.," We find that the $\beta$ parameter is fairly constant over the fields and filters $(\beta
\approx 4.0)$ and only $R_{0}$ changes significantly."
" To model Ro as a function of position, we fit a 2-dimensional polynomial function to the SExtracted values for r59."," To model $R_{0}$ as a function of position, we fit a 2-dimensional polynomial function to the SExtracted values for $r_{50}$."
" This constrains the PSF size on every position, for every field and filter."," This constrains the PSF size on every position, for every field and filter."
 We find that there is a ~30% difference in Ro between the image center and boundaries., We find that there is a $\sim$ difference in $R_{0}$ between the image center and boundaries.
" As this, in our ground-based wide-field survey, is by far the dominating effect in the apparent surface brightnesses of our sources, we do not assume an intrinsic size distribution for the sources in the main simulations of this paper."," As this, in our ground-based wide-field survey, is by far the dominating effect in the apparent surface brightnesses of our sources, we do not assume an intrinsic size distribution for the sources in the main simulations of this paper."
" If we consider a certain intrinsic magnitude distribution of galaxies, the recovered distribution after source extraction and colour selection will look different due to statistical fluctuations in the measurement."," If we consider a certain intrinsic magnitude distribution of galaxies, the recovered distribution after source extraction and colour selection will look different due to statistical fluctuations in the measurement."
 In our analysis we attempt to correct for this effect called Eddington bias (??)..," In our analysis we attempt to correct for this effect called Eddington bias \citep{eddington13, teerikorpi04}."
 It is hard to estimate this bias analytically because the size of the magnitude scatter is an increasing function of magnitude., It is hard to estimate this bias analytically because the size of the magnitude scatter is an increasing function of magnitude.
" Also, when approaching the completeness limit of the survey, only the brighter objects will be detected."," Also, when approaching the completeness limit of the survey, only the brighter objects will be detected."
 What generally happens is that intrinsically faint objects will on average look brighter than they are., What generally happens is that intrinsically faint objects will on average look brighter than they are.
 The Eddington bias can be estimated by comparing the intrinsic magnitudes of the injected sources to the recovered magnitudes., The Eddington bias can be estimated by comparing the intrinsic magnitudes of the injected sources to the recovered magnitudes.
" Such a comparison is shown in Fig. 4,,"," Such a comparison is shown in Fig. \ref{fig:eddingtonbias},"
 stressing the importance of that effect for faint magnitudes., stressing the importance of that effect for faint magnitudes.
" We want to inject sources with the same magnitude distribution as the intrinsic distribution, to get an unbiased result."," We want to inject sources with the same magnitude distribution as the intrinsic distribution, to get an unbiased result."
" As the bias is expected to be largest for fainter sources, it is especially important to correctly model the faint-end of the intrinsic distribution."," As the bias is expected to be largest for fainter sources, it is especially important to correctly model the faint-end of the intrinsic distribution."
" Here we adopt a LF that is consistent with the deepest LBG survey, conducted by ?.."," Here we adopt a LF that is consistent with the deepest LBG survey, conducted by \cite{bouwens07}. ."
efficiency required.,efficiency required.
 The process of chemical enrichment i5 rather fast. since it is primarily driven by massive OB stars with lifetimes of order a few million years.," The process of chemical enrichment is rather fast, since it is primarily driven by massive OB stars with lifetimes of order a few million years."
 If formation redshifts zp5 are assumed for the more abundant component of faint galaxies (which contribute the most to the ICM because of their high ejected fractions). then by z~1.5 most of the metals have been released to the intracluster medium. which results in no further evolution of Zicy.," If formation redshifts $z_F\simgt 2$ are assumed for the more abundant component of faint galaxies (which contribute the most to the ICM because of their high ejected fractions), then by $z\sim 1.5$ most of the metals have been released to the intracluster medium, which results in no further evolution of $Z_{\rm ICM}$."
 Hence. the lack of evolution in the metal abundance of the ICM observed at moderate redshifts is consistent with a picture where most of the metals are expelled from the population of faint ellipticals.," Hence, the lack of evolution in the metal abundance of the ICM observed at moderate redshifts is consistent with a picture where most of the metals are expelled from the population of faint ellipticals."
 Were recent and big mergers to contribute significantly to the metal abundance of the ICM. then a strong drop in Zicy should be expected by Lo1-1.5.," Were recent and big mergers to contribute significantly to the metal abundance of the ICM, then a strong drop in $Z_{\rm ICM}$ should be expected by $z\sim 1-1.5$."
 Upeoming X-ray observations of clusters withAXAF andXMM will elucidate this point., Upcoming X-ray observations of clusters with and will elucidate this point.
 The strong degeneracy between age and metallicity thwarts any attempt at estimating the star formation history of early-type galaxies., The strong degeneracy between age and metallicity thwarts any attempt at estimating the star formation history of early-type galaxies.
 Hence. evolutionary studies must include some model in which both age and metallicity are related.," Hence, evolutionary studies must include some model in which both age and metallicity are related."
 A simple chemical enrichment model has been deseribed in this paper. where we have tried to reduce the many factors ocewring in galaxy evolution down to the most basic parameters.," A simple chemical enrichment model has been described in this paper, where we have tried to reduce the many factors occurring in galaxy evolution down to the most basic parameters."
 We believe that infall of gas. outflows from supernova-triggered winds and possible variations in the star formation efficiency can collectively determine chemical enrichment.," We believe that infall of gas, outflows from supernova-triggered winds and possible variations in the star formation efficiency can collectively determine chemical enrichment."
 The results from our simple models demonstrate that outflows can generate the range in metallicity required for the observed color-magnitude relation (figure 1). whereas the other principal parameters. associated with infall of primordial gas or with the star formation efficiency. cannot account for the observations.," The results from our simple models demonstrate that outflows can generate the range in metallicity required for the observed color-magnitude relation (figure 1), whereas the other principal parameters, associated with infall of primordial gas or with the star formation efficiency, cannot account for the observations."
 This agrees with dynamical-spectrophotometric relations such as the Faber-Jackson correlation between central velocity dispersion and absolute luminosity (Faber Jackson 1976))., This agrees with dynamical-spectrophotometric relations such as the Faber-Jackson correlation between central velocity dispersion and absolute luminosity (Faber Jackson \markcite{fj76}) ).
 The ejected fraction of gas should be a function of the mass of the galaxy., The ejected fraction of gas should be a function of the mass of the galaxy.
 It could be argued that there might be a correlation between star formation and galaxy mass so that stars would be preferentially formed in more massive galaxies., It could be argued that there might be a correlation between star formation and galaxy mass so that stars would be preferentially formed in more massive galaxies.
 This would increase the ejected fraction in these galaxies., This would increase the ejected fraction in these galaxies.
 However. the color-magnitude diagram would then be strongly altered. blueing the bright end of the red sequence.," However, the color-magnitude diagram would then be strongly altered, blueing the bright end of the red sequence."
 One way out of this would include other mechanisms “conspiring” to restore the redness of the brightest galaxies., One way out of this would include other mechanisms “conspiring” to restore the redness of the brightest galaxies.
 Therefore. we conclude that the simplest explanation for the color-magnitude relation comes from a range of metal abundances caused by the correlation between galaxy mass and ejected fraction.," Therefore, we conclude that the simplest explanation for the color-magnitude relation comes from a range of metal abundances caused by the correlation between galaxy mass and ejected fraction."
 We emphasize that observational evidence concerning this point is still in a primitive stage. and thus a significant age spread cannot be ruled out.," We emphasize that observational evidence concerning this point is still in a primitive stage, and thus a significant age spread cannot be ruled out."
 However. observations of the Fornax cluster by Kuntschner Davies seem to point to a metallicity spread as being responsible for the color-magnitude relation.," However, observations of the Fornax cluster by Kuntschner Davies \markcite{kd98} seem to point to a metallicity spread as being responsible for the color-magnitude relation."
 Other factors such as an IMF with a variable high mass slope or cutoff or variable stellar yields could in principle decrease the effect of outflows on the resulting stellar populations., Other factors such as an IMF with a variable high mass slope or cutoff or variable stellar yields could in principle decrease the effect of outflows on the resulting stellar populations.
 However. if such factors were to play a significant role in affecting the scatter of the color-magnitude relation. the expected correlation of these factors with galaxy mass should have other observable implications.," However, if such factors were to play a significant role in affecting the scatter of the color-magnitude relation, the expected correlation of these factors with galaxy mass should have other observable implications."
 The combination of these chemical enrichment tracks. with the latest population synthesis models from BC99 allows us to estimate the spectrophotometric properties of cluster early-type galaxies., The combination of these chemical enrichment tracks with the latest population synthesis models from BC99 allows us to estimate the spectrophotometric properties of cluster early-type galaxies.
 Using the color-magnitude relation and. the luminosity function of local clusters as constraints. clusters can be simulated over a wide range of redshifts for different input parameters and star formation scenarios.," Using the color-magnitude relation and the luminosity function of local clusters as constraints, clusters can be simulated over a wide range of redshifts for different input parameters and star formation scenarios."
 A strong degeneracy is found when varying infall parameters (the rate. timescale and delay of infall) or the star formation efficiency.," A strong degeneracy is found when varying infall parameters (the rate, timescale and delay of infall) or the star formation efficiency."
 This is just a mapping of the degenerate enrichment tracks shown in figures | and 2 with respect to metallicity and C—V. color. respectively.," This is just a mapping of the degenerate enrichment tracks shown in figures 1 and 2 with respect to metallicity and $U-V$ color, respectively."
 Three different star formation scenarios are also considered: monolithie collapse. and two hierarchical. models with formation redshifts dependent on the luminosity of the galaxy.," Three different star formation scenarios are also considered: monolithic collapse, and two hierarchical models with formation redshifts dependent on the luminosity of the galaxy."
 The predictions for these models are not as degenerate at high redshifts <=>1. especially for age-sensitive observables such as the mass-to-light ratio.," The predictions for these models are not as degenerate at high redshifts $z\simgt 1$, especially for age-sensitive observables such as the mass-to-light ratio."
" The most remarkable difference between the models can be shown in the predicted color-magnitude relations in figure 4: hierarchical models (H. and IH) clearly display at high redshift a population of early-type galaxies which fall conspicuously blueward of the “main sequence"" red envelope: these blue outliers are so far the best candidates for characterizing cluster evolution.", The most remarkable difference between the models can be shown in the predicted color-magnitude relations in figure 4: hierarchical models (H and IH) clearly display at high redshift a population of early-type galaxies which fall conspicuously blueward of the “main sequence” red envelope: these blue outliers are so far the best candidates for characterizing cluster evolution.
 A hierarchical scenario. (H-model) presents these outliers as the brightest cluster galaxies. whereas an inverted hier- 3.4truein +0.2truein archy (IH-model) identifies them with a faint populatior of dwarf galaxies.," A hierarchical scenario (H-model) presents these outliers as the brightest cluster galaxies, whereas an inverted hier- 3.4truein +0.2truein archy (IH-model) identifies them with a faint population of dwarf galaxies."
 Monolithic collapse results in no major difference in the residuals from the linear fit with respect to luminosity., Monolithic collapse results in no major difference in the residuals from the linear fit with respect to luminosity.
 A complete sample of three blue outhers down to F814Wz21 has been confirmed to be members of cluster CIOO16+416 (z= 0.545) using serendipitous observations of these candidates by Belloni Rósser and the MORPHS collaboration (Dressler et al. 1999))., A complete sample of three blue outliers down to F814W=21 has been confirmed to be members of cluster Cl0016+16 $z=0.545$ ) using serendipitous observations of these candidates by Belloni Rösser \markcite{br96} and the MORPHS collaboration (Dressler et al. \markcite{dr99}) ).
 They are also classified as post-starburst (E+A or k+a) galaxies (Dressler Gunn 1983)). a clear sign of recent star formation activity.," They are also classified as post-starburst (E+A or k+a) galaxies (Dressler Gunn \markcite{dg83}) ), a clear sign of recent star formation activity."
 The observed equivalent widths are matched against the predictions of population synthesis models and an upper limit to the age between 0.5 and 2 Gyr is inferred for a range of metallicities 0.2<Z/Z..2.5. with the younger estimates corresponding to the higher metallicities.," The observed equivalent widths are matched against the predictions of population synthesis models and an upper limit to the age between 0.5 and 2 Gyr is inferred for a range of metallicities $0.2 < Z/Z_\odot < 2.5$, with the younger estimates corresponding to the higher metallicities."
 This sets an upper limit ο<1 on the epoch of formation of these galaxies. favoring a hierarchical clustering scenario where late merging stages could still be associated with significant star formation.," This sets an upper limit $z_F\simlt 1$ on the epoch of formation of these galaxies, favoring a hierarchical clustering scenario where late merging stages could still be associated with significant star formation."
 It is still a matter of debate whether the spectral signature of young stars in these galaxies corresponds to a large fraction of the galaxy mass., It is still a matter of debate whether the spectral signature of young stars in these galaxies corresponds to a large fraction of the galaxy mass.
 Such quantitative estimates must be performed in order to ascertain whether the star formation process that imprinted the E+A signature on these galaxies played a dominant role in accounting for the observed stellar populations., Such quantitative estimates must be performed in order to ascertain whether the star formation process that imprinted the E+A signature on these galaxies played a dominant role in accounting for the observed stellar populations.
 The evolution of mass-to-light ratios and magnesium abundances can also be explored with these simulated clusters., The evolution of mass-to-light ratios and magnesium abundances can also be explored with these simulated clusters.
 Both give the same degeneracy for a range of toy enrichment models. and a significant departure at high redshift (z= 1) between different star formation scenarios.," Both give the same degeneracy for a range of toy enrichment models, and a significant departure at high redshift $z\simgt 1$ ) between different star formation scenarios."
 The comparison between stellar M/L ratios and observations (that trace the total mass) yield a roughly linear correlation, The comparison between stellar $M/L$ ratios and observations (that trace the total mass) yield a roughly linear correlation
Using these. the continuity equation ancl (he equations of motion for each species. expressed in the I-franme. are: wwhere e is the magnitude of the electron charge.,"Using these, the continuity equation and the equations of motion for each species, expressed in the H-frame, are: where $e$ is the magnitude of the electron charge."
 In the II-Irame. all space derivatives disappear.," In the H-frame, all space derivatives disappear."
 Conservation of magnetic Πας. V.D=0. is automatic. and the remaining Maxwell's equations (Ampere. Faraday. and Coulomb law. respectively) become: wwhere p is the charge density.," Conservation of magnetic flux, $\mathbf{\nabla}
\cdot \mathbf{B} = 0$, is automatic, and the remaining Maxwell's equations (Ampere, Faraday and Coulomb law, respectively) become: where $\rho$ is the charge density."
 From (A10)). the charge density must vanish in the I-frame.," From \ref{coulomb}) ), the charge density must vanish in the H-frame."
" In combination with the continuity equation. we gel wwhere ng.5,j are constants."," In combination with the continuity equation, we get where $n_0$ $\gamma_0$ are constants."
" The restriction to purely transverse electric fields. (which is implied in the way Ampere's law is expressed above) means that the radial current. must vanish: you,=u,n."," The restriction to purely transverse electric fields (which is implied in the way Ampere's law is expressed above) means that the radial current must vanish: $n_+u_{x+} 
= u_{x-}n_-$."
 In this case. the net force acting on the plasma in the (ranusverse direction vanishes. so that νι+uy. d8 constant.," In this case, the net force acting on the plasma in the transverse direction vanishes, so that $u_{y,z+}+u_{y,z-}$ is constant."
" In keeping with the approximation of toroidal fields (corresponding to the z-direction in the plane wave approximation) and radial propagation (r-direction). we set this constant to zero. so that uw,=—u, and"," In keeping with the approximation of toroidal fields (corresponding to the $z$ -direction in the plane wave approximation) and radial propagation $x$ -direction), we set this constant to zero, so that $u_{y+}= - u_{y-}$ and"
line profiles in one or several spectra taken at various rotational phases.,line profiles in one or several spectra taken at various rotational phases.
" The output is then a coarse model of the abundance distribution of the element in magnetic latitude, effectively a very low resolution 1D map."," The output is then a coarse model of the abundance distribution of the element in magnetic latitude, effectively a very low resolution 1D map."
 This modelling is repeated for various elements., This modelling is repeated for various elements.
" Itis important to understand that the abundance model used by ZEEMAN was adopted to describe the kind of abundance variations observed in 53 Cam (HD 65339), a magnetic Ap star in which there are huge differences in large-scale mean abundances between the two hemispheres surrounding the two"," It is important to understand that the abundance model used by ZEEMAN was adopted to describe the kind of abundance variations observed in 53 Cam (HD 65339), a magnetic Ap star in which there are huge differences in large-scale mean abundances between the two hemispheres surrounding the two"
spread functions obtained onVesta.,spread functions obtained on.
. In order to match the observations. these were rotated to match the satellite position angle for each observation of a field. coadded and slightly convolved with a gaussian to match the actual FWHM of the combined map.," In order to match the observations, these were rotated to match the satellite position angle for each observation of a field, coadded and slightly convolved with a gaussian to match the actual FWHM of the combined map."
" For our reduction methods and projection into mmap pixels at 70 and 100 jm and aat 160 jim. we have PSF FWHM for the 70. 100. and 160 um maps of 6.46"".. 7.390.10"".. and 11.29x0."," For our reduction methods and projection into map pixels at 70 and 100 $\mu$ m and at 160 $\mu$ m, we have PSF FWHM for the 70, 100, and 160 $\mu$ m maps of , $\pm$, and $\pm$."
1/.. The FWHM values are from gaussian fits to the core of the observed PSF., The FWHM values are from gaussian fits to the core of the observed PSF.
 For the 100 and 160 jim widths we quote the error of the mean of measurements from five different fields., For the 100 and 160 $\mu$ m widths we quote the error of the mean of measurements from five different fields.
 All PEP blank fields benefit from extensive multi-wavelength coverage that is allowing guided extraction based on source positions at shorter wavelengths. where the depth and resolution of the observations are higher.," All PEP blank fields benefit from extensive multi-wavelength coverage that is allowing guided extraction based on source positions at shorter wavelengths, where the depth and resolution of the observations are higher."
 This approach resolves most of the blending issues encountered in dense fields and allows straightforward multi-wavelength association (Magnelli et al. 2009.. 2011:," This approach resolves most of the blending issues encountered in dense fields and allows straightforward multi-wavelength association (Magnelli et al. \cite{magnelli09}, \cite{magnelli11};"
 Roseboom et al 2010)., Roseboom et al. \cite{roseboom10}) ).
 However. to use this powerful method. prior source catalogs have to contain all the sources in the PACS images.," However, to use this powerful method, prior source catalogs have to contain all the sources in the PACS images."
 Deep MIPS 24 jm observations. available for all our blank fields. should fulfill this eriterion since they have higher resolution and are deeper than our current PACS observations.," Deep MIPS 24 $\mu$ m observations, available for all our blank fields, should fulfill this criterion since they have higher resolution and are deeper than our current PACS observations."
 Moreover. since the 24 jim emission ts strongly correlated with the far-infrared emission. those catalogs will not contain a large excess of sources without far-infrared counterparts.," Moreover, since the 24 $\mu$ m emission is strongly correlated with the far-infrared emission, those catalogs will not contain a large excess of sources without far-infrared counterparts."
 This. largely avoids deblending far-infrared sources into several unrealistic counterparts. as could happen when using an optical prior catalog with very high source density.," This largely avoids deblending far-infrared sources into several unrealistic counterparts, as could happen when using an optical prior catalog with very high source density."
 Figure 5. illustrates the validity of the MIPS 24 jm observations as PACS prior source positions., Figure \ref{fig: MIPS PACS} illustrates the validity of the MIPS 24 $\mu$ m observations as PACS prior source positions.
 At 100 um. models and observations predict typical PACS-to-MIPS flux ratios in the range 5-50.," At 100 $\mu$ m, models and observations predict typical PACS-to-MIPS flux ratios in the range 5-50."
 A MIPS 24 jm catalog 50 times deeper than the PACS observations is thus suited to perform guided source extraction., A MIPS 24 $\mu$ m catalog $50$ times deeper than the PACS observations is thus suited to perform guided source extraction.
 This ts illustrated. for GOODS-S. in the panel of Figure 5.. where the observed PACS population Hes well-below the boundary of the parameter space reachable by the MIPS 24 jim catalog.," This is illustrated, for GOODS-S, in the panel of Figure \ref{fig: MIPS PACS}, where the observed PACS population lies well-below the boundary of the parameter space reachable by the MIPS 24 $\mu$ m catalog."
 In all our blank fields. deep MIPS 24 um catalogs fulfill this criterion (1.e.. GOODS-S/N. COSMOS. LH. ECDFS. EGS...)).," In all our blank fields, deep MIPS 24 $\mu$ m catalogs fulfill this criterion (i.e., GOODS-S/N, COSMOS, LH, ECDFS, )."
 At 160 pm. models and observations have typical PACS-to-MIPS flux ratios in the range 15-150.," At 160 $\mu$ m, models and observations have typical PACS-to-MIPS flux ratios in the range 15-150."
 In all but one field. the deep MIPS 24 ym observations are at least 150 times deeper than our PACS observations: thus. they can be used as prior source positions.," In all but one field, the deep MIPS 24 $\mu$ m observations are at least 150 times deeper than our PACS observations; thus, they can be used as prior source positions."
 In GOODS-S. the deepest MIPS 24 um observations are only 100 times deeper than our PACS observations.," In GOODS-S, the deepest MIPS 24 $\mu$ m observations are only 100 times deeper than our PACS observations."
 This limitation can be observed. in the panel of Figure 5.. as a slight truncation. at faint 160. pm flux density. of the high-end of the dispersion of the PACS-to-MIPS flux ratio.," This limitation can be observed, in the panel of Figure \ref{fig: MIPS PACS}, as a slight truncation, at faint 160 $\mu$ m flux density, of the high-end of the dispersion of the PACS-to-MIPS flux ratio."
 This truncation will introduce. at faint flux density. incompleteness in our prior catalog.," This truncation will introduce, at faint flux density, incompleteness in our prior catalog."
 However. we also observe that even at this faint 160 jm flux density. the bulk of the population has a PACS-to-MIPS flux ratio of ~60.," However, we also observe that even at this faint 160 $\mu$ m flux density, the bulk of the population has a PACS-to-MIPS flux ratio of $\thicksim60$."
 The incompleteness introduced by the lack of MIPS 24 jim priors should thus be low or at least lower than the incompleteness introduced by source extraction methods at such low S/N. This was checked by comparing the GOODS-S 160 jim catalog obtained using blind source extraction with that obtained using guided source extraction: we find no significant difference. at faint 160 jm flux densities. in the number of sources in those two catalogs.," The incompleteness introduced by the lack of MIPS 24 $\mu$ m priors should thus be low or at least lower than the incompleteness introduced by source extraction methods at such low S/N. This was checked by comparing the GOODS-S 160 $\mu$ m catalog obtained using blind source extraction with that obtained using guided source extraction: we find no significant difference, at faint 160 $\mu$ m flux densities, in the number of sources in those two catalogs."
 In line with these finding. Magdis et al. (," In line with these finding, Magdis et al. ("
1n prep) find very low fractions of 244m undetected sources i1 very deep data from the GOODS-Herschel key program. <2% for ratios of detection limits S(100)/S(24)>43 and «1% for S(160)/S(24)> 130.,"in prep) find very low fractions of $\mu$ m undetected sources in very deep data from the GOODS-Herschel key program, $<2\%$ for ratios of detection limits $>$ 43 and $<1\%$ for $>$ 130."
 Therefore. for all fields with deep MIPS 24 jum observations. we also extract source catalogs with a PSF-fitting method using 24 im source positions as priors and following the method described in Magnelli et al. (2009)).," Therefore, for all fields with deep MIPS 24 $\mu$ m observations, we also extract source catalogs with a PSF-fitting method using 24 $\mu$ m source positions as priors and following the method described in Magnelli et al. \cite{magnelli09}) )."
 We used the same PSFs and aperture corrections as for the blind source extraction., We used the same PSFs and aperture corrections as for the blind source extraction.
 Blind and prior catalogs were compared to verify the consistency between those two methods., Blind and prior catalogs were compared to verify the consistency between those two methods.
 Completeness. fraction of spurious sources and flux reliability were estimated by running Monte Carlo simulations.," Completeness, fraction of spurious sources and flux reliability were estimated by running Monte Carlo simulations."
 Up to 10000 artificial sources were added to PACS science maps. and then extracted with the same techniques and configurations adopted for real source extraction.," Up to 10000 artificial sources were added to PACS science maps, and then extracted with the same techniques and configurations adopted for real source extraction."
 In. order to avoid crowding. many such frames were created. each including a limited number of artificial sources.," In order to avoid crowding, many such frames were created, each including a limited number of artificial sources."
 The number of frames and the number of sources added in each one depend on the size of the field under analysis and range between 20 and 500 sources (GOODS fields or COSMOS) per frame. repeated up to reaching the total of 10000.," The number of frames and the number of sources added in each one depend on the size of the field under analysis and range between 20 and 500 sources (GOODS fields or COSMOS) per frame, repeated up to reaching the total of 10000."
 These synthetic sources cover a large range in flux. extending down to 0.5c (c being the measured rms noise in the PACS maps).," These synthetic sources cover a large range in flux, extending down to $\sigma$ $\sigma$ being the measured rms noise in the PACS maps)."
 The flux distribution follows the detected number counts. extrapolated to fainter level by means of the most successful fitting backward evolutionary model predictions (see Berta et al. 2011)).," The flux distribution follows the detected number counts, extrapolated to fainter level by means of the most successful fitting backward evolutionary model predictions (see Berta et al. \cite{berta11}) )."
 Sources are modelled using the Vesta PSF. manipulated as described above.," Sources are modelled using the Vesta PSF, manipulated as described above."
 Figure 6 shows an example of results in the GOODS-N field at 160 jim. Completeness is defined here as the fraction of sources that have been detected with a photometric accuracy of at least (Papovich et al. 2004))., Figure \ref{fig:sims} shows an example of results in the GOODS-N field at 160 $\mu$ m. Completeness is defined here as the fraction of sources that have been detected with a photometric accuracy of at least (Papovich et al. \cite{papovich04}) ).
 Spurious sources are defined as those extracted above 3c with an input flux lower than 3o(Image)., Spurious sources are defined as those extracted above $\sigma$ with an input flux lower than $\sigma$ (Image).
 The systematic flux boosting in the blind extraction 1s corrected in the final blind catalog on the basis of these simulations., The systematic flux boosting in the blind extraction is corrected in the final blind catalog on the basis of these simulations.
 olse was estimated by extracting fluxes through10000 apertures randomly positioned. on residual maps., Noise was estimated by extracting fluxes through10000 apertures randomly positioned on residual maps.
 Figure 7 shows the distribution of the extracted fluxes. peaking around zero. as expected for a well subtracted background. and showing a Gaussian profile.," Figure \ref{fig:goodsnnoisehisto} shows the distribution of the extracted fluxes, peaking around zero, as expected for a well subtracted background, and showing a Gaussian profile."
 Figures 8 and 9. show the 100 jim and 160 pm maps of the GOODS-N and Abell 2218 fields as obtained during, Figures \ref{fig:goodsnsdp} and \ref{fig:a2218sdp} show the 100 $\mu$ m and 160 $\mu$ m maps of the GOODS-N and Abell 2218 fields as obtained during
seven medividual liue indices to an average iron indicator(Feo.,seven individual line indices to an average iron indicator.
 Furthermore. we defiuec a nean Bahuer iudex tthat served as a temperature imdicator.," Furthermore, we defined a mean Balmer index that served as a temperature indicator."
 The same iudicees were measured on spectra of the chemically homogeneous chster AMISH. in addition to standard stars aud svuthetic spectra.," The same indices were measured on spectra of the chemically homogeneous cluster M55, in addition to standard stars and synthetic spectra."
 These iudices were used to estimate he depenudeace of oon teniperature and surface eravity and to establish au analytical fuuctio1/TM=f(Fe).. (OI5)).," These indices were used to estimate the dependence of on temperature and surface gravity and to establish an analytical function, )."
 The eor i ithe absolute iro1 abundance calibration is of the order + 0.1 to 0.3 dex., The error in the absolute iron abundance calibration is of the order $\pm$ 0.1 to 0.3 dex.
 Furthermore. wio aeasured Me. Ca. CN. and CII iudices for tie aan M55 seCra to study f16 abundance variations mn the cdiffereut popul:ous;," Furthermore, we measured Mg, Ca, CN, and CH indices for the and M55 spectra to study the abundance variations in the different populations."
 The [a/Fo| ratio is fairly flat OVer a wio rage of anctallicities. indicating a prolouged enriclunent by nassive (M > 1| Mj) stars.," The $\alpha$ /Fe] ratio is fairly flat over a wide range of metallicities, indicating a prolonged enrichment by massive (M $>$ 10 ) stars."
" Moreover, we showed that the strong CN and CIT variations (which rack been fouiud oll the RGB before. see e.g. 72)) are also ound among tie stars in the ASTO/SDBG regiou. i.c. hese variations nkot possibly lave a primordial origin πο are not due to musing effects"," Moreover, we showed that the strong CN and CH variations (which had been found on the RGB before, see e.g. \citealt{H/R:00}) ) are also found among the stars in the MSTO/SBG region, i.e. these variations most possibly have a primordial origin so are not due to mixing effects."
 While the combined CN|CII abuudauc| sunoothly increases with metallicity. he enrichment in € “and N is auti-correlated.," While the combined CN+CH abundance smoothly increases with metallicity, the enrichment in C and N is anti-correlated."
 The most netalrich stars show an extreme enrichment in the whereas 1ietal-poor stars are scattered to high CII abunances. probably pointing to a fast C emiclineut by more massive AGB stars.," The most metal-rich stars show an extreme enrichment in the whereas metal-poor stars are scattered to high CH abundances, probably pointing to a fast C enrichment by more massive AGB stars."
 The abundance patterns of the stars in aare uconuuon among the globular cluster population of our Milkv Wav., The abundance patterns of the stars in are uncommon among the globular cluster population of our Milky Way.
 This refers LO ouly to the iron abuudauce but aso to the lighter elemeut abuudances., This refers not only to the iron abundance but also to the lighter element abundances.
 The strong abundance variatious of f1C ight eleineuts indicate that experienced a very coupex eurchnmeut historv aud that he progenitor of fLs object must have heen a far more massive object ha was able to retain ejecta by its sbsequenut generations of stars., The strong abundance variations of the light elements indicate that experienced a very complex enrichment history and that the progenitor of this object must have been a far more massive object that was able to retain ejecta by its subsequent generations of stars.
 Whether this enrichment was due to i0niogeneous or episodie star formation must be left to a nore detailed analysis that iucludes 1oration on s- aud r-process elements. which would allow more accurate models of the star formation rate ancl tje initial stellar mass distributiois to be derived.," Whether this enrichment was due to homogeneous or episodic star formation must be left to a more detailed analysis that includes information on s- and r-process elements, which would allow more accurate models of the star formation rate and the initial stellar mass distributions to be derived."
 Over fle past years. άν studies have revealed more zd more xeculiaxities ofCoen.," Over the past years, many studies have revealed more and more peculiarities of."
 Deep ]photometry enabled a laore detailed iuquiry of the bifrcation of the MS found by 7. which can most probably be ¢*xplained as a1 Ie overabunance of the iuermediate iuetallicity population (? and ? )). lus complicating f1e interxetatiou o: the cheimical-enrichiuent history ofCen.," Deep photometry enabled a more detailed inquiry of the bifurcation of the MS found by \citet{A:97}, which can most probably be explained as an He overabundance of the intermediate metallicity population \citealt{N:04} and \citealt{P/V:05}) ), thus complicating the interpretation of the chemical-enrichment history of."
 Up to now here no selfcousistent modes exist for tlre origin ofCoen. but most stidies suggest a coniex formation sce14110 in order to explain the uumsual observed properties othus elobulu cluster.," Up to now there no self-consistent models exist for the origin of, but most studies suggest a complex formation scenario in order to explain the unusual observed properties of this globular cluster."
 Our study provides fiwther evidence of a scenario in which sowas embeded in a formerly larger ealactic cutiv that was captured and disrupted bv the Milkv. Wavy., Our study provides further evidence of a scenario in which was embedded in a formerly larger galactic entity that was captured and disrupted by the Milky Way.
 Iu ow previous stuy (0). we show that μας experieiced. an extended star-formation listory over a perio of at least 3 Cyr.," In our previous study \citep{H/K:04}, we show that has experienced an extended star-formation history over a period of at least 3 Gyr."
 Iu coiubiuatioji with the abundance patteri» presented iu this stiX. the conmbiued information sires niu similarities witji what is found for nearby dwarf galaxies that are known to have experienced rather coulex star-formation processes TU). (?).," In combination with the abundance patterns presented in this study, the combined information shares many similarities with what is found for nearby dwarf galaxies that are known to have experienced rather complex star-formation processes \citep[e.g.][]{S/V:03, T/V:02, L/M:03}. \citep{G:99}."
 ? (e.c.2).," \citet{H/G:01} \citep[e.g.][]{N/F/M:96},"
Our analysis is restricted to observations made with the High Energy Transmission Grating Spectrometer.,Our analysis is restricted to observations made with the High Energy Transmission Grating Spectrometer.
 The HETGS offers better resolution than the Reflection Grating Spectrometer. as well as coverage across the full 0.3-10.0 keV band.," The HETGS offers better resolution than the Reflection Grating Spectrometer, as well as coverage across the full 0.3-10.0 keV band."
 When the equivalent neutral hyrdogen density i$ too high. much of the source continuum spectrum is scattered out of the line of sight.," When the equivalent neutral hyrdogen density is too high, much of the source continuum spectrum is scattered out of the line of sight."
 This must be avoided as absorption features are measured relative to à continuum., This must be avoided as absorption features are measured relative to a continuum.
 A number of clear absorption edges are detected in Cygnus X-I. which has an equivalent neutral hydrogen column density of Ny=6.2«107!emo? (Schulz et 22002).," A number of clear absorption edges are detected in Cygnus X-1, which has an equivalent neutral hydrogen column density of $N_{H} =
6.2\times 10^{21}~ {\rm cm}^{-2}$ (Schulz et 2002)."
 However. an estimated column density of 8.0«107!em does not allow the absorption edges in XTE J1550—564 to be studied in detail (Miller et 22003).," However, an estimated column density of $8.0\times 10^{21}~ {\rm cm}^{-2}$ does not allow the absorption edges in XTE $-$ 564 to be studied in detail (Miller et 2003)."
 We therefore restricted our analysis to sources equal to or below approximately 6«107!em7.," We therefore restricted our analysis to sources equal to or below approximately $6\times 10^{21}~ {\rm
cm}^{-2}$."
 Our analysis was also restricted by the need to select variable and transient sources., Our analysis was also restricted by the need to select variable and transient sources.
 Observations of transient sources. with large missions can be difficult. and relatively few sources with low or moderate column densities have been observed on multiple occasions.," Observations of transient sources with large missions can be difficult, and relatively few sources with low or moderate column densities have been observed on multiple occasions."
 The sources and observations selected for our analysis are listed in Table |., The sources and observations selected for our analysis are listed in Table 1.
 Different source types. companion types. and orbital periods are included in the sample.," Different source types, companion types, and orbital periods are included in the sample."
 When observing bright sources using the HETGS. the ACIS-S array of CCDs must be run in “continuous clocking” mode to prevent photon pile-up.," When observing bright sources using the HETGS, the ACIS-S array of CCDs must be run in “continuous clocking” mode to prevent photon pile-up."
 For consistency. the observations considered in this work employed this observing mode.," For consistency, the observations considered in this work employed this observing mode."
 The only exception is a single observation of GX 339-4 in a low flux state (obsid 4420: see Table 1)., The only exception is a single observation of GX $-$ 4 in a low flux state (obsid 4420; see Table 1).
" An observation of Cygnus X-] in the low/hard state that was not taken in. ""continuous clocking” mode (obsid 107) suffered heavy photon pile-up. complicating absorption. spectroscopy (see Juett. Schulz. Chakrabarty 2004). and was therefore rejected."," An observation of Cygnus X-1 in the low/hard state that was not taken in “continuous clocking” mode (obsid 107) suffered heavy photon pile-up, complicating absorption spectroscopy (see Juett, Schulz, Chakrabarty 2004), and was therefore rejected."
 For more information on the specific nature of HETGS observations made in “continuous clocking” mode. please see Miller et ((2006b) or Cackett et ((2008b).," For more information on the specific nature of HETGS observations made in “continuous clocking” mode, please see Miller et (2006b) or Cackett et (2008b)."
" Most of the spectra considered in this work were obtained using the ""TGCat"" data center (see http://tgcat.mitedu).", Most of the spectra considered in this work were obtained using the “TGCat” data center (see http://tgcat.mit.edu).
 This facility is run by the X-ray Center and provides first-order HETGS spectra and responses derived using up-to-date CIAO software and calibrations., This facility is run by the X-ray Center and provides first-order HETGS spectra and responses derived using up-to-date CIAO software and calibrations.
 An error in the instrument offsets used to observe ΧΤΕ J1817—-330 required custom processing as per the procedure outlined in Miller et ((2006b) and Cackett et ((2008b)., An error in the instrument offsets used to observe XTE $-$ 330 required custom processing as per the procedure outlined in Miller et (2006b) and Cackett et (2008b).
 Two observations of 4U 1820-30 were previously reduced and analyzed by Cackett et ((2008b) (obsid 6633 and 6634). and the same spectra are used in this work.," Two observations of 4U $-$ 30 were previously reduced and analyzed by Cackett et (2008b) (obsid 6633 and 6634), and the same spectra are used in this work."
" Using CIAO version 4.0.2. we combined the first-order MEG spectra and instrument response files using the CIAO tool sspectra""."," Using CIAO version 4.0.2, we combined the first-order MEG spectra and instrument response files using the CIAO tool spectra”."
 The same procedure was repeated for the first-order HEG spectra., The same procedure was repeated for the first-order HEG spectra.
 Again owing to the pointing error. only the minus-side first-order spectra of XTE J1817—330 were used in our analysis.," Again owing to the pointing error, only the minus-side first-order spectra of XTE $-$ 330 were used in our analysis."
" To create distinct spectra of Cygnus X-2 in the flaring. horizontal. and normal branches of its ""Z track. we employed exactly the same selection criteria and procedure as Schulz et ((2009) to both observations (obtaining a total of six spectra)."," To create distinct spectra of Cygnus X-2 in the flaring, horizontal, and normal branches of its “Z” track, we employed exactly the same selection criteria and procedure as Schulz et (2009) to both observations (obtaining a total of six spectra)."
" The ""agle"" script was used in the ISIS analysis package (Houck Denicola 2000) to create lighteurves and. color-color diagrams that were used to create spectra from each branch.", The “aglc” script was used in the ISIS analysis package (Houck Denicola 2000) to create lightcurves and color-color diagrams that were used to create spectra from each branch.
 All of the spectral fits reported in this work were made using XSPEC version 12 (Arnaud Dorman 2000)., All of the spectral fits reported in this work were made using XSPEC version 12 (Arnaud Dorman 2000).
 Unless otherwise stated. errors are 1o errors.," Unless otherwise stated, errors are $1\sigma$ errors."
 The true neutral absorption column density observed in a given spectrum should not be a function of the continuum flux model., The true neutral absorption column density observed in a given spectrum should not be a function of the continuum flux model.
 However. to ensure model-independent results. we fit for prominent neutral photoelectric absorption edges individually — in narrow wavelength ranges — using local power-law models for the continuum.," However, to ensure model-independent results, we fit for prominent neutral photoelectric absorption edges individually – in narrow wavelength ranges – using local power-law models for the continuum."
 The O K. Fe L. and Ne K edges were fit in the20-25A..16-I8A.. and bands. respectively.," The O K, Fe L, and Ne K edges were fit in the, and bands, respectively."
 At longer wavelengths. the MEG has a higher effective area than the HEG: moreover. it covers longer wavelengths than the HEG.," At longer wavelengths, the MEG has a higher effective area than the HEG; moreover, it covers longer wavelengths than the HEG."
" Fits to absorption. edges were therefore made to the combined first-order MEG spectrum from each observation,", Fits to absorption edges were therefore made to the combined first-order MEG spectrum from each observation.
 In many of the spectra. it was quickly apparent that simple step-function edge models do not fully describe the data.," In many of the spectra, it was quickly apparent that simple step-function edge models do not fully describe the data."
" We therefore used the ""tbnew"" model (Wilms et 22009). which includes up-to-date cross-sections and detailed. edge structure."," We therefore used the “tbnew” model (Wilms et 2009), which includes up-to-date cross-sections and detailed edge structure."
" A new functionality in ""tbnew"" can be used to fit the column density in an individual edge by setting the overall column density and abundance of all elements (apart from the element of interest) to zero. and restricting the column density to negative values for the parameter of interest. ("," A new functionality in “tbnew” can be used to fit the column density in an individual edge by setting the overall column density and abundance of all elements (apart from the element of interest) to zero, and restricting the column density to negative values for the parameter of interest. ("
Negative values instruct the model to return the column density for the element: positive. values return the abundance of à given element relative to hydrogen.),Negative values instruct the model to return the column density for the element; positive values return the abundance of a given element relative to hydrogen.)
 All fitting parameters relating to grain properties were fixed at their default value., All fitting parameters relating to grain properties were fixed at their default value.
" In our fits. then. ""tbnew functioned as a model with only one variable parameter (the column density of the element of interest)."," In our fits, then, “tbnew” functioned as a model with only one variable parameter (the column density of the element of interest)."
 Due to a combination of a relatively high total absorption column and the particular choice of instrumental pointing offsets used. useful constraints on the O K edge could not be obtained from existing data on GX 339-4. 4U 1820—30. and Cygnus X-2.," Due to a combination of a relatively high total absorption column and the particular choice of instrumental pointing offsets used, useful constraints on the O K edge could not be obtained from existing data on GX $-$ 4, 4U $-$ 30, and Cygnus X-2."
 We note that Yao et (2009) were able to study the Oxygen edge in Cygnus X-2 by adding multiple spectra. but this procedure is inconsistent with the aim of this study.," We note that Yao et (2009) were able to study the Oxygen edge in Cygnus X-2 by adding multiple spectra, but this procedure is inconsistent with the aim of this study."
 To estimate the luminosity of each source in à given observation. we fit the first-order HEG spectra in the 1.2—10.0 keV range using simple absorbed continuum models.," To estimate the luminosity of each source in a given observation, we fit the first-order HEG spectra in the 1.2--10.0 keV range using simple absorbed continuum models."
 The equivalent neutral hydrogen column density was allowed to vary but values were found to be broadly consistent with fits to individual edges., The equivalent neutral hydrogen column density was allowed to vary but values were found to be broadly consistent with fits to individual edges.
 These models should be regarded as fiducial., These models should be regarded as fiducial.
 Some of the fits obtained are not formally acceptable. owing," Some of the fits obtained are not formally acceptable, owing"
The cause of these residuals is once again the differcices in the treatinent of the effective pixel windows: The HEALDix pixel window is computed by wniformly averagine over the full «kx. whereas the simulation pipeline takes iuto account the actual poiutiug directions of the satellie.,"The cause of these residuals is once again the differences in the treatment of the effective pixel windows: The HEALPix pixel window is computed by uniformly averaging over the full sky, whereas the simulation pipeline takes into account the actual pointing directions of the satellite."
 Sub-pixel variations iu the CMD sky. therefore leads to sienificant differences iu the two estimates on small scales., Sub-pixel variations in the CMB sky therefore leads to significant differences in the two estimates on small scales.
" The effect of such pixel window variations on the 5-vear WMAP power spectrum will be cousidered im a future pa201,", The effect of such pixel window variations on the 5-year WMAP power spectrum will be considered in a future paper.
 The heart of the simulation pipeline described iu Seclon 2 is the real-space convolution algoritluu defined bx Equation L., The heart of the simulation pipeline described in Section \ref{sec:pipeline} is the real-space convolution algorithm defined by Equation \ref{eq:convolution}.
 For this operation to be computationally feaside we have to be able to evaluate the beam response function cτήςκ] at any position., For this operation to be computationally feasible we have to be able to evaluate the beam response function quickly at any position.
 The real beam maps. however. are provided to us in the form of two-dimensional pixelized images with relatively coarse resolution.," The real beam maps, however, are provided to us in the form of two-dimensional pixelized images with relatively coarse resolution."
 It is therefore necessary to establish a fast aud accurate interpolation scheme., It is therefore necessary to establish a fast and accurate interpolation scheme.
 We adoot a bicubic spline for this purpose. and review here one specific implementation of this coucept.," We adopt a bicubic spline for this purpose, and review here one specific implementation of this concept."
 Note that inost of the following is standard textbook material (e.¢..Press2002).. aud is included here oulv for easy. reference.," Note that most of the following is standard textbook material \citep[e.g.,][]{press:2002}, and is included here only for easy reference."
 Suppose we are eiven some tabulated two-dimensional fiction fOr.y) over a regular exid. and want to interpolate at arbitrary »ositious Gry.vy) Within this exid.," Suppose we are given some tabulated two-dimensional function $f(x,y)$ over a regular grid, and want to interpolate at arbitrary positions $(x_0, y_0)$ within this grid."
 One particularly appealing approach for doing so are by mecaus of bicubic splines. wuch are biccubic polvnomials inc and y. The coefficieuts 0;; are defiued separately for cach grid cell. and our task is to compute these eiveu the tabulated function fGr.yg).," One particularly appealing approach for doing so are by means of bicubic splines, which are bi-cubic polynomials in $x$ and $y$, The coefficients $a_{ij}$ are defined separately for each grid cell, and our task is to compute these given the tabulated function $f(x,y)$."
 Note that ouce we have these cocfiicicuts. any spline evaluation will be very fast. since it essentialv ainounts to performing a vectorauatrix-vector multiplication with a 1«Lt matrix.," Note that once we have these coefficients, any spline evaluation will be very fast, since it essentially amounts to performing a vector-matrix-vector multiplication with a $4\times4$ matrix."
 Let us first consider a cell defined over the unit square. having corners (e.gy)=(00.0). (1.0). (0.1) and (1.1). (," Let us first consider a cell defined over the unit square, having corners $(x,y) = (0,0)$, $(1,0)$, $(0,1)$ and $(1,1)$. ("
Note that this assumption does not imply auv restriction of the problem. since any exid cell iu a regular exid may be linearV transformed iuto the unit square.),"Note that this assumption does not imply any restriction of the problem, since any grid cell in a regular grid may be linearly transformed into the unit square.)"
 Assume also that we know the fiction values f(r.g) and the first- aud second-order deivatives. fi.Gey). fyCeug) aud Έργωνug) at all four corners. (," Assume also that we know the function values $f(x,y)$ and the first- and second-order derivatives, $f_x(x,y)$, $f_y(x,y)$ and $f_{xy}(x,y)$ at all four corners. ("
"ere subscript . denotes derivatives. f,=dfde.)","Here subscript $x$ denotes derivatives, $f_x = df/dx$ .)"
 The coefficients of the bicubic spline are then defined such that that both the function values aud the derivatives match. at all four corners.," The coefficients of the bicubic spline are then defined such that that both the function values and the derivatives match, at all four corners."
 With four equations for each of four corners. there is a total of 16 independent equations for the 16 independent spline cocficicnts. a;;. aud the spline is therefore uniquely defiued.," With four equations for each of four corners, there is a total of 16 independent equations for the 16 independent spline coefficients, $a_{ij}$, and the spline is therefore uniquely defined."
 Writing out Equation Bh explicitly. we obtain the following set of linear equations. The remaining problem is then to estinate the first- and second-order derivatives at all eid. points. and several approaches iiv be used for this.," Writing out Equation \ref{eq:spline_equations} explicitly, we obtain the following set of linear equations, The remaining problem is then to estimate the first- and second-order derivatives at all grid points, and several approaches may be used for this."
 We adoot a spline based imetlod for this step as well., We adopt a spline based method for this step as well.
 Fist. we compute a standard one-dimensional natural splinealone all. and y coordinate lues. using standard inethods.," First, we compute a standard one-dimensional natural splinealong all $x$ and $y$ coordinate lines, using standard methods."
 The result from this operation is the set of all pure secoud-order derivatives. foaGe.y) and fyyGe. y). at cach eric point.," The result from this operation is the set of all pure second-order derivatives, $f_{xx}(x,y)$ and $f_{yy}(x,y)$ , at each grid point."
For the passbands we show in Fig.,For the passbands we show in Fig.
" 12 two plots involving the passbandsand H,.", \ref{fig:Hipp-diag} two plots involving the passbandsand $H_{p}$.
" In the left panel where we display G—H, with respect to Ggp-Grp,, we notice a deviation from the main trend for Ggp-Gpp>4."," In the left panel where we display $G-H_{p}$ with respect to $-$, we notice a deviation from the main trend for $-$ $\gtrsim4$."
 This deviation is caused by cool metal poor stars with Teg« 2500 K and [M/H]«-1.5 dex., This deviation is caused by cool metal poor stars with $T_{\rm{eff}}<$ 2500 K and $<-1.5$ dex.
" For this reason, we have computed two distinct relationships involving Gpgp-Ggp aandG— H,."," For this reason, we have computed two distinct relationships involving $-$ and$G-H_{p}$ ."
 These relationships are displayed in Table 4 and Fig. 12.., These relationships are displayed in Table \ref{table:coeficients_Hippa} and Fig. \ref{fig:Hipp-diag}. .
Centaurus A (NGC 5128. Cen A) is the closest (distance d~3.4 Mpe: Israel 1998) and one of the best studied active galaxies.,"Centaurus A (NGC 5128, Cen A) is the closest (distance $d \sim 3.4$ Mpc; Israel 1998) and one of the best studied active galaxies."
 Optically. Cen A is an elliptical galaxy undergoing late stages of a merger event with a small spiral galaxy.," Optically, Cen A is an elliptical galaxy undergoing late stages of a merger event with a small spiral galaxy."
 Radio observations detected a complex FR I morphology with a subparsec-seale Jet and counter-jet. a one-sided kiloparsec-scale jet. two radio lobes and extended diffusive emission.," Radio observations detected a complex FR I morphology with a subparsec-scale jet and counter-jet, a one-sided kiloparsec-scale jet, two radio lobes and extended diffusive emission."
 VLBI observations of the subparsec-scale jet indicate that Cen A is a non-blazar source with a jet inclination angle i-50° (Tingay et al., VLBI observations of the subparsec-scale jet indicate that Cen A is a non-blazar source with a jet inclination angle $i \gppr 50^{\circ}$ (Tingay et al.
 1998). or perhaps somewhat smaller if large-scale observations are reliable tracers (Hardeastle et al.," 1998), or perhaps somewhat smaller if large-scale observations are reliable tracers (Hardcastle et al."
 2003)., 2003).
 The center of its activity is a supermassive black hole (BH) with a mass inferred to be in the range Hum(0.5—1.2)xI0M. (Marconi et al.," The center of its activity is a supermassive black hole (BH) with a mass inferred to be in the range $m_{\rm BH} 
 \simeq (0.5-1.2) \times 10^8 M_{\odot}$ (Marconi et al."
 2006: Hirring-Neumayer et al.," 2006; H\""arring-Neumayer et al."
" 2006). corresponding to a Schwarzschild scale r,=(1.573.6)x10"" Cen A is the only AGN of the non-blazar type detected at MeV (COMPTEL: Steinle et al."," 2006), corresponding to a Schwarzschild scale $r_s \simeq (1.5-3.6) \times 10^{13}$ Cen A is the only AGN of the non-blazar type detected at MeV (COMPTEL: Steinle et al."
 1998) and GeV energies (EGRET: Sreekumar et al., 1998) and GeV energies (EGRET: Sreekumar et al.
 1999)., 1999).
 The nuclear spectral energy distribution (SED) of Cen A. as inferred from non-simultaneous data. appears to consist of two peaks. one reaching its maximum at several times 10' Hz and one peaking around 0.1 MeV (Chiaberge et al.," The nuclear spectral energy distribution (SED) of Cen A, as inferred from non-simultaneous data, appears to consist of two peaks, one reaching its maximum at several times $10^{13}$ Hz and one peaking around $0.1$ MeV (Chiaberge et al."
 2001: Meisenheimer et al., 2001; Meisenheimer et al.
 2007)., 2007).
 The SED below | GeV has been successfully modeled within a simple jet synchrotron self-Compton (SSC) framework. assuming Cen A to be a misaligned BL Lac object (Chiaberge et al.," The SED below 1 GeV has been successfully modeled within a simple jet synchrotron self-Compton (SSC) framework, assuming Cen A to be a misaligned BL Lac object (Chiaberge et al."
 2001)., 2001).
 In the early days of gamma-ray astronomy. a tentative detection (> 4o) of Cen A at very high energies >0.3 TeV was reported during a phase of high X-ray activity in 1972-1974 (Grindlay 1975).," In the early days of gamma-ray astronomy, a tentative detection $> 4 \sigma$ ) of Cen A at very high energies $>0.3$ TeV was reported during a phase of high X-ray activity in 1972-1974 (Grindlay 1975)."
 H.E.S.S. results (Aharonian et al., H.E.S.S. results (Aharonian et al.
" 2009a) have established Cen A as a TeV emitting source (the second radio galaxy after M87) with integral VHE flux of ~1% of the Crab Chandra and XMM-Newton observations between 2 and 7 keV indicate that the nuclear X-ray continuum spectrum in Cen A may consist of both a disk and a jet component. the disk contribution being consistent with a hybrid disk configuration where a standard disk is truncated at r, and replaced by an ADAF in the inner regions close to the central black hole (Evans et al."," 2009a) have established Cen A as a TeV emitting source (the second radio galaxy after M87) with integral VHE flux of $\sim 1\%$ of the Crab Chandra and XMM-Newton observations between 2 and 7 keV indicate that the nuclear X-ray continuum spectrum in Cen A may consist of both a disk and a jet component, the disk contribution being consistent with a hybrid disk configuration where a standard disk is truncated at $r_t$ and replaced by an ADAF in the inner regions close to the central black hole (Evans et al."
 2004; cf., 2004; cf.
 also Pellegrini et al., also Pellegrini et al.
 2005 and Meisenheimer et al., 2005 and Meisenheimer et al.
 2007)., 2007).
 A transition to an inner ADAF disk could also explain the lack of a big blue bump UV feature expected in the standard disk scenario (Marconi et al., A transition to an inner ADAF disk could also explain the lack of a big blue bump UV feature expected in the standard disk scenario (Marconi et al.
 2001)., 2001).
 The aceretion rate for Cen A seems uncertain by about an order of magnitude. with model-dependent estimates ranging from several 107 to some 107riu.," The accretion rate for Cen A seems uncertain by about an order of magnitude, with model-dependent estimates ranging from several $10^{-4}$ to some $10^{-3}\,\dot{m}_{\rm Edd}$."
 Taking the measured nuclear X-ray luminosity of L.~5x10+! erg/s (Evans et al., Taking the measured nuclear X-ray luminosity of $L_x \sim 5 \times 10^{41}$ erg/s (Evans et al.
 2004) as a robust upper limit to a possible ADAF disk contribution gives fit5.0.004. Which for the canonical viscosity parameter wv=0.3 is still below the critical mass accretion rate Titem0.307iau required for à two-temperature ADAF to occur (Narayan et al.," 2004) as a robust upper limit to a possible ADAF disk contribution gives $\dot{m} \lppr 0.004 \dot{m}_{\rm Edd}$, which for the canonical viscosity parameter $\alpha \simeq 0.3$ is still below the critical mass accretion rate $\dot{m}_{\rm crit} \simeq 0.3\,\alpha^2\,\dot{m}_{\rm Edd}$ required for a two-temperature ADAF to occur (Narayan et al."
 1998; Υ If the first SED peak below 10'7 Hz is indeed caused by synchrotron emission from the jet (Chiaberge et al., 1998; Yi If the first SED peak below $10^{14}$ Hz is indeed caused by synchrotron emission from the jet (Chiaberge et al.
 2001: Meisenheimer et al., 2001; Meisenheimer et al.
 2007). inverse Compton upscattering in a conventional homogeneous SSC framework is unable to account for VHE y-rays in the TeV regime.," 2007), inverse Compton upscattering in a conventional homogeneous SSC framework is unable to account for VHE $\gamma$ -rays in the TeV regime."
 On the other hand. it could be that the situation for Cen A is similar to that for M 87. where efficient particle acceleration close to the BH horizon seems to be responsible for the production of the observed TeV y-rays (Aharonian et al.," On the other hand, it could be that the situation for Cen A is similar to that for M 87, where efficient particle acceleration close to the BH horizon seems to be responsible for the production of the observed TeV $\gamma$ -rays (Aharonian et al."
 2009b; Rieger Aharonian 2008a. henceforth: RAOSa).," 2009b; Rieger Aharonian 2008a, henceforth: RA08a)."
 Here we analyze possible VHE characteristics associated with this scenario., Here we analyze possible VHE characteristics associated with this scenario.
 We show that for parameters inferred from observations. inverse Compton upseattering of ADAF disk photons by centrifugally accelerated electrons could result in variable (~1 hr) VHE y-rays with a relatively hard TeV spectrum.," We show that for parameters inferred from observations, inverse Compton upscattering of ADAF disk photons by centrifugally accelerated electrons could result in variable $\sim 1$ hr) VHE $\gamma$ -rays with a relatively hard TeV spectrum."
 We show that the mechanism considered is unable to accelerate protons to ultra high energy cosmic-ray (UHECR) energies. although shear acceleration along the jet could potentially provide a means.," We show that the mechanism considered is unable to accelerate protons to ultra high energy cosmic-ray (UHECR) energies, although shear acceleration along the jet could potentially provide a means."
 Magnetic fields are widely considered to play a key role in the formation of collimated relativistic outflows from compact objects., Magnetic fields are widely considered to play a key role in the formation of collimated relativistic outflows from compact objects.
 According to. e.g. MHD scenarios. magnetic. flux dragged in by the accretion flow and suitably amplified by," According to, e.g., MHD scenarios, magnetic flux dragged in by the accretion flow and suitably amplified by"
detected.,detected.
 The oulv measured “bascline flux” is the light falling within a resolution clement due to several stars im the lighly erowded fields., The only measured “baseline flux” is the light falling within a resolution element due to several stars in the highly crowded fields.
 The Lhnuunositv function of ΑΟ sources αι be specified., The luminosity function of M31 sources must be specified.
 For the disk. we take Rand 7 baud luninosity functions from Aamou Soncira (1982).," For the disk, we take $R$ and $I$ band luminosity functions from Mamon Soneira (1982)."
 For the bulgc. we take the 7 band frou Terudrup. Frogel Whitford (1990).," For the bulge, we take the $I$ band from Terndrup, Frogel Whitford (1990)."
 Data for the R band is scarce. so we average Gu logd /NV/dAM) V. aud 7 baud data for Mg>0 (using Terndrup et al. (," Data for the $R$ band is scarce, so we average (in $\log dN/dM$ ) $V$ and $I$ band data for $M_R>0$ (using Terndrup et al. ("
1990) for 7 and Woltziman et al. (,1990) for $I$ and Holtzman et al. (
1998) for V).,1998) for $V$ ).
 For Mg< Owe attach a power law slope of 0.59 taken from the MACTIO project data (Alves 2001)., For $M_R<0$ we attach a power law slope of 0.59 taken from the MACHO project data (Alves 2001).
 The mass function of lenses. both stellar and the MACTIO component. is somewhat problematic.," The mass function of lenses, both stellar and the MACHO component, is somewhat problematic."
 For the stellar compoucut. we use the exponential Chabrier (2001) mass function. down to 0.0LAZ...," For the stellar component, we use the exponential Chabrier (2001) mass function, down to $0.01 M_\odot$."
 This is steeply decreasing. so there is little mass in the lowest decade (the brown dwarts}.," This is steeply decreasing, so there is little mass in the lowest decade (the brown dwarfs)."
 Varving the stellar mass fiction in acceptable ranges has little effect unless for example there is a large component of brown dwarfs (Daltz Silk 2001)., Varying the stellar mass function in acceptable ranges has little effect unless for example there is a large component of brown dwarfs (Baltz Silk 2001).
 The uean stellar mass of about 0.537.. is what dominates he rate and timescale frou self leusiug., The mean stellar mass of about $0.5 M_\odot$ is what dominates the rate and timescale from self lensing.
" We have also investigated a Scalo (1986) mass function. which has a slightly ligher mean mass. thus longer timescales aud ower rates,"," We have also investigated a Scalo (1986) mass function, which has a slightly higher mean mass, thus longer timescales and lower rates."
 The differences are uot very large however., The differences are not very large however.
 For lack of convincing evidence to the contrary. we take a fixed mass for ALACΠο.," For lack of convincing evidence to the contrary, we take a fixed mass for MACHOs."
 Based on Alcock et (2000) we assunie adnass of 3/8 dex relative to solar (z:0.92211.]. and we test values of OAL. and LOAL.. as well.," Based on Alcock et (2000) we assume a mass of $-3/8$ dex relative to solar $(\approx 0.422 M_\odot)$, and we test values of $0.1 M_\odot$ and $1.0 M_\odot$ as well."
 We rote here that ATACTIO amass can have a laree effect ou he expected timescales and rates., We note here that MACHO mass can have a large effect on the expected timescales and rates.
 Larger masses would indicate a lower rate and longer eveuts. while smaller nasses give a higher rate but shorter events.," Larger masses would indicate a lower rate and longer events, while smaller masses give a higher rate but shorter events."
 This is discussed further iu the next section., This is discussed further in the next section.
 Iu Fies. 1-, In Figs. \ref{fig:map1}-
-6 we plot event rate contours for 77 baud observations., \ref{fig:map_mass} we plot event rate contours for $R$ band observations.
 The contours for £ bind are very similar., The contours for $I$ band are very similar.
 The only pronounced difference is in the bulec. where he Z baud huumositv function is quite shallow. there is a significantly lareer rate in the most central L square archuinutes.," The only pronounced difference is in the bulge, where the $I$ band luminosity function is quite shallow, there is a significantly larger rate in the most central 4 square arcminutes."
 While it is desirable to detect events iu two wands to test that the fluxenfiencemoent las a coustaut color (in time). as should be the case for gravitational eusing. we will not include this criterion.," While it is desirable to detect events in two bands to test that the flux has a constant color (in time), as should be the case for gravitational lensing, we will not include this criterion."
 The separate event rates are verv smuilu. thus we ceem it uulikelv that he joiut event rate will be much differeut.," The separate event rates are very similar, thus we deem it unlikely that the joint event rate will be much different."
 Iu Fie., In Fig.
 1. we ot the rate contours for self lensing aud for M31 halos with a NIACTIIO fraction AAlcock et al. (, \ref{fig:map1} we plot the rate contours for self lensing and for M31 halos with a MACHO fraction Alcock et al. (
"2000) Cfi,= 0.2) aud a core radius of 2 kpc.",2000) $f_b=0.2$ ) and a core radius of 2 kpc.
 Both round (y= 1) and flattened (q= 0.3) halos are illustrated., Both round $q=1$ ) and flattened $q=0.3$ ) halos are illustrated.
 These maps are given as contours of coustant rate. m units of events + aremin 7.," These maps are given as contours of constant rate, in units of events $^{-1}$ $^{-2}$ ."
 In Fig., In Fig.
" 20 we plot rate contours again for f,=0.2. but compare the small (6.=1 kpc) aud laree (Gr—5 kpe) core cases. for both round aud fattened halos."," \ref{fig:map2} we plot rate contours again for $f_b=0.2$, but compare the small $r_c=1$ kpc) and large $r_c=5$ kpc) core cases, for both round and flattened halos."
 In Fig., In Fig.
 2. we illustrate the event rate from Milky Way ATACTOs. asstumineg both round aud flattened cases again.," \ref{fig:map3} we illustrate the event rate from Milky Way MACHOs, assuming both round and flattened cases again."
 The rate should be related to the surface brightucss. also illustrated.," The rate should be related to the surface brightness, also illustrated."
 In fact a naive calculation indicates that the rate from a constant optical depth of lenses (sch as a Alilkv Way population. which svouldut vary much over the ΑΙ]. fields) should be proportional to the square root of the surface brightness.," In fact a naive calculation indicates that the rate from a constant optical depth of lenses (such as a Milky Way population, which wouldn't vary much over the M31 fields) should be proportional to the square root of the surface brightness."
 This can be seen from the following siuple arguneut., This can be seen from the following simple argument.
 The nunuber of monitored sources is xoportional to the surface brightness (the proportionality constant depeuds on huninosity function). but the noise evel increases as the square root of the surface brieltucss. recessitating an ducrease dmi magnification bv the same actor to obtain an equivaleut signal to noise.," The number of monitored sources is proportional to the surface brightness (the proportionality constant depends on luminosity function), but the noise level increases as the square root of the surface brightness, necessitating an increase in magnification by the same factor to obtain an equivalent signal to noise."
 Since the oeak magnification of the event is proportional to the inverse of the iaupact parameter. the total cross section goes down by this square root of surface brightuess.," Since the peak magnification of the event is proportional to the inverse of the impact parameter, the total cross section goes down by this square root of surface brightness."
 Thus. he ΠΙΟ of nionitored sources times the cross section is xoportional to the square root of the surface brightuess.," Thus, the number of monitored sources times the cross section is proportional to the square root of the surface brightness."
" This aremmenut breaks down at very high surface brightucss where the magnification required implies events whose ""ll width at half παπα timescales are too short to detect. however. this regine is not reached for N31 for the nlasses assumed."," This argument breaks down at very high surface brightness where the magnification required implies events whose full width at half maximum timescales are too short to detect, however, this regime is not reached for M31 for the masses assumed."
 Frou Fig., From Fig.
 3 we see that this calculation is reasonable. as the shape of rate contours matches the shape of the surface brightuecss coutours. aud the rate of decline is roughly half ou the logarithmic scale illustrated.," \ref{fig:map3} we see that this calculation is reasonable, as the shape of rate contours matches the shape of the surface brightness contours, and the rate of decline is roughly half on the logarithmic scale illustrated."
 The dattening of the Milky Wav halo only changes the jormalizatiou of the rates. not the shape of the contours.," The flattening of the Milky Way halo only changes the normalization of the rates, not the shape of the contours."
 Combining all of these componcuts. we illustrate the otal expected event rate.," Combining all of these components, we illustrate the total expected event rate."
 In the bottom paucl of Fig. 1L.," In the bottom panel of Fig. \ref{fig:map_dist},"
 we plot coutours of the total microlensing rate. from solf cusing aud ALACTIO halos for both the Milkv. Way and NI.," we plot contours of the total microlensing rate, from self lensing and MACHO halos for both the Milky Way and M31."
 The self lensing dominates in the iuer 5 kpc. mit outside. the halo provides most of the eveuts.," The self lensing dominates in the inner 5 kpc, but outside, the halo provides most of the events."
 Changing the halo fraction fj las little effect on the shape of the contours. aud ouly iu the region where the self chasing and halo lensing are comparable (roughly speaking within the 0.3 events ? + contour assuming a halo).," Changing the halo fraction $f_b$ has little effect on the shape of the contours, and only in the region where the self lensing and halo lensing are comparable (roughly speaking within the 0.3 events $^{-2}$ $^{-1}$ contour assuming a halo)."
 The overall normalization of the eveut rate away from the bulee cau give a clear measuremeut of fr., The overall normalization of the event rate away from the bulge can give a clear measurement of $f_b$.
 For example. comparing a halo to the case of a halo. the inner contours Gwithin Levent ? 3) are not much affected since self leusiug dominates aud the of the outer coutours is very simular since it is the halo that dominates there iu both cases.," For example, comparing a halo to the case of a halo, the inner contours (within 1 event $^{-2}$ $^{-1}$ ) are not much affected since self lensing dominates and the of the outer contours is very similar since it is the halo that dominates there in both cases."
 Between the 1.0 and 0.3 contours the event rate drops more quickly in the halo case since this is the region where the microlensing rate from the halo aud stellar components are comparable., Between the 1.0 and 0.3 contours the event rate drops more quickly in the halo case since this is the region where the microlensing rate from the halo and stellar components are comparable.
 This is clear from inspecting the top paucl of Fig., This is clear from inspecting the top panel of Fig.
 1. (the self leusing rate) aud comparing to the bottom panel (the AD halo lensing rate) which is trivially rescaled according ο MACTIO fraction., \ref{fig:map1} (the self lensing rate) and comparing to the bottom panel (the M31 halo lensing rate) which is trivially rescaled according to MACHO fraction.
 Fig., Fig.
 1 shows the difference iu the rate contours for round q= Land dattened 4=0.3 halos., \ref{fig:map_dist} shows the difference in the rate contours for round $q=1$ and flattened $q=0.3$ halos.
 The two cases appear to )o Casily distinguishable. especially along the major axis.," The two cases appear to be easily distinguishable, especially along the major axis."
 Iu the bottom panel of Fig. 5..," In the bottom panel of Fig. \ref{fig:map_sn},"
 we again plot contours of he total microleusing rate. this time varving the halo core radius from 1.2.5.10 Ipc.," we again plot contours of the total microlensing rate, this time varying the halo core radius from $1,2,5,10$ kpc."
 The significant differeuce i3 on he far side. aloug the minor axis.," The significant difference is on the far side, along the minor axis."
 A crude measurement of core radius may thus be possible., A crude measurement of core radius may thus be possible.
 Tere we see the utility of using the raw event rates to determine parameters., Here we see the utility of using the raw event rates to determine parameters.
 We do not uced to evaluate the optical depth to do so., We do not need to evaluate the optical depth to do so.
 Since in the end we are interested iu the halo parameters like NLACIIO fraction aud flattening. the optical depth is secondary.," Since in the end we are interested in the halo parameters like MACHO fraction and flattening, the optical depth is secondary."
 The Eiusteiu time is the fuudiuuneutal timescale paralcterizing the variability dueto Ieusine. but it is," The Einstein time is the fundamental timescale parameterizing the variability dueto lensing, but it is"
by Walboru et al. (,by Walborn et al. (
2002) to include the new types of O2 aud O3.5 to delineate the behavior of the NUL. αδένας N features seen in the earliest types.,"2002) to include the new types of O2 and O3.5 to delineate the behavior of the N, N, and N features seen in the earliest types."
 Even in the age of large multi-object sirveys ouly a few tens of stars are kuown with O203.5 types., Even in the age of large multi-object surveys only a few tens of stars are known with O2–O3.5 types.
 Although very rare. their influence is far-reaching as they are expected to evolve rapidly iuto nitrogen rich WolfRawvet stars (WN types). plausible progenitors of supernovae and. potentially. eanuna-ray bursts (Sinartt 2009].," Although very rare, their influence is far-reaching as they are expected to evolve rapidly into nitrogen rich Wolf–Rayet stars (WN types), plausible progenitors of supernovae and, potentially, gamma-ray bursts (Smartt 2009)."
 Observatious with the 2-degree Field (2dF) instrmucut at the Anelo-Australian Telescope revealed a new O2-tvpe star on the western fringes of 30 Doradus (Figure 1)). with a radial velocity of —85 ‘lower than the svstemic velocity ofnearby massive stars (e.g.. Bosch. Terlevich Terlevich 2009).," Observations with the 2-degree Field (2dF) instrument at the Anglo-Australian Telescope revealed a new O2-type star on the western fringes of 30 Doradus (Figure \ref{fig1}) ), with a radial velocity of $\sim$ lower than the systemic velocity of nearby massive stars (e.g., Bosch, Terlevich Terlevich 2009)."
 New epoch spectroscopy of this star. 30 Dor 016 in the VLT-FLAMES Tarantula Survey (Evaus et al.," New multi-epoch spectroscopy of this star, 30 Dor 016 in the VLT-FLAMES Tarantula Survey (Evans et al."
 2010). now enables us to rule out the presence of a close massive colupanion to a high level of confidence. sugeesting that the star night have been ejected from the denser central reeion.," 2010), now enables us to rule out the presence of a close massive companion to a high level of confidence, suggesting that the star might have been ejected from the denser central region."
" Tere. we combine these observations with new ultraviolet (UV) spectroscopy of #0016. some of the first data taken with the Cosinic Origins Spectrograph (COS) on theT). which reveal the star to have one of the highest wind terminal velocities secu to date in any massive star,"," Here, we combine these observations with new ultraviolet (UV) spectroscopy of 016, some of the first data taken with the Cosmic Origins Spectrograph (COS) on the, which reveal the star to have one of the highest wind terminal velocities seen to date in any massive star."
" 30 Dor O16 (o 0052 337 OOSSSS. 6==- 69° O07! 2207336, J2000) was observed with HST-COS as part of the Servicing Mission Observatory Verification (SMOV) program in 2009 July usine the CGI3B0ALD and CAGOAD eratiuss in the far-UW channel."," 30 Dor 016 $\alpha$ $^{\rm h}$ $^{\rm m}$ 88, $\delta$ $-$ $^\circ$ $'$ 36, J2000) was observed with }-COS as part of the Servicing Mission Observatory Verification (SMOV) program in 2009 July using the G130M and G160M gratings in the far-UV channel."
 The data were obtained as part of a focus-check ru carly in the SAIOV phase of COS operations so we do not have full waveleneth coverage as the gratiugs, The data were obtained as part of a focus-check run early in the SMOV phase of COS operations so we do not have full wavelength coverage as the gratings
In connection to the much debated primordial lithium abundance. and its relation to the observed lithium abundance in metal-poor dwarfs (the so-called Spite-plateau). we checked the status of this element in our two program stars.,"In connection to the much debated primordial lithium abundance, and its relation to the observed lithium abundance in metal-poor dwarfs (the so-called Spite-plateau), we checked the status of this element in our two program stars."
 We deterninec the abundance from the 5.. 6). 8 ," We determined the abundance from the \ref {T-param}, \ref {F-Liline}) \ref {F-LivFe} "
analvsis threads provided by the SScicuce SupportCenuter®.,analysis threads provided by the Science Support.
". We selected data with ""Diffuse events. which have the highest probability of being a photon."," We selected data with “Diffuse” events, which have the highest probability of being a photon."
 Iu addition. we filtered out events with earth zenith angles exreater than 1057 to reduce the contamination from Earth albedo eanuna-ravs.," In addition, we filtered out events with earth zenith angles greater than $105^\circ$ to reduce the contamination from Earth albedo gamma-rays."
 The instrument response fuuctious (IRFs). “PONVV3_DDIFFUSE™ ire used.," The instrument response functions (IRFs), DIFFUSE” are used."
 We limited our analysis using data between 0.5 aud 20 GeV with which the point-spread-fiuiction is better than ~1 degree such that the contamination by the Galactic plane ciission is nmdunuized., We limited our analysis using data between 0.5 and 20 GeV with which the point-spread-function is better than $\sim 1$ degree such that the contamination by the Galactic plane emission is minimized.
 Furthermore. the sensitivity is more.," Furthermore, the sensitivity is more."
. Iu Figure 1. the photon map im the 0.520 CeV band iu the vicinity of Terzau 5 is shown.," In Figure 1, the photon map in the 0.5–20 GeV band in the vicinity of Terzan 5 is shown."
 Although stroug Calactie plane emissiou is seen near Terzan 5. a eanamnia-rav source at the position of Terzau 5 is clearly detected as an isolated source at a level of ~2760 (see below).," Although strong Galactic plane emission is seen near Terzan 5, a gamma-ray source at the position of Terzan 5 is clearly detected as an isolated source at a level of $\sim 27\sigma$ (see below)."
 We used. to deteriine the position of the ganuua-rav position., We used to determine the position of the gamma-ray position.
" Iu order to miinuze the contamination from nearby sources and diffuse enuüssion. we inchuded Calactie diffuse model vv(02.ft) aud isotropic backerouud vvοκε), as well as all poiut sources m the bright source (Abdo et al."," In order to minimize the contamination from nearby sources and diffuse emission, we included Galactic diffuse model v02.fit) and isotropic background v02.txt), as well as all point sources in the bright source (Abdo et al."
" 2009): version of 2010 January) within a region of interest of 195"" centered on Terzan 5.", 2009b; version of 2010 January) within a region of interest of $15^\circ$ centered on Terzan 5.
 The best-fit pposition of Terzan 5r is R.A.—17hlsmn0s.— decl.=-[dISud5s (J2000) with a error of 0.097 (includiug a svstemiatie error based ou the bright source catalog).," The best-fit position of Terzan 5 is R.A.=17h48m00s, decl.=-24d48m15s (J2000) with a error of $0.09^\circ$ (including a systematic error based on the bright source catalog)."
" The optical ceuter of Terza His at R.A.=17h(δι, clecL=-2IdE61£88 (J2000). which is 0.037 from the ppositiou."," The optical center of Terzan 5 is at R.A.=17h48m05s, decl.=-24d46m48s (J2000), which is $0.03^\circ$ from the position."
 Therefore the ssource is consistent with the location of Terzan 5., Therefore the source is consistent with the location of Terzan 5.
 Iu addition. it is clear frou the test-statistic (TS) map in Figure 1 that the source is highly significant iu the 0.520 GeV band aud the optical ceuter of Terzan 5 falls ou he peak of the TS map.," In addition, it is clear from the test-statistic (TS) map in Figure 1 that the source is highly significant in the 0.5--20 GeV band and the optical center of Terzan 5 falls on the peak of the TS map."
 Also shown in Figure 1l is the 1020 GeV image aud its TS map: the gamma-ray source jas less than lo detection significance., Also shown in Figure 1 is the 10–20 GeV image and its TS map; the gamma-ray source has less than $4\sigma$ detection significance.
 We also divided he image iuto four parts with roughly equal exposure iue., We also divided the image into four parts with roughly equal exposure time.
 Terzan 5 is always seen with no apparent flaring. indicating that the gamma-rays are not from any kind of Hares.," Terzan 5 is always seen with no apparent flaring, indicating that the gamma-rays are not from any kind of flares."
 We performed spectral analysis by using maxim ikclihood technique implemented byyflike., We performed spectral analysis by using maximum likelihood technique implemented by.
 Like spatial analysis. we also included diffuse emission and bright »oiut sources to Obtain a simltancous fit to the uubiuned data.," Like spatial analysis, we also included diffuse emission and bright point sources to obtain a simultaneous fit to the unbinned data."
 All bright point sources were modeled with simple vower-laws., All bright point sources were modeled with simple power-laws.
 We first fit the spectrum of Terzan 5 with a siuple power-law: the best-fitting photon index D is 2540.1 (errors are statistical oulv)., We first fit the spectrum of Terzan 5 with a simple power-law; the best-fitting photon index $\Gamma$ is $2.5\pm0.1$ (errors are statistical only).
 However. as shown w othe sanuna-eray cussion frou L7 Tuc as well as other MSPs. the cuerey spectrum is likely to be im the orm of an exponential eutoff power-law (Aldo et al.," However, as shown by the gamma-ray emission from 47 Tuc as well as other MSPs, the energy spectrum is likely to be in the form of an exponential cutoff power-law (Abdo et al."
 2009a.2009C).," 2009a,2009c)."
 We show the sspectruuir of Terzan 5 in Figure 2 and it is clear that he energy distribution appears to turi over at energies above ~5 GeV. We then re-fit the spectrum with au exponeutial cutoff power-law model: the photon index is P=1940.2 and the cutoff energy is Zi=3.8+1.2 GeV. The additional cutoff componcut is statistically mangesienificant at level., We show the spectrum of Terzan 5 in Figure 2 and it is clear that the energy distribution appears to turn over at energies above $\sim 5$ GeV. We then re-fit the spectrum with an exponential cutoff power-law model; the photon index is $\Gamma=1.9\pm0.2$ and the cutoff energy is $E_c=3.8\pm1.2$ GeV. The additional cutoff component is statistically significant at level.
 The resulting TS value. indicates the significance of the source detection," The resulting TS value, which indicates the significance of the source detection"
 , 
as the condition to determine the trigger time and. to ect the straight line at [ate stages.,as the condition to determine the trigger time and to get the straight line at late stages.
 Llowever. we must bear in mind that it is in fact not an easy task.," However, we must bear in mind that it is in fact not an easy task."
 First. to take the process we need to follow the orphan as long as possible. and the simple. cliscovery of an orphan is obviously insullicient.," First, to take the process we need to follow the orphan as long as possible, and the simple discovery of an orphan is obviously insufficient."
 Note that currently optical afterglows from most well-localized (ας can be observed. for only [ess than LOO days., Note that currently optical afterglows from most well-localized GRBs can be observed for only less than 100 days.
 Lt is quite unlikely at we can follow an orphan for a period longer than that., It is quite unlikely that we can follow an orphan for a period longer than that.
 ulecond. since the orphan is usually very faint. errors in the neasured magnitudes will seriously:A prevent us from deriving 1e straight line.," Second, since the orphan is usually very faint, errors in the measured magnitudes will seriously prevent us from deriving the straight line."
 Due to all these dillieulties. à satisfactory light curve is usually hard to get for most orphans.," Due to all these difficulties, a satisfactory light curve is usually hard to get for most orphans."
 We see that measurement of the GRB beaming angle using orphan searches is not as simple as we originally expected., We see that measurement of the GRB beaming angle using orphan searches is not as simple as we originally expected.
 La fact. it is impractical to some extent.," In fact, it is impractical to some extent."
 Recently it was suggested by Rhoacs (2001) that CRB afterglows can be ellectIy identified by snapshot observations made with three or more optical filters., Recently it was suggested by Rhoads (2001) that GRB afterglows can be effectly identified by snapshot observations made with three or more optical filters.
 The method has been successfully applied to GRB 001011. by Ciorosabel et al. (, The method has been successfully applied to GRB 001011 by Gorosabel et al. (
2001).,2001).
 Lt is believed that this method is also helpful for orphan afterglow searches., It is believed that this method is also helpful for orphan afterglow searches.
 However. please note that a jetted GRB orphan and an FORB one still cannot be discriminated cirectly.," However, please note that a jetted GRB orphan and an FGRB one still cannot be discriminated directly."
 We have shown that the derivation of a satisfactory light curve for an orphan afterglow is cillicult., We have shown that the derivation of a satisfactory light curve for an orphan afterglow is difficult.
 Lhe major problem is that we do not know the trigger time., The major problem is that we do not know the trigger time.
 Anyway. there are still some possible solutions that may help to determine the onset of an orphan afterglow.," Anyway, there are still some possible solutions that may help to determine the onset of an orphan afterglow."
 Firstly. of course we should improve our detection limit so that the orphan afterglow could be followed as long as possible.," Firstly, of course we should improve our detection limit so that the orphan afterglow could be followed as long as possible."
 “Phe longer we observe. the more likely that. we can get the true late-time light curve slope.," The longer we observe, the more likely that we can get the true late-time light curve slope."
 Secondly. we know that FORBs usually manifest themselves as fast. X-ray transients or N-ray-GRBs.," Secondly, we know that FGRBs usually manifest themselves as fast X-ray transients or X-ray-GRBs."
 Loan orphan can be identifie to associate with such a transient. then it is most. likely an FORB one.," If an orphan can be identified to associate with such a transient, then it is most likely an FGRB one."
 In this case. the trigger time can be wel determined.," In this case, the trigger time can be well determined."
 ‘Vhirdly. maybe in some rare cases we are so lucky tha the rising phase of the orphan could be observed.," Thirdly, maybe in some rare cases we are so lucky that the rising phase of the orphan could be observed."
 For a jettec GRB orphan the maximum optical (lux is usually reachec within one or two days and for an FORB orphan it is even within hours., For a jetted GRB orphan the maximum optical flux is usually reached within one or two days and for an FGRB orphan it is even within hours.
 Phen the uncertainty in trigger time is greatly reduced., Then the uncertainty in trigger time is greatly reduced.
 Additionally. a jetted GARB orphan dillers markedly rom an FORB one during the rising phase.," Additionally, a jetted GRB orphan differs markedly from an FGRB one during the rising phase."
 The former can »¢ brightened by more than one magnitude in several hours (sce Figures 1 4). while the brightening of the latter can iarcdy be observed.," The former can be brightened by more than one magnitude in several hours (see Figures 1 — 4), while the brightening of the latter can hardly be observed."
 So. if an orphan afterglow with a short »eriod. o£. brightening is observed. then it is most. likely a jetted GRB orphan.," So, if an orphan afterglow with a short period of brightening is observed, then it is most likely a jetted GRB orphan."
 Of course. we should. first be certain hat it is not a supernova.," Of course, we should first be certain that it is not a supernova."
 Fourthly. valuable clues may come from racio observations.," Fourthly, valuable clues may come from radio observations."
 In radio bands. the light curve should. be üghlv variable at carly stages due to interstellar medium scintillation. and it will become much smoother at late imes.," In radio bands, the light curve should be highly variable at early stages due to interstellar medium scintillation, and it will become much smoother at late times."
 So the variability in radio light curves provides useful information on the trigger time., So the variability in radio light curves provides useful information on the trigger time.
 nd [ifthlv. in he future maybe gravitational wave radiation or neutrino radiation associated with GRBs could. be detected. due to orogresses in technology. then the trigger time of an orphan could be determined. directly. and. accurately.," And fifthly, in the future maybe gravitational wave radiation or neutrino radiation associated with GRBs could be detected due to progresses in technology, then the trigger time of an orphan could be determined directly and accurately."
 In fact. with he successful detection of &ravitational waves or neutrino emission. our understanding on GIU progenitors will surely »' promoted. greatly. (Paolis ct al.," In fact, with the successful detection of gravitational waves or neutrino emission, our understanding on GRB progenitors will surely be promoted greatly (Paolis et al."
 2001)., 2001).
 Sixthlv. the redshift of the orphan afterglow can help us ereatly in determining the isotropic energy involved. which itself is helpful for inferring the trigger time.," Sixthly, the redshift of the orphan afterglow can help us greatly in determining the isotropic energy involved, which itself is helpful for inferring the trigger time."
 Seventhlv. the microlensing ellect may be of some help.," Seventhly, the microlensing effect may be of some help."
 Since the size of the radiation zone of a jetted GARB orphan is much smaller than that of an FORB one. they should behave cillerently when microlensec.," Since the size of the radiation zone of a jetted GRB orphan is much smaller than that of an FGRB one, they should behave differently when microlensed."
 Finally. although a successful detection of some orphan alterglows does not directly mean that CtBs be collimated. the negative detection of any orphans can always place both a stringent lower limit on the beaming angle for GRBs and a reasonable upper Limit for the rate of FGRBs.," Finally, although a successful detection of some orphan afterglows does not directly mean that GRBs be collimated, the negative detection of any orphans can always place both a stringent lower limit on the beaming angle for GRBs and a reasonable upper limit for the rate of FGRBs."
 ‘To successfully produce a CRB. the blastwave should. be ultra-relativistic. with Lorentz factor tvpically larger than 100 1000.," To successfully produce a GRB, the blastwave should be ultra-relativistic, with Lorentz factor typically larger than 100 — 1000."
 Llowever. in almost all popular progenitor models. the environment. is unavoidably barvon-rich.," However, in almost all popular progenitor models, the environment is unavoidably baryon-rich."
 We believe that only in very rare cases can an ultra-relativistic blastwave successfully break out to give birth toa CARB. and there should be much more Failed. CRBs. Le. fireballs with Lorentz factor much less than 100 but still much larger than unity.," We believe that only in very rare cases can an ultra-relativistic blastwave successfully break out to give birth to a GRB, and there should be much more failed GRBs, i.e., fireballs with Lorentz factor much less than 100 but still much larger than unity."
 In fact. this possibility has also been mentioned by a number of authors. such as Alésszarros Waxman (2001).," In fact, this possibility has also been mentioned by a number of authors, such as Mésszárros Waxman (2001)."
 Owing to the existence of FORBs. there should. be many orphan alterelows even if GRBs are due to isotropic fireballs.," Owing to the existence of FGRBs, there should be many orphan afterglows even if GRBs are due to isotropic fireballs."
 “Phen the simple discovery. of orphan afterelows does not necessarily mean that GRBs be highly collimated., Then the simple discovery of orphan afterglows does not necessarily mean that GRBs be highly collimated.
 ‘To make use of information from orphan afterglow surveys correctly. we should first know how to discriminate a jetted CGRB orphan and an FORB one.," To make use of information from orphan afterglow surveys correctly, we should first know how to discriminate a jetted GRB orphan and an FGRB one."
 This can be done only by checking the detailed afterglow light curve., This can be done only by checking the detailed afterglow light curve.
 However. we have shown that the derivation of a satisfactory light. curve for an orphan afterglow is dillicult.," However, we have shown that the derivation of a satisfactory light curve for an orphan afterglow is difficult."
 Phe major problem is that we do not know the trigger time., The major problem is that we do not know the trigger time.
 In Section 3.2. some possible solutions to the problem are suggested.," In Section 3.2, some possible solutions to the problem are suggested."
 Unfortunately many of these solutions are still quite impractical in the foresceable future. which means measure of GRB beaming angle using orphan afterglow searches is extremely dillieult. currently.," Unfortunately many of these solutions are still quite impractical in the foreseeable future, which means measure of GRB beaming angle using orphan afterglow searches is extremely difficult currently."
 However. special attention. should be paid. to the second. solution.," However, special attention should be paid to the second solution."
 Usually. FORBs manifested themselves as fast X-ray transients during the main burst phase. while jetted but off-axis GRBs went unattended completely.," Usually, FGRBs manifested themselves as fast X-ray transients during the main burst phase, while jetted but off-axis GRBs went unattended completely."
 H£ the fast A-ray transients, If the fast X-ray transients
We have examined the 5—rav emission properties of a group of GCs.,We have examined the $\gamma-$ ray emission properties of a group of GCs.
 By investigating the possible correlations between the 5—ray power and a number of cluster properties. we shed light on the origin of the 5—ravs from these GC's.," By investigating the possible correlations between the $\gamma-$ ray power and a number of cluster properties, we shed light on the origin of the $\gamma-$ rays from these GCs."
 First of all. the correlation between L. and D. suggests the high energy radiation are intimately related to (he population of dvnamically-formed objects. which are presumably. MSPs. confirming Abdo et al. (," First of all, the correlation between $L_{\gamma}$ and $\Gamma_{c}$ suggests the high energy radiation are intimately related to the population of dynamically-formed objects, which are presumably MSPs, confirming Abdo et al. ("
201011) who used 8 GCs in their study.,2010a) who used 8 GCs in their study.
 Together with the lack of anv correlation with M4- and hence the cluster mass. this is fully consistent with the inference suggested by IIui et al. (," Together with the lack of any correlation with $M_{V}$ and hence the cluster mass, this is fully consistent with the inference suggested by Hui et al. ("
2010) and consolidates the dviaimical formation scenario of AISPs in GCs.,2010) and consolidates the dynamical formation scenario of MSPs in GCs.
" Apart from D. we have found that £, is also positively correlated with [Fe/H]."," Apart from $\Gamma_{c}$, we have found that $L_{\gamma}$ is also positively correlated with $\left[{\rm Fe/H}\right]$."
 This is well-consistent with the tendency deduced from studyiug the radio MSP population in GC's (Thai et al., This is well-consistent with the tendency deduced from studying the radio MSP population in GCs (Hui et al.
 2010) and the fact that the GC possesses the highest Ρο also has the highest £L. (Tam et al., 2010) and the fact that the GC possesses the highest [Fe/H] also has the highest $L_{\gamma}$ (Tam et al.
 2010)., 2010).
 Ivanova (2006) proposes that the absence of the outer convective zone in metal-poor main sequence donor stus in (he mass range of 0.85... - 1.25.M.. im comparison to their metal rich counterparts can be responsible. since the absence of magnetic braking in such stars precludes orbital shrinkage. thereby. significantly reducing the binary. parameter space for the production of bright LAINBs.," Ivanova (2006) proposes that the absence of the outer convective zone in metal-poor main sequence donor stars in the mass range of $0.85\msun$ - $1.25 \msun$, in comparison to their metal rich counterparts can be responsible, since the absence of magnetic braking in such stars precludes orbital shrinkage, thereby, significantly reducing the binary parameter space for the production of bright LMXBs."
 For a conventional scenario. MSPs are the old pulsars (hat. have passed through the death-line in 7?—P diagram which are subsequent=< spun-up in the binaries.," For a conventional scenario, MSPs are the old pulsars that have passed through the death-line in $P-\dot{P}$ diagram which are subsequently spun-up in the binaries."
 As the metalicitv determines the parameter space for successful Roche-lohe overflow. it is also a kev parameter in determining the intrinsic number of ASPs in a GC (IIui et al.," As the metalicity determines the parameter space for successful Roche-lobe overflow, it is also a key parameter in determining the intrinsic number of MSPs in a GC (Hui et al."
 2010: Ivanova 2006)., 2010; Ivanova 2006).
 We note that the link between the LAINBs in extragalactic GCs and the metalicity is somewhat weaker than with the cluster mass (e.g. Sivakolf et al., We note that the link between the LMXBs in extragalactic GCs and the metalicity is somewhat weaker than with the cluster mass (e.g. Sivakoff et al.
 2007: Nim et al., 2007; Kim et al.
 2006: Kundu οἱ al., 2006; Kundu et al.
 2002). whieh is different. from the inference drawn from our investigation of the Galactic MSP-hosting or 5 —rav selected clusters.," 2002), which is different from the inference drawn from our investigation of the Galactic MSP-hosting or $\gamma-$ ray selected clusters."
 ILowever. a direct comparison between these (wo populations has to be cautious.," However, a direct comparison between these two populations has to be cautious."
 As the MSPs are long-lived and are produced by (he previous generations of LMXDs. their dvnamical properties might be different from that of the LAINB population currently observed.," As the MSPs are long-lived and are produced by the previous generations of LMXBs, their dynamical properties might be different from that of the LMXB population currently observed."
 Since the relaxation time al (he cluster core is generally longer than the lifetime of LAINBs. the cluster is continuously evolved with mass segregalion at the cluster center which can result in a varving formation rate of compact binaries (cf.," Since the relaxation time at the cluster core is generally longer than the lifetime of LMXBs, the cluster is continuously evolved with mass segregation at the cluster center which can result in a varying formation rate of compact binaries (cf."
 the discussion in IIui οἱ al., the discussion in Hui et al.
 2010)., 2010).
 Also. while a large number of LMXD-hosting GCs in Virgo cluster earlv-tvpe galaxies have relaxation times >2.5 Gvr. there is no sinele GC in our Galaxy with a relaxation timescale larger (han (hiis value contains an active LMXD (cL.," Also, while a large number of LMXB-hosting GCs in Virgo cluster early-type galaxies have relaxation times $>2.5$ Gyr, there is no single GC in our Galaxy with a relaxation timescale larger than this value contains an active LMXB (cf."
 Sivakolf et al., Sivakoff et al.
 2007)., 2007).
 Although the reason is still unclear. this suggests possible dilferent properties between (he Milkv. Way GC's and the extragalactic ones.," Although the reason is still unclear, this suggests possible different properties between the Milky Way GCs and the extragalactic ones."
 Further investigations are required to understand (he difference., Further investigations are required to understand the difference.
loss of evolved stars. (Ciotti&Ostriker1997)..,loss of evolved stars. \citep{Ciotti1997}. .
 Quatacrt(2001) model the gas supply in the ceutral parsec of the Galactic center due to the latter process., \cite{Quataert2004} model the gas supply in the central parsec of the Galactic center due to the latter process.
 Winds from luassive stars eau provide ~102Mvx+ of eas. with a few percent. ~10ML.yr+. of the gas flowine in toward the central massive black hole.," Winds from massive stars can provide $\sim 10^{-3}\msun {\rm yr^{-1}}$ of gas, with a few percent, $\sim 10^{-5}\msun {\rm yr^{-1}}$, of the gas flowing in toward the central massive black hole."
 Quataert.(2001) shows that the observed Imminosity frou: Ser A* can indeed be explained by relatively ineficicut accretion of eas originating from stellar winds., \cite{Quataert2004} shows that the observed luminosity from Sgr A* can indeed be explained by relatively inefficient accretion of gas originating from stellar winds.
 Elliptical galaxies with quicscent massive black holes. systems for which we have both accurate massive black role inasses and data about their simroundiuss. lint hat stellar winds may be a significant source of fuel for he massive black hole.," Elliptical galaxies with quiescent massive black holes, systems for which we have both accurate massive black hole masses and data about their surroundings, hint that stellar winds may be a significant source of fuel for the massive black hole."
 The hot eas of the iuterstellar ueciun. lending itself to X-ray observations. cannot  the sole source of fuel for at least some inassive dack holes.," The hot gas of the interstellar medium, lending itself to X-ray observations, cannot be the sole source of fuel for at least some massive black holes."
 In particular. some massive black holes are xiehter than one would expect for inefficient accretion. mt siguif&cantlv less bright than for normal accretion (Soriaetal.2006a).," In particular, some massive black holes are brighter than one would expect for inefficient accretion, but significantly less bright than for normal accretion \citep{Soria2006a}."
. The N-rav Iuuünosity cau vary by orders of magnitude displaving no relationship )etxeeen massiveblack hole mass or the Bondi accretion rate (Pellegrini2005)., The X-ray luminosity can vary by orders of magnitude displaying no relationship between massiveblack hole mass or the Bondi accretion rate \citep{pellegrini2005}.
. It is likely that wari gas that das not vet been thermalized or virialized originating roni stellar winds aud supernovae from near the massive lack hole provides a significant amount of material for accretion. possibly an order of magnitude larger than the Doudi accretion rate of hot interstellar iuediua eas alone (Soriaetal.200G6)).," It is likely that warm gas that has not yet been thermalized or virialized originating from stellar winds and supernovae from near the massive black hole provides a significant amount of material for accretion, possibly an order of magnitude larger than the Bondi accretion rate of hot interstellar medium gas alone \citep{Soria2006b}."
. We attempt iu this paper a simple estimate of how uuch recycled eas is available for accretion outo a nassive black hole iu differcut stellar systems. from elobular clusters to galaxies. includiug dwarf spheroicdals. clear star clusters in the cores of late type galaxies and carly type normal galaxies.," We attempt in this paper a simple estimate of how much recycled gas is available for accretion onto a massive black hole in different stellar systems, from globular clusters to galaxies, including dwarf spheroidals, nuclear star clusters in the cores of late type galaxies and early type normal galaxies."
 We show that the amount of fuel available to massive black holes through stellar winds in quiesceut galaxies is indeed mioeager. aud unless extreme couditious are uct. X-ray detection of massive black holes iu globular clusters aud low-mass galaxies is expected to be uuconmuuion.," We show that the amount of fuel available to massive black holes through stellar winds in quiescent galaxies is indeed meager, and unless extreme conditions are met, X-ray detection of massive black holes in globular clusters and low-mass galaxies is expected to be uncommon."
 To inodel the accretion rate. we iuust choose 3-dimensional stellar distributions for the various stellar systems we consider heres," To model the accretion rate, we must choose 3-dimensional stellar distributions for the various stellar systems we consider here."
 For elobular clusters aud dwart spheroidals we assume the stars to be distributed following a Planner profile:2 where ο=Πω is the core radius.," For globular clusters and dwarf spheroidals we assume the stars to be distributed following a Plummer profile:, where $a=R_{\rm eff}$ is the core radius."
 Early type galaxies and nuclear clusters are modeled as IHoruquist spheres: where the scale leugth kj2Rog/1.51., Early type galaxies and nuclear clusters are modeled as Hernquist spheres: where the scale length $r_h\approx R_{\rm eff}/1.81$.
 To fully define the stellar svstems we have oulv to relate the stellar ass. Misa to the effective radius. Pg.," To fully define the stellar systems we have only to relate the stellar mass, $M_{\rm stellar}$, to the effective radius, $R_{\rm eff}$."
 For globulu clusters. we recall that simulations by Bammeardtetal.(2005.2001) sugecst that elobular clusters withmassive black holes have relatively larec cores 4~l|3 pe (seealsoTreutietal.2007).," For globular clusters, we recall that simulations by \cite{Baumgardt2005,Baumgardt2004} suggest that globular clusters withmassive black holes have relatively large cores $a\sim 1-3$ pc \citep[see also][]{Trenti2007}."
. Consistent results were found using Monte Carlo sunulatious (Uiubreitetal.2009). ancl in analytical models (Iegeieetal.2007)., Consistent results were found using Monte Carlo simulations \citep{Umbreit2009} and in analytical models \citep {Heggie2007}.
. The core radii (where measured) of globular clusters hosting intermediate mass black hole eaudidates. are roughly consistent with the values we considered. rangiue from approx 0.5 pe in ALLS (Gerssen et al.," The core radii (where measured) of globular clusters hosting intermediate mass black hole candidates, are roughly consistent with the values we considered, ranging from approx 0.5 pc in M15 (Gerssen et al."
 2002. core radius from the catalog presented im Iuris et al. 2010?))," 2002, core radius from the catalog presented in Harris et al. ),"
. up to few pe in omega Centauri (Novola ct al., up to few pc in omega Centauri (Noyola et al.
 2008)., 2008).
" For carly type galaxies. we adopt the fits by Shenetal. for stellar-iass vs effective radius in Sloan Digital Sky Survey galaxies: The scatter is roughly 0.2 dex for stellar masses between 105M and LOYALL one=OBLOBYL|CU1029ME, JJ."," For early type galaxies, we adopt the fits by \cite{Shen2003} for stellar-mass vs effective radius in Sloan Digital Sky Survey galaxies: The scatter is roughly 0.2 dex for stellar masses between $10^8\msun$ and $10^{10}\msun$: $\sigma_{\ln
 R}=0.34+0.13/[1+(M_{\rm stellar}/4\times10^{10}\msun)]$ ."
 We note that for 5 galaxies (NGC 1697. NGC 3277. NGC 1561. NGC 5815. NGC 821) where measurements of the effective radius are available (aloug with stellar masses. black hole masses. and gas deusitv- see Soriaetal.(200623) and Marconi&IIuut. (2003))) the fits derived bv Shenetal.(2003) provide values of 1ο effective radius roughly times lareer than the neasured value.," We note that for 5 galaxies (NGC 4697, NGC 3377, NGC 4564, NGC 5845, NGC 821) where measurements of the effective radius are available (along with stellar masses, black hole masses, and gas density- see \cite{Soria2006a} and \cite{MarconiHunt2003}) ) the fits derived by \cite{Shen2003} provide values of the effective radius roughly times larger than the measured value."
 This is likely due to Shenetal.(2003) definition of effective radius as the radius cuclosing 5 x cent of the Petrosian flix., This is likely due to \cite{Shen2003} definition of effective radius as the radius enclosing 50 per cent of the Petrosian flux.
 This definition differs from he standard definition of projected radius euclosiug half of the total huuinosity., This definition differs from the standard definition of projected radius enclosing half of the total luminosity.
 We therefore scale the fit for carly vpe galaxies by a factor of 0.55 for consistency., We therefore scale the fit for early type galaxies by a factor of 0.55 for consistency.
 As shown )clow (Fig. 3)), As shown below (Fig. \ref{size}) )
 this small correction does not influeucc he accretion rate we derive., this small correction does not influence the accretion rate we derive.
 For dwarf spheroidals. we fit the data presented iu Walkeretal.(2009.2010).," For dwarf spheroidals, we fit the data presented in \cite{Walker2009, Walker2010}."
.. We asstune a constant mniass-o-light ratio of two for the visible component. aud derive stellar masses from the total huninosities:kpc.. (Lywhere the uncertainties iu the slope and in the normalization are 0.06 aud 0.2 dex respectively.," We assume a constant mass-to-light ratio of two for the visible component, and derive stellar masses from the total luminosities:, where the uncertainties in the slope and in the normalization are 0.06 and 0.2 dex respectively."
 Finally for nuclear clusters we ft the stellar lass vs effective radius data preseuted in Seth (2008).. leading to: =7.9 kpe.. where the uncertainties im the slope and iu the normalizationare 0.05 and 0.3 dex respectively.," Finally for nuclear clusters we fit the stellar mass vs effective radius data presented in \cite{Seth2008}, , leading to: =7.9 , where the uncertainties in the slope and in the normalizationare 0.05 and 0.3 dex respectively."
 These scaliues are shown in Figure 1., These scalings are shown in Figure 1.
caution isin limite,< 5.22 where CCL is central confidence limit.
d Unlikethe !Ie4. lowdeuteriumnumber statisticsdoes notappeardue tothe sulfe," Using a standard model prior assuming $\nnu \ge 3.0$ \cite{prior}, the corresponding CL upper limits are: $\nnu < 5.19$ for D/H = 2.78 $\times 10^{-5}$; $\nnu < 4.20$ for D/H = 2.49 $\times 10^{-5}$."
r[rom oflargefinding svstematics. high-r," For comparison, we also quote the corresponding limits based on 4: $\nnu < 3.40$ for $Y_P = 0.238$; $\nnu < 3.64$ for $Y_P
= 0.244$ also assuming the prior of $\nnu > 3.0$."
edshift Itissvstemssimply well-suitedbyforac," Also forcomparison, we note that note that the CMB itself also constrains $\nnu$ \cite{hann,kssg,crot}."
curate determinations. ," From the WMAP data alone, $\nnu < 6$ CL) \cite{crot}. ."
Given clifficulty thatDpredictions from WALAP agree «quitewell with observations.," Note that it is conceivable that an evolving nonstandard component could lead to different $\nnu$ at the BBN and CMB epochs; as the data improve, this could be tested."
" D/I wecan now useDto place an interesting limitonNg. Dis nolas sensilive toIN,ugas ed is.butnonetheless itdoes have asignif", The new power of D to probe early universe physics will grow with the increasing precision in $\eta_{\rm CMB}$ and particularly with increasing accuracy in observed D/H. A measurement in D will allow it to become the dominant constraint on $\nnu$ \cite{cfo2}.
icant dependence., Primordial nucleosynthesis has entered a new era.
 The relative errorinthe obser," With the precision observations of WMAP, the CMB has become the premier cosmic baryometer."
ved.abundance of D/II ranges from 7-104... depending on what svstems arechosen for averaging.," The independent BBN and CMB predictions for $\eta$ are in good agreement (particularly when D is used in BBN), indicating that cosmology has passed a fundamental test."
 If thefive most reliable svstemsare chosen.," Moreover, this agreement allows us to use BBN in a new way, as the CMB removes $\eta$ as a free parameter."
" the peak ofthe.N ur likelihood distributionliesat οι223.0. with awidth ofNN, ugzz 1.0 as seen in Fig.3.. However. ifwe limit our sample"," One can then adopt the standard BBN predictions, and use $\eta_{\rm CMB}$ to infer primordial abundances; by comparing these to light element abundances in different settings, one gains new insight into the astrophysics of stars, regions, cosmic rays, and chemical evolution, to name a few examples."
" tothe two Dsystems multiple absorption leatures observed. then (thepeak shifts to IN,ar &2.2. wilha widthof "," Alternately, WMAP transforms BBN into a sharper probe of new physics in the early universe; with $\eta_{\rm CMB}$ fixed, of the light elements constrain non-standard nucleosynthesis, with $\nnu$ being one example."
"ANON,uar & 0."," As BBN assumes a new role, much work remains to be done."
7.Giventhe low numberof observations., To leverage the power of the WMAP precision requires the highest possible precision in light element observations.
 it isdiffieult toqualify theseresults.The differences c, Further improvements in the primordial D abundance can open the door to D as a powerful probe of early universe physics.
ould be statisticalin, Improved 3 observations can offer new insight into stellar and chemical evolution.
 nature.orcould be hinting at NV(6) !(7) | (S) f= 302. (9) 2.101(10) ! (1h)(12)," And perhaps most pressing, the WMAP prediction for primordial 4 and particularly 7 are higher than the current observed abundances; it remains to be resolved what systematic effects (or new physics!)"
 ! ! Nu) ! (14) ! (15) i414, has led to this discrepancy.
 (16) (11) (13) mbox (68% CCL), WMAP also demands improvements in BBN theory.
" 1.261 (19) ?Note thatwehave neglectedthe CMDB'sown scusitivitytoIN,our: since t"," While the basic calculation is sound, accuracy of the WMAP light element predictions \\ref{fig:abs-MAP}) ) is or soon will be limited by the errors in BBN theory."
lhe CMBvaluesforàaud cH are essentially inde," These in turn arise from uncertainty in nuclear reaction cross sections \cite{nuc,cfo1}. ."
pendent [0.6.0].this does not biasour results. butmeans that oursis a morecouscrvative ," In particular,the 7 prediction is completely dominated by the nuclear errors, especially that in the $\he3(\alpha,\gamma)\be7$ "
In van den Bereh (2009) it was speculated that the observation Chat S0 ealaxies are. on average. 1.0 mag and 0.3 mag Inter. respectively. than E and Sa galaxies. indicates (hat {vpical lenticular galaxies have lost about half of their initial luminous mass.,"In van den Bergh (2009) it was speculated that the observation that S0 galaxies are, on average, 1.0 mag and 0.8 mag fainter, respectively, than E and Sa galaxies, indicates that typical lenticular galaxies have lost about half of their initial luminous mass."
 Alternatively one might. of course. argue that faint low-mass spirals are more likely to have been stripped of gas bv ram pressure than are Iuminous hieh-mass spirals.," Alternatively one might, of course, argue that faint low-mass spirals are more likely to have been stripped of gas by ram pressure than are luminous high-mass spirals."
 Ii other words both location in the cluster environment. or low parent galaxy. mass. might have [avored the transformation of spirals into lenticulers.," In other words both location in the cluster environment, or low parent galaxy mass, might have favored the transformation of spirals into lenticulars."
 However. if ram-pressure stripping (Gunn Gott 1972) had transformecl cluster Sa galaxies into lenticulars one would have expected (he Iraction of all early-(wpe galaxies that are assigned (o the SO class would be higher in clusters than ib is in (hie field.," However, if ram-pressure stripping (Gunn Gott 1972) had transformed cluster Sa galaxies into lenticulars one would have expected the fraction of all early-type galaxies that are assigned to the S0 class would be higher in clusters than it is in the field."
 Unexpectedly. (he data in Table 1 show that the fraction of all E + 50 + Sa galaxies that are lenticulars is 40/121 (3354)) for clusters. 17/45 (38%)) in groups. and 24/70 jin the field.," Unexpectedly, the data in Table 1 show that the fraction of all E + S0 + Sa galaxies that are lenticulars is 40/121 ) for clusters, 17/45 ) in groups, and 24/70 )in the field."
 In other words the fraction of all earlv-tvpe galaxies that are of tvpe SO appears to be more-or-less independent of environment., In other words the fraction of all early-type galaxies that are of type S0 appears to be more-or-less independent of environment.
 Llowever. (he reader is cautioned (hat this conclusion is based on a rather small data sample and should be re-investigated when larger databases becomes available.," However, the reader is cautioned that this conclusion is based on a rather small data sample and should be re-investigated when larger databases becomes available."
 In. particular. if would be very important to check if the fraction of all early-twpe CE+S0+Sa) galaxies that is of type 90 is larger in verv rich. clusters than it is in other environments.," In particular, it would be very important to check if the fraction of all early-type (E+S0+Sa) galaxies that is of type S0 is larger in very rich clusters than it is in other environments."
 In summary. it is found that (on average) SO galaxies are (in all environments) only half as luminous as objects of tvpes E and Sa.," In summary, it is found that (on average) S0 galaxies are (in all environments) only half as luminous as objects of types E and Sa."
 In (his sense S0 ealaxies are therefore not. as Hubble (1936) suggested. intermediate between tvpes E and Sa.," In this sense S0 galaxies are therefore not, as Hubble (1936) suggested, intermediate between types E and Sa."
 This conclusion is independently confirmed by the work of Nair (2009. p.74) who shows that. in a sample of 13534 Sloan Digital Skv Survey images. (he Petrosian (1976) radii of SO galaxies are significantly smaller than are those of both E and Sa galaxies.," This conclusion is independently confirmed by the work of Nair (2009, p.74) who shows that, in a sample of 13534 Sloan Digital Sky Survey images, the Petrosian (1976) radii of S0 galaxies are significantly smaller than are those of both E and Sa galaxies."
and the strength of the bright spot ingress feature means that we cannot constrain full fit using the MCMC model used previously.,and the strength of the bright spot ingress feature means that we cannot constrain a full fit using the MCMC model used previously.
" The modela confirms the bright spot flux has decreased considerably, although an orbital hump is still visible."," The model confirms the bright spot flux has decreased considerably, although an orbital hump is still visible."
" The white dwarf flux remains almost unchanged, although the disc appears brighter."," The white dwarf flux remains almost unchanged, although the disc appears brighter."
" The fit to the data is good, indicating that the models derived from the 2007 data (and used to derive our system parameters) are reliable."," The fit to the data is good, indicating that the models derived from the 2007 data (and used to derive our system parameters) are reliable."
 In section 3.2.2 we noted that the shape of the light curve in Fig., In section \ref{sec:2354} we noted that the shape of the light curve in Fig.
 1 indicated possible bright spot egress features around phases 1.060 and 1.080., \ref{figure:lightcurves} indicated possible bright spot egress features around phases 1.060 and 1.080.
 Fig., Fig.
 2 shows that our model has fit the bright spot egress feature at phase 1.080., \ref{fig:eclipses} shows that our model has fit the bright spot egress feature at phase 1.080.
 Given the strength and shape of the bright spot features and general scatter present in the light curve we cannot be certain if the bright spot positions have been correctly identified by our, Given the strength and shape of the bright spot features and general scatter present in the light curve we cannot be certain if the bright spot positions have been correctly identified by our
non-I&epleriau motion due to gravitational iuteractious between the planets aud lost star.,non-Keplerian motion due to gravitational interactions between the planets and host star.
 To search for the best-fitting. two-planet orbital solution for cach time series we use the partially-lueanized technique prescuted by 7.. as implemented iu the software suiteRVLIN.," To search for the best-fitting, two-planet orbital solution for each time series we use the partially-linearized technique presented by \citet{wrighthoward}, as implemented in the software suite."
 We estimate the paralucter uncertainties using a Alarkov-Chain Monte Carlo (AICAIC) aleorithia. as described by 2..," We estimate the parameter uncertainties using a Markov-Chain Monte Carlo (MCMC) algorithm, as described by \citet{bowler10}."
 We obtained imitial-epoch observations of aat Lick Observatory in 2005 February. and since the- we have obtained RRV ineasurcmeuts.," We obtained initial-epoch observations of at Lick Observatory in 2005 February, and since then we have obtained RV measurements."
 After noticing time-correlated RV variations. we beean additional monitoring at Necks Observatory in 2008 December. where we have obtained aadditional RV iieasurenieuts.," After noticing time-correlated RV variations, we began additional monitoring at Keck Observatory in 2008 December, where we have obtained additional RV measurements."
 The RVs from both observatories are listed in Table L. along with the Julian Dates (JD) of observation aud the ternal measurement nucertainties (without jitter).," The RVs from both observatories are listed in Table \ref{tab:rvA}, along with the Julian Dates (JD) of observation and the internal measurement uncertainties (without jitter)."
 Fie., Fig.
 dl. shows the RV time series from both observatorics. where the error bars represent the quadrature stun of the internal errors aud Sis oot," \ref{fig:orbitA} shows the RV time series from both observatories, where the error bars represent the quadrature sum of the internal errors and 5 of jitter."
 jitter. ? reported evidence of a two-pluiet system aroundSex.. but the data at the time could not provide a unique orbital solution.," \citet{bowler10} reported evidence of a two-planet system around, but the data at the time could not provide a unique orbital solution."
 Au additional season of observations has provided stronger constraints on the possible orbits of the two planets., An additional season of observations has provided stronger constraints on the possible orbits of the two planets.
 We fitted a model consisting of two non-interacting planets anda sstar orbiting their mutual ceuter of mass., We fitted a model consisting of two non-interacting planets and a star orbiting their mutual center of mass.
 We fud that two Ixepleriaus provide au acceptable fit to the data with annis scatter of G.S aand a reduced = LLL , We find that two Keplerians provide an acceptable fit to the data with an rms scatter of 6.8 and a reduced $ = \chisA$ .
"The inner planct has a period of /AZP=155.2E2 dave. velocity senüaniplitude A=33:221..6Ἐν, aud eccentricity ο=O1sl+0.029."," The inner planet has a period of $P = \pAb \pm \peAb$ days, velocity semiamplitude $K =
\kAb \pm \keAb$, and eccentricity $e = \eAb \pm \eeAb$."
 The outer planct has 21 days. AK=235429Ll. and e=(0.112c 0.061.," The outer planet has $P = \pAc \pm \peAc$ days, $K = \kAc \pm \keAc$, and $e = \eAc \pm \eeAc$ ."
" Tosether with our stellar mass estimate these spectroscopic orbital paramicters vield senmiinuajor axes = AAU and minimum planet masses Ls(Alf,a)MEsine[1.112.221=[16.1.1]Mis."," Together with our stellar mass estimate these spectroscopic orbital parameters yield semimajor axes $\{a_b,a_c\} =
\{\arelAb,\arelAc\}$ AU and minimum planet masses $\{M_b,M_c\}\sin{i} = \{\msiniAb,\msiniAc\}$."
 A amore detailed. dynamical analysis prescuted in 6 revises this two-Keplerian solution under the coustraint of loug-term stability.," A more detailed, dynamical analysis presented in \ref{sec:dynamical} revises this two-Keplerian solution under the constraint of long-term stability."
 We beean mouitoring aat Lick Observatory in 2007 July 1and have obtained RRV aeasuremenuts., We began monitoring at Lick Observatory in 2007 July and have obtained RV measurements.
 Tuuc-correlated variations in the starsRVs prompted additional monitoring at Ίνους Observatory where we have obtained nunueasureinents since 2007 October., Time-correlated variations in the star'sRVs prompted additional monitoring at Keck Observatory where we have obtained measurements since 2007 October.
 The RVs from both, The RVs from both
As eXpected. the reduction in the data-set increases the statistical error (Fig. 9..,"As expected, the reduction in the data-set increases the statistical error (Fig. \ref{fig:stat_cuts},"
 compare to Fig. 3): , compare to Fig. \ref{fig:stat_dip}) );
on the other hand the systematic error is highly reduced as can be seen comparing Fig., on the other hand the systematic error is highly reduced as can be seen comparing Fig.
 IO. to Fig. 8.., \ref{fig:syst_cuts} to Fig. \ref{fig:syst_gal}.
 Anyway this technique is limited by the presence of residual emission at high galactic latitudes: in Fig., Anyway this technique is limited by the presence of residual emission at high galactic latitudes; in Fig.
 10 we can see the effect of the emission of Magellanic Clouds that are at 307 of galactic latitude., \ref{fig:syst_cuts} we can see the effect of the emission of Magellanic Clouds that are at $-30^{\circ}$ of galactic latitude.
 At 30 GHz their signals uncertainty produces an error of ~ on G., At 30 GHz their signals uncertainty produces an error of $\sim$ on $G$.
" The ""weight function"" technique. allows us to improve the calibration accuracy."," The “weight function"" technique allows us to improve the calibration accuracy."
 Results on the optimization of a are shown in Fig. 11.., Results on the optimization of $\alpha$ are shown in Fig. \ref{fig:alpha_det}.
 The optimum choice of a depends on both frequency. and integration time., The optimum choice of $\alpha$ depends on both frequency and integration time.
 The frequency dependency is obvious. since foreground emission and noise levels are different at the various frequencies.," The frequency dependency is obvious, since foreground emission and noise levels are different at the various frequencies."
 The integration. time dependence comes from the fact that the systematic. error is independent of time. while white noise scales as 1/Vr.," The integration time dependence comes from the fact that the systematic error is independent of time, while white noise scales as $1/\sqrt{\tau}$."
 The « step in simulations is 0.125 at both frequencies., The $\alpha$ step in simulations is 0.125 at both frequencies.
 On the I-hour time scale. we find that the best result is with w=1.5 at 30 GHz and «=0.625 at 100 GHz: on a 24-hour time scale the best result is with «=2.875 at 30 GHz and α=0.75 at 100 GHz.," On the 1-hour time scale, we find that the best result is with $\alpha=1.5$ at 30 GHz and $\alpha=0.625$ at 100 GHz; on a 24-hour time scale the best result is with $\alpha=2.875$ at 30 GHz and $\alpha=0.75$ at 100 GHz."
scale leneth set equal to0.22240.,scale length set equal to$0.2R_{\rm NC}$.
 We will explore in detail how (he present results depend on models with different initial radial profiles (e.e.. Nine or Sérrsic models) in future work.," We will explore in detail how the present results depend on models with different initial radial profiles (e.g., King or Sérrsic models) in future work."
 To construct a model in dynamical equilibrium for a NC with a MBIT located at its center. we adopt the following two steps.," To construct a model in dynamical equilibrium for a NC with a MBH located at its center, we adopt the following two steps."
 First. the initial mass of the MDILI in our isolated NC model is set to the mass of each individual star τι) in the NC.," First, the initial mass of the MBH in our isolated NC model is set to the mass of each individual star $m_{\rm star}$ ) in the NC."
" Second. we run the isolated model such that the initial MDII mass (144,) is increased. steadily and slowly to finally reach any adopted. Afpy value within 20 fay (ee. aciabatic growth of the MDII)."," Second, we run the isolated model such that the initial MBH mass $m_{\rm star}$ ) is increased steadily and slowly to finally reach any adopted $M_{\rm BH}$ value within $20$ $t_{\rm dyn}$ (i.e., adiabatic growth of the MBH)."
 During {his isolated evolution of the NC. the stellar clistribution of the NC can adiabatically evolve into a new dynamical equilibrium.," During this isolated evolution of the NC, the stellar distribution of the NC can adiabatically evolve into a new dynamical equilibrium."
 We then use (his new radial distribution of the stars for our progenitor NCs which are subsequently merged., We then use this new radial distribution of the stars for our progenitor NCs which are subsequently merged.
 We have confirmed that with time steps as small as 4.5x104 vr for models with 0.025. the NC's with MIBIIs are stable after 20/444.," We have confirmed that with time steps as small as $4.5 \times 10^4$ yr for models with $F_{\rm BH}\le 0.025$ , the NCs with MBHs are stable after $20$ $t_{\rm dyn}$."
 The changes to the central stellar densities due to adiabatie MBII growth in models with MDlIIs are only. a [actor of ~2 in comparison with those with no MDII., The changes to the central stellar densities due to adiabatic MBH growth in models with MBHs are only a factor of $\sim 2$ in comparison with those with no MBH.
 This effect is much smaller than the [actor of ten change in central stellar density cue to MIBIT heating. as shown later.," This effect is much smaller than the factor of ten change in central stellar density due to MBH heating, as shown later."
 We are therefore able to probe the effects ol MIBUs in NC merger remnants on the inner stellar densities of the remnants., We are therefore able to probe the effects of MBHs in NC merger remnants on the inner stellar densities of the remnants.
" The two NCs in a NC merger are referred (o as NCT and NC? and (he relative positions and velocities of NC2 with respect to NCI are set to be (Αν. M. Z,) and (U,. Vi. JV). respectively,"," The two NCs in a NC merger are referred to as NC1 and NC2 and the relative positions and velocities of NC2 with respect to NC1 are set to be $X_{\rm r}$, $Y_{\rm r}$, $Z_{\rm r}$ ) and $U_{\rm r}$, $V_{\rm r}$, $W_{\rm r}$ ), respectively."
" Although the relative positions and velocities of NC2 are [ree parameters. and we investigated models with different values for these 6 parameters. we only show the results ol the models with (Αν. ὃν. Z,)2(4. 0.5. 0) and (U,. Ἐν, W,)e(-1. 0. 0)."," Although the relative positions and velocities of NC2 are free parameters, and we investigated models with different values for these 6 parameters, we only show the results of the models with $X_{\rm r}$, $Y_{\rm r}$, $Z_{\rm r}$ )=(4, 0.5, 0) and $U_{\rm r}$, $V_{\rm r}$, $W_{\rm r}$ )=(-1, 0, 0)."
" The total number of stellar particles used in a model for NC merging is 4x10°. allowing us to conduct a large parameter study (e.g... μι and Ἐν. and C,) lor NCC evolution with MDIIs."," The total number of stellar particles used in a model for NC merging is $4 \times 10^5$, allowing us to conduct a large parameter study (e.g., $F_{\rm BH}$ and $Y_{\rm r}$, and $U_{\rm r}$ ) for NC evolution with MBHs."
" We follow the dvnamical evolution of (wo merging NC's for 20 fag, within which the two NCs merge with each other completely to form a new NC.", We follow the dynamical evolution of two merging NCs for $20$ $ t_{\rm dyn}$ within which the two NCs merge with each other completely to form a new NC.
 The (wo AIBIIs in the newly formed. NC can dift. around the central region of the AC alter the DIIs form a very close pair owing to their orbital decay caused by dynamical friction against the NC stars., The two MBHs in the newly formed NC can drift around the central region of the NC after the BHs form a very close pair owing to their orbital decay caused by dynamical friction against the NC stars.
 We note that a Newtonian gravilational force is always assumed (outside of ες) during simulations with GRAPE (we do not investigate MDII merging through eravitational wave radiation)., We note that a Newtonian gravitational force is always assumed (outside of ${\epsilon}_{\rm g}$ ) during simulations with GRAPE (we do not investigate MBH merging through gravitational wave radiation).
 We assume that the MBII pair can merge to form a single MDII akin to the merging of stellaa-1nass DIIs in dense star clusters (e.g.. Quinlan Shapiro 1989) and adopt the following (wo steps to obtain the final stellar distribution in the NC merger.," We assume that the MBH pair can merge to form a single MBH akin to the merging of stellar-mass BHs in dense star clusters (e.g., Quinlan Shapiro 1989) and adopt the following two steps to obtain the final stellar distribution in the NC merger."
 First. (he MBlIs in the merger remnant are replaced with a single MBII with position and velocity equal to the mass center of the (wo MDlIIs.," First, the MBHs in the merger remnant are replaced with a single MBH with position and velocity equal to the mass center of the two MBHs."
 This is done after 20 faci. when the single NC is already formed and cvnamically relaxed.," This is done after $20$ $t_{\rm dyn}$ , when the single NC is already formed and dynamically relaxed."
" Second. we follow the evolution of the NC merger remnant with the new ABIL for a further 20 fa, of the original NC's. so"," Second, we follow the evolution of the NC merger remnant with the new MBH for a further $20$ $ t_{\rm dyn}$ of the original NCs, so"
Power-law disk models such as the Minimum-Mass Solar Nebula (hereafter MMSN: (1981))) allow the advectiou-diffusion equation to be solved analytically. at least in steady. state.,"Power-law disk models such as the Minimum-Mass Solar Nebula (hereafter MMSN; ) allow the advection-diffusion equation to be solved analytically, at least in steady state."
 Some aspects of time-depeudent evolution can also be determined analytically for this class of disk moclels., Some aspects of time-dependent evolution can also be determined analytically for this class of disk models.
 Throughout this section. all clisk models are cousicered to be infinite in radius as well as steady.," Throughout this section, all disk models are considered to be infinite in radius as well as steady."
 While uurealistic. this is techuically convenieut. aud we are still able to identify results tliat are likely to be seusitive to the details of the outer boundary couditious: for example. the mean orbital lifetime.," While unrealistic, this is technically convenient, and we are still able to identify results that are likely to be sensitive to the details of the outer boundary conditions: for example, the mean orbital lifetime."
" For reference. the MMSN model adopted here Las mean surface deusity Xxr.| and aspect ratio firxrhe, "," For reference, the MMSN model adopted here has mean surface density $\bar{\Sigma}\propto r^{-3/2}$ and aspect ratio $h/r\propto r^{1/4}$."
A steady-state distribution of planets. f(J). satislies where the right-hand side is a source term representing the rate of formation of planets at radiusn ry withn angular momentum J=Mj{SyaA— /GM.ry.— ," A steady-state distribution of planets, $f(J)$, satisfies where the right-hand side is a source term representing the rate of formation of planets at radius $r_p$ with angular momentum $J=M_p\sqrt{GM_*r_p}$ ."
Analyticn solutionsn to Eq.E (11))fae , Analytic solutions to Eq. \ref{eq:steadystate}) )
existn when mean torque and the diffusion coefficient are both power-laws in J: aud the source teriu is a Dirac delta fuuction where A is the rate of planet formation at Jy., exist when mean torque and the diffusion coefficient are both power-laws in $J$: and the source term is a Dirac delta function where $\Lambda$ is the rate of planet formation at $J_S$.
" We see iuunediately that the flux of planets interior C£,) and exterior (EF,) to the source are both constant aud related to each other by First we consider the limiting behavior as J—x.", We see immediately that the flux of planets interior $(F_J^-)$ and exterior $(F_J^+)$ to the source are both constant and related to each other by First we consider the limiting behavior as $J\rightarrow\infty$.
 The local timescale for secular inward migration is given by finie=J/|U()]. and the local diffusion timescale is given by {μμ=J2DCS).," The local timescale for secular inward migration is given by $t_{\rm{mig}}= J/|\bar{\Gamma}(J)|$, and the local diffusion timescale is given by $t_{\rm{diff}}=J^2/D(J)$."
" The ratio. /qip//igXxJ""!V indicates that the mean torque becomes asyinptotically. negligible ifa—3-1<0. ("," The ratio, $t_{\rm diff}/t_{\rm
 mig}\propto J^{\alpha-\beta+1}$ indicates that the mean torque becomes asymptotically negligible if $\alpha-\beta+1<0$. ("
This condition holds for the minimume-nmass solar nebula. in which DP.x—J/? aud Dx J.),"This condition holds for the minimum-mass solar nebula, in which $\bar{\Gamma}\propto -J^{-2}$ and $D\propto J$ .)"
 For such disks the solution to Eq. (11)), For such disks the solution to Eq. \ref{eq:steadystate}) )
 at large J exterior to the sourcebecomes, at large $J$ exterior to the sourcebecomes
and. rearranging. More specifically. for NGC 4258 we find This warp radius is closer to the black hole than the inner masers and we consider this in. more detail in Section 3.4..,"and, rearranging, More specifically, for NGC 4258 we find This warp radius is closer to the black hole than the inner masers and we consider this in more detail in Section \ref{sec:grav}."
 The motion of the infalling gas in NGC 4258 cannot be measured directly so we have to estimate the mass accretion rate. AL. indirectly.," The motion of the infalling gas in NGC 4258 cannot be measured directly so we have to estimate the mass accretion rate, $\dot M$, indirectly."
 We use the bolometric luminosity of the system and assume that where € is the accretion clliciency of a Werr black hole. €zzOL.," We use the bolometric luminosity of the system and assume that where $\epsilon$ is the accretion efficiency of a Kerr black hole, $\epsilon \approx 0.1$."
 The bolometric luminosity of NGC 4258 is about 4.10712eres. loc," The bolometric luminosity of NGC 4258 is about $4\times 10^{42}\,\rm erg \, s^{-1}$."
eThis corresponds to à mass accretion. rate of if the disc is in a steady state., This corresponds to a mass accretion rate of if the disc is in a steady state.
 We explore the consequences of the assumption that the disc is in steady state., We explore the consequences of the assumption that the disc is in steady state.
 When we vary i2 we want properties of the disc at R=uus to be be fixed and so we choose Ry= Roop., When we vary $\beta$ we want properties of the disc at $R=R_{\rm warp}$ to be be fixed and so we choose $R_0=R_{\rm warp}$ .
" We lind the surface density using equation (21)) to be Capronictal.(2007). used the same model for the disc with à,=const but varied 7/2 with a power law in 2."," We find the surface density using equation \ref{sigma}) ) to be where \cite{C07} used the same model for the disc with $\alpha_1=\,\rm
const$ but varied $H/R$ with a power law in $R$."
 Using the surface density of the disc we can find the total mass of the observable disc to be i| zx2. or. if 3=2 then Lor NGC 4258. with 3=2. we find ‘This is much smaller than the mass of the black hole but in the next section we consider if this is. or could be. large enough for our clise to be self-gravitating.," Using the surface density of the disc we can find the total mass of the observable disc to be if $\beta \ne 2$, or, if $\beta=2$ then For NGC 4258, with $\beta=2$, we find This is much smaller than the mass of the black hole but in the next section we consider if this is, or could be, large enough for our disc to be self-gravitating."
 Having calculated the mass of the observed. maser cise we check if the disc is stable against the elfects of self gravity., Having calculated the mass of the observed maser disc we check if the disc is stable against the effects of self gravity.
 IC it were unstable against self gravity then it would collapse into bound fragments locally., If it were unstable against self gravity then it would collapse into bound fragments locally.
 Lf the mass of the disc satisfies the inequality then the cise is stable (Loomre1964:Binney&‘Tremaine 1987).," If the mass of the disc satisfies the inequality then the disc is stable \citep{T64,BT87}."
. For HI=0.001 this corresponds. to a critical disc mass of 3.78«10:M..," For $H/R=0.001$ this corresponds to a critical disc mass of $3.78\times 10^4\,\rm M_\odot$."
 For 4=2. using equation (43)). we see that we need 7/170.0006 For a disc which is stable against self gravity.," For $\beta=2$, using equation \ref{discmass}) ), we see that we need $H/R>0.0006$ for a disc which is stable against self gravity."
 Now we have constrained HB to the approximate limits of if our model is correct., Now we have constrained $H/R$ to the approximate limits of if our model is correct.
 Using equation. (36)) we find that for 9=2 our warp radius is limited to ‘This is a relatively small range., Using equation \ref{rwarp2}) ) we find that for $\beta=2$ our warp radius is limited to This is a relatively small range.
 We note that this range [or fs is completely. inside the inner. observed: maser points.," We note that this range for $R_{\rm
 warp}$ is completely inside the inner observed maser points."
 Capronictal.(2007). found that the warp racius was approximately equal to or smaller than the inner maser but we find that it is at most around hall way between the black hole and the inner mascr., \cite{C07} found that the warp radius was approximately equal to or smaller than the inner maser but we find that it is at most around half way between the black hole and the inner maser.
 We note that this mass just takes into account the mass of the disc of the observed: masers., We note that this mass just takes into account the mass of the disc of the observed masers.
 For our steady. state solution. the surface density increases as we move towards the black hole and so. if we calculate the mass of the disc including inner regions. then our disc soon becomes eravitating.," For our steady state solution, the surface density increases as we move towards the black hole and so, if we calculate the mass of the disc including inner regions, then our disc soon becomes self-gravitating."
 Lf the inner parts of the disc were not in steady state or i£ f/f were much larger there then we could over come this problem., If the inner parts of the disc were not in steady state or if $H/R$ were much larger there then we could over come this problem.
 In our model. dillerent radii of the disc communicate through the two viscosities.," In our model, different radii of the disc communicate through the two viscosities."
 Discs of non-nesligible mass could also communicate through gravitational torques., Discs of non-negligible mass could also communicate through gravitational torques.
 We consider here how these torques would allect equation (23)). Nava, We consider here how these torques would affect equation \ref{main}) ).
kshin(2005) considered. the. eravitational torque between two rings at racii Z2 and {1 of masses AZ ancl Mj respectively which are inclined at an angle 5 to each other., \cite{N05} considered the gravitational torque between two rings at radii $R$ and $R_1$ of masses $M$ and $M_1$ respectively which are inclined at an angle $\gamma$ to each other.
 The torque exerted by the second ring on the first is wherer and ry are the position vectors around the rings, The torque exerted by the second ring on the first is where$\bm{r}$ and $\bm{r_1}$ are the position vectors around the rings
fraction of the diffuse light.,fraction of the diffuse light.
 Some of these predictions have been confirmed in the Virgo cluster where an important amount of diffuse light have been observed in regions near to the brightest cluster galaxy M87 and the subgroup formed by M84 and M86 (Aguerri et al., Some of these predictions have been confirmed in the Virgo cluster where an important amount of diffuse light have been observed in regions near to the brightest cluster galaxy M87 and the subgroup formed by M84 and M86 (Aguerri et al.
 2005: Mihos et al., 2005; Mihos et al.
 2005)., 2005).
 Little is known about the diffuse light in groups of galaxies., Little is known about the diffuse light in groups of galaxies.
 Pildis et al. (, Pildis et al. (
1995b) studied the diffuse light in. 12. galaxy groups. finding that only one. HCG 94. has diffuse light in the group potential (with a lumimosity of 7£7).,"1995b) studied the diffuse light in 12 galaxy groups, finding that only one, HCG 94, has diffuse light in the group potential (with a luminosity of $L^{*}$ )."
 In. contrast. the other groups do not contain more than 1/377 in diffuse light.," In contrast, the other groups do not contain more than $1/3 L^{*}$ in diffuse light."
 Feldmeier et al. (, Feldmeier et al. (
2003b) and Castro-Rodriguez et al. (,2003b) and Castro-Rodriguez et al. (
2003) measured the intragroup light (IGL) by searching for intragroup planetary nebulae (IGPNe) in the M81 and Leo groups. respectively.,"2003) measured the intragroup light (IGL) by searching for intragroup planetary nebulae (IGPNe) in the M81 and Leo groups, respectively."
 They found that at most a few percent of the light of these groups is located in the intragroup region., They found that at most a few percent of the light of these groups is located in the intragroup region.
 In contrast. White et al. (," In contrast, White et al. ("
2003) found that the fraction of diffuse light in HCG 90 was 38-48%.,2003) found that the fraction of diffuse light in HCG 90 was $\%$.
 Da Rocha de Oliveia (2005) also measured the fraction of intragroup light in three Hickson groups., Da Rocha de Oliveia (2005) also measured the fraction of intragroup light in three Hickson groups.
 They found the the IGL contributes 0-45% to the total galaxy light., They found the the IGL contributes $\%$ to the total galaxy light.
 The broad range in the observed diffuse light fraction was interpreted 1n the sense that these groups being in different states of evolution., The broad range in the observed diffuse light fraction was interpreted in the sense that these groups being in different states of evolution.
 The aim of this paper is to study the amount of diffuse light in HCG 44 through the detection of IGPNe. to give a deseription of the evolutionary state of the group. and to investigate the implications of the combined data for the groups analysed so far.," The aim of this paper is to study the amount of diffuse light in HCG 44 through the detection of IGPNe, to give a description of the evolutionary state of the group, and to investigate the implications of the combined data for the groups analysed so far."
 The paper is organized as follows: in Section 2 we present a description of the group HCG 44., The paper is organized as follows: in Section 2 we present a description of the group HCG 44.
 The observations and data reduction are described in Section 3., The observations and data reduction are described in Section 3.
 The detection of IGPNe in HCG 44 is deseribed in Section 4. and the fraction of IGL is discussed in Section 5.," The detection of IGPNe in HCG 44 is described in Section 4, and the fraction of IGL is discussed in Section 5."
 In Section 6 we analyze the dependence of the diffuse light fraction on the galaxy content of compact groups. and the conclusions are given in Section 7.," In Section 6 we analyze the dependence of the diffuse light fraction on the galaxy content of compact groups, and the conclusions are given in Section 7."
 HCG 44 ts an association of four galaxies: NGC 3190. NGC 3193. NGC 3185 and NGC 3187. located within a circle of 16.4 aremin diameter and centered at a(/2000) 210:18:05. 6(J2000)2421:48:44!.," HCG 44 is an association of four galaxies: NGC 3190, NGC 3193, NGC 3185 and NGC 3187, located within a circle of 16.4 arcmin diameter and centered at $\alpha(J2000)=$ 10:18:05, $\delta(J2000)=$."
. The mean velocity of the galaxies in the group is 1379 km s!. and the galaxy velocity dispersion is 219 km s! (Hickson et al.," The mean velocity of the galaxies in the group is 1379 km $^{-1}$, and the galaxy velocity dispersion is 219 km $^{-1}$ (Hickson et al."
 1992)., 1992).
 This implies a group distance of 18.4 Mpe. assuming Hy=75 km s! Mpe.," This implies a group distance of 18.4 Mpc, assuming $H_{0}=75$ km $^{-1}$ $^{-1}$."
 The distance to the galaxies of this group was also obtained from the Tully-Fisher (TF) relation and the surface brightness fluctuations method (SBF)., The distance to the galaxies of this group was also obtained from the Tully-Fisher (TF) relation and the surface brightness fluctuations method (SBF).
 Williams et al. (, Williams et al. (
1991) measure the TF distances of the three spiral galaxies in the group (NGC 3190. NGC 3185 and NGC 3187).,"1991) measure the TF distances of the three spiral galaxies in the group (NGC 3190, NGC 3185 and NGC 3187)."
 They conclude that these three galaxies are at à common distance of 19 Mpc.corresponding to a distance modulus of 31.4.," They conclude that these three galaxies are at a common distance of 19 Mpc,corresponding to a distance modulus of 31.4."
 This distance is in good agreement with that obtained from their recessional velocities. and will be the adopted distance to the group in the present paper.," This distance is in good agreement with that obtained from their recessional velocities, and will be the adopted distance to the group in the present paper."
 Tonry et al. (, Tonry et al. (
2001) computed the distance modulus of the elliptical galaxy in the association. NGC 3193. using surface brightness fluctuations.,"2001) computed the distance modulus of the elliptical galaxy in the association, NGC 3193, using surface brightness fluctuations."
 They obtained a distance modulus of 32.7]. corresponding a distance of 35 Mpe.," They obtained a distance modulus of 32.71, corresponding a distance of 35 Mpc."
 Thus. this galaxy is located at a much larger distance than the three spirals and has a large peculiar velocity with respect to the Hubble flow.," Thus, this galaxy is located at a much larger distance than the three spirals and has a large peculiar velocity with respect to the Hubble flow."
 These results show that HCG 44 consists of three spiral galaxies., These results show that HCG 44 consists of three spiral galaxies.
 The brightest galaxy. NGC 3190. is an almost edge on early-type spiral. showing a strong dust lane and disturbed outer isophotes.," The brightest galaxy, NGC 3190, is an almost edge on early-type spiral, showing a strong dust lane and disturbed outer isophotes."
 Close to NGC 3190 is located the faintest galaxy of the group. NGC 3187.," Close to NGC 3190 is located the faintest galaxy of the group, NGC 3187."
 This 1s a peculiar barred galaxy with two open arms., This is a peculiar barred galaxy with two open arms.
 However. Rubin et al. (," However, Rubin et al. ("
1991) proposed that NGC 3187 is not really a barred galaxy. and what we are observing are two tidal tails coming out of the plane of a spiral galaxy.,"1991) proposed that NGC 3187 is not really a barred galaxy, and what we are observing are two tidal tails coming out of the plane of a spiral galaxy."
 They also found strange velocity patterns in these two galaxies. concluding that this is à consequence of a recent tidal interaction.," They also found strange velocity patterns in these two galaxies, concluding that this is a consequence of a recent tidal interaction."
 This interaction is also visible in HIE: Williams et al. (, This interaction is also visible in HI: Williams et al. (
1991) found a faint HI bridge. connecting NGC 3190 and NGC 3187.,"1991) found a faint HI bridge, connecting NGC 3190 and NGC 3187."
 This was the only gas detectec outwards the galaxies., This was the only gas detected outwards the galaxies.
 They conclude that HCG 44 is a dynamically young group of galaxies., They conclude that HCG 44 is a dynamically young group of galaxies.
 The third spiral galaxy of the group. NGC 3185. does not show signs of interactions.," The third spiral galaxy of the group, NGC 3185, does not show signs of interactions."
 It has a nuclear emission knot surrounded by a ring of HII regions with no Ha emission within., It has a nuclear emission knot surrounded by a ring of HII regions with no $\alpha$ emission within.
 This galaxy has been reported to be a Seyfert 2 (Huchra Burg 1992)., This galaxy has been reported to be a Seyfert 2 (Huchra Burg 1992).
 Table | shows the main characteristics of the galaxies in HCG 44., Table 1 shows the main characteristics of the galaxies in HCG 44.
 In the present study we will try to give a constraint to the evolutionary state of the group by measuring the amount of [GL in HCG 44., In the present study we will try to give a constraint to the evolutionary state of the group by measuring the amount of IGL in HCG 44.
 We have observed one field centered on HCG 44 at « (J2000)=10:17:58. 6 (J2000)=+21:48:44 in December 2003. using the Wide Field Camera (WFC) at the 2.5m Isaae Newton Telescope (INT) located in La Palma insland.," We have observed one field centered on HCG 44 at $\alpha$ (J2000)=10:17:58, $\delta$ (J2000)=+21:48:44 in December 2003, using the Wide Field Camera (WFC) at the 2.5m Isaac Newton Telescope (INT) located in La Palma insland."
 The WFC is an optical mosaic camera mounted at the prime focus of the telescope., The WFC is an optical mosaic camera mounted at the prime focus of the telescope.
 It consists of 4 thinned EEV 2kx4k CCDs with a pixel size of 0.33/pixel.," It consists of 4 thinned EEV 2kx4k CCDs with a pixel size of 0.33""/pixel."
 This gives a total field of view of 3434/.," This gives a total field of view of $'
\times$ $'$."
 The galaxy group was imaged through a B band broad filter and an [OIL] narrow band filter., The galaxy group was imaged through a B band broad filter and an [OIII] narrow band filter.
 The broad-band filter was centered at 4407 A and had a width of 10224. and the narrow-band filter was centered at 5027 À and had a width of 60 A.," The broad-band filter was centered at 4407 $\AA$ and had a width of $\AA$ , and the narrow-band filter was centered at 5027 $\AA$ and had a width of 60 $\AA$."
 The exposure times were 83000 s and 24x600 s for the [OIII| and B band images. respectively.," The exposure times were $\times$ 3000 s and $\times$ 600 s for the [OIII] and B band images, respectively."
 The images were obtained under photometric conditions and the final seeing was 1.5 aresec in both filter., The images were obtained under photometric conditions and the final seeing was 1.5 arcsec in both filter.
 After stacking all the images the total effective area was 874.13 aremin*., After stacking all the images the total effective area was 874.13 $^{2}$.
 Figure | shows the B band image of the group., Figure 1 shows the B band image of the group.
 The data were reduced using the mosaic IRAF tasks package MSCRED., The data were reduced using the mosaic IRAF tasks package MSCRED.
 The images were corrected by dark. bias and flat-," The images were corrected by dark, bias and flat-field."
 In addition tothe standard flat-fields. we created a," In addition tothe standard flat-fields, we created a"
"where z is the redshift. (see Table 1 for values of cach burst). d; is the luminosity distance of the source. and the concordance cosmology with O4=0.7 and £2,,=0.3 is adopted in the calculation.","where $z$ is the redshift (see Table 1 for values of each burst), $d_L$ is the luminosity distance of the source, and the concordance cosmology with $\Omega_{\Lambda}=0.7$ and $\Omega_m = 0.3$ is adopted in the calculation."
 Aclopting Ly;=££.;. we then progressively increase the total energy in the blastwave £z;=X; by adding £i; in each step.," Adopting $E_{k,i}=\xi E_{\gamma,i}$, we then progressively increase the total energy in the blastwave $E_k = \Sigma E_{k,i}$ by adding $E_{k,i}$ in each step."
 For each time step. we calculate the lighteurve eiving the available fy.," For each time step, we calculate the lightcurve giving the available $E_k$."
 his results in a series of lighteurve solutions., This results in a series of lightcurve solutions.
 The final lighteurve is then derived by jumping to progressively higher level solutions due to additional energy injections in each time step (see also Maxham Zhang 2009)., The final lightcurve is then derived by jumping to progressively higher level solutions due to additional energy injections in each time step (see also Maxham Zhang 2009).
" This would result in a series of elitches"" inthe lighteurves. cach representing injection of energy. from. 7-th shell into the blastwave."," This would result in a series of “glitches” inthe lightcurves, each representing injection of energy from $i$ -th shell into the blastwave."
 Jowdes the energy. we also derive the (lower limit) Lorentz factor 5; of each shell.," Besides the energy, we also derive the (lower limit) Lorentz factor $\gamma_i$ of each shell."
" ""This parameter is important. especially for early. shells. since it determines the deceleration time of a certain shell."," This parameter is important, especially for early shells, since it determines the deceleration time of a certain shell."
 This is particularly relevant for the first shell., This is particularly relevant for the first shell.
 Phe Lorentz factors of later shells are also relevant [fot two reasons., The Lorentz factors of later shells are also relevant fot two reasons.
" First. they can be used to caleulate the elective Lorentz factor of a ""merged"" shell after adding energy to an existing shell."," First, they can be used to calculate the effective Lorentz factor of a “merged” shell after adding energy to an existing shell."
 This is needed to calculate the deceleration time of the blastwave solutions., This is needed to calculate the deceleration time of the blastwave solutions.
" Second. since the observed time for a late energy. injection is defined by (Alaxham Zhang 2009) where /,.; and ρω are the times of ejection and collision measured in the rest frame of the central engine."," Second, since the observed time for a late energy injection is defined by (Maxham Zhang 2009) where $t_{ej}$ and $t_{col}$ are the times of ejection and collision measured in the rest frame of the central engine."
 The effect of ~ becomes progressively less important. since at large / ο... he second term in Eq.(4)) becomes negligible so that the observed collision time is essentially defined by the ejection ime.," The effect of $\gamma$ becomes progressively less important, since at large $t_{ej}$ 's, the second term in \ref{collisiontime}) ) becomes negligible so that the observed collision time is essentially defined by the ejection time."
 In any case. we derive the constraints on 5 for each ime bin using the pair opacity argument as described below.," In any case, we derive the constraints on $\gamma$ for each time bin using the pair opacity argument as described below."
 To derive a constraint. on the Lorentz factor. we rave collected the spectral parameters and the observed niaximum photon energy ZZ|ausi for cach time bin.," To derive a constraint on the Lorentz factor, we have collected the spectral parameters and the observed maximum photon energy $E_{\rm{\oplus,max},i}$ for each time bin."
 One can hen derive the maximum photon energy in the cosmological ocal frame. be. Fux=Loyμμ.|c)," One can then derive the maximum photon energy in the cosmological local frame, i.e. $E_{\rm{max},i}=E_{\rm{\oplus,max},i}(1+z)$."
 Requiring the vain production optical depth to be less than unity for f= Laaxas We can write a general constraint in the parameter space of A? and ~ (where {0 is the distance of the emission region [rom the central engine. Gupta Zhang 2008: Zhang Peer 2009). Le. where er is the Thompson cross section. 3 represents he slope of the power law component for GRBs 000002D and 090510 and the Band. function high energy. spectral xwameter for GRBs 080916€7 ancl 000926. anc fü (n units of ergs-em2«s 4) can be written. as TREEANa[e][Eweayeexp)a)(100keV) ourfor the Dand ‘unction model. and fo=ANcAZ(LO0keV) for the simple power law model where lL and A are normalization actors (both normalized to 100 keV).," Requiring the pair production optical depth to be less than unity for $E = E_{\rm{max},i}$ , we can write a general constraint in the parameter space of $R$ and $\gamma$ (where $R$ is the distance of the emission region from the central engine, Gupta Zhang 2008; Zhang Pe'er 2009), i.e. where $\sigma_T$ is the Thompson cross section, $\beta$ represents the slope of the power law component for GRBs 090902B and 090510 and the Band function high energy spectral parameter for GRBs 080916C and 090926A, and $f_0$ (in units of $\rm{ergs} \cdot \rm{cm}^{-2} \cdot s^{-1}$ ) can be written as $f_0 =A \cdot \Delta T \left[ \f{E_p (\alpha - \beta)}{2 + \alpha}\right]^{\alpha - \beta} \rm{exp}(\beta - \alpha)(100 \quad \rm{keV})^{-\alpha}$ for the Band function model, and $f_0=K \cdot \Delta T (100 \quad \rm{keV})^{-\beta}$ for the simple power law model, where $A$ and $K$ are normalization factors (both normalized to 100 keV)."
 The approximation CQ)oπώςd)7/01} (Svensson LOST) is adopted o perform the calculation., The approximation $\rm{C}(\beta) \simeq (7/6)(- \beta)^{5/3}/(1-\beta)$ (Svensson 1987) is adopted to perform the calculation.
 In. order to further constrain 5. one needs to make an assumption about /?.," In order to further constrain $\gamma$, one needs to make an assumption about $R$."
" Without other independent. constraints. we apply the conventional assumption of internal shocks. so that Ais)=ze"" where of is the observed. minimum variability time scale."," Without other independent constraints, we apply the conventional assumption of internal shocks, so that $R(\gamma)=\gamma^2 c \f{\delta t}{1+z}$, where $\delta t$ is the observed minimum variability time scale."
 Combining Le.(5)). the lower limit for > is derived. for each time bin of each burst (see also Lithwick Sari 2001. Abdo et al.," Combining \ref{Solveme}) ), the lower limit for $\gamma$ is derived for each time bin of each burst (see also Lithwick Sari 2001, Abdo et al."
 2009)., 2009).
 In our calculation. we generally adopt 5; as the derived. lower limit.," In our calculation, we generally adopt $\gamma_i$ as the derived lower limit."
 This is because the derived: Lorentz factors of other GRBs using the afterglow deceleration constraint (Liang ct al., This is because the derived Lorentz factors of other GRBs using the afterglow deceleration constraint (Liang et al.
 2010) or photosphere constraint (Peer et al., 2010) or photosphere constraint (Pe'er et al.
 2011) are all below or consistent with these lower limits derived from the opacity constraints (Abdo et al., 2011) are all below or consistent with these lower limits derived from the opacity constraints (Abdo et al.
 2009a.b. 2010: Ackermann et al.," 2009a,b, 2010; Ackermann et al."
 2010)., 2010).
 Feeding this data into our shell mocel code. letting cach shell be ejected. with energv. Ly; ancl Lorentz factor 5; at time equal to that of the beginning of the bin time. we can calculate the early blastwave evolution and LAT band (integrated over >LOO MeV) lighteurve for the four CRBs.," Feeding this data into our shell model code, letting each shell be ejected with energy $E_{k,i}$ and Lorentz factor $\gamma_i$ at time equal to that of the beginning of the bin time, we can calculate the early blastwave evolution and LAT band (integrated over $>100$ MeV) lightcurve for the four GRBs."
 To mateh the observed. steep decay (with slope ~1.5). we adopt a radiative fireball solution or an acliahatic fireball solution with steep electron. energy. index.," To match the observed steep decay (with slope $\sim -1.5$ ), we adopt a radiative fireball solution or an adiabatic fireball solution with steep electron energy index."
 [ven though cach solution (for à fixed kinetic energv) has a steep decay slope. the overall lighteurve shows a shallower decay due to piling up of successive shells ejected later. with elitches introduced by jumping among the solutions.," Even though each solution (for a fixed kinetic energy) has a steep decay slope, the overall lightcurve shows a shallower decay due to piling up of successive shells ejected later, with glitches introduced by jumping among the solutions."
 As an example. the radiative model lishteurve of CRB 080016C' as compared with observation is presented in Fig.l.," As an example, the radiative model lightcurve of GRB 080916C as compared with observation is presented in Fig.1."
 Phe top nel shows the long term evolution. while the bottom panel is the zoomed-in carly afterglow lighteurve.," The top panel shows the long term evolution, while the bottom panel is the zoomed-in early afterglow lightcurve."
 The dotted lines denote the blastwave solutions with progressively increasing otal energy., The dotted lines denote the blastwave solutions with progressively increasing total energy.
 The lowest one corresponds to the first time jn. the second. lowest. corresponds to adding the energy. of he second time bin. etc.," The lowest one corresponds to the first time bin, the second lowest corresponds to adding the energy of the second time bin, etc."
 Since the lighteurve is chopped. into. discrete. time jns. the blastwave energy. is added in discrete steps.," Since the lightcurve is chopped into discrete time bins, the blastwave energy is added in discrete steps."
 This introduces some artificial elitches in the lighteurve., This introduces some artificial glitches in the lightcurve.
 Such an approximation is more realistic for GRBs with cistinet emission episodes., Such an approximation is more realistic for GRBs with distinct emission episodes.
 For ΙΙ 080916C.. the lighteurve is more appropriately approximated as a continuous wind with variable luminosity.," For GRB 080916C, the lightcurve is more appropriately approximated as a continuous wind with variable luminosity."
 Phe artificial glitches should appear to be more smeared., The artificial glitches should appear to be more smeared.
 For this reason. we have smoothed the elitches to make more natural transitions between solutions.," For this reason, we have smoothed the glitches to make more natural transitions between solutions."
 The model afterglow parameters (the fraction of electron energv ος. the fraction of magnetic energv cg. and the number density 7) are presented in Table 1.," The model afterglow parameters (the fraction of electron energy $\epsilon_e$, the fraction of magnetic energy $\epsilon_B$, and the number density $n$ ) are presented in Table 1."
 These are in eeneral consistent. with the parameter constraints derived bv Kumar Barniol Duran (2009. 2010).," These are in general consistent with the parameter constraints derived by Kumar Barniol Duran (2009, 2010)."
 In general. the model lighteurve. of GRB 080016C cannot fit the carly LAT cata.," In general, the model lightcurve of GRB 080916C cannot fit the early LAT data."
 Making the model suitable to fit the late-time steep decay. the early mocdel lighteurve level is too low to account for the observed data.," Making the model suitable to fit the late-time steep decay, the early model lightcurve level is too low to account for the observed data."
 Alternatively. one can make the early mocdel lighteurve match the observed lux level.," Alternatively, one can make the early model lightcurve match the observed flux level."
 Then inevitably the late time afterglow. level exceeds the observed level significantby due to the continuous energy injection., Then inevitably the late time afterglow level exceeds the observed level significantly due to the continuous energy injection.
 We believe that if the LAT band emission alter Zou originates from the external shock. then the LAT emission during the prompt emission phase be solely interpreted by the external shock model.," We believe that if the LAT band emission after $T_{90}$ originates from the external shock, then the LAT emission during the prompt emission phase be solely interpreted by the external shock model."
 Phe external shock contribution is relatively small. especially during carly epochs when energy in the blastwave is small," The external shock contribution is relatively small, especially during early epochs when energy in the blastwave is small."
 As a result. the GeV. emission during the prompt phase must be of an," As a result, the GeV emission during the prompt phase must be of an"
"(exposure of 5mn); the middle spectrum is from the INT on June 25, 2008 (exposure of 200 sec).","(exposure of 5mn); the middle spectrum is from the INT on June 25, 2008 (exposure of 200 sec)."
" Note that the extremities of this INT spectrum (bluewards of ~ 5000A and redwards of ~ 7000A) are not usable for determining the fluxes because of the onset of a strong vignetting in the camera, which is difficult to correct for in the reduction (the bump seen in the continuum around 5000 A is also artificial)."," Note that the extremities of this INT spectrum (bluewards of $\sim$ $\AA$ and redwards of $\sim$ $\AA$ ) are not usable for determining the fluxes because of the onset of a strong vignetting in the camera, which is difficult to correct for in the reduction (the bump seen in the continuum around 5000 $\AA$ is also artificial)."
" All three spectra are calibrated, and the differences in ordinates mainly reflect the difference in atmospheric transparency at the moment of the observations (except that the upper spectrum has been offset upwards by 300 units for clarity)."," All three spectra are calibrated, and the differences in ordinates mainly reflect the difference in atmospheric transparency at the moment of the observations (except that the upper spectrum has been offset upwards by 300 units for clarity)."
" The emission features detected comprise the Balmer lines of hydrogen (Ha, Hf, Hy, H6), lines of neutral helium (7065, 6678, 5876, 5015, 4921 A), the Hell lines at 5411 and 4686 A and the broad CIII/NIII AA 4640 and CIV 44 5805 A features."," The emission features detected comprise the Balmer lines of hydrogen $\alpha$, $\beta$, $\gamma$, $\delta$ ), lines of neutral helium (7065, 6678, 5876, 5015, 4921 $\AA$ ), the HeII lines at 5411 and 4686 $\AA$ and the broad CIII/NIII $\lambda\lambda$ 4640 and CIV $\lambda\lambda$ 5805 $\AA$ features."
 The slightly higher, The slightly higher
while for a=3 and larger a give more negative powers of συ and combinations of logs or arctangents.,while for $\alpha=3$ and larger $\alpha$ give more negative powers of $\sigma_0$ and combinations of logs or arctangents.
 A natural choice lor fo is to make ay=1. so that no is the number of quasars with Py=2. and d measures the minimum Hux in units of the characteristic flux.," A natural choice for $f_0$ is to make $\sigma_0=1$, so that $n_0$ is the number of quasars with $P_N=P_{\rm los}$ and $\Phi$ measures the minimum flux in units of the characteristic flux."
 Lt is easy to see that decreasing fuii. i6. increasing e$. leads to larger map but that the gains are small once 9=>1.," It is easy to see that decreasing $f_{\rm min}$, i.e. increasing $\Phi$, leads to larger $\bar{n}_{\rm eff}$ but that the gains are small once $\Phi\gg 1$."
 For fui~fo mop is mo up to a numerical constant of order unity. which reinforces the discussion in the text. 5.. ?..," For $f_{\rm min}\sim f_0$ $\bar{n}_{\rm eff}$ is $n_0$ up to a numerical constant of order unity, which reinforces the discussion in the text. \ref{sec:systematics}, \citet{cooray02}."
 Bo E? .?.., \ref{fig:DLAhalo} \citet{omeara07} \citet{prochaska10}.
 Bo D. ?.. 2. D. ," \ref{fig:DLAhalo} \ref{fig:DLAhalo} \citet{mcdonald05}, \citealt{mcdonald05} \ref{fig:DLAhalo} "
 , 
refspecred)).,).
 The inost prominent spectral features of cach spectruni are indicated in the seventh colhuun of he catalog (Table D)., The most prominent spectral features of each spectrum are indicated in the seventh column of the catalog (Table 4).
 An ciission line flag was given o each object., An emission line flag was given to each object.
 A value of 0 corresponds to galaxies without observed enission lines. a value of 1 corresponds o galaxies showing any cussion line.," A value of 0 corresponds to galaxies without observed emission lines, a value of 1 corresponds to galaxies showing any emission line."
 Two galaxies with road Ciuission lines (Αν) were assigned a value of 2., Two galaxies with broad emission lines (AGNs) were assigned a value of 2.
 As an example of the data obtained duriug our survey. tle spectra of 5 cluster 1uienmibers are shown in Fig. 2..," As an example of the data obtained during our survey, the spectra of 5 cluster members are shown in Fig. \ref{memb_spectra}."
 Frou op to bottom. the spectra are arranged from carly type ealaxies to late type galaxies.," From top to bottom, the spectra are arranged from early type galaxies to late type galaxies."
 The ealaxy spectroscopic ype as defined in Dressler et al. (, The galaxy spectroscopic type as defined in Dressler et al. (
1999) is also eiven.,1999) is also given.
 The ost conuuon spectral features are iudicated by dashed Ines. as explained iu the figure caption.," The most common spectral features are indicated by dashed lines, as explained in the figure caption."
 The umber of coufirmed cluster members obtained i our spectroscopic survey is comparable to other surveys of distaut clusters as. e.g... MS1051-03 (Donahue et al.," The number of confirmed cluster members obtained in our spectroscopic survey is comparable to other surveys of distant clusters as, e.g., MS1054-03 (Donahue et al."
 1998: Tran et al., 1998; Tran et al.
 1999: van Dokkuii ct al., 1999; van Dokkum et al.
 1999: van Dokkua et al., 1999; van Dokkum et al.
 2000) aud the supercluster Cl 16011]1301 at :=0.90 (Cal Lubin 2001)., 2000) and the supercluster Cl 1604+4304 at $z=0.90$ (Gal Lubin 2004).
" Iu addition to the number of secure iienibers, we have 15 objects at the cluster redshift with less secure redshifts."," In addition to the number of secure members, we have 15 objects at the cluster redshift with less secure redshifts."
 In Table 5 we also present the coordinates aud redshifts of the nou-cluster nienibers., In Table 5 we also present the coordinates and redshifts of the non-cluster members.
 The erouud-based photometric catalog itself was usec to estimate the success rate of our spectroscopic survey., The ground-based photometric catalog itself was used to estimate the success rate of our spectroscopic survey.
 Since the inaeiug ata were obtained with LRIS. we restrict the analysis to the 199. « 6/551 field of view of LRIS.," Since the imaging data were obtained with LRIS, we restrict the analysis to the 9 $\times$ 54 field of view of LRIS."
 We computed the ratio of the umber of object with spectroscopic redshifts o the number of objects in the photometric catalogue that were tarected for spectroscopy as a function of R magnitude., We computed the ratio of the number of object with spectroscopic redshifts to the number of objects in the photometric catalogue that were targeted for spectroscopy as a function of R magnitude.
 The data were binnecl iu AR=045 imag intervals., The data were binned in $\Delta R=0.5$ mag intervals.
 The ratio is observed to be nearly coustaut between the iuterval 20<Rc21 with a mean value of 0.89 and a dispersion of 0.07., The ratio is observed to be nearly constant between the interval $20 < R < 24$ with a mean value of 0.89 and a dispersion of 0.07.
 Fie., Fig.
 3 shows the distribution in redshift space of the 202 ealaxies for which a secure estimate of he redshift was obtained., \ref{redshift_histo} shows the distribution in redshift space of the 202 galaxies for which a secure estimate of the redshift was obtained.
 The bin size of the histogram was fixed to ΑΔ.Ξ001.," The bin size of the histogram was fixed to $\Delta
z=0.04$."
 celearly appears as the most siguificant structure in the distribution. with a mecian redshift of +=(L837 (3o-clipped mean of +=2E 0.83760.0010) and 102 calaxics between 2=(Al and +=OT.," clearly appears as the most significant structure in the distribution, with a median redshift of $z=0.837$ $\sigma$ -clipped mean of $\bar{z}=0.8376 \pm 0.0010$ ) and 102 galaxies between $z=0.81$ and $z=0.87$."
 All these galaxies are located in the 6788 « 6788 region covered w FORSI. which is equivalent to an area of 3.1 Ape « 3.1 Alpe at the cluster redshift.," All these galaxies are located in the 8 $\times$ 8 region covered by FORS1, which is equivalent to an area of 3.1 Mpc $\times$ 3.1 Mpc at the cluster redshift."
 A secondary peak in the histoeriuu is clearly seen at 2—0.61. where 31 galaxies have been confirmed in the rauge 0.60<i0.68.," A secondary peak in the histogram is clearly seen at $z \sim 0.64$, where 31 galaxies have been confirmed in the range $0.60 < z < 0.68$."
 The spatial distribution of this eroup of galaxies is quite elongated in the North-South direction. extending across the field," The spatial distribution of this group of galaxies is quite elongated in the North-South direction, extending across the field"
south. possibly due to the tit in the plane of he skv.,"south, possibly due to the tilt in the plane of the sky."
 Some of the inhomogcucities sccu in the two-dimensional nuage can also (o seen m these profiles., Some of the inhomogeneities seen in the two-dimensional image can also be seen in these profiles.
 The ratio of the 2-1S(1) over the 1-081) intesity varies betwee1 about 0.1 in the W aid E peaks of emission to about O.OL in the coudeusatio1 detected iu the W positiou 15 ssouth of the midplane., The ratio of the 2-1S(1) over the 1-0S(1) intensity varies between about 0.1 in the W and E peaks of emission to about 0.04 in the condensation detected in the W position $\sim$ south of the midplane.
 Auoticr interesting resit which emerges frou the spectra aud the intensity profiles is that the cussion in extends over the whole central torus., Another interesting result which emerges from the spectra and the intensity profiles is that the emission in extends over the whole central torus.
 However. lis quite weak. 10 of the 1-0S(1).," However, is quite weak, $\sim$ of the 1-0S(1)."
 The eenmissjonu iu the 1-08(1) liue of the of NGC 22316 is compared in this section to the predictions of the NII98 theoretical models., The emission in the 1-0S(1) line of the of NGC 2346 is compared in this section to the predictions of the NH98 theoretical models.
 The NII98 models comte the emission expected from tori (or shells or clumps) ex»osed to the racdiaion field of the hot central star and expanding mske the remmaut O he wind ejected by the central sar in 1S XOevious red giant phase., The NH98 models compute the emission expected from tori (or shells or clumps) exposed to the radiation field of the hot central star and expanding inside the remnant of the wind ejected by the central star in its previous red giant phase.
 As the ceiral star evolves iuilally at πι ΕΠ toward ligher effective teuperatures aud the1i along the white dwarf cooliic track. the torus CXpalicos radially with τοιοι] coustan velocivo and decreasing deusitv.," As the central star evolves initially at constant luminosity toward higher effective temperatures and then along the white dwarf cooling track, the torus expands radially with roughly constant velocity and decreasing density."
 The models consider the effects of UV aud soft N-ray radiation on he neutral eas aud follow the time dependent chemistry forΠω. solving or the chemical aud teuerature structure and the emergeut specruin (iu t1¢ folowing. the PDR spectrum) of the cvolving torus.," The models consider the effects of UV and soft X-ray radiation on the neutral gas and follow the time dependent chemistry for, solving for the chemical and temperature structure and the emergent spectrum (in the following, the PDR spectrum) of the evolving torus."
 The orus expands inside the mate‘Tha ejected by the s avins previous phase as red giant., The torus expands inside the material ejected by the star in its previous phase as red giant.
 Since its velocity Is larger than that of the wind itself. it gives origin to a Srock weuch heats aud compresses the gas. which theu enüts mtense lines of vibrationally excitedIT».," Since its velocity is larger than that of the wind itself, it gives origin to a shock which heats and compresses the gas, which then emits intense lines of vibrationally excited."
.. NIIOS consider the enuüssiou of J shocks. since the importance of mnaguctic ficld in PNe is not clear and. in this range of shock velocities. the Hine inteusitv is maxima in J shocks.," NH98 consider the emission of J shocks, since the importance of magnetic field in PNe is not clear and, in this range of shock velocities, the line intensity is maximum in J shocks."
slopes similarly close to ]. whilst the correlation coefficients are ~ 0.9 too.,"slopes similarly close to 1, whilst the correlation coefficients are $\sim$ 0.9 too."
 The present-day dynamical masses are therefore quite well reproduced by the models., The present-day dynamical masses are therefore quite well reproduced by the models.
 Note that the errors for the MSHOS5 based fits are always smaller than the fits with the here-derived values., Note that the errors for the MSH05 based fits are always smaller than the fits with the here-derived values.
 This 1s because the MSHOS5 values involve πο errors. and the fit only contains errors in the dynamical masses.," This is because the MSH05 values involve no errors, and the fit only contains errors in the dynamical masses."
 The values derived here values also have their own error estimate., The values derived here values also have their own error estimate.
 In Figs., In Figs.
 4. to 6. the dynamical masses from Table 2 (open circles) are shown together with the present-day, \ref{fig:comp_I} to \ref{fig:comp_V} the dynamical masses from Table \ref{tab:dyn} (open circles) are shown together with the present-day
preparation).,preparation).
 The number of galaxies in our survey is too small to evaluate the presence of a dip at ff~13.5., The number of galaxies in our survey is too small to evaluate the presence of a dip at $H\sim13.5$.
 The counts in the 13<H«13.5 and 13.5<H14 bins (5547 and 05c8. respectively) are very similar: (he LF in this region is (hus consistent wilh either a flat. rising. or declining slope.," The counts in the $13<H<13.5$ and $13.5<H<14$ bins $55\pm7$ and $68\pm8$, respectively) are very similar; the LF in this region is thus consistent with either a flat, rising, or declining slope."
 We determine the total Z-band luminosity of ALG4IL by extrapolating the liminosity function., We determine the total -band luminosity of A1644 by extrapolating the luminosity function.
 For a magnitude-limited survey described bv a Schechter function Che observed fraction of the total light is given by Pla+2.L4/ία2). where Er.y) is the incomplete Gamma functüon and ορ and L are the luminosities corresponding to the completeness limit and A/*.," For a magnitude-limited survey described by a Schechter function the observed fraction of the total light is given by $\Gamma(\alpha+2,L_{min}/L^*)/\Gamma(\alpha+2)$, where $\Gamma(x,y)$ is the incomplete Gamma function and $L_{min}$ and $L^*$ are the luminosities corresponding to the completeness limit and $M^*$."
 With a completeness limit of //=16. the fitted Schechter parameters imply that we observe of the total light.," With a completeness limit of $H=16$, the fitted Schechter parameters imply that we observe of the total light."
 Our photometric survey covers a square field 9 f? Mpc? in area;, Our photometric survey covers a square field 9 $h^{-2}$ $^2$ in area.
 The photometry is therefore complete within 0.5(95.7 Mpc?)/?=1.5h1 Mpe of the center of the field., The photometry is therefore complete within $0.5(9\:h^{-2}$ $^2)^{1/2}=1.5\:h^{-1}$ Mpc of the center of the field.
 Inside this radius the total Iuminositv is Ly—76204x107h?L.: the quoted error in Ly rellects the uncertainty in the LF parameters., Inside this radius the total luminosity is $L_H=7.6\pm0.4\times10^{12}\:h^{-2}\:L_{\odot}$; the quoted error in $L_H$ reflects the uncertainty in the LF parameters.
 For comparison. we integrate the visible LF in a smaller 0.32 deg? region of A644 (IXashikawaetal.1995).," For comparison, we integrate the visible LF in a smaller 0.82 $^2$ region of A1644 \citep{kas95}."
". Using their values of a. Mg. and AM"". the total Z-band. light within L.1 5! Mpe is LgeL1x1072h? L.."," Using their values of $\alpha$ , $M^*_R$, and $M^{lim}_R$, the total -band light within 1.1 $h^{-1}$ Mpc is $L_R\sim1.1\times10^{12}\:h^{-2}\:L_\odot$ ."
 Within the same radius we compute the Ipuminosity and use (vpical galactic colors aud (/—4/1).=0.85 to convertLf photometry toR., Within the same radius we compute the }-band luminosity and use typical galactic colors and $(R-H)_\odot=0.85$ to convert photometry to.
 The result is Lj;=5.120.3x107h.2L. which implies Lj~1.122:0.06x1077L.. in excellent agreement with Ixashikawa et al.," The result is $L_H=5.1\pm0.3\times10^{12}\:h^{-2}\:L_\odot$ which implies $L_R\sim1.12\pm0.06\times10^{12}\:h^{-2}\:L_\odot$, in excellent agreement with Kashikawa et al."
 The agreement implies that the optical Iuminosity of A1644 is only slightly affected by factors such as dust extinction and recent star formation activity., The agreement implies that the optical luminosity of A1644 is only slightly affected by factors such as dust extinction and recent star formation activity.
 Figure 12. shows the radial M/Lj profile., Figure \ref{fig-ml} shows the radial $M/L_H$ profile.
 The mass-to-light ratio is flat for R=O.4h! Ape. suggesting that the dark matter Iraction is constant outside this radius.," The mass-to-light ratio is flat for $R\gtrsim0.4\:h^{-1}$ Mpc, suggesting that the dark matter fraction is constant outside this radius."
 The increased M/Lat BRE0.35h.1 Mpe dis a result of a depressed luminosity near the cluster core., The increased $M/L$ at $R\lesssim0.35\:h^{-1}$ Mpc is a result of a depressed luminosity near the cluster core.
 At the limiting photometric radius of 1.5 f! Mpe the caustic and. virial mass-to-light ratios are M/Ly28213hM.fL. and M/Ly=12726hM./L.., At the limiting photometric radius of 1.5 $h^{-1}$ Mpc the caustic and virial mass-to-light ratios are $M/L_H=82\pm13\:h\:M_\odot/L_\odot$ and $M/L_H=127\pm26\:h\:M_\odot/L_\odot$.
" For A1644. Girardietal.(2000) obtain AM/Lp,e250hW/L. within 1.5 f| Mpe."," For A1644, \citet{gir00} obtain $M/L_{B_j}\sim250\:h\:M_\odot/L_\odot$ within 1.5 $h^{-1}$ Mpc."
" Transforming from D; to1 gives M/Lj,~40hM./L. Lor their data.", Transforming from $B_j$ to gives $M/L_H\sim40\:h\:M_\odot/L_\odot$ for their data.
 This value is roughly half of our caustic estimate., This value is roughly half of our caustic estimate.
 Decause our measured masses are almost exactly the same. the difference in JV/L is due to their largerluminosity.," Because our measured masses are almost exactly the same, the difference in $M/L$ is due to their largerluminosity."
 Our Iuminosityv. determination is based on CCD photometry and agrees well with the optical CCD photometryof, Our luminosity determination is based on CCD photometry and agrees well with the optical CCD photometryof
spectral features and is between the and silicate features.,spectral features and is between the and silicate features.
 Being an intermediate mid-infrared wavelength. it is not as dominated bv luminosity from the hot dust associated with AGN or the cool dust associated with a starburst as would be a shorter or longer wavelength.," Being an intermediate mid-infrared wavelength, it is not as dominated by luminosity from the hot dust associated with AGN or the cool dust associated with a starburst as would be a shorter or longer wavelength."
" In Figure 6. luminosities pL,(15jmi) ave compared to the EW of the PAIL feature."," In Figure 6, luminosities $\nu$ $_{\nu}$ $\mu$ m) are compared to the EW of the PAH feature."
 This Figure shows our most important results., This Figure shows our most important results.
 Ht shows the dramatic range in dust continuum huninosilies that is covered bv the sample. a [actor of 2.5 x 107 in luminositv. a range that encompasses virtually all extragalactic sources observed so [ar wilh Spitzer. regardless of selection criterion.," It shows the dramatic range in dust continuum luminosities that is covered by the sample, a factor of 2.5 x $^{4}$ in luminosity, a range that encompasses virtually all extragalactic sources observed so far with $Spitzer$, regardless of selection criterion."
" The faintest source is source SBIL in Tables 2 and 3. a blue compact dwarf in Bootes with log pL, (15j/i) = 41.85 (eres 1): the most luminous sources are sources AGNI and AGN21 in Tables 4 and 5. with AGNI] being an absorbed silicate source and AGN21 an emission silicate source. with log pL, (15jm) = 16.2. ("," The faintest source is source SB11 in Tables 2 and 3, a blue compact dwarf in Bootes with log $\nu$ $_{\nu}$ $\mu$ m) = 41.85 (ergs $^{-1}$ ); the most luminous sources are sources AGN11 and AGN21 in Tables 4 and 5, with AGN11 being an absorbed silicate source and AGN21 an emission silicate source, with log $\nu$ $_{\nu}$ $\mu$ m) = 46.2. ("
"Source AGN3 in Table 5. the QSO at z = 2.4 discussed in section 2.3. does not have a measurement of pL, (15;jan) because the observed rest-frame spectrum does not extend toum.","Source AGN3 in Table 5, the QSO at z = 2.4 discussed in section 2.3, does not have a measurement of $\nu$ $_{\nu}$ $\mu$ m) because the observed rest-frame spectrum does not extend to."
". It certainly is among the sources with log vL,(15jm) > 45.0 (eres +) so is included in the average for this luminosity bin discussed below in section 3.2.)", It certainly is among the sources with log $\nu$ $_{\nu}$ $\mu$ m) $>$ 45.0 (ergs $^{-1}$ ) so is included in the average for this luminosity bin discussed below in section 3.2.)
 Figure 6 shows a well defined gap in the distribution of PAIL strength at < EW(6.2;n)) «0.5jm., Figure 6 shows a well defined gap in the distribution of PAH strength at $<$ ) $<$.
". 21 of the 60 sources show EW(6.2jm)) 20.47pm. and the remaining sources all have EW(6.2,0m)) «0.37jan."," 21 of the 60 sources show ) $>$, and the remaining sources all have ) $<$."
. We also note that the “pure” starbursts in show a lower limit for EW(6.2jm)) at about this value: 21 of 22 DBrandl et al.," We also note that the ""pure"" starbursts in \citet{bra06} show a lower limit for ) at about this value; 21 of 22 Brandl et al."
 starbursts have EEW(6.2j/m1))) >O., starbursts have ) $>$.
4yan.. We interpret these empirical results for both our 10 mJv sample and the Brandl et al., We interpret these empirical results for both our 10 mJy sample and the Brandl et al.
 sample to mean that sources with EW(6.2j)) > are pure starbursts., sample to mean that sources with ) $>$ are pure starbursts.
" Sources in which the strength of the PAIL feature is diluted by additional mid-infrared continuum arising from an AGN would show EW(G.2;an)) <0.4jun.. and we consider such sources as composite starburstΕΑΝ,"," Sources in which the strength of the PAH feature is diluted by additional mid-infrared continuum arising from an AGN would show ) $<$, and we consider such sources as composite starburst+AGN."
 Sources with the smallest values of EW(6.2jm)) are dominated by the AGN component., Sources with the smallest values of ) are dominated by the AGN component.
 These interpretations lead to the classifications shown in Figure 6., These interpretations lead to the classifications shown in Figure 6.
" For starbursts with EW(6.2;0))2O4yem.. the median log pL, (15jmi) = 43.1."," For starbursts with $>$, the median log $\nu$ $_{\nu}$ $\mu$ m) = 43.1."
" For composite sources with « «0.4jm.. the median log pL, (15jm) = 44.0."," For composite sources with $<$ $<$, the median log $\nu$ $_{\nu}$ $\mu$ m) = 44.0."
" For AGN sources with EW(G6.2jm))«0.1jan.. the median log pL, (155m) = 45.0."," For AGN sources with $<$, the median log $\nu$ $_{\nu}$ $\mu$ m) = 45.0."
We are grateful to Dr. A. Ohsawa [rom Tokvo University for help in the first stage of ihe experiment and (to Dr. M. Olsen for reading the manuscript.,We are grateful to Dr. A. Ohsawa from Tokyo University for help in the first stage of the experiment and to Dr. M. Olsen for reading the manuscript.
 This work was partially supported by FAPERJ (Research Foundation of the State of Rio de Janeiro) in Brazil., This work was partially supported by FAPERJ (Research Foundation of the State of Rio de Janeiro) in Brazil.
1n Saumon Marley (2008) we demonstrated that by increasing the cloud sedimentation efficiency ficqg as a brown cdwarl cools [rom Teg=1400 to Ix. (the predicted model colors reproduce those across the L to T transition.,"In Saumon Marley (2008) we demonstrated that by increasing the cloud sedimentation efficiency $f_{\rm sed}$ as a brown dwarf cools from $T_{\rm eff}=1400$ to $\,$ K, the predicted model colors reproduce those across the L to T transition."
 In the previous section we likewise showed that increasing fractional eloudiness αἱ fixed fi. has the same result., In the previous section we likewise showed that increasing fractional cloudiness – at fixed $f_{\rm sed}$ – has the same result.
 This leads us to consider how to distinguishe the (wo cases., This leads us to consider how to distinguish the two cases.
 As shown in Figure La partly cloudy (72) profile (based on a [ως2 cloud) can be nearly identical to a model with a thinner homogeneous cloud but (he spectrum from these two models are not necessarily the same because the former uses ((1) to compute the flux., As shown in Figure 1 a partly cloudy $T(P)$ profile (based on a $f_{\rm sed}=2$ cloud) can be nearly identical to a model with a thinner homogeneous cloud but the spectrum from these two models are not necessarily the same because the former uses (1) to compute the flux.
 In the partly cloudy case some flux from deep. hot regions of the atmosphere (Fue is escaping through the clear regions (hat are otherwise totallv shielded by (he cloud in the homogeneous case (see the middle panel of Figure 7 of Ackerman&Morley. (2001))).," In the partly cloudy case some flux from deep, hot regions of the atmosphere ${\cal F}_{\rm hole}$ is escaping through the clear regions that are otherwise totally shielded by the cloud in the homogeneous case (see the middle panel of Figure 7 of \citet{Ack01}) )."
 Thus we expect that even for identical Z(77) profiles (he emission spectra will differ., Thus we expect that even for identical $T(P)$ profiles the emission spectra will differ.
 Indeed that is the case as shown in Figure 4 which shows spectra computed from proliles shown in Figure 1., Indeed that is the case as shown in Figure 4 which shows spectra computed from profiles shown in Figure 1.
 Focusing on the J band. which features the lowest molecular opacity ancl ihe deepest. atmospheric window in the near-infrared (Ackerman&Marley2001).. the ereatest (lux is found lor the clouclless model.," Focusing on the $J$ band, which features the lowest molecular opacity and the deepest atmospheric window in the near-infrared \citep{Ack01}, the greatest flux is found for the cloudless model."
 The homogenous cloudy. feq=2 model is faintest. with the fi=4 case falling in between.," The homogenous cloudy $f_{\rm sed}=2$ model is faintest, with the $f_{\rm sed}=4$ case falling in between."
 Even though the partly cloudy f=0.5 model has essentially the same thermal profile as the fq=4 model. it is brighter in the J band. because some [lux is escaping from deeper in the atmosphere.," Even though the partly cloudy $h=0.5$ model has essentially the same thermal profile as the $f_{\rm sed}=4$ model, it is brighter in the $J$ band because some flux is escaping from deeper in the atmosphere."
 Of course flux conservation requires (hat the partly cloudy model must be fainter al other wavelenetlis. here in A band.," Of course flux conservation requires that the partly cloudy model must be fainter at other wavelengths, here in $K$ band."
 Thus the model spectra are increasinely bluer in (he near-intrarecl [rom faa 240 fre=4 bo the partly cloudy model., Thus the model spectra are increasingly bluer in the near-infrared from $\fsed=2$ to $\fsed=4$ to the partly cloudy model.
 Figure 4 shows that the partly cloudy model is verv close to the foeq=4 homogeneous cloudy model at wavelengths where the [ιν is low and emitted from the upper atmosphere. ancl intermediate between. fi.=4 and cloudless in (he Jifdy [lux peaks where part of the flux comes from the deeper atmosphere.," Figure 4 shows that the partly cloudy model is very close to the $\fsed=4$ homogeneous cloudy model at wavelengths where the flux is low and emitted from the upper atmosphere, and intermediate between $\fsed=4$ and cloudless in the $JHK$ flux peaks where part of the flux comes from the deeper atmosphere."
 Thus. for a given Zr ancl gravity. the presence of holes in the cloud cover have a cliscernible effect on (he neaur-inlrared spectrum.," Thus, for a given $\teff$ and gravity, the presence of holes in the cloud cover have a discernible effect on the near-infrared spectrum."
 For a given observed spectrum. where Zug. gravity aud composition are nol knownpriori how can we distinguish a partly from a homogeneous cloudy atmosphere?," For a given observed spectrum, where $\teff$, gravity and composition are not known, how can we distinguish a partly from a homogeneous cloudy atmosphere?"
 We explored (his problem by fitting the near-infrared partly cloudy model spectra with our laree library ol cloudy models. using the method of Crushingetal. (2003).. and allowing Tig. gravity. and freq (to vary freely.," We explored this problem by fitting the near-infrared partly cloudy model spectra with our large library of cloudy models, using the method of \citet{Cus08}, , and allowing $\teff$ , gravity, and $\fsed$ to vary freely."
 We find that in general. the best Πο cloudy model has the same eravity. (he same Zar (or slightly higher by ~ 100IX) and a higher f/.4 depending on h.," We find that in general, the best fitting cloudy model has the same gravity, the same $\teff$ (or slightly higher by $\sim 100\,$ K) and a higher $\fsed$ depending on $h$."
 The fitted cloudy spectra are close to the partly cloudy spectra. ancl some of the dillerences can be attributed to the grid spacing of the cloudy models.," The fitted cloudy spectra are close to the partly cloudy spectra, and some of the differences can be attributed to the grid spacing of the cloudy models."
Itappears that the Ην colors of,Itappears that the $JHK$ colors of
detected as a satellite of another galaxy during its history.,detected as a satellite of another galaxy during its history.
 These timesteps are plotted as circles (panel 14(d)))., These timesteps are plotted as circles (panel \ref{fig:gal4}) ).
" The bottom panels of figure 14 show the origins of the mass, separated into two components: merger and accretion."," The bottom panels of figure \ref{fig:mass_hist} show the origins of the mass, separated into two components: merger and accretion."
 Smooth accretion is shown in blue and mergers in red., Smooth accretion is shown in blue and mergers in red.
" A negative value of merger or accretion, respectively, means that the galaxy loses mass to either another galaxy (fragmentation) or the background (evaporation)."," A negative value of merger or accretion, respectively, means that the galaxy loses mass to either another galaxy (fragmentation) or the background (evaporation)."
" These are the two components of the derivative of the blue curve shown in the upper panel, since with our definition, all mass is acquired by either merger or smooth accretion, and lost by fragmentation or evaporation."," These are the two components of the derivative of the blue curve shown in the upper panel, since with our definition, all mass is acquired by either merger or smooth accretion, and lost by fragmentation or evaporation."
 Those four galaxies have very different mass accretion histories., Those four galaxies have very different mass accretion histories.
" The galaxy in panel undergoes a major merger that can be seen in the lower panel of (a),, at t~5.1 Gyr."," The galaxy in panel undergoes a major merger that can be seen in the lower panel of , at $t \simeq 5.1$ Gyr."
" The galaxy in panel shows the opposite behaviour: it does not experience any merger and grows smoothly by accreting gas until {~7 Gyr, then maintains a constant mass until the end of the simulation, passively turning its gas reservoir into stars."," The galaxy in panel shows the opposite behaviour: it does not experience any merger and grows smoothly by accreting gas until $t\simeq 7$ Gyr, then maintains a constant mass until the end of the simulation, passively turning its gas reservoir into stars."
" In panel(c), the galaxy grows mainly through accretion until it reaches a maximum mass at t~7 Gyr, and then interacts with another structure and loses more mass than it gains from mergers, and ends with a somewhat lower mass."," In panel, the galaxy grows mainly through accretion until it reaches a maximum mass at $t\simeq 7$ Gyr, and then interacts with another structure and loses more mass than it gains from mergers, and ends with a somewhat lower mass."
" Galaxy in panel shows quite an unusual behaviour: after entering the level 3 box at {~5Gyr, it grows from both mergers and accretion, and is suddenly accreted by a more massive galaxy, becomes a satellite, then loses about one third of its mass, which feeds the host galaxy."," Galaxy in panel shows quite an unusual behaviour: after entering the level 3 box at $t \simeq 5\text{ Gyr}$, it grows from both mergers and accretion, and is suddenly accreted by a more massive galaxy, becomes a satellite, then loses about one third of its mass, which feeds the host galaxy."
 It then leaves its host galaxy and continues to lose mass through evaporation., It then leaves its host galaxy and continues to lose mass through evaporation.
" These behaviours are quite typical of what we can see in our simulations, with high-mass central galaxies undergoing mergers and accreting, and lower-mass, isolated galaxies accreting gas before their growth is stopped."," These behaviours are quite typical of what we can see in our simulations, with high-mass central galaxies undergoing mergers and accreting, and lower-mass, isolated galaxies accreting gas before their growth is stopped."
" We computed the accretion fraction by considering, at the last output, the origin of each particle: particles belonging to the galaxy at the first time of detection were defined as ""initial""; particles that came originally from the background, and had never belonged toanother structure were labelled “accretion”;"," We computed the accretion fraction by considering, at the last output, the origin of each particle: particles belonging to the galaxy at the first time of detection were defined as “initial”; particles that came originally from the background, and had never belonged toanother structure were labelled “accretion”;"
Two observations were iade ou the central region of the p Oph cloud with the ACIS-I array consisting of four abutted ταν CCDs.,Two observations were made on the central region of the $\rho$ Oph cloud with the ACIS-I array consisting of four abutted X-ray CCDs.
" The first observation (here aud after. obs.1) covered a LES 171EE area including cores D. C. E. aud F. while the second observation (0bs.2) covered the center of core A (Motte,Aucdeé.&Nor1998)."," The first observation (here and after, obs.1) covered a $\times$ 4 area including cores B, C, E, and F, while the second observation (obs.2) covered the center of core A \citep{Motte1998}."
. The level 2 data are retrieved from the N-rav Counter (CNC) archive. iu which the data degradation caused by the increase of charge transfer inefficiency (CTI) in orbit is corrected.," The level 2 data are retrieved from the X-ray Center (CXC) archive, in which the data degradation caused by the increase of charge transfer inefficiency (CTI) in orbit is corrected."
 N-ray events are selected with-— the erades 0. 2. 3. Land 6.," X-ray events are selected with the grades 0, 2, 3, 4, and 6."
 After the processing. 2100 ks effective exposure time is obtained from cach observation.," After the processing, $\approx$ 100 ks effective exposure time is obtained from each observation."
 The log of the observations is listed in Table |, The log of the observations is listed in Table \ref{tab:obs}.
" Iu these two fields. 18 late AL chwarts have beeu reported. based on the water vapor absorption at A = 2.12.5 pau (Wilking. Crecne, Meyer 1999: Cushing. Tokunaga. Ἱνουανασα 2000)."," In these two fields, 18 late M dwarfs have been reported, based on the water vapor absorption at $\lambda$ = 2.4–2.5 $\mu$ m (Wilking, Greene, Meyer 1999; Cushing, Tokunaga, Kobayashi 2000)."
" Amoug them. 8 sources have the upper limit of mass less than 0.08 AL... which we call ""bonasfide brown chwarts” (here and after. DDz)."," Among them, 8 sources have the upper limit of mass less than 0.08 $_{\odot}$, which we call ``bona-fide brown dwarfs” (here and after, BDs)."
" The other 10 sources have a mass in the transition region of 0.08 NL... hence called ""candidate brown dwarts” (CBDs)}."," The other 10 sources have a mass in the transition region of 0.08 $_{\odot}$, hence called “candidate brown dwarfs” (CBDs)."
 Their names aud spectral types ave shown in Table 2.., Their names and spectral types are shown in Table \ref{tab:BDs}.
 Using the conumuiad. we pick up —100 X-rav sources frou cach field above the sienificance criterion of *.," Using the command, we pick up $\sim$ 100 X-ray sources from each field above the significance criterion of $^{-7}$."
 Infrared (IR) counterparts from the catalog of Barsouvetal.(1997) are searched aud the position is cross-correlated to that of the N-rav source., Infrared (IR) counterparts from the catalog of \citet{Barsony1997} are searched and the position is cross-correlated to that of the X-ray source.
 Systematic coordinate offset of the frame is then fine-tuned το fit the IR frame., Systematic coordinate offset of the frame is then fine-tuned to fit the IR frame.
 After the offset correction. tle relative position crror (lo) is 1722.," After the offset correction, the relative position error $\sigma$ ) is 2."
 We find X-rav counterparts frou 5 IR positions iu a 26 eror radius (2711) out of the 18 catalogued BDs aud CBDs (GY 310. CY 31. CY 37. CY 59. aud CY 326).," We find X-ray counterparts from 5 IR positions in a $\sigma$ error radius 4) out of the 18 catalogued BDs and CBDs (GY 310, GY 31, GY 37, GY 59, and GY 326)."
 The N-rav positions and relative offsets from the IR sources are given in Table 2.., The X-ray positions and relative offsets from the IR sources are given in Table \ref{tab:BDs}.
 The Naax counts are extracted from a circle of a half radius of the poiut-spread function. (PSF) around the N-rav position., The X-ray counts are extracted from a circle of a half radius of the point-spread function (PSF) around the X-ray position.
 Since no apparent X-ray sources are fouud ina 256 error radius 11) of the other 13 catalogued DDs aud CBDs. we define a circle with a half radius of PSF around each IR. position.," Since no apparent X-ray sources are found in a $\sigma$ error radius 4) of the other 13 catalogued BDs and CBDs, we define a circle with a half radius of PSF around each IR position."
 Then we nanually count the X-ray photous iu the circle., Then we manually count the X-ray photons in the circle.
 We rote that a rather παπα source radius is selected so as to maximize the signal-to-noise (S/N) ratio. yarticularly. for fait N-rav sources;," We note that a rather small source radius is selected so as to maximize the signal-to-noise (S/N) ratio, particularly, for faint X-ray sources."
 Nevertheless. as ds denmoustrated iu the 5 bright sources. the yosition error between IB and N-ravs is always «λαο than the source radius. because both have eenerallv simular depeudence ou the source off-axis auele: both have the smaller values for the sources with smaller offaxis augle.," Nevertheless, as is demonstrated in the 5 bright sources, the position error between IR and X-rays is always smaller than the source radius, because both have generally similar dependence on the source off-axis angle; both have the smaller values for the sources with smaller off-axis angle."
 Therefore most of the N-rav photons for the relevant BDs aud CBDs. if any. may fall in the source circles.," Therefore most of the X-ray photons for the relevant BDs and CBDs, if any, may fall in the source circles."
 The N-rav flux lius counted are given in Table 2.., The X-ray flux thus counted are given in Table \ref{tab:BDs}.
" The mean background counts are estinated Yoni source-free regions of a G3-arcnuin? aud a 5O-arciuin? area du the ACIS-I fields for obs.1 aud obs.2. respectively,"," The mean background counts are estimated from source-free regions of a $^2$ and a $^2$ area in the ACIS-I fields for obs.1 and obs.2, respectively."
 The soft band (0.52.0 se-V) background counts (n. units. of 27 counts 7) are 2.3 aud 2.2. for obs.l aud obs.," The soft band (0.5–2.0 keV) background counts (in units of $^{-2}$ counts $^{-2}$ ) are 2.3 and 2.2, for obs.1 and obs."
 2. respectively. while those iu the hard (2.09.0 keV) xuid are about 3 times larger. 6.5 and 6.5 for obs.1 and obs.," 2, respectively, while those in the hard (2.0–9.0 keV) band are about 3 times larger, 6.8 and 6.5 for obs.1 and obs."
 2., 2.
 The background counts in cach source area are given in Table 2., The background counts in each source area are given in Table 2.
 We then separately calculate the confidence level (CL) of the N-ray detection for the soft. hard aud total (0.59.0 keV) bauds.," We then separately calculate the confidence level $CL$ ) of the X-ray detection for the soft, hard and total (0.5–9.0 keV) bands."
" Based ou the Poisson statistics. the CL is defined. as: where Ny and Vy, ave the detected aud the backeround counts in the source cirele. respectively (sce e.g... Gehrels L986. and references therein)."," Based on the Poisson statistics, the $CL$ is defined as; where $N_{0}$ and $N_{bg}$ are the detected and the background counts in the source circle, respectively (see e.g., Gehrels 1986, and references therein)."
 We set the detection (or the upper lait) criterion that the CL should be larger than 0.999 (23.30) in any of the 3 energy band data., We set the detection (or the upper limit) criterion that the $CL$ should be larger than 0.999 $\sigma$ ) in any of the 3 energy band data.
 In Table 2.. we show the iiaxinuuu CL value for cach source.," In Table \ref{tab:BDs}, we show the maximum $CL$ value for each source."
 For sources located in both fields of view (CY 111. CY 163. and CY 202). we also estimate the CL for the combined data as well as the separate data.," For sources located in both fields of view (GY 141, GY 163, and GY 202), we also estimate the $CL$ for the combined data as well as the separate data."
 Towever. no higher CL value is obtained from all the sources.," However, no higher $CL$ value is obtained from all the sources."
 As are sununarized in Table 2.. bright N-ravs," As are summarized in Table \ref{tab:BDs}, , bright X-rays"
reproduces the analytic distributions very well. aud this verifies the overall iiethod.,"reproduces the analytic distributions very well, and this verifies the overall method."
 Finally. the cut-sky power spectimm with ouc-sigima confidence regions is shown in three panels iu Figure 5.. focusing on different (-rauges. uamely all Cs. the SYN~| transition region. aud the low S/N region.," Finally, the cut-sky power spectrum with one-sigma confidence regions is shown in three panels in Figure \ref{fig:TT_spectrum}, focusing on different $\ell$ -ranges, namely all $\ell$ 's, the $S/N \sim 1$ transition region, and the low $S/N$ region."
 This completes the ligh-f temperature analysis validation., This completes the $\ell$ temperature analysis validation.
 We now consider polarization analysis. aud construct a new low-f simulation for this purpose.," We now consider polarization analysis, and construct a new $\ell$ simulation for this purpose."
 This simulation does uot inue any planned experiment. but is rather designed to lighheht the analysis method itself.," This simulation does not mimic any planned experiment, but is rather designed to highlight the analysis method itself."
" Specifically, we drew a new CAB realization from the best-fit WALAP ACDAL spectra that includes a non-zero tensor contribution. incliding multipoles up to fans=180. and convolved this with a 37 PWIAL Gaussian beam. aud pixclized it at Noa=Ol."," Specifically, we drew a new CMB realization from the best-fit WMAP $\Lambda$ CDM spectrum that includes a non-zero tensor contribution, including multipoles up to $\ell_{\textrm{max}}=150$, and convolved this with a $3^{\circ}$ FWHM Gaussian beam, and pixelized it at $N_{\textrm{side}} = 64$."
 Uniform noise of Seis RATS was added to the temperature compoucut. and Lis RAIS to the polarization componcuts.," Uniform noise of $5\mu\textrm{K}$ RMS was added to the temperature component, and $1\mu\textrm{K}$ RMS to the polarization components."
 The S-vear WMADP polarization sky mask was imposed on the data., The 5-year WMAP polarization sky mask was imposed on the data.
" We allowed for uou-zero CIT, CIF, CPE aud CPP spectra. but fixed CF?=CPP(0,"," We allowed for non-zero $C_{\ell}^{TT}$, $C_{\ell}^{TE}$, $C_{\ell}^{EE}$ and $C_{\ell}^{BB}$ spectra, but fixed $C_{\ell}^{TB}
= C_{\ell}^{EB} = 0$."
 These spectra were then individually binned to maintain a reasonable signalto-noise per bin. (, These spectra were then individually binned to maintain a reasonable signal-to-noise per bin. (
Details ou how to introduce individual binning of each power προςπα were receutly deseribed by Eviksen and Wels. 2008.),"Details on how to introduce individual binning of each power spectrum were recently described by Eriksen and Wehus, 2008.)"
 Again. a tuned Cassia proposal density was used in the MCAIC step.," Again, a tuned Gaussian proposal density was used in the MCMC step."
 A total of 0000 samples were produced over 12 chains. and the CPU time per sample was 55 seconds. for a total of ~200 CPU hours.," A total of 000 samples were produced over 12 chains, and the CPU time per sample was 55 seconds, for a total of $\sim200$ CPU hours."
" Iu Figure 6 we show one C, chain for each of the our sanled spectra. for the last (and therefore most difficult) bin in cach case."," In Figure \ref{fig:pol_trace_plots} we show one $C_{\ell}$ chain for each of the four sampled spectra, for the last (and therefore most difficult) bin in each case."
 Note that the CFF aud CPP spectra lave csseutially vanishing signal-to-noise. ancl herefore these chains reach zero values.," Note that the $C_{\ell}^{EE}$ and $C_{\ell}^{BB}$ spectra have essentially vanishing signal-to-noise, and therefore these chains reach zero values."
 Clearly. we see hat mixing properties of these chains are satisfactory. and the correlation leugths are quite short.," Clearly, we see that mixing properties of these chains are satisfactory, and the correlation lengths are quite short."
 In Figure 7 we show the Celman-Rubin statistics or each of the four power spectra. aud with the single exception of the very last bin of CEP. all R values are well below 1.1.," In Figure \ref{fig:gr_polarization} we show the Gelman-Rubin statistics for each of the four power spectra, and with the single exception of the very last bin of $C_{\ell}^{EE}$, all $R$ values are well below 1.1."
 Thus. all spectra have couvereed well everywhere.," Thus, all spectra have converged well everywhere."
" Finally, in Έπος ὃ we show the reconstructed uarginal power spectra for cach polarization compoucut. overplotted ou the input spectrum."," Finally, in Figure \ref{fig:pol_spectrum} we show the reconstructed marginal power spectra for each polarization component, overplotted on the input spectrum."
 The agreement is very good., The agreement is very good.
 Note. however. that these spectra are direct uarginals. aud not a joiut πλακα likelihood estimate.," Note, however, that these spectra are direct marginals, and not a joint maximum likelihood estimate."
 They are therefore uot individual uubiased estimators., They are therefore not individual unbiased estimators.
 Tn particular. the marginal CPE power spectrüuni is yased slightly high because of the combination of he CITCEE(CTE)?=0 positivity coustraint aud relatively low signal-to-noise.," In particular, the marginal $C_{\ell}^{EE}$ power spectrum is biased slightly high because of the combination of the $C_{\ell}^{TT}C_{\ell}^{EE} - (C_{\ell}^{TE})^2 > 0$ positivity constraint and relatively low signal-to-noise."
 Cousideration of tle joiut volavization posterior. which au unbiased estimator. is xostponed to a future publication.," Consideration of the joint polarization posterior, which an unbiased estimator, is postponed to a future publication."
"spectra with a sum of the disc blackbody component (DISKBB) and Comptonization(EQPAIR, Coppi 1999).","spectra with a sum of the disc blackbody component ) and Comptonization, Coppi 1999)."
" The code gives the ratio between the power in seed photons, {ς and hot electrons, £;,."," The code gives the ratio between the power in seed photons, $\ell_s$ and hot electrons, $\ell_h$."
" This ratio, £,/£,, depends mostly on the geometry of the accretion flow and defines the spectral shape of the hard X-ray continuum."," This ratio, $\ell_h/\ell_s$, depends mostly on the geometry of the accretion flow and defines the spectral shape of the hard X-ray continuum."
" Typically, the hard state is characterized by £j,/£,>>1, (ultra) soft state by £n/€s<1 and very high/intermediate state by €,/€s;~1."," Typically, the hard state is characterized by $\ell_h/\ell_s \gg 1$, (ultra) soft state by $\ell_h/\ell_s \ll 1$ and very high/intermediate state by $\ell_h/\ell_s \sim 1$."
" The other important model parameters include the optical depth, 7, the temperature of the seed photons, kT, and the ratio of the nonthermal-to-thermal compactness €nin/l:n-"," The other important model parameters include the optical depth, $\tau$ the temperature of the seed photons, $kT_s$ , and the ratio of the nonthermal-to-thermal compactness $\ell_{nth}/\ell_{th}$."
 Theindex of the injected non-thermal electrons was fixed at [inj=2.5 in all but 14 cases for which the fits resulted in 1«Γι«3., Theindex of the injected non-thermal electrons was fixed at $\Gamma_{\rm inj} = 2.5$ in all but 14 cases for which the fits resulted in $1 < \Gamma_{\rm inj} < 3$.
 The model is not very sensitive to the changes of the total compactness έιοι=£y+ές. TheEQPAIR, The model is not very sensitive to the changes of the total compactness $\ell_{tot} = \ell_h+\ell_s$.
 also accounts for a reflection of the hard X-rays from a cold medium (presumably an accretion disc)., The also accounts for a reflection of the hard X-rays from a cold medium (presumably an accretion disc).
 This reflected component is parametrized by the reflection amplitude and ionization parameter., This reflected component is parametrized by the reflection amplitude and ionization parameter.
" The complete model used in was defined asCONSTANT*WABS(DISKBB--EQPAIR), where allows for normalization between PCA and HEXTE data andWABS models the Galactic absorption with Ny fixed at 0.8x10??cm? (Done Gierlirisski 2003, and references therein)."," The complete model used in was defined as, where allows for normalization between PCA and HEXTE data and models the Galactic absorption with $N_H$ fixed at $\times 10^{22}$ $^{-2}$ (Done Gierlińsski 2003, and references therein)."
" The model is particularly well suited for our study because it allowes for straight forward scaling of the spectra between the accreting black holes of different mass by applying due corrections to the seed photons temperature, while keeping the geometry of accretion constant."," The model is particularly well suited for our study because it allowes for straight forward scaling of the spectra between the accreting black holes of different mass by applying due corrections to the seed photons temperature, while keeping the geometry of accretion constant."
 We modeled 94 hard state spectra of the outburst and 38 representative soft state spectra; 132 data sets in total., We modeled 94 hard state spectra of the outburst and 38 representative soft state spectra; 132 data sets in total.
 The times of the data sets that we used are indicated in Fig., The times of the data sets that we used are indicated in Fig.
" laa. We set a lower limit of 0.4 keV on the disc photons temperature,ΚΤω, and in the case of the hard"," \ref{fig:loop}a a. We set a lower limit of 0.4 keV on the disc photons temperature,$kT_{bb}$, and in the case of the hard"
the irregularly spaced ws identified as a modified /=3 mode.,the irregularly spaced $\nu_8$ identified as a modified $\ell\!=\!3$ mode.
" They have labelled these modified modes as /,,,=0. 1. 2 and 3. corresponding to the { value of the component that has the greatest Kinetic energy in the expansion of the eigenfunctions using the axisymmetric spherical harmonies Y,"""," They have labelled these modified modes as $l_m\!=\!0$ , $1$, $2$ and $3$, corresponding to the $\ell$ value of the component that has the greatest kinetic energy in the expansion of the eigenfunctions using the axisymmetric spherical harmonics $Y_{\ell}^{m=0}$."
" The amplitude modulation with rotation phase for modes of /,,=0. 1. 2 and 3 has been predicted (seeFig.8ofSaio.Ryabchikova&Sachkov 2010)."," The amplitude modulation with rotation phase for modes of $l_m\!=\!0$, $1$, $2$ and $3$ has been predicted \citep[see Fig.\,8 of][]{Saio10}."
. They assumed that the pulsation and magnetic axes in 11217 are aligned. with the magnetic geometry given by the parameters ὁ=1377. 3=1507. as determined by Bagnuloetal.(1995).," They assumed that the pulsation and magnetic axes in 1217 are aligned, with the magnetic geometry given by the parameters $i=137^{\circ}$, $\beta=150^{\circ}$, as determined by \citet{Bagnulo95}."
.. A single peak at the pulsation maximum. in phase with the magnetic maximum. is expected for the modified dipole. quadrupole and octopole modes.," A single peak at the pulsation maximum, in phase with the magnetic maximum, is expected for the modified dipole, quadrupole and octopole modes."
 For modified radial modes the amplitude modulation is smaller. with the pulsation maximum expected to occur at magnetic minimum.," For modified radial modes the amplitude modulation is smaller, with the pulsation maximum expected to occur at magnetic minimum."
 Does this theoretical model well explain the structure in the observed amplitude modulation?, Does this theoretical model well explain the structure in the observed amplitude modulation?
" All observed frequencies exhibit an amplitude modulation which. in general. peaks around the magnetic maximum. consistent with their being modes of /,,,=1. 2 or 3."," All observed frequencies exhibit an amplitude modulation which, in general, peaks around the magnetic maximum, consistent with their being modes of $l_m\!=\!1$, $2$ or $3$."
 However. more detailed structure is also observed.," However, more detailed structure is also observed."
 The modulation of £j and vx at some rotational cycles in 1986 is particularly hard to explain: a pulsation minimum is observed at magnetic maximum., The modulation of $\nu_1$ and $\nu_8$ at some rotational cycles in 1986 is particularly hard to explain: a pulsation minimum is observed at magnetic maximum.
" While this might seem to imply a radial mode geometry. pulsation maximum is not observed at magnetic minimum. but rather at the first and third quarter of the magnetic cycle. which is inconsistent with a /,,,=0 mode."," While this might seem to imply a radial mode geometry, pulsation maximum is not observed at magnetic minimum, but rather at the first and third quarter of the magnetic cycle, which is inconsistent with a $l_m\!=\!0$ mode."
" The best-fit model of 11217 by Saio.Ryabchikova&Sachkov(2010) does have /,,,20 and /,,,=1 modes closely spaced in frequency. and #7, is identified as an /,,,=1 mode in this model."," The best-fit model of 1217 by \citet{Saio10} does have $l_m\!=\!0$ and $l_m\!=\!1$ modes closely spaced in frequency, and $\nu_1$ is identified as an $l_m\!=\!1$ mode in this model."
" It is conceivable that 7, might behave as a combination of /,,,=0 and /,,,=1 modes.", It is conceivable that $\nu_1$ might behave as a combination of $l_m\!=\!0$ and $l_m\!=\!1$ modes.
" However. a linear combination of the /,,,=0 and /,,=1 modulation does not suffice to explain the observed modulation for 7, and vs."," However, a linear combination of the $l_m\!=\!0$ and $l_m\!=\!1$ modulation does not suffice to explain the observed modulation for $\nu_1$ and $\nu_8$."
" Furthermore. s is identified as an /,,,—3 mode in this model. and is well separated in frequency from the nearest radial mode."," Furthermore, $\nu_8$ is identified as an $l_m\!=\!3$ mode in this model, and is well separated in frequency from the nearest radial mode."
 Observed structure in the modulation that is more complex is even more difficult to explain by mode geometry distortion., Observed structure in the modulation that is more complex is even more difficult to explain by mode geometry distortion.
 If this is indeed the correct explanation. then it would appear that the distortion to the mode geometry can change over a remarkably short period of time. and a new mechanism would be required to explain this.," If this is indeed the correct explanation, then it would appear that the distortion to the mode geometry can change over a remarkably short period of time, and a new mechanism would be required to explain this."
 It is already well known that there is a phase difference between radial velocity variations and luminosity variations. basec on simultaneous spectroscopic and photometric observations of 11217 ¢Sachkovetal.2006:Ryabehikova2007) and other roAp stars (e.g.Sachkovetal.2008:Mkrtichian2008).," It is already well known that there is a phase difference between radial velocity variations and luminosity variations, based on simultaneous spectroscopic and photometric observations of 1217 \citep{Sachkov06, Ryab07} and other roAp stars \citep[e.g.][]{Sachkov08,Mkrtichian08}."
. There are also phase differences in the radial velocity variations of absorption lines of different elements which. due to chemica stratification in the atmosphere of roAp stars. may be attributed to depth effects (Ryabchikovaetal.2007).," There are also phase differences in the radial velocity variations of absorption lines of different elements which, due to chemical stratification in the atmosphere of roAp stars, may be attributed to depth effects \citep{Ryab07}."
. However. the rotationa phase lag observed between different modes in the wavelet analysis is different: a lag in the rotational modulation as opposed to a lag in the pulsations themselves.," However, the rotational phase lag observed between different modes in the wavelet analysis is different: a lag in the rotational modulation as opposed to a lag in the pulsations themselves."
 Magnetic Doppler imaging of 11217 by Lüftingeretal.(2010) found quite interesting elemental abundance patterns., Magnetic Doppler imaging of 1217 by \citet{Luftinger10} found quite interesting elemental abundance patterns.
 Regions of abundance enhancement or depletion were seen around either the rotation phase when the positive magnetic pole is visible. or where the magnetic equatorial region dominates the visible surface. depending on the chemical element.," Regions of abundance enhancement or depletion were seen around either the rotation phase when the positive magnetic pole is visible, or where the magnetic equatorial region dominates the visible surface, depending on the chemical element."
 Most interesting is that the enhancements for different elements were shifted in longitude relative to each other., Most interesting is that the enhancements for different elements were shifted in longitude relative to each other.
 Since the observations in 1986 and 2000 were in the photometric 72 band. a range of atmospheric depths was being observed.," Since the observations in 1986 and 2000 were in the photometric $B$ band, a range of atmospheric depths was being observed."
 The different modes have slightly different pulsation cavities. and amplitude and phase variations are strongly depth dependent in roAp stars in general. so it is plausible that this could explain the phase behaviour.," The different modes have slightly different pulsation cavities, and amplitude and phase variations are strongly depth dependent in roAp stars in general, so it is plausible that this could explain the phase behaviour."
 Once again. it seems that the phase difference can change over a short period of time.," Once again, it seems that the phase difference can change over a short period of time."
 It is apparent from a comparison of the amplitudes at maximum in both refcross| sGandsthal. inadditiontolhevariationinpowerductorotational fimescale," It is apparent from a comparison of the amplitudes at maximum in both \\ref{cross1_86} and \ref{cross1} that, in addition to the variation in power due to rotational modulation, the intrinsic amplitude of each mode varies over as short a timescale as one rotational period d)."
variationshacebeenobservedinolherroApstars. suchas 660435," Short-timescale variations have been observed in other roAp stars, such as 60435 \citep{Matthews87}."
(modi, It is difficult to resolve power variations on even shorter timescales for 1217 owing to the modulation caused by rotation.
," Could these power variations on timescales shorter than the rotation period be responsible for the behaviours that have been observed, namely structure in the rotation modulation and phase difference between modes?"
ul and vx bein, If the pulsation energy in a mode varies considerably over a few days then it is conceivable that this could result in the behaviour seen.
g at a minimum at both full and half rotation phase occasionally in. 1986. and a feature in 2000 in which. at the first pulsation maxima. several frequencies appear to show two distinct maxima.," We are then left, however, with several coincidences, such as $\nu_1$ and $\nu_8$ being at a minimum at both full and half rotation phase occasionally in 1986, and a feature in 2000 in which, at the first pulsation maxima, several frequencies appear to show two distinct maxima."
 While a change of power in the modes is certainly responsible for some of the observed features. it seems likely there are other processes involved as well.," While a change of power in the modes is certainly responsible for some of the observed features, it seems likely there are other processes involved as well."
 As previously mentioned. Kurtzetal.(2005). speculated that the total pulsational energy could be conserved. with nonlinear interactions transferring energy between modes.," As previously mentioned, \citet{Kurtz05a} speculated that the total pulsational energy could be conserved, with nonlinear interactions transferring energy between modes."
 reftotalpow shows the total power from all modes as a function of time., \\ref{totalpow} shows the total power from all modes as a function of time.
 While it can be seen that the power at maximum reaches approximately the same value at several maxima. both in 1986 and 2000. there are two notable exceptions. specifically the third maximum in 1986 which only reaches just over half the height of the other maxima. and the first maximum in 2000. which exhibits the previously mentioned double peak.," While it can be seen that the power at maximum reaches approximately the same value at several maxima, both in 1986 and 2000, there are two notable exceptions, specifically the third maximum in 1986 which only reaches just over half the height of the other maxima, and the first maximum in 2000, which exhibits the previously mentioned double peak."
 Caution is required in relating pulsation power to the pulsation energy. the determinationof which requires a complete characterisation of the modes.," Caution is required in relating pulsation power to the pulsation energy, the determinationof which requires a complete characterisation of the modes."
 We have reanalysed the 1986 and 2000 multisite photometric observations of the roAp star 11217. using a weighting scheme to minimize the noise level.," We have reanalysed the 1986 and 2000 multisite photometric observations of the roAp star 1217, using a weighting scheme to minimize the noise level."
 Despite the improvement in the noise level. the ‘missing’ frequencies ο and v> are still not detectable in," Despite the improvement in the noise level, the `missing' frequencies $\nu_6$ and $\nu_7$ are still not detectable in"
"Equation (29)) is obtained by eliminating Z,4 aud J,, from equation (26)) aud equation (28)).",Equation \ref{ieq4}) ) is obtained by eliminating $I_{n+1}^{+}$ and $I_{n+1}^{-}$ from equation \ref{ieq2a}) ) and equation \ref{ieq3a}) ).
 We can write r aud / operators for the composite cell as aud where J is the identity matrix and aud Similarly. MQ+L.02) is define.," We can write $r 
$ and $t$ operators for the composite cell as and where $I$ is the identity matrix and and Similarly, $\Sigma(n+1,n+2)$ is defined."
 Iu order to obtain plivsical interpretation of the equatious (31)) - (31)) we expand the operator inverse lu a power series., In order to obtain physical interpretation of the equations \ref{ieq5a}) ) - \ref{ieq5b}) ) we expand the operator inverse in a power series.
 For exatple.," For example,"
the production rate of accreting white dwarfs. but find that in their. globular cluster models. the accreting white dwarfs are heavier. and so more likely to be SNIa progenitors.,"the production rate of accreting white dwarfs, but find that in their globular cluster models, the accreting white dwarfs are heavier, and so more likely to be SNIa progenitors."
 Other studies have predicted higher numbers of accreting white dwarfs (??).. corresponding to 7=5. but did not consider SNIa progenitors specifically.," Other studies have predicted higher numbers of accreting white dwarfs \citep{DiStefano1994,Davies1995}, corresponding to $\eta$ =5, but did not consider SNIa progenitors specifically."
 ? find no enhancement of double white dwarf binaries. but this study does not discuss SNla progenitors specifically.," \citet{Shara2006} find no enhancement of double white dwarf binaries, but this study does not discuss SNIa progenitors specifically."
 ? find an enhancement of merging double white dwarfs above the Chandrasekhar mass of ή=3- 13 compared to a field population with the same metallicity and age as the population in the globular clusters. but no significant enhancement (jj=0.3- 1.2) when compared to field population with solar metallicity.," \citet{Ivanova2006} find an enhancement of merging double white dwarfs above the Chandrasekhar mass of $\eta=$ 3-13 compared to a field population with the same metallicity and age as the population in the globular clusters, but no significant enhancement $\eta=0.3-1.2$ ) when compared to field population with solar metallicity."
 For the SD scenario. an alternative approach is to compare to observations of similar systems.," For the SD scenario, an alternative approach is to compare to observations of similar systems."
 This is not possible for the DD scenario. due to a lack of observational systems to compare to.," This is not possible for the DD scenario, due to a lack of observational systems to compare to."
 With their accreting massive white dwarfs. SD SNla progenitors are somewhat similar to cataclysmic variables (CVs) and LMXBs in their formation and evolution.," With their accreting massive white dwarfs, SD SNIa progenitors are somewhat similar to cataclysmic variables (CVs) and LMXBs in their formation and evolution."
 The bright LMXB population in globular clusters is quite well studied. as they can be seen to large distances with Chandra. and they have been found to be over-abundant by a factor of ~ 100 (22??)..," The bright LMXB population in globular clusters is quite well studied, as they can be seen to large distances with Chandra, and they have been found to be over-abundant by a factor of $\sim$ 100 \citep{Clark1975,Sarazin2003,Jordan2007,Voss2009}."
 The CV population is much less understood. as they are much harder to identify.," The CV population is much less understood, as they are much harder to identify."
 Only a small sample has been found in recent years. consistent with an over-production by a factor of «few (e.g.222).. but completeness is à serious issue. and higher enhancement factors are therefore not ruled out.," Only a small sample has been found in recent years, consistent with an over-production by a factor of $\sim$ few \citep[e.g.][]{Pooley2006,Dieball2007,Knigge2008}, but completeness is a serious issue, and higher enhancement factors are therefore not ruled out."
 Observations of novae in M31 suggests en enhancement factor of «10 (2).., Observations of novae in M31 suggests en enhancement factor of $\sim$ 10 \citep{Henze2009}.
 The SD SNIa progenitors have white dwarfs with masses near Mc. more similar to the masses of neutron stars than to those of most CVs.," The SD SNIa progenitors have white dwarfs with masses near $M_C$, more similar to the masses of neutron stars than to those of most CVs."
 They therefore sink the the center more easily and experience more dynamical encounters than more typical white dwarf systems. which leads to a higher expected enhancement.," They therefore sink the the center more easily and experience more dynamical encounters than more typical white dwarf systems, which leads to a higher expected enhancement."
 From the discussion above we conclude that 77 is most likely greater than one and lowerthan 10., From the discussion above we conclude that $\eta$ is most likely greater than one and lowerthan 10.
 However. it is clear that the results are very poorly constrained. and models with 7 outside this range can not be discarded.," However, it is clear that the results are very poorly constrained, and models with $\eta$ outside this range can not be discarded."
 It is therefore important to constrain this fraction from observations., It is therefore important to constrain this fraction from observations.
 Besides 7. the fraction of SNlae that explodes in globular clusters also depends on the fraction of stellar mass that resides in the globular clusters. μου=Μα. where Mec is the total mass of the population of globular clusters and M; is the total mass of all the other stars.," Besides $\eta$, the fraction of SNIae that explodes in globular clusters also depends on the fraction of stellar mass that resides in the globular clusters, $F_{M,GC}=M_{GC}/M_{F}$, where $M_{GC}$ is the total mass of the population of globular clusters and $M_{F}$ is the total mass of all the other stars."
 For a sample of N SNlae. the expected number that explodes in globular clusters 1s then: The mass fraction Fayce varies strongly between galaxies.," For a sample of $N$ SNIae, the expected number that explodes in globular clusters is then: The mass fraction $F_{M,GC}$ varies strongly between galaxies."
 The Milky Way has a low abundance of globular clusters. with Fapg¢e~0.15€ (e.g.thecatalogueof?)..," The Milky Way has a low abundance of globular clusters, with $F_{M,GC}\sim0.1$ \citep[e.g. the catalogue of][]{Harris1996}."
 Therefore only ~10% of the Milky Way LMXBs (seee.g.?).. and based on the considerations above. probably ~1% of the CVs. are in globular clusters.," Therefore only $\sim10$ of the Milky Way LMXBs \citep[see e.g.][]{Liu2007}, and based on the considerations above, probably $\sim1$ of the CVs, are in globular clusters."
 This is in stark contrast to many elliptical galaxies with rich globular cluster systems. where in some cases Fajcoc can be larger than (e.g.?).. and the majority of bright LMXBs are in globular clusters (2)..," This is in stark contrast to many elliptical galaxies with rich globular cluster systems, where in some cases $F_{M,GC}$ can be larger than \citep[e.g.][]{Harris1999}, and the majority of bright LMXBs are in globular clusters \citep{Angelini2001}."
 Correspondingly. if the SNIa enhancement is a factor of 10. about of the SNlae in these galaxies must be formed in globular clusters.," Correspondingly, if the SNIa enhancement is a factor of 10, about of the SNIae in these galaxies must be formed in globular clusters."
 Averaging over the population of nearby galaxies yields a fraction of SNlae in globular clusters of ~1—3-1075 (2).. most likely a few per cent.," Averaging over the population of nearby galaxies yields a fraction of SNIae in globular clusters of $\sim1-3\cdot10^{-3}\eta$ \citep{Pfahl2009}, most likely a few per cent."
 A complicating factor that was not taken into account in previous studies is the fact that the rate of type [a supernovae Roar decreases with age for a coeval population of stars., A complicating factor that was not taken into account in previous studies is the fact that the rate of type Ia supernovae $R_{SNIa}$ decreases with age for a coeval population of stars.
 In general the distribution of globular cluster ages is different from that of the field stars., In general the distribution of globular cluster ages is different from that of the field stars.
 Therefore where {ος is the age of the globular clusters and f£; 1s the age of the field stars., Therefore where $t_{GC}$ is the age of the globular clusters and $t_{f}$ is the age of the field stars.
 For early-type galaxies ος~fj. whereas the bulk of the field population of late-type galaxies tends to be significantly younger than the globular cluster population.," For early-type galaxies $t_{GC}\sim t_f$, whereas the bulk of the field population of late-type galaxies tends to be significantly younger than the globular cluster population."
 Yeo 18 the globular cluster enhancement per unit stellar mass. compared to a field population of age.," $\eta_{co}$ is the globular cluster enhancement per unit stellar mass, compared to a field population of ."
 The exact shape of the delay-time distribution (DTD. the SNIa rate as a function of time for a coeval population of stars) is not known. but it has been shown to decrease strongly by a factor of >10 from young environments «1 Gyr to older environments ~10 Gyr (e.g.?)..," The exact shape of the delay-time distribution (DTD, the SNIa rate as a function of time for a coeval population of stars) is not known, but it has been shown to decrease strongly by a factor of $>10$ from young environments $<$ 1 Gyr to older environments $\sim10$ Gyr \citep[e.g.][]{Maoz2010}."
 Therefore ~50-85% of all type la supernovae explode within the first Gyr after star formation (e.g.?).., Therefore $\sim$ of all type Ia supernovae explode within the first Gyr after star formation \citep[e.g.][]{Maoz2010}.
 However. the current star-formation density is much lower than at redshifts I. and comparing the local rate of star formation ? to the stellar mass density ?? leads to a fraction of stars in the local universe that were formed less than | Gyr ago of ~2%.," However, the current star-formation density is much lower than at redshifts 1, and comparing the local rate of star formation \citet{Hanish2006} to the stellar mass density \citet{Salucci1999,Cole2001} leads to a fraction of stars in the local universe that were formed less than 1 Gyr ago of $\sim2$."
. Despite the high fraction of prompt SNlae for a population of stars. the local population will therefore be dominated by the tardy component.," Despite the high fraction of prompt SNIae for a population of stars, the local population will therefore be dominated by the tardy component."
 Combining the fractions found by ? with the local rate of star formation ? and stellar mass density ??.. only x20 per cent of the local SNlae are expected to belong to the prompt component.," Combining the fractions found by \citet{Sullivan2006} with the local rate of star formation \citet{Hanish2006} and stellar mass density \citet{Salucci1999,Cole2001}, only $\lesssim20$ per cent of the local SNIae are expected to belong to the prompt component."
 For most local galaxies. the ratio Λου=PSBusputo) will therefore be higher than what could be expected from the DTD.," For most local galaxies, the ratio $R_{GC/F}=\frac{R_{SNIa}(t_{GC})}{R_{SNIa}(t_{f})}$ will therefore be higher than what could be expected from the DTD."
 It is typically in the range ~0.1—I., It is typically in the range $\sim0.1-1$.
 For early-type galaxies. the typical age of the field population is similar to the age of the globular clusters. and therefore Λου~1.," For early-type galaxies, the typical age of the field population is similar to the age of the globular clusters, and therefore $R_{GC/F}\sim1$."
 Late-type galaxies can have significant populations of young stars for which the SNIa rate is more than a magnitude higher than for the old population of stars in their globular clusters., Late-type galaxies can have significant populations of young stars for which the SNIa rate is more than a magnitude higher than for the old population of stars in their globular clusters.
 However. the vast majority of late-type galaxies also have older stellar components. and Rec; will therefore almost always be higher than 0.1.," However, the vast majority of late-type galaxies also have older stellar components, and $R_{GC/F}$ will therefore almost always be higher than 0.1."
 The association of type Ia supernovae with globular clusters relies on the spatial coincidence., The association of type Ia supernovae with globular clusters relies on the spatial coincidence.
 If a type la supernova is found to have exploded at the same position as a globular cluster. it have exploded inside the globular cluster.," If a type Ia supernova is found to have exploded at the same position as a globular cluster, it have exploded inside the globular cluster."
 If not. then a globular cluster origin is definitely excluded.," If not, then a globular cluster origin is definitely excluded."
 However.the distribution of GC luminosities is wide. and many observations are only sensitive to the bright end of the GC luminosity function.," However,the distribution of GC luminosities is wide, and many observations are only sensitive to the bright end of the GC luminosity function."
 ? showed that for 7=10 approximately of all," \citet{Pfahl2009}
 showed that for $\eta$ =10 approximately of all"
only to address the time evolution of high energy radiation. but also to use it as an age calibrator when the stellar high- emissions can be measured.,"only to address the time evolution of high energy radiation, but also to use it as an age calibrator when the stellar high-energy emissions can be measured."
 This age indicator is very interesting because it will be based on the star's own properties and will be useful in a regime (>| , This age indicator is very interesting because it will be based on the star's own properties and will be useful in a regime $>1$ 
a).,a).
 As [our examples are not statistically relevant. we have carried out an analvsis of the differences between (he reconstructed ancl original spectra lor 5000 stars chosen at random from the seventh data release of the SDSS (Abazajianetal.2009).," As four examples are not statistically relevant, we have carried out an analysis of the differences between the reconstructed and original spectra for 5000 stars chosen at random from the seventh data release of the SDSS \citep{abazajian09}."
. We have verified that a sample of (hiis size chosen at random covers all y—r bins and provides reliable statistics., We have verified that a sample of this size chosen at random covers all $g-r$ bins and provides reliable statistics.
 The quality is characterized. al each wavelength. by the 5th. 50th and 95th percentile of the distribution of relative errors [rom (he reconstructed spectrum aud (he original one.," The quality is characterized, at each wavelength, by the 5th, 50th and 95th percentile of the distribution of relative errors from the reconstructed spectrum and the original one."
 The results are shown in the upper-left panel of Fig. 5.., The results are shown in the upper-left panel of Fig. \ref{fig:statistical_difference}.
 As stated. the 50th percentile (the median) is represented as a black curve and indicates that half of the stars can be reconstructed with relative errors smaller (han (rom «4200 to 9000 A)).," As stated, the 50th percentile (the median) is represented as a black curve and indicates that half of the stars can be reconstructed with relative errors smaller than (from $\sim$ 4200 to 9000 )."
 The 5th and 95th percentiles (blue and red curves) are also indicated in the upper left panel of Fig. 5.., The 5th and 95th percentiles (blue and red curves) are also indicated in the upper left panel of Fig. \ref{fig:statistical_difference}.
 Ht is demonstrated that (he reconstructions can be done with relative errors well below [or of the stars., It is demonstrated that the reconstructions can be done with relative errors well below for of the stars.
 OF course. (his does not rule out the presence of of the stars with relative reconstruction errors potentially larger than 1054.," Of course, this does not rule out the presence of of the stars with relative reconstruction errors potentially larger than ."
.. For reference. in Fig.," For reference, in Fig."
 5 reconstructions with the first three (lower left panel) aud four (lower right panel) principal components as obtained from MeGurketal.(2010) are compared with the original spectra., \ref{fig:statistical_difference} reconstructions with the first three (lower left panel) and four (lower right panel) principal components as obtained from \cite{mcgurk10} are compared with the original spectra.
 These plots summarize the quality of the PCA recreations., These plots summarize the quality of the PCA recreations.
 Although PCA reconstructions wilh relative errors below or of the order of are possible for of the stars. a fraction of stellar spectra will incur (even knowing exactly (he projections along the principal components) relative errors larger thanLOY.," Although PCA reconstructions with relative errors below or of the order of are possible for of the stars, a fraction of stellar spectra will incur (even knowing exactly the projections along the principal components) relative errors larger than."
.. Note also that the improvement on (he reconstruction is marginal when using four instead of three principal components., Note also that the improvement on the reconstruction is marginal when using four instead of three principal components.
 An inclication of the quality of the PCA reconstruction is that the difference between the initial magnitudes and the reconstructed magnitudes has a standard deviation of 0.008 for g. r and ;/ when using 4 principal components.," An indication of the quality of the PCA reconstruction is that the difference between the initial magnitudes and the reconstructed magnitudes has a standard deviation of 0.008 for $g$, $r$ and $i$ when using 4 principal components."
 When using only one principal component. this number increases up to 0.03 lor gy and r and to 0.05 [or 7.," When using only one principal component, this number increases up to 0.03 for $g$ and $r$ and to 0.05 for $i$."
 It is important to realize that the residuals shown in Fig., It is important to realize that the residuals shown in Fig.
 5 are significantly hieher for wavelengths with lines than in continuum regions., \ref{fig:statistical_difference} are significantly higher for wavelengths with lines than in continuum regions.
 This suggests that the PCA reconstruction is reproducing well the continuum shape. but not so the lines’ strength.," This suggests that the PCA reconstruction is reproducing well the continuum shape, but not so the lines' strength."
 However. lines are crucial for recovering information on surface gravitv and chemical composition.," However, lines are crucial for recovering information on surface gravity and chemical composition."
 A possibility for improvement is therefore to perlorm PCA on continuun-corrected spectra., A possibility for improvement is therefore to perform PCA on continuum-corrected spectra.
 If iusteacl of using the original spectra as reference. reconstructions are compared with the spectra projected onto the space spanned by the first three principal components. the results are (hose shown in the upper right panel of Fig. 5..," If instead of using the original spectra as reference, reconstructions are compared with the spectra projected onto the space spanned by the first three principal components, the results are those shown in the upper right panel of Fig. \ref{fig:statistical_difference}."
 It is clear from this plot Chat our method is able to reliably extract the projection along the first three principalcomponents from photometric information., It is clear from this plot that our method is able to reliably extract the projection along the first three principalcomponents from photometric information.
results from the effects of dust obscuration in and around (he starlorminge regions. particularly for those techniques which depend upon optical or UV data (seethereviewbyCalzetti2001).,"results from the effects of dust obscuration in and around the star-forming regions, particularly for those techniques which depend upon optical or UV data \citep[see the review by][]{Calzetti01}."
. A fairly direct technique. which has enjoved extensive use in the determination of star formation rates. is the measurement of hydrogen recombination line fluxes (BellοMaddox1998:Pascualοἱal.2001:Yanet1999:Dopita2002b..(onamebuta lew).," A fairly direct technique, which has enjoyed extensive use in the determination of star formation rates, is the measurement of hydrogen recombination line fluxes \citep[][ to name but
a few]{Bell01,Gallego95,Jones01, Moorwood00,Tresse98,Pascual01,Yan99,Dopita02b}."
 Provided that the rreeion can absorb all the EUV photons produced by (he central star. this should be a reliable technique. since the flux in anv hydrogen line is simply. proportional to (he number of photons produced by (he hot stars. which is proportional to the birthrate of massive stars.," Provided that the region can absorb all the EUV photons produced by the central star, this should be a reliable technique, since the flux in any hydrogen line is simply proportional to the number of photons produced by the hot stars, which is proportional to the birthrate of massive stars."
 This relationship has been well calibrated at solar metallicity for the Ha line 1993): There exist a number of wavs in which this relationship might break down.," This relationship has been well calibrated at solar metallicity for the $\alpha $ line \citep{Dopita94,Kennicutt98}: There exist a number of ways in which this relationship might break down."
 First. the rreeion might be optically-thin to the EUV photons in some directions.," First, the region might be optically-thin to the EUV photons in some directions."
 In this case the recombination [Iux will provide an underestimate of the star formation rate. and the appropriate correction [actor is difficult to estimate.," In this case the recombination flux will provide an underestimate of the star formation rate, and the appropriate correction factor is difficult to estimate."
 Second. there may be dust in front of the rregion which both reddens and absorbs the recombination lines.," Second, there may be dust in front of the region which both reddens and absorbs the recombination lines."
 In this case. the corrections for dust absorption can be made using a loreground screen approximation.," In this case, the corrections for dust absorption can be made using a foreground screen approximation."
 This appears to work extraordinarily well in many galaxies (Dell&Kennicutt2001:Dopitaetal.2002b:Kewley&Dopita 2002).," This appears to work extraordinarily well in many galaxies \citep{Bell01, Dopita02b,Kewley02}."
. Third. dust may be contained in dense. oplically-Chick. clouds within or surrounding the rreeion.," Third, dust may be contained in dense, optically-thick, clouds within or surrounding the region."
 In this case the optical recombination lines are entirely absorbed in lines of sieht passing through foreground clouds., In this case the optical recombination lines are entirely absorbed in lines of sight passing through foreground clouds.
" However. the radio thermal continuum is transmitted by such clouds. so this factor can be estimated as a 7""grev screen by comparison of the optical and the radio data."," However, the radio thermal continuum is transmitted by such clouds, so this factor can be estimated as a “grey” screen by comparison of the optical and the radio data."
 Such clouds will re-emit the incident radiation in the far-IR. ancl this emission mav also be used to estimate the stellar EUV thus., Such clouds will re-emit the incident radiation in the far-IR and this emission may also be used to estimate the stellar EUV flux.
 A fourth possibility is that dust within the ionized gas itself competes with the gas to absorb the EUV photons from the central star(s)., A fourth possibility is that dust within the ionized gas itself competes with the gas to absorb the EUV photons from the central star(s).
 This possibilitv. first seriously equantified by Petrosian.Silk&Field(1972).. has been cliscussecl by a number of authors since (PanagiaShields&Iwennicutt1995:Bottorlfetal. 1993).," This possibility, first seriously quantified by \citet{Petrosian72}, has been discussed by a number of authors since \citep{Panagia74, Mezger74,
Natta76, Sarazin77, Smith78, Shields95, Bottorff98}."
. More recently ils effect has investigated and quantiliecl (as far as possible by direct observation) im a series of recent. papers bv Inoue and his collaborators, More recently its effect has investigated and quantified (as far as possible by direct observation) in a series of recent papers by Inoue and his collaborators
nunmber counts and color-magnitude distribution for various classes of objects.,number counts and color-magnitude distribution for various classes of objects.
 We have used published template SEDs. huminosity lunctions and general evolution models for ellipticals. spirals. and starbursts. as well as Type 1l and Type 2 AGN.," We have used published template SEDs, luminosity functions and general evolution models for ellipticals, spirals, and starbursts, as well as Type 1 and Type 2 AGN."
 For ellipticals. spirals and slavburst/lin galaxies we used templates from Coleman et al. (," For ellipticals, spirals and starburst/Im galaxies we used templates from Coleman et al. ("
1980) at optical wavebancds. combined with multiwaveband data from Schmitt et al. (,"1980) at optical wavebands, combined with multiwaveband data from Schmitt et al. ("
1997) extending up to X-ray energies.,1997) extending up to X-ray energies.
 For Type | AGN we used composite spectra from Cristiani Vio (1990) supplemented again bv Sehimitt οἱ al. (, For Type 1 AGN we used composite spectra from Cristiani Vio (1990) supplemented again by Schmitt et al. (
1997) for X-ray energies. while our Type 2 AGN template was taken from Della Ceca et al. (,"1997) for X-ray energies, while our Type 2 AGN template was taken from Della Ceca et al. ("
2000).,2000).
 For the non-active galaxies we adopted the same Iuminosity function and evolution as determined by Loveday et al. (, For the non-active galaxies we adopted the same luminosity function and evolution as determined by Loveday et al. (
1992). while lor the AGN we used the Type 1 luminosity [funetion and evolution recently determined by Bovle et al. (,"1992), while for the AGN we used the Type 1 luminosity function and evolution recently determined by Boyle et al. ("
2000).,2000).
 We applied ihe Tvpe 1 LF to the Type 2 AGN by assuming that the ratio of Type 1/2 remains constant with redshift. is determined by a torus with opening angle 607. and (hat the emission from the torus is isotropic at GO jan (thus normalizing the SEDs at this frequenev).," We applied the Type 1 LF to the Type 2 AGN by assuming that the ratio of Type 1/2 remains constant with redshift, is determined by a torus with opening angle $\arcdeg$, and that the emission from the torus is isotropic at 60 $\mu$ m (thus normalizing the SEDs at this frequency)."
 These are all fairly extreme oversimplilications. and we will present more detailed modelling in IXoekemoer (2001) in the context of the entire set of sources from the 940 ksec catalog.," These are all fairly extreme oversimplifications, and we will present more detailed modelling in Koekemoer (2001) in the context of the entire set of sources from the 940 ksec catalog."
 For the moment. however. we note that (he results are not dramatically sensitive to details such as the precise ratio of Tvpe 1/2 (and whether it varies with redshift).," For the moment, however, we note that the results are not dramatically sensitive to details such as the precise ratio of Type 1/2 (and whether it varies with redshift)."
 We simulated the expected fluxes in the optical using the filter throughput curves for HST/WEDCO?2. and similarly the Chandra fluxes in the soft ancl hard bands were simulated. using the available sensitivity cata [or ACIS-I as a function of energy.," We simulated the expected fluxes in the optical using the filter throughput curves for /WFPC2, and similarly the Chandra fluxes in the soft and hard bands were simulated using the available sensitivity data for ACIS-I as a function of energy."
 In Figure 5.. we present (he histogram of the J magnitude distribution of the observed optical counterparts of the Chandra sources. along with predicted curves (to be discussed in more detail our forthcoming paper) lor ellipticals. spirals. starbursts. and AGN. based on the above models. an area of sky corresponding to our three WEDPC? fields(a total of τι] arcmin?). and detection thresholds for the 300B ksec Chandra. X-ray. data as described bv Tozzi οἱ al. (," In Figure \ref{fig:popns}, we present the histogram of the $I$ magnitude distribution of the observed optical counterparts of the Chandra sources, along with predicted curves (to be discussed in more detail our forthcoming paper) for ellipticals, spirals, starbursts, and AGN, based on the above models, an area of sky corresponding to our three WFPC2 fields(a total of 17.1 $^2$ ), and detection thresholds for the 300 ksec Chandra X-ray data as described by Tozzi et al. ("
2001).,2001).
 We also show the sum of the contributions from each tvpe., We also show the sum of the contributions from each type.
 It is clearfrom the predictions in Figure 5. that the majority of the N-rav. source optical counterparts are expected to be relatively bright. as observed.," It is clearfrom the predictions in Figure \ref{fig:popns} that the majority of the X-ray source optical counterparts are expected to be relatively bright, as observed."
 The eroup includes ellipticals. spirals. starbursts. and Tvpe 1 and Type 2 AGN.," The group includes ellipticals, spirals, starbursts, and Type 1 and Type 2 AGN."
 More interesting. the optically faint population (JZ24— 25) of X-ray source counterparts is expected to consist only of higher-redshift Type 2 AGN (2~ 2).," More interesting, the optically faint population $I\gtrsim 24 - 25$ ) of X-ray source counterparts is expected to consist only of higher-redshift Type 2 AGN $z \sim 2$ )."
 Furthermore. the models suggest that these would be softer than their lower-redshift counterparts. by virtue of the predicted higher redshifts causing more X-rav emission to be shifted into the soft. band.," Furthermore, the models suggest that these would be softer than their lower-redshift counterparts, by virtue of the predicted higher redshifts causing more X-ray emission to be shifted into the soft band."
 This prediction agrees with (he observed. X-ray hardness ratios: the optically faint sources are not as hard in (he X-rays as the optically brighter ones., This prediction agrees with the observed X-ray hardness ratios: the optically faint sources are not as hard in the X-rays as the optically brighter ones.
" Moreover. the one object in this [aint group for which we have a preliminary redshilt (J033208.2—214153) is à NELG with 2:=2.45. leading to an X-ray huninosity estimate of &3x107Ἱ erg !, in the rest frame enerev range of 1.7—35 keV."," Moreover, the one object in this faint group for which we have a preliminary redshift $-$ 274153) is a NELG with $z=2.45$, leading to an X-ray luminosity estimate of $ \approx
3\times 10^{43}$ erg $^{-1}$ , in the rest frame energy range of $1.7-35\,{\rm keV}$ ."
Emploving the EO5s described briefly in Section 2. we compute the neutron star moment of inertia with the RAS! code developed and made available to the publie by Nikolaos stergioulas (Stergioulas&Friedman1995)..,"Employing the EOSs described briefly in Section 2, we compute the neutron star moment of inertia with the $RNS$ code developed and made available to the public by Nikolaos Stergioulas \citep{Stergioulas:1994ea}."
 The code solves the hvdrostatie and Einstein's [ield equations for mass distributions rotating rigidly under the assumption of stationary ancl axial symmetry. about. Che rotational axis. and reflectional svaumetry. about the equatorial plane.," The code solves the hydrostatic and Einstein's field equations for mass distributions rotating rigidly under the assumption of stationary and axial symmetry about the rotational axis, and reflectional symmetry about the equatorial plane."
" RNS calculates the angular momentum J as (Stergioulas2003) where 77"" is the energv-monmentum tensor of stellar matter S Is Ue INilling vector in azimuthal direction rellecting axial symmetry. and is a proper 3-volume element (gy=det(y,;) is thedeterminant of the 3-metric)."," $RNS$ calculates the angular momentum $J$ as \citep{Stergioulas:2003yp}
 where $T^{\mu\nu}$ is the energy-momentum tensor of stellar matter $\xi^{\nu}_{(\phi)}$ is the Killing vector in azimuthal direction reflecting axial symmetry, and $dV=\sqrt{-g}d^3x$ is a proper 3-volume element $g\equiv \det(g_{\alpha\beta})$ is thedeterminant of the 3-metric)."
 In Eq. (9)), In Eq. \ref{eq.2}) )
" P is the pressure. € is the mass-enerey clensitv. and 4 is the unit tnme-like satislying uu,=—1."," $P$ is the pressure, $\epsilon$ is the mass-energy density, and $u^\mu$ is the unit time-like four-velocity satisfying $u^{\mu}u_{\mu}=-1$."
 For axial-symmetrie stars it takes the form w=ul(1.0.0.0). where Q is (he stars angular velocity.," For axial-symmetric stars it takes the form $u^{\mu}=u^t(1,0,0,\Omega)$, where $\Omega$ is the star's angular velocity."
 Under this condition Eq. (8)), Under this condition Eq. \ref{eq.1}) )
 reduces to It should be noted that the moment of inertia cannot be caleulated directly as an integral quantity over the source of gravitational field (Stergioulas2003).., reduces to It should be noted that the moment of inertia cannot be calculated directly as an integral quantity over the source of gravitational field \citep{Stergioulas:2003yp}.
 In addition. there exists no unique generalization of the Newtonian definition of the moment of inertia in General Relativity and therelore 7=//Q is a natural choice for caleulating this important quantity.," In addition, there exists no unique generalization of the Newtonian definition of the moment of inertia in General Relativity and therefore $I=J/\Omega$ is a natural choice for calculating this important quantity."
 For rotational frequencies much lower than the lxepler frequency (the highest possible rotational rate supported by a given EOS). Le. fi.<<1 (v= O/(2x)). the deviations from spherical svnuuetry are very small. so Chat Cie moment of inertia can be approximated from spherical stellar models.," For rotational frequencies much lower than the Kepler frequency (the highest possible rotational rate supported by a given EOS), i.e. $\nu/\nu_k<<1$ $\nu=\Omega/(2\pi)$ ), the deviations from spherical symmetry are very small, so that the moment of inertia can be approximated from spherical stellar models."
 In what follows we review briefly this slow-rotation approximation. see e.g. (IIartle 1967)..," In what follows we review briefly this slow-rotation approximation, see e.g. \citep{Hartle:1967he}. ."
 In (the slow-rotational limit the metric can be written in spherical coordinates as (in geomeltrized units G=¢ 1), In the slow-rotational limit the metric can be written in spherical coordinates as (in geometrized units $G=c=1$ )
"For each experiment listed in the previous section, we obtain p(nr|d,H1) by analyzing simulated data generated from the model 1.","For each experiment listed in the previous section, we obtain $p(n_T|{\bf d},\mathcal{H}_1)$ by analyzing simulated data generated from the model $\mathcal{H}_1$."
" We assign the base cosmological parameters the fiducial values Q,h?= 0.022, Q.h?=0.105, 0,=1.04, T=0.09, A,=2.23x1079, n,= 0.97, r=0.1, and simulate a different dataset asnr is incremented in steps of |δ,,|=0.1 across the prior range nr€[—0.5,0.5]°."," We assign the base cosmological parameters the fiducial values $\Omega_b
h^2 = 0.022$ , $\Omega_c h^2 = 0.105$ , $\theta_s = 1.04$, $\tau = 0.09$, $A_s = 2.23\times 10^{-9}$, $n_s = 0.97$ $r = 0.1$ , and simulate a different dataset as$n_T$ is incremented in steps of $|\delta_{n_T}|= 0.1$ across the prior range $n_T \in
[-0.5,0.5]$."
". We use MCMC to constrainr and nr for each dataset; since the base parameters QA?, Q-h?, 0,, T, As, and n, have little effect on the B-mode signal, we only vary r and nr within the chains."," We use MCMC to constrain$r$ and $n_T$ for each dataset; since the base parameters $\Omega_bh^2$, $\Omega_c h^2$ , $\theta_s$, $\tau$, $A_s$, and $n_s$ have little effect on the B-mode signal, we only vary $r$ and $n_T$ within the chains."
" The theoretical temperature and polarization C;- spectra are generated out to /—2000 with footnotehttp:/(Lewisetal. /camb.info2000), and the parameter estimation is performed using (Lewis&Bridle 2002).."," The theoretical temperature and polarization $C_\ell$ -spectra are generated out to $\ell=2000$ with \citep{Lewis:1999bs}, , and the parameter estimation is performed using \citep{Lewis:2002ah}."
" For each dataset, convergence is measured across four chains using the Gelman-Rubin R statistic."," For each dataset, convergence is measured across four chains using the Gelman-Rubin R statistic."
" The constraints on r and nr are in general correlated, but the parameter uncertainties can be minimized by choosing the pivot scale corresponding to the multipole at which they become uncorrelated, k.10ΊΜρε-16.."," The constraints on $r$ and $n_T$ are in general correlated, but the parameter uncertainties can be minimized by choosing the pivot scale corresponding to the multipole at which they become uncorrelated, $k_* \simeq 10^{-4}{\rm
Mpc}^{-1}\ell_*$."
" This pivot scale depends on the data, and will be different for each experiment: @,= 10,30,65,150, and 300 for Planck, Planck+PolarBear, Planck--QUIET (II), CMBPol, and the ideal experiment (Zhao&Baskaran2009;ZhaoZhang 2009)."," This pivot scale depends on the data, and will be different for each experiment: $\ell_* = 10, 30, 65, 150,$ and 300 for Planck, Planck+PolarBear, Planck+QUIET (II), CMBPol, and the ideal experiment \citep{Zhao:2009mj,Zhao:2009rt}."
" By constraining r(k.), we minimize the effects of correlations. in our comparisonsof constraints across experiments."," By constraining $r(k_*)$, we minimize the effects of correlations in our comparisonsof constraints across experiments."
 We present results in Figure 3 and Table 1., We present results in Figure 3 and Table 1.
" In Figure 3, the data points represent the actual evaluations of InBoi; the curves are obtained via quadratic regression."," In Figure 3, the data points represent the actual evaluations of $\ln B_{01}$; the curves are obtained via quadratic regression."
" The gray shaded region, nr>0.15, is ruled out by nucleosynthesis constraints on the energy density of gravitational waves with power law spectra (Stewart&Brandenberger2008).."," The gray shaded region, $n_T > 0.15$, is ruled out by nucleosynthesis constraints on the energy density of gravitational waves with power law spectra \citep{Stewart:2007fu}."
" We find that Planck by itself will not find decisive (strong) evidence for nrZ0 unless [nz|>0.5 (0.43); in combination with PolarBear and QUIET (II) these same levels of evidence are achieved for |nr|z0.36 (0.28) and 0.29 (0.25), respectively."," We find that Planck by itself will not find decisive (strong) evidence for $n_T \neq 0$ unless $|n_T| > 0.5$ (0.43); in combination with PolarBear and QUIET (II), these same levels of evidence are achieved for $|n_T| \approx 0.36$ (0.28) and $0.29$ (0.25), respectively."
 These detection thresholds are ruled out for power law spectra., These detection thresholds are ruled out for power law spectra.
" The constraint from nucleosynthesis should, however, be applied with care since the assumption of a power law tensor spectrum is not alwaysate?."," The constraint from nucleosynthesis should, however, be applied with care since the assumption of a power law tensor spectrum is not always."
". Meanwhile, a future space-based mission with the specifications of CMBPol will provide decisive evidence of nr#0 for |nr|>0.15 - just on the edge of the excluded region, and strong evidence for |nr|>0.12."," Meanwhile, a future space-based mission with the specifications of CMBPol will provide decisive evidence of $n_T \neq 0$ for $|n_T| \geq 0.15$ – just on the edge of the excluded region, and strong evidence for $|n_T| \geq 0.12$."
" Lastly, an ideal satellite experiment will perform even better: not only will it support a decisive (strong) confirmation of nr40 for |nr|>0.03 (0.025), but it will provide strong evidence for nr=0, favor the null hypothesis Ho, if |nr|<0.01."," Lastly, an ideal satellite experiment will perform even better: not only will it support a decisive (strong) confirmation of $n_T \neq 0$ for $|n_T| > 0.03$ (0.025), but it will provide strong evidence for $n_T = 0$, favor the null hypothesis $\mathcal{H}_0$, if $|n_T| < 0.01$."
 These results are summarized in Table 1., These results are summarized in Table 1.
 The previous findings apply to Hi with fiducial r=0.1., The previous findings apply to $\mathcal{H}_1$ with fiducial $r=0.1$.
" However, the error on nr,which largely determines the Bayes factor, depends on the base value of r."," However, the error on $n_T$,which largely determines the Bayes factor, depends on the base value of $r$."
 We now examine whether and how our conclusions change when r is also allowed to vary., We now examine whether and how our conclusions change when $r$ is also allowed to vary.
" The preferred approach to this problem would be apply the same MCMC analysis on data sets generated from a range of fiducial r, in addition to nr."," The preferred approach to this problem would be apply the same MCMC analysis on data sets generated from a range of fiducial $r$, in addition to $n_T$."
" This method, however, is time consuming and more efficient approaches exist."," This method, however, is time consuming and more efficient approaches exist."
" The previous results from the MCMC analysis show that the posterior distributions of r(k.) and nr are nearly Gaussian and not too strongly correlated, and so a Fisher matrix analysis should provide reliable constraints (Perottoetal.2006).."," The previous results from the MCMC analysis show that the posterior distributions of $r(k_*)$ and $n_T$ are nearly Gaussian and not too strongly correlated, and so a Fisher matrix analysis should provide reliable constraints \citep{Perotto:2006rj}."
" A forecast of parameter constraints can be obtained relatively easily by Taylorexpanding thelog-likelihood function,In £(@|d), about the best-fit parameter values, 6, and examining the 2""-order coefficient, TheFisher information matrix, F;;, encodes parameter correlations and measures the steepness of the likelihood function in the direction of each parameter 0;."," A forecast of parameter constraints can be obtained relatively easily by Taylorexpanding thelog-likelihood function,$\ln \mathcal{L}(\bm \theta | \bf d)$ , about the best-fit parameter values, $\bar{\bm \theta}$ , and examining the$^{nd}$ -order coefficient, TheFisher information matrix, $F_{ij}$ , encodes parameter correlations and measures the steepness of the likelihood function in the direction of each parameter $\theta_i$ ."
" The minimum precision with which parameter 0; can be measured is set by the Cramer-Rao bound (Tegmark 1997),,"," The minimum precision with which parameter $\theta_i$ can be measured is set by the Cramer-Rao bound \citep{Tegmark:1996bz}, ,"
"analyses of the OC candidates, and derive astrophysical parameters radit)) of the confirmed OCs and two previously studied objects.","analyses of the OC candidates, and derive astrophysical parameters ) of the confirmed OCs and two previously studied objects."
 In Sect., In Sect.
 6 we estimate the cluster mass stored in stars., \ref{Mass} we estimate the cluster mass stored in stars.
 In Sect., In Sect.
 7 we discuss the results and investigate the relationship between derived parameters., \ref{sec:6} we discuss the results and investigate the relationship between derived parameters.
" Finally, in Sect."," Finally, in Sect."
 8 we present concluding remarks., \ref{sec:7} we present concluding remarks.
" Froebrich,Scholz&Raftery(2007) have published a catalogue of 1021 star cluster candidates with |b|<20° and all Galactic longitudes."," \citet{Froebrich07} have published a catalogue of 1021 star cluster candidates with $|b|\,\leq\,20^\circ$ and all Galactic longitudes."
" They identify overdensities in the 2MASS database that are classified according to a quality flag, with 0 and 1 for the most probable star clusters and 2 - 5 for possible star clusters."," They identify overdensities in the 2MASS database that are classified according to a quality flag, with 0 and 1 for the most probable star clusters and 2 - 5 for possible star clusters."
" Bica,Bon-atto&Camargo(2008) explored FSR overdensities, with quality flags 0 and 1, in bulge/disk directions at |έ<60°."," \citet{Bica08} explored FSR overdensities, with quality flags 0 and 1, in bulge/disk directions at $|\ell|\,\leq\,60^\circ$."
" The sample consisted of 20 star cluster candidates and resulted in 4 new, 2 previously known OCs, 5 uncertain cases, and 9 probable field fluctuations."," The sample consisted of 20 star cluster candidates and resulted in 4 new, 2 previously known OCs, 5 uncertain cases, and 9 probable field fluctuations."
" Bonatto&Bica(2008b) analysed 28 FSR, cluster candidates projected nearly towards the anti-centre (160°«4x 200°) and confirm 6 new and 9 previously known OCs, 6 uncertain cases, and 7 probable fluctuations of the stellar field."," \citet{Bonatto08} analysed 28 FSR cluster candidates projected nearly towards the anti-centre $160^\circ\,\leq\,\ell\,\leq 200^\circ$ ) and confirm 6 new and 9 previously known OCs, 6 uncertain cases, and 7 probable fluctuations of the stellar field."
 The present FSR overdensity sample is listed in Table 1.., The present FSR overdensity sample is listed in Table \ref{tab1}.
 Some of these objects have previous identifications (Table 2))., Some of these objects have previous identifications (Table\ref{tab2}) ).
 The Koposovetal.(2008) analysis of CMDs for 5 clusters is showed in Table 2.., The \citet{Koposov08} analysis of CMDs for 5 clusters is showed in Table \ref{tab2}.
" They concluded that FSR 795 (Koposov 10), Cz 22, FSR 828 (Koposov 43), FSR 856 (Koposov 53) and Cz 24 are clusters."," They concluded that FSR 795 (Koposov 10), Cz 22, FSR 828 (Koposov 43), FSR 856 (Koposov 53) and Cz 24 are clusters."
 The derived parameters for them and the present ones (Tables 3 and 4 ) agree well., The derived parameters for them and the present ones (Tables \ref{tab3} and \ref{tab4} ) agree well.
" Kumar,Keto&Clerkin(2006) studied KKC1 (FSR, 788) and found that it is a cluster (Sect. 5)).", \citet{Kumar06} studied KKC1 (FSR 788) and found that it is a cluster (Sect. \ref{sec:5}) ).
 We derive parameters for the previously catalogued OCs Cz 22 and NGC2234., We derive parameters for the previously catalogued OCs Cz 22 and NGC2234.
" Yadav&Sagar(2004) derived for Cz 22 a radius of 1.8’, metallicity of 0.08, E(B—V)=0.45+0.05, age of the 20050 Myr and dg=3.0+0.2 kpc."," \citet{Yadav04} derived for Cz 22 a radius of 1.8', metallicity of 0.08, $E(B-V)=0.45\pm0.05$, age of the $200\pm50$ Myr and $d_{\odot}=3.0\pm0.2$ kpc."
 NGC2234 does not have parameters derived so far., NGC2234 does not have parameters derived so far.
" Some clusters are seen in visible bands (Fig. 1)),"," Some clusters are seen in visible bands (Fig. \ref{fig:1}) ),"
 while others are essentially infrared objects (Fig. 2))., while others are essentially infrared objects (Fig. \ref{fig:2}) ).
" photometry (Skrutskieetal.,2006) in the J, H, and Ks; bands was extracted in circular regions centred on the coordinates of the FSR objects usingVizieR?."," photometry \citep{Skrutskie06} in the $J$ , $H$, and $K_s$ bands was extracted in circular regions centred on the coordinates of the FSR objects using."
. Wide extraction areas are essential for producing RDPs (Sect.A4 ) with a high contrast against the background and for a consistent field-star decontamination (Sect.3.1))., Wide extraction areas are essential for producing RDPs \ref{sec:4} ) with a high contrast against the background and for a consistent field-star decontamination \ref{sec:3.1}) ).
 We started by assuming the FSR coordinates to centre the photometry extraction., We started by assuming the FSR coordinates to centre the photometry extraction.
" Next, we computed the RDP (Sect. 4))"," Next, we computed the RDP (Sect. \ref{sec:4}) )"
 to check cluster centring., to check cluster centring.
 In some cases the RDP built with the original FSR coordinates presented a dip at the centre., In some cases the RDP built with the original FSR coordinates presented a dip at the centre.
" Then, new central coordinates are searched (after field-star decontamination - Sect. 3.1))"," Then, new central coordinates are searched (after field-star decontamination - Sect. \ref{sec:3.1}) )"
 to maximise the star-counts in the innermost RDP bin (e.g. Bonatto&Bica 2009c))., to maximise the star-counts in the innermost RDP bin (e.g. \citealt{Bonatto09c}) ).
" To uncover the intrinsic CMD morphology from the background stars, we applied the field-star decontamination procedure."," To uncover the intrinsic CMD morphology from the background stars, we applied the field-star decontamination procedure."
" This algorithm works on a statistical basis by measuring the relative number densities of probable cluster and field stars in cubic CMD cells that have axes along the J, (J—H) and (J—K;) magnitude and colours."," This algorithm works on a statistical basis by measuring the relative number densities of probable cluster and field stars in cubic CMD cells that have axes along the $J$ , $(J-H)$ and $(J-K_{s})$ magnitude and colours."
These are the colours that provide the maximum distinction among CMD sequences for star,These are the colours that provide the maximum distinction among CMD sequences for star
The last wo difficulties of the axisvuunetric model can be ποιονμαt relaxed by adding au unresolved. polarized source idu tie nuiddle of the western arm. where its unusually sraielt part (see Fig.,"The last two difficulties of the axisymmetric model can be somewhat relaxed by adding an unresolved polarized source in the middle of the western arm, where its unusually straight part (see Fig."
 5) aud a steep III eradicut on his disk side are suggestive for au externa easons conression (ITavies et al., 5) and a steep HI gradient on this disk side are suggestive for an external gas compression (Haynes et al.
 1989)., 1989).
 Towever. the diffiatics of the spira ar model can oulv be improved by adding a widespreacl. significant axisviuncetric magnetic field.," However, the difficulties of the spiral arm model can only be improved by adding a widespread, significant axisymmetric magnetic field."
 Attempts to reproduce hne variations of facc-on corrected niaenetic pitch angles ce xih the azimnuthal anele in tlic|o disk are shown in Fie., Attempts to reproduce the variations of face-on corrected magnetic pitch angles $\psi$ with the azimuthal angle in the disk are shown in Fig.
 10., 10.
 The observed changes of t and especially a jump near the azinnthal anele of 90 rule out a purely axisviinieric niasjetic ποια.," The observed changes of $\psi$, and especially a jump near the azimuthal angle of $90\degr$, rule out a purely axisymmetric magnetic field."
 Towever. addition of the ciscussec uupolarized region to our axisviuietric nocel vields the jump a the correct position. though its exact shape in our suple noctel is still far from reality.," However, addition of the discussed unpolarized region to our axisymmetric model yields the jump at the correct position, though its exact shape in our simple model is still far from reality."
 The spiral arm uodoels shown in Fie., The spiral arm models shown in Fig.
 9a aud b also have sone di» at about 90°. however hey vield abrupt jumps of c at 1507 alc 3307.," 9a and b also have some dip at about $^{o}$, however they yield abrupt jumps of $\psi$ at $150\degr$ and $330\degr$."
 These eatures do rot depend ou model paraleters. nor ou the iuclusion or exclusion of low-brightuess regious iu model naps.," These features do not depend on model parameters, nor on the inclusion or exclusion of low-brightness regions in model maps."
 They naturally result from the spiral aria shape aud cannot )o removed Without changing the basic uodel assinuptions., They naturally result from the spiral arm shape and cannot be removed without changing the basic model assumptions.
 Iu the azimuthal augle range of 2707 to 3307 he spiral arii imodel deviates also from the data mich nore than tlat assuninug the axisvuumetric field., In the azimuthal angle range of $270\degr$ to $330\degr$ the spiral arm model deviates also from the data much more than that assuming the axisymmetric field.
 Despite very strong density waves NGC 3627 still shows clear signaures of axisviuuetne. dvuamno-tvpe naenetic fields.," Despite very strong density waves NGC 3627 still shows clear signatures of axisymmetric, dynamo-type magnetic fields."
 At pxent it is hard to szwowhether it dominates the «ik feld. showing oulv locally effects of exterial conression. or whether it cocsists with he deusitv-Avave componeut as au nnuportaut coustitucut of the οobal magnetic field.," At present it is hard to say whether it dominates the disk field, showing only locally effects of external compression, or whether it coexists with the density-wave component as an important constituent of the global magnetic field."
 A detailec discrimination )etween these possibilities needs observations with a considerably higher resolution complemened by extensive coluputatious of a wlde exid of detailed quantitative nodels of NCC 3627. which is bevoud t16 scope of this uper.," A detailed discrimination between these possibilities needs observations with a considerably higher resolution complemented by extensive computations of a whole grid of detailed quantitative models of NGC 3627, which is beyond the scope of this paper."
 The strounglv interacting Leo Triplet ealaxv NGC 3627 has been observed at 10.55 GIIz with the 100-11 ΑΠii radio telescope., The strongly interacting Leo Triplet galaxy NGC 3627 has been observed at 10.55 GHz with the 100-m MPIfR radio telescope.
 Total power aud polarization maps with a resolution of 1/13. very scusitive to extended. diffuse polarized οιμοι were obtained.," Total power and polarization maps with a resolution of 13, very sensitive to extended, diffuse polarized emission were obtained."
 Their analysis iu the σοιext of optical. CO and Πα data vielded the followi18o results:," Their analysis in the context of optical, CO and $\alpha$ data yielded the following results:"
Ry is uceligible).,$R_H$ is negligible).
 As the distance determined by. Welch et al. (, As the distance determined by Welch et al. (
1987) of 61 kpc has now been used. as opposed to 70 kpe. its Mug and Ago. values have changed accordingly.,"1987) of 61 kpc has now been used, as opposed to 70 kpc, its $M_{total}$ and $M_{gas}$ values have changed accordingly."
 Ou the other hand. according to Iuukel. Demers. Tewin (1996) most of the mass of the LAIC is located within the inner 5 deg. we are thus uot making a big mistake by using the g associated to the inner region of L2 deg (Lequeux ct al.," On the other hand, according to Kunkel, Demers, Irwin (1996) most of the mass of the LMC is located within the inner 5 $\deg$, we are thus not making a big mistake by using the $\mu$ associated to the inner region of 4.2 $\deg$ (Lequeux et al."
 1979): apparently there is no massive dark halo in LMC (I&uukel et al., 1979); apparently there is no massive dark halo in LMC (Kunkel et al.
 1997)., 1997).
 The Π I core of I Zw LO was studied by Gottesinan Weliachew (1972) aud its correspouding πας adopted by οςΓρ Lequeux et al.From the ευ values derived by Brinks EKlein (1988). we fined povalue of 0.11 for the northern cloud of II Zw LO (sec Table 7).," The H I core of II Zw 40 was studied by Gottesman Weliachew (1972) and its corresponding $\mu$ was adopted by CCPS Lequeux et al.. the $M_{total}$ values derived by Brinks Klein (1988), we find $\mu$ value of 0.14 for the northern cloud of II Zw 40 (see Table 7)."
 This low value of p might imply the presence of a senificant amount of dark matter., This low value of $\mu$ might imply the presence of a significant amount of dark matter.
 IC 10., IC 10.—
 The Kepleriu estinate of Aft (Shostak 1971) was denrved within a radius which is very close to (Ry=LOkpe. if the distance to the galaxy is taken to Pube3 Mpc).," The Keplerian estimate of $M_{total}$ (Shostak 1974) was derived within a radius which is very close to $R_H$ $R_H$ =4.0 kpc, if the distance to the galaxy is taken to be 3 Mpc)."
 Recent deteziinations of the distance to IC 10 put it close to 1. Alpe \pe(e.g.. Wilson et al.," Recent determinations of the distance to IC 10 put it close to 1 Mpc (e.g., Wilson et al."
 1996)., 1996).
 This value contrasts with the 3 adopted by Lequeux et al., This value contrasts with the 3 Mpc adopted by Lequeux et al.
 from Sandage Tamunann (1975)., Sandage Tammann (1975).
 We have adopted 1.5 Mpc and at this distance j£—0.51., We have adopted 1.5 Mpc and at this distance $\mu = 0.51$.
 IL Zw το NGC 6822., II Zw 70 NGC 6822.—
" The total masses of these two ealaxies are derived within a radius which is ereater than their Ry, values by about actor of two (Dalkowski et al.", The total masses of these two galaxies are derived within a radius which is greater than their $R_H$ values by about a factor of two (Balkowski et al.
 1978: Cotteinan Weliachew 1977)., 1978; Gottesman Weliachew 1977).
 By using these Αμ] values. we may. be underestimating the value of µ as compared with the values derived for other galaxies iu the sample.," By using these $M_{total}$ values, we may be underestimating the value of $\mu$ as compared with the values derived for other galaxies in the sample."
 A very detailed modeling of the rotation curve of these two galaxies is needed to kuow the contribution of a dark halo to the total mass., A very detailed modeling of the rotation curve of these two galaxies is needed to know the contribution of a dark halo to the total mass.
 NGC το., NGC 4449.—
 The total mass of this galaxy. within a radius of 37 kpe (by far guter than its optical ταςτις) has been estimated receutlvbv Dajaja. considera]Huchtiieier. Klein (1991).," The total mass of this galaxy, within a radius of 37 kpc (by far greater than its optical radius) has been estimated recently by Bajaja, Huchtmeier, Klein (1994)."
 Its po=0.052 is dv lower than those usually estimated for dwarf imregulu galaxies. in particular. lower than the other galaxies of our sample.," Its $\mu = 0.052$ is considerably lower than those usually estimated for dwarf irregular galaxies, in particular, lower than the other galaxies of our sample."
 The rotation curve iudicates the presence of dark matter in its extended II I halo but. as iu the case of NGC 6822 and II Zw 70. à very detailed modeling of its rotation curve is still needed.," The rotation curve indicates the presence of dark matter in its extended H I halo but, as in the case of NGC 6822 and II Zw 70, a very detailed modeling of its rotation curve is still needed."
 It is interesting to note that the mean ji value presented in Table 7 differs oulv by 2 the mean jp value obtained by CCPS., It is interesting to note that the mean $\mu$ value presented in Table 7 differs only by 2 the mean $\mu$ value obtained by CCPS.
 Cohuuus 5 aud 6 of Table 7 preseut the hel aud the oxygen abuudances by mass. the data are the same as those preseuted by. CCPS.," Columns 5 and 6 of Table 7 present the helium and the oxygen abundances by mass, the data are the same as those presented by CCPS."
 In the last two lines of Tables 9 and Ll we preseut the C/O. AY/AO. aud Z/O values derived by CCPSfrom their sample of regular galaxies.," In the last two lines of Tables 9 and 11 we present the C/O, $\Delta Y/\Delta {\rm O}$, and $Z$ /O values derived by CCPS their sample of irregular galaxies."
 More recent determinations of He abundances permit to derive other AY/AO valucs., More recent determinations of He abundances permit to derive other $\Delta Y/\Delta {\rm O}$ values.
From the data of Izotov. Thuan. Lipovetski (1997) on extragalactic I II regions it is obtained that AY/AO=3.1+1.1L.," the data of Izotov, Thuan, Lipovetski (1997) on extragalactic H II regions it is obtained that $\Delta Y/\Delta {\rm O} = 3.1 \pm 1.4$."
" Based onu observatious by many authors Olive. Steigman. Skilhnan(1997) obtain a preealactic helimm abunudauce. Y, of 0.231 d 0.002. alternatively Izotov ct al."," Based on observations by many authors Olive, Steigman, Skillman(1997) obtain a pregalactic helium abundance, $Y_p$, of 0.234 $\pm$ 0.002, alternatively Izotov et al."
" find Y,=0.2135+0.003.", find $Y_p = 0.243 \pm 0.003$.
" By adoptiug Y,=0.210+0.006 and combining this value with the Y' and O abundances of the ealactic IT II τοσο AIL. that amount to O.280 +4 0.006 and (8.69£1.3)«107. respectively (Poeinmibert. Torres-Peimbert. Ruiz 1992). it follows that AY/AO=L6XLl."," By adopting $Y_p = 0.240 \pm 0.006$ and combining this value with the $Y$ and O abundances of the galactic H II region M17, that amount to 0.280 $\pm$ 0.006 and $(8.69 \pm 1.3) \times 10^{-3}$, respectively (Peimbert, Torres-Peimbert, Ruiz 1992), it follows that $\Delta Y/\Delta {\rm O} = 4.6 \pm 1.1$."
 We have added 0.08 dex to the eascous O abundance to consider the fraction of O atoms eiuhedded in dust (Esteban et al., We have added 0.08 dex to the gaseous O abundance to consider the fraction of O atoms embedded in dust (Esteban et al.
 1998)., 1998).
 Finally.from fine structure in the main uen based. on Iipparcos pirallaxes Pagel Portinari (1995) obtain that AY/AO=5.6cx6.," Finally, fine structure in the main sequence based on Hipparcos parallaxes Pagel Portinari (1998) obtain that $\Delta Y/\Delta {\rm O} = 5.6 \pm 3.6$ ."
 These three AY/AO values are in good agreement with the value preseuted in Tables 9 aud 11., These three $\Delta Y/\Delta {\rm O}$ values are in good agreement with the value presented in Tables 9 and 11.
 The properties of the typical nregular galaxw were obtainedfrom the galaxies preseuted in Table 7 aud are eiven in the last row of this table., The properties of the typical irregular galaxy were obtained the galaxies presented in Table 7 and are given in the last row of this table.
 We have computed closed-box models with continuous SERs aud cdiffercut ages for the typical nreeular galaxy., We have computed closed-box models with continuous SFRs and different ages for the typical irregular galaxy.
 All the models reproduce the observational constraints. f=0.288 aud O = 2.589ο ," All the models reproduce the observational constraints, $\mu = 0.288$ and O = $2.589 \times 10^{-3}$."
For the typical iimeeular ealaxy we do not know the amount of M. therefore the observed po value is a lower limit to arg.," For the typical irregular galaxy we do not know the amount of $M_{nb}$, therefore the observed $\mu$ value is a lower limit to $\mu_{IMF}$."
" Consequently. we lave computed models for a range of (001.85) values: we think it is unlikely that the 7 valueis smaller than oue (see Table 1). and r£, 18 the value for AZ,=0.0. 6 can not be higher than 7,4; because AM, would become uceative."," Consequently, we have computed models for a range of $r(0.01,85)$ values; we think it is unlikely that the $r$ valueis smaller than one (see Table 1), and $r_{max}$ is the value for $M_{nb} = 0.0$, $r$ can not be higher than $r_{max}$ because $M_{nb}$ would become negative."
 In Table 8 we preseut the model results for the different mass fractious defined in this paper., In Table 8 we present the model results for the different mass fractions defined in this paper.
" Thedistributions of ων and Mj, for differcut (0.01.85) values are plotted in Figure 1."," Thedistributions of $M_{sub}$ and $M_{nb}$ for different $r(0.01,85)$ values are plotted in Figure 1."
" this figure it can be seen that ζω dacreases with r and Ad, decreases with rk.", this figure it can be seen that $M_{sub}$ increases with $r$ and $M_{nb}$ decreases with $r$ .
" The increase of M, with r is due to an", The increase of $M_{sub}$ with $r$ is due to an
Nou-geuerie beliasior can occur at isolated spatia points where either πῳ or Q.y vanishes.,"Non-generic behavior can occur at isolated spatial points where either $\pi_Q$ or $Q,_\theta$ vanishes."
 In the former case. the absence of Vi where πω=0 aud its flatucss Wwlore Tem Valow P.- and thus P toremain ποσαive for a lone time.," In the former case, the absence of $V_1$ where $\pi_Q
= 0$ and its flatness where $\pi_Q \approx 0$ allow $P,_\tau$ and thus $P$ toremain negative for a long time."
 Since Q.;——πιoeop21 .€2 will erow exnentiallv in opposite directions on either side of the points where mo=0 producing a characterisic appareut discontiuuitv.," Since $Q,_\tau = \pi_Q \,e^{-2P}$, $Q$ will grow exponentially in opposite directions on either side of the points where $\pi_Q = 0$ producing a characteristic apparent discontinuity."
 O1i the other laxd. if Q.gz0. I. can remain large for a loug time causing a spiky feature iu P.," On the other hand, if $Q,_\theta \approx 0$, $P,_\tau$ can remain large for a long time causing a spiky feature in $P$."
 Both tv)08 ο feaures sharpen aud narrow with time., Both types of features sharpen and narrow with time.
 T1ο features aud their association with i1r-egenerie poiuts are shown in Fie. 5.., The features and their association with non-generic points are shown in Fig. \ref{ber-fig5}.
" Tje presence of his non-geucric belavlo vat isolated spatial poiuts leads to a dependence of simulation resul""5 Oll he sxitial resolution.", The presence of this non-generic behavior at isolated spatial points leads to a dependence of simulation results on the spatial resolution.
 The finer the spatial resolu1011.i he closer will a grid. poiit be to the non-geueric poiut.," The finer the spatial resolution, the closer will a grid point be to the non-generic point."
" Near these nOon-exnere polls. the generic procCSS Of approach to 0xP..<21 will occur but slowy απο either mo or Onzxο,"," Near these non-generic points, the generic process of approach to $0 \le P,_\tau < 1$ will occur but slowly since either $\pi_Q$ or $Q,_\theta \approx 0$."
 Tie closer one ds to à non-geueric site. the lo1ος rtjs process will take.," The closer one is to a non-generic site, the longer this process will take."
 Tlu saiver resolution code will have narrower spiky Caures at which it takes longer for P.- to move into the rauge [0.1).," Thus a finer resolution code will have narrower spiky features at which it takes longer for $P,_\tau$ to move into the range $[0,1)$."
 Some ονidence for this is secu in Fig., Some evidence for this is seen in Fig.
 |. where he fer spatial resolution simulation divergCR Yo nthe coarser one aud will be considered in detail elsewhere |22].., \ref{ber-fig4} where the finer spatial resolution simulation diverges from the coarser one and will be considered in detail elsewhere \cite{ber-bggm}. .
 Finalv. we note that V5 is analogous to the MSS potential.," Finally, we note that $V_2$ is analogous to the MSS potential."
 One may consider, One may consider
Gi) At any eiven radius A. the energy spectruu of CRs is a power law. N(z)wz? for SinEXfua. with sc0 and with total energy. Ley.,"(ii) At any given radius $R$, the energy spectrum of CRs is a power law, $N(\vep)\propto\vep^{-2-x}$ for $\vep_{\min}<\vep<\vep_{\max}$, with $x>0$ and with total energy $\ECR$."
" The spectrmu can be expressed as where we assumed that (fyax/fmin)""Xl. (ii) The minimal. maximal aud total cosiiic ray euereles are power law functions of the radius. Under the above asstuuptions. the spectrum of escaped particles is giveu by with For the case 6,,;,= 0. this reduces to equation (28) of Ohiraetal.(200901."," The spectrum can be expressed as where we assumed that $(\vep_{\max}/\vep_{\min})^{-x}\ll1$ (iii) The minimal, maximal and total cosmic ray energies are power law functions of the radius, Under the above assumptions, the spectrum of escaped particles is given by with For the case $\al_{min}=0$ , this reduces to equation (28) of \citet{Ohira09}."
 Equation (5) is valid for c7(0., Equation $\eqref{eq:GeneralPowerlaw}$ is valid for $x>0$.
 We note that for the lamiting value. ο=0. a logarithmic correction ds introduced to. the spectrum of escaped. CRs. duc to the logarithinic depeudeuce of the total CR energy. on Duiuanae Lor=logCziuaxCuin)N(s).," We note that for the limiting value, $x=0$, a logarithmic correction is introduced to the spectrum of escaped CRs, due to the logarithmic dependence of the total CR energy on $\vep_{\min,\max}$, $\ECR=\log(\vep_{\max}/\vep_{\min})\vep^2N(\vep)$."
 For c«0. the energv carried by the CRs is dominated by the particles with larecst cucreics. Toauas," For $x<0$, the energy carried by the CRs is dominated by the particles with largest energies, $\vep=\vep_{max}$."
 The resulting escaped spectrin safisfes ace=AEfOpar 0d is not scusitive to the form of the instantaneous spectra., The resulting escaped spectrum satisfies $\xesc=\al_E/\al_{max}$ and is not sensitive to the form of the instantaneous spectrum.
 We next apply the above general result to simple cases. focusing ou a blast wave of fixed energy which starts off ultra-relativistic. and then decelerates to non relativistic velocity.," We next apply the above general result to simple cases, focusing on a blast wave of fixed energy which starts off ultra-relativistic, and then decelerates to non relativistic velocity."
" The non relativistic aud relativistic stages are analyzed in and respectively,", The non relativistic and relativistic stages are analyzed in and respectively.
" The spectiua resulting frou, the combination of the two stages is addressed iu??.", The spectrum resulting from the combination of the two stages is addressed in.
". Perhaps the simplest case to consider is the case of constant CR uunimeal energy £444, aud total energy. Ley: (ασ.μην= 0)"," Perhaps the simplest case to consider is the case of constant CR minimal energy $\vep_{\min}$ and total energy $\ECR$ $\al_E,\al_{\min}=0$ )."
 This is expected in the Sedovw-Tavlor phase of non relativistic blast waves., This is expected in the Sedov-Taylor phase of non relativistic blast waves.
" The cuerev in CRs is. donunated. bv the relativisticB CRs. 72Di0,07. and isB conunuonlv assumed to be a coustaut fraction f of the total euergv. £ in the svstem."," The energy in CRs is dominated by the relativistic CRs, $\vep>m_pc^2$, and is commonly assumed to be a constant fraction $f$ of the total energy $E$ in the system."
 Heuce £444~nyc aud Log=FE. both iudepeudeut of the shock radius.," Hence $\vep_{\min}\sim m_pc^2$ and $\ECR=fE$, both independent of the shock radius."
 Eq., Eq.
 iuplies that the escaped spectrum dis the same as the lustantaneous spectruui. This result cau be obtained directly from Eq.," implies that the escaped spectrum is the same as the instantaneous spectrum, This result can be obtained directly from Eq."
 bx noting that the eutire spectrun. up to the maximal ΟΠΟΙΟΥ μις18). is independent of radius.," by noting that the entire spectrum, up to the maximal energy $\vep_{\max}(R)$, is independent of radius."
 We next consider the case of ultra-relativistic expansion., We next consider the case of ultra-relativistic expansion.
 Below and in we make the following assumptions iu addition to assuniptious (1)-(1) (iv) The minimal CR energy is the energy of the thermal particles. (v) The CR pressure is a radius incependeut fraction fcg of. the moment fux iu+ the shock frame.B peuXPop.Di nuplving (vi) The maximal CR euergv is the maximal cucrey of CRs that are confined by a fluid rest frame magnetic Ποιά. Boos (equivalent to Diffusive Shock Acceleration in the Bolu linüt). where Eon.~DDBaa is the electric field iu the observer frame corresponding to a maeuetic fleld δν~(SzI?pe?egn)7? in the rest frame of the shocked plasma. assumed to carry a constant fraction ey of the iuiomentun flux. and dR~R/T is the maximal distance that a cosmic rav can propagate alone the electric field in the observer frame.," Below and in we make the following assumptions in addition to assumptions (i)-(iii) (iv) The minimal CR energy is the energy of the thermal particles, (v) The CR pressure is a radius independent fraction $f_{\text{CR}}$ of the momentum flux in the shock frame, $p_{\text{CR}}\propto \Gamma^2\rho$, implying (vi) The maximal CR energy is the maximal energy of CRs that are confined by a fluid rest frame magnetic field $B_{\text{rest}}$ (equivalent to Diffusive Shock Acceleration in the Bohm limit), where $E_{\text{obs}}\sim \Gamma B_{\text{rest}}$ is the electric field in the observer frame corresponding to a magnetic field $B_{\text{rest}}\sim (8\pi\Gamma^2\rho
c^2\ep_B)^{1/2}$ in the rest frame of the shocked plasma, assumed to carry a constant fraction $\ep_B$ of the momentum flux, and $\de R\sim R/\Gamma$ is the maximal distance that a cosmic ray can propagate along the electric field in the observer frame."
" We next cousider a Dlanudford- Melxee (energy.cou-serving:Dlaudford&AIcIxec1976)/ shock expanding iuto a uniform οςαπ,", We next consider a Blandford- McKee \citep[energy conserving;][]{Blandford76} shock expanding into a uniform medium.
 By assumption ag=0., By assumption $\al_E=0$.
" Using equations(9). ejas=1/2 and ayy,=3 are obtained."," Using equations, $\al_{\max}=1/2$ and $\al_{\min}=3$ are obtained."
 Using we fiud wxhee or The spectral index of escaped CRs. given by Eq.(," Using we find $\xesc=-5x$, or The spectral index of escaped CRs, given by Eq.,"
10).. may be surprisingly hard if the instantaneous spect (equ.|2]) is softer than a flat spectu. ic. 2>0.," may be surprisingly hard if the instantaneous spectrum (equ.[2]) is softer than a flat spectrum, i.e. $x>0$."
 The basic reason for this is the fact that the miniual CR OLCYSV Sayin0 changes with radius much faster than the maximal Pic?cucreyv. miplviug that at later times (correspondiue to lower escaped energies) there is uch less CR energy at the escaping. high eud ofthe spectrua.," The basic reason for this is the fact that the minimal CR energy $\vep_{\min}\sim \Gamma^2m_pc^2$ changes with radius much faster than the maximal energy, implying that at later times (corresponding to lower escaped energies) there is much less CR energy at the escaping, high end of the spectrum."
 For example. consider the conmouly asstuuedt Diffusive Shock Acceleration (DSA) mechanisia (srvinskii1977: 1978).. which for ultra-relativistic shocks with isotropic. xnalbauele scattering. leads to an mstantaneous spectrum Nxe78? ο&Waxinan2005:Bednuarz&OstrowskiL998:irketal. 2000).," For example, consider the commonly assumed Diffusive Shock Acceleration (DSA) mechanism \citep{Krymskii77, Axford77, Bell78, Blandford78}, which for ultra-relativistic shocks with isotropic, small-angle scattering, leads to an instantaneous spectrum $N\propto \vep^{-20/9}$ \citep{Keshet05,Bednarz98,Kirk00}."
. Using Eq.(," Using Eq.,"
"10).. this iuplics a very lard escaping spectrum. Niexs 7. We emphasize that DSA has not been shown to work based on first principles aud even if it docs. the resulting spectrum is sensitive to the ποσαατα mechanism (οιο, which is poorly nuderstoocd."," this implies a very hard escaping spectrum, $\Nesc\propto \vep^{-8/9}$ We emphasize that DSA has not been shown to work based on first principles and even if it does, the resulting spectrum is sensitive to the scattering mechanism \citep[e.g.][]{Keshet05,Keshet06} which is poorly understood."
 Iu fact. the instantaneous spectrum does nof necessarily need to havea power-law form (c.g.Caprioli or to have a constant spectral iudex(e.g.Ellison&Double2001)..," In fact, the instantaneous spectrum does not necessarily need to havea power-law form \citep[e.g.][]{Caprioli09,Ohira09} or to have a constant spectral \citep[e.g.][]{Ellison04}.."
use the data from and use their magnitude and colors in a 25/2 diameter aperture.,use the data from and use their magnitude and colors in a $25\farcs2$ diameter aperture.
" At the redshift of Coma, this corresponds to a physical size of 11.71 kpc, quite closely approximating our ~14 kpc aperture at z~0.8."," At the redshift of Coma, this corresponds to a physical size of $11.71$ kpc, quite closely approximating our $\sim 14$ kpc aperture at $z\sim 0.8$."
 Fig., Fig.
" 1 shows that the single burst model provides a remarkably good fit to the red sequence observed in the high redshift clusters, confirming that the location of the CM sequence observed in distant clusters requires high redshifts of formation, and that the slope is consistent with a correlation between galaxy metal content and luminosity."," \ref{cm} shows that the single burst model provides a remarkably good fit to the red sequence observed in the high redshift clusters, confirming that the location of the CM sequence observed in distant clusters requires high redshifts of formation, and that the slope is consistent with a correlation between galaxy metal content and luminosity."
" Perhaps the most interesting result of our analysis is that the red sequence in our clusters is well populated at magnitudes brighter than ~22, but unusually ‘empty’ at fainter magnitudes."," Perhaps the most interesting result of our analysis is that the red sequence in our clusters is well populated at magnitudes brighter than $\sim
22$, but unusually `empty' at fainter magnitudes."
 The histograms in Fig., The histograms in Fig.
" 1 show the number of cluster members within ~30 from the best fit relation, after averaging over 100 Monte Carlo realizations of the statistical subtraction."," \ref{cm} show the number of cluster members within $\sim 3\sigma$ from the best fit relation, after averaging over $100$ Monte Carlo realizations of the statistical subtraction."
 The paucity of low-luminosity red galaxies at high-z occurs at magnitudes well above our completeness limit and in all the clusters under investigation., The paucity of low–luminosity red galaxies at high–z occurs at magnitudes well above our completeness limit and in all the clusters under investigation.
" There is no clear evidence for such a deficiency in c11040.7-1155 (z— 0.7) but, given its very low fraction of objects with absorption-line spectra, it cannot be ruled out statistically either."," There is no clear evidence for such a deficiency in $1040.7$ $1155$ $z=0.7$ ) but, given its very low fraction of objects with absorption–line spectra, it cannot be ruled out statistically either."
" In order to quantify this effect, we combine the histograms shown in Fig."," In order to quantify this effect, we combine the histograms shown in Fig."
 1 correcting colors and magnitudes to a common redshift —0.75., \ref{cm} correcting colors and magnitudes to a common redshift $=0.75$.
 The result is shown in panel (a) of Fig. 3.., The result is shown in panel (a) of Fig. \ref{histo}.
 Panel (b) shows the corresponding result for the Coma cluster., Panel (b) shows the corresponding result for the Coma cluster.
" For the high-z clusters, non-members have been excluded as described in 833."," For the high–z clusters, non–members have been excluded as described in 3."
 The dashed histograms shows the corresponding result when membership is based solely on photometric redshifts., The dashed histograms shows the corresponding result when membership is based solely on photometric redshifts.
" In Coma, membership information is available from spectroscopy for a large number of galaxies and we have corrected the number of red galaxies in each magnitude bin for background and foreground contamination using a redshift catalog kindly provided by Matthew Colless and the same procedure as in(2003)."," In Coma, membership information is available from spectroscopy for a large number of galaxies and we have corrected the number of red galaxies in each magnitude bin for background and foreground contamination using a redshift catalog kindly provided by Matthew Colless and the same procedure as in."
". The histogram of the EDisCS clusters shows a decrease in the number of < 0.4L, red-sequence galaxies.", The histogram of the EDisCS clusters shows a decrease in the number of $\lesssim 0.4$ $_*$ red–sequence galaxies.
" This effect is present in all our clusters individually, with the possible exception of c11040.7—1155, as discussed above."," This effect is present in all our clusters individually, with the possible exception of $1040.7$ $1155$, as discussed above."
" Indeed, the ‘luminosity function’ of the red galaxies in these clusters shows the same decrease despite the variety in cluster properties such as velocity dispersion, richness, concentration and substructure (White et al.;"," Indeed, the `luminosity function' of the red galaxies in these clusters shows the same decrease despite the variety in cluster properties such as velocity dispersion, richness, concentration and substructure (White et al.;"
" Halliday et al.,"," Halliday et al.,"
 in , in preparation).
"Unfortunately, such a deficiency coincides with the preparation).well-known ‘dip’ in the luminosity function of the Coma cluster1977)."," Unfortunately, such a deficiency coincides with the well–known `dip' in the luminosity function of the Coma cluster."
". However, the behaviour of the Coma cluster seems quite ‘untypical’.(2003),"," However, the behaviour of the Coma cluster seems quite `untypical'.,"
", for example, have shown that the luminosity function of early (passive) spectral types increases going to fainter magnitudes in clusters in the 2dF survey."," for example, have shown that the luminosity function of early (passive) spectral types increases going to fainter magnitudes in clusters in the 2dF survey."
 After correcting for passive evolution with the single burst model shown in Figs., After correcting for passive evolution with the single burst model shown in Figs.
" 1 and 2, the histograms shown in Fig."," \ref{cm} and \ref{coma}, the histograms shown in Fig."
 3 are significantly different., \ref{histo} are significantly different.
of the Le LL 4686 Aline.,of the He II 4686 line.
" Strong Balmer emission is tvpical of cwarf novae in quiescence. although the Lle LL 4686 line is present in some chwarl novae (eg YZ πο, Shafter Llessman 1988). but not in others (eg SS νο Alartinez-Pais et al 1994)."," Strong Balmer emission is typical of dwarf novae in quiescence, although the He II 4686 line is present in some dwarf novae (eg YZ Cnc, Shafter Hessman 1988), but not in others (eg SS Cyg Martinez-Pais et al 1994)."
 The second epoch observations were taken on the same night as we obtained observations using the NOT when RAT J1953|1859 was in outburst., The second epoch observations were taken on the same night as we obtained observations using the NOT when RAT J1953+1859 was in outburst.
 The exposure time was 90 sec with a further 12 sec for readout., The exposure time was 90 sec with a further 12 sec for readout.
 By the epoch of the third observation. the source had returned to quiescence and the exposure time was 240 sec with a further 25 sec for readout.," By the epoch of the third observation, the source had returned to quiescence and the exposure time was 240 sec with a further 25 sec for readout."
 We show the mean of the spectra taken in the blue and, We show the mean of the spectra taken in the blue and
Asstuning that spectral pulse lag is due to sole proper timescale. ic. AfXL/D. and using the relation of Eq. 1..,"Assuming that spectral pulse lag is due to some proper timescale, i.e. $\Delta t \propto 1/{\cal D}$, and using the relation of Eq. \ref{t_jeqn},"
 we find that also the jet-break time 7;XL/D.," we find that also the jet-break time $\tau_j \propto
1/{\cal D}$."
 Somehow tho jet-breals time depends on the initial concitious (as reflected in the Doppler factor during the CRB phase}. aud those conditions are maintained iu the afterelow.," Somehow the jet-break time depends on the initial conditions (as reflected in the Doppler factor during the GRB phase), and those conditions are maintained in the afterglow."
" This suggests that the relations L,4(07;) aud Lig(7) discussedin Section 2 could be manifestations of the same effect.", This suggests that the relations $L_{pk}(\tau_j)$ and $E_{iso}(\tau_j)$ discussed in Section \ref{datasection} could be manifestations of the same effect.
" For sake of argument. if we asstune that £,, is constant over a burst duration. hen we have £;,,Γένος Where trop Is the mast duration."," For sake of argument, if we assume that $L_{pk}$ is constant over a burst duration, then we have $E_{iso}
= L_{pk} t_{tot}$, where $t_{tot}$ is the burst duration."
" In our sample. burst duration. which is typically ty¢~10 seconds. varies within a factor of 2 while L,;, aud Ly,¢ vary over a actor LOO."," In our sample, burst duration, which is typically $t_{tot} \sim 10$ seconds, varies within a factor of $~2$ while $L_{pk}$ and $E_{tot}$ vary over a factor $\sim 100$."
" This makes seuse because τε Is equal to the lifetime of the central eugime and ms is not affected by Lkmenmaties πα]κο L,j; ud E44."," This makes sense because $t_{tot}$ is equal to the lifetime of the central engine and thus is not affected by kinematics, unlike $L_{pk}$ and $E_{tot}$."
" Take fne; to be essentially coustaut conipared to Ly, and Ej... then. to the exteut at Ly, is coustaut over the burst chivation. we sxpect Lys. Lys "," Taking $t_{tot}$ to be essentially constant compared to $L_{pk}$ and $E_{iso}$, then, to the extent that $L_{pk}$ is constant over the burst duration, we expect $E_{iso} \sim L_{pk}$ ."
"The variabilitv-haninositv relationship (Reichartetal.2001) would imaply vat dinuner burts are less variable iu haninositv and thus we expect they will have the strongest correlation E;4,Ly. (they come closest to the assumption of constant luminosity over the burst duration). while brighter. more variable bursts will appear more chaotic: a trend that appears to be reflected in the data (see Fieures 5 aud 6))."," The variability-luminosity relationship \citep{rlfr+01} would imply that dimmer burts are less variable in luminosity and thus we expect they will have the strongest correlation $E_{iso} \sim L_{pk}$ (they come closest to the assumption of constant luminosity over the burst duration), while brighter, more variable bursts will appear more chaotic; a trend that appears to be reflected in the data (see Figures \ref{Lvtlag} and \ref{Eisovtj}) )."
" Thus. overall. it is not surprising that both £,, aud Γον, have similar slopes in 7j."," Thus, overall, it is not surprising that both $L_{pk}$ and $E_{iso}$ have similar slopes in $\tau_j$."
 Given that observed. timescales in general vary asfx τό. and. as cliscussed above. Iuninosities also appear to be functions of the Doppler boost. we are led to the intieuing possibility that all of he velatiouships described here (Equs. 1.. 2...," Given that observed timescales in general vary as $t \propto
\tau/{\cal D}$ , and, as discussed above, luminosities also appear to be functions of the Doppler boost, we are led to the intriguing possibility that all of the relationships described here (Eqns. \ref{t_jeqn}, \ref{Leqn},"
 7 83) depend on one kincmatic variable: D., \ref{jpnlageqn} \ref{jdslageqn}) ) depend on one kinematic variable: ${\cal D}$.
" Thus he existence of the relationships between spectral ag. Af. jet-break times. 7; and peal. luiuosity. Ly, (or Nyy). would be evideuce for variation in notion amoung CRBs."," Thus the existence of the relationships between spectral lag, $\Delta t$, jet-break times, $\tau_j$ and peak luminosity, $L_{pk}$ (or $N_{pk}$ ), would be evidence for variation in motion among GRBs."
 We here propose that. iu act. kinematic variation is the dominant source of variety observed among GRBs.," We here propose that, in fact, kinematic variation is the dominant source of variety observed among GRBs."
 The specific rature of this kinematic variation is still uuclemr., The specific nature of this kinematic variation is still unclear.
" Specifically, is it the opening augle 0 of the jet. or is the Lorentz factor > the dominant source of variation in D (Equ. 1D)?"," Specifically, is it the opening angle $\theta$ of the jet, or is the Lorentz factor $\gamma$ the dominant source of variation in ${\cal D}$ (Eqn. \ref{deltaeqn}) )?"
 This question will be explored with three possible models., This question will be explored with three possible models.
 This model was put forward by Frailetal.(2001)., This model was put forward by \cite{fksd01}.
. Frailetal.(2001) determine the opening anele of the jets from the observed jet-break times. assundüg TjOX05 (e.g.Sarietal.1999).. and roni this infer that there exists in CRBs a rauge in jet-openuiug angles.," \citet{fksd01} determine the opening angle of the jets from the observed jet-break times, assuming $\tau_j \propto \theta_j^{8/3}$ \citep[e.g.][]{sph99}, and from this infer that there exists in GRBs a range in jet-opening angles."
 Frailetal.(2001) have aken a simple jet where the Loreutz factor docs rot vary with angle (1.0. a non-structered jet} and he observer is effectively looking straight at the ceuter of the jet., \citet{fksd01} have taken a simple jet where the Lorentz factor does not vary with angle (i.e. a non-structered jet) and the observer is effectively looking straight at the center of the jet.
 Correcting for the ecometiy of he explosion. gamnuunua-ray energies then appear iurowlv chastered: the most energetic GRBs thus rave the narrowest jets.," Correcting for the geometry of the explosion, gamma-ray energies then appear narrowly clustered; the most energetic GRBs thus have the narrowest jets."
 If we adopt this model. and combine this with our result (Equ. 1)).," If we adopt this model, and combine this with our result (Eqn. \ref{t_jeqn}) ),"
 Atx05  and using AfxL/D. we find (στο we have taken στXAf).," $\tau_j \propto \Delta t \propto
\theta_j^{8/3}$ , and using $\Delta t \propto 1/{\cal D}$, we find (where we have taken $\tau_j \propto \Delta t$ )."
 Because relativistic bemuiug is strongest along the line of sight. material moving directly toward the observer will donünate the cussion.," Because relativistic beaming is strongest along the line of sight, material moving directly toward the observer will dominate the emission."
" For au observer located along the axis of the jet. i.c. 0,zz0. this translates into 0;x5779 (Dx> or (,.=0 in Equ. Lj)."," For an observer located along the axis of the jet, i.e. $\theta_v \approx 0$, this translates into $\theta_j \propto \gamma^{-3/8}$ ${\cal D} \propto
\gamma$ for $\theta_v = 0$ in Eqn. \ref{deltaeqn}) )."
 We thus find. in this ramework. that the fastests GRBs. with the üehest 5. have the narrowest jets.," We thus find, in this framework, that the fastests GRBs, with the highest $\gamma$ , have the narrowest jets."
 A prediction of this model is that uot ouly should there be a Varlation iu opening angles 0; amoug bursts. mt they should be related to Loreutz factor ? iu his proportion.," A prediction of this model is that not only should there be a variation in opening angles $\theta_j$ among bursts, but they should be related to Lorentz factor $\gamma$ in this proportion."
" A progenitor model must predict hat objects of a given jet angle 0; bo produced with a probability P~Pons0°X0,OL where Frailctal.(2001) have shown that Pop,x0,al"," A progenitor model must predict that objects of a given jet angle $\theta_j$ be produced with a probability $P \sim
P_{obs}/\theta_j^2 \propto \theta_j^{-4.54}$, where \citet{fksd01}
 have shown that $P_{obs} \propto \theta_j^{-2.54}$."
 We note here that Reichart&Yost(2002). have yoluted out that the observed distribution of aueles may be biased: wide jets are less effective iu ring away the cireunburst dust. and thereby will more often be optically undetectable (dark) hau narrow jets.," We note here that \citet{ry01} have pointed out that the observed distribution of angles may be biased; wide jets are less effective in burning away the circumburst dust, and thereby will more often be optically undetectable (dark) than narrow jets."
" This ""Mauy Morphologies scenario asses hat the observed variation amone CRBs is au intrinsicfeature of the burst population. 1.0. there exists a spectrun of GRB Lorentz factors (and corresponding hInuniuosities) aud of jet sizes (wide and narrow opening aneles)"," This “Many Morphologies” scenario assumes that the observed variation among GRBs is an intrinsicfeature of the burst population, i.e. there exists a spectrum of GRB Lorentz factors (and corresponding luminosities) and of jet sizes (wide and narrow opening angles)."
 It is unclear why there is sucha broad range of afterglow opening angeles (ranging from3 to more than 25 deerces:, It is unclear why there is sucha broad range of afterglow opening angles (ranging from3 to more than 25 degrees;
can be carried. out for the How structure in the equatorial jane.,can be carried out for the flow structure in the equatorial plane.
 In Fig., In Fig.
 2 density isolines ancl velocity vectors in this jane for the region with dimensions [rom 2 to LO. on axis X and from —3 to 342. on axis Y are presented., 2 density isolines and velocity vectors in this plane for the region with dimensions from 2 to $10R_\odot$ on axis $X$ and from $-3$ to $3R_\odot$ on axis $Y$ are presented.
 In Fig., In Fig.
 2 our Dowlines are shown as well. labelled by markers e. 7b. οἱ and τα.," 2 four flowlines are shown as well, labelled by markers $a$ ', $b$ ', $c$ ' and $d$ '."
 Phese Howlines illustrate the directions of matter lows in the system., These flowlines illustrate the directions of matter flows in the system.
 The analysis of results presented in Fig., The analysis of results presented in Fig.
 2 verifies the above conclusion that the part of matter of the stream falls in the disc at once (Llowline ). and then loses the angular momentum under the action of numerical viscosity and accretes.," 2 verifies the above conclusion that the part of matter of the stream falls in the disc at once (flowline $d$ '), and then loses the angular momentum under the action of numerical viscosity and accretes."
 “The obtained quantitative evaluations show. hat in steady-state regime the fraction of accreted matter. or the given semidetached binary. is approximately equal to 75 per cents of the total amount of matter injected into the syslem.," The obtained quantitative evaluations show, that in steady-state regime the fraction of accreted matter, for the given semidetached binary, is approximately equal to 75 per cents of the total amount of matter injected into the system."
 The part of matter. that remains in the svstem and influences the [low structure (lowlines ‘a’. 7b. and c in Fig.," The part of matter, that remains in the system and influences the flow structure (flowlines $a$ ', $b$ ', and $c$ ' in Fig."
 2) is of special interest., 2) is of special interest.
 Hereafter we shall name this part of matter by a circumbinary envelope., Hereafter we shall name this part of matter by a circumbinary envelope.
" Lt should. be noted. that a significant part of the gas of cireumbinary envelope (see Dowlines *e anc"") interacts with the matter ejected. from the surface of mass-Iosing star."," It should be noted, that a significant part of the gas of circumbinary envelope (see flowlines $a$ ' and $b$ ') interacts with the matter ejected from the surface of mass-losing star."
 Ehe influence of this part of cireumbinary envelope on the flow structure results in considerable change of the mass transfer regime., The influence of this part of circumbinary envelope on the flow structure results in considerable change of the mass transfer regime.
 The detailed: analysis of this effect. will be presented. in subsection 3.3 of this paper., The detailed analysis of this effect will be presented in subsection 3.3 of this paper.
 Another part of cireumbinary envelope (see Dowline ο}. makes a revolution around. the accretor and shocks the stream edge. facing the orbital movement.," Another part of circumbinary envelope (see flowline $c$ ') makes a revolution around the accretor and shocks the stream edge, facing the orbital movement."
 This interaction results in a significant change of the general How structure in the system and. in. particular. in absence of hotspot/ in the disc. as well as to the formation of an extended: shock wave. located: along the stream edge.," This interaction results in a significant change of the general flow structure in the system and, in particular, in absence of `hotspot' in the disc, as well as to the formation of an extended shock wave, located along the stream edge."
 Detailed description of the inlluence of this part of cireumbinary envelope on the morphology of eas Lows in the system is presented below., Detailed description of the influence of this part of circumbinary envelope on the morphology of gas flows in the system is presented below.
would introduce au uucertainty of <2% iu the ejecta mass. if the template with the nearest erid temperature is used.,"would introduce an uncertainty of $<2\%$ in the ejecta mass, if the template with the nearest grid temperature is used."
 Such a sinall variation of the ejecta mass has a negligible effect on the SNR inner structure., Such a small variation of the ejecta mass has a negligible effect on the SNR inner structure.
 As indicated in 823.2. the scalability of an SNR solution also requires that its initial coudition (Le.. SN ejecta profiles) to be scalable with respect to the surrounding inedium.," As indicated in 2.2, the scalability of an SNR solution also requires that its initial condition (i.e., SN ejecta profiles) to be scalable with respect to the surrounding medium."
 We find that such an initial couditiou can be set up within the uncertainty of SN ejecta models., We find that such an initial condition can be set up within the uncertainty of SN ejecta models.
" We adopt the density aud velocity profiles of a post-cellagration stellar remuaut of a Type Ia SN as proposed by Dwarkadas&Chevalier (1005): where p, aud ey are the correspondiug values at the characteristic radius ry.", We adopt the density and velocity profiles of a post-deflagration stellar remnant of a Type Ia SN as proposed by \citet{DC98}: : where $\rho_s$ and $v_s$ are the corresponding values at the characteristic radius $r_s$.
 The ejecta extends toa radius r; so that Qutside r; is the ambient gas with an assumed uniform density py., The ejecta extends to a radius $r_i$ so that Outside $r_i$ is the ambient gas with an assumed uniform density $\rho_a$.
 To make the initial conditiot scalable. we set two düuneusionless paraimeters. ancl to be the same lor all SNRs iu the consideration.," To make the initial condition scalable, we set two dimensionless parameters, and to be the same for all SNRs in the consideration."
 The four Eqs. (35))-(38)), The four Eqs. \ref{eq:SNIaMnorm}) \ref{eq:fm}) )
 thus determiue the four parameters: rjry.ps. aud es.," thus determine the four parameters: $r_s, r_i, \rho_s$, and $v_s$ ."
" From these equations. it is also easy to slow that where;r=η; aud 32=‘2be3,(el:.21)—(2492an>4qua123:t+Eo 1)."," From these equations, it is also easy to show that where $x\equiv r_s/r_i$ and $\beta= 24 x^3 (e^{1/x}-1) - (24x^2 + 12x + 4 + x^{-1})$ ."
 Thus i and e; depend. only on the assumed constants. f; aud fie.," Thus $x$ and $v_s$ depend only on the assumed constants, $f_i$ and $f_m$."
 Similarly. the ratio. px/pa=fet+. is again the same for various ambient densities.," Similarly, the ratio, $\rho_s/\rho_a= f_i e^{1/x-1}$, is again the same for various ambient densities."
 Thus. we cau get auy desirable SNR from a pre-simmulated template witli the above scalable initial condition.," Thus, we can get any desirable SNR from a pre-simulated template with the above scalable initial condition."
 To make the initial [ree expausiou a good approximation to be described by Eq. (31)).," To make the initial free expansion a good approximation to be described by Eq. \ref{eq:SNIainitprof}) ),"
" we ueed to have fy, much less than one (e.g. 10.1 in our examinations: no significantdifference is found if [4,710 5)."," we need to have $f_m$ much less than one (e.g., $10^{-4}$ in our examinations; no significantdifference is found if $f_m$ $10^{-6}$ )."
 Theparameter f; (adopted to be 10)determines the shape of the initial ejecta profile: a, Theparameter $f_i$ (adopted to be 10)determines the shape of the initial ejecta profile; a
The brightest cluster galaxy (BCG) in A3112 exhibits strong optical line emission and a powerful radio source.,The brightest cluster galaxy (BCG) in A3112 exhibits strong optical line emission and a powerful radio source.
" It was targeted with IRAC and MIPS observations by ?,, who find a weak MIR excess atmicron."," It was targeted with IRAC and MIPS observations by \citet{Quillen08}, who find a weak MIR excess at."
. They derive an infrared luminosity of 2.2x1019 Lo which equates to an SFR of 4 (2))., They derive an infrared luminosity of $\times 10^{10}$ $_\odot$ which equates to an SFR of 4 \citealt{O'Dea08}) ).
" The BLAST results are at face value inconsistent with this SFR, with a 2σ detection at of 57+28 mJy and upper limits of 64 and 46 mJy at 350 and (assuming three times the map r.m.s.)."," The BLAST results are at face value inconsistent with this SFR, with a $\sigma$ detection at of $\pm$ 28 mJy and upper limits of 64 and 46 mJy at 350 and (assuming three times the map r.m.s.)."
 This translates to an upper limit of 3.1x10? Lo for the FIR luminosity and 0.6 for the SFR., This translates to an upper limit of $\times 10^{9}$ $_\odot$ for the FIR luminosity and 0.6 for the SFR.
" However, theSpitzer and BLAST luminosities are derived using different methods and the Spitzer-derived value is potentially over-estimated due to the MIR contribution of an AGN."," However, the and BLAST luminosities are derived using different methods and the }-derived value is potentially over-estimated due to the MIR contribution of an AGN."
" The presence of an AGN is consistent with the results of ?,, who find an X-ray point source coincident with the core of the BCG and an X-ray excess associated with radio lobes."," The presence of an AGN is consistent with the results of \citet{Takizawa03}, who find an X-ray point source coincident with the core of the BCG and an X-ray excess associated with radio lobes."
" Spectral analysis identified a power-law component with index 1.9, which confirms this galaxy to host an AGN."," Spectral analysis identified a power-law component with index 1.9, which confirms this galaxy to host an AGN."
 The X-ray excess is also explained by ? in terms of relativistic electrons accelerated by a central source., The X-ray excess is also explained by \citet{Bonamente07} in terms of relativistic electrons accelerated by a central source.
" The BLAST limit is at the lower end of the SFR values found both by ? and by us with the UV detection of the BCG by GALEX (1.5+,, cf."," The BLAST limit is at the lower end of the SFR values found both by \citet{{O'Dea08}} and by us with the UV detection of the BCG by GALEX (1.5, cf."
" Section 3.1)), which is also likely to be contaminated by the signature of the AGN."," Section \ref{cmembs}) ), which is also likely to be contaminated by the signature of the AGN."
 The cluster colour-magnitude (CM) diagram enables us to select galaxies with respect to their overall unobscured star-formation activity., The cluster colour-magnitude (CM) diagram enables us to select galaxies with respect to their overall unobscured star-formation activity.
" As already pointed out in Sect. 3.1,,"," As already pointed out in Sect. \ref{cmembs},"
" a large number of objects lie on the cluster RS, identifying them as passively evolving ellipticals."," a large number of objects lie on the cluster RS, identifying them as passively evolving ellipticals."
" Moreover, we find the region redwards of the RS to be populated by 26 galaxies (i.e., of the optical sample) showing colours about 0.1—0.2 magnitudes redder than the RS."," Moreover, we find the region redwards of the RS to be populated by 26 galaxies (i.e., of the optical sample) showing colours about 0.1–0.2 magnitudes redder than the RS."
 The combination of BLAST with optical and near-IR data can help in understanding the nature of these systems., The combination of BLAST with optical and near-IR data can help in understanding the nature of these systems.
" We thus stack the three sub-catalogues of blue galaxies (21 objects below the RS), RS galaxies (99 objects) and very red galaxies (26 objects redder than the RS)."," We thus stack the three sub-catalogues of blue galaxies (21 objects below the RS), RS galaxies (99 objects) and very red galaxies (26 objects redder than the RS)."
" We then derive the mean star-formation rate from the FIR luminosity, as in Section 3.2.."," We then derive the mean star-formation rate from the FIR luminosity, as in Section \ref{indsources}."
" The results are presented in Table 3, showing that the majority of the stacked sub-mm emission from our cluster member catalogue comes from optically blue (i.e. star-forming) galaxies."," The results are presented in Table 3, showing that the majority of the stacked sub-mm emission from our cluster member catalogue comes from optically blue (i.e. star-forming) galaxies."
 The bulk of their emission is clearly detected atmicron., The bulk of their emission is clearly detected at.
" On the other hand, RS galaxies show no significant emission in any BLAST band, confirming these systems as largely evolved, dust-free galaxies; consistently, their derived SFR is"," On the other hand, RS galaxies show no significant emission in any BLAST band, confirming these systems as largely evolved, dust-free galaxies; consistently, their derived SFR is"
 arate The ratio of these two rates vields since (he ratio in equation 25 is <1 lor ey«€c. we conclude that ΙΝΕ5 with separations RyoBRaleyulefey Ge. KDDs with esB€ e) tend to be broken up by passingg NMBOs.,"a rate The ratio of these two rates yields Since the ratio in equation \ref{e600} is $<1$ for $v_B<v$, we conclude that KBBs with separations $R_B> R_H (v_H/v)^2$ (i.e. KBBs with $v_B < v$ ) tend to be broken up by passing KBOs."
 Binaries with separations of Rey=Ryley/v0)* or less. tend to survive.," Binaries with separations of $R_{crit}= R_H
(v_H/v)^2$ or less, tend to survive."
 The cross section for the £L? mechanism is therefore reduced with respect to the sub-IHill case., The cross section for the $L^3$ mechanism is therefore reduced with respect to the sub-Hill case.
" The probability of having a IKDBO within /2,;, of a given KDO is (VO)/(pRiv)Re, where (XO)/(pIt*e) is the volume number densitv. of erpINDOs."," The probability of having a KBO within $R_{crit}$ of a given KBO is $(\Sigma \Omega)/(\rho R^3
v)~ R_{crit}^3$ where $(\Sigma \Omega)/(\rho R^3 v)$ is the volume number density of KBOs."
" :The flix of. INDOs into− area 75,59 is. (XO)/(pItv)..-ορ.""ENcrit"," The flux of KBOs into area $R_{crit}^2$ is $(\Sigma
\Omega)/(\rho R^3 v)~v R_{crit}^2$."
 The super-Iill formation rate for tight binaries with separations e2... via the L mechanism. is therefore (see also Nolletal. (2007))).," The super-Hill formation rate for tight binaries with separations $\sim R_{crit}$, via the $L^3$ mechanism, is therefore (see also \citet{N07}) )."
 In addition to tight5 binaries with separations ofΠρri and less. (here exist a second class of binaries wilh larger separations.," In addition to tight binaries with separations of$R_{crit}$ and less, there exist a second class of binaries with larger separations."
 Binaries will separations Ry>Roy ave constantly created and destroved. via the Z mechanism., Binaries with separations $R_B>R_{crit}$ are constantly created and destroyed via the $L^3$ mechanism.
 KDDs can form from two KDOs that approach each other with relative velocity 0j<e while a third NBO removes energy. through gravitational scattering. enabling the INDOs to get bound.," KBBs can form from two KBOs that approach each other with relative velocity $v_B \lesssim v$ while a third KBO removes energy, through gravitational scattering, enabling the KBOs to get bound."
 Since we are selecting bodies with relative velocities ~ey or less. the number of INRBOs that can form binaries with separation Ry=Bgy(vg/veg)? is reduced by ~(eg/c0)*.," Since we are selecting bodies with relative velocities $\sim v_B$ or less, the number of KBOs that can form binaries with separation $R_B= R_H
 (v_H/v_B)^2$ is reduced by $\sim (v_B/v)^3$."
" The lormation rate for binaries with separation Ry=Bgy(vg/veg)? is These wider binaries (2p> f,,5) have a higher formation rate compared to the tight ones which have a separation eορ.", The formation rate for binaries with separation $R_B=R_H (v_H/v_B)^2$ is These wider binaries $R_B>R_{crit}$ ) have a higher formation rate compared to the tight ones which have a separation $\sim R_{crit}$.
 The ratio of the formation rate (equation 27)) to the destruction rate (equation 24)) vields an equilibrium abundance of binaries per ABO at any given time that is given by The number of binaries scales as (/25/Rjj) ., The ratio of the formation rate (equation \ref{e169}) ) to the destruction rate (equation \ref{e101}) ) yields an equilibrium abundance of binaries per KBO at any given time that is given by The number of binaries scales as $(R_B/R_H)^{3/2}$ .
" Binaries with separation £25 are therefore (plRony?c(v/vg)? mes more common than those with separation A,,;; provided", Binaries with separation $R_B$ are therefore $(R_B/R_{crit})^{3/2}\sim(v/v_B)^3$ times more common than those with separation $R_{crit}$ provided
Aluch larger5 velocities are induced. however. if the elfect ol ram.pressure acceleration by the shocked IGM gas (often referred to as entrainment) is considered.,"Much larger velocities are induced, however, if the effect of ram–pressure acceleration by the shocked IGM gas (often referred to as entrainment) is considered."
 Dehind the initial row shock. the clouds find themselves in a shocked. laver of IGM. moving outwards at speeds. approaching that of he bow shock.," Behind the initial bow shock, the clouds find themselves in a shocked layer of IGM, moving outwards at speeds approaching that of the bow shock."
 Phe clouds will be accelerated: within this mecium until they pass across the contact discontinuity into he radio cocoon. where the pressure is the same as in the shocked laver of gas but the density is much lower. and they are no longer accelerated: there is essentially no mixing of he hot intercloud gas across this contact discontinuity (e.g. vorman 11982).," The clouds will be accelerated within this medium until they pass across the contact discontinuity into the radio cocoon, where the pressure is the same as in the shocked layer of gas but the density is much lower, and they are no longer accelerated; there is essentially no mixing of the hot inter–cloud gas across this contact discontinuity (e.g. Norman \nocite{nor82}."
. During the time AY’ for which a cloud is between the »»w shock and the contact. eliscontinuitv. the momentunir imparted to the cloud. by the shocked. IGM. can be approximated to first order as rzez2nsmpME. where à; is the cloud size. ος is the bow shock velocity. my is the post.shock number density of the inter.cloud gas and my is the proton mass.," During the time $\Delta T$ for which a cloud is between the bow shock and the contact discontinuity, the momentum imparted to the cloud by the shocked IGM can be approximated to first order as $r_{\rm c}^2 v_{\rm s}^2
n_{\rm g} m_{\rm p} \Delta T$, where $r_{\rm c}$ is the cloud size, $v_{\rm s}$ is the bow shock velocity, $n_{\rm g}$ is the post–shock number density of the inter–cloud gas and $m_{\rm p}$ is the proton mass."
" The mass of the cloud is of order rn,my. where ne is the cloud number density. aid the timescale AY is of order Die. where D is the distance between the bowshock and the contact discontinuity: therefore. the velocity to which the cloud is accelerated is In the radio source evolution models of Kaiser Alexander (7).. radio sources grow selfsimilarly ancl D is found to be about of the distance between the ACGN and the bow shock (?):: for the radio source passing through the emission line region atradius 15 kkpe then. D~0.5 kkpe."," The mass of the cloud is of order $r_{\rm c}^3 n_{\rm c} m_{\rm p}$, where $n_{\rm c}$ is the cloud number density, and the timescale $\Delta
T$ is of order $D / v_{\rm s}$, where $D$ is the distance between the bow–shock and the contact discontinuity; therefore, the velocity to which the cloud is accelerated is In the radio source evolution models of Kaiser Alexander \shortcite{kai97a}, radio sources grow self–similarly and $D$ is found to be about of the distance between the AGN and the bow shock \cite{kai99a}; ; for the radio source passing through the emission line region atradius $\sim 15$ kpc then, $D \sim 0.5$ kpc."
 Assuming a density ratio of Ημης107 for pressure equilibrium. between the clouds (1°~10 WIN) and. the surrounding IGM (27~107 Wis). and a shock velocity of ος~0.056 from typical hot-spot advance velocities (e.g. Liu. Pooley Lileyv 1992).. then a cloud of size ro Lppe will e accelerated to1. comparable to the velocities observed. in the small radio sources (the actual velocities may need to be slightly higher since the radio galaxies are relieved to lie close to the plane of the sky).," Assuming a density ratio of $n_{\rm g} / n_{\rm c} \sim 10^{-4}$ for pressure equilibrium between the clouds $T \sim 10^4$ K) and the surrounding IGM $T \sim 10^8$ K), and a shock velocity of $v_{\rm s} \sim 0.05c$ from typical hot-spot advance velocities (e.g. Liu, Pooley Riley \nocite{liu92}, then a cloud of size $r_{\rm c} \sim 1$ pc will be accelerated to, comparable to the velocities observed in the small radio sources (the actual velocities may need to be slightly higher since the radio galaxies are believed to lie close to the plane of the sky)."
 The spread in projected. cloud. velocities Crom clouds. of dilferent. sizes and from clouds accelerated through dillerent regions of the row shock will lead. to the broad. velocity. dispersions., The spread in projected cloud velocities from clouds of different sizes and from clouds accelerated through different regions of the bow shock will lead to the broad velocity dispersions.
 The acceleration of the emission line gas clouds by the radio bow shocks therefore explains the distorted velocity. profiles and arge line widths observed in small radio sources., The acceleration of the emission line gas clouds by the radio bow shocks therefore explains the distorted velocity profiles and large line widths observed in small radio sources.
 lt is interesting to note that the acquired cloud velocities are proportional to the bowshock velocity ος., It is interesting to note that the acquired cloud velocities are proportional to the bow–shock velocity $v_{\rm s}$.
 If the bowshock velocity increases with radio power (redshift). as has been sugeested from spectral ageing measurements of hotspot advance velocities (e.g. Liu. Pooley Riley 1992).. this would. explain why greater velocity widths are seen in high redshift sources than low reclshilt SOULCES.," If the bow–shock velocity increases with radio power (redshift), as has been suggested from spectral ageing measurements of hotspot advance velocities (e.g. Liu, Pooley Riley \nocite{liu92}, this would explain why greater velocity widths are seen in high redshift sources than low redshift sources."
 The ionisation state of the large radio sources indicates that the dominant sourceof ionising photons in these sources is the AGN., The ionisation state of the large radio sources indicates that the dominant source of ionising photons in these sources is the AGN.
 Since the properties of the AGN are. not expected. to change dramatically between small ancl large radio sources. the eas surrounding the small sources should receive a similar Lux of photoionising radiation.," Since the properties of the AGN are not expected to change dramatically between small and large radio sources, the gas surrounding the small sources should receive a similar flux of photoionising radiation."
 The lower ionisation state seen in the spectra of these galaxies arises in part due to compression of emission line gas clouds by the radio source shocks. decreasing the ionisation parameter.," The lower ionisation state seen in the spectra of these galaxies arises in part due to compression of emission line gas clouds by the radio source shocks, decreasing the ionisation parameter."
 The presence of extra. (softer) ionising photons associated with the shocks further inlluences the ionisation state., The presence of extra (softer) ionising photons associated with the shocks further influences the ionisation state.
 Bicknell ((19007: see also Dopita and Sutherland have investigated the emission. line. luminosity that can be generated by radio source shocks expanding through a single.phase ISM with a powerlaw clensity graclicnt. porfry).," Bicknell (1997; see also Dopita and Sutherland \nocite{bic97,dop96} have investigated the emission line luminosity that can be generated by radio source shocks expanding through a single–phase ISM with a power–law density gradient, $\rho(r) = \rho_{\rm
0} (r/r_{\rm 0})^{-\delta}$ ."
 Por à=2. they show that the work done on the ISAL by the expanding radio cocoon CPdV) is approximately half of the energy supplied by the radio jet: if the shock is fully radiative then a significant. proportion of this energy is [ed into emission line lIuminositv.," For $\delta = 2$, they show that the work done on the ISM by the expanding radio cocoon $P{\rm d}V$ ) is approximately half of the energy supplied by the radio jet; if the shock is fully radiative then a significant proportion of this energy is fed into emission line luminosity."
 The luminosity of the OLLI] 5007 emission line can be estimated as where £4 is the monochromatic power of the radio source at L4AcGllz. and &i4 is the conversion factor from the energy flux of the jet to the monochromatic radio power ab 14GllIz. which Bicknell shortceitebicü7— estimate to be of order LOηςUn," The luminosity of the [OIII] 5007 emission line can be estimated as where $P_{1.4}$ is the monochromatic power of the radio source at GHz, and $\kappa_{\rm 1.4}$ is the conversion factor from the energy flux of the jet to the monochromatic radio power at GHz, which Bicknell \\shortcite{bic97} estimate to be of order $10^{-10.5}$."
 AdoptingH his value. taking the flux density of a typical z~1 3C€H source at an observed. frequency. of αν to be ὃν. and assuming that the OLI](?).. then for 6=2 the observed OL] 3727 emission line flux. produced. by the shocks is calculated to be ΟΙ)~310Peergsss teem 27.," Adopting this value, taking the flux density of a typical $z
\sim 1$ 3CR source at an observed frequency of GHz to be Jy, and assuming that the [OII], then for $\delta = 2$ the observed [OII] 3727 emission line flux produced by the shocks is calculated to be $f({\rm
[OII]}) \sim 3 \times 10^{-15}$ $^{-1}$ $^{-2}$."
 Οἱ his. probably between a third anda half (that is. 1 to 1.5 eergsss 7) will fall within the projected sky area from which the spectrum was extracted.," Of this, probably between a third anda half (that is, 1 to $1.5 \times
10^{-15}$ $^{-1}$ $^{-2}$ ) will fall within the projected sky area from which the spectrum was extracted."
 This predicted emission line (ux can be compared to the OIL 3727 emission line Duxes observed in the data (Pable 12). which lie in the range 0.55 to 5..10Ls 1 73 with the smaller radio sources tvpically having the higher values (sec also Figure 6)).," This predicted emission line flux can be compared to the [OII] 3727 emission line fluxes observed in the data (Table \ref{props}) ), which lie in the range $\sim 0.5$ to $5
\times 10^{-15}$ $^{-1}$ $^{-2}$ with the smaller radio sources typically having the higher values (see also Figure \ref{EWsize}) )."
 These results are completely consistent with a small. (factors of 2 to 5) boosting of the emission line unminosities of small sources due to the extra energy. input rom the shocks., These results are completely consistent with a small (factors of 2 to 5) boosting of the emission line luminosities of small sources due to the extra energy input from the shocks.
 Once the radio source shocks have passed. bevond 10 emission line clouds. the shockinduced. emission. line unminosity will fall.," Once the radio source shocks have passed beyond the emission line clouds, the shock–induced emission line luminosity will fall."
 Under the simplest assumptions. once © jets. pass bevond the confining ISM the pressure inside 10 Cocoon will drain away. and the cocoon wall shocks will no longer be pressure driven (e.g. Dopita 1999).," Under the simplest assumptions, once the jets pass beyond the confining ISM the pressure inside the cocoon will drain away, and the cocoon wall shocks will no longer be pressure driven (e.g. Dopita \nocite{dop99}."
. These garocks will pass into à momentum conserving phase: their 2locity will decrease roughly asοςoxrr2 and so since —1e shock Luminosity per unit area scales as c2. the shockinduced. emission line Luminosity will fall as r +.," These shocks will pass into a momentum conserving phase; their velocity will decrease roughly as$v_{\rm s} \propto r^{-2}$ , and so since the shock luminosity per unit area scales as $v_{\rm s}^3$, the shock--induced emission line luminosity will fall as $r^{-4}$ ."
 Although these assumptions are oversimplified. taking no account of confinement by an intracluster medium. for. example.," Although these assumptions are oversimplified, taking no account of confinement by an intracluster medium for example,"
" (""extremelyRidewav1994:Thompsonefa£1999:Daddia£.2000)."," \citep[``extremely red galaxies'', hereafter 
ERGs; e.g.][]{Els88,Mcc92,Hu94,Tho99,Dad00}."
". A—>5. (221) efal,1997;Süavellie£a£.1999:Soileral.1999). "," $R-K > 5$ $z \gtrsim\ 1$ \citep[e.g.][]{Spi97,Sti99,Soi99} "
used to directly determine the origin of the N-ray emission. which carries little distance information.,"used to directly determine the origin of the X-ray emission, which carries little distance information."
 The interpretatiou of the enussionu depends scusitively on the assumed cool (A-vayv-absorbine) aud hot gas distributions., The interpretation of the emission depends sensitively on the assumed cool (X-ray-absorbing) and hot gas distributions.
 Spectroscopic information on the X-ray oenmission has been obtained from rocket experiments (10) and nxxe recently from oobservatious. but only for a ummber of sample regions (c.e.. (11))).," Spectroscopic information on the X-ray emission has been obtained from rocket experiments \cite{mcc02}
 and more recently from observations, but only for a number of sample regions (e.g., \cite{yos09}) )."
 There are also large uucertaiuties iu the contributions fron faint discrete sources aud other irvelevant phenomena such as solar wind charge exchange (SWCN) to the cinission., There are also large uncertainties in the contributions from faint discrete sources and other irrelevant phenomena such as solar wind charge exchange (SWCX) to the emission.
 A breakthrough for the study of the elobal hot eas has Όσοι mace from the use of the N-rav absorption line spectroscopy (c.@.. (12:13:14:15:16:17:18:19: 20))).," A breakthrough for the study of the global hot gas has been made from the use of the X-ray absorption line spectroscopy (e.g., \cite{fut04, wan05,wil05,yw05,yw06,yw07a,yw07b,yao08,yao09}) )."
 While absorption line spectroscopy is comonly used in optic‘al and UV studies of the iuterstellay medium (ISM). this technique became feasible in the soft X-ray rogiux onlv with erating spectra from aandNewton.," While absorption line spectroscopy is commonly used in optical and UV studies of the interstellar medium (ISM), this technique became feasible in the soft X-ray regime only with grating spectra from and."
.. Uulike the emissiou. which is sensitive to the density structure. absorption lines produced by ious such as O VIL ο VITL and Ne IX (Fig.," Unlike the emission, which is sensitive to the density structure, absorption lines produced by ions such as O VII, O VIII, and Ne IX (Fig."
 1 1)) dixectly probe their column deusities. which are proportional to the mass of the hot gas.," 1 \ref{fig:f1}) ) directly probe their column densities, which are proportional to the mass of the hot gas."
 The relative strengths of such absorption lines give direct ciagnostics «X the thermal. chemical and/or kinetic properties of the hot eas.," The relative strengths of such absorption lines give direct diagnostics of the thermal, chemical and/or kinetic properties of the hot gas."
 Although the absorption lines are rarely resolved iu the spectra (with a resolution of ~LOO)500kins PWIHIAD). the velocity dispersion of the hot gas can be derived from the relative line saturation of different. transitions of same ion species (ως. Ka vs. K »).," Although the absorption lines are rarely resolved in the spectra (with a resolution of $\sim 400-500 {\rm~km~s^{-1}}$ FWHM), the velocity dispersion of the hot gas can be derived from the relative line saturation of different transitions of same ion species (e.g., $\alpha$ vs. $\beta$ )."
 Because the Keshell trausitious of carbon through iron are all in the X-rav reguue. the sale techπιο can be used to study. the ISM im csseutially all phases (cold. wari. aud hot) and forts (atomic. molecular. and dust erain: (16))).," Because the K-shell transitions of carbon through iron are all in the X-ray regime, the same technique can be used to study the ISM in essentially all phases (cold, warm, and hot) and forms (atomic, molecular, and dust grain; \cite{yw06}) )."
 Fithermore. the measurements are insensitive to the absorption bv the cool ISM (kT2104 Is) aud to the SWCN.," Furthermore, the measurements are insensitive to the photo-electric absorption by the cool ISM $kT \lesssim 10^4$ K) and to the SWCX."
 Therefore. the N-ray absorption line spectroscopy allows us to probe the global ISMunubiasedly aloug a sight line.," Therefore, the X-ray absorption line spectroscopy allows us to probe the global ISM unbiasedly along a sight line."
 The effectiveness of the teclinique can be further cubanced when multiple sight lines are analyzed jointly (0... (18))) and/or enüssion data are Included (ee. (19))).," The effectiveness of the technique can be further enhanced when multiple sight lines are analyzed jointly (e.g., \cite{yw07b}) ) and/or emission data are included (e.g., \cite{yao08}) )."
 We cau then infer differeutial properties of hot eas between sight lines of differcut depths or dir'ectious and/or estimate the pathleusth and deusitv ofthe hot eas., We can then infer differential properties of hot gas between sight lines of different depths or directions and/or estimate the pathlength and density of the hot gas.
 The application of this X-ray tomoeraply. though only to a very limited iuuber of sight lines so far. has led to the first characterization of the elobal hot eas:," The application of this X-ray tomography, though only to a very limited number of sight lines so far, has led to the first characterization of the global hot gas:"
ALL galaxies thus acelecl were visually checked: to prevent duplication due to mis-identification or positional errors.,All galaxies thus added were visually checked to prevent duplication due to mis-identification or positional errors.
 About of the galaxies in the sample belong to smereed” images. where the image parameters output by the APAL refer to à combined image of the galaxy in question and other overlapping stars or galaxies (classification label NI in Table 2..," About of the galaxies in the sample belong to “merged” images, where the image parameters output by the APM refer to a combined image of the galaxy in question and other overlapping stars or galaxies (classification label $\ge$ 81 in Table \ref{tab:catalogue}."
 The diameters and magnitudes of. these ealaxies will of course be uncertain., The diameters and magnitudes of these galaxies will of course be uncertain.
 We have visually assessed cach of these objects to ensure that the galaxy in question is bright enough to be included in the sample., We have visually assessed each of these objects to ensure that the galaxy in question is bright enough to be included in the sample.
 The UW Schmidt. plates have generous overlaps with neighbouring plates. since their centres are 5 degrees apart whereas the usable areas of these. plates are 6.2. degrees square.," The UK Schmidt plates have generous overlaps with neighbouring plates, since their centres are 5 degrees apart whereas the usable areas of these plates are 6.2 degrees square."
 X relative magnitude system is thus established bv matching the magnitudes of galaxies in these overlap regions., A relative magnitude system is thus established by matching the magnitudes of galaxies in these overlap regions.
 CCD observations of galaxy. sequences on a lareec fraction of of these plates are used. to relate. it to the b; magnitude svstem (Ravehaucdhury2002)., CCD observations of galaxy sequences on a large fraction of of these plates are used to relate it to the $b_J$ magnitude system \cite{somak:2002}.
. Since total magnitudes of the calibrating galaxies are used. the quoted magnitudes refer. to the total magnitude of the sample ealaxies.," Since total magnitudes of the calibrating galaxies are used, the quoted magnitudes refer to the total magnitude of the sample galaxies."
 The galaxy magnitudes were corrected for Galactic extinction according to Burstein [llciles (1982) reddening values. based. of LE E. column densities. using a gas-to-dust ratio of εξ4.0«E(D.—V).," The galaxy magnitudes were corrected for Galactic extinction according to Burstein Heiles \shortcite{burstein:82} reddening values based of H I column densities, using a gas-to-dust ratio of $A_B = 4.0*E(B-V)$."
 The magnitude limit of b;=16.7 was imposed.affer correction for extinction., The magnitude limit of $b_J=16.7$ was imposed correction for extinction.
 Alost of the observations were performed. with the FLALR-Η fibre spectrograph (hereafter FLALR) system at the Ulx Schmidt. ‘Telescope (UIST) at Siding Spring Observatory (SSO) in Australia. over à S-vear period from mid. 1991 to carly 1996.," Most of the observations were performed with the FLAIR-II fibre spectrograph (hereafter FLAIR) system at the UK Schmidt Telescope (UKST) at Siding Spring Observatory (SSO) in Australia, over a 5-year period from mid 1991 to early 1996."
 The FLALR system (Parker&Watson1994)— was, The FLAIR system \cite{pw:1994} was
the external Compton component.,the external Compton component.
" The peak photon energies ancl peak pF, fluxes. eres ? +. of the Compton and svnchrotvon components are determined [rom simultaneous nmulüiwavelength observations."," The peak photon energies and peak $\nu F_{\nu}$ fluxes, $\nu F_{\nu} = 
10^{-10} \, F_{-10}$ ergs $^{-2}$ $^{-1}$, of the Compton and synchrotron components are determined from simultaneous multiwavelength observations."
" In (he lolowing. photon energies are given in dimensionless units €—πωο=10""e,. and we deline ej2B/D,,—23x2.9101BG),"," In the following, photon energies are given in dimensionless units $\epsilon = h \nu / m_e c^2 = 10^n \,
\epsilon_n$, and we define $\epsilon_B \equiv B / B_{\rm cr} = 
2.3 \times 10^{-14} \, B({\rm G})$."
 The jets in blazars are generally believed to be oriented close to the line of sight where the Doppler beaminge factor DzzE., The jets in blazars are generally believed to be oriented close to the line of sight where the Doppler beaming factor $D \approx \Gamma$.
 Thus. for simplicity. we assume 2=TD in the following.," Thus, for simplicity, we assume $D = \Gamma$ in the following."
e The model parameters can then be estimated from the observables through the expressions and “ERC” refer to the svuchrotvon. SSC. andexternal Compton componeils. respectively. ancl €; is (he mean photon energy of the external soft photon field in the stationary frame of the AGN.," The model parameters can then be estimated from the observables through the expressions The subscripts “sy,"" “SSC,"" and “ERC"" refer tothe synchrotron, SSC, and external Compton components, respectively, and $\estar$ is the mean photon energy of the external soft photon field in the stationary frame of the AGN."
" The factor f, in equations (5 ) (0) is à normalization actor defined through f,d5n,(5)57=ferD?Nef. and fasc in equation (1)) is a correction [actor between the νΕ peak value and the total energv output in the σος; component. wich differ significantly due to the substantial spectral broadness of the 525C emission."," The factor $\fsp$ in equations \ref{nfnsy}) ) – \ref{nfnssc}) ) is a normalization factor defined through $\int_1^{\infty} d\gamma \, n_e (\gamma) \, \gamma^2 = \gcr^2 \, n_e
\, \fsp$, and $\fssc$ in equation \ref{nfnssc}) ) is a correction factor between the $\nfn$ peak value and the total energy output in the SSC component, which differ significantly due to the substantial spectral broadness of the SSC emission."
 Typically. fase0.1.," Typically, $\fssc \sim 0.1$."
 For the more strongly. peaked svnchrotron aud ERC components. the corresponding correction [actor is fa.àfire~ 1.," For the more strongly peaked synchrotron and ERC components, the corresponding correction factor is $\fsy \approx \ferc \sim 1$ ."
" Combining the above estimates. and defining dj,=1075do; cm and 24,Use2=105R44 em. we find"," Combining the above estimates, and defining $d_L = 10^{28} \, 
d_{28}$ cm and $R_{\rm sc} = 10^{18} \, R_{{\rm sc}, 18}$ cm, we find"
those of ?..,those of \citet{hec2000}. .
 ? also document the cyclic long-term spectral variations of over a time interval from 1973 to 2002., \citet{mirosh2002} also document the cyclic long-term spectral variations of over a time interval from 1973 to 2002.
 To shed more light on the differences between these two RVs studies. to obtain truly reliable orbital elements ofCas. and to exclude possible | d aliases of the 204 d period. we combined our efforts and analysed the two sets of spectra. complemented by more recent observations from Ondreejov and additional spectra from the Dominion Astrophysical (DAO). Haute Provence (OHP) and Castanet-Tolosan Observatories.," To shed more light on the differences between these two RVs studies, to obtain truly reliable orbital elements of, and to exclude possible 1 d aliases of the 204 d period, we combined our efforts and analysed the two sets of spectra, complemented by more recent observations from Ondřeejov and additional spectra from the Dominion Astrophysical (DAO), Haute Provence (OHP) and Castanet-Tolosan Observatories."
 The RVs in all these spectra were measured by both measuring techniques — alternatively used by ? and ? — and analysed in several different ways., The RVs in all these spectra were measured by both measuring techniques – alternatively used by \citet{hec2000} and \citet{mirosh2002} – and analysed in several different ways.
 Here we present the results of our investigation., Here we present the results of our investigation.
 We also studied the long-term and rapid spectral variations of in our data., We also studied the long-term and rapid spectral variations of in our data.
 We have collected and analysed series of electronic. spectra from five observatories., We have collected and analysed series of electronic spectra from five observatories.
 They cover the time interval from 1993 to 2010., They cover the time interval from 1993 to 2010.
 The journal of the observations is in Table I.. where the wavelength range. time interval covered. the number of spectra. and the spectral lines are given.," The journal of the observations is in Table \ref{spectra}, where the wavelength range, time interval covered, the number of spectra, and the spectral lines are given."
 For more details on the individual datasets. readers are referred to Appendix A:," For more details on the individual datasets, readers are referred to Appendix \ref{apen}."
 We focused our study on the lines in the region. which are available for all spectra. although several echelle spectra cover almost the whole visible region of the electromagnetic spectrum.," We focused our study on the lines in the region, which are available for all spectra, although several echelle spectra cover almost the whole visible region of the electromagnetic spectrum."
 In particular. we studied the following spectral lines:Ha...Α..Α.. and À.," In particular, we studied the following spectral lines:, and ."
. No dramatic changes were found in these line profiles., No dramatic changes were found in these line profiles.
" The and lines exhibit double-peaked emissions with the well-known V/R variations (changes in the relative strength of the shorter wavelength. ""violet"". to the longer wavelength. ""red"". peak) on the timeseale of several years."," The and lines exhibit double-peaked emissions with the well-known $V/R$ variations (changes in the relative strength of the shorter wavelength, “violet”, to the longer wavelength, “red”, peak) on the timescale of several years."
 Over the whole time interval covered by our spectra. the line was observed as a strong. basically single-peaked emission. having à peak intensity between 3.5 and 5.0 in the units of the continuum level.," Over the whole time interval covered by our spectra, the line was observed as a strong, basically single–peaked emission, having a peak intensity between 3.5 and 5.0 in the units of the continuum level."
 [ts V/R variations manifest themselves as a relative shift in the emission peak with respect to the centre of the emission profile., Its $V/R$ variations manifest themselves as a relative shift in the emission peak with respect to the centre of the emission profile.
 Several shallow absorptions can be noted in the line in some of the studied spectra. but most of them are the telluric water vapour lines.," Several shallow absorptions can be noted in the line in some of the studied spectra, but most of them are the telluric water vapour lines."
 Ocassionally. some weak shallow absorptions of probably stellar origin were seen. bu= they disappeared in less than several tens of days. and we found no regularity in their appearance and disappearance.," Ocassionally, some weak shallow absorptions of probably stellar origin were seen, but they disappeared in less than several tens of days, and we found no regularity in their appearance and disappearance."
 The line consists of a double-peaked emission filling a large part of the rotationally broadened photospheric (or pseudophotospheric) absorption., The line consists of a double–peaked emission filling a large part of the rotationally broadened photospheric (or pseudophotospheric) absorption.
 The whole line is very weak and can only be measured reliably on the spectra with high S/N., The whole line is very weak and can only be measured reliably on the spectra with high $S/N$.
 The emission peaks rise only a few percent above the continuum level., The emission peaks rise only a few percent above the continuum level.
 Nevertheless. the time variations are seen most prominently in this line.," Nevertheless, the time variations are seen most prominently in this line."
 The red peak of the emission disappeared almost completely at certain times., The red peak of the emission disappeared almost completely at certain times.
 It is hard to say whether these variations represent only real long-term changes or whether they are partly caused by line blending., It is hard to say whether these variations represent only real long-term changes or whether they are partly caused by line blending.
 The and double emission lines are even weaker than the line. and their peak intensity never exceeds of the continuum level.," The and double emission lines are even weaker than the line, and their peak intensity never exceeds of the continuum level."
 The more recent evolution of the line. profile is shown in Fig. .., The more recent evolution of the line profile is shown in Fig. \ref{haevol}.
 All line profiles shown were obtained after RJD = 52225 and were not included in the study by ?.., All line profiles shown were obtained after RJD = 52225 and were not included in the study by \citet{hec2000}.
 A similar sequences of theA..A. and line profiles are shown in Fig. 2..," A similar sequences of the, and line profiles are shown in Fig. \ref{heevol}."
 All displayed spectra are from Ondreejov. to compare the data with the same resolution.," All displayed spectra are from Ondřeejov, to compare the data with the same resolution."
 There are. however. the huge differences in the flux scale betweenΠα..A.. A. and lines.," There are, however, the huge differences in the flux scale between, , and lines."
" We fitted the line profiles with a Gaussian profile to obtain their peak intensity (/, hereafter) and full width at half maximum (FWHM hereafter).", We fitted the line profiles with a Gaussian profile to obtain their peak intensity $I_{\rm p}$ hereafter) and full width at half maximum (FWHM hereafter).
" This procedure naturally returns a value of /,. which is slightly less than the very maximum of the emissionprofile. whichis affected by both theV/R variations and blending with the neighbouring telluric lines."," This procedure naturally returns a value of $I_{\rm p}$ , which is slightly less than the very maximum of the emissionprofile, whichis affected by both the$V/R$ variations and blending with the neighbouring telluric lines."
Transiting planets provide à wealth of information on. the structure and formation of planets.,Transiting planets provide a wealth of information on the structure and formation of planets.
" The measurement of planet radius combined with its mass has found a surprising diversity in the mean densities anc in particular ""inflated"" hot Jupiters."," The measurement of planet radius combined with its mass has found a surprising diversity in the mean densities and in particular “inflated"" hot Jupiters."
 Spectroscopic measurement of the Rossiter-McLaughlin effect on the radial velocity during transits indicates that some of these planets may not be aligned with the rotation axes of their stars (see references in Winn (2010)))., Spectroscopic measurement of the Rossiter-McLaughlin effect on the radial velocity during transits indicates that some of these planets may not be aligned with the rotation axes of their stars (see references in \cite{2010arXiv1001.2010W}) ).
 The diversity in the observed spin-orbit misalignments is somewhat similar to that seen earlier in period and eccentricity distribution of planets detected by radial velocity surveys (see refs in Udry&Santos(2007) and references therein)., The diversity in the observed spin-orbit misalignments is somewhat similar to that seen earlier in period and eccentricity distribution of planets detected by radial velocity surveys (see refs in \cite{2007ARA&A..45..397U} and references therein).
 The recent sharp rise in the detections of transiting planets is the outcome of successful ground-based wide transit searches surveys among which WASP (Pollaccoetal.2006) is the most prolific., The recent sharp rise in the detections of transiting planets is the outcome of successful ground-based wide transit searches surveys among which WASP \citep{2006PASP..118.1407P} is the most prolific.
 These discoveries have stimulated theoretical investigations of alternative formation. scenarios to. the migration theory (Linetal.1996:Wu&Murray2003)..," These discoveries have stimulated theoretical investigations of alternative formation scenarios to the migration theory \citep{1996Natur.380..606L,2003ApJ...589..605W}."
 These alternative theories account for the discoveries of eccentric hot Jupiters on orbits not aligned with the rotation equator of their star (Wu&Murray2003:Fabrycky 2009).," These alternative theories account for the discoveries of eccentric hot Jupiters on orbits not aligned with the rotation equator of their star \citep{2003ApJ...589..605W, 2009ApJ...696.1230F,2008ApJ...678..498N,2009MNRAS.395.2268B}."
 The star ((TYC2 7522-505-1) at a(2000): 236.015. 0(2000): —35° 552.97. was observed in 2006 and 2007 by the WASP-south telescope (Pollaccoetal.2006).," The star (TYC2 7522-505-1) at $\alpha$ (2000): 36.07s, $\delta$ (2000): $-35^\circ$ 52.9”, was observed in 2006 and 2007 by the WASP-south telescope \citep{2006PASP..118.1407P}."
 It is a V=9.79 magnitude star with a Tycho (B-V) color of0.73 which is indicative of a G8 spectral type., It is a $V=9.79$ magnitude star with a Tycho $-$ V) color of0.73 which is indicative of a G8 spectral type.
 The Infra-red Flux Method (IRFM) (Blackwell&Shallis1977).. using GALEX. TYCHO-2. USNO-B1.0 R-magnitude. and 2MASS band photometry. yields a distance of 8747 pe.," The Infra-red Flux Method (IRFM) \citep{1977MNRAS.180..177B}, using GALEX, TYCHO-2, USNO-B1.0 R-magnitude, and 2MASS broad-band photometry, yields a distance of $\pm7$ pc."
 iis identified in the CCDM catalogue 23596-3502)) as the A component of a system of three stars., is identified in the CCDM catalogue ) as the A component of a system of three stars.
 The B component is à [5th magnitude red star. 4 aresee south of A. and the third component C is a 10th magnitude star118299.. 664)) 142 aresee north of A. The radial velocity of 664 is 4.7 aand stable over two years (Mayor priv com.)," The B component is a 15th magnitude red star, 4 arcsec south of A, and the third component C is a 10th magnitude star, ) 142 arcsec north of A. The radial velocity of HD224664 is 4.7 and stable over two years (Mayor priv com.)"
 but differs from the WASP-8 value ofs!., but differs from the WASP-8 value of.
. The proper motions of the components also differs., The proper motions of the components also differs.
 It is therefore unlikely that C and A are physically associated., It is therefore unlikely that C and A are physically associated.
 We measured the photometry and position of aand its nearby star (B component) with the Euler CCD camera of the 1.2m swiss Euler telescope at La Silla (see reftigwaspSuna., We measured the photometry and position of and its nearby star (B component) with the Euler CCD camera of the 1.2m swiss Euler telescope at La Silla (see \\ref{fig:wasp8_ima}) ).
Bycomparingwithnearbystars. weobtainedamagnitude 4.7. Am;=3.5.," By comparing with nearby stars, we obtained a magnitude difference $\Delta\mathrm{m}_V=4.7$ , $\Delta\mathrm{m}_I=3.5$."
 A separation and a projected angle was measured on the deconvolved images (Gillonetal.2007) and we obtained 4.834 0.017 and PA=170.7+ 0.1°(only internal errors being considered)., A separation and a projected angle was measured on the deconvolved images \citep{2007ASPC..366..113G} and we obtained $4.83\pm0.01$ ” and $\mathrm{PA}=170.7\pm0.1$ (only internal errors being considered).
 Assuming that aand its B. component are part of a multiple system. the color indices would represent those of an M star.," Assuming that and its B component are part of a multiple system, the color indices would represent those of an M star."
" A similar photometric analysis of the individual 2MASS archive images indicates that Am,=2.7. Amy= 2.2. and Amy=2.1. which are also indicative of an M star."," A similar photometric analysis of the individual 2MASS archive images indicates that $\Delta\mathrm{m}_J=2.7$, $\Delta\mathrm{m}_H=2.2$ , and $\Delta\mathrm{m}_K=2.1$, which are also indicative of an M star."
 The value mentioned in the Washington Visual Double Star Catalog measured 70 years ago indicates 4.07 and PA=170°(Masonetal. 2001)..," The value mentioned in the Washington Visual Double Star Catalog measured 70 years ago indicates 4.0"" and \citep{2001AJ....122.3466M}. ."
 This suggestslittle. if any. relative motion of the two stars over the 70-year," This suggestslittle, if any, relative motion of the two stars over the 70-year"
(2006).,.
. The combination of (hese studies now leads to a confinned population of 342 Also included in our catalog are the new GC candidates from //57 STIS imaging from Tlarrisetal.(2002).. labelled CLOO-CLOG. and trom (M57 ACS imaging from (2006).. labelled CI11-CI79.," The combination of these studies now leads to a confirmed population of 342 Also included in our catalog are the new GC candidates from $HST$ STIS imaging from \cite{hhhm02}, labelled C100-C106, and from $HST$ ACS imaging from \cite{harris06}, labelled C111-C179."
 All these previous studies have their own internal numbering svslenms. which makes the cluster identifications somewhat confusing at this point.," All these previous studies have their own internal numbering systems, which makes the cluster identifications somewhat confusing at this point."
 Here we define a new. homogeneous listing combining all this material and with a single numbering svslenm.," Here we define a new, homogeneous listing combining all this material and with a single numbering system."
 Our catalog of the GCs of NGC 5128 is given in Table 1.., Our catalog of the GCs of NGC 5128 is given in Table \ref{tab:cat_GC}.
" La successive columns. the Table eives (he new cluster name in order of increasing right ascension: (he previous names of the cluster in (he literature: right ascension and declination (J2000); the projected radius from the center of NGC 5128 in arcminutes: the U. DB. V. R. and 7 photometric indices and (heir measured uncertainties: the C. AL. and Z3 photometric indices and their uncertainties: the colors UL—D. B—-V.V—R.V—I. M— Tq. C—M. and C—T3: and. lastly. the weighted mean velocity v, and its associated uncertaintv from all previous studies."," In successive columns, the Table gives the new cluster name in order of increasing right ascension; the previous names of the cluster in the literature; right ascension and declination (J2000); the projected radius from the center of NGC 5128 in arcminutes; the $U$, $B$, $V$, $R$ , and $I$ photometric indices and their measured uncertainties; the $C$ , $M$ , and $T_1$ photometric indices and their uncertainties; the colors $U-B$, $B-V$, $V-R$, $V-I$, $M-T_1$ , $C-M$, and $C-T_1$; and, lastly, the weighted mean velocity $v_r$ and its associated uncertainty from all previous studies."
 All CDVRI photometry is from the imagingsurvey described in Peng.Ford.&Freeman(2004a)., All $UBVRI$ photometry is from the imagingsurvey described in \cite{pff04I}.
". The CALT, data are from ILlarrisetal.(2004)..", The $CMT_1$ data are from \cite{hhg04II}.
" The mean velocities are weighted averages with weights on each individual measurement equal to 2,7 where 7, is the quoted velocity uncertainty [rom each study.", The mean velocities are weighted averages with weights on each individual measurement equal to $\varepsilon_{v}^{-2}$ where $\varepsilon_{v}$ is the quoted velocity uncertainty from each study.
" The uncertainty in the mean velocity is then <z,>=($27;Da7)τι", The uncertainty in the mean velocity is then $<\varepsilon_v> = (\sum \varepsilon_{i}^{-2})^{-1/2}$.
 There are no individual uncertainties supplied for the velocities lor clusters studied by Lesser.Harris.&Harris(1986).. but their study reports that the mean velocity uncertainty for clusters with Ry.<Ll is 25 km !and for Ry.> Lis 44 km |.," There are no individual uncertainties supplied for the velocities for clusters studied by \cite{hhh86}, but their study reports that the mean velocity uncertainty for clusters with $R_{gc} < 11'$ is 25 km $^{-1}$and for $R_{gc} > 11'$ is 44 km $^{-1}$."
 We have adopted these values accordingly for their The study by Harrisetal.(1992) also does not report velocityuncertainties: however. these clustershave allbeen recently measured byPeng.Ford.&Freeman (200428)...," We have adopted these values accordingly for their The study by \cite{hghh92} also does not report velocityuncertainties; however, these clustershave allbeen recently measured by\cite{pff04I}. ."
 The rms seatter of the ILurisetal.(1992) values from theirs was 58 km |., The rms scatter of the \cite{hghh92} values from theirs was 58 km $^{-1}$ .
 This value has, This value has
the middle-aged Vela pulsar (?)..,the middle-aged Vela pulsar \citep{vela1}.
" We place the source at (R.A., Decl.)"," We place the source at (R.A., Decl.)"
" = (128.8463, -45.1735), the position of Vela."," = (128.8463, -45.1735), the position of Vela."
" For the background, we simulate photons from the two diffuse background models used in the IFGL catalog analysis (?),, gli_tem_v02—a model of the Galactic diffuse background due to cosmic rays—and isotropicv02—an isotropic background including contributionsiem. from unresolved extragalactic point sources and instrumental backgrounds."," For the background, we simulate photons from the two diffuse background models used in the 1FGL catalog analysis \citep{1fgl}, —a model of the Galactic diffuse background due to cosmic rays—and }---an isotropic background including contributions from unresolved extragalactic point sources and instrumental backgrounds."
" In all, we simulate one year of integration using the spacecraft pointing history from 2009."," In all, we simulate one year of integration using the spacecraft pointing history from 2009."
 'The normalization of Eq., The normalization of Eq.
 10 is chosen to yield a bright source with an integral photon flux from 100 MeV to 100 GeV of Fsim=1075s-!..," \ref{eq:vela_spec} is chosen to yield a bright source with an integral photon flux from 100 MeV to 100 GeV of $\mcf_{sim}\equiv
10^{-5}$."
" We are interested in detection of dim sources, so from this set of photons we select subsets emulating sources with appropriately lower fluxes, e.g. Frar=10-9? s!, by (a) drawing the target number, Λα. of photons from a Poisson distribution with mean NiotX and (b) selecting a subset of Nia, of the originalFtar/Fsim photon set at random (without replacement)."," We are interested in detection of dim sources, so from this set of photons we select subsets emulating sources with appropriately lower fluxes, e.g. $\mcf_{tar} = 10^{-8}$ , by (a) drawing the target number, $N_{tar}$, of photons from a Poisson distribution with mean $N_{tot}\times\mcf_{tar}/\mcf_{sim}$ and (b) selecting a subset of $N_{tar}$ of the original photon set at random (without replacement)."
" In this way, we can generate ensembles of statistically independent point sources over a range of fluxes from a single Monte Carlo data set."," In this way, we can generate ensembles of statistically independent point sources over a range of fluxes from a single Monte Carlo data set."
" While we use a single realization of the diffuse photons, we effectively generate a new iteration by randomizing these photons in phase for each ensemble member as we discuss below."," While we use a single realization of the diffuse photons, we effectively generate a new iteration by randomizing these photons in phase for each ensemble member as we discuss below."
 To determine the weights (Eq. 9)) we emplo," To determine the weights (Eq. \ref{eq:weights}) ),"
ygtsrcprob., we employ.
. This Science Tool combines the source models used to generate the Monte Carlo data) with the instrument(those response function to determine the observed source rates and hence the weights., This Science Tool combines the source models (those used to generate the Monte Carlo data) with the instrument response function to determine the observed source rates and hence the weights.
" These weights are valid for the simulated point source flux 75, and must be scaled for the dim ensemble members: w;;.(wom,—1)x "," These weights are valid for the simulated point source flux $\mcf_5$, and must be scaled for the dim ensemble members: $w_{tar}^{-1} - 1 = (w_{sim}^{-1} - 1)\times\mcf_{sim}/\mcf_{tar}$ ."
The Monte Carlo Fsim/Frar-events as generated by have no pulsation., The Monte Carlo events as generated by have no pulsation.
" During simulation, each photon is “tagged” with an identifier for its originating source."," During simulation, each photon is “tagged” with an identifier for its originating source."
" We assign phases from a uniform distribution to the diffuse background, and for the point source we draw phases from an assumed light curve, typically a normalized sum of wrapped Gaussians."," We assign phases from a uniform distribution to the diffuse background, and for the point source we draw phases from an assumed light curve, typically a normalized sum of wrapped Gaussians."
 'Type I error stems from two sources., Type I error stems from two sources.
" First, there is the chance of a fluctuation in the test statistic (TS) sufficiently large to pass the established threshold for rejection of the null hypothesis, i.e., claiming detection of a pulsar."," First, there is the chance of a fluctuation in the test statistic (TS) sufficiently large to pass the established threshold for rejection of the null hypothesis, i.e., claiming detection of a pulsar."
" As long as we understand the null distribution of the TS, this particular source of error is easy to control: we simply determine in advance our tolerance to false positives and set the TS threshold accordingly."," As long as we understand the null distribution of the TS, this particular source of error is easy to control: we simply determine in advance our tolerance to false positives and set the TS threshold accordingly."
 We must be cautious about applying the asymptotic calibration of the null distribution to small sample sizes., We must be cautious about applying the asymptotic calibration of the null distribution to small sample sizes.
" For these cases, it is important to verify the chance probability with a Monte Carlo simulation."," For these cases, it is important to verify the chance probability with a Monte Carlo simulation."
" A second, more insidious source of error arises from the strong influence of the data selection scheme on the pulsed this dependence stemming from the energy-dependentS/N, psf, source confusion, the strong Galactic diffuse, and the exponential suppression of pulsar emission above a few GeV. To find the best cuts, one is tempted to use the TS itself as a metric, a procedure which invalidates its calibration."," A second, more insidious source of error arises from the strong influence of the data selection scheme on the pulsed S/N, this dependence stemming from the energy-dependent psf, source confusion, the strong Galactic diffuse, and the exponential suppression of pulsar emission above a few GeV. To find the best cuts, one is tempted to use the TS itself as a metric, a procedure which invalidates its calibration."
 Failure to account for this change increases the probability of false positives., Failure to account for this change increases the probability of false positives.
 Stringent cuts may also make the asymptotic calibration poorer., Stringent cuts may also make the asymptotic calibration poorer.
 Probability-weighted statistics eliminate these problems., Probability-weighted statistics eliminate these problems.
" Since the weights naturally go to zero for photons with neglible signal, one could in principle include LAT data in the TS. ("," Since the weights naturally go to zero for photons with neglible signal, one could in principle include LAT data in the TS. ("
"In practice, little signal is contained in photons more than 2? from the source.","In practice, little signal is contained in photons more than $2^{\circ}$ from the source.)"
" Weighting provides an amorphous, optimal selection reflecting, e.g., the proximity of the Galactic plane or the estimated pulsar cutoffenergy?."," Weighting provides an amorphous, optimal selection reflecting, e.g., the proximity of the Galactic plane or the estimated pulsar cutoff."
. And this single selection incurs no probability of Type I error beyond that due to statistical fluctuations., And this single selection incurs no probability of Type I error beyond that due to statistical fluctuations.
" Finally, the weighted statistic is less susceptible to small-sample effects since all relevant information is included, though for particularly weak signals Monte Carlo validation remains important."," Finally, the weighted statistic is less susceptible to small-sample effects since all relevant information is included, though for particularly weak signals Monte Carlo validation remains important."
" To make these claims concrete, we compare the weighted H-test (Ηορυ) and the standard H-test (Πορ) computed over a grid of cuts on photon position and energy 2))"," To make these claims concrete, we compare the weighted $H$ -test $H_{20w}$ ) and the standard $H$ -test $H_{20}$ ) computed over a grid of cuts on photon position and energy (Figure \ref{ch5_plot8}) )."
" The unweighted statistics show strong T'S (Figurepeaks for certain energy thresholds and extraction radii, and these peaks vary from realization to realization, precluding an calculation of an optimal aperture."," The unweighted statistics show strong TS peaks for certain energy thresholds and extraction radii, and these peaks vary from realization to realization, precluding an calculation of an optimal aperture."
" The weighted statistics, on the other hand, are largely insensitive to the data selection and perform best for a simple prescription: use as many photons as is practical."," The weighted statistics, on the other hand, are largely insensitive to the data selection and perform best for a simple prescription: use as many photons as is practical."
" We are thus free to usethe same loose cuts for all sources, maintaining good performance (peak TS) without the need to tune."," We are thus free to usethe same loose cuts for all sources, maintaining good performance (peak TS) without the need to tune."
 Releasee 7 (SDSS-DR7)., e 7 (SDSS-DR7).
highest regularisation which provided a fit to the observations compatible with S/N of the data.,highest regularisation which provided a fit to the observations compatible with $S/N$ of the data.
" Analysing the fit of individual profiles, we found synthetic spectrum deviating systematically for a couple of lines of each element, while the rest of lines were fitted rather well."," Analysing the fit of individual profiles, we found synthetic spectrum deviating systematically for a couple of lines of each element, while the rest of lines were fitted rather well."
" To minimise the influence of the errors in atomic data, we allowed the code to correct the oscillator strengths of these lines in the course of inversion."," To minimise the influence of the errors in atomic data, we allowed the code to correct the oscillator strengths of these lines in the course of inversion."
" In Table 5 we provide the information about ion, wavelength, excitation potential, initial oscillator strength, and corrected oscillator strength of the spectral lines used in DI inversion."," In Table \ref{DIlines} we provide the information about ion, wavelength, excitation potential, initial oscillator strength, and corrected oscillator strength of the spectral lines used in DI inversion."
 We present spherical maps of the distribution of chemical elements in Fig. 8.., We present spherical maps of the distribution of chemical elements in Fig. \ref{Fig8}.
" The fit of the observed profiles of Y, Sr, Ti, and Cr is shown in Figs. 9,, 10,, 11,,"," The fit of the observed profiles of Y, Sr, Ti, and Cr is shown in Figs. \ref{fitY}, , \ref{fitSr}, \ref{fitTi},"
" and 12,, respectively."," and \ref{fitCr}, respectively."
" For line at 4077.71A,, we found a much stronger contribution of the blending spectral line of at 4077.51 iin the synthetic spectrum than appears in observations."," For line at 4077.71, we found a much stronger contribution of the blending spectral line of at 4077.51 in the synthetic spectrum than appears in observations."
" The correction of the oscillator strength for this particular Cr line by one order of magnitude allowed a better fit of the observed profile, reducing the standard deviation for Sr from to0."," The correction of the oscillator strength for this particular Cr line by one order of magnitude allowed a better fit of the observed profile, reducing the standard deviation for Sr from to."
"65%.. For the other chemical elements, the standard deviation of the final profile fit is for Y, for Ti, and for Cr."," For the other chemical elements, the standard deviation of the final profile fit is for Y, for Ti, and for Cr."
 These results are consistent with the quality of our data., These results are consistent with the quality of our data.
" From the DI surface maps we found that all chemical elements concentrate in the same spot, observed at phases 0.2-0.4."," From the DI surface maps we found that all chemical elements concentrate in the same spot, observed at phases 0.2–0.4."
 A secondary chemical spot exists for Ti and Cr and is visible at phase range 0.8-1.0., A secondary chemical spot exists for Ti and Cr and is visible at phase range 0.8–1.0.
" However, the abundance gradients relative to the mean stellar composition are different for the four investigated elements."," However, the abundance gradients relative to the mean stellar composition are different for the four investigated elements."
" The largest gradient (1.3 dex) is found for Y. Sr shows less of a contrast (0.6 dex), which is comparable to that of Ti (0.5 dex)."," The largest gradient (1.3 dex) is found for Y. Sr shows less of a contrast (0.6 dex), which is comparable to that of Ti (0.5 dex)."
" Finally, a very low contrast (0.15 dex) is observed for Cr."," Finally, a very low contrast (0.15 dex) is observed for Cr."
typical distance set by the diffusion length LaVs/KB(E) E.,typical distance set by the diffusion length $L_{\rm d} \sim V_{\rm s}/\kappa_{\rm B}(E) \propto E$ .
" The diagonally shaded area is the region more than 4.6 diffusion lengths ahead of the shock, in which 99 per cent of the particles should be located (F(p)=F(p)ofev/vo-- 0.01F(p)o)."," The diagonally shaded area is the region more than $4.6$ diffusion lengths ahead of the shock, in which 99 per cent of the particles should be located $F(p)=F(p)_0\int e^{-\Delta x/x_0}=0.01 F(p)_0$ )."
" In this model the attainable electron energy is limited mostly by synchrotron losses, and considerably less than the proton energy at an age of ~1300 yr."," In this model the attainable electron energy is limited mostly by synchrotron losses, and considerably less than the proton energy at an age of $\sim 1300$ yr."
 The high-energy electrons therefore diffuse over smaller distances compared to protons., The high-energy electrons therefore diffuse over smaller distances compared to protons.
" The horizontally shaded region in the electron plot shows the region more than 4.6 loss-limited diffusion lengths ahead of the shock, (Lioss,a=VW2Ktioss; with tios;=/orB? 61m2c3 "," The horizontally shaded region in the electron plot shows the region more than $4.6$ loss-limited diffusion lengths ahead of the shock, $L_{\rm loss,d} =\sqrt{2 \kappa t_{\rm loss}}$, with $t_{\rm loss}=6 \pi m_{\rm e}^2 c^3/\sigma_T B^2 E$ )."
In Fig., In Fig.
" 16 we follow E).the population of protons that were injected during the first 300 yr of the simulation, and track their distribution in the energy-radius plane as the simulation progresses."," \ref{fig:nxu_time} we follow the population of protons that were injected during the first 300 yr of the simulation, and track their distribution in the energy-radius plane as the simulation progresses."
" At the end of the simulation (at t&1500 yr), they constitute about 10 per cent of the total proton population."," At the end of the simulation (at $t\approx 1500$ yr), they constitute about 10 per cent of the total proton population."
 The maximum energy in the distribution of these protons turns out to be similar to that of the entire proton poulation., The maximum energy in the distribution of these protons turns out to be similar to that of the entire proton poulation.
" This is due to the fact that for this particular model (ISM«p10p), the Sedov-Taylor time is roughly equal to the time at which we start tracking the population of particles."," This is due to the fact that for this particular model $\kappa_B$ 10p), the Sedov-Taylor time is roughly equal to the time at which we start tracking the population of particles."
" As we discussed earlier, the acceleration efficiency is highest around the Sedov-Taylor transition, after which the maximum energy of the particles only increases by a factor of a few."," As we discussed earlier, the acceleration efficiency is highest around the Sedov-Taylor transition, after which the maximum energy of the particles only increases by a factor of a few."
 We have determined that the overall spectrum is somewhat steeper than the canonical g=2 power law., We have determined that the overall spectrum is somewhat steeper than the canonical $q=2$ power law.
" We attribute this to the losses that are not taken into account in the analytical calculations for planar, steady shocks."," We attribute this to the losses that are not taken into account in the analytical calculations for planar, steady shocks."
" It is therefore interesting to look at the spectrum at the shock, one diffusion length La(Emax) upstream and downstream, and compare it to the spectrum of all particles in the SNR."," It is therefore interesting to look at the spectrum at the shock, one diffusion length $L_{\rm d}(E_{\rm max})$ upstream and downstream, and compare it to the spectrum of all particles in the SNR."
 In Fig., In Fig.
 17 we show these spectra for the CSM&gp10 model for electrons and protons., \ref{fig:spectimeloc} we show these spectra for the $\kappa_B$ 10 model for electrons and protons.
 It becomes apparent that the spectrum at the shock follows the analytically predicted power law slope quite closely., It becomes apparent that the spectrum at the shock follows the analytically predicted power law slope quite closely.
 Upstream of the shock only, Upstream of the shock only
"with (σος,=PAY(0) for galaxies and shear.",with $(\bit{C}_\ell)_{ij}^{XY} = \tilde{P}_{ij}^{XY}(\ell)$ for galaxies and shear.
 The minimum marginalized error of ga is =(F“ie.," The minimum marginalized error of $q_\alpha$ is $\sigma(q_\alpha) =
(F^{-1})_{\alpha\alpha}^{1/2}$."
" Independent Fisher matrices are additive;o(da) a prior on qa, op(da), can be introduced via ΕΠΟΝ=Fya+op""(qa)."," Independent Fisher matrices are additive; a prior on $q_\alpha$, $\sigma_{\rm P}(q_\alpha)$ , can be introduced via $F_{\alpha\alpha}^{\rm new} = F_{\alpha\alpha}
+\sigma_{\rm P}^{-2}(q_\alpha)$."
" We extend the additive and multiplicative shear power spectrum errors in Hutereretal.(2006) to include the galaxy power spectrum errors: where p* determines how strongly the additive errors of two different bins are correlated, and n* and ¢* account for the scale dependence of the additive errors."," We extend the additive and multiplicative shear power spectrum errors in \citet{huterer06} to include the galaxy power spectrum errors: where $\rho^X$ determines how strongly the additive errors of two different bins are correlated, and $\eta^X$ and $\ell_*^X$ account for the scale dependence of the additive errors."
 Note that the multiplicative error of galaxy number density is degenerate with the galaxy clustering bias and is hence absorbed by b;., Note that the multiplicative error of galaxy number density is degenerate with the galaxy clustering bias and is hence absorbed by $b_i$.
" At the levels of systematics future surveys aim to achieve, the most important aspect of the (shear) additive error is its amplitude (Hutereretal. 2006),, so we simply fix p*=1 and n*=0."," At the levels of systematics future surveys aim to achieve, the most important aspect of the (shear) additive error is its amplitude \citep{huterer06}, so we simply fix $\rho^X = 1$ and $\eta^X = 0$."
" For more comprehensive accounts of the above systematic uncertainties, see Hutereretal.(2006);Jain"," For more comprehensive accounts of the above systematic uncertainties, see \citet{huterer06, jain06, ma06, zhan06d}."
" Forecasts on dark energy (2006)..constraints are sensitive to the priors on the shear multiplicative errors (op(f;’)) and the amplitudes of the shear additive errors (A7), so we list them in1."," Forecasts on dark energy constraints are sensitive to the priors on the shear multiplicative errors $\sigma_\mathrm{P}(f_i^\gamma)$ ) and the amplitudes of the shear additive errors $A_i^\gamma$ ), so we list them in."
. See Wittman(2005);Masseyetal.(2007);Paulin-Henrikssonetal.(2008) for detailed work on these systematic uncertainties and Zhanetal.(2009) for a discussion on and A7 for LSST.," See \citet{wittman05,massey07a,paulin-henriksson08} for detailed work on these systematic uncertainties and \citet{zhan09} for a discussion on $\sigma_\mathrm{P}(f_i^\gamma)$ and $A_i^\gamma$ for LSST."
 It has been demonstrated that small op(f;’)and stable point spread function in space leads to better shear measurements (Kasliwaletal., It has been demonstrated that small and stable point spread function in space leads to better shear measurements \citep{kasliwal08}.
" In the absence of a detailed investigation, we simply 2008)..choose values or priors of these systematic error parameters somewhat arbitrarily between what might be achieved by space projects and what have been used in LSST forecasts."," In the absence of a detailed investigation, we simply choose values or priors of these systematic error parameters somewhat arbitrarily between what might be achieved by space projects and what have been used in LSST forecasts."
" We infer from the Sloan Digital Sky Survey galaxy angular power spectrum (Tegmarketal.2002) that the additive galaxy power spectrum error due to extinction, photometry calibration, and seeing will be at (A7)?=107 level."," We infer from the Sloan Digital Sky Survey galaxy angular power spectrum \citep{tegmark02} that the additive galaxy power spectrum error due to extinction, photometry calibration, and seeing will be at $(A_i^\mathrm{g})^2 = 10^{-8}$ level."
" Since the amplitude of is fairly low compared to the galaxy power spectra, its Afvalue does not affect the forecasts much."," Since the amplitude of $A_i^\mathrm{g}$ is fairly low compared to the galaxy power spectra, its value does not affect the forecasts much."
" In summary, the parameter set includes 11 cosmological parameters and 170 nuisance parameters."," In summary, the parameter set includes 11 cosmological parameters and 170 nuisance parameters."
" The cosmological parameters are wo, Wa, the matter density Wm, the baryon density wp, the angular size of the sound horizon at the last scattering surface θς, the curvature parameter Q,, the scalar spectral index ng, the running of the spectral index ας, the primordial Helium fraction Y,, the election optical depth 7, and the normalization of the primordial curvature power spectrum A2."," The cosmological parameters are $w_0$ , $w_{\rm a}$, the matter density $\omega_{\rm m}$ , the baryon density $\omega_{\rm b}$ , the angular size of the sound horizon at the last scattering surface $\theta_{\rm s}$, the curvature parameter $\Omega_{\rm k}$ , the scalar spectral index $n_{\rm s}$, the running of the spectral index $\alpha_{\rm s}$, the primordial Helium fraction $Y_{\rm p}$, the election optical depth $\tau$, and the normalization of the primordial curvature power spectrum $\Delta_{\rm R}^2$."
" Note that and 7 are solely constrained by the cosmic microwave Y,background (CMB), which is introduced as priors."," Note that $Y_{\rm p}$ and $\tau$ are solely constrained by the cosmic microwave background (CMB), which is introduced as priors."
" The nuisance parameters include 40 bias parameters, 40 rms parameters, 40 galaxy clustering bias parameters, 30 galaxy additive noise parameters, 10 shear additive noise parameters, and 10 parameters for shear calibration errors."," The nuisance parameters include 40 bias parameters, 40 rms parameters, 40 galaxy clustering bias parameters, 30 galaxy additive noise parameters, 10 shear additive noise parameters, and 10 parameters for shear calibration errors."
 We use multipoles 40<ἐ2000 for WL and 40<£«3000 for BAO., We use multipoles $40\le \ell \le 2000$ for WL and $40 \le \ell \le 3000$ for BAO.
" In addition, we require A2(£/DA;z)<0.4 for BAO to reduce the influence of nonlinear evolution."," In addition, we require $\Delta_\delta^2(\ell/D_A; z) < 0.4$ for BAO to reduce the influence of nonlinear evolution."
" The lower cut in @ is to minimize the dependence of the forecasts on particular models of dark energy perturbation and the integrated Sachs-Wolfe effect, which affect only very large scales."," The lower cut in $\ell$ is to minimize the dependence of the forecasts on particular models of dark energy perturbation and the integrated Sachs–Wolfe effect, which affect only very large scales."
" presents the forecasts of lo error contours of the dark energy EOS parameters wo and ww, for the ideal 10k survey WL (solid line), BAO (dotted line), SNe line), joint BAO and WL (dashed and the three (dot-dashedcombined(shaded area)."," presents the forecasts of $\sigma$ error contours of the dark energy EOS parameters $w_0$ and $w_{\rm a}$ for the ideal 10k survey WL (solid line), BAO (dotted line), SNe (dot-dashed line), joint BAO and WL (dashed line), and the three combined(shaded area)."
" Since different line),probes have different parameter degeneracy directions in the full parameter space, including both cosmological parametersandnuisanceparameters as thebias and rms parameters), a joint (suchanalysis can reduce the error significantly."," Since different probes have different parameter degeneracy directions in the full parameter space, including both cosmological parametersandnuisanceparameters (such as thebias and rms parameters), a joint analysis can reduce the error significantly."
 One example is that the BAO technique, One example is that the BAO technique
binary WDC 01590-2255 and has a slightly fainter (Am20.3) companion al a separation of 8.6 aresec which was not included in the spectrograph slit.,binary WDC 01590-2255 and has a slightly fainter $\Delta m \simeq 0.3$ ) companion at a separation of 8.6 arcsec which was not included in the spectrograph slit.
 We obtained. however. one spectrum of the companion giving a radial velocity of 29.6+1.2 km +.," We obtained, however, one spectrum of the companion giving a radial velocity of $29.6 \pm 1.2$ km $^{-1}$."
" This is marginally consistent with the center of mass velocity of the binary. V,=32.92.1] km |l."," This is marginally consistent with the center of mass velocity of the binary, $V_0=32.9 \pm 2.1$ km $^{-1}$."
 The radial velocity orbit of AA Cet is well defined., The radial velocity orbit of AA Cet is well defined.
 The star appears to be a rather ivpical contact binary with a mass ratio of αρ=0.35x0.02., The star appears to be a rather typical contact binary with a mass ratio of $q_{\rm sp}=0.35 \pm 0.02$.
 The spectral tvpe in IIDII. AT/SV + G. might reflect the combined contribution of both visual components.," The spectral type in HDH, A7/8V + G, might reflect the combined contribution of both visual components."
" However. DB—V=0.38 (Tyeho-2) corresponds to ΕΟΝ rather than ΑΣ, so (hat the spectral Classification may have sulfered from contaminationbv (he visual companion."," However, $B-V=0.38$ (Tycho-2) corresponds to F3V rather than A7/8V, so that the spectral classification may have suffered from contaminationby the visual companion."
 The color measurement 5—y=0.256 (Woll&IXern1933). also suggests E3V. Chambliss(1981). gave the spectral (vpe of the binary as F2 and noted that the companion. with a spectral (vpe οἱ F5. shows sharp. double-Iimed spectra. indicating that itself it is a close binary system.," The color measurement $b-y=0.256$ \citep{WK83} also suggests F3V. \citet{chamb81} gave the spectral type of the binary as F2 and noted that the companion, with a spectral type of F5, shows sharp, double-lined spectra, indicating that itself it is a close binary system."
 Our single spectrum of the companion does not show any doubling of the lines while the BF is very sharp as expected for a slowly rotating single star., Our single spectrum of the companion does not show any doubling of the lines while the BF is very sharp as expected for a slowly rotating single star.
 RW Dor CUP 24763. LD 269320) has been known as an variable since its discovery by Leavitt in 1906: but it was Hertzsprung(1928) who classified it as à W UMa svstem.," RW Dor (HIP 24763, HD 269320) has been known as an variable since its discovery by Leavitt in 1906; but it was \citet{hertz28} who classified it as a W UMa system."
 It has been a subject of numerous photometric studies., It has been a subject of numerous photometric studies.
" The only spectroscopic radial velocity orbit is bv Hilditehetal.(1992) who found Vj=665448 kan ft. Ay=130.55T kms ! and A»=191.5d3.1 km |. thus implying gq,=0.68d0.04."," The only spectroscopic radial velocity orbit is by \citet{hild92} who found $V_0= 66.5 \pm 4.8$ km $^{-1}$ , $K_1=130.5 \pm 5.7$ km $^{-1}$ and $K_2=191.5 \pm 3.1$ km $^{-1}$ , thus implying $q_{\rm sp}=0.68 \pm 0.04$."
" Our orbit is different in that Vj is by 25 km ! smaller and both semi-amplitudes A; are larger: (he mass ratio is. however. similar: q,=0.632:0.03."," Our orbit is different in that $V_0$ is by 25 km $^{-1}$ smaller and both semi-amplitudes $K_i$ are larger; the mass ratio is, however, similar: $q_{\rm sp}=0.63 \pm 0.03$."
 An under-estimation of the semi-amplitudes is a typical problem of insullicient resolution which max have been (he result of the use of the ποο (CCE). in contrast to our much better resolving BF technique.," An under-estimation of the semi-amplitudes is a typical problem of insufficient resolution which may have been the result of the use of the cross-correlation function (CCF), in contrast to our much better resolving BF technique."
 On the other hand. our phase coverage is verv sparse. with only 3 observations not falling; within the conjunetions.," On the other hand, our phase coverage is very sparse, with only 3 observations not falling within the conjunctions."
 Thilditehetal.(1992). assumed a spectral (wpe of IKIV following Martonοἱal.(1989)., \citet{hild92} assumed a spectral type of K1V following \citet{mart89}.
". D—V—0.66 CIEveho-2) suggests an earlier spectral (wpe of about G4/5V with Vina,= 10.97.", $B-V=0.66$ (Tycho-2) suggests an earlier spectral type of about G4/5V with $V_{\rm max}=10.97$ .
 The binary is a contact svstem of theW-tvpe. (theless massive. but brighter componen is eclipsed at (he primary eclipse.," The binary is a contact system of theW-type, theless massive, but brighter component is eclipsed at the primary eclipse."
at 1.4 GHz but lacks an optical SDSS counterpart to a limit of r»23.l.,at 1.4 GHz but lacks an optical SDSS counterpart to a limit of $r > 23.1$.
" The brightest radio source FIRST J122542.2+295616 (S,, = 13.78 mJy) was automatically selected by A-means as a possible association.", The brightest radio source FIRST J122542.2+295616 $S_{1.4}$ = 13.78 mJy) was automatically selected by $K$ -means as a possible association.
 However. it was later manually discarded as a possible ‘impostor’ since its optical counterpart 1s listed as extended by the SDSS pipeline.," However, it was later manually discarded as a possible `impostor' since its optical counterpart is listed as extended by the SDSS pipeline."
 Analysis of the LLAT data shows no high-energy photons with energies above 10 GeV. In this case. the brightest radio source FIRST J131603.04-543629 1 = 26.89 mJy) is steep and falls in the neighbourhood of a SDSS optical object flagged as extended.," Analysis of the LAT data shows no high-energy photons with energies above 10 GeV. In this case, the brightest radio source FIRST J151603.0+545629 $S_{1.4}$ = 26.89 mJy) is steep and falls in the neighbourhood of a SDSS optical object flagged as extended."
" FIRST J151444.1-545027 ($4,, 2 4.9] mJy) should also be examined as a potential counterpart.", FIRST J151444.1+545027 $S_{1.4}$ = 4.91 mJy) should also be examined as a potential counterpart.
 At Sia = 77.77 mJy. FIRST J152757.5+414708 is the dominant radio source within the y- ray error region.," At $S_{1.4}$ = 77.77 mJy, FIRST J152757.5+414708 is the dominant radio source within the $\gamma$ -ray error region."
 It is also detected by WENSS and GBo. but falls outside the locus of association determined by A-means.," It is also detected by WENSS and GB6, but falls outside the locus of association determined by $K$ -means."
 Further analysis shows that its spectral index is rather steep qo)=—1.04., Further analysis shows that its spectral index is rather steep $\alpha_{92} = -1.04$.
 FIRST J152735.2+414839 (511 = 2.93 mly) is most likely associated with a pair of interacting galaxies at 5=0.149., FIRST J152735.2+414839 $S_{1.4}$ = 2.93 mJy) is most likely associated with a pair of interacting galaxies at $z=0.149$.
 Three prominent ROSAT sources are found in or around this region: IRXS J155357.14+495930 (with a photometric redshift ς= 0.425). IRXS J155437.5+495915 (QSO. 5Ξ 0.905). and IRXS J155254.9+495818 (no spectroscopy).," Three prominent ROSAT sources are found in or around this region: 1RXS J155357.1+495930 (with a photometric redshift $z=0.425$ ), 1RXS J155437.5+495915 (QSO, $z=0.905$ ), and 1RXS J155254.9+495818 (no spectroscopy)."
 However. none is radio loud.," However, none is radio loud."
" The brightest radio source inside FIRST J155234.8+495446 (S4, = 7.72 mJy) reveals a steep radio spectrum «y»=—0.98 and no obvious optical counterpart.", The brightest radio source inside FIRST J155234.8+495446 $S_{1.4}$ = 7.72 mJy) reveals a steep radio spectrum $\alpha_{92} = -0.98$ and no obvious optical counterpart.
 IFGL J1553.9+4952 hàs the highest energy y-ray photon (E = 265.4 GeV) detected among the unassociated ssources in the “overlap region’., 1FGL J1553.9+4952 has the highest energy $\gamma$ -ray photon (E = 265.4 GeV) detected among the unassociated sources in the `overlap region'.
" FIRST J162715.3+321652 (S4, = 14.68 mJy) is steep in radio and remains undetected in the optical by SDSS down to a limit of ¢>23.1. ", FIRST J162715.3+321652 $S_{1.4}$ = 14.68 mJy) is steep in radio and remains undetected in the optical by SDSS down to a limit of $r > 23.1$ 
M). but the proposed scenario provides no explanation for the svstematic suppression of horizoutal aud normal branches as 22.9 keV count rate drops.,"), but the proposed scenario provides no explanation for the systematic suppression of horizontal and normal branches as 2–2.9 keV count rate drops."
 The above discussion has mostly focused on the role of iu the Z source tracks., The above discussion has mostly focused on the role of in the Z source tracks.
 As already meutioned in refsecintro.. motion along atoll tracks appears to be uostlv the result of changes inα," As already mentioned in \\ref{sec:intro}, motion along atoll tracks appears to be mostly the result of changes in."
ν The spectral fits by LRIIU9 support this., The spectral fits by LRH09 support this.
 In this respect. it is interestius to xut to the atoll lowerbanana branch in the ΠΙΟ of162.. which appears to be a continuation of he presumably dadriveu secular motion observed in the Z-like phase of the outburst.," In this respect, it is interesting to point to the atoll lower-banana branch in the HID of, which appears to be a continuation of the presumably driven secular motion observed in the Z-like phase of the outburst."
 DLowever. the presence of hvsteresis in the state ransitions (Cdacdstoueetal.2007) and the phenomenon of parallel tracks (Méndezetal.1998). observed in other atoll NS-LAINBs sugeest that a time averaged response o changes in umight be involved as well (vanderIklis2001).," However, the presence of hysteresis in the state transitions \citep{gldogi2007} and the phenomenon of parallel tracks \citep{mevava1998a} observed in other atoll NS-LMXBs suggest that a time averaged response to changes in might be involved as well \citep{va2001}."
. The bhuuinositv rauge over which kIlz QPOs are detected in sspans a factor of ~1520. which is wider than seen in any other NS-LAINB (Fordetal.2000).," The luminosity range over which kHz QPOs are detected in spans a factor of $\sim$ 15–20, which is wider than seen in any other NS-LMXB \citep{fovame2000}."
. However. there is a aly large gap in luminosity in which uo kHz QPOs are detected. correspouding to selections CGIs. Iu sclections C and II the source shows Sco-like Z behavior. but is wissing the horizoutal aud upper normal branches. where nost of the kIIz QPO detections iu the Sco-like Z sources we made (sec.e.g..vanderIKlisetal.1997:1998:Tomanetal. 2002).," However, there is a fairly large gap in luminosity in which no kHz QPOs are detected, corresponding to selections G–K. In selections G and H the source shows Sco-like Z behavior, but is missing the horizontal and upper normal branches, where most of the kHz QPO detections in the Sco-like Z sources are made \citep[see, e.g.,][]{vawiho1997,zhstsw1998,hovajo2002}."
. The behavior of iu selections IKK is similar to that of the brieht atoll sources CX 9419. GN 911. and GN 311. for which uo kz QPOs have been reported either (see.e...Wij-uandsetal. 1998b).," The behavior of in selections I–K is similar to that of the bright atoll sources GX 9+9, GX 9+1, and GX 3+1, for which no kHz QPOs have been reported either \citep[see, e.g.,][]{wivava1998}."
. Surprisingly. wo did not detect ΚΣ QPOs iu the Cye-like Z selectious. despite the fact that all three persistent Cye-like Z sources have shown kIIz QPOs (Wijnandsetal.19982:Jouker1998.2002).," Surprisingly, we did not detect kHz QPOs in the Cyg-like Z selections, despite the fact that all three persistent Cyg-like Z sources have shown kHz QPOs \citep{wihova1998,jowiva1998,jovaho2002}."
. As pointed out in §??.. however. selections A aud B also show some differences from the Cye-like Z sources iu eris of CD/IIID structure.," As pointed out in \ref{sec:comparison}, however, selections A and B also show some differences from the Cyg-like Z sources in terms of CD/HID structure."
 Selection C is missing its iorizontal brauch. on which most kIIz OPO detections were made in the Cyve-like Z sources.," Selection C is missing its horizontal branch, on which most kHz QPO detections were made in the Cyg-like Z sources."
 Finally. the fact hat the Z-source-like and atoll-source-Iike kIIz QPOs in aare well separated in duninositv aud have distinct xoperties (such as Q-value aud xis amplitudes) suggests hat they imueht be the result of different excitation uechauisus. not only iu but also in other Z aud atoll sources.," Finally, the fact that the Z-source-like and atoll-source-like kHz QPOs in are well separated in luminosity and have distinct properties (such as Q-value and rms amplitudes) suggests that they might be the result of different excitation mechanisms, not only in but also in other Z and atoll sources."
 Quasi-periodic long-term variability has been observed in numerous LAINBs (Charlesetal.2008:Durant 2010).," Quasi-periodic long-term variability has been observed in numerous LMXBs \citep{chclco2008,ducore2010}."
. The loue-term modulatious seen in the ΟΠΟΙΟΥ light curve of aare closely related to the eradual changes im the CDAND tracks of the source. aud we therefore sugeest that they are the result of changes inM.," The long-term modulations seen in the low-energy light curve of are closely related to the gradual changes in the CD/HID tracks of the source, and we therefore suggest that they are the result of changes in."
. They are only seen at intermediate bhuuinositfies (not at the peak of the outburst or during the decay)., They are only seen at intermediate luminosities (not at the peak of the outburst or during the decay).
" To καν the time dependence of the long-term modulations we created a dynamical power spectrum of the long-term low-energv light curve (see.c.g.Clarksonetal.2003).. by combining Lonib-Scarele periodograis (Scarele1952) of 75-dav intervals, with the start dates of the intervals shifting bv five davs."," To study the time dependence of the long-term modulations we created a dynamical power spectrum of the long-term low-energy light curve \citep[see, e.g.,][]{clchco2003}, by combining Lomb-Scargle periodograms \citep{sc1982} of 75-day intervals, with the start dates of the intervals shifting by five days."
 The resulting απαλά] power προσ reveals that the period of the loue-termi modulatious varies between ~20 50 days., The resulting dynamic power spectrum reveals that the period of the long-term modulations varies between $\sim$ 20–50 days.
 Caven the strong variations in their period. the loue-term variatious are probably not the result of orbital modulations.," Given the strong variations in their period, the long-term variations are probably not the result of orbital modulations."
 We also note that the sharp dips that are present near the maxima of the first few cycles are not related to the absorption eveuts that are often seen in ligh-nchnation LMXDs: here they are the result of spectral changes associated with the source eutering the horizoutal brauch., We also note that the sharp dips that are present near the maxima of the first few cycles are not related to the absorption events that are often seen in high-inclination LMXBs; here they are the result of spectral changes associated with the source entering the horizontal branch.
 The lack of a known orbital period for ccoluplicates the interpretation of the lome-term modulations. although. given the brightuess and duration of the outburst. the orbital periodof is likely to be on the order of davs or longer (IIO07).," The lack of a known orbital period for complicates the interpretation of the long-term modulations, although, given the brightness and duration of the outburst, the orbital periodof is likely to be on the order of days or longer (H07)."
 Accretion disk precession as the result of radiatiou-induced warping has becu suggested as a source for loue-term modulation iun some LAINBs (Pringle1996:Wijers&Pringle1999:OgilvieDubus 2001).. although such modulations are usually discussed in terms of changes In viewing angle or obscuration (which we rule out as a source of subclass transitions in 162- sce refsec:nature)).," Accretion disk precession as the result of radiation-induced warping has been suggested as a source for long-term modulation in some LMXBs \citep{pr1996,wipr1999,ogdu2001}, although such modulations are usually discussed in terms of changes in viewing angle or obscuration (which we rule out as a source of subclass transitions in - see \\ref{sec:nature}) )."
 Although uot explicitly discussed in these works. a precessing warped dise could perhaps also result iu actual modulatious inM.. as the result of varviug torques fromthe secondary.," Although not explicitly discussed in these works, a precessing warped disc could perhaps also result in actual modulations in, as the result of varying torques fromthe secondary."
 Two NS LAINBs have shown modulatious that may ve relevant to the discussion of the long-term variations iu162., Two NS LMXBs have shown modulations that may be relevant to the discussion of the long-term variations in.
. Shihetal.(2005) report on uodulatious with a period of ~ LO days iu the NS LAINB IU 165653., \citet{shbich2005} report on modulations with a period of $\sim$ 40 days in the NS LMXB 4U 1636–53.
 These modulations are accompanied by rausitions between the island state and lower banana xyauch (seealsoBellowetal.2007) anc are therefore ikelv the result of modulations in A/., These modulations are accompanied by transitions between the island state and lower banana branch \citep[see also][]{behomo2007} and are therefore likely the result of modulations in .
. Sinular to162.. the modulations iu 1U 163653 were not xeseut at every luminosity level: they oulv appeared after the lone-term average luninosity of the source mad shown a decrease.," Similar to, the modulations in 4U 1636–53 were not present at every luminosity level; they only appeared after the long-term average luminosity of the source had shown a decrease."
 Shihetal.(2005) areuc that such a decrease could lower the irradiation of the outer accretion disc. resulting iun a drop in its temperature aud vossibly bringing it mto a regime of unstable accretion hat results in luit evcle behavior.," \citet{shbich2005} argue that such a decrease could lower the irradiation of the outer accretion disc, resulting in a drop in its temperature and possibly bringing it into a regime of unstable accretion that results in limit cycle behavior."
 Based ou the leneth ancl Inuimositv of its outburst. lis expected to have an orbital period ou the order of davs or more (IT07). which is longer than IU 163653 (3.8 hrs).," Based on the length and luminosity of its outburst, is expected to have an orbital period on the order of days or more (H07), which is longer than 4U 1636–53 (3.8 hrs)."
 Prestunably. it therefore also has a larger accretion disc. which means that the ouset of such au instability could already. occur at a higher buuinositv. iu line with what we observe for 162.," Presumably, it therefore also has a larger accretion disc, which means that the onset of such an instability could already occur at a higher luminosity, in line with what we observe for."
. The loue-term: modulations in νο X-2 (Wijuauds are accompanied by strong changes between various types of Z tracks (Ixuulkersetal. 1996).. simular to what we observe in ι05.," The long-term modulations in Cyg X-2 \citep{wikusm1996,pakima2000} are accompanied by strong changes between various types of Z tracks \citep{kuvava1996}, similar to what we observe in ."
. Although the modulations in (νο N-2 appear to be less regularthan in 162.. Bovd&Sinale(2001) find that the lengths of the modulations cycles in (νο A-2 are consistent with beime integer multiples (1.11) of," Although the modulations in Cyg X-2 appear to be less regularthan in , \citet{bosm2004} find that the lengths of the modulations cycles in Cyg X-2 are consistent with being integer multiples (1–14) of"
run) has the effect of strongly increasing the positive evolution of in the central region of g531. which turns out to be over— by +=0.,"run) has the effect of strongly increasing the positive evolution of in the central region of g51, which turns out to be over--enriched by $z=0$."
 This leads to the counter-intuitive conclusion that the lack of low—z star formation should generate an increase of the enrichment of the hot gas., This leads to the counter-intuitive conclusion that the lack of $z$ star formation should generate an increase of the enrichment of the hot gas.
 In order to investigate the origin of this increase. we show in Figure 3. the emission-weighted metallicity maps of the reference rrun of g51 at z0. along with those of the CS and CMS runs.," In order to investigate the origin of this increase, we show in Figure \ref{Fig:maps} the emission–weighted metallicity maps of the reference run of g51 at $z=0$, along with those of the CS and CMS runs."
 Quite apparently. the metal distribution in the CS simulation is more clumpy than in the reference run.," Quite apparently, the metal distribution in the CS simulation is more clumpy than in the reference run."
 At the cluster centre. a high iis clearly visible. which boosts the central emission weighted metallicity shown in Fig.2..," At the cluster centre, a high is clearly visible, which boosts the central emission weighted metallicity shown in \ref{Fig:ZFe_red}."
" Indeed. while the emission-weighted iinereauses by about a factor two within 0.2/2,«5. we verified that the mass—weighted estimate within the same radius increases only by about 10 per cent."," Indeed, while the emission–weighted increases by about a factor two within $0.2R_{180}$, we verified that the mass–weighted estimate within the same radius increases only by about 10 per cent."
 In the reference run. the metals released in the high density clumps disappear from the hot diffuse medium due to the efficient gas cooling.," In the reference run, the metals released in the high density clumps disappear from the hot diffuse medium due to the efficient gas cooling."
 As a result. the reference run has a globally higher level of diffuse enrichment. but a lower level of enrichment inside the high-density gas clumps. which dominate the emission—weighted estimate of..," As a result, the reference run has a globally higher level of diffuse enrichment, but a lower level of enrichment inside the high–density gas clumps, which dominate the emission–weighted estimate of."
 These results demonstrate that the strongly positive evolution of the metallicity in the CMS run is driven by the accretion of highly enriched dense clumps., These results demonstrate that the strongly positive evolution of the metallicity in the CMS run is driven by the accretion of highly enriched dense clumps.
 Inhibiting also the production of metals below redshift unity (CMS run) allows us to characterize the role payed by gas—dynamical processes in redistributing metals produced at higher redshift., Inhibiting also the production of metals below redshift unity (CMS run) allows us to characterize the role played by gas--dynamical processes in redistributing metals produced at higher redshift.
 As shown in the bottom—eft panel of Fig.3.. metal clumps are less pronounced than in the CS run.," As shown in the bottom–left panel of \ref{Fig:maps}, metal clumps are less pronounced than in the CS run."
 The global enrichment level of the ICM is now significantly ower than in the reference run. although an enhancement in the innermost regions is still visible.," The global enrichment level of the ICM is now significantly lower than in the reference run, although an enhancement in the innermost regions is still visible."
" The resulting mass—weighted metallicity within 0.277,50 at z=O ""ecreuses by ~60 per cent wih respect to the reference run.", The resulting mass–weighted metallicity within $0.2R_{180}$ at $z=0$ decreases by $\sim 60$ per cent with respect to the reference run.
 Therefore. the stability of the emission—weighted metallicity is due to he competing effects of a more clumpy distribution of metals and of a decrease of the overall ICM metal budget.," Therefore, the stability of the emission–weighted metallicity is due to the competing effects of a more clumpy distribution of metals and of a decrease of the overall ICM metal budget."
 The maps of Fig.3 also illustrate tqe role of gas-dynamical effects in redistributing highly enriched gas., The maps of \ref{Fig:maps} also illustrate the role of gas–dynamical effects in redistributing highly enriched gas.
 Merging clumps within the custer virial region leave behind them over-enriched tails of stripped gas. which is tempting o explain as due to ram—pressure strisping.," Merging clumps within the cluster virial region leave behind them over–enriched tails of stripped gas, which is tempting to explain as due to ram--pressure stripping."
 However. a significant contribution could well be orovided by viscous stripping.," However, a significant contribution could well be provided by viscous stripping."
 Since the SPH scheme is known to be generally characterized by a large numerical viscosity. this may induce an excess of Eus Strripping from merging halos.," Since the SPH scheme is known to be generally characterized by a large numerical viscosity, this may induce an excess of gas stripping from merging halos."
 ? showed that he effect of including the Svitzer-Braginskil viscosity, \cite{2006MNRAS.371.1025S} showed that the effect of including the Spitzer-Braginskii viscosity
The central star masses obtained in this paper have been derived from Fig.,The central star masses obtained in this paper have been derived from Fig.
 2 by comparing their location ou the IIR. diagram with the Vassiliadis&Wood(1991). tracks for stars with LAIC metallicity (Z = 0.008)., 2 by comparing their location on the HR diagram with the \cite{Vw:94} tracks for stars with LMC metallicity (Z = 0.008).
 Note that the progenitors of the PNe we studied have a range of initial metallicities. aud using sinele metallicities for all the tracks las the potential to introduce additional uncertainty iu the determination of mdividual masses.," Note that the progenitors of the PNe we studied have a range of initial metallicities, and using single metallicities for all the tracks has the potential to introduce additional uncertainty in the determination of individual masses."
 We have not plotted or derived masses for the stars that lie below the evolutionary tracks (AIG L1. MG 16. Mo 7. Sa 117 and Mo 17).," We have not plotted or derived masses for the stars that lie below the evolutionary tracks (MG 14, MG 16, Mo 7, Sa 117 and Mo 47)."
 We did not have 1686 fluxes (or he 1686 iueasured fux is verv small) for MIC L1. MC 16. Mo 7 aud Mo. LF aud therefore their central star parameters are very uncertain.," We did not have 4686 fluxes (or the 4686 measured flux is very small) for MG 14, MG 16, Mo 7 and Mo 47 and therefore their central star parameters are very uncertain."
 The ceutral star of Sa 117 is only mareinally detected above the jebula., The central star of Sa 117 is only marginally detected above the nebula.
 We did not estimate the ceutral star masses for MC 19. Sa Lola. aud SAIP 88 that have iimch larger i1uninosities than those euconipassed by the highest mass evolutionary track.," We did not estimate the central star masses for MG 45, Sa 104a, and SMP 88 that have much larger luminosities than those encompassed by the highest mass evolutionary track."
 Caven the compact nature of hese three PNoe. our photometric technique fails in subtracting the true nebular contribution from the stellar aperture.," Given the compact nature of these three PNe, our photometric technique fails in subtracting the true nebular contribution from the stellar aperture."
 J 5 has been excluded as well from the following analysis because its magnitude was measured roni saturated data and because most of its Balmer ciuission appears to be comune from the ceutral star (Shawctal.2006)., J 5 has been excluded as well from the following analysis because its magnitude was measured from saturated data and because most of its Balmer emission appears to be coming from the central star \citep{Shaw:06}.
. The core masses and the morphological classification of the nebulae are stuumarized iu Table 5., The core masses and the morphological classification of the nebulae are summarized in Table 5.
 The Vassiliadis&Wood(1991) LAIC models are more efficient at producing He-buruiug post-AGD tracks for lower mass progenitors. which they argue is a natural consequence of the mass-loss behavior during the AGB phase.," The \cite{Vw:94} LMC models are more efficient at producing He-burning post-AGB tracks for lower mass progenitors, which they argue is a natural consequence of the mass-loss behavior during the AGB phase."
 The IHe-buruiug or I-buriiug nature of the post-AGB track depends on whether tle star leaves the AGB when hielimu-shell or when hbydrogeu-shell burning is dominant., The He-burning or H-burning nature of the post-AGB track depends on whether the star leaves the AGB when helium-shell or when hydrogen-shell burning is dominant.
 However. the mechanism that coutrols the departure of the star from the AGB is unknown and therefore artificially defined in the stellar evolutionary models.," However, the mechanism that controls the departure of the star from the AGB is unknown and therefore artificially defined in the stellar evolutionary models."
 From our data we caunot constrain the nature of the track. so when possible we have estimated the masses from both the W-buruine aud the We-burning LMC tracks.," From our data we cannot constrain the nature of the track, so when possible we have estimated the masses from both the H-burning and the He-burning LMC tracks."
 Note that the central star temperatures aud Iuuinosities (aud therefore the masses) have been computed uuder the assuiiption of a non-hbinary ceutral star. ic. asundug that all the measured flix arises from the central star.," Note that the central star temperatures and luminosities (and therefore the masses) have been computed under the assumption of a non-binary central star, i.e. assuming that all the measured flux arises from the central star."
 The reliability of tlis assumption has been addressed in Villaveretal.(2001). where we explored the possibility of light from a stellar companion contaminating the photometric measurciments., The reliability of this assumption has been addressed in \cite{Vss:04} where we explored the possibility of light from a stellar companion contaminating the photometric measurements.
 A siguificaut contribution from a stellar companion to the measured flux in the STIS/50C'CD bandpass can be excluded eiven the additional restriction that a known distance imniposes ou the measured flux., A significant contribution from a stellar companion to the measured flux in the STIS/50CCD bandpass can be excluded given the additional restriction that a known distance imposes on the measured flux.
 It is important to note that our analysis does not rule out the possibility of a binary companion to the ceutral star: we only exclude colupanions with fluxes in the STIS bandpass that are comparable to that of the ionizing source., It is important to note that our analysis does not rule out the possibility of a binary companion to the central star: we only exclude companions with fluxes in the STIS bandpass that are comparable to that of the ionizing source.
 Given the large amount of observational evideuce that shows fundamental differences iu the physical and chemical properties among PN morphological classes. it has been suggested that the initial mass of he progenitor star determines the morphology of the PN.," Given the large amount of observational evidence that shows fundamental differences in the physical and chemical properties among PN morphological classes, it has been suggested that the initial mass of the progenitor star determines the morphology of the PN."
 In particular. the N and O chemical euricliiieut ound in the Galactic bipolar aud extremely asvuuuetric morphological classes (Cree1971:Peiibert1978:Torres-Penmbert&Penubert1997) together with their lower average distance from the Galactic plane (Corradi&Schavarz1995:Mauchadoetal.2000:Stanghellini2002b:Parker2006).. suggests hat the bipolar class nusht evolve frou nore massive progenitors and eiveu the initialfinal mass relation uassive progenitors nplv massive central stars.," In particular, the N and O chemical enrichment found in the Galactic bipolar and extremely asymmetric morphological classes \citep{Gre:71,Pei:78,Tpp:97} together with their lower average distance from the Galactic plane \citep{Cs:95, Metal:00, Svmg:02,
ParK:06}, suggests that the bipolar class might evolve from more massive progenitors and given the initial–final mass relation massive progenitors imply massive central stars."
 The correlation between the ceutral star mass aud the PN uorphologv has been explored for Calactic samples by several authors (Stanghelliui.Corradi.&Scliwuz1993:Amunuel1995:Corny.Stasinska.&Tylenda1997:Staneghelinietal.20025). who have found slightly different mass distributions for the ceutral stars of svauiuetric and axisvunuectiic PNe.," The correlation between the central star mass and the PN morphology has been explored for Galactic samples by several authors \citep{Scs:93,Amn:95,Gst:97,Svmg:02} who have found slightly different mass distributions for the central stars of symmetric and axisymmetric PNe."
 Iu the sample of, In the sample of
due to hardware limitations (hat arise [rom acquiring (he auto-correlations in 64-1ae chunks everv LO ms.,due to hardware limitations that arise from acquiring the auto-correlations in 64-lag chunks every 10 ms.
 Auto-correlations are also acquired in each sub-band with the eross-correlator hardware. although only (vo products al a time per antenna max be acquired.," Auto-correlations are also acquired in each sub-band with the cross-correlator hardware, although only two products at a time per antenna may be acquired."
 Each StB and BIB contains a PC/1042- embedded: processor mezzanine card running real-time Linux., Each StB and BlB contains a PC/104+ embedded processor mezzanine card running real-time Linux.
 PC/104+ is an inexpensive and hieh performance technology for (is purpose., PC/104+ is an inexpensive and high performance technology for this purpose.
 The StD computing requirements are (he most stringent because real-time delay (racking and phase model generation. integration control. and data accquisition must be performed.," The StB computing requirements are the most stringent because real-time delay tracking and phase model generation, integration control, and data acquisition must be performed."
 The BIB computing requirements are less stringent. requiring only monitor aud control operations since the flow of all correlation coellicient dala is CPU-independent.," The BlB computing requirements are less stringent, requiring only monitor and control operations since the flow of all correlation coefficient data is CPU-independent."
 This arrangement ellectively eliminates anv bottlenecks to the data flow., This arrangement effectively eliminates any bottlenecks to the data flow.
 The data rate produced by the correlator is governed by several factors., The data rate produced by the correlator is governed by several factors.
 The correlator hardware is capable of producing data al an extremely. rapid rate. so data rate limitations are sel by a combination of factors. including configuration of the CBE computers. their performance and network topology. and not least scientific necessity.," The correlator hardware is capable of producing data at an extremely rapid rate, so data rate limitations are set by a combination of factors, including configuration of the CBE computers, their performance and network topology, and not least scientific necessity."
 The standard correlator configuration is a 1 Gigabit Ethernet link from each of 128 BIBs for the visibility data. providing the capability for dumping all spectral channels every. 11 ms. and a 1 Gigabil Ethernet link from each BIB lor real-time phased. data.," The standard correlator configuration is a 1 Gigabit Ethernet link from each of 128 BlBs for the visibility data, providing the capability for dumping all spectral channels every 11 ms, and a 1 Gigabit Ethernet link from each BlB for real-time phased data."
 Thus. the maximum data rate to ihe computing cluster is 128 Gbps.," Thus, the maximum data rate to the computing cluster is 128 Gbps."
 A BIB can be upgraded with 10 Gigabit Ethernet for a maximum data rate of 1.28 Tbps., A BlB can be upgraded with 10 Gigabit Ethernet for a maximum data rate of 1.28 Tbps.
 With the planned number of CBE computers. all spectral channels can be dumped every 100 ms. for a data rate of 167 mega-visibilities per second in a 32-station correlator.," With the planned number of CBE computers, all spectral channels can be dumped every 100 ms, for a data rate of 167 mega-visibilities per second in a 32-station correlator."
 The actual dump times used will be determined by science objectives. arrav configuration. aud data storage capabilities.," The actual dump times used will be determined by science objectives, array configuration, and data storage capabilities."
 On the timescale of early 2012. (vpical data rates produced by the correlator are expected to be at the more modest rate of about 20 MDps. with a maximum rate of 75 Mbps.," On the timescale of early 2012, typical data rates produced by the correlator are expected to be at the more modest rate of about 20 MBps, with a maximum rate of 75 MBps."
 One of the major goals of the EVLA project was to replace the software of the VLA. much of whieh was written over 20 vears ago and was becoming more and more dilfHicult io maintain.," One of the major goals of the EVLA project was to replace the software of the VLA, much of which was written over 20 years ago and was becoming more and more difficult to maintain."
 The new hardware of the EVLA requires much more software to control it. and because the instrument is so much more capable than the VLA. the control and user software is necessarily more complex.," The new hardware of the EVLA requires much more software to control it, and because the instrument is so much more capable than the VLA, the control and user software is necessarily more complex."
 While more complex. the intent of the new software in the end is to make the process of observing with the EVLA much more accessible to the astrononmer who is not necessarily intimately familiar with the theory and techniques of radio interferometry.," While more complex, the intent of the new software in the end is to make the process of observing with the EVLA much more accessible to the astronomer who is not necessarily intimately familiar with the theory and techniques of radio interferometry."
galaxies(ECGs:IHubble1936) (e.g...Ixauffiiaunetal.1993:Daugh1996)... (c.g...Eisensteinetal.2005).. o. 6,"\citep[EGs:][]{Hubble} \citep[e.g.,][]{kauffmann_93, baugh_96}, \citep[e.g.,][]{eisenstein_05}. \citep[e.g.,][]{bertola_75, illingworth_77, binney_78},"
 “dynamical masses” that are indepeudent of stellarxopulation assunuptious (c.g..Padmanabhanetal.2001:Boltonetal. 2008b).," $\sigma$ ${\sigma}$ “dynamical masses” that are independent of stellar-population assumptions \citep[e.g.,][]{padmanabhan_04, bolton_08b}."
". Dynamical masses can then iu mn be used to trace the evolution of ECGs at fixed nass ίσιο,vanderMarel&Dokki2007:Welctal.2008:Cappellariet 2009).. indicating a manced dynamical history despite ecucrally passive star-ormation histories at 2<1 (e.gThomasetal.2005: 2008)."," Dynamical masses can then in turn be used to trace the evolution of EGs at fixed mass \citep[e.g.,][]{vdm_07, vdw_08, cappellari_09}, indicating a nuanced dynamical history despite generally passive star-formation histories at $z < 1$ \citep[e.g.,][]{thomas_05,cool_08}."
. Stellar velocity dispersion is also the uost important single predictor of stroug gravitational ensine cross sectious(6.8.TheTurneretal.1981:Doltouetal. 2008a).. and cau used in colbination with stroug leusing observations to constrain the central iiass-density structure of elliptical galaxies at cosmological distances (e.g...Noopimans&Treu2002:TrewIKoop-mans2001:[oopniausetal. 2006).," Stellar velocity dispersion is also the most important single predictor of strong gravitational lensing cross sections \citep[e.g.,][]{Turner, bolton_08a}, and can be used in combination with strong lensing observations to constrain the central mass-density structure of elliptical galaxies at cosmological distances \citep[e.g.,][]{kt02,tk04,koopmans_06}."
. Stellar velocity dispersions are tied to nearly all other properties of ECs through iuultiple enpirieal scaling relations., Stellar velocity dispersions are tied to nearly all other properties of EGs through multiple empirical scaling relations.
 Faber& found a correlation between luuinositics of early-type galaxies and them velocity. dispersious σ known as the Faber-Jacksou Relation (FIR)., \citet{FJR} found a correlation between luminosities of early-type galaxies and their velocity dispersions ${\sigma}$ known as the Faber-Jackson Relation (FJR).
 The relation of INormendy(1977). ties the surface brightuess (p. with the effective radius Ro., The relation of \citet{Kormendy} ties the surface brightness $\langle \rm I \rangle _e$ with the effective radius $\rm R_e$.
 Both the FIR aud ISormendy relations can be viewed as projections of the “fundamental plane”Bernardi(EP.e.2..Djorgovski&Davis1987:Dressleretal.1987:2003c¢) within the space spannedby logy)Re. aud logy0.," Both the FJR and Kormendy relations can be viewed as projections of the “fundamental plane” \citep[FP, e.g.,][]{Djorgovski, Dressler, Bernardi03III}
 within the space spanned by $\rm \log_{10} R_e$, $\rm \langle I \rangle _e$ and $\rm \log_{10}{\sigma}$."
 Furthenuore. centralblackhole mass hasT.been found tobe correlated with the velocity dispersionof thebulge via the ΛΙ relation(e.g..Ferrarese&—Merritt2000:Goebhlrdt 2009)..," Furthermore, central blackhole mass has been found to be correlated with the velocity dispersionof the bulge via the $\rm M_{BH} - {\sigma}$ \citep[e.g.,][]{Ferrarese, Gebhardt, Kormendy09}. ."
 Together. these relations provide multiple coustraimts ou the structure. formation. aud evolution of ECs ..," Together, these relations provide multiple constraints on the structure, formation, and evolution of EGs ."
In H.5 this circumstellar absorption is seen as well. but in addition the other four spectra show variability in the line wings. in particular in the red one.,"In $\beta$ this circumstellar absorption is seen as well, but in addition the other four spectra show variability in the line wings, in particular in the red one."
 This is probably a signature of the circumstellar emission arising in the corotating clouds. well seen in the two FEROSspectra (2). for Ha.," This is probably a signature of the circumstellar emission arising in the corotating clouds, well seen in the two FEROSspectra \citep{2008A&A...482..255R} for $\alpha$."
 All lines in the observed range follow a similar variation pattern. varying both in strength and in profile.," All lines in the observed range follow a similar variation pattern, varying both in strength and in profile."
 The lines showing strong broadening wings have a larger amplitude in V due to variation in these wings. but the profile variability is better seen in weaker lines. like 44713.," The lines showing strong broadening wings have a larger amplitude in $W_\lambda$ due to variation in these wings, but the profile variability is better seen in weaker lines, like 4713."
 In addition to the well known stellar and lines. there is significant variability at Aa4045 aand bluewards of Hel4922. at Àez4911AA.," In addition to the well known stellar and lines, there is significant variability at $\lambda \approx 4045$ and bluewards of 4922, at $\lambda \approx 4911$."
. We identify the features with the forbidden lines Her4045 QPo> 5*Pyand ΟΙ Q4P.—=44P). features well known in extreme Helium stars (2)..," We identify the features with the forbidden lines 4045 $2^3P\rightarrow5^3P$ ) and 4911 $2^1P\rightarrow4^1P$), features well known in extreme Helium stars \citep{1998ApJ...496..395B}. ."
colour-colour plot used in the 2QZ to select quasars (Croometal. 2004)..,colour-colour plot used in the 2QZ to select quasars \citep{2004mas..conf...57C}.
 As Figures 12) and 19 only contain objects that have U-hancl photometry. in Figure 14. we generated the same colow-colour plot in Figure 11.. but. only for objects that had. U-bancl photometry so as to make a fair comparison.," As Figures \ref{UVX} and \ref{multiplot} only contain objects that have U-band photometry, in Figure \ref{UonlyKX} we generated the same colour-colour plot in Figure \ref{colourcolourplot}, but only for objects that had U-band photometry so as to make a fair comparison."
" Comparing Figures 12. and 19 to Figure 14. qualitatively, the INN. method immediately. appeared. more ellective than the UVX method and comparable to the 2QZ multicolour method."," Comparing Figures \ref{UVX} and \ref{multiplot} to Figure \ref{UonlyKX}, qualitatively, the KX method immediately appeared more effective than the UVX method and comparable to the 2QZ multicolour method."
 We examined. this quantitatively by measuring the percentage of quasars in our sample that would not be selected. by the UVX. and. 20Z multi-color methods. in total and as a function of colour. and compared us to our WKN method variant.," We examined this quantitatively by measuring the percentage of quasars in our sample that would not be selected by the UVX and 2QZ multi-color methods, in total and as a function of colour, and compared this to our KX method variant."
 In. Figure 12. we use a colour criterion of (by« -0.36 to select. quasars as an xample of a typical UVX method criterion. based on Smith al. (," In Figure \ref{UVX} we use a colour criterion of $U - b_J <$ -0.36 to select quasars as an example of a typical UVX method criterion, based on Smith et al. ("
1997). Bovleetal.(1990):LaFranca (1997)..,"1997), \citet{1990MNRAS.243....1B,1997AJ....113.1517L}."
 Using this cut 13 of the 69 quasars. or194... were not selected in Figure 12..," Using this cut 13 of the 69 quasars, or, were not selected in Figure \ref{UVX}."
 Breaking this into red ancl blue quasars. where red quasars satisfy 5;Aom 3.5. 3 (10) ( [dA (58) red (blue) quasars were not selected.," Breaking this into red and blue quasars, where red quasars satisfy $ b_J - K \geq$ 3.5, 3 (10) of 11 (58) red (blue) quasars were not selected."
 The UVX method. failed. to select. of the red. quasars compared to of the blue quasars., The UVX method failed to select of the red quasars compared to of the blue quasars.
 In. Figure 13. we applied. the selection criterion used in the 2QZ (Croomctal.2004).. the criterion is marked by a dashed line ancl objects below or to the left of the line were selected as quasars.," In Figure \ref{multiplot} we applied the selection criterion used in the 2QZ \citep{2004mas..conf...57C}, the criterion is marked by a dashed line and objects below or to the left of the line were selected as quasars."
 This selection criterion failed to select 5 of the 69 quasars. corresponding of the quasars.," This selection criterion failed to select 5 of the 69 quasars, corresponding to of the quasars."
 Broken into red ancl blue quasars. 1 and 4 blue quasars were missed. equating to and.," Broken into red and blue quasars, 1 red and 4 blue quasars were missed, equating to and."
 For the IXX method. variant used. here. in Figure 14 we applied an example of a suitable colour-based. selection criterion. and. plotted it as a dotted line in Figure 1H. with objects below the line selected as quasars.," For the KX method variant used here, in Figure \ref{UonlyKX} we applied an example of a suitable colour-based selection criterion, and plotted it as a dotted line in Figure \ref{UonlyKX} with objects below the line selected as quasars."
 The details of our example selection criterion are listed in Table 2.., The details of our example selection criterion are listed in Table \ref{examplekxtable}.
 Our example selection criterion fails to select 7 quasars. 1 red and 6 blue. corresponding to of all the quasars and and of the red ancl blue quasars respectively.," Our example selection criterion fails to select 7 quasars, 1 red and 6 blue, corresponding to of all the quasars and and of the red and blue quasars respectively."
 As we knew where the quasars were located on the colour-colour plot before defining a suitable colour-hasecl selection. criterion: comparing the results of our example KX method selection criterion. to the results of the UWA and. 2QZ methods is potentially an unfair comparison., As we knew where the quasars were located on the colour-colour plot before defining a suitable colour-based selection criterion; comparing the results of our example KX method selection criterion to the results of the UVX and 2QZ methods is potentially an unfair comparison.
 As an alternative. we used the proximity to the stellar locus as a selection criterion i.c. whether a quasar was obscured by the stellar locus.," As an alternative, we used the proximity to the stellar locus as a selection criterion i.e. whether a quasar was obscured by the stellar locus."
 In Figure 14.. 7 quasars were clearly obscured by the stellar locus. 1 τοῦ and 6 blue.," In Figure \ref{UonlyKX}, 7 quasars were clearly obscured by the stellar locus, 1 red and 6 blue."
 This corresponds to of all the quasars and «| both. the red. and. blue quasars., This corresponds to of all the quasars and of both the red and blue quasars.
 Comparing all these percentages we found that the KA: method: variant was quantitatively superior to the UVN method. as the UVX method selected less quasars ancl was clearly. biassed towards the selection of blue quasars.," Comparing all these percentages we found that the KX method variant was quantitatively superior to the UVX method, as the UVX method selected less quasars and was clearly biassed towards the selection of blue quasars."
 We also found. that quantitatively the KAN method variant is comparable to the 2QZ multicolour method in the number of quasars selected: however. the WX method variant is superior as the 20Z multicolour did demonstrate a bias towards the selection of blue quasars while the KAN method. variant did not.," We also found that quantitatively the KX method variant is comparable to the 2QZ multicolour method in the number of quasars selected; however, the KX method variant is superior as the 2QZ multicolour did demonstrate a bias towards the selection of blue quasars while the KX method variant did not."
 Our results are strong experimental support that compared. to existing methods. such as the UVX and 2QZ multicolor methods. the IX method. and in particular our variant. is," Our results are strong experimental support that compared to existing methods such as the UVX and 2QZ multicolor methods, the KX method, and in particular our variant, is"
Knowing the host galaxy magnitude. we can estimate the redshift of IES 06474250.,"Knowing the host galaxy magnitude, we can estimate the redshift of 1ES 0647+250."
 Sbarufatti et al. (, Sbarufatti et al. (
"2005) demonstrated that the distribution of the absolute magnitudes of BL Lac host galaxies is almost Gaussian with an average of M, = -22.8 and o = 0.5. and that BL Lac host galaxies can therefore be used as a standard candle to estimate their distances.","2005) demonstrated that the distribution of the absolute magnitudes of BL Lac host galaxies is almost Gaussian with an average of $M_R$ = -22.8 and $\sigma$ = 0.5, and that BL Lac host galaxies can therefore be used as a standard candle to estimate their distances."
 Before using their method. we first have to transform the apparent H-band magnitude of the host galaxy to apparent R-band magnitude.," Before using their method, we first have to transform the apparent $H$ -band magnitude of the host galaxy to apparent $R$ -band magnitude."
 Since the observed A—H colour depends on redshift. we have to determine the redshift by iteration. starting from z = 0 and using Eq. (," Since the observed $R-H$ colour depends on redshift, we have to determine the redshift by iteration, starting from z = 0 and using Eq. ("
2) in Sbarufatti et al. (,2) in Sbarufatti et al. (
2005) and a typical BL Lac host galaxy colourR-H = 2.2 +0.4 (Hyvónnen et al.,2005) and a typical BL Lac host galaxy colour $R-H$ = 2.2 $\pm$ 0.4 (Hyvönnen et al.
 2007)., 2007).
 This iteration yields R(host) 2 19.1 and z 2 0.408 in the adopted cosmology., This iteration yields R(host) = 19.1 and z = 0.408 in the adopted cosmology.
 To compute the uncertainty in the derived redshift. we use the estimated Ico fitting uncertainty of the host galaxy magnitude of 0.2 mag.," To compute the uncertainty in the derived redshift, we use the estimated $\sigma$ fitting uncertainty of the host galaxy magnitude of 0.2 mag."
 Performing the redshift iteration. at m(host) + 0.2 mag and m(host) - 0.2 mag yields an error of 40.03 for z. By adding to this in quadrature the inherent uncertainty in the method (Az=0.05; Sbarufatti et al., Performing the redshift iteration at m(host) + 0.2 mag and m(host) - 0.2 mag yields an error of $\pm$ 0.03 for z. By adding to this in quadrature the inherent uncertainty in the method $\Delta z = 0.05$; Sbarufatti et al.
 2005). we derive the final error in z to be 40.06.," 2005), we derive the final error in z to be $\pm$ 0.06."
 The effective radius of the host galaxy is 16640733.122 which translates into $.641.7 kpe at z = 0.41. consistent with typical values found in the near-infrared (NIR) for blazar host galaxies (e.g. Kotilainen et al.," The effective radius of the host galaxy is $\pm$ 3, which translates into $\pm$ 1.7 kpc at z = 0.41, consistent with typical values found in the near-infrared (NIR) for blazar host galaxies (e.g. Kotilainen et al."
 1998a.b). which lends further credibility to our estimate of the redshift.," 1998a,b), which lends further credibility to our estimate of the redshift."
 There have been several previous attempts to derive the host galaxy properties of TES 0647+250 with varying success., There have been several previous attempts to derive the host galaxy properties of 1ES 0647+250 with varying success.
 Falomo Kotilainen (1999) found the object to be unresolved from 900 sec NOT R-band imaging taken under very good seeing conditions (0665)., Falomo Kotilainen (1999) found the object to be unresolved from 900 sec NOT $R$ -band imaging taken under very good seeing conditions 65).
 They derived a lower limit of z > 0.3. assuming it is hosted by a typical elliptical galaxy.," They derived a lower limit of z $>$ 0.3, assuming it is hosted by a typical elliptical galaxy."
 Scarpa et al. (, Scarpa et al. (
2000) obtained a 600 sec HST F702W band image. as part of their BL Lac snapshot survey.,"2000) obtained a 600 sec HST F702W band image, as part of their BL Lac snapshot survey."
 They found the surface brightness profile to be consistent with the PSF anc derived an upper limit R > 19.1 for the apparent magnitude of the host galaxy., They found the surface brightness profile to be consistent with the PSF and derived an upper limit R $>$ 19.1 for the apparent magnitude of the host galaxy.
 Based on this upper limit. Sbarufatti et al. (," Based on this upper limit, Sbarufatti et al. ("
2005) derived a lower limit of z > 0.47 for the redshift.,2005) derived a lower limit of z $>$ 0.47 for the redshift.
 Finally. Nilsson et al. (," Finally, Nilsson et al. ("
"2003) found that [ES 0647+250 was unresolved in a 900 see NOT R-band image. taken under - [00 seeing conditions,","2003) found that 1ES 0647+250 was unresolved in a 900 sec NOT $R$ -band image, taken under $\sim$ 0 seeing conditions."
 Meisner Romani (2010) were able to resolve the host galaxy from 1200 sec i’-band imaging at the WIYN 3.6m telescope at Kitt Peak National Observatory. under very good seeing conditions (07668).," Meisner Romani (2010) were able to resolve the host galaxy from 1200 sec $i'$ -band imaging at the WIYN 3.6m telescope at Kitt Peak National Observatory, under very good seeing conditions 68)."
 They derived apparent /’-band magnitudes of 16.1 and 19.040.1 for the nucleus and the host galaxy. respectively.," They derived apparent $i'$ -band magnitudes of 16.1 and $\pm$ 0.1 for the nucleus and the host galaxy, respectively."
 However. their data analysis did not allow them to estimate the effective radius of the host galaxy.," However, their data analysis did not allow them to estimate the effective radius of the host galaxy."
 Based on the host magnitude. and using the method of Sbarufatti et al. (," Based on the host magnitude, and using the method of Sbarufatti et al. ("
2005). Meisner Romani (2010) report imaging redshift of z = 0.45+0.08.,"2005), Meisner Romani (2010) report imaging redshift of z = $\pm$ 0.08."
 We note that the detection of the host galaxy by Meisner Romani is not well documented. in the sense that they do not show the image of the field. the radial profiles vs. the models. nor the comparison with the PSF.," We note that the detection of the host galaxy by Meisner Romani is not well documented, in the sense that they do not show the image of the field, the radial profiles vs. the models, nor the comparison with the PSF."
 Especially. the lack of an estimate of the effective radius translates into à poorer constraint on the redshift. than that reported in this work.," Especially, the lack of an estimate of the effective radius translates into a poorer constraint on the redshift, than that reported in this work."
 Knowledge of the redshift is of critical importance to the VHE spectra of blazars. due to the absorption of VHE photons via pair production on the EBL.," Knowledge of the redshift is of critical importance to the VHE spectra of blazars, due to the absorption of VHE photons via pair production on the EBL."
 This absorption is energy-dependent and increases strongly with redshift. distorting the VHE spectra of distant objects.," This absorption is energy-dependent and increases strongly with redshift, distorting the VHE spectra of distant objects."
 Our redshift estimate. z = 0.4120.06. places thus important constraints on the gamma-ray properties of [ES 0647-250. and it is consistent with a picture where the VHE photons are mostly absorbed and the gamma-ray spectrum of IES 06474250 is dominated by the EBL.," Our redshift estimate, z = $\pm$ 0.06, places thus important constraints on the gamma-ray properties of 1ES 0647+250, and it is consistent with a picture where the VHE photons are mostly absorbed and the gamma-ray spectrum of 1ES 0647+250 is dominated by the EBL."
 BL Lae hosts are often surrounded by a significant excess of nearby galaxies (e.g. Falomo et al., BL Lac hosts are often surrounded by a significant excess of nearby galaxies (e.g. Falomo et al.
 2000)., 2000).
 To see if there is an overdensity of galaxies around TES 06474250. we counted all the resolved objects within a projected distance of 27755," To see if there is an overdensity of galaxies around 1ES 0647+250, we counted all the resolved objects within a projected distance of 5"
The large-scale distribution of superclusters is shown in Fig.,The large-scale distribution of superclusters is shown in Fig.
 | in cartesian coordinates., \ref{fig:sclxyz} in cartesian coordinates.
 These coordinates are defined as in? and in2:: where d is the comoving distance. and οἱ and 7 are the SDSS survey coordinates.," These coordinates are defined as in and in: where $d$ is the comoving distance, and $\lambda$ and $\eta$ are the SDSS survey coordinates."
 gave detailed description of the scale distribution of rich superclusters., gave detailed description of the large-scale distribution of rich superclusters.
 The idea of the principal component analysis is to find a small number of linear combinations of correlated parameters to describe most of the variation in the dataset with a small number of new uncorrelated parameters., The idea of the principal component analysis is to find a small number of linear combinations of correlated parameters to describe most of the variation in the dataset with a small number of new uncorrelated parameters.
 The PCA transforms the data to à new coordinate system. where the greatest variance by any projection of the data lies along the first coordinate (the first principal component). the second greatest variance — along the second coordinate. and so on.," The PCA transforms the data to a new coordinate system, where the greatest variance by any projection of the data lies along the first coordinate (the first principal component), the second greatest variance – along the second coordinate, and so on."
 There are as many principal components as there are parameters. but typically only the first few are needed to explain most of the total variation.," There are as many principal components as there are parameters, but typically only the first few are needed to explain most of the total variation."
" Principal components PCy (x€E; v€N,4) are a linear combination of the original parameters: where -1Xali)x| are the coefficients of the linear transformation. V; are the original parameters and Λο is the number of the original parameters."," Principal components $x$ $x \in \mathbb{N}$, $x \leq N_{tot})$ are a linear combination of the original parameters: where $-1 \leq a(i)_x \leq 1$ are the coefficients of the linear transformation, $V_i$ are the original parameters and $N_{\mathrm{tot}}$ is the number of the original parameters."
 PCA ts suitable tool to study simultaneously correlations between a large number of parameters. for finding subsets in data. and detecting outliers.," PCA is suitable tool to study simultaneously correlations between a large number of parameters, for finding subsets in data, and detecting outliers."
 Linear combinations of principal components can be used to reproduce parameters characterising objects in the dataset., Linear combinations of principal components can be used to reproduce parameters characterising objects in the dataset.
 Principal components can be used to derive sealing relations., Principal components can be used to derive scaling relations.
 If data points lie along a plane. defined by the first two principal components. then the scaling relations along this plane are defined by the third principal component (?).," If data points lie along a plane, defined by the first two principal components, then the scaling relations along this plane are defined by the third principal component ."
. For the analysis we use standardised parameters. centred on their means (V;—Vj) and normalised (divided by their standard deviations. σσV;)).," For the analysis we use standardised parameters, centred on their means $ V_{i} - \overline{V_{i}})$ and normalised (divided by their standard deviations, $\sigma( V_{i}))$."
 Therefore we obtain for the scaling relations: For PCA. the parameters should be normally distributed.," Therefore we obtain for the scaling relations: For PCA, the parameters should be normally distributed."
 Therefore we use the logarithms of parameters in most cases: this makes the distributions more gaussian. and the range over which their values span are smaller. especially for luminosities and volumes.," Therefore we use the logarithms of parameters in most cases; this makes the distributions more gaussian, and the range over which their values span are smaller, especially for luminosities and volumes."
 We do not use logarithms of morphological data. in order to not to exclude from the analysis those with negative values of shapefinders. which may oceur in the case of compact superclusters with a complex overall morphology," We do not use logarithms of morphological data, in order to not to exclude from the analysis those with negative values of shapefinders, which may occur in the case of compact superclusters with a complex overall morphology."
(??).. Figures 2. and 3. show the distribution of the values of the standardised parameters., Figures \ref{fig:scl90para5distr} and \ref{fig:scl90para4distr} show the distribution of the values of the standardised parameters.
 Deviations from the normal distribution are mostly caused by the most luminous (or by the poorest for the shape parameter) superclusters in our sample., Deviations from the normal distribution are mostly caused by the most luminous (or by the poorest for the shape parameter) superclusters in our sample.
 In Table 1 we give the mean values and standard deviations of supercluster parameters., In Table \ref{tab:msd} we give the mean values and standard deviations of supercluster parameters.
" For poor superclusters of ""spider"" morphology the shape parameter is not always well defined(?).", For poor superclusters of “spider” morphology the shape parameter is not always well defined.
. For five systems the value of the shape parameter ΓΚ.>4: therefore we also calculated the mean value and standard deviation of the shape parameter without these systems (denoted as ΚΚ)., For five systems the value of the shape parameter $|K_1/K_2| > 4$; therefore we also calculated the mean value and standard deviation of the shape parameter without these systems (denoted as $K_1/K_2^*$ ).
 This effect does not affect the values of other parameters. thus we did not exclude these systems from our calculations.," This effect does not affect the values of other parameters, thus we did not exclude these systems from our calculations."
 We present in tables the values of principal components and the standard deviations. proportion of variance. and cumulative variance of principal components.," We present in tables the values of principal components and the standard deviations, proportion of variance, and cumulative variance of principal components."
 The values of components show the importance of the original parameters in. each PCx., The values of components show the importance of the original parameters in each PCx.
 We plot the principal planes for superclusters., We plot the principal planes for superclusters.
 For the calculations we used command fromR. an open-source free statistical environment developed under the GNU GPL|1g96.," For the calculations we used command from, an open-source free statistical environment developed under the GNU GPL."
 To study correlations between properties of superclusters. we applied Spearman's rank correlation test. in which the value of the correlation coefficient r shows the presence of correlation (rz| for perfect correlation).anticorrelation (p.=-] for perfect anticorrelation). or the absence of correlations when px.," To study correlations between properties of superclusters, we applied Spearman's rank correlation test, in which the value of the correlation coefficient $r$ shows the presence of correlation $r = 1$ for perfect correlation),anticorrelation $r = -1$ for perfect anticorrelation), or the absence of correlations when $r \approx 0$ ."
important term is the work done by the azimuthal flow against the azimuthalCag component of magnetic stress.,"important term is $\efrate_\text{mag}^4$, the work done by the azimuthal flow against the azimuthal component of magnetic stress."
" Its contribution to Emag decreases rapidly, however, falling below 50% at r~30 (i.e. well below the surface, near the sonic one)."," Its contribution to $\efrate_\text{mag}$ decreases rapidly, however, falling below $50\%$ at $r
\approx 30$ (i.e. well below the surface, near the sonic one)."
 It is then taken over by Cla which describes the flow of magnetic enthalpy stored in the azimuthal field.," It is then taken over by $\efrate_\text{mag}^2$, which describes the flow of magnetic enthalpy stored in the azimuthal field."
" Ol has minor significance in the 3D simulation, which may be due to the perturbed toroidal field having also a By component (a rigid displacement of a pure azimuthal field in the r—const. plane introduces a non-azimuthal component)."," $\efrate_\text{mag}^1$ has minor significance in the 3D simulation, which may be due to the perturbed toroidal field having also a $B_\vartheta$ component (a rigid displacement of a pure azimuthal field in the $r=\const$ plane introduces a non-azimuthal component)."
 is insignificant in both cases., $\efrate_\text{mag}^3$ is insignificant in both cases.
 The strong decrease of Emag in Casthe 3D simulation is caused by the decrease of Cla, The strong decrease of $\efrate_\text{mag}$ in the 3D simulation is caused by the decrease of $\efrate_\text{mag}^2$.
" We find a net outflow of magnetic enthalpy through the lateral boundaries of the computational volume at the height of the jet front, with peak rates of about 0.15 in the 2.5D case and 0.05 in the 3D case."," We find a net outflow of magnetic enthalpy through the lateral boundaries of the computational volume at the height of the jet front, with peak rates of about $0.15$ in the 2.5D case and $0.05$ in the 3D case."
" The outflow is transient in the 2.5D case, vanishing quickly after the jet front leaves the computational volume."," The outflow is transient in the 2.5D case, vanishing quickly after the jet front leaves the computational volume."
" In the 3D case, however, it turns into an inflow of the order —0.05 which persists until the end of the simulation."," In the 3D case, however, it turns into an inflow of the order $-0.05$ which persists until the end of the simulation."
" The energy in the radial magnetic field increases correspondingly, mainly outside the jet at 9>5.7°."," The energy in the radial magnetic field increases correspondingly, mainly outside the jet at $\vartheta>5.7\degree$."
 The red line in Fig., The red line in Fig.
" 6 shows the magnetic flux E contained within an angle 9«5.7? from the axis, divided by its initial value."," \ref{fig:magflux} shows the magnetic flux $\Xi$ contained within an angle $\vartheta<5.7\degree$ from the axis, divided by its initial value."
" For comparison, the green curve shows &*, the flux of only those field lines that have the same direction as the initial field (the green and the red curves coincide in the 2.5D case)."," For comparison, the green curve shows $\Xi^+$, the flux of only those field lines that have the same direction as the initial field (the green and the red curves coincide in the 2.5D case)."
" Although the 2.5D jet fills only part of the 5.7? cone, it causes a significant reduction of &."," Although the 2.5D jet fills only part of the $5.7\degree$ cone, it causes a significant reduction of $\Xi$."
" This reflects the lateral expansion of the jet due to the pressure exerted by B,.", This reflects the lateral expansion of the jet due to the pressure exerted by $B_\varphi$.
" There is less reduction in the 3D case, with = being near the original value at very large distances."," There is less reduction in the 3D case, with $\Xi$ being near the original value at very large distances."
" The difference becomes evident where the 3D jet is unstable, showing that it is due to the dissipation of the toroidal field."," The difference becomes evident where the 3D jet is unstable, showing that it is due to the dissipation of the toroidal field."
Both vortex creep and. rotochenücal heating niechanisnis depend on| rotational kinetic cnerey.,Both vortex creep and rotochemical heating mechanisms depend on rotational kinetic energy.
 According to ?.. onlv these two mechanisms will be Huportant at time-scales comparable to PSR JO[37s age.," According to \citet{2010A&A...522A..16G}, only these two mechanisms will be important at time-scales comparable to PSR J0437's age."
 Our measurement of the bulk surface teiiperature. 1.25«10T3.5510 KI. is iore precise aud slightly higher than the temxature found by EKO1.," Our measurement of the bulk surface temperature, $1.25\times10^5\leq T \leq3.55\times10^5$ K, is more precise and slightly higher than the temperature found by K04."
 Iu Figure L top. of ?.. this pished the data point from about 1-0 from the upper model curve to about L.5-0 from the model curve.," In Figure 4, top, of \citet{2010A&A...522A..16G}, this pushed the data point from about $\sigma$ from the upper model curve to about $\sigma$ from the model curve."
 Although the allowed range of surface T ds in agreement with the more uncertain WOL nuüeasurenaent. we stress that the iuportaut result of our analysis is a muuch increased coufidence im the thermal interpretation of the pulsar FUV spectra (IKO1 allowed for a non-thermal interpretation as well).," Although the allowed range of surface $T$ is in agreement with the more uncertain K04 measurement, we stress that the important result of our analysis is a much increased confidence in the thermal interpretation of the pulsar FUV spectrum (K04 allowed for a non-thermal interpretation as well)."
 As well as residual heat in the interior and anv heating uechanisni discussed above. the surface temperature xofile of the pulsar will be affected by. the energetics of spin-down induced magnetospheric activity.," As well as residual heat in the interior and any heating mechanism discussed above, the surface temperature profile of the pulsar will be affected by the energetics of spin-down induced magnetospheric activity."
 A larec amount of energv is available from the loss of rotational sinctic enerev. E;=28<WP8 3. but the uajoritv of this will be released as a relativistic wind.," A large amount of energy is available from the loss of rotational kinetic energy, $\dot{E}_i=2.8\times10^{33}$ $^{-1}$, but the majority of this will be released as a relativistic wind."
 Some fraction of this power is. however. released as uaenetospheric photon cussion (ΙΟ accompany the article cascades).," Some fraction of this power is, however, released as magnetospheric photon emission (which accompany the particle cascades)."
 Hligli-enerey maeuctospheric partic—CR are responsible for the non-thermal emission from the oulsar. but it is generally believed that some fraction of the particle fix returns to the NS surface along the ficld lines. heating the polar caps.," High-energy magnetospheric particles are responsible for the non-thermal emission from the pulsar, but it is generally believed that some fraction of the particle flux returns to the NS surface along the field lines, heating the polar caps."
 Iudoeed. this is believed o be the cause of soft ταν thermal cussion with T=108 IIS and projected areas umchi simaller thau the size of a NS(?)..," Indeed, this is believed to be the cause of soft X-ray thermal emission with $T\ga10^6$ K and projected areas much smaller than the size of a NS \citep{2007arXiv0710.3517H}."
" In the case of JOIX37. it is reasonable to assume iat the hotter black-body components fitted above. with a combined huuiuositv of Li,~107 |. are also volar caps heated in a simular way to other pulsars."," In the case of J0437, it is reasonable to assume that the hotter black-body components fitted above, with a combined luminosity of $L_{\rm hot}\sim10^{30}$ $^{-1}$, are also polar caps heated in a similar way to other pulsars."
 The rermal X-ray efficieuey of the order jz3&100?," The thermal X-ray efficiency of the order $\eta\approx3\times10^{-4}$ \citep{2007MNRAS.376L..67G,2008AIPC..983..171K}."
 (2?).. ? (λεν 13)). 13)). (7).. (23... (?7)..," \citet{2007arXiv0710.3517H} \citep{1995JApA...16..375D}, \ref{MW3}) \ref{MW3} \ref{MW3}) \citep{2009ApJ...706L..56A}. \citep{2010ApJS..187..460A}. \citep{2006ApJ...638..951Z,2007ApJ...670..668B}."
 2 , \citet{2007ApJ...670..668B} 
mean [ree path is A=lI/popa;. where p is the density of dark matter.,"mean free path is $\lambda = 1/\rho\sigma_{DM}$, where $\rho$ is the density of dark matter."
 An optical depth can be defined 7=r/A. which distinguishes dillerent physical regimes.," An optical depth can be defined $\tau \equiv r/\lambda$, which distinguishes different physical regimes."
 In regions which are optically thick 721. the dark matter behaves as a fIuid: whereas. for regions which are optically thin 7SI. the dynamics closely resembles two body relaxation in globular clusters.," In regions which are optically thick $\tau \gg 1$, the dark matter behaves as a fluid; whereas, for regions which are optically thin $\tau \lesssim 1$, the dynamics closely resembles two body relaxation in globular clusters."
 The range of cross sections consistent with experimental constraints. vel eiving the required rates of evolution. imply that dark halos will probably be optically thin το)<1 at their Characteristic scale radius re (Wandelt et al.," The range of cross sections consistent with experimental constraints, yet giving the required rates of evolution, imply that dark halos will probably be optically thin $\tau\left(r_s\right)\lesssim 1$ at their characteristic scale radius $r_s$ (Wandelt et al."
 2000; Davé et al., 2000; Davé et al.
" 2000). but of course can be oplically thick in the inner regions r<r, where the densities are higher (provided a>1)."," 2000), but of course can be optically thick in the inner regions $r\ll r_s$ where the densities are higher (provided $\alpha>1$ )."
 Numerical investigations of SIDAL halo evolution have been carried oul by several eroups., 	Numerical investigations of SIDM halo evolution have been carried out by several groups.
 Yoshida et al. (, Yoshida et al. (
2000a) and Moore et al. (,2000a) and Moore et al. (
2000) simulated S1DM halos in the optically thick or fluid limit. which. as mentioned above. is probably not the relevant scenario [or SIDM.,"2000) simulated SIDM halos in the optically thick or fluid limit, which, as mentioned above, is probably not the relevant scenario for SIDM."
 Burkert (2000) aid IXochanek White (2000) simulated isolated halos employing a range of cross sections nearly consistent with the optically thin requirement., Burkert (2000) and Kochanek White (2000) simulated isolated halos employing a range of cross sections nearly consistent with the optically thin requirement.
 Both groups found that halos develop shallow cores for a modest period of time before the onset of core collapse. but. disagree on the core collapse timescale.," Both groups found that halos develop shallow cores for a modest period of time before the onset of core collapse, but disagree on the core collapse timescale."
 Davé οἱ al. (, Davé et al. (
2000) aid. Yoshida et al. (,2000) and Yoshida et al. (
2000b) simulated optically (hin halos in cosmological settings. which include infall and merging.,"2000b) simulated optically thin halos in cosmological settings, which include infall and merging."
 Thev observed evolution towards reduced central densities and shallower inner profiles. effects increasing with increasing cross section: and neither saw any evidence [or core collapse.," They observed evolution towards reduced central densities and shallower inner profiles, effects increasing with increasing cross section; and neither saw any evidence for core collapse."
 Their results are in broad agreement with each other and span the range [rom cdwarf galaxies to clusters., Their results are in broad agreement with each other and span the range from dwarf galaxies to clusters.
 Alternative to N-body techniques. Lannestead. (2000) and Fimani. D'Onghia. Chinearini (2001) have carried. out. integrations of the collisional Doltzmann equation.," Alternative to N-body techniques, Hannestead (2000) and Firmani, D'Onghia, Chincarini (2001) have carried out integrations of the collisional Boltzmann equation."
 Firmani et al., Firmani et al.
's simulation differs from previous investigations in that they considered. a velocity dependent cross section σxο'.,'s simulation differs from previous investigations in that they considered a velocity dependent cross section $\sigma \propto v^{-1}$.
 Also Dalberg. Shapiro Inagaki (2001) examined SIDAL halo evolution via a time-dependent eravothermal numerical calewlation.," Also Balberg, Shapiro Inagaki (2001) examined SIDM halo evolution via a time-dependent gravothermal numerical calculation."
 All three find the development of shallower central slopes and less concentrated cores than CDM would produce. consistent with (he quoted N-body results. although Balbere et al. (," All three find the development of shallower central slopes and less concentrated cores than CDM would produce, consistent with the quoted N-body results, although Balberg et al. ("
2001) obtained a collapse timescale roughly. an order of magnitude lareer than that seen bv Burkert (2000) and IXochanek White (2000).,2001) obtained a collapse timescale roughly an order of magnitude larger than that seen by Burkert (2000) and Kochanek White (2000).
 In sum. the most relevant numerical studies performed to date indicate that. for appropriate dark matter scattering cross sections. collisions can effectivelv reduce dark matter central densities for normal galaxies.," In sum, the most relevant numerical studies performed to date indicate that, for appropriate dark matter scattering cross sections, collisions can effectively reduce dark matter central densities for normal galaxies."
 A niunber ol authors have obtained constraints on συ from analytical and semi-analvtical arguments., 	 	A number of authors have obtained constraints on $\sigma_{DM}$ from analytical and semi-analytical arguments.
" Strong lensing events are extremely sensitive to the inner profiles ancl shapes of dark halos in clusters of galaxies. aud are (hus a powerful probe of SIDM. which has enabled several authors to place constraints on gpa, (Miralda-Escudé 2000: Wxithe. Turner Spergel 2001: Meneehetti et al."," Strong lensing events are extremely sensitive to the inner profiles and shapes of dark halos in clusters of galaxies, and are thus a powerful probe of SIDM, which has enabled several authors to place constraints on $\sigma_{DM}$ (Miralda-Escudé 2000; Wyithe, Turner Spergel 2001; Meneghetti et al."
 2001)., 2001).
" Mo and Mao (2000) determined what value of gpa, would produce a correct Tullv-Fisher relation for SIDM halos.", Mo and Mao (2000) determined what value of $\sigma_{DM}$ would produce a correct Tully-Fisher relation for SIDM halos.
 Further constraints can be placed on SIDM because of the existence of subhalos in larger halos: heat (transfer to a cool subhalo from the, Further constraints can be placed on SIDM because of the existence of subhalos in larger halos: heat transfer to a cool subhalo from the
interpolated on a 5 (3 for TW να) kan |! grid. and henY averaecQ,"interpolated on a 5 (3 for TW Hya) km $^{-1}$ grid, and then averaged."
NTΤΟ(s Weefoes avo plottedN : Figure Tore22.., Line composites are plotted in Figure \ref{fig:fluxfit_plot1}.
 About half d.of Liuthe line conipositecompositesan are single-peaked.in while half have evidence for somewhat double-peaked xofiles.," About half of the line composites are single-peaked, while half have evidence for somewhat double-peaked profiles."
" Two source coπρο AA Tau sU depressiousτον. that and.likely Aur.incousisthavecut with strong centraldisk. clission a areIxepleriau disk. with the latter. siupleuufortunately. having fromno observable ines with Ay, 220."," Two source composites, AA Tau and SU Aur, have strong central depressions that are likely inconsistent with simple disk emission from a Keplerian disk, with the latter, unfortunately, having no observable lines with $J_\mathrm{up}>$ 20."
 Our sample also includes a fow sonrces known to be strongly centrally (AS 205 and DR ct 22011). peakedthe overal ine shape consistentTan: Bastwith the sun of a withI&epleriau profile ⋜⋯≼↧⋜↧↴∖↴↕∪↖↖↽≼∐∖↴↘↽↖↖↽↕∐≼↧⋖↕⋟∪↕↑∪⋯≻↕≺↧⋜∐⊔∖," Our sample also includes a few sources known to be strongly centrally peaked (AS 205 N and DR Tau; Bast et 2011), with the overall line shape consistent with the sum of a Keplerian profile and a slow disk wind \citep{Pontoppidan11}."
↑⋜↕↕∙⊇∩∐⋟∙∙∖↖⊽↸∖≼↧∪ ↕∪↑↕⊔⋜∐↘↽↸∖⋜∐⊔∖↕−↥⋅∪↥⋅↑↑∪⋯∪≼∐∖↕∪↥⋅∏∐≼∐∖↥⋅↴∖↴↑⋜⋯≼⇂↑∐↸∖↴∖↴↸∖↸∖↘⋜↧↸⊳ ↴∖↴⊓⋅⋯⊳⊓∐⋅↸∖↴∖↴∙⋜⋯≼↧↕∐↴∖↴↑↸∖⋜∥⊔≯∪↸⊳∏↴∖↴↕∐∖↥⋅↸∖∪∐⋜↧≼∐∖↥⋅↕↖⇁⋜↧↑↕," We do not make an effort to model or understand these exact structures, and instead focus here on a derivation of inner radii from the line wings."
∪∐∪↕⋟↕∐∐↸∖↥⋅ ↥⋅⋜↧≼∐↕↕≯↥⋅∪⋯↑∐↸∖∐⋯∖↖↖↽↕∐∶↴∙∷∖↴∙⊟≻↥⋅⋯∪↥⋅↸∖↕∐⊣∐∖↻↑∐↴∖↴↑∏≼∐↸∖↴∖↴∪⋡ ∪↖↽↸∖↥⋅⋜↧∐∐∐↸∖↴∖↴∐⋜∏⋉∖↴∖↴∙∏↑∐↕∑↕∐∶↴∙⊾∐↕∶↴∙⊾∐↸∖↥⋅≓↥⋅↸∖↴∖↴≺≻↕∏↑↕∪∐≼↧⋜↧↑⋜↧↕≯↥⋅∪⋯ VLT-CRIRES. we direct the reader to Poutoppidaual. (2011).. Bastetal. (2011).. and BBrown ct ((2011. iu preparation).," For more in-depth studies of overall line shapes, utilizing higher-resolution data from VLT-CRIRES, we direct the reader to \citet{Pontoppidan11}, \citet{Bast11}, and Brown et (2011, in preparation)."
" While temperature€ profilesD have€ been measuredetr for outer disk dust (c.¢..Andrewsetal.2009:Isella 2009).. the temperature profile for iuner disks or for tnolecnlax line-cmittine layers is πιοσος,"," While temperature profiles have been measured for outer disk dust \citep[e.g.,][]{Andrews09, Isella09}, the temperature profile for inner disks or for molecular line-emitting layers is unmeasured."
 In fact. it is believed. that the disk upper atmosphere is thermally decoupled from the dust. aud its temperature is set bv a coniplex balance of gas heating aud cooling (Classgold&Najita2001:KamDullemond 2001).," In fact, it is believed that the disk upper atmosphere is thermally decoupled from the dust, and its temperature is set by a complex balance of gas heating and cooling \citep{Glassgold01, Kamp04}."
.. Therefore. we have chosen a model that makes a ΙΙια. nuuber of assunirptious about the underline temperature.," Therefore, we have chosen a model that makes a minimal number of assumptions about the underlying temperature."
 Iu addition. our model was designed to provide a robust wav to determine the CO inner radius. without the nieasurenaent of this radius depending strongly on the choice of model.," In addition, our model was designed to provide a robust way to determine the CO inner radius, without the measurement of this radius depending strongly on the choice of model."
 Tn other words. it allows for a good fit to the line wines (and hence Ry)independently of velocity portions of the line profile.," In other words, it allows for a good fit to the line wings (and hence $R_\mathrm{in}$ ) of lower-velocity portions of the line profile."
 We lave chosen to model the line profiles as ciissiou, We have chosen to model the line profiles as emission
"Canuna-Rav bursts (GRBs) are the brightest electromagnetic explosions iu the universe (for a recent review, see Pirau 2000).","Gamma-Ray bursts (GRBs) are the brightest electromagnetic explosions in the universe (for a recent review, see Piran 2000)."
 Popuar models for their ceutral enenme divide iuto two main classes: (1) the collavse of a lnassive star to a black hole (DIT) (AlacFadven. Woosley. Ποσο 2001. and references therein): (1) the coaescelicc5 of a binary svsteni mvolviug a neutron star (NS) and :i DII or a NS as a companion (c.g. Eichler et al.," Popular models for their central engine divide into two main classes: (i) the collapse of a massive star to a black hole (BH) (MacFadyen, Woosley, Heger 2001, and references therein); (ii) the coalescence of a binary system involving a neutron star (NS) and a BH or a NS as a companion (e.g. Eichler et al."
 1989 Janka et al., 1989; Janka et al.
 1999)., 1999).
 The observe association of loue-duration CRBs with star forming regious (Djorgovski et al, The observed association of long-duration GRBs with star forming regions (Djorgovski et al.
 2001c. aud references therein). aud the possible superuowi signatures in rapidly-decaving afterglows (Bloom et al," 2001c, and references therein), and the possible supernova signatures in rapidly-decaying afterglows (Bloom et al."
 1999: I&ulkaurni et al., 1999; Kulkarni et al.
 2000: Reichart 2001) favors he first class., 2000; Reichart 2001) favors the first class.
 Both classes of models associate GRB progenitors with compact objects (BIL or NS) that are the Cle products in the evolution of massive stars., Both classes of models associate GRB progenitors with compact objects (BH or NS) that are the end products in the evolution of massive stars.
 ence. tlre GRB formation historv is expected to ollow the cosmic star formation dhüstorv (Totani 1997. 1999: Wijes e al.," Hence, the GRB formation history is expected to follow the cosmic star formation history (Totani 1997, 1999; Wijers et al."
 1998: Blain Natarajau 2000) u» to the highes redshifts (2~2 Yoat which the first ecucration of stars iav have formed (Barkana Loch 2001)., 1998; Blain Natarajan 2000) up to the highest redshifts $z\sim 20$ ) at which the first generation of stars may have formed (Barkana Loeb 2001).
 GRBs mieh therefore provide an ideal probe of cosmic star formatio at all redshifts that iu particular is unaffected by dus obscuration (e.g. Blain Naarajan 2000: Porciani Madan 2001).," GRBs might therefore provide an ideal probe of cosmic star formation at all redshifts that in particular is unaffected by dust obscuration (e.g., Blain Natarajan 2000; Porciani Madau 2001)."
 In fact. the top-heavy inilal ΝΕ fuucti (INE) predicted. for the first stars {Brouun. Coppi. Larsou 1999. 2002: Abel. Drva1 Norman 2000. 2002. Nakamura Unmemura 2001) favors massive stars wclic. are the likely source of GRB progenitors.," In fact, the top-heavy initial mass function (IMF) predicted for the first stars (Bromm, Coppi, Larson 1999, 2002; Abel, Bryan, Norman 2000, 2002, Nakamura Umemura 2001) favors massive stars which are the likely source of GRB progenitors."
 GRB afterglows provide a unique probe of the ie redshift universe (Lamb Reichart 2WOO: Clardi Loc 2000)., GRB afterglows provide a unique probe of the high redshift universe (Lamb Reichart 2000; Ciardi Loeb 2000).
 The bright. carly opticaLUV hnimositv of a CRB afterglow is expected to outshine its host galaxy. eve1 more so at ligh redshifts when the typical galaxies are less massive than their present-day counterparts (Barkana Loeb 2001).," The bright, early optical-UV luminosity of a GRB afterglow is expected to outshine its host galaxy, even more so at high redshifts when the typical galaxies are less massive than their present-day counterparts (Barkana Loeb 2001)."
 The broad-band afterglow spectrmu extends 1uto the far UV and so the absorption features imprinted ( nit by the iuterveniug intergalactie medium (IGM) can ο used to infer the evolution of the ueutral hydrogen yaction aud the metal abundance of the IGAL during he epoch of reionization., The broad-band afterglow spectrum extends into the far UV and so the absorption features imprinted on it by the intervening intergalactic medium (IGM) can be used to infer the evolution of the neutral hydrogen fraction and the metal abundance of the IGM during the epoch of reionization.
" In difference from galaxies and (pasas, Which fade rapidly with increasing redshift due to he iucrease m their huuinosity distance. CRB afterglows uaintain an almost constant infrared flux with iucreasing redshift at a fixed time lag after the GRB trigeerfelon] in the 6observer frame (Ciardi Loeb 2000)."," In difference from galaxies and quasars, which fade rapidly with increasing redshift due to the increase in their luminosity distance, GRB afterglows maintain an almost constant infrared flux with increasing redshift at a fixed time lag after the GRB trigger in the observer frame (Ciardi Loeb 2000)."
 This follows from he cosinological timestretching of the afterglow trausieut (which is intrinsically brighter at earlier tines) and frou i vfavorable A -correction im the afterglow spectra., This follows from the cosmological time–stretching of the afterglow transient (which is intrinsically brighter at earlier times) and from a favorable $K$ -correction in the afterglow spectrum.
 TheSwiftsatellitet.. planned for lunch in 2003. is (sxpected to localize roughly oue GRB per day.," The, planned for launch in 2003, is expected to localize roughly one GRB per day."
 Sorting out the sbset of all CRBs which originate at high redshifts DE ) would be of particular interest., Sorting out the subset of all GRBs which originate at high redshifts $z\ga 5$ ) would be of particular interest.
 Observers may ¢4uplov a simple strategy for this purpose., Observers may employ a simple strategy for this purpose.
 Photometric (lata from a small telescope should be used at first to ideutiVv those CRBs which possess a Lya trough at a wavelength of 0.734u(l|23/6 due to absorption by the IGAL., Photometric data from a small telescope should be used at first to identify those GRBs which possess a $\alpha$ trough at a wavelength of $0.73\mu{\rm m}(1+z)/6$ due to absorption by the IGM.
 Follow-up spetroscopy of those CRBs could then be (lone on a LO-in class telescope., Follow-up spectroscopy of those GRBs could then be done on a 10-m class telescope.
 Iu designing this observing strategy it is muporant to forecast which fraction of all GRBs originate from different redshifts., In designing this observing strategy it is important to forecast which fraction of all GRBs originate from different redshifts.
 For example. it would be impractica to search for those very high redshits which auouut to a fraction smaller than 10. of all GRBs. ivecamse barely a snele one of thei would be found bvSwift over several vears of operation.," For example, it would be impractical to search for those very high redshifts which amount to a fraction smaller than $10^{-3}$ of all GRBs, because barely a single one of them would be found by over several years of operation."
 Iun this paper. we use existing observational aud theoretical work on the cosnüc star formation history to predict the fraction of all GRBs that are expected to originate at differeut redshifts.," In this paper, we use existing observational and theoretical work on the cosmic star formation history to predict the fraction of all GRBs that are expected to originate at different redshifts."
 In order to keep our resuts eeneral. we mdse predictious about«ff GRBs without reference to the detection threshold or redshift horizou of any particular instimuent.," In order to keep our results general, we make predictions about GRBs without reference to the detection threshold or redshift horizon of any particular instrument."
 To ascertain. however. what t1ο," To ascertain, however, what the"
The VLBI images of SN11993J keep a high degree of circularity during the whole expansion.,The VLBI images of 1993J keep a high degree of circularity during the whole expansion.
 A quantitative representation of the degree of circularity of the shell is the fractional uncertainty of the radius determined with the CPM (1. e.. the scatter of radial positions of a given contour with respect to the shell center. in units of the source radius; see Appendix | of Marcaide et al.," A quantitative representation of the degree of circularity of the shell is the fractional uncertainty of the radius determined with the CPM (i. e., the scatter of radial positions of a given contour with respect to the shell center, in units of the source radius; see Appendix 1 of Marcaide et al."
 2000. for more details)., \cite{Marcaide2009} for more details).
 The degree of circularity of the supernova. computed this way. is typically around2-4%.. as can be seen in Fig. 8..," The degree of circularity of the supernova, computed this way, is typically around, as can be seen in Fig. \ref{SN93J-circul},"
 with the exception of some epochs with low dynamic ranges., with the exception of some epochs with low dynamic ranges.
 Similar results were also reported in Bietenholz et al. (200100)., Similar results were also reported in Bietenholz et al. \cite{Bietenholz2001}) ).
 Such a circularity in the images must be due to a high degree of isotropy in the angular distribution of the ejecta velocities (and. therefore. in the distribution of the CSM).," Such a circularity in the images must be due to a high degree of isotropy in the angular distribution of the ejecta velocities (and, therefore, in the distribution of the CSM)."
 However. the symmetry of the radio shell not only depends on its circularity. but also on the intensity distribution mside it.," However, the symmetry of the radio shell not only depends on its circularity, but also on the intensity distribution inside it."
" To study the azimuthal intensity distribution in the shell. we computed. for each epoch since 1995, the angular distribution of flux density in a ring of radius equal to the radial position of the brightness peak."," To study the azimuthal intensity distribution in the shell, we computed, for each epoch since 1995, the angular distribution of flux density in a ring of radius equal to the radial position of the brightness peak."
 For every epoch. we used a convolving beam with FWHM equal to 0.5 times the shell radius.," For every epoch, we used a convolving beam with FWHM equal to 0.5 times the shell radius."
 In Fig., In Fig.
 9 we show the time evolution of the angular intensity distribution in the 11993) shell. obtained from a linear interpolation between epochs.," \ref{AzimDistri} we show the time evolution of the angular intensity distribution in the 1993J shell, obtained from a linear interpolation between epochs."
 In the cases of epochs observed less than 50 days apart. we selected only one for the interpolation. that of highest dynamierange’.," In the cases of epochs observed less than 50 days apart, we selected only one for the interpolation, that of highest dynamic."
.. The minimum-to-maximum intensity ratio at each epoch typically ranges between 0.7 and 0.9. indicating that the shell emission is homogeneous to a level of ~80%..," The minimum-to-maximum intensity ratio at each epoch typically ranges between 0.7 and 0.9, indicating that the shell emission is homogeneous to a level of $\sim$."
 From Fig., From Fig.
 9 we arrive at a clear conclusion: there are some regions where the shell is clearly brighter (1. e.. has hot spots). and these regions persist in time for periods of the order of a thousand days.," \ref{AzimDistri} we arrive at a clear conclusion: there are some regions where the shell is clearly brighter (i. e., has hot spots), and these regions persist in time for periods of the order of a thousand days."
 Unfortunately. the dynamic range of the images is not high enough to ensure a single interpretation of the azimuthal evolution of the radio shell.," Unfortunately, the dynamic range of the images is not high enough to ensure a single interpretation of the azimuthal evolution of the radio shell."
 The first hot spot is located in the west (1. e.. position angle of 270 degrees in Fig. 9))," The first hot spot is located in the west (i. e., position angle of 270 degrees in Fig. \ref{AzimDistri}) )"
 and is present from the beginning of the interpolation up to day ~ 1600 after explosion., and is present from the beginning of the interpolation up to day $\sim$ 1600 after explosion.
 There is another. less clear. hot spot present during approximately the same time range. but located in the east (1. e.. position angle of 90 degrees).," There is another, less clear, hot spot present during approximately the same time range, but located in the east (i. e., position angle of 90 degrees)."
 This hot spot seems to decompose in several parts at some epochs. which drift towards north and/or south.," This hot spot seems to decompose in several parts at some epochs, which drift towards north and/or south."
 Beginning on day ~1600 after explosion. this second hot spot seems to be finally decomposed into two hot spots. one towards the south (reaching a position angle ~ 160 degrees) and the other towards the north (reaching a position angle -O degrees).," Beginning on day $\sim$ 1600 after explosion, this second hot spot seems to be finally decomposed into two hot spots, one towards the south (reaching a position angle $\sim$ 160 degrees) and the other towards the north (reaching a position angle $\sim$ 0 degrees)."
 These two new hot spots persist in time beyond day 3500 after explosion., These two new hot spots persist in time beyond day 3500 after explosion.
 From that epoch onwards. the dynamic range of our images Is too low to reach to any robust conclusion about the evolution of the angular brightness pattern.," From that epoch onwards, the dynamic range of our images is too low to reach to any robust conclusion about the evolution of the angular brightness pattern."
 It is remarkable that the first hot spot located at a position angle of 270 degrees disappears more or less at the same time as the other hot spot evolves into two hot spots which shift to their final positions at 160 and 0 degrees., It is remarkable that the first hot spot located at a position angle of 270 degrees disappears more or less at the same time as the other hot spot evolves into two hot spots which shift to their final positions at 160 and 0 degrees.
 Another possible interpretation of Fig., Another possible interpretation of Fig.
 9. 1s that the hot spot located at 270 degrees could shift to 160 degrees on day ~ 1600. and the one located at 90 degrees could shift to ~O degrees at roughly the same time.," \ref{AzimDistri} is that the hot spot located at 270 degrees could shift to 160 degrees on day $\sim$ 1600, and the one located at 90 degrees could shift to $\sim$ 0 degrees at roughly the same time."
 These interpretations of Fig., These interpretations of Fig.
 9 differ from the evolution reported in Bietenholz. Bartel Rupen (2003)).," \ref{AzimDistri} differ from the evolution reported in Bietenholz, Bartel Rupen \cite{Bietenholz2003}) )."
 According to these authors. an additional hot spot should be visible at 180 degrees from day 774 to day 1258. which is not seen in Fig. 9..," According to these authors, an additional hot spot should be visible at 180 degrees from day 774 to day 1258, which is not seen in Fig. \ref{AzimDistri}."
 However. as we noticed above. for some epochs like that of day 1177. the wide hot spot at 90 degrees seems to decompose in several parts. and one of the parts shifts close to the south. thus making the figure compatible with the reported hot spot in Bietenholz et al. (2003).," However, as we noticed above, for some epochs like that of day 1177, the wide hot spot at 90 degrees seems to decompose in several parts, and one of the parts shifts close to the south, thus making the figure compatible with the reported hot spot in Bietenholz et al. \cite{Bietenholz2003}) )."
 According to Bietenholz et al. (2003)).," According to Bietenholz et al. \cite{Bietenholz2003}) ),"
 another, another
which can be solved αποσαν for p. eiveu Mj. σεwives 55. and ὃν,"which can be solved numerically for $\mu$, given $\mathcal{M}_i$ , $\gamma_i$ , $\gamma_b$ , and $\delta$."
 For ó=1. 5;=55 the obvious solution is p=1.," For $\delta = 1$, $\gamma_i=\gamma_b$ the obvious solution is $\mu = 1$."
 For our problem we expect 5;=5/3 aud 24=3., For our problem we expect $\gamma_i = 5/3$ and $\gamma_b = 4/3$.
 This Equation (B5)) is displaved for 6=107 ME à—10? in the left panel of Figure BLIu the strong (external) shock Liuit. αντíο Is casy i see that approximately pXv.," This gives Equation \ref{eq:B5}) ) is displayed for $\delta = 10^{-2}$ and $\delta = 10^{-3}$ in the left panel of Figure \ref{bubshock}.In the strong (external) shock limit, $\mu\mathcal{M}_i \gg 1$, it is easy to see that approximately $\mu \propto \sqrt{\delta}$."
 Empirically we fined in this limit when à<1 that pp~ονος κο that Oy0204.2 ," Empirically we find in this limit when $\delta \ll 1$ that $\mu \sim 2 \sqrt{\delta}$, so that $v_\rmn{sb}
\approx 2 v_\rmn{si}$."
"Ax M;>1. the solution pp>1. so At,>1 also applies."," As $\mathcal{M}_i \rightarrow 1$, the solution $\mu
\rightarrow 1$ , so $\mathcal{M}_b \rightarrow 1$ also applies."
 The more general solutions for snall to moderate incident shock streneths are shown for two values of 6 as solid curves iu Figure DI.., The more general solutions for small to moderate incident shock strengths are shown for two values of $\delta$ as solid curves in Figure \ref{bubshock}.
" The lower bouncl for e, 1s given by ον=c4niftyAGCMUVI8)| aud is shown in each case by a dotted curve."," The lower bound for $v_\rmn{sb}$ is given by $c_b =
v_\rmn{si}\sqrt{\gamma_b/\gamma_i}~[1/(\mathcal{M}_i\sqrt{\delta})]$ and is shown in each case by a dotted curve."
" We note that the solution shown iu Figure Bl is liosu ideutical to the case of 2;=54. since the internal shock. in the bubbleis barely supersonic with MM,21 due to the large sound speed in the bubble."," We note that the solution shown in Figure \ref{bubshock} is almost identical to the case of $\gamma_i =\gamma_b$, since the internal shock in the bubble is barely supersonic with $\mathcal{M}_b
\gtrsim 1$ due to the large sound speed in the bubble."
" This can be easily seen by takiug the ratio ofthe corresponding solid-to-dotted lines which provides ,M for cach external Mach umber M;.", This can be easily seen by taking the ratio of the corresponding solid-to-dotted lines which provides $\mathcal{M}_b$ for each external Mach number $\mathcal{M}_i$.
 We can understand the eeucral behavior of an increasing shock speed iuside a low-density bubble relative to the incident shock speed for smaller Mach αμνους Mi; by the following line of arguments., We can understand the general behavior of an increasing shock speed inside a low-density bubble relative to the incident shock speed for smaller Mach numbers $\mathcal{M}_i$ by the following line of arguments.
" For small Mach παος, both waves are just nonlinear sound waves. so cach propagates near the local sound speed. which is much larger in the bubble."," For small Mach numbers, both waves are just nonlinear sound waves, so each propagates near the local sound speed, which is much larger in the bubble."
 It turus out for large Mach numbers M; that the pressure just behind the peuctrating shock is smaller tha- the external post-sliock pressure by a factor that scales with the density contrast 6., It turns out for large Mach numbers $\mathcal{M}_i$ that the pressure just behind the penetrating shock is smaller than the external post-shock pressure by a factor that scales with the density contrast $\delta$ .
 This pressure drop comes frou tlie rarefaction goimg back iuto the shocked ICAL, This pressure drop comes from the rarefaction going back into the shocked ICM.
 For weak shocks that rarefaction is weak (provided the original babble was in pressure equilibrium)., For weak shocks that rarefaction is weak (provided the original bubble was in pressure equilibrium).
 The right panel in Figure BL shows the behavior of rey correspouding to the shock solutions in the left figureme ane., The right panel in Figure \ref{bubshock} shows the behavior of $v_\rmn{CD}$ corresponding to the shock solutions in the left figure panel.
" Tn the limit /4/72,Mjὃν1. the expression for ec in Equation] (B2)) takes the form eop/eg©(2/64|1)V55/05;/mµ."," In the limit $\mu^2 \mathcal{M}_i^2\gg 1$, the expression for $v_\rmn{CD}$ in Equation \ref{eq:B1}) ) takes the form $v_\rmn{CD}/v_\rmn{si} \approx (2/(\gamma_b+1))
\sqrt{\gamma_b/\delta\gamma_i}~\mu$."
 Note- that the limitnol ασ2ας2o2941 requires: the internal: bubile {(pseudo-) temperature not to be too hieh: aud inplies a lower limit ou the bubble deusitv contrast of 6210? assunüng the original bubblewas in pressure equilibria.," Note that the limit $\mu^2
\mathcal{M}_i^2\gg 1$ requires the internal bubble (pseudo-) temperature not to be too high and hence implies a lower limit on the bubble density contrast of $\delta\gtrsim 10^{-3}$ assuming the original bubblewas in pressure equilibrium."
" Applying our enipirical result for strong shockswith107z8«1(uunelv. µ~ὃνδ). we would expect topσαΣά,|2;0 1.5. which is within about of the exactsolutious in this But."," Applying our empirical result for strong shockswith$10^{-3}\lesssim\delta \ll 1$(namely, $\mu \sim 2 \sqrt{\delta}$ ), we would expect $v_\rmn{CD}/v_\rmn{si}\rightarrow (4/(\gamma_b+1))\sqrt{\gamma_b/\gamma_i} \sim
1.5$ , which is within about of the exactsolutions in this limit."
 This value for cepey is also a reasonable VEMestimate at moderate shock nunibers. sav Vf;2 23.," This value for $v_\rmn{CD}/v_\rmn{si}$ is also a reasonable estimate at moderate shock numbers, say $\mathcal{M}_i\ga 3$ ."
 For M;z2 the limit ecp>ey .. applies.," For $\mathcal{M}_i\ga 2$ the limit $v_\rmn{CD}>
v_\rmn{si}$ still applies."
 AsM; 2 (22))), As$\mathcal{M}_i$ \ref{fig:images} \ref{eq:delta})
 AsM; 2 (22)))., As$\mathcal{M}_i$ \ref{fig:images} \ref{eq:delta})
The above initial conditions are chosen to reproduce — às closely as possible — the initial conditions of the 2D model by Lefloch Lazaretf (1994).,The above initial conditions are chosen to reproduce – as closely as possible – the initial conditions of the 2D model by Lefloch Lazareff (1994).
 We note that from the outset the cloud is over-pressured. and left to its own devices would simply disperse on a timescale of ~|Tyr.," We note that from the outset the cloud is over-pressured, and left to its own devices would simply disperse on a timescale of $\sim 1\,{\rm Myr}$."
 Fig., Fig.
 15 shows the evolution of the cloud., \ref{fig.rdiseq} shows the evolution of the cloud.
 The tonizing flux propagates upwards and rapidly boils off the outer layers on the near side of the cloud., The ionizing flux propagates upwards and rapidly boils off the outer layers on the near side of the cloud.
 At ¢~0.036Myr (Fig.," At $t\sim 0.036\,{\rm Myr}$ (Fig."
 15aa) a shock front starts to compress the remaining neutral gas., \ref{fig.rdiseq}a a) a shock front starts to compress the remaining neutral gas.
 At the same time. the north hemisphere starts to expand due to the thermal pressure of the atomic hydrogen.," At the same time, the north hemisphere starts to expand due to the thermal pressure of the atomic hydrogen."
 ΑΙ ~0.13Myr (Fig.," At $t\sim 0.13\,{\rm Myr}$ (Fig."
 I5bb) a dense. prolate. approximately ellipsoidal core forms.," \ref{fig.rdiseq}b b) a dense, prolate, approximately ellipsoidal core forms."
 By t~0.18Myr (Fig.," By $t\sim 0.18\,{\rm Myr}$ (Fig."
 15ec). the prolate core has semi-major axis 0.08pe and semi-minor axis 0.02pe; its mass is ~6M.," \ref{fig.rdiseq}c c), the prolate core has semi-major axis $0.08\,{\rm pc}$ and semi-minor axis $0.02\,{\rm pc}$; its mass is $\sim 6\,{\rm M}_\odot$."
 It is therefore thermally sub-eritical. and does not collapse to form a star.," It is therefore thermally sub-critical, and does not collapse to form a star."
 Instead 1t is steadily ablated by ionization., Instead it is steadily ablated by ionization.
 By t~0.21Myr (Fig.," By $t\sim 0.21\,{\rm Myr}$ (Fig."
 15dd). the remnants of the cloud start to develop a cometary tail.," \ref{fig.rdiseq}d d), the remnants of the cloud start to develop a cometary tail."
 By /~2.5Myr (not shown on Fig. 15)).," By $t\sim 2.5\,{\rm Myr}$ (not shown on Fig. \ref{fig.rdiseq}) ),"
 the last vestiges of the cloud are ionized. and they are ~28pe from the tonizing star.," the last vestiges of the cloud are ionized, and they are $\sim 28\,{\rm pc}$ from the ionizing star."
 Fig., Fig.
 16. plots the total mass of neutral gas against time., \ref{fig.rdimass} plots the total mass of neutral gas against time.
 The undulations seen at ¢~0.25Myr. and at f~0.5Myr are acoustic oscillations. excited as the cloud responds to the increase in external pressure.," The undulations seen at $t\sim 0.25\,{\rm Myr}$, and at $t\sim 0.5\,{\rm Myr}$ are acoustic oscillations, excited as the cloud responds to the increase in external pressure."
 Gritschneder et al. (, Gritschneder et al. (
2009: hereafter GO9) have also simulated radiatively driven compression.,2009; hereafter G09) have also simulated radiatively driven compression.
 However. the cloud that GO9 treat (with mass 96 M... radius 1.6pc. and temperature IO K) ts much more massive and much colder than the one we treat here (20M... 0.5pe. 100K). and therefore it is much less resistant to compression and more prone to triggered gravitational collapse.," However, the cloud that G09 treat (with mass $96\,{\rm M}_\odot$ radius $1.6\,{\rm pc}$, and temperature $10\,{\rm K}$ ) is much more massive and much colder than the one we treat here $20\,{\rm M}_\odot$, $0.5\,{\rm pc}$, $100\,{\rm K}$ ), and therefore it is much less resistant to compression and more prone to triggered gravitational collapse."
 Furthermore. in their first two simulations. GO9 use a larger ionizing flux than we do.," Furthermore, in their first two simulations, G09 use a larger ionizing flux than we do."
 As a consequence. the clouds in their simulations are more strongly compressed than ours. particularly at the leading edge (i.e. the edge exposed directly to the tonizing flux). and are triggered into gravitational collapse.," As a consequence, the clouds in their simulations are more strongly compressed than ours, particularly at the leading edge (i.e. the edge exposed directly to the ionizing flux), and are triggered into gravitational collapse."
 In contrast. our cloud is more mildly compressed. and evolves towards a centrally condensed configuration but never becomes gravitationally unstable.," In contrast, our cloud is more mildly compressed, and evolves towards a centrally condensed configuration but never becomes gravitationally unstable."
 We have introduced a new technique for treating the propagation of tonizing radiation in SPH simulations of self-gravitating gas dynamics., We have introduced a new technique for treating the propagation of ionizing radiation in SPH simulations of self-gravitating gas dynamics.
 The method uses the HEALPix algorithm to tessellate the celestial sphere. and solves the equation of ionization equilibrium along the rays associated with each tessera: rays are split hierarchically to produce greater resolution wherever 1t is required. 1e. to ensure that the resolution of the radiation transfer matches the resolution of the hydrodynamics. locally.," The method uses the HEALPix algorithm to tessellate the celestial sphere, and solves the equation of ionization equilibrium along the rays associated with each tessera; rays are split hierarchically to produce greater resolution wherever it is required, i.e. to ensure that the resolution of the radiation transfer matches the resolution of the hydrodynamics, locally."
 This makes the algorithm very computationally efficient., This makes the algorithm very computationally efficient.
 The algorithm. has been incorporated. into the new Smoothed Particle Hydrodynamies code SEREN (Hubber et al.," The algorithm has been incorporated into the new Smoothed Particle Hydrodynamics code SEREN (Hubber et al.,"
 i preparation). and tested against a number of known analytic and semi-analytic problems.," in preparation), and tested against a number of known analytic and semi-analytic problems."
 These tests are presented here., These tests are presented here.
 The code follows the expansion of a spherically symmetric. in a. non-self-gravitating gas (Spitzer solution): the expansion of a spherically symmetric in a self-gravitating gas (new semi-analytic solution described in Sec.??)): the rocket acceleration and subsequent ablation of amassive cloud irradiated by an ionizing star on one side (Oort Spitzer 1955): and the radiatively driven compression of a pre-existing dense core engulfed by an expandingregion., The code follows the expansion of a spherically symmetric in a non–self-gravitating gas (Spitzer solution); the expansion of a spherically symmetric in a self-gravitating gas (new semi-analytic solution described in \ref{semi-analytic}) ); the rocket acceleration and subsequent ablation of a massive cloud irradiated by an ionizing star on one side (Oort Spitzer 1955); and the radiatively driven compression of a pre-existing dense core engulfed by an expanding.
 The code will be used in future to explore the role of regions in triggering and regulating star formation.injecting turbulent energy into the interstellar medium. and eroding molecular clouds.," The code will be used in future to explore the role of s in triggering and regulating star formation,injecting turbulent energy into the interstellar medium, and eroding molecular clouds."
continuum to the template stars accounts lor veiling in DQ Tau.,continuum to the template stars accounts for veiling in DQ Tau.
 The technique produced eood photospheric fits in the echelle orders of interest which when subtracted from DQ Tau succeeded in removing lines from the photosphere (see Figure 1)., The technique produced good photospheric fits in the echelle orders of interest which when subtracted from DQ Tau succeeded in removing lines from the photosphere (see Figure 1).
 We subtracted the night sky lines for [O I| A6300 and [O I] A5577 by using (wo extraction window sizes. one narrow and one wide.," We subtracted the night sky lines for [O I] $\lambda$ 6300 and [O I] $\lambda$ 5577 by using two extraction window sizes, one narrow and one wide."
 Dy subtracting. will appropriate scaling. the narrow window spectrum from the wide window spectrum. il was possible to create a prolile of only the night skv line which could then be used for subtraction.," By subtracting, with appropriate scaling, the narrow window spectrum from the wide window spectrum, it was possible to create a profile of only the night sky line which could then be used for subtraction."
 We replaced the original order with the skv-subtracted order in only the wavelength range affected by the night sky line. wilh the skv-subiracted segment scaled to fit (he original spectrum.," We replaced the original order with the sky-subtracted order in only the wavelength range affected by the night sky line, with the sky-subtracted segment scaled to fit the original spectrum."
 This technique was very successful in producing night-sky subtracted spectrum for the [O I] A6300 line (Figure 2)., This technique was very successful in producing night-sky subtracted spectrum for the [O I] $\lambda$ 6300 line (Figure 2).
 The same technique was used to remove the night skv in the [O I] A5577 line. which had brighter night skv emission and weaker emission [from the object. creating a noisier residual line profile than [O I] A6300.," The same technique was used to remove the night sky in the [O I] $\lambda$ 5577 line, which had brighter night sky emission and weaker emission from the object, creating a noisier residual line profile than [O I] $\lambda$ 6300."
 The observing run vielded fourteen nights of spectra. including the forbidden lines of interest aud other prominent photospheric features with which we could trace the orbital molion of (he primary ancl secondary.," The observing run yielded fourteen nights of spectra, including the forbidden lines of interest and other prominent photospheric features with which we could trace the orbital motion of the primary and secondary."
 Onlv eleven of (he fourteen spectra were used in measuring radial velocities of the secondary and primary for purposes of comparison to the orbital elements., Only eleven of the fourteen spectra were used in measuring radial velocities of the secondary and primary for purposes of comparison to the orbital elements.
 The radial velocities measured in our data came from measuring shifts in lil AGTQOT. Ca LI AGTIT.T. and Al | A6696.02. which vou can see in Figure 3.," The radial velocities measured in our data came from measuring shifts in Li I $\lambda$ 6707, Ca I $\lambda$ 6717.7, and Al I $\lambda$ 6696.02, which you can see in Figure 3."
 The vertical error bars represent one standard deviation in the average of radial velocities measured from double-gaussian fits to those three absorption lines., The vertical error bars represent one standard deviation in the average of radial velocities measured from double-gaussian fits to those three absorption lines.
 The radial velocity measurements allowed us lo adjust slightly the period found in Mathieuetal.(1997).. which gave P = 15.8043 + 0.0024 days.," The radial velocity measurements allowed us to adjust slightly the period found in \citet{mat97}, which gave P = 15.8043 $\pm$ 0.0024 days."
 Our observations were 110 epochs since the (ime of periastron passage. T = 24409582.54 + 0.05 JD.," Our observations were 170 epochs since the time of periastron passage, T = 2449582.54 $\pm$ 0.05 JD."
 We found the best fit between our data aud the orbit of came when we shortened the period to 15.8016 ctis days., We found the best fit between our data and the orbit of \citet{mat97} came when we shortened the period to 15.8016 $\pm^{0.002}_{0.006}$ days.
 Signal for the [O I] A6300 line in DQ Tau was very good throughout the run and the line profile remains unchanged as the stellar velocities approach their maximun. as shown in Figure 4.," Signal for the [O I] $\lambda$ 6300 line in DQ Tau was very good throughout the run and the line profile remains unchanged as the stellar velocities approach their maximum, as shown in Figure 4."
 The permitted line Ile I A5876 both splits and shows intensity variation as, The permitted line He I $\lambda$ 5876 both splits and shows intensity variation as
which possess higher N/O ratios.,which possess higher N/O ratios.
 We now discuss some of the statistical aspects of our measurements., We now discuss some of the statistical aspects of our measurements.
 In doing so we note that all means. errors. and standard deviations relating to our sample and given below were iniüiallv computed in linear space and (hen converted (o their corresponding logarithmic quantities.," In doing so we note that all means, errors, and standard deviations relating to our sample and given below were initially computed in linear space and then converted to their corresponding logarithmic quantities."
 This is not necessarily (rue lor values οποίος from other papers. however.," This is not necessarily true for values quoted from other papers, however."
 The log of the weighted mean of N/O [or the 52 objects Iving on the plateau is -1.43 (+.0084/-.0085). where the values in parenthesis represent the error in the mean. not the standard deviation. ancl were derived from observational uncertainties quoted in column (4) ol Table 62003)...," The log of the weighted mean of N/O for the 52 objects lying on the plateau is -1.43 (+.0084/-.0085), where the values in parenthesis represent the error in the mean, not the standard deviation, and were derived from observational uncertainties quoted in column (4) of Table \ref{bigtable}."
 The value for plateau objects with O/II below 7.8 is -1.44 (+.011/-.012). while above 7.8 it is measured to be -1.41 (7.012/-.013). so there is no evidence of metallicity dependence of the mean.," The value for plateau objects with O/H below 7.8 is -1.44 (+.011/-.012), while above 7.8 it is measured to be -1.41 (+.012/-.013), so there is no evidence of metallicity dependence of the mean."
 These results are in good agreement with those of Izotovetal.(1999).. who obtained -1.47 (6=4.14) or (heir total sample. -1.60 (0= z.02) for their low metallicity (Ο/Η < 7.6) objects. and -1.46 (4.14) lor their high metallicity (O/II > 7.6) objects.," These results are in good agreement with those of \cite{izotov99}, who obtained -1.47 $\sigma = \pm$ .14) for their total sample, -1.60 $\sigma = \pm$ .02) for their low metallicity (O/H $<$ 7.6) objects, and -1.46 $\pm$ .14) for their high metallicity (O/H $>$ 7.6) objects."
 Likewise. our resulis are in close agreement wilh Garnett(1990).. who found log(N/O) = -1.46 (4+.10/-.13) for plateau objects.," Likewise, our results are in close agreement with \cite{garnett90}, who found log(N/O) = -1.46 (+.10/-.13) for plateau objects."
 Finally. the standard deviation about the weighted mean for our plateau objects. expressed logarithmically. is 27.071ο nearly an order of magnitude larger (han (he error in the mean.," Finally, the standard deviation about the weighted mean for our plateau objects, expressed logarithmically, is +.071/-.084, nearly an order of magnitude larger than the error in the mean."
 An interesting question pertaining to the distribution of points in the N/O-O/II plane concerns the nature of the observed N/O scatter (as measured by (he standard deviation) of the plateau objects and to what degree it is related {ο errors in abundance measurements., An interesting question pertaining to the distribution of points in the N/O-O/H plane concerns the nature of the observed N/O scatter (as measured by the standard deviation) of the plateau objects and to what degree it is related to errors in abundance measurements.
 That is to sav. is the spread in N/O associated with the plateau due mostly (o intrinsic or statistical scatter?," That is to say, is the spread in N/O associated with the plateau due mostly to intrinsic or statistical scatter?"
 To investigate this point futher. we assumed a Gaussian distribution in the parent N/O plateau population. as suggested bv the distribution shape in Figure 13.. aud performed a \-square analysis of the observed point distribution of logN/O) for the plateau using our calculated weighted mean value for log(N/O) of -1.43 along with the established errors in the abundances. as given in column (4) of Table 6..," To investigate this point further, we assumed a Gaussian distribution in the parent N/O plateau population, as suggested by the distribution shape in Figure \ref{n2ohisto}, and performed a $\chi$ -square analysis of the observed point distribution of log(N/O) for the plateau using our calculated weighted mean value for log(N/O) of -1.43 along with the established errors in the abundances, as given in column (4) of Table \ref{bigtable}."
 We found that (he value lor the reduced. \-square® for the 52 platea objects is 1.244. consistent with a probability of about. that our sample of objects could not have been drawn randomly from a parent," We found that the value for the reduced $\chi$ for the 52 plateau objects is 1.244, consistent with a probability of about that our sample of objects could not have been drawn randomly from a parent"
emission bump seen at about 3 jim wavelength is characteristic for Herbig AeBe stars and has been interpreted either by the presence of a circumstellar disk with an inner hole (Hillenbrand et al.,emission bump seen at about 3 $\mu$ m wavelength is characteristic for Herbig AeBe stars and has been interpreted either by the presence of a circumstellar disk with an inner hole (Hillenbrand et al.
 1992). by spherical envelopes (Hartmann et al.," 1992), by spherical envelopes (Hartmann et al."
 1993) or the combination of both (Miroshnichenko et al., 1993) or the combination of both (Miroshnichenko et al.
 1999)., 1999).
 While there is general consensus that the Herbig Ae stars are surrounded by circumstellar disks similar to those of T Tauri stars during most of their pre-main-sequence phase (Natta et al., While there is general consensus that the Herbig Ae stars are surrounded by circumstellar disks similar to those of T Tauri stars during most of their pre-main-sequence phase (Natta et al.
 2001). only one out of seven Herbig Be stars was detected by mm-interferometry (Natta et al.," 2001), only one out of seven Herbig Be stars was detected by mm-interferometry (Natta et al."
 2000)., 2000).
 Extended halos and envelopes in the near- (Leinert et al., Extended halos and envelopes in the near- (Leinert et al.
 2001) and mid-infrared (Prusti et al., 2001) and mid-infrared (Prusti et al.
 1994) are more frequently observed around more massive Herbig Be stars., 1994) are more frequently observed around more massive Herbig Be stars.
 However. these observational differences could be due to a faster evolution of massive stars and differences in the relative timescales of the PMS phases. which limit the detection of disks around early B stars to the very early stage of their evolution.," However, these observational differences could be due to a faster evolution of massive stars and differences in the relative timescales of the PMS phases, which limit the detection of disks around early B stars to the very early stage of their evolution."
 We suggest that our spectroscopic signatures of ongoing accretion and the infrared excess can best be combined in terms of an accretion disk around IRSI., We suggest that our spectroscopic signatures of ongoing accretion and the infrared excess can best be combined in terms of an accretion disk around IRS1.
 We have calculated the spectral energy distribution of an active viscous aceretion disk including radiative heating by photospheric radiation from IRSI., We have calculated the spectral energy distribution of an active viscous accretion disk including radiative heating by photospheric radiation from IRS1.
" The radial temperature dependence of the optically thick. geometrically thin disk is then assumed to be [5,001ων) σα."," The radial temperature dependence of the optically thick, geometrically thin disk is then assumed to be $T(r) = [T_{acc}(r)^{4} + T_{rad}(r)^{4}]^{1/4}$ ."
 We use a standard o-disk Pringle 1974)., We use a standard $\alpha$ -disk Pringle 1974).
 Its accretion disk temperature profile is given by In the flat disk approximation its temperature profile due to irradiation only is Emerging spectral energy distributions have been computed for varying inner disk radi R; and aceretion rates Mos., Its accretion disk temperature profile is given by In the flat disk approximation its temperature profile due to irradiation only is Emerging spectral energy distributions have been computed for varying inner disk radii $_{i}$ and accretion rates $\dot{M}_{acc}$.
 As shown in Fig., As shown in Fig.
 14. the fit of the startdisk SED to the dereddened photometry of IRS] is consistent with a dusty. optically thick accretion disk.," \ref{herbig_accretion1} the fit of the star+disk SED to the dereddened photometry of IRS1 is consistent with a dusty, optically thick accretion disk."
 Tab., Tab.
 8 summarizes the model parameters of the system., \ref{properties_mir1} summarizes the model parameters of the system.
 Next we consider whether our data could also allow an envelope: Our spectrophotometry of IRSI obtained in the narrow-band silicate filter at 9.7 j/m shows a weak absorption feature (Τοτμ~ 0.2 + 0.1) which is consistent with the total line-of-sight extinction towards the source according to, Next we consider whether our data could also allow an envelope: Our spectrophotometry of IRS1 obtained in the narrow-band silicate filter at 9.7 $\mu$ m shows a weak absorption feature $\tau_{9.7 \mu m} \sim$ 0.2 $\pm$ 0.1) which is consistent with the total line-of-sight extinction towards the source according to
stars like DY Cen as well.,stars like DY Cen as well.
 The extreme Fe celicieucy is suggested to be a result of the accretion of winuowed gas from dust (Jeffery Heber 1993)., The extreme Fe deficiency is suggested to be a result of the accretion of winnowed gas from dust (Jeffery Heber 1993).
 The surface abundances of RCBs and EHes have been estimated by Asplund οἱ al. (, The surface abundances of RCBs and EHes have been estimated by Asplund et al. (
2000). Rao Lambert (2003. 2001). Jeffery (1996). Paucey et al. (,"2000), Rao Lambert (2003, 2004), Jeffery (1996), Pandey et al. ("
2001) aud Paucley et al. (,2001) and Pandey et al. (
200la).,2004a).
 Both RCBs and EHes show the majority. minority division proposed by Lambert Rao (1991).," Both RCBs and EHes show the majority, minority division proposed by Lambert Rao (1994)."
 Mainly they are differentiated by Fe abundance., Mainly they are differentiated by Fe abundance.
 The majority cluster around [Fe] of —1 and the minority show a larger deficiency about —1.7 or more., The majority cluster around [Fe] of $-$ 1 and the minority show a larger deficiency about $-$ 1.7 or more.
 Since a C/He of is assumed for all stars (except the minority RCB star Cen for which a value of is suggested -Aspluud et al., Since a C/He of is assumed for all stars (except the minority RCB star Cen for which a value of is suggested -Asplund et al.
 1998). the absolute numbers cai be compared.," 1998), the absolute numbers can be compared."
 15 stars out of 19 analysed RCBs comprise the majority auc 12 out of 14. EHes aualysed constitute the majority class., 15 stars out of 19 analysed RCBs comprise the majority and 12 out of 14 EHes analysed constitute the majority class.
 The {minority RC‘Bs are VCCraA. VZSSer. SSer and V8olCCen and the 2 minority EHes are BD +10 2179 and AAqr.," The 4 minority RCBs are CrA, Sgr, Sgr and Cen and the 2 minority EHes are BD +10 2179 and Aqr."
 The mean abundances (normalised to logXpye(X) = 12.15 with 4i as the atomic weight) of each group are shown iu Table 1., The mean abundances (normalised to $\log\Sigma\mu_X\epsilon$ (X) = 12.15 with $\mu$ as the atomic weight) of each group are shown in Table 1.
 The dispersion around the mean in each group is surprisingly small particularly for the majority groups of RCBs aud EHes  0.27 ¢ex., The dispersion around the mean in each group is surprisingly small particularly for the majority groups of RCBs and EHes $\sim$ 0.27 dex.
 Only H aud the s-process elements slow a little more dispersion., Only H and the $s$ -process elements show a little more dispersion.
 The similarity in the abundance pattern of the majority RCBs aud EHe (Fe of 6.5 and 6.8. respectively) is striking.," The similarity in the abundance pattern of the majority RCBs and EHe (Fe of 6.5 and 6.8, respectively) is striking."
 The mean cliference for 15 elements is 0.23 dex., The mean difference for 15 elements is 0.23 dex.
 However H. N. Ne aud Me show siguilicaut dilfereuces.," However H, N, Ne and Mg show significant differences."
 Tle minority groups RCBs αμα EHes (Fe of 5.7 for both) also show simall differeuces (« 0.13 dex) or most elements except Si. Ca (μιαν be P and 5c).," The minority groups RCBs and EHes (Fe of 5.7 for both) also show small differences $<$ 0.13 dex) for most elements except Si, Ca (may be P and Sc)."
 The fact that the H abundance for the majority of RCBs is lower by 1.0 dex compared to EHes aud the N abuudance is also higher by 0.3 dex inση suggestMOD that RCBs are a later pliase in evolution to EHes. However. the larger abundance of Ne and Me in EHes furthur indicates that HN is converted to Νο and Νο by alpha processing. thus EHes might be a later phase to RCBs as is expected [rom the tracks of post AGB stars in the log g. log Tay plane.," The fact that the H abundance for the majority of RCBs is lower by 1.0 dex compared to EHes and the N abundance is also higher by 0.3 dex might suggest that RCBs are a later phase in evolution to EHes, However, the larger abundance of Ne and Mg in EHes furthur indicates that $^{14}$ N is converted to $^{22}$ Ne and $^{25}$ Mg by alpha processing, thus EHes might be a later phase to RCBs as is expected from the tracks of post AGB stars in the log $g$, log $T_{\rm eff}$ plane."
 Figure 1 shows [N/Fe] versus Fe and [N/M]versus M (the metalicity parameter) for both eroups of RCBs aud EHes., Figure 1 shows [N/Fe] versus Fe and [N/M]versus M (the metalicity parameter) for both groups of RCBs and EHes.
 Clearly. most of the RCBs have N abuudauces that are predicted frou conversion of initial C aud O to N or even more.," Clearly, most of the RCBs have N abundances that are predicted from conversion of initial C and O to N or even more."
 In some cases C. produced in the He burning. uight also have been converted to N. The newly discovered RCB star OOpli may be one such aud illustrates the N euliauceiuent. prominently (Rao Lambert 2003).," In some cases C, produced in the He burning, might also have been converted to N. The newly discovered RCB star Oph may be one such and illustrates the N enhancement prominently (Rao Lambert 2003)."
 Although RCCrB and OOph have very similar line spectra ancl physical parameters. V2552 Oph shows much strouger lines than BR. CrB. On the otlier hand. the N abundance iu EHes," Although CrB and Oph have very similar line spectra and physical parameters, V2552 Oph shows much stronger lines than R CrB. On the other hand, the N abundance in EHes"
devoted to the progenitors of SNIa supernovae. including the analysis of time delays aud the mass ranges (2.. 2.. 2 and ?)).,"devoted to the progenitors of SNIa supernovae, including the analysis of time delays and the mass ranges \citet{han:04}, , \citet{yungelson:04}, , \citet{garnavich:05} and \citet{belczynski:05}) )."
 The GOODS data are now cousisteut with siguilicautly larger delays fof order 1 Gyr. including the lifetime of the star) aud exclude delays less than 2 Gyr at the 95 coufidence level (22)..," The GOODS data are now consistent with significantly larger delays (of order 4 Gyr, including the lifetime of the star) and exclude delays less than 2 Gyr at the 95 confidence level \citep{strolger:04,dahlen:04}."
 In the context of the normal mocle (Aloclel 0). we fined that these observations are well reproduced if ~1% of intermediate mass stars lead to type Ia supernovae aud if the typical delay between the formation of the white dwarf aud the explosion is 3—3.5Gyr.," In the context of the normal mode (Model 0), we find that these observations are well reproduced if $\sim 1\ \%$ of intermediate mass stars lead to type Ia supernovae and if the typical delay between the formation of the white dwarf and the explosion is $\sim 3-3.5\ \mathrm{Gyr}$."
 The resulting comparison between our theoretical prediction aud the data is shown in the lower panel of Figure where the effect of the time delay is quite apparent aud is chielly responsible for the peak iu the SN rate at z~I., The resulting comparison between our theoretical prediction and the data is shown in the lower panel of Figure \ref{fig:model0SN} where the effect of the time delay is quite apparent and is chiefly responsible for the peak in the SN rate at $z \sim 1$.
" While this comiparisou is made using our best fit inodel with Agi,=LO’M... the resulting rate for type Ia supernovae would be quite similar lor other choices of Aj."," While this comparison is made using our best fit model with $M_\mathrm{min} = 10^{7}\ \mathrm{M_{\odot}}$, the resulting rate for type Ia supernovae would be quite similar for other choices of $M_\mathrm{min}$."
 For au alternative approach see ??..," For an alternative approach see \citet{scann:05,mannucci:05}."
 To test the sensitivity of the result to the time delay. we show in Figure 7. the predicted SNIa rates using a time delay of 2.0 and LO Cyr. compared with our best fit value of 3.2 Gyr.," To test the sensitivity of the result to the time delay, we show in Figure \ref{fig:SNIa}
 the predicted SNIa rates using a time delay of 2.0 and 4.0 Gyr, compared with our best fit value of 3.2 Gyr."
 Also shown in Figure 7 (upper panel) is the seusitivity to the adopted intermeciate mass rauge., Also shown in Figure \ref{fig:SNIa} (upper panel) is the sensitivity to the adopted intermediate mass range.
 Our best fit model assumes a range of 2 - 8 M..Also plotted are models where the lower end of the mass range is 1.5 and 3 , Our best fit model assumes a range of 2 - 8 $_\odot$.Also plotted are models where the lower end of the mass range is 1.5 and 3 $_\odot$.
Finally. in the upper panel of Figuree 5.. we compare our predictions of tvpe Ia to tvpe II supernovae.," Finally, in the upper panel of Figure \ref{fig:model0SN}, we compare our predictions of type Ia to type II supernovae."
 We see that these are quite consistent. with the local rate (2).., We see that these are quite consistent with the local rate \citep{cappellaro:99}.
 The ratio drops olf at redshifts zo=1 due to the time delay in produciug type Ia events., The ratio drops off at redshifts $z \ga 1$ due to the time delay in producing type Ia events.
 Furthermore. when SN Ia explosions do occur. structures are larger aud mass outflows are suppressed (see discussion iu the next section).," Furthermore, when SN Ia explosions do occur, structures are larger and mass outflows are suppressed (see discussion in the next section)."
 Thus. as a consequence of the SN Ia time delay. we predict that while 50% of iron iu structures is produced by type la supernovae. this fraction is only 10*€ in the ICM.," Thus, as a consequence of the SN Ia time delay, we predict that while $\sim 50\ \%$ of iron in structures is produced by type Ia supernovae, this fraction is only $\sim 10\ \%$ in the IGM."
 As shown in ?.. the normal mode of star formation. labelled Model 0 there as well as here. is uot capable of reiouiziug the Uuiverse at high redshilt.," As shown in \citet{daigne:04}, the normal mode of star formation, labelled Model 0 there as well as here, is not capable of reionizing the Universe at high redshift."
" Indeed. at a redshift z=17. ouly 1.6 ioniziug photons per baryon are available compared to the requisite value of approximately 20 asstuning a clumpiuess factor. Ci,=LO (2).. It was also shown in ? that Model 0 alone is not capable of explaining the observed abundauce patterus in the extremely irou-poor stars. CS 22919-037 (??).. HE 0107-5210 (??).. HE 1327-2326 (?)) and G 77-61 (2))."," Indeed, at a redshift $z = 17$, only 1.6 ionizing photons per baryon are available compared to the requisite value of approximately 20 assuming a clumpiness factor, $C_\mathrm{H\;\scriptscriptstyle{II}} = 10$ \citep{ricotti:04b}.. It was also shown in \citet{daigne:04} that Model 0 alone is not capable of explaining the observed abundance patterns in the extremely iron-poor stars, CS 22949-037 \citep{depagne:02,israelian:04}, HE 0107-5240 \citep{christlieb:04,bessell:04}, HE 1327-2326 \citet{frebel:05}) ) and G 77-61 \citet{plez:05}) )."
 The necessity ofa massive mode of star formation. active at high redshilt has become an integral part of our emergiug picture of the growth of galactic structures.," The necessity of a massive mode of star formation, active at high redshift has become an integral part of our emerging picture of the growth of galactic structures."
 However. there is au active debate as to the exact nature of the massive mode.," However, there is an active debate as to the exact nature of the massive mode."
 As in ?.. we cousider three possibilities for tlie massive mocle.," As in \citet{daigne:04}, we consider three possibilities for the massive mode."
 1) stars with masses in the range 10 — 100 M... Model 1: these stars terminate as type II supernovae.," 1) stars with masses in the range 40 – 100 $_\odot$ , Model 1; these stars terminate as type II supernovae."
 2) stars withmasses inthe range 110 — 260 NL...Model 2a: these stars terminate as," 2) stars withmasses inthe range 140 – 260 $_\odot$ ,Model 2a; these stars terminate as"
 Abstract u,"of instantons in the Euclidean plane, is given \cite{Coleman85}
 to one-loop accuracy."
sing a, Here $S(\phi_{cl})$ is the instanton action.
method based onintegrating the Euclidea, The coefficient ${\cal D}$ represents the effect of quantum fluctuations around the instanton configuration and arises from the Gaussian approximation to the functional integral.
n Gree, This is the object whose computation we will consider here.
n! function., It is given in general form by the second equation relating it to the one-loop effective action.
 Amore elegan, The operators $\calm$ are the fluctuation operators obtained by taking the second functional derivative of the action at the instanton and vacuum background field configurations.
t method, The prime on the determinant implies omitting of the two translation zero modes.
 for computing functiona, The first prefactor $S(\phi_{cl})/2\pi$ takes into account the integration of the translation mode collective coordinates.
ldeterminants. using(he ," Finally, the counterterm action $S_{ct}$ in the exponent will absorb the ultraviolet divergences of ${\cal D}$."
Gel[and- Yaelom the," One may also include a corresponding determinant for fermions, which for massless fermions is even known analytically \cite{Nielsen:1976hs,Nielsen:1977aw}."
orem. has beenapplied recently to, For finite masses is has been computed recently \cite{Burnier:2005he}.
 avarietw. ofsvstems., This paper is organized as follows: In the next section we present the basic equations for the Abelian Higgs model and its instanton.
 This methodruns into difliculti, The fluctuation operator and its partial wave reduction is presented in section \ref{fluctuations}.
esif thebackground fiek," Two methods for computing fluctuation integrals, one based on integratingEuclidean Green' s functions, as it was used inRef. \cite{Baacke:1994bk},"
l has nontr, and the Gel'fand-Yaglom method are introduced in section \ref{twomethods} and compared.
ivial topology. asis the requir," This includes the application for a single channel problem, as present here in the Faddeev-Popov sector, and to a coupled-channel problem, as present here for the gauge-Higgs sector."
essome modifications of the Gel fand-Yaglom method which arethe main subjectofthis work.We presenthere both. the Green. sfunction and theGel fand-Yaglom method and compare t," In section \ref{specifix} we adress some specific problems: in subsection \ref{swave} we discuss the s-wave problem which arises do to the topological nature of the background field and which constitutes the main purpose of this manuscript, in subsection \ref{zeromode} the zero mode problem which has well-known solutions for both the Green's function and the Gel'fand-Yaglom method, and in subsection \ref{renorm} the renormalization, which here amounts to as simple subtraction."
henumerical results in detai," The numerical results, in particular a comparison of both methods and the final results for the effective action are presented in section \ref{numerix}. ."
l., A summary and conclusions are presented in section \ref{summary}. .
The Barium stars have close ties with symbiotic stars as well as with planctary nebulae.,The Barium stars have close ties with symbiotic stars as well as with planetary nebulae.
 Several extrinsic S stars have been found to exhibit svmbiotic-like features. (c.g. Ake et al., Several extrinsic S stars have been found to exhibit symbiotic-like features (e.g. Ake et al.
 1991). while several svmbiotio stars are also known to present overabundances of s-process elements (Smith et al.," 1991), while several symbiotic stars are also known to present overabundances of s-process elements (Smith et al."
 1996... 1997: Pereira οἱ al.," 1996, 1997; Pereira et al."
 2005)., 2005).
 The D-ἵνρο svimbiotic stars are the closest relatives to Darium stars. (Schmid. Nussbaumer L993: Pereira. ct al., The D'-type symbiotic stars are the closest relatives to Barium stars (Schmid Nussbaumer 1993; Pereira et al.
 2005: Jorissen et al., 2005; Jorissen et al.
 2005). especially considering some of them are surrounded. by apparently nebulae.," 2005), especially considering some of them are surrounded by apparently nebulae."
 Schwarz (1991) discovered an inner ane outer nebula around one of hese. AS 201. of which the outer nebula is likely to bea PN (ejected by the WD dwarf).," Schwarz (1991) discovered an inner and outer nebula around one of these, AS 201, of which the outer nebula is likely to be a PN (ejected by the WD dwarf)."
 Miszalski et al. (, Miszalski et al. (
20110) found svmbiotic characteristics in the Galactic Bulee PN Al 2-29. which also exhibits inner and outer nebulae. however he secondary has vet to observed against the elare of the wimary.,"2011c) found symbiotic characteristics in the Galactic Bulge PN M 2-29, which also exhibits inner and outer nebulae, however the secondary has yet to observed against the glare of the primary."
 Appendix A deseribes the discovery of a bipolar nebula around LID 330036 (Cn 1-1). which if considered to oe a nebula. would add. further evidence to the ink between Darium stars with PNe and barium enhanced D-type svmbiotic stars.," Appendix \ref{sec:app} describes the discovery of a bipolar nebula around HD 330036 (Cn 1-1), which if considered to be a nebula, would add further evidence to the link between Barium stars with PNe and barium enhanced D'-type symbiotic stars."
 Observing a svstem such as A 70 implies that the initial mass ratio must have been close to unity., Observing a system such as A 70 implies that the initial mass ratio must have been close to unity.
 The rarity of such a configuration may be used. as an argument against the present. formation scenario. and indeed an identical approach was taken by Corradi (2003) concerning the potential presence of Mira secondaries in ολο," The rarity of such a configuration may be used as an argument against the present formation scenario, and indeed an identical approach was taken by Corradi (2003) concerning the potential presence of Mira secondaries in PNe."
 Such an A 70-like configuration5 can in principle occur since Lucy (2006) found. an excess of so-called. twins. Le. svstems with mass ratios between 0.98 and 1.," Such an A 70-like configuration can in principle occur since Lucy (2006) found an excess of so-called twins, i.e. systems with mass ratios between 0.98 and 1."
 As further binaries similar to A TO and WeBo 1 are found. then these probabilities may have to be revised in favour of a greater frequency of twins.," As further binaries similar to A 70 and WeBo 1 are found, then these probabilities may have to be revised in favour of a greater frequency of twins."
 This would foster a greater overlap between svmbiotic stars (at least those of vellow or D'-tvpe) and PNe (Jorissen et al., This would foster a greater overlap between symbiotic stars (at least those of yellow or D'-type) and PNe (Jorissen et al.
 2005). with the formal cdilference becoming notional.," 2005), with the formal difference becoming notional."
 Wide binaries will interact and produce genuine PNe in a wide varicty of cases. however only a relatively narrow range is currently observed (e.g. De Marco 2009).," Wide binaries will interact and produce genuine PNe in a wide variety of cases, however only a relatively narrow range is currently observed (e.g. De Marco 2009)."
 The measurement of nebular s-process abuncances in PNe has considerable potential to improve AGB nucleosynthesis models (e.g. Sterling Dinerstein 2008. hereafter. SDOS: ]|xarakas et al.," The measurement of nebular s-process abundances in PNe has considerable potential to improve AGB nucleosynthesis models (e.g. Sterling Dinerstein 2008, hereafter SD08; Karakas et al."
 2009: lxarakas Lugaro 2010)., 2009; Karakas Lugaro 2010).
 These abundances are a valuable constraint upon the number of third. dredge-up episodes experienced curing the thermallyv-pulsing AGB phase., These abundances are a valuable constraint upon the number of third dredge-up episodes experienced during the thermally-pulsing AGB phase.
 Of particular interest are Type-I PNe whose Lle- and N-rich abundances are well-reproduced in models that require a progenitor mass 2+ M. to achieve hot bottom burning., Of particular interest are Type-I PNe whose He- and N-rich abundances are well-reproduced in models that require a progenitor mass $>4$ $_\odot$ to achieve hot bottom burning.
 Quantifving the stellar s-process abundances of A 70 via high-resolution spectroscopy will therefore be of great. interest to Compare against the Type-L nebula abundance., Quantifying the stellar s-process abundances of A 70 via high-resolution spectroscopy will therefore be of great interest to compare against the Type-I nebula abundance.
 The high surface brightness of A το compared to c.g. WeBo | may also allow nebula s-process abundances to be measured. via NER spectroscopy., The high surface brightness of A 70 compared to e.g. WeBo 1 may also allow nebula s-process abundances to be measured via NIR spectroscopy.
 In principle the s-process abundances of Tvpe-I PNe should be relatively straight-forware to understand. however no firm patterns have been found so far (Ixaralkas et al.," In principle the s-process abundances of Type-I PNe should be relatively straight-forward to understand, however no firm patterns have been found so far (Karakas et al."
 2009)., 2009).
 SDOS noted that binary interactions may be responsible [or reducing their measured s-process abundances. however the paucity of known binaries in their sample meant this remained untested.," SD08 noted that binary interactions may be responsible for reducing their measured s-process abundances, however the paucity of known binaries in their sample meant this remained untested."
 New discoveries of binary central stars in the SDOS sample should therefore help resolve the issue., New discoveries of binary central stars in the SD08 sample should therefore help resolve the issue.
 Miszalski et al. (, Miszalski et al. (
2011b) recently. found. a close binary in NGC 6778 which is a bipolar Evpe-E PN in the SDOS sample with strong Hle and. N enhancement (le/ll=0.155 and N/O-—]|0.78. Perinotto. Morbidelli Scatarzi 2004).,"2011b) recently found a close binary in NGC 6778 which is a bipolar Type-I PN in the SD08 sample with strong He and N enhancement (He/H=0.155 and $+$ 0.78, Perinotto, Morbidelli Scatarzi 2004)."
 Lt is possible that. post-CI2 binaries may. reduce s-process abundances to à greater extent than wider binary systenis. making wider binaries a potentially more reliable probe of s- abundances in PNe.," It is possible that post-CE binaries may reduce s-process abundances to a greater extent than wider binary systems, making wider binaries a potentially more reliable probe of s-process abundances in PNe."
 Ehe growing sample of A 70 and, The growing sample of A 70 and
dynamical timescales of matter orbiting close to à NS.,dynamical timescales of matter orbiting close to a NS.
 For this reason. ΚΣ QPOs are potential tools to probe general relativity in the strone-eravitational field. regime (vanIxlis 2005).. and constrain the NS equation of state CMiller.Lamb&Cook1998).," For this reason, kHz QPOs are potential tools to probe general relativity in the strong-gravitational field regime \citep{v2005}, and constrain the NS equation of state \citep{mil1998}."
. since the launch of the ltossi A-Rav Timing Explorer (RATE) in 1995. ΚΙ QPOs have been detected in about 30 NS LAINBs (for a review see vanderWlhis 2005)).," Since the launch of the Rossi X-Ray Timing Explorer (RXTE) in 1995, kHz QPOs have been detected in about 30 NS LMXBs (for a review see \citealt{v2005}) )."
 Most of these sources show two simultaneous kIIz QPOs. usually called the lower and the upper kIIz QDO. with frequencies that can drift as a function of time in the range 250-1200 Iz (vanderIxlis 2004)).," Most of these sources show two simultaneous kHz QPOs, usually called the lower and the upper kHz QPO, with frequencies that can drift as a function of time in the range 250-1200 Hz \citealt{v2004}) )."
 Studies of these kIIz QPOs show that QPO frequencies are related to other properties of the source: ee. on short time-scales (within a day or less) QPO frequencies are well correlated. with the intensity of the source. whereas on long time-scales this correlation breaks down and intensity-frequency diagrams show the so-called “parallel tracks” (Méndezetal. 1999)).," Studies of these kHz QPOs show that QPO frequencies are related to other properties of the source; e.g. on short time-scales (within a day or less) QPO frequencies are well correlated with the intensity of the source, whereas on long time-scales this correlation breaks down and intensity-frequency diagrams show the so-called “parallel tracks” \citealt{m1999}) )."
. Ehe. frequencies of the kllz QPOs correlate also with the position of the source in the colour-colour diagram. and with parameters of spectral components used. to describe the X-ray spectrum of these sources (Wijnandsetal.1997... MéndezandvanderWhis 1999... Ixaaretetal. 1999... DiSalvoetal. 2001)).," The frequencies of the kHz QPOs correlate also with the position of the source in the colour-colour diagram, and with parameters of spectral components used to describe the X-ray spectrum of these sources \citealt{w1997}, \citealt{mv1999}, \citealt{k1999}, \citealt{ds2001}) )."
 Nevertheless. it is still unclear. which physical parameters drive the QPO frequency. although there are. indications that mass accretion rate. mi. plays a kev role (Milleretal.1998).," Nevertheless, it is still unclear which physical parameters drive the QPO frequency, although there are indications that mass accretion rate, $\dot{m}$, plays a key role \citep*{mil1998}."
 Several models. have been proposed to explain the ΚΣ QPOs (c.g.. Miller.Lamb&Psaltis1998b.. Stella&Vetri 1905... Abraniowiezetal. 2003)). as well as the connection between high-frequency QPOs ancl other time variability usually present in power density spectra. (for a review of variability at. low frequencies see vanderWis 2001)).," Several models have been proposed to explain the kHz QPOs (e.g., \citealt{mlp1998}, \citealt{sv1998}, \citealt{a2003}) ), as well as the connection between high-frequency QPOs and other time variability usually present in power density spectra (for a review of variability at low frequencies see \citealt{v2001}) )."
 Despite these efforts. there is still no single model that is able to explain in a self-consistent way all the ΟΡΟ Kile QPOs are characterised. by three parameters: centroid frequeney i. quality factor Q=£/FMHM. where PAWIAL is the fullewidth at half-maximum of the QPO. and fractional rms amplitude.," Despite these efforts, there is still no single model that is able to explain in a self-consistent way all the QPO KHz QPOs are characterised by three parameters: centroid frequency $\nu$, quality factor $Q=\nu/FWHM$, where $FWHM$ is the full-width at half-maximum of the QPO, and fractional rms amplitude."
 Systematic analyses of these ΚΙ QPO properties have been done for a large number of sources (e.g.Jonkerctal.2000:vanStraatenetDietal.2005:Méndez2006:Barret.Olive&Aliller 2006).," Systematic analyses of these kHz QPO properties have been done for a large number of sources \citep[e.g.][]{j2000,van2000,ds2001,mvf2001,h2002,van2002,dmv2003,b2005a,b2005b,a2005,m2006,bom2006}."
. Those studies show that. in cach source the quality factor and the rms amplitude of the lower kllz QPO increase with the centroid [requeney. of the QPO until they reach a masini value. after which they decrease as the frecqucney continues to increase (e.g. Méndezctal.2001... DiSalvoetal. 2003.. Barretctal. 2005b:: see Méndez2006/— for a compilation of results).," Those studies show that, in each source the quality factor and the rms amplitude of the lower kHz QPO increase with the centroid frequency of the QPO until they reach a maximum value, after which they decrease as the frequency continues to increase (e.g. \citealt*{mvf2001}, \citealt*{dmv2003}, \citealt{b2005b}; see \citealt{m2006} for a compilation of results)."
 Phe upper kIlz ODPO cloes not show the same trend: in this case the quality factor usually does not change with the centroid frequency while the rms amplitude stavs more or less constant at lower frequencies and then decreases as the frequency increases (vanStraatenetal. 2002:: vanStraatenetal. 2003: Barretetal. 2005a:: Altamiranoctal.2008)). Jarretetal.(2005b) and interpreted the drop of the quality factor of the lower ΚΣ QPO at high frequencies in the LAINBs 4U 1636536 and 4U 1608522 as a signature of the inner disk radius reaching the innermost stable circular. orbit (ISCO). and. starting from that assumption they estimated the mass ancl the radius of the compact object in these two systems.," The upper kHz QPO does not show the same trend; in this case the quality factor usually does not change with the centroid frequency while the rms amplitude stays more or less constant at lower frequencies and then decreases as the frequency increases \citealt{van2002}; \citealt{van2003}; \citealt{b2005a}; \citealt{a2008}) \citet{b2005b} and interpreted the drop of the quality factor of the lower kHz QPO at high frequencies in the LMXBs 4U 1636–536 and 4U 1608–522 as a signature of the inner disk radius reaching the innermost stable circular orbit (ISCO), and starting from that assumption they estimated the mass and the radius of the compact object in these two systems."
 However. Aléndez(2006) argued against this idea ancl suggested that the drop of Q and rms in individual sources might be related (at least in part) to changes of the properties of the accretion Llow in these Following those results. here we investigate the properties of the ΚΣ QPOs for the transient NS LAINB NTE 1701462.," However, \citet{m2006} argued against this idea and suggested that the drop of $Q$ and rms in individual sources might be related (at least in part) to changes of the properties of the accretion flow in these Following those results, here we investigate the properties of the kHz QPOs for the transient NS LMXB XTE J1701–462."
 This source was detected for the first time on 2006 January LS with the AL-Sky monitor on-boare RATE (Remillareletal.2006)., This source was detected for the first time on 2006 January 18 with the All-Sky monitor on-board RXTE \citep{r2006}.
. As reported by Homan(2007a).. Linetal.(2009a).. AXresuetal.(2010) and Llomanetal.(2010).. this is the only source so far that showed both Z and atoll behaviour (for more details about the Z and atoll classes see Llasinger&vanderIxlis 1989)).," As reported by \citet{h2007ate}, \citet{l2009a}, \citet{a2010} and \citet{h2010}, this is the only source so far that showed both Z and atoll behaviour (for more details about the Z and atoll classes see \citealt{hv1989}) )."
 Phe luminosity. range covered by NPE J1701462. from. Eclelington limit to quiescence. gives us a unique opportunity to study κ» QPO properties in dillerent states and. more importantly. at clüllerent mass accretion rates in the same svstem. which could provide vital information to understand. the origin and the mechanisms that drive the properties of these In section. 2 we describe the observations and the data analysis. and in section 3 we present our results.," The luminosity range covered by XTE J1701–462, from Eddington limit to quiescence, gives us a unique opportunity to study kHz QPO properties in different states and, more importantly, at different mass accretion rates in the same system, which could provide vital information to understand the origin and the mechanisms that drive the properties of these In section 2 we describe the observations and the data analysis, and in section 3 we present our results."
 Ln section 4 we discuss those results in the context of current ideas concerning the mechanisms behind the kIIz QPOs in LAINBs. and in section 5 we summarise our conclusions.," In section 4 we discuss those results in the context of current ideas concerning the mechanisms behind the kHz QPOs in LMXBs, and in section 5 we summarise our conclusions."
 We analysed all the publie cata of the LAINB NTIS J1701462 collected with the Proportional Counter Array (PCA) on board of RNTVE (Bradt.Rothschild&Swank1993:: Jabocaetal. 2006))., We analysed all the public data of the LMXB XTE J1701--462 collected with the Proportional Counter Array (PCA) on board of RXTE \citealt{b1993}; \citealt{ja2006}) ).
 There are S66 observations of this source in the ΙΝΕΣ archive. for a total exposure time of ~ 3 Ms. During these observations the source showed several tvpe-L X-ray bursts that we excluded from our analysis (see Linetal.2009h for a detailed analysis of the bursts)," There are 866 observations of this source in the RXTE archive, for a total exposure time of $\sim$ 3 Ms. During these observations the source showed several type-I X-ray bursts that we excluded from our analysis (see \citealt{l2009b} for a detailed analysis of the bursts)."
 ‘To search for ΚΣ QPOs. we created Lealiv-normalised power density spectra using Event mode data with 1255/5 time resolution covering the full PCA οποιον bane. nominally from 2 to 60 keV. We created. Fourier power density spectra from. 16-seconds. cata segments. using 1/4096 s time resolution such that the frequency. range is defined. from 0.0625 IIz to 2048 Lz.," To search for kHz QPOs, we created Leahy-normalised power density spectra using Event mode data with $\mu s$ time resolution covering the full PCA energy band, nominally from 2 to 60 keV. We created Fourier power density spectra from 16-seconds data segments, using 1/4096 s time resolution such that the frequency range is defined from 0.0625 Hz to 2048 Hz."
 We removed. detector drop-outs: no cdead-time correction or subtraction of background. contribution were done to calculate the power density spectra., We removed detector drop-outs; no dead-time correction or subtraction of background contribution were done to calculate the power density spectra.
 We created: one averaged: power. density spectrum for cach observation that we visually inspected to search for the presence of QPOs with characteristic frequencies in the range from 200 Lz to 1200 Lz., We created one averaged power density spectrum for each observation that we visually inspected to search for the presence of QPOs with characteristic frequencies in the range from 200 Hz to 1200 Hz.
 We found kllz QPOs in 14 out of the 866 observations that we, We found kHz QPOs in 14 out of the 866 observations that we
The VLA data exhibit substantial variability.,The VLA data exhibit substantial variability.
 We show the higher quality GGL lighteurve together with that from in. Vig.ὃν 1.., We show the higher quality GHz lightcurve together with that from in Fig. \ref{OptVarFig}.
 The radio is clearly stronglye variable and shows both large Dares and dips not cdissimilar to those seen byChandra., The radio is clearly strongly variable and shows both large flares and dips not dissimilar to those seen by.
 Phe most dramatic feature rises from almost zero [lux to the highest peak in about mamin. as was also the case in the dataset presented by Miller-Jonesetal. (2008)..," The most dramatic feature rises from almost zero flux to the highest peak in about min, as was also the case in the dataset presented by \citet{MillerJones:2008a}."
. No clear correlation between radio ancl X- is apparent to the eve. however.," No clear correlation between radio and X-ray is apparent to the eye, however."
 To further test this. we calculate the eross-correlation function between the rav and radio data and show this in Fig. 6..," To further test this, we calculate the cross-correlation function between the X-ray and radio data and show this in Fig. \ref{CCFFig}."
 No compelling correlation (or anti-correlation) is present although an unremarkable peak is present at zero lag., No compelling correlation (or anti-correlation) is present although an unremarkable peak is present at zero lag.
 Since WSRTL is a linear array. it covers a full svnthesis in 12 hours and hence is not capable of the high time-resolution achieved by the VLA.," Since WSRT is a linear array, it covers a full synthesis in 12 hours and hence is not capable of the high time-resolution achieved by the VLA."
 Nevertheless the source does show significant. variability over this period. even if a xossible correlation with N-rav/optical is dillicult to infer.," Nevertheless the source does show significant variability over this period, even if a possible correlation with X-ray/optical is difficult to infer."
" When the observation is split in 2 sub-intervals. 18:4024:00 ancl 00:00.05:13. the resulting [lux densities are: S,=).25d0.04 mm.Jy. and ου=0.14d:0.04 mm.Jy. respectively."," When the observation is split in 2 sub-intervals, 18:40--24:00 and 00:00–05:13, the resulting flux densities are: $S_1
= 0.25 \pm 0.04$ mJy and $S_2 = 0.14 \pm 0.04$ mJy respectively."
 The second interval. covering D2F2. overlaps with the first xwt of the VLA observation. which shows a significant increase at GGL beginning at 08:00 UTE (with a peak lux density of mmy).," The second interval, covering D2–F2, overlaps with the first part of the VLA observation, which shows a significant increase at GHz beginning at 03:00 UT (with a peak flux density of mJy)."
 However. the VLA Ware only lasts or 1 hour. of which only about one-half was covered. by WSL.," However, the VLA flare only lasts for $\sim1$ hour, of which only about one-half was covered by WSRT."
 Finer sub-intervals proved impractical as there was insullicient coverage of the UV plane to isolate flux. fromC'vg., Finer sub-intervals proved impractical as there was insufficient coverage of the UV plane to isolate flux from.
. Previous sections of this paper have focused. primarily on one or two bands: we will broaden our scope here to questions best addressed. with the whole SED., Previous sections of this paper have focused primarily on one or two bands; we will broaden our scope here to questions best addressed with the whole SED.
" We show the complete radioN-rav SED in Fig. τν,", We show the complete radio–X-ray SED in Fig. \ref{SEDFig}.
 We have also compiled all the data »oints. as plotted. in Table 4 to allow easier comparison with future models.," We have also compiled all the data points, as plotted, in Table \ref{DataTable} to allow easier comparison with future models."
 We include a. point representing just the lickering Component in the optical to represent a lower Limi on the accretion light., We include a point representing just the flickering component in the optical to represent a lower limit on the accretion light.
" We adopt the extinction curve of Fitzpatrick(1999) in the optical and UV. Indebetouwetal.(2005). for the Spifzer/LRAC data and assume zl»,Ayc0.5 following Chapmanetal.(2009).."," We adopt the extinction curve of \citet{Fitzpatrick:1999a} in the optical and UV, \citet{Indebetouw:2005a} for the /IRAC data and assume $A_{24\mu m} / A_{\rm K} \simeq 0.5$ following \citet{Chapman:2008a}."
 Our dataset. should supersede that used by Naravanctal. for future modelling of., Our dataset should supersede that used by \citet{Narayan:1997a} for future modelling of.
Cvg.. Compared to earlier work we now have simultaneous X-ray ancl optical data. shorter wavelength coverage extending into the UV. and simultaneous radio observations.," Compared to earlier work we now have simultaneous X-ray and optical data, shorter wavelength coverage extending into the near-UV, and simultaneous radio observations."
 In Fig., In Fig.
 S— we illustrate the additional constraints now possible. showing Model 1: of Naravanet.al.(1997) overlaid on our SED after scaling. downwards to fit our Xeray spectrum.," \ref{ADAFFig} we illustrate the additional constraints now possible, showing Model 1 of \citet{Narayan:1997a} overlaid on our SED after scaling downwards to fit our X-ray spectrum."
 Chis is of course not intended to. be a detailed. model fit., This is of course not intended to be a detailed model fit.
 Not. only should a new model be computed to fit a lower X-ray luminosity. but there have xen refinements in mocdelling of advective acerction Lows in he last decade as well.," Not only should a new model be computed to fit a lower X-ray luminosity, but there have been refinements in modelling of advective accretion flows in the last decade as well."
 Our main point is to stress the strong constraint provided by the low near-UV flux., Our main point is to stress the strong constraint provided by the low near-UV flux.
 Model 1 was an acceptable fit to the SED data available to Naravanetal.(1997) but clearly over-predicts the near-UV. substantially compared to our new data., Model 1 was an acceptable fit to the SED data available to \citet{Narayan:1997a} but clearly over-predicts the near-UV substantially compared to our new data.
 Alternative models with winds oesented. by Quataert&Naravan(1999)... on the other mance. would be consistent with the UV data.," Alternative models with winds presented by \citet{Quataert:1999a}, on the other hand, would be consistent with the UV data."
 This constraint on the UV to X-ray. [lux ratio can be used to constrain current and future mocdels., This constraint on the UV to X-ray flux ratio can be used to constrain current and future models.
 The flux of the optical Uickering component. falls at. an intriguing location in the SED (Fig. τὸ)., The flux of the optical flickering component falls at an intriguing location in the SED (Fig. \ref{SEDFig}) ).
 Ht is a little above a straight extrapolation of either the X-ray or racio power-laws., It is a little above a straight extrapolation of either the X-ray or radio power-laws.
 An extrapolation of the radio is plausible. as a Ilat- is expected to continue until a break to optically thin svnchrotron at higher frequencies.," An extrapolation of the radio is plausible, as a flat-spectrum is expected to continue until a break to optically thin synchrotron at higher frequencies."
 We would not expect a straight extrapolation of the X-ray spectrum at all. anc," We would not expect a straight extrapolation of the X-ray spectrum at all, and"
 We would not expect a straight extrapolation of the X-ray spectrum at all. ancl," We would not expect a straight extrapolation of the X-ray spectrum at all, and"
uxightest 20bCIUS system.,brightest 2dFGRS system.
 However. as shown in Fig. 5..," However, as shown in Fig. \ref{chiang},"
 his comes at the expense of producing a set of objects that are significantly more racially oriented than those found in he 2dE€GH5., this comes at the expense of producing a set of objects that are significantly more radially oriented than those found in the 2dFGRS.
 Also shown in Fig., Also shown in Fig.
 H1. is the distribution of systems ound in the 22 Llubble Volume mock catalogues of. 7.. , \ref{dist_hv_chi} is the distribution of systems found in the 22 Hubble Volume mock catalogues of \citet{2000MNRAS.319..168C}. .
After tuning x to be L1 to recover the 2dECGIUS structure orientation distribution. the Llubble Volume mocks are xoadlv similar to the 2BASICC ones. with the abundance of the most luminous systems being almost unchanged.," After tuning $\chi$ to be $1.11$ to recover the 2dFGRS structure orientation distribution, the Hubble Volume mocks are broadly similar to the 2BASICC ones, with the abundance of the most luminous systems being almost unchanged."
 The roltom row of table 1. contains statistics for the systems found in these Hubble Volume mocks., The bottom row of table \ref{stats} contains statistics for the systems found in these Hubble Volume mocks.
 We have described. a simple. algorithm with which to define connected structure within galaxy redshift) surveys. and applied it to the δολ.," We have described a simple algorithm with which to define connected structure within galaxy redshift surveys, and applied it to the 2dFGRS."
 This algorithm: explicitly addresses the recdshilt-space cistortion associated with rapidly moving galaxies within groups and clusters., This algorithm explicitly addresses the redshift-space distortion associated with rapidly moving galaxies within groups and clusters.
" The 7.603 ΓΙ connected structures at zx0.12 containing at least two members range up to 2005.!Alpe in extent. but are mostly associations of two L, galaxies."," The $7,603$ 2dFGRS connected structures at $z\leq0.12$ containing at least two members range up to $\sim 200\Mpc$ in extent, but are mostly associations of two $L_*$ galaxies."
 Quantifving object sizes via their total luminosities. corrected. for the survey Dux limits. we find that the largest svstems are filamentary in nature and have 64 luminosities of almost 10H5?L..," Quantifying object sizes via their total luminosities, corrected for the survey flux limits, we find that the largest systems are filamentary in nature and have $\bj$ luminosities of almost $10^{14}\Lsol$."
 Applying the same algorithm to mock 2dECHts catalogues. constructed. using laree-volume cark matter simulations and the semi-analvtical model of 2... we find a broadly. similar cistribution of structures to those in the real data.," Applying the same algorithm to mock 2dFGRS catalogues, constructed using large-volume dark matter simulations and the semi-analytical model of \citet{2005MNRAS.356.1191B}, we find a broadly similar distribution of structures to those in the real data."
 There are. however. a few cillerences in detail.," There are, however, a few differences in detail."
 Many of these result. from the fact that the model places too many Lzzἓν galaxies into groups and clusters compared with the 2dGIS., Many of these result from the fact that the model places too many $L\lsim L_*$ galaxies into groups and clusters compared with the 2dFGRS.
 This biases the orientation distribution of the svstems containing at least 20 galaxies to contain more racially aligned objects in the mock survey than in the 2dEGIU., This biases the orientation distribution of the systems containing at least $20$ galaxies to contain more radially aligned objects in the mock survey than in the 2dFGRS.
 Applying a crude correction to the algorithm to enable it to recover the same orientation distribution in the mock survey as it does in the 2dECGHIS leads to the largest mock structures being significantly less luminous than those in the ας., Applying a crude correction to the algorithm to enable it to recover the same orientation distribution in the mock survey as it does in the 2dFGRS leads to the largest mock structures being significantly less luminous than those in the 2dFGRS.
 lt is clear that at least some of the cdillerencesga between the properties of the structures in the 24EGIGS and the mock catalogues arise from inadedquacies in the galaxy formation model that was used. to construct the mocks., It is clear that at least some of the differences between the properties of the structures in the 2dFGRS and the mock catalogues arise from inadequacies in the galaxy formation model that was used to construct the mocks.
 We have attempted to overcome these inadequacies as far as possible through empirical corrections., We have attempted to overcome these inadequacies as far as possible through empirical corrections.
 Our analysis indicates that the largest filamentary structures seen in the 2dEGIU are not reproduced in the mock catalogues., Our analysis indicates that the largest filamentary structures seen in the 2dFGRS are not reproduced in the mock catalogues.
 However. while this iscrepaney could signal a failure. of the. standard cosmological model on large scales. it seems more plausible that it reflects a shortcoming in the predictions of our models of galaxy formation for the abundance and spatial clistribution of galaxies on small scales.," However, while this discrepancy could signal a failure of the standard cosmological model on large scales, it seems more plausible that it reflects a shortcoming in the predictions of our models of galaxy formation for the abundance and spatial distribution of galaxies on small scales."
 ΡΟΝΑΛΝΤ acknowledges an STEC PhD studentship and CSE a Roval Socicty Wolfson Research Merit award., DNAM acknowledges an STFC PhD studentship and CSF a Royal Society Wolfson Research Merit award.
 We thank Raul Angulo and Carton Baugh [or assistance in the production of the 2BASICC mock surveys., We thank Raul Angulo and Carlton Baugh for assistance in the production of the 2BASICC mock surveys.
 We also thank Ixevin.Pimblett and. the referee for useful. comments that improved the quality of this manuscript., We also thank KevinPimblett and the referee for useful comments that improved the quality of this manuscript.
stars are found.,stars are found.
 The presence of low age objects and the rapidly rotating configuration may be taken to define the thin disk., The presence of low age objects and the rapidly rotating configuration may be taken to define the thin disk.
 For V « -10. [U| > 60 and ο” juiuinnun stellar age is about 2 10? vr.," For $V$ $<$ -40, $\vert U \vert$ $>$ 60 and $\vert W \vert$ $>$ 30 km $\rm
s^{-1}$ the minimum stellar age is about 2 $10^9$ yr."
 The disappearauce of the vounger stellar component may be assiuned to mar the transition to the thick disk., The disappearance of the younger stellar component may be assumed to mark the transition to the thick disk.
 For V « -80. |U] > 100 and |W]| > 60 kins! the stellar population exhibit a common age c 1019 yy.," For $V$ $<$ -80, $\vert U \vert$ $>$ 100 and $\vert W \vert$ $>$ 60 km $\rm
s^{-1}$ the stellar population exhibit a common age $\geq$ $10^{10}$ yr."
 For increasing values of [OVV.3T| no substantial increase in age is observed. while the average location of the main sequence shifts more aud more to the blue.," For increasing values of $\vert U,V,W \vert$ no substantial increase in age is observed, while the average location of the main sequence shifts more and more to the blue."
 The metal poor cononeut j 410 3) ds best isolated by the condition V. « -180 laus.| iilo population)., The metal poor component $<$ 4 $10^{-3}$ ) is best isolated by the condition $V$ $<$ -180 km $\rm s^{-1}$ (halo population).
 For what coucerns the chemical composition. we notice 16 departure frou a rapidly rotating coufiguration (-30 <Vo<lO0kms +) at wibout -0.6: this kinematical change is possibly related to ie age increase mentioned before. which takes place at simular values of this space velocity componcut.," For what concerns the chemical composition, we notice the departure from a rapidly rotating configuration (-30 $< V <$ 10 km $\rm s^{-1}$ ) at about -0.6; this kinematical change is possibly related to the age increase mentioned before, which takes place at similar values of this space velocity component."
 The σοι age for large space velocity suggests that 10 substantial age spread exists in the iuuer halo. at least in the local sample.," The common age for large space velocity suggests that no substantial age spread exists in the inner halo, at least in the local sample."
 Πές of a progressive decrease of the netal content with iucreasine |D.V.1T]. come from the distributions with aat various V: this poiut. together with the abseuce of age spread at large CU.V.VW. is more in favour of a model iu which the bulk of the inner halo formed in a continuous coherent process - collapse of a gaseous nass. as advocated by ουσια et al. (," Hints of a progressive decrease of the metal content with increasing $\vert U,V,W \vert$ come from the distributions with at various $V$: this point, together with the absence of age spread at large $U,V,W$, is more in favour of a model in which the bulk of the inner halo formed in a continuous coherent process - collapse of a gaseous mass, as advocated by Eggen et al. ("
1962) aud Saudage Fouts (1987) - than a niodel in which accretion and meresiug are prevailing.,1962) and Sandage Fouts (1987) - than a model in which accretion and merging are prevailing.
 Undoubtly episodes of mereie have taken. and are takine. place (as exemplified by the case of the dif cllitpical ealaxy in Sagittarius. Ibata et al.," Undoubtly episodes of merging have taken, and are taking, place (as exemplified by the case of the dwarf ellitpical galaxy in Sagittarius, Ibata et al."
 1991). but their effects have not been enough as to cancel the overall kinematical aud chemical structure left over by the collapse aud spin- of the original protogalaxy. at least in the ducer halo reeglon.," 1994), but their effects have not been enough as to cancel the overall kinematical and chemical structure left over by the collapse and spin-up of the original protogalaxy, at least in the inner halo region."
This is valid for 3.603<logTay4.123.,This is valid for $3.603 \leq \log T_{\rm eff} \leq 4.123$.
 The error in the bolometric correction using V. is severely dominated by the reddening correction and is around 0.15 magnitudes., The error in the bolometric correction using $V$ is severely dominated by the reddening correction and is around 0.15 magnitudes.
" We contemplated using A instead because reddening has such little effect. but because. BC), is such a steep Iuncüon of the Zur. the errors are virtually identical."," We contemplated using $K$ instead because reddening has such little effect, but because $BC_{K}$ is such a steep function of the $T_{\rm eff}$, the errors are virtually identical."
 We were now able to determine the stars’ logL/L. using the 9MC's distauce modulus of 18.9 (van den Bergh 2000)., We were now able to determine the stars' $\log L/L_\odot$ using the SMC's distance modulus of 18.9 (van den Bergh 2000).
 The results are shown in Table 2.., The results are shown in Table \ref{tab:derived}.
 Qut of our original list of G77 lareets. we identified 116 stars as candidate SAIC supergiants and an additional 16 stars as probable SAIC supergiants.," Out of our original list of 677 targets, we identified 176 stars as candidate SMC supergiants and an additional 16 stars as probable SMC supergiants."
 ILowever. many of our targets are bright and thus have been previously classified.," However, many of our targets are bright and thus have been previously classified."
 As shown in Table 1.. a literature search vielded spectral classifications for of our program targets.," As shown in Table \ref{tab:allobs}, a literature search yielded spectral classifications for of our program targets."
 Among these. the stars we identified as SAIC supergiants were indeed idenüfied as supergiants in the literature. and the stars we identified as foreground stars were indeed identified as clwarls in the literature.," Among these, the stars we identified as SMC supergiants were indeed identified as supergiants in the literature, and the stars we identified as foreground stars were indeed identified as dwarfs in the literature."
 llowever. this doesnt hold true on a star-bv-star basis.," However, this doesn't hold true on a star-by-star basis."
 We believe that in most cases the literature luminosity classes are at fault because they are based on spectral lines instead of racial velocity measurements and the incorrect resulis make use of low-dispersion spectra., We believe that in most cases the literature luminosity classes are at fault because they are based on spectral lines instead of radial velocity measurements and the incorrect results make use of low-dispersion objective-prism spectra.
 When determining (he classification of an SAIC star. (he process is made more difficult by the SAIC’s low metallicity.," When determining the classification of an SMC star, the process is made more difficult by the SMC's low metallicity."
 Thus. stars with weak metal lines may be misclassified as dwarls when they are in [act SAIC supergiants.," Thus, stars with weak metal lines may be misclassified as dwarfs when they are in fact SMC supergiants."
 In order to futher cheek that our survey did not exclude any of the most. huminous menibers. we examined the Evans Howartlh (2008) survey of radial velocities ancl spectral (vpes for a variety of SAIC members.," In order to further check that our survey did not exclude any of the most luminous members, we examined the Evans Howarth (2008) survey of radial velocities and spectral types for a variety of SMC members."
 However. his list of E- and G- stus begins below our Taint magnitude limit (corresponding to 124. ) and hence does not contain anv highly ]uminous and massive members.," However, his list of F- and G- stars begins below our faint magnitude limit (corresponding to $M_\odot$ ) and hence does not contain any highly luminous and massive members."
 Desides looking at literature classifications. we also examined our blue spectra and determined crude spectral types based on prominent metal lines for 209 stars. or of our observed sample.," Besides looking at literature classifications, we also examined our blue spectra and determined crude spectral types based on prominent metal lines for 209 stars, or of our observed sample."
 These results are also shown in Table 1.., These results are also shown in Table \ref{tab:allobs}.
 Once again. overall we identified our category 1 stars as supergiants and our category 3 stars as clwarls but for many individual cases this fails.," Once again, overall we identified our category 1 stars as supergiants and our category 3 stars as dwarfs but for many individual cases this fails."
 These failures reinforced. our distrust in the abilities of spectral types to faithfully discriminate SAIC supergiants [rom foreground dwarls. particularly for Inter stars.," These failures reinforced our distrust in the abilities of spectral types to faithfully discriminate SMC supergiants from foreground dwarfs, particularly for fainter stars."
 We therefore put no weight on the spectral classifications and didn't use them further., We therefore put no weight on the spectral classifications and didn't use them further.
 We were now able to evaluate our studys completeness before placing (he stars on the IIBD., We were now able to evaluate our study's completeness before placing the stars on the HRD.
 Firstly. we didnt observe all 677 of our selected targets.," Firstly, we didn't observe all 677 of our selected targets."
 But. our literature search only," But, our literature search only"
For microquasar examples we consider Cvgnus X-1 (Young et al.,For microquasar examples we consider Cygnus X-1 (Young et al.
 2001) and $5483 (Ixatz Piran 1932: Begelman et al., 2001) and SS433 (Katz Piran 1982; Begelman et al.
 2006: Blundell et al., 2006; Blundell et al.
 2005:2007)., 2005;2007).
" For the former. we take M= 10M... M~10PA, vi. and n,=10007,"," For the former, we take $M= 10M_\odot$ , $\dot M\sim 10^{19} M_\sun$ /yr, and $r_o=1000 r_g$."
 ÀUr =ry~L5xο Eq. (23))," At $r=r_g\sim 1.5 \times 10^6$ cm, Eq. \ref{23}) )"
" then gives /,,~0.03(zu)(2x)v(AU vr. ", then gives $t_{w}\sim 0.03\left({s\epsilon_{ed}\over 0.01}\right)^{-2}\left({\alpha\over 0.3}\right)^{-9/5}\left({\theta\over 0.03 \ {\rm rad}}\right)^2$ yr.
For this case too. the first inequality in (24)) is easily satisfied [rom (27)).," For this case too, the first inequality in \ref{23b}) ) is easily satisfied from \ref{24c}) )."
 The second inequality in (24)) allows use of the second value in (26))., The second inequality in \ref{23b}) ) allows use of the second value in \ref{ineq}) ).
 The companion mass to e.g. (νο N-1 is al least 90141. so for accretion al LOAL. ντ. accretion can be powered long after the wobble time.," The companion mass to e.g. Cyg X-1 is at least $M_\sun$ so for accretion at $10^{-7}M_\odot$ /yr, accretion can be powered long after the wobble time."
 For $8433 (e.g. Degelman et al., For SS433 (e.g. Begelman et al.
" 2006) Af=I0.U.. and we take the inner radius 10""em."," 2006) $M=10M_\odot$, and we take the inner radius $r\sim r_g\sim 1.5 \ts 10^{6}$ cm."
" The accretion rate that makes it to the inner region. relevant for the jets. is Mj~2x L0Me/s. This is to be distinguished from the super-Eddington accretion rate of Mou>10*M5, at the disc cireularization radius of ri.~10cm."," The accretion rate that makes it to the inner region, relevant for the jets, is ${\dot M}_{in}\sim 2\times 10^{19}$ g/s. This is to be distinguished from the super-Eddington accretion rate of ${\dot M}_{out}\ge 10^3 {\dot M}_{in}$ at the disc circularization radius of $r_{circ}\sim 10^{12}$ cm."
 Begelman et al. (, Begelman et al. (
"2006) argue that the much of the mass is taken out by a wind at reAahcLor,10H cm.",2006) argue that the much of the mass is taken out by a wind at $r\sim{r_{circ}\over 10}\sim 10^5r_g\sim 10^{11}$ cm.
" We therefore take 7,7LO°r, for the outer radius of the disc supplying mass to the inner jet and use M; for the relevant accretion rate.", We therefore take $r_o\sim 10^5r_g$ for the outer radius of the disc supplying mass to the inner jet and use ${\dot M}_{in}$ for the relevant accretion rate.
" We then obtain /,~0.04(22)(3)a(uu vr. ", We then obtain $t_{w}\sim 0.04\left({s\epsilon_{ed}\over 0.01}\right)^{-2}\left({\alpha\over 0.3}\right)^{-9/5}\left({\theta\over 0.03 \ {\rm rad}}\right)^2$ yr.
For $5483. like Cvgnuus X-1. the first inequality in (24)) is easily satisfied from (27)) ancl a conipanion mass of ~20.4... (based on crudely averaging recent mass estimates of Lopez et al.," For SS433, like Cygnus X-1, the first inequality in \ref{23b}) ) is easily satisfied from \ref{24c}) ) and a companion mass of $\sim 20M_\odot$ (based on crudely averaging recent mass estimates of Lopez et al."
 2006 and Lillwvig and Gies 2008) allows use of the second value in (26)) lor the second inequalitv in (24))., 2006 and Hillwig and Gies 2008) allows use of the second value in \ref{ineq}) ) for the second inequality in \ref{23b}) ).
 This implies that accretion will be fueled long alter the wobble time., This implies that accretion will be fueled long after the wobble time.
 Again. we have not considered relativistic effects.," Again, we have not considered relativistic effects."
 We can compare the stochastic wander just estimated [or 55433 wilh the data of Blundell et al. (, We can compare the stochastic wander just estimated for SS433 with the data of Blundell et al. (
2005.2007). who monitored fluctuations in the speed and direction of the inner jets.,"2005,2007), who monitored fluctuations in the speed and direction of the inner jets."
 Table 1 of Blundell et al. (, Table 1 of Blundell et al. (
2007) shows that. when averaged over several clay (ime scales. wander angles of ~0.5—0.7 degrees were obtained.,"2007) shows that when averaged over several day time scales, wander angles of $\sim 0.5-0.7$ degrees were obtained."
 This is roughly consistent with our result above: Converting units. out result [or 55433 can be written 8—1.7(15davsE) deg.," This is roughly consistent with our result above: Converting units, out result for SS433 can be written $\theta\sim 1.7\left({t_w\over 15 {\rm days}}\right)^{1/2}$ deg."
" There is likely à maximum time scale /,,,,,, which is the value of /,; above which the stochastic wander is tempered by some negative feedback [rom forces not considered in the present work."," There is likely a maximum time scale $t_{w,max}$ which is the value of $t_w$ above which the stochastic wander is tempered by some negative feedback from forces not considered in the present work."
" Thus Jie<lame, M the wander is to be calculated with our approximations."," Thus $t_w\le t_{w,max}$ if the wander is to be calculated with our approximations."
 One limit on {μι comes from the small wander angle approximation that allowed our use of a 2-D Carlesian approximation., One limit on $t_w$ comes from the small wander angle approximation that allowed our use of a 2-D Cartesian approximation.
 Hlowever. for a precessing and nodding svstem like $5433 (e.g. Fabrika 2004). the 162 dav precession (ime scale or the 6.3 clay nodding time scale may provide (he maxium ἐν appropriate for computing untenipered stochastic wander.," However, for a precessing and nodding system like SS433 (e.g. Fabrika 2004), the 162 day precession time scale or the 6.3 day nodding time scale may provide the maxium $t_w$ appropriate for computing untempered stochastic wander."
" We ο not determine /,,,,,,here or study Iarge angle wobble but note that a persistent leature of stochastic wander is its non-periodicitv. which distinguishes it [rom systematic precession induced by binary companions (e.g. Terquem et al."," We do not determine $t_{w,max}$here or study large angle wobble but note that a persistent feature of stochastic wander is its non-periodicity, which distinguishes it from systematic precession induced by binary companions (e.g. Terquem et al."
 1999)., 1999).
diffuse surrounding gas can help us understand the physical processes that govern galaxy evolution in general.,diffuse surrounding gas can help us understand the physical processes that govern galaxy evolution in general.
" The imetallicity of stars aud eas in galaxies is known to correlate stronglv with their huninosities, circular velocities and stellar masses (c.g. Lequeuxetal.1979:Garnett2002: 2005))."," The metallicity of stars and gas in galaxies is known to correlate strongly with their luminosities, circular velocities and stellar masses (e.g. \citealt{L79,G02,T04,G05}) )."
 However. the plivsical processes that drive these correlations are not vet fully understood.," However, the physical processes that drive these correlations are not yet fully understood."
 Mathews&Baker(1971) and Larson(1974) first sugeested that interstellar gas can be driven out of galaxies. by supernova explosions asoutflows., \citet{MB71} and \citet{L74} first suggested that interstellar gas can be driven out of galaxies by supernova explosions as.
.. They predicted that galaxies of smaller mass have lower metal abundances because their lower escape velocities allow freshly. enriched gas to be more efficiently. removed., They predicted that galaxies of smaller mass have lower metal abundances because their lower escape velocities allow freshly enriched gas to be more efficiently removed.
" The input of energy from supernova explosions is now routincly incorporated ito livdrodynainical simulations of galaxy formation, either in the form of thermal heating or ‘kinetic feedback, whereby radial moincntiun kicks are lnparted to particles surrounding sites of star formation in the galaxy."," The input of energy from supernova explosions is now routinely incorporated into hydrodynamical simulations of galaxy formation, either in the form of thermal heating or `kinetic feedback', whereby radial momentum kicks are imparted to particles surrounding sites of star formation in the galaxy."
 Although these simulations are now able to demonstrate that galactic outflows can vield à good imatch to the observed imass-inetallicity relation (c.g. Ixobayashietal.2007:Scannapiccoctal. 2008)). this does not mean that outflows are the only process at work in regulating the metallicities of real galaxies.," Although these simulations are now able to demonstrate that galactic outflows can yield a good match to the observed mass-metallicity relation (e.g. \citealt{K07,S08}) ), this does not mean that outflows are the only process at work in regulating the metallicities of real galaxies."
" Brooksetal.(2007) argue that a (SFE) is required to explain observations, i addition to supernova feedback."," \citet{B07} argue that a (SFE) is required to explain observations, in addition to supernova feedback."
" In this scenario, less massive galaxies convert their gas reservoirs into stars over longer timescales than more massive galaxies."," In this scenario, less massive galaxies convert their gas reservoirs into stars over longer timescales than more massive galaxies."
" Therefore, less massive galaxies have higher gas-to-stellar mass ratios aud are consequently less inctal-rich."," Therefore, less massive galaxies have higher gas-to-stellar mass ratios and are consequently less metal-rich."
" Motivated bw their work on momentumn-driven winds in smoothed particle hwdrodynainics (SPH) simulations, Finlator&Davé(2008) have also suggested that both ietal-rich outflows at all masses aud a variable star formation efficiency. inust play roles in explaining the observed mass-mnetallicity relation for nearby galaxies."," Motivated by their work on momentum-driven winds in smoothed particle hydrodynamics (SPH) simulations, \citet{FD08} have also suggested that both metal-rich outflows at all masses and a variable star formation efficiency must play roles in explaining the observed mass-metallicity relation for nearby galaxies."
" Alternatively, Dalcantonctal.(2004) suggest that can regulate inctallicity in disc galaxies."," Alternatively, \citet{D04} suggest that can regulate metallicity in disc galaxies."
 Given that lower mass galaxies teud to have lower star formation rates (due to the fact that their coll gas densities are lower). a met dilution takes place when the time-scale for star formation falls below the time-scale for accretion of metal-poor gas.," Given that lower mass galaxies tend to have lower star formation rates (due to the fact that their cold gas densities are lower), a net dilution takes place when the time-scale for star formation falls below the time-scale for accretion of metal-poor gas."
 This would drive down the low mass cud of the mass-inctallicity relation., This would drive down the low mass end of the mass-metallicity relation.
" Finally, (IMF) have also been cited as another factor that might mfluence the mass-inctallicity relation."," Finally, (IMF) have also been cited as another factor that might influence the mass-metallicity relation."
" Ióppoen,Weidner&INroupa(2007) propose that a SFR-dependent (aid therefore stellar inass-dependent) IMF causes different galaxies to produce different. effective oxvgen vields.", \citet{KWK07} propose that a SFR-dependent (and therefore stellar mass-dependent) IMF causes different galaxies to produce different effective oxygen yields.
 This hwpothesis is based, This hypothesis is based
pattern in which the flux maximum after the deeper eclipses is larger than the maximum after the shallower eclipses.,pattern in which the flux maximum after the deeper eclipses is larger than the maximum after the shallower eclipses.
" We attribute this to Doppler beaming, see Section??.."," We attribute this to Doppler beaming, see Section\ref{sec_lc_BF}."
" To determine the system properties, we modelled the light curve with the code written by TRM (foradescriptionofthecode,see?,Appendix A).."," To determine the system properties, we modelled the light curve with the code written by TRM \citep[for a description of the code, see][Appendix
A]{CopperwheatMarsh2010}."
" This code uses grids of points to model the two stars, taking into account limb darkening, gravity darkening, Doppler beaming and gravitational lensing when the white dwarf eclipses its companion."," This code uses grids of points to model the two stars, taking into account limb darkening, gravity darkening, Doppler beaming and gravitational lensing when the white dwarf eclipses its companion."
" It assumes the ellipsoidally deformed star to be in corotation with the binary orbit, which is usually a good assumption because of the large tidal interactions between the two binary components."," It assumes the ellipsoidally deformed star to be in corotation with the binary orbit, which is usually a good assumption because of the large tidal interactions between the two binary components."
 Reprocessing of light from the sdB by the WD is included in the light curve models as well (“reflection effect”).," Reprocessing of light from the sdB by the WD is included in the light curve models as well (“reflection effect"")."
 To speed up the computation of the models used in this paper we implemented a new option whereby a finer grid can be used along the track of the white dwarf as it eclipses the sdB. This reduces the overall number of points needed to model the light curve to the demanding precision required to model theKepler data., To speed up the computation of the models used in this paper we implemented a new option whereby a finer grid can be used along the track of the white dwarf as it eclipses the sdB. This reduces the overall number of points needed to model the light curve to the demanding precision required to model the data.
" In addition, we only used the finely-spaced grid during the eclipse phases, taking care to make the model values continuous when changing between grids by applying normalisation factors (very close to unity) to the coarse grid fluxes."," In addition, we only used the finely-spaced grid during the eclipse phases, taking care to make the model values continuous when changing between grids by applying normalisation factors (very close to unity) to the coarse grid fluxes."
 We used ~100000 (~37000) grid points for the fine (coarse) grids for the sdB and 3000 for the white dwarf.," We used $\sim 100\,000$ $\sim 37\,000$ ) grid points for the fine (coarse) grids for the sdB and $3000$ for the white dwarf."
" To model the finite exposures more accurately during the eclipses, where smearing occurs due to the 1mm integration time, we calculated 7 points for each exposure (i.e., one point for every ~10s) and took their trapezoidal average."," To model the finite exposures more accurately during the eclipses, where smearing occurs due to the m integration time, we calculated 7 points for each exposure (i.e., one point for every $\sim 10\,$ s) and took their trapezoidal average."
" We used model spectra to compute the gravity darkening coefficient (GDC) of the sdB and the limb darkening coefficients for both the sdB and the white dwarf, which are all important parameters for the modeling of a close binary’s light curve."," We used model spectra to compute the gravity darkening coefficient (GDC) of the sdB and the limb darkening coefficients for both the sdB and the white dwarf, which are all important parameters for the modeling of a close binary's light curve."
" The GDC is needed to model the effects of the white dwarf’s gravity on the sdB, which slightly distorts the sdB’s shape."," The GDC is needed to model the effects of the white dwarf's gravity on the sdB, which slightly distorts the sdB's shape."
 The bolometric flux from a stellar surface depends on the local gravity as Tοςg® in which 6 is the bolometric GDC., The bolometric flux from a stellar surface depends on the local gravity as $T^4\propto g^{\beta_{b}}$ in which $\beta_{b}$ is the bolometric GDC.
" For radiative stars, By=1 (?).."," For radiative stars, $\beta_{b}=1$ \citep{von-Zeipel1924}."
" We observe the band-limited stellar flux, not the bolometric flux, and hence we require a different coefficient defined by Iος g?*."," We observe the band-limited stellar flux, not the bolometric flux, and hence we require a different coefficient defined by $I \propto g^{\beta_{K}}$ ."
" The GDC for theKepler bandpass, 3x was computed from in which I is the photon-weighted bandpass-integrated specific intensity at µ=1 and TERT=B—0.25."," The GDC for the bandpass, $\beta_K$ was computed from in which $I$ is the photon-weighted bandpass-integrated specific intensity at $\mu=1$ and $\frac{\mathrm{d} \log T}{\mathrm{d} \log
 g}=\frac{\beta_{b}}{4}=0.25$."
" We used a grid of sdB atmosphere models calculated from the LTE model atmosphere grid of ? using the Linfor program (?) and assumed Tig= 34500K, logg=5.5, log(nHe/nuH)=—1.5 and log(Z/Zo)=—2."," We used a grid of sdB atmosphere models calculated from the LTE model atmosphere grid of \citet{HeberReid2000} using the Linfor program \citep{Lemke1997} and assumed $T_{\rm{eff}}=34\,500$ K, $\log g=5.5$, $\log \left(n_{\rm{He}}/n_{\rm{H}}\right) = -1.5$ and $\log \left(Z/Z_\odot\right)=-2$."
" To estimate the interstellar reddening, we compared the observed B—V colour of —0.20+0.01 mag (?) with the colours expected from a model atmosphere."," To estimate the interstellar reddening, we compared the observed $B-V$ colour of $-0.20\pm0.01\,$ mag \citep{AllardWesemael1994} with the colours expected from a model atmosphere."
 We found an intrinsic colourof B-—V=—0.26 mag and consequently adopted a reddening of E(B—V) 0.06.," We found an intrinsic colourof $B-V=-0.26\,$ mag and consequently adopted a reddening of $E(B-V)=0.06$ ."
 To account for this interstellar reddening, To account for this interstellar reddening
Vaucouleurs 1958. 1975).,"Vaucouleurs 1958, 1975)."
 Thus. if the Local Ciroup — Sculptor Group concentration is modeled as a cylinder like filament aligned aloug the Superealactic Y-axis. this projection slows the typical displacement [rom the ceuter of that concentration.," Thus, if the Local Group – Sculptor Group concentration is modeled as a cylinder like filament aligned along the Supergalactic Y-axis, this projection shows the typical displacement from the center of that concentration."
 Figure 5 elves the appearance that the transition galaxies show a concentration to the center of this filament similar to that seen by the spirals. while the dIs appear to have larger radial distances.," Figure 8 gives the appearance that the transition galaxies show a concentration to the center of this filament similar to that seen by the spirals, while the dIs appear to have larger radial distances."
 Figure 9 is a histogram of the racial distances from this axis sorted by galaxy type., Figure 9 is a histogram of the radial distances from this axis sorted by galaxy type.
 Average racial distances aud staucdard deviations have been calculated for each of the types., Average radial distances and standard deviations have been calculated for each of the types.
 Here we are including the dE galaxies for tle first time., Here we are including the dE galaxies for the first time.
 The distances for the Local Croup dE galaxies are takeu [rom Mateo (1993) and van deu Bergh (2000)., The distances for the Local Group dE galaxies are taken from Mateo (1998) and van den Bergh (2000).
 The distances of the six kuown Sculptor Group dEs come from Jerjeu et ((10998: NGC 59. SC 22. ESO 29[-CCOT0. ESO 210-C030). Ixarachenutsev. et ((2000: ESO. 110-005). aud Jerjen Rejkuba (2001: ESO 510-G032).," The distances of the six known Sculptor Group dEs come from Jerjen et (1998: NGC 59, SC 22, ESO 294-G010, ESO 540-G030), Karachentsev et (2000: ESO 410-G005), and Jerjen Rejkuba (2001: ESO 540-G032)."
 The confirms the unpression that the radial distributions of the trausition galaxies are very similar to those of the spiral galaxies and dE galaxies aud distinctly different. Grom those of the dis., The confirms the impression that the radial distributions of the transition galaxies are very similar to those of the spiral galaxies and dE galaxies and distinctly different from those of the dIs.
 It the sealaxies are separated into the Local aud Sculptor groups. the offset is still present.," If the galaxies are separated into the Local and Sculptor groups, the offset is still present."
 The main dillereuce is the siguificant population of dis more than 1. Mpe from the cloud axis., The main difference is the significant population of dIs more than 1 Mpc from the cloud axis.
 The bimocdality of the dE distribution simply reflects the [act that most of these galaxies are either satellites of AL 31 (with au ollset from the Superealactic Y-axis of 0.7 Mpc) or the Milky Way (withli uo offset)., The bimodality of the dE distribution simply reflects the fact that most of these galaxies are either satellites of M 31 (with an offset from the Supergalactic Y-axis of 0.7 Mpc) or the Milky Way (with no offset).
 Figure 10 shows the results of the calculation of the distauces of the cl. trausition. and dE galaxies to the nearest spiral galaxy. inspired by the results of Figures 8 aud 9.," Figure 10 shows the results of the calculation of the distances of the dI, transition, and dE galaxies to the nearest spiral galaxy inspired by the results of Figures 8 and 9."
 In this figure. the Sculptor Group dwarfs are noted by dots in thehistograms”.," In this figure, the Sculptor Group dwarfs are noted by dots in the."
 The main difference between the cll ancl tranM.itionitiou galaxies in Figure 10 is the lack of trausitiontransitio ealaxies at large clistauces. with the result that the average clistauce for the dIs is almost a factor oL two larger than that of the transition galaxies.," The main difference between the dI and transition galaxies in Figure 10 is the lack of transition galaxies at large distances, with the result that the average distance for the dIs is almost a factor of two larger than that of the transition galaxies."
 This is a margiually strouger result [rom tliat shown in Figure 9 (0.32/0.58 = a factor of 1.1 for average radial distance from the Cloud axis versus 0.92/0.50 = a factor of 1.9 [or average cdistauce to the nearest spiral)., This is a marginally stronger result from that shown in Figure 9 (0.82/0.58 $=$ a factor of 1.4 for average radial distance from the Cloud axis versus 0.92/0.50 $=$ a factor of 1.9 for average distance to the nearest spiral).
 The Ix-5 test indicates that all three clistributious in Figure 10 are significantly dillerent., The K-S test indicates that all three distributions in Figure 10 are significantly different.
 Comparing the trausition galaxies to the other two samples vields ouly a probability that the transition galaxies come from the saline saiple as the cls aud only an probability of comune Crom the same sample as the dEs., Comparing the transition galaxies to the other two samples yields only a probability that the transition galaxies come from the same sample as the dIs and only an probability of coming from the same sample as the dEs.
 The distauces calculated for Figure 10 carry a larger degree of uncertaiuty than those in Figure, The distances calculated for Figure 10 carry a larger degree of uncertainty than those in Figure
"where p, is the critical mass density of the universe today.",where $\rho_{c_0}$ is the critical mass density of the universe today.
" The lensing equation for the GNFW profile is &eiven bvvoy y=rο...µια): ς€=Fro and 5d/=JEια.ο)αι are the position vectors in the lens plane ancl (he source plane respectively. gir)=teuduJi(QuRz)UT(Qr and where jf, is à parameter on which the efficiency of producing mulüple images is strongly X,⋅∖"," The lensing equation for the GNFW profile is given by $y=x-\mu_s g(x)/x$ ; $\vec{\xi}=\vec{x}r_s$ and $\vec{\eta}=\vec{y}r_s d^A_S/d^A_L$ are the position vectors in the lens plane and the source plane respectively, $g(x) \equiv
\int_0^x u du \int_0^{\infty} \left(u^2 +z^2\right)^{-\alpha/2}
\left[\left(u^2+z^2\right)^{1/2} +1\right]^{-3+\alpha} dz$, and where $\mu_s$ is a parameter on which the efficiency of producing multiple images is strongly dependent."
" — ∢⋅1dipP2(he Fi.critical surface masssue⋅⋅ ⇁⇁⋅density.⋅ and⇀⊻≓⇀⊻⇀⊻∕↼⊻↴ djdependent.↽ = dzdy,/di."," Here $\Sigma_{\rm
cr}={c^2\over 4\pi G}\,{d^A_S\over d^A_L d^A_{LS}}$ is the critical surface mass density, and $d^A_R=d^A_L d^A_{LS}/d^A_S$."
HereThe lensing equation curves are svnuuelrical wilh respect to the origin., The lensing equation curves are symmetrical with respect to the origin.
 Multiple images can be formed when |y|<yer. where yey is the maximum value of y when .r<0 or the minimum value for ac>0.," Multiple images can be formed when $|y|\leq y_{\rm cr}$, where $y_{\rm cr}$ is the maximum value of $y$ when $x<0$ or the minimum value for $x>0$."
 Generally speaking. there exist three images for |y|<ye.," Generally speaking, there exist three images for $|y|< y_{\rm cr}$ ."
 We will just consider ihe outermost two images stretched bv the splitting angle A@ when more than two images are formed., We will just consider the outermost two images stretched by the splitting angle $\Delta\theta$ when more than two images are formed.
 Therefore. we can write the cross-section as o(M.z)£zyr2U(CM)—NO) with AG>AG) in the lens plane for multiple images produced bv à GNEW lens at z.," Therefore, we can write the cross-section as $\sigma\left(M,z\right) \approx \pi y_{\rm cr}^2
r_s^2\,\vartheta\left(\Delta\theta - \Delta\theta_0\right)$ with $\Delta\theta>\Delta\theta_0$ in the lens plane for multiple images produced by a GNFW lens at $z$."
 Ποιο splitting angle A@ isgiven by M)ο and ry is the positive root of the lensing equation οἱ.)=0.," Here splitting angle $\Delta\theta$ isgiven by $\Delta\theta={r_s\Delta x/d^A_L}
\approx{2 x_0 r_s/d^A_L}$ and $x_0$ is the positive root of the lensing equation $y(x)=0$."
" In (his letter. we assume spatially [Iat ACDAM moclels characterized bv (he matter density parameter QO,. vacuum enerev density parameter O4."," In this letter, we assume spatially flat $\Lambda$ CDM models characterized by the matter density parameter $\Omega_{\mathrm
m}$, vacuum energy density parameter $\Omega_{\Lambda}$."
" For both PL-ACDAI and RSI-ACDM models. we take cosmological parameters to be the new result from the WMAD: Hubble constant f=0.71. O4,=0.27. og=0.84 (7?) and M4=1.5x1077TAL."," For both $\Lambda$ CDM and $\Lambda$ CDM models, we take cosmological parameters to be the new result from the WMAP: Hubble constant $h=0.71$, $\Omega_{\mathrm m}=0.27$, $\sigma_8=0.84$ \citep{2003ApJS..148....1B,2003ApJS..148..175S} and $M_{c1}=1.5\times10^{13}h^{-1}M_{\sun}$."
 As mentioned above. (he lensing probability depend strongly on (he abundance of viralized dark halos.," As mentioned above, the lensing probability depend strongly on the abundance of viralized dark halos."
 The mass function of dark halos directly involve the calculation of primordial power of density (Inetuation., The mass function of dark halos directly involve the calculation of primordial power of density fluctuation.
 According to Eq.(1)). it is clear that the effect of running spectral index on mass [function of halos cause the difference of lensing probabilities between the two models.," According to \ref{prob}) ), it is clear that the effect of running spectral index on mass function of halos cause the difference of lensing probabilities between the two models."
 Alrough the redshift distribution of quasars in the JVAS/CLASS survey is still poorly known. the prediction of 2? model and the CLASS lensing sub-sample redshift measurements suggest that the recdshilt distribution for CLASS unlensed sourcescan be modelled by a Gaussian distribution with mean redshift <2.>=1.27 (?) ancl dispersion o.—0.95 (???).. ," Although the redshift distribution of quasars in the JVAS/CLASS survey is still poorly known, the prediction of \cite{1990MNRAS.247...19D} model and the CLASS lensing sub-sample redshift measurements suggest that the redshift distribution for CLASS unlensed sourcescan be modelled by a Gaussian distribution with mean redshift $<z_s>$=1.27 \citep{2000AJ....119.2629M} and dispersion $\sigma_z$ =0.95 \citep{2002PhRvL..89o1301C,2003MNRAS.341...13B,2003MNRAS.341....1M}. ."
Thus in this letter we adopt the Gaussian redshift distribution of quasars wilh the mean, Thus in this letter we adopt the Gaussian redshift distribution of quasars with the mean
to 100 AL... but changes in the mass range ancl IMIF slope will affect the LyC production substantially.,"to 100 $M_{\odot}$, but changes in the mass range and IMF slope will affect the LyC production substantially."
 For example. differences in (he IME have been associated with higher Jeans nasses in low-metallicitv gas in the high-redshift IGM (Abel 2002: Bromm Loeb 2003). and Trmiinson (2007) ancl Smith (2009) noted the potential influence of CAIB temperature on modes of high-redshift star ommnation.," For example, differences in the IMF have been associated with higher Jeans masses in low-metallicity gas in the high-redshift IGM (Abel 2002; Bromm Loeb 2003), and Tumlinson (2007) and Smith (2009) noted the potential influence of CMB temperature on modes of high-redshift star formation."
 Consequentiv. most cosmological simulations or calculations include a metallicity-induced IAIF (transition (Iren Shull 2010) between low-metallicity Population ILI star ormation and metal-enhanced Population LL.," Consequently, most cosmological simulations or calculations include a metallicity-induced IMF transition (Trenti Shull 2010) between low-metallicity Population III star formation and metal-enhanced Population II."
 The number of LvC photons produced per total mass in star formation depends on the IMF of the stellar population and is given by the conversion [actor Que., The number of LyC photons produced per total mass in star formation depends on the IMF of the stellar population and is given by the conversion factor $Q_{\rm LyC}$.
 We calculate (his conversion bx integrating the total number of LyC photons produced over the entire mass in star formation., We calculate this conversion by integrating the total number of LyC photons produced over the entire mass in star formation.
 llere. Q(ii) is the lifeüme-integrated number of LvC photons as a funcüon of mass calculated. from. stellar atmosphere models and evolutionary (tracks.," Here, $Q(m)$ is the lifetime-integrated number of LyC photons as a function of mass calculated from stellar atmosphere models and evolutionary tracks."
" The IME. Auma is integrated over (he mass range mug,-m-—nugas. where m is expressed in solar units."," The IMF, $\Psi (m) = Km^{-\alpha}$ , is integrated over the mass range $m_{\rm min} < m < m_{\rm max}$, where $m$ is expressed in solar units."
 In the SFR simulator discussed in Section 3.3. the user can choose between a normal and broken IME. power law.," In the SFR simulator discussed in Section 3.3, the user can choose between a normal and broken IMF power law."
 The lower integration limit in (he numerator. mop. is (he mass at which stars no longer produce significant amounts of LvC photons.," The lower integration limit in the numerator, $m_{\rm OB}$, is the mass at which stars no longer produce significant amounts of LyC photons."
 In our calculator. we use and compare (wo models (hat caleulate Q().," In our calculator, we use and compare two models that calculate $Q(m)$."
 First. using stellar atmospheres aud evolutionary tracks SSutherland SShull. unpublished). we [ind (hat. over its main-sequence and post-main-sequence lifetime. an OB star of mass m produces a total number Vive=Quali)xLO of ionizing photons. where Qu;21—10 over the mass range n=30—100 and for metallicities Z=(0.02—2.0)Z..," First, using stellar atmospheres and evolutionary tracks Sutherland Shull, unpublished), we find that, over its main-sequence and post-main-sequence lifetime, an OB star of mass $m$ produces a total number $N_{\rm LyC} = Q_{63}(m) \times 10^{63}$ of ionizing photons, where $Q_{63} \approx 1-10$ over the mass range $m = 30-100$ and for metallicities $Z =( 0.02 - 2.0) Z_{\odot}$."
 We have filled our results to the form Qgsg;Gn)2Am—DB. lor m>mop=B/A (the mass mop defines the effective lower limüt for stars (hat produce sienifieaut. numbers of LvC photons).," We have fitted our results to the form $Q_{63}(m) \approx Am - B$, for $m \geq m_{\rm OB} = B/A$ (the mass $m_{\rm OB}$ defines the effective lower limit for stars that produce significant numbers of LyC photons)."
 For metalliciües in (he range 0.002<Z0.04 (whereZ=Z.0.02 is the solar metallicitv)ancl [for masses 15<m100. the fitted coefficients are B=1.578 and ACZ)=0.0050—1.059Z.," For metallicities in the range $0.002 \leq Z \leq 0.04$ (where$Z = Z_{\odot} = 0.02$ is the solar metallicity)and for masses $15 < m < 100$, the fitted coefficients are $B = 1.578$ and $A(Z) = 0.0950 - 1.059Z$."
 Thus. [or Z=Z.&0.02. we have A=0.0738 and mop=21.4... while [or Z—0.1Z.=0.002 we have A=0.0929 and mop=17M...," Thus, for $Z = Z_{\odot} \approx 0.02$, we have $A = 0.0738$ and $m_{\rm OB} = 21.4\,M_{\odot}$, while for $Z = 0.1 Z_{\odot} = 0.002$ we have $A = 0.0929$ and $m_{\rm OB} = 17\,M_{\odot}$."
 Inserting these values for Q(in)into equation (8). we integrate these LvC photon vields over the IME. to derive (he conversion coefficient. Qo. from in star formation to manber of LvC," Inserting these values for $Q(m)$into equation (8), we integrate these LyC photon yields over the IMF, to derive the conversion coefficient, $Q_{\rm LyC}$ , from in star formation to of LyC"
guider images taken simultaneously with the VIRUS-P data.,guider images taken simultaneously with the VIRUS-P data.
 Typically. ten stars per guider frame were available for photometry.," Typically, ten stars per guider frame were available for photometry."
 We have switched from the standard stars to the science targets with gaps of less than 5 minutes and assumed the conditions to be constant over that time and between the standard star and galaxy positions to make the absolute flux calibration., We have switched from the standard stars to the science targets with gaps of less than 5 minutes and assumed the conditions to be constant over that time and between the standard star and galaxy positions to make the absolute flux calibration.
 The observations of standard stars were taken during the most photometrically stable periods during each night to mitigate this potential source of error., The observations of standard stars were taken during the most photometrically stable periods during each night to mitigate this potential source of error.
 Even so. the final flux calibration factor we apply may have systematic errors.," Even so, the final flux calibration factor we apply may have systematic errors."
 We assess this error by considering the 5 observations of 2 standards. PG1708+602 and Feige 34. taken along with the UGC 7321] data and the 3 observations of 1 standard. Feige 110. taken along with the UGC 1281 data.," We assess this error by considering the 5 observations of 2 standards, PG1708+602 and Feige 34, taken along with the UGC 7321 data and the 3 observations of 1 standard, Feige 110, taken along with the UGC 1281 data."
 The distribution in flux calibrations is wavelength-independent over our observed range with a rms and rms respectively., The distribution in flux calibrations is wavelength-independent over our observed range with a rms and rms respectively.
 These estimates also capture possible variation in transparency with on-sky position., These estimates also capture possible variation in transparency with on-sky position.
 They are reported in TableA2. along with the possible error in the extinction curve between the effective wavelength of the guider and the wavelength of Ha., They are reported in Table\ref{tab_lims} along with the possible error in the extinction curve between the effective wavelength of the guider and the wavelength of $\alpha$.
 For the non-photometric data on UGC 7321. we measured a median zeropoint change. Azp. of 0.276 magnitudes and a rrange of 0.171-0.382 magnitudes over the two nights.," For the non-photometric data on UGC 7321, we measured a median zeropoint change, $\Delta\mbox{zp}$, of 0.276 magnitudes and a range of 0.171-0.382 magnitudes over the two nights."
 The more nearly photometric data on UGC 1281 had median Azp =0.057 magnitudes and a rrange of 0.043-0.077 magnitudes over the three nights., The more nearly photometric data on UGC 1281 had median $\Delta\mbox{zp}=$ 0.057 magnitudes and a range of 0.043-0.077 magnitudes over the three nights.
 The choice of sky subtraction is particularly important for this work which reaches for flux limits far below the average sky brightness., The choice of sky subtraction is particularly important for this work which reaches for flux limits far below the average sky brightness.
 If the science field were covered with source emission. sky nods would be necessary.," If the science field were covered with source emission, sky nods would be necessary."
 Then. the time variability of the OH and geocoronal Ha sky lines would form important systematic error sources.," Then, the time variability of the OH and geocoronal $\alpha$ sky lines would form important systematic error sources."
 Fortunately. the large VIRUS-P field of view and selection of extremely thin. edge-on target galaxies affords a subset of fibers that contain a negligible amount of source flux to serve as simultaneously measured sky fibers.," Fortunately, the large VIRUS-P field of view and selection of extremely thin, edge-on target galaxies affords a subset of fibers that contain a negligible amount of source flux to serve as simultaneously measured sky fibers."
 We selected fibers sufficiently far from the major axis such that the models predicted jj«210.7! ere/s/em?/LI (with the baseline T=1«103! +). or 100. below the expected peak surface brightness. to be used for sky subtraction.," We selected fibers sufficiently far from the major axis such that the models predicted $\mu < 2 \times 10^{-21}$ $^2$ (with the baseline $\Gamma=4\times 10^{-14}$ $^{-1}$ ), or $\times$ below the expected peak surface brightness, to be used for sky subtraction."
 This cut left and of the fibers for sky estimation in UGC 7321 and UGC 1281 respectively., This cut left and of the fibers for sky estimation in UGC 7321 and UGC 1281 respectively.
 We experimented with moving this sky fiber cut up and down by a factor of five and found no difference in the final upper limits to the UVB strength., We experimented with moving this sky fiber cut up and down by a factor of five and found no difference in the final upper limits to the UVB strength.
 Depending on the number of fibers co-added. the statistical Ha flux errors presented here reach to « dimmer than the sky level.," Depending on the number of fibers co-added, the statistical $\alpha$ flux errors presented here reach to $\times$ dimmer than the sky level."
 Without simultaneously measured sky background. the systematics of sky nods would quickly dominate the limits.," Without simultaneously measured sky background, the systematics of sky nods would quickly dominate the limits."
 The data reduction. optimal background subtraction. and search for emission lines were completed with algorithms developed for a Lyman-o emitter survey (?)..," The data reduction, optimal background subtraction, and search for emission lines were completed with algorithms developed for a $\alpha$ emitter survey \citep{Adam10a}."
 We summarize here the important steps., We summarize here the important steps.
 First. overscans and à master bias frame are subtracted from each frame.," First, overscans and a master bias frame are subtracted from each frame."
 The wavelength solution for each fiber is fit às a fourth order polynomial to 30 emission lines from HgCd lamps passing through the entire telescope light path., The wavelength solution for each fiber is fit as a fourth order polynomial to $\sim30$ emission lines from HgCd lamps passing through the entire telescope light path.
 The residuals to the solution are of order one hundredth of a resolution element., The residuals to the solution are of order one hundredth of a resolution element.
 Flat fields precise to <1% are made from twilight flats with the solar spectrum removed by a b-spline fit (?) and division., Flat fields precise to $<1\%$ are made from twilight flats with the solar spectrum removed by a b-spline fit \citep{Die93} and division.
 This fit method is the same as we apply to fitting and subtracting the sky background and has important advantages over data interpolation., This fit method is the same as we apply to fitting and subtracting the sky background and has important advantages over data interpolation.
 By avoiding data resampling. we keep the errors largely uncorrelated.," By avoiding data resampling, we keep the errors largely uncorrelated."
 Small distortions of the instrument camera over a regular pixel grid lead to the spectrum from each fiber being sampled at slightly different wavelengths., Small distortions of the instrument camera over a regular pixel grid lead to the spectrum from each fiber being sampled at slightly different wavelengths.
 By considering a collection of fibers together in a fit. the spectrum is oversampled. and we can recover nearly blended features.," By considering a collection of fibers together in a fit, the spectrum is oversampled, and we can recover nearly blended features."
 This method delivers an optimal spectral model robust against cosmic rays and without the residuals that linear interpolation can create., This method delivers an optimal spectral model robust against cosmic rays and without the residuals that linear interpolation can create.
 A thorough description of b-spline fits as applied to astronomy datasets can be found in ?.., A thorough description of b-spline fits as applied to astronomy datasets can be found in \citet{Kel03}.
 The next step in the data reduction is to fit and subtract a b-spline sky background modelled from selected sky fibers., The next step in the data reduction is to fit and subtract a b-spline sky background modelled from selected sky fibers.
 Next. cosmic rays are masked by finding all pixels that deviate from the other pixels in the same fiber by some large threshold value.," Next, cosmic rays are masked by finding all pixels that deviate from the other pixels in the same fiber by some large threshold value."
 Some dim cosmic rays are missed by this step. but are rejected when combining multiple frames.," Some dim cosmic rays are missed by this step, but are rejected when combining multiple frames."
 We have chosen a threshold that misses the weakest ~20% of cosmic rays for direct masking in this work., We have chosen a threshold that misses the weakest $\sim$ of cosmic rays for direct masking in this work.
 The exact threshold does not affect the results., The exact threshold does not affect the results.
 The frame is then flux calibrated with the non-photometric zeropoint correction and airmass correction applied., The frame is then flux calibrated with the non-photometric zeropoint correction and airmass correction applied.
 Finally. a one dimensional final spectrum for each fiber position is created by combining all the frames taken at the same dither position and running across the 5 pixel cross-dispersion aperture.," Finally, a one dimensional final spectrum for each fiber position is created by combining all the frames taken at the same dither position and running across the 5 pixel cross-dispersion aperture."
 For the final estimate to be immune to remaining cosmic rays we have used the brweight estimator (2) at this step., For the final estimate to be immune to remaining cosmic rays we have used the biweight estimator \citep{Bee90} at this step.
 Our pipeline makes no cross-talk correction since we restrict our cross-dispersion apertures to 5 pixels where the fiber separations are typically ὃ pixels and the cross-dispersion FWHMs are typically 4 pixels., Our pipeline makes no cross-talk correction since we restrict our cross-dispersion apertures to 5 pixels where the fiber separations are typically 8 pixels and the cross-dispersion FWHMs are typically 4 pixels.
 This leads to. at most. LO% contamination from neighboring fibers and becomes especially trivial when considering large collections of fibers as an aperture.," This leads to, at most, $10\%$ contamination from neighboring fibers and becomes especially trivial when considering large collections of fibers as an aperture."
 The scattered light properties of the instrument have been characterized in? and. particularly at Ha wavelengths. no scattered light or ghost patterns are found.," The scattered light properties of the instrument have been characterized in \citet{Ada08} and, particularly at $\alpha$ wavelengths, no scattered light or ghost patterns are found."
 The spectral resolution varies by <5% for all fibers at a common wavelength due to careful design and alignment of the spectrograph camera., The spectral resolution varies by $<5\%$ for all fibers at a common wavelength due to careful design and alignment of the spectrograph camera.
 We have made no corrections by convolution to à common resolution., We have made no corrections by convolution to a common resolution.
 The effect of the spectral resolution variation and the background subtraction scheme is to leave residuals under bright skylines., The effect of the spectral resolution variation and the background subtraction scheme is to leave residuals under bright skylines.
 We characterize the spectral resolution systematic in §3.5.., We characterize the spectral resolution systematic in \ref{sec_lim}.
 Given the large number of independent spectral elements in VIRUS-P data (126.000 in each dither). we must choose a high significance cut.," Given the large number of independent spectral elements in VIRUS-P data (126,000 in each dither), we must choose a high significance cut."
 At 5o significance. the chance of noise leading to a detection at a particular wavelength in a particular dither is only 1 in 14.000.," At $\sigma$ significance, the chance of noise leading to a detection at a particular wavelength in a particular dither is only 1 in 14,000."
 We choose to quote this limit as sufficiently conservative., We choose to quote this limit as sufficiently conservative.
 We describe here an automated emission line search algorithm to work with a sky background and continuum subtracted spectrum or stacks of spectra., We describe here an automated emission line search algorithm to work with a sky background and continuum subtracted spectrum or stacks of spectra.
 By applying this search. we robustly find all significant emission lines at all redshifts.," By applying this search, we robustly find all significant emission lines at all redshifts."
 In practice. we find no significant Ha emission with plausible velocity offsets in any fiber for either galaxy.," In practice, we find no significant $\alpha$ emission with plausible velocity offsets in any fiber for either galaxy."
 Plausible velocity offsets are determined by the HI rotation curves., Plausible velocity offsets are determined by the HI rotation curves.
 In UGC 7321. for example. the rotation curve is flat over our data range with variations of only £10 km s...," In UGC 7321, for example, the rotation curve is flat over our data range with variations of only $\pm$ 10 km $^{-1}$."
 The gas dispersion is measured in the HI data to be near 7 km + subject to the limitation of the 5 km ! resolution (?).., The gas dispersion is measured in the HI data to be near 7 km $^{-1}$ subject to the limitation of the 5 km $^{-1}$ resolution \citep{Uso03}. .
 Over a very conservative £100 km ! (2.2A)) range around, Over a very conservative $\pm$ 100 km $^{-1}$ ) range around
encounters (ri;>dry).,encounters $r_{peri} > 4 r_d$ ).
 However. for close encounters (ry;>2r4) signilicant deviations are founcl.," However, for close encounters $r_{peri} > 2 r_d$ ) significant deviations are found."
 In this regime the analvtical caleulations overestimate the angular momentum loss by up to a [actor 3., In this regime the analytical calculations overestimate the angular momentum loss by up to a factor 3.
 Comparing hvperbolie. parabolic ancl elliptical svstems. il was found that the mass and periastvon of the secondary. determine the location of the angular momentum (ransler within the disc.," Comparing hyperbolic, parabolic and elliptical systems, it was found that the mass and periastron of the secondary determine the location of the angular momentum transfer within the disc."
 In hyperbolic encounters. the velocity has no influence on the location. but instead determines the interaction time and therefore (he percentage of the maximum angular momentum loss that is actually incurred during the encounter.," In hyperbolic encounters, the velocity has no influence on the location, but instead determines the interaction time and therefore the percentage of the maximum angular momentum loss that is actually incurred during the encounter."
 There are strong indications that the angular momentum loss is actually the same for different elliptical orbits with the salle periastron. it just takes much longer for svstems with highly elliptical orbits to reach this state.," There are strong indications that the angular momentum loss is actually the same for different elliptical orbits with the same periastron, it just takes much longer for systems with highly elliptical orbits to reach this state."
 Generally. (he angular momentum loss in the inner regions (which is the most relevant to the angular momentum problem) is underestimated if the entire disc is included in the calculation.," Generally, the angular momentum loss in the inner regions (which is the most relevant to the angular momentum problem) is underestimated if the entire disc is included in the calculation."
 The relative difference is most significant for distant encounters. where up to a factor of 15 at a periastron of 450 AU was found.," The relative difference is most significant for distant encounters, where up to a factor of 15 at a periastron of 450 AU was found."
 This implies that a succession of distant. encounters might well be able to transport a higher amount of angular momentum outwards (han previously thought., This implies that a succession of distant encounters might well be able to transport a higher amount of angular momentum outwards than previously thought.
 This result is supported by the finding that successive encounters can achieve (he same (il nol more) relative angular momentum loss than in the first encounter., This result is supported by the finding that successive encounters can achieve the same (if not more) relative angular momentum loss than in the first encounter.
 To answer (his question quanttativelv. one would need the probability [or repeated encounters in ebusters of high stellar density (ypically LO! stars 7) which to our knowledge has not been investigated so far.," To answer this question quantitatively, one would need the probability for repeated encounters in clusters of high stellar density (typically $^4$ stars $^{-3}$ ) which to our knowledge has not been investigated so far."
 However. Bonnelletal.(2001). and found (hat 5 (to LO per cent of stars in such an environment undergo a single encounter of 100 AU and closer within the first 2-3 Myr.," However, \cite{bonnell:mnras01} and \cite{scally:mnras01} found that 5 to 10 per cent of stars in such an environment undergo a single encounter of 100 AU and closer within the first 2-3 Myr."
 For longer time scales (> 10* vr) their results differ: Scallv&Clarke(2001) find under 30 per cent of stars undergo such close collisions. whereas Bonnelletal.(2001). conclude that nearly all stars have experienced such a close encounter.," For longer time scales $>$ $^7$ yr) their results differ: \cite{scally:mnras01} find under 30 per cent of stars undergo such close collisions, whereas \cite{bonnell:mnras01} conclude that nearly all stars have experienced such a close encounter."
 Whichever scenario is right. close encounters are clearly ofa rare event in such environments.," Whichever scenario is right, close encounters are clearly a rare event in such environments."
 Bearing in mind. that distant encounters will be more likely. possible loss of angular momentum may therefore be significant.," Bearing in mind, that distant encounters will be more likely, possible loss of angular momentum may therefore be significant."
 For close encounters nearly 50 per cent of the angular momentum can be removed [rom within the original disc radius., For close encounters nearly 50 per cent of the angular momentum can be removed from within the original disc radius.
 Although the transport of angular momentum might not be predominantly due to encounters. (μον may nevertheless play an important part.," Although the transport of angular momentum might not be predominantly due to encounters, they may nevertheless play an important part."
 Finally. it was demonstrated that for close encounters. (he area affected. by angular momentum loss can reach [ar inside the disc (for the non-penetrating encounters considered here down to 20 AU).," Finally, it was demonstrated that for close encounters, the area affected by angular momentum loss can reach far inside the disc (for the non-penetrating encounters considered here down to 20 AU)."
 The actual increase in angular momentum near the center occurs, The actual increase in angular momentum near the center occurs
momentum for a given surface rotation velocity.,momentum for a given surface rotation velocity.
 Lt also has a strong shear laver at the convective boundary that can drive additional transport of chemical elements., It also has a strong shear layer at the convective boundary that can drive additional transport of chemical elements.
 Dillerent models. for stellar. rotation have. not. been compared directly on à. common numerical platform alongside otherwise identical input physies before., Different models for stellar rotation have not been compared directly on a common numerical platform alongside otherwise identical input physics before.
 From the Cambridge: stellar evolution. code. (IEigeleton|1971:Polsetal.1995) we have produced a code capable of modelling rotating stars in 1D. under the shellular rotation hypothesis of Zahn(1992).," From the Cambridge stellar evolution code \citep{Eggleton71,Pols95} we have produced a code capable of modelling rotating stars in 1D under the shellular rotation hypothesis of \citet{Zahn92}."
. The code. (Rotating Stellar Evolution). can be easily programmed to run with different physics for stellar rotation and can model both radiative and convective zones under a range of cillerent assumptions.," The code, (Rotating Stellar Evolution), can be easily programmed to run with different physics for stellar rotation and can model both radiative and convective zones under a range of different assumptions."
 This allows us to compare a variety of models for stellar rotation and determine what. if anv. observable traits could be used to distinguish between them.," This allows us to compare a variety of models for stellar rotation and determine what, if any, observable traits could be used to distinguish between them."
 We foresee two possibilities: either we can identify clear observational tests to eliminate certain models or the models show no testable dilference in which case a simplified mocel could be formulated to provide the same results., We foresee two possibilities; either we can identify clear observational tests to eliminate certain models or the models show no testable difference in which case a simplified model could be formulated to provide the same results.
 In section 2 we outline the physical ingredients to and the cillerent models already implemented., In section 2 we outline the physical ingredients to and the different models already implemented.
 In section 3 we present a comparison of the evolutionary predictions for each model., In section 3 we present a comparison of the evolutionary predictions for each model.
 In section 4 we present our summary. and conclusions., In section 4 we present our summary and conclusions.
 Llere we present the physical ingredients of the numerical code.ROSE. used to implement. the models of. stellar rotation.," Here we present the physical ingredients of the numerical code, used to implement the models of stellar rotation."
 is based on the Cambridge stellar evolution code.STABS.," is based on the Cambridge stellar evolution code,."
. Originally written by Eseleton(1971).. the code has been modified many times over the past thirty vears.," Originally written by \citet{Eggleton71}, the code has been modified many times over the past thirty years."
 For details of the last significant update see Stanclilfe&Elelridee (2009)., For details of the last significant update see \citet{Eldridge09}.
. We now solve the four structure equations. seven chemical equations and. now the angular velocity. equation in a single. implicit. Newton-Raphson iterative step.," We now solve the four structure equations, seven chemical equations and now the angular velocity equation in a single, implicit, Newton-Raphson iterative step."
" We caleulate +L He. ""He. 47°C. HN. !*O and 7""Ne implicitly and. 39 other isotopic abundances can be calculated. explicitly."," We calculate $^1$ H, $^4$ He, $^3$ He, $^{12}$ C, $^{14}$ N, $^{16}$ O and $^{20}$ Ne implicitly and 39 other isotopic abundances can be calculated explicitly."
 Lhe nuclear reaction rates were updated by Polsetal.(1995). and Stanclilfe anc are based on the reaction rates of CaughlanFowler (1988).., The nuclear reaction rates were updated by \citet{Pols95} and \citet{Stancliffe05} and are based on the reaction rates of \citet{Caughlan88}. .
 The opacities were last updated by IEldridge&Tout.(2004) and are based on the OPAL opacitics (lelesias&Rogers1996) at high temperatures and Fergusonetal.(2005) at. low temperatures., The opacities were last updated by \citet{Eldridge04} and are based on the OPAL opacities \citep{Iglesias96} at high temperatures and \citet{Ferguson05} at low temperatures.
" Also included: are ""urther corrections for major molecular opacities (Stanclille&Glebbeek 9005).", Also included are further corrections for major molecular opacities \citep{Stancliffe08}.
 The equation. of state is that. of Polsοἱal.(1995)... convection is treated by mixine-leneth heory (BohnVitense1958). and a model for convective overshooting (Schróder.Pols&Eeeleton1997). is included.," The equation of state is that of \citet{Pols95}, convection is treated by mixing-length theory \citep{Bohm58} and a model for convective overshooting \citep{Schroder97} is included."
 Whilst the code has a number of models for mass loss orogrammed. we restrict ourselves to the mass-loss rates of Vink.deIxoter&Lamers(2001). for massive stars.," Whilst the code has a number of models for mass loss programmed, we restrict ourselves to the mass-loss rates of \citet{Vink01} for massive stars."
 These rates apply to non-rotating stars and are moclified as explained in section 2.4.., These rates apply to non-rotating stars and are modified as explained in section \ref{massloss}.
 The centrifugal force. caused bv. rotation allects the welrostatic balance of the star. effectively reducing the local eravity.," The centrifugal force caused by rotation affects the hydrostatic balance of the star, effectively reducing the local gravity."
 On a surface. of constant radius the centrifugal orce acts more strongly at the equator than the poles so he distortion of the star depends on co-latitude ancl our assumption of spherical svnimetry is no longer valid., On a surface of constant radius the centrifugal force acts more strongly at the equator than the poles so the distortion of the star depends on co-latitude and our assumption of spherical symmetry is no longer valid.
 Tassoul(1978) showed that. except. for stars that are. close to critical rotation. the elect of rotational deformation remains axially svmmetric.," \citet{Tassoul78} showed that, except for stars that are close to critical rotation, the effect of rotational deformation remains axially symmetric."
 Enhanced: mass loss from the surface cause of rotation generally keeps stars rotating sullicientlv xdow critical., Enhanced mass loss from the surface because of rotation generally keeps stars rotating sufficiently below critical.
 Even when this is not the case it is only he outer most lavers that are allected., Even when this is not the case it is only the outer most layers that are affected.
 In. models where he angular momentum cistribution in convective regions is uniform the rotation rate may approach critical there but recause convective turbulence is already. considered. to be Tully asvmmetric. we do not need to consider further axial instabilities owing to the rotation.," In models where the angular momentum distribution in convective regions is uniform the rotation rate may approach critical there but because convective turbulence is already considered to be fully asymmetric, we do not need to consider further non-axial instabilities owing to the rotation."
 We adopt similar adjustments to the stellar structure equations to those deseribed by IEndal&Sofia(1976) and Mevnet&Maecder(1997)., We adopt similar adjustments to the stellar structure equations to those described by \citet{Endal76} and \citet{Meynet97}.
. First we define Sp to bea surface of constant pressure. P.," First we define $S_P$ to be a surface of constant pressure, $P$."
 Vp is the volume contained. within Sp and rp is the radius of a sphere with volume Vp=πι /3., $V_P$ is the volume contained within $S_P$ and $r_P$ is the radius of a sphere with volume $V_P=4\pi r_P^3/3$ .
 The equation of continuity is then preserved in its non rotating form. where mp is the mass enclosed. within Sp and p is the density. on the isobar which is assumed to be uniform.," The equation of continuity is then preserved in its non rotating form, where $m_P$ is the mass enclosed within $S_P$ and $\rho$ is the density on the isobar which is assumed to be uniform."
 As we discuss in section 2.6— we expect variables aud chemical abundances to be uniform across isobars. owing to the strong horizontal turbulence caused. by the strong density stratification present in stars (Zahn1992)., As we discuss in section \ref{rotation} we expect variables and chemical abundances to be uniform across isobars owing to the strong horizontal turbulence caused by the strong density stratification present in stars \citep{Zahn92}.
. Phe local gravity vector is where © is the local angular velocity., The local gravity vector is where $\Omega$ is the local angular velocity.
 Lo proceed further we define the average of a quantity over Sp as where der is a surface element of Sp., To proceed further we define the average of a quantity over $S_P$ as where $d\sigma$ is a surface element of $S_P$.
 Using this notation the equation of hyclrostatic equilibrium becomes where and gar=[gr]., Using this notation the equation of hydrostatic equilibrium becomes where and $g_{\rm eff}\equiv |{\boldsymbol g}_{\rm eff}|$.
 Hence with the new definition of variables we can retain the same 1D hyclrostatie equilibrium equation modified by a factor of fp which tends to unity for no rotation., Hence with the new definition of variables we can retain the same 1D hydrostatic equilibrium equation modified by a factor of $f_P$ which tends to unity for no rotation.
 The equation for radiative equilibrium. is. similarly moclified to where Lp is the total οποιον Ες through Sp. P is the pressure. 7 ds the temperature. #is the opacity. ( is," The equation for radiative equilibrium is similarly modified to where $L_P$ is the total energy flux through $S_P$ , $P$ is the pressure, $T$ is the temperature, $\kappa$is the opacity, $a$ is"
where The couductivitv tensor related to electrou-pliouon scattering can be written (again in rotating coordinates) as We then obtain where the quantitics play the vole of damping frequencies in the two different directious.,where The conductivity tensor related to electron-phonon scattering can be written (again in rotating coordinates) as We then obtain where the quantities play the role of damping frequencies in the two different directions.
" By trausforming back to nou-rotatiug coordinates we funally ect from which the dielectric tensor follows as Iu the previous expressions. the off-diagonal terius correspond to the (unou-dissipative) Hall couductivity. aud S, ή are defined as 5. Din 3.1 but with R.L.P replaced by further rotatiou by an angle à accounts for the misalignement between B aud τ aud gives the diclectric teusor ef"" H in the same fori as in eq. (11))."," By transforming back to non-rotating coordinates we finally get from which the dielectric tensor follows as In the previous expressions, the off-diagonal terms correspond to the (non-dissipative) Hall conductivity, and $S^{tot}$ , $D^{tot}$ are defined as $S,D$ in \ref{cold} but with $R,L,P$ replaced by A further rotation by an angle $\alpha$ accounts for the misalignement between $\mathbf{B}$ and $z$ and gives the dielectric tensor $\epsilon^{tot}_{ij}$ in the same form as in eq. \ref{maxw}) )."
 We have repeated the computation of the monochromatic absorption coefficients by following the same method as iu 3.1... but using the diclectric tensor ej.," We have repeated the computation of the monochromatic absorption coefficients by following the same method as in \ref{cold}, but using the dielectric tensor $\epsilon^{tot}_{ij}$ ."
 The conductivites σι. have been computed umucrically for the appropriate values of B. p aud T9.," The conductivites $\sigma_{\|, \perp}$ have been computed numerically for the appropriate values of $B$, $\rho$ and $T$."
. The inclusion of electron-plionou damping seriously affects the emission properties of the surface. as can be seen from Figures 2. and 5 where the augle-averaged aud augle-depeudenut emissivitv is shown.," The inclusion of electron-phonon damping seriously affects the emission properties of the surface, as can be seen from Figures \ref{alpha_tot} and \ref{alpha_ang_phon} where the angle-averaged and angle-dependent emissivity is shown."
 Below ~1 keV the cuussivity declines quite rapidly with decreasing photon cucrev., Below $\sim 1$ keV the emissivity declines quite rapidly with decreasing photon energy.
 There is now a stroug depenudenuce ou the magnetic fieldstrength. with the suppression beiug more pronounced at lowerfields.," There is now a strong dependence on the magnetic fieldstrength, with the suppression being more pronounced at lowerfields."
 This is mainly due to the role, This is mainly due to the role
Over the past decade. a large number of so-called Lyman-a (να) emitters have been discovered at high redshift.,"Over the past decade, a large number of so-called $\alpha$ $\alpha$ ) emitters have been discovered at high redshift."
 Several techniques have been employed in the search for these galaxies. but the by far most common method is that of narrow-band imaging. where a narrow-band filter is tuned to Lye within a particular narrow redshift range.," Several techniques have been employed in the search for these galaxies, but the by far most common method is that of narrow-band imaging, where a narrow-band filter is tuned to $\alpha$ within a particular narrow redshift range."
 Objects with large equivalent widths (EWs) are thus selected by comparing the colours in the narrow-band image and complementary broad-band images., Objects with large equivalent widths (EWs) are thus selected by comparing the colours in the narrow-band image and complementary broad-band images.
 Spectroscopically confirmed Lya emitters now include several hundreds of sources at redshifts ~~3 (e.g.. Moller Warren 1993: Cowie Hu 1998; Steidel et al.," Spectroscopically confirmed $\alpha$ emitters now include several hundreds of sources at redshifts $z \sim 3$ (e.g., ller Warren 1993; Cowie Hu 1998; Steidel et al."
 2000; Fynbo et al., 2000; Fynbo et al.
 2001. 2003: Matsuda et al.," 2001, 2003; Matsuda et al."
 2005: Venemans et al., 2005; Venemans et al.
 2007: Nilsson et al., 2007; Nilsson et al.
 2007; Ouchi et al., 2007; Ouchi et al.
 2008). 2—1.5 (Finkelstein et al.," 2008), $z \sim 4.5$ (Finkelstein et al."
 2007). 2—5.7 (Malhotra et al.," 2007), $z \sim 5.7$ (Malhotra et al."
 2005: Shimasaku et al., 2005; Shimasaku et al.
 2006; Tapken et al., 2006; Tapken et al.
 2006) and ~6.5 (Taniguchi et al., 2006) and $z \sim 6.5$ (Taniguchi et al.
 2005: Kashikawa et al., 2005; Kashikawa et al.
 2006)., 2006).
 However. in the low redshift range. between :~1.6 corresponding to the atmospheric cut-off in the UV and -~3. little progress has been made.," However, in the low redshift range, between $z \approx 1.6$ corresponding to the atmospheric cut-off in the UV and $z \sim 3$, little progress has been made."
 In practice. the lower redshift limit is in fact higher than:~1.6 because of the drop-off in CCD sensitivity and a more typical lower redshift limit is 2~2.0.," In practice, the lower redshift limit is in fact higher than $z \approx 1.6$ because of the drop-off in CCD sensitivity and a more typical lower redshift limit is $z \sim 2.0$."
 Eight narrow-band surveys have so far been published below :~3: Fynbo et al. (, Eight narrow-band surveys have so far been published below $z \sim 3$; Fynbo et al. (
1999). Pentericei et al. (,"1999), Pentericci et al. ("
2000). Stiavelli et al. (,"2000), Stiavelli et al. ("
2001). Fynbo et al. (,"2001), Fynbo et al. ("
2002. 2003a. 20050). Francis et al. (,"2002, 2003a, 2003b), Francis et al. ("
2004) and Venemans et al. (,2004) and Venemans et al. (
2007).,2007).
 Furthermore. Van Breukelen et al. (," Furthermore, Van Breukelen et al. ("
2005) published a sample of Ένα emitters (LAEs) at -~2.5 using integral-field spectroscopy.,2005) published a sample of $\alpha$ emitters (LAEs) at $z \sim 2.5$ using integral-field spectroscopy.
 The difficulty in observing the Ένα line between redshifts 2.<3 lies in the low throughput of optical systems. the low efficiency of CCDs in this wavelength range. and higher extinction in the atmosphere.," The difficulty in observing the $\alpha$ line between redshifts $2 < z < 3$ lies in the low throughput of optical systems, the low efficiency of CCDs in this wavelength range, and higher extinction in the atmosphere."
 Even so. the advantage of a smaller luminosity distance is rewarding in that a higher limit equals the same limit as surveys at higher redshift.," Even so, the advantage of a smaller luminosity distance is rewarding in that a higher limit equals the same limit as surveys at higher redshift."
 It also facilitates follow-up observations into the nature of these objects., It also facilitates follow-up observations into the nature of these objects.
 At higher redshifts. Lya emitters have been observed to be increasingly bluer. younger and smaller with increasing redshift.," At higher redshifts, $\alpha$ emitters have been observed to be increasingly bluer, younger and smaller with increasing redshift."
 At >~3. Gawiser et al. (," At $z \sim 3$, Gawiser et al. ("
2006) inferred stellar masses of afew «105 M... almost no dust extinction. and ages of the order of 100 Myr.,"2006) inferred stellar masses of a few $\times 10^8$ $_{\odot}$, almost no dust extinction, and ages of the order of $100$ Myr."
 In a follow-up paper. Gawiser et al. (," In a follow-up paper, Gawiser et al. ("
2007) studied a stacked sample of 52 Lya emitters without Spitzer detections and confirmed their results of young ages and that no dust appears to be present in these systems. although they inferred slightly higher masses.,"2007) studied a stacked sample of 52 $\alpha$ emitters without Spitzer detections and confirmed their results of young ages and that no dust appears to be present in these systems, although they inferred slightly higher masses."
 The galaxies in their sample with Spitzer detections are presented in Lai et al. (, The galaxies in their sample with Spitzer detections are presented in Lai et al. (
2008).,2008).
 For these galaxies. older ages and higher masses are reported and the authors propose that τ~3 Lya emitters may have a wide range of properties.," For these galaxies, older ages and higher masses are reported and the authors propose that $z \sim 3$ $\alpha$ emitters may have a wide range of properties."
 In Nilsson et al. (, In Nilsson et al. (
2007). a stacked sample of Ίνα emitters at 2=3.15 were studied.,"2007), a stacked sample of $\alpha$ emitters at $z = 3.15$ were studied."
 Here. small masses and low dust contents were inferred. but the ages Were unconstrained.," Here, small masses and low dust contents were inferred, but the ages were unconstrained."
 At even higher redshift. Pirzkal et al. (," At even higher redshift, Pirzkal et al. ("
2007) showed that a sample of |<:<5.7 Lya emitters had very young ages of a few Myr and small stellar masses. in the range 10°= M...,"2007) showed that a sample of $4 < z < 5.7$ $\alpha$ emitters had very young ages of a few Myr and small stellar masses, in the range $10^6 - 10^8$ $_{\odot}$."
 These results agreed well with those of Finkelstein et al. (, These results agreed well with those of Finkelstein et al. (
2007). who studied almost 100 Ένα emitters at >=[.5.,"2007), who studied almost 100 $\alpha$ emitters at $z = 4.5$."
 Finkelstein et al. (, Finkelstein et al. (
2008) reported. studying a different sample. finding very dusty. massive galaxies with “Ayeoy as high as 4.5 magnitudes and masses as high as several S109 M. at :=L5.,"2008) reported, studying a different sample, finding very dusty, massive galaxies with $A_{1200}$ as high as 4.5 magnitudes and masses as high as several $\times 10^{10}$ $_{\odot}$, at $z = 4.5$."
 They argued that they observed a bimodality in the properties of Ίνα emitters: young and blue galaxies versus old and dusty., They argued that they observed a bimodality in the properties of $\alpha$ emitters; young and blue galaxies versus old and dusty.
 Thus. the properties of ὁ Lyo emitters are poorly constrained. but these galaxies tend to be considered young. blue. small and dust-free.," Thus, the properties of $z \geq 3$ $\alpha$ emitters are poorly constrained, but these galaxies tend to be considered young, blue, small and dust-free."
 With the data presented here. we aim to extend the study of the properties of Lyn emitters to lower redshifts. where a wider range of the SED can be studied in the optical/infrared and the luminosity distance is smaller. allowing a more detailed analysis.," With the data presented here, we aim to extend the study of the properties of $\alpha$ emitters to lower redshifts, where a wider range of the SED can be studied in the optical/infrared and the luminosity distance is smaller, allowing a more detailed analysis."
 This paper is organised as follows., This paper is organised as follows.
 Section ?? presents the observations leading. to our sample. as well as the," Section \ref{sec:obs} presents the observations leading to our sample, as well as the"
"(30) where of=30,17/2.", where $A=3\Omega_mH^2/2$.
 Note that. as shown in Castro et al. (," Note that, as shown in Castro et al. ("
2003) we take advantage of an algebraic convenience by using the geometric mean of the matter power spectra. this is well justified since at [arge separations (where the approximation may break down) any pair correlations are down weighted by the form of the Bessel functions.,"2003) we take advantage of an algebraic convenience by using the geometric mean of the matter power spectra, this is well justified since at large separations (where the approximation may break down) any pair correlations are down weighted by the form of the Bessel functions."
 This is fed into equations (23)) then (24)) so that we have an expression for the expected covariance of the 3D cosmic shear estimator f(32) ΕΓΩ” the prefactor AQ. the angular size or area of the survey. comes from final integrations over angle @ (see Ixitehing et al..," This is fed into equations \ref{est}) ) then \ref{est2}) ) so that we have an expression for the expected covariance of the 3D cosmic shear estimator ) )A^2 _h r” F_K(r^g,r')F_K(r^h,r”) , the prefactor $\Delta\Omega$, the angular size or area of the survey, comes from final integrations over angle $\thetab$ (see Kitching et al.,"
 2007 for more information), 2007 for more information).
 We usethis final expressionin Section 2..," We usethis final expressionin Section \ref{Photometric 3D Shear
 Estimator}. ."
moderately fast nova.,moderately fast nova.
 Lis post-nova. quiescen maenituce was thought to be 222 mag (Duerbeck 1987). but a recent 5»ectroscopic search has located it at VIs. 7 away from ῃs previously estimated position (Bianchini et a.," Its post-nova quiescent magnitude was thought to be $>$ 22 mag (Duerbeck 1987), but a recent spectroscopic search has located it at $V \sim 18$, $''$ away from its previously estimated position (Bianchini et al."
 2001)., 2001).
 The 5)eciranm shows a blue continuum with a slope cjracteristic Q lan«pticallv thick disc. on which are superimposed strong Ioll. JAILACTLE. and moderate Balmer emission lines.," The spectrum shows a blue continuum with a slope characteristic of an optically thick disc, on which are superimposed strong HeII, NIII/CIII, and moderate Balmer emission lines."
" The divalent width of 20 measured. by Dianchini et al.d-VL). entered into the VW(4a) inclination correlation cliagram (Warner 1986). indicates an inclination of 65 ""n16"," The $\alpha$ equivalent width of 20 measured by Bianchini et al.(2001), entered into the $W(H\alpha)$ – inclination correlation diagram (Warner 1986), indicates an inclination of $\sim$ $^{\circ}$."
 log of our photometric observations is included in ‘Table 1., The log of our photometric observations is included in Table 1.
 The longest of our light curves is clisplaved in Fig., The longest of our light curves is displayed in Fig.
 iuad srows a Clear modulation with a period near 2 h. From the Fourier transform of the entire data set WE Ηιοαδο a perio of 1.977 h. The mean light curve at this period. is shown in Fie. 2..," \ref{lcrscar}
 and shows a clear modulation with a period near 2 h. From the Fourier transform of the entire data set we measure a period of 1.977 h. The mean light curve at this period is shown in Fig. \ref{rscar_av}."
 As expected rom the profile. the Fourier spectrum is rich in harmonies: the first. third. and. higher harmonics are quite strong but the second harmonic is very weak.," As expected from the profile, the Fourier spectrum is rich in harmonics; the first, third and higher harmonics are quite strong but the second harmonic is very weak."
 Prewhitening of the light curve at the fundamental and harmonics leaves no significant. features., Prewhitening of the light curve at the fundamental and harmonics leaves no significant features.
 We cannot tell from our short. baseline whether the »oriocic brightness variation is an orbital or a superhump mociuation., We cannot tell from our short baseline whether the periodic brightness variation is an orbital or a superhump modulation.
 From the gradient of the Εκ in the spectrum of tS Car. which resembles that of an optically thick acerction disc (AJàanchini et al.," From the gradient of the flux in the spectrum of RS Car, which resembles that of an optically thick accretion disc (Bianchini et al."
 2001) and shows that the svstem is in he high AZ state characteristic of an old nova. ancl he short orbital. period (implying a low mass ratio)) we ονρος the accretion disc to be permanently perturbed into αι οὓς'entrie shape.," 2001) and shows that the system is in the high $\dot{M}$ state characteristic of an old nova, and the short orbital period (implying a low mass ratio), we expect the accretion disc to be permanently perturbed into an eccentric shape."
 The period we have found. is therefore xobady à superhump period. and the orbital period will be a low »ercent shorter.," The period we have found is therefore probably a superhump period, and the orbital period will be a few percent shorter."
 “Phe profile of the light modulation is charac‘teristic of à superhump., The profile of the light modulation is characteristic of a superhump.
" liS Car joins the small group of classical novae with orbita periods shorter than 2 h. The others are RW UAL Gun 1.419 h: Retter Lipkin »2001). GQ Mus (12,4 = 1.425 i Diaz et al."," RS Car joins the small group of classical novae with orbital periods shorter than 2 h. The others are RW UMi $P_{orb}$ = 1.419 h: Retter Lipkin 2001), GQ Mus $P_{orb}$ = 1.425 h: Diaz et al."
" 1995). CP Pup (73,4 = 1474 h. P, = 1.500 i Patterson Warner 1998). and V1974 ονο (D, = 1.950 h. Py, = 2.039 h: Hetter. Leibowitz Ofek 1997)."," 1995), CP Pup $P_{orb}$ = 1.474 h, $P_{sh}$ = 1.500 h: Patterson Warner 1998), and V1974 Cyg $P_{orb}$ = 1.950 h, $P_{sh}$ = 2.039 h: Retter, Leibowitz Ofek 1997)."
 Fora disc inclination of 65. the correction in magnitude to the standard inclination of 57 is 0.4 (Warner 1995).," For a disc inclination of $^{\circ}$ , the correction in magnitude to the standard inclination of $^{\circ}$ is $-0.4$ (Warner 1995)."
 At, At
sample consists of 6880 galaxies located in similar physical regions for each galaxy clusters (7< 27299).,sample consists of 6880 galaxies located in similar physical regions for each galaxy clusters $r<2r_{200}$ ).
 The substructure was studied using the DS statistical test., The substructure was studied using the DS statistical test.
 The percentage of clusters with substructure is strongly sensitive to the galaxy population mapped by the different clusters., The percentage of clusters with substructure is strongly sensitive to the galaxy population mapped by the different clusters.
" Thus. 11% and 33% of the clusters show substructure in the inner regions (r.€ 7200) when galaxies brighter than M,=-20 or -19 are considered. respectively."," Thus, $\%$ and $\%$ of the clusters show substructure in the inner regions $r<r_{200}$ ) when galaxies brighter than $_{r}=-20$ or $-19$ are considered, respectively."
 The fraction of cluster with substructure in their outskirts (F2 7200) Is much larger. being 55% and 57% in the two considered cases.," The fraction of cluster with substructure in their outskirts $r>r_{200}$ ) is much larger, being $\%$ and $\%$ in the two considered cases."
 No correlation between substructure and global cluster properties (cr. fp and Am>) has been found.," No correlation between substructure and global cluster properties $\sigma_{c}$, $f_{b}$ and $\Delta m_{12}$ ) has been found."
" We have also studied the galaxies located in substructures by the selection of a value of 0, that distinguishes between galaxies inside and outside substructures.", We have also studied the galaxies located in substructures by the selection of a value of $\delta_{c}$ that distinguishes between galaxies inside and outside substructures.
" The value of 6, was chosen by comparing the o values measured for the galaxies in the clusters and those values of 6 from the MC simulations used in the normalization of the DS test.", The value of $\delta_{c}$ was chosen by comparing the $\delta$ values measured for the galaxies in the clusters and those values of $\delta$ from the MC simulations used in the normalization of the DS test.
 This comparison was done individually cluster by cluster. or comparing the global distribution of 6 values obtained from stacking the data of the individual clusters into an ensemble one.," This comparison was done individually cluster by cluster, or comparing the global distribution of $\delta$ values obtained from stacking the data of the individual clusters into an ensemble one."
" In order to avoid possible bias problems with different galaxy population traced by the clusters. we have also considered two different galaxy populations. one formed by those galaxies brighter than M,=—20 located in clusters at z«0.1 (called ECI) and the other formed by galaxies brighter than M,=—19 in clusters at z«0.07 (called EC 2)."," In order to avoid possible bias problems with different galaxy population traced by the clusters, we have also considered two different galaxy populations, one formed by those galaxies brighter than $M_{r}=-20$ located in clusters at $z<0.1$ (called EC1) and the other formed by galaxies brighter than $M_{r}=-19$ in clusters at $z<0.07$ (called EC 2)."
found by Baheall West (1992). but has a Ἡute correlation leeth at zero separation.,"found by Bahcall West (1992), but has a finite correlation length at zero separation."
 We think this is llOro roOssolade because the correlation leusth should re fuite a the continua limit. namely for the matter field.," We think this is more reasonable because the correlation length should be finite at the continuum limit, namely for the matter field."
 By usino€» the X-ray selected clusters oue cau ercatly OVCTCOMC he projection effects which might have affected he optica cluster samples selected from the distributio1 of galaxies projected on the sky., By using the X-ray selected clusters one can greatly overcome the projection effects which might have affected the optical cluster samples selected from the distribution of galaxies projected on the sky.
 Although the NBACs clusters are nof eeuuine X-ray selected clusters auk lave ducoupleeness due to the missing poor ACO clusters. t10v are indeed three-dimensioually bou Svstenis axd tie σαupling is nearly free from false detectiono roverestination of richness.," Although the XBACs clusters are not genuine X-ray selected clusters and have incompleteness due to the missing poor ACO clusters, they are indeed three-dimensionally bound systems and the sampling is nearly free from false detection or overestimation of richness."
 The BCS clusters are sclected purely from their X-ray properties. ai also have icelieible projection effects.," The BCS clusters are selected purely from their X-ray properties, and also have negligible projection effects."
 However. since the nunbe roof N-raw clusters is not vot large euouch toimake a sutficieutly large volume-linited sample. the CFs eastred from he NBAC's aud the BCS clusters have large uncertainies compared to those of optical clusters.," However, since the number of X-ray clusters is not yet large enough to make a sufficiently large volume-limited sample, the CFs measured from the XBACs and the BCS clusters have large uncertainties compared to those of optical clusters."
 Tje clustering streneth of these X-ray clusters is in general lower than what is expected from the ry versus darelation of optical clusters., The clustering strength of these X-ray clusters is in general lower than what is expected from the $r_0$ versus $d_c$ relation of optical clusters.
 This is probably due to the| fact tha the N-rav hDuumositv of X-ray clusters is rot an excellent measure of the cluster richness or mass., This is probably due to the fact that the X-ray luminosity of X-ray clusters is not an excellent measure of the cluster richness or mass.
 The XN-rav bhuuinositv of a cluster depends ou he environment aud activity as well as its dynamical τιdass., The X-ray luminosity of a cluster depends on the environment and activity as well as its dynamical mass.
 In fact. Fieure lof David. Forman Jones (1999) shows that the clusters very bright in ταν beoue to various richness classes.," In fact, Figure 4 of David, Forman Jones (1999) shows that the clusters very bright in X-ray belong to various richness classes."
 Cülbauk. Dower. €fastander (2001) also found that N-ray selection nuüdisses sone significant rich clusters while optical scleclon cal detect all X-ray clusters.," Gilbank, Bower, Castander (2001) also found that X-ray selection misses some significant rich clusters while optical selection can detect all X-ray clusters."
 However. there is a fix4d of tje clustering streneth of the ταν clusters increasing as the mean separation iucreases.," However, there is a trend of the clustering strength of the X-ray clusters increasing as the mean separation increases."
" Despite the laree τιwertaintics, the correlation length of the X-rav clusters is Neher in amplitude compared to Croft et al. ("," Despite the large uncertainties, the correlation length of the X-ray clusters is higher in amplitude compared to Croft et al. ("
1997)s expectation.,1997)'s expectation.
 We couclude tha the Abell aud the APM clusters do have CFs statisically cousistent with each other and show a simular riciness dependence relation of the clustering streneth., We conclude that the Abell and the APM clusters do have CFs statistically consistent with each other and show a similar richness dependence relation of the clustering strength.
 It s1ould. be again emphasized that our results have becu obtained bv applving the sale method of analyzing the observational data and calculating the CT., It should be again emphasized that our results have been obtained by applying the same method of analyzing the observational data and calculating the CF.
The magnetosphere of a magnetar provides a particularly interesting medium for the propagation of electromagnetic waves.,The magnetosphere of a magnetar provides a particularly interesting medium for the propagation of electromagnetic waves.
 Magnetars are characterized by exceptionally. large magnetic fields that can be several times larger than the «quantum critical field strength. (2)..., Magnetars are characterized by exceptionally large magnetic fields that can be several times larger than the quantum critical field strength \citep{mereghetti-2008}.
 Because the magnetic fieles are so laree. the Luetuations of the vacuum of quantunm electrodynamies (QED) inlluence the propagation of light.," Because the magnetic fields are so large, the fluctuations of the vacuum of quantum electrodynamics (QED) influence the propagation of light."
 Specifically. the vacuum clleets add nonlinear terms to the wave equations of light in the presence large magnetic fields.," Specifically, the vacuum effects add nonlinear terms to the wave equations of light in the presence large magnetic fields."
 Ln addition. the magnetosphere of a magnetar contains a plasma which alters the clispersion relationship for light.," In addition, the magnetosphere of a magnetar contains a plasma which alters the dispersion relationship for light."
 Because of the unique optical conditions in the magnetospheres of magnetars. they. provide excellent arenas to explore nonlinear vacuum elfects arising due to quantum electrodynamies.," Because of the unique optical conditions in the magnetospheres of magnetars, they provide excellent arenas to explore nonlinear vacuum effects arising due to quantum electrodynamics."
 The influence of QED vacuum cllects from. strong magnetic fields in the vicinities of magnetized stars has oeviouslv. been studied by several authors., The influence of QED vacuum effects from strong magnetic fields in the vicinities of magnetized stars has previously been studied by several authors.
 The combined QED vacuum and plasma medium is discussed in detail in he context of neutron stars in 7.., The combined QED vacuum and plasma medium is discussed in detail in the context of neutron stars in \citet{meszarosbook}.
 Vacuum effects have been ound to dominate the polarization properties and transport of X-ravs in the strong magnetic fields near neutron stars (222777).," Vacuum effects have been found to dominate the polarization properties and transport of X-rays in the strong magnetic fields near neutron stars \citep{PhysRevD.19.3565, PhysRevLett.41.1544, 1981ApJ...251..695M,
 1980ApJ...238.1066M, 1983ZhETF..84.1217G}."
 Detailed consideration of magnetic vacuum elfects is therefore critical to an understanding of emissions [roni uehly magnetized stars., Detailed consideration of magnetic vacuum effects is therefore critical to an understanding of emissions from highly magnetized stars.
 Alost stuclies of waves in systems including plasmas or vacuum effects approach the problem. perturbatively. which imits the applicability of their results.," Most studies of waves in systems including plasmas or vacuum effects approach the problem perturbatively, which limits the applicability of their results."
 The purpose of the esent paper is to examine the combined impact of the QLD vacuum and a magnetized plasma using nonpoerturbative methods to fully preserve the nonlinear interaction between the fields., The purpose of the present paper is to examine the combined impact of the QED vacuum and a magnetized plasma using nonperturbative methods to fully preserve the nonlinear interaction between the fields.
 Neutron stars may be capable of producing very intense clectromagnetic waves. comparable to the ambient magnetic [ield.," Neutron stars may be capable of producing very intense electromagnetic waves, comparable to the ambient magnetic field."
 For example. a coupling. between plasma waves ancl seismic activity in the crust could. produce an Alfvénn wave with a very large amplitude (22)...," For example, a coupling between plasma waves and seismic activity in the crust could produce an Alfvénn wave with a very large amplitude \citep{1989ApJ...343..839B,1995MNRAS.275..255T}."
 Leven if they may. not be produce directly. electromagnetic waves naturally clevelop through he interactions between Alfvénn waves.," Even if they may not be produced directly, electromagnetic waves naturally develop through the interactions between Alfvénn waves."
 To lowest order in the size of the wave. Alfvénn waves do πο suller from shock formation (7) whereas electromagneic waves do (22): therefore. how to stabilise the propagation of the the latter is the focus of this paper.," To lowest order in the size of the wave, Alfvénn waves do not suffer from shock formation \citep{Thom98} whereas electromagnetic waves do \citep{heyl1998electromagnetic,Heyl98mhd}; therefore, how to stabilise the propagation of the the latter is the focus of this paper."
 lt such a magnetospheric disturbance results in electromagneic. waves of sullicienthy large amplitude and low [recueney. then nonperturbative techniques. are required. to characterize the wave.," If such a magnetospheric disturbance results in electromagnetic waves of sufficiently large amplitude and low frequency, then nonperturbative techniques are required to characterize the wave."
 The importance. of studying suc 1a system nonperturbatively is particularly well illustrated by the fact that some nonlinear wave xhaviour is 'undamentallvy nonperturbative. as is generally jo CASE WLth solitons (2)...," The importance of studying such a system nonperturbatively is particularly well illustrated by the fact that some nonlinear wave behaviour is fundamentally nonperturbative, as is generally the case with solitons \citep{rajaraman1982solitons}."
" In. order to. handle. the oblem nonperturbatively. we choose to study waves whose μα»wetime cle»ndence is described by the parameter 5= οἱ, where e is a constant speed of propagation through re medium in the x-direction."," In order to handle the problem nonperturbatively, we choose to study waves whose spacetime dependence is described by the parameter $S=x-vt$ , where $v$ is a constant speed of propagation through the medium in the $\bhat{x}$ -direction."
 In the study of waves. one normally chooses the ansatz οἱHaodlkxi ," In the study of waves, one normally chooses the ansatz $e^{i(\omega t - {\bf k}\cdot{\bf x})}$ ."
llowever. in this xeture. a numerical study would. typically treat the self-interactions «cX the electromagnetic field. by summing the interactions of finitely many Fourier modes.," However, in this picture, a numerical study would typically treat the self-interactions of the electromagnetic field by summing the interactions of finitely many Fourier modes."
 So. this ansatz conllicts with our goal of stuclving the nonlinear interactions o all. orders.," So, this ansatz conflicts with our goal of studying the nonlinear interactions to all orders."
 In contrast. a plane wave ansatz given hy ssoel allows us to study a simple wave structure to all orders withot(t any reference to individual Fourier modes.," In contrast, a plane wave ansatz given by $S=x-vt$ allows us to study a simple wave structure to all orders without any reference to individual Fourier modes."
 We mock| a magnetar atmosphereby including the, We model a magnetar atmosphereby including the
"For a Ilubble constant. denoted. Ly=(100kms!Mpe.1). we wn ihe WALIAP- (plus BAO+ Ly) parameters. Ομ=0.02255+0.00054 and Q,,47=0.1352+40.0036 (INomatsu 22011) relative to a critical density p,=L.8785x1077/?> g .","For a Hubble constant denoted $H_0 = (100~ {\rm km~s}^{-1}~{\rm Mpc}^{-1}) \, h$, we adopt the WMAP-7 (plus BAO+ $H_0$ ) parameters, $\Omega_b h^2 = 0.02255\pm0.00054$ and $\Omega_m h^2 = 0.1352\pm0.0036$ (Komatsu 2011) relative to a critical density $\rho_{\rm cr} = 1.8785 \times 10^{-29}~h^2$ g $^{-3}$."
" From the corresponding helium mass fraction Y=0.2477dk0.0029 (Peimbert 22007). we adopt a mean hydrogen imunber density. In a fully ionized IGA. the CMD optical depth back to 2,4 can be written as the integral ol n.cqdít. the electron density times the Thomson cross section along proper length. for a standard ΛΟΡΝΤ cosmology (Q,,+Q4= 1) with Hs)=Ho|[Q,,(1+zyeyQj)− ↴⊺∐↕⊳∖⇁↕↕∐≼↲≸↽↔↴↕⋅≀↧↴↥≺∢≀↧↴"," From the corresponding helium mass fraction $Y = 0.2477\pm0.0029$ (Peimbert 2007), we adopt a mean hydrogen number density, In a fully ionized IGM, the CMB optical depth back to $z_{\rm rei}$ can be written as the integral of $n_e \sigma_T d \ell$, the electron density times the Thomson cross section along proper length, for a standard $\Lambda$ CDM cosmology $\Omega_m + \Omega_{\Lambda} = 1$ ) with $H(z) = H_0 [\Omega_m (1+z)^3 + \Omega_{\Lambda}]^{1/2}$."
"∐∣↽≻≼↲≼⇂∪∐≼↲≀↧↴∐≀↧↴↥⋡∖↽∐≺∢≀↧↴∐∡∖≼⋝⊳↔∐∏∐≪↽∖∖≼↲∐↳≀↧↴∥↲⋝∖⊽≀↧↴∐∃∩∩⊾⋝⋅ In the high-redshift limit. when O,,(1+2)?2»O4. this expression simplifies to independent of  to lowest order."," This integral can be done analytically (Shull Venkatesan 2008), In the high-redshift limit, when $\Omega_m (1+z)^3 \gg \Omega_{\Lambda}$, this expression simplifies to independent of $h$ to lowest order."
" The helium ancl electron densities are written my=yn and ο,=ng(l-dy) lor sinely ionized helium. where y=nyc/ng(Y/4)/(1—Y)220.0823 bv number."," The helium and electron densities are written $n_{\rm He} = y n_H$ and $n_e = n_H (1+y)$ for singly ionized helium, where $y = n_{\rm He}/n_{\rm H} = (Y/4)/(1-Y) \approx 0.0823$ by number."
" To these formulae. we add Az,2 0.002. from electrons donated bv rreionized αἱ 2<3 (Shull 22010)."," To these formulae, we add $\Delta \tau_e \approx 0.002$ , from electrons donated by reionized at $z \leq 3$ (Shull 2010)."
" Helium therefore contributes ~&8% to 7,. and a fully ionized IGM produces 7,=0.050. 0.060. and 0.070 back to redshifts τα=7. 8. and 9. respectively."," Helium therefore contributes $\sim$ to $\tau_e$, and a fully ionized IGM produces $\tau_e = 0.050$, 0.060, and 0.070 back to redshifts $z_{\rm rei} = 7$, 8, and 9, respectively."
 A comoving volume of 1. Mpc? contains Vy=5.6x10° hydrogen atoms., A comoving volume of 1 $^3$ contains $N_H = 5.6 \times 10^{66}$ hydrogen atoms.
" Our simple ionization criterion requires a SFR densitv that produces a number of LvC photons equal to Ny over a hydrogen recombination time. free=|n,aTCy]5"," Our simple ionization criterion requires a SFR density that produces a number of LyC photons equal to $N_H$ over a hydrogen recombination time, $t_{\rm rec} = [n_e \alpha_H^{(B)} C_H]^{-1}$."
" The hydrogen Case-B recombination rate coefficient k Ferland 2006)is a(T)z(2.59x10Pem?s57,08), scaled to an LGM temperature MUNT=ndo(10!“ ΤΙ."," The hydrogen Case-B recombination rate coefficient (Osterbrock Ferland 2006) is $\alpha_H^{(B)}(T) \approx (2.59 \times 10^{-13}~{\rm cm}^3~{\rm s}^{-1}) T_4^{-0.845}$, scaled to an IGM temperature $T = (10^4~{\rm K})T_4$ ."
" For typical IGM ionization histories and photoelectric heating rates. numerical ions "" diffuse photoionized filaments of hydrogen havetemperatures ranging Irom5000 IX ""Mto20.000 Ix. (Davé"," For typical IGM ionization histories and photoelectric heating rates, numerical simulations predict that diffuse photoionized filaments of hydrogen havetemperatures ranging from 5000 K to 20,000 K (Davé"
D = 2.6. and a particular seed whose((7.4).. (744))) point is low in Figure 4..,"$D$ = 2.6, and a particular seed whose, ) point is low in Figure \ref{fig4}."
 The effects of g are minimal on the locus of the lower envelope of the individual points: (he minimunm e is achieved [or g>0.5., The effects of $g$ are minimal on the locus of the lower envelope of the individual points; the minimum $a$ is achieved for $g\ge0.5$.
 We tried such a wide range of models that we doubt (hat there is an drastically lower. (, We tried such a wide range of models that we doubt that there is an drastically lower. (
d) No useful estimate of is possible because inefficient scattering can be produced bv exireme clumping (as small a D as allowed) and with no uniform component.,d) No useful estimate of is possible because inefficient scattering can be produced by extreme clumping (as small a $D$ as allowed) and with no uniform component.
 For D = 2.3. an e Lis needed to fit for some distributions of clumps.," For $D$ = 2.3, an $a\sim1$ is needed to fit for some distributions of clumps."
 For D = 2.6. is about 0.8.," For $D$ = 2.6, is about 0.8."
 The dust geometry (hat produced did not allow @ to be above 0.6. but il was chosen to have especially efficient scattering.," The dust geometry that produced did not allow $a$ to be above 0.6, but it was chosen to have especially efficient scattering."
 Alternatively. very optically thick models that have low stellar extinctions as seen from some viewing angles can fit observed fIuxes with very high albedos.," Alternatively, very optically thick models that have low stellar extinctions as seen from some viewing angles can fit observed fluxes with very high albedos."
 For instance. we have fitted the point in Figure 1. withmoclels.. = 8. « = 0.85.," For instance, we have fitted the point in Figure \ref{fig1} with, = 8, $a$ = 0.85."
 We have no doubt that many optically Chick hierarchical models could fit the observations as well., We have no doubt that many optically thick hierarchical models could fit the observations as well.
 Perhaps such extreme models could be ruled out with Eu-inlrared (FUR) fluxes. although the low absorption tends (ο compensate lor the hieh optical depth.," Perhaps such extreme models could be ruled out with far-infrared (FIR) fluxes, although the low absorption tends to compensate for the high optical depth."
 Furthermore. the FIR arises [rom dust surrounding the star in all directions. while the scattering is mainly [rom dust close to the line of sight.," Furthermore, the FIR arises from dust surrounding the star in all directions, while the scattering is mainly from dust close to the line of sight."
 In any case. these models are hardly reasonable on physical grounds.," In any case, these models are hardly reasonable on physical grounds."
 2 and WUT observed at (Wilt οἱ al., and HUT observed at (Witt et al.
 1993)., 1993).
 Uniform models predict e 70.45 if of the stellar extinction occurs within the nebula., Uniform models predict $a\sim$ 0.45 if of the stellar extinction occurs within the nebula.
 IBerarchical models can fit the observation (not plotted. but in the upper right corner of Figures 1. 3) with α = 0.8 with τιZ4.," Hierarchical models can fit the observation (not plotted, but in the upper right corner of Figures 1 – 3) with $a$ = 0.8 with $\tau_0\gtrsim4$."
 Of course. we make no claim that such a high e is correct.," Of course, we make no claim that such a high $a$ is correct."
 On the other haad. we can fit (he point with e = 0.4. lower than the uniform models.," On the other hand, we can fit the point with $a$ = 0.4, lower than the uniform models."
 Once again we see that the observations are subject to a very ambiguous interpretation., Once again we see that the observations are subject to a very ambiguous interpretation.
 Durgh. MeCandliss. Feldman (2002) used a uniform model for 220223 with = 2.4.," Burgh, McCandliss, Feldman (2002) used a uniform model for 2023 with = 2.4."
 They derived an albedo of 0.39(2 atAA..., They derived an albedo of $0.39^{+0.12}_{-0.05}$ at.
 Our hierarchical model shown in Figure L.. with «à = 0.6. could accommodate their observations. and others that scatter light inefliciently could have αο»1.," Our hierarchical model shown in Figure \ref{fig1}, with $a$ = 0.6, could accommodate their observations, and others that scatter light inefficiently could have $a\sim1$."
 Figure G shows the albedos derived. [rom uniform models. using the scattering and ex(netions from (he hierarchical model (a.g.D.τι) = 11). plotted against the stellar extinctions at each viewing angle.," Figure \ref{fig6} shows the albedos derived from uniform models, using the scattering and extinctions from the hierarchical model $(a,\,g,\,D,\,\tau_0)$ = 1), plotted against the stellar extinctions at each viewing angle."
 The albedo used to generate the scattered [Iuxes and extinctions. 0.6. is marked by the dashed line.," The albedo used to generate the scattered fluxes and extinctions, 0.6, is marked by the dashed line."
 The distribution of points for the hierarchical model with = 2 is virtually identical., The distribution of points for the hierarchical model with = 2 is virtually identical.
 We see that the minimum « derived [from uniform modelsis 0-0.32: (the average for 0.6<m1.6 is 70.42.," We see that the minimum $a$ derived from uniform modelsis $\sim$ 0.32; the average for $0.6\le\tau_{\rm
ext}\le1.6$ is $\sim$ 0.42."
 At moderate extinction. leading to bright," At moderate extinction, leading to bright"
Iuub position and for determing the coordinates ou the Sun in the DEI images.,limb position and for determining the coordinates on the Sun in the BFI images.
 For the lelioscisimology analysis we used the Ca IT data series., For the helioseismology analysis we used the Ca H data series.
 We first aligned the images and determined the helioeraphic coordinates of cach image., We first aligned the images and determined the heliographic coordinates of each image.
 Then. we chose several poiuts ou the Suu within the SOT field of view. ax the ceutral points for the Postel’s projection (see below).," Then, we chose several points on the Sun within the SOT field of view, as the central points for the Postel's projection (see below)."
 We tracked the central poiuts with the local differcutial rotation rate (Snodgrass1981).. aud remapped cach image into the heliographie coordinates by using the Postel’s projection.," We tracked the central points with the local differential rotation rate \citep{1984SoPh...94...13S}, and remapped each image into the heliographic coordinates by using the Postel's projection."
 Using the tracked aud remapped nuages. we carried out the time-cistance analysis (Duvalletal.1997:I&osovichev&DuvallL997) το measure variations of acoustic travel times and detect subsurface flow structures.," Using the tracked and remapped images, we carried out the time-distance analysis \citep{1997SoPh..170...63D, 1997ASSL..225..241K}
 to measure variations of acoustic travel times and detect subsurface flow structures."
 The SOT observations of the regions close to the limb were carried out with fixed telescope pointines., The SOT observations of the regions close to the limb were carried out with fixed telescope pointings.
 Although he image stabilization svstem. the correlation tracker (CT: Shimizuetal. 2008)). was turned on. the ficld of view was graduallv drifting toward the disk ceuter mainly duc o the limb darkening.," Although the image stabilization system, the correlation tracker (CT; \citealt{2008SoPh..249..221S}) ), was turned on, the field of view was gradually drifting toward the disk center mainly due to the limb darkening."
" Therefore. we aligned the images by ensunueg that the limb stavs in the same position iu the ficld of view, aud then determined the solar coordinates of cach image."," Therefore, we aligned the images by ensuring that the limb stays in the same position in the field of view, and then determined the solar coordinates of each image."
 When we observe resious near the solar limb. oreshorteniug is significant. and appropriate remapping is required. for the data analysis.," When we observe regions near the solar limb, foreshortening is significant, and appropriate remapping is required for the data analysis."
 We used the Postel’s azimuthal equidistaut projection (c.¢..Dogartetal.1995:Zaatrictal. 2008)..," We used the Postel's azimuthal equidistant projection \citep[e.g.,][]{1995ESASP.376b.147B,2008JPhCS.118a2090Z}."
 The projected map is what we would observe bv looking directly from above the region., The projected map is what we would observe by looking directly from above the region.
 For he dataset taken at the disk center. however. we did rot project the muages. because the distortion effect is ieelieible there.," For the dataset taken at the disk center, however, we did not project the images, because the distortion effect is negligible there."
 Also. since for the disk ceuter dataset he SOT observed the region tracking its ceuter with the rotation rate of the Sun. we did not apply any further racking.," Also, since for the disk center dataset the SOT observed the region tracking its center with the rotation rate of the Sun, we did not apply any further tracking."
" For the timedistance analysis. cross-correlation ""unctious of the surface wavefield of the 5-10àn oscillations were caleulated from the tracked aud projected datasets."," For the time–distance analysis, cross-correlation functions of the surface wavefield of the 5-min oscillations were calculated from the tracked and projected datasets."
 We measured the acoustic (phase) travel times for several distances bv fitting a Cabor-type wavelet to the cross-correlation functious (I[&osovichev&DuvallLO97).., We measured the acoustic (phase) travel times for several distances by fitting a Gabor-type wavelet to the cross-correlation functions \citep{1997ASSL..225..241K}.
 For cach distance A. we averaged the oscillation signals over an amuulus of the radius A around a target point. aud then cross-correlated the averaged signals with the oscillation sienal observed at the target point.," For each distance $\Delta$, we averaged the oscillation signals over an annulus of the radius $\Delta$ around a target point, and then cross-correlated the averaged signals with the oscillation signal observed at the target point."
 We obtained outward (from the target to the auuulus) aud nsvard (from the anuuulus to the target) travel times at each point in the field of view for a set of travel distances A., We obtained outward (from the target to the annulus) and inward (from the annulus to the target) travel times at each point in the field of view for a set of travel distances $\Delta$.
 The differeuce of the outward and inward travel times indicates the diverging(converging flow around the target poiut iu the region of wave propagation below the simface., The difference of the outward and inward travel times indicates the diverging/converging flow around the target point in the region of wave propagation below the surface.
 Note that for iuproviug the signal-to-noise ratio we applied phase-speed filters following Duvalletal. (1997).. , Note that for improving the signal-to-noise ratio we applied phase-speed filters following \citet{1997SoPh..170...63D}. .
The outwardinward travel-time difference maps of the north polar region are illustrated in Figure 1.., The outward–inward travel-time difference maps of the north polar region are illustrated in Figure \ref{fig:PL_tmapp4}. .
" Panels (a). (b). aud (0) show the travel times for the distances. A. of S.L. TL. aud 21.1 Maii. (or 0.77. 1.27. and 1.77) respectively,"," Panels (a), (b), and (c) show the travel times for the distances, $\Delta$, of $8.4$, $14.4$, and $21.1$ Mm, (or $0.7^\circ$, $1.2^\circ$, and $1.7^\circ$ ) respectively."
 The black regions. where the outward travel times are shorter than the iwward travel times. indicate divergiug flows. while the white regions correspond to convereiue flows.," The black regions, where the outward travel times are shorter than the inward travel times, indicate diverging flows, while the white regions correspond to converging flows."
 The dark cells with white bouudaries are supereranular cells., The dark cells with white boundaries are supergranular cells.
 Iu the maps for the largest auuuli (panel c). the supergranular patterus are rather faint.," In the maps for the largest annuli (panel c), the supergranular patterns are rather faint."
 Judging from the penetratius depths of the acoustic ravs. this indicates that the supergranules are not much deeper than. sav. 5 Mui which is consistent with other helioscisinoloey results (0.9...Woodard2007:Sekiietal.2007).," Judging from the penetrating depths of the acoustic rays, this indicates that the supergranules are not much deeper than, say, $5$ Mm, which is consistent with other helioseismology results \citep[e.g.,][]{ 2007ApJ...668.1189W,2007PASJ...59..637S}."
 Tereatter. we use oulv the travel times for A=11.1 Nn. because these travel-time maps (panel b) show the supergrauular patterus most clearly.," Hereafter, we use only the travel times for $\Delta=14.4$ Mm, because these travel-time maps (panel b) show the supergranular patterns most clearly."
 Figure ldd shows a [-hour averaged intensity nuage m the Ca II line of the north polar region., Figure \ref{fig:PL_tmapp4}d d shows a 4-hour averaged intensity image in the Ca H line of the north polar region.
 It is well-known that 3upergranulation is seen as a bright network structure in the chromosphere because magnetic field is concentrated at the supererauulation boundaries., It is well-known that supergranulation is seen as a bright network structure in the chromosphere because magnetic field is concentrated at the supergranulation boundaries.
 Iu this chromospheric iuage the network brighteniugs. though faint. are seen. and their distribution is consistent with the supereranular )undaries detected in the outwardnmsvard travel-timie naps (panels a to c).," In this chromospheric image the network brightenings, though faint, are seen, and their distribution is consistent with the supergranular boundaries detected in the outward–inward travel-time maps (panels a to c)."
 Iu Figure 1.. the outwardinward traveltime difference naps of the south polar region (panel e). a region near he east lub (panel f) and a region around the disk. center (panel ο) are shown.," In Figure \ref{fig:PL_tmapp4}, the outward–inward travel-time difference maps of the south polar region (panel e), a region near the east limb (panel f), and a region around the disk center (panel g) are shown."
 Figure 2. shows the mine outwardnmsvurd traveltine difference maps of the south vole obtained for cach of the nine observing ruus in March of 2010., Figure \ref{fig:PL_SP9} shows the nine outward–inward travel-time difference maps of the south pole obtained for each of the nine observing runs in March of 2010.
 Iu these maps. the supererauular patterus in both volar regions aud the east lib region are seen as clearly as dn the travel time map of the disk ceuter.," In these maps, the supergranular patterns in both polar regions and the east limb region are seen as clearly as in the travel time map of the disk center."
 In the ligh-atitude region. however. the cells seem to align iu the direction roughly from north to south. with some tilt.," In the high-latitude region, however, the cells seem to align in the direction roughly from north to south, with some tilt."
 The ‘aliguumeut” patterns exist in both of the north aud south volar regions: Figure 2. suggests that the alieniaeut! is xobablv a characteristic structure in the polar regions., The `alignment' patterns exist in both of the north and south polar regions; Figure \ref{fig:PL_SP9} suggests that the `alignment' is probably a characteristic structure in the polar regions.
 There also seem to be areas with weak divereing flows )tween the aligned cells., There also seem to be areas with weak diverging flows between the aligned cells.
 The aliguiment seems to be coherent for a distance of 2-3 cells., The alignment seems to be coherent for a distance of 2-3 cells.
 For a quantitative characterization of the aliguineut. we calculated two-dimensional correlations of the travel-time difference maps.," For a quantitative characterization of the alignment, we calculated two-dimensional correlations of the travel-time difference maps."
 Figure 3. shows the correlation functions of the traveltime differcuce maps for the north polar region and the lower-latitude regions as well., Figure \ref{fig:PL_cor} shows the correlation functions of the travel-time difference maps for the north polar region and the lower-latitude regions as well.
 The correlation function of the north polar datasets (paucl d) does indicate a striking alieunnmient iu the map. ie.. the correlation is the strongest iu the northeast-soutlwest direction.," The correlation function of the north polar datasets (panel d) does indicate a striking alignment in the map, i.e., the correlation is the strongest in the northeast-southwest direction."
 Ou the other laud. for the disk ceuter aud the cast lah region maps (panels e aud f) the correlation shows no particular preference iu direction: uamely it shows a nearly random distribution.," On the other hand, for the disk center and the east limb region maps (panels e and f) the correlation shows no particular preference in direction; namely, it shows a nearly random distribution."
" Actually. the strength of the ""alignment? differs from dataset to dataset."," Actually, the strength of the `alignment' differs from dataset to dataset."
 The aliguaent. however. does exist in the averaged correlation functions of the travel-time difference maps. calculated for different latitudes (Figure 1)).," The alignment, however, does exist in the averaged correlation functions of the travel-time difference maps, calculated for different latitudes (Figure \ref{fig:PL_corav}) )."
 The aligumieut is most notable at the highest latitude. as shown in the bottom panel.," The alignment is most notable at the highest latitude, as shown in the bottom panel."
 Thealiguiment is alinost in the north-south direction.but not precisely.," Thealignment is almost in the north-south direction,but not precisely."
 We estimated the mean direction and its variance for the nine datasets., We estimated the mean direction and its variance for the nine datasets.
 We measured the peak position angle aloug a 20-Ab, We measured the peak position angle along a 20-Mm
 We measured the peak position angle aloug a 20-Abn, We measured the peak position angle along a 20-Mm
Since the FORSI spectra did not include Hc. we obtained two additional low-dispersion spectra with the ESO Paint Object Spectrograph and Camera (EFOSC?) attached to the New Technology Telescope (NTT) at La Silla Observatory Οἱ UT 2008 Oct 23.,"Since the FORS1 spectra did not include $\alpha$, we obtained two additional low-dispersion spectra with the ESO Faint Object Spectrograph and Camera (EFOSC2) attached to the New Technology Telescope (NTT) at La Silla Observatory on UT 2008 Oct 23."
 We used Grism 11 which has 300 lines per mm and a blaze wavelength of 4000A., We used Grism 11 which has 300 lines per mm and a blaze wavelength of 4000.
. The slit-width was set to ] aresecond. which resulted in a spectral resolution of 14A.," The slit-width was set to 1 arcsecond, which resulted in a spectral resolution of $\sim 14$."
. The exposure time of each spectrum was 1500 seconds., The exposure time of each spectrum was 1500 seconds.
 Observations were carried out at the parallactic angle and were flux calibrated with the flux standard Feige 110., Observations were carried out at the parallactic angle and were flux calibrated with the flux standard Feige 110.
 Figure 1. compares the low-resolution spectrum ofII lines obtained with EFOSC? to the higher resolution spectrum of FORSI., Figure \ref{fig-spol} compares the low-resolution spectrum of lines obtained with EFOSC2 to the higher resolution spectrum of FORS1.
 The flux and circular polarization spectra clearly show the «c components. proving NLTT 10480 to be magnetic.," The flux and circular polarization spectra clearly show the $\sigma$ components, proving NLTT 10480 to be magnetic."
 Finally. we obtained a set of echelle spectra of NLTT 10480 with the X-shooter spectrograph attached to the UT2 (Kueyen) at Paranal Observatory.," Finally, we obtained a set of echelle spectra of NLTT 10480 with the X-shooter spectrograph attached to the UT2 (Kueyen) at Paranal Observatory."
 The spectra were obtained at four epochs (UT 2010 Dee 10. 2011 Jan 9 and 26. and March 3).," The spectra were obtained at four epochs (UT 2010 Dec 10, 2011 Jan 9 and 26, and March 3)."
 The 2011 Mar 3 spectrum was of much poorer quality and was excluded from the analysis., The 2011 Mar 3 spectrum was of much poorer quality and was excluded from the analysis.
 The spectra were obtained with the slit-width set to 0.5. 0.9. and 0.6 aresecond for the UVB. VIS. and NIR arms. respectively.," The spectra were obtained with the slit-width set to 0.5, 0.9, and 0.6 arcsecond for the UVB, VIS, and NIR arms, respectively."
 This set-up delivered a resolving power of 9100 for UVB. 8800 for VIS. and 6200 for NIR.," This set-up delivered a resolving power of 9100 for UVB, 8800 for VIS, and 6200 for NIR."
 The exposure time for each exposure was 2400 seconds., The exposure time for each exposure was 2400 seconds.
 Table | summarizes our spectroscopic observations., Table \ref{tbl-log} summarizes our spectroscopic observations.
 The signal-to-noise ratio in. the summed X-shooter spectrum is S/Nx53 per binned-pixel at4000A.. while it is +120 in the summed FORS]I spectrum and =65 in the summed EFOSC2 spectrum at the same wavelength.," The signal-to-noise ratio in the summed X-shooter spectrum is $S/N\approx53$ per binned-pixel at, while it is $\approx 120$ in the summed FORS1 spectrum and $\approx 65$ in the summed EFOSC2 spectrum at the same wavelength."
 We searched for photometric measurements using VizieR. The Two Micron. All Sky Survey (2MASS) listed infrared JHK magnitudes. but only the 7 magnitude was of acceptable quality.," We searched for photometric measurements using VizieR. The Two Micron All Sky Survey (2MASS) listed infrared $JHK$ magnitudes, but only the $J$ magnitude was of acceptable quality."
 We also used the acquisition images from the X-shooter observations to estimate à V magnitude for NLTT 10480., We also used the acquisition images from the X-shooter observations to estimate a $V$ magnitude for NLTT 10480.
 We used 11 acquisition images of Feige 110 obtained between UT 2010 Dec 10 and 2011 Jan 1. and set the zero point.," We used 11 acquisition images of Feige 110 obtained between UT 2010 Dec 10 and 2011 Jan 1, and set the zero point."
 Next. we determined an average V magnitude for NLTT 10480 using our five acquisition images.," Next, we determined an average $V$ magnitude for NLTT 10480 using our five acquisition images."
 We employed the atmospheric extinction. table of Patatetal. (2011).., We employed the atmospheric extinction table of \citet{pat2011}. .
 Table 2. lists the photometric measurements., Table \ref{tbl-phot} lists the photometric measurements.
 The SPM Catalog provides a photographic B magnitude (18.08+ 0.16)., The SPM Catalog provides a photographic $B$ magnitude $18.08\pm0.16$ ).
 However. due to large uncertainties in the SPM and other photographic magnitudes. these are not as useful as our V magnitude and the 2MASS J magnitudes.," However, due to large uncertainties in the SPM and other photographic magnitudes, these are not as useful as our $V$ magnitude and the 2MASS $J$ magnitudes."
 The 2MASS K magnitude is unreliable and the H magnitude is uncertain., The 2MASS $K$ magnitude is unreliable and the $H$ magnitude is uncertain.
 The index B—V=0.59+0.17 loosely constrains the temperature in the range 5100€Tay<6700 K. but the more precise index V—Jz1.49+0.09 implies that NLTT 10480 ts à cool white dwarf with Zrz5050+150 K (see Table 3 and Sect.," The index $B-V=0.59\pm0.17$ loosely constrains the temperature in the range $5\,100\la T_{\rm eff}\la 6\,700$ K, but the more precise index $V-J=1.49\pm0.09$ implies that NLTT 10480 is a cool white dwarf with $T_{\rm eff}\approx 5\,050\pm150$ K (see Table \ref{tbl-model} and Sect."
 3.1)., 3.1).
 NLTT 10480 is also characterized by a large proper-motion of ~0.5” yyr! (Table 2))., NLTT 10480 is also characterized by a large proper-motion of $\sim0.5\arcsec$ $^{-1}$ (Table \ref{tbl-phot}) ).
 The kinematical properties were determined using the proper-motion and the X-shooter radial velocity measurement (see Sect., The kinematical properties were determined using the proper-motion and the X-shooter radial velocity measurement (see Sect.
 4)., 4).
 We calculated a grid of model atmospheres for cool hydrogen- white dwarfs., We calculated a grid of model atmospheres for cool hydrogen-rich white dwarfs.
 The models are in convective and radiative equilibrium with the total flux converged to better than in all layers., The models are in convective and radiative equilibrium with the total flux converged to better than in all layers.
 The model grid covers the effective temperature range 4900<Tayx6000 K in 100 Ksteps and the surface gravity range 7.5.€logg<8.5 in steps of 0.25 dex.," The model grid covers the effective temperature range $4\,900\le T_{\rm eff}\le 6\,000$ K in 100 Ksteps and the surface gravity range $7.5\le \log{g}\le8.5$ in steps of 0.25 dex."
 The adopted treatment of the convective energy transport, The adopted treatment of the convective energy transport
using (extrapolated) radio luminosity functions for several different populations of sources.,using (extrapolated) radio luminosity functions for several different populations of sources.
" In this model, radio sources dominate the counts above ~200 mJy, while below sources dominate down to beyond our detection threshold."," In this model, radio sources dominate the counts above $\sim 200$ mJy, while below sources dominate down to beyond our detection threshold."
" Figure 4 shows an approximate agreement between the model and our observations, although the average power-law slope between 10 and 200 mJy of 0.83 is flatter than the value of 0.91 derived from our data."," Figure \ref{fig:bootes_dif_source_counts} shows an approximate agreement between the model and our observations, although the average power-law slope between 10 and 200 mJy of 0.83 is flatter than the value of 0.91 derived from our data."
 For the models that are discussed here we find that all predicted source counts deviate from the observed source counts., For the models that are discussed here we find that all predicted source counts deviate from the observed source counts.
 The model source count slopes appear to be influenced mostly by the assumed contribution of sources., The model source count slopes appear to be influenced mostly by the assumed contribution of sources.
" On the other hand, the observational results from ? also deviate from our result."," On the other hand, the observational results from \citet{ishwara2010} also deviate from our result."
 More source counts from similar deep surveys at this frequency are needed to put stronger constraints on the source count models., More source counts from similar deep surveys at this frequency are needed to put stronger constraints on the source count models.
" Preliminary source counts from a deep GMRT 153 MHz survey three times the area of our current survey (>1000 sources; Intema et al.,"," Preliminary source counts from a deep GMRT 153 MHz survey three times the area of our current survey $>1000$ sources; Intema et al.,"
 in preparation) match up closely with our current results., in preparation) match up closely with our current results.
 And future source counts from the ongoing GMRT 153 MHz sky survey (TGSS) should provide a more robust reference to compare the source count models and our results against., And future source counts from the ongoing GMRT 153 MHz sky survey (TGSS) should provide a more robust reference to compare the source count models and our results against.
" Because of the good match in resolution between the GMRT 153 MHz image and the deep WSRT 1.4 GHz image from ?,, we can accurately determine spectral indices over a decade in frequency."," Because of the good match in resolution between the GMRT 153 MHz image and the deep WSRT 1.4 GHz image from \citet{devries2002}, we can accurately determine spectral indices over a decade in frequency."
 The survey depths at 153 MHz and 1.4 GHz are equal for sources with a spectral index of —1.6., The survey depths at 153 MHz and 1.4 GHz are equal for sources with a spectral index of $-1.6$.
" Due to the high detection rate of 1.4 GHz sources at 153 MHz positions (Section 3.2)), we do an automated search for 1.4 GHz counterparts within 25"" of the 153 MHz sources and ignore all sources for which we don't find counterparts."," Due to the high detection rate of 1.4 GHz sources at 153 MHz positions (Section \ref{sec:bootes_compl}) ), we do an automated search for 1.4 GHz counterparts within $25\arcsec$ of the 153 MHz sources and ignore all sources for which we don't find counterparts."
 The spectral indices of 417 matched sources are plotted in Figure 5.., The spectral indices of 417 matched sources are plotted in Figure \ref{fig:bootes_spectral}.
" We find à median spectral index of —0.76, which is similar to the median values of —0.79 (?),, —0.85 (?),, —0.82 (7) and —0.78 (?) found for similar high-resolution, low-frequency surveys at 74 and 153 MHz."," We find a median spectral index of $-0.76$ , which is similar to the median values of $-0.79$ \citep{cohen2004}, $-0.85$ \citep{ishwara2007}, $-0.82$ \citep{sirothia2009} and $-0.78$ \citep{ishwara2010} found for similar high-resolution, low-frequency surveys at 74 and 153 MHz."
" The small differences are most likely caused by differences in the completeness limits of the catalogs, as the median spectral index varies with flux density (see below)."," The small differences are most likely caused by differences in the completeness limits of the catalogs, as the median spectral index varies with flux density (see below)."
" Figure 5 also plots the median spectral index in 6 logarithmic flux bins, which clearly highlights the flattening trend of the mean spectral index towards lower flux densities."," Figure \ref{fig:bootes_spectral} also plots the median spectral index in 6 logarithmic flux bins, which clearly highlights the flattening trend of the mean spectral index towards lower flux densities."
 The unique combination of our deep 153 MHz catalog and the very deep 1.4 GHz catalog makes that the median spectral index is unbiased down to the lowest 153 MHz flux densities., The unique combination of our deep 153 MHz catalog and the very deep 1.4 GHz catalog makes that the median spectral index is unbiased down to the lowest 153 MHz flux densities.
" The median spectral index is ~—0.9 for =0.5 Jy sources, and flattens to ~—0.7 for S50 mJy sources."," The median spectral index is $\sim -0.9$ for $\gtrsim 0.5$ Jy sources, and flattens to $\sim -0.7$ for $\lesssim 50$ mJy sources."
" A similar trend appears to be present in the spectral index distribution by ? for sources between 153 MHz and various frequencies (610 MHz and higher), but may be biased by catalog flux limits at the higher frequencies."," A similar trend appears to be present in the spectral index distribution by \citet{ishwara2010} for sources between 153 MHz and various frequencies (610 MHz and higher), but may be biased by catalog flux limits at the higher frequencies."
" A similar flattening trend is also seen at both lower and higher frequencies, e.g., between 74 MHz and 1.4 GHz by ? and ?,, between 1.4 GHz and 325 MHz by ?,, between 325 MHz and 1.4 GHz by ? and ?,, between 610 MHz and 1.4 GHz by ?,, and between 1.4 and 5 GHz by ?.."," A similar flattening trend is also seen at both lower and higher frequencies, e.g., between 74 MHz and 1.4 GHz by \citet{cohen2004} and \citet{tasse2006}, between 1.4 GHz and 325 MHz by \citet{devries2002}, between 325 MHz and 1.4 GHz by \citet{zhang2003} and \citet{owen2009}, between 610 MHz and 1.4 GHz by \citet{bondi2007}, and between 1.4 and 5 GHz by \citet{prandoni2006}."
" Recently, ? found that, for a near-complete sample of radio galaxies, there is no evidence for spectral steepening or flattening due to redshifted curved radio spectra."," Recently, \citet{bornancini2010} found that, for a near-complete sample of radio galaxies, there is no evidence for spectral steepening or flattening due to redshifted curved radio spectra."
" In fact, most of their sources have straight power-law spectra from 74 MHz to 4.8 GHz."," In fact, most of their sources have straight power-law spectra from 74 MHz to 4.8 GHz."
 This suggests that the observedspectral flattening towards lower flux densities results dominantly from a correlation between source luminosity and spectral index (P—a correlation)., This suggests that the observedspectral flattening towards lower flux densities results dominantly from a correlation between source luminosity and spectral index $P-\alpha$ correlation).
" This correlation is found to exist for galaxies (e.g.,?).."," This correlation is found to exist for galaxies \citep[e.g.,][]{blundell1999}."
" According to the models by ? and ?,, galaxies are the dominant 153 MHz source population in our sample at higher flux levels (20—200 mJy), which can explain part of the flattening observation."," According to the models by \citet{jackson2005} and \citet{wilman2008}, galaxies are the dominant 153 MHz source population in our sample at higher flux levels $\gtrsim 20-200$ mJy), which can explain part of the flattening observation."
" For lower flux levels, the flattening trend continues, which suggests that either galaxies are still a significant source population, or the galaxies dominate and also follow a P—a correlation."," For lower flux levels, the flattening trend continues, which suggests that either galaxies are still a significant source population, or the galaxies dominate and also follow a $P-\alpha$ correlation."
 From Figure 5 we highlight a small groupof 16 USS sources that have a spectral indices lower than —1.3., From Figure \ref{fig:bootes_spectral} we highlight a small groupof 16 USS sources that have a spectral indices lower than $-1.3$ .
 The, The
Z is sealed uuiforiulv by the same factor.,$Z$ is scaled uniformly by the same factor.
 A slightly snaller change iu Z in selected regions may also give vise to sinilar change in the resultant bhunuinositv., A slightly smaller change in $Z$ in selected regions may also give rise to similar change in the resultant luminosity.
 Frou the results presented later where we try to adjust the Z profile to match the Iuninositv. it turus out that the required maxima change in Z is not much simaller than what is indicated by this simple analysis.," From the results presented later where we try to adjust the $Z$ profile to match the luminosity, it turns out that the required maximum change in $Z$ is not much smaller than what is indicated by this simple analysis."
 For the purpose of this work we herefore estimate a reasonable error of in the huninositv arising from possible uncertainties in the heavy clement abundance and/or opacities., For the purpose of this work we therefore estimate a reasonable error of in the luminosity arising from possible uncertainties in the heavy element abundance and/or opacities.
 Since this is wich larger than the estimated uncertainties from other sources we asstune a total uncertantv of iu computed huninosity., Since this is much larger than the estimated uncertainties from other sources we assume a total uncertainty of in computed luminosity.
" There are uncertainties iu other nuclear reaction rates which will also affect the computed huninosity. but again if these are within Liuits eiven by 3POh, he error iu Iuunünosity from these is ouly about."," There are uncertainties in other nuclear reaction rates which will also affect the computed luminosity, but again if these are within limits given by BP95, the error in luminosity from these is only about."
 Thus the integrated Iuuinositv is consistent with the observed value witlin rese uncertamties for a reasonable Z profile., Thus the integrated luminosity is consistent with the observed value within these uncertainties for a reasonable $Z$ profile.
 It may be noted that all these results are obtaiue using the pp reaction cross-section to be Sy., It may be noted that all these results are obtained using the pp reaction cross-section to be $S_0$.
 If he recent value adopted bx BP95 (0.955859) was used. he computed luminosity would be about lower. while or the normal value of Z the computed Iunuinositv would )o significantly lower than the observed. value.," If the recent value adopted by BP95 $0.9558S_0$ ) was used, the computed luminosity would be about lower, while for the normal value of $Z$ the computed luminosity would be significantly lower than the observed value."
 This leads us fo sumuise that the cross-section for the pp-reaction rate needs to be increased to its earlier value eiven bv Dahcall (1989))., This leads us to surmise that the cross-section for the pp-reaction rate needs to be increased to its earlier value given by Bahcall \cite{bah89}) ).
. Similar couclusious were also reached earlier bv Αα Chitre (1995))., Similar conclusions were also reached earlier by Antia Chitre \cite{ac95}) ).
 Iu order to obtain a better estimate for the cross-section of pp reaction. we try to compute the luminosity using different values for the cross-section of the pp reaction. with the normal value of Zang=0.018.," In order to obtain a better estimate for the cross-section of pp reaction, we try to compute the luminosity using different values for the cross-section of the pp reaction, with the normal value of $Z_\mathrm{surf}=0.018$."
 From these results we can identify the rauge of cross-section values which vield the computed huninositv within of the observed value., From these results we can identify the range of cross-section values which yield the computed luminosity within of the observed value.
" This can be treated as the helioseisiic estimate for the cross-section of pp reaction. which turus out to be (1.15+0.25)ς107"" MeV. barns. where the quoted errors correspond. to an uncertainty. of in the computed luminosity."," This can be treated as the helioseismic estimate for the cross-section of pp reaction, which turns out to be $(4.15\pm0.25)\times10^{-25}$ MeV barns, where the quoted errors correspond to an uncertainty of in the computed luminosity."
" This range is cousisteut with the value adopted by Bahlcall (1989)). but slightly lareer than he more recent value adopted x BPO,"," This range is consistent with the value adopted by Bahcall \cite{bah89}) ), but slightly larger than the more recent value adopted by BP95."
 All the inversion results prescuted 5ο far were obtained using α=(0 in equation (6)). which vield xofiles that require no opacity modifications. but the computed huuinositv may not match the observed. value.," All the inversion results presented so far were obtained using $\alpha=0$ in equation \ref{chisq}) ), which yield profiles that require no opacity modifications, but the computed luminosity may not match the observed value."
 It is possible to adjust the opacity or equivaleutlv the jieavy element abundauce to obtain the correct observed ininositv by choosing a suitably lhuge value of o iu equation (6))., It is possible to adjust the opacity or equivalently the heavy element abundance to obtain the correct observed luminosity by choosing a suitably large value of $\alpha$ in equation \ref{chisq}) ).
 However. such profiles may not be unique as only one parameter namely. the luminosity is fitted by," However, such profiles may not be unique as only one parameter namely, the luminosity is fitted by"
bolometric corrections from which the relative AGN/SD contribution can be derived.,bolometric corrections from which the relative AGN/SB contribution can be derived.
 We then discuss how our results improve the optical classification and fit into the question ol the growing AGN contribution with IR. liminosity (Section 5)., We then discuss how our results improve the optical classification and fit into the question of the growing AGN contribution with IR luminosity (Section 5).
 The application of our method to high-redshift sources and possible. alternate variants are dealt with in Section 6. while the conclusions are drawn in Section 7.," The application of our method to high-redshift sources and possible, alternate variants are dealt with in Section 6, while the conclusions are drawn in Section 7."
" Throughout (his paper we have made use of the concordance cosmology from (he WALADP)) skv sturvev, with Ly=70.5 km ! |. Q,,=0.27 and Qy=0.73 (LHnshaw οἱ al."," Throughout this paper we have made use of the concordance cosmology from the ) sky survey, with $H_0=70.5$ km $^{-1}$ $^{-1}$, $\Omega_m=0.27$ and $\Omega_\Lambda=0.73$ (Hinshaw et al."
 2009)., 2009).
 In the wake of (he indications [rom many previous studies. in Paper II we already looked for the possibility of a larger AGN incidence at higher Iuminosities. and found evidence of an increasing (rend.," In the wake of the indications from many previous studies, in Paper II we already looked for the possibility of a larger AGN incidence at higher luminosities, and found evidence of an increasing trend."
 Our preliminary resulis were anvwav incomplete due to the limited statistics., Our preliminary results were anyway incomplete due to the limited statistics.
 We note that the existence of such a correlation is a cornerstone in the present knowledge of ULIRGs. but remains a rather statement (hat has never received a (treatment.," We note that the existence of such a correlation is a cornerstone in the present knowledge of ULIRGs, but remains a rather statement that has never received a treatment."
 In particular. in order (to achieve a comprehensive description of the entire ULIRG luminosity range. especially at the higher end. one has to abandon the widely adopted flux threshold of 1 Jv at GO yan (ham Sanders 1993) and to allow for faàinter objects.," In particular, in order to achieve a comprehensive description of the entire ULIRG luminosity range, especially at the higher end, one has to abandon the widely adopted flux threshold of 1 Jy at 60 $\mu$ m (Kim Sanders 1998) and to allow for fainter objects."
 In the light of these considerations. the optimal candidates lor tliis study have (o be found within the PSC: survey (Saunders et al.," In the light of these considerations, the optimal candidates for this study have to be found within the $z$ survey (Saunders et al."
 2000). which covers the 84 per cent οἱ the skv down to a flux density of 20.6 Jv at GO jn. The PSC catalog contains more than a thousand ULIRGs. almost two hundreds of which have been observed bySpi/zer.," 2000), which covers the 84 per cent of the sky down to a flux density of $\sim$ 0.6 Jy at 60 $\mu$ m. The $z$ catalog contains more than a thousand ULIRGs, almost two hundreds of which have been observed by."
. Among the latter. no archival data are available at present [or ~15 sources of the 1 Jv sample. and a handful of the observed objects were not detected at 58 jun. This seems to be due to an offset in the target pointing and/or to an insullicient exposure time (see the Appendix for more detail).," Among the latter, no archival data are available at present for $\sim$ 15 sources of the 1 Jy sample, and a handful of the observed objects were not detected at 5–8 $\mu$ m. This seems to be due to an offset in the target pointing and/or to an insufficient exposure time (see the Appendix for more detail)."
 Within (he remaining entry list. we have applied an additional filler related to the quality of (he available measure of the I luminosity. as explained later on.," Within the remaining entry list, we have applied an additional filter related to the quality of the available measure of the IR luminosity, as explained later on."
 We have also decided to drop 3€ 273. since its UR luminosity lies in (he ULIBG range only as a consecuence of ils quasar nature. and represents a minor fraction of the bolometric emission.," We have also decided to drop 3C 273, since its IR luminosity lies in the ULIRG range only as a consequence of its quasar nature, and represents a minor fraction of the bolometric emission."
 Our final sample consists of 164 sources. of which TQ have been already. analysed in our previous The highest redshift is 2=0.342. and the huninositv range 107<Ly;/L.«10! is adequately probed in all ils extent (see Fig. 1)).," Our final sample consists of 164 sources, of which 70 have been already analysed in our previous The highest redshift is $z=0.342$, and the luminosity range $10^{12} < L_\mathit{IR}/L_\odot < 10^{13}$ is adequately probed in all its extent (see Fig. \ref{zl}) )."
 We stress (that. this sample is [fully, We stress that this sample is fully
confident with the ACIS-I spectral fitting even in the rather carly phase of the Chandra iission.,confident with the ACIS-I spectral fitting even in the rather early phase of the $Chandra$ mission.
 lu the ACTS-I field. LO Class Is and 16 Class Ls have been reported with uear- to far-IR observations.," In the ACIS-I field, 10 Class Is and 16 Class $_c$ s have been reported with near- to far-IR observations."
" Among them. we detect N-ravs from 7 Class Is and 11 Class Is above the detection limit of ~1025 Cres κ,"," Among them, we detect X-rays from 7 Class Is and 11 Class $_c$ s above the detection limit of $\sim10^{28}$ ergs $^{-1}$."
 Thus the Neray detection rates are as hiel as TO in both Class Is and Class Ls. The lack of X- from the other Class Ts could be partly due to short time variability., Thus the X-ray detection rates are as high as 70 in both Class Is and Class $_c$ s. The lack of X-rays from the other Class $_c$ s could be partly due to short time variability.
 For example. WL 21 (No S) and YLW 16D (No.60) are hardly visible. except when they exhibit au ταν flare (see Figure 2a aud 21).," For example, WL 21 (No 8) and YLW 16B (No.60) are hardly visible, except when they exhibit an X-ray flare (see Figure 2a and 2j)."
 Also lone-term variability. like the Ll-veay evele of solar activity. may uot be ignored.," Also long-term variability, like the 11-year cycle of solar activity, may not be ignored."
 We lence suspect that all the Class Ts. at least those in the p Oph cloud. are potential N-ray sources.," We hence suspect that all the Class $_c$ s, at least those in the $\rho$ Oph cloud, are potential X-ray sources."
" Carkuer. Ἱνοσα]ς, Feigelsou (1998) compiled the N-ray emission from YSOs usingROSAT PSPC aud reported that the detection rate from Class Ls was ouly ~ above the detection limit of 107? eres st."," Carkner, Kozak, Feigelson (1998) compiled the X-ray emission from YSOs using PSPC and reported that the X-ray detection rate from Class $_c$ s was only $\sim$ above the detection limit of $10^{29}$ ergs $^{-1}$."
 Our hieh detection rate of Class Is (70 %)) is due to the higher seusitivitv of Chandra. especially in the hard N-ray band.," Our high detection rate of Class $_c$ s $\sim$ 70 ) is due to the higher sensitivity of , especially in the hard X-ray band."
 In fact. if we convert the flix of the 15 Class Tes to the PSPC counts using thesoftware! we fiud ouly 1: sources fall above the PSPC lower liit ( cts 4). even in their flare phases.," In fact, if we convert the flux of the 18 Class $_c$ s to the PSPC counts using the, we find only 4 sources fall above the PSPC lower limit $\approx$ $^{-3}$ cts $^{-1}$ ), even in their flare phases."
 This correspouds to the PSPC detection rate of ~20%., This corresponds to the PSPC detection rate of $\sim$ 20.
. To search for N-ravs frou an even τοσα phase than Class I. sve check hard N-vay cuhaucements frou 11. starless cores (Motte. André.. Neri 1998) in the ACIS-I field.," To search for X-rays from an even younger phase than Class I, we check hard X-ray enhancements from 41 starless cores (Motte, André,, Neri 1998) in the ACIS-I field."
 The 38 keV band photon fluxes iu a 137 radius circle around the 1300 gam sources are either below the 3 6 significance level (37 sources) or are contanunated bv nearby YSOs (1 sources)., The 3–8 keV band photon fluxes in a $''$ radius circle around the 1300 $\mu$ m sources are either below the 3 $\sigma$ significance level (37 sources) or are contaminated by nearby YSOs (4 sources).
" Iu our field of view. 3 BDs and | BD,s have been reported with infrared spectroscopy (Wilkiug. Greene. Meyer 1999: Cushing. Tokunaga. Iobavashi 20003."," In our field of view, 3 BDs and 4 $_c$ s have been reported with infrared spectroscopy (Wilking, Greene, Meyer 1999; Cushing, Tokunaga, Kobayashi 2000)."
" We detect N-ravs from 1 BD (CY 310. No.76) and 1 BD, (CY 326. No.S1)."," We detect X-rays from 1 BD (GY 310, No.76) and 1 $_c$ (GY 326, No.81)."
 We should note that ROSAT also found N-ravs from another BD CY 202 CNeuláauuser et al., We should note that ROSAT also found X-rays from another BD GY 202 (Neuhäuuser et al.
 1999)., 1999).
 The ages of these stars are estimated to be iu the rauee of 10° yr (Willing. Greene. Moever 1999: Cushing. Tokunaga. Ikobavashi 2000).," The ages of these stars are estimated to be in the range of $\times$ $^{6}$ yr (Willing, Greene, Meyer 1999; Cushing, Tokunaga, Kobayashi 2000)."
 Interestingly. the other ποταν BDs aud BD.» have systematically older ages of «109 vy.," Interestingly, the other non-X-ray BDs and $_c$ s have systematically older ages of $\times$ $^{6}$ yr."
" The N-rav properties of the DD aud BD, are sinulato Class IT|Ts: relatively low absorption 2.310272 em2) and teiiperature (0.92.0 keV).", The X-ray properties of the BD and $_c$ are similarto Class II+IIIs: relatively low absorption $\times$ $^{22}$ $^{-3}$ ) and temperature (0.9–2.0 keV).
" Both have Lyf/Ljy,; of about 3410 Like typical low mass YSOs."," Both have $L_{X}$ $L_{\rm bol}$ of about $\times$ $^{-4}$, like typical low mass YSOs."
 Although the N-vavs show aperiodic variability. no flare-like eveut is found.," Although the X-rays show aperiodic variability, no flare-like event is found."
 Using the J aud Z7 baud maguitudes of Barsouy ct al. (, Using the $J$ and $H$ band magnitudes of Barsony et al. (
1997). we display the relation between the N-rav absorption column (Nyy) aud the IR color (7ff) in Figure 3.,"1997), we display the relation between the X-ray absorption column $N_{\rm H}$ ) and the IR color $J-H$ ) in Figure 3."
 From this fleure. we see that δι ds roughly proportional to (77T).," From this figure, we see that $N_{\rm H}$ is roughly proportional to $J-H$ )."
 The best-fit linear relation is (Ny τοσα 7) = (L.2G40.08){(7F IT) | (0.652:0.09)E... where the data points of No.l. 8. 23. and 77 are excluded for the fitting (see the next paragraph).," The best-fit linear relation is $N_{\rm H}$ $^{22}$ $^{-2}$ ) = $\pm$ $J-H$ ) + $\pm$, where the data points of No.1, 8, 23, and 77 are excluded for the fitting (see the next paragraph)."
 The offset of 0.65 mae corresponds to that of the zero-reddening I-M type stars (Cox 2000)., The offset of 0.65 mag corresponds to that of the zero-reddening K-M type stars (Cox 2000).
 Using the relation of A and infrared= extinction ofthe p Ophl cloud (Martin Whittet 1990). we obtain a relation of Ny ?| = (1.5940. 10)«1023 AL. which should be compared to Np {cm3] — 1.591023 A. in the interstellar space of our Calaxy (Predehl Sclunitt 1995).," Using the relation of $A_{\rm v}$ and infrared extinction of the $\rho$ Oph cloud (Martin Whittet 1990), we obtain a relation of $N_{\rm H}$ $^{-2}$ ] = $\pm$ $\times$ $^{21}$ $A_{\rm v}$, which should be compared to $N_{\rm H}$ $^{-2}$ ] = $\times$ $^{21}$ $A_{\rm
v}$ in the interstellar space of our Galaxy (Predehl Schmitt 1995)."
 Large Nyy excesses are found iu 3 Class ILL: WL 12 (No.1). WE 21 (No 8). aud EL 29 (No.23).," Large $N_{\rm H}$ excesses are found in 3 Class $_c$ s: WL 12 (No.1), WL 21 (No 8), and EL 29 (No.23)."
 Since the N-ravs would be emitted frou the stellar surface or dnuermost disk. these Class Ls should have extra infrared photons conmüug from outer regions.," Since the X-rays would be emitted from the stellar surface or innermost disk, these Class $_c$ s should have extra infrared photons coming from outer regions."
 One possibility is that IR photons from the stellar surface escape above or below the accretion disk or torus. then the euvelope gas scatters the IR photous into our line of sight.," One possibility is that IR photons from the stellar surface escape above or below the accretion disk or torus, then the envelope gas scatters the IR photons into our line of sight."
 Since the scattering efficiency is larger at shorter waveleneths. this process makes apparent (7) fF) smaller than that expected fromNu.," Since the scattering efficiency is larger at shorter wavelengths, this process makes apparent $J-H$ ) smaller than that expected from$N_{\rm H}$."
 An unclassified source. CY 312 (No.77) also shows laree Nyy excess.," An unclassified source, GY 312 (No.77) also shows large $N_{\rm H}$ excess."
 The ταν properties of this source. ugh AL. Nyy. magnetic field. and Ly(flare) (Ly (quiesceut} are more small to Class Is than Class ID|UIs (see also figures 1. 6. and 7). hence CY 312 may be a Class I. We display. the relation between absorption (Ny)," The X-ray properties of this source, high $kT$, $N_{\rm H}$ , magnetic field, and $L_{X}$ $L_{X}$ (quiescent) are more similar to Class Is than Class II+IIIs (see also figures 4, 6, and 7), hence GY 312 may be a Class I. We display the relation between absorption $N_{\rm H}$ )"
clustering of a system in which all objects have the same mass.,clustering of a system in which all objects have the same mass.
 This allows us to describe a hierarchical model of clustering with different mass “particles” at each level of the hierarchy by rescaling 8., This allows us to describe a hierarchical model of clustering with different mass “particles” at each level of the hierarchy by rescaling $\beta$.
" Next, because halos, galaxies and clusters of galaxies that are mostly relaxed and have a virial ratio greater than about 0.86 have a negative specific heat, they approximately form a set of microcanonical ensembles."," Next, because halos, galaxies and clusters of galaxies that are mostly relaxed and have a virial ratio greater than about $0.86$ have a negative specific heat, they approximately form a set of microcanonical ensembles."
 Hence their internal energies are largely inaccessible to the rest of the universe., Hence their internal energies are largely inaccessible to the rest of the universe.
" In particular, small dense groups are more likely to be virialized than larger clusters because their dynamical timescales, given by TaynX(Gp)~'/? are shorter."," In particular, small dense groups are more likely to be virialized than larger clusters because their dynamical timescales, given by $\tau_\mathrm{dyn} \propto (G \rho)^{-1/2}$ are shorter."
 This allows us to describe virialized groups of galaxies as individual particles that can be treated as modified point masses., This allows us to describe virialized groups of galaxies as individual particles that can be treated as modified point masses.
" Finally, merging particles that are bound to each other can be treated"," Finally, merging particles that are bound to each other can be treated"
"the bispectra f,g: where the denominator is the variance of the local bispectrum, for triangles with £1Z2¢3.","the bispectra $f,g$: where the denominator is the variance of the local bispectrum, for triangles with $\ell_1 \neq \ell_2 \neq \ell_3$."
 The correlation coefficient between a bispectrum 5 and the local bispectrum 0/9? is: with o being IR or radio., The correlation coefficient between a bispectrum $b^\alpha$ and the local bispectrum $b^\mathrm{loc}$ is: with $\alpha$ being IR or radio.
" Figure 14 shows that, for €«200, the correlation between radio and local bispectra decreases quickly, so that the two bispectra may be distinguished efficiently."," Figure \ref{costhetafg} shows that, for $\ell<200$, the correlation between radio and local bispectra decreases quickly, so that the two bispectra may be distinguished efficiently."
" Conversely, even when using a large multipole range, the IR bispectrum is significantly correlated with the local one."," Conversely, even when using a large multipole range, the IR bispectrum is significantly correlated with the local one."
" 'The contribution of the bispectrum of a point source population α to fwr is: This equation is the usual bias (7) of the local- NG estimator, when the local bispectrum has the form of Eq. (13))."," The contribution of the bispectrum of a point source population $\alpha$ to $f_\mathrm{NL}$ is: This equation is the usual bias \citep{Serra2008} of the local-optimised NG estimator, when the local bispectrum has the form of Eq. \ref{eq:cmbispsw}) )."
 A more comprehensive computation of Af&; is achievable by applying the full local estimator described in Sect. ??.., A more comprehensive computation of $\Delta f_\mathrm{NL}^{\alpha}$ is achievable by applying the full local estimator described in Sect. \ref{sect:fnlestim}.
" We built up this estimator using the full transfer function from the latest version of CAMB (?) with WMAPT--BAO--HO0 cosmological parameters (?),, and we tested the estimator on simulations from ?.."," We built up this estimator using the full transfer function from the latest version of CAMB \citep{Lewis2000}
 with WMAP7+BAO+H0 cosmological parameters \citep{Larson2011}, and we tested the estimator on simulations from \cite{Elsner2009}."
 We found the previously noted result that the variance of the estimator increases with fwr.., We found the previously noted result that the variance of the estimator increases with $f_\mathrm{NL}$.
" It is unbiased in the range we have tested (0€fur,« 200)."," It is unbiased in the range we have tested $0
\leq f_\mathrm{NL} \leq 200$ )."
" We used this fwr estimator on two sets of simulated maps: maps containing all the point sources, and maps with only sources below the flux limit of Planck's Early Release Compact Source Catalogue (ERCSC) (?),, namely S. =0.5, 0.5, 0.3, 0.3, 0.3, 0.25 Jy as a function of frequency."," We used this $f_\mathrm{NL}$ estimator on two sets of simulated maps: maps containing all the point sources, and maps with only sources below the flux limit of Planck's Early Release Compact Source Catalogue (ERCSC) \citep{Planck-Collaboration-ERCSC}, namely $S_c
=$ 0.5, 0.5, 0.3, 0.3, 0.3, 0.25 Jy as a function of frequency."
" Moreover, we have computed the estimator at three resolutions, ἔπιακ, recalibrating the Sprim normalisation in each case."," Moreover, we have computed the estimator at three resolutions, $\ell_\mathrm{max}$, recalibrating the $\mathrm{S}_\mathrm{prim}$ normalisation in each case."
 Tables 1 and 2 summarise these results., Tables \ref{fnlradtable} and \ref{fnlirtable} summarise these results.
" The bias ΔΙΑ (see Table 1)) is negative on large angular scales, for £4=50."," The bias $\Delta f_\mathrm{NL}^\mathrm{RAD}$ (see Table \ref{fnlradtable}) ) is negative on large angular scales, for $\ell_\mathrm{max}=50$."
 The bias due to radio sources becomes positive at higher multipoles in agreement with ?.., The bias due to radio sources becomes positive at higher multipoles in agreement with \cite{Serra2008}.
 This is due to the CMB bispectrum being negative in the SW-dominated regime and the radio bispectrum being positive., This is due to the CMB bispectrum being negative in the SW-dominated regime and the radio bispectrum being positive.
" The bias increases by 5 orders of magnitude at the highest resolution, max= 2048.The reason for the rapid increase of the bias with Cmax relates to the weight of"," The bias increases by 5 orders of magnitude at the highest resolution, $\ell_\mathrm{max}=2048$ .The reason for the rapid increase of the bias with $\ell_{\mathrm{max}}$ relates to the weight of"
As expected. the two prescriptions for the advectec »erturbations are equivalent in the limit of vanishing ει and c».,"As expected, the two prescriptions for the advected perturbations are equivalent in the limit of vanishing $\epsilon_1$ and $\epsilon_2$."
" These parameters are very small for the seconc and third /=1 acoustic modes: eq€»~0.03. anc ).015 respectively for ry,=2.55, (note that these two modes have a higher [requency than the second: anc hire) S.ASI modes as discussed in Section. 5.2.2))", These parameters are very small for the second and third $l=1$ acoustic modes: $\epsilon_1 \sim \epsilon_2 \sim 0.03$ and $0.015$ respectively for $r_\sh=2.5r_*$ (note that these two modes have a higher frequency than the second and third SASI modes as discussed in Section \ref{sec:SASI_spectrum}) ).
 The vigh frequency approximation is thus well justified. anc he two prescriptions are in reasonable agreement: the damping rates agree within LO15% for the second moco. and <5% for the third. mode.," The high frequency approximation is thus well justified and the two prescriptions are in reasonable agreement: the damping rates agree within $10-15\%$ for the second mode, and $<5\%$ for the third mode."
 These two modes are enough to conclude that SASL is not a purely acoustic instability since the second and third /—1 SASL modes are unstable., These two modes are enough to conclude that SASI is not a purely acoustic instability since the second and third $l=1$ SASI modes are unstable.
 Phe approximation is slightly less good for the fundamental acoustic mode: in this case ejc€~ 0.1., The approximation is slightly less good for the fundamental acoustic mode: in this case $\epsilon_1 \sim \epsilon_2 \sim 0.1$ .
 Ehe damping rates in the two prescriptions dilfer by 30%. but the modes are still definitely stable whatever the prescription.," The damping rates in the two prescriptions differ by $\sim 30\%$, but the modes are still definitely stable whatever the prescription."
 In this section. we study in detail the frequeney spectrum expected from acvective-acoustic ancl purely acoustic cveles.," In this section, we study in detail the frequency spectrum expected from advective-acoustic and purely acoustic cycles."
 In the subsection 5.1. we study a simple tov model (?).. which allows an analytical study of the frequeney spectrum.," In the subsection \ref{sec:toy_model}, we study a simple toy model \citep{foglizzo09}, which allows an analytical study of the frequency spectrum."
 In the following subsection 5.2.1. we then give an approximate egeneralisation to the more realistic model of SASL used. in Sections 3 and. 4.," In the following subsection \ref{sec:spherical}, we then give an approximate generalisation to the more realistic model of SASI used in Sections \ref{sec:radial_time} and \ref{sec:acoustic_modes}."
 This analvsis confirms the validity of the argument presented in Section 3..., This analysis confirms the validity of the argument presented in Section \ref{sec:radial_time}.
 Furthermore it allows a direct comparison between anabytical expectations and the frequeney spectrum. of SASL., Furthermore it allows a direct comparison between analytical expectations and the frequency spectrum of SASI.
 This direct. comparison leads to the same conclusion about the instability mechanism. in favour of the advective-acoustic cvele.," This direct comparison leads to the same conclusion about the instability mechanism, in favour of the advective-acoustic cycle."
 We consider the toy model introduced by 2.., We consider the toy model introduced by \citet{foglizzo09}.
 Lt consists of a planar shock Iving above a zone of deceleration imposed by an external potential step., It consists of a planar shock lying above a zone of deceleration imposed by an external potential step.
 Phe potential step is localisecl within a length. seale of ἐν. ancl is separated. [rom the shock by a region of size Lf where the How is uniform.," The potential step is localised within a length scale of $H_\nabla$, and is separated from the shock by a region of size $H$ where the flow is uniform."
 The eas is assumed to be perfect. acliabatie (with an adiabatic index = 4/3). and non-sell-eravitating.," The gas is assumed to be perfect, adiabatic (with an adiabatic index $\gamma=4/3$ ), and non-self-gravitating."
 Phe direction perpendicular to the shock is called z. ancl referred. to as vertical.," The direction perpendicular to the shock is called $z$, and referred to as vertical."
 Modes. have a transverse structure along e (parallel to the shock). which is referred. to as the horizontal direction.," Modes have a transverse structure along $x$ (parallel to the shock), which is referred to as the horizontal direction."
 “Phe domain is à box of horizontal size L., The domain is a box of horizontal size $L$.
" After a Fourier transform in time and horizontal direction .r. the cigenmoces are characterised by their. complex frequency a ancl the number n, of horizontal wavelengths in the width of the box."," After a Fourier transform in time and horizontal direction $x$, the eigenmodes are characterised by their complex frequency $\omega$ and the number $n_x$ of horizontal wavelengths in the width of the box."
 The horizontal wave number is then: Vhe reader is referred to?) for more details about this tov model. the equations governing it. anc the numerical method used to solve them.," The horizontal wave number is then: The reader is referred to \citet{foglizzo09} for more details about this toy model, the equations governing it, and the numerical method used to solve them."
" In the remaining of this subsection. the numerical calculations have used the parameters: L=641. M,=o. livfil=0.01. and 6Cy=015."," In the remaining of this subsection, the numerical calculations have used the parameters: $L=6H$, $\M_1=\infty$ , $H_\nabla/H=0.01$, and $c_{\rm in}^2/c_{\rm out}^2 = 0.75$."
 Cycle constants Q and & describing the acveetive-acoustic ancl purely acoustic evcle can be defined. as in Section 2. (but here without any approximation)., Cycle constants $Q$ and $R$ describing the advective-acoustic and purely acoustic cycle can be defined as in Section \ref{sec:review} (but here without any approximation).
 An cigenmode with a complex eigenfrequeney ow must then verily Equation (5)). and contains both excles in some proportion.," An eigenmode with a complex eigenfrequency $\omega$ must then verify Equation \ref{eq:QR}) ), and contains both cycles in some proportion."
 In order to separate the two evcles ancl study their properties independentIy from cach other. we follow ? in considering advective-acoustic modes verifving: which corresponds to a situation where the acoustic wave propagating downward would be artificially removed.," In order to separate the two cycles and study their properties independently from each other, we follow \citet{foglizzo09} in considering advective-acoustic modes verifying: which corresponds to a situation where the acoustic wave propagating downward would be artificially removed."
 Similarly. purely. acoustic modes follow: which signifies that the advected: entropy-vorticity wave is ignored.," Similarly, purely acoustic modes follow: which signifies that the advected entropy-vorticity wave is ignored."
 This is equivalent to. the method described in Section 4 to compute purely acoustic modes., This is equivalent to the method described in Section \ref{sec:acoustic_modes} to compute purely acoustic modes.
 As in ?.. we deline new evele constants Qo and {η that do not include the propagation of the waves between the shock and the potential step.," As in \citet{foglizzo09}, we define new cycle constants $Q_0$ and $R_0$ that do not include the propagation of the waves between the shock and the potential step."
" These are defined as: where AS and KT are the vertical numbers of the advected: wave. ancl of the acoustic waves propagating down (1) and up(-): Equations (24)) and (26)) are combined to obtain the condition verified by an acvective-acoustic mocle: where Trae ds the duration of a one dimensional acdvective-acoustic evele (A=0. fe= 1): Equation 31. can be solved. approximately in the regime where the growth rate is low (o; w,) and where the acoustic wave is propagating ..- 0)."," These are defined as: where $k_z^{\rm adv}$ and $k_z^\pm$ are the vertical numbers of the advected wave, and of the acoustic waves propagating down (+) and up(-): Equations \ref{eq:Q}) ) and \ref{eq:Q0}) ) are combined to obtain the condition verified by an advective-acoustic mode: where $\tau_{\rm aac}$ is the duration of a one dimensional advective-acoustic cycle $k_x = 0$, $\mu = 1$ ): Equation \ref{eq:Qmode} can be solved approximately in the regime where the growth rate is low $\omega_i \ll \omega_r$ ) and where the acoustic wave is propagating $\mu^2>0$ )."
 1n this case. the modulus of this complex relation gives access to the erowth rate (7): In a similar wav. the frequency may. beobtained from the argument of the same relation. which gives an information on the wave phase:," In this case, the modulus of this complex relation gives access to the growth rate \citep{foglizzo09}: : In a similar way, the frequency may beobtained from the argument of the same relation, which gives an information on the wave phase:"
We have shown that the reprocessed cussion of the disk ilhuuinated by the star is à very powerful conustraiut ou the disk presence and/or properties.,We have shown that the reprocessed emission of the disk illuminated by the star is a very powerful constraint on the disk presence and/or properties.
 In fact. the effect is “stronecr than stellar eclipses that we studied in 87? (secalso 2)..," In fact, the effect is “stronger” than stellar eclipses that we studied in \ref{sec:eclipses} \citep[see also][]{NS03}."
 The luminous stars enüt most of their raciatiou in the visible aud UV ranges., The luminous stars emit most of their radiation in the visible and UV ranges.
 The disk re-processes this enission in the NIR baud which then appears much xiehter than the star itself in the same frequency., The disk re-processes this emission in the NIR band which then appears much brighter than the star itself in the same frequency.
 We rave seen that the reprocessed NIB. disk emission is up to a factor of 100 üieher than tha of the star., We have seen that the reprocessed NIR disk emission is up to a factor of 100 higher than that of the star.
 At the same ine eclipses vield an effect of order unity., At the same time eclipses yield an effect of order unity.
 Analvziug the predicted NIR light curves for 8S2 we ound that ai optically thin disk with a very small inner tole Rin&O ds ruled out., Analyzing the predicted NIR light curves for S2 we found that an optically thin disk with a very small inner hole $R_{\rm in}\simeq 0$ is ruled out.
 The disk emission would have )een seen by now. whereas ohservatious do not show uv varkülitv iu S2 A baud fluxes.," The disk emission would have been seen by now, whereas observations do not show any variability in S2 $K$ band fluxes."
" We then tested disks with 1011-2010 values of P. axd found that only for rather large values of Ri,20.1"" such disks are ροήτος."," We then tested disks with non-zero values of $R_{\rm in}$, and found that only for rather large values of $R_{\rm in}\simgt 0.1$ such disks are permitted."
 Tn 9?? we explored the eclipses of the individual stars bv the putative optically hick disk., In \ref{sec:eclipses} we explored the eclipses of the individual stars by the putative optically thick disk.
 To observe such eclipses one should be able to resolve iudividual stir orbits. which is extremely difficult aud has been made possible ouly for our Calactic Center (see??)..," To observe such eclipses one should be able to resolve individual star's orbits, which is extremely difficult and has been made possible only for our Galactic Center \citep[see][]{Schoedel03,Ghez03a}."
" At the sae ine. simular eclipses of stars of the cluster should also be ουαπλο, and hence one mav hope to detect the disk ""shadow ou the backeround emission of the nuclear cluster."," At the same time, similar eclipses of stars of the cluster should also be occurring, and hence one may hope to detect the disk “shadow” on the background emission of the nuclear cluster."
 In doiug the calculations below. we will be concerned with the optical-UV emission rather than with the infrared. as we were in the previous sections.," In doing the calculations below, we will be concerned with the optical-UV emission rather than with the infrared, as we were in the previous sections."
 Our workingo assunption is that the visible aud UV. flux incident on the disk is absorbed and reprocessed iuto the near mfrared eniüssion (see 77)). reflecting only a σα]. fraction of the radiation in the visible-UV rauge.," Our working assumption is that the visible and UV flux incident on the disk is absorbed and reprocessed into the near infrared emission (see \ref{sec:reprocessed}) ), reflecting only a small fraction of the radiation in the visible-UV range."
 Hence we treat the disk as an optically thick absorbing surface in this section., Hence we treat the disk as an optically thick absorbing surface in this section.
 We will only cousider disks with uo inner holes. ic. Ra=0. since the iustruucut resolution (for other than eealactic centers) is usually worse than the actual non-zero value of Rh.," We will only consider disks with no inner holes, i.e. $R_{\rm in}=0$, since the instrument resolution (for other than galactic centers) is usually worse than the actual non-zero value of $R_{\rm
in}$."
 Note that an enhanced emission from the iuuer hole could iu principle be detected. butasymmetry is currently impossible to resolve.," Note that an enhanced emission from the inner hole could in principle be detected, but is currently impossible to resolve."
 Iu addition. the star cluster is assumed to be spherically svuunoctric.," In addition, the star cluster is assumed to be spherically symmetric."
 For this reason the angle 9 is no louger of miportanuce., For this reason the angle $\beta$ is no longer of importance.
 Tustead we define the wy coordinate svsteni. with : axis directed straight to us. and. aud yas in Fig. 13..," Instead we define the $xyz$ coordinate system, with $z$ axis directed straight to us, and $x$ and $y$ as in Fig. \ref{fig:shadow}."
 The ue axis is positive where the disk is closer to the observer., The $x$ axis is positive where the disk is closer to the observer.
 We also define he column density of stars along the line of sight. JNGe.gy). as the integral of the star density. oR). through the line of sight. from the disk to the observer. located at infinity. where 7=x if the line of sight does not intercept the disk projection. and 2!-diske the respective ;-co01dinate of the disk iu the opposite case.," We also define the column density of stars along the line of sight, $N(x,y)$, as the integral of the star density, $n(\vec{R})$, through the line of sight from the disk to the observer, located at infinity, where $z'=-\infty$ if the line of sight does not intercept the disk projection, and $z'=z_{\rm disk}$, the respective $z$ -coordinate of the disk in the opposite case."
" For definitiveness. we take the spherically svuuuetric density profile n(R)xRU with a=Lt for RcBou~10"" selven bv ?. aud consider the case where RourmResp."," For definitiveness, we take the spherically symmetric density profile $n(R) \propto R^{-\alpha}$ with $\alpha = 1.4$ for $R<R_{cusp} \sim 10''$ given by \cite{Genzel03}
 and consider the case where $R_{\rm out} \ll R_{cusp}$."
 Tn Fig., In Fig.
 13. we show the resulting map of the stellar column density for the disk iuclinatiou angle / =SO”., \ref{fig:shadow} we show the resulting map of the stellar column density for the disk inclination angle $i$ =.
 The projection of the disk shadow is clearly seen., The projection of the disk shadow is clearly seen.
 The boundaries of the disk appear as sharp discontiuuities i the surface brightuess of the star cluster., The boundaries of the disk appear as sharp discontinuities in the surface brightness of the star cluster.
 This effect is the strongest near the side of the disk that is closer to the observer (positive .c in Figure 13))., This effect is the strongest near the side of the disk that is closer to the observer (positive $x$ in Figure \ref{fig:shadow}) ).
 Also note that the star cluster unuage appears anisotropic on all scales smaller than the disk outer radius., Also note that the star cluster image appears anisotropic on all scales smaller than the disk outer radius.
" This fact allows us to introduce an ""anisotropy measure. AL defined as where Ας) is the anele-averaged number count of stars at projected distance + from the star cluster ceuter away: Tere we used in the plane of the kv the communion polar (r| o) coordinates centered ou the black hole."," This fact allows us to introduce an “anisotropy measure”, $A$, defined as where $\overline{N}(r)$ is the angle-averaged number count of stars at projected distance $r$ from the star cluster center away: Here we used in the plane of the sky the common polar $r-\phi$ ) coordinates centered on the black hole."
 We also, We also
the iron line band in the 4.5 - 7.5 keV region.,the iron line band in the 4.5 - 7.5 keV region.
 Galactic absorption was included using the XSPEC was model with Ny values given in NO7., Galactic absorption was included using the XSPEC $\it{wabs}$ model with $N_{\rm H}$ values given in N07.
 NO7 found that some of the observations in our sample show additional effects of ionized absorption local to the AGN., N07 found that some of the observations in our sample show additional effects of ionized absorption local to the AGN.
 We accounted for this in cases where it was required using the XSTAR table model cies described in NO7. with parameters fixed to those found by NO7.," We accounted for this in cases where it was required using the XSTAR table model $\it{cwa18}$ described in N07, with parameters fixed to those found by N07."
 The power-law index and normalization were left free to vary., The power-law index and normalization were left free to vary.
 The data/model ratios are shown in Fig., The data/model ratios are shown in Fig.
 | where the ratio of the time-averaged spectrum to a power-law model excluding 4.5-7.5 keV has also been overplotted., 1 where the ratio of the time-averaged spectrum to a power-law model excluding 4.5-7.5 keV has also been overplotted.
 An excess in the iron line region over the fitted continuum implies iron line variability. and the errors shown in Fig.," An excess in the iron line region over the fitted continuum implies iron line variability, and the errors shown in Fig."
 | provide a crude visual impression of the significance of those variations., 1 provide a crude visual impression of the significance of those variations.
 We have also made a more explicit estimate of the significance of any line variability by performing additional simulations of the expected rms spectrum of a power-law continuum with no emission line components., We have also made a more explicit estimate of the significance of any line variability by performing additional simulations of the expected rms spectrum of a power-law continuum with no emission line components.
 A continuum light curve was simulated by using the fakcil function in XSPEC to create a power-law spectrum for each 10005 time bin., A continuum light curve was simulated by using the $\it{fakeit}$ function in XSPEC to create a power-law spectrum for each 1000s time bin.
 The model is the same as the continuum used to fit the real rms spectrum (i.e. those shown in Fig., The model is the same as the continuum used to fit the real rms spectrum (i.e. those shown in Fig.
 |). but the normalization of the power-law for each bin was set such that the total count rate of the four continuum bins (i.e. those between 2.5-4.6 keV and 7.4-10.0 keV). matched the observed count rate in this energy range.," 1), but the normalization of the power-law for each bin was set such that the total count rate of the four continuum bins (i.e. those between 2.5-4.6 keV and 7.4-10.0 keV), matched the observed count rate in this energy range."
 The +.6-7.4 keV interval is excluded in the renormalization. as this will contain any contribution by line components. whereas the rest of the energy range should contain only the continuum.," The 4.6-7.4 keV interval is excluded in the renormalization, as this will contain any contribution by line components, whereas the rest of the energy range should contain only the continuum."
 These simulations therefore yield fake light curves in each energy bin. based solely on the observed continuum spectrum and light curve. with random Poisson noise.," These simulations therefore yield fake light curves in each energy bin, based solely on the observed continuum spectrum and light curve, with random Poisson noise."
 These simulations were repeated 1000 times and the excess variance spectrum was calculated for each one. just as it was for the real light curve.," These simulations were repeated 1000 times and the excess variance spectrum was calculated for each one, just as it was for the real light curve."
 We can then compare how many times the excess variance in the fake continuum rms spectrum exceeds that of the observed rms spectrum. which contains the emission line.," We can then compare how many times the excess variance in the fake continuum rms spectrum exceeds that of the observed rms spectrum, which contains the emission line."
 This then yields the probability that the observed variance exceeds the continuum model by chance. and hence the significance of the line variations.," This then yields the probability that the observed variance exceeds the continuum model by chance, and hence the significance of the line variations."
 We deem an excess in an individual to be significant if its confidence level exceeds95%., We deem an excess in an individual to be significant if its confidence level exceeds.
. In Table |. we list all all bins with a confidence level of at leastος. as several adjacent bins with moderately high confidence might indicate a broad variability excess. even if individually they do not all exceed confidence.," In Table 1, we list all all bins with a confidence level of at least, as several adjacent bins with moderately high confidence might indicate a broad variability excess, even if individually they do not all exceed confidence."
 Simple disk models for Fe Ka line emission predict that the line should respond rapidly to changes in the illuminating continuum flux so the rms spectrum for such an object would have a power- and iron line excess that matches the time-averaged spectrum., Simple disk models for Fe $\alpha$ line emission predict that the line should respond rapidly to changes in the illuminating continuum flux so the rms spectrum for such an object would have a power-law and iron line excess that matches the time-averaged spectrum.
 In contrast. the rms spectra in Fig.," In contrast, the rms spectra in Fig."
 | display a range of iron line variability profiles and there is no clear overall trend between the ime-averaged and rms spectra., 1 display a range of iron line variability profiles and there is no clear overall trend between the time-averaged and rms spectra.
 Half of the sample (9/18 observations) show at least one bin with significant line variability at9550., Half of the sample (9/18 observations) show at least one bin with significant line variability at.
.. A further four show ower-contidence }) excesses only. but in the cases of ICG-5-23-16() and NGC 4051 these might well be real. as they exhibit more than one bin with such an excess.," A further four show lower-confidence ) excesses only, but in the cases of MCG-5-23-16(2) and NGC 4051 these might well be real, as they exhibit more than one bin with such an excess."
 Ark 564 contains a single excess bin at confidence. which is suggestive. but marginal.," Ark 564 contains a single excess bin at confidence, which is suggestive, but marginal."
 NGC 4395 contains a single bin at confidence which we do not consider significant., NGC 4395 contains a single bin at confidence which we do not consider significant.
 Of the observations with significant line variability. two (NGC 35160) and NGC 550619) show definitive broad line variability. in that there are two adjacent bins with excess variations at c95% confidence.," Of the observations with significant line variability, two (NGC 3516(2) and NGC 5506(1)) show definitive broad line variability, in that there are two adjacent bins with excess variations at $>95$ confidence."
 However. a further three observations. NGC 3783. MCG-6-30-15¢1) and NGC S548(2) almost certainly have broad line variability as well. based on moderately significant excesses adjacent to the more significant bins.," However, a further three observations, NGC 3783, MCG-6-30-15(1) and NGC 5548(2) almost certainly have broad line variability as well, based on moderately significant excesses adjacent to the more significant bins."
 NGC στο. Mrk 766). MCG-6-30-15¢2) and NGC 7314¢1) show signitieant. but narrow excesses.," NGC 4151(2), Mrk 766(3), MCG-6-30-15(2) and NGC 7314(1) show significant, but narrow excesses."
 The diversity of behaviour increases further when the strength of the variability excess is compared to the time-averaged line profile., The diversity of behaviour increases further when the strength of the variability excess is compared to the time-averaged line profile.
 The correspondence is generally poor., The correspondence is generally poor.
 For example. NGC 3516(2) and NGC 55480) have line variability. especially in the red wing. that is stronger than the time-averaged spectrum. 6-30-15¢1)," For example, NGC 3516(2) and NGC 5548(2) have line variability, especially in the red wing, that is stronger than the time-averaged spectrum. MCG-6-30-15(1)"
 has a variable. broad iron line that is as strong as the time-averaged line profile. as does NGC 3783 (although its iron line red wing is not as strong as in MCG-6-30-15).," has a variable, broad iron line that is as strong as the time-averaged line profile, as does NGC 3783 (although its iron line red wing is not as strong as in MCG-6-30-15)."
 Sometimes. a broad iron line and red wing is seen in the time-averaged spectrum. but the variability excess is narrow. and tends to the blue side of the line.," Sometimes, a broad iron line and red wing is seen in the time-averaged spectrum, but the variability excess is narrow, and tends to the blue side of the line."
 Examples are Mrk 766(3). MCG-6-30-15(2) and NGC 151.," Examples are Mrk 766(3), MCG-6-30-15(2) and NGC 7314(1)."
 NGC 41510) is unique in displaying a significantly variable narrow component to the red side of the line. greatly in excess of the time averaged profile.," NGC 4151(2) is unique in displaying a significantly variable narrow component to the red side of the line, greatly in excess of the time averaged profile."
 Many observations show no evidence for line variability at all. despite a clear emission (narrow and/or broad) in their time averaged spectra.," Many observations show no evidence for line variability at all, despite a clear emission (narrow and/or broad) in their time averaged spectra."
 The rms spectra can crudely be classified. into three non-exclusive groups., The rms spectra can crudely be classified into three non-exclusive groups.
 The first class are those with red wing variability. the second. those with blue excess variations. and lastly there are those with little or no evidence for broad or energy shifted iron line variations at all.," The first class are those with red wing variability, the second, those with blue excess variations, and lastly there are those with little or no evidence for broad or energy shifted iron line variations at all."
 Here we discuss each class in turn. but before doing so. we consider the 6.4 keV line core. which may well have a different origin to the broad line. outside the accretion disk.," Here we discuss each class in turn, but before doing so, we consider the 6.4 keV line core, which may well have a different origin to the broad line, outside the accretion disk."
 N07 found that a narrow component of the iron line at 6.4 keV was ubiquitous throughout their sample., N07 found that a narrow component of the iron line at 6.4 keV was ubiquitous throughout their sample.
 The fact that it is narrow and found at the non-redshifted energy of fluorescence for neutral iron suggests that it originates at a large distance from the black hole., The fact that it is narrow and found at the non-redshifted energy of fluorescence for neutral iron suggests that it originates at a large distance from the black hole.
 The most likely location is the molecular torus (Ghiselini. Haardt Matt 1994: Krolik. Madau Zycki 1994) and such a line would be expected to be constant because any variations in the power-law continuum will be averaged out over the light-erossing time. which is expected to be several years for a typical pe-scale torus.," The most likely location is the molecular torus (Ghiselini, Haardt Matt 1994; Krolik, Madau Zycki 1994) and such a line would be expected to be constant because any variations in the power-law continuum will be averaged out over the light-crossing time, which is expected to be several years for a typical pc-scale torus."
 This agrees with the fact that no observation other than MCG-6-30-15¢1). which has a broad variable iron line excess. shows a significantly variable excess in the 6.2-6.6 keV bin.," This agrees with the fact that no observation other than MCG-6-30-15(1), which has a broad variable iron line excess, shows a significantly variable excess in the 6.2-6.6 keV bin."
 In all cases. the variability at 6.4 keV is suppressed compared to the time average spectrum.," In all cases, the variability at 6.4 keV is suppressed compared to the time average spectrum."
 Clearly the narrow core of the iron line is far less variable than the continuum. supporting an origin in distant material.," Clearly the narrow core of the iron line is far less variable than the continuum, supporting an origin in distant material."
 A number of observations in Table | show variability excesses that extend below 6.4 keV. In many the excesses are observed in multiple. consecutive bins.," A number of observations in Table 1 show variability excesses that extend below 6.4 keV. In many the excesses are observed in multiple, consecutive bins."
 In some cases. the red wing is as variable as the continuum. e.g. NGC 3783 and MCG-6-30-15¢1). but in others. the line is more variable: eg. NGC 35160) and NGC S548(2).," In some cases, the red wing is as variable as the continuum, e.g. NGC 3783 and MCG-6-30-15(1), but in others, the line is more variable: e.g. NGC 3516(2) and NGC 5548(2)."
 The observation that the red wing is as variable as the continuum is consistent with the simplest interpretation of disk reflection., The observation that the red wing is as variable as the continuum is consistent with the simplest interpretation of disk reflection.
We note that the residuals from the model fits shown in Figure 1. are relatively large al ον0.6—0.7 keV. To (ry and reduce the residuals we fitted the data using the previous models. each modified by an absorption. namely phabs or tbabs in NSPEC.,"We note that the residuals from the model fits shown in Figure \ref{fig_spec} are relatively large at $\sim 0.6-0.7$ keV. To try and reduce the residuals we fitted the data using the previous models, each modified by an absorption, namely phabs or tbabs in XSPEC."
 We find that the resulting fits are not improved with respect to our previous results., We find that the resulting fits are not improved with respect to our previous results.
 For the timing analvsis we only used PN data. extracted by applying the filtering criteria and extraction region previously described in relobser: the filtered file was then barycentrically corrected.," For the timing analysis we only used PN data, extracted by applying the filtering criteria and extraction region previously described in \\ref{obser}; the filtered file was then barycentrically corrected."
 In order to search for an N-ravy modulation at the sspin period. we first determined a predicted pulse period at the epoch of our oobservalions. assuming a linear spin-down rate and using the radio measurements (DeweyIIobbsetal. 2004).," In order to search for an X-ray modulation at the spin period, we first determined a predicted pulse period at the epoch of our observations, assuming a linear spin-down rate and using the radio measurements \citep{dtws85,hlk04}."
.. We calculate 2=0.495355469 s Cf=2.0187523 Iz) at the midpoint of ow observation (MJD 53.047.6).," We calculate $P = 0.495355469$ s $f = 2.0187523$ Hz) at the midpoint of our observation (MJD 53,047.6)."
 As elitches and/or deviations [rom a linear spin-down may alter (he period evolution. we then searched for à pulsed signal over a wider frequency range centered on /=2.01875 IIz.," As glitches and/or deviations from a linear spin-down may alter the period evolution, we then searched for a pulsed signal over a wider frequency range centered on $f = 2.01875$ Hz."
 We searched for pulsed. emission using (wo methods., We searched for pulsed emission using two methods.
 In the first method we implement the Z7 test (Buccherietal.1983)... with the number of harmonics n being varied from 1 to 5.," In the first method we implement the $Z^{2}_{n}$ test \citep{buc83}, with the number of harmonics $n$ being varied from 1 to 5."
 In the second method we caleulate the Ravleieh statistic (deJager1991:Mardia1972). and then calculate the maximun likelihood periodogram (MLDP. Zaneetal. 2002)) using the C statistic (Cash1979). to determine significant. periodicities in the data sets.," In the second method we calculate the Rayleigh statistic \citep{dej91,mar72} and then calculate the maximum likelihood periodogram (MLP, \citealt{za02}) ) using the $C$ statistic \citep{cas79} to determine significant periodicities in the data sets."
 We do not find anv significant peak near to the predicted Irequency with either method. either using the whole 0.3—10 keV energy band or restricting the search to the 0.3—1.5 keV band.," We do not find any significant peak near to the predicted frequency with either method, either using the whole $0.3-10$ keV energy band or restricting the search to the $0.3-1.5$ keV band."
 By folding the light curve of on the radio frequency ancl fitting it with a sinusoid. we determine an upper limit for the pulsation of in modulation amplitude (defined as (ΕπBin)/(FinesΕμ) where Fa» xd Fy; are the maximum and minimum of the pulse light curve).," By folding the light curve of on the radio frequency and fitting it with a sinusoid, we determine an upper limit for the pulsation of in modulation amplitude (defined as $(F_{max}-F_{min})/(F_{max}+F_{min})$ where $F_{max}$ and $F_{min}$ are the maximum and minimum of the pulse light curve)."
 We have presented the results from the [ist oobservation ofD23344-61., We have presented the results from the first observation of.
. The source has been positively detected in all EPIC instruments. alihough the X-ray. emission is verv faint and the spectrum does not have a high enough," The source has been positively detected in all EPIC instruments, although the X-ray emission is very faint and the spectrum does not have a high enough"
In order to treat the time-dependent electron dynamics ancl radiation transler problem in (he emitting volume. we solve simultaneously the kinetic equation for the relativistic electrons. and for the photons. llere. (d/dl)y is (he radiative energy. loss rate for the electrons. Q.(5./) is the sum of the external injection rate QM [rom Eq.,"In order to treat the time-dependent electron dynamics and radiation transfer problem in the emitting volume, we solve simultaneously the kinetic equation for the relativistic electrons, and for the photons, Here, $(d\gamma / dt)_{\rm loss}$ is the radiative energy loss rate for the electrons, $Q_e (\gamma, t)$ is the sum of the external injection rate $Q_e^{\rm inj}$ from Eq."
 1. and the intrinsic +> pair production rate. πι0) abd ptable.) ave the photon emission and absorption rates corresponding to the various radiation mechanisms. and /jj=(3/4)ο ," \ref{Qe} and the intrinsic $\gamma\gamma$ pair production rate, $\dot n_{\rm ph, em} (\epsilon, t)$ and $\dot n_{\rm ph, abs} (\epsilon, t)$ are the photon emission and absorption rates corresponding to the various radiation mechanisms, and $t_{\rm ph, esc} = (3/4) \, R_b/c$."
In Eq. 4..," In Eq. \ref{e_evolution},"
 electron cooling is approximated as a continuous function of time (ie.. the energv of an individual electron is described as a differentiable function of time).," electron cooling is approximated as a continuous function of time (i.e., the energy of an individual electron is described as a differentiable function of time)."
 This would be inaccurate if a significant contribution to the cooling rate were due to Compton scattering in the Ixlein-Nishina limit since in (hat case. the electron is transferring virtually all of ils energy to a solt photon in a sinele scattering event.," This would be inaccurate if a significant contribution to the cooling rate were due to Compton scattering in the Klein-Nishina limit since in that case, the electron is transferring virtually all of its energy to a soft photon in a single scattering event."
 Hlowever. in (he parameter ranges which we are primarily interested in. electron cooling is dominated by svuchrotvon losses and Compton scattering in the Thomson regime. for which Eq.," However, in the parameter ranges which we are primarily interested in, electron cooling is dominated by synchrotron losses and Compton scattering in the Thomson regime, for which Eq."
 4. is a good approximation., \ref{e_evolution} is a good approximation.
 In Eq. 5..," In Eq. \ref{ph_evolution},"
 the emissivity term contains the contribution [from Compton scattering into a given photon energy interval., the emissivity term contains the contribution from Compton scattering into a given photon energy interval.
" since in all model situations considered here. the Thomson depth of the emitting region is Ty«10"". the modification of the photon spectrum due to scattering of photons out of a eiven photon energy range is neglieible."," Since in all model situations considered here, the Thomson depth of the emitting region is $\tau_{\rm T} \ll 10^{-6}$, the modification of the photon spectrum due to scattering of photons out of a given photon energy range is negligible."
 The relevant electron cooling rates and photon enissivities and opacilies are evaluated using the well-tested subroutines of the jet radiation transfer code described in detail in BoUcher.Alause.&Schlickeiser(1997). and Dóttcher&Bloom(2000)., The relevant electron cooling rates and photon emissivities and opacities are evaluated using the well-tested subroutines of the jet radiation transfer code described in detail in \cite{bms97} and \cite{bb00}.
. The full Nishina cross section lor Compton scattering and the complete. analytical solution Lor (he +> pair production spectrum of Bótteher&Schlickeiser(1997). are used.," The full Klein-Nishina cross section for Compton scattering and the complete, analytical solution for the $\gamma\gamma$ pair production spectrum of \cite{bs97} are used."
 The discretized electron continuitv equation can be written in the form of a iri-diagonal matrix as in (1999).. which can be readily solved. using the standard routine of (1992).," The discretized electron continuity equation can be written in the form of a tri-diagonal matrix as in \cite{cg99}, which can be readily solved using the standard routine of \cite{press92}."
. This procedure turns out to be very stable iL instead of the sharp cutoffs of the electron injection function (1)). we introduce continuous (iransitions {ο verv sleep to mimic these eutoffs.," This procedure turns out to be very stable if, instead of the sharp cutoffs of the electron injection function \ref{Qe}) ), we introduce continuous transitions to very steep power-laws to mimic these cutoffs."
" Specifically. we add a low-energv branch with Q,(5:/)x5? for"," Specifically, we add a low-energy branch with $Q_e (\gamma; t) \propto \gamma^2$ for"
We obtain different spectral types for the secondary star in /' and z/ (SpT?= M5.5. SpT-= M4).,"We obtain different spectral types for the secondary star in $i^\prime$ and $z^\prime$ $_{i^\prime}\approx$ M5.5, $_{z^\prime}\approx$ M4)."
 Since we did not observe the stars in both filters on the same night. the brightness of either companion might have changed from one observation to the next if the stars are variable.," Since we did not observe the stars in both filters on the same night, the brightness of either companion might have changed from one observation to the next if the stars are variable."
 We tentatively assign the secondary spectral type 541., We tentatively assign the secondary spectral type $\pm$ 1.
 Our primary star is also known as CD-25 4322B. the secondary star in à wide double system with 4322.," Our primary star is also known as CD-25 4322B, the secondary star in a wide double system with CD-25 4322."
 Our wide but faint secondary component is not. however. found in any catalogue.," Our wide but faint secondary component is not, however, found in any catalogue."
" The star CD-25 4322 is an F-star (FO/F3V.??) and not within our field of view (CCDMseparation»=12.4"".epoch1897.2).."," The star CD-25 4322 is an F-star \citep[F0/F3V, ][]{Dommanget2002, Perryman1997} and not within our field of view \citep[CCDM separation $\rho=12.4\arcsec$, epoch 1897, ][]{Dommanget2002}."
 Because of the faintness of our secondary companion. it was not detected at the time of observation and not observed in //.," Because of the faintness of our secondary companion, it was not detected at the time of observation and not observed in $i^\prime$."
 Since our primary star is the secondary star in à system with an F-star primary. it is not included in the statistical analysis.," Since our primary star is the secondary star in a system with an F-star primary, it is not included in the statistical analysis."
" This is à known binary system also known as GJ 2060 (?).. which was concluded by ? to probably be part of a quadruple system with another close. equal mass M dwarf binary at a separation of p=67.2""."," This is a known binary system also known as GJ 2060 \citep{Zuckerman2004}, which was concluded by \citet{AllenReid2008} to probably be part of a quadruple system with another close, equal mass M dwarf binary at a separation of $\rho=67.2\arcsec$."
 GJ 2060 is a likely member of the ~50 MMyr old AB Dor association (?).., GJ 2060 is a likely member of the $\sim$ Myr old AB Dor association \citep{Zuckerman2004}.
 We obtain spectral types MI+M3. while ? find spectral types MO.5+M1.5.," We obtain spectral types M1+M3, while \citet{Daemgen2007} find spectral types M0.5+M1.5."
 The primary star is a known variable star (V372 Pup)., The primary star is a known variable star (V372 Pup).
" ?. determine the binary separation and position angle to be p=0.175"" and 9=143.71° (epoch 2002.83). while we find p=0.485"" and 6=169.97. indicating significant orbital motion."," \citet{Daemgen2007} determine the binary separation and position angle to be $\rho=0.175\arcsec$ and $\theta=143.71\degr$ (epoch 2002.83), while we find $\rho=0.485\arcsec$ and $\theta=169.9\degr$, indicating significant orbital motion."
 The primary star of this triple system is also known as LHS 2005. a high proper motion star.," The primary star of this triple system is also known as LHS 2005, a high proper motion star."
" Our separation and position angle for the tertiary component. which is also known as LHS 2004. is p=8.429"" and @=26.17."," Our separation and position angle for the tertiary component, which is also known as LHS 2004, is $\rho=8.429\arcsec$ and $\theta=26.1\degr$."
" This is consistent with data from the 2MASS PSC (?) for the star JO8224787-572645| with a separation 8.6"" and position angle @=23° (epoch 1999.99) and is indicative of orbital motion.", This is consistent with data from the 2MASS PSC \citep{Cutri2003} for the star J08224787-5726451 with a separation $8.6\arcsec$ and position angle $\theta=23\degr$ (epoch 1999.99) and is indicative of orbital motion.
 LHS 2004 and LHS 2005 form à known common proper motion pair., LHS 2004 and LHS 2005 form a known common proper motion pair.
 The close secondary was not previously known., The close secondary was not previously known.
 The wide companion was noticed at the time of observation and fitted into the field of view by placing the primary star in the corner of the detector for the z'-band observations., The wide companion was noticed at the time of observation and fitted into the field of view by placing the primary star in the corner of the detector for the $z^\prime$ -band observations.
" The wide companion ts outside the field of view in /""-band.", The wide companion is outside the field of view in $i^\prime$ -band.
 Since the C component separation from the primary ts greater than6”.. it is not included in the statistical analysis.," Since the C component separation from the primary is greater than, it is not included in the statistical analysis."
 The secondary star is previously unknown., The secondary star is previously unknown.
 Only /'-band images could be used in our analysis since the secondary star was too faint in z'., Only $i^\prime$ -band images could be used in our analysis since the secondary star was too faint in $z^\prime$.
 The position angle. separation. and individual spectral types are therefore obtained from the i'-band observation.," The position angle, separation, and individual spectral types are therefore obtained from the $i^\prime$ -band observation."
" The companion is J21103096-2710513 at a 2MASS PSC distance of 9.4"" and position angle 313°(epoch1998.59,?).."," The companion is J21103096-2710513 at a 2MASS PSC distance of $9.4\arcsec$ and position angle $\theta=313\degr$ \citep[epoch 1998.59, ][]
{Cutri2003}."
" We find a separation p.=9.50"". which is greater than our limits for completeness."," We find a separation $\rho=9.50\arcsec$, which is greater than our limits for completeness."
 The system is therefore not included in the statistical analysts., The system is therefore not included in the statistical analysis.
 This is a known visual binary system where the primary star (also known as V* FG Aqr or GJ 852A) and the secondary star (J22171870-0848186. or GJ 852B) are both flare stars (2)..," This is a known visual binary system where the primary star (also known as V* FG Aqr or GJ 852A) and the secondary star (J22171870-0848186, or GJ 852B) are both flare stars \citep{Gershberg1999}."
" The tertiary companion. close to our secondary star GJ 852B at ppc=0.97"" and gc=316.77. was discovered by ? atp=0.978"" and 6=305.87 (epoch2001.60). hence the system shows orbital motion."," The tertiary companion, close to our secondary star GJ 852B at $\rho_\mathrm{BC}=0.97\arcsec$ and $\theta_\mathrm{BC}=316.7\degr$, was discovered by \citet{Beuzit2004} at $\rho=0.978\arcsec$ and $\theta=305.8\degr$ (epoch2001.60), hence the system shows orbital motion."
 TheC component is in our observations too faint to be resolved in / band., TheC component is in our observations too faint to be resolved in $i^\prime$ band.
 Photometric measurements in 7 for the B component therefore include the very faint flux from the close C component., Photometric measurements in $i^\prime$ for the B component therefore include the very faint flux from the close C component.
" The 2MASS PSC (?) infer à proximity of 7.8"" and position angle of #=213° (epoch 1998.79). relating the positions of GJ 852 A and GJ 852 B. Our measured separation between these stars is p=7.95"" and position angle @=213.27."," The 2MASS PSC \citep{Cutri2003} infer a proximity of $7.8\arcsec$ and position angle of $\theta=213\degr$ (epoch 1998.79), relating the positions of GJ 852 A and GJ 852 B. Our measured separation between these stars is $\rho=7.95\arcsec$ and position angle $\theta=213.2\degr$."
" Also known as GJ 4282. this flare star was discovered to be a binary by ?.. who derived a separation ofp=1.66"" and position angle @=272.25° for epoch 1997.6."," Also known as GJ 4282, this flare star was discovered to be a binary by \citet{McCarthy2001}, who derived a separation of $\rho=1.66\arcsec$ and position angle $\theta=272.25\degr$ for epoch 1997.6."
 ? observed a separation ofp=1.571” and 8=279.73* for epoch 2005.44., \citet{Daemgen2007} observed a separation of $\rho=1.571\arcsec$ and $\theta=279.73\degr$ for epoch 2005.44.
" We find p=1.421"" and 8=98.67. a separation that agrees with previous observations but at a position angle that is clearly inconsistent with the previous measurements by ? and ?.."," We find $\rho=1.421\arcsec$ and $\theta=98.6\degr$, a separation that agrees with previous observations but at a position angle that is clearly inconsistent with the previous measurements by \citet{Daemgen2007} and \citet{McCarthy2001}."
 With an estimated orbital period of approximately 380 years. we need to assume that our primary star (the eastern component) is actually the secondary star of ? and ?.. and our revised position angle is in that case @=278.67. indicating orbital motion.," With an estimated orbital period of approximately 380 years, we need to assume that our primary star (the eastern component) is actually the secondary star of \citet{Daemgen2007} and \citet{McCarthy2001}, and our revised position angle is in that case $\theta=278.6\degr$, indicating orbital motion."
 Since in our observations the eastern star is slightly brighter than the western component. one or both of the stars might be variable. causing the discrepancy in position angle between our observations and the observations by ? and ?..," Since in our observations the eastern star is slightly brighter than the western component, one or both of the stars might be variable, causing the discrepancy in position angle between our observations and the observations by \citet{McCarthy2001} and \citet{Daemgen2007}."
 We assign the stars spectral types M2.5 and M3. respectively. in agreement with °2((M3+M3) and ? (eastern component M2.5. western component M2.6).," We assign the stars spectral types M2.5 and M3, respectively, in agreement with \citet{Daemgen2007}( (M3+M3) and \citet{Shkolnik2009} (eastern component M2.5, western component M2.6)."
 ? estimate the age of the system to be MMyr., \citet{Shkolnik2009} estimate the age of the system to be Myr.
" This flare star, which is also known as GJ 865. was identified by ? as a possible member of the ~600 MMyr Hyades supercluster."," This flare star, which is also known as GJ 865, was identified by \citet{Montes2001} as a possible member of the $\sim600$ Myr Hyades supercluster."
 The star GJ 865 is part of a known triple system., The star GJ 865 is part of a known triple system.
" We observed the two close components. separated by p=0.842"", which ts in agreement with the separation»=0.770"" and position angle 6=16° found by ? for epoch 1991.25."," We observed the two close components, separated by $\rho=0.842\arcsec$, which is in agreement with the separation $\rho=0.770\arcsec$ and position angle $\theta=16\degr$ found by \citet{Perryman1997}
 for epoch 1991.25."
" The third companion ts outside our field of view. with a separation from our primary star of p230.4"" ?).."," The third companion is outside our field of view, with a separation from our primary star of $\rho=30.4\arcsec$ \citep[epoch 1974, ][]{Dommanget2002}."
 While we could not find the spectral type of this companion in literature. the V magnitudes of the three companions differ only slightly (V4= =12.0. =12.1. =12.3. 2.where the close components are B and and we assume that the third component is also an M star.," While we could not find the spectral type of this companion in literature, the V magnitudes of the three companions differ only slightly \citep[$V_\mathrm{A}= =12.0, =12.1, =12.3, ][where the close components are B and and we assume that the third component is also an M star."
 We therefore include this systemin the binary statistics as an M dwarf binary/multiple system., We therefore include this systemin the binary statistics as an M dwarf binary/multiple system.
 This couple of high proper motion stars (2). are also known as LSR J22403-4931W (our primary star) and LSR J22403-4931E located at RA = 118.96s. Dec = -49?331'," This couple of high proper motion stars \citep{Lepine2005} are also known as LSR J22403-4931W (our primary star) and LSR J22403-4931E located at RA = 18.96s, Dec = (J2000)."
"001.4""7(J2000). ?. found p=4.2"" and 8=40° for epoch 1999.72.", \citet{Cutri2003} found $\rho=4.2\arcsec$ and $\theta=40\degr$ for epoch 1999.72.
" We measure p=4.039"" and 0= 41.07.", We measure $\rho=4.039\arcsec$ and $\theta=41.0\degr$ .
 The binary character of this high proper motion star. also known as NLTT 58589. was discovered by ?.. who derived the same individual spectral types M2+M2. as we do.," The binary character of this high proper motion star, also known as NLTT 58589, was discovered by \citet{Daemgen2007}, , who derived the same individual spectral types M2+M2, as we do."
" We find p= 1.989"". in good agreement with the ? separation p=1.904"" for epoch 2005.54. although our measured position angle @=355.7? disagrees with the ? result of 0=265.307 by"," We find $\rho=1.989\arcsec$ , in good agreement with the \citet{Daemgen2007} separation $\rho=1.904\arcsec$ for epoch 2005.54, although our measured position angle $\theta=355.7\degr$ disagrees with the \citet{Daemgen2007} result of $\theta=265.30\degr$ by"
= Fe»G,= )^2.
NG Equation (3)) is a prescription lor computing the rotational diffusion coefficient. [rom scaltering experiments., Equation \ref{eq_diff2}) ) is a prescription for computing the rotational diffusion coefficient from scattering experiments.
 This prescription will be applied in the next section., This prescription will be applied in the next section.
" We can estimate the order of magnitude of the rotational diffusion coefficient bv noting that CALjo/a=Vii. the relative velocity of Ady and Ms. and that a single close encounter produces a change in ( of the fiekl star of order Vy,x«."," We can estimate the order of magnitude of the rotational diffusion coefficient by noting that $\sqrt{G\m12/a}=V_{bin}$, the relative velocity of $M_1$ and $M_2$, and that a single close encounter produces a change in $\ell$ of the field star of order $V_{bin}\times a$."
 The rate of close encounters is ~2nCManonga/oy with ny and oy; the number density and Ld velocity dispersion of the field stars (Paper D)., The rate of close encounters is $\sim 2\pi G\m12\nf a/\sf$ with $\nf$ and $\sf$ the number density and 1d velocity dispersion of the field stars (Paper I).
" Thus (AC)z(aV,J?x2Gλα(σι and where py2mn.", Thus $\langle \Delta \ell^2\rangle \approx (aV_{bin})^2\times 2\pi G\m12\nf a/\sf$ and where $\rf\equiv \mf\nf$.
 The same encounters that induce rotational diffusion will also cause the binary to harden. according to equation (4h)).," The same encounters that induce rotational diffusion will also cause the binary to harden, according to equation \ref{eq_harden}) )."
 The hardening rate may be written Ie)1. o wilh //zz15 for a hare binary (e.g. Quinlan (1996)))., The hardening rate may be written ) = with $H\approx 15$ for a hard binary (e.g. \citet{qui96}) ).
" Thus | with ""MHEa(didly(l/a).", Thus ] with $t^{-1}_{hard}\equiv a(d/dt)(1/a)$.
" Equation (3)) suggests Chat rotational diffusion occurs on a (ime scale that is of order {οΠΠ, times the hardening time. orthat the binary. will rotate"," Equation \ref{eq_compare}) ) suggests that rotational diffusion occurs on a time scale that is of order $\m12/\mf$ times the hardening time, orthat the binary will rotate"
uncertainties are given in parentheses.,uncertainties are given in parentheses.
 The emission measure Is defined as EA/—nigV. where V is the volume contributing to the emission and for solar abundances the hydrogen density myzeO85...," The emission measure is defined as $EM = n_\mathrm{e} n_\mathrm{H} V$, where $V$ is the volume contributing to the emission and for solar abundances the hydrogen density $n_\mathrm{H} \simeq 0.85 n_\mathrm{e}$."
 The temperatures and emission measures of all speetra show a dominant region between | and 2.5 MK., The temperatures and emission measures of all spectra show a dominant region between 1 and 2.5 MK.
 The two dominant temperature components are about 1.2 and 3 MK., The two dominant temperature components are about 1.2 and 2.3 MK.
" Using EUVE, Schmitt et al. ("," Using EUVE, Schmitt et al. ("
1996) derived a DEM ity a peak temperature of 1.6 MK based on Fe-lines only.,1996) derived a DEM with a peak temperature of 1.6 MK based on Fe-lines only.
" This is in satisfactory agreement with our results,", This is in satisfactory agreement with our results.
 The total emission measures summed over all temperature components are about GC1).«10°? ? for LETGS and 09623).<107 ? for RGS+MOS., The total emission measures summed over all temperature components are about $4.6(.4) \times 10^{50}$ $^{-3}$ for LETGS and $3.9(.3) \times 10^{50}$ $^{-3}$ for RGS+MOS.
 These are similar to the total E of L5ς10? ? found by Schmitt et al. (, These are similar to the total $EM$ of $4.5 \times 10^{50}$ $^{-3}$ found by Schmitt et al. (
1996).,1996).
 The determination of abundances is complicated by several factors., The determination of abundances is complicated by several factors.
" The many weak L-shell lines. which are absent in the atomic code (see difference between Col. """," The many weak L-shell lines, which are absent in the atomic code (see difference between Col. """
"MEKAL"" and KELLY"" of Table 2) can produce a ""pseudo-continuum"" (sse σα, Fig.","MEKAL"" and ""KELLY"" of Table 2) can produce a ""pseudo-continuum"" (see e.g. Fig."
 2a between 42 and 58 A). which bias the ueletermination of the real but very weak continuum.," 2a between 42 and 58 ), which bias the determination of the real but very weak continuum."
 Several fits to the LETGShe spectrum were made: to the total spectrum. b) to the total spectrum with selected aylines in the wavelength range from 40 to 100A.. to limit the influence of the inaccuracy of atomic data of Ne-. Mg-. and Si- L-shell lines. andο) to a line spectrum with lines of Table 1 and lines with a statistical significance > do in the wavelength range above 40 ((see Table 5).," Several fits to the LETGS spectrum were made: a) to the total spectrum, b) to the total spectrum with selected lines in the wavelength range from 40 to 100, to limit the influence of the inaccuracy of atomic data of Ne-, Mg-, and Si- L-shell lines, and c) to a line spectrum with lines of Table 1 and lines with a statistical significance $\ga$ $\sigma$ in the wavelength range above 40 (see Table 5)."
 During our investigations the absolute (relative, During our investigations the absolute (relative
" anew density p’=p(I/1""Y. and the same velocity.","a new density $\rho' = \rho (R/R')^3$, and the same velocity."
 In practice. for each new model. CMFGEN adapts its 80-point spatial grid to cover each optical-depth decade with at least tive points.," In practice, for each new model, CMFGEN adapts its 80-point spatial grid to cover each optical-depth decade with at least five points."
 For model D. the grid contains only 50 radial points.," For model D, the grid contains only 50 radial points."
 In refcomp..//h. bs... dependentmodcls(noletbatourmodelswerenoltailoredtomaltchan ion," In \\ref{comp_with_obs}, we present a sample of comparisons to observations to the performance of these time-dependent models (note that our models were not tailored to match any specific observation)."
dMéssilefROiehth," For the “early” model D, observations are only starting now to be available through, e.g., the SWIFT satellite (Brown et al."
hΙΟ inomirconl," 2007), and the corresponding simulations for model D, thus, remain largely unconstrained (but see Quimby et al."
 gsta, 2007; Dessart et al.
, 2007).
rlingn lL wi," To illustrate the bolometric luminosity and color evolution of our four models, we present in Fig."
lhproperliesquilelgpicalofypel{ PS NeCLeonardetal," \ref{fig_lc} their light curves covering from the UV to the near-IR, with properties quite typical of Type II-P SNe (Leonard et al."
 2002: Pastorclloctal., 2002; Pastorello et al.
 2006: Dessartedal, 2006; Dessart et al.
 2007), 2007).
 We. start our discussion. of utime-dependence effects. on Type II SNe. by focusing on the properties of the ejecta., We start our discussion of time-dependence effects on Type II SNe by focusing on the properties of the ejecta.
 In Fig. 2..," In Fig. \ref{fig_h_he},"
 we show the ionization fraction for hydrogen (left) and helium (right) for model A ut the end of the time sequence. ddays after the explosion.," we show the ionization fraction for hydrogen (left) and helium (right) for model A at the end of the time sequence, days after the explosion."
 Hydrogen recombination occurs just above the photosphere but inepresentasamplcofcomparisonsloobserval ancthÉotimesdepeidbntsmhedal than in the steady- ΙΕ ΙΡ abundant in the later model.," Hydrogen recombination occurs just above the photosphere but less efficiently in the time-dependent model than in the steady-state model, neutral hydrogen being 3 orders of magnitude more abundant in the later model."
 In the time-dependent model. two additional features of interest are the presence of fully ionized," In the time-dependent model, two additional features of interest are the presence of fully ionized"
"1998)]], is higher than the value adopted for the nebular component.","], is higher than the value adopted for the nebular component."
 This produces an imperfect match between gas and star metallicity in our photoionization models., This produces an imperfect match between gas and star metallicity in our photoionization models.
" As pointed out by Dopitaetal.(2006), the main effect of this is that the computed stellar UV photon field result slightly softer."," As pointed out by \citet{dopita06}, the main effect of this is that the computed stellar UV photon field result slightly softer."
" To investigate how this discrepancy affects our results, we built a model with a perfect match between nebular and stellar metallicities and compared the result with another model whose metallicities are in disagreement."," To investigate how this discrepancy affects our results, we built a model with a perfect match between nebular and stellar metallicities and compared the result with another model whose metallicities are in disagreement."
 This latter was built using a SED with 12+log(O/H)=8.69 obtained by linear interpolation of the spectra with Z= 0.02 and Z= 0.008., This latter was built using a SED with 12+log(O/H)=8.69 obtained by linear interpolation of the spectra with $Z$ = 0.02 and $Z$ = 0.008.
 In Figure 1 we show the histogram with the comparison of some emission line intensities ratio predicted by these models., In Figure \ref{f1a} we show the histogram with the comparison of some emission line intensities ratio predicted by these models.
" We can see that, with exception of Ro3index(notshowninFig. 1))"," We can see that, with exception of index (not shown in Fig. \ref{f1a}) )"
"showsasmalldeviation, i.e.about12"," shows a small deviation, i.e. about, which corresponds to variations in the oxygen abundance from calibrations using this line ratio by only 0.02 dex."
"96,, whichcorresponc linemethodsandcanonlyaff ectUestimatesindiagnosticdiagramswhichusethe| found that critical line ratios changed by 0.1 dex or less, except for the 1]46300/Ha ratio,"," Thus, the disagrement between the nebular and stellar metallicity have little influence on the $Z$ determinations from strong-line methods and can only affect $U$ estimates in diagnostic diagrams which use the found that critical line ratios changed by 0.1 dex or less, except for the $\lambda$ $\alpha$ ratio,"
Qur value of » is significantly larger than that reported| by Zhangetal.(2001).. 0.07.,"Our value of $n$ is significantly larger than that reported by \citet{zmg+01}, $n=1.81 \pm 0.07$ ."
 We find that if we phase-connect only the same 300-day data set they used. we obtain a value n=1.822:0.01. in agreement with their result.," We find that if we phase-connect only the same 300-day data set they used, we obtain a value $n = 1.82 \pm
0.01$, in agreement with their result."
 Thus their measurement was Clearly conlaminatecl by (imine noise and/or elitch recovery. and affected by. the relatively small time baseline used to measured n.," Thus their measurement was clearly contaminated by timing noise and/or glitch recovery, and affected by the relatively small time baseline used to measured $n$."
 The value of η=2.140x0.009 is sienilicantlv less (han that for simple magnetic dipole radiation. 7=3.," The value of $n=2.140 \pm 0.009$ is significantly less than that for simple magnetic dipole radiation, $n=3$."
 In fact. all measurements of »? (hus [ar are less (han 3.," In fact, all measurements of $n$ thus far are less than 3."
 Several explanations for this have been. proposed., Several explanations for this have been proposed.
 Loss of angular momentum owing to a particle wind (which voung pulsars are well known to have) could account For this (Manchester&Peterson1989)., Loss of angular momentum owing to a particle wind (which young pulsars are well known to have) could account for this \citep{mp89}.
. Another explanation is that the neutron star loses additional rotational energy by toreuing a disk of supernova lallback material (Menouetal.2001)., Another explanation is that the neutron star loses additional rotational energy by torquing a disk of supernova fallback material \citep{mph01}.
. Another explanation is a time-varving magnetic field (Dlandford&Romani1983)., Another explanation is a time-varying magnetic field \citep{br88}.
. The presence of a (me-varving magnetic field can be determined by measuring a value of the third. frequency. derivative larger or smaller (han that predicted by the spin-down model., The presence of a time-varying magnetic field can be determined by measuring a value of the third frequency derivative larger or smaller than that predicted by the spin-down model.
 The simple spin-down model given in Equation 1 assumes a constant value of A. which is only. valid if (he magnetic field. moment ol inertia. and angle between the spin ancl magnetic axes are all constant.," The simple spin-down model given in Equation 1 assumes a constant value of $K$, which is only valid if the magnetic field, moment of inertia, and angle between the spin and magnetic axes are all constant."
 With present data. the third frequency derivative is not measurable for bbecause of contamination from (nming noise.," With present data, the third frequency derivative is not measurable for because of contamination from timing noise."
 Ht ds possible (hat. as observations continue. {his parameter will be measurable.," It is possible that, as observations continue, this parameter will be measurable."
 For both the Crab pulsar and PSR B1509—58. values of v have been measured and are consistent wilh the spin-down law elal. 2005).," For both the Crab pulsar and PSR $-$ 58, values of $\nudotdotdot$ have been measured and are consistent with the spin-down law \citep{lps93,lkgm05}."
. We [ound that the best description of the vvr of dedata include a gliteh at NJD 51335412., We found that the best description of the yr of data include a glitch at MJD $51335 \pm 12$.
 Our partially phase-colierent analysis shows a clear discontinuitv in P (Figures 1 and 2))., Our partially phase-coherent analysis shows a clear discontinuity in $\dot{\nu}$ (Figures \ref{fig:nudot} and \ref{fig:nudot_resid}) ).
 The fully phase coherent analysis confirms (his result., The fully phase coherent analysis confirms this result.
 This glitch. was previously reported by Zhangetal.(2001).. at MJD 51325+45 and later refuted by Custunanoetal.(2003).. who claimed that the data could be described by fitting higher order derivatives. (hat is. timing noise.," This glitch was previously reported by \citet{zmg+01}, at MJD $51325 \pm 45$ and later refuted by \citet{cmm03}, who claimed that the data could be described by fitting higher order derivatives, that is, timing noise."
 The detected gliteh has a small magnitude in both Av/v and AZz/P which Cusumanoetal.(2003) cite as evidence that no glitch occurred., The detected glitch has a small magnitude in both $\Delta{\nu}/{\nu}$ and $\Delta{\dot{\nu}}/{\dot{\nu}}$ which \citet{cmm03} cite as evidence that no glitch occurred.
 llowever. fitting derivatives to the data shows that the residuals increase cdramatically when filling over the epoch of the reported elitch.," However, fitting derivatives to the data shows that the residuals increase dramatically when fitting over the epoch of the reported glitch."
 This is exactly what is expected from a glitch. and is not expected from mine noise. which increases residuals eracually as observations are added.," This is exactly what is expected from a glitch, and is not expected from timing noise, which increases residuals gradually as observations are added."
 In addition. (he partially coherent analysis shows a clear discontinuity in P near (within uncertainties) the epoch of the eliteh found by the phase-coherent analysis (Figure," In addition, the partially coherent analysis shows a clear discontinuity in $\dot{\nu}$ near (within uncertainties) the epoch of the glitch found by the phase-coherent analysis (Figure"
"In this appendix we compile the information about the sky coordinates of the slits and its height (RA (J2000), Dec (J2000), Ay), the correspondent face-on polar coordinates measured from the kinematic centre of the galaxies (r, 0), the cross-correlated velocities evaluated from the observed spectra (νους), the velocity dispersion (oy,,,) and the number of lines detected (niin) and effectively used on the calculations (nus).","In this appendix we compile the information about the sky coordinates of the slits and its height (RA (J2000), Dec (J2000), $\Delta$ y), the correspondent face-on polar coordinates measured from the kinematic centre of the galaxies (r, $\theta$ ), the cross-correlated velocities evaluated from the observed spectra $_{obs}$ ), the velocity dispersion $\sigma_{v_{obs}}$ ) and the number of lines detected $_{lin}$ ) and effectively used on the calculations $_{us}$ )."
that there is no substantial racial dispersal of the metals from the Galactocentric radius where they are produced.,that there is no substantial radial dispersal of the metals from the Galactocentric radius where they are produced.
 A similar result has been also recently reported by. 2.., A similar result has been also recently reported by \citet{spito08}.
 Aloreover. Figures 3 and 4 show that the small fraction of the rising gas escaping to the coronal sector moves racially preferentially outward rather than inward.," Moreover, Figures \ref{fig:colden} and \ref{fig:vneg} show that the small fraction of the rising gas escaping to the coronal sector moves radially preferentially outward rather than inward."
 This is due to the decrease of the centripetal component of the gravity with height and to the conservation of the angular momentum (??)..," This is due to the decrease of the centripetal component of the gravity with height and to the conservation of the angular momentum \citep{shafi76,breg80}."
 The tendency of the MGE gas to move outward. is however. contrasted. by its interaction with the hot. halo (which is assumed at rest)," The tendency of the MGF gas to move outward is however, contrasted by its interaction with the hot halo (which is assumed at rest)."
 The fountain transfers part. of its angular momentum to the halo and thus tends to reduce its racial displacement outward. (see below)., The fountain transfers part of its angular momentum to the halo and thus tends to reduce its radial displacement outward (see below).
 A more quantitative insight of the evolution of the gas circulation is given by Fig. 5.., A more quantitative insight of the evolution of the gas circulation is given by Fig. \ref{fig:angmo}.
 The top panel shows the loss of angular momentum of the SN LL ejecta due to the, The top panel shows the loss of angular momentum of the SN II ejecta due to the
consistent with a picture in which ACN are considered tracers of large scale structures in the universe (¢.e.. Calli et al.,"consistent with a picture in which AGN are considered tracers of large scale structures in the universe (e.g., Gilli et al."
 2003). however they tend to avoid the ceutral reeions of clusters.," 2003), however they tend to avoid the central regions of clusters."
 More ACN ichtifications around clusters are needed to bridge the gap between moderate density euvironmmoeuts (filaments) and ligh-deusity regions (clusters)., More AGN identifications around clusters are needed to bridge the gap between moderate density environments (filaments) and high-density regions (clusters).
 The other two ACNs (ID=63HN) aud ID=1503HN) in Table TU and Fie. 8))," The other two AGNs (ID=63 and ID=1503 in Table \ref{tab_field}
 and Fig. \ref{el_membs}) )"
" have redshifts of z=0.993 Laud z=0.7139. respectively, auc are not cluster members."," have redshifts of z=0.9934 and z=0.7439, respectively, and are not cluster members."
 Their uct counts im the [0.5-10] keV. baud are 53.197 aud [1019 respectively., Their net counts in the [0.5-10] keV band are 53.197 and 44.019 respectively.
 Their ταν fuxes aud unmumnosilos are elven in Table 3.1L.1.., Their X-ray fluxes and luminosities are given in Table \ref{tab_agns}.
 The cluscr N-rav flux measured by ROSAT PSPC in the |0.5-2| keV band within a 23 arcnuün radius aperture is f-—(2240.2)Eή10JP3ergsbem27? (Della Ceca et al.," The cluster X-ray flux measured by ROSAT PSPC in the [0.5-2] keV band within a 3 arcmin radius aperture is $f_x=(2.2\pm0.2)\times 10^{-13} \
erg \ s^{-1} \ cm^{-2}$ (Della Ceca et al."
 2000)., 2000).
 Tie four N-vayv point sources re»orted in this section are located within the above aperture. however ID=1503 was masked out in the PSPC fux estimation (Della Ceca et al.," The four X-ray point sources reported in this section are located within the above aperture, however ID=1503 was masked out in the PSPC flux estimation (Della Ceca et al."
 2000)., 2000).
 Frou the N-ray flixes presented in Table Dnll. we estimate that the RCISAT fiux of int1ο [0.5-2| keV baud was overestimated wv about due to contamination from the other three ACNs.," From the X-ray fluxes presented in Table \ref{tab_agns}, we estimate that the ROSAT flux of in the [0.5-2] keV band was overestimated by about due to contamination from the other three AGNs."
 The extensive spectroscopic survey that we have cared ou on aalows us to firmly characterize its dvuaimical state., The extensive spectroscopic survey that we have carried out on allows us to firmly characterize its dynamical state.
 The coverage of the cluster field) was performed iu the most uniforii possible mamner. allowing us to spectroscopically confini 102 cluster members.," The coverage of the cluster field was performed in the most uniform possible manner, allowing us to spectroscopically confirm 102 cluster members."
 The picture derived froni this sample confrius previous fudiugs frou X-ray* observations., The picture derived from this sample confirms previous findings from X-ray observations.
" Cluster galaxies are observed to fori substructures that coincide with those iu the extended X-""o endsson.", Cluster galaxies are observed to form substructures that coincide with those in the extended X-ray emission.
 Furthermore. weak leusing data based on ο inagiug (Jee et al.," Furthermore, weak lensing data based on ACS imaging (Jee et al."
 2001) show that the three mavor chmips of baryous (hot eas aud galaxies) are associated to three separated dark matter halos., 2004) show that the three mayor clumps of baryons (hot gas and galaxies) are associated to three separated dark matter halos.
 The simple analvsis of the cluster galaxy distribution in velocity space preseuted iu section rofealg/stgivesaveloeitudispersionof- 1600 lau 3 to he whole cluster structure., The simple analysis of the cluster galaxy distribution in velocity space presented in section \\ref{gal_dist} gives a velocity dispersion of $\sim$ 1600 km $^{-1}$ to the whole cluster structure.
 This value is somewhat higher hai that measured for MS1051I (Tran ct al., This value is somewhat higher than that measured for MS1054 (Tran et al.
 1999) at Z=0.833 aud almost the same. within the uucertaiuties. o the one measured or RN τοσο|6708 (Cüola et al.," 1999) at z=0.833 and almost the same, within the uncertainties, to the one measured for RX J1716.6+6708 (Gioia et al."
 1999). another dynamically voung galaxy chister at z=(0.81.," 1999), another dynamically young galaxy cluster at z=0.81."
 This overall velocity dispersion tfurus out to © huger than that expected from the σT relation. iudicating the unrelaxed state of the cluster.," This overall velocity dispersion turns out to be larger than that expected from the $\sigma-T$ relation, indicating the unrelaxed state of the cluster."
" The same analysis allowed us to estimate the velocity dispersion or both the northern :id southeru clumps. which are iu agreement with the «jserved aoLy (Wu. Fang Xu 1995) aud £,a7 (Naο Wu 2000) rolatious for clusters."," The same analysis allowed us to estimate the velocity dispersion for both the northern and southern clumps, which are in agreement with the observed $\sigma-T_X$ (Wu, Fang Xu 1998) and $L_x-\sigma$ (Xue Wu 2000) relations for clusters."
" Iu terms of total cluscr mass, it is not possible to eive a reliable estimate based on the observed velocity dispersion de to the unuvirialised. state of the cluster."," In terms of total cluster mass, it is not possible to give a reliable estimate based on the observed velocity dispersion due to the unvirialised state of the cluster."
 Naunerical DIRuulatious (see Roettiger. Loken Durus 1997) show that mereers make the gas evolve cüffereutlv from the cars uatter. affecting the livdrostatic equilibritiu of the eas ac. therefore. the dynauical mass estimates based ou the cluster N-ray emission as well.," Numerical simulations (see Roettiger, Loken Burns 1997) show that mergers make the gas evolve differently from the dark matter, affecting the hydrostatic equilibrium of the gas and, therefore, the dynamical mass estimates based on the cluster X-ray emission as well."
 The evidence presented in this worl: as well iu others (Alaughan et al., The evidence presented in this work as well in others (Maughan et al.
 2003: Jee et al., 2003; Jee et al.
 200 }srows that this is the case forJ0152., 2004) shows that this is the case for.
7-1357.. Iu fact. the predicted AZo relation for galaxy clusters (Bryan Norman 1998) is unable to reconcile the weak leusiug nass (Jee et al.," In fact, the predicted $M-\sigma$ relation for galaxy clusters (Bryan Norman 1998) is unable to reconcile the weak lensing mass (Jee et al."
 2001) with the overall velocity dispersion presented in this paper., 2004) with the overall velocity dispersion presented in this paper.
 A velocity dispersion of abot tl600 Isus >1 would correspond toa virial mass more than a Actor of two ercater than the weals leusine lueasmummenie, A velocity dispersion of about 1600 km $^{-1}$ would correspond to a virial mass more than a factor of two greater than the weak lensing measurement.
lir Ii the case of the northern aud soutiru subclusters. our niass esnuates roni Eq.," In the case of the northern and southern subclusters, our mass estimates from Eq."
 1 are in close agreement. within the unucertaiuties. with those Ton the weak lensing aud N-rav analyses for thο se substructures and within apertures of ~ 00 Ispe iu radius.," \ref{virmass} are in close agreement, within the uncertainties, with those from the weak lensing and X-ray analyses for the same substructures and within apertures of $\sim$ 400 kpc in radius."
" The specrophotonmetrie information of a sigificaut yactjon of ealaxies down to ~RA""| has allowed us o characterize the galaxy populations oei1357.", The spectrophotometric information of a significant fraction of galaxies down to $\sim R^*+1$ has allowed us to characterize the galaxy populations in.
. Iu terus of spectroscopic classification. we found hne expectec spectral typedensity reation.," In terms of spectroscopic classification, we found the expected spectral type–density relation."
 The high density regions of the cluster are dominaed by red passive ealaxies. most of them classified as k type.," The high density regions of the cluster are dominated by red passive galaxies, most of them classified as k type."
 The lower density reeious in the cluster periphery. ou the other haud. are dominated by star-forming [ΟΠ galaxies.," The lower density regions in the cluster periphery, on the other hand, are dominated by star-forming [OII] galaxies."
 All galaxies showing on-going star-forming activity clearly avoid the, All galaxies showing on-going star-forming activity clearly avoid the
separation of variables in the form. with arbitrary constants ej and es.,separation of variables in the form with arbitrary constants $c_{\rm 1}$ and $c_{\rm 2}$.
 The scattering of stars by shearing. short lived density waves leads to independent diffusion of stars in radial action angular momentun space.," The scattering of stars by shearing, short lived density waves leads to independent diffusion of stars in radial action – angular momentum space."
 This diffusion process has various implications., This diffusion process has various implications.
 The radial action integral is related to. the peculiar velocities of the stars as ‘Thus a distribution function of the form implies à exp07/2o5(1)2 dependence of the velocity distribution with a predicted radial velocity. dispersion of a.) = VEI|Dil2)., The radial action integral is related to the peculiar velocities of the stars as Thus a distribution function of the form implies a $\exp{- u^2 / 2 \sigma^2_{\rm u}(t)}$ dependence of the velocity distribution with a predicted radial velocity dispersion of $\sigma_{\rm u}(t)$ = $\sqrt{\kappa ( c_{\rm 1} + \tilde{D}_{\rm 11} t /2)}$.
 Such a vise of the velocity dispersion with time fits ideally to the actual agevelocity dispersion. relation observed. in the solar. neighbourhoo: (cf., Such a rise of the velocity dispersion with time fits ideally to the actual age–velocity dispersion relation observed in the solar neighbourhood (cf.
 Fuchs et al., Fuchs et al.
 2001 for à recent review of the observationa data), 2001 for a recent review of the observational data).
 Unfortunatelv the diffusion coellicicnts cannot be estimated quantitatively. because the constant |o|7. which »wameterizes the white noise. is not known a priori.," Unfortunately the diffusion coefficients cannot be estimated quantitatively, because the constant $|\Phi_0|^2$, which parameterizes the white noise, is not known a priori."
 Bu judging from the shape of the heating law (46) wave | star scattering of the kind cliseussed here might well have plavec an important role in the Milkv Way disc., But judging from the shape of the heating law (46) wave – star scattering of the kind discussed here might well have played an important role in the Milky Way disc.
 Whether this is he only disc heating mechanism is still a matter of debate (Fuchs et al., Whether this is the only disc heating mechanism is still a matter of debate (Fuchs et al.
 2001)., 2001).
" The ciffusion of the guiding centre radii of the stellar orbits can be estimated [rom the ratio of the dilfusion coelIicients. As shown above &D,,L/(24,) is proportional to the square of the radial velocity dispersion. o0)."," The diffusion of the guiding centre radii of the stellar orbits can be estimated from the ratio of the diffusion coefficients, As shown above $\kappa D_{\rm 11} t/(2 J_{\rm 1})$ is proportional to the square of the radial velocity dispersion, $\sigma^2_{\rm u}(t)$."
 According to epievclic theory (cf., According to epicyclic theory (cf.
" equation. 20) so that the dispersion of the guiding centre radii of the stellar orbits is given hy Using the parameter values estimated above equation (49) implies V/=(2e,/O. if α Dat rotation curve is assumed."," equation 20) so that the dispersion of the guiding centre radii of the stellar orbits is given by Using the parameter values estimated above equation (49) implies $\sqrt{\langle x^2_{\rm g} \rangle} = 0.2 \sigma_{\rm u}/\Omega_{\rm
0}$, if a flat rotation curve is assumed."
 A star with an age of 5 Cars like the Sun has typically in the solar neighbourhood a velocity. dispersion of 50 km/s. Thus VATES = 400 pe = 0.05 rj in the solar neighbourhood. if a local angular velocity of Ου = 26 km/s/kpe is adopted.," A star with an age of 5 Gyrs like the Sun has typically in the solar neighbourhood a velocity dispersion of 50 km/s. Thus $\sqrt{\langle x^2_{\rm g} \rangle}$ = 400 pc = 0.05 $r_{\rm
0}$ in the solar neighbourhood, if a local angular velocity of $\Omega_{\rm 0}$ = 26 km/s/kpc is adopted."
 This confirms the conclusion of Binney Lacey (1988) that the cliffusion of guiding centre radii driven by à rapid succession of spiral density waves ts rather small., This confirms the conclusion of Binney Lacey (1988) that the diffusion of guiding centre radii driven by a rapid succession of spiral density waves is rather small.
 “Phis assumes that disc heating by transient. spiral density waves is the only disc heating mechanism., This assumes that disc heating by transient spiral density waves is the only disc heating mechanism.
 However. if the Sun has indeed. drifted from its birth place nearly- 2 kpe racially outwards to its present ealactocentric raclius as suggested by Wielen. Fuchs. Dettbarn (996) and Wielen Wilson (1997). this would mean that there must be other dynamical heating mechanisms of the galactic disc.," However, if the Sun has indeed drifted from its birth place nearly 2 kpc radially outwards to its present galactocentric radius as suggested by Wielen, Fuchs, Dettbarn (1996) and Wielen Wilson (1997), this would mean that there must be other dynamical heating mechanisms of the galactic disc."
 Lt was shown by Fuchs. Dettbarn. Wiclen (1994) theoretically ancl by numerical simulations that SpitzerSchwarzschild cillusion of stars duc to gravitational encounters with massive molecular clouds. for instance. leads to a much more pronounced diffusion of the euiding centre radii of the stellar orbits. even if the mechanism does not heat the disc ellectively.," It was shown by Fuchs, Dettbarn, Wielen (1994) theoretically and by numerical simulations that Spitzer–Schwarzschild diffusion of stars due to gravitational encounters with massive molecular clouds, for instance, leads to a much more pronounced diffusion of the guiding centre radii of the stellar orbits, even if the mechanism does not heat the disc effectively."
 ] thank X. Just and 1t. Wielen for helpful discussions., I thank A. Just and R. Wielen for helpful discussions.
 I am also grateful to the anonymous referee. whose comments [σας to an improvement of the paper.," I am also grateful to the anonymous referee, whose comments lead to an improvement of the paper."
of success for the ATP class on any particular trial.,of success for the $k^{\rm th}$ class on any particular trial.
 The vector G; is also considered to be missing data. aud is introduced to simplify coustruction of the Gibbs sampler.," The vector ${\bf G}_i$ is also considered to be missing data, and is introduced to simplify construction of the Gibbs sampler."
 The new values of the mussingο data simulated in the data aueimoeutationoO step are then used to simulate Lew values of the regression aud Caussian mixture parameters., The new values of the missing data simulated in the data augmentation step are then used to simulate new values of the regression and Gaussian mixture parameters.
" The second stage of the Cabbs sampler simulates values of the regression parameters. 0, given the curreutvalues of wef and jg."," The second stage of the Gibbs sampler simulates values of the regression parameters, $\theta$, given the currentvalues of $xi$ and $\eta$."
 The third stage simulates values of the mixture paramcters. c. given the current values of © and 1.," The third stage simulates values of the mixture parameters, $\psi$ , given the current values of $\xi$ and $\eta$."
 The fourth stage uses the new values of 0 aud c to update the paramcters of the prior deusity., The fourth stage uses the new values of $\theta$ and $\psi$ to update the parameters of the prior density.
 The values of the parameters are saved. aud the process is repeated. creating a Markov Chain.," The values of the parameters are saved, and the process is repeated, creating a Markov Chain."
 After à large umber of iterations. the Markov Chain converges. and the saved values of 0 and co from the latter part of the aleoritlian may then he treated as a random draw from the posterior distribution. p(£.ole.4g).," After a large number of iterations, the Markov Chain converges, and the saved values of $\theta$ and $\psi$ from the latter part of the algorithm may then be treated as a random draw from the posterior distribution, $p(\theta,\psi|x,y)$."
 Methods for simulatingC» random variables from the distributions used for this Cilobs sampler are described in various works (e.s..Ripley1987:Pressetal.1992:Gelman 2001)..," Methods for simulating random variables from the distributions used for this Gibbs sampler are described in various works \citep[e.g.,][]{rip87,numrec,gelman04}. ."
 A Gibbssampler for the Cussiau mixture model is, A Gibbssampler for the Gaussian mixture model is
occur in NDAÀEs and originate the fast variability in the prompt emissions of GRBs (Janiuk et al.,occur in NDAFs and originate the fast variability in the prompt emissions of GRBs (Janiuk et al.
 2004. 2007: Masacda et al.," 2004, 2007; Masada et al."
 2007)., 2007).
 1n this study. we investigate the structure and stability of NDAEs by taking into account the convective energy transfer in the vertical direction. which has not been considered in detail in the previous studies.," In this study, we investigate the structure and stability of NDAFs by taking into account the convective energy transfer in the vertical direction, which has not been considered in detail in the previous studies."
 In the context of standard accretion. disks which is radiation pressure-dominated. some authors have inferred the importance of vertical convective motions (Disnovatvi-Ixosan Blinnikoy 1977: Shakura et al.," In the context of standard accretion disks which is radiation pressure-dominated, some authors have inferred the importance of vertical convective motions (Bisnovatyi-Kogan Blinnikov 1977; Shakura et al."
 1978: Milsom et al., 1978; Milsom et al.
 1994: Blaes Socrates. 2001: Saddowski et al., 1994; Blaes Socrates 2001; Sa̧ddowski et al.
 2011) ancl some recent studies have shown the importance of convective motions in the hwperaceretion. Hows (Milosavljevic ct al., 2011) and some recent studies have shown the importance of convective motions in the hyperaccretion flows (Milosavljevic et al.
 2010: Sekiguchi Shibata 2010)., 2010; Sekiguchi Shibata 2010).
 Due to the vertical convection. the internal energy stored in the gas would not be advected inward but transported upward. which alters the equation of energy conservation.," Due to the vertical convection, the internal energy stored in the gas would not be advected inward but transported upward, which alters the equation of energy conservation."
 We present the equilibrium solutions of convective NDAEs. discuss their stability. ancl propose the new scenario for the evolution of NDAs that can account [or the violent time variability in the prompt. emission. of GRBs.," We present the equilibrium solutions of convective NDAFs, discuss their stability, and propose the new scenario for the evolution of NDAFs that can account for the violent time variability in the prompt emission of GRBs."
 In the following discussion. we adopt equations describing the steady structure of a hyperaceretion disk. based: on Newtonian gravity.," In the following discussion, we adopt equations describing the steady structure of a hyperaccretion disk based on Newtonian gravity."
 Angular velocity. of eas particles can be approximated as Weplerian: Qtr)=(6MPES where Ad ds the mass of the black hole.," Angular velocity of gas particles can be approximated as Keplerian: $\Omega (r)=(GM/r^3)^{1/2}$, where $M$ is the mass of the black hole."
" Expressions for mass conservation. angular momentum conservation. hydrostatic balance ancl a-viscosity are given. respectively. where e,. X. p. p and ff denote the radial. velocity. surface mass density. kinematic viscosity coefficient. pressure and scale height of the accretion disk. respectively: AZ and a are the mass aceretion rate ancl viscosity parameter."," Expressions for mass conservation, angular momentum conservation, hydrostatic balance and $\alpha$ -viscosity are given, respectively, where $v_r$, $\Sigma$, $\nu$, $p$ and $H$ denote the radial velocity, surface mass density, kinematic viscosity coefficient, pressure and scale height of the accretion disk, respectively; $\dot{M}$ and $\alpha$ are the mass accretion rate and viscosity parameter."
 Llere he pressure p is composed of three ternis: poPars| pase where Prats Pans pa are the radiation. pressure. he gas pressure. the pressure of the degenerate. particles. respectively (for their mathematical description see Section 2.1 of IXMO2).," Here the pressure $p$ is composed of three terms: $p=p_{\rm rad}+p_{\rm gas}+p_{\rm d}$ , where $p_{\rm rad}$, $p_{\rm gas}$, $p_{\rm d}$ are the radiation pressure, the gas pressure, the pressure of the degenerate particles, respectively (for their mathematical description see Section 2.1 of KM02)."
" We set inner radius of the aceretion disk. ri, o be the radius of the innermost stable circular orbit around a Schwarzschild black hole. rg,=Bre. where re=26Mfc is the Schwarzschilel radius."," We set inner radius of the accretion disk, $r_{\rm in}$ to be the radius of the innermost stable circular orbit around a Schwarzschild black hole, $r_{\rm in}=3r_S$, where $r_S=2GM/c^2$ is the Schwarzschild radius."
" Lo addition. we should consider he equation of energy conservation: where Q and Q, are the viscous heating rate and neutrino cooling rate per unit surface area."," In addition, we should consider the equation of energy conservation: where $Q^+$ and $Q_{\nu}^-$ are the viscous heating rate and neutrino cooling rate per unit surface area."
" As for the right hand side. the energy dissipation rate per unit surface area can be described as and the neutrino cooling rate Q is composed. of [our lernis: where dx. dii,fives DO. Qusauen are the neutrino emissivity due to the electron/positron capture by a nucleon AN. due to the cleetron-positron pair annihilation. due to the nucleon-nucleon bremsstrahlung. ancl the plasmon decay. respectively (see Section 2.8 of Ixohri et al."," As for the right hand side, the energy dissipation rate per unit surface area can be described as and the neutrino cooling rate $Q^-$ is composed of four terms: where $\dot{q}_{Ne}$, $\dot{q}_{e^+ e^-}$, $\dot{q}_{\rm brems}$ and $\dot{q}_{\rm plasmon}$ are the neutrino emissivity due to the electron/positron capture by a nucleon $N$, due to the electron-positron pair annihilation, due to the nucleon-nucleon bremsstrahlung, and the plasmon decay, respectively (see Section 2.3 of Kohri et al."
 2005)., 2005).
 The left hand side is often called as the acdvective cooling rate: which means the inward flux of the gas energy. along the flow., The left hand side is often called as the advective cooling rate: which means the inward flux of the gas energy along the flow.
 Here s denotes the entropy. per unit mass. s=(yd|Saad fp. where sy4 and ὅμως are the entropy density of the radiation and the gas. respectively (sec Section 2.3 of IxMO2).," Here $s$ denotes the entropy per unit mass, $s=(s_{\rm rad}+s_{\rm
gas})/\rho$ , where $s_{\rm rad}$ and $s_{\rm gas}$ are the entropy density of the radiation and the gas, respectively (see Section 2.3 of KM02)."
" In the following ciiscussions. we approximated dsdr as s/r. and deline the total cooling rate as QQ,|Q, "," In the following discussions, we approximated $ds/dr$ as $s/r$, and define the total cooling rate as $Q^- \equiv Q_{\nu}^-
+Q_{\rm adv}^- $."
Lt would be obvious that the radiative cooling is negligible., It would be obvious that the radiative cooling is negligible.
 In order to see cllects of convection in an hvperaccretion disk. we should. estimate. a typical timescale for the convective motion of the blob in the vertical direction Fou and compare it with timescale for the inward advection Gas.," In order to see effects of convection in an hyperaccretion disk, we should estimate a typical timescale for the convective motion of the blob in the vertical direction $t_{\rm conv}$ and compare it with timescale for the inward advection $t_{\rm adv}$."
 The acceleration of the blob in the accretion disk due to the vertical buovancy would. be the same order of magnitude as that due to the gravitational force. Le. O(r)7z2 where is the vertical coordinate measured from the equatorial plane.," The acceleration of the blob in the accretion disk due to the vertical buoyancy would be the same order of magnitude as that due to the gravitational force, i.e. $\sim \Omega (r)^2 z$ where $z$ is the vertical coordinate measured from the equatorial plane."
" Then the convective speed along the vertical direction comming [rom zinf2) should be and then the timescale for the blob which is emerged at 2CLf) and transported convectively can be estimated as On the other μαμα, advection timescale can be estimated as ∐⋖⊾↓⋅⋖⋅∖∖⊽⋖⊾≼⇍∪⊔≼∙⋖⋅⊔∣↓⋅⋜⋯⊾∪⊔≼↛⋜↧⋡∖⋖⋅⋡∖∖∖⋰↓↿↓↥⇀⋃∿↓∪⊽⋝⇀⊔⋅⋡∖⋯∙ ⊥⋡ ⇀∖≼⇍≼⇍"," Then the convective speed along the vertical direction comming from $z_{\rm min}~(\ll z)$ should be and then the timescale for the blob which is emerged at $z(<H)$ and transported convectively can be estimated as On the other hand, advection timescale can be estimated as Here we concentrate on cases with $\dot{M}\lesssim 10^{-3}M_{\odot}{\rm sec}^{-1}$."
∪↓⋅∠⇂⊀↓⊔⋏↳≱↿∪↓∖⋥∖∐⊔∢⋅⊓∙↣," According to KM02 etc.,"
 such an accretion disk is very optically thick with respect of photons ancl not so dense or hot enough to emit neutrinos elliciently., such an accretion disk is very optically thick with respect of photons and not so dense or hot enough to emit neutrinos efficiently.
 Llowever. when the convection timescale is shorter than the advection timescale. the energy dissipated in the aceretion Low would. not. be adveetecd radially inward. but would be convected. upwarel. and as a result the gas at a certain radius would be heated more ellicientlv than in the case without convection.," However, when the convection timescale is shorter than the advection timescale, the energy dissipated in the accretion flow would not be advected radially inward, but would be convected upward, and as a result the gas at a certain radius would be heated more efficiently than in the case without convection."
 Let, Let
relation. when the bolometric correction becomes insensitive to temperature. (which occurs longward of about one micron for G and Ix spectral tvpes. tvpical of Cepheids.),"relation, when the bolometric correction becomes insensitive to temperature (which occurs longward of about one micron for G and K spectral types, typical of Cepheids.)"
 The areal variations (vpically amount to only around 0.3-0.4 mag im total amplitude. (, The areal variations typically amount to only around 0.3-0.4 mag in total amplitude. (
Those over LOO days can have amplitudes of 0.6-0.8 mag).,Those over 100 days can have amplitudes of 0.6-0.8 mag).
 This is to be compared with observed D-band amplitudes that can exceed 2 mag or I-band amplitudes that can reach 1 mag., This is to be compared with observed B-band amplitudes that can exceed 2 mag or I-band amplitudes that can reach 1 mag.
 Even just a [actor of three decrease in amplitude provides for almost a factor of 10 decrease in ihe number of randomlv-phased observations needed to reach the same error on (he mean magnitude [or a given variable star., Even just a factor of three decrease in amplitude provides for almost a factor of 10 decrease in the number of randomly-phased observations needed to reach the same error on the mean magnitude for a given variable star.
 There are vet further advantages to the mid-infrared., There are yet further advantages to the mid-infrared.
 The effects of line blanketing. the process by which energy is removed from the optical and UV. aud is subsequently thermalized and redistributed to the optical/uear-intrarecl (back-warming). are expected to be much smaller at mid-infraredwavelengths!.," The effects of line blanketing, the process by which energy is removed from the optical and UV and is subsequently thermalized and redistributed to the optical/near-infrared (back-warming), are expected to be much smaller at mid-infrared."
. Most importantly. because the reddening is so low in comparison to the optical. 3.6 jan provides an opportunity for a very clean and direct test for anv metallicity effects.," Most importantly, because the reddening is so low in comparison to the optical, 3.6 $\mu$ m provides an opportunity for a very clean and direct test for any metallicity effects."
 For the HST Key Project determination of the extragalactic distance scale. a list of identified svstematic uncertainties set its finally quoted aceuracy al £10%..," For the HST Key Project determination of the extragalactic distance scale, a list of identified systematic uncertainties set its finally quoted accuracy at $\pm$."
 The dominant svslelmatics were: (a) the zero point of the Leavitt Law: (b) the differential metallicity corrections to the PL zero point: (c) reddening corrections: (d) calibration/instrumental uncerlainties: (e) crowding effects and παν HIST. PSF uncertainties and evolution. with lime/posilion., The dominant systematics were: (a) the zero point of the Leavitt Law; (b) the differential metallicity corrections to the PL zero point; (c) reddening corrections; (d) calibration/instrumental uncertainties; (e) crowding effects and finally HST PSF uncertainties and evolution with time/position.
 In this paper. we discuss the improvements (hat are coming [romSpitzer. and that will eventually come from JWST.," In this paper, we discuss the improvements that are coming from, and that will eventually come from JWST."
 We show in Figures la and b απο models for solar-metallicily supergiant stars. wilh ellective temperatures and eravilies of 4000Ix. and log(g)—0. consistent with those of Cepheids.," We show in Figures 1a and b Kurucz models for solar-metallicity supergiant stars, with effective temperatures and gravities of 4000K and log(g)=0, consistent with those of Cepheids."
 Note that the IRAC band 1: at 3.6 jan is devoid of any molecular bands: however. IRAC band 2 at 4.5 yan overlaps with the broad. CO molecular bands in the approximate wavelength range of 4 to 6 jm. There are (vo immediate conclusions from these plots.," Note that the IRAC band 1 at 3.6 $\mu$ m is devoid of any molecular bands; however, IRAC band 2 at 4.5 $\mu$ m overlaps with the broad CO molecular bands in the approximate wavelength range of 4 to 6 $\mu$ m. There are two immediate conclusions from these plots."
 First. Figure la illustrates thesmooth continuum. over the 3.6 jim band. and as expected. its suitability for distance determinations.," First, Figure 1a illustrates thesmooth continuum over the 3.6 $\mu$ m band, and as expected, its suitability for distance determinations."
 Figure Ib illustrates that the 4.5 yam band may not be a suitable distance indicator for Cepheids., Figure 1b illustrates that the 4.5 $\mu$ m band may not be a suitable distance indicator for Cepheids.
 We are currently exploring the use of the 4.5 jan band as a metallicity indicator for Cepheids (Scowerolt aL. in preparation).," We are currently exploring the use of the 4.5 $\mu$ m band as a metallicity indicator for Cepheids (Scowcroft , in preparation)."
and poy=eC—n) is the number density required for corotation. then the requirement is (hat the multiplicitv. M—(n.+nρου. be greater than unity.,"and $\rho_{\rm GJ}=e(n_+-n_-)$ is the number density required for corotation, then the requirement is that the multiplicity, $M=(n_++n_-)/\rho_{\rm GJ}$, be greater than unity."
 The requirement on the parallel. current density for screening of OEq4j/0/ can be estimated by noting (hat the maximum current density is when the electrons aud positrons are flowing in opposite directions al relativistic speeds., The requirement on the parallel current density for screening of ${\partial E_{{\rm ind}\parallel}/\partial t}$ can be estimated by noting that the maximum current density is when the electrons and positrons are flowing in opposite directions at relativistic speeds.
 This maximum is pcc., This maximum is $e(n_++n_-)c=M\rho_{\rm GJ}c$ .
" Apart fron factors of order unity. one has J.)/peje2r/Mry; which is nich less than unity for kr<r,—c/w."," Apart from factors of order unity, one has $J_{{\rm sc}\parallel}/M\rho_{\rm GJ}c\approx r/Mr_{\rm lc}$, which is much less than unity for $r\ll r_{\rm lc}=c/\omega$."
 I follows that pair creation (in laree-amplitucle oscillations) provides an adequate source of charges to ensure that parallel current screening occurs in (he inner magnetosphere., It follows that pair creation (in large-amplitude oscillations) provides an adequate source of charges to ensure that parallel current screening occurs in the inner magnetosphere.
 However. parallel current screening must break down in the outer magnetosphere.," However, parallel current screening must break down in the outer magnetosphere."
 Perpendicular current screening involves different plivsies [rom parallel current screening., Perpendicular current screening involves different physics from parallel current screening.
 We discuss (his from two complementary. viewpoints., We discuss this from two complementary viewpoints.
 The equivalent dielectric tensor of anv plasma at very low Irequencies may be approximated by a perpendicular- component 1407/05> and a parallel component 1705/47.>7 where the unit. terms corresponds to vacuum.," The equivalent dielectric tensor of any plasma at very low frequencies may be approximated by a perpendicular component $1 + c^2/v_A^2$ and a parallel component $1 - \omega_p^2/\omega^2$, where the unit terms corresponds to vacuum."
 Here the Allven speed is e4=D/(ug)*7. where 1 is the mass density.," Here the $\acute{\rm v}$ en speed is $v_A = B/(\mu_0\eta)^{1/2}$, where $\eta$ is the mass density."
" In a conventional plasma. one has ο«ο, but in à pulsar plasma. one has (4>>c."," In a conventional plasma, one has $v_A \ll c$, but in a pulsar plasma, one has $v_A \gg c$."
 ]lence. (he perpendicular response of a pulsar plasma is effectively the same as if (he plasma were absent.," Hence, the perpendicular response of a pulsar plasma is effectively the same as if the plasma were absent."
" The perpendicular response links (he current density. J_. to the displacement current, z;QE01."," The perpendicular response links the current density, ${\bi J}_\perp$, to the displacement current, $\varepsilon_0 \partial{\bi E}_\perp/\partial t$."
" It follows that the plasma can supply only a fraction 7/0,«1 of the current required to screen the displacement current.", It follows that the plasma can supply only a fraction $c^2/v_A^2 \ll 1$ of the current required to screen the displacement current.
 [In contrast. interpreting —«7 as a second lime derivative. the parallel response corresponds to 0.4)/Ol=τα which leads to large amplitude electric oscillations in a pulsar plasma (Levinsonetal.2005).," In contrast, interpreting $-\omega^2$ as a second time derivative, the parallel response corresponds to $\partial J_\parallel/\partial t = \omega_p^2\varepsilon_0 E_\parallel$, which leads to large amplitude electric oscillations in a pulsar plasma \citep{Letal05}."
. The perpendicular plasma response (at very low frequencies) can be understood in terms ol the so-called polarization drift., The perpendicular plasma response (at very low frequencies) can be understood in terms of the so-called polarization drift.
 Due to QE.Οἱ. à particle with charge q and mass m drilis across the magnetic field lines αἱ a velocity /(ΠΕΟΙ.," Due to $\partial{\bi E}_\perp/\partial t$, a particle with charge $q$ and mass $m$ drifts across the magnetic field lines at a velocity $(m/qB^2) \partial{\bi E}_\perp/\partial t$."
" For an inductive electric field due to the magnetic field varving at frequency vw=2z/P. the polarization ον is smaller than (he dift caused by the inductive electric field by a factor of w/Q, (see equation (10)). where O,=eB/im is the evelotvon frequency."," For an inductive electric field due to the magnetic field varying at frequency $\omega=2\pi/P$, the polarization drift is smaller than the drift caused by the inductive electric field by a factor of $\omega/\Omega_e$ (see equation (10)), where $\Omega_e=eB/m$ is the cyclotron frequency."
 Summiig over all charges. (his leads to a current density Jo=(c/e3)z)0E./Ol. which reproduces the result implied by the plasma response tensor. providing a physical interpretation of (his response.," Summing over all charges, this leads to a current density ${\bi J}_\perp = (c^2/v_A^2) \varepsilon_0 \partial{\bi E}_\perp/\partial t$, which reproduces the result implied by the plasma response tensor, providing a physical interpretation of this response."
 In summary. (he parallel component of the displacement current can be screened by a plasma current. which. however. is unstable to large-amplitude oscillations.," In summary, the parallel component of the displacement current can be screened by a plasma current, which, however, is unstable to large-amplitude oscillations."
 The perpendicular, The perpendicular
 Since 7. used proper motions ancl parallaxes obtained: by the Hipparcos satellite (7). to investigate the kinematics of the Solar neighbourhood. it has been clear that the local distribution function (bDE)) is far from smooth.," Since \cite{WD98} used proper motions and parallaxes obtained by the Hipparcos satellite \citep{Hipparcos} to investigate the kinematics of the Solar neighbourhood, it has been clear that the local distribution function ) is far from smooth."
 In particular. the distribution of stars in the C.V. is dominated by a number of streams. all of which are thought to be dynamical in origin (e.g.?)..," In particular, the distribution of stars in the $U,V$ is dominated by a number of streams, all of which are thought to be dynamical in origin \citep[e.g.][]{Faea05}."
 Recently 7.heneclorthSLO argued that. part of this substructure could be explained by a recent inner Lindblad resonance (LL). a conclusion he supported. with reference to the distribution in angle coordinates of stars observed by the Geneva-Copenhagen survey (GO$8: ?2)..," Recently \citet[henceforth S10]{Se10} argued that part of this substructure could be explained by a recent inner Lindblad resonance (ILR), a conclusion he supported with reference to the distribution in angle coordinates of stars observed by the Geneva-Copenhagen survey \citep*[GCS:][]{GCS09}."
 This conclusion was supported by 2? who looked at stars in the Solar neighbourhood observed by the Racial Velocity Experiment (RAVE:2). and the Sloan Digital Sky Survey (SDSS:?).., This conclusion was supported by \cite*{HaSePr11} who looked at stars in the Solar neighbourhood observed by the Radial Velocity Experiment \citep[RAVE:][]{RAVE1_short} and the Sloan Digital Sky Survey \citep[SDSS:][]{SDSS7_short}.
 In this paper L reexamine S10's conclusion that the clistribution of stars in the Solar neighbourhood show signs of an inner Lindblad resonance (ILIU., In this paper I reexamine S10's conclusion that the distribution of stars in the Solar neighbourhood show signs of an inner Lindblad resonance (ILR).
 E compare the GCS sample of stars in the Solar neighbourhood. to a dynamical model., I compare the GCS sample of stars in the Solar neighbourhood to a dynamical model.
 This allows me to separate selection ellects from genuine substructure in the local and to develop some understanding of the impact of selection cllects on the observed properties of any substructure that is found in the localDr.," This allows me to separate selection effects from genuine substructure in the local, and to develop some understanding of the impact of selection effects on the observed properties of any substructure that is found in the local."
 E then explore he impact of selection ellects on simple models of an ILI or an outer Lindblad resonance (OLR)., I then explore the impact of selection effects on simple models of an ILR or an outer Lindblad resonance (OLR).
 1n Section ?? | discuss angle-action coordinates. how hey might be used to determine the dynamical origin of observed. kinematic substructure. and their relationship to kinematics in the Solar neighbourhood.," In Section \ref{sec:AAcoords} I discuss angle-action coordinates, how they might be used to determine the dynamical origin of observed kinematic substructure, and their relationship to kinematics in the Solar neighbourhood."
 In Section 3. 1 eive numerical details of the assumptions made and the ohase-mixed. dynamical model considered., In Section \ref{sec:num} I give numerical details of the assumptions made and the phase-mixed dynamical model considered.
 In. Section. ?? ] explore the appearance in angle coordinates of the solar neighbourhood in a phase-mixed model. whieh E then use in Section 5 to interpret the distribution in angle coordinates of stars observed by the GCS.," In Section \ref{sec:smooth} I explore the appearance in angle coordinates of the solar neighbourhood in a phase-mixed model, which I then use in Section \ref{sec:GCS} to interpret the distribution in angle coordinates of stars observed by the GCS."
 Section 6. discusses simple models which include a resonant component. and uses them to better understand the GC's data.," Section \ref{sec:resmod} discusses simple models which include a resonant component, and uses them to better understand the GCS data."
 Three actions J; and three conjugate angle coordinates 80; provide canonical coordinates for stars orbiting in the eravitational potential of the Galaxy., Three actions $J_i$ and three conjugate angle coordinates $\theta_i$ provide canonical coordinates for stars orbiting in the gravitational potential of the Galaxy.
 For a particle on any orbit the actions are conserved. quantities ancl the angles increase linearly with time. 6;(/)=6;(0)| O;/. where £2; is a frequency.," For a particle on any orbit the actions are conserved quantities and the angles increase linearly with time, $\theta_i(t) = \theta_i(0)+\Omega_it$ , where $\Omega_i$ is a frequency."
 This means that J can be thought of as labelingan orbit. and @ as describing a point on that orbit.," This means that $\bolJ$ can be thought of as labelingan orbit, and $\bolth$ as describing a point on that orbit."
Ehe usual,The usual
ueutriuo species?,neutrino species”.
 To perforin the study. we use the statistical 4? technique. with the code described by Fiorentinietal.(1998) and Lisietal.(1999).," To perform the study, we use the statistical $\chi^2$ technique, with the code described by \citet{Fi98} and \citet{Li99}."
. This code allows to analyze the coustraints that the measured Ie. D aud [ Li abundances put on jj; aud IN.," This code allows to analyze the constraints that the measured He, D and $^7$ Li abundances put on $\eta$ and $N_\nu$."
 For the primordial D abundance. we use the value obtiiued by Pottiuietal. (2008).," For the primordial D abundance, we use the value obtained by \citet{P08}."
. As for ‘Li. its value derived from observations of low-inetallicitv halo stars (Asphiudetal.2006) i5 ~ 5 times lower than the one obtained from the WALAP analysis (Duuklevetal.2009).," As for $^7$ Li, its value derived from observations of low-metallicity halo stars \citep{As06} is $\sim$ 5 times lower than the one obtained from the WMAP analysis \citep{D09}."
. Because mechauisiuas that may lead to a reduction of the * Li primordial abundance. such as diffusion or rotationally iuduced mixing. are nof well understood and we do not kuow how to correct for them. we have adopted the value of the primordial abundance of “Li abundance as derived from the 5yr WMAP data of Dunkleyetal.(2009).," Because mechanisms that may lead to a reduction of the $^7$ Li primordial abundance, such as diffusion or rotationally induced mixing, are not well understood and we do not know how to correct for them, we have adopted the value of the primordial abundance of $^7$ Li abundance as derived from the 5yr WMAP data of \citet{D09}."
".. The predicted primordial abundances of light clemeuts depend ou the adopted neutron life-time 5,.", The predicted primordial abundances of light elements depend on the adopted neutron life-time $\tau_{\rm n}$.
" We lave considered two values. the old one. 5, = 885.1 + 0.9 s (Arzimanoyetal. 2000).. aud the new oue. 5, = BNr8 + 0.5 5 (Serebrovetal.2005.2008)."," We have considered two values, the old one, $\tau_{\rm n}$ = 885.4 $\pm$ 0.9 s \citep{A00}, and the new one, $\tau_{\rm n}$ = 878.5 $\pm$ 0.8 s \citep{S05,S08}."
". With the old value5 of 7, aud our best value of the primordial He abundance. Y, = (0.25654 0.0010(stat.)"," With the old value of $\tau_{\rm n}$ and our best value of the primordial He abundance, $Y_p$ = $\pm$ 0.0010(stat.)"
τε obtainedO.0050(svst.).," $\pm$ 0.0050(syst.),"
" me mun (= 0.610521) is when ny = ""0.10 and I 6.2:nin68.", the minimum $\chi^2_{min}$ (= 0.640524) is obtained when $\eta_{10}$ = 6.47 and $N_\nu$ = 3.68.
 4017The value ofiy is in agreenie withiy = derived from the WALAP data (Dunkley 2009)., The value of $\eta_{10}$ is in agreement with $\eta_{10}$ = $\pm$ 0.17 derived from the WMAP data \citep{D09}.
". If instead the new value of 5, is adopted with the same value of 35. then the ini (= 0.619816) is obtained when iy = 6.51 and ἂν = on3.80."," If instead the new value of $\tau_{\rm n}$ is adopted with the same value of $Y_p$ , then the minimum $\chi^2_{min}$ (= 0.619816) is obtained when $\eta_{10}$ = 6.51 and $N_\nu$ = 3.80."
" We note that ay aud IN, oulv sheltly depend ou the value of the “Li abundance.", We note that $\eta_{10}$ and $N_\nu$ only slightly depend on the value of the $^7$ Li abundance.
 They are by and24. respectively. if the observed ‘Li decreasedabundance by. otal.(2006) is adopted.," They are decreased by and, respectively, if the observed $^7$ Li abundance by \citet{As06} is adopted."
" The ijoiut ft of y aud ;V, is shown iu Figures 2aa ind 2 for the two values of z,.", The joint fit of $\eta$ and $N_\nu$ is shown in Figures \ref{fig2}a a and \ref{fig2}b b for the two values of $\tau_{\rm n}$.
" The 1o (4? A2,, = 1.0) aud 26 (47. = 2.71) deviations are shown respectively bv the thin \2,,,,aud thick solid lues.", The $\sigma$ $\chi^2$ – $\chi^2_{min}$ = 1.0) and $\sigma$ $\chi^2$ – $\chi^2_{min}$ = 2.71) deviations are shown respectively by the thin and thick solid lines.
" We fiud the equivdent ο of light ucutrino species to be in. the range. JN,- = ο.USD (20) (Fig.", We find the equivalent number of light neutrino species to be in the range $N_\nu$ = $^{+0.80}_{-0.70}$ $\sigma$ ) (Fig.
" s 2aa) in: the first⋅ case. and AN,E = UULUN (20) (Fig."," \ref{fig2}a a) in the first case, and $N_\nu$ = $^{+0.80}_{-0.70}$ $\sigma$ ) (Fig."
 M 2bb) inR the second case., \ref{fig2}b b) in the second case.
 Both of these values are ouly mareinally consistent (at the 20 level) with the value of 2.99032EO.011 (Casoetal.1998). shownby the exponentialdashed line. nuplving deviations from SBBN.," Both of these values are only marginally consistent (at the $\sigma$ level) with the experimental value of $\pm$ 0.011 \citep{Ca98} shown by the dashed line, implying deviations from SBBN."
" We note that. although both values are consistent with JSy = Lt+ 1.5 derived from the analysis of ον WMADP observations (Komatsuetal.2009).. the primordial helium abundance sets tiehter coustraints on the effective mmuiber of neutrino species than the CMD data. the error bars of JN, being approximately half as large in the first case as compared to the latter case."," We note that, although both values are consistent with $N_\nu$ = 4.4 $\pm$ 1.5 derived from the analysis of 5yr WMAP observations \citep{K09}, the primordial helium abundance sets tighter constraints on the effective number of neutrino species than the CMB data, the error bars of $N_\nu$ being approximately half as large in the first case as compared to the latter case."
" We present here a new determination of the primorcia helium mass fraction Y,low by linear regressions of a sample of 9:3 spectra of 86 mctallicity extragalactic ID reeglons.", We present here a new determination of the primordial helium mass fraction $Y_p$ by linear regressions of a sample of 93 spectra of 86 low-metallicity extragalactic H regions.
 Iu this new deteruunation of νι we have taken into account thelatest developiueuts concerning severa known svstemiatic effects.," In this new determination of $Y_p$, we have taken into account thelatest developments concerning several known systematic effects."
 We have used Aoute Carlo methods to solve simultaneously for the effects of collisional aud fluorescent cuhancemenuts of Te recombination lines. of collisional aud. fluorescent excitation of lydrogen oenüssion lines. of uuderlviug stellar Πο absorption. of possible teniperature differences between the Ie! and. [O. ul) zones. aud of the ionization correction factor [CF (Ue! | IE?! ).," We have used Monte Carlo methods to solve simultaneously for the effects of collisional and fluorescent enhancements of He recombination lines, of collisional and fluorescent excitation of hydrogen emission lines, of underlying stellar He absorption, of possible temperature differences between the $^+$ and [O ] zones, and of the ionization correction factor $ICF$ $^+$ + $^{2+}$ )."
 We have obtained the following results: 1l., We have obtained the following results: 1.
" Our best vm is Y, = 0.2565 + O.00L0(stat.)", Our best value is $Y_p$ = 0.2565 $\pm$ 0.0010(stat.)
 + 0.0050(svst.).," $\pm$ 0.0050(syst.),"
 or larger than the value derived from the microwave backerouud vacation fiuctuation lucasurements assuming SBBN., or larger than the value derived from the microwave background radiation fluctuation measurements assuming SBBN.
" In order to bring this high value of Y, iuto agreciuent with the deuteriunu and Syr WALAP imeasurements. an equivalent πο of neutrino flavors in the range 3.68 3.80. depending on the lifetime of the neutron. is required."," In order to bring this high value of $Y_p$ into agreement with the deuterium and 5yr WMAP measurements, an equivalent number of neutrino flavors in the range 3.68 – 3.80, depending on the lifetime of the neutron, is required."
 This is higher than the canonical value of 3 aud nmiplies the existence ofdeviations frou: SBBN, This is higher than the canonical value of 3 and implies the existence ofdeviations from SBBN.
 ., 2.
 The dV/4Z slope derived frou the ο ΟΠ linear reeression is equal to 1.62 + 0.29(stat.).," The $dY/dZ$ slope derived from the $Y$ – O/H linear regression is equal to 1.62 $\pm$ 0.29(stat.),"
 shallower thu the previous determinationbv Izotovetal.(2007 ).., shallower than the previous determinationby \citet{I07}. .
 Y.LL thauks the staff of the Astronomy. Department at the Universitv of Virginia aud of the Max. Plauck Tustitute for BRadioastronomiw in Boun. Cermauy for wari hospitality.," Y.I.I. thanks the staff of the Astronomy Department at the University of Virginia and of the Max Planck Institute for Radioastronomy in Bonn, Germany for warm hospitality."
dispersion of infrared dark clouds (Sridharanetal.,dispersion of infrared dark clouds \citep{s05}.
2005)..- Lusicle rjj. where the binary itself may reside. gas falls freely onto the central stars.," Inside $r_{\rm in}$, where the binary itself may reside, gas falls freely onto the central stars."
" If the binary separation. to be denoted as eq,;.lot exceeds rj.inu then each orbitingo star is surrouucded by its own zone of infall."," If the binary separation, to be denoted as $a_{\rm tot}$, exceeds $r_{\rm in}$, then each orbiting star is surrounded by its own zone of infall."
 In that case. eit becomes tlie appropriate inner boundary.," In that case, $a_{\rm tot}$ becomes the appropriate inner boundary."
" This comparison ol ayy relative to ry effectively distinguishes two cases: “hard” binaries. in which the relative speed ol the component stars is supersonic with respect to the gas aud ""soft"" binaries. [or which this speed is subsouicrij)."," This comparison of $a_{\rm tot}$ relative to $r_{\rm in}$ effectively distinguishes two cases: “hard” binaries, in which the relative speed of the component stars is supersonic with respect to the gas and “soft” binaries, for which this speed is subsonic."
. We shall concentrate on the first case. since it yields. as we shall see in Section La simplified [orm of the acoustic disturbance.," We shall concentrate on the first case, since it yields, as we shall see in Section 4, a simplified form of the acoustic disturbance."
 We also require that our propagatione regione is not so spatially extended that the dominant eravitatioual force is from interior gas rather than the stars., We also require that our propagation region is not so spatially extended that the dominant gravitational force is from interior gas rather than the stars.
 Thus. we are coufined within anotler radius rq. where the mass of background gas rivals that of the stars.," Thus, we are confined within another radius $r_{\rm gas}$, where the mass of background gas rivals that of the stars."
 For au H» number deusity of 101cin. represeiating the most compact regions of infrared dark clouds. we find that LAL. is contained inAU.," For an ${\rm H}_2$ number density of $10^7\,\,{\rm cm}^{-3}$, representating the most compact regions of infrared dark clouds, we find that $1\,\,\Msun$ is contained in."
. Beyond even this point. theory indicates. and observations confirm (e.g.Butler&Tan2009).. that the mass deusity. p [alls off in respouse to the self-gravity of the cloud as a whole.," Beyond even this point, theory indicates, and observations confirm \citep[e.g.][]{bt09}, that the mass density $\rho$ falls off in response to the self-gravity of the cloud as a whole."
 This outermost radius is tlie Jeaus leneth Ay. where Our wave analysis is (hus valid within a somewhat restricted. but well-defined. cdyuamic range.," This outermost radius is the Jeans length $\lambda_J$, where Our wave analysis is thus valid within a somewhat restricted, but well-defined, dynamic range."
 By the same token. weeainnot model. using this method. binaries embedded within the deuse cores Characterizing low-mass star formation euvirouments (seeHaischetal.2001.olcandidatestellar patrs)..," By the same token, we model, using this method, binaries embedded within the dense cores characterizing low-mass star formation environments \citep[see][for observations of candidate stellar pairs]{h04}."
 Here. the entire cloud mass is comparable to the stellar A44. audAy.," Here, the entire cloud mass is comparable to the stellar $M_{\rm tot}$, and."
 Physically. the dynamics inside such a dense core is dominated by infall onto the binary. unless the cloud is stabilized by tension iu its internal maenetic field.," Physically, the dynamics inside such a dense core is dominated by infall onto the binary, unless the cloud is stabilized by tension in its internal magnetic field."
 Acoustic waves lay propagate outside the cloud. but their source would be both the stars aud the deuse core gas.," Acoustic waves may propagate outside the cloud, but their source would be both the stars and the dense core gas."
 We now introduce our central object. the binary.," We now introduce our central object, the binary."
 Let the component stars have masses A4 and, Let the component stars have masses $M_1$ and
In our analvsis we use the standard 47 method.,In our analysis we use the standard $\chi^2$ method.
 The analvsis is done minimizing the value of weitghed \7: where i0; is the weight of the -th SN Ia. m; is ils B-band effective apparent magnitude. and mVmode Pis its magnitude as predicted with the models introduced before and thoroughly discussed in (RubanoandSeudellaro2001).," The analysis is done minimizing the value of weitghed $\chi^2$ : where $w_i$ is the weight of the $i$ -th SN Ia, $m_i$ is its $B$ -band effective apparent magnitude, and $m^{model}_i$ is its magnitude as predicted with the models introduced before and thoroughly discussed in \citep{rub01}."
. In the first model. it is possible to eliminate 7 from Eqs. (3))," In the first model, it is possible to eliminate $\tau$ from Eqs. \ref{eq3}) )"
 and (4)). and to obtainan analviical expression for //(z).," and \ref{eq4}) ), and to obtainan analytical expression for $H(z)$."
 Thus. it is possibleto compute i from Eqs. (10))," Thus, it is possibleto compute $m$ from Eqs. \ref{eq10}) )"
 and (11)). and 4? as afunction of 7 and my.," and \ref{eq11}) ), and $\chi^2$ as afunction of $\tau$ and $m_0$."
 Firstly. we use GO SN La data and get the 47 minimum at mg=2401. 7;=104. with v=176 per degree of freedom.," Firstly, we use 60 SN Ia data and get the $\chi^2$ minimum at $m_0=24.01$, $\tau_0=1.04$, with $\chi^2 = 1.77$ per degree of freedom."
 As it is unsatisfactory. we reject data which are out of the σ level. as done in (Perlmutteretal.1999.," As it is unsatisfactory, we reject data which are out of the $\sigma$ level, as done in \citep{per99}."
a).. A[ter data rejection. the 4? mininiunm drops down to 47=1.195 per degree of [reedom.," After data rejection, the $\chi^2$ minimum drops down to $\chi^2=1.195$ per degree of freedom."
 It is definitelydefinitely. within one sigma level of tlthe expectedyecled value of 47., It is definitely within one sigma level of the expected value of $\chi^2$.
 The minimum 1now |has other values than my=23.985 and 7=1.268., The minimum now has other values than $m_0=23.985$ and $\tau_0=1.268$.
 If we accept the value of this mininnun. we obtain. from Eqs. (," If we accept the value of this minimum, we obtain, from Eqs. ("
"4) and (5). +. ,,4=0.15.","4) and (5), $H_{0}=70kms^{-1}Mpc^{-1}$ , $\Omega _{m0}=0.15$."
 The situation is illustrated in Figs., The situation is illustrated in Figs.
 1. 3., 1 – 3.
 The second model has only been tested and fitted with 56 data of SNe la. The number of parameters in this case is equal to three., The second model has only been tested and fitted with 56 data of SNe Ia. The number of parameters in this case is equal to three.
" The trie minimum of the 47 is at mi=23.98. 7,=0.5. and A=1.182."," The true minimum of the $\chi ^{2}$ is at $m_{0}=23.98$, $\tau _{0}=0.8$, and $\lambda
=1.182$."
 We find a value of 47=1.1906. which is definitely within one sigma level of expected value.," We find a value of $\chi ^{2}=1.1906$, which is definitely within one sigma level of expected value."
 After such value we obtain from Eqs. (3)), After such value we obtain from Eqs. \ref{eq8}) )
" and (9) that O,,4,=0.17.", and (9) that $\Omega _{m0}=0.17$.
 The 4? value is afunction of three arbitrary values: mpi. 7). and A.," The $\chi ^{2}$ value is afunction of three arbitrary values: $m_{0}$ , $\tau _{0}$ , and $\lambda $ ."
 Therefore. the 4? as a function of all parameters is impossible to plot. but we can nonetheless plot several slits.," Therefore, the $\chi ^{2}$ as a function of all parameters is impossible to plot, but we can nonetheless plot several slits."
 The situation is illustrated in Figs., The situation is illustrated in Figs.
 4. 3., 4 – 8.
accreting matter. anc so have an elfective surface pressure that adds to the total energy of the system.,"accreting matter, and so have an effective surface pressure that adds to the total energy of the system."
 In addition to the surface. pressure. we also note that the haloes are not necessarily in a steady state.," In addition to the surface pressure, we also note that the haloes are not necessarily in a steady state."
 The density of matter increases with redshift proportional to (1|zy* and so ata redshift of z=6. the mean matter density of the Universe is higher by a factor of almost 350.," The density of matter increases with redshift proportional to $(1+z)^3$, and so at a redshift of $z=6$, the mean matter density of the Universe is higher by a factor of almost $350$."
 The higher density implies a larger merger rate for these dark matter halocs and hence a shorter time between mergers., The higher density implies a larger merger rate for these dark matter haloes and hence a shorter time between mergers.
 Thus haloes are less likely to be in a steady state at. high redshift., Thus haloes are less likely to be in a steady state at high redshift.
 Finally. the virial theorem. relates time-averaged values for the kinetic and potential energies.," Finally, the virial theorem relates time-averaged values for the kinetic and potential energies."
 However. we do not have the time resolution requirecl for such a calculation.," However, we do not have the time resolution required for such a calculation."
 We therefore use instantaneous measurements of the. kinetic ancl potential energies. with the understanding that this will induce scatter in the energies of our haloes.," We therefore use instantaneous measurements of the kinetic and potential energies, with the understanding that this will induce scatter in the energies of our haloes."
 In Figure 2.. we show the ratio of λοςτα for all idoes in the MecdRes run at 2=6.," In Figure \ref{Virial}, we show the ratio of $2E_{\rm{K}}/|E_{\rm{G}}|$ for all haloes in the MedRes run at $z=6$."
 For α virialized dark matter halo. this should be approximately equal to 1.," For a virialized dark matter halo, this should be approximately equal to $1$."
 Llowever. we find that the median ratio is 1.3. with fewer han 0.2% having a virial ratio less than unitv at 2= 6.," However, we find that the median ratio is $1.3$, with fewer than $0.2\%$ having a virial ratio less than unity at $z=6$ ."
 At higher redshifts. the median ratio increases slightly to 1.5at z—10.," At higher redshifts, the median ratio increases slightly to $1.5$ at $z=10$."
 We note that LHetznecker&Burkert(2006) ound similar results. albeit at lower redshifts.," We note that \citet{Hetz06} found similar results, albeit at lower redshifts."
 Dhese results imply that very few of our haloes are actually virialized evaluated. using the above definition., These results imply that very few of our haloes are actually virialized evaluated using the above definition.
 However. Bettctal.(2007) labeled haloes with a ratio between 0.5 and 1.5 as relaxed. and Netoctal.(2007). set the upper limit as 1.35.," However, \citet{Bett07} labeled haloes with a ratio between $0.5$ and $1.5$ as relaxed, and \citet{Neto07} set the upper limit as $1.35$."
 We find that 95% of our haloes Gt the Bettetal.(2007) criterion. while 73% [it the Netoetal.(2007). criterion.," We find that $95\%$ of our haloes fit the \citet{Bett07} criterion, while $73\%$ fit the \citet{Neto07} criterion."
 In order to verify that we have the necessary particle resolution to capture the angular momoentum properties of haloes we ran three runs that had identical initial conditions. but. dillerent. resolutions.," In order to verify that we have the necessary particle resolution to capture the angular momentum properties of haloes we ran three runs that had identical initial conditions, but different resolutions."
 This was achieved. by creating the initial conditions for a 10247 sized. run (IliRes) and then lumping particles to create a 512° (Medltes) and 2567 (Loltes) set of initial conditions., This was achieved by creating the initial conditions for a $1024^3$ sized run (HiRes) and then lumping particles to create a $512^3$ (MedRes) and $256^3$ (LoRes) set of initial conditions.
 Thus. each particle in the AlecdRes run has the total mass of δ particles in the Ηλος run. ancl is assigned the average position and velocity of those S particles.," Thus, each particle in the MedRes run has the total mass of $8$ particles in the HiRes run, and is assigned the average position and velocity of those 8 particles."
 The LoRes run is similarly averaged out of the Medltes run., The LoRes run is similarly averaged out of the MedRes run.
 We note. however. that due to computational limitations. we were unable to run the entire box at the highest resolution.," We note, however, that due to computational limitations, we were unable to run the entire box at the highest resolution."
 Fherefore. we kept only. one-eighth. of the box at the highest. resolution. and. Iumped the rest of the box to the medium resolution.," Therefore, we kept only one-eighth of the box at the highest resolution, and lumped the rest of the box to the medium resolution."
 In order to avoid biases due to the interaction of dillering mass particles in the LiRes run. we only kept haloes which were entirely composed of the high resolution particles.," In order to avoid biases due to the interaction of differing mass particles in the HiRes run, we only kept haloes which were entirely composed of the high resolution particles."
 This ensures that he haloes used for comparison are representative of the üghest resolution., This ensures that the haloes used for comparison are representative of the highest resolution.
 We used the centre of mass to Cross-match haloes across the three runs., We used the centre of mass to cross-match haloes across the three runs.
 We mateh 85% of the aaloes between runs., We match $85\%$ of the haloes between runs.
 The unmatched haloes are likely cases where the group finder has joined neighboring groups with a enuous bridge at à higher resolution that does not exist at ower resolution., The unmatched haloes are likely cases where the group finder has joined neighboring groups with a tenuous bridge at a higher resolution that does not exist at lower resolution.
 In this situation. the centre of mass would x very different between resolutions.," In this situation, the centre of mass would be very different between resolutions."
 In Figure 23.. we compare the halo mass. spin. kineticσε encreyv. potential energy. and total angular momentum tween the Loltes and Medltes simulations.," In Figure \ref{CT_test}, we compare the halo mass, spin, kinetic energy, potential energy, and total angular momentum between the LoRes and MedRes simulations."
 Phe bottom right panel shows the cosine of the angle between the angular momentum vectors in the two simulations., The bottom right panel shows the cosine of the angle between the angular momentum vectors in the two simulations.
 Table 2. lists the mean and standard deviation of the fractional dillerence of those same quantities as a function of number of particles in the Loltes run., Table \ref{Comp_stats} lists the mean and standard deviation of the fractional difference of those same quantities as a function of number of particles in the LoRes run.
 We also include the ollset in the centre of mass position. which was used to eross-match the haloes.," We also include the offset in the centre of mass position, which was used to cross-match the haloes."
 We find good agreement in the masses of individual haloes. with a mean fractional dillerence. of 144. at. the Lowest xwtiele resolution (haloes with less than 1.000. particles).," We find good agreement in the masses of individual haloes, with a mean fractional difference of $14\%$ at the lowest particle resolution (haloes with less than $1,000$ particles)."
 Llowever. there is some spread in calculating the kinetic and potential energies. with differences up to 30% in the smallest xn.," However, there is some spread in calculating the kinetic and potential energies, with differences up to $30\%$ in the smallest bin."
 Phe angular momentum has the largest. variation of 10 quantities used to calculate AL, The angular momentum has the largest variation of the quantities used to calculate $\lambda$.
 For the smallest haloes. we find a mean fractional difference of 73%. which only ecreases to 25% in the [largest haloes (haloes with more iur 10.000 particles.," For the smallest haloes, we find a mean fractional difference of $73\%$, which only decreases to $25\%$ in the largest haloes (haloes with more than $10,000$ particles."
 We also find that the direction. of 1C cngular momentum vector ds biased at low particle resolution., We also find that the direction of the angular momentum vector is biased at low particle resolution.
 These findings lead to a large spread in the spin xwanmeter for the same haloes at dillering resolution., These findings lead to a large spread in the spin parameter for the same haloes at differing resolution.
 There does not appear to be any systematic olfset in A between resolutions. as the top right panel of Figure 3. shows.," There does not appear to be any systematic offset in $\lambda$ between resolutions, as the top right panel of Figure \ref{CT_test} shows."
 This is unlike Trentietal.(2010) who found that for haloes with less than LOO particles. the spin parameter measurement is biased high at lower resolution.," This is unlike \citet{Trenti10} who found that for haloes with less than 100 particles, the spin parameter measurement is biased high at lower resolution."
 While we do not show the comparison between the Medltes and the Hiltes subregion. we find the same trends. withincreasing resolution.," While we do not show the comparison between the MedRes and the HiRes subregion, we find the same trends withincreasing resolution."
 One possible explanation for the larger dispersion in A may be the dillieultv in defining an outer edge or boundary for dark matter haloes., One possible explanation for the larger dispersion in $\lambda$ may be the difficulty in defining an outer edge or boundary for dark matter haloes.
 A particle at. the edge adds little to the, A particle at the edge adds little to the
star in the range GSIV-KAIII with 4100.ει<5100 K and Alo~OAAL. although a tentative measurement of the rotational broadening suggests A/»=>0.0..,star in the range G8IV-K4III with $4100\leq T_{eff} \leq 5100$ K and $M_2\sim 0.4 M_{\odot}$ although a tentative measurement of the rotational broadening suggests $M_2\geq0.9 M_{\odot}$.
 On the other hand. the orbital period is 7?=1.552 days (O02) which is very similar to that of GX 339-4.," On the other hand, the orbital period is $P=1.552$ days (O02) which is very similar to that of GX 339-4."
 The stripped-giant model (see above equations) for this P yields 0.16<=Alo<1.001. with 4880>ειc457 K. which is highly consistent with the observations.," The stripped-giant model (see above equations) for this $P$ yields $0.16\leq M_2 \leq 1.09 M_{\odot}$ with $4880 \geq T_{eff} \geq 4574$ K, which is highly consistent with the observations."
" In table 2 we compare the observed properties of the companion in XTE JISS0-S64 with those obtained through the stripped-giant model and the parameters are in excellent Since its discovery in 1998. XTE ΤΙ550-564 has undergone two more X-ray outbursts suggesting a mass transfer rate close to Ady,"," In table \ref{j1550} we compare the observed properties of the companion in XTE J1550-564 with those obtained through the stripped-giant model and the parameters are in excellent Since its discovery in 1998, XTE J1550-564 has undergone two more X-ray outbursts suggesting a mass transfer rate close to $\dot{M_{ct}}$."
" OU2 estimate Ma=0.17.10""M. yr| which yields AlsAL,5.1071.", O02 estimate $\dot{M_2}=0.1-7\times10^{-9} M_{\odot}$ $^{-1}$ which yields $\dot{M_2}/\dot{M_{ct}}\sim 1.5\times10^{-2}-1$.
 During the 1998 outburst. Homanet measured a maximum X-ray flux y=LAT.10T erg Lem 7 which results in Lx(peak)~4.94107 erg 1 Gl~5.3 kpe: O02) and MMΝτο100CAL. * (eq 10).," During the 1998 outburst, \cite{Ho01} measured a maximum X-ray flux $F_X=1.47\times10^{-7}$ erg $^{-1}$ $^{-2}$ which results in $L_X(peak) \sim 4.94\times10^{38}$ erg $^{-1}$ $d\sim 5.3$ kpc; O02) and $\dot{M_1}\sim 8.72\times10^{-8} M_{\odot}$ $^{-1}$ (eq \ref{m1p}) )."
" By combining the observational constraints to Als and Al, we obtain a predicted duty cycle in the range ΕΕ~O128.035107.", By combining the observational constraints to $\dot{M_2}$ and $\dot{M_1}$ we obtain a predicted duty cycle in the range $-\dot{M_2}/\dot{M_1} \sim 0.12-8.03\times10^{-2}$.
 As expected. these values are largerthat those typical of classical transients (e. 5. V404 Cyg) which have longer outburst recurrence times.," As expected, these values are largerthat those typical of classical transients (e. g. V404 Cyg) which have longer outburst recurrence times."
 We get to reproduce these values by considering stripped-giant companions with Ale=0.258. for which we predict Ab in agreement with the observations.," We get to reproduce these values by considering stripped-giant companions with $M_2 \geq 0.28$, for which we predict $-\dot{M_2}$ in agreement with the observations."
 We want to note that XTE JISS0-S64 is also interesting because is one of only four SXTs for which the Very High X-ray state has been observed (ο. 5. Sobezaketal.1999:: GX 339-4 is one of the other three)., We want to note that XTE J1550-564 is also interesting because is one of only four SXTs for which the Very High X-ray state has been observed (e. g. \citealt{So99}; GX 339-4 is one of the other three).
 Moreover Hannikainenetal.(2001) observed relativistic plasma ejections at radio wavelenghts indicating that XTE ΤΙ550-564 is a microquasar as well., Moreover \cite{Ha01} observed relativistic plasma ejections at radio wavelenghts indicating that XTE J1550-564 is a microquasar as well.
 We have applied the stripped-giant model to the BH LMXBs GX 339-4 and XTE J1550-564., We have applied the stripped-giant model to the BH LMXBs GX 339-4 and XTE J1550-564.
 These systems share the following (i) Orbital periods in the range 1.5-1.7 Gi» Transient behaviour with frequent X-ray (ii) The Very High state has been observed (a total of only + system have shown this X-ray (iv) Both are For the case of XTE 1550-564. where the companion star has been detected and its stellar parameters constrained. we find that the proposed evolutionary model successfully reproduces all the observables.," These systems share the following (i) Orbital periods in the range 1.5-1.7 (ii) Transient behaviour with frequent X-ray (iii) The Very High state has been observed (a total of only 4 system have shown this X-ray (iv) Both are For the case of XTE J1550-564, where the companion star has been detected and its stellar parameters constrained, we find that the proposed evolutionary model successfully reproduces all the observables."
 Therefore. it seems probable that XTE J1550-564 harbours a stripped-giant companion.," Therefore, it seems probable that XTE J1550-564 harbours a stripped-giant companion."
 The case of GX339 is less straightforward since the companion star has not yet been observed., The case of GX339 is less straightforward since the companion star has not yet been observed.
" Only through the detection of the NIII/CIII Bowen lines arising from the irradiated donor a lower limit CA,317 km lj to the velocity of the companion was established by H03.", Only through the detection of the NIII/CIII Bowen lines arising from the irradiated donor a lower limit $K_{em}\sim 317$ km $^{-1}$ ) to the velocity of the companion was established by H03.
 We have applied the K-correction to this νι velocity and derived Aly56M. including the error bars in /(ÀJ) reported by H03., We have applied the K-correction to this $K_{em}$ velocity and derived $M_X \geq 6 M_{\odot}$ including the error bars in $f(M)$ reported by H03.
 This value represents a solid lower limit to the mass of the BH in this LMXB., This value represents a solid lower limit to the mass of the BH in this LMXB.
 This result comes from the assumption that the companion is a stripped-giant with the minimum possible mass., This result comes from the assumption that the companion is a stripped-giant with the minimum possible mass.
 Although there is not a definitive evidence for a stripped-giant donor in this system. this model is favoured by the ~1.7 d orbital period which clearly points to an evolved. companion.," Although there is not a definitive evidence for a stripped-giant donor in this system, this model is favoured by the $\sim 1.7$ d orbital period which clearly points to an evolved companion."
 Moreover this evolutionary model is consistent with the transient behaviour of the source and also with the large number of X-ray outbursts displayed., Moreover this evolutionary model is consistent with the transient behaviour of the source and also with the large number of X-ray outbursts displayed.
 The radius and luminosity predicted by the stripped-giant model also explain the non-detectionof the companion by SFCOI., The radius and luminosity predicted by the stripped-giant model also explain the non-detectionof the companion by SFC01.
 However. the above lower limit to Ady is quite conservative and unrealistically small since the companion is nof an Helium white dwarf because it would not fill a 1.7 d Roche lobe.," However, the above lower limit to $M_{X}$ is quite conservative and unrealistically small since the companion is not an Helium white dwarf because it would not fill a 1.7 d Roche lobe."
 Furthermore. the AZ predicted by the minimum mass solution yields an outburst duty eycle which is much too long to explain the frequent X-ray activity in GX 339-4. with 4 outbursts in the last 10 years.," Furthermore, the $\dot{M_2}$ predicted by the minimum mass solution yields an outburst duty cycle which is much too long to explain the frequent X-ray activity in GX 339-4, with 4 outbursts in the last 10 years."
" Assuming the ratio M3Ma for GX 339-4 is similar than for XTE 11550-564 (AlAla>14510 3) we estimate Als>1.2LOMOAR, yr+ which results in Mo>0.3M.."," Assuming the ratio $\dot{M_2}/\dot{M_{ct}}$ for GX 339-4 is similar than for XTE J1550-564 $\dot{M_2}/\dot{M_{ct}}\geq 1.5\times10^{-2}$ ) we estimate $\dot{M_2} \geq 1.2\times10^{-10} M_{\odot}$ $^{-1}$, which results in $M_2\geq0.3 M_{\odot}$."
 If we combine this limit with the K-correction we obtain Aly>6.6TOM. considering the error bar in f(AL)., If we combine this limit with the K-correction we obtain $M_{X}\geq6.6-7.7M_{\odot}$ considering the error bar in $f(M)$.
 Although this lower limit is less secure than the one obtained through the minimum mass solution it is probably more realistic and better explains the frequent X-ray activity displayed by this source., Although this lower limit is less secure than the one obtained through the minimum mass solution it is probably more realistic and better explains the frequent X-ray activity displayed by this source.
 Note that the stripped-giant model is only valid for A.50.45.M.. and hence if we consider heavier evolved companions (e. g. giant stars) with AM»AL we would obtain higher Ady values., Note that the stripped-giant model is only valid for $M_c \la 0.45 M_{\odot}$ and hence if we consider heavier evolved companions (e. g. giant stars) with $M_2 \geq M_c \ga 0.45 M_{\odot}$ we would obtain higher $M_{X}$ values.
 However. as we explain770.45. in section 3. this possibility is at odds with the mean density of the donor derived from the orbital We have applied the K-correction to the BH LMXB GX 339-4.," However, as we explain in section \ref{companion}, this possibility is at odds with the mean density of the donor derived from the orbital We have applied the K-correction to the BH LMXB GX 339-4."
 By considering the limit case where the emission line is formed at the limb of the irradiated region of the companion we derive a solid lower limit to My=GAL. including the error bars in f(AL)., By considering the limit case where the emission line is formed at the limb of the irradiated region of the companion we derive a solid lower limit to $M_{X}\geq 6 M_{\odot}$ including the error bars in $f(M)$.
 Here we have only assumed Als50.166A4.. the lower limit allowed by the stripped giant model.," Here we have only assumed $M_2\geq0.166 M_{\odot}$, the lower limit allowed by the stripped giant model."
 We find that the stripped-giant evolutionary model explains the non-detection of the companion by SFCO! and the X-ray behaviour ofthe source., We find that the stripped-giant evolutionary model explains the non-detection of the companion by SFC01 and the X-ray behaviour ofthe source.
In particular. we propose M»770.3.. for which we predict Ab large enough to explain the frequent X-ray outbursts displayed by this source.,"In particular, we propose $M_{2}\ga0.3M_{\odot}$, for which we predict $\dot{M_{2}}$ large enough to explain the frequent X-ray outbursts displayed by this source."
 This limit results in Ady<TAL. ., This limit results in $M_{X}\ga7M_{\odot}$ .
 From the maximum mass solution we find q 0.125., From the maximum mass solution we find $q\leq0.125$ .
" On the other hand. we have also shown that the stripped-giant model successfully explains the observable properties (Alo. Ro. 7,py and AL } of the akin LMXB XTE"," On the other hand, we have also shown that the stripped-giant model successfully explains the observable properties $M_2$ , $R_2$ , $T_{eff}$ and $\dot{M}_2$ ) of the akin LMXB XTE"
"subsequent Hubble time, tidal stripping and evaporation remove most low-mass clusters, and the higher-mass ones are significantly eroded (seeVesperini2010,forareview)..","subsequent Hubble time, tidal stripping and evaporation remove most low-mass clusters, and the higher-mass ones are significantly eroded \citep[see][for a review]{ves10}."
 These factors combined mean that the initial mass in the GC system should have been many times larger than it is now., These factors combined mean that the initial mass in the GC system should have been many times larger than it is now.
" By contrast, the BH mass has been continually growing over the same time through gas accretion and stellar capture, though its most rapid growth stage would have been at early times (cf."," By contrast, the BH mass has been continually growing over the same time through gas accretion and stellar capture, though its most rapid growth stage would have been at early times (cf."
 the references cited above)., the references cited above).
" In other words, in their early stages the total mass in the GC population must have been much larger than the initial BH mass (an order of magnitude or more)."," In other words, in their early stages the total mass in the GC population must have been much larger than the initial BH mass (an order of magnitude or more)."
" It is only now, after a Hubble time’s worth of evolution in opposite senses, that their total masses are nearly crossing."," It is only now, after a Hubble time's worth of evolution in opposite senses, that their total masses are nearly crossing."
 The case of the SO galaxies is extremely puzzling., The case of the S0 galaxies is extremely puzzling.
" There seems to be no obvious way in which the data for these systems is more uncertain than for the E and S galaxies, leaving us in the position of questioning the sample and/or classification."," There seems to be no obvious way in which the data for these systems is more uncertain than for the E and S galaxies, leaving us in the position of questioning the sample and/or classification."
" As already discussed, the two most discordant 905 have black hole masses which are upper limits and there appears to be no obvious way in which they can be moved to more closely agree with the majority of the galaxies in our sample."," As already discussed, the two most discordant S0s have black hole masses which are upper limits and there appears to be no obvious way in which they can be moved to more closely agree with the majority of the galaxies in our sample."
" Interestingly, they deviate from the norm in the same sense as the MW and NGC 5128 (discussed above)."," Interestingly, they deviate from the norm in the same sense as the MW and NGC 5128 (discussed above)."
" The four galaxies which are the most discordant then (1 E, 1, S and 2 S0 - roughly 1096 of our sample) all deviate in the sense that their values are too small compared withNec;; and without the two discordant S0s, the SO sample overall becomes less peculiar."," The four galaxies which are the most discordant then (1 E, 1, S and 2 S0 - roughly $10\%$ of our sample) all deviate in the sense that their values are too small compared with; and without the two discordant S0s, the S0 sample overall becomes less peculiar."
" However, all four ”discordant” galaxies have normal specific frequencies for their galaxy type - i.e. is normal when compared to the luminosity/mass of the whole galaxy."," However, all four ""discordant"" galaxies have normal specific frequencies for their galaxy type - i.e. is normal when compared to the luminosity/mass of the whole galaxy."
" This suggests to us that the formation of GCs is more strongly correlated with overall galaxy properties, and that in some cases is a later or less rapid development."," This suggests to us that the formation of GCs is more strongly correlated with overall galaxy properties, and that in some cases is a later or less rapid development."
 On observational grounds there is much room for improvement to explore this intriguing correlation further with bigger samples., On observational grounds there is much room for improvement to explore this intriguing correlation further with bigger samples.
" Galaxies with already-known BH masses can be imaged with deep wide-field photometry to determine their cluster populations, while the cores of many nearby galaxies with well determined values can be investigated to determine new BH masses."," Galaxies with already-known BH masses can be imaged with deep wide-field photometry to determine their cluster populations, while the cores of many nearby galaxies with well determined values can be investigated to determine new BH masses."
 Some dozens of new datapoints can be added to the current list., Some dozens of new datapoints can be added to the current list.
" Larger samples should also allow exploration of wider ranges of galaxy environment and host galaxy type, and perhaps allow us to uncover more direct causal links between these old substructures."," Larger samples should also allow exploration of wider ranges of galaxy environment and host galaxy type, and perhaps allow us to uncover more direct causal links between these old substructures."
" We thank Nadine Neumayer, Karl Gebhardt, and Andreas Burkert for helpful discussions."," We thank Nadine Neumayer, Karl Gebhardt, and Andreas Burkert for helpful discussions."
" The majority of this work was undertaken during a visit to ESO in Garching, sponsored by the ESO visitor programme."," The majority of this work was undertaken during a visit to ESO in Garching, sponsored by the ESO visitor programme."
 WEH also acknowledges financial support through a grant from the Natural Sciences and Engineering Research Council of Canada., WEH also acknowledges financial support through a grant from the Natural Sciences and Engineering Research Council of Canada.
Figure 2(upper panels) shows the evolution of (he major ice mantle species.,Figure 2(upper panels) shows the evolution of the major ice mantle species.
 H52CO and CIIL;OIL are the most abundant organic species in ice mantles., $_2$ CO and $_3$ OH are the most abundant organic species in ice mantles.
 Thev are formed from the carbon atom ab / <2 x 10? vr and from CO at later tine., They are formed from the carbon atom at $t < $ 2 $\times$ $^5$ yr and from CO at later time.
 Fieure 2(lower panels) shows the evolution of the isotope ratios of the ice mantle species., Figure 2(lower panels) shows the evolution of the isotope ratios of the ice mantle species.
 Carbon atoms and carbon monoxides in the gas phase are adsorbed aud form more complex species bv grain surface reactions., Carbon atoms and carbon monoxides in the gas phase are adsorbed and form more complex species by grain surface reactions.
 Before 10? vr. the isotope ratio of carbon atoms on grain surfaces is almost the same as in (he gas phase.," Before $^5$ yr, the isotope ratio of carbon atoms on grain surfaces is almost the same as in the gas phase."
 Carbon monoxide. on the other hand. is directly absorbed on grain surfaces and is also formed by the grain surface reactions of the carbon-bearng species.," Carbon monoxide, on the other hand, is directly absorbed on grain surfaces and is also formed by the grain surface reactions of the carbon-bearing species."
 Then (he isotope ratio of CO on grain surfaces is slightly different from that in (lie gas phase., Then the isotope ratio of CO on grain surfaces is slightly different from that in the gas phase.
 The isotope ratios of ice mantle species depend mainly on whether the species are formed [rom the carbon atom or the CO molecule: the isotope ratio is larger than 60 if the species are formed [rom C atom. while the ratio is smaller (han 60 if the species are formed Irom CO.," The isotope ratios of ice mantle species depend mainly on whether the species are formed from the carbon atom or the CO molecule; the isotope ratio is larger than 60 if the species are formed from C atom, while the ratio is smaller than 60 if the species are formed from CO."
 For example. CIE;OLL is formed from the carbon atom and its isotope ratio is 81 at / = 2 x I0? vr.," For example, $_3$ OH is formed from the carbon atom and its isotope ratio is 81 at $t$ = 2 $\times$ $^5$ yr."
" After 2 x 10? vr. CHOU are formed from the CO molecule and the isotope ratio decreases to 53 at 10"" vr. which is almost the same as the isotope ratio of CO."," After 2 $\times$ $^5$ yr, $_3$ OH are formed from the CO molecule and the isotope ratio decreases to 53 at $^6$ yr, which is almost the same as the isotope ratio of CO."
 HIICOOLL is an exception., HCOOH is an exception.
 It is formed from in the gas pliase and adsorbed onto the grain surfaces., It is formed from $^+$ in the gas phase and adsorbed onto the grain surfaces.
 The isotope ratio of IICOOLL is similar to that of in the gas phase., The isotope ratio of HCOOH is similar to that of $^+$ in the gas phase.
 Isotope ratios of ice species in higher (5x10? 7) and lower (5x10*E 7) density models are listed in Table 4., Isotope ratios of ice species in higher $5 \times 10^5$ $^{-3}$ ) and lower $5 \times 10^3$ $^{-3}$ ) density models are listed in Table 4.
 Boogert et al. (, Boogert et al. (
2000: 2002) found that the solid COs/F CO» ratio is similar to the solid CO/U CO ratio towards NGC 7538 IRS 9. and suggested that CO» is formed from CO on erain surfaces. rather (han trom the carbon atom in the gas phase.,"2000; 2002) found that the solid $_2$ $^{13}$ $_2$ ratio is similar to the solid $^{13}$ CO ratio towards NGC 7538 IRS 9, and suggested that $_2$ is formed from CO on grain surfaces, rather than from the carbon atom in the gas phase."
 In our model. COs is formed in the gas-phase via the reaction of an O atom with ΠΟ. which is formed [rom carbon atom. and adsorbed onto grain surfaces.," In our model, $_2$ is formed in the gas-phase via the reaction of an O atom with HCO, which is formed from carbon atom, and adsorbed onto grain surfaces."
 Then the isotope ratio of COs is similar, Then the isotope ratio of $_2$ is similar
within the data reductionpackage?.,within the data reduction.
". Under this scheme, the master sky spectrum is iteratively subtracted from each object spectrum and the residual assessed while fitting for line scaling, small velocity offsets (at the sub-pixel level) between the template and the data, and employing a smoothing filter to account for PSF variations."," Under this scheme, the master sky spectrum is iteratively subtracted from each object spectrum and the residual assessed while fitting for line scaling, small velocity offsets (at the sub-pixel level) between the template and the data, and employing a smoothing filter to account for PSF variations."
" With more data at hand, Wild&Hewett(2005) implemented a Principle Components Analysis (PCA) approach to the problem of correction of poor PSF residual sky subtraction."," With more data at hand, \citet{Wild05} implemented a Principle Components Analysis (PCA) approach to the problem of correction of poor PSF residual sky subtraction."
" This methodology, first proposed by Kurtz&Mink(2000),, has been successfully implemented with AAOmega data at the AAT by both the WiggleZ (Drinkwateretal.2009) and GAMA (Driveretal.2009) survey projects."," This methodology, first proposed by \citet{Kurtz00}, has been successfully implemented with AAOmega data at the AAT by both the WiggleZ \citep{WiggleZ} and GAMA \citep{GAMA} survey projects."
" It has been adopted as an option within the AAOmega data reduction environment for moderate signal-to-noise extragalactic The (N--S) observing technique was first deployed at the AAT by Glazebrook&Bland-Hawthorn(2001) for use with the LDSS slit-mask system, building on the earlier work of Cuillandreetal.(1994) and theVient technique."," It has been adopted as an option within the AAOmega data reduction environment for moderate signal-to-noise extragalactic The (N+S) observing technique was first deployed at the AAT by \citet{Glazebrook01} for use with the LDSS slit-mask system, building on the earlier work of \citet{Cuillandre94}
 and the technique."
" The premise of N4-S observing is to perform quasi-continuous observations of both target and blank sky (adjacent to the target) through the identical light paths, hence preserving the temporal and optical structure of theon andoff target sky spectra."," The premise of N+S observing is to perform quasi-continuous observations of both target and blank sky (adjacent to the target) through the identical light paths, hence preserving the temporal and optical structure of the and target sky spectra."
" The principle is identical to that of beam switching, but achieves a high chopping frequency (30sseconds to 2mminute dwell times) without incurring the onerous CCD read-out times and read-noise associated with classical beam switching at this frequency."," The principle is identical to that of beam switching, but achieves a high chopping frequency seconds to minute dwell times) without incurring the onerous CCD read-out times and read-noise associated with classical beam switching at this frequency."
" One therefore requires an observational scheme whereby charge can be accumulated on the CCD for multiple independent observations, totaling an observational time of the order mminutes (sufficient to reach the sky limited regime for observation with the low resolution AAOmega gratings of R~1350), and then readout the entire observation in a single mminute) readout."," One therefore requires an observational scheme whereby charge can be accumulated on the CCD for multiple independent observations, totaling an observational time of the order minutes (sufficient to reach the sky limited regime for observation with the low resolution AAOmega gratings of $\sim$ 1350), and then readout the entire observation in a single minute) readout."
" This mitigates the impact of readout noise, while still allowing independent quasi-continuous observations of target--sky position pairs."," This mitigates the impact of readout noise, while still allowing independent quasi-continuous observations of target+sky position pairs."
" Much has already been written about the mechanics of CCD charge shuffling (Cuillandreetal.1994;Glazebrook&Bland-Hawthorn2001;Abrahametal. 2004),, here we merely note that charge accumulated in one pixel of a CCD can be somewhat arbitrarily moved across the CCD, essentially instantaneously, with no loss of signal integrity."," Much has already been written about the mechanics of CCD charge shuffling \citep{Cuillandre94,Glazebrook01,gdds}, here we merely note that charge accumulated in one pixel of a CCD can be somewhat arbitrarily moved across the CCD, essentially instantaneously, with no loss of signal integrity."
" The CCD charge transfer phenomenon is fundamental to the basic operation of a CCD, with all charge accumulated in an ordinary observations essentially being charge across the CCD to the readout register(s) before readout."," The CCD charge transfer phenomenon is fundamental to the basic operation of a CCD, with all charge accumulated in an ordinary observations essentially being charge across the CCD to the readout register(s) before readout."
" Prolonged experiments indicate that, with modern CCDs, charge transfer between pixels is essentially loss-less (a charge transfer efficiency of 100%)) at least in the limit of low signal levels (high-signal high-frequency data leaving some unfortunate charge transfer inefficiency residuals)."," Prolonged experiments indicate that, with modern CCDs, charge transfer between pixels is essentially loss-less (a charge transfer efficiency of ) at least in the limit of low signal levels (high-signal high-frequency data leaving some unfortunate charge transfer inefficiency residuals)."
" Furthermore, while a full CCD readout may take 2mminutes, transferring charge around the CCD is practically instantaneous."," Furthermore, while a full CCD readout may take minutes, transferring charge around the CCD is practically instantaneous."
" Hence provided sufficient is available on the CCD, one can follow the nod-and-shuffle procedure and accumulate charge with the"," Hence provided sufficient is available on the CCD, one can follow the nod-and-shuffle procedure and accumulate charge with the"
elobular cluster Luminosity function: (2) stellar superclusters formed in gas-rich mergers of galaxies (77):(3) end-products of small-scale primordial density Ductuations. in dense environments. (2): (4) tidallv stripped. nucleated cls (UINs. 2?)) or simply cHEN’s with very lowsurface brightness outer components (cf. 2)).,"globular cluster luminosity function; (2) stellar superclusters formed in gas-rich mergers of galaxies \citep{FK02,FK05};(3) end-products of small-scale primordial density fluctuations in dense environments \citep{PDGJ01}; (4) tidally stripped nucleated dEs (dEN's, \citealp{BCD01,Goerdt+08}) ) or simply dEN's with very lowsurface brightness outer components (cf. \citealp{Drinkwater+03}) )."
 None of the concepts is completely ruled out or confirmed vet., None of the concepts is completely ruled out or confirmed yet.
 The dynamical ML. ratios of UCDs are on average about twice as large as those of Galactic globular clusters of comparable metallicity (e.g.2222).. although environmental cilferences exist (see below).," The dynamical M/L ratios of UCDs are on average about twice as large as those of Galactic globular clusters of comparable metallicity \citep[e.g.][]{DHK08,Mieske+08,FLGS08,Taylor+10}, although environmental differences exist (see below)."
 Lt has been shown that about 1/4 ofthe M/L olfset with respect to globular clusters is oobablv clue to dynamical evolution of the latter (?).., It has been shown that about 1/4 of the M/L offset with respect to globular clusters is probably due to dynamical evolution of the latter \citep{KM09}.
 The remaining olfset in M/L indicates that UCDs may mark the onset of dark matter domination in small stellar svstenmis (?7).. or indeed. probe a variation of the LAL (??)..," The remaining offset in M/L indicates that UCDs may mark the on-set of dark matter domination in small stellar systems \citep{Gilmore+07,Goerdt+08}, , or indeed probe a variation of the IMF \citep{DHK08,MK08}."
 ? state a need in observations aimed at the studies of UCDs stellar. populations and age determination in xuticular. required to explain the low dynamical A/L ratios in Fornax UCDs compared to those in the Virgo cluster.," \citet{Mieske+08} state a need in observations aimed at the studies of UCDs stellar populations and age determination in particular, required to explain the low dynamical $M/L$ ratios in Fornax UCDs compared to those in the Virgo cluster."
 Llere we re-analvse the same observational data applying a »owerful full-spectral fitting technique allowing us to obtain simultaneously internal kinematics and stellar population ooperties in the largest. UCD sample available until now., Here we re-analyse the same observational data applying a powerful full-spectral fitting technique allowing us to obtain simultaneously internal kinematics and stellar population properties in the largest UCD sample available until now.
 We also improve some data reduction steps. necessary oecause of the more stringent requirements for stellar population analvsis regarding sky subtraction.," We also improve some data reduction steps, necessary because of the more stringent requirements for stellar population analysis regarding sky subtraction."
 Another motivation for re-analvsing these data was to clouble-check he velocity dispersion. measurements for certain CCDs., Another motivation for re-analysing these data was to double-check the velocity dispersion measurements for certain UCDs.
 ? used. late-type giant stars from c Cen having metallicities of around —1.0 dex as stellar templates., \citet{Mieske+08} used late-type giant stars from $\omega$ Cen having metallicities of around $-1.0$ dex as stellar templates.
 While this is close to the average UCD metallicity. UCDs span a wider range of metallicities and for metal-rich objects the template mismatch due to the metallicity dillerence. may allect velocity dispersion measurements às sugeested in ?..," While this is close to the average UCD metallicity, UCDs span a wider range of metallicities and for metal-rich objects the template mismatch due to the metallicity difference may affect velocity dispersion measurements as suggested in \citet{Chilingarian06}."
 The paper is organised as follows: in Section 2 we describe spectroscopic data reduction and. analysis. as well as complementary archival LIST cata used. to extend. the sample of UCDs with known structural parameters: the results of the full spectral fitting are presented in Section 3: comparison of kinematical and stellar population properties of UCDs with earlv-tvpe galaxies and a general discussion about the origin of UCDs is given in Section 4.," The paper is organised as follows: in Section 2 we describe spectroscopic data reduction and analysis, as well as complementary archival HST data used to extend the sample of UCDs with known structural parameters; the results of the full spectral fitting are presented in Section 3; comparison of kinematical and stellar population properties of UCDs with early-type galaxies and a general discussion about the origin of UCDs is given in Section 4."
 We used the data obtained in the course of the study ofCSSs in the Fornax cluster (program 078.D-0496. PL: L. Infante).," We used the data obtained in the course of the study of CSSs in the Fornax cluster (program 078.B-0496, P.I.: L. Infante)."
 The datasets are publicly available through the ESO DataArchivel., The datasets are publicly available through the ESO Data.
. The observations were collected at the ESO Very Large ‘Telescope with the FLAMES/Ciralle spectrograph (?) in the multi-object “ALEDUSA® mocoe. using the LER9 setup giving à resolving power /?z17000 in the wavelength range 51205450 iin the service mode in 14 observing blocks (OB) between June and December 2007 with the total integration time of 0000 sec.," The observations were collected at the ESO Very Large Telescope with the FLAMES/Giraffe spectrograph \citep{Pasquini+02} in the multi-object “MEDUSA” mode, using the HR9 setup giving a resolving power $R\approx17000$ in the wavelength range 5120–5450 in the service mode in 14 observing blocks (OB) between June and December 2007 with the total integration time of 000 sec."
 ALL particular details about observations are eiven in ?.., All particular details about observations are given in \citet{Mieske+08}.
 We use the distance modulus of the Fornax cluster mAJ=31.39 mag (?) corresponding to the distance 19 Alpe and the spatial scale 92 pe , We use the distance modulus of the Fornax cluster $m-M = 31.39$ mag \citep{Freedman+01} corresponding to the distance 19 Mpc and the spatial scale 92 pc $^{-1}$.
In order to perform the stellar population analysis we had to improve the data reduction and sky subtraction with respect to the requirements for the kinematical analysis presented in. 7.. therefore we had to introduce. several accditional steps before ancl after standard ESO FLANMIZS pipeline data reduction.," In order to perform the stellar population analysis we had to improve the data reduction and sky subtraction with respect to the requirements for the kinematical analysis presented in \citet{Mieske+08}, therefore we had to introduce several additional steps before and after standard ESO FLAMES pipeline data reduction."
 The first additional pre-processing step is to apply the Laplacian cosmic ray cleaning algorithm (7) to the original science Frames and mask all the regions allected by cosmic pav hits in every individual frame., The first additional pre-processing step is to apply the Laplacian cosmic ray cleaning algorithm \citep{vanDokkum01} to the original science frames and mask all the regions affected by cosmic ray hits in every individual frame.
 The second step. the «πιο light subtraction. is of a great importance for the success of our study.," The second step, the diffuse light subtraction, is of a great importance for the success of our study."
 The simultaneous calibration (SimCal) Ph-Ar lamp inside the spectrograph was switched on during the observations., The simultaneous calibration (SimCal) Th-Ar lamp inside the spectrograph was switched on during the observations.
 The average [lux level in the SimCal fibres exceeded: those of scientific targets by at least two orders of maenitucle., The average flux level in the SimCal fibres exceeded those of scientific targets by at least two orders of magnitude.
 Therefore. the scattered light from bright. are lines at a level of 12 per cent severely contaminated the neighbouring fibres.," Therefore, the scattered light from bright arc lines at a level of 1–2 per cent severely contaminated the neighbouring fibres."
 “Phere is also a smooth dilfuse light component in the spectrograph. having however. only little effects on the Iat-fielcing.," There is also a smooth diffuse light component in the spectrograph, having however, only little effects on the flat-fielding."
 To account for this contamination. we created. a decicated scattered. light modelling algorithm.," To account for this contamination, we created a dedicated scattered light modelling algorithm."
 Since FLAALES fibres are sparsely placed on a CCD plane: the mecian inter-ibre distance is 14.3 pixels while the fibre PMUILAL is around. 4 pixels. therefore it is possible to use inter-fibre gaps to estimate the scattered light contribution.," Since FLAMES fibres are sparsely placed on a CCD plane: the median inter-fibre distance is 14.3 pixels while the fibre $FWHM$ is around 4 pixels, therefore it is possible to use inter-fibre gaps to estimate the scattered light contribution."
 We use fibre traces derived. from a [lat field το identify inter-fibre gaps which normally should not contain any signal., We use fibre traces derived from a flat field to identify inter-fibre gaps which normally should not contain any signal.
 Phen. we assume that all signal detected in the gaps represent a superposition of scattered light and global diffuse light.," Then, we assume that all signal detected in the gaps represent a superposition of scattered light and global diffuse light."
 In the beginning we smooth this contribution along dispersion. with a boxear of 4 pix. then we fit it across dispersion at every position along fibre traces between each pair of SimC'al fibres using the 3-rel order smoothing splines.," In the beginning we smooth this contribution along dispersion with a boxcar of 4 pix, then we fit it across dispersion at every position along fibre traces between each pair of SimCal fibres using the 3-rd order smoothing splines."
 We use the spline interpolation instead of smoothing splines in à small region of the frame containing a parasite signal generated by the CCD read-out amplifier., We use the spline interpolation instead of smoothing splines in a small region of the frame containing a parasite signal generated by the CCD read-out amplifier.
 The two-dimensional scattered light model constructed in this fashion is ereatec ancl subtracted from every spectral image., The two-dimensional scattered light model constructed in this fashion is created and subtracted from every spectral image.
 In Fig 1. we present a fragment of a spectral image before and after scattered light subtraction., In Fig \ref{figsc} we present a fragment of a spectral image before and after scattered light subtraction.
 Then. the corrected. files are used. to. feed. the ESO FLAMIZS. data reduction pipeline to. proceed through all steps up-to the linearisation of extracted spectra.," Then, the corrected files are used to feed the ESO FLAMES data reduction pipeline to proceed through all steps up-to the linearisation of extracted spectra."
 Then. we apply the third. post-processing step including the adjustment of the wavelength scale to account. for hehocentrie radial velocity corrections. sky subtraction. ane combination of spectra for multiple exposures.," Then, we apply the third, post-processing step including the adjustment of the wavelength scale to account for heliocentric radial velocity corrections, sky subtraction, and combination of spectra for multiple exposures."
 ALL further data analysis is performed on individual one-dimensiona extracted spectra of every object., All further data analysis is performed on individual one-dimensional extracted spectra of every object.
 We fitted the high-resolution (7). simple stellar. population (SSP) models against the observationa data using the mocification of the full spectra fitting technique (??7)..," We fitted the high-resolution \citep{LeBorgne+04} simple stellar population (SSP) models against the observational data using the modification of the full spectral fitting technique \citep{CPSA07,CPSK07}."
 The original version of cannot be used cirectly with our data as we clic for FLAALES-LRO4 observations (??).. because the spectra resolutionof FLAALES in the LIRO setup exceeds that of the stellar. population models (22= 10000).," The original version of cannot be used directly with our data as we did for FLAMES-LR04 observations \citep{Chilingarian+08,CCB08}, , because the spectral resolutionof FLAMES in the HR9 setup exceeds that of the stellar population models $R \approx 10000$ )."
A total of 32 Monte Carlo simulations were ruu to examine the various input parameters described above.,A total of 32 Monte Carlo simulations were run to examine the various input parameters described above.
 Resulting observable distributions for the baseline simulations are eiven in Tables 3 and £ and diaeramuucd in Fieures { aud 5., Resulting observable distributions for the baseline simulations are given in Tables 3 and 4 and diagrammed in Figures 4 and 5.
 Figure | diagrams the derived LEs. ΑΓ). for bascline parameters aud for each of the MEs examined.," Figure 4 diagrams the derived LFs, $\Phi(M_{bol})$, for baseline parameters and for each of the MFs examined."
 Also labelled in this plot (and subsequent figures) are the approximate Mygs for spectral types (SpT) Lo. L5. T5. aud T8. based ou eipirical measurements by Colimowskietal.(2001).," Also labelled in this plot (and subsequent figures) are the approximate $M_{bol}$ s for spectral types (SpT) L0, L5, T5, and T8, based on empirical measurements by \citet{gol04}."
. At bright magnitudes. there is a peak at Ai~13 (SpT z LO) which is less pronounced for the steeper MES but yields the same density of objects (0.01 pe? mae 1) for all MEs.," At bright magnitudes, there is a peak at $M_{bol} \sim 13$ (SpT $\lesssim$ L0) which is less pronounced for the steeper MFs but yields the same density of objects (0.01 $^{-3}$ $^{-1}$ ) for all MFs."
 This peak is almost cutirely comprised of low mass stars (0.08 «OM OIM.) and the fixed density reflects the adopted normalization.," This peak is almost entirely comprised of low mass stars (0.08 $<$ M $<$ 0.1 $_{\sun}$ ), and the fixed density reflects the adopted normalization."
" The drop off iu @(AL,.,) toward brighter Iumiuuosities is an artifact of the upper mass limit (0.1 NE.) of the simulatious.", The drop off in $\Phi(M_{bol})$ toward brighter luminosities is an artifact of the upper mass limit (0.1 $_{\sun}$ ) of the simulations.
" At Af.~15 (SpT ~ L5) there is a local minim in $(375,,). a feature that has also been seen in the simulations of aud Allenetal.(2004.their“TroughD7).."," At $M_{bol} \sim 15$ (SpT $\sim$ L5) there is a local minimum in $\Phi(M_{bol})$, a feature that has also been seen in the simulations of \citet{cha03} and \citet[their ``Trough B'']{all04}."
" The origin of this trough nav be seen in the divergence of the evolutionary tracks in Figure 2 around T,¢¢1500 I& (corresponding to Mj,~15).", The origin of this trough may be seen in the divergence of the evolutionary tracks in Figure 2 around $_{eff} \sim 1800$ K (corresponding to $M_{bol} \sim 15$ ).
 At late ages. this teiiperature straddles the WBAMIAL and hence most brown dwarf have cooled to lower temperatures and fainter hpunuinosities.," At late ages, this temperature straddles the HBMM, and hence most brown dwarfs have cooled to lower temperatures and fainter luminosities."
 Sources older than 1 Cor tend to dominate the overall population for a flat birthrate (seo 5 LA): hence. the narrow ranee of masses sampling these liunosities at late ages implies fewer sources overall.," Sources older than 1 Gyr tend to dominate the overall population for a flat birthrate (see $\S$ 4.1); hence, the narrow range of masses sampling these luminosities at late ages implies fewer sources overall."
 Note that shallower power laws produce a more pronounced trough., Note that shallower power laws produce a more pronounced trough.
 Toward fainter magnitudes. ΑΓ) rises. more significantly for steeper power laws due to the exeater proportion of low mass (and hence intrinsically faiuter for a eiven age) brown dwarts.," Toward fainter magnitudes, $\Phi(M_{bol})$ rises, more significantly for steeper power laws due to the greater proportion of low mass (and hence intrinsically fainter for a given age) brown dwarfs."
 Each distribution exhibits a broad poa- these faiut uaenitudes. with the location of the maxim depending ou the steepness of the ME: Mj~1δ for a = ( and Af;~22 for a = 2.," Each distribution exhibits a broad peak at these faint magnitudes, with the location of the maximum depending on the steepness of the MF: $M_{bol} \sim 18$ for $\alpha$ = 0 and $M_{bol} \sim 22$ for $\alpha$ = 2."
 Indeed. bevoud Ai;~18 (SpT — T7). there is a substautial iucrease im he contrast between the various ATFs. with up to 25 times more brown dwarfs between à = 2 aud 0 at Miu21.," Indeed, beyond $M_{bol} \sim 18$ (SpT $\sim$ T7), there is a substantial increase in the contrast between the various MFs, with up to 25 times more brown dwarfs between $\alpha$ = 2 and 0 at $_{bol} \sim 21$."
 The lognormal Φ(Ανω) lies between those of the a = 0.5 aud 1.0 MES. and is generally flat votween 18€M4<21.," The lognormal $\Phi(M_{bol})$ lies between those of the $\alpha$ = 0.5 and 1.0 MFs, and is generally flat between $18 \lesssim M_{bol} \lesssim 21$."
" Below Mp~22. there is a steep drop off in all of the 9(1,,) distributions due to th. the adopted lower mass limit (0.01 ML. for the simulations diagranuned in Figure 1) and the adopted uaxiuun aee (10 Cir)."," Below $M_{bol} \sim 22$, there is a steep drop off in all of the $\Phi(M_{bol})$ distributions due to both the adopted lower mass limit (0.01 $_{\sun}$ for the simulations diagrammed in Figure 4) and the adopted maximum age (10 Gyr)."
 A lower minima mass and/or aud an older population would result in à turnover in the LF at fainter maguitudes., A lower minimum mass and/or and an older population would result in a turnover in the LF at fainter magnitudes.
 Figure 5 compares the Φε) distributions for the same simulations., Figure 5 compares the $\Phi(T_{eff})$ distributions for the same simulations.
" The bright magnitude peak seeu in the 9(M,) distribution is evideut at Tepe,~2500.—2700 Ts. although it likely underestimates the actual uunuber of stars/brown dwarfs at these hieher temperatures because of the 0.1 AL. upper mass cutoff."," The bright magnitude peak seen in the $\Phi(M_{bol})$ distribution is evident at $T_{eff} \sim 2500-2700$ K, although it likely underestimates the actual number of stars/brown dwarfs at these higher temperatures because of the 0.1 $_{\sun}$ upper mass cutoff."
" The trough in $(A7,,) is also seen here. albeit somewhat less pronounced. around 1800.2000 I& (SpT — L3-L5). again due to the rapid cooling of brown dwarfs at these temperatures."," The trough in $\Phi(M_{bol})$ is also seen here, albeit somewhat less pronounced, around 1800–2000 K (SpT $\sim$ L3-L5), again due to the rapid cooling of brown dwarfs at these temperatures."
" At lower T;5 gs. all of the distributions rise. with the steeper power laws yielding at least an order of magnitude more cold brown dwarts (Ty¢¢~500 Ix} than warm ones (T,¢¢~2000 IX)."," At lower $T_{eff}$ s, all of the distributions rise, with the steeper power laws yielding at least an order of magnitude more cold brown dwarfs $_{eff} \sim 500$ K) than warm ones $_{eff} \sim 2000$ K)."
 At 1000 Ts (SpT ~ TG). there is a factor of 8 difference between a = 0 and 2. anc a factor of 30 difference at 500 Ix. The resulting densities of cold brown cliwarts are fairly high. predicting roughly 25 brown dwarfs with 100 z Γι Z 800 Is within 5 pe of the Suu for a = 1.," At 1000 K (SpT $\sim$ T6), there is a factor of 8 difference between $\alpha$ = 0 and 2, and a factor of 30 difference at 500 K. The resulting densities of cold brown dwarfs are fairly high, predicting roughly 25 brown dwarfs with 400 $\lesssim$ $_{eff}$ $\lesssim$ 800 K within 5 pc of the Sun for $\alpha$ = 1."
 This is, This is
al (he location of 12-11.,at the location of r2-71.
 We therefore assume r2-71 is an LMXD system., We therefore assume r2-71 is an LMXB system.
 No reliable variability was detected in the r2-71 error circle. so that we did not detect the optical counterpart of the ARN.," No reliable variability was detected in the r2-71 error circle, so that we did not detect the optical counterpart of the XRN."
 A dillerence image of the region confirms the lack of significant variability., A difference image of the region confirms the lack of significant variability.
 The optical data therefore place an upper-limit on the B-bancl brightness of the outburst of B>25.5., The optical data therefore place an upper-limit on the $B$ -band brightness of the outburst of $B\geq25.5$.
 The corresponding upper-limit on the V-band humninosity along with the X-ray Iuminosity measured from (he spectrum provide a prediction of <1.6 davs for the orbital period ol the LAINB svstem., The corresponding upper-limit on the $V$ -band luminosity along with the X-ray luminosity measured from the spectrum provide a prediction of $\leq$ 1.6 days for the orbital period of the LMXB system.
 Support for this work was provided by NASA through erant number GO-9087 from the Space Telescope Science Institute and through erant number GO-3103X [rom the X-Ray Center., Support for this work was provided by NASA through grant number GO-9087 from the Space Telescope Science Institute and through grant number GO-3103X from the X-Ray Center.
 MRG acknowledges support from NASA LTSA grant. NAG5-10889., MRG acknowledges support from NASA LTSA grant NAG5-10889.
 SSAI acknowledges the support of the IIRC contract NAS8-03060., SSM acknowledges the support of the HRC contract NAS8-03060.
 JEM acknowledges the support ol NASA erant NNGO-5GD31G., JEM acknowledges the support of NASA grant NNG0-5GB31G.
Extended X-ray absorption fine structures (EXAFS) refer to the oscillatory appearance of X-ray spectra at the short wavelength side of an atomic edge.,Extended X-ray absorption fine structures (EXAFS) refer to the oscillatory appearance of X-ray spectra at the short wavelength side of an atomic edge.
 When an electron can be emitted from an atom due to absorption of an X-ray photon. back-scattering of the photo-electron wave by the surrounding atoms causes interferences which may prevent the absorption of the X-ray photon in the first place.," When an electron can be emitted from an atom due to absorption of an X-ray photon, back-scattering of the photo-electron wave by the surrounding atoms causes interferences which may prevent the absorption of the X-ray photon in the first place."
 This process is determined by the distances of the emitting atom to its neighbours., This process is determined by the distances of the emitting atom to its neighbours.
 This interference behaviour will cause a sinusoidal structure of the absorption cross-section with wavelength., This interference behaviour will cause a sinusoidal structure of the absorption cross-section with wavelength.
 Since the photo-electron will normally be absorbed within short distance by the medium into which it is emitted. the EXAFS spectral structure will only show the average local surroundings of emitting atoms.," Since the photo-electron will normally be absorbed within short distance by the medium into which it is emitted, the EXAFS spectral structure will only show the average local surroundings of emitting atoms."
 Whereas crystalline structures. which are repetitive over large distances. can be studied by X-ray diffraction techniques. EXAFS were recognized as an important tool to study amorphous materials (see e.g. 2)).," Whereas crystalline structures, which are repetitive over large distances, can be studied by X-ray diffraction techniques, EXAFS were recognized as an important tool to study amorphous materials (see e.g. \cite{Sayers}) )."
 The availability of high intensity X-ray facilities therefore has made the study of EXAFS an established technique in many fields of the materials sciences., The availability of high intensity X-ray facilities therefore has made the study of EXAFS an established technique in many fields of the materials sciences.
 For astronomy. the availability of a new generation of large X-ray telescopes like aandXMM-Newton... with their high resolution X-ray spectrometers. was already early recognized as an opportunity to observe EXAFS of interstellar dust and hence study the character of the solid material of dust particles (see.," For astronomy, the availability of a new generation of large X-ray telescopes like and, with their high resolution X-ray spectrometers, was already early recognized as an opportunity to observe EXAFS of interstellar dust and hence study the character of the solid material of dust particles (see."
 e.g. ?))., e.g. \cite{Woo}) ).
 However. until now only limited possible observations of interstellar EXAFS have been reported (?.. 2.. 2)).," However, until now only limited possible observations of interstellar EXAFS have been reported \cite{Petric}, \cite{Ueda}, \cite{jlee}) )."
 The high intensity of the ground based X-ray sources used by the material sciences for EXAFS studies means that signal to noise ratio is extremely high., The high intensity of the ground based X-ray sources used by the material sciences for EXAFS studies means that signal to noise ratio is extremely high.
 In contrast. in astronomical sources noise is a serious problem for EXAFS studies.," In contrast, in astronomical sources noise is a serious problem for EXAFS studies."
 In addition. since EXAFS extend over a broad range in wavelengths. stability and knowledge of the instrument effective area and response is needed to a very high level of accuracy.," In addition, since EXAFS extend over a broad range in wavelengths, stability and knowledge of the instrument effective area and response is needed to a very high level of accuracy."
 iis one of the brightest X-ray sources in the sky and its emission is subject to interstellar absorption., is one of the brightest X-ray sources in the sky and its emission is subject to interstellar absorption.
 It is located at a distance of about 2.8 kpe (?) at a galactic latitude of 23.8°. which means the source ts situated about 1.1 kpe above the galactic plane.," It is located at a distance of about 2.8 kpc \citep{Bradshaw99} at a galactic latitude of $23.8^\circ$, which means the source is situated about 1.1 kpc above the galactic plane."
 This is well above the scale height of neutral interstellar material in the galaxy., This is well above the scale height of neutral interstellar material in the galaxy.
 For this reason the expected total column density of in front of the source can be derived from surveys and is estimated at about 19£3«1079?.., For this reason the expected total column density of in front of the source can be derived from surveys and is estimated at about $19 \pm 3 \times 10^{20}$.
 This corresponds quite well with the absorption derived from low energy X-ray spectra (?).., This corresponds quite well with the absorption derived from low energy X-ray spectra \citep{deVries03}.
" Using a dust to gas ratio of Nj/A,=2.0«1031 cin7 (2). we get a total of about | magnitude of extinctior at optical wavelengths.", Using a dust to gas ratio of $N_H/A_v=2.0 \times 10^{21}$ ${\rm cm}^{-2}$ \citep{Vuong} we get a total of about 1 magnitude of extinction at optical wavelengths.
 Comparing this with a general extinction of about 1.9 magnitude/kpe (2) in the plane of the galaxy and keeping in mind that the line of sight to this high latitude source only traverses part of its total length through the molecular disk of the galaxy it is safe to assume that all low energy X-ray absorption is due to the common diffuse material present in the galactic interstellar medium., Comparing this with a general extinction of about 1.9 magnitude/kpc \citep{Savage} in the plane of the galaxy and keeping in mind that the line of sight to this high latitude source only traverses part of its total length through the molecular disk of the galaxy it is safe to assume that all low energy X-ray absorption is due to the common diffuse material present in the galactic interstellar medium.
 In cold parts of this medium absorption by solid dust particles will play a significant role., In cold parts of this medium absorption by solid dust particles will play a significant role.
 The high intensity of the X-ray flux from provides high signal to noise ratio spectra in relatively short exposure times., The high intensity of the X-ray flux from provides high signal to noise ratio spectra in relatively short exposure times.
 This allows for a detailed study of the X-ray absorption characteristics of the interstellar medium., This allows for a detailed study of the X-ray absorption characteristics of the interstellar medium.
 In addition the high likelihood of absorption by solid matter makes this source ideally suited to look for EXAFS., In addition the high likelihood of absorption by solid matter makes this source ideally suited to look for EXAFS.
 The RGS_ instrument (?) provides high resolution X-ray spectra in the soft energy band (6 - 38 A))., The RGS instrument \citep{herder} provides high resolution X-ray spectra in the soft energy band (6 - 38 ).
 In this energy band the predominant interstellar absorption features are caused by the elements oxygen. nitrogen. neon and iron (see Fig. 1)).," In this energy band the predominant interstellar absorption features are caused by the elements oxygen, nitrogen, neon and iron (see Fig. \ref{spect}) )."
 Neon and nitrogen are thought to be present mainly in atomic gas phase. while tron will be mainly chemically bound in compounds contained in interstellar dust.," Neon and nitrogen are thought to be present mainly in atomic gas phase, while iron will be mainly chemically bound in compounds contained in interstellar dust."
 Oxygel Is one of the most abundant elements and causes the most prominent features in the spectrum. notably the deep Oxygen edge at around 23A..," Oxygen is one of the most abundant elements and causes the most prominent features in the spectrum, notably the deep Oxygen edge at around 23."
 Oxygen is expected to be partly in (atomic) gas phase and partly bound in various chemical compounds in solid form., Oxygen is expected to be partly in (atomic) gas phase and partly bound in various chemical compounds in solid form.
 Here we concentrate on signatures (EXAFS) of solids around the oxygen edge., Here we concentrate on signatures (EXAFS) of solids around the oxygen edge.
In this paper. we model the diffuse field. structure of astrophysical regions.,"In this paper, we model the diffuse field structure of astrophysical regions."
 ltecombinations within these regions emit radiation in the various hydrogen line spectra anc Balmer and higher continua which is an observed characteristic of them., Recombinations within these regions emit radiation in the various hydrogen line spectra and Balmer and higher continua which is an observed characteristic of them.
 Emission in the Lyman continuum. however. is energetic enough to ionize other hydrogen atoms. and so is trapped within the nebula.," Emission in the Lyman continuum, however, is energetic enough to ionize other hydrogen atoms, and so is trapped within the nebula."
 This radiation field is believed to have a significant fraction of the energy density of the direct ionizing continuum in some parts of the region. and so it is important to model it correctly.," This radiation field is believed to have a significant fraction of the energy density of the direct ionizing continuum in some parts of the region, and so it is important to model it correctly."
 Phis is particularly relevant when modelling the complex dynamics of the nebulae. or the emission from the internal features such as the tails of cometary globules in the Helix planetary nebula (CODellοἱal.2007 )..," This is particularly relevant when modelling the complex dynamics of the nebulae, or the emission from the internal features such as the tails of cometary globules in the Helix planetary nebula \citep{odell07}. ."
 lützerveld(2005). has suggested that diffuse fields may oe particularly important at the edges of regions. in some regimes.," \cite{ritze05} has suggested that diffuse fields may be particularly important at the edges of regions, in some regimes."
 This would seem to suggest that the dilf'use ield may have a more significant impact on their overall evolution than previously assumed., This would seem to suggest that the diffuse field may have a more significant impact on their overall evolution than previously assumed.
 However. Htitzerveld uses à simple outward-only treatment of the dilfuse radiation ransport. and also assumes that the absorption coelfTicient is comparable for diffuse and direct radiation fields. although it is acknowledged that in reality the direct photons are likely o have à harder spectrum and. will thus be significantly niore penetrating.," However, Ritzerveld uses a simple outward-only treatment of the diffuse radiation transport, and also assumes that the absorption coefficient is comparable for diffuse and direct radiation fields, although it is acknowledged that in reality the direct photons are likely to have a harder spectrum and will thus be significantly more penetrating."
 To investigate the validity of these conclusions. in his paper we apply detailed. diserete-orcinate angular integration to investigate the validity of several approximate numerical transport. schemes.," To investigate the validity of these conclusions, in this paper we apply detailed discrete-ordinate angular integration to investigate the validity of several approximate numerical transport schemes."
 To simplify the problem. we assume a pure-hyvdrogen nebula. without dust. ancl use a simple two-frequeney approximation to the radiation Low.," To simplify the problem, we assume a pure-hydrogen nebula, without dust, and use a simple two-frequency approximation to the radiation flow."
 With our more detailed modelling. we find. that the cliffuse field. can indeed: dominate. for the situations lützerveld deseribes.," With our more detailed modelling, we find that the diffuse field can indeed dominate for the situations Ritzerveld describes."
 However. where the diffuse Ποιά dominates. it will twpically also be outwardlv-beamed. aud therefore be indistinguishable from the direct Geld for most purposes.," However, where the diffuse field dominates, it will typically also be outwardly-beamed and therefore be indistinguishable from the direct field for most purposes."
 For most astrophysically relevant conditions. the usual on-the-spot approximation is shown to give accurate results through most of a spherical nebula. except for à region close to the star where it the cilluse Ποια.," For most astrophysically relevant conditions, the usual on-the-spot approximation is shown to give accurate results through most of a spherical nebula, except for a region close to the star where it the diffuse field."
 We also assess the accuracy of the Edcington cillusion approximation for the diffuse field. transfer. which may be a useful means of moclelling diffuse transport effects. in multidimensional simulations.," We also assess the accuracy of the Eddington diffusion approximation for the diffuse field transfer, which may be a useful means of modelling diffuse transport effects in multidimensional simulations."
 In the present paper. we neglect the effects. of. dust and heavy elements in the region.," In the present paper, we neglect the effects of dust and heavy elements in the region."
 This is a reasonable assumption for the case of cosmological regions: however. there is observational evidence for the importance of dust. absorption within the ionizecl eas in galactic regions (Cesarskyetal.2000:Robberto2005).," This is a reasonable assumption for the case of cosmological regions; however, there is observational evidence for the importance of dust absorption within the ionized gas in galactic regions \citep{cesar00,robbe05}."
. We brielly discuss the impact dust might have on our results., We briefly discuss the impact dust might have on our results.
 We use a simple. model ofΕΠ regions to. study the diffuse field structure., We use a simple model of regions to study the diffuse field structure.
 Me. consider steady. spherically symmetric pure-hyvdrogen regions. with the radiation field in two frequency. components: higher frequency. radiation propagating clirectly from a central point source.and," We consider steady, spherically symmetric pure-hydrogen regions, with the radiation field in two frequency components: higher frequency radiation propagating directly from a central point source,and"
for as many stars as necessary. until the total luminosity reaches the desired: value of Ly.,"for as many stars as necessary, until the total luminosity reaches the desired value of $L_V$."
 Sinee a laree number of the stars in the realization will be low-mass stars too faint to be observed. we keep only the photometric information of stars brigther than an arbitrary cutoll absolute magnitude Ady=5.," Since a large number of the stars in the realization will be low-mass stars too faint to be observed, we keep only the photometric information of stars brigther than an arbitrary cutoff at absolute magnitude $M_V=5$."
 Although we discard these atvery faint stars. it is important to emphasize that their Iuminosities contribute to the total luminosity of the system.," Although we discard these very faint stars, it is important to emphasize that their luminosities contribute to the total luminosity of the system."
 The magnitude cutoll was chosen at Ady=5 since it. is fainter han the turn-oll of a 13.4 Gyr old. population of ike metallicity (AJ;= 4)., The magnitude cutoff was chosen at $M_V=5$ since it is fainter than the turn-off of a 13.4 Gyr old population of halo-like metallicity $M_V=4$ ).
 This ensures that the turn-olf will be brigther than our cutoll for a population of any given age., This ensures that the turn-off will be brigther than our cutoff for a population of any given age.
 Nevertheless. the fraction of these. stars hat will be observable will be determined. by the Gaia magnitude cut-oll (V< 20).," Nevertheless, the fraction of these stars that will be observable will be determined by the Gaia magnitude cut-off $V<20$ )."
 Following this recipe ensures hat our random realization accurately represents both the uminosity Function of the stars given by the SELL as well as he total number of stars in à system with total luminosity Ly.," Following this recipe ensures that our random realization accurately represents both the luminosity function of the stars given by the SFH, as well as the total number of stars in a system with total luminosity $L_V$."
 Finally. we randomly assign the photometric properties generated with this procedure. to the N-bocky particles of the simulated satellites as explained in Sec.," Finally, we randomly assign the photometric properties generated with this procedure, to the N-body particles of the simulated satellites as explained in Sec."
 4.3 in BOS. and then compute. using the recipe detailed in Sec.," 4.3 in B05, and then compute, using the recipe detailed in Sec."
 4.1 in Bos. the Galatie longitude. latitude. parallax. radial velocities and proper motions with their corresponding errors. for each simulated satellite star within the completeness limit ofGaia (V< 20).," 4.1 in B05, the Galatic longitude, latitude, parallax, radial velocities and proper motions with their corresponding errors, for each simulated satellite star within the completeness limit of Gaia $V<20$ )."
 In this section we use a typical satellite stream with a chosen dynamical age. luminosity. orbit ancl SELL in order o explain the morphology of the pole count map and. the methodology devised to detect in it the signature produced wv the stream.," In this section we use a typical satellite stream with a chosen dynamical age, luminosity, orbit and SFH in order to explain the morphology of the pole count map and the methodology devised to detect in it the signature produced by the stream."
" For the present and all following experiments. role count maps were produced with a 72τὸ spherically uniform grid. position ancl velocity tolerances of δν=de,=5° and including from the simulated catalogues only hose stars with positive parallax with errors less than 30 »v cent ancl with |b|>107. to avoid the Galactic Plane."," For the present and all following experiments, pole count maps were produced with a $72 \times 72$ spherically uniform grid, position and velocity tolerances of $\delta\psi_r=\delta\psi_v=5^\circ$ and including from the simulated catalogues only those stars with positive parallax with errors less than $30$ per cent and with $|b| > 10^\circ$, to avoid the Galactic Plane."
 For this example we chose satellite S2 at a dynamical age of 5.85 Gyr. with an elongated. ancl inclined. orbit. a Carina-tvpe SELL and total luminosity of 310 L..," For this example we chose satellite S2 at a dynamical age of 5.85 Gyr, with an elongated and inclined orbit, a Carina-type SFH and total luminosity of $3\times10^8$ $_\odot$."
 The corresponding Galactocentrie sky distribution is shown in Fie. 6.., The corresponding Galactocentric sky distribution is shown in Fig. \ref{fig:spatial_s2}.
 Phe color scale of the figure indicates the particles? CGalactocentrie distances., The color scale of the figure indicates the particles' Galactocentric distances.
 The mGC€3 pole count map which corresponds to this simulated stream alone is shown in Fig., The mGC3 pole count map which corresponds to this simulated stream alone is shown in Fig.
 πι and the mGC€3 pole count map of this stream embecdtde in the Galactic background. (with errors) described in Sec. 77..," \ref{fig:polemap_s2}a a; and the mGC3 pole count map of this stream embedded in the Galactic background (with errors) described in Sec. \ref{s:mgc3_galmap_errs},"
 is shown in bie., is shown in Fig.
 ΤΡ). In this figure. the signature of the stream in pole counts is a barely perceptible excess aroune (ομωςGrote)=(57.35.yt.," \ref{fig:polemap_s2}b b. In this figure, the signature of the stream in pole counts is a barely perceptible excess around $(\phi_{pole},\theta_{pole})=(85^\circ,35^\circ)$."
 This is the kind. of feature we need to detect in pole count maps in an automated fashion. in order to evaluate the method's capabilities to detect tida streams of various characteristics.," This is the kind of feature we need to detect in pole count maps in an automated fashion, in order to evaluate the method's capabilities to detect tidal streams of various characteristics."
 Since the Galactic background. leaves a smooth signature in the pole count maps. we can use the stanclare image processing technique of to remove galaxie&s contribution.," Since the Galactic background leaves a smooth signature in the pole count maps, we can use the standard image processing technique of to remove its contribution."
 Unsharp masking consists in subtracting from the original image a image. in which the value of cach pixel corresponds to the median. value in its neighbourghood.," Unsharp masking consists in subtracting from the original image a image, in which the value of each pixel corresponds to the median value in its neighbourghood."
 Phe subtracted image or. in this case. the subtractec pole count map has a much more uniform backerouncl and the contrast of localized excesses is enhanced.," The subtracted image or, in this case, the subtracted pole count map has a much more uniform background and the contrast of localized excesses is enhanced."
 The smoothed image. made from the pole count map on Fig.," The smoothed image, made from the pole count map on Fig."
 ΤΟ using a neighbourhood of 5ο pixels. is shown in Fig.," \ref{fig:polemap_s2}b b using a neighbourhood of $5\times5$ pixels, is shown in Fig."
 Tec. “Phe subtracted pole count map is shown in Fig., \ref{fig:polemap_s2}c c. The subtracted pole count map is shown in Fig.
 τος for the present example., \ref{fig:polemap_s2}d d for the present example.
 In this subtracted map the streams signature is much more evident than it was in the original pole count map (Fig., In this subtracted map the stream's signature is much more evident than it was in the original pole count map (Fig.
 bb)., \ref{fig:polemap_s2}b b).
 The color scale in the subtracted map indicates the amplitude or height of the excesses in units of the backgrounds standard deviation e. and clearly shows that the stream in this example is detected at the ~Te level in the subtracted pole count map: whereas in original map the excess appears only at the ~260 level.," The color scale in the subtracted map indicates the amplitude or height of the excesses in units of the background's standard deviation $\sigma$, and clearly shows that the stream in this example is detected at the $\sim7\sigma$ level in the subtracted pole count map; whereas in original map the excess appears only at the $\sim2\sigma$ level."
 The subtractecl pole count map of Fig., The subtracted pole count map of Fig.
 dd still shows signs of non-uniformity., \ref{fig:polemap_s2}d d still shows signs of non-uniformity.
 Some regions in the subtracted map. particularly near an excess. appear with pole counts below the background (i.e. negative sigma amplitudes in Fig.," Some regions in the subtracted map, particularly near an excess, appear with pole counts below the background (i.e. negative sigma amplitudes in Fig."
 vdd)., \ref{fig:polemap_s2}d d).
 ‘This is caused by an oversubtraction of the background clue to the excess itself which increases the median value of the pole counts in pixels surrounding it in the smoothed image.," This is caused by an oversubtraction of the background due to the excess itself, which increases the median value of the pole counts in pixels surrounding it in the smoothed image."
 Also. spurious detections tend to arise at the 2003.56 leve due to imperfections in the background. subtraction.," Also, spurious detections tend to arise at the $2-3.5\sigma$ level due to imperfections in the background subtraction."
 In the examples of following sections we consider excess detections as those corresponding to excess counts with amplitudes larger than 4a., In the examples of following sections we consider excess detections as those corresponding to excess counts with amplitudes larger than $4\sigma$.
" We also require |6,,,,]<δθ consistently with our avoidance zone of |b|>10"," We also require $|\theta_{pole}|<80^\circ$, consistently with our avoidance zone of $|b|>10^\circ$."
 In the following section we systematically apply this procedure to recover the simulated. streams from. the detection of excesses in mGC€3 pole count maps., In the following section we systematically apply this procedure to recover the simulated streams from the detection of excesses in mGC3 pole count maps.
 In this section we explore the cllicieney of the method in recovering simulated. streams uncer different conditions of total Iuminosity. SELL and orbital parameters.," In this section we explore the efficiency of the method in recovering simulated streams under different conditions of total luminosity, SFH and orbital parameters."
from equation |.. slightly overestimating the stellar inclination and thus underestimating the planet mass.,"from equation \ref{eq1}, slightly overestimating the stellar inclination and thus underestimating the planet mass."
" ? used astrometric observations to tightly constrain the orbital parameters of HD 22049 b (4,=3043.8 deg).", \citet{Benedict06} used astrometric observations to tightly constrain the orbital parameters of HD 22049 b $i_{p}=30\pm3.8$ deg).
" The inclination of the planetary orbit lies within the range estimated here for 7, (44u deg) and the best-fitting stellar axial inclination (27-33 deg) determined by ? from the modelling of spots.", The inclination of the planetary orbit lies within the range estimated here for $i_{*}$ $44_{-15}^{+24}$ deg) and the best-fitting stellar axial inclination (27–33 deg) determined by \citet{Croll06} from the modelling of spots.
 Also. a circumstellar dise with /=25 deg was found by ??..," Also, a circumstellar disc with $i$ =25 deg was found by \citet{Greaves98,Greaves05}."
 All these values suggest that the system is well aligned., All these values suggest that the system is well aligned.
 The stars with previously published rotation periods (seconc section of Table L3) are analysed in ?.., The stars with previously published rotation periods (second section of Table \ref{Rot}) ) are analysed in \citet{Watson10}. .
 We removed the sin/ ambiguity from the planetary minimum mass. mysini. using the inclination of the stellar rotation axis. under the assumption that the rotation axis is aligned with the planetary orbital axis.," We removed the $\sin{i}$ ambiguity from the planetary minimum mass, $m_{p}\sin{i}$, using the inclination of the stellar rotation axis, under the assumption that the rotation axis is aligned with the planetary orbital axis."
 Several systems contain. multiple planets allowing the mass of fourteen planets to be calculated., Several systems contain multiple planets allowing the mass of fourteen planets to be calculated.
 The majority of the planets are calculated to have inclinations greater than 30 deg so the planetary masses are not more than twice the minimum mass., The majority of the planets are calculated to have inclinations greater than 30 deg so the planetary masses are not more than twice the minimum mass.
 All but one of the planets (HD 92788) have calculated masses below the brown-dwarf mass limit ( 13.17). supporting their status as planets.," All but one of the planets (HD 92788) have calculated masses below the brown-dwarf mass limit $\simeq$ 13 $M_{J}$ ), supporting their status as planets."
 The lower limit of esin/ for HD 69830 and HD 92788 is approximately zero. which leads to a minimum inclination of O deg.," The lower limit of $v \sin i$ for HD 69830 and HD 92788 is approximately zero, which leads to a minimum inclination of 0 deg."
 As a result. the maximum planetary masses cannot be determined.," As a result, the maximum planetary masses cannot be determined."
 The calculated mass of HD 92788 b (28 AZ; is found to be much larger than the brown dwarf limit due to the low inclination predicted from the rotation period (8.1H. deg)., The calculated mass of HD 92788 b (28 $M_{J}$ ) is found to be much larger than the brown dwarf limit due to the low inclination predicted from the rotation period $8_{-8}^{+14}$ deg).
" The lower range of the mass (9 A7,;) still allows the possibility that it is a planet. however there is evidence to suggest that it could be a very low- brown dwarf."," The lower range of the mass (9 $M_{J}$ ) still allows the possibility that it is a planet, however there is evidence to suggest that it could be a very low-mass brown dwarf."
 Similarly. the inclination of HD 69830 is found to be low (13.25 deg) and as a result. the planets are calculated to be over four times the minimum mass.," Similarly, the inclination of HD 69830 is found to be low $13_{-13}^{+27}$ deg) and as a result, the planets are calculated to be over four times the minimum mass."
 This suggests that the planets are in the Saturn-mass rather than Neptune-mass regime., This suggests that the planets are in the Saturn-mass rather than Neptune-mass regime.
 HD 69830 and HD 92788 are the stars with the lowest esin? which leads to the low inclinations., HD 69830 and HD 92788 are the stars with the lowest $v \sin i$ which leads to the low inclinations.
 Due to the difficulty in measuring such small values. other determinations in the literature find higher values of esin/ (L1 km + 2 and L.8 km 19 respectively).," Due to the difficulty in measuring such small values, other determinations in the literature find higher values of $v \sin i$ (1.1 km $^{-1}$ \citet{Lovis06} and 1.8 km $^{-1}$ \citet{Mayor04}, respectively)."
 Using these values pushes the inclinations to 55− deg and 53a deg. resulting in the plane masses being not much above the minimum mass.," Using these values pushes the inclinations to $58_{-32}^{+32}$ deg and $53_{-20}^{+37}$ deg, resulting in the planet masses being not much above the minimum mass."
 To determine the nature of these objects. aconsensus on the value of ¢sins must be found.," To determine the nature of these objects, a consensus on the value of $v \sin i$ must be found."
 HD 89744b has one of the highest minimum-mss companions discovered and may be a low mass brown dwarf if the inclination were low enough., HD 89744b has one of the highest minimum-mass companions discovered and may be a low mass brown dwarf if the inclination were low enough.
 The moderate inclination. 54Te leads to a mass range of 8-15. M; which does not rule this out: however. the calculated value falls below the brown dwarf limit. which suggests that the companion is a very massive planet.," The moderate inclination, $54_{-12}^{+36}$, leads to a mass range of 8–15 $M_{J}$ which does not rule this out; however, the calculated value falls below the brown dwarf limit, which suggests that the companion is a very massive planet."
 The H K records of 36 exoplanet host stars and photometric observations. of HD 130322. were analysed. for periodicities associated with stellar rotation., The H K records of 36 exoplanet host stars and photometric observations of HD 130322 were analysed for periodicities associated with stellar rotation.
 An increased H K dataset allowed previously unknown rotation periods to be determined., An increased H K dataset allowed previously unknown rotation periods to be determined.
 Ten stars exhibit periodicities that are consistent with /?.. resin; and £2... the rotation period estimated from the average Magnetic activity. and are therefore inferred to be due to rotational modulation.," Ten stars exhibit periodicities that are consistent with $R_*$, $v \sin i$ and $P_{calc}$, the rotation period estimated from the average magnetic activity, and are therefore inferred to be due to rotational modulation."
 HD 9651.HD 130322 and HD 22049 show the recurrence of strong and similar periodicities over many seasons whieh we attribute to rotation.," HD 3651,HD 130322 and HD 22049 show the recurrence of strong and similar periodicities over many seasons which we attribute to rotation."
 The rotation period of HD 36531 has been, The rotation period of HD 3651 has been
"a?/3,b?/3, and c?/3, where a, b, and c are the semi- axes, with a>bc.","$a^2/3, b^2/3$, and $c^2/3$ , where $a$ , $b$ , and $c$ are the semi-principal axes, with $a \geq b \geq c$."
" Hence, the square roots of the eigenvalues are proportional to the lengths of the semi-principal axes."," Hence, the square roots of the eigenvalues are proportional to the lengths of the semi-principal axes."
" We then keep the length of the semi- axis fixed (but the orientation can change) and recalculate S by summing over all particles within an ellipsoidal shell with semi-major axis a=r and axis ratios b/a and c/a, but with the new orientation."," We then keep the length of the semi-major axis fixed (but the orientation can change) and recalculate $\mat{S}$ by summing over all particles within an ellipsoidal shell with semi-major axis $a=r$ and axis ratios $b/a$ and $c/a$, but with the new orientation."
 This iteration is repeated until convergence is reached., This iteration is repeated until convergence is reached.
 As a convergence criterion we require that the fractional difference between two iteration steps in both axis ratios is smaller than 10-?., As a convergence criterion we require that the fractional difference between two iteration steps in both axis ratios is smaller than $10^{-3}$.
" When referring to the radius or distance from the center for an ellipsoidal shape, we always mean the semi-major axis a."," When referring to the radius or distance from the center for an ellipsoidal shape, we always mean the semi-major axis $a$."
 There are many other methods for shape determination used in the literature., There are many other methods for shape determination used in the literature.
" We present tests and comparisons in a companion paper (?),, which further motivates our choice of procedure, since other methods can lead to a significant bias in the measured shape."," We present tests and comparisons in a companion paper \citep{2011arXiv1107.5582Z}, which further motivates our choice of procedure, since other methods can lead to a significant bias in the measured shape."
 For measuring the halo shape it is essential to exclude all particles that are in subhalos., For measuring the halo shape it is essential to exclude all particles that are in subhalos.
 Not removing subhalo particles can lead to artificially low axis ratios (spikes) at the location of the subhalos (see also ?))., Not removing subhalo particles can lead to artificially low axis ratios (spikes) at the location of the subhalos (see also \citealt{2011arXiv1107.5582Z}) ).
" In Figure 11,, we show the median axis ratios b/a and c/a as well as the triaxiality parameter for the different matter components at z72."," In Figure \ref{fig:shape}, we show the median axis ratios $b/a$ and $c/a$ as well as the triaxiality parameter for the different matter components at $z \approx 2$."
" Ellipsoids are called oblate if 0€T<1/3, triaxial if and prolate if 2/3€T<1. 2/3"," Ellipsoids are called oblate if $0 \leq T \leq 1/3$, triaxial if $1/3 < T < 2/3$ , and prolate if $2/3 \leq T \leq 1$."
",In the non-radiative case B, the dark matter shows the well known behavior from N-body simulations where the halo shape is relatively round near the virial radius but becomes progressively prolate czzb« a) towards the center, reaching b/a~0.55 (i.e.and c/a7:0.4 e.g., ??7).."," In the non-radiative case B, the dark matter shows the well known behavior from N-body simulations where the halo shape is relatively round near the virial radius but becomes progressively prolate (i.e. $c \approx b < a$ ) towards the center, reaching $b/a \approx 0.55$ and $c/a \approx 0.4$ \citep[see also, e.g.,][]{2005ApJ...627..647B, 2006MNRAS.367.1781A, 2009MNRAS.398L..21S}."
" In the dissipative case A, the dark matter shape is much rounder at the center: b/a70.95 and c/ae0.8, and the overall shape is oblate instead of prolate."," In the dissipative case A, the dark matter shape is much rounder at the center: $b/a \approx 0.95$ and $c/a \approx 0.8$ , and the overall shape is oblate instead of prolate."
" Such transformation has been seen in previous studies (e.g., "," Such transformation has been seen in previous studies \citep[e.g.,][]{1991ApJ...377..365K, 1994ApJ...422...11E, 1994ApJ...431..617D, 2004ApJ...611L..73K, 2010MNRAS.406..922T, 2011ApJ...734...93L}."
"In particular, ? find very similar axis ratios in their smooth particle hydrodynamics (SPH) simulations: b/a=0.95, =0.8—0.9."," In particular, \cite{2010MNRAS.407..435A} find very similar axis ratios in their smooth particle hydrodynamics (SPH) simulations: $b/a \approx 0.95$, $c/a \approx 0.8-0.9$."
" The change in the shape with radius isc/a gradual and is best demonstrated by the triaxiality parameter T', which steadily decreases from T=0.8 outside the virial radius to Tzz0.2 at the center."," The change in the shape with radius is gradual and is best demonstrated by the triaxiality parameter $T$, which steadily decreases from $T \approx 0.8$ outside the virial radius to $T \approx 0.2$ at the center."
 The baryons in run A form a strongly flattened distribution., The baryons in run A form a strongly flattened distribution.
" The gas settles into a rather thin disk, with c/a7:0.2 (which includes the hot and warm gas phases; the cold gas disk is still thinner — see Figure 1)), as opposed to an almost prolate elongated shape in run B without dissipation."," The gas settles into a rather thin disk, with $c/a \approx 0.2$ (which includes the hot and warm gas phases; the cold gas disk is still thinner – see Figure \ref{fig:disc}) ), as opposed to an almost prolate elongated shape in run B without dissipation."
" The stars also form an oblate disc structure, with a minimum c/a&0.3, although it is not as thin as the gaseous disk."," The stars also form an oblate disc structure, with a minimum $c/a \approx 0.3$, although it is not as thin as the gaseous disk."
 The stellar particles experience gravitational scattering from fluctuation of the potential as soon as they form and therefore diffuse away from the plane of the disk., The stellar particles experience gravitational scattering from fluctuation of the potential as soon as they form and therefore diffuse away from the plane of the disk.
" Near the center, the stellar distribution becomes less flattened as the disk transitions into a bulge."," Near the center, the stellar distribution becomes less flattened as the disk transitions into a bulge."
 The shape of the stellar distribution in the outskirts of the halo has a large scatter because of the low particle number and is not meaningful., The shape of the stellar distribution in the outskirts of the halo has a large scatter because of the low particle number and is not meaningful.
 The shape of the total matter distribution is then a consequence of the combination of the individual matter component shapes and their relative importance as a function of radius (shown in Figure 5))., The shape of the total matter distribution is then a consequence of the combination of the individual matter component shapes and their relative importance as a function of radius (shown in Figure \ref{fig:fraction}) ).
" In the dissipative run A, the shape is approximately round at r>O.1r299p,A, but sharply turns oblate at the inner radii where baryons dominate the mass also?).."," In the dissipative run A, the shape is approximately round at $r > 0.1\, r_\mathrm{200b,A}$, but sharply turns oblate at the inner radii where baryons dominate the mass \citep[see also][]{2010MNRAS.405.1119K}."
" In the innermost region, the matter distribution(see is determined by the more round bulge."," In the innermost region, the matter distribution is determined by the more round bulge."
" This detailed shape structure of the mass distribution is important for accurate modeling of the strong gravitational lensing effect due to massive elliptical galaxies, which we discuss in Section ??.."," This detailed shape structure of the mass distribution is important for accurate modeling of the strong gravitational lensing effect due to massive elliptical galaxies, which we discuss in Section \ref{sec:discussion}."
" Over the three epochs that we investigate in detail, we do not find any significant changes in the overall shape of the matter distribution."," Over the three epochs that we investigate in detail, we do not find any significant changes in the overall shape of the matter distribution."
" Generally, the shape converges farther from center than the density profile."," Generally, the shape converges farther from center than the density profile."
" For example, ? found that the convergence radius for the shape in a pure N-body simulations was a factor 3 larger than the convergence radius for the density profile."," For example, \cite{2009MNRAS.398L..21S} found that the convergence radius for the shape in a pure N-body simulations was a factor 3 larger than the convergence radius for the density profile."
 One should keep this in mind when interpreting the results in Figure 11.., One should keep this in mind when interpreting the results in Figure \ref{fig:shape}.
 Why does baryon dissipation change the shape of the dark matter distribution so drastically at the center?, Why does baryon dissipation change the shape of the dark matter distribution so drastically at the center?
 One intuitive interpretation is that dark matter particles respond to the flattened gravitational potential near the disk and transform their orbital structure., One intuitive interpretation is that dark matter particles respond to the flattened gravitational potential near the disk and transform their orbital structure.
 Low-angular momentum box orbits may be replaced by more round tube orbits., Low-angular momentum box orbits may be replaced by more round tube orbits.
" Indeed, we show later in Figure 15 that the average angular momentum of dark matter particles at the center increases by a factor of several relative to the non-dissipative run."," Indeed, we show later in Figure \ref{fig:angularmomentum_contraction_radius} that the average angular momentum of dark matter particles at the center increases by a factor of several relative to the non-dissipative run."
" In addition to studying individual particle orbits, we can conduct test of this idea basedon theglobal shape of the dark mattera halo."," In addition to studying individual particle orbits, we can conduct a test of this idea basedon theglobal shape of the dark matter halo."
" If the oblate spheroid shape of dark matter follows the shapeof the baryon disk, the orientation of the inner spheroid should align with that of the disk, regardless ofthe orientation of dark matter near the virial radius."," If the oblate spheroid shape of dark matter follows the shapeof the baryon disk, the orientation of the inner spheroid should align with that of the disk, regardless ofthe orientation of dark matter near the virial radius."
(or destructively).,(or destructively).
 Both the typical timescale and the frequency baudwidth are small., Both the typical timescale and the frequency bandwidth are small.
 The modulation iudex equals one., The modulation index equals one.
 The timescale is dependent ou the relative velocities of the pulsu. the interstellar medium aud the Earth.," The timescale is dependent on the relative velocities of the pulsar, the interstellar medium and the Earth."
 For the WENSS obscrvatious of pulsars typical timescales are 1 to 10 aimutes and typical baucwidths are 10 Uz to 500 kKIIz., For the WENSS observations of pulsars typical timescales are 1 to 10 minutes and typical bandwidths are 10 Hz to 500 kHz.
 This ueans that for almost all pulsars any variations due to diffractive scintillation are averaged out over the 5 MIIZ WENSS bandwidth aud when the 6 « 15 short observations spread over 6 « 12 hours are combined., This means that for almost all pulsars any variations due to diffractive scintillation are averaged out over the 5 MHz WENSS bandwidth and when the 6 $\times$ 18 short observations spread over 6 $\times$ 12 hours are combined.
 Ouly for PSR Boso9|7 Lave the diffractive scintillation timescale and bandwidth large οποιο] that some effect relmains., Only for PSR B0809+74 are the diffractive scintillation timescale and bandwidth large enough that some effect remains.
 From the equations eiven by Walker (1998) one finds a timescale of 12 minutes and a bandwidth of 500 kIIz., From the equations given by Walker \cite*{wal98} one finds a timescale of 12 minutes and a bandwidth of 500 kHz.
 The actual value of the typical scintillation timescale and bandwidth are even higher. since several authors have already shown that the Tavlor-Cordes distance inodel (Tavlor&Cordes.1993) gives too small predictions for this pulsar (e.g. Rickett ct 22000).," The actual value of the typical scintillation timescale and bandwidth are even higher, since several authors have already shown that the Taylor-Cordes distance model \cite{tc93} gives too small predictions for this pulsar (e.g. Rickett et 2000)."
 — Diffractive scintillation can explain the WENSS image of this pulsar reffeuuaps)), \nocite{rcm00} Diffractive scintillation can explain the WENSS image of this pulsar ).
 As LO auinutes is the time between two observatious of a ποια iu one nuüosuc. flux cdenusitv variations on that time scale cause spokes in the map.," As 40 minutes is the time between two observations of a field in one mosaic, flux density variations on that time scale cause spokes in the map."
 Such spokes can also be seen in the complete map of PSR D0329|51 rof£Be:0329))., Such spokes can also be seen in the complete map of PSR B0329+54 \\ref{fig:0329}) ).
 Refractive scintillation is caused bv the focussing effect. of à large scattering region., Refractive scintillation is caused by the focussing effect of a large scattering region.
 The timescales and bandwidths involved are ιο. larger than iu the case of diffractive scintillation., The timescales and bandwidths involved are much larger than in the case of diffractive scintillation.
 The modulation iudex is also 3inaller., The modulation index is also smaller.
" The sciutillation bandwidth is of the order of the observing frequency,", The scintillation bandwidth is of the order of the observing frequency.
 Refractive time scales for the pulsars detected in the WENSS vary from a couple of davs to several vears aud the expected modulation index from 0.05 to 0.3., Refractive time scales for the pulsars detected in the WENSS vary from a couple of days to several years and the expected modulation index from 0.05 to 0.3.
 Tf the refractive time scale is less than he time between observations of the same mosaic (couple of davs to several vears). auv flux deusifv variation will be averaged out when the mosaics are conibiued.," If the refractive time scale is less than the time between observations of the same mosaic (couple of days to several years), any flux density variation will be averaged out when the mosaics are combined."
 Ilowever. stone flux density variations between 12 hour sessions cause a rine at the first erating rine of the svuthesised beam.," However, stong flux density variations between 12 hour sessions cause a ring at the first grating ring of the synthesised beam."
 Since the mutual distances between the dishes are multiples of 72 ui the rine will have radius of 72 im / (c 325 MITz) radians. in right ascension aud {τνCOsCCÓ in declination.," Since the mutual distances between the dishes are multiples of 72 m, the ring will have radius of 72 m / $c/$ 325 MHz) radians, in right ascension and $\times ~\cosec ~\delta$ in declination."
 The second aud higher erating rings are uot visible. since data far from the field ceuter gets a low weighting factor when the final iniage is created.," The second and higher grating rings are not visible, since data far from the field center gets a low weighting factor when the final image is created."
 It is hard to eive good estinates for the expected ciffractive and refractive scintillation timescales., It is hard to give good estimates for the expected diffractive and refractive scintillation timescales.
 They depend on the often poorly known pulsar velocity., They depend on the often poorly known pulsar velocity.
 For aree pulsar velocities (compared to the velocity of the iuterstellar medi. beiug about 50/3) the dependence is as one over the square root of this velocity.," For large pulsar velocities (compared to the velocity of the interstellar medium, being about 50 km/s) the dependence is as one over the square root of this velocity."
 Since some oilsar velocities uieht be up to several hundred kilometers oer second. this cannot o neglected.," Since some pulsar velocities might be up to several hundred kilometers per second, this cannot be neglected."
 1 divided the pulsars hat are detecte iu the WENSS in two groups. based ou heir expected refractive modulation dex if weir velocity is neglected.," I divided the pulsars that are detected in the WENSS in two groups, based on their expected refractive modulation index if their velocity is neglected."
 Both groups had simular relative deviations )etxeeen their mieasured aud expected fux deusities., Both groups had similar relative deviations between their measured and expected flux densities.
 The observe nodulation index is abot 0.1. much areor than the expected value of. abot 02.," The observed modulation index is about 0.4, much larger than the expected value of about 0.2."
 The WENSS pulsar flux densities vary more due ο refractive scintillation than. predicted. bv the equations., The WENSS pulsar flux densities vary more due to refractive scintillation than predicted by the equations.
 This has οσα observed before by several authors aud is attributed o the asstuption that the turbulence iu the interstellar uediunu has a Ixoliiogorov spectrum BBlaudford Naravan. 1985).," This has been observed before by several authors and is attributed to the assumption that the turbulence in the interstellar medium has a Kolmogorov spectrum Blandford Narayan, 1985)."
 The NWSS flux clensities are even more affected by scintillation effects.," \nocite{bn85}
 The NVSS flux densities are even more affected by scintillation effects."
 Each point iu the NVSS maps is an average of abou three snapshots., Each point in the NVSS maps is an average of about three snapshots.
 Two of these three are taken rielit after cach other (snapshot series are taken at constant decluation and increasing right ascension. see fleuve 7 in Couou et 119985) aud very little averaging takes place.," Two of these three are taken right after each other (snapshot series are taken at constant declination and increasing right ascension, see figure 7 in Condon et 1998) and very little averaging takes place."
 The expected refractive modulation iudex at 1100 MITIZz is larger than at the WENSS frequency., The expected refractive modulation index at 1400 MHz is larger than at the WENSS frequency.
 The expected diffractive frequency bandwidth is also larger at, The expected diffractive frequency bandwidth is also larger at
 , 
Ihnes.,lines.
 We therefore leave a detailed discussion of the hare N-vav continuum. which should also iuchide data for the οποιον range 0.5-10 keV. to a future article.," We therefore leave a detailed discussion of the hard X-ray continuum, which should also include data for the energy range 0.5-10 keV, to a future article."
 Towever. in order to test the dependence of the measured line flix estimates on the assumned continuum shape we tested various coutiuuun models. the results of which cau be found in Table 1..," However, in order to test the dependence of the measured line flux estimates on the assumed continuum shape we tested various continuum models, the results of which can be found in Table \ref{tbl-fits}."
 It is surprising that the best fit to the PDS-spectruu iu a statistical seuse is provided by a power law inodel plus Ine emission., It is surprising that the best fit to the PDS-spectrum in a statistical sense is provided by a power law model plus line emission.
 However. as the 1ieasured line flux depends ou the continuum model chosen. we have to take the uncertaintv about the nature of the contiuunun inte account.," However, as the measured line flux depends on the continuum model chosen, we have to take the uncertainty about the nature of the continuum into account."
 Tt is clear from spectral fits to the narrower 30-100 keV spectral range that the πο of a thermal componcut with Τις L2 keV has little effect on the estimated Hux., It is clear from spectral fits to the narrower 30-100 keV spectral range that the inclusion of a thermal component with = 4.2 keV has little effect on the estimated flux.
 Certainly. for this narrow range a power law js a reasonable approximation for the continuum.," Certainly, for this narrow range a power law is a reasonable approximation for the continuum."
 As he energv range is smaller. there is more statistical uncertainty about the photon index. aud therefore the line fux is 1nore uncertain.," As the energy range is smaller, there is more statistical uncertainty about the photon index, and therefore the line flux is more uncertain."
 Iudeed the significance of the iue cinission drops from the 56 to the 3.16 level., Indeed the significance of the line emission drops from the $5\sigma$ to the $3.4\sigma$ level.
 The photon index versus line flux confidence contours for this ΟΠΟΙΟΥ range is shown in Figure 2.., The photon index versus line flux confidence contours for this energy range is shown in Figure \ref{fig-contour}.
 The 30 upper limit ou he flux iu both lines is 3.510./s.. based on the K100 keV energev range.," The $3\sigma$ upper limit on the flux in both lines is $3.5\ 10^{-5}$, based on the 30-100 keV energy range."
 This upper limit is comparable o the line flux at 1157. keV recently. obtained from CCRO-COMPTEL data. (3.340.6)107 confidence range). see Ividin(1997).," This upper limit is comparable to the line flux at 1157 keV recently obtained from CGRO-COMPTEL data, $(3.3 \pm 0.6)\ 10^{-5}$ confidence range), see \citet{Iyudin97}."
. However. both neasurelents are consistent even the systematic uncertainties for the COMPTEL measurement (Duprazetal. 1997).," However, both measurements are consistent given the systematic uncertainties for the COMPTEL measurement \citep{Dupraz97}."
. Although it is difficult to combine the COMPTEL and the PDS results. due to the unkuown nature of the systematic error. the fact that there are now two independent measurements of Lue cussion associated with the ddecay mereases the credibility of the detections.," Although it is difficult to combine the COMPTEL and the PDS results, due to the unknown nature of the systematic errors, the fact that there are now two independent measurements of line emission associated with the decay increases the credibility of the detections."
 We therefore suggest adopting a line flux for Cas A of (2.5£1.0)10°fs. which is consistent with both the PDS and COMPTEL lueasurenmoents.," We therefore suggest adopting a line flux for Cas A of $(2.5 \pm 1.0)\, 10^{-5}$, which is consistent with both the PDS and COMPTEL measurements."
 Since the initial discovery of the inuclear decay lines by CGRO-COMPTEL (Uvucin199 8).. our knowledge of the formation aud decay of thas substantially iuproved.," Since the initial discovery of the nuclear decay lines by CGRO-COMPTEL \citep{Iyudin94}, our knowledge of the formation and decay of has substantially improved."
 Recently. the decay time of thas been accurately measured to be 85.1250.9 vr by three adependent experiments (Almacetal.1998:Correseo905:Normanetal. 1005).," Recently, the decay time of has been accurately measured to be $85.4 \pm 0.9$ yr by three independent experiments \citep{Ahmad98,Goerres98,Norman98}. ."
 As the Cas A supernova was xobablv observed by the English astronomer J. Flaustecd i A.D. 1680 (Ashworth1980).. the age of Cas A is ~ tooo20 vi.," As the Cas A supernova was probably observed by the English astronomer J. Flamsteed in A.D. 1680 \citep{Ashworth80}, the age of Cas A is $\sim$ 320 yr."
 A good alternative is to use the kincmatic age of ie fast moving optical knots. 330 vr (ThorstensenWw 0101. but the age difference is so small that it has little Που on the inferred range of initial nunass.," A good alternative is to use the kinematic age of the fast moving optical knots, 330 yr \citep{Thorstensen01}, but the age difference is so small that it has little effect on the inferred range of initial mass."
 The line fux of (2.5+L0)10?fs. combined with the ddecay time and a distance to Cas A of 3.1!Mi kpe 1995).. vields an initial nuuassintherauge (0.82.5)10IAL with 1210.ΤΙ. ccorrespondiug to the adopted ffiux and distance to Cas A. This is rather hieh compared to model predictions. which usually indicate nuuasses below 104ML. exeept for progenitor masses around acad above 25M. citepTiuuues96..," The line flux of $(2.5 \pm 1.0)\, 10^{-5}$, combined with the decay time and a distance to Cas A of $3.4^{+0.3}_{-0.1}$ kpc \citep{Reed95}, yields an initial mass in the range $(0.8 - 2.5)\ 10^{-4}$, with $1.2\ 10^{-4}$ corresponding to the adopted flux and distance to Cas A. This is rather high compared to model predictions, which usually indicate masses below $10^{-4}$, except for progenitor masses around and above $\sim$ \\citep{Timmes96}."
 For that reason. Mochizuldetal.(1999) made the interesting suggestiou that the ddecay. may be delayed. as à result of complete ionization of14TH... inhibiting the decay of bby the capture of a Ix-shell electron.," For that reason \citet{Mochizuki99} made the interesting suggestion that the decay may be delayed, as a result of complete ionization of, inhibiting the decay of by the capture of a K-shell electron."
 ITowever. recently Lamune(2001€) showed that the electrou temperature im the ejecta was probably never high euough to seriously affect the cldlecay.," However, recently \citet{Laming01c} showed that the electron temperature in the ejecta was probably never high enough to seriously affect the decay."
 The production of lucreases with the size of the helium core of the progenitor. mit material falling back on the neutron star or black hole LBnits the amouut of ejectedΤ," The production of increases with the size of the helium core of the progenitor, but material falling back on the neutron star or black hole limits the amount of ejected."
"ι, Model ealeiulatious show hat massive stars have more fall back. but pre-supernova wind loss may haut the amount of material falling back (Tinuuesetal.1996)."," Model calculations show that massive stars have more fall back, but pre-supernova wind loss may limit the amount of material falling back \citep{Timmes96}."
. This agrees with the idea that the xogenitor of Cas A was a not too massive (~ 30M.) WolfRavet star that suffered heavy mass loss (Vinkctal.1996)., This agrees with the idea that the progenitor of Cas A was a not too massive $\sim$ ) Wolf-Rayet star that suffered heavy mass loss \citep{Vink96}.
. Additionally. assvimetries in the explosion may rave inercased the amount of ssvuthesized (Nagatakietal.1998).," Additionally, assymetries in the explosion may have increased the amount of synthesized \citep{Nagataki98}."
. The likely presence of a neutron star (Chakrabartyetal.2001) in Cas A further constrains the explosion scenario for Cas A. as too mmch fall back would have resulted iu the formation of a black hole.," The likely presence of a neutron star \citep{Chakrabarty01} in Cas A further constrains the explosion scenario for Cas A, as too much fall back would have resulted in the formation of a black hole."
 Although we have now finally detected the uuuclear decay lines at 67.9 keV and 78.1 keV. interesting observations remain to be done with future hard N-ray aud Canunaray ndssous.," Although we have now finally detected the nuclear decay lines at 67.9 keV and 78.4 keV, interesting observations remain to be done with future hard X-ray and Gamma-ray missions."
" The solid state detectors ou hoard Tutegral will be able to meastre the line broadening of the ]lhne accurately, aud coustrain the properties of the hard N-rav coutimmiuu further."," The solid state detectors on board Integral will be able to measure the line broadening of the line accurately, and constrain the properties of the hard X-ray continuum further."
 Iu addition. hard N-rav experiments using multi-aver mirrors will be able to map the spatial distribution of inu Cas A on the arciuinute scale.," In addition, hard X-ray experiments using multi-layer mirrors will be able to map the spatial distribution of in Cas A on the arcminute scale."
" Support for this work was provided by the NASA through Chandra Postdoctoral Fellowship Award πμ) PFO-LOOLL issued by the Claudra N-rayv Observatory Center. which is operated by the Sinithonian Astrophysical Observatory for and on behalf of NASA under contract NASS-39073,"," Support for this work was provided by the NASA through Chandra Postdoctoral Fellowship Award Number PF0-10011 issued by the Chandra X-ray Observatory Center, which is operated by the Smithonian Astrophysical Observatory for and on behalf of NASA under contract NAS8-39073."
 JAIL was supported by basic research fuuds of the Office of NavalResearch This research has made use of SANDAS linearized and cleaned event files (Rev.2.1.1) produced at the BeppoSAX Scicuce Data Ceuter., JML was supported by basic research funds of the Office of NavalResearch This research has made use of SAXDAS linearized and cleaned event files (Rev.2.1.4) produced at the BeppoSAX Science Data Center.
»gerite equal to 3.1 For LIDS (104 - 050). and 21.6 for DoS (144 - 050) using an excitation temperature of 10 Ix. This temperature. taken as a kinetic temperature is that at. which chemical fractionation should be efficient.,"$\sum_{i}^{}g_{i}e^{E_{i}/kT_{ex}}$ equal to 3.1 for HDS $_{0,1}$ - $_{0,0}$ ), and 21.6 for $_2$ S $_{1,1}$ - $_{0,0}$ ) using an excitation temperature of 10 K. This temperature, taken as a kinetic temperature is that at which chemical fractionation should be efficient."
 The observed transitions are obviously not enough to calculate the excitation temperature in each source., The observed transitions are obviously not enough to calculate the excitation temperature in each source.
 Nevertheless. it is possible to estimate a reliable value lor the excitation temperature using the kinetic temperature of the gas found in (he literature.," Nevertheless, it is possible to estimate a reliable value for the excitation temperature using the kinetic temperature of the gas found in the literature."
 Mentenetal.(LOST) (vespectivelvDachilleretal.1990). derived a kinetic temperature in L1689N (respectively Bl) of  12 Ix based on their ammonia observations., \citet{menten87} \citep[respectively][]{bachiller90} derived a kinetic temperature in L1689N (respectively B1) of $\sim$ 12 K based on their ammonia observations.
 Blakeetal.(1995) estimated T; between 20 and 40 Ix for the core of IRASAA based on their CS ancl HeCO observations., \citet{blake95} estimated $_k$ between 20 and 40 K for the core of IRAS4A based on their CS and $_2$ CO observations.
 Ward-Thompsonetal.(1996). found that T; lies in the range of 15-20 Ix for IRAS2 from their infall model., \citet{ward96} found that $_k$ lies in the range of 15-20 K for IRAS2 from their infall model.
 VanDishoecketal.(1995) estimated a rotational temperature of ~ 12 Ix from two IDS lines towards IRASIG6293., \citet{vandishoeck95} estimated a rotational temperature of $\sim$ 12 K from two HDS lines towards IRAS16293.
 In the three last sources. the Class (0 sources. temperature gradients are known {ο be present. ancl Cae quoted estimates refer to the outer regions of the envelopes of these sources.," In the three last sources, the Class 0 sources, temperature gradients are known to be present, and the quoted estimates refer to the outer regions of the envelopes of these sources."
 Very likely the present 1IDS and DoS observations probe in [act those external regions too., Very likely the present HDS and $_2$ S observations probe in fact those external regions too.
" In the following. we will assume that T., is the same for IDS and DeS. namely that the 2 molecules originate in the same region."," In the following, we will assume that $_{ex}$ is the same for HDS and $_2$ S, namely that the 2 molecules originate in the same region."
 Luckily enough. the calculation of the N(DaS)/ N(IIDS) ratio does not depend so nich on the excitation temperature in the 10 - 50 Ix range. as the energy levels compared are DoS has para aud ortho forms.," Luckily enough, the calculation of the $_2$ S)/N(HDS) ratio does not depend so much on the excitation temperature in the 10 - 50 K range, as the energy levels compared are $_2$ S has para and ortho forms."
 The observed 144 - Oo.) (ransiGion is the lowest line in the ortho Iadder.," The observed $_{1,1}$ - $_{0,0}$ transition is the lowest line in the ortho ladder."
 To derive the D55/IIDS ratio. the DeS column density. was caleulated for the ortho levels only. and (then extrapolated to a total column density. assuming an ortlio to para ratio of 2.," To derive the $_2$ S/HDS ratio, the $_2$ S column density was calculated for the ortho levels only, and then extrapolated to a total column density assuming an ortho to para ratio of 2."
 The derived. D5S/ILIDS ratios have been computed using equations (1 - 3) and are reported in Table 3.., The derived $_2$ S/HDS ratios have been computed using equations (1 - 3) and are reported in Table \ref{table3}.
 Ilverogen sulfide is traditionally believed to fori on (he grain surfaces. since gas pliase reactions in cold gas are not efficient enough to account for the observed II58 abunclances (e.g.Tielens&Allamandola1987:Minhοἱal.1989).," Hydrogen sulfide is traditionally believed to form on the grain surfaces, since gas phase reactions in cold gas are not efficient enough to account for the observed $_2$ S abundances \citep[e.g.][]{tielens87,minh89}."
. In dense clouds sulfur is believed to be mostly neutral and initiates the chain reaction: 1l;5 isthought to be the precursor to the Πο molecule. via a dissociative recombination.," In dense clouds sulfur is believed to be mostly neutral and initiates the chain reaction: $_3$ $^+$ is thought to be the precursor to the $_2$ S molecule, via a dissociative recombination."
 As aanust be of eqs(63)) aud (6051) So Freidinaun equation aud Ravchaudhuri equation must hold at the same time. or must not hok simultaneously.,"], As a must be of \ref{time_time_Einstein}) ) and \ref{space_space_Einstein}) ) So Freidmann equation and Raychaudhuri equation must hold at the same time, or must not hold simultaneously."
 Thestatement of (Wane&Stemlardt1998) aud (Weinber&I&uuionukowski2002) that when dark euerev does not cluster on the scale of ealaxv clusters. Ravehaudlimi equation cau be use to describe the evolution of the over-dense region bu Freidimann equation does not hold is an incorrec statement.," Thestatement of \citep{WangSteinhardt1} and \citep{NWeinberg} that when dark energy does not cluster on the scale of galaxy clusters, Raychaudhuri equation can be used to describe the evolution of the over-dense region but Freidmann equation does not hold is an incorrect statement."
 Let us sav more explicitly. when dark energy docs uot cluster on the ealaxy clusters. hence a dari enerev exists wlich describe the flowing of dark euergv outside the over-deuse region. the basic equation which should be used to describe the evolution of the region is not the eqcÀ2) of (Wane&Stein L998).. it should be our eq(2))," Let us say more explicitly, when dark energy does not cluster on the galaxy clusters, hence a dark energy exists which describe the flowing of dark energy outside the over-dense region, the basic equation which should be used to describe the evolution of the over-denseregion is not the eq(A2) of \citep{WangSteinhardt1}, it should be our \ref{ZGEconserve}) )."
 Our eq(2)) is not obtained by variable separatiou iu solving Einstein equation., Our \ref{ZGEconserve}) ) is not obtained by variable separation in solving Einstein equation.
 We obtained it bv euergv conservation. so we include the effects of the dark energv cureut on the evolution of the over-deuse region.," We obtained it by energy conservation, so we include the effects of the dark energy current on the evolution of the over-dense region."
 Let us emphasize again that the problem iu the existing works (Wang&Steinhardt1908) and (Weinber&Iamionkowski2002) is. when writing down the basic equations describing the evolution of the over-deuse region they assumed that dark eunergv moves svuchrououslv with ordinary matters. please see eq(À2) of (Wane&Steinhardt1998).. but when writing down equations which will be used to describe the density of dark cuereies in the over-deuse reeions. please see eq(AG) of AVang&Steinhardt1998)... a different assumption is made.," Let us emphasize again that the problem in the existing works \citep{WangSteinhardt1} and \citep[]{NWeinberg} is, when writing down the basic equations describing the evolution of the over-dense region they assumed that dark energy moves synchronously with ordinary matters, please see eq(A2) of \citep{WangSteinhardt1}, but when writing down equations which will be used to describe the density of dark energies in the over-dense regions, please see eq(A6) of \citep{WangSteinhardt1}, a different assumption is made."
 That is. dark euergv onlv moves svuchronously with ordinary matters on IIubble scales.," That is, dark energy only moves synchronously with ordinary matters on Hubble scales."
 Just as we pointed out in (Zeng&Cao2005) and iu the conchision section of this paper., Just as we pointed out in \citep[]{SphereI} and in the conclusion section of this paper.
 Iu realities. dar cherey should have some degree of cluster behaviors ou the galaxw clusters.," In realities, dark energy should have some degree of cluster behaviors on the galaxy clusters."
 We can muaeie. ordinary matters cluster and form potential wells. when dark cherey falls in ancl some degree of dark energvs clustering will occur either.," We can imagine, ordinary matters cluster and form potential wells, when dark energy falls in and some degree of dark energy's clustering will occur either."
 So the actual case of dark enerevs clustering phenomenon should lie between the following two extreme cases., So the actual case of dark energy's clustering phenomenon should lie between the following two extreme cases.
 The two extreme cases are. dark cuerev moves svuchronouslv with ordinary matters on both Iubble scales and galaxy cluster scales or dark euergv only moves svuchrouously witli ordinary matters on IIubble scale but could not fall iu the potential wells formed by the over-deuse matter reeion at all.," The two extreme cases are, dark energy moves synchronously with ordinary matters on both Hubble scales and galaxy cluster scales or dark energy only moves synchronously with ordinary matters on Hubble scale but could not fall in the potential wells formed by the over-dense matter region at all."
 We study the first extreme case in (Zeug&Cao2005) and the second extreme case in this paper., We study the first extreme case in \citep[]{SphereI} and the second extreme case in this paper.
 A natural question is. can the results of (Wang&Steinhardt1998) lie between our two extreme cases?," A natural question is, can the results of \citep[]{WangSteinhardt1} lie between our two extreme cases?"
 If this is the case. then although iucousisteut. the treatinent of (Wane&SteinlardtL998) can be thought as some kinds of approximation of realities.," If this is the case, then although inconsistent, the treatment of \citep[]{WangSteinhardt1} can be thought as some kinds of approximation of realities."
 We will see iu the following that this is not the case., We will see in the following that this is not the case.
 We compared the results of ¢’s dependence on αἱ aud Ὁνεα in FIC.9. and 10.. ΕΙ is 3-duneusional. 10 is 2-dinensional.," We compared the results of $\zeta^\prime$ s dependence on $w$ and $\Omega_{mb,ta}$ in \ref{zetaCompare}
 and \ref{zetaCompare2d}, \ref{zetaCompare} is 3-dimensional, \ref{zetaCompare2d} is 2-dimensional."
 When this paper and its sibling one (Zeug& are put on the e-prepriut arXive and submitted to Astrophysical Journals. we are told that just recently. many authors have studied this problem in different depth.," When this paper and its sibling one \citep[]{SphereI} are put on the e-preprint arXive and submitted to Astrophysical Journals, we are told that just recently, many authors have studied this problem in different depth."
 Such as (van 2005).. (Battve&Weller 2003)... (I&olvisto 2005).. (Mota&vandeBruck 2001).. (Nunes&Mota and CManera&Mota 2005)..," Such as \citep[]{BM05}, , \citep[]{BW03}, , \citep[]{Koi05}, , \citep[]{MB04}, , \citep[]{NM04} and \citep[]{NM05}. ."
 We believe there, We believe there
(T).,\citep{mcquinn2009a}.
 Establishing the volume-averagecl evolution of ΙΔ temperatures provides a baseline against whieh to measure these Luetuations., Establishing the volume-averaged evolution of IGM temperatures provides a baseline against which to measure these fluctuations.
 The timing and amplitude of the increase inZ5.. the changes in aand the evolution of the scatter. will each be essential ingredients for understanding the role of pphotoheating in the thermal balance of the IGM. and. for formulating a more robust picture of when and how rreionization occurred.," The timing and amplitude of the increase in, the changes in and the evolution of the scatter will each be essential ingredients for understanding the role of photoheating in the thermal balance of the IGM, and for formulating a more robust picture of when and how reionization occurred."
 The authors would like to thank Bryan. Penprase for reducing much of the low-redshift LILRIES data. and the anonymous. referee. for their helpful —suggestions.," The authors would like to thank Bryan Penprase for reducing much of the low-redshift HIRES data, and the anonymous referee for their helpful suggestions."
 We also. wish to recognize and acknowledge the very significant cultural. role ancl reverence that the summit of Alauna |xea. has always had within the indigenous Llawalian community., We also wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community.
 We are most fortunate to have the opportunity to conduct. observations from. this mountain., We are most fortunate to have the opportunity to conduct observations from this mountain.
 The hvdrodvnamical simulations used. in this work were performed using the Darwin Supercomputer of. the University. of Cambridge High. Performance Computing Service (http/www.hpce.cam.ac.uk/). provided. by Dell Ine. using Strategic Iesearch. Infrastructure Funding from the Higher. Eclucation Funding Council lor England.," The hydrodynamical simulations used in this work were performed using the Darwin Supercomputer of the University of Cambridge High Performance Computing Service (http://www.hpc.cam.ac.uk/), provided by Dell Inc. using Strategic Research Infrastructure Funding from the Higher Education Funding Council for England."
 GB acknowledges financial support from the Ixavli foundation., GB acknowledges financial support from the Kavli foundation.
 JB has been supported by an ARC Australian postdoctoral fellowship (DDP0984947)., JB has been supported by an ARC Australian postdoctoral fellowship (DP0984947).
 WS has been supported by the National Science Foundation through grant. AST-0606868., WS has been supported by the National Science Foundation through grant AST-0606868.
 Capturing the small-scale structure in the high-redshift [forest poses a significant challenge for cosmological simulations., Capturing the small-scale structure in the high-redshift forest poses a significant challenge for cosmological simulations.
 As discussed by 2.. most of the transmission in the forest at 25 comes from. voids. which are less well resolved. in SPL simulations than the filaments that clominate the characteristics of the forest at 2~3.," As discussed by \citet{boltonbecker2009}, most of the transmission in the forest at $z \gtrsim 5$ comes from voids, which are less well resolved in SPH simulations than the filaments that dominate the characteristics of the forest at $z \sim 2-3$."
 Ideally: one would use both a large simulation box (/z40 AIMpe). and. high resolution. (MiX10b TAL).," Ideally, one would use both a large simulation box $l \gtrsim 40$ Mpc), and high resolution $M_{\rm gas} \lesssim 10^5\,{h^{-1}}\,{\rm M}_\odot$ )."
 Computational constraints. however. required us to focus on obtaining the necessary mass resolution. which was found to be à more stringent requirement for the curvature.," Computational constraints, however, required us to focus on obtaining the necessary mass resolution, which was found to be a more stringent requirement for the curvature."
 To check our convergence with mass resolution ancl box size. we ran a set of comparison simulations (runs Itl 11).," To check our convergence with mass resolution and box size, we ran a set of comparison simulations (runs R1 – R4)."
 In these runs we used the same thermal history as in run €15. but varied the box size and mass resolution.," In these runs we used the same thermal history as in run C15, but varied the box size and mass resolution."
 Compared to run C15. which uses £=10 .MMpe. 0=Ὁ512% particles and Adj.—02101bTAL. he mass resolution was lowered by up to a factor of 64. and the box size was increased by up to a factor of four in ength.," Compared to run C15, which uses $L = 10$ Mpc, $n = 2 \times 512^3$ particles and $M_{\rm gas} = 9.2 \times 10^{4}\,h^{-1}\,M_{\odot}$, the mass resolution was lowered by up to a factor of 64, and the box size was increased by up to a factor of four in length."
 The optical depths in each simulation were rescaled such that the mean fluxes were equal after the spectra were re-normalized in .MMpe sections (Section 2?7))., The optical depths in each simulation were rescaled such that the mean fluxes were equal after the spectra were re-normalized in Mpc sections (Section \ref{sec:mean_flux}) ).
 The curvature was then computed using the procedure outlined in Section ??.. with the modification that noise-free spectra were used. and. no b-spline fits were performed.," The curvature was then computed using the procedure outlined in Section \ref{sec:method_summary}, with the modification that noise-free spectra were used and no b-spline fits were performed."
 The convergence results are shown in Figure Al.. where we plot the change in wwith respect to run C15.," The convergence results are shown in Figure \ref{fig:curv_convergence}, where we plot the change in with respect to run C15."
 We are nearly converged with box size at all τοσα., We are nearly converged with box size at all redshifts.
 At a fixed resolution. aabwavs decreases by less than 0.03 when increasing the box size from 10 to MMpe.," At a fixed resolution, always decreases by less than 0.03 when increasing the box size from 10 to Mpc."
 For the curvature values measured in the data. this corresponds to a temperature difference of less than 900K. X. box. size. correction calculated. from these results was applied to the simulation curvature values when fitting the temperatures.," For the curvature values measured in the data, this corresponds to a temperature difference of less than K. A box size correction calculated from these results was applied to the simulation curvature values when fitting the temperatures."
 At 2<+ we are well converged: with mass resolution. although the convergence is less clear at higher redshifts.," At $z < 4$ we are well converged with mass resolution, although the convergence is less clear at higher redshifts."
 At z=4.915. he increase in wwhen increasing the number of particles from 2.256° 02. 512 is 0.058.," At $z = 4.915$, the increase in when increasing the number of particles from $2 \times 256^3$ to $2 \times 512^3$ is 0.058."
" We can estimate the gains from an aclelitional factor of eight in mass resolution by comparing ο 223.991. which has a similar change in wwhen increasing the number of particles from 21258"" to 2.256""."," We can estimate the gains from an additional factor of eight in mass resolution by comparing to $z = 3.991$, which has a similar change in when increasing the number of particles from $2 \times 128^3$ to $2 \times 256^3$."
 In that case. further increasing the mass resolution wa factor οἱ eigh increased xbv only 0.014. wuch at z=4.915 would correspond to a change in temporature of roughly KK. While we do not apply a mass resolulion correction to our results. therefore. we can be reasonadv. confident that the gains [rom going to higher resolution would be small. and that they would only be significant our highest redshift bins where the correction is likely to be smaller than the errors.," In that case, further increasing the mass resolution by a factor of eight increased by only 0.014, which at $z = 4.915$ would correspond to a change in temperature of roughly K. While we do not apply a mass resolution correction to our results, therefore, we can be reasonably confident that the gains from going to higher resolution would be small, and that they would only be significant our highest redshift bins where the correction is likely to be smaller than the errors."
In Figure 4. we show how the mean fluence predictions can be expected to vary from vear to vear. based on the number of bursts in the ssumple and the variance in luence in this population.,"In Figure \ref{fig:fourfermi} we show how the mean fluence predictions can be expected to vary from year to year, based on the number of bursts in the sample and the variance in fluence in this population."
 This figure has been created using a simulation of LAXE observations. and assuming randomly occurring bursts with the flux and redshift distribution of he population.," This figure has been created using a simulation of LAT observations, and assuming randomly occurring bursts with the flux and redshift distribution of the population."
 Phe upper two distribuions show the numberof high-redshift (1<2 6) bursts faling in the field of view of the detector over a period of 1 (up»er-Ieft) and 5 (upper-right) vears: this follows a Poisson clistribution., The upper two distributions show the number of high-redshift $1<z<6$ ) bursts falling in the field of view of the detector over a period of 1 (upper-left) and 5 (upper-right) years; this follows a Poisson distribution.
 As rcfore. we do not account for the possibility of the spacecraft autonomously slewing to view events with he LAT after ing triggered. by the CDM. or another ex»riment.," As before, we do not account for the possibility of the spacecraft autonomously slewing to view events with the LAT after being triggered by the GBM or another experiment."
 The ower panels show how the stacked Duence collected can be expected to vary [rom the predictions in the oevious plots., The lower panels show how the stacked fluence collected can be expected to vary from the predictions in the previous plots.
 For ALAGIC. we begin by considering the vear-Lo-vear probability that a given number of high-redshift CRBs will occur in a region of sky where they can observed with a low energv threshold.," For MAGIC, we begin by considering the year-to-year probability that a given number of high-redshift GRBs will occur in a region of sky where they can observed with a low energy threshold."
 By multiplying the duty evele of the instrument (10 per cent) with the sky coverage (11.7 per cent [or Gree=40 deg). we lind that only —1 per cent of bursts can be observed. with a reasonably low οποίον threshold.," By multiplying the duty cycle of the instrument (10 per cent) with the sky coverage (11.7 per cent for $\theta_{max}= 40$ deg), we find that only $\sim$ 1 per cent of bursts can be observed with a reasonably low energy threshold."
 Our sample consists of 145 bursts seen over 54 months. 96 of which are at 2>>1. and therefore the expected. number of bursts per vear is somewhat less than 1.," Our sample consists of 145 bursts seen over 54 months, 96 of which are at $z>1$, and therefore the expected number of bursts per year is somewhat less than 1."
 Therefore. we begin by predicting the probability that any bursts will be visible.," Therefore, we begin by predicting the probability that any bursts will be visible."
 Once we understand this probability. we will look at the photon statistics for a single burst.," Once we understand this probability, we will look at the photon statistics for a single burst."
 The sky coverage of the telescope increases approximately as the square. of. the maximum allowed angle [rom zenith., The sky coverage of the telescope increases approximately as the square of the maximum allowed angle from zenith.
 However. we find that the number of photons wedieted: from distant. (2= 1) bursts. does not increase sienilicanthy bevoncd an angle. of about 40 degrees. as the encrev threshold. of the instrument rises above the energies at which the universe is transparent," However, we find that the number of photons predicted from distant $z>1$ ) bursts does not increase significantly beyond an angle of about 40 degrees, as the energy threshold of the instrument rises above the energies at which the universe is transparent"
scaling relations including the ΤΕΕ in more realistic situations in a forthcoming paper.,scaling relations including the TFR in more realistic situations in a forthcoming paper.
 This work was supported in part by the Grant-in-Aid for the Scientific Research Fund (17104002 and 18749007) of the Ministry of Education. Culture. Sports. Science and Technology of Japan. and by a Nagasaki University president's Fund grant.," This work was supported in part by the Grant-in-Aid for the Scientific Research Fund (17104002 and 18749007) of the Ministry of Education, Culture, Sports, Science and Technology of Japan, and by a Nagasaki University president's Fund grant."
 HK is supported by the Japan Society for the Promotion of Science for Young Scientists (1589)., HK is supported by the Japan Society for the Promotion of Science for Young Scientists (1589).
images. it was necessary to do the background subtraction from each frame before flat-fielding by means of normalized differential sky flats (Hunt et al. 1994)),"images, it was necessary to do the background subtraction from each frame before flat-fielding by means of normalized differential sky flats (Hunt et al. \cite{hunt}) )"
 in order to eliminate the contribution of the thermal emission from the telescope that becomes significant for this band., in order to eliminate the contribution of the thermal emission from the telescope that becomes significant for this band.
 Finally. the frames were combined together to produce the final source frame. using a new algorithm. invented by Hook and Fruchter (1997)) in order to combine multiple stacks of dithered. undersampled image frames.," Finally, the frames were combined together to produce the final source frame, using a new algorithm, invented by Hook and Fruchter \cite{hook}) ) in order to combine multiple stacks of dithered, undersampled image frames."
 Por the identification of the IR counterparts of radio sources we relied on the following informations: the most accurate radio positions available and the optical positions of stars visible in our IR frames., For the identification of the IR counterparts of radio sources we relied on the following informations: the most accurate radio positions available and the optical positions of stars visible in our IR frames.
 Concerning the radio positions. for the sources," Concerning the radio positions, for the sources"
das ever been detected.,has ever been detected.
 I focus here on the Taurus and Ophiuchus star forming regious. the oulv oucs or Which high-resolution nultiplicitv. photometric aud willuneter survevs have a hieh completcucss rate.," I focus here on the Taurus and Ophiuchus star forming regions, the only ones for which high-resolution multiplicity, photometric and millimeter surveys have a high completeness rate."
 The wo clouds contribute an almost equal umber of binaries o the sample., The two clouds contribute an almost equal number of binaries to the sample.
 Furthermore. both regious have similar stellar age distributions (median age around ADAG. Ophiuchus being probably slighter vounecr ou average han Taurus) and their mass function fully samples the 15M. rauge (e.e..Lulunan&Rieke1999:Luh- 2000).," Furthermore, both regions have similar stellar age distributions (median age around Myr, Ophiuchus being probably slighter younger on average than Taurus) and their mass function fully samples the $M_\odot$ range \citep[e.g.,][]{luhman99, luhman00}."
. Finally. Taurus represents an instance of distributed star formation. while Opliuclus is a more clustered cuvironment.," Finally, Taurus represents an instance of distributed star formation, while Ophiuchus is a more clustered environment."
 These two clouds therefore offer a elobal view of the carly stages of planet formation amoue solar-type ancl lower-iass stars., These two clouds therefore offer a global view of the early stages of planet formation among solar-type and lower-mass stars.
 I first address the question of the presence of dust iu the planet-forming region. namely the innermost few AU around each component. within binary svstems.," I first address the question of the presence of dust in the planet-forming region, namely the innermost few AU around each component, within binary systems."
 To probe the presence of an optically thick dusty iuner disk. I used near- to mid-imfrared colors.," To probe the presence of an optically thick dusty inner disk, I used near- to mid-infrared colors."
 I selected the following standard thresholds to conclude that a circtustellar disk is present: [3.6][8.0]2 O.Simag. WON>1.25 imag. KoLoc 02l5auuas. 0»ipaa>LT (eqsClozactal.2009:McCabeet2006:Boutemps 2001).," I selected the following standard thresholds to conclude that a circumstellar disk is present: $[3.6]-[8.0] \ge 0.8$ mag, $K-N \ge
1.75$ mag, $K-L \ge 0.35$ mag, $\alpha_{2-14\mu\mathrm{m}}>-1.7$ \citep[e.g.,][]{cieza09, mccabe06, bontemps01}."
. About of the PAIS binaries considered. here. have Spitzer/IRAC colors. which are used whenever available.," About of the PMS binaries considered here have /IRAC colors, which are used whenever available."
 Ciezaetal.(2009). have demonstrated that tighter binaries have a auch lower probability of hostiug circunistellar dust., \cite{cieza09} have demonstrated that tighter binaries have a much lower probability of hosting circumstellar dust.
 The same effect is observed here in a somewhat smaller sample., The same effect is observed here in a somewhat smaller sample.
 The media separatiou of binaries with au imuer disk iu this sample is about AAU. whereas that of cdisk-free biniaries is AAU.," The median separation of binaries with an inner disk in this sample is about AU, whereas that of disk-free binaries is AU."
 The simplest interpretation of this trend is that disks iu tieht binaries are dissipated auch faster than iu wide «κος (Ciezaetal.2009.Irausab.inprep.)..," The simplest interpretation of this trend is that disks in tight binaries are dissipated much faster than in wide systems \citep[][Kraus et al., in prep.]{cieza09}."
 To extend upon this previous analysis. I used the two-sided Fischer exact test to determine the probability that wide and tieht binarics have a differcut proportion of diskless systems. using a sliding threshold to split the sample.," To extend upon this previous analysis, I used the two-sided Fischer exact test to determine the probability that wide and tight binaries have a different proportion of diskless systems, using a sliding threshold to split the sample."
 As shown in veffiie:proba.. the difference is significant at the 20 level or higher for a wide range of threshold separations.," As shown in \\ref{fig:proba}, the difference is significant at the $\sigma$ level or higher for a wide range of threshold separations."
 Du particular. this analysis reveals thatLO0AT.," In particular, this analysis reveals that."
 On the other haud. there is no statistical difference between binaries wider than LOOAAT and single stars.," On the other hand, there is no statistical difference between binaries wider than AU and single stars."
 While near- aud iid-infrared cinission best traces the presence of dust within a few AU of star. oulv long-wavelength fiux measurements can probe the tota dust mass of protoplauctary disks (c.g.Beckwithctal. 1990).," While near- and mid-infrared emission best traces the presence of dust within a few AU of star, only long-wavelength flux measurements can probe the total dust mass of protoplanetary disks \citep[e.g.,][]{beckwith90}."
. From the sample defined above. I sclectec those objects which show evidence of an optically thick iuncr disk (as defined above) aud have beeu obserwe« in the (sub)nülluneter.," From the sample defined above, I selected those objects which show evidence of an optically thick inner disk (as defined above) and have been observed in the (sub)millimeter."
 The median separation iu this subsample of LL binaries is AAT., The median separation in this subsample of 44 binaries is AU.
 While the 85040 survey of Ophliuchus is not vet as complete as that of Taurus. the existing 1.3nun observations of PAIS stars are generally less sensitive to cold dust.," While the $\mu$ m survey of Ophiuchus is not yet as complete as that of Taurus, the existing 1.3mm observations of PMS stars are generally less sensitive to cold dust."
 Since sine both waveleneths vield similar conclusions but with lower significance for the αι one. I focus here on 85021 micasurcmicuts.," Since using both wavelengths yield similar conclusions but with lower significance for the 1.3mm one, I focus here on $\mu$ m measurements."
 As has long been kuown. tight binaries have a differeut distribution of subimillineter fluxes than wide oues. witli a nmeh lower median fux (12uuuJv vs 5OnuuJw at 85a using a 100AU. separation threshold) aud ouly very few hieh-flux Asystems (Jensenetal.1996:Αιdrews&Williams2005).," As has long been known, tight binaries have a different distribution of submillimeter fluxes than wide ones, with a much lower median flux mJy vs mJy at $\mu$ m using a AU separation threshold) and only very few high-flux systems \citep{jensen96, andrews05}."
. I compared the distributions of δῦθ μι fluxes for tight and wide binarics defined by the sale sliding threshold as above using the conservative survival analysis Peto-Peutrice Ceneralized Wilcoxon test to account for upper lits., I compared the distributions of $\mu$ m fluxes for tight and wide binaries defined by the same sliding threshold as above using the conservative survival analysis Peto-Pentrice Generalized Wilcoxon test to account for upper limits.
 I find that wide aud tieht binarics are differeut at the 26 level or higher if the separation threshold is iu the AAU ranee (see rofüe:proba))., I find that wide and tight binaries are different at the $\sigma$ level or higher if the separation threshold is in the AU range (see \\ref{fig:proba}) ).
 I therefore conclude thats, I therefore conclude that.
ubindllancterfluc Ou the other haud. the distribution of S50j;nu fluxes for wide binarics is indistinemshable from that of single stars.," On the other hand, the distribution of $\mu$ m fluxes for wide binaries is indistinguishable from that of single stars."
 Tn past studies. it has been assumed that a reduced (sub)nilliueter fiux necessuilv miplies a reduced. total dust mass independently of the disk properties 2005).," In past studies, it has been assumed that a reduced (sub)millimeter flux necessarily implies a reduced total dust mass independently of the disk properties \citep[for instance, see the prescription used
by][]{andrews05}."
. While this is true iu general. it is unclear whether his assuniption is valid for severcly truncated disks or Which optical depth effects may become iuportaut.," While this is true in general, it is unclear whether this assumption is valid for severely truncated disks for which optical depth effects may become important."
 The model constructed by Jeusenetal.(1996)— seems o support this hvpothesis. but these authors assumed hat tight binarics are always surrounded by a massive αποπαν structure. which we now know is rare.," The model constructed by \cite{jensen96} seems to support this hypothesis, but these authors assumed that tight binaries are always surrounded by a massive circumbinary structure, which we now know is rare."
 To revisit this issuc. I have computed a erid of radiative rausfer models using the AICFOST code (Pinte2006) to compute the 850411 flux of a disk witha typical Str)xrt surface4. density profile. au AAU inner radius and a flaring power law P(r)xsb.," To revisit this issue, I have computed a grid of radiative transfer models using the MCFOST code \citep{pinte06} to compute the $\mu$ m flux of a disk with a typical $\Sigma(r) \propto r^{-1}$ surface density profile, an AU inner radius and a flaring power law $H(r)\propto
r^{1.125}$."
 Emission roni the central star is modeled as a TII. 22. yhotosphere aud a distance of 1LOppc is assmmed.," Emission from the central star is modeled as a K, $L_\odot$ photosphere and a distance of pc is assumed."
 The dust is asstuned to be made of astronomical silicates witli aa77 power law size distribution raueging from 0.0371 o lumuu., The dust is assumed to be made of astronomical silicates with a $a^{-3.5}$ power law size distribution ranging from $\mu$ m to mm.
 The only variables in the model are the dis- outer radius. Πε aud the total dust mass. κει," The only variables in the model are the disk outer radius, $R_{out}$, and the total dust mass, $M_{dust}$."
 vefiie:diskimass demonstrates that the proportionality vetween total dust mass and subiillimeter fiux observed or large disks breaks down for Rowe& 30AAU as the disk becomes optically thick to its own emission.," \\ref{fig:diskmass} demonstrates that the proportionality between total dust mass and submillimeter flux observed for large disks breaks down for $R_{out} \lesssim
30$ AU as the disk becomes optically thick to its own emission."
 Disk truucation by an outer stellar component is dependent on the orbital parameters aud lass ratio of the binary system (CArtviuowicz&Lubow1991)., Disk truncation by an outer stellar component is dependent on the orbital parameters and mass ratio of the binary system \citep{artymowicz94}.
 It is therefore not possible to uniquelv associate a binary separation with a fidalh-set value of Rong., It is therefore not possible to uniquely associate a binary separation with a tidally-set value of $R_{out}$.
 The ratio between these quantities is typically in the broad 2.55 range., The ratio between these quantities is typically in the broad 2.5–5 range.
 Svstenuis whose separation is less than AAT are therefore expected to possess disks whose outer radius is 10AU or less., Systems whose separation is less than AU are therefore expected to possess disks whose outer radius is AU or less.
 In this coufiguration. total disk masses of atA least ˣ; are necessary to produce 850441. fluxes as low as ~20 30nuuJy.," In this configuration, total disk masses of at least $M_{J}$ are necessary to produce $\mu$ m fluxes as low as $\sim20$ mJy."
 In the sample studied here. about a third (6 out of 19) of all binaries that are tighter than LOOAAT and possess an inner disk have an 850402 flux that is higher than 30uunJv.," In the sample studied here, about a third (6 out of 19) of all binaries that are tighter than AU and possess an inner disk have an $\mu$ m flux that is higher than mJy."
 Therefore.," Therefore,"
Subewart D. stars are mostly assumed to be extreme horizontal branch stars. i-c.. core helium burning stars with a thin inert hydrogen. envelope (??).. In.,"Subdwarf B stars are mostly assumed to be extreme horizontal branch stars, i.e., core helium burning stars with a thin inert hydrogen envelope \citep{Heber1986, SafferBergeron1994}."
 order to reach such high temperattres and surface eravities. the progenitor must have lost almost its entire hydrogen. envelope.," In order to reach such high temperatures and surface gravities, the progenitor must have lost almost its entire hydrogen envelope."
 The majority of sdDs is expected to have lost its envelope via binary interaction channels. as elaborated by ??..," The majority of sdBs is expected to have lost its envelope via binary interaction channels, as elaborated by \citet{HanPodsiadlowski2002, HanPodsiadlowski2003}."
 Our tareet. (νι 7975824). is à subdwarl D star (sdD) with a white cwarl (WD) companion in a 0.403739(8)clay orbit (Morales-Rueca et al.," Our target, (KIC 7975824), is a subdwarf B star (sdB) with a white dwarf (WD) companion in a 0.403739(8)day orbit (Morales-Rueda et al."
 2003). which identifies the theoretical formation channel for this system as the second common-envelope ejection channel of Han et al. (," 2003), which identifies the theoretical formation channel for this system as the second common-envelope ejection channel of Han et al. ("
2002. 2003).,"2002, 2003)."
 In this scenario the white dwarf is engulfed by the sd progenitor as it ascends the first giant branch., In this scenario the white dwarf is engulfed by the sdB progenitor as it ascends the first giant branch.
 The white D.cwarl will deposit its angular momentum in the atmosphere of the giant. and μαn up the envelope until it is ejected., The white dwarf will deposit its angular momentum in the atmosphere of the giant and spin up the envelope until it is ejected.
 There. are two subchannels to this scenario. depending on the initial mass of 1e progenitor.," There are two subchannels to this scenario, depending on the initial mass of the progenitor."
 Lf sufficiently massive. it will ignite helium non-degenerativelv. and the resulting extended horizontal branch (LLIB) star will have a mass of ~0.35 M..," If sufficiently massive, it will ignite helium non-degeneratively, and the resulting extended horizontal branch (EHB) star will have a mass of $\sim 0.35\,$ $_\odot$."
 The more common scenario. starting with a roughly solar-mass giant. produces an ELLB star with a mass that must be very close to the helium flash mass of 0.47 M..," The more common scenario, starting with a roughly solar-mass giant, produces an EHB star with a mass that must be very close to the helium flash mass of $0.47\,$ $_\odot$."
 A third possibility occurs when the white dwarf companion cjects the envelope before the core has attained sullicient mass to ignite helium., A third possibility occurs when the white dwarf companion ejects the envelope before the core has attained sufficient mass to ignite helium.
 In this case the remaining core will evolve directly to the white chvarl cooling track., In this case the remaining core will evolve directly to the white dwarf cooling track.
 On its way it crosses the domain of the ELLB stars. but without helium ignition the period in which it appears as an sdB star is brief. making this channel a very small contributor to the sdB population.," On its way it crosses the domain of the EHB stars, but without helium ignition the period in which it appears as an sdB star is brief, making this channel a very small contributor to the sdB population."
 For a recent extensive review on hot subcwarl stars. their evolution and observed. properties. see ?..," For a recent extensive review on hot subdwarf stars, their evolution and observed properties, see \citet{Heber2009}."
 The exact physical details: involved. in common-envelope ejection are notwell understood., The exact physical details involved in common-envelope ejection are notwell understood.
 This uncertainty| is commonly. embodied. in the ellicleney parameter. a. which denotes the amount of orbital energy used. to eject the envelope (seeeg.?7?).," This uncertainty is commonly embodied in the efficiency parameter $\alpha$, which denotes the amount of orbital energy used to eject the envelope \citep[see e.g.][]{de-Kool1990, HuNelemans2007}."
 LEclipsing subdwarl jnaries could. help constrain the permitted values of a. ot studies have hitherto been hampered by the fact mat both καWD and. sdB|Mecivarf binaries have Pürtuallv invisible companions ancl are herelore single ined. leaving the masses indeterminate.," Eclipsing subdwarf binaries could help constrain the permitted values of $\alpha$, but studies have hitherto been hampered by the fact that both sdB+WD and sdB+M-dwarf binaries have virtually invisible companions and are therefore single lined, leaving the masses indeterminate."
 Firmly establishing je parameters of both components of a post-CE system 1erefore has substantial implications not just for confirming iat our formaion scenarios are correct. bu also in order to une future binary population synthesis stulies by confining iC 0 poramelt«Y.," Firmly establishing the parameters of both components of a post-CE system therefore has substantial implications not just for confirming that our formation scenarios are correct, but also in order to tune future binary population synthesis studies by confining the $\alpha$ parameter."
 The targe stuclied here. 340.. is an sdD star. cliscoverecLo by the survey (?)..," The target studied here, , is an sdB star discovered by the survey \citep{Downes1986}. ."
equation (actually a quadratic in ww? where w is the frequency of oscillation) results. becoming aquintic equation in o wilh the inclusion of advection.,"equation (actually a quadratic in $\omega ^2$ where $\omega $ is the frequency of oscillation) results, becoming a quintic equation in $\omega$ with the inclusion of advection."
" We find (hat in bot cases for 5~4/3. for all except the highest values of the ratio of the shock radius to the radius of the inner boundary. modes with /=1 grow the fastest Gin fact for cases where the postshock radial velocity. u,=0. no other nonradial modes grow)."," We find that in both cases for $\gamma\sim 4/3$, for all except the highest values of the ratio of the shock radius to the radius of the inner boundary, modes with $l=1$ grow the fastest (in fact for cases where the postshock radial velocity, $u_r=0$, no other nonradial modes grow)."
 This suggests that [or /21 in 4=4/3 gas in (his regime. postshock advection is not crucial to the operation of the instability.," This suggests that for $l=1$ in $\gamma =4/3$ gas in this regime, postshock advection is not crucial to the operation of the instability."
 Thus in eeneral these results will support the conclusions of Blondin&Mezzacappa(2006) that the instability. proceeds by the growth of trapped waves in (his regime., Thus in general these results will support the conclusions of \citet{blondin05} that the instability proceeds by the growth of trapped waves in this regime.
 Nevertheless. regions of | and 4 parameter space exist where we find modes (hat are only unstable in the presence of postshock advection. which we interpret as an advective-acoustic evcle. as suggested by Galletti&Foglizzo(2005) and Foelizzoetal.(2007).," Nevertheless, regions of $l$ and $\gamma$ parameter space exist where we find modes that are only unstable in the presence of postshock advection, which we interpret as an advective-acoustic cycle, as suggested by \citet{galletti05}
 and \citet{foglizzo06}."
. In both cases. the frequencies of the erowing modes are similar. suggesting that frequency alone is not a good discriminator of the mechanism of instability.," In both cases, the frequencies of the growing modes are similar, suggesting that frequency alone is not a good discriminator of the mechanism of instability."
 As will be seen below. this might be expected in a comparison of a perturbation advected radially between the shock aud inner boundary. ancl a sound wave traveling essentially laterally around the shock.," As will be seen below, this might be expected in a comparison of a perturbation advected radially between the shock and inner boundary, and a sound wave traveling essentially laterally around the shock."
 We consider an unperturbed model in which spherically accreting plasma is cleceleratec al a spherically symmetrical shock. before accreting onto a protoneutron star.," We consider an unperturbed model in which spherically accreting plasma is decelerated at a spherically symmetrical shock, before accreting onto a protoneutron star."
 The accretion shock is at radius ri. aud we take an inner boundary. at rj. maintained al constant pressure. where plasma cools and decouples from the postshock flow.," The accretion shock is at radius $r_s$, and we take an inner boundary at $r_i$, maintained at constant pressure, where plasma cools and decouples from the postshock flow."
 The postshock flow is modeled bv the Bernoulli equation. as given in Appendix A. Gas with polvtropie index 5<1.5 decelerates. and gas wilh 521.5 accelerates away [rom the shock towards the inner boundary.," The postshock flow is modeled by the Bernoulli equation, as given in Appendix A. Gas with polytropic index $\gamma < 1.5$ decelerates, and gas with $\gamma > 1.5$ accelerates away from the shock towards the inner boundary."
 We shall be solely concerned with 5«1.5., We shall be solely concerned with $\gamma < 1.5$.
 The dominant variations with radius are in pressure and density. as shown in Figure 1.," The dominant variations with radius are in pressure and density, as shown in Figure 1."
 To treat the perturbation. we follow in large part the methods and notation of Vishniac who derive an approximate dispersion relation [or application to shocks with arbitrarypostshock structure.," To treat the perturbation, we follow in large part the methods and notation of \citet{vishniac89} who derive an approximate dispersion relation for application to shocks with arbitrarypostshock structure."
 In spherical coordinates. we write the hvdrodynanmic equations: an equation of continuity and momentum equations in the +. ϐ and © directions as Continuity:," In spherical coordinates, we write the hydrodynamic equations; an equation of continuity and momentum equations in the $r$ , $\theta$ and $\phi$ directions as Continuity:"
Altogether 709 archival plates taken between 1931 aud 1905 of the Sonnebere astrograplis 100 nin. 170 mim and 140 nun were used for investigating the lone-teri vchaviour of S 10917 ΑΙ.,"Altogether 709 archival plates taken between 1934 and 1995 of the Sonneberg astrographs 400 mm, 170 mm and 140 mm were used for investigating the long-term behaviour of S 10947 Aql."
 Tab., Tab.
 1 eives the details of hese iieasurements., \ref{phot} gives the details of these measurements.
 Unfortunately. the object is invisible on all plates of the Sounebere sky patrol.," Unfortunately, the object is invisible on all plates of the Sonneberg sky patrol."
 Spectroscopic observations of S 10917 Aql do rot exist. mt the kind of brightuess changes together with the detected N-rav enmdssion ποσα to iudicate that it is a chromospherically active binary of the RS ϱVu type.," Spectroscopic observations of S 10947 Aql do not exist, but the kind of brightness changes together with the detected X-ray emission seem to indicate that it is a chromospherically active binary of the RS CVn type."
 The major results of the variability study cau be stbunarized as follows: According to the classical interpretation of RS CVu stars the brightucss changes cau be interpreted solely by starspot activities in a binary system (e.g. Cover 1976)., The major results of the variability study can be summarized as follows: According to the classical interpretation of RS CVn stars the brightness changes can be interpreted solely by starspot activities in a binary system (e.g. Geyer 1976).
" But until now it was not vet possible to uuaubiguouslv explain the plivsical processes in RS CVu πίτσας,", But until now it was not yet possible to unambiguously explain the physical processes in RS CVn systems.
 This is because photooelectrie aud spectroscopic observations are not available to a sufficicut extent since the phenomenon was discovered bv Hall (1972)., This is because photoelectric and spectroscopic observations are not available to a sufficient extent since the phenomenon was discovered by Hall (1972).
 Systematic changes of the orbital period are observed also iu most other RS CV svsteiis., Systematic changes of the orbital period are observed also in most other RS CVn systems.
 Wall EI&reiuer (1980) and ITall ((19580) gave a compilation of 31 such objects where both. decreasing aud increasing periods are found in the ratio of abou 2:1.," Hall Kreiner (1980) and Hall (1980) gave a compilation of 34 such objects where both, decreasing and increasing periods are found in the ratio of about 2:1."
 The value of dllog P/dt = 2.3 « 5 for S 10917 is large but not extraordinary., The value of log $P$ $t$ = –2.3 $\times$ $^{-6}$ for S 10947 is large but not extraordinary.
 It is surpassed oulv bv SZ Psc (5.25 « ο) CQ Aur (2.15. « ) aud AR Mon(1.22 & 9).," It is surpassed only by SZ Psc (–5.25 $\times$ $^{-6}$ ), CQ Aur (–2.45 $\times$ $^{-6}$ ) and AR Mon (–1.22 $\times$ $^{-6}$ )."
 Iu anv case. huge period changes are an imdicatiou of rapid evolutionary efects (e.g. p. 127 iu Ixopal 19785).," In any case, large period changes are an indication of rapid evolutionary efects (e.g. p. 427 in Kopal 1978)."
 However. it is dificult to estimate more details. such as mass loss or mass transfer rates iu RS οδι stars because the period changes may be caused by effects which are not directly related to the mass trausfer i the binary svete.," However, it is difficult to estimate more details, such as mass loss or mass transfer rates in RS CVn stars because the period changes may be caused by effects which are not directly related to the mass transfer in the binary system."
 As far as known. RS CVu stars have binary components of," As far as known, RS CVn stars have binary components of"
Analytical approximations for the evolution of large.scale structure (LSS) are based ou the paradigm that simall initial perturbations erow by eravitational instability. which is in furu implemented iu the simplest matter nodel. dust. (Peebles 1980. Zeldovich Novikov 1983. Sahni Coles 1995. aud rof.,"Analytical approximations for the evolution of large–scale structure (LSS) are based on the paradigm that small initial perturbations grow by gravitational instability, which is in turn implemented in the simplest matter model, `dust' (Peebles 1980, Zel'dovich Novikov 1983, Sahni Coles 1995, and ref."
 therein)., therein).
 Towever. this approximation has some linütations: one has to restrict he application to the carly stages of structure formation and when the effects on the evolution of pliysical processes different frou eravitational instability are negligible.," However, this approximation has some limitations: one has to restrict the application to the early stages of structure formation and when the effects on the evolution of physical processes different from gravitational instability are negligible."
 Iu his paper we purport to generalize this matter model iu order to overcome some of these Lautatious., In this paper we purport to generalize this matter model in order to overcome some of these limitations.
 One of the problems at the later stages of LSS evolution is the formation of multistream regions. Lo.. regions where particles of dust come together with verv different velocities.," One of the problems at the later stages of LSS evolution is the formation of multi–stream regions, i.e., regions where particles of dust come together with very different velocities."
 This fact manifests itself as the emergence of caustics in the density field. where the velocity field is “vertical” G.c.. where it acquires an infinite derivative at a poiut) and later ou multiplv valued.," This fact manifests itself as the emergence of caustics in the density field, where the velocity field is “vertical” (i.e., where it acquires an infinite derivative at a point) and later on multiply valued."
 This problem arises from insisting on following the trajectory of cach particle of dust., This problem arises from insisting on following the trajectory of each particle of dust.
" We therefore propose a set of hvdrodsisuniclike equations for thegraincd fields. which trace the average motion rather than that of individual particles,"," We therefore propose a set of hydrodynamic–like equations for the fields, which trace the average motion rather than that of individual particles."
 A substautial iugredieut of this approach is that the coarseerained velocity evolves wader the combined action of gravity and forces due to velocity dispersion (ie. because particles of dust do not move exactly with the coarsegrained velocity).," A substantial ingredient of this approach is that the coarse–grained velocity evolves under the combined action of gravity and forces due to velocity dispersion (i.e., because particles of dust do not move exactly with the coarse–grained velocity)."
" We cannot resort to lvdrodvuanue cousiderations of local equilibrimu but make instead use of ""equations of state as phenomenological matter models without any further justification.", We cannot resort to hydrodynamic considerations of local equilibrium but make instead use of `equations of state' as phenomenological matter models without any further justification.
] Tn these models the pressure is assunied isotropic and may onlv depend on the (coarseeraimed) density. that is p=plo}.," In these models the pressure is assumed isotropic and may only depend on the (coarse–grained) density, that is, $p=p(\varrho)$."
 This asstuuption makes the problem accessible to analytical study aud helps. to ilunimate our major arguient that the presence of forces which counteract the eravitational attraction is a basic step in uuderstanding the οσαος of selferavitating matter: a detailed study of the origin and properties of pressure forces is carried out clsewlere (Buchert 1uneneg 1998)., This assumption makes the problem accessible to analytical study and helps to illuminate our major argument that the presence of forces which counteract the gravitational attraction is a basic step in understanding the dynamics of self–gravitating matter; a detailed study of the origin and properties of pressure forces is carried out elsewhere (Buchert nguez 1998).
 Tha the putative problem is far more couples. than re dus case already becomes clear in the investigation of the onedimensional EulerNewton svstemi with the siuuple matter model p.Xο (Góttz 195858)., That the putative problem is far more complex than the dust case already becomes clear in the investigation of the one–dimensional Euler–Newton system with the simple matter model $p \propto \varrho$ (Göttz 1988).
 Góttz has shown iit solutious to the ouedimensional problem can be ecnerated by solutions of the SineCordon equation., Göttz has shown that solutions to the one–dimensional problem can be generated by solutions of the Sine–Gordon equation.
 This wellstudied equation has a rich spectrum of solutions vat includes solitous., This well–studied equation has a rich spectrum of solutions that includes solitons.
" Cóttz also pointed out that au asviuptotic Nsoliton state is generic. Ίνοι, will be realized almost independently of the initial data."," Göttz also pointed out that an asymptotic N–soliton state is generic, i.e., will be realized almost independently of the initial data."
 We see already in this comparatively simple case. that we are faced with a generic picture which is completely differcut from what οσος in a cosmology based on dust imattor: 4.veclal nonlinear features build up structures at large times which areabsent in the dust cosmoloey.," We see already in this comparatively simple case, that we are faced with a generic picture which is completely different from what emerges in a cosmology based on dust matter: special nonlinear features build up structures at large times which are in the dust cosmology."
 This illustrates that the complexity introduced by a pressure term could bear farreaching surprises., This illustrates that the complexity introduced by a pressure term could bear far–reaching surprises.
 We also want to stress that the iutroductiou of a pressure term is not, We also want to stress that the introduction of a pressure term is not
an embedded “hot spot” in the accretion disk shows the rieht trend for the visibilies. but the values for the UT3-UT4 and UT2-UT4 baseline are higher than for our models which already eive slightlv too high values compared to the observations.,"an embedded ""hot spot"" in the accretion disk shows the right trend for the visibilities, but the values for the UT3-UT4 and UT2-UT4 baseline are higher than for our models which already give slightly too high values compared to the observations."
 The main reason lor the hieher visibilities resulting from (he model applied by Malbetetal.(2005). is the single power law approach which provides less MIR. flux compared to our mocels., The main reason for the higher visibilities resulting from the model applied by \citet{malbet} is the single power law approach which provides less MIR flux compared to our models.
 We also compared our models to the measured NII visibilities from Malbetetal.(2005)., We also compared our models to the measured NIR visibilities from \citet{malbet}.
. We restricted ourselves to those observations where the object was clearly resolved., We restricted ourselves to those observations where the object was clearly resolved.
 The resulis are given in Table 8.., The results are given in Table \ref{table_NIRvisi}.
 Except lor (the observations done with north-west baseline of the Palomar Testbed Interferometer (PTI/NW) both of our models agree with the NIR visibilities within the error bars., Except for the observations done with north-west baseline of the Palomar Testbed Interferometer (PTI/NW) both of our models agree with the NIR visibilities within the error bars.
 Concerning the predicted “hot spot” in the accretion disk (Malbetοἱal.2005) our observations do not vield new insights into its nature as (hev do not have the required spatial resolution to confirm its existence.," Concerning the predicted ""hot spot"" in the accretion disk \citep{malbet} our observations do not yield new insights into its nature as they do not have the required spatial resolution to confirm its existence."
 Also the calibrated phase of our observations do nol contain anv information on which basis we could speculate about this possible second companion., Also the calibrated phase of our observations do not contain any information on which basis we could speculate about this possible second companion.
 We presented (he first multi-baseline MIR. interferometric observations of FU Orionis with MIDI/VLTII., We presented the first multi-baseline MIR interferometric observations of FU Orionis with MIDI/VLTI.
 The findings can be summarized as follows:, The findings can be summarized as follows:
"rate(vM77, where is the index of the dependence of the inner disk radius on the mass accretion rate. Rj,«Mo, a=2/7 if the inner dise radius is approximated by the Alfven radius).","rate$\dot{\nu}\propto \dot{M}^{1-\alpha/2}$, where $\alpha$ is the index of the dependence of the inner disk radius on the mass accretion rate, $R_{in}\propto\dot{M}^{-\alpha}$, $\alpha=2/7$ if the inner disc radius is approximated by the Alfven radius)."
 As the peak X-ray flux shown by the source during both 2008 outbursts is roughly half that of the 2004 outburst. the spin up rate is expected to scale accordingly. provided that the flux is a good tracer of the mass accretion rate.," As the peak X-ray flux shown by the source during both 2008 outbursts is roughly half that of the 2004 outburst, the spin up rate is expected to scale accordingly, provided that the flux is a good tracer of the mass accretion rate."
 We thus expect Pos2.5x107 Hz s! during each of the outbursts shown by the source in 2008.," We thus expect $\dot{\nu}\approx
2.5\times10^{-13}$ Hz $^{-1}$ during each of the outbursts shown by the source in 2008."
 While the upper limit to the September 2008 outburst spin up 1s of the same order as this value. the upper limit to the August 2008 data is one order of magnitude larger and can therefore not be considered as a tight constraint.," While the upper limit to the September 2008 outburst spin up is of the same order as this value, the upper limit to the August 2008 data is one order of magnitude larger and can therefore not be considered as a tight constraint."
 This can also be viewed by considering the 3 σ upper limit to the difference between the spin frequencies at the beginning of the 2008 September and August outbursts. vsos—voy<0.45ur Hz.," This can also be viewed by considering the 3 $\sigma$ upper limit to the difference between the spin frequencies at the beginning of the 2008 September and August outbursts, $\nu_{S08}-\nu_{A08}<0.45\:\mu$ Hz."
 Neglecting any spin down in-between the two outbursts. the spin up during the 2008 August episode cannot be larger than luos]$1x107 Hz s! to account for this difference.," Neglecting any spin down in-between the two outbursts, the spin up during the 2008 August episode cannot be larger than $|\dot{\nu}_{A08}|\simlt
1\times10^{-12}$ Hz $^{-1}$ to account for this difference."
 This reasonable upper limit is already smaller by a factor of two than the upper limit found from timing analysis of that outburst alone., This reasonable upper limit is already smaller by a factor of two than the upper limit found from timing analysis of that outburst alone.
 The comparison of the spin frequency measured at the beginning of the 2008 August outburst with that of the end of the 2004 episode indicates that the spin frequency has decreased during quiescence., The comparison of the spin frequency measured at the beginning of the 2008 August outburst with that of the end of the 2004 episode indicates that the spin frequency has decreased during quiescence.
 Summing in quadrature the statistical error to the systematics induced by the uncertainty in the source position (see Sec. 3.4)).," Summing in quadrature the statistical error to the systematics induced by the uncertainty in the source position (see Sec. \ref{sec:evol}) ),"
" we quote an average spin-down rate during quiescence of r,=(4.1+1.2)x107 Hz sl.", we quote an average spin-down rate during quiescence of $\dot{\nu}_{sd}=(-4.1\pm1.2)\times10^{-15}$ Hz $^{-1}$.
 A spin down at a rate of (-5.5x1.2)107 Hz s! extending over ~10 vr. has already been measured byHO8.. from the401 Hz AMSP.JI808.," A spin down at a rate of $(-5.5\pm1.2)\times 10^{-16}$ Hz $^{-1}$ extending over $\sim 10$ yr, has already been measured by, from the401 Hz AMSP,."
4-30658. Riggio et al. (, Riggio et al. (
2010. in prep.),"2010, in prep.)"
 found an average spin down rate of (5.541.2)x107 Hz s! for the case ofJ1751-305.. while only an upper limit (||€2»I0 Hz κ confidence level) could be set instead by?.. forJ1756.," found an average spin down rate of $(-5.5\pm1.2)\times10^{-15}$ Hz $^{-1}$ for the case of, while only an upper limit $|\dot{\nu}|\leq
2\times10^{-15}$ Hz $^{-1}$, confidence level) could be set instead by, for."
9-2508.. Similarly to HOS. we discuss the spin down measured from 1n terms of: (1) magneto-dipole radiation. (11) emission of gravitational waves. and (11) the propeller effect.," Similarly to H08, we discuss the spin down measured from in terms of: (i) magneto-dipole radiation, (ii) emission of gravitational waves, and (iii) the propeller effect."
 The spin down luminosity of a rotating magnetosphere. Le-απΙνν. has been evaluated by in the limit of force-free magneto-hydrodynamies as. Ly=(lo+sin?ayP(Qzvy Je. where a is the latitude of the magnetic poles. J is the NS moment of inertia and µ is the magnetic dipole.," The spin down luminosity of a rotating magnetosphere, $L_{sd}=4\pi^2I\nu\dot{\nu}$, has been evaluated by in the limit of force-free magneto-hydrodynamics as, $L_{sd}=(1+\sin^2{\alpha})\mu^2(2\pi\nu)^4/c^3$ , where $\alpha$ is the latitude of the magnetic poles, $I$ is the NS moment of inertia and $\mu$ is the magnetic dipole."
" This translates into a spin down rate. v4;=Ly/(AmIv)=[30-sina)/Qsin o)](V,4/221)..where Na=-QO/Ayοὗsin« isthe usual expression for the torque acting on a magnetised rotator in vacuum."," This translates into a spin down rate, $\dot{\nu}_{sd}=L_{sd}/(4\pi^2 I \nu)=
[3(1+\sin^2{\alpha})/(2\sin^2{\alpha})] (N_{vac}/2\pi I)$ ,where $N_{vac}= - (2/3) \mu^2 (2\pi\nu/c)^3 \sin^2{\alpha}$ isthe usual expression for the torque acting on a magnetised rotator in vacuum."
" The estimate of v, we have given translates into a value of the magnetic dipole ofji&1.12)10761°(Lesino!? G em? where Lys is the moment of inertia in units of 10 & em."," The estimate of $\dot{\nu}_{sd}$ we have given translates into a value of the magnetic dipole of $\mu\simeq1.1(2)\times10^{26}
\;I_{45}^{1/2}\;(1+\sin^2{\alpha})^{-1/2}$ G $^{3}$, where $I_{45}$ is the moment of inertia in units of $10^{45}$ g $^2$."
 This estimates translates into a magnetic field. Bz2.2(4)x105sin?ay’? G at the magnetic poles of a 10 km NS.," This estimates translates into a magnetic field, $B\simlt
2.2(4)\times10^{8} \;I_{45}^{1/2}\;(1+\sin^2{\alpha})^{-1/2}$ G at the magnetic poles of a 10 km NS."
 Considering α=0. an upper limit of ~3κ10° G (3c confidence level) on the magnetic field is obtained.," Considering $\alpha=0$, an upper limit of $\simeq 3\times10^{8}$ G $\sigma$ confidence level) on the magnetic field is obtained."
 This estimate fits well into the expected range of magnetic field strengths for the AMSPs to be the progenitors of recycled radio millisecond pulsars (~105— 10° ο)., This estimate fits well into the expected range of magnetic field strengths for the AMSPs to be the progenitors of recycled radio millisecond pulsars $\simeq 10^8$ $10^9$ G).
 It is also compatible with the requirements set on the dipole strength by the maximum and minimum accretion rate experienced by the source while showing pulsations., It is also compatible with the requirements set on the dipole strength by the maximum and minimum accretion rate experienced by the source while showing pulsations.
 For pulsations to be observed. the magnetospheric radius has to lie between the NS radius. Ray. and the corotation radius. Re=(GGMJAnV)? (23.6 mi km forJ00291. where mj: is the NS mass in units of 1.4 M...," For pulsations to be observed, the magnetospheric radius has to lie between the NS radius, $R_{NS}$, and the corotation radius, $R_{C}=(GM/4\pi^2\nu^2)^{1/3}$ $23.6$ $_{1.4}^{1/3}$ km for, where $_{1.4}$ is the NS mass in units of 1.4 $_{\odot}$ )."
 The minimum flux at which we observe pulsations during the 2008 outbursts is [οςας=(1.840.4)107! ere em? s7! (MID 54696.751)., The minimum flux at which we observe pulsations during the 2008 outbursts is $F_{2.5-25}=(1.8\pm0.4)\times10^{-10}$ erg $^2$ $^{-1}$ (MJD 54696.751).
" Assuming as the bolometric correction factor that derived by GOS (2.54) anc that the observed X-ray flux reflects the mass aceretion rate. this translates into M,50.9x107 mj! Ryo d; Μ. yr. where Rjo is the radius of the NS in units of 10 km. and is the distance to the source in units of 4 kpe."," Assuming as the bolometric correction factor that derived by G05 (2.54) and that the observed X-ray flux reflects the mass accretion rate, this translates into $\dot{M}_{min}\simeq0.9\times10^{-10}$ $_{1.4}^{-1}$ $_{10}$ $_4^2$ $_{\odot}$ $^{-1}$, where $_{10}$ is the radius of the NS in units of 10 km, and $_4$ is the distance to the source in units of 4 kpc."
" Considering the value quoted by GOS for the peak flux during the 2004 outburst. the maximum accretion rate at which pulsations were observed can be estimated as Mj,=4.7x107 mj! Rio di M. yr!"," Considering the value quoted by G05 for the peak flux during the 2004 outburst, the maximum accretion rate at which pulsations were observed can be estimated as $\dot{M}_{max}\simeq4.7\times10^{-10}$ $_{1.4}^{-1}$ $_{10}$ $_4^2$ $_{\odot}$ $^{-1}$."
 Using the expressions derived by?.. the presence of pulsations at these two limiting aceretion rates indicates that the magnetic dipole has to lie in the range. (0.2 — 21)*1079 dy G em. fully compatible withour estimate.," Using the expressions derived by, the presence of pulsations at these two limiting accretion rates indicates that the magnetic dipole has to lie in the range, (0.2 – $\times 10^{26}$ $_4$ G $^{3}$, fully compatible withour estimate."
 As the minimum flux at which pulsations are observed is likely overestimatec by a factor of ~2 because of the contribution of V709 Cas. the upper limit to the magnetic dipole is likely to be a factor V2 smaller.," As the minimum flux at which pulsations are observed is likely overestimated by a factor of $\sim
2$ because of the contribution of V709 Cas, the upper limit to the magnetic dipole is likely to be a factor $\sqrt{2}$ smaller."
 Considering also the dynamical estimate of the maximum mass-accretiol rate derived by BO7 from the spin up rate observed during the 2004outburst. the lower limit to the dipole strength increases to 0.6x1079 G em. still compatible with the estimate derived here.," Considering also the dynamical estimate of the maximum mass-accretion rate derived by B07 from the spin up rate observed during the 2004outburst, the lower limit to the dipole strength increases to $\times 10^{26}$ G $^{-3}$, still compatible with the estimate derived here."
 Our estimate of the magnetic field strength 1s also compatible with the upper limit estimated by TO8 from the X-ray quiescent luminosity. <3x10° G. using the criteria stated by and2.," Our estimate of the magnetic field strength is also compatible with the upper limit estimated by T08 from the X-ray quiescent luminosity, $<3\times10^8$ G, using the criteria stated by and."
. The spin down torque associated with the emission of gravitational radiation has been proposed to explain the non- of acereting pulsars with frequencies higher than =730 Hz (?.. see for models describing mechanism that can lead to a non-zero mass quadrupole for an accreting pulsar).," The spin down torque associated with the emission of gravitational radiation has been proposed to explain the non-detection of accreting pulsars with frequencies higher than $\approx730$ Hz , see for models describing mechanism that can lead to a non-zero mass quadrupole for an accreting pulsar)."
 In this case. the spin-down torque is. Nei=-(32/9)GO?(2av/er ?)..," In this case, the spin-down torque is, $N_{GW}=
-(32/5)GQ^2(2\pi\nu/c)^5$ ."
 Under the hypotheses that the spin down of is due only to this mechanism and that the torque due to the GW emission is constant. our measure of the average spin down translates into an estimate of the average mass quadrupole moment. Q~1.2(2)x1076ne 5 enr.," Under the hypotheses that the spin down of is due only to this mechanism and that the torque due to the GW emission is constant, our measure of the average spin down translates into an estimate of the average mass quadrupole moment, $Q\simeq1.2(2)\times10^{36}\;I_{45}^{1/2}$ g $^2$."
 Considering the upper limit at the 37 confidence level. ο52x10 g eni. the maximum amplitude at the Earth of the emitted GW is therefore. Aic24.6G(vrO/det=3x1077 di ne (?)..," Considering the upper limit at the $\sigma$ confidence level, $Q\simlt 2\times10^{36}$ g $^{2}$ , the maximum amplitude at the Earth of the emitted GW is therefore, $h_C\simlt
4.6G(2\pi\nu)^2Q/dc^4\simlt 3\times10^{-28}$ $d_4^{-1}$ $I_{45}^{1/2}$ ."
 Assuming that the spin down during quiescence of and 1s driven by the emission of GW and that the NS in these systems have a similar mass quadrupole. the spin down driven by the emission of GW should be =(598.9/101.0)7?~7.6 times larger in than in J1808.4—3658.," Assuming that the spin down during quiescence of and is driven by the emission of GW and that the NS in these systems have a similar mass quadrupole, the spin down driven by the emission of GW should be $\approx (598.9/401.0)^5\simeq7.6$ times larger in than in ."
 The large uncertainties affectingthe spin down estimates in both sources do not allow us to check whether this prediction is compatible with observations., The large uncertainties affectingthe spin down estimates in both sources do not allow us to check whether this prediction is compatible with observations.
retarders as the polarization modulator (MartínezPilletetal. 2010:: see also Jochumetal. 2003.. MartínezPilletetal.2004... and Álvarez-Herreroetal. 2006)).,"retarders as the polarization modulator \citealt{Pillet}; see also \citealt{2003SPIE.4843...20J}, , \citealt{2004SPIE.5487.1152M}, and \citealt{2006SPIE.6265E.132A}) )."
 IMaX is one of the post-focus instruments of the Im telescope. which flew over the Artic in a stratospheric balloon from June 8 to 13. 2010 (Bartholetal.2010).," IMaX is one of the post-focus instruments of the 1m telescope, which flew over the Artic in a stratospheric balloon from June 8 to 13, 2010 \citep{Barthol}."
. In this way. continuous observations of the Sun were possible avoiding most of the Earth atmosphere.," In this way, continuous observations of the Sun were possible avoiding most of the Earth atmosphere."
 Table 1. summarizes the basic parameters of the instrument., Table \ref{cap9:imaxtable} summarizes the basic parameters of the instrument.
 IMaX provides capabilities for obtaining polarimetric images near the diffraction limit of (07111 at 525 nm). with a SNR of about 1000.," IMaX provides capabilities for obtaining polarimetric images near the diffraction limit of 11 at 525 nm), with a SNR of about $1000$."
" The instrument has several observing modes in which the number of wavelengths is varied from 3 through 12 (one of them is always reserved for the continuum). but the ""regular"". so-called vector spectropolarimetric. mode is one that scans the line at 5 wavelength points in 33 s. Will it be possible to accurately infer the full vector magnetic field from the regular IMaX measurements using appropriate inversion techniques?"," The instrument has several observing modes in which the number of wavelengths is varied from 3 through 12 (one of them is always reserved for the continuum), but the “regular”, so-called vector spectropolarimetric, mode is one that scans the line at 5 wavelength points in 33 s. Will it be possible to accurately infer the full vector magnetic field from the regular IMaX measurements using appropriate inversion techniques?"
 Answering this question is the main aim of the present paper., Answering this question is the main aim of the present paper.
 To assess the accuracy to which the magnetic field strength. inclination. azimuth. and line-of-sight (LOS) velocity can be determined. we here simulate an IMaX observation.," To assess the accuracy to which the magnetic field strength, inclination, azimuth, and line-of-sight (LOS) velocity can be determined, we here simulate an IMaX observation."
 We use radiative magnetohydrodynamic (MHD) models to synthesize the Stokes profiles of the photospherie. lines at 525.02 and 525.06 nm., We use radiative magnetohydrodynamic (MHD) models to synthesize the Stokes profiles of the photospheric lines at 525.02 and 525.06 nm.
 These two lines. very close in. wavelength and hence observable with the same pre-filter. were considered for the IMaX instrument since the beginning of the design phase.," These two lines, very close in wavelength and hence observable with the same pre-filter, were considered for the IMaX instrument since the beginning of the design phase."
 In fact. part of the results of this paper provided the rationale for selecting one of the lines instead of the other.," In fact, part of the results of this paper provided the rationale for selecting one of the lines instead of the other."
 An earlier investigation on magnetic inferences from filtergrams with limited wavelength sampling was carried out by Grahametal. (2002).., An earlier investigation on magnetic inferences from filtergrams with limited wavelength sampling was carried out by \citet{2002SoPh..208..211G}.
 They used Milne-Eddington (ME) profiles to simulate the observations., They used Milne-Eddington (ME) profiles to simulate the observations.
 Our paper can be considered as an extension of their work. since MHD simulations provide a more realistic description of the solar photosphere.," Our paper can be considered as an extension of their work, since MHD simulations provide a more realistic description of the solar photosphere."
 The simulated Stokes profiles are degraded by telescope diffraction and detector pixel size to a spatial resolution of 80 km on the solar surface. and then sampled at five wavelengths (four within the line plus another in the nearby continuum) to mimic the nominal vector spectropolarimetric mode of IMaX. From these data we determine the magnetic field vector and LOS velocity using ME inversions and compare them with the parameters resulting from the inversion of fully resolved and critically sampled profiles.," The simulated Stokes profiles are degraded by telescope diffraction and detector pixel size to a spatial resolution of 80 km on the solar surface, and then sampled at five wavelengths (four within the line plus another in the nearby continuum) to mimic the nominal vector spectropolarimetric mode of IMaX. From these data we determine the magnetic field vector and LOS velocity using ME inversions and compare them with the parameters resulting from the inversion of fully resolved and critically sampled profiles."
 To simulate à real observation. the typical noise of IMaX measurements 1s added to the profiles.," To simulate a real observation, the typical noise of IMaX measurements is added to the profiles."
 The paper is structured as follows: Sect., The paper is structured as follows: Sect.
 2. describes the spatial degradation of the simulated Stokes profiles and the effects of the tunable filter on the spectra.," \ref{simulandoimax}
 describes the spatial degradation of the simulated Stokes profiles and the effects of the tunable filter on the spectra."
 In that Section we also analyze the effects of noise and the drawbacks of selecting only a few wavelength positions across the line., In that Section we also analyze the effects of noise and the drawbacks of selecting only a few wavelength positions across the line.
 Section 3 deals with the results of ME inversions., Section \ref{cap9:inversion} deals with the results of ME inversions.
 There we estimate the uncertainties of the retrieved physical parameters., There we estimate the uncertainties of the retrieved physical parameters.
 In Sect., In Sect.
 4 we summarize the main conclusions of this work., \ref{sec:conclu} we summarize the main conclusions of this work.
 To simulate an IMaX observation we use model atmospheres from the radiative MHD calculations of Vógleretal.(2005).., To simulate an IMaX observation we use model atmospheres from the radiative MHD calculations of \citet{2005A&A...429..335V}.
 They were initialized with a distribution of mixed polarity fields with an average magnetic field strength of (8)~200 G atlogr =-—l., They were initialized with a distribution of mixed polarity fields with an average magnetic field strength of $\langle B\rangle\sim200$ G at $\log\tau=-1$.
 The snapshot used here was taken when (5) had decayed to about ~ 140 G. We have chosen this particular run because it contains both network- and internetwork-like regions.," The snapshot used here was taken when $\langle
 B\rangle$ had decayed to about $\sim$ 140 G. We have chosen this particular run because it contains both network- and internetwork-like regions."
 The extent of the computational box is 288«x100 pixels. with a spatial sampling of 20.8 km (070287) in the horizontal direction and 14. km in the vertical direction.," The extent of the computational box is $288\times288\times100$ pixels, with a spatial sampling of 20.8 km $0\farcs0287$ ) in the horizontal direction and 14 km in the vertical direction."
 The bottom of the box ts located 800 km below r=1., The bottom of the box is located 800 km below $\tau =1$.
 More details about this run can be found in Khomenkoetal.(2005).., More details about this run can be found in \citet{khomenko}.
 Since the work of Vógleretal.(2005).. simulations of higher numerical resolution have become available.," Since the work of \citet{2005A&A...429..335V}, simulations of higher numerical resolution have become available."
 They certainly represent a significant step forward. but we believe they would not change our conclusions. at least for the larger magnetic structures present in the network and most of the internetwork — the ones observed by IMaX during its first flight and also by Hinode since its launch in 2006.," They certainly represent a significant step forward, but we believe they would not change our conclusions, at least for the larger magnetic structures present in the network and most of the internetwork – the ones observed by IMaX during its first flight and also by Hinode since its launch in 2006."
 The reason is that the simulations of Vógleretal.(2005) have been confronted with observations thoroughly with excellent results.," The reason is that the simulations of \citet{2005A&A...429..335V}
 have been confronted with observations thoroughly with excellent results."
 This indicates that they already provide a very good descriptio=) of the solar atmosphere., This indicates that they already provide a very good description of the solar atmosphere.
 The MHD models are used to generate the observatiornr by synthesizing the Stokes 7. Q. U. and V profiles with the SIR code (RuizCobo&DelToroIntesta1992).," The MHD models are used to generate the observations by synthesizing the Stokes $ I$, $Q$, $U$, and $V$ profiles with the SIR code \citep{1992ApJ...398..375R}."
. The spectral synthesis is performed in a wavelength range that spans | nm and includes the lines at 525.02 and 525.06 nm., The spectral synthesis is performed in a wavelength range that spans 1 nm and includes the lines at 525.02 and 525.06 nm.
 The wavelength step is 1 pm., The wavelength step is 1 pm.
 Next. the monochromatic images are spatially degraded as the Sunrise/IMaX system does.," Next, the monochromatic images are spatially degraded as the /IMaX system does."
 The modulation transfer function (MTF) of the whole system Is depicted in Fig., The modulation transfer function (MTF) of the whole system is depicted in Fig.
 1. and includes the | m aperture of the telescope. the central obscuration of the entrance pupil (caused by the secondary mirror). and the effects of Image pixelation.," \ref{fig:continuo} and includes the 1 m aperture of the telescope, the central obscuration of the entrance pupil (caused by the secondary mirror), and the effects of image pixelation."
 The spatially degraded images are binned by a factor 2. hence their sampling is almost identical to that of IMaX with a pixel size of 07055.," The spatially degraded images are binned by a factor 2, hence their sampling is almost identical to that of IMaX with a pixel size of $0\farcs055$."
 The original continuum contrast of decreases only by due to diffraction and CCD pixelation., The original continuum contrast of decreases only by due to diffraction and CCD pixelation.
 After that we convolve the Stokes profiles with a Gaussian of 6 pm FWHM to account for the limited spectral resolving power of the Fabry-Pérrot éttalon., After that we convolve the Stokes profiles with a Gaussian of 6 pm FWHM to account for the limited spectral resolving power of the Fabry-Pérrot éttalon.
 Finally. we add noise and select four wavelengthsamples across the line plus a wavelength point in the nearby continuum.," Finally, we add noise and select four wavelengthsamples across the line plus a wavelength point in the nearby continuum."
cilepjonds..,\\citep{jon05}.
 A vector showing 10 visual magnitudes of extinction (IndebetowwLebolskv1935) as well as the AGB limit are included in the IR CMD.," A vector showing 10 visual magnitudes of extinction \citep{ind05,rie85} as well as the AGB limit are included in the IR CMD."
 While the reddening vector Lakes into account the wavelength dependent extinction from dust. it does not include the cireumstellar emission. which can be significant at longer wavelengths.," While the reddening vector takes into account the wavelength dependent extinction from dust, it does not include the circumstellar emission, which can be significant at longer wavelengths."
" The AGB limit was determined by assuming a bolometric correction at 3.6 ool +3 magnitudes for an M5 star. +2 magnitudes for a GO star and M),,=—7.1 1983).. and is depicted in Figure 5. as a line connecting the AGB limit for these two stellar twpes."," The AGB limit was determined by assuming a bolometric correction at 3.6 of +3 magnitudes for an M5 star, +2 magnitudes for a G0 star and $_{bol}$ $-$ 7.1 \citep{woo83}, and is depicted in Figure \ref{IR_cmd} as a line connecting the AGB limit for these two stellar types."
 Above the plotted AGB limit we detect two optically classified RSGs and one optically classified AGB star., Above the plotted AGB limit we detect two optically classified RSGs and one optically classified AGB star.
 The object optically classified as an AGB star lies just within the blue boundary of region (b) and could easily be a slightly reddened RSG., The object optically classified as an AGB star lies just within the blue boundary of region (b) and could easily be a slightly reddened RSG.
 There are also six objects brighter than. but rechward of the AGB limit that are optically classified as AGB stars.," There are also six objects brighter than, but redward of the AGB limit that are optically classified as AGB stars."
 Dased on (heir positions in the optical CMD. the brightest (μου of these six objects are likely reddened RSCs. while the fainter three are consistent with mass-losing AGB stars (see 82? for a description of the elfect of mass-loss on the [3.6]— 4.5] color).," Based on their positions in the optical CMD, the brightest three of these six objects are likely reddened RSGs, while the fainter three are consistent with mass-losing AGB stars (see \ref{mass_loss} for a description of the effect of mass-loss on the $-$ [4.5] color)."
 There is considerable overlap in the lower part of the IR CMD between stellar (vpes., There is considerable overlap in the lower part of the IR CMD between stellar types.
 llowever. the luminosity of the red giant. branch tip (TRGB) does enable us to separate red giants from the other stellar (vpes.," However, the luminosity of the red giant branch tip (TRGB) does enable us to separate red giants from the other stellar types."
 Figure G shows the 3.6 luminosity function for all objects detected at both 3.6 and 4.5jim., Figure \ref{lum_fn} shows the 3.6 luminosity function for all objects detected at both 3.6 and 4.5.
 Dased on the abrupt drop in the 3.6 luminosity function. we adopt a 3.6 aabsolute magnitude of the TRGB to be —6.6.," Based on the abrupt drop in the 3.6 luminosity function, we adopt a 3.6 absolute magnitude of the TRGB to be $-$ 6.6."
 This value for the TRGB is slightly brighter than the value adopted by vanLoonetal.(2005). for the LAIC (L’ = —6.4). though given the uncertainty in the distance modulus to WLM (5 0.08 magnitudes) and the bin size of our luminosity function (0.25 magnitudes) (hese values agree reasonably well.," This value for the TRGB is slightly brighter than the value adopted by \citet{van05}
 for the LMC $^\prime$ = $-$ 6.4), though given the uncertainty in the distance modulus to WLM $\pm$ 0.08 magnitudes) and the bin size of our luminosity function (0.25 magnitudes) these values agree reasonably well."
 For the objects detected at both 3.6 and 4.5. of the total 3.6 [flux of 46.5 mJv is [rom stars brighter than the TRGB. which are predominantly ACB stars.," For the objects detected at both 3.6 and 4.5, of the total 3.6 flux of 46.5 mJy is from stars brighter than the TRGB, which are predominantly AGB stars."
 The right panel of Figure 5. shows the IR. CAD of objects detected in V. 1. and at 3.6 and 4.5jam. separated. according to their optically selected stellar (wpe.," The right panel of Figure \ref{IR_cmd} shows the IR CMD of objects detected in V, I, and at 3.6 and 4.5, separated according to their optically selected stellar type."
 The optically detected AGB stars have typical IR. colors of —0.25« [3.6]— £0.25. with the exception of a few luminous red sources.," The optically detected AGB stars have typical IR colors of $-$ $<$ $-$ $<$ 0.25, with the exception of a few luminous red sources."
 The RSGs have a similar distribution. although no RSGs with red II. colors awe detected. as any reddening would cause a RSG to be misidentified as an AGB star in the optical.," The RSGs have a similar distribution, although no RSGs with red IR colors are detected, as any reddening would cause a RSG to be misidentified as an AGB star in the optical."
 Nearly all of the blue objects detected in the optical and IR. are found between —5cMa;—5 and —0.3«|3.6]— 4.5] «0.5., Nearly all of the blue objects detected in the optical and IR are found between $-$ $<$ $_{3.6}$$<$$-$ 5 and $-$ $<$ $-$ $<$ 0.5.
 We also detect a few. IR Iuminous, We also detect a few IR luminous
emission in these particular sources is likely to be a &ood indicator of the intrinsic luminosity of the ACN.,emission in these particular sources is likely to be a good indicator of the intrinsic luminosity of the AGN.
 For AGNs with strong contributions from. star-formation. the Jeu] emission may contaminate the measured. Lux measured from low-resolution Spizer-2108 spectroscopy (?)..," For AGNs with strong contributions from star-formation, the ] emission may contaminate the measured flux measured from low-resolution -IRS spectroscopy \citep{melendez08a}."
 For those galaxies which we find to be dominated. by star formation at mid-Ilt. wavelengths (i.e. ACN contributions of <50 percent: see Section 3.4)). we conservatively apply a small cownwareds correction factor of z1.5 (?) to our measured Dux to account for the Fe 11] contamination.," For those galaxies which we find to be dominated by star formation at mid-IR wavelengths (i.e., AGN contributions of $< 50$ percent; see Section \ref{subsec:spitz_spec_decomps}) ), we conservatively apply a small downwards correction factor of $\approx 1.5$ \citep{melendez08a}
 to our measured flux to account for the [Fe ] contamination."
 Our final adopted luminosities cover the range. Loneπε(0.15 20)1033Cres," Our final adopted luminosities cover the range, $L_{\rm [OIV]} \approx (0.15$ $20) \times 10^{41} \ergps$."
 The low-resolution mid-LH spectra of typical Tvpe-2 AGNs at vest-Lrame Az4 15qun. are composed of three primary components: 1) à power-law like thermal ACN dust continuum: 2) a star-formation component which arises from the super-position of PALL features: ancl 3) a silicate absorption feature at Az9.7qum. produced by the hot dust continuum. being absorbed. by cooler dust. on parsec scales (e.g... 2: 7: νι ?)).," The low-resolution mid-IR spectra of typical Type-2 AGNs at rest-frame $\lambda \approx 4$ $15 \um$ are composed of three primary components: 1) a power-law like thermal AGN dust continuum; 2) a star-formation component which arises from the super-position of PAH features; and 3) a silicate absorption feature at $\lambda \approx 9.7
\um$ produced by the hot dust continuum being absorbed by cooler dust on parsec scales (e.g., \citealt{GA09}; \citealt{gallimore10}; \citealt{mullaney10}; \citealt{tommasin10}) )."
 Therefore. as expected. we find that the mid-LHIt spectra for the majority of our candidate Compton-thick AGNs contain both an AGN produced continuum and strong polvevclic aromatic hydrocarbon (PALD) features. which are associated with starburst activity in the cireumnuclear photodissociation regions of the host galaxy.," Therefore, as expected, we find that the mid-IR spectra for the majority of our candidate Compton-thick AGNs contain both an AGN produced continuum and strong polycyclic aromatic hydrocarbon (PAH) features, which are associated with starburst activity in the circumnuclear photodissociation regions of the host galaxy."
 Here we outline our spectral decomposition routine to determine the relative contributions of starburst (SB) activity and the ACN continuum in our 14 Compton-thick AGN candidates (oe. the SBuXAGN ratio). and measure the intrinsic luminosity of the central source. from the ACN produced mid-LR. continuum at 6tum (e.g.. 2)).," Here we outline our spectral decomposition routine to determine the relative contributions of starburst (SB) activity and the AGN continuum in our 14 Compton-thick AGN candidates (i.e., the SB:AGN ratio), and measure the intrinsic luminosity of the central source from the AGN produced mid-IR continuum at $6 \um$ (e.g., \citealt{lutz04}) )."
 Using a purpose-built IDL-based routine. we fit the Las spectroscopy for cach of the Lt candidate. Compton-thick AGNs with a combined standard starburst’ template and an AGN power-law component (with spectral index. 4°) convolved with a 7. extinction curve (0(À)) of the form. where e. b and & are constants. and. 7 is the optical Within the fitting we use four possible starburst templates which cover a realistic range of physical and theoretical scenarios: 1) low-resolution Spifzer-LRS spectroscopy of the archetypal starburst galaxy. MS2: 2) a combined 5 starburst template of local pure star-forming galaxies presented in 2:7 3) a theoretical radiative transfer model of a pure circummuclear starburst region at pomM kpe with LanzmLOL. (25 hereafter. SIXOT): and 4) a theoretical radiative transfer model of a nuclear star cluster at i«0.35 kpe with Ziz107L. (SINOT).," Using a purpose-built -based routine, we fit the IRS spectroscopy for each of the 14 candidate Compton-thick AGNs with a combined standard starburst template and an AGN power-law component (with spectral index, $k$ ) convolved with a \citet{draine07}
 extinction curve $\rho ( \lambda )$ ) of the form, where $a$, $b$ and $k$ are constants, and $\tau$ is the optical Within the fitting we use four possible starburst templates which cover a realistic range of physical and theoretical scenarios: 1) low-resolution -IRS spectroscopy of the archetypal starburst galaxy, M82; 2) a combined -IRS starburst template of local pure star-forming galaxies presented in \citet{brandl06}; 3) a theoretical radiative transfer model of a pure circumnuclear starburst region at $r \approx 3$ kpc with $L_{\rm IR}
\approx 10^{10} \Lsun$ \citealt{siebenmorgen07}; hereafter, SK07); and 4) a theoretical radiative transfer model of a nuclear star cluster at $r < 0.35$ kpc with $L_{\rm IR} \approx 10^{10} \Lsun$ (SK07)."
 The best resulting model parameters derived from the minimum. Chi-squared. fit to the IRS data are given in ‘Table 20 and shown in Fig. 4.., The best resulting model parameters derived from the minimum Chi-squared fit to the IRS data are given in Table \ref{tab:ir_phot_spec} and shown in Fig. \ref{fig:decomps}.
 We note that none of the ACGNs in our sample have mid-LHt spectral features which are consistent with the theoretical nuclear star cluster moclel. and hence. the best-Lit spectral model for cach are that of an AGN combined with one of the three cireumnuclear starburst templates.," We note that none of the AGNs in our sample have mid-IR spectral features which are consistent with the theoretical nuclear star cluster model, and hence, the best-fit spectral model for each are that of an AGN combined with one of the three circumnuclear starburst templates."
 Dased on the mid-Ilt spectral-fits. we also derive the approximate contribution of the ACN to the mid-L emission for each of the sources: see column (7) of ‘Table 2..," Based on the mid-IR spectral-fits, we also derive the approximate contribution of the AGN to the mid-IR emission for each of the sources; see column (7) of Table \ref{tab:ir_phot_spec}."
 We find that although these AGNs were selected to be strong and. Nu]emitters (i.c... opticallv-dominate Sevfert. galaxies). the mid-IIt. spectra of =50 percent. of the sources are consistent with being dominated by star-formation activity.," We find that although these AGNs were selected to be strong and ]emitters (i.e., optically-dominated Seyfert galaxies), the mid-IR spectra of $\approx 50$ percent of the sources are consistent with being dominated by star-formation activity."
 Indeed. on the basis of these spectra decompositions. the mid-Ilt spectroscopy. lor one source (SDSS | 130550) is consistent with there being no AGN component. despite this source clearly being identifiec as an AGN at optical wavelengths.," Indeed, on the basis of these spectral decompositions, the mid-IR spectroscopy for one source (SDSS $+$ 130550) is consistent with there being no AGN component, despite this source clearly being identified as an AGN at optical wavelengths."
 In order to estimate the intrinsic AGN luminosity anc hence place limits on the X-ray absorption in these sources. we use the measured AGN power-law parameters to derive 6jun luminosities (Loja).," In order to estimate the intrinsic AGN luminosity and hence place limits on the X-ray absorption in these sources, we use the measured AGN power-law parameters to derive $6\um$ luminosities $L_{6 \mu
 m}$ )."
 The uncertainties of these 6pun κος are established by considering a weighted: spread in the measured 6pum fluxes. from all statistically valid starburst template fits (Le. we reject all statistically poor fits at the 95 per cent level).," The uncertainties of these $6 \um$ fluxes are established by considering a weighted spread in the measured $6 \um$ fluxes from all statistically valid starburst template fits (i.e., we reject all statistically poor fits at the 95 per cent level)."
 The mean le uncertainty is x0.1 dex., The mean $1\sigma$ uncertainty is $\approx 0.1$ dex.
 See column (8) of Table 2.., See column (8) of Table \ref{tab:ir_phot_spec}. .
 We estimate the 6pum continuum luminosities for 13 of our 14 candidate Compton-thick AGNs and conservatively estimate an upper limit for the 6jum continuum. flux. of «107 mJy for SDSS | 130550., We estimate the $6 \um$ continuum luminosities for 13 of our 14 candidate Compton-thick AGNs and conservatively estimate an upper limit for the $6 \um$ continuum flux of $< 10^{-2}$ mJy for SDSS $+$ 130550.
" We find. using our adopted cosmology. that the AGNs cover more than 2 decades in 6pun luminosity. with Loja,2(0.1 20)107ergs "," We find using our adopted cosmology, that the AGNs cover more than 2 decades in $6\um$ luminosity, with $\nu L_{6\mu
 m} \approx (0.1$ $20) \times 10^{43} \ergps$ ."
We have selected a sample. of 14 bright. X-ray undetected AGNs from. the =100. deg? overlap region between the SDSS-DRT and 2NATM surveys.," We have selected a sample of 14 bright, X-ray undetected AGNs from the $\approx 100$ $^2$ overlap region between the SDSS-DR7 and 2XMMi surveys."
 These sources Πο at z0.03 0.2 and host moderate to highly Iuminous AGNs with de-reddened Loup(0.2 500)«1077eres (i.c.. similar to those of typical nearby Sevfert galaxies).," These sources lie at $z \sim 0.03$ –0.2 and host moderate to highly luminous AGNs with de-reddened $L_{\rm [OIII]}
\approx (0.2$ $500) \times 10^{42} \ergps$ (i.e., similar to those of typical nearby Seyfert galaxies)."
 Our 14 targets all have fx/four<1. implying strong intrinsic absorption of their X-ray Εαν and many (possibly all) ave likely Compton-thick AXGNs.," Our 14 targets all have $f_X /
f_{\rm [OIII]} < 1$, implying strong intrinsic absorption of their X-ray flux and many (possibly all) are likely Compton-thick AGNs."
 In the absence of X-ray spectroscopic data. in section 3. we derived AGN-procuced emission line and. continuum luminosity measurements in order to independently constrain the intrinsic luminosity of these candidate Compton-thick AXCGNs.," In the absence of X-ray spectroscopic data, in section \ref{sec:midir_spec_photom} we derived AGN-produced emission line and continuum luminosity measurements in order to independently constrain the intrinsic luminosity of these candidate Compton-thick AGNs."
 In this section. we use these intrinsic luminosities in conjunction with X-ray constraints from data to test whether these objects are indeed Compton-thick ACGNs.," In this section, we use these intrinsic luminosities in conjunction with X-ray constraints from data to test whether these objects are indeed Compton-thick AGNs."
 We then use these results to place new constraints on the space density. and relative mass-aceretion rates of Compton-thick XCGNs in the nearby Universe (2~ 0.1).," We then use these results to place new constraints on the space density and relative mass-accretion rates of Compton-thick AGNs in the nearby Universe $z
\sim 0.1$ )."
 Previously. strong. relativelyhigh-excitation emission lines.," Previously, strong, relativelyhigh-excitation emission lines,"
There are a number of numerical works in which such a highly nonaxisymmetric structure is the outcome alter onset of dynamical instability of cilferentiallv rotating stars with a high value of 3 (e.g. Williams Tohline LOST. 1988: llouser Centrella 1996).,"There are a number of numerical works in which such a highly nonaxisymmetric structure is the outcome after onset of dynamical instability of differentially rotating stars with a high value of $\beta$ (e.g., Williams Tohline 1987, 1988; Houser Centrella 1996)."
 Phe outcome in the simulations for unstable stars of a high value of 3 found in the present numerical computation is qualitatively the same as that in previous papers., The outcome in the simulations for unstable stars of a high value of $\beta$ found in the present numerical computation is qualitatively the same as that in previous papers.
 Phus. we do not discuss the results for such cases in the following.," Thus, we do not discuss the results for such cases in the following."
 After the perturbation saturates. the amplitude of 9 settles down toward a value of order 0.1.," After the perturbation saturates, the amplitude of $\eta$ settles down toward a value of order 0.1."
 The approximate final values of η are(, The approximate final values of $\eta$ are.
11) Comparing the results of (Qu=(5/3.0.3) and (5/3. 0.1) for the identical value of C. it is found that [or the smaller value of lay is larger.," Comparing the results of $(\Gamma, \hat A)=(5/3, 0.3)$ and (5/3, 0.1) for the identical value of $C_a$, it is found that for the smaller value of $\hat A$, $\eta_f$ is larger."
 This implies that a stronger degree of differential rotation makes the magnitude of the nonaxisvmmetric deformation larger., This implies that a stronger degree of differential rotation makes the magnitude of the nonaxisymmetric deformation larger.
 Lt is also found that for the smaller value of E. the final value coL: salles," It is also found that for the smaller value of $\Gamma$, the final value of $\eta$ is smaller."
 Phi because the stars of smaller, This is because the stars of smaller
unclittered picture of the local behavior of the lens equation near a critical point. we sel ας—0.,"uncluttered picture of the local behavior of the lens equation near a critical point, we set $dz_+= 0$."
 1 ας -—0.dz-—dzE.ancl from equation (61)). This is the quadratic behavior of (he lens equation near a critical point.," If $dz_+ =0$, $dz = dz_- E_-$,and from equation \ref{eqLomega}) ), This is the quadratic behavior of the lens equation near a critical point."
 The role of the eritical direction is clear., The role of the critical direction is clear.
 Hf τς is a critical point. (wo images separated along the critical direction al D—cudlFf ave from a same source.," If $z_\circ$ is a critical point, two images separated along the critical direction at $ z = z_\circ \pm |dz_-|E_-$ are from a same source."
" I o is (he caustic point corresponding to 2, under (he lens equation. then the position of the source. w=ow. that produces the (wo images is such that the shilt dw is in(he same direction as the gradient of the Jacobian determinant VJ—(JoJo) ab το."," If $\omega_\circ$ is the caustic point corresponding to $z_\circ$ under the lens equation, then the position of the source, $\omega = \omega_\circ + \delta\omega$, that produces the two images is such that the shift $\delta\omega$ is inthe same direction as the gradient of the Jacobian determinant $\nabla J = (J_+, J_-)$ at $z_\circ$."
 See Fie., See Fig.
 1l., 1.
 We refer to this caustic point ως as thepoint Lor w, We refer to this caustic point $\omega_\circ$ as the for $\omega$.
 Then. two images of & can be found in (he critical direction from the critical point τος ο=το|dz|E where dz oy|= o= mu..," Then, two images of $\omega$ can be found in the critical direction from the critical point $z_\circ$ : $ z = z_\circ \pm |dz_-|E_-$ where |dz_-| = = = ."
that due to the peculiar morphology of dwart galaxies. inore Clectrous escape from the galaxy because of the ↸⊳∪↴∖↴∐∏↸⊳↥⋅⋜↧⋅↖⇁≼∐↕−,"that due to the peculiar morphology of dwarf galaxies, more electrons escape from the galaxy because of the cosmic ray diffusion."
"↥∎∏↴∖↴↕∪∐∙↕≧∪⋅↖⇁↕↸∖↸∖↑⋜↧↕∙⋖⊇∩∩⊤⋟∐⋜↧↖↽↸∖⋜↧↕↴∖↴∪↕≯⋯∐∐↧ a Μο] ου5-1 0-0 the sources they studied. aud postulated that this 03may ibe idue to a changein the mean qo, ratio for objects with Lynn) τν. however. their sources are mich htl away aud may not he to the low metallicity star⋅⋅ forming galaxies⋅ FE∶ study in the local universe."," \citet{Boyle07} have also found a high $_{24}$ $\pm$ 0.02 for the sources they studied, and postulated that this may be due to a change in the mean $_{24}$ ratio for objects with $_\nu$ $\mu$ m) $<$ mJy, however, their sources are much further away and may not be comparable to the low metallicity star forming galaxies we study in the local universe."
 5 uunber of physical paraicters. such as Ε if BH + ⋅ BH— f," A number of physical parameters, such as the metallicity, dust grain size distribution, and temperature may affect the shape of the infrared SED."
"or⋅ correlatious6 between log(L, _/Le)8 :9 [o] the galaxies iu our sample with those 24pm ο..."," Consequently, we search for correlations between the q ratios of the galaxies in our sample with those parameters."
 Ourratios saluple v nuc tallicity pane of Lie.δν σοι, Our sample covers a metallicity range of $\le$ $\le$ 8.9.
 inetallicity galaxics. luminosity Loy. Phe Thesvibols usually low. even though there are notable exceptious such as SBS0335-052E (Houck et al. 2001b).. thustheciission of UV elt might iof be fully reprocessed bv the dust aud re-euütted Cluission. counter balance ea," In low metallicity galaxies, the dust content is usually low, even though there are notable exceptions such as SBS0335-052E \citep{Houck04b}, thus the emission of UV light might not be fully reprocessed by the dust and re-emitted at the infrared wavelengths."
ch Wowever. these galaxies DCDs though. are typically svuchrotron radiation.," However, these galaxies might have a quenched synchrotron radiation."
 This cau in size. and have reasons inchiding a lack of (wit. normal galaxies) which particles producing supernovae to produce cosimic radio enuisskmu. the escape of fast cosmic ravs frou the ealaxy. otc.," This can be attributed to various reasons including a lack of supernovae remnants which accelate particles producing radio emission, the escape of fast cosmic rays from the galaxy, etc."
 These two competing factors. dust aud racio other (see Dell 2003).," These two competing factors, dust and radio emission, counter balance each other \citep[see][]{Bell03}."
. at theinfraredwavelengths. siuall. less than —1kkpe welt have a quenched fewer TTT regions with massive stars v0 att," BCDs though, are typically small, less than $\sim$ kpc in size, and have fewer HII regions with massive stars (w.r.t."
ributed to various heat the dust aud so supernovae reniuants which accelate rays., normal galaxies) which heat the dust and go supernovae to produce cosmic rays.
 As a result the averaging effects in the sampling of the properties of the interstellar ποπι which result from the limited spatial, As a result the averaging effects in the sampling of the properties of the interstellar medium which result from the limited spatial
The formation of pores by the process of coalescence at the photosphere is revealed by both remote observations ancl previous numerical simulations (???)..,"The formation of pores by the process of coalescence at the photosphere is revealed by both remote observations and previous numerical simulations \citep[]{vrabec1974,zwaan1985,cheung2010}."
 However. the mechanism that transfers (he magnetic [lux from the tachocline. which is believed to be the origin of the active region magnetic field. to the solar surface is still to be determined.," However, the mechanism that transfers the magnetic flux from the tachocline, which is believed to be the origin of the active region magnetic field, to the solar surface is still to be determined."
 To date. global scale simulations of the solar interior can not vel resolve individual flix tubes.," To date, global scale simulations of the solar interior can not yet resolve individual flux tubes."
 Here. we examine the evolution of the magnetic flux rope in the deep convection zone ancl the photospheric and coronal response to ils emergence.," Here, we examine the evolution of the magnetic flux rope in the deep convection zone and the photospheric and coronal response to its emergence."
 The horizontal flux rope at 2=—10 Mm. shown by Figure 2.. rises in (he central section due to the depletion of the density and upwelling convective flows.," The horizontal flux rope at $z = -10$ Mm, shown by Figure \ref{initrope}, rises in the central section due to the depletion of the density and upwelling convective flows."
 However. (he two ends of the central section are embedded in large-scale cownflows present in the convection zone when the flux rope is initiated at /=0:00:00.," However, the two ends of the central section are embedded in large-scale downflows present in the convection zone when the flux rope is initiated at $t = 0:00:00$."
 The downllows are illustrated by the blue isosurlaces and color contours in Figure 2.., The downflows are illustrated by the blue isosurfaces and color contours in Figure \ref{initrope}. .
 Panel (a) of Figure 4. shows the structure of u. on the c—z plane al /=4:50:00. when the downllows are still present in the convection zone al the two ends of (he emerged [ας rope.," Panel (a) of Figure \ref{y=0} shows the structure of $u_{z}$ on the $x-z$ plane at $t = 4:50:00$, when the downflows are still present in the convection zone at the two ends of the emerged flux rope."
 The region of the convective downflows in Panel (a) of Figure 4. appears in great. accordance with the black ancl green. contour lines indicating (he polarity of the pores., The region of the convective downflows in Panel (a) of Figure \ref{y=0} appears in great accordance with the black and green contour lines indicating the polarity of the pores.
 This consistency. between (he down flowing and magnetic concentrated regions suggests a causal relationship between the formation of the magnetic pores and the large-scale downllows., This consistency between the down flowing and magnetic concentrated regions suggests a causal relationship between the formation of the magnetic pores and the large-scale downflows.
 Figure 5. illustrates the temporal evolution of the 3-D magnetic field. colored bv the 4. value of the local plasma curing the rising of the central section of the flux rope.," Figure \ref{dipole} illustrates the temporal evolution of the 3-D magnetic field, colored by the $u_{z}$ value of the local plasma during the rising of the central section of the flux rope."
 The long-lasting. large-scale downflow. indicated by the blue color. crags down the (wo endpoints of the rising part and fixes them in (the deep convection zone. forming an QO-shape emerged flix rope within 2.5 hours.," The long-lasting, large-scale downflow, indicated by the blue color, drags down the two endpoints of the rising part and fixes them in the deep convection zone, forming an $\Omega$ -shape emerged flux rope within 2.5 hours."
 The cownflow maintains the pores and prevents the two pores of opposite polarities[rom separation or, The downflow maintains the pores and prevents the two pores of opposite polaritiesfrom separation or
between the lens and source. respectively.,"between the lens and source, respectively."
" The deflection angle for the light ray is given as follows where o, and o, are the positions of the binary system in the lens plane and A4, and Af are mass of the lenses.", The deflection angle for the light ray is given as follows where $\underline{\varrho}_{1}$ and $\underline{\varrho}_{2}$ are the positions of the binary system in the lens plane and $M_{1}$ and $M_{2}$ are mass of the lenses.
 Equation {11) as the lens equation is a fifth order equation and in general the solution is not trivial., Equation \ref{lense}) ) as the lens equation is a fifth order equation and in general the solution is not trivial.
 One of the possible solution for solving the lens equation is the inverse ray shooting method (Kayseretal.1986:Schneider&Wiess 1987).," One of the possible solution for solving the lens equation is the inverse ray shooting method \cite{kay86,sw87}."
. In this method we follow the position of the light ray that shoots from the observer to the lens plane. knowing the position of the lenses we can calculate the deflection angle and substituting in the lens equation results in the position of the source.," In this method we follow the position of the light ray that shoots from the observer to the lens plane, knowing the position of the lenses we can calculate the deflection angle and substituting in the lens equation results in the position of the source."
 We pixelize the source and the lens plane and for each light ray passing from the lens plane and hitting the source plane. we count the number of hits inside each pixel.," We pixelize the source and the lens plane and for each light ray passing from the lens plane and hitting the source plane, we count the number of hits inside each pixel."
 These numbers identify the magnification pattern in the source plane., These numbers identify the magnification pattern in the source plane.
 We use tree code method as we describe it later. for generating the image and the magnification of the source star.," We use tree code method as we describe it later, for generating the image and the magnification of the source star."
 In order to simplify our caleulation we take the dimensionless parameters in the lens equation., In order to simplify our calculation we take the dimensionless parameters in the lens equation.
" Let us define the overall Einstein radius as follows: We normalize the lens equation to this length scale. which results in: Where.=DifD. gílig.r=€/ReH and the deflection angle is given by: and j/=Mj;/CU,|Ale) or,=ofite."," Let us define the overall Einstein radius as follows: We normalize the lens equation to this length scale, which results in: where $\underline{x}={D_{l}}/{D_{s}}\times \underline{\eta}/{R_{E}}$, $\underline{r}=\underline{\xi}/R_{E}$ and the deflection angle is given by: and $\mu_i = M_i/(M_1+M_2)$, $\underline{r}_{i} =
\underline{\varrho}_{i}/ R_{E}$."
 We take a straight line for the path of the center of mass of the parent star and planet at the lens plane., We take a straight line for the path of the center of mass of the parent star and planet at the lens plane.
 Taking the mass of parent star larger than the mass of planet. the parent star follows approximately a straight line as follows: where vy is defined as the minimum impact parameter of source star from the center of the cartesian coordinate system. normalized to the Einstein radius. /o is time of impact parameter. and à is angle between .r-axis and the trajectory of the source star.," Taking the mass of parent star larger than the mass of planet, the parent star follows approximately a straight line as follows: where $u_{0}$ is defined as the minimum impact parameter of source star from the center of the cartesian coordinate system, normalized to the Einstein radius, $t_{0}$ is time of impact parameter, and $\alpha$ is angle between $x$ -axis and the trajectory of the source star."
 The rotation of the planet around the parent star makes an cycloid like pattern on the source plane which is given by: where à is the projection of the planet orbit on the lens plane normalized to the Einstein radius. z is the angular velocity of planet around the source star which can be obtained from the Kepler's third law: and e is the orbital radius of the planet. ? is the deviation of the normal vector to the orbital plane ofthe planet from our line of sight.," The rotation of the planet around the parent star makes an cycloid like pattern on the source plane which is given by: where $\tilde{a}$ is the projection of the planet orbit on the lens plane normalized to the Einstein radius, $\omega$ is the angular velocity of planet around the source star which can be obtained from the Kepler's third law: and $a$ is the orbital radius of the planet, $\delta$ is the deviation of the normal vector to the orbital plane of the planet from our line of sight."
 For the Hot Jupiters due to the tidal interaction of the planet and the parent star we set the eccentricity to zero and one angle is sufficient for describing the orbital plane deviation. .7 is angle between the trajectory of the source star and the projected major axis of the planet and y is initial phase of the planet.," For the Hot Jupiters due to the tidal interaction of the planet and the parent star we set the eccentricity to zero and one angle is sufficient for describing the orbital plane deviation, $\beta$ is angle between the trajectory of the source star and the projected semi-major axis of the planet and $\varphi$ is initial phase of the planet."
 In order to generate the light curve. we need the relative velocity of the binary lens with the parent star and companion planet.," In order to generate the light curve, we need the relative velocity of the binary lens with the parent star and companion planet."
" The relative transverse velocity of the source-observer line of sight with respect to the lens at the lens plane is given by (Kayseretal.1986): where ey. e, and e, are the two dimensional transverse velocities of the center of mass of the lens system. source and observer with respect to the line of sight respectively and Di£D. is the ratio of the distance of the lens to the source."," The relative transverse velocity of the source-observer line of sight with respect to the lens at the lens plane is given by \cite{kay86}: where $\underline{v_l}$, $\underline{v_s}$ and $\underline{v_o}$ are the two dimensional transverse velocities of the center of mass of the lens system, source and observer with respect to the line of sight respectively and $x=D_l/D_s$ is the ratio of the distance of the lens to the source."
 The velocity of the observer is obtained from the local measurements of the solar system in the Galactic frame., The velocity of the observer is obtained from the local measurements of the solar system in the Galactic frame.
 The velocity of the stars in the Bulge is given by the dispersion velocity in this structure and the velocity of the stars in the disk is obtained from the combination of the dispersion and global velocities of the stars (Binney&Tremaine1987)., The velocity of the stars in the Bulge is given by the dispersion velocity in this structure and the velocity of the stars in the disk is obtained from the combination of the dispersion and global velocities of the stars \cite{bin}.
. Since the lens is a binary system. that will rotate around the center of mass during the microlensing of the parent star and the companion planet.," Since the lens is a binary system, that will rotate around the center of mass during the microlensing of the parent star and the companion planet."
 For simplify in our calculation we fix the position of the binary system and obtain the relative motion of the source objects with respect to the rotating binary system., For simplify in our calculation we fix the position of the binary system and obtain the relative motion of the source objects with respect to the rotating binary system.
 The situation is similar to the studying of the motion of an object in rotating non-intertidal reference frame in the classical mechanics., The situation is similar to the studying of the motion of an object in rotating non-intertidal reference frame in the classical mechanics.
 In the reference frame of the binary system we do the following coordinate transformation for the position of the source object where © is the angular velocity of the binary lens.which is given by and αι is the apparent separation of the two lenses from each other and cis the deviation of the normal vector to the binary plane from the line of sight.," In the reference frame of the binary system we do the following coordinate transformation for the position of the source object where $\Omega$ is the angular velocity of the binary lens,which is given by and $d_\bot$ is the apparent separation of the two lenses from each other and $\psi$ is the deviation of the normal vector to the binary plane from the line of sight."
 For generating the light curve we should note that there are two source objects. the parent star and the planet.," For generating the light curve we should note that there are two source objects, the parent star and the planet."
" The total flux receiving by the observer then is the accumulation of the magnitied flux of each component (Han&Gould1996:GriestHu1992): where the 7, and £5, are the intrinsic flux of the parent star and the planet and 21, and 4, are the corresponding magnifications."," The total flux receiving by the observer then is the accumulation of the magnified flux of each component \cite{hg97,gh92}: where the $F_{\star}$ and $F_p$ are the intrinsic flux of the parent star and the planet and $A_\star$ and $A_p$ are the corresponding magnifications."
 Let us detine the ratio of the intrinsic flux of the planet to the flux of the parent star by 5={ην which is much smaller than one (i.e. =<< 1)., Let us define the ratio of the intrinsic flux of the planet to the flux of the parent star by $\varepsilon = F_p/F_\star$ which is much smaller than one (i.e. $\varepsilon\ll 1$ ).
 The total magnitication can be written as: For a typical case of the binary lens and a main sequence parent star with an Hot Jupiter companion. the trajectory of the source in the source plane with the corresponding caustic lines is shown in Figure (1)).," The total magnification can be written as: For a typical case of the binary lens and a main sequence parent star with an Hot Jupiter companion, the trajectory of the source in the source plane with the corresponding caustic lines is shown in Figure \ref{fig1}) )."
"the other molecules(IICN..IINC..SiO.. ΟΦ), but notΗν, which peaks in the south at the position of a 2| ppoiut source.","the other molecules, ), but not, which peaks in the south at the position of a 24 point source."
 Although this source is clearly ideutified as an iregion from the characteristic appearance of a 2| iuner bubble surrouuded by a ring of 5 eenission (e.g...?).. the detection of a hot core molecule identifies the location of the ceutral exciting source.," Although this source is clearly identified as an region from the characteristic appearance of a 24 inner bubble surrounded by a ring of 8 emission \citep[e.g.,][]{Watson:2008}, the detection of a hot core molecule identifies the location of the central exciting source."
 The chemical difference irafio] between the southern source sugeests either a different Iuuinosity for the exciting source or a different evolutionary state., The chemical difference ratio) between the southern source suggests either a different luminosity for the exciting source or a different evolutionary state.
 Figure 15 shows 00.011. a chump drawn fon the ΠΟΡΟ sirver catalog αμα classified as protostellar from the CLIMIPSE/AUPSCAL iuages due to the presence of 21 ppoiut sources within a dark extiuction feature without extended 8 or 214an eenission.," Figure \ref{ExampleProtostellar2} shows $-$ 00.411, a clump drawn from the HOPS survey catalog and classified as protostellar from the GLIMPSE/MIPSGAL images due to the presence of 24 point sources within a dark extinction feature without extended 8 or 24 emission."
 The spatial coincidence of the 21 ppoiut sources and the 8 eextiuctiou feature sugecsts that the 21 ppoiut sources are associated with the chump. aud the MALT90 pilot survey data confirms this association.," The spatial coincidence of the 24 point sources and the 8 extinction feature suggests that the 24 point sources are associated with the clump, and the MALT90 pilot survey data confirms this association."
 The Hiuteerated intensity contours trace the 5 eenission extinction feature., The integrated intensity contours trace the 8 emission extinction feature.
 There is ecluission at the same velocity at the position of the xiehtest 21 »poiut source., There is emission at the same velocity at the position of the brightest 24 point source.
 Since Ες is normally associated with outflow activity iu oxotostars (e.g.7).. a detection of this line at the same velocity as the ΟΠ) is strong evidence that the 21 »poiut source is associated with this chuup.," Since emission is normally associated with outflow activity in protostars \citep[e.g.,][]{Lopez-Sepulcre:2011}, a detection of this line at the same velocity as the clump is strong evidence that the 24 point source is associated with this clump."
 Figure 16 shows (322.668 00.038. a clump drawn ron the GLIAIPSE-Dark catalog and classified as quiescent from the GLIMPSE/MIPSGAL images due to the lack of 8 or 21 eenmission inside the 5 cextinetion feature.," Figure \ref{ExampleQuiescent} shows $-$ 00.038, a clump drawn from the GLIMPSE-Dark catalog and classified as quiescent from the GLIMPSE/MIPSGAL images due to the lack of 8 or 24 emission inside the 8 extinction feature."
 As a quiescent chuup iu the carly stages of evolution. this object displays less complex chemistry than clumps in more evolved stages with oulv the four main lines(ΧΟΠ.TING...WCO!.. aud HIICN)) detected.," As a quiescent clump in the early stages of evolution, this object displays less complex chemistry than clumps in more evolved stages with only the four main lines, and ) detected."
 The ünteerated iutensitv cussion shows two distinct peaks associated with two of the darkest 5 coxtinction features., The integrated intensity emission shows two distinct peaks associated with two of the darkest 8 extinction features.
 The velocity field of sshows that these two peaks are at very simular velocities (-GIlus + and -65.6 laws 1). strongly suggesting that both peaks are at the same distance aud that the entire extinction feature is a single plivsical object.," The velocity field of shows that these two peaks are at very similar velocities (-64 km $^{-1}$ and -65.6 km $^{-1}$ ), strongly suggesting that both peaks are at the same distance and that the entire extinction feature is a single physical object."
 We use the ? rotation curve to calculate a kincmatic distance for this chup: the near distance is £27 kpc and the far distance is 9.25 kpe., We use the \citet{Clemens:1985} rotation curve to calculate a kinematic distance for this clump; the near distance is 4.27 kpc and the far distance is 9.25 kpc.
 Because we see the clump as au extinction feature against the diffuse Calactic background. if is reasonable to assume that the near distance is correct.," Because we see the clump as an extinction feature against the diffuse Galactic background, it is reasonable to assume that the near distance is correct."
 The MALTI90 map therefore allows us (1) to identify which extinction features are likely a suele plysical object versus a chance projection and (2) to assign a distance which is useful for auv further study of this object., The MALT90 map therefore allows us (1) to identify which extinction features are likely a single physical object versus a chance projection and (2) to assign a distance which is useful for any further study of this object.
An aclequately broad dist size spectrum would then affect the grain-grain interactions bv changing the form of e...,An adequately broad dust size spectrum would then affect the grain-grain interactions by changing the form of $v_c$.
 We can evaluate the importance of this effect by caleulating ihe width of the dust spectrum. (Ar/7) required for the difference in headwind induced velocily to equal the velocity induced by the eddies which dominate dust-dust collisions in our model from Eq. 17.., We can evaluate the importance of this effect by calculating the width of the dust spectrum $\Delta \tau/\tau$ ) required for the difference in headwind induced velocity to equal the velocity induced by the eddies which dominate dust-dust collisions in our model from Eq. \ref{v2}.
 We therefore caleulate the minimum .Az/7 lor which a spectrum would influence our results., We therefore calculate the minimum $\Delta \tau/\tau$ for which a spectrum would influence our results.
 The lager the Av/r we calculate. the broader the spectrum our model can accommodate.," The larger the $\Delta \tau/\tau$ we calculate, the broader the spectrum our model can accommodate."
 For 0.5 AU <R« 8 AU and 1)!<a«107. we find that ihe minimum .Nr/7 lor which a spectrum would affect our results is 0.12. in regime 3.2.," For $0.5$ AU $<R<$ $8$ AU and $10^{-4}<\alpha<10^{-2}$, we find that the minimum $\Delta \tau/\tau$ for which a spectrum would affect our results is $0.12$, in regime $3.2$."
 For Epstein drag. this is also Ary/ry while for Stokes crag this implies Ary/ry=0.06.," For Epstein drag, this is also $\Delta r_d/r_d$ while for Stokes drag this implies $\Delta r_d/r_d=0.06$."
 Draine(2006) gives an observationally derived spectrum for small grains that deviates from our Gaussian., \citet{draine2006} gives an observationally derived spectrum for small grains that deviates from our Gaussian.
 However. for most of the planetesimal growth. the grains sizes (hal we model are much larger (han (he micron grain sizes in the Draine spectrum.," However, for most of the planetesimal growth, the grains sizes that we model are much larger than the micron grain sizes in the Draine spectrum."
 While larger scale erain-grain collisions will produce some detritus down to the micron scales. we cease to model the spectrum on (these scales once the bulk of the dust mass is predominately comprised of larger grains.," While larger scale grain-grain collisions will produce some detritus down to the micron scales, we cease to model the spectrum on these scales once the bulk of the dust mass is predominately comprised of larger grains."
 There are lew observational constraints on (he grain spectrum on scales much larger (han microns., There are few observational constraints on the grain spectrum on scales much larger than microns.
" This latter circumstance justifies our having pursued the simple ""dust of a single size al any one (ime approach herein.", This latter circumstance justifies our having pursued the simple “dust of a single size at any one time” approach herein.
 The benefit is that the basic physics can be identified at each stage of growth. the formalism is simple. aud meaningful constraints in erowth times can be ealeulated analvtically.," The benefit is that the basic physics can be identified at each stage of growth, the formalism is simple, and meaningful constraints in growth times can be calculated analytically."
 We have developed a simple model to estimate the effects of disc turbulence on planetesimal erowth We show that turbulence has (wo competing influences: (1) It increases (he collisional velocity of dust grains which increases their interaction [or growth. (, We have developed a simple model to estimate the effects of disc turbulence on planetesimal growth We show that turbulence has two competing influences: (1) It increases the collisional velocity of dust grains which increases their interaction for growth. (
2) It increases the velocity which determines the scale height of the dust laver in the disc which decreases the volume clensity lowering the interaction for growth.,2) It increases the velocity which determines the scale height of the dust layer in the disc which decreases the volume density lowering the interaction for growth.
 Since the growth rate of erains depends on the ratio of these two velocities. (he evolution of protoplanetesimal formation depends on the evolution of (his ratio.," Since the growth rate of grains depends on the ratio of these two velocities, the evolution of protoplanetesimal formation depends on the evolution of this ratio."
 Because the coupling of the gas to the dust evolves wilh grain size. (he ratio is not a constant.," Because the coupling of the gas to the dust evolves with grain size, the ratio is not a constant."
 Our work differs from previous studies bv explicitly incorporting the dynamical evolution of dust grain size and the dust settling and considering disces with and without dead zones., Our work differs from previous studies by explicitly incorporting the dynamical evolution of dust grain size and the dust settling and considering discs with and without dead zones.
 We identify the range of turbulent strength. measured by a. the range of dust sticking efficiency. measured by c. and (he disc radius range For which protoplanetesimal formation progresses (o (he gravitational instability phase on observtionally constrained (ime scales vr. D'Alessioetal. (2005))).," We identify the range of turbulent strength, measured by $\alpha$, the range of dust sticking efficiency, measured by $c$, and the disc radius range for which protoplanetesimal formation progresses to the gravitational instability phase on observtionally constrained time scales $(<10^6)$ yr, \citet{d'Alessio05}) )."
 The allowed ranges emerge [rom constraints on (1) the total, The allowed ranges emerge from constraints on (1) the total
orbit. determination setup was chosen.,orbit determination setup was chosen.
 The AMI values in that analysis were determined. in. the standard: orbit determination procedure at the AIUD. with fit ares as long as possible for a successful. that is defined. as leading to a small rms error. orbit determination.," The AMR values in that analysis were determined in the standard orbit determination procedure at the AIUB, with fit arcs as long as possible for a successful, that is defined as leading to a small rms error, orbit determination."
 The results are illustrated in reAM BR-LLAMB.., The results are illustrated in \\ref{LAMR-HAMR}.
. No general trend in the AMI variations could. be determined. for either LLAATR. or LAMIR objects., No general trend in the AMR variations could be determined for either HAMR or LAMR objects.
" The relative variations of the AMI, values of the LAMB objects were larger. than the AMI variations of the LLAALR values."," The relative variations of the AMR values of the LAMR objects were larger, than the AMR variations of the HAMR values."
 Phe AMI variations of the LAMIR objects were of the order of several 100 percent., The AMR variations of the LAMR objects were of the order of several 100 percent.
 All orbits were predicted and compared to additional observations of the same object. which were not used. for orbit. determination.," All orbits were predicted and compared to additional observations of the same object, which were not used for orbit determination."
 The additional observations were all checked via orbit determination. to ensure that they belong to the same object.," The additional observations were all checked via orbit determination, to ensure that they belong to the same object."
 refdüistances shows the angular distances between the predicted. cphemeris— and observations., \\ref{distances} shows the angular distances between the predicted ephemeris and observations.
 “Phe values ae averaged over alb distances SOdcays alter— orbit determination and their standard deviations serve as error refdistancesaa shows that lor object LOS241A. one orbit produces the largest’ distances of one degree.," The values are averaged over all distances days after orbit determination and their standard deviations serve as error \\ref{distances}a a shows that for object E08241A, one orbit produces the largest distances of one degree."
 This orbit does not show up prominently in the orbital parameter, This orbit does not show up prominently in the orbital parameter
In this paper we have addressed the question of whether dust cooling can lead to the fragmentation of low-metallicity star-forming clouds.,In this paper we have addressed the question of whether dust cooling can lead to the fragmentation of low-metallicity star-forming clouds.
 For this purpose we performed numerical simulations to follow the thermodynamical and chemical evolution of collapsing clouds., For this purpose we performed numerical simulations to follow the thermodynamical and chemical evolution of collapsing clouds.
" The chemical model included a primordial chemical network together with a description of dust evolution, where the dust temperature was calculated by solving self-consistently the thermal energy equilibrium We performed three sets of simulations, two at low resolution and one at high resolution (Table 1))"," The chemical model included a primordial chemical network together with a description of dust evolution, where the dust temperature was calculated by solving self-consistently the thermal energy equilibrium We performed three sets of simulations, two at low resolution and one at high resolution (Table \ref{tsim}) )."
" All simulations had an initial cloud mass of 1000 Mo, number density of 10? cm, and temperature of 300K. We tested two different metallicities (10Z; and 10-?Z5), and also the inclusion of small amounts of turbulent and rotational We found in all simulations that dust can effectively cool the gas, for number densities higher than 10!!'cm?."," All simulations had an initial cloud mass of 1000 $_{\odot}$, number density of $^5$ $^{-3}$, and temperature of 300K. We tested two different metallicities $^{-4} {\rm Z}_{\odot}$ and $^{-5} {\rm Z}_{\odot}$ ), and also the inclusion of small amounts of turbulent and rotational We found in all simulations that dust can effectively cool the gas, for number densities higher than $10^{11} \rm cm^{-3}$."
" An increase in metallicity implies a higher dust-to-gas ratio, and consequently stronger cooling by dust."," An increase in metallicity implies a higher dust-to-gas ratio, and consequently stronger cooling by dust."
" This is reflected in a lower temperature of the dense gas in the higher metallicity For the low resolution case, we tested the effect of adding turbulence and rotation."," This is reflected in a lower temperature of the dense gas in the higher metallicity For the low resolution case, we tested the effect of adding turbulence and rotation."
" These diminish the infall velocity, leading to different fluid elements undergoing different amounts of compressional heating."," These diminish the infall velocity, leading to different fluid elements undergoing different amounts of compressional heating."
" This lack of heating allows the gas to reach a lower We found that the transport of angular momentum to smaller scales lead to the formation of a disk-like structure, which then fragmented into a number of low mass We conclude that the dust is already an efficient coolant even at metallicities as low as 107? or 107Z;, in agreement with previous works (Clarketal,2008;Omukaial.,2006,2008).."," This lack of heating allows the gas to reach a lower We found that the transport of angular momentum to smaller scales lead to the formation of a disk-like structure, which then fragmented into a number of low mass We conclude that the dust is already an efficient coolant even at metallicities as low as $^{-5}$ or $^{-4}Z_{\odot}$, in agreement with previous works \citep{2008ApJ...672..757C, 2010ApJ...722.1793O, 2002ApJ...571...30S, 2006MNRAS.369.1437S, 2006ApJ...642L..61T, 2008ApJ...676L..45T}."
 Our results support the idea that dust cooling can play an role in the of molecular clouds and theimportant evolution of the stellar, Our results support the idea that dust cooling can play an important role in the fragmentation of molecular clouds and the evolution of the stellar
 Our results support the idea that dust cooling can play an role in the of molecular clouds and theimportant evolution of the stellarf, Our results support the idea that dust cooling can play an important role in the fragmentation of molecular clouds and the evolution of the stellar
 Our results support the idea that dust cooling can play an role in the of molecular clouds and theimportant evolution of the stellarfr, Our results support the idea that dust cooling can play an important role in the fragmentation of molecular clouds and the evolution of the stellar
 Our results support the idea that dust cooling can play an role in the of molecular clouds and theimportant evolution of the stellarfra, Our results support the idea that dust cooling can play an important role in the fragmentation of molecular clouds and the evolution of the stellar
 Our results support the idea that dust cooling can play an role in the of molecular clouds and theimportant evolution of the stellarfrag, Our results support the idea that dust cooling can play an important role in the fragmentation of molecular clouds and the evolution of the stellar
 Our results support the idea that dust cooling can play an role in the of molecular clouds and theimportant evolution of the stellarfragm, Our results support the idea that dust cooling can play an important role in the fragmentation of molecular clouds and the evolution of the stellar
 Our results support the idea that dust cooling can play an role in the of molecular clouds and theimportant evolution of the stellarfragme, Our results support the idea that dust cooling can play an important role in the fragmentation of molecular clouds and the evolution of the stellar
 Our results support the idea that dust cooling can play an role in the of molecular clouds and theimportant evolution of the stellarfragmen, Our results support the idea that dust cooling can play an important role in the fragmentation of molecular clouds and the evolution of the stellar
 Our results support the idea that dust cooling can play an role in the of molecular clouds and theimportant evolution of the stellarfragment, Our results support the idea that dust cooling can play an important role in the fragmentation of molecular clouds and the evolution of the stellar
 Our results support the idea that dust cooling can play an role in the of molecular clouds and theimportant evolution of the stellarfragmenta, Our results support the idea that dust cooling can play an important role in the fragmentation of molecular clouds and the evolution of the stellar
 Our results support the idea that dust cooling can play an role in the of molecular clouds and theimportant evolution of the stellarfragmentat, Our results support the idea that dust cooling can play an important role in the fragmentation of molecular clouds and the evolution of the stellar
 Our results support the idea that dust cooling can play an role in the of molecular clouds and theimportant evolution of the stellarfragmentati, Our results support the idea that dust cooling can play an important role in the fragmentation of molecular clouds and the evolution of the stellar
 Our results support the idea that dust cooling can play an role in the of molecular clouds and theimportant evolution of the stellarfragmentatio, Our results support the idea that dust cooling can play an important role in the fragmentation of molecular clouds and the evolution of the stellar
 Our results support the idea that dust cooling can play an role in the of molecular clouds and theimportant evolution of the stellarfragmentation, Our results support the idea that dust cooling can play an important role in the fragmentation of molecular clouds and the evolution of the stellar
"where ng; aud aj; are the uuuboer deusity of molecular hnwvdrogen and the total uunuber density in cell /j respectively, í(osnd y are cell indices in the + aud RB directions. and dV}; is the volume of cell 47.","where $n_{{\rm H_2},ij}$ and $n_{ij}$ are the number density of molecular hydrogen and the total number density in cell $ij$ respectively, $i$ and $j$ are cell indices in the $z$ and $R$ directions, and $dV_{ij}$ is the volume of cell $ij$."
 This equation is valid since the only moment on the exid originated in the jet. and since the simulations are stopped before any eas flows off the eril.," This equation is valid since the only momentum on the grid originated in the jet, and since the simulations are stopped before any gas flows off the grid."
 Note that we ouly consider uonmentuni trausferred to ambient molecules because we we onlv interested in how efficient YSO jets are at accelerating molecules. not atoms.," Note that we only consider momentum transferred to ambient molecules because we are only interested in how efficient YSO jets are at accelerating molecules, not atoms."
" TWis we ignore albicut uolecules which have been dissociated in the acceleration IEOCCSS,", Thus we ignore ambient molecules which have been dissociated in the acceleration process.
 Table 2 shows the fraction of momentum iu ambicw nolecules for all the sinulatious after 300 vrs., Table \ref{fractions} shows the fraction of momentum in ambient molecules for all the simulations after 300 yrs.
 For completeness we also show J£. the total fraction of nonientun transterred to ambient eas. whether molecular or atonic.," For completeness we also show ${\cal F}_{\rm total}$, the total fraction of momentum transferred to ambient gas, whether molecular or atomic."
" The first interesting point to note fom Table 2 is that he amount of momentum residing iu ambicut molecules in these simulations is typically an order of magnitude ess thai the total momentum contaimed on the οτι,", The first interesting point to note from Table \ref{fractions} is that the amount of momentum residing in ambient molecules in these simulations is typically an order of magnitude less than the total momentum contained on the grid.
" Noο, however. iow significant amounts of niomoeutunm are Leisferred. to t1e züubient mediumwhole. especialA in those cases where the jet deusitv matches that of its euvironnmient."," Note, however, how significant amounts of momentum are transferred to the ambient medium, especially in those cases where the jet density matches that of its environment."
 This is as oue would expect., This is as one would expect.
 What is perhaps surprising at first is the low efficiency of momentum transfer to ambicut eas that remains din molecular form in the post-bow shock zone., What is perhaps surprising at first is the low efficiency of momentum transfer to ambient gas that remains in molecular form in the post-bow shock zone.
" Comparison between Zi and Fy, for inodels A aud C and models D aud C clearly shows that the imonmeutuni transfer effiiiencwv from the jet to the aubicut media with iucreasing deusitv.", Comparison between ${\cal F}_{\rm total}$ and ${\cal F}_{\rm H_2}$ for models A and C and models B and G clearly shows that the momentum transfer efficiency from the jet to the ambient medium with increasing density.
 This result is particularly marked in the case of post-shock abient molecules., This result is particularly marked in the case of post-shock ambient molecules.
 Although further sinulatious should be performed to confrin this fineine. it is physically plausible.," Although further simulations should be performed to confirm this finding, it is physically plausible."
 Cooling causes the bow shock to be narrower niniore aerodyvuiuuic)thau in the adiaatic case. thus reducing its cross-sectional area.," Cooling causes the bow shock to be narrower more aerodynamic) than in the adiabatic case, thus reducing its cross-sectional area."
 Owiously this leads to a reduction in rate at which momentum is transferred ron fie jet to its surroundings., Obviously this leads to a reduction in rate at which momentum is transferred from the jet to its surroundings.
 The fact that the effect is nore marked for post-shock amveut uolecules mist reflect changes in the shape of the bow (as opposed. to πο clanees d its cross sectional area) with increased cooling., The fact that the effect is more marked for post-shock ambient molecules must reflect changes in the shape of the bow (as opposed to pure changes in its cross sectional area) with increased cooling.
 Since we are simmlating svstenis here which are xobablv of low deusitv m comparison to typical YSO jets. our results sueecst that radiative bow shocks. from at least heavy and equal density jets (with respect o the environment). are not very good at accelerating aubieut uolecules without causing dissociation.," Since we are simulating systems here which are probably of low density in comparison to typical YSO jets, our results suggest that radiative bow shocks, from at least heavy and equal density jets (with respect to the environment), are not very good at accelerating ambient molecules without causing dissociation."
 This result also x)uts to the fact that iu he case of such jets. the jet nay carry muuch more momentum than one might jdvelv estimate based on a rough balance with the moimeutum in any associated observed molecular flow.," This result also points to the fact that in the case of such jets, the jet may carry much more momentum than one might naively estimate based on a rough balance with the momentum in any associated observed molecular flow."
 We now turn fto differences in the efficiency of moment trausfer in pulsed versus steady jets., We now turn to differences in the efficiency of momentum transfer in pulsed versus steady jets.
 The topic of differences iu οὐταπο rates will be discussed more fully in 83.5., The topic of differences in entrainment rates will be discussed more fully in 3.5.
" rettau,,olshousgrey scaleplotsofthedistributionof τα andofje", \\ref{tau_mol} shows grey-scale plots of the distribution of $|\vec{u}|$ and of jet gas for models C $\frac{v_1}{v_0}=0$ )
The data-set. used in (he present work (the same as in D10) consists of a sample of 4x90sec images acquired in (he FGOGW (V) and 4x90sec images in FSItW filters obtained wilh the Advanced. Camera for Survevs (ACS: GO-I10775. PI: Sarajedini). complemented with 2x1100sec and 2x1200sec images in F606W ancl 2xH100sec and 2x1200sec images obtained with the Field Planetary Camera 2 (WEDC?: GO-6113. PI: Paresce) on board the Ilubble Space Telescope.,"The data-set used in the present work (the same as in B10) consists of a sample of $4\times90sec$ images acquired in the F606W $V$ ) and $4\times90sec$ images in F814W filters obtained with the Advanced Camera for Surveys (ACS; GO-10775, PI: Sarajedini), complemented with $2\times1100sec$ and $2\times1200sec$ images in F606W and $2\times1100sec$ and $2\times1200sec$ images obtained with the Field Planetary Camera 2 (WFPC2; GO-6113, PI: Paresce) on board the Hubble Space Telescope."
 The ACS data-set samples the cluster central regions. while the WFDPC? one covers an area located between one and two hall-mass radii (see Figure 1)).," The ACS data-set samples the cluster central regions, while the WFPC2 one covers an area located between one and two half-mass radii (see Figure \ref{map}) )."
" The detailed description of the data reduction. photometric and astrometric solution procedures is given in DIO and the sample used in the present analvsis contains (lie szune ""bona-ide"" stars selected on the basis of the quality of the point-spread-Dunction filling (asDAOPIIOTIIsharpnessparameter:Stetson 1987)."," The detailed description of the data reduction, photometric and astrometric solution procedures is given in B10 and the sample used in the present analysis contains the same “bona-fide” stars selected on the basis of the quality of the point-spread-function fitting \citep[as measured by the
 DAOPHOTII sharpness parameter;][]{stet87}."
. The CMDs of the two data-sets are shown in Figure 2.., The CMDs of the two data-sets are shown in Figure \ref{cmd}.
 Stars brighter than /=16 and J=19.5 are saturated in the ACS and WEPC? samples. respectively.," Stars brighter than $I=16$ and $I=19.5$ are saturated in the ACS and WFPC2 samples, respectively."
 DIO also performed a detailed photometric completeness study. based on artificial star experiments. where artificial stars were added to the original FLT frames and the whole data reduction procedure was repeated.," B10 also performed a detailed photometric completeness study, based on artificial star experiments, where artificial stars were added to the original FLT frames and the whole data reduction procedure was repeated."
 From the resulting catalogue. listing the input and output. positions and magnitudes for more (han 500.000 artificial stars. DIO estimated that the photometric completeness drops below al J~22.5 in the innermost region of the cluster. and al 7—25 for the WEPC2 data-set.," From the resulting catalogue, listing the input and output positions and magnitudes for more than 500,000 artificial stars, B10 estimated that the photometric completeness drops below at $I\sim 22.5$ in the innermost region of the cluster, and at $I\sim 25$ for the WFPC2 data-set."
 In order to estimate the binary. fraction of MIO. we followed the method extensively described in Bellazzinietal.(2002) and Sollimaetal.(2007.herealter901)..," In order to estimate the binary fraction of M10, we followed the method extensively described in \citet{bell02} and \citet[][hereafter
 S07]{sol07}."
 The basic idea is (hal (he magnitude of a binary svstem corresponds to the Iuminositv of the primary (ore massive) star. increased by the contribution of the companion of an amount that depends on the mass ralio of the (wo components (¢= M3/M4).," The basic idea is that the magnitude of a binary system corresponds to the luminosity of the primary (more massive) star, increased by the contribution of the companion of an amount that depends on the mass ratio of the two components $q=M_2/M_1$ )."
 In fact. since the stars along the MS follow a mass-Inminositv relation. (he luninosity of a binary can be written in terms of (he mass ratio of the two components.," In fact, since the stars along the MS follow a mass-luminosity relation, the luminosity of a binary can be written in terms of the mass ratio of the two components."
 By definition. 0«q<1 andlor g=1 (equal-mass binary) the svstem appears 0.75 magnitudes brighter (han the single component. while ihe luminosity enhancement decreases lor decreasing q.," By definition, $0<q\le 1$ andfor $q=1$ (equal-mass binary) the system appears $\sim 0.75$ magnitudes brighter than the single component, while the luminosity enhancement decreases for decreasing $q$ ."
 The spanning of all the possible, The spanning of all the possible
evolutionary models. as an extra check ou our basic inodel(& rofseciMainu-Sequeuce-Collisiou-Tiiie)).,"evolutionary models, as an extra check on our basic model \\ref {sec:Main-Sequence-Collision-Time}) )."
 Iu PARAMETERSDENSILYreferas CM ΣΠ μμ μμ πι TI.(9).ομυς AND STELLARAN {μαμα RADIUS (42) FOR oesWDs aunANDsofdusten, In \\ref{gas_ICM} we discuss how the ejected material from a stellar collision interacts with the ICM and how it can clear signatures of dust emission.
i feonclusion.., We conclude in \\ref{conclusion}.
 We define a collision between two stars with radi Ry aud Re to occur whenever their distance dRy|Ro., We define a collision between two stars with radii $R_{1}$ and $R_{2}$ to occur whenever their distance $d\leq R_{1}+R_{2}$.
" The: average local collision- time: Tip(1.2)(0) for: oue star of] type ""1 to collide with a star of type 72 can be written as (compare to Binney Tremaine 1987 their eq."," The average local collision time $T_{\rm coll}^{(1,2)}(r)$ for one star of type “1” to collide with a star of type “2” can be written as (compare to Binney Tremaine 1987 their eq."
 8-122) where vy. is the nuniber deusitv of field stir 727 and stars of type l. Mq» their masses. and 6 the one-dimensional velocity dispersion (assunüug a Maxwellian velocity distribution for both species with c(r)-—VIVE |.05(70)2)/2).," 8-122) where $n_{1,2}$ is the number density of field stars “2” and stars of type “1”, $M_{1,2}$ their masses, and $\sigma$ the one-dimensional velocity dispersion (assuming a Maxwellian velocity distribution for both species with $\sigma(r)=\sqrt{(\sigma_1(r)^2+\sigma_2(r)^2)/2}$ )."
 To get the total umuber of collisions per uuit time in the cluster between these two species eq.," To get the total number of collisions per unit time in the cluster between these two species, eq."
 Lis inteerated over the whole cluster. where ris the radial position in the cluster.," \ref{eq:local-coll-time}
 is integrated over the whole cluster, where $r$ is the radial position in the cluster."
 Iu order to account for a continuous stellar iuass spectruni and the mass-radius relationship of stars. we take local averages Ryote) aud ος) at position r.," In order to account for a continuous stellar mass spectrum and the mass-radius relationship of stars, we take local averages $R_{1,2}(r)$ and $M_{1,2}(r)$ at position $r$."
 We find that in the N-body model for MIS these profiles. as well as yer). can be well represented bv. power-laws over a sufficicutly large range of (O25pe«r<2pc.," We find that in the N-body model for M15 these profiles, as well as $n_{1,2}(r)$, can be well represented by power-laws over a sufficiently large range of $0.025\,{\rm pc}<r<2\,{\rm pc}$."
 Tusicle of 0.025pe there are almost no MSSs. while outside of zLpe the contribution of the integrand iu eq.," Inside of $0.025\, {\rm pc}$ there are almost no MSSs, while outside of $\approx1\,{\rm pc}$ the contribution of the integrand in eq."
 2 becomes rapidly negligible., \ref{eq:totat-coll-rate} becomes rapidly negligible.
 We do not cousider collisions between MSSs and NSs as the NS reteution fraction in GC's is expected to be low (Pfalil Rappaport 2001: Dull et al., We do not consider collisions between MSSs and NSs as the NS retention fraction in GCs is expected to be low (Pfahl Rappaport 2001; Dull et al.
 1997)., 1997).
 We also do not consider collisions betweeu eqauts aud AISSs as the escape velocity at the surface of a eiut. and even more so the expected cucrey of the ejected material. is an order of magnitude lower than for AISSs.," We also do not consider collisions between giants and MSSs as the escape velocity at the surface of a giant, and even more so the expected energy of the ejected material, is an order of magnitude lower than for MSSs."
 For simplicity we choose a constant ¢=11kins as 7 does not vary ich within Lpc (Eas . conrare Dull et al.," For simplicity we choose a constant $\sigma=11\, 
{\rm km\, s}^{-1}$, as $\sigma$ does not vary much within $1\, {\rm pc}$ $\pm 1\, {\rm km\, s}^{-1}$ ; compare Dull et al."
 1997) and also agrees with the value obtained by MeNiimara Diimugardt (2001) for MI5 for a similar region (r«0.5z(Spec)., 1997) and also agrees with the value obtained by McNamara Baumgardt (2004) for M15 for a similar region $(r<0.3'\approx 0.8\rm{ pc})$.
 The slight variatious within Lpe are accounted for in the error estimates of the collision rates.," The slight variations within $1\, {\rm pc}$ are accounted for in the error estimates of the collision rates."
 With all quautities given as power-laws. we solve eq.," With all quantities given as power-laws, we solve eq."
 2 analytically.," \ref{eq:totat-coll-rate}
 analytically."
 Our calculations are based ou the results of N-body simulations by Batineardt et ((2003). which were scaled to ft the velocity dispersion profile of M15 in McNamara et ((2001).," Our calculations are based on the results of $N$ -body simulations by Baumgardt et (2003), which were scaled to fit the velocity dispersion profile of M15 in McNamara et (2004)."
 Their model consisted of mitiallv. 130.072 stars with a realistic mass spectrum. and included a treatineut of stellay evolution aud the Galactic tidal field.," Their model consisted of initially $130,072$ stars with a realistic mass spectrum, and included a treatment of stellar evolution and the Galactic tidal field."
 They also take iuto accouut velocity kicks iurparted to NSs at birth aud consider two extreme cases. one where all NSs are retained. aud one where all NSs ire removed from the cluster.," They also take into account velocity kicks imparted to NSs at birth and consider two extreme cases, one where all NSs are retained, and one where all NSs are removed from the cluster."
 Here we oulv consider the latter case. since. as mentioned before. the actual NS retention fraction is expected to be very low.," Here we only consider the latter case, since, as mentioned before, the actual NS retention fraction is expected to be very low."
 Tn Table 1 the fit parameters for o. R. R and AL foy WDs and AISSs in MIS are shown.," In Table \ref{tab:Parameters-fits} the fit parameters for $n$, $R$, $R^2$ and $M$ for WDs and MSSs in M15 are shown."
 As can be seen. through niass scerceation. MSSs are amore abundant outside lpe while the more massive WDs dominate the central 0.75pe where collisious are most likely to happen.," As can be seen, through mass segregation, MSSs are more abundant outside $1\,{\rm pc}$ while the more massive WDs dominate the central $0.75\,{\rm pc}$ where collisions are most likely to happen."
 As a consequence. we should expect more collisions between WDs and AISSs than between MSSs.," As a consequence, we should expect more collisions between WDs and MSSs than between MSSs."
 From eq. 2..," From eq. \ref{eq:totat-coll-rate},"
" we obtain ONGALSWpdf=(2m1).10ESE auc ON,ollALSALESdt—(1X1)«105NYl where NollXY is the number of collisions between No aud Y."," we obtain $dN_{coll,MS-WD}/dt=(2\pm1)\times10^{-7}\,{\rm yr}^{-1}$ and $dN_{coll,MS-MS}/dt=(4\pm1)\times10^{-8}\,{\rm yr}^{-1}$, where $N_{coll,X-Y}$ is the number of collisions between $X$ and $Y$."
 It follows that. eiven the current state of MID. we expect one collision every (522)<108s between a WD aud a MSS aud every (841)ςἸθvr a collision between two AISSs. resultiue iu oue collision every (12322)«10°vy that releases lieh-velocity eas into the ICAL," It follows that, given the current state of M15, we expect one collision every $(5\pm2)\times10^{6}\,{\rm yr}$ between a WD and a MSS and every $(3\pm1)\times10^{7}\,{\rm yr}$ a collision between two MSSs, resulting in one collision every $(4\pm2)\times10^{6} 
\,{\rm yr}$ that releases high-velocity gas into the ICM."
 It is rather remarkable low closely this timescale coincides with the estimated ICAL dust lifetime. sugecsting a direct connection between dust clearing aud stellar collisions.," It is rather remarkable how closely this timescale coincides with the estimated ICM dust lifetime, suggesting a direct connection between dust clearing and stellar collisions."
 Using a simular approach. we estimate the DS formation rate. defiuiug BSs as two merged MSSs with a combined mass >LAL... significautly larger than the MS turn-off mass (0.58M ..).," Using a similar approach, we estimate the BS formation rate, defining BSs as two merged MSSs with a combined mass $>1\,{\rm M}_{\odot}$, significantly larger than the MS turn-off mass $0.8\,{\rm M}_{\odot}$ )."
 After binnine all MSSs iuto (LIAL. bins. we determine the collision rate between all mass bins with combined mass >LAL...," After binning all MSSs into $0.1\,{\rm M}_{\odot}$ bins, we determine the collision rate between all mass bins with combined mass $>1\,{\rm M}_{\odot}$."
 This also allows us to cletermune the expected mass spectrum for DSs for conmparisou with future observations., This also allows us to determine the expected mass spectrum for BSs for comparison with future observations.
 We obtain a total collision rate of (6.L—£0.7)«10.%AlyyI which. together with the 6—7 DSs observed im MID. niplies an average BS lifetime of about 1Cx.," We obtain a total collision rate of $(6.4\pm0.7)\times10^{-3}\,{\rm 
Myr}^{-1}$ which, together with the $6-7$ BSs observed in M15, implies an average BS lifetime of about $1\,{\rm Gyr}$."
 This is also consistent with recent BS evolution models (c.e.. Leigh et 22007: Sills et 22001).," This is also consistent with recent BS evolution models (e.g., Leigh et 2007; Sills et 2001)."
 Towever. we note that this is certainly an upper luit. given that the presence of binaries would increase the formation rate through binary mergers aud resonant interactions (Freeeau et 220014: Alapelli et 22001).," However, we note that this is certainly an upper limit, given that the presence of binaries would increase the formation rate through binary mergers and resonant interactions (Fregeau et 2004; Mapelli et 2004)."
 For example. for a Pluuuner sphere with a Iroupa mass function raugine from 0.3 to 3.0ΔΕ. aud a binary fraction of 30%. the rate of collisions mediated by binaryv-sinegle aud binary-binary interactions can be l order of magnitude larecr than from sinele-sinele interactions (Chatterjee et 22008).In Figure 1 the mass distribution for BSs is shown.," For example, for a Plummer sphere with a Kroupa mass function ranging from $0.3$ to $3.0\,\rm{M_\odot}$ and a binary fraction of $30\%$, the rate of collisions mediated by binary-single and binary-binary interactions can be $\sim 1$ order of magnitude larger than from single-single interactions (Chatterjee et 2008).In Figure \ref{fig:bs_mass} the mass distribution for BSs is shown."
 As expected it decreases for higher mass DSs. since the umber deusity for the lower mass MSSs is wach higher compared to that for the close to turn-off AISSs.," As expected it decreases for higher mass BSs, since the number density for the lower mass MSSs is much higher compared to that for the close to turn-off MSSs."
which relates the observed proper-motion dispersion to the observed. dispersion aloug the expected. correlation.,which relates the observed proper-motion dispersion to the observed dispersion along the expected correlation.
" Assuming any deviation from the line to represents the total error of the data point. an estimate of ge, cau be obtained by the dispersion of data points perpeucdicularly to tlie line: Top-right panel of Fig."," Assuming any deviation from the line to represents the total error of the data point, an estimate of $\sigma_{\rm err}$ can be obtained by the dispersion of data points perpendicularly to the line: Top-right panel of Fig."
 7 shows the histograms of the :-displacement dispersions along (filled circles) aud perpeudicular (open circles) to the expected. correlations., \ref{fig:ipm} shows the histograms of the $x$ -displacement dispersions along (filled circles) and perpendicular (open circles) to the expected correlations.
 Poisson error bars aud Gaussian best fits are also shown., Poisson error bars and Gaussian best fits are also shown.
 Standard deviations σι and ao are computed as the 68.27! percentile of the distribution residuals around their median value., Standard deviations $\sigma_{\parallel}$ and $\sigma_{\perp}$ are computed as the $^{\rm th}$ percentile of the distribution residuals around their median value.
 The bottom-right panel shows the same [or gy-axis displacemeut clispersious., The bottom-right panel shows the same for $y$ -axis displacement dispersions.
 Taking the average of σι and o_ from the displacements along randy. we had σι20.50 mas ando20.12 mas.," Taking the average of $\sigma_{\parallel}$ and $\sigma_{\perp}$ from the displacements along $x$ and $y$ , we had $\sigma_{\parallel}\simeq0.50$ mas and $\sigma_{\perp}\simeq 0.15$ mas."
 By using the previous equations L.. 3 aud L. we obtained an intrinsic dispersiou of vigi=0.860.27 mas vr.| which is in remarkable agreement with the value op=0.83250.07 mas | measured by Anderson van der Marel (201)) using a time baseline almost 9 times larger CLOT years 1172 days!)," By using the previous equations \ref{eq1}, \ref{eq3} and \ref{eq4}, we obtained an intrinsic dispersion of $\sigma_{\rm intr} =
0.86 \pm 0.27$ mas $^{-1}$, which is in remarkable agreement with the value $\sigma_{\mathrm{1-D}} = 0.83\pm0.07$ mas $^{-1}$ measured by Anderson van der Marel (2010) using a time baseline almost 9 times larger (4.07 years 172 days!),"
 aud more images., and more images.
 This result is even more astonishing if we consider that we did not use local transformations (see. e.g.. Bedin et 22003: Ancerson et 22006. Anderson vau der Marel 2010) which would further reduce systematic residuals in the GD solution. as well as auy correction [or breathiiο Gwhich cau introduce small low-order terms) or charge-trausfer iuelficieucy. Gwhichli is already plaguing this new camera: see Figure §)).," This result is even more astonishing if we consider that we did not use local transformations (see, e.g., Bedin et 2003; Anderson et 2006, Anderson van der Marel 2010) which would further reduce systematic residuals in the GD solution, as well as any correction for breathing (which can introduce small low-order terms) or charge-transfer inefficiency (which is already plaguing this new camera; see Figure \ref{fig:cti}) )."
 As a [inal external check on the achieved accuracy. we can assume the uncertainties on £1 to cancel out and £2 aud. £3 to equally contribute to a (=Vστο+gps=2x op).," As a final external check on the achieved accuracy, we can assume the uncertainties on $E1$ to cancel out and $E2$ and $E3$ to equally contribute to $\sigma_\perp$ $=\sqrt{\sigma_{E2}^2+\sigma_{E3}^2}=\sqrt{2}\times\sigma_{E}$ )."
 Having ~9 exposures per epoch. we cau infer a 1-D positional accuracy of 0.008 pixels. ~0.3 mas V2). which is consistent with the value reported in Fig. 5..," Having $\sim$ 9 exposures per epoch, we can infer a 1-D positional accuracy of 0.008 pixels, $\sim$ 0.3 mas $\sqrt{9-1}\times\sigma_\perp/\sqrt{2}$ ), which is consistent with the value reported in Fig. \ref{fig:res}."
 Ht should also be noted that. at this level of accuracy. there is a considerable interplay between the derived PSF models aud the GD solution. which mieht play some role on the achievable astrometric precision.," It should also be noted that, at this level of accuracy, there is a considerable interplay between the derived PSF models and the GD solution, which might play some role on the achievable astrometric precision."
 On account of breathing and other phenomena. the distortion solution is not perfectly stable over tune.," On account of breathing and other phenomena, the distortion solution is not perfectly stable over time."
 The impact of breathing is not well enough understood to predict its inpact on the distortion. so the best we can hope to achieve is an average distortiou solution aud a seuse of how stable the solution is about this average.," The impact of breathing is not well enough understood to predict its impact on the distortion, so the best we can hope to achieve is an average distortion solution and a sense of how stable the solution is about this average."
 It is typically the low-order terms that are the most time-variable. so it made sense above to coustruct the best siugle-chip-based solution first aud ouly later to consider the less accurate larger-seale terms that relate the two chips to a common frame.," It is typically the low-order terms that are the most time-variable, so it made sense above to construct the best single-chip-based solution first and only later to consider the less accurate larger-scale terms that relate the two chips to a common frame."
 We do that here with the uuderstaudiug. that for the highest-precision dillerential astrometry. it is always best to perform the measurements as locally as possible. provided that there are an adequate uumber of relereuce stars.," We do that here with the understanding, that for the highest-precision differential astrometry, it is always best to perform the measurements as locally as possible, provided that there are an adequate number of reference stars."
 Some projects. however havelew reference objects aud require knowledge," Some projects, however havefew reference objects and require knowledge"
"The highest number statistic is provided by the study of RBGO09, and when compared with this study. the K-S test yields a probability of that the clump mass distributions in G304.74 and the other IRDCs are drawn from the same parent distribution.","The highest number statistic is provided by the study of RBG09, and when compared with this study, the K-S test yields a probability of that the clump mass distributions in G304.74 and the other IRDCs are drawn from the same parent distribution."
 This probability drops significantly when smaller samples are used in the test (Table 8.. Col. (," This probability drops significantly when smaller samples are used in the test (Table \ref{table:KS}, Col. ("
4)).,4)).
 Moreover. according to the K-S test. there is a probability (Diyas= 0.001) that the RBGO9 and RJSO6 clump masses represent the subsamples of the same underlying parent distribution.," Moreover, according to the K-S test, there is a probability $D_{\max}=0.001$ ) that the RBG09 and RJS06 clump masses represent the subsamples of the same underlying parent distribution."
 For this test. clump masses from RBGO9 were also multiplied by 0.8 to compare with the RJSO6 masses which were based on the value Kjamm=0.1 nr !.," For this test, clump masses from RBG09 were also multiplied by 0.8 to compare with the RJS06 masses which were based on the value $\kappa_{\rm 1.2mm}=0.1$ $^2$ $^{-1}$ ."
 For the clump masses between ~30 and 3000 Meo. RBGO9 derived an IRDC clump mass spectrum with a slope of a=€ 1.760.05. which is consistent with the mass functions derived for high-mass star-forming regions. and also resembles the mass function of Galactic stellar clusters (see RBGO9 and references therein).," For the clump masses between $\sim30$ and 3000 $_{\sun}$, RBG09 derived an IRDC clump mass spectrum with a slope of $\alpha=1.76\pm0.05$ , which is consistent with the mass functions derived for high-mass star-forming regions, and also resembles the mass function of Galactic stellar clusters (see RBG09 and references therein)."
 Note. however. that RBGO9 merged all their clumps into a single mass function. whereas we have used only starless clumps in deriving the cumulative mass functions.," Note, however, that RBG09 merged all their clumps into a single mass function, whereas we have used only starless clumps in deriving the cumulative mass functions."
 RJSO6 found a Salpeter-like (aw=2.35: Salpeter 1955)) mass function for their cold IRDC clumps (a=2.1+0.4 at Mz100 Mo)., RJS06 found a Salpeter-like $\alpha=2.35$; \cite{salpeter1955}) ) mass function for their cold IRDC clumps $\alpha=2.1\pm0.4$ at $M\gtrsim100$ $_{\sun}$ ).
 The IRDC clump mass spectra derived by RJSO6 and RBGO9 are comparable to those predicted by turbulent fragmentation models (see Sect., The IRDC clump mass spectra derived by RJS06 and RBG09 are comparable to those predicted by turbulent fragmentation models (see Sect.
 6.7 and references therein)., 6.7 and references therein).
 In addition to the clump mass distribution. 1t is also useful to determine how clumps are spatially distributed within the cloud in order to unveil the presence of a possible preferred length-scale of fragmentation (e.g.. Munozetal. 2007)).," In addition to the clump mass distribution, it is also useful to determine how clumps are spatially distributed within the cloud in order to unveil the presence of a possible preferred length-scale of fragmentation (e.g., \cite{munoz2007}) )."
 For this purpose. we determined the clump-separation distributions and the number distributions of the projected separation distance between nearest in G304.74. and in nine other IRDCs for comparison.," For this purpose, we determined the clump-separation distributions and the number distributions of the projected separation distance between nearest in G304.74, and in nine other IRDCs for comparison."
 We chose those IRDCs from the sample of RJSO6 which contain the largest number of clumps. ie. MSXDC G023.60+00.00. G024.334-00.11. G028.37+00.07. G028.53-00.25.. G031.97--00.07.. G034.43-00.24. and G035.39-00.33.," We chose those IRDCs from the sample of RJS06 which contain the largest number of clumps, i.e., MSXDC G023.60+00.00, G024.33+00.11, G028.37+00.07, G028.53-00.25, G031.97+00.07, G034.43+00.24, and G035.39-00.33."
 Moreover. we determined. the spatial distribution of YSOs in the IRDC MSXDC G048.65-00.29 studied by van der Wiel Shipman (2008).," Moreover, we determined the spatial distribution of YSOs in the IRDC MSXDC G048.65-00.29 studied by van der Wiel Shipman (2008)."
 For these analyses. we selected only those sources that are clearly associated (in the plane of the sky) with their parental dark cloud (e.g.. clumps that lie within. the dark filaments).," For these analyses, we selected only those sources that are clearly associated (in the plane of the sky) with their parental dark cloud (e.g., clumps that lie within the dark filaments)."
 Thus. we excluded the millimetre clumps MM |. 3. and 5 from G023.60+00.00. MM 2. 5. and 7 from G024.334-00.11. MM 3. 5. 7. 8. 12. 13. 18 from 6G028.37--00.07. MM I and 2 from G035.39-00.33. and YSOs S4. 10. 17. 18. 19. and 20 from GO048.65-00.29.," Thus, we excluded the millimetre clumps MM 1, 3, and 5 from G023.60+00.00, MM 2, 5, and 7 from G024.33+00.11, MM 3, 5, 7, 8, 12, 13, 18 from G028.37+00.07, MM 1 and 2 from G035.39-00.33, and YSOs S4, 10, 17, 18, 19, and 20 from G048.65-00.29."
 In addition to the observed spatial distributions. we also determined the distributions expected from random positions of the same number of objects as the observed samples have.," In addition to the observed spatial distributions, we also determined the distributions expected from random positions of the same number of objects as the observed samples have."
 The areas over which the objects were randomly distributed were chosen so that they approximate the observed dark cloud areas: the IRDC areas were estimated by rectangles which just cover the observed dark clouds., The areas over which the objects were randomly distributed were chosen so that they approximate the observed dark cloud areas; the IRDC areas were estimated by rectangles which just cover the observed dark clouds.
 When needed. these rectangles were rotated with respect to the (a@.0)-coordinate system.," When needed, these rectangles were rotated with respect to the $(\alpha,\delta)$ -coordinate system."
 The random distributions were generated à hundred times per cloud and the resulting averaged histograms were used in comparisons with observed spatial distributions., The random distributions were generated a hundred times per cloud and the resulting averaged histograms were used in comparisons with observed spatial distributions.
 Figure 8 (top) shows the observed clump-separation distribution in G304.74. and the distribution expected for the same number of randomly positioned clumps over minimum rectangular area which encloses the dark cloud (~29.8 arcmin," Figure \ref{figure:dist} (top) shows the observed clump-separation distribution in G304.74, and the distribution expected for the same number of randomly positioned clumps over minimum rectangular area which encloses the dark cloud $\sim29.8$ $^2$ )."
") The mean and its standard deviation. and median of the clump separations in. G304.74 are log((r).p./AU)= (4.907055x10° AU) and log(,,,/AU)=5.759 (5.74x10° AU). respectively."," The mean and its standard deviation, and median of the clump separations in G304.74 are $\log(\langle r \rangle_{\rm obs}/{\rm AU})=5.690\pm0.041$ $4.90^{+0.48}_{-0.44}\times10^5$ AU) and $\log(\tilde{r}_{\rm obs}/{\rm AU})=5.759$ $5.74\times10^5$ AU), respectively."
" These values are similar to those of randomly positioned clumps. for which the mean and median are log(6)444/AU)=5.67420.061 and log(54,/AU)=5.738+0.084 (see Table 9))."," These values are similar to those of randomly positioned clumps, for which the mean and median are $\log(\langle r \rangle_{\rm ran}/{\rm AU})=5.674\pm0.061$ and $\log(\tilde{r}_{\rm ran}/{\rm AU})=5.738\pm0.084$ (see Table \ref{table:separations}) )."
 The latter two values and their +-errors quoted represent the average values and their standard deviations derived from the 100 generated random distributions., The latter two values and their $\pm$ -errors quoted represent the average values and their standard deviations derived from the 100 generated random distributions.
 According to the K-S test. the probability that the observed distribution and the generated random distribution represent the same underlying distribution is100%.," According to the K-S test, the probability that the observed distribution and the generated random distribution represent the same underlying distribution is."
. Statistics of the clump-separation distributions in other IRDCs studied by RJSO6 and van der Wiel Shipman (2008) are listed in Table 9.., Statistics of the clump-separation distributions in other IRDCs studied by RJS06 and van der Wiel Shipman (2008) are listed in Table \ref{table:separations}.
 The columns of this table are the following: (1) IRDC name: (2) number of clumps used in the analysis (see above): (3) distance: (4) area used to create the random distributions (see above); (5) and (6) mean and median of the observed clump-separation distribution (ου. and Fons (7) and (8) mean and median of the corresponding random distribution (Uo) and Fan) (9) and (10) ratios between the observed and random mean and median separations (quoted errors are propagated from the standard deviations of (7) and 7) (11) probability given by the K-S test that the observed and random distributions are drawn from the same underlying distribution., The columns of this table are the following: (1) IRDC name; (2) number of clumps used in the analysis (see above); (3) distance; (4) area used to create the random distributions (see above); (5) and (6) mean and median of the observed clump-separation distribution $\langle r \rangle_{\rm obs}$ and $\tilde{r}_{\rm obs}$ ); (7) and (8) mean and median of the corresponding random distribution $\langle r \rangle_{\rm ran}$ and $\tilde{r}_{\rm ran}$ ); (9) and (10) ratios between the observed and random mean and median separations (quoted errors are propagated from the standard deviations of $\langle r \rangle$ and $\tilde{r}$ ); (11) probability given by the K-S test that the observed and random distributions are drawn from the same underlying distribution.
 Theobserved clump separations are mostly similar to those expected from random distributions., Theobserved clump separations are mostly similar to those expected from random distributions.
 This 1s evident from the ratios Cos/Οδ and Pay/745 Which are close to unity. and from the K-S probabilities which are high (~71— 10056) except," This is evident from the ratios $\langle r \rangle_{\rm obs}/\langle r \rangle_{\rm ran}$ and $\tilde{r}_{\rm obs}/\tilde{r}_{\rm ran}$ which are close to unity, and from the K-S probabilities which are high $\sim71-100\%$ ) except"
considerable delay (at least ~ 3058) between the collapse (as signalled by the initial neutrino aud eravitational wave signal) aud the launch of the GRB explosion.,considerable delay (at least $\sim$ s) between the collapse (as signalled by the initial neutrino and gravitational wave signal) and the launch of the GRB explosion.
 There are. however. upper limits to the delay.," There are, however, upper limits to the delay."
 The explosion must occur. after all. before the disk accretes.," The explosion must occur, after all, before the disk accretes."
" Using the convection dominated accretion flow (CDAF) solutions from Narayan. Piran. unu (2001). we fiud that for accretion rates above 0,0537,s.| and a total mass acereted hrough the disk less than LOAL... the total time including the delav since the collapse plus the must duration can not be hieher than 200s."," Using the convection dominated accretion flow (CDAF) solutions from Narayan, Piran, Kumar (2001), we find that for accretion rates above $0.05 M_\odot s^{-1}$ and a total mass accreted through the disk less than $10M_\odot$, the total time including the delay since the collapse plus the burst duration can not be higher than 200s."
 Those disks which do not explode before this time will iot explode before the disk dissipates., Those disks which do not explode before this time will not explode before the disk dissipates.
 Requiring that the accretion rate is at least LODAZ.s+ places an upper limit on the disk orluation radius (the radius at which the angular uomentunm in the intalling stellar wmaterial supports it agaistOo the C»eravitational pull of the black hoBN, Requiring that the accretion rate is at least $0.05 M_\odot s^{-1}$ places an upper limit on the disk formation radius (the radius at which the angular momentum in the infalling stellar material supports it against the gravitational pull of the black hole).
 Similarly. requiring that the disk imaiutains its accretion rate long enough to survive the delay times given above places a lower limit on the disk formation radius.," Similarly, requiring that the disk maintains its accretion rate long enough to survive the delay times given above places a lower limit on the disk formation radius."
 Usine the CDAF solutions from Naravan ct al. (, Using the CDAF solutions from Narayan et al. (
"2001) and assuming that the disk à viscosity ~O.0L0.1. Mp,>O.05ALxἩ, facerction25 κ. a total mass accreted through the disk =10M.. with at least LAS. in the disk. vields a range of disk formation radi from kia.","2001) and assuming that the disk $\alpha$ viscosity $\sim 0.01-0.1$, $\dot{M}_{\rm D} > 0.05 M_\odot s^{-1}$, $t_{\rm accretion} > 40 {\rm
s}$ , a total mass accreted through the disk $= 10 M_\odot$ with at least $1 M_\odot$ in the disk, yields a range of disk formation radii from km."
 This corresponds to specific stellar ijular momenta iu the range: 3&1005τνVole10M?9s i.," This corresponds to specific stellar angular momenta in the range: $3\times 10^{16} - 5 \times 10^{17} {\rm cm^2 \,
s^{-1}}$ ."
" Although this ⋅⋅is a narrow range of. stellar angular momenta. it does lie within many ( the current rotating models ίσιο, IHegero 2002)."," Although this is a narrow range of stellar angular momenta, it does lie within many of the current rotating models (e.g. Heger 2002)."
 For neutrino-driven explosions from black- hole accretion disks. we can derive the remmanut lass of black holes.," For neutrino-driven explosions from black hole accretion disks, we can derive the remnant mass of black holes."
 Stars between ~20LOAL.. are likely to have weak supernova explosions which ultimately lead to cousiderable fallback aud the formation of a black hole (Frver 1999).," Stars between $\sim
20-40M_\odot$ are likely to have weak supernova explosions which ultimately lead to considerable fallback and the formation of a black hole (Fryer 1999)."
 If these stars have insufficient angular momentum. thev produce a range of black hole masses between 215AL: (νο Ialogera 2001).," If these stars have insufficient angular momentum, they produce a range of black hole masses between $2-15\,M\odot$ (Fryer Kalogera 2001)."
 If instead. they are rapidly rotating. they can form hvperuovae and lower umass black holes (Nalguuura et al.," If instead, they are rapidly rotating, they can form hypernovae and lower mass black holes (Nakamura et al."
 2000)., 2000).
 Simulations bv AMacFackven. Woosloev. Ποσο (2001) show that ~10 ss after their weak explosious. the iufall rates of these stars will drop below our critical densities (assunuüug disk accretion rates iu the range: 0.05LAL.s ty and will drive explosions.," Simulations by MacFadyen, Woosley, Heger (2001) show that $\sim
10^{4}$ s after their weak explosions, the infall rates of these stars will drop below our critical densities (assuming disk accretion rates in the range: $0.05-1 M_\odot s^{-1}$ ) and will drive explosions."
" These ""collapsar type ID objects will rauge from 2SAL..."," These “collapsar type II” objects will range from $2-5
M_\odot$."
 For direct collapse black holes which are the nore likely CRB candidate. the curreuthy most reliable progenitors (rotating LO.GO AL. stars). vield black hole remmauts masses to range within 11-224... with disk accretion rates in the range: 051815+.," For direct collapse black holes which are the more likely GRB candidate, the currently most reliable progenitors (rotating 40,60 $M_\odot$ stars), yield black hole remnants masses to range within $M_\odot$ with disk accretion rates in the range: $0.05-1 M_\odot
s^{-1}$."
 Tf other effects (o6. disk winds. nagnetic fields) are iuportant. these masses could ο lower.," If other effects (e.g. disk winds, magnetic fields) are important, these masses could be lower."
 But not all stars will form CRBs., But not all stars will form GRBs.
 For stars with iusufficieut augular momentum to xoduce these disk accretion rates. weak or no explosions are produced. aud the remmant cau be uuch nore massive (up to the mass of the star).," For stars with insufficient angular momentum to produce these disk accretion rates, weak or no explosions are produced, and the remnant can be much more massive (up to the mass of the star)."
 This work has been fundedby DOE SciDAC erant προς. DE-FCO2-01ER1176. a LANL- ASCT eraut. and NASA NAC5-9192.," This work has been fundedby DOE SciDAC grant number DE-FC02-01ER41176, a LANL-based ASCI grant, and NASA NAG5-9192."
 , 
"vanishing minors in A/,.",vanishing minors in $M_\nu$.
 Out of these fifteen only seven patterns [Table-I] viz., Out of these fifteen only seven patterns [Table-I] viz.
" νι ida. By. B,. Bs. By and D can accommodate the neutrino oscillation data."," $A_1$ , $A_2$ , $B_3$ , $B_4$, $B_5$, $B_6$ and $D$ can accommodate the neutrino oscillation data."
 OF all the allowed two zero minors in (heneutrino mass matrix only three cases {οι By and D. provide non-trivial zero minors. all other cases reduce to two zero textures when confronted with the neutrino oscillation data.," Of all the allowed two zero minors in theneutrino mass matrix only three cases $B_5$, $B_6$ and $D$ provide non-trivial zero minors, all other cases reduce to two zero textures when confronted with the neutrino oscillation data."
 We work in a basis where Mj is diagonal (Mp=dieag(r.y.z)). ancl the neulvino mixing arises solely [rom Mg.," We work in a basis where $M_D$ is diagonal $M_D = diag(x,y,z)$ ), and the neutrino mixing arises solely from $M_R$."
 In this basis. a zero entry in Mg propagates asa vanishing minor in the ellective neutrino mass matrix 1.," In this basis, a zero entry in $M_R$ propagates asa vanishing minor in the effective neutrino mass matrix $M_\nu$."
 Here. we focus on Bs ancl D; class of vanishing minors.," Here, we focus on $B_5$ and $B_6$ class of vanishing minors."
" To obtain the classes. D; and 1 of neutrino mass matrices. we extend the Standard. Model (8M) by adding three right-handed neutrino singlets vj, and one scalar singlet 4."," To obtain the classes $B_5$ and $B_6$ of neutrino mass matrices, we extend the Standard Model (SM) by adding three right-handed neutrino singlets $\nu_{R_i}$ and one scalar singlet $\chi$."
 In order to enable (he seesaw mechanism for suppressing the neutrino masses Ay must have the following structures for 25 and D: leading to the following effective neutrino mass matrices (through theseesaw mechanism A general procedure for enforcing zero textures in arbitrary entries of the fermion mass matrices using abelian family svnunetries has been outlined in [12]., In order to enable the seesaw mechanism for suppressing the neutrino masses $M_R$ must have the following structures for $B_5$ and $B_6$: leading to the following effective neutrino mass matrices through theseesaw mechanism A general procedure for enforcing zero textures in arbitrary entries of the fermion mass matrices using abelian family symmetries has been outlined in \cite{12}.
. The svmmetry realization of all the allowed. one zero ancl (wo zero textures was recently presented in [13]., The symmetry realization of all the allowed one zero and two zero textures was recently presented in \cite{13}.
. For the svmnmelry realization of D; and Dg textures of (wo zero minors we consider a small evelic eroup Z4 which corresponds to the minimal group since Z» leads to a non-ciagonal charged lepton and Dirac neutrino mass matrix., For the symmetry realization of $B_5$ and $B_6$ textures of two zero minors we consider a small cyclic group $Z_3$ which corresponds to the minimal group since $Z_2$ leads to a non-diagonal charged lepton and Dirac neutrino mass matrix.
" Under Z4 the SAI Iiegs doublet remains invariant and the leptonic fields are assumed totransform as:here w— σε) 6777"".", Under $Z_3$ the SM Higgs doublet remains invariant and the leptonic fields are assumed totransform as:where $\omega$= $e^{i 2 \pi/3}$ .
" Hence the bilinearsEET τς.Dy{μι and —uD, rj. relevant for. M; and Mp transform. as The SM Iliggs doublet remains invariant under Z4 leading to diagonal M; and A/p."," Hence the bilinears $\overline{D}_{L_j} l_{R_k}$ and $\overline{D}_{L_j}\nu_{R_k}$ , relevant for $M_l$ and $M_D$ transform as The SM Higgs doublet remains invariant under $Z_3$ leading to diagonal $M_l$ and $M_D$ ."
 The, The
such a scenario does appear to be able to accommodate all the features of the observed oscillations.,such a scenario does appear to be able to accommodate all the features of the observed oscillations.
 Since we observe the system towards the end of an outburst. the radial density distribution is not expected to be that of a steady-state disc.," Since we observe the system towards the end of an outburst, the radial density distribution is not expected to be that of a steady-state disc."
 Disc instability calculations usually show a broad peak in the density at roughly the eireularisation radius towards the end of the outburst., Disc instability calculations usually show a broad peak in the density at roughly the circularisation radius towards the end of the outburst.
 Such an empty disc would be in particular susceptible to stream overllow. and again the obvious region for streamedisc interaction would be near the circularisation radius where the density peaks and the stream is flowing towards the orbital plane again.," Such an 'empty' disc would be in particular susceptible to stream overflow, and again the obvious region for stream-disc interaction would be near the circularisation radius where the density peaks and the stream is flowing towards the orbital plane again."
 We detected coherent continuum ancl emission. line oscillations in the chwarf nova V2051 Oph on decline from a normal outburst., We detected coherent continuum and emission line oscillations in the dwarf nova V2051 Oph on decline from a normal outburst.
 Accretion disc emission extends from. very close to the white dwarf out to the outer parts of the primary toche lobe., Accretion disc emission extends from very close to the white dwarf out to the outer parts of the primary Roche lobe.
 The disc emission lines display a persistent blue o red asymmetry. with the blue peak being stronger in all he Helium lines as well as the Balmer lines. except Ho which las a stronger red peak.," The disc emission lines display a persistent blue to red asymmetry, with the blue peak being stronger in all the Helium lines as well as the Balmer lines, except $\alpha$ which has a stronger red peak."
 The eclipse light. curves are also uehly asvmmetric which suggests that the blue side of the disc makes a larger contribution to the emission compare ο the red-shifted side., The eclipse light curves are also highly asymmetric which suggests that the blue side of the disc makes a larger contribution to the emission compared to the red-shifted side.
 The continuum oscillations are most likely to originate on the surface of a spinning white dwarf with spin perio 56.125 and temperature around. 1200018. Ehe amplitude of the oscillation in the continuum. varies between 0 and.4%.. and disappears during white dwarf eclipse.," The continuum oscillations are most likely to originate on the surface of a spinning white dwarf with spin period 56.12s and temperature around 15000K. The amplitude of the oscillation in the continuum varies between 0 and, and disappears during white dwarf eclipse."
 Phe Balmer ane Ielium L emission lines oscillate strongly ata period of 29.88., The Balmer and Helium I emission lines oscillate strongly at a period of 29.8s.
" The line kinematies as well as the eclipse constraints indicate these to come from a non-axisvmmetric bulge in the disc a a radius of 12+2/2,4.", The line kinematics as well as the eclipse constraints indicate these to come from a non-axisymmetric bulge in the disc at a radius of $12\pm2R_{wd}$.
 Phe corresponding Ixepler orbit has a period of 488s. and. corresponds well with the observec amplitude variations (0-4%)) on this period.," The corresponding Kepler orbit has a period of 488s, and corresponds well with the observed amplitude variations ) on this period."
 The oscillating ine emission is observed to go from maximum blue-shift to maximum red-shift every 29.88. but not vice. versa.," The oscillating line emission is observed to go from maximum blue-shift to maximum red-shift every 29.8s, but not vice versa."
 This. ogether with the regular modulation. of the oscillation amplitudes can be explained. by intervening eas above the orbital plane. close to the white cwarf.," This, together with the regular modulation of the oscillation amplitudes can be explained by intervening gas above the orbital plane, close to the white dwarf."
 This is supported » an uneclipsed component in both the continuum. and ines., This is supported by an uneclipsed component in both the continuum and lines.
 In the Balmer lines this component is centered on zero velocity and basa EWLLM of 1000 kms +., In the Balmer lines this component is centered on zero velocity and has a FWHM of 1000 km $^{-1}$.
 Alternatively. the emission is beamed away [from the white ναί," Alternatively, the emission is beamed away from the white dwarf."
 The close correspondence between the location of the oscillations and the circularisation radius of the svsteni as well as the disc asvmnmetry may indicate the relevance of stream overllow to the presence of vertically extended bulges in the disc., The close correspondence between the location of the oscillations and the circularisation radius of the system as well as the disc asymmetry may indicate the relevance of stream overflow to the presence of vertically extended bulges in the disc.
 More observations of this kind as well as more detailed simulations of such a scenario are required to confirm its feasibility in the light of producing DNOs., More observations of this kind as well as more detailed simulations of such a scenario are required to confirm its feasibility in the light of producing DNOs.
 Predictions of our interpretation are the persistent. presence of 56.128/28.06s. oscillations from. the white dwarf., Predictions of our interpretation are the persistent presence of 56.12s/28.06s oscillations from the white dwarf.
 This period should be detected at other epochs. most likely in the UV.," This period should be detected at other epochs, most likely in the UV."
 The UV also provides opportunities to measure the spin of the white chvarl directlv. using the rotational broadening of white dwarf absorption lines (Sion 1999)), The UV also provides opportunities to measure the spin of the white dwarf directly using the rotational broadening of white dwarf absorption lines (Sion \nocite{sion})
 The UV also provides opportunities to measure the spin of the white chvarl directlv. using the rotational broadening of white dwarf absorption lines (Sion 1999))., The UV also provides opportunities to measure the spin of the white dwarf directly using the rotational broadening of white dwarf absorption lines (Sion \nocite{sion})
"(i) The colour-magnitude relation (CMIU) and colour-velocity dispersion relation (Colt) of BCGs are significantly Hatter in. slope(-hyTAL,ori and digTononi ) than the respective relations for non-BCG I2/80 galaxies of comparable (high) Iuminositv.",(i) The colour-magnitude relation (CMR) and colour-velocity dispersion relation $\sigma$ R) of BCGs are significantly flatter in ${{d(g-r)}\over{d M_r}}$ and ${{d(g-r)}\over{d{\rm log}~\sigma}}$ ) than the respective relations for non-BCG E/S0 galaxies of comparable (high) luminosity.
 The cifferenee in slope is about a factor of two. whether we define the gor colour using k-corrected model magnitudes or rest-frame magnitudes derived. fron integrating the SDSS spectra.," The difference in slope is about a factor of two, whether we define the $g-r$ colour using k-corrected model magnitudes or rest-frame magnitudes derived from integrating the SDSS spectra."
" Εςας are also. on average. ~0.01 mag redder in model magnitudes (k-corrected to rame) than E/SOs of the same M, or e. but with less or no olfset in spectra-derived colours."," BCGs are also, on average, $\sim 0.01$ mag redder in model magnitudes (k-corrected to rest-frame) than E/S0s of the same $M_r$ or $\sigma$, but with less or no offset in spectra-derived colours."
 The hierarchical merging model of Lucia and Blaizot (2007) predicts a Lat CAL for BCGs as a result. of late assembly from a laree number of red. progenitors which ormed their stars. very much earlier (2~ 5)., The hierarchical merging model of Lucia and Blaizot (2007) predicts a flat CMR for BCGs as a result of late assembly from a large number of red progenitors which formed their stars very much earlier $z\sim 5$ ).
 This mocel included a very carly truncation of star-Lormation., This model included a very early truncation of star-formation.
" Skelton. Bell and Somerville (2009) present a simplified: model in which dev mergers of already. merged. LE/SOs on a ""creation red sequence! mildly atten the CALR slope at. higher uminosities."," Skelton, Bell and Somerville (2009) present a simplified model in which dry mergers of already merged E/S0s on a `creation red sequence' mildly flatten the CMR slope at higher luminosities."
 Phere may indeed. be some Uattening in the sight end of the CALR for all I2/80s (see Paper D. but. for DOGs we find much more. although the BCG CAL is not entirely flat.," There may indeed be some flattening in the bright end of the CMR for all E/S0s (see Paper I), but for BCGs we find much more, although the BCG CMR is not entirely flat."
 This suggests the BCGs or their. progenitors evolve by a less extreme scenario than the first. of these nmocels but perhaps with a higher dev merger rate compared to the E/SO0s in the second. model., This suggests the BCGs or their progenitors evolve by a less extreme scenario than the first of these models but perhaps with a higher dry merger rate compared to the E/S0s in the second model.
 In. addition to being Hattened. the BCG CMM is olfset. rechwarels. (," In addition to being flattened, the BCG CMR is offset redwards. ("
ii) As a simple quantifier of radial colour gradient. we use 4reyqgiglαν with. the elfective⋅. radiie ερες) and πρ). correctedZEE to the rest-frame by linearly interpolating between the racii fitted in the bands ο. r. 7 and z.,"ii) As a simple quantifier of radial colour gradient we use ${{{\rm r}_{eff}(g)}\over{{\rm r}_{eff}(r)}}-1$, with the effective radii ${\rm r}_{eff}(g)$ and ${\rm r}_{eff}(r)$ , corrected to the rest-frame by linearly interpolating between the radii fitted in the bands $g$, $r$, $i$ and $z$."
" We show that at least for galaxies with angular rry radii above 1.8 aresce. this ratio is well and linearly correlated to diosdigri across the observed range of colour gradients and. galaxy. [uminosities.ri and estimate: =A""desidrni~87/4a=,tyigi1)."," We show that at least for galaxies with angular $r_{eff}$ radii above 1.8 arcsec, this ratio is well and linearly correlated to ${{d(g-r)}\over {d(\rm log~r)}}$ across the observed range of colour gradients and galaxy luminosities, and estimate ${{d(g-r)}\over {d(\rm log~r)}}\simeq -0.87 ({{{\rm r}_{eff}(g)}\over{{\rm r}_{eff}(r)}}-1)$."
 Phe large scatter in this correlation. which we initiallyTES estimated. as 0.122. is reduced to a much more acceptable 0.056 if only galaxies with ες larger than 1.5 aresee are included.," The large scatter in this correlation, which we initially estimated as 0.122, is reduced to a much more acceptable 0.056 if only galaxies with $r_{eff}$ larger than 1.8 arcsec are included."
 After excluding the rcg<LS aresec. galaxies and a [ow others which we believed to be spiral types. we found for the E/SOs a mean colour eracient. using our measure. of 0.11115+0.00061 with a comparable ealaxv-to galaxy scatter 0.1172.," After excluding the $r_{eff}<1.8$ arcsec galaxies and a few others which we believed to be spiral types, we found for the E/S0s a mean colour gradient, using our measure, of $0.11115\pm 0.00061$ with a comparable galaxy-to galaxy scatter 0.1172."
" For the Ad,22.5 non-BCG the mean is similar at 0.10550+0.00098. (scatter. 0.1141). and. for max-DCCGs the mean is 0.08142+0.00114 (scatter 0.0764).", For the $M_r<-22.5$ non-BCG the mean is similar at $0.10550\pm 0.00098$ (scatter 0.1141) and for max-BCGs the mean is $0.08142\pm 0.00114$ (scatter 0.0764).
" ""Therefore we find at high significance that Εςος have a latter (by an average of 234) radial colour gradient. than other high luminosity spheroidals.", Therefore we find at high significance that BCGs have a flatter (by an average of $23\%$ ) radial colour gradient than other high luminosity spheroidals.
 This again could be due to intensified: merging in the cluster-core environment., This again could be due to intensified merging in the cluster-core environment.
 La Barbera et al. (, La Barbera et al. (
2005). and similarly Wo ancl Im. (2005). reported mean colour graclients in E/SOs of all luminosities were weaker by almost a [actor two in the richest clusters CN;2 50) compared to the lield. ancl suggested this was because formation histories in denser cluster environments included: more. elliptical-elliptical mergers (c.g. “Tran et. al.,"2005), and similarly Ko and Im (2005), reported mean colour gradients in E/S0s of all luminosities were weaker by almost a factor two in the richest clusters $N_{gal}>50$ ) compared to the field, and suggested this was because formation histories in denser cluster environments included more elliptical-elliptical mergers (e.g. Tran et al."
 2005). which reduce colourmetallicity gradients (Ixobavashi 2004).," 2005), which reduce colour/metallicity gradients (Kobayashi 2004)."
" The simulations of Bovlan-Ixolchin. Ma and Quataert (2006) account for the steeper Z2. L of BCGs. Le. their ‘abnormally’ large sizes (e.g. Bernardi 2009). as the result of repeated: ""dry (dissipationless. non-star-forming) mergers. ancl especially of the anisotropic acerction of smaller spheroidals in near-radial. low angular momentum orbits. which might occur preferentially in a cluster core."," The simulations of Boylan-Kolchin, Ma and Quataert (2006) account for the steeper $R_e$ $L$ of BCGs, i.e. their `abnormally' large sizes (e.g. Bernardi 2009), as the result of repeated `dry' (dissipationless, non-star-forming) mergers, and especially of the anisotropic accretion of smaller spheroidals in near-radial, low angular momentum orbits, which might occur preferentially in a cluster core."
 A few BC's have been observed: undergoing such mergers (Liu et al., A few BCGs have been observed undergoing such mergers (Liu et al.
 2008: Tran et al., 2008; Tran et al.
 2008)., 2008).
 Di Matteo ct al. (, Di Matteo et al. (
2009) predict [rom simulations that the metallicity gradient in a dissipationless (ανν). merger remnant will consistently be =0.6 the mean of the progenitor galaxies’ graclicnts (but not reduced to zero) (,2009) predict from simulations that the metallicity gradient in a dissipationless (`dry') merger remnant will consistently be $\simeq 0.6$ the mean of the progenitor galaxies' gradients (but not reduced to zero). (
ii) In non-BCG E/SO0s. we examine the trends in mean colour gracicnt as a function of other galaxy properties.,"iii) In non-BCG E/S0s, we examine the trends in mean colour gradient as a function of other galaxy properties."
" We ind a dependence of colour gradient on absolute magnitude Al. with a broad. peak in colour gradient at Al,c—22 and a decrease to lower and higher [uminosities."," We find a dependence of colour gradient on absolute magnitude $M_r$, with a broad peak in colour gradient at $M_r\simeq - 22$ and a decrease to lower and higher luminosities."
 The uminosity dependence is relatively mild. less than a factor 1.5. which may explain why it was not seen by La Barbera et al. (," The luminosity dependence is relatively mild, less than a factor 1.5, which may explain why it was not seen by La Barbera et al. ("
2005).,2005).
 However. Spolaor et al. (," However, Spolaor et al. ("
2009) do [find a uminositv dependence similar to ours.,2009) do find a luminosity dependence similar to ours.
" Colour graclients end to decrease with increasing velocity dispersion. a. by almost 1/2 between 150 and 300 km s confirming the sugeestion in our Paper Ll that the trends with Ad, and e are clilferent. ("," Colour gradients tend to decrease with increasing velocity dispersion $\sigma$, by almost 1/2 between 150 and 300 km $\rm s^{-1}$, confirming the suggestion in our Paper I that the trends with $M_r$ and $\sigma$ are different. ("
iv) Colour gradients in E/SOs show strong correlations with some other galaxy properties.,iv) Colour gradients in E/S0s show strong correlations with some other galaxy properties.
 Colour gradients increase. by about a factor of two. with from small to larger ellective radius. up toa maximum at 8-12 kpe (depending on luminosity).," Colour gradients increase, by about a factor of two, with from small to larger effective radius, up to a maximum at 8-12 kpc (depending on luminosity)."
 A positive correlation with radius was prevously reported by Tamura and Ohta (2003) for a small sample of I5/S0s in Abell 2199., A positive correlation with radius was prevously reported by Tamura and Ohta (2003) for a small sample of E/S0s in Abell 2199.
" At even larger racii we find the mean colour eracicnts decrease. but this is actually because of a reduced gradient in the most luminous (M,<— 23) galaxies."," At even larger radii we find the mean colour gradients decrease, but this is actually because of a reduced gradient in the most luminous $M_r<-23$ ) galaxies."
 If E/SOS are divided by Luminosity. within low/mocerate luminosity intervals there is simply a steep increase in colour eracient with rr.," If E/S0s are divided by luminosity, within low/moderate luminosity intervals there is simply a steep increase in colour gradient with $\rm r_{eff}$."
" We find colour gradients to be negatively correlatec with 10log&|M, (the e residual relative to (7[|M,)) ane Diass density. (σpLu2 } ", We find colour gradients to be negatively correlated with $\rm 10~log~\sigma+M_r$ (the $\sigma$ residual relative to $\langle \sigma|M_r\rangle$ ) and mass density $\sigma^2/\rm r_{eff}^2$ ).
OfB course. those cquauatrtresnm are relatec a high density implies a high e at à given dynamic mass (rather than luminosity).," Of course, these quantities are related – a high density implies a high $\sigma$ at a given dynamic mass (rather than luminosity)."
" These negative correlations do no seem to be caused by a selection ellect (from the Εν limi of the sample). as they are seen. within a wide range of narrow Luminosity intervals. being strongest. for LySOs of mocderate/high luminosity 21«M,<24. ("," These negative correlations do not seem to be caused by a selection effect (from the flux limit of the sample), as they are seen within a wide range of narrow luminosity intervals, being strongest for E/S0s of moderate/high luminosity $-21<M_r<-24$. ("
v) We also examine the trend in colour gradient. with the ‘mean stellar ages’ estimated (Callazzi et al.,v) We also examine the trend in colour gradient with the `mean stellar ages' estimated (Gallazzi et al.
 2005. 2006) lor most of these galaxies using 5 indices from the SDSS spectra.," 2005, 2006) for most of these galaxies using 5 indices from the SDSS spectra."
 In. non-BCG I5/SOs the colour gradients are strongest. for relatively voung ages of 4.5 Gyr (which nw signify the presence. of vounger. stellar populations or more extended: star-formation. rather than the galaxies being vounger) and decrease by up to a factor of two to the oldest ages of 11 Gyr.," In non-BCG E/S0s the colour gradients are strongest for relatively young ages of 4–5 Gyr (which may signify the presence of younger stellar populations or more extended star-formation, rather than the galaxies being younger) and decrease by up to a factor of two to the oldest ages of 11 Gyr."
 This may be primarily because older stellar populations have experienced more mergers and interactions. especially at high redshifts.," This may be primarily because older stellar populations have experienced more mergers and interactions, especially at high redshifts."
 E£arlv-tvpe galaxies which ceased forming stars and joined the red sequence more recently (e.g. post-mereersof spirals at 2« 1) would tend to have stronger colour gradients. iit is dry mergers (occurring alter the end of star-formation) that Dlatten the gradients.," Early-type galaxies which ceased forming stars and joined the red sequence more recently (e.g. post-mergersof spirals at $z<1$ ) would tend to have stronger colour gradients, if it is dry mergers (occurring after the end of star-formation) that flatten the gradients."
 Llowever. there is a drop in mean colour gradient for the," However, there is a drop in mean colour gradient for the"
(Table 12).,(Table \ref{tab:templates}) ).
 While the cilference in. the \7 between various mocels (e.g. one-component exponential versus one-Component Gaussian) is formally statistically significant. it. corresponds to less than change in. the Ay72 value relative to the 7null hypothesis” of a zero IHlux in the 508 keV band over the entire. cata set.," While the difference in the $\chi^2$ between various models (e.g. one-component exponential versus one-component Gaussian) is formally statistically significant, it corresponds to less than change in the $\Delta
\chi^2$ value relative to the “null hypothesis” of a zero flux in the 508--514 keV band over the entire data set."
 t this level. a particular value of Ay? for a given model might be sensitive to the subtle features of the data set.," At this level, a particular value of $\Delta \chi^2$ for a given model might be sensitive to the subtle features of the data set."
 Our experiments with different background. mioclels have indeed shown that the ranking of models in terms of A7 can slightly vary., Our experiments with different background models have indeed shown that the ranking of models in terms of $\chi^2$ can slightly vary.
 For example. the ranking of the Gaussian|Caussian and Gaussian|exponential. models. in. Table 1 can change depending on the particular background moclel.," For example, the ranking of the Gaussian+Gaussian and Gaussian+exponential models in Table \ref{tab:templates} can change depending on the particular background model."
 Despite the difference in the functional forms. the Hux in the central component does not.depend: strongly on the model used: Ἡ varies between S4107 and 9310.photsem? for all two-components mocels.," Despite the difference in the functional forms, the flux in the central component does notdepend strongly on the model used; it varies between $8.4~10^{-4}$ and $9.3~10^{-4} \pscm2$ for all two-components models."
 Using the one-component exponential model (the first mocel in eq. 3)), Using the one-component exponential model (the first model in eq. \ref{eq:e2}) )
" with M;=3° and M,=2 we τος to vary the centroid of the distribution over a few degrees around the GC anc caleulated the changes in the 47."," with $W_l=3$ and $W_b=2$, we tried to vary the centroid of the distribution over a few degrees around the GC and calculated the changes in the $\chi^2$."
 The best-litting position is at (fb)=(OV0.27) and the minimal X7 dilfers from the value at (26)=(0.0) by 2.3.," The best-fitting position is at $(l,b)=(-0.1^\circ,-0.2^\circ)$ and the minimal $\chi^2$ differs from the value at $(l,b)=(0,0)$ by 2.3."
 While this means that formally the statistics of accumulated data is already. sullicient to measure sub-deerce shifts of the centroid. we believe that systematic uncertainties and the obvious crucdeness of the spatial model preclude: any firm conclusion.," While this means that formally the statistics of accumulated data is already sufficient to measure sub-degree shifts of the centroid, we believe that systematic uncertainties and the obvious crudeness of the spatial model preclude any firm conclusion."
 We can conservatively conclude from this exercise that the position of the centroid is consistent within ~0.2° with the position of the dynamic centre of the Milky Wav., We can conservatively conclude from this exercise that the position of the centroid is consistent within $\sim$ with the position of the dynamic centre of the Milky Way.
 lligdon.Lingenfelter.&Itothschild(2009) have suggested hat a significant [fraction of positrons is annihilating in a “Tilted Disk” of neutral gas inside the central 3 kpe region of the Galaxy., \citet{2009ApJ...698..350H} have suggested that a significant fraction of positrons is annihilating in a “Tilted Disk” of neutral gas inside the central 3 kpc region of the Galaxy.
 This 7Tilted Disk” is one of the components of he Ferriere.Gillard.&Jean(2007) model of the interstellar eas distribution in the innermost part of the Milky Way. xwed on earlier. results of Liszt&Burton(1950)— (see 1996).. ," This “Tilted Disk” is one of the components of the \citet{2007A&A...467..611F} model of the interstellar gas distribution in the innermost part of the Milky Way, based on earlier results of \citet{1980ApJ...236..779L}
 \citep[see also][]{1996IAUS..169..297L}. ."
Phe Tilted Disk (scebie.4in in projection to the sky xdane has an apparent size of —18 by —5 and is tilted by," The Tilted Disk \citep[see
 Fig. 4 in][]{2007A&A...467..611F} in projection to the sky plane has an apparent size of $\sim$ by $\sim$ and is tilted by"
weaker.,weaker.
 The peak strength of the secondary maximum increases will wavelength. (hat is. il is smallest in /3-band and highest in A-band.," The peak strength of the secondary maximum increases with wavelength, that is, it is smallest in $B$ -band and highest in $K$ -band."
 In Figure 12. we have plotted a zoomed part of the J- and A-band lisht curves around (he secondary maximum., In Figure \ref{fig:gauss_sec_max} we have plotted a zoomed part of the $J$ - and $K$ -band light curves around the secondary maximum.
 One can separate the two components: a steadily declining flux from the primary outburst on top of which is superimposed additional flux from the secondary maxinmmn., One can separate the two components: a steadily declining flux from the primary outburst on top of which is superimposed additional flux from the secondary maximum.
" The first component we will call (he ""underlvineg flux.", The first component we will call the “underlying flux”.
" The secondary maximum is [lux additional and separate to that of the linearlv-decaving Πανκ,", The secondary maximum is flux additional and separate to that of the linearly-decaying flux.
 Hence. it seems likely (hat ils origin is also separate from the processes governing (he primary outburst.," Hence, it seems likely that its origin is also separate from the processes governing the primary outburst."
 We estimated (he peak times in each bad by fitting two-sided Gaussians to the secondary maximum., We estimated the peak times in each band by fitting two-sided Gaussians to the secondary maximum.
 Dwo-sided Gaussians were used as (μον provided a much better fit than a single Gaussian., Two-sided Gaussians were used as they provided a much better fit than a single Gaussian.
 The data were first detrended for (he underlving flux by removing a linear component fitted (to the data either side of (he secondary maximum., The data were first detrended for the underlying flux by removing a linear component fitted to the data either side of the secondary maximum.
 The best fit Gaussian parameters are shown in Table 2.., The best fit Gaussian parameters are shown in Table \ref{tab:sec_max_fits}.
" The secondary maximum peaked in both wavebands al (he same time: in the J-band. the fitted peak time was MJD re (1-0) while for A-band it was MJD t1 (1-σ], "," The secondary maximum peaked in both wavebands at the same time: in the $J$ -band, the fitted peak time was MJD $^{+1.5}_{-1.8}$ $\sigma$ ) while for $K$ -band it was MJD $^{+2.1}_{-1.8}$ $\sigma$ )."
We reiterate here that the second. MOST radio detection was made near the peak of (he secondary maximum., We reiterate here that the second MOST radio detection was made near the peak of the secondary maximum.
 It is not known whether a radio source was present before or alter this detection as observations were not conducted., It is not known whether a radio source was present before or after this detection as observations were not conducted.
 Although there is no obvious change in the RNTE/ASM light curve. there may be ellects seen in the RNTE/PCA data which will be presented elsewhere (Ixalemci οἱ al..," Although there is no obvious change in the RXTE/ASM light curve, there may be effects seen in the RXTE/PCA data which will be presented elsewhere (Kalemci et al.,"
 in prep.)., in prep.).
 Alter the secondary maximiun. the OIR light curves return to the original decline rate of the primary maximum until reaching previous quiescent levels.," After the secondary maximum, the OIR light curves return to the original decline rate of the primary maximum until reaching previous quiescent levels."
 To understand the source of the secondary. maximum emission. we have constructed a spectral energy distribution (SED) of the flux from the secondary maximum only at the time when the second MOST radio detection was made (MJD 52437).," To understand the source of the secondary maximum emission, we have constructed a spectral energy distribution (SED) of the flux from the secondary maximum only at the time when the second MOST radio detection was made (MJD 52487)."
" The OIR magnitudes of 4U 1543-47 were first corrected for interstellar extinction using E(D— V) = 0.5 d 0.05 1908), Ay = 3.2 E(D— V) = 1.6 (Zombeck1990).. Αρ Αι = 1.324 and A, Αι. = 0.432. Αι Αιξ 0.282 and Ay Αν = 0.112 (RiekeandLebolsky1985)."," The OIR magnitudes of 4U 1543-47 were first corrected for interstellar extinction using $B-V$ ) = 0.5 $\pm$ 0.05 \citep{oro98}, $_V$ = 3.2 $B-V$ ) = 1.6 \citep{zom90}, $_B$ $_V$ = 1.324 and $_I$ $_V$ = 0.482, $_J$ $_V$ = 0.282 and $_K$ $_V$ = 0.112 \citep{rie85}."
. As there were no D.V or I observations made on (his date. we extrapolated the optical light curves to estimate (heir magnitudes.," As there were no $B, V$ or $I$ observations made on this date, we extrapolated the optical light curves to estimate their magnitudes."
" For this date we estimate the secondary maxinum magnitudes at (he peak to be ,—14.2. V;—14.2 and /,213.9."," For this date we estimate the secondary maximum magnitudes at the peak to be $B_o$ =14.2, $V_o$ =14.2 and $I_o$ =13.9."
" We estimated the magnitude of the underlving flux. at the time of the secondary. maxinmn peak to be B, = 14.5. V, = 14.6 and £, = 14.6."," We estimated the magnitude of the underlying flux at the time of the secondary maximum peak to be $B_o$ = 14.5, $V_o$ = 14.6 and $I_o$ = 14.6."
 In the, In the
"gives us the most complete picture of the spatial distribution of the various molecules, which is crucial to studying variations in the chemistry with the MALT90 sources.","gives us the most complete picture of the spatial distribution of the various molecules, which is crucial to studying variations in the chemistry with the MALT90 sources."
" Mapping artifacts are seen in many of our maps, typically manifesting as stripes in the direction of scans."," Mapping artifacts are seen in many of our maps, typically manifesting as stripes in the direction of scans."
 Our sources were generally mapped with scans of constant Galactic longitude so that each strip in Galactic longitude uses the same reference spectrum., Our sources were generally mapped with scans of constant Galactic longitude so that each strip in Galactic longitude uses the same reference spectrum.
" Noise or gain variations in this reference spectrum can therefore produce stripes in the map, and this phenomenon is particularly prevalent in sources observed in bad weather."," Noise or gain variations in this reference spectrum can therefore produce stripes in the map, and this phenomenon is particularly prevalent in sources observed in bad weather."
 We chose to map using scans of constant Galactic longitude for the pilot survey because most extended structures in the Galactic plane are parallel to the plane., We chose to map using scans of constant Galactic longitude for the pilot survey because most extended structures in the Galactic plane are parallel to the plane.
" Thus, noise stripes are easier to identify, since they typically run perpendicular to real features."," Thus, noise stripes are easier to identify, since they typically run perpendicular to real features."
 We mapped two sources (G305.887+00.016and G308.058—00.397) in both Galactic longitude and latitude to see if this would mitigate the striping., We mapped two sources $+$ 00.016and $-$ 00.397) in both Galactic longitude and latitude to see if this would mitigate the striping.
 Figure 12 shows the two individual maps for G308.058—00.397 as well as the combination of both maps for a signal-free ccube., Figure \ref{CrossMap} shows the two individual maps for $-$ 00.397 as well as the combination of both maps for a signal-free cube.
 The striping visible in the scan direction in both individual maps is significantly reduced in the combined image., The striping visible in the scan direction in both individual maps is significantly reduced in the combined image.
 We therefore decided to map using scans of both constant Galactic longitude and latitude in the full MALT90 survey., We therefore decided to map using scans of both constant Galactic longitude and latitude in the full MALT90 survey.
 Figure 19 shows the central portion of the maps for the source G321.935—00.007 in aandHCO*., Figure \ref{Infall} shows the central portion of the maps for the source $-$ 00.007 in and.
. The line shows self-absorption at the systemic velocity (traced by the wwhich shows little or no , The line shows self-absorption at the systemic velocity (traced by the which shows little or no non-gaussianity).
"In the lower-right portion of the map,non-gaussianity). this self-absorption shows an asymmetric profile with brighter blue-shifted emission."," In the lower-right portion of the map, this self-absorption shows an asymmetric profile with brighter blue-shifted emission."
" Such a profile is characteristic of infall of cold gas toward a hot central source (e.g.,?).."," Such a profile is characteristic of infall of cold gas toward a hot central source \citep[e.g.,][]{Mardones:1997}."
" This characteristic shape is not present in the upper-left of the map, where we see a red-shifted profile usually associated with expansion."," This characteristic shape is not present in the upper-left of the map, where we see a red-shifted profile usually associated with expansion."
 It is possible that infall is happening only in part of this source or that other kinematic complexity is present; the large variance of this complex line shape over the source demonstrates the value of mapping at high velocity resolution., It is possible that infall is happening only in part of this source or that other kinematic complexity is present; the large variance of this complex line shape over the source demonstrates the value of mapping at high velocity resolution.
 The many lines observed in MALTO90 provide information about the evolutionary state of the clumps observed., The many lines observed in MALT90 provide information about the evolutionary state of the clumps observed.
" This information can be combined with morphological classification and dust temperature determination from spectral-energy distribution fitting (e.g.,11) to constrain the evolutionary state of a clump."," This information can be combined with morphological classification and dust temperature determination from spectral-energy distribution fitting \citep[e.g.,][]{Rathborne:2010, Peretto:2010} to constrain the evolutionary state of a clump."
 As a short example we present three sources in different morphological states and show what information can be gained from the molecular lines in each case., As a short example we present three sources in different morphological states and show what information can be gained from the molecular lines in each case.
" Figure 14 shows G330.873—00.361, a clump drawn from the HOPS survey catalog and classified as an rregion from the GLIMPSE/MIPSGAL images due to its strong extended 8 and 24 eemission."," Figure \ref{ExampleHII} shows $-$ 00.361, a clump drawn from the HOPS survey catalog and classified as an region from the GLIMPSE/MIPSGAL images due to its strong extended 8 and 24 emission."
" The presence of ((Jig= 51—41) emission identifies the hot core associated with a massive protostar since this molecule is seen only in warm (T'> 100 K) and dense (n> 10? cm?) regions and is often detected in rregions (e.g., ?).."," The presence of $J_K = 5_1 - 4_1$ ) emission identifies the hot core associated with a massive protostar since this molecule is seen only in warm $T >$ 100 K) and dense $n >$ $^{5}$ $^{-3}$ ) regions and is often detected in regions \citep[e.g.,][]{Purcell:2006}. ."
 The location of the core is also the position of maximum integrated intensity for most of, The location of the core is also the position of maximum integrated intensity for most of
we could also expect that the number of X-ray sources has a stronger dependence on the total mass than on the encounter rate for the low-density core globular clusters.,we could also expect that the number of X-ray sources has a stronger dependence on the total mass than on the encounter rate for the low-density core globular clusters.
 M12 1s a relatively low-density core globular cluster with 0772 of core radius and 2/16 of half-mass radius (Harris 1996. version of 2003 February).," M12 is a relatively low-density core globular cluster with $\farcm$ 72 of core radius and $\farcm$ 16 of half-mass radius (Harris 1996, version of 2003 February)."
 It i near the galactic disk (/=15°72. bΞ3260591) κο there are not so many (foreground or background) stars in the region as on the galactic disk.," It is near the galactic disk $l=15\fdg72$, $b=26\fdg31$ ) so there are not so many (foreground or background) stars in the region as on the galactic disk."
 The absolute visual magnitude of M12 ts -7.32., The absolute visual magnitude of M12 is -7.32.
 The distance to MI2 is 4.9 kpe and the extinction toward M12 is E[B-V|20.19 corresponding to a neutral hydrogen column density Ny=1.0 «107! cen (derived from Ny=5.3 « 10? E[B-V| cem? by Predehl Schmitt 1995)., The distance to M12 is 4.9 kpc and the extinction toward M12 is E[B-V]=0.19 corresponding to a neutral hydrogen column density $_\mathrm{H}$ $\times10^{21}$ $^{-2}$ (derived from $_\mathrm{H}$ $\times$ $^{21}$ E[B-V] $^{-2}$ by Predehl Schmitt 1995).
 We used these values in the following analysis., We used these values in the following analysis.
 According to a previous optical study. MI2 is an (optical) variable-poor cluster (Malakhova et al.," According to a previous optical study, M12 is an (optical) variable-poor cluster (Malakhova et al."
 1997)., 1997).
 Until 2001. only à few optical variables have been identified to be a W Vir variable (Sawyer 1938; Clement et al.," Until 2001, only a few optical variables have been identified to be a W Vir variable (Sawyer 1938; Clement et al."
 1988) or a W UMa variable (von Braun et al., 1988) or a W UMa variable (von Braun et al.
 2002)., 2002).
 In addition. some UV-bright stars have been discovered in the past decades (e.g. Zinn et al.," In addition, some UV-bright stars have been discovered in the past decades (e.g. Zinn et al."
 1972; Harris et al., 1972; Harris et al.
 1983: Geffert et al., 1983; Geffert et al.
 1991)., 1991).
 Previous observation of M12 with HEAO-1 and Einstein (Hertz WWood 1985) and with ROSAT in its All Sky Survey (Verbunt et al., Previous observation of M12 with HEAO-1 and Einstein (Hertz Wood 1985) and with ROSAT in its All Sky Survey (Verbunt et al.
 1995) did not detect a source., 1995) did not detect a source.
 The ROSAT upper limit is the lowest: ιοοσον<1.7«107 ssl em., The ROSAT upper limit is the lowest: $f_{0.5-2.5\mathrm{keV}}<1.7\times 10^{-13}$ $^{-1}$ $^{-2}$.
 In 52 we describe the observation and analysis of XX-ray data., In $\S2$ we describe the observation and analysis of X-ray data.
 The ooptical data is presented in 53., The optical data is presented in $\S3$.
 In 54. We discuss the source identification and in 55 compare our results with other globular clusters., In $\S4$ We discuss the source identification and in $\S5$ compare our results with other globular clusters.
 M12 was observed on 2004 July 17 for 26.6 ks with the Advanced CCD Imaging Spectrometer (ACIS) on the XX-Ray Observatory (ObsID 4530)., M12 was observed on 2004 July 17 for 26.6 ks with the Advanced CCD Imaging Spectrometer (ACIS) on the X-Ray Observatory (ObsID 4530).
 The telescope aim point is on the ACIS back-illuminated S3 chip., The telescope aim point is on the ACIS back-illuminated S3 chip.
 The data were taken in the timed mode with a frame transfer time of 3.24 s and were telemetered to the ground in faint mode., The data were taken in the timed mode with a frame transfer time of 3.24 s and were telemetered to the ground in faint mode.
 The field of view of ACIS S3 chip (~ 8.3 « 8.3 aremin’)” covering the whole radius of M12., The field of view of ACIS S3 chip $\sim$ 8.3 $\times$ 8.3 $^{2}$ covering the whole half-mass radius of M12.
 In this paper. we only consider the data taken with the S3 chip.," In this paper, we only consider the data taken with the S3 chip."
 We usedCIAO.. version 3.4 provided by the XX-Ray Center to perform data reduction and analysis.," We used, version 3.4 provided by the X-Ray Center to perform data reduction and analysis."
 We reprocessed the level | event files withCALDB.. version 3.4.2.," We reprocessed the level 1 event files with, version 3.4.2."
 The reprocessing included flagging and filtering out the cosmic rays and creating à new bad pixel file by using package., The reprocessing included flagging and filtering out the cosmic rays and creating a new bad pixel file by using package.
 The data were also filtered with the (Advanced Satellite for Cosmology and Astrophysics) grades of 0. 2. 3. 4. and 6 which is the standard value to optimize the mstrumental signal-to-background ratio.," The data were also filtered with the (Advanced Satellite for Cosmology and Astrophysics) grades of 0, 2, 3, 4, and 6 which is the standard value to optimize the instrumental signal-to-background ratio."
 We only processed the events extracted with photon energies in the range of 0.3-7 keV. Periods of high background flares (count rate > 5 counts ss! which is inspected from the entire area of chip SI) were eliminated., We only processed the events extracted with photon energies in the range of 0.3-7 keV. Periods of high background flares (count rate $>$ 5 counts $^{-1}$ which is inspected from the entire area of chip S1) were eliminated.
 The final effective exposure time was 26.5 ks., The final effective exposure time was 26.5 ks.
 The package was employed to detect X-ray sources inside the ACIS-S3 chip., The package was employed to detect X-ray sources inside the ACIS-S3 chip.
 The wavelet scales (also the sizes of the point spread function. PSF) were set to be a series from | to 16 increasing by a factor of 2.," The wavelet scales (also the sizes of the point spread function, PSF) were set to be a series from 1 to 16 increasing by a factor of $\sqrt{2}$."
 We also set the detection signal threshold to be 1079 such that there will be at most one false detection (fake source) caused by background fluctuation., We also set the detection signal threshold to be $10^{-6}$ such that there will be at most one false detection (fake source) caused by background fluctuation.
 The data was divided into three energy bands: soft band (0.3-] keV). medium band (1-2 keV). and hard band (2-7 keV).," The data was divided into three energy bands: soft band (0.3-1 keV), medium band (1-2 keV), and hard band (2-7 keV)."
 We performed with exposure maps on the total energy band (0.3-7 keV) and also the three sub-bands with the parameters described above., We performed with exposure maps on the total energy band (0.3-7 keV) and also the three sub-bands with the parameters described above.
 We then produced à master source list which was the combined source list of the 4 energy bands., We then produced a master source list which was the combined source list of the 4 energy bands.
 We detected 20 sources in the whole ACIS-S3 chip and 6 of them are inside the half-mass radius of M12., We detected 20 sources in the whole ACIS-S3 chip and 6 of them are inside the half-mass radius of M12.
 Figure | shows the resultant source detection on the chip., Figure 1 shows the resultant source detection on the chip.
 Table | shows the information of the 20 sources ordered by increasing unabsorbed flux within 0.3-7 keV. The columns list the source name. the position of the source (J2000.0). the net counts (source counts excluding the background contribution) in the three bands CXan. Xmedium. and μια). and the unabsorbed flux within 0.3-7 keV and 0.5-2.5 keV. The photon counts from the three bands were extracted from the source region corresponding to the 30 ," Table 1 shows the information of the 20 sources ordered by increasing unabsorbed flux within 0.3-7 keV. The columns list the source name, the position of the source (J2000.0), the net counts (source counts excluding the background contribution) in the three bands $X_\mathrm{soft}$, $X_\mathrm{medium}$ , and $X_\mathrm{hard}$ ), and the unabsorbed flux within 0.3-7 keV and 0.5-2.5 keV. The photon counts from the three bands were extracted from the source region corresponding to the $\sigma$ ellipse."
background counts were extracted from an annulus centered at the individual source and outside the 30 ellipse region.," Furthermore, the background counts were extracted from an annulus centered at the individual source and outside the $\sigma$ ellipse region."
 The unabsorbed flux was calculated from the source counts rate by assuming a power law model with a column density Ny = 107! cem and a photon index of 2., The unabsorbed flux was calculated from the source counts rate by assuming a power law model with a column density $_\mathrm{H}$ = $10^{21}$ $^{-2}$ and a photon index of 2.
 We also estimated the possible number of background sources., We also estimated the possible number of background sources.
 If we consider the 14 sources outside the cluster half- radius às background sources. then we can scale the backgroundsources inside the half-mass radius by the area," If we consider the 14 sources outside the cluster half-mass radius as background sources, then we can scale the backgroundsources inside the half-mass radius by the area"
Couneil for travel funding to La Palma.,Council for travel funding to La Palma.
 Some of the clata »esented in this paper were obtained from the Multimission Archive at the Space Telescope Science Institute (NLAST)., Some of the data presented in this paper were obtained from the Multimission Archive at the Space Telescope Science Institute (MAST).
 SISeb is operated by the Association of Universities. [or tesearch in Astronomy. Inc.. under NASA contract NAS5S-26555.," STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555."
 Support for ALAS for non-LIS'T data is provided by he NASA Ollice of Space Science via erant NACG5-75s4 and ov other grants and contracts., Support for MAST for non-HST data is provided by the NASA Office of Space Science via grant NAG5-7584 and by other grants and contracts.
 This research has mace use of the NASA/IPAC Extragalactic Database (NED) which is operated. by the Jet Propulsion Laboratory. California Institute of Technology. under contract with the National Acronautics and Space Administration.," This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration."
 , 
a power-law of index 4/3 in energy.,a power-law of index $4/3$ in energy.
 G is the gravitational constant., $G$ is the gravitational constant.
" Z and I are respectively the Riemann and the gamma functions, with Z(8/3)«1.2842 and T(8/3)«1.5046."," $\zeta$ and $\Gamma$ are respectively the Riemann and the gamma functions, with $\zeta\left(8/3\right)\approx 1.2842$ and $\Gamma\left(8/3\right)\approx 1.5046$."
" Hard X-rays are assumed to originate from the corona, a spherical region of radius R, (see Fig. B.2.))."," Hard X-rays are assumed to originate from the corona, a spherical region of radius $R_{\rm{c}}$ (see Fig. \ref{fig_corona}) )."
" The density of non-thermal X-rays follows where K, is a normalization constant and p the spectral index.", The density of non-thermal X-rays follows where $K_{\rm{c}}$ is a normalization constant and $p$ the spectral index.
" For simplicity, we assume that X-rays are emitted radially outside the corona (if p> Κε)."," For simplicity, we assume that X-rays are emitted radially outside the corona (if $\rho> R_{\rm{c}}$ )."
" If L, is the total luminosity of the corona, we have Hence the density of non-thermal X-rays outside the corona is where (if p# (s)2) If X-ray photons are homogeneous and isotropic inside the corona (p« Κο). then Gamma rays are injected on the axis of the accretion disk at an altitude z."," If $L_{\rm{c}}$ is the total luminosity of the corona, we have Hence the density of non-thermal X-rays outside the corona is where (if $p\neq 2$ ) If X-ray photons are homogeneous and isotropic inside the corona $\rho<R_c$ ), then Gamma rays are injected on the axis of the accretion disk at an altitude $z$."
" If z<R., gamma rays first cross the corona over a distance /p given by and escape at the point N (see Fig. B.2.))."," If $z< R_{\rm{c}}$, gamma rays first cross the corona over a distance $l_0$ given by and escape at the point N (see Fig. \ref{fig_corona}) )."
 We average over an isotropic distribution of pitch angle between both photons 6., We average over an isotropic distribution of pitch angle between both photons $\theta_0$.
 The integral over the length path in the full expression of the total optical depth (Eq. A1)), The integral over the length path in the full expression of the total optical depth (Eq. \ref{tau_gg}) )
 is trivial since there is an invariance in / for homogeneous target photon density., is trivial since there is an invariance in $l$ for homogeneous target photon density.
" The gamma-ray opacity inside the corona is Outside the corona, X-ray photonsare anisotropic and not homogeneous."," The gamma-ray opacity inside the corona is Outside the corona, X-ray photonsare anisotropic and not homogeneous."
" The angle of interaction is related to the length path / where Jp is given in Eq. (B6)),"," The angle of interaction is related to the length path $l$ where $l_0$ is given in Eq. \ref{l0}) ),"
" / is the distance NP, and p is the distance to the interaction point from the center OP such that The gamma-ray optical depth is then The total optical depth is Tj=Tint+ Text-"," $l$ is the distance NP, and $\rho$ is the distance to the interaction point from the center OP such that The gamma-ray optical depth is then The total optical depth is $\tau_{\gamma\gamma}=\tau_{\rm{int}}+\tau_{\rm{ext}}$ ."
specify a Gaussian or à Lorentzian profile with an assumed linewidth.,specify a Gaussian or a Lorentzian profile with an assumed linewidth.
 However. the intrinsic line profile of PAH emission bands ts distinctly non-Gaussian and non-Lorentzian due to the effects of anharmonicity and the accompanying red-shading (??).. ," However, the intrinsic line profile of PAH emission bands is distinctly non-Gaussian and non-Lorentzian due to the effects of anharmonicity and the accompanying red-shading \citep{1987ApJ...315L..61B, pech}."
Here. we will adopt Lorentzian profiles. fully realizing that this implies that this procedure will force the fit of the observed broader and red-shaded bands to blends by emission from multiple species.," Here, we will adopt Lorentzian profiles, fully realizing that this implies that this procedure will force the fit of the observed broader and red-shaded bands to blends by emission from multiple species."
 We will adopt an intrinsic Lorentzian linewidth of 6 em! for the out-of-plane bending modes and note that this 1s somewhat less than the measurements (~ 10 !) at ~700K for pyrene and coronene (?).., We will adopt an intrinsic Lorentzian linewidth of 6 $^{-1}$ for the out-of-plane bending modes and note that this is somewhat less than the measurements $\sim$ 10 $^{-1}$ ) at $\sim$ 700K for pyrene and coronene \citep{1995A&A...299..835J}.
" However. our ""choice"" to fit the observed. inherently asymmetric line profiles of the out-of-plane bending modes with symmetric calculated profiles forces us to adopt a somewhat small intrinsic line profile."," However, our “choice” to fit the observed, inherently asymmetric line profiles of the out-of-plane bending modes with symmetric calculated profiles forces us to adopt a somewhat small intrinsic line profile."
 We will assess the effect of these assumptions on our fiting results later on., We will assess the effect of these assumptions on our fitting results later on.
 Lastly. we mention that the relative strength. of the bands in the caleulated spectrum will also depend on the internal energy (eg..," Lastly, we mention that the relative strength of the bands in the calculated spectrum will also depend on the internal energy (eg.,"
 temperature) of the emitting species and hence on the absorbed photon energy and the temperature cascade., temperature) of the emitting species and hence on the absorbed photon energy and the temperature cascade.
 However. over the limited. wavelength range considered here. this effect is very small and we will here simply adopt a single absorbed UV photon energy (6.5 eV) characteristic for the benign conditions of the PDR in NGC 7023 (?)..," However, over the limited wavelength range considered here, this effect is very small and we will here simply adopt a single absorbed UV photon energy (6.5 eV) characteristic for the benign conditions of the PDR in NGC 7023 \citep{2009EAS....35..133J}."
 This corresponds to a peak temperature of ~900K for a 50 C-atom PAH., This corresponds to a peak temperature of $\sim$ 900K for a 50 C-atom PAH.
 The database evaluates the temperature for each PAH and follows the temperature cascade consistently., The database evaluates the temperature for each PAH and follows the temperature cascade consistently.
 Although our wavelength range ts limited. we choose to use the temperature cascade to represented the most physically accurate approach.," Although our wavelength range is limited, we choose to use the temperature cascade to represented the most physically accurate approach."
 The results for the fits of the three extracted BSS component signals are presented in Figure 7.. broken down in categories of PAH size and charge.," The results for the fits of the three extracted BSS component signals are presented in Figure \ref{fig:fit_matrix}, broken down in categories of PAH size and charge."
 The small ( «50 C atoms) and the large (250 C atoms) PAHs. as well as the cation. neutral. and anion species were separated out in order to judge each subgroupOs contribution to the fit.," The small ( $<$ 50 C atoms) and the large $\geq$ 50 C atoms) PAHs, as well as the cation, neutral, and anion species were separated out in order to judge each subgroupÕs contribution to the fit."
 A fit to the raw observed spectra at à typical position. was also made (Figure 8))., A fit to the raw observed spectra at a typical position was also made (Figure \ref{fig:fitvbss}) ).
 The results are summarized in Table .., The results are summarized in Table \ref{tab:tab1}.
 It should be emphasized that the contribution of individual species was quantified in terms of emission intensity. not in terms of abundance.," It should be emphasized that the contribution of individual species was quantified in terms of emission intensity, not in terms of abundance."
" Figure 8. shows a comparison between the PAH™ and PAH? contributions of the database fit (top). and the PAH and PAH"" contributions in the BSS decomposition (bottom)."," Figure \ref{fig:fitvbss} shows a comparison between the $^+$ and $^0$ contributions of the database fit (top), and the $^+$ and $^0$ contributions in the BSS decomposition (bottom)."
 The results of the database fits highlight various trends., The results of the database fits highlight various trends.
 First. except for the VSG spectrum. the overall contribution of large versus small PAHs seems very even.," First, except for the VSG spectrum, the overall contribution of large versus small PAHs seems very even."
 This may arise from the three times greater number of smaller PAHs in the database., This may arise from the three times greater number of smaller PAHs in the database.
 Remarkably. although they represent only of the database. the main features of each spectrum are generated by the larger PAHs while the continuum and less dominant features arereproduced primarily by the smaller PAHs.," Remarkably, although they represent only of the database, the main features of each spectrum are generated by the larger PAHs while the continuum and less dominant features arereproduced primarily by the smaller PAHs."
" Second. both the fit of the observed raw spectra shown m Figure 8. and the various PAH charge state contributions shown in the right side of Figure 7. clearly shows that the dominant contributors to the 11.0 jm band are PAH™ while the bulk of the [1.2 4m feature is due to PAH"" species."," Second, both the fit of the observed raw spectra shown in Figure \ref{fig:fitvbss} and the various PAH charge state contributions shown in the right side of Figure \ref{fig:fit_matrix} clearly shows that the dominant contributors to the 11.0 $\mu$ m band are $^+$ while the bulk of the 11.2 $\mu$ m feature is due to $^0$ species."
 This behavior. based on the spectra of hundreds of PAHs. confirms the early suggestion. based on a handful of experimental PAH spectra. that the emission between 10.8 and 11.1 um can be used as a tracer of PAH cations (?)..," This behavior, based on the spectra of hundreds of PAHs, confirms the early suggestion, based on a handful of experimental PAH spectra, that the emission between 10.8 and 11.1 $\mu$ m can be used as a tracer of PAH cations \citep{hudgins}."
 It should also be noted that the BSS extracted VSGsignal has two strong absorption features at about 11.0 and 12.6 jm. These probably arise from cross mixing as deseribed earlier and are likely artificial (Appendix AppendixA:))., It should also be noted that the BSS extracted VSGsignal has two strong absorption features at about 11.0 and 12.6 $\mu$ m. These probably arise from cross mixing as described earlier and are likely artificial (Appendix \ref{sec:appendixa}) ).
 Therefore. the fit was also performed with a linear interpolation over these points.," Therefore, the fit was also performed with a linear interpolation over these points."
 This fit produced almost identical results., This fit produced almost identical results.
 Common concerns regarding the PAH Database fitting methods are uniqueness and degeneracy., Common concerns regarding the PAH Database fitting methods are uniqueness and degeneracy.
 In the case of PAHs with a limited wavelength range. these concerns must be approached in a different way.," In the case of PAHs with a limited wavelength range, these concerns must be approached in a different way."
 This is further discussed and investigated in Appendix AppendixB:., This is further discussed and investigated in Appendix \ref{sec:appendixb}.
". These studies show that if the database is tasked to fit the BSS extracted ΡΑΗ spectra with only PAH"" species. this is not possible. further strengthening the attribution of the 11.0 jm feature to PAH”."," These studies show that if the database is tasked to fit the BSS extracted $^+$ spectra with only $^0$ species, this is not possible, further strengthening the attribution of the 11.0 $\mu$ m feature to $^+$."
" On the other hand. if the database attempts to fit the BSS extracted PAH"" signal with only PAH. a suitable fit is provided."," On the other hand, if the database attempts to fit the BSS extracted $^0$ signal with only $^+$, a suitable fit is provided."
 However. without any limitations of the database fit. the reduced norm fit chooses predominately PAH™ to fit the BSS extracted PAH™ signal and PAH to fit the BSS extracted PAH® signal (Table 1)).," However, without any limitations of the database fit, the reduced norm fit chooses predominately $^+$ to fit the BSS extracted $^+$ signal and $^0$ to fit the BSS extracted $^0$ signal (Table \ref{tab:tab1}) )."
 This only shows that PAH cations have emission features that peak through the 10 - 15 jm range and it is important to employ more than one method to apply as many astronomical constraints as possible., This only shows that PAH cations have emission features that peak through the 10 - 15 $\mu$ m range and it is important to employ more than one method to apply as many astronomical constraints as possible.
 Investigating the spectra and examining the spatial distribution of the extracted emission. components. we recognize four aspects that vary with spatial position: the [11.0]/[11.2] jm ratio. the red wing of the 11.2 jim feature. the precise peak position of the 11.2 ym band. and the weak features at 12.0. 12.7. and 13.5 jm. In the following section we discuss these variations in the context of Signal 1. 2. and 3. which will now be referred to as PAH”. PAH™. and VSGs. as emission feature carriers.," Investigating the spectra and examining the spatial distribution of the extracted emission components, we recognize four aspects that vary with spatial position: the [11.0]/[11.2] $\mu$ m ratio, the red wing of the 11.2 $\mu$ m feature, the precise peak position of the 11.2 $\mu$ m band, and the weak features at 12.0, 12.7, and 13.5 $\mu$ m. In the following section we discuss these variations in the context of Signal 1, 2, and 3, which will now be referred to as $^0$ , $^+$ , and VSGs, as emission feature carriers."
An alternative approach to the 2D MGE fit of an image. using Gaussians with the same PA and the same centre. consists of transforming the whole problem into à NNLS problem. that can be solved with the Lawson Hanson (1974) algorithm.,"An alternative approach to the 2D MGE fit of an image, using Gaussians with the same PA and the same centre, consists of transforming the whole problem into a NNLS problem, that can be solved with the Lawson Hanson (1974) algorithm."
 This can be done by generating a large grid of all possible Gaussians that may end up in the final solution., This can be done by generating a large grid of all possible Gaussians that may end up in the final solution.
" We sample e; logarithmically with Ruin€0jXPha for every choice of 7 we sample qd, linearly with 0<qd,«1.", We sample $\sigma_j$ logarithmically with $R_{\rm min}<\sigma_j<R_{\rm max}$; for every choice of $\sigma_j$ we sample $q'_j$ linearly with $0<q'_j<1$.
 The non-negative superposition of the Gaussians that best fit the data is then found with NNLS., The non-negative superposition of the Gaussians that best fit the data is then found with NNLS.
 This approach is memory intensive since a copy of the data has to be kept in memory for every Gaussian inthe grid: a LOO.100 grid requires 107 copies of the photometric data. yet it is already feasible if only the sectors are used.," This approach is memory intensive since a copy of the data has to be kept in memory for every Gaussian inthe grid: a $100\times100$ grid requires $10^4$ copies of the photometric data, yet it is already feasible if only the sectors are used."
 The advantage of this method is that it is to find he lowest X solution (although it may not be unique) within he accuracy imposed by the adopted grid of Gaussians., The advantage of this method is that it is to find the lowest $\chi^2$ solution (although it may not be unique) within the accuracy imposed by the adopted grid of Gaussians.
 A big disadvantage is that in practice many more Gaussians are used py the NNLS algorithm to produce a fit with the same \7 as ound with our nonlinear algorithm of Section 3.3.., A big disadvantage is that in practice many more Gaussians are used by the NNLS algorithm to produce a fit with the same $\chi^2$ as found with our nonlinear algorithm of Section \ref{sec:2d}.
 This is in general an important point. since one often needs to use the MGE xrametrization to perform subsequent calculations whose speed depends on the number of Gaussians: the. computation. of the xotential scales linearly. with the number ;N. of Gaussians. while or example the solution of the Jeans equations scales as V7 (Emsellem et 119942).," This is in general an important point, since one often needs to use the MGE parametrization to perform subsequent calculations whose speed depends on the number of Gaussians: the computation of the potential scales linearly with the number $N$ of Gaussians, while for example the solution of the Jeans equations scales as $N^2$ (Emsellem et 1994a)."
 As an example we have used a LOO.100 grid of (a.q) values (107 Gaussians) to produce an MGE model for NGC 4342 using the same input photometry of Section 3.3..," As an example we have used a $100\times100$ grid of $(\sigma,q')$ values $10^4$ Gaussians) to produce an MGE model for NGC 4342 using the same input photometry of Section \ref{sec:2d}."
 The NNLS algorithm gave a best solution with 38 positive Gaussians and an error only slightly smaller than that of the 13 Gaussians nonlinear solution of Fig., The NNLS algorithm gave a best solution with 38 positive Gaussians and an error only slightly smaller than that of the 13 Gaussians nonlinear solution of Fig.
 (RMS error of 1.7 per cent. to be compared with 1.8 per cent for the nonlinear solution).," \ref{fig:n4342_profiles} (RMS error of 1.7 per cent, to be compared with 1.8 per cent for the nonlinear solution)."
" Since the NNLS solution is ill-conditioned it may be possible to extract a subsample from the 38 Gaussians that gives essentially the same \j,.., of the best solution.", Since the NNLS solution is ill-conditioned it may be possible to extract a subsample from the 38 Gaussians that gives essentially the same $\chi^2_{\rm best}$ of the best solution.
 In particular one would like to tind the set of Gaussians that still verifies X.« Vea where ¢ represents a chosen fractional tolerance.," In particular one would like to find the set of Gaussians that still verifies $\chi^2 < (1+\epsilon)\; \chi^2_{\rm best}$ , where $\epsilon$ represents a chosen fractional tolerance."
 Unfortunately this is a combinatorial minimization problem whose, Unfortunately this is a combinatorial minimization problem whose
The study of luminous and dark matter in elliptical galaxies is crucial to understanding the formation of massive galaxies in our Universe.,The study of luminous and dark matter in elliptical galaxies is crucial to understanding the formation of massive galaxies in our Universe.
 In. hierarchical models. ellipticals are the result. of interactions ancl mergers of spiral galaxies (e.g. Blumenthal et al.," In hierarchical models, ellipticals are the result of interactions and mergers of spiral galaxies (e.g. Blumenthal et al."
 1984)., 1984).
 This is in contrast to a scenario in which they form from a monolithic collapse (c.g. Egecn et al, This is in contrast to a scenario in which they form from a monolithic collapse (e.g. Eggen et al.
 1962: Cranato. et al., 1962; Granato et al.
 2004)., 2004).
 The most massive elliptical galaxies. with barvonie masses AZ>LOMAL.. are challenging because they should have formed. in the very carly universe and at the same time undergone a Large deal of merging.," The most massive elliptical galaxies, with baryonic masses $M>10^{11}M_{\odot}$, are challenging because they should have formed in the very early universe and at the same time undergone a large deal of merging."
" There is now growing evidence that massive galaxies (Ad,~101 AL.) did exist at 2~2.", There is now growing evidence that massive galaxies $M_* \sim 10^{11}$ $_\odot$ ) did exist at $z\sim 2$.
 Some work suggests that they were much smaller and denser than their. local counterparts of the same stellar mass (e.g. Trujillo ct al., Some work suggests that they were much smaller and denser than their local counterparts of the same stellar mass (e.g. Trujillo et al.
 2006: van Dokkum ct al., 2006; van Dokkum et al.
 2008: Cimatti et al., 2008; Cimatti et al.
 2008: Saracco et al., 2008; Saracco et al.
 2009) and that similar compact. galaxies to those observed at. high-redshift do not exist in the local universe (e.g. Trujillo et al., 2009) and that similar compact galaxies to those observed at high-redshift do not exist in the local universe (e.g. Trujillo et al.
 2009)., 2009).
 These results raised the question of what process or processes have acted to increase the sizes of these objects to make them consistent with the larger sizes we see at late times (e.g. van Dokkunm et al., These results raised the question of what process or processes have acted to increase the sizes of these objects to make them consistent with the larger sizes we see at late times (e.g. van Dokkum et al.
 2008: Fan et al., 2008; Fan et al.
 2008)., 2008).
 Aozanson et al. (, Bezanson et al. (
2009) showed that the stellar density within the central | kpe of cllipticals at z2.3 is similar to that for nearby ellipticals (they diller by only a factor of 2. compared. to a difference of a factor of ~100 if the comparison is done within the hall-light raclius).,"2009) showed that the stellar density within the central 1 kpc of ellipticals at $z\sim 2.3$ is similar to that for nearby ellipticals (they differ by only a factor of $\sim 2$, compared to a difference of a factor of $\sim 100$ if the comparison is done within the half-light radius)."
 This suggests an inside-out. hierarchical growth scenario dominated by dry. minor mergers which add mass primarily to the outer regions (e.g. Loeb Peebles 2003: Bournaud et al.," This suggests an inside-out, hierarchical growth scenario dominated by dry minor mergers which add mass primarily to the outer regions (e.g. Loeb Peebles 2003; Bournaud et al."
 2007: Naab et al., 2007; Naab et al.
 2007: Hopkins et al., 2007; Hopkins et al.
 2009)., 2009).
the pulsar position is determined from the annual variation of TOAs as the Earth moves about its orbit. proper motion is determined from a secular variation of this annual signal.,"the pulsar position is determined from the annual variation of TOAs as the Earth moves about its orbit, proper motion is determined from a secular variation of this annual signal."
 Timing noise or other svstematic effects can contaminate such measurements., Timing noise or other systematic effects can contaminate such measurements.
 We now believe that the previously reported. value of PSR DI9134-168 proper motion 1989) was biased by timing noise. a problem which was exacerbated by the concentrated but c-bienniallv spaced observing campaigns frequently emploved for this source.," We now believe that the previously reported value of PSR B1913+16's proper motion \citep{tw89} was biased by timing noise, a problem which was exacerbated by the concentrated but $\sim$ biennially spaced observing campaigns frequently employed for this source."
 To circumvent these problems. we observed PSR D19134-16 several times over the course of calendar νου 2004 to achieve thorough data coverage around the Earth's orbit.," To circumvent these problems, we observed PSR B1913+16 several times over the course of calendar year 2004 to achieve thorough data coverage around the Earth's orbit."
 By merging the 2004 data with observations made in 1985-1988. which also had good coverage throughout (hose vears. we have now obtained a robust measurement of the pulsars proper motion.," By merging the 2004 data with observations made in 1985-1988, which also had good coverage throughout those years, we have now obtained a robust measurement of the pulsar's proper motion."
 See Section 5Hr for farther analvses of the proper motion result., See Section \ref{sec:vel} for further analyses of the proper motion result.
 As in other pulsars. the measured spindown rate f is assumed {ο be the result of an electromagnetic braking torque on the spinning. strongly magnetized neutron star.," As in other pulsars, the measured spindown rate $\dot f$ is assumed to be the result of an electromagnetic braking torque on the spinning, strongly magnetized neutron star."
 Its value is deterministic and (at the level of accuracy. quoted in Table 2) independent of the span of data over which it is fitted., Its value is deterministic and (at the level of accuracy quoted in Table 2) independent of the span of data over which it is fitted.
" In addition.the pulsar experienced a well-defined. ""classical elitch in May 2003."," In addition,the pulsar experienced a well-defined “classical” glitch in May 2003."
 The magnitude Af/f—3.7x10! of the event is smaller than almost all seen in (he population of normal (not recycled) pulsars. with only some of the elitches in PSR. D03554-54 having a comparably small magnitude (Melatos&Urama 2010).," The magnitude $\Delta
f/f=3.7\times10^{-11}$ of the event is smaller than almost all seen in the population of normal (not recycled) pulsars, with only some of the glitches in PSR B0355+54 having a comparably small magnitude \citep{mel08,cu10}."
. Ours is only the second eliteh to be detected in a reeveled pulsar. with the other (the smallest known amone all pulsars) occurring in the millisecond. pulsar PSR D1321—24 in globular cluster M28 (Cognard&Backer2004).," Ours is only the second glitch to be detected in a recycled pulsar, with the other (the smallest known among all pulsars) occurring in the millisecond pulsar PSR $-$ 24 in globular cluster M28 \citep{cb04}."
. The remaining Ging parameters — hieher-order derivatives f. n aand (in some lits) another small frequency discontinuity. in mid-1992 were introduced (o the timing solution in an manner. in order to “whiten” the remaining post-lit residuals.," The remaining timing parameters — higher-order derivatives $\ddot
f$, $\dddot f$, and (in some fits) another small frequency discontinuity in mid-1992 — were introduced to the timing solution in an manner, in order to “whiten” the remaining post-fit residuals."
 Although we olfer no clear or unique physical interpretation for these parameters. (heir combined effects are almost certainly a consequence of stochastic timing-noise processes in the neutron star interior (Cordes&Downs1985:Arzommanianetal.1994:Urama2006).," Although we offer no clear or unique physical interpretation for these parameters, their combined effects are almost certainly a consequence of stochastic timing-noise processes in the neutron star interior \citep{cd85,aet94,ulw06}."
. Unlike the case ol the well-fitted May 2003 eliteh. the values of these fitted parameters are not independent of the data span analyzed and cannot be expected to extrapolate (he timing behavior accurately to future epochs.," Unlike the case of the well-fitted May 2003 glitch, the values of these fitted parameters are not independent of the data span analyzed and cannot be expected to extrapolate the timing behavior accurately to future epochs."
 Icdentifvine the mid-1992 behavior as a discrete event is highly uncertain. in part because of coarse sampling around (hat time.," Identifying the mid-1992 behavior as a discrete event is highly uncertain, in part because of coarse sampling around that time."
 Our data can be fit almost as well by introducing several additional Irequency. derivatives instead of a second discrete event., Our data can be fit almost as well by introducing several additional frequency derivatives instead of a second discrete event.
 sinilar results were obtained by fitting multiple harmonically related sinusoids to the timing noise with the routine “FITWAVES” (LIlobbsetal.2004) of program TEMPO? (IIobbsοἱal.2006:Edwardsetal. 2006).. instead of the multiple frequency. derivatives described above.," Similar results were obtained by fitting multiple harmonically related sinusoids to the timing noise with the routine “FITWAVES” \citep{het04} of program TEMPO2 \citep{het06,eet06}, instead of the multiple frequency derivatives described above."
 since we are unable {ο converge on a unique glitch parameter solution for the mid-1992 behavior. we do not include this event in Table 2..," Since we are unable to converge on a unique glitch parameter solution for the mid-1992 behavior, we do not include this event in Table \ref{table:astromfits}. ."
"ULIRGs (Li, = 10'7L.). which in the local universe are known to be mergers of gas rich galaxies. are thought to play a critical role in galaxy evolution.","ULIRGs $_{IR}$ $\geq 10^{12} L_{\odot}$ ), which in the local universe are known to be mergers of gas rich galaxies, are thought to play a critical role in galaxy evolution."
 It 1s therefore crucial to understand the conditions. dynamics. chemistry and energetics of this stage of evolution. in which dissipative collapse accompanies the transformation of gas rich galaxies into ellipticals (Lonsdale et al.," It is therefore crucial to understand the conditions, dynamics, chemistry and energetics of this stage of evolution, in which dissipative collapse accompanies the transformation of gas rich galaxies into ellipticals (Lonsdale et al."
 2006)., 2006).
 As part of the Key Project on local galaxies. we are carrying out a far-infrared (FIR) spectroscopic survey of all 21 ULIRGs im the Revised Bright Galaxy Survey (Sanders et al.," As part of the Key Project on local galaxies, we are carrying out a far-infrared (FIR) spectroscopic survey of all 21 ULIRGs in the Revised Bright Galaxy Survey (Sanders et al."
 2003)., 2003).
 Previous work on ULIRGs with the Infrared Space Observatory (ISO) Long Wavelength Spectrometer (LWS) found deficits in far-infrared atomic and ionized fine-structure line emission relative to their FIR luminosities (Luhman et al. 1998)), Previous work on ULIRGs with the Infrared Space Observatory (ISO) Long Wavelength Spectrometer (LWS) found deficits in far-infrared atomic and ionized fine-structure line emission relative to their FIR luminosities (Luhman et al. \cite{Luhman98}) )
 accompanied by prominent molecular absorption in excited transitions of molecules such as OH and H:O rarely seen in other galaxies (Fischer et al. 1999))., accompanied by prominent molecular absorption in excited transitions of molecules such as OH and $_2$ O rarely seen in other galaxies (Fischer et al. \cite{Fischer99}) ).
 The deficits. often based only on a few non-detections. were postulated to result from the high ratios of UV radiation density to particle density in the nuclet of these galaxies (Malhotra et al.," The deficits, often based only on a few non-detections, were postulated to result from the high ratios of UV radiation density to particle density in the nuclei of these galaxies (Malhotra et al."
 2001. Luhman et al.," 2001, Luhman et al."
 2003. Abel et al.," 2003, Abel et al."
 2009). high gas density (e.g. Negishi et al.," 2009), high gas density (e.g. Negishi et al."
 2001) and high FIR opacity and/or high lummosity-to-mass ratio (Gonzállez-Alfonso et al., 2001) and high FIR opacity and/or high luminosity-to-mass ratio (Gonz\'{a}llez-Alfonso et al.
 2004. 2008. hereafter GAO4. GAOS). but because of the paucity of diagnostic line detections this puzzle remained unresolved.," 2004, 2008, hereafter GA04, GA08), but because of the paucity of diagnostic line detections this puzzle remained unresolved."
 GAO4 and GAOS showed that the high excitation molecular absorptions m both Arp 220 and Mrk 231 are radiatively pumped. consistent with high radiation density to particle density.," GA04 and GA08 showed that the high excitation molecular absorptions in both Arp 220 and Mrk 231 are radiatively pumped, consistent with high radiation density to particle density."
" They identified far-infrared absorption by OH. H:O. NHs. NH. and ""OH. but the identifications of the latter species were uncertain due to the low resolution of the LWS."," They identified far-infrared absorption by OH, $_2$ O, $_3$, NH, and $^{18}$ OH, but the identifications of the latter species were uncertain due to the low resolution of the LWS."
 The PACS ULIRG spectroscopic survey is designed to kinematically identify the 10nized. atomic and molecular regions and to study the conditions of the interstellar medium. thereby illuminating the nature of this important evolutionary phase.," The PACS ULIRG spectroscopic survey is designed to kinematically identify the ionized, atomic and molecular regions and to study the conditions of the interstellar medium, thereby illuminating the nature of this important evolutionary phase."
 In this first paper we present our initial results on Mrk 231. the most luminous of the local ULIRGs (L(8-1000 pm) = 3.2 x 10% Ls) and a type |. low-ionization broad absorption line (LoBAL) active galactic nucleus (AGN) at an adopted distance of 172 Mpe (z=0.04217).," In this first paper we present our initial results on Mrk 231, the most luminous of the local ULIRGs (L(8–1000 $\mu$ m) = 3.2 $\times$ $^{12}$ $_{\odot}$ ) and a type 1, low-ionization broad absorption line (LoBAL) active galactic nucleus (AGN) at an adopted distance of 172 Mpc (z=0.04217)."
 Its central quasar is covered by a semi-transparent dusty shroud producing about 3.1 magnitudes of extinction at 4400 A (Reynolds et al., Its central quasar is covered by a semi-transparent dusty shroud producing about 3.1 magnitudes of extinction at 4400 $\AA$ (Reynolds et al.
 2009) and is at the center of a rotating. nearly face-on molecular disk (Downes Solomon 1998).," 2009) and is at the center of a rotating, nearly face-on molecular disk (Downes Solomon 1998)."
 Based primarily on results. Veilleux et al. (," Based primarily on results, Veilleux et al. ("
2009) estimate that the average AGN contribution to the bolometric luminosity in. ULIRGs its 35 — and that for Mrk 231 the AGN contribution is ~ by most estimation techniques.,2009) estimate that the average AGN contribution to the bolometric luminosity in ULIRGs is 35 – and that for Mrk 231 the AGN contribution is $\sim$ by most estimation techniques.
 The contribution of an advanced 120 — 250 Myr nuclear starburst Is estimated at 25 — based on near infrared observations of Mrk 231 by Davies et al. (, The contribution of an advanced 120 – 250 Myr nuclear starburst is estimated at 25 – based on near infrared observations of Mrk 231 by Davies et al. (
2007).,2007).
 The observations were taken with the Photodetector Array Camera and Spectrometer (PACS) integral field spectrometer (Poglitsch et al., The observations were taken with the Photodetector Array Camera and Spectrometer (PACS) integral field spectrometer (Poglitsch et al.
 2010) on board the Space Observatory (Pilbratt et al., 2010) on board the Space Observatory (Pilbratt et al.
 2010) in high spectral sampling range spectroscopy mode using small chop-nod cycles., 2010) in high spectral sampling range spectroscopy mode using small chop-nod cycles.
" Scans covering the range + 1300 km s were taken around five fine- lines and a longer range scan included the OH 119 m Πιν 8/2 — 3/2 A-doublet transitions. the '""OH 120 m counterparts. and the [NI] 122 jem fine-structure line."," Scans covering the range $\pm$ 1300 km $^{-1}$ were taken around five fine-structure lines and a longer range scan included the OH 119 $\mu$ m $^{2}\Pi_{3/2}$ 5/2 – 3/2 $\Lambda-$ doublet transitions, the $^{18}$ OH 120 $\mu$ m counterparts, and the [NII] 122 $\mu$ m fine-structure line."
 The OH 79 um Πιο Πιν 1/2 - 3/2 A-doublet transitions. the nearly superposed '*OH counterparts. and the H1O 78.7 pm 423 — 3)2 line were observed in parallel on the blue array.," The OH 79 $\mu$ m $^{2}\Pi_{1/2}$ – $^{2}\Pi_{3/2}$ 1/2 – 3/2 $\Lambda-$ doublet transitions, the nearly superposed $^{18}$ OH counterparts, and the $_2$ O 78.7 $\mu$ m $_{23}$ – $_{12}$ line were observed in parallel on the blue array."
 The basic data reduction was done using the standard PACS reduction and calibration pipeline (ipipe) included in. HIPE, The basic data reduction was done using the standard PACS reduction and calibration pipeline (ipipe) included in HIPE
to the expected vj) but it could also be a signal related to granulation.,to the expected $\nu\ind{\rm max}$ ) but it could also be a signal related to granulation.
 Up to now. the background of all the precedent CoRoT solar-like targets (HD 49933. HD 175726. HD 181420. HD 181906 and HD 49385) has been correctly characterized by a single component in the Harvey model (?) that has been associated to granulation.," Up to now, the background of all the precedent CoRoT solar-like targets (HD 49933, HD 175726, HD 181420, HD 181906 and HD 49385) has been correctly characterized by a single component in the Harvey model \citep{1985ESASP.235..199H} that has been associated to granulation."
 However. when comparing the spectrum of HD 170987 to the one of the Sun obtained using the VIRGO instrument (?) and to solar-type stars observed by the Kepler satellite (Chaplin et al.," However, when comparing the spectrum of HD 170987 to the one of the Sun obtained using the VIRGO instrument \citep{1995SoPh..162..101F} and to solar-type stars observed by the Kepler satellite (Chaplin et al."
 2010) we see that in these cases a second Harvey power law has been used to take into account some extra power located around 1000 Hz (time-scale close to 80 s)., 2010) we see that in these cases a second Harvey power law has been used to take into account some extra power located around 1000 $\mu$ Hz (time-scale close to 80 s).
 Based on the smoothed PSD we can therefore not conclude that the spectrum shows p-mode oscillations while we see some excess power centered at ~ Hz.," Based on the smoothed PSD we can therefore not conclude that the spectrum shows p-mode oscillations while we see some excess power centered at $\sim$ $\,\mu$ Hz."
 For the precise analysis of the acoustic. background. different strategies have been followed to study the bump at 1000 Hz.," For the precise analysis of the acoustic background, different strategies have been followed to study the bump at 1000 $\mu$ Hz."
 We start by assuming that the bump around 3004 Hz originates from granulation and the one at ~ 1000 Hz could originate from a shorter convective scale or by faculae.," We start by assuming that the bump around $\mu$ Hz originates from granulation and the one at $\sim$ $\,\mu$ Hz could originate from a shorter convective scale or by faculae."
 The faculaes are the bright points seen on visual solar images often close to the dark sunspots., The faculaes are the bright points seen on visual solar images often close to the dark sunspots.
 They are due to changes in the opacity caused by a strong magnetic field which means that we see the inside rather than the surface of the granulation and as the temperature is higher inside the granulation cells than at their surfaces the faculaes appear brighter than there surroundings (?).., They are due to changes in the opacity caused by a strong magnetic field which means that we see the inside rather than the surface of the granulation and as the temperature is higher inside the granulation cells than at their surfaces the faculaes appear brighter than there surroundings \citep{2004ApJ...607L..59K}.
 The carateristic timescale of the faculae is shorter than the time-scale of the granulation cells because the faculaes only sample the edges of the granulation cells., The carateristic timescale of the faculae is shorter than the time-scale of the granulation cells because the faculaes only sample the edges of the granulation cells.
 Following Harvey (1985) we model the smoothed PSD in the range [200 - Hz with a background model containing two components plus the photon-noise contribution (c) that dominate the PSD at high frequency. 1.8. Here. στων and taeT are the amplitudes of the background signal of granulation and the second convective component or faculae respectively. τ Is the time-scale. and eran and peu are two constants.," Following Harvey (1985) we model the smoothed PSD in the range [200 - $\mu$ Hz with a background model containing two components plus the photon-noise contribution $c$ ) that dominate the PSD at high frequency, i.e. Here, $\sigma\ind{gran}$ and $\sigma\ind{facu}$ are the amplitudes of the background signal of granulation and the second convective component or faculae respectively, $\tau$ is the time-scale, and $a_{\rm gran}$ and $a_{\rm facu}$ are two constants."
 Because we are modelling a smoothed version of the PSD we can assume that the error between the model and the observations are normally distributed., Because we are modelling a smoothed version of the PSD we can assume that the error between the model and the observations are normally distributed.
 We can therefore fit the model to the observations by means of least squares., We can therefore fit the model to the observations by means of least squares.
 Using the robust non-linear least squares curve fitting IDL package MPFIT (http://www.physies.wisc.edu/- eraigm/idl/idl.html) we obtain a granulation time-scale of 3832228 s and à second component with a time-scale of € 551 s. We then assumed that the second bump. around 1000 Hz. is caused by p modes.," Using the robust non-linear least squares curve fitting IDL package MPFIT $\sim$ craigm/idl/idl.html) we obtain a granulation time-scale of $\pm$ 28 s and a second component with a time-scale of $\pm$ 51 s. We then assumed that the second bump, around 1000 $\mu$ Hz, is caused by p modes."
 Thus. for the background fitting. we use the first two terms of equation (2) — the photon noise and one Harvey model component- and fitted à Gaussian function to the second bump.," Thus, for the background fitting, we use the first two terms of equation (2) – the photon noise and one Harvey model component– and fitted a Gaussian function to the second bump."
 This led to a very similar fit compared to the previous one. with the same parameters for the granulation time-scale (see Fig. 9)).," This led to a very similar fit compared to the previous one, with the same parameters for the granulation time-scale (see Fig. \ref{back}) )."
 Consequently. both assumptions could be correct and we cannot disentangle which one is the best one at this stage of the analysis.," Consequently, both assumptions could be correct and we cannot disentangle which one is the best one at this stage of the analysis."
 In order to determine whether HD 170987 presents solar-like oscillations. we have applied several methods.," In order to determine whether HD 170987 presents solar-like oscillations, we have applied several methods."
 One of them consists of searching for the signature of the mean large separation of a solar-like oscillating signal in. the autocorrelation of the time series., One of them consists of searching for the signature of the mean large separation of a solar-like oscillating signal in the autocorrelation of the time series.
 As proposed by ?.. in a refined application of the Wiener-Khinchine theorem. this autocorrelation is calculated as the Fourter spectrum of the windowed Fourier spectrum.," As proposed by \cite{2006MNRAS.369.1491R}, in a refined application of the Wiener-Khinchine theorem, this autocorrelation is calculated as the Fourier spectrum of the windowed Fourier spectrum."
 ? subsequently used a narrower window to look for the variation of the large separation with frequency., \citet{2009A&A...506..435R} subsequently used a narrower window to look for the variation of the large separation with frequency.
 ? have shown how to optimize the method and to determine its reliability., \cite{2009A&A...508..877M} have shown how to optimize the method and to determine its reliability.
 They have scaled the autocorrelation function according to the noise contribution. in order to statistically test its significance.," They have scaled the autocorrelation function according to the noise contribution, in order to statistically test its significance."
 Then. when the envelope autocorrelation function (EACF) gives a signal above a defined threshold level. the null hypothesis can be rejected. and a reliable large separation can be derived.," Then, when the envelope autocorrelation function (EACF) gives a signal above a defined threshold level, the null hypothesis can be rejected, and a reliable large separation can be derived."
 For a blinc analysis of the mean value. (Av). of the large separation and a rejection of the null hypothesis at the level The method has shown to be efficient in low signal-to-noise cases. such as the CoRoT target HD 175726 (?) orin the KIV target with a height-to-background ratio ® as low as Other methods have been used giving a mean large separation between 54 and 56 μΗΖ (??)..," For a blind analysis of the mean value, $\dnumoy$, of the large separation and a rejection of the null hypothesis at the level The method has shown to be efficient in low signal-to-noise cases, such as the CoRoT target HD 175726 \citep{2009A&A...506...33M} or in the K1V target with a height-to-background ratio $\HBR$ as low as Other methods have been used giving a mean large separation between 54 and 56 $\mu$ Hz \citep{2010MNRAS.402.2049H,2010A&A...511A..46M}."
 Indeed. using the method described in ?.. we have calculated the power spectrum (PS) of the power spectrum (PS2) between 100 and 10000 iJ: Hz.," Indeed, using the method described in \citet{2010A&A...511A..46M}, we have calculated the power spectrum (PS) of the power spectrum (PS2) between 100 and 10000 $\mu$ Hz."
 We select the highest peak and we assume that it corresponds to half of the mean large separation., We select the highest peak and we assume that it corresponds to half of the mean large separation.
 Then. we cut the original PSD in boxes of 600 μΗ7. shifted every 60 μΗΖ and we compute the PS? of each box," Then, we cut the original PSD in boxes of 600 $\mu$ Hz, shifted every 60 $\mu$ Hz and we compute the PS2 of each box"
and Peitemery4XLO|.,"and $\rho_{BH-He,merg} \sim 4\times10^{-4}$."
" The required number of events is Veyacpc7XLO? (6,/0.05)>7 (CE/0.8)? (D/10sec) (u/0.1AM.).1 (1/2000pe)! and Neigs~4X10° (6,,/0.05)2 CE/0.8)? (D/10sec) (1/0.4.).1 (4/2000:pe)!.", The required number of events is $N_{BH-WD} \sim 7\times 10^9 $ $(\epsilon_m/0.05)^{-2}$ $(F/0.8)^2$ $(T/10 ~\mbox{sec})$ $(\mu/0.1M_\odot)^{-4}$ $(d/2000Mpc)^{4}$ and $N_{BH-He} \sim 4\times 10^7$ $(\epsilon_m/0.05)^{-2}$ $(F/0.8)^2$ $(T/10 ~\mbox{sec})$ $(\mu/0.4M_\odot)^{-4}$ $(d/2000Mpc)^{4}$.
 We might be able to select only nearby events by using redshift observations of the afterglows. if available.," We might be able to select only nearby events by using redshift observations of the afterglows, if available."
" When we analyze the nearest. 7 events in a νου, the (vpical distance d is proportional to nF7."," When we analyze the nearest $n$ events in a year, the typical distance $d$ is proportional to $n^{1/3}$."
 Since the number of events needed to detect the association is xd!n. the number of vears it takes to collect samples Ison1/7," Since the number of events needed to detect the association is $\propto d^4 \propto n^{4/3}$, the number of years it takes to collect samples is $\propto n^{1/3}$."
" When we collect only the nearest event in a vear p?=I. the number of events needed to detect the association is μμapc10* (6,/0.05)7 CE/0.8). (D/10sec) (Qu/O.1ML)! οMyr.teal1).I and Neygi~200 (6,,/0.05)? CE/0.8)? (T/10sec) (0/O4AL.)| (R/LLMyr.teal1)2°. or equivalently. it takes LOT vears and 200 vears to collect the samples."," When we collect only the nearest event in a year $n=1$, the number of events needed to detect the association is $N_{BH-WD}\sim 10^7$ $(\epsilon_m/0.05)^{-2}$ $(F/0.8)^2$ $(T/10 ~\mbox{sec})$ $(\mu/0.1M_\odot)^{-4}$ $(R/0.15 ~\mbox{Myr}^{-1}\mbox{gal}^{-1})^{-4/3}$ and $N_{BH-He} \sim 200$ $(\epsilon_m/0.05)^{-2}$ $(F/0.8)^2$ $(T/10 ~\mbox{sec})$ $(\mu/0.4M_\odot)^{-4}$ $(R/14 ~\mbox{Myr}^{-1}\mbox{gal}^{-1})^{-4/3}$, or equivalently, it takes $10^7$ years and 200 years to collect the samples."
 The ranges of Neywep and Neyqus due to the uncertainty of the formation rates are 10—10! and 37—10°. respectively.," The ranges of $N_{BH-WD}$ and $N_{BH-He}$ due to the uncertainty of the formation rates are $10^6-10^{11}$ and $37-10^5$, respectively."
 Thus. it is unlikely (hat one can detect an association between GRBs and gravitational waves from DII-WD or BDII-IIe binaries.," Thus, it is unlikely that one can detect an association between GRBs and gravitational waves from BH-WD or BH-He binaries."
 ILowever. with a relatively small umber sample. it is still possible to set a tight upper limit on the amplitude ol the gravitational waves.," However, with a relatively small number sample, it is still possible to set a tight upper limit on the amplitude of the gravitational waves."
 If we have Nayavpius=30 events of DII-WD or DII-IIe binaries al anv distances and we detect no signal of gravitational waves. we can give an upper limit on the mean amplitude of the events Λι«7.2x10.(Neywpe/30).UP/10κου).," If we have $N_{BH-WD/He}=30$ events of BH-WD or BH-He binaries at any distances and we detect no signal of gravitational waves, we can give an upper limit on the mean amplitude of the events $h_{c}< 7.2\times
10^{-23}(N_{BH-WD/He}/30)^{-1/4}(T/10~\mbox{sec})^{1/4}$."
 We have estimated the strains of gravitational waves [rom some of the most widely discussed. current GARB progenitor stellar svstems., We have estimated the strains of gravitational waves from some of the most widely discussed current GRB progenitor stellar systems.
 If some fraction of GRBs are produced bv double neutron star or neutron star black hole mergers. the eravilational wave chirp signal of the in-spiral phase should be detectable by the advanced. LIGO within one vear. associated with the GRB electromagnetic signal.," If some fraction of GRBs are produced by double neutron star or neutron star – black hole mergers, the gravitational wave chirp signal of the in-spiral phase should be detectable by the advanced LIGO within one year, associated with the GRB electromagnetic signal."
 We have also estimated the signals from the black hole ring-clown phase. as well as the possible contribution of a bar configuration from gravitational instability in the accretion disk following tidal disruption or infall in GR scenarios.," We have also estimated the signals from the black hole ring-down phase, as well as the possible contribution of a bar configuration from gravitational instability in the accretion disk following tidal disruption or infall in GRB scenarios."
 The assumed values of (he parameters related to the gravitational energy emitted during merging and ring-«down phase may be verv optimistic., The assumed values of the parameters related to the gravitational energy emitted during merging and ring-down phase may be very optimistic.
 Thus. our calculations may be regarded as order-of-magnitude estimates for the wpper-limits to the strains.," Thus, our calculations may be regarded as order-of-magnitude estimates for the upper-limits to the strains."
 Among the other progenitor scenarios. (he signals from black hole — Helium star and black hole — white cwarf merger GRB progenitors are the least likely to be detectable. due to the low estimates obtained for the maxinum non-axisvnunelrical perturbations.," Among the other progenitor scenarios, the signals from black hole – Helium star and black hole – white dwarf merger GRB progenitors are the least likely to be detectable, due to the low estimates obtained for the maximum non-axisymmetrical perturbations."
 For another possible tvpe of GRB progenitor. (he massive rotating stellar collapses or collapsars. the non-axisvimetrical perturbations may be stronger. ancl the estimated formation rates are much higher (han for other progenitors. with tvpical distances correspondinely much nearer (ο Earth.," For another possible type of GRB progenitor, the massive rotating stellar collapses or collapsars, the non-axisymmetrical perturbations may be stronger, and the estimated formation rates are much higher than for other progenitors, with typical distances correspondingly much nearer to Earth."
 This tvpe of progenitor is of special interest. since it has so [ar received (he most observational support," This type of progenitor is of special interest, since it has so far received the most observational support"
"where X, idis the surface density of the cell in the SPH simulation.",where $\Sigma_{\rm cell}$ is the surface density of the cell in the SPH simulation.
 In this model. when the cloud is resolved. we use the surface density as calculated in the simulations.," In this model, when the cloud is resolved, we use the surface density as calculated in the simulations."
 When the cloud is unresolved. we adopt a subresolution surface density comparable to observed values of GMCs2006).," When the cloud is unresolved, we adopt a subresolution surface density comparable to observed values of GMCs."
. We then determine the ffraction of the neutral ISM utilising the analytic formalism of and(2010)., We then determine the fraction of the neutral ISM utilising the analytic formalism of and.