source,target " In addition to these simulations, several other tests were performed to check whether the Wiener deconvolution introduces a significant bias in the astrometry or photometry of the data used in this work:"," In addition to these simulations, several other tests were performed to check whether the Wiener deconvolution introduces a significant bias in the astrometry or photometry of the data used in this work:" (kulkarnietal.2010).,\citep{Kul10}. .. Phe sub-DLAs in this work have a slightly lower mean velocity width than the total sub-DLA »»pulation of ;esu—1107., The sub-DLAs in this work have a slightly lower mean velocity width than the total sub-DLA population of 107. +. The complex. velocity »ofiles seen in some absorption line svstems have often been attributed to merging or interacting galaxies (DPetitjean.Sri-anand&Lecoux2002:Quast.ReimersBaade 2008).," The complex velocity profiles seen in some absorption line systems have often been attributed to merging or interacting galaxies \citep{Petit02, QRB08}." . The »ofiles for both the svstems in the spectrum of 0051 are not unusually broad. each extending ~100 ο.," The profiles for both the systems in the spectrum of $-$ 0051 are not unusually broad, each extending $\sim$ 100." Lf he interacting galaxies seen to the south of this field. are indeed: responsible for the absorption line svstem. then at east in this case interacting galaxies surprisingly cdo not seem to produce a complex velocity. structure.," If the interacting galaxies seen to the south of this field are indeed responsible for the absorption line system, then at least in this case interacting galaxies surprisingly do not seem to produce a complex velocity structure." At smaller impact parameters the profiles may show signs of broader velocity profiles., At smaller impact parameters the profiles may show signs of broader velocity profiles. The inclination of the disk to the QSO line of sight possibly. plavs a large part in the kinematic width of the absorption profiles., The inclination of the disk to the QSO line of sight possibly plays a large part in the kinematic width of the absorption profiles. lt is interesting to note that although the recent compilation of Noterdaemeοἳal.(2005) focused on DLA systems (77 total systems were included. in the sample. with only 7 sub-DLAs and all had log on(20.0).L oncofthesystemswithahigh fraction wasin factasdbritto," It is interesting to note that although the recent compilation of \citet{Not08b} focused on DLA systems (77 total systems were included in the sample, with only 7 sub-DLAs and all had log $>$ 20.0), one of the systems with a high molecular fraction was in fact a sub-DLA." n Similarlyhighmoleculerichsubmolecular2003.ApJ.592.S19 Lshavealsobeensceninolherinvestigalions(Quast. Heimers&DagagleΗΠΑΡΗΝΟ," Similarly high molecule rich sub-DLAs have also been seen in other investigations \citep{QRB08, Not08a}." Lt would. be interesting to expand. the number of HH» measurements in sub-DLAs to see if they are. perhaps also have high molecular fractions. and thus favoring the scenario where the lower LE 1 column clensities are due to the conversion of gas from neutral to molecular.," It would be interesting to expand the number of $_2$ measurements in sub-DLAs to see if they are perhaps also have high molecular fractions, and thus favoring the scenario where the lower H I column densities are due to the conversion of gas from neutral to molecular." Although the number of DLAs or sub-DLAs that have been observed with high quality spectra has increased. there is still a very small number of galaxies that have been confirmed. at the redshift of the absorber with followup spectroscopic measurements.," Although the number of DLAs or sub-DLAs that have been observed with high quality spectra has increased, there is still a very small number of galaxies that have been confirmed at the redshift of the absorber with followup spectroscopic measurements." Even fewer DLAs have spectra of the host ealaxy of high cnough S/N that can be used to determine the properties of the galaxy’s stellar population such as the star formation rate (SER). masses and star formation histories via spectral template fitting and emission line diagnostics.," Even fewer DLAs have spectra of the host galaxy of high enough S/N that can be used to determine the properties of the galaxy's stellar population such as the star formation rate (SFR), masses and star formation histories via spectral template fitting and emission line diagnostics." Followup spectroscopy is clearly necessary to link the properties we see in absorption such as the metallicity. kinematics. and abundance patterns with the properties of the stellar populations of the host galaxies.," Followup spectroscopy is clearly necessary to link the properties we see in absorption such as the metallicity, kinematics, and abundance patterns with the properties of the stellar populations of the host galaxies." DLAs ancl DLAs are likely to arise in a range of environments. a larger sample with imaging and spectroscopy of the host. galaxies would reveal any potential dichotomy in the populations.," DLAs and sub-DLAs are likely to arise in a range of environments, a larger sample with imaging and spectroscopy of the host galaxies would reveal any potential dichotomy in the populations." The sub-DLA svstems in this sample seem to arise in à range of environments themselves. from the inner region of a possible carly tvpe galaxy in the case of the sub-DLA in SDSS 0021. from the periphery of a luminous star forming galaxy in SDSS J10090 0026 and from the outskirts of an interacting pair of galaxies in SDSS | 0051.," The sub-DLA systems in this sample seem to arise in a range of environments themselves, from the inner region of a possible early type galaxy in the case of the sub-DLA in SDSS $-$ 0021, from the periphery of a luminous star forming galaxy in SDSS $-$ 0026 and from the outskirts of an interacting pair of galaxies in SDSS $-$ 0051." llowever. in all cases we observe luminous galaxies that are the likely host galaxies of these metal rich absorbers.," However, in all cases we observe luminous galaxies that are the likely host galaxies of these metal rich absorbers." A large sample of both spectroscopic ancl photometric measurements of DLA and sub-DLA host galaxies will allow for stuclving trends between luminosity. impact. parameter. and SER.," A large sample of both spectroscopic and photometric measurements of DLA and sub-DLA host galaxies will allow for studying trends between luminosity, impact parameter, and SFR." Higher spatial resolution imaging with the LIST would also allow for detailed information on the morphology of the absorbing galaxies., Higher spatial resolution imaging with the HST would also allow for detailed information on the morphology of the absorbing galaxies. We thank the exceptionally helpful stall of SOAR. for their assistance during the observing runs., We thank the exceptionally helpful staff of SOAR for their assistance during the observing runs. The SOAR. Telescope is à joint project o£ Conselho Nacional ce Pesquisas Cientificas ο Tecnologicas CNPq-Brazil. The University of North Carolina at Chapel Hill. Michigan State University. and the National Optical Astronomy Observatory.," The SOAR Telescope is a joint project of: Conselho Nacional de Pesquisas Cientificas e Tecnologicas CNPq-Brazil, The University of North Carolina at Chapel Hill, Michigan State University, and the National Optical Astronomy Observatory." LRAL is distributed by the National Optical Astronomy Observatory. which is operated by the Association of Universities for Research in Astronomy (AURA) under cooperative agreement with the National Science Foundation.," IRAF is distributed by the National Optical Astronomy Observatory, which is operated by the Association of Universities for Research in Astronomy (AURA) under cooperative agreement with the National Science Foundation." We thank the anonvmous referee. for the helpful. comments in the preparation of this manuscript., We thank the anonymous referee for the helpful comments in the preparation of this manuscript. VPIx acknowledges partial support from the National Science Foundation grant AS'T-, VPK acknowledges partial support from the National Science Foundation grant AST-0908890. "resolution dark matter region. cucompassing all matter out to5ray. lias particle mass iip=1.1065«10°AL... while eas particles are placed inside 374; and lave initial IMASSCS Hog,—2.2131&10? AL...","resolution dark matter region, encompassing all matter out to$5~r_{\mathrm{vir}}$, has particle mass $m_{\mathrm{DM}}=1.1065 \times 10^6~M_{\sun}$, while gas particles are placed inside $3~r_{\mathrm{vir}}$ and have initial masses $m_{\mathrm{gas}}=2.2131 \times 10^5~M_{\sun}$ ." There are typically ~1000000 eas aud lich resolution dark matter particles each in the refined regions of the resiauulations. with the exact number depending on the halo mass aud the ecolctry of the Lagrangian region that collapses iuto the >=0 halo.," There are typically $\sim 1000000$ gas and high resolution dark matter particles each in the refined regions of the resimulations, with the exact number depending on the halo mass and the geometry of the Lagrangian region that collapses into the $z=0$ halo." The simulations were evolved using the parallel SPI code (?).., The simulations were evolved using the parallel SPH code \citep{gasoline}. solves the equations of Lydrodvuamiics using SPIT aud selferavity using the DarnesIIut tree algorithm (?).. and inchides radiative cooling. an ultraviolet (UW) backeround. star formation. aud energetic and chemical feedback.," solves the equations of hydrodynamics using SPH and self-gravity using the Barnes-Hut tree algorithm \citep{bh86}, and includes radiative cooling, an ultraviolet (UV) background, star formation, and energetic and chemical feedback." The coolinge is calculated frou the contributions of both primordial gas and metals as Aos(:.p.T.Z)=NurueuaitzpT)01ManzCep T) ," The cooling is calculated from the contributions of both primordial gas and metals as $\Lambda_{\mathrm{tot}}(z, \rho, T, Z) = \Lambda_{\mathrm{HI, HeI, HeII}}(z,\rho, T) + \frac{Z}{Z_{\sun}}\Lambda_{\mathrm{metal},Z_{\sun}}(z, \rho, T)$ ." The first term enuplovs atomic cooling based on a gas with primordial composition heated by a uuiforii UV ioniziug backgrouud. adopted from Taardt ADMadau (npreparation:sce?) with rates cocficicut closely matching those cited in ?.. while the metal cooling erid is constructed using Cloudy (version 07.02. last described bv ?)). assunmüng ionization equilibrium. as described iun ?..," The first term employs atomic cooling based on a gas with primordial composition heated by a uniform UV ionizing background, adopted from Haardt Madau \citep[in preparation; see][]{hm01} with rates coefficient closely matching those cited in \citet{Abel97}, while the metal cooling grid is constructed using Cloudy (version 07.02, last described by \citet{CLOUDY}) ), assuming ionization equilibrium, as described in \citet{sws09}." The UV background is used im order to calculate the metal cooling rates selfconsisteutly., The UV background is used in order to calculate the metal cooling rates self-consistently. The cooling lookup table is linearly interpolated im three dimensions (ie. p. 2. T) and scaled linearly withmetallicity.," The cooling lookup table is linearly interpolated in three dimensions (i.e., $\rho$, $z$, $T$ ) and scaled linearly withmetallicity." " The star formation and feedback recipes are based on the ""blastwave model” described in detail iu ?.. but with the addition of clustered supernovae to account for the clustered: nature of star formation."," The star formation and feedback recipes are based on the “blastwave model” described in detail in \citet{Stinson06}, but with the addition of clustered supernovae to account for the clustered nature of star formation." Star formation can occur in gas particles that are dense (yun=0.1cur 3) and cool (Zi4«=15.000 IN). calibrated to match the ? Sclunidt Law for the Isolated Model Milky Way in ?..," Star formation can occur in gas particles that are dense $n_{\rm min}=0.1~\mathrm{cm^{-3}}$ ) and cool $T_{\rm max} = 15,000$ K), calibrated to match the \citet{kennicutt98} Schmidt Law for the Isolated Model Milky Way in \citet{Stinson06}." At the resolution of these simulations. cach star article represents a large umber of stars (6.32<104 ALL).," At the resolution of these simulations, each star particle represents a large number of stars $6.32\times 10^4~M_{\sun}$ )." Thus. cach particle has its stars partitioned into amass bius based on the initial mass function xeseuted im ?..," Thus, each particle has its stars partitioned into mass bins based on the initial mass function presented in \citet{Kroupa93}." These masses are correlated to stellar Metinies as described in 7.., These masses are correlated to stellar lifetimes as described in \citet{Raiteri96}. We stochastically determine when a star particle releases feedback energy so that a uiininin of 30 supernovae worth of energy is released conciurentlv to reflect the clustered nature of star ormation., We stochastically determine when a star particle releases feedback energy so that a minimum of $30$ supernovae worth of energy is released concurrently to reflect the clustered nature of star formation. The explosion of these stars is treated using he analytic model for blastwaves prescuted in ? as described in detail in ?.., The explosion of these stars is treated using the analytic model for blastwaves presented in \citet{MO77} as described in detail in \citet{Stinson06}. While the blast radius is calculated using the full energy output ofthe supernova. ess than half of that energw is transferred to the stwwromuding ISM. ων=τν10° cres.," While the blast radius is calculated using the full energy output of the supernova, less than half of that energy is transferred to the surrounding ISM, $E_{SN}=4\times10^{50}$ ergs." The rest of he supernova energy is radiated away., The rest of the supernova energy is radiated away. Tron aud oxyeeu are produced in SNIT according to the analytic fits used in 7.., Iron and oxygen are produced in SNII according to the analytic fits used in \citet{Raiteri96}. The iron aud oxvecn are distributed to the same eas Within the blast radius as is the supernova energy ejected from SNII., The iron and oxygen are distributed to the same gas within the blast radius as is the supernova energy ejected from SNII. Each SNIa produces 0.63A. ou and 0.13.AL. oxveeu (7). and it is ejected into the nearest eas particle for SNIa., Each SNIa produces $0.63~M_{\sun}$ iron and $0.13~M_{\sun}$ oxygen \citep{Thielemann86} and it is ejected into the nearest gas particle for SNIa. We have implemented diffusion of all scalar SPU «quantities. particularly πιστα! coutent aud thermal ΟΠΟΙΟΥ. as described in. 2.. which is required to correctly model even simple processes such as convection and Ravleigh-Tavlor imstabilities (?) and to account formusing in turbulent outflows.," We have implemented diffusion of all scalar SPH quantities, particularly metal content and thermal energy, as described in \citet{sws09}, which is required to correctly model even simple processes such as convection and Rayleigh-Taylor instabilities \citep{wadsley-etal08} and to account formixing in turbulent outflows." MUGS galaxies are labelled by their group umber in the list returned by the fricucs-of-fricuds algoritlun., MUGS galaxies are labelled by their group number in the list returned by the friends-of-friends algorithm. The simulations analyzed in this work are MUGS @1536. e5b661. οτ151. eld7al ePlGl7. e282187. e?2795. and e21331L.," The simulations analyzed in this work are MUGS $1536$, $5664$, $7124$, $15784$, $21647$, $22437$, $22795$, and $24334$." Ouly stars within the virial radius of the main ealaxy are considered., Only stars within the virial radius of the main galaxy are considered. The mean metallicity of stars formed iu the simulation is shown in Figure 3. as a function of their formation redshift., The mean metallicity of stars formed in the simulation is shown in Figure \ref{figure:zevol} as a function of their formation redshift. The solid line shows the results for all stars within MUGS simulated ealaxies. aud shows that stellar inetallicities rise frou —23. for those formed at 210. to nearly solar for those formed at 2=0.," The solid line shows the results for all stars within MUGS simulated galaxies, and shows that stellar metallicities rise from $\sim -3$, for those formed at $z \ga 10$, to nearly solar for those formed at $z=0$." Our siaulatious are of L galaxies. while the majority of star formation at lnieh redshift occurred in larecr galaxies. which formed their metals earlier than less massive ealaxies.," Our simulations are of $L^*$ galaxies, while the majority of star formation at high redshift occurred in larger galaxies, which formed their metals earlier than less massive galaxies." Our determünatious may therefore uuderestinate the metallicities of a universal sample of stars formed at biel redshift., Our determinations may therefore underestimate the metallicities of a universal sample of stars formed at high redshift. " We have coufirmed that our results are consistent with those obtained with completely differeut codes: the dotted line. which shows the star-formation-ratc-weighted mean metallicity of eas from the GADGET2 siuulations of ? (the ""SER-weighted"" line in their figure 2) aud should be directly comparable. slows reasonable aereenieut with our results over the eutie range Oτς6 that they plotted."," We have confirmed that our results are consistent with those obtained with completely different codes: the dotted line, which shows the star-formation-rate-weighted mean metallicity of gas from the GADGET2 simulations of \citet{do07} (the “SFR-weighted” line in their figure 2) and should be directly comparable, shows reasonable agreement with our results over the entire range $0 \le z \le 6$ that they plotted." " Where our results deviate from those of ?.. it is iu the sense that the MUCGS ietallicities are lower,"," Where our results deviate from those of \citet{do07}, it is in the sense that the MUGS metallicities are lower." The best observational mieasurenaents of stellar imetallicitv as à function of formation redslüft come from ?.. who performed spectral svuthesis modelling of SDSS ealaxies at redshifts rangiug from 0.1 to 3.," The best observational measurements of stellar metallicity as a function of formation redshift come from \citet{panter-etal08}, who performed spectral synthesis modelling of SDSS galaxies at redshifts ranging from $0.1$ to $3$ ." The mean metallicities ofstars iuferred to have formed at cach redshift is shown as the dot-dashed line in Figure 3.., The mean metallicities ofstars inferred to have formed at each redshift is shown as the dot-dashed line in Figure \ref{figure:zevol}. . Unlike the simulation predictions. the observations show essentially uo drop iu stellar metallicity out to += 3.," Unlike the simulation predictions, the observations show essentially no drop in stellar metallicity out to $z=3$ ." This is mainly because the total stellar mass is dominated bv the most massive galaxies. which formed most of," This is mainly because the total stellar mass is dominated by the most massive galaxies, which formed most of" of the same population (σα.οἱal.2002:Grimm.Qillanov.&Sunvaev 2003).,"of the same population \citep{kilgard02,grimm03}." . It is useful to study. objects both below and above this limit to understauxd the properties of the full population., It is useful to study objects both below and above this limit to understand the properties of the full population. The identification of counterparts of these N-rav sources al other. wavelenetls is important to understand the physical nature of these objects (Liu.Bregman.Ward.&Zezas 2004)..," The identification of counterparts of these X-ray sources at other wavelengths is important to understand the physical nature of these objects \citep{liu02,pakull02,kaaret03,zampieri04,liu04,kaaret04b}." Classification of the spectral types of the companion stars should directly constrain the evolutionary history of the binary systems., Classification of the spectral types of the companion stars should directly constrain the evolutionary history of the binary systems. Spectroscopy of companion stars might permit measurement of radial velocity curves providing direct constraints on the compact object mass., Spectroscopy of companion stars might permit measurement of radial velocity curves providing direct constraints on the compact object mass. Characterization of the environments in whieh the X-ray sources are [found should provide clues to their formation (Ixaaretetal.2004:Soriaet 2004).," Characterization of the environments in which the X-ray sources are found should provide clues to their formation \citep{kaaret04a,soria04}." .. IIere. we report on IIubble Space Telescope and Chandra X-Ray Observatory observations of the lace-on spiral galaxy NGC 1073 (= LGC 2210)," Here, we report on Hubble Space Telescope and Chandra X-Ray Observatory observations of the face-on spiral galaxy NGC 1073 (= UGC 2210)." " This ealaxyv contains an ""Intermediate X-ray Object. INO 5. reported in the catalog of Colbert.&Piak (2002).."," This galaxy contains an “Intermediate X-ray Object”, IXO 5, reported in the catalog of \citet{colbert02}. ." " This object. has an X-ray luminosity of ~2xLO""ergs! which is below the Edclington luminosity lor a POAL. black hole."," This object has an X-ray luminosity of $\sim 2 \times 10^{39} \rm \, erg \, s^{-1}$ which is below the Eddington luminosity for a $20 M_{\odot}$ black hole." " However. it is significantly brighter (han anv persistent black hole X-rav binary in the Alilky Way and les at the transition between standard black hole X-ray binaries and ultraluminous X-ray SOULCES,"," However, it is significantly brighter than any persistent black hole X-ray binary in the Milky Way and lies at the transition between standard black hole X-ray binaries and ultraluminous X-ray sources." NGC L073 is a member of a Gelt group of galaxies containing the bright Sevlert ealaxv NGC LOGS and some additional [ainter companions., NGC 1073 is a member of a tight group of galaxies containing the bright Seyfert galaxy NGC 1068 and some additional fainter companions. We adopt a distance to NGC 1073 of 16.4 Alpe based on a radial velocity corrected. for infall of the local group toward Virgo of 1147 km/s as reported in the LEDA catalog and a IIubble constant. of το km/s/Mpe., We adopt a distance to NGC 1073 of 16.4 Mpc based on a radial velocity corrected for infall of the local group toward Virgo of 1147 km/s as reported in the LEDA catalog and a Hubble constant of 70 km/s/Mpc. . NGC 1073 is notable because several quasars lie near the light of sight. (Arp&Su-lentic1979)., NGC 1073 is notable because several quasars lie near the light of sight \citep{arp79}. . The presence of several objects in the field with both X-rav. and oplical emission permits us (o obtain accurate relative astrometry of the X-rav ancl optical images., The presence of several objects in the field with both X-ray and optical emission permits us to obtain accurate relative astrometry of the X-ray and optical images. There are only two potential optical counterparts to the brightest X-ray source in the galaxy., There are only two potential optical counterparts to the brightest X-ray source in the galaxy. We describe the observations and analysis in 2. and discuss the results in 3.," We describe the observations and analysis in 2, and discuss the results in 3." Observations of NGC 10723. were made using the Advanced Camera for Surveys (ACS) on the Ilubble Space Telescope (UST) under. GO program 10001. (PI lNaaret)., Observations of NGC 1073 were made using the Advanced Camera for Surveys (ACS) on the Hubble Space Telescope (HST) under GO program 10001 (PI Kaaret). Images were obtained in the broad band filters F435W (Johnson D) and F606W (Droad V) using the Wide-Field Camera (WFC)., Images were obtained in the broad band filters F435W (Johnson B) and F606W (Broad V) using the Wide-Field Camera (WFC). Al the observations were made on 18 Nov 2003., All the observations were made on 18 Nov 2003. The poinüng was offset from either (he X-ray source position or the galaxy nucleus in order to include {wo quasars known to emit both optical light and X-ravs in the ACS field of view to allow us to align the X-ray. auc optical images., The pointing was offset from either the X-ray source position or the galaxy nucleus in order to include two quasars known to emit both optical light and X-rays in the ACS field of view to allow us to align the X-ray and optical images. Each observation consisted. of a (wo point line dither pattern with a pair of cosnmüc-rayv split images obtained at each point in the pattern., Each observation consisted of a two point line dither pattern with a pair of cosmic-ray split images obtained at each point in the pattern. The totalexposure was 2160 s [or the F435W image and 2240 s for the F606W image., The totalexposure was 2160 s for the F435W image and 2240 s for the F606W image. mass.,mass. Close pairs are dominated by galaxies in massive halos., Close pairs are dominated by galaxies in massive halos. " Hence, our results indicate that galaxies which formed the bulk of their stars at high redshift are today in clusters, in which there is little ongoing star formation."," Hence, our results indicate that galaxies which formed the bulk of their stars at high redshift are today in clusters, in which there is little ongoing star formation." " Since clusters formed from overdense regions in the early Universe, our results imply that cosmic star formation has moved from dense to ever less dense regions."," Since clusters formed from overdense regions in the early Universe, our results imply that cosmic star formation has moved from dense to ever less dense regions." This is qualitatively consistent with the findings of Poggiantietal. (2006)., This is qualitatively consistent with the findings of \citet{EDisCS06}. ". However, whereas Poggianti et al."," However, whereas Poggianti et al." " measure instantaneous star formation rates in cluster galaxies identified over a wide range of redshifts (the SDSS at zc0, and the ESO Distant Cluster Survey for 0.4Q. is These solutious are shown in Fig.," The complete solution, the number of grains in bin $k$ for $t>0$, is These solutions are shown in Fig." 2 along with the results of the numerical simulation., \ref{fig:cna} along with the results of the numerical simulation. The numerical results agree exactly with the analytic solution., The numerical results agree exactly with the analytic solution. The extra grains in the last bin in the simulation (Figs., The extra grains in the last bin in the simulation (Figs. 2bb and 244) are the result of a last bin. that gralus cau grow into but not out of.," \ref{fig:cna}b b and \ref{fig:cna}d d) are the result of a last bin, that grains can grow into but not out of." The number of graius in the last biu should be interpreted as representing all the grains of that sizelarger. or as the total nuuber of grains in the tail of the analytic distribution.," The number of grains in the last bin should be interpreted as representing all the grains of that size, or as the total number of grains in the tail of the analytic distribution." A second case that can be solved analytically is that of a linear kernel. Ay;=8()+J) (?)..," A second case that can be solved analytically is that of a linear kernel, $K_{ij}=\beta(i+j)$ \citep{wetherill90}. ." The nuuber of graius that remain after time / in tliis case is and the distribution is These functions are also compared with the results of simulation in Fig. 2.., The number of grains that remain after time $t$ in this case is and the distribution is These functions are also compared with the results of simulation in Fig. \ref{fig:cna}. Again. the numerical results agree well with the aualytie solution uutil euougli time has passed that a significant uuumber of grains is iu the tail of the distribution. above the largest bin used in the simulation.," Again, the numerical results agree well with the analytic solution until enough time has passed that a significant number of grains is in the tail of the distribution, above the largest bin used in the simulation." While these tests are not applicable in the case of a real. physical kernel. they provide some measure of confidence in the numerical algorithia.," While these tests are not applicable in the case of a real, physical kernel, they provide some measure of confidence in the numerical algorithm." The grain opacity. αν. for a particular grain size was fouud from the grains extinction cross section. which was computed from Mie theory (2). using au approximation suggested by Dr. J. Cuzzi (personal communication).," The grain opacity, $\kappa_\nu$, for a particular grain size was found from the grain's extinction cross section, which was computed from Mie theory \citep{hulst57} using an approximation suggested by Dr. J. Cuzzi (personal communication)." " If the size parameter of a grain of radius « is ar=2z0/AÀ. where A is the waveleneth of the impinging photons. then the scattering elliciency (Q. of the grain is well approximated by Here n, and »; are the real and imaginary refractive Iudices of thegrain material respectively."," If the size parameter of a grain of radius $a$ is $x=2\pi{a}/\lambda$, where $\lambda$ is the wavelength of the impinging photons, then the scattering efficiency $Q_s$ of the grain is well approximated by Here $n_r$ and $n_i$ are the real and imaginary refractive indices of thegrain material respectively." " The absorption efficiency. Q, is approximated. [or all grain sizes. by"," The absorption efficiency $Q_a$ is approximated, for all grain sizes, by" lane appears across the granule and roughly along the field lines.,lane appears across the granule and roughly along the field lines. " The magnetic field vector has different azimuths at both sides of this dark lane and as the plasma evolves, the granule splits in two and so does the loop."," The magnetic field vector has different azimuths at both sides of this dark lane and as the plasma evolves, the granule splits in two and so does the loop." At the end of the process the negative footpoint is divided in two while the positive one still links both loops., At the end of the process the negative footpoint is divided in two while the positive one still links both loops. " The azimuth of the magnetic field is parallel to the line dividing both parts of the loop, showing that the evolution of the loop is driven by the dynamics of the local granulation."," The azimuth of the magnetic field is parallel to the line dividing both parts of the loop, showing that the evolution of the loop is driven by the dynamics of the local granulation." This 1s compatible with the relatively weak field strength (B)=176x4G (filling factor 30+ 1%)) found for this loop., This is compatible with the relatively weak field strength $\langle B\rangle=176\pm 4$ G (filling factor $30\pm 1$ ) found for this loop. " From Mg b magnetograms, the magnetic flux density for the loop of Fig."," From Mg b magnetograms, the magnetic flux density for the loop of Fig." | is 15 Mx em™., \ref{loop1} is 15 Mx $^{-2}$. " The temperature minimum marks just the lower boundary of the chromosphere, hence, this flux density can be used to compute the rate of magnetic energy injected to the chromosphere by the loop."," The temperature minimum marks just the lower boundary of the chromosphere, hence, this flux density can be used to compute the rate of magnetic energy injected to the chromosphere by the loop." " Assuming the same magnetic filling factor as in the photosphere (30%)) and an inclination of magnetic fields. 25° as shown by the reconstructed loops field lines at the temperature minimum region, the magnetic field strength is B=55 G. This number is consistent with estimating the magnetic field strength at the apex as B'~BR?/R? (from magnetic flux conservation), R being the radius of the photospheric footpoints and Δ΄ the radius of the loop cross section at the temperature minimum."," Assuming the same magnetic filling factor as in the photosphere $30$ ) and an inclination of magnetic fields $~25^\circ$ as shown by the reconstructed loops field lines at the temperature minimum region, the magnetic field strength is $B=55$ G. This number is consistent with estimating the magnetic field strength at the apex as $B'\approx BR^{2}/R'^2$ (from magnetic flux conservation), $R$ being the radius of the photospheric footpoints and $R'$ the radius of the loop cross section at the temperature minimum." " From the reconstruction, we find that, around 500 km, R?/R?=0.25."," From the reconstruction, we find that, around 500 km, $R^2/R'^2 \approx 0.25$." " Therefore, the magnetic field strength must be 52 G. The magnetic field energy density associated to such a field is Ej,=B?/8xx120 erg cm™."," Therefore, the magnetic field strength must be 52 G. The magnetic field energy density associated to such a field is $E_{\rm mag}=B^2/8\pi\approx 120$ erg $^{-3}$." " The ascent velocity of the apex of the reconstructed loop at chromospheric heights is v~12 km s, which gives a magnetic energy rate of Εμμ=1.4x10° ere em? s! over the entire solar surface."," The ascent velocity of the apex of the reconstructed loop at chromospheric heights is $v\sim 12$ km $^{-1}$, which gives a magnetic energy rate of $E_{\rm mag}v=1.4\times 10^8$ erg $^{-2}$ $^{-1}$ over the entire solar surface." However. we must correct this number by the portion of the area occupied by the emerging loops.," However, we must correct this number by the portion of the area occupied by the emerging loops." The loop of Fig., The loop of Fig. " | is typical —other events show similar magnetic fluxes, spatial and temporal scales."," \ref{loop1} is typical —other events show similar magnetic fluxes, spatial and temporal scales." " Thus, we take as the magnetic energy flux derived here as representative of the emergence process."," Thus, we take as the magnetic energy flux derived here as representative of the emergence process." " From the analysis of the Hinode data used here, MartínezGonzález&BellotRubio(2009) report an emergence rate of 0.02 loops h! aresec37, of them reaching the chromosphere."," From the analysis of the Hinode data used here, \cite{marian_09} report an emergence rate of 0.02 loops $^{-1}$ $^{-2}$, of them reaching the chromosphere." " Assuming a mean lite time of the loop in the chromosphere of ~1050 s, and estimating their area roughly from"," Assuming a mean life time of the loop in the chromosphere of $\sim 1050$ s, and estimating their area roughly from" volume.,volume. We also consider the possibility that galaxy 3 can photo-ionise the blob., We also consider the possibility that galaxy 3 can photo-ionise the blob. However. 1f we assume a power law for the spectrum and extrapolating from the HST/B and HST/V detections we find that the UV luminosity of galaxy 3 ds not sufficient to photo-iontse the blob. unless highly collimated towards the blob.," However, if we assume a power law for the spectrum and extrapolating from the HST/B and HST/V detections we find that the UV luminosity of galaxy 3 is not sufficient to photo-ionise the blob, unless highly collimated towards the blob." We have no reason to believe that this ts the Case., We have no reason to believe that this is the case. The second possibility is that the blob Lya emission ts somehow related to starburst driven. superwind outflows.," The second possibility is that the blob $\alpha$ emission is somehow related to starburst driven, superwind outflows." A starburst would be expected to be located within the blob to create such a Lyn halo and no central continuum source has been detected., A starburst would be expected to be located within the blob to create such a $\alpha$ halo and no central continuum source has been detected. Even though a very massive starburst can be made invisible in the UV/optical range by dust obscuration. it should be visible in the IR. te. the bands.," Even though a very massive starburst can be made invisible in the UV/optical range by dust obscuration, it should be visible in the IR, i.e. the bands." The third option is that the Ένα emission is due to cold accretion of predominantly neutral. filamentary gas onto a massive dark matter halo.," The third option is that the $\alpha$ emission is due to cold accretion of predominantly neutral, filamentary gas onto a massive dark matter halo." For cold accretion. the bulk of the Ένα emission is produced by collisional excitation. rather than recombination.," For cold accretion, the bulk of the $\alpha$ emission is produced by collisional excitation, rather than recombination." Recently. Dijkstra et al.," Recently, Dijkstra et al." 2006(a.b) presented a theoretical model for Ένα cooling flows. along with predictions of the emission line profile and the shape of the surface brightness function.," 2006(a,b) presented a theoretical model for $\alpha$ cooling flows, along with predictions of the emission line profile and the shape of the surface brightness function." The S/N of our spectrum is not high enough to allow a comparison of emission line profiles., The S/N of our spectrum is not high enough to allow a comparison of emission line profiles. However. the surface brightness profile matches well the predictions for a centrally illuminated. collapsing clouc of Dijkstra et al.," However, the surface brightness profile matches well the predictions for a centrally illuminated, collapsing cloud of Dijkstra et al." 2006(a). see Fig.," 2006(a), see Fig." 1., 1. Further tests are needec to determine how well their model fits., Further tests are needed to determine how well their model fits. " To test whether this blob can be filamentary gas accreting ""cold"" onto à companitor galaxy. we also conducted the following experiment: we calculated the Ένα surface brightness in a 1004 100. kpe (projected) region for a proto-galaxy of ""cooling"" radiatiol only (so all contributions from regions with young stars were removed. as well as all emission. in general. from gas closer than 10 kpe to any star-forming region)."," To test whether this blob can be filamentary gas accreting “cold” onto a companion galaxy, we also conducted the following experiment: we calculated the $\alpha$ surface brightness in a $\times$ 100 kpc (projected) region for a proto-galaxy of “cooling” radiation only (so all contributions from regions with young stars were removed, as well as all emission, in general, from gas closer than 10 kpc to any star-forming region)." The calculation was based on a cosmological simulation of the formation and evolution of an M3I-like disk galaxy (Sommer-Larsen 2009: Portinari Sommer-Larsen 2005)., The calculation was based on a cosmological simulation of the formation and evolution of an M31-like disk galaxy (Sommer-Larsen 2005; Portinari Sommer-Larsen 2005). The results at:~3 are presented in Sommer-Larsen (2005). and get to a surface brightness about an order of magnitude lower than the observed level.," The results at $z\sim3$ are presented in Sommer-Larsen (2005), and get to a surface brightness about an order of magnitude lower than the observed level." This is interesting. and nay point to a cold aceretion origin of the blob Lya emission on a larger scale. such as filamentary gas accretion onto a galaxy-group sized halo.," This is interesting, and may point to a cold accretion origin of the blob $\alpha$ emission on a larger scale, such as filamentary gas accretion onto a galaxy-group sized halo." Another possibility is that the periods with high surface brightness are shorter than 2.5 Myr (the resolution of the simulation)., Another possibility is that the periods with high surface brightness are shorter than 2.5 Myr (the resolution of the simulation). Given that in a search volume of about 40000 co-moving Mpc. only one such blob has been detected. it is actually comforting. that we could not reproduce the blob characteristics. by cold accretion onto this. randomly selected. M31-like galaxy.," Given that in a search volume of about 40000 co-moving $^3$, only one such blob has been detected, it is actually comforting, that we could not reproduce the blob characteristics, by cold accretion onto this, randomly selected, M31-like galaxy." This has to be a rare phenomenon., This has to be a rare phenomenon. A test for the cold accretion model would be to observe the Balmer lines., A test for the cold accretion model would be to observe the Balmer lines. For collisionally excited hydrogen. neglecting extinction effects. the flux in Ha should only be about 3.5 percent of the Lya flux. whereas for recombining. photo-ionized gas this ratio is ~11.5 (Brocklehurst 1971).," For collisionally excited hydrogen, neglecting extinction effects, the flux in $\alpha$ should only be about 3.5 percent of the $\alpha$ flux, whereas for recombining, photo-ionized gas this ratio is $\sim 11.5$ (Brocklehurst 1971)." Hence. the relative Ha luminosity is expected to be significantly larger in the latter case.," Hence, the relative $\alpha$ luminosity is expected to be significantly larger in the latter case." The situation is similar for H7. and whereas the Ha line will be very difficult to detect from the ground. ) should be observable.," The situation is similar for $\beta$, and whereas the $\alpha$ line will be very difficult to detect from the ground, $\beta$ should be observable." We have here reported the results of an extensive multi-wavelength investigation of a redshift +=3.16 Lyo emitting blob discovered in the GOODS South field., We have here reported the results of an extensive multi-wavelength investigation of a redshift $z = 3.16$ $\alpha$ emitting blob discovered in the GOODS South field. " The blob has a diameter larger than 60 kpe diameter and a total lummosity of Lis,~10’ erg 1."," The blob has a diameter larger than 60 kpc diameter and a total luminosity of $\mathrm{L}_{\mathrm{Ly}\alpha} \sim 10^{43}$ erg $^{-1}$." Deep HST imaging show no obvious optical counterpart. and the lack of X-ray or IR. emission suggest there are no AGN or dusty starburst components associated with at least the centroid of the blob.," Deep HST imaging show no obvious optical counterpart, and the lack of X-ray or IR emission suggest there are no AGN or dusty starburst components associated with at least the centroid of the blob." Two galaxies within a LO” radius have photometric redshifts consistent with the redshift of the blob. but follow-up spectroscopy Is needed to establish if there 1s a connection.," Two galaxies within a $10''$ radius have photometric redshifts consistent with the redshift of the blob, but follow-up spectroscopy is needed to establish if there is a connection." We have run simulations of Ένα surface brightness arising from cold aceretion and found that such extended Lyn emission may be explained by aceretion along a filament onto a galaxy group sized dark matter halo., We have run simulations of $\alpha$ surface brightness arising from cold accretion and found that such extended $\alpha$ emission may be explained by accretion along a filament onto a galaxy group sized dark matter halo. Another possibility is that such emission in very short lived. 1.e. significantly shorter than the 2.5 Myr resolutiot of our simulation.," Another possibility is that such emission in very short lived, i.e. significantly shorter than the 2.5 Myr resolution of our simulation." " We argue that other previously suggested origins of Lya blobs (hidden AGN and ""super-winds"") can be ruled out in this case due to the lack of detected continuum counter-parts.", We argue that other previously suggested origins of $\alpha$ blobs (hidden AGN and “super-winds”) can be ruled out in this case due to the lack of detected continuum counter-parts. Hence. though our cold accretion simulatior cannot perfectly match our data. it is the only explanation that is plausible.," Hence, though our cold accretion simulation cannot perfectly match our data, it is the only explanation that is plausible." Our results combined with the fact that previously studied blobs appear to be caused by superwinds and/or AG, Our results combined with the fact that previously studied blobs appear to be caused by superwinds and/or AGN for constraining the total number of GCs around NCC 7811. since the inner points can be fit by many profiles that have quite different outer profiles aud therefore total uumber.,"for constraining the total number of GCs around NGC 7814, since the inner points can be fit by many profiles that have quite different outer profiles and therefore total number." The observation oL very low or zero GC surface deusity in the outer auuuli strongly suggests that we have observed the entire radial extent of this galaxys QC system., The observation of very low or zero GC surface density in the outer annuli strongly suggests that we have observed the entire radial extent of this galaxy's GC system. For the SBF distance modulus. 3’ equals 11.5 kpc.," For the SBF distance modulus, $\arcm$ equals 11.5 kpc." For comparison. we uote that if we projected the Milky Way's GC system outo tlie Y-Z plane (where Y is the Galactocentric1 coordinate iu the direction of Galactic rotation aud Z is the height above or below the plane) aud caleulated a radial distance for each GC. of them would have racial distauces of 11.5 kpe or less (Harris 1996).," For comparison, we note that if we projected the Milky Way's GC system onto the $Y$ $Z$ plane (where $Y$ is the Galactocentric coordinate in the direction of Galactic rotation and $Z$ is the height above or below the plane) and calculated a radial distance for each GC, of them would have radial distances of 11.5 kpc or less (Harris 1996)." The information coutaiued in the corrected GC radial profile cau be used to calculate the total uunber of GCs around NGC 781., The information contained in the corrected GC radial profile can be used to calculate the total number of GCs around NGC 7814. Since we have combiued HST data with wider-field WIYN data. we can directly determine the total number of GCs without the extrapolation from sinaller racius hat would have been necessary had we used HST data alone.," Since we have combined HST data with wider-field WIYN data, we can directly determine the total number of GCs without the extrapolation from smaller radius that would have been necessary had we used HST data alone." There are two ways to compute the otal number: oue is to integrate the best-fit deVaucouleurs profile from r = 0 to an outer radius. and he other is to sum the actual data points. ie. by multiplying the surface deusity at each point. iu he profile by the area of the associated auuulus aud sumone over all radii.," There are two ways to compute the total number: one is to integrate the best-fit deVaucouleurs profile from $r$ $=$ 0 to an outer radius, and the other is to sum the actual data points, i.e., by multiplying the surface density at each point in the profile by the area of the associated annulus and summing over all radii." Both methods produce a total number of GCs for the galaxy. corrected [or maguitude incompleteness. missing spatial coverage. and contamination from non-GCs.," Both methods produce a total number of GCs for the galaxy, corrected for magnitude incompleteness, missing spatial coverage, and contamination from non-GCs." " The best-fit deVaucouleurs law provides a good fit to the radial profile data between 70.8 and 1.7"". ancl either slightly or significantly overestimates the data elsewhere."," The best-fit deVaucouleurs law provides a good fit to the radial profile data between $\sim$ $\arcm$ and $\arcm$, and either slightly or significantly overestimates the data elsewhere." For this reason we have used both methods — integrating the profile and summiug the actual data — to calculate the total number of GCs in NGC 7811L., For this reason we have used both methods — integrating the profile and summing the actual data — to calculate the total number of GCs in NGC 7814. Because the GC surface density is cousistent with zero from Ὁ outward. aud the deVaucouleurs fuuctiou consistently overestimates the data points beyond that radius. we stop the iutegration or sunmumatiou at tliat poiut. (," Because the GC surface density is consistent with zero from $\arcm$ outward, and the deVaucouleurs function consistently overestimates the data points beyond that radius, we stop the integration or summation at that point. (" Below we cliscuss tlie possible impact of our choice of integration limit ou the final results.),Below we discuss the possible impact of our choice of integration limit on the final results.) Summineg the data points in the profile to 3 vields a total of 140 GC's [or NGC 7811., Summing the data points in the profile to $\arcm$ yields a total of 140 GCs for NGC 7814. Integer:ing the best-fit deVaucouleurs law from 0 to 3. vields 190 GCs., Integrating the best-fit deVaucouleurs law from 0 to $\arcm$ yields 190 GCs. The total number of CCs can be normalized by luminosity or mass of the galaxy iu order to facilitate comparison of NGC Tells GC system to that of other galaxies., The total number of GCs can be normalized by luminosity or mass of the galaxy in order to facilitate comparison of NGC 7814's GC system to that of other galaxies. The specific [requency. ον. is the number of GCs uormalized by luminosity aid is defiued as (Harris&vandenBergh|1981).," The specific frequency, $S_N$, is the number of GCs normalized by luminosity and is defined as \citep{hvdb81}." . The total. extinction-corrected. face-on maguittde lor NGC δα is WE = 10.20 (ROB: deVaucouleurs et 11991).," The total, extinction-corrected, face-on magnitude for NGC 7814 is $V^T_0$ $=$ 10.20 (RC3; deVaucouleurs et 1991)." Since Ros for this galaxy is 2.75. virtually all of the galaxy light. is located within 3.," Since $R_{25}$ for this galaxy is $\arcm$, virtually all of the galaxy light is located within $\sim$ $\arcm$." Therefore. integrating the QC profile to yf and then using the total luminosity to calculate Sy is a reasonable approach.," Therefore, integrating the GC profile to $\arcm$ and then using the total luminosity to calculate $S_N$ is a reasonable approach." Asstumine the SBF clistauce modulus vields a total absolute maguitude of MU = —20.10., Assuming the SBF distance modulus yields a total absolute magnitude of $M^T_V$ $=$ $-$ 20.40. Combining this with, Combining this with The comparison may also be carried out in terms of the mean of the Doppler shifts and. separately. half the difference.,"The comparison may also be carried out in terms of the mean of the Doppler shifts and, separately, half the difference." For a uniformly glowing ring the former would be the systemic velocity and the latter the rotation speed of the orbiting ring., For a uniformly glowing ring the former would be the systemic velocity and the latter the rotation speed of the orbiting ring. Fig., Fig. 6 shows the variation of the apparent rotational speec with time and Fig., 6 shows the variation of the apparent rotational speed with time and Fig. 7 the apparent systemic recession., 7 the apparent systemic recession. These figures may be compared with the corresponding Figs.5 anc 6 in Bowler (2010a)., These figures may be compared with the corresponding Figs.5 and 6 in Bowler (2010a). As in Fig., As in Fig. 5. the model calculations are made for the narrower source distribution from Fig.| and a short decay time of about | day.," 5, the model calculations are made for the narrower source distribution from Fig.1 and a short decay time of about 1 day." The assumed rotational speed of the ring was 230 kms7~!. which gives the best representatior of the He I data. as for the model in Bowler (2010a).," The assumed rotational speed of the ring was 230 km $^{-1}$, which gives the best representation of the He I data, as for the model in Bowler (2010a)." The agreement between the model and the data is very good: i particular the phasing of the variations relative to Julian date is not a free parameter. yet here the model and the data agree to within a day.," The agreement between the model and the data is very good; in particular the phasing of the variations relative to Julian date is not a free parameter, yet here the model and the data agree to within a day." It is also important that with such a short decay time there is no freedom in the model to accentuate the magnitude of the variations of the rotational and recessional velocities with time. because these details are dominated by the geometry of the source and not by the decay time.," It is also important that with such a short decay time there is no freedom in the model to accentuate the magnitude of the variations of the rotational and recessional velocities with time, because these details are dominated by the geometry of the source and not by the decay time." If the wider source distribution in Fig.]. were employed. the depth of the ninima in rotational speed would decrease by 10 km s! and the amplitude of the recessional oscillations by 25 km s7!.," If the wider source distribution in Fig.1 were employed, the depth of the minima in rotational speed would decrease by 10 km $^{-1}$ and the amplitude of the recessional oscillations by 25 km $^{-1}$." Obviously. as the source distribution flattens out completely the oscillations in both quantities vanish.," Obviously, as the source distribution flattens out completely the oscillations in both quantities vanish." Thus for geometries giving flatter source distributions than those illustrated in Fig.l the agreement between model and data would become progressively worse for He I. An assumed decay time greater than | day would not succeed in producing oscillations of the magnitudes shown in Figs., Thus for geometries giving flatter source distributions than those illustrated in Fig.1 the agreement between model and data would become progressively worse for He I. An assumed decay time greater than 1 day would not succeed in producing oscillations of the magnitudes shown in Figs. 5-7., 5-7. The new model also matches the He data. originally presented in. Blundell. Bowler Schmidtobreick (2008) and again in Bowler (2010a).," The new model also matches the $\alpha$ data, originally presented in Blundell, Bowler Schmidtobreick (2008) and again in Bowler (2010a)." The new model has less flexibility than the old. but a longer damping time is again needed to generate a sequence of spectra with comparatively small oscillations in the heights of the Ha horns.," The new model has less flexibility than the old, but a longer damping time is again needed to generate a sequence of spectra with comparatively small oscillations in the heights of the $\alpha$ horns." This 15 reflected in very small snaking in the Ha analogue of Fig., This is reflected in very small snaking in the $\alpha$ analogue of Fig. 5: to a first approximation the red and blue components attributed to the cireumbinary disk run railroad straight over 30 consecutive days (and can be traced beyond JD +294 until flaring leads to some obscuratior. Bowler 2010b).," 5; to a first approximation the red and blue components attributed to the circumbinary disk run railroad straight over 30 consecutive days (and can be traced beyond JD +294 until flaring leads to some obscuration, Bowler 2010b)." The Ha data are best represented with a decay time of about 3 days and as in Bowler (2010a) a rotational speed rather over 250 km s7!., The $\alpha$ data are best represented with a decay time of about 3 days and as in Bowler (2010a) a rotational speed rather over 250 km $^{-1}$. As the source distribution is flattened the indentations in rotational speed drop in magiitude faster than those in recessional speed and as for He I the narrower distribution in Fig., As the source distribution is flattened the indentations in rotational speed drop in magnitude faster than those in recessional speed and as for He I the narrower distribution in Fig. | is preferred over the broader., 1 is preferred over the broader. As for the He I data. the," As for the He I data, the" Unlike for many other millisecond pulsars (cf.,Unlike for many other millisecond pulsars (cf. Table 6.7 of Becker 2009 for à summary). modeling the X-ray spectrum of PSR J1824-2452A with a power-law does not require any additional blackbody component (c.g. associated with thermal emission from heated polar caps) to get an acceptable spectral fit.," Table 6.7 of Becker 2009 for a summary), modeling the X-ray spectrum of PSR J1824-2452A with a power-law does not require any additional blackbody component (e.g. associated with thermal emission from heated polar caps) to get an acceptable spectral fit." All combinations of blackbody normalizations and temperatures that were fitted along the power-law model gave reduced X7-values which didn't indicate a higher likelihood for such a model than the fits to a single power-law., All combinations of blackbody normalizations and temperatures that were fitted along the power-law model gave reduced $\chi^2$ -values which didn't indicate a higher likelihood for such a model than the fits to a single power-law. " The F-test statistic for adding the extra blackbody spectral component to the power-law model, thus, is very low."," The F-test statistic for adding the extra blackbody spectral component to the power-law model, thus, is very low." " Nevertheless, the high photon statistics provided by the archival Chandra data allows us to constrain the temperature of a presumed thermal polar cap."," Nevertheless, the high photon statistics provided by the archival Chandra data allows us to constrain the temperature of a presumed thermal polar cap." " Defining the size of the polar cap as the foot points of the neutron star’s dipolar magnetic field. the radius of the polar cap area is given by p=V258R./cP with R being the neutron star radius, c the velocity of light and P the pulsar rotation period (see e.g. Michel 1991)."," Defining the size of the polar cap as the foot points of the neutron star's dipolar magnetic field, the radius of the polar cap area is given by $\rho=\sqrt{2\pi R^3/c P}$ with $R$ being the neutron star radius, c the velocity of light and P the pulsar rotation period (see e.g. Michel 1991)." " For PSR J1824-2452A, with a rotation period of 3.05 ms this yields a polar cap radius of p—2.62 km."," For PSR J1824-2452A, with a rotation period of 3.05 ms this yields a polar cap radius of $\rho\sim 2.62$ km." " As a thermal spectral component of a heated polar cap contributes mostly below ~1 keV, the fitted column absorption is found to be a steep function of the blackbody emitting area (corresponding to the model normalization) and temperature."," As a thermal spectral component of a heated polar cap contributes mostly below $\sim 1$ keV, the fitted column absorption is found to be a steep function of the blackbody emitting area (corresponding to the model normalization) and temperature." To determine a polar cap temperature upper limit which is in agreement with the fitted power-law model and column absorption we fixed the absorption of the composite model as well as the power-law photon index to the upper bound set by the 1o confidence range deduced in the power-law fit., To determine a polar cap temperature upper limit which is in agreement with the fitted power-law model and column absorption we fixed the absorption of the composite model as well as the power-law photon index to the upper bound set by the $1\sigma$ confidence range deduced in the power-law fit. The power-law normalization was fixed to the lo lower bound as this led to a higher temperature upper limit., The power-law normalization was fixed to the $1\sigma$ lower bound as this led to a higher temperature upper limit. We then computed the confidence ranges of the blackbody normalization and temperatures by leaving these parameters tree., We then computed the confidence ranges of the blackbody normalization and temperatures by leaving these parameters free. " The resulting contours, computed for two parameters of interest, are shown in Figure 17.."," The resulting contours, computed for two parameters of interest, are shown in Figure \ref{figure17}." " The blackbody normalization in XSPEC is proportional to Pin!oipe in which pj, is the blackbody radius of the emitting area and dio,, is the pulsar distance in units of 10 kpc."," The blackbody normalization in XSPEC is proportional to $\rho^2_{km}/d^2_{10\,kpc}$ in which $\rho_{km}$ is the blackbody radius of the emitting area and $d_{10\,kpc}$ is the pulsar distance in units of 10 kpc." For a distance of 5.6 kpc towards M28 and a polar cap radius of 2.62 km we thus obtain a normalization of 21.88., For a distance of 5.6 kpc towards M28 and a polar cap radius of 2.62 km we thus obtain a normalization of 21.88. " Assuming a contribution from one polar cap only we can set a 3e temperature upper limit of 7,7<1.3x10° K. This upper limit is at the same level as the temperatures fitted for the thermal components in the spectra of c.g. the solitary millisecond pulsar PSR J2124—3358 or of PSR J0437 —4715 (cf.", Assuming a contribution from one polar cap only we can set a $3\sigma$ temperature upper limit of $T_{pc}^\infty < 1.3 \times 10^6$ K. This upper limit is at the same level as the temperatures fitted for the thermal components in the spectra of e.g. the solitary millisecond pulsar PSR $2124-3358$ or of PSR $0437-471$ 5 (cf. Table 6.7 in Becker 2009)., Table 6.7 in Becker 2009). Converting the temperature upper limit into a flux upper limit yields fiosev<1.5x107ergsstem. corresponding to <4% of the non-thermal energy flux within 0.3—8 keV. The best-fit spectral models andparameters used to describe the spectra of the X-ray detected globular cluster millisecond pulsars are summarized in Table 8..," Converting the temperature upper limit into a flux upper limit yields $f_{bb, 0.3 - 8\,\,keV}\le 1.5 \times 10^{-14}\,\, {\rm ergs\,\,s}^{-1}\,{\rm cm}^{-2}$, corresponding to $\le 4$ of the non-thermal energy flux within $0.3-8$ keV. The best-fit spectral models andparameters used to describe the spectra of the X-ray detected globular cluster millisecond pulsars are summarized in Table \ref{t:gc_psr_spec}. ." 18740097).,18740097). TN also has been supported by the same grants 118104003 and 19740094)., TN also has been supported by the same grants 18104003 and 19740094). TTT has been supported by the Special Coordination Funds for Promotion Science and Technology (SCF) commissioned by the MEXT (MEXT) of Japan., TTT has been supported by the Special Coordination Funds for Promotion Science and Technology (SCF) commissioned by the MEXT (MEXT) of Japan. We fully utilized the NASA's Astrophysics Data System Abstract Service (ADS). 2.2..," We fully utilized the NASA's Astrophysics Data System Abstract Service (ADS). \ref{subsec:method}," Edward(1983). Philipp(1985)... Alaa ," \citet{edward85} \citet{philipp85}, \ref{fig:sio2}a " Table 4. lists (he expected Zi; to Spencer 1.1 [Iux ratios. as derived lor known L aud T odwarfs.,"Table \ref{tab:ratio} lists the expected $H_{MK}$ to Spencer 1.7 flux ratios, as derived for known L and T dwarfs." The values have heen computed. from flux. calibrated near-intrared spectra., The values have been computed from flux calibrated near-infrared spectra. All T dwarf ratios were calculated from spectra downloaded from Adam Bureasser’s T. cwarl archive (http://web.mit.edu/ajb/www/tdwarf)., All T dwarf ratios were calculated from spectra downloaded from Adam Burgasser's T dwarf archive (http://web.mit.edu/ajb/www/tdwarf). The L dwarl ratios were calculated from Ian AMeLean's BDSS archive (MeLeanοἱal.2003)., The L dwarf ratios were calculated from Ian McLean's BDSS archive \citep{mcl}. . The ratio values are flat for L dwarls (73.5) and increase from ~4 for earlv-tvpe T. dwarls to 11 for the TY dwarf. 24M0345-60.," The ratio values are flat for L dwarfs $\sim$ 3.5) and increase from $\sim4$ for early-type T dwarfs to $\sim$ 11 for the T7 dwarf, 2M0348-60." " II the candidate is à late-tvpe T dwarf. as indicated bv its J—A color. then its fay, /Spencer 1.7 flux ratio should be on the order of 10 (Table 4))."," If the candidate is a late-type T dwarf, as indicated by its $J-K$ color, then its $H_{MK}$ /Spencer 1.7 flux ratio should be on the order of 10 (Table \ref{tab:ratio}) )." To calculate the fIux ratio of the candidate. the ratio is calibrated for the main binary svstem. the L3/L3 2M1146--22.," To calculate the flux ratio of the candidate, the ratio is calibrated for the main binary system, the L3/L3 2M1146+22." Since no flux standards were observed. we use [hax calibrated spectra of objects similar to that of the primary.," Since no flux standards were observed, we use flux calibrated spectra of objects similar to that of the primary." " The raw count rate of the primary and the candidate companion were measured at both yy, and Spencer 1.7 using the method describedin Section 2.2..", The raw count rate of the primary and the candidate companion were measured at both $H_{MK}$ and Spencer 1.7 using the method described in Section \ref{sec:datared}. The measured raw count rate ratio for 2M11462-22 is 2.22:0.]anc l the candidate companion is 1.7+1.1., The measured raw count rate ratio for 2M1146+22 is $2.2 \pm 0.1$ and the candidate companion is $1.7 \pm 1.1$. The values derived from flux calibrated spectra of the L2 dwarf 2M00154-35 and the L4 heal Gliese 165B are 3.5 ancl 3.3 respectively 2003).., The values derived from flux calibrated spectra of the L2 dwarf 2M0015+35 and the L4 dwarf Gliese 165B are 3.5 and 3.3 respectively \citep{mcl}. These values are about m(higher than the raw ratio lor 2M11464-22., These values are about higher than the raw ratio for 2M1146+22. Hence. the ratio Lor the candidateis expec dilo e- higher. raising it to 2.641.1.," Hence, the ratio for the candidate is expected to be $\sim$ higher, raising it to $2.6 \pm 1.1$." " We surmise that it does not exhibit anv sienilicant methane absorption, as would be expected for a very late-tvpe T. dwarl."," We surmise that it does not exhibit any significant methane absorption, as would be expected for a very late-type T dwarf." The observed ratio between £74; and Spencer 1.7 for the candidate is also similar to the ratio of the bandwidths of the two filters (NJ~0.35jun.AS=70.15 jun). 72.3.," The observed ratio between $H_{MK}$ and Spencer 1.7 for the candidate is also similar to the ratio of the bandwidths of the two filters ${\Delta}H \sim 0.35~{\mu}m, {\Delta}S = {\sim}0.15~{\mu}m$ ), ${\sim}2.3$." Since the InSb detectors have a relatively uniform response wilh wavelength. this is consistent with a flat spectrum source.," Since the InSb detectors have a relatively uniform response with wavelength, this is consistent with a flat spectrum source." It is concluded that (his eandidate companion to 2M11462-22 is not a low-mass brown dwarf companion., It is concluded that this candidate companion to 2M1146+22 is not a low-mass brown dwarf companion. We have completed a thorough. statistically well-defined search for wide companions to ultracool dwarls.," We have completed a thorough, statistically well-defined search for wide companions to ultracool dwarfs." Previous large-scale survevs (Douyetal.2003:Gizis2003) usecl oplical imaging and concentrated on searching lor companions al small separations: our survev is (he first to sample the full T. dwarf regime at separations [rom a few tens {ο thousands of AU.," Previous large-scale surveys \citep{bouy03,gizis03} used optical imaging and concentrated on searching for companions at small separations; our survey is the first to sample the full T dwarf regime at separations from a few tens to thousands of AU." We can ealeulate an upper limit on the frequeney of companions al those separations from our null results., We can calculate an upper limit on the frequency of companions at those separations from our null results. We use a basic Poisson distribution to determine the probability of getting a null detection given the number of observations: Freq). where Nop. is the number of observations (132) and Freq is the lrequency of companions.," We use a basic Poisson distribution to determine the probability of getting a null detection given the number of observations: $Prob(Null) = \exp(-N_{obs}{\times}Freq)$ , where $N_{obs}$ is the number of observations (132) and $Freq$ is the frequency of companions." We determine a conservative upper limit when the probability. of obtaining, We determine a conservative upper limit when the probability of obtaining There is a large body of literature on the issue of polarized foreground cleaning for the B-mode detection.,There is a large body of literature on the issue of polarized foreground cleaning for the $B$ -mode detection. Our method is one specific (and relatively simpler) example., Our method is one specific (and relatively simpler) example. " For the other methods in the literature, see review articles (Dunkleyetal.2009;Fraisse and references therein."," For the other methods in the literature, see review articles \citep{dunkley/etal:2008,fraisse/etal:prep} and references therein." This paper is organized as follows., This paper is organized as follows. " In Section 2,, we show how the detector noise and the lensing noise influence the statistical errors on r."," In Section \ref{sec:noise}, we show how the detector noise and the lensing noise influence the statistical errors on $r$." " In Section 3,, we describe our method for estimating r in the presence of the Galactic foreground and the dominant scalar E-mode polarization."," In Section \ref{sec:method}, we describe our method for estimating $r$ in the presence of the Galactic foreground and the dominant scalar $E$ -mode polarization." " In Section 4,, we describe our simulation including CMB, detector noise, and foreground."," In Section \ref{sec:simulation}, we describe our simulation including CMB, detector noise, and foreground." " In Section 5,, we presentthe main results of this paper."," In Section \ref{sec:results}, we presentthe main results of this paper." We conclude in Section 6.., We conclude in Section \ref{sec:conclusion}. " Before we study the effect of the foreground, we show how the detector noise and the lensing noise influence our ability to detect r."," Before we study the effect of the foreground, we show how the detector noise and the lensing noise influence our ability to detect $r$." " The detector noise enters into the likelihood of r via the noise power spectrum, NPP."," The detector noise enters into the likelihood of $r$ via the noise power spectrum, $N_l^{BB}$." " Assuming white noise, we write the noise power spectrumas where wp1/2 is the noise in Stokes parameters Q or U per pixel whose solid angle, gives /Qpix=1 arcmin."," Assuming white noise, we write the noise power spectrumas where ${w}_p^{-1/2}$ is the noise in Stokes parameters $Q$ or $U$ per pixel whose solid angle, $\Omega_{\rm pix}$, gives $\sqrt{\Omega_{\rm pix}}=1$ arcmin." " This quantity is useful OQpix,because one can compare various experiments on the same scale.", This quantity is useful because one can compare various experiments on the same scale. Current and future experiments use many order 10?— detectors to reduce the noise equivalent(of temperature10?) (NET) down to a few wK arcmin level., Current and future experiments use many (of order $10^3-10^4$ ) detectors to reduce the noise equivalent temperature (NET) down to a few $\mu$ K arcmin level. Is this sufficient for detecting primordial B modes?, Is this sufficient for detecting primordial $B$ modes? " For comparison, the expected sensitivity of Planck combining 70, 100, and 143 GHz is wp//?=63 uK arcmin In 2005)."," For comparison, the expected sensitivity of combining 70, 100, and 143 GHz is ${w}_p^{-1/2}=63~{\mu}$ K arcmin \citep[see, e.g., Appendix A of][]{zaldarriaga/etal:prep, planck:bb}." ".Figure 2,, we compare the noise power spectra for WpV/?_2 and 10 LA arcmin to the primordial and lensing B modes."," In Figure \ref{fig:clnoise}, we compare the noise power spectra for $w_p^{-1/2}=2$ and 10 $\mu$ K arcmin to the primordial and lensing $B$ modes." " For r=107° and the 10 wK arcmin noise, only a few modes (1=2, 3, and 4) are above noise."," For $r=10^{-3}$ and the 10 $\mu$ K arcmin noise, only a few modes $l=2$, 3, and 4) are above noise." " For the 2 arcmin noise, the noise power spectrum is below the wKlensing B-mode power spectrum, and thus noise is no longer the limiting factor (unless we “de-lens” maps and remove the lensing noise)."," For the 2 $\mu$ K arcmin noise, the noise power spectrum is below the lensing $B$ -mode power spectrum, and thus noise is no longer the limiting factor (unless we ``de-lens'' maps and remove the lensing noise)." How would this influence our ability to detect r?, How would this influence our ability to detect $r$? " To see this, let us calculate the likelihood of r for a given noise level."," To see this, let us calculate the likelihood of $r$ for a given noise level." " For simplicity, we assume that we cover the full sky and the noise per pixel is Then, one can write down the probability distribution function of the measured B-mode power spectrum, CPP, for a given value of r as (e.g.,Equation(8)ofHamimeche&Lewis2008) where cg is the primordial B-mode power spectrum from gravitational waves with r=1, and cf is the secondary B mode from gravitational lensing."," For simplicity, we assume that we cover the full sky and the noise per pixel is Then, one can write down the probability distribution function of the measured $B$ -mode power spectrum, $\hat{C}_l^{BB}$, for a given value of $r$ as \citep[e.g., Equation~(8) of][]{hamimeche/lewis:2008} where $c_l^{GW}$ is the primordial $B$ -mode power spectrum from gravitational waves with $r=1$, and $c_l^L$ is the secondary $B$ mode from gravitational lensing." We then use Bayes’ theorem to calculate the likelihood for r as L(r|CP®)ο. P(CPP|r)., We then use Bayes' theorem to calculate the likelihood for $r$ as ${\cal L}(r|\hat{C}^{BB}_l)\propto P(\hat{C}^{BB}_l|r)$ . " To calculate the likelihood, we set the measured power spectrum to be CPB=Tinputc?©+ and sum the log-likelihood over multipoles up ckto NPP,Imax: Figure 3 shows the likelihood of r for the input value of rinput=107? and las=2, 5, 10, and 100."," To calculate the likelihood, we set the measured power spectrum to be $\hat{C}^{BB}_l=r_{\rm input}c_l^{GW}+c_l^L+N_l^{BB}$ , and sum the log-likelihood over multipoles up to $l_{\rm max}$: Figure \ref{fig:like} shows the likelihood of $r$ for the input value of $r_{\rm input}=10^{-3}$ and $l_{\rm max}=2$, 5, 10, and 100." " One useful number to keep in mind is that a multipole, |=2, is sufficient for detecting r=107%, if the noise is smaller than 10 arcmin."," One useful number to keep in mind is that a multipole, $l=2$, is sufficient for detecting $r=10^{-3}$, if the noise is smaller than $10~{\mu}$ K arcmin." " However, the precision on r does not improve wKbeyond |=5."," However, the precision on $r$ does not improve beyond $l=5$." This is apparent also in Figure 2:: the noise power spectrum exceeds the signal at |>5., This is apparent also in Figure \ref{fig:clnoise}: the noise power spectrum exceeds the signal at $l\ge 5$. " We can improve the precision further if we lower the noise level to, say, 2 j4K arcmin."," We can improve the precision further if we lower the noise level to, say, $2~{\mu}$ K arcmin." " Even so, the gravitational lensing prevents us from improving on the precision beyond |—10 if r=107%. ("," Even so, the gravitational lensing prevents us from improving on the precision beyond $l\sim 10$ if $r=10^{-3}$. (" "If there were no lensing in the universe, we would be able to continue to improve on the precision, as indicated by the dashed lines.)","If there were no lensing in the universe, we would be able to continue to improve on the precision, as indicated by the dashed lines.)" " In fact, 2 4K arcmin is essentially the same as zero detector noise, as the lensing term dominates the error budget."," In fact, $2~{\mu}$ K arcmin is essentially the same as zero detector noise, as the lensing term dominates the error budget." " Again, this is apparent in Figure 2.."," Again, this is apparent in Figure \ref{fig:clnoise}. ." " Of course, these results are overlyoptimistic, as the error would be dominated by the foreground rather than by the detector noise."," Of course, these results are overlyoptimistic, as the error would be dominated by the foreground rather than by the detector noise." " Nevertheless, it is still useful to knowwhat would be possible when we ignore the foreground."," Nevertheless, it is still useful to knowwhat would be possible when we ignore the foreground." " To quantify the precision on r, it is convenient to use the variance, σὲ, given by the second moment of the"," To quantify the precision on $r$ , it is convenient to use the variance, $\sigma^2_r$ , given by the second moment of the" dl shows nunerical calculations of the quiesceut radiation conipoueuts of Ser A,1 shows numerical calculations of the quiescent radiation components of Sgr $^*$. " These iuclude svuchrotron and SSC cinission fou the magnetized ADAF within 4220 of the GCDIT eurecs). N-vav aud TeV emission from the compact plerion atscales A—(3 LO)«1026σ οκ]. and the emission from the larecr pleriou curves) inflated tope scales in the process of couvective (aud possibly also ciffusive} propagation of the accelerated electrons on timescales <1ηνι, "," These include synchrotron and SSC emission from the magnetized ADAF within $r_{rad}\approx 20$ of the GCBH ), X-ray and TeV emission from the compact plerion atscales $R\sim (3$ – $10)\times 10^{16}\,\rm cm$ ), and the emission from the larger plerion ) inflated to scales in the process of convective (and possibly also diffusive) propagation of the accelerated electrons on timescales $\lesssim 10^4\,\rm yr$." Maguetic field in the latter. By=LlopC. is asstuned higher than By=θὀθμέ in the TeV plerion.," Magnetic field in the latter, $B_2 = 140\,\rm \mu G$, is assumed higher than $B_{1}=90\,\rm \mu G$ in the TeV plerion." This is in agreement with the expected merease of the naenetic field downstream of the shock in typical pulsar Xenons (dd&eunel&Coroniti198D)... and is explained by deceleration and compression of the plasiua.," This is in agreement with the expected increase of the magnetic field downstream of the shock in typical pulsar plerions \citep{kc84}, and is explained by deceleration and compression of the plasma." But it is also xossible that Bo109 explains the X-rav flares with very short viriabilitv scales., Synchrotron emission of electrons accelerated to $\gamma > 10^{6}$ explains the X-ray flares with very short variability scales. " Furthermore. while propagating through the first few τοις of Rs. thes electrons have sufficieut time. ~10?s, to cool in the hie[um B fields there down to ><3.105 to produce fares in the NIR domain."," Furthermore, while propagating through the first few tens of $R_{S}$, these electrons have sufficient time, $\sim 10^3 \,\rm s$, to cool in the high $B$ fields there down to $\gamma \lesssim 3\times 10^3$ to produce flares in the NIR domain." " Self-absorbed flares at =100CIIz detectoca ou = Ldav timescales after the X-ray flares (Zhaoctal.WwX01) could be explained by the radiation from these sau ectrons at later stages/larger distances of the outburst i- +16 ""expandiusg source’ scenario."," Self-absorbed flares at $\lesssim 100\,\rm GHz$ detected on $\lesssim 1\,$ day timescales after the X-ray flares \citep{zha04} could be explained by the radiation from these same electrons at later stages/larger distances of the outburst in the `expanding source' scenario." Tn 22 we show the flare fluxes expected iu this model., In 2 we show the flare fluxes expected in this model. After shock-acceleration close to the BID and injection iuto collinated wind outflow with speed c/2. ‘lectrous propagate through the iuner r210 330 reeiou on timescale ρω=1200s. after which the radiation losses rop because of wind expansion and decline of B.," After shock-acceleration close to the BH and injection into collimated wind outflow with speed $c/2$, electrons propagate through the inner $r\simeq$ 30 region on timescale $t_{esc}=1200\,\rm s$, after which the radiation losses drop because of wind expansion and decline of $B$." The solid. dashed. aud dot-dashed curves show svuchrotron aud Compton fluxes produced at times s; 8 aud hh after the onset of the fare.," The solid, dashed, and dot-dashed curves show synchrotron and Compton fluxes produced at times s, s and hr after the onset of the flare." The electron injection time profile is Lyia(f)=Lyf|tftj)?. with ty=720s.," The electron injection time profile is $L_{e.flare}(t)= L_{0}/ (1+t/t_0)^{2}$, with $t_0 = 720\,\rm s$." The mean maenetic field in ADAF outflow could be enhanced at the faring state. so we take B=25.," The mean magnetic field in ADAF outflow could be enhanced at the flaring state, so we take $B=25\,\rm G$." The Compton fluxes shown (thin curves) clearly demonstrate that no detectable TeV flares should be expected during powerful N-rav flares., The Compton fluxes shown (thin curves) clearly demonstrate that no detectable TeV flares should be expected during powerful X-ray flares. Thüs is in agreement with the uou-detection of TeV flux variations curing niuiv davs of observation with the TESS telescopes. whereas the N-vay flares occur with frequency of 1 per dax (Baganoffetal.2003).," This is in agreement with the non-detection of TeV flux variations during many days of observation with the HESS telescopes, whereas the X-ray flares occur with frequency of $\sim 1$ per day \citep{Chandra}." . A ainodel consisting of magnetized coronal ADAF (svuchrotron) racio emission within z20Rs of the GCDII. and of a black-hole pleriou powered by a wind from the ADAF resolves many puzzling observations of Ser A.," A model consisting of magnetized coronal ADAF (synchrotron) radio emission within $\approx 20~R_{\rm S}$ of the GCBH, and of a black-hole plerion powered by a wind from the ADAF resolves many puzzling observations of Sgr $^\ast$." X-rav flares are svuchrotron radiation of clectrous accelerated through first-order Ferma process bv shocks within a few of the GCBU., X-ray flares are synchrotron radiation of electrons accelerated through first-order Fermi process by shocks within a few of the GCBH. Electrous accelerated to >2105 at the wind termination shock at Z3«10M cu creates the CGCDII pleriou.," Electrons accelerated to $\gamma\gtrsim 10^8$ at the wind termination shock at $\gtrsim 3\times 10^{16}\,$ cm creates the GCBH plerion." " Its svuchrotron N-rav cussion has beeu resolved as iu 21.1"" source with Chaudra (Baganoffetal.Ww 103).", Its synchrotron X-ray emission has been resolved as an $\simeq 1.4^{\prime\prime}$ source with Chandra \citep{Chandra}. .. The imulti-TeV electrous Compton scatter the radio photous from aud FIR pliotous from the dust ring of Ser A West to produce the TeV ciission., The multi-TeV electrons Compton scatter the radio photons from and FIR photons from the dust ring of Sgr A West to produce the TeV emission. TeV emission from the GCDIT pleriou is nearly stationary because the cooling time of TeV electrons is ~LOO vrs., TeV emission from the GCBH plerion is nearly stationary because the cooling time of TeV electrons is $\sim 100$ yrs. A vjet-ADAF” inodel for has Όσοι. proposed bv Falcke&Alarkoff(2000). and Yuan.Alarkoff.&Fal-cke (2002).," A “jet-ADAF"" model for has been proposed by \citet{fm00} and \citet{ymf02}." . Our model though also based on cucrey outflow from the ADAF. differs ereath.," Our model, though also based on energy outflow from the ADAF, differs greatly." In particular. the quiescent aud flaring X-ray components are produced at different sites.," In particular, the quiescent and flaring X-ray components are produced at different sites." " The origin of the N-rav aud NIR flares are explained as svuchrotron cussion of electrons accelerated durimg episodes of instabilities very close to the BID. not as Compton radiation in the SSC scenario of the “jet-ADAF"" model."," The origin of the X-ray and NIR flares are explained as synchrotron emission of electrons accelerated during episodes of instabilities very close to the BH, not as Compton radiation in the SSC scenario of the ``jet-ADAF"" model." Tnportautly. the TeV flux cannot be casily explained if the observed X-ravs were due to the SSC uechauisui iu the vicinity of the GCDIT. as suggested by Falcke&Markotff(2000).," Importantly, the TeV flux cannot be easily explained if the observed X-rays were due to the SSC mechanism in the vicinity of the GCBH, as suggested by \citet{fm00}." . Propagation of GeW electrons from the plerion. on tmescales of >L0'xy with speeds ~LOOkms tcould senificautlv contribute to the radio svuchrotron flux of Ser A West.," Propagation of GeV electrons from the plerion on timescales of $\gtrsim 10^4 \,\rm yr$ with speeds $\sim 100 \,\rm km\, s^{-1}$ could significantly contribute to the radio synchrotron flux of Sgr A West." In particular. it could explain the sugeested routhermal origin of radiation in the bar of Ser A West (Wrightetal. 1987).. formed in the outflow direction.," In particular, it could explain the suggested nonthermal origin of radiation in the bar of Sgr A West \citep{bar}, , formed in the outflow direction." We also predict that quasistationary Compton aud emisstrahluug fluxes fromthe pc-scale pleriou. comcideut with the central parts of Ser A West. will be siguificautly detected and possibly resolved with CLAST at GeV energies.," We also predict that quasi-stationary Compton and bremsstrahlung fluxes from the pc-scale plerion, coincident with the central parts of Sgr A West, will be significantly detected and possibly resolved with GLAST at GeV energies." But the expected liehly variable Compton counterpart of the svuchrotron N-ray flares from the CCBIU vicinity is too weal. to be detectable with GCLAST, But the expected highly variable Compton counterpart of the synchrotron X-ray flares from the GCBH vicinity is too weak to be detectable with GLAST formation length. which costs much shorter (ime than the fist. principle method. utilizing the Lienard-Wiechert potential.,"formation length, which costs much shorter time than the first principle method utilizing the Lienard-Wiechert potential." In (his paper. we rather use the first principle method to obtain the spectrum as exact as possible.," In this paper, we rather use the first principle method to obtain the spectrum as exact as possible." We adopt the field description method developed by Giacalone Jokipii (1999) and used by Reville lIxirk (2010)., We adopt the field description method developed by Giacalone Jokipii (1999) and used by Reville Kirk (2010). " We asstune isotropic turbulent magnetic fields which have broader power spectra Ayia,=LOOxAya, aud caleulate the radiation spectra in the regime of 158 (vith no useful upper lait)."," This method results in relatively weak constraints, as is clear from the rather wide $\sigma$ contours shown in figure \ref{C_M_contour} (black contours); the deduced mass and concentration are $M_{\rm vir}=1.6^{+1.1}_{-0.8}\times 10^{15}$ $^{-1}$, and $c_{\rm vir}>5.8$ (with no useful upper limit)." " The latter method of estimating the cluster mass. frou the Jeans equation with assiuned profiles. is less precise than the other methods. vielding a partial degeucracy between ej, aud Af, as shown m figure 10."," The latter method of estimating the cluster mass, from the Jeans equation with assumed profiles, is less precise than the other methods, yielding a partial degeneracy between $c_{\rm vir}$ and $M_{\rm vir}$ as shown in figure \ref{C_M_contour}." We thus expect this coustraiut to be weak., We thus expect this constraint to be weak. The observed. galaxy uunber density essentially determines eae) through eq. COX. aud ," The observed galaxy number density essentially determines $n_{\rm gal}(r)$ through eq. \ref{eq:galaxy number surface density}) )," the observed projected velocity dispersion determines a degenerate combination of o? aud 3 at cach radius through eq. (5)).," and the observed projected velocity dispersion determines a degenerate combination of $\sigma_r^2$ and $\beta$ at each radius through eq. \ref{projected velocity dispersion}) )." This vields a degeneracy where for any asstuned (70). the Jeans equation vields an Mr) that is consistent with the ealaxy dynamical data.," This yields a degeneracy where for any assumed $\beta(r)$, the Jeans equation yields an $M(r)$ that is consistent with the galaxy dynamical data." Iu the actual fitting though. this degeneracy is partially broken bv the strict analytical forms assuiied for the various input profiles.," In the actual fitting though, this degeneracy is partially broken by the strict analytical forms assumed for the various input profiles." Figure & shows that the best-fit NEW. mass profile from the Joans equation is i good agreement with the mass profiles from the other methods.," Figure \ref{mass profile comparison} shows that the best-fit NFW mass profile from the Jeans equation is in good agreement with the mass profiles from the other methods." " To eget more useful coustramts on ej, aud Mg. we conie the two cvnamical methods. 156. the caustics and the Jeaus equation."," To get more useful constraints on $c_{\rm vir}$ and $M_{\rm vir}$, we combine the two dynamical methods, i.e., the caustics and the Jeans equation." From the caustics method we ake ouly the coustraint on AM. siuce the mass profile at sÁnall radii is uncertain in this method due to the xeakdown of the E;=0.5 assumption (see discussion in the previous subsection).," From the caustics method we take only the constraint on $M_{\rm vir}$, since the mass profile at small radii is uncertain in this method due to the breakdown of the $F_{\beta}=0.5$ assumption (see discussion in the previous subsection)." Figure 10. shows that the conibined constraiuts (ereen contours) are stronger and in good agreement with the values derived from the chsing and X-ray data by LOS (who asstmed iu this xuwtieular analysis au NEW profile for the total mass density aud a double beta model for the gas mass deusity xofile).," Figure \ref{C_M_contour} shows that the combined constraints (green contours) are stronger and in good agreement with the values derived from the lensing and X-ray data by L08 (who assumed in this particular analysis an NFW profile for the total mass density and a double beta model for the gas mass density profile)." " Iu particular. the combined dvuamical methods vield 1-6 limits of AA,=340.0&101 lhPAD. ane Con>19.1."," In particular, the combined dynamical methods yield $\sigma$ limits of $M_{\rm vir}=(1.3\pm 0.4) \times 10^{15}$ $^{-1}$ $_{\odot}$ and $c_{\rm vir}>13.4$." Tn this section we sunmnnaarize various wavs of defining a iuitiug radius for Al689., In this section we summarize various ways of defining a limiting radius for A1689. One wav to define the edge of he cluster is to use the observed galaxy uunuber density xofile., One way to define the edge of the cluster is to use the observed galaxy number density profile. The fits that we have used in eqs. (1)), The fits that we have used in eqs. \ref{Sigma_tot}) ) aud (6)) do iof have a sharp cutoff iu the uuuber deusity of ealaxies., and \ref{beta model}) ) do not have a sharp cutoff in the number density of galaxies. We thus define an edge as the radius where we cau no ouecr detect cluster iienibers above the coutzibution of he (nou-cluster) background galaxy level., We thus define an edge as the radius where we can no longer detect cluster members above the contribution of the (non-cluster) background galaxy level. For A689 this volt is visible in figure 1.., For A1689 this point is visible in figure \ref{galaxy surface number density}. Specifically. the cluster radial edge was estimated to be where ΣΠ>AChe/C and MoafC\Delta C_{\rm bg}/C_{\rm bg}$ and $\Sigma_{\rm gal}/C_{\rm bg}<\Delta C_{\rm bg}/C_{\rm bg}$ including uncertainties in $\Sigma_{\rm gal}/C_{\rm bg}$ , yielding a limiting radius of $2.1_{-0.7}^{+0.8}$ $^{-1}$ Mpc, where the $\sigma$ uncertainties account also for the errors in the various fitting parameters in eq. \ref{Sigma_tot}) )." Tudepeucently. the velocity caustic fits to the projected velocity dispersion data shown in figure 2 vield a very similar value for the πιο radius. 2.12+0.07 Lh! Alpc. where the error includes an estimate of the effect of Poisson noise in the observed umber of galaxies.," Independently, the velocity caustic fits to the projected velocity dispersion data shown in figure \ref{velocity space diagram} yield a very similar value for the limiting radius, $2.12\pm0.07$ $^{-1}$ Mpc, where the error includes an estimate of the effect of Poisson noise in the observed number of galaxies." We caution that in simulations the caustics often flatten but do not reach zero at the virial radius: also. the shape of the caustics is somewhat dependent on the particular line of sight (D99).," We caution that in simulations the caustics often flatten but do not reach zero at the virial radius; also, the shape of the caustics is somewhat dependent on the particular line of sight (D99)." ITowever. the caustics are generally more cleanly defined iu data ou real clusters than in N-body shuulatious (Rines et 22003).," However, the caustics are generally more cleanly defined in data on real clusters than in N-body simulations (Rines et 2003)." Both of these methods vield a cluster edee luting radius of ~2 h! Mpe., Both of these methods yield a cluster edge limiting radius of $\sim 2$ $^{-1}$ Mpc. " A similar value was also independently derived from our leusine and Nav analysis, wlüch depends mostly on the projected DAL distribution,"," A similar value was also independently derived from our lensing and X-ray analysis, which depends mostly on the projected DM distribution." We found the virial radius to be 2.11022 ht Mpc (L0)., We found the virial radius to be $2.14^{+0.27}_{-0.29}$ $^{-1}$ Mpc (L08). We conclude that all these different data sets agree reasonably well both in terms of the virial, We conclude that all these different data sets agree reasonably well both in terms of the virial Finally. we argued that in the radiation reaction-limited regime the >-rav luminosity of pulsars should scale linearly. with the spin-down enerev. Eq. (5)).,"Finally, we argued that in the radiation reaction-limited regime the $\gamma$ -ray luminosity of pulsars should scale linearly with the spin-down energy, Eq. \ref{11}) )." The coefficients of this proportionality depend both on the overall geometry of the inclination angle of the magnetic dipole with respect to the axis) through the parameters ie; and on the im the gap through the parameter 7 Owhich. im (urn. depends on microphysics of the acceleration precesses).," The coefficients of this proportionality depend both on the overall geometry of the inclination angle of the magnetic dipole with respect to the axis) through the parameters $\eta_G$ and on the in the gap through the parameter $\eta$ (which, in turn, depends on microphysics of the acceleration precesses)." This prediction is in contrast to the currently assumed scaling of the 5-rav. luminosity with the available potential. xVEsp.," This prediction is in contrast to the currently assumed scaling of the $\gamma$ -ray luminosity with the available potential, $\propto \sqrt{\dot{E}_{SD}}$." Observationallv. when compared with the scaling of xVEsp. all models underpredict the huninositv of pulsars and thus [ail to describe the observed population (e.g..Pierbattistaetal.2011) (foralternativeinterpretationseeλα(ους&Romani 2011)..," Observationally, when compared with the scaling of $\propto \sqrt{\dot{E}_{SD}}$, all models underpredict the luminosity of pulsars and thus fail to describe the observed population \cite[\eg][]{2011arXiv1103.2682P} \citep[for alternative interpretation of data see][]{2011ApJ...727..123W}." The proposed linear scaling of the 5-rav Iuminositv. with the spin down energy naturally predicts more energetic pulsars., The proposed linear scaling of the $\gamma$ -ray luminosity with the spin down energy naturally predicts more energetic pulsars. llere we outlined a framework to explain the non-thermal radiation lvom gaps in the maegnetosphere of pulsars., Here we outlined a framework to explain the non-thermal radiation from gaps in the magnetosphere of pulsars. More detailed calculations of the emitted οποιον spectra are needed., More detailed calculations of the emitted energy spectra are needed. A major complication in including the IC loses in the radiation codes results from the fact that in the INN regime. an accelerating ool a given strength does not lead to a fixed energy of a particle.," A major complication in including the IC loses in the radiation codes results from the fact that in the KN regime, an accelerating of a given strength does not lead to a fixed energy of a particle." This means (hat a particle is either accelerated or decelerated depending on the photon density and the value of the and does not reach a steady. energy., This means that a particle is either accelerated or decelerated depending on the photon density and the value of the and does not reach a steady energy. This implies that in this regime acceleration is vighly non-stationary., This implies that in this regime acceleration is highly non-stationary. The addition of curvature radiation can. however. establish a steady state.," The addition of curvature radiation can, however, establish a steady state." Thus. curvature radiation. even if not dominating the total gamma-ray luninosity. nav dictate the particle's final energy.," Thus, curvature radiation, even if not dominating the total gamma-ray luminosity, may dictate the particle's final energy." A number of additional factors must be taken into account to construct a comprehensive nodel of the higher energy emission., A number of additional factors must be taken into account to construct a comprehensive model of the higher energy emission. Most important is the intrinsically non-isotropic distribution ol soft photons., Most important is the intrinsically non-isotropic distribution of soft photons. A more detailed structure of the lines within the ineed (o be taken into account. including modifications due to magnetospheric currents.," A more detailed structure of the lines within the need to be taken into account, including modifications due to magnetospheric currents." Also. particle trajectories may not exactly follow the lines due (o various drift elfects.," Also, particle trajectories may not exactly follow the lines due to various drift effects." An important modification could be the IC scattering of ihe surface thermal emission closer to the surface of the iin the slot gaps (Arons1983) (incomparison.CrabdoesnotWeisskoplοἱal. 2004)..," An important modification could be the IC scattering of the surface thermal emission closer to the surface of the in the slot gaps \citep{1983ApJ...266..215A} \citep[in comparison, Crab does not show any thermal component][]{2004ApJ...601.1050W}." Our model is based on the assumption (hat emission is generated within the light eviinder., Our model is based on the assumption that emission is generated within the light cylinder. The main argument for this is that, The main argument for this is that activity levels depend primarily on Rossby number. which is a key parameter describing the efficiency of a magnetic dynamo (Durney Robinson 1982: Robinson Durney 1982).,"activity levels depend primarily on Rossby number, which is a key parameter describing the efficiency of a magnetic dynamo (Durney Robinson 1982; Robinson Durney 1982)." Supporting evidence for an explanation involving saturation of magnetic flux generation comes from direct measurements of magnetic flux in fast rotating M-dwarts (Saar 1991: Reiners et al., Supporting evidence for an explanation involving saturation of magnetic flux generation comes from direct measurements of magnetic flux in fast rotating M-dwarfs (Saar 1991; Reiners et al. 2009) and from chromospheric magnetic activity indicators. which also show show saturation at Rossby numbers of —0.1 (Cardini Cassatella 2007: Marsden. Carter Donati 2009).," 2009) and from chromospheric magnetic activity indicators, which also show show saturation at Rossby numbers of $\simeq 0.1$ (Cardini Cassatella 2007; Marsden, Carter Donati 2009)." A caveat to this conclusion is that the convective turnover times and hence Rossby numbers of the lowest mass stars in our sample are uncertain., A caveat to this conclusion is that the convective turnover times and hence Rossby numbers of the lowest mass stars in our sample are uncertain. In. fact the semi-empirical scaling of 7.xLiu. wasdesigned to minimise the scatter at large Rossby numbers (Pizzolato et al., In fact the semi-empirical scaling of $\tau_c \propto L_{\rm bol}^{-1/2}$ was to minimise the scatter at large Rossby numbers (Pizzolato et al. 2003)., 2003). " Clearly. better theoretical calculations of 7, ure desirable for AZ«0.5M..."," Clearly, better theoretical calculations of $\tau_c$ are desirable for $M<0.5\,M_{\odot}$." The phenomenon of super-saturation does not seem to be well described by Rossby numbers calculated using similar 7. estimates., The phenomenon of super-saturation does not seem to be well described by Rossby numbers calculated using similar $\tau_c$ estimates. Some G- and K-dwarfs show super-saturation atlogNyy2—1.8. but using the same 7. values that tidy up the low-activity side of Fig.," Some G- and K-dwarfs show super-saturation at$\log N_R \simeq -1.8$, but using the same $\tau_c$ values that tidy up the low-activity side of Fig." 6. implies that M-dwarfs do not super-saturate unless at logNyx—2.5., \ref{comblxlbol} implies that M-dwarfs do not super-saturate unless at $\log N_R \simeq -2.5$. This suggests that super-saturation may not be intrinsic to the dynamo mechanism: a point of view supported by the lack of super-saturation in the chromospheric emission from very rapidly rotating G- and K-dwarfs (Marsden. Carter Donati 2009).," This suggests that super-saturation may not be intrinsic to the dynamo mechanism; a point of view supported by the lack of super-saturation in the chromospheric emission from very rapidly rotating G- and K-dwarfs (Marsden, Carter Donati 2009)." It is worth noting that the lack of super-saturation in M-dwarfs is probably not related to any fundamental change in dynamo action. such as a switch from an interface dynamo to a distributed dynamo as the convection zone deepens.," It is worth noting that the lack of super-saturation in M-dwarfs is probably not related to any fundamental change in dynamo action, such as a switch from an interface dynamo to a distributed dynamo as the convection zone deepens." There are sufficient M-dwarfs in Fig., There are sufficient M-dwarfs in Fig. 6 with AZ70.35M.. which should still have radiative cores (Siess et al.," \ref{comblxlbol} with $M>0.35\,M_{\odot}$, which should still have radiative cores (Siess et al." 2000). to demonstrate that they also show no signs of super-saturation at the Rossby numbers of super-saturated G- and K-dwarfs.," 2000), to demonstrate that they also show no signs of super-saturation at the Rossby numbers of super-saturated G- and K-dwarfs." Steppien et al. (, Stȩppień et al. ( 2001). put. forward a hypothesis that. a latitudinal dependence of the heating flux at the base of the convection zone is caused by the polar dependence of the local gravity in rapid rotators.,2001) put forward a hypothesis that a latitudinal dependence of the heating flux at the base of the convection zone is caused by the polar dependence of the local gravity in rapid rotators. This could result in strong poleward updrafts in the convection zone that sweep magnetic flux tubes to higher latitudes. leaving an equatorial band that is free from magnetically active regions. hence reducing the tilling factor of magnetically active regions in the photosphere. chromosphere and corona.," This could result in strong poleward updrafts in the convection zone that sweep magnetic flux tubes to higher latitudes, leaving an equatorial band that is free from magnetically active regions, hence reducing the filling factor of magnetically active regions in the photosphere, chromosphere and corona." In this model super-saturation occurs when the ratio of centrifugal acceleration at the surface of the radiative core to the local gravitational acceleration reaches some critical value ., In this model super-saturation occurs when the ratio of centrifugal acceleration at the surface of the radiative core to the local gravitational acceleration reaches some critical value $\gamma$. " i.e. where AZ, and /%,. are the mass and radius of the radiative core.", i.e. where $M_c$ and $R_c$ are the mass and radius of the radiative core. " Leaving aside the issue of what happens in fully convective stars. we can make the approximation that A4,42,7 is approximately proportional to the central density. so that the period {δις at which super-saturation would be evident depends on central density as /,Xp,un (assuming that the convection zone rotates as a solid body)."," Leaving aside the issue of what happens in fully convective stars, we can make the approximation that $M_c R_c^{-3}$ is approximately proportional to the central density, so that the period $P_{ss}$ at which super-saturation would be evident depends on central density as $P_{\rm ss} \propto \rho_c^{-1/2}$ (assuming that the convection zone rotates as a solid body)." The central density as a function of mass is very time dependent on the PMS., The central density as a function of mass is very time dependent on the PMS. " At MMyr a star of 0.3Al. has p,=3000 kemm. while a 0.9AZ. star has p,=6000 mm (Siess et al."," At Myr a star of $0.3\,M_{\odot}$ has $\rho_c = 3000$ $^{-3}$, while a $0.9\,M_{\odot}$ star has $\rho_c = 6900$ $^{-3}$ (Siess et al." 2000)., 2000). At MMyr however. the core of the 0.3A7. star is nearly three times denser. while the 0.917. star is almost unchanged.," At Myr however, the core of the $0.3\,M_{\odot}$ star is nearly three times denser, while the $0.9\,M_{\odot}$ star is almost unchanged." Thanks to the inverse square root dependence on density however. one would eXpect super-saturation to occur at quite similar periods in objects with a range of masses and certainly with a variation that is much smaller than if super-saturation occurred at a fixed Rossby number.," Thanks to the inverse square root dependence on density however, one would expect super-saturation to occur at quite similar periods in objects with a range of masses and certainly with a variation that is much smaller than if super-saturation occurred at a fixed Rossby number." However. there is no evidence of super-saturation in the chromospheric activity of G- and K-dwarfs which coronally super-saturated (Marsden et al.," However, there is no evidence of super-saturation in the chromospheric activity of G- and K-dwarfs which coronally super-saturated (Marsden et al." 2009). and this argues that a simple restriction of the filling factor due to a polar concentration of the magnetic field is not the solution.," 2009), and this argues that a simple restriction of the filling factor due to a polar concentration of the magnetic field is not the solution." Jardine Unruh (1999) have shown that dynamo saturation or complete filling by active regions may not be necessary to explain the observed plateau in X-ray activity and its subsequent decline at very fast rotation rates., Jardine Unruh (1999) have shown that dynamo saturation or complete filling by active regions may not be necessary to explain the observed plateau in X-ray activity and its subsequent decline at very fast rotation rates. In their model. centrifugal orces act to strip the outer coronal volume. either because the jxlasma pressure exceeds what can be contained by closed magnetic oops (see also Ryan et al.," In their model, centrifugal forces act to strip the outer coronal volume, either because the plasma pressure exceeds what can be contained by closed magnetic loops (see also Ryan et al." 2005) or because the coronal plasma becomes radiatively unstable beyond the Keplerian co-rotation radius (Collier Cameron 1988)., 2005) or because the coronal plasma becomes radiatively unstable beyond the Keplerian co-rotation radius (Collier Cameron 1988). The reduced coronal volume is initially balanced by a rising coronal density. causing a saturation Hateau. but at extreme rotation rates. as more of the corona is orced open. the X-ray emission measure falls (see also Jardine 2004).," The reduced coronal volume is initially balanced by a rising coronal density, causing a saturation plateau, but at extreme rotation rates, as more of the corona is forced open, the X-ray emission measure falls (see also Jardine 2004)." We might expect centrifugal effects to become signiticant in the most rapidly rotating stars and whilst there will clearly be a correlation with Rossby number. there will be an important difference in mass dependence.," We might expect centrifugal effects to become significant in the most rapidly rotating stars and whilst there will clearly be a correlation with Rossby number, there will be an important difference in mass dependence." The key dimensionless parameter in the centrifugal stripping model is ἂν. the co-rotation radius expressed as a multiple of the stellar radius where /? is the rotation period.," The key dimensionless parameter in the centrifugal stripping model is $\alpha_c$, the co-rotation radius expressed as a multiple of the stellar radius where $P$ is the rotation period." Thus coronal activity should saturate at some small value of ἂν and then super-saturate at an even smaller a..., Thus coronal activity should saturate at some small value of $\alpha_c$ and then super-saturate at an even smaller $\alpha_c$. " In the samples considered here there is a two order of magnitude range in /? but a much smaller range in Abert, ", In the samples considered here there is a two order of magnitude range in $P$ but a much smaller range in $M_{\ast}^{1/3} R_{\ast}^{-1}$. Hence we expect to see saturation and super-saturation occur at short periods corresponding to some critical values of a..., Hence we expect to see saturation and super-saturation occur at short periods corresponding to some critical values of $\alpha_c$. " However. in stars with lower masses and smaller radii. these critical αν values will be reached at periods. such that {ονxAZ7287, which in NGC 2547 varies from 0.9 (in solar units) for the most massive stars in our sample to 0.5 in the lowest mass stars."," However, in stars with lower masses and smaller radii, these critical $\alpha_c$ values will be reached at periods, such that $P_{ss} \propto M^{-1/2} R^{3/2}$, which in NGC 2547 varies from 0.9 (in solar units) for the most massive stars in our sample to 0.5 in the lowest mass stars." Hence super-saturation in the M-dwarfs would occur at shorter periods than for K-dwarfs by a factor approaching 2., Hence super-saturation in the M-dwarfs would occur at shorter periods than for K-dwarfs by a factor approaching 2. To test these ideas Fig., To test these ideas Fig. " 7. shows L,/Li.4 as a function of both logNyy and a,. with the stars grouped into mass subsets in a similar way to sections 3 and +4."," \ref{rkplot} shows $L_{x}/L_{\rm bol}$ as a function of both $\log N_R$ and $\alpha_c$, with the stars grouped into mass subsets in a similar way to sections 3 and 4." The stellar radii and masses for the comparison samples were estimated from their luminosities and the Siess et al. (, The stellar radii and masses for the comparison samples were estimated from their luminosities and the Siess et al. ( 2000) models as described in sections 3 and +.,2000) models as described in sections 3 and 4. The o. parameter. like the rotation period. is a poor predictor of what happens to X-ray activity in the slowly-rotating and low-activity regimes.," The $\alpha_c$ parameter, like the rotation period, is a poor predictor of what happens to X-ray activity in the slowly-rotating and low-activity regimes." " Saturated levels of coronal activity are reachec for a,= 10-30. dependent on the mass of the star."," Saturated levels of coronal activity are reached for $\alpha_c = 10$ –30, dependent on the mass of the star." We interpre this to mean that centrifugal forces have a negligible effect on coronal structures in this regime., We interpret this to mean that centrifugal forces have a negligible effect on coronal structures in this regime. " For large values of à, and concomitantly large values of logNyy we suppose that corona activity is determined by the efficiency of the magnetic dynamo. hence explaining the reasonably small scatter within the shadec area of the left hand panel of Fig. 7.."," For large values of $\alpha_c$ and concomitantly large values of $\log N_R$ we suppose that coronal activity is determined by the efficiency of the magnetic dynamo, hence explaining the reasonably small scatter within the shaded area of the left hand panel of Fig. \ref{rkplot}." " On the other hand. super- seems to be achieved when a,2.5 and the modes scatter within the shaded area of the right hand panel of Fig. 7.."," On the other hand, super-saturation seems to be achieved when $\alpha_c \la 2.5$ and the modest scatter within the shaded area of the right hand panel of Fig. \ref{rkplot}," " compared with that for logAy1.8 in the left hand panel. suggests that centrifugal effects may start to control the level of X-ray emission somewhere between this value anda,~ 10."," compared with that for $\log N_R < -1.8$ in the left hand panel, suggests that centrifugal effects may start to control the level of X-ray emission somewhere between this value and $\alpha_c \sim 10$ ." In this model it now becomes clear that the reason we have no clear evidence for super-saturation in M-dwarfs is that they are no spinning fast enough for their coronae to be affected by centrifuga forces., In this model it now becomes clear that the reason we have no clear evidence for super-saturation in M-dwarfs is that they are not spinning fast enough for their coronae to be affected by centrifugal forces. There are only two very low-mass M-dwarfs in our sample, There are only two very low-mass M-dwarfs in our sample compensation of the above mentioned effects or (1) a negligibly small absorption of the y--rays and (1) a y--ray production mechanism. which has a weak dependence on the orbital phase.,"compensation of the above mentioned effects or (i) a negligibly small absorption of the -rays and (ii) a -ray production mechanism, which has a weak dependence on the orbital phase." The latter could be the case for e.g. a large production region in or IC scattering to proceed in the deep Klein-Nishina regime with the cross section oj. only changing marginally with 8., The latter could be the case for e.g. a large production region in or IC scattering to proceed in the deep Klein-Nishina regime with the cross section $\sigma_{\rm ic}$ only changing marginally with $\theta$. To explain the variability of the observed flux as a function of the separation distance one possibility is to. introduce non-radiative (adiabatic) losses. which would dominate in over the whole orbital period (see Fig.44 in 2)).," To explain the variability of the observed flux as a function of the separation distance one possibility is to introduce non-radiative (adiabatic) losses, which would dominate in over the whole orbital period (see 4 in \citet{khangulyan}) )." Moreover. the observed lightcurve with à number of humps and dips suggests a rather complicated dependence of the non-radiative losses on the separation distance.," Moreover, the observed lightcurve with a number of humps and dips suggests a rather complicated dependence of the non-radiative losses on the separation distance." Given the complexity of the self-consistent calculation of the adiabatic losses. TeV data were used to infer a possible profile of the losses.," Given the complexity of the self-consistent calculation of the adiabatic losses, TeV data were used to infer a possible profile of the losses." In particular. one may expect the adiabatic loss rate to have a peak close to periastron together with two smaller peaks located at orbital positions characterized by a true anomaly of 4=+75°.," In particular, one may expect the adiabatic loss rate to have a peak close to periastron together with two smaller peaks located at orbital positions characterized by a true anomaly of $\theta\approx\pm75^{\circ}$." Those smaller peaks may be linked to the impact of the stellar disc. as indicated in Fig. 4..," Those smaller peaks may be linked to the impact of the stellar disc, as indicated in Fig. \ref{cool}," when the pulsar exits the equatorial wind and thus the loss rate due to interference with the outflow The predicted TeV lightcurves including different possible cooling profiles. Fig. 4..," when the pulsar exits the equatorial wind and thus the loss rate due to interference with the outflow The predicted TeV lightcurves including different possible cooling profiles, Fig. \ref{cool}," give an overall qualitative agreement with the data (see Fig. 5))., give an overall qualitative agreement with the data (see Fig. \ref{lc_model}) ). Profiles with a simple evolution of the cooling rate such as the dashed curves in Figs., Profiles with a simple evolution of the cooling rate such as the dashed curves in Figs. " 4 and 5 do not account for the TeV data close to periastron (4= £70""),", \ref{cool} and \ref{lc_model} do not account for the TeV data close to periastron $\theta\approx\pm70^{\circ}$ ). Naturally. the best agreement is achieved by a cooling function featuring two additional peaks that account for the potential impact of the stellar dise (black solid curve in Figs.," Naturally, the best agreement is achieved by a cooling function featuring two additional peaks that account for the potential impact of the stellar disc (black solid curve in Figs." 4 and 5))., \ref{cool} and \ref{lc_model}) ). The predicted lighteurve shows the moderate impact of anisotropic IC. scattering while still being qualitatively compatible with the Regarding X-ray emission. the predicted lighteurves corresponding to the presented cooling coefficients only show a weak degree of agreement to the data (Fig. 3)).," The predicted lightcurve shows the moderate impact of anisotropic IC scattering while still being qualitatively compatible with the Regarding X-ray emission, the predicted lightcurves corresponding to the presented cooling coefficients only show a weak degree of agreement to the data (Fig. \ref{x-ray}) )." The most prominent disagreement stems from pre periastron data for binary separation distances r>2x10em.," The most prominent disagreement stems from pre periastron data for binary separation distances $r>2\times10^{13}\,\mbox{\rm cm}$." This basically indicates a more complicated +-dependence of the magnetic field in the production region than the symmetric B(r)«16/r assumed in this study., This basically indicates a more complicated $r$ -dependence of the magnetic field in the production region than the symmetric $B(r)\propto1/r$ assumed in this study. There is qualitative agreement for the post periastron. lighteurve (red symbols) as far as flux level and global evolution is concerned., There is qualitative agreement for the post periastron lightcurve (red symbols) as far as flux level and global evolution is concerned. Introducing à second peak close to periastron in the black solid model curve seems also not Justified in. X-rays even if improving the prediction compared to the red dashed simple curve., Introducing a second peak close to periastron in the black solid model curve seems also not justified in X-rays even if improving the prediction compared to the red dashed simple curve. In conclusion. none of the suggested model curves accounts quantitatively for the observational data in this energy regime based on a simple phase dependence of the B-field.," In conclusion, none of the suggested model curves accounts quantitatively for the observational data in this energy regime based on a simple phase dependence of the $B$ -field." This requires additional assumptions on the orbital phase dependence of the magnetic Although any detailed discussion of the ratio of TeV and X-ray fluxes requires rather accurate calculations and goes beyond the scope of this paper. a qualitative explanation for a sharp increase of the X-ray flux before periastron passage may be suggested here.," This requires additional assumptions on the orbital phase dependence of the magnetic Although any detailed discussion of the ratio of TeV and X-ray fluxes requires rather accurate calculations and goes beyond the scope of this paper, a qualitative explanation for a sharp increase of the X-ray flux before periastron passage may be suggested here." In the framework of dominant non-radiative losses. a decrease of the IC flux by a factor of 3 should be caused by an equivalent enhancement of the non-radiative losses.," In the framework of dominant non-radiative losses, a decrease of the IC flux by a factor of 3 should be caused by an equivalent enhancement of the non-radiative losses." This may be achieved with an increase of the ram pressure in the stellar outflow. so that the PW termination shock moves closer to the pulsar (roughly by a factor of 3).," This may be achieved with an increase of the ram pressure in the stellar outflow, so that the PW termination shock moves closer to the pulsar (roughly by a factor of 3)." Such à scenario is naturally provided by the pulsar crossing the dense stellar disc., Such a scenario is naturally provided by the pulsar crossing the dense stellar disc. This would not significantly change the density of the tareet photons (assuming the shock is located close to the pulsar). but should lead to a significant increase of the magnetic field in the production region (again by a factor of 3).," This would not significantly change the density of the target photons (assuming the shock is located close to the pulsar), but should lead to a significant increase of the magnetic field in the production region (again by a factor of 3)." Thus. it is indeed natural to expect an increase of the synchrotron flux by one order of magnitude.," Thus, it is indeed natural to expect an increase of the synchrotron flux by one order of magnitude." On the other hand. it has to be noted that the overall orbital behavior of the X-ray flux cannot be explained by means of these simple arguments.," On the other hand, it has to be noted that the overall orbital behavior of the X-ray flux cannot be explained by means of these simple arguments." In this regard it is noteworthy that the increase in pre perisatron X-ray emission coincides with the position of the stellar disc (see black points and vertical dashed line in Fig. 3))., In this regard it is noteworthy that the increase in pre perisatron X-ray emission coincides with the position of the stellar disc (see black points and vertical dashed line in Fig. \ref{x-ray}) ). The steepest increase of the emission is roughly aligned with the equatorial stellar plane where the dise density is presumed to be highest., The steepest increase of the emission is roughly aligned with the equatorial stellar plane where the disc density is presumed to be highest. Again. it 15 difficult to account for the behavior of the post periastron data (red points) in this model picture.," Again, it is difficult to account for the behavior of the post periastron data (red points) in this model picture." Although the data are not yet significant enough to be conclusive regarding the existence of two dips in the TeV lightcurve. the symmetry of the presented feature in the VHE regime with respect to periastron and the correlation with a significant rise of the X-ray emission at the same separation distance are certainly notable.," Although the data are not yet significant enough to be conclusive regarding the existence of two dips in the TeV lightcurve, the symmetry of the presented feature in the VHE regime with respect to periastron and the correlation with a significant rise of the X-ray emission at the same separation distance are certainly notable." It could be well explained by a non monotonic adiabatic cooling profile. tracing a change in the shock region's size and magnetic field conditions induced e.g. by stellar matter outflows of increased density such as the stellar disc.," It could be well explained by a non monotonic adiabatic cooling profile, tracing a change in the shock region's size and magnetic field conditions induced e.g. by stellar matter outflows of increased density such as the stellar disc." Future observations in the VHE regime with instruments such as CTA or II should shed light on this interesting question., Future observations in the VHE regime with instruments such as CTA or II should shed light on this interesting question. "We observed 2MASS 1207 in queue-mode on 2008 March 29 UT and in classical-mode on 2010 March 31 UT and 2010 April 1 UT at Gemini-South, with its highly sensitive Thermal-Region Camera Spectrograph (T-ReCS;?)..","We observed 2MASS 1207 in queue-mode on 2008 March 29 UT and in classical-mode on 2010 March 31 UT and 2010 April 1 UT at Gemini-South, with its highly sensitive Thermal-Region Camera Spectrograph \citep[T-ReCS;][]{1998SPIE.3354..534T}." " We used the Si-2 filter (Acai 8.74um), which is relatively insensitive to extinction/silicate absorption from a potential edge-on disk/shell, while being similarly sensitive as the N-bandfiltei], and mostly immune to variations in precipitable water vapor (?).."," We used the Si-2 filter $\lambda_{central}=8.74\micron$ ), which is relatively insensitive to extinction/silicate absorption from a potential edge-on disk/shell, while being similarly sensitive as the N-band, and mostly immune to variations in precipitable water vapor \citep{2008SPIE.7016E..63M}." " Our data were taken in ~320 s on-source blocks, which corresponds to ~18 minutes clock-time when including chop-nod and other overheads."," Our data were taken in $\sim$ 320 s on-source blocks, which corresponds to $\sim$ 18 minutes clock-time when including chop-nod and other overheads." These long integration sequences are required to build up enough S/N to shift and add on 2MASS 1207 A. Combining the data in larger blocks appears to degrade our image quality due to guiding/nod-offset errors., These long integration sequences are required to build up enough S/N to shift and add on 2MASS 1207 A. Combining the data in larger blocks appears to degrade our image quality due to guiding/nod-offset errors. " We reduced our data with the custom T-ReCS IDL software MEFTOOLS v.5.0, which allows the user to interactively display individual T-ReCS saveset frames and remove those with bad electronic artifacts/noise properties."," We reduced our data with the custom T-ReCS IDL software MEFTOOLS v., which allows the user to interactively display individual T-ReCS saveset frames and remove those with bad electronic artifacts/noise properties." We used this to discard approximately of our frames and produce combined ~320 s chop-nod subtracted images., We used this to discard approximately of our frames and produce combined $\sim$ 320 s chop-nod subtracted images. " For each of these images, we fit 2MASS 1207 A with a 2D Gaussian ellipsoid using the IDL software suite MPFIT (?).."," For each of these images, we fit 2MASS 1207 A with a 2D Gaussian ellipsoid using the IDL software suite MPFIT \citep{2009ASPC..411..251M}." " We discard images where the fit centroid error on 2MASS 1207 A is 20.5 pixels (0.045"")."," We discard images where the fit centroid error on 2MASS 1207 A is $\ge$ 0.5 pixels (0.045"")." This keeps our final combined image free of degradation from shift and add errors (T-ReCS' image quality is typically ~0.3” FWHM).," This keeps our final combined image free of degradation from shift and add errors (T-ReCS' image quality is typically $\sim$ 0.3"" FWHM)." Discarding frames with large centroid errors also has the benefit of selecting the frames with the best image quality (FWHM image quality cannot be accurately measured because of the low S/N on 2MASS 1207 A in a single frame)., Discarding frames with large centroid errors also has the benefit of selecting the frames with the best image quality (FWHM image quality cannot be accurately measured because of the low S/N on 2MASS 1207 A in a single frame). " Our selection leaves us with 15 ~320 s blocks, which are then weighted by the S/N of the Gaussian ellipsoid fit, and combined."," Our selection leaves us with 15 $\sim$ 320 s blocks, which are then weighted by the S/N of the Gaussian ellipsoid fit, and combined." " While 14 out of 25 blocks from 2010 March 31 UT were usable, only one out of the 6 blocks from 2008 March 29 UT and none of the blocks from 2010 April 1 UT passed our centroid error cut."," While 14 out of 25 blocks from 2010 March 31 UT were usable, only one out of the 6 blocks from 2008 March 29 UT and none of the blocks from 2010 April 1 UT passed our centroid error cut." The image quality from 2010 April 1 UT appears to have been significantly degraded by a error., The image quality from 2010 April 1 UT appears to have been significantly degraded by a nod-return/guiding error. A summary of our observations and weather conditions is presented in Table ∙, A summary of our observations and weather conditions is presented in Table \ref{observations}. " Our final combined image is 4749 s on-source (9498 s open-shutter, including chop-nod subtraction), and is shown in Figure ∙ "," Our final combined image is 4749 s on-source (9498 s open-shutter, including chop-nod subtraction), and is shown in Figure \ref{2MASS 1207_image}." "Figure|l] shows 2MASS 1207 A at the center of the two red circles, and a green circle at the near-IR determined position of 2MASS 1207 b (sep=0.773”,PA=125.37°;?)."," Figure \ref{2MASS 1207_image} shows 2MASS 1207 A at the center of the two red circles, and a green circle at the near-IR determined position of 2MASS 1207 b \citep[sep=0.773"", PA=125.37$^{\circ}$." " The measured FWHM of 2MASS 1207 A is 0.30”, so the core of the 2MASS 1207 A"," The measured FWHM of 2MASS 1207 A is 0.30"", so the core of the 2MASS 1207 A" high S/Nratio-.. we introduced the same “smearing” in the simulated BFs.,"high S/N, we introduced the same “smearing” in the simulated BFs." We calculated three BFs for each exposure and stacked them together: one simulated observation 6.6 minutes before the photon midpoint. one at the photon midpoint and one 6.6 minutes after the photon midpoint.," We calculated three BFs for each exposure and stacked them together: one simulated observation 6.6 minutes before the photon midpoint, one at the photon midpoint and one 6.6 minutes after the photon midpoint." We convolved each simulated BF with a Gaussian of σ = 2.5 knys. representing roughly the resolution of the spectrograph in the wavelength range used.," We convolved each simulated BF with a Gaussian of $\sigma$ = 2.5 km/s, representing roughly the resolution of the spectrograph in the wavelength range used." In addition to the parameters describing the binary system. one parameter is included that scales all simulated BFs to the observed BFs.," In addition to the parameters describing the binary system, one parameter is included that scales all simulated BFs to the observed BFs." The primary star has a slightly higher luminosity than the secondary., The primary star has a slightly higher luminosity than the secondary. Also. the template used might fit one of the two stars better than the other one.," Also, the template used might fit one of the two stars better than the other one." Therefore. we included another parameter scaling the height of the kernels of the two stars relative to each other.," Therefore, we included another parameter scaling the height of the kernels of the two stars relative to each other." As mentioned in the beginning of this section. all spectra have been normalized.," As mentioned in the beginning of this section, all spectra have been normalized." During the eclipses the absolute amount of light changes., During the eclipses the absolute amount of light changes. Hence the depths of the absorption lines change relative to the normalized continuum. and therefore the height of the BFs also change.," Hence the depths of the absorption lines change relative to the normalized continuum, and therefore the height of the BFs also change." This has to be incorporated in the calculations of the BFs., This has to be incorporated in the calculations of the BFs. We performed a fit using all 46 spectra obtained out of eclipse and during the primary and secondary eclipses., We performed a fit using all 46 spectra obtained out of eclipse and during the primary and secondary eclipses. The derived values for the parameters are given in column four of Table 2.., The derived values for the parameters are given in column four of Table \ref{tab:fit}. The measured BFs and the best fits can be seen in Fig., The measured BFs and the best fits can be seen in Fig. 8. for the primary eclipse and in Fig., \ref{fig:bf_primary} for the primary eclipse and in Fig. 9. for the secondary eclipse., \ref{fig:bf_secondary} for the secondary eclipse. The uncertainties were calculated using the bootstrap method deseribed in Pressetal.(1992)., The uncertainties were calculated using the bootstrap method described in \cite{Press1992}. . Using the methods described in Section 3.1. and Section 3.2 we obtained values for the orbital parameters of CCyg and for the stellar parameters of the two stars., Using the methods described in Section \ref{sect:center} and Section \ref{sect:shape} we obtained values for the orbital parameters of Cyg and for the stellar parameters of the two stars. The time of periastron passage of the primary (T). the longitude of the periastron (c). and the eccentricity (e) were determined in all three fits. and agree with each other to within. the ]-«- level.," The time of periastron passage of the primary (T), the longitude of the periastron $\omega$ ), and the eccentricity $e$ ) were determined in all three fits, and agree with each other to within the $\sigma$ level." " Using the values from Giménez&Margrave(1985) for w (48.26+0.01"") and the apsidal motion rate (0.000705+40.00004 17/cycle). and taking the time difference into account. one would derive an w of 49.3]+0.067 for the time of our observations."," Using the values from \cite{Gimenez1985} for $\omega$ $48.26\pm 0.01^{\circ}$ ) and the apsidal motion rate $\pm$ $^{\circ}$ /cycle), and taking the time difference into account, one would derive an $\omega$ of $49.31^{\circ} \pm 0.06^{\circ} $ for the time of our observations." This. i5 also the value stated in Table 2.., This is also the value stated in Table \ref{tab:fit}. . " The parameter for the semi-amplitude of the secondary (K,) (90.0+0.1 km/s) falls outside the ]-«- range of the literature. value (91.1+0.4 km/s).", The parameter for the semi-amplitude of the secondary $K_{s}$ ) $90.0\pm0.1$ km/s) falls outside the $\sigma$ range of the literature value $91.1\pm0.4$ km/s). This difference can also be seen in the values for the projected semi-major axis of the system (asin/)., This difference can also be seen in the values for the projected semi-major axis of the system $a \sin i$ ). The uncertainty in the radial-velocity of the center of gravity of the system (y) includes the uncertainty of the radial-velocity in our template star. HD222368 (5.6+0.3 km/s. Udryetal... 1999)).," The uncertainty in the radial-velocity of the center of gravity of the system $\gamma$ ) includes the uncertainty of the radial-velocity in our template star, HD222368 $5.6\pm0.3$ km/s, \citeauthor{Udry1999} \citeyear{Udry1999}) )." " Our calculated masses for the two components in CCyg are M, = 1.355x0.004 M. and M, = 1.32740.003 M...", Our calculated masses for the two components in Cyg are $M_{p}$ = $\pm$ $M_{\odot}$ and $M_{s}$ = $\pm$ $M_{\odot}$. " These values lie in between the values calculated by Andersenetal.(1987) M, = 1.391z0.016 M.« and M, = 1.347x0.013 M... and the values given by Giménez&Margrave(1985) M,, = 1.3340.03 M. and M, = 1.29+0.03 M..."," These values lie in between the values calculated by \cite{Andersen1987} $M_{p}$ = $\pm$ $M_{\odot}$ and $M_{s}$ = $\pm$ $M_{\odot}$, and the values given by \cite{Gimenez1985} $M_{p}$ = $\pm$ $M_{\odot}$ and $M_{s}$ = $\pm$ $M_{\odot}$." The stellar parameters obtained in Section 3.1. are derived by analyzing the shape of the rotation anomaly in the radial velocity., The stellar parameters obtained in Section \ref{sect:center} are derived by analyzing the shape of the rotation anomaly in the radial velocity. The method relies on a clean subtraction of the foreground star from the obtained spectra before calculating the BF's. which depend on orbital parameters derived from out-of-eclipse measurements. values for the stellar radii. the stellar limb-darkening and the light ratio between the two stars during the subtraction process. which have been taken from the literature.," The method relies on a clean subtraction of the foreground star from the obtained spectra before calculating the BF's, which depend on orbital parameters derived from out-of-eclipse measurements, values for the stellar radii, the stellar limb-darkening and the light ratio between the two stars during the subtraction process, which have been taken from the literature." In Section 3.2.. the change in the shape of the absorption lines is used instead of the rotation anomaly.," In Section \ref{sect:shape}, the change in the shape of the absorption lines is used instead of the rotation anomaly." Looking at Figs., Looking at Figs. and 9.. one can see that the simulated BFs are somewhat “rounder” during eclipses than the observed BFs.," \ref{fig:bf_primary} and \ref{fig:bf_secondary}, one can see that the simulated BFs are somewhat “rounder” during eclipses than the observed BFs." This can clearly be seen during the central phase of the primary eclipse (Fig., This can clearly be seen during the central phase of the primary eclipse (Fig. 8 panels in the second row) and during the secondary eclipse (Fig. 9))., \ref{fig:bf_primary} panels in the second row) and during the secondary eclipse (Fig. \ref{fig:bf_secondary}) ). The agreement between the measured BF and the observed BF can be improved if « ts included in the fit., The agreement between the measured BF and the observed BF can be improved if $u$ is included in the fit. The derived values for η would be 0.9+0.1 for the primary and 0.8+0.1 for the secondary., The derived values for $u$ would be $0.9\pm0.1$ for the primary and $0.8\pm0.1$ for the secondary. " As these values are probably too high (Gray 2005)) and the derived values for8 would not change significantly (6, = —0.6+14° and B, 2 —0.3+ 1.27). we kept u fixed to 0.6 in the final fits."," As these values are probably too high \citeauthor{Gray2005} \citeyear{Gray2005}) ) and the derived values for $\beta$ would not change significantly $\beta_{p}$ = $-0.6\pm 1.4^{\circ}$ and $\beta_{s}$ = $-0.3\pm 1.2^{\circ}$ ), we kept $u$ fixed to 0.6 in the final fits." Including solar-like differential rotation. the orbital inclination and the stellar radit as free parameters in the fits also leads to a better agreement between data and simulation.," Including solar-like differential rotation, the orbital inclination and the stellar radii as free parameters in the fits also leads to a better agreement between data and simulation." However. the derived differential rotation. parameters are negative for both stars; theangular rotation speed is faster at the poles than at the equator.," However, the derived differential rotation parameters are negative for both stars; theangular rotation speed is faster at the poles than at the equator." Furthermore. the fitted radi are not in agreement with the literature values; the primary radius is increased relative to the literature. value and the secondary decreased relative to its literature value.," Furthermore, the fitted radii are not in agreement with the literature values; the primary radius is increased relative to the literature value and the secondary decreased relative to its literature value." The value for the orbital inclination of CCye in the literature is, The value for the orbital inclination of Cyg in the literature is Tn this paper. we add a collisional chuhamcement due to the atimosphere.,"In this paper, we add a collisional enhancement due to the atmosphere." " Although the simple power-law radial density profile of the atinosphiere (Equation (6))) is used for the derivation of final masses, (QM. Mg). the simmlation. iucorporates a amore realistic profile provided by the foriiulae of Inaba&Tkoma(2003)."," Although the simple power-law radial density profile of the atmosphere (Equation \ref{eq:atm_dens}) )) is used for the derivation of final masses $M_{\rm ca}$, $M_{\rm fa}$ ), the simulation incorporates a more realistic profile provided by the formulae of \citet{inaba_ikoma03}." . The opacity of the enmbrvo's atinosphere in their model is eiven bx HOmWea|fea. Where Kea. is the eas opacity. bey is the opacity of grains having au interstellar size distribution. aud f is the erain depletion factor.," The opacity of the embryo's atmosphere in their model is given by $\kappa = \kappa_{\rm gas} + f \kappa_{\rm gr}$, where $\kappa_{\rm gas}$ is the gas opacity, $\kappa_{\rm gr}$ is the opacity of grains having an interstellar size distribution, and $f$ is the grain depletion factor." Following Inaba Tkoma. we adopt The cnhancement factor R./R> due to the atinosplhiere is shown in Fig. 2..," Following Inaba Ikoma, we adopt The enhancement factor $R_{\rm e}/R$ due to the atmosphere is shown in Fig. \ref{fig:enhanced_radius}." " We perform the starting from planctesimals of mass iy and radius ry with e=2)(δημ)/? and Pp=Leen5m around the central star of mass AM. with a set of cight concentric auuuli at 3.2. 1.5. 6.1. 9.0. 12. 18. 25. and AAU containing X4, aud X, for q=3/2."," We perform the starting from planetesimals of mass $m_0$ and radius $r_0$ with $e = 2 i = (2 m_0/M_*)^{1/3}$ and $\rho_{\rm p} = 1\,{\rm g\,cm}^{-3}$ around the central star of mass $M_\sun$ with a set of eight concentric annuli at 3.2, 4.5, 6.4, 9.0, 13, 18, 25, and AU containing $\Sigma_{\rm gas}$ and $\Sigma_{\rm s}$ for $q = 3/2$." " To compute Qj. we use Equation (5)) with Qu,27.0«10 ereοtS (15. Qu.=2]locecni ο7. 4,=119. aud Co.=9 (Benz&Asphaug1999:Stewart&Leinhardt 2009)."," To compute $Q_{\rm D}^*$, we use Equation \ref{eq:qd}) ) with $Q_{\rm 0s}=7.0 \times 10^7$ ${\rm erg}\, {\rm g}^{-1}$, ${\beta_{\rm s}}=-0.45$, $Q_{\rm 0g}=2.1$ ${\rm cm}^3\,{\rm g}^{-2}$ , ${\beta_{\rm g}} = 1.19$, and $C_{\rm gg} = 9$ \citep{benz99,stewart09}." ".. We artificially apply the eas surface density evolution in the form Ma,HE=XaExplτων dep). where Tugvas.dey is the ogas depletion timescale. which we set to Tease=105 years."," We artificially apply the gas surface density evolution in the form $\Sigma_{\rm gas} = \Sigma_{\rm gas,0}\exp(-t/T_{\rm gas,dep})$ , where $T_{\rm gas,dep}$ is the gas depletion timescale, which we set to $T_{\rm gas,dep} = 10^7$ years." " Assuming a constant X4, gives almost the samc results for fual enibrvo masses. because we consider tine spas fXTonsdeg"," Assuming a constant $\Sigma_{\rm gas}$ gives almost the same results for final embryo masses, because we consider time spans $t \leq T_{\rm gas,dep}$." Fig., Fig. 6 shows the at G.LAAU for f=0.01., \ref{fig:comp_growth} shows the at AU for $f=0.01$ . Once embryo masses exceed the Mars mass. atmosphere substantially accelerates the embryo erowth.," Once embryo masses exceed the Mars mass, atmosphere substantially accelerates the embryo growth." For Sy©2leem? (34.MMSN). the atinosplhere leads to further enmibrvo growth.," For $\Sigma_0 \geq 21\,{\rm g\,cm}^{-2}$ $3\times$ MMSN), the atmosphere leads to further embryo growth." " Nevertheless. emibrvos finally attain asviuptotic Lassen,"," Nevertheless, embryos finally attain asymptotic masses." Results for these simulations are ΕΠ in Fie. 3..," Results for these simulations are summarised in Fig. \ref{fig:final_mass_r10}," " where the cmbrvo masses after 10"" voars are compared to analytical foriuulae for final eiibrvo masses.", where the embryo masses after $10^7$ years are compared to analytical formulae for final embryo masses. " Eunibrvo masses finally reach Af, mede⋅⋅ SAAT- (Xj=unτιίσοι ""EN7) 1OAAT- (Sy=42lecm2 *). and 20AAU- (Sy2=Tlecm 7)."," Embryo masses finally reach $M_{\rm a}$ inside AU $\Sigma_0 = 7.1\,{\rm g\,cm}^{-2}$ ), AU $\Sigma_0 = 21\,{\rm g\,cm}^{-2}$ ), and AU $\Sigma_0 = 71\,{\rm g\,cm}^{-2}$ )." " However. enibrvos exceed AL, inside AAT for Xy=—.Tlgon2 "," However, embryos exceed $M_{\rm a}$ inside AU for $\Sigma_0 = 71\,{\rm g\,cm}^{-2}$ ." Thisqo excess comes from] theclubrvo growth through collisional accretion with bodies drifting from outside. which effect we did not considerinthe analysisdescribed im Section," This excess comes from theembryo growth through collisional accretion with bodies drifting from outside, which effect we did not considerinthe analysisdescribed in Section" "particle and containing a specifie number of companion particles. generally referred. to as. “neighbours”: formally. this translates into the following relation: where IN,4, stands for the number of neighbours and iN is the number of particles within distance ; from the target xwticle j.","particle and containing a specific number of companion particles, generally referred to as “neighbours”; formally, this translates into the following relation: where $N_{ngbs}$ stands for the number of neighbours and $N$ is the number of particles within distance $h_j$ from the target particle $j$." Phe above equation is solved. iteratively with a rewton-Raphson method. until the dillerence between the wo sides falls below a certain tolerance Adaptive softening lengths can be activated both when he code works in TreePM mode and when it uses the ‘Tree-only algorithm., The above equation is solved iteratively with a Newton-Raphson method until the difference between the two sides falls below a certain tolerance Adaptive softening lengths can be activated both when the code works in TreePM mode and when it uses the Tree-only algorithm. En the latter case the softening lengths are left. varving without boundaries according to the local eatures of the particle distribution: in the former case we co instead. allow for the presence of a minimum and maximum value for the softening lengths., In the latter case the softening lengths are left varying without boundaries according to the local features of the particle distribution; in the former case we do instead allow for the presence of a minimum and maximum value for the softening lengths. As explained in Sec., As explained in Sec. 3.2.1 of BINOOD. the existence of à minimum value is not crucial and only prevents the simulation [rom becoming overly expensive in terms of computational time: conversely. the upper bound. is introduced to ensure that the long-range orce (the particle-mesh contribution) is negligible on the scales where softening is important. so that errors. arising rom the non-mocification of the long range force are under control.," $3.2.1$ of BK09, the existence of a minimum value is not crucial and only prevents the simulation from becoming overly expensive in terms of computational time; conversely, the upper bound is introduced to ensure that the long-range force (the particle-mesh contribution) is negligible on the scales where softening is important, so that errors arising from the non-modification of the long range force are under control." Phese bounds are expressed in terms of the splitting scale rs. the scale (generally of order the grid spacing) where he splitting of the potential in a long-range and short-range component is performed: choosing ρω&— results in the ong-range contribution being below 1% of the total force at scales where softening is important.," These bounds are expressed in terms of the splitting scale $r_s$, the scale (generally of order the grid spacing) where the splitting of the potential in a long-range and short-range component is performed; choosing $h_{max} \simeq \frac{r_s}{2}$ results in the long-range contribution being below $1\%$ of the total force at scales where softening is important." Although we always impose a lower limit to the softening length when using the code in its TreeP mode. we did not find the presence of an upper limit to haveM dramatic consequences on the results. especially when using the adaptive formalism in its full. CONSCLVALIVE version.," Although we always impose a lower limit to the softening length when using the code in its TreePM mode, we did not find the presence of an upper limit to have dramatic consequences on the results, especially when using the adaptive formalism in its full, conservative version." In this section we present some of the tests. performed in order to check the correctness of the. implementation and explore the ecneral ellects of adaptive softening when simulating cdillerent physical scenarios., In this section we present some of the tests performed in order to check the correctness of the implementation and explore the general effects of adaptive softening when simulating different physical scenarios. We will initially: show the behaviour of the code in simulating simple systems. of well-known properties: the force profile of a Plummer ancl Lernquist models are investigated. and their temporal evolution in anc out of equilibrium: the density profile of a polvtrope and the behaviour of its total energy in time is also shown.," We will initially show the behaviour of the code in simulating simple systems, of well-known properties; the force profile of a Plummer and Hernquist models are investigated, and their temporal evolution in and out of equilibrium; the density profile of a polytrope and the behaviour of its total energy in time is also shown." Most. of these examples are present already in PALOT and were specifically chosen to test. our In all the numerical simulations presented in this section we adopt units of mass Af]=1. length 47]=1 ancl C—1.," Most of these examples are present already in PM07 and were specifically chosen to test our In all the numerical simulations presented in this section we adopt units of mass $[M]=1$, length $[R]=1$ and $G=1$." As a result. the energy. per unit mass is measured in units of GAL/R and time in (CAL/RE)5.," As a result, the energy per unit mass is measured in units of $GM/R$ and time in $(GM/R^3)^{-1/2}$." " The system considered. here consists of a set of IN. particles distributed according toa ""Plummer"" profile: llere the total mass AZ and the scale radius r; are set equal to unity.", The system considered here consists of a set of $N$ particles distributed according to a “Plummer” profile: Here the total mass $M$ and the scale radius $r_s$ are set equal to unity. Phe idea is to evaluate the resulting gravitational force profile ancl investigate its dependence on the choice of softening., The idea is to evaluate the resulting gravitational force profile and investigate its dependence on the choice of softening. Once this is accomplished. we concentrate on the behaviour of the total energy. as the svstem is let evolve in This test is identical to that presented. by PALOT and we refer to section 4.3 of their paper or alternatively to ? [or details on the setup of the initial The test was run using dillerent. number of particles and both Trec-onlv ancl TreePM. algorithms for. the evaluation of the gravitational force: the results behave as expected in the dilferent cases and here we show only those obtained using the pure Tree method on IN=1000 lig., Once this is accomplished we concentrate on the behaviour of the total energy as the system is let evolve in This test is identical to that presented by PM07 and we refer to section 4.3 of their paper or alternatively to \citet{aarseth74} for details on the setup of the initial The test was run using different number of particles and both Tree-only and TreePM algorithms for the evaluation of the gravitational force; the results behave as expected in the different cases and here we show only those obtained using the pure Tree method on $N=1000$ Fig. 1 shows the averaged: square errors. (ASL) of the simulated. force field. corresponding to dilferent. choices of both fixed ancl adaptive &ravitational softening., \ref{ase} shows the averaged square errors (ASE) of the simulated force field corresponding to different choices of both fixed and adaptive gravitational softening. " ""This quantity measures the deviation of the force experienced by particles at different radii from the analytical value. given by and it is defined as where f; is the force on particle 7 and five. is the maximum value of the exact solution."," This quantity measures the deviation of the force experienced by particles at different radii from the analytical value, given by and it is defined as where $f_i$ is the force on particle $i$ and $f_{max}$ is the maximum value of the exact solution." For a discussion on, For a discussion on with a speed of approximately 250 km s. greater than half the separation of the centres of the fitted Gaussians. the brightest spot rotating close to the compact object and its aceretion disk.,"with a speed of approximately 250 km $^{-1}$, greater than half the separation of the centres of the fitted Gaussians, the brightest spot rotating close to the compact object and its accretion disk." There are more recent observations concerning the putative circumbinary disk., There are more recent observations concerning the putative circumbinary disk. First. it has been observed in Brackett y (Perez Blundell 2009) over about one orbital period.," First, it has been observed in Brackett $\gamma$ (Perez Blundell 2009) over about one orbital period." The extracted rotational velocity is again 200 km s! but the signal is squeezed between probable accretion disk lines. which complicates its extraction.," The extracted rotational velocity is again $\sim$ 200 km $^{-1}$ but the signal is squeezed between probable accretion disk lines, which complicates its extraction." Secondly. observations in both Hw and Hf suggest that the apparent circumbinary disk lines are not attenuated by the wind from the accretion disk and hence their source is indeed (Perez Blundell 2010).," Secondly, observations in both $\alpha$ and $\beta$ suggest that the apparent circumbinary disk lines are not attenuated by the wind from the accretion disk and hence their source is indeed (Perez Blundell 2010)." | consider such other possible models for the origin of these split lines as have occurred to me., I consider such other possible models for the origin of these split lines as have occurred to me. They are not plausible because of the marked degree to which the red and blue narrow components of Ha in Blundell. Bowler Schmidtobreick (2008) are unmoving over more than two orbits. which is naturally explained by the disk model.," They are not plausible because of the marked degree to which the red and blue narrow components of $\alpha$ in Blundell, Bowler Schmidtobreick (2008) are unmoving over more than two orbits, which is naturally explained by the disk model." The relevant spectra were taken nightly from Julian Date 2453000 + 245.5 to 4 274.5 and only one observation was missed during this period (Blundell. Bowler Schmidtobreick 2008).," The relevant spectra were taken nightly from Julian Date 2453000 + 245.5 to + 274.5 and only one observation was missed during this period (Blundell, Bowler Schmidtobreick 2008)." After JD +274 there are only data at +281 and +282 before another fairly unbroken sequence commenced on JD +287., After JD +274 there are only data at +281 and +282 before another fairly unbroken sequence commenced on JD +287. This was at the onset of an optical outburst. preceding a radio flare. and the stationary lines broadened: an effect attributed to the unveiling of the accretion disk (Bowler 2010).," This was at the onset of an optical outburst, preceding a radio flare, and the stationary lines broadened; an effect attributed to the unveiling of the accretion disk (Bowler 2010)." Up to JD +274 Ha and He I were usually fitted with three Gaussians. à broad Gaussian (representing an origin in the wind for Ha) and two narrower.," Up to JD +274 $\alpha$ and He I were usually fitted with three Gaussians, a broad Gaussian (representing an origin in the wind for $\alpha$ ) and two narrower." Where redshifts or Doppler speeds are quoted in this paper. they refer to the centroids of the fitted Gaussians: the relationship between these fitted parameters and the real structure of the source may not be straightforward.," Where redshifts or Doppler speeds are quoted in this paper, they refer to the centroids of the fitted Gaussians; the relationship between these fitted parameters and the real structure of the source may not be straightforward." The H« data have already been analysed in Blundell. Bowler & Schmidtobreick (2008) and I have used the results of those publishedanalyses.," The $\alpha$ data have already been analysed in Blundell, Bowler $\&$ Schmidtobreick (2008) and I have used the results of those publishedanalyses." The evolution with time of the split spectral profiles of Hw and of He I at both 6678 and 7065 iis elegantly presented in Fig.2 of Schmidtobreick & Blundell (2006b)., The evolution with time of the split spectral profiles of $\alpha$ and of He I at both 6678 and 7065 is elegantly presented in Fig.2 of Schmidtobreick $\&$ Blundell (2006b). In that figure it is immediately obvious that the red and blue components of the split lines alternate in intensity and that the relative intensity in the He I lines varies nuch nore than He., In that figure it is immediately obvious that the red and blue components of the split lines alternate in intensity and that the relative intensity in the He I lines varies much more than $\alpha$. The red side tends to be stronger overall., The red side tends to be stronger overall. The results of fitting Gaussian profiles to the He I lines have not been published. so for the purposes of this paper I have nade ny own fits to the spectra for the He I 6678 line. displayed in Fig.2 of Schmidtobreick Blundell (2006b).," The results of fitting Gaussian profiles to the He I lines have not been published, so for the purposes of this paper I have made my own fits to the spectra for the He I 6678 line, displayed in Fig.2 of Schmidtobreick Blundell (2006b)." Since this paper involves a comparison of Ha and He LI note here some remarks relevant to the reliability of the fitted parameters in the two cases.," Since this paper involves a comparison of $\alpha$ and He I, I note here some remarks relevant to the reliability of the fitted parameters in the two cases." As far as Ha is concerned. inspection of the top panel of Fig.1 of Blundell. Bowler Schmidtobreick (2008) shows that the structure of the line Is dominated by a pair of relatively narrow Gaussians sitting on top of a broader component.," As far as $\alpha$ is concerned, inspection of the top panel of Fig.1 of Blundell, Bowler Schmidtobreick (2008) shows that the structure of the line is dominated by a pair of relatively narrow Gaussians sitting on top of a broader component." In Fig.2 of Schmidtobreick Blundell (2006b) this can be followed until JD +270. after which a minor component becomes visible in the blue on a few occasions.," In Fig.2 of Schmidtobreick Blundell (2006b) this can be followed until JD +270, after which a minor component becomes visible in the blue on a few occasions." These additional components are also plotted in the lower panel of that figure., These additional components are also plotted in the lower panel of that figure. Fitting of two narrow and one broad Gaussian in most cases Well represented the spectra: additional terms would either have picked up very minor aspects or have over parametrised the data., Fitting of two narrow and one broad Gaussian in most cases well represented the spectra; additional terms would either have picked up very minor aspects or have over parametrised the data. Least squares fitting to a complicated shape in terms of many parameters always suffers from the problems of correlated parameters and the existence of local minima in which a fitting program can get trapped: this is not so serious a problem when fitting to three Gaussians as fitting to five. as is necessary after JD +287 (Bowler 2010).," Least squares fitting to a complicated shape in terms of many parameters always suffers from the problems of correlated parameters and the existence of local minima in which a fitting program can get trapped; this is not so serious a problem when fitting to three Gaussians as fitting to five, as is necessary after JD +287 (Bowler 2010)." Such problems can be dealt with by exploring the parameter space and making independent fits., Such problems can be dealt with by exploring the parameter space and making independent fits. The data for Blundell. Bowler Schmidtobreick (2008) were fitted independently with two different least squares programs and for Ha the narrow lines seldom differed by more than a Doppler shift of 10 km s7!.," The data for Blundell, Bowler Schmidtobreick (2008) were fitted independently with two different least squares programs and for $\alpha$ the narrow lines seldom differed by more than a Doppler shift of 10 km $^{-1}$." This is reflected in the random seatter of the results in the lower panel of Fig.l of Blundell. Bowler Schmidtobreick (2008) and the reproduction of those data in Fig.1 of the present paper.," This is reflected in the random scatter of the results in the lower panel of Fig.1 of Blundell, Bowler Schmidtobreick (2008) and the reproduction of those data in Fig.1 of the present paper." " The He I| spectra are noisier than Ha and uncertainties correspondingly larger,", The He I spectra are noisier than $\alpha$ and uncertainties correspondingly larger. Fig.2 of Schmidtobreick & Blundell (2006b) makes it clear that after JD +287 the He and He I profiles broaden considerably and become much more complicated., Fig.2 of Schmidtobreick $\&$ Blundell (2006b) makes it clear that after JD +287 the $\alpha$ and He I profiles broaden considerably and become much more complicated. It is not easy to identify Gaussian components from the circumbinary disk and Blundell. Bowler & Schmidtobreick (2008) considered only spectra up to JD +274.," It is not easy to identify Gaussian components from the circumbinary disk and Blundell, Bowler $\&$ Schmidtobreick (2008) considered only spectra up to JD +274." Similarly. I discuss here only the analysis of He I data up to that date.," Similarly, I discuss here only the analysis of He I data up to that date." I present results for He 16678z not significantly different from the He I 7065 lline. as may be seen from Fig.2 of Schmidtobreick Blundell (2006b).," I present results for He I 6678; not significantly different from the He I 7065 line, as may be seen from Fig.2 of Schmidtobreick Blundell (2006b)." Fits were made to three Gaussian components in every case. because three were clearly necessary for Ho. and yielded two narrow components (standard deviation approximately 2 ) and a third with standard deviation approximately 7.," Fits were made to three Gaussian components in every case, because three were clearly necessary for $\alpha$, and yielded two narrow components (standard deviation approximately 2 ) and a third with standard deviation approximately 7." . This third component may not be associated with the wind from the accretion disk because the width does not reflect precession and nodding in the way of the much broader wind component in He (Blundell. Bowler Schmidtobreick 2008).," This third component may not be associated with the wind from the accretion disk because the width does not reflect precession and nodding in the way of the much broader wind component in $\alpha$ (Blundell, Bowler Schmidtobreick 2008)." It is possible that the tails represent a lower intensity higher speed source within the rim of the circumbinary disk., It is possible that the tails represent a lower intensity higher speed source within the rim of the circumbinary disk. The third component does improve the fits but any further additions would certainly overparametrise the data., The third component does improve the fits but any further additions would certainly overparametrise the data. Here | am concerned only with the signal from the narrow components., Here I am concerned only with the signal from the narrow components. The results of fits made in the preparation of Blundell. Bowler Schmidtobreick (2008) have not been published. so I digitised the spectra published in Schmidtobreick Blundell (2006b). much as I digitised the later period of Ha data in Bowler (2010) and made my own fits. the results of which I compared with the earlier work.," The results of fits made in the preparation of Blundell, Bowler Schmidtobreick (2008) have not been published, so I digitised the spectra published in Schmidtobreick Blundell (2006b), much as I digitised the later period of $\alpha$ data in Bowler (2010) and made my own fits, the results of which I compared with the earlier work." The random errors on He I narrow components are about 30 km s. except where a component ts both dim and very much out of place. when," The random errors on He I narrow components are about 30 km $^{-1}$ , except where a component is both dim and very much out of place, when" us confidence in the reality of the compact objects in the nebula.,us confidence in the reality of the compact objects in the nebula. " Unfortunately, the B and V images are too noisy to confirm their existence in these bands although upper limits can be given."," Unfortunately, the B and V images are too noisy to confirm their existence in these bands although upper limits can be given." The high contrast B and V and images are shown in Figure 3.. Based upon, The high contrast B and V and images are shown in Figure \ref{psrFig2}. " Cardelli,Clayton,&Mathis(1989) we expect E(V-R) and E(B-R) to be — 0.5 and 1.2 respectively, and this extinction probably accounts for the non-detection in the B and V bands."," Based upon \citet{car89} we expect E(V-R) and E(B-R) to be $\sim$ 0.5 and 1.2 respectively, and this extinction probably accounts for the non-detection in the B and V bands." " The results of our photometry, with the measured coordinates of the compact objects inside of the nebula, are presented in Table 3.."," The results of our photometry, with the measured coordinates of the compact objects inside of the nebula, are presented in Table \ref{Fluxes}." " In conclusion we note that the object οἱ is well inside the typical HRC pointing uncertainty, x1"", marked in Figure 2 as a circle around the pulsar position."," In conclusion we note that the object o1 is well inside the typical HRC pointing uncertainty, $\lesssim 1 \arcsec$, marked in Figure \ref{psrFig} as a circle around the pulsar position." We propose that this is the best candidate for the optical counterpart of the pulsar., We propose that this is the best candidate for the optical counterpart of the pulsar. From these observations we confirm the presence of an optical, From these observations we confirm the presence of an optical Space-time in the vicinity of a rotating black hole is described. by the Werr metric.,Space-time in the vicinity of a rotating black hole is described by the Kerr metric. La Bover-Linceuist coordinates this metric reads: where The photon trajectory may be specified. by. two constants of motion (the component of angular momentum. parallel to the symmetry axis / and the Carter constant Q) which can be expressed in terms of the direction cosines e; of the photon momentum k and the comoving tetrad A:., In Boyer-Lindquist coordinates this metric reads: where The photon trajectory may be specified by two constants of motion (the component of angular momentum parallel to the symmetry axis $l$ and the Carter constant $Q$ ) which can be expressed in terms of the direction cosines $e_{\hat{i}}$ of the photon momentum ${\bf k}$ and the comoving tetrad $\lambda_{\hat{i}}$. where g is the Werr metric tensor and h is the transverse projecting operator defined bv h=g|uw:u ancl u denotes the four velocity of the source given where and € is the angular velocity of the lare by: Note that such a definition does not violate (for the parameters considered in Section 3) the obvious condition that the source must follow a timelike worlcdline: The necessary components of the comoving tetrad and photon momentum are: and where w=σα is the angular velocity of the [rame dragging and £=€|(7., where ${\bf g}$ is the Kerr metric tensor and ${\bf h}$ is the transverse projecting operator defined by ${\bf h}={\bf g}+{\bf u\cdot u}$ and ${\bf u}$ denotes the four velocity of the source given where and $\Omega$ is the angular velocity of the flare by: Note that such a definition does not violate (for the parameters considered in Section 3) the obvious condition that the source must follow a timelike worldline: The necessary components of the comoving tetrad and photon momentum are: and where $\omega=2ar/A$ is the angular velocity of the frame dragging and $L=Q+l^{2}$. The directional cosines can be expressed as functions of polar V. and azimuthal e angles in the rest frame of the source in the usual wav: Lere we chose the local z axis to point in the ὃν direction and the local x axis in Ve direction., The directional cosines can be expressed as functions of polar $\Psi$ and azimuthal $\Phi$ angles in the rest frame of the source in the usual way: Here we chose the local z axis to point in the $\partial_{r}$ direction and the local x axis in $\partial_{\theta}$ direction. We can now combine the above equations to obtain the desired set of two equations [or the two constants of motion / and (Q: All components containing £ in Eq., We can now combine the above equations to obtain the desired set of two equations for the two constants of motion $l$ and $Q$ : All components containing $L$ in Eq. Dl cancel out miraculously anc we obtain relatively simple quadratic equation for / which has the solution: , B1 cancel out miraculously and we obtain relatively simple quadratic equation for $l$ which has the solution: with The discovery of planets around other stars has placed our Solar Svstem in context aud stimulated speculation on the Irequency of habitable planets aud life in the Universe.,The discovery of planets around other stars has placed our Solar System in context and stimulated speculation on the frequency of habitable planets and life in the Universe. Very cool dwarf stars (wilh late IX and early M spectral (vpes) are of special significance to such investigations because (he two principle detection techniques. Doppler radial velocity (RV) and (transit photometry. are more sensitive to smaller planets around smaller stars.," Very cool dwarf stars (with late K and early M spectral types) are of special significance to such investigations because the two principle detection techniques, Doppler radial velocity (RV) and transit photometry, are more sensitive to smaller planets around smaller stars." Such stars are also much less Iuminous (han solar-twpe stars. the circumstellar habitable zone is closer (Ixastingetal.1993).. aud. planets within the habitable zone are therefore more detectable (Gaidosetal.2007).," Such stars are also much less luminous than solar-type stars, the circumstellar habitable zone is closer \citep{Kasting1993}, and planets within the habitable zone are therefore more detectable \citep{Gaidos2007}." . These stars test models of planet formation: for example. core-accretion models predict fewer gas elants and more “failed” cores (Laughlinetal.]xennedy&Ixenvon 2008).. consistent with the lower Lrequeney of giant planets ancl higher frequency of low-mass planets compared (o G stars (Johnsonetal.2007;Cummingοἱ2008:Mavorοἱal. 2009).," These stars test models of planet formation: for example, core-accretion models predict fewer gas giants and more ""failed"" cores \citep{Laughlin2004,Kennedy2008}, consistent with the lower frequency of giant planets and higher frequency of low-mass planets compared to G stars \citep{Johnson2007a,Cumming2008,Mayor2009}." . Finally. late Ix and early AI cdiwarls constitute Cirvee-quarters of all stars in the Galaxy. and their contribution weighs heavily in anv cosmic accounting of planets or life.," Finally, late K and early M dwarfs constitute three-quarters of all stars in the Galaxy, and their contribution weighs heavily in any cosmic accounting of planets or life." Most confirmed. exoplanets have been found by the Doppler technique. which can detect planets of a few Earth masses on short-period orbits around bright late F- to early ]x-tvpe stars (Alavorοἱal.2009:Llowardet2010).," Most confirmed exoplanets have been found by the Doppler technique, which can detect planets of a few Earth masses on short-period orbits around bright late F- to early K-type stars \citep{Mayor2009,Howard2010}." . There are also Doppler searches Lor planets around very cool dwarls (Zechmeisterοἱal.2009;Appset2010:Bean2010:Forveilleetal. 2011).," There are also Doppler searches for planets around very cool dwarfs \citep{Zechmeister2009,Apps2010,Bean2010,Forveille2011}." . The CoRoT andAepler missions have successfully extended the search for small planets to space using the transit technique., The CoRoT and missions have successfully extended the search for small planets to space using the transit technique. " TheAepler spacecraft is monitoring ~150.000 stars. including approximately 24.000 Ix-tvpe stars and 3000 M-t(vpe stars(Datalhaetal. 2010).. and has discovered hundreds of candidate planets with radii 2, "," The spacecraft is monitoring $\sim$ 150,000 stars, including approximately 24,000 K-type stars and 3000 M-type stars\citep{Batalha2010}, , and has discovered hundreds of candidate planets with radii $R_p$ " stars.,stars. " Additionally, we expect that the range of metallicities present among the field stars includes the metallicities of the clusters."," Additionally, we expect that the range of metallicities present among the field stars includes the metallicities of the clusters." " The radius distributions of the three clusters and the field stars overlap, with a bimodal distribution most prominent for stars in NGC 6791."," The radius distributions of the three clusters and the field stars overlap, with a bimodal distribution most prominent for stars in NGC 6791." " In general, the stars with radii in the range 5-9 Ro are most likely less-evolved H-shell burning stars ascending the red-giant branch, while the stars with radii 1189 are most likely He-core burning red-clump stars (?2?).."," In general, the stars with radii in the range 5-9 $_{\odot}$ are most likely less-evolved H-shell burning stars ascending the red-giant branch, while the stars with radii $\sim$ $_{\odot}$ are most likely He-core burning red-clump stars \citep{miglio2009,kallinger2010,mosser2010}." " This shows that for the clusters, a significant fraction of stars are still in the (less-evolved) H-shell burning phase, while for the field stars the majority of the stars are in the He-core burning red-clump phase."," This shows that for the clusters, a significant fraction of stars are still in the (less-evolved) H-shell burning phase, while for the field stars the majority of the stars are in the He-core burning red-clump phase." This is also confirmed by the locations of the stars in the colour-magnitude diagram in Fig. 1.., This is also confirmed by the locations of the stars in the colour-magnitude diagram in Fig. \ref{CMD6791}. " The H-R diagrams of the different clusters look very similar but with an offset with respect to one another, most notably in log Te, but also in logL/Lo (see Fig. 6))."," The H-R diagrams of the different clusters look very similar but with an offset with respect to one another, most notably in $\log T_{\rm eff}$ , but also in $\log L/ \rm L_{\odot}$ (see Fig. \ref{HRclusters}) )." For an explanation of this we have again used models., For an explanation of this we have again used models. From the right panels of Fig., From the right panels of Fig. 5 it is clear that both mass and metallicity influence the location of a star in the H-R diagram., \ref{resmodels} it is clear that both mass and metallicity influence the location of a star in the H-R diagram. " When leaving all other parameters the same, stars with higher metallicities shift to lower effective temperatures and luminosities, while higher masses give higher effective temperatures and luminosities."," When leaving all other parameters the same, stars with higher metallicities shift to lower effective temperatures and luminosities, while higher masses give higher effective temperatures and luminosities." NGC 6791 has a significantly higher metallicity and consists of lower mass stars compared to NGC 6819 (see Table 1 and lower left panel of Fig. 2))., NGC 6791 has a significantly higher metallicity and consists of lower mass stars compared to NGC 6819 (see Table \ref{cluster_param} and lower left panel of Fig. \ref{resclusters}) ). So both mass and metallicity add to the separation of the location of the two clusters in the H-R diagram., So both mass and metallicity add to the separation of the location of the two clusters in the H-R diagram. To quantify this shift further we computed the change in both effective temperature and luminosity for models in the range 1.0 « logL/Lo « 2.0 and 3.6 «ΙοσΤε « 3.75 due to a change in mass or metallicity., To quantify this shift further we computed the change in both effective temperature and luminosity for models in the range 1.0 $<$ $\log L/ \rm L_{\odot}$ $<$ 2.0 and 3.6 $<$ $\log T_{\rm eff}$ $<$ 3.75 due to a change in mass or metallicity. We change the mass from ~1.7 Μο (NGC 6819) to «1.3 Μο (NGC 6791) for models with constant metallicity of 0.06 dex (similar to the metallicity of NGC 6819)., We change the mass from $\sim$ 1.7 $_{\odot}$ (NGC 6819) to $\sim$ 1.3 $_{\odot}$ (NGC 6791) for models with constant metallicity of 0.06 dex (similar to the metallicity of NGC 6819). This change in mass induces a change in logΤεῃ of —0.016 and in logL/Lo of 0.05., This change in mass induces a change in $\log T_{\rm eff}$ of $-$ 0.016 and in $\log L/ \rm L_{\odot}$ of 0.05. For the metallicity we compute the difference in logTe for models with M = 1.3 Mo (NGC 6791) due to a metallicity change from 0.06 dex (NGC 6819) to 0.4 dex (NGC 6791)., For the metallicity we compute the difference in $\log T_{\rm eff}$ for models with $M$ = 1.3 $_{\odot}$ (NGC 6791) due to a metallicity change from 0.06 dex (NGC 6819) to 0.4 dex (NGC 6791). This change in metallicity induces a difference in logTeg of —0.014 and in logL/L of 0.03., This change in metallicity induces a difference in $\log T_{\rm eff}$ of $-$ 0.014 and in $\log L/ \rm L_{\odot}$ of 0.03. Applying the total shifts logΤομ = —0.03 and logL/Lo = 0.02 to the data of NGC 6819 indeed places the data roughly at the position of the observations of NGC 6791 (see gray dots on the right-hand side of Fig. 6))., Applying the total shifts $\log T_{\rm eff}$ = $-$ 0.03 and $\log L/ \rm L_{\odot}$ = 0.02 to the data of NGC 6819 indeed places the data roughly at the position of the observations of NGC 6791 (see gray dots on the right-hand side of Fig. \ref{HRclusters}) ). From this analysis we can conclude that both the metallicity and mass difference between the clusters contribute to the observed shift in the position in the H-R diagram., From this analysis we can conclude that both the metallicity and mass difference between the clusters contribute to the observed shift in the position in the H-R diagram. " For NGC 6811 no direct metallicity determination is available and so far solar metallicity has been assumed, similar to the metallicity of NGC 6819."," For NGC 6811 no direct metallicity determination is available and so far solar metallicity has been assumed, similar to the metallicity of NGC 6819." In that respect the offset of the NGC 6811 compared to NGC 6819 should be mostly due to the difference in mass., In that respect the offset of the NGC 6811 compared to NGC 6819 should be mostly due to the difference in mass. From the models with [Fe/H] = 0.06 dex we find that an increase in mass from 1.7 Μο (NGC 6819) to 2.6 Μο (NGC 6811) would cause an offset in logTeg of the order of 0.03 and an offset in logL/Lo of about 0.05., From the models with [Fe/H] = 0.06 dex we find that an increase in mass from 1.7 $_{\odot}$ (NGC 6819) to 2.6 $_{\odot}$ (NGC 6811) would cause an offset in $\log T_{\rm eff}$ of the order of 0.03 and an offset in $\log L/ \rm L_{\odot}$ of about 0.05. Shifting the position of the red-giant branch of NGC 6819 (dashed line in Fig. 6)), Shifting the position of the red-giant branch of NGC 6819 (dashed line in Fig. \ref{HRclusters}) ) by these amounts would result in the position indicated with the dashed-dotted line in Fig. 6.., by these amounts would result in the position indicated with the dashed-dotted line in Fig. \ref{HRclusters}. This location is not consistent with the observations and indicates that the metallicity of NGC 6811 is subsolar., This location is not consistent with the observations and indicates that the metallicity of NGC 6811 is subsolar. " Therefore, we used a metallicity for NGC 6811 of —0.35 dex."," Therefore, we used a metallicity for NGC 6811 of $-$ 0.35 dex." The additional shift induced by this metallicity would shift the red-giant branch of NGC 6819 to the position indicated with the dashed-dotted-dotted-dotted line in Fig. 6.., The additional shift induced by this metallicity would shift the red-giant branch of NGC 6819 to the position indicated with the dashed-dotted-dotted-dotted line in Fig. \ref{HRclusters}. " This could be consistent with the observations, if we assume that the observed stars of NGC 6811 are red-clump stars."," This could be consistent with the observations, if we assume that the observed stars of NGC 6811 are red-clump stars." " However, if the stars in NGC 6811 are ascending the red-giant branch, it would mean that the observed offset of the locations of the stars with respect to NGC 6819is even larger and a metallicity of —0.66 6)). ? "," However, if the stars in NGC 6811 are ascending the red-giant branch, it would mean that the observed offset of the locations of the stars with respect to NGC 6819is even larger and a metallicity of $-$ \ref{HRclusters}) \citet{kallinger2010} " with respect to the first order terms.,with respect to the first order terms. The resultant equations of motion are cvelic in the variables / and 42. and hence by applving the local WIKD method one may seek solutions in (he form of normal modes by expanding anv perturbation where 0X and 9N are the real amplitudes. which are constant in space and (me. Αι} is the real radial wavenumber. 77 is (he nonnegative (integer) azimuthal mode number. ο=DawtHw ds (he complex Irequencey of excited waves. and c.c. means (he complex conjugate.," The resultant equations of motion are cyclic in the variables $t$ and $\varphi$, and hence by applying the local WKB method one may seek solutions in the form of normal modes by expanding any perturbation where $\delta \Sigma$ and $\delta \aleph$ are the real amplitudes, which are constant in space and time, $k_r (r)$ is the real radial wavenumber, $m$ is the nonnegative (integer) azimuthal mode number, $\omega=\Re \omega +i\Im \omega$ is the complex frequency of excited waves, and $\mathrm{c.\,c.}$ means the complex conjugate." The solution in such a form represents a spiral plane wave with n arms., The solution in such a form represents a spiral plane wave with $m$ arms. " The inaeginaryv part olo corresponds to a growth (Sw> 0) or decay (Sie«0) of the components in lime. X4 and 84xexp(3o/). ancl (he real part to a rotation with constant angular velocity Q,iip=Xm."," The imaginary part of $\omega$ corresponds to a growth $\Im \omega >0$ ) or decay $\Im \omega <0$ ) of the components in time, $\Sigma_1$ and $\aleph_1 \propto \exp (\Im \omega t)$, and the real part to a rotation with constant angular velocity $\Omega_{\mathrm{p}}=\Re \omega/m$." Thus. when Sw>0. the medium transfers its energy to the growing wave and oscillation buildup occurs.," Thus, when $\Im \omega >0$, the medium transfers its energy to the growing wave and oscillation buildup occurs." " It is important to note that in the WIND method. the racial wavenumber is presumed io be of the form where A is a large parameter and V(r) is à smooth. slowly varving function of the radial distance r. ie. dIn/,/dIny=O(1). and |/,]r21."," It is important to note that in the WKB method, the radial wavenumber is presumed to be of the form where ${\cal{A}}$ is a large parameter and $\Psi (r)$ is a smooth, slowly varying function of the radial distance $r$, i.e., $\mathrm{d} \ln k_r / \mathrm{d}\ln r =O(1)$, and $|k_r| r \gg 1$." Paralleling the analysis leading (o equation (84) in Griv et al. (, Paralleling the analysis leading to equation (34) in Griv et al. ( "1999). il is straightforward (ο show that where X4(/——2€)=0. so by considering only growing perturbations we neglected the effects of the initial conditions. 2,=w—mQ is the Doppler-shifted (in a rotating reference frame) wavelrequency. O(r) is the angular velocity of differential rotation at the distance r ","1999), it is straightforward to show that where $\Sigma_1 (t \rightarrow -\infty) = 0$, so by considering only growing perturbations we neglected the effects of the initial conditions, $\omega_*= \omega-m\Omega$ is the Doppler-shifted (in a rotating reference frame) wavefrequency, $\Omega (r)$ is the angular velocity of differential rotation at the distance $r$ " magnetic indices do. we can determine (he period of the evele by correlating the zonal-Llow pattern with itself after a shift in time.,"magnetic indices do, we can determine the period of the cycle by correlating the zonal-flow pattern with itself after a shift in time." Using this we estimate the length of solar cycle 23 (o be about 11.7 vears., Using this we estimate the length of solar cycle 23 to be about 11.7 years. This is shorter (han the length defined as the time elapsed between the minimun in solar activity. indices., This is shorter than the length defined as the time elapsed between the minimum in solar activity indices. For cvcle 23 the period derived from suuspot numbers is about 12.6 vears (see Hathaway 2010)., For cycle 23 the period derived from sunspot numbers is about 12.6 years (see Hathaway 2010). We conclude by reiterating (hat solar dynamics. in particular the solar rotation rate ancl zonal [lows were different for (he evele 24 minimum compared with the evele 22 minimum.," We conclude by reiterating that solar dynamics, in particular the solar rotation rate and zonal flows were different for the cycle 24 minimum compared with the cycle 23 minimum." We find that solar zonal flows returned to their mean-minimum state before solar magnetic indices did curing the end of solar evele 23., We find that solar zonal flows returned to their mean-minimum state before solar magnetic indices did during the end of solar cycle 23. This work utilizes data obtained by the Global Oscillation Network Group (GONG) project. managed by the National Solar Observatory. which is operated by AURA. Inc. under a cooperalive agreement wilh the National Science Foundation.," This work utilizes data obtained by the Global Oscillation Network Group (GONG) project, managed by the National Solar Observatory, which is operated by AURA, Inc. under a cooperative agreement with the National Science Foundation." The data were acquired bv instruments operated by the Bie Bear Solar Observatory. High. Altitude. Observatory. Learmonth Solar Observatory. Udaipur Solar Observatory. Instituto de Astrolisico de Canarias. and Cerro Tololo Inter-American Observatory.," The data were acquired by instruments operated by the Big Bear Solar Observatory, High Altitude Observatory, Learmonth Solar Observatory, Udaipur Solar Observatory, Instituto de Astrofisico de Canarias, and Cerro Tololo Inter-American Observatory." This work also utilizes data from the Solar Oscillations Iuivestigation/ Michelson Doppler Lnager (SOL/AIDI) on the Solar aud Heliospheric Observatory (SOHO)., This work also utilizes data from the Solar Oscillations Investigation/ Michelson Doppler Imager (SOI/MDI) on the Solar and Heliospheric Observatory (SOHO). SOIIO is a project of international cooperation between ESA and NASA., SOHO is a project of international cooperation between ESA and NASA. SD acknowledges support [rom NSF grant ATM 0348827 and NASA erant NNXIO0AEGOC., SB acknowledges support from NSF grant ATM 0348837 and NASA grant NXX10AE60G. aapparent column density profiles are shown in Fig 3..,apparent column density profiles are shown in Fig \ref{fig: OVI-AOD}. " Since the metal lines come close to zero flux in several cases, we also performed Voigt profile fitting to check for unresolved saturation."," Since the metal lines come close to zero flux in several cases, we also performed Voigt profile fitting to check for unresolved saturation." " Fitting was performed on the aand lines Cin both clouds, and results are shown in Table 3.. We fit the No"," Fitting was performed on the and lines in both clouds, and results are shown in Table \ref{tab: profile_fitting}." n-detection]ine in both strong components of the metal-poor cloud., We fit the line in both strong components of the metal-poor cloud. " ""The profile fits yield: a higher: column density: (~0.4 dex) an is obtained in the optically thin case, but with correspondingly larger errors (~0.3 such that the two measurements are in statistical agreement."," The profile fits yield a higher column density $\sim 0.4\dex$ ) than is obtained in the optically thin case, but with correspondingly larger errors $\sim 0.3\dex$ ), such that the two measurements are in statistical agreement." "dex), 'The aapparent column density curves of the ccloud shown in Figure 3 show some evidence of asymmetry in the pprofile, indicating that a two-component fit may be justified for theVI."," The apparent column density curves of the cloud shown in Figure \ref{fig: OVI-AOD} show some evidence of asymmetry in the profile, indicating that a two-component fit may be justified for the." ". We performed fits using both a single and a double-component model, using two independant fitting codes, and taking into account the tabulated COS line-spread functions, but the S/N was not sufficient to distinguish between the two cases."," We performed fits using both a single and a double-component model, using two independant fitting codes, and taking into account the tabulated COS line-spread functions, but the S/N was not sufficient to distinguish between the two cases." This is reflected in the large parameter errors for the two component fit., This is reflected in the large parameter errors for the two component fit. " The total column density is the same in with 1 or 2 components, and is ~0.4dex higher than was obtained above by assuming the gas is optically"," The total column density is the same in with 1 or 2 components, and is $\sim 0.4\dex$ higher than was obtained above by assuming the gas is optically" and learn more about the role of substellar companions lor the formation of single and close binary. sdBs.,and learn more about the role of substellar companions for the formation of single and close binary sdBs. The double-lined spectroscopic WD+BD system WDO00137—2349 is a binary very similar to J08204-0008. but in a later stage of evolution.," The double-lined spectroscopic WD+BD system $-$ 349 \citep{maxted06} is a binary very similar to J0820+0008, but in a later stage of evolution." It consists of a lle-core white dwarl of 0.39M... orbited by a 0.05344. brown dwarl in 0.0803 davs.," It consists of a He-core white dwarf of $0.39\,M_{\rm \odot}$ orbited by a $0.053\,M_{\rm \odot}$ brown dwarf in 0.0803 days." When evolving on the white cdwarf cooling sequence J082054-0008 will therefore appear as a (win to 00137—349 once it is cooled down to the effective temperature of the latter (15000Ix).," When evolving on the white dwarf cooling sequence J08205+0008 will therefore appear as a twin to $-$ 349 once it is cooled down to the effective temperature of the latter $15\,000\,{\rm K}$ )." Based on observations at the La Silla Observatory of the European Southern Observatory for programmes number 082.D-0649 and 084.D-0348 and on observations with the Southern Astrophysical Research (SOAR) telescope operated bv the U.S. National Optical Astronomy Observatory (NOAQ). the MinistA@Qrio da Ciencia e Tecnologia of the Federal Republic of Brazil (AICT). the University of North Carolina al Chapel Lill (UNC). and. Michigan state University (MSU).," Based on observations at the La Silla Observatory of the European Southern Observatory for programmes number 082.D-0649 and 084.D-0348 and on observations with the Southern Astrophysical Research (SOAR) telescope operated by the U.S. National Optical Astronomy Observatory (NOAO), the Ministério da Ciencia e Tecnologia of the Federal Republic of Brazil (MCT), the University of North Carolina at Chapel Hill (UNC), and Michigan State University (MSU)." Based on observations collected with the Flemish 1.2-m Mercator Telescope at the toque de los Muchachos. La Palma. Spain.," Based on observations collected with the Flemish 1.2-m Mercator Telescope at the Roque de los Muchachos, La Palma, Spain." A.T. and $.G. are supported by the Deutsche Forschungsgemeinschaft (DEG) through grants HIE1356/45-1 and WE1356/49-1l., A.T. and S.G. are supported by the Deutsche Forschungsgemeinschaft (DFG) through grants HE1356/45-1 and HE1356/49-1. RO... acknowledges funding from the European. Research Council under the European (PROSPERITY). as well as from the Research Council of IX.U.Leuven grant agreement GOA/2008/04.," acknowledges funding from the European Research Council under the European Community's Seventh Framework Programme (FP7/2007–2013)/ERC grant agreement $^{\underline{\mathrm o}}$ 227224 ), as well as from the Research Council of K.U.Leuven grant agreement GOA/2008/04." the nominal absorption. the cllective temperature limit on iis ττουν (using Ny=5«107em 7).,"the nominal absorption, the effective temperature limit on is eV (using $\NH=\expnt{5}{21}\,\percmsq$ )." While the count-rate limit is tighter for0257.. the higher likely distance and. absorption (although the DAL is lower) mean that the limit is comparable. ουν (for Ny=2Q7em 7).," While the count-rate limit is tighter for, the higher likely distance and absorption (although the DM is lower) mean that the limit is comparable, eV (for $\NH=\expnt{2}{22}\,\percmsq$ )." Alternately. if we take blackbody emission. at a fixed temperature of 140eeV. we ect luminosity limits of 107745EHeres1 and 3.⋅I07dzο»ergslop.," Alternately, if we take blackbody emission at a fixed temperature of eV we get luminosity limits of $\expnt{1}{32}d_{3.4}^2\,\ergsec$ and $\expnt{3}{32}d_{5.2}^2\,\ergsec$." " ""Phe temperature imits for both sources are considerably cooler than for for almost all absorptions values.", The temperature limits for both sources are considerably cooler than for for almost all absorptions values. Similarly. Phe Iuminosity imits for both sources are typically below that of for a range of input spectra. often by several orders. of magnitude.," Similarly, The luminosity limits for both sources are typically below that of for a range of input spectra, often by several orders of magnitude." Only for the lowest. temperature considered (10006 ancl absorptions at the high end of the considered range V)do our limits become less constraining. although we must consider the correlation between distance and.;|Ng.. where a Larger true distance would also be associated with more absorption and hence an even weaker limit.," Only for the lowest temperature considered eV) and absorptions at the high end of the considered range do our limits become less constraining, although we must consider the correlation between distance and, where a larger true distance would also be associated with more absorption and hence an even weaker limit." We also consider a non-thermal spectrum (power-law with photon indexof 2). which gives limits of 4.10745eres+ and S10742seresT for πο," We also consider a non-thermal spectrum (power-law with photon indexof 2), which gives limits of $\expnt{4}{31}d_{3.4}^2\,\ergsec$ and $\expnt{8}{30}d_{5.2}^2\,\ergsec$ for and." The X-ray emission from wavas assumed to be largely due to cooling emission from the neutron star surface2007).. with only a small contribution from an extended nebula2," The X-ray emission from was assumed to be largely due to cooling emission from the neutron star surface, with only a small contribution from an extended nebula." 009). Lowe expect similar emission from DhRILXESJ0S47 aand0257.. it would be diminished due to their older ages (characteristic ages of 0.8 and MMyr. respectively. MMsyr for 1458)).," If we expect similar emission from RRATs and, it would be diminished due to their older ages (characteristic ages of 0.8 and Myr respectively, Myr for )." In the neutrino-dominated cooling regime. the temperature declines slowly with time. with surface temperature /1/122004).," In the neutrino-dominated cooling regime, the temperature declines slowly with time, with surface temperature $\sim t^{-1/12}$." .. The transition to photon-cominatecl cooling tvpically occurs around 1.0Myr. ancl after that. the decline is much. steeper ancl dependentM on the nature of the envelope. but exponents of 13 are common.," The transition to photon-dominated cooling typically occurs around Myr, and after that the decline is much steeper and dependent on the nature of the envelope, but exponents of 1–3 are common." So in the Worst Case. and assuming that characteristic age is correlated with true age (something that is not necessarily true: e.g. 2009)) we would expect tiny temperatures < I0eV [or RRATS πο that would be undetectable.," So in the worst case, and assuming that characteristic age is correlated with true age (something that is not necessarily true; e.g., ) we would expect tiny temperatures $<10\,$ eV for RRATs and that would be undetectable." However. we know of other neutron stars with similar characteristic ages with luminosities of ~LO’eres (eg. PSR 52 with characteristic age ATAIvr: 2005)).," However, we know of other neutron stars with similar characteristic ages with luminosities of $\sim 10^{33}\,\ergsec$ (e.g., PSR $-$ 52 with characteristic age Myr; )." We also know that characteristic age (and even true age) do not always correlate strictly with ellective temperature2008)., We also know that characteristic age (and even true age) do not always correlate strictly with effective temperature. . So while it is tempting to sav that the BRILXES studied. bere are older and. colder than11058... that may be misleading.," So while it is tempting to say that the RRATs studied here are older and colder than, that may be misleading." While the unknown distance and column densities limit the strength of any conclusions. our data may actually provide upper limits on the luminosities of two sources that point to a range in X-ray enission among the RATS.," While the unknown distance and column densities limit the strength of any conclusions, our data may actually provide upper limits on the luminosities of two sources that point to a range in X-ray emission among the RRATs." The RRALs lie close to the INS in the £-P. plane in a region with few other pulsars. and appear like the INS to have preferentially long periods (although there are substantial selection effects: 2009)).," The RRATs lie close to the INS in the $P$ $\dot P$ plane in a region with few other pulsars, and appear like the INS to have preferentially long periods (although there are substantial selection effects; )." Our X-ray non-detections of the RRATS are actually consistent over most. of the range in Ny with emission like that seen from the INS: blackbodies with AY=40100eV and luminosities 1077nergs ," Our X-ray non-detections of the RRATs are actually consistent over most of the range in $\NH$ with emission like that seen from the INS: blackbodies with $kT=40-100\,$ eV and luminosities $\sim 10^{32}\,\ergsec$ ." They are generally consistent with a cooling sequence that also includes the vounger pulsars like PSR. D0656|14 and PSR. 522009).. although the details of the emission. are dillieult. and there could. be a small contribution from magnetic field decaybelow).," They are generally consistent with a cooling sequence that also includes the younger pulsars like PSR B0656+14 and PSR $-$ 52, although the details of the emission are difficult and there could be a small contribution from magnetic field decay." . While the characteristic ages of the INS are a factor of 48 older than those of the RATS considered here. the true ages are likely comparable2009:: 20073).," While the characteristic ages of the INS are a factor of 4–8 older than those of the RRATs considered here, the true ages are likely comparable; )." I£ tho RIRATS and the INS were drawn from a single cooling sequence that evolved. with the characteristic age. we would expect aand tto [ie somewhere between 140006V. 1458)) and ceV. (the mean of the INS). with the Iuminosity declining accordingly.," If the RRATs and the INS were drawn from a single cooling sequence that evolved with the characteristic age, we would expect and to lie somewhere between eV ) and eV (the mean of the INS), with the luminosity declining accordingly." In that case the RRAPS could be at ~107eres for much of the considered range in Ny. and. significantly deeper observations would be required. to uncerstand the true nature of their emission.," In that case the RRATs could be at $\sim 10^{32}\,\ergsec$ for much of the considered range in $\NH$, and significantly deeper observations would be required to understand the true nature of their emission." Considering true age rather than characteristic age complicates the situation as the RRATs do not have any such measurements. but the general argument still holds.," Considering true age rather than characteristic age complicates the situation as the RRATs do not have any such measurements, but the general argument still holds." The X-ray luminosity of iis above the spin-down luminosity & (—3.10eres 1). implving that rotationally-powerecd non-thermal processes cannot drive the X-ray emission. contrary to what is seen for many rotation-powered pulsars wOGbulconsisten wilh thei nS.," The X-ray luminosity of is above the spin-down luminosity $\dot E$ $\sim \expnt{3}{32}\,\ergsec$ ), implying that rotationally-powered non-thermal processes cannot drive the X-ray emission, contrary to what is seen for many rotation-powered pulsars but consistent with the INS." Thenon thermatcontributionstol hen rayemission fromVs aand wiouldbelo?)l ∢⋅↓⋅⋏∙≟≱∖⋡∣⋊⋅⇂∪∖∖⊽∪⊔↓⋅↓↓⊔⊔↿⊳∖∢⊾∖⇁⋖⋅⊔⇂∪↓⋅ s ⋅ optimistic values of the distance ancNy.," The non-thermal contributions to the X-ray emission from RRATs and would be $10^{28-29}\,\ergsec$, below our limits even for optimistic values of the distance and." .. Pherefore ∪⊔↓⋅∐⊔↓⊲↓↿⊳∖≼∼⋜⋯⊔∪↿↓⋅∢⊾⋜↧∐∙∖⇁≼∼∢≱↓↕≻⇂↓⋅⋜↧↕↓↥↿↓↕⋖⋅⋖⋅⇀∖↓≻∢⋅≼∙⊓⋅∠⇂⇂∢⋅∖⇁⋖⋅⇂∪⇂∎ ⊔∪⊔−⇂↓↕∢⊾↓⋅⊔↓⋜↧↓∢⊾↓↥↓↕≻≻↕∢≱↓, Therefore our limits cannot really constrain the expected level of non-thermal emission from these sources. ↕∐⋅∪⊔↓↿↓↕∢⊾⊳∖⋖⋅⊳∖∪⊔↓⋅⊓⋅⋡∖⋡∖∖⊽∢⋅⊔∪↿∢⋅⋡∣⇂↥∪⊔⋏∙≟∐⋡ hat the observed. spin-down luminosity appears too low o power the extended X-ray emission. observed: around ((interpreting it as a pulsar wind nebula) requiring some other encrev source2009).. which is also a xossible conclusion about the nebula around. the INS tX 37542008).," We note, though, that the observed spin-down luminosity appears too low to power the extended X-ray emission observed around (interpreting it as a pulsar wind nebula) requiring some other energy source, which is also a possible conclusion about the nebula around the INS RX $-$ 3754." . A final possibility for the enission of iis that. while the spectrum is thermal. the emission we see iscooling augmented by magnetic field decay.," A final possibility for the emission of is that, while the spectrum is thermal, the emission we see iscooling augmented by magnetic field decay." therein).. While the exact. field. decay mechanisms anc timescales are still uncertain 1992)... field decay may. be relevant for objects of ages «LAlvr and magnetic fields 72 107€ 2009).. which is the correct range For the RIALS considered here.," While the exact field decay mechanisms and timescales are still uncertain , field decay may be relevant for objects of ages $<1\,$Myr and magnetic fields $>\expnt{2}{13}\,$ G , which is the correct range for the RRATs considered here." We would, We would populations in the outer disk of NGC 7793 (Figure Sbb-d.f-h).,"populations in the outer disk of NGC 7793 (Figure \ref{profile}b b-d,f-h)." Selection boxes used to separate stars into different populations are marked on the color-magnitude diagram in Figure 4.. Since theGal, Selection boxes used to separate stars into different populations are marked on the color-magnitude diagram in Figure \ref{cmdboxes}. axyCount tool does not provide direct information on the color of background galaxies. we require an alternative method for determiming the galaxy number counts.," Since the tool does not provide direct information on the color of background galaxies, we require an alternative method for determining the galaxy number counts." Following ?.. we employ the data from the William Herschel Deep Field (WHDF.?) το estimate the contamination from the faint background galaxy population.," Following \citet{vlajic09}, we employ the data from the William Herschel Deep Field \citep[WHDF,][]{metcalfe01} to estimate the contamination from the faint background galaxy population." " We determine the number counts within the asymptotic giant branch (AGB) box directly from the WHDF data. while for the stellar populations reaching fainter magnitudes than probed with WHDF ""e main sequence (MS) and red giant branch (RGB) stars) salaxywe use the method described in ? to caleulate the number counts."," We determine the number counts within the asymptotic giant branch (AGB) box directly from the WHDF data, while for the stellar populations reaching fainter magnitudes than probed with WHDF (i.e. main sequence (MS) and red giant branch (RGB) stars) we use the method described in \citet{vlajic09} to calculate the galaxy number counts." " We calculate the /""-band number counts of all galaxies in WHDF and fit linearly the (log of) differential number counts in 0.5 mag bins.", We calculate the $i'$ -band number counts of all galaxies in WHDF and fit linearly the (log of) differential number counts in $0.5$ mag bins. In order to determine the galaxy counts below the limit of the WHDF survey we assume that the counts in the bins 2—3 magnitudes below the survey limit follow the same linear trend (in the log space) as the counts in the brighter bins used in the fit., In order to determine the galaxy counts below the limit of the WHDF survey we assume that the counts in the bins $2-3$ magnitudes below the survey limit follow the same linear trend (in the log space) as the counts in the brighter bins used in the fit. We finally correct the derived. galaxy number counts using completeness curves of our data., We finally correct the derived galaxy number counts using completeness curves of our data. The resulting background galaxy counts 3.9E2.1. 511 (4447) and 5248 (4947) aremin7. arefor the AGB. RGB and MS selection regions. respectively. the SE (NW) field. (," The resulting background galaxy counts are $3.9\pm2.1$, $51\pm7$ $44\pm7$ ) and $52\pm8$ $49\pm7$ ) $^{-2}$, for the AGB, RGB and MS selection regions, respectively, for the SE (NW) field. (" Quoted errors are variance. as estimated by GalaxyCount.),"Quoted errors are variance, as estimated by .)" While contamination-subtracted profiles of RGB stars largely confirm the finding from Figures Saa.e (with the distinction that the RGB profile for the NW field falls off more steeply and RGB stars are only detected out to 10) we detect no main sequence stars and all objects within our MS selection box can be attributed to the contaminating background galaxy population (the galaxy number counts for the MS selection box are ~2—3 times higher than the derived star counts for this color-magnitude region).," While contamination-subtracted profiles of RGB stars largely confirm the finding from Figures \ref{profile}a a,e (with the distinction that the RGB profile for the NW field falls off more steeply and RGB stars are only detected out to $10'$ ) we detect no main sequence stars and all objects within our MS selection box can be attributed to the contaminating background galaxy population (the galaxy number counts for the MS selection box are $\sim2-3$ times higher than the derived star counts for this color-magnitude region)." We detect AGB stars out to 8—9' (8.5—9.5 kpe). after which their number counts fall bellow the estimated background galaxy level.," We detect AGB stars out to $8-9'$ $8.5-9.5$ kpc), after which their number counts fall bellow the estimated background galaxy level." As we show in ?.. at the high galactic latitudes of the Sculptor Group. contamination from the Milky Way stars is negligible (??)..," As we show in \citet{vlajic09}, at the high galactic latitudes of the Sculptor Group, contamination from the Milky Way stars is negligible \citep{robin03,sharma11}." ? find a break in the radial profile of young and intermediate age stars in the outer disk of NGC 7793 (their HST/ACS fields overlap significantly with our SE field). with the scale length of a stellar population being shorter for younger stars.," \citet{radburnsmith11b} find a break in the radial profile of young and intermediate age stars in the outer disk of NGC 7793 (their HST/ACS fields overlap significantly with our SE field), with the scale length of a stellar population being shorter for younger stars." This 15 largely consistent with the star counts profiles we derive., This is largely consistent with the star counts profiles we derive. Due to the higher level of contamination in our ground based data we see no MS stars. in agreement with the short scale length for this population found by ?:: similarly. we find AGB stars to be more extended than the MS population. with the RGB stars having the largest scale length.," Due to the higher level of contamination in our ground based data we see no MS stars, in agreement with the short scale length for this population found by \citet{radburnsmith11b}; similarly, we find AGB stars to be more extended than the MS population, with the RGB stars having the largest scale length." Comparing the RGB profiles of NGC 7793 and NGC 300 (?.Figure9) we find that the counts in the outermost bins shown in Figure 5bb are —2 times lower than corresponding counts in the most distant bins in the outer disk of NGC 300., Comparing the RGB profiles of NGC 7793 and NGC 300 \citep[Figure~9]{vlajic09} we find that the counts in the outermost bins shown in Figure \ref{profile}b b are $\sim2$ times lower than corresponding counts in the most distant bins in the outer disk of NGC 300. This is yet another piece of evidence supporting our earlier finding of an extended exponential disk in NGC 300 (??)..," This is yet another piece of evidence supporting our earlier finding of an extended exponential disk in NGC 300 \citep{blandhawthorn05,vlajic09}." While our CMD of NGC 300 reaches 4 mag below the tip of the RGB. compared to only 2.5 mag in NGC 7793. background galaxy number counts increase rapidly with magnitude and the counts in the faintest magnitude bins dominate the total galaxy counts.," While our CMD of NGC 300 reaches 4 mag below the tip of the RGB, compared to only 2.5 mag in NGC 7793, background galaxy number counts increase rapidly with magnitude and the counts in the faintest magnitude bins dominate the total galaxy counts." Our CMDs of NGC 300 and NGC 7793 reach same apparent depth (~26.5—27 mag) and hence experience roughly the same contamination by faint background galaxies., Our CMDs of NGC 300 and NGC 7793 reach same apparent depth $\sim26.5-27$ mag) and hence experience roughly the same contamination by faint background galaxies. The difference in star counts in the outermost bins therefore does not reflect the difference in galaxy number counts but in star counts. and is an additional independent confirmation of the extended exponential disk in NGC 300 out to at least 10 disk scale lengths.," The difference in star counts in the outermost bins therefore does not reflect the difference in galaxy number counts but in star counts, and is an additional independent confirmation of the extended exponential disk in NGC 300 out to at least $10$ disk scale lengths." The power of resolved stellar photometry over surface photometry is most easily recognized if star counts are transformed into measurements of effective surface brightness and compared with existing surface brightness data., The power of resolved stellar photometry over surface photometry is most easily recognized if star counts are transformed into measurements of effective surface brightness and compared with existing surface brightness data. It has been shown in a number of works recently (222?) that this approach allows one to reach surface brightnesses 3-4 mag arcsec below the limit of surface photometry," It has been shown in a number of works recently \citep{blandhawthorn05,irwin05,dejong07,radburnsmith11a} that this approach allows one to reach surface brightnesses $3-4$ mag $^{-2}$ below the limit of surface photometry." " We divide the data in 0.5’ wide annuli and calculate surface brightness in each annulus as: Here. N,j, is a number of pixels in an annulus. f, and fy are radial completeness factors and i; are magnitudes of stars within a given annulus."," We divide the data in $0.5'$ wide annuli and calculate surface brightness in each annulus as: Here, $N_{pix}$ is a number of pixels in an annulus, $f_{g'}$ and $f_{i'}$ are radial completeness factors and $m_{i}$ are magnitudes of stars within a given annulus." Radial completeness of our data is lowest in the innermost annulus (45%) due to crowding. andincreases to an average of 87% in the outermost disk.," Radial completeness of our data is lowest in the innermost annulus $45\%$ ) due to crowding, and increases to an average of $87\%$ in the outermost disk." " To convert surface brightness to units of mag arcsec we multiply the effective flux under the logarithm with the inverse of the square of the GMOS pixel size (1 pix= 0.146"") which is equal to F""=1/0.14672 47.", To convert surface brightness to units of mag $^{-2}$ we multiply the effective flux under the logarithm with the inverse of the square of the GMOS pixel size $1$ $=0.146''$ ) which is equal to $F''=1/0.146^2=47$ . them to previous findines.,them to previous findings. " Throughout this Letter we asstume IL,250 lain IN and qo=0.5.", Throughout this Letter we assume $_{o}$ =50 km $^{-1}$ $^{-1}$ and $_{o}$ =0.5. un The cluster A2256 was observed by the BeppoSAX satellite (Boclla et al., The cluster A2256 was observed by the BeppoSAX satellite (Boella et al. 1997a) at two differeut epochs: between the 11” and the 12/ of February 1998 and between the 25 and the 267 of February 1999., 1997a) at two different epochs; between the $^{th}$ and the $^{th}$ of February 1998 and between the $^{th}$ and the $^{st}$ of February 1999. We will discuss here data from the MECS iustrunueut onboard BeppoSAN: a joint analysis of the MECS and PDS spectra of À2256 is presented in Fusco-Femiano et al. (, We will discuss here data from the MECS instrument onboard BeppoSAX; a joint analysis of the MECS and PDS spectra of A2256 is presented in Fusco-Femiano et al. ( 2000).,2000). The MECS (Boclla et al., The MECS (Boella et al. 1997b) is preseutlv conrposed of two units working iu the 110 keV energv rauec., 1997b) is presently composed of two units working in the 1–10 keV energy range. At 6 keV. the enerev resolution is —854 and the aneular resolution is 70.7 (FWHIAL).," At 6 keV, the energy resolution is $\sim$ and the angular resolution is $\sim$ $^{\prime}$ (FWHM)." Standard reduction procedures and screening criteria have been adopted to produce linearized aud equalized eveut files., Standard reduction procedures and screening criteria have been adopted to produce linearized and equalized event files. Data preparation and luearization was performed using theSANDAS package under euvironnment., Data preparation and linearization was performed using the package under environment. The total effective exposure time for the two observation was 1.3.10? s. All spectral fits lave been performed using XSPEC Ver., The total effective exposure time for the two observation was $\times$ $^5$ s. All spectral fits have been performed using XSPEC Ver. 10.00., 10.00. Quoted confidence intervals are for 1 interesting pariter (ic. Ay?= 1). unless otlicrwise stated.," Quoted confidence intervals are for 1 interesting parameter (i.e. $\Delta \chi^2 =1$ ), unless otherwise stated." Spectral distortions introduced by the energy depeudeut PSF must be accounted for when ροής spatially resolved spectroscopy of galaxy clusters., Spectral distortions introduced by the energy dependent PSF must be accounted for when performing spatially resolved spectroscopy of galaxy clusters. As for the analvsis of other BeppoSAX observations of clusters (6.9. A2319. Moleudi et al.," As for the analysis of other BeppoSAX observations of clusters (e.g. A2319, Molendi et al." 1999). we have taken them iuto account uxing the program publicly available within the latest release.," 1999), we have taken them into account using the program publicly available within the latest release." We remark that we fit spectra individually., We remark that we fit spectra individually. This is not what is typically done when performing spatially resolved spectroscopy of clusters with ASC'A data., This is not what is typically done when performing spatially resolved spectroscopy of clusters with ASCA data. Hore spectra accumulated from different regions are typically analyzed simultancously. the reason being that the correction to be applied to a given reeion depends on the temperature of all the others.," Here spectra accumulated from different regions are typically analyzed simultaneously, the reason being that the correction to be applied to a given region depends on the temperature of all the others." The lack of a strong dependence of the MECS PSF ou cuerey allows us to avoid such complications., The lack of a strong dependence of the MECS PSF on energy allows us to avoid such complications. " For each of the two observations we have acciunulated spectra frou 6 anuular regions ceutered ou the main X- cinission peak of A2256. with inner aud outer radii of 07-2"", 27-1 |'-6'. 6-N'. 8-12"" and 12/-16"" "," For each of the two observations we have accumulated spectra from 6 annular regions centered on the main X-ray emission peak of A2256, with inner and outer radii of $^{\prime}$ $^{\prime}$ , $^{\prime}$ $^{\prime}$, $^{\prime}$ $^{\prime}$, $^{\prime}$ $^{\prime}$, $^{\prime}$ $^{\prime}$ and $^{\prime}$ $^{\prime}$." We have also accumulated: a global spectrum from a circle with radius 16’., We have also accumulated a global spectrum from a circle with radius $^{\prime}$. The background subtraction has been performed usine spectra extracted from blauk sky eveut files iu the same region of the detector as the source., The background subtraction has been performed using spectra extracted from blank sky event files in the same region of the detector as the source. A correction for ie absorption caused bv the stroneghback supporting the aetector window has Όσοι applied for the 8/-12 annulus. where the annular part of the strougback is contained.," A correction for the absorption caused by the strongback supporting the detector window has been applied for the $^{\prime}$ $^{\prime}$ annulus, where the annular part of the strongback is contained." " For ie GS"" aud 12-16"" annuli. where the stroughack covers uly a siiall fraction of the available area. we have chosen o exclude the regious shadowed by the strougback."," For the $^{\prime}$ $^{\prime}$ and $^{\prime}$ $^{\prime}$ annuli, where the strongback covers only a small fraction of the available area, we have chosen to exclude the regions shadowed by the strongback." For ie 5b imunennost anuuli the enerev range considered for PAectral fitting was 2-10 keV: for the outermost aunuulus. ιο fit was restricted to the 2-8 keV energy range to μπιτ PAρουται] distortions which could be caused by au imcorrect oXXckeround subtraction (see De Grandi Moleudi 1999a for details).," For the 5 innermost annuli the energy range considered for spectral fitting was 2-10 keV; for the outermost annulus, the fit was restricted to the 2-8 keV energy range to limit spectral distortions which could be caused by an incorrect background subtraction (see De Grandi Molendi 1999a for details)." Source aud. background. spectra accinaulated for cach of the two observations have then been sununed together., Source and background spectra accumulated for each of the two observations have then been summed together. We have fitted cach spectrmu with a MERAL model absorbed by the Galactic line of sight equivalent Lydrogeu column density. Nyy. of LI1«10?9 cu7.," We have fitted each spectrum with a MEKAL model absorbed by the Galactic line of sight equivalent hydrogen column density, $N_H$, of $\times 10^{20}$ $^{-2}$." The temperature and abundance we derive from the elobal spectra are respectively 7.50.1 keV and 0.25-50.02. solar units.," The temperature and abundance we derive from the global spectrum are respectively $\pm 0.1$ keV and $\pm 0.02$, solar units." Iu feure d we show the tempcrature and abuudance profiles obtained from our six zumnular regions., In figure 1 we show the temperature and abundance profiles obtained from our six annular regions. A constaut does not xovide a good fit to the temperature or the abundance xofile (see table 1)., A constant does not provide a good fit to the temperature or the abundance profile (see table 1). As in Molondi et al. (, As in Molendi et al. ( "1999). we have used the Fe Τι, Ine as an independent estimator of the ICAL temperature.","1999), we have used the Fe $_{\alpha}$ line as an independent estimator of the ICM temperature." Cousidering the lanited uunuber of counts available in he line. we have performed the analysis ou 2 annuli with bouudiue radii. 0-8 and s/12'. the verv snall Fe abundauce measured in the 12'-16/ auuulus preveuts us roni deriving a reliable line ceutroid for this region.," Considering the limited number of counts available in the line, we have performed the analysis on 2 annuli with bounding radii, $^{\prime}$ $^{\prime}$ and $^{\prime}$ $^{\prime}$, the very small Fe abundance measured in the $^{\prime}$ $^{\prime}$ annulus prevents us from deriving a reliable line centroid for this region." We ive fitted cach spectra with a bromisstralilung modcl dus a line. both at a redshift of z=0.057 (ZDBREMSS and ZCGAUSS iodels in NSPEC). absorbed bv the ealactic Ny.," We have fitted each spectrum with a bremsstrahlung model plus a line, both at a redshift of z=0.057 (ZBREMSS and ZGAUSS models in XSPEC), absorbed by the galactic $N_{H}$." A systematic negative shift of 10 eV has j'en ducluded in the centroid energv to account for a slight nüsscalibration of the enerev pulscheight-chanucl relationship near the Fe πο, A systematic negative shift of 40 eV has been included in the centroid energy to account for a slight misscalibration of the energy pulseheight-channel relationship near the Fe line. To couvert the energv centroid into a temperature we have derived an cucrey centroid vs. temperature relationship., To convert the energy centroid into a temperature we have derived an energy centroid vs. temperature relationship. This has Όσοι doue by simulating thermal spectra. using the MERAL model and the MECS response matrix. aud fitting them with the BHue model which has been used to fit the real data.," This has been done by simulating thermal spectra, using the MEKAL model and the MECS response matrix, and fitting them with the same model, which has been used to fit the real data." " We derive a temperate of 8.0!) keV for the inner radial biu aud of 3.2! 32 keV for the outer onc,", We derive a temperature of $^{+0.9}_{-1.0}$ keV for the inner radial bin and of 3.2 $^{+2.8}_{-1.7}$ keV for the outer one. Thus. our two independent measurements of the temperature profile are in good agreement with cach other.," Thus, our two independent measurements of the temperature profile are in good agreement with each other." As shown iu figure 2. we have divided the MECS inage of A2256 into 1 sectors: NW. SW. SE iud NE. cach sector has been divided into | aunuli with bounding radii. 2'- Uo δι S-12/ and 12-16.," As shown in figure 2, we have divided the MECS image of A2256 into 4 sectors: NW, SW, SE and NE, each sector has been divided into 4 annuli with bounding radii, $^{\prime}$ $^{\prime}$, $^{\prime}$ $^{\prime}$, $^{\prime}$ $^{\prime}$ and $^{\prime}$ $^{\prime}$." The backeround. subtraction has been performed using spectra extracted frour blank sky event files in the same region of the detector as the source., The background subtraction has been performed using spectra extracted from blank sky event files in the same region of the detector as the source. Correction or exclusion of the regious shadowed by the strougback supporting the detector window have been performed as in the previous subsection., Correction or exclusion of the regions shadowed by the strongback supporting the detector window have been performed as in the previous subsection. The energy ranges aud the spectral models adopted for fitting are the same used for the azinmthally averaged spectra., The energy ranges and the spectral models adopted for fitting are the same used for the azimuthally averaged spectra. Iu figures 3 aud Lowe show respectively the temperature and abundance profiles obtained frou the spectral fits for each of the 1 sectors., In figures 3 and 4 we show respectively the temperature and abundance profiles obtained from the spectral fits for each of the 4 sectors. In table 1 we report the best fitting constant temperatures auc abundances for the profiles shown in figures 3 and 14., In table 1 we report the best fitting constant temperatures and abundances for the profiles shown in figures 3 and 4. Note that iu all the profiles we have included. the measure obtained for the central circular reeion with radius 2/., Note that in all the profiles we have included the measure obtained for the central circular region with radius $^{\prime}$. All sectors. except for the SW sector. show a statistically siguif&cant temperature decrease with increasing radius.," All sectors, except for the SW sector, show a statistically significant temperature decrease with increasing radius." In the NW sector the temperature decreases conutinmouslv as the distance frou the cluster ceuter increases., In the NW sector the temperature decreases continuously as the distance from the cluster center increases. " In theSE aud NE sectors the temperature first increases, reaching a asian in either the second (NE sector) or third (SE sector) auuulus. aud then decreases."," In theSE and NE sectors the temperature first increases, reaching a maximum in either the second (NE sector) or third (SE sector) annulus, and then decreases." Iuterestiuglv. a fit to the temperatures of," Interestingly, a fit to the temperatures of" "μμ... where v is the observed frequency. 2 is the observed size of the afterglow. and 5, is the tvpical Lorentz [actor of theelectrons emitting al v."," , where $\nu$ is the observed frequency, $R_{\perp}$ is the observed size of the afterglow, and $\gamma_{e}$ is the typical Lorentz factor of theelectrons emitting at $\nu$." For simplicity we use /2(/) For the relativistic case. while Ro)x2(/)! for the non-relativistic case.Dynamics:," For simplicity we use $R_{\perp}(t)=4 \gamma(t) c t/(1+z)$ for the relativistic case, while $R_{\perp}(t) \propto \beta(t) t$ for the non-relativistic case.:" Iu the initial stage /.«/;. the Lorentz factor is constant 5~g.," In the initial stage $t&540//y).U! for thick shells.," In the interval $t_{i}3.7. The characteristic wave strain fh.c4x107 is also comparable to that invoked by Bildsten(1998) to explain the observed range of f, in low-mass X-ray binaries."," Note that, for a neutron star accreting matter at the rate $\dot{M}_{\rm a} \approx 10^{-11} \Msun \, {\rm yr}^{-1}$ (like SAX $-$ 3658),it takes only $10^{7}$ yr to reach $S/N > 3$ The characteristic wave strain $h_{\rm c} \sim 4\times 10^{-25}$ is also comparable to that invoked by \citet{bil98} to explain the observed range of $f_*$ in low-mass X-ray binaries." An observationally testable scaling between δι and the magnetic dipole moment has been predicted (Melatos&Payne2005)., An observationally testable scaling between $h_{\rm c}$ and the magnetic dipole moment has been predicted \citep{mel05}. . The analvsis in 82. and 84. applies to a biaxial star whose principal axis of inertia coincides with (he magnetic axis of svimietry. and is therefore inclined with respect to the angulw momentum axis in general (lor a4 0)., The analysis in \ref{sec:gwfreq} and \ref{sec:snr} applies to a biaxial star whose principal axis of inertia coincides with the magnetic axis of symmetry and is therefore inclined with respect to the angular momentum axis in general (for $\alpha \neq 0$ ). Such a star precesses 2001).. a fact. neglected in our analvsis up to this point in order (o maintain consistency with Bonazzola&Gourgoulhon(1996).," Such a star precesses \citep{cut01}, a fact neglected in our analysis up to this point in order to maintain consistency with \citet{bon96}." ". The latter authors explicitly disregarded precession. arguing that most of the stellar interior is a fluid. (ervstalline crust <0.02,). so that the precession Lrequency is reduced. by ~10°? relative to a rigid star 1974).."," The latter authors explicitly disregarded precession, arguing that most of the stellar interior is a fluid (crystalline crust $\lesssim 0.02 M_*$ ), so that the precession frequency is reduced by $\sim 10^{5}$ relative to a rigid star \citep{pin74}. ." Equations (4)) and (5)) clisplay this clearly., Equations \ref{eq:hplus}) ) and \ref{eq:hcross}) ) display this clearly. They. are structurally identical to the equations in both Bonazzola&Gourgoulhon(1996) and Zimmermann&Szedenits (1979).. but these papers solve different physical problems.," They are structurally identical to the equations in both \citet{bon96} and \citet{zim79}, , but these papers solve different physical problems." In. Zimmermann&Szedenits(1979).. O differs [rom the pulsar spin frequency by. the body-lrame precession frequency. as expected [or a precessing. rigid. Newtonian star. whereas in Bonazzola&Gourgoulhon (1996)... ο exaclly equals the pulsar spin frequency. as expected for a Gnagneticallv) distorted. (but nonprecessing) [Iuid star.," In \citet{zim79}, $\Omega$ differs from the pulsar spin frequency by the body-frame precession frequency, as expected for a precessing, rigid, Newtonian star, whereas in \citet{bon96}, $\Omega$ exactly equals the pulsar spin frequency, as expected for a (magnetically) distorted (but nonprecessing) fluid star." Moreover. 0(whichreplaces a) in," Moreover, $\theta$(whichreplaces $\alpha$ ) in" thas providing a tieliter uppor lanit than above.,thus providing a tighter upper limit than above. The lack of a point source in the eroune based L aud N observations also places upper limits ou the mud-IR cluission. though less tight due to the lower scusitivity aud spatial resolution (FA(L)«12ο7s!n!| and Εν)«6.0&10Poergenὃνtyan +).," The lack of a point source in the ground based L and N observations also places upper limits on the mid-IR emission, though less tight due to the lower sensitivity and spatial resolution $F_\lambda(\mathrm{L})<1.2\xten{-12}\ERG\CM\2\S\1\MIC\1$ and $F_\lambda(\mathrm{N})<6.0\xten{-13}\ERG\CM\2\S\1\MIC\1$ )." Finally. tvpe 2 AGNs are usually characterized by ionization coues detected either iu line images or in excitation maps. Le. ratios between high and low excitation lines (usually. aad IIn)) revealing lüeher excitation thau the surrounding medium.," Finally, type 2 AGNs are usually characterized by ionization cones detected either in line images or in excitation maps, i.e. ratios between high and low excitation lines (usually and ) revealing higher excitation than the surrounding medium." Iu NGC 1915. the equivalent width of aad he ratio indeed show a cone inorphologv but the behaviour is the opposite of what expected. ic. the excitation within the cone ds lower than im the surroundings and the H»/Paa ratio increases up to ~5 (see Fig.," In NGC 4945 the equivalent width of and the ratio indeed show a cone morphology but the behaviour is the opposite of what expected, i.e. the excitation within the cone is lower than in the surroundings and the $_2$ $\alpha$ ratio increases up to $\sim 5$ (see Fig." 244)., \ref{fig:line}d d). Two processes could be responsible for the chhanced CCLUISSION. either shocks caused by the interaction οποσα the supernova-driven wind aud the interstellar uediun or exposure to a strong N-rav dominated photon fux euutted by the ACN., Two processes could be responsible for the enhanced emission – either shocks caused by the interaction between the supernova-driven wind and the interstellar medium or exposure to a strong X-ray dominated photon flux emitted by the AGN. But im auv case there is absolutely uo indication of the strong UV £fx which oxoduces “standard” ACN ionization cones., But in any case there is absolutely no indication of the strong UV flux which produces “standard” AGN ionization cones. We find. therefore. no evidence for the expected AGN narkers in our NICAIOS data.," We find, therefore, no evidence for the expected AGN markers in our NICMOS data." Although uo trace of its presence las Όσοι fouud in these data. the existence of an obscured ACN in the uucleus of NGC 1915 is uuquestionably indicated bv the X-rays (Iwasawa ct al. 1993..," Although no trace of its presence has been found in these data, the existence of an obscured AGN in the nucleus of NGC 4945 is unquestionably indicated by the X-rays (Iwasawa et al. \cite{iwasawa93}," Done et al. 1996))., Done et al. \cite{done96}) ). Recent. hieh signal-to-noise observations bv BeppoSAN (Caminazzi ct al. 2000))," Recent, high signal-to-noise observations by BeppoSAX (Guainazzi et al., \cite{guainazzi}) )" lave coufirimed the previous indications of variability from Cduea observations (Bwasasva et al. 1993)):, have confirmed the previous indications of variability from Ginga observations (Iwasawa et al. \cite{iwasawa93}) ): in the 13-200 keV baud. where he trausuütted spectruui is observed. the Πο curve shows fluctuations with au extrapolated doubliug/halviug nue scale of F~3B5«101 s.," in the 13-200 keV band, where the transmitted spectrum is observed, the light curve shows fluctuations with an extrapolated doubling/halving time scale of $\tau\sim 3-5\xten{4}\S$ ." These time scales aud amplitudes essentially exclude any known process for producing the high euergv N-avs other than accretion outo a supermassive black hole., These time scales and amplitudes essentially exclude any known process for producing the high energy X-rays other than accretion onto a supermassive black hole. Making the oobserved in the Dband with BeppoSAN would require about 10000 of the most Iuninous X-ray binaries observed in our Galaxy (6.8. Scorpio-X1) aud ouly a few of this objects are known., Making the observed in the band with BeppoSAX would require about 10000 of the most luminous X-ray binaries observed in our Galaxy (e.g. Scorpio-X1) and only a few of this objects are known. Alternatively. very hot plana (XT— a few keV)). due to superuovae. Las beeu observed in the sspectruni of starburst galaxies. but at higher eucergies (>30keV) the cussion is essentially ucelieible (Cappi et al. 1999::," Alternatively, very hot plasma $KT\sim$ a few ), due to supernovae, has been observed in the spectrum of starburst galaxies, but at higher energies $>30\KEV$ ) the emission is essentially negligible (Cappi et al. \cite{cappi};" Persic et al. 1998)):, Persic et al. \cite{persic}) ); whereas the ciission of NGC1915 peaks between 30 andLOOkeV.., whereas the emission of NGC4945 peaks between 30 and. Also. eiven that the N-rav cussion is observed through a gaseous absorbing colin density of a few times2.. both the 10000 zuperluuninous X-rav binaries aud the very hot SN wiud should be hiddeu by this huge gaseous colui.," Also, given that the X-ray emission is observed through a gaseous absorbing column density of a few times, both the 10000 superluminous X-ray binaries and the very hot SN wind should be hidden by this huge gaseous column." I is very difficult to fud a geometry for the eas distribution that could produce this effect., It is very difficult to find a geometry for the gas distribution that could produce this effect. We therefore conclude hat the presence of aa ACN xovides the oulv plausible origin of the iud N-ray enmission., We therefore conclude that the presence of an AGN provides the only plausible origin of the hard X-ray emission. The above considerations combined with the abseuce of any evidence for the preseuce of an ACN at other wavelengths has important consequences irrespective of the relative. aud unknown. coutzibutious of the starburst and AGN to the total bolometric bhDuuinositv.," The above considerations combined with the absence of any evidence for the presence of an AGN at other wavelengths has important consequences irrespective of the relative, and unknown, contributions of the starburst and AGN to the total bolometric luminosity." " This is illustrated. below by considering the extreme possibilities that the huninositv is dominated either by the starburst or the AGN,", This is illustrated below by considering the extreme possibilities that the luminosity is dominated either by the starburst or the AGN. " Most previous studies have conchided that the FIR cluission iu NGC 1915 can be attributed solely to starburst activity (e.g. Noornnect 1993.. Moorwood Oliva 199μα) without invoking the preseuce of an ACN,"," Most previous studies have concluded that the FIR emission in NGC 4945 can be attributed solely to starburst activity (e.g. Koornneef \cite{koorn}, Moorwood Oliva \cite{moorwood94a}) ) without invoking the presence of an AGN." " We uote that. on average. active galaxies are characterized bv Leyp/Lp,- ratios quuch larecr than starbursts and this fact was sometimes invoked to discern starbursts from ACNs (see the discussion in Cenzel et al. 1998)3."," We note that, on average, active galaxies are characterized by $L_{FIR}/L_{Br\gamma}$ ratios much larger than starbursts and this fact was sometimes invoked to discern starbursts from AGNs (see the discussion in Genzel et al. \cite{genzel98}) )." In this regard. NGC 1915 has a starburst-like ratio: Dein!LiecddsLO? (from observed wwith Ay=llSmag).," In this regard, NGC 4945 has a starburst-like ratio: $\LFIR/L_\mathrm{Br\gamma}\sim1.4\xten{5}$ (from observed with 15mag)." This is similar to the value for the prototypical starburst galaxy M82 (Leyζω. LO. Ricke et al. LO80}).," This is similar to the value for the prototypical starburst galaxy M82 $\LFIR/L_\mathrm{Br\gamma}\sim3.4\xten{5}$ , Rieke et al. \cite{rieke80}) )," sugecsting that the FIR ciission of NCC 1915 may arise from the starburst., suggesting that the FIR emission of NGC 4945 may arise from the starburst. Coenze et al (1998)), Genzel et al. \cite{genzel98}) ) showed that. when considerimg the reddening correction derived frou the mud-IR ustaly πιο larecr than from the optical and near-IR the observed II hune cussion fromm he starburst translates iuto an iowizine hunünositv comparable to the FIR huuinositv.," showed that, when considering the reddening correction derived from the mid-IR -- usually much larger than from the optical and near-IR – the observed H line emission from the starburst translates into an ionizing luminosity comparable to the FIR luminosity." Indeed. if iu NGC 1915 the bulk of II cuuission is hidden bv just -—L15inag. |... and the observed starburst activity is entirely responsible for the FIR.," Indeed, if in NGC 4945 the bulk of H emission is hidden by just 45mag, $\LFIR/L_\mathrm{ion}\sim 1$ and the observed starburst activity is entirely responsible for the FIR." Although all the bolometric luminosity could be eecnerated bv a starburst it is also possible to construct starburst models which are cousisteut with the observed near iufrared propertics but eenerate a much lower total huninosity., Although all the bolometric luminosity could be generated by a starburst it is also possible to construct starburst models which are consistent with the observed near infrared properties but generate a much lower total luminosity. " It is important to recall that Lepy/Lpr- represents the ratio between star formation rates averaged over two differentDr timescales.. ic.. 24qnNLO’ vrs aud 10^8$ yrs and $<10^7$ yrs, respectively." Therefore. this ratio strongly depends on the past star formation history.," Therefore, this ratio strongly depends on the past star formation history." For example. objects," For example, objects" The Zanstra temperature measures the ratio of the amount of ionizing radiation to the amount of radiation in the visual spectrum.,The Zanstra temperature measures the ratio of the amount of ionizing radiation to the amount of radiation in the visual spectrum. Tz(H) uses the H5 flux and thus measures the amount of radiation which can ionize hydrogen. while Tz( Hell) measures the amount of radiation which can completely ionize helium.," $_{Z}$ (H) uses the $\beta$ flux and thus measures the amount of radiation which can ionize hydrogen, while $_{Z}$ (HeII) measures the amount of radiation which can completely ionize helium." In converting the ratio to à temperature it is assumed that the stellar spectrum is a blackbody. that all the ionizing radiation 1s absorbed by the nebula. and that the continuum visual flux is measured by the stellar magnitude.," In converting the ratio to a temperature it is assumed that the stellar spectrum is a blackbody, that all the ionizing radiation is absorbed by the nebula, and that the continuum visual flux is measured by the stellar magnitude." Zanstra temperatures have been measured for many years and several papers have published extensive tables of these temperatures (e.g. Phillips (2003)))., Zanstra temperatures have been measured for many years and several papers have published extensive tables of these temperatures (e.g. Phillips \cite{phillips}) ). The most uncertain measurement in the determination is the stellar magnitude because. as discussed above. nebular light must be avoided.," The most uncertain measurement in the determination is the stellar magnitude because, as discussed above, nebular light must be avoided." The values we have found are listed in cols., The values we have found are listed in cols. 5 and 6 of Table 4+ and are not essentially different from those given in the literature., 5 and 6 of Table 4 and are not essentially different from those given in the literature. One of the most discussed aspects of the results can be seen in the table: in about of the nebulae the value of Tz(H) ts substantially lower than Tz(Hell)., One of the most discussed aspects of the results can be seen in the table: in about of the nebulae the value of $_{Z}$ (H) is substantially lower than $_{Z}$ (HeII). " The reason for this has been debated in the literature: the most often cited reason is the assumption that the nebula is ""optically deep’ to radiation which tonizes hydrogen is wrong and that some of this radiation escapes the nebula without being registered.", The reason for this has been debated in the literature; the most often cited reason is the assumption that the nebula is 'optically deep' to radiation which ionizes hydrogen is wrong and that some of this radiation escapes the nebula without being registered. This has the consequence that Tz(H) is too low and that Tz(Hell) is the more nearly correct value., This has the consequence that $_{Z}$ (H) is too low and that $_{Z}$ (HeII) is the more nearly correct value. It is difficult to confirm this because not only is the total nebular mass uncertain. its distribution in the nebula is also unknown.," It is difficult to confirm this because not only is the total nebular mass uncertain, its distribution in the nebula is also unknown." Another explanation for this difference could also be that the stellar spectrum is not well represented by a blackbody., Another explanation for this difference could also be that the stellar spectrum is not well represented by a blackbody. The Energy Balance method. first introduced by Stoy (1933). neasures the average excess energy per ionizing photon.," The Energy Balance method, first introduced by Stoy \cite{stoy}, measures the average excess energy per ionizing photon." This can be found from the ratio of the intensity of collisionally excited nebular lines to Hf., This can be found from the ratio of the intensity of collisionally excited nebular lines to $\beta$. It has the advantage that only the nebular spectrum has to be known: no measurement of the central star flux is necessary., It has the advantage that only the nebular spectrum has to be known; no measurement of the central star flux is necessary. It has the further advantage that itis applicable both to optically thin as well as optically thick nebulae., It has the further advantage that it is applicable both to optically thin as well as optically thick nebulae. The method is also independent of the nebular model as long as all the collisionally excited lines are measured., The method is also independent of the nebular model as long as all the collisionally excited lines are measured. [Ii practice sometimes a correction must be made for unmeasured lines., In practice sometimes a correction must be made for unmeasured lines. The entire spectrum must be measured but for most P the visible and ultraviolet lines are the most important., The entire spectrum must be measured but for most PN the visible and ultraviolet lines are the most important. For very low temperature central stars the infrared nebular spectrum car be the most Important., For very low temperature central stars the infrared nebular spectrum can be the most important. Once the ratio of collisional line intensity to Hf (called R) is known a difficulty arises in interpreting this measurement 1 terms of a stellar effective temperature: it is necessary to know whether the star emits as a blackbody or some particular model atmosphere., Once the ratio of collisional line intensity to $\beta$ (called R) is known a difficulty arises in interpreting this measurement in terms of a stellar effective temperature; it is necessary to know whether the star emits as a blackbody or some particular model atmosphere. Since this is not known it is assumed here that the star emits as a blackbody., Since this is not known it is assumed here that the star emits as a blackbody. Preite-Martinez Pottasch (1983) have calculated the effective temperatures found when a variety of model atmospheres of different effective temperatures are used as tonizing source., Preite-Martinez Pottasch \cite{pmp} have calculated the effective temperatures found when a variety of model atmospheres of different effective temperatures are used as ionizing source. They found that for a fixed value of the ratio R the model atmospheres give a slightly lower value of effective temperature than the blackbody., They found that for a fixed value of the ratio R the model atmospheres give a slightly lower value of effective temperature than the blackbody. The exact status of the nebula also has an effect on the effective temperature found., The exact status of the nebula also has an effect on the effective temperature found. Preite-Martinez Pottasch calculated three cases., Preite-Martinez Pottasch \cite{pmp} calculated three cases. In the first case the nebula ts optically thin to all ionizing radiation., In the first case the nebula is optically thin to all ionizing radiation. In the second case the nebula is optically thick to He tonizing radiation and in the third case the nebula is optically thick to all tonizing radiation., In the second case the nebula is optically thick to $^+$ ionizing radiation and in the third case the nebula is optically thick to all ionizing radiation. These authors compare the effective temperatures derived for 52 central star using all of these three assumptions., These authors compare the effective temperatures derived for 52 central star using all of these three assumptions. They find that all three assumptions give similar results., They find that all three assumptions give similar results. We have redone the calculations using the case which is thick to He ionizing radiation and thin to hydrogen tonizing radiation (case two): the effective temperatures found are listed in col.8 of Table 4., We have redone the calculations using the case which is thick to $^+$ ionizing radiation and thin to hydrogen ionizing radiation (case two); the effective temperatures found are listed in col.8 of Table 4. As can be seen from the table. temperatures can now be found even when the central star is unobservable.," As can be seen from the table, temperatures can now be found even when the central star is unobservable." The Energy balance temperature is rather similar to the Hell Zanstra temperature Tz(Gell). sometimes slightly lower. sometimes slightly higher.," The Energy balance temperature is rather similar to the HeII Zanstra temperature $_{Z}$ (HeII), sometimes slightly lower, sometimes slightly higher." Stellar temperatures may also be obtained from a model atmosphere analysis of the spectrum., Stellar temperatures may also be obtained from a model atmosphere analysis of the spectrum. Because high resolution spectra are needed this has only been done for very bright stars., Because high resolution spectra are needed this has only been done for very bright stars. The results can be found in Mendez et al. (1988)..," The results can be found in Mendez et al. \cite{mendez}," Kudritzki et al., Kudritzki et al. (1997) and Pauldrach et al. (2004).., \cite{kudritzki} and Pauldrach et al. \cite{pauldrach}. As Pauldrach et al., As Pauldrach et al. (2004) point out. the model atmosphere analysis is difficult: the results using hydrogen line profiles can differ according to which hydrogen line is used.," \cite{pauldrach} point out, the model atmosphere analysis is difficult; the results using hydrogen line profiles can differ according to which hydrogen line is used." Mendez et al., Mendez et al. (1988) Kudritzki et al., \cite{mendez} Kudritzki et al. (1997) base their temperatures on the analysis of hydrogen and helium line profiles while Pauldrach et al.," \cite{kudritzki} base their temperatures on the analysis of hydrogen and helium line profiles while Pauldrach et al." (2004) base their temperatures on the analysis of metal line profiles in the ultraviolet., \cite{pauldrach} base their temperatures on the analysis of metal line profiles in the ultraviolet. The results are quite similar., The results are quite similar. The results are given in Table 3 where. considering the consistency of the different determinations. we estimate the error to be of the order of 10 to155€.," The results are given in Table 3 where, considering the consistency of the different determinations, we estimate the error to be of the order of 10 to." Although only six spectroscopic temperatures have been measured for our nebulae. it is interesting to compare them with what has been found from the Zanstra and Energy Balance methods.," Although only six spectroscopic temperatures have been measured for our nebulae, it is interesting to compare them with what has been found from the Zanstra and Energy Balance methods." For two of the nebulae. 4418 and 66826. no Tz(Hell) can be measured.," For two of the nebulae, 418 and 6826, no $_{Z}$ (HeII) can be measured." " In both cases there is good agreement between the spectroscopic temperature and Το, derived from Tz(H) and Ty».", In both cases there is good agreement between the spectroscopic temperature and $_{eff}$ derived from $_{Z}$ (H) and $_{EB}$. " In two other cases. 33242 and 11535. there 1s reasonably good agreement between the spectroscopic temperature and T,;, derived from Tz(Hell) and Trp. but definitely higher than that found from Tz(H)."," In two other cases, 3242 and 1535, there is reasonably good agreement between the spectroscopic temperature and $_{eff}$ derived from $_{Z}$ (HeII) and $_{EB}$, but definitely higher than that found from $_{Z}$ (H)." This could also be true for 22448 because the spectroscopic temperature is more uncertain for this central star., This could also be true for 2448 because the spectroscopic temperature is more uncertain for this central star. [t is definitely not true for the central star of 22392 where both TzGHell) and Tyg indicate a very much higher temperature., It is definitely not true for the central star of 2392 where both $_{Z}$ (HeII) and $_{EB}$ indicate a very much higher temperature. This will presently be discussed in more detail., This will presently be discussed in more detail. can be taken care of by recentering the particles.,can be taken care of by recentering the particles. In. this case. every expansion of the SCE system is taken about its centre of mass. alleviating the need to recentre the particle.," In this case, every expansion of the SCF system is taken about its centre of mass, alleviating the need to recentre the particle." We check the accuracy of this modification hy monitoring the conservation of linear momentum of the SCE centre of mass of a spherical stellar system. and the separation of a binary svstem of spherical galaxies (one SCE: one Tree) in a circular and stable orbit.," We check the accuracy of this modification by monitoring the conservation of linear momentum of the SCF centre of mass of a spherical stellar system, and the separation of a binary system of spherical galaxies (one SCF; one Tree) in a circular and stable orbit." Figure 10. shows the separation between an SCE and a Tree spheroid of equal mass. both with 2500 particles. in a circular orbit.," Figure \ref{binary} shows the separation between an SCF and a Tree spheroid of equal mass, both with 2500 particles, in a circular orbit." We show an example of the evolution of the total angular momentum of the system. in Figure (7aa) and although |L| is intrinsically near zero we see that it. varies no more than over the length of the run., We show an example of the evolution of the total angular momentum of the system in Figure \ref{angmom}a a) and although $|{\bf L}|$ is intrinsically near zero we see that it varies no more than over the length of the run. Figure (ΡΟ) shows the absolute variation of the z-component of L., Figure \ref{angmom}b b) shows the absolute variation of the $z$ -component of ${\bf L}$. The system in this case is a Lowered Evans Model with 20000 particles with “Pree particles., The system in this case is a Lowered Evans Model with 20000 particles with Tree particles. We investigate the performance of the SCETIUEE code on a system which is not initially in equilibrium., We investigate the performance of the SCFTREE code on a system which is not initially in equilibrium. " For this purpose we perform simulations on the collapse of a uniform density spherical distribution of particles with random: velocities scaled. such that the initial virial ratio of the system QVAW|,=1/2.", For this purpose we perform simulations on the collapse of a uniform density spherical distribution of particles with random velocities scaled such that the initial virial ratio of the system $\left|2T/W\right|_0=1/2$. Following the thorough investigation by llozumi and Llernquist (1995) of the pure SCE code in similar non-equilibrium states. we trace the evolution of the virial ratio from its initial value of 1/2.," Following the thorough investigation by Hozumi and Hernquist (1995) of the pure SCF code in similar non-equilibrium states, we trace the evolution of the virial ratio from its initial value of $1/2$." " Our purpose here is not to perform a detailed investigation of the accuracy of the dynamical evolution but as a qualitative check that the combined SCE ancl Tree. codes behave as expected. and the virial ratio oscillates about the equilibrium: value of YA],=L0."," Our purpose here is not to perform a detailed investigation of the accuracy of the dynamical evolution but as a qualitative check that the combined SCF and Tree codes behave as expected, and the virial ratio oscillates about the equilibrium value of $\left|2T/W\right|_0=1.0$." The results are shown for a typical run containing 20000 particles. of which are randomly allocated as tree particles.," The results are shown for a typical run containing 20000 particles, of which are randomly allocated as tree particles." The truncation parameters for the SCE part are η=16 and /=6. Fieure(S)), The truncation parameters for the SCF part are $n=16$ and $l=6$. \ref{density}) ) shows the plot of final density profile of the sae system after a period of/=120., shows the plot of final density profile of the same system after a period of $t=120$. The separate profiles of the Tree and SCE svstems of particles are shown. together with the total profile of all of the particles.," The separate profiles of the Tree and SCF systems of particles are shown, together with the total profile of all of the particles." In the example ga10wn the system undergoes homologous collapse (Fillmore CGoldreich 1984: Gunn 1977) evolving to a density. profile pcr77., In the example shown the system undergoes homologous collapse (Fillmore Goldreich 1984; Gunn 1977) evolving to a density profile of $\rho \sim r^{-2.5}$. Powards the core of the system in this example 1e number of particles is too small to adequately. resolve vw detailed evolution HMozumi Lernquist (1995) who used. hundreds of thousands of particles and. obtained: adequate resolution to resolve the —attening of the core.), Towards the core of the system in this example the number of particles is too small to adequately resolve the detailed evolution Hozumi Hernquist (1995) who used hundreds of thousands of particles and obtained adequate resolution to resolve the flattening of the core.) We have seen from the previous tests that the code. is, We have seen from the previous tests that the code is shown in Fig.8.,shown in Fig.8. We can see that the duration distribution of 1224 BATSE bursts is bimodal., We can see that the duration distribution of 1234 BATSE bursts is bimodal. The first is centered around (he a small value of 7790=0.21ο0.3 seconds and the second is centered. around the a large value 790=40/o60 seconds. where 790 is the duration [ου of the bursts to occur.," The first is centered around the a small value of $T90=0.2\;to\;0.3$ seconds and the second is centered around the a large value $T90=40\;to\;60$ seconds, where $T90$ is the duration for of the bursts to occur." The arrow in Fig.8 shows the duration of the FRED GLE., The arrow in Fig.8 shows the duration of the FRED GLE. We can see that its duration (416 seconds) is still inside that of the BATSE 790 distribution., We can see that its duration (416 seconds) is still inside that of the BATSE $T90$ distribution. The counting rate of scintillator detectors at ground level is subject to several sources of modulation., The counting rate of scintillator detectors at ground level is subject to several sources of modulation. The main ones ave due to atmospheric pressure variation. solar activity and the 24 hours sidereal anisotropy.," The main ones are due to atmospheric pressure variation, solar activity and the 24 hours sidereal anisotropy." However. (he temporal scales of these modulation phenomena are much larger than the GLEs duration.," However, the temporal scales of these modulation phenomena are much larger than the GLEs duration." In the case of a tracking telescope like the TUPI it is necessary {ο take into account the eeonmagnetic effect responsible lor the muon flix dependence on azimuth angle (see section 3)., In the case of a tracking telescope like the TUPI it is necessary to take into account the geomagnetic effect responsible for the muon flux dependence on azimuth angle (see section 3). Again the temporal seale to observe this effect is much larger than the GLEs duration., Again the temporal scale to observe this effect is much larger than the GLEs duration. In order to take into account possible anomalous pressure variations as being responsible of the GLEs. we have monitored the barometric pressure and included (his in our data acquisition svstem.," In order to take into account possible anomalous pressure variations as being responsible of the GLEs, we have monitored the barometric pressure and included this in our data acquisition system." Every 10 seconds the counting rate and the atmospheric pressure are registered., Every 10 seconds the counting rate and the atmospheric pressure are registered. Under normal conditions. (he daily (24 h) variations of the atmospheric pressure present a maximum value and a mininunm value.," Under normal conditions, the daily (24 h) variations of the atmospheric pressure present a maximum value and a minimum value." This tendency has been found during the raster scan where GLEs have been found., This tendency has been found during the raster scan where GLEs have been found. Fig.9 summarizes the situation where the pressure lime series on 2003/12/02 is shown in the upper panel and ils corresponding fast. Fourier transformation (FFT) is shown in the lower panel., Fig.9 summarizes the situation where the pressure time series on 2003/12/02 is shown in the upper panel and its corresponding fast Fourier transformation (FFT) is shown in the lower panel. The arrow in (he upper figure indicates the beeinning of the GLE., The arrow in the upper figure indicates the beginning of the GLE. The absence of peaks in the power spectrum means that (here are no scintillation phenomena as indications of anomalies., The absence of peaks in the power spectrum means that there are no scintillation phenomena as indications of anomalies. The power spectrum gives an estimate of the mean square fluctuations at Irequeney. f anel. consequently. of the variations over a lime scale of order L//.," The power spectrum gives an estimate of the mean square fluctuations at frequency f and, consequently, of the variations over a time scale of order $1/f$." For the pressure case. the spectral density. varies as 1/[075 and this quite steep spectral density is close to a correlated Brownian noise with 1//7. over many decades. or in other words. over all the 12 hours of the raster scan.," For the pressure case, the spectral density varies as $1/f^{1.96}$ and this quite steep spectral density is close to a correlated Brownian noise with $1/f^2$, over many decades, or in other words, over all the 12 hours of the raster scan." Consequently. pressure variation could not be a cause of the origin of the first GLE.," Consequently, pressure variation could not be a cause of the origin of the first GLE." A similar situation has been found for the second GLE., A similar situation has been found for the second GLE. There are several reports of ground level observations. of solar flares. especially those of," There are several reports of ground level observations, of solar flares, especially those of" Let us now calculate p. for non-relativistic electrons within the turbulent volume. aud consequently the energy spectrum of electrons.,"Let us now calculate $p_{esc}$ for non-relativistic electrons within the turbulent volume, and consequently the energy spectrum of electrons." " For simplicity. let us take the turbulent region to be rectangular. with the long axis. z. parallel to the direction of the bulk flow. with z=0 and 2=Ly üxed to the downstream and upstream boundaries of the region respectively,"," For simplicity, let us take the turbulent region to be rectangular, with the long axis, $z$, parallel to the direction of the bulk flow, with $z=0$ and $z=L_F$ fixed to the downstream and upstream boundaries of the region respectively." Ly is taken to be the extent of the region of turbulent. flow. which is presumed to be the entire distance between the reconnection sheet and the top of the soft. X-ray loop.," $L_F$ is taken to be the extent of the region of turbulent flow, which is presumed to be the entire distance between the reconnection sheet and the top of the soft X-ray loop." This distance is (vpically of size 101 cn for solar [lares (Tsuneta1996)., This distance is typically of size $10^{10}$ cm for solar flares \citep{Tsuneta}. ". The largest eddy size in the turbulence. Ly is set by the width of the outflow. tvpically 10σηι,"," The largest eddy size in the turbulence, $L_T$ is set by the width of the outflow, typically $10^8$ cm." Thus the turbulent volume consists of a number of cells. each of which flows downward from the reconnection point towards the loop-top.," Thus the turbulent volume consists of a number of cells, each of which flows downward from the reconnection point towards the loop-top." An electron escapes the acceleration region only when it reaches the X-ray loop at the base of the turbulent region., An electron escapes the acceleration region only when it reaches the X-ray loop at the base of the turbulent region. These individual cells may be associaetd with single bursts or fragments of X-ray emission. and (hus are responsible for the temporal structure of impulsive flares.," These individual cells may be associaetd with single bursts or fragments of X-ray emission, and thus are responsible for the temporal structure of impulsive flares." In order to escape the region wilh enerev E(A). an electron must stream [rom its location in the region at some height z to the boundary at 2=0 alter (he A/th reflection without further reflection.," In order to escape the region with energy $E(M)$, an electron must stream from its location in the region at some height $z$ to the boundary at $z=0$ after the $M$ th reflection without further reflection." We will assume that the electrons are contained in (he region in tlie i—y plane by evration around laree scale field lines., We will assume that the electrons are contained in the region in the $x-y$ plane by gyration around large scale field lines. To further simplifv the problem. we shall assume that the electron density remains uniform throughout the turbulent region.," To further simplify the problem, we shall assume that the electron density remains uniform throughout the turbulent region." We also neglect the bulk flow speed. v;=8x10* em ! since the legth of the downflow region is roughly 1010 cm.," We also neglect the bulk flow speed, $v_f = 8 \times 10^7$ cm $^{-1}$ \citep{Tsuneta} since the legth of the downflow region is roughly $10^{10}$ cm." This gives a flow time from (he reconnection reeion to the loop-top of 1005. The acceleration process is lixed (o the much shorter 1s time scale by the temporal size of the observed energy release [ragments and the ΑΔΗ) eddy turnover time., This gives a flow time from the reconnection region to the loop-top of $100$ s. The acceleration process is fixed to the much shorter $1$ s time scale by the temporal size of the observed energy release fragments and the MHD eddy turnover time. Thus. bulk flow into the flare loop is not likely to be a dominant process in culling off the acceleration.," Thus, bulk flow into the flare loop is not likely to be a dominant process in cutting off the acceleration." Take (he mean z-component of the distance streamed between reflections to be À.: A. carries ai energv dependence inherited from the energy dependence of the pitch scattering., Take the mean $z$ -component of the distance streamed between reflections to be $\lambda_z$; $\lambda_z$ carries an energy dependence inherited from the energy dependence of the pitch scattering. The probability of escaping al 2=0 alter the A/th reflection from a point at height z is given by and (he mean escape probability of electrons distributed uniformly across the length of {he region is, The probability of escaping at $z=0$ after the $M$ th reflection from a point at height $z$ is given by and the mean escape probability of electrons distributed uniformly across the length of the region is Comparison with previous data.,Comparison with previous data. Upper panels: velocity dispersion. lower panels: rotation curve.," Upper panels: velocity dispersion, lower panels: rotation curve." Different sources are marked with different symbols as explained in the captions., Different sources are marked with different symbols as explained in the captions. Notice that. in general. the P.A. of different authors do not exactly coincide.," Notice that, in general, the P.A. of different authors do not exactly coincide." Those which are different from ours by more than 5° are the following: Bicknell et al., Those which are different from ours by more than $^{\circ}$ are the following: Bicknell et al. 1989 and Stiavelli et al., 1989 and Stiavelli et al. 1993 adopted P.A.284 for NGC 1399 (instead of 1127); van der Marel Franx 1993 adopted for NGC 1374 (instead of 120°): D95 adopted , 1993 adopted $^{\circ}$ for NGC 1399 (instead of $^{\circ}$ ); van der Marel Franx 1993 adopted $^{\circ}$ for NGC 1374 (instead of $^{\circ}$ ); D95 adopted $^{\circ}$ "Description: These disks show significant effects arising from (a) evolution of dust to larger sizes (this version nuelt be an anemic disk): (b) the combined effects of accretion aud photoevaporation: aud (c) the ανασα] effects of forming plancts on the structure. accretion rate aud dust content of the ner disks (b and ο could be ""cold disks” or transitional disks im the more narrow seuse of definition #11) Conuueuts: This is oue of the more coufused terms.","Description: These disks show significant effects arising from (a) evolution of dust to larger sizes (this version might be an anemic disk); (b) the combined effects of accretion and photoevaporation; and (c) the dynamical effects of forming planets on the structure, accretion rate and dust content of the inner disks (b and c could be “cold disks"" or transitional disks in the more narrow sense of definition 1) Comments: This is one of the more confused terms." If definition 4633 is used. for transitional disk. it iucludes pre-transitional disk. transitional disks in the narrow sense of definition. #11 (also cold disks). aud anemic disks.," If definition 3 is used, for transitional disk, it includes pre-transitional disk, transitional disks in the narrow sense of definition 1 (also cold disks), and anemic disks." Tf vou use it. be sure to define it. (," If you use it, be sure to define it. (" NJE) (CL) Connunents: If definition #233 is used for transitional disk. this is one variant of a transitional disk. (,"NJE) (CL) Comments: If definition 3 is used for transitional disk, this is one variant of a transitional disk. (" LII) Description: Tadicator of a plauctary svstei given that larec. planctary-inass bodies are required in order to induce and maintain the collisional cascade.,"LH) Description: Indicator of a planetary system given that large, planetary-mass bodies are required in order to induce and maintain the collisional cascade." Iu our Solar System. the Asteroid Belt aud the EKuiper Belt are well-separated debris belts that would be considered a teuuous debris disk if viewed from afar. (," In our Solar System, the Asteroid Belt and the Kuiper Belt are well-separated debris belts that would be considered a tenuous debris disk if viewed from afar. (" CL) (DW) (BAT) Description: Hilleubraud et al. (,CL) (DW) (BM) Description: Hillenbrand et al. ( "1992. ApJ. 397. 613) dubbed intermediate mass objects falline iuto this category ""Group HI Ac/Be stars.","1992, ApJ, 397, 613) dubbed intermediate mass objects falling into this category “Group III"" Ae/Be stars." Conuueuts Note that these clefinitions are all quite different from one another., Comments: Note that these definitions are all quite different from one another. If vou use this terii. be sure to define it. (," If you use this term, be sure to define it. (" BAD,BM) thermal emission aud scattering efficiencies. respectively.,"thermal emission and scattering efficiencies, respectively." Dust temperature at a distance d (ii parsecs) from the star can be calculated as T;=p M6Leadpl64yoLB qeIN Q4(T). where μμis dust gram size dn pr. aud Γον is stellar Dunünositv in LOPS lo ," Dust temperature at a distance $d$ (in parsecs) from the star can be calculated as $T_d\,=\,$ $\,a$$_{\mu m}^{-1/6}$$\,L$$_{*,38}^{1/6}$$\,d$$_{pc}^{-1/3}$$\,$ K \citep{vanburen88, kruegelbook}, where $a_{\mu m}$is dust grain size in $\mu m$ and $L_{*,38}$ is stellar luminosity in $^{38}$ $\,$ $^{-1}$." P(QL4) is the (normalized) scatteriue function that coutrols the amount of forward scattering. and is given by: For g= 0. scattering is isotropic and 2? does not depend ou the scattering angle Οι," $P(\theta_{sca})$ is the (normalized) scattering function that controls the amount of forward scattering, and is given by: For $g=0$ , scattering is isotropic and $P$ does not depend on the scattering angle $\theta_{sca}$." g=1l ameans full forward scattering., $g=1$ means full forward scattering. We have varied g between 0 and 0.5. in steps of 0.2.," We have varied $g$ between 0 and 0.8, in steps of 0.2." " Since ej, aud é€., are in general not kuown. we have chosen to test three different cases: (eg. €seq) = (1.0. 0.0). (0,0. 1.0). and (0.5. 0.5). ic. thermal emissiou oulv. scattering only. aix equal coutributious from both processes."," Since $\epsilon_{th}$ and $\epsilon_{sca}$ are in general not known, we have chosen to test three different cases: $\epsilon_{th}$, $\epsilon_{sca}$ ) = (1.0, 0.0), (0.0, 1.0), and (0.5, 0.5), i.e. thermal emission only, scattering only, and equal contributions from both processes." The shape ofthe thermal emission depends ou the dust teiiperature distribution: we investieate ceutral stars with huninosities (102. 10°. 101..," The shape of the thermal emission depends on the dust temperature distribution: we investigate central stars with luminosities $^2$, $^3$, $^4$." . Finally. the resulting projection of the 3D-eeoioetrv onto the plane of the sky is robiuned to the pixclscale of the NÀCO images and smoothed with a gaussian PSF having EWIIM equivalent to the angular resolution of our lniaeges.," Finally, the resulting projection of the 3D-geometry onto the plane of the sky is rebinned to the pixel-scale of the NACO images and smoothed with a gaussian PSF having FWHM equivalent to the angular resolution of our images." L shows the best-fit results of our bow-shock modeling for the feature N7.," $\,$ \ref{X7fit} shows the best-fit results of our bow-shock modeling for the feature X7." " We have tested the three ciffereut conibinatious of (eg. Ese). aud five values of g=(0.0. 0.2. OL 0.6. 0,8)."," We have tested the three different combinations of $\epsilon_{th}$, $\epsilon_{sca}$ ), and five values of $g$ =(0.0, 0.2, 0.4, 0.6, 0.8)." In 1L. however. we show only those values that result in good fits. except for the leftanost panels (blue contours). which we show to illustrae the behaviour of purely thermal emission.," In $\,$ \ref{X7fit}, however, we show only those values that result in good fits, except for the left-most panels (blue contours), which we show to illustrate the behaviour of purely thermal emission." Thermal emissiou is dominant in the vicinity of the star. but cannot fit the exteuded tail that we observe in XT. unless the central star is much brighter than the cases investigated here.," Thermal emission is dominant in the vicinity of the star, but cannot fit the extended tail that we observe in X7, unless the central star is much brighter than the cases investigated here." This. iowever. is not plausible since X7 is very faint iu the I&- (see discussion below).," This, however, is not plausible since X7 is very faint in the K-band (see discussion below)." The tail of the bow-shock is uuch better described by scattering., The tail of the bow-shock is much better described by scattering. For (eg. €seq )=C0.5. 1.5). we show only the solution for L..=10°L....," For $\epsilon_{th}$, $\epsilon_{sca}$ )=(0.5, 0.5), we show only the solution for $_{*}$ $^2$." We choose o do so because the difference in resulting contours for he three stellar Iuninosities is πια]. and eives the same solution for the plivsicallv most interesting paraiucter. fy.," We choose to do so because the difference in resulting contours for the three stellar luminosities is small, and gives the same solution for the physically most interesting parameter, $R_{0}$." " Tn cases when scattering is duportant (ex, 20.5). more Oorward scattering (large ο). results iu a lore compact nodel. thus not fitting well the outercontours."," In cases when scattering is important $\epsilon_{sca}\geq$ 0.5), more forward scattering (large g) results in a more compact model, thus not fitting well the outercontours." There is no significant infiuence of the parameters ou the mner contours. due to relatively simall size of the feature. aud sanootlinge.," There is no significant influence of the parameters on the inner contours, due to relatively small size of the feature, and smoothing." These differences cau be better observed iu case of N23., These differences can be better observed in case of X3. For each set of parameters (Cip. εκαι S) We have tested different. values of Ry.," For each set of parameters $\epsilon_{th}$, $\epsilon_{sca}$, g), we have tested different values of $R_0$." By changing Ry. the model preserves the same shape ofthe contours. but is as a whole expanded or shruuken.," By changing $R_0$ , the model preserves the same shape of the contours, but is as a whole expanded or shrunken." Therefore in 1 we plot wo values of Ry for cach set of parameters.," Therefore in $\,$ \ref{X7fit} we plot two values of $R_0$ for each set of parameters." We close values in the wav that shows how the chauee in Ry affects the fit., We chose values in the way that shows how the change in $R_0$ affects the fit. By changing its value by larger amount. the fit becomes inadequate.," By changing its value by larger amount, the fit becomes inadequate." The best solutious for differeut sets of parameters are obtained for Ryz 2.540503. and PA 507. measured east of north.," The best solutions for different sets of parameters are obtained for $R_0\approx\,$ $\cdot$ $^{15}$ cm, and $\,$ $\,$ $^\circ$, measured east of north." Note that in this case the best results are obtained using the simple analytic two-dimensional solution 1)).," Note that in this case the best results are obtained using the simple analytic two-dimensional solution $\,$ \ref{Req}) )." Both XN? aud X3 have an nuuusuallv arrow appearance. and therefore are best fitted with inclination angles close to 907.," Both X7 and X3 have an unusually narrow appearance, and therefore are best fitted with inclination angles close to $^\circ$." NT coincides with ai point source αἲ shorter wavelengths (seco. discussion ol proper lotions du section 3))., X7 coincides with a point source at shorter wavelengths (see discussion on proper motions in section \ref{sec:pm}) ). Photometric measurements eive T=18.940.1 and W=16.940.1 (2).., Photometric measurements give $\pm$ 0.1 and $\pm$ 0.1 \citep{schoedel10}. For the local extinction at the position of NT we assume Ap =2.5 (7).., For the local extinction at the position of X7 we assume $_K$ =2.5 \citep{schoedel10}. Iu section 7.1 we discuss possible stellar types aud Huplicatious this has ou the external wind parameters., In section \ref{X7discuss} we discuss possible stellar types and implications this has on the external wind parameters. Fig.5 shows the best-fit results of our bow-shock modeling for the feature N3.," $\,$ \ref{X3fit} shows the best-fit results of our bow-shock modeling for the feature X3." This feature is very cloneated iik a satisfactory ft cannot be obtained using the analytic 2D solution., This feature is very elongated and a satisfactory fit cannot be obtained using the analytic 2D solution. It requires a narrow model (see Section 1.1.2)). with small opening angles Oy.," It requires a narrow model (see Section \ref{narrow}) ), with small opening angles $\theta_0$." As in the case of A3. the outer contours are represented better iu models with lower g. while larger g values result iu more compact inner contours.," As in the case of X7, the outer contours are represented better in models with lower $g$, while larger $g$ values result in more compact inner contours." [ere it is even more evident that therma enissjon gives a too compact model., Here it is even more evident that thermal emission gives a too compact model. The elougated tai of N3 can oulv be well fitted with models that iuclude scattering.,The elongated tail of X3 can only be well fitted with models that include scattering. Therefore we show ouly these solutions. iu pairs of two ciffercut values of Ry.," Therefore we show only these solutions, in pairs of two different values of $R_0$." The best fit solutions give Ryzm 1.510 oun. with 042307. 7 90°. and =5h5° ," The best fit solutions give $R_0\approx\,$ $\cdot$ $^{16}$ cm, with $\theta_0$ $^{\circ}$, $i\,$ $\,$ $^\circ$, and $\,$ $\,$ $^\circ$." Tn coutrast to NT. there is no detectable point source at the position of X3 iu our s-baud images.," In contrast to X7, there is no detectable point source at the position of X3 in our $_S$ -band images." Local extinction at the position of NJ is Ag 22.7 (?).., Local extinction at the position of X3 is $_K\approx$ 2.7 \citep{schoedel10}. In section 7.2 we discuss the possible nature of this source and the Huplicatious this has ou the external wind parameters., In section \ref{X3discuss} we discuss the possible nature of this source and the implications this has on the external wind parameters. 6 shows a 3D reconstruction of some of the features found iu the ceutral parsec of the Galaxy.," $\,$ \ref{GC3D} shows a 3D reconstruction of some of the features found in the central parsec of the Galaxy." The shaded area represents the disk of clockawise-rotating stars (CWS: ?: Tu 7j)and the colored spheresare the stellar nienibers.," The shaded area represents the disk of clockwise-rotating stars (CWS; \citealt{paum06}; ; \citealt{beloborodov06}; ; \citealt{lu09}) ),and the colored spheresare the stellar members." " The positious of the stars aud the disk parineters (resty.He )m(C0.2. -0.79. 0.6) axe from ον, "," The positions of the stars and the disk parameters $n_x, n_y, n_z$ )=(-0.12, -0.79, 0.6) are from \citet{paum06}. ." The stars are represented by differentcolors according to their distance from the observer (green is closer aud violet is further away frou us)., The stars are represented by differentcolors according to their distance from the observer (green is closer and violet is further away from us). ? show how a threc-dimensioual separation r frou the center can be estimated by comparing the proper motion par) of a star to the three-dimeusional velocity dispersion o. The probability that a star at the position + , \citet{eckart02} show how a three-dimensional separation $r$ from the center can be estimated by comparing the proper motion $_{PM}$ ) of a star to the three-dimensional velocity dispersion $\sigma$ The probability that a star at the position $r$ shock aud 2.17<3” for the outer (western) shock.,shock and $''\times3''$ for the outer (western) shock. " Although these inteeration areas are small we corrected for backerouud level by running INEAN on a nearby region 15.6""«13.2"","," Although these integration areas are small, we corrected for background level by running IMEAN on a nearby region $''\times13.2''$." These corrections were « in all cases., These corrections were $<$ in all cases. The results aro eiven in Table 2.., The results are given in Table \ref{tab:fluxden}. " The resulting spectral indices are Gout = U.6640,03 and a;, 0.06,", The resulting spectral indices are $\alpha_{out}$ = $\pm$ 0.03 and $\alpha_{in}$ = $\pm$ 0.06. There is no clear evidence for a significant difference in the spectral indices of the two parts of k25., There is no clear evidence for a significant difference in the spectral indices of the two parts of k25. The values are very close to each other and there are no data that demand a spectral wreak between 1.L and 13 Giz., The values are very close to each other and there are no data that demand a spectral break between 1.4 and 43 GHz. The outer shock structure is brighter than the iuner feature at all Yrequencies we lave measured., The outer shock structure is brighter than the inner feature at all frequencies we have measured. Our attempts to measure the magnitudes of the eradicuts in the surface brightuess have con. less than rewarding., Our attempts to measure the magnitudes of the gradients in the surface brightness have been less than rewarding. To make progress with his approach. it would be necessary to have a resolution aud seusitivity at least equal to those of fig. 3..," To make progress with this approach, it would be necessary to have a resolution and sensitivity at least equal to those of fig. \ref{fig:regions}." Our only indicative conclusion is that he ratio of the normalized eradicuts of the outer o the inner shock structures is greater than one at and below 5 GIIz. aud less than one above 10 CIIz.," Our only indicative conclusion is that the ratio of the normalized gradients of the outer to the inner shock structures is greater than one at and below 5 GHz, and less than one above 10 GHz." However. the beamsizes curploved even for lis comparison are judged to be too large for any reasonable accuracy.," However, the beamsizes employed even for this comparison are judged to be too large for any reasonable accuracy." We conclude that there is verv little or no difference between the two shocks (except for the total flux density) and neither is discerniblv exotic., We conclude that there is very little or no difference between the two shocks (except for the total flux density) and neither is discernibly exotic. Civen the ever iucreasing uuuber of X-ray detections of radio jets. we take the absence of evidence for peculiarity iu these putative shock features to be cousistent with the idea that N-ray Cluission is relatively ΟΛΟΙ for radio jets with a reasonable velocity towards us (i.e. two-sided N-ray jets are rare: we cannot cite even a single convincing example).," Given the ever increasing number of X-ray detections of radio jets, we take the absence of evidence for peculiarity in these putative shock features to be consistent with the idea that X-ray emission is relatively common for radio jets with a reasonable velocity towards us (i.e. two-sided X-ray jets are rare; we cannot cite even a single convincing example)." Iu this section we discuss οοποτα] aspects of the possible euissiou processes aud for cach jet feature tabulate the kev parameters for cach process., In this section we discuss general aspects of the possible emission processes and for each jet feature tabulate the key parameters for each process. Iu section 2? we compare the processes for cach feature in turn., In section \ref{sec:eval} we compare the processes for each feature in turn. There are two basic problems: how to estimate the emitting volume (which infiuences the calculated value of the equipartition magnetic field strength) and what coustraints σα there be ou the Doppler beaming factor. 6 (which governs the 10 caleulatious).," There are two basic problems: how to estimate the emitting volume (which influences the calculated value of the equipartition magnetic field strength) and what constraints might there be on the Doppler beaming factor, $\delta$ (which governs the IC calculations)." Iun general. we have clected to use the largest reasonable volume. with the Neray and highest resolution radio maps as a euide.," In general, we have elected to use the largest reasonable volume, with the X-ray and highest resolution radio maps as a guide." Table Lt provides the dimnensious and shapes of our assmuptious., Table \ref{tab:regions} provides the dimensions and shapes of our assumptions. Iu some or possibly all cases the actual volumes nav be sunaller hau that assumed. aud that would lead to arecr equipartition magnetic field streueths for svuchrotron models or higher electron densities or thermal bremsstraliluug models.," In some or possibly all cases the actual volumes may be smaller than that assumed, and that would lead to larger equipartition magnetic field strengths for synchrotron models or higher electron densities for thermal bremsstrahlung models." " To acconunodate relativistic beaming from bulk jet fluid velocities (DP.-(1Ryle. jay/e), we will derive svuchrotron parameters for a few representative values of à=L/T(1)cost) (0 is he angele between the jet direction aud the line of sieht)."," To accommodate relativistic beaming from bulk jet fluid velocities $\Gamma=(1-\beta^2)^{-1/2}$ ; $\beta$ =v/c), we will derive synchrotron parameters for a few representative values of $\delta=1/\Gamma(1-\beta~cos\theta)$ $\theta$ is the angle between the jet direction and the line of sight)." For thermal models we assume there is no »oanuing aud for IC/CMD models we solve for the characteristic value of 0 for which P=8., For thermal models we assume there is no beaming and for IC/CMB models we solve for the characteristic value of $\theta$ for which $\Gamma=\delta$ . We found no evidence that the outer shock iu k25 is disceruiblv exotic iu the radio (section 3)). but from the X-ray morphology of K25. it is evident that the N-rav aud radio emissious are co-spatial.," We found no evidence that the outer shock in k25 is discernibly exotic in the radio (section \ref{sec:results}) ), but from the X-ray morphology of k25, it is evident that the X-ray and radio emissions are co-spatial." This demoustrates that the suggestion of IIIISSV. that the N-rav emission might originate in auch sanaller volhune than the radio oenuüssion. is not supported bv the new data.," This demonstrates that the suggestion of HHSSV, that the X-ray emission might originate in a much smaller volume than the radio emission, is not supported by the new data." The svuchrotron parameters listed in Table 6 are typical for FRI jets., The synchrotron parameters listed in Table \ref{tab:sync} are typical for FRI jets. With beaming. the intrinsic power of the source drops.," With beaming, the intrinsic power of the source drops." Since we posit uo chanee in emitting volume. the field drops as well.," Since we posit no change in emitting volume, the field drops as well." The halfite for clectrous respousible for 2 keV cussion ἔτι} increases as the Ποιά drops. but eventually the IC losses dominate aud so Τα decreases.," The halflife for electrons responsible for 2 keV emission $\tau_{\frac{1}{2}}$ ) increases as the field drops, but eventually the IC losses dominate and so $\tau_{\frac{1}{2}}$ decreases." " Since we have chosen to use tle largest allowable cutting volume iu each case. the actual value of the magnetic Ποια streneth may be larger than indicated. aud this would decrease τα,"," Since we have chosen to use the largest allowable emitting volume in each case, the actual value of the magnetic field strength may be larger than indicated, and this would decrease $\tau_{\frac{1}{2}}$." The classical objection to the svuchrotrou model arises for those features which have an obvious inflection in their spectra to acconunodate a flatter N-rav spectrin than would be anticipated bv the segment connecting to optical or radio data., The classical objection to the synchrotron model arises for those features which have an obvious inflection in their spectra to accommodate a flatter X-ray spectrum than would be anticipated by the segment connecting to optical or radio data. Two possibleescapes from this objection are: (a) the existence of adistinct spectral, Two possibleescapes from this objection are: (a) the existence of adistinct spectral These estimates for the orientation of the spin vector are in good agreement with a number of other efforts to estimate the of A*’s accretion flow.,These estimates for the orientation of the spin vector are in good agreement with a number of other efforts to estimate the properties of Sgr A*'s accretion flow. " Estimates based upon fitting propertieslonger wavelengthSgr observations with numerical models of radiatively inefficient accretion flows produce position angles and inclination estimates with large uncertainties, though these are nevertheless consistent with the results obtained here (?).."," Estimates based upon fitting longer wavelength observations with numerical models of radiatively inefficient accretion flows produce position angles and inclination estimates with large uncertainties, though these are nevertheless consistent with the results obtained here \citep{Huan-Cai-Shen-Yuan:07}." It is also in excellent agreement with more recent attempts to probe the spin orientation using the mm-VLBI data from the 2007 epoch (??)..," It is also in excellent agreement with more recent attempts to probe the spin orientation using the mm-VLBI data from the 2007 epoch \citep{Huan-Taka-Shen:09,Dext-Agol-Frag-McKi:10}." " As before it is not possible to assess consistency with models that employ different plasma distributions near the black hole (e.g.,?), qualitativelythough they tend to imply similarly large viewing We angles."," As before it is not possible to assess consistency with models that employ qualitatively different plasma distributions near the black hole \citep[e.g., ][]{Mark-Bowe-Falc:07}, though they tend to imply similarly large viewing angles." "find similar spin orientations to those inferred from modelling of infrared polarization observations of Sgr A*’s flaring emission, though in this case the uncertainties are considerable (e.g.,?).."," We find similar spin orientations to those inferred from modelling of infrared polarization observations of Sgr A*'s flaring emission, though in this case the uncertainties are considerable \citep[e.g., ][]{Meye_etal:07}." " we find with the spin directions obtained Similarly,from modeling the consistencyspectrum and general relativistic MHD simulations, despite polarizationpreferring usingsignificantly smaller spin magnitudes (?).."," Similarly, we find consistency with the spin directions obtained from modeling the spectrum and polarization using general relativistic MHD simulations, despite preferring significantly smaller spin magnitudes \citep{Shch-Penn-McKi:10}." " Unlike the estimates in ?,, there is no any allowed solution for the spin vector that aligns with longereither of the stellar disks in the inner of the Galactic center reported(?).."," Unlike the estimates in \citet{Brod_etal:09}, there is no longer any allowed solution for the spin vector that aligns with either of the reported stellar disks in the inner $0.2\,\pc$ of the Galactic center \citep{Genz_etal:03}." " However, our revised position 0.2pcangle estimates are consistent with with the feature in ?,, bolstering the beinginterpretationaligned of this as X-rayrelated to a reportedpossible jet."," However, our revised position angle estimates are consistent with being aligned with the X-ray feature reported in \citet{Muno_etal:08}, bolstering the interpretation of this as related to a possible jet." " Note, however, this interpretation may be inconsistent with the low spin magnitudes we prefer."," Note, however, this interpretation may be inconsistent with the low spin magnitudes we prefer." The constraints upon the accretion model parameters obtained in the previous sections have for future mm-VLBI experiments., The constraints upon the accretion model parameters obtained in the previous sections have implications for future mm-VLBI experiments. " With these it is implicationspossible both to make for the visibilities on the various possible predictionsbaselines, as well as expectedidentify which baselines are most to substantial to the BL06 model likelyparameter provideestimation."," With these it is possible both to make predictions for the expected visibilities on the various possible baselines, as well as identify which baselines are most likely to provide substantial improvements to the BL06 model parameter estimation." " To estimate these, improvementshere we compute the as well as the variance associated with averagethe visibilityuncertainty in the amplitudesmodel parameters, weighted by the posterior probability distributions we have obtained using the combined mm-VLBI data set, following the method of ?.."," To estimate these, here we compute the average visibility amplitudes as well as the variance associated with the uncertainty in the model parameters, weighted by the posterior probability distributions we have obtained using the combined mm-VLBI data set, following the method of \citet{Fish-Brod-Doel-Loeb:09}." " The probability-weighted mean visibility profile of the scatter-broadened 230GHz emission from Sgr A* is elongated in the (+u,+v) direction (Figure 10))."," The probability-weighted mean visibility profile of the scatter-broadened $230\,\GHz$ emission from Sgr A* is elongated in the $(+u,+v)$ direction (Figure \ref{fig:heat}) )." " For the moderately high values of 0 favored by the mm-VLBI data, the profile is dominated by Doppler-boosted emissionintensity on the approaching side of the accretion flow (e.g., in the northeast of lower left panel of Figure 3))."," For the moderately high values of $\theta$ favored by the mm-VLBI data, the intensity profile is dominated by Doppler-boosted emission on the approaching side of the accretion flow (e.g., in the northeast of lower left panel of Figure \ref{fig:bestfit}) )." This portion of the emission is elongated parallel to the projected direction of the black hole spin vector., This portion of the emission is elongated parallel to the projected direction of the black hole spin vector. " Since the effective size of the emission is larger along the projected spin axis, the correlated flux density falls off faster with baseline length for baselines that are sensitive to structure in this direction than in the perpendicular direction."," Since the effective size of the emission is larger along the projected spin axis, the correlated flux density falls off faster with baseline length for baselines that are sensitive to structure in this direction than in the perpendicular direction." Our estimates of RIAF parameters suggest that a mm-VLBI baseline oriented southwest-northeast will detect more correlated flux density than an equal-length baseline oriented southeast-northwest., Our estimates of RIAF parameters suggest that a mm-VLBI baseline oriented southwest-northeast will detect more correlated flux density than an equal-length baseline oriented southeast-northwest. The standard deviation of the visibility amplitudes provides an estimate of which baselines would provide maximal additional constraints on RIAF model parameters equal sensitivity at all sites)., The standard deviation of the visibility amplitudes provides an estimate of which baselines would provide maximal additional constraints on RIAF model parameters (assuming equal sensitivity at all sites). Previous computations(assuming based on the 2007 epoch of data indicated that the largest scatter occurred at baseline lengths of approximately 3GA and with orientations perpendicular to the Hawaii-SMT baseline (?)..," Previous computations based on the 2007 epoch of data indicated that the largest scatter occurred at baseline lengths of approximately $3\,{\rm G}\lambda$ and with orientations perpendicular to the Hawaii-SMT baseline \citep{Fish-Brod-Doel-Loeb:09}." These findings still hold in light of the 2009 data., These findings still hold in light of the 2009 data. " Among observing baselines in the next few years, Chile-SPT and possibleChile-LMT probe the region of highest standard deviation, followed by baselines between the LMT and the continental US."," Among possible observing baselines in the next few years, Chile-SPT and Chile-LMT probe the region of highest standard deviation, followed by baselines between the LMT and the continental US." Our model suggests that the LMT-SMT and LMT-CARMA baselines will detect well over 1Jy.," Our model suggests that the LMT-SMT and LMT-CARMA baselines will detect well over $1\,\Jy$." " The increased sensitivity provided by phased ALMA may be important on the baselines to Chile, as the probability-weighted mean visibility amplitudes are >0.1Jy on the Chile-SMT baseline, <0.1Jy over most of the (u,v) track of the Chile— baseline, and smaller still on the longer baselines to Chile."," The increased sensitivity provided by phased ALMA may be important on the baselines to Chile, as the probability-weighted mean visibility amplitudes are $\gtrsim 0.1\,Jy$ on the Chile–SMT baseline, $\lesssim 0.1\,\Jy$ over most of the $(u,v)$ track of the Chile--CARMA baseline, and smaller still on the longer baselines to Chile." " However, the standard deviation of the predicted model visibility amplitudes is several x10mJy on these baselines, leading to uncertainties of tens of percent in model amplitude "," However, the standard deviation of the predicted model visibility amplitudes is several $\times 10\,\mJy$ on these baselines, leading to uncertainties of tens of percent in model amplitude predictions." "Further mm-VLBI data, either in the form of higher predictions.sensitivity on existing baselines or detections on new baselines, will both reduce these uncertainties and test the RIAF model with increasing rigor."," Further mm-VLBI data, either in the form of higher sensitivity on existing baselines or detections on new baselines, will both reduce these uncertainties and test the RIAF model with increasing rigor." The significantly increased number of long-baseline,The significantly increased number of long-baseline To interpret the large-scale alignments of quasar optical polarization vectors observed at redshifts z~ | (Hutsemékkers 1998:: Hutsemékkers and Lamy 2001: Hutsemékkers et al. 2005)),To interpret the large-scale alignments of quasar optical polarization vectors observed at redshifts $z\sim$ 1 (Hutsemékkers \cite{HUT98}; Hutsemékkers and Lamy \cite{HUT01}; Hutsemékkers et al. \cite{HUT05}) ) polarization induced by photon-pseudoscalar mixing along the line of sight has been invoked (Hutsemékkers 1998:; Jain et al. 2002))., polarization induced by photon-pseudoscalar mixing along the line of sight has been invoked (Hutsemékkers \cite{HUT98}; Jain et al. \cite{JAI02}) ). Photon-pseudoscalar mixing generates dichroism and. birefringence. the latter transforming linear polarization into circular polarization and vice-versa along the line of sight.," Photon-pseudoscalar mixing generates dichroism and birefringence, the latter transforming linear polarization into circular polarization and vice-versa along the line of sight." If photon-pseudoscalar mixing produces the linear polarization needed to explain the observed alignments. a comparable amount of circular polarization would be expected (Raffelt and Stodolsky 1988: Jain et al. 2003: ," If photon-pseudoscalar mixing produces the linear polarization needed to explain the observed alignments, a comparable amount of circular polarization would be expected (Raffelt and Stodolsky \cite{RAF88}; Jain et al. \cite{JAI02}; ;" Das et al. 2005::, Das et al. \cite{DAS04}; Gnedin et al. 2007::, Gnedin et al. \cite{GNE07}; Hutsemékkers et al. 2008::, Hutsemékkers et al. \cite{HUT08}; Payez et al. 2008))., Payez et al. \cite{PAY08}) ). Hence. we present accurate circular polarizatior measurements for a sample of quasars whose polarizatior vectors are coherently oriented.," Hence, we present accurate circular polarization measurements for a sample of quasars whose polarization vectors are coherently oriented." The optical circular polarization. of quasars has. rarely been measured., The optical circular polarization of quasars has rarely been measured. Our new observations. data reduction. anc a compilation of published measurements are presented 1 Sect. 2.," Our new observations, data reduction, and a compilation of published measurements are presented in Sect. \ref{sec:data}." Implications for the photon-pseudoscalar mixing mechanism are discussed in Sect. 3.1., Implications for the photon-pseudoscalar mixing mechanism are discussed in Sect. \ref{sec:discuss1}. The detection. of significant circular polarization im two objects and its consequence for quasar physics are presented in Sect. 3.2.., The detection of significant circular polarization in two objects and its consequence for quasar physics are presented in Sect. \ref{sec:discuss2}. The observations were carried out on April 18-20. 2007 at the European Southern Observatory (ESO. La Silla) using the 3.6m telescope equipped with the ESO Faint Object Spectrograph and Camera EFOSC?.," The observations were carried out on April 18-20, 2007 at the European Southern Observatory (ESO, La Silla) using the 3.6m telescope equipped with the ESO Faint Object Spectrograph and Camera EFOSC2." Circular polarization was measured using a super-achromatic quarter-wave (1/4) retarder plate (QWP). which transforms the circular polarization into linear polarization. and a Wollaston prism. which splits the linearly polarized beam into two orthogonally polarized images of the object (Saviane et al. 2007)).," Circular polarization was measured using a super-achromatic quarter-wave $\lambda$ /4) retarder plate (QWP), which transforms the circular polarization into linear polarization, and a Wollaston prism, which splits the linearly polarized beam into two orthogonally polarized images of the object (Saviane et al. \cite{SAV07}) )." " The CCD was used in unbinned mode. which corresponds to a scale of 0.157"" /pixel on the sky."," The CCD was used in unbinned mode, which corresponds to a scale of $\arcsec$ /pixel on the sky." All measurements were performed through a Bessel V filter (VstG4]: central wavelength: 5476A:: FWHM: 1132 A)., All measurements were performed through a Bessel V filter $\#$ 641; central wavelength: 5476; FWHM: 1132 ). At least one pair of exposures with the QWP rotated to the angles —45? and +45° was secured for each target.," At least one pair of exposures with the QWP rotated to the angles $-45 \degr$ and $+45 \degr$ was secured for each target." Frames were dark-subtracted and flat-fielded., Frames were dark-subtracted and flat-fielded. The circular polarization po. Le.. the normalized Stokes V/7 parameter. was extracted from each pair of frames using a procedure used to measure the normalized Stokes Q/7 and U/I parameters and described in Lamy and Hutsemékkers (1999)) and Sluse et al. (2005)).," The circular polarization $p_{\rm circ}$ , i.e., the normalized Stokes $V/I$ parameter, was extracted from each pair of frames using a procedure used to measure the normalized Stokes $Q/I$ and $U/I$ parameters and described in Lamy and Hutsemékkers \cite{LAM99}) ) and Sluse et al. \cite{SLU05}) )." Errors were estimated from the photon noise., Errors were estimated from the photon noise. Seeing was typically around 1., Seeing was typically around $\arcsec$. Owing to the variable atmospheric extinction (thin to thick cirrus). some exposures had to be repeated to reach a sufficient signal-to-noise ratio.," Owing to the variable atmospheric extinction (thin to thick cirrus), some exposures had to be repeated to reach a sufficient signal-to-noise ratio." The performances of the instrument were checked during our run and during the setup night (April 17) using an unpolarized standard star and a star with high and slowly variable circular polarization. LP 790—20 (West 1989:; Jordan and Friedrich 2002)).," The performances of the instrument were checked during our run and during the setup night (April 17) using an unpolarized standard star and a star with high and slowly variable circular polarization, LP $-$ 20 (West \cite{WES89}; Jordan and Friedrich \cite{JOR02}) )." The results. discussed in Saviane et al. (2007)).," The results, discussed in Saviane et al. \cite{SAV07}) )," demonstrated the quality of the instrumental setup., demonstrated the quality of the instrumental setup. LP 790-20 was also used to fix the sign of the circular polarization. Le. Pur>O when the electric vector rotates counter-clockwise as seen by an observer facing the object.," LP $-$ 20 was also used to fix the sign of the circular polarization, i.e., $p_{\rm circ} > 0$ when the electric vector rotates counter-clockwise as seen by an observer facing the object." To evaluate the cross-talk between linear and circular polarization. we measured the circular polarization of linearly polarized stars.," To evaluate the cross-talk between linear and circular polarization, we measured the circular polarization of linearly polarized stars." These observations were repeated several times during our observing run., These observations were repeated several times during our observing run. Hilt 652 was observed during the setup night., Hilt 652 was observed during the setup night. The results are given in Table | together with the published linear polarization (1.9. the polarization degree pis and the polarization position angle μμ).," The results are given in Table \ref{tab:datastd} together with the published linear polarization (i.e. the polarization degree $p_{\rm lin}$ and the polarization position angle $\theta_{\rm lin}$ )." Uncertainties are smaller than in Saviane et al. (2007)), Uncertainties are smaller than in Saviane et al. \cite{SAV07}) ) because of the availability of repeated observations., because of the availability of repeated observations. Although the objects are highly linearly polarized. we measure a null circular polarization.," Although the objects are highly linearly polarized, we measure a null circular polarization." Combining the data of Hilt 652 and Ve 6-23. which have similar. polarization angles. we derive the 3o upper limit to the circular polarization due to cross-talk in the V filter [οPlinl< 0.0075.," Combining the data of Hilt 652 and Ve $-$ 23, which have similar polarization angles, we derive the $\sigma$ upper limit to the circular polarization due to cross-talk in the V filter $|p_{\rm circ} / p_{\rm lin}| \lesssim$ 0.0075." Our new measurements ofquasar circular polarization are reported in Table 2 with Io photon-noise errors., Our new measurements ofquasar circular polarization are reported in Table \ref{tab:dataqso} with $\sigma$ photon-noise errors. The targets are extracted from the sample of 355 polarized quasars defined inHutsemékkers et al. (200501).," The targets are extracted from the sample of 355 polarized quasars defined inHutsemékkers et al. \cite{HUT05}) )," as well as their B1950, as well as their B1950 llere ross is the core radius of the à model. and ioa is the inner limiting radius of the cooling flow. allowing us to avold infinitics at rp=0. Πρι. ,"Here $r_{\rm core}$ is the core radius of the $\beta$ model, and $r_{\rm inner}$ is the inner limiting radius of the cooling flow, allowing us to avoid infinities at $r=0$. $n_{\rm e1}$," no» ancl nos are scale electron densities and Zig. 75» and Zi scale temperatures: Tia Corresponds to the temperature of the non-cooling gas.," $n_{\rm e2}$ and $n_{\rm e3}$ are scale electron densities and $T_{\rm e1}$, $T_{\rm e2}$ and $T_{\rm e3}$ scale temperatures; $T_{\rm e3}$ corresponds to the temperature of the non-cooling gas." ]t is clear that matching temperatures and densities allows us to write all the scale factors in terms of Όρο and Zi., It is clear that matching temperatures and densities allows us to write all the scale factors in terms of $n_{\rm e3}$ and $T_{\rm e3}$. The results are only weakly dependent on riii so long as it is small ancl we fix it at a value corresponding to 0.01. aresec in what follows., The results are only weakly dependent on $r_{\rm inner}$ so long as it is small and we fix it at a value corresponding to 0.01 arcsec in what follows. The parameters e and b set the slope of the density and temperature distributions: for a realistic cooling mocel we expect @20 and b«0. so that density increases aud temperature decreases with decreasing radius.," The parameters $a$ and $b$ set the slope of the density and temperature distributions; for a realistic cooling model we expect $a>0$ and $b<0$, so that density increases and temperature decreases with decreasing radius." The ideal gas law implies that. pressure goes as riu, The ideal gas law implies that pressure goes as $r^{-(a+b)}$. A the atmosphere is required to be close to. hyvdrostatie equilibrium. then matching mass as a function of radius inside and outside the cooling zone leads to a constraint on rojo] as a function ofa and b: and if we assume some law for the radial dependence ⋅ .. ∪⇂↓≻↓⋅⋖⊾⊳∖⊳∖⊔↓⋅∢⊾↿∖∫↗∖∣⋮↓≱∖≼∙∪⊔≱∖↓≱∖⊓⊾⊔⇂∖∖⊽↓↿⇂↥∪∣⋡≱∖∢⋅↓⋅∖⇁⋜∐↓∪⊔≱∖∪⇂. . . other cooling regions) then the model has only five. [ree parameters: S. Powe. @ dos and nma. the last being a normalis:ion parameter that can be determined in the fit.," If the atmosphere is required to be close to hydrostatic equilibrium, then matching mass as a function of radius inside and outside the cooling zone leads to a constraint on $r_{\rm cool}$ as a function of $a$ and $b$: and if we assume some law for the radial dependence of pressure $P \propto r^{-1}$ is consistent with observations of other cooling regions) then the model has only five free parameters: $\beta$, $r_{\rm core}$, $a$, $T_{\rm e3}$ and $n_{\rm e3}$, the last being a normalisation parameter that can be determined in the fit." " In addition. such a model can only be physically realistic if the cooling time at ri, is comparable to the svstem lifetime. or the Hubble time: (Sarazin 1986) where 7,4 is in vears. &gZ in keV and ny, inom"," In addition, such a model can only be physically realistic if the cooling time at $r_{\rm cool}$ is comparable to the system lifetime, or the Hubble time: (Sarazin 1986) where $\tau_{\rm cool}$ is in years, $k_B T$ in keV and $n_p$ in $^{-3}$." We fit a range of representative cooling models to the data., We fit a range of representative cooling models to the data. As before. 3 was chosen from a small number of possible values (0.5. 0.667. 0.9) while roo. ranged from 1000 aresec.," As before, $\beta$ was chosen from a small number of possible values (0.5, 0.667, 0.9) while $r_{\rm core}$ ranged from 1--1000 arcsec." We tried. values of 1. 1.5. 2. 5 ancl 10 keV for kglis.," We tried values of 1, 1.5, 2, 5 and 10 keV for $k_B T_{\rm e3}$." 0 was allowed to take the values 1.5. 1.75 or 2.0.," $a$ was allowed to take the values 1.5, 1.75 or 2.0." No model consisting of a cooling How alone was a good Lit to the data., No model consisting of a cooling flow alone was a good fit to the data. A number of models consisting of a cooling Low and a central point source were comparable in goodness of fit to the combination of J-mocdel and point source discussed above. but most of these were ruled out by the constraint on cooling time.," A number of models consisting of a cooling flow and a central point source were comparable in goodness of fit to the combination of $\beta$ -model and point source discussed above, but most of these were ruled out by the constraint on cooling time." Those that were not have small core radii. low external temperatures and steep temperature and. density power laws: for example. the model with Aedi;=1.5 keV. a= 240. 3=0.667. bore=Meas40 aresee is an acceptable fit to the ΕΙ radial profile (47= 25).," Those that were not have small core radii, low external temperatures and steep temperature and density power laws: for example, the model with $k_B T_{\rm e3} = 1.5$ keV, $a=2.0$ , $\beta=0.667$, $r_{\rm core} = r_{\rm cool} = 40$ arcsec is an acceptable fit to the HRI radial profile $\chi^2=25$ )." In this moclel just under LO per cent of the total counts (10004 100) are assigned to the cooling Hlow component., In this model just under 10 per cent of the total counts $1000 \pm 100$ ) are assigned to the cooling flow component. The nominal cooling time at the core radius is 2«1017 vears: the mass deposition rate is approximately 4044. + and the implied densities at 20 kpe correspond roughly with those required [or pressure equilibrium. with the cold. gas inferred. from. observations of the extended. emission-line region (Boisson 11989)., The nominal cooling time at the core radius is $2 \times 10^{10}$ years; the mass deposition rate is approximately $40 M_\odot$ $^{-1}$ and the implied densities at 20 kpc correspond roughly with those required for pressure equilibrium with the cold gas inferred from observations of the extended emission-line region (Boisson 1989). Though the details of the model may not be correct. this shows that the extended emission of οσα plausibly be modelled as a cooling How of this tvpe.," Though the details of the model may not be correct, this shows that the extended emission of can plausibly be modelled as a cooling flow of this type." A strong nuclear source is still necessary: the tux of the point-like component in the cooline-Low mocel is reduced bv only ~L per cent compared to that derived. [from the simple o-mioctel fits of section 3.., A strong nuclear source is still necessary; the flux of the point-like component in the cooling-flow model is reduced by only $\sim 1$ per cent compared to that derived from the simple $\beta$ -model fits of section \ref{analysis}. We have carried out the first. separation. of nuclear and ealaxy-scale extended: X-ray emission in a BL Lac object ancl found evidence that ünhabits a dense anc. presumably. rapidly cooling region of X-rav emission. a much more extreme environment than those found for Ἱνρίσα ETE radio galaxies: we have shown that it can be modelled as a cooling Dow in low-temperature cluster gas.," We have carried out the first separation of nuclear and galaxy-scale extended X-ray emission in a BL Lac object and found evidence that inhabits a dense and, presumably, rapidly cooling region of X-ray emission, a much more extreme environment than those found for `typical' FRI radio galaxies; we have shown that it can be modelled as a cooling flow in low-temperature cluster gas." Lf this result were extended to other BL Lac objects. it. would cause cdillieulties for models that seek to unify FRIs and DL Lacs. and might imply some causal relationship between a dense and rapidly cooling atmosphere and the DL Lac phenomenon.," If this result were extended to other BL Lac objects, it would cause difficulties for models that seek to unify FRIs and BL Lacs, and might imply some causal relationship between a dense and rapidly cooling atmosphere and the BL Lac phenomenon." However. it may. be that365. with its high power and intermediate racio structure. is not representative of the BL Lac class.," However, it may be that, with its high power and intermediate radio structure, is not representative of the BL Lac class." Further observations are planned both to verify the thermal nature of the galaxy-scale halo and to see whether iis unusual among BL Lacs in this respect., Further observations are planned both to verify the thermal nature of the galaxy-scale halo and to see whether is unusual among BL Lacs in this respect. We are grateful to Guy Pooley for allowing us to use his VLA observations of365. and to the VLA Analysts for help in recovering the VLA. cata from. the archive.," We are grateful to Guy Pooley for allowing us to use his VLA observations of, and to the VLA Analysts for help in recovering the VLA data from the archive." This research has made use of the NASA/LPAC Extragalactic Database (NIED) which is operated by the Jet Propulsion Laboratory. California Institute of Technology. under contract with NASA.," 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 NASA." The Digitized Sky Surveys were produced at the Space Telescope Science. Institute under U.S. Government erant. NAC W-2166., The Digitized Sky Surveys were produced at the Space Telescope Science Institute under U.S. Government grant NAG W-2166. The National ltadio Astronomy Observatory is operated: by Associated Universities Inc... uncer co-operative agreement with the National Science Foundation.," The National Radio Astronomy Observatory is operated by Associated Universities Inc., under co-operative agreement with the National Science Foundation." This work was supported. by NASAerant. NAG 5-2312 and PPARC grant. GIt/Ix98582., This work was supported by NASAgrant NAG 5-2312 and PPARC grant GR/K98582. positions. plus shear estimates which have been corrected for circularisation of the galaxies bv the PSE. and anisotropic smearing due to e.g. tracking errors.,"positions, plus shear estimates which have been corrected for circularisation of the galaxies by the PSF, and anisotropic smearing due to e.g. tracking errors." This catalogue was combined with the photometric redshift catalogue for the COMIDO-IT survey., This catalogue was combined with the photometric redshift catalogue for the COMBO-17 survey. The resulting catalogue included 52139 galaxies. 23102 of which had. reliable. photometric redshifts assigned: the remaining galaxies vielded ambiguous redshift: probabilities or were fainter than the 7?=24 reliability limit for redshifts in the survey.," The resulting catalogue included 52139 galaxies, 23102 of which had reliable photometric redshifts assigned; the remaining galaxies yielded ambiguous redshift probabilities or were fainter than the $R=24$ reliability limit for redshifts in the survey." This remainder of galaxies was Lageccl as having unreliable redshifts: the faint galaxies were assigned an optional redshift which we use below when stated., This remainder of galaxies was flagged as having unreliable redshifts; the faint galaxies were assigned an optional redshift which we use below when stated. Following Brown et al (2003). Section 4. we use a mecian-magnitude mecdian-redshift. relation to assign this redshift: the median /? magnitude of the faint sample is /?=24.9. corresponding to a median redshift z20.950.05.," Following Brown et al (2003), Section 4, we use a median-magnitude median-redshift relation to assign this redshift; the median $R$ magnitude of the faint sample is $R=24.9$, corresponding to a median redshift $z\simeq 0.95\pm0.05$." We will now use the models. developed. above to assess he evidence for evolution of the matter distribution from he COMDO-17 survev., We will now use the models developed above to assess the evidence for evolution of the matter distribution from the COMBO-17 survey. We begin by making a minimal direct. detection of evolution. by comparing the growth. of he lensing signal with recdshift to that expected with a ruly unevolving matter clistribution.," We begin by making a minimal direct detection of evolution, by comparing the growth of the lensing signal with redshift to that expected with a truly unevolving matter distribution." We σο on to tse our »henomoenological model of an evolving power spectrum to constrain the rate of evolution., We go on to use our phenomenological model of an evolving power spectrum to constrain the rate of evolution. Finally. we return to full power spectra models including cosmological parameters. in order to constrain the cosmological constant from the rate of growth of the shear signal with recshilt.," Finally, we return to full power spectra models including cosmological parameters, in order to constrain the cosmological constant from the rate of growth of the shear signal with redshift." As a preliminary first. step in using 3-D shear data to measure evolution. we will demonstrate. that the data exclude a non-evolving matter distribution. given the present-day normalisation of the matter power spectrum σκυ anc a ACDAL eeometry.," As a preliminary first step in using 3-D shear data to measure evolution, we will demonstrate that the data exclude a non-evolving matter distribution, given the present-day normalisation of the matter power spectrum $\sigma_{8,0}$ and a $\Lambda$ CDM geometry." Lt is important to realise that his simplest step is already effectively achieved. by 2D cosmic shear surveys. if the median redshift of the survey is well estimated.," It is important to realise that this simplest step is already effectively achieved by 2D cosmic shear surveys, if the median redshift of the survey is well estimated." " That is to sav. the amplitude. of the ojected 2D shear field correlation functions measured with cosmic shear surveys (see e.g. van Waerbeke Mollier 2003. telregier. 2003 for reviews) at à median redshift z,,~1 is inconsistent with that expected for an unevolving power spectrum. both caleulated for example with eo=0.84c1.04 (ef"," That is to say, the amplitude of the projected 2D shear field correlation functions measured with cosmic shear surveys (see e.g. van Waerbeke Mellier 2003, Refregier 2003 for reviews) at a median redshift $z_m \sim 1$ is inconsistent with that expected for an unevolving power spectrum, both calculated for example with $\sigma_{8,0}=0.84\pm0.04$ (c.f." Spergel et al 2003)., Spergel et al 2003). " For example. at an angular scale of 1. Cyz9940.4)«10.3 for z,,=1 in these surveys. whereas Cy is predicted to be (5.140.8).10l at 1 in à model with unevolving power (1.0. with the power expected for ACDAL at the present day as in section. 2.1. but unchanged in the past). σκυ=0.84+0.04 and ACDAL ecometry (0,,=0.3.44101.44) 12km s 1j calculated: using equation (19))."," For example, at an angular scale of $1'$, $C_0\simeq (3.2\pm0.4)\times10^{-4}$ for $z_m=1$ in these surveys, whereas $C_0$ is predicted to be $(5.1\pm0.8)\times10^{-4}$ at 1' in a model with unevolving power (i.e. with the power expected for $\Lambda$ CDM at the present day as in section 2.1, but unchanged in the past), $\sigma_{8,0}=0.84\pm0.04$ and $\Lambda$ CDM geometry $(\Omega_m=0.3, \Omega_{\rm tot}=1, H_0=72$ km $^{-1}$ $^{-1}$ ) calculated using equation \ref{eq:pg}) )." However. we will see that there is considerable power in using the redshift information for each galaxy. as we will obtain significantly more accurate measurements of the evolution. and will be able to exelude no-growth moclels regardless of present-day power spectrum normalisation.," However, we will see that there is considerable power in using the redshift information for each galaxy, as we will obtain significantly more accurate measurements of the evolution, and will be able to exclude no-growth models regardless of present-day power spectrum normalisation." We begin by making a clireet detection of evolution with the 3-D shear field., We begin by making a direct detection of evolution with the 3-D shear field. " We can do this by caleulating the X7 fit of the no-evolution model to the data. and comparing with the 4? lit for. sav. an evolving AC DAL model (ο=0.3.44,Ly=72kms + Alpely dn the Gest instance both with σκυ=OS4 (ef"," We can do this by calculating the $\chi^2$ fit of the no-evolution model to the data, and comparing with the $\chi^2$ fit for, say, an evolving $\Lambda$ CDM model $(\Omega_m=0.3, \Omega_{\rm tot}=1, H_0=72$ km $^{-1}$ $^{-1}$ ), in the first instance both with $\sigma_{8,0}=0.84$ (c.f." Spergel et al 2003)., Spergel et al 2003). In the next. section we will examine the ellect of varving this normalisation ancl mareinalising over cosmological parameters., In the next section we will examine the effect of varying this normalisation and marginalising over cosmological parameters. " Phe sum we require for our X7 fit is given by where 5, and 5» are the two components of shear for a particular galaxy. in the frame where the ;r-axis is the line joining the two galaxies in question: wj; are à set of weights which we will choose presently."," The sum we require for our $\chi^2$ fit is given by where $\gamma_1$ and $\gamma_2$ are the two components of shear for a particular galaxy, in the frame where the $x$ -axis is the line joining the two galaxies in question; $w_{ij}$ are a set of weights which we will choose presently." / anc j are indices for different galaxies. and Cy and C2 are the expected correlation functions between the two galaxies in the mocel. calculated. using equations (21)) and (22)).," $i$ and $j$ are indices for different galaxies, and $C_1$ and $C_2$ are the expected correlation functions between the two galaxies in the model, calculated using equations \ref{ctheta1}) ) and \ref{ctheta2}) )." Hore we choose a simple weighting us;=Lat. j. where e is the variance in one shear component.," Here we choose a simple weighting $w_{ij}=1/\sigma_\gamma^4$, $i \ne j$ , where $\sigma_\gamma$ is the variance in one shear component." " We choose this weighting as the error upon 51,51,; is entirely dominated by the random orientation of galaxies: therefore we have neglected: olf-diagonal elements. of the covariance matrix of errors upon 1,51,;."," We choose this weighting as the error upon $\gamma_{1,i} \gamma_{1,j}$ is entirely dominated by the random orientation of galaxies; therefore we have neglected off-diagonal elements of the covariance matrix of errors upon $\gamma_{1,i} \gamma_{1,j}$." 1n addition. we neglect the smoothing error associated with our redshift uncertainty of As=0.05: assessment of the impact of this small smoothing term is left for future investigation.," In addition, we neglect the smoothing error associated with our redshift uncertainty of $\Delta z\simeq 0.05$; assessment of the impact of this small smoothing term is left for future investigation." We are also invoking the Central Limit Theorem in order to use 47 to estimate uncertainties upon parameters. as aay one product of galaxy shears does not have a Gaussian error.," We are also invoking the Central Limit Theorem in order to use $\chi^2$ to estimate uncertainties upon parameters, as any one product of galaxy shears does not have a Gaussian error." In order to remove the impact of intrinsic alignments between galaxies. due to physical galaxy alignment instead of apparent alignment due to lensing. we reject galaxy pairs which are within A:=0.05 of cach other. if their comoving separation Is less than I\lpe.," In order to remove the impact of intrinsic alignments between galaxies, due to physical galaxy alignment instead of apparent alignment due to lensing, we reject galaxy pairs which are within $\Delta z = 0.05$ of each other, if their comoving separation is less than 1Mpc." We also remove. with the same prescription. near galaxy pairs in the background. without redshift information. assigning to them the mecdian recdshift as described in Section 3.," We also remove, with the same prescription, near galaxy pairs in the background without redshift information, assigning to them the median redshift as described in Section 3." Phe weighting equation (34)) is 1/02 since. if our shear estimator 5; is near Ciaussian. we find that the probability distribution of si; (1.0. two independent Gaussian variables multiplied together) is given by where Ay is a modified Bessel function of the second kind.," The weighting equation \ref{chi2}) ) is $1/\sigma_\gamma^4$ since, if our shear estimator $\gamma_i$ is near Gaussian, we find that the probability distribution of $\gamma_i \gamma_j$ (i.e. two independent Gaussian variables multiplied together) is given by where $K_0$ is a modified Bessel function of the second kind." Εις probability distribution. Prob(y). has variance a? as stated: this is found to be an excellent match to the variance of measured 5;*5; (both have value 0.311).," This probability distribution, ${\rm Prob}(y)$, has variance $\sigma_\gamma^4$ as stated; this is found to be an excellent match to the variance of measured $\gamma_i \gamma_j$ (both have value $0.31^4$ )." " Phe no-evolution mocdoel we select is as described above. Le. ACDAL(Q,,=03.0,1.4 12km + +)"," The no-evolution model we select is as described above, i.e. $\Lambda$ CDM $(\Omega_m=0.3, \Omega_{\rm tot}=1, H_0=72$ km $^{-1}$ $^{-1}$ )" for sources at redshifts 20.9.,for sources at redshifts $z\simlt 0.9$. Αι higher redshifts. the 4000 break featurcomehichouralgorilhimisbasedisredshi fle and," At higher redshifts, the $\,$ break feature on which our algorithm is based is redshifted out of our observational wavelength range." " 0.3A,obsere (nur."," Taking into account our completeness in spectral data (section \ref{data}) ), only 53 of the 323 sources in the Drinkwater et al." ek ingi, \shortcite{Drinkwater1997} sample have been analysed using our algorithm. pong: 1 urcomplelten," Since we are limited to redshifts $z\simlt 0.9$, it is possible that we are biased towards detecting relatively large galaxy contributions." "essi, ", Our results may thus not be representative for the whole sample of Parkes quasars. We have two strong pieces of observational evidence that supports a minimal galaxy contribution from the high redshift’ Parkes sources: First. a| sources with 220.5Lx appear very compact in dy (eg.," We have two strong pieces of observational evidence that supports a minimal galaxy contribution from the high redshift Parkes sources: First, all sources with $z\simgt0.5$ appear very compact in $K$ (eg." Fie. 9)).," Fig. \ref{Kfracvsz}) )," and exhibit. broacd-line equivalent widths typical of those observed. in. optically-selected: quasars., and exhibit broad-line equivalent widths typical of those observed in optically-selected quasars. Second. significantly high. levels of linear polarisation. (Z:5'X have been observed in the near-LHHi in several sources at zzl.. (see Alasci 1997).," Second, significantly high levels of linear polarisation $\simgt5\%$ ) have been observed in the near-IR in several sources at $z\simgt1$ (see Masci 1997)." This stronely inclicates tha the emission is dominated by a non-thermal mechanism., This strongly indicates that the emission is dominated by a non-thermal mechanism. Ht is important to note however that the number ol sources in which a polarisation has been searched for is too low to draw any reasonable conclusion., It is important to note however that the number of sources in which a polarisation has been searched for is too low to draw any reasonable conclusion. Further polarimetric studies of preferably the reddest. quasars are necessary. to asses the importance of a host galaxy component., Further polarimetric studies of preferably the reddest quasars are necessary to asses the importance of a host galaxy component. The next significant step in improving the algorithm presented. here for. determining. the galaxy contribution would be to completely discard our assumption of a power-law lor the shape of the underlying quasar spectrum., The next significant step in improving the algorithm presented here for determining the galaxy contribution would be to completely discard our assumption of a power-law for the shape of the underlying quasar spectrum. Although a simple power-law is a good overall representation [or the around A=00... generic cquasar spectra also include a complex blend of emission line features superimposed on the continuum about this region.," Although a simple power-law is a good overall representation for the around $\lambda\simeq4000$, generic quasar spectra also include a complex blend of emission line features superimposed on the continuum about this region." As seen in most compilations of composite QSO spectra (eg., As seen in most compilations of composite QSO spectra (eg. Francis et al., Francis et al. 1991). wavelengths shortwards of 3TOOA are contaminalec bv a Balmer coninuum. where emission from the convergence of high order Balmer lines can introduce a steep rise in this part of the spectrum.," 1991), wavelengths shortwards of $3700$ are contaminated by a Balmer coninuum, where emission from the convergence of high order Balmer lines can introduce a steep rise in this part of the spectrum." Furthermore there is also a complex blend of Fell emission setting in at these wavelengths., Furthermore there is also a complex blend of FeII emission setting in at these wavelengths. " ""These considerations therefore invalidate our assumption of a pure power-law for the ""smooth"" quasar spectrum.", These considerations therefore invalidate our assumption of a pure power-law for the “smooth” quasar spectrum. Nonetheless. itis likely that the omission of these acdclitional intrinsic features at AZ4000A will have led us to overestimate the galaxy. contribution on average.," Nonetheless, it is likely that the omission of these additional intrinsic features at $\lambda\simlt4000$ will have led us to overestimate the galaxy contribution on average." This paper has explored. whether emission [rom the host ealaxies of Parkes quasars can significantly contribute to the relatively large spread in D;—A colours observed., This paper has explored whether emission from the host galaxies of Parkes quasars can significantly contribute to the relatively large spread in $B_{J}-K$ colours observed. If the hosts are classical eiant cllipticals ancl their lux. strongly contributes. then this would. be expected. since. elliptical colours are known to be quite red in 5Aiozoze2," If the hosts are classical giant ellipticals and their flux strongly contributes, then this would be expected since elliptical colours are known to be quite red in $B-K$ to $z\sim2$." We have devised. an algorithm that measures the relative galaxy contribution in each source in. an unbiased wav using the characteristic 4000 break featurcofelliplicalgalaagS EDs.," We have devised an algorithm that measures the relative galaxy contribution in each source in an unbiased way using the characteristic $\,$ break feature of elliptical galaxy SEDs." " Thebasisofthealgorithminvol| break feature clisapears and what is left is a ""smooth? spectrum. containing no breaks."," The basis of the algorithm involves subtracting a generic elliptical SED from each source spectrum until the $\,$ break feature disapears and what is left is a “smooth” spectrum containing no breaks." " This ""smooth"" spectrum. we refer to as the underlving quasar spectrum.", This “smooth” spectrum we refer to as the underlying quasar spectrum. The only requirement by our algorithm: is that this remaining spectrum be smooth., The only requirement by our algorithm is that this remaining spectrum be smooth. The ealactic contribution. relative to the total light at any wavelength is estimated from the amount of galaxy subtracted.," The galactic contribution, relative to the total light at any wavelength is estimated from the amount of galaxy subtracted." Phe main conclusions are: 1., The main conclusions are: 1. " For 20.9. (Lor which the J4000A. feat irren rui iiam en).we findbroadandalmostbim Most, sources ""alli70%)ya Πάνο σαίακν fractions⋅."," For $z\simlt0.9$ , (for which the $\,$ feature remains observable in our spectra), we find broad and almost bimodal distributions in the relative galaxy fraction in $B_{J}$ and $K$." " doutofour. at atienqthe 36are leveli ""in bot Db, and A.", Most sources $\simgt70\%$ ) have galaxy fractions $<0.3$ at the $3\sigma$ level in both $B_{J}$ and $K$. "tono, remainder have large galaxy contributions and are predominately low redshift galaxies with strong VA breaks."," The remainder have large galaxy contributions and are predominately low redshift galaxies with strong $\,$ breaks." . Vloftheselatlersourcesarespaliallyectendedandresoleedon ancl Αρα images., All of these latter sources are spatially extended and resolved on $B_{J}$ and $K$ -band images. In particular. there is a clear distinction in the ποσα of the 4000A break forresoleedandunresolvedsources.," In particular, there is a clear distinction in the strength of the $\,$ break for resolved and unresolved sources." indent2., 2. Usinglhescestimales. wefindlhalthemoeanl bandmagniludcofthehostgalaricso f flalspectrumradioqua sarsisconsistent ACN.," Using these estimates, we find that the mean $K$ -band magnitude of the host galaxies of flat spectrum radio quasars is consistent with that of extended radio galaxies at $z\simlt0.9$." indenta , This is consistent with the unified model for radio-loud AGN. , 3. Bysublractingthegalarycontributionincachbandpass fromlheobser colours of Parkes sources. we find that at. predominately the 26 confidence level. the relatively large spread in colours still remains.," By subtracting the galaxy contribution in each bandpass from the observed $B_{J}-K$ colours of Parkes sources, we find that at predominately the $2\sigma$ confidence level, the relatively large spread in colours still remains." We conclude that in a majority of cases. the relatively red colours must be dueto a mechanism other than that contributed by a cred” stellar component.," We conclude that in a majority of cases, the relatively red colours must be dueto a mechanism other than that contributed by a “red” stellar component." PJM acknowledges support from an APRA Scholarship. anc RLW from an ARC research erant.," FJM acknowledges support from an APRA Scholarship, and RLW from an ARC research grant." The gravitational instability. picture involves the erowth of carly time primordial fluctuatious into the actual large-scale structure observed through the ealaxv distribution.,The gravitational instability picture involves the growth of early time primordial fluctuations into the actual large-scale structure observed through the galaxy distribution. This erowth depends in principle ou the underlying theory of eravity and the cosmic expansion history., This growth depends in principle on the underlying theory of gravity and the cosmic expansion history. It is therefore important to be able to measure the growth history to obtain useful cosmological informations., It is therefore important to be able to measure the growth history to obtain useful cosmological informations. Oue wav of determining the erowth of structure is through the apparent anisotropy of the galaxy distribution in redshift space. caused by the dinc-of-sieht (LOS) component of the ealaxies peculiar velocities.," One way of determining the growth of structure is through the apparent anisotropy of the galaxy distribution in redshift space, caused by the line-of-sight (LOS) component of the galaxies peculiar velocities." Ou laree scales under the linear perturbations regine. the two-point correlation function preseuts a squashine iong the LOS aud correspoudiuglv the power προςται appears euhanced for wavevectors directed along the LOS (Ixaiser1987)..," On large scales, under the linear perturbations regime, the two-point correlation function presents a squashing along the LOS and correspondingly the power spectrum appears enhanced for wavevectors directed along the LOS \citep{1987MNRAS.227....1K}." The anisotropies are governed by the parameter ο) that depends on the growth functiou and galaxy bias., The anisotropies are governed by the parameter $\beta$ that depends on the growth function and galaxy bias. Redshift-space distortious (RSDs) lave been the subject of many analyses. as reviewed in ILuuiltou (1998)..," Redshift-space distortions (RSDs) have been the subject of many analyses, as reviewed in \cite{1998ASSL..231..185H}." Examples of recent studies involving the latest large survevs are the following., Examples of recent studies involving the latest large surveys are the following. The Two-Deeree Field Galaxy Redshift Survey enabled the RSD measurements ou the correlation function (Peacocketal.2001:Tawkinsetal.2003). and power spectrum (Percivaletal.2001).," The Two-Degree Field Galaxy Redshift Survey enabled the RSD measurements on the correlation function \citep{2001Natur.410..169P,2003MNRAS.346...78H} and power spectrum \citep{2004MNRAS.353.1201P}." The Sloan Digital Sky Survey permitted other RSD measurements on the correlation function (Zchavictal. and power spectrum (Teemarketal.2001. 2006).. ," The Sloan Digital Sky Survey permitted other RSD measurements on the correlation function \citep{2005ApJ...621...22Z,2008ApJ...676..889O,2009MNRAS.393.1183C,2009MNRAS.396.1119C} and power spectrum \citep{2004ApJ...606..702T,2006PhRvD..74l3507T}. ." The VIMOS-VLT Deep Survey and the 298LÀCO Survey were used in Cuzzoetal.(2008) for RSD deteriuatious from the correlation function., The VIMOS-VLT Deep Survey and the 2SLAQ Survey were used in \cite{2008Natur.451..541G} for RSD determinations from the correlation function. After this work was subiuitted RSD studies on the WigeleZao aud BOSS catalogs also appeared (Blakeetal.2011:Reid2012).," After this work was submitted RSD studies on the WiggleZ and BOSS catalogs also appeared \citep{2011MNRAS.415.2876B,2012arXiv1203.6641R}." Since the linear theory description starts to be valk ouly at very laree scales. aud lacking a complete mode for general nou linear cosuic fluctuations. au extension of the theoretical description has been attempted to non linear aud quasilinear scales thanks to enmipirica miothods based ou the so-called streaming model (Pechles 1980).. consisting of linear theory aud a couvolution ou the LOS with a velocity distribution.," Since the linear theory description starts to be valid only at very large scales, and lacking a complete model for general non linear cosmic fluctuations, an extension of the theoretical description has been attempted to non linear and quasi-linear scales thanks to empirical methods based on the so-called streaming model \citep{1980lssu.book.....P}, consisting of linear theory and a convolution on the LOS with a velocity distribution." The mode was first adopted ou small scales and highly uou linear reeime to describe the fineers-ofCod (FOC) elongation along the LOS due to random motions of virialize: objects (Jackson1972)., The model was first adopted on small scales and highly non linear regime to describe the fingers-of-God (FOG) elongation along the LOS due to random motions of virialized objects \citep{1972MNRAS.156P...1J}. Also. fitting fuuctious base on simulation results have been used. for iustance. im Tatton&Cole(1999).. Tinkeretal.(2006) and (2007)..," Also, fitting functions based on simulation results have been used, for instance, in \cite{1999MNRAS.310.1137H}, \cite{2006MNRAS.368...85T} and \cite{2007MNRAS.374..477T}." Recently. it was shown by Percival&White(2000) that on quasi-luear scales a streamuue node with a Gaussian velocity dispersion is a eood ecucral fit to the redshift-space power spectruu.," Recently, it was shown by \cite{2009MNRAS.393..297P} that on quasi-linear scales a streaming model with a Gaussian velocity dispersion is a good general fit to the redshift-space power spectrum." The eooduess of the streaming model was also demonstrated lately for exaniple. in Cuzzoetal.(2008).. C'abró&Caztanaga (2009a).. Blakeetal. (2011).. Beutleretal. (2012).. Ablarullictal.(2012) aud Chuang&Wang(2011)..," The goodness of the streaming model was also demonstrated lately, for example, in \cite{2008Natur.451..541G}, \cite{2009MNRAS.393.1183C}, \cite{2011MNRAS.415.2876B}, \cite{2012MNRAS.423.3430B}, \cite{2012arXiv1203.1002M} and \cite{2011arXiv1102.2251C}." We caution that the model breaks down at siuall scales., We caution that the model breaks down at small scales. This happeus even for au unbiased dark matter model (sec. for example. Taruvactal. (2010))) and complex galaxy bias issues niavbe required to be uncer strict control (like shown in Okunura&Jing(2011):ReidWhite (2011))).," This happens even for an unbiased dark matter model (see, for example, \cite{2010PhRvD..82f3522T}) ) and complex galaxy bias issues maybe required to be under strict control (like shown in \cite{2011ApJ...726....5O,2011MNRAS.417.1913R}) )." Also. low modes represeutiug large scales are saluplecd in simulations finite volume boxes melt plav a role (Matsubara2008:Taruvactal.2009).. especially if their effect is of the order of a few percent and in the presence of bias. that might further reduce sampling cficiency.," Also, how modes representing large scales are sampled in simulations finite volume boxes might play a role \citep{2008PhRvD..77f3530M,2009PhRvD..80l3503T}, especially if their effect is of the order of a few percent and in the presence of bias, that might further reduce sampling efficiency." Nonetheless; being aware that there exist in the literature works that claim either a good or nof sogood performance of the streaming model. aud that anyway often use it as benchmark. due to its theoretical siuplicditv and appeal. in this work we will rely on a," Nonetheless, being aware that there exist in the literature works that claim either a good or not sogood performance of the streaming model, and that anyway often use it as benchmark, due to its theoretical simplicity and appeal, in this work we will rely on a" ΛΑΟΙ> Owhenever 2=0 and M;; is positive definite. and therefore P cannot become negative.,"${\rm D}P/{\rm D}t>0$ whenever $P=0$ and $M_{ij}$ is positive definite, and therefore $P$ cannot become negative." According to equation (ΑΕ., According to equation \ref{dqdt}) "full combination of data yields M,«1.31eV, compared with M,«2.34eV when the XLF is not used 1)).","full combination of data yields $\Mnu<1.31\eV$, compared with $\Mnu<2.34\eV$ when the XLF is not used )." Joint constraints on and Qmh? are shown in for a flat cosmology., Joint constraints on and $\Omegam h^2$ are shown in for a flat cosmology. " The strong correlation in this plane is due to the fact that the CMB data constrain directlyZeq;, Which is a degenerate combination of and Qmh?, as discussed previously in2."," The strong correlation in this plane is due to the fact that the CMB data constrain directly, which is a degenerate combination of and $\Omegam h^2$, as discussed previously in." ". The combination of data that we use places tight constraints onQm,, so significant improvement can be obtained by incorporating a direct measurement of the Hubble constant; throughout this section we use a Gaussian prior, h=0.742+0.036, based on the results of(2009)."," The combination of data that we use places tight constraints on, so significant improvement can be obtained by incorporating a direct measurement of the Hubble constant; throughout this section we use a Gaussian prior, $h=0.742 \pm 0.036$, based on the results of." . The constraints thus obtained are listed in2., The constraints thus obtained are listed in. ". We note that, ordinarily, the combination of and CMB dataprovides a tight constraint on Ho2008); however, this is not the case when is free."," We note that, ordinarily, the combination of and CMB dataprovides a tight constraint on $H_0$; however, this is not the case when is free." The reason why can be seen in4., The reason why can be seen in. ". The green contours in the figure show constraints obtained from combining the CMB,feas,, SNIa and BAO data (without a prior on Ho)."," The green contours in the figure show constraints obtained from combining the CMB, SNIa and BAO data (without a prior on $H_0$ )." " A correlation in this plane occurs naturally in the analysis, since X-ray observations of clusters measure a degenerate combination of the cosmic baryon fraction, Ων/Ώνι, and distance."," A correlation in this plane occurs naturally in the analysis, since X-ray observations of clusters measure a degenerate combination of the cosmic baryon fraction, $\Omegab/\Omegam$, and distance." " When is fixed, CMB data place tight constraints on the baryon fraction, though not on the Hubble parameter, and so the combination of CMB and data produces tight constraints on both Ho and Q»/Qm."," When is fixed, CMB data place tight constraints on the baryon fraction, though not on the Hubble parameter, and so the combination of CMB and data produces tight constraints on both $H_0$ and $\Omegab/\Omegam$." " When is free, however, the CMB constraints in this plane are degenerate along nearly the same axis as the and so the inclusion of additional, independent distance measurements is necessary to place a constraint on Ho."," When is free, however, the CMB constraints in this plane are degenerate along nearly the same axis as the and so the inclusion of additional, independent distance measurements is necessary to place a constraint on $H_0$." The combination with a direct measurement of Ho (blue contours) significantly improves matters., The combination with a direct measurement of $H_0$ (blue contours) significantly improves matters. " As shows, the addition of the XLF data improves the constraint on somewhat, from Nes=3.610% to Neg=3.4406 (68.3 per cent confidence)."," As shows, the addition of the XLF data improves the constraint on somewhat, from $\Neff=3.6_{-0.6}^{+0.7}$ to $\Neff=3.4_{-0.5}^{+0.6}$ (68.3 per cent confidence)." " The mechanism for this improvement is a degeneracy between Qu? and og, shown in5,, which the XLF data reduce through their constraint on os."," The mechanism for this improvement is a degeneracy between $\Omegam h^2$ and $\sigma_8$, shown in, which the XLF data reduce through their constraint on $\sigma_8$." " The addition of nuisance parameters in the form of curvature, tensors, and non-zero neutrino mass tends to weaken the constraints on and Ho along their primary degeneracy axis, similarly to what was observed in5."," The addition of nuisance parameters in the form of curvature, tensors, and non-zero neutrino mass tends to weaken the constraints on and $H_0$ along their primary degeneracy axis, similarly to what was observed in." "2.. lists the constraints obtained with and without the Ho prior when various nuisance parameters are marginalized over, as well as when the XLF data are included in the fit."," lists the constraints obtained with and without the $H_0$ prior when various nuisance parameters are marginalized over, as well as when the XLF data are included in the fit." " As the table shows, the inclusion of the prior on Ho effectively eliminates the degeneracies between and the nuisance parameters; in particular, the constraint on obtained whenmarginalizing over curvature, tensors and neutrino mass simultaneously, Neg= 05, is very similar to those obtained when the nuisance parameters are fixed, Noe= 3.670%."," As the table shows, the inclusion of the prior on $H_0$ effectively eliminates the degeneracies between and the nuisance parameters; in particular, the constraint on obtained whenmarginalizing over curvature, tensors and neutrino mass simultaneously, $\Neff=3.7_{-0.8}^{+0.7}$ , is very similar to those obtained when the nuisance parameters are fixed, $\Neff=3.6_{-0.6}^{+0.7}$ ." With so much extra, With so much extra "sub-areminute scales, the statistical error rises due to the intrinsic ellipucity contribution which has a white noise power spectrum (assuming the intrinsic ellipucities are uncorrelated and randomly oriented).","sub-arcminute scales, the statistical error rises due to the intrinsic ellipticity contribution which has a white noise power spectrum (assuming the intrinsic ellipticities are uncorrelated and randomly oriented)." However the statistical errors are roughly constant over the range of scales that provide the cosmological information (100—(« 104)., However the statistical errors are roughly constant over the range of scales that provide the cosmological information $100 < \ell < 10^4$ ). This is useful for setting the permissible level of residual systematics., This is useful for setting the permissible level of residual systematics. One of the main sources of error in the shear estimates comes from the convolution of the image by the point spread function (PSF)., One of the main sources of error in the shear estimates comes from the convolution of the image by the point spread function (PSF). This function is known (albeit noisily) at the positions of the stars in the image., This function is known (albeit noisily) at the positions of the stars in the image. " As the PSF varies across the image, one must interpolate this l'uncton to the positions of the galaxies."," As the PSF varies across the image, one must interpolate this function to the positions of the galaxies." An incorrect model of the PSF leads to an error in the estimated (pre-seeing) galaxy shape and hence in the shear correlation., An incorrect model of the PSF leads to an error in the estimated (pre-seeing) galaxy shape and hence in the shear correlation. " Coherent PSF patterns have non-zero two-point functions, which add to the lensing induced correlations in galaxy ellipticiües."," Coherent PSF patterns have non-zero two-point functions, which add to the lensing induced correlations in galaxy ellipticities." This systematic error can exceed statisücal errors in lensing measurements if the PSF is not modeled sufficiently accurately (Hoekstra2004)., This systematic error can exceed statistical errors in lensing measurements if the PSF is not modeled sufficiently accurately \citep{Ho04}. ". We will not consider here errors due to removal of the PSF from the galaxy shapes if the PSF at the location of the galaxy is known correctly (e.g.Kaiser,Squires,&Broadhurst1995;Kaiser2000:Bacon 2003)."," We will not consider here errors due to removal of the PSF from the galaxy shapes if the PSF at the location of the galaxy is known correctly \citep[e.g.][]{KSB,Ka00,BJ02,RB03}." . We are only concerned here with the estimation of the PSF at each galaxy's location., We are only concerned here with the estimation of the PSF at each galaxy's location. PSF interpolation error has been one of the primary sources of systematic error in most of the lensing measurements published to date (errors in the shear calibration and redshift distribution are the other main sources)., PSF interpolation error has been one of the primary sources of systematic error in most of the lensing measurements published to date (errors in the shear calibration and redshift distribution are the other main sources). Given a model lor PSF anisotropy we can calculate how well the power spectrum would need to be corrected to be well below the statistical errors., Given a model for PSF anisotropy we can calculate how well the power spectrum would need to be corrected to be well below the statistical errors. The stausucal error curves in Figure 1. give a good indication of the upper limit on coherent residual systematic errors if they are not to dominate the error budget., The statistical error curves in Figure \ref{fig:stats} give a good indication of the upper limit on coherent residual systematic errors if they are not to dominate the error budget. " Thus at /1000. or 10 areminute scales, the coherent residual should be well below 0.001 (so that its square is smaller than the statistical error curves)."," Thus at $l\sim 1000$, or 10 arcminute scales, the coherent residual should be well below $0.001$ (so that its square is smaller than the statistical error curves)." Generic models of PSF patterns do not exist; the amplitudes measured in current data (before any corrections) are in the range with varying coherence scales., Generic models of PSF patterns do not exist; the amplitudes measured in current data (before any corrections) are in the range with varying coherence scales. " Telescopes that will be built with lensing as a primary science goal are expected to do better than these, and may have PSF modeling software like TinyTim for HST, but even [or the best-designed telescope, the galaxy shapes will require correction using data on stars."," Telescopes that will be built with lensing as a primary science goal are expected to do better than these, and may have PSF modeling software like TinyTim for HST, but even for the best-designed telescope, the galaxy shapes will require correction using data on stars." In this paper we describe two methods which in combination can remove the systematic elfeets of asymmetric PSFs in large imaging surveys., In this paper we describe two methods which in combination can remove the systematic effects of asymmetric PSFs in large imaging surveys. A method based on a principal component analysis (PCA) of the PSF was the subject of a recent paper (Jarvis&Jain2004)., A method based on a principal component analysis (PCA) of the PSF was the subject of a recent paper \citep{Ja05}. ". Essentially, it detects and models components of the PSF pattern which appear in many dilferent images."," Essentially, it detects and models components of the PSF pattern which appear in many different images." " For example, guiding errors have the same elfect on every stàr in an exposure, so ils pattern is a constant in Gr.7). with a coefficient which varies [rom exposure to exposure."," For example, guiding errors have the same effect on every star in an exposure, so its pattern is a constant in $(x,y)$, with a coefficient which varies from exposure to exposure." The principal component corresponding to this is therefore a constant., The principal component corresponding to this is therefore a constant. " Focus errors are similarly recurring; astigmatism produces a characteristic pattern when the telescope is slightly above locus, and the opposite pattern when below."," Focus errors are similarly recurring; astigmatism produces a characteristic pattern when the telescope is slightly above focus, and the opposite pattern when below." That is. there is a fixed (;r.y) pattern which is modulated by a coefficient for each exposure. (," That is, there is a fixed $(x,y)$ pattern which is modulated by a coefficient for each exposure. (" There may be more than one principal component corresponding to [ocus if the variation is not quite linear as the telescope gets more out of focus.),There may be more than one principal component corresponding to focus if the variation is not quite linear as the telescope gets more out of focus.) " In general, the principal components should model any pattern due to a recurrent physical cause."," In general, the principal components should model any pattern due to a recurrent physical cause." The second method discussed in this paper tackles PSF patters that no not recur in dillerent exposures., The second method discussed in this paper tackles PSF patters that no not recur in different exposures. In, In Ins, In particular chip 2. containing the putative clark lump) show no colour slices for which a.)73.,"particular chip 2, containing the putative dark lump) show no colour slices for which $\sigma_{\rm col}>3$." We do. however. see a Toy=46 detection for the 7ff=2.312 bin in chip 1.," We do, however, see a $\sigma_{\rm col}=3.46$ detection for the $I-H=2.312$ bin in chip 1." This marginal detection corresponds to the sequence visible with colours 0.4 mag redder than the Abell 1942 sequence in Fig. 4.., This marginal detection corresponds to the sequence visible with colours $\sim 0.4$ mag redder than the Abell 1942 sequence in Fig. \ref{fig-colmag}. Phese colours are consistent with those of carly-ἵνρο galaxies at 2=0.5., These colours are consistent with those of early-type galaxies at $z=0.5$. However. when the positions of the 25 ealaxies in this bin are plotted on the sky. they show no obvious clustering and are spread nearly evenly across the four quacrants of chip 1.," However, when the positions of the 25 galaxies in this bin are plotted on the sky, they show no obvious clustering and are spread nearly evenly across the four quadrants of chip 1." They are therefore not likely to be in physical association., They are therefore not likely to be in physical association. Similarly. a slight overdensity is secninthe £df=1.112 and 1.212 bins in chip 2 but these ealaxies show no angular clustering and are not co-located with the dark lump region.," Similarly, a slight overdensity is seen in the $I-H = 1.112$ and $1.212$ bins in chip 2 but these galaxies show no angular clustering and are not co-located with the dark lump region." Erben reported a slight. overdensity of galaxies in their /-band image approximately GO aresec [rom the location of the mass peak ancl close to the X-ray source., Erben reported a slight overdensity of galaxies in their $I$ -band image approximately 60 arcsec from the location of the mass peak and close to the X-ray source. We also detect this marginal concentration in the matched {- and /f-bancl catalogues (Figure 5))., We also detect this marginal concentration in the matched $I$ - and $H$ -band catalogues (Figure \ref{fig-overdensity}) ). However. when we examine the location of those galaxies in this excess region on the colour-magnitude relation. no obvious trend is found.," However, when we examine the location of those galaxies in this excess region on the colour-magnitude relation, no obvious trend is found." Even allowing for field contamination. at most 2-3 galaxics have J4H colours appropriate for a high redshift cluster aud the colour variation from galaxy to galaxy is considerable.," Even allowing for field contamination, at most 2-3 galaxies have $I-H$ colours appropriate for a high redshift cluster and the colour variation from galaxy to galaxy is considerable." Next. we turn our attention to the faintest. //-band objects in the CIRSL imageimage.," Next, we turn our attention to the faintest $H$ -band objects in the CIRSI image." As we showed in $2. the reduced. A-correction in the //-band makes it possible that a distant cluster could be seen in the ΕΙ image but not in the Z-band data (ef," As we showed in $\S$ 2, the reduced $k$ -correction in the $H$ -band makes it possible that a distant cluster could be seen in the CIRSI image but not in the $I$ -band data (c.f." Figure 1)., Figure 1). 1n this case we utilised a SExtractor catalogue based only on the /f-bancl image. foregoing the formal magnitude limit on the assumption that. the magnitude-dependent selection function is positionally invariant across the detectors (Caray ot al.," In this case we utilised a SExtractor catalogue based only on the $H$ -band image, foregoing the formal magnitude limit on the assumption that the magnitude-dependent selection function is positionally invariant across the detectors (Gray et al." 2000)., 2000). Figure 6 shows the location of all the sources that consist of at least 5 connected pixels whose surface brightness lies la above the mean background., Figure 6 shows the location of all the sources that consist of at least 5 connected pixels whose surface brightness lies $\sigma$ above the mean background. Again. the number of sources within an aperture centred on the location of the dark lump deviates by less that le from the mean value determined. for 10. rancomly-placed apertures on the same chip.," Again, the number of sources within an aperture centred on the location of the dark lump deviates by less that $1\sigma$ from the mean value determined for 10 randomly-placed apertures on the same chip." This statement is true both for sources to //=22 and to the catalogue limit. and for apertures of 18 and 36 aresee radii (corresponding to the La and 2a dispersion for the centroid of the Erben et al.," This statement is true both for sources to $H=22$ and to the catalogue limit, and for apertures of 18 and 36 arcsec radii (corresponding to the $1\sigma$ and $2\sigma$ dispersion for the centroid of the Erben et al." mass peak)., mass peak). As shown previously in £2. we expect a significantly stronger signal in the case of even a richness class 11 cluster al 2c].," As shown previously in $\S2$, we expect a significantly stronger signal in the case of even a richness class II cluster at $z\simeq 1$." In conclusion. neither the colour-based nor the Z£-band search. has turned. up a convincing case for any physical association of background sources in the region of the mass peak.," In conclusion, neither the colour-based nor the $H$ -band search has turned up a convincing case for any physical association of background sources in the region of the mass peak." Most importantly. the colours of sources in this region show a wide variation and. to a faint /-limit. no excess is visible.," Most importantly, the colours of sources in this region show a wide variation and, to a faint $H$ -limit, no excess is visible." Lavine discounted. the possibility. of a conventional xkeround. cluster of galaxies. we next attempt to place imits on the Z/-band luminosity associated with the mass »ealk and hence the mass-to-light ratio of the structure which will depends on its (unknown) redshift.," Having discounted the possibility of a conventional background cluster of galaxies, we next attempt to place limits on the $H$ -band luminosity associated with the mass peak and hence the mass-to-light ratio of the structure which will depends on its (unknown) redshift." " We first consider. the area. around. the X-ray. source ocated at à=14389228, 8=3733/11""."," We first consider the area around the X-ray source located at $\alpha=14^{\rm h} 38^{\rm m} 22.8^{\rm s}$, $\delta=3^{\circ} 33\arcmin 11\arcsec$." No obvious infrared. source is found at this location., No obvious infrared source is found at this location. We sum the Ilux of all the non-stellar objects within a radius of 20 arcsec ji are contained in the photometric catalogue described in Section 3. to ff=22., We sum the flux of all the non-stellar objects within a radius of 20 arcsec that are contained in the photometric catalogue described in Section \ref{sec-obs} to $H=22$. Comparing to the tux contained in 26 control apertures distributed on the three non-cluster chips we find the Dux in the aperture containing 10 X-ray source is only 1.46 above the mean., Comparing to the flux contained in 26 control apertures distributed on the three non-cluster chips we find the flux in the aperture containing the X-ray source is only $\sigma$ above the mean. Similarly. we examine the (ux of objects within lI) aresec of the location of the mass concentration.," Similarly, we examine the flux of objects within 50 arcsec of the location of the mass concentration." Again. rere is no significant excess of [ux compared. to ju within control apertures.," Again, there is no significant excess of flux compared to that within control apertures." kept in πα.,kept in mind. Threedimensional simulations of galaxy formation have shown that a galactic halo is built up by nergecrs of preexisting subchuups. rather than bv continuous acerction of smooth eas.," Three–dimensional simulations of galaxy formation have shown that a galactic halo is built up by mergers of pre–existing subclumps, rather than by continuous accretion of smooth gas." At the current resolution of simulations the fraction of the intalline mass in these chumps is ~LO% (e.e@. Yoshida ct al., At the current resolution of simulations the fraction of the infalling mass in these clumps is $\approx 10\%$ (e.g. Yoshida et al. 2000)., 2000). Since the slope of the subclump massfunctiou is ΙΑΛΙxALtS. the simulations might aÀleady lave convereed ou the total clumped mass.," Since the slope of the subclump mass–function is $dN/dM \propto M^{-1.8}$, the simulations might already have converged on the total clumped mass." " Even stronger subchunpine. however. should not effect the overall euergv budget: as long as the eas contracts aud maintains its circular velocity. it has to dissipate the cuerey given im eq. δι,"," Even stronger sub--clumping, however, should not effect the overall energy budget: as long as the gas contracts and maintains its circular velocity, it has to dissipate the energy given in eq. \ref{eq:rad}." Furthermore. the eas in small sub.clumps cau be y.ripped from the iuereiug DM sub.clamps. either by the external UV. background. or bv chump collisions.," Furthermore, the gas in small sub–clumps can be stripped from the merging DM sub–clumps, either by the external UV background, or by clump–clump collisions." The barvous falling iuto the halo are then dispersed iuto re iuferclump medimn aud shockheated. iuplyvius that icr contraction and dissipation closely resenubles the VAnooth accretion scenario.," The baryons falling into the halo are then dispersed into the inter–clump medium and shock–heated, implying that their contraction and dissipation closely resembles the smooth accretion scenario." The strength of the iuterual VArocks are deteriuued by the strezuime velocities. which ποΊσα simulations find to be siguificautlv siinaller than ιο velocity dispersion of the halo.," The strength of the internal shocks are determined by the streaming velocities, which numerical simulations find to be significantly smaller than the velocity dispersion of the halo." As a cousequenece. ie duternal shocks are not likely to heat the gasto eiperatures above Z2:6& 10]. where He! line cooling would start to dominate over Ίσα cooling.," As a consequence, the internal shocks are not likely to heat the gasto temperatures above $T\approx 6\times 10^4$ K, where $^+$ line cooling would start to dominate over $\alpha$ cooling." We have asstuned that the dissipated energy is released πι Ίνα cooling alone., We have assumed that the dissipated energy is released in $\alpha$ cooling alone. Tudeed. for a pure ID]We gas of primordial composition. this is a safe assunuption. since cooling shuts off abruptly below the collisional excitation temperature of Tz 101. However. in the preseuce of molecules auc heavy elements radiative cooling is possible below 10'K. The cooling tine for Ίνα cooling at the of the cooling curve ijs giveu bv faq=OMN2)kpη Agoop where Noum2«810??eresteu? and s is the barvon umber deusityv corresponding to an overdensity of z200 at the time of collapse.," Indeed, for a pure H+He gas of primordial composition, this is a safe assumption, since cooling shuts off abruptly below the collisional excitation temperature of $T\approx 10^4$ K. However, in the presence of molecules and heavy elements, radiative cooling is possible below $10^4$ K. The cooling time for $\alpha$ cooling at the of the cooling curve is given by $t_{\rm cool}= (3/2) n k_{\rm B} T_{\rm vir} / n^2 \Lambda_{\rm cool}$ , where $\Lambda_{\rm cool}\approx 2\times 10^{-22}~{\rm erg~s^{-1}~cm^{3}}$ and $n$ is the baryon number density corresponding to an overdensity of $\approx 200$ at the time of collapse." " We have used Z4 in this expression. rather thau the eas temperatiwe Tox LOA. since it is the former that characterizes the gravitational binding energv that is racdiated away,"," We have used $T_{\rm vir}$ in this expression, rather than the gas temperature $T\approx 10^4$ K, since it is the former that characterizes the gravitational binding energy that is radiated away." We find that the cooling time is hetween 615% of the dynamical time. tay=νπρ for the halos considered here.," We find that the cooling time is between $6-45\%$ of the dynamical time, $t_{\rm dyn}=1/\sqrt{6\pi G\rho}$ for the halos considered here." The requirement that tooo.7fqq then nuüplies that the eas temperature will be near. but somewhat below. the temperature T~0 ΤΙ where the cooling function peaks.," The requirement that $t_{\rm cool}\approx t_{\rm dyn}$ then implies that the gas temperature will be near, but somewhat below, the temperature $T\approx10^{4.1}$ K where the cooling function peaks." " Now consider the cooling of metalenriched οas,", Now consider the cooling of metal–enriched gas. Although non-Lvo cooling is possible at T 10. the cooling function below this temperature drops sharply.," Although $\alpha$ cooling is possible at $T<10^4$ K, the cooling function below this temperature drops sharply." As long asthe inctalicity is Z«0.1Z ... molecular cooling or cooling by atoms heavier than He is at least a factor of zzLOOO less efficieut then cooling via the Lvo peak.," As long asthe metalicity is $Z<0.1 Z_\odot$ , molecular cooling or cooling by atoms heavier than He is at least a factor of $\approx 1000$ less efficient then cooling via the $\alpha$ peak." Since initially the nou-Lya cooling time exceeds the dynamical time by a factor of GO150. and fofxpL7. Lv cooling dominates until the density is cuhanced by a factor of E«10ος10°. or until radial contraction factors of 1560.," Since initially the $\alpha$ cooling time exceeds the dynamical time by a factor of $60-450$, and $t_{\rm cool}/t_{\rm dyn}\propto \rho^{-1/2}$, $\alpha$ cooling dominates until the density is enhanced by a factor of $4\times10^3 - 2\times10^5$, or until radial contraction factors of $15-60$." We therefore conclude that the bulk of the binding energv is likely released iu Lye cooling. uutil the iietalicitv builds up to near-solar levels.," We therefore conclude that the bulk of the binding energy is likely released in $\alpha$ cooling, until the metalicity builds up to near-solar levels." Dust absorption cau strouslv suppress the Ίνα flux escaping from a media that is optically thick to Lya photons: this is thought to be the reason why carly Lya surveys did uot detect protogalaxies (see Pritchet 1991)., Dust absorption can strongly suppress the $\alpha$ flux escaping from a medium that is optically thick to $\alpha$ photons; this is thought to be the reason why early $\alpha$ surveys did not detect proto–galaxies (see Pritchet 1994). " ουσ], however. Lya cutting galaxies have been fouud at highredshift (e.g. Thi et al."," Recently, however, $\alpha$ emitting galaxies have been found at high–redshift (e.g. Hu et al." 1998). as expected i models with lower galactic dust abundance. aud. iuhomogeneous dust distribution (Taian Spaaus 1999).," 1998), as expected in models with lower galactic dust abundance, and inhomogeneous dust distribution (Haiman Spaans 1999)." Furthermore. the dust abundance i the early. spatially extended. collapsing plase of the highredshift halos is likely to be sienificantly lower than inside starforming galaxies.," Furthermore, the dust abundance in the early, spatially extended, collapsing phase of the high–redshift halos is likely to be significantly lower than inside star–forming galaxies." The typical Lya luminosities we derive are ~1005thoresἩν ," The typical $\alpha$ luminosities we derive are $\sim 10^{43-44}~{\rm erg~s^{-1}}$ ." Our halos are expected to be mostly ueutral. and since they are embedded. in the UV. background. they will couvert a fraction x(45 of the incident ionizing radiation to Lya radiation (Could Weinhere 1996).," Our halos are expected to be mostly neutral, and since they are embedded in the UV background, they will convert a fraction $\approx 0.5$ of the incident ionizing radiation to $\alpha$ radiation (Gould Weinberg 1996)." It is interesting to uote that for a UW backeround flux of Ὁx103(heíl3.6oV)beCrestomTeba oj. the resulting Lvo radiation would be at a level of ο10% of our coolingsignal.," It is interesting to note that for a UV background flux of $5\times 10^{-22}~(h\nu/13.6~{\rm eV})^{-1.7}~{\rm erg~s^{-1}~cm^{-2}~Hz^{-1}~sr^{-1}}$ , the resulting $\alpha$ radiation would be at a level of $5-10\%$ of our coolingsignal." Tn addition to the Ίσα flux expected from individual halos. we have computed the coutribution to the extragalactic UV backerouud from halos below the detection threshold. by sununine the flux of these sources.," In addition to the $\alpha$ flux expected from individual halos, we have computed the contribution to the extragalactic UV background from halos below the detection threshold, by summing the flux of these sources." 9a We fud the amplitude for this backeround to be quite 4nall. at the level of =10CRSAL.vvr + for all masses: (2) added aceretion luminosity to the ZAAIS luminosity when estimating disk irradiation: and (3) emploved the moclels (for AL=1001M which is appropriate) to estimate the radius of the accreting protostar.,"effective temperature that sets the accretion rate, so that $\dot{M}_{\star d}\geq 10^{-5.3} \varepsilon M_\odot$ $^{-1}$ for all masses; (2) added accretion luminosity to the ZAMS luminosity when estimating disk irradiation; and (3) employed the models (for $\dot{M}_{\star d} = 10^{-4} M_\odot$ $^{-1}$, which is appropriate) to estimate the radius of the accreting protostar." " Although rather approximate. these amendments are of diminishing importance as AZ,y increases beyond ~20M..."," Although rather approximate, these amendments are of diminishing importance as $M_{\star f}$ increases beyond $\sim 20M_\odot$." Given the expected range of disk. radii. all the disks presented in figure 3. are candidates for Lragmentation.," Given the expected range of disk radii, all the disks presented in figure \ref{frag} are candidates for fragmentation." " The expected disk. radius crosses the fragmentation boundary for AL,= 3.5M.. and the two remain almost equal until Af,pcJOAZ.: fragmentation is marginal in this range."," The expected disk radius crosses the fragmentation boundary for $M_{\star f}\simeq 3.5 M_\odot$ , and the two remain almost equal until $M_{\star f}\simeq 10 M_\odot$; fragmentation is marginal in this range." " Fragmentation becomes increasingly likely as the mass increases. though slowly: Aoi: is within a factor of 2 of Ry lor AM,gp<28BAL.."," Fragmentation becomes increasingly likely as the mass increases, though slowly: $R_{\rm crit}$ is within a factor of 2 of $R_d$ for $M_{\star f} < 23 M_\odot$." " For M,g2 57M... Roy drops below the range of disk radii implied by the dispersion of /; given below equation (25)) αν indicated by the grav region in figure 3.."," For $M_{\star f}> 57M_\odot$ , $R_{\rm crit}$ drops below the range of disk radii implied by the dispersion of $f_j$ given below equation \ref{theta_j_evaluation}) ) – as indicated by the gray region in figure \ref{frag}." Phe specific masses quoted depend on our mocel for angular momentum. particularly as the critical radius is relatively constant in the range 100-150 AU.," The specific masses quoted depend on our model for angular momentum, particularly as the critical radius is relatively constant in the range 100-150 AU." Reeall however. that the disk angular momentuni derives [rom a turbulent velocity field ancl is. therefore quite stochastic.," Recall, however, that the disk angular momentum derives from a turbulent velocity field and is therefore quite stochastic." The spread in j predicted by a Ciaussian mocel for the velocity field allows for the frequent formation of disks. twice as large as predicted. in equation (30))., The spread in $j$ predicted by a Gaussian model for the velocity field allows for the frequent formation of disks twice as large as predicted in equation \ref{Rd_from_Rc}) ). Likewise. much smaller disks (by about a factor of nine) can form equally casily [rom a chance cancellation within the core velocity. field.," Likewise, much smaller disks (by about a factor of nine) can form equally easily from a chance cancellation within the core velocity field." This dispersion in expected radii is indicated. as à shaded: band in figure 3..., This dispersion in expected radii is indicated as a shaded band in figure \ref{frag}. Remember also that we adopted a conservative estimate of the disk angular momentum: otherwise. disk fragmentation would have been even more prevalent.," Remember also that we adopted a conservative estimate of the disk angular momentum; otherwise, disk fragmentation would have been even more prevalent." Taking these points into account. we can craw a few conclusions with relative certainty.," Taking these points into account, we can draw a few conclusions with relative certainty." Up to this point we have adopted s=0.5 as the fiducial accretion elliciencv. following(2003).," Up to this point we have adopted $\varepsilon= 0.5$ as the fiducial accretion efficiency, following." . In the theory of(2000)... 5 is set by the ejection of material by a centrally-collimated protostcllar wind.," In the theory of, $\varepsilon$ is set by the ejection of material by a centrally-collimated protostellar wind." show that © is quite insensitive to the ratio of infall and outflow momentum Iluxes., show that $\varepsilon$ is quite insensitive to the ratio of infall and outflow momentum fluxes. Nevertheless. (0.5 is only an estimate and 2 could well vary during accretion.," Nevertheless, 0.5 is only an estimate and $\varepsilon$ could well vary during accretion." This is especially trueif the protostellar wind were everto truncate aceretion. as 2(f)»O when this happens.," This is especially trueif the protostellar wind were everto truncate accretion, as $\varepsilon(t)\rightarrow 0$ when this happens." We brielly consider other values here., We briefly consider other values here. " The primary ellect of varving z. while fixing M,y. Xa. and &,. is to change the core mass required to make a star of that mass."," The primary effect of varying $\varepsilon$, while fixing $M_{\star f}$, $\Sigma_{\rm cl}$, and $k_\rho$ , is to change the core mass required to make a star of that mass." Suppose we halve z. so that AZ. must double.," Suppose we halve $\varepsilon$, so that $M_c$ must double." " Phe aceretion time then increases. ancl Aly, decreases. bv a factor 214 (for Ay= 3/2)."," The accretion time then increases, and $\dot{M}_{\star d}$ decreases, by a factor $2^{1/4}$ (for $k_\rho=3/2$ )." This mildly stabilizes the disk., This mildly stabilizes the disk. But at the same time. Z2. has been increased by 2/7. 7 has gone up by 277. and. Rap has expanded by 277.2," But at the same time, $R_c$ has been increased by $2^{1/2}$, $j$ has gone up by $2^{3/4}$, and $R_{d,f}$ has expanded by $2^{3/2}$." Balancing these contributions. we expect lowering ο to destabilize the disk.," Balancing these contributions, we expect lowering $\varepsilon$ to destabilize the disk." This was predicted also in equation (35)). where lowering 5 is seen to decrease stability in an active disk.," This was predicted also in equation \ref{Scalings}) ), where lowering $\varepsilon$ is seen to decrease stability in an active disk." Passive disks are extremely insensitive to 2, Passive disks are extremely insensitive to $\varepsilon$. ligure (4)) corroborates our expectation by showing that lower values of 2 correspond to less stable clisks., Figure \ref{diskseff}) ) corroborates our expectation by showing that lower values of $\varepsilon$ correspond to less stable disks. Indeed. the mass at which fragmentationsets in is sensitive to specifically. Aagx5 while the criticalcisk radius is relatively constant.,"Indeed, the mass at which fragmentationsets in is sensitive to $\varepsilon$ , specifically, $M_{\rm crit} \propto\varepsilon^{2.6}$ , while the criticaldisk radius is relatively constant." Does this mean that a decline in core ellicieney over time destabilizes disks?, Does this mean that a decline in core efficiency over time destabilizes disks? Probably not. since," Probably not, since" to choose a more general correction model than the EQS approach.,to choose a more general correction model than the E05 approach. For this purpose. a Q-model (Coleetal.2005)) was used with 6 and Q as free parameters. which seems to be more appropriate for dark energy models with dynamical equation of state.," For this purpose, a Q-model \cite{Cole05}) ) was used with $b$ and $Q$ as free parameters, which seems to be more appropriate for dark energy models with dynamical equation of state." In Fig., In Fig. 2. we illustrate the effect of fast transitions in the correlation function at low redshift by considering three different values for w- and setting wo=—1., \ref{fig:xi} we illustrate the effect of fast transitions in the correlation function at low redshift by considering three different values for $w_+$ and setting $w_-=-1$. " In each plot. the effect of changing the transition epoch (a,) is shown."," In each plot, the effect of changing the transition epoch $a_t$ ) is shown." The remaining cosmological parameters were set to the best values obtained in Ferramacho et al. (, The remaining cosmological parameters were set to the best values obtained in Ferramacho et al. ( 2009) when considering a free but constant value for w.,2009) when considering a free but constant value for $w$. The bias parameter was marginalized over in all the plots for a better comparison of the effects in the overall shape., The bias parameter was marginalized over in all the plots for a better comparison of the effects in the overall shape. Matter fluctuation amplitude. measured by ος. might therefore be different for the different models.," Matter fluctuation amplitude, measured by $\sigma_8$, might therefore be different for the different models." Transitions between woo=-0.2 and we=-] do not change the overall shape of the correlation function. even if we consider transitions at relatively low redshifts.," Transitions between $w_+=-0.2$ and $w_-=-1$ do not change the overall shape of the correlation function, even if we consider transitions at relatively low redshifts." In this case. the predicted matter distribution with the adopted model for dark energy cannot be distinguished from the same distributior obtained with a standard ACDM model.," In this case, the predicted matter distribution with the adopted model for dark energy cannot be distinguished from the same distribution obtained with a standard $\Lambda$ CDM model." However. when we let w— be closer to 0. some interesting effects appear in the predicted correlation function. noticeably at intermediate anc large scales.," However, when we let $w_+$ be closer to $0$, some interesting effects appear in the predicted correlation function, noticeably at intermediate and large scales." We observe then a relative increase of the power at these scales. which boosts the amplitude of the baryonic peak (to a small degree when we=—O.1 and much larger wher Woo- Q) and shifts its position. and furthermore the global shape of the correlation function is modified.," We observe then a relative increase of the power at these scales, which boosts the amplitude of the baryonic peak (to a small degree when $w_+=-0.1$ and much larger when $w_+=0$ ) and shifts its position, and furthermore the global shape of the correlation function is modified." These effects show that the matter distribution is sensitive to fast and strong variations in the dark energy equation of state and provides in principle a good probe to test such models., These effects show that the matter distribution is sensitive to fast and strong variations in the dark energy equation of state and provides in principle a good probe to test such models. Also. in the view of these results changes in the correlation function for these models cannot be fully reproduced with à single geometrical factor. as for instance the A parameter from EOS.," Also, in the view of these results changes in the correlation function for these models cannot be fully reproduced with a single geometrical factor, as for instance the $A$ parameter from E05." So. the full shape of the correlation function (or of the matter power spectrum) must be taken into account when studying models that have an effect on both the correlation function form and the position of the baryonic peak due to other effects than angular diameter distance changes.," So, the full shape of the correlation function (or of the matter power spectrum) must be taken into account when studying models that have an effect on both the correlation function form and the position of the baryonic peak due to other effects than angular diameter distance changes." The precision of the SDSS LRG measurements on the correlation function is not high. but as an example the model with w==—0.1 and a transition redshift fixed at z;=0.5 has a y reduced of 2 in comparison with the concordance model. suggesting that a transition is preferred at Γ c using only the correlation function data.," The precision of the SDSS LRG measurements on the correlation function is not high, but as an example the model with $w_+=-0.1$ and a transition redshift fixed at $z_t=0.5$ has a $\chi^2$ reduced of 2 in comparison with the concordance model, suggesting that a transition is preferred at 1 $\sigma$ using only the correlation function data." That transitions in w at redshifts as high as | could leave an imprint on the correlation function is an interesting issue requiring a further investigation., That transitions in $w$ at redshifts as high as 1 could leave an imprint on the correlation function is an interesting issue requiring a further investigation. Below. we look into the impact on these models of the joint analysis of data from galaxy distribution. CMB anisotropies and SN Ia. Let us start our analysis by taking the case of transitions occurring at a rate typical of the Hubble time.," Below, we look into the impact on these models of the joint analysis of data from galaxy distribution, CMB anisotropies and SN Ia. Let us start our analysis by taking the case of transitions occurring at a rate typical of the Hubble time." As seen above. with Γ~|. the parametrization provided by Eq.," As seen above, with $\Gamma \sim 1$, the parametrization provided by Eq." 8 becomes almost equivalent to the CPL parametrization., \ref{wqz} becomes almost equivalent to the CPL parametrization. It is interesting to compare the effect of considering Γ=|. which fulfills the condition w;(z=0)wy. as requested when deriving the CPL parametrization. and a slightly lower value for Γ like 0.85. which provides a better agreement for the overall shape of the W(z) curve in both parametrizations.," It is interesting to compare the effect of considering $\Gamma=1$, which fulfills the condition $w_t^{'}(z=0)=w_1$, as requested when deriving the CPL parametrization, and a slightly lower value for $\Gamma$ like 0.85, which provides a better agreement for the overall shape of the $w(z)$ curve in both parametrizations." of the neutron superfiuid in the direction perpendicular to za.,of the neutron superfluid in the direction perpendicular to $\vec{\omega}_n$. When BRL (the stroug-drag limut). the second term ou the right-hand side dominates.," When $R\gg 1$ (the strong-drag limit), the second term on the right-hand side dominates." This eutails that the neutron vortices mostly follow the plasima motion., This entails that the neutron vortices mostly follow the plasma motion. When R=x. which is the case on which this paper focuses. the vortices ect piuued to the plasma.," When $R=\infty$, which is the case on which this paper focuses, the vortices get pinned to the plasma." In this limit. the plasina and the neutron superftuid interact exclusively via the MagnusoO force arisingc» from the relative motion between the neutron vortices aud ueutron supoerfiuid.," In this limit, the plasma and the neutron superfluid interact exclusively via the Magnus force arising from the relative motion between the neutron vortices and neutron superfluid." We choose the ibackerouudC» state as follows: 1., We choose the background state as follows: 1. the z-axis 4. is directed along QaQ: 2., the $z$ -axis is directed along $\Omega$; 2. " the neutron vortices are aligned wit[um Q=O., and are at rest in the rotating frame: 3."," the neutron vortices are aligned with $\vec{\Omega}=\Omega \vec{e}_z$, and are at rest in the rotating frame; 3." ? in the sale frame. he plasiua has a background velocity @y= Wyte. which is directed along the vortices: Ll.," in the same frame, the plasma has a background velocity $\vec{w}_0=w_0 \vec{e}_z$ , which is directed along the vortices; 4." the moa- magnetic fick is cirected aloug the vortices. B=Be..," the mean magnetic field is directed along the vortices, $\vec{B}=B \vec{e}_z$." We consider waves which are propagating along the z-axis., We consider waves which are propagating along the z-axis. " We are interested in the waves for which the restoring force is the combination of lvdromaguctic stress. the Coriolis force, aud the Maeuus force."," We are interested in the waves for which the restoring force is the combination of hydromagnetic stress, the Coriolis force, and the Magnus force." " This means that the wave must be nearly incompressible, which impplics Here Aris the wavevector. 06,,, is the neutron/proton velocity perturbation due to the wave."," This means that the wave must be nearly incompressible, which implies Here $\vec{k}$ is the wavevector, $\vec{\delta v}_{n,p}$ is the neutron/proton velocity perturbation due to the wave." Iuconipressibility and assuued homogeneity of the background state imply διup0.," Incompressibility and assumed homogeneity of the background state imply $\delta \psi_{n,p}=0$." " Let us introduce the Lagraugiau displacement vectors £,, of the neutron aud protou fiuids frou their background positions. with àe,,,=D'S."," Let us introduce the Lagrangian displacement vectors $\vec{\xi}_{n,p}$ of the neutron and proton fluids from their background positions, with $\vec{\delta v}_{n,p}=D_t^{n,p}\vec{\xi}_{n,p}$." We are looking for the solutions of theform where σ is the angular frequency of the wave., We are looking for the solutions of theform where $\sigma$ is the angular frequency of the wave. We now perturb Equations (3)). (1)). aud (6)): we set R=x in the latter.," We now perturb Equations \ref{n1}) ), \ref{np}) ), and \ref{mutfr1}) ); we set $R=\infty$ in the latter." " To the linear order in the velocity perturbation. we have: Tere ey,=νBB.(lip,} is the Alfven velocity in the plasina."," To the linear order in the velocity perturbation, we have: Here $c_A=\sqrt{B B_{\rm cr}/(4\pi \rho_p)}$ is the Alfven velocity in the plasma." Substituting these iuto Eqs. (34) , Substituting these into Eqs. \ref{n1}) ) "and (11). aud using V«&—/&«& together with óc,=/o&, and e,=/(a|kweg)&,. we get 2 linear vector equations for ¢, aud &,."," and \ref{np}) ), and using $\nabla\times\vec{\xi}=i\vec{k}\times \vec{\xi}$ together with $\vec{\delta v}_n= i\sigma \vec{\xi}_n$ and $\vec{\delta v}_p=i(\sigma+kw_0) \vec{\xi}_p $, we get 2 linear vector equations for $\vec{\xi}_n$ and $\vec{\xi}_p$." " It is now couveuieut to proceed as follows: Let us represcut a vector b£=£.0,|MUT£46,oy by a complex number 5ὁ=ἐν|/£,.Sy", It is now convenient to proceed as follows: Let us represent a vector $\vec{\xi}=\xi_x \vec{e}_x+\xi_y \vec{e}_y$ by a complex number $\tilde{\xi}=\xi_x+i\xi_y$. Then a vector €;«S© is represented by i£., Then a vector $\vec{e}_z\times \vec{\xi}$ is represented by $i\tilde{\xi}$. By using this. we can immediately rewrite the 2 real vector equations as 2 complex scalar equations: where 0—60|kwg.," By using this, we can immediately rewrite the 2 real vector equations as 2 complex scalar equations: where $\bar{\sigma}=\sigma+kw_0$." This pair of equation viclds inunuediatelv the complex dispersion relation: The dispersion relation for arbitrary R is derived. for completeness. in Appendix A. Iu the nest 2 sections we consider 2 applicatious of the relation Eq. (11)).," This pair of equation yields immediately the complex dispersion relation: The dispersion relation for arbitrary $R$ is derived, for completeness, in Appendix A. In the next 2 sections we consider 2 applications of the relation Eq. \ref{maineq}) )." lu this section we assume that there is no O-directed relative proton-neutrou flow. L0. we assume wy=0.," In this section we assume that there is no $\vec{\Omega}$ -directed relative proton-neutron flow, i.e. we assume $w_0=0$." " We also set om. to zero. since the ratio of the viscous to hvdromaeuetico stress is oCIVCLL Ins With these simplifications. the dispersion relation (11)) elves It is iuiportaut to note that iu this expression e, dis a function of onlv the proton deusity p, (0=BDaf1zp,)."," We also set $\nu_{\rm ee}$ to zero, since the ratio of the viscous to hydromagnetic stress is given by With these simplifications, the dispersion relation \ref{maineq}) ) gives It is important to note that in this expression $c_A$ is a function of only the proton density $\rho_p$ $c_A^2 \equiv B B_{\rm cr}/4\pi \rho_p$ )." All observed maguetars are slowly rotating. with O~ lrad/s. The observed lowest angular frequency for a magnetar ΟΡΟ is IslIz. thus σ~ να. The stu of Magnus and Coriolis forces. represented by the terms with OQ. contribute only a fraction 00/0 to the wave frequency.," All observed magnetars are slowly rotating, with $\Omega\sim 1$ rad/s. The observed lowest angular frequency for a magnetar QPO is $18$ Hz, thus $\sigma \sim 113$ rad/s. The sum of Magnus and Coriolis forces, represented by the terms with $\Omega$ , contribute only a fraction $\delta \sigma/\sigma$ to the wave frequency," which was also observed for the ILC: ammonia component and the hot dense disk observed by Martin-Pintacloetal.(1995).,which was also observed for the HC ammonia component and the hot dense disk observed by \citet{martin-pintado95}. . However. no absorption is observed at the ammonia broad absorption velocity of —50kkms ! which Martín-Pintadoetal.(1993.1995). interpreted as occurring [rom post-shocked elumps.," However, no absorption is observed at the ammonia broad absorption velocity of $-$ $s^{-1}$ which \citet{martin-pintado93,martin-pintado95} interpreted as occurring from post-shocked clumps." Aecordinglv. the ICN absorption most likely originates from the same volume of gas as (he ammonia hot core component and (he dense disk.," Accordingly, the HCN absorption most likely originates from the same volume of gas as the ammonia hot core component and the dense disk." In contrast to the J=38.10.11.12.14. transitions appearing as absorption lines toward the continuum. the /=9 transition is found in emission.," In contrast to the $J=8,10,11,12,13,14$ transitions appearing as absorption lines toward the continuum, the $J=9$ transition is found in emission." Blending with an unknown line cannot be ruled out entirely. but to the best of our knowledge there is no known transition of a different molecule. aud no trace of a =9 absorption (which would modify (he of the blending line) is seen.," Blending with an unknown line cannot be ruled out entirely, but to the best of our knowledge there is no known transition of a different molecule, and no trace of a $J=9$ absorption (which would modify the emission-profile of the blending line) is seen." Moreover. the (blueshifted) velocity ancl the line width correspond well to the velocities and linewidths of the J=8.10.11.12.13.14 transitions.," Moreover, the (blueshifted) velocity and the line width correspond well to the velocities and linewidths of the $J=8,10,11,12,13,14$ transitions." In parücular the linewidth argument is compelling. since other emission lines are much broader tthe linewidth of the HIIC-N. J=21—20 transition is 27 km |. 1992)).," In particular the linewidth argument is compelling, since other emission lines are much broader the linewidth of the $_7$ N $J=21-20$ transition is 27 km $^{-1}$, \citealp{mar92}) )." These facts suggest that the /=9 (ransilion is a weak maser amplilvine the continuum., These facts suggest that the $J=9$ transition is a weak maser amplifying the continuum. Its optical depth has a dillerent sign. but is similar in value to the absorption lines.," Its optical depth has a different sign, but is similar in value to the absorption lines." Tlow can this maser be understood?, How can this maser be understood? A quantitative analvsis would require quite detailed modeling of the pumping mechanism. which is not feasible because many of the transition rates (in particular collision rales between. vibrational states and within the vibrationally excited state) are not or only poorly known.," A quantitative analysis would require quite detailed modeling of the pumping mechanism, which is not feasible because many of the transition rates (in particular collision rates between vibrational states and within the vibrationally excited state) are not or only poorly known." However. one can argue as follows that this óransitlion is easily perturbed or inverted: The splitting due to (-tvpe doubling is much smaller than the rotational splitting.," However, one can argue as follows that this transition is easily perturbed or inverted: The splitting due to $\ell$ -type doubling is much smaller than the rotational splitting." Considering (he rotational level svstem /—8. J=9 and assuming that the excitation temperature of the J=9e—8e is ο. while the excitation temperature for the f. (upper) states is taken to be TAPS!=TO*4AT (with AT«T? ). one can show that inversion oceurs (777< 0) if the following condition 1s niet: In terms of occupation mumbers. a dillerence AT = means that [or an excitation temperature of 560 Ix. the occupation of the J=Of level needs to be elevated in population bv only with respect to a completely thermalized distribution to invert the direct (-0vpe transition.," Considering the rotational level system $J=8$, $J=9$ and assuming that the excitation temperature of the $J=9e-8e$ is $T_{\rm ex}^{9e,8e}$ (and equal to $T_{\rm ex}^{8f,8e}$ ), while the excitation temperature for the $f$ (upper) states is taken to be $T_{\rm ex}^{9f,8f} = T_{\rm ex}^{9e,8e} + \Delta T$ (with $\Delta T \ll T_{\rm ex}^{9e,8e}$ ), one can show that inversion occurs $T_{\rm ex}^{9f,9e} < 0$ ) if the following condition is met: In terms of occupation numbers, a difference $\Delta T$ = means that for an excitation temperature of 560 K, the occupation of the $J=9f$ level needs to be elevated in population by only with respect to a completely thermalized distribution to invert the direct $\ell$ -type transition." If one considers the populations relative to the vibrational ground state. similar argumentis can be made.," If one considers the populations relative to the vibrational ground state, similar arguments can be made." A similar svstem is the ammonia molecule. where the inversion," A similar system is the ammonia molecule, where the inversion" in particular. which may affect the brightness (and to a lesser extent the IR colors) of the sources.,"in particular, which may affect the brightness (and to a lesser extent the IR colors) of the sources." Depending on the typical disk flaring angles. which are enhanced by the UV radiation within the HII region (Robbertoetal.2002). the sample of edge-on disks may be relevant.," Depending on the typical disk flaring angles, which are enhanced by the UV radiation within the HII region \citep{Robberto02} the sample of edge-on disks may be relevant." We shall assume that they still represent a small contamination. since they tend to move the sources beyond our 2115 limit for cluster membership.," We shall assume that they still represent a small contamination, since they tend to move the sources beyond our 15 limit for cluster membership." Probably more important ts the fact. also found by R1O. that ~11% of the point-like sources in the ISPI catalog do not show NIR colors compatible with reddened photospherie. colors.," Probably more important is the fact, also found by R10, that $\sim$ of the point-like sources in the ISPI catalog do not show NIR colors compatible with reddened photospheric colors." Their position in the )) diagram ts compatible with the reddened CTTSs locus introduced by Meyeretal.(1997) reffig:dereddening)). ttheir photometry is indicative of strong excess emission fromcircumstellar disks.," Their position in the ) diagram is compatible with the reddened CTTSs locus introduced by \citet{Meyer97} ), their photometry is indicative of strong excess emission fromcircumstellar disks." Following Meyer(1996).. we split our candidate members sample in two subgroups.," Following \citet{Mey96}, we split our candidate members sample in two subgroups." Η the observed colors are compatible with reddened CTTSs colors. then we deredden the observed colors taking the CTTSs locus as reference.," If the observed colors are compatible with reddened CTTSs colors, then we deredden the observed colors taking the CTTSs locus as reference." Otherwise. in order to minimize the effects of eventual NIR excesses from circumstellar disks. we deredden our sources in the H)) diagram taking the 2 Myr old isochrone shown by RIO as the reference locus.," Otherwise, in order to minimize the effects of eventual NIR excesses from circumstellar disks, we deredden our sources in the ) diagram taking the 2 Myr old isochrone shown by R10 as the reference locus." In both cases. our dereddening algorithm moves the observed photometry to the reference locus (either the CTTSs locus or the isochrone) along the reddening direction. computed using the Cardellietal.(1989) reddening law.," In both cases, our dereddening algorithm moves the observed photometry to the reference locus (either the CTTSs locus or the isochrone) along the reddening direction, computed using the \citet{Cardelli00} reddening law." Figure graphically shows our dereddening algorithm., Figure graphically shows our dereddening algorithm. The set of Ay estimates is then locally averaged following the same strategy described in Sect., The set of $_V$ estimates is then locally averaged following the same strategy described in Sect. "??.. In this case. we adopt a maximum angular resolution of 1.500 pixels (~7.5"")) to allow our algorithm to find a good number of cluster members in the outskirts of the Nebula. where the surface density of stars is generally low (see Fig. 2))."," In this case, we adopt a maximum angular resolution of 1,500 pixels $\sim$ ) to allow our algorithm to find a good number of cluster members in the outskirts of the Nebula, where the surface density of stars is generally low (see Fig. )." The resulting extinction map. with the associated error map. are shown in Fig.," The resulting extinction map, with the associated error map, are shown in Fig." 6. We find that in the direction of the Trapezium cluster the ON extinction 1s generally Ay <3. with a clear increase (Ay 26) in correspondence of the dark ridge along the north-east edge of the HII region. which ts therefore a foreground structure.," We find that in the direction of the Trapezium cluster the ON extinction is generally $A_V\lesssim$ 3, with a clear increase $A_V\gtrsim$ 6) in correspondence of the dark ridge along the north-east edge of the HII region, which is therefore a foreground structure." The ridge is part of a larger bow-shaped feature extending from the east to the north of the ON., The ridge is part of a larger bow-shaped feature extending from the east to the north of the ON. These findings are fully consistent with the map derived by O'Dell&Yusef-Zadeh(2000) combining radio and optical measurements over an area 360425” wwide around 6! Ori-C. Alongside with the previous studies illustrated in Sect.?," These findings are fully consistent with the map derived by \citet{odell2000} combining radio and optical measurements over an area $\times$ wide around $\theta^1$ Ori-C. Alongside with the previous studies illustrated in Sect.," ?.. our map (Fig. 4), our map (Fig. ) ) shows that the OMC-1 surface density generally increases towards the Trapezium., shows that the OMC-1 surface density generally increases towards the Trapezium. In particular. we find that the Trapezium cluster is located in front of a region (Ayz30) extending ~ tto the north of 6! Ori-C. This region is delimited to the side by a sharp edge: the optical thickness of the OMC-I decreases steeply by ~20 magnitudes in a few areminutes.," In particular, we find that the Trapezium cluster is located in front of a region $A_V\gtrsim30$ ) extending $\sim$ to the north of $\theta^1$ Ori-C. This region is delimited to the south-east side by a sharp edge: the optical thickness of the OMC-1 decreases steeply by $\sim$ 20 magnitudes in a few arcminutes." This edge corresponds to the Orton Bar. the bright feature directly discernible in the ISPI image (right panel in Fig. 4)).," This edge corresponds to the Orion Bar, the bright feature directly discernible in the ISPI image (right panel in Fig. )." The steep drop of extinction can be confirmed even by a direct inspection of the Images., The steep drop of extinction can be confirmed even by a direct inspection of the images. It is quite evident that the density of faint and red stars suddenly increases to the south of the Orion Bar., It is quite evident that the density of faint and red stars suddenly increases to the south of the Orion Bar. A similar extinction drop is found also to the north-eastern edge of the extinction peak. in correspondence of the dark structure. known as the Dark Bay or Fish Mouth. seen in absorption in the optical images of the ON.," A similar extinction drop is found also to the north-eastern edge of the extinction peak, in correspondence of the dark structure, known as the Dark Bay or Fish Mouth, seen in absorption in the optical images of the ON." Elsewhere. the extinction smoothly decreases down to Ay>4 with increasing distance from the Trapezium cluster.," Elsewhere, the extinction smoothly decreases down to $A_V\gtrsim4$ with increasing distance from the Trapezium cluster." On larger scales. the OMC-1 extinctior map shows a north-south pattern.," On larger scales, the OMC-1 extinction map shows a north-south pattern." The elongated extinction ridge ts distributed over the full extent of the survey. reaching the OMC-2/3 star forming region to the north of the ONC (Peterson&Megeath2008).," The elongated extinction ridge is distributed over the full extent of the survey, reaching the OMC-2/3 star forming region to the north of the ONC \citep{Peterson2008}." . The extinction map thus follows the dense filament traced by the molecular column density data of Goldsmithetal.(1907). , The extinction map thus follows the dense filament traced by the molecular column density data of \citet{gold97}. . To compare our extinction map with the one of SFD98. we degrade our spatial resolution down to their value.," To compare our extinction map with the one of SFD98, we degrade our spatial resolution down to their value." " The pixel-by-pixel ratio ri,=ΑνFD)/AyCUSPJ) is plotted in Fig.", The pixel-by-pixel ratio $r_{A_{V}}=A_V(SFD)/A_V(ISPI)$ is plotted in Fig. as a function of AyUSΡΟ., as a function of $A_V(ISPI)$. For low extinction values. the SFD98 values generally overestimate the extinction by a factor of 1.5—2. consistently with what found by Arce&Goodman(1999).," For low extinction values, the SFD98 values generally overestimate the extinction by a factor of 1.5--2, consistently with what found by \citet{Arce99}." ", Moreover. consistently with Dobashietal.(2005).. the SFD98 values are systematically larger than ours. the ratio increasing in the 3€ry,x5 range with the Ay(/SPI) extinction."," Moreover, consistently with \citet{dobashi05}, the SFD98 values are systematically larger than ours, the ratio increasing in the $3\lesssim r_{A_{V}}\lesssim5$ range with the $A_V(ISPI)$ extinction." This is indicative of the fact that SFD98 map is not accurate either in high extinction regions or in regions with high extinction gradients., This is indicative of the fact that SFD98 map is not accurate either in high extinction regions or in regions with high extinction gradients. As proposed in the 3-D model of the ON by O'Dellet (2009).. the boundary between the HII region and the bulk of the neutral matter is made up by a geometrically thin anc optically thick shell swept up by stellar winds.," As proposed in the 3-D model of the ON by \citet{ODell2009}, the boundary between the HII region and the bulk of the neutral matter is made up by a geometrically thin and optically thick shell swept up by stellar winds." Given this model. we argue that the extinction in the Dark Bay directior and the broad feature around it are spatially correlated. the former being a clump of high column density gas inside the remnant of the neutral shell located between the observer anc the Trapezium (seeFig.4inODelletal.2009).," Given this model, we argue that the extinction in the Dark Bay direction and the broad feature around it are spatially correlated, the former being a clump of high column density gas inside the remnant of the neutral shell located between the observer and the Trapezium \citep[see Fig.~4 in][]{ODell2009}." . On larger scales. the ON isnever thinner than Ay ~2 and this is compatible with the presence of a foreground neutral veil (ΟDelletal.2009).," On larger scales, the ON isnever thinner than $A_V\sim$ 2 and this is compatible with the presence of a foreground neutral veil \citep{ODell2009}." . Furthermore. a north-south pattern is evident. similarly to what is found for the OMC-1 extinctior map reffig:buildavmap)).," Furthermore, a north-south pattern is evident, similarly to what is found for the OMC-1 extinction map )." This pattern roughly follows the elongation of the ONC observed by Hillenbrand& (1998).. indicating that the cluster is still partially embedded in the OMC-1.," This pattern roughly follows the north-south elongation of the ONC observed by \citet{HillenbrandHartmann1998}, , indicating that the cluster is still partially embedded in the OMC-1." As pointed out by Hartmann& (2007).. this suggest that it might be better to view," As pointed out by \citet{HartmannBurkert2007}, , this suggest that it might be better to view" "Motivated by the scalings discussed in (he previous section. we focus on subsonic. compact vorlices that have horizontal extent A, comparable to the vertical scale height IH. which is much smaller than the distance r to the protostar: ΑΠ~e/o<1 and AfreeofBo«1.","Motivated by the scalings discussed in the previous section, we focus on subsonic, compact vortices that have horizontal extent $\Lambda_r$ comparable to the vertical scale height $H$, which is much smaller than the distance $r$ to the protostar: $\Lambda_r/H\sim\epsilon/Ro\lesssim1$ and $\Lambda_r/r\sim\epsilon\delta/Ro\ll 1$." This allows us to make (wo kev approximations to the hvdrodynamics., This allows us to make two key approximations to the hydrodynamics. The first simplification we make is the Cartesian approximation (Goldreich 1965): we simulate the hydrodynamics only within a small patch of the disk that co-rotates with the gas at some fiducial radius 7j.," The first simplification we make is the Cartesian approximation \citep{goldreich65b}: we simulate the hydrodynamics only within a small patch of the disk $(\Delta r\ll r_0,\Delta\phi\ll 2\pi)$ that co-rotates with the gas at some fiducial radius $r_0$." We map this pateh of the disk onto a Cartesian grid: r—ry4. ro(ó—69)y. z—£0; —90. 0sSy. and re—d.," We map this patch of the disk onto a Cartesian grid: $r-r_0 \rightarrow x$, $r_0(\phi - \phi_0) \rightarrow y$, $z\rightarrow z$, $v_r \rightarrow v_x$, $v_{\phi} \rightarrow v_y$, and $v_z\rightarrow v_z$." The background shear and mean thermodynamic variables have radial gradients that vary on the length scale Ár which is much larger than the characteristic size of a subsonic vortex., The background shear and mean thermodynamic variables have radial gradients that vary on the length scale $r$ which is much larger than the characteristic size of a subsonic vortex. " For example. let 4 represent anv background disk variable: then the variation 98 over the size of a vortex is: 0q/q~(OlInq/Or)A.eA,/r«1."," For example, let $\bar{q}$ represent any background disk variable; then the variation $\delta\bar{q}$ over the size of a vortex is: $\delta\bar{q}/\bar{q} \sim (\partial\ln\bar{q}/\partial r)\Lambda_r\sim \Lambda_r/r\ll 1$." This allows us to neglect radial eradients of (he mean thermodynamic variables and to linearize the Ixeplerian shear Low., This allows us to neglect radial gradients of the mean thermodynamic variables and to linearize the Keplerian shear flow. The (me-independent. axisvuunetric base Keplerian flow in the rotating frame. which we denote wilh overbars. is then: where T. p. p. Save (he mean temperature. density. pressure. and entropy. respectively. which depend only on the vertical coordinate z.," The time-independent, axisymmetric base Keplerian flow in the rotating frame, which we denote with overbars, is then: where $\bar{T}$, $\bar{\rho}$ , $\bar{p}$ , $\bar{s}$ are the mean temperature, density, pressure, and entropy, respectively, which depend only on the vertical coordinate $z$." We have defined: O4=On(0). pi=pyRT. lig=RIO. and R is the gas constant.," We have defined: $\Omega_0\equiv\Omega_K(r_0)$, $p_0\equiv\rho_0\mathcal{R}T_0$, $H_0^2\equiv\mathcal{R}T_0/\Omega_0^2$, and $\mathcal{R}$ is the gas constant." The errors in making this Cartesian approximation are oL order O(ed.07).," The errors in making this Cartesian approximation are of order $\mathcal{O}(\epsilon\delta,\delta^2)$." Note that neglecting radial gradients of the background disk properties effectively filters out Rossby waves (which require a gradient in the background vorticity) ancl large-scale baroclinic instabilities., Note that neglecting radial gradients of the background disk properties effectively filters out Rossby waves (which require a gradient in the background vorticity) and large-scale baroclinic instabilities. Our rationale for (his is that if there were indeed large-scale baroclinic instabilities. (aev would produce large. supersonic vortices which would rapidly decay [rom radiation of acoustic waves aud shocks.," Our rationale for this is that if there were indeed large-scale baroclinic instabilities, they would produce large, supersonic vortices which would rapidly decay from radiation of acoustic waves and shocks." The second simplification we make is the anelastic approximation: all variables are expandedin powersof the Mach munber v=εν+0) +... p=ερ..., The second simplification we make is the anelastic approximation: all variables are expandedin powersof the Mach number $\mathbf{v} = \epsilon(\mathbf{\bar{v}} + \mathbf{\tilde{v}}) + ...\;$ ; $p=\bar{p} + \epsilon^2\tilde{p} + ...\;$ ; "ellipses, determined by the assumed kinematical parameters.","ellipses, determined by the assumed kinematical parameters." " For the vertical distribution, we assumed an exponential profile exp(—z/h,), with h,=200 pc."," For the vertical distribution, we assumed an exponential profile $\exp(-z/h_{z})$, with $h_{z} = 200$ pc." " For the gas velocity dispersion, we used oy;=8 km s! over the entire disk."," For the gas velocity dispersion, we used $\sigma_{\rm{\hi }} = 8$ km $^{-1}$ over the entire disk." The models are almost indistinguishable for differences in σῃι of +4 km s'., The models are almost indistinguishable for differences in $\sigma_{\rm{\hi }}$ of $\pm 4$ km $^{-1}$. " All the models were smoothed to the spatial resolution of the observations, thus they also reproduce beam-smearing effects."," All the models were smoothed to the spatial resolution of the observations, thus they also reproduce beam-smearing effects." " In figure 5,, we compare position-velocity diagrams from the models and the data."," In figure \ref{fig:pvModels}, we compare position-velocity diagrams from the models and the data." " For NGC 7589, we took a slice through the datacubes along a position angle of 305°."," For NGC 7589, we took a slice through the datacubes along a position angle of $305^{\circ}$." This is a mean value between our result of 307?.7 and that of 302? by ?.., This is a mean value between our result of $307^{\circ}.7$ and that of $302^{\circ}$ by \citet{Pickering1997}. " For Malin 1, we took slice along a position angle of 35°."," For Malin 1, we took a slice along a position angle of $35^{\circ}$." This is a mean value for thea major axis., This is a mean value for the major axis. " For both galaxies, the observed datacubes (left panels of figure 5)) show the presence of emission at high rotational velocities near the galaxy centre (κ€ 20"")."," For both galaxies, the observed datacubes (left panels of figure \ref{fig:pvModels}) ) show the presence of emission at high rotational velocities near the galaxy centre $R \lesssim 20''$ )." " The “slowly rising curve"" models (right panels) do not reproduce such emission, as the is spread from low rotational velocities near the centre to high rotational velocities at large radii."," The “slowly rising curve” models (right panels) do not reproduce such emission, as the is spread from low rotational velocities near the centre to high rotational velocities at large radii." " On the contrary, in the ""steeply rising curve"" models (middle panels) the emission is concentrated at high rotational velocities, as seen in the data."," On the contrary, in the “steeply rising curve” models (middle panels) the emission is concentrated at high rotational velocities, as seen in the data." Both models show tails of emission toward the systemic velocity due to beam-smearing effects., Both models show tails of emission toward the systemic velocity due to beam-smearing effects. " Overall, the observed data are reproduced better by the ""steeply rising curve"" models based on our new results than by the “slowly rising curve"" models based on those by ?.."," Overall, the observed data are reproduced better by the “steeply rising curve” models based on our new results than by the “slowly rising curve” models based on those by \citet{Pickering1997}." " We also note that the ""slowly rising curve"" model of NGC 7589 at large radii (R z 50"") exhibits emission at rotational velocities higher than those observed.", We also note that the “slowly rising curve” model of NGC 7589 at large radii (R $\gtrsim 50''$ ) exhibits emission at rotational velocities higher than those observed. This demonstrates that the rotation curve by ? is over-estimated in the outer regions., This demonstrates that the rotation curve by \citet{Pickering1997} is over-estimated in the outer regions. The steeply rising rotation curves found for Malin 1 and NGC 7589 suggest that GLSB galaxies have a dynamical behaviour more similar to a HSB than to a LSB galaxy., The steeply rising rotation curves found for Malin 1 and NGC 7589 suggest that GLSB galaxies have a dynamical behaviour more similar to a HSB than to a LSB galaxy. " To determine the relative contributions of luminous (gas and stars) and dark matter to the gravitational potential, we built mass models following ?.."," To determine the relative contributions of luminous (gas and stars) and dark matter to the gravitational potential, we built mass models following \citet{Begeman1987}." The contribution of the gaseous disk was computed using the surface density profiles derived from the total maps (figure 6))., The contribution of the gaseous disk was computed using the surface density profiles derived from the total maps (figure \ref{fig:HIprofile}) ). These were multiplied by a factor (1--z) to correct for cosmological dimming and by a factor 1.4 to take into account the presence of Helium., These were multiplied by a factor $(1+z)^{4}$ to correct for cosmological dimming and by a factor 1.4 to take into account the presence of Helium. Molecular and ionized gas were not explicitly considered in the mass model., Molecular and ionized gas were not explicitly considered in the mass model. " However,"," However," To determine the size of the region. within which the source.plusbackground counts are extracted we adopt the empirical method. described. by Nandra et al. (,To determine the size of the region within which the source–plus–background counts are extracted we adopt the empirical method described by Nandra et al. ( 2002).,2002). Tests are performed. in. which the radius of the circular aperture within which the source.plusbackground. counts are summed. varies (from one trial to the next) between lSaarcsec., Tests are performed in which the radius of the circular aperture within which the source–plus–background counts are summed varies (from one trial to the next) between arcsec. We find that a radius of 12aaresec. maximises the significance of the stacked signal and hence this optimal extraction radius is adopted for the analysis that follows., We find that a radius of arcsec maximises the significance of the stacked signal and hence this optimal extraction radius is adopted for the analysis that follows. This extraction radius is about 3 times the on-axis LIWILAL of the PSE (Llasinger ct al., This extraction radius is about 3 times the on-axis HWHM of the PSF (Hasinger et al. 2001)., 2001). We also note that the visible disk of a \lilky Way type galaxy at z=0.1 subtencs an angular radius of zz Saaresce., We also note that the visible disk of a Milky Way type galaxy at z=0.1 subtends an angular radius of $\approx8$ arcsec. To assess the significance of the stacked. signal we estimate the background. by averaging the counts in 60 l2aaresce apertures randomly positioned. within annular regions centered on the positions of the sample. galaxies with inner and outer radii of 20 and aarcsec respectively., To assess the significance of the stacked signal we estimate the background by averaging the counts in 60 arcsec apertures randomly positioned within annular regions centered on the positions of the sample galaxies with inner and outer radii of 20 and arcsec respectively. Yo avoid. contamination from X-ray detections. in the background. estimation. regions close to X-ray sources (840 aaresce) are excluded.," To avoid contamination from X-ray detections in the background estimation, regions close to X-ray sources $8-40$ arcsec) are excluded." Phe smooth background. map produced by the task of CLAO was also used to estimate the background., The smooth background map produced by the task of CIAO was also used to estimate the background. Although no significant differences are found. the background. estimated in the latter case is systematically lower and hence. the detection significance of the stacked signal is somewhat higher.," Although no significant differences are found, the background estimated in the latter case is systematically lower and hence, the detection significance of the stacked signal is somewhat higher." We adopt a conservative approach and estimate the background. from the science image rather than the smooth-— background map., We adopt a conservative approach and estimate the background from the science image rather than the smooth background map. However. it should be noted that use ofthe background map does not alter any of the conclusions.," However, it should be noted that use of the background map does not alter any of the conclusions." " In practice. 2dEGIU galaxies associated. (« Saarescc) with X-rav sources detected in the total kkeV) band above the false probability threshold. of 10."" are excluded from the stacking analvsis."," In practice, 2dFGRS galaxies associated $<8$ arcsec) with X-ray sources detected in the total keV) band above the false probability threshold of $10^{-5}$ are excluded from the stacking analysis." As already discussed. in the previous section this detection limit. corresponds to a soft band. kkeV) detection threshold. of about te which translates to a tvpical on-axis point source [Dux of f(0.52keV)zm410Perestem ," As already discussed in the previous section this detection limit corresponds to a soft band keV) detection threshold of about $4\sigma$ which translates to a typical on-axis point source flux of $f\rm (0.5-2\,keV)\approx4\times10^{-15}\rm\, erg\, s^{-1}\, cm^{-2}$ ." Such a low detection threshold. is essential to study the mean properties of X-pav weak sources. the signal of which would. otherwise be diluted by brighter ones.," Such a low detection threshold is essential to study the mean properties of X-ray weak sources, the signal of which would otherwise be diluted by brighter ones." X-ray detected 2dPGIUS galaxies may cdiller in their nature from X-rav [aint galaxies., X-ray detected 2dFGRS galaxies may differ in their nature from X-ray faint galaxies. lt is clear that summing counts of different classes of objects is meaningless., It is clear that summing counts of different classes of objects is meaningless. We lind a total of 7 2dCRS galaxies associated (< Saarescc) with X-ray. detections above the total band. kkeV) alse probability. threshold of 10.7., We find a total of 7 2dFGRS galaxies associated $<8$ arcsec) with X-ray detections above the total band keV) false probability threshold of $10^{-5}$. Two of them exhibit clear evidence for ACN activity such as broad emission ine optical spectra. high X-rav.tooptical luminosity ratios (Lx/Lg>1) and X-ray luminosities Lxzm107ergs," Two of them exhibit clear evidence for AGN activity such as broad emission line optical spectra, high X-ray–to–optical luminosity ratios $L_X/L_B>-1$ ) and X-ray luminosities $L_X\approx10^{42}\,\rm erg\,s^{-1}$." Another three 2dEGIUS galaxies have narrow emission line optical spectra. Lx/Lg&1. relatively hard X-ray spectral »operties and soft band. kkeV) X-ray. [uminosities in he range 0.3.5.10eres!.," Another three 2dFGRS galaxies have narrow emission line optical spectra, $L_X/L_B\approx-1$ , relatively hard X-ray spectral properties and soft band keV) X-ray luminosities in the range $0.3-5 \times 10^{42} \,\rm erg\,s^{-1}$." Phe evidence above suggests obscured or weak GN. activity., The evidence above suggests obscured or weak AGN activity. " Finally two 2dGIU ealaxies have optical spectra exhibiting both absorption ancl narrow emission lines. Lyflee2. soft X-ray spectra and Lxm2510Hergs suggesting either ""normal galaxies or LLAGNs."," Finally two 2dFGRS galaxies have optical spectra exhibiting both absorption and narrow emission lines, $L_X/L_B\approx-2$, soft X-ray spectra and $L_X\approx2 \times 10^{41}\,\rm erg\,s^{-1}$, suggesting either `normal' galaxies or LLAGNs." Detailed. analysis of these galaxies. will be oesented in a forthcoming paper (Ceorgakakis et al., Detailed analysis of these galaxies will be presented in a forthcoming paper (Georgakakis et al. in reparation)., in preparation). Finally. counts associated with the wings of the PSE of xight X-ray sources might erroneously increase the stacking signal significance.," Finally, counts associated with the wings of the PSF of bright X-ray sources might erroneously increase the stacking signal significance." Therefore. to avoid. contamination of he stacking signal from nearby X-ray sources we have excluded from the analysis 2dEGIUS galaxies that [ie close (κ:40 aarcsec) to N-rayv detections (total of 21).," Therefore, to avoid contamination of the stacking signal from nearby X-ray sources we have excluded from the analysis 2dFGRS galaxies that lie close $<40$ arcsec) to X-ray detections (total of 21)." Therelore. a total of 28 2dEBRGS sources either lie close to (21: 8dO aaresee) or are associated with (total of 7: «Saaresec) X-ray detections.," Therefore, a total of 28 2dFRGS sources either lie close to (21; $8-40$ arcsec) or are associated with (total of 7; $<8$ arcsec) X-ray detections." Εις reduces the number of galaxies used in the stacking analysis to LOS., This reduces the number of galaxies used in the stacking analysis to 198. The stacking results for the 2dEGIU galaxies. are summzarised in Table 3.., The stacking results for the 2dFGRS galaxies are summarised in Table \ref{stacking_tbl}. The X-ray [lux in this table is estimated. from the raw net counts after. correcting individual galaxies for (1) the elect of vignetting estimated rom the corresponding exposure map and (ii) the energy raction outside the adopted aperture of aaresec using the encircled. energy. corrections recently derived. by Chizzarei (2001a. 2001b) for both the PN and the MOS detectors (sce section ??)).," The X-ray flux in this table is estimated from the raw net counts after correcting individual galaxies for (i) the effect of vignetting estimated from the corresponding exposure map and (ii) the energy fraction outside the adopted aperture of arcsec using the encircled energy corrections recently derived by Ghizzardi (2001a, 2001b) for both the PN and the MOS detectors (see section \ref{obs}) )." The countsto[Iux conversion factor has oen derived: assuming a power-law with spectral index P=L7 and Galactic absorption (see section ??))., The counts–to–flux conversion factor has been derived assuming a power-law with spectral index $\Gamma=1.7$ and Galactic absorption (see section \ref{obs}) ). The X-ray uminosities in Fable 3. are estimated using the X-ray. [lux derived from the stacking analysis and the mean redshift of cach subsample also listed in this table., The X-ray luminosities in Table \ref{stacking_tbl} are estimated using the X-ray flux derived from the stacking analysis and the mean redshift of each subsample also listed in this table. The soft-band vields a statistically significant signal for both the whole sample and for the I2/8S0 and spiral galaxy sub-sanmples., The soft-band yields a statistically significant signal for both the whole sample and for the E/S0 and spiral galaxy sub-samples. On the contrary stacking of the hard. bane counts did not result in a significant signal for either of the samples., On the contrary stacking of the hard band counts did not result in a significant signal for either of the samples. For the kkeV. band 3e upper limits are estimated assuming Poisson statistics for the backgrounc stacked. counts., For the keV band $3\sigma$ upper limits are estimated assuming Poisson statistics for the background stacked counts. Unfortunately. the estimated. upper limits are not tight enough to stronely constrain the X-ray spectra moperties of the spiral ancl elliptical1 Sgalaxy subsamples.," Unfortunately, the estimated upper limits are not tight enough to strongly constrain the X-ray spectral properties of the spiral and elliptical galaxy subsamples." 1 To further assess the confidence level of the stackesignal in both the soft. and the hard bands we perform extensive simulations: mock catalogs are constructed by, To further assess the confidence level of the stackedsignal in both the soft and the hard bands we perform extensive simulations: mock catalogs are constructed by 7 write the OCD [ree energies in the form where JCA) takes care of the quantum effects in the gas-liquid phase. and FisC0X) is the vibrational contribution to the [ree energv (2).. ?,"\citet{1992ApJ...388..521I} write the OCP free energies in the form where $J(\Lambda)$ takes care of the quantum effects in the gas-liquid phase, and $\Fvib(\Lambda)$ is the vibrational contribution to the free energy \citep{1970A&A.....8..398K}. ." have shown that Fun/In;SONATH can be fitted by a weightedex sum of two Debve [ree energies:ex where a=0.5711. Ay= 1.0643. Ao= 2.9438. and Lr) is given bv The function JOA) is known (?) to have the the high-temperature limit A?/12.," \citet{1992ApJ...388..521I} have shown that $\Fvib/\sum N_ikT$ can be fitted by a weighted sum of two Debye free energies: where $\alpha=0.5711$, $\Lambda_1=1.0643$ , $\Lambda_2=2.9438$ and $L(x)$ is given by The function $J(\Lambda)$ is known \citep{1972A&A....16...72S} to have the the high-temperature limit $\Lambda^2/12$." At low temperatures the OCD liquid should resemble a bee lattice. with the ions vibrating about their equilibrium positions.," At low temperatures the OCP liquid should resemble a bcc lattice, with the ions vibrating about their equilibrium positions." " This leads toa (X) proportional to A: according to ?.. J(A)—1.069804 (although their foregoing fit for Fig, vields Fi,—0.76753)."," This leads toa $J(\Lambda)$ proportional to $\Lambda$: according to \citet{1992ApJ...388..521I}, $J(\Lambda)\rightarrow1.06980\Lambda$ (although their foregoing fit for $\Fvib$ yields $\Fvib\rightarrow0.76758\Lambda$ )." They then sugeest a functional form for JCA) that interpolates between (hese limits., They then suggest a functional form for $J(\Lambda)$ that interpolates between these limits. But (his leads to a non-monotonic entropy. (I-derivative of the eas-liquid Focp): in partücular. (he specific heat has the required 7? dependenceat low T. but with the wrong sign!," But this leads to a non-monotonic entropy (T-derivative of the gas-liquid $\FOCP$ ); in particular, the specific heat has the required $T^3$ dependenceat low $T$, but with the wrong sign!" Rather than adopt Iben et al, Rather than adopt Iben et al. /s J(A). we note that. for A<>1 it tends to 0.76758. and therelore set The OCP [ree energies include the contribution of the translationaldegrees of freedom.,"'s $J(\Lambda)$, we note that, for $\Lambda << 1$, $\Fvib/\sum N_ikT$ tends to $3\ln\Lambda-1-1.49602$, whereas for $\Lambda >> 1$ it tends to $0.76758\Lambda$, and therefore set The OCP free energies include the contribution of the translationaldegrees of freedom." " Since our[ree energy. already includes $5 F(T.V..V;). we must. in order to obtain Feo. EF"" [rom each one of the Foop's. Thus.finally."," Since ourfree energy already includes $\sum F(T,V,N_i)$ , we must, in order to obtain $F_{CQ}$ , $F^0$ from each one of the $\FOCP$ 's. Thus,finally," depends only on rotational frequency.,depends only on rotational frequency. from now studied inerfiabinodes in spheres with arbitrary polytropic density profile., from now studied inertial-modes in spheres with arbitrary polytropic density profile. Thev expressed the spatial structure of cach inertialinode as a sm of spherical harmonic functions and curls of the spherical harmonics., They expressed the spatial structure of each inertial-mode as a sum of spherical harmonic functions and curls of the spherical harmonics. They presented some cigenfrequenucies for. eg. ο=1 polvtrope.," They presented some eigenfrequencies for, e.g., $n=1$ polytrope." We will compare our results against theirs., We will compare our results against theirs. Iuertial-1nodes have also been attacked uuuercally. via inteeration of the characteristics2001).. the finite difference method1997).. aud the spectral method(2001).," Inertial-modes have also been attacked numerically, via integration of the characteristics, the finite difference method, and the spectral method." . There are two purposes to this paper., There are two purposes to this paper. First. it las down the foundation for Paper IL where we discuss our attempt to solve the tidal Q problem.," First, it lays down the foundation for Paper II where we discuss our attempt to solve the tidal $Q$ problem." Second. it presents a new series of exact solutions to iuertial-110des in spheres with power-law deusitv profile. as well as approximate solutions for spleres with au arbitrary (but sinoothlv varving) deusitv profile.," Second, it presents a new series of exact solutions to inertial-modes in spheres with power-law density profile, as well as approximate solutions for spheres with an arbitrary (but smoothly varying) density profile." Our approach centers on the abilitv to reduce the partial differential equation governing fluid motion in a rotating sphere to ordinary differcutial equations., Our approach centers on the ability to reduce the partial differential equation governing fluid motion in a rotating sphere to ordinary differential equations. This scuu-analvtical approach produces results that are both casily reproducible aud have clear plysical interpretations., This semi-analytical approach produces results that are both easily reproducible and have clear physical interpretations. The mathematics are concentrated im 2.., The mathematics are concentrated in \ref{sec:structure}. We then expose properties of inertialinodes that are relevant for its interaction with the tidal perturbatious 3))., We then expose properties of inertial-modes that are relevant for its interaction with the tidal perturbations \ref{sec:property}) ). A discussion section 1)) follows in which we cousicer the validity of our asstuuptious., A discussion section \ref{sec:discussion}) ) follows in which we consider the validity of our assumptions. Readers iuterested in the tidal dissipation problem alone are referred to 85. for a brief παν of the features of immertiablinodes upon which we build our theory of tidal dissipation (Paper IT)., Readers interested in the tidal dissipation problem alone are referred to \ref{sec:summary} for a brief summary of the features of inertial-modes upon which we build our theory of tidal dissipation (Paper II). Readers interested in setting only a favor of how inertialiuodeslook like are referredto Pies., Readers interested in getting only a favor of how inertial-modeslook like are referredto Figs. 11 12.., \ref{fig:plota} \ref{fig:density-surf}. The accompanving description (853.1)) as well as a comparison between inertial-modes and the more conuuonlv known eravitv- and pressure-nuodes (83.5]) lay prove useful as well., The accompanying description \ref{subsec:graphic}) ) as well as a comparison between inertial-modes and the more commonly known gravity- and pressure-modes \ref{subsec:differing}) ) may prove useful as well. This section documents our effort iu obtainiug senianalytical eieeufuuctious for ποαπο»., This section documents our effort in obtaining semi-analytical eigenfunctions for inertial-modes. The relevant equation of motion is first introduced in §2.1.., The relevant equation of motion is first introduced in \ref{subsec:equation}. We then deal with iucreasinglv more complicated aud more realisticcases., We then deal with increasingly more complicated and more realisticcases. This proceeds from simple uniform density spheres 2.2)). to power-law density spheres 2.3)). aud lastly to spheres with realistic planetary density profiles (§2.1)) Consider a planet spinning with a uniform augular velocity of Q pointing in the z direction.," This proceeds from simple uniform density spheres \ref{subsec:constantrho}) ), to power-law density spheres \ref{subsec:powerlaw}) ), and lastly to spheres with realistic planetary density profiles \ref{subsec:approximate}) ) Consider a planet spinning with a uniform angular velocity of $\boldOmega$ pointing in the $\boldz$ direction." " Iu the rotating frame. the equations for mnonieutuni and mass conservation read where € is the displacement vector. while p’. p! aud &/ are the Eulerian perturbations to pressure. density aud eravitational potential. respectively,"," In the rotating frame, the equations for momentum and mass conservation read where $\boldxi$ is the displacement vector, while $p^\prime$, $\rho^\prime$ and $\Phi^\prime$ are the Eulerian perturbations to pressure, density and gravitational potential, respectively." We ignore rotational deformation to the lyclrostatic structure. as wellas the centrifugal force associated with the perturbation.," We ignore rotational deformation to the hydrostatic structure, as wellas the centrifugal force associated with the perturbation." Both these terms are smaller by a factor ~(Q/OQyae)? than the terms we keep. with Όμως being the break-up spiu-rate of the plauct.," Both these terms are smaller by a factor $\sim (\Omega/\Omega_{\rm max})^2$ than the terms we keep, with $\Omega_{\rm max}$ being the break-up spin-rate of the planet." This factor is ~LO% for Jupiter and much s1ualler for close-in extra-solar planets which likely have reached spin-svuchrouization with the orbit., This factor is $\sim 10\%$ for Jupiter and much smaller for close-in extra-solar planets which likely have reached spin-synchronization with the orbit. " We restrict ourselves to adiabatic perturbations. hence the Lagrangian pressure and density perturbations are related to cach other by poo where the adiabatic iudex Ty=@lup/@lup|, and is related to the speed of sound by T4=ep/p."," We restrict ourselves to adiabatic perturbations, hence the Lagrangian pressure and density perturbations are related to each other by = _1 where the adiabatic index $\Gamma_1 = \partial \ln p/\partial \ln \rho|_s$ and is related to the speed of sound by $\Gamma_1 = c_s^2\,\rho/p$." The interiors of eiaut planets are couvectively uustable. with a low degree of super-aciabaticity. as is guaranteed by the fact that the convective velocity is fairly subsonic.," The interiors of giant planets are convectively unstable, with a low degree of super-adiabaticity, as is guaranteed by the fact that the convective velocity is fairly subsonic." This allows us to treat the fluid as neutrally buovaut., This allows us to treat the fluid as neutrally buoyant. Setting the frequency to zero. we obtain. dr| d," Setting the frequency to zero, we obtain, = ." "r’ Given the following expression which relates the Lagrangian aud the Eulerian perturbations im a quantity X. 6éN = | EVN, equations aud combine to vield yo Dy and the right-hand side of equation can be simplified iuto - pl peep) WV το. where we have introduced a new scalar C=-- ( | )—-- ία2p | )."," Given the following expression which relates the Lagrangian and the Eulerian perturbations in a quantity $X$, X = + X, equations and combine to yield = _1 and the right-hand side of equation can be simplified into - + - = - ) - = - ^2 , where we have introduced a new scalar = ( + ) = ( c_s^2 + )," saluple there also 3 galaxies (two among those analyzed in this work) with au iuterinediate value of 5.,sample there also 3 galaxies (two among those analyzed in this work) with an intermediate value of $\gamma$. See Tab., See Tab. ora summary of the breakdown of the objects iuto the litferent classes., \ref{nuker} for a summary of the breakdown of the objects into the different classes. Since we were forced to Use several filters for the analysis of the surface brightuess profile. there is the possibility that the cescription of a given galaxy changes when observed in differeut bands.," Since we were forced to use several filters for the analysis of the surface brightness profile, there is the possibility that the description of a given galaxy changes when observed in different bands." However. the colmparison of the parameters derived froma Nuker fits ou the same ealaxyv dmaeed wit1i OST in different filters (Ravindranathetal.2001) indicates that. although differences are present. the cassification iuto Ῥοπα-law aud core galaxies ds indepeudeut on waveleneth.," However, the comparison of the parameters derived from Nuker fits on the same galaxy imaged with HST in different filters \citep{ravi01} indicates that, although differences are present, the classification into power-law and core galaxies is independent on wavelength." Nonetheless. we prefer to explo this issue dn nore detail for our sample.," Nonetheless, we prefer to explore this issue in more detail for our sample." The images usec in this work rauge from the V to the II baud., The images used in this work range from the V to the H band. We here consider the 21 galaxics for which images taken in both these bands are available. to test the robustness of the Nuker classification over the largest breadth of wavelength.," We here consider the 21 galaxies for which images taken in both these bands are available, to test the robustness of the Nuker classification over the largest breadth of wavelength." Nine objects must be discarded since them V band images are saturated (3). heavily affected by dust Ch) or as the orescence of a single iuage iu the archive preveuts cosniüc-caw rejection (2).," Nine objects must be discarded since their V band images are saturated (3), heavily affected by dust (4) or as the presence of a single image in the archive prevents cosmic-ray rejection (2)." —Xf the 12 remaiming objects. xiehtuess profiles of 11 ealaxies have been alreacky preseuted in the literature (sec the articles cited in Table 3. Laueretal.(2001) and Faberetal. (1997))). leaving to us ouly the analvsis of the V baud image of COC 7191 ALD 81).," Of the 12 remaining objects, brightness profiles of 11 galaxies have been already presented in the literature (see the articles cited in Table 3, \citet{lauer04} and \citet{faber97}) ), leaving to us only the analysis of the V band image of UGC 7494 (M 84)." No discordaut Nuker classification has been fouud. wither supporting its independence ou the observing baud.," No discordant Nuker classification has been found, further supporting its independence on the observing band." Examining Eqs. [4.. 24.. ,"Examining Eqs. \ref{eq:psi}, , \ref{eq:dpsi1}, ," and 23. we see that. when 5$ is small. the triaxial structure of the halo manifests itself only through multiplicative prefactors.," and \ref{eq:dpsi} we see that, when $S$ is small, the triaxial structure of the halo manifests itself only through multiplicative prefactors." This is not a generic behaviour for all potentials: it is true of this model because. when Sis small. all terms carry factors of the same power of qx. the normalising ratio that carries information about the length of the axis hidden along the line of sight.," This is not a generic behaviour for all potentials; it is true of this model because, when $S$ is small, all terms carry factors of the same power of $q_X$, the normalising ratio that carries information about the length of the axis hidden along the line of sight." All terms in the potential that are important when 5 is small are proportional to .V or Y. giving each term an overall normalisation of qx. and similarly all important terms in its derivative are dimensionless in lengths giving each term a normalisation of qx.," All terms in the potential that are important when $S$ is small are proportional to $\mathcal{X}$ or $\mathcal{Y}$, giving each term an overall normalisation of $q_X$, and similarly all important terms in its derivative are dimensionless in lengths giving each term a normalisation of $q_X$." When 5 is large. or were there any terms that carried unequal powers of qx. this simple multiplicative renormalisation due to triaxial structure would no longer hold.," When $S$ is large, or were there any terms that carried unequal powers of $q_X$, this simple multiplicative renormalisation due to triaxial structure would no longer hold." However. given that there is good evidence that galactic cores are very small (Wallington&Narayan (C1993))) and that galaxy density profiles are generally isothermal over the central region to which strong lensing is sensitive. this straightforward analysis indicates that triaxiality will not independently lead to any significant change in the shape of the lensing potential and thus creates no significant errors in the measurement of the Hubble parameter. as indicated in our simulations.," However, given that there is good evidence that galactic cores are very small \cite{wall}) ) and that galaxy density profiles are generally isothermal over the central region to which strong lensing is sensitive, this straightforward analysis indicates that triaxiality will not independently lead to any significant change in the shape of the lensing potential and thus creates no significant errors in the measurement of the Hubble parameter, as indicated in our simulations." The multiplicative factors introduced by the triaxial structure of the lensing halo are apparent in the varied values of the normalisation of the potential by returned for different orientations of the triaxial halos., The multiplicative factors introduced by the triaxial structure of the lensing halo are apparent in the varied values of the normalisation of the potential $b_{\rm E}$ returned for different orientations of the triaxial halos. To complete our understanding of the problem of Hubble parameter estimation from triaxial lens systems. we now look to the fully general case in which the elliptical power law model is fit with both Hubble and slope parameters left free to vary.," To complete our understanding of the problem of Hubble parameter estimation from triaxial lens systems, we now look to the fully general case in which the elliptical power law model is fit with both Hubble and slope parameters left free to vary." We tit this general model to the same family of halos described in Section ??.., We fit this general model to the same family of halos described in Section \ref{sec:FS1}. . " The complete posterior probability distribution for one of the halos. the prolate halo oriented at SO"" such that the ellipticity is approaching the maximum. is shown in Figure 4.. again absent the well-constrained and independent orientation angle @ to make the plot clearer."," The complete posterior probability distribution for one of the halos, the prolate halo oriented at $80^{\rm o}$ such that the ellipticity is approaching the maximum, is shown in Figure \ref{plot:figure4}, again absent the well-constrained and independent orientation angle $\theta$ to make the plot clearer." The well-known degeneracy between the Hubble parameter and the slope parameter 7 is clearly visible. but interestingly. is not the only strong degeneracy present.," The well-known degeneracy between the Hubble parameter $h$ and the slope parameter $\eta$ is clearly visible, but interestingly, is not the only strong degeneracy present." Both the Hubble parameter and the density profile slope are also strongly degenerate with the normalisation of the potential be. and with the source position«1.," Both the Hubble parameter and the density profile slope are also strongly degenerate with the normalisation of the potential $b_E$, and with the source position." The regions of highest likelihood (indicated by the shading) are centred on the true parameter values: however. the most-probable parameter values obtained by marginalizing over all other parameters give consistently high values for the Hubble parameter and low values for the profile slope. indicating that while the true parameter values give a slightly higher likelihood value than others. there are other likely parameter value combinations including low values for jj and high values for / that occupy significantly larger volumes in parameter space.," The regions of highest likelihood (indicated by the shading) are centred on the true parameter values; however, the most-probable parameter values obtained by marginalizing over all other parameters give consistently high values for the Hubble parameter and low values for the profile slope, indicating that while the true parameter values give a slightly higher likelihood value than others, there are other likely parameter value combinations including low values for $\eta$ and high values for $h$ that occupy significantly larger volumes in parameter space." Were the errors in thisproblem Gaussian. the maximum-likelihood parameter estimates should correspondtothe most-probable marginalized parameter value:," Were the errors in thisproblem Gaussian, the maximum-likelihood parameter estimates should correspondtothe most-probable marginalized parameter value;" partially cleared or ultra-settled (note that there several partially cleared. (inner. hole sources) in Taurus but. these have bluer Ix - SN] colours than those sources in Figure 6 and we would not be able to identify these sources as such in the absence of 245m data).,partially cleared or ultra-settled (note that there several partially cleared (inner hole sources) in Taurus but these have bluer K - [8] colours than those sources in Figure 6 and we would not be able to identify these sources as such in the absence of $24 \mu$ m data). By contrast. around 30% of disc bearing objects in IC. 348 have spectral slopes in the colour range 0.7«dyS]L2 in which dises are eithor partially cleared or ultra-settled.," By contrast, around $30 \%$ of disc bearing objects in IC 348 have spectral slopes in the colour range $0.7 < K - [8] < 1.2$ in which discs are either partially cleared or ultra-settled." The INS probability of these distributions being the same is 10., The KS probability of these distributions being the same is $10^{-5}$. 7 We thus conclude that the distribution of Ix - S] colours in IC 348 and in Taurus are very dillerent once one includes all objects (regardless of whether they are detected. at 245m)., We thus conclude that the distribution of K - [8] colours in IC 348 and in Taurus are very different once one includes all objects (regardless of whether they are detected at $24 \mu$ m). We can estimate the fraction of dise bearing svstenis that are partially cleared or ultra-settled by adding all the sources in the colour range 0.7LL, This is generally the case for $S/N(H\alpha) > 4.4$. For the ten strongest Io cutter the ratio is /Tlo.=0.2140.05., For the ten strongest $\alpha$ emitter the ratio is $\alpha = 0.21\pm0.05$. The maxininua line fux ratio 11]]658.2/TIo is limited to 15 in the fit., The maximum line flux ratio $\alpha$ is limited to 0.5 in the fit. Iu order to make use of the pre-filter fluxes. the line Hux estimated from this line fit is subtracted from the pre-filter fix allowine for the filter transmission at the specific wavelength of the line.," In order to make use of the pre-filter fluxes, the line flux estimated from this line fit is subtracted from the pre-filter flux allowing for the filter transmission at the specific wavelength of the line." The line corrected pre-filter flax - and its error - is included as an additional continua data »oiut for an iniproved line fit., The line corrected pre-filter flux - and its error - is included as an additional continuum data point for an improved line fit. Examples for fits to different ines are shown iu the righ panels of 11. where the erved pre-filter fluxes are marked as solid bars with heir errors. aud the corrected pre-filter fluxes as dashed LBies.," Examples for fits to different lines are shown in the right panels of 1, where the observed pre-filter fluxes are marked as solid bars with their errors, and the corrected pre-filter fluxes as dashed lines." Both values are also marked in the SED plots iu the oft paucls., Both values are also marked in the SED plots in the left panels. Iu the next step. for every of he eight redshifts determined above. template spectra mublished by Iàiunev et al. (," In the next step, for every of the eight redshifts determined above, template spectra published by Kinney et al. (" 1996) were fitted to the SED derived from the multi-filter plotometiy.,1996) were fitted to the SED derived from the multi-filter photometry. This is done bx ueans of colors. similar to the multi-color classification xocedure described in Wolf et al. (," This is done by means of colors, similar to the multi-color classification procedure described in Wolf et al. (" 2001). vielding a most xobable template spectrum.,"2001), yielding a most probable template spectrum." In order to achieve better fits o the data. we allow for an extra reddening correction of the template spectra up to Ejy of 0.3.," In order to achieve better fits to the data, we allow for an extra reddening correction of the template spectra up to $E_{\rm B-V}$ of 0.3." The latter Is nuportau for distant samples which coutain generally xiehter and more massive galaxies with more reddening han the Kiunuev et al., The latter is important for distant samples which contain generally brighter and more massive galaxies with more reddening than the Kinney et al. templates (see sect., templates (see sect. 3.5)., 3.5). Since we want to determine the fluxes in the euission ines from the signal excesses in the veto filters above he coutinuun (see step 1). line free template spectra are weded.," Since we want to determine the fluxes in the emission lines from the signal excesses in the veto filters above the continuum (see step 4), line free template spectra are needed." Thus. the IKiuuev-Calzetti template spectra were altered by cutting out the xoimüuent enission lines.," Thus, the Kinney-Calzetti template spectra were altered by cutting out the prominent emission lines." As consequence. those filter data where secondary ciissiou LBres are expected. are not usable for the fit.," As a consequence, those filter data where secondary emission lines are expected, are not usable for the fit." Thus. the SED fit ix purely based ou the continuum part of the spectra.," Thus, the SED fit is purely based on the continuum part of the spectra." For the template spectruni which fits best to the served SED a reduced 4? is derived., For the template spectrum which fits best to the observed SED a reduced $\chi^2$ is derived. The fit to the continu spectrum provides. for cach of the cight possible liue identifications. also a Lew contimmiun level at the waveleneth of the FP window. which is marked in either of the Lue plots in Fig.11 as a dotted horizoutal line.," The fit to the continuum spectrum provides, for each of the eight possible line identifications, also a new continuum level at the wavelength of the FP window, which is marked in either of the line plots in 1 as a dotted horizontal line." The error bar is estimated from the quality of the coutinuun fit. aud is colparable to that of the pre-filter fix.," The error bar is estimated from the quality of the continuum fit, and is comparable to that of the pre-filter flux." Ideally. this continua fiux level should agree with the corrected pre- flux (step 1)," Ideally, this continuum flux level should agree with the corrected pre-filter flux (step 1)." A high discrepancy between the two, A high discrepancy between the two "the transverse and radial magnetic field dispersions, respectively.","the transverse and radial magnetic field dispersions, respectively." " For example, oy=(B?)!/? and the definition of op, is analogous."," For example, $\sigma_{bt}=\langle B_{t}^{2}\rangle^{1/2}$ and the definition of $\sigma_{br}$ is analogous." The meaning of the curves is the same as in Figure 2., The meaning of the curves is the same as in Figure 2. " For the absolute value of the radial component of the magnetic field, the isotropic case corresponds to 0.5."," For the absolute value of the radial component of the magnetic field, the isotropic case corresponds to 0.5." " For magnetic anisotropy, isotropic case corresponds to vanishing f, and tangential and radial cases to negative and positive DB, respectively."," For magnetic anisotropy, isotropic case corresponds to vanishing $\beta$, and tangential and radial cases to negative and positive $\beta$, respectively." Horizontal dotted lines correspond to isotropic configurations., Horizontal dotted lines correspond to isotropic configurations. Figure 4 demonstrates that the radiative run with field-aligned thermal conduction shows a weak bias for tangential orientation of the magnetic fields., Figure 4 demonstrates that the radiative run with field-aligned thermal conduction shows a weak bias for tangential orientation of the magnetic fields. " We stress that this feature, although technically corresponding to a region resolved by up to 16 grid zones, is only tentative and that higher resolution runs are required to make any definite statements about its nature."," We stress that this feature, although technically corresponding to a region resolved by up to 16 grid zones, is only tentative and that higher resolution runs are required to make any definite statements about its nature." " In à companion paper (Ruszkowski Oh 2010b, we make a step in this direction by systematically submitted)studying the substructure parameter space and the substructure impact on the HBI in isolated cool cores in non-cosmological simulations."," In a companion paper (Ruszkowski Oh 2010b, submitted) we make a step in this direction by systematically studying the substructure parameter space and the substructure impact on the HBI in isolated cool cores in non-cosmological simulations." There is also a tentative decrement in the anisotropy parameter at intermediate radii for all four runs., There is also a tentative decrement in the anisotropy parameter at intermediate radii for all four runs. This may be caused by partial trapping of gravity modes ," This may be caused by partial trapping of gravity modes \citep{rebusco08, ruszkowski10}." At larger radii there appears to be slight radial bias (??)..in the orientation of the magnetic field., At larger radii there appears to be a slight radial bias in the orientation of the magnetic field. a This could be attributed to the accretion along the filaments as the magnetic fields are expected to be locally preferentially tangential to these structures (?) or to inhomogeneous radial flows in general., This could be attributed to the accretion along the filaments as the magnetic fields are expected to be locally preferentially tangential to these structures \citep{bruggen05b} or to inhomogeneous radial flows in general. " The right panel of Figure 4 shows the anisotropy parameter (6, for the velocity field.", The right panel of Figure 4 shows the anisotropy parameter $\beta_{v}$ for the velocity field. The definition of this quantity is analogous to that for the magnetic fields with velocity dispersions replacing the magnetic fields dispersions., The definition of this quantity is analogous to that for the magnetic fields with velocity dispersions replacing the magnetic fields dispersions. " However, the velocity dispersion is measured with respect to the mean streaming velocity of the cluster."," However, the velocity dispersion is measured with respect to the mean streaming velocity of the cluster." This figure bears an interesting resemblance to its magnetic counterpart., This figure bears an interesting resemblance to its magnetic counterpart. There is even stronger tangential bias in the velocity field in the radiative run with anisotropic thermal conduction than for the magnetic anisotropy parameter for the same run., There is even stronger tangential bias in the velocity field in the radiative run with anisotropic thermal conduction than for the magnetic anisotropy parameter for the same run. " However, there is a significant scatter in these quantities and firm conclusion about the trend could be drawn from averaging over many clusters."," However, there is a significant scatter in these quantities and firm conclusion about the trend could be drawn from averaging over many clusters." " The exact values also depend on such factors as the definitions of the cluster center and its bulk velocity, and whether the quantities are mass-weighted or not."," The exact values also depend on such factors as the definitions of the cluster center and its bulk velocity, and whether the quantities are mass-weighted or not." " Nevertheless, some similarity in these quantities is not unexpected simply due to the fact that the magnetic field is frozen to the gas and follows it."," Nevertheless, some similarity in these quantities is not unexpected simply due to the fact that the magnetic field is frozen to the gas and follows it." " However, unlike the velocity field, the magnetic field has a “memory” of past gas displacement, so the two anisotropy parameters are not expected to be identical."," However, unlike the velocity field, the magnetic field has a “memory” of past gas displacement, so the two anisotropy parameters are not expected to be identical." Intermediate radii tend to have relatively more tangential velocity field., Intermediate radii tend to have relatively more tangential velocity field. owe describe the set-up of our sinulations including simulation parameters and technique. cosmolocical model. chemistry. and radiative feedback.,"we describe the set-up of our simulations including simulation parameters and technique, cosmological model, chemistry, and radiative feedback." Iu Section refsecidataset πο present the characteristics of the simulated data set of pregalactic objects identified iu our simulations and used for further analysis., In Section \\ref{sec:dataset} we present the characteristics of the simulated data set of pregalactic objects identified in our simulations and used for further analysis. In Section refsecistats we use the data set as a whole to develop fitting fornmlaes for the fraction of eas that cau cool. vecolmme dense and thus be available for star formation with aud without the presence of a background xhotodissociatiug flux.," In Section \\ref{sec:stats} we use the data set as a whole to develop fitting formulaes for the fraction of gas that can cool, become dense and thus be available for star formation with and without the presence of a background photodissociating flux." In Section refseciprofile we use radial profiles to show the internal collapse characteristics of these structures., In Section \\ref{sec:profile} we use radial profiles to show the internal collapse characteristics of these structures. We consider voth the time evolution of a single peak for a fixed vackeround photodissociatiug fiux aud also how the internal properties of a eiven cloud chauge at fixed redshift when the level of photoclissociating flux ds varied., We consider both the time evolution of a single peak for a fixed background photodissociating flux and also how the internal properties of a given cloud change at fixed redshift when the level of photodissociating flux is varied. Anued with these examples of the internal evolution aud structure of the collapsing clouds. we discuss in Section refsce:discussion the neglect of selfshiclding and photodetaclient in our sinulatious aud then use a simple analytical aremmenut to illuninuate the esseutial plivsics of the collapse.," Armed with these examples of the internal evolution and structure of the collapsing clouds, we discuss in Section \\ref{sec:discussion} the neglect of self-shielding and $^-$ photodetachment in our simulations and then use a simple analytical argument to illuminate the essential physics of the collapse." We stunimarize our results in Section οΠΠ, We summarize our results in Section \\ref{sec:summary}. A selfteousistent three dimensional cosinologica siuulatiou of the collapse of low mass (Lo? 10 AL.) protogalaxies at high redshift (302 19) requires both large enough simulation volume to model the eravitationa tidal forces at work during the formation epoch aud high spatial (aud mass) resolution to probe within the smal collapsing clouds., A self-consistent three dimensional cosmological simulation of the collapse of low mass $10^5$ – $10^7 \Ms$ ) protogalaxies at high redshift $30 > z > 19$ ) requires both large enough simulation volume to model the gravitational tidal forces at work during the formation epoch and high spatial (and mass) resolution to probe within the small collapsing clouds. One techuique that has receuth beeu able to achieve the large dynamic range necessary to slie heht on the collapse aud fragmentation of these first star producing structures is adaptive imesh refinement (AMR)., One technique that has recently been able to achieve the large dynamic range necessary to shed light on the collapse and fragmentation of these first star producing structures is adaptive mesh refinement (AMR). The three dimensional AMIR algorithm used in our snuulatious is described more fully elsewhere (Bryan 1999: Brvau Norman 1997. 1999: Norman Divan 1998).," The three dimensional AMR algorithm used in our simulations is described more fully elsewhere (Bryan 1999; Bryan Norman 1997, 1999; Norman Bryan 1998)." Briefly. the code uses an adaptive hierarchy of rectaneular erid patches at various levels of resolution very sinular to the aleorithiu described bv Berger Collela (1989).," Briefly, the code uses an adaptive hierarchy of rectangular grid patches at various levels of resolution very similar to the algorithm described by Berger Collela (1989)." Each erid patch covers some region within its parent erid needius additional refinement and may itself become a parent erid to an even higher resolution child eric., Each grid patch covers some region within its parent grid needing additional refinement and may itself become a parent grid to an even higher resolution child grid. We take the ratio of parent to child exid imesh spacing to be two., We take the ratio of parent to child grid mesh spacing to be two. The dark matter is followed using methods similar to those presented by Couchinan (1991) aud the eas lbydrodvuauics uses the artificial viscosity method of Stone Norman (1992)., The dark matter is followed using methods similar to those presented by Couchman (1991) and the gas hydrodynamics uses the artificial viscosity method of Stone Norman (1992). " We use a flat. low matter deusitv model for our sinulatious with Qy=0.1. 0,=0.05. O4=0.6. 7;—0.65. σς=O8. ands=1 where O9. O5. aud Ὃν are the fraction of the critical cnerey deusitv cried iu uourclativistic matter. barvous. and vactuun euergyv. respectively. fi is the dimensionless IIubble parameter in units of 100Ἐν σε isthe density fluctuation normalization iu a sphere of radius S5+ Mpe. and ( ds the slope of the primordial density perturbation power spectrum."," We use a flat, low matter density model for our simulations with $\Omega_0=0.4$, $\Omega_b=0.05$, $\Omega_\Lambda=0.6$, $h=0.65$, $\sigma_8=0.8$, and $n=1$ where $\Omega_0$, $\Omega_b$, and $\Omega_\Lambda$ are the fraction of the critical energy density carried in nonrelativistic matter, baryons, and vacuum energy, respectively, $h$ is the dimensionless Hubble parameter in units of $100$, $\sigma_{8}$ is the density fluctuation normalization in a sphere of radius $8h^{-1}$ Mpc, and $n$ is the slope of the primordial density perturbation power spectrum." The paralcters are chosen to provide good consistenev wi observation., The parameters are chosen to provide good consistency with observation. The fluctuation normalization is cousisteut with the CAIB quadimpole as measured by CODE (Bunun White 1997) aud also with observations of the uunuber density of galaxy clusters (White. Efstathiou Freuls 1993: Boud Myers 1996).," The fluctuation normalization is consistent with the CMB quadrupole as measured by COBE (Bunn White 1997) and also with observations of the number density of galaxy clusters (White, Efstathiou Frenk 1993; Bond Myers 1996)." Q4/2 is consistent. with big bane uucleosvuthesis aud the measured abundance of primordial deuteriunu (Copi Scehranuu. Turner 1995: Durles Tytler 1998). and 4 is consistent with the upper nut (O40.7) of Maoz Ris (1993) and the best fit xumneters of Ostriker Steinhardt (1995).," $\Omega_b h^{2}$ is consistent with big bang nucleosynthesis and the measured abundance of primordial deuterium (Copi, Schramm, Turner 1995; Burles Tytler 1998), and $\Omega_\Lambda$ is consistent with the upper limit $\Omega_\Lambda < 0.7$ ) of Maoz Rix (1993) and the best fit parameters of Ostriker Steinhardt (1995)." The simulations are initialized at 2=99 with density rturbatious generated for the above model using the Eieusteiu IIu (1998) transfer functions in a comoving simulation vohuue of 1 Mpe?., The simulations are initialized at $z=99$ with density perturbations generated for the above model using the Eisenstein Hu (1998) transfer functions in a comoving simulation volume of $1$ $^3$. This simulation volume is large enough to eusure that the fundamental mode in the box remains linear at the lowest redshifts considered. here., This simulation volume is large enough to ensure that the fundamental mode in the box remains linear at the lowest redshifts considered here. Ao low resolution run is used firs to ideutifv a region of active structure formation., A low resolution run is used first to identify a region of active structure formation. Iu order to achieve high mass resolution iu the reeion of interest the simulation is reinitialized with niultiple static refinement levels surroundiug the chosen region such tha cach successive static parent exid contaius the laeraneian volue of its child eric., In order to achieve high mass resolution in the region of interest the simulation is reinitialized with multiple static refinement levels surrounding the chosen region such that each successive static parent grid contains the lagrangian volume of its child grid. " This results iu à nass resolution iu the initial conditions for the region of interest of 1.278(38.25).M.. for the eas (dark matter). respectively,"," This results in a mass resolution in the initial conditions for the region of interest of $4.78 (38.25) \Ms$ for the gas (dark matter), respectively." In addition. that region is allowed to dvuauuicallv refine so that the local Jeaus length is resolved at all times by at least four erid zones and no eril cell contaius more than four times the initial eas mass clement 178M.) or ten times the initial dark matter elemeut (382.5 M...," In addition, that region is allowed to dynamically refine so that the local Jeans length is resolved at all times by at least four grid zones and no grid cell contains more than four times the initial gas mass element $4.78 \Ms$ ) or ten times the initial dark matter element $382.5 \Ms$ )." We lunit the total refinement to 11 levels within a GI? top evi which results iu a asin clvnamic range of 1.018.576.," We limit the total refinement to $14$ levels within a $64^3$ top grid which results in a maximum dynamic range of $1,048,576$." The comoving spatial resolution of 0.95 pc at mani refinement translates iuto a plivsical spatial resolution of 0.03 pe (0.05 pe) at ;—30 (2=19). respectively.," The comoving spatial resolution of $0.95$ pc at maximum refinement translates into a physical spatial resolution of $0.03$ pc $0.05$ pc) at $z=30$ $z=19$ ), respectively." We cal a peak “collapsed” when it reaches maximal refinement., We call a peak “collapsed” when it reaches maximal refinement. Ouce this occurs. we still wish to follow the subsequent evolution of structure iu the region. but are uuiutereste in the details of the collapsed peak.," Once this occurs, we still wish to follow the subsequent evolution of structure in the region, but are uninterested in the details of the collapsed peak." In order to prevent the peak from collapsing further (which could cause ποτσα instabilities). we introduce a formi of artificial pressure support.," In order to prevent the peak from collapsing further (which could cause numerical instabilities), we introduce a form of artificial pressure support." This is doue by defining. for cach cell. au effective pressure Which is the exeater of the thermal pressure and KGprAsμι where py ds the barvon density in the cell. Av; is the cell width on the finest level aud je=1.22074 is the usual mean mass per particle.," This is done by defining, for each cell, an effective pressure which is the greater of the thermal pressure and $K G \rho_b^2 \Delta x_f^2 / \mu$, where $\rho_b$ is the baryon density in the cell, $\Delta x_f$ is the cell width on the finest level and $\mu=1.22 m_H$ is the usual mean mass per particle." The cdimensiouless constant A is set to 100. a value which spreads the mass over a spherical region with a radius of several cells.," The dimensionless constant $K$ is set to 100, a value which spreads the mass over a spherical region with a radius of several cells." The foin of this expression is chosen by matching the thermal energv and eravitational sclfenerey of the eas: notice also that it results in a polvtropic equation of state., The form of this expression is chosen by matching the thermal energy and gravitational self-energy of the gas; notice also that it results in a polytropic equation of state. " We also smooth. the gravitational potential by LAr, which helps to reduce the amplitude of the artificial pressure support required.", We also smooth the gravitational potential by $4 \Delta x_f$ which helps to reduce the amplitude of the artificial pressure support required. Although introducing artificial pressure support causes us to lose information about the detailed morphology of the immer d... 2 pe (~1% of the virial radius) of the peak after collapse. it should uot affect the determination of cooled eas fractious in Section since the cooling region lies outside of the collapsed core.," Although introducing artificial pressure support causes us to lose information about the detailed morphology of the inner $1$ – $2$ pc $\sim 1$ of the virial radius) of the peak after collapse, it should not affect the determination of cooled gas fractions in Section \\ref{sec:stats} since the cooling region lies outside of the collapsed core." Our data set consists of results from four simulatious starting from ideutical cosmological initial couditious on the density fields., Our data set consists of results from four simulations starting from identical cosmological initial conditions on the density fields. Three of the simulations follow the, Three of the simulations follow the (29) and (30) in Chapter 7 of Chandrasekhar(1969).,(29) and (30) in Chapter 7 of \cite{Ch69}. . The solutions of equations (13)) aud (143) for a direct. configuration are: where For adjoint configurations. we only need to interchange «7 and A7.," The solutions of equations \ref{ch1}) ) and \ref{ch2}) ) for a direct configuration are: where For adjoint configurations, we only need to interchange $\omega^2$ and $\lambda^2$ ." The signs of wand A are determined by the sign of f (which is predetermined by the specilied axis ratios). through Eq. (2))," The signs of $\omega$ and $\lambda$ are determined by the sign of $f$ (which is predetermined by the specified axis ratios), through Eq. \ref{eqn:f}) )" and the relationship. With these constants and the Bernoulli's function in hand. we can solve for 77 throughout the interior of the configuration.," and the relationship, With these constants and the Bernoulli's function in hand, we can solve for $H$ throughout the interior of the configuration." In the incompressible case (n= 0). we know from (he classical analvtical results that the adopted: velocity [ield generates equilibrium structures that are uniform clensity ellipsoids.," In the incompressible case $n=0$ ), we know from the classical analytical results that the adopted velocity field generates equilibrium structures that are uniform density ellipsoids." llence. we can obtain Riemann S-tvpe ellipsoids directly by setting up a mass distribution that is confined by the ellipsoidal surface defined by three axes e. ὁ and c: (hen we solve Poisson's equation to get the potential everywhere: finally. w amd A can be determined by equations (15)) and (16)).," Hence, we can obtain Riemann S-type ellipsoids directly by setting up a mass distribution that is confined by the ellipsoidal surface defined by three axes $a$, $b$ and $c$; then we solve Poisson's equation to get the potential everywhere; finally, $\omega$ and $\lambda$ can be determined by equations \ref{omega}) ) and \ref{lambda}) )." Compressible polvtropic models (7> 0) having the same flow pattern as (hat. of Riemann ellipsoids (given by Eq. 3)).," Compressible polytropic models $n>0$ ) having the same flow pattern as that of Riemann ellipsoids (given by Eq. \ref{vel}) )," can also be constructed by an iterative procedure (hat is verv similar to IHachisus SCF method (Ilachisu 1986a).., can also be constructed by an iterative procedure that is very similar to Hachisu's SCF method \citep{H86A}. . The main steps of this method include: (i) set up a trial ellipsoidal mass distribution defined by (he choice of a. b. and c. then solve Poisson's equation to obtai the gravitational potential evervwhere (thedetailsofourPoissonsolverarediscussedinCohl&Tohline 1999): (11) caleulate Cy. ο and A using the three boundary. conditions as discussed above: ii) calculate the enthalpy everywhere inside the configuration using Eq. (6)): (," The main steps of this method include: (i) set up a trial ellipsoidal mass distribution defined by the choice of $a$, $b$, and $c$, then solve Poisson's equation to obtain the gravitational potential everywhere \citep[the details of our Poisson solver are discussed in][]{CT99}; (ii) calculate $C_1$, $\omega$ and $\lambda$ using the three boundary conditions as discussed above; (iii) calculate the enthalpy everywhere inside the configuration using Eq. \ref{bernoulli}) ); (" iv)caleulate the new “trial” densitw distribution according to the relationshipbetween the density ancl enthalpy for a polvtrope.,"iv)calculate the new “trial"" density distribution according to the relationshipbetween the density and enthalpy for a polytrope." These steps are repeated until the model converges., These steps are repeated until the model converges. therefore using (1)) aud (6)). we lave we can obtain the mass of the μαμα. fluctuations. Ημ WS so that bvsubstituting (6)) in (8)) we have Assmuiug that universe is just composed of dark matter aud DE. so that bv using the following data (FujiandMaeda2003:Waterhouse2006) and p= p.n coutormal transforiiation. we can rewrite Eq. (7)),"therefore using \ref{4}) ) and \ref{6}) ), we have we can obtain the mass of the small fluctuations, $ m_{min}$ as so that bysubstituting \ref{6}) ) in \ref{8}) ) we have Assuming that universe is just composed of dark matter and DE, so that by using the following data \citep{1,14} and $\rho=e^{\frac{3\beta\phi}{M_{pl}}}\widetilde{\rho}, $ in conformal transformation, we can rewrite Eq. \ref{7}) )" as By ectting the parameters of the Eq. (5)), as By getting the parameters of the Eq. \ref{5}) ) " as we obtain Oi,17:5«LONGee.", as we obtain $\phi_{min}=1.1775\times10^{18}Gev$. " We have drown Vto).V,(o) and Vo4o). bv these coustauts for more introduction."," We have drown $V(\phi), V_{,\phi}(\phi)$ and $V_{,\phi\phi}(\phi)$, by these constants for more introduction." " From figure (1) it is ποσα that this potential satisfies the coustraints of (ποιν2000),", From figure $(1)$ it is seen that this potential satisfies the constraints of \citep{23}. " Ον definition. gives W(®) the dimensions of an enerev density. therefore. according to (Weinbere2008:terhouse 200G6).. one can define DE deusitv. as by ταπιο use of o,,5;, and other coustauts ο,δια and s. we can obtain density of DE as por=3.31«10 Geet."," Our definition, gives $V(\Phi)$ the dimensions of an energy density, therefore, according to \citep{10,14}, one can define DE density, as by making use of $\phi_{min}$ and other constants $a, b, q $ and $n$, we can obtain density of DE as $\rho_{DE}=3.34\times10^{-47}Gev^{4}$ ." This result exactly is equalled with main quantity which is brought iu (Waterhouse2006)., This result exactly is equalled with main quantity which is brought in \citep{14}. ". Now we want obtain i)s,,7, for this model.", Now we want obtain $m_{min}$ for this model. " Asstmine the mnatter is the atmosphere of the earth with p=|x1071eel, using relation (01) one can compte ijni), as We should note tha Manin Us stuall fluctuation around imiuimuun"," Assuming the matter is the atmosphere of the earth with $\widetilde{\rho}=4\times10^{-21}Gev^{4}$ , using relation \ref{9}) ) one can compute $m_{min}$ as We should note that $m_{min}$ is small fluctuation around minimum." "i Πονονα, we obtain the relation between τω) aud ποιοΤαΟΠΟΥ tensor as Iu Jordan frame we lave THGy=3pp. by substituting p=wp we have TlGay,=(3ejp. But in Eiusteiu frame we obtain from relation (12)) we have T""!jg)—p. this micas that w=0."," However, we obtain the relation between $V_{,\phi}(\phi)$ and momentum-energy tensor as In Jordan frame we have $\tilde{T}^{\mu\nu} \tilde{g}_{\mu\nu}=3\tilde{p}-\tilde{\rho}$, by substituting $\tilde{p}=\omega\tilde{\rho}$ we have $\tilde{T}^{\mu\nu}\tilde{g}_{\mu\nu}=(3\omega-1)\tilde{\rho}.$ But in Einstein frame we obtain from relation \ref{12}) ) we have $ \tilde{T}^{00}\tilde{g}_{00}= -\tilde{\rho}$, this means that $\omega=0$." " Eveutuallv we ciui obtain by substituting (13)) iu Eq.(10)). we have by nakine use of the value of 0,,;, aud other relevant constant we obtain T""=6.5«10όσους. for this model."," Eventually we can obtain by substituting \ref{13}) ) in \ref{10}) ), we have by making use of the value of $\phi_{min}$ and other relevant constant we obtain $T^{00}=6.5\times10^{-48}Gev^{4}$ for this model." " This is another result which is agree with other Now we want focus ou the chameleou behavior iu the earlier uuiverse by w= Ll. of course note that in earlier unuiverse. we use we define Q,, as where p.=3 PAL."," This is another result which is agree with other Now we want focus on the chameleon behavior in the earlier universe by $\omega=-1$ , of course note that in earlier universe, we use we define $\Omega_{m}$ as where $\rho_{c}=3H^{2}M_{pl}^{2}$ ." Therefore from Eq. (9)), Therefore from Eq. \ref{9}) ) we obtain for investigating the cosmology behavior we consider two reenues.," we obtain for investigating the cosmology behavior we consider two regimes," models usually are in good agreement.,models usually are in good agreement. Exceptions are the temperature for LL 40. derived. by RPDM. and the temperatures for M 3. 15.," Exceptions are the temperature for H $-$ 40 derived by RPDM, and the temperatures for M $-$ 15." Phe deviating value for LE 40 even by RPDAL can probably be attributed to the AdGS6 line. which they usec as a temperature indicator.," The deviating value for H $-$ 40 given by RPDM can probably be attributed to the 4686 line, which they used as a temperature indicator." We refer to the discussion in 5..., We refer to the discussion in \ref{pni:ind}. For M 15 we find a higher stellar temperature than other authors., For M $-$ 15 we find a higher stellar temperature than other authors. The largest discrepaney is with the value from INST., The largest discrepancy is with the value from AK87. This can probably be attributed to the fact that INST. did: not report a detection of the A4686 line in their spectrum (although a detection. of roughly the same strength. as RPDAL was reported in Aller Ixeves 1985)., This can probably be attributed to the fact that AK87 did not report a detection of the 4686 line in their spectrum (although a detection of roughly the same strength as RPDM was reported in Aller Keyes 1985). Since M 15 has a WC]-tvpe central star. part of the A4686 Dux may originate from the central star.," Since M $-$ 15 has a [WC]-type central star, part of the 4686 flux may originate from the central star." Unfortunately. no detection oftheriv] A4740 line has ever been reported. so that no alternative temperature sensitive line is available.," Unfortunately, no detection of the 4740 line has ever been reported, so that no alternative temperature sensitive line is available." La view ofthis. the central star temperature for M 15 should. be viewed with some caution.," In view of this, the central star temperature for M $-$ 15 should be viewed with some caution." We conclude that the temperature determination. for the central stars in Chis sample is fairly reliable. although the situation for M 15 is not completely clear.," We conclude that the temperature determination for the central stars in this sample is fairly reliable, although the situation for M $-$ 15 is not completely clear." This confirms our results from Paper Lin which we found the temperature determination to be robust., This confirms our results from Paper I in which we found the temperature determination to be robust. In 5. the electron temperatures derived by clilferent authors are compared., In \ref{te:tab} the electron temperatures derived by different authors are compared. The electron temperature determined ον iis a weighted mean of the temperature in the nebula: 7; = feted|nzdV.," The electron temperature determined by is a weighted mean of the temperature in the nebula: $\overline{T_{\rm e}}$ = $\int n_{\rm e}^2 T_{\rm e} \md V / \int n_{\rm e}^2 \md V$." The observational material shows a aree spread in most cases. even when the same method is used.," The observational material shows a large spread in most cases, even when the same method is used." This indicates that the electron. temperature determination. at least in those cases where diagnostic lines iive been used. is not very. reliable.," This indicates that the electron temperature determination, at least in those cases where diagnostic lines have been used, is not very reliable." Ελπίς is in agreement with our results in Paper I. Note the large dillerence between heNi] andΟΠΠ] temperatures in the case of M 23., This is in agreement with our results in Paper I. Note the large difference between the and temperatures in the case of M $-$ 23. This cüllerence is not caused by measurement error., This difference is not caused by measurement error. For this articular object. the temperature derived. from theNu] ines has no physical meaning (Liu. private communication).," For this particular object, the temperature derived from the lines has no physical meaning (Liu, private communication)." The electron temperatures derived from our method are in most cases just outside the range of values found. with ine diagnostics: three times at the low end and. twice at he high end., The electron temperatures derived from our method are in most cases just outside the range of values found with line diagnostics; three times at the low end and twice at the high end. The results from Paper | indicate that the electron temperature cetermination with our method should » robust., The results from Paper I indicate that the electron temperature determination with our method should be robust. Ht is not apparent to us why the average values of the electron temperature derived from line diagnostics clo not coincide with our results., It is not apparent to us why the average values of the electron temperature derived from line diagnostics do not coincide with our results. Fhis might indicate a problem. although the fact that we find both higher and lower results is not indicative of a svstematic ellect.," This might indicate a problem, although the fact that we find both higher and lower results is not indicative of a systematic effect." Nevertheless. this issue should be investigated further in future research. using a larger sample.," Nevertheless, this issue should be investigated further in future research, using a larger sample." 1n ο the electron. densities derived. by different authors are compared., In \ref{ne:tab} the electron densities derived by different authors are compared. Phe electrondensity determined. by lis a weighted mean of the density in the nebula: m; = |ned.nocd’.," The electrondensity determined by is a weighted mean of the density in the nebula: $\overline{n_{\rm e}}$ = $\int n_{\rm e}^3 \md V / \int n_{\rm e}^2 \md V$." “Phere are enormous differences between 10 various determinations in the literature. even when the Lgame method. has been applied.," There are enormous differences between the various determinations in the literature, even when the same method has been applied." This indicates that the etermination of densities with line diagnostics is unreliable. which confirms our results in Paper LE. Also note the 'normous cdillerences between theSu].Clit} and. ensities for M 20 derived by Water et al. (1996)...," This indicates that the determination of densities with line diagnostics is unreliable, which confirms our results in Paper I. Also note the enormous differences between the, and densities for M $-$ 20 derived by Kaler et al. \cite{c2:kalerea2}." Our values ciller substantially from the values given hy IUDA. although they are based on the same observationa ata.," Our values differ substantially from the values given by RPDM, although they are based on the same observational data." This is because we use a completely different methoc to determine the density., This is because we use a completely different method to determine the density. For three out of fivenebulae we find results which are within the range of values foun with other methods., For three out of fivenebulae we find results which are within the range of values found with other methods. For M 4 we find a value which is a bit larger., For M $-$ 4 we find a value which is a bit larger. The results in Paper L indicate that our determination of the density is somewhat susceptible to measurement errors and. errors in the model assumptions., The results in Paper I indicate that our determination of the density is somewhat susceptible to measurement errors and errors in the model assumptions. This might provide an explanation for the discrepancy., This might provide an explanation for the discrepancy. The [act that we model only the core region of M 23 provides an explanation for the very. high. density we find for this nebula., The fact that we model only the core region of M $-$ 23 provides an explanation for the very high density we find for this nebula. Webster (1976). and. Bolli Stanghellini (1994. using the same spectrum) also find a high value using theIN] line ratio.," Webster \cite{c2:web76} and Boffi Stanghellini (1994, using the same spectrum) also find a high value using the line ratio." Pheiv] lines are expected to be formed predominantlv in the core region ancl hence this would confirm our results., The lines are expected to be formed predominantly in the core region and hence this would confirm our results. On the other hand. the excitation in the core is too high to form large amounts of .," On the other hand, the excitation in the core is too high to form large amounts of $^+$ ." Hence the Si] lines can be expected to originate predominantly, Hence the lines can be expected to originate predominantly i] Fieure 7..,in Figure \ref{fig:irzoom}. Iu both imaecs. the position of iis iudieated with a 07323 circle coufideuce). aud the average locations of the two lobes of the radio jet are illustrated with diamonds (Bowerctal.2005).," In both images, the position of is indicated with a 3 circle confidence), and the average locations of the two lobes of the radio jet are illustrated with diamonds \citep{bow05}." . There are clearly several füut infrared sources within the error circle of Hu the images taken in July 2001 απο panels. Fig. 7)).," There are clearly several faint infrared sources within the error circle of in the images taken in July 2004 (right panels, Fig. \ref{fig:irzoom}) )." The brightest of these. at the southwest edge. las AT= aud L'=13.3.," The brightest of these, at the southwest edge, has $K^\prime = 15.3$ and $L^\prime = 13.3$." Althoueh the A nuage from 2003 is not scusitive chough to reveal this source. it does appear to be preseut at the same duteusitv in L/ in 2003.," Although the $K$ image from 2003 is not sensitive enough to reveal this source, it does appear to be present at the same intensity in $L^\prime$ in 2003." " There mav also be several fainter sources near the detection tliresliold of A""~17 inthe A"" nuage frou July 2001.", There may also be several fainter sources near the detection threshold of $K^\prime \sim 17$ in the $K^\prime$ image from July 2004. Again. the δ΄ images from 2003 are uot seusitive enough to determine whether auy of these brightened.," Again, the $K$ images from 2003 are not sensitive enough to determine whether any of these brightened." Therefore. we are not able to uuiunubiguously identify the infrared counterpart to290031... but can can rule out with confidence that its infrared counterpart has A«15.," Therefore, we are not able to unambiguously identify the infrared counterpart to, but can can rule out with confidence that its infrared counterpart has $K<15$." Finally. we note that the A’ aud £’ images exteud no more than ssouth ofÀ.. and do not cover the region where the diffuse X-ray cnussion brightened.," Finally, we note that the $K^\prime$ and $L^\prime$ images extend no more than south of, and do not cover the region where the diffuse X-ray emission brightened." Therefore. we have obtained nuages with wider ficlds-ofview in order to search for gas aud dust that nmüeht have contributed to the brightening of the diffuse emission.," Therefore, we have obtained images with wider fields-of-view in order to search for gas and dust that might have contributed to the brightening of the diffuse emission." " In Figure δι, we preseut a LAST ju image of the Galactic ceuter taken in 1998 August with the Near Infrared Camera and"," In Figure \ref{fig:paalpha}, we present a 1.87 $\mu$ m image of the Galactic center taken in 1998 August with the Near Infrared Camera and" of particles having radius-depeudeut mass.,of particles having radius-dependent mass. Thus. their results can be directly compared with our results without much complication.," Thus, their results can be directly compared with our results without much complication." In the text. they stated that the hardening rate became coustant for the value of ΑΝ around 2—1107.," In the text, they stated that the hardening rate became constant for the value of $N$ around $2\sim 4 \times 10^5$." For their LOOK run. Apy=0.00125. which is 1/s of the value we usec.," For their 400K run, $M_{BH}=0.00125$, which is 1/8 of the value we used." Uufortuuatelv. the siauulation was stopped before we would expect to to see whether the loss-cone depletion would or would nof occur.," Unfortunately, the simulation was stopped before we would expect to to see whether the loss-cone depletion would or would not occur." Uulike the previous two papers. Milosavljevió&Aer-vitt(2001) calculated the actual merecr of two ealaxics with central black holes. as Makino(1997) did.," Unlike the previous two papers, \citet{MilosavljevicMerritt2001} calculated the actual merger of two galaxies with central black holes, as \citet{Makino1997} did." The difference between Milosavljevió&Merritt(2001) and Makino(1997) is that the former started with a galaxy model with a deusitv cusp with pxr? around the central black hole. while the latter used a Wine model with a finite core as the initial model.," The difference between \citet{MilosavljevicMerritt2001} and \citet{Makino1997} is that the former started with a galaxy model with a density cusp with $\rho \propto r^{-2}$ around the central black hole, while the latter used a King model with a finite core as the initial model." For simulations of mergers of elliptical galaxies with massive central black holes (LO°AL.. or larger). a galaxy model with finite-size core would be more appropriate. since the shallow “cusp” of such large ellipticals corresponds to a cutoff of the distribution function at finite energy.," For simulations of mergers of elliptical galaxies with massive central black holes $10^8 \msun$ or larger), a galaxy model with finite-size core would be more appropriate, since the shallow “cusp” of such large ellipticals corresponds to a cutoff of the distribution function at finite energy." The stellar distribution in the central region of spiral galaxies is consistent with a cusp of pxor7.," The stellar distribution in the central region of spiral galaxies is consistent with a cusp of $\rho \propto r^{-2}$." Therefore. for sinulatious of 1uergers of spiral galaxies. the initial model used by Milosavljevió&Moeritt(2001) may be more appropriate.," Therefore, for simulations of mergers of spiral galaxies, the initial model used by \citet{MilosavljevicMerritt2001} may be more appropriate." " Allosavljoevió&Merritt(2001) performed three rus with als. 161. anc 991 stars. aud found that the hardening rate was independent of the nunber of particles,"," \citet{MilosavljevicMerritt2001} performed three runs with 8K, 16K and 32K stars, and found that the hardening rate was independent of the number of particles." As discussed in their paper. this result was steuuued from the fact that the loss cone was nof depleted in their simulations. because of two reasons.," As discussed in their paper, this result was stemmed from the fact that the loss cone was not depleted in their simulations, because of two reasons." The first is that the initial ceutral density of their model was high. since they tailored the distribution function so that the progenitor galaxies hack ceutral cusps around the black holes.," The first is that the initial central density of their model was high, since they tailored the distribution function so that the progenitor galaxies had central cusps around the black holes." This is a situation very different frou that used in other studies. where black holes were placed off-ceuter in a single galaxy or placed at the ceuters of galaxies with relatively large cores.," This is a situation very different from that used in other studies, where black holes were placed off-center in a single galaxy or placed at the centers of galaxies with relatively large cores." Since the initial stellar deusitv around the black holes is very high. the binary initially hardens very rapidly.," Since the initial stellar density around the black holes is very high, the binary initially hardens very rapidly." A binary with a small semi-major axis has a small interaction cross section. which implies that it takes a long time to deplete the nearby stars.," A binary with a small semi-major axis has a small interaction cross section, which implies that it takes a long time to deplete the nearby stars." The second reason is the relatively small uuuber of particles cuploved iu their simulation. which resulted im rather laree random velocities.," The second reason is the relatively small number of particles employed in their simulation, which resulted in rather large random velocities." Therefore. Drownuiui motion of the binary covered a fairly large radius.," Therefore, Brownian motion of the binary covered a fairly large radius." Even in their largest calculation with 321s particles. the total mass of the stars which can cuter the region covered by the Brownian notion of the black hole binary is much larecr than he mass ejected bv the binary.," Even in their largest calculation with 32K particles, the total mass of the stars which can enter the region covered by the Brownian motion of the black hole binary is much larger than the mass ejected by the binary." Thus. the verv high initial central deusitv aud the relatively πα] nuuber of particles conspired together to prevent the loss cone roni being depleted.," Thus, the very high initial central density and the relatively small number of particles conspired together to prevent the loss cone from being depleted." If Milosavljovió&Alerritt(2001) could have used a uuch larger umber of particles. the wandering distauce would have shruuk. aud the loss cone would have con. formed carly ou.," If \citet{MilosavljevicMerritt2001} could have used a much larger number of particles, the wandering distance would have shrunk, and the loss cone would have been formed early on." According to their own estimate (AGlosavljevié&Morvitt2001).. for [N>2<10° the loss cone depletion becomes important.," According to their own estimate \citep{MilosavljevicMerritt2001}, for $N>2\times 10^5$ the loss cone depletion becomes important." To stuumarize. there is no real discrepancy among the results of full N-body simulations.," To summarize, there is no real discrepancy among the results of full $N$ -body simulations." observed weaker depeudeuce of the hardening rate han obtained iu the present study. simply because his calculations were not long enough.," observed weaker dependence of the hardening rate than obtained in the present study, simply because his calculations were not long enough." Milosavljevió&Mes-rit(2001) found no dependence on NW. essentially )ecause the nuuber of particles they used was too small or the loss cone to be depleted.," \citet{MilosavljevicMerritt2001} found no dependence on $N$, essentially because the number of particles they used was too small for the loss cone to be depleted." As first sueeested by BBR and confirmed by a uunuber of followup works. if the hardening timescale of the black tole binary is proportional to the relaxation timescale of he parent galaxy. the evolution timescale of typical black tole binaries in elliptical galaxies excecds the Hubble iue bv many orders of magnitude.," As first suggested by BBR and confirmed by a number of followup works, if the hardening timescale of the black hole binary is proportional to the relaxation timescale of the parent galaxy, the evolution timescale of typical black hole binaries in elliptical galaxies exceeds the Hubble time by many orders of magnitude." In other words. dünaries are unlikely to merece through eucouuters witli ficld stars and eravitational wave radiation.," In other words, binaries are unlikely to merge through encounters with field stars and gravitational wave radiation." Our results strongly sugeest that the hardening nuescale is indeed determined by the relaxation nuescale. for large enoush NN and after the binary )ecomies sufficieutlv hard.," Our results strongly suggest that the hardening timescale is indeed determined by the relaxation timescale, for large enough $N$ and after the binary becomes sufficiently hard." This implies that eravitational interaction with field stars is iusufficieut to let the binary nerec., This implies that gravitational interaction with field stars is insufficient to let the binary merge. There are a nunber of alternative mechanisms that uav lead to the mereer of the black hole binary., There are a number of alternative mechanisms that may lead to the merger of the black hole binary. If there is a significant amount of eas left at the ceuter. or if gas is supplied from the disk during the merecr event. it would certainly chauge the cutive picture.," If there is a significant amount of gas left at the center, or if gas is supplied from the disk during the merger event, it would certainly change the entire picture." However. iu the case of aanereer of two cllipticals. there is not much cold gas left iu the resulting galaxy.," However, in the case of a merger of two ellipticals, there is not much cold gas left in the resulting galaxy." Iu this case. the most likely outcome is that the binary. stuck at a certain seni-auajor axis. staves at the center of the loss conc.," In this case, the most likely outcome is that the binary, stuck at a certain semi-major axis, stays at the center of the loss cone." Itf the eccentricity of the binary goes up. the timescale of orbital evolution bv eravitational wave radiation is reduced significantly.," If the eccentricity of the binary goes up, the timescale of orbital evolution by gravitational wave radiation is reduced significantly." Roughly speaking. if the eccentricity reaches 0.9. a fair fraction of the binary black holes would merge in a time less than the ITubble time.," Roughly speaking, if the eccentricity reaches 0.9, a fair fraction of the binary black holes would merge in a time less than the Hubble time." Some of the early N-body simmlations aud scattering experiments have focused on this possibility. (Malkinoetal.1993:Mikkola&Valtonen 1992).," Some of the early $N$ -body simulations and scattering experiments have focused on this possibility \citep{Makinoetal1993,MikkolaValtonen1992}." . Tlowever. the eeneral couscusts seenis to be that the eccentricity docs not chanee much during the hardening.," However, the general consensus seems to be that the eccentricity does not change much during the hardening." This situation can change if there are more than two massive black holes., This situation can change if there are more than two massive black holes. If the binary black hole has a lone lifetime. it is quite natural to assume that some of the galaxies which contain binary black holes will undergo a further mereer with another galaxy with a central massive black hole or a binary.," If the binary black hole has a long lifetime, it is quite natural to assume that some of the galaxies which contain binary black holes will undergo a further merger with another galaxy with a central massive black hole or a binary." H£ we regard the black holes as poiut-mass particles interacting through Newtoman gravitv. then with three (or more) black holes we expect at most one black hole binary to be left in the galaxy. having ejected all other black holey. by the gravitational slingshot οςατάκα (Saslawetal. 1971).," If we regard the black holes as point-mass particles interacting through Newtonian gravity, then with three (or more) black holes we expect at most one black hole binary to be left in the galaxy, having ejected all other black holes by the gravitational slingshot mechanism \citep{SaslawValtonenAarseth1974}." . ILowever. here the eccentricity effects nüehlt play an inportant role.," However, here the eccentricity effects might play an important role." Simple estimates assumune a thermal distribution of eccentricities (λαο&Ebisuzaki1991) sugeest that. during repeated three body interactions. the eccentricity of the binary cau reach a very lieh value. resulting in quick merge through eravitatioual wave radiation.," Simple estimates assuming a thermal distribution of eccentricities \citep{MakinoEbisuzaki1994} suggest that, during repeated three body interactions, the eccentricity of the binary can reach a very high value, resulting in quick merging through gravitational wave radiation." Iu principle. it is possible that multiple black holes form a stable hierarchical svsteuni. where evolution of the outer binary is halted because of the loss cone depletion.," In principle, it is possible that multiple black holes form a stable hierarchical system, where evolution of the outer binary is halted because of the loss cone depletion." In this case. however. the inner binary would typically have a seni-mnajor axis of orde 1/10 of that of," In this case, however, the inner binary would typically have a semi-major axis of orde 1/10 of that of" the uv coverage of the observations. and imaged again.,"the uv coverage of the observations, and imaged again." The first step of our fitting procedure is to reproduce the observed continuum by creating regions whose sizes and densities are based on ?. for G10.47+0.03 and ? for SgrB2-M. For SgrB2-N. we use similar models as for G10.47--0.03 since the 1.3cm data of ? are not sufficient in terms of angular resolution and wavelength.," The first step of our fitting procedure is to reproduce the observed continuum by creating regions whose sizes and densities are based on \citet{Cesaroni10} for G10.47+0.03 and \citet{dePree98} for SgrB2-M. For SgrB2-N, we use similar models as for G10.47+0.03 since the 1.3cm data of \citet{Gaume95} are not sufficient in terms of angular resolution and wavelength." Sizes and densities of the regions are slightly modified to fit the observed continuum., Sizes and densities of the regions are slightly modified to fit the observed continuum. The hypercompact regions Bl and B2 in G10.4740.03 and K2 in SgrB2-N have thus density gradients (with r and outer radii of 1590 AU in BI. 950 AU in B2 and 1000 AU in K2). while all other regions have constant densities.," The hypercompact regions B1 and B2 in G10.47+0.03 and K2 in SgrB2-N have thus density gradients (with $r^{-1.5}$ and outer radii of 1590 AU in B1, 950 AU in B2 and 1000 AU in K2), while all other regions have constant densities." ? and ? also give spectral types of the exciting stars. which are converted to luminosity following ?..," \citet{Cesaroni10} and \citet{dePree98} also give spectral types of the exciting stars, which are converted to luminosity following \citet{Panagia73}." These stars heat the dust and are. for simplicity. placed in the plane of the sky. except for two regions in SgrB2-M. The dust density distribution is adapted to fit the line observations.," These stars heat the dust and are, for simplicity, placed in the plane of the sky, except for two regions in SgrB2-M. The dust density distribution is adapted to fit the line observations." Figure 11 shows the column densities in x. y. and z directions of the three models that are described in the following.," Figure \ref{fig:coldens} shows the column densities in x, y, and z directions of the three models that are described in the following." The model consists of a clump centered at BI whose density follows a Gaussian with 7x10 H» em? at the half-power radius of 7000 AU., The model consists of a clump centered at B1 whose density follows a Gaussian with $7\times 10^7$ $_2$ $^{-3}$ at the half-power radius of 7000 AU. This dust is heated by BI with 10° L«. B2 with 8.3x10 Ls. and A with 4.6x10 1...," This dust is heated by B1 with $10^5$ $_\odot$, B2 with $8.3\times 10^4$ $_\odot$, and A with $4.6\times 10^4$ $_\odot$." The intrinsic line width (FWHM) is 8.3 km s!., The intrinsic line width (FWHM) is 8.3 km $^{-1}$. The model output is compared to the observations in Fig. 12.., The model output is compared to the observations in Fig. \ref{fig:g10_mod}. In the model for SgrB2-N. the dust is heatedby K2 with 10° L. and K3 with 8.3x10+ Ls.," In the model for SgrB2-N, the dust is heatedby K2 with $10^5$ $_\odot$ and K3 with $8.3\times 10^4$ $_\odot$." The dust density follows a Gaussian centered at K2 with 7x10’ H» em at the half-power radius of 10 AU., The dust density follows a Gaussian centered at K2 with $7\times 10^7$ $_2$ $^{-3}$ at the half-power radius of $^4$ AU. An additional core (Gaussian with 5x105 Hs em at the half-power radius of 1000 AU) 3000 AU 1n front of K2 provides the strong absorption., An additional core (Gaussian with $5\times 10^8$ $_2$ $^{-3}$ at the half-power radius of 1000 AU) 3000 AU in front of K2 provides the strong absorption. The intrinsic line width is 10 km s!., The intrinsic line width is 10 km $^{-1}$. Figure 13 shows the comparison to the observations., Figure \ref{fig:b2n_mod} shows the comparison to the observations. In this model. the dust density follows two radial power laws with index 1.5. centered at FIf and F3.," In this model, the dust density follows two radial power laws with index 1.5, centered at F1f and F3." The first one starts with 5.5x105 Hs em at a radius of 660 AU. the latter one with 5»105 H» em? at 750 AU.," The first one starts with $5.5\times 10^8$ $_2$ $^{-3}$ at a radius of 660 AU, the latter one with $5\times 10^8$ $_2$ $^{-3}$ at 750 AU." Inside this latter radius. there is an region that contains a star of 8x10 Lis.," Inside this latter radius, there is an region that contains a star of $8\times 10^4$ $_\odot$." Additionally. a larger region is located 5000 AU closer to us with a star of 2.5x10° Ls - F3 is thus split into these two different regions.," Additionally, a larger region is located 5000 AU closer to us with a star of $2.5\times 10^5$ $_\odot$ - F3 is thus split into these two different regions." Fle with 2.5x10 Ls is located 2000 AU farther away from us than the other regions to facilitate absorption (Fig. 11))., F1e with $2.5\times 10^4$ $_\odot$ is located 2000 AU farther away from us than the other regions to facilitate absorption (Fig. \ref{fig:coldens}) ). Further heating is provided by Fle. FIf. F2. F4 teach 5.4x107 Li). Fla (3.8x107 Lis). and F3a (2.5x107 L..).," Further heating is provided by F1c, F1f, F2, F4 (each $5.4\times 10^4$ $_\odot$ ), F1a $3.8\times 10^4$ $_\odot$ ), and F3a $2.5\times 10^4$ $_\odot$ )." The intrinsic line width is 6.7 km s!., The intrinsic line width is 6.7 km $^{-1}$. A comparison to the observations is shown in Fig. 14.., A comparison to the observations is shown in Fig. \ref{fig:b2m_mod}. These models are as simple as possible to approach a good fit to the observations. but are not unique.," These models are as simple as possible to approach a good fit to the observations, but are not unique." The model maps shown in Figs., The model maps shown in Figs. 12 to 14. would appear more similar to the data 1f corresponding noise was added., \ref{fig:g10_mod} to \ref{fig:b2m_mod} would appear more similar to the data if corresponding noise was added. This noise also makes it difficult to constram more complicated models. since it is not clear how much of the clumpy substructure is real (which is on the order of only 2 or 3 times the rms noise) In. this section. we discuss implications from. the observational results and the modeling efforts.," This noise also makes it difficult to constrain more complicated models, since it is not clear how much of the clumpy substructure is real (which is on the order of only 2 or 3 times the rms noise) In this section, we discuss implications from the observational results and the modeling efforts." As explained in Sect. ??..," As explained in Sect. \ref{sec:results}," lower limits on optical depth and HCN column density can be derived from the absorption lines (Table 2))., lower limits on optical depth and HCN column density can be derived from the absorption lines (Table \ref{tab:abslines}) ). Outstanding 1s K2 in SgrB2-N. where the line ts optically thick.," Outstanding is K2 in SgrB2-N, where the line is optically thick." The column densities of hot HCN toward the regions where it is detected are at least a few times 10? cm. which translates into H» column densities of 1077 to 107? ο” even for a high HCN fractional abundance of 107.," The column densities of hot HCN toward the regions where it is detected are at least a few times $10^{19}$ $^{-2}$, which translates into $_2$ column densities of $^{24}$ to $10^{25}$ $^{-2}$ even for a high HCN fractional abundance of $10^{-5}$." This represents only the molecular gas at temperatures above roughly 300 K. In the models. the mass above 300 K is 350 M. in G10.47+0.03. 500 M. in SgrB2-N. and 200 M. in SgrB2-M. Such large quantities of hot molecular gas are necessary to explain the observations. and challenge theories of massive star formation.," This represents only the molecular gas at temperatures above roughly 300 K. In the models, the mass above 300 K is 350 $_\odot$ in G10.47+0.03, 500 $_\odot$ in SgrB2-N, and 200 $_\odot$ in SgrB2-M. Such large quantities of hot molecular gas are necessary to explain the observations, and challenge theories of massive star formation." Current hydrodynamical simulations. produce far too little hot molecular gas (e.g.2.withatotalmassof1000 M... both absolute and relative to the total mass. since the highly inhomogeneous structure (filamentary disks) does not lead to diffusion of the heating radiation.," Current hydrodynamical simulations produce far too little hot molecular gas \citep[e.g.][with a total mass of 1000 M$_\odot$]{Peters10}, both absolute and relative to the total mass, since the highly inhomogeneous structure (filamentary disks) does not lead to diffusion of the heating radiation." This is probably due to the lower initial mass and hence lower column densities and dust optical depths of these models. and it is to be hoped that in the future simulations of cores as massive as the ones presented in the current paper will reproduce our results.," This is probably due to the lower initial mass and hence lower column densities and dust optical depths of these models, and it is to be hoped that in the future simulations of cores as massive as the ones presented in the current paper will reproduce our results." Also a high abundance of HCN (on the order of 1077) in the dense. warm gas Is needed. since the dust densities of our models are consistent with dust continuum data from the SMA and a lower abundance would mean an even higher mass of the hot gas.," Also a high abundance of HCN (on the order of $10^{-5}$ ) in the dense, warm gas is needed, since the dust densities of our models are consistent with dust continuum data from the SMA and a lower abundance would mean an even higher mass of the hot gas." We expect future chemical models to compute such à high HCN abundance. probably through high-temperature gas-phase reactions.," We expect future chemical models to compute such a high HCN abundance, probably through high-temperature gas-phase reactions." Although HCN thermalizes to the ambient dust temperature. the population difference between the two (-type levels is very small. making them sensitive to the exact excitation conditions.," Although HCN thermalizes to the ambient dust temperature, the population difference between the two $\ell$ -type levels is very small, making them sensitive to the exact excitation conditions." " The line optical depth is proportional to the population difference. where T, and T, are the excitation temperatures for the lower and upper state. respectively."," The line optical depth is proportional to the population difference, where $T_{\rm l}$ and $T_{\rm u}$ are the excitation temperatures for the lower and upper state, respectively." " A difference of between 7| and 7, causes r to change by more than70%:: inversion occurs if 7, is larger than ΤΙ.", A difference of between $T_{\rm l}$ and $T_{\rm u}$ causes $\tau$ to change by more than; inversion occurs if $T_{\rm u}$ is larger than $T_{\rm l}$ . The two levels are independently coupled to the ground vibrational state through the I4j:m transitions. which determine the excitation temperatures.," The two levels are independently coupled to the ground vibrational state through the $\mu$ m transitions, which determine the excitation temperatures." If these are different. the analysis would be far more difficult. as one would have to know the exact I4jm radiation field. where lines could slightly affect the optical depths.," If these are different, the analysis would be far more difficult, as one would have to know the exact $\mu$ m radiation field, where lines could slightly affect the optical depths." However. there is no such mechanismknown. and an extreme sub-thermal population difference. which would," However, there is no such mechanismknown, and an extreme sub-thermal population difference, which would" which are crucial lor solar activity. mav take place there (Dikpati&Gilman&Cally 2007).,"which are crucial for solar activity, may take place there \citep{dik05,gil07}." . MIID waves and oscillations in the tachocline may play a sienilicant role in both cases: thev may redistribute the angular momentum in the horizontal direction aud some of (hem may become unstable due to the differential rotation. leading to magnetic fIux emergence al the solar surface.," MHD waves and oscillations in the tachocline may play a significant role in both cases: they may redistribute the angular momentum in the horizontal direction and some of them may become unstable due to the differential rotation, leading to magnetic flux emergence at the solar surface." Therefore. to study the complete spectrum of possible wave modes in this svstem is of vital importance.," Therefore, to study the complete spectrum of possible wave modes in this system is of vital importance." The tachocline is verv thin compared to the solar radius. therefore the ordinary shallow water approximation mocdilfied by (he presence of a horizontal large-scale magnetic fiekl can be easily applied (Gilman2000).," The tachocline is very thin compared to the solar radius, therefore the ordinary shallow water approximation modified by the presence of a horizontal large-scale magnetic field can be easily applied \citep{gil00}." . The spectrum of various shorter scale shallow water MIID waves has been recently studied in Cartesian coordinates by Sceliecterοἱal.(2001)., The spectrum of various shorter scale shallow water MHD waves has been recently studied in Cartesian coordinates by \citet{sch01}. . However. global wave mocles. those with a wavelength comparable to the solar radius. must be considered in spherical coordinates.," However, global wave modes, those with a wavelength comparable to the solar radius, must be considered in spherical coordinates." Recently. Zaqarashvilietal.(2007) have studied the spherical shallow water ALLID waves in the simplest case. in which the hieh frequency. branch i.e. magnetic Poincaré waves (or magneto-gravitv waves) and the influence of the tachocline thickness on the wave dvnamics have been ignored (that is. when the surface eravily speed is much higher than the surface rotation speed).," Recently, \citet{zaq07} have studied the spherical shallow water MHD waves in the simplest case, in which the high frequency branch i.e. magnetic Poincaré waves (or magneto-gravity waves) and the influence of the tachocline thickness on the wave dynamics have been ignored (that is, when the surface gravity speed is much higher than the surface rotation speed)." This approximation has enabled us to study (he dynamics of elobal magnetic Rossby waves in the lower. strongly stable part of the tachocline. but it fails in the upper. weakly stable overshoot region. where a negative buovancy due to the subaciabatic stratification strongly reduces the gravity speed (Gilman2000).," This approximation has enabled us to study the dynamics of global magnetic Rossby waves in the lower, strongly stable part of the tachocline, but it fails in the upper, weakly stable overshoot region, where a negative buoyancy due to the subadiabatic stratification strongly reduces the gravity speed \citep{gil00}." . In this letter. we present the analvlical spectrum of global linear shallow water MILD waves lor bot parts of the tachocline in the absence of differential rotation.," In this letter, we present the analytical spectrum of global linear shallow water MHD waves for both parts of the tachocline in the absence of differential rotation." We use the linearized shallow water MIID equations in the rotating spherical coordinate, We use the linearized shallow water MHD equations in the rotating spherical coordinate search for gravitational waves is one of the most important tasks in modern astronomy and physics.,Search for gravitational waves is one of the most important tasks in modern astronomy and physics. Various techniques are used to look for gravitational waves in a very broad range of frequencies (rom 101 (Baskaran.Grishehuk2006) to (LIGO2003).., Various techniques are used to look for gravitational waves in a very broad range of frequencies from $10^{-18}$ \citep{bgp2006} to \citep{LIGOwebsite}. " Pulsar timing provides a unique access for observations in a low-frequeney band (10.Ην«ως10"" Mz) (Sazhin1978:Detweiler1979:Bertotti.Carr&Rees 1983)."," Pulsar timing provides a unique access for observations in a low-frequency band $10^{-7} ~\mathrm{Hz}x. df oreduces to the Calilean boost (9)).","The relativistic dispersion$E(p) = \sqrt{m^2 c^4 + c^2 p^2}$ implies the Hamiltonian and the semi-relativistic boost operator In the non-relativistic limit, when $c \rightarrow \infty$, it reduces to the Galilean boost \ref{galileanboost}) )." The generating function in the form of relativistic plaue wave then gives semi-relativistic poblvuonials Tuthe non-rclativistie limit 7727>H2., The generating function in the form of relativistic plane wave then gives semi-relativistic polynomials Inthe non-relativistic limit $H^{SRS}_n \rightarrow H^S_{n} $. " The first three polyionmials coincide exactly with the Schréddinger polvuouiials Ip!Cr.f)e. IL,(SRS)47D|: iAP. I(SRS)=r?m|hb.Het. while. starting. from. the fourthJ one we have relativistic corrections of order 1/607."," The first three polynomials coincide exactly with the Schröddinger polynomials $H^{SRS}_1 (x,t) = x$, $H^{(SRS)}_2(x,t) = x^2 + i \frac{\hbar}{m} t$ , $H^{(SRS)}_3 = x^3 + i\frac{\hbar}{m} 3 x t$, while starting from the fourth one we have relativistic corrections of order $1/c^2$." For complex valued space coordinate as it appears in 2|1 dimensional Chern-Simous theory [1].. zeros of these polwuouuals describe a motion of poiut vortices in the plane.," For complex valued space coordinate $x$, as it appears in 2+1 dimensional Chern-Simons theory \cite{PG}, zeros of these polynomials describe a motion of point vortices in the plane." Equations of inotion for No vortices are (ks = L.....N) Using Schróddiuger's log V transform: [5Γ |. W2ch and identity the Schróddiuger equation (1)) can be rewritten in the form," Equations of motion for $N$ vortices are (k = 1,...,N): Using Schröddinger's log $\Psi$ transform \cite{S}, , $\Psi = e^{\ln \Psi}$ , and identity the Schröddinger equation \ref{Schrodinger}) ) can be rewritten in the form" We run several 3D numerical models in order to understand the chemical and dynamical evolution of the ISM in dSphs as a function of several parameters like the SEIL and the amount of dark matter.,We run several 3D numerical models in order to understand the chemical and dynamical evolution of the ISM in dSphs as a function of several parameters like the SFH and the amount of dark matter. Given the large amount of epu time required to complete a single model. we could not explore avast region of the parameter space: instead. we tailorec our galaxy model on Draco and considered SLLs similar to those supported by the observations for this galaxy.," Given the large amount of cpu time required to complete a single model, we could not explore a vast region of the parameter space; instead, we tailored our galaxy model on Draco and considered SFHs similar to those supported by the observations for this galaxy." " AME the adopted SELs last 3 Cvr and give rise to the same fina amount Ad,=5.610"" M. of stellar mass.", All the adopted SFHs last 3 Gyr and give rise to the same final amount $M_{\star}=5.6\times 10^5$ $_{\odot}$ of stellar mass. The stars are supposed to form in a sequencei of instantaneous identica bursts separated by. quicscent periods: dillerent Ες diller bv the assumed number of bursts. but the total number of SNIL (but not SNla) is always the same.," The stars are supposed to form in a sequence of instantaneous identical bursts separated by quiescent periods; different SFHs differ by the assumed number of bursts, but the total number of SNII (but not SNIa) is always the same." Although the total energy released by the SNe is orders of magnitude larger than the binding energy of the ISM. the ealaxy retains almost the totality of its initial gas. unless rather light clark haloes are assumed.," Although the total energy released by the SNe is orders of magnitude larger than the binding energy of the ISM, the galaxy retains almost the totality of its initial gas, unless rather light dark haloes are assumed." This is due to the huge efficiency of the radiative cooling. despite the low mean metallicity (Z—107? Z.) of the eas.," This is due to the huge efficiency of the radiative cooling, despite the low mean metallicity $Z\sim 10^{-2}$ $\rm Z_{\odot}$ ) of the gas." For most. parameter combinations tested. in this stuck. such ellective radiative losses prevent the gas to slowly accumulate the SN energy.," For most parameter combinations tested in this study, such effective radiative losses prevent the gas to slowly accumulate the SN energy." With our assumptions. the galaxy never gets rid of its gas. unless the potential well is rather shallow (see Section 5.3)): in this latter case a galactic wind starts quite soon and the ealaxy looses all its eas in less than 200 Myr.," With our assumptions, the galaxy never gets rid of its gas, unless the potential well is rather shallow (see Section \ref{sec:draco-s}) ); in this latter case a galactic wind starts quite soon and the galaxy looses all its gas in less than 200 Myr." ln the light of the above cliscussion. we conclude that the dark halo of Draco must be massive and extended in order to retain the gas for a period of several Gyr. the duration of its star formation.," In the light of the above discussion, we conclude that the dark halo of Draco must be massive and extended in order to retain the gas for a period of several Gyr, the duration of its star formation." This in turn implies the need of an external mechanism to remove the gas and end the star formation. as gas stripping and/or tidal interaction bv the Galaxy (?)..," This in turn implies the need of an external mechanism to remove the gas and end the star formation, as gas stripping and/or tidal interaction by the Galaxy \citep{mayer2005}." The above arguments highlight the crucial role played by the radiative cooling in our mocdoels: would these losses be less substantial. galactic winds could develop more easily and the evolutionary scenario would drastically change.," The above arguments highlight the crucial role played by the radiative cooling in our models: would these losses be less substantial, galactic winds could develop more easily and the evolutionary scenario would drastically change." A correct evaluation of the radiative losses in the numerical simulations is thus of the utmost importance., A correct evaluation of the radiative losses in the numerical simulations is thus of the utmost importance. Unfortunately. it is known that in numerical hvdrocynamies several factors concur to degrade an accurate estimate of these losses.," Unfortunately, it is known that in numerical hydrodynamics several factors concur to degrade an accurate estimate of these losses." More confusing. some [actors lead to an overestimate. while others to an underestimate.," More confusing, some factors lead to an overestimate, while others to an underestimate." Overestimates occur particularly αἲ the contact discontinuities separating hot rarelieck ancl cold. dense gas phases because the intrinsic diffusion of the numerical scheme spreads these discontinuities over several mesh points creating a gas phase with intermediate densities and temperatures characterized by a large emissivity., Overestimates occur particularly at the contact discontinuities separating hot rarefied and cold dense gas phases because the intrinsic diffusion of the numerical scheme spreads these discontinuities over several mesh points creating a gas phase with intermediate densities and temperatures characterized by a large emissivity. Although several physical processes (such as turbulences and. heat conduction) really smear out these ciscontinuities. the numerical spread is likely to be larger than the physical one.," Although several physical processes (such as turbulences and heat conduction) really smear out these discontinuities, the numerical spread is likely to be larger than the physical one." Underestimates as well as overestimates of the radiative cooling at the contact discontinuities may occur when in the numerical code a cooling curve calculated in a regime of ionization equilibrium is implemented. (as we actually do), Underestimates as well as overestimates of the radiative cooling at the contact discontinuities may occur when in the numerical code a cooling curve calculated in a regime of ionization equilibrium is implemented (as we actually do). Η has become common practice to analyse and. interpret the observed. abundance and. distribution of high-redshift galaxies by approximating a limited survey volume to a single-epoch snapshot of the Universe (Ellis2007).,It has become common practice to analyse and interpret the observed abundance and distribution of high-redshift galaxies by approximating a limited survey volume to a single-epoch snapshot of the Universe \citep{Ellis07}. . The observed. data is then compared. to theoretical predictions which were calculated. for an idealized snapshot of. this nature., The observed data is then compared to theoretical predictions which were calculated for an idealized snapshot of this nature. Llowever. in actual observations. an increase in the distance along the line-of-sight corresponds to an earlier cosmic time at which the properties of the surveyed galaxy population may change.," However, in actual observations, an increase in the distance along the line-of-sight corresponds to an earlier cosmic time at which the properties of the surveyed galaxy population may change." " The “snapshot approximation"" is adequate for galaxy surveys at low redshifts. when galaxy halos are common and their mass function is not evolving rapidly with cosmic time."," The “snapshot approximation” is adequate for galaxy surveys at low redshifts, when galaxy halos are common and their mass function is not evolving rapidly with cosmic time." At these low redshifts. a relatively small region of space spanning a narrow redshift range can still be sulficientIv large to contain an adequate sample of these abundant objects.," At these low redshifts, a relatively small region of space spanning a narrow redshift range can still be sufficiently large to contain an adequate sample of these abundant objects." However. the validity of the approximation should be carefully. examined at high. redshifts when massive ealaxies are rare and their abundance varies exponentially with redshift.," However, the validity of the approximation should be carefully examined at high redshifts when massive galaxies are rare and their abundance varies exponentially with redshift." To illustrate the situation at. high. redshifts. [et us consider two regions of the same shape centered at dilferent redshifts and containing the same number of galaxy halos of a particular mass.," To illustrate the situation at high redshifts, let us consider two regions of the same shape centered at different redshifts and containing the same number of galaxy halos of a particular mass." The region centered at the higher redshift will span a larger range in redshift for two reasons., The region centered at the higher redshift will span a larger range in redshift for two reasons. First. since halos of a given mass are rarer at a higher redshift. he higher redshift region must have a larger comoving size han the one at smaller redshift for each to contain the same number of halos.," First, since halos of a given mass are rarer at a higher redshift, the higher redshift region must have a larger comoving size than the one at smaller redshift for each to contain the same number of halos." Second. the same comoving distance corresponds to a larger redshift interval at higher. recshift han at lower redshift (ic. dz (Ον. where \ is he comoving length and the Hubble parameter. (2). is an increasing function of z).," Second, the same comoving distance corresponds to a larger redshift interval at higher redshift than at lower redshift (i.e. $dz = [H(z)/c] d\chi$ , where $\chi$ is the comoving length and the Hubble parameter, $H(z)$, is an increasing function of $z$ )." The dilference between snapshot analvsis (on a space-like hypersurface) and that along the ight-cone is becoming increasinglyrelevant with purported, The difference between snapshot analysis (on a space-like hypersurface) and that along the light-cone is becoming increasinglyrelevant with purported larger clistances from the SMDLL which cancelled most of the angular momentum of the gas. or cooling of a large quantity of hot gas that already had a specific angular momentunm much smaller than that of the Galaxy (hot gas can be supported by its pressure in accdition to rotation).,"larger distances from the SMBH, which cancelled most of the angular momentum of the gas, or cooling of a large quantity of hot gas that already had a specific angular momentum much smaller than that of the Galaxy (hot gas can be supported by its pressure in addition to rotation)." In these conditions. it is reasonable to expect that the disk will settle into a local thermal equilibrium. in which the gas is heated via turbulence generated by self-gravitation (Ciammie.2001) and is cooled by radiation.," In these conditions, it is reasonable to expect that the disk will settle into a local thermal equilibrium, in which the gas is heated via turbulence generated by self-gravitation \citep{Gammie01} and is cooled by radiation." Phe magnitude of viscosity a- parameter. and the disk cooling time. foo... are then coupled by (Gammie.2001:Levin.2003:Riceetal..2005):: where 5 is the adiabatic index of gas.," The magnitude of viscosity $\alpha$ -parameter, and the disk cooling time, $t_{\rm cool}$, are then coupled by \citep{Gammie01,Levin03b,Rice05}: where $\gamma$ is the adiabatic index of gas." As we shall see low. for the parameters of interest. the evolution of the disk after star formation is turned on proceeds on a time scale again shorter than the local viscous time.," As we shall see below, for the parameters of interest, the evolution of the disk after star formation is turned on proceeds on a time scale again shorter than the local viscous time." Therefore. »ow: we assume that the disk is in the Bhiydrostatie and hermal equilibrium. but not in a steady aceretion state. when the accretion rate AIR)= const.," Therefore, below we assume that the disk is in the hydrostatic and thermal equilibrium, but not in a steady accretion state, when the accretion rate $\dot M(R) =$ const." We now estimate he conditions in the disk (as a function of radius £2) when it reaches surface density large enough to suller local eravitational collapse., We now estimate the conditions in the disk (as a function of radius $R$ ) when it reaches surface density large enough to suffer local gravitational collapse. Star formation is a local process in his approach. and dillerent rings in the disk could become eravitationally unstable at cüfferent times.," Star formation is a local process in this approach, and different rings in the disk could become gravitationally unstable at different times." The appropriate accretion disk equations for Qo~1 ave been discussed by many authors (see references in the Introduction)., The appropriate accretion disk equations for $Q\sim 1$ have been discussed by many authors (see references in the Introduction). The hvdrostatie balance condition vields where ὃς is the isothermal sound speed. 7? ancl p are the total pressure and gas density. Z7 is the disk scale height and OF=(CMpgg/IU|o2/R7) is the Ixeplerian. angular frequeney at radius Z7 from the black hole.," The hydrostatic balance condition yields where $c_s$ is the isothermal sound speed, $P$ and $\rho$ are the total pressure and gas density, $H$ is the disk scale height and $\Omega^2 = (G\mbh/R^3 + \sigma_v^2/R^2)$ is the Keplerian angular frequency at radius $R$ from the black hole." " a, here is the stellar velocity dispersion just outside the SMDLL radius of inlluence. ic. where the total stellar mass becomes larger than Mpg."," $\sigma_v$ here is the stellar velocity dispersion just outside the SMBH radius of influence, i.e. where the total stellar mass becomes larger than $\mbh$." Using equation 2.. the disk midplane density is determined by inversion of the definition of Toomre(1964) Q-parametoer: Lo solve for temperature of the disk. we should specify heating and cooling rates per unit area of the disk.," Using equation \ref{cs}, the disk midplane density is determined by inversion of the definition of \cite{Toomre64} $Q$ -parameter: To solve for temperature of the disk, we should specify heating and cooling rates per unit area of the disk." The former is coupled to the rate of the mass transfer through the disk. AL: The aceretion rate is given by where “=2ifp is the disk surface densitv.," The former is coupled to the rate of the mass transfer through the disk, $\dot M$: The accretion rate is given by where $\Sigma = 2 H \rho$ is the disk surface density." The kinematic viscosity 7 in terms of the Shakura&Sunvaev(1073) prescription is v=ασ.," The kinematic viscosity $\nu$ in terms of the \cite{Shakura73} prescription is $\nu = \alpha c_s H$." Marginally stable selt-eravitating disks are believed to have a~1 (Lin&Prinele.Ganimic.2001:Riceetal..2005). generated by spiral density. waves.," Marginally stable self-gravitating disks are believed to have $\alpha\sim 1$ \citep{Lin87,Gammie01,Rice05} generated by spiral density waves." The cooling rate of the disk (per side per unit surface area) is given by where τς&Xj2 is the optical depth of the disk., The cooling rate of the disk (per side per unit surface area) is given by where $\tau = \kappa \Sigma/2$ is the optical depth of the disk. " ""his expression allows one to switch smoothly from the optically hick 7rZ»1 to the optically thin 7«1 radiative cooling inits.", This expression allows one to switch smoothly from the optically thick $\tau\gg 1$ to the optically thin $\tau \ll 1$ radiative cooling limits. We approximate the opacity coefficient. & following ‘Table 3 in the Appendix of Bell&Lin(1994)., We approximate the opacity coefficient $\kappa$ following Table 3 in the Appendix of \cite{Bell94}. . For the woblem at hand. it is just the first four entries in the ‘Table are important as disk solutions with 722000 Ix are hermally unstable(seealsoAppendixDBinFhompsonetal..2005) since opacity rises as quickly as &«xT? in that region.," For the problem at hand, it is just the first four entries in the Table are important as disk solutions with $T\simgt 2000 $ K are thermally \citep[see also Appendix B in][]{Thompson05} since opacity rises as quickly as $\kappa \propto T^{10}$ in that region." This rather simple approximation to the opacities is justified for the order of magnitude parameter study that we intend to perform here., This rather simple approximation to the opacities is justified for the order of magnitude parameter study that we intend to perform here. In addition. we set à minimum. emperature of 1°=40 I for our solutions.," In addition, we set a minimum temperature of $T=40$ K for our solutions." Even without any eas accretion. realistic gas disks near galactic centres will be rated by external stellar radiation to elfective temperatures of this order or slightly larger.," Even without any gas accretion, realistic gas disks near galactic centres will be heated by external stellar radiation to effective temperatures of this order or slightly larger." Phe main conclusions of this iur do not sensitively depend on the exact value of the minimunm temperature or exact opacity law., The main conclusions of this paper do not sensitively depend on the exact value of the minimum temperature or exact opacity law. The upper panel of Figure 1 shows the resulting disk “mass” clelined as A4;=ποτ and the midplane, The upper panel of Figure \ref{fig:fig1} shows the resulting disk “mass” defined as $M_d = \pi \Sigma R^2$ and the midplane temperature atmospheres and therefore spectra replete with dense and complex molecularlines.,temperature atmospheres and therefore spectra replete with dense and complex molecular. Although these spectra have been analysed by a few stellar. spectroscopists. the abundance studies are generally limited to very few elements aud isotopic ratios.," Although these spectra have been analysed by a few stellar spectroscopists, the abundance studies are generally limited to very few elements and isotopic ratios." The ACD phase of stellar evolution concludes. with a rapid phase of evolution to the tip of the white dwarf cooling track., The AGB phase of stellar evolution concludes with a rapid phase of evolution to the tip of the white dwarf cooling track. This post-AGB (PAGB) phase takes a star in a few thousand vears or so from a cool AGB star to a verv hot central star of a planetary nebula and onto a white dwarl cooling track., This post-AGB (PAGB) phase takes a star in a few thousand years or so from a cool AGB star to a very hot central star of a planetary nebula and onto a white dwarf cooling track. Alone this track. the star's spectrum is amenable to straightforward abundance analysis and thus olfers apparently a way to infer the abundance changes brought by the PACGD stars AGD progenitor.," Along this track, the star's spectrum is amenable to straightforward abundance analysis and thus offers apparently a way to infer the abundance changes brought by the PAGB star's AGB progenitor." This inference is. of course. dependent on the assumption that the composition of an AGB star is exactly preserved by the DACGD star.," This inference is, of course, dependent on the assumption that the composition of an AGB star is exactly preserved by the PAGB star." Observations of certain PAGB stars show that us is a false assumption., Observations of certain PAGB stars show that this is a false assumption. " For example. several PACGI stars show abundance anomalies correlated with the condensation temperature Ted [ου dust grains to MNnse out of gas of normal composition (see Van Winekel2003 n""for à review) a process we refer to as ""dust-gas "," For example, several PAGB stars show abundance anomalies correlated with the condensation temperature $_C$ for dust grains to condense out of gas of normal composition (see Van Winckel 2003 for a review) – a process we refer to as `dust-gas winnowing'." "Other PAGB candidate stars show abundance anomalies correlated with the ionization potential of the neutral atoms (Rao Reclely 2005) a process we refer to as ""the FLP ellect'.", Other PAGB candidate stars show abundance anomalies correlated with the ionization potential of the neutral atoms (Rao Reddy 2005) – a process we refer to as `the FIP effect'. Given that the PACGD phase is rapid. the number of identified PACGB stars is relatively small and the number subjected to an abundance analysis is. of course. even smaller.," Given that the PAGB phase is rapid, the number of identified PAGB stars is relatively small and the number subjected to an abundance analysis is, of course, even smaller." In this paper. we report abundance analyses for 11 candidate PAGB stars and have compiled. abundance data of previously analysed PAGB stars in an attempt to seek explanations for the diverse compositions of these objects.," In this paper, we report abundance analyses for 11 candidate PAGB stars and have compiled abundance data of previously analysed PAGB stars in an attempt to seek explanations for the diverse compositions of these objects." Our sample stars are presented in Table 1. and displayed in he IRAS two colour diagram Figure 1. which has proven o be a powerful tool for identifving candidate PAGB stars (van der Veen Habing 1988: Suárrez et al., Our sample stars are presented in Table 1 and displayed in the IRAS two colour diagram Figure \ref {loci1} which has proven to be a powerful tool for identifying candidate PAGB stars (van der Veen Habing 1988; Suárrez et al. 2006: Szezerba et al., 2006; Szczerba et al. 2007)., 2007). " Nine of our eleven stars have measured LAS luxes and are identified in Figure1: the stars. HD. 107369 and DD |39"" 4926 were not detected by LAS."," Nine of our eleven stars have measured IRAS fluxes and are identified in Figure \ref{loci1}; the stars, HD 107369 and BD $^{o}$ 4926 were not detected by IRAS." lt is known that zone |. of IRAS two colour diagram o» van cer Veen Παρί LOSS corresponds to. [luxes rom stellar photospheres warmer than 2000K. Phe LAS colours of Zones L-LL signify the emergence and evolution of circumstellar shell (CS) produced. by increasing large mass-loss at AGB., It is known that zone 1 of IRAS two colour diagram by van der Veen Habing 1988 corresponds to fluxes from stellar photospheres warmer than 2000K. The IRAS colours of Zones II-III signify the emergence and evolution of circumstellar shell (CS) produced by increasing large mass-loss at AGB. Sources at Zone IV. are at the super-wind phases or sliehth bevond., Sources at Zone IV are at the super-wind phases or slightly beyond. Zone Vo contains objects with only signature of cold dust shell as the mass-Ioss has stopped hence warm dust is not being added., Zone V contains objects with only signature of cold dust shell as the mass-loss has stopped hence warm dust is not being added. The objects with detached: cold. CS would be seen at region Vila. while objects in zone Vib contains objects with warm as well as cold CS.," The objects with detached cold CS would be seen at region VIa, while objects in zone VIb contains objects with warm as well as cold CS." Phe Zone VIL and dashed region is dominated by DAGDs with PN like colours., The Zone VII and dashed region is dominated by PAGBs with PN like colours. Our sample stars IAS05208-2035.js LAS ()o-232]. Ihe BN2611 and LAS01259S23 belong to zone Illa. Ith andIN. ονwhere signatures of CS formed. by. increased mass-loss at AGB are evident.," Our sample stars IRAS 05208-2035, IRAS 07140-2321, IRAS 12538-2611 and IRAS 01259+6823 belong to zone IIIa, IIIb and IV where signatures of CS formed by increased mass-loss at late AGB are evident." ΗνΑν 17279-1119 (zone Vib) seems to ves the hot as well as cold. clust shell while HAS.07331des|0021. LRAS 22223|4327. LRAS 5 have PN like ," IRAS 17279-1119 (zone VIb) seems to possess the hot as well as cold dust shell while IRAS 07331+0021, IRAS 22223+4327, IRAS 08187-1905 have PN like colours." "Ligh-resolution optical spectra. were obtained at the W.J. MeDonald Observatory with the 2.7m Harlan. J.. Smith rellector. and the ""Tull. coudé spectrograph (Pull et al.", High-resolution optical spectra were obtained at the W.J. McDonald Observatory with the 2.7m Harlan J. Smith reflector and the Tull coudé spectrograph (Tull et al. 1995) with a resolving power of 60.000.," 1995) with a resolving power of 60,000." Spectral coverage in à single exposure from this cross-cispersed echelle spectrograph is complete up to and extensive but incomplete at longer wavelengths., Spectral coverage in a single exposure from this cross-dispersed echelle spectrograph is complete up to and extensive but incomplete at longer wavelengths. A S/N— ratio of δ0-100 over much of the spectral range was achieved., A S/N ratio of 80-100 over much of the spectral range was achieved. Figure 2 contains à [ew representative spectra to illustrate the quality of typical spectra., Figure \ref {loci2} contains a few representative spectra to illustrate the quality of typical spectra. = |-- CB » (tii ny)» C's i ,"_p^* h^*+ ( - )^2, C_1 _l ( - ), C_2 _l ." It is straightforward to check that the derivative ofV7 with respect to /* is zero: hence our results are independent of (he choice of /*., It is straightforward to check that the derivative of$\tilde{\chi}^2$ with respect to $h^*$ is zero; hence our results are independent of the choice of $h^*$ . We take h*=0.65., We take $h^*=0.65$. " For a given choice of ny,,. we can minimize (he modilied X7 statistic of Eq.(3.1)) to find the best fit O°m and PNA)py(z) (parametrized by ρε.D 7=1. 2. .... ng).bin "," For a given choice of $n_{bin}$, we can minimize the modified $\chi^2$ statistic of \ref{eq:chi2mod}) ) to find the best fit $\Omega_m^{obs}$ and $\rho_X(z)$ (parametrized by $\rho_i$, $i=1$, 2, ..., $n_{bin}$ )." We can find one sigma5 error bars by finding values with (Ay)?=1 from the minimum., We can find one sigma error bars by finding values with $(\Delta \chi)^2 = 1$ from the minimum. For each model in Table 1. we obtainfour sets of best fit parameters.," For each model in Table 1, we obtain sets of best fit parameters." We apply. [our different constraints to the arbitrary finetion ον) in order to discover which one allows a eood fit., We apply four different constraints to the arbitrary function $\rho_X(z)$ in order to discover which one allows a good fit. The four constraints are: d) px(z)=px(0)constant: ie. a cosmological constant moclel: and Gv) completely unconstrained py(z).," The four constraints are: (i) $\rho_X(z)=\rho_X(0) = {\rm constant}$; i.e., a cosmological constant model; (ii) $\rho_X'(z) \geq 0$; (iii) $\rho_X'(z) < 0$; and (iv) completely unconstrained $\rho_X(z)$." For each of these constraints. we find (he best fit parameters.," For each of these constraints, we find the best fit parameters." Figure 4 shows our results: panels (a) and (b) correspond to the AIP Carclassian aud quintessence models described in Table 1 respectively., Figure 4 shows our results: panels (a) and (b) correspond to the MP Cardassian and quintessence models described in Table 1 respectively. For simulated data of Model 1 of Table 1. a cosmologicalo constant model. we find that Qnm is estimated correctly to accuracy. regardless of the assumption made about P(z).," For simulated data of Model 1 of Table 1, a cosmological constant model, we find that $\Omega_m^{obs}$ is estimated correctly to accuracy, regardless of the assumption made about $\rho_X'(z)$." " For Model 2 (MP Cardassian) and Model 3 (quintessence). Fig.d(a) and (b) show the best fit obs O77. under all ofthe four constraints above. for nj, values ranging from 1 to 10."," For Model 2 (MP Cardassian) and Model 3 (quintessence), Fig.4(a) and (b) show the best fit $\Omega_m^{obs}$ , under all ofthe four constraints above, for $n_{bin}$ values ranging from 1 to 10." We find that assuming the wrong, We find that assuming the wrong the numerical simulations.,the numerical simulations. We take the trace of equation (7)) with k=k’ aud integrate over m. thereby removing the 6-fuuction iu time aud vielcling To obtain the final expression we have replaced the ensemble average with au average over time / (assuming ergodicity). replaced the integral over τε[75€.56] by an integral over a finite interval that is sufficieutly larger than the velocity correlation time 7. in order to eusure convergeuce (1 is the sinallest integer required lor couvergence). aud integrated over the direction of k.," We take the trace of equation \ref{eq:corr_v_k}) ) with $\mathbf{k}=\mathbf{k}'$ and integrate over $\tau$, thereby removing the $\delta$ -function in time and yielding To obtain the final expression we have replaced the ensemble average with an average over time $t$ (assuming ergodicity), replaced the integral over $\tau \in [-\infty, \infty]$ by an integral over a finite interval that is sufficiently larger than the velocity correlation time $\tau_c$ in order to ensure convergence $n$ is the smallest integer required for convergence), and integrated over the direction of $\mathbf{k}$." We then determine the spatial correlator (η) (rom F(A) by uunerically integrating equation (S)) using a modified Simpson's We then seek solutious of equation (5)) in the form Mj(r./)=AMj(r)exp(A/).," We then determine the spatial correlator $\kappa_L(r)$ from $F(k)$ by numerically integrating equation \ref{eq:kappa_L_F}) ) using a modified Simpson's We then seek solutions of equation \ref{eq:M_L}) ) in the form $M_L(r,t)=M_L(r)\exp(\lambda t)$ ." The equations are solved utunerically using a fourth-orcer BRuuge-Ixutta method. (for details see MalyshkiuBoldyrey (2007)))., The equations are solved numerically using a fourth-order Runge-Kutta method (for details see \cite{malyshkinb2007}) ). " The maguetic spectrum function. Εμ.) cau be determined from AL;(r./!) by (see Monin&Yaglom (1971))) Iu the next section. we shall compare the Ixazautsev- magnetic. spectrum iοπήggFyfh)o, and the erowth rate A with the magnetic spectrum £p(&) aud the erowth rate that are obtained from the direct. numerical simulations."," The magnetic spectrum function $F_B(k,t)$ can be determined from $M_L(r,t)$ by (see \cite{moniny1971}) ) In the next section we shall compare the Kazantsev magnetic spectrum $2 \pi k^2F_B(k)$ and the growth rate $\lambda$ with the magnetic spectrum $\hat E_B(k)$ and the growth rate that are obtained from the direct numerical simulations." First. we concentrate ο the direct numerical simulatious (DNS).," First, we concentrate on the direct numerical simulations (DNS)." We report the results of tluree cases., We report the results of three cases. Case ] represents a strougly dillusive test case., Case 1 represents a strongly diffusive test case. We take v=1 in anticipation that the velocity will then inherit the properties of the lorce. especially its short-time correlation.," We take $\nu=1$ in anticipation that the velocity will then inherit the properties of the force, especially its short-time correlation." Hence we expect that the results of the numerical simulations and the Ixazautsev model will be in agreement., Hence we expect that the results of the numerical simulations and the Kazantsev model will be in agreement. We choose a sinall value of the magnetic resistivity. jj=0.0008. eusuriug that the dynaimo is excited aud the magnetic field is resolved.," We choose a small value of the magnetic resistivity, $\eta=0.0008$, ensuring that the dynamo is excited and the magnetic field is resolved." Case 2 represents a more turbulent scenario., Case 2 represents a more turbulent scenario. We take v=1)0.007., We take $\nu=\eta=0.007$. Thus the nonlinear term in the momentum equation (10)) is important aud the turbulent ecddies should have a correlation time 7. that is of the order of the eddy turnover time aid is much louger than the correlation time of the force., Thus the nonlinear term in the momentum equation \ref{eq:momentum}) ) is important and the turbulent eddies should have a correlation time $\tau_c$ that is of the order of the eddy turnover time and is much longer than the correlation time of the force. This particular value of 5 (7) is chosen to correspondto, This particular value of $\eta$ $\nu$ ) is chosen to correspondto corresponding to 7 structures per level.,corresponding to $7$ structures per level. The lower panels of Figure presents the spatial distributions of the could distributed with these fractal parameters: from the left to right. the panels. present the first to the fifth hierarchy. of fractal structure: the large circle in all panels corresponds to the lowest (zeroth) level of the fractal hierarchy. ancl has a radius of Rive.," The lower panels of Figure \ref{fig1} presents the spatial distributions of the could distributed with these fractal parameters; from the left to right, the panels present the first to the fifth hierarchy of fractal structure; the large circle in all panels corresponds to the lowest (zeroth) level of the fractal hierarchy and has a radius of $R_{max}$." The lower left-most panel. presents the case with f=I. the first fractal hierarchy.," The lower left-most panel presents the case with $h=1$, the first fractal hierarchy." " Here there are seven source regions rancomly scattered within £2,,;. each with a radius of Rote=HusL+~0291,,,,."," Here there are seven source regions randomly scattered within $R_{max}$, each with a radius of $R_{cloud} = R_{max} L^{-1} \sim 0.29 R_{max}$." In the panel immediately to the right. the second fractal hierarchy. f=2. is considered. and each of the emission clouds in the f=1 level has been broken up into seven smaller clouds. cach with a radius of Rajon=uusb7~OUS. with each cloud being randomly scattered. within the circle of the f=1 cloud.," In the panel immediately to the right, the second fractal hierarchy, $h=2$, is considered, and each of the emission clouds in the $h=1$ level has been broken up into seven smaller clouds, each with a radius of $R_{cloud} = R_{max} L^{-2} \sim 0.08 R_{max}$, with each cloud being randomly scattered within the circle of the $h=1$ cloud." This process to f=5 in the right-most panel., This process to $h=5$ in the right-most panel. This right-most. panel consists of 77=16807 individual emission clouds. cach with a radius of Lope=Riek7~DOO2ZR va.," This right-most panel consists of $7^5=16807$ individual emission clouds, each with a radius of $R_{cloud} = R_{max} L^{-5} \sim 0.002 R_{max}$ ." " Phe upper panels consider a similar procedure. but instead of scattering clouds in cach hierarchy within the boundaries defined by the hierarchy below it. the clouds are scattered. randomly within /5,,,. providing an overall random distribution."," The upper panels consider a similar procedure, but instead of scattering clouds in each hierarchy within the boundaries defined by the hierarchy below it, the clouds are scattered randomly within $R_{max}$, providing an overall random distribution." It is immediately apparent that the fractal distributions diller significantly from the random distributions and possess structure on a number of scales (as expected for fractal distributions), It is immediately apparent that the fractal distributions differ significantly from the random distributions and possess structure on a number of scales (as expected for fractal distributions). ligure 2. presents the microlensing light curves for the sources at cach hierarchy. presented in Figure 1: note that or the simulations presented in this paper. it is assumed hat the source region remains [fixed and unvarving as it is swept bv the microlensing caustic: such variability would further complicate the resulting light curve. confusing he microlensing signature.," Figure \ref{fig2} presents the microlensing light curves for the sources at each hierarchy presented in Figure \ref{fig1}; note that for the simulations presented in this paper, it is assumed that the source region remains fixed and unvarying as it is swept by the microlensing caustic; such variability would further complicate the resulting light curve, confusing the microlensing signature." " The dashed line in each panel corresponds microlensing light curve for a source of unit radius. corresponding to Z, in this case. and the surface rightness of cach source hierarchy. has been adjusted: so hat it matches this light curve after the caustic has passed he emission region."," The dashed line in each panel corresponds microlensing light curve for a source of unit radius, corresponding to $R_{max}$ in this case, and the surface brightness of each source hierarchy has been adjusted so that it matches this light curve after the caustic has passed the emission region." In the left-most. panel. the source region consists of a small number of relatively large sources. a situation which is rellected. in the light) curve. which exhibits substantial variations about the unit radius source light curve.," In the left-most panel, the source region consists of a small number of relatively large sources, a situation which is reflected in the light curve, which exhibits substantial variations about the unit radius source light curve." Moving towards the right of the top panels of ligure 2.. as the source size decreases and their number increases. the size of the deviations from the unit. source decreases. becoming imperceptible in the final frame of the panel. representing the resultant light curve of 16807 randomly clistributecl sources.," Moving towards the right of the top panels of Figure \ref{fig2}, as the source size decreases and their number increases, the size of the deviations from the unit source decreases, becoming imperceptible in the final frame of the panel, representing the resultant light curve of 16807 randomly distributed sources." Considering the lower panels of Figure 2. reveals that. as expected. the lowest fractal hierarchy. produces a similar light curve to the random clistribution of sources. a situation which is apparent in the second hierarchy.," Considering the lower panels of Figure \ref{fig2} reveals that, as expected, the lowest fractal hierarchy produces a similar light curve to the random distribution of sources, a situation which is apparent in the second hierarchy." In. moving to higher fractal. hierarchies (towards the right). however. it is seen that there is a pronounced. dillerence between the light curves from the fractal distributions and the random," In moving to higher fractal hierarchies (towards the right), however, it is seen that there is a pronounced difference between the light curves from the fractal distributions and the random" with a corresponding slope z0.15.,with a corresponding slope $\approx0.15$. " Their dependence on environment is much smaller, ~0.03—0.06 for a projected local density in the range 0.1—10, which corresponds to a slope ~0.015—0.03 that closely agrees with the results of our analysis."," Their dependence on environment is much smaller, $\sim0.03-0.06$ for a projected local density in the range $0.1-10$, which corresponds to a slope $\sim0.015-0.03$ that closely agrees with the results of our analysis." Cooper et al. (, Cooper et al. ( "2010) analyzed the (U—B)rest color searching for a dependence on environment for galaxies from the DEEP2 sample, in the mass range 10.6AL,,,, will evolve on their propeller spin-down (racks until they. reach Prainm0yo/aj'? at an age This age lor pulsar Gurnoll is close to (yng For almost all cases."," Pulsars with $\dot{M} > \dot{M}_{min}$ will evolve on their propeller spin-down tracks until they reach $P_{death} = (B_{\bot,12}/\alpha)^{1/2}$ at an age This age for pulsar turnoff is close to $t_{max}$ for almost all cases." " Even for the track at Mus with a=0.3 we lind /;5,,5=0.55,,,,."," Even for the track at $\dot{M}_{min}$ with $\alpha = 0.3$ we find $t_{death} = 0.5 t_{max}$." " At times close to /,,,, evolution is rapid.", At times close to $t_{max}$ evolution is rapid. Few pulsars are observed al late times (long periods) along the propeller spin-down tracks., Few pulsars are observed at late times (long periods) along the propeller spin-down tracks. Therefore pulsar Curnolf will not effect the distribution of pulsars in the P— diagram except for the lowest M., Therefore pulsar turnoff will not effect the distribution of pulsars in the $P-\dot{P}$ diagram except for the lowest $\dot{M}$. " The spindown lifetime /,,4,, 1s plausible in view of the low M values obtained for the pulsar tracks.", The spindown lifetime $t_{max}$ is plausible in view of the low $\dot{M}$ values obtained for the pulsar tracks. A time dependent disk would reach AZLOS—LO! ems ton timescales eLOY vis.," A time dependent disk would reach $\dot{M} \approx 10^8 -10^{10}$ gm $^{-1}$ on timescales $\sim 10^{8}$ yrs." If the disk is depleted before the pulsar completes its evolution the pulsar will switch to the pure dipole spin-down track corresponding to its magnetic field., If the disk is depleted before the pulsar completes its evolution the pulsar will switch to the pure dipole spin-down track corresponding to its magnetic field. The number AV of pulsars with magnetic field 2] and mass inflow rate M in a period interval AP? at period P? is llere A is (he birthrate of pulsars in thegalaxy. and I(P. D). the fraction of the galactic disk volume in which pulsars of period P and period derivative P are observable. describes selection effects.," The number $\Delta N$ of pulsars with magnetic field $B_{\bot}$ and mass inflow rate $\dot{M}$ in a period interval $\Delta P$ at period $P$ is Here $R$ is the birthrate of pulsars in thegalaxy, and $P$, $\dot{P}$ ), the fraction of the galactic disk volume in which pulsars of period $P$ and period derivative $\dot{P}$ are observable, describes selection effects." For simplicity we take [(2?. D) to be constant. assuming that the variation in [CP P) is negligible compared to the variation of DP.," For simplicity we take $P$, $\dot{P}$ ) to be constant, assuming that the variation in $P$, $\dot{P}$ ) is negligible compared to the variation of $\dot{P}$." We further assume that one and only one track (3.5)passes through each point in the P— plane. such that the plane can be divided into strips separated by chosen (23.5) (racks.," We further assume that one and only one track $\beta,\gamma$ )passes through each point in the $P-\dot{P}$ plane, such that the plane can be divided into strips separated by chosen $\beta,\gamma$ ) tracks." For each strip we count the pulsars in equal sized period bins and construct the histogram of AN., For each strip we count the pulsars in equal sized period bins and construct the histogram of $\Delta N$ . We then choose a representative, We then choose a representative emissivity index. q=3.,"emissivity index, q=3." " A more thorough exploration of the parameter space was performed by computing the value of \2,, for a grid of 156 models per epoch spanning 26 between 40° <7 < 907. and 6 values for the inner radius spanning 500 < €; < 3000. expressed in units of the gravitational radius. r, = GM,/c."," A more thorough exploration of the parameter space was performed by computing the value of ${\chi}_{red}^2$ for a grid of 156 models per epoch spanning 26 between ${^\circ}$ ${\le}$ ${i}$ ${\le}$ ${^\circ}$, and 6 values for the inner radius spanning 500 ${\le}$ ${\xi}_{i}$ ${\le}$ 3000, expressed in units of the gravitational radius, ${r_g}$ = ${_{\bullet}}/c^2$." The remaining parameters are fixed as listed in Table 4., The remaining parameters are fixed as listed in Table 4. where O; represents the observed normalized line profile intensities. Αι. the model normalized line profile intensities. v is (he number of degrees of Ireedom and 9 the uncertainty in the observed normalized line profile intensities. taken to be for both epochs.," where ${O_j}$ represents the observed normalized line profile intensities, ${M_j}$, the model normalized line profile intensities, ${\nu}$ is the number of degrees of freedom and ${\delta}$ the uncertainty in the observed normalized line profile intensities, taken to be for both epochs." The summation was performed over the velocity span of the broad La line as specified in Table 5., The summation was performed over the velocity span of the broad ${\alpha}$ line as specified in Table 5. " The minimum \2,,, computed for the 2010 data was unity indicating that the axis-synmietric disk plus inflow model provided an excellent representation of those data.", The minimum ${\chi}_{red}^2$ computed for the 2010 data was unity indicating that the axis-symmetric disk plus inflow model provided an excellent representation of those data. " A contour plot of the 42, surface. presented in Figure 7. shows that there are multiple combinations of disk inclination and inner radius that can minimize X2, for each epoch."," A contour plot of the ${\chi}_{red}^2$ surface, presented in Figure 7, shows that there are multiple combinations of disk inclination and inner radius that can minimize ${\chi}_{red}^2$ for each epoch." Thus. the model representations of the data presented in Fig.," Thus, the model representations of the data presented in Fig." 6 are bv no means unique., 6 are by no means unique. " However. (he [acl iab the red and blue 42,,, contours do not overlap suggests that there is no single disk model iab can smmiltaneouslv explain both the 1999 and 2010 observations."," However, the fact that the red and blue ${\chi}^2_{min}$ contours do not overlap suggests that there is no single disk model that can simultaneously explain both the 1999 and 2010 observations." There could even be wo disks., There could even be two disks. But. the most conservative interpretation is that there is just one disk for which 1e inclination did not change between 1999 and 2010.," But, the most conservative interpretation is that there is just one disk for which the inclination did not change between 1999 and 2010." In this case the size of the disk must have changed., In this case the size of the disk must have changed. The arrow in Fig., The arrow in Fig. " 7 represents (he feas! size evolution solution which implies iab Che disk is highly inclined. / = 82° + 1°. which presumably. aided in its detection. aud ve inner radius of the disk decreased Lrom 2770r, + 182r, in 1999 to 2200r, = 216r, in 2010. the implications of which are discussed further in Section 4.7."," 7 represents the ${\it least}$ size evolution solution which implies that the disk is highly inclined, ${i}$ = ${^\circ}$ ${\pm}$ ${^\circ}$, which presumably aided in its detection, and the inner radius of the disk decreased from ${r_g}$ ${\pm}$ ${r_g}$ in 1999 to ${r_g}$ ${\pm}$ ${r_g}$ in 2010, the implications of which are discussed further in Section 4.7." That the inflow plus disk model is able to reproduce the rather complex shapes observed for the broad La emission line profiles in NGC 4203 allows the sizes of the inflow and disk components to be estimated., That the inflow plus disk model is able to reproduce the rather complex shapes observed for the broad ${\alpha}$ emission line profiles in NGC 4203 allows the sizes of the inflow and disk components to be estimated. The mass distribution determines that the size of the inflow is, The mass distribution determines that the size of the inflow is ones. and the conundrums they pose are even more mysterious (Plataisetal.2011).,"ones, and the conundrums they pose are even more mysterious \citep{pla11}." Both the degenerate binaries and all kinds of stragglers are thought to be products of the evolution of binary systems in a dense stellar environment. and their peculiarities are most probably promoted or even induced by interactions between cluster members (Ferraro2006;Plataisetal.2011).," Both the degenerate binaries and all kinds of stragglers are thought to be products of the evolution of binary systems in a dense stellar environment, and their peculiarities are most probably promoted or even induced by interactions between cluster members \citep{fer06,pla11}." As such. they provide a link between classical stellar evolution and dynamical evolution of the cluster. being a valuable observational template against which the dynamical models of stellar aggregates can be tested.," As such, they provide a link between classical stellar evolution and dynamical evolution of the cluster, being a valuable observational template against which the dynamical models of stellar aggregates can be tested." The straggler-related goal of the present survey is to verify the membership of straggler candidates selected from the proper-motion catalogue of w Cen by Bellinietal.(2009).. and to establish how frequent binary systems are in the straggler population.," The straggler-related goal of the present survey is to verify the membership of straggler candidates selected from the proper-motion catalogue of $\omega$ Cen by \citet{bel09}, and to establish how frequent binary systems are in the straggler population." We monitored selected targets in w Cen with the help of VIMOS - à multi-purpose instrument mounted in the Nasmyth B focus of the ESO VLT-Unit 3 telescope., We monitored selected targets in $\omega$ Cen with the help of VIMOS – a multi-purpose instrument mounted in the Nasmyth B focus of the ESO VLT-Unit 3 telescope. For the present survey It was working as a multi-object spectrograph., For the present survey it was working as a multi-object spectrograph. To adapt it to the observations of blue stragglers. we selected the HR blue mode with wavelength range 4100 — 6300Á.. resolutio 2050 — 2550 (150 — 120 km s!) and dispersion 0.5 Aj/pixel.," To adapt it to the observations of blue stragglers, we selected the HR blue mode with wavelength range 4100 – 6300, resolution 2050 – 2550 (150 – 120 km $^{-1}$ ) and dispersion 0.5 /pixel." A VIMOS spectroscopy run consists of pre-1maging and spectroscopic follow-up., A VIMOS spectroscopy run consists of pre-imaging and spectroscopic follow-up. The pre-imaging frames of ω Ce were obtained on 2010.16.01 to serve as a basis for the preparation of masks with slits centered on objects chose for the survey., The pre-imaging frames of $\omega$ Cen were obtained on 2010.16.01 to serve as a basis for the preparation of masks with slits centered on objects chosen for the survey. The spectroscopic monitoring was performec during ten nights in February and March 2010., The spectroscopic monitoring was performed during ten nights in February and March 2010. On every night one ~30 min observation was made. consisting of acquisition-imaging. two spectroscopic integrations of 580 sec.," On every night one $\sim$ 30 min observation was made, consisting of acquisition-imaging, two spectroscopic integrations of 580 sec." each. up to three flat-field exposures. and helium-neon lamp exposure for wavelength calibration.," each, up to three flat-field exposures, and helium-neon lamp exposure for wavelength calibration." " The VIMOS field of view. which is composed of four 7x8 aremin quadrants served by independent CCDs and separated by about 2 aremin gaps. was centered on Gr.San = 26 46.3. 4772755 1.8"")."," The VIMOS field of view, which is composed of four $\times$ 8 arcmin quadrants served by independent CCDs and separated by about 2 arcmin gaps, was centered on $\alpha, \delta)_{2000}$ = $^{\rm h}$ 26 $^{\rm m}$ $^{\rm s}$, $^\circ$ )." A log of the observations is presented in Table 1.. in which date and airmass are given for the start of the exposures. and the seeing is averaged over each observation.," A log of the observations is presented in Table \ref{tab:log}, in which date and airmass are given for the start of the exposures, and the seeing is averaged over each observation." The target objects were selected from variable star catalog of Kaluznyetal.(2004).. henceforth identified by a number preceded with V or NV. and proper-motion catalog of Bellinietal.(2009).. henceforth identified by à number preceded with B. We adopted the following selection criteria: Photometrically detected pulsating stars. whose intrinsic variations of radial velocity could mask orbital effects. were excluded from the sample.," The target objects were selected from variable star catalog of \citet{kal04}, henceforth identified by a number preceded with V or NV, and proper-motion catalog of \citet{bel09}, henceforth identified by a number preceded with B. We adopted the following selection criteria: Photometrically detected pulsating stars, whose intrinsic variations of radial velocity could mask orbital effects, were excluded from the sample." The selection procedure was rather tedious. and trying to maximize the number of photometric variables in the sample we were forced to relax the second criterion.," The selection procedure was rather tedious, and trying to maximize the number of photometric variables in the sample we were forced to relax the second criterion." After a few trials we decided to focus on 8l objects: 61 straggler candidates and 20 photometric variables. among which NV332. NV334 and NV361 had membership probabilities equal to84%.. and64%.. respectively.," After a few trials we decided to focus on 81 objects: 61 straggler candidates and 20 photometric variables, among which NV332, NV334 and NV361 had membership probabilities equal to, and, respectively." We deliberately included V209 — a system thoroughly investigated by Kaluznyetal.(20074) — with the intention. to use it as an indicator of the quality and reliability of velocity measurements., We deliberately included V209 – a system thoroughly investigated by \citet{kal07a} – with the intention to use it as an indicator of the quality and reliability of velocity measurements. In the sample there are a few blue objects which. strictly speaking. do not conform to the classical definition of blue stragglers. because they are located not on the main-sequence extension. but to the left of it.," In the sample there are a few blue objects which, strictly speaking, do not conform to the classical definition of blue stragglers, because they are located not on the main-sequence extension, but to the left of it." We included them in order to maximize the total number of slits., We included them in order to maximize the total number of slits. VIMOS spectra can be calibrated automatically by the ESO-VIMOS pipeline. which. however. cannot be trusted.," VIMOS spectra can be calibrated automatically by the ESO-VIMOS pipeline, which, however, cannot be trusted." This is because the spectra of some slits extend below 2=5000A. where calibration lamp lines are scarce (ESO2011).. and some of them are very weak.," This is because the spectra of some slits extend below $\lambda=5000$, where calibration lamp lines are scarce \citep{eso11}, and some of them are very weak." While Giuffridaetal.(2010) wrote an interactive procedure within the pipeline. which allowed for a better control of each calibration step. we decided to reduce the data manually. using standard procedures.," While \citet{giu10} wrote an interactive procedure within the pipeline which allowed for a better control of each calibration step, we decided to reduce the data manually, using standard procedures." We started from seitraw frames and proceeded through object identification. slit extraction. flatfielding. science aperture extraction. lamp aperture extraction. wavelength calibration and normalization of the spectra.," We started from raw frames and proceeded through object identification, slit extraction, flatfielding, science aperture extraction, lamp aperture extraction, wavelength calibration and normalization of the spectra." Unfortunately. all flat-field images in quadrants 3 and 4 were contaminated by internal reflections.," Unfortunately, all flat-field images in quadrants 3 and 4 were contaminated by internal reflections." We were forced to substitute the affected image-sections with smooth fits. which. of course. degraded the quality of the corresponding sections of the spectra.," We were forced to substitute the affected image-sections with smooth fits, which, of course, degraded the quality of the corresponding sections of the spectra." Seven slits produced no useful data., Seven slits produced no useful data. In five cases the target aperture could not be reliably extracted or the spectrum was too, In five cases the target aperture could not be reliably extracted or the spectrum was too otal power spectrum. and Züa is the peak flux ο τα1e uaser feature.,"total power spectrum, and $I_{\rm max}$ is the peak flux of the maser feature." D is the magnetic field streueth axd 0 he anele between the maguetic fold lues aud the li1e of sight., $B$ is the magnetic field strength and $\theta$ the angle between the magnetic field lines and the line of sight. The Appk cocficient depends on the masi18o ivperfne components., The $A_{\rm F-F'}$ coefficient depends on the masing hyperfine components. The Apge coefficients have 30011 determined by calculating v frou svuthetic V-spectra. determined for a seres of magnetic field streneths B. axd or the different laperfine components.," The $A_{\rm F-F'}$ coefficients have been determined by calculating $P_{\rm V}$ from synthetic V-spectra, determined for a series of magnetic field strengths $B$, and for the different hyperfine components." Some cxampCR of svuwetic V-spectra for the three hvperfue lines are shown 1in Fie.l.. The B.Py relation is shown in Fig., Some examples of synthetic V-spectra for the three hyperfine lines are shown in Fig.\ref{vs}. The $B-P_{\rm V}$ relation is shown in Fig. 2 for diff(vent lvperfine components aud line widths.," \ref{bv} for different hyperfine components and line widths." For the dierent hvperfüne transitions separately. FG find Appo=O013.0.08 and 0.01 for the 76.65 aud 5o| transitions respectively.," For the different hyperfine transitions separately, FG find $A_{\rm F-F'} = 0.013, 0.08$ and $0.01$ for the $7-6, 6-5$ and $5-4$ transitions respectively." For the fitted combinatious of hivperfiue coiipouents we ecnerally fiud Apgcz 0.011. , For the fitted combinations of hyperfine components we generally find $A_{\rm F-F'} \approx 0.011$ "We used the upgraded dual-channel W/D GGIIz) receiver at (he James Clerk Maxwell. Telescope at mami atop Manna Kea in Llawaii. operating single sideband (SSB). to observe the CO J=G65 line (4.4 GGIIz) in 2220 on Mareh 15th 2009 under dry conditions (7555ey),~0.04—-0.06).","We used the upgraded dual-channel W/D GHz) receiver at the James Clerk Maxwell Telescope at m altitude atop Mauna Kea in Hawaii, operating single sideband (SSB), to observe the CO J=6–5 line $\rm \nu _{rest}$ GHz) in 220 on March 15th 2009 under dry conditions $\rm \tau_{225\,GHz}$$\sim $ $-$ 0.06)." " To ensure the flattest baselines possible. but also measure the corresponding dust continuum at A4,4424. we used the fastest beam switching mode available (continuum mode) with a beam switch frequency. of Comet Hz and a throw of 30” (in azimuth)."," To ensure the flattest baselines possible, but also measure the corresponding dust continuum at $\rm \lambda _{obs}$ $\mu $ m, we used the fastest beam switching mode available (continuum mode) with a beam switch frequency of $\rm f_{bmsw}$ Hz and a throw of $30''$ (in azimuth)." The ACSIS was usec at its widest mode of GGIIz (~780kkimss tat GGIZz) and two separate (unings. vielding an effective bandwidth of 3.235GlIIz (1400 1).," The ACSIS was used at its widest mode of GHz $\sim$ $^{-1}$ at GHz) and two separate tunings, yielding an effective bandwidth of $\rm 3.235\,GHz $ $\sim $ $^{-1}$ )." This was necessary in order to cover the widest known CO line in local ULIRGs (FWZI~900 ')., This was necessary in order to cover the widest known CO line in local ULIRGs $\sim$ $^{-1}$ ). " The (vpical system temperatures were T,74(2000—3000) Idx. with a median of Ty..~+2500 Wis (including atmospheric absorption)."," The typical system temperatures were $\rm T_{sys}$$\sim $ $-$ K, with a median of $\rm T_{sys}$$\sim $ K (including atmospheric absorption)." " The beam size at GGIIz is Ojppw —8"".", The beam size at GHz is $\rm \Theta _{HPBW}$ $''$. Good pointing with such narrow beams is crucial and was checked everv mmins using both absolute W/D and differential pointing with the 33 receiver GGIIz). vielding σι (rms) (Figure 1).," Good pointing with such narrow beams is crucial and was checked every mins using both absolute W/D and differential pointing with the 3 receiver GHz), yielding $\rm \sigma _x$$\sim $$\sigma_y$$\sim $ $''$ (rms) (Figure 1)." " The aperture efficiency at GGITz is 0.03. estimated from the Ruze formula for an membrane (ransniission. an rms dish surface accuracy of 725400. and a jj,420.68 (aperture effiieney lor a perfect dish. with the illumination taper applied at the JCMT). and verified with observations of Venus."," The aperture efficiency at GHz is $\eta ^* _a$ =0.32, estimated from the Ruze formula for an membrane transmission, an rms dish surface accuracy of $\sim $ $\mu $ m, and a $\rm \eta ^* _{a,0}$ =0.68 (aperture efficiency for a perfect dish with the illumination taper applied at the JCMT), and verified with observations of Venus." The flux calibration uncertainty is estimated with repeated observations of compact spectral line standards and is ~254., The flux calibration uncertainty is estimated with repeated observations of compact spectral line standards and is $\sim 25\%$. Individual spectra were examined. edited for bad channels. ancl co-added (both. W/D channels) to vield the final spectrum shown in Figure 2 overlaid with CO 32 (JCMT). and the HCN J210. CS J=32 lines obtained with the IRAM 30-m telescope (from. Greve οἱ al.," Individual spectra were examined, edited for bad channels, and co-added (both W/D channels) to yield the final spectrum shown in Figure 2 overlaid with CO 3–2 (JCMT), and the HCN J=1–0, CS J=3–2 lines obtained with the IRAM 30-m telescope (from Greve et al." 2009)., 2009). " The agreement between overall FWZIs and line centers is excellent although the CO J=65 line becomes weak towards (he velocity range where the high clensity tracer CS J=32 line (n,7-2x10? *) becomes especially strong. (see discusion in section 3)."," The agreement between overall FWZI's and line centers is excellent although the CO J=6–5 line becomes weak towards the velocity range where the high density tracer CS J=3–2 line $\rm n_{cr}$$\sim $ $\times$ $^5$ $^{-3}$ ) becomes especially strong (see discusion in section 3)." The integrated CO J=65 line [ιν is estimated from, The integrated CO J=6–5 line flux is estimated from Mercury-manganese (HgMn) stars is one of the sub-classes of early-type chemically peculiar (CP) stars.,Mercury-manganese (HgMn) stars is one of the sub-classes of early-type chemically peculiar (CP) stars. " HgMn stars show an overabundance of Hg, Mn, Y, Sr, and other, mostly heavy, chemical elements."," HgMn stars show an overabundance of Hg, Mn, Y, Sr, and other, mostly heavy, chemical elements." " These stars are often found in close binaries and belong to the temperature range of ,2299500-16000 K, corresponding to the spectral classes from AO to B5 (?).."," These stars are often found in close binaries and belong to the temperature range of 9500–16000 K, corresponding to the spectral classes from A0 to B5 \citep{Dworetsky:1993}." " Earlier it was thought that HgMn stars show no rotational spectral variability, meaning that the atmospheres of these stars are horizontally homogeneous."," Earlier it was thought that HgMn stars show no rotational spectral variability, meaning that the atmospheres of these stars are horizontally homogeneous." " However, the variability discovered in a spectral line of Hg in a And (?) has changed this picture."," However, the variability discovered in a spectral line of Hg in $\alpha$ And \citep{Adelman:2002} has changed this picture." ? show that the observed variability is related to presence of chemical spots., \citet{Adelman:2002} show that the observed variability is related to presence of chemical spots. " In the case of Ap stars, the presence of spots is usually caused by the magnetic field."," In the case of Ap stars, the presence of spots is usually caused by the magnetic field." The study by ? aimed at the search for magnetic field in a And proved an absence of the global magnetic field sufficient to cause the chemical spot formation., The study by \citet{Wade:2006a} aimed at the search for magnetic field in $\alpha$ And proved an absence of the global magnetic field sufficient to cause the chemical spot formation. " Detection of spots increased the interest towards HgMn stars, resulting in a discovery of seven more spotted HgMn stars: HR 1185 and HR 8723 (?),, AR Aur (??),, HD 11753, HD 53244, HD 221507 (?),, and HD 32964 (?).."," Detection of spots increased the interest towards HgMn stars, resulting in a discovery of seven more spotted HgMn stars: HR 1185 and HR 8723 \citep{Kochukhov:2005}, AR Aur \citep{Hubrig:2006, Folsom:2010}, HD 11753, HD 53244, HD 221507 \citep{Briquet:2010}, and HD 32964 \citep{Makaganiuk:2011b}." " At the same time, all systematic studies of the magnetic field in HgMn stars reported its absence (?????).."," At the same time, all systematic studies of the magnetic field in HgMn stars reported its absence \citep{Shorlin:2002, Wade:2006a, Folsom:2010, Auriere:2010, Makaganiuk:2011a}." " In the best cases, an upper limit set on the strength of the mean longitudinal magnetic field is a few Gauss (??).."," In the best cases, an upper limit set on the strength of the mean longitudinal magnetic field is a few Gauss \citep{Auriere:2010, Makaganiuk:2011a}." " The source ((HD 11753, HIP 8882, HR 558) is a slowly-rotating, bright (V2 5.11) and cool (Teg=10700K,?) HgMn star."," The source (HD 11753, HIP 8882, HR 558) is a slowly-rotating, bright $\,=\,5.11$ ) and cool \citep[\Teff$=10700$~K,][]{Smith:1993a} HgMn star." " ? suggested that the radial velocity of vvaries with a period of more than 30 days, which means that this star is a spectroscopic binary with a single spectrum."," \citet{Dworetsky:1982} suggested that the radial velocity of varies with a period of more than 30 days, which means that this star is a spectroscopic binary with a single spectrum." ? found the orbital period of 41.489+0.019 d forPhe., \citet{Leone:1999} found the orbital period of $41.489\pm0.019$ d for. ". Employing the IUE spectra and the spectrum synthesis method, ???? determined abundances of Cr, Mn, Fe, Mg, Al, Si, Zn, Cu, Co, Ni, and Hg."," Employing the IUE spectra and the spectrum synthesis method, \citet{Smith:1993a, Smith:1993b, Smith:1994, Smith:1997} determined abundances of Cr, Mn, Fe, Mg, Al, Si, Zn, Cu, Co, Ni, and Hg." " ? and ? used optical spectra to determine abundances of Mn and Hg, respectively."," \citet{Jomaron:1999} and \citet{Dolk:2003} used optical spectra to determine abundances of Mn and Hg, respectively." " ? found a stratification of gallium, based on the analysis of the UV lines of this element."," \citet{Smith:1996} found a stratification of gallium, based on the analysis of the UV lines of this element." " He concluded that Ga shows an increase of concentration, starting from logTsq99=40.3 towards the upper layers of the stellar atmosphere."," He concluded that Ga shows an increase of concentration, starting from $\log\tau_{5000}\,=\,+0.3$ towards the upper layers of the stellar atmosphere." ? discovered chemical spots onPhe., \citet{Briquet:2010} discovered chemical spots on. ". Using a large number of observations, the authors found variability in the spectral lines of Ti, Sr, and Y with a 91554 period."," Using a large number of observations, the authors found variability in the spectral lines of Ti, Sr, and Y with a 54 period." " They reconstructed surface maps for the two sets of spectra of this star, separated by 65 days."," They reconstructed surface maps for the two sets of spectra of this star, separated by 65 days." " Based on the differences in their maps, the authors suggest an evolution of spots, similar to the phenomenon discovered by ? in « And."," Based on the differences in their maps, the authors suggest an evolution of spots, similar to the phenomenon discovered by \citet{Kochukhov:2007} in $\alpha$ And." There were no previous magnetic field studies ofPhe., There were no previous magnetic field studies of. . This star was included in the sample of HgMn stars for which we performed a magnetic field survey with HARPSpol (?).., This star was included in the sample of HgMn stars for which we performed a magnetic field survey with HARPSpol \citep{Makaganiuk:2011a}. " The spectropolarimetric observations of ccover its full rotational period, enabling us to measure the magnetic field at each rotational phase."," The spectropolarimetric observations of cover its full rotational period, enabling us to measure the magnetic field at each rotational phase." Based on these high-quality data we also reconstructed surface maps of variable chemical elements and tested the presence of extreme vertical stratification for some of them., Based on these high-quality data we also reconstructed surface maps of variable chemical elements and tested the presence of extreme vertical stratification for some of them. In Sect., In Sect. 2 we describe the observations and data reduction., \ref{obs} we describe the observations and data reduction. The least-squares deconvolution (LSD) and the measurements of the longitudinal magnetic field are presented in Sect. 3.., The least-squares deconvolution (LSD) and the measurements of the longitudinal magnetic field are presented in Sect. \ref{mf}. Section 4 describes investigation of the line profile variability., Section \ref{lpv} describes investigation of the line profile variability. Surface maps of chemical elements derived with the Doppler imaging technique are discussed in Sect. 5.., Surface maps of chemical elements derived with the Doppler imaging technique are discussed in Sect. \ref{DI}. The stratification analysis is presented in Sect. 6.., The stratification analysis is presented in Sect. \ref{strat}. Section 7 summarises our results and discusses them in the context of previous studies of aand recent theoretical diffusion calculations., Section \ref{disc} summarises our results and discusses them in the context of previous studies of and recent theoretical diffusion calculations. " The star wwas observed in January 2010, using a newly-built HARPS polarimeter (??) at the 3.6-m ESO telescope in La Silla, Chile."," The star was observed in January 2010, using a newly-built HARPS polarimeter \citep{Snik:2011, Piskunov:2011} at the 3.6-m ESO telescope in La Silla, Chile." All observations were done with the circular polarimeter., All observations were done with the circular polarimeter. chcomraging. with estimated escape rates sunuuimng up to 10 per cent of the initial galaxw mass over an Iubble time.,"encouraging, with estimated escape rates summing up to 10 per cent of the initial galaxy mass over an Hubble time." Iu the present paper we cousiderably extend these two previous investigations. by assuune that the ealaxics are triaxial ellipsoids ancl two cases are considered: when the center of mass of the ellipsoid is at rest at the equilibriun poiut of ie field generated bv the cluster. and when it is placed on a cieulu orbit around the center of a spherically sviuuetrie cluster.," In the present paper we considerably extend these two previous investigations, by assuming that the galaxies are triaxial ellipsoids and two cases are considered: when the center of mass of the ellipsoid is at rest at the equilibrium point of the field generated by the cluster, and when it is placed on a circular orbit around the center of a spherically symmetric cluster." After deriviug the equations of the motion of a star inside an oscillating ealaxy. we integrate ποσαν these equatious wider different initial conditions realized by using a Monte-Carlo extraction.," After deriving the equations of the motion of a star inside an oscillating galaxy, we integrate numerically these equations under different initial conditions realized by using a Monte-Carlo extraction." The paper is organized as follows., The paper is organized as follows. In Sect., In Sect. 2 we briefly review the proper physical setting of the problem. and iu Sect.," 2 we briefly review the proper physical setting of the problem, and in Sect." 3 we describe the adopted galaxy aud cluster models., 3 we describe the adopted galaxy and cluster models. Iu Sect., In Sect. [woe describe in the uunerical integration schemo. while iu Sect.," 4 we describe in the numerical integration scheme, while in Sect." Swe present the main results. that axe finally sunuuarized and discussed in Sect.," 5 we present the main results, that are finally summarized and discussed in Sect." 6., 6. In the Appoeudix. the specific technique adopted to obtain the gravitational fiek inside the ealaxy models aud other useful dynamical quantities are briefly described.," In the Appendix, the specific technique adopted to obtain the gravitational field inside the galaxy models and other useful dynamical quantities are briefly described." " Following the analytical treatment of CO9S8, we start presenting the simple case of a spiuless galaxy with its center of lass at rest at the center of a triaxial ealaxy cluster."," Following the analytical treatment of CG98, we start presenting the simple case of a spinless galaxy with its center of mass at rest at the center of a triaxial galaxy cluster." In ος df was shown that the ealactic equilibrium configurations correspoud tfo the ealaxy inertia ellipsoid orieuted aloug the CTF principal directions: without loss of generality we assume that in the (inertial) Cartesian coordinate system €. the CTF tensor T is in diagoual form. with componcuts 7; (/=1.2.3).," In CG98 it was shown that the galactic equilibrium configurations correspond to the galaxy inertia ellipsoid oriented along the CTF principal directions: without loss of generality we assume that in the (inertial) Cartesian coordinate system $C$, the CTF tensor $\Tc$ is in diagonal form, with components $\Ti$ $(i=1,2,3)$." " By using three successive counterclockwise rotations Qo around ae axis. s around q/ axis and c arouud z"" axis). CG98 showed that the linearized equatious of motion for the ealaxy near the equilibrium configurations cau be written as where AT);=TiTj. and Jf; are the priucipal colmpouncuts of the galaxy inertia teusor."," By using three successive counterclockwise rotations $\varphi$ around $x$ axis, $\vartheta$ around $y'$ axis and $\psi$ around $z''$ axis), CG98 showed that the linearized equations of motion for the galaxy near the equilibrium configurations can be written as where $\DTij \equiv \Ti-\Tj$, and $\Ii$ are the principal components of the galaxy inertia tensor." If we also assume that Tj=T5> and fyx[5o>1 we get (Gradshteyn&Ryzhik2000) 'Thus, for these asymptotics we have if /ó«&1, and if(ó>>1."," If $\l\delta\ll 1$, then $P_\l^m(\cos\theta)\simeq P_\l^m(0)$, where while for $\l\delta\gg 1$ we get \citep{gr} Thus, for these asymptotics we have if $\l\delta\ll 1$, and if$\l\delta\gg 1$." " For odd £--m, as seen from Eq.(18)), Gm—0 if £0«1°."," For odd $\l+m$, as seen from \ref{rec3}) ), $a^r_{\l,m}=0$ if $\l\delta\ll 1$." ". That means that the main term in Eq.(15)), proportional to 6/7 is related with the even harmonics €+m=2n,n 1,2...."," That means that the main term in \ref{rec}) ), proportional to $\delta/\pi$ is related with the even harmonics $\l+m=2n, n=1,2 \ldots$ ." " The leading term, which determines the sign of a7,4,, is D(i-m-5) in the denominator of Eq.(19))."," The leading term, which determines the sign of $a^r_{\l+\Delta,m}$ is $\Gamma(\frac{1-\l-m-\Delta}{2})$ in the denominator of \ref{rec4}) )." " For that term we have and for A=4k,k1,2... the sign of aj,A,, is the same, as for aj."," For that term we have and for $\Delta=4k, k=1,2\ldots$ the sign of $a^r_{\l+\Delta,m}$ is the same, as for $a^r_{\l,m}$." " Taking into account that for dj,, estimator the order of signs for £,m and €+A,m is crucial, we can conclude that the compensation of the central part of the signal requires A=4k,k1,2...."," Taking into account that for $d^r_{\l,m}$ estimator the order of signs for $\l,m$ and $\l+\Delta,m$ is crucial, we can conclude that the compensation of the central part of the signal requires $\Delta=4k, k=1,2\ldots$." " However, it does not guarantee that for £ó>>1 modes A=4k criteria leads the compensation of the signal."," However, it does not guarantee that for $\l\delta\gg 1$ modes $\Delta=4k$ criteria leads the compensation of the signal." " To show this let us describe the asymptotic /ó>>1, when the symmetry of the dem coefficients is determined by Eq.(17))."," To show this let us describe the asymptotic $\l\delta\gg 1$, when the symmetry of the $a_{\lm}$ coefficients is determined by \ref{rec2}) )." " As one can see from this equation, if (--m=4k,k1,2... the sign of aj,4 is now determined by the combination sin[(¢+$)6] and does not show any 4k-correlation at all."," As one can see from this equation, if $\l+m= 4k, k=1,2\ldots$ the sign of $a^r_{\l+\Delta,m}$ is now determined by the combination $\sin\left[(\l+\frac{1}{2})\delta\right]$ and does not show any $4k$ -correlation at all." " Moreover, according to the properties of the sine mode the shift of the argument ὁ by the factor A=4k just transforms it to the combination Thus, one can see that 4k-correlation requiressome restriction on the ó-parameter Thus, for k=1 and m=1 the halfwidth of the rectangular area must be close to 6= 7/2."," Moreover, according to the properties of the sine mode the shift of the argument $\l$ by the factor $\Delta=4k$ just transforms it to the combination Thus, one can see that $4k$ -correlation requiressome restriction on the $\delta$ -parameter Thus, for $k=1$ and $m=1$ the halfwidth of the rectangular area must be close to $\delta=\pi/2$ ." " If, for example,"," If, for example," (or initial densities). may be significantly cilferent in the enuous ISM.,"(or initial densities), may be significantly different in the tenuous ISM." lo particular. non-thermal chemistry in C-shocks or turbulent vortices may play an important role in he chemistry of the dilfuse gas (seee.g.22?)..," In particular, non-thermal chemistry in C-shocks or turbulent vortices may play an important role in the chemistry of the diffuse gas \citep[see e.g.][]{Federmanetal96,Shefferetal08,Godardetal09}." Alternatively. arge scale galactic processes not considered. in our model may be required to accurately model the chemistry in diffuse molecular gas. such as galactic rotation. the gravitational ield clue to the disk. and/or large scale magnetic fields.," Alternatively, large scale galactic processes not considered in our model may be required to accurately model the chemistry in diffuse molecular gas, such as galactic rotation, the gravitational field due to the disk, and/or large scale magnetic fields." We lope to pursue studies involving such large scale dynamics and chemistry in the future., We hope to pursue studies involving such large scale dynamics and chemistry in the future. In observational investigations where the [actor is derived. solely from. CO) observations. the CO linewidths are used to. derive. masses through the virial theorem.," In observational investigations where the factor is derived solely from CO observations, the CO linewidths are used to derive masses through the virial theorem." Ifthe bulk of the gas is in molecular form. then iis emploved along with the CO linewidth derived. tto estimate the ITactor via Equation 1..," If the bulk of the gas is in molecular form, then is employed along with the CO linewidth derived to estimate the factor via Equation \ref{Xfac}." " Phe key assumption here is that the observed: clouds are in virial equilibrium (e.g.22).. which is the interpretation of the observed. power-law linowidth e, size I? relationship o.xIU (e.g.?2).."," The key assumption here is that the observed clouds are in virial equilibrium \citep[e.g.][]{Young&Scoville91, Solomonetal87}, which is the interpretation of the observed power-law linewidth $\sigma_v$ size $R$ relationship $\sigma_v \propto R^{0.5}$ \citep[e.g.][]{Larson81, Solomonetal87}." Measurements of the molecular mass through independent. observations. such as dust-based emission or extinction. can also provide estimates ofNg.," Measurements of the molecular mass through independent observations, such as dust-based emission or extinction, can also provide estimates of." .. These can be combined. with CO observations to calculate the [Tactor., These can be combined with CO observations to calculate the factor. As discussed in Section ??.. a discrepancy in the derived [factor based on virialized. clouds or based on independent nmunmiass estimates is found in low metallicity systems. such as the SAIC (7???)," As discussed in Section \ref{introsec}, a discrepancy in the derived factor based on virialized clouds or based on independent mass estimates is found in low metallicity systems, such as the SMC \citep[][]{Bolattoetal08, Rubioetal04, Israel97, Leroyetal07, Leroyetal09}." " The velocity. dispersions in. our models follow the observed. m,xRRνο relationship.+ (Shetty4 et al."," The velocity dispersions in our models follow the observed $\sigma_v \propto R^{0.5}$ relationship (Shetty et al." In reparation). as found in numerous similar turbulent clou models (e.g.2?7)..," In preparation), as found in numerous similar turbulent cloud models \citep[e.g.][]{Klessen00, Ostrikeretal01, Federrathetal10}." We have calculated the factors in model MCs assuming independent. knowledge ofNyy. so no assumption of a linewidth-size. scaling. or of virializecl clouds (or cores). is necessary.," We have calculated the factors in model MCs assuming independent knowledge of, so no assumption of a linewidth-size scaling, or of virialized clouds (or cores), is necessary." In our analysis of otal column densities and. integrated. intensities. we finc jad factor is primarily controlled. by the CO abundance. ai ius ultimately by cloud properties. most. responsible for ο.'O formation: the metallicity. density. or background. UV OEacliation field.," In our analysis of total column densities and integrated intensities, we find that factor is primarily controlled by the CO abundance, and thus ultimately by cloud properties most responsible for CO formation: the metallicity, density, or background UV radiation field." This variation in the 7actor is most drastic - upto several orders of magnitude - in mocdels with metallicities. densities. or UV radiation fields ilferent from the Milky. Wavy.," This variation in the factor is most drastic - upto several orders of magnitude - in models with metallicities, densities, or UV radiation fields different from the Milky Way." These results are in agreement with models showing an increased ITactor for low metallicity svstems (7?)..," These results are in agreement with models showing an increased factor for low metallicity systems \citep{Maloney&Black88, Israel97}." The diserepaney. between [factor estimates based on νακος. svstenis. ancl those based on independent. nmineasures can be explained by he selective photoclissociation —of CO— ἵπ low —clensity regions.," The discrepancy between factor estimates based on virialized systems, and those based on independent measures can be explained by the selective photodissociation of CO in low density regions." — The CO bright objects thus only trace highest. density gas. which is surrounded: by lower clensity molecular material. with little or no CO emission (?2??7.PaperLLMolina.etal.inprep.)..," The CO bright objects thus only trace highest density gas, which is surrounded by lower density molecular material, with little or no CO emission \citep[][Paper II, Molina et al. in prep.]{Maloney&Black88,Bolattoetal08, Grenieretal05, Wolfireetal10}." In low metallicity or low density systems. we only find the [factor to be constant at the very highest. densities (Figs.," In low metallicity or low density systems, we only find the factor to be constant at the very highest densities (Figs." Gbb 6dd). though the vast majority of observed: points clearly show a gradient in the flactor with density.," \ref{XvsAv}b b \ref{XvsAv}d d), though the vast majority of observed points clearly show a gradient in the factor with density." For the high density Model n1000. (Fig Gee). the flactor increases with increasing density due to CO: line saturation (Fig.," For the high density Model n1000 (Fig \ref{XvsAv}c c), the factor increases with increasing density due to CO line saturation (Fig." Hcc). though the range of iis only 22 orders of magnitudo.," \ref{wvsav}c c), though the range of is only 2 orders of magnitude." " The idea that CO observations accurately provide miss estimates. with VeVo... of virialized clouds needs to. be allirmed quantitatively,"," The idea that CO observations accurately provide mass estimates, with $\approx$, of virialized clouds needs to be affirmed quantitatively." Previous clforts to address this issue have usually involved: static models., Previous efforts to address this issue have usually involved static models. 2? constructed. clouds models with microturbulent velocities consistent with the observed Linewidth-size relationship., \citet{Kutner&Leung85} constructed clouds models with microturbulent velocities consistent with the observed linewidth-size relationship. Γον found that the [factor still strongly depends on the temperature. as well as the density and CO abundance.," They found that the factor still strongly depends on the temperature, as well as the density and CO abundance." Using photodissociation region models. ?7— found that microturbulenee cannot reproduce the observed. CO line profiles.," Using photodissociation region models, \citet{Wolfireetal93} found that microturbulence cannot reproduce the observed CO line profiles." The CO intensity. and hence the factor. is sensitive to other parameters responsible for CO formation.," The CO intensity, and hence the factor, is sensitive to other parameters responsible for CO formation." With the radiative transfer. calculations xrformed on the 3D. MIID simulations including chemistry discussed. here. we can further investigate how various urbulent velocity [fields inlluence. €CO emission. as well as 1e cloud. characteristics that alfect the factor in a range of environments.," With the radiative transfer calculations performed on the 3D MHD simulations including chemistry discussed here, we can further investigate how various turbulent velocity fields influence CO emission, as well as the cloud characteristics that affect the factor in a range of environments." Such an analysis would. address the following issues: llow well do CO peaks trace coherent. objects in spectral PPV) cubes?, Such an analysis would address the following issues: How well do CO peaks trace coherent objects in spectral (PPV) cubes? Ldentifving coherent. objects from. spectral cubes has proved to be quite challenging. as à consequence of line-of-sight. projection (27).," Identifying coherent objects from spectral cubes has proved to be quite challenging, as a consequence of line-of-sight projection \citep{Adler&Roberts92,Pichardoetal00}." Low well do CO linewidths encode information on the dynamics of the cloud?, How well do CO linewidths encode information on the dynamics of the cloud? Projection ellects may also skew the linewidth - size power law scalings κ.)..," Projection effects may also skew the linewidth - size power law scalings \citep{Ballesteros-Paredesetal99,Ballesteros-Paredes&MacLow02,Shettyetal10}." Wa CO bright core can be accurately identified. is the observed. linewidth representative of the intrinsic. velocity dispersion?," If a CO bright core can be accurately identified, is the observed linewidth representative of the intrinsic velocity dispersion?" “To what extent does turbulence alfect the CO emission. and thus the," To what extent does turbulence affect the CO emission, and thus the" The ASCA observaion of were carried out ou September 21-25th. 1995.,"The ASCA observation of were carried out on September 24-25th, 1995." Daa were screeued aud aualyzed using the standard precedure described in the 2iwallable a the ASCA Cuest ObserverFacility!., Data were screened and analyzed using the standard procedure described in the available at the ASCA Guest Observer. . In. particular. data were rejected churing times whei the satelite was traversing regiος of low Cut-Ol ‘Rigidity (COR <6) and when the Ea‘th lim elevation angle was <10°.," In particular, data were rejected during times when the satellite was traversing regions of low Cut-Off Rigidity (COR $\le 6$ ) and when the Earth limb elevation angle was $\leq$ $^\circ$." The data were also masked spatially in order to remove the outer rine of high baesground as well as the calibration sot‘ceevents?., The data were also masked spatially in order to remove the outer ring of high background as well as the calibration source. . We also performed. background. rejectlon on GIS daa based ou the rise-time of the sigal., We also performed background rejection on GIS data based on the rise-time of the signal. The SIS x‘reening criteria for ext‘acting specral information were very similar to the ones applie to the CIS: same minimun elevation angle and salue minipiunm rigklitv cuteJL., The SIS screening criteria for extracting spectral information were very similar to the ones applied to the GIS: same minimum elevation angle and same minimum rigidity cutoff. Because o ‘the possibiity for contamihation intie. SIS of [luo'escence lines of oxygen from the Eartls atmosphere. data selection Was done ou the brielt-Earth auele. and only data above 1607 (20°) for tle 8150 (SIS1 were retainecl.," Because of the possibility for contamination in the SIS of fluorescence lines of oxygen from the Earth's atmosphere, data selection was done on the bright-Earth angle, and only data above $^\circ$ $^\circ$ ) for the SIS0 (SIS1) were retained." Fiualy. only. everts with CCD eraces Q. 2. 3. were isec in furtl ey:lalysis.," Finally, only events with CCD grades 0, 2, 3, or 4 were used in further analysis." The position of tle source [rom the i1lage analysis Is COUSINEL uowith with ROSAT al EINSTEIN j»ositions (Meregletietal.1995:Criudlay 1981)..," The position of the source from the image analysis is consistent with with ROSAT and EINSTEIN positions \cite{tz2:mereghetti95aa,grindlay84apjl}." In order to check for time aud specral variability. we have »oduced backgrour dsubtractec ight curves. as wel as |ardnuess-intenity aud coOr-color diagranms.," In order to check for time and spectral variability, we have produced background subtracted light curves, as well as hardness-intenity and color-color diagrams." This W.howed that the source is 'eiiarkably steady within our observajon. botl in intensity ald spectral slape.," This showed that the source is remarkably steady within our observation, both in intensity and spectral shape." The GIS spectrum was extracted fro na circilar 'eelon of adius 7! ceered αἱ the ition of he με..., The GIS spectrum was extracted from a circular region of radius $^\prime$ centered at the position of the source. lu order to correctly Ἡ he contributio1 from the gaactic plane diffuse emissiOL. we lave extracted. the background. from ultiple jelds withi1i the FOV of he instrument.," In order to correctly subtract the contribution from the galactic plane diffuse emission, we have extracted the background from multiple fields within the FOV of the instrument." Te salue I)cedure was applied to te SIS daa. except that à stualler region. (315'/ racius) was used to extract tle source spectrun.," The same procedure was applied to the SIS data, except that a smaller region $^\prime$ $^{\prime\prime}$ of radius) was used to extract the source spectrum." As mentioned alx)ve. 10 spect‘al variatlous coud be found within the observatiou. we have thereOre conjued for each detector he whole data se o derive a time averaged spectrum.," As mentioned above, no spectral variations could be found within the observation, we have therefore combined for each detector the whole data set to derive a time averaged spectrum." The spectral anaysis has )eel restrictec to the (0.5 to 10 keV range [or he CHUS2 :uud GIS3 and 0.L 0.5 to 10 keV for SISO aud 5191.," The spectral analysis has been restricted to the 0.8 to 10 keV range for the GIS2 and GIS3 and 0.4, 0.5 to 10 keV for SIS0 and SIS1." In these energy bands. the source count rates are 17.20-70.03. 7250.03. 1020.03 and. 1270.03 counts inthe GIS2. GIS3. SISO. SISI respectively.," In these energy bands, the source count rates are $\pm$ 0.03, $\pm$ 0.03, $\pm$ 0.03 and $\pm$ 0.03 count $^{ \rm -1}$ in the GIS2, GIS3, SIS0, SIS1 respectively." All fits were done using XSPEC version 10.00., All fits were done using XSPEC version 10.00. We startec by fitting tie cletectors separately aud then. merged them in a combined |-detector auaysis.," We started by fitting the detectors separately and then, merged them in a combined 4-detector analysis." Remarkable agreement is loud between all he detectors and weec decide to seej» the normalization equal [or all 1ie. [our instruüunments., Remarkable agreement is found between all the detectors and we decide to keep the normalization equal for all the four instruments. Leaving he relative uornalizaious of he four data sets as [ree parameters gives cousisteut results: the only noticeable difference is that it leads to a reduction of the reduced 4? values of ayout 0.2 (for more than 1300 degrees of (reecdonu)., Leaving the relative normalizations of the four data sets as free parameters gives consistent results; the only noticeable difference is that it leads to a reduction of the reduced $\chi^{2}$ values of about 0.2 (for more than 1300 degrees of freedom). Given previous observatious of the source. we first fit the spectrum with a siugle absorbed. power law.," Given previous observations of the source, we first fit the spectrum with a single absorbed power law." ΤΙe power law fit is uot good as there is a clear mw enerey excess which is uot accounted for iu the residuals., The power law fit is not good as there is a clear low energy excess which is not accounted for in the residuals. We then tried to fit this excess witli lackbodsy (BB) componeut., We then tried to fit this excess with a blackbody (BB) component. This results iu a enilicant inmxovement of the fits (N47>200)., This results in a significant improvement of the fits $\Delta\chi^2 \ge 200$ ). sine advautage of the better spectral resolution the SIS. we have checked that adding such a CJi couponent is also required when fitting the SISO at ASIST spectra (NA?>150 for LOS degrees [9]- [reeclom).," Taking advantage of the better spectral resolution of the SIS, we have checked that adding such a soft component is also required when fitting the SIS0 and SIS1 spectra $\Delta\chi^2 \ge 150 $ for 408 degrees of freedom)." We have also tried to [it the soft component with a multi-color cisx blackbody (DBB. itsuca et al.," We have also tried to fit the soft component with a multi-color disk blackbody (DBB, Mitsuda et al." 198D)., 1984). This moclel provides an ectally eood fi., This model provides an equally good fit. The Ay? is less than LO (1313 cLo..) for the two models., The $\Delta\chi^2$ is less than 10 (1313 d.o.f) for the two models. Other moclels such as a thermal B'enisstrahlung. a cutoff. power aw. Or a broken Ρε»ver law combined with a BB or a DBB could fi ue data as well but the flatuess ol the spectrum auc the restricted energy range o “ASCA does not allow to put interesting constralus on the itte paralneters.," Other models such as a thermal Bremsstrahlung, a cutoff power law, or a broken power law combined with a BB or a DBB could fit the data as well but the flatness of the spectrum and the restricted energy range of ASCA does not allow to put interesting constraints on the fitted parameters." The source flux at the tiue of our observation was within of the flux see iby SAN aud within ol the one observed by RATE., The source flux at the time of our observation was within of the flux seen by SAX and within of the one observed by RXTE. Likewise. the source spectrum was also very lard. and a soft component was also present: therefore it was legitimate to use the SAN and RATE models to try to fit the ASCA data as well.," Likewise, the source spectrum was also very hard and a soft component was also present; therefore it was legitimate to use the SAX and RXTE models to try to fit the ASCA data as well." This model is made of the stun of eitlier a BB or DBB componen aud the so-called, This model is made of the sum of either a BB or DBB component and the so-called This model is made of the stun of eitlier a BB or DBB componen aud the so-called., This model is made of the sum of either a BB or DBB component and the so-called "The average value of the correction from Avsyes; to Av is of the order of values of Av and the smallest ratio vymax/Av, the correction can be as high as [Avguess—Av| can be 10 times the estimate of the stellar noise contribution.","The average value of the correction from $\dnug$ to $\dnumoy$ is of the order of values of $\dnumoy$ and the smallest ratio $\numax / \dnumoy$, the correction can be as high as $|\dnug-\dnumoy|$ can be 10 times the estimate of the stellar noise contribution." " At low frequency, with an observing run not much longer than the mode lifetimes (?),, the realization noise dominates the background noise and the mean accuracy of the determination of Av is uniform, at about wHz."," At low frequency, with an observing run not much longer than the mode lifetimes \citep{baudin2010}, the realization noise dominates the background noise and the mean accuracy of the determination of $\dnumoy$ is uniform, at about $\mu$ Hz." We are aware that any bias in the e(Ay) input relation will induce a bias in the results.," We are aware that any bias in the $\varepsilon (\dnumoy)$ input relation will induce a bias in the results." We therefore took care to insure the iterative process to be unbiased., We therefore took care to insure the iterative process to be unbiased. Analysis of synthetic data indicates that the precision gained with this method is of order 10 times better than that obtained with conventional methods (?).., Analysis of synthetic data indicates that the precision gained with this method is of order 10 times better than that obtained with conventional methods \citep{2010arXiv1008.2959H}. " This new method based on a simple hypothesis and an automated procedure removes any ambiguity on the identification of the modes (Fig. 3)),"," This new method based on a simple hypothesis and an automated procedure removes any ambiguity on the identification of the modes (Fig. \ref{identi}) )," despite the complexity induced by mixed modes., despite the complexity induced by mixed modes. Mode identification is derived by looking at the closest ridge., Mode identification is derived by looking at the closest ridge. " In particular, we provide a straightforward determination of the mode radial orders, which were previously unknown."," In particular, we provide a straightforward determination of the mode radial orders, which were previously unknown." Radial eigenfrequencies are located at: Ridges were already shown in previous works., Radial eigenfrequencies are located at: Ridges were already shown in previous works. " While ? and ? looked at single stars separately, ? and ? used manual fine-tuning of the large separation to align the radial modes of a large sample of stars."," While \cite{2009Natur.459..398D} and \cite{2010A&A...509A..73C} looked at single stars separately, \cite{2010ApJ...713L.176B} and \cite{huber2010} used manual fine-tuning of the large separation to align the radial modes of a large sample of stars." " However, the radial modes were identified in only one third of the spectra by ?,, but they also showed the ridges with varying e in the folded and collapsed power spectrum."," However, the radial modes were identified in only one third of the spectra by \cite{huber2010}, but they also showed the ridges with varying $\varepsilon$ in the folded and collapsed power spectrum." In most regions of the oscillation spectra we observe the presence of both radial and non-radial modes., In most regions of the oscillation spectra we observe the presence of both radial and non-radial modes. " Realization noise causes the height of the individual modes to show considerable variability, but on average, the ratio between the dipole and radial mode height is approximately independent of Vmax."," Realization noise causes the height of the individual modes to show considerable variability, but on average, the ratio between the dipole and radial mode height is approximately independent of $\numax$." " Although, at very low Vmax there is some reduction in the strength of the dipole mode."," Although, at very low $\numax$ there is some reduction in the strength of the dipole mode." We also make clear that the larger spread of the ridges corresponding to dipole modes (Fig. 3)), We also make clear that the larger spread of the ridges corresponding to dipole modes (Fig. \ref{identi}) ) " is due to the presence of many mixed modes, as already noticed (??).."," is due to the presence of many mixed modes, as already noticed \citep{2009A&A...506...57D,2010ApJ...713L.176B}." The universal pattern makes it easier to identify them opening up the possibility of exploring the conditions in the inner layers of thered giants., The universal pattern makes it easier to identify them opening up the possibility of exploring the conditions in the inner layers of thered giants. " Despite their low amplitudes and the resulting poor signal, €=3 modes have been detected in Kepler data on red giants (??).."," Despite their low amplitudes and the resulting poor signal, $\ell=3$ modes have been detected in Kepler data on red giants \citep{2010ApJ...713L.176B,huber2010}." Our results represent the first such detection in CoRoT data., Our results represent the first such detection in CoRoT data. " Their identification gives access to the fine structure of the oscillation spectra, as modes of different angular degree probe different depths within the star."," Their identification gives access to the fine structure of the oscillation spectra, as modes of different angular degree probe different depths within the star." " Their detection and complete characterization will first be derived from the universal pattern, then the small differences to this pattern will be exploited to characterize in detail a given object (?).."," Their detection and complete characterization will first be derived from the universal pattern, then the small differences to this pattern will be exploited to characterize in detail a given object \citep{2010arXiv1009.1024M}." More than magnitude than mg—13 observed with CoRoT show solar-like oscillations., More than magnitude than $m\ind{R}=13$ observed with CoRoT show solar-like oscillations. " In the remainder, we observe a large proportion of classical pulsators or of giants with a so large radius that the oscillations occur at a too low frequency for a positive detection."," In the remainder, we observe a large proportion of classical pulsators or of giants with a so large radius that the oscillations occur at a too low frequency for a positive detection." " In a very limited number of cases at very low frequency, the possible confusion between radial and dipole modes is not clearly solved."," In a very limited number of cases at very low frequency, the possible confusion between radial and dipole modes is not clearly solved." This confusion increases toward dimmer targets with lower quality time series., This confusion increases toward dimmer targets with lower quality time series. " Among the positive detection of bright stars, we did not observe any outliers when performing the correlation with the universal pattern."," Among the positive detection of bright stars, we did not observe any outliers when performing the correlation with the universal pattern." " For this procedure to be effective, we require that the modes have a significant height-to-background ratio."," For this procedure to be effective, we require that the modes have a significant height-to-background ratio." Hence for all high signal-to-noise targets (?) we are able to derive corrected values for the large frequency spacing., Hence for all high signal-to-noise targets \citep{2010A&A...517A..22M} we are able to derive corrected values for the large frequency spacing. It is recognized that the majority of the red giants in the CoRoT field of view are in their post-flash helium-burning phase (?).., It is recognized that the majority of the red giants in the CoRoT field of view are in their post-flash helium-burning phase \citep{2009A&A...503L..21M}. " In terms of stellar evolution, the demonstration of the universal regular pattern of red giants proves that these red giants have similar and homologous interior structures."," In terms of stellar evolution, the demonstration of the universal regular pattern of red giants proves that these red giants have similar and homologous interior structures." " On the other hand, despite the agreement of the fit in & with the Solar value, we have verified that the method does not work with subgiants or main-sequence stars (????).."," On the other hand, despite the agreement of the fit in $\varepsilon$ with the Solar value, we have verified that the method does not work with subgiants or main-sequence stars \citep{2009A&A...506...51B,2009A&A...507L..13B,2010ApJ...713..935B,2010arXiv1003.4368D}. ." We explain this by, We explain this by Molecular lines at high redshift have generated cousiderable interest as probes of the gaseous content of carly Ooealaxies. as siguifiersoO of star formation. and as indicators of AGN activation processes.,"Molecular lines at high redshift have generated considerable interest as probes of the gaseous content of early galaxies, as signifiers of star formation, and as indicators of AGN activation processes." Thermal lines of species like CO trace large masses of molecular Lyvdrogen. typically ~10°—1011A7;. if detected in the distant universe.," Thermal lines of species like CO trace large masses of molecular hydrogen, typically $\sim 10^9 - 10^{11} M_{\sun}$, if detected in the distant universe." According to AGN activation scenarios developed over the past decade. it seenis likely that many quasars aud active galaxies turi ou when fue in the form of molectlar eas is forced iuto a ealactic uucleus during the course of an interac‘tion or merecr between two galaxies.," According to AGN activation scenarios developed over the past decade, it seems likely that many quasars and active galaxies turn on when fuel in the form of molecular gas is forced into a galactic nucleus during the course of an interaction or merger between two galaxies." " This model commects IB-hunünous galaxies aud classical quasars in au evolutionary sequence that leads frou concentration of eas in the nucleus through its cousuniptiou or exptusion. eventually revealing a mature. optically bright AGN (οι, Sanders et al 1988: Barnes aud Wernquist 1996)."," This model connects IR-luminous galaxies and classical quasars in an evolutionary sequence that leads from concentration of gas in the nucleus through its consumption or expulsion, eventually revealing a mature, optically bright AGN (e.g., Sanders et al 1988; Barnes and Hernquist 1996)." During this sequence the courpressed gas may pass through a huninous nuclear starbursting phase., During this sequence the compressed gas may pass through a luminous nuclear starbursting phase. Using molecular lines we hope to study these processes as they occured in the carly universe., Using molecular lines we hope to study these processes as they occured in the early universe. The observations push current instruments to thei hits. aud consequently oulv a few sources have becu detected at hiel-:.," The observations push current instruments to their limits, and consequently only a few sources have been detected at $z$." Several of these detectious have been aided by a boost from eravitatioual leusine., Several of these detections have been aided by a boost from gravitational lensing. " Below T summarize the observational situation with regardOo to thermal (1οι, wou-maser) molecular lines. inchidingeC» discussion of a new detection of CO from a lensed quasar at 2=2.61."," Below I summarize the observational situation with regard to thermal (i.e., non-maser) molecular lines, including discussion of a new detection of CO from a lensed quasar at $z = 2.64$." I also briefly discuss an ongoing new search for TeO masers at high redshift., I also briefly discuss an ongoing new search for $_2$ O masers at high redshift. Iu the late SO's. with improvements in nd]uneter telescope seusitivities and impetus from far-IR detections by IRAS. TR-luninous galaxies and nearby ACNs Όσσα1i to be observed iu molecular emission lines [primarily CO(L0)].," In the late 80's, with improvements in millimeter telescope sensitivities and impetus from far-IR detections by IRAS, IR-luminous galaxies and nearby AGNs began to be observed in molecular emission lines [primarily CO(1–0)]." The AGNs detected included. Mrk 231 (Saunders et al 1987). Mrk 1011 (Saunders. Scoville. Soifer 1988). T Zw 1 (Barvainis. Aloiu. Antonucci 1989). and a few other low-: quasars (Sanders ct al 1989: Alloiu ct al 1992).," The AGNs detected included Mrk 231 (Sanders et al 1987), Mrk 1014 (Sanders, Scoville, Soifer 1988), I Zw 1 (Barvainis, Alloin, Antonucci 1989), and a few other $z$ quasars (Sanders et al 1989; Alloin et al 1992)." Revealiis naps of the nuceus of NOGC1068 in both CO aud UCN, Revealing maps of the nucleus of NGC1068 in both CO and HCN AlISE values lor dillerent values of the softening. for different number of particles in the configuration. and. in the case of the power softening. dillerent values of the exponent p. roughly in the range from 2 to S.,"$MISE$ values for different values of the softening, for different number of particles in the configuration, and, in the case of the power softening, different values of the exponent $p$, roughly in the range from 2 to 8." For all types of softening the AZSE as a Function ofο curves are very similar to those of Figure 1.. so we will not repeat them here.," For all types of softening the $MISE$ as a function of $\epsilon$ curves are very similar to those of Figure \ref{repeat}, so we will not repeat them here." Figure 17. compares the optimal softening μη) for the power law softening - as a function of the exponent p - and for the spline softening., Figure \ref{eps_p_spline} compares the optimal softening $\epsilon_{opt}$ ) for the power law softening - as a function of the exponent $p$ - and for the spline softening. The values were obtained. from six hundred realisations of a Plummer sphere of 10 000 particles each. two hundred realisations of 30 000 particles ancl sixty 100 000 particle realisations.," The values were obtained from six hundred realisations of a Plummer sphere of 10 000 particles each, two hundred realisations of 30 000 particles and sixty 100 000 particle realisations." " We note that e,;;; Increases with p.", We note that $\epsilon_{opt}$ increases with $p$. Thus comparing p = 2.0 to p = 7.0 we fine an increase in cou; Of roughly a factor of two., Thus comparing $p$ = 2.0 to $p$ = 7.0 we find an increase in $\epsilon_{opt}$ of roughly a factor of two. Tho c;;; value for the spline is somewhat larger than that of the highest p values., The $\epsilon_{opt}$ value for the spline is somewhat larger than that of the highest $p$ values. As expected. the optimal softening decreases with increasing number of particles IN.," As expected, the optimal softening decreases with increasing number of particles $N$." The (loge) does not depend notably on the power p., The $\Delta(log\epsilon_{opt})$ does not depend notably on the power $p$. Figure IN compares the minimum. value for radial Mish (MESE) for the same cases as the previous figure., Figure \ref{MISE_p_spline} compares the minimum value for radial $MISE$ $MISE_{opt}$ ) for the same cases as the previous figure. " We note that AZ/SE, decreases with p.", We note that $MISE_{opt}$ decreases with $p$. " Thus comparing p — 234 t0 p 2 7.0 we find a decrease in AZSE, of roughly304.", Thus comparing $p$ = 2.0 to $p$ = 7.0 we find a decrease in $MISE_{opt}$ of roughly. ".. Phe ALS, value for the spline is of the order of that of the highest p values.", The $MISE_{opt}$ value for the spline is of the order of that of the highest $p$ values. As expected. the corresponding minimum errors decrease with increasing number of particles N.," As expected, the corresponding minimum errors decrease with increasing number of particles $N$." The A(logMμη) does not depend. notably on the power p., The $\Delta(logMISE_{opt})$ does not depend notably on the power $p$. Figure 19. compares the optimal softening and the corresponding racial MS47 values as a function of IN for the spline softening and for the power softening for exponents p — 2 and p — 5., Figure \ref{N_p_spline} compares the optimal softening and the corresponding radial $MISE$ values as a function of $N$ for the spline softening and for the power softening for exponents $p$ = 2 and $p$ = 5. Power laws are satisfactory approximations in all cases. given by and The values of the coellicients are given in Table 3..," Power laws are satisfactory approximations in all cases, given by and The values of the coefficients are given in Table \ref{tab:spline_p}." The small differences between the coellicients for the Plummer sphere ancl Plummer softening given here and those given in Table |. are due to the fact that here we have used radial ALISL while in Table 1. ALASL., The small differences between the coefficients for the Plummer sphere and Plummer softening given here and those given in Table \ref{tab:hpd} are due to the fact that here we have used radial $MISE$ while in Table \ref{tab:hpd} $MASE$. " From this table. as well as [rom Figure 19.. we see that the MS£, as a function of N is more or less the same for the p — 5 and the spline."," From this table, as well as from Figure \ref{N_p_spline}, we see that the $MISE_{opt}$ as a function of $N$ is more or less the same for the $p$ = 5 and the spline." The p = 2 case gives somewhat bigger values of ALLS£u., The $p$ = 2 case gives somewhat bigger values of $MISE_{opt}$. All the above argue that the spline softening as well as the higher values of the power in the power softening give a better representation of the force than the standard Plummer softening., All the above argue that the spline softening as well as the higher values of the power in the power softening give a better representation of the force than the standard Plummer softening. Phe dillerence. however. is not as big as one could have inferred [rom Figure 16.. since some of the dillerence is compensated by an adjustment in c;," The difference, however, is not as big as one could have inferred from Figure \ref{compare_soft}, since some of the difference is compensated by an adjustment in $\epsilon_{opt}$." Thus Figures 17. and IS argue for an improvement of30%.. with corresponding changes of «op. of a factor of two.," Thus Figures \ref{eps_p_spline} and \ref{MISE_p_spline} argue for an improvement of, with corresponding changes of $\epsilon_{opt}$ of a factor of two." This improvement is nevertheless non-neglieible. since it would take an increase of the number ofparticles of roughly to achieve it (cf.," This improvement is nevertheless non-negligible, since it would take an increase of the number of particles of roughly to achieve it (cf." section 3.2))., section \ref{sec:plummer_opt}) ). } The fact that the corresponding value of cop is higher is also an advantage. since. for equally good representations of the forces in the mass distribution. a larger softening allows for large time-steps. and therefore shorter CPU execution times.," The fact that the corresponding value of $\epsilon_{opt}$ is higher is also an advantage, since, for equally good representations of the forces in the mass distribution, a larger softening allows for large time-steps, and therefore shorter CPU execution times." Last but not least the spline softening necessitates considerably. less CPU time per call., Last but not least the spline softening necessitates considerably less CPU time per call. This gain in time depends on whether one programs in fortran or C. on what the exponent of the power is. and on the compiler used.," This gain in time depends on whether one programs in fortran or C, on what the exponent of the power is, and on the compiler used." We have found ratios roughly between 2 and. 10., We have found ratios roughly between 2 and 10. Dv making some modifications to the standard. treecode (Barnes and Llut 1986) it is possible to implement it on a GRAPE svstem (Makino 1991)., By making some modifications to the standard treecode (Barnes and Hut 1986) it is possible to implement it on a GRAPE system (Makino 1991). In. particular the tree should not be descended for cach particle separately. but for rlocks of particles. as initially proposed by Barnes (1990).," In particular the tree should not be descended for each particle separately, but for blocks of particles, as initially proposed by Barnes (1990)." Increasing the number of particles in the block makes the interaction list longer and the treecode more accurate., Increasing the number of particles in the block makes the interaction list longer and the treecode more accurate. The articular implementation on the Marseille CRAP svstenis is described in A198. together with some discussion on its »erformance and accuracy.," The particular implementation on the Marseille GRAPE systems is described in A+98, together with some discussion on its performance and accuracy." We have made caleulations of M.SZ using the GRAPE reecode and radial ΑΙ with the standard. one. for various values of the tolerance and the number of particles AN.," We have made calculations of $MASE$ using the GRAPE treecode and radial $MISE$ with the standard one, for various values of the tolerance and the number of particles $N$." The dilferences between the values corresponding to the same number of particles and dillerent tolerances is rather small., The differences between the values corresponding to the same number of particles and different tolerances is rather small. In. particular the values obtained with a tolerance of 0.5 or 0.7 are very near those obtained with the direct summation., In particular the values obtained with a tolerance of 0.5 or 0.7 are very near those obtained with the direct summation. Only for tolerances larger than 1 do the MASE values increase significantly. and even so the cdillerences with the direct summation are always considerably smaller than those obtained by changing the number of particles by factors as those considered e.g. in Figure 1..," Only for tolerances larger than 1 do the $MASE$ values increase significantly, and even so the differences with the direct summation are always considerably smaller than those obtained by changing the number of particles by factors as those considered e.g. in Figure \ref{repeat}." In this paper we have discussed the value of the softening that allows us to best approximate the true forces within a given mass distribution in an N-body simulation., In this paper we have discussed the value of the softening that allows us to best approximate the true forces within a given mass distribution in an N-body simulation. We have first worked. with the Plummer sphere and confirmed. previous results that. for a given number of xwiicles No there is an optimal softening which gives the ost approximations to the forces.," We have first worked with the Plummer sphere and confirmed previous results that, for a given number of particles $N$, there is an optimal softening which gives the best approximations to the forces." For smaller. values of he softening the noise introduces errors. while for larger here is a svstematic bias from the Newtonian force results.," For smaller values of the softening the noise introduces errors, while for larger there is a systematic bias from the Newtonian force results." We calculated the dependence of the optimal softening on he number of particles No ancl confirmed. ancl extencded he results of M96 anc AJOS., We calculated the dependence of the optimal softening on the number of particles $N$ and confirmed and extended the results of M96 and A+98. We compared. the results, We compared the results SPI simulation meluding dark matter and gas.,SPH simulation including dark matter and gas. Theoretically. (he mechanism giving rise to these displacements involves a high velocity substructure passing through the center of the parent cluster halo.," Theoretically, the mechanism giving rise to these displacements involves a high velocity substructure passing through the center of the parent cluster halo." Assessing the feasibility to accommodate that kind of events in the ACDM context. could be used as a test for the validitv of the model.," Assessing the feasibility to accommodate that kind of events in the $\Lambda$ CDM context, could be used as a test for the validity of the model." Unfortunately. deriving the relative velocity from observations is a non-trivial task. because of statistical and svstematical uncertainties. making diflieult the comparison to theoretical models.," Unfortunately, deriving the relative velocity from observations is a non-trivial task, because of statistical and systematical uncertainties, making difficult the comparison to theoretical models." The separation between the DM and gas components is a much better defined quantity. mostly affected by statistical errors in (he measurement process. but not so much by svstematic or model-cdepencent uncertainties.," The separation between the DM and gas components is a much better defined quantity, mostly affected by statistical errors in the measurement process, but not so much by systematic or model-dependent uncertainties." In (his paper we derive. for (he first time. (he expected physical 2D separation distribution [or clusters with a DM mass larger than 1015..," In this paper we derive, for the first time, the expected physical 2D separation distribution for clusters with a DM mass larger than $ 10^{14}$." ; We find that around 154 to 2% of these clusters show DM-gas separations equal or larger (han the observed in the Bullet Cluster., We find that around $1\%$ to $2\%$ of these clusters show DM-gas separations equal or larger than the observed in the Bullet Cluster. Thus. the existence of Bullet Clusters should not be considered as a challenge to the ACDM model as it has been recently claimed.," Thus, the existence of Bullet Clusters should not be considered as a challenge to the $\Lambda$ CDM model as it has been recently claimed." Even though the fractions of expected bullets in our ACDAM simulation basically coincide with (he previous work of ILavashi&White(2006).. (he comparison between the two results should be taken with a bit of eaution.," Even though the fractions of expected bullets in our $\Lambda$ CDM simulation basically coincide with the previous work of \cite{Hayashi06}, the comparison between the two results should be taken with a bit of caution." As we mentioned before. the definition of a Bullet cluster in ILavashi&White(2006) is different than in our case.," As we mentioned before, the definition of a Bullet cluster in \cite{Hayashi06} is different than in our case." Moreover. the dvnamical origin of the large displacements in our clusters seems (ο be more varied (han (he scenario of a single dominant substructure passing through the cluster.," Moreover, the dynamical origin of the large displacements in our clusters seems to be more varied than the scenario of a single dominant substructure passing through the cluster." Nevertheless. the striking coincidence of the predicted bullet fractions between the Millenium N-bocly simulation ancl the MareNostrum SPI simulation suggests that indeed it is possible to produce a bullet-like configuration with substructure velocities as low as ~2400 km/s. The approach we use and (he results we found are above all a necessary complement to the work of Πάνας&White(2006) and Lee&Komatsu(2010).," Nevertheless, the striking coincidence of the predicted bullet fractions between the Millenium N-body simulation and the MareNostrum SPH simulation suggests that indeed it is possible to produce a bullet-like configuration with substructure velocities as low as $\sim 2400$ km/s. The approach we use and the results we found are above all a necessary complement to the work of \citet{Hayashi06} and \citet{lee}." . We give inlormation about the configuration space rather Chan the velocity space. which can be compared in a more straightforward wav to observations as it has been done in the recent. work of on a small sample of 38 clusters. who find an acceptable agreement wilh our theoretical predictions.," We give information about the configuration space rather than the velocity space, which can be compared in a more straightforward way to observations as it has been done in the recent work of \cite{shan} on a small sample of 38 clusters, who find an acceptable agreement with our theoretical predictions." The Full distribution of these displacements can be considered as new prediction of the ACDAML model. which could eventually be compared against observations.," The full distribution of these displacements can be considered as new prediction of the $\Lambda$ CDM model, which could eventually be compared against observations." Upcoming large optical ancl N-rays survevs can make (his feasible in (he next vears., Upcoming large optical and X-rays surveys can make this feasible in the next years. in the D1 aud D2 Ποιά». which are good caudidates for being either carly L dwarfs or high redshift quasars (see Fig. 7)).,"in the D1 and D2 fields, which are good candidates for being either early L dwarfs or high redshift quasars (see Fig. \ref{naines}) )." They are given in Tab., They are given in Tab. 3., 3. Πο] redshift quasars with /i1.5 will be distinguixhable from brown dwarts either by near-infrared photometry or by proper motion lnueasurenmients., High redshift quasars with $i'-z' >1.5$ will be distinguishable from brown dwarfs either by near-infrared photometry or by proper motion measurements. The formation and evolution of low-mass stars ina binary system is a common phenomenon which leads to the interesting class of cataclysmic variables., The formation and evolution of low-mass stars in a binary system is a common phenomenon which leads to the interesting class of cataclysmic variables. In deep surveys one expects to detect a few cases of WD-AL dwarf pairs., In deep surveys one expects to detect a few cases of WD-M dwarf pairs. Ravinoud et al. (2003)), Raymond et al. \cite{Raymond2003}) ) ideutified ~ 100 white dwarfAI dwarf pairs in the SDSS survey with g«20., identified $\sim$ 100 white dwarf-M dwarf pairs in the SDSS survey with $g < 20$. Using additional spectroscopy. they achieve an efficiency. of ~GO% in findiug white dwuf-M dwarf pains because of the coutamination by galaxies iu the interesting colour PC@IOUS.," Using additional spectroscopy, they achieve an efficiency of $\sim 60\%$ in finding white dwarf-M dwarf pairs because of the contamination by galaxies in the interesting colour regions." We simulated saluple of uuresolved AL dawarts | white dwarfs systems by inereius their fluxes., We simulated a sample of unresolved M dwarfs + white dwarfs systems by merging their fluxes. Typical colours of these simulated systems are given in Fig., Typical colours of these simulated systems are given in Fig. ὃ as star syuibols., \ref{binaires} as star symbols. The location of these systems is clearly outside the single star locus in the ο vs 5!i diagraiun., The location of these systems is clearly outside the single star locus in the $g'-r'$ vs $r'-i'$ diagram. However they lic in a region where we expect contamination by compact ealaxics aud quasars., However they lie in a region where we expect contamination by compact galaxies and quasars. Their identification will |© CARY using proper motions. all these objects being intrinsically faint. and are hence detected ouly in the solar neighbourhood.," Their identification will be easy using proper motions, all these objects being intrinsically faint, and are hence detected only in the solar neighbourhood." As incutioned above. the stellar samples are contaminated by non-stellar sources.," As mentioned above, the stellar samples are contaminated by non-stellar sources." As a laree fraction of those fall iuse the stellar locus aud stellar binaries aud white dwarfs are also expected outside the main sequence (see Fig., As a large fraction of those fall inside the stellar locus and stellar binaries and white dwarfs are also expected outside the main sequence (see Fig. 2). oulv proper motions can be used to clean our saluple and remove galaxies aud quasars.," 2), only proper motions can be used to clean our sample and remove galaxies and quasars." Iu the following all objects classified. as stellar are kept., In the following all objects classified as stellar are kept. Iu Fig., In Fig. 9 histograms in go/on. /—7 and it/ for he D1 feld are shown. with model predictions for cach population. thin disc. thick disc. and splieroid.," \ref{histD1} histograms in $g'-r'$, $r'-i'$ and $i'-z'$ for the D1 field are shown, with model predictions for each population, thin disc, thick disc, and spheroid." Model predictions are acceptable for all three populations. which are better separated in the 1” colour.," Model predictions are acceptable for all three populations, which are better separated in the $r'-i'$ colour." Figure 10 shows the g/.—5 vs’ i diagrain for cach CFIITLS field. compared with model predictions. where the grevscale indicates the umuber of stars.," Figure \ref{histall} shows the $g'-r'$ vs $r'-i'$ diagram for each CFHTLS field, compared with model predictions, where the greyscale indicates the number of stars." The colow-colour Giagrais in the three fields are similar. and model predictions are in good ecucral agreement with the data.," The colour-colour diagrams in the three fields are similar, and model predictions are in good general agreement with the data." We notice. jowever. a few significant differences:," We notice, however, a few significant differences:" derived for the SGBs.,derived for the SGBs. Oxvgen and carbon abundances have been computed from the equivalent widths of the triplet and the lines respectively. and the derived values have then been corrected for non-local (hermodvnanuc equilibrium effects.," Oxygen and carbon abundances have been computed from the equivalent widths of the triplet and the lines respectively, and the derived values have then been corrected for non-local thermodynamic equilibrium effects." For O abundances these corrections were derived by interpolating the eric by Gratton et al. (, For O abundances these corrections were derived by interpolating the grid by Gratton et al. ( 1999); for C abundances we adopted the empirical relation obtained by interpolating the values listed by Tomkin et al. (,1999); for C abundances we adopted the empirical relation obtained by interpolating the values listed by Tomkin et al. ( 1992).,1992). The resulting average abundances for the SGD sample are [C/Fe|=—0.16+0.02 (0=0.17) and [O/Fe|—0.29=0.02 (o= 0.17)., The resulting average abundances for the SGB sample are $=-0.16\pm 0.02$ $\sigma = 0.17$ ) and $=0.29\pm 0.02$ $\sigma = 0.17$ ). No measurements have been possible for the very fast rotating BSSs and lor a [ew other objects (see Table 1)., No measurements have been possible for the very fast rotating BSSs and for a few other objects (see Table 1). IIence. we were able to measure both the C and O abundances only lor 11. BSSs. out of 20 observed.," Hence, we were able to measure both the C and O abundances only for 11 BSSs, out of 20 observed." Figure 3. shows the results obtained in the [C'/Fe]|-[O/Fe] plane.," Figure \ref{abb} shows the results obtained in the $-$ [O/Fe] plane." The values measured for the 11. DSSs are in agreement with those of the SGDs. with no evidence of depletion either in carbon or in oxveen.," The values measured for the 11 BSSs are in agreement with those of the SGBs, with no evidence of depletion either in carbon or in oxygen." We finally notice that also in the 3 cases for which only the oxvgen ihe carbon abundance has been measured. (see Table 1). the values obtained are in agreement with those of the οὓς.," We finally notice that also in the 3 cases for which only the oxygen the carbon abundance has been measured (see Table 1), the values obtained are in agreement with those of the SGBs." Belore discussing in details (he main findings of the present work it is necessary (o verily whether some of the investigated stars do not belong to the cluster., Before discussing in details the main findings of the present work it is necessary to verify whether some of the investigated stars do not belong to the cluster. In particular. live D5S9s have been found to display anomalous μαι which may cast some doubts about (heir menbership.," In particular, five BSSs have been found to display anomalous $V_{\rm rad}$, which may cast some doubts about their membership." Ilowever. DS5s #442424 and 4664677 have measured proper motions well in agreement with those of the cluster members (Anderson et al.," However, BSSs 42424 and 64677 have measured proper motions well in agreement with those of the cluster members (Anderson et al." 2006)., 2006). All the other objects have measured rotational velocities significantly larger than expected for normal stars of the sanie spectral tvpe. thus making unlikely that they belong to the field.," All the other objects have measured rotational velocities significantly larger than expected for normal stars of the same spectral type, thus making unlikely that they belong to the field." We have also used the Desancoon Galactic model (Robin et al., We have also used the Besançoon Galactic model (Robin et al. 2003) to derive the radial velocity and metallicity distributions of the Galactic field stars in the direction of M4. within the same magnitude and colour intervals shared by our BSS sample.," 2003) to derive the radial velocity and metallicity distributions of the Galactic field stars in the direction of M4, within the same magnitude and colour intervals shared by our BSS sample." The Vi4 distribution is peaked at —14.6kins and has a dispersion c=50.7kms.+.," The $V_{\rm rad}$ distribution is peaked at $-14.6\kms$ and has a dispersion $\sigma = 50.7\kms$." As a consequence. the probability that the DSSs with anomalous radial velocity belong to the field is always smaller than1.," As a consequence, the probability that the BSSs with anomalous radial velocity belong to the field is always smaller than." 756.. The theoretical metallicity distribution of field stars is peaked at [Fe/II]2.—0.1720.02 (6= 0.45)., The theoretical metallicity distribution of field stars is peaked at $=-0.17\pm 0.02$ $\sigma = 0.45$ ). The iron abundance measured in two of the five DSSs with anomalous radial velocity (|Fe/II]|2-—1.35 [or 3£442424. and —1.23 lor #664677) clearly is lareely inconsistent with the field value and concordant. within the errors. with that of M4 stars.," The iron abundance measured in two of the five BSSs with anomalous radial velocity $=-1.35$ for 42424, and $-1.23$ for 64677) clearly is largely inconsistent with the field value and concordant, within the errors, with that of M4 stars." " Based on these considerations we therefore conclude that all the BSSs with anomalous Vi,4 are indeed members of MA.", Based on these considerations we therefore conclude that all the BSSs with anomalous $V_{\rm rad}$ are indeed members of M4. We notice that if (he discrepancies were caused by (he orbital motion in binary svstenis.," We notice that if the discrepancies were caused by the orbital motion in binary systems," the increasing formation height combined with the decrease in field strength with height (Solankietal.1996).,the increasing formation height combined with the decrease in field strength with height \citep{Solanki+others1996}. . The peak amplitude of unipolar cuts as a function of ji is similar to the center-side amplitude i1 the bipolar cuts., The peak amplitude of unipolar cuts as a function of $\mu$ is similar to the center-side amplitude in the bipolar cuts. The total polarization (circular and linear) ts larger in the bipolar features consistent with the unipolar features being smaller flux concentrations which do not expand as strongly as the bipolar features., The total polarization (circular and linear) is larger in the bipolar features consistent with the unipolar features being smaller flux concentrations which do not expand as strongly as the bipolar features. " Since we do not see as many unipolar features in (in fact none were included in the analysis) this indicates that either the unipolar features further expand with height (assuming the NaD, signal is formed higher than the Fe lines and appear bipolar in NaD,. or they are not strong enough to reach or to be visible at the formation height of the NaD, signal in the NFI data."," Since we do not see as many unipolar features in $_{1}$ (in fact none were included in the analysis) this indicates that either the unipolar features further expand with height (assuming the $_{1}$ signal is formed higher than the Fe lines and appear bipolar in $_{1}$, or they are not strong enough to reach or to be visible at the formation height of the $_{1}$ signal in the NFI data." " Due to the larger width and lower Landé g-factor of the NaD, line. together with the NFI not being as sensitive as SP. the NFI data may sample only the stronger. larger magnetic features."," Due to the larger width and lower Landé $g$ -factor of the $_{1}$ line, together with the NFI not being as sensitive as SP, the NFI data may sample only the stronger, larger magnetic features." " Note that the NaD, signal does not necessarily come from a greater height (deWijnetal.2009).", Note that the $_{1}$ signal does not necessarily come from a greater height \citep{deWijn+others2009}. . Besides the geometry (tube or sheet) the choice of flux tube radius at z-O km. so. is the most important factor determining the expansion of the thin flux tubes (Fig. 7)).," Besides the geometry (tube or sheet) the choice of flux tube radius at $z$ =0 km, $r_0$, is the most important factor determining the expansion of the thin flux tubes (Fig. \ref{fig:tube-r}) )." Note that the values of ο considered here (140. 200. 400 and 600 km.," Note that the values of $r_0$ considered here (140, 200, 400 and 600 km." ς=Q corresponds to 7=| in the external atmosphere) are comparable to or larger than the pressure scale height. .e.. outside the strict validity range of the thin flux tube approximation.," $z=0$ corresponds to $\tau=1$ in the external atmosphere) are comparable to or larger than the pressure scale height, i.e., outside the strict validity range of the thin flux tube approximation." " The absolute expansion is significantly stronger for 1,2400 and 600 km than for the tubes with smaller radii (although the relative expansion. (7(2)/7(0). 1s the same for all)."," The absolute expansion is significantly stronger for $r_0$ =400 and 600 km than for the tubes with smaller radii (although the relative expansion, $r(z)/r(0)$, is the same for all)." Compared to the choice of radius. the choice of internal model (facular or plage) or Bo (magnetic field strength at «Ξ0 km. 1300 or 1400 G) does not produce dramatically different expansion rates as shown in Fig. 7..," Compared to the choice of radius, the choice of internal model (facular or plage) or $B_0$ (magnetic field strength at $z$ =0 km, 1300 or 1400 G) does not produce dramatically different expansion rates as shown in Fig. \ref{fig:tube-r}." The plage and network models used here describe the network and plage regions as à whole. re.. they do not specifically address flux tubes.," The plage and network models used here describe the network and plage regions as a whole, i.e., they do not specifically address flux tubes." The discrepancy between these models and flux tube models. such as. e.g.. Briand&Solanki(1995)... is largest in the low photosphere where the temperature rise Is stronger in the flux tube nodels.," The discrepancy between these models and flux tube models, such as, e.g., \cite{Briand+Solanki1995}, is largest in the low photosphere where the temperature rise is stronger in the flux tube models." This leads to slightly stronger expansion of the tube in the lower layers., This leads to slightly stronger expansion of the tube in the lower layers. " In the following. we show synthetic observables from slabs with the facular model as the internal atmosphere and B,21300 G. where By corresponds to B in the the flux tube at =0."," In the following, we show synthetic observables from slabs with the facular model as the internal atmosphere and $B_0$ =1300 G, where $B_{0}$ corresponds to $B$ in the the flux tube at $=0$." Ratios resulting from different models (atmospheric model. Bo) are not significantly different from the ones shown here.," Ratios resulting from different models (atmospheric model, $B_0$ ) are not significantly different from the ones shown here." " The radial cuts in NaD, and Fe become more asymmetric towards the limb (Fig. 8).", The radial cuts in $_{1}$ and Fe become more asymmetric towards the limb (Fig. \ref{fig:tube-res}) ). Local maxima in the cuts are produced close to the boundaries of the flux tube due to the hot-wall effect., Local maxima in the cuts are produced close to the boundaries of the flux tube due to the hot-wall effect. " When the tube radius. ro. is comparable to the pressure scale height (140 km or 200 km) the tube does not expand enough or at heights low enough to produce clearly bipolar features in the Fe and NaD, observables as shown in Fig. 9ten.."," When the tube radius, $r_{0}$, is comparable to the pressure scale height (140 km or 200 km) the tube does not expand enough or at heights low enough to produce clearly bipolar features in the Fe and $_{1}$ observables as shown in Fig. \ref{fig:tube-ratio}." Only when the tube radius is > 400 km do bipolar features begin to appear at j/20.5., Only when the tube radius is $\ge$ 400 km do bipolar features begin to appear at $\mu$ =0.5. The smallest ratios are from the Ro=600 km case where the expansion of the magnetic field is the strongest., The smallest ratios are from the $R_{0}$ =600 km case where the expansion of the magnetic field is the strongest. Using the amplitude instead of area results in slightly different ratios., Using the amplitude instead of area results in slightly different ratios. The differences between area and amplitude are largest for the smallest j7-values. but both observables show the same trends.," The differences between area and amplitude are largest for the smallest $\mu$ -values, but both observables show the same trends." The effect of convolving and rebinning the observables to Hinode resolution only slightly alters the ratios., The effect of convolving and rebinning the observables to Hinode resolution only slightly alters the ratios. Normalizing the Stokes V profiles to the local continuum intensity prior to computing the observables (area. amplitude) slightly changes the ratios.," Normalizing the Stokes $V$ profiles to the local continuum intensity prior to computing the observables (area, amplitude) slightly changes the ratios." " The NaD, ratios are slightly higher than the Fe ratios. contrary to the observations."," The $_{1}$ ratios are slightly higher than the Fe ratios, contrary to the observations." ll=odpl1=0pt mnlessbox-oliboxzolit22-0dp22-0pt Active Galactic Nuclei (ACN) in general. but quasars iu particular are very powerful sources of radiation.,"1=0pt 2=0pt Active Galactic Nuclei (AGN) in general, but quasars in particular are very powerful sources of radiation." The ACN huninosity. £ is typically high compared to its Eddinetou lait. Leaq (0.001 πιωL1 Lgg)," The AGN luminosity, $L$ is typically high compared to its Eddington limit, $L_{\rm Edd}$ (0.001 $L_{\rm Edd}\simless L \simless 1~L_{\rm Edd}$ )." The spectral energy distribution (SED) of ACN is very broad., The spectral energy distribution (SED) of AGN is very broad. It spans the wavelength range from radio to lard N-ravs aud even TeV. Most of the ACN luminosity is iu the opticalUV.IR bands but some significant fraction is in the N-rav baud., It spans the wavelength range from radio to hard X-rays and even TeV. Most of the AGN luminosity is in the optical–UV–IR bands but some significant fraction is in the X-ray band. These ACN radiation properties aud the ACN ceutral location in their host ealaxics imply that they plav a very inportanut role in determing the ionization structure aud dviuauues of matter not only iu their vicinity but also ou larger. galactic and even intergalactic scales (Ciotti Oztriker. 1997. 2001: ine 2003: Mii. Quataert. Thompson 2005: Sazouov et al.," These AGN radiation properties and the AGN central location in their host galaxies imply that they play a very important role in determining the ionization structure and dynamics of matter not only in their vicinity but also on larger, galactic and even intergalactic scales (Ciotti Ostriker, 1997, 2001; King 2003; Murray, Quataert, Thompson 2005; Sazonov et al." 2005: Springel. Di Matteo IHeruquist 2005: IToplius et al.," 2005; Springel, Di Matteo Hernquist 2005; Hopkins et al." 2005: Wane. Chen. IIn aud references therein).," 2005; Wang, Chen, Hu and references therein)." There are many inclications that support this sugeestion. for example tle preseuce of broad cussion lines (BELs) in ACN spectra.," There are many indications that support this suggestion, for example the presence of broad emission lines (BELs) in AGN spectra." BELs ave one of the defining spectral features of ACN., BELs are one of the defining spectral features of AGN. Thev are observed in optical (OPT) and ultraviolet (UV) spectra and have line wines extending to velocities up to 105Ensft., They are observed in optical (OPT) and ultraviolet (UV) spectra and have line wings extending to velocities up to $10^4~{\rm km~s^{-1}}$. " Tt ds fairly well established that the primary plysical mechanisin for production of BELs is photoionization by the compact continua source of ACN,", It is fairly well established that the primary physical mechanism for production of BELs is photoionization by the compact continuum source of AGN. Detailed photoionization calculations vield relatively tight constraints on the physical couditions of the cutting gas such as the temperature. density. ionization level. aud chemical abundances (e... Ferlaud et al.," Detailed photoionization calculations yield relatively tight constraints on the physical conditions of the emitting gas – such as the temperature, density, ionization level, and chemical abundances (e.g., Ferland et al." 1998: Παπά Ferland 1999: Krolik 1999 and references therein)., 1998; Hamman Ferland 1999; Krolik 1999 and references therein). The width of BELs indicates that the photoiouized eas is supersonic., The width of BELs indicates that the photoionized gas is supersonic. The shape aud position of the line profiles cau be explained by lines forming either iu a region without preferred velocity direction and with a nearly spherical distributionor at the base of a wind from an accretion disk (Murrav et al., The shape and position of the line profiles can be explained by lines forming either in a region without preferred velocity direction and with a nearly spherical distribution at the base of a wind from an accretion disk (Murray et al. 1995. hereafter MCCV: Dottorff et.," 1995, hereafter MCGV; Bottorff et." al 1997)., al 1997). In the latter case. the BELs can form where the outflow expausion velocity is low compared to the rotational velocity (AICCAY).," In the latter case, the BELs can form where the outflow expansion velocity is low compared to the rotational velocity (MCGV)." Not all gas in AGN shaves the properties of the oue responsible for BELs., Not all gas in AGN shares the properties of the one responsible for BELs. Some quasars show broad absorption lines (BALs) which are the most dramatic /es3ideuce for well-organized outflows in ACN., Some quasars show broad absorption lines (BALs) which are the most dramatic evidence for well-organized outflows in AGN. BALs are almost always blueshitted relative to the emission-line rest frame. indicatiug the presence of outflows frou the active uucleus. with velocities as laxge as 0.2 e (c.g... Turnshek 1998).," BALs are almost always blueshifted relative to the emission-line rest frame, indicating the presence of outflows from the active nucleus, with velocities as large as 0.2 c (e.g., Turnshek 1998)." BALs are observed not only iu the UV but also in the N-ravs., BALs are observed not only in the UV but also in the X-rays. For example. Clartas. Draudt Callagher (2003) discovered a very broad absorption line iu the X-raw spectrum of Ῥ L115|so.," For example, Chartas, Brandt Gallagher (2003) discovered a very broad absorption line in the X-ray spectrum of PG 1115+80." Other evidence for ACN outflows include narrow absorption lines (NALS)., Other evidence for AGN outflows include narrow absorption lines (NALs). UV spectra of some quasars show NALS which are blueshifted bw as much as c 50000 lans+ (Ibunaun ct al., UV spectra of some quasars show NALs which are blueshifted by as much as $\sim$ 50000 ${\rm km~s^{-1}}$ (Hamann et al. 1997)., 1997). NALS are, NALs are The reionization of the universe. which took pace arounel a redshift of 10.5. (Ixomatsuetal.POLL). iss generally believed to be driven primarily by ionizing photons from early “Population HE. (pop-Hll) stars.,"The reionization of the universe, which took place around a redshift of 10.5 \citep{komatsu11}, is generally believed to be driven primarily by ionizing photons from early `Population III' (pop-III) stars." As hese stars form from primordial unenriched. metal-frec| hydrogen and helium. they undergo a formation procCss that ds substantially different from that of later popuation Land IE stars.," As these stars form from primordial unenriched, metal-free hydrogen and helium, they undergo a formation process that is substantially different from that of later population I and II stars." Simulations of the production of peyp-LLL stars (Abel.Brvan&Norman2000:Dromm.CoopiLar-man2008) generally find an initial mass function (LM) that is heavily biased. towards high masses. 10. 1000AL.," Simulations of the production of pop-III stars \citep{abel02,bromm02,tan&mckee04,yoshida06,norman08} generally find an initial mass function (IMF) that is heavily biased towards high masses, 10 – 1000." .. A considerable fraction of the radiant energy fron these stars is released at. ionizing wavelengths («912 A)) which allows reionization of the universe to be completed on the timescale required by forest data (Beckerctal.2001).," A considerable fraction of the radiant energy from these stars is released at ionizing wavelengths $< 912$ ), which allows reionization of the universe to be completed on the timescale required by forest data \citep{becker01}." . Despite their. importance in cosmology and impact on IGM evolution. pop-Lll stars οςontinue to evade direct. detection.," Despite their importance in cosmology and impact on IGM evolution, pop-III stars continue to evade direct detection." Detecting the recishifed UN. emission from pop-Lll stars is a primary eoal of the upcomingTelescope. though even with the state of the art sensitivity of this instrument detecting individual metal-[ree stars will be challenging. (iwelbere.Zackrisson&Scott.2011).," Detecting the redshifted UV emission from pop-III stars is a primary goal of the upcoming, though even with the state of the art sensitivity of this instrument detecting individual metal-free stars will be challenging \citep{rydberg11}." . Searchine for indirect. evidence of these stars ane their integrated: cosmological impact is therefore the primary, Searching for indirect evidence of these stars and their integrated cosmological impact is therefore the primary no standard star calibrations and our velocities are measured solely with respect to the Th/Ar lamp.,no standard star calibrations and our velocities are measured solely with respect to the Th/Ar lamp. " For short span observations such a primitive procedure still yields root-mean-square (RMS) residuals in the m/s range, for stars brighter than mag."," For short span observations such a primitive procedure still yields root-mean-square (RMS) residuals in the m/s range, for stars brighter than mag." " As demonstrated— in refs2,, for intensively observed, strictly periodic stars, any long-term effects of a floating instrumental zero-point may be removed with some assurance, yielding again RMS residuals less than m/s, over one year span of data."," As demonstrated in \\ref{s2}, for intensively observed, strictly periodic stars, any long-term effects of a floating instrumental zero-point may be removed with some assurance, yielding again RMS residuals less than m/s, over one year span of data." In total 158 radial velocity measurements of V440 Per were obtained with PST from 2007 August 15 till 2008 July 03., In total 158 radial velocity measurements of V440 Per were obtained with PST from 2007 August 15 till 2008 July 03. 'To reach signal-to-noise ratio of 70 we exposed spectra for min and up to several spectra were obtained per night., To reach signal-to-noise ratio of 70 we exposed spectra for min and up to several spectra were obtained per night. The observed velocities are listed in Table 1 published in the electronic form., The observed velocities are listed in Table \ref{t1} published in the electronic form. Phase-folded data with fitted Fourier series refs2)) are displayed in refASCI.., Phase-folded data with fitted Fourier series \\ref{s2}) ) are displayed in \\ref{ASC1}. In refASC2 we plot residuals of the first order and the second order fits pulsation phase and time., In \\ref{ASC2} we plot residuals of the first order and the second order fits pulsation phase and time. " Inspection of the plots demonstrates that our coverage was reasonably uniform, both in time and in frequency."," Inspection of the plots demonstrates that our coverage was reasonably uniform, both in time and in frequency." From the residuals we estimate standard error of our individual measurements as m/s. The plot of the phase-folded radial velocities reveals near sinusoidal variations with peak-to-peak amplitude of km/s. Some data consistency checks are due prior to drawing any final conclusions., From the residuals we estimate standard error of our individual measurements as m/s. The plot of the phase-folded radial velocities reveals near sinusoidal variations with peak-to-peak amplitude of km/s. Some data consistency checks are due prior to drawing any final conclusions. Cepheid phases and frequencies are known to vary slightly., Cepheid phases and frequencies are known to vary slightly. " Additionally, the instrument stability over months needs checking, too."," Additionally, the instrument stability over months needs checking, too." A preliminary nonlinear least squares fit of our data with the Fourier series of three harmonics terms (third order fit) yielded no significant 2nd harmonics of the main frequency nor the period derivative term., A preliminary nonlinear least squares fit of our data with the Fourier series of three harmonics terms (third order fit) yielded no significant 2nd harmonics of the main frequency nor the period derivative term. " Our fitted frequency of 0.13206+ 0.00001c/d is less accurate, yet consistent within errors with the frequency derived by combining our data with the earlier measurements of Burki&Benz(1982),, ArellanoFerro(1984) and Gorynyaetal.(1992,1996,1998).."," Our fitted frequency of $0.13206\pm 0.00001$ c/d is less accurate, yet consistent within errors with the frequency derived by combining our data with the earlier measurements of \citet{BB82}, \citet{arr84} and \citet{Gor92,Gor96,Gor98}." " Comparison of the data shows, that the weighted zero point shift of our velocities with respect to the previous authors is —26.3+0.2 km/s. The RMS deviation from the Fourier fit of all our data was 164m/s, well in excess of m/s obtained for the first part of the dataset."," Comparison of the data shows, that the weighted zero point shift of our velocities with respect to the previous authors is $-26.3\pm 0.2$ km/s. The RMS deviation from the Fourier fit of all our data was m/s, well in excess of m/s obtained for the first part of the dataset." " Worse, inspection of the residuals plotted against time sometimes revealed non-gaussian, bi-modal distribution."," Worse, inspection of the residuals plotted against time sometimes revealed non-gaussian, bi-modal distribution." The origin of both effects seems to be instrumental., The origin of both effects seems to be instrumental. " To confirm that, we expanded our Fourier model by including two linear terms proportional to the time interval from the mid-epoch and to the hourangle of the star at the moment of observation."," To confirm that, we expanded our Fourier model by including two linear terms proportional to the time interval from the mid-epoch and to the hourangle of the star at the moment of observation." " The fitted values of these instrumental correction coefficients were significant at 6c and 5o level, respectively."," The fitted values of these instrumental correction coefficients were significant at $\sigma$ and $\sigma$ level, respectively." " From the overall covariance matrix we find maximum absolute value of the correlation coefficients of 0.30, consistent with little interference between different fitted terms."," From the overall covariance matrix we find maximum absolute value of the correlation coefficients of 0.30, consistent with little interference between different fitted terms." " These instrumental corrections reached up to X100 m/s. At this stage, we have no explanation for these corrections."," These instrumental corrections reached up to $\pm 100$ m/s. At this stage, we have no explanation for these corrections." " Our final second order Fourier fit, supplemented with the instrumental correction terms, yielded RMS deviation of m/s, consistent with that obtained from the short-span observations."," Our final second order Fourier fit, supplemented with the instrumental correction terms, yielded RMS deviation of m/s, consistent with that obtained from the short-span observations." The values of the Fourier parameters of V440 Per radial velocity curve are listed in Table 2 (for exact formulae defining Fourier parameters and their errors see Appendix A))., The values of the Fourier parameters of V440 Per radial velocity curve are listed in Table \ref{t2} (for exact formulae defining Fourier parameters and their errors see Appendix \ref{sa}) ). Pulsation mode of a Cepheid can be established by measuring Fourier phase ¢21 of its light curve (Antonelloetal.1990) or radial velocity curve (Kienzleetal.1999)., Pulsation mode of a Cepheid can be established by measuring Fourier phase $\phi_{21}$ of its light curve \citep{APR90} or radial velocity curve \citep{kie99}. ". This Fourier parameter does not depend on the pulsation amplitude of the star and for each mode it follows a different, defined progression with the pulsation period."," This Fourier parameter does not depend on the pulsation amplitude of the star and for each mode it follows a different, progression with the pulsation period." " For periods at which the two $21 progressions are well separated, secure mode identification can be achieved."," For periods at which the two $\phi_{21}$ progressions are well separated, secure mode identification can be achieved." In we plot velocity $21 of short period Galactic, In \\ref{ASC3} we plot velocity $\phi_{21}$ of short period Galactic In the light of this very strong TTV detection. the original science goal based on multi-color photometry becomes relegated to supporting evidence.,"In the light of this very strong TTV detection, the original science goal based on multi-color photometry becomes relegated to supporting evidence." Despite the TTV. we captured the crucial part of the egress where the planet crosses the limb of the star. which results in a weak detection of a g'—z' color signature (on the order of one millimag). consistent with the modeled one. though offset (Fig. 1).," Despite the TTV, we captured the crucial part of the egress where the planet crosses the limb of the star, which results in a weak detection of a $g'-z'$ color signature (on the order of one millimag), consistent with the modeled one, though offset (Fig. \ref{gtc806}) )." This offset is plausible. given the clear evidence of transparency variations Just after the transit. revealed by increased scatter in the photometry.," This offset is plausible, given the clear evidence of transparency variations just after the transit, revealed by increased scatter in the photometry." This could in turn affect the measured out-of-transit flux., This could in turn affect the measured out-of-transit flux. However. even without a true detection of the transit color signature. we can constrain the the ature of any false positive.," However, even without a true detection of the transit color signature, we can constrain the the nature of any false positive." " The photometry does clearly excludes the possibility of any strong ""Sependency of transit depth on color. which one would expect from a blend with any color difference between the components. as proposed by Tingley (2004)) and utilized by O°’Donovan et al. (2006))."," The photometry does clearly excludes the possibility of any strong dependency of transit depth on color, which one would expect from a blend with any color difference between the components, as proposed by Tingley \cite{tin2004}) ) and utilized by O'Donovan et al. \cite{odo2006}) )," ODonovan et al. (2007)).," O'Donovan et al. \cite{odo2007}) )," Cochran et al. (201 1).," Cochran et al. \cite{coc2011}) )," and Ballard et al. (2011))., and Ballard et al. \cite{bal2011}) ). " We ""Serived an equation that is similar in principle to BLENDER (Torres et al 2004.2011)). but much simplified. to limit the possible color difference between the target star and any contaminating eclipsing binaries (CEBs)."," We derived an equation that is similar in principle to BLENDER (Torres et al \cite{tor2004,tor2011}) ), but much simplified, to limit the possible color difference between the target star and any contaminating eclipsing binaries (CEBs)." " It relates the blended eclipse depth in Z (dep) to that in σ΄ using only the depth of the unblended eclipse depth in g’ and z' ( dep. and «ερ. respectively) and the £'—z' color difference between the target star and the blending eclipsing binary (Αν)— z): where where we set /,45,,=|. which yields a differential blended eclipse depth in zZ'."," It relates the blended eclipse depth in $z'$ $d_{CEB,g}$ ) to that in $g'$ using only the depth of the unblended eclipse depth in $g'$ and $z'$ ( $d_{EB,g}$ and $d_{EB,z}$ , respectively) and the $g'-z'$ color difference between the target star and the blending eclipsing binary $\Delta(g'-z')$ ): where where we set $f_{target,g}=1$, which yields a differential blended eclipse depth in $z'$." If we set dep.=dep. ACg!—τσ) must be less than about 0.02.," If we set $d_{EB,z} = d_{EB,g}$, $\Delta(g'-z')$ must be less than about 0.02." Relaxing this constraint to allow ανν to vary as much as from ερ. à reasonable value. constrains A(g’—z') to about 0.25 for lightly blended eclipses (s frg) to 0.05 for highly blended eclipses (fu2» fen).," Relaxing this constraint to allow $d_{EB,z}$ to vary as much as from $d_{EB,g}$, a reasonable value, constrains $\Delta(g'-z')$ to about 0.25 for lightly blended eclipses $f_{target} \sim f_{EB}$ ) to 0.05 for highly blended eclipses $f_{target} \gg f_{EB}$ )." While this does not absolutely rule out the possibility that the transit of may be due to a blend. it does suggest that it is unlikely.," While this does not absolutely rule out the possibility that the transit of may be due to a blend, it does suggest that it is unlikely." While the GTC showed a clear advance of the transit egress. we would not have been able to detect any changes in transit duration due to the partial coverage of the transit.," While the GTC showed a clear advance of the transit egress, we would not have been able to detect any changes in transit duration due to the partial coverage of the transit." To verify the stellar parameters given in the Kepler Input Catalogue for the host star. KIC 3832474 5206K.logg= 4.53). we took spectra of KOI 806 and several other similar stars with the 2.5 meter Nordic Optical Telescope (NOT). using grism #55 at a resolving power R=830 over the wavelength interval5100-90004.," To verify the stellar parameters given in the Kepler Input Catalogue for the host star, KIC 3832474 $T_{\rm eff} = 5206 K$ , $\log g = 4.53$ ), we took spectra of KOI 806 and several other similar stars with the 2.5 meter Nordic Optical Telescope (NOT), using grism 5 at a resolving power R=830 over the wavelength interval." . The spectra were calibrated in wavelength against Ne lines from are images taken with the same instrumental configuration as the target and flux normalized to unity at the wavelength interval7400-7500A., The spectra were calibrated in wavelength against Ne lines from arc images taken with the same instrumental configuration as the target and flux normalized to unity at the wavelength interval. . Uncertainty in instrumental response correction is less than10%., Uncertainty in instrumental response correction is less than. . We corrected the spectra for telluric absorption. though some residuals at the strongest telluric oxygen band at around remain due to differentairmasses of target and tellurie standard star (see Fig. 2)).," We corrected the spectra for telluric absorption, though some residuals at the strongest telluric oxygen band at around remain due to differentairmasses of target and telluric standard star (see Fig. \ref{spectrum}) )." We obtained the spectral classification of the host star, We obtained the spectral classification of the host star "and thus that D,,<ἰ-Lo.",and thus that $D_m < \lambda_z < L_0$. For a fixed value of οἱ in this range. 0B/Bo ts a decreasing function of .t_ so the requirement OB/Bo<| now sets a lower limit to 2_. obtainable by rewriting Eq. (21):," For a fixed value of $\lambda_z$ in this range, $\delta B/B_0$ is a decreasing function of $\lambda_\perp$ so the requirement $\delta B/B_0 < 1$ now sets a lower limit to $\lambda_\perp$, obtainable by rewriting Eq. \ref{dminterp}) ):" " With D, known and assumed values of ;,L and οἱ Eq. (215) "," With $D_m$ known and assumed values of $\lambda_z$ and $\lambda_\perp$, Eq. \ref{dminterp}) )" yields a cubic equation that may be solved exactly for (58/80) (although the resulting expression is not particularly informative)., yields a cubic equation that may be solved exactly for $(\delta B/B_0)^2$ (although the resulting expression is not particularly informative). " Putting 2t-=Lo and ΞWo gives 0B8/B4 0.12. the minimum value consistent with D,,."," Putting $\lambda_z = L_0$ and $\lambda_\perp = W_0$ gives $\delta B/B_0 = 0.12$ , the minimum value consistent with $D_m$." In Figure | we show the allowed region of Ct...t_) space. bounded by ÀA-=Lo. tL=Wo and 6B/By=1.," In Figure \ref{fig:lengths} we show the allowed region of $\lambda_z,\lambda_\perp$ ) space, bounded by $\lambda_z = L_0$, $\lambda_\perp = W_0$ and $\delta B/B_0 = 1$." From Eq. (24)), From Eq. \ref{eq:lperp}) ) " in the case 0B/By=l|. we can show that; has a minimum value of 4D,/357=1.75D,,3.5x107 em here."," in the case $\delta B/B_0 = 1$, we can show that $\lambda_\perp$ has a minimum value of $4 D_m/3^{3/4} = 1.75D_m = 3.5\times10^7$ cm here." The energy in perturbations must be at least ~1% of the energy of the background field., The energy in perturbations must be at least $\sim 1\%$ of the energy of the background field. The possibility remains of a much higher energy contained in the turbulent perturbations (see Figure 2)). even sufficient to power the whole flare if OB/Bo=1.," The possibility remains of a much higher energy contained in the turbulent perturbations (see Figure \ref{fig:lengthsB}) ), even sufficient to power the whole flare if $\delta B/B_{0}\simeq 1$." In most of the allowed region K is of the order of unity 0.1]>1.," Nonetheless, we can have significant anisotropy $\lambda_z$ and $\lambda_\perp$ substantially different from one another) without also having $K >>1$." Correlation lengths may not. however. be very much less than the natural scales of the magnetic loop.," Correlation lengths may not, however, be very much less than the natural scales of the magnetic loop." The theory by ? was applied by ? (ο the thermal loops observed by the TRACE spacecraft in the extreme ultraviolet range to determine the magnetic turbulence level in thermal loops.," The theory by \citet{1978PhRvL..40...38R} was applied by \citet{2006ApJ...646..615G} to the thermal loops observed by the TRACE spacecraft in the extreme ultraviolet range to determine the magnetic turbulence level in thermal loops." The authors found a level of the order of 0B/Bo=0.025— 0.075., The authors found a level of the order of $\delta B/B_{0}\simeq 0.025-0.075$ . More recently it was pointed out by ? that by taking into account certain features related to the Kubo number. the higher value of the order of 6B/Byz0.05—0.7 could instead be inferred from the data. values high enough for field-line braiding to lead to sufficient continuous. small scale reconnection events to account for coronal heating.," More recently it was pointed out by \citet{2010ApJ...719.1912B} that by taking into account certain features related to the Kubo number, the higher value of the order of $\delta B/B_{0}\simeq 0.05-0.7$ could instead be inferred from the data, values high enough for field-line braiding to lead to sufficient continuous, small scale reconnection events to account for coronal heating." It should be noted that these estimates for quiet non-flaring loops appear to be as high as the faring loop estimates., It should be noted that these estimates for quiet non-flaring loops appear to be as high as the flaring loop estimates. Furthermore. these high values of 9B/By=0.7 seem to contradict the observations ofnon-thermal broadening if interpreted as turbulent velocities.," Furthermore, these high values of $\delta B/B_{0}\simeq 0.7$ seem to contradict the observations of non-thermal broadening if interpreted as turbulent velocities." " The corresponding MHD turbulence velocities v~B_/Bov,=50—700 km/s for v4=1000 km/s appear much higher than the typical velocities of tens of km/s inferred from non-thermal line broadening (???).."," The corresponding MHD turbulence velocities ${\rm v}\sim B_{\perp}/B_{0} {\rm v}_{A} \simeq 50-700$ km/s for ${\rm v}_{A}\simeq 1000$ km/s appear much higher than the typical velocities of tens of km/s inferred from non-thermal line broadening \cite[][]{1997SoPh..173..243D,1999ApJ...513..969H,2009ApJ...705L.208I}." For the solar flare conditions discussed by ?.. the non-thermal broadening ts instead measured in the range of 100-200 km/s (222?) so. 6B/Bo=0.1—0.2 is indeed consistent with these observations.," For the solar flare conditions discussed by \citet{2011ApJ...730L..22K}, the non-thermal broadening is instead measured in the range of 100-200 km/s \citep{1982SoPh...78..107A,1983SoPh...86...49D,1989ApJ...344..991F,1999A&A...342..279P} so, $\delta B/B_{0}\simeq 0.1-0.2$ is indeed consistent with these observations." We note that the thermal particles are nore likely to be influenced by E_xB drift. which is dominant for particles whose speeds is comparable to or less thai the Alfven speed.," We note that the thermal particles are more likely to be influenced by $\mathbf{E}_{\perp}\times \mathbf{B}$ drift, which is dominant for particles whose speeds is comparable to or less than the Alfven speed." The observed appearance of TRACE loops would then constrain 6B/Bo to even lower values than those found by ?.., The observed appearance of TRACE loops would then constrain $\delta B/B_{0}$ to even lower values than those found by \citet{2006ApJ...646..615G}. " Alternatively. the ratio of magnetic and kinetic energies in the turbulence is far from unity and hence the simple relation v~B_/Bov, is not applicable."," Alternatively, the ratio of magnetic and kinetic energies in the turbulence is far from unity and hence the simple relation ${\rm v}\sim B_{\perp}/B_{0} {\rm v}_{A}$ is not applicable." We considered the cross-field transport of fast electrons inside coronal loops., We considered the cross-field transport of fast electrons inside coronal loops. Our analysis was based on a novel method. which exploits the imaging capabilities for determining the value of the magnetic diffusion coefficient in thick target loops.," Our analysis was based on a novel method, which exploits the imaging capabilities for determining the value of the magnetic diffusion coefficient in thick target loops." By “thick target” we mean that the flaring loop is dense enough to guarantee that the electrons remain in the loop while they are accelerated and emit HXRs. and hence that they are well-observed with X-ray imaging instruments.," By “thick target” we mean that the flaring loop is dense enough to guarantee that the electrons remain in the loop while they are accelerated and emit HXRs, and hence that they are well-observed with X-ray imaging instruments." Various possible regimes of cross-field transport of non-thermal electrons were discussed and applied to the interpretation of the data., Various possible regimes of cross-field transport of non-thermal electrons were discussed and applied to the interpretation of the data. The importance of the Kubo number K as a governing parameter was emphasized and results applicable to both the quasilinear (K«1) and trapping limits (K>>1) were collected., The importance of the Kubo number $K$ as a governing parameter was emphasized and results applicable to both the quasilinear $K\ll 1$ ) and trapping limits $K\gg 1$ ) were collected. The combination of theory and observation allows us to place interesting constraints on the relative level of magnetic fluctuations and on the Kubo number in flaring loops., The combination of theory and observation allows us to place interesting constraints on the relative level of magnetic fluctuations and on the Kubo number in flaring loops. These are summarized in Figs.(1)-(2)., These are summarized in Figs.(1)-(2). By identifying parallel and perpendicular correlation lengths with the two integral scales of the visible HXR loop. we found 6B/By=0.1 and also K=O.4.," By identifying parallel and perpendicular correlation lengths with the two integral scales of the visible HXR loop, we found $\delta B/B_{0}\simeq 0.1$ and also $K\simeq 0.4$ ." This quasilinear estimate for 6B/By shows that magnetic fluctuations with energy of at least ~1% of the energy of the background field can be inferred from measurements of the magnetic diffusion coefficient., This quasilinear estimate for $\delta B/B_{0}$ shows that magnetic fluctuations with energy of at least $\sim 1\%$ of the energy of the background field can be inferred from measurements of the magnetic diffusion coefficient. We note that although the size of the HXR emitting region is likely to be governed by parallel and perpendicular transport. continuing theoretical effort is needed to describe the electror dynamics more accurately. in particular regarding the treatment of the impact of energy loss. acceleration and non-linearity Οἱ transport.," We note that although the size of the HXR emitting region is likely to be governed by parallel and perpendicular transport, continuing theoretical effort is needed to describe the electron dynamics more accurately, in particular regarding the treatment of the impact of energy loss, acceleration and non-linearity on transport." compute several flux statistics (??7)..,"compute several flux statistics \citep{bolton08,viel04,viel08voids}." Many systematic effects have been carefully addressed including metal lines contamination and continuum fitting errors., Many systematic effects have been carefully addressed including metal lines contamination and continuum fitting errors. The median redshift of the sample isat z—2.2., The median redshift of the sample isat $z=2.2$. " From this data set we extracted the cumulative distribution of voids in the transmitted flux, i.e. connected regions with flux above the mean level, which at z2 appear to trace reasonably well underdense regions."," From this data set we extracted the cumulative distribution of voids in the transmitted flux, i.e. connected regions with flux above the mean level, which at $z\sim 2$ appear to trace reasonably well underdense regions." " As for the sample of galaxy groups, it contains 40 objects selected by ? so that gas properties can be derived out to r2500 for all of them (rA is the radius encompassing an average density of Axρε, being ρε the cosmic critical density)."," As for the sample of galaxy groups, it contains 40 objects selected by \cite{sun08} so that gas properties can be derived out to $r_{2500}$ for all of them $r_\Delta$ is the radius encompassing an average density of $\Delta \times\rho_{\rm c}$, being $\rho_{\rm c}$ the cosmic critical density)." " ? analysed this sample to derive the scaling relation between entropy and temperature at different overdensities and found an excess of entropy at T500, with respect to the baseline value calibrated by ? from non-radiative hydrodynamical simulations of clusters, although this excess is smaller than suggested by previous analyses (e.g. ??7).."," \cite{sun08} analysed this sample to derive the scaling relation between entropy and temperature at different overdensities and found an excess of entropy at $r_{500}$, with respect to the baseline value calibrated by \cite{voit05} from non–radiative hydrodynamical simulations of clusters, although this excess is smaller than suggested by previous analyses \citep[e.g.][]{ponman03,pratt05,piffaretti05}. ." " Moreover, they also found that the excess entropy is larger at 2500, thus confirming that any non-gravitational process has a larger effect in the central regions of groups."," Moreover, they also found that the excess entropy is larger at $r_{2500}$, thus confirming that any non–gravitational process has a larger effect in the central regions of groups." " In we show a projected slice whose thickness is 8 comoving Figure[I]h~'Mpc of the gas distribution at z=2.2 and z—0, for the default run and for the (300,10) run."," In Figure \ref{fig1} we show a projected slice whose thickness is 8 comoving $\hm$ of the gas distribution at $z=2.2$ and $z=0$ for the default run and for the (300,10) run." " Even by adding this strong pre-heating, at z—2.2 the skeleton of the cosmic web at densities around the mean is still preserved."," Even by adding this strong pre–heating, at $z=2.2$ the skeleton of the cosmic web at densities around the mean is still preserved." " The main differences arise in dense structures, whose filling factor is small."," The main differences arise in dense structures, whose filling factor is small." At z—0 the effect of pre-heating is quite visible as well: the mildly non-linear cosmic web evolves and gives rise to clusters of galaxies and galaxy groups., At $z=0$ the effect of pre–heating is quite visible as well: the mildly non-linear cosmic web evolves and gives rise to clusters of galaxies and galaxy groups. " These very non-linear structures tend to be puffier and smoother compared to the reference case, with a suppression of the number of small halos that trace the filaments."," These very non-linear structures tend to be puffier and smoother compared to the reference case, with a suppression of the number of small halos that trace the filaments." From the snapshots at z—2.2 we extract a mock set of 1000 QSO spectra in random directions., From the snapshots at $z=2.2$ we extract a mock set of 1000 QSO spectra in random directions. " Then, we smooth the spectra over a scale of 1 comoving h!Mpc, to be less sensitive to small structures at and around the Jeans length that might not be properly resolved by our simulations."," Then, we smooth the spectra over a scale of 1 comoving $\hm$, to be less sensitive to small structures at and around the Jeans length that might not be properly resolved by our simulations." " We then compute the number of voids in the flux distribution, having size larger than a given value and compare the pre-heated runs with the default one."," We then compute the number of voids in the flux distribution, having size larger than a given value and compare the pre–heated runs with the default one." " As shown by ?,, the reference run provides results in excellent agreement with the data."," As shown by \cite{viel08voids}, the reference run provides results in excellent agreement with the data." " Results are presented in Figure Bl. where the shaded area indicates the uncertainty in the observed mean flux level, which sets the criterion for the selection of voids."," Results are presented in Figure \ref{fig2}, where the shaded area indicates the uncertainty in the observed mean flux level, which sets the criterion for the selection of voids." " Among all the possible uncertainties in the astrophysical and cosmological parameters, this error has the largest effect on the void statistics (see ? for more details)."," Among all the possible uncertainties in the astrophysical and cosmological parameters, this error has the largest effect on the void statistics (see \citealt{viel08voids} for more details)." " Therefore, we take it as a rough estimate of the error."," Therefore, we take it as a rough estimate of the error." We remind that the total error budget must also take into account the contributions from all the other parameters and it is larger than the one shown here., We remind that the total error budget must also take into account the contributions from all the other parameters and it is larger than the one shown here. " For example, a ~3 times higher temperature of the IGM at the mean density would boost the number of 30 comoving h~'Mpc voids up to a factor 1.5, bringing some of the models in better agreement with the observations."," For example, a $\sim 3$ times higher temperature of the IGM at the mean density would boost the number of 30 comoving $\hm$ voids up to a factor 1.5, bringing some of the models in better agreement with the observations." " Basically, the error bars represented by the shaded area do not take into account different thermal histories for the low density IGM and/or different cosmological scenarios (warm dark matter or extra power at intermediate scales) that are more extensively discussed in ?.."," Basically, the error bars represented by the shaded area do not take into account different thermal histories for the low density IGM and/or different cosmological scenarios (warm dark matter or extra power at intermediate scales) that are more extensively discussed in \cite{viel08voids}." " In the left panel, we address the role of a different overdensity threshold for heating, keeping fixed the entropy floor at 300 keV cm?."," In the left panel, we address the role of a different overdensity threshold for heating, keeping fixed the entropy floor at 300 keV $^2$." " Clearly, heating up the whole IGM (i.e. dn=—1) substantially increases the number of voids since the neutral fraction will be reduced by the very large amount of heating."," Clearly, heating up the whole IGM (i.e. $\delta_{\rm h}=-1$ ) substantially increases the number of voids since the neutral fraction will be reduced by the very large amount of heating." " If we increase the overdensity threshold to 6,=3 and 10, then the void fraction is in better agreement with the default case, as expected, but there is a tendency to under-predict the number of large void regions."," If we increase the overdensity threshold to $\delta_h=3$ and 10, then the void fraction is in better agreement with the default case, as expected, but there is a tendency to under-predict the number of large void regions." " This result might seem counter-intuitive, since a heating of the IGM should reduce the hydrogen neutral fraction."," This result might seem counter–intuitive, since a heating of the IGM should reduce the hydrogen neutral fraction." " However, we found that the gas in the relatively low density environments of the pre-heated runs is denser compared to the default run and thereby carries with it a larger neutral hydrogen fraction."," However, we found that the gas in the relatively low density environments of the pre–heated runs is denser compared to the default run and thereby carries with it a larger neutral hydrogen fraction." The opposite trend takes place in overdense regions where the default simulation is denser than the corresponding pre-heated ones., The opposite trend takes place in overdense regions where the default simulation is denser than the corresponding pre--heated ones. At low redshifts the volume filling factor of underdense (overdense) regions gets larger (smaller) in all the models but the overall effect is a reduction of the size of large voids compared to the REF case since in the pre-heated runs the voids are less empty., At low redshifts the volume filling factor of underdense (overdense) regions gets larger (smaller) in all the models but the overall effect is a reduction of the size of large voids compared to the REF case since in the pre--heated runs the voids are less empty. " The (300,30) is closer to the default case than the (300,10) owing to the decrease of the volume filling factor of the heated regions with increasing óc."," The (300,30) is closer to the default case than the (300,10) owing to the decrease of the volume filling factor of the heated regions with increasing $\delta_{\rm c}$." " In the right panel of Figure D] we show the effect of changing the entropy floor, while keeping the overdensity threshold for heating fixed at δν=10."," In the right panel of Figure \ref{fig2} we show the effect of changing the entropy floor, while keeping the overdensity threshold for heating fixed at $\delta_{\rm h}=10$." Increasing the entropy floor has the effect of lowering the fraction of large voids: at z=4 the heating of dense gas particles at 6>10 makes them leave quickly their halos and reach the low density IGM: these particles have usually a larger fraction of neutral hydrogen that can cause absorptions in the mock spectra that are extracted at z—2.2., Increasing the entropy floor has the effect of lowering the fraction of large voids: at $z=4$ the heating of dense gas particles at $\delta > 10$ makes them leave quickly their halos and reach the low density IGM: these particles have usually a larger fraction of neutral hydrogen that can cause absorptions in the mock spectra that are extracted at $z=2.2$. At z=0 we identify galaxy groups in our simulations by running a friends-of-friends algorithm with b—0.15 for the linking length in units of the mean dark matter (DM) interparticle separation., At $z=0$ we identify galaxy groups in our simulations by running a friends–of–friends algorithm with $b=0.15$ for the linking length in units of the mean dark matter (DM) interparticle separation. The centre of each group is then identified with the position of the DM particle having the minimum value of thegravitational potential., The centre of each group is then identified with the position of the DM particle having the minimum value of thegravitational potential. " Following ?,, we compute for each group the temperature TA within TA (for A—500 and 2500) by excluding the core region within 0.15rsoo."," Following \cite{sun08}, , we compute for each group the temperature $T_\Delta$ within $r_{\Delta}$ (for $\Delta=500$ and 2500) by excluding the core region within $0.15\,r_{500}$." " Then we measure the profiles of the electron number density, ne(r), and of the gas temperature, T(r)."," Then we measure the profiles of the electron number density, $n_{\rm e}(r)$, and of the gas temperature, $T(r)$." The values of entropy Ka at ra are then computed as KA= A- ," The values of entropy $K_\Delta$ at $r_\Delta$ are then computed as $K_{\Delta}=T_{\Delta}/n_{\rm e,\Delta}^{2/3}$ ." "X-ray temperatures are computed following theprescriptionαν by ?,,which represents an extension to low- systems (Tx«3 keV, relevant for our analysis) of the spectroscopic-like temperature, originally introduced by ?.."," $X$ –ray temperatures are computed following theprescription by \cite{vikhlinin06}, ,which represents an extension to low--temperature systems $T_X< 3$ keV, relevant for our analysis) of the spectroscopic–like temperature, originally introduced by \cite{mazzotta2004}. ." " In Figure we compare the relation between entropy and temperature for our simulated groups to the observational data by ?,, for four of our simulatedboxes."," In Figure \ref{fig3} we compare the relation between entropy and temperature for our simulated groups to the observational data by \cite{sun08}, , for four of our simulatedboxes." variability has a clear impact on the sample's morphological makeup.,variability has a clear impact on the sample's morphological makeup. We have created a sample of 123 variable radio sources using two epoch observations of a zero-dec strip toward the south Galactic cap., We have created a sample of 123 variable radio sources using two epoch observations of a zero-dec strip toward the south Galactic cap. This sample spans the range of radio flux densities from ~2 to 1000 mJy., This sample spans the range of radio flux densities from $\sim2$ to 1000 mJy. " It presents both in size and radio flux density coverage a unique starting point for variability studies of more normal, less AGN-dominated galaxies, especially toward the lower flux density limits."," It presents both in size and radio flux density coverage a unique starting point for variability studies of more normal, less AGN-dominated galaxies, especially toward the lower flux density limits." We compared both our variable and non-variable samples to the Sloan Digital Sky Survey optical data., We compared both our variable and non-variable samples to the Sloan Digital Sky Survey optical data. We found that the quasar fraction of the sample sharply declines as a function of declining radio flux density levels., We found that the quasar fraction of the sample sharply declines as a function of declining radio flux density levels. " T'his is consistent with earlier findings that the radio source population demographics change as one samples at progressively lower flux density levels: AGN-dominated systems tend to be found at the brighter radio flux density levels (>10 mJy), whereas star-forming and normal galaxies dominate the counts at sub-mJy flux density levels (at 1.4 GHz, e.g., Windhorst 2003)."," This is consistent with earlier findings that the radio source population demographics change as one samples at progressively lower flux density levels: AGN-dominated systems tend to be found at the brighter radio flux density levels $> 10$ mJy), whereas star-forming and normal galaxies dominate the counts at sub-mJy flux density levels (at 1.4 GHz, e.g., Windhorst 2003)." " Our variable sample contains a consistently higher fraction of quasars than the non-variable control sample, independent of radio flux density."," Our variable sample contains a consistently higher fraction of quasars than the non-variable control sample, independent of radio flux density." " While this explains part of our almost 2x higher optical matching rate of the variable sample compared to the non-variable one (quasars are easier to detect at a given brightness limit than galaxies), it does imply that our variable sample contains on average slightly brighter sources (though not significantly so, see Sect. ??))."," While this explains part of our almost $2\times$ higher optical matching rate of the variable sample compared to the non-variable one (quasars are easier to detect at a given brightness limit than galaxies), it does imply that our variable sample contains on average slightly brighter sources (though not significantly so, see Sect. \ref{apmid}) )." " Based on relative number statistics, we estimate that quasars are about 5 times more likely to harbor a variable radio source than galaxies."," Based on relative number statistics, we estimate that quasars are about 5 times more likely to harbor a variable radio source than galaxies." " However, at flux density levels <20 mJy, the majority of (radio) variable sources are identified as galaxies."," However, at flux density levels $< 20$ mJy, the majority of (radio) variable sources are identified as galaxies." " And finally, galaxies and quasars that harbor a variable radio source exhibit, on average, bluer optical colors than hosts of non-variable sources."," And finally, galaxies and quasars that harbor a variable radio source exhibit, on average, bluer optical colors than hosts of non-variable sources." " All of this underlines the fact that both galaxies and quasars can harbor variable radio sources, albeit at different occurrence rates."," All of this underlines the fact that both galaxies and quasars can harbor variable radio sources, albeit at different occurrence rates." " Some of this is obviously due to the beamed nature of the (variable) quasars, enhancing the variability both by boosting their brightnesses and shortening the"," Some of this is obviously due to the beamed nature of the (variable) quasars, enhancing the variability both by boosting their brightnesses and shortening the" the Centre National d'Etudes Spatiales of France and the Korean Ministry of Science and Technology.,the Centre National d'Etudes Spatiales of France and the Korean Ministry of Science and Technology. We thank the many members of the ALFALFA team who have contributed to the acquisition and processing of the ALFALFA dataset over the last six years., We thank the many members of the ALFALFA team who have contributed to the acquisition and processing of the ALFALFA dataset over the last six years. RG and MPH are supported by NSF grant AST-0607007 and by a grant from the Brinson Foundation., RG and MPH are supported by NSF grant AST-0607007 and by a grant from the Brinson Foundation. Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation. the Participating Institutions. the National Science Foundation. the U.S. Department of Energy. the National Aeronautics and Space Administration. the Japanese Monbukagakusho. the Max Planck Society. and the Higher Education Funding Council for England.," Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England." The SDSS Web Site is http://www.sdss.org/. In this paper. UV/optical colours are measured by convolving the SDSS images to match the poorer resolution of the GALEX NUV images.," The SDSS Web Site is http://www.sdss.org/. In this paper, UV/optical colours are measured by convolving the SDSS images to match the poorer resolution of the GALEX NUV images." In some of our galaxies. the half-light semi-minor axis bsy becomes similar to or smaller than the size of the ~4 pixel PSF of the GALEX NUV images.," In some of our galaxies, the half-light semi-minor axis $b_{50}$ becomes similar to or smaller than the size of the $\sim 4$ pixel PSF of the GALEX NUV images." In this regime. the 2- colour and SFR measurements may no longer be valid.," In this regime, the 2-zone colour and SFR measurements may no longer be valid." In addition. the GALEX MIS images are relatively shallow. so the 2-zone measurements of the NUV fluxes may have large errors if the signal-to-noise is low.," In addition, the GALEX MIS images are relatively shallow, so the 2-zone measurements of the NUV fluxes may have large errors if the signal-to-noise is low." In order to quantify these effects more precisely. we have performed simulations by transforming the images of nearby galaxies so that they have similar magnitudes and apparent size ranges to the galaxies in the samples studied in this paper.," In order to quantify these effects more precisely, we have performed simulations by transforming the images of nearby galaxies so that they have similar magnitudes and apparent size ranges to the galaxies in the samples studied in this paper." We select 52 galaxies from the GALEX Nearby Galaxies Survey (NGS. GildePazetal. (2007))) with images available from the SDSS.," We select 52 galaxies from the GALEX Nearby Galaxies Survey (NGS, \citet{Gildepaz07}) ) with images available from the SDSS." We only select isolated galaxies with apparent sizes (ox) less than 5 aremin. where the image is not contaminated by foreground or background objects.," We only select isolated galaxies with apparent sizes $D_{25}$ ) less than 5 arcmin, where the image is not contaminated by foreground or background objects." " We begin by measuring NUV— rand A,ΝΟΥ—r) from these images (shown in purple in Figure A3).", We begin by measuring $NUV-r$ and $\Delta_{o-i}(NUV-r)$ from these images (shown in purple in Figure A3). The nearby sample turns out to have a similar distribution of these two parameters as the GASS (shown in black on in Figure A3)., The nearby sample turns out to have a similar distribution of these two parameters as the GASS (shown in black on in Figure A3). We then create a library of 60.000 simulated images.," We then create a library of 60,000 simulated images." " For each nearby galaxy image. we select a value of 5a, and r-band apparent"," For each nearby galaxy image, we select a value of $b_{50}$ and $r$ -band apparent" galaxies are confined to a ~2 Mpc thick plane (seen side on in Figure 6)).,galaxies are confined to a $\sim 2$ Mpc thick plane (seen side on in Figure \ref{figure:SGxz}) ). Seen from above (Fig. 5)), Seen from above (Fig. \ref{figure:SGxy}) ) the MW and M31 PoS are both highly inclined with respect to the supergalactic plane., the MW and M31 PoS are both highly inclined with respect to the supergalactic plane. " As discussed in Metzetal.(2007) there is no apparent spatial connection between the MW and M31 PoS as the M31 PoS is inclined at ~55° to the MW PoS. It is, however, notable that the PoS of both galaxies is well aligned with an axis between the two major mass distributions within 20 Mpc: the Virgo and Fornax clusters (Karachentsevetal.2003).."," As discussed in \citet{Metz07} there is no apparent spatial connection between the MW and M31 PoS as the M31 PoS is inclined at $\sim 55^{\circ}$ to the MW PoS. It is, however, notable that the PoS of both galaxies is well aligned with an axis between the two major mass distributions within 20 Mpc: the Virgo and Fornax clusters \citep{Karachentsev03}. ." This was remarked upon by Navarroetal.(2004) in their study of the galaxies of the local supergalacticplane?., This was remarked upon by \citet{Navarro04} in their study of the galaxies of the local supergalactic. . Here they found that not only are the satellites of nearby early-type galaxies preferentially confined to polar planes relative to their disks but that the galaxy disk is orientated along the major axis of surrounding LSS material., Here they found that not only are the satellites of nearby early-type galaxies preferentially confined to polar planes relative to their disks but that the galaxy disk is orientated along the major axis of surrounding LSS material. " This is also the case for the MW and M31, where as seen in reffigure:SGxy and 6,, the PoS are highly inclined to the stellar disks of their hosts."," This is also the case for the MW and M31, where as seen in \\ref{figure:SGxy} and \ref{figure:SGxz}, the PoS are highly inclined to the stellar disks of their hosts." It is our thesis that the observed affinity between the planar distribution of outer halo GCs and that of the MW satellites implies a common origin., It is our thesis that the observed affinity between the planar distribution of outer halo GCs and that of the MW satellites implies a common origin. " In this scenario, the outer halo GCs are accreted to the MW as part of galaxies from the surrounding LSS."," In this scenario, the outer halo GCs are accreted to the MW as part of galaxies from the surrounding LSS." They enter as entities residing in dark matter subhalos in LSS filaments that stream into the MW dark matter halo., They enter as entities residing in dark matter subhalos in LSS filaments that stream into the MW dark matter halo. " Upon entry, potential subhalos may deliver the GCs from their natal dark matter subhalos via tidal disruption and dispersal of dwarf galaxies (akin to the simulations of Libeskindetal. 2010)) or from the early tidal disruption of a moderate mass galaxy (like that envisaged by Kroupaetal. 2010))."," Upon entry, potential subhalos may deliver the GCs from their natal dark matter subhalos via tidal disruption and dispersal of dwarf galaxies (akin to the simulations of \citeauthor{Libeskind10} \citeyear{Libeskind10}) ) or from the early tidal disruption of a moderate mass galaxy (like that envisaged by \citeauthor{Kroupa10} \citeyear{Kroupa10}) )." We discount the possibility of ”free-floating” GCs as this would imply dark matter dominance and in the case of at least one of the outer halo GCs (Pal 14; Jordietal. 2009)) there is no evidence for dark matter.," We discount the possibility of ""free-floating"" GCs as this would imply dark matter dominance and in the case of at least one of the outer halo GCs (Pal 14; \citeauthor{Jordi09} \citeyear{Jordi09}) ) there is no evidence for dark matter." We see in the spatial distribution of the outer halo GCs evidence of their accretion origin., We see in the spatial distribution of the outer halo GCs evidence of their accretion origin. This is a direct observation of the importance of accretion to galaxy formation as inferred from the properties of the MW GC system in the seminal work of (1978).., This is a direct observation of the importance of accretion to galaxy formation as inferred from the properties of the MW GC system in the seminal work of \citet{SZ}. " The only direct observations of this process of globular cluster accretion are in the disrupting Sagittarius dwarf (delivering at least five GCs into the MW halo: DaCosta 1995; Martinez-Delgadoetal. 2002; Law&Majewski 2010)), perhaps in the case of the putative Canis Major dwarf (Martinetal.2004)and in the globular clusters of M31 associated with tidal stellar streams in the vicinity of M31 (Mackeyetal. 2010).."," The only direct observations of this process of globular cluster accretion are in the disrupting Sagittarius dwarf (delivering at least five GCs into the MW halo: \citeauthor{DaCostaArmandroff95} \citeyear{DaCostaArmandroff95}; \citeauthor{MartinezDelgado02} \citeyear{MartinezDelgado02}; \citeauthor{Law10} \citeyear{Law10}) ), perhaps in the case of the putative Canis Major dwarf \citep{Martin04} and in the globular clusters of M31 associated with tidal stellar streams in the vicinity of M31 \citep{Mackey10}. ." "The statistics of catastrophic events in ecoplivsics (e.e.. earthquakes. laudslides. forest fires) as well as in astroplivsics (οιο,,BS. auroral substoris. solar and stellar flares. pulsar elitches) is ecuerally quautified iu a Ίος” versus loe-size histogram. which often exhibits a powerlaw-like fuuction. also called occurrence frequency distribution.","The statistics of catastrophic events in geophysics (e.g., earthquakes, landslides, forest fires) as well as in astrophysics (e.g., auroral substorms, solar and stellar flares, pulsar glitches) is generally quantified in a log-number versus log-size histogram, which often exhibits a powerlaw-like function, also called occurrence frequency distribution." The most widely known example is the distrjbutiou of earthquakes. maeuitucles. which has a powerlaw slope of a~2.0 for the differeutial frequeney distribution (Turcotte 1999). the Cartenbere-Richter (1951) law.," The most widely known example is the distribution of earthquakes magnitudes, which has a powerlaw slope of $\alpha \approx 2.0$ for the differential frequency distribution (Turcotte 1999), the so-called Gutenberg-Richter (1954) law." " Bak. Taug. aud Wieseufeld (1987. 1988) introduced the theoretical concept of sclborganized criticality (SOC). which has been initially applied to sandpile avalanches at a critical augle of repose. but has been generalized to nonlinear dissipative svstenis that are driven iu a critical state,"," Bak, Tang, and Wiesenfeld (1987, 1988) introduced the theoretical concept of self-organized criticality (SOC), which has been initially applied to sandpile avalanches at a critical angle of repose, but has been generalized to nonlinear dissipative systems that are driven in a critical state." Comprehecusive reviews on this subject cau be found for applications in ecoplivsics (Turcotte 1999). solar physics (Charbounean ct al.," Comprehensive reviews on this subject can be found for applications in geophysics (Turcotte 1999), solar physics (Charbonneau et al." 2001). and astrophysics (Asclwwande1 2010).," 2001), and astrophysics (Aschwanden 2010)." Talhnarks of SOC systems are the scale-free powerlaw distributious of various event parameters. such as the peak cnerev dissipation rate P. the total euergv E. or the tine duration Z of events;," Hallmarks of SOC systems are the scale-free powerlaw distributions of various event parameters, such as the peak energy dissipation rate $P$ the total energy $E$ , or the time duration $T$ of events." While the powerlaw shape of the distribution function can be explained by the statistics of nonlinear processes that have an exponential C»erowth pliase auc saturate after a rancdon time terval (c.e..Oo Willis aud Yule 1922: Fermi 1919: Rosuer aud Vaiana 1978: Asclavaucden et al.," While the powerlaw shape of the distribution function can be explained by the statistics of nonlinear processes that have an exponential growth phase and saturate after a random time interval (e.g., Willis and Yule 1922; Fermi 1949; Rosner and Vaiana 1978; Aschwanden et al." 1998). uo general ticoretical iiodel has Όσοι developed that predicts the numerical value of the powerlaw slope of SOC paraujeter distributions.," 1998), no general theoretical model has been developed that predicts the numerical value of the powerlaw slope of SOC parameter distributions." Simple aualvtical models that characterize the nouliuear erowth phase with au exponeuial erowth time 7e; and the random distribution of risctimes with an average value of £4. predict a powerlaw slope of ap=1{ἐςήτοι for the peak. dissipation rate (e.g... Rosner and Vaiana 1978: Asclavanden ct al.," Simple analytical models that characterize the nonlinear growth phase with an exponential growth time $\tau_G$ and the random distribution of risetimes with an average value of $t_S$, predict a powerlaw slope of $\alpha_P = 1 + t_S/\tau_G$ for the peak dissipation rate (e.g., Rosner and Vaiana 1978; Aschwanden et al." 1998).butobservations of the time scales," 1998),butobservations of the time scales" "The dwarf satellite galaxies of the Milky Way are the most ""ark matter dominated systems known to date in the Universe.",The dwarf satellite galaxies of the Milky Way are the most dark matter dominated systems known to date in the Universe. They represent a heterogeneous population in terms of their stellar properties such as luminosity. star formation and chemical enrichment histories (222)..," They represent a heterogeneous population in terms of their stellar properties such as luminosity, star formation and chemical enrichment histories \citep{mateo,dolphin,martin}." Yet. the mass enclosed within a radius of 300 tor 600) pe appears to be roughly constant (222)...," Yet, the mass enclosed within a radius of 300 (or 600) pc appears to be roughly constant \citep{gilmore07,strigari07,strigari08}." This could imply a minimum mass seale for the existence of dwarf spheroidal galaxies. as originally suggested by ?..," This could imply a minimum mass scale for the existence of dwarf spheroidal galaxies, as originally suggested by \citet{mateo}." It is currently unclear whether this is due to the mierophysies of the dark matter particles. or to astrophysical processes that inhibit star formation on small scales.," It is currently unclear whether this is due to the microphysics of the dark matter particles, or to astrophysical processes that inhibit star formation on small scales." " For Weakly Interacting Massive Particles (WIMPs). collisional damping and free streaming are expected to cut off the power spectrum at masses of ~10""M. (e.g.2) or smaller."," For Weakly Interacting Massive Particles (WIMPs), collisional damping and free streaming are expected to cut off the power spectrum at masses of $\sim 10^{-6} \sm$ \citep[e.g.][]{green} or smaller." Then. in models which assume these as dark matter particles wwarm dark matter (WDM). X cold dark matter (CDM)]. a minimum mass scale for dwarf spheroidals can only result as a consequence of astrophysical processes that affect the collapse of baryons and the formation of stars on small galactic scales.," Then, in models which assume these as dark matter particles warm dark matter (WDM), $\Lambda$ cold dark matter (CDM)], a minimum mass scale for dwarf spheroidals can only result as a consequence of astrophysical processes that affect the collapse of baryons and the formation of stars on small galactic scales." For example. 1e presence of a strong photo-ionizing background (possibly associated to the reionization of the Universe) can suppress accretion and cooling in low-mass haloes.," For example, the presence of a strong photo-ionizing background (possibly associated to the reionization of the Universe) can suppress accretion and cooling in low-mass haloes." " This is because the heating of 1e gas Will raise its pressure and therefore may suppress its colla»se in haloes with virial velocities 30—50kms (e.g.22222,andreferencestherein)..."," This is because the heating of the gas will raise its pressure and therefore may suppress its collapse in haloes with virial velocities $\lesssim 30-50\,{\rm km}{\rm s}^{-1}$ \citep[e.g.][and references therein]{Efstathiou_1992,Quinn_Katz_Efstathiou_1996,Thoul_Weinberg_1996,Gnedin_2000,Okamoto_Gao_Theuns_2008}." This has often been considered as a vossible solution to the excess of small scale structures found in CDM and in particular in /N-body simulations of galaxysize systems (222222).," This has often been considered as a possible solution to the excess of small scale structures found in CDM and in particular in $N$ -body simulations of galaxysize systems \citep{kwg,klypin99,moore99,bullock00,somerville,benson}." In addition. in systems with virial temperature below 107 K gas cannot cool via hydrogen line emission. and must rely on the highly inefficient cooling through collisional excitations of L1» molecules (22).," In addition, in systems with virial temperature below $10^4$ K gas cannot cool via hydrogen line emission, and must rely on the highly inefficient cooling through collisional excitations of $\mathrm{H}_2$ molecules \citep{haiman,kravtsov2004}." In this Letter we discuss the existence of a common mass scale for Milky Way satellites using results from high resolution /V- simulations of galaxy-size haloes coupled with semi-analytic techniques to model the evolution of the baryonic component of galaxies., In this Letter we discuss the existence of a common mass scale for Milky Way satellites using results from high resolution $N$ -body simulations of galaxy-size haloes coupled with semi-analytic techniques to model the evolution of the baryonic component of galaxies. This approach allows us to identify the dark matter substructures that host stars and to characterise their stellar properties., This approach allows us to identify the dark matter substructures that host stars and to characterise their stellar properties. At the same time. the high resolution of the simulations used in this study permits a reliable determination of the internal dynamical properties of these satellites.," At the same time, the high resolution of the simulations used in this study permits a reliable determination of the internal dynamical properties of these satellites." As we shall describe below. we find that the dark matter mass within 600 pe for the model satellites shows very little scatter from object to object.," As we shall describe below, we find that the dark matter mass within 600 pc for the model satellites shows very little scatter from object to object." This is in very good agreement with the observational results by 22..," This is in very good agreement with the observational results by \citet{strigari07,strigari08}." Interestingly. our model also reproduces the very wide range of luminosities observed for the satellite galaxies around the Milky Way.," Interestingly, our model also reproduces the very wide range of luminosities observed for the satellite galaxies around the Milky Way." " In this study. we use a high-resolution resimulation of a ""Milky Way” halo from the GÀ series described in ? and ?.."," In this study, we use a high-resolution resimulation of a `Milky Way' halo from the GA series described in \citet{Stoehr_etal_2002} and \citet{Stoehr_etal_2003}." The candidate “Milky Way? halo was selected as a relatively isolated halo with a quiet. merging history (last major merger at 2c 2) and with maximum rotational velocity close to 220 +., The candidate `Milky Way' halo was selected as a relatively isolated halo with a `quiet' merging history (last major merger at $z > 2$ ) and with maximum rotational velocity close to $\sim 220$ . . The halo. selected from an intermediate resolution cosmological simulation. was then re-simulated at four progressively higher resolutions using," The halo, selected from an intermediate resolution cosmological simulation, was then re-simulated at four progressively higher resolutions using" he loop cross-section area. which is a free parameter in he model.,"the loop cross-section area, which is a free parameter in the model." The loop 1uodel spectra are fitted with single cluperature (1-T) τος. spectra (the same as those used to. svuthesize them)., The loop model spectra are fitted with single temperature (1-T) model spectra (the same as those used to synthesize them). " The fitting provides a vest-tit ""average temperature Ty;. aud an analytical ionnalization factor. which. multiplied by the loop cross-section area. vields the emissiou measure."," The fitting provides a best-fit “average” temperature $T_{fit}$, and an analytical normalization factor, which, multiplied by the loop cross-section area, yields the emission measure." The 1-T fitting is performed in the 0.8-10 keV sub-baud., The 1-T fitting is performed in the 0.8-10 keV sub-band. This allows us ο compare Ty; to the teuperature of the hot component of the multi-ttempcrature fitting of the data. at least for Τε&10 ME.," This allows us to compare $T_{fit}$ to the temperature of the hot component of the multi-temperature fitting of the data, at least for $T_{fit} \ga 10$ MK." Whenever fitting the observation data requires the combination of two model loops. we svuthesize the otal Cluission at a given time by sununuiug the two focal plane spectra oue for each loop. with the appropriate cross-section area at that time.," Whenever fitting the observation data requires the combination of two model loops, we synthesize the total emission at a given time by summing the two focal plane spectra – one for each loop, with the appropriate cross-section area – at that time." We then analyze the resulting sequence of spectra. one for cach time. as we clo for single loop spectra: we derive the light curve aud fit the spectra with single tempecratiure models.," We then analyze the resulting sequence of spectra, one for each time, as we do for single loop spectra: we derive the light curve and fit the spectra with single temperature models." The modeling of this flare will be described following the flare evolution., The modeling of this flare will be described following the flare evolution. It will frst address the dare peak. ioc. phases Rl aud Di in Fie. l..," It will first address the flare peak, i.e. phases R1 and D1 in Fig. \ref{fig:datlc}," then the first decay (D2). aud fnally the second. peak and the late decay (R2. D3 and DI).," then the first decay (D2), and finally the second peak and the late decay (R2, D3 and D4)." We model the initial aud most intense phase of the fare with a sinele flaring loop: we will call itA., We model the initial and most intense phase of the flare with a single flaring loop; we will call it. The modeling requires. first of all. that we set the loop eugth.," The modeling requires, first of all, that we set the loop length." As mentioned in Section 2.. the empirical scaling aws applied to phase DI provide an upper limit Ly)...=1.6«10/9 cm.," As mentioned in Section \ref{sec:obs}, the empirical scaling laws applied to phase D1 provide an upper limit $L_{max} = 1.6 \times 10^{10}$ cm." In the lack of a well-defined path in the LT diagraia. aud therefore of reliable information about he heating decay. any leugth shorter than this may be appropriate.," In the lack of a well-defined path in the n-T diagram, and therefore of reliable information about the heating decay, any length shorter than this may be appropriate." We will show here results for three oop half-leugtlis. vauncly the upper luit £=1.6«1019 cu. au intermediate value £=1.0.1010 cin and the hal£length obtained for he flare (0.7<1029 cm. Reale et al.," We will show here results for three loop half-lengths, namely the upper limit $L = 1.6 \times 10^{10}$ cm, an intermediate value $L = 1.0 \times 10^{10}$ cm and the half-length obtained for the flare $0.7 \times 10^{10}$ cm, Reale et al." 1988)., 1988). The initial base pressures are py=3 dyne 7 for the first wo. and py=1.3. dvue * Dffor the last leneth value.," The initial base pressures are $p_0 = 3$ dyne $^{-2}$ for the first two, and $p_0 = 4.3$ dyne $^{-2}$ for the last length value." The flare peak is driven by a strong heat pulse., The flare peak is driven by a strong heat pulse. The time dependence of the heat pulse is described in Section 3.1.., The time dependence of the heat pulse is described in Section \ref{sec:setup}. The data indicate a very rapid increase of the temperature and therefore an nupulsive heating., The data indicate a very rapid increase of the temperature and therefore an impulsive heating. Typically in flares (and in thei simulations as well) the cussion nieasure still increases well after the heating has been turned off (c.g. Svestka 1976)., Typically in flares (and in their simulations as well) the emission measure still increases well after the heating has been turned off (e.g. Svestka 1976). The temperature is a better tracer of the heating duration. because the efficicut thermal conduction makes it promptly decrease as the heating decreases.," The temperature is a better tracer of the heating duration, because the efficient thermal conduction makes it promptly decrease as the heating decreases." Fie., Fig. 2. aud the time evolution of the harcluess ratio (Fie. 1)), \ref{fig:datnt} and the time evolution of the hardness ratio (Fig. \ref{fig:datlc}) ) sugeest a duration of the order of 500 s: the choice of a pulse duration οί=600 s is good for all our simulations of this flare phase., suggest a duration of the order of 500 s; the choice of a pulse duration $\delta t_H = 600$ s is good for all our simulations of this flare phase. A hint for the pulse lutensity comes from the flar maxinmui temperature., A hint for the pulse intensity comes from the flare maximum temperature. I is reached after a few secouds and then remains steady as long as the heating is constant. because hermal couduction rapidly balances the heating.," It is reached after a few seconds and then remains steady as long as the heating is constant, because thermal conduction rapidly balances the heating." By applying the loop scaling laws (Rosner et al., By applying the loop scaling laws (Rosner et al. " 1978) wit[um logT=7.6 (Section 2)). we obtain that. if the heating were distributed uniformly iu a loop of lalfleneth 101"" cni. its dutensity would be of the order of: For this phase of the flare. we have considered two alternative spatial distributions of the heat pulse along the loop: i) just above the footpoiuts (sg0.11, aud σ—0.035): 3) centered at the apex (sy=L aud a=0.35)."," 1978) with $\log T = 7.6$ (Section \ref{sec:obs}) ), we obtain that, if the heating were distributed uniformly in a loop of half-length $10^{10}$ cm, its intensity would be of the order of: For this phase of the flare, we have considered two alternative spatial distributions of the heat pulse along the loop: i) just above the footpoints $s_0 = 0.1 L$ and $\sigma = 0.03 L$ ); ii) centered at the apex $s_0 = L$ and $\sigma = 0.3 L$ )." The width of the heating distribution iufiueuces the simulation results little., The width of the heating distribution influences the simulation results little. We will not report on the whole exploration of the space of the model parameters that we performed. but ouly ou sole cases providing representative results;," We will not report on the whole exploration of the space of the model parameters that we performed, but only on some cases providing representative results." We will discuss results for the three loop leneths listed iu Section 1.1.1.., We will discuss results for the three loop lengths listed in Section \ref{sec:llen}. " For the intermediate loop length (£=1010 cni). we show results for two cases. ie. a leat pulse concentrated at the loop footpoiuts with a maxima intensity of Ty=60 ere cm? Ἡ, and a heating deposited at the loop apex with a mnaxiuun intensity Il,=1 cg s 1."," For the intermediate loop length $L=10^{10}$ cm), we show results for two cases, i.e. a heat pulse concentrated at the loop footpoints with a maximum intensity of $H_0 = 60$ erg $^{-3}$ $^{-1}$, and a heating deposited at the loop apex with a maximum intensity $H_0 = 12$ erg $^{-3}$ $^{-1}$." For the smallest length. we show results for a heat pulse concentrated at the loop footpoiuts with a maxinunun intensity of Hy=85 erg ὃς +.," For the smallest length, we show results for a heat pulse concentrated at the loop footpoints with a maximum intensity of $H_0 = 85$ erg $^{-3}$ $^{-1}$." " For the longest loop. we show results for a heat pulse at the loop apex with a maxima intensity of Z7=10 erg i)> st,"," For the longest loop, we show results for a heat pulse at the loop apex with a maximum intensity of $H_0 = 10$ erg $^{-3}$ $^{-1}$." The evolution of the flaring plasma confined in a loop is well-known from extensive previous modeling studies (e.g. Peres ct al., The evolution of the flaring plasma confined in a loop is well-known from extensive previous modeling studies (e.g. Peres et al. 1982)., 1982). The eloba characteristics of the evolution do not depend ou he details of the heating (see also Section 5.53): the lea o»ilse makes the temperature Increase up to several tens MES. along the whole loop ina few seconds. due o the Heh plasma thermal conduction: the deuse chromosphere a he loop footpoiuts is heated violeutlv. aud expauds upwards with a strong evaporation frout.," The global characteristics of the evolution do not depend on the details of the heating (see also Section \ref{sec:evol}) ): the heat pulse makes the temperature increase up to several tens MK along the whole loop in a few seconds, due to the high plasma thermal conduction; the dense chromosphere at the loop footpoints is heated violently, and expands upwards with a strong evaporation front." The upcoming plasma fillsup the loop. very dvuamically frst and then more graduallv. approaching anew hydrostatic equilibrium at a much lieher pressure.," The upcoming plasma fillsup the loop, very dynamically first and then more gradually, approaching a new hydrostatic equilibrium at a much higher pressure." The loop A-rav emission mereases mostlv following the increase of cinission iueasure., The loop X-ray emission increases mostly following the increase of emission measure. As the heating stops (or, As the heating stops (or For u223. we obtain a fractal dimension of 2. which is precisely the value suggested by observations (Pictronero et al.,"For n=3, we obtain a fractal dimension of 2, which is precisely the value suggested by observations (Pietronero et al.," 1996: Svlos Labiui et ab.," 1996; Sylos Labini et al.," 1998) but values given in the above list are all compatible with our network., 1998) but values given in the above list are all compatible with our network. Lindner et al (1996) considered the range over which filamentary structures exist. from the observational point of view.," Lindner et al (1996) considered the range over which filamentary structures exist, from the observational point of view." Following the magnetic interpretation assumed here. the lower limit corresponds to the smaller scale below which primordial magnetic fields were destroved iu the radiation-doniunuated era bv cifferent mechamisis. mainly Silk damping (Silk. 1968: Jedamzik. Natalinic aud Oliuto. 1996) and magnetic diffusion (Lesch aud Birk. 1998).," Following the magnetic interpretation assumed here, the lower limit corresponds to the smaller scale below which primordial magnetic fields were destroyed in the radiation-dominated era by different mechanisms, mainly Silk damping (Silk, 1968; Jedamzik, Katalinic and Olinto, 1996) and magnetic diffusion (Lesch and Birk, 1998)." Super horizon scale maeuetic fields during this epoch. today of the order of 10. Mpe. were unaffected by. these processes and this horizon scale should be identified with the lower luit. below which the fractal ecometry is lost.," Super horizon scale magnetic fields during this epoch, today of the order of 10 Mpc, were unaffected by these processes and this horizon scale should be identified with the lower limit, below which the fractal geometry is lost." The upper Huit should be ereater than the typical distance of the deepest survevs. about LOO Mpc.," The upper limit should be greater than the typical distance of the deepest surveys, about 100 Mpc." Therefore the distance range is relatively short. 10-100 Alpe.," Therefore the distance range is relatively short, 10-100 Mpc." Tn the best case with a size ratio equal to 3. there would only be octahedra. sub-octahedra and sub-ub-octaliedra. nothing more.," In the best case with a size ratio equal to 3, there would only be octahedra, sub-octahedra and sub-sub-octahedra, nothing more." Even the lowest size octahedra would probably be unrecoguizable., Even the lowest size octahedra would probably be unrecognizable. We also conclude that ο<2., We also conclude that $n \le 2$. This situation is sinular to that depicted by Linduer et al (1996)., This situation is similar to that depicted by Lindner et al (1996). "distribution of stars with metallicity. in turn. influences the calculation of the average κMg/H7]and ,| shown in table 3.","distribution of stars with metallicity, in turn, influences the calculation of the average $[_{*}]$and $[_{*}]$ shown in table 3." For the ancl models clearly there is very little dillerence in these average values. whereas for and models the average «ος>] varies from |0.507 to. |0.32.," For the and models clearly there is very little difference in these average values, whereas for and models the average $[_{*}]$ varies from +0.507 to +0.32." Therefore. we conclude that the elect. of »op LL pair-creation SNe cannot be detected i£ ellipticals ormed out of initial merging of primordial gas (infall cases).," Therefore, we conclude that the effect of pop III pair-creation SNe cannot be detected if ellipticals formed out of initial merging of primordial gas (infall cases)." The cases and labelled DII and bl labelled BL (no chemical enrichment from stars in the range 40-100A7. in pop LE and the following populations). predict in genera ower «AlgíPFev]. «Mg/H>.) and -- han the corresponding cases where chemical. enrichmen rom those stars is taken into account (see Table 3).," The cases and labelled BH and b1 labelled BH (no chemical enrichment from stars in the range $M_{\odot}$ in pop III and the following populations), predict in general lower $[_{*}]$, $[_{*}]$ and $[_{*}]$ than the corresponding cases where chemical enrichment from those stars is taken into account (see Table 3)." This elfect is not negligible as shown for the Milkv Way by De Donder Vanbeveren (2003)., This effect is not negligible as shown for the Milky Way by De Donder Vanbeveren (2003). However. if we consider this »ossibilitv only. in pop ILE stars. then only negligible effects are produced on the results. and for this reason we did. not show this case.," However, if we consider this possibility only in pop III stars, then only negligible effects are produced on the results, and for this reason we did not show this case." The cases£2. and54. dillering for the pop LLL vields. indicate that the vields of LV02 and UN are similar. whereas the old. vields hy OFLS3 produce quite dilferent results especially in the predicted κοο7] which raises up to 4.66 as opposed to ~0.3 in the other two cases.," The cases, and, differing for the pop III yields, indicate that the yields of HW02 and UN are similar, whereas the old yields by OFE83 produce quite different results especially in the predicted $[_{*}]$ which raises up to 4.66 as opposed to $\sim 0.3$ in the other two cases." This is due to the fact that the vields of OFLES3 do not contain Fe-peak elements for pair-creation SNe whereas the other vields do., This is due to the fact that the yields of OFE83 do not contain Fe-peak elements for pair-creation SNe whereas the other yields do. Clearly this case should. be ciscarded because it is at odd. with observations which indicate a xMgfPFe7] ~0.2-0.3 (e.g. Thomas ct al., Clearly this case should be discarded because it is at odd with observations which indicate a $[_{*}]$ $\sim$ 0.2-0.3 (e.g. Thomas et al. 2002: PALOL) in ellipticals., 2002; PM04) in ellipticals. The strongly. bimodal cases and eS). where the first stellar generations are made only of pair-creation SNe. show that. if the phase during which only very massive stars form. is quite short (<105 vears). nothing changes relative to the standard case.," The strongly bimodal cases and ), where the first stellar generations are made only of pair-creation SNe, show that, if the phase during which only very massive stars form, is quite short $< 10^{7}$ years), nothing changes relative to the standard case." H£ instead. the duration of the massive stars phase is as long as 0.1 Car. then we obtain a too high metallicity for the next stellar generations (see «ΑΗ and «FeíH4] in model e3)). with the consequence of obtaining too high metallicity indices and too red integrated colors.," If instead, the duration of the massive stars phase is as long as 0.1 Gyr, then we obtain a too high metallicity for the next stellar generations (see $[_{*}]$ and $[_{*}]$ in model ), with the consequence of obtaining too high metallicity indices and too red integrated colors." We tried to adjust the star formation and infall parameters but. could. not. fine any. acceptable solution., We tried to adjust the star formation and infall parameters but could not find any acceptable solution. Therefore. such a case should. be discarded.," Therefore, such a case should be discarded." The zilure of bimodal star formation in elliptical galaxies had already been: discussed. by Gibson. (1996)., The failure of bimodal star formation in elliptical galaxies had already been discussed by Gibson (1996). In. particular. rw showed that this assumption leads to a metallicity -uminosity relation at variance with observations.," In particular, he showed that this assumption leads to a metallicity -luminosity relation at variance with observations." It is worth noting that in the case we adopted a blast wave energy .or pair-creation. SNeTU of⋅ 5-107752 erg per SN.ane whereas in. all he other cases we assumed the canonical value of 1075 org.," It is worth noting that in the case we adopted a blast wave energy for pair-creation SNe of $5 \cdot 10^{52}$ erg per SN, whereas in all the other cases we assumed the canonical value of $10^{51}$ erg." In this case a very carly (/~2-10° vears) galactic wind develops due to the energy. injected. by pair-creation SNe. and it does not destroy the galaxy. provided. that only a small fraction of gas is lost. then star formation starts again with a normal AIF when the gas has cooled down (at ~0.1 Gyr).," In this case a very early $t \sim 2 \cdot 10^{6}$ years) galactic wind develops due to the energy injected by pair-creation SNe, and it does not destroy the galaxy provided that only a small fraction of gas is lost, then star formation starts again with a normal IMF when the gas has cooled down (at $\sim 0.1$ Gyr)." After this point. the evolution is the same as in the standard case with galacic winds produced by normal type Il and la SNe.," After this point, the evolution is the same as in the standard case with galactic winds produced by normal type II and Ia SNe." Clearly. this is a rather arbitrary situation since there is the possibiity of destroving the whole object but we mace these assuniptions only for the sake of testing the chemical effects of a generation of very massive stars.," Clearly, this is a rather arbitrary situation since there is the possibility of destroying the whole object but we made these assumptions only for the sake of testing the chemical effects of a generation of very massive stars." Always in case e4.. [rom he point of view of the enrichment of the intracluster medium (ICM). it is worth noting that," Always in case , from the point of view of the enrichment of the intracluster medium (ICM), it is worth noting that" where Typ~1000οcu? is the moment of imertia of the white dwarf.,"If $B_p=10^9$ G, the expected spin down rate is where $I_{\rm WD} \sim 10^{50} ~{\rm g~cm^2}$ is the moment of inertia of the white dwarf." Even with long term monitoring. such a sinall spindown rate is difficult to measure.," Even with long term monitoring, such a small spindown rate is difficult to measure." The apparent optical/IR maeuitude of a white dwarf a a distauce of 8.5 kpe dis (27-30)., The apparent optical/IR magnitude of a white dwarf at a distance of 8.5 kpc is $\sim$ (27-30). Extinction would further suppress the optical flux., Extinction would further suppress the optical flux. Deep IR. exposure with large telescopes παν lead to the discovery of the couuterpar of GCRT J1715-3009. especially if the source is at a closer distance than that of the Galactic ceuter.," Deep IR exposure with large telescopes may lead to the discovery of the counterpart of GCRT J1745-3009, especially if the source is at a closer distance than that of the Galactic center." Line features. if detected. would eive a direct measuremoeut of the maguetic field streugth through Zeeiiau spectroscopy to test the hypothesis (Wickramasinghe Ferrario 2000).," Line features, if detected, would give a direct measurement of the magnetic field strength through Zeeman spectroscopy to test the hypothesis (Wickramasinghe Ferrario 2000)." We have shown that the cuigiatic trausicut radio source GCRT JLF15-3009 could be uuderstood within the hypothesis that it is a white dwarf pulsar., We have shown that the enigmatic transient radio source GCRT J1745-3009 could be understood within the hypothesis that it is a white dwarf pulsar. If this liypothesis is correct. the detection of this powerful bursting radio source therefore suggests the discovery of such a new type of pulsating. occasionally radio-loud. strongly magnetized white dwarts.," If this hypothesis is correct, the detection of this powerful bursting radio source therefore suggests the discovery of such a new type of pulsating, occasionally radio-loud, strongly magnetized white dwarfs." " The study of this object and future more objects Gf discovered) would also shed light on the poorly understood coherent radio ocnüssioun imechanis (οιο, Melrose 2001 for a review) of their brethren. neutron star pulsars."," The study of this object and future more objects (if discovered) would also shed light on the poorly understood coherent radio emission mechanism (e.g. Melrose 2004 for a review) of their brethren, neutron star pulsars." Detecting such a transient white dwarf pulsar also sugeests that some “dead” neutron star pulsars not deep below the death line may become active again occasionally if strong suuspot-like maguetic fields cimerge into their polar cap regions., Detecting such a transient white dwarf pulsar also suggests that some “dead” neutron star pulsars not deep below the death line may become active again occasionally if strong sunspot-like magnetic fields emerge into their polar cap regions. These trausient radio pulsars are awaiting being discovered., These transient radio pulsars are awaiting being discovered. We thank S. BR. Ikulkarni for drawing our attention to this new phenomenon. D. Lai aud J. Dvks for helpful cliscussion. and au anonvimous referee for helpful commucuts during the reviews.," We thank S. R. Kulkarni for drawing our attention to this new phenomenon, D. Lai and J. Dyks for helpful discussion, and an anonymous referee for helpful comments during the reviews." This work is supported by NASA NNGOLGD5SLC (BZ and JG) aud bv eraut 1 POS3D 029 26 of the Polish State Committee for Scientific Research (JC)., This work is supported by NASA NNG04GD51G (BZ and JG) and by grant 1 P03D 029 26 of the Polish State Committee for Scientific Research (JG). grain temperature. which can be used to indicate the intensity of the ambient stellar radiation. at least two bands are needed at wavelengths =90tum.,"grain temperature, which can be used to indicate the intensity of the ambient stellar radiation, at least two bands are needed at wavelengths $\ga 90~\micron$." Furthermore. we require in the FIR to a FIR colour-ecolourdiagram.," Furthermore, we require in the FIR to a FIR colour–colour." charaacteristies., acteristics. bendolO with (Pilbrattetal.2010)... whose long-wavelength coverage is particularly. useful to examine the robustness of our analysis against the inclusion of long-wavelength data.," with \citep{pilbratt10}, whose long-wavelength coverage is particularly useful to examine the robustness of our analysis against the inclusion of long-wavelength data." In this paper. we aim of FIR mapping data by deriving some fundamental quantities about dust (dust temperature. dust optical depth. ete.).," In this paper, we aim of FIR mapping data by deriving some fundamental quantities about dust (dust temperature, dust optical depth, etc.)." At the same time. we try to clarify the relation between global (tintegrated) quantities and spatially resolved quantities.," At the same time, we try to clarify the relation between global (integrated) quantities and spatially resolved quantities." Some important features in the FIR colourcolour diagram of a spatially resolved image is also focused on., Some important features in the FIR colour–colour diagram of a spatially resolved image is also focused on. The method used in this paper is general and can be applied to future data taken by or the Atacama Large Millimetre/submillimetre |Array This1 paper is organized as follows., The method used in this paper is general and can be applied to future data taken by or the Atacama Large Millimetre/submillimetre Array This paper is organized as follows. We explain the data analysis in Section ??.. and describe some basic results related to global properties such as morphology and radialdependence in Section ??..," We explain the data analysis in Section \ref{sec:data}, and describe some basic results related to global properties such as morphology and radialdependence in Section \ref{sec:result}." We investigate the distribution of dust temperatures and the colour-colour diagram in Section 22.., We investigate the distribution of dust temperatures and the colour–colour diagram in Section \ref{sec:temperature}. We discuss the results obtained for MS881 in general contexts in Section ??.., We discuss the results obtained for 81 in general contexts in Section \ref{sec:discussion}. Finally. Section 2? gives the conclusion.," Finally, Section \ref{sec:conclusion} gives the conclusion." The distance to 881 is assumed to be MMpe (Freedmanetal.1994). throughout this paper., The distance to 81 is assumed to be Mpc \citep{freedman94} throughout this paper. At this distance. aaremin corresponds to kkpe.," At this distance, arcmin corresponds to kpc." 881 was observed by AKAR///FIS as a pointed observation (PI: FIS Team)., 81 was observed by /FIS as a pointed observation (PI: FIS Team). The data are taken from Data Archives and Transmission Photometric observations were performed with four bands: NO6O60 (central wavelength: pum). Lum). jum). and NT160(160 pum) with an observational mode of FISOL tphotometrv/mapping mode). a reset interval of ss and a scan speed of 15 arcsec s+.," The data are taken from Data Archives and Transmission Photometric observations were performed with four bands: 60 (central wavelength: $\micron$ ), $\micron$ ), $\micron$ ), and 160 $\micron$ ) with an observational mode of FIS01 (photometry/mapping mode), a reset interval of s and a scan speed of 15 arcsec $^{-1}$ ." We utilize the images of the 65 ium. 90 Lum. and 140 pum bands.," We utilize the images of the 65 $\micron$, 90 $\micron$, and 140 $\micron$ bands." The quality of the 160 jum band image is not good enough for our purpose., The quality of the 160 $\micron$ band image is not good enough for our purpose. The FIS observation of 881 is composed of two pointings: one covers almost all the 881 area except for the south-east edge. which is observed by the second observation.," The FIS observation of 81 is composed of two pointings: one covers almost all the 81 area except for the south-east edge, which is observed by the second observation." We combine those two images to obtain the entire M881 image after the background subtraction (Section 2.39). and the analysis procedures before combining the images are identical for the two images.," We combine those two images to obtain the entire 81 image after the background subtraction (Section \ref{subsec:bak}) ), and the analysis procedures before combining the images are identical for the two images." " The measured FWHMs of point spread function are 377. 39"", and 5s"" (Kawadaetal.2007)... which correspond to 650 pe. 690 pe. and 1000 pe. respectively. at M881."," The measured FWHMs of point spread function are $37''$, $39''$, and $58''$ \citep{kawada07}, which correspond to 650 pc, 690 pc, and 1000 pc, respectively, at 81." Thus. internal structures such as spiral arms can be clearly identified on the images (Section 22).," Thus, internal structures such as spiral arms can be clearly identified on the images (Section \ref{subsec:morphology}) )." The raw data were reduced by using the FIS Slow-Scan Tool (version 20070914: Verdugo.Yamamura.&Pearson2007)). The process includes flagging of bad data. measurement of sky signal. dark and. response correction. flat-fielding. and construction of co-added images.," The raw data were reduced by using the FIS Slow-Scan Tool (version 20070914; \citealt*{verdugo07}) The process includes flagging of bad data, measurement of sky signal, dark and response correction, flat-fielding, and construction of co-added images." We used the local-flat for the flat-fielding., We used the local-flat for the flat-fielding. The output image grid size is chosen to be 307. which is about half of the beam size of 140 jum.," The output image grid size is chosen to be 30”, which is about half of the beam size of 140 $\micron$." M econf irmedthatthefollowingresullsarenolsensilivelolhesclectionoft , We confirmed that the following results are not sensitive to the selection of the grid size. It is Known that the AKARI//FIS detectors underestimate the total flux probably because of the slow response (Shirahataetal.2008)., It is known that the /FIS detectors underestimate the total flux probably because of the slow response \citep{shirahata08}. Thus. we multiply the correction factors for the intensity. 1.7 for pumend90 pum. and 1.9. for pum. ecemultipliedlocachband.," Thus, we multiply the correction factors for the intensity, 1.7 for $\micron$ and $\micron$, and 1.9 for $\micron$, are multiplied to each band." Decauscthefactorsacresimilartoalllheban ," Because the factors are similar to all the bands, the colours (flux ratios) and dust temperatures are not significantly affected by this correction." "Since the intensity at the central wavelength is derived by assuminga flat spectrum (7/,,= constant) in the ΕΙΡ Slow-Sean Tool. colour correction should be applied."," Since the intensity at the central wavelength is derived by assuminga flat spectrum $\nu I_\nu =\mbox{constant}$ ) in the FIS Slow-Scan Tool, colour correction should be applied." We applied correction to the, We applied correction to the covariance requirements imposed on thediscrete relationsbetween (hegenerators,The subspaces ${\bf{\cal{A}}}_0 $ and ${\bf{\bar{\cal{A}}}}_0$ form zero-graded subalgebras. ofthe algebra. 2. Al present. based on thequark model. despite the factthat isolated quarks cannot be , These algebras can be made if we add to each of them the unit element $\bf{1}$ acting as identity and considered as being of grade $0$. observed. The onlyexperimentally accessible states areeither (hree-quark or (hree-anti-quark combinations (fermions) or (hequark-anti-quark states (bosons). Whenever onehas todo wilh a," If we want the products between the generators $\theta^A$ and the conjugate ones ${\bar{\theta}}^{\dot{B}}$ to be included into the greater algebra spanned by both types of generators, we should consider all possible products, which will be included in the linear subspaces with a definite grade." trilinear combinat, of the resulting algebra ${\cal{A}} \otimes {\bar{\cal{A}}}$. ion of fields (or operators). onemustinvestigate the behavior of such states underpermutations. Letus introduce NV generators spanning alinear space overcomplex numbers. satisIving following relations," In order to decide which expressions are linearly dependent, and what is the overall dimension of the enlarged algebra generated by $\theta^A$ 's and their conjugate variables ${\bar{\theta}}^{\dot{D}}$ 's, we must impose on them some binary commutation relations." whichare acubic generalization of anti-commnutation inthe ususal, The fact that the conjugate generators are of grade $2$ maysuggest that they behave like products of two ordinary generators $\theta^A \theta^B$. (binary)case (see e.g.[0].. |0])): OOFAS= jg?gCg*," Such a choice was often made (see, e.g., \cite{Kerner3}, \cite{Kerner5} and \cite{VARKBLR}) )." " =porgio"", (1) theprimitive cubic root of1. Wehave j Fand 14j P0. We withshall jalso e'™%.in"," However, this does not enable one to make a distinction between the conjugate generators and the products of two ordinary ones, and it would be better to be able to make the difference." "troduce similar of conjugale ""nS- p ggc gà-j 0Cp98. (2) A. evading.Letus consideringdenote this algebraby We shall gradeendow elements. this algebraand withanatural"," Due to the binary nature of “mixed"" products, another choice is possible, namely, to impose the following relations: In what follows, we shall deal with the first two simplest realizations of such algebras, spanned by two or three generators." Z4(! being grade ," Consider the case when $A, B,.. = 1,2$." Thethegrades generators modulo@!as 1that theproducts their 01109conjugates linear subspaceof2. grade2. andthe cubicaddproductsup 0-9P3.so0C of grade0.Similarly.," The algebra contains numbers, two generators of grade $1$ , $\theta^1$ and $\theta^2$, their four independent products (of grade $2$ ), and two independent cubic expressions, $\theta^1 \theta^2 \theta^1$ and $\theta^2 \theta^1 \theta^2$ ." " spanallquadratic a expressions generators. ofaye productsin conjugateagainof grade0. 9-30liketheare cubic gradeproducts24-2 od4,7;4's,"," Similar expressions can be produced with conjugate generators ${\bar{\theta}}^{\dot{C}}$; finally, mixed expressions appear, like four independent grade $0$ terms $\theta^1 {\bar{\theta}}^{\dot{1}}$ , $\theta^1 {\bar{\theta}}^{\dot{2}}$ , $\theta^2 {\bar{\theta}}^{\dot{1}}$ and $\theta^2 {\bar{\theta}}^{\dot{2}}$." Ll., 4. whereas their cubic Combinedare associativity., Let us consider multilinear forms defined on the algebra ${\cal{A}} \otimes {\bar{\cal{A}}}$. these cubic relations imposefinite dimension the generatedwithChe Z4 As matterof Lact.eubic expressions on the algebra thatbythedoes not graded gener," Because only cubic relations are imposed on products in ${\cal{A}}$ and in $\bar{\cal{A}}$, and the binary relations on the products of ordinary and conjugate elements, we shall fix our attention on tri-linear and bi-linear forms, conceived as mappings of ${\cal{A}} \otimes {\bar{\cal{A}}}$ into certain linear spaces over complex numbers." ators.identically.a The pro, Let us consider a tri-linear form $\rho^{\alpha}_{ABC}$. ofis immediate: are 0.2cm hiehestorder vanish9-398gCgP j pPgcggP equalto IN 4-N?(Αν N)/3:theN generators of gradeL.the NV? independent products of two generators.," Obviously, as by virtue of the commutation relations \ref{ternary1}) ) it follows that we must have Even in this minimal and discrete case, there are covariant and contravariant indices: the lower and the upper indices display the inverse transformation property." and (NV?— N)/3 independent cubicexpressions. because the cubeof any generatormust be zero.and the remaining.N*—N ternary products aredivided by 3.bv virtueofthe constitutive," If a given cyclic permutation is represented by a multiplication by $j$ for the upper indices, the same permutation performed on the lower indices is represented by multiplication by the inverse, i.e. $j^2$ , so that they compensate each other." relations (1)). The conjugate generators97 spanan algebra A isomorphicwithA. Both algebras splitquite naturallyintosumsof linear subspaces with definite grades: , Similarreasoning leads to the definitionof the conjugateforms$ \rho^{{\dot{\alpha}}}_{{\dot{C}}{\dot{B}}{\dot{A}}}$ satisfying the relations \ref{defrhomatrix3}) ) with $j$ replaced by $j^2$ : rqc——o€ and ry=0.,$x_1=-\infty$ and $x_2=0$. In both cases pp=0 and po=x., In both cases $p_1=0$ and $p_2=\infty$. Eq., Eq. ο is sometimes called thee, \ref{eq:adj} is sometimes called the. "quation, Using these conditions in Eq.", Using these conditions in Eq. 4 we obtain the (wo fundamental expressions: in (he upstream region. and in the downstream region.," \ref{eq:toadjoint} we obtain the two fundamental expressions: in the upstream region, and in the downstream region." In order to keep the notation as simple as possible we inverted all primed ancl unprimed variables. so that Che physical quantities are all expressed. as funelions of unprimed variables.," In order to keep the notation as simple as possible we inverted all primed and unprimed variables, so that the physical quantities are all expressed as functions of unprimed variables." " The indexes ""1 and 72"" refer respectively (0 quantities in the upstream and downstream fluid.", The indexes “1” and “2” refer respectively to quantities in the upstream and downstream fluid. Αρ) is the spectrum of accelerated particles at the shock location., $N_0(p)$ is the spectrum of accelerated particles at the shock location. " Clearly the distribution function of the accelerated particles is continuous across (he shock. namely lim,4,ποp)=πανΧο No(p)."," Clearly the distribution function of the accelerated particles is continuous across the shock, namely $\lim_{x\to 0^{-}}N_{1}(x,p)=\lim_{x\to 0^{+}} N_{2}(x,p) = N_{0}(p)$ ." The lower limit οἱ integration in Eqs., The lower limit of integration in Eqs. 7 ancl 8 is p instead of zero because of the definition of the function G. solution of Eq.," \ref{eq:N1} and \ref{eq:N2} is $p$ instead of zero because of the definition of the function $\cG$, solution of Eq." G (see Appendix)., \ref{eq:adj} (see Appendix). From the physics point of view. it is obvious that it must be so. because the contribution to the spectrum al a eiven momentum p can only come from particles with larger momentum that lose energv through svnchrotron losses.," From the physics point of view, it is obvious that it must be so, because the contribution to the spectrum at a given momentum $p$ can only come from particles with larger momentum that lose energy through synchrotron losses." The functions ορ) are defined as: which only depend on quantiües evaluated al the shock., The functions $\phi_{i}(p)$ are defined as: which only depend on quantities evaluated at the shock. It should be noted that Eqs., It should be noted that Eqs. 7 anc 8. deline the spectrum at anv location upstream ancl downstream in terms of No(p) and ó once the functions 64 aud Gs are known., \ref{eq:N1} and \ref{eq:N2} define the spectrum at any location upstream and downstream in terms of $N_0(p)$ and $\phi$ once the functions $\cG_1$ and $\cG_2$ are known. The solution al the shock. NoCGp). must be derived by using the boundary condition at the shock location.," The solution at the shock, $N_0(p)$, must be derived by using the boundary condition at the shock location." On the other hand. the Green function of the adjoint equation. G. is easily calculated. (see Appendix) to be: llere we introduced 2=1/p and the function 7. which is defined as follows: The main difference between (he approach described here and (he approach of Biermann(1984) is in the fact that our approach (previously mastered by Webb for diffusion coefficient independent of momentun) allows one to write the distribution function A(r./) as an integralon momentum of the distribution function at the," On the other hand, the Green function of the adjoint equation, $\cG$, is easily calculated (see Appendix) to be: Here we introduced $z=1/p$ and the function $\tau$, which is defined as follows: The main difference between the approach described here and the approach of \cite{webb} is in the fact that our approach (previously mastered by \cite{webbfritz} for diffusion coefficient independent of momentum) allows one to write the distribution function $N(x,t)$ as an integralon momentum of the distribution function at the" We have used the square/rectangular boxes covering the selected features for the study.,We have used the square/rectangular boxes covering the selected features for the study. Then we have summed up all the pixel intensity values covered by the box and extracted the cumulative intensity of a chosen feature for the entire 6-hours duration of observations., Then we have summed up all the pixel intensity values covered by the box and extracted the cumulative intensity of a chosen feature for the entire 6-hours duration of observations. The light curves of all the UVBPs. UVNWs. and UVBGs have been derived and plotted them as a function of time.," The light curves of all the UVBPs, UVNWs, and UVBGs have been derived and plotted them as a function of time." We have done a power spectrum analysis on the time series data to determine the period of intensity oscillations associated with these features., We have done a power spectrum analysis on the time series data to determine the period of intensity oscillations associated with these features. There was an indication of the existence of longer-period of oscillations in chromospheric bright points and network elements from Call H-line observations., There was an indication of the existence of longer-period of oscillations in chromospheric bright points and network elements from CaII H-line observations. Since it was only a duration of time sequence of observations. 1t was difficult to investigate on the longer period of oscillations (Kariyappa. et al.," Since it was only a 35-minute duration of time sequence of observations, it was difficult to investigate on the longer period of oscillations (Kariyappa, et al." 2006)., 2006). In order to confirm on the existence of longer period of oscillations. in this paper. we have analyzed a long time sequence of uv images (6 hours of observations) obtained on May 24. 2003 with TRACE in 1600 A UV continuum.," In order to confirm on the existence of longer period of oscillations, in this paper, we have analyzed a long time sequence of uv images (6 hours of observations) obtained on May 24, 2003 with TRACE in 1600 $\AA$ UV continuum." We identified and chosen 15 uv bright points (UVBPs). 15 uv network elements (UVNWs). and 15 uv background regions (UVBGs) from the time sequence of uv images.," We identified and chosen 15 uv bright points (UVBPs), 15 uv network elements (UVNWs), and 15 uv background regions (UVBGs) from the time sequence of uv images." We derived the cumulative intensity values of the UVBPs. UVNWs. and UVBGs using SSW in IDL.," We derived the cumulative intensity values of the UVBPs, UVNWs, and UVBGs using SSW in IDL." To calculate the intensity we have put the rectangular or square boxes covering the selected features., To calculate the intensity we have put the rectangular or square boxes covering the selected features. We derived the intensity time series of all the ultraviolet bright points (UVBPs). uv network (UVNWs) and uv background regions (UVBGs).," We derived the intensity time series of all the ultraviolet bright points (UVBPs), uv network (UVNWs) and uv background regions (UVBGs)." As an example we have shown the time series of the two UVBPs (UVBPI and UVBP2) from our selection in the upper panel of Fig.1., As an example we have shown the time series of the two UVBPs (UVBP1 and UVBP2) from our selection in the upper panel of Fig.1. The time series of UVBPs show a small fluctuations in their intensity values., The time series of UVBPs show a small fluctuations in their intensity values. In addition there is an indication of longer period., In addition there is an indication of longer period. To determine the period of intensity oscillations. we have done the power spectrum analysis using their time series data.," To determine the period of intensity oscillations, we have done the power spectrum analysis using their time series data." The power spectra for UVBPI and UVBP2 are shown in the lower panel of Fig.1., The power spectra for UVBP1 and UVBP2 are shown in the lower panel of Fig.1. It is clearly seen from the power spectra the existence of significant prominent peak around 5.5 hours in both the cases., It is clearly seen from the power spectra the existence of significant prominent peak around 5.5 hours in both the cases. Similarly. we have shown the time series and power spectra for two uv network elements (UVNW] and UVNW?) respectively in the upper and lower panels of Fig.2.," Similarly, we have shown the time series and power spectra for two uv network elements (UVNW1 and UVNW2) respectively in the upper and lower panels of Fig.2." As we could see from the power spectrum plots that the uv network elements exhibit around 4.6 hours of period of intensity oscillations., As we could see from the power spectrum plots that the uv network elements exhibit around 4.6 hours of period of intensity oscillations. In the upper and lower panels of Fig.3. we have presented the time series and power spectra for two background regions (UVBGI and UVBG2).," In the upper and lower panels of Fig.3, we have presented the time series and power spectra for two background regions (UVBG1 and UVBG2)." The background regions will be associated with around 3.4 hours of period of intensity oscillations., The background regions will be associated with around 3.4 hours of period of intensity oscillations. We have performed the cross spectrum analysis on the uv bright points and uv network elements of May 22. 2003 to compare with May 24. 2003 observations.," We have performed the cross spectrum analysis on the uv bright points and uv network elements of May 22, 2003 to compare with May 24, 2003 observations." We found that both the data sets show a coherent in phase there is a single dominate period associated with uv bright points (around 5.5 hours) and uv network elements (4.6 hours)., We found that both the data sets show a coherent in phase there is a single dominate period associated with uv bright points (around 5.5 hours) and uv network elements (4.6 hours). It has high coherence between May 22 and 24 uv bright point and uv network modulation., It has high coherence between May 22 and 24 uv bright point and uv network modulation. This, This not solve Lydrodvnamical and radiative transfer equations simultaneously. the evolution of species other (han neutral and ionized hydrogen such as molecular hydrogen. for example is not crucial in this model. although these species were formally included in our calculations.,"not solve hydrodynamical and radiative transfer equations simultaneously, the evolution of species other than neutral and ionized hydrogen – such as molecular hydrogen, for example – is not crucial in this model, although these species were formally included in our calculations." Let us briefly. summarize (he approximations we take., Let us briefly summarize the approximations we take. " First of all. hvdro and RT are computed separately, i.e. photoheating due to diffuse radiation has no dynamical effect on the gas."," First of all, hydro and RT are computed separately, i.e. photoheating due to diffuse radiation has no dynamical effect on the gas." Secondly. we omit (he time derivative in the RT equation in favor of simple photon statistics. so (hat al Chis stage we cannot properly compute OQ(v/c) ellects.," Secondly, we omit the time derivative in the RT equation in favor of simple photon statistics, so that at this stage we cannot properly compute ${\cal O}(v/c)$ effects." We also employ linite angular resolution for the diffuse flux. but. fortunately. due to the almost isotropic nature of this diffuse component and its small value. this approximation has negligible ellect on the shape and speed of I-Ironts.," We also employ finite angular resolution for the diffuse flux, but fortunately, due to the almost isotropic nature of this diffuse component and its small value, this approximation has negligible effect on the shape and speed of I-fronts." In addition. we eroup nearby stellar sources once they creale sienilicant reeions around them.," In addition, we group nearby stellar sources once they create significant regions around them." Finally. we use just one spectral group for the raciation. therefore. we cannot study Ie reionization in these particular calculations.," Finally, we use just one spectral group for the radiation, therefore, we cannot study He reionization in these particular calculations." One question which can be immediately addressed by our simulations is whether underdense regions (like voids) are ionized before overdense regions (like filaments)., One question which can be immediately addressed by our simulations is whether underdense regions (like voids) are ionized before overdense regions (like filaments). Our full RT simulations ina 7h!\pe volume show a picture of stellar reionization in which photons initially do not travel fay from ionizing sources. in contrast with images from the simulations by Gnedin (2000).," Our full RT simulations in a $7h^{-1}\mpc$ volume show a picture of stellar reionization in which photons initially do not travel far from ionizing sources, in contrast with images from the simulations by Gnedin (2000)." Fig., Fig. 2. shows that although ionizing photons stream preferentially into Che voids. regions do not grow bieger (han a few hundred thousand kpe until alter most of the gas close to sources is already ionized.," \ref{fig:2d_oka} shows that although ionizing photons stream preferentially into the voids, regions do not grow bigger than a few hundred thousand kpc until after most of the gas close to sources is already ionized." This result differs [rom that of Gnedin (2000). who found voids ionizing before regions had percolated.," This result differs from that of Gnedin (2000), who found voids ionizing before regions had percolated." This counter-intuitive result stems [rom Gnedins inclusion of a homogeneous UV. background which is not present in our simulation until the volume is fully ionized., This counter-intuitive result stems from Gnedin's inclusion of a homogeneous UV background which is not present in our simulation until the volume is fully ionized. In a sense. radiative transfer in our work is much more local. since the mean [ree path of ionizing photons in the fully ionized medium is much smaller than the box size.," In a sense, radiative transfer in our work is much more local, since the mean free path of ionizing photons in the fully ionized medium is much smaller than the box size." Host halos — and on larger scales dense filamentary structures around star forming proto-galaxies — serve as efficient sinks of radiation delaving global reionization by a significant fraction of the IIubble time., Host halos – and on larger scales dense filamentary structures around star forming proto-galaxies – serve as efficient sinks of radiation delaying global reionization by a significant fraction of the Hubble time. Only after these regions are ionized does radiation break out into the low-densitv IGM. sweeping quickly through the rest of the volume.," Only after these regions are ionized does radiation break out into the low-density IGM, sweeping quickly through the rest of the volume." A related question on how many photons per hvdrogen atom would be needed to cause complete overlap — has atiracted. a lot of attention in recent literature, A related question – on how many photons per hydrogen atom would be needed to cause complete overlap – has attracted a lot of attention in recent literature Type Ta supernovae (SNe Ia) are considered to be the most reliable distance indicators on extragalactic. even cosinological distance scales (ee. Cubsonetal.2000.Riessetab.L998.Tanaial.1996b and references therein),"Type Ia supernovae (SNe Ia) are considered to be the most reliable distance indicators on extragalactic, even cosmological distance scales (e.g. \cite{key1,par,perl1,riess2,hamuy1} and references therein)." " This is mainly based on their exceptional brightness aud honioseucitv. despite of he existence of ""peculii SNe Ta. such as SN 1991T or SN 1991bg (e.g. Filippeuko. 1997))."," This is mainly based on their exceptional brightness and homogeneity, despite of the existence of “peculiar” SNe Ia, such as SN 1991T or SN 1991bg (e.g. \cite{filip1}) )." " Althoush the frequency of these “standard bombs (Jhaeal.. 1999)) 1 OW. regular monitoring of nnnnerous ealaxies (ο,ο, we the Lick Observatory Supernova Search. the Nearby Cralaxies Supernova Search. ete.)"," Although the frequency of these “standard bombs” \cite{jha}) ) is low, regular monitoring of numerous galaxies (e.g. by the Lick Observatory Supernova Search, the Nearby Galaxies Supernova Search, etc.)" supplies nore than a hundred Type Ia SN eveuts per wear., supplies more than a hundred Type Ia SN events per year. The reliability of SN-based distances d9 duereased we the umber of bright. xwelbobserved. nearby SNe Ia iu host ealaxies whose distances cau also ve determined by other methods. such as Cepheids (Sahactal..1997.Cabsonet2000.Jha 1999)). Tully-Fisher relation. or surface brightuess fluctuation (e.g. Riessetal.. 1996)).," The reliability of SN-based distances is increased by the number of bright, well-observed, nearby SNe Ia in host galaxies whose distances can also be determined by other methods, such as Cepheids \cite{saha,key1,jha}) ), Tully-Fisher relation, or surface brightness fluctuation (e.g. \cite{riess1}) )." Tn this paper we present an updated distance to the type 2 Sevfert ealaxy NCC 6951 via the Type Ta SN 2000E. This ealaxy has received considerable attention recently especially its active nucleus. and cincmnnuclear star-foriuug rine (Boer&Schulz.1993.I&ohuoetal..1999.Perez 2000)).," In this paper we present an updated distance to the type 2 Seyfert galaxy NGC 6951 via the Type Ia SN 2000E. This galaxy has received considerable attention recently, especially its active nucleus and circumnuclear star-forming ring \cite{boer,barth,elm,kohno,perez}) )." Its cüstauce has been determined via Tulls-Fisher relation by several eroups., Its distance has been determined via Tully-Fisher relation by several groups. Dottinellietal..1981 eives fiy=231.055 mag for the true distauce modulus (corresponding to 23.1 Mpc). while Tully.1988. lists 2L1 Mpe Gay=21.91 imag).," \cite{bott} gives $\mu_{\rm 0} = 31.85$ mag for the true distance modulus (corresponding to 23.4 Mpc), while \cite{tully} lists 24.1 Mpc $\mu_{\rm 0} = 31.91$ mag)." SN 2000E has occurred just outside the origin of the long. northern spiral aru. in a relatively low surface brightuess region (Fig).," SN 2000E has occurred just outside the origin of the long, northern spiral arm, in a relatively low surface brightness region (Fig.1)." This SN was discovered by C. Valentini aud coworkers (Valentinictal..2000)) 0n Jau.26. 2000. and inunediately announced to be a Type Ta eveut by Turatto et al. (," This SN was discovered by G. Valentini and coworkers \cite{valent}) ) on Jan.26, 2000, and immediately announced to be a Type Ia event by Turatto et al. (" ef,cf. TAUC 7351)., IAUC 7351). They reported the appearance ofS111.SILL.dr. andtir. the usual ious characterizing Type Ia SNe. aud also the presence of Na D indicating considerable reddening.," They reported the appearance of, and, the usual ions characterizing Type Ia SNe, and also the presence of Na D indicating considerable reddening." The occurrence of SN 20001 was particularly interesting. because it appeared just a few mouths after the imaxiumuu of the Type II SN 199901. the first SN observed in NGC 6951.," The occurrence of SN 2000E was particularly interesting, because it appeared just a few months after the maximum of the Type II SN 1999el, the first SN observed in NGC 6951." SN 19990] was located closer to the bar-donmuuated central region. but definitely outside the circumaunuclear regiue where star-forming processes are nost active (Perezetal.. 2000)).," SN 1999el was located closer to the bar-dominated central region, but definitely outside the circumnuclear regime where star-forming processes are most active \cite{perez}) )." The expected αμα brieltucss of SNe Ia at the distance of NCC 6951 (about 13.5 mae) indicates that SN 2000E offers a good chance to increase the sample of bright. well-observed SNe Ta. The comparison of distances eternuned via SNe Ia aud other methods may result iu the refinement of the distance measuring techniques and the cosmuüc distance scale itself.," The expected maximum brightness of SNe Ia at the distance of NGC 6951 (about 13.5 mag) indicates that SN 2000E offers a good chance to increase the sample of bright, well-observed SNe Ia. The comparison of distances determined via SNe Ia and other methods may result in the refinement of the distance measuring techniques and the cosmic distance scale itself." This is especially portal in the case of SNe. because they are used to nieasuringe cosinological distances. where other methods often do not work. aud its technique relies on a relatively σπα]. uunnber of local calibrator SNe.," This is especially important in the case of SNe, because they are used to measuring cosmological distances, where other methods often do not work, and its technique relies on a relatively small number of local calibrator SNe." In the followines the new photometric aud spectroscopic observations of SN 2000TL are described then the results are preseuted. and discussed., In the followings the new photometric and spectroscopic observations of SN 2000E are described then the results are presented and discussed. The CCD-photometric observatious were obtained with four telescopes: the 2s cni Schinidt-Casscerain αἲ the campus site of University of Szeged (X11). the," The CCD-photometric observations were obtained with four telescopes: the 28 cm Schmidt-Cassegrain at the campus site of University of Szeged 1), the" This is the second paper in a series that investigates the 3.4 pan carbonaceous dust. absorption feature in sources that show a strong absorption-like feature at —10 jin but no detectable polvevelic aromatic hydrocarbon (PALL) emission eatures in ground-based δ13 pim. (ice. whole the IN-band) spectra.,"This is the second paper in a series that investigates the 3.4 $\mu$ m carbonaceous dust absorption feature in sources that show a strong absorption-like feature at $\sim$ 10 $\mu$ m but no detectable polycyclic aromatic hydrocarbon (PAH) emission features in ground-based 8–13 $\mu$ m (i.e., whole the $N$ -band) spectra." The [first paper discusses NGC 5506. (Imanishi 2000)., The first paper discusses NGC 5506 (Imanishi 2000). Roche ct al. (, Roche et al. ( 1991) performed. extensive. erouncl-owed S13 jm spectroscopy of the nuclei of nearby. active ealaxies (mostly z « 0.05). and classified them. into the ollowing three groups: (1) those dominated. by the family of emission features from small molecules called. PAIS (2040 carbon atoms per molecule: Allamancdola. Γιου» Barker 1989). (2) those with a featureless continuum. and (3) those that. display an absorption-like feature at ~ 10 jum. Each group of sources is regarded: as. respectively. (1) hose powered by star-forming activity. (2) those powered »v unobscured active galactic nuclei (Ας) activity. and (3) those powered by obscured AGN activity. for which the silicate dust absorption feature at 7.7 pii is expected to be resent.,"1991) performed extensive ground-based 8–13 $\mu$ m spectroscopy of the nuclei of nearby active galaxies (mostly $z$ $<$ 0.05), and classified them into the following three groups: (1) those dominated by the family of emission features from small molecules called PAHs (20--40 carbon atoms per molecule; Allamandola, Tielens Barker 1989), (2) those with a featureless continuum, and (3) those that display an absorption-like feature at $\sim$ 10 $\mu$ m. Each group of sources is regarded as, respectively, (1) those powered by star-forming activity, (2) those powered by unobscured active galactic nuclei (AGNs) activity, and (3) those powered by obscured AGN activity, for which the silicate dust absorption feature at $\sim$ 9.7 $\mu$ m is expected to be present." Sources in the third eroup. in particular those with a strong silicate dust absorption feature. are expected to be ughly obscured Ας and thus can be used to investigate he properties of the intervening medium along our Line-of- through the study of infrared. absorption features.," Sources in the third group, in particular those with a strong silicate dust absorption feature, are expected to be highly obscured AGNs, and thus can be used to investigate the properties of the intervening medium along our line-of-sight through the study of infrared absorption features." However. the attribution of the strong absorption-like eature ab 10. jum detected. in many ground-based δ13 ju spectra to the 9.7 qun silicate dust. absorption has oven questioned: based. on theObservatory (190) spectra. (Clavel et al.," However, the attribution of the strong absorption-like feature at $\sim$ 10 $\mu$ m detected in many ground-based 8–13 $\mu$ m spectra to the 9.7 $\mu$ m silicate dust absorption has been questioned based on the ) spectra (Clavel et al." 1999: Genzel et al., 1999; Genzel et al. 1998)., 1998). Strong PALL emission at ded jum from star-forming activity and continuum Εαν. that increases with wavelength: coull oduce an apparent strong absorption-like feature at 10 jam. One can attempt to estimate the strength of the 7.7 pam PALL emission. based on the observed Dux of the PALL emission at S.6 pm and 11.3. ja in grouncd-based S.19 jum spectra (Dudley 1999) by assuming that the 7.7 fum, Strong PAH emission at 7.7 $\mu$ m from star-forming activity and continuum flux that increases with wavelength could produce an apparent strong absorption-like feature at $\sim$ 10 $\mu$ m. One can attempt to estimate the strength of the 7.7 $\mu$ m PAH emission based on the observed flux of the PAH emission at 8.6 $\mu$ m and 11.3 $\mu$ m in ground-based 8–13 $\mu$ m spectra (Dudley 1999) by assuming that the 7.7 $\mu$ m for the parameter values adopted. here.,for the parameter values adopted here. “The uniform distribution. gle)=Lfewas. which is the distribution advocated by Llarercaves (1996). and. Mateo (1993).. is obtained by setting a=30.," The uniform distribution $\varphi(e) = 1/e_{\rm max}$, which is the distribution advocated by Hargreaves \cite{har} and Mateo \cite{mat}, is obtained by setting $\alpha = \beta = 0$." The argument of the periastron wis obviously cistributed randomly between aw=0 andi=2s., The argument of the periastron $\omega$ is obviously distributed randomly between $\omega=0$ and $\omega=2\pi$. Therefore. Averagingὃνo the nth velocity moment of the specific binary LOSVD (15)) over w involves the integral which can only be non-zero if m is even.," Therefore, Averaging the $n^{\rm th}$ velocity moment of the specific binary LOSVD \ref{mome}) ) over $\omega$ involves the integral which can only be non-zero if $n$ is even." " We will therefore consider only the even moments and make the transformation =2n in which case The integrations over 7 and m are pretty straightforward. and one obtains the following expression for the moments fis, : The next step is the integration over the semi-major axis e. making use olf (20)) : Finally. we are left with the integration over all possible values of the eccentricitv."," We will therefore consider only the even moments and make the transformation $n \rightarrow 2n$ in which case The integrations over $i$ and $m$ are pretty straightforward and one obtains the following expression for the moments $\tilde{\mu}_{2n}$ : The next step is the integration over the semi-major axis $a$, making use of \ref{disa}) ): Finally, we are left with the integration over all possible values of the eccentricity." Making use of the lemma one finds that: For eas=0. only the terms with m|2n.&=0 survive.," Making use of the lemma one finds that: For $e_{\rm max}=0$, only the terms with $m+2n-k=0$ survive." This is only possible if i=0 and &=27 and (51)) reduces to the expression for the moments of the LOSVD for circular orbits., This is only possible if $m=0$ and $k=2n$ and \ref{momavere}) ) reduces to the expression for the moments of the LOSVD for circular orbits. In the next. paragraph. we discuss how the velocity dispersion. of the binary LOSVD for non-circular orbits depends on the distributions of the different orbital parameters.," In the next paragraph, we discuss how the velocity dispersion of the binary LOSVD for non-circular orbits depends on the distributions of the different orbital parameters." Another important point that will be addressed is the way the shape of the observed LOSVD depends onthe binary[raction., Another important point that will be addressed is the way the shape of the observed LOSVD depends onthe binaryfraction. "(AGN, starburst. late auc early type ealaxies). are still far roni being well established.","(AGN, starburst, late and early type galaxies), are still far from being well established." Optical spectroscopy for a complete sample οἳ aut radio SOULCCS would be the luost cirect way Or a proper cassification of the optical counterparts., Optical spectroscopy for a complete sample of faint radio sources would be the most direct way for a proper classification of the optical counterparts. Towever. the very faint imaenitudes of a siguificaut raction of the objects associated to fait raclio sources Lnuudkes lis approach dithcul even for Suiclass clescopes.," However, the very faint magnitudes of a significant fraction of the objects associated to faint radio sources makes this approach difficult even for 8m–class telescopes." Alternatively. approximate classification of the counterparts can be achieved using photometric (colours) and radio (spectral index) data.," Alternatively, approximate classification of the counterparts can be achieved using photometric (colours) and radio (spectral index) data." The purpose of this work is to shed some light into the nature of these sources by studyiug a new faint radio suuple for which we have aualvzed the radio spectral properties aud derived photometric optical ideuntifications down to faint optical aud I& baud magnitudes., The purpose of this work is to shed some light into the nature of these sources by studying a new faint radio sample for which we have analyzed the radio spectral properties and derived photometric optical identifications down to faint optical and K band magnitudes. To further strenethen these goals we have observed a region of the sky at 6 cn centered in the Lockinan Iole. where excellent data are already available at 20 ci (de Ruiter et al..," To further strengthen these goals, we have observed a region of the sky at 6 cm centered in the Lockman Hole, where excellent data are already available at 20 cm (de Ruiter et al.," 1997). in the far-infrared baud (Fadda et al..," 1997), in the far-infrared band (Fadda et al.," 2002: Rodighicro et al., 2002; Rodighiero et al. iu preparation). iu the near infrared aud optical bauds (Schinidt et al..," in preparation), in the near infrared and optical bands (Schmidt et al.," 1998: Lehman et al..," 1998; Lehmann et al.," 2000: Lelunann et al..," 2000; Lehmann et al.," 2001: Wilson et al..," 2001; Wilson et al.," 2001) and in the X- baud (Ilasiuser et aL.," 2001) and in the X-ray band (Hasinger et al.," 2001)., 2001). In Sect., In Sect. 2 we give a general description of the radio observations. while the radio catalogue aud the source counts are presented im Sect.," 2 we give a general description of the radio observations, while the radio catalogue and the source counts are presented in Sect." 3., 3. Iu Sect., In Sect. [woe present he associations ofthe 6 ci sources with the radio (20011). nearmfrared. optical. and N-rav sources.," 4 we present the associations of the 6 cm sources with the radio (20cm), near–infrared, optical, and X-ray sources." Finally. Sect.," Finally, Sect." 5 is devoted to the discussion of our results. while Sect.," 5 is devoted to the discussion of our results, while Sect." 6 sunnuarizes our conclusions., 6 summarizes our conclusions. The VLA observations were done in three ruus of eleveu hours each ou January 16. 17 aud 19. 1999 at. 1835 aud 45885 Az with a bandwidth of 50 MIIz iu C coufiguration.," The VLA observations were done in three runs of eleven hours each on January 16, 17 and 19, 1999 at 4835 and 4885 MHz with a bandwidth of 50 MHz in C configuration." " A total of seven poiutiues in a hexagonal erid with a size of Opyyup/V¥2 -—6.1 arcmin Ovhere Opywyp is the full-width at halfpower of the primary beam. 9 arciuiu at 5 GIIz) plus one at the center were observed for l hours each around the ROSAT ultra-decp TRI feld center RA(2000j= 10752""138) DEC(2000)= 57728!is”,"," A total of seven pointings in a hexagonal grid with a size of $\theta_{\rm FWHP}/\sqrt{2} \sim$ 6.4 arcmin (where $\theta_{\rm FWHP}$ is the full-width at half-power of the primary beam, 9 arcmin at 5 GHz) plus one at the center were observed for 4 hours each around the ROSAT ultra-deep HRI field center RA(2000)= $^h52^m43^s$, DEC(2000)= $^{\circ}28^{\prime} 48^{\prime\prime}$." This choice of poiutiug positions was adopted in order to obtain a reasonably uniform niis noise level iu the iuner part of the ROSAT ultra deep IIRI field., This choice of pointing positions was adopted in order to obtain a reasonably uniform rms noise level in the inner part of the ROSAT ultra deep HRI field. All the data were analyzed using the NRAQO AIPS reuction package., All the data were analyzed using the NRAO AIPS reduction package. The data were calibrated using 3€ 286 as priuary flux density calibrator (assuming a fiux deusity of 7.5103 Jv at 1835 MITz aud 7.1617 Jv at £885 MITz) and the source 1035561 as a phase and secondary amplitude calibrator., The data were calibrated using 3C 286 as primary flux density calibrator (assuming a flux density of 7.5103 Jy at 4835 MHz and 7.4617 Jy at 4885 MHz) and the source 1035+564 as a phase and secondary amplitude calibrator. For each of the seven fields we constructed au image of 10511051 pixels. with a pixelsize of 1.0 arcsec.," For each of the seven fields we constructed an image of $\times$ 1024 pixels, with a pixel-size of 1.0 arcsec." Each observation was cleaned using the task INLACGT. using a restoriug beam of LxlL arcsec.," Each observation was cleaned using the task IMAGR, using a restoring beam of $\times$ 4 arcsec." The nus noise levels in the cleaned (uot primary beam corrected) images are uniform and of the order of 11 yi Jy., The rms noise levels in the cleaned (not primary beam corrected) images are uniform and of the order of 11 $\mu$ Jy. Finally. using the AIPS task LGEOM. HGEONM and LTESS. we have combined all the seven poitines. creating a single mosaic nap of 420158. pixels.," Finally, using the AIPS task LGEOM, HGEOM and LTESS, we have combined all the seven pointings, creating a single mosaic map of $\times$ 2048 pixels." Contour plot of the mosaic nap Is shown in Fie. 1.., Contour plot of the mosaic map is shown in Fig. \ref{F1}. As expected. the mosaic map has a regular noise distribution: a circular ceutral region with a flat nolse distribution. smrounded by an outer region where the nolse Increases for mereasing distance frou the ceuter.," As expected, the mosaic map has a regular noise distribution: a circular central region with a flat noise distribution, surrounded by an outer region where the noise increases for increasing distance from the center." No structures or irreeularities were found iu the runs nolse map., No structures or irregularities were found in the rms noise map. " The rus values as a function of the distance from the field center are well fitted by 10 function: iust,y y) — S2 LL dy where 0,5, is the off-axis anele iu arcmin.", The rms values as a function of the distance from the field center are well fitted by the function: $\theta_{off}$ ) = 8.2 $\times$ $^{-5} \times \theta_{off}^{5.05} $ + 11 $\mu$ Jy where $\theta_{off}$ is the off-axis angle in arcmin. 700Measureineuts| of 1611115 ose at viulous distances from the field ceuter and the fitting function are shown in Fig. 2.., Measurements of the rms noise at various distances from the field center and the fitting function are shown in Fig. \ref{F2}. Caiven the rapid increase of the rius noise at large off-axis aneles. we have linited the extraction of the sources to an area with θε «10 arcmin. corresponding to 0.087 square degree.," Given the rapid increase of the rms noise at large off-axis angles, we have limited the extraction of the sources to an area with $\theta_{off} \leq$ 10 arcmin, corresponding to 0.087 square degree." The criterion we adopted for including a source in the catalogue is that its peak flux deusitv. Sp. is 215 times the average rmi value at the off-axis auele of the source (sce Fig. 2)).," The criterion we adopted for including a source in the catalogue is that its peak flux density, $_{\rm P}$, is $\geq$ 4.5 times the average rms value at the off-axis angle of the source (see Fig. \ref{F2}) )." In order to choose the threshold in Sp we analyzed the map with the negative peaks using ciffercut, In order to choose the threshold in $_{\rm P}$ we analyzed the map with the negative peaks using different OGLE-051019.64685812.3 offers us an outstanding opportunity to derive a very accurate distance to the LMC using an empirical surface brightness color relation (di Benedetto 1998. Groenewegen 2004. IXervella et al.,"OGLE-051019.64-685812.3 offers us an outstanding opportunity to derive a very accurate distance to the LMC using an empirical surface brightness – color relation (di Benedetto 1998, Groenewegen 2004, Kervella et al." 2004. di Benedetto 2005).," 2004, di Benedetto 2005)." We would like to note here. that another calibration given by van Belle (1999) is not. accurate enough for our purpose (e.g. about. LO only. due to the lower accuracy of their measured angular diameters).," We would like to note here, that another calibration given by van Belle (1999) is not accurate enough for our purpose (e.g. about 10 only, due to the lower accuracy of their measured angular diameters)." Given the long period of the svstem it was not possible to obtain eclipse light curves in all passbands. and as a result we computed the magnitudes and colors of the individual Cmponents by deriving the brightness ratios in different bands from an extrapolation of the I-band solution (e.g. taking into account the inlormation about the temperatures of both components).," Given the long period of the system it was not possible to obtain eclipse light curves in all passbands, and as a result we computed the magnitudes and colors of the individual components by deriving the brightness ratios in different bands from an extrapolation of the $I$ -band solution (e.g. taking into account the information about the temperatures of both components)." since all available empirical surface brightness-color relations are based on magnitudes calibrated onto the Johnson svstem. we transformed our photometry (to (his svstem using the equations given by Carpenter et al. (," Since all available empirical surface brightness-color relations are based on magnitudes calibrated onto the Johnson system, we transformed our photometry to this system using the equations given by Carpenter et al. (" 2001). and Bessell and Brett (1983).,"2001), and Bessell and Brett (1988)." Adopting the reddening law of Schlegel et al. (, Adopting the reddening law of Schlegel et al. ( 1993) and a reddening of E(B-V) = 0.146 mag as derived from the OGLE redelening maps. the reddening-free magnitudes and colors of the individual components were calculated.,"1998) and a reddening of E(B-V) = 0.146 mag as derived from the OGLE reddening maps, the reddening-free magnitudes and colors of the individual components were calculated." These are listed in Table 3., These are listed in Table 3. " The distance in parsecs follows then directly from the Lacy. (LOTT) equation: d(pe)=1.337x10""r(bim)/z(Gmnas) The linear diameter (1) comes [rom the analvsis of the svstem while the angular diameter (42) is derived from the surface brightness-color relations (e.g. my=9—Mog(,). where Ὦ is the surface brightness in a given band. and my is the unreddened magnitude of a given star in this band)."," The distance in parsecs follows then directly from the Lacy (1977) equation: $ d(pc) = 1.337 \times 10^{-5}r(km)/ \varphi(mas)$ The linear diameter (r) comes from the analysis of the system while the angular diameter $\varphi$ ) is derived from the surface brightness-color relations (e.g. $ m_{0} = S - 5 log(\varphi)$, where S is the surface brightness in a given band, and $ m_{0}$ is the unreddened magnitude of a given star in this band)." Calculating the respective surface brightnesses of the components οἱ 635812.3 [rom their (V-IxX) colors and using the calibration of di Benedetto ο”(2005))5) obtained for a mixed sample of giant and dwarf stars. we obtain distances of (50.4— 1.3) kpe lor the primary. ancl (50.0 & 1.4) kpe for the secondary. component. corresponding to distance moduli of (18.51 4 0.06) mae and (18.49+ 0.06) mae. respectively.," Calculating the respective surface brightnesses of the components of OGLE-051019.64-685812.3 from their (V-K) colors and using the calibration of di Benedetto (2005) obtained for a mixed sample of giant and dwarf stars, we obtain distances of (50.4 $\pm$ 1.3) kpc for the primary, and (50.0 $\pm$ 1.4) kpc for the secondary component, corresponding to distance moduli of (18.51 $\pm$ 0.06) mag and (18.49 $\pm$ 0.06) mag, respectively." Very similar results (see Table 2) are obtained using the (V-IX) colors and the calibrations of di Benedetto (1993). Groenewegen (2004). IXervella (2004).," Very similar results (see Table 2) are obtained using the (V-K) colors and the calibrations of di Benedetto (1998), Groenewegen (2004), Kervella (2004)." It has been shown bv Di Benedetto (1998. 2005) that the surface brightness — color relations for late-tvpe cdwarf ancl giant stus are consistent wilh each other at the level ol l.," It has been shown by Di Benedetto (1998, 2005) that the surface brightness – color relations for late-type dwarf and giant stars are consistent with each other at the level of 1." To demonstrate the verv low sensitivity of our derived distance value on the adopted surface brightness - color relation. we present in Table 2 the distances of the two," To demonstrate the very low sensitivity of our derived distance value on the adopted surface brightness - color relation, we present in Table 2 the distances of the two" from both ionizing aud Lyinan-Werner UV radiation.,from both ionizing and Lyman-Werner UV radiation. To show clearly the dependence of ealaxv properties on dust destruction. we use a simple one-zoue galaxy model.," To show clearly the dependence of galaxy properties on dust destruction, we use a simple one-zone galaxy model." The paper is organized as follows., The paper is organized as follows. describe the dust evolution model., In $\S2$ we describe the dust evolution model. In 63 we explain our one-zone galaxy model., In $\S3$ we explain our one-zone galaxy model. In 51 we present the results., In $\S4$ we present the results. Iu $5 we discuss the effects of the dust size evolution ou II» formation process aud couclude by sunuumizime our results., In $\S5$ we discuss the effects of the dust size evolution on $_{2}$ formation process and conclude by summarizing our results. " Throughout this paper we adopt the cosimological parameters frou the third-vear WALAP results (Sperecletal.2007).. Oy= 0.76. Oy=021. OQ,=0.0L and H2,=τὸΚιν!Atpe dl "," Throughout this paper we adopt the cosmological parameters from the third-year $WMAP$ results \citep{Spe07}, $\Omega_{\Lambda}=0.76$ , $\Omega_{M}=0.24$, $\Omega_{b}=0.04$, and $H_{0}=73\ {\rm km}\ {\rm s}^{-1}\ {\rm Mpc}^{-1}$ ." SNe II are believed to be the dominant sources of dust at high redshift of +>5 because of short lifetimes (5$ because of short lifetimes $<10^{7}\ {\rm yr}$ ) of their massive progenitors \citep[e.g.][]{Dwe07, Gal10}." . Dust formation in the ejecta of primordial SNe II has been investigated theoretically (Toclinioff&Dwelk 2010).," Dust formation in the ejecta of primordial SNe II has been investigated theoretically \citep{Tod01, Noz03, Che10}." . The amount and the size distributions of dust eraius injected iuto ISM have been investigated by cousideriug the destruction iu SN remmauts (SNRs) (Bianchi&Schneider2007: 2010).," The amount and the size distributions of dust grains injected into ISM have been investigated by considering the destruction in SN remnants (SNRs) \citep{Bia07, Noz07, Nat08, Sil10}." ". Althoueh how much dust really forms iu the ejecta has been still under debate (I&ozasactal.2009.for review)... the recent observatious of Cas-A SNR revealed the presence of ~0.07AL, dust condensed iu the ejecta (Barlowctal.2010:Sibthorpeetal. 2010).. which is consistent with the dust mass predicted by the theoretical mocel takiug iuto account formation and destruction processes of dust iu a Type IIb SN (Nozawaetal. 2000)."," Although how much dust really forms in the ejecta has been still under debate \citep[][for review]{Koz09}, the recent observations of Cas-A SNR revealed the presence of $\sim0.07\ M_{\odot}$ dust condensed in the ejecta \citep{Bar10, Sib10}, which is consistent with the dust mass predicted by the theoretical model taking into account formation and destruction processes of dust in a Type IIb SN \citep{Noz10}." .. Valiantectal.(2009) and. Dwels&Cherchueff(2010). have proposed that the contribution from asvuiptotie giant brauch (ACB) stars du the ποιοςκατ quasar JILLLs|5251 cannot be neelected for the total dust budget even at i~6., \citet{Val09} and \citet{Dwe10} have proposed that the contribution from asymptotic giant branch (AGB) stars in the high-redshift quasar J1148+5251 cannot be neglected for the total dust budget even at $z\sim6$. However. the size distribution of dust forme in the imass-loss wind of ACD stars has uot been fully studied vet (Ferrarotti&Cail2006:Zhukovskaetal. 2008).," However, the size distribution of dust formed in the mass-loss wind of AGB stars has not been fully studied yet \citep{Fer06, Zhu08}." . If type Ia SNe could occur in such an carly epoch. they are unlikely to be efficient sources of dust (Nozawa et al.," If type Ia SNe could occur in such an early epoch, they are unlikely to be efficient sources of dust (Nozawa et al." 2010 in preparation)., 2010 in preparation). Therefore. in order to follow the evolution of dust size distribution and reveal the resulting influence on galaxy evolution. we consider SNe II as the source of dust in the carly Universe.," Therefore, in order to follow the evolution of dust size distribution and reveal the resulting influence on galaxy evolution, we consider SNe II as the source of dust in the early Universe." The basic quantity for governing the production aud destruction historv of dust by SNe ID is the rate of SN II explosions. *ux(£). given by where Wit) is the SFR at time f. ο) is the stellay IME. τί) is the lifetime of a star whose mass is mn aud mis aud TEN aro the pper aud lower mass linüts of SN II progenitors. respectively.," The basic quantity for governing the production and destruction history of dust by SNe II is the rate of SN II explosions, $\gamma_{\rm SN}(t)$, given by where $\Psi(t)$ is the SFR at time $t$, $\phi(m)$ is the stellar IMF, $\tau(m)$ is the lifetime of a star whose mass is $m$ and $m_{\rm SN}^{u}$ and $m_{\rm SN}^{l}$ are the upper and lower mass limits of SN II progenitors, respectively." " In this paper we adopt the Salpeter IMF (04)win2°, (Salpeter1955))) with the stellar mass range between 0.1AL. aud GOAL... we assume ils=SM and ni=10AL. (IHereeretal. 2003)."," In this paper we adopt the Salpeter IMF $\phi(m)\propto m^{-2.35}$, \citep{Sal55}) ) with the stellar mass range between $0.1\ M_{\odot}$ and $60\ M_{\odot}$, we assume $m_{\rm SN}^{l}=8\ M_{\odot}$ and $m_{\rm SN}^{u}=40\ M_{\odot}$ \citep{Her03}." . For τη). we adopt the model of gzero-Inetallicity stars without mass loss (Schaerer2002).," For $\tau(m)$, we adopt the model of zero-metallicity stars without mass loss \citep{Sch02}." . Iu this paper. we do not consider Population IIT stars. for simplicity.," In this paper, we do not consider Population III stars, for simplicity." In the forthcoming paper. we will consider possible contribution of Population III stars.," In the forthcoming paper, we will consider possible contribution of Population III stars." Population III stars formed out of the omuordial eas are considered to be much more nassive than Population T/T stars (Yoshidaetal.2008:Brownet2009.for reviews)... and hus the primordial IME Ιστ be biased. toward a higher mass (ZLO AZ.) than that in the oeseut Universe.," Population III stars formed out of the primordial gas are considered to be much more massive than Population I/II stars \citep[][for reviews]{Yos08, Bro09}, and thus the primordial IMF might be biased toward a higher mass $\gtrsim10\ M_{\odot}$ ) than that in the present Universe." Furthermore. Population III stars as massive as {0—260AL. are predicted o end their lives as pair-dustabilitv SNe (PISNeIlereer&Woosley2002) and to produce a large züunount of metals aud dust (Nozawaetal.2003:Schueideretal. 2001).," Furthermore, Population III stars as massive as $140-260\ M_{\odot}$ are predicted to end their lives as pair-instability SNe \citep[PISNe][]{Her02} and to produce a large amount of metals and dust \citep{Noz03, Sch04}." . However. Jogecrstetal.(20104). and Jogeerstetal.(20105) address the erowius nucleosvuthetie forensic evidence that the majority of primordial stars may have been 1510A£.. objects.," However, \citet{Jog10a} and \citet{Jog10b} address the growing nucleosynthetic 'forensic' evidence that the majority of primordial stars may have been $15-40\ M_{\odot}$ objects." On the other haud. once the gas is curiched up to a critical metallicity of Z~10%10 Z..formation of low-mass stars is trigecred. leading to the transition of the star formation node from massive population III stars to low-mass population 1Ἡ stars. if dust present (Omukaietal.2005:Sclineider 2010)..," On the other hand, once the gas is enriched up to a critical metallicity of $Z\simeq10^{-6}-10^{-5}\ Z_{\odot}$ ,formation of low-mass stars is triggered, leading to the transition of the star formation mode from massive population III stars to low-mass population I/II stars, if dust present \citep{Omu05, Sch06, Sch10, Omu10}. ." If there is no dust. the trausition of," If there is no dust, the transition of" e.g.. the relationship between star formation rate and euerev injected iuto the ISM by supernovae. he II» formation timescale (aud. its dependeuce on metallicity). aud the turbulent dimension of he ISM (used. to relate the driving leneth scale o the characteristic cloud size modulo a free oxumwneter),"e.g., the relationship between star formation rate and energy injected into the ISM by supernovae, the $_2$ formation timescale (and its dependence on metallicity), and the turbulent dimension of the ISM (used to relate the driving length scale to the characteristic cloud size modulo a free parameter)." As fur as possible. these are drawn ron observations of the Milky. Way.," As far as possible, these are drawn from observations of the Milky Way." We are left with three free parameters., We are left with three free parameters. First. here is an unknown scaling factor relating the diving leneth of turbulence to the size of gravitationally youd Clamps. which we call 6.," First, there is an unknown scaling factor relating the driving length of turbulence to the size of gravitationally bound clumps, which we call $\delta$." Secoud. the point at which the star formation timescale trausitions rom the free fall time to the Is formation time ispriori unknown.," Second, the point at which the star formation timescale transitions from the free fall time to the $_2$ formation time is unknown." Third. the mass accretion vate. AM. which is related to the driving leneth and turbulent velocity. is a free parameter.," Third, the mass accretion rate, $\dot{M}$, which is related to the driving length and turbulent velocity, is a free parameter." In Section |. via comparison to the present sample of ealaxies. we coustrain à.," In Section \ref{sec:results} via comparison to the present sample of galaxies, we constrain $\delta$." " Iu practice. we also treat he Toonmre Q panuneter of the eas as a ""senui-rec parameter. allowing it to change somewhat rou the observed value."," In practice, we also treat the Toomre $Q$ parameter of the gas as a ``semi-free'' parameter, allowing it to change somewhat from the observed value." With these assumptions in hand. we may fit he model to a galaxy by comparing the observed sincmatics.II CO. and star formation rate xofiles to those predicted bv the model.," With these assumptions in hand, we may fit the model to a galaxy by comparing the observed kinematics, CO, and star formation rate profiles to those predicted by the model." The resulting fit vields the disk mass accretion rate and several other paraneters that may be checked against expectations: the free fall time (or density) for the largest sclteravitating structures. the daiving leneth of turbulence. aud the approximate velocity of radial inflow.," The resulting fit yields the disk mass accretion rate and several other parameters that may be checked against expectations: the free fall time (or density) for the largest self-gravitating structures, the driving length of turbulence, and the approximate velocity of radial inflow." Iu the remainder of this section. we discuss our asstuuptious in slielitly more detail justify them. via comparison to observation and theory. aud note the physics that we neglect.," In the remainder of this section, we discuss our assumptions in slightly more detail, justify them via comparison to observation and theory, and note the physics that we neglect." "ISAM: Following. e.g. MacLow&EKlessen (2001).. we view the ISM as à sinele turbulent eas,"," Following, e.g., \citet{MacLow}, we view the ISM as a single turbulent gas." Iu this picture. the vain. cold. aud molecular phases of the ISM are a single eutitv.," In this picture, the warm, cold, and molecular phases of the ISM are a single entity." Locally. the exact phase of the gas may depend ou the local pressure. moetallicitv. stellar radiation field. stellar winds. aud shocks.," Locally, the exact phase of the gas may depend on the local pressure, metallicity, stellar radiation field, stellar winds, and shocks." Here we view these factors as secondary. makiug a few siniplifviug assumptions.," Here we view these factors as secondary, making a few simplifying assumptions." The equilibiuun between the different plases of the ISM aud the equilibrium between turbulence and star formation depends on three local timescales: the turbulent crossing time fh. the molecule formation timescale Ü and the local free fall timescale te of a cloud.Turbulence," The equilibrium between the different phases of the ISM and the equilibrium between turbulence and star formation depends on three local timescales: the turbulent crossing time $t_{\rm turb}^{l}$ , the molecule formation timescale $t_{\rm mol}^{l}$, and the local free fall timescale $t_{\rm ff}^{l}$ of a cloud." : First. we assue that the eas is turbulent. so that the turbulent velocity is the relevant one throughout the disk (iiaking the exact temperature of the eas is largely irrelevant).," First, we assume that the gas is turbulent, so that the turbulent velocity is the relevant one throughout the disk (making the exact temperature of the gas is largely irrelevant)." We asstune that this turbulence is driven by SNe aud that they input their energv in turbulent eddies that have a characteristic leugth scale. Jay. aud a characteristic velocity. Crop.," We assume that this turbulence is driven by SNe and that they input their energy in turbulent eddies that have a characteristic length scale, $l_{\rm driv}$, and a characteristic velocity, $v_{\rm turb}$." Lhis driving leneth scale may be the characteristic length scale of a SN bubble. bu it oes not lave to be so.," This driving length scale may be the characteristic length scale of a SN bubble, but it does not have to be so." It may be set bv the iuteraction of multiple SN bubbles or of a SN with the surrounding ISM., It may be set by the interaction of multiple SN bubbles or of a SN with the surrounding ISM. We note tha based on simulations. the assiuuption of a single daiving scale may be a simplification (Joung&MaeLow 2006).," We note that based on simulations, the assumption of a single driving scale may be a simplification \citep{JoungMacLow}." . The VBO3 iodel does no address the spatial imhomogencity of the turbuleu daiving nor the mechanics of turbulent driving aud dissipation., The VB03 model does not address the spatial inhomogeneity of the turbulent driving nor the mechanics of turbulent driving and dissipation. It is assumed that the energv mpu rate into the ISM due ta SNe. Bex. is cascaded to smaller scales without losses bv turbulence.," It is assumed that the energy input rate into the ISM due to SNe, $\dot{E}_{\rm SN}$, is cascaded to smaller scales without losses by turbulence." At scales smaller than the size of the larecs selferavitatins clouds the energy is dissipated via cloud contraction aud star formation., At scales smaller than the size of the largest selfgravitating clouds the energy is dissipated via cloud contraction and star formation. We refer to AlaeLow&Ποσο(2001). for a review of these topics., We refer to \citet{MacLow} for a review of these topics. We linut our analytical model to the first euergv sink which is the scale where the clouds become sclferavitating., We limit our analytical model to the first energy sink which is the scale where the clouds become selfgravitating. We can connect the energy iuput iuto the ISM by SNe directly to the star formation rate., We can connect the energy input into the ISM by SNe directly to the star formation rate. With the asstunption of a constant initial mass function (INE) independent of environment one cau write where AA is the unit surface clement of the disk., With the assumption of a constant initial mass function (IMF) independent of environment one can write where $\Delta A$ is the unit surface element of the disk. The factor of proportionality. © relates the local SN enerev input to the local star formation rate and is asstuned to be independent of loca conditions., The factor of proportionality $\xi$ relates the local SN energy input to the local star formation rate and is assumed to be independent of local conditions. € is normalized using Galactic observations by iuteerating over the Galactic disk aud results in &=L6«10.* Y)? (sce VDO3).," $\xi$ is normalized using Galactic observations by integrating over the Galactic disk and results in $\xi=4.6 \times 10^{-8}$ $^{2}$ (see VB03)." The adopted energy that is injected into the ISM ls ο=10409 ores based ou muuerical studies bv Thorutouetal.(1998).., The adopted energy that is injected into the ISM is $E^{\rm kin}_{\rm SN}=10^{50}$ ergs based on numerical studies by \citet{Thornton}. The final two parts of Equation 1 assune that stars form over a characteristic scaleequal to the driving leneth aud equate energev output frou SNe with the energy transported by turbulence (see VDO3)., The final two parts of Equation \ref{eq:energyflux} assume that stars form over a characteristic scaleequal to the driving length and equate energy output from SNe with the energy transported by turbulence (see VB03). Considering the apparent οσοπιο population of low huninosity ACN at microjansikay levels. care is needed when interpreting racio source counts in terms of the evolution of the star formation rate in the Universe.,"Considering the apparent emerging population of low luminosity AGN at microjansky levels, care is needed when interpreting radio source counts in terms of the evolution of the star formation rate in the Universe." We plan to expand on this work by using our deeper (7μὴν per beam over the whole Exteuded CDES region) radio observations (Milleretal.2008) anc the receutly released 2 MecChandra data (Luoetal.2008).., We plan to expand on this work by using our deeper $7~\mu$ Jy per beam over the whole Extended CDFS region) radio observations \citep{mil08} and the recently released 2 MsecChandra data \citep{luo08}. . AX two-pole accretion model. based on the doubc-peak pulse profile and the «ominance of the first harnjonic in the optical anc X-ray power spectra. has been xoposed. for RA J0558|5353 (Allan et al.,"A two-pole accretion model, based on the double-peak pulse profile and the dominance of the first harmonic in the optical and X-ray power spectra, has been proposed for RX J0558+5353 (Allan et al." 1996)., 1996). Our data show pulses (Fig., Our data show pulses (Fig. 2) which at imes are dillerent between odd. and even ones., 2) which at times are different between odd and even ones. " Together wih the observation that. the »ower of the enission-line. pulsc""s appears mainlv at the first harmonic. our spectra corrol»o»rate for a two-pole accretion region as well."," Together with the observation that the power of the emission-line pulses appears mainly at the first harmonic, our spectra corroborate for a two-pole accretion region as well." The puse shows a semi-umplitucde o “408435 km f., The pulse shows a semi-amplitude of $\pm$ 35 km $^{-1}$. For a Keplerian velocity of 408 km + the location of the pulsations would be placed. bevoncd the tidal radius of the accretion disc.," For a Keplerian velocity of 408 km $^{-1}$, the location of the pulsations would be placed beyond the tidal radius of the accretion disc." In addition. such a location for a highly-ionized region is problematic.," In addition, such a location for a highly-ionized region is problematic." LE pulsations are eencrally related to the transition region between the disc and the magnetic field of the white dwarf (Lamb 1988). and in particular the accretion-curtain model seems plauside to interpret the double-pulse ofLE (EX Hya in Rosen et al.," pulsations are generally related to the transition region between the disc and the magnetic field of the white dwarf (Lamb 1988), and in particular the accretion-curtain model seems plausible to interpret the double-pulse of (EX Hya in Rosen et al." Loss; AO Pse in Hellier et al., 1988; AO Psc in Hellier et al. 1991: see also Fig., 1991; see also Fig. 11)., 11). Each pulse maximum in the continuum. most ikelv.," Each pulse maximum in the continuum, most likely," "magnitudes using K=K,+0.044.",magnitudes using $K= K_{\rm s}+0.044$. The resulting zero point differences should be less than 0.02 magnitudes (Alvesetal.2002).., The resulting zero point differences should be less than 0.02 magnitudes \citep{2002ApJ...573L..51A}. " For the Ks photometry, the distance modulus to a red clump giant in the outer disk would be: wwhere we adopted Ax./(A;—Ακ.)=0.73, (J—K,)o=0.7040.05 and Mx,=—1.652:0.03 as the mean values for the red clump giants of the Milky Way disk (Alvesetal.2002).."," For the Ks photometry, the distance modulus to a red clump giant in the outer disk would be: where we adopted $A_{K_{\rm s}}/(A_J-A_{K_{\rm s}})=0.73$, $(J-K_{\rm s})_0=0.70\pm 0.05$ and $M_{K_{\rm s}}=-1.65\pm 0.03$ as the mean values for the red clump giants of the Milky Way disk \citep{2002ApJ...573L..51A}." There should be negligible metallicity dependence of these mean values because we are looking at a stellar population of the Milky Way disk that should be similar to that of the Solar neighbourhood where Hipparcos distances of clump giants were calibrated., There should be negligible metallicity dependence of these mean values because we are looking at a stellar population of the Milky Way disk that should be similar to that of the Solar neighbourhood where Hipparcos distances of clump giants were calibrated. " Adopting these means magnitudes and colours, and the reddening coefficients (Cardellietal.1989) yields: Using this equation we computed the distance modulus (and distance in kpc) for every"," Adopting these means magnitudes and colours, and the reddening coefficients \citep{1989ApJ...345..245C} yields: Using this equation we computed the distance modulus (and distance in kpc) for every" We see that the surface density of Compton-thick sources expected in a 220 ks exposure (equal in length to the initial Chandra observation of the HDF-N and its vicinity by Hornschemeier et al.,We see that the surface density of Compton-thick sources expected in a 220 ks exposure (equal in length to the initial Chandra observation of the HDF-N and its vicinity by Hornschemeier et al. 2001) with Chandra ACIS chip is about 200., 2001) with Chandra ACIS chip is about 200. A chip is S.N aremin or 0.0178 sq deg which means that 3—4 faint hard sources are expected in such an exposure., A chip is $8\times8$ arcmin or 0.0178 sq deg which means that 3–4 faint hard sources are expected in such an exposure. If the ACIS-I array is use. with j times the area. then the number rises to about 10 ¢given the degradation of sensitivity off axis: most of the photons detected are above 6 keV).," If the ACIS-I array is use, with 4 times the area, then the number rises to about 10 (given the degradation of sensitivity off axis: most of the photons detected are above 6 keV)." The sources have redshifts of 3—7 and are basically detectable because of the inverse K-correction., The sources have redshifts of 3–7 and are basically detectable because of the inverse K-correction. Most of the Compton-thick above +=3 become detectable in deeper exposures of | Ms. In an. XMM pn chip exposure of similar duration. concentrating on the 5-10 keV band. we have about 40 sources detected per square degree. mostly in the redshift range of 2-5.," Most of the Compton-thick above $z=3$ become detectable in deeper exposures of 1 Ms. In an XMM pn chip exposure of similar duration, concentrating on the 5–10 keV band, we have about 40 sources detected per square degree, mostly in the redshift range of 2–5." The field of view is about 0.2 sq deg (30 aremin diameter) leading to about 8 sources detected per 220 ks exposure. similar to the yield from Chandra.," The field of view is about 0.2 sq deg (30 arcmin diameter) leading to about 8 sources detected per 220 ks exposure, similar to the yield from Chandra." Source confusion should not be a problem at such high photon energies., Source confusion should not be a problem at such high photon energies. The adopted WEN model thus predicts that the direct absorbed emission from some Compton-thick quasars is detectable by Chandra and XMM with similar yields., The adopted WFN model thus predicts that the direct absorbed emission from some Compton-thick quasars is detectable by Chandra and XMM with similar yields. The absorbed primary emission from these sources will be very hard and most will be detected close to the threshold for detection CIO counts for Chandra. 30 for XMM}. as discussed in section 2.1.," The absorbed primary emission from these sources will be very hard and most will be detected close to the threshold for detection (10 counts for Chandra, 30 for XMM), as discussed in section 2.1." Scattered emission may however allow the sources to be detected also in softer energy bands., Scattered emission may however allow the sources to be detected also in softer energy bands. The appearance of such objects in the optical and near infrared bands depends on the rate of star formation., The appearance of such objects in the optical and near infrared bands depends on the rate of star formation. If this rate is low then they should appear as redshifted early-type bulges. without strong emission lines. and if high they will be brighter and of much later spectral type. probably with emission lines.," If this rate is low then they should appear as redshifted early-type bulges, without strong emission lines, and if high they will be brighter and of much later spectral type, probably with emission lines." So far only one source with a spectrum consistent with being Compton thick has been reported (Norman et al 20013: its redshift =3.8., So far only one source with a spectrum consistent with being Compton thick has been reported (Norman et al 2001); its redshift $z=3.8$. The observed X-ray emission in this case is not the absorbed direct radiation but a reflected component., The observed X-ray emission in this case is not the absorbed direct radiation but a reflected component. Only a guess can be made as to the power of the direct component., Only a guess can be made as to the power of the direct component. It is this direct absorbed component of such sources which is important for the spectral peak of the XRB., It is this direct absorbed component of such sources which is important for the spectral peak of the XRB. Our model predicts that more than half the sources detected in a Ms exposure with Chandra will have redshifts ranging from 2—8., Our model predicts that more than half the sources detected in a Ms exposure with Chandra will have redshifts ranging from 2–8. Most of them would have / band magnitudes exceeding 24. i.e. are optically faint according to the definition of Alexander et al (2001).," Most of them would have $I$ band magnitudes exceeding 24, i.e. are optically faint according to the definition of Alexander et al (2001)." The precise magnitudes would depend upon the star formation rate in the host galaxy., The precise magnitudes would depend upon the star formation rate in the host galaxy. If we assume that the obscured black hole growth phase coincides with the major star formation phase in the galaxy. then the star formation rate must be tens M.vr. +.," If we assume that the obscured black hole growth phase coincides with the major star formation phase in the galaxy, then the star formation rate must be tens $\Msunpyr$ ." Then the 2 (and approximately /) magnitude of the hosts will be about 24 for objects at 2—3 (e.g. Pettini et al 2001)., Then the $R$ (and approximately $I$ ) magnitude of the hosts will be about 24 for objects at $z\sim 3$ (e.g. Pettini et al 2001). Objects at +—6 will be about 1.5 mag fainter., Objects at $z\sim 6$ will be about 1.5 mag fainter. Alexander et al (2001) have 47 objects fainter than £=24 (I5 with £ 25.3). which is about half the number we predict.," Alexander et al (2001) have 47 objects fainter than $I=24$ (15 with $I>25.3$ ), which is about half the number we predict." At this stage we consider that our model remains viable. with a factor of two in number densities arrangeable by a small alteration of some of the parameters (e.g. the gas fraction and/or the gas metallicity: note that most of the sourcesare predicted to be," At this stage we consider that our model remains viable, with a factor of two in number densities arrangeable by a small alteration of some of the parameters (e.g. the gas fraction and/or the gas metallicity: note that most of the sourcesare predicted to be" showed exceptional agreement.,showed exceptional agreement. In the non-linear regime. the maximum reached by the magnetic energy in the ideal ALI simulation matches that of Malagolietal.(1996). to within," In the non-linear regime, the maximum reached by the magnetic energy in the ideal MHD simulation matches that of \citet{mala96} to within." ‘This allows us to be confident of the behaviour of in simulating the WII instability., This allows us to be confident of the behaviour of in simulating the KH instability. The inclusion of multifluic effects. introduces new length scales into the system., The inclusion of multifluid effects introduces new length scales into the system. These include the cliffusion length scales of the magnetic field due to ambipolar resistivity. and the rather computationally challenging whistler waves arixng from the Hall effect.," These include the diffusion length scales of the magnetic field due to ambipolar resistivity, and the rather computationally challenging whistler waves arising from the Hall effect." The. Hall termi is handled by using the explicit Llall Dillusion Scheme (LIDS) (O'Sullivan&Downes2006.2007).," The Hall term is handled by using the explicit Hall Diffusion Scheme (HDS) \citep{osd06, osd07}." . Although the code naturally does not resolve waves of vanishing wavelength. resolution studies were performed in. Paper Lo of both ambipolar ancl Lall-cominatecd flows and the results indicated. that a resolution of G400.200...1 is sullicient to capture the initial growth and saturation of the instability.," Although the code naturally does not resolve waves of vanishing wavelength, resolution studies were performed in Paper I of both ambipolar and Hall-dominated flows and the results indicated that a resolution of $6400\times200\times1$ is sufficient to capture the initial growth and saturation of the instability." Subsequently. the dynamics are captured at least qualitatively.," Subsequently, the dynamics are captured at least qualitatively." In order to ensure that the smallest-scale clispersive cllects were in. place when examining whether they are sullicienthy resolved. the highest values for the ambipolar ancl Hall resistivity. used in. Paper LE were implemented. for these resolution studies.," In order to ensure that the smallest-scale dispersive effects were in place when examining whether they are sufficiently resolved, the highest values for the ambipolar and Hall resistivity used in Paper I were implemented for these resolution studies." " As indicated in refsubsec:computational-parameters.. this highest. value. of ambipolar resistivity. in Paper L| is equivalent to. the value implemented. in this paper (with magnetic Itevnolds number Rey,= 28.4). while the amount of Llall resistivity implemented. in this study. is equivalent to the simulation with only moderate Llall resistivity. from. Paper Lb (with magnetic Itevnolds number Ley,= 284)."," As indicated in \\ref{subsec:computational-parameters}, this highest value of ambipolar resistivity in Paper I is equivalent to the value implemented in this paper (with magnetic Reynolds number $Re_{\rm m} = 28.4$ ), while the amount of Hall resistivity implemented in this study is equivalent to the simulation with only moderate Hall resistivity from Paper I (with magnetic Reynolds number $Re_{\rm m} = 284$ )." We ares therefore. confident that the. multilluid dvnamies resulting [rom the non-icleal cllects in these simulations are well resolved and that our. conclusions as to the physical processes occurring are well-founcdecd.," We are, therefore, confident that the multifluid dynamics resulting from the non-ideal effects in these simulations are well resolved and that our conclusions as to the physical processes occurring are well-founded." In order to observe the dillerences in the evolution of the Wl instability with the inclusion of multilluid elfects. several aspects of the evolution are examined and compared to those from simulations carried. out in ideal ALLO and in pure hiverodynamics (seeJones2011.forfurtherdetailssimulation results).," In order to observe the differences in the evolution of the KH instability with the inclusion of multifluid effects, several aspects of the evolution are examined and compared to those from simulations carried out in ideal MHD and in pure hydrodynamics \citep[see][for further details of the simulation results]{jones11}." The study of the growth of the instability is carried out through measuring the evolution of a number of parameters with time., The study of the growth of the instability is carried out through measuring the evolution of a number of parameters with time. In particular. we measure the transverse kinetic οποιον and the magnetic energy in the system where Dy is the magnitude of the magnetic field at /=0.," In particular, we measure the transverse kinetic energy and the magnetic energy in the system where $B_0$ is the magnitude of the magnetic field at $t=0$." Xny growth of ἐν is due to the growth of the instability. as the entire plasma flow is initially in the jy-direction. with only a very small perturbation in the .c- direction. Vhe WL instability leads to an interaction between the two dasnmias on either side of the initial interface.," Any growth of $\Ek{x}$ is due to the growth of the instability, as the entire plasma flow is initially in the $y$ -direction, with only a very small perturbation in the $x$ -direction, The KH instability leads to an interaction between the two plasmas on either side of the initial interface." " In. particular. in ideal. AULD. the plasmas are seen to wincd-up. leading to he ""Ixelvin's cats eve” vortex."," In particular, in ideal MHD, the plasmas are seen to wind-up, leading to the “Kelvin's cat's eye” vortex." The inclusion of multilluid cllects can alfect. this evolution. in a number of wavs., The inclusion of multifluid effects can affect this evolution in a number of ways. Llowever. it: can be seen that this multilluid set-up does not event the development of the classic vortex in the neutral ΜΗ (see Fig. 12).," However, it can be seen that this multifluid set-up does not prevent the development of the classic vortex in the neutral fluid (see Fig. \ref{weak_32wide_NI3_v_80.eps}) )." As described. in Paper 1. analysis of the transverse kinetic energy in the svstem allows for study of the growth rate of the instabilitv.," As described in Paper I, analysis of the transverse kinetic energy in the system allows for study of the growth rate of the instability." Figure 2. plots the growth. of the kinetic energy resulting from the instability in the ideal and ΜπΕις MED. cases. as well as the hyvdrodynamic case.," Figure \ref{nonideal_logKEx} plots the growth of the kinetic energy resulting from the instability in the ideal and multifluid MHD cases, as well as the hydrodynamic case." Lt can be seen that the linear growth of the instability clilfers very little with the inclusion of multilluid etfects., It can be seen that the linear growth of the instability differs very little with the inclusion of multifluid effects. Le will be seen that the instability is developing in a way very dilferent to the ideal ΑΔΗΠΟ case. vet the linear growth rates are found to be within of each other.," It will be seen that the instability is developing in a way very different to the ideal MHD case, yet the linear growth rates are found to be within of each other." The stepping iu time of positious x aud velocities v is accomplished with a staucarcl second order leapfrog integration in comoving coordinates. the cosmological model determining the scale [actor a{/): Here a. Hz àfa. aud the gravitational potential ® are determined at time !/+iN.,"The stepping in time of positions ${\bf x}$ and velocities ${\bf v}$ is accomplished with a standard second order leapfrog integration in comoving coordinates, the cosmological model determining the scale factor $a(t)$ : Here $a$, $H\equiv \dot{a}/a$ , and the gravitational potential $\Phi$ are determined at time $t+\onehalf \Delta t$." One advautage of the TPAL approach is that it allows the use of multiple time steps., One advantage of the TPM approach is that it allows the use of multiple time steps. Tree particles are required to take at least two steps per PM step. but each particle las au iucdividual time step so that finer time resolutiou cau be used if required.," Tree particles are required to take at least two steps per PM step, but each particle has an individual time step so that finer time resolution can be used if required." Particles are arranged in au hierarchy oL time bins differing by a factor of two. in the manner of Heruquist&Ixatz(1980): where Mpa; is the PM time step auc the integer s>1.," Particles are arranged in an hierarchy of time bins differing by a factor of two, in the manner of \citet{HernKatz89}: where $\Delta t_{PM}$ is the PM time step and the integer $s\geq 1$." Iu a seuse TPM operates along the sale lines as a tree code. except that the particles in the s=0 time step biu are haudlect differently from the rest.," In a sense TPM operates along the same lines as a tree code, except that the particles in the $s=0$ time step bin are handled differently from the rest." A cdiagramauatic representation of the time stepping is shown in Fie. for the case when all tree particles are in the longest time step bin. s= 1.," A diagrammatic representation of the time stepping is shown in $.$ \\ref{fig:tstep} for the case when all tree particles are in the longest time step bin, $s=1$ ." Beeiunine at time /. the PM particle positions are moved forward to midstep (eq.," Beginning at time $t$, the PM particle positions are moved forward to midstep (eq." [laa] with A’=Af py)., \ref{eqn:leapfrog}a a] with $\Delta t =\Delta t_{PM}$ ). The tidal poteutial is then [ouud. aud the tree particles are evolved [forward one full step with Al=Mpy/2.," The tidal potential is then found, and the tree particles are evolved forward one full step with $\Delta t =\Delta t_{PM}/2$." The PAL potential is updated (eq., The PM potential is updated (eq. [Ibb]). and for a second time the tree particles are evolved for one full step. to time /+Mpa;.," \ref{eqn:leapfrog}b b]), and for a second time the tree particles are evolved for one full step, to time $t+\Delta t_{PM}$." Finally. the PM particle velocities aud. positions are updated to the end of the step (eq.," Finally, the PM particle velocities and positions are updated to the end of the step (eq." [Lec-d])., \ref{eqn:leapfrog}c c-d]). To repeat the TPMI algoritlim in more detail: Identify tree regious aud the particles in each region., To repeat the TPM algorithm in more detail: Identify tree regions and the particles in each region. This is doue by ideutifviug PM cells above a given density threshokl. described iu refsec:xdomdec..," This is done by identifying PM cells above a given density threshold, described in \\ref{sec:domdec}." Adjoiniug cells are then grouped into isolated tree regious. as described inBOX.," Adjoining cells are then grouped into isolated tree regions, as described in." Push PM particles to midstep (eq., Push PM particles to midstep (eq. [1aa])., \ref{eqn:leapfrog}a a]). " Fiudthe tidal potential 9.,; for each tree region.", Find the tidal potential $\Phi_{ext}$ for each tree region. First the total potential is computedonthe evid in the staudard PAL inanner., First the total potential is computedonthe grid in the standard PM manner. Then for each of thetree regions. a small portion of the grid," Then for each of thetree regions, a small portion of the grid" grealer is 1e abuudance of heavies relative to light s-process elemeuts.,greater is the abundance of heavies relative to light $s$ -process elements. Busso et al. (, Busso et al. ( 2001) used the clistribtion of the ratio of heavy s-process celements (lis) to the light s-process (1s) elements with respec to metallicity to characterize various parameters of neutron exposures curing the third dredgeup pase in ACB stars eg.,2001) used the distribution of the ratio of heavy $s$ -process celements (hs) to the light $s$ -process (ls) elements with respect to metallicity to characterize various parameters of neutron exposures during the third dredgeup phase in AGB stars eg. mass of PC pocket in the inter shell regions., mass of $^{13}$ C pocket in the inter shell regions. Reddy et al. (, Reddy et al. ( 2002) showed tha the variation ofthe [hs/Is] with respect to metallicity in post -AGDB stars (hat went through thi«d dredgeup) is characterized by a model ST/1.5 of Busso et al. (,2002) showed that the variation of the [hs/ls] with respect to metallicity in post -AGB stars (that went through third dredgeup) is characterized by a model ST/1.5 of Busso et al. ( 2001).,2001). A plot of [Y/M] and [Zr/M] versus [M] for RCBs and EHes (ligure | ) shows that the enhanucemelts are positive aud both show a similar rauge in their abuucdauces., A plot of [Y/M] and [Zr/M] versus [M] for RCBs and EHes (figure 4 ) shows that the enhancements are positive and both show a similar range in their abundances. We compared the run of the ratio of [Is/hs] for RCBs ancl EHes with respect to the metallicity parameter [M]., We compared the run of the ratio of [ls/hs] for RCBs and EHes with respect to the metallicity parameter [M]. The estimates for EHes are based ou the upper limits for the heavy. s-process elements aud. includes data from our ongoing analysis of the HST UV spectra., The estimates for EHes are based on the upper limits for the heavy $s$ -process elements and includes data from our ongoing analysis of the $HST$ UV spectra. Estimates of AAqr aud the born again eiant. Sakurai's object (during May - Oct 1996) are also included for comparison.," Estimates of Aqr and the born again giant, Sakurai's object (during May - Oct 1996) are also included for comparison." Both the groups RCBs and EHes blend together emphasizing the similarity in their I5/hs ratios., Both the groups RCBs and EHes blend together emphasizing the similarity in their ls/hs ratios. Figure 5 shows a comparison of the trend of [ls/hs] in RCB aud EHe stars along with that shown by post- AGB stars (Redcly et al., Figure 5 shows a comparison of the trend of [ls/hs] in RCB and EHe stars along with that shown by post- AGB stars (Reddy et al. 2002) aud the Busso et al’s (2001) model ST/1.5., 2002) and the Busso et al's (2001) model ST/1.5. It is, It is inclination. 2 stellar noise parameters (1 noise profile with a slope fixed at 2).,"inclination, 2 stellar noise parameters (1 noise profile with a slope fixed at 2)." In Fig., In Fig. | we present the global fitting of the power spectrum used by BO9. obtained with the MLE for their scenario | (see also Sect. 5.2)).," \ref{fig_MLE_181420} we present the global fitting of the power spectrum used by B09, obtained with the MLE for their scenario 1 (see also Sect. \ref{results}) )." The input parameters are close to the estimated values obtained in BOO., The input parameters are close to the estimated values obtained in B09. It arises that when the signal-to-noise ratio of the power spectrum ts too low. the MLE converges to a manifestly incorrect solution.," It arises that when the signal-to-noise ratio of the power spectrum is too low, the MLE converges to a manifestly incorrect solution." In BOS. the mode widths and heights of the external modes (lower and higher frequency) were rejected. in order to keep only the reliable fit values obtained with 10 overtones.," In B09, the mode widths and heights of the external modes (lower and higher frequency) were rejected, in order to keep only the reliable fit values obtained with 10 overtones." When the mode height becomes too low. the estimator tends to exactly fit some individual spikes of the power spectrum. that 15. extremely high and narrow (very apparent in the frequency range [1100-1300] uHz).," When the mode height becomes too low, the estimator tends to exactly fit some individual spikes of the power spectrum, that is, extremely high and narrow (very apparent in the frequency range [1100-1300] µHz)." " Hereafter we speak of ""Dirac-Iike"" convergence.", Hereafter we speak of “Dirac-like” convergence. Such a behavior ts not surprising since the MLE consists of maximizing the similarity between the data and the model., Such a behavior is not surprising since the MLE consists of maximizing the similarity between the data and the model. The Bayesian approach allows us to avoid such solutions., The Bayesian approach allows us to avoid such solutions. Bayesian methods have been widely used in the deconvolution of astronomical images since the time of the restoration project for HST (?).. and also in cosmology (e.g. ?)) in order to fully exploit available reliable prior knowledge.," Bayesian methods have been widely used in the deconvolution of astronomical images since the time of the restoration project for HST \citep{Bertero_95}, and also in cosmology (e.g. \citealt{Trotta_08}) ) in order to fully exploit available reliable prior knowledge." Bayesian reasoning often arises unconsciously: e.g. in the solar case. if the MLE estimator gives a value of the rotational splitting near 0.82 Hz instead of =0.41 μΗΖ and an inclination of 0° instead of =90°. we reject that solution because we know it is wrong. not on the basis of a statistical criterion.," Bayesian reasoning often arises unconsciously: e.g. in the solar case, if the MLE estimator gives a value of the rotational splitting near 0.82 $\mu$ Hz instead of $\simeq0.41\ \mu$ Hz and an inclination of $^\circ$ instead of $\simeq90^\circ$, we reject that solution because we know it is wrong, not on the basis of a statistical criterion." The same occurred in BOO when eliminating the estimates of the external mode heights and widths., The same occurred in B09 when eliminating the estimates of the external mode heights and widths. They seemed wrong although they were statistically correct. since they occurred at a local minimum of the parameter space.," They seemed wrong although they were statistically correct, since they occurred at a local minimum of the parameter space." " The Bayesiar approach consists of using all of the prior information ""T"" that we have.", The Bayesian approach consists of using all of the prior information “I” that we have. Bayes theorem can be expressed as: The Bayesian approach. compared with MLE. modifies the likelihood Ομ].D into a posterior distribution PGUD.D) which takes into account the prior information PGUD.," Bayes theorem can be expressed as: The Bayesian approach, compared with MLE, modifies the likelihood $P({\rm D} | \lambda,\rm{I})$ into a posterior distribution $P(\lambda | {\rm D,I})$ which takes into account the prior information $P(\lambda |{\rm I})$." The P(D|D is a normalization term., The $P({\rm D | I})$ is a normalization term. In this paper we consider only the simplest way of applying the Bayesian approach. ie. the maximum a posteriori estimator (MAP): Note the normalization term Is not included and will not be taken into account in the following.," In this paper we consider only the simplest way of applying the Bayesian approach, i.e. the maximum a posteriori estimator (MAP): Note the normalization term is not included and will not be taken into account in the following." Often. the prior is written as a Gaussian function centered around the expected value of the free parameter: Therefore. the function to be minimized can be expressed as: The AAP MAPtsis the crudest Bayesian approach. but it allows usu to improve the fits noticeably.," Often, the prior is written as a Gaussian function centered around the expected value of the free parameter: Therefore, the function to be minimized can be expressed as: The MAP is the crudest Bayesian approach, but it allows us to improve the fits noticeably." In this section. we discuss the importance of carefully selecting the priors.," In this section, we discuss the importance of carefully selecting the priors." Indeed. as can be anticipated when looking at Eq. 5..," Indeed, as can be anticipated when looking at Eq. \ref{Eq_MAP}," putting a stronger prior (1. e. narrow variance) may introduce à bias: the risk is to obtain exactly the value that we were expecting., putting a stronger prior (i. e. narrow variance) may introduce a bias: the risk is to obtain exactly the value that we were expecting. As an example. Fig.," As an example, Fig." 2. (top) presents a simulation of the power spectrum of a single overtone featuring degrees £6= [0.2]. with =3. which corresponds to the maximum SNR of HD 181420 (B09).," \ref{fig_simu_MAP} (top) presents a simulation of the power spectrum of a single overtone featuring degrees $\ell = [0,2]$ , with $\ =\ 3$, which corresponds to the maximum SNR of HD 181420 (B09)." We have tested the MAP fitting procedure by using a set of priors of the same value but with linearly increasing variance., We have tested the MAP fitting procedure by using a set of priors of the same value but with linearly increasing variance. The only free parameter that we have kept is the splitting frequency., The only free parameter that we have kept is the splitting frequency. Fig., Fig. 2. (bottom) shows the value of the estimated splitting frequency as a function of the prior variance., \ref{fig_simu_MAP} (bottom) shows the value of the estimated splitting frequency as a function of the prior variance. " The ""true"" splitting corresponds to the value used to build the noisy power spectrum. while the “prior” splitting ts the value that we think to be true and the “MLE” splitting i5 the value obtained with the MLE."," The “true” splitting corresponds to the value used to build the noisy power spectrum, while the “prior” splitting is the value that we think to be true and the “MLE” splitting is the value obtained with the MLE." When oie tends to 0. the output estimate tends to the prior value. whereas as Cui. tends to infinity the estimated output tends to the MLE estimate.," When $\sigma\ind{prior}^2$ tends to 0, the output estimate tends to the prior value, whereas as $\sigma\ind{{prior}}^2$ tends to infinity the estimated output tends to the MLE estimate." " So. the a priori probability does not help us find theÉ""true"" value when the prior is wrong."," So, the a priori probability does not help us find theÊ“true” value when the prior is wrong." It just tends towards the prior value as a function of the prior's strength., It just tends towards the prior value as a function of the prior's strength. In other terms. the MAP does not push the solution to converge towards the local minimum that we may expect to be," In other terms, the MAP does not push the solution to converge towards the local minimum that we may expect to be" France. and the VizieR online database (see Ochsenbeinοἱal(2000))).,"France, and the VizieR online database (see \citet{vizier}) )." We have also made extensive use of information aud code from Pressetal.(1992)., We have also made extensive use of information and code from \citet{nrc}. . We have used digitized images [rom the Palomar Sky Survey (available from form)). which were produced at the Space Telescope Science Institute under U.S. Government erant NAC? W-2166.," We have used digitized images from the Palomar Sky Survey (available from ), which were produced at the Space Telescope Science Institute under U.S. Government grant NAG W-2166." The images ol these surveys are based ou photographic data obtained using the Oschin Schinidt Telescope on Palomar Mountain aud the Ul Schinidt Telescope., The images of these surveys are based on photographic data obtained using the Oschin Schmidt Telescope on Palomar Mountain and the UK Schmidt Telescope. Facilities:, Facilities: The lack of color eradieuts can also be demonstrated by measmiue the difference iu colors between the outer reeious of the LAICCs. which does not include their cores. and thei core colors.,"The lack of color gradients can also be demonstrated by measuring the difference in colors between the outer regions of the LMCGs, which does not include their cores, and their core colors." " We apply this test bv dividing ealaxies into their inner parts (p= 2”)) and the rest of the ealaxics’ light at r >2"".", We apply this test by dividing galaxies into their inner parts $r=$ ) and the rest of the galaxies' light at r $>2$. . The results of this comparison are shown by the solid triangles ou Figure 7., The results of this comparison are shown by the solid triangles on Figure 7. Again. we find few Perseus LAICCs with siguificaut. color eradieuts between the ceuters and outer regions.," Again, we find few Perseus LMCGs with significant color gradients between the centers and outer regions." The few LAICCs that do show significant ditfereuces could be galaxies with stellar populations at different ages and metallicities iu their cores and cuvelopes., The few LMCGs that do show significant differences could be galaxies with stellar populations at different ages and metallicities in their cores and envelopes. Some non-aumcleated LAICCs also have red cores. possibly the result of dust. very old stellar populations. or accreted elobular clusters (Lotz ct al.," Some non-nucleated LMCGs also have red cores, possibly the result of dust, very old stellar populations, or accreted globular clusters (Lotz et al." 2001)., 2001). A few dEs in the Virgo cluster also contain blue uuclei. but the majority of nucleated objects have a central color simular to their host ealaxics (Durrell 1997).," A few dEs in the Virgo cluster also contain blue nuclei, but the majority of nucleated objects have a central color similar to their host galaxies (Durrell 1997)." Further observations. especially spectroscopy. will be necessary to determine if recent star formation could have produced the bluer nuclei.," Further observations, especially spectroscopy, will be necessary to determine if recent star formation could have produced the bluer nuclei." The carly-type dwarf to giant ratio (EDCR: Secker ILuvis 1996: Phillipps et al., The early-type dwarf to giant ratio (EDGR; Secker Harris 1996; Phillipps et al. L998) provides a quantitative measure of the form of the huuiunositv function. where ealaxies are selected both by Iuninosity aud morphology (Driver. Couch. Phillipps 1998).," 1998) provides a quantitative measure of the form of the luminosity function, where galaxies are selected both by luminosity and morphology (Driver, Couch, Phillipps 1998)." Bi our 173 arcmin? survey of the Perseus cluster. we fud 160 candidate carly-type duit elliptical-like LAICCGs with Mp<11 (Paper II). eiving a surface jnunber density of —1 ? or ~2000 carky-type LMCCs 7.," In our 173 $^{2}$ survey of the Perseus cluster, we find 160 candidate early-type dwarf elliptical-like LMCGs with $_{\rm B} < -11$ (Paper II), giving a surface number density of $\sim$ 1 $^{-2}$ or $\sim$ 2000 early-type LMCGs $^{-2}$." The eiaut galaxy. deusitv is ~260 eiuts 2., The giant galaxy density is $\sim$ 260 giants $^{-2}$. This eives an EDGR ratio of ~8. which is lower than the Virgo or Coma value at the brighter magnitude luit Mi=12.5 (e.g. Ferguson Saudage 1991: Secker ILhbuxis 1996).," This gives an EDGR ratio of $\sim$ 8, which is lower than the Virgo or Coma value at the brighter magnitude limit $_{\rm B} = -12.5$ (e.g., Ferguson Sandage 1991; Secker Harris 1996)." For LMCCs with Mp«12.5. we find a sinface deusity of ~0.5 7 or 1000 7.," For LMCGs with $_{\rm B} < -12.5$, we find a surface density of $\sim$ 0.5 $^{-2}$ or $\sim$ 1000 $^{-2}$." This eves an EDGR ratio of ~ Ll. compared with the values 9.[ and 9.3 computed in the Coma aud Vireo clusters (Seeker Tlarris 1996).," This gives an EDGR ratio of $\sim$ 4, compared with the values 9.4 and 9.3 computed in the Coma and Virgo clusters (Secker Harris 1996)." Table 2 lists the values of the EDGR computed for Perseus aud values frou the Vireo and Coma clusters., Table 2 lists the values of the EDGR computed for Perseus and values from the Virgo and Coma clusters. This result sueecsts that the EDGR ratio at the ceuter of the Perseus cluster is lower than published values for the less dense Virgo cluster and integrated value for the Coma cluster (Ferguson Saudage 1991: Secker Παντ]ς 1996)., This result suggests that the EDGR ratio at the center of the Perseus cluster is lower than published values for the less dense Virgo cluster and integrated value for the Coma cluster (Ferguson Sandage 1991; Secker Harris 1996). The EDGR ratio was fouud by Fergusou Saudace (1991) to correlate with galaxy eroup density. with denser eroups displaving higher EDCRs.," The EDGR ratio was found by Ferguson Sandage (1991) to correlate with galaxy group density, with denser groups displaying higher EDGRs." Other studies suggest au opposite trend for rich clusters. such that denser cluster reeious contain lower EDGR ratios (Phillipps ct al.," Other studies suggest an opposite trend for rich clusters, such that denser cluster regions contain lower EDGR ratios (Phillipps et al." 1998)., 1998). A reduced surface deusitv of LMCCs near the center of a rich cluster has been noted before (Thompson Gregory 1993: Driver et al., A reduced surface density of LMCGs near the center of a rich cluster has been noted before (Thompson Gregory 1993; Driver et al. 1998: Adami et al., 1998; Adami et al. 2000). and is possibly the result of galaxw destruction rather than initial couclitious (Conselice 2002: 813).," 2000), and is possibly the result of galaxy destruction rather than initial conditions (Conselice 2002; 4.3)." As pointed out by Thompson Creeory (1993) in the Coma cluster. the processes creating LAICGs from stripping could become so efficient in the cores of rich clusters that many LAICCs are destroved. or disrupted to the point where they are too faint to be detected.," As pointed out by Thompson Gregory (1993) in the Coma cluster, the processes creating LMCGs from stripping could become so efficient in the cores of rich clusters that many LMCGs are destroyed, or disrupted to the point where they are too faint to be detected." Iu Paper II e argued that for Perseus LAICCGs fainter than Mp.~15. there is anu increase in the scatter about the universal linear C'MB established for eiaut ellipticals (Bower et al.," In Paper II we argued that for Perseus LMCGs fainter than $_{\rm B} \sim -15$, there is an increase in the scatter about the universal linear CMR established for giant ellipticals (Bower et al." 1992) (sce Figure 2)., 1992) (see Figure 2). This increase cannot be accounted for by photometric errors for svstenis more luuimous than Mp~12.5 (Paper ID., This increase cannot be accounted for by photometric errors for systems more luminous than $_{{\rm B}} \sim -12.5$ (Paper II). Evidence that faint cluster dE galaxies scatter sienificautly frou a linear CAIR have been available for some time (c.e.. Caldwell Bothun 1987). but tlis has vet to be fully characterized. explained. or appreciated.," Evidence that faint cluster dE galaxies scatter significantly from a linear CMR have been available for some time (e.g., Caldwell Bothun 1987), but this has yet to be fully characterized, explained, or appreciated." To uuderstaud and characterize the galaxies that make up this scatter. we lait our detailed analysis to the sample of early-type Perseus LAICCs with Mp<—12.5 listed in Table 1 aud displaved in Figure 1.," To understand and characterize the galaxies that make up this scatter, we limit our detailed analysis to the sample of early-type Perseus LMCGs with $_{\rm B} < -12.5$ listed in Table 1 and displayed in Figure 1." The origin of the relationship between the colors and magnitudes of eiut cluster elliptical galaxies has been debated since its initial characterization by Sandage Visvanathan (1978). but it is now generally regarded as a relatiouship between a galaxvs mass (traced by its magnitude) aud metallicity (traced by its color). with the stars in cach galaxy at similarly old ages (Arimoto Yoshii 1987: Bower ct al.," The origin of the relationship between the colors and magnitudes of giant cluster elliptical galaxies has been debated since its initial characterization by Sandage Visvanathan (1978), but it is now generally regarded as a relationship between a galaxy's mass (traced by its magnitude) and metallicity (traced by its color), with the stars in each galaxy at similarly old ages (Arimoto Yoshii 1987; Bower et al." 1992)., 1992). This idea is supported through studies of cluster galaxies at higher redshifts. where the scatter in the coloranaguitude relationship remains low (Ellis et al.," This idea is supported through studies of cluster galaxies at higher redshifts, where the scatter in the color-magnitude relationship remains low (Ellis et al." 1997: Stautord. Eisenhardt Dickinson 1997).," 1997; Stanford, Eisenhardt Dickinson 1997)." Metallicity as a driver of cluster ealaxy colors is also au inherent aspect of various formation models (Arimoto Yoshii 1987: EKKauffiuauun Charlot 1998)., Metallicity as a driver of cluster galaxy colors is also an inherent aspect of various formation models (Arimoto Yoshii 1987; Kauffmann Charlot 1998). Below we demonstrate what our broadband UBR colors tell us about the nature of the stellar populations in LAICCs: specifically we demonstrate that the red colors of some LAICGs πρίν that they must be particularly metal eunched and that this enhanced eurichumenut is at least partially the cause of the larec scatter of these galaxies from the color-anaguitude relationship., Below we demonstrate what our broadband UBR colors tell us about the nature of the stellar populations in LMCGs; specifically we demonstrate that the red colors of some LMCGs imply that they must be particularly metal enriched and that this enhanced enrichment is at least partially the cause of the large scatter of these galaxies from the color-magnitude relationship. As we argue in 83.2 the internal colors of Perseus LAICGs are nearly homogeneous. such that we can o a first approximation consider their stars as single stellar populations (SSPs). to place coustraiuts on their ages. inetallicities and stellar masses.," As we argue in 3.2 the internal colors of Perseus LMCGs are nearly homogeneous, such that we can to a first approximation consider their stars as single stellar populations (SSPs), to place constraints on their ages, metallicities and stellar masses." We investigate he properties of these stellar populations by comparing spectral enerey distributions of LMCGs to the stellar »opulatiou svuthesis models of Worthev (199£). iucludiug he Padova isochrone library (Bertelli et al.," We investigate the properties of these stellar populations by comparing spectral energy distributions of LMCGs to the stellar population synthesis models of Worthey (1994), including the Padova isochrone library (Bertelli et al." 199E)., 1994). Figure 5 shows model (UC.B))(B.R)y color-color racks at three different ages (7=18.12.5 Cis). plotted as a function of metallicity. with cach panel showing a different age. alone with the Perseus cluster data.," Figure 8 shows model $(U-B)_{0} - (B-R)_{0}$ color-color tracks at three different ages $\tau = 18, 12, 5$ Gyrs), plotted as a function of metallicity, with each panel showing a different age, along with the Perseus cluster data." All ealaxies fall along. or close to these Worthev (1991) isochrones.," All galaxies fall along, or close to these Worthey (1994) isochrones." If Perseus cluster galaxies contain stellar populatious formed at roughly the same time. aud are old. as clusters ellipticals are thought to be (es. Iuutschuer Davies 1998: Trager et al.," If Perseus cluster galaxies contain stellar populations formed at roughly the same time, and are old, as clusters ellipticals are thought to be (e.g., Kuntschner Davies 1998; Trager et al." 2000). then Perseus. eiaut ellipticals have near solu metallicity stellar populations. while the Perseus LALCGs consist of stars with a range of lower metallicities.," 2000), then Perseus giant ellipticals have near solar metallicity stellar populations, while the Perseus LMCGs consist of stars with a range of lower metallicities." Figure 9 shows corresponding color-color diagrams of, Figure 9 shows corresponding color-color diagrams of Ounce the velocity exceeds the local souud of speed in the halo. shocks are created which quickly act to mix the bubble with its stwroundineg.,"Once the velocity exceeds the local sound of speed in the halo, shocks are created which quickly act to mix the bubble with its surrounding." In the following calculation the velocity is not allowed to exceed the speed of sound. Cος. and in that case fp is reduced until εξος πι(17)...," In the following calculation the velocity is not allowed to exceed the speed of sound, $c_{\rm s}$, and in that case $H_{\rm P}$ is reduced until $v=c_{\rm s}$ in." A model is a model with arbitrary high L. so effectively the bubbles always accelerate until the speed. of sound. at which time they are broken aud mixed.," A model is a model with arbitrary high $L$, so effectively the bubbles always accelerate until the speed of sound, at which time they are broken and mixed." The Flux of euergv per τα surface per unit mass ls:Fehmporateradicuts which is determined by the halo profile from the simulation at each time. aud the mixing leneth L.," The Flux of energy per unit surface per unit mass is:, which is determined by the halo profile from the simulation at each time, and the mixing length $L$." Cp is the coustaut pressure heat capacity aud is related to py Cpοαμ]. A numerical solution of the mixing leneth model requires evaluation of the incomime aud outeoime Huxes from the boundaries of cach racial shell., $C_{\rm P}$ is the constant pressure heat capacity and is related to $\hat{\mu}$ by $C_{\rm P}=5/(2\hat{\mu}).$ A numerical solution of the mixing length model requires evaluation of the incoming and outgoing fluxes from the boundaries of each radial shell. The Huxes depend on the temperature eradicut between each shell aud the oues directly below and above it. and interpolation of thermodvuamic properties frou he shell centres to the shells edges is required.," The fluxes depend on the temperature gradient between each shell and the ones directly below and above it, and interpolation of thermodynamic properties from the shell centres to the shell's edges is required." A solution using an explicit ummerical scheme (ith the Huxes determined at the beeimning of cach timestep) requires extremely suall timesteps to avoid negative eniperafures. so an dHuplieit scheme which solves sinultaneouslv for all the temperatures aud fluxes at he cud of cach timestep in cach convective area was nupleiieuted.," A solution using an explicit numerical scheme (with the fluxes determined at the beginning of each timestep) requires extremely small timesteps to avoid negative temperatures, so an implicit scheme which solves simultaneously for all the temperatures and fluxes at the end of each timestep in each convective area was implemented." This is done by inversion of the threc-diagonal matrix which is obtained by discretization of(18)., This is done by inversion of the three-diagonal matrix which is obtained by discretization of. . Tn the coutext of the chuup heating discussed. iu this paper. it should be emphasized that the couvection is not between the cold gas iu the clamps aud the hot surrounding.," In the context of the clump heating discussed in this paper, it should be emphasized that the convection is not between the cold gas in the clumps and the hot surrounding." It is only within the hot component. aud is the result of heating aud cooling of that component.," It is only within the hot component, and is the result of heating and cooling of that component." The convection model assmues hear perturbations within a single sas phase which separates mto two phases (hot buovanut bubbles. and cold sinking gas).," The convection model assumes linear perturbations within a single gas phase which separates into two phases (hot buoyant bubbles, and cold sinking gas)." The propagation of clumps. which have a typical over-densities of <1000 is followed explicitly using the Xocesses described in - 52.," The propagation of clumps, which have a typical over-densities of $\gsim 1000$ is followed explicitly using the processes described in - ." 11... The ICAL is mülkdlv magnetized. with the non-hermal magnetic pressure contributing at most 104 of the total pressure (7).," The ICM is mildly magnetized, with the non-thermal magnetic pressure contributing at most $10\%$ of the total pressure \citep{churazov08}." This effect could lead to jieat-flux buovaut iustabilitv (Πο2) even when he eutropy profile is monotonically increasing provided here is a temperature inversion near the core (1fdrc ).," This effect could lead to heat-flux buoyant instability \citep[HBI; ][]{parrish09} even when the entropy profile is monotonically increasing provided there is a temperature inversion near the core $dT/dr>0$ )." These instabilities act to align the magnetic fields perpendicular to the temperature eradicut. iu a inanner that suppresses further conduction (?)..," These instabilities act to align the magnetic fields perpendicular to the temperature gradient, in a manner that suppresses further conduction \citep{parrish09}." Couvective motions are also somewhat suppressed even for inateriid that is) lydrodvuamically couvectively unstable (dsfdr«0)., Convective motions are also somewhat suppressed even for material that is hydrodynamically convectively unstable $ds/dr<0$ ). Future work could. aud. should. use a revised mixing leneth theory for which the driver of convection is temperature inversion rather than entropy inversion.," Future work could, and should, use a revised mixing length theory for which the driver of convection is temperature inversion rather than entropy inversion." Such a model would need to take to account the saturation of the instability as the magnetic fields align themselves. baring in mind that heating by clumps is closely related. to turbulence driving by chumps.," Such a model would need to take into account the saturation of the instability as the magnetic fields align themselves, baring in mind that heating by clumps is closely related to turbulence driving by clumps." Also. the largely reduced convection streneth that is cluded to im (??) must be evaluated.," Also, the largely reduced convection strength that is eluded to in \citep{parrish08b, parrish09} must be evaluated." Ultimately. the convection here is invoked to smooth over local instabilities for which. at least according to the spherical calculations. steep of more than an order of maeuitude im use and cutropy form at the spatial resolution lit (thin red line of 3)).," Ultimately, the convection here is invoked to smooth over local instabilities for which, at least according to the spherical calculations, steep gradients of more than an order of magnitude in temperature and entropy form at the spatial resolution limit (thin red line of )." These extreme eradicuts (that are also present at edges of radio bubbles in clusters) are far from linear perturbations. aud the validity of the linear analysis of the various convection prescriptions is highly questionable.," These extreme gradients (that are also present at edges of radio bubbles in clusters) are far from linear perturbations, and the validity of the linear analysis of the various convection prescriptions is highly questionable." Tn the current implementation. when clumps are destroved. their mass is added to the hot component iustautlv.," In the current implementation, when clumps are destroyed, their mass is added to the hot component instantly." In realitv. the process of IKIT fragmentation. followed bv small scale evaporation aud conductiou of the debris will vield a auultiphased gas. with au effective entropy aud temperature which is between the values of the hot and cold phases.," In reality, the process of KH fragmentation, followed by small scale evaporation and conduction of the debris will yield a multiphased gas, with an effective entropy and temperature which is between the values of the hot and cold phases." As will be shown ater (81)). the chump density and chump destruction rate increase towards the ceutre so effective cooler aud ower cutropy values are expected there.," As will be shown later ), the clump density and clump destruction rate increase towards the centre so effective cooler and lower entropy values are expected there." The radiative signature of eas heating through all the temperatures j)etween LOL to the cluster ambicut gas temperature of ~3«101 is expected to be significantly different roni that of radiative cooling since it is governed bv ieating processes (enmissionspectrumfromheatinggas.in ??)..," The radiative signature of gas heating through all the temperatures between $10^4K$ to the cluster ambient gas temperature of $\sim 3\times 10^7K$ is expected to be significantly different from that of radiative cooling since it is governed by heating processes \citep[emission spectrum from heating gas, albeit by other heating mechanisms have been studies in][]{voit97,oh04}." A framework of heating aud cooling processes ini avers between hot aud cold inedia have beeu proposed wn," A framework of heating and cooling processes in layers between hot and cold media have been proposed by \citet{begelman90,gnat10}." " The observational signature of chump break up would require detailed 3D simulation of chip interactions with cluster core gas. and imultiphased modeling of the radiative signature during the heating process, and is bevoud the scope of this work."," The observational signature of clump break up would require detailed 3D simulation of clump interactions with cluster core gas, and multiphased modeling of the radiative signature during the heating process, and is beyond the scope of this work." Iustead. we will plot below the mass weighted cutropy aud temperature of the two components.," Instead, we will plot below the mass weighted entropy and temperature of the two components." This is a lower lait for the observed cutropy and temperature as the chumps contribution to the huninositv. particularly at N-rav wavelength. is probably small.," This is a lower limit for the observed entropy and temperature as the clumps' contribution to the luminosity, particularly at X-ray wavelength, is probably small." Plivsically. it correspouds to the thermodvuauiuc properties expected in the event of full misxine between the cold aud hot phase.," Physically, it corresponds to the thermodynamic properties expected in the event of full mixing between the cold and hot phase." The actual temperature and profileexpected from the multiphase gas is thus bracketed between the hot only component. and the mass weighting between," The actual temperature and profileexpected from the multiphase gas is thus bracketed between the hot only component, and the mass weighting between" maximum at the time of core collapse and decreases again in the post-core-collapse phase.,maximum at the time of core collapse and decreases again in the post-core-collapse phase. " However, the ionization rate in all multiple-component models is always larger than that in the reference system."," However, the ionization rate in all multiple-component models is always larger than that in the reference system." " Fig.2 shows the time evolution of the volume-integrated ionization rate for SG (Asc(a, t)) and FG (Arc(a,t)) binaries, for a=5x10?R;/N."," \ref{fig:volumeionrate} shows the time evolution of the volume-integrated ionization rate for SG $\Delta_{SG}(a,t)$ ) and FG $\Delta_{FG}(a,t)$ ) binaries, for $a=5\times 10^{-2} R_t/N$." SG binaries are preferentially located in the cluster inner regions and so are disrupted more efficiently than FG binaries., SG binaries are preferentially located in the cluster inner regions and so are disrupted more efficiently than FG binaries. " The time evolution of Asc(a,t)/Ara(a,t) is plotted in Fig.3.."," The time evolution of $\Delta_{SG}(a,t)/\Delta_{FG}(a,t)$ is plotted in \ref{fig:ratiorate}." " As the cluster evolves and the two populations tend to mix, Asc(a,t)/Arc(a,t) tends to decrease."," As the cluster evolves and the two populations tend to mix, $\Delta_{SG}(a,t)/\Delta_{FG}(a,t)$ tends to decrease." " However, the mixing is not complete by the end of the time interval spanned by this study (t~ 40trn,sq(0)), so the SG binary disruption rate is always larger than that of FG binaries."," However, the mixing is not complete by the end of the time interval spanned by this study $t\sim 40 t_{rh,SG}(0)$ ), so the SG binary disruption rate is always larger than that of FG binaries." Fig., Fig. " 4 plots N,,sc(a)/N»,rc(a), calculated at the end of each simulation, as a function of binary semi-major axis."," \ref{fig:numberratio} plots $N_{b,SG}(a)/N_{b,FG}(a)$, calculated at the end of each simulation, as a function of binary semi-major axis." " In all cases, SG binary disruption is significantly enhanced compared to that of the FG binary population."," In all cases, SG binary disruption is significantly enhanced compared to that of the FG binary population." Fig., Fig. " 5 shows the ratios of the final to the initial number of binaries for the SG and the FG population, Ni,sc(a)/Ns,(a)ini and Nirc(a)/Nw,(a)in;«, and illustrates the extent of the binary disruption in our multiple population clusters, as well as the preferential disruption of SG binaries."," \ref{fig:numberbinaries} shows the ratios of the final to the initial number of binaries for the SG and the FG population, $N_{b,SG}(a)/N_{b,SG}(a)_{init}$ and $N_{b,FG}(a)/N_{b,FG}(a)_{init}$, and illustrates the extent of the binary disruption in our multiple population clusters, as well as the preferential disruption of SG binaries." " Finally, in Fig.6 we plot the time evolution of No,sa(a,t), Nwrc(a,t), and their ratio, for two different values of a for simulationr10.."," Finally, in \ref{fig:timenumber} we plot the time evolution of $N_{b,SG}(a,t)$, $N_{b,FG}(a,t)$, and their ratio, for two different values of $a$ for simulation." This figure illustrates the extent of the early (pre-core collapse) disruption of binaries due to the presence of the high-density SG subsystem., This figure illustrates the extent of the early (pre-core collapse) disruption of binaries due to the presence of the high-density SG subsystem. " Binary disruption further increases during core collapse, and finally slows down during the post-core collapse phase."," Binary disruption further increases during core collapse, and finally slows down during the post-core collapse phase." The preferential disruption of SG binaries continues for the whole simulation., The preferential disruption of SG binaries continues for the whole simulation. " The results presented in this paper show that the properties of binary stars are significantly affected by the initial structure of a cluster hosting multiple populations, and may contain important clues to the formation and evolutionary history of multiple populations."," The results presented in this paper show that the properties of binary stars are significantly affected by the initial structure of a cluster hosting multiple populations, and may contain important clues to the formation and evolutionary history of multiple populations." The central result of our study is that significant differences in the numbers of FG and SG binaries is a, The central result of our study is that significant differences in the numbers of FG and SG binaries is a (Uugerechtsetal.2000).. Campbell&Thompson1981).. 197E:Willuer1976).," \citep{ung00}, \citep{elmegreen77,campthomp84}. \citep{martin73,wynnwilliams74,willner76}." . L28«104E. o>10/5«&1 (Scovilleetal.1986)..," $L > 8 \times 10^{4}~ L_{\odot}$ $\phi > 10^{48} ~{\rm s}^{-1}$ \citep{werner79,lugo04}. \citep{scoville86outflows}." Pratapetal.(L989) TCO! ~1’ oof wwith rresolution., \citet{pratap89} $^+$ $\sim$ of with resolution. They found evidence for a shell-like structure on scales of aroundL., They found evidence for a shell-like structure on scales of around. . Wilsonetal.(1983). observed aabsorption toward1.. and Telecel.Wilson.&Johu-ston(L981) mapped the absorption with the VLA.," \citet{wilson83} observed absorption toward, and \citet*{henkel84} mapped the absorption with the VLA." The absorption traces wari gas with a high coluun deusity of aaud is centered near GO+.., The absorption traces warm gas with a high column density of and is centered near $-60$. The emission. on the other haud. is centered near 56.5ον," The emission, on the other hand, is centered near $-56.5$." ", The systemic velocity for this source is ~57 citepvdtüO..", The systemic velocity for this source is $\sim 57$ \\citep{vdt00}. More recently. Zhengetal.(2001) mapped cCluission from a iore extended region m75238.," More recently, \citet{zheng01} mapped emission from a more extended region in." . This ciuission probably probes the outer cuvelope ax indicated by the colder temperature and the sanaller column deusitv., This emission probably probes the outer envelope as indicated by the colder temperature and the smaller column density. Usiug both sinele-dish aud interferometer observations of various nolecular tracers. vanderTaketal.(2000) studied the deusitv aud teirperature structure of both the cold outer euvelope and the warm inner material (21072000 AU).," Using both single-dish and interferometer observations of various molecular tracers, \citet{vdt00} studied the density and temperature structure of both the cold outer envelope and the warm inner material (240–72000 AU)." The inner wart region is characterized by temperatures of a few hundred Ix. Outflows are often preseut toward protostars. aud lis no exception.," The inner warm region is characterized by temperatures of a few hundred K. Outflows are often present toward protostars, and is no exception." Campbell(1981). observed wwith the VLA at 5 and 15 ΟΠ., \citet{campbell84} observed with the VLA at 5 and 15 GHz. " She fouud a pair of very conipaet lobes of coutinuuu radiation. separated oe1 declination by0.27. with eiuission extending out to +2”"".."," She found a pair of very compact lobes of continuum radiation, separated in declination by, with emission extending out to $\pm$." Πο preferred model involves a bipolar i0nized outflow from a late Ο star. collimated by a core of dense eas oxtending from «65 AU to 225.000 AU.," Her preferred model involves a bipolar ionized outflow from a late O star, collimated by a core of dense gas extending from $<$ 65 AU to $>$ 25,000 AU." Further, Further ‘Transiting planets are an important. source of information on the formation. structure and evolution of extra-solar planets.,"Transiting planets are an important source of information on the formation, structure and evolution of extra-solar planets." We are monitoring known transiting planetary systems in radial velocity with the SODPIIILS spectrograph in the Northern hemisphere and. LLARDPS spectrograph in the Southern: hemisphere. to refine⋅ our knowledge of the dynamics. of these systems. notably the orbital. eccentricity.D. spin-orbit angle and. presence of additional companions ??.ESOProg. 0812.C-0312)..," We are monitoring known transiting planetary systems in radial velocity with the SOPHIE spectrograph in the Northern hemisphere and HARPS spectrograph in the Southern hemisphere to refine our knowledge of the dynamics of these systems, notably the orbital eccentricity, spin-orbit angle and presence of additional companions \citep[e.g.][ESO Prog. 0812.C-0312]{Loeillet2008,Hebrard2008}." In this paper. we analyse our new SODLLILI velocity data for two transiting planetary svstems. WASI and WASP-14.," In this paper, we analyse our new SOPHIE radial-velocity data for two transiting planetary systems, WASP-12 and WASP-14." Both are characterized by close-in but apparently eccentric orbits. and. therefore. represen potentially.. important. svstems to constrain. the migration.. tidal. and thermal evolution. of⋅ gas giant. planets.," Both are characterized by close-in but apparently eccentric orbits, and therefore represent potentially important systems to constrain the migration, tidal and thermal evolution of gas giant planets." We⇁ combine. our racdial-velocitv. data with. previously. published. data ane a realistic treatment of correlated noise to calculate upcdatec constraints on the orbital eccentricities., We combine our radial-velocity data with previously published data and a realistic treatment of correlated noise to calculate updated constraints on the orbital eccentricities. Lhe companion of the 11:7th-magnitude star WASDP-12 is a particularly interesting example (?.hereafterLO9).., The companion of the 11.7th-magnitude star WASP-12 is a particularly interesting example \citep[][hereafter H09]{Hebb2009}. 1 orbits extremely close to its host star. even by the standards," It orbits extremely close to its host star, even by the standards" Semi-analvtie models of galaxy formation aim to predict the evolution of population properties such as the distributions of stellar mass. luminosity. star formation rate. size. rotation velocity. morphology. gas content and metallicity. as well as the sealing relations linking these properties.,"Semi-analytic models of galaxy formation aim to predict the evolution of population properties such as the distributions of stellar mass, luminosity, star formation rate, size, rotation velocity, morphology, gas content and metallicity, as well as the scaling relations linking these properties." They. follow astrophysical processes alfecting the barvonic components using a series of analytic. physically based mocels which are embedded either in an analytic representation (7777). or in," They follow astrophysical processes affecting the baryonic components using a series of analytic, physically based models which are embedded either in an analytic representation \citep{White1991,Kauffmann1993, Cole1994,Somerville1999} or in" Weak leusiug. the distortion of observed galaxy shapes w the eravitational potential of large-scale structure. las ereat potential to help determine cosmological xuwalneters (Albrechtetal.2006:Tockstra&Jain2008:etal 2006)..,"Weak lensing, the distortion of observed galaxy shapes by the gravitational potential of large-scale structure, has great potential to help determine cosmological parameters \citep{TaskForce, HoekstraJain, Huterer, Mellier, Munshi, Peacock}." " Leusiug by ealaxy clusters can constraiu he mass and mass distribution of those clusters (Ixaiser 2007).. which has implications for the amplitude of the uatter power spectrum oy. the matter deusity O,,.and he evolution of dark energv (Alavianetal.2009:Wane&Steinhardt1998:Albrechtetal."," Lensing by galaxy clusters can constrain the mass and mass distribution of those clusters \citep{KaiserSquires, SchneiderBook, Johnston}, which has implications for the amplitude of the matter power spectrum $\sigma_8$, the matter density $\Omega_m$,and the evolution of dark energy \citep{Marian, Wang, TaskForce}." 2006).. Since the lensing cross-section varies with the distances vetwween the observer. the lens. aud the lensed galaxy. it is also possible to obtain information about the tince-dependent cosmic geometry.," Since the lensing cross-section varies with the distances between the observer, the lens, and the lensed galaxy, it is also possible to obtain information about the time-dependent cosmic geometry." Tomography cau constraiu xuwanieters such as the dark cnerey density O4 aud its equation of state dw (πα1999) and can also est general relativity on large scales (Zhaooetal. 2009)., Tomography can constrain parameters such as the dark energy density $\Omega_{\Lambda}$ and its equation of state $w$ \citep{Hu} and can also test general relativity on large scales \citep{Zhao}. . Tomoeraphic analvsis for cosmologyrequires deep. wide. high-resolution surveys (Berustein2007:Alyechtetal.2006:Peacock 2006). so there is ereat potential for results from upconuünug larec-scale surveys such as the Dark Enerey Survey (DES: http://www.darkenergysurvey.org).," Tomographic analysis for cosmologyrequires deep, wide, high-resolution surveys \citep{Bernstein, TaskForce, Peacock}, so there is great potential for results from upcoming large-scale surveys such as the Dark Energy Survey (DES; )." Tomoerapliv has previously been observed around a sanall nuniber of clusters., Tomography has previously been observed around a small number of clusters. The chauge in shear with redshift can be observed by dinning source galaxies into redshift slices and determining the amplitude of the signal iu cach bin around single clusters. as \ledeziuskietal.(20101). aud Tavloretal.(2001) have done: in addition Tavloroetal. fit a three-dimeusional eravitational potential for the clusters in their survey.," The change in shear with redshift can be observed by binning source galaxies into redshift slices and determining the amplitude of the signal in each bin around single clusters, as \citet{Medezinski} and \citet{Taylor} have done; in addition \citeauthor{Taylor} fit a three-dimensional gravitational potential for the clusters in their survey." Cavazzi&Soucail(2007) aud Shanctal.(2011) take an inverse approach. using the expected chauge with redshift to iufer the redshift of poteutial clusters identified through shear peaks aud to distinguish noise peaks from real clusters.," \citet{Gavazzi} and \citet{Shan} take an inverse approach, using the expected change with redshift to infer the redshift of potential clusters identified through shear peaks and to distinguish noise peaks from real clusters." Simonetal.(2011) look for shear peaks in three-dimensional convergence maps of the Abell 901/902 superchister. detecting additional structure behiud the known clusters uxiug the lensing streneth at a series of redshift slices.," \citet{Simon} look for shear peaks in three-dimensional convergence maps of the Abell 901/902 supercluster, detecting additional structure behind the known clusters using the lensing strength at a series of redshift slices." Here we restrict ourselves to the question of the redslüft-distance relation. using a stacked sample of many clusters rather than making a detection for single clusters in high signal-to-noise data.," Here we restrict ourselves to the question of the redshift-distance relation, using a stacked sample of many clusters rather than making a detection for single clusters in high signal-to-noise data." Tn this work. we detect lensing around the clusters in Stripe 82 of the Sloan Digital Sky Survey (SDSS). a region observed nultiple times so that it probes ~2 magnitudes deeper than the SDSS sample overall. reaching a depth completeness) of 23 in the {- baud (Yorketal.2000:Fricmman2008:Anis 2011).," In this work, we detect lensing around the clusters in Stripe 82 of the Sloan Digital Sky Survey (SDSS), a region observed multiple times so that it probes $\sim2$ magnitudes deeper than the SDSS sample overall, reaching a depth completeness) of 23 in the $i$ -band \citep{SDSS, Stripe82, Annis}." . Like the DES. Stripe 82 of the SDSS achieves its depth by coadding many images of the same region of the sky.," Like the DES, Stripe 82 of the SDSS achieves its depth by coadding many images of the same region of the sky." This process can introduce svstematic errors to the lensing signal (Schneideretal.2006.Part3. 83.3)). πο one motivation for this study is to check if coadding adversely affects the cluster lensing signal.," This process can introduce systematic errors to the lensing signal \citealt[Part 3, \S 3.3]{SchneiderBook}) ), so one motivation for this study is to check if coadding adversely affects the cluster lensing signal." The deeper sample also opens up the possibility of detecting tomography., The deeper sample also opens up the possibility of detecting tomography. Iu principle. tomography offers the pronise of determining cosmological paraicters. but in this study we aim only to detect the ereater shear in distant ealaxies.," In principle, tomography offers the promise of determining cosmological parameters, but in this study we aim only to detect the greater shear in distant galaxies." Ον lensing and cluster data are described in 8??.., Our lensing and cluster data are described in \ref{Data}. . We analyze the data usinga Likclhood method described im 877.., We analyze the data usinga likelihood method described in \ref{LMethod}. . Results of the analysis are given in 8?77.., Results of the analysis are given in \ref{Results}. . mass-lIoss events.,mass-loss events. According to our simulations. large regions of neutral gas surrounding the molecular envelopes of AGB stars should be expected.," According to our simulations, large regions of neutral gas surrounding the molecular envelopes of AGB stars should be expected." These large regions of gas are formed [rom the mass-loss experienced by the star during the AGB evolution., These large regions of gas are formed from the mass-loss experienced by the star during the AGB evolution. These large shells should be detectable at inlrared wavelengths., These large shells should be detectable at infrared wavelengths. We thank M. L. Norman and the Laboratory for Computational Astrophvsies lor the use of ZEUS-3D. We also want to thank Emanuel Vassiliadis for his Iruitful comments at the begining of (his work and for providing us will some of his models., We thank M. L. Norman and the Laboratory for Computational Astrophysics for the use of ZEUS-3D. We also want to thank Emanuel Vassiliadis for his fruitful comments at the begining of this work and for providing us with some of his models. EV is grateful to Tariq Shahbaz and Letizia Stanghellini for their careful reading of the manuscript ancl (heir valuable comments., EV is grateful to Tariq Shahbaz and Letizia Stanghellini for their careful reading of the manuscript and their valuable comments. The work of EV and. AM is supported by the Spanish DGES grant PDB97-1435-C02-01., The work of EV and AM is supported by the Spanish DGES grant PB97-1435-C02-01. GGS is partially supported by erants fron DGADPA-UNAM (IN130693. IN117799 IN114199) and CONACYT (32214-E).," GGS is partially supported by grants from DGAPA-UNAM (IN130698, IN117799 IN114199) and CONACyT (32214-E)." error bars are the average and dispersion of this quantity the triangular point for the dwarf spheroicdals ancl the square point for the elobulars anc UCDs taken together.,error bars are the average and dispersion of this quantity – the triangular point for the dwarf spheroidals and the square point for the globulars and UCDs taken together. The dwarl spheroidals deviate by about two sigma from hose svstems lving on the FP (this probably unclerstates he significance as the οἱset becomes more pronounces al ower luminosities)., The dwarf spheroidals deviate by about two sigma from those systems lying on the FP (this probably understates the significance as the offset becomes more pronounced at lower luminosities). 77 is a plot of logl(at/GauL) Vs. og(L) for these same svsems., 7 is a plot of $\log(\sigma^4/Ga_0L)$ vs. $\log(L)$ for these same systems. ‘This is proportional to ÀT/L as determined from the E.J relation (AIOND)., This is proportional to M/L as determined from the FJ relation (MOND). Again the WO points with error bars are the mean and dispersion of this quantity for the να spheroidals (triangle) and separately he globulars and CCDs (square)., Again the two points with error bars are the mean and dispersion of this quantity for the dwarf spheroidals (triangle) and separately the globulars and UCDs (square). Here we see that there is no significant cillerence between these classes of objects: the dwarl spheroidals lie on the universal Faber-Jackson relation defined by the more compact. pressure-supported objects., Here we see that there is no significant difference between these classes of objects; the dwarf spheroidals lie on the universal Faber-Jackson relation defined by the more compact pressure-supported objects. Luminous elliptical galaxies. cdwarl elliptical galaxies. ultra-compact chyvarts. and globular star clusters are high surface brightness objects.," Luminous elliptical galaxies, dwarf elliptical galaxies, ultra-compact dwarfs, and globular star clusters are high surface brightness objects." Ligh surface brightness implies high internal acceleration: Le.. the gravitational acceleration at Roy ds roughly ten times larger than eo. the fundamenta MOND acceleration parameter.," High surface brightness implies high internal acceleration; i.e., the gravitational acceleration at $\mathit{R_{eff}}$ is roughly ten times larger than $a_0$, the fundamental MOND acceleration parameter." This means that. in the context of MOND. such objects. should. be describe essentially by Newtonian dynamics within an| cllective radius. In that respect. it is not surprising that this wide range of gravitationally bound. pressure-supportec structures fall on a EP that reflects the Newtonian viria relation.," This means that, in the context of MOND, such objects should be described essentially by Newtonian dynamics within an effective radius, In that respect, it is not surprising that this wide range of gravitationally bound pressure-supported structures fall on a FP that reflects the Newtonian virial relation." Of course there are variations: the globular clusters do not lie precisely upon the same FP as the cllipticals. but then the the data shown here is heterogeneous. an," Of course there are variations: the globular clusters do not lie precisely upon the same FP as the ellipticals, but then the the data shown here is heterogeneous, and" image. after the model subtraction. shows the disk structure mapped by the 5; shape parameter.,"image, after the model subtraction, shows the disk structure mapped by the $b_4$ shape parameter." In our spectroscopic study. 14 galaxies in the immediate surrounding of NGC 4756 are considered. 8 of which have redshifts accordant to the group.," In our spectroscopic study, 14 galaxies in the immediate surrounding of NGC 4756 are considered, 8 of which have redshifts accordant to the group." Among them. we identifv two new eroup members. one of which is a dI. and measured (he previously unknown svstenic velocily of a third member. Leda 83619.," Among them, we identify two new group members, one of which is a dE, and measured the previously unknown systemic velocity of a third member, Leda 83619." We complement our data wilh Dressler and Garcia(1993) samples in order to characterize the elobal group properties., We complement our data with \citet{Dress88} and \citet{gar93} samples in order to characterize the global group properties. Table 9 includes 11 galaxies from Dressler&Shectman(1988). with svstemic velocities in the range of 3200. 4950 kins | and additionally 2 galaxies rom Garcia(1993)... which are not included either in our or in the Dressler&Shectinan(1988). sample.," Table \ref{tab8} includes 11 galaxies from \citet{Dress88} with systemic velocities in the range of 3200 – 4950 km $^{-1}$ and additionally 2 galaxies from \citet{gar93}, which are not included either in our or in the \citet{Dress88} sample." The member galaxies listed by Giuricinetal.(2000) are actually too distant (on average more than 1 Alpe) from NGC 4756 to have any direct influence on NGC 4756. and we therelore preter not to include them in our list of group members.," The member galaxies listed by \citet{giu00} are actually too distant (on average more than 1 Mpc) from NGC 4756 to have any direct influence on NGC 4756, and we therefore prefer not to include them in our list of group members." The number ofmembers of the NGC 4756 group is then 22 galaxies., The number of of the NGC 4756 group is then 22 galaxies. From the above list of galaxies. the average svstemic velocity of the group is 4068 km |. with a median velocity of 4074 kms | and a velocity dispersion of 459 km 1.," From the above list of galaxies, the average systemic velocity of the group is 4068 km $^{-1}$, with a median velocity of 4074 km $^{-1}$ and a velocity dispersion of 459 km $^{-1}$." " Adopting Il, = 70 km ! +. we derived a distance of 58 Mpe for the NGC 4756 eroup."," Adopting $_0$ = 70 km $^{-1}$ $^{-1}$, we derived a distance of 58 Mpc for the NGC 4756 group." Figure 9 shows the distribution of the absolute total magnitudes and of the systemic velocities of the 22 fiducial candidate members., Figure \ref{figure9} shows the distribution of the absolute total magnitudes and of the systemic velocities of the 22 fiducial candidate members. The magnitude panel (Figure 9)) reveals that all galaxies belong to intermediate and lowluminosity galaxy classes (van 1998)., The magnitude panel (Figure \ref{figure9}) ) reveals that all galaxies belong to intermediate and low–luminosity galaxy classes \citep{vdb98}. . The (incomplete) svstemic velocity distribution (each velocity bin is 150 km !) of the group shows that our 8 galaxies lie within a velocity range of the order of 1500 kms ! a tvpical velocity range of loose groups once their centers have been identified, The (incomplete) systemic velocity distribution (each velocity bin is 150 km $^{-1}$ ) of the group shows that our 8 galaxies lie within a velocity range of the order of 1500 km $^{-1}$ a typical velocity range of loose groups once their centers have been identified "Re=eftfv aud the maguetic Bevuodls umber Ri»=ef η, ",$Re \equiv c_s H/\nu$ and the magnetic Reynodls number $Rm \equiv c_s H/\eta$ . Specifically. it has been shown that Re aud Riv. or alternatively the magnetic Praudtl ummber Pin= RinfRe. determine whether turbulence is sustained iu zero uct flux. wustratified simulations (Fromanectal.2007:Sinon&Lawley 2009).," Specifically, it has been shown that $Re$ and $Rm$, or alternatively the magnetic Prandtl number $Pm=Rm/Re$ , determine whether turbulence is sustained in zero net flux, unstratified simulations \citep{fro07,sh09}." . To see if these results hold iu stratified domains. we perform three smiulatious with differing values of viscosity and resistivity: Re=so0 with Pii21 (hereafter Resd0Pml). Re-58500 with Piui22 (Resd0Pin2). anc Re=1600 with Ότιι-- (ποσοΟι).," To see if these results hold in stratified domains, we perform three simulations with differing values of viscosity and resistivity: Re=800 with Pm=4 (hereafter Re800Pm4), Re=800 with Pm=2 (Re800Pm2), and Re=1600 with Pm=2 (Re1600Pm2)." Exinuuation of Figure Ll of Fromaneetal.(2007) or Table 1 of Simon&Tawley(2009) show that none of these woul sustain turbulence in an unstratified domains with no net field. regardless of whether Zeus or Athena is usec for the simulations.," Examination of Figure 11 of \citet{fro07} or Table 1 of \citet{sh09} show that none of these would sustain turbulence in an unstratified domains with no net field, regardless of whether Zeus or Athena is used for the simulations." We have coufiniied these results for uustratified domains with our own Athena calculations., We have confirmed these results for unstratified domains with our own Athena calculations. Figue 195 shows the stress as a function of time for the three simulations with a logarithmic vertical scale., Figure \ref{f:stressdis} shows the stress as a function of time for the three simulations with a logarithmic vertical scale. The behavior of Res00Piul aud RelGOOPim2 is rather different from the wustratified domains where the siauulatious decay rapidly to zero on timescales of 10-20 orbits after the initial lincar erowth of the MBI., The behavior of Re800Pm4 and Re1600Pm2 is rather different from the unstratified domains where the simulations decay rapidly to zero on timescales of 10-20 orbits after the initial linear growth of the MRI. Even Resd00Pin2. which drops rapidly to a dimensionless stress of ~10? and then ~10! in the stratified domain. decays much mere rapidly aud contiuues to even lower values in the wustratified domain.," Even Re800Pm2, which drops rapidly to a dimensionless stress of $\sim 10^{-3}$ and then $\sim 10^{-4}$ in the stratified domain, decays much more rapidly and continues to even lower values in the unstratified domain." The behavior of the stratified domains is also considerably more complicated., The behavior of the stratified domains is also considerably more complicated. Turbulence never decays away completely. but vigorous iubuleuce is not sustaimecd iu aiv of the calculations or longer than 100 orbits.," Turbulence never decays away completely, but vigorous turbulence is not sustained in any of the calculations for longer than 100 orbits." The auplitude of variability is large. and turbulence decays 5owlv on timescales of iuucdreds of orbits.," The amplitude of variability is large, and turbulence decays slowly on timescales of hundreds of orbits." The Bel600P112 aud Res00P112 runs th show a recovery nearly to peak values after spending over LOO orbital periods in staguation or slow decay!, The Re1600Pm2 and Re800Pm2 runs both show a recovery nearly to peak values after spending over 100 orbital periods in stagnation or slow decay! Using the criteria of Fromangetal.(2007).. we would xobablv have labeled the BRes00Piil run as having sustained turbulence (over the first 100 orbits. which is the baseline. used there). the RelGOOPm2 ruu as nareinal. and the BRes00Piil as either mareinal or iof having sustained turbulence. although the complex variabilitv of the stratified ruus makes this somewhat subjective.," Using the criteria of \citet{fro07}, we would probably have labeled the Re800Pm4 run as having sustained turbulence (over the first 100 orbits, which is the baseline used there), the Re1600Pm2 run as marginal, and the Re800Pm4 as either marginal or not having sustained turbulence, although the complex variability of the stratified runs makes this somewhat subjective." Figure 11 of Fromiaug&Papaloizou(2007) maps out a locus of sustained turbulence in Re Dii space. and it’s notable that Που! aud Rel600Pm2 simulations are on the cusp of showiug sustained turbulence while ResOOPim2 more firmly iu the nou-turbuleut regime.," Figure 11 of \citet{fp07} maps out a locus of sustained turbulence in Re – Pm space, and it's notable that Re800Pm4 and Re1600Pm2 simulations are on the cusp of showing sustained turbulence while Re800Pm2 more firmly in the non-turbulent regime." Therefore. it would secu that stratification slightly increases the parameter space for which sustained turbulence is possible. but does not qualitatively alter the conclusion that turbulence dies out or sufficiently low Pin or sufficiently high Re.," Therefore, it would seem that stratification slightly increases the parameter space for which sustained turbulence is possible, but does not qualitatively alter the conclusion that turbulence dies out for sufficiently low Pm or sufficiently high Re." It is suggestive that all three sets of dissipation terms show sustained turbulence m unustratified boxes once a ret toroidal field is iuposed (Simon&Tawley2009)., It is suggestive that all three sets of dissipation terms show sustained turbulence in unstratified boxes once a net toroidal field is imposed \citep{sh09}. . As noted previously. it is conceivable that main impact of stratification is the production of toroidal field. which hen lead to cuhanced turbulence.," As noted previously, it is conceivable that main impact of stratification is the production of toroidal field, which then lead to enhanced turbulence." The turbulence iu the stratified ruus is significantly less vigorous. but this may ve consistent withthe ruis field streneths in the stratified sinulations beme much weaker than the toroidal fields considered by Simon&Tawley(2009).. Iu Figure 16 we plot the time average power spectra of the maenetic cuerey density from ResdoPint aid Rel600Pm2. including SGIRIZI for comparison.," The turbulence in the stratified runs is significantly less vigorous, but this may be consistent withthe rms field strengths in the stratified simulations being much weaker than the toroidal fields considered by \citet{sh09}, In Figure \ref{f:psdis} we plot the time average power spectra of the magnetic energy density from Re800Pm4 and Re1600Pm2, including S64R1Z4 for comparison." Sinceo the magnetic cucrey 1i the Ποσοτι drops rapiclv to a low amplitude. we have elected. to exelude it.," Since the magnetic energy in the Re1600Pm2 drops rapidly to a low amplitude, we have elected to exclude it." Of course. the amplitude of the power spectimm depoeuds on the interval used in the time average. which is 25-100 orbits.," Of course, the amplitude of the power spectrum depends on the interval used in the time average, which is 25-100 orbits." The Res00Piil aud Rel600Piíi2 power spectra are simular in shape. falling off somewhat more rapidly than SGIRIZL as k increases.," The Re800Pm4 and Re1600Pm2 power spectra are similar in shape, falling off somewhat more rapidly than S64R1Z4 as $k$ increases." The power iu Resd0Pin lin exceeds that in RelGO00Pm2 at all Αν , The power in Re800Pm4 in exceeds that in Re1600Pm2 at all $k$ . Note that these two calculations have the sale resistivity but Bes00DPnil has a higher viscosity.," Note that these two calculations have the same resistivity but Re800Pm4 has a higher viscosity," and respectively (Table 2)).,and respectively (Table \ref{tab:model_parameters}) ). This is entirely consistent with the presence of in the centre of the core which should be destroyed by CO and is also consistent with integrated intensity maps of these species which show the CO isotopes are only weakly present above the background molecular cloud., This is entirely consistent with the presence of in the centre of the core which should be destroyed by CO and is also consistent with integrated intensity maps of these species which show the CO isotopes are only weakly present above the background molecular cloud. More modest depletion is implied for the data and the modelling suggests that this species is depleted within r«0.3R., More modest depletion is implied for the data and the modelling suggests that this species is depleted within $r < 0.3R$. Little freeze-out of CS is implied by the modelling which calls for a depletion only within the central regions at r«0.1R., Little freeze-out of CS is implied by the modelling which calls for a depletion only within the central regions at $r < 0.1R$. " The core (envelope) and outflow parameters of the best fit model are summarised in Table 2,, the modelled spectra are shown in Figure 9.."," The core (envelope) and outflow parameters of the best fit model are summarised in Table \ref{tab:model_parameters}, the modelled spectra are shown in Figure \ref{fig:cc_mopra_model}." " Based on the best fit model of Mopra data, we further refined the input parameters to replicate the blue-shifted line wings found in the ATCA line profiles."," Based on the best fit model of Mopra data, we further refined the input parameters to replicate the blue-shifted line wings found in the ATCA line profiles." We adopted an ‘hourglass’-shaped outflow model (?) with an opening angle of 50 degrees., We adopted an `hourglass'-shaped outflow model \citep{Rawlings2004} with an opening angle of 50 degrees. " In order to reproduce the centre line intensity, the core density has to be doubled from the Mopra data model (Table 2))."," In order to reproduce the centre line intensity, the core density has to be doubled from the Mopra data model (Table \ref{tab:model_parameters}) )." " The outflow density is also an order of magnitude higher and temperature of 50 K to give the line wings intensity, this is consistent with the suggestion that the Mopra data suffers from beam dilution as the source does not fill up the beam, and that the interferometric data has filtered out the extended structure of the core."," The outflow density is also an order of magnitude higher and temperature of 50 K to give the line wings intensity, this is consistent with the suggestion that the Mopra data suffers from beam dilution as the source does not fill up the beam, and that the interferometric data has filtered out the extended structure of the core." " The extent of the line wings are reproduced with an outflow velocity of 12s!,, while a turbulent velocity of 3.0 ggives the smooth blending profile between the centre line component and the outflow line wings; the outflow is oriented such that the blue-shifted outflow lobe is south-west of the source and the red-shifted lobe falls outside of the primary beam."," The extent of the line wings are reproduced with an outflow velocity of 12, while a turbulent velocity of 3.0 gives the smooth blending profile between the centre line component and the outflow line wings; the outflow is oriented such that the blue-shifted outflow lobe is south-west of the source and the red-shifted lobe falls outside of the primary beam." The abundance has to be increased by two orders of magnitude in order to reproduce the observed intensity., The abundance has to be increased by two orders of magnitude in order to reproduce the observed intensity. This is consistent with the findings of ? that abundance is enhanced in outflows., This is consistent with the findings of \citet{Rawlings2004} that abundance is enhanced in outflows. Shown in Figure 10 are sample spectra of the observed ATCA overlain on the model spectra., Shown in Figure \ref{fig:HCOp_model_atca} are sample spectra of the observed ATCA overlain on the model spectra. " In summary, self-consistent radiative transfer model was generated usinga the size, temperature, density and abundances reported in ?.."," In summary, a self-consistent radiative transfer model was generated using the size, temperature, density and abundances reported in \citet{Lo2007}." " Supersonic infall and turbulence and heavy depletion of CO, due to freeze-out, is required to produce a good fit to the line widths, shapes and strengths."," Supersonic infall and turbulence and heavy depletion of CO, due to freeze-out, is required to produce a good fit to the line widths, shapes and strengths." iis located in the G333 giant molecular cloud complex which has been the subject of a multi-molecular line survey project carried out by the authors., is located in the G333 giant molecular cloud complex which has been the subject of a multi-molecular line survey project carried out by the authors. Several papers of results have now been published from this work (???) and so it is now," Several papers of results have now been published from this work \citep{Bains2006, Wong2008, Lo2009} and so it is now" deblending algorithm. consisting of the following. tasks: (1) Two Gaussians. of the same FWHM and with fixed angular separation but otherwise unconstrained. were fitted simultaneously to each spectral resolution element. (,"deblending algorithm, consisting of the following tasks: (1) Two Gaussians, of the same FWHM and with fixed angular separation but otherwise unconstrained, were fitted simultaneously to each spectral resolution element. (" 2) The variation with wavelength of the resulting parameters FWHM and centroid location was fitted by low-order polynomials. (,2) The variation with wavelength of the resulting parameters FWHM and centroid location was fitted by low-order polynomials. ( 3) Another double-Gaussian fit was performed. now with only the two amplitudes as free parameters.,"3) Another double-Gaussian fit was performed, now with only the two amplitudes as free parameters." The algorithm is described in more detail by Lopez et ((1998))., The algorithm is described in more detail by Lopez et \cite{lopez98}) ). Inspection of the residual maps revealed no significant deviation from this model., Inspection of the residual maps revealed no significant deviation from this model. The resulting one-dimensional spectra were recorded as MIDAS table files. thus avoiding loss of information due to data rebinning.," The resulting one-dimensional spectra were recorded as MIDAS table files, thus avoiding loss of information due to data rebinning." Wavelength calibration frames were obtained from comparison lamp spectra. usually based on Helium/Argon lines.," Wavelength calibration frames were obtained from comparison lamp spectra, usually based on Helium/Argon lines." The observing conditions were in many cases not photometric. and standard star spectra for flux. calibration purposes were obtained in only a few nights.," The observing conditions were in many cases not photometric, and standard star spectra for flux calibration purposes were obtained in only a few nights." Therefore only a relative. flux. calibration could be attempted., Therefore only a relative flux calibration could be attempted. Two of the pre-monitoring observations were made through à narrow slit. which in one case was not even aligned.," Two of the pre-monitoring observations were made through a narrow slit, which in one case was not even aligned." We explain below how these measurements could be incorporated into the analysis., We explain below how these measurements could be incorporated into the analysis. Altogether. 19 sets of spectra could be secured. of which 14 were obtained in the course of the monitoring.," Altogether, 19 sets of spectra could be secured, of which 14 were obtained in the course of the monitoring." Most spectra are of very high quality. some with a continuum S/N ratio exceeding 100 in component A. Examples of the spectra are presented in reffig:spectra:: the range in S/N ratio is bracketed by these example data. with most spectra looking rather similar to the February 1995 ones.," Most spectra are of very high quality, some with a continuum S/N ratio exceeding 100 in component A. Examples of the spectra are presented in \\ref{fig:spectra}; the range in S/N ratio is bracketed by these example data, with most spectra looking rather similar to the February 1995 ones." The high quality of the data enabled us to monitor the of both components. which has the advantage over the conventional broad-band magnitudes that it is a brightness measure uncontaminated by emission lines and their possibly different variability patterns.," The high quality of the data enabled us to monitor the of both components, which has the advantage over the conventional broad-band magnitudes that it is a brightness measure uncontaminated by emission lines and their possibly different variability patterns." However. absolute photometric calibration from standard stars was usually not possible. and we had to design a method to compare spectra taken at different epochs.," However, absolute photometric calibration from standard stars was usually not possible, and we had to design a method to compare spectra taken at different epochs." In the following we motivate and outline this procedure., In the following we motivate and outline this procedure. After placing the spectra on a relative. flux. scale. we measured the fluxes and equivalent widths of all major emission lines in both components (Ly&. A1400. 1549. and IIIJ] 41909).," After placing the spectra on a relative flux scale, we measured the fluxes and equivalent widths of all major emission lines in both components $\alpha$, $\lambda$ 1400, $\lambda$ 1549, and ] $\lambda$ 1909)." Local continua were estimated by fitting straight lines to predefined wavebands known to be largely devoid of emission and absorption lines eexamples in reffig;spectra))., Local continua were estimated by fitting straight lines to predefined wavebands known to be largely devoid of emission and absorption lines examples in \\ref{fig:spectra}) ). Although a direct comparison of line strengths between different epochs is not possible. there is one strong piece of evidence that the lines have remained. essentially constant over the time span observed: The flux ratio between the same lines in components A and B. independent of the absolute scale. has stayed at a consistently constant value of 2.85+0.07 for all lines.," Although a direct comparison of line strengths between different epochs is not possible, there is one strong piece of evidence that the lines have remained essentially constant over the time span observed: The flux ratio between the same lines in components A and B, independent of the absolute scale, has stayed at a consistently constant value of $2.85\pm 0.07$ for all lines." This implies either a time delay of much less than a month (the separation between data points during the periods of quasi-continuous monitoring). which is highly improbable. or simply constancy of the line fluxes as such.," This implies either a time delay of much less than a month (the separation between data points during the periods of quasi-continuous monitoring), which is highly improbable, or simply constancy of the line fluxes as such." Adopting the latter hypothesis. we were then able to recalibrate the spectra by scaling them to equal emission line fluxes.," Adopting the latter hypothesis, we were then able to recalibrate the spectra by scaling them to equal emission line fluxes." As reference we usedCIV.. a prominent line that ts surrounded by clearly identifiable continuum windows visible also at low spectral resolution.," As reference we used, a prominent line that is surrounded by clearly identifiable continuum windows visible also at low spectral resolution." For each pair of spectra we computed a seale factor so that the flux of component A assumed an arbitrary but constant value. and applied this factor to both spectra.," For each pair of spectra we computed a scale factor so that the flux of component A assumed an arbitrary but constant value, and applied this factor to both spectra." The, The The Hamillonian of the svstem of a πουν falling. particle described in((2.2)) is nothing but the (half the) momentum square of the and is conserved along the equation of motion.,The Hamiltonian of the system of a freely falling particle described in\ref{eqAction}) ) is nothing but the (half the) momentum square of the and is conserved along the equation of motion. The Hamiltonian H auc thepath parameter p are canonical conjugates., The Hamiltonian ${\cal H}$ and thepath parameter $p$ are canonical conjugates. There is no external force for a particle freely falling in a curved space time as defined bv (the metric. hence this is an exact parallel with the non-relativistic case discussed above where the kinetic energv is conserved.," There is no external force for a particle freely falling in a curved space time as defined by the metric, hence this is an exact parallel with the non-relativistic case discussed above where the kinetic energy is conserved." The resulting variational principle is a principle of extrem path parameter p. or equivalently a principle of extrenmun proper time 7. Recall the action in ((2.2)) and define Sp. S= Ldp:: Sy = αρ (QT) and the A variation of the action 9 is given by AS = — HAp..(48) Since the Hamiltonian is conserved. AS= AS) —HAp.. hence ASy=0.," The resulting variational principle is a principle of extremum path parameter $p$, or equivalently a principle of extremum proper time $\tau$ Recall the action in \ref{eqAction}) ) and define $S_0$, S = dp ; S_0 = dp , and the $\Delta$ variation of the action $S$ is given by S = - p. Since the Hamiltonian is conserved, S= S_0 - p, hence $\Delta S_0 =0$." From Sy=[2Hdp. ()2AS)=2HAp.," From $S_0 = \int 2 {\cal H} dp$, $0= \Delta S_0 = 2 {\cal H} \Delta p$." Expressing in terms of the A variation of the proper time. Q— AS) = 2HAp= - Np= _\ lau-— — ουν (," Expressing in terms of the $\Delta$ variation of the proper time, 0= S_0 = 2 p = - p=- = - ." Expressing in terms of the A variation of the proper time. Q— AS) = 2HAp= - Np= _\ lau-— — ουν (5," Expressing in terms of the $\Delta$ variation of the proper time, 0= S_0 = 2 p = - p=- = - ." Expressing in terms of the A variation of the proper time. Q— AS) = 2HAp= - Np= _\ lau-— — ουν (50," Expressing in terms of the $\Delta$ variation of the proper time, 0= S_0 = 2 p = - p=- = - ." Expressing in terms of the A variation of the proper time. Q— AS) = 2HAp= - Np= _\ lau-— — ουν (50)," Expressing in terms of the $\Delta$ variation of the proper time, 0= S_0 = 2 p = - p=- = - ." Way. after w Cen (Harris1996)).,"Way, after $\omega$ Cen \citealt{har96}) )." " AI 51 aud w Cen represent the high mass tail of the CC mass distribution. aud show many similarities. worth of deeper insight: i) both have intrinsic dispersion iu unctallicity |Fo/TI]. even if of differeut aniplitude: ii) they are either associated to (M51) or suspected to be born iu (w Cen) a dwarf galaxv: ii) both lie in the intermediate reeion Gin the AZ, vs half mass radius) between Ultra Compact Dwarfs (UCDs) aud CC's. very close to the low-nass lit of the UCDs (sce Fig."," M 54 and $\omega$ Cen represent the high mass tail of the GC mass distribution, and show many similarities, worth of deeper insight: i) both have intrinsic dispersion in metallicity [Fe/H], even if of different amplitude; ii) they are either associated to (M 54) or suspected to be born in $\omega$ Cen) a dwarf galaxy; iii) both lie in the intermediate region (in the $M_V$ vs half mass radius) between Ultra Compact Dwarfs (UCDs) and GCs, very close to the low-mass limit of the UCDs (see Fig." Lin Tolstoyetal.2009:Mackey&vandeuBerelh2005:Federicietal. 2007)).," 1 in \citealt{tol09,mac05,fed07}) )." All these similarities may led to the legitimate suspicion hat M 51 and z Cen could be siblings. or at least next of cin.," All these similarities may led to the legitimate suspicion that M 54 and $\omega$ Cen could be siblings, or at least next of kin." In particular BOs speculated that the residual of the (future) complete dissolution of the Ser ealaxy will leave a lone-living conrpact remnant composed by a bulk of uetal-poor stars (the original M51 cluster) plus a lesser »»pulatiou of ποτάσον stars from the original nucleus of Ser (Sgr.N).," In particular B08 speculated that the residual of the (future) complete dissolution of the Sgr galaxy will leave a long-living compact remnant composed by a bulk of metal-poor stars (the original M54 cluster) plus a lesser population of metal-rich stars from the original nucleus of Sgr (Sgr,N)." This would be very similar to the current status of w Cen (see Paucinoetal...2000.. and references herein). suggesting that this puzzling svete iav. have ormed through an analogous process.," This would be very similar to the current status of $\omega$ Cen (see \citealt{pan00}, and references therein), suggesting that this puzzling system may have formed through an analogous process." Iu this paper we investigate this scenario in further detail. comparing newly obtained abundance analysis roni high dispersion spectra of M51 (auc Ser.N) stars with simular data for vw Cen taken from the literature.," In this paper we investigate this scenario in further detail, comparing newly obtained abundance analysis from high dispersion spectra of M54 (and Sgr,N) stars with similar data for $\omega$ Cen taken from the literature." The only previous study of M 51 based on high resolution spectroscopy was that of Brownotal.(1999.hereinafterDWG99) who analyzed five eiut stars., The only previous study of M 54 based on high resolution spectroscopy was that of \citet[hereinafter BWG99]{bro99} who analyzed five giant stars. They found an average Fe/I]2—1.55 dex and evidence of proton-capture reactions (low O. cnhauced Na and Al) in the abundance ratios of one. perhaps two stars.," They found an average $=-1.55$ dex and evidence of proton-capture reactions (low O, enhanced Na and Al) in the abundance ratios of one, perhaps two stars." Qur study is based ou the FLAMES (CIRAFFE iux UVES) spectra of 76 stars on the red giant brauch (RGB) of M 51. and of 25 stars belougine to the Ser dSph nucleus: the two samples are selected from the RGDs of the two populations that are well separate in the CMD (Bos).," Our study is based on the FLAMES (GIRAFFE and UVES) spectra of 76 stars on the red giant branch (RGB) of M 54, and of 25 stars belonging to the Sgr dSph nucleus; the two samples are selected from the RGBs of the two populations that are well separated in the CMD (B08)." A full description of the analysis and results will be presented elsewhere (Carretta et al., A full description of the analysis and results will be presented elsewhere (Carretta et al. 2010. in preparation).," 2010, in preparation)." In this Letter we only show results concerning Fe. Na. O and the two α clements Me. Si.," In this Letter we only show results concerning Fe, Na, O and the two $\alpha-$ elements Mg, Si." Towever. our abundance analysis traces as closely as possible the homogeneous procedures adopted for other GCs (see Carrettaotαἱ.2009a.) and references," However, our abundance analysis traces as closely as possible the homogeneous procedures adopted for other GCs (see \citealt{car09a,car09b} and references." thorein??.. w Cen has been extensively studied at high spectral resolution., $\omega$ Cen has been extensively studied at high spectral resolution. We consider here the following data sets: The average metallicity for M 51 derived frou neutral Fe lines is 1.559+0.021 dex (a=0.189 dex. 76 stars). Which[Fe/MJ= is almost coincidenut with the value obtained by DWG99.," We consider here the following data sets: The average metallicity for M 54 derived from neutral Fe lines is $=-1.559\pm 0.021$ dex $\sigma=0.189$ dex, 76 stars), which is almost coincident with the value obtained by BWG99." We obtained au average |Fe/II| value. of 0.622£0.068 dex. o=0.353 dex for the 25 stars of the Ser dSpli uucleus.," We obtained an average [Fe/H] value of $-0.622\pm 0.068$ dex, $\sigma=0.353$ dex for the 25 stars of the Sgr dSph nucleus." Since internal errors iu. in our analysis are ~0.02 dex.54. as proposed by Sarajedini&Lavdeu(1995) aud Bos.," Since internal errors in in our analysis are $\sim 0.02$ dex, as proposed by \citet{sar95} and B08." Tn Fig., In Fig. |. we compare metallicity distribution functions (MIDF) in M Si) Ser dSph uucleus (our data)and w Cen (Staufordetal.2007.. O03).," \ref{f:metM54SGRN51} we compare metallicity distribution functions (MDF) in M $+$ Sgr dSph nucleus (our data)and $\omega$ Cen \citealt{sta07}, O03)." MIDFs are formally different. however. similarities may be traced in the elobal appearence.," MDFs are formally different, however, similarities may be traced in the global appearence." In both cases: The same couclisious are also evident for w Con iu Fie., In both cases: The same conclusions are also evident for $\omega$ Cen in Fig. 9 of Norrisetal.(1996)., 9 of \citet{nor96}. . While the exact relative fraction of the various component is obviously affected by differeut selection effects acting in the differcut samples. the sinularity of the overall shape is well established aud intrigue.," While the exact relative fraction of the various component is obviously affected by different selection effects acting in the different samples, the similarity of the overall shape is well established and intriguing." The Ni-O anticorrelatious. obtained for M 51 (our data} and for w Cen (NDC95) are shown iu Fie.2., The Na-O anticorrelations obtained for M 54 (our data) and for $\omega$ Cen (NDC95) are shown in Fig.2. They are the two most pronounced known examples of O-depletions auticorrelated with Na-culancements amone RGB stars in GCs., They are the two most pronounced known examples of O-depletions anticorrelated with Na-enhancements among RGB stars in GCs. " The interquartile range of the distribution of ratios. assmnued as a quantitative measure of the [D/Na]extension of the anticorrelatiou (see Carretta= 2006)) ave IQR[O/Na]—1.169. and 1.310. for M5l and uw Cen. respectively,"," The interquartile range of the distribution of [O/Na] ratios, assumed as a quantitative measure of the extension of the anticorrelation (see \citealt{car06}) ) are IQR[O/Na]=1.169 and 1.310 for M54 and $\omega$ Cen, respectively." While the Primorcial compoucnt fractions (26+6% and 3149%. respectively: see definition iu Carrettaetal. 2009a)) are very similar to the average fraction of first eeneration stars in other CC's (about 33%)). AL 51 has the highest fractions of second generation stars with extreme composition found up to date: Extσι = Payc .," While the Primordial component fractions $26\pm 6\%$ and $31\pm 9\%$, respectively: see definition in \citealt{car09a}) ) are very similar to the average fraction of first generation stars in other GCs (about ), M 54 has the highest fractions of second generation stars with extreme composition found up to date: $_{\rm M~54}$ = $28\% \pm 6\%$ ." The values of TOR casily exceccing the previous record detained by NCC 2808 (Carrettact 200943). M 51 aud w Cen uicely extend to the," The values of IQR easily exceeding the previous record detained by NGC 2808 \citealt{car09a}) ), M 54 and $\omega$ Cen nicely extend to the" that the velocity field v(x.€) is not mirror svinnmeltric. sav. possesses nonzero kinetic helicity H—[v-(Vεναz0 (Steenbeck.Krause&Radler1966:Molfatt1978).,"that the velocity field ${\bf v}({\bf x, t})$ is not mirror symmetric, say, possesses nonzero kinetic helicity $H=\int {\bf v}\cdot ({\nabla \times {\bf v}})\, d^3 x\neq 0$ \citep{skr,moffatt78}." . Assume that (the velocitylocity [InctnationsUnetuations Ihave the typical correlation scalele fy./). ancland (he typicaltypica rms value vy. and the plasma has kinematic viscosity v and magnetic cilfusivity 7 (he latCer is proportional to electrical resistivity).," Assume that the velocity fluctuations have the typical correlation scale $l_0$, and the typical rms value $v_0$, and the plasma has kinematic viscosity $\nu$ and magnetic diffusivity $\eta$ (the latter is proportional to electrical resistivity)." " The range of scales available for velocity. ancl magnetic fluctuations can be characterized bv the Revnolds number Re~{μον and the magnetic Revnolds number Im~ο/η, respectively."," The range of scales available for velocity and magnetic fluctuations can be characterized by the Reynolds number ${\rm Re}\sim l_0v_0/\nu$ and the magnetic Reynolds number ${\rm Rm}\sim l_0v_0/\eta$, respectively." In astrophysical applications both numbers are very large (for example. in a protogalaxy. where dynamo action is believed to operate. Re and Rin reach values ~10? and —1075. respectively).," In astrophysical applications both numbers are very large (for example, in a protogalaxy, where dynamo action is believed to operate, ${\rm Re}$ and ${\rm Rm}$ reach values $\sim 10^{5}$ and $\sim 10^{26}$, respectively)." Their ratio. the magnetic Prandtl number Pim=Ran/Re can be either large or small," Their ratio, the magnetic Prandtl number ${\rm Pm=Rm/Re}$ can be either large or small." For example. in galaxies and galaxy clusters pum1. while in planets and stellar interiors Pm«1.," For example, in galaxies and galaxy clusters ${\rm Pm}\gg 1$, while in planets and stellar interiors ${\rm Pm}\ll 1$." Because of the vast range of scales available for magnetic aud velocity [Inctuations. ancl generally strongly disparate magnetic and velocity dissipation scales. present-day direct numerical simulations cannot directly address astrophvsical magnetohvdrodvnamic (MIID) regimes.," Because of the vast range of scales available for magnetic and velocity fluctuations, and generally strongly disparate magnetic and velocity dissipation scales, present-day direct numerical simulations cannot directly address astrophysical magnetohydrodynamic (MHD) regimes." Ixdeed. maximal Bevnolds and magnetic Hevnolds numbers accessible with numerical simulations are hopelessly small. of the order of 10*—10. in which case the typical magnetic Prandtl numbers are. not sienificantly different from Pa~1.," Indeed, maximal Reynolds and magnetic Reynolds numbers accessible with numerical simulations are hopelessly small, of the order of $10^3-10^4$, in which case the typical magnetic Prandtl numbers are not significantly different from ${\rm Pm}\sim 1$." A physical picture of magnetic dvnamo action and an elfective analvlic Lramework for investigating astrophysical dvnamo action are therefore in demand., A physical picture of magnetic dynamo action and an effective analytic framework for investigating astrophysical dynamo action are therefore in demand. The first step in understanding dynamo action is to understand (he initial. kinematic stage of magnetic [ield amplification.," The first step in understanding dynamo action is to understand the initial, kinematic stage of magnetic field amplification." In (hiis regime. the magnetic [field is weak and does not affect the velocity fluctuations.," In this regime, the magnetic field is weak and does not affect the velocity fluctuations." Magnetic field evolution is therefore fully described bv the induction equation in which the velocity [field is prescribed independently of the magnetic field., Magnetic field evolution is therefore fully described by the induction equation in which the velocity field is prescribed independently of the magnetic field. An elfective freunework in this case is provided by the so-called model. where the velocity field is assumed to be a random Gaussian field.," An effective framework in this case is provided by the so-called Kazantsev-Kraichnan model, where the velocity field is assumed to be a random Gaussian short-time-correlated field." ‘This formal simplification allows for analvlic solutions of the mocel while capturing the essential physics of the phenomenon., This formal simplification allows for analytic solutions of the model while capturing the essential physics of the phenomenon. We should note however that even with (his simplification the model is nontrivial and its general solution is not known., We should note however that even with this simplification the model is nontrivial and its general solution is not known. Onlv certain special cases have been solved so far. which reveal a good agreement wilh numerical simulations in the parameter range accessible to. numerics (e.g...Maronllaugen.Brandenburg&Dobler2004:DoldyrevCattaneo 2004).," Only certain special cases have been solved so far, which reveal a good agreement with numerical simulations in the parameter range accessible to numerics \citep[e.g.,][]{maron,haugen,boldyrev-cattaneo}." . The Ixazantsev-Ixraichnan dynamo model allows one to answer the fundamental questions concerning the possibility of turbulent. dynamo action for given Revnolds ancl magnetic Revnolds numbers. (he spectrum of growing magnetic fluctuations. the conditions for magnetic fiekl amplification. etc.," The Kazantsev-Kraichnan dynamo model allows one to answer the fundamental questions concerning the possibility of turbulent dynamo action for given Reynolds and magnetic Reynolds numbers, the spectrum of growing magnetic fluctuations, the conditions for large-scale magnetic field amplification, etc." In many instances. (he results obtzined in munerical sinmlations were predicted by the model well before such simulations," In many instances, the results obtained in high-resolution numerical simulations were predicted by the model well before such simulations" burning is ruled out by the lack of appreciable N enrichment.,burning is ruled out by the lack of appreciable N enrichment. Sodium stands apart from this picture: [Na/Fe] =|0.8 is neither a ratio found among normal stars nor easily accounted for on nucleosynthetic grounds.," Sodium stands apart from this picture: [Na/Fe] $= +0.8$ is neither a ratio found among normal stars nor easily accounted for on nucleosynthetic grounds." The Na abundance appears to be affected by non-LTE effects., The Na abundance appears to be affected by non-LTE effects. Non-LTE analysis of Na T lines by Takeda Takada-Hidai (1994) indicates the non-LTE corrections GMogc( in lines at 4979. 5683. 5688. and 8195 iis -0.06. -0.15. -0.20 and -0.94 dex respectively at temperature 6000 K and gravity 0.5 dex.," Non-LTE analysis of Na I lines by Takeda Takada-Hidai (1994) indicates the non-LTE corrections $\Delta log\epsilon(X)$ in lines at 4979, 5683, 5688, and 8195 is -0.06, -0.15, -0.20 and -0.94 dex respectively at temperature 6000 K and gravity 0.5 dex." (0.2 em Operation of the s-process would be expected to lead to overabundances of Y and Zr but underabundances (relative to Fe) are found., 0.2 cm Operation of the $s$ -process would be expected to lead to overabundances of Y and Zr but underabundances (relative to Fe) are found. At [Fe/H] ~1. Y and Zr underabundances are not found among normal stars.," At [Fe/H] $\simeq -1$, Y and Zr underabundances are not found among normal stars." Thus. the Y and Zr abundances for IRAS 1809542704 present a puzzle.," Thus, the Y and Zr abundances for IRAS 18095+2704 present a puzzle." It is not clear if the same puzzle is provided by the heavier elements Ba. La. and Nd for which the s-process would provide some enrichment.," It is not clear if the same puzzle is provided by the heavier elements Ba, La, and Nd for which the $s$ -process would provide some enrichment." Barium is nominally consistent with the Y and Zr in suggesting a slight underabundance ([Ba/Fe] =— 0.2)., Barium is nominally consistent with the Y and Zr in suggesting a slight underabundance ([Ba/Fe] $=-0.2$ ). Our search for La and Nd proved unsuccessful and the upper limits [La/Fe] ~ [Nd/Fe] 0 are consistent with results for normal stars and also with the Y. Zr. and Ba abundances for TRAS 18095-2704.," Our search for La and Nd proved unsuccessful and the upper limits [La/Fe] $\simeq$ [Nd/Fe] $\simeq 0$ are consistent with results for normal stars and also with the Y, Zr, and Ba abundances for IRAS 18095+2704." The r-process Eu abundance is that expected for a normal star: any s-process contribution to Eu is expected to be very slight even had the S-process operated in TRAS 1809542704. (Sneden et al., The $r$ -process Eu abundance is that expected for a normal star; any $s$ -process contribution to Eu is expected to be very slight even had the $s$ -process operated in IRAS 18095+2704 (Sneden et al. 2010)., 2010). In summary. Y and Zr underabundances represent a puzzle.," In summary, Y and Zr underabundances represent a puzzle." One is struck by the fact that Y and Zr with Al have condensation emperatures among the highest of the elements in Table 4., One is struck by the fact that Y and Zr with Al have condensation temperatures among the highest of the elements in Table 4. All are underabundant relative to expectation., All are underabundant relative to expectation. We noted above that he abundances do not always correlate well with condensation emperature., We noted above that the abundances do not always correlate well with condensation temperature. But elements with condensation temperatures hotter han 1550K generally appear among the most underabundant. the set includes Al. Ca. Sc. Ti. Y. Zr. and Ba. (," But elements with condensation temperatures hotter than 1550K generally appear among the most underabundant - the set includes Al, Ca, Sc, Ti, Y, Zr, and Ba. (" "La and Nd also ""all in the set but upper limits to their abundances restricts their relevance here.)",La and Nd also fall in the set but upper limits to their abundances restricts their relevance here.) At [Fe/H] :0.3. the Ca and Ti abundance should be judged with respect to their overabundance relative to Fe by about 0.3 dex in normal stars. te. add about =0.3 dex to the entries for [X/Fe] in Table 5 when judging abundance anomalies according to condensation temperature.," At [Fe/H] $\leq -0.3$, the Ca and Ti abundance should be judged with respect to their overabundance relative to Fe by about 0.3 dex in normal stars, i.e., add about $-0.3$ dex to the entries for [X/Fe] in Table 5 when judging abundance anomalies according to condensation temperature." Then. the [X/Fe] for Al. Ca. Ti. Y. Zr. and Ba are quite similar for these elements of a similar condensation temperature.," Then, the [X/Fe] for Al, Ca, Ti, Y, Zr, and Ba are quite similar for these elements of a similar condensation temperature." Scandium appears to be mildly overabundant with respect to the speculation that elements of the highest condensation temperature (Te:1500 K) are underabundant in IRAS. 180952704., Scandium appears to be mildly overabundant with respect to the speculation that elements of the highest condensation temperature $_C > 1500$ K) are underabundant in IRAS 18095+2704. In spite of the above remarks about abundances and condensation. temperatures. similarities. with the compositions of some RV Tauri variables are present.," In spite of the above remarks about abundances and condensation temperatures, similarities with the compositions of some RV Tauri variables are present." Among RV. Tauri variables and the presumably closely related W Vir. variables (Maas et al., Among RV Tauri variables and the presumably closely related W Vir variables (Maas et al. 2007). the correlation between abundance anomalies and condensation temperature runs from strong to weak.," 2007), the correlation between abundance anomalies and condensation temperature runs from strong to weak." IRAS 1809542704 definitely falls among the latter group., IRAS 18095+2704 definitely falls among the latter group. There is a fair correspondence between the composition of IRAS 18054-2704 and the RV Tauri variable AI Sco (Giridhar et al., There is a fair correspondence between the composition of IRAS 1805+2704 and the RV Tauri variable AI Sco (Giridhar et al. 2005) (Figure 19)).7 In part. Figure 19 may reflect the fact that systematic errors (e.g.. non-LTE effects) are of similar magnitude for the two stars with similar atmospheric parameters: (fap. logο. Fe/1 (6500. 40.5. 0.9) for IRAS 1809542704. and (5300. 0.25. -0.7) for AI Sco.," 2005) (Figure \ref{f_AI_SCO}) In part, Figure \ref{f_AI_SCO} may reflect the fact that systematic errors (e.g., non-LTE effects) are of similar magnitude for the two stars with similar atmospheric parameters: $T_{\rm eff}$, $\log\,g$, $[Fe/H]$ )=(6500, +0.5, $-$ 0.9) for IRAS 18095+2704 and (5300, 0.25, -0.7) for AI Sco." Stars exhibiting a striking correlation involving condensation temperature seem certain to be binaries with a circumbinary disk providing infall of gas but not dust onto the star responsible for the anomalies (Van Winckel 2003)., Stars exhibiting a striking correlation involving condensation temperature seem certain to be binaries with a circumbinary disk providing infall of gas but not dust onto the star responsible for the anomalies (Van Winckel 2003). For those stars (e.g... AI Sco) with hints of a correlation involving the condensation temperature. their binary status is unknown.," For those stars (e.g., AI Sco) with hints of a correlation involving the condensation temperature, their binary status is unknown." Certainly. the lack of a strong radial velocity variation for IRAS. 1809542704 may suggest that is a single star.," Certainly, the lack of a strong radial velocity variation for IRAS 18095+2704 may suggest that it is a single star." But. perhaps. a wind off the star. as may be suggested by the strong blue asymmetry for strong lines. provides the site for dust-gas separation.," But, perhaps, a wind off the star, as may be suggested by the strong blue asymmetry for strong lines, provides the site for dust-gas separation." In summary. we suppose that IRAS |80954-2704 may be related to a RV Tauri variable. probably one ctjat has evolved to hotter temperatures beyond the instability strip.," In summary, we suppose that IRAS 18095+2704 may be related to a RV Tauri variable, probably one that has evolved to hotter temperatures beyond the instability strip." (0.2 em Abundance analysis of TRAS 1809542704. classified as a proto-planetary nebula by Hrivnak et al. (, 0.2 cm Abundance analysis of IRAS 18095+2704 classified as a proto-planetary nebula by Hrivnak et al. ( 1988) suggests the star left the AGB before thermal pulses had the opportunity to enrich the atmosphere in the principal products from He-shell burning ¢C and s-process nuclides).,1988) suggests the star left the AGB before thermal pulses had the opportunity to enrich the atmosphere in the principal products from He-shell burning (C and $s$ -process nuclides). The star is not exceptional in this regard - see. for example. the abundance analyses of post-AGB stars reviewed by Van Winckel (2003).," The star is not exceptional in this regard - see, for example, the abundance analyses of post-AGB stars reviewed by Van Winckel (2003)." If the stars Fe abundance is adopted as a reference. the composition of IRAS 1809542704 is normal except for an underabundance of Al. Y and Zr.," If the star's Fe abundance is adopted as a reference, the composition of IRAS 18095+2704 is normal except for an underabundance of Al, Y and Zr." A speculation was offered that elements including AI. Y. and Zr having a condensation temperature hotter than 13500 K are underabundant.," A speculation was offered that elements including Al, Y, and Zr having a condensation temperature hotter than 1500 K are underabundant." This suggests that the atmosphere is depleted in those elements that condense most readily into dust grains., This suggests that the atmosphere is depleted in those elements that condense most readily into dust grains. Perhaps. the wind which is suggested by the pronounced blue asymmetry to the lines of strong lines removes grains selectively.," Perhaps, the wind which is suggested by the pronounced blue asymmetry to the lines of strong lines removes grains selectively." Although a variety of spectroscopic indicators provide a consistent set of atmospheric parameters. the high-resolution optical spectra offer evidence that IRAS 18095427045 atmosphere," Although a variety of spectroscopic indicators provide a consistent set of atmospheric parameters, the high-resolution optical spectra offer evidence that IRAS 18095+2704's atmosphere" "the case for the CO index CO,, used by Dovon ct al. (1994).","the case for the CO index $_{sp}$ used by Doyon et al. \shortcite{do:94}," . which extends over a restframe wavelength range of 2.3202.400 jin and would have been allected by large ane uncertain telluric absorption anc emission for the highes redshilt galaxies in the present sample., which extends over a restframe wavelength range of 2.320–2.400 $\mu$ m and would have been affected by large and uncertain telluric absorption and emission for the highest redshift galaxies in the present sample. Thus we only presen gi values in this paper., Thus we only present $_{EW}$ values in this paper. A further advantage of the Oz definition of Puxlev et al., A further advantage of the $_{EW}$ definition of Puxley et al. (1997). is that it is almost completely: unalfecte bv velocity. dispersion. elfects. due to the wide range of wavelength over which the absorption is measured.," \shortcite{pu:97} is that it is almost completely unaffected by velocity dispersion effects, due to the wide range of wavelength over which the absorption is measured." Puxlev et al., Puxley et al. (1997). find the velocity dispersion corrections to be insignificant. which we confirmed by smoothing low-velocity-dispersion galaxy spectra to an effective velocity dispersion of 500 +.," \shortcite{pu:97} find the velocity dispersion corrections to be insignificant, which we confirmed by smoothing low-velocity-dispersion galaxy spectra to an effective velocity dispersion of 500 $^{-1}$." The resulting change in gi was 70.254. very much smaller than the random errors.," The resulting change in $_{EW}$ was $\sim$ , very much smaller than the random errors." The errors on the COpgy values include three components., The errors on the $_{EW}$ values include three components. “Phe first was calculated. [rom the standard deviation in the fitted continuum points. on the assumption that the noise level remains constant through the CO absorption. giving an error on both the continuum level and on the mean level in the CO absorption. which were aded in quadrature.," The first was calculated from the standard deviation in the fitted continuum points, on the assumption that the noise level remains constant through the CO absorption, giving an error on both the continuum level and on the mean level in the CO absorption, which were added in quadrature." Lhe second error component comes from the formal error. provided by the continuum fitting procedure., The second error component comes from the formal error provided by the continuum fitting procedure. This procedure could. leave a residual tilt or curvature in the spectrum. and the formal error was used to quantify this contribution.," This procedure could leave a residual tilt or curvature in the spectrum, and the formal error was used to quantify this contribution." The final component was an estimate of the error. induced. by redshift and wavelength. calibration uncertainties., The final component was an estimate of the error induced by redshift and wavelength calibration uncertainties. All three errors were of similar sizes. with only the first varving from spectrum to spectrum. as a result of signal-to-noise variations (see Fig.," All three errors were of similar sizes, with only the first varying from spectrum to spectrum, as a result of signal-to-noise variations (see Fig." 1). and all three were actelecl in quadrature to give the value quoted in Table 1.," 1), and all three were added in quadrature to give the value quoted in Table 1." The equivalent. widths of €O absorption features for the sample of BCCGs. observed. in this. study are. presented in Table 1., The equivalent widths of CO absorption features for the sample of BCGs observed in this study are presented in Table 1. " The data included. in this table are bell (1958) catalogue numbers (column 1). BCG names (column 2). COr values with Loo errors (column 3). recession velocity in (column 4). absolute R-bancl magnitude corresponding to the metric luminosity L,, ((column 5).r structure parameter (a) (column 6) and the magnitude residual relative to the best-lit £,, o relation (column 7). (columns 47 are all taken from Lauer Postman (1994).. who assumed a Lubble constant of SO kms‘Mpc +)."," The data included in this table are Abell \shortcite{ab:58} catalogue numbers (column 1), BCG names (column 2), $_{EW}$ values with $\sigma$ errors (column 3), recession velocity in $^{-1}$ (column 4), absolute R-band magnitude corresponding to the metric luminosity $L_m$ (column 5), structure parameter $\alpha$ ) (column 6) and the magnitude residual relative to the best-fit $L_m$ $\alpha$ relation (column 7), (columns 4–7 are all taken from Lauer Postman \shortcite{la:94}, who assumed a Hubble constant of 80 $^{-1}$ $^{-1}$ )." Columns S and 9 contain velocity dispersions anc Me» metallicity indices. where available. from Faber οἱ al. (1989).," Columns 8 and 9 contain velocity dispersions and $_2$ metallicity indices, where available, from Faber et al. \shortcite{fa:89}." . We find the mean COpiy value for the 21. BCCs (3.3540.03) to be ellectively identical to that of the Coma cluster ellipticals +0.04) (Alobasher&James1999).. and to that of the 31 cllipticals from a range ol clusters discussed by James Alobasher (1999). (3.29-£0.06).," We find the mean $_{EW}$ value for the 21 BCGs $\pm$ 0.03) to be effectively identical to that of the Coma cluster ellipticals $\pm$ 0.04) \cite{mo:99}, and to that of the 31 ellipticals from a range of clusters discussed by James Mobasher \shortcite{ja:99} $\pm$ 0.06)." " Phe cluster and BCG distributions lie between the distributions of ""isolated? and ""group! field cllipticals discussed by Jamies Mobasher (1999) and shown in Fig.", The cluster and BCG distributions lie between the distributions of `isolated' and `group' field ellipticals discussed by James Mobasher \shortcite{ja:99} and shown in Fig. 2a., 2a. The major cilference between the BCG ey values and those of other cllipticals is the remarkably small range in the former: the stancarel deviation for BCCs is 0.156. compared to 0.240 for Coma ellipticals. 0.337 for general cluster galaxies. aud 0.422 for cluster plus field. ellipticals.," The major difference between the BCG $_{EW}$ values and those of other ellipticals is the remarkably small range in the former: the standard deviation for BCGs is 0.156, compared to 0.240 for Coma ellipticals, 0.337 for general cluster galaxies, and 0.422 for cluster plus field ellipticals." Indeed. the scatter in BCG CO absorption strengths is that. predicted: from jo error estimates on the individual pg values. ancl so 10 intrinsic scatter may be much smaller still.," Indeed, the scatter in BCG CO absorption strengths is that predicted from the error estimates on the individual $_{EW}$ values, and so the intrinsic scatter may be much smaller still." Given the small number of BCC galaxies. a Ixolmogorov-Smirnov test cannot distinguish. between the distributions of BCC and ‘luster or Coma galaxies in Figs.," Given the small number of BCG galaxies, a Kolmogorov-Smirnov test cannot distinguish between the distributions of BCG and cluster or Coma galaxies in Figs." 2b and 2c. but there is less van chance that the BOCs are drawn from the same parent population as all the non-BCC ellipticals. and. less ian hance that they are from the same population as field ellipticals (Pig.," 2b and 2c, but there is less than chance that the BCGs are drawn from the same parent population as all the non-BCG ellipticals, and less than chance that they are from the same population as field ellipticals (Fig." 2a)., 2a). The BCGs are drawn from a much narrower region of the galaxy luminosity function than are the comparison samples in Fig., The BCGs are drawn from a much narrower region of the galaxy luminosity function than are the comparison samples in Fig. 2. which could allect the interpretation of this result.," 2, which could affect the interpretation of this result." The 21 DCCGs have a range in Mj of-22.0 to -23.1. little. more than a magnitude.," The 21 BCGs have a range in $_R$ of-22.0 to -23.1, little more than a magnitude." R-bancl photometry is not available for all the comparison galaxies. but good. estimates can be mace fron published. optical and," R-band photometry is not available for all the comparison galaxies, but good estimates can be made from published optical and" "mean values of 6.8+0.8Mo(Kkms!pc?)*! and 3.33:0.8Mo(Kkms!pc?)-1, respectively (the quoted errorsrepresent the lo uncertainty in the mean).","mean values of $6.8\pm0.8\,\xcounits$ and $3.3\pm0.8\,\xcounits$, respectively (the quoted errorsrepresent the $\sigma$ uncertainty in the mean)." " B08 derive 7.673Mc(Kkms~!pc?)-! for the extragalactic ensemble (the errors represent the scatter in the data), which is in good agreement with the M33 inner disk value."," B08 derive $7.6^{+3.9}_{-2.6}\,\xcounits$ for the extragalactic ensemble (the errors represent the scatter in the data), which is in good agreement with the M33 inner disk value." " We test the significance of the difference between the M33 inner and outer disk means with a Student’s t-test, which yields a probability of ~1% for the null hypothesis that both means are equal."," We test the significance of the difference between the M33 inner and outer disk means with a Student's t-test, which yields a probability of $\sim1\%$ for the null hypothesis that both means are equal." This implies that the average cconversion factor for the outer disk GMCs is in fact smaller (by about a factor of two) than the extragalactic and the M33 inner disk average., This implies that the average conversion factor for the outer disk GMCs is in fact smaller (by about a factor of two) than the extragalactic and the M33 inner disk average. " This finding is contrary to the expectations based on environmental conditions, which suggested a somewhat higher conversion factor (Section 3))."," This finding is contrary to the expectations based on environmental conditions, which suggested a somewhat higher conversion factor (Section \ref{environ}) )." One factor that could influence ((and is particularly relevant in outer disks) is a decreasing fraction of CO emitting iin the more dust and metal-poor environment at larger radii (see Section 3))., One factor that could influence (and is particularly relevant in outer disks) is a decreasing fraction of CO emitting in the more dust and metal-poor environment at larger radii (see Section \ref{environ}) ). We therefore compare our measurements to complementary eestimates in M33 from(2010)., We therefore compare our measurements to complementary estimates in M33 from. ". They estimate ffrom dust modeling (thus tracing the entire ddistribution under the assumption that gas and dust are well mixed) and find values of »6.3Mo(Kkms! απ ~4.7Mo(Kkms!pc?)7! for the innerpc?)-! and outer part of M33, respectively."," They estimate from dust modeling (thus tracing the entire distribution under the assumption that gas and dust are well mixed) and find values of $\sim6.3\,\xcounits$ and $\sim4.7\,\xcounits$ for the inner and outer part of M33, respectively." " These numbers are in good agreement with our virial mass estimates, which argues against a significant amount of CO-dark aat large radii."," These numbers are in good agreement with our virial mass estimates, which argues against a significant amount of CO-dark at large radii." " We note that because the values are averages over a large area, the application of these values to our specific region does not rule out conclusively unaccounted forH»."," We note that because the values are averages over a large area, the application of these values to our specific region does not rule out conclusively unaccounted for." ". Taken at face value, however, the lower average conversion factor we measure for the outer disk clouds could be interpreted as a higher fractional CO abundance, i.e, more “CO per Πο»."," Taken at face value, however, the lower average conversion factor we measure for the outer disk clouds could be interpreted as a higher fractional CO abundance, i.e., more “CO per '." " This is highly unlikely, however, given the much lower dust-to-gas ratios and metallicities at larger radii in M33 (compare Section "," This is highly unlikely, however, given the much lower dust-to-gas ratios and metallicities at larger radii in M33 (compare Section \ref{environ}) )." "On the other hand, sscales3)). inversely with the brightness temperature: acoc 1988)."," On the other hand, scales inversely with the brightness temperature: $\aco\propto{\rm T_{B}}^{-1}$ ." " Thus, the more likely explanation seems to be the"," Thus, the more likely explanation seems to be the" see that the lensing tail is relatively important above about 20mm.Jy and more so for higher redshift submnm galaxies.,see that the lensing tail is relatively important above about mJy and more so for higher redshift submm galaxies. The cumulative source counts. are used to determine the density of sources above a given Hux on the sky.," The cumulative source counts, are used to determine the density of sources above a given flux on the sky." This is a useful quantity for making observational predictions for surveys., This is a useful quantity for making observational predictions for surveys. Examining the contribution to source counts as a function of fui. as ceseribecl above. we set. somewhat arbitrarily (though consistent with ? and 7?7)) a characteristic magnification for lensing events of fin2.," Examining the contribution to source counts as a function of $\mu_\rmn{min}$, as described above, we set, somewhat arbitrarily (though consistent with \citealt{Negrello07} and \citealt{Perrotta02}) ), a characteristic magnification for lensing events of $\mu_\rmn{min}=2$." In Fig., In Fig. " 6 we plot the contribution as a function of Sur for various redshifts. as well as the ‘best’ and ""maximal estimates for the average over all redshiftsο"," \ref{fig:mmu-combo} we plot the contribution as a function of $\Sobs$ for various redshifts, as well as the `best' and `maximal' estimates for the average over all redshifts." This quantifies the probability that an object. observed a some Sui has been lensed with a magnificationὃν >greater than 2., This quantifies the probability that an object observed at some $\Sobs$ has been lensed with a magnification greater than $2$. One could easily obtain similar results for any other c.vice of minimal amplification., One could easily obtain similar results for any other choice of minimal amplification. There have been several attempts to characterise the redshift’ distribution of SALGs., There have been several attempts to characterise the redshift distribution of SMGs. ποσα p1enomenological models do exist. (e.g.7) we focus on estimates based purely on observational data.," Though phenomenological models do exist \citep[e.g.,][]{Granato01} we focus on estimates based purely on observational data." ? obtained a Large number of spectroscopic redshifts for radio selected: galaxies. while 7? obtained both spectroscopic ancl photometric recdshifts in the COODS-North survey. and ?/— used. racio/submim photometric redshifts in the SCUBA Half Degree Survey (SHADES).," \citet{Chapman05} obtained a large number of spectroscopic redshifts for radio selected galaxies, while \citet{Pope06} obtained both spectroscopic and photometric redshifts in the GOODS-North survey, and \citet{Aretxaga07} used radio/submm photometric redshifts in the SCUBA Half Degree Survey (SHADES)." All three are consistent with ao Gaussian distribution centred at ο=2.2+0.1 and with e=O0.8+0.1.," All three are consistent with a Gaussian distribution centred at $z=2.2 \pm 0.1 $ and with $\sigma=0.8 \pm 0.1$." ‘This is the distribution we use to obtain the average over redshift in Fie.6.. The results are. nearly identical. when varving the peak redshift by Εθι1., This is the distribution we use to obtain the average over redshift in Fig.\ref{fig:mmu-combo}. The results are nearly identical when varying the peak redshift by $\pm0.1$. Fig., Fig. 6 shows that for sources with Son.c 20mJw the probability of strong lensing is already LO20 per cent for any reasonable redshift distribution.," \ref{fig:mmu-combo} shows that for sources with $\Sobs \simeq 20\,$ mJy the probability of strong lensing is already 10–20 per cent for any reasonable redshift distribution." Empirical evidence suggests that this may be a conservative estimate. since at the moment all sources detected with Son. 20mJy at S50 jn have been claimed to be Ilensecd.," Empirical evidence suggests that this may be a conservative estimate, since at the moment all sources detected with $\Sobs \ga 20\,$ mJy at $850\,\mu$ m have been claimed to be lensed." We can also look at the average amplification as a function of observed Lux density. given by This is shown in Fig.," We can also look at the average amplification as a function of observed flux density, given by This is shown in Fig." 7 across a range of redshifts., \ref{fig:ave} across a range of redshifts. One can see a change in behaviour at higher and lower lux densities. depending on the source redshift.," One can see a change in behaviour at higher and lower flux densities, depending on the source redshift." Below about 35mm.Jv the mean anplification increases with recshilt. while above 35 mv it decreases with redshift.," Below about mJy the mean amplification increases with redshift, while above $35\,$ mJy it decreases with redshift." This is cue to the change in dominance between the (ijz1 peak and the high j£ tail. an effect that can be seen in the bottom panel of Fig. 3..," This is due to the change in dominance between the $\mu \simeq 1$ peak and the high $\mu$ tail, an effect that can be seen in the bottom panel of Fig. \ref{fig:z2-amp-combo}." ? discuss how they may have underestimated the lensing, \citet{Hilbert07} discuss how they may have underestimated the lensing aud others zero.,and others zero. " Alter diflerentiating aud combining compouents. we have: The linear term (the first term) in Eq (1)) gives. for instance thelorce dP,/df on the binary systel: The force computecl is applied to the total mass. so we find the iudividual black hole velocity by time integrating Eq (16)). using d!=b/vg. auddividing the result by 215."," After differentiating and combining components, we have: The linear term (the first term) in Eq \ref{kickEQ}) ) gives, for instance theforce $dP_x/dt$ on the binary system: The force computed is applied to the total mass, so we find the individual black hole velocity by time integrating Eq \ref{dP_x/dt}) ), using $dt= b/v_0$, anddividing the result by $2m$." " The velocities are estimated in Ans fora,Sa.2 nm. e2 1. and sRz5 (closest approach = Lr): Similarly."," The velocities are estimated in $km/s$ for $a_x\approx a_z\approx m$ , $v \approx 1$ , and $\frac{m}{b} \approx \frac{1}{2}$ (closest approach $= 4m$ ): Similarly," 5 Jupiter masses.,5 Jupiter masses. " The latter is twice the M sin(i) = 2M,,,,of Gl 876b (??) and HIP79431b (?),, previously the highest mass planets found by radial velocity monitoring of M dwarfs, and above the 3.8 or 3.4 (from two degenerate solutions) of the OGLE-2005-BLG-071Lb (?) microlensing planet."," The latter is twice the M sin(i) = of Gl 876b \citep{Delfosse1998,Marcy1998} and HIP79431b \citep{Apps2010}, previously the highest mass planets found by radial velocity monitoring of M dwarfs, and above the 3.8 or 3.4 (from two degenerate solutions) of the OGLE-2005-BLG-071Lb \citep{Dong2009} microlensing planet." " The MOV Gl 676A however is significantly more massive (0.71Mo,, Table 1)) than the M4V G1876 (0.33Μο?) and the M3V HIP79431 (0.49Μο?).."," The M0V Gl 676A however is significantly more massive (0.71, Table \ref{table:stellar}) ) than the M4V Gl 876 \citep[0.33~\Msol][]{Correia2010} and the M3V HIP79431 \citep[0.49~\Msol][]{Apps2010}." The higher mass of its planet therefore remains in approximate line with the current upper envelope of the planetary versus stellar mass diagram., The higher mass of its planet therefore remains in approximate line with the current upper envelope of the planetary versus stellar mass diagram. " These most massive planets are rare at any stellar mass, with an occurence rate under1%,, suggesting that they can form only under the most favorable conditions."," These most massive planets are rare at any stellar mass, with an occurence rate under, suggesting that they can form only under the most favorable conditions." " They have been suggested to form through gravitational instability, with their lower mass counterparts forming by core accretion."," They have been suggested to form through gravitational instability, with their lower mass counterparts forming by core accretion." " Proto-planetary disks of any realistic mass, however, are expected be gravitationally stable out to beyond 10 AU."," Proto-planetary disks of any realistic mass, however, are expected be gravitationally stable out to beyond 10 AU." " If Gl 676Ab formed through gravitational instability, it would therefore have undergone much inward migration, through a very massive disk."," If Gl 676Ab formed through gravitational instability, it would therefore have undergone much inward migration, through a very massive disk." How it could escape accreting enough mass during this migration to become a brown dwarf is unclear., How it could escape accreting enough mass during this migration to become a brown dwarf is unclear. " Gl 676A and HIP 12961 increase the sample of M dwarfs with giant planets (Saturn-mass and above) from 7 to 9, and therefore offer an opportunity to evaluate the trend (??) for giant planets being more common around more metal-rich M dwarfs."," Gl 676A and HIP 12961 increase the sample of M dwarfs with giant planets (Saturn-mass and above) from 7 to 9, and therefore offer an opportunity to evaluate the trend \citep{Johnson2009,Schlaufman2010} for giant planets being more common around more metal-rich M dwarfs." " Adopting the very recent ? metallicity calibration of the Mx, vs V-Ks plane, which finds metallicities approximately half-way between those of the earlier ? and ? calibrations, the metallicities of Gl 676A and HIP 12961 are 0.18 and —0.07."," Adopting the very recent \cite{Schlaufman2010} metallicity calibration of the $_{K_s}$ vs $_S$ plane, which finds metallicities approximately half-way between those of the earlier \citet{Bonfils2005} and \citet{Johnson2009} calibrations, the metallicities of Gl 676A and HIP 12961 are $0.18$ and $-0.07$." " Both values are above the [Fe/H] = -0.17 average metallicity for the solar neighborhood in the ? metallicity scale, the latter very significantly so."," Both values are above the [Fe/H] = -0.17 average metallicity for the solar neighborhood in the \cite{Schlaufman2010} metallicity scale, the latter very significantly so." " The two new planets therefore clearly reinforce the incipient trend, and help suggest that more massive planets are found around more metal-rich M-dwarfs."," The two new planets therefore clearly reinforce the incipient trend, and help suggest that more massive planets are found around more metal-rich M-dwarfs." , "intermediate region (transition from optically thick to optically thin) in the outward radial direction, which is shielded from the direct irradiation and is not in good agreement with the FLD approximation.","intermediate region (transition from optically thick to optically thin) in the outward radial direction, which is shielded from the direct irradiation and is not in good agreement with the FLD approximation." Approximating the frequency dependence of the stellar spectrum by gray (frequency averaged) Planck mean opacities results in an overestimation of the optical depth in the infrared part and an underestimation of the absorption in the ultraviolet part of the stellar spectrum (see Fig. 2))., Approximating the frequency dependence of the stellar spectrum by gray (frequency averaged) Planck mean opacities results in an overestimation of the optical depth in the infrared part and an underestimation of the absorption in the ultraviolet part of the stellar spectrum (see Fig. \ref{Opacities}) ). This leads to an under- or overestimation of the radiative force onto dust grains at the first absorption peak depending on the stellar luminosity due to less absorption of the most energetic UV photons or stronger absorption of the photons at the peak of the stellar black body spectrum., This leads to an under- or overestimation of the radiative force onto dust grains at the first absorption peak depending on the stellar luminosity due to less absorption of the most energetic UV photons or stronger absorption of the photons at the peak of the stellar black body spectrum. " Secondly, the gray approximation results in an underestimation of the resulting temperature deeply inside the disk due to absorption of the infrared photons already at inner disk radii."," Secondly, the gray approximation results in an underestimation of the resulting temperature deeply inside the disk due to absorption of the infrared photons already at inner disk radii." The quantitative amount of the resulting deviations depends in general on the specific stellar and dust properties., The quantitative amount of the resulting deviations depends in general on the specific stellar and dust properties. " Due to the steep decay of the stellar black body spectrum at high frequencies, the difference of the gray and frequency dependent radiative force turns out to be very small in this specific setup."," Due to the steep decay of the stellar black body spectrum at high frequencies, the difference of the gray and frequency dependent radiative force turns out to be very small in this specific setup." " On the other hand, consideration of the frequency dependence is essential to limit the deviations in the resulting temperature profile to less than (compared to for gray irradiation plus FLD, see Fig. 5))."," On the other hand, consideration of the frequency dependence is essential to limit the deviations in the resulting temperature profile to less than (compared to for gray irradiation plus FLD, see Fig. \ref{Tau1e+2_Irradiation+FLD_radial}) )." These issues are well illustrated in Fig. 2.., These issues are well illustrated in Fig. \ref{Opacities}. " The figure shows the frequency dependent opacities of ?,, the approximated frequency averaged value of the Planck mean opacity regarding the stellar effective surface temperature as well as the black body spectrum of the central star (to visualize the amount of radiative flux which is emitted per frequency bin)."," The figure shows the frequency dependent opacities of \citet{Draine:1984p594}, the approximated frequency averaged value of the Planck mean opacity regarding the stellar effective surface temperature as well as the black body spectrum of the central star (to visualize the amount of radiative flux which is emitted per frequency bin)." Each dot in the figure marks the mid-frequency of the correspondingly chosen frequency bin., Each dot in the figure marks the mid-frequency of the correspondingly chosen frequency bin. The effects on the resulting temperature profile and radiative force cannot be generalized easily., The effects on the resulting temperature profile and radiative force cannot be generalized easily. " They depend on the underlying dust model and strongly on the properties of the central star, which yield a shift of the peak position of the black body spectrum in Fig."," They depend on the underlying dust model and strongly on the properties of the central star, which yield a shift of the peak position of the black body spectrum in Fig." 2 according to Wien's displacement law νροικοςT., \ref{Opacities} according to Wien's displacement law $\nu_\mathrm{peak} \propto T$. " In the specific setup of ? the Planck mean opacity at the black body peak position is higher than the frequency dependent ones, leading to a slightly higher radiative force."," In the specific setup of \citet{Pascucci:2004p39} the Planck mean opacity at the black body peak position is higher than the frequency dependent ones, leading to a slightly higher radiative force." The strong overestimation of the opacity in the infrared regime leads to the huge discrepancy of the gray approximation in the radial temperature profile through the disk., The strong overestimation of the opacity in the infrared regime leads to the huge discrepancy of the gray approximation in the radial temperature profile through the disk. The parallelization of the radiation transport scheme and the GMRES solver (see Sect., The parallelization of the radiation transport scheme and the GMRES solver (see Sect. " 2.4 for details of how the solver works) are taken care of by the PETSc library (Portable, Extensible Toolkit for Scientific computation), see also ?.."," \ref{sect:gmres} for details of how the solver works) are taken care of by the PETSc library (Portable, Extensible Toolkit for Scientific computation), see also \cite{petsc-efficient}." To test the parallel speedup of the implemented radiation transport module we perform two tests with an extended version of the circumstellar disk setup introduced in Sect. 3.1.., To test the parallel speedup of the implemented radiation transport module we perform two tests with an extended version of the circumstellar disk setup introduced in Sect. \ref{sect:setup}. We adopt the most optically thick setup for Tssonm=100 and expand it to three dimensions assuming axial symmetry., We adopt the most optically thick setup for $\tau_{550\mbox{nm}} = 100$ and expand it to three dimensions assuming axial symmetry. All runs include frequency dependent irradiation and Flux Limited Diffusion., All runs include frequency dependent irradiation and Flux Limited Diffusion. " The tests run for 10 main iterations, which consume the main computational effort for the approximate solver (later on, near equilibrium, the internal iterations needed decrease strongly)."," The tests run for 10 main iterations, which consume the main computational effort for the approximate solver (later on, near equilibrium, the internal iterations needed decrease strongly)." The number of internal iterations of the approximate implicit solver is fixed to 100 to guarantee the same amount of computation in all runs during this benchmark test., The number of internal iterations of the approximate implicit solver is fixed to 100 to guarantee the same amount of computation in all runs during this benchmark test. " Due to the parallel Block-Jacobian pre-conditioner, the number of needed internal iterations (for a specified accuracy) normally increases with increasing number of processors."," Due to the parallel Block-Jacobian pre-conditioner, the number of needed internal iterations (for a specified accuracy) normally increases with increasing number of processors." " The precise value for the increase is strongly problem dependent (B. F. Smith, member of the development team of the PETSc library, private communication)."," The precise value for the increase is strongly problem dependent (B. F. Smith, member of the development team of the PETSc library, private communication)." " The parallel domain (the linear system of equations) is split in the azimuthal and polar direction only, which insures good speedup and efficiency."," The parallel domain (the linear system of equations) is split in the azimuthal and polar direction only, which insures good speedup and efficiency." Decomposing the domain in the radial direction would decrease the parallel performance due to the fact that in the ray-tracing routine it is necessary to compute and therefore communicate the flux from the central sink cell to the outer boundary from the inside outward., Decomposing the domain in the radial direction would decrease the parallel performance due to the fact that in the ray-tracing routine it is necessary to compute and therefore communicate the flux from the central sink cell to the outer boundary from the inside outward. " Since the knowledge of the flux at the inner cell interface is needed to compute the flux at the outer interface, this method is hardly parallelizable as a domain decomposition."," Since the knowledge of the flux at the inner cell interface is needed to compute the flux at the outer interface, this method is hardly parallelizable as a domain decomposition." The measured times t» to {ῃ (n is the number of processors) represent the wall clock time per main iteration per grid cell without the non-recurring initialization and finalization of the code., The measured times $t_2$ to $t_n$ $n$ is the number of processors) represent the wall clock time per main iteration per grid cell without the non-recurring initialization and finalization of the code. We perform runs with 2 up to 64 processors due to the fact that single job submission is not available on the cluster we use., We perform runs with 2 up to 64 processors due to the fact that single job submission is not available on the cluster we use. " Cases, in which the local cache size would exceed the parallel decomposed problem size, are not taken into account, ie. no misleading super linear speedup for high number of used processors is shown here."," Cases, in which the local cache size would exceed the parallel decomposed problem size, are not taken into account, i.e. no misleading super linear speedup for high number of used processors is shown here." " The speedup S is calculated as the ratio of the ‘serial’ run time compared to the wall clock time used by the parallel run: S=f2/t,.", The speedup $S$ is calculated as the ratio of the `serial' run time compared to the wall clock time used by the parallel run: $S=t_2 / t_n$. " The efficiency E is determined via E=f/(t,n)S/n.", The efficiency $E$ is determined via $E = t_2 / (t_n ~ n) = S/n$. " Each run for a specific grid and a specific number of processors is performed three times and averaged afterwards, but the differences of the resulting run times are negligible."," Each run for a specific grid and a specific number of processors is performed three times and averaged afterwards, but the differences of the resulting run times are negligible." All tests are performed on a 64-Bit Opteron cluster consisting of 80 nodes with two CPUs each., All tests are performed on a 64-Bit Opteron cluster consisting of 80 nodes with two CPUs each. The runs during this test are performed on a grid consisting of 64x256 grid cells., The runs during this test are performed on a grid consisting of $64 \mbox{ x } 64 \mbox{ x } 256$ grid cells. " Each processor covers therefore a (64x64256)/n subdomain, depending on the number of processors used."," Each processor covers therefore a $\left(64 \mbox{ x } 64 \mbox{ x } 256\right) / n$ subdomain, depending on the number of processors used." This test shows the speedup one can gain when running a fixed problem on more and more processors., This test shows the speedup one can gain when running a fixed problem on more and more processors. " Therefore, the parallel efficiency declines stronger than in the following growing grid test due to the fact that with the usage of an increasing number of processors one lower the amount of computation and increase the amount of communication"," Therefore, the parallel efficiency declines stronger than in the following growing grid test due to the fact that with the usage of an increasing number of processors one lower the amount of computation and increase the amount of communication" cCluission is in the fast cooling regime.,emission is in the fast cooling regime. Within thin svuchrotron. there Is uo wav to obtain a>3/2.," Within thin synchrotron, there is no way to obtain $\alpha > -3/2$." This carlyrecognized requirement (Ikatz 1991) is πι) Inescapable iat it has been dubbed the ‘line of death’., This early–recognized requirement (Katz 1994) is so inescapable that it has been dubbed the `line of death'. Observations are notoriousvy discordan 3th this prediction., Observations are notoriously discordant with this prediction. Preece 44501999) have shown that. for more than 10 bursts. is distributed like a bell between 2 aud 0. with mean a~--l.," Preece (1999) have shown that, for more than 1000 bursts, $\alpha$ is distributed like a bell between $-2$ and $0$, with mean $\bar{\alpha} \approx -1$." The tail of us distribution also contains a few tens of objects with a~--1., The tail of this distribution also contains a few tens of objects with $\alpha \approx +1$. Α1 example of rese can be found in FronteraeL.. 1999 (CRB 970111). which is istructive since BeppoSAX has better coverage of the critical. lowplotouenerev region.," An example of these can be found in Frontera, 1999 (GRB 970111), which is instructive since BeppoSAX has better coverage of the critical, low–photon–energy region." In articular. BATSE secs to loose seusitivitv below ~--30keV. bu this ds sil iof chough to explain away the discrepancy witi the theory.," In particular, BATSE seems to loose sensitivity below $\approx 30\; keV$, but this is still not enough to explain away the discrepancy with the theory." " Also. Preecel... 1999. showed that the timeintegrated spectra energv5 distribution lasa peak a a ohotou euergy ej,2200keV. aud that 6,4: liHSavery sΠα]. variauce from burst ο burst."," Also, Preece, 1999, showed that the time–integrated spectral energy distribution has a peak at a photon energy $\epsilon_{pk} \approx 200\; keV$, and that $\epsilon_{pk}$ has a very small variance from burst to burst." Again. this does not seem dependent upou DATSIEs lack of seuxistivitv above TOOkeV. and again this has uo explanation1 within he classic fireball nioel.," Again, this does not seem dependent upon BATSE's lack of sensistivity above $700\; keV$, and again this has no explanation within the classic fireball model." " Any theorist who worked ou blazars will s:Ww that he root of he cdisagrecicut is the neglect of Tuverse Conipto1 processes, bu the trickX here is ueXt to ideutity the culprit. on which evervoue agrees. but to devIsc a firebal LOCel that siuiootilv incorporates it."," Any theorist who worked on blazars will say that the root of the disagreement is the neglect of Inverse Compton processes, but the trick here is not to identify the culprit, on which everyone agrees, but to devise a fireball model that smoothly incorporates it." One should remeuber that the «etails of the5 felill evolution aregeneric.4.0... they do not depen dipon auv doetaile« pro]xdy M the source. so that thines lise the radius at which the firebal becomes opticatlv thin (to pairs or barvouic electrons). the radius at which accelerajon ends.l hne equipartition iaenetie field. aud so on. are all reliably. and imescaably fixed bv the outflow's elobal proTonics.," One should remember that the details of the fireball evolution are, they do not depend upon any detailed property of the source, so that things like the radius at which the fireball becomes optically thin (to pairs or baryonic electrons), the radius at which acceleration ends, the equipartition magnetic field, and so on, are all reliably and inescapably fixed by the outflow's global properties." A step toward the solution has been nicee by 6hisellini anc Celotti (1999) who remarked that at least soue bursts have comραους parameters f=LOL10ergs1300/2yc91.," A step toward the solution has been made by Ghisellini and Celotti (1999) who remarked that at least some bursts have compactness parameters $l = 10 (L/10^{53}\; erg\; s^{-1}) (300/\gamma)^5\gg 1$." Under hese conditiols. a pair plasina will Ori. near vtlornalized at kTzinc. aud wit1 Thomson opical depth rr5-10.," Under these conditions, a pair plasma will form, nearly thermalized at $kT \approx m_e c^2$, and with Thomson optical depth $\tau_T \approx 10$." " The uocdificatious which this plasma will bri18o o the bursts spcchruna are currently uukuOW. ut it nay be remarked that this ""Oconfiguration wi1 o optica lvtuck to oth lüehCLOYSV svuchrotron photons due to nonthermal ele(ος aοςeleriuted at he 1iternal shocss. and to lowenergev eveotron photons enited by tιο fierinal asina. but it will be optical vtin in the intermediate regio1 reached DV CVClotron οποίος upscattered via IC processes off nou.thermal electroas."," The modifications which this plasma will bring to the burst's spectrum are currently unknown, but it may be remarked that this configuration will be optically thick to both high–energy synchrotron photons due to non–thermal electrons accelerated at the internal shocks, and to low–energy cyclotron photons emitted by the thermal plasma, but it will be optically thin in the intermediate region reached by cyclotron photons upscattered via IC processes off non–thermal electrons." " A lwle along this ine(hoe... upscatterine of cyclotron photous by highlv relativistic ekΤΟΙΣ} is dn xeparatioi (Vietri 2000a). ""t it relmaims to be seen whether it (like any other nodel. of course) can simulancously explain the spectral shape iux| the narrow range of the specral distrition peak energy ey."," A model along this line, upscattering of cyclotron photons by highly relativistic electrons) is in preparation (Vietri 2000a), but it remains to be seen whether it (like any other model, of course) can simultaneously explain the spectral shape and the narrow range of the spectral distribution peak energy $\epsilon_{pk}$." As vemarked several times already. the fireball evolution is independent of the source nature.," As remarked several times already, the fireball evolution is independent of the source nature." The oulv existing constraint is the maxiuun amount of barvon contamination. which is This is a remarkably siaalb value: since the inferred LDhunuinosities exceed the," The only exisiting constraint is the maximum amount of baryon contamination, which is This is a remarkably small value: since the inferred luminosities exceed the" our clusters in y-ray vers.,our clusters in $\gamma$ -ray vers. X-ray luminosity for the 3 models., X-ray luminosity for the 3 models. Also in this case we show two y-ray upper limits from VERITAS (?) and preliminary FERMI (?) observations respectively., Also in this case we show two $\gamma$ -ray upper limits from VERITAS \citep{1992A&AS...95..129P} and preliminary FERMI \citep{2009arXiv0912.3346M} observations respectively. " A quasi—linear correlation is predicted, and is found less scattered than that between ""-ray and radio luminosities since it compares two purely thermal quantities (also in the case of models 2 and 3 CRp are scaled with thermal energy according with the profile in Figure 4))."," A quasi--linear correlation is predicted, and is found less scattered than that between $\gamma$ -ray and radio luminosities since it compares two purely thermal quantities (also in the case of models 2 and 3 CRp are scaled with thermal energy according with the profile in Figure \ref{img_xcr}) )." The FERMI results are still consistent with the models for CRp presented in this paper., The FERMI results are still consistent with the models for CRp presented in this paper. As shown by ?) the expected - flux increases substantially if we consider a spatial CR proton distribution so the radio emission actually fits the observations in morphology., As shown by \citet{2010MNRAS.401...47D} the expected $\gamma$ -ray flux increases substantially if we consider a spatial CR proton distribution so the radio emission actually fits the observations in morphology. We therefore expect a rejection or confirmation of our models in the very near future., We therefore expect a rejection or confirmation of our models in the very near future. " We use a constrained, cosmological MHD SPH simulation with a semianalytic model for galactic magnetic outflows, to obtain a sample of 16 galaxy clusters with thermal properties similar to clusters in the Local Universe."," We use a constrained, cosmological MHD SPH simulation with a semianalytic model for galactic magnetic outflows, to obtain a sample of 16 galaxy clusters with thermal properties similar to clusters in the Local Universe." Further we assume 3 different, Further we assume 3 different without contamination by the primary.,without contamination by the primary. The simulated star is readily seen in Figure 2.., The simulated star is readily seen in Figure \ref{fig2}. Large errors in the reported orbital parameters allow for the possibility that the companion remained unresolved due to chance alienment during the observation., Large errors in the reported orbital parameters allow for the possibility that the companion remained unresolved due to chance alignment during the observation. " The values and computed errors in separation and position angle. derived from the binary orbital calculator. are 0.190"".tls and 274°1"" yespectively."," The values and computed errors in separation and position angle, derived from the binary orbital calculator, are ${0.19''} \ ^{+0.07}_{-0.18}$ and ${274\arcdeg} \ ^{+180}_{-2}$ respectively." Hence the putative companion could have been located al almost any position iin ils orbit by the epoch of the observation., Hence the putative companion could have been located at almost any position in its orbit by the epoch of the observation. However. (here is further evidence against (is possibility.," However, there is further evidence against this possibility." In the case of a chance alignment. anv substellar companion would still cause excess enission at mid inlrared wavelengths.," In the case of a chance alignment, any substellar companion would still cause excess emission at mid infrared wavelengths." This is primarily due to the size dillerence between brown clwarls and white dwarls: a ratio of 10:1 in radius., This is primarily due to the size difference between brown dwarfs and white dwarfs; a ratio of 10:1 in radius. Ht is not possible for a significant oceultation to occur., It is not possible for a significant occultation to occur. At most. a white dwarf could block only ~1€ of the light from an orbiting brown cw.," At most, a white dwarf could block only $\sim1$ of the light from an orbiting brown dwarf." As mentioned above. a value of L'=11.4020.06 mag was measured for van Maanen |," As mentioned above, a value of $L^{'}=11.40\pm0.06$ mag was measured for van Maanen 2." This is to be compared with the value predicted for a 6750 IX white dwarf. Lo=11.43 mag.," This is to be compared with the value predicted for a 6750 K white dwarf, $L^{'}=11.43$ mag." " The combined flux of the white dwarf plus a 50M, brown clwarl at 5 Gyr would have a maenitude of L'=11.09 mag.", The combined flux of the white dwarf plus a $50M_{\rm J}$ brown dwarf at 5 Gyr would have a magnitude of $L^{'}=11.09$ mag. Hence it is concluded. there is no excess emission at this wavelength., Hence it is concluded there is no excess emission at this wavelength. Furthermore. the published£SO observations place even stronger constraints on the absence of flax from a brown chwarl around. van Alaanen 2.," Furthermore, the published observations place even stronger constraints on the absence of flux from a brown dwarf around van Maanen 2." A recent model. 2003) of the flux from a 5 Gyr. 25M; brown ciwarl was integrated over the 15.0;an filler LAW3.," A recent model \citep*{bur03} of the flux from a 5 Gyr, $25M_{\rm J}$ brown dwarf was integrated over the $15.0\mu$ m filter LW3." This results in a flux of about 1.0mJy in this filter., This results in a flux of about 1.0mJy in this filter. The reported measurement taken at van Maanen 2 in 1997 was 0.50.2 mJv., The reported measurement taken at van Maanen 2 in 1997 was $0.5\pm0.2$ mJy. This measurement is consistent with photospheric flux from the white dwarl ancl an of 5o most likely would have been detected., This measurement is consistent with photospheric flux from the white dwarf and an of $5\sigma$ most likely would have been detected. If the/8O results are correct ancl the models are right. any companion with Teg2500 IN is ruled out — this includes 10 Gyr old brown dwarls with Af>35.Mj (Burrowsetal.1997.2003).," If the results are correct and the models are right, any companion with $T_{\rm eff} \ga500$ K is ruled out – this includes 10 Gyr old brown dwarfs with $M\geq35M_{\rm J}$ \citep{bur97,bur03}." Table 1 summarizes all existing photometric data on van Maanen 2 ancl (hie corresponding [Iuxes are plotted in Figure 3.., Table \ref{tbl-1} summarizes all existing photometric data on van Maanen 2 and the corresponding fluxes are plotted in Figure \ref{fig3}. It should be clear from the figure that the measured fluxes are all consistent will a single white dwarf with a temperature around 6300 Ix., It should be clear from the figure that the measured fluxes are all consistent with a single white dwarf with a temperature around 6800 K. "is below the number of major mergers of the corresponding hosts, as clearly seen in Figure 8 when comparing dotted to solid lines.","is below the number of major mergers of the corresponding hosts, as clearly seen in Figure \ref{fig:number_densities} when comparing dotted to solid lines." " This apparent discrepancy is explained, first of all, by the fact that when two haloes merge, their host galaxies will merge at some later time only if the new satellite halo loses enough mass to fall below the resolution limit of the simulation."," This apparent discrepancy is explained, first of all, by the fact that when two haloes merge, their host galaxies will merge at some later time only if the new satellite halo loses enough mass to fall below the resolution limit of the simulation." " Moreover, in the current treatment of galaxy mergers, when a galaxy becomes a satellite, it loses its hot gas component; cooling is then inhibited and the stellar component grows only moderately from the cold gas previously available."," Moreover, in the current treatment of galaxy mergers, when a galaxy becomes a satellite, it loses its hot gas component; cooling is then inhibited and the stellar component grows only moderately from the cold gas previously available." " Therefore, although a given FOF halo merger may be counted as a major merger, by the time the corresponding galaxy merger occurs it may fall below our chosen threshold for a major merger."," Therefore, although a given FOF halo merger may be counted as a major merger, by the time the corresponding galaxy merger occurs it may fall below our chosen threshold for a major merger." " In any case, despite the fact that the number of major mergers is lower for galaxies than for haloes, the number of mergers of galaxies more massive than (Mg>4x101957! M) is still large enough to explain the observed number densities of bright quasars."," In any case, despite the fact that the number of major mergers is lower for galaxies than for haloes, the number of mergers of galaxies more massive than $M_G \gtrsim 4\times 10^{10} ~h^{-1} \rm{M}_{\odot}$ ) is still large enough to explain the observed number densities of bright quasars." " Taken at face value, the galaxy model would then predict that the SDSS luminous quasars detected at z>2 should be hosted by galaxies as massive as >4x101957!M."," Taken at face value, the galaxy model would then predict that the SDSS luminous quasars detected at $z>2$ should be hosted by galaxies as massive as $\gtrsim 4\times 10^{10}~h^{-1} \rm{M}_{\odot}$." " Given that virial relations point to BHs more massive than >3x108Mo, this would suggest an increase, by a factor of >3, of the BH-to-stellar mass ratio with respect to local values (?).."," Given that virial relations point to BHs more massive than $\gtrsim 3\times 10^{8} \rm{M}_{\odot}$, this would suggest an increase, by a factor of $\gtrsim 3$, of the BH-to-stellar mass ratio with respect to local values \citep{HaringRix}." " In addition, we find that the clustering of galaxies with stellar mass Mg>4x101057!Mi is too weak to match the observed quasar clustering."," In addition, we find that the clustering of galaxies with stellar mass $M_{G}\geq 4 \times 10^{10} ~h^{-1} \rm{M}_{\odot}$ is too weak to match the observed quasar clustering." " To better address the connection with the semianalytical galaxy models, we compare our results with the outputs of the detailed model for the coevolution of quasars and galaxies presented in ? and ?.."," To better address the connection with the semianalytical galaxy models, we compare our results with the outputs of the detailed model for the coevolution of quasars and galaxies presented in \citet{marulli08} and \citet{bonoli09}." " Figure 9 shows the bias of luminous optical quasars derived using the model of ?,, built on the assumption that quasar activity is triggered during galaxy mergers."," Figure \ref{fig:bias_QSO} shows the bias of luminous optical quasars derived using the model of \citet{marulli08}, built on the assumption that quasar activity is triggered during galaxy mergers." " In ? we showed that such a model predicts well the clustering properties of Observed optical quasars at a variety of redshifts and luminosities, independent of the specific light curve characterizing the active phase of a BH."," In \citet{bonoli09} we showed that such a model predicts well the clustering properties of observed optical quasars at a variety of redshifts and luminosities, independent of the specific light curve characterizing the active phase of a BH." " In the upper panel of Figure 9, the bias of bright quasars in the model is compared with the bias of randomly selected dark-matter subhaloes with the same mass distribution as the ones hosting the quasars."," In the upper panel of Figure \ref{fig:bias_QSO}, the bias of bright quasars in the model is compared with the bias of randomly selected dark-matter subhaloes with the same mass distribution as the ones hosting the quasars." " The ratio between the two-point correlation functions of the two samples is shown in the lower panel: the excess bias is at most ~5%, except at z=5, where the small number of simulated quasars results in a statistically unreliable result."," The ratio between the two-point correlation functions of the two samples is shown in the lower panel: the excess bias is at most $\sim 5\%$, except at $z=5$, where the small number of simulated quasars results in a statistically unreliable result." " It is clear that if bright quasars were hosted by DM subhaloes less massive than inferred from the clustering analysis, the BH-to-stellar mass ratio would be even higher (see also the discussion in ?))."," It is clear that if bright quasars were hosted by DM subhaloes less massive than inferred from the clustering analysis, the BH-to-stellar mass ratio would be even higher (see also the discussion in \citet[e.g.,][]{ShankarCrocce}) )." " To address, in an independent way, the evolution of the average expected relation between the BH and its host, we compute the expected baryonic mass locked in BHs following the method outlined by previous authors (e.g.,?????):: first, we map haloes to their appropriate virial velocities V,;, at a given redshift z applying the virial theorem (e.g.,?)."," To address, in an independent way, the evolution of the average expected relation between the BH and its host, we compute the expected baryonic mass locked in BHs following the method outlined by previous authors \citep[e.g.,][]{Ferrarese02,Ciras05,Shankar06,ShankarMathur,ShankarCrocce}: first, we map haloes to their appropriate virial velocities $V_{\rm vir}$ at a given redshift $z$ applying the virial theorem \citep[e.g.,][]{BarkanaLoeb}." " We then link V to the velocity dispersion o as calibrated in the local universe by, e.g., ?,, and finally we compute the associated BH mass via the local Mgy—o relation (e.g.,?).."," We then link $V_{\rm vir}$ to the velocity dispersion $\sigma$ as calibrated in the local universe by, e.g., \citet{Ferrarese02}, , and finally we compute the associated BH mass via the local $M_{\rm BH}-\sigma$ relation \citep[e.g.,][]{Tundo07}." " If we assume that these BHs are accreting at an Eddington ratio A>0.5, we find that, at z=4, all haloes above ~5x10?7!M, can indeed host a BH luminous enough to be recorded in the high-z quasar sample of ?.."," If we assume that these BHs are accreting at an Eddington ratio $\lambda\gtrsim 0.5$, we find that, at $z=4$, all haloes above $\sim 5\times 10^{12} h^{-1} \rm{M}_{\odot} $ can indeed host a BH luminous enough to be recorded in the $z$ quasar sample of \citet{shen09}." " This simple exercise proves that if quasars are associated to normally biased haloes, the ratio between BH mass and halo mass could be similar to that observed locally."," This simple exercise proves that if quasars are associated to normally biased haloes, the ratio between BH mass and halo mass could be similar to that observed locally." " In the present work we exploited the large halo and galaxy samples extracted from the Millennium Simulation to test the idea that ""merger bias"", a tendency of recently merged systems to be more strongly clustered on large scales than typical systems of similar mass, could help reconcile the apparent discrepancy between the observed abundance and clustering of high redshift quasars with those predicted for massive dark haloes."," In the present work we exploited the large halo and galaxy samples extracted from the Millennium Simulation to test the idea that “merger bias”, a tendency of recently merged systems to be more strongly clustered on large scales than typical systems of similar mass, could help reconcile the apparent discrepancy between the observed abundance and clustering of high redshift quasars with those predicted for massive dark haloes." " Previous studieshave, in fact, shown that the quasar number density and clustering can be simultaneously explained theoretically either by models"," Previous studieshave, in fact, shown that the quasar number density and clustering can be simultaneously explained theoretically either by models" " = --2, wherey Ry—((1-=py/(pv+ py), 2R,))(1)pv and p, being respectively the energy densities in relativistic neutrinos and photons."," , = ( 1 + ) where $R_\nu \equiv \rho_\nu/(\rho_\nu+\rho_\gamma)$ , $\rho_\nu$ and $\rho_\gamma$ being respectively the energy densities in relativistic neutrinos and photons." " 'To compute these expressions, we adapted for our analysis an already modified version of CMBFAST (?), named CROSS.CCMBFAST (?).."," To compute these expressions, we adapted for our analysis an already modified version of CMBFAST \citep{CMBFAST}, named CMBFAST \citep{CCMBF}." " For a given cosmology and emissivity function j(v,z) (see Eqs. (2))"," For a given cosmology and emissivity function $\bar{j}(\nu,z)$ (see Eqs. \ref{dtcib}) )" and (3))) our code calculates the C7' from Eq. (8))," and \ref{biais}) )), our code calculates the $C_{\ell}^{\rm{cr}}$ from Eq. \ref{cross_cl}) )" and at the same time the predicted power spectrum of the CIB fluctuations described in Eq. (4)), and at the same time the predicted power spectrum of the CIB fluctuations described in Eq. \ref{CIBpow}) ) and already illustrated in Fig. 1.., and already illustrated in Fig. \ref{compar_cl}. " It also gives the standard CMBFAST outputs, including the CMB temperature power In Fig. 2,,"," It also gives the standard CMBFAST outputs, including the CMB temperature power In Fig. \ref{cross}," " we present our predictions for the CIB-CMB cross-correlation, at several FIR wavelengths and for different instruments, namely: IRAS at 100 um, SPIRE at 250, 350 and 500 wm and HFI at 350, 550, 850, 1380, and 2097 pum."," we present our predictions for the CIB-CMB cross-correlation, at several FIR wavelengths and for different instruments, namely: IRAS at 100 $\mu m$, SPIRE at 250, 350 and 500 $\mu m$ and HFI at 350, 550, 850, 1380, and 2097 $\mu m$." " We note that at 350 wm the SPIRE- and Planck-- predicted spectra differ slightly from each other, due to the difference in wavelength bandwidth of the two instruments."," We note that at 350 $\mu m$ the SPIRE- and - predicted spectra differ slightly from each other, due to the difference in wavelength bandwidth of the two instruments." " In a fashion similar to previous galaxy-ISW cross-correlations (see the references in Section 1)), we note that the cross-correlation peaks around £~10-30, and quickly vanishes at higher multipoles."," In a fashion similar to previous galaxy-ISW cross-correlations (see the references in Section \ref{sec:introduction}) ), we note that the cross-correlation peaks around $\ell\simeq10\textendash30$, and quickly vanishes at higher multipoles." Comparing the signal at the different wavelengths shows that the amplitude of the cross-correlation signal is maximum at a wavelength ~250jm., Comparing the signal at the different wavelengths shows that the amplitude of the cross-correlation signal is maximum at a wavelength $\simeq 250~\mu m$. " 'This is not entirely surprising, since this wavelength roughly corresponds to the maximum of the observed CIB spectral energy distribution (see?,forreference).."," This is not entirely surprising, since this wavelength roughly corresponds to the maximum of the observed CIB spectral energy distribution \citep[see][for reference]{CIB_SED}." " It should be also noted that these results are not exact at the highest /s since the non-linear counterpart to the ISW effect, called the Rees-Sciama effect, contributes at those scales (see?,foradiscussion)."," It should be also noted that these results are not exact at the highest $\ell$ s since the non-linear counterpart to the ISW effect, called the Rees-Sciama effect, contributes at those scales \citep[see][for a discussion]{RSeffect}." " However, in our case the linear part of the ISW largely dominates at the observed peak in Fig. 2.."," However, in our case the linear part of the ISW largely dominates at the observed peak in Fig. \ref{cross}." We now investigate the detection level of the ISW effect using CMB-CIB cross-correlation by performing a signal-to-noise ratio analysis., We now investigate the detection level of the ISW effect using CMB-CIB cross-correlation by performing a signal-to-noise ratio analysis. " Using the power spectra computed in the previous section, we can write for each given frequency v the total signal-to-noise ratio of the ISW detection as: [81K = where the total (or cumulative) signal-to-noise is summed over multipoles between /=2 and fmax<100 where the signal has its major contribution (see previous section, Fig. 2))."," Using the power spectra computed in the previous section, we can write for each given frequency $\nu$ the total signal-to-noise ratio of the ISW detection as: ]^2 ) = where the total (or cumulative) signal-to-noise is summed over multipoles between $\ell=2$ and $\ell_{\rm{max}} \leqslant 100$ where the signal has its major contribution (see previous section, Fig. \ref{cross}) )." " In this section, we first consider the ideal situation where the CIB and CMB maps used for cross-correlation are noiseless and cover the whole sky; with these assumptions we obtain the highest possible signal-to-noiseratio, the only limitation being the cosmic variance."," In this section, we first consider the ideal situation where the CIB and CMB maps used for cross-correlation are noiseless and cover the whole sky; with these assumptions we obtain the highest possible signal-to-noiseratio, the only limitation being the cosmic variance." In Fig., In Fig. " 3 we present our prediction for the CIB-CMB cross-correlation in the case of a full-sky CIB map, by the previously mentionned instruments and"," \ref{plotsnr} we present our prediction for the CIB-CMB cross-correlation in the case of a full-sky CIB map, by the previously mentionned instruments and" "model, and thus there is some element of doubt as to the value obtained for our mass ratio and thus donor mass.","model, and thus there is some element of doubt as to the value obtained for our mass ratio and thus donor mass." " It is at this point we draw the readers attention to our 2010 data, shown in Fig. 6.."," It is at this point we draw the readers attention to our 2010 data, shown in Fig. \ref{figure:ctcv2354_2009_2010}." " The eclipse dated 2010 May 3 (centre panel) shows clear bright spot ingress and egress features, with a clear orbital hump visible from phases 0.70-0.95."," The eclipse dated 2010 May 3 (centre panel) shows clear bright spot ingress and egress features, with a clear orbital hump visible from phases 0.70–0.95." " The system is much brighter in this state than the 2007 data previously modelled, in part due to a dramatic increase in bright spot flux."," The system is much brighter in this state than the 2007 data previously modelled, in part due to a dramatic increase in bright spot flux." " As with CTCV 1300 we carried out a downhill simplex method to vary all parameters bar q, Ad, Rw/a and Uw."," As with CTCV 1300 we carried out a downhill simplex method to vary all parameters bar $q$ , $\Delta\phi$, $R_{w}/a$ and $U_{w}$." " Our fit to the eclipse of May 3 is especially pleasing, as its excellent agreement with the light curve confirms that our 2007 model correctly identified the bright spot egress feature and thus the mass ratio obtainedis reliable."," Our fit to the eclipse of May 3 is especially pleasing, as its excellent agreement with the light curve confirms that our 2007 model correctly identified the bright spot egress feature and thus the mass ratio obtainedis reliable." about a 25% error [or the SDSS data when using Criterion 1. model selection.,about a $25\%$ error for the SDSS data when using Criterion 1 model selection. Similarly. we find about 7995 error for the ESOLY data and 39% error for SDSS data when using BIC model selection.," Similarly, we find about $79\%$ error for the ESOLV data and $39\%$ error for SDSS data when using BIC model selection." The values of NA lor Criterion 2 error for some of the SDSS experiments reflect models where (here were no nonpredefined components: in this case (he error measure is undefined., The values of NA for Criterion 2 error for some of the SDSS experiments reflect models where there were no nonpredefined components; in this case the error measure is undefined. Note that. in all these cases. the unknown classes had very small mass. which explains why no nonpredefined components were found.," Note that, in all these cases, the unknown classes had very small mass, which explains why no nonpredefined components were found." In particular. class 0 and class 4 collectively comprise less than 154 of the SDSS data.," In particular, class 0 and class 4 collectively comprise less than $1\%$ of the SDSS data." Thus. when these classes are missing. we would not expect to find nonpredefined components in the solution unless bot 1) there are more (han 100 components in the model aud 2) the model criterion selects a solution of (his size.," Thus, when these classes are missing, we would not expect to find nonpredefined components in the solution unless both 1) there are more than 100 components in the model and 2) the model criterion selects a solution of this size." The Criterion 3 error measures how well the model can assign objects to known classes., The Criterion 3 error measures how well the model can assign objects to known classes. For this we obtained about a 32% error lor ESOLV. data and 7% error for SDSS data using Criterion 1 model selection., For this we obtained about a $32\%$ error for ESOLV data and $7\%$ error for SDSS data using Criterion 1 model selection. When using DIC model selection we obtained 33% error [or ESOLY data and 9% error for SDSS data., When using BIC model selection we obtained $33\%$ error for ESOLV data and $9\%$ error for SDSS data. We find the overall τος presented here very promising., We find the overall results presented here very promising. The tests done here have demonstrated the efficacy of the class discovery. problem and approaches., The tests done here have demonstrated the efficacy of the class discovery problem and approaches. However. more work will be required to develop a mature technology for highly reliable new class discovery.," However, more work will be required to develop a mature technology for highly reliable new class discovery." We would like to thank the NASA Appliecl Information Svstems Research Program [ου supporting us in this elfort under contract NAS5-02093., We would like to thank the NASA Applied Information Systems Research Program for supporting us in this effort under contract NAS5-02098. One of the authors (DB) would like to thank Oler Lalav lor supplving the ESO-LV. data., One of the authors (DB) would like to thank Ofer Lahav for supplying the ESO-LV data. determination.,determination. Phe remaining LS orbital determinations are new., The remaining 18 orbital determinations are new. We follow the procedure. described. in. ὃν using the ‘floating mean’ periodogram (e.g. 7)). which consists in fitting the data with a model composed of à sinusoid plus a constant of the form: where f is the frequeney Cf. = L/period) and fis the observation time.," We follow the procedure described in \citet{MoralesRueda03}, using the `floating mean' periodogram (e.g. \citealt{Cumming99}) ), which consists in fitting the data with a model composed of a sinusoid plus a constant of the form: where $f$ is the frequency $f$ = $1/$ period) and $t$ is the observation time." We obtain the X72 of the fits as a function of frequeney and select the minima of this X7 function., We obtain the $\chi^2$ of the fits as a function of frequency and select the minima of this $\chi^2$ function. By fitting the svstemic velocity. +. at the same time as A and fy. we correct a failing of the Lomb-Scargle (2?) periodogram which starts by subtracting the mean of the data and then fits a plain sinusoid.," By fitting the systemic velocity, $\gamma$, at the same time as $K$ and $t_0$, we correct a failing of the Lomb-Scargle \citep{Lomb76,Scargle82} periodogram which starts by subtracting the mean of the data and then fits a plain sinusoid." The floating mean periodogram works better than the Lomb-Scargle periodogram for small numbers of points., The floating mean periodogram works better than the Lomb-Scargle periodogram for small numbers of points. We obtain the X7 of the lit as a function of f and then identify minima in this function., We obtain the $\chi^2$ of the fit as a function of $f$ and then identify minima in this function. In Table 2 we give the orbital parameters for each sdB binary., In Table \ref{tab:results} we give the orbital parameters for each sdB binary. listing To. the svsemic velocity. 5. the racial velocity semi-amplitude. Ix. and the reduced x7 achieved for the best alias.," listing $_{0}$, the systemic velocity, $\gamma$, the radial velocity semi-amplitude, K, and the reduced $\chi^2$ achieved for the best alias." We also give the period of an INth alias. aud the dillerence in V7 between this alias and the best alias.," We also give the period of an $N$ th alias, and the difference in $\chi^2$ between this alias and the best alias." Lo most cases we list the Ni= 2nd alias. and find a significant v difference between these best ancl second-best aliases.," In most cases we list the $N = 2$ nd alias, and find a significant $\chi^2$ difference between these best and second-best aliases." llowever. [for some sysenis (POO958-073. POGI000|408. 11230|052. P€GHLA03|316. PGIG648|536. IKDPD2215|5037 and PO2331|038) we find that the best alias is surrouncled » many other aliases which are very close in period and with a similar X7.," However, for some systems (PG0958-073, PG1000+408, PG1230+052, PG1403+316, PG1648+536, KPD2215+5037 and PG2331+038) we find that the best alias is surrounded by many other aliases which are very close in period and with a similar $\chi^2$." In some sense these svstenis are not solved since 1ese Close aliases are as significant as the best alias. but they re sulliciently close and span a sullicicntly small range that ur criterion is satisfied.," In some sense these systems are not solved since these close aliases are as significant as the best alias, but they are sufficiently close and span a sufficiently small range that our criterion is satisfied." For the purposes of Table 2. when 1 nearest. competing aliases are so close in period it makes =nore sense to compare with the next of aliases. so for jese systems we choose to give the Nth alias for which the »eriod differs bv more than 5 per cent from the best alias.," For the purposes of Table \ref{tab:results} when the nearest competing aliases are so close in period it makes more sense to compare with the next of aliases, so for these systems we choose to give the $N$ th alias for which the period differs by more than $5$ per cent from the best alias." In ul cases this results in a significant difference in X7 between us alias and the best alias., In all cases this results in a significant difference in $\chi^2$ between this alias and the best alias. ‘The results of folding the racial velocities of cach object on its orbital period are plotted in Figure 1.., The results of folding the radial velocities of each object on its orbital period are plotted in Figure \ref{fig:phasefold}. Phe error bars on the radial velocity points are. in most cases. smaller than the size of the symbol uscc to displav them.," The error bars on the radial velocity points are, in most cases, smaller than the size of the symbol used to display them." The periodograms (4? versus orbital frequency) for the 28 objects listed in Table 2 are given in Figures 2. and 3.., The periodograms $\chi^2$ versus orbital frequency) for the 28 objects listed in Table \ref{tab:results} are given in Figures \ref{fig:pgram1} and \ref{fig:pgram2}. Each panel includes a blow-up of the region in frequency where the minimum X? is Found., Each panel includes a blow-up of the region in frequency where the minimum $\chi^2$ is found. Lt is clear from these figures hat in the majority ο [cases there is a significant dillerence in 47 between the bes alc the second alias., It is clear from these figures that in the majority of cases there is a significant difference in $\chi^2$ between the best and the second alias. Exceptions are he seven svstenis we hiwe previously discussed. in which here are many aliases €lose in frequency. ancl significance othe best alias., Exceptions are the seven systems we have previously discussed in which there are many aliases close in frequency and significance to the best alias. The xdow-ups illustrate that the frequency range covered by these alternate aliases is very small. so we can determine the penod to within 5 per cent of the ruc value with confidentes," The blow-ups illustrate that the frequency range covered by these alternate aliases is very small, so we can determine the period to within $5$ per cent of the true value with confidence." Two other systems we wish to uehlieht are DC12452|1tJS ane EC22202-1834., Two other systems we wish to highlight are PG1452+198 and EC22202-1834. In. Table 2 we compared the first and second aliases for these systenis. which are very similar in significance.," In Table \ref{tab:results} we compared the first and second aliases for these systems, which are very similar in significance." The periodograms or each of these two svstems show that the two aliases are discrete and. separate| without the continuous range of intermediate aliases whic1 we see in the previously discussed seven systems., The periodograms for each of these two systems show that the two aliases are discrete and separate without the continuous range of intermediate aliases which we see in the previously discussed seven systems. For each system. either one of these two solutions could. represent the “true” period. and the \7 cillerenee is too small to avour one over the other.," For each system, either one of these two solutions could represent the `true' period, and the $\chi^2$ difference is too small to favour one over the other." However. in both cases the period dillerence between the two aliases is verv small ancl our criterion for solution is satisfied no matter which we believe o be the true perio.," However, in both cases the period difference between the two aliases is very small and our criterion for solution is satisfied no matter which we believe to be the true period." We therefore include these systems wi1 those we consider to be solved., We therefore include these systems with those we consider to be solved. 1n Table 3 we List [or cach system the probability that the true orvital period. lies further than | and 5 per cent from our favoured vaue. using the Bavesian calculation detailed in ? and ?..," In Table \ref{tab:probs} we list for each system the probability that the true orbital period lies further than 1 and 5 per cent from our favoured value, using the Bayesian calculation detailed in \citet{MoralesRueda03} and \citet{Marsh95}." MὉ consider a period to be robust when the probajlitw is below 0.1 per cent (or -3λ in the log scale)., We consider a period to be robust when the probability is below 0.1 per cent (or -3 in the log scale). This is not fufilled to within 1 per cent of our favoured period For 7 of«our 28 sources., This is not fulfilled to within 1 per cent of our favoured period for 7 of our 28 sources. The worst example is D€11519|640: or this svstem the probability that the true period is more tjin l per cent dillerent. from our favoured value is 0.98 in the Log scale. or greater than 10 per cent.," The worst example is PG1519+640: for this system the probability that the true period is more than 1 per cent different from our favoured value is $-0.98$ in the log scale, or greater than 10 per cent." well as the barvou fraction within 1 Mpc aud 3 Alpe are quoted in the abstract or the coufidence level.,well as the baryon fraction within 1 Mpc and 3 Mpc are quoted in the abstract for the confidence level. " The mass within 5 \Ipe is (1.9£0.9)&Lol?M, and the Iuiinous matter fraction is"," The mass within 5 Mpc is $(1.9 \pm 0.9) \times 10^{15}\, M_\odot$ and the luminous matter fraction is." The temperature profiles we obtain are nearly all couvectively stable. ic. <⊐∼∼3.within ∙the maxinnua observed.. extent of the∙∙ chister ~3.3 Ape.," The temperature profiles we obtain are nearly all convectively stable, i.e., $\vert {d \ln T \over d \ln \rho}\vert < {2\over 3}$, within the maximum observed extent of the cluster $\sim$ 3.3 Mpc." ων The few models that violate this coustraint lie between the 90% 99% confidence contours at low values of Pp; and a and thus are statistically less ikelv to be acceptable solutions auvwav., The few models that violate this constraint lie between the and confidence contours at low values of $R_{\rm DM}$ and $\alpha$ and thus are statistically less likely to be acceptable solutions anyway. Iu summa. I fud uo evidence for steep temperature eradieuts in Coma that might indicate nonlydrostatic or other exotic couditions.," In summary, I find no evidence for steep temperature gradients in Coma that might indicate nonhydrostatic or other exotic conditions." " Based ou their N-body simulatious of a standard colkd-darkauatter dominated Universe. Navarro. Freuk. White. CNEW) find that the radial dark matter density profiles of svsteius rangius from dwarf galaxies to rich clusters of ealaxies can be well described by the simple function p= rír,Y. where à. is the characteristic overdensity of the halo in terms of the critical density peur aud ry is a characteristic scale radius."," Based on their $N$ -body simulations of a standard cold-dark-matter dominated Universe, Navarro, Frenk, White \cite{nfw} (NFW) find that the radial dark matter density profiles of systems ranging from dwarf galaxies to rich clusters of galaxies can be well described by the simple function $\rho = \delta_c \rho_{\rm crit}/(r/r_s)(1+r/r_s)^2$ , where $\delta_c$ is the characteristic overdensity of the halo in terms of the critical density $\rho_{\rm crit}$ and $r_s$ is a characteristic scale radius." The best ft of this fiction to the Coma temperature data is obtained for re~0.5 Mpe and spas~Los1028 ο cm7.," The best fit of this function to the Coma temperature data is obtained for $r_s \sim 0.5$ Mpc and $\delta_c \rho_{\rm crit} \sim 4 \times 10^{-26}$ g $^{-3}$." However. this fit is formally unacceptable: the minimum 4 of 31.5 for 15 degrees of freedoms cau be rejected at ereater than confidence.," However, this fit is formally unacceptable: the minimum $\chi^2$ of 31.5 for 15 degrees of freedom can be rejected at greater than confidence." The central temperature iu the best-fit mocel is rather high ~16.5 keV but drops rapidly to —5 keV at rj aud thereafter continues to fall. although more geraduallv.," The central temperature in the best-fit model is rather high $\sim$ 16.5 keV but drops rapidly to $\sim$ 8 keV at $r_s$ and thereafter continues to fall, although more gradually." The steep temperature gradient near the ceuter of the cluster is incousisteut with the observed data for Coma., The steep temperature gradient near the center of the cluster is inconsistent with the observed data for Coma. This also appears to be the case for the rich cluster Abell 2256 where the NEW halo function predicts a considerably steeper temperature profile iu the center of the cluster than observed? On the other liaud. the NEW fiction appears to be an acceptable description of the optically-cerived average nass profile of galaxy clusters?) ," This also appears to be the case for the rich cluster Abell 2256 where the NFW halo function predicts a considerably steeper temperature profile in the center of the cluster than \cite{kop} On the other hand, the NFW function appears to be an acceptable description of the optically-derived average mass profile of galaxy \cite{carl} " Equation (20)) uses the gravitational potential at the both euds of the clagonal for the linear interpolation.,Equation \ref{interpolation2}) ) uses the gravitational potential at the both ends of the diagonal for the linear interpolation. This interpolation is not unique: we can use the bi-linear interpolation iu the coarse cell surface., This interpolation is not unique; we can use the bi-linear interpolation in the coarse cell surface. The result depends little on the interpolation adopted., The result depends little on the interpolation adopted. The cell number at the both euds of the diagoual depends ou the even-odd parity of j aud &., The cell number at the both ends of the diagonal depends on the even-odd parity of $ j $ and $ k $. Equation (20)) should be modified appropriately when either j or & are eve, Equation \ref{interpolation2}) ) should be modified appropriately when either $ j $ or $ k $ are even. Equatious (11))-(16)) are central dillerence. our dillerence equations are the second. order accurate except across the grid level boundaries.," Equations \ref{gx}) \ref{gz}) ) are central difference, our difference equations are the second order accurate except across the grid level boundaries." Since equations (19)) aud (20)) are the first order accurate. our difference equatious are only the first order accurate across the boundaries.," Since equations \ref{interpolation1}) ) and \ref{interpolation2}) ) are the first order accurate, our difference equations are only the first order accurate across the boundaries." We need the gravity at the cell center in the hydrodyuaimical computation., We need the gravity at the cell center in the hydrodynamical computation. The gravity at the cell center is evaluated to be the average of those at the opposing cell sur(aces. e.g.. We examine tlie accuracy of the gravity at the cell center in 81.," The gravity at the cell center is evaluated to be the average of those at the opposing cell surfaces, e.g., We examine the accuracy of the gravity at the cell center in 4." Our difference equation can be solved with a simple point Jacobi iteration or red-black iteration but with too many times iteration of the order of N7., Our difference equation can be solved with a simple point Jacobi iteration or red-black Gauss-Seidel iteration but with too many times iteration of the order of $ N ^2 $. Thus we adopt the multi-grid iteration for to accelerate the convergence., Thus we adopt the multi-grid iteration for to accelerate the convergence. We employ the Full Multi-Cirid (FMC) scheme. Le.. the algorithin shown tu Press&Teukolsky(1991). in our paper.," We employ the Full Multi-Grid (FMG) scheme, i.e., the algorithm shown in \citet{press91} in our paper." Our numerical procedures are rather complicated partly because the FMC1 scheme is complicated auc partly because our nested. eric is complex., Our numerical procedures are rather complicated partly because the FMG scheme is complicated and partly because our nested grid is complex. Thus. we first outline our scheme in the following.," Thus, we first outline our scheme in the following." Detailed nunerical procedures are shown later., Detailed numerical procedures are shown later. Essence of the multi-erid iteration is to obtain a better initial guess for finer grids [rom au approximate solutious on coarser erids (see.e.g..Wesseling1992:Briggs.Henson.&MeCoruick2000.forthebasicofmulti-erid iteration)..," Essence of the multi-grid iteration is to obtain a better initial guess for finer grids from an approximate solutions on coarser grids \citep[see, e.g.,][for the basic of multi-grid iteration]{wesseling92,briggs00}." . When grids are coarse. the computation cost 1s less.," When grids are coarse, the computation cost is less." When tuterpolatec for a fine grkl. the solution ou a coarse grid is a good initial guess aud a better solution ou the fine eric is obtained by only a few times iteratious.," When interpolated for a fine grid, the solution on a coarse grid is a good initial guess and a better solution on the fine grid is obtained by only a few times iterations." Asa coarse grid. we use another nested grid which covers the same computation volume with a ↥⋅≺↵∖∖↽≺↵↕⋅≛∖⊽⋜⋯≺⊔⋜↕↓⋅∑≟≺↵↕⋅∣," As a coarse grid, we use another nested grid which covers the same computation volume with a fewer $ N $ and larger $ h $." ∣⋅↥∖↓∩⋅≺↵⊳∖↥↽≻≺↵∢↝∐↕∢⋅⋜↕↥⊽∖⊽∖∖↽≺↵⇂⊳∖≺↵↕∐≺↵∐≺↵⊳∖↕≺↵≺⇂∑≟↕⋅↕≺⇂⊳∖∩⋅↸⋡⋤∖⊽⋅∣∣⋝∶⋜⋮⊇∣∣⋅⊇∣∣∣∣⋝−↸↨⊇∣∣ >−∙22h). ⋅⋅⋅⋅⋅ ⋜↕∐≺⊔−≻−⋅−≻⊔−∣∣∣∣⋝⋅⋜↕⊳∖≺↵∐↕↥↽≻∩↕⋅⋜⋃⋅↥⊽∖⊽∖∖↽∩↓⋅⊆↓∐∑∸∐≺↵⊳∖↕≺↲≺⇂∑∸↕⋅∐⇂⊳∖↥∩⋅∢∙∩∐↕↥↽≻⋯⋜↕⊔∩∐∩∐↕∐≺↵∐≺↲⊳∖↕≺↵≼⇂∑∸↕⋅∐∩↥ ⋜⋮⋀∖⊽⋅∣∣⋝∶↸⋮⊇⊔⋅∣∣∣∣⋝↸⋮⊳∖≺↵≺↵⊂⊲⋜↕↥↽≻↕≺↵↥⋅∪∩∎⊟↕⋅↕≺⋯↠∖⋅∐↩⊔↠∖∩∐⋅⋅∖↽↥∖↓∢∙⊂⊲∩⋅∐↥∢∙↕⊆⊇∪∩∩⋅↥∎∩↓⋅∐≺↵↕⋅≺↵⋜↕⊳∖∩↥∏∐∑∸∩∐⋯⊔⋅MOchoiceof coarsening)...," More specifically we use the nested grids of $ (N, \, h) $ = $ ( 2 ^{n-1}, \, 2 h_0) $, $ ( 2 ^{n-2}, \, 2 ^2 h _0) $, ...., and $ (2 ^2, \, 2 ^{n-2} h _0 ) $, as temporarily working nested grids for computation on the nested grid of $ (N, \, h ) $ = $ (2^n, \, h _0) $ \citep[see Chapter 9 of][for the reasoning on our choice of coarsening]{briggs00}." Furthermore. we introduce two uniform grids one of which has 2” cells auc the other of which has ouly 1 cell.," Furthermore, we introduce two uniform grids one of which has $ 2^3 $ cells and the other of which has only 1 cell." Both the uniform grids covers the whole computation domaiu which is covered only with the largest eric in the nested eric., Both the uniform grids covers the whole computation domain which is covered only with the largest grid in the nested grid. Introduction of these temporarily working erids increases the total number of cells in our computation ouly a factor of 8/7., Introduction of these temporarily working grids increases the total number of cells in our computation only a factor of 8/7. Accordingly the computation ou these working nested grids is ouly a minor fraction., Accordingly the computation on these working nested grids is only a minor fraction. "collisional heating dominates the atomic gas and the excitation of hydrogen, such as in shocks or clouds in hot gas, can the intrinsic ratios be significantly different (seee.g.Ferlandetal.2009),, but these processes are not expected to dominate most galaxies within our sample.","collisional heating dominates the atomic gas and the excitation of hydrogen, such as in shocks or clouds in hot gas, can the intrinsic ratios be significantly different \citep[see e.g.][]{Ferland09}, but these processes are not expected to dominate most galaxies within our sample." " An additional reason to include AGN is that, in accordance with our main aim, separating out the contribution of AGN from lower S/N samples may prove problematic as the weak diagnostic lines become lost within the noise."," An additional reason to include AGN is that, in accordance with our main aim, separating out the contribution of AGN from lower S/N samples may prove problematic as the weak diagnostic lines become lost within the noise." Approximately of the full SDSS sample considered here are duplicate observations of galaxies (i.e. ~4% of the sample are pairs)., Approximately of the full SDSS sample considered here are duplicate observations of galaxies (i.e. $\sim4$ of the sample are pairs). We have not removed these from the sample so as to include the intrinsic scatter due to observational uncertainties in the subsequent analysis., We have not removed these from the sample so as to include the intrinsic scatter due to observational uncertainties in the subsequent analysis. " The labelsec:EWissue of simply using directly the equivalent widths of the Balmer lines as proxies for the line fluxes when calculating the Balmer decrement can be seen in figure 2 which shows the spread of the equivalent width based Balmer decrement (log[EW(Ho))EW(Hp))]) against the “true” Balmer decrement determined from the stellar continuum-subtracted line fluxes (log(Ha//H£))) for the SN(Ha,,H8)) sample.", The issue of simply using directly the equivalent widths of the Balmer lines as proxies for the line fluxes when calculating the Balmer decrement can be seen in figure \ref{fig:EW_HaHb} which shows the spread of the equivalent width based Balmer decrement $\log[$ $]$ ) against the “true” Balmer decrement determined from the stellar continuum-subtracted line fluxes )) for the ) sample. " Both the EW Balmer decrement and the flux Balmer decrement have been normalised to the intrinsic ratio of 2.86, appropriate for a low density gas of T=ιο KK. One of the first obvious issues to be corrected for is the variation of the underlying stellar continuum between the aand wwavelengths."," Both the EW Balmer decrement and the flux Balmer decrement have been normalised to the intrinsic ratio of 2.86, appropriate for a low density gas of $T=10^4$ K. One of the first obvious issues to be corrected for is the variation of the underlying stellar continuum between the and wavelengths." " In the left diagram of figure 3,, we show the distribution of log[EW(Ho))/EW(Hp))], uncorrected for the continuum flux variation, while on the right the more accurate form of the EW Balmer decrement is used: log[EW(Ho))/EW(Hp))]+ log[F,(Ha@)/F,(H8)], where F;(Ha) is the continuum flux atHa,, determined from a 200 pixel median smoothing of the emission-line subtracted continuum."," In the left diagram of figure \ref{fig:EW_HaHb}, we show the distribution of $\log[$ $]$, uncorrected for the continuum flux variation, while on the right the more accurate form of the EW Balmer decrement is used: $\log[$ $] + \log[{\rm F}_{\lambda}(\ha)/{\rm F}_{\lambda}(\hb)]$ , where ${\rm F}_{\lambda}(\ha)$ is the continuum flux at, determined from a 200 pixel median smoothing of the emission-line subtracted continuum." When uncorrected for the underlying continuum variation there is a clear systematic offset of the EW Balmer decrement from the 1:1 relation of ~0.1 dex.," When uncorrected for the underlying continuum variation there is a clear systematic offset of the EW Balmer decrement from the 1:1 relation of $\sim 0.1$ dex." " Correcting for the continuum variation removes this offset, yet a significant spread remains."," Correcting for the continuum variation removes this offset, yet a significant spread remains." This spread is due to the effect of the stellar Balmer absorption features., This spread is due to the effect of the stellar Balmer absorption features. " Without these, EW(Ho))XxF,(Ho) should be, by definition, the flux of the line."," Without these, $\times{\rm F}_{\lambda}(\ha)$ should be, by definition, the flux of the line." " The colors in figure 3aa indicate the median aabsorption index (HóAs,, of the sample in each pixel."," The colors in figure \ref{fig:EW_HaHb}a a indicate the median absorption index \citep[\hd$_{\rm Abs}$ of the sample in each pixel." " As the figure shows, while the absolute strength of the stellar Balmer absorption features does play a part in the observed offset of the SDSS galaxies' EW Balmer decrements, the dominant mechanism for the offset and spread is the strength of the stellar absorption features to the emission lines."," As the figure shows, while the absolute strength of the stellar Balmer absorption features does play a part in the observed offset of the SDSS galaxies' EW Balmer decrements, the dominant mechanism for the offset and spread is the strength of the stellar absorption features to the emission lines." " This can be seen by the distribution of the equivalent width of the eemission line indicated by the colours in figure 3bb, where there is a clear gradient of decreasing EW(Ha)) with increasing offset from the line."," This can be seen by the distribution of the equivalent width of the emission line indicated by the colours in figure \ref{fig:EW_HaHb}b b, where there is a clear gradient of decreasing ) with increasing offset from the line." " As the emission lines become weaker overall, the stellar absorption features, which are <10A aas discussed in section ??,, obscure a greater fraction of rrelative to aand therefore lead to a larger offset."," As the emission lines become weaker overall, the stellar absorption features, which are $<$ as discussed in section \ref{sec:balmer}, obscure a greater fraction of relative to and therefore lead to a larger offset." " As discussed in the introduction, the best way to compensate for the effect of the stellar absorption features on the emission lines is to fit the stellar continuum as done within the MPA/JHU SDSS database."," As discussed in the introduction, the best way to compensate for the effect of the stellar absorption features on the emission lines is to fit the stellar continuum as done within the MPA/JHU SDSS database." " However, when only poor quality spectra are available such as for high redshift galaxies, the determination of the Balmer absorption features may be unreliable."," However, when only poor quality spectra are available such as for high redshift galaxies, the determination of the Balmer absorption features may be unreliable." One possible approach when faced with low resolution spectra is to assume that the absorption equivalent width is constant for both Balmer lines across the whole sample., One possible approach when faced with low resolution spectra is to assume that the absorption equivalent width is constant for both Balmer lines across the whole sample. " While figure 1 clearly shows that the absorption EW is the same for all the Balmer lines, it provides a first step when information is sparse and uncertainties large."," While figure \ref{fig:EW_Balmer} clearly shows that the absorption EW is the same for all the Balmer lines, it provides a first step when information is sparse and uncertainties large." " When a constant Balmer absorption correction R is assumed for both EW(Ho)) and EW(Hp),, a correction factor of R=4A iis determined when the offset of the SDSS galaxies’ EW Balmer decrements to the measured rratios is minimized using an error-based weighting."," When a constant Balmer absorption correction $R$ is assumed for both ) and ), a correction factor of $R=4$ is determined when the offset of the SDSS galaxies' EW Balmer decrements to the measured ratios is minimized using an error-based weighting." " The inclusion of this simple correction factor improves the situation when compared to that shown in figure 3,, but with a still significant scatter of σ—0.1 dex around the expected value and an extended tail of objects towards lower values."," The inclusion of this simple correction factor improves the situation when compared to that shown in figure \ref{fig:EW_HaHb}, but with a still significant scatter of $\sigma\sim0.1$ dex around the expected value and an extended tail of objects towards lower values." Both the scatter and the tail arise due to the assumption of a constant offset (i.e. Balmer absorption) for the whole sample., Both the scatter and the tail arise due to the assumption of a constant offset (i.e. Balmer absorption) for the whole sample. " The value determined is biased towards high EW(Ha)) galaxies, as these galaxies both dominate the sample and have lower uncertainties, as discussed in section 200a)"," The value determined is biased towards high ) galaxies, as these galaxies both dominate the sample and have lower uncertainties, as discussed in section \ref{sec:SDSSsample}." " When split into bins of different EW(Ho)), more accurate fits with differing correction factors are obtained."," When split into bins of different ), more accurate fits with differing correction factors are obtained." " In figure 4,, we show the fits for the galaxies split into four bins; 0.5«log(EW(Ho))< 1.0, 1.0$ 6 Gyr), one third were part of the thick disk, and the remainder were 1.5–6 Gyr thin disk members." " Abundance analysis shows that WASP-37 has enhanced alpha elements and although this is not accounted for in the simulation, we estimate that it increases the probability of thick disk membership but that it is also equally likely to be part of the old thin disk."," Abundance analysis shows that WASP-37 has enhanced alpha elements and although this is not accounted for in the simulation, we estimate that it increases the probability of thick disk membership but that it is also equally likely to be part of the old thin disk." It is reassuring that this independent analysis also finds that WASP-37 is part of an old population., It is reassuring that this independent analysis also finds that WASP-37 is part of an old population. " To determine the properties of the planet, we simultaneously modelled the SuperWASP, LT and FTN light curves and the CORALIE and SOPHIE radial velocities with a global MCMC fit."," To determine the properties of the planet, we simultaneously modelled the SuperWASP, LT and FTN light curves and the CORALIE and SOPHIE radial velocities with a global MCMC fit." Details of this process are described in?) and ?.., Details of this process are described in \citet{Cameron07} and \citet{Pollacco08}. " The free parameters in the fit are: orbital period /?: transit epoch Ty): transit duration Zaye: ratio of planet to star radius (405/£0, ): impact parameter 4; RV semi-amplitude Jv: Lagrangian elements €cosc and esinc where e is the eccentricity and w is the longitude of periastron; and the systematic offset velocity .", The free parameters in the fit are: orbital period $P$ ; transit epoch $T_{0}$; transit duration $T_{\rm dur}$; ratio of planet to star radius $(R_{\rm p}/R_{*})^{2}$ ; impact parameter $b$; RV semi-amplitude $K$; Lagrangian elements $e\cos \omega$ and $e \sin \omega$ where $e$ is the eccentricity and $\omega$ is the longitude of periastron; and the systematic offset velocity $\gamma$. " In this parucular case, two systematic velocities were fit to allow [or instrumental olfsets between the SOPHIE and CORALIE datasets."," In this particular case, two systematic velocities were fit to allow for instrumental offsets between the SOPHIE and CORALIE datasets." " We propagated the uncertainty in the stellar mass through to the derived parameters == 0.925 4 0.120., see Section ??))."," We propagated the uncertainty in the stellar mass through to the derived parameters = 0.925 $\pm$ 0.120, see Section \ref{check}) )." " We used the 4 coelficient ??. non-linear limb darkening coefficients for the appropriate stellar temperature and photometric passband appropriate for each light curve, see Table 5.."," We used the 4 coefficient \citet{claret00, claret04} non-linear limb darkening coefficients for the appropriate stellar temperature and photometric passband appropriate for each light curve, see Table \ref{ld}." The limb darkening coefficients are re-calculated at each step in the MCMC chain to take into account the uncertainties in the stellar temperature and radius., The limb darkening coefficients are re-calculated at each step in the MCMC chain to take into account the uncertainties in the stellar temperature and radius. The photometric error bars were scaled to account for any underestimations so that the best fitung model results in - = \7/dof = 1 (dof = number of points —number of fitted parameters)., The photometric error bars were scaled to account for any underestimations so that the best fitting model results in $\chi^{2}_{\rm red}$ = $\chi^{2}$ /dof = 1 (dof = number of points $-$number of fitted parameters). The radial velocity error bars did not require rescaling with a Jitter term in order to obtain - = |., The radial velocity error bars did not require rescaling with a jitter term in order to obtain $\chi^{2}_{\rm red}$ = 1. " The RMS of the residuals [romthe best-fit model are: ΜΙΝΑ, = 0.0292 mag, RMS,;y = 0.0013 mag,ΜΕΡΙ = 0.0025 mag,RMSsopie = 0.0194 land RMScortie = 0.0380 1"," The RMS of the residuals fromthe best-fit model are: $_{\rm WASP}$ = 0.0292 mag, $_{\rm LT}$ = 0.0013 mag,$_{\rm FTS}$ = 0.0025 mag,$_{\rm SOPHIE}$ = 0.0194 and $_{\rm CORALIE}$ = 0.0380 ." ", By removing the oullying point at 8.064 !., we obtain RMSCopvu: = 00164 4."," By removing the outlying point at 8.064 , we obtain $_{\rm CORALIE}$ = 0.0164 ." 2012).,. ". Given the very deep near-IR observations used in this work, the sampling of the low-mass end of the GSMF is considerably finer than most previous surveys, on average by 0.5 dex up to z~1.8 and by 0.1 dex at z~4, and at the same time the conservative photometric cut (Ks< 25.5) ensures reliable results even at the lowest masses."," Given the very deep near-IR observations used in this work, the sampling of the low-mass end of the GSMF is considerably finer than most previous surveys, on average by 0.5 dex up to $z\sim 1.8$ and by 0.1 dex at $z\sim 4$, and at the same time the conservative photometric cut $K_S<25.5$ ) ensures reliable results even at the lowest masses." The only comparable study sampling similar or slightly lower stellar masses is the one of Mortlocketal.(2011)., The only comparable study sampling similar or slightly lower stellar masses is the one of \cite{mortlock11}. ". This work is somewhat peculiar, being obtained from a set of biased pointings specifically designed to contain as many massive galaxies as possible, and a posteriori corrected to account for this bias."," This work is somewhat peculiar, being obtained from a set of biased pointings specifically designed to contain as many massive galaxies as possible, and a posteriori corrected to account for this bias." " They pushed their detection to H=26.8 at a 5c level, while our sample, although extracted from images of similar depth, was cut at a brighter limit to ensure good photometric quality."," They pushed their detection to $H=26.8$ at a $5\sigma$ level, while our sample, although extracted from images of similar depth, was cut at a brighter limit to ensure good photometric quality." " They also did not include any K band data, which is important to estimate reliable stellar masses."," They also did not include any $K$ band data, which is important to estimate reliable stellar masses." " Finally, since our studyis based on 14 bands of photometry (insteadof6bandsasMortlocketal. 2011),, our work also relies on good quality photometric redshifts."," Finally, since our studyis based on 14 bands of photometry \citep[instead of 6 bands as][]{mortlock11}, our work also relies on good quality photometric redshifts." " Despite the limited sky area, the bright-end tail is comparable overall within the uncertainties with that inferred by large surveys over the whole redshift range (with the exception of the 1.4—2.5 redshift interval, which, as discussed above, is affected by the presence of overdensities)."," Despite the limited sky area, the bright-end tail is comparable overall within the uncertainties with that inferred by large surveys over the whole redshift range (with the exception of the $1.4-2.5$ redshift interval, which, as discussed above, is affected by the presence of overdensities)." " The only severe disagreement is found when comparing our results in the highest redshift interval to Gonzálezetal. (2011),, who,"," The only severe disagreement is found when comparing our results in the highest redshift interval to \cite{gonzalez11}, , who," example)... roughly 32 INDOs and Centaurs have been checked for variability ancl this has vielded only 14 known rotational periods.,", roughly 32 KBOs and Centaurs have been checked for variability and this has yielded only 14 known rotational periods." A Wat rotational light curve could be due to 2000 LD4 being viewed pole-on or due to its being nearly round. ancl without. large regional albedo differences., A flat rotational light curve could be due to 2000 $EB_{173}$ being viewed pole-on or due to its being nearly round and without large regional albedo differences. " The absence of anv signilicant rotational variability and the bright appearance of 2000 LED, relative to other INDOs has allowed us to measure the objects phase curve. the first for anv NBO other than Pluto (Rabinowilz&Schaeler2001)."," The absence of any significant rotational variability and the bright appearance of 2000 $EB_{173}$ relative to other KBOs has allowed us to measure the object's phase curve, the first for any KBO other than Pluto \citep{ras01}." . In Figure 2. we compare the phase curve (o planet Pluto (the largest known IXDO). outer solar-svstem satellites Rhea. Nereid. and Titania. and also to the dark main-belt asteroid (24) Themis.," In Figure 2, we compare the phase curve to planet Pluto (the largest known KBO), outer solar-system satellites Rhea, Nereid, and Titania, and also to the dark main-belt asteroid (24) Themis." These examples have been chosen because they span the range of small-augle phase curves that have been well measured for bodies that might have surfaces similar to 2000. ED474., These examples have been chosen because they span the range of small-angle phase curves that have been well measured for bodies that might have surfaces similar to 2000 $EB_{173}$. Nereid is particularly interesting because it might be a captured. INDO (Schaefer&Schaefer1995.2000). and because it also exhibits a prominent opposition surge (Schaefer&Tourtellotte 2001)..," Nereid is particularly interesting because it might be a captured KBO \citep{scs95,scs00} and because it also exhibits a prominent opposition surge \citep{sct01}. ." " It is apparent thal 2000 ED4z, has an opposition surge with a slope intermediate in amplitude among the comparisons in Figure 2. (", It is apparent that 2000 $EB_{173}$ has an opposition surge with a slope intermediate in amplitude among the comparisons in Figure 2. ( This is also confirmed. by comparing Vopp(07)—Vopp(27)=0.31 with the tabulated values in Table II of (2001)..),This is also confirmed by comparing $V_{OPP}(0 \degr)-V_{OPP}(2 \degr)=0.31$ with the tabulated values in Table II of \citet{sct01}. .) The surge is much steeper than for PIuto. Rhea. aud most main-belt asteroids. but 10b as steep as (he surges observed Lor Nereid and Titania.," The surge is much steeper than for Pluto, Rhea, and most main-belt asteroids, but not as steep as the surges observed for Nereid and Titania." Unlike these (wo satellites which iwe narrow opposition surges. 2000 ιτ also has a wide surge comparable to Rhea and (24) Themis.," Unlike these two satellites which have narrow opposition surges, 2000 $EB_{173}$ also has a wide surge comparable to Rhea and (24) Themis." Strong and narrow opposition surges have also been measured [or particulate naterials of hieh albedo. for which the cause is attributed to coherent backscatter 2000).," Strong and narrow opposition surges have also been measured for particulate materials of high albedo, for which the cause is attributed to coherent backscatter \citep{nel98,nel00}." ". It is thus possible that the influence of coherent backscatter is modest or 2000 EDB4z, in comparison will Nereid ancl Titania.", It is thus possible that the influence of coherent backscatter is modest for 2000 $EB_{173}$ in comparison with Nereid and Titania. This might also indicate a relatively ow albedo [or 2000 EDz., This might also indicate a relatively low albedo for 2000 $EB_{173}$. However. because the high-albedo surfaces of Pluto and Rhea (0.6) have even weaker opposition surges. this conclusion can not be drawn.," However, because the high-albedo surfaces of Pluto and Rhea (0.6) have even weaker opposition surges, this conclusion can not be drawn." Owing to the intermediate slope of the opposition surge in 2000 ED424. the comparison wilh Nereid does 100 allow anv confident conclusion concerning the possibility that Nereid is a captured IKDO.," Owing to the intermediate slope of the opposition surge in 2000 $EB_{173}$, the comparison with Nereid does not allow any confident conclusion concerning the possibility that Nereid is a captured KBO." Despite the relatively broad opposition surge for 2000. £D474. (he laxge amplitude that we derive (B(O)21.7 with confidence) shows Chat coherent backscattering is likely an important influence.," Despite the relatively broad opposition surge for 2000 $EB_{173}$, the large amplitude that we derive $B(0)>1.7$ with confidence) shows that coherent backscattering is likely an important influence." This can be tested by looking lor a wavelength: dependence to the width of the opposition surge. 5h.," This can be tested by looking for a wavelength dependence to the width of the opposition surge, $h$." For shadow-hiding. (here is no wavelength: dependence.," For shadow-hiding, there is no wavelength dependence." For coherent-backscattering. scale linearly with wavelength of observation (lapke 1993)..," For coherent-backscattering, $h$ scale linearly with wavelength of observation \citep{hap93}. ." Our R-band observations vield 5—0.050 rad., Our R-band observations yield $h=0.050$ rad. For the V-band. we should therefore expect fh=0.050x(5500.1/7000.1)0.039 rad if coherent-backscattering is the dominant cause. and f=0.050 rad if shadow-hidiug isdominant.. Unfortunately. our observations are not sullicientlv precise to measure (his smalldifference.," For the V-band, we should therefore expect $h= 0.050 \times (5500 \AA /7000 \AA)=0.039$ rad if coherent-backscattering is the dominant cause, and $h = 0.050$ rad if shadow-hiding isdominant.. Unfortunately, our observations are not sufficiently precise to measure this smalldifference." However. in the near future. a simple," However, in the near future, a simple" fg—i) or (g—r).,$(g - i)$ or $(g - r)$. We can also see that the best SDSS color (Figure 5b) for metallicity resolution is (yg—r). but that the SDSS photometry is not seusitive enough to this difference in colors to distinguish. Boo Is level of metallicity spread with the photometric errors of the SDSS.," We can also see that the best SDSS color (Figure 5b) for metallicity resolution is $(g-r)$, but that the SDSS photometry is not sensitive enough to this difference in colors to distinguish Boo I's level of metallicity spread with the photometric errors of the SDSS." " In Figure 6. we compare the Stróuuugren auc Washington filters. and. construct. two uew iudices: my,=(C—Tj),(FyT5)) aud ii=(C—by(byy."," In Figure 6, we compare the Strömmgren and Washington filters, and construct two new indices: $m_*=(C-T_1)_0-(T_1-T_2)_0$ and $m_{**}=(C-b)_0-(b-y)_0$." The moivaliol 1s to avokl the colapse of the metallicity seusitivity of the n7-1udex ou the lower-RGB. aid to attempt o replace tle v-filter with the broader C-filter.," The motivation is to avoid the collapse of the metallicity sensitivity of the $m_1$ -index on the lower-RGB, and to attempt to replace the $v$ -filter with the broader $C$ -filter." " We see that the most successful combination. which 1naiut:üus reasonable [Fe/H]|-resolution over the whole RGB whilst allowing Or lucreasiug »hotoinetric ucertainties towards the lower-RGB. is shown in Figure 6h. with niat""s.(C—Tio."," We see that the most successful combination, which maintains reasonable [Fe/H]-resolution over the whole RGB whilst allowing for increasing photometric uncertainties towards the lower-RGB, is shown in Figure 6h, with $m_{**} \; vs.\; (C-T_1)_0$ ." This result allows us to use £ filters. CTiby. which saves observing time aud keeys 0.3) dex [Fe/H]-resoluion for stars with —1.5«[Fe/H]—1.0.," This result allows us to use 4 filters, $CT_1by$, which saves observing time and keeps $\sim 0.3$ dex [Fe/H]-resolution for stars with $-1.5<[Fe/H]<-4.0$." Figure Οἱ shows that we could use Cby for uetallicity esimates —1.5«[Fe/H]<—1.0. but these color-color plots are not sensiive to age on he RGB.," Figure 6i shows that we could use $Cby$ for metallicity estimates $-1.5<[Fe/H]<-4.0$, but these color-color plots are not sensitive to age on the RGB." Figs.6a. b e show that ig will remain preferred or systems with ). ," Figs.6a, b c show that $m_0$ will remain preferred for systems with $-1.0<[Fe/H]<-2.0$ ." In Figure δα b. we compare the Strómiugren axl Wasilugton systems. respectively.," In Figure 8a b, we compare the Strömmgren and Washington systems, respectively." This work will be expanded in HWD. but a simple closed-)ox chenuical evolution model is run for a total population of a few thousaucd stars with a couseryalive raige of —1.0<[Fe/H2.5. ages 10—12 Gyr. where we added photometric τιicertainles on tie RGB. aud we expect it to rise to least al dje MSTO.," This work will be expanded in HWD, but a simple closed-box chemical evolution model is run for a total population of a few thousand stars with a conservative range of $-1.0<[Fe/H]<-3.5$, ages $10-12$ Gyr, where we added photometric uncertainties on the RGB, and we expect it to rise to at least at the MSTO." We need at least photometry at the MSTO to cletermije if there are age spreads present. since the isoclrones exhibi ta charee of ~0.06 mag in (C—Ty for each Gyr ist age (better tian (B—1) also).," We need at least photometry at the MSTO to determine if there are age spreads present, since the isochrones exhibit a change of $\sim 0.06$ mag in $(C - T_1)$ for each Gyr in age (better than $(B-I)$ also)." We show that there would have to be much deepe| Strémimeren p10t0metry. [or auy age spread to be seen. bu that the metallicity spread is mainalned.," We show that there would have to be much deeper Strömmgren photometry for any age spread to be seen, but that the metallicity spread is maintained." In the Washiugton syseni. it is clear that this level of j»Xhotoimetric uucertainty would reveal au age spread [9] 2] Gyr. and no age-spread is observed.," In the Washington system, it is clear that this level of photometric uncertainty would reveal an age spread of $> 1$ Gyr, and no age-spread is observed." Taking the most couservative metallicity range of —1.5<[Fe/H]uw—2.5. the Strónuugren system gives the upper RGB stars (from HWD) twice the metallicity resolution of the Washinetou system at comparable S/N. However. both Strónuugren- and. Washington-color conversions to [Fe/H]-values fail at the lower RGB. due to a combination of temperature and line-blanketing ellects..," Taking the most conservative metallicity range of $-1.5 < [Fe/H] < -2.5$, the Strömmgren system gives the upper RGB stars (from HWD) twice the metallicity resolution of the Washington system at comparable S/N. However, both Strömmgren- and Washington-color conversions to [Fe/H]-values fail at the lower RGB, due to a combination of temperature and line-blanketing effects.," as well as au increase in photometjc uncertainties at [aint maeuitucles., as well as an increase in photometric uncertainties at faint magnitudes. This range in [Fe/H] produces .N(g—r)~0.1 dex. Ng—)-O.l dex. Mg—r0.2 dex. and ACC’—7)~0.2 dex. which is still half what we can achieve i ithe (C—T1) and tle StrÓmangren sys(ein.," This range in [Fe/H] produces $\Delta (g-r) \sim 0.1$ dex, $\Delta (g-i) \sim 0.1$ dex, $\Delta (g-r) \sim 0.2$ dex, and $\Delta (C-i) \sim 0.2$ dex, which is still half what we can achieve in the $(C-T_1)$ and the Strömmgren system." HWB and HWD find that the Washiugt«i1 filters are better stΠίος to dSph population studies than the Slozui filters., HWB and HWD find that the Washington filters are better suited to dSph population studies than the Sloan filters. The Str6mumeren phoOnuetry is more sensitive to the metallicity than the Washinetou «lata for metal-poor systems on tie upper RGB., The Strömmgren photometry is more sensitive to the metallicity than the Washington data for metal-poor systems on the upper RGB. However. the dSplishave so few upper RGB stars. we have to look for a better index han may alone.," However, the dSphshave so few upper RGB stars, we have to look for a better index than $_1$ alone." Washiigtou photometry (C— Ti)-color, Washington photometry $(C-T_1)$ -color r high-z. jr)~rlen 52 75<| a>4. high-n higher-z low-/ , $r^{1/2}$ $z$ $\mu(r) \sim r^{1/n}$ $n$ $n<1$ $n>4$ $n$ $n$ $n$ the blue/long-dashed and green/solid curves level out after about 45 years.,the blue/long-dashed and green/solid curves level out after about 45 years. This is interesting in comparison with the current status of the observations., This is interesting in comparison with the current status of the observations. " Since by now only one periapse passage of S2 has been observed in 2002, one would not expect to have detected an IBH from the actual 92 data so far."," Since by now only one periapse passage of S2 has been observed in 2002, one would not expect to have detected an IBH from the actual S2 data so far." " This is particularly true since the assumed level of accuracy was not reached during the first years of the observations (1992 - 2002), and radial velocity information is only available after 2002 (with the exception of one point in 2000)."," This is particularly true since the assumed level of accuracy was not reached during the first years of the observations (1992 - 2002), and radial velocity information is only available after 2002 (with the exception of one point in 2000)." " Hence, the first real chance to detect an IBH will be after the next S2 periapse passage, which will happen in 2018."," Hence, the first real chance to detect an IBH will be after the next S2 periapse passage, which will happen in 2018." " Here we consider other perturbations that could induce changes in S2’s orbital angular momentum, potentially complicating the signal from an IBH."," Here we consider other perturbations that could induce changes in S2's orbital angular momentum, potentially complicating the signal from an IBH." We find that almost all such alternative perturbations are small compared to the torque produced by an IBH., We find that almost all such alternative perturbations are small compared to the torque produced by an IBH. " Angles quoted in this section are intrinsic, not astrometric."," Angles quoted in this section are intrinsic, not astrometric." " As noted above, current data are able to determine the orbital angles (cv,Ω, i) of $2 with an accuracy of about one degree."," As noted above, current data are able to determine the orbital angles $\varpi,\Omega,i$ ) of S2 with an accuracy of about one degree." " Changes induced by an IBH per orbit of S2 are 10?degsA(i,Ω)€1deg (Figure 2)."," Changes induced by an IBH per orbit of S2 are $10^{-3} \mathrm{deg} \simless \Delta(i,\Omega) \simless 1 \mathrm{deg}$ (Figure 2)." Frame-dragging effects from a spinning MBH include an additional in-plane precession term as well as a precession of the orbital plane., Frame-dragging effects from a spinning MBH include an additional in-plane precession term as well as a precession of the orbital plane. " Defining 7’ and 1’ as the inclination and nodal angle of S2's orbit with respect to the MBH's equatorial plane, to lowest PN order, frame dragging induces changes per revolution in the angle of periapse and the line of nodes, respectively, where and χ<1 is the dimensionless spin of the MBH (e.g.Merrittetal.2010)."," Defining $i^\prime$ and $\Omega^\prime$ as the inclination and nodal angle of S2's orbit with respect to the MBH's equatorial plane, to lowest PN order, frame dragging induces changes per revolution in the angle of periapse and the line of nodes, respectively, where and $\chi\le 1$ is the dimensionless spin of the MBH \citep[e.g.][]{MAMW2010}." . The orbital inclination 7’ remains unchanged., The orbital inclination $i^\prime$ remains unchanged. " For $2, the spin contribution to advance of the periapse is ~1% of the Schwarzschild contribution even for x—1 and so can be ignored."," For S2, the spin contribution to advance of the periapse is $\sim 1\%$ of the Schwarzschild contribution even for $\chi=1$ and so can be ignored." " The nodal advance is ΔΩ’=0.002xdeg, too small to be detectable in the next few decades of monitoring, and smaller than the changes induced by an IBH in almost all of the runs carried out here (Fig."," The nodal advance is $\Delta\Omega^\prime \approx 0.002\,\chi\,\rm deg$, too small to be detectable in the next few decades of monitoring, and smaller than the changes induced by an IBH in almost all of the runs carried out here (Fig." 2)., 2). Effects of frame dragging are only likely to be important for stars much closer to SgrA* than S2 (Merrittetal.2010).. (, Effects of frame dragging are only likely to be important for stars much closer to $^*$ than S2 \citep{MAMW2010}. ( Frame dragging could nevertheless be relevant to the orbit of an IBH.,Frame dragging could nevertheless be relevant to the orbit of an IBH. " For the IBH orbit with smallest a (0.3 mpc) and largest e (0.9) considered here, the precession time drops to ~300x! yr.)"," For the IBH orbit with smallest $a$ $0.3$ mpc) and largest $e$ $0.9$ ) considered here, the precession time drops to $\sim 300\chi^{-1}$ yr.)" " If the gravitational potential due to the distributed mass is appreciably non-spherical, the resultant torques could affect all of the orbital elements of S2 aside from a."," If the gravitational potential due to the distributed mass is appreciably non-spherical, the resultant torques could affect all of the orbital elements of S2 aside from $a$." " For instance, the nuclear bar described by Alard(2001) has been modelled as a triaxial spheroid with central density ~150Mgpc (Rodriguez-Fernandez&Combes 2008)."," For instance, the nuclear bar described by \citet{alard01} has been modelled as a triaxial spheroid with central density $\sim 150 \msun \mathrm{pc}^{-3}$ \citep{combes08}." ". In the most extreme? case, the nuclear star cluster (NSC) of the Milky Way could be stratified on triaxial ellipsoids at all radii."," In the most extreme case, the nuclear star cluster (NSC) of the Milky Way could be stratified on triaxial ellipsoids at all radii." " A homogeneous, non-rotating triaxial bar induces changes in the inclination and nodal angle of a test star orbiting near the MBH, with characteristic time scale (Merritt&Vasiliev2010,equations11-15).."," A homogeneous, non-rotating triaxial bar induces changes in the inclination and nodal angle of a test star orbiting near the MBH, with characteristic time scale \citep[][equations 11-15]{MV10}." " Here, p; is the density of the triaxial component, and (Τα,Τε) are the dimensionless coefficients, of order unity, that Ty,define the shape of the triaxial component (Chandrasekhar1969);; the torque in the (i,1) principal plane is proportional to T;—T;, etc."," Here, $\rho_t$ is the density of the triaxial component, and $(T_x,T_y,T_z)$ are the dimensionless coefficients, of order unity, that define the shape of the triaxial component \citep{chandra69}; the torque in the $(i,j)$ principal plane is proportional to $T_i-T_j$, etc." " For $2, the angular reorientation over one orbit due to torques from a triaxial bar would be of order undetectable even if py©10°Μαρςὃ, the approximate density of the NSC at 1 pc from SgrA*."," For S2, the angular reorientation over one orbit due to torques from a triaxial bar would be of order undetectable even if $\rho_b\approx 10^5\msun \mathrm{pc}^{-3}$, the approximate density of the NSC at $1$ pc from $^*$." "relaxation: Discreteness in the distribution of stars and stellar remnants is also a potential source of torque. """, Discreteness in the distribution of stars and stellar remnants is also a potential source of torque. “ "Vector resonant relaxation"" produces changes in the direction of the orbital angular momentum of order per radial period, where m is the mass of a background star and N is the number of such stars within S2’s orbit.","Vector resonant relaxation” produces changes in the direction of the orbital angular momentum of order per radial period, where $m$ is the mass of a background star and $N$ is the number of such stars within S2's orbit." " Writing N= M,/m, with M, the distributed mass within"," Writing $N=M_\star/m$ , with $M_\star$ the distributed mass within" than expected. the observations for this GOV star are close to predictions.,"than expected, the observations for this G0V star are close to predictions." The mode visibility 7; and r are free parameters in the reference fitting., The mode visibility $r_1$ and $r_2$ are free parameters in the reference fitting. The values obtained are given in Table 6 for fits A and B. Both results are consistent., The values obtained are given in Table \ref{tab:vis} for fits A and B. Both results are consistent. These values are compatible with theoretical values computed with the CoRoT limb-darkening laws by ?.., These values are compatible with theoretical values computed with the CoRoT limb-darkening laws by \citet{Sing10}. As a further test. we considered the sum of visibilities of modes over an interval that is equal to ]+n4n.," As a further test, we considered the sum of visibilities of modes over an interval that is equal to $1+r_1^2+r_2^2$." The fitted values are listed in Table 6.., The fitted values are listed in Table \ref{tab:vis}. According to ?.. this 1s comparable to the quantity (Κος)ΔΙο)=3.10.," According to \citet{Michel09}, , this is comparable to the quantity $(R_\mathrm{osc}/R_{l=0})^2=3.10$." The second includes modes up to /=4. whereas the first includes modes only up to /22.," The second includes modes up to $l=4$ , whereas the first includes modes only up to $l=2$." Nevertheless. the agreement between fits A and B and the theoretical expectation is met within the error bars.," Nevertheless, the agreement between fits A and B and the theoretical expectation is met within the error bars." Using photometric observations from the CoRoT space telescope spanning 117 days and a duty cycle of90%.. we measured a rotation period Py=12.3+0.15 days for the GO main sequence star52265.. thanks to a modulation in the light curve induced by photospheric activity.," Using photometric observations from the CoRoT space telescope spanning 117 days and a duty cycle of, we measured a rotation period $P_\mathrm{rot}=12.3\pm0.15$ days for the G0 main sequence star, thanks to a modulation in the light curve induced by photospheric activity." We have clearly detected solar-like oscillations in 52265.. and characterised 31 p modes in the range wwith degrees /=0. 1. and 2.," We have clearly detected solar-like oscillations in , and characterised 31 p modes in the range with degrees $l=0$, 1, and 2." We observed lifetimes for these modes ranging between 0.5 and 3 days., We observed lifetimes for these modes ranging between 0.5 and 3 days. mmode lifetimes are shorter than the solar ones. but significantly longer than the lifetimes previously observed in F stars. confirming that mode lifetimes decrease as the effective temperature increases.," mode lifetimes are shorter than the solar ones, but significantly longer than the lifetimes previously observed in F stars, confirming that mode lifetimes decrease as the effective temperature increases." Moreover. we observed for tthat the variation in lifetimes with frequency is not monotonic and shows a elear S shape.," Moreover, we observed for that the variation in lifetimes with frequency is not monotonic and shows a clear S shape." The fitted maximum bolometrie amplitude for radial modes is 3.96+0.24 ppm. which is marginally higher than the theoretical models of ? but still compatible within. the error bars.," The fitted maximum bolometric amplitude for radial modes is $3.96\pm0.24$ ppm, which is marginally higher than the theoretical models of \citet{Samadi07} but still compatible within the error bars." In the past. several analyses have shown smaller amplitudes than predicted; however. they were F stars. whereas iis a GO star. hence more like the Sun.," In the past, several analyses have shown smaller amplitudes than predicted; however, they were F stars, whereas is a G0 star, hence more like the Sun." Nevertheless. this star is over metallic.," Nevertheless, this star is over metallic." ? have shown that the surface metallicity has a strong impact on the efficiency of the mode driven by turbulent convection: the lower the surface metal abundance. the weaker the driving.," \citet{Samadi10a} have shown that the surface metallicity has a strong impact on the efficiency of the mode driven by turbulent convection: the lower the surface metal abundance, the weaker the driving." These authors have precisely quantified this effect for the CoRoT target HD 49933. which is a rather metal-poor star compared to the Sun since for this star [Fe/H]=—0.37.," These authors have precisely quantified this effect for the CoRoT target HD 49933, which is a rather metal-poor star compared to the Sun since for this star $\feh=-0.37$." found that ignoring the surface metal abundance of this target results in a significant underestimation of the observed mode amplitudes., found that ignoring the surface metal abundance of this target results in a significant underestimation of the observed mode amplitudes. The theoretical scaling law by ? (see Eq. 15)), The theoretical scaling law by \citet{Samadi07} (see Eq. \ref{eq:scalamp}) ) was obtained on the basis of a series of 3D hydrodynamical models with a solar metal abundance., was obtained on the basis of a series of 3D hydrodynamical models with a solar metal abundance. Given the result of ??.. we would expect for hhigher theoretical mode amplitudes than predicted by the theoretical scaling law of ?..," Given the result of \citet{Samadi10b,Samadi10a}, we would expect for higher theoretical mode amplitudes than predicted by the theoretical scaling law of \citet{Samadi07}." However. the amount by which the theoretical amplitudes are expected to increase remains to be precisely quantified and compared to the uncertainties associated with the present seismic data.," However, the amount by which the theoretical amplitudes are expected to increase remains to be precisely quantified and compared to the uncertainties associated with the present seismic data." For52265.. we found that the mean large and small separations are Av=98.340.1μΗΖ and dor=8.1+0.2uHz and that 692 does not significantly decrease with frequency.," For, we found that the mean large and small separations are $\Dnu = 98.3 \pm 0.1\muHz$ and $\overline{\delta_{02}} = 8.1\pm 0.2\muHz$ and that $\delta_{02}$ does not significantly decrease with frequency." These quantities are typical of a — 1.2-solar-mass star that 1s still on the main sequence (seepreparatorymodelsby?).., These quantities are typical of a $\sim$ 1.2-solar-mass star that is still on the main sequence \citep[see preparatory models by][]{Soriano07}. Moreover. ddoes not show any mixed modes. as is the case for the more evolved GO star HD 49385 (?)..," Moreover, does not show any mixed modes, as is the case for the more evolved G0 star HD 49385 \citep{Deheuvels10}." The variation of Av with frequency shows an oscillation that we interpret as a possible signature of the second helium-ionisation region., The variation of $\Delta\nu$ with frequency shows an oscillation that we interpret as a possible signature of the second helium-ionisation region. Thanks to accurate eigenfrequency measurements(the erroris aboutffor the modes with the highest amplitudes) and to fine measurements of fundamental parameters obtained with the Narval spectrograph.," Thanks to accurate eigenfrequency measurements(the erroris aboutfor the modes with the highest amplitudes) and to fine measurements of fundamental parameters obtained with the Narval spectrograph," parameter at t=104 yr is between 2 and 100.,parameter at $t=10^4$ yr is between 2 and 100. The dust distribution reaches a quasi-steady state at t—10* yr., The dust distribution reaches a quasi-steady state at $t=10^{4}$ yr. We see that the particle mass is constant as a function of height at t=104 yr., We see that the particle mass is constant as a function of height at $t=10^4$ yr. " As turbulence effectively mixes the particles, and as bouncing prevents further growth or fragmentation (the dust growth is halted), both the masses and porosities of the aggregates are similar at all heights where dust is present."," As turbulence effectively mixes the particles, and as bouncing prevents further growth or fragmentation (the dust growth is halted), both the masses and porosities of the aggregates are similar at all heights where dust is present." We will see in the next section that this is only true if the turbulence parameter is rather modest., We will see in the next section that this is only true if the turbulence parameter is rather modest. A value of a=107? results in height-dependent particle mass., A value of $\alpha=10^{-2}$ results in height-dependent particle mass. We also see from these simulations that a higher turbulence value reduces the mass of particles and increases the dust scale height., We also see from these simulations that a higher turbulence value reduces the mass of particles and increases the dust scale height. " If turbulence is strong enough, the dust scale height can be similar to the gas scale height and the disk atmosphere remains dusty at all times."," If turbulence is strong enough, the dust scale height can be similar to the gas scale height and the disk atmosphere remains dusty at all times." " However, such high turbulence value prevents any significant dust growth, which is not a fertile environment for planet formation (see next Section)."," However, such high turbulence value prevents any significant dust growth, which is not a fertile environment for planet formation (see next Section)." " In this Section we use the complete Braunschweig model (see Paper I for details), the value of the turbulence parameter is a=10-4 and 10:73."," In this Section we use the complete Braunschweig model (see Paper I for details), the value of the turbulence parameter is $\alpha=10^{-4}$ and $10^{-2}$." " The calculations are performed with both the Okuzumi porosity model (CB1, CB3) and the Ormel porosity model (CB2, CB4) because we want to investigate how sensitive the outcome of dust growth is to the used hit&sstick porosity model within the context of our model."," The calculations are performed with both the Okuzumi porosity model (CB1, CB3) and the Ormel porosity model (CB2, CB4) because we want to investigate how sensitive the outcome of dust growth is to the used stick porosity model within the context of our model." " In the simplified Braunschweig collision model, the growth is halted by bouncing immediately if the particles enter the bouncing regime."," In the simplified Braunschweig collision model, the growth is halted by bouncing immediately if the particles enter the bouncing regime." " However, in the complete Braunschweig model, there channels for growth beyond the hit&sstick border line (that is where Econ ὃΕποι)."," However, in the complete Braunschweig model, there channels for growth beyond the stick border line (that is where $E_{\mathrm{coll}} > 5 E_{\mathrm{roll}}$ )." The most important area is in the regime where a small porous projectile collides with a heavy porous target (see Fig.11 of Paper I)., The most important area is in the regime where a small porous projectile collides with a heavy porous target (see Fig.11 of Paper I). " Due to these “green” areas at intermediate collision energies, particles in the CB1 and"," Due to these “green” areas at intermediate collision energies, particles in the CB1 and" dust. erains.,dust grains. " Pherelore the metallicity Z(z). relative to the local solar value. Z.. can be written: From the formalism in section 2.1.. the mass clensity in dust. relative to the local density. ,(2)/£824(0). can be determined. and. is found to be independent. of the galaxy properties rj and 7g. depending only on our evolution parameters. 0 and ar."," Therefore the metallicity $Z(z)$, relative to the local solar value, $Z_{\odot}$, can be written: From the formalism in section \ref{ev}, the mass density in dust relative to the local density, $\Omega_{d}(z)/\Omega_{d}(0)$, can be determined and is found to be independent of the galaxy properties $r_{0}$ and $\tau_{B}$, depending only on our evolution parameters, $\delta$ and $z_{dust}$ ." " This is given by The gas ratio. 2,(0)/Q,(2). is adopted from studies of the evolution in gas content of damped Ly-a systems."," This is given by The gas ratio, $\Omega_{g}(0)/\Omega_{g}(z)$, is adopted from studies of the evolution in gas content of damped $\alpha$ systems." These svstenis are believed to account for at least SO% of the eas content in the form of neutral hydrogen at reclshilts 222 (Lanzetta et al., These systems are believed to account for at least $80\%$ of the gas content in the form of neutral hydrogen at redshifts $z\simgt2$ (Lanzetta et al. 1991)., 1991). We adopt the empirical fit of Lanzetta et al. (, We adopt the empirical fit of Lanzetta et al. ( "1995). who find that the observed evolution in οί) is well represented by Ορ)=O,(0)exptaz). where a=0.60.15 and O.S3+0.15 for qu=0 and qu=0.5 respectively.","1995), who find that the observed evolution in $\Omega_{g}(z)$ is well represented by $\Omega_{g}(z)=\Omega_{g}(0)\exp(\alpha z)$, where $\alpha=0.6\pm0.15$ and $0.83\pm0.15$ for $q_{0}=0$ and $q_{0}=0.5$ respectively." Figure 2 shows the range in relative metallicity implied bv our evolutionary dust. model (equations 19 and 13)) as a function of redshift. for two values of qu., Figure \ref{metfit} shows the range in relative metallicity implied by our evolutionary dust model (equations \ref{mdg} and \ref{omegev}) ) as a function of redshift for two values of $q_{0}$. The. solid and dashed. lines correspond to respectively qa=0 and qu=0.5 and the regions between these lines correspond to the ranges assumed for our assumed model parameters: 6Xnnacx 20and 05«0«0.05., The solid and dashed lines correspond to respectively $q_{0}=0$ and $q_{0}=0.5$ and the regions between these lines correspond to the ranges assumed for our assumed model parameters: $6\leq z_{dust}\leq20$ and $-0.5<\delta<-0.05$. For comparison. the mean metallicities ZzQ.1Z. and Zz0.012 observed in damped: Ly-a systems at 2:z2.2 and the Lyman forest at 5 respectively are also shown.," For comparison, the mean metallicities $Z\approx 0.1Z_{\odot}$ and $Z\approx 0.01Z_{\odot}$ observed in damped $\alpha$ systems at $z\approx2.2$ and the Lyman forest at $z\simgt2.5$ respectively are also shown." These agree well with our model predictions. suggesting that our model assumptions will provide a reliable measure of dust evolution which are at least compatible with other indirect estimates.," These agree well with our model predictions, suggesting that our model assumptions will provide a reliable measure of dust evolution which are at least compatible with other indirect estimates." Using the formalism of Alasci Webster (1995). and replacing the parameters rg and ry by their assumed redshift dependence as defined in section 2.1.. Fig.," Using the formalism of Masci Webster (1995) and replacing the parameters $\tau_{B}$ and $r_{0}$ by their assumed redshift dependence as defined in section \ref{ev}, , Fig." 3. shows probability density. functions p(r|z) for the total opticaldepth up to redshifts 2 —1. 3 and 5.," \ref{pdfs2} shows probability density functions $p(\tau\, |\,z)$ for the total opticaldepth up to redshifts $z=$ 1, 3 and 5." Results are shown [or two sets of galaxy parameters (7. Te). with four sets of evolutionary parameters (9. τω) for each.," Results are shown for two sets of galaxy parameters $\tau_{g}$, $\tau_{B}$ ), with four sets of evolutionary parameters $\delta$ , $z_{dust}$ ) for each." The area under any normalised curve in Fig., The area under any normalised curve in Fig. 3. gives the fraction of lines-o[-sight. to that redshift which have optical depths within some interval 0οTas., \ref{pdfs2} gives the fraction of lines-of-sight to that redshift which have optical depths within some interval $0\rightarrow\tau_{max}$. Lowards high redshifts. we find that obscuration depends most sensitively on the parameter 7. in other words. on the covering factor of absorbers (equation. 100).," Towards high redshifts, we find that obscuration depends most sensitively on the parameter $\tau_{g}$, in other words, on the covering factor of absorbers (equation \ref{tg2}) )." Figure 3. shows that as the amount of dust at high. redshift. decreases. ic.," Figure \ref{pdfs2} shows that as the amount of dust at high redshift decreases, ie.," as 9 and τις decrease. the curves show little horizontal shift towards larger optical depths from z= 110 z—5.," as $\delta$ and $z_{dust}$ decrease, the curves show little horizontal shift towards larger optical depths from $z=1$ to $z=5$." " A significant shift becomes noticeable however for the weaker evolution cases. and is largest for ""no evolution’ (solid lines)."," A significant shift becomes noticeable however for the weaker evolution cases, and is largest for `no evolution' (solid lines)." Phis behaviour is further investigated below., This behaviour is further investigated below. In order to give a clearer comparison between the amount of obscuration and strength of evolution implied by our model parameters (Ty.Te.ὃνSaar) we have caleulated the mean and variance in total optical depth as a function of redshift.," In order to give a clearer comparison between the amount of obscuration and strength of evolution implied by our model parameters $\tau_{g},\,\tau_{B},\,\delta,\,z_{dust}$ ), we have calculated the mean and variance in total optical depth as a function of redshift." Formal derivations of these quantities are given in the appendix., Formal derivations of these quantities are given in the appendix. Here. webrielly. discuss their general dependence on the model parameters., Here webriefly discuss their general dependence on the model parameters. A quantity first worth considering. is the number of galaxies interceptecl along the lince-ol-sight., A quantity first worth considering is the number of galaxies intercepted along the line-of-sight. " In a qu=0.5 (A=0) universe. the average number of intersections within a scale length rg of a galaxy’s center by a light rav to some redshift is given by Where 9 and 7, are defined in equations (9)) and (10)) respectively."," In a $q_{0}=0.5$ $\Lambda=0$ ) universe, the average number of intersections within a scale length $r_{0}$ of a galaxy's center by a light ray to some redshift is given by Where $\delta$ and $\tau_{g}$ are defined in equations \ref{rozev}) ) and \ref{tg2}) ) respectively." In the case where we haveno-evotilion. ic.," In the case where we have, ie." where 6=0 and SayeOe. aN for a dust lew that scales inversely with wavelength. (ie.," where $\delta=0$ and $z_{max}=\infty$, and for a dust law that scales inversely with wavelength (ie." £yx1/AÀ which is à good approximation ab ÀZ2500A)). exact expressions follow for the mean and variance in total optical depth along the line-of-5ight.," $\xi_{\lambda}\propto 1/\lambda$ which is a good approximation at $\lambda\simgt2500$ ), exact expressions follow for the mean and variance in total optical depth along the line-of-sight." The mean optical depth can be written: and the variance: The variance (equation 16)) or scatter about the mean to some redshift’ provides a more convenient. measure of reddening., The mean optical depth can be written: and the variance: The variance (equation \ref{varnoev}) ) or `scatter' about the mean to some redshift provides a more convenient measure of reddening. " The mean optical depth has a simple linear dependence on the parameters z, and rg and thus gives no indication of the degree to which each of these parameters contributes to the scatter.", The mean optical depth has a simple linear dependence on the parameters $\tau_{g}$ and $\tau_{B}$ and thus gives no indication of the degree to which each of these parameters contributes to the scatter. As seen. [rom the probability distributions in Fig. 3..," As seen from the probability distributions in Fig. \ref{pdfs2}," there is a relatively large scatter about the mean optical depth to any redshift., there is a relatively large scatter about the mean optical depth to any redshift. From equation (16)). it is seen that the strongest. dependence. of. the variance is on the central absorber optical depth 7g.," From equation \ref{varnoev}) ), it is seen that the strongest dependence of the variance is on the central absorber optical depth $\tau_{B}$." Thus. larger values of re (which imply harder-edged! disks). are expected to introduce considerable scatter amongst random incividual lines of sight. even to relatively low recdshift.," Thus, larger values of $\tau_{B}$ (which imply `harder-edged' disks), are expected to introduce considerable scatter amongst random individual lines of sight, even to relatively low redshift." In Fig. 4..," In Fig. \ref{meantaus}," we show how the mean optical depth varies as a Function ofredshift for a range of evolutionary. parameters., we show how the mean optical depth varies as a function ofredshift for a range of evolutionary parameters. " ‘Strong evolution! is characterised by 8=05. zi=6 (dot-dashed: curves). às compared to the ""no. ""weak and ""moderate! evolution. cases. indicated."," `Strong evolution' is characterised by $\delta=-0.5$, $z_{dust}=6$ (dot-dashed curves), as compared to the `no', `weak' and `moderate' evolution cases indicated." " The mean optical depth IHattens out considerably towards high redshift in the strong evolution case. and gradually steepens as 9 and 2,54 are increased."," The mean optical depth flattens out considerably towards high redshift in the strong evolution case, and gradually steepens as $\delta$ and $z_{dust}$ are increased." Note that no such flattening is expected. in mean reddening for the no evolution case (Fig., Note that no such flattening is expected in mean reddening for the no evolution case (Fig. 4cc)., \ref{meantaus}c c). The mean optical depth to redshifts 221 in evolution mocdels can be reduced by [actors of at leastthree. even for low to moderately low evolution strengths.," The mean optical depth to redshifts $z\simgt1$ in evolution models can be reduced by factors of at leastthree, even for low to moderately low evolution strengths." Figure 4dd shows the sealing of mean optical depth with respect to the evolutionary parameters., Figure \ref{meantaus}d d shows the scaling of mean optical depth with respect to the evolutionary parameters. Lt is seenthat reddening depends: most sensitively on the parameter. à. which controls the rate of evolution in galactic dust. scale raciius ry.,"It is seenthat reddening depends most sensitively on the parameter $\delta$ , which controls the rate of evolution in galactic dust scale radius $r_{0}$ ." A similar trend is followed in bie. 5..," A similar trend is followed in Fig. \ref{vars}, ," which shows the dependence of variance in optical depth on evolution as a, which shows the dependence of variance in optical depth on evolution as a the value obtained w ancl (2009)... aux exhibits smaller nucertaiuties.,"the value obtained by and , and exhibits smaller uncertainties." Likewise. the estimate is consistent with a Weald derived from the NASA/IPAC Extragalactic Database (NED-D) master list of ealaxy distances. which features over 2300 distances for the LMC 57 The authors prior cstimates were inferred bx applying a Calactic classical Cepheid calibration to the LAIC photometiy of and (2002).," Likewise, the estimate is consistent with a mean derived from the NASA/IPAC Extragalactic Database (NED-D) master list of galaxy distances, which features over 300 distances for the LMC $^,$ The author's prior estimates were inferred by applying a Galactic classical Cepheid calibration to the LMC photometry of and ." . calibration is based primarily ou the efforts of fellow researchers who established classical Cepheids as ποιος» of Calactic opeu clusters and secured precise rigonoletric parallaxes)., calibration is based primarly on the efforts of fellow researchers who established classical Cepheids as members of Galactic open clusters and secured precise trigonometric parallaxes. . The latest OGLE LAIC observalous inclicate wat 6 Scuti stars exhibit a steeper Wesenleit slope than classical Cepheids pulsating iu the Mudamental mode3. see2010).," The latest OGLE LMC observations indicate that $\delta$ Scuti stars exhibit a steeper Wesenheit slope than classical Cepheids pulsating in the fundamental mode, see." The pulsation nodes of 6 Scuti variables may be constrained by overlavius a target demoeraplicalong with RR Lyrae aud type II Cepheid variables which are often detected in tandemupon the calibrated LAIC Wesenheit template., The pulsation modes of $\delta$ Scuti variables may be constrained by overlaying a target demographic—along with RR Lyrae and type II Cepheid variables which are often detected in tandem—upon the calibrated LMC Wesenheit template. SX Phe variables appear toward the shorter-period extension of the à Scuti regine on the Weseuhlcit diagram (Fig. 3))., SX Phe variables appear toward the shorter-period extension of the $\delta$ Scuti regime on the Wesenheit diagram (Fig. \ref{fig3}) ). The distance to variable stars in globular clusters may be established by comparing the observed Wescuheit magnitudes to the calibrated LAIC template. which exhibits extensive statistics and period coverage for iununerable variable types.," The distance to variable stars in globular clusters may be established by comparing the observed Wesenheit magnitudes to the calibrated LMC template, which exhibits extensive statistics and period coverage for innumerable variable types." " The distance modulus for MS from the analysis is: fy=15.12+0.01(0,.)d: 0.20(0). That agrees with estimate of jn19.08.", The distance modulus for M3 from the analysis is: $\mu_0=15.12\pm0.01 (\sigma_{\bar{x}}) \pm 0.20 (\sigma )$ That agrees with estimate of $\mu_0\simeq15.08$. " distances to globular clusters are established. from the magnitude of the horizontal The distauce modulus for w Ceu from the aforementioned approach is: ji=13.104-0.01(0,)5E0.0060).", distances to globular clusters are established from the magnitude of the horizontal The distance modulus for $\omega$ Cen from the aforementioned approach is: $\mu_0=13.49\pm0.01 (\sigma_{\bar{x}}) \pm 0.09 (\sigma )$ . Estimates in the literature for w Cen span a range: fyc123.4].>13.762006)..., Estimates in the literature for $\omega$ Cen span a range: $\mu_0\simeq13.41\rightarrow13.76$. The photometry characterizing variables du w Cen was obtained somewhat indirectly2007)., The photometry characterizing variables in $\omega$ Cen was obtained somewhat indirectly. . Securing multiepoch. Z-biik observations is therefore desirable to permit : more confident determination of the zero-point. and enable further constmünts on the effects of chemical composition on the hlunünosities of RR Lyrae variables.," Securing multiepoch $I$ -band observations is therefore desirable to permit a more confident determination of the zero-point, and enable further constraints on the effects of chemical composition on the luminosities of RR Lyrae variables." Stars ine Cen exhibit a sizeable spread in inetallicity at a common zero-poiu owing to the presence of multiple populations LO2|FefH|7».2.|L 2000)).," Stars in $\omega$ Cen exhibit a sizeable spread in metallicity at a common zero-point owing to the presence of multiple populations $-1.0\ge [Fe/H] \ge-2.4$, )." Evaluating the correlation between the distance modulus computed for a given RR Lyrac variable ancl its abundance vields direct constraints ou the effects of moetalliitv2009)., Evaluating the correlation between the distance modulus computed for a given RR Lyrae variable and its abundance yields direct constraints on the effects of metallicity. ". An analysis of the variable stars im ΑΠΟ vields: jy=11.09+0.02(0,)c0.0600) (caution warranted. see below)."," An analysis of the variable stars in M13 yields: $\mu_0=14.09\pm0.02 (\sigma_{\bar{x}}) \pm 0.06 (\sigma )$ (caution warranted, see below)." That may agree with the infrared weighted solution of jy=1125 by(1992).. but the estimate is slenificautly smaller than the distance modulus for M13 cited by (pj211.13).," That may agree with the infrared weighted solution of $\mu_0=14.25$ by, but the estimate is significantly smaller than the distance modulus for M13 cited by $\mu_0\simeq14.43$ )." The observations of MIS are from a series of studies that detected at least 1 SX Phe variables. 5 RR Lyrae variables (E RRe aud 1 RRab). aud 3 type II Cepheids2005).," The observations of M13 are from a series of studies that detected at least 4 SX Phe variables, 5 RR Lyrae variables (4 RRc and 1 RRab), and 3 type II Cepheids." .. The νους wore conducted as part of renewed efforts to secure inultibancd photometric parameters for variable stars in globular clusters1939.. 2001.," The surveys were conducted as part of renewed efforts to secure multiband photometric parameters for variable stars in globular clusters, ,." .mainDodyCitationEud1925]pk03.piüs. Applving the RR Lyrae variable period-reddening calibration of to the ΑΠΟ data vields a quean colour excess of: Lp49—06+0.02(0) (caution warranted. see below).," Applying the RR Lyrae variable period-reddening calibration of to the M13 data yields a mean colour excess of: $E_{B-V}=0.06 \pm 0.02 (\sigma )$ (caution warranted, see below)." The VFRR Lyrae variable period-colour relation derived by vields £y;=105dx0.02(0) (Epy= 0.01)., The RR Lyrae variable period-colour relation derived by yields $E_{V-I}=0.05\pm0.02 (\sigma)$ $E_{B-V}\simeq0.04$ ). The estimates are arecr than the reddening inferred from the NED extinction calculator for the direction toward ΑΠΟ (Epy= 0.02).The consensus position is that the ine of sight toward MIS is unobseured. however he Wesenheit approach isextinction free and," The estimates are larger than the reddening inferred from the NED extinction calculator for the direction toward M13 $E_{B-V}\simeq0.02$ ).The consensus position is that the line of sight toward M13 is unobscured, however the Wesenheit approach isextinction free and" deline the Superealactic Plane. for instance) and still not interfere with the internal dynamics of galaxy groups.,"define the Supergalactic Plane, for instance) and still not interfere with the internal dynamics of galaxy groups." It is dillicull to understand. however. how the most massive dark matter objects could manage to avoid accreting any luminous matter at all.," It is difficult to understand, however, how the most massive dark matter objects could manage to avoid accreting any luminous matter at all." 3., 3. The observed velocities of galaxies are not those of their dark matter halos: the luminous matter is “sloshing around” insile the dark potential well., The observed velocities of galaxies are not those of their dark matter halos; the luminous matter is “sloshing around” inside the dark potential well. This is probably a more attractive idea than the previous (vo. though a mechanism lor such internal motion is lacking.," This is probably a more attractive idea than the previous two, though a mechanism for such internal motion is lacking." 4., 4. Peculiar velocities on this scale are not. produced by gravitational interaction. but perhaps by some remnant of “primeval turbulence.," Peculiar velocities on this scale are not produced by gravitational interaction, but perhaps by some remnant of “primeval turbulence.”" This is an old idea in the context of the formation of galaxies., This is an old idea in the context of the formation of galaxies. ILeisenberg (in Πον]ο (1949))) required some original motion in order for matter to chunp together in galaxies: but this kind of motion is probably unimportant on galactic scales (Peebles1993) (page 541).," Heisenberg (in \citet{H49}) ) required some original motion in order for matter to clump together in galaxies; but this kind of motion is probably unimportant on galactic scales \citep{P93} (page 541)." 5., 5. We might have had bad luck with data. an unfortunate set of observations giving a misleading result of the sort that Ekholmetal.(2001) encountered.," We might have had bad luck with data, an unfortunate set of observations giving a misleading result of the sort that \citet{EBT01} encountered." Of course this is harder lo arrange wilh a much lareer sample. and in particular it is hard (o understuxd how (he very even distribution of peculiar velocity wilh absolute magnitude could have been produced by anv reasonable selection of data.," Of course this is harder to arrange with a much larger sample, and in particular it is hard to understand how the very even distribution of peculiar velocity with absolute magnitude could have been produced by any reasonable selection of data." It has indeed been argued above that the data sets at hand do not sample the true underlying cyvuanucs well: but that is in Che context of a particular model (isotropic or simple anisotropic expansion)., It has indeed been argued above that the data sets at hand do not sample the true underlying dynamics well; but that is in the context of a particular model (isotropic or simple anisotropic expansion). 6., 6. That idea leads on to the possibility that we are using the wrong kinematic mocel., That idea leads on to the possibility that we are using the wrong kinematic model. There is indeed a general expansion of the Local Volume: but perhaps there is some clilferent motion., There is indeed a general expansion of the Local Volume; but perhaps there is some different motion. This is a most attractive idea in thal no current notions of cosmology or plivsics need necessarily be discarded. or even greatly revised: however. it is not obvious to how to pursue it.," This is a most attractive idea in that no current notions of cosmology or physics need necessarily be discarded or even greatly revised; however, it is not obvious to how to pursue it." The fact that no clear trend shows up in the plots of deviation versus the various spatial directions shows (hat no simple modification of the present models. (1ncluding. for instance. a nonlinear effect of Virgocentric flow) is likely to be of use.," The fact that no clear trend shows up in the plots of deviation versus the various spatial directions shows that no simple modification of the present models (including, for instance, a nonlinear effect of Virgocentric flow) is likely to be of use." An examination of the kinematics of galaxies within 10 Mpe of the Alilky Waa’ has thrown up some surprises and one deep puzzle., An examination of the kinematics of galaxies within 10 Mpc of the Milky Way has thrown up some surprises and one deep puzzle. An overall anisotropic expansion. expected from the distribution of galaxies in the Local Volume. can be caleulated: but the uncertainty of its details and its strong dependence on (he particular data set chosen indicate that it is nol a useful description.," An overall anisotropic expansion, expected from the distribution of galaxies in the Local Volume, can be calculated; but the uncertainty of its details and its strong dependence on the particular data set chosen indicate that it is not a useful description." brightness gas is at least 1.5 times hotter than the surrounding gas or that the regions of lower surface brightness would be filled with a relativistic ,brightness gas is at least 1.5 times hotter than the surrounding gas or that the regions of lower surface brightness would be filled with a relativistic plasma. No indication of emission from a hot plasma is seen in plasma.the harder X-ray band (2.0- keV)., No indication of emission from a hot plasma is seen in the harder X-ray band (2.0-7.0 keV). " Therefore, we expect the regions of lower surface brightness to be cavities filled with a currently undetected relativistic plasma, a morphology seen in other galaxies and galaxy clusters and known as ghost cavities (Heinzetal. 2002)."," Therefore, we expect the regions of lower surface brightness to be cavities filled with a currently undetected relativistic plasma, a morphology seen in other galaxies and galaxy clusters and known as ghost cavities \citep{hei02}." . Emission from ghost cavities are generally detected in low-frequency radio data (e.g. Giacintucci et al., Emission from ghost cavities are generally detected in low-frequency radio data (e.g. Giacintucci et al. 2009)., 2009). " NGC 1316 exhibits signs of a recent merger, including nuclear and a disturbed morphology seen in the optical and activityinfrared dust distribution as well as the tidal tails first noted by Schweizer(1980)."," NGC 1316 exhibits signs of a recent merger, including nuclear activity and a disturbed morphology seen in the optical and infrared dust distribution as well as the tidal tails first noted by \citet{sch80}." . Each wavelength provides different insights into the merger event and the resulting structure of NGC 1316., Each wavelength provides different insights into the merger event and the resulting structure of NGC 1316. " Below, we discuss the distribution of the infrared-emitting dust and estimate the mass of the galaxy that collided with NGC 1316 from the measured dust mass."," Below, we discuss the distribution of the infrared-emitting dust and estimate the mass of the galaxy that collided with NGC 1316 from the measured dust mass." We also use the morphology of the large scale radio and X-ray emission (Figure 4)) to constrain the recent outburst history of the central SMBH., We also use the morphology of the large scale radio and X-ray emission (Figure \ref{xmm}) ) to constrain the recent outburst history of the central SMBH. " To measure the dust emission in the bands, we performed aperture photometry on the infrared images after subtracting a model of the stellar emission."," To measure the dust emission in the bands, we performed aperture photometry on the infrared images after subtracting a model of the stellar emission." Elliptical apertures (Figure 8)) were chosen to include dust features seen atµπι., Elliptical apertures (Figure \ref{phot}) ) were chosen to include dust features seen at. ". For the southeastern region, we used an ellipse with a major axis of 56.58, a minor axis of 46/66, and a position angle of (east of north) centered at (3*22""425.75, -37?113'02/11)."," For the southeastern region, we used an ellipse with a major axis of 8, a minor axis of 6, and a position angle of (east of north) centered at $3^{h}22^{m}42^{s}.75$, $\arcmin$ 1)." " For the northwestern region, we used an ellipse witha major axis of 86"", a minor axis of 54”, and a position angle of centered at (322""40*47, 111'53/’00)."," For the northwestern region, we used an ellipse witha major axis of $\arcsec$, a minor axis of $\arcsec$, and a position angle of centered at $3^{h}22^{m}40^{s}.47$ , $\arcmin$ 0)." The counts in each aperture were background, The counts in each aperture were background Eclipsing binaries are great stellar laboratories for gathering information on stellar surface. strueture.,Eclipsing binaries are great stellar laboratories for gathering information on stellar surface structure. During eclipses. varying parts of the stellar disk are obscured. allowing the observer to gather spatially resolved information.," During eclipses, varying parts of the stellar disk are obscured, allowing the observer to gather spatially resolved information." Without eclipses. this information is difficult to access.," Without eclipses, this information is difficult to access." The crossing of a companion in front of a rotating star causes a change in the line profile of the eclipsed star as. for example. it first covers mainly the part of the stellar surface which is moving towards the observer.," The crossing of a companion in front of a rotating star causes a change in the line profile of the eclipsed star as, for example, it first covers mainly the part of the stellar surface which is moving towards the observer." This change in the line profile results in a change in the center of gravity of the line and therefore in a change in the measured radial-velocity of the star., This change in the line profile results in a change in the center of gravity of the line and therefore in a change in the measured radial-velocity of the star. The strength and shape of this rotation effect is a function of the projection of the stellar axes on the sky. its inclination (for stars with differential rotation). the projected rotational velocity. the stellar radius. the radius of the companion. the stellar darkening. and the orbital parameters of the system.," The strength and shape of this rotation effect is a function of the projection of the stellar axes on the sky, its inclination (for stars with differential rotation), the projected rotational velocity, the stellar radius, the radius of the companion, the stellar limb-darkening, and the orbital parameters of the system." The rotation effect was first observed by Rossiter(1924) in 6 Lyrae. and by MeLaughlin(1924) in the Algol system.," The rotation effect was first observed by \cite{Rossiter1924} in $\beta$ Lyrae, and by \cite{McLaughlin1924} in the Algol system." The theory of the rotation effect is well understood (e.g. Kopal 1959.. Hosokawa 195... Ohtaetal. 2005.. and Giménez 2006)).," The theory of the rotation effect is well understood (e.g. \citeauthor{Kopal1959} \citeyear{Kopal1959}, \citeauthor{Hosokawa1953} \citeyear{Hosokawa1953}, \citeauthor{Otha2005} \citeyear{Otha2005}, and \citeauthor{Gimenez2006} \citeyear{Gimenez2006}) )." In contrast. observations of the rotation effect in eclipsing binary systems are rare (e.g. Hube&Couch 1982. and Worek 1996)).," In contrast, observations of the rotation effect in eclipsing binary systems are rare (e.g. \citeauthor{Hube1982} \citeyear{Hube1982} and \citeauthor{Worek1996} \citeyear{Worek1996}) )." Observation and analysis of the RM effect has recently received renewed interest. caused by the possibility of observing the spin-orbital alignment for transiting exoplanet systems (e.g. Quelozetal. 2000 and Winnetal. 2006)) and the potential to observe features of the planetary atmosphere (Snellen.2004).," Observation and analysis of the RM effect has recently received renewed interest, caused by the possibility of observing the spin-orbital alignment for transiting exoplanet systems (e.g. \citeauthor{Queloz2000} \citeyear{Queloz2000} and \citeauthor{Winn2006} \citeyear{Winn2006}) ) and the potential to observe features of the planetary atmosphere \citep{Snellen2004}." . For the successful observation and interpretation of the rotation effect in a planetary system. the required S/N and precision m radial velocity are significantly higher than those required to analyze the RM effect in a stellar binary system.," For the successful observation and interpretation of the rotation effect in a planetary system, the required S/N and precision in radial velocity are significantly higher than those required to analyze the RM effect in a stellar binary system." However. the difficulty in analyzing a stellar binary system lies in the fact that one has to deal with the additional light from the eclipsing foreground star.," However, the difficulty in analyzing a stellar binary system lies in the fact that one has to deal with the additional light from the eclipsing foreground star." The spectral lines of the two stars normally blend during the eclipses. which makes an analysis of the rotation effect in the framework of the change of the center of gravity during an eclipse difficult.," The spectral lines of the two stars normally blend during the eclipses, which makes an analysis of the rotation effect in the framework of the change of the center of gravity during an eclipse difficult." Nevertheless. the observation of the rotation effect is of astrophysical interest in binary systems. as 1t might reveal the orientation of the stellar rotation axes and provide information about stellar surface velocity. fields.," Nevertheless, the observation of the rotation effect is of astrophysical interest in binary systems, as it might reveal the orientation of the stellar rotation axes and provide information about stellar surface velocity fields." The knowledge of these quantities might help to answer questions related to binary formation and evolution. and to the study of apsidal motion.," The knowledge of these quantities might help to answer questions related to binary formation and evolution, and to the study of apsidal motion." Accordingly. our aim in this research is twofold: D to develop a method for deriving information about the orientation of the stellar rotation axes m an eclipsing system with two nearly equally bright components: ID) to apply it to an astrophysically interesting system. V1143CCyg (e.g. Andersenetal. 1987:: Giménez&Margrave 1985)).," Accordingly, our aim in this research is twofold: I) to develop a method for deriving information about the orientation of the stellar rotation axes in an eclipsing system with two nearly equally bright components; II) to apply it to an astrophysically interesting system, Cyg (e.g. \citeauthor{Andersen1987} \citeyear{Andersen1987}; \citeauthor{Gimenez1985} \citeyear{Gimenez1985}) )." CCyg (Table 1)) is a bright system consisting of two PSV stars. and has a high eccentricity (e= 0.54) that makes it an ideal candidate for testing a new algorithm.," Cyg (Table \ref{tab:v1143cyg}) ) is a bright system consisting of two F5V stars, and has a high eccentricity $e=0.54$ ) that makes it an ideal candidate for testing a new algorithm." Because of the high eccentricity. the spectral lines are not as extensively blended during eclipses.," Because of the high eccentricity, the spectral lines are not as extensively blended during eclipses." CCyg is a young (2-10° yr) system (Andersenetal. 1987)). and the measured apsidal motion. Le. the precession of the orbit in its own plane," Cyg is a young $2\cdot10^{9}$ yr) system \citeauthor{Andersen1987} \citeyear{Andersen1987}) ), and the measured apsidal motion, i.e. the precession of the orbit in its own plane" A single star is formed at 0.054Myr and reaches a mass of 3.69M.. by 0.3Myr.,"A single star is formed at $0.054\,{\rm Myr}$ and reaches a mass of $3.69 M_{\odot}$ by $0.3\,{\rm Myr}$." Four stars are formed in this simulation.the first. after 0.057Myr. and the other three in a burst around 0.072Myr.," Four stars are formed in this simulation,the first after $0.057\,{\rm Myr}$, and the other three in a burst around $0.072\,{\rm Myr}$." All four stars remain bound at 0.3Myr as an hierarchical quadruple consisting of a pair of close binary systems.," All four stars remain bound at $0.3\,{\rm Myr}$ as an hierarchical quadruple consisting of a pair of close binary systems." The more massive binary comprises 1.52 and 0.89M. stars in an orbit with @=15au and e=0.13.," The more massive binary comprises 1.52 and $0.89 M_{\odot}$ stars in an orbit with $a=15\,{\rm au}$ and $e=0.13$." The less massive binary comprises 0.91 and 0.69M... stars 1n an orbit with ¢@=12au and e=0.05.," The less massive binary comprises 0.91 and $0.69 M_{\odot}$ stars in an orbit with $a=12\,{\rm au}$ and $e=0.05$." The two binary systems are in a wide orbit around each other with «a~S0au and e~0.09.," The two binary systems are in a wide orbit around each other with $a \sim 80\,{\rm au}$ and $e \sim 0.09$." Four stars form in this simulation., Four stars form in this simulation. The primary star forms at 0.055Myr and eventually acquires a mass of 1.433M...," The primary star forms at $0.055\,{\rm Myr}$ and eventually acquires a mass of $1.43 M_{\odot}$." The remaining three stars form between 0.069 and 0.079 Myr.," The remaining three stars form between 0.069 and $0.079\,{\rm Myr}$ ." By 0.3Myr there is a massive triple comprising a close binary (component masses 1.43 and 0.70M... semi-major axis Sau) with a third star (0.853M.) in a wide orbit around this binary.," By $0.3\,{\rm Myr}$ there is a massive triple comprising a close binary (component masses 1.43 and $0.70 M_\odot$ , semi-major axis $a=5\,{\rm au}$ ) with a third star $0.83 M_{\odot}$ ) in a wide orbit around this binary." Thefourth star has 0.60M.. and has been ejected with a large dise early in the interaction process., Thefourth star has $0.60 M_{\odot}$ and has been ejected with a large disc early in the interaction process. Five stars are formed. the first at 0.053 Myr. and the rest between 0.070 and 0.076Myr.," Five stars are formed, the first at $0.053\,{\rm Myr}$ , and the rest between 0.070 and $0.076\,{\rm Myr}$." Three of the stars are ejected. leaving a close binary with component masses 1.46 and 1.28M... semi-major axis ¢=19au and eccentricity e=0.21.," Three of the stars are ejected, leaving a close binary with component masses $1.46$ and $1.28 M_{\odot}$, semi-major axis $a=19\,{\rm au}$ and eccentricity $e=0.21$." Unusually. the most massive star at the end of the simulation is the second object to form. rather than the first as in all other simulations.," Unusually, the most massive star at the end of the simulation is the second object to form, rather than the first as in all other simulations." Eight objects are formed in this simulation. including three brown dwarves.," Eight objects are formed in this simulation, including three brown dwarves." The primary star forms at 0.053Myr. and five further objects. including the three brown dwarves. form in a burst around 0.064Myr: the final two stars form at 0.09Myr.," The primary star forms at $0.053\,{\rm Myr}$, and five further objects, including the three brown dwarves, form in a burst around $0.064\,{\rm Myr}$; the final two stars form at $0.09\,{\rm Myr}$." Five objects are ejected almost immediately. leaving a triple system. which. despite the ejections Is very loose: the main binary has 5220au.," Five objects are ejected almost immediately, leaving a triple system, which, despite the ejections is very loose; the main binary has $a \approx 220\,{\rm au}$." After 0.17Myr the third component of the triple is ejected and the remaining binary is somewhat hardened to «~125au.," After $0.17\,{\rm Myr}$ the third component of the triple is ejected and the remaining binary is somewhat hardened to $a \sim 125\,{\rm au}$." Six stars and one brown dwarf are formed., Six stars and one brown dwarf are formed. The primary star forms at 0.055Myr. and four further stars and the brown dwarf form in à burst around 0.071Myr: the final star forms at 0.092Myr.," The primary star forms at $0.055\,{\rm Myr}$, and four further stars and the brown dwarf form in a burst around $0.071\,{\rm Myr}$; the final star forms at $0.092\,{\rm Myr}$." Two stars and the brown dwarf are ejected. leaving two close binaries in an hierarchical quadruple.," Two stars and the brown dwarf are ejected, leaving two close binaries in an hierarchical quadruple." The more massive binary comprises 1.03 and 0.711. stars m an orbit with α=|Sau.," The more massive binary comprises 1.03 and $0.71 M_{\odot}$ stars in an orbit with $a=15\,{\rm au}$." The less massive binary comprises 0.73 and 0.71Ms. stars in an orbit with ¢=16au.," The less massive binary comprises 0.73 and $0.71 M_{\odot}$ stars in an orbit with $a=16\,{\rm au}$." The two binary systems are in a wider orbit around each other with o~180au and e~0.09.," The two binary systems are in a wider orbit around each other with $a \sim 180\,{\rm au}$ and $e \sim 0.09$." However. this system is unstable. and at 0.24Myr the 0.73M.. star is ejected in a 4-body encounter. leaving the more massive binary hardened to a=4au (below our ability to resolve the dynamics properly) and the 0.71M. star in a 270au orbit around this binary. t-e. an hierarchical triple.," However, this system is unstable, and at $0.24\,{\rm Myr}$ the $0.73 M_{\odot}$ star is ejected in a 4-body encounter, leaving the more massive binary hardened to $a = 4\,{\rm au}$ (below our ability to resolve the dynamics properly) and the $0.71 M_{\odot}$ star in a $270\,{\rm au}$ orbit around this binary, i.e. an hierarchical triple." Only two stars are formed in this simulation., Only two stars are formed in this simulation. The primary star is formed at 0.057Myr and ends up with 3.19M...," The primary star is formed at $0.057\,{\rm Myr}$ and ends up with $3.19 M_{\odot}$." The secondary star forms at 0.142Myr and ends up with 0.48M...They form a wide binary system with ¢=170au and e=0.15.," The secondary star forms at $0.142\,{\rm Myr}$ and ends up with $0.48 M_{\odot}$.They form a wide binary system with $a=170\,{\rm au}$ and $e=0.15$." The large mass ratio 1s due to the very late formation time of the secondary star and its distance from the primary., The large mass ratio is due to the very late formation time of the secondary star and its distance from the primary. A single star is formed at 0.055Myr and reaches a mass of 3.33M. by 0.3Myr.," A single star is formed at $0.055\,{\rm Myr}$ and reaches a mass of $3.35 M_{\odot}$ by $0.3\,{\rm Myr}$ ." A total of seven objects is formed. the first at 0.057Myr. another five in à burst around 0.064Myr. and a final object at 0.081Myr.," A total of seven objects is formed, the first at $0.057\,{\rm Myr}$, another five in a burst around $0.064\,{\rm Myr}$, and a final object at $0.081\,{\rm Myr}$." Three stars are ejected. leaving two close binary systems 1 an hierarchical quadruple.," Three stars are ejected, leaving two close binary systems in an hierarchical quadruple." The more massive binary comprises 1.20 and 0.89M.. stars in an orbit with ¢=061au and e= 0.63.," The more massive binary comprises 1.20 and $0.89 M_{\odot}$ stars in an orbit with $a=11\,{\rm au}$ and $e = 0.63$ ." The less massive binary comprises 0.29 and 0.041M.. stars In a orbit with &=38au and e=0.33; this is the onlyexample of a brown dwarf in a binary or multiple system in all our simulations.," The less massive binary comprises 0.29 and $0.041 M_{\odot}$ stars in an orbit with $a=38\,{\rm au}$ and $e = 0.33$; this is the onlyexample of a brown dwarf in a binary or multiple system in all our simulations." The two binary systems are in a very wide orbit around each other with a~1500 au. A single star is formed at0.055Myr and reaches a mass of 2.62M.. by 0.3Myr.," The two binary systems are in a very wide orbit around each other with $a \sim 1500\,{\rm au}$ A single star is formed at$0.055\,{\rm Myr}$ and reaches a mass of $2.62 M_{\odot}$ by $0.3\,{\rm Myr}$." "magnetic field of 1 uG and a local electron density of 0.03 cm? (??), a Faraday thickness of 1 rad m? corresponds to only 40 pc, which is difficult to reconcile with the smoothness of the Galactic synchrotron foreground unless the structures to the Sun.","magnetic field of $1\ \mu$ G and a local electron density of $0.03$ $^{-3}$ \citep{GomezBenjaminCox2001,CordesLazio2002}, a Faraday thickness of 1 rad $^{-2}$ corresponds to only 40 pc, which is difficult to reconcile with the smoothness of the Galactic synchrotron foreground unless the structures to the Sun." " Assuming that the emitting patches are approximately as thick as they are wide, at 90’ scales implies that the clouds are closer than 1.6 kpc."," Assuming that the emitting patches are approximately as thick as they are wide, at $90'$ scales implies that the clouds are closer than 1.6 kpc." " Polarization observations at lower frequencies are required to follow the depolarization and determine the exact The ""front"" was tentatively interpreted by ? as a large scale structure formation shock at the interface between the Perseus cluster and the Perseus-Pisces super cluster.", Polarization observations at lower frequencies are required to follow the depolarization and determine the exact The “front” was tentatively interpreted by \citet{DeBruynBrentjens2005} as a large scale structure formation shock at the interface between the Perseus cluster and the Perseus-Pisces super cluster. " It was unclear at that time whether the ""front"" extended much beyond the primary beam of the WSRT.", It was unclear at that time whether the “front” extended much beyond the primary beam of the WSRT. " As can be seen in the image at $=+42 rad m""? in Fig. A3,,"," As can be seen in the image at $\phi=+42$ rad $^{-2}$ in Fig. \ref{brentjens_perseusmosaic_fig:rmcube-3}," it does., it does. " The location of the ""front"" is indicated by the dashed line in Fig. 6..", The location of the “front” is indicated by the dashed line in Fig. \ref{brentjens_perseusmosaic_fig:wolleben-overlay}. It runs from line of sight 32 via lines of sight 18 and 12 to line of sight 19., It runs from line of sight 32 via lines of sight 18 and 12 to line of sight 19. Association with the Perseus cluster is therefore unlikely., Association with the Perseus cluster is therefore unlikely. The excess of +40 to +50 rad m? in $ of the structures observed by ? with respect to the background sources was based on a small number of polarized sources near the centre of the mosaic., The excess of $+40$ to $+50$ rad $^{-2}$ in $\phi$ of the structures observed by \citet{DeBruynBrentjens2005} with respect to the background sources was based on a small number of polarized sources near the centre of the mosaic. " ? have since published a comprehensive RM catalogue based on a re-analysis of 375543 NVSS sources, allowing a more detailed analysis."," \citet{TaylorStilSunstrum2009} have since published a comprehensive RM catalogue based on a re-analysis of 543 NVSS sources, allowing a more detailed analysis." de Bruyn et al. (, de Bruyn et al. ( in prep.),in prep.) have conducted WSRT observations of more than 200 polarized sources in and around this area during the 2004/2005 winter season., have conducted WSRT observations of more than 200 polarized sources in and around this area during the 2004/2005 winter season. Those data will be reported ina subsequent paper., Those data will be reported ina subsequent paper. Figure 9 illustrates the relation between the ?emission..," Figure \ref{brentjens_perseusmosaic_fig:comparison-with-background} illustrates the relation between the \citet{TaylorStilSunstrum2009} ." " The logarithmic grey scale image represents the |F(9)| at a particular Faraday depth and horizontal position in a 1? thick horizontal slab through the α=320"" and 6= +41°48’12”."," The logarithmic grey scale image represents the $|F(\phi)|$ at a particular Faraday depth and horizontal position in a $1\degr$ thick horizontal slab through the $\alpha =3^\mathrm{h}20^\mathrm{m}$ and $\delta= +41\degr 48\arcmin 12\arcsec$ ." The ? sources are those within a 4° thick horizontal slab centred at the same," The \citet{TaylorStilSunstrum2009} sources are those within a $4\degr$ thick horizontal slab centred at the same." position.. from ? partly overlap with the ? selection.," from \citet{DeBruynBrentjens2005} partly overlap with the \citet{TaylorStilSunstrum2009} selection." " Where they do, the rotation measures agree within the error bars."," Where they do, the rotation measures agree within the error bars." The tick marks indicate the right ascension at the centre of the slabs., The tick marks indicate the right ascension at the centre of the slabs. " The dashed lines are the background points convolved with a Gaussian kernel of Aa=5"" FWHM.", The dashed lines are the background points convolved with a Gaussian kernel of $\Delta\alpha=5^\mathrm{m}$ FWHM. Both dashed curves show a clear trend in the background RM., Both dashed curves show a clear trend in the background RM. " in the polarized emission at $ó>+12 anda«3°17""."," in the polarized emission at $\phi > +12$ and $\alpha < 3^\mathrm{h}17^\mathrm{m}$." This suggests that there is an area behind the emission at high ¢ with a relatively uniform Faraday thickness of —45+5 rrad ?., This suggests that there is an area behind the emission at high $\phi$ with a relatively uniform Faraday thickness of $-45\pm5$ rad $^{-2}$. The fact that the excess extends to the westernmost edge of the image rules out a cluster origin., The fact that the excess extends to the westernmost edge of the image rules out a cluster origin. " The scatter in background RMs is relatively large, as is the scatter in the Faraday depth of polarized emission."," The scatter in background RMs is relatively large, as is the scatter in the Faraday depth of polarized emission." Whether this scatter can be explained adequately by a turbulent magnetized ISM or by the IGM around the background sources needs to be investigated using numerical MHD simulations., Whether this scatter can be explained adequately by a turbulent magnetized ISM or by the IGM around the background sources needs to be investigated using numerical MHD simulations. The large scale magnetic field in the vicinity of the Sun is estimated at 1.4 wG and points towards 1~80? (??)..," The large scale magnetic field in the vicinity of the Sun is estimated at 1.4 $\mu$ G and points towards $l \approx 80\degr$ \citep{HanQiao1994,SunEtAl2008}. ." " The Faraday depth at /~150° should therefore be slightly negative, which is clearly not observed."," The Faraday depth at $l \approx 150\degr$ should therefore be slightly negative, which is clearly not observed." The most prominent polarized features are instead observed at positive Faraday, The most prominent polarized features are instead observed at positive Faraday of the turbulent structure of the aaround the SAIC by Mulleretal.(2004).,of the turbulent structure of the around the SMC by \cite{muller2004}. ".. Finally, we see in Figure 3 that model 2. can convineinely reproduce the observed loop! olf the north-eastern corner of the SAIC."," Finally, we see in Figure \ref{fig:fig3} that model 2 can convincingly reproduce the observed 'loop' off the north-eastern corner of the SMC." Mulleretal(2003). report that the loop is found within a contiguous velocity range., \cite{muller2003} report that the loop is found within a contiguous velocity range. A study of their Figures 3 and 4 reveals that the bulk of the loop is consistent. with the velocity-shifted northern component. and that the bottom of the loop is delimited by the velocity and brighter southern component.," A study of their Figures 3 and 4 reveals that the bulk of the loop is consistent with the velocity-shifted northern component, and that the bottom of the loop is delimited by the lower-velocity and brighter southern component." We show in Figuree 4 the position-racius projection of the simulations., We show in Figure \ref{fig:fig4} the position-radius projection of the simulations. We see that in both cases. two filaments emanate from. the forming SMC.," We see that in both cases, two filaments emanate from the forming SMC." The. actual Magellanic AMüdege may be regarded: as the more nearby component. whereas the tidal counterpart to the Bridge extends more racially.," The actual Magellanic Bridge may be regarded as the more nearby component, whereas the tidal counterpart to the Bridge extends more radially." Importantlv. both models. predict an extremely large linc-of-sight depth for the SAIC (including the Bridge. SAIC ancl counter-arm) consistent with some previous numerical simulation results (c.g.Ciardiner.Sawa&bFuji-moto LOO4):: and also a line of sight depth through the Bridge which is consistent with the ~5 kpe line-of-sight measured between adjacent. stellar clusters by Batinelli(1998). in the Magellanic Bridec.," Importantly, both models predict an extremely large line-of-sight depth for the SMC (including the Bridge, SMC and counter-arm) consistent with some previous numerical simulation results \citep[e.g.][]{gsf94}; and also a line of sight depth through the Bridge which is consistent with the $\sim$ 5 kpc line-of-sight measured between adjacent stellar clusters by \cite{demers} in the Magellanic Bridge." Although neither of the two models can reproduce the observations fully self-consistently. we find that the three Κον large-scale features in the Magellanie Bridge are produced by these two models.," Although neither of the two models can reproduce the observations fully self-consistently, we find that the three key large-scale features in the Magellanic Bridge are produced by these two models." This suggests that the scenario where the Bridge is the result of a tidal interaction between the Clouds and the Galaxy for the last 0.2 Cave is essentially important in explaining fundamental properties of scale organisation of the ISM in the MD., This suggests that the scenario where the Bridge is the result of a tidal interaction between the Clouds and the Galaxy for the last 0.2 Gyr is essentially important in explaining fundamental properties of large-scale organisation of the ISM in the MB. The lack of exact reproduction at this stage may be due to insullicientIy complex simulations. which exclude LSAT focdback processes.," The lack of exact reproduction at this stage may be due to insufficiently complex simulations, which exclude ISM feedback processes." We note that other large-scale numerical simulations. such as those by Gardiner.Sawa&Fujimoto(1994) are also unable to clearly reproduce the loop feature.," We note that other large-scale numerical simulations, such as those by \cite{gsf94} are also unable to clearly reproduce the loop feature." Future and more sophisticated. models with gas dynamics ancl star formation will confirm whether the tidal interaction model can explain both the two kinematical properties (ναι. the bimodal kinematics and the velocity. olfset) and the presence of the giant. lloop in a self-consistent manner.," Future and more sophisticated models with gas dynamics and star formation will confirm whether the tidal interaction model can explain both the two kinematical properties (i.e., the bimodal kinematics and the velocity offset) and the presence of the giant loop in a self-consistent manner." Given the preliminary. nature of these results in. predicting the formation of the Bridge ‘loop’. it is appropriate to explore alternative processes which also may develop similar structures such as shells.," Given the preliminary nature of these results in predicting the formation of the Bridge 'loop', it is appropriate to explore alternative processes which also may develop similar structures such as 'shells'." Processes such as the stellarwind. SNe and HV impacts are conumonty-cited in the literature as. shell-[ormation mechanisms.," Processes such as the stellar-wind, SNe and HVC impacts are commonly-cited in the literature as shell-formation mechanisms." Using the canonical formulations to estimate the total input energv by Weaveretal.(1977).— (shell evolution powered bv stellar winds) along with data. of the basic characteristics of the observed loop (11—1.3 kpce). ancl based on its observed velocity. position in the “high velocity’ component which has a limiting velocity dispersion of 30 νι we estimate an cnerey requirements for the shell," Using the canonical formulations to estimate the total input energy by \cite{weaver} (shell evolution powered by stellar winds) along with data of the basic characteristics of the observed loop (R=1.3 kpc), and based on its observed velocity position in the 'high velocity' component which has a limiting velocity dispersion of $\sim$ 30 , we estimate an energy requirements for the shell" stars of future GCs may be triggered.,stars of future GCs may be triggered. In a first step. we limit our study to the propagation of the shell throughout the hot protogalactic background in which the ος are initially embedded. this part of the shell propagation being much longer than the propagation throughout the cloud (see Fig. 1)).," In a first step, we limit our study to the propagation of the shell throughout the hot protogalactic background in which the PGCCs are initially embedded, this part of the shell propagation being much longer than the propagation throughout the cloud (see Fig. \ref{fig:RsHPB}) )." The outline of the paper is as follows., The outline of the paper is as follows. In Sect., In Sect. 2. we solve the perturbecl equations of continuity and. motion for transverse Lows within the shell (ie. the swept cloud) in order to identify the conditions supporting a successful shell transverse collapse.," 2, we solve the perturbed equations of continuity and motion for transverse flows within the shell (i.e. the swept cloud) in order to identify the conditions supporting a successful shell transverse collapse." We also discuss in turn the impact of the different parameters acting upon the shell collapse and. thus. upon the temporal growth of the shell fragments in which further star formation may be stimulated.," We also discuss in turn the impact of the different parameters acting upon the shell collapse and, thus, upon the temporal growth of the shell fragments in which further star formation may be stimulated." In Sect., In Sect. 3. we show how the conditions required to stimulate a star formation episode within the shell provides a natural explanation to the observed metallicity range of halo GC's and how the shape of their metallicity spectrum constitutes the next step to work on.," 3, we show how the conditions required to stimulate a star formation episode within the shell provides a natural explanation to the observed metallicity range of halo GCs and how the shape of their metallicity spectrum constitutes the next step to work on." Sect., Sect. 4 describes some ellects which our forthcoming computations should take into account in order to refine the present. model., 4 describes some effects which our forthcoming computations should take into account in order to refine the present model. Finally. our conclusions are presented in Sect.," Finally, our conclusions are presented in Sect." 5., 5. " The shell will in general contain perturbed: (transverse) velocity, components. anc perturbations in the column density whose development leads to the transverse collapse of the swept PGCC and. thereby. to the formation of a second. stellar. generation."," The shell will in general contain perturbed (transverse) velocity components and perturbations in the column density whose development leads to the transverse collapse of the swept PGCC and, thereby, to the formation of a second stellar generation." We now derive the conditions to ect such a collapsing shell., We now derive the conditions to get such a collapsing shell. Phe elementary method described below is adopted., The elementary method described below is adopted. The computations are based on the linear perturbed equations of continuity ancl motion for transverse flows in the shell (e.g. Elmegreen 1994)., The computations are based on the linear perturbed equations of continuity and motion for transverse flows in the shell (e.g. Elmegreen 1994). " The perturbed.— equation of continuity (mass conservatlon)— is where subscript T means that the gracient component uneler consideration is the transverse one. and the perturbed equation of motion (momentum conservation) is In these equations. A. and V, are respectively the radius and the velocity of the shell. σου is the προurbed surface cdensitv. a, is the perturbecl surface. density. 60 is the perturbecl (transverse) velocity. ὃν is the velocity dispersion of the material inside the shell. gi is the perturbed eravity. this one being related to the surface density through (Elmegreen 1994): As mentioned above. the evolution of the shell is studied while propagating through the hot background. ic. when the whole clouc has been swept inside the shell."," The perturbed equation of continuity (mass conservation) is where subscript T means that the gradient component under consideration is the transverse one, and the perturbed equation of motion (momentum conservation) is In these equations, $R_s$ and $V_s$ are respectively the radius and the velocity of the shell, $\sigma _0$ is the unperturbed surface density, $\sigma _1$ is the perturbed surface density, $v$ is the perturbed (transverse) velocity, $c_s$ is the velocity dispersion of the material inside the shell, $g_1$ is the perturbed gravity, this one being related to the surface density through (Elmegreen 1994): As mentioned above, the evolution of the shell is studied while propagating through the hot background, i.e. when the whole cloud has been swept inside the shell." The hot backerounc being a cdilluse medium. the shell mass 1(0) does not increase any longer at this stage of its propagation and is given by the mass M of the progenitor cloud.," The hot background being a diffuse medium, the shell mass $M_s(t)$ does not increase any longer at this stage of its propagation and is given by the mass $M$ of the progenitor cloud." " The unperturbed surface density of the shell is thus given by Equation 1 shows that the cevelopment with time of any perturbation of the shell surface density (Oa,/Ol2» 0) is inhibited by the stretching of the perturbecl region. due to the shell expansion (i.c. V52Q0. first term on the right hand-side. hereafter rhs) while the convergence of the perturbed flows supports the growth of the perturbation (second. term on the rhs)."," The unperturbed surface density of the shell is thus given by Equation \ref{eq:per_cont} shows that the development with time of any perturbation of the shell surface density $\partial \sigma _1 / \partial t > 0$ ) is inhibited by the stretching of the perturbed region due to the shell expansion (i.e. $V_s > 0$, first term on the right hand-side, hereafter rhs) while the convergence of the perturbed flows supports the growth of the perturbation (second term on the rhs)." Equation 2 shows that an initial transverse Llow of material along the shell develops (OrfOt> 0) only if the selt-gravitv (third term on the rhs) overcomes the stabilizing ellects of the stretching (first terni on the rhs) and of the internal pressure (second term on the rhs). here represented by the shell sound speed squared.," Equation \ref{eq:per_motion} shows that an initial transverse flow of material along the shell develops $\partial v/ \partial t > 0$ ) only if the self-gravity (third term on the rhs) overcomes the stabilizing effects of the stretching (first term on the rhs) and of the internal pressure (second term on the rhs), here represented by $c_s^2$, the shell sound speed squared." In order to solve Eqs.l and 2. properly. we now turn to the determination of the expansion law of the shell. ic. AH) and Ἐν(δν while it propagates throughout the hot protogalactic background.," In order to solve \ref{eq:per_cont} and \ref{eq:per_motion} properly, we now turn to the determination of the expansion law of the shell, i.e. $R_s(t)$ and $V_s(t)$, while it propagates throughout the hot protogalactic background." The equations describing the propagation of a shell are as follow (Castor et al., The equations describing the propagation of a supernova-driven shell are as follow (Castor et al. 1975)., 1975). "Antarctic Plateau, especially the Kunlun Station under construction by the Polar Research Institute of China provides a unique opportunity for wide field astronomical(PRIC), surveys targeting cosmological studies.","Antarctic Plateau, especially the Kunlun Station under construction by the Polar Research Institute of China (PRIC), provides a unique opportunity for wide field astronomical surveys targeting cosmological studies." " Astronomical site survey of Dome A, Antarctica was enabled by the International Polar Year (IPY) endorsed PANDA program (Yangetal.2009) led by the PRIC and the Chinese Center for Antarctica Astronomy (CCAA)."," Astronomical site survey of Dome A, Antarctica was enabled by the International Polar Year (IPY) endorsed PANDA program \citep{Yang09} led by the PRIC and the Chinese Center for Antarctica Astronomy (CCAA)." Several international teams contributed to this effort., Several international teams contributed to this effort. " In particular, the power and on-site laboratory system built by the University of New South Wales (BUN’S) has provided the platform for all the site survey instruments."," In particular, the power and on-site laboratory system built by the University of New South Wales (BUN'S) has provided the platform for all the site survey instruments." " In its two years’ operation, the site survey effort proves practically all aspects of the theoretical expectations of the Dome A site for astronomical observations."," In its two years' operation, the site survey effort proves practically all aspects of the theoretical expectations of the Dome A site for astronomical observations." Preliminary analyses show that the boundary layer of atmospheric turbulence to be around 10—20 meters during the Antarctic winter (Ashleyetal.2010)., Preliminary analyses show that the boundary layer of atmospheric turbulence to be around $10-20$ meters during the Antarctic winter \citep{ashley10}. ". Similar to the relatively better studied neighboring Dome C site (Fossatetal. the Dome site may enjoy free atmospheric seeing 2010),,conditions of aboutA 0.3 arcsec seeing above this boundary layer, thus making it an ideal site for high angular resolution wide area surveys."," Similar to the relatively better studied neighboring Dome C site \citep{fossat10}, the Dome A site may enjoy free atmospheric seeing conditions of about 0.3 arcsec seeing above this boundary layer, thus making it an ideal site for high angular resolution wide area surveys." " The temperature at Dome A is around —60 to —70°C, making it the coldest spot on the surface of the Earth."," The temperature at Dome A is around $-60$ to $-70 \degree{C}$, making it the coldest spot on the surface of the Earth." This implies a very low thermal background emission in the thermal infrared., This implies a very low thermal background emission in the thermal infrared. The Dome site is thus also the best site for astronomical observationsA in the near infrared wavelength region., The Dome A site is thus also the best site for astronomical observations in the near infrared wavelength region. One other especially exciting property of the site is the lack of water vapors due to the high altitude and the low temperature., One other especially exciting property of the site is the lack of water vapors due to the high altitude and the low temperature. This implies that the site is also ideal for terahertz observations which have been impossible from any temperate sites on Earth., This implies that the site is also ideal for terahertz observations which have been impossible from any temperate sites on Earth. " While quantitative site properties are still under analyses and longer term monitoring are still needed to firmly establish the astronomical potential of the Dome A site, there is no doubt that a survey project at Dome A can be highly complimentary to programs such as the Large Synoptic Survey (LSST,LSSTScienceCollaborations the Joint Dark EnergyMission?, andEuclid?."," While quantitative site properties are still under analyses and longer term monitoring are still needed to firmly establish the astronomical potential of the Dome A site, there is no doubt that a survey project at Dome A can be highly complimentary to programs such as the Large Synoptic Survey \citep[LSST,][]{lsst09}, the Joint Dark Energy, and." ". 2009),,For example, a survey at Dome A can provide near infrared data that compliments the deep optical band survey of the LSST; a deep survey in the near infrared combined with the optical data from LSST can reveal high redshift objects at z~10, which are not detectable in the optical."," For example, a survey at Dome A can provide near infrared data that compliments the deep optical band survey of the LSST; a deep survey in the near infrared combined with the optical data from LSST can reveal high redshift objects at $z\sim10$, which are not detectable in the optical." The Kunlun Dark Universe Survey Telescope (KDUST) is a 6-to-8-meter wide-area survey telescope being designed by the CCAA., The Kunlun Dark Universe Survey Telescope (KDUST) is a 6-to-8-meter wide-area survey telescope being designed by the CCAA. " The preliminary design includes a 3x3 square degree optical camera with 0"".15 pixel, and an infrared camera of 1x square degree at 0"".1/pixel optimized for 1—3.5 uum surveys."," The preliminary design includes a $3\times3$ square degree optical camera with $0''.15$ pixel, and an infrared camera of $1\times1$ square degree at $0''.1$ /pixel optimized for $1-3.5$ $\mu$ m surveys." One of the key science missions of KDUST is to investigate the mystery of the accelerated cosmic expansion (Riessetal.1998;Perlmutter using multiple techniques.," One of the key science missions of KDUST is to investigate the mystery of the accelerated cosmic expansion \citep{riess98,perlmutter99a} using multiple techniques." " In this paper, we estimate"," In this paper, we estimate" " In this paper, we estimate1"," In this paper, we estimate" " In this paper, we estimate19"," In this paper, we estimate" " In this paper, we estimate199"," In this paper, we estimate" " In this paper, we estimate1999"," In this paper, we estimate" " In this paper, we estimate1999)"," In this paper, we estimate" regions where all the three IR bands overlap.,regions where all the three IR bands overlap. To facilitate the comparison. Fig.," To facilitate the comparison, Fig." 9bb displays the 330 MHz continuum image of IC 443 with a grayscale selected to emphasize the brightest radio emission., \ref{ir-radio}b b displays the 330 MHz continuum image of IC 443 with a grayscale selected to emphasize the brightest radio emission. An impressive agreement is observed in location. size and shape between the NIR emission detected in the H and J bands and the flattest spectral feature as traced by the a contours along the eastern edge of IC 443.," An impressive agreement is observed in location, size and shape between the NIR emission detected in the H and J bands and the flattest spectral feature as traced by the $\alpha_{74}^{330}$ contours along the eastern edge of IC 443." This correspondence begins in the northernmost part of the remnant and extends down to positions near dee.~+22° 25’.," This correspondence begins in the northernmost part of the remnant and extends down to positions near $\sim+22^{\circ}\,25^{\prime}$ ." From Fig., From Fig. 9bb it is also notable that the brightest radio synchrotron emission perfectly matches the bright emission in the NIR bands., \ref{ir-radio}b b it is also notable that the brightest radio synchrotron emission perfectly matches the bright emission in the NIR bands. As noticed by ?.. at this site the predominant constituent of the emission in the J and H bands is the [Fell] line. with a minor contribution from other multi-10nized spectes like [Nell]. |Nell]. [Sill]. [SHI]. ete.," As noticed by \citet{rho01}, at this site the predominant constituent of the emission in the J and H bands is the [FeII] line, with a minor contribution from other multi-ionized species like [NeII], [NeIII], [SiII], [SIII], etc." ?. proposed a model in which the infrared emission from the tonized species in the east bright radio limb of IC 443 comes from shattered dust produced by a fast dissociating J-type shock., \citet{rho01} proposed a model in which the infrared emission from the ionized species in the east bright radio limb of IC 443 comes from shattered dust produced by a fast dissociating J-type shock. The present accurate comparison between radio spectral indices and IR emission confirms this model., The present accurate comparison between radio spectral indices and IR emission confirms this model. In effect. the passage of a dissociative shock through a molecular cloud not only dissociates molecules but also tonize the atoms.," In effect, the passage of a dissociative shock through a molecular cloud not only dissociates molecules but also ionize the atoms." Such collisional ionization is responsible for the thermal absorbing electrons that produce the peculiar very flat spectrum areas observed all along the eastern border of IC 443., Such collisional ionization is responsible for the thermal absorbing electrons that produce the peculiar very flat spectrum areas observed all along the eastern border of IC 443. This interpretation is 1n agreement with studies based on CO and X-ray observations which conclude that the large molecular cloud complex is located in front of IC 443 (??)..," This interpretation is in agreement with studies based on CO and X-ray observations which conclude that the large molecular cloud complex is located in front of IC 443 \citep{cor77,tro06}." Evidence for a similar situation has also been observed in the ringlike morphology of 3C 391 (?).. another SNR known to be interacting with a molecular cloud.," Evidence for a similar situation has also been observed in the ringlike morphology of 3C 391 \citep{bro05}, another SNR known to be interacting with a molecular cloud." Towards the interior of the bright eastern shell. the spectral index gradually steepens with position in coincidence with a decrease in the intensity of the radio emission.," Towards the interior of the bright eastern shell, the spectral index gradually steepens with position in coincidence with a decrease in the intensity of the radio emission." " Widely distributed K, band emission is observed in the 2MASS image in this part of the remnant. which was proposed to delineate H» shocked gas from the region interacting with the adjacent molecular cloud."," Widely distributed $K_{s}$ band emission is observed in the 2MASS image in this part of the remnant, which was proposed to delineate $_{2}$ shocked gas from the region interacting with the adjacent molecular cloud." " In contrast to the excellent agreement between the tonic emitting gas and the flattest spectrum features found in the eastern bright limb. no much obvious correspondence is observed in the southern part of IC 443 with the exception of a spectral component located at the northern extreme of the ridge. near R.A.=061G""45, dee.=22335’."," In contrast to the excellent agreement between the ionic emitting gas and the flattest spectrum features found in the eastern bright limb, no much obvious correspondence is observed in the southern part of IC 443 with the exception of a spectral component located at the northern extreme of the ridge, near $=06^{\mathrm{h}}\,16^{\mathrm{m}}\,45^{\mathrm{s}}$, $=22^{\circ}\,35^{\prime}$." This poor IR/radio-spectrum correspondence is consistent with the hypothesis proposed before. in which the flat spectrum features in this part of IC 443 have a non-thermal origin.," This poor IR/radio-spectrum correspondence is consistent with the hypothesis proposed before, in which the flat spectrum features in this part of IC 443 have a non-thermal origin." In the remainder of this section we attempt to infer. using our new measurements at low radio frequencies. the physical properties of the area of thermal absorption seen in Fig.," In the remainder of this section we attempt to infer, using our new measurements at low radio frequencies, the physical properties of the area of thermal absorption seen in Fig." 9aa spatially coincident with the ionized fine-structure line emitting atoms. te. the eastern half of the SNR.," \ref{ir-radio}a a spatially coincident with the ionized fine-structure line emitting atoms, i.e. the eastern half of the SNR." At radio wavelengths. the emissionmeasure (EM) ts given by.," At radio wavelengths, the emissionmeasure (EM) is given by," we present our results and discussion in Sections 4 and Ότι and we conclude in Section 6..,we present our results and discussion in Sections \ref{results}~ and \ref{discuss}; and we conclude in Section \ref{conclusion}. Data on very low mass binaries (VLAIBs) — binaries with a otal svstem mass of «0.2 MM. | have been collated in the (VLAIBA.see?)Burgasser...," Data on very low mass binaries (VLMBs) – binaries with a total system mass of $< 0.2$ $_\odot$ – have been collated in the \citep[VLMBA, see][]{Burgasser07}." Given that the majority of these systems have primary masses less than he hvdrogen-burning limit (mig=0.08 MM... the VLAIBA data have the potential to provide an excellent constraint on he hypothesis that substellar binaries formi via a dilferent mechanism or in a dillerent environment to stellar binaries.," Given that the majority of these systems have primary masses less than the hydrogen-burning limit $m_{\rm H} = 0.08$ $_\odot$ ), the VLMBA data have the potential to provide an excellent constraint on the hypothesis that substellar binaries form via a different mechanism or in a different environment to stellar binaries." " As of September 2010. the VLMBA [ists 99 systems. our of which lack robust separation measurements and a ""urther system has a planctary-mass companion."," As of September 2010, the VLMBA lists 99 systems, four of which lack robust separation measurements and a further system has a planetary-mass companion." That leaves 94 systems to compare with numerical simulations., That leaves 94 systems to compare with numerical simulations. We define the multiplicity of VL.MBs as where J is the number of binary systems ancl S is the number of single svstems., We define the multiplicity of VLMBs as where $B$ is the number of binary systems and $S$ is the number of single systems. We ignore triple ancl higher-order systems for the remainder of this paper., We ignore triple and higher-order systems for the remainder of this paper. The overall multiplicity of VLMDs is open to debate., The overall multiplicity of VLMBs is open to debate. Dased on potentially uncliscovered svstems. ο suggest a a value of 0.26 4 0.10.," Based on potentially undiscovered systems, \citet{Basri06} suggest a a value of 0.26 $\pm$ 0.10." This would argue in favour of he VLMDs as a continuous population. as the multiplicity of M-cdwarls ancl οκναί is O42 and (0.58. respectively (?7) possibly indicating a smooth decrease in multiplicity with decreasing primary mass.," This would argue in favour of the VLMBs as a continuous population, as the multiplicity of M-dwarfs and G-dwarfs is 0.42 and 0.58, respectively \citep{Fischer92,Duquennoy91} possibly indicating a smooth decrease in multiplicity with decreasing primary mass." However. ? argue that the VLMDA data is consistent with an overall multiplicity of ).15. representing a distinct cut-olf from the stellar binary regine.," However, \citet{Thies07} argue that the VLMBA data is consistent with an overall multiplicity of 0.15, representing a distinct cut-off from the stellar binary regime." In Fig., In Fig. 1 we plot the separation distribution of the observed VLAIBs. distinguishing between systems observed in the Galactic field (the hashed histogram) and systems observed in various clusters (the open histogram).," \ref{VLMBA_sepdata} we plot the separation distribution of the observed VLMBs, distinguishing between systems observed in the Galactic field (the hashed histogram) and systems observed in various clusters (the open histogram)." Phe majority of hese systems lie in à small separation range (1.— 30aau with a peak around 5aau)., The majority of these systems lie in a small separation range $\sim 1-30$ au with a peak around au). Phe total area of the histogram corresponds to the observed binary fraction of VEM objects. VAS (?)..," The total area of the histogram corresponds to the observed binary fraction of VLM objects, 0.15 \citep{Close03}." lt is important to note that most of the observed VLAIBs are in the field., It is important to note that most of the observed VLMBs are in the field. Vhis means that their birth cluster ias disrupted and that we are mostly observing an alreacly cdsnamically processed VLALB population., This means that their birth cluster has disrupted and that we are mostly observing an already dynamically processed VLMB population. Unfortunately we lave no information on the birth clusters of these svstenis., Unfortunately we have no information on the birth clusters of these systems. Several authors have attempted to fit the VLMDB data with logiu-normal distributions similar to those that are used to fit Ge. We and. Αννας in the field. respectively) field)...," Several authors have attempted to fit the VLMB data with $_{10}$ -normal distributions similar to those that are used to fit G-, K- and M-dwarfs in the field \citep[][respectively]{Duquennoy91,Mayor92,Fischer92} ." " ? fit the VLAIB separation distribution with a logjo-normal distribution with mean 4.6aau and. variance 9),.,,4=0.4. and an overall substcllar multiplicity of 0.15. (the (solid) brown line in Fig. 1))."," \citet{Thies07} fit the VLMB separation distribution with a $_{10}$ -normal distribution with mean au and variance $\sigma_{\rm log_{10}\,a} = 0.4$, and an overall substellar multiplicity of 0.15 (the (solid) brown line in Fig. \ref{VLMBA_sepdata}) )." llowever. there are. some outlving systems wilh very short and long separations. and ο argue for a wider distribution. based on the hypothesis that there may be unresolved short-periock VLMDs with separations less than laau (?) and (at the time) the tentative discovery of VLAIBs with separations in excess of 100aau (e.g.?7?)..," However, there are some outlying systems with very short and long separations, and \citet{Basri06} argue for a wider distribution, based on the hypothesis that there may be unresolved short-period VLMBs with separations less than au \citep{Maxted05} and (at the time) the tentative discovery of VLMBs with separations in excess of au \citep[e.g.][]{Close03,Bouy06}." The former is still the subject of debate. with claims hat the peak in the VLAIB separation distribution may be tween 1. Saau (?).. though ? suggests that few VLMDs exist with separations < aau.," The former is still the subject of debate, with claims that the peak in the VLMB separation distribution may be between 1 – au \citep{Burgasser07}, , though \citet{Joergens08} suggests that few VLMBs exist with separations $<$ au." The latter appears to he xwtlv vinelicatecd by recent eliscoveries of wider svstems in he Geld (Ixónnigstuhl-1. AD. α=18007: 2M0126AD.a=5100au. 7: 2MI25SAD.α=6700au. 2)). although surveys should. be sensitive to VLAIBs with separations vctween LO 2POQaau (?)..," The latter appears to be partly vindicated by recent discoveries of wider systems in the field \citealp[K{\""o}n nigstuhl-1 AB, $a = 1800$; \citealp[2M0126AB, $a = 5100$ au,][]{Artigau07}; \citealp[2M1258AB, $a = 6700$ au,][]{Radigan09}) ), although surveys should be sensitive to VLMBs with separations between 10 – au \citep{Burgasser07}. ." " 7. proposed a wider logys-normal fit to the data with mean 4.6aau and variance 03,44un0.85. and an overall substellar multiplicity of 0.26 (the (dot-dashed) magenta line in Fig. 1)."," \citet{Basri06} proposed a wider $_{10}$ -normal fit to the data with mean au and variance $\sigma_{\rm log_{10}\,a} = 0.85$, and an overall substellar multiplicity of 0.26 (the (dot-dashed) magenta line in Fig. \ref{VLMBA_sepdata}) )." For comparison. in Fig.," For comparison, in Fig." 1. we also show the logio- fits for Ποιά Al-clwarls (7.the(dashed)blueline) and field C-dwarfs C2.the(dotted)redline)..," \ref{VLMBA_sepdata} we also show the $_{10}$ -normal fits for field M-dwarfs \citep[][the (dashed) blue line]{Fischer92} and field G-dwarfs \citep[][the (dotted) red line]{Duquennoy91}." Details of the parameters for the logjo-normal fits are given in Table 1.., Details of the parameters for the $_{10}$ -normal fits are given in Table \ref{lognormfits}. Lt is also interesting to trace the possible evolution of the mass ratio cüstribution., It is also interesting to trace the possible evolution of the mass ratio distribution. " For each system. the mass ratio. q. is defined as where mj and nm, are the masses of the primary. and secondary components. respectively."," For each system, the mass ratio, $q$, is defined as where $m_{\rm p}$ and $m_{\rm s}$ are the masses of the primary and secondary components, respectively." In Fig., In Fig. 2 we show the observed mass ratio distribution of the VLAIBA data. normalised to the total number of systems (94).," \ref{VLMBA_qdata} we show the observed mass ratio distribution of the VLMBA data, normalised to the total number of systems (94)." Almost half the VLALBs in the sample have a nis ratio approaching unity. and the majority of the other systems havehigh (2 00.7) values of q.," Almost half the VLMBs in the sample have a mass ratio approaching unity, and the majority of the other systems havehigh $>$ 0.7) values of $q$." LU Scorpii is a recurrent nova (RN) which has undergone recorded Outbursts in 1505. 1906. 1οιτ. 1986. L945. 1969. 1979. 1987. and 1999 (2). before a further outburst. pealed on 2010 January 28.190.17 UTE (2)..,"U Scorpii is a recurrent nova (RN) which has undergone recorded outbursts in 1863, 1906, 1917, 1936, 1945, 1969, 1979, 1987, and 1999 \citep{schaeferlong} before a further outburst peaked on 2010 January $28.19\pm0.17$ UT \citep{schaefer}." Phe mean recurrence time is 10.3. vears (τις, The mean recurrence time is 10.3 years \citep{schaeferlong}. " U Seo is an eclipsing binary with an orbital. inclinationD of⋅ ~82 ""n(7) and is. semi-detached. with⊀ an orbital. period.. of⋅ 21.23σοι days ""(?2)..", U Sco is an eclipsing binary with an orbital inclination of $\sim82^{\circ}$ \citep{thoroughgood} and is semi-detached with an orbital period of $\simeq$ 1.23 days \citep{schaefer&ringwald}. U DcSeo consists. of⋅ à white. dwarl⋅ (WD)⇁ primary⊀ and a probable subgiant. secondary with. a spectral tvpe in. the range Weny (7).9 to GO (?).. with the white chwarf having a mass close to the Chanclrasekhar) limit20. (2-- 137A/.) 2(?).. cp," U Sco consists of a white dwarf (WD) primary and a probable subgiant secondary with a spectral type in the range K2 \citep{anupama} to G0 \citep{hanes}, with the white dwarf having a mass close to the Chandrasekhar limit $\simeq 1.37 M_{\odot}$ ) \citep{thoroughgood}." The svstem is. at a distance of 12+2 kkpce and is far out of the galactic plane at a height of —4.5 kkpe (?).., The system is at a distance of $12\pm2$ kpc and is far out of the galactic plane at a height of $\sim4.5$ kpc \citep{schaeferlong}. 7 interprets the outbursts as being due to à thermonuclear runaway (PNR) on the surface of the white dwarf., \cite{starrfield} interprets the outbursts as being due to a thermonuclear runaway (TNR) on the surface of the white dwarf. " Phe PNR occurs when the temperature and density at the base of the laver accreted [rom the secondary reach criticalκ Hvalues ""Olof ~XY10"" KIS HandCL ~τπτ102 2 respective“CSMCIV ∖∙ TEre", The TNR occurs when the temperature and density at the base of the layer accreted from the secondary reach critical values of $\simeq 10^{8}$ K and $\simeq 10^{19}$ $^{-2}$ respectively \citep{starrfield}. recurrence; ütime scale ledis consistentsient withvill nthe nova‘ outburst∐∣↕↕ models of 2.. ⇂↓↕⋅⇀↗↽, The recurrence time scale is consistent with the nova outburst models of \cite{yaron}. "∐Phe energy.” released.|M Tfrom ""the hvdrogsen burning. is. sullicients to allow heavier. elements undergo nuclear fusion.", The energy released from the hydrogen burning is sufficient to allow heavier elements to undergo nuclear fusion. ThisMEM .continues until. theby energy generation is limited by the long. temperature independent half-lives of some isotopes involved in the CNO evele such as HO and PN. The 2010 outburst was anticipated by ? who planned a multiwavelength observing progranuue ahead of time: this resulted. in the 2010. outburst of U Sco having the best emporal! coverageS of anv nova event so far.," This continues until the energy generation is limited by the long, temperature independent half-lives of some isotopes involved in the CNO cycle such as $^{14}$ O and $^{13}$ N. The 2010 outburst was anticipated by \cite{schaefer04} who planned a multiwavelength observing programme ahead of time; this resulted in the 2010 outburst of U Sco having the best temporal coverage of any nova event so far." This led to he discovery: of new phenomena such as aperiodicmM dips ⊀⊀in he light. curve and Dares κ(7: Schaefer;. et al., This led to the discovery of new phenomena such as aperiodic dips in the light curve and flares \cite{pagnotta}; Schaefer et al. in. prep)., in prep). sThe apparent onset of⋅ optical. Hickering. on day 8 of the outburst (?); has been identified.» as an example of such a [are., The apparent onset of optical flickering on day 8 of the outburst \citep{worters} has been identified as an example of such a flare. sPhe spectral evolution. between outbursts is. consistent.. as : : ↓≱∖↿⇂↥∢⋅↓≻↓↕∪⋯⊔↓⋖⋅↿↓⋅⊔∼∢⋅∖," The spectral evolution between outbursts is consistent, as is the photometric evolution." ⇁∪⋯↓∪⊔⊳∙↗↓≻↓⋅⋖⊾⊳∖∢⋅⊔↿⊔∢⊾⋜⊔⋅−∐↘⊳∖↓≻∢⊾≼∼↿↓⋅⋜⊔⋟⇂. . ; ↓↕∢⋅⋯∐∣⋡⊔↓⋅≱∖↥∖∖⊽↓↕⊲⊔∼↓↥⊳∖↓↥∪∖∖⊽∣⋡↓⋅∪⋯⇂∐↥↦∐∢⊾↥↦∐⋖⋅∐↦⋜⋯∠⇂↻↥ emission lines.," \cite{banerjee} present near-IR spectra of the outburst which show broad, , and emission lines." " The lines give an upper limit on the ejected mass of 9.71x9.2910.""AZ. (7).", The lines give an upper limit on the ejected mass of $9.71\pm9.29 \times 10^{-5}M_{\odot}$ \citep{banerjee}. The helium abundance. N(He) ΑΗ). of U Seo is highly uncertain (7) with estimates ranging from 0.16 (2) 10 4.5 (72)..," The helium abundance, $N$ $N$ (H), of U Sco is highly uncertain \citep{diaz} with estimates ranging from 0.16 \citep{iijima} to 4.5 \citep{evans}." Xn accurate determination of the helium abundance in U Sco is necessary as some studies. have suggested that. unlike. classical. novae. the WD ..is acereting. helium-rich. material ⋠⋅from the secondary star.," An accurate determination of the helium abundance in U Sco is necessary as some studies have suggested that, unlike classical novae, the WD is accreting helium-rich material from the secondary star." As a result. the physies. of⋅ the xeTNR has been moclified⋠⋅ 2? for ⋅⋅⇁↴the case of U Sco.," As a result, the physics of the TNR has been modified by \cite{Starrfield2} for the case of U Sco." sTo .explain the. presence in to⋅⊀ re system of a helium-rich. donor star. ? proposed. an evolutionary sequence in which a helium-rich. primary filled --s Roche lobe ancl transfered materialto the secondary in," To explain the presence in the system of a helium-rich donor star, \cite{hachisukato} proposed an evolutionary sequence in which a helium-rich primary filled its Roche lobe and transfered materialto the secondary in" Galaxy clusters are natural laboratories for studying a variety of astrophysical processes and for testing cosmological models.,Galaxy clusters are natural laboratories for studying a variety of astrophysical processes and for testing cosmological models. In particular. the masses and mass profiles of clusters have proved to be useful for constraining cosmological parameters (e.g. Bridle et al.," In particular, the masses and mass profiles of clusters have proved to be useful for constraining cosmological parameters (e.g. Bridle et al." 1999: Reiprich Bóhhringer 2002: Voit 2005: Allen et al., 1999; Reiprich Böhhringer 2002; Voit 2005; Allen et al. 2008: Vikhlinin et al., 2008; Vikhlinin et al. 2009)., 2009). Gravitational lensing is frequently used to map the evolution of cluster mass profiles. ellipticities. and substructure.," Gravitational lensing is frequently used to map the evolution of cluster mass profiles, ellipticities, and substructure." One approach is to perform detailed modeling of individual clusters using strong and weak lensing (e.g.. Abdelsalam et al.," One approach is to perform detailed modeling of individual clusters using strong and weak lensing (e.g., Abdelsalam et al." 1998: Broadhurst et al., 1998; Broadhurst et al. 2005: Leonard et al., 2005; Leonard et al. 2007: Limousin et al., 2007; Limousin et al. 2007: Richard et al., 2007; Richard et al. 2007)., 2007). However. since this kind of approach requires deep data for individual clusters that exhibit numerous lensed images. the results may not be representative of the vast majority of clusters.," However, since this kind of approach requires deep data for individual clusters that exhibit numerous lensed images, the results may not be representative of the vast majority of clusters." A complementary approach is to measure the statistics of lensed ares in large samples of clusters., A complementary approach is to measure the statistics of lensed arcs in large samples of clusters. Lensing statisties thus provide another means to study clusters as a population., Lensing statistics thus provide another means to study clusters as a population. For the past decade there has been debate concerning theoretical lensing statistics predictions and their confrontation with observations., For the past decade there has been debate concerning theoretical lensing statistics predictions and their confrontation with observations. Bartelmann et al. (, Bartelmann et al. ( 1998: B98) performed lensing simulations using artificial sources at redshift z—| by ray tracing through the tive most massive clusters formed in a cosmological N-body dark matter simulation (Kauffmann et al.,1998; B98) performed lensing simulations using artificial sources at redshift $z=1$ by ray tracing through the five most massive clusters formed in a cosmological N-body dark matter simulation (Kauffmann et al. 1999)., 1999). The observed number of giant ares. with length-to-width ratio 7w=10 anc Ro21.5 mag. present over the whole sky was estimated by extrapolating< from observations of a subsample of X-ray selected clusters from the Einstein Extended Medium Sensitivity Survey (EMSS). and compared to the theoretical ealeulation.," The observed number of giant arcs, with length-to-width ratio $l/w \geq 10$ and $R<21.5$ mag, present over the whole sky was estimated by extrapolating from observations of a subsample of X-ray selected clusters from the Einstein Extended Medium Sensitivity Survey (EMSS), and compared to the theoretical calculation." B98 founc hat the estimated number of observed arcs is larger by almost an order of magnitude than the number predicted by the now-standard ACDM model., B98 found that the estimated number of observed arcs is larger by almost an order of magnitude than the number predicted by the now-standard $\Lambda {\rm CDM}$ model. Later estimates of lensed ares statistics in clusters rom both the Las Campanas Distant Cluster Survey (Zaritsky Gonzales 2003: ares with/avIO and A«21.5 mag) and the Red-Sequence Cluster Survey (RCS: Gladders et al., Later estimates of lensed arcs statistics in clusters from both the Las Campanas Distant Cluster Survey (Zaritsky Gonzales 2003; arcs with $l/w \geq 10$ and $R<21.5$ mag) and the Red-Sequence Cluster Survey (RCS; Gladders et al. 2003) confirmed he estimates of the observed number of ares derived by B98., 2003) confirmed the estimates of the observed number of arcs derived by B98. Most recently. Hennawi et al. (," Most recently, Hennawi et al. (" 2008) analyzed a sample of 240 clusters. optically selected from the Sloan Digital Sky Survey (SDSS). and ound that 10420% of them are strong lenses. similar to the,"2008) analyzed a sample of 240 clusters, optically selected from the Sloan Digital Sky Survey (SDSS), and found that $10\% - 20\%$ of them are strong lenses, similar to the" layer. the spine and fan have collapsed towards one another. and the current spreads along the fan both along and across the driving direction.,"layer, the spine and fan have collapsed towards one another, and the current spreads along the fan both along and across the driving direction." The tilt and magnitude of the arising current concentration depend on the imposed driving speed and imposed 7 as will be discussed later., The tilt and magnitude of the arising current concentration depend on the imposed driving speed and imposed $\eta$ as will be discussed later. Typically the tilt of the current sheet overshoots initially and the sheet experiences a few oscillations before settling to a stable angle., Typically the tilt of the current sheet overshoots initially and the sheet experiences a few oscillations before settling to a stable angle. Due to the imposed constant 7. reconnection takes place in the current sheet. and a near steady-state balance between the flux advected into the current sheet and the reconnected flux exiting the sheet through a reconnection jet is reached (see below).," Due to the imposed constant $\eta$, reconnection takes place in the current sheet, and a near steady-state balance between the flux advected into the current sheet and the reconnected flux exiting the sheet through a reconnection jet is reached (see below)." This picture is maintained with only minor changes until the termination of the experiments., This picture is maintained with only minor changes until the termination of the experiments. From the 2D experiment it is seen that the evolution reaches a quasi-steady-state., From the 2D experiment it is seen that the evolution reaches a quasi-steady-state. In order for it to be physically meaningful to search for sealing relations. we must first check if such a quasi-steady-state also exists in. the. 3D simulations.," In order for it to be physically meaningful to search for scaling relations, we must first check if such a quasi-steady-state also exists in the 3D simulations." To determine. this we examine some of the characteristic parameters addressed in the Sweet-Parker (??) 2D reconnection model.," To determine this we examine some of the characteristic parameters addressed in the Sweet-Parker \citep{1957JGR....62..509P,1958IAUS....6..123S} 2D reconnection model." In order to define the characteristic size of the current layer we define the boundary of the layer to be the surface at which the current modulus |J] falls to of its peak value (this peak occurring at the null)., In order to define the characteristic size of the current layer we define the boundary of the layer to be the surface at which the current modulus $|{\bf J}|$ falls to of its peak value (this peak occurring at the null). In 3D this provides three characteristic length scales that are here listed in. descending. order: The (L) in the plane of the shear perturbation (here the vy- the extent of the sheet in the direction perpendicular to this plane and parallel to the current at the null (here the z direction) which we denote here by the Gs). and finally thethickness. /. of the sheet (measured in the z=0 plane).," In 3D this provides three characteristic length scales that are here listed in descending order; The $L$ ) in the plane of the shear perturbation (here the $xy$ -plane), the extent of the sheet in the direction perpendicular to this plane and parallel to the current at the null (here the $z$ direction) which we denote here by the $w$ ), and finally the, $l$, of the sheet (measured in the $z=0$ plane)." First we estimate the amount of magnetic flux. being transported into the sheet — for which one needs to know both the inflow velocity perpendicular to the current sheet and the magnetic vector aligned with the sheet., First we estimate the amount of magnetic flux being transported into the sheet – for which one needs to know both the inflow velocity perpendicular to the current sheet and the magnetic vector aligned with the sheet. For the purposes of making such an estimate. we measure these values at the centre of the inflow region just outside the current sheet.," For the purposes of making such an estimate, we measure these values at the centre of the inflow region just outside the current sheet." We also consider the outflow Jet velocity. measured toward the outflow edge of the current sheet.," We also consider the outflow jet velocity, measured toward the outflow edge of the current sheet." shows four combinations of these variables as functions of time from experiment “C3”.," shows four combinations of these variables as functions of time from experiment “C3""." The top left frame represents the component of the magnetic field parallel to the current sheet., The top left frame represents the component of the magnetic field parallel to the current sheet. It shows an initial build-up followed by a near linear decline in magnitude., It shows an initial build-up followed by a near linear decline in magnitude. The latter 15 a consequence of the depletion of the magnetic field in the inflow region due to the limited length scale of the driving in the y-direction., The latter is a consequence of the depletion of the magnetic field in the inflow region due to the limited length scale of the driving in the $y$ -direction. The top right panel shows the inflow velocity. which ts found to reach a stable level with only a slow decay with time.," The top right panel shows the inflow velocity, which is found to reach a stable level with only a slow decay with time." The lower left frame shows the ratio of the outflow velocity and the Alfvénn speed in the inflow region (akin to the reconnection rate in the Sweet-Parker model). which reaches a nearly stable value at the same time as the magnetic field component reached its peak value.," The lower left frame shows the ratio of the outflow velocity and the Alfvénn speed in the inflow region (akin to the reconnection rate in the Sweet-Parker model), which reaches a nearly stable value at the same time as the magnetic field component reached its peak value." Finally the lower right frame shows the ratio of the length scale of the inflow region times the inflow velocity and the thickness of the outflow region times the outflow velocity., Finally the lower right frame shows the ratio of the length scale of the inflow region times the inflow velocity and the thickness of the outflow region times the outflow velocity. In the 2D Sweet Parker analysis this relation constitutes mass conservation. and here we can see that it reaches a stable value declining only slowly with time.," In the 2D Sweet Parker analysis this relation constitutes mass conservation, and here we can see that it reaches a stable value declining only slowly with time." It is interesting to note that this stable value is somewhat greater, It is interesting to note that this stable value is somewhat greater the higher inclination is correct. the total mass of the galaxy. would be 0.75?=2.4 times smaller.,"the higher inclination is correct, the total mass of the galaxy would be $0.75^{-3} = 2.4$ times smaller." While this is a significant difference. it does not change our final conclusion.," While this is a significant difference, it does not change our final conclusion." If the relation Mayx1rRuasa HOlds at these velocities. we can compare NGC 1961 to the Milky Way (644=220 km |) and infer that NGC 1961 has six times the dynamical mass of the Milky Wax.," If the relation $M_{\text{dyn}} \propto V_{\text{max}}^3$ holds at these velocities, we can compare NGC 1961 to the Milky Way $v_{\text{circ}} = 220$ km $^{-1}$ ) and infer that NGC 1961 has six times the dynamical mass of the Milky Way." " Similarly. its 2\LASS K-band magnitude is -26.0. which for an assumed mass-Lo-light ratio of 0.6 (Bell and de Jong 2001) corresponds to a stellar mass of 3x10!M., (which is also six (mes the stellar mass of the Milky Way)."," Similarly, its 2MASS K-band magnitude is -26.0, which for an assumed mass-to-light ratio of 0.6 (Bell and de Jong 2001) corresponds to a stellar mass of $3\times10^{11} M_{\odot}$ (which is also six times the stellar mass of the Milky Way)." Extrapolating from the Ly— relation for elliptical galaxies. we therefore expect NGC 1961 to have an unusually bright X-rav halo (Lossg21xLO! erg + for the diffuse emission). making this galaxy an ideal target [or identilving extended. X-ray. emission.," Extrapolating from the $L_X - L_K$ relation for elliptical galaxies, we therefore expect NGC 1961 to have an unusually bright X-ray halo $L_{0.5-2 \text{ keV}} \approx 1\times10^{41}$ erg $^{-1}$ for the diffuse emission), making this galaxy an ideal target for identifying extended X-ray emission." The virial radius of the Milky Wav is ~250 kpe (Shattow and Loeb 2009. IXIvpin. Zhao. and Somerville 2002). so bv extension the virial radius of NGC 1961 would be around 450kpc?.," The virial radius of the Milky Way is $\sim 250$ kpc (Shattow and Loeb 2009, Klypin, Zhao, and Somerville 2002), so by extension the virial radius of NGC 1961 would be around 450." . Within this radius. NGC 1961 has several. much smaller. companions (Gottesman el al.," Within this radius, NGC 1961 has several, much smaller, companions (Gottesman et al." 2002. Haan et al.," 2002, Haan et al." 2008). including three cwarls (gi<10M. ) at 120. 140. and 160 kpe. and several slightly larger galaxies al 200-500 kpe distances.," 2008), including three dwarfs $M_{\text{HI}} < 10^9 M_{\odot}$ ) at 120, 140, and 160 kpc, and several slightly larger galaxies at 200-500 kpc distances." It is therefore the dominant ealaxv in a small group. but no IGM emission is observed.," It is therefore the dominant galaxy in a small group, but no IGM emission is observed." We adopt for this galaxy. a distance of 56 Mpe (NASA Extragalactic Database average). which matches independent measurenienis of distances to other galaxies in the group (Gottesman οἱ al.," We adopt for this galaxy a distance of 56 Mpc (NASA Extragalactic Database average), which matches independent measurements of distances to other galaxies in the group (Gottesman et al." 2002). and is probably uncertain to1056.," 2002), and is probably uncertain to." .. At this distance. 1 arcminute corresponds to 16 kpe.," At this distance, 1 arcminute corresponds to 16 kpc." Our observing strategy was (o use a 2x2 mosaic with the ACIS-I array on the Chandra N-rav Observatory. which allowed us to sample the extended emission out to about 260 kpc (17) - roughly 2/3 of the virial radius (see Figure 1).," Our observing strategy was to use a $\times$ 2 mosaic with the ACIS-I array on the Chandra X-ray Observatory, which allowed us to sample the extended emission out to about 260 kpc (17') - roughly 2/3 of the virial radius (see Figure 1)." The observations (obs ids 10528-10531) were approved [ον 35 ks each. ancl ranged [rom 31.75-33.25 ks of good time.," The observations (obs ids 10528-10531) were approved for 35 ks each, and ranged from 31.75-33.25 ks of good time." We also observed {wo background fields (obs ids 10532.10533) for 10.14 and 10.02 ks.," We also observed two background fields (obs ids 10532,10533) for 10.14 and 10.02 ks." All observations were taken in VFAINT mode with ACHIS-I. The data were processed using CIAO. version 4.1.2. and the latest calibration files.," All observations were taken in VFAINT mode with ACIS-I. The data were processed using CIAO, version 4.1.2, and the latest calibration files." Data taken during flares were excised. but the observations were remarkably clean. with only about 0.4 ks of bad time to remove from the total integration time for each observation.," Data taken during flares were excised, but the observations were remarkably clean, with only about 0.4 ks of bad time to remove from the total integration time for each observation." A 0.6-6 keV image was produced for point source detection (using the WAVDETECT algorithm in CLAO)., A 0.6-6 keV image was produced for point source detection (using the WAVDETECT algorithm in CIAO). For the rest of the analysis. we use a 0.6-2.0 keV image for observations of the hot halo. and a 2.0-6.0 keV image for constraints on contamination [rom emission [rom X-ray binaries. as discussed in section 3.4.," For the rest of the analysis, we use a 0.6-2.0 keV image for observations of the hot halo, and a 2.0-6.0 keV image for constraints on contamination from emission from X-ray binaries, as discussed in section 3.4." "producing a low-energv power-law spectrum. wf,xv.","producing a low-energy power-law spectrum, $\nu F_\nu \propto \nu$." Both power-laws are limited to about one order of magnitude in i) The flare ends with a sharp decay at a lime that coincides with the transition {ο the spherical phase., Both power-laws are limited to about one order of magnitude in (iii) The flare ends with a sharp decay at a time that coincides with the transition to the spherical phase. If (he breakout is ultva relativistic (Le. 55421) then Lx12 and TxobsL4. until the spherical phase emission (iv) After the flare ends. spherical evolution dietates a steady decay of the huninositv.," If the breakout is ultra relativistic (i.e., $\g_{f,0} \gg 1$ ) then $L \propto t_{obs}^{-2}$ and $T \propto t_{obs}^{-1}$, until the spherical phase emission (iv) After the flare ends, spherical evolution dictates a steady decay of the luminosity." " At first. while relativistic shells dominate the emission. Lx/,L!."," At first, while relativistic shells dominate the emission, $L \propto t_{obs}^{-1.1}$." " Later. at obs5. once Newtonian shells become transparent Lox1,477."," Later, at $t_{NW}^{obs}$ , once Newtonian shells become transparent $L \propto t_{obs}^{-0.35}$." Note that during the latter phase the total emitted energv increases with (v)\ The post [lare temperature decays at firstH αἱ a steady rate of. about ἐνO.6 generated| during the spherical phase.," Note that during the latter phase the total emitted energy increases with (v) The post flare temperature decays at first at a steady rate of about $t_{obs}^{-0.6}$, generated during the spherical phase." A sharp drop in the temperature is observed when shells which were nol loaded by pairs during the shock crossing οSoM< 0.5) dominate the emission., A sharp drop in the temperature is observed when shells which were not loaded by pairs during the shock crossing $v_s \lesssim 0.5$ ) dominate the emission. The drop is typically from the X-ray range to the UV. and it is observed at about LO).obs (vi) The energv emitted before the steep temperature drop is often comparable to that emitted during the breakout flare.," The drop is typically from the X-ray range to the UV, and it is observed at about $10~t_{NW}^{obs}$ (vi) The energy emitted before the steep temperature drop is often comparable to that emitted during the breakout flare." Thus. We apply our model (o a range of observed and lwpothesizecl explosions findingthe folowing predictions:," Thus, We apply our model to a range of observed and hypothesized explosions findingthe following predictions:" is done m Figure 4..,is done in Figure \ref{fig:ld_ui}. Again. the linear approximation (Equation (33))) is quite accurate and agrees well with the full numerical results for Ü;x0.1.," Again, the linear approximation (Equation \ref{eq:ldtt}) )) is quite accurate and agrees well with the full numerical results for $\bar{\ui} \lesssim 0.1$." As expected. the difference between the numerical results and the linear approximation increases as the flow velocity gets faster.," As expected, the difference between the numerical results and the linear approximation increases as the flow velocity gets faster." However. for U;=0.2 the relative difference between the full solution and the approximation is only around for the forward wave and for the backward wave.," However, for $\bar{\ui} = 0.2$ the relative difference between the full solution and the approximation is only around for the forward wave and for the backward wave." This means that for realistic flow velocities observed in coronal magnetic loops (e.g..Brekkeetal.1997:Winebarger2001. 2002).. Equation (33)) correctly describes the behavior of the damping length.," This means that for realistic flow velocities observed in coronal magnetic loops \citep[e.g.,][]{brekke,winebarger01,winebarger02}, Equation \ref{eq:ldtt}) ) correctly describes the behavior of the damping length." In summary. in this Section. we have confirmed. that the analytical expressions obtained in the TT and TB approximations and for slow. sub-Alfvénnic flows are very accurate even when these expressions are used outside their domain of strict. validity.," In summary, in this Section we have confirmed that the analytical expressions obtained in the TT and TB approximations and for slow, sub-Alfvénnic flows are very accurate even when these expressions are used outside their domain of strict validity." This result enables us to use Equation (33)). Le.. the key equation of this investigation. when realistic values of frequency. flow velocity. and the rest of relevant parameters obtained from the observations are used.," This result enables us to use Equation \ref{eq:ldtt}) ), i.e., the key equation of this investigation, when realistic values of frequency, flow velocity, and the rest of relevant parameters obtained from the observations are used." Naturally. kink waves propagating in nonuniform magnetic flux tubes are spatially damped by resonant absorption.," Naturally, kink waves propagating in nonuniform magnetic flux tubes are spatially damped by resonant absorption." In the static case. TGV showed that the damping length is inversely proportional to the frequency.," In the static case, TGV showed that the damping length is inversely proportional to the frequency." Here we have investigated analytically and numerically the spatial damping of resonant kink waves in a transversely nonuniform magnetic waveguide in the presence of longitudinal background flow., Here we have investigated analytically and numerically the spatial damping of resonant kink waves in a transversely nonuniform magnetic waveguide in the presence of longitudinal background flow. Longitudinal flow breaks the equivalence between forward and backward propagating waves with respect to the flow direction., Longitudinal flow breaks the equivalence between forward and backward propagating waves with respect to the flow direction. The wavelength and the damping length due to resonant absorption are both affected by the flow., The wavelength and the damping length due to resonant absorption are both affected by the flow. For sub-Alfvénnic flows. the backward wavelength is shorter than that of the forward wave. and backward waves are damped 1 shorter length scales than forward waves.," For sub-Alfv\'ennic flows, the backward wavelength is shorter than that of the forward wave, and backward waves are damped in shorter length scales than forward waves." However. as in TGV we have found that the damping length of both forward and backward propagating waves is inversely proportional to the frequency.," However, as in TGV we have found that the damping length of both forward and backward propagating waves is inversely proportional to the frequency." MHD seismology based on propagating waves has attracted limited attention and definitely less than its counterpart basec on standing kink waves., MHD seismology based on propagating waves has attracted limited attention and definitely less than its counterpart based on standing kink waves. Standing kink MHD waves are rare phenomena as they need a violent and energetic event such as a solar flare for their excitation (see.e.g..Aschwandenet 1999).," Standing kink MHD waves are rare phenomena as they need a violent and energetic event such as a solar flare for their excitation \citep[see, e.g.,][]{ash,naka}." . In the absence of flow and for coronal loop standing oscillations (see.e.g..Nakariakov2008:Goossensetal. 2008).. MHD seismology has beei used to obtain information of the plasma physical conditions.," In the absence of flow and for coronal loop standing oscillations \citep[see, e.g.,][]{nakaofman,goossens2002,arregui07,arregui08,goossens08}, MHD seismology has been used to obtain information of the plasma physical conditions." Particularly. for à given set of parameters provided by the observations. ie.. period. damping time. and wavelength in the case of standing waves. Arreguietal.(2007) and Goossensetal.(2008) showed that the possible values of v4;. £. and //R which are consistent with the theory form a one-dimensional curve in the three-dimensional parameter space.," Particularly, for a given set of parameters provided by the observations, i.e., period, damping time, and wavelength in the case of standing waves, \citet{arregui07} and \citet{goossens08} showed that the possible values of $\vai$, $\zeta$, and $l/R$ which are consistent with the theory form a one-dimensional curve in the three-dimensional parameter space." In principle. any. point of this curve can equally explain the observations.," In principle, any point of this curve can equally explain the observations." Soleretal.(2010) and Arregui&Ballester(2011) showed that more constrained estimations of v4; and //R can be given in the case of prominence thread oscillations as the limit Z>>| can be adopted., \citet{solerfine} and \citet{arreguiballester} showed that more constrained estimations of $\vai$ and $l/R$ can be given in the case of prominence thread oscillations as the limit $\zeta \gg 1$ can be adopted. More recently. Arregui&AsensioRamos(2011) found that more accurate estimations of the parameters are possible by combining the analytical theory of Goossensetal.(2008) with statistical Bayesian analysis.," More recently, \citet{bayesian} found that more accurate estimations of the parameters are possible by combining the analytical theory of \citet{goossens08} with statistical Bayesian analysis." In the presence of flows. Terradasetal.(2011) have recently explained also for standing waves that the flow velocity can be estimated from the wave phase difference along the magnetic loop.," In the presence of flows, \citet{terradasletterflow} have recently explained also for standing waves that the flow velocity can be estimated from the wave phase difference along the magnetic loop." On the contrary. propagating MHD waves are ubiquitous in the solar atmosphere (see.e.g..Tomezyketal.2007; and provide a huge reservoir of possibilities for seismology.," On the contrary, propagating MHD waves are ubiquitous in the solar atmosphere \citep[see, e.g.,][]{tomczyk07,tomczyk09} and provide a huge reservoir of possibilities for seismology." Some examples of MHD, Some examples of MHD The consequences of radio jets impacting on density inhomogencities have been invoked to explain many properties of high redshift radio sources. such as bending aud asvmametries in arm length.,"The consequences of radio jets impacting on density inhomogeneities have been invoked to explain many properties of high redshift radio sources, such as bending and asymmetries in arm length." Evidence for this is seen in the Form of correlations between emission-line gas and the side of the radio galaxy with the shorter arm-length. or higher depolarisation (MeCarthy. van Breugel Ixapahi 1991: Liu Pooley 1991).," Evidence for this is seen in the form of correlations between emission-line gas and the side of the radio galaxy with the shorter arm-length, or higher depolarisation (McCarthy, van Breugel Kapahi 1991; Liu Pooley 1991)." The extent to which this is related to the so-called. “alignment ellect whereby. the axis of extended optical continuum and line emission is found to be co-aligned with the radio axis. is unclear. although many. attempts to explain radio-optical alignments involve a dense external medium.," The extent to which this is related to the so-called “alignment effect” whereby the axis of extended optical continuum and line emission is found to be co-aligned with the radio axis, is unclear, although many attempts to explain radio-optical alignments involve a dense external medium." Such a medium is needed. for example. to act as the source of a scattering surface for quasar light from the ACN (Bremer. Fabian Crawford LOOT). or as à medium for jet-induced star formation DDest. Longair ltóttteering 1996 references therein)," Such a medium is needed, for example, to act as the source of a scattering surface for quasar light from the AGN (Bremer, Fabian Crawford 1997), or as a medium for jet-induced star formation Best, Longair Rötttgering 1996 references therein)." 3C441 is à z—0.708 radio galaxy with an asvmametric radio structure. which appears to be a rare example of a radio source with a red aligned component outside the racio lobes.," 3C441 is a $z=0.708$ radio galaxy with an asymmetric radio structure, which appears to be a rare example of a radio source with a red aligned component outside the radio lobes." Such a component is clearly hard to obtain in either Jet-induced star formation or scattered quasar mocoels., Such a component is clearly hard to obtain in either jet-induced star formation or scattered quasar models. This red component is seen just. bevonc the end of the shorter. north-west radio lobe component ο of Eisenharelt Chokshi (1990): see 11].," This red component is seen just beyond the end of the shorter, north-west radio lobe [component `c' of Eisenhardt Chokshi (1990); see 1]." Vhis lobe appears to possess a radio jet which bends round to the west at the tip of the obe., This lobe appears to possess a radio jet which bends round to the west at the tip of the lobe. Just to the south of the red component. mostIy within he radio lobe. is à are-shaped clump of emission line gas seen in the Ouj372.7 emission line image of MeCarthy. van Breugel Spinrad (1994).," Just to the south of the red component, mostly within the radio lobe, is a arc-shaped clump of emission line gas seen in the ]372.7 emission line image of McCarthy, van Breugel Spinrad (1994)." Spectroscopy of the Orr] emission ine by MeCarthy. Baum Spinrad (1996) shows that this emission line material is redshilted by zzSOO km + with respect to the radio galaxy. and weak emission extends to just bevond the red component.," Spectroscopy of the ] emission line by McCarthy, Baum Spinrad (1996) shows that this emission line material is redshifted by $\approx 800\;$ km $^{-1}$ with respect to the radio galaxy, and weak emission extends to just beyond the red component." In this paper. we use our own spectroscopy. infrared and radio imaging. and archive data from the(1517) (also presented in Best. Longair Rotttegering 19970) to attempt to explain the properties of 3C441 in terms of models for the interaction of radio jets with their environments.," In this paper, we use our own spectroscopy, infrared and radio imaging, and archive data from the (also presented in Best, Longair Rötttgering 1997c) to attempt to explain the properties of 3C441 in terms of models for the interaction of radio jets with their environments." In. particular. we address the problems of the origin of the red continuum light. from the aligned component and the properties of the extended emission line region.," In particular, we address the problems of the origin of the red continuum light from the aligned component and the properties of the extended emission line region." We assume an Einstein de Sitter cosmology with a Hubble constant Jo=50 km *Alpe L, We assume an Einstein – de Sitter cosmology with a Hubble constant $H_0=50\;$ km $^{-1}$ $^{-1}$. We obtained an optical spectrum with USES on the 4.2-m, We obtained an optical spectrum with ISIS on the 4.2-m curve rather than a straight line.,curve rather than a straight line. Consequently. it does not match well the prediction by the singular isothermal sphere (SIS) halo moclel (see. e... Li&Ostriker 2002)).," Consequently, it does not match well the prediction by the singular isothermal sphere (SIS) halo model (see, e.g., \citealt{LO02}) )." " Phe failure of the SIS moclel is evident for My,107M. as noticed by several authors citealtLOO2.INWN OT.DIuse))."," The failure of the SIS model is evident for $\Mvir \ga 10^{13} \Msun$ as noticed by several authors \\citealt{LO02,KW01,Blu86}) )." This result confirms the critical halo mass AL.~LOM below which the barvonie ellects start to become significant. for the inner halo dynamics and structure., This result confirms the critical halo mass $M_c \sim 10^{13} \Msun$ below which the baryonic effects start to become significant for the inner halo dynamics and structure. However. even for My107. the SIS model is not. very. successful in matching the empiricallv determined (Mo) curve.," However, even for $\Mvir \la 10^{13} \Msun$ the SIS model is not very successful in matching the empirically determined $\sigma(\Mvir)$ curve." " Εις implies that the SIS mocel is not precise as a ""elobal model of the ealactic halo despite the fact that a range of observational constraints support the isothermal profile for the inner part of the halo (sce Chae2010) and references. theirin).", This implies that the SIS model is not precise as a `global model' of the galactic halo despite the fact that a range of observational constraints support the isothermal profile for the inner part of the halo (see \citealt{Cha10} and references theirin). " Phe underprediction of σ bv the SIS. model for AM,1077M. probably rellects the neglected. concentration of the halo.", The underprediction of $\sigma$ by the SIS model for $\Mvir \la 10^{13} \Msun$ probably reflects the neglected concentration of the halo. The curvature in the Ada relation may reflect the systematic variation of halo concentration but may. also imply. the varving barvonic elfects on the halo structures., The curvature in the $\Mvir$ $\sigma$ relation may reflect the systematic variation of halo concentration but may also imply the varying baryonic effects on the halo structures. The internal structures of the haloes may. be constrained by combining dynamical constraints with the empirical Adve relation (in preparation)., The internal structures of the haloes may be constrained by combining dynamical constraints with the empirical $\Mvir$ $\sigma$ relation (in preparation). In Fig., In Fig. 4. we compare the abundance matching Alvi relations at 2=1 and 0., \ref{MvirV} we compare the abundance matching $\Mvir$ $\sigma$ relations at $z=1$ and $0$. This comparison shows little sign of evolution in the Afi relation for the strong lensing probed range σ300kms| (AgXLOMPALS: see 82)., This comparison shows little sign of evolution in the $\Mvir$ $\sigma$ relation for the strong lensing probed range $\sigma \la 300\kms$ $\Mvir \la 10^{14.6} \Msun$; see 2). The near constaney in the Ao» relation with z implies that the HLME and the VDE are coevolving in parallel., The near constancy in the $\Mvir$ $\sigma$ relation with $z$ implies that the HMF and the VDF are coevolving in parallel. Namely. as the halo grows in mass over cosmic time. the central stellar velocity dispersion grows in accordance.," Namely, as the halo grows in mass over cosmic time, the central stellar velocity dispersion grows in accordance." The natural question to ask is then what the origin of this coevolution is., The natural question to ask is then what the origin of this coevolution is. We discuss this in 85., We discuss this in 5. Alternatively. we may transform the HILME into à VDE using the z=0 relation of Fig.," Alternatively, we may transform the HMF into a VDF using the $z=0$ relation of Fig." and assuming a certain evolution of the Adve relation., \ref{MvirV} and assuming a certain evolution of the $\Mvir$ $\sigma$ relation. 4.Fig., Fig. 5. shows the VDEs predicted. from the HIIMES assuming zero evolution of the Al-0 relation., \ref{VDFhalo} shows the VDFs predicted from the HMFs assuming zero evolution of the $\Mvir$ $\sigma$ relation. In Fig., In Fig. 5. the HME-converted. VDEs are compared with the observationally derived local. VDES and the lensing constrained VDEs at >=]., \ref{VDFhalo} the HMF-converted VDFs are compared with the observationally derived local VDFs and the lensing constrained VDFs at $z=1$. The VDEsat 220 are in excellent. agreement with cach other., The VDFs at $z=0$ are in excellent agreement with each other. The VDEs at >=] are also in agreement with each other., The VDFs at $z=1$ are also in agreement with each other. This exercise shows that under the simple assumption of the constancy of the AZou-o relation in time. the evolution of the LEME predicted by the current ICDM cosmology can match well the evolution of the VDE constrained by strong lensing μαatistics for ο—zx1.," This exercise shows that under the simple assumption of the constancy of the $\Mvir$ $\sigma$ relation in time, the evolution of the HMF predicted by the current $\LCDM$ cosmology can match well the evolution of the VDF constrained by strong lensing statistics for $0 \la z \la 1$." Alany recent surveys of galaxies have been used to constrain he evolution of galaxies through the LE or/and the SAL., Many recent surveys of galaxies have been used to constrain the evolution of galaxies through the LF or/and the SMF. The results are at variance., The results are at variance. Many results argue for relatively ittle evolution in the number density. of most massive ealaxiecs and greater evolution of less massive galaxies over cosmic time. aa stellar mass-downsizing (anti-ucrarchical) behaviour (e.g... Cimattictal.2006:FontanaAMarchesinietal. 2009)). although there are results that do not particularly support a mass-clownsizing evolution (e.g. Delletal.2004:Faber2007:Brown2008:Hbertal. 2010)).," Many results argue for relatively little evolution in the number density of most massive galaxies and greater evolution of less massive galaxies over cosmic time, a “stellar mass-downsizing” (anti-hierarchical) behaviour (e.g., \citealt{Cim06,Fon06,Poz07,Con07,Sca07,Coo08,Per08,Mar09}) ), although there are results that do not particularly support a mass-downsizing evolution (e.g., \citealt{Bel04,Fab07,Bro08,Ilb09}) )." The variance for the evolution of the SME is not well understood but may be cue to errors in measurements and modelling of the SME. (see Longhetti&Saracco 2009)) and galaxy sample biases caused by cosmic variance (see. og. Faberetal.2007:Cattaneo2008:Stringer for cliscussions).," The variance for the evolution of the SMF is not well understood but may be due to errors in measurements and modelling of the SMF (see \citealt{LS09}) ) and galaxy sample biases caused by cosmic variance (see, e.g., \citealt{Fab07,Cat08,Str08} for discussions)." We have seen in the previous section that the strong lensing constrained VDE evolution. is in line with the, We have seen in the previous section that the strong lensing constrained VDF evolution is in line with the the large change of. flux at a column depth XEzs105 gemE7.,"the large change of flux at a column depth $\Sigma \approx 10^{8}$ $\mathrm{g\,cm}^{-2}$." A small amount of. carbon burning5 occurs al ~~107-105 5@em7.," A small amount of carbon burning occurs at $\Sigma \sim 10^{12}$ $10^{13}$ $\mathrm{g\,cm}^{-2}$." Deep crustal heatingg occurs for column depths 10P 3. > ⋅ ≸↽↔↴≺∢∐↓−≤∣∖∣↵≤∐≱↓⋎≸≟≺∢↕∐−⋅⊺↥∐↲∐∏⇀∏↽≻↕⋅∪∐↥≼↲⋝∖⊽∐∪∖∖↽⊳∖," Deep crustal heating occurs for column depths $10^{15}$ $\mathrm{g\,cm}^{-2} \lesssim \Sigma \lesssim 10^{17}$ $\mathrm{g\,cm}^{-2}$." ⇁⊔⋯↴↥∐↓∪⊳∖⊽↥∪↓⊔∐↲≼↲↕∐↲↕⋅≸↽↔↴⋡∖↽≸≟≼↲↕∐↲↕⋅≀⋯↲≼⇂∣↽≻∡∖⇁≼⇂≼↲≼↲↕↽≻ crustal heating is directed inward. in agreement with Brown(2000).," The flux profile shows that most of the energy generated by deep crustal heating is directed inward, in agreement with \citet{B00}." . The burning of hydrogen ancl helium near the surface of an accreting neutron star releases a substantial amount of energy within the star., The burning of hydrogen and helium near the surface of an accreting neutron star releases a substantial amount of energy within the star. Consequently. (he thermal profile of the outer crust. including (he superburst ignition region. is rather sensitive to the magnitude and physical location of this energv. generation.," Consequently, the thermal profile of the outer crust, including the superburst ignition region, is rather sensitive to the magnitude and physical location of this energy generation." To account for (his. previous authors sel ihe temperature at a given. column depth to coincide with estimates [rom investigations of hydrogen and helium ignition.," To account for this, previous authors set the temperature at a given column depth to coincide with estimates from investigations of hydrogen and helium ignition." However. the thermal profile in (his region is a sensitive [function of many. variables. including the mass accretion rate (e.e.. compare (he two models in 22). stellar radius. ancl composition of the accreted) gas.," However, the thermal profile in this region is a sensitive function of many variables, including the mass accretion rate (e.g., compare the two models in 2), stellar radius, and composition of the accreted gas." Since we include both hydrogen ancl helium energy. generation rates in our energy conservation equation. we make no assumptions regarding (he temperature al a given depth in the accreted laver.," Since we include both hydrogen and helium energy generation rates in our energy conservation equation, we make no assumptions regarding the temperature at a given depth in the accreted layer." Thus. we are able (to determine (he thermal profile of the outer crust sell-consistentlv.," Thus, we are able to determine the thermal profile of the outer crust self-consistently." Not only does (his improve the accuracy of our calculation. but it also gives us the freedom to vary. physical parameters such as the eas composition and stellar radius sell-consistently.," Not only does this improve the accuracy of our calculation, but it also gives us the freedom to vary physical parameters such as the gas composition and stellar radius self-consistently." As noted earlier. all of the svstems in which astronomers have observed superbursts exhibit normal Type I X-ray bursts as well.," As noted earlier, all of the systems in which astronomers have observed superbursts exhibit normal Type I X-ray bursts as well." To do a rigorous calculation of the thermal profile of the outer crust. one would need to conduct a fully. tme-dependent. caleulation of nuany successive normal bursts. which is bevond the scope of this study.," To do a rigorous calculation of the thermal profile of the outer crust, one would need to conduct a fully time-dependent calculation of many successive normal bursts, which is beyond the scope of this study." Our calculation is quasistatic. so the composition and thermal profile of the erust in the the normal burst ignition region is essentially computed via stable (hough rapid) hydrogen and helium burning.," Our calculation is quasistatic, so the composition and thermal profile of the crust in the the normal burst ignition region is essentially computed via stable (though rapid) hydrogen and helium burning." Since the timescale over which normal bursts occur (hours (to davs) is much shorter than the timescale over which superbursis occur (vears (o. possibly decades). anv effects. that hydrogen and helium burning have on the thermal profile of (he superburst ignition region will be due to the time-averaged hydrogen and helium nuclear energy. generation rate.," Since the timescale over which normal bursts occur (hours to days) is much shorter than the timescale over which superbursts occur (years to possibly decades), any effects that hydrogen and helium burning have on the thermal profile of the superburst ignition region will be due to the time-averaged hydrogen and helium nuclear energy generation rate." The {ime-averaged energy generation rate is the same regardless of the manner in whieh the [uel is burned., The time-averaged energy generation rate is the same regardless of the manner in which the fuel is burned. Therefore. our method should be sufficiently accurate for our purposes.," Therefore, our method should be sufficiently accurate for our purposes." To demonstrate the importance of hydrogen aud helium burning on the thermal prolile of the outer crust. we plot in Figure 3 the temperature as a function of column density. [or two svstenmis with different accreted gas compositions.," To demonstrate the importance of hydrogen and helium burning on the thermal profile of the outer crust, we plot in Figure 3 the temperature as a function of column density for two systems with different accreted gas compositions." ILvdrogen burning releases much more enerev per eram of accreted fuel than helium burning., Hydrogen burning releases much more energy per gram of accreted fuel than helium burning. Therefore. (he maximum temperature," Therefore, the maximum temperature" We previously celined overachievers as students who ente‘ed the university with low SAT scores. but earned high upper division GPAs.,"We previously defined overachievers as students who entered the university with low SAT scores, but earned high upper division GPAs." " Similarly. tje underachievers had high. SAT sco""es but performed poorly in college."," Similarly, the underachievers had high SAT scores but performed poorly in college." We further refine our defiliition ofthese eroups as follows., We further refine our definition of these groups as follows. Lu Figre δν which displays upper GPA versus combined SAT. we fit a liue to the ridge of highest densiiv fereen curve).," In Figure 8, which displays upper GPA versus combined SAT, we fit a line to the ridge of highest density (green curve)." We then calculate the staucard devia101 ¢X population density distribution in t direction perpendicular to this line., We then calculate the standard deviation of population density distribution in the direction perpendicular to this line. " Students that ie more than +1.25 SD above the line (wi GPAs greater than 3.5) are defined as overachievers. all (jose who are more than -1.25 SD bek he line (with GPAs less than 2.5) are defiued as uder""acuievers."," Students that lie more than +1.25 SD above the line (with GPAs greater than 3.5) are defined as overachievers, and those who are more than -1.25 SD below the line (with GPAs less than 2.5) are defined as underachievers." The outcome of this proced is displayed in Figure 8. in which the overachievers :we | he upper left (red are female stucler due are tale students) aud the underachievers are in 11 ower right.," The outcome of this procedure is displayed in Figure 8, in which the overachievers are in the upper left (red are female students, blue are male students) and the underachievers are in the lower right." " Au analysis of the two populations reveals that Ove""ulchievers are predominantly (61 perceLU) emale aid uncderachievers are overwhelminglyOre (79 percen uale.", An analysis of the two populations reveals that overachievers are predominantly (64 percent) female and underachievers are overwhelmingly (79 percent) male. See Figure 5 for gender distributiOlls: tote the overall population of our data set has a male:female ratio of 15:55., See Figure 8 for gender distributions; note the overall population of our data set has a male:female ratio of 45:55. Table 3 aud. | dispay he breakdown by major aud egeuder for the over aud underachievers., Table 3 and 4 display the breakdown by major and gender for the over and underachievers. Social sciences dominate both categories. although oue should be careful in considering the distribution by major.," Social sciences dominate both categories, although one should be careful in considering the distribution by major." We deli1ecl over- aπω dunclerachievers relative to the GPA vs. SAT trend computed across all 12 majors., We defined over- and underachievers relative to the GPA vs. SAT trend computed across all 12 majors. Some majors. whose average upper GPAs deviate [rom the group average. will tend to overpopulate one of the two eroups.," Some majors, whose average upper GPAs deviate from the group average, will tend to overpopulate one of the two groups." For example. Spanish has a high. average upper GPA (3.61) aid economics Las a |NW one (2.97).," For example, Spanish has a high average upper GPA (3.61) and economics has a low one (2.97)." This contributes to the overrepreseutation of Spanish majors among the overachievers. auc of economics majors amoung the uucderachievers.," This contributes to the overrepresentation of Spanish majors among the overachievers, and of economics majors among the underachievers." Π our primary interest were the clisributiou aπωlong majors. we could correct for these variations in average upper GPA by converting to SD units relative to mean for each major.," If our primary interest were the distribution among majors, we could correct for these variations in average upper GPA by converting to SD units relative to mean for each major." Note that Sociology. which contributes the single largest eroup of overachievers. has an average upper CPA of 3.18. which is close to the average of 3.20 for he 12 majors as a whole.," Note that Sociology, which contributes the single largest group of overachievers, has an average upper GPA of 3.18, which is close to the average of 3.20 for the 12 majors as a whole." Thus. in the case of Sociology. the overrepreseutation of overachievers is 100 clue to systematically higher grades.," Thus, in the case of Sociology, the overrepresentation of overachievers is not due to systematically higher grades." One might guess that these two groups could be identified using bieh school GPA., One might guess that these two groups could be identified using high school GPA. Figure 9. in which the horizontal axis is Ας. shows a wide rauge for both populations.," Figure 9, in which the horizontal axis is $_{HS}$, shows a wide range for both populations." Many. of the uxlerachievers have low high school GPA relative to what their SAT scores would have precictec. aud lower than the average for adiuitted: UO students.," Many of the underachievers have low high school GPA relative to what their SAT scores would have predicted, and lower than the average for admitted UO students." Figure LO shows that women tend to outperform men in upper GPA at any fixed. value of SAT score., Figure 10 shows that women tend to outperform men in upper GPA at any fixed value of SAT score. This is related to the fact that women aclunittecd to the University tend to have higher high school CPAs., This is related to the fact that women admitted to the University tend to have higher high school GPAs. In the best fit preclictive model we cliseussed above. women would have higher combined (SAT + HSCPA) z scores than men at fixed values of SAT score.," In the best fit predictive model we discussed above, women would have higher combined (SAT + HSGPA) z scores than men at fixed values of SAT score." One might reasonably associate mastery of a subject with GPA > 3.5 — roughly. the minimum," One might reasonably associate mastery of a subject with GPA $>$ 3.5 – roughly, the minimum" This configuration favors an inclination of about 50.1°.,This configuration favors an inclination of about $50.1^{\circ}$. The primary star would fill up its Roche lobe at about whilst the secondary component at about87%., The primary star would fill up its Roche lobe at about whilst the secondary component at about. . The second possible configuration is a system where the secondary star fills up its Roche lobe (Sol 2 in Table 3))., The second possible configuration is a system where the secondary star fills up its Roche lobe (Sol 2 in Table \ref{tab_lc}) ). This configuration is closer to that found in the literature., This configuration is closer to that found in the literature. " Under this assumption, we found an inclination of about 48.1°."," Under this assumption, we found an inclination of about $48.1^{\circ}$." " The volumes of the Roche lobes are filling up at about and for the primary and the secondary components, respectively."," The volumes of the Roche lobes are filling up at about and for the primary and the secondary components, respectively." " As ? already mentioned and no matter the chosen configuration, the inclination is well between 45° and 55° but, with the present investigation, we note that we improved, with more accuracy, the true value of the inclination."," As \citet{howarth91} already mentioned and no matter the chosen configuration, the inclination is well between $^{\circ}$ and $^{\circ}$ but, with the present investigation, we note that we improved, with more accuracy, the true value of the inclination." " In both configurations, we included the reflection effects which are not negligible when one star fills out a large fraction of its Roche lobe."," In both configurations, we included the reflection effects which are not negligible when one star fills out a large fraction of its Roche lobe." We also note that there is no photometric evidence of a non-zero eccentricity., We also note that there is no photometric evidence of a non-zero eccentricity. The error bars given in Table 3 are established by exploring the parameter space., The error bars given in Table \ref{tab_lc} are established by exploring the parameter space. We fixed one parameter and let the others, We fixed one parameter and let the others to one.,to one. " The term has been chosen here merely to reflect the fact that the ""goodness of fit” is calculated in the same way as a reduced chi-squared.", The term has been chosen here merely to reflect the fact that the “goodness of fit” is calculated in the same way as a reduced chi-squared. However. it should be interpreted as a relative merit value to compare different fits rather than an absolutely measurement of fit quality.," However, it should be interpreted as a relative merit value to compare different fits rather than an absolutely measurement of fit quality." Recent publications show that nebular emission lines can play an extremely important role in fitting SEDs (Zackrisson et al., Recent publications show that nebular emission lines can play an extremely important role in fitting SEDs (Zackrisson et al. 2008. Schaerer de Barros 2009. Raiter et al.," 2008, Schaerer de Barros 2009, Raiter et al." 2010)., 2010). In order to properly take into account this potentially large effect of gas emission in young. star-bursting galaxies. an add-on to the GALAXEV code was created.," In order to properly take into account this potentially large effect of gas emission in young, star-bursting galaxies, an add-on to the GALAXEV code was created." The nebular gas contributes with a continuum component and an emission-line component., The nebular gas contributes with a continuum component and an emission-line component. The continuum addition was caleulated from the Starburst99 models (Leitherer et al., The continuum addition was calculated from the Starburst99 models (Leitherer et al. 1999) with a Salpeter IMF with slope a=2.35 in the mass range 1100 M... (the Salpeter IMF is also used in the GALAXEV models)., 1999) with a Salpeter IMF with slope $\alpha = 2.35$ in the mass range $1 - 100$ $_{\odot}$ (the Salpeter IMF is also used in the GALAXEV models). The emission-line strengths were calculated using the MAPPINGS phototonisation code (Kewley et al., The emission-line strengths were calculated using the MAPPINGS photoionisation code (Kewley et al. 2011. in. prep.).," 2011, in prep.)." Both nebular continuum and emission-line strengths were calculated on a grid of ages (for the continuum in 36 steps between and 100 Myrs and for the emission lines in six steps between ] and 20 Myrs) and metallicities (same as available in GALAXEV. see below) and for each fit. the nearest values for these parameters were used.," Both nebular continuum and emission-line strengths were calculated on a grid of ages (for the continuum in 36 steps between 1 and 100 Myrs and for the emission lines in six steps between 1 and 20 Myrs) and metallicities (same as available in GALAXEV, see below) and for each fit, the nearest values for these parameters were used." The emission-lines were scaled with the Ha flux and the number of ionising photons im the galaxy spectra produced by GALAXEV., The emission-lines were scaled with the $\alpha$ flux and the number of ionising photons in the galaxy spectra produced by GALAXEV. For an illustration of the added nebular emission. see Fig. Τ..," For an illustration of the added nebular emission, see Fig. \ref{fig:nebex}." In practice. the emission line strengths as well as the continuum contribution become negligible at ages >20 Myrs.," In practice, the emission line strengths as well as the continuum contribution become negligible at ages $\gtrsim 20$ Myrs." In this publication. we choose to fit only two single stellar populations (SSP) models. as the nebular emission addon becomes too complicated with any other star formatio history.," In this publication, we choose to fit only two single stellar populations (SSP) models, as the nebular emission add-on becomes too complicated with any other star formation history." For all models. dust is added according to Calzetti et al. (," For all models, dust is added according to Calzetti et al. (" 2000).,2000). The parameter space allowed is detailed 1 Table 4.., The parameter space allowed is detailed in Table \ref{tab:params}. For the metallicity. the steps allowed are Z/Z..— 1.0.," For the metallicity, the steps allowed are $Z / Z_{\odot} = 0.005, 0.02, 0.2, 0.4, 1.0$ ." Only fluxes in the bands from By te the Ss.0j/m bands are used. as there are large uncertainties 1 the models at wavelengths below the Lya line. and at restframe mid-IR wavelengths.," Only fluxes in the bands from Bj to the $8.0\mu$ m bands are used, as there are large uncertainties in the models at wavelengths below the $\alpha$ line, and at restframe mid-IR wavelengths." The observed Lyn flux. as calculatec from the narrow-band photometry. was subtracted from the Bj band before fitting to avoid uncertainties in the fitting of the Ένα line itself.," The observed $\alpha$ flux, as calculated from the narrow-band photometry, was subtracted from the Bj band before fitting to avoid uncertainties in the fitting of the $\alpha$ line itself." Correspondingly. the Lya line was also subtracted from the nebular emission add-on.," Correspondingly, the $\alpha$ line was also subtracted from the nebular emission add-on." When the spectrum of a very young SSP is added to an older SSP spectrum. the older spectrum will need to comprise avery large mass fraction in order to be seen. as the young SSP," When the spectrum of a very young SSP is added to an older SSP spectrum, the older spectrum will need to comprise a very large mass fraction in order to be seen, as the young SSP" most massive galaxy in the eroup was assumed.,most massive galaxy in the group was assumed. The index is applied to the sample of ealaxy eroups studied for this paper as well as the M81 and NGC 2103 eroups aud the Local Group., The index is applied to the sample of galaxy groups studied for this paper as well as the M81 and NGC 2403 groups and the Local Group. Note that the nuuboers resulting from these caleulations are arbitrary: in order to use the index to rank our observation sample. we have normalized cach variable to the niacin for our sample.," Note that the numbers resulting from these calculations are arbitrary; in order to use the index to rank our observation sample, we have normalized each variable to the maximum for our sample." A robust statistic would need to include a normalization of the indices to some standard aud appropriate weighting of cach variable., A robust statistic would need to include a normalization of the indices to some standard and appropriate weighting of each variable. Fortunately. for the purposes of this study it is only necessary to rau- the eroups relative to one another.," Fortunately, for the purposes of this study it is only necessary to rank the groups relative to one another." We define the evidence for recent or ongoiug interactions as follows: Uere. the first factor deseribes the degree of disturbed morphology: the second factor the star formation rates. and the third factor accounts for AGN activity.," We define the evidence for recent or ongoing interactions as follows: Here, the first factor describes the degree of disturbed morphology; the second factor the star formation rates, and the third factor accounts for AGN activity." Nya is the umber of eroup ealaxies exhibiting tidal tails or bridecs., $N_{Tidal}$ is the number of group galaxies exhibiting tidal tails or bridges. SFR is the average star formation rate of eroup galaxies. calculated following Ποστ (1998).. usus Galactic extiuction-corrected Ta huuiuosities 11IIUCIS study of I&eunicuttetal. (2008)..," $SFR$ is the average star formation rate of group galaxies, calculated following \citet{ken98}, using Galactic extinction-corrected $\alpha$ luminosities 11HUGS study of \citet{ken08}. ." For ealaxies with no Ia hunuinosity measurement iu the ΜΗ survey (Ixeunicuttetal.2008).. the τρ survey detection Lit was assumed.," For galaxies with no $\alpha$ luminosity measurement in the 11HUGS survey \citep{ken08}, the 11HUGS survey detection limit was assumed." NacxACO is the umber of ogroup oealaxics classifiec as any type of. ACN ⇁⋅⇁⋅≽inNED-., $N_{\rm{AGN}}$ is the number of group galaxies classified as any type of AGN in. . We applied Equation (1) to the five galaxy eroups., We applied Equation (1) to the five galaxy groups. The results are tabulated in Tables 8. ane 9.., The results are tabulated in Tables \ref{ind_ev_val} and \ref{ind_ev_rank}. To avoid giving any one factor an artificially hieh or low weight. we assign a rank from 1-6 for cach variable. aud add the ranks for the fina ranking order for our sample.," To avoid giving any one factor an artificially high or low weight, we assign a rank from 1-6 for each variable, and add the ranks for the final ranking order for our sample." Since this ranking scheme is. at best. an ad-lioc indicator of ongoing interactions. we also tested altcrnate versions of Equation (1).," Since this ranking scheme is, at best, an ad-hoc indicator of ongoing interactions, we also tested alternate versions of Equation (1)." We tested cach permutation of two of the three factors. as well as cach factor individually. aud each version that we tester vielded a shehtly different result.," We tested each permutation of two of the three factors, as well as each factor individually, and each version that we tested yielded a slightly different result." Since none of the factors is an ivou-clacd iudicator of ongoing interactions in and of itself. we concluded that it is best to use all available evidence in raukius the ealaxy groups with respect to one another.," Since none of the factors is an iron-clad indicator of ongoing interactions in and of itself, we concluded that it is best to use all available evidence in ranking the galaxy groups with respect to one another." The ALS group has the highest interaction iudex. while the NCC 15 eroup ranks lowest.," The M81 group has the highest interaction index, while the NGC 45 group ranks lowest." " Based upou these ταπο», we expect that the AÍSI group should coutain the most ET clouds. followed by NGC 672. CVn EL. NGC. 2103. and NGC 15."," Based upon these rankings, we expect that the M81 group should contain the most HI clouds, followed by NGC 672, CVn I, NGC 2403, and NGC 45." To place these calculations iu contest. we have also calculated the interaction index for the Local Group.," To place these calculations in context, we have also calculated the interaction index for the Local Group." The Local Group measurements are included in boldface in Tables δ aud 9.., The Local Group measurements are included in boldface in Tables \ref{ind_ev_val} and \ref{ind_ev_rank}. We consider the Local Group to consist of the Milky War. AI33. and MOL since Local Croup chwart ealaxies would not be visible from the distances of the groups we observed.," We consider the Local Group to consist of the Milky Way, M33, and M31 since Local Group dwarf galaxies would not be visible from the distances of the groups we observed." We calculate the M31 aud AI33 star formation rate from the 111IIUCOS survey Ilo huuimositv. aud assmnue the widely-accepted star formation rate of d M | for the Milky Wav.," We calculate the M31 and M33 star formation rate from the 11HUGS survey $\alpha$ luminosity, and assume the widely-accepted star formation rate of 1 $_{\odot}$ $^{-1}$ for the Milky Way." The Local Croup ranks secoud to the M81 eroup in interaction evidence., The Local Group ranks second to the M81 group in interaction evidence. We wish to point out a few notable areas where our ranking scheme is lacking., We wish to point out a few notable areas where our ranking scheme is lacking. Firstly. we have uot attempted to put a quantitative timescale on the index.," Firstly, we have not attempted to put a quantitative timescale on the index." This is because the factors we take iuto account have different (and largely uuknowni) durations. expecially iu relation to iuteractious. and combining these different timescales is a daunting problem.," This is because the factors we take into account have different (and largely unknown) durations, especially in relation to interactions, and combining these different timescales is a daunting problem." Secoudly. we have no method iu ace for predicting the quantity of IE clouds that ought to he present or their properties based ou he interaction iudices.," Secondly, we have no method in place for predicting the quantity of HI clouds that ought to be present or their properties based on the interaction indices." Rather. we predict whether a given ealaxy eroup is more likelv than another o host III clouds at all.," Rather, we predict whether a given galaxy group is more likely than another to host HI clouds at all." Finally. we have not considered possible cross-correlation of the three Actors.," Finally, we have not considered possible cross-correlation of the three factors." Observations of the M81 aud NGC 2103 evoups aro summarized in Clynowetletal.(2008). Clyvnowethetal. (2009).. and Chynowethetal. (2002).," Observations of the M81 and NGC 2403 groups are summarized in \citet{chy08}, \citet{chy09}, and \citet{chy11}." .. We observed the CVn 1. NGC 672. and NGC 15 groups iun 232 sessions between Jauuuy and August 2009.," We observed the CVn I, NGC 672, and NGC 45 groups in 32 sessions between January and August 2009." We combined the observing sessions iuto 9 maps enconipassiug theeroup galaxies., We combined the observing sessions into 9 maps encompassing thegroup galaxies. Maps were made bv moving the telescope in declination aud sampling every 3! at, Maps were made by moving the telescope in declination and sampling every $\arcmin$ at We have. however. made a major assumption. that the disk mass Is much less than the BH mass (and the mode is everywhere slow).,"We have, however, made a major assumption, that the disk mass is much less than the BH mass (and the mode is everywhere slow)." In generality. and to second-order in «ΑΓΙ. the WKB dispersion relation can be written (for a gas disk) where \= SS (?)Fine Whenever the right-hand side of Equation 22. is negative. the modes are unstable and grow exponentially.," In generality, and to second-order in $|kR|^{-1}$, the WKB dispersion relation can be written (for a gas disk) where = s \citep{lau:spiral.wave.dispersion.relations} Whenever the right-hand side of Equation \ref{eqn:dispersion} is negative, the modes are unstable and grow exponentially." Take the case of interest. a global 5—| mode in a relatively cold disk.," Take the case of interest, a global $m=1$ mode in a relatively cold disk." " For convenience take the limit &20 and c,=0: Equation 22. becomes ($-1)r-20145-2 where is roughlyCFR the Senetdisk mmass fraction inside A.", For convenience take the limit $k=0$ and $c_{s}=0$; Equation \ref{eqn:dispersion} becomes ( -1 = (1+s) - where is roughly the disk mass fraction inside $R$. The RHS is negative for fu>tltoyG—sy!.," The RHS is negative for $\tilde{f}_{d} > (1+s)^{2}\,(3-s)^{-1}$." Tf the potential is near-Keplerian. then S—]/2. so this just becomes fy=1/10.," If the potential is near-Keplerian, then $s\sim-1/2$, so this just becomes $\tilde{f}_{d}\gtrsim 1/10$." In greater detail. consider the special case of a cold Mestel 1) disk around a BH. with an 272| mode and mass ratio enclosed in some radius v—μεςRy/Myy: the full dispersion relation fromEquation 22. is then ( κ...n -—- 0E9] where for a local mode. ΚΑΙ>| and y+0. while for a global mode [AR]>O but IX0CGC2».," In greater detail, consider the special case of a cold Mestel $\eta=1$ ) disk around a BH, with an $m=1$ mode and mass ratio enclosed in some radius $y\equiv M_{d}((-3+\sqrt{17})/4\approx0.281$ $\tilde{f}_{d}=0.11$ ), and local modes unstable for $|kR|>(1+2\,y)/y$." The solutions for arbitrary power-law disks 7 are tedious. but for global modes can be well approximatedby v20.07+0.09740.07iP40.04jp.," The solutions for arbitrary power-law disks $\eta$ are tedious, but for global modes can be well approximatedby $y>0.07+0.09\,\eta+0.07\,\eta^{2}+0.04\,\eta^{3}$." More generally. for the power-law disk+BH and the stellar dispersion relation. the minimum radius at. which instability appears (noting that the term |AR|exp[--|AA|} is maximized for kR|=1/9) is given by," More generally, for the power-law disk+BH and the stellar dispersion relation, the minimum radius at which instability appears (noting that the term $|kR|\,\exp{\{-\beta\,|kR| \}}$ is maximized for $|kR|=1/\beta$ ) is given by." For small 3 this is just v21.35.2(1—9/2Y'!.," For small $\beta$ this is just $y\gtrsim 1.35\,\beta\,(1-\eta/2)^{-1}$ ." If the disk does not extend to these masses. then it will be everywhere locally stable.," If the disk does not extend to these masses, then it will be everywhere locally stable." It is also immediately clear that if 3>L/(oe(t3—1 60.2-0.3 for the interesting range of 1). then the disk is everywhere locally stable independent of M;/Muygy (this is just ο—DL).," It is also immediately clear that if $\beta \ge 1/(\alpha\,e\,(3-\eta))$ $\approx0.2-0.3$ for the interesting range of $\eta$ ), then the disk is everywhere locally stable independent of $M_{d}/M_{\rm BH}$ (this is just $Q\gtrsim1$ )." This instability criteria agrees well with what is seen in simulations: for the simulations discussed in [.. the mode growth rate and maximum mode amplitudes are plotted as a function of Ma/Moyo at radii [Ope near the BH radius of influence in Figure 6 of ? (see also Figure 12 of 29).," This instability criteria agrees well with what is seen in simulations; for the simulations discussed in \ref{sec:intro}, the mode growth rate and maximum mode amplitudes are plotted as a function of $M_{d}/M_{\rm enc}$ at radii $\sim10\,$ pc near the BH radius of influence in Figure 6 of \citet{hopkins:inflow.analytics} (see also Figure 12 of \citealt{hopkins:zoom.sims}) )." Around these values of v or /;. rapid growth rates for the 572| mode appear at these radii.," Around these values of $y$ or $\tilde{f}_{d}$, rapid growth rates for the $m=1$ mode appear at these radii." So at least at larger radii. mode growth is possible.," So at least at larger radii, mode growth is possible." What is the nature of these modes?, What is the nature of these modes? " Note that the side of Equation 26 is real: as such. to lowest order in the WKB approximation. the unstable branch must correspond to an with the real part of aw. Ret)=0,©."," Note that the right-hand side of Equation \ref{eqn:mestel.modes} is real; as such, to lowest order in the WKB approximation, the unstable branch must correspond to an with the real part of $\omega$, ${\rm Re}(\omega)=\Omega_{p}=\Omega$." In other words. the system can develop modesthat are globally unstable. where v is not very small.," In other words, the system can develop modesthat are globally unstable, where $y$ is not very small." This suggests a picture in which the 7=| modes first appear at large radii — some Ai where Αρ/Moi~1. wwhere the potential is only transitioning to Keplerian. and where it can be globally unstable.," This suggests a picture in which the $m=1$ modes first appear at large radii – some $R_{\rm crit}$ where $M_{d}/M_{\rm BH}\sim1$, where the potential is only transitioning to Keplerian, and where it can be globally unstable." " The pattern speed £2, will simply reflect OU44).", The pattern speed $\Omega_{p}$ will simply reflect $\Omega(R_{\rm crit})$. But f the mode can propagate inwards at constant ©). it will eventually be a slow mode. relative to the local ©.," But f the mode can propagate inwards at constant $\Omega_{p}$, it will eventually be a slow mode, relative to the local $\Omega$." This is. in fact. what is seen in simulations (see 5 below).," This is, in fact, what is seen in simulations (see \ref{sec:sims} below)." How does this occur?, How does this occur? For now. we will remain in the WKB approximation and consider how such a mode (stable or unstable) might evolve.," For now, we will remain in the WKB approximation and consider how such a mode (stable or unstable) might evolve." " Given a mode. the wave packets themselves propagate with approximate group velocity v,=dco/dk=signa(es—GS)te) or FGM42.2KOT! for slow modes."," Given a mode, the wave packets themselves propagate with approximate group velocity $v_{g}={\rm d}\omega/{\rm d}k = {\rm sign}(k)\,(c_{s}^{2}-G\,\Sigma)/(\omega-\Omega)$ or $\pi\,G\,\Sigma\,\Omega^{-1}+2\,c_{s}^{2}\,k\,\Omega^{-1}$ for slow modes." " For a cold disk this is simply v,στ&e—zo R[KR[!: and since wOG) and the mode is global. this is ~VG."," For a cold disk this is simply $v_{g}\approx(\omega-\varomega)\,R\,|kR|^{-1}$ ; and since $\omega\sim\Omega(R_{\rm crit})$ and the mode is global, this is $\sim V_{c}(R_{\rm crit})$." The timescale for the mode to travel is just the dynamical time at this critical radius., The timescale for the mode to travel is just the dynamical time at this critical radius. " If the mass profile is too shallow. and c, or σ remains constant at small radii. then the wave will refract back at some Q barrier at some minimum radius (for constant 7. refraction occurs with gm1/2. the same criteria that 2? show applies for modes in a pure fluid disk with a hard outer edge)."," If the mass profile is too shallow, and $c_{s}$ or $\sigma$ remains constant at small radii, then the wave will refract back at some $Q$ barrier at some minimum radius (for constant $\beta$, refraction occurs with $\eta<1/2$, the same criteria that \citet{ostriker:eccentric.waves.via.forcing} show applies for modes in a pure fluid disk with a hard outer edge)." In non-linear simulations. this typically leads to pile-up of inflows. gradually steepening the profile: the consequences of this for setting galaxy profile shapes is discussed in ?..," In non-linear simulations, this typically leads to pile-up of inflows, gradually steepening the profile; the consequences of this for setting galaxy profile shapes is discussed in \citet{hopkins:cusp.slopes}." Here. the mass profile is fixed: but provided the mass profile is sufficiently steep such that the RHS of Equation a remains finite as r= O. thenmodes can propagate through to A— 0.," Here, the mass profile is fixed; but provided the mass profile is sufficiently steep such that the RHS of Equation \ref{eqn:slowmode.dispersion.gas} remains finite as $r\rightarrow0$ , thenmodes can propagate through to $R=0$ ." Provided that the sound speed isfinite. wave packets in a gaseous disk ean propagate through the OLR to r= o. eventually becoming simple sound waves.," Provided that the sound speed isfinite, wave packets in a gaseous disk can propagate through the OLR to $r\rightarrow\infty$ , eventually becoming simple sound waves." This is discussed in ? —because the waves can freely escape carrying the mode energy and angular momentum (and will reflect off small radii as above). infinite," This is discussed in \citet{adams89:eccentric.instab.in.keplerian.disks} –because the waves can freely escape carrying the mode energy and angular momentum (and will reflect off small radii as above), infinite" Note that the WAIAP team initializes their search at the CMD dipole. which is the dominant component in their data set.,"Note that the WMAP team initializes their search at the CMB dipole, which is the dominant component in their data set." However. this is in our sctting equivalent to imitializiug at zero. siuce our simulation does not iuclude a dipole.," However, this is in our setting equivalent to initializing at zero, since our simulation does not include a dipole." Taking the difference between the two final solutions. we have verified that the peak-to-peak residuals iu the two maps are less than 0.1 gs. of which essentially all is concentrated im a single dipole coumponcut.," Taking the difference between the two final solutions, we have verified that the peak-to-peak residuals in the two maps are less than 0.1 $\mu$ K, of which essentially all is concentrated in a single dipole component." The solution is thus independent of initialization. aud the only difference lies in computational speed.," The solution is thus independent of initialization, and the only difference lies in computational speed." Finally. note that even though the two maps are internally iudistinguishable. they are both quite different from the isotropic reference map.," Finally, note that even though the two maps are internally indistinguishable, they are both quite different from the isotropic reference map." To be precise. the RAIS difference between the derived maps and the isotropic reference map is 0.91 gS. with a spatial pattern similar to the overall WALTAP scaunuiug pattern.," To be precise, the RMS difference between the derived maps and the isotropic reference map is 0.91 $\mu$ K, with a spatial pattern similar to the overall WMAP scanning pattern." "The mean, ó, and the standard deviation, o,, of the following quantity are calculated: Iteratively 3σ outliers are rejected and after convergence their fraction is given by f;,.","The mean, $\delta_z$, and the standard deviation, $\sigma_z$, of the following quantity are calculated: Iteratively $\sigma$ outliers are rejected and after convergence their fraction is given by $f_{3\sigma}$." " By doing so, the outlier fraction Ίσ is not independent of the scatter o,."," By doing so, the outlier fraction $f_{3\sigma}$ is not independent of the scatter $\sigma_z$." " Therefore, we additionally report the quantity {οι which is the fraction of objects for which Az>0.15."," Therefore, we additionally report the quantity $f_{0.15}$ which is the fraction of objects for which $\Delta z>0.15$." As described above every photo-z code gives a confidence estimate for each object., As described above every $z$ code gives a confidence estimate for each object. and the COMBO code report confidence intervals on the redshift while uses the ODDS parameter., and the COMBO code report confidence intervals on the redshift while uses the ODDS parameter. " It is obvious that an end-user will reject objects that clearly have uncertain photo-z estimates, although it is a-priori unclear how to define these objects."," It is obvious that an end-user will reject objects that clearly have uncertain $z$ estimates, although it is a-priori unclear how to define these objects." Since the codes do not estimate confidence measures in identical ways it is not possible to apply a universal threshold., Since the codes do not estimate confidence measures in identical ways it is not possible to apply a universal threshold. " We can get an idea of appropriate thresholds for the different codes by varying the cuts on the confidence intervals or the ODDS parameter, respectively."," We can get an idea of appropriate thresholds for the different codes by varying the cuts on the confidence intervals or the ODDS parameter, respectively." " Thus, we see how the quantities ó;, στ, and fis change with the completeness of the remaining sample."," Thus, we see how the quantities $\delta_z$, $\sigma_z$, and $f_{3\sigma}$ change with the completeness of the remaining sample." When using and the COMBO code all objects with a probability vs. redshift distribution that is too wide are rejected by the following criterion: with o being the half-width of the confidence interval and A the parameter that is varied from 0 to 1., When using and the COMBO code all objects with a probability vs. redshift distribution that is too wide are rejected by the following criterion: with $\sigma$ being the half-width of the confidence interval and $A$ the parameter that is varied from 0 to 1. The fraction of rejected objects is then called r4 and the completeness then becomes compl.=1—r4., The fraction of rejected objects is then called $r_A$ and the completeness then becomes $\mathrm{compl.}=1-r_A$. In we reject all objects with: with A varied from to0%., In we reject all objects with: with $A$ varied from to. . The ODDS parameter put out by does not allow to vary the completeness over a large interval since a lot of objects are assigned an ODDS value of 1., The ODDS parameter put out by does not allow to vary the completeness over a large interval since a lot of objects are assigned an ODDS value of 1. " In this way diagrams showing ó, σε, and fi, vs. completeness are created."," In this way diagrams showing $\delta_z$, $\sigma_z$, and $f_{3\sigma}$ vs. completeness are created." " While 6, is almost independent of completeness the dependencies of c; and /3, on completeness for selected setups are shown in Fig. 4..", While $\delta_z$ is almost independent of completeness the dependencies of $\sigma_z$ and $f_{3\sigma}$ on completeness for selected setups are shown in Fig. \ref{fig:char_line}. From the preceding paragraphs it should be clear that the choice of A in Eq., From the preceding paragraphs it should be clear that the choice of $A$ in Eq. 3 and Eq., \ref{eq:completeness} and Eq. 4 as a criterion for a reliable redshift estimate is somewhat arbitrary., \ref{eq:completeness_ODDS} as a criterion for a reliable redshift estimate is somewhat arbitrary. " After careful investigation of all characteristic line plots for all setups we decided to fix the cut for the rejection of uncertain objects in at σ>0.125, in the COMBO code at σ>0.15 and in at ODDS«0.95."," After careful investigation of all characteristic line plots for all setups we decided to fix the cut for the rejection of uncertain objects in at $\sigma>0.125$, in the COMBO code at $\sigma>0.15$ and in at $ODDS<0.95$." This appears to eliminate the most uncertain objects in the datasets studied here., This appears to eliminate the most uncertain objects in the datasets studied here. There is clearly some amount of degeneracy between the quantities defined in this section., There is clearly some amount of degeneracy between the quantities defined in this section. " If the photo-z error distribution was purely Gaussian, scatter and bias would be sufficient numbers to characterise the accuracy of one particular setup."," If the $z$ error distribution was purely Gaussian, scatter and bias would be sufficient numbers to characterise the accuracy of one particular setup." " As described above, this is not the case for real data (see also Fig."," As described above, this is not the case for real data (see also Fig." 5 6))., \ref{fig:zz_BCH_C5}~ \ref{fig:zz_BCH_B5}) ). " Usually, there is a core which might be offset by some bias and there are very extended wings containing catastrophic outliers."," Usually, there is a core which might be offset by some bias and there are very extended wings containing catastrophic outliers." This complex error distribution is not easily described by a few numbers and a specific choice must be a compromise between clarity and degeneracy., This complex error distribution is not easily described by a few numbers and a specific choice must be a compromise between clarity and degeneracy. with respect to (ry.@y).,with respect to $r_0$ $\Phi_0$ ). " n; is the observed number of galaxies in bin ὁ and nm., the predicted number for any assumed. pair of lens parameters.", $n_{r}^{i}$ is the observed number of galaxies in bin $i$ and $n_{ex}^{i}$ the predicted number for any assumed pair of lens parameters. " We have binned the data in such away that n7,=20.", We have binned the data in such a way that $n_{ex}^{i}=20$. This procedure was carried out for several hundred samples of 500 galaxies., This procedure was carried out for several hundred samples of $500$ galaxies. The reconstructed (r7.909) are plotted on figure (6)).," The reconstructed $(r_0,\Phi_0)$ are plotted on figure \ref{recon_dis}) )." We can see that there is a great dispersion in the reconstructed cata., We can see that there is a great dispersion in the reconstructed data. This arises from the fact that the statistic of the reconstructed sources is fairly insensitive to the Lens parameters., This arises from the fact that the statistic of the reconstructed sources is fairly insensitive to the lens parameters. Therefore the above 47 is small for a wide range of parameters over which the minimum can be found., Therefore the above $\chi^2$ is small for a wide range of parameters over which the minimum can be found. Although this method of finding confidence regions for the lens parameters in the absence of polarization information may not be optimal. it does however given some idea of the advantages of using polarimetric data (see Fie.," Although this method of finding confidence regions for the lens parameters in the absence of polarization information may not be optimal, it does however given some idea of the advantages of using polarimetric data (see Fig." 2)., 2). As we have already mentioned. if one does not use the polarization to determine the orientation of the source galaxy. the only measurable quantities are the image parameters.," As we have already mentioned, if one does not use the polarization to determine the orientation of the source galaxy, the only measurable quantities are the image parameters." " We are thus left with five unknown parameters (£,:2Mανν0) but still have only 3 equations. and so it is impossible to solve the svstem."," We are thus left with five unknown parameters $(l_s, \Delta l_s, \alpha_{s}, \Gamma, \theta)$ but still have only $3$ equations, and so it is impossible to solve the system." Η we assume only that the lens is spherically svnunetric. and. as before. that the centre of the lens is known. so that the angle 8 is determined. and that the polarization has been measured. then the system of equations (10)).(11)) and (13)) will contain three unknowns ελ.D).," If we assume only that the lens is spherically symmetric, and, as before, that the centre of the lens is known, so that the angle $\theta$ is determined, and that the polarization has been measured, then the system of equations \ref{sr1}) \ref{sr2}) ) and \ref{sr4}) ) will contain three unknowns $(l_s, \Delta l_s, \Gamma)$ ." I is thus possible to deduce the remaining source parameters as well as E., It is thus possible to deduce the remaining source parameters as well as $\Gamma$. From equations (10)) and (13)) one can show that E is given by lem Η there is no measurement error and if the lens is really spherical. this method would provide an exact. determination of the lens parameters.," From equations \ref{sr1}) ) and \ref{sr4}) ) one can show that $\Gamma$ is given by 1cm If there is no measurement error and if the lens is really spherical, this method would provide an exact determination of the lens parameters." Of course these assumptions are not very realistic. and it is interesting to investigate the case described by equation (18)) when there is à measurement error ay.," Of course these assumptions are not very realistic, and it is interesting to investigate the case described by equation \ref{solr}) ) when there is a measurement error $\alpha_s$." In order tocarry out this analysis. we have reconstructed E for 10000 randomly selected galaxies as before. and including a random error on the measurement of os.," In order tocarry out this analysis, we have reconstructed $\Gamma$ for $10 000$ randomly selected galaxies as before, and including a random error on the measurement of $\alpha_s$." " Fig.7 shows the mean error in percent on the value obtained for E GNE,=(bP,E)/E where E, and E are the inferred and the actual value) as a function of the error. measured in degrees. on a, (Aa.=Ja;o. )."," \ref{errsph} shows the mean error in percent on the value obtained for $\Gamma$ $\Delta\Gamma_{r}=(\Gamma_{r}-\Gamma)/\Gamma$ where $\Gamma_{r}$ and $\Gamma$ are the inferred and the actual value) as a function of the error, measured in degrees, on $\alpha_s$ $\Delta\alpha_{s}=|\alpha_{s}^{r}-\alpha_s|$ )." " Evidently. if one can measure à, to within a few degrees. it is possible to locally cetermine E to a precision of around 204 using just one galaxy."," Evidently, if one can measure $\alpha_{s}$ to within a few degrees, it is possible to locally determine $\Gamma$ to a precision of around $20\%$ using just one galaxy." " We generated two samples of galaxies with a gaussian error distribution on a, with a standard deviation of 2.5""and 5"".", We generated two samples of galaxies with a gaussian error distribution on $\alpha_s$ with a standard deviation of $2.5^{o}$and $5^{o}$ . The uncertainty in the effective redshift of the mass belonging (ο M31 is taken to be about of the circular velocity.,The uncertainty in the effective redshift of the mass belonging to M31 is taken to be about of the circular velocity. This seems reasonable but. as for many of the other parameter uncertainties. i( is an intuitive guess.," This seems reasonable but, as for many of the other parameter uncertainties, it is an intuitive guess." The distance is from (he survev by MeConnachie et al. (, The distance is from the survey by McConnachie et al. ( 2005). but the adopted standard deviation is larger than (the stated measurement error.,"2005), but the adopted standard deviation is larger than the stated measurement error." The allowed perpendicular distance d_ of the effective center of the mass of M31 from the observed center of the galaxy is 10 kpc. about the optical width of the galaxy.," The allowed perpendicular distance $d_\perp$ of the effective center of the mass of M31 from the observed center of the galaxy is 10 kpc, about the optical width of the galaxy." The mass of LAIC is allowed a larger range because it is interesting to see whether the dvnamics give some indication of its likely value., The mass of LMC is allowed a larger range because it is interesting to see whether the dynamics give some indication of its likely value. The distance and its uncertainty are from Freedman οἱ al. (, The distance and its uncertainty are from Freedman et al. ( 2001).,2001). van der Marel et al. (, van der Marel et al. ( 2002) describe an uncertainty of about 1 kpc in the position of the optical center of the LMC.,2002) describe an uncertainty of about 1 kpc in the position of the optical center of the LMC. The choice d.=2 kpe for the offset from the dark matter halo thus seems justified but maybe overly optimistic., The choice $d_\perp=2$ kpc for the offset from the dark matter halo thus seems justified but maybe overly optimistic. Ht is adopted because an offset much larger than (his significantlv shilts the LAIC angular position. confusing the meaning of (he measured proper motions.," It is adopted because an offset much larger than this significantly shifts the LMC angular position, confusing the meaning of the measured proper motions." The LAIC proper motions in Table 1 are from Ixallivavalil et al. (, The LMC proper motions in Table 1 are from Kallivayalil et al. ( 2006). and the adopted standard deviations for 47 are their stated errors (wilh no allowance for possible motion of the stars relative to a dark matter halo).,"2006), and the adopted standard deviations for $\chi^2$ are their stated errors (with no allowance for possible motion of the stars relative to a dark matter halo)." The galaxies M33 and 10160 are in this analvsis because their proper motions (Drunthaler et al., The galaxies M33 and IC10 are in this analysis because their proper motions (Brunthaler et al. 2005: Drunthaler et al., 2005; Brunthaler et al. 2007) are important. constraints., 2007) are important constraints. The stated uncertainties in (he measured proper motions are treated as standard deviations., The stated uncertainties in the measured proper motions are treated as standard deviations. The allowed perpendicular olfset α is more generous than for the LAIC because the angular positions are much less sensitive to d., The allowed perpendicular offset $d_\perp$ is more generous than for the LMC because the angular positions are much less sensitive to $d_\perp$. The larger allowance in the distance to IC10 seems warranted by its low galactic latitude (Sanna et al., The larger allowance in the distance to IC10 seems warranted by its low galactic latitude (Sanna et al. 2008: Nim et al., 2008; Kim et al. 2009)., 2009). The galaxy NGC3109 is included because this relatively small spiral with its scattering of dwarl companions is in a low density region on the edge of or just outside LG., The galaxy NGC3109 is included because this relatively small spiral with its scattering of dwarf companions is in a low density region on the edge of or just outside LG. At this location the redshift and distance of NGC23109 is expected (to give a particularly direct constraint on the LG mass., At this location the redshift and distance of NGC3109 is expected to give a particularly direct constraint on the LG mass. The distance is [rom Dalcanton et al. (, The distance is from Dalcanton et al. ( 2009). with standard deviation larger than the measurement error.,"2009), with standard deviation larger than the measurement error." The object NGC300 is meant (o represent the mass belonging to (his galaxy aud to AI55., The object NGC300 is meant to represent the mass belonging to this galaxy and to M55. Ht may also represent the tidal field of the more distant galaxies in (he Sculptor Group., It may also represent the tidal field of the more distant galaxies in the Sculptor Group. To accommodate (his. the allowed ranges of posiüon and redshift are broader (han the assignments lor the nearer objects.," To accommodate this, the allowed ranges of position and redshift are broader than the assignments for the nearer objects." The object Maffei is similarly meant to represent the mass around 1342 and Madfei P: and perhaps also the tidal effect of more distant mass in roughly the same direction., The object Maffei is similarly meant to represent the mass around IC342 and Maffei 1 and perhaps also the tidal effect of more distant mass in roughly the same direction. This first exploration of how the orbit of the LMC relative to ihe MW might be affected by large mass concentrations external to the LG compares models with and without. Malfei., This first exploration of how the orbit of the LMC relative to the MW might be affected by large mass concentrations external to the LG compares models with and without Maffei. The nearby galaxy NGC 4258 is another remarkable object. with a disk of gas in its nucleus that emits radio waves via maser emission [rom water molecules (Mivoshi οἱ al.,"The nearby galaxy NGC 4258 is another remarkable object, with a disk of gas in its nucleus that emits radio waves via maser emission from water molecules (Miyoshi et al." 1995: Greenhill et al., 1995; Greenhill et al. 1995: Herrnstein et al., 1995; Herrnstein et al. 1998)., 1998). Raclio interferometry measurements have shown that the eas lollows circular orbits with a nearly perfect Keplerian velocity prolile (expb?. see Fig.," Radio interferometry measurements have shown that the gas follows circular orbits with a nearly perfect Keplerian velocity profile $v \propto r^{-1/2}$, see Fig." 1)., 1). Furthermore. the acceleration of the gas has been measured and it loo is consistent wilh Ixeplerian cdvnaanics (Brage et al.," Furthermore, the acceleration of the gas has been measured and it too is consistent with Keplerian dynamics (Bragg et al." 2000)., 2000). From these measurements it is inferred that there is a dark object with a mass of 3.5x10*M.. confined within ~4xLo? m of the center of NGC 4258., From these measurements it is inferred that there is a dark object with a mass of $3.5\times10^7 M_\odot$ confined within $\sim4\times10^{15}$ m of the center of NGC 4258. The case for this dark mass being a DII is again extremely slrong., The case for this dark mass being a BH is again extremely strong. Supermassive DIIs have been inferred in (he nuclei of many other nearby galaxies by means of optical observations. especially with the IIubble Space Telescope (IXormendy. Richstone 1995: Pinkney et al.," Supermassive BHs have been inferred in the nuclei of many other nearby galaxies by means of optical observations, especially with the Hubble Space Telescope (Kormendy Richstone 1995; Pinkney et al." 2003)., 2003). One or two galaxies have coherent. gas disks at the center whose orbital velocities provide information on the enclosed mass., One or two galaxies have coherent gas disks at the center whose orbital velocities provide information on the enclosed mass. For the rest. one measures (he velocity dispersion of stars near the center of (he galaxy. and applies (he virial iheorem essentially a statistical version of equation (2) io inler the enclosed. mass.," For the rest, one measures the velocity dispersion of stars near the center of the galaxy and applies the virial theorem — essentially a statistical version of equation (2) — to infer the enclosed mass." Masses in the range 1053. to 3x10??M. have been estimated by this means in about 20 galaxies., Masses in the range $10^6M_\odot$ to $3\times10^{9.5}M_\odot$ have been estimated by this means in about 20 galaxies. Although the constraints on the radii of the dark mass concentrations in these ealactic nuclei is relatively poor (compared to Ser A* or NGC 4253). nevertheless the case for identifving the objects as supermassive DIIs is strong.," Although the constraints on the radii of the dark mass concentrations in these galactic nuclei is relatively poor (compared to Sgr A* or NGC 4258), nevertheless the case for identifying the objects as supermassive BHs is strong." Central black hole masses are difficult to measure for more distant galaxies., Central black hole masses are difficult to measure for more distant galaxies. Techniques such as “reverberation mappiug (see llorne et al., Techniques such as “reverberation mapping” (see Horne et al. 2004) — another application of the virial theorem = can be used if the black hole is an AGN and shows variability., 2004) — another application of the virial theorem — can be used if the black hole is an AGN and shows variability. Such methods are less accurate (han the ones described above. but thev are valuable since they provide black hole mass estimates for a large sample of galaxies.," Such methods are less accurate than the ones described above, but they are valuable since they provide black hole mass estimates for a large sample of galaxies." " The two categories of BIIs described above are clearly very distinct Irom each other. with verv different masses: M.~[few—204M., for stellar-mass DIIs in NRBs and M—105—107?AL, for supermassive DIIs in AGN."," The two categories of BHs described above are clearly very distinct from each other, with very different masses: $M \sim {\rm few} -20M_\odot$ for stellar-mass BHs in XRBs and $M\sim 10^6-10^{9.5}M_\odot$ for supermassive BHs in AGN." The DIIs in XRDs are clearly the remnants of very massive stars (sav. with initial masses Af> 30M.) at the end of their lives., The BHs in XRBs are clearly the remnants of very massive stars (say with initial masses $M>30M_\odot$ ) at the end of their lives. But how exactly are the BIls in galactic nuclei formed. and how do thev evolve?," But how exactly are the BHs in galactic nuclei formed, and how do they evolve?" Observations have revealed interesting correlations between (he supermassive BIIs in the nuclei of galaxies and (he properties of their host galaxies., Observations have revealed interesting correlations between the supermassive BHs in the nuclei of galaxies and the properties of their host galaxies. For instance. the DII mass appears to be roughly," For instance, the BH mass appears to be roughly" For almost a decade. it has been known that the power spectra of solar acoustic mocles are asvnnuelric. velocity has more power on (he low Irequency side ancl intensity has more power on the high frequency side of (he power maxima (e.g.Duvallοἱal.1993).,"For almost a decade, it has been known that the power spectra of solar acoustic modes are asymmetric, velocity has more power on the low frequency side and intensity has more power on the high frequency side of the power maxima \citep[e.g.][]{duv93}." . The asvininelry reversal between velocity and intensity is thought to be due to the correlated backeround noise contribution to the intensity power spectra (Nigam et al., The asymmetry reversal between velocity and intensity is thought to be due to the correlated background noise contribution to the intensity power spectra (Nigam et al. 1998)., 1998). It is debated whether (he asvimmetry reversal occurs invelocity (Roxburel&Vorontsov1997) or intensity. (Nigametal.1998). or both (Ixummar&Basu1999).," It is debated whether the asymmetry reversal occurs invelocity \citep{rav97} or intensity \citep{nig98} or both \citep{kab99}." . Theoretical models predict asvimmnietries that depend on (the source depth and tvpe (Ixumar&Basu1999:Georgobianietal. 2000b).," Theoretical models predict asymmetries that depend on the source depth and type \citep{kab99,dg00b}." . Roxburgh&Vorontsov(1997). considered the superposition ol dipole ancl quadrupole sources; Nigametal.(1998). used a combination of monopole aud dipole terms: Kumar&Basu(1999) show Chat the asymmetry reversal could be triggered even bx dipole or euadrupole sources alone.," \citet{rav97} considered the superposition of dipole and quadrupole sources; \citet{nig98} used a combination of monopole and dipole terms; \citet{kab99} show that the asymmetry reversal could be triggered even by dipole or quadrupole sources alone." Sinnuations of the shallow upper laver of the solar convective zone have resonant acoustic modes like (he Sun., Simulations of the shallow upper layer of the solar convective zone have resonant acoustic modes like the Sun. The emergent intensity and (he velocity in (he photosphere have asvuunelric spectra with the opposite asvinmetry (Georgobianiοἱal.2000a)., The emergent intensity and the velocity in the photosphere have asymmetric spectra with the opposite asymmetry \citep{dg00a}. . In this letter we calculate (he temperature and velocity power spectra at the continuum optical depth 7=1 and at the eeomelrieal depth corresponding to «€7>=1., In this letter we calculate the temperature and velocity power spectra at the continuum optical depth $\tau = 1$ and at the geometrical depth corresponding to $<\tau>=1$. At unit continuum optical depth the velocity and temperature have opposite asymmetry. wilh the velocity having more low-Irequency power and (he intensity more high frequency power.," At unit continuum optical depth the velocity and temperature have opposite asymmetry, with the velocity having more low-frequency power and the intensity more high frequency power." At fixed geometrical depth. however. the velocity ancl temperature have the same asvnunelry. more low frequency power. for the funclamental mode.," At fixed geometrical depth, however, the velocity and temperature have the same asymmetry, more low frequency power, for the fundamental mode." These results indicate that the asvmimetry reversal is caused by radiative transfer effects. and not bv correlated noise.," These results indicate that the asymmetry reversal is caused by radiative transfer effects, and not by correlated noise." We use a three - dimensional hydrodvnamic code of Stein&Nordlundences(herein) {ο simulate the upper lavers of the solar convection zone., We use a three - dimensional hydrodynamic code of \citet[and references therein]{san98} to simulate the upper layers of the solar convection zone. The computational domain covers 6 Mm by 6 Mm horizontally and 3 Mm in vertical direction. [rom 0.5 Mm above the 7=1 surface to 2.5 Mm beneath it.," The computational domain covers 6 Mm by 6 Mm horizontally and 3 Mm in vertical direction, from 0.5 Mm above the $\tau = 1$ surface to 2.5 Mm beneath it." The model includes non-gray. LTE radiative transfer.," The model includes non-gray, LTE radiative transfer." LLorizontal boundaries are periodic. while vertical ones are transmitting.," Horizontal boundaries are periodic, while vertical ones are transmitting." The spatial resolution is 100 km horizontally and ~ 50 km vertically. with a finer eric interpolated for solving the radiative transfer equation.," The spatial resolution is 100 km horizontally and $\sim$ 50 km vertically, with a finer grid interpolated for solving the radiative transfer equation." The radiation fiekl is caleulated by solving the Feautrier equation along a vertical and 4 straight inclined rays. after averaging the Planck [function into four bins by wavelength sorted according to opacity (c£Nordlund 1991)..," The radiation field is calculated by solving the Feautrier equation along a vertical and 4 straight inclined rays, after averaging the Planck function into four bins by wavelength sorted according to opacity \citep[cf][]{nor82,nas90,nas91}. ." Snapshots are saved at 30 s intervals., Snapshots are saved at 30 s intervals. We have simulated 43 hours, We have simulated 43 hours eravitational potential is deep chough to retain the ionized eas (Le. CoreZ20ks 7).,gravitational potential is deep enough to retain the ionized gas (i.e. $v_{\rm circ}\ga 20{\rm km ~ s^{-1}}$ ). Hence. the photo-evaporation is quite devastating for fluctuations with lower masses aud ater collapse epochs.," Hence, the photo-evaporation is quite devastating for fluctuations with lower masses and later collapse epochs." " Intriguingly, a steep transition of Ένας for Core20κας coincidentally lies ou a line of 10111” constant 6. be. Op/pτε20."," Intriguingly, a steep transition of $f_{\rm star}$ for $v_{\rm circ}\la 20{\rm km s^{-1}}$ coincidentally lies on a line of nearly constant $\sigma$, i.e., $\delta\rho/\rho \approx 2\sigma$." This means that in nore than of the halos with eee&20x18.+. the star ornmation is strouely suppressed by the carly rciouization.," This means that in more than of the halos with $v_{\rm circ}\la 20{\rm km s^{-1}}$, the star formation is strongly suppressed by the early reionization." Tu the preseut μαπο. the star formation is assumed o proceed iu local free-fall time.," In the present simulation, the star formation is assumed to proceed in local free-fall time." This leads to the physically αιμαια. star formation rate., This leads to the physically maximal star formation rate. Tence. the obtained stellar faction iu a halo should be regarded as a naximal oue.," Hence, the obtained stellar fraction in a halo should be regarded as a maximal one." If the star formation proceeds iu a longer nuescale. barvon gas in a halo with coin20m| could be almost completely ploto-evaporated after the roionization.," If the star formation proceeds in a longer timescale, baryon gas in a halo with $v_{\rm circ}\la 20{\rm km s^{-1}}$ could be almost completely photo-evaporated after the reionization." On the other laud. fluctuations with Core=201s bis like to be impervious to the photo-cvaporation. since the gravitational potential is deep enough to retain the ionized eas.," On the other hand, fluctuations with $v_{\rm circ}\ga 20{\rm km s^{-1}}$ is like to be impervious to the photo-evaporation, since the gravitational potential is deep enough to retain the ionized gas." " To examine the the dependence of results on assumed UVB intensity (Z4). we also perform several ruus with fo,=1."," To examine the the dependence of results on assumed UVB intensity $I_{21}$ ), we also perform several runs with $I_{21}=1$." In this case. a steep transition of foray is slightlv shifted to higher a as δρέρ~2.50.," In this case, a steep transition of $f_{\rm star}$ is slightly shifted to higher $\sigma$ as $\delta\rho/\rho \approx 2.5\sigma$." Thus. it turus out that the results are not stronely dependcut ou the UVB lutensity.," Thus, it turns out that the results are not strongly dependent on the UVB intensity." Such iuseusitiveness may be understood by the weak dependence of the sclfshiclding ou the UV intensity seen In equation (2))., Such insensitiveness may be understood by the weak dependence of the self-shielding on the UV intensity seen in equation \ref{nshield}) ). Finally. to check the uummerical effects; we analyze the convergence of the ruus with changing the mass resolution and softening leneth.," Finally, to check the numerical effects, we analyze the convergence of the runs with changing the mass resolution and softening length." " In Figure 2.. the left panel shows the final stellar fraction (foray) iu runs with Ma=6«10.14, and τοδε10. while the right panel is with ALi=οςLOPAL. aud :.c15."," In Figure \ref{fig2}, the left panel shows the final stellar fraction $f_{\rm star}$ ) in runs with $M_{\rm vir} = 6\times 10^7 M_\odot$ and $z_{\rm c}\simeq 10$, while the right panel is with $M_{\rm vir} = 6\times 10^6 M_\odot $ and $z_{\rm c}\simeq 15$." " They are at the transition region of fora, In Figure ", They are at the transition region of $f_{\rm star}$ in Figure \ref{fig1}. The horizontal axis in Figure 2 is the softening leneth e for eravity., The horizontal axis in Figure \ref{fig2} is the softening length $\epsilon$ for gravity. Four different curves correspond to the differcut uuubers of particles used iu the simulations., Four different curves correspond to the different numbers of particles used in the simulations. " We cau see that foray almost couverees, if Napa22)? aud ife20x<10 20pe."," We can see that $f_{\rm star}$ almost converges, if $N_{\rm SPH}\ga 2^{15}$ and if $\epsilon \la 10-20{\rm pc}$ ." Thus. the present smuulatioun with e= and Napg=25(Np) is ulikelv to suffer from nuuerical effects.," Thus, the present simulation with $\epsilon=20{\rm pc}$ and $N_{\rm SPH}=2^{15}(=N_{\rm DM})$ is unlikely to suffer from numerical effects." The present nmuuerical simulations predict strong negative feedback ou the formation of dwarf galaxies with Core&20a5 , The present numerical simulations predict strong negative feedback on the formation of dwarf galaxies with $v_{\rm circ} \la 20 {\rm km~s^{-1}}$. Based on faa. We cau make a rough estimation of the mass-to-light ratios (M/L) for finally formed ealaxics.," Based on $f_{\rm star}$, we can make a rough estimation of the mass-to-light ratios $M/L$ ) for finally formed galaxies." " If we assume των,=3 for pus n solar units. forar=0.01 correPD to Ma/L""m=2.6«10? and fear01 to AA/L=2.6vun«10°."," If we assume $M_{\rm star}/L=3$ for stars in solar units, $f_{\rm star}=0.01$ corresponds to $M_{\rm vir}/L =2.6 \times 10^{3}$ and $f_{\rm star}=0.1$ to $M_{\rm vir}/L= 2.6 \times 10^{2}$." But. values cannot be compared directly the observed AL of satellite galaxies. because a quite large fraction (typically more than 90 percent) of dark matter halos of satellites can be tidally stripped. as shown bv Kravtsov.Cuedin&Whypin(2001).," But, these values cannot be compared directly with the observed $M/L$ of satellite galaxies, because a quite large fraction (typically more than 90 percent) of dark matter halos of satellites can be tidally stripped, as shown by \citet{Kravtsov04}." . Thus. the eventual ML of satellites is likely to decrease by a factor of 10. ce. AV/L=2.6«10° for Ένα=0.01.," Thus, the eventual $M/L$ of satellites is likely to decrease by a factor of 10, e.g. $M/L =2.6 \times 10^{2}$ for $f_{\rm star}=0.01$." Local Croup chvart galaxies (dSphs aud divs) exhibit a wide rauge of ML. which is from a few up to z100 (vandeuBerel1999:Mateo1905:Thepashita.Takeuchi.&Tama1998).," Local Group dwarf galaxies (dSphs and dIrrs) exhibit a wide range of $M/L$, which is from a few up to $\approx 100$ \citep{vdB99,Mateo98,Hirashita98}." . Hence. the formiect ealaxies with fa;20.01 mar account for the Local Group dwarf galaxies.," Hence, the formed galaxies with $f_{\rm star} \ga 0.01$ may account for the Local Group dwarf galaxies." The preseut simulation predicts that oulv few percent of fluctuations result iu faa;20.01. if ConeZO20kmas+.," The present simulation predicts that only a few percent of fluctuations result in $f_{\rm star} \ga 0.01$, if $v_{\rm circ}\la 20{\rm km s^{-1}}$." Tf the star formation rate is lower. the probability is reduced further.," If the star formation rate is lower, the probability is reduced further." Hence. such intrinsically low-unass halos may be too few to account for all Galactic satellites.," Hence, such intrinsically low-mass halos may be too few to account for all Galactic satellites." One possibility to reconcile this discrepancy could be a model sugeested by Eravtsov.Cuediu&IEklvpiu(2001)., One possibility to reconcile this discrepancy could be a model suggested by \citet{Kravtsov04}. . They found that of small halos originate iu considerably larger systems with >109A/.. which survived the tidal stripping. and sugeest that the Galactic satellites are deseeudauts of relatively massive svstenis which formed at ligher redshifts.," They found that of small halos originate in considerably larger systems with $\ga 10^9 M_\odot$, which survived the tidal stripping, and suggest that the Galactic satellites are descendants of relatively massive systems which formed at higher redshifts." Iu our simulation. systems larger than LOCAL. are not subject to the UVB feedback.," In our simulation, systems larger than $10^8 M_\odot$ are not subject to the UVB feedback." Thus. their model secs viable to account for the nuniber of Local Group dwarf galaxies.," Thus, their model seems viable to account for the number of Local Group dwarf galaxies." We are grateful the referee. who provided helpful columents on this paper.," We are grateful to the referee, who provided helpful comments on this paper." " We thank A. Ferrara. T. IWitavama. Is. Ounnuku. IX. Wada. N. Yoshida. aud ο, White for stimulating discussion."," We thank A. Ferrara, T. Kitayama, K. Omukai, K. Wada, N. Yoshida, and S. White for stimulating discussion." The TAICS has heen developed in a project which Center for Computational Physics. University of Tsukuba propelled in the course of JSPS BResearcl-for-the-Euture program of Computational Science. aud. Eneiecring.," The HMCS has been developed in a project which Center for Computational Physics, University of Tsukuba propelled in the course of JSPS Research-for-the-Future program of Computational Science and Engineering." The analysishas been made with computational facilities at Center for Computational Sciences In Vuiversity of Tsukuba and Rikkvo Cuiversity., The analysishas been made with computational facilities at Center for Computational Sciences in University of Tsukuba and Rikkyo University. We acknowledee Research Grant. from Japan Society for the Promotion of Science (15710122:IIS. 15310060:NIU).," We acknowledge Research Grant from Japan Society for the Promotion of Science (15740122:HS, 15340060:MU)." LAIC! ancl SMC.,LMC and SMC. In addition. Paezviski&Pindor(2000) showed that the OGLE LAIC Cepheids. in (he period range of 1.1 between 0.05 and 0.1 seems to reproduce the right normalization at radio wavelengths. if combine with a magnetic field close to equipartition.," A value of $\gamma$ between 0.05 and 0.1 seems to reproduce the right normalization at radio wavelengths, if combined with a magnetic field close to equipartition." Other values of the density. profile power law index would. instead: require unacceptable values of 1. As discussed. above. neutralino annihilation produce. a Continuum y-ray spectrum. originating from the decay. of neutral pions. which in turn come from the hacronization process of quark-antiquark pairs.," Other values of the density profile power law index would instead require unacceptable values of B. As discussed above, neutralino annihilation produce a continuum $\gamma$ -ray spectrum, originating from the decay of neutral pions, which in turn come from the hadronization process of quark-antiquark pairs." " Referring to the paper of Gondolo and Silk (1999) we write the contribution of the spike as where A,=1.5[EU2|Hus]1/2 and Y. is the number of photons produced. per annihilation."," Referring to the paper of Gondolo and Silk (1999) we write the contribution of the spike as where $R_{\rm in} = 1.5 \left[ (20 R_{\rm S})^2+R_{\rm core}^2 \right]^{1/2} $ and $Y_{\gamma}$ is the number of photons produced per annihilation." ‘This formula is valid in the case of adiabatic accretion from an initial power law density profile., This formula is valid in the case of adiabatic accretion from an initial power law density profile. LE one considers an initialzso/frerimat profile. (ie. a profile with a Lat central core). the enhancement of the Dux in the Galactic Center would be negligible compared. to radiation. from annihilations along the line of sight (see Gondolo and Silk. 1999).," If one considers an initial profile (i.e. a profile with a flat central core), the enhancement of the flux in the Galactic Center would be negligible compared to radiation from annihilations along the line of sight (see Gondolo and Silk, 1999)." We show in figure 2. the expected fluxes for a subset of supersvmmetrie models and the same values of as in figure l., We show in figure \ref{gammas} the expected fluxes for a subset of supersymmetric models and the same values of $\gamma$ as in figure \ref{synchro}. A value of 54 between 0.05 ancl 0. can reproduce the normalization of the observed Dux., A value of $\gamma$ between 0.05 and 0.1 can reproduce the normalization of the observed flux. This is fully consistent with the result. found in the previous section., This is fully consistent with the result found in the previous section. Larger values of 5 are also able to reproduce the EGRET normalization. as shown in figure 3..," Larger values of $\gamma$ are also able to reproduce the EGRET normalization, as shown in figure \ref{reqgamma}. ." In particular we found that even if most of the models would require a> ofthe order of 0.1 or lower. some of them could &o as high as ο21.," In particular we found that even if most of the models would require a $\gamma$ of the order of 0.1 or lower, some of them could go as high as $\gamma \approx 1$." Those models correspond to very low predicted Duxes. and are thought to require an important level of fine-tuning ofthe seven input. parameters.," Those models correspond to very low predicted fluxes, and are thought to require an important level of fine-tuning of the seven input parameters." For comparison we also show he expected results in à scenario without the central spike. in which case a range of ? between 1 and 2 is required.," For comparison we also show the expected results in a scenario without the central spike, in which case a range of $\gamma$ between 1 and 2 is required." Finally in figure 4 we show the required. eross sections o reproduce the EGRET data normalization for all the supersvmmetrie models and four dillerent values of 5 (in the case of presence of the central spike)., Finally in figure \ref{cross} we show the required cross sections to reproduce the EGRET data normalization for all the supersymmetric models and four different values of $\gamma$ (in the case of presence of the central spike). Here again it is possible o read out the range of values of 7 which can reproduce the observed. EGRET normalization with cross sections close to hose predicted in our supersvmametrie scenario., Here again it is possible to read out the range of values of $\gamma$ which can reproduce the observed EGRET normalization with cross sections close to those predicted in our supersymmetric scenario. In the framework of a halo model with a spike around the central black hole. we showed that a consistent scenario can be built. reproducing at the same time both the radio and eania-ray enission.," In the framework of a halo model with a spike around the central black hole, we showed that a consistent scenario can be built, reproducing at the same time both the radio and gamma-ray emission." Observed radio. emission can be explained hy synchrotron emission of secondary ος|pairs in the Galactic magnetic field., Observed radio emission can be explained by synchrotron emission of secondary e-e+pairs in the Galactic magnetic field. Phe enhancement of annihilation rate due to the central spike and. svachrotron self-absorption were the two main ingredients of our calculation., The enhancement of annihilation rate due to the central spike and synchrotron self-absorption were the two main ingredients of our calculation. Despite the lack of distinctive features of continuum eanmnma-rav emission. we find full consistencv of the results obtained with the radio emission. the EGRET tus normalization being reproduced with values of zz0.1. when assuming profiles with a central spike.," Despite the lack of distinctive features of continuum gamma-ray emission, we find full consistency of the results obtained with the radio emission, the EGRET flux normalization being reproduced with values of $\gamma \approx0.1$, when assuming profiles with a central spike." The argument can also be turned the other way round and interpreted as à measure of the Galactic magnetic field: we can in fact decide to select the values of 5 reproducing the normalization of the observed. gamnma-ray. emission. (figure 3)). and eo back to figure 1. to read out the corresponding value of BY. which for most of the mocdoels is indeed of order the equipartition value. thus confirming the consistency of OUL scenario.," The argument can also be turned the other way round and interpreted as a 'measure' of the Galactic magnetic field: we can in fact decide to select the values of $\gamma$ reproducing the normalization of the observed gamma-ray emission (figure \ref{reqgamma}) ), and go back to figure \ref{synchro} to read out the corresponding value of $B^*$, which for most of the models is indeed of order the equipartition value, thus confirming the consistency of our scenario." Fortheoming experiments. such as GLAST. will probe energies well above the LECRET measurements. up to 300 GeV. A sharp cutolf around. the neutralino mass is predicted for this scenario. i£ the annihilation radiation gives the dominant. contribution to normalization.," Forthcoming experiments, such as GLAST, will probe energies well above the EGRET measurements, up to 300 GeV. A sharp cutoff around the neutralino mass is predicted for this scenario, if the annihilation radiation gives the dominant contribution to normalization." " Furthermore other ""smoking gun signatures. such as narrow hieh energyganuna ray lines could give further information and constraints on neutralino properties or halo profiles."," Furthermore other 'smoking gun' signatures, such as narrow high energygamma ray lines could give further information and constraints on neutralino properties or halo profiles." hbiehichissuf ficientlodelerminevelocitydispersionsdounto~ 60 km I.,$b$ which is sufficient to determine velocity dispersions down to $\sim$ 60 km $^{-1}$. In all. three fibre configurations were observed.," In all, three fibre configurations were observed." Spectra were extracted. [rom the raw data frames. wavelength. calibrated and. sky-subtracted using the AAO 2dlde softwarepackage’.," Spectra were extracted from the raw data frames, wavelength calibrated and sky-subtracted using the AAO 2dfdr software." .. Recshifts were determined. via cross-correlation for the absorption line spectra and/or the direct. measurement of emission lines., Redshifts were determined via cross-correlation for the absorption line spectra and/or the direct measurement of emission lines. The 2dE spectroscopic observations focussed on. the determination of accurate velocity dispersions of earlv-tvpe ealaxies in the Norma cluster for a Fundamental Plane analysis of the cluster., The 2dF spectroscopic observations focussed on the determination of accurate velocity dispersions of early-type galaxies in the Norma cluster for a Fundamental Plane analysis of the cluster. The primary target list. therefore consisted of known bright ellipticals in the cluster (Woucelt Ixraan-Ixorteweg 2001)., The primary target list therefore consisted of known bright ellipticals in the cluster (Woudt Kraan-Korteweg 2001). Llowever. we used the spare fibres of the 2.1 spectrograph to extend the redshift coverage of the Norma cluster.," However, we used the spare fibres of the 2dF spectrograph to extend the redshift coverage of the Norma cluster." Galaxies were primarily selected from. the optical catalogue of Woucdt Ixraan-Ixortewese (2001) and the 24LASS NSC. indicated by “Wixi? and JJ. respectively in Table 2..," Galaxies were primarily selected from the optical catalogue of Woudt Kraan-Korteweg (2001) and the 2MASS XSC, indicated by `WKK' and J', respectively in Table \ref{2dftable}." Additional galaxies were identified on deep Z: images taken with the ESO/ALPC 2.2-m telescope and the Wide Field Imager (see Sect., Additional galaxies were identified on deep $R_C$ images taken with the ESO/MPG 2.2-m telescope and the Wide Field Imager (see Sect. 4)., 4). These ave identified as “ZOAJJ° in Table 2.., These are identified as J' in Table \ref{2dftable}. ltedshifts were obtained for 182 galaxies. 53 of which had a previous measurement.," Redshifts were obtained for 182 galaxies, 53 of which had a previous measurement." bor 76 galaxies. multiple measurements were obtained to gauge the internal accuracy of the 2clF spectrograph.," For 76 galaxies, multiple measurements were obtained to gauge the internal accuracy of the 2dF spectrograph." Table 20 shows a representative sample of the results obtained [rom the 201 spectroscopy., Table \ref{2dftable} shows a representative sample of the results obtained from the 2dF spectroscopy. The full table is available online., The full table is available online. Figure 3 shows a comparison of the measurecl 301 heliocentric velocities with measurements from the literature., Figure \ref{2dfcompext} shows a comparison of the measured 2dF heliocentric velocities with measurements from the literature. The vast) majority. of these previous measurements were obtained in the course of our ZOA redshift survey (SAAQO: Wouelt et al., The vast majority of these previous measurements were obtained in the course of our ZOA redshift survey (SAAO: Woudt et al. 1999: AHEPOS: \Wouelt et al., 1999; MEFOS: Woudt et al. 2004)., 2004). Phe overall agreement is very good: with a dispersion of m4 = 124 km | (based on 51 galaxies).," The overall agreement is very good: with a dispersion of $\sigma_{\rm ext, all}$ = 124 km $^{-1}$ (based on 51 galaxies)." Only one galaxy revealed a cliscrepent heliocentric velocity: for. 66329. the 2dlE spectroscopy. resulted in poc4749+35 km as compared to the previously. low signal-to-noise value for this galaxy of 2477 +4 250 km s (Wouclt et al.," Only one galaxy revealed a discrepent heliocentric velocity; for 6329, the 2dF spectroscopy resulted in $v = 4749 \pm 35$ km $^{-1}$ as compared to the previously low signal-to-noise value for this galaxy of 2477 $\pm$ 250 km $^{-1}$ (Woudt et al." 1999)., 1999). We then compared the δα results with a subset of the literature sample. namely those for which redshifts were obtained with the MIZEOS multi-fibre spectrograph (Woucelt et al.," We then compared the 2dF results with a subset of the literature sample, namely those for which redshifts were obtained with the MEFOS multi-fibre spectrograph (Woudt et al." 2004)., 2004). This subset has the most accurate redshifts available for the Norma cluster., This subset has the most accurate redshifts available for the Norma cluster. There are. 16 galaxies in common between 2k anc MEEFOS (the filled circles. in Fig. 3))., There are 16 galaxies in common between 2dF and MEFOS (the filled circles in Fig. \ref{2dfcompext}) ). The agreement is again excellent. with a lower rms σκιΕως = 31 km 5) than the previous comparison (which included the SAAQ measurements) Given the primary goal of obtaining accurate velocity dispersions from the 201 spectroscopy. we have observed a aree number of galaxies repeatedly to gauge the internal uncertainty: 69 galaxies were observed twice and 7 galaxies iwl three independent velocity. measurements.," The agreement is again excellent, with a lower rms $\sigma_{\rm ext, MEFOS}$ = 31 km $^{-1}$ ) than the previous comparison (which included the SAAO measurements), Given the primary goal of obtaining accurate velocity dispersions from the 2dF spectroscopy, we have observed a large number of galaxies repeatedly to gauge the internal uncertainty: 69 galaxies were observed twice and 7 galaxies had three independent velocity measurements." For these repeated: observations we find σαν = 33 km s over the entire range of observed: velocities., For these repeated observations we find $\sigma_{\rm int}$ = 33 km $^{-1}$ over the entire range of observed velocities. This is comparable to he external comparison with the ALEFOS spectroscopy., This is comparable to the external comparison with the MEFOS spectroscopy. Dased on these independent evaluations. we have assigned a standard error of 35 km * to each of the 2dE. velocities.," Based on these independent evaluations, we have assigned a standard error of 35 km $^{-1}$ to each of the 2dF velocities." With the new δα observations described: above. racial," With the new 2dF observations described above, radial" Figure 2 shows the background-subtracted X-ray light eurve with I ks binning lor source PNAMAL J043527.2-144301.,Figure 2 shows the background-subtracted X-ray light curve with 1 ks binning for source 2XMM J043527.2-144301. The source light eurve clearly shows two flares that occurred after an lial quiescent period of al least 65 ks (including a time interval in the middle of the observation affected by proton flare)., The source light curve clearly shows two flares that occurred after an initial quiescent period of at least 65 ks (including a time interval in the middle of the observation affected by proton flare). The source first flare was very strong: in (he energy range (0.2-7.5) keV the peak count rate reached in the light curve was (0.11-0.12) counts !. depending on the choice of binning.," The source first flare was very strong; in the energy range (0.2-7.5) keV the peak count rate reached in the light curve was (0.11-0.12) counts $^{-1}$, depending on the choice of binning." However during the quiescent period the source was very faint. with an average count rate of 0.0021 counts ll corresponding (o an increase of more (han 52 in the count rate from quiescent to peak.," However during the quiescent period the source was very faint, with an average count rate of 0.0021 counts $^{-1}$, corresponding to an increase of more than 52 in the count rate from quiescent to peak." The second flare in the same energy. band had peak count rate of 0.055 counts |., The second flare in the same energy band had peak count rate of 0.055 counts $^{-1}$. Both flares show [ast-rise. exponential-decay profile with a rise time of ~3 ks and similar e-folding decay times of (4.320.7) ks and (4.53:1.0) ks for the first aud second flare respectively.," Both flares show fast-rise, exponential-decay profile with a rise time of $\sim$ 3 ks and similar e-folding decay times of $(4.3\pm0.7)$ ks and $(4.5\pm1.0)$ ks for the first and second flare respectively." We compared the position of source 2XMM JO48527.2-144801 with error radius of with available optical/IR. catalogs., We compared the position of source 2XMM J043527.2-144301 with error radius of with available optical/IR catalogs. " We found a faint 2MAÀSS counterpart (2MASS J04352724-1443017) only from the position. with 0.08 and (/—N,)=L163:0.10 (Fig 3. Table 1)."," We found a faint 2MASS counterpart (2MASS J04352724-1443017) only from the position, with $K_{s}=14.35\pm0.08$ and $(J-K_{s})=1.16\pm0.10$ (Fig 3, Table 1)." " There is only one source in a 4"" radius in the near-inlrared band of DSS image. which is not visible at other wavelengths (Fig."," There is only one source in a $4\arcsec$ radius in the near-infrared band of DSS image, which is not visible at other wavelengths (Fig." 3)., 3). We also found a counterpart of our source in the USNO-DBDI.O catalog aud Guide Star Catalog GSC-2.3 with offset of0., We also found a counterpart of our source in the USNO-B1.0 catalog and Guide Star Catalog GSC-2.3 with offset of. "9"".. The USNO-B1.0 counterpart has R-band magnitude of 19.37 and near-IR band magnitude of 17.9.", The USNO-B1.0 counterpart has R-band magnitude of 19.37 and near-IR band magnitude of 17.9. Whereas GSC counterpart is identified only in neaw-IR (0.35 band). no detection in F (red). J (blue) and V (green) photographic band.," Whereas GSC counterpart is identified only in near-IR $0.8\micron$ band), no detection in F (red), J (blue) and V (green) photographic band." G5C-2.3 catalog is based on ground-based photographic plate material., GSC-2.3 catalog is based on ground-based photographic plate material. The majority of stars visible in these cameras plates awe very red late-twpe stars. in agreement with the 2MAÀSS characterization (see next paragraph).," The majority of stars visible in these cameras plates are very red late-type stars, in agreement with the 2MASS characterization (see next paragraph)." To assign a spectral class to source 2NMM J043527.2-144301. we compared the 24ÀSS colors of this source with the colors of other M and found that the CJ—H). (HE—Ni) and (7—AN.) colors are best matched (he spectral class M8.5V. To conlivm the spectral class. in Fig.," To assign a spectral class to source 2XMM J043527.2-144301, we compared the 2MASS colors of this source with the colors of other M and found that the $(J-H)$, $(H-K_{s})$ and $(J-K_{s})$ colors are best matched the spectral class M8.5V. To confirm the spectral class, in Fig." d we compare source 2NMM JO43527.2-144301 with data from Gizis et al. (, 4 we compare source 2XMM J043527.2-144301 with data from Gizis et al. ( 2000. (heir,"2000, their" with4 shocksdee (9,with shocks \citealt{cw84}) ). AQ uses the PARAMESHARAMES librarybrary to handle adaptive (7).mesh FLASHrefinement (?)) and the Message-Passing Interface library to achieve parallelization., FLASH uses the PARAMESH library to handle adaptive mesh refinement \citealt{mom00}) ) and the Message-Passing Interface library to achieve parallelization. In a previous paper (?)). we presented a first set of results concerning a jet less dense than the ambient medium. with density contrast vy=nfiLO where 54 1s the ambient density and 1; is the density of the jet) which emits X-rays in good agreement with the X-ray emission observed in 1154 (2).," In a previous paper \citealt{bop04}) ), we presented a first set of results concerning a jet less dense than the ambient medium, with density contrast $\nu = n_{\rm a}/n_{\rm j} = 10$ (where $n_{\rm a}$ is the ambient density and $n_{\rm j}$ is the density of the jet) which emits X-rays in good agreement with the X-ray emission observed in 154 \citealt{ffm02}) )." ? have shown the validity of the physical principle on which our model is based: a supersonic jet traveling through the ambient medium produce a shock at the jet/ambient interaction front leading to X-ray emission in good agreement with observations., \citet{bop04} have shown the validity of the physical principle on which our model is based: a supersonic jet traveling through the ambient medium produce a shock at the jet/ambient interaction front leading to X-ray emission in good agreement with observations. In the present paper. we study the effects on the jet dynamics of varying the parameters. such as the ambient-to-jet density ratio. v=naf03. and the Mach number. AL=cfe through a wide rarge. to determine the range of parameters which can give rise to X-ray emission consistent with observations.," In the present paper, we study the effects on the jet dynamics of varying the parameters, such as the ambient-to-jet density ratio, $\nu = n_{\rm a}/n_{\rm j}$, and the Mach number, $M = v_{\rm j}/c_{\rm a}$, through a wide range, to determine the range of parameters which can give rise to X-ray emission consistent with observations." Note that we use this definition for the Mach number to be able to compare the jet velocity with the ambient sound speed. to have information on how much the jet Is supersonic.," Note that we use this definition for the Mach number to be able to compare the jet velocity with the ambient sound speed, to have information on how much the jet is supersonic." The paper is structured as follow: Sect., The paper is structured as follow: Sect. 2. describes the model and the numerical setup: in Sect., \ref{The model} describes the model and the numerical setup; in Sect. 3. we discuss the results of our numerical simulations; finally Sect., \ref{Results} we discuss the results of our numerical simulations; finally Sect. 4. is devoted to summary and conclusions.," \ref{Discussion and conclusions} is devoted to summary and conclusions." In Appendix AppendixA: we discuss our method to synthesize X-ray emission from our numerical simulations.," In Appendix \ref{synthesizing the X-ray spectra} we discuss our method to synthesize X-ray emission from our numerical simulations." We model the propagation of a constantly driven protostellarJet through an isothermal and homogeneous medium., We model the propagation of a constantly driven protostellar jet through an isothermal and homogeneous medium. We assume that the fluid is fully tonized and that it can be regarded as a perfect gas with a ratio of specific heats ~=5/2., We assume that the fluid is fully ionized and that it can be regarded as a perfect gas with a ratio of specific heats $\gamma = 5/3$. Also we assume a negligible magnetic field., Also we assume a negligible magnetic field. The jet evolution is deseribed by the fluid equations of mass. momentum and energy conservation. taking into account the effects of radiative losses and thermal conduction where f is the time. p the mass density. v the plasma velocity. p. the pressure. 4 the heat flux. » and ayy are the electron and hydrogen density respectively. P(T) is the optically thin. radiative losses function per unit. emission measure (for the P(T) we use a functional. form. which takes into account: free-free. bound-free. bound-bound and 2 photons emission. see ο 2:; 2). T the plasma temperature. and whereE is the total energy and e the specific internal energy.," The jet evolution is described by the fluid equations of mass, momentum and energy conservation, taking into account the effects of radiative losses and thermal conduction where $t$ is the time, $\rho$ the mass density, $\bf v$ the plasma velocity, $p$ the pressure, $q$ the heat flux, $n_e$ and $n_H$ are the electron and hydrogen density respectively, $P(T)$ is the optically thin radiative losses function per unit emission measure (for the P(T) we use a functional form, which takes into account: free-free, bound-free, bound-bound and 2 photons emission, see \citealt{rs77}; \citealt{mgv85}; \citealt{km00}) ), $T$ the plasma temperature, and where $E$ is the total energy and $\epsilon$ the specific internal energy." We use the equation of state for an ideal gas Following ?.. we use an interpolation expression for the thermal conductive flux of the form which allows for a smooth transition between the classical and saturated conduction regime.," We use the equation of state for an ideal gas Following \citet{db93}, we use an interpolation expression for the thermal conductive flux of the form which allows for a smooth transition between the classical and saturated conduction regime." In the above expression. q.i represents the classical conductive flux (?)) where &(T)=9.2«10*T? eres + ! ! is the thermal conductivity.," In the above expression, $q_{\rm spi}$ represents the classical conductive flux \citealt{spi62}) ) where $\kappa (T) = 9.2\times10^{-7} T^{5/2}$ erg $^{-1}$ $^{-1}$ $^{-1}$ is the thermal conductivity." " The saturated flux. 4,44. 1s (2) where o0.3 (2:: 2.. and references therein) and c, is the isothermal sound speed."," The saturated flux, $q_{\rm sat}$, is \citealt{cm77}) ) where $\phi\sim0.3$ \citealt{1984ApJ...277..605G}; \citealt{1989ApJ...336..979B}, and references therein) and $c_{\rm s}$ is the isothermal sound speed." We adopt a 2-D cylindrical GG 2) coordinate system with the jet axis coincident with the +-axis.," We adopt a $2$ -D cylindrical $r, z$ ) coordinate system with the jet axis coincident with the $z$ -axis." For the different cases analyzed. we have chosen different ranges for the radial and longitudinal dimensions of the computational grid to follow in all cases the jet/ambient interaction for at least 20-50 years: the computational grid size varies from z300 AU to zz600 AU in the i direction and from =6000 AU to +3«10! AU in the : direction.," For the different cases analyzed, we have chosen different ranges for the radial and longitudinal dimensions of the computational grid to follow in all cases the jet/ambient interaction for at least 20-50 years: the computational grid size varies from $\approx 300$ AU to $\approx 600$ AU in the $r$ direction and from $\approx6000$ AU to $\approx 3\times10^{4}$ AU in the $z$ direction." completeness. we outline here.,"completeness, we outline here." ο adopted a simple stellar model in which a thin outer shell of mass M. is spun up by addition of angular momentum 2M from the interior of the star., \cite{applegate92} adopted a simple stellar model in which a thin outer shell of mass $M_s$ is spun up by addition of angular momentum $\Delta J$ from the interior of the star. The energy required to do this is given by his equation 2s. where εδ =O.©. is the angular velocity of cüllerential rotation between the outer shell (Q.) and the stellar interior (Q.).," The energy required to do this is given by his equation 28, where $\Omega_{dr}$ = $\Omega_s - \Omega_*$ is the angular velocity of differential rotation between the outer shell$\Omega_s$ ) and the stellar interior $\Omega_*$ )." depp is theclleetive moment of inertia given by. where ἐς and {ν are the moments of inertia of the outer shell and the stellar interior. respectively.," $I_{eff}$ is theeffective moment of inertia given by, where $I_s$ and $I_*$ are the moments of inertia of the outer shell and the stellar interior, respectively." " TFypicallv. for an outer shell mass of Al,=OLA. £,=f; and therefore in equation we can substitute 24,5;=£,. where 4,=2/3ALAP."," Typically, for an outer shell mass of $M_s = 0.1M$, $I_s = I_*$ and therefore in equation \ref{eqn:deltaE} we can substitute $2I_{eff} = I_s$, where $I_s = 2/3 M_sR^2$." The £24 term on the left-hand side of equation 4 is normally small (but see later) anc can be set to zero., The $\Omega_{dr}$ term on the left-hand side of equation \ref{eqn:deltaE} is normally small (but see later) and can be set to zero. We can therefore re-express equation 4. as. In the model outlined in ?.. variations in the quadrupole moment. €. of the star are driven by the stellar activity cvcle.," We can therefore re-express equation \ref{eqn:deltaE} as, In the model outlined in \cite{applegate92}, variations in the quadrupole moment, $Q$, of the star are driven by the stellar activity cycle." Magnetic. fields. are supposed. to drive the angular momentum transfer from within the star., Magnetic fields are supposed to drive the angular momentum transfer from within the star. For instance. if angular momentum is transported from the core of the star to its envelope. the star will become more oblate ancl its quadrupole moment will increase.," For instance, if angular momentum is transported from the core of the star to its envelope, the star will become more oblate and its quadrupole moment will increase." ? computes the rate of change of the stellar quacdrupole as a function of the angular moment transport in his equation 26. where © is the stellar angular rotation velocity.," \cite{applegate92} computes the rate of change of the stellar quadrupole as a function of the angular momentum transport in his equation 26, where $\Omega$ is the stellar angular rotation velocity." As outlined in Section 2.. a change in the stellar quadrupole moment Ieads to a corresponding change in the orbital period given by equation 2.. where e is the orbital separation between. in this case. the star and the planet.," As outlined in Section \ref{sec:applegate}, a change in the stellar quadrupole moment leads to a corresponding change in the orbital period given by equation \ref{eqn:deltaP}, where $a$ is the orbital separation between, in this case, the star and the planet." We now have three equations. with equation 6. relating AL to AJ. equation 7 relating AQ to AJ. and finally equation relating AP to AQ.," We now have three equations, with equation \ref{eqn:deltaE2} relating $\Delta E$ to $\Delta J$, equation \ref{eqn:deltaQ} relating $\Delta Q$ to $\Delta J$, and finally equation \ref{eqn:deltaP} relating $\Delta P$ to $\Delta Q$." Given that stellar activity eveles are rather variable. there is no well-defined amplitude or period of variation to be expected from Applegate's models.," Given that stellar activity cycles are rather variable, there is no well-defined amplitude or period of variation to be expected from Applegate's models." The one constraint that we can invoke is a restriction on the energv budget allowed to drive the quadrupole moment., The one constraint that we can invoke is a restriction on the energy budget allowed to drive the quadrupole moment. With this in mind. we can use the last 3 equations to relate the (as vet undefined) energy budget to the change in the orbital period AL’ giving. which can be rearranged to give Η we assume that the power available to drive the quadrupole changes is some fraction. f. of the stellar luminosity then we obtain a total energy budget of A=FLT. where 7 is the timescale over which the quadrupole changes occur.," With this in mind, we can use the last 3 equations to relate the (as yet undefined) energy budget to the change in the orbital period $\Delta P$ giving, which can be rearranged to give If we assume that the power available to drive the quadrupole changes is some fraction, $f$, of the stellar luminosity then we obtain a total energy budget of $\Delta E = fLT$ , where $T$ is the timescale over which the quadrupole changes occur." Since stellar activity eveles tend to be of the order of vears or decades (e.g. 21). there is potentially a large energy. budget available for driving orbital period. changes.," Since stellar activity cycles tend to be of the order of years or decades (e.g. \citealt{saar99}) ), there is potentially a large energy budget available for driving orbital period changes." Η this energy is supplied. by the nuclear luminosity of the star with no energy storage in the convection zone then (?)) the star will exhibit RAIS luminosity variations of We set the available energy budget such that the luminosity variations never exceed. some fraction a of the total stellar luminosity., If this energy is supplied by the nuclear luminosity of the star with no energy storage in the convection zone then \citealt{applegate92}) ) the star will exhibit RMS luminosity variations of We set the available energy budget such that the luminosity variations never exceed some fraction $\alpha$ of the total stellar luminosity. Vhis sets our energy budget as While we have used Luminosity variations to set our energv budget we note that such variations will be strict upper limits., This sets our energy budget as While we have used luminosity variations to set our energy budget we note that such variations will be strict upper limits. Indeed. it is not clear that any luminosity changes would be observable.," Indeed, it is not clear that any luminosity changes would be observable." I£ the thermal timescale of the envelope is much larger than the timescale of activity eveles then the observed Luminosity may. hardly vary., If the thermal timescale of the envelope is much larger than the timescale of activity cycles then the observed luminosity may hardly vary. To test this. we have examined the standard solar model (SSAL) used by 2? ane estimated the thermal timescale of the convective envelope (the lower boundary of which we have taken to lie at a radius R=0 0713863H8.).," To test this, we have examined the standard solar model (SSM) used by \cite{boothroyd03} and estimated the thermal timescale of the convective envelope (the lower boundary of which we have taken to lie at a radius $R = 0.713863R_{\odot}$ )." For cach shell in the SSM the therma energy due to fully ionised hydrogen. helium and associate ree electrons was calculated (hvdrogen and helium are fully jonised. except for the very uppermost regions near the xhotosphere).," For each shell in the SSM the thermal energy due to fully ionised hydrogen, helium and associated free electrons was calculated (hydrogen and helium are fully ionised except for the very uppermost regions near the photosphere)." From this we determine a thermal timescale of 73.000 vears for the Sun's convective envelope.," From this we determine a thermal timescale of 73,000 years for the Sun's convective envelope." This is likely o be a lower limit (but a reasonable estimate nonetheless) since we have not included the thermal energy [rom metals., This is likely to be a lower limit (but a reasonable estimate nonetheless) since we have not included the thermal energy from metals. We conclude. therefore. that any luminosity variations on he timescale of 10'sor 100's of vears may. be damped considerably. ancl would be potentially unobservable.," We conclude, therefore, that any luminosity variations on the timescale of 10'sor 100's of years may be damped considerably, and would be potentially unobservable." Armed with a prescription for defining the energy xidget available to the star to drive AQ (but being aware of he possible reservations so far described). we can caleulate orbital period modulations via equation. 9..," Armed with a prescription for defining the energy budget available to the star to drive $\Delta Q$ (but being aware of the possible reservations so far described), we can calculate orbital period modulations via equation \ref{eqn:deltaP2}. ." Following ?.. he amplitude of the orbital period. modulation. and the amplitude of the oscillation observed in an ο6 diagram are related. by This. combined. with equation 9 and setting 3= ΑΛ. leads to potential OC! variations in the observed planetary transit times of the order.," Following \cite{applegate92}, , the amplitude of the orbital period modulation and the amplitude of the oscillation observed in an $O-C$ diagram are related by This, combined with equation \ref{eqn:deltaP2} and setting $\beta = M_s/M$ , leads to potential $O-C$ variations in the observed planetary transit times of the order," Following ?.. he amplitude of the orbital period. modulation. and the amplitude of the oscillation observed in an ο6 diagram are related. by This. combined. with equation 9 and setting 3= ΑΛ. leads to potential OC! variations in the observed planetary transit times of the order.—," Following \cite{applegate92}, , the amplitude of the orbital period modulation and the amplitude of the oscillation observed in an $O-C$ diagram are related by This, combined with equation \ref{eqn:deltaP2} and setting $\beta = M_s/M$ , leads to potential $O-C$ variations in the observed planetary transit times of the order," "The ultra-faint dwarfs in the first group. and the classical dSph noted in? are the best candidates for an observed population of primordial fossils, with stellar spheroids not significantly modified by tides.","The ultra-faint dwarfs in the first group, and the classical dSph noted in \cite{RicottiGnedin:05} are the best candidates for an observed population of primordial fossils, with stellar spheroids not significantly modified by tides." " However, as noted in Paper I. classical dwarfs with Ly>10L. are too bright to be hosted in halos with CarΌρη lor egi=20 kms Llor3O0kms !."," However, as noted in Paper I, classical dwarfs with $L_V > 10^6 L_\odot$ are too bright to be hosted in halos with $v_{max}=0 halos with Xy:>10 FL. 7."," Throughout this work, and in Paper I, we compare the observed Milky Way satellites to our luminous $z=0$ halos with $\Sigma_V > 10^{-1.4}$ $_\odot$ $^{-2}$." We are also able to use our simulations to study the distribution of a hereto undetected population of ultra-faints with Sy<10+4 L. ? and LyZ10! L..," We are also able to use our simulations to study the distribution of a hereto undetected population of ultra-faints with $\Sigma_V < 10^{-1.4}$ $_\odot$ $^{-2}$ and $L_V \simlt 10^4$ $_\odot$." " The possible existence and undetectability of this population was first noticed in BROY, [rom the analysis of RGOS simulations (see also Ricott 2010 for a review)."," The possible existence and undetectability of this population was first noticed in BR09, from the analysis of RG05 simulations (see also Ricotti 2010 for a review)." " However, using independent arguments, ?. have also proposed the existence of this population they refer to as “stealth galaxies.”"," However, using independent arguments, \cite{Bullocketal:10} have also proposed the existence of this population they refer to as “stealth galaxies.”" " In this section, we compare the distributions of non-fossils and true-fossils to the galactocentric radial distribution of the observed Milky Way satellites."," In this section, we compare the distributions of non-fossils and true-fossils to the galactocentric radial distribution of the observed Milky Way satellites." We first compare the galactocentric radial distributions of our simulations to observations., We first compare the galactocentric radial distributions of our simulations to observations. We then make detailed comparisons between the observed cumulative luminosity function of the Milky Way satellites and the simulated cumulative luminosity functions of our non-fossil and true fossil populations., We then make detailed comparisons between the observed cumulative luminosity function of the Milky Way satellites and the simulated cumulative luminosity functions of our non-fossil and true fossil populations. " Note, that our simulated cumulative luminosity functions only include stellar populations formed before reionization."," Note, that our simulated cumulative luminosity functions only include stellar populations formed before reionization." " Therefore, we refer to our simulated cumulative luminosity functions as primordial cumulative luminosity functions."," Therefore, we refer to our simulated cumulative luminosity functions as primordial cumulative luminosity functions." Any star formation that may take place in halos WIN trae>μμ alter reionizauion is not accounted [or in our simulated luminosity functions., Any star formation that may take place in halos with $v_{max}>v_{filt}$ after reionization is not accounted for in our simulated luminosity functions. " Thus, only the cumulative luminosity function of true fossils can be directly compared to observations, while the luminosities of the non-fossils are lower limits."," Thus, only the cumulative luminosity function of true fossils can be directly compared to observations, while the luminosities of the non-fossils are lower limits." Figure | shows the galactocentric radial distribution of all the simulated and observed Milky Way satellites., Figure \ref{RD.all} shows the galactocentric radial distribution of all the simulated and observed Milky Way satellites. " In the left panel of Figure 1,, we compare observations to simulations without correcting Lor the sensitivity limits of the SDSS (??) or whether a satellite is a fossil."," In the left panel of Figure \ref{RD.all}, we compare observations to simulations without correcting for the sensitivity limits of the SDSS \citep{Walshetal:09,Koposovetal:07} or whether a satellite is a fossil." " In the right panel, we show all the satellites again, now applying the ? limits to the simulated halos around MW.? and MW.3."," In the right panel, we show all the satellites again, now applying the \cite{Walshetal:09} limits to the simulated halos around MW.2 and MW.3." Figure 2 shows the galactocenuric radial distribution for onlythe observed and simulatedfossils., Figure \ref{RD.fos} shows the galactocentric radial distribution for onlythe observed and simulated. As in Figure 1.. the right and left panels show the simulated true fossils with and without the ? corrections.," As in Figure \ref{RD.all}, the right and left panels show the simulated true fossils with and without the \cite{Walshetal:09} corrections." " The observational and theoretical fossil definitions are discussed in Sections 3. and ??,, respectively."," The observational and theoretical fossil definitions are discussed in Sections \ref{Obser}~ and \ref{Fossil}, respectively." " Our simulations do not account for tidal stripping of stars, and do not reproduce the properües of the inner ultra-[aint dwarls, and we do not include them in Figure 2.."," Our simulations do not account for tidal stripping of stars, and do not reproduce the properties of the inner ultra-faint dwarfs, and we do not include them in Figure \ref{RD.fos}. ." the modification of the shape of the MDF by the selection of metal- candidates.,the modification of the shape of the MDF by the selection of metal-poor candidates. " Consequently, a comparison to our prediction is valid for [Fe/H]«—2.5.."," Consequently, a comparison to our prediction is valid for $<-2.5$." " In our analysis, for a given model (SFR and IMF of PoplII/I and PoplIID), we count the number of low mass stars created at each redshift."," In our analysis, for a given model (SFR and IMF of PopII/I and PopIII), we count the number of low mass stars created at each redshift." " As the iron abundance in the ISM is also calculated as a function of the redshift, the metallicity of the stellar population at each redshift is known 2.1))."," As the iron abundance in the ISM is also calculated as a function of the redshift, the metallicity of the stellar population at each redshift is known )." " The value of the MDF in a given iron abundance bin, is given by the number of stars that are still shining today and were created at times when the iron abundance was within this bin."," The value of the MDF in a given iron abundance bin, is given by the number of stars that are still shining today and were created at times when the iron abundance was within this bin." The MDF for several possible PoplII star formation histories are plotted along with the observation in3., The MDF for several possible PopIII star formation histories are plotted along with the observation in. ". The solid black line corresponds to the normal mode, i.e. a Salpeter IMF starting at 0.1 Mo."," The solid black line corresponds to the normal mode, i.e. a Salpeter IMF starting at 0.1 $_\odot$." " A massive mode is then added with a Salpeter IMF with different lower masses: 36.5 Mo (red dashed), 30 Me (black dotted) and 8 Μο (black dot-dashed)."," A massive mode is then added with a Salpeter IMF with different lower masses: 36.5 $_\odot$ (red dashed), 30 $_\odot$ (black dotted) and 8 $_\odot$ (black dot-dashed)." The minimum mass of 36.5 corresponds to our best model., The minimum mass of 36.5 corresponds to our best model. " Note that the value of the upper limit of the IMFs is not a key parameter, in constrast to the lower one, due to the steep slope of the IMF."," Note that the value of the upper limit of the IMFs is not a key parameter, in constrast to the lower one, due to the steep slope of the IMF." " For —4 «[Fe/H]«-—2.5, the slope of the MDF is well reproduced by PoplI alone."," For $-4<$ $<-2.5$, the slope of the MDF is well reproduced by PopII alone." " The reality of the drop observed at [Fe/H]~ —3.6 (compare the thin solid black line to the thick black histogram) is still debated (e.g., ?))."," The reality of the drop observed at $\sim-3.6$ (compare the thin solid black line to the thick black histogram) is still debated (e.g., \citealt{2009arXiv0901.0617K}) )." " The prediction of several models for the MDF is discussed in ?,, where the authors conclude that none of them are able to explain the tail at [Fe/H]«—4, except a stochastic enrichment model (e.g. ?))."," The prediction of several models for the MDF is discussed in \citet{2008arXiv0809.1172S}, where the authors conclude that none of them are able to explain the tail at $<-4$, except a stochastic enrichment model (e.g. \citealt{2006ApJ...641L..41K}) )." " In our model, as in Karlsson's model, the presence of a massive mode implies the early production of iron, which has an impact on the low metallicity MDF: very few low mass stars at zero or quasi-null metallicity are expected in such a scenario, i.e., effectively as a prompt initial enrichment (PIE)."," In our model, as in Karlsson's model, the presence of a massive mode implies the early production of iron, which has an impact on the low metallicity MDF: very few low mass stars at zero or quasi-null metallicity are expected in such a scenario, i.e., effectively as a prompt initial enrichment (PIE)." The cut-off on the MDF at low metallicity depends on the lower mass of the massive mode., The cut-off on the MDF at low metallicity depends on the lower mass of the massive mode. " Given the paucity of stars with [Fe/H]<—3.5, it is difficult to accurately discriminate between different star formation histories presently."," Given the paucity of stars with $\lesssim -3.5$, it is difficult to accurately discriminate between different star formation histories presently." " Indeed, PoplII stars do not modify the MDF at —3.5<[Fe/H]< —2.5, as long as their minimal mass is larger than about 30Mo."," Indeed, PopIII stars do not modify the MDF at $-3.5<$ $< -2.5$, as long as their minimal mass is larger than about 30." . We now focus on the giants of the ESO-LP (?) which contain the abundances of 17 elements from C to Zn for all of the observed stars., We now focus on the giants of the ESO-LP \citep{2004A&A...416.1117C} which contain the abundances of 17 elements from C to Zn for all of the observed stars. " Following the nomenclature proposed in ?,, very metal-poor (VMP) stars correspond to a metallicity [Fe/H]«—2, extremely metal-poor (EMP) stars to [Fe/H]«—3, ultra metal-poor (UMP) stars to [Fe/H]«--4 and hyper metal-poor (HMP) stars to [Fe/H]<—5."," Following the nomenclature proposed in \citet{2005ARA&A..43..531B}, , very metal-poor (VMP) stars correspond to a metallicity ${\rm [Fe/H]}<-2$, extremely metal-poor (EMP) stars to ${\rm [Fe/H]}<-3$, ultra metal-poor (UMP) stars to $<-4$ and hyper metal-poor (HMP) stars to ${\rm [Fe/H]}<-5$." Some UMP stars are also carbon-enhanced metal-poor (CEMP) stars with [C/Fe]>+1., Some UMP stars are also carbon-enhanced metal-poor (CEMP) stars with $>+1$. " The ESO-LP contains 35 VMP stars, which includes 22 EMP stars."," The ESO-LP contains 35 VMP stars, which includes 22 EMP stars." The star in their sample with the next to lowest iron abundance (CS 22949-037; [Fe/H] = -3.97) is a CEMP star., The star in their sample with the next to lowest iron abundance (CS 22949-037; [Fe/H] = -3.97) is a CEMP star. " Note that 38°245 (?) has [Fe/H]=-4.19; unfortunately, ? and ? do not provide O abundances, and only an upper limit to the abundance of C. One result of this survey has been the reduction of the scatter in different element abundances as correlated against [Fe/H] (e.g Mg, Ca, Cr and Ni)."," Note that $^\circ$ 245 \citep{1984ApJ...285..622B} has [Fe/H]=-4.19; unfortunately, \citet{2004A&A...416.1117C} and \citet{1984ApJ...285..622B} do not provide O abundances, and only an upper limit to the abundance of C. One result of this survey has been the reduction of the scatter in different element abundances as correlated against [Fe/H] (e.g Mg, Ca, Cr and Ni)." " According to ?,, this is contrary to the long- hypothesis that, at such low metallicity, one observes the nucleosynthetic products of only a few or even a single SN II (??).."," According to \citet{2005ARA&A..43..531B}, this is contrary to the long-standing hypothesis that, at such low metallicity, one observes the nucleosynthetic products of only a few or even a single SN II \citep{1998ApJ...507L.135S,2000ApJ...531L..33T}." The lack of scatter in these abundances could be explained by a well-mixed ISM., The lack of scatter in these abundances could be explained by a well-mixed ISM. The CEMP stars references are retrieved from the SAGA presented in ?.., The CEMP stars references are retrieved from the SAGA presented in \citet{2008PASJ...60.1159S}. Abundances derived from 1D and 3D model atmospheres and references are gathered in1., Abundances derived from 1D and 3D model atmospheres and references are gathered in. ". At the lowest metallicity, HE 0107-5240 and HE 1327-2326 are both HMP and CEMP stars."," At the lowest metallicity, HE 0107-5240 and HE 1327-2326 are both HMP and CEMP stars." The very specific chemical pattern of these starsis assumed to be related to the first stages of star formation., The very specific chemical pattern of these starsis assumed to be related to the first stages of star formation. The UMP star HE 13004-0157 with [Fe/H]=-3.88 has an abundance, The UMP star HE 1300+0157 with [Fe/H]=-3.88 has an abundance outer profile remains fixed while the central regions undergo eravothermal contraction.,outer profile remains fixed while the central regions undergo gravothermal contraction. The tically influence profiles also show mild concavity in the [αἱο a feature. which resmbles the observed. profiles given by Curillmair ct al. (," The tidally influenced profiles also show mild concavity in the fall-off, a feature which resmbles the observed profiles given by Grillmair et al. (" 1995.1996). who interpreted their observations asfails.,"1995,1996), who interpreted their observations as." However. the feature evident here is not an unbouncl tidal tail but a bound halo region which has been partially cleared through orbital resonances.," However, the feature evident here is not an unbound tidal tail but a bound halo region which has been partially cleared through orbital resonances." The evolution. of the profile of the mass spectral index is shown in Figure 4., The evolution of the profile of the mass spectral index is shown in Figure \ref{fig:arp_comp}. Mass segregation occurs in every case. regardless of the strength. of tidal heating.," Mass segregation occurs in every case, regardless of the strength of tidal heating." Alost low-mass stars evaporate while the &=1.0 cluster disrupts às indicated. by the strong Uattening of (2?) at all radii., Most low-mass stars evaporate while the $\kappa=1.0$ cluster disrupts as indicated by the strong flattening of $\beta(R)$ at all radii. Phe other cases show Ilattening of the spectrum in the core and steepening in the halo with cillerences that increase with eccentricity., The other cases show flattening of the spectrum in the core and steepening in the halo with differences that increase with eccentricity. Lhe increasing dilferences result from the shorter evolutionary time scales at high eccentricitv for orbits with equal. apocenter., The increasing differences result from the shorter evolutionary time scales at high eccentricity for orbits with equal apocenter. Aside [rom dillerences in time scale. the evolution of the mass spectral index does not depend. significantly: on orbit.," Aside from differences in time scale, the evolution of the mass spectral index does not depend significantly on orbit." Phe spectral index remains approximatelv constant in time near the initial half-mass racius of the cluster., The spectral index remains approximately constant in time near the initial half-mass radius of the cluster. However. the half-mass racius is relatively constant only in the most eccentric cases and undergoes considerable evolution whre tidal effects are strong.," However, the half-mass radius is relatively constant only in the most eccentric cases and undergoes considerable evolution whre tidal effects are strong." The mass spectrum of observed. clusters is not. well-described by a single power-law index over the mass range considered. here., The mass spectrum of observed clusters is not well-described by a single power-law index over the mass range considered here. Harris Pudritz (1994) find a change in slope near 107M..., Harris Pudritz (1994) find a change in slope near $10^5 \msun$. Phis trend is evident in Table 6 which compares [its to the mass spectrum. using three. dilferent models: a single power law. a two-component power law and a Gaussian magnitude distribution.," This trend is evident in Table \ref{tab:mass_comp} which compares fits to the mass spectrum using three different models: a single power law, a two-component power law and a Gaussian magnitude distribution." The single power law shows a relatively Hat spectrum in agreement with Llarris Dudritz (1994)., The single power law shows a relatively flat spectrum in agreement with Harris Pudritz (1994). Phe two-component power law shows a fairly steep dependence for AZ72.2101M. and a nearly [lat spectrum for masses below that., The two-component power law shows a fairly steep dependence for $M>2.2\times 10^5 \msun$ and a nearly flat spectrum for masses below that. " The Gaussian magnitude distvibution peaks at 2.7«10""M... consistent with the Component power Law."," The Gaussian magnitude distribution peaks at $2.7\times 10^5 \msun$, consistent with the two-component power law." Likelihood ratio tests show that the single power law can be rejected in favor of both the Gaussian magnitude distribution and two-component model at better than confidence., Likelihood ratio tests show that the single power law can be rejected in favor of both the Gaussian magnitude distribution and two-component model at better than confidence. The Gaussian and two-component power law can be discriminated with onlv confidence., The Gaussian and two-component power law can be discriminated with only confidence. However. because the data is so sparse. we adopt the single power law as the simplest. model which provides a tenable description of the overall cluster. mass distribution.," However, because the data is so sparse, we adopt the single power law as the simplest model which provides a tenable description of the overall cluster mass distribution." (Charbouneanetal.2000:Tenry2000).. (Miralda-Escudé2002).. (Tolman2009).. (Sasselov," \citep{Charbonneau2000, Henry2000}, \citep{MiraldaEscude2002}. \citep{Holman2005, Agol2005, Heyl2007, Ford2007, Simon2007, Kipping2009a, Kipping2009b}. \citep{Sasselov2003,Patzold2004,Carone2007,Levrard2009}." OGLE-TR-LI3b was reported by Udalskietal.(2002) as a planet candidate trausiting a K-dwarf |I—1LL: RA(I2000)210:52:21.10.. DecJ2000)=61:26:18.5].," OGLE-TR-113b was reported by \citet{Udalski2002c} as a planet candidate transiting a K-dwarf [I=14.4; RA(J2000)=10:52:24.40, Dec(J2000)=–61:26:48.5]." Its planetary nature was coufirmed by Bouchyetal.(2001) and Iouackietal.(2001)., Its planetary nature was confirmed by \citet{Bouchy2004} and \citet{Konacki2004}. . OCLE-TR-113 is an excellent target for differential photometry. since it is located in a dense region of the sky toward the Calactie plane and has wmunerous nearby. bright comparison stars.," OGLE-TR-113 is an excellent target for differential photometry, since it is located in a dense region of the sky toward the Galactic plane and has numerous nearby, bright comparison stars." We observed six transits of OGLE-TR-113b as part of a larecr campaign to detect transit timine variations of OGLE plaucts (Adams2010).., We observed six transits of OGLE-TR-113b as part of a larger campaign to detect transit timing variations of OGLE planets \citep{Adams2010PhD}. All transits were observed in the Sloan // baud with the dual-CCD iustruincut AlasIC on the Magellan Telescopes. located at Las Campanas Observatory in Chile.," All transits were observed in the Sloan $i'$ –band with the dual-CCD instrument MagIC on the Magellan Telescopes, located at Las Campanas Observatory in Chile." " Both MaegIC CCDs have low readout noise (about 6 c- per pixel). stall fields-ofview aud high-resolution pixels (SITe: 112""«112"". or 0.7069 per pixel: c2v: JN"".δν or 000 per pixel). which both minimizes blends and produces stellar inages that are spread over many pixels (typical PWIIM1020 pixels depending ou secing and biuniug)."," Both MagIC CCDs have low readout noise (about 6 e- per pixel), small fields-of-view and high-resolution pixels (SITe: $142\arcsec\times142\arcsec$, or $0.\arcsec 069$ per pixel; e2v: $38\arcsec\times38\arcsec$, or $0.\arcsec037$ per pixel), which both minimizes blends and produces stellar images that are spread over many pixels (typical FWHM=10–20 pixels depending on seeing and binning)." This last feature reduces differeutial pixel response effects and increases the total nunber of photous that cau be collected per frame. without requiring defocusing.," This last feature reduces differential pixel response effects and increases the total number of photons that can be collected per frame, without requiring defocusing." The SITe eain was 2.0 c-/ADU. while the οὖν eiu was 2.1 e-/ADU in 2008 aud 0.5 ο-‘ADU iu 2009 (due to cneineering changes).," The SITe gain was 2.0 e-/ADU, while the e2v gain was 2.4 e-/ADU in 2008 and 0.5 e-/ADU in 2009 (due to engineering changes)." The main advantage of the οὖν is its frame-trauster capability: the readout time per frame is only 5s in standard readout mode and 0.0038 in frame trausfer mode. surpassing the 23s reacout time of the SITe chip aud other couveutional CCDs.," The main advantage of the e2v is its frame-transfer capability: the readout time per frame is only 5s in standard readout mode and 0.003s in frame transfer mode, surpassing the 23s readout time of the SITe chip and other conventional CCDs." We used AlaeIC-SITe for two transits in January 2007 and February 2008. lenceforth denoted by their UT dates as 20070130 and 20080225.," We used MagIC-SITe for two transits in January 2007 and February 2008, henceforth denoted by their UT dates as 20070130 and 20080225." MagIC-e2yv was used for four additional transits between April 2008 aud May 2009 (20080121. 20080511. 20090315. ancl 20090510).," MagIC-e2v was used for four additional transits between April 2008 and May 2009 (20080424, 20080514, 20090315, and 20090510)." The wieltly sky couditiousranged from plotometiic to partly cloudy., The nightly sky conditionsranged from photometric to partly cloudy. Therefore. exposure times wereadjusted," Therefore, exposure times wereadjusted" with the probable descendants of the sstar-formung galaxy population 2008).,with the probable descendants of the star-forming galaxy population . . This evidence thus confinia the plausibility of the rapid bulge formation seen at tin the SINS ealaxies being followed by a few Cwr of rapid SABID assciuubly. ultimately resulting in spheroids aud bulges that obey the local rrelation.," This evidence thus confirm the plausibility of the rapid bulge formation seen at in the SINS galaxies being followed by a few Gyr of rapid SMBH assembly, ultimately resulting in spheroids and bulges that obey the local relation." fouud similar delaved SMDIT formation in the sub-mun galaxy population at (ος Figure 5)). suggesting that the time lag between 1ack holes aud bulges may be a οςinmon phenomenon in rapidly forming galaxies at high redshift.," found similar delayed SMBH formation in the sub-mm galaxy population at (see Figure \ref{mbh}) ), suggesting that the time lag between black holes and bulges may be a common phenomenon in rapidly forming galaxies at high redshift." Towever. this trend is nof universal: quasars and radio galaxies at simular redshifts are suspected to lieabeve local black hole scaling relations. with black holes that are over-massive for their host bulees by up to aud exceeding an order of magnitudet," However, this trend is not universal; quasars and radio galaxies at similar redshifts are suspected to lie local black hole scaling relations, with black holes that are over-massive for their host bulges by up to and exceeding an order of magnitude." his These systems populate the 1729]highestWal mass cud of the lack hole mass function. with black hole masses of 1ο.10? aalveady in place at2.," These systems populate the highest mass end of the black hole mass function, with black hole masses of $> 10^8-10^9$ already in place at." It may therefore be that lack holes in these differeut mass/activity regimes grow in very differenf circumstances and cousequenutlv relate o their bulges very cdiffercuthy., It may therefore be that black holes in these different mass/activity regimes grow in very different circumstances and consequently relate to their bulges very differently. If this is the case. the challenge is then to locate the mechanism(s) that brine hese varied high-redshift formation processes togetler iuto the black hole scaling relations observed at 2=0.," If this is the case, the challenge is then to locate the mechanism(s) that bring these varied high-redshift formation processes together into the black hole scaling relations observed at $z = 0$." Iu stacked. average spectra of SINS sstar-formunge galaxies. we have detected broad ciission nuderneath the much brighter narrow aaud ecnission lines.," In stacked, average spectra of SINS star-forming galaxies, we have detected broad emission underneath the much brighter narrow and emission lines." " This broad emission accounts for ~ oot the total Thuninosity of these ealaxics aud can be parameterized equally well with a single broad line (""broad line” of FWITME ~ 1500 1) and with a two Gaussian fit to both the peruütted aud forbidden lines (""broad wings” of PFWIIM ~ 550 1]."," This broad emission accounts for $\sim$ of the total luminosity of these galaxies and can be parameterized equally well with a single broad line (“broad line"" of FWHM $\sim$ 1500 ) and with a two Gaussian fit to both the permitted and forbidden lines (“broad wings"" of FWHM $\sim$ 550 )." The huuinosity and FWIIM of the broad component increascs with increasing ealaxy mass and therefore with SFR., The luminosity and FWHM of the broad component increases with increasing galaxy mass and therefore with SFR. This broad component is found both in known AGN and in stacked spectra of svstenis that have not beeu previously identified as ACN., This broad component is found both in known AGN and in stacked spectra of systems that have not been previously identified as AGN. There is some evidence that the broad enmüssion is more luuünous in galaxy centers. as opposed to in the outer regions. but the sjeuificauce of these detections are low.," There is some evidence that the broad emission is more luminous in galaxy centers, as opposed to in the outer regions, but the significance of these detections are low." We cannot empircallv determine whether this broad cluission is due to ligh-velocity ealactic winds aud the associated shocks or to the BLR cinission of AGN., We cannot empirically determine whether this broad emission is due to high-velocity galactic winds and the associated shocks or to the BLR emission of AGN. Iu he former case. we fud that simple scaling aretuenuts show that the luuinosity and FWIIM of the broad cnussion can plausibly be accounted for via shocking of he ambicut interstellar media frou supernovac-driven ealactic winds.," In the former case, we find that simple scaling arguments show that the luminosity and FWHM of the broad emission can plausibly be accounted for via shocking of the ambient interstellar media from supernovae-driven galactic winds." These winds would then be cjectiug uatter from the host galaxy at rates slightly exceeding he star formation rate. in keeping with expectations roni the inetallicitv evolution of these galaxies and with ultraviolet interstellar absorptiou-line studies at similar redshifts.," These winds would then be ejecting matter from the host galaxy at rates slightly exceeding the star formation rate, in keeping with expectations from the metallicity evolution of these galaxies and with ultraviolet interstellar absorption-line studies at similar redshifts." On the other haud. the broad cussion may be eenerated in a DLR: in this case. we can estimate the black hole masses aud DImuuaimosities necessary to fuel the observed cussion for cach of three ealaxy mass bius.," On the other hand, the broad emission may be generated in a BLR; in this case, we can estimate the black hole masses and luminosities necessary to fuel the observed emission for each of three galaxy mass bins." " We find that the measured SMDIT masses correlate with the host galaxw masses. as expected from local scaling relations. but that the SMDIIS are siguificautlv ""uaderanuassive for their bulges when compared with local Rehati"," We find that the measured SMBH masses correlate with the host galaxy masses, as expected from local scaling relations, but that the SMBHs are significantly under-massive for their bulges when compared with local relations." dhiss lar result has huge uucertainties. it is consistent with the emoereiug picture of galaxy. assembly at2.2 d which a gasaich disk fragiueuts iuto lavee C1 kpe)] super-star-forming clumps that then iiegrate mto the galaxy ceuter ou Coi-tiniescales to form a nasceut bulec.," While this result has large uncertainties, it is consistent with the emerging picture of galaxy assembly at, in which a gas-rich disk fragments into large $\ge 1$ kpc) super-star-forming clumps that then migrate into the galaxy center on Gyr-timescales to form a nascent bulge." The bulge would then form first through this process aud only later completely asseiible its black hole., The bulge would then form first through this process and only later completely assemble its black hole. The obvious direction for future research is to determine the source of the broad eenmission in ligh-redshitt star-forming galaxies., The obvious direction for future research is to determine the source of the broad emission in high-redshift star-forming galaxies. This will most Likely require detailed examination of iudividual ealaxics., This will most likely require detailed examination of individual galaxies. Among the diagnostics that will be useful for this task are comparisoux with X-ray data aud deep inteerations in rest-frame UV/optical wavebauds to spatially resolve e.g. UV interstellar absorption lines aud broad Baler cussion., Among the diagnostics that will be useful for this task are comparisons with X-ray data and deep integrations in rest-frame UV/optical wavebands to spatially resolve e.g. UV interstellar absorption lines and broad Balmer emission. We thank the ESO staff. especially those at Paranal Observatory. for their helpful and cutlusiastic support during the many observing runs aud several wears over which the SINS project was carried out.," We thank the ESO staff, especially those at Paranal Observatory, for their helpful and enthusiastic support during the many observing runs and several years over which the SINS project was carried out." We also ackuowledge the SINFONI aud PARSEC teams. whose hard work on the instrunneut and laser paved the wav for the success of the SINS observations.," We also acknowledge the SINFONI and PARSEC teams, whose hard work on the instrument and laser paved the way for the success of the SINS observations." Tus paper has additionally beuefited siguificautly frou many euliehteuiug conversations with colleagues. iucludiug FEréddérric Bournaud. Mohan CGaueshalingam. Wevin Tene. Phil Hopkins. Chiis Mcl&ee. Jeffrey Silverman. aud Thea Steele.," This paper has additionally benefited significantly from many enlightening conversations with colleagues, including Fréddérric Bournaud, Mohan Ganeshalingam, Kevin Heng, Phil Hopkins, Chris McKee, Jeffrey Silverman, and Thea Steele." Finally. we thauk the referee. whose detailed and insightful comments ercatlv improved the quality of this paper.," Finally, we thank the referee, whose detailed and insightful comments greatly improved the quality of this paper." , The misalignment of the dises in the Haro 6-10 binary system might suggest the formation mechanism of the system itself.,The misalignment of the discs in the Haro 6-10 binary system might suggest the formation mechanism of the system itself. Such a misalignment cannot be caused by an infall of external material with a different angular momentum onto the binary orbit. because the accretion would have re-aligned the two dises (2)..," Such a misalignment cannot be caused by an infall of external material with a different angular momentum onto the binary orbit, because the accretion would have re-aligned the two discs \citep[][]{Bateetal2000}." Only the infall on one of the components might lead to a tilt of that component. when the transported angular momentum 1s large enough.," Only the infall on one of the components might lead to a tilt of that component, when the transported angular momentum is large enough." Also capture of the companion is an unlikely explanation. because for solar-mass stars the capture rates are insufficient even when circumstellar disces increase the interaction cross section considerably (?)..," Also capture of the companion is an unlikely explanation, because for solar-mass stars the capture rates are insufficient even when circumstellar discs increase the interaction cross section considerably \citep[][]{Heller1995}." 2? (22?)..," \citet{Boffinetal1998} \citep[][]{MoeckelBally2006, MoeckelBally2007a, MoeckelBally2007b}." While studies to date typically quote an average value of the + parameter [rom the clusters in (heir samples. it is not clear (hat this quantity is meaningful.,"While studies to date typically quote an average value of the $r$ parameter from the clusters in their samples, it is not clear that this quantity is meaningful." Comparing the values directly is complicated by the fact that some studies only use RGB stars. while others include subgiants. dwarfs. and even AGB stars as well.," Comparing the values directly is complicated by the fact that some studies only use RGB stars, while others include subgiants, dwarfs, and even AGB stars as well." Since chwarls. with their hotter atmospheres. are less likely to show significant CN absorption. their inclusion may bias the value downward.," Since dwarfs, with their hotter atmospheres, are less likely to show significant CN absorption, their inclusion may bias the value downward." The same holds true for the inclusion of AGB stars. since they are nearly alwavs CN-weakdiscussion).," The same holds true for the inclusion of AGB stars, since they are nearly always CN-weak." . The study by.(2010).. comprised entirely of AIS dwarls. reported an average of 7r=0.8240.29. while the average of (he r values reported bv [or the giants in (heir sample is 0.61.," The study by, comprised entirely of MS dwarfs, reported an average of $r = 0.82 \pm 0.29$, while the average of the $r$ values reported by for the giants in their sample is 0.61." Together. these results indicate that for the clusters in their samples. both of which span a large range of and luminosity. the CN-strong stars are in the minority.," Together, these results indicate that for the clusters in their samples, both of which span a large range of and luminosity, the CN-strong stars are in the minority." llowever. studies of Na and O abundances in cluster giants by suggest that the ratio is much higher. with enriched stars comprising of the total (r2 1).," However, studies of Na and O abundances in cluster giants by suggest that the ratio is much higher, with enriched stars comprising of the total $r > 1$ )." The compilation by of giants from 10 clusters gives an average ratio of 1.72. which agrees well with(2009b.," The compilation by of giants from 16 clusters gives an average ratio of 1.72, which agrees well with." c¢).. While it is puzzling that (wo samples of cluster eiants would vield such discrepant results. this may result [rom a bias toward more luminous clusters. since their inclusion. would artificially inflate the fraction of CN-strong stars in the sample.," While it is puzzling that two samples of cluster giants would yield such discrepant results, this may result from a bias toward more luminous clusters, since their inclusion would artificially inflate the fraction of CN-strong stars in the sample." " Table 5 lists (he mean r values alongside the mean M, values for our sample and the three GCs from the literature.", Table \ref{tabcnratioMv} lists the mean $r$ values alongside the mean $M_V$ values for our sample and the three GCs from the literature. The increase in (r) with (M4) is apparent. indicating that conclusions drawn based upon the CN ratio must account for anv potential biases [rom including or excluding massive GC's in the sample.," The increase in $\langle r \rangle$ with $\langle M_V\rangle$ is apparent, indicating that conclusions drawn based upon the CN ratio must account for any potential biases from including or excluding massive GCs in the sample." represents the highest resolution. homogenous spectral data set vet used to obtain an orbital solution for LS 5039.,"represents the highest resolution, homogenous spectral data set yet used to obtain an orbital solution for LS 5039." Given the lack of X-ray eclipses we could not use the special mode in WD code developed. for modeling the orbits of X-ray binaries., Given the lack of X-ray eclipses we could not use the special mode in WD code developed for modeling the orbits of X-ray binaries. Therefore. we analysed LS 5039 as a single. line spectroscopic binary without any (X-ray) light curves.," Therefore, we analysed LS 5039 as a single line spectroscopic binary without any (X-ray) light curves." This limitation allowed us to determine only the mass function. f(m). as a function of dilferent inclination angles. ;.," This limitation allowed us to determine only the mass function, $f(m)$, as a function of different inclination angles, $i$." We could not determine the exact values of the inclination. 7. and the mass ratio. q.," We could not determine the exact values of the inclination, $i$, and the mass ratio, $q$." However. knowledge of the primarys mass. Ado. allowed: us to narrow the possible parameter space.," However, knowledge of the primary's mass, $M_{\rm O}$, allowed us to narrow the possible parameter space." As described previously. we adopted the 3.906 d period as à fixed. parameter during the modelling.," As described previously, we adopted the 3.906 d period as a fixed parameter during the modelling." The computed value of Zo = UID 2455017.08 was used as the epoch of periastron., The computed value of $T_{0}$ = HJD 2455017.08 was used as the epoch of periastron. The computed orbital parameters are given in reforbitpar where they are compared to the results of 005 and AOO., The computed orbital parameters are given in \\ref{orbitpar} where they are compared to the results of C05 and A09. Phe RV curve implied by the solution is shown in Fig. 2..," The RV curve implied by the solution is shown in Fig. \ref{rvfit}," bottom., bottom. Our values and the ones published by C05 are based only on velocity points from the Ho lines. while A09 applied the velocities of every. available LI. HeL. and Le line. a process which combines lines from two clillerent sources on and near the O star as mentioned in Section ??..," Our values and the ones published by C05 are based only on velocity points from the He lines, while A09 applied the velocities of every available H, He, and He line, a process which combines lines from two different sources on and near the O star as mentioned in Section \ref{RV}." In general. our computed orbital parameters are close to earlier solutions. but there are some clilferences.," In general, our computed orbital parameters are close to earlier solutions, but there are some differences." The value of the computed systemic racial velocity. V5. was significantly higher (bv 15 to 20 km 1) for cach line tvpe (ILL. He and Le 10) in C05 than what we found.," The value of the computed systemic radial velocity, $V_{\gamma}$, was significantly higher (by 15 to 20 km $^{-1}$ ) for each line type (H, He and He ) in C05 than what we found." Phe possibility of a real change in the svstem RY over a lew vears is very small. so the cause of the dillerence is likely clue to ciüllerences in cata analyses.," The possibility of a real change in the system RV over a few years is very small, so the cause of the difference is likely due to differences in data analyses." One of the main goals of our investigation was to obtain stronger constraints on thecompanion., One of the main goals of our investigation was to obtain stronger constraints on the. C05 executed detailed light curve simulations using their orbital solution for LS 5039: they found. that if the inclination angle is around. 307. then photometric variability caused. by the distortion of the primary should be of the order of 0.01 mag near periastron.," C05 executed detailed light curve simulations using their orbital solution for LS 5039; they found that if the inclination angle is around $^{\circ}$, then photometric variability caused by the distortion of the primary should be of the order of 0.01 mag near periastron." I£ the change in brightness is 0.01 mag or less then the inclination is 30° or less., If the change in brightness is 0.01 mag or less then the inclination is $^{\circ}$ or less. An inclination less than 307. in turn. implies that the mass of the compact object is too high (> 3.0 M... €05) to be a neutron star.," An inclination less than $^{\circ}$ , in turn, implies that the mass of the compact object is too high $>$ 3.0 $_{\odot}$, C05) to be a neutron star." Lacking the necessary 2-3 mmag photometric accuracy required. they could not check their scenario.," Lacking the necessary 2-3 mmag photometric accuracy required, they could not check their scenario." As described in Section. ??.. our new analysis of the orbital parameters of LS 5039 is based on an independent homogeneous radial velocity data set.," As described in Section \ref{orbit}, our new analysis of the orbital parameters of LS 5039 is based on an independent homogeneous radial velocity data set." Our results are in good agreement with the one presented. hy C05 Photometric data from theAZOST satellite (6649 incliviclual brightness measurements through 106. days between July 7 and July 23) did not show any variability ereater than a few mmag., Our results are in good agreement with the one presented by C05 – Photometric data from the satellite (6649 individual brightness measurements through 16 days between July 7 and July 23) did not show any variability greater than a few mmag. To quantify the frequency content of the light. curve. we performed. a period. analysis of the full dataset using the software (Lenz&Breger 2004).," To quantify the frequency content of the light curve, we performed a period analysis of the full dataset using the software \citep{Lenz2004}." . “Phe resulting frequency spectrum does not contain any significant peak with an zunplitude greater than 0.002 mag., The resulting frequency spectrum does not contain any significant peak with an amplitude greater than 0.002 mag. Moreover. the orbital period does not jump out of the noise either.," Moreover, the orbital period does not jump out of the noise either." Asa cdillerent approach. we phased the light," Asa different approach, we phased the light" In a maegnitude-Imited polarimetric survey. the observed polarization CDF of all stus Gncluding non-detections) above the observational apparent magnitude limit would be constructed.,"In a magnitude-limited polarimetric survey, the observed polarization CDF of all stars (including non-detections) above the observational apparent magnitude limit would be constructed." A predicted degree of polarization CDF in the same region of the sky. al the same limiting magnitude. should be simulated.," A predicted degree of polarization CDF in the same region of the sky, at the same limiting magnitude, should be simulated." The ratios of the degrees of polarization al a given percentile value in the observed and simulated. CDFs will give (he normalization factor., The ratios of the degrees of polarization at a given percentile value in the observed and simulated CDFs will give the normalization factor. This normalization factor can then be used to calibrate the predicted. degrees of starlight polarization to actual observations., This normalization factor can then be used to calibrate the predicted degrees of starlight polarization to actual observations. The simulations presented here attempt to bridge the gap between (theory. and observation bx making testable predictions for starlight polarization observations based on models of the large-scale structure of the Galactic magnetic field., The simulations presented here attempt to bridge the gap between theory and observation by making testable predictions for starlight polarization observations based on models of the large-scale structure of the Galactic magnetic field. These predictions. when combined with NIR polarization observations. can be used to test the models for the large-scale magnetic field and their physical underpinnines.," These predictions, when combined with NIR polarization observations, can be used to test the models for the large-scale magnetic field and their physical underpinnings." Polarization of background starlight is insensitive to magnetic reversals and cannot. address the presence or location of reversals., Polarization of background starlight is insensitive to magnetic reversals and cannot address the presence or location of reversals. However. these polarizations can allow (esting for (he existence and nature of the poloidal component of the Galactic magnetic field. since all SO models vield similar polarization predictions across the skv and all AO models vield similar predictions that are distinctly different from the SO models.," However, these polarizations can allow testing for the existence and nature of the poloidal component of the Galactic magnetic field, since all S0 models yield similar polarization predictions across the sky and all A0 models yield similar predictions that are distinctly different from the S0 models." The predicted longitude shift of the polarization null points with magnetic pitch. angle. demonstrated in Models 19-24 (a small shift is seen all of the models. however only Models 19-24 svstematically vary (he pitch angle). may [acilitate an observational test for the Galactic magnetic pitch. angle in the disk. similar to the work of Heiles(1996).," The predicted longitude shift of the polarization null points with magnetic pitch angle, demonstrated in Models 19-24 (a small shift is seen all of the models, however only Models 19-24 systematically vary the pitch angle), may facilitate an observational test for the Galactic magnetic pitch angle in the disk, similar to the work of \citet{H96}." . This test is fandaamentallv different from. previous attempts to use Faraday rotation of pulsars and extragalactie sources to model (he magnetic pitchangle (Rand&Ixulkarni1989:Menοἱal.2008:NotaIxatgert2010:VanEcket 2011)..," This test is fundamentally different from previous attempts to use Faraday rotation of pulsars and extragalactic sources to model the magnetic pitchangle \citep{RK89,MFH08,NK10,VE11}. ." shape of the plots in Fie.,shape of the plots in Fig. 1 would appear to make such fine tuuiug au unurealistie possibility., \ref{fig1} would appear to make such fine tuning an unrealistic possibility. There would appear to be three possible explanations for the lack of a time dilation effect iu quasar lielt curves. all of which conflict with broad consensus m the astronomical community.," There would appear to be three possible explanations for the lack of a time dilation effect in quasar light curves, all of which conflict with broad consensus in the astronomical community." Firstly. time dilation might not in fact be a property of the Universe. which would effectively mean that the Universe was not expanding.," Firstly, time dilation might not in fact be a property of the Universe, which would effectively mean that the Universe was not expanding." Apart from the overwheliimg support for the big baug theory. the direct incasurements of tine dilation quoted above strouely argue against this.," Apart from the overwhelming support for the big bang theory, the direct measurements of time dilation quoted above strongly argue against this." The second possibilty is that quasars are not at cosmological distances., The second possibilty is that quasars are not at cosmological distances. This is an areuinentOo which was hotly disputed iu ↓↸∖↕≝⊔∩↴∖↴∙↖↖↽↕↑∐⋜⋯⋜∖⊔⋜∖↥⋅∶↴∙⊾↕∐∶↴∙⊾↸⊳∪∐↴∖↴↸∖∐↴∖↴∏↴∖↴↕≯⋜∏↽≺∏∐⋅↕∐∶↴∙⊾ ≼⊳∪↴∖↴⋯∪↕∪," This is an argument which was hotly disputed in the 1970s, with an emerging consensus favouring cosmological distances." ∶↴⋁↕↸⊳⋜↧↕≼∐↴∖↴↑⋜⋯↸⊳↸∖↴∖↴∙↽∕∏∐↴∖↴∐⋜↧↴∖↴↴∖↴∏↴⋝↴∖↴↸∖≺∣⋯∖∐↑↕⋅↖↽ ⋝↸∖↸∖∐↴∖↴⊓⋅∪∐∶↴∙⊾↕⋅↖⇁↸⊳∪∐∐↥⋅↕⋯∖≺∏⋝∙↖⇁↴∖↴↑, This has subsequently been strongly confirmed by studies of quasar host galaxies at high redshift. ∏≼∐↸∖↴∖↴∪↕⋟≺∣∏⋜↧↴∖↴⋜∐⋅∐∪↴∖↴↑ ∶↴∙⊾⋜↧↕⋜↧⊼↕↸∖↴∖↴⋜↧↑∐↕∶↴∙⊾∐↥⋅↸∖≼↴∖↴∐↕↕⋟↑∙↽∕∏∐∖↑∐∐⋅≼↧↻∪↴∖∷∖↴∏⋝∐↕↑⋅↖↽ is that the observed variatious are not intrinsic o the quasars but caused by some intervening oocess at lower redshift. such as eravitationa uicroleusiue.," The third possibility is that the observed variations are not intrinsic to the quasars but caused by some intervening process at lower redshift, such as gravitational microlensing." Althoueh this idea has been strouelv argued. (Παπίας1996).. there is an opposing view that variations du quasars are doniünate wi odnstabilities in the central accretion disc.," Although this idea has been strongly argued \citep{h96}, there is an opposing view that variations in quasars are dominated by instabilities in the central accretion disc." The reality of this moce of variability iu active ealactic wiclei is supported bw detailed observations of Sevtert ealaxies (Petersonetal.1999) alu eravitationallv lensed quasars (Ikundióοal. 1991).. where the preseuce of intrinsic variations cannot be in doubt.," The reality of this mode of variability in active galactic nuclei is supported by detailed observations of Seyfert galaxies \citep{p99} and gravitationally lensed quasars \citep{k97}, where the presence of intrinsic variations cannot be in doubt." The debate centres on whether this imechanisni is responsible for the long timescale large amplitude variations which dominate the power spectra discussed in this paper., The debate centres on whether this mechanism is responsible for the long timescale large amplitude variations which dominate the power spectra discussed in this paper. Taking the various argunieuts outlined above at face value. aud accepting the case against nücroleusimg. there does not appear to beo a satisfactory explanation for the abseuce of a time dilation effect in quasar power spectra.," Taking the various arguments outlined above at face value, and accepting the case against microlensing, there does not appear to be a satisfactory explanation for the absence of a time dilation effect in quasar power spectra." The arguments resting on an expanding Universe and cosmological distances for quasars secur bevoud challeuse., The arguments resting on an expanding Universe and cosmological distances for quasars seem beyond challenge. The argunent against iuicrolensiug ijs nof so secure., The argument against microlensing is not so secure. Apart from the statistical evidence from quasar light curves (Wawkins1996).. mucrolensing bas been unambieuously shown to take place in gravitationally lensed quasar systenis (Peltetal.1998).. aud dominates at long timescales.," Apart from the statistical evidence from quasar light curves \citep{h96}, microlensing has been unambiguously shown to take place in gravitationally lensed quasar systems \citep{p98}, and dominates at long timescales." If this were a general phenonmenou in quasars at cosmological distances then the apparent abseuce of a time dilation effect in quasar hight curves would be explained., If this were a general phenomenon in quasars at cosmological distances then the apparent absence of a time dilation effect in quasar light curves would be explained. I thank Cerson Coldhaber for a valuable sugecstion for the presentation of the data., I thank Gerson Goldhaber for a valuable suggestion for the presentation of the data. We now briefly discuss observations of several coronal IIXR aud continua 5-ray sources and consider whether ICS may play a role in the observed. emission.,We now briefly discuss observations of several coronal HXR and continuum $\gamma$ -ray sources and consider whether ICS may play a role in the observed emission. Observations of coronal continui ταν (200-800 keV) sources associated with three extremely powerful N-class flares were preseuted by?., Observations of coronal continuum $\gamma$ -ray (200-800 keV) sources associated with three extremely powerful X-class flares were presented by. . The flares occured ou 2003 October 28 (X17: disk ceuter). 2005 Jauuuv 20 (N71: WG1). and 2005. September 7 (2XlT: solar limb).," The flares occurred on 2003 October 28 $>$ X17; disk center), 2005 January 20 (X7.1; W61), and 2005 September 7 $>$ X17; solar limb)." Early in cach event. footpoiut —ciission dominated the coutimmim y-ray cuussion.," Early in each event, footpoint emission dominated the continuum $\gamma$ -ray emission." Later. duriug the (exponential) decay phase of the +-rayv cussion. the coronal sotree becanie iore proineunt than the footpoiut cussion.," Later, during the (exponential) decay phase of the $\gamma$ -ray emission, the coronal source became more prominent than the footpoint emission." The photon spectral index of the coronal source ireach case was signific:uitlv harder (6z 2) than that of the foot-point soirees (a23. 1)., The photon spectral index of the coronal source in each case was significantly harder $\alpha\approx 1.5-$ 2) than that of the foot-point sources $\alpha\approx 3-$ 4). The authors sugeest the coronal sources result from non-jcrmal bremissrahluug cuuission., The authors suggest the coronal sources result from non-thermal bremsstrahlung emission. The» photon spectral oeudices are ad. or near. the theoreticval Tait of Lerua bremsstralline cussion ac require a non-vernal electroi distribution with a ow-enerev cutoff DE.>1 MeV in all cases(?):5 see also SIL.," The photon spectral indices are at, or near, the theoretical limit of non-thermal bremsstrahlung emission and require a non-thermal electron distribution with a low-energy cutoff $E_c>1$ MeV in all cases; see also 4." Cüveu iat the electroji transit tine of MeV electrous is much shorter than their collisional loss time for typical coronal conditions in a flare. electron trapping is needed to xoduce the coronal source.," Given that the electron transit time of MeV electrons is much shorter than their collisional loss time for typical coronal conditions in a flare, electron trapping is needed to produce the coronal source." Iu the specific example of 1ο fare on 2005 January 20. suggest that svuchrotrou osses dominate electron energy losses aud the observed -rav cluission between 800 keV can be explained by wenisstrahlune cussion frou electrous with a energies >£O-—8 MeV. Tf the trap is stable. the cutissiou vecolmes thick-target aud the total energv iu >8 MeV eleetrous is estimated to be ~1075 eres.," In the specific example of the flare on 2005 January 20, suggest that synchrotron losses dominate electron energy losses and the observed $\gamma$ -ray emission between $-$ 800 keV can be explained by bremsstrahlung emission from electrons with a energies $>E_c=8$ MeV. If the trap is stable, the emission becomes thick-target and the total energy in $>8$ MeV electrons is estimated to be $\sim 10^{28}$ ergs." It should vc noted that while EED ciuission contributes to this oioton energy range (20% of the total ciission for he isotropic case) the net effect is to harden the photon spectrin somewhat., It should be noted that while EEB emission contributes to this photon energy range $\sim 20\%$ of the total emission for the isotropic case) the net effect is to harden the photon spectrum somewhat. Dowever. for a highlv anisotropic electron spectitmm EED could be respousible for a larger raction of the ουμπα οταν eniüssion for a favorable viewiues ecometry.," However, for a highly anisotropic electron spectrum EEB could be responsible for a larger fraction of the continuum $\gamma$ -ray emission for a favorable viewing geometry." ΑΙΑΠΟ considered the coutinuuni οταν Cluission roni the flare on 2005 .Runuuv 20., MM10 considered the continuum $\gamma$ -ray emission from the flare on 2005 January 20. Thev fud that ICS represents a viable alternative to bremsstrahhme Cluission iu the seuse that only a modest uumuber of ultra-relativistic clectrous are needed to account for the observed continu 5-1av source in terms of ICS., They find that ICS represents a viable alternative to bremsstrahlung emission in the sense that only a modest number of ultra-relativistic electrons are needed to account for the observed continuum $\gamma$ -ray source in terms of ICS. Iu particular. they estimate that as long as an (sotropic power-law) electron cucrey distribution function exteuds to >LOO MeV. a total of ~10°! clectrous with energies >0.5 MeV are sufficient to account for the source.," In particular, they estimate that as long as an (isotropic power-law) electron energy distribution function extends to $>100$ MeV, a total of $\sim 10^{31}$ electrons with energies $>0.5$ MeV are sufficient to account for the source." With a source volume of ~5«1025 ancl an ziibieut density of LOS 7. a umber deusity of just 200 > >0.5 AleV electron is needed. or a fraction of only 2&10 of the ambient electrous.," With a source volume of $\sim 5\times 10^{28}$ $^{-3}$ and an ambient density of $10^8$ $^{-3}$, a number density of just 200 $^{-3}$ $>0.5$ MeV electron is needed, or a fraction of only $2\times 10^{-6}$ of the ambient electrons." As noted in 822.1. an error in the analysis of MMIO resulted in over-optinüstic ICS enissivities.," As noted in 2.1, an error in the analysis of MM10 resulted in over-optimistic ICS emissivities." Our calculations lead to a revised estimate for the total ummber of electrons required to account for the observed οταν cluission reported bv for the 2005 January 20 flare that is a factor ~500 larger (10? cj 2) which. if the electron cnerey distribution indeed exteuds continuously to 100 MeV miplies a fraction of of the ambient electrous are accelerated to high energies.," Our calculations lead to a revised estimate for the total number of electrons required to account for the observed $\gamma$ -ray emission reported by for the 2005 January 20 flare that is a factor $\sim 500$ larger $10^5$ $^{-3}$ ) which, if the electron energy distribution indeed extends continuously to $\sim 100$ MeV implies a fraction of of the ambient electrons are accelerated to high energies." If the electrous respousible for the emission are rapped near the loop top. they will have a pancakxe-ike anisotropy which. as shown iu 8323 requires fewer clectrous for a favorable viewing ecometry.," If the electrons responsible for the emission are trapped near the loop top, they will have a pancake-like anisotropy which, as shown in 3 requires fewer electrons for a favorable viewing geometry." If this is the case. the required number of electrons can perhaps he reduced to ὃς104 ? electrous. again normedized oa reference enerev of 0.5 MeV. As noted above. IKkrucker et al.," If this is the case, the required number of electrons can perhaps be reduced to $-2\times 10^4$ $^{-3}$ electrons, again normalized to a reference energy of $0.5$ MeV. As noted above, Krucker et al." fiud that the energy coutent of the electrons 2E.=8 MeV needed to account or the observed emission in terms of bremsstrahhime emission is ~1075 oves in total, find that the energy content of the electrons $>E_c=8$ MeV needed to account for the observed emission in terms of bremsstrahlung emission is $\sim\!10^{28}$ ergs in total. The implied umuber of cucrectic clectrons required to account for the source, The implied number of energetic electrons required to account for the source and by Swiss National Foundation (SNSF) grant PBEZ2-108928.,and by Swiss National Foundation (SNSF) grant PBEZ2-108928. " We would like to thank the anonymous referee for his constructive comments.RHESSL,(XRT),,GOES,, FOXSI."," We would like to thank the anonymous referee for his constructive comments., ." ". Using Kramers’ simplified differential bremsstrahlung cross-section Q(e,E)=Z?52&eE in Eq. (4)),"," Using Kramers' simplified differential bremsstrahlung cross-section $Q(\varepsilon, E)=\bar{Z}^2\frac{\kappa_{BH}}{\epsilon E}$ in Eq. \ref{eq:int}) )," " one arrives at: Where Z? z1.44 in the corona, &gg—$ ar?m.c?=7.9x10-” cm? keV, B(x,a,b) is the incomplete beta function, and: Similar to Brown, 2002, except that we provide for the emission below the low-energy cutoff."," one arrives at: Where $\bar{Z^2}\approx$ 1.44 in the corona, $\kappa_{BH}$ $\frac{8}{3} \, \alpha \, r_e^2 \, m_ec^2$ $\times$ $^{-25}$ $^2$ keV, $B(x,a,b)$ is the incomplete beta function, and: Similar to Brown, 2002, except that we provide for the emission below the low-energy cutoff." " In the absence of low-energy cutoff E—0), or at least as long as £?>E2—2KN, we have: where B(a,b) is the Beta function."," In the absence of low-energy cutoff $E_1$ =0), or at least as long as $\varepsilon^2 \ge E_1^2-2KN$, we have: where $B(a,b)$ is the Beta function." " Le. the emissivity at a certain photon energy ε is constant along the path of the beam, until u decreases to #1, i.e. e&V2KN, after which it falls rapidly with increasing N, as shown in Fig. 7.."," I.e. the emissivity at a certain photon energy $\varepsilon$ is constant along the path of the beam, until $u$ decreases to $\approx$ 1, i.e. $\varepsilon \approx \sqrt{2KN}$, after which it falls rapidly with increasing $N$, as shown in Fig. \ref{fig:dI_dN}." Using the Kramers cross-section however does not yield a wholly accurate photon spectrum for e1000$, implying that the metagalactic radiation field exhibits inhomogeneities at the scale of $\simeq1$ Mpc \citealt{Reimers04,Shull04,Zheng04b}) )." There is also some evidence for an anti-correlation between 5 and the density of the absorbers (Reimersetal.2004:Shull 2004)).," There is also some evidence for an anti-correlation between $\eta$ and the density of the absorbers \citealt{Reimers04,Shull04}) )." Semi-analvtical mocdels. (Lleapetal.2000:Smettect 2002)) suggest that a soft. UVB with a significant. stellar contribution is required. to. reproduce the high opacity regions (7> 200). while the observed opacity gaps (η<100) have been attributed to hard sources near the line-of-sight creating pockets of highly. ionized. helium.," Semi-analytical models \citealt{Heap00,Smette02}) ) suggest that a soft UVB with a significant stellar contribution is required to reproduce the high opacity regions $\eta>200$ ), while the observed opacity gaps $\eta<100)$ have been attributed to hard sources near the line-of-sight creating pockets of highly ionized helium." The small-scale variations in a could also be attributed to a spread in QSO spectral indices Clelferetal.2002:Scott 2004)). local density variations Miralda-Iscudéetal.2000) ). finite QSO lifetimes (Reimersetal. 2005b)). intrinsic absorption within the nuclei of active galaxies. (Jalkobsenοἱal.2003:Shulletal. 2004)) or the filtering of QSO radiation by radiative transfor elfects (Shulletal.2004:Maselli&Ferrara 2005)).," The small-scale variations in $\eta$ could also be attributed to a spread in QSO spectral indices \citealt{Telfer02,Scott04}) ), local density variations \citealt{MiraldaEscude00}) ), finite QSO lifetimes \citealt{Reimers05b}) ), intrinsic absorption within the nuclei of active galaxies \citealt{Jakobsen03,Shull04}) ) or the filtering of QSO radiation by radiative transfer effects \citealt{Shull04,Maselli05}) )." Llowever. the exact nature of these fluctuations and. their interpretation is unclear.," However, the exact nature of these fluctuations and their interpretation is unclear." In this paper we use realistic and forest spectra. constructed from. state-of-the-art. hvedrodynamical simulations of a Universe. to test. the reliability of using line profile fitting techniques to infer the UVB softness parameter. defined as the ratio of the rand metagalactic ionization. rates. S=Lug.," In this paper we use realistic and forest spectra, constructed from state-of-the-art hydrodynamical simulations of a Universe, to test the reliability of using line profile fitting techniques to infer the UVB softness parameter, defined as the ratio of the and metagalactic ionization rates, $S=\Gamma_{\rm HI}/\Gamma_{\rm HeII}$." We obtain improved. estimates of the UVB softness parameter and its uncertainty using published estimates of the and forest. opacity., We obtain improved estimates of the UVB softness parameter and its uncertainty using published estimates of the and forest opacity. We concentrate on the redshill range 2.«zz<3 where the Hluctuations of the mean opacity are still moderate ancl reionization is probably mostly complete., We concentrate on the redshift range $2πι iv imaginary tine 7=J/AL. where J=l/kgT aud Af is called the Trotter umber.," According to the Feynman path integral formulation of the quantum statistical mechanics \citep{Fey72} the partition function of interacting distinguishable particles is given by the trace of the density matrix $\hat{\rho}(\beta) = e^{-\beta\hat{H}}$ as where the action $S(R_{i},R_{i+1};\tau)$ is taken over the path $R_{i} \rightarrow R_{i+1}$ in imaginary time $\tau = \beta/M$, where $\beta = 1/k_{\text{B}}T$ and $M$ is called the Trotter number." " The trace implies a closed path (Ra,= Ry).", The trace implies a closed path $R_{M}=R_{0}$ ). For simulation we use the pair approximation iu the action (Storer1968:Ceperley1995). for the Coulomb interaction of charges.," For simulation we use the pair approximation in the action \citep{Storer68,Ceperley95} for the Coulomb interaction of charges." This is exact iu the lait AMoo»xe however. chemical accuracy is reached with sufficieutlv large AL. ic. 1l enough 7.," This is exact in the limit $M\rightarrow\infty$, however, chemical accuracy is reached with sufficiently large $M$, i.e. small enough $\tau$." Samplingiu the configuration space {AR} in NWT euseiible is carried out using the Metropolis aleorithin (Aletropolisc£a£1953) with bisection moves and displaceiieut moves (Chakravartyctal.1998).," Sampling in the configuration space $\{ R_i \}_i^\infty$ in $NVT$ ensemble is carried out using the Metropolis algorithm \citep{Metro53} with bisection moves and displacement moves \citep{Chakravarty98}." . The total energy is calculated using the virial estimator (Ποιαctαἱ.1982)., The total energy is calculated using the virial estimator \citep{Herman82}. . The error estimate in the PIAIC scheme is commonly eivon in powers of the imaecinary time time-step 7 (Ceperley1995)., The error estimate in the PIMC scheme is commonly given in powers of the imaginary time time-step $\tau$ \citep{Ceperley95}. .. Therefore. in order to systematically determine the thermal effects on the svstem we have carried out all the simulatious with 7=0.ES. where Ly denotes the wut of ILutrec.," Therefore, in order to systematically determine the thermal effects on the system we have carried out all the simulations with $\tau = 0.03 E_\text{H}^{-1}$, where $E_\text{H}$ denotes the unit of Hartree." Thus. the temperatures aud the Trotter number AL are related by T—(kgMr) *. where kp is the Boltzmann constant.," Thus, the temperatures and the Trotter number $M$ are related by $T=(k_{\text{B}}M\tau)^{-1}$ , where $k_{\text{B}}$ is the Boltzmann constant." " Iu the following we mainly use the atomic units. where the leneths. energies and iuasses are given in the uuits of Bola radius (αμ). Hartree (Eg) aud free electron mass (84). respectively,"," In the following we mainly use the atomic units, where the lengths, energies and masses are given in the units of Bohr radius $a_0$ ), Hartree $E_\text{H}$ ) and free electron mass $m_\text{e}$ ), respectively." " Thus. for the mass of the electrons we take m.= and for the protons nn,ου.107,5..."," Thus, for the mass of the electrons we take $m_\text{e}=1$ and for the protons $m_\text{p} = 1.83615267248\times 10^{3}m_\text{e}$." Conversion of the units of energv is given by Ej=219171.63L3705em|z27.2 eV. aud correspoudingly. Ay=3.1668152«10ον|.," Conversion of the units of energy is given by $E_\text{H} = 219474.6313705\text{cm}^{-1} \approx 27.2$ eV, and correspondingly, $k_{\text{B}} = 3.1668152\times 10^{-6} E_\text{H} \rm{K}^{-1}$." The statistical standard error of the mean (SEM) with 2SEM limits is used as au error estimate for the evaluated observables.," The statistical standard error of the mean (SEM) with $2\, $ SEM limits is used as an error estimate for the evaluated observables." " For the NVT siumlations we place one Πω ion. ο, three protons aud two electrons. iuto a cubic box aud apply periodic boundary conditions aud the miüiuimuiuu iuaee principle."," For the $NVT$ simulations we place one $_3^+$ ion, i.e. three protons and two electrons, into a cubic box and apply periodic boundary conditions and the minimum image principle." The simulations are performed in tlicο different super cell(box) volumes: (300600y. (10004)? and (5044)?," The simulations are performed in three different super cell (box) volumes: $(300a_0)^3$, $(100a_0)^3$ and $(50a_0)^3$." " These correspond to the mass densities of ~1.255«105ean3 x2.988«10""open aud ~2710SUE respectively,"," These correspond to the mass densities of $\sim 1.255\times 10^{-6}~\rm{gcm}^{-3}$, $\sim 3.388\times 10^{-5}~\rm{gcm}^{-3}$ and $\sim 2.710\times 10^{-4}~\rm{gcm}^{-3}$, respectively." The deusitv has no essential effect at low T. where dissociation rarely takes place.," The density has no essential effect at low $T$, where dissociation rarely takes place." At higher T. however. the fiute density gives vise to the molecular recombination baancing the more frequent dissociation.," At higher $T$, however, the finite density gives rise to the molecular recombination balancing the more frequent dissociation." It should be pointed out that application of the Wun nuage principle with ouly one molecular ion in the periolic super cel lua both give rise to the finite- effects aud also disccard 1ueher density distribution effects. Le. yagiueuts of SOVCEal ious in the simulation box.," It should be pointed out that application of the minimum image principle with only one molecular ion in the periodic super cell may both give rise to the finite-size effects and also disregard higher density distribution effects, i.e. fragments of several ions in the simulation box." Thus. the lower theLens itv the beter woe ΠΜ2ο the finite-size effects. w.πο in this work are uceligihle. if not absent.," Thus, the lower the density the better we minimize the finite-size effects, which in this work are negligible, if not absent." The zero density lmit cannot be reached due to the finite T., The zero density limit cannot be reached due to the finite $T$. To avoid all these ambiguitics we define our targets as molecular energeties. molecular partition function aud other related molecular quantities.," To avoid all these ambiguities we define our targets as molecular energetics, molecular partition function and other related molecular quantities." Therefore. iu the following. we also exclude the trivial contribution from the center-of-mass thermal dvuamics aud cucrey 2hyT to the molecular quantities.," Therefore, in the following, we also exclude the trivial contribution from the center-of-mass thermal dynamics and energy $\tfrac{3}{2}\kB T$ to the molecular quantities." The nuclear quanti dyvuauics. which was shown to be essential at low T. turus out to be neglieible at higher temperatures.," The nuclear quantum dynamics, which was shown to be essential at low $T$, turns out to be negligible at higher temperatures." It is included. however. to be cousistent with the low temperature results aud our earlier study.," It is included, however, to be consistent with the low temperature results and our earlier study." For more details about the model aud a discussion about the here neglected coutribution from the exchange interaction see KvlaupaaandRautala(2010).., For more details about the model and a discussion about the here neglected contribution from the exchange interaction see \cite{Kylanpaa10jcp}. In Fie., In Fig. 1 the .NVT total energv (canonical euseuible internal energy) of the IT. ion aud its fragments is shown as d function of temperature., \ref{Fig1} the $NVT$ total energy (canonical ensemble internal energy) of the $_3^+$ ion and its fragments is shown as a function of temperature. The molecular euergv does not include the ceuter-of-nass translational kinetic euerev 2hgsT., The molecular energy does not include the center-of-mass translational kinetic energy $\tfrac{3}{2}\kB T$. The data from simulations are given as circles. Squares aud triaueles correspouding to the tbree densities.," The data from simulations are given as circles, squares and triangles corresponding to the three densities." The PIMC data is also given in Tables 1. aud 2., The PIMC data is also given in Tables \ref{Table1} and \ref{Table2}. ", The solid lines at To«1000 I& are fitted to analvtical model forms but at higher temperatures lines are for euiding the eve. only."," The solid lines at $T < 4000$ K are fitted to analytical model forms but at higher temperatures lines are for guiding the eye, only." Our low temperature fit and analytical model. Eq.(," Our low temperature fit and analytical model, Eq.," 7).. is given as a blue dashed line and is discussed in the next sections in more detail, is given as a blue dashed line and is discussed in the next sections in more detail. For conrparisou the enereics from the fitted partition function of NealeandTenuvsou(1995). is shown as black dots., For comparison the energies from the fitted partition function of \cite{Neale95ApJ} is shown as black dots. These two do not manifest dissociation. and therefore. are not relevant at “higher 7.," These two do not manifest dissociation, and therefore, are not relevant at ""higher $T$ ""." The horizoutal dash-dotted lines show the zero IKclviu energies for the ion and its fragments inEq., The horizontal dash-dotted lines show the zero Kelvin energies for the ion and its fragments in. "(2).. One of these lines prescuts the energv for the ""barrier to luearitv. ic. the energv needed for the transformation to linear molecular ecometry."," One of these lines presents the energy for the ""barrier to linearity"", i.e. the energy needed for the transformation to linear molecular geometry." It is also seen to be roughly the barrier to dissociation within the considered molecular deusities., It is also seen to be roughly the barrier to dissociation within the considered molecular densities. Above 1000 IX the density dependence is clearly secu as varviug composition of fragmeuts., Above $4000$ K the density dependence is clearly seen as varying composition of fragments. In the range from 1000to 10000 I& the changing dissociation recombination balauce leads to distinctly different enereeties. aud above that. at our highest simulation temperatures the thermal ionization of hydrogen atoms starts contributiug to the energv.," In the range from $4000$to $10000$ K the changing dissociation recombination balance leads to distinctly different energetics, and above that, at our highest simulation temperatures the thermal ionization of hydrogen atoms starts contributing to the energy." " However, it is worth pointing out that the teirperature limits of these three ranges. ie. O0—1000 "," However, it is worth pointing out that the temperature limits of these three ranges, i.e. $0-4000$ " Neither distances. nor even redshifts (including photometric ones) are currently measured lor the whole 2\IASS NSC (although some attempts are being made regarding photo-z's. see ?. and ?)).,"Neither distances, nor even redshifts (including photometric ones) are currently measured for the whole 2MASS XSC (although some attempts are being made regarding $z$ 's, see \citealt{Jar04} and \citealt{FraPea}) )." We ihus need to deduce effective distances of galaxies from their fluxes. with the use of the luminosity function (LF) in the A band.," We thus need to deduce effective distances of galaxies from their fluxes, with the use of the luminosity function (LF) in the $K$ band." " If all the galaxies had the same luminosity. sav L,. the relation between the observed fIux 5 and distance r would be straightlorward: r=yL,/4x5."," If all the galaxies had the same luminosity, say $L_*$, the relation between the observed flux $S$ and distance $r$ would be straightforward: $r=\sqrt{L_*\slash 4\pi S}$." However. galaxies have different morphologies. masses and luminosities. aud obviously their LF is not a Dirac’s delta (on the contrary. it is verv broad).," However, galaxies have different morphologies, masses and luminosities, and obviously their LF is not a Dirac's delta (on the contrary, it is very broad)." " Therefore an estimated cdistauce of a galaxy with a given fIux must have a scatter,", Therefore an estimated distance of a galaxy with a given flux must have a scatter. Constructing (he estimator. a first choice could be the conditional mean. tthe expectation value for r given 5.," Constructing the estimator, a first choice could be the conditional mean, the expectation value for $r$ given $S$." Instead. we think that it is better to choose the conditional [or reg (a median value of distance given the flux).," Instead, we think that it is better to choose the conditional for $r_\mathrm{eff}$ (a median value of distance given the flux)." We consider it being more adequate to our problem: the same number of galaxies with a given [hix have distances smaller and greater than the mecian., We consider it being more adequate to our problem: the same number of galaxies with a given flux have distances smaller and greater than the median. " Detailed calculations. presented in Appendix ?? (see also 2)). show that for the A band LF as given by ον, aa Sehechter [unction (7). with M,=—23.83+blogh£0.03 and à=—1.1640.04. (his effective distance for the magnitude Jy equals to This proxy of distance is used in Figure 2.. which dillers from Figure 1. by a different scaling of {he r-axis."," Detailed calculations, presented in Appendix \ref{App:r_eff} (see also \citealt{Pe93}) ), show that for the $K$ band LF as given by \cite{6dF_Fi}, a Schechter function \citep{Sche} with $M_*=-23.83+5\log h\pm0.03$ and $\alpha=-1.16\pm0.04$, this effective distance for the magnitude $K$ equals to This proxy of distance is used in Figure \ref{Fig:growth.r}, which differs from Figure \ref{Fig:growth.N} by a different scaling of the $x$ -axis." The growth of the clustering dipole up to the completeness limit of the 2\IASS XSC is now evident., The growth of the clustering dipole up to the completeness limit of the 2MASS XSC is now evident. Additionally. note that the growth has an essentially constant slope for rar>150 Mpc/h. Ix;>12 mag.," Additionally, note that the growth has an essentially constant slope for $r_\mathrm{eff}>150\Mpch$ , $K_s>12$ mag." An interesting feature is the behavior of the Galactic Cartesian components of the dipole., An interesting feature is the behavior of the Galactic Cartesian components of the dipole. The and z ones are virtually constant lor reg>150Mpc/h: however. the y component still erows even al the limit of the catalog. similarly as does the total amplitude.," The $x$ and $z$ ones are virtually constant for $r_\mathrm{eff}>150\Mpch$; however, the $y$ component still grows even at the limit of the catalog, similarly as does the total amplitude." This could point to some systematic effect. related to masking and filling of the Zone of Avoidance.," This could point to some systematic effect, related to masking and filling of the Zone of Avoidance." We have however checked (hat. the sanie qualitative behavior of the three components is observed [or different shapes of the mask and the way it is filled: what is more. the effect exists even if we calculate the dipole having removed [rom the catalog all the galaxies with |b]<10 (leaving the resulting strip completely devoid of galaxies).," We have however checked that the same qualitative behavior of the three components is observed for different shapes of the mask and the way it is filled; what is more, the effect exists even if we calculate the dipole having removed from the catalog all the galaxies with $|b|<10\dgr$ (leaving the resulting strip completely devoid of galaxies)." We have also observed that adding to the sample the LGA galaxies that were not present in our catalog has virtually no influence on theamplitude of the dipole ancl only slightly changes the values, We have also observed that adding to the sample the LGA galaxies that were not present in our catalog has virtually no influence on theamplitude of the dipole and only slightly changes the values The X-ray source AX 2315.592 (CP Lue) was cliscovered by Alisaki et al (1995) usingA data.,The X-ray source AX J2315–592 (CP Tuc) was discovered by Misaki et al (1995) using data. Follow up observations by Thomas Reinsch (1995) iclentified! the optical counterpart (V ~17) and suggested it was a polar (or XM Ler) svstem., Follow up observations by Thomas Reinsch (1995) identified the optical counterpart $V\sim$ 17) and suggested it was a polar (or AM Her) system. These are cataclysmic variables - CVs - in which the accreting white dwacl has a sulliciently strong magnetic field to lock the spin of the white dwarf into svachronous rotation with the binary orbital period., These are cataclysmic variables - CVs - in which the accreting white dwarf has a sufficiently strong magnetic field to lock the spin of the white dwarf into synchronous rotation with the binary orbital period. Ifthe photometric variation of SO min is attributed to its orbital period (Alisaki et al 1996). then this would place it at the shorter end. of the polar orbital period distribution.," If the photometric variation of 89 min is attributed to its orbital period (Misaki et al 1996), then this would place it at the shorter end of the polar orbital period distribution." CP Tue shows a prominent dip which in X-rays lasts approximately half the orbital evele (Misaki et al 1996)., CP Tuc shows a prominent dip which in X-rays lasts approximately half the orbital cycle (Misaki et al 1996). Misaki et al suggested that this clip is caused by the accretion stream far from the white dwarl obscuring our line of sight tothe bright aceretion region since the dip was deeper in soft X-ravs compared to hard. N-ravs., Misaki et al suggested that this dip is caused by the accretion stream far from the white dwarf obscuring our line of sight to the bright accretion region since the dip was deeper in soft X-rays compared to hard X-rays. In all other polars where absorption dips are seen in hard. N-ravs. they are visible for only ~0.1 of a evele.," In all other polars where absorption dips are seen in hard X-rays, they are visible for only $\sim$ 0.1 of a cycle." In some of the polars which show these hard X-rays clips. a much broader dip is also seen in the EUV these broader dips are thought to be due to the aceretion column obscuring the acerction region anc have not. been seen in hard X-ravs.," In some of the polars which show these hard X-rays dips, a much broader dip is also seen in the EUV – these broader dips are thought to be due to the accretion column obscuring the accretion region and have not been seen in hard X-rays." One of the defining properties of polars is their high level of polarisation., One of the defining properties of polars is their high level of polarisation. “Vo confirm the polar nature of CP ‘Tuc we have obtained the first optical polarimetric data of this source., To confirm the polar nature of CP Tuc we have obtained the first optical polarimetric data of this source. To complement these data and to determine the nature of the dip feature we obtained: quasi-simultaneous A-rav data using theRNY satellite (Brac. Rothschile. Swank 1993).," To complement these data and to determine the nature of the dip feature we obtained quasi-simultaneous X-ray data using the satellite (Bradt, Rothschild, Swank 1993)." The most prominent feature of the X-ray light curve is the deep cip first noted in data by Misaki ct al (1996)., The most prominent feature of the X-ray light curve is the deep dip first noted in data by Misaki et al (1996). We use this dip to derive an precise ephemeris for CP Tuc using data from which is in the public archive (CIS: 0.5]2keV) (Misakl et al 1996).SAN CMECS: 1.10keV) and (120keV) (both Wheatley. in prep).," We use this dip to derive an precise ephemeris for CP Tuc using data from which is in the public archive (GIS: 0.5–12keV) (Misaki et al 1996), (MECS: 1–10keV) and (1–20keV) (both Wheatley, in prep)." Since the data obtained using anc are described elsewhere we will not cliscuss them in any detail here., Since the data obtained using and are described elsewhere we will not discuss them in any detail here. There are several issucs with the Toe-in imetlocl. one of the principal being vertical parallax due to τουςome.,"There are several issues with the Toe-in method, one of the principal being vertical parallax due to keystoning." Because the projections are taken at an anele. successive planes perpendicular to the viewer will o μοντ] distorted.," Because the projections are taken at an angle, successive planes perpendicular to the viewer will be slightly distorted." The distortion is inverted iu he LIIS and RIS images., The distortion is inverted in the LHS and RHS images. As a result. when mereine he two images. there will be a mismatch in the outer volts. rosIting ina blurred nage.," As a result, when merging the two images, there will be a mismatch in the outer points, resulting in a blurred image." It should be noted hat kevstonius is closely related to the distance of the camera tot16 object. and is more inportait when beige close from the 3D scene.," It should be noted that keystoning is closely related to the distance of the camera to the object, and is more important when being close from the 3D scene." The second issue with the Toc-in inetrod lies in the fact that the eves will have to adjust from a convergent to a divergeit position iu order to scan the depth dimension., The second issue with the Toe-in method lies in the fact that the eyes will have to adjust from a convergent to a divergent position in order to scan the depth dimension. For extended objects this can result in strone discomfort for the viewers. and even an impossibility to merec the oft and right nuages if the couvergine/diverging anele )oconies TOO iuportaut.," For extended objects this can result in strong discomfort for the viewers, and even an impossibility to merge the left and right images if the converging/diverging angle becomes too important." Woodsetal.(1993) discuss the various distortions preseut in stereo pairs in great details. and we refer the interested reader to his article for more cdetails.," \cite{Woods93} discuss the various distortions present in stereo pairs in great details, and we refer the interested reader to his article for more details." The Offset (or Off-axis) method addresses aux solves the problems of the Toc-in projection. aud is in that SOLIS soluetimes considered to he iorecorrect.," The Offset (or Off-axis) method addresses and solves the problems of the Toe-in projection, and is in that sense sometimes considered to be more." m this case. the LIIS and ROS look at he 3D scene 111 pualel directions. aud offset oa distance g.," In this case, the LHS and RHS look at the 3D scene in parallel directions, and offset by a distance $\eta$." This imetlkxl does not create auv kevstoniusB. aud ensures that tl1ο eves remain diu the same )osition when scanning the cepth dimension of he LOCCustructed 3D picture.," This method does not create any keystoning, and ensures that the eyes remain in the same position when scanning the depth dimension of the reconstructed 3D picture." An ilustration of the nethod is shown in Fig. 2.., An illustration of the method is shown in Fig. \ref{fig:view}. One o the inherent drawYC. x50 this inethod is that the ouside regions of the LUS and RUS fields do not overlap - aud hence must be ake1 off the final nuage., One of the inherent drawbacks of this method is that the outside regions of the LHS and RHS fields do not overlap - and hence must be taken off the final image. Choosing between the Toc-in aud he Offset iuiethod to create sereo pairs is entirely 1p te» the creator of the pair., Choosing between the Toe-in and the Offset method to create stereo pairs is entirely up to the creator of the pair. As we will discuss in he next Section. the Toe-in uecthod can provide οχος‘lent stereo pairs under certain circuustamces the sOCTO) pairs shown in Fig.," As we will discuss in the next Section, the Toe-in method can provide excellent stereo pairs under certain circumstances; the stereo pairs shown in Fig." 1 ive for example con created usine the Toc-in projection 1nethod. an doin the Biochemistry literature. lualiv torials describing the creation of stereo pairs use the Toc-in uctrod (6.8.Tavinan1987:Robinson1989:Stocποτ1001:BerryandBaker 2010).," \ref{Fig:para_cross_sphere} have for example been created using the Toe-in projection method, and in the Biochemistry literature, many tutorials describing the creation of stereo pairs use the Toe-in method \citep[e.g.][]{Hayman87,Robinson89,Stockert94,Berry10}." . Furthermore. nues. itrημας Dluitations of the software or progranumuiug laneswee used to create the stereo pair müeht require a trace-off between feasibility and quality. as we wiIl show in Sec. ??..," Furthermore, sometimes, intrinsic limitations of the software or programming language used to create the stereo pair might require a trade-off between feasibility and quality, as we will show in Sec. \ref{Sec:tools}." The last step recmired to construct a stereo pair consists iu placing he LIIS aud RUS images sice-by-xdes, The last step required to construct a stereo pair consists in placing the LHS and RHS images side-by-side. The distauce between the two images is nof critical., The distance between the two images is not critical. This reflect the fact that the imterpupillary distance is not unifori across the population. but varies with aee. eeuder. aud race.," This reflect the fact that the interpupillary distance is not uniform across the population, but varies with age, gender, and race." Specifically. Dodgson(2001) mentions a mcan iuterpupilhuw distawe of 63 mun or adults. with the vast majority bug within a το nuu raice.," Specifically, \cite{Dodgson04} mentions a mean interpupillary distance of 63 mm for adults, with the vast majority lying within a 50-75 mm range." Iu this articleawe have used point-to-)olut separations ()otwoeen tre LOS ane RUS images) rangiue from 3.5Π €u to ὉΠ cuni clepending on the stereo dr. andi ina uatter of per‘sonal opinion as to which value is most comfortable.," In this article, we have used point-to-point separations (between the LHS and RHS images) ranging from 3.5 cm to 5 cm depending on the stereo pair, and it is a matter of personal opinion as to which value is most comfortable." Iicreasiue the imnter-nuage distance aOVE 6 cimi is not advisable. as the stereo xür nieht become harder to visualize for people with a smaller iuterpupilary distaice than average.," Increasing the inter-image distance above 6 cm is not advisable, as the stereo pair might become harder to visualize for people with a smaller interpupillary distance than average." For screo pairs to be recognized as a valuable tool bv the Astrophysics community requires them to be extremely easy to create. maplemient and link to the data set.," For stereo pairs to be recognized as a valuable tool by the Astrophysics community requires them to be extremely easy to create, implement and link to the data set." Let us consider the 3D data set used to produce Fie. 1..," Let us consider the 3D data set used to produce Fig. \ref{Fig:para_cross_sphere}," which can dxοσα as a cloud of points in 3D space., which can be seen as a cloud of points in 3D space. There exist many methods in order to easilv produce stereo pairs fixma such a data cube. aud it woul be minposside to list hem all here.," There exist many methods in order to easily produce stereo pairs from such a data cube, and it would be impossible to list them all here." Some conmnuniercal software οςσος ean prodice stereo pars with a single mouse click - the stereo vais shown iu Sec., Some commercial software packages can produce stereo pairs with a single mouse click - the stereo pairs shown in Sec. " 77 were for example procuced with the ""CTware.", \ref{Sec:Alex} were for example produced with the software. Alternatively. many scientists rave developed their own software. specifically tailored to their OW. data type and Orla," Alternatively, many scientists have developed their own software, specifically tailored to their own data type and format." Such ¢ustomized or conuuerclal software are caoible of creating excellent stereo urs. and are usually designed well enough not to have too steep learning cülurves.," Such customized or commercial software are capable of creating excellent stereo pairs, and are usually designed well enough not to have too steep learning curves." Tere. we prorose an alterniitive. off-the-shelf. efficieutl way to produce stereo pairs using he programing languageON.," Here, we propose an alternative, off-the-shelf, efficient way to produce stereo pairs using the programming language." . This method. which we will refer to as he (STi) is based on our own experiucutatiojo ancl ds extremely sraiehttorwar¢ to iuplemieut. even for people with litle/uo experience with tis language.," This method, which we will refer to as the (sTi) is based on our own experimentation, and is extremely straightforward to implement, even for people with little/no experience with this language." Furthermore. creating stereo pairs with erauts access to a large collection of non-plottiug modules to work ou the data cube beforchand.," Furthermore, creating stereo pairs with grants access to a large collection of non-plotting modules to work on the data cube beforehand." This provies the more advanced user witla the freedom to potentially redice. sort. fif and clean the data set before creating a stereo pair - a strong advantage as conrparec to οςununercal software which often requires specific put. :uid does not enable direct data interaction.," This provides the more advanced user with the freedom to potentially reduce, sort, fit and clean the data set before creating a stereo pair - a strong advantage as compared to commercial software which often requires specific input, and does not enable direct data interaction." Qur sTi method is used ou the Tocdnu projection deseribed previously. 11 taccotuts for current laitation in the plotting nodule. iu which several projection parameters are currently hx-coded aud," Our sTi method is based on the Toe-in projection described previously, but accounts for current limitation in the plotting module, in which several projection parameters are currently hard-coded and" ΙΟ (?).. the bound density maximum algorithin (BDAL) (7). and SKID (see http ref: http:WAhpec.astro.washington.edu/tools).,"(HFOF) \citep*{gott}, the bound density maximum algorithm (BDM) \citep{kly}, and SKID (see http ref: http://www-hpcc.astro.washington.edu/tools)." Each of these algorithms has its own advantages and weaknesses. so that arguably none of them is completely satisfactory vet.," Each of these algorithms has its own advantages and weaknesses, so that arguably none of them is completely satisfactory yet." In this work. we use the algorithm: proposed. by 2)... which combines ideas used in other group finding techniques with a topological approach for finding substructure candidates.," In this work, we use the algorithm proposed by \citet{volker2}, which combines ideas used in other group finding techniques with a topological approach for finding substructure candidates." " can handle haloes of arbitrary shape. does not require an iterative procedure. for. finding. subhalo candidates. and is capable of detecting arbitrary levels of ""subhalos within subhalos'."," can handle haloes of arbitrary shape, does not require an iterative procedure for finding subhalo candidates, and is capable of detecting arbitrary levels of `subhalos within subhalos'." ln this section. we briclly sumnmarise how the method works.," In this section, we briefly summarise how the method works." In a [first step. a standard: friends-of-[riends. (FOE) algorithm is used το icentify virialized parent haloes.," In a first step, a standard friends-of-friends (FOF) algorithm is used to identify virialized parent haloes." The FOR algorithm links together all particle pairs with separation less than a linking length b., The FOF algorithm links together all particle pairs with separation less than a linking length $b$ . We adopt the standard. value 6=0.2. in. units of the mean particle separation. which selects. groups of particles with overdensities close to the value precictecd by the spherical collapse model for the virialized regions of haloes.," We adopt the standard value $b=0.2$ in units of the mean particle separation, which selects groups of particles with overdensities close to the value predicted by the spherical collapse model for the virialized regions of haloes." The next step is to compute an estimate of the local density at the position of cach particle in the group., The next step is to compute an estimate of the local density at the position of each particle in the group. To this end. we employ an adaptive kernel interpolation method similar to the one used in smoothed. particle hyvdrodynamics.," To this end, we employ an adaptive kernel interpolation method similar to the one used in smoothed particle hydrodynamics." In the resulting clensity field. we define ascandidates locally overdense regions which are enclosed by isocdensity contours that traverse a saddle point.," In the resulting density field, we define as locally overdense regions which are enclosed by isodensity contours that traverse a saddle point." Our method for finding these regions can be visualisecl as follows: we reconstruct. the density. field. by considering particles in order of decreasing density. thus working our way from high to low density.," Our method for finding these regions can be visualised as follows: we reconstruct the density field by considering particles in order of decreasing density, thus working our way from high to low density." This corresponds to gradually lowering a global threshold in the density Ποια sampled by the simulation particles., This corresponds to gradually lowering a global threshold in the density field sampled by the simulation particles. Isolated overdense regions grow slowly in size during this process., Isolated overdense regions grow slowly in size during this process. When two such separate regions coalesce to form a single region. their density contours join at a saddle point.," When two such separate regions coalesce to form a single region, their density contours join at a saddle point." Each time such an event occurs. we have found two substructure canicliclates.," Each time such an event occurs, we have found two substructure candidates." " After the regions containing substructure candidates have been identified. we apply an unbinding procedure where we Lloratively reject all particles with positive total energy in order to eliminate ""background! particles that do not belong to the subhalo."," After the regions containing substructure candidates have been identified, we apply an unbinding procedure where we iteratively reject all particles with positive total energy in order to eliminate `background' particles that do not belong to the subhalo." For the purposes of this study. we consider all substructures that survive this unbinding procedure. and still have at least LO self-bound particles. to be genuine subhalos.," For the purposes of this study, we consider all substructures that survive this unbinding procedure, and still have at least $10$ self-bound particles, to be genuine subhalos." In summary. the algorithm: cdecomposes a given particle group into a set of disjoint and. sell-bound substructures. each of which is identified as a locally overdense region in the density field of the background halo.," In summary, the algorithm decomposes a given particle group into a set of disjoint and self-bound substructures, each of which is identified as a locally overdense region in the density field of the background halo." Note that classifies all the particles inside a FOL eroup either as belonging to a bound substructure or as being unbound., Note that classifies all the particles inside a FOF group either as belonging to a bound substructure or as being unbound. Phe selt-bhound part of the FOL background halo itself will then also appear in the substructure List., The self-bound part of the FOF background halo itself will then also appear in the substructure list. We will exelude it when referring to subhalos or substructures in the following analysis., We will exclude it when referring to subhalos or substructures in the following analysis. The sample of parent haloes used. for studsing the mass function analysis consists of 6. 5. 34 ancl 100 haloes in the mass ranges S68«107 1.79.107 (from simulations 191 and 82). 6.90-1077. 1.27104 (from simulations D2). 1012 2.0.1077 (from simulation M3) and 7.0«107 2.01012.1M. (from simulation M3).," The sample of parent haloes used for studying the mass function analysis consists of $6$, $5$, $34$ and $100$ haloes in the mass ranges $8.68\times10^{14}$ $1.79\times10^{15}$ (from simulations B1 and S2), $6.99\times10^{13}$ $1.27\times10^{14}$ (from simulations B2), $7.0\times10^{12}$ $2.0\times10^{13}$ (from simulation M3) and $7.0\times10^{11}$ $2.0\times10^{12}\,h^{-1}{\rm M}_{\odot}$ (from simulation M3)." The resulting. subhalo mass functions are shown in Fie. 1.., The resulting subhalo mass functions are shown in Fig. \ref{fig:fig1}. In the first four panels. we plot the dillerential mass tunctions for parent haloes ofcilferent mass.," In the first four panels, we plot the differential mass functions for parent haloes of different mass." The histograms are computed by stacking all the haloes in the eiven range of mass and the error bars represent. Poisson errors., The histograms are computed by stacking all the haloes in the given range of mass and the error bars represent Poisson errors. “The solid ine in cach of the panels is a power-law fit to the measured differential mass function: the fit is performed using the least absolute deviation method over the range of mass shown by he line., The solid line in each of the panels is a power-law fit to the measured differential mass function; the fit is performed using the least absolute deviation method over the range of mass shown by the line. In all the cases the 4ope of this unrestricted. fit is close to (it is equal to V.98 for the top left panel. 0.97 or the top right panel. 1.11 for the micelle left panel and 1.13 for the middle right panel).," In all the cases the slope of this unrestricted fit is close to $-1$ (it is equal to $-0.98$ for the top left panel, $-0.97$ for the top right panel, $-1.11$ for the middle left panel and $-1.13$ for the middle right panel)." Llowever. we note that the owest mass bins. which have the smallest statistical errors. are best fit with a slightly shallower slope: if we restrict the it to the 4 lowest mass bins the slope is 0.94 for the top eft. panel and 0.85 for the middle left. panel.," However, we note that the lowest mass bins, which have the smallest statistical errors, are best fit with a slightly shallower slope: if we restrict the fit to the $4$ lowest mass bins the slope is $-0.94$ for the top left panel and $-0.85$ for the middle left panel." These are closer to the value OLS. measured by 7). [or a single cluster simulation of extremely. high-resolution.," These are closer to the value $-0.8$, measured by \citet*{amina} for a single cluster simulation of extremely high-resolution." Also note that à slope shallower than —1 at the low-mass end. implies that the integrated: mass in substructures remains bounded. and is dominated by themost massive subhalos., Also note that a slope shallower than $-1$ at the low-mass end implies that the integrated mass in substructures remains bounded and is dominated by themost massive subhalos. IH is likely that our subhalo mass functions are steepenecl somewhat by a cut-olf in abundance for very massive substructures., It is likely that our subhalo mass functions are steepened somewhat by a cut-off in abundance for very massive substructures. The bottom left panel of Fig., The bottom left panel of Fig. 1. shows the cumulative, \ref{fig:fig1} shows the cumulative The star. ISWASP 251549.2 hhereafter) was observed. by the WASDP-South instrument as part of the WASP survey.,"The star, 1SWASP $-$ 251549.2 hereafter) was observed by the WASP-South instrument as part of the WASP survey." “Phe WASP. survey. is described in? and ?.., The WASP survey is described in \citet{2006PASP..118.1407P} and \citet{2008ApJ...675L.113W}. The cata from this survey are automatically processed. and analysed. in order to identify stars with lightcurves that contain transit-like features that may indicate the presence of a planetary. companion., The data from this survey are automatically processed and analysed in order to identify stars with lightcurves that contain transit-like features that may indicate the presence of a planetary companion. The candidate selection. methods can be found. in ον. 7.. and references therein.," The candidate selection methods can be found in \citet{2007MNRAS.380.1230C}, \citet{2008MNRAS.385.1576P}, and references therein." In. practice. these automatic methods produce tens of thousands of candidates. so we use a database to store the results of the automatic analysis plus other information available for the stars such as catalogue photometry and astrometry.," In practice, these automatic methods produce tens of thousands of candidates, so we use a database to store the results of the automatic analysis plus other information available for the stars such as catalogue photometry and astrometry." This. makes it possible to cllicicnthy reject. large. numbers of candidates that are unlikely to host planets using a variety. of criteria such as eclipse depth ancl the noise level in the lishteurve., This makes it possible to efficiently reject large numbers of candidates that are unlikely to host planets using a variety of criteria such as eclipse depth and the noise level in the lightcurve. The number of candidates that remain after sifting is small enough to make selection by inspection of the available data by a small number of people feasible., The number of candidates that remain after sifting is small enough to make selection by inspection of the available data by a small number of people feasible. Ehe same database can also be used to identify eclipsing binary stars by mocdifving the sifting criteria., The same database can also be used to identify eclipsing binary stars by modifying the sifting criteria. wwas spotted by one of us (PM) while looking at lighteurves of stars with deep eclipses and low reduced proper motions. Le. stars that may be eclipsing binary subcwarls.," was spotted by one of us (PM) while looking at lightcurves of stars with deep eclipses and low reduced proper motions, i.e., stars that may be eclipsing binary subdwarfs." Catalogue photometry and astromoetrv of aare summarized. in. ‘Table 1.., Catalogue photometry and astrometry of are summarized in Table \ref{mags}. The automatic transit detection algorithm correctly identified a period of dd rom 6633 observations of this star obtained with the WASD-South instrument., The automatic transit detection algorithm correctly identified a period of d from 6633 observations of this star obtained with the WASP-South instrument. The observations were obtained. with a single camera through a broad-band filter nnm) xtween 2006 August LO and 2007 December 31., The observations were obtained with a single camera through a broad-band filter nm) between 2006 August 10 and 2007 December 31. Phe WASP? xhotometry is shown as a function of orbital phase in Fig. 1.., The WASP photometry is shown as a function of orbital phase in Fig. \ref{lcfit}. The deeper of the two eclipses in the lighteurve shows a Lat section between a sharp ingress and egress., The deeper of the two eclipses in the lightcurve shows a flat section between a sharp ingress and egress. This type of iehteurve is produced by the eclipse of one star by a larger »it Cooler star., This type of lightcurve is produced by the eclipse of one star by a larger but cooler star. Ht is not. possible to produce a lighteurve with these properties if both the stars in the binary. are on he main sequence., It is not possible to produce a lightcurve with these properties if both the stars in the binary are on the main sequence. For this reason we organised Follow-up observations of this unusual object., For this reason we organised follow-up observations of this unusual object. We observed the egress phases of two eclipses of uusing the VCP CCD photometer on the SAO. 1.0-m telescope., We observed the egress phases of two eclipses of using the UCT CCD photometer on the SAAO 1.0-m telescope. “Phe star approximately 2.5 magnitudes. fainter, The star approximately 2.5 magnitudes fainter Collisional excitations by electrons are incorporated through the van Regemorter formula (?) and cross-sections for collisional ionization by electrons are calculated by the methods of ?..,Collisional excitations by electrons are incorporated through the van Regemorter formula \citep{VRegemorter1962} and cross-sections for collisional ionization by electrons are calculated by the methods of \citet{Cox2000}. In the case of H collisions. the approximate description of ??.. as implemented by ? with the correction of ? and multiplied by Sy. has been used.," In the case of H collisions, the approximate description of \citet{Drawin1968, Drawin1969}, as implemented by \citet{SteenbockHolweger1984} with the correction of \citet{Lambert1993} and multiplied by $\rm S_{H}$, has been used." As we do not intend to constrain Sy. we treat it as a free parameter and adopt values of 0 (no neutral H collisions). 0.001 and 1 (Drawin’s prescription).," As we do not intend to constrain $\rm S_{H}$, we treat it as a free parameter and adopt values of 0 (no neutral H collisions), 0.001 and 1 (Drawin's prescription)." This allows us to assess the importance of H collisions on the NLTE corrections., This allows us to assess the importance of H collisions on the NLTE corrections. For all calculations. the oscillator strength value. fj. has been set to a minimum of 107 when there is no reliable data or the £ value for a given line is below this minimum.," For all calculations, the oscillator strength value, $f_{ij}$ has been set to a minimum of $10^{-3}$ when there is no reliable data or the $f$ value for a given line is below this minimum." This minimum ts set as the scaling between the cross-sections and the f value breaks down for weak and forbidden lines (?).., This minimum is set as the scaling between the cross-sections and the $f$ value breaks down for weak and forbidden lines \citep{Lambert1993}. In this work. we have adopted plane-parrallel models.," In this work, we have adopted plane-parrallel models." These models are used. rather than the Kuruez 1996 models as was done in ?.. as needs a specific format for its input. this is provided by theMARCS. details of which can be found in ?..," These models are used, rather than the Kurucz 1996 models as was done in \citet{Hosfordetal2009}, as needs a specific format for its input, this is provided by the, details of which can be found in \citet{Asplundetal1997}." 3D models lead toan even steeper temperature gradient. and hence cooler temperatures in the line forming region (?).. but the use of these more sophisticated models is beyond the scope of this work.," 3D models lead toan even steeper temperature gradient, and hence cooler temperatures in the line forming region \citep{Asplund2005}, but the use of these more sophisticated models is beyond the scope of this work." The NLTE code used to produce Fe line profiles and equivalent widths (Wi) is a modified version of (?).., The NLTE code used to produce Fe line profiles and equivalent widths $W_{\rm \lambda}$ ) is a modified version of \citep{Carlsson1986}. This is a multi-level radiative transfer program for solving the statistical equilibrium and radiative transfer equations., This is a multi-level radiative transfer program for solving the statistical equilibrium and radiative transfer equations. The code we adopted is a version modified by R. Collet to include the effects of line-blocking (?).., The code we adopted is a version modified by R. Collet to include the effects of line-blocking \citep{Colletetal2005}. To do this. they sampled metal line opacities for 9000 wavelength points between 1000 aand 20000 aand added them to the standard background continuous opacities.," To do this, they sampled metal line opacities for 9000 wavelength points between 1000 and 20000 and added them to the standard background continuous opacities." They found that. for metal-poor stars. the difference between NLTE Fe abundances derived from lines excluding and including line-blocking by metals in the NLTE calculations is of the order of 0.02 dex or less.," They found that, for metal-poor stars, the difference between NLTE Fe abundances derived from lines excluding and including line-blocking by metals in the NLTE calculations is of the order of 0.02 dex or less." For this work. we have chosen six of our original program stars (?) that approximately represent the limits of our physical parameters. te. one of the more metal-rich. one of the less metal-rich. one of the hotter. one of the cooler etc.," For this work, we have chosen six of our original program stars \citep{Hosfordetal2009} that approximately represent the limits of our physical parameters, i.e. one of the more metal-rich, one of the less metal-rich, one of the hotter, one of the cooler etc." Table | indicates the stellar parameters for which model atmospheres were created., Table \ref{Table1} indicates the stellar parameters for which model atmospheres were created. For the HD stars gravities were used., For the HD stars gravities were used. For the other three stars. lower and upper limits on log g are given by theoretical isochrones (see?)..," For the other three stars, lower and upper limits on log $g$ are given by theoretical isochrones \citep[see][]{Hosfordetal2009}." In the case of LP815-43. there is uncertainty as to whether it is just above or just below the main-sequence turnoff.," In the case of LP815-43, there is uncertainty as to whether it is just above or just below the main-sequence turnoff." The final temperatures are interpolated between these values using a final log ς that represents the star at 12.5 Gyr (Table 2))., The final temperatures are interpolated between these values using a final log $g$ that represents the star at 12.5 Gyr (Table \ref{Table2}) ). This study ts primarily concerned with the formation of lines., This study is primarily concerned with the formation of lines. In Fig. l..," In Fig. \ref{fig:departplots}," we present the departure coefficients. ΗΕ o. for the lower (left hand side) and upper (right hand side) levels of all lines we have measured in the star HD140283 in paper L calculated for three Sy values.," we present the departure coefficients, $b_{i}=n_{i}/n_{i}^{\rm LTE}$ , for the lower (left hand side) and upper (right hand side) levels of all lines we have measured in the star HD140283 in paper I, calculated for three $\rm S_{H}$ values." The two sets of lines in each plot. coloured.," The two sets of lines in each plot, coloured." red and blue. represent levels that fall above and below the midpoint of our excitation energy range. 1.9. 1.83 eV where our highest lower level of the transition ts at 3.65 eV. and 5.61 eV where our highest upper transition level is at 6.87 eV. This is done to better visualise the effects of NLTE on different levels of the atom.," red and blue, represent levels that fall above and below the midpoint of our excitation energy range, i.e. 1.83 eV where our highest lower level of the transition is at 3.65 eV, and 5.61 eV where our highest upper transition level is at 6.87 eV. This is done to better visualise the effects of NLTE on different levels of the atom." We see that in all cases the levels are under-populated compared to LTE at tso99«1l., We see that in all cases the levels are under-populated compared to LTE at $\tau_{\rm 5000} < $ 1. " This is primarily due to the effects of overionization where J,B, for lines formed from the levels of the atom at around y~ 4 eV below the continuum. due to the UV photons having energies = 3-4 eV. This causes all levels of the atom to become greatly depopulated. as can be seen from the blue lines."," This is primarily due to the effects of overionization where $J_{\nu} > B_{\nu}$ for lines formed from the levels of the atom at around $\chi \sim$ 4 eV below the continuum, due to the UV photons having energies $\approx$ 3-4 eV. This causes all levels of the atom to become greatly depopulated, as can be seen from the blue lines." The coupling of the higher levels through collisions and of the lower levels through the large number of strong lines sharing upper levels implies that relative to one another the level populations approximately follow the Boltzmann distribution., The coupling of the higher levels through collisions and of the lower levels through the large number of strong lines sharing upper levels implies that relative to one another the level populations approximately follow the Boltzmann distribution. Because of photoionization. the Saha equilibrium between and is not fulfilled however and the departure coefficients of levels are less than unity.," Because of photoionization, the Saha equilibrium between and is not fulfilled however and the departure coefficients of levels are less than unity." In deeper levels of the atmosphere. this leads to both upper and lower levels of a transition being equally affected by the above phenomena (Fig | — right hand side).," In deeper levels of the atmosphere, this leads to both upper and lower levels of a transition being equally affected by the above phenomena (Fig \ref{fig:departplots} – right hand side)." For this reason. the source functions for lines forming at these depths are relatively unaffected in this region. as Sx(pper/Plower)By. and follow a Planckian form (Fig.," For this reason, the source functions for lines forming at these depths are relatively unaffected in this region, as $S \approx (b_{\rm upper}/b_{\rm lower})B_{\nu}$, and follow a Planckian form (Fig." 2 — right hand panel)., \ref{fig:sjbplots} – right hand panel). " The combined effect of the above processes. Le. depopulation and relatively unaffected source functions. leads to a smaller W, and thus weaker lines. and increased abundances compared to the LTE case."," The combined effect of the above processes, i.e. depopulation and relatively unaffected source functions, leads to a smaller $W_{\rm \lambda}$ and thus weaker lines, and increased abundances compared to the LTE case." " For stronger lines. forming further out in the atmosphere.there is a divergence between bsp, and bi, and the source function thus diverges from the Planck function (Fig."," For stronger lines, forming further out in the atmosphere,there is a divergence between $b_{\rm upper}$ and $b_{\rm lower}$ and the source function thus diverges from the Planck function (Fig." 2. — left hand panel)., \ref{fig:sjbplots} – left hand panel). " In the case where S« B,. the source function compensatesslightly for"," In the case where $S^l_\nu < B_\nu$ , the source function compensatesslightly for" high enough to have some consequences on the dynamical and radiative properties. anc on the evolutionary. history. of the system.,"high enough to have some consequences on the dynamical and radiative properties, and on the evolutionary history, of the system." In the canonical view. the keV ravs from X-ray binaries with an O star are powered by the accretion of gas either in a wind focused by the Roche-lohe of the donor star or captured. directly. from the wind out-lowing from the donor star.," In the canonical view, the keV X-rays from X-ray binaries with an O star are powered by the accretion of gas either in a wind focused by the Roche-lobe of the donor star or captured directly from the wind out-flowing from the donor star." In the focused. wind scenario. an accretion disk is expected to form around the compact star. similar to that in systems with Roche-lobe filling mass-ransfer. as the accreting gas carries substantial specific angular momentum.," In the focused wind scenario, an accretion disk is expected to form around the compact star, similar to that in systems with Roche-lobe filling mass-transfer, as the accreting gas carries substantial specific angular momentum." In the direct. wind. capture scenario. oovided that the specific angular momentum of the gas is sullicienthy small. an extensive aceretion disk might not be ormed and the accretion inflow would be practically racial and resemble that of a Bondi-Hovle How.," In the direct wind capture scenario, provided that the specific angular momentum of the gas is sufficiently small, an extensive accretion disk might not be formed and the accretion inflow would be practically radial and resemble that of a Bondi-Hoyle flow." A eccentricitv would give a lower specific angular momentun in the wind material that is swept up by the accreting star., A eccentricity would give a lower specific angular momentum in the wind material that is swept up by the accreting star. So far observations e.g. X-ray observations by and (Alartocchiaetal.2005:Boseh-Ramonetal. 2007)]] have not shown evidence of an acerction disk in LS 5039.," So far observations [e.g. X-ray observations by and \citep{Martocchia2005,Bosch-Ramon2007}] ] have not shown evidence of an accretion disk in LS 5039." LE LS 5039 has an extremely high orbital eccentricity as originally measured. the lack of an accretion disk around its compact star would need certain non-trivial explanations (cf.," If LS 5039 has an extremely high orbital eccentricity as originally measured, the lack of an accretion disk around its compact star would need certain non-trivial explanations (cf." the situation in the Be X-ray. binaries)., the situation in the Be X-ray binaries). The lower eecentricity may ease the situation somewhat. allowing racial gas inflow for a substantial distance before reaching the compact accretor.," The lower eccentricity may ease the situation somewhat, allowing radial gas inflow for a substantial distance before reaching the compact accretor." Then. if there is an accretion disk. it would. not be expected. to be a Large and. dense disk because such a clisk would generate significant thermal soft keV. X-rays. which are not detected in theChandra. and. other X-ray observations.," Then, if there is an accretion disk, it would not be expected to be a large and dense disk because such a disk would generate significant thermal soft keV X-rays, which are not detected in the, and other X-ray observations." Our smaller value of eccentricity reduces the discrepancy between the low observed X-ray. variability and what would be expected [rom wind accretion with Boneli-Llovle like radial inflow BondiLlovle (1944).. Bosch-Itamonetal. (2005)... C05].," Our smaller value of eccentricity reduces the discrepancy between the low observed X-ray variability and what would be expected from wind accretion with Bondi-Hoyle like radial inflow \citet{Bondi1944}, \citet{Bosch-Ramon2005}, C05]." Ixnown black-hole high-mass X-ray. binaries tend. to have small orbital eccentricity. unlike the X-ray pulsars (see (Liu.vanParadijs&denHeuvel2005.2006. 200723).," Known black-hole high-mass X-ray binaries tend to have small orbital eccentricity, unlike the X-ray pulsars (see \citep{Liu2005,Liu2006,Liu2007}) )." rav binaries with a black hole and an Ο donor star are very rare. and Cvg X-1 is the currently only known system in the Milkv Way.," X-ray binaries with a black hole and an O donor star are very rare, and Cyg X-1 is the currently only known system in the Milky Way." The confirmation of LS 5039 as a black-hole hieh-mass X-rav binary in which a massive O donor star and a black hole revolve around each other in an eccentric orbit important implications on how such svstenis are formed and how massive binaries evolve., The confirmation of LS 5039 as a black-hole high-mass X-ray binary in which a massive O donor star and a black hole revolve around each other in an eccentric orbit important implications on how such systems are formed and how massive binaries evolve. In LS 5039. the compact star's progenitor. at à certain stage. should be more massive than the current O donor star. otherwise it would not have evolved to form the compact star.," In LS 5039, the compact star's progenitor, at a certain stage, should be more massive than the current O donor star, otherwise it would not have evolved to form the compact star." O stars have very short life spans (7 a few Myr). thus LS 5039 as must be vounger than a few million vears.," O stars have very short life spans $\sim$ a few Myr), thus LS 5039 as must be younger than a few million years." This is supported by the fact that LS 5039 has a highly eccentric xnarv orbit. which has vet to becircularized [rom a »esumed: recent. supernova event.," This is supported by the fact that LS 5039 has a highly eccentric binary orbit, which has yet to be from a presumed recent supernova event." However. it is unclear whether the progenitor of the O star or the progenitor of he compact star had the larger initial mass. evolution of the progenitor of the compact star could. well » trigeered by a mass transfer process. in which the system was compact enough to allow the progenitor of the current O star to overfill its Roche-lobe and transfer material to the xogenitor of the compact star. (," However, it is unclear whether the progenitor of the O star or the progenitor of the compact star had the larger initial mass, evolution of the progenitor of the compact star could well be triggered by a mass transfer process, in which the system was compact enough to allow the progenitor of the current O star to overfill its Roche-lobe and transfer material to the progenitor of the compact star. (" For more on the evolution of very massive binaries. see c.g. Dalton&Sarazin(1995):VanBever&Vanbeveren(2003):DionneRobert (2006)..),"For more on the evolution of very massive binaries, see e.g. \citet{Dalton1995,VanBever2003,Dionne2006}. .)" If LS 5039 was indeed. formed. through this mass-transfer channel. among the fewer than 200 known high-mass X-ray. binaries in the Alilky Way would imply that a black-hole high-mass X-ray might be formed in close massive binarics more casily than previously thought.," If LS 5039 was indeed formed through this mass-transfer channel, among the fewer than 200 known high-mass X-ray binaries in the Milky Way would imply that a black-hole high-mass X-ray might be formed in close massive binaries more easily than previously thought." Young stellar. clusters in. star-forming galaxies may well be populated by LS 5039-type sources and are potentially Ciev-TeV. οταν sources., Young stellar clusters in star-forming galaxies may well be populated by LS 5039-type sources and are potentially Gev-TeV $\gamma$ -ray sources. Our simultaneous optical photometry [rom theALOST space telescope anc high resolution cchelle optical spectroscopy from the ANU 2.3m. Telescope have put constraints on the orbital parameters of the LS 5039 system., Our simultaneous optical photometry from the space telescope and high resolution echelle optical spectroscopy from the ANU 2.3m Telescope have put constraints on the orbital parameters of the LS 5039 system. In particular we obtained a mass function. 0.0049+0.0006 NL. and an orbital eccentricity e=0.244 0.08., In particular we obtained a mass function $f(m) \approx0.0049 \pm 0.0006$ $_{\odot}$ and an orbital eccentricity $e=0.24\pm0.08$ . The maximum. photometric variation of LS 5039 in theAOST light curve was 2 mmae., The maximum photometric variation of LS 5039 in the light curve was 2 mmag. Our value for the eccentricity of 0.24-£0.08 is a little smaller than previous determinations., Our value for the eccentricity of $\pm$ 0.08 is a little smaller than previous determinations. Ehe lower eccentricity implies that the wind material that is captured and falls into the Roche lobe of the compact star has a lower specific angular momentum., The lower eccentricity implies that the wind material that is captured and falls into the Roche lobe of the compact star has a lower specific angular momentum. Thus it may not lead to the formation of a large-scale optically thick accretion disk. and the accretion inllow is practically racial resembling that of a Bondi-Llovle Low.," Thus it may not lead to the formation of a large-scale optically thick accretion disk, and the accretion inflow is practically radial resembling that of a Bondi-Hoyle flow." Finally (rom EW measurements of the Ho line. we derived that the mass loss rate from the O-tvpe primary through stellar wind is 3.7 to4810 M. + similar to values obtained hy other workers.," Finally from EW measurements of the $\alpha$ line, we derived that the mass loss rate from the O-type primary through stellar wind is 3.7 to4.8$\times 10^{-7}$ $_{\odot}$ $^{-1}$, similar to values obtained by other workers." Our observations do not show evidence of dense clumps in the stellar wind., Our observations do not show evidence of dense clumps in the stellar wind. of the short lifetimes of the relativistic electrons. it is difficult (o interpret the large size ol radio halos as the result of the diffusion of the relativistie electrons injected. [rom radio ealaxies (JaffeLOTT)...,"of the short lifetimes of the relativistic electrons, it is difficult to interpret the large size of radio halos as the result of the diffusion of the relativistic electrons injected from radio galaxies \citep{jaf77}." Consequently. lor the formation of radio halos. a significant level of re-acceleration might be involved.," Consequently, for the formation of radio halos, a significant level of re-acceleration might be involved." The secondary electron model first proposed by provides a different scenario for the origin of the radio halo and can avoid the problem of re-acceleration lor the relativistic electrons in the primary electron models., The secondary electron model first proposed by \citet{den80} provides a different scenario for the origin of the radio halo and can avoid the problem of re-acceleration for the relativistic electrons in the primary electron models. However. this model encounters serious problems when comparing wilh observations seeBrunetti 2002).," However, this model encounters serious problems when comparing with observations \citep[for a recent review, see][]{bru02}." . Coma C in the Coma cluster is (he prototvpe of radio halos in galaxy clusters., Coma C in the Coma cluster is the prototype of radio halos in galaxy clusters. Being the best studied example. Coma € has been observed at many different radio wavebancds 1993:Deissοἱal.1997:Thierbach.Klein.&Wiele," Being the best studied example, Coma C has been observed at many different radio wavebands \citep*[e.g.,][]{sch87,kim90,ven90,gio93,dei97,thi03}." binski 2003).. argued that (he measurement at 2.7 GlIIz by Schlickeiseretal.(LOST) is too low and suggested that the integrated spectrum might have no tendency to steepen as suggested by Schlickeiseretal.(1987): however. this strong steepening of the radio spectrum at hieh frequencies was confirmed by Thierbachetal.(2003).," \citet{dei97} argued that the measurement at 2.7 GHz by \citet{sch87} is too low and suggested that the integrated spectrum might have no tendency to steepen as suggested by \citet{sch87}; however, this strong steepening of the radio spectrum at high frequencies was confirmed by \citet{thi03}." ". Giovanniniοἱal.(1993) used the radio data al 1380 MIIz (IxXimetal.1990). and 326 MIIz (Venturietal.1990). to derive (he radial distribution of the spectral index in Coma C. and they found a central ""plateau with a size of ~15' for the spectral-index distribution."," \citet{gio93} used the radio data at 1380 MHz \citep{kim90} and 326 MHz \citep{ven90} to derive the radial distribution of the spectral index in Coma C, and they found a central “plateau"" with a size of $\sim15\arcmin$ for the spectral-index distribution." In the central region. the value of (he spectral index is ~0.5: in the outside region. the spectral index strongly steepens as the raclius increases.," In the central region, the value of the spectral index is $\sim0.8$; in the outside region, the spectral index strongly steepens as the radius increases." Observations with and the (RATE)) have detected a hard X-ray (INR) excess with respect to thermal emission Irom the Coma cluster (Fusco-Femianoetal.1999:Rephaeli.Gruber.&Blanco1999;RephaeliGruber2002).," Observations with and the ) have detected a hard X-ray (HXR) excess with respect to thermal emission from the Coma cluster \citep*{fus99,rep99,rep02}." . The IDNR. excesses [rom several other clusters have also been reported (Ixaastraetal.1999:Fusco-Femianoetal.2000.2001:Gruber&Rephaeli 2002).," The HXR excesses from several other clusters have also been reported \citep{kaa99,fus00,fus01,gru02}." . The most favored mechanism ol the ΗΝ excess is inverse Compton scattering (LCS) of the cosmic microwave background (CMD) photons by relativistic electrons., The most favored mechanism of the HXR excess is inverse Compton scattering (ICS) of the cosmic microwave background (CMB) photons by relativistic electrons. Since these electrons with energy 5~10! will also produce radio svnchrotron radiation. (he ΗΝ excesses and radio halos may originate from the same electron population.," Since these electrons with energy $\gamma\sim10^{4}$ will also produce radio synchrotron radiation, the HXR excesses and radio halos may originate from the same electron population." In the Coma cluster. the volume-averaged values of magnetic fields deduced from the comparison of the radio with the IIXI. excess enission is ~ 0.1 iG. (Fusco-Femianoetal.1999:Rephaeli&Gruber2002).," In the Coma cluster, the volume-averaged values of magnetic fields deduced from the comparison of the radio with the HXR excess emission is $\sim$ 0.1--0.3 $\mu$ G \citep{fus99,rep99,rep02}." . These low values of field strength are not consistent with those deduced [rom the measurements of Faraday rotation., These low values of field strength are not consistent with those deduced from the measurements of Faraday rotation. Clarke.INronberg.&Bohringer(2001) have shown that many clusters have relatively large (~ 48 µία) fields., \citet*{cla01} have shown that many clusters have relatively large $\sim$ 4–8 $\mu$ G) fields. For the Coma cluster. Iximetal.(1990). found a central field strength of 1.72:0.9 iG. and Ferettietal.(1995) estimated the strength to be GEL µία. It is (hus very important to see whether it is possible to produce the observed INR. excess via," For the Coma cluster, \citet{kim90} found a central field strength of $1.7\pm0.9\ \mu$ G, and \citet{fer95} estimated the strength to be $6\pm1\ \mu$ G. It is thus very important to see whether it is possible to produce the observed HXR excess via" Related to the sudden increase of the energy density at deconlinement. (here are (wo further points to note.,"Related to the sudden increase of the energy density at deconfinement, there are two further points to note." " In the region 7. 2.4$." The Swift observations fud these sources at Iuninosities <1.10eves.," The Swift observations find these sources at luminosities $\lesssim 1 \times 10^{40} \rm \, erg \, s^{-1}$." There are several other ULXs that appear in the scep power-law state at similar uunmnosities(Feng&Ἱνααστοτ2005)., There are several other ULXs that appear in the steep power-law state at similar luminosities\citep{Feng05}. . The steep powcr-aw state tends to occur at the ποο Iuninosities seen roni accreting stellarauass black holes., The steep power-law state tends to occur at the highest luminosities seen from accreting stellar-mass black holes. These ULXs may represent a high ποσατν extension of he steep aw state, These ULXs may represent a high luminosity extension of the steep power-law state. NGC 1395 has heen referred to as the least huuimous ype 1 Sevtert galaxy (Moranctal.1999) due to measurements of vervolow lhuuinosities with ROSAT., NGC 4395 has been referred to as the least luminous type 1 Seyfert galaxy \citep{Moran99} due to measurements of very low luminosities with ROSAT. More receut observatious covering a broader energy band Sugeest an average Μπ near 9«107eresL|1 in the 0.5-10 keV. biuxd (Moranetal.2005)... within th range seen οι ULAs.," More recent observations covering a broader energy band suggest an average luminosity near $9 \times 10^{39} \rm \, erg \, s^{-1}$ in the 0.5-10 keV band \citep{Moran05}, within the range seen from ULXs." The helt curve of the nucleus:4. of NGC 1395. shows a strong flare near MJD 5162, The light curve of the nucleus of NGC 4395 shows a strong flare near MJD 54624. We use a simple absorbed power-law model to couvert the Swift count rates to fluxes., We use a simple absorbed power-law model to convert the Swift count rates to fluxes. Following Morauctal.(1999).. we adopt an absorption column density Vy1079cm7.," Following \citet{Moran99}, , we adopt an absorption column density $N_H = 1.6 \times 10^{20} \rm \, cm^{-2}$ ." " We use a photon index DP—1.5 which produces a harducss of 0.7. in reasonable aerecmenut with the measured νιdues,"," We use a photon index $\Gamma = 1.5$ which produces a hardness of 0.7, in reasonable agreement with the measured values." The true X-ray spectrum of NGC 1395 X-1 is more complex. than this. but this approximation shouk suf&cieut to produce rough fiux estimates;," The true X-ray spectrum of NGC 4395 X-1 is more complex than this, but this approximation should sufficient to produce rough flux estimates." The peak counting rate observed is 0.81 ος and corresponds to a Bux of L5«10Merecu28+ in the 0.5-10 keV banda id a huninosity of 9.1«10/9eres! at the distance of 1.1 Alpe.," The peak counting rate observed is 0.84 c/s and corresponds to a flux of $4.5 \times 10^{-11} \rm \, erg \, cm^{-2} \, s^{-1}$ in the 0.5-10 keV band and a luminosity of $9.1 \times 10^{40} \rm \, erg \, s^{-1}$ at the distance of 4.1 Mpc." This is several times higher than auy flux previously reported from NGC L395 X-1., This is several times higher than any flux previously reported from NGC 4395 X-1. The spectral evolujon of the nuclear XN-raw source In NGC 1395 1s incosistent with being constant., The spectral evolution of the nuclear X-ray source in NGC 4395 is inconsistent with being constant. The C/DoF for a mode of constant larcducss is 27.9/6 corresponding to a preyhability of occurence of 1.0«10.+., The $\chi^2$ /DoF for a model of constant hardness is 27.9/6 corresponding to a probability of occurrence of $1.0\times 10^{-4}$. The spectrum appearsto harden at the lowest flux levels observed., The spectrum appears to harden at the lowest flux levels observed. O'Neilletal.(2006). found a simular treud conpariue two Cliauclra observations of NGC 1395 aud sugeested that the cause ds variable absorption., \citet{ONeill06} found a similar trend comparing two Chandra observations of NGC 4395 and suggested that the cause is variable absorption. NGC 1395 is known to exhibit dramaic long-term spectral variabilitv ou time scales of severa] vears., NGC 4395 is known to exhibit dramatic long-term spectral variability on time scales of several years. Such cinatic variabilitv is uot apparent in the Swift data. but this may be because the Swift data cover oulv oue vear.," Such dramatic variability is not apparent in the Swift data, but this may be because the Swift data cover only one year." The monitoring pregranis. described here demoustrate that Swift cau be used to measure the fiux aud spectral evolution of ULXs aια AGN on time scales of months to vears., The monitoring programs described here demonstrate that Swift can be used to measure the flux and spectral evolution of ULXs and AGN on time scales of months to years. For the nucear source in NGC L395. the trend for larder spectra at ower fluxes seen in two Claucdra observations (O'Neilletal.2006) is comfrmed with a sample of more than 700 observations aud the highest X-rav Dunuinositv ever «Xcon. 9&T0eyesἘν was recorded.," For the nuclear source in NGC 4395, the trend for harder spectra at lower fluxes seen in two Chandra observations \citep{ONeill06} is confirmed with a sample of more than 100 observations and the highest X-ray luminosity ever seen, $9 \times 10^{40} \rm \, erg \, s^{-1}$, was recorded." The three ULNs monitored do not show siguificaut changes in spectral sate over mouths to vears., The three ULXs monitored do not show significant changes in spectral state over months to years. Two of the ULXs. NGC 5108 δν aud NGC 1395 X-I. remain iu a soft spectral sate. equivalent to a photon iudex softer than 2.6. as their fiux varies bv factors of ~9.," Two of the ULXs, NGC 5408 X-1 and NGC 4395 X-1, remain in a soft spectral state, equivalent to a photon index softer than 2.6, as their flux varies by factors of $\sim 9$." " The other ULX. IHohubere IN N-1. remains ina lard spectral state. equivalent to a photon iudex near 1.9. as its flux varies by a factor of 7 inobservations spread over several vears and with Gsotropic) huuinosities up to 2.5«1tHUyes P, "," The other ULX, Holmberg IX X-1, remains in a hard spectral state, equivalent to a photon index near 1.9, as its flux varies by a factor of 7 inobservations spread over several years and with (isotropic) luminosities up to $2.8 \times 10^{40} \rm \, erg \, s^{-1}$ ." This behavior may sutOOroost an unusually massive compact object., This behavior may suggest an unusually massive compact object. seems to point to mode conversion as the likely candidate to explain our findings.,seems to point to mode conversion as the likely candidate to explain our findings. This statement could be strengthened by performing intensity observations at different heights in. the atmosphere. i order to check upon the nature of the waves.," This statement could be strengthened by performing intensity observations at different heights in the atmosphere, in order to check upon the nature of the waves." If we do not observe any high-frequeney acoustic enhancement with height. this will imply that they are incompressible waves (?). and we can rule out mode conversion as the physical mechanism behind low-frequency acoustic absorption and high-frequency acoustic enhancement.," If we do not observe any high-frequency acoustic enhancement with height, this will imply that they are incompressible waves \citep{Cal08}, and we can rule out mode conversion as the physical mechanism behind low-frequency acoustic absorption and high-frequency acoustic enhancement." The wave behavior with height is even more extremely important to investigate another interesting issue., The wave behavior with height is even more extremely important to investigate another interesting issue. While fast magnetoacoustic waves are refracted backwards. slow-magnetoacoustic waves can travel in the atmosphere.," While fast magnetoacoustic waves are refracted backwards, slow-magnetoacoustic waves can travel in the atmosphere." Thus the latter could play a major role in the chromospheric heating (?).., Thus the latter could play a major role in the chromospheric heating \citep{Jef06}. This opens up a new interesting scenario: these observations have shown that the magnetism of the Quiet Sun affects the nature of the waves with increasing activity. which could even imply that the chromospheric heating varies with the solar cycle.," This opens up a new interesting scenario: these observations have shown that the magnetism of the Quiet Sun affects the nature of the waves with increasing activity, which could even imply that the chromospheric heating varies with the solar cycle." Nowadays. the nature of the Quiet Sun magnetism and its link with solar activity as the dependence of chromospheric heating on the state of the solar activity cycle is hotly debated (2?)..," Nowadays, the nature of the Quiet Sun magnetism and its link with solar activity as the dependence of chromospheric heating on the state of the solar activity cycle is hotly debated \citep{Cat99,Alm09}." To work out this it will be extremely important to check upon the different contributions coming from regions which have a strong relatively uniform magnetic field. e.g. sunspots and active regions. with that (f any) from regions in which the field direction is very variable. like the intranetwork.," To work out this it will be extremely important to check upon the different contributions coming from regions which have a strong relatively uniform magnetic field, e.g. sunspots and active regions, with that (if any) from regions in which the field direction is very variable, like the intranetwork." The results of this further work will help us settle the debate about the origin of the quiet Sun magnetism., The results of this further work will help us settle the debate about the origin of the quiet Sun magnetism. Furthermore the investigation will also be important to check the possibility of using the solar eycle changes induced in the p-mode parameters as precursors of solar activity., Furthermore the investigation will also be important to check the possibility of using the solar cycle changes induced in the $p$ -mode parameters as precursors of solar activity. We hope to extend this analysis during the peculiar extended minimum of activity cycle 23. in. which some frequency shifts are not following the traditional activity indexes (??)..," We hope to extend this analysis during the peculiar extended minimum of activity cycle 23, in which some frequency shifts are not following the traditional activity indexes \citep{Broo09, Sal09}." Additionally. the interpretation of the observational findings in terms of mode conversion helps us to understand why low-frequency acoustic enhancement is essentially located around sunspots and active regions.," Additionally, the interpretation of the observational findings in terms of mode conversion helps us to understand why low-frequency acoustic enhancement is essentially located around sunspots and active regions." We have shown that the magnetic field strength and inclination control the locations where mode transmission and/or conversion might occur., We have shown that the magnetic field strength and inclination control the locations where mode transmission and/or conversion might occur. Transmission from acoustic to slow MHD waves between 2 mHz 129⋅ 4.6dav between the first⋅ and. fourth⋅ overtones ,. ⋃∖⊓⋅⊔∠↓⋖⊾⋖⋅∣⋜↧⇂⋡↓≤"," The velocity Fourier parameters of the s-Cepheids display a very characteristic progression with period, which is attributed to the 2:1 resonance at $P\! =\! 4.2\! -\! 4.6$ day between the first and fourth overtones \citep{kie99, FEU00}." ⋗≤⋗≤⋗∶↓⊲⋖⊾⋯⇍↓∐↓⊔⋏∙≟⋖⊾↓⋅∢⊾↿⋜↧↓⊳⇉∪∪∪⊐↦⇂⊔⇂∪↓⋅⋯⊔⋜⋯⊾↓∙∖⇁⊳⇁⋅ any detailed: modeling of this progression and. pinpointing of⋅ the resonance position2. is. hampered by a scarcity. of⋅ the sCepheids. with: 2 5.5day. with. ALY] Pup being. the only secure identification.," Unfortunately, any detailed modeling of this progression and pinpointing of the resonance position is hampered by a scarcity of the s-Cepheids with $P > 5.5$ day, with MY Pup being the only secure identification." " One more candidate. V440. Per (P=7.57 has been identified by."" Kienzle etονal."," One more candidate, V440 Per $P = 7.57$ day), has been identified by \citet{kie99}. ." "(1999).. of . ⊀⊲ ""M ] ⋅ the. ""ND the first.⋅ overtone sequence. On.⊀ this [uncamental mode pulsators""M xis. Ixienzlec"," They noted, that the velocity Fourier phase $\phi_{21}$ places this Cepheid away from the fundamental mode sequence and possibly onto the first overtone sequence." tal.(1999). proposed that V44O0 Per is an overtone pulsator.," On this basis, \citet{kie99} proposed that V440 Per is an overtone pulsator." " This hypothesis was further supported w determination of the phasc-lag between the light curve and the racial velocity. curve. A®,=obOpnag7. which laced V440. Per away from the funcamental sequence as well (Osglozactal.2000)."," This hypothesis was further supported by determination of the phase-lag between the light curve and the radial velocity curve, $\Delta\Phi_1=\phi_1^{V_r}-\phi_1^{mag}$, which placed V440 Per away from the fundamental sequence as well \citep{Og00}." . Llowever. V440. Per is a small amplitude. nearly sinusoidal variable.," However, V440 Per is a small amplitude, nearly sinusoidal variable." Lyven the best. then available racial velocity data (Burki&Benz1982). vielded large errors of⋅ the Ist harmonies⊀ Fourier.s parameters., Even the best then available radial velocity data \citep{BB82} yielded large errors of the 1st harmonics Fourier parameters. MThe ⊔↓⋖⋅⋜↧⊳∖⊔↓⋅⋖⊾⊔↓∢⋅↓∐⋖⋅↓⋅↓⋅∪↓⋅∪⋅⇂↓↕⋖⋅≻↓↥⋜↧⊳∖⋖⊾−↓⋜↧⋃∆≺↓⋅∖∖⋎⋜↧⊳∖⇂⋜⊔⋅⋃," The measurement error of the phase-lag $\Delta\Phi_1$ was large, too." ⋖⋅⋡∣∪∪⋡↓° 1 ? This. and inconsistencey. with their hvdrodynamie pulsation models led Szaboetal.(2007) to. dispute the mode identification of V440 Per.," This, and inconsistency with their hydrodynamic pulsation models led \citet{SZ07} to dispute the mode identification of V440 Per." They noted that the membership| of this Cepheid in the funcamental mode sequence could not be rejected at the 3a confidence level., They noted that the membership of this Cepheid in the fundamental mode sequence could not be rejected at the $3\sigma$ confidence level. “Phey argued that V440 Per is not an overtone pulsator. but. rather a fundamental mode Cepheid ofa verylow amplitude.," They argued that V440 Per is not an overtone pulsator, but rather a fundamental mode Cepheid of a verylow amplitude." In the present paper we report results of an extensive, In the present paper we report results of an extensive "opacity coefficient (8,x vey. which in turn carries the information on erain erowth iu the disk.","opacity coefficient $\kappa_{\nu} \propto \nu^{\beta}$ ), which in turn carries the information on grain growth in the disk." " For example. in the Ravleigli-Jeaus regiae for a completely optically thin enission. A=ja2,"," For example, in the Rayleigh-Jeans regime for a completely optically thin emission, $\beta=\alpha-2$." [Iowever. since the hypotheses of completely optically thin emüssioun in the Ravleigh-Jeans regime are not always realized even at these long wavelengths. modelling of the disk cussion is required.," However, since the hypotheses of completely optically thin emission in the Rayleigh-Jeans regime are not always realized even at these long wavelengths, modelling of the disk emission is required." We modelled the measured disk sub-iuu SED of the 53-1536 binary system by using a modified version je two-laver passively irradiated disk models (Chiang&Coldveich1997:Dullemoudctal. 2001).. as described in Riccietal.(2010α.1).," We modelled the measured disk sub-mm SED of the 253-1536 binary system by using a modified version of the two-layer passively irradiated disk models \citep{Chiang:1997,Dullemond:2001}, as described in \citet{Ricci:2010a,Ricci:2010b}." . The effective telpcrature of je two stellar companions were derived by converting je spectral types adopted in Section 2.2 with the cluperature scale of Lulimanetal.(2003)., The effective temperature of the two stellar companions were derived by converting the spectral types adopted in Section \ref{sec:X-Shooter} with the temperature scale of \citet{Luhman:2003}. . By using ιο Palla&Staller(1999) PAIS evolutionary tracks aud jew multi-baud optical photometry aud spectroscopy. DaRioetal.(2010) recently derived a new estimate for ιο ONC mean age of about 2 Myr.," By using the \citet{Palla:1999} PMS evolutionary tracks and new multi-band optical photometry and spectroscopy, \citet{DaRio:2010} recently derived a new estimate for the ONC mean age of about 2 Myr." With these same PAIS evolutionary tracks and age. the values for the stellar masses and are about 2 AJ... 12 L. oy 253-1536a aud about 0.3 MmiuinositiesAL... 0.2 £.. for 253-152 respectively.," With these same PMS evolutionary tracks and age, the values for the stellar masses and luminosities are about 2 $M_{\odot}$, 12 $L_{\odot}$ for 253-1536a and about 0.3 $M_{\odot}$, 0.2 $L_{\odot}$ for 253-1536b, respectively." The angular resolutions of the EVLA and SAMA observations do not allow us to properly coustrain the radial profile of the dust surface density in the two disks., The angular resolutions of the EVLA and SMA observations do not allow us to properly constrain the radial profile of the dust surface density in the two disks. For this reason. we consider im this analysis disks with truucated power-law surface densities (MauerXrc for pRoy and Nays=0 foror Rou} with possible p-values between 0 aud 1.5. as obtained. through hieh-aueular resolution sub-nuunu nuaenie of disks iu nearby SFRs (Andrews&Williaius2007).," For this reason, we consider in this analysis disks with truncated power-law surface densities $\Sigma_{\rm{dust}} \propto r^{-p}$ for $r < R_{\rm{out}}$ and $\Sigma_{\rm{dust}}=0$ for $r > R_{\rm{out}}$ ) with possible $p$ -values between 0 and 1.5, as obtained through high-angular resolution sub-mm imaging of disks in nearby SFRs \citep{Andrews:2007}." . As for the disk outer radius A. the TST aud SMA observations constrained value of Rouzc280 AU the 253-1536a disk aud derived an upper limit of or60 AU for he uuresolved253-1536) disk.," As for the disk outer radius $R_{\rm{out}}$, the HST and SMA observations constrained a value of $R_{\rm{out}} \approx 280$ AU for the 253-1536a disk and derived an upper limit of 60 AU for the unresolved 253-1536b disk." " Since the A, of the 253-1536h disk is not determined by the observations. in the following analysis we will cousider two different yossibilities. namely 2,4;= 10 aud GO AU."," Since the $R_{\rm{out}}$ of the 253-1536b disk is not determined by the observations, in the following analysis we will consider two different possibilities, namely $R_{\rm{out}} = $ 40 and 60 AU." Simaller disks with Row<30 AU always fail to reproduce the measured (sub-)uuu fluxes of253-1536b., Smaller disks with $R_{\rm{out}} \simless 30~$ AU always fail to reproduce the measured (sub-)mm fluxes of253-1536b. This is due to the fact hat the emission of such siunall aud deuse disks becomes optically thick and. as a consequence. uudoerestinates he relatively large (sub-)nuu fluxes of 253-1536h (Testietal. 9001).," This is due to the fact that the emission of such small and dense disks becomes optically thick and, as a consequence, underestimates the relatively large (sub-)mm fluxes of 253-1536b \citep[][]{Testi:2001}." .. Note that these possible values for the outer radius of the 253-1536) disk are all siguificautly ower than the estimated radius of the Roche lobo. i.c. 2100 AU (fomPaczviski1971.usingourestimatesforasalowerlinutforthebinarysenianajor axis)..," Note that these possible values for the outer radius of the 253-1536b disk are all significantly lower than the estimated radius of the Roche lobe, i.e. $\simgreat 100$ AU \citep[from ][using our estimates for the stellar masses, and the projected physical separation as a lower limit for the binary semi-major axis]{Paczynski:1971}. ." This neans that the material in the disk lies well inside the stable zone in the Roche lobe., This means that the material in the disk lies well inside the stable zone in the Roche lobe. Another important parameter is the disk inclination. defined as the angle between the disk axis aud the line-ofsieht.," Another important parameter is the disk inclination, defined as the angle between the disk axis and the line-of-sight." " By taking the ratio of the two projected disk aNCS Jn the TST Tages, we estimated iu inclination ""Eliedfor the 253-15:36a clisk."," By taking the ratio of the two projected disk axes in the HST images, we estimated an inclination $i \sim 55^{\circ}$ for the 253-1536a disk." This procedure cauiot he to the sinaller 225331536) disk. which las iot been (etected by OST.," This procedure cannot be applied to the smaller 253-1536b disk, which has not been detected by HST." Tie X-Shooter spectra show tlat the 253-15361y star ds sieificaitly less extineted than its stellar colmpanion., The X-Shooter spectra show that the 253-1536b star is significantly less extincted than its stellar companion. This indicaes that the 253-1536b ¢isk. is likely less inclined tha1i the companion., This indicates that the 253-1536b disk is likely less inclined than the companion. For this «isk. we considered a rage of ]JOSS]deiuclinations between 07 and 507, For this disk we considered a range of possibleinclinations between $^{\circ}$ and $^{\circ}$. With the parameters ottlinecd above we determined the spectral iudex ο) of the dust οoicitv coefficieut by fitting the loug-wave SED with the wo-laver disk models (secRiccietal., With the parameters outlined above we determined the spectral index $\beta$ of the dust opacity coefficient by fitting the long-wave SED with the two-layer disk models \citep[see][]{Ricci:2010a}. 2010a).. Ταde 2 shows the i values for the possible cliftevent Aa sudcoustrame ; for the 5:-1536b disk. and in the p=l1 case.," Table \ref{tab:models} shows the constrained $\beta$ -values for the possible different $R_{\rm{out}}$ and $i$ for the 253-1536b disk, and in the $p=1$ case." The difference between the estinated values for the 25:M1536b disk is eiven by fie different contribution of the inner optica thick regions to the total cnussion., The difference between the estimated $\beta$ -values for the 253-1536b disk is given by the different contribution of the inner optically thick regions to the total emission. The decrease of Ros. or the increase of/ which increases the Lue-ofsight optical depth of the disk. makes this contribution more important.," The decrease of $R_{\rm{out}}$, or the increase of $i$, which increases the line-of-sight optical depth of the disk, makes this contribution more important." As a consequence. ) becomes larger. i.c. the specrun of the dust cuuissivity steepous. to compensate or the op»osite effect elven by optically thick eiissionu.," As a consequence, $\beta$ becomes larger, i.e. the spectrum of the dust emissivity steepens, to compensate for the opposite effect given by optically thick emission." To better quantify the value of > for the 253-L536) disk. üeh-augular resohοι. Πάσα 1s jiceded. to. directly coustrain its outer radius. and therefore the nupact of ie optically thick inner regions to its total emission.," To better quantify the value of $\beta$ for the 253-1536b disk, high-angular resolution imaging is needed to directly constrain its outer radius, and therefore the impact of the optically thick inner regions to its total emission." The miportaut poiit fo be noticed vere is that for all 16 possible values of tie disk parameters (this result is iichanuged for posside other p-values setween 0 aud 1.5). je J-value constraine for 253-1536 yas lueer than for oe53-15362a.," The important point to be noticed here is that for all the possible values of the disk parameters (this result is unchanged for possible other $p$ -values between 0 and 1.5), the $\beta$ -value constrained for 253-1536b is larger than for 253-1536a." The index carries information oi the size (jas of largest grains in the dust xopulajon of the outer disk (e.gYo.Nattaetal., The $\beta$ -index carries information on the size $a_{\rm{max}}$ of the largest grains in the dust population of the outer disk \citep[e.g.][]{Natta:2007}. 2007).. values lower than about 11.5 can only be expaine wih the xesence of grains as large as at least 0.1 luuui., $\beta$ -values lower than about $1-1.5$ can only be explained with the presence of grains as large as at least $0.1-1~$ mm. Converting au estimate for 34ito one for µιας Is particularly difficult because of our ignorance on the plisvical‘chemical properties ofthe probe dust., Converting an estimate for $\beta$ into one for $a_{\rm{max}}$ is particularly difficult because of our ignorance on the phsyical/chemical properties of the probed dust. However. for all the dust models cousidered iu the literature. a gen valo:uiticorrelatiou between and (anas Is generally obtained for 3S1.5 ," However, for all the dust models considered in the literature, a general anticorrelation between $\beta$ and $a_{\rm{max}}$ is generally obtained for $\beta \simless 1.5$ ." Under the assution that the chemustiv/shape of the dust erains in the wo disks is the same and cousideriie that the dust evolution models iu disks with the coustrained plysical properties predict a slope 4which is rearly ideutical (Birusticletal. 2011).. this means that the observational," Under the assumption that the chemistry/shape of the dust grains in the two disks is the same and considering that the dust evolution models in disks with the constrained physical properties predict a slope $q$which is nearly identical \citep{Birnstiel:2011}, , this means that the observational" (Gould.Flyun (Czis1997). ," \citep{gfb98,gr99} \citep{g97} " found indicate that a sieuificant component of the imeasured redshifts aust be intrinsic.,found indicate that a significant component of the measured redshifts must be intrinsic. The consequences of this couclusion are enormous., The consequences of this conclusion are enormous. Twish to thank an anonviuious referee for several helpful zugeestious pertaining to the prescutation of these results., I wish to thank an anonymous referee for several helpful suggestions pertaining to the presentation of these results. thereby make an important contribution toward answering the questions about the origin of water in planetary systenis.,thereby make an important contribution toward answering the questions about the origin of water in planetary systems. We are grateful to Tin van lxempen lor helpful comments about (he manuscript., We are grateful to Tim van Kempen for helpful comments about the manuscript. Research at Centre for Star and Planet Formation is huided by the Danish National Research Foundation and (he University of Copenhagens programme of excellence., Research at Centre for Star and Planet Formation is funded by the Danish National Research Foundation and the University of Copenhagen's programme of excellence. Research in astrochemistry in Leiden is supported by a Spinoza Grant Irom the Netherlands Organization for Scientific Research (NWO) and à NOVA erant., Research in astrochemistry in Leiden is supported by a Spinoza Grant from the Netherlands Organization for Scientific Research (NWO) and a NOVA grant. This paper is based on data from the Submillimeter Array: the Submillimeter Array is a joint project between the Smithsonian Astrophysical Observatory and the Academia Sinica Institute of Astronomy ancl Astrophysics aud is [ποος bv the Smithsonian Institution and the Academia Sinica., This paper is based on data from the Submillimeter Array: the Submillimeter Array is a joint project between the Smithsonian Astrophysical Observatory and the Academia Sinica Institute of Astronomy and Astrophysics and is funded by the Smithsonian Institution and the Academia Sinica. CL error circle. which is consistent with the three we found (C1-C3. their positions are given in Table 4)).,"CL error circle, which is consistent with the three we found (C1–C3, their positions are given in Table \ref{posc}) )." " The brightest candidate (Cl = J16281083—4838560)) is located at 2"" from the nominal position of the X-ray source. and the other two candidates are closer to it. but several magnitudes fainter."," The brightest candidate (C1 = ) is located at $2\arcsec$ from the nominal position of the X-ray source, and the other two candidates are closer to it, but several magnitudes fainter." None of the candidates is seen in any of the optical images. which is consistent with the strong absorption towards this region (/=335.37. b=+0.1°. Ay=12.3 mag: Beckmann et al. 2005)).," None of the candidates is seen in any of the optical images, which is consistent with the strong absorption towards this region $l = 335.3\degr$, $b = +0.1\degr$, $A_V = 12.3$ mag; Beckmann et al. \cite{Bec05}) )." At this point. there is no preferred candidate: astrometry alone cannot help us identify the. counterpart. ofJ16283—4838.. until subaresecond positioning such as that achievable with is available for this source.," At this point, there is no preferred candidate: astrometry alone cannot help us identify the counterpart of, until subarcsecond positioning such as that achievable with is available for this source." " A logN- logS diagram of the sources in our K, frame shows that there is a probability of finding at least one unrelated NIR source brighter than CI within the CL error. which increases to and for C2 and C3. respectively."," A $\log N$ $\log S$ diagram of the sources in our $K_{\mathrm s}$ frame shows that there is a probability of finding at least one unrelated NIR source brighter than C1 within the CL error, which increases to and for C2 and C3, respectively." This result indicates that Cl is the strongest counterpart candidate., This result indicates that C1 is the strongest counterpart candidate. The faintness of all counterpart candidates makes it difficult to obtain their spectra. Cl being the only case in which we succeeded.," The faintness of all counterpart candidates makes it difficult to obtain their spectra, C1 being the only case in which we succeeded." Given this situation. a careful extraction of the spectrum was performed. especially in terms of sky subtraction and the removal of telluric features.," Given this situation, a careful extraction of the spectrum was performed, especially in terms of sky subtraction and the removal of telluric features." In Fig. 2..," In Fig. \ref{spectra}," we present the NIR spectra of this object taken with the red grism of SOFI (the blue grism spectrum shows a large absorption. which renders it useless).," we present the NIR spectra of this object taken with the red grism of SOFI (the blue grism spectrum shows a large absorption, which renders it useless)." As can be seen in Fig. 2..," As can be seen in Fig. \ref{spectra}," the uncertainty in the continuum position is3-8%.. allowing us to identify only a few features in it. which are listed in Table 5..," the uncertainty in the continuum position is, allowing us to identify only a few features in it, which are listed in Table \ref{lines}." " The Bry line at 2.1655 jm ts clearly seen in emission,", The $\gamma$ line at 2.1655 $\mu$ m is clearly seen in emission. Other hydrogen lines are not detected. probably because their intensities would be below the continuum noise level.," Other hydrogen lines are not detected, probably because their intensities would be below the continuum noise level." In the spectrum of C1. the 1.7002 ym and 2.0581 ym lines are also present. visible in absorption and emission. respectively.," In the spectrum of C1, the 1.7002 $\mu$ m and 2.0581 $\mu$ m lines are also present, visible in absorption and emission, respectively." The 2.112/2.113 um line is marginally detected at the 2c level., The 2.112/2.113 $\mu$ m line is marginally detected at the $\sigma$ level. Since hydrogen and helium lines are the main spectral features. some in emission. C] may be an early-type star.," Since hydrogen and helium lines are the main spectral features, some in emission, C1 may be an early-type star." We also searched for ionized helium features., We also searched for ionized helium features. According to Hanson et al. (2005)).," According to Hanson et al. \cite{Han05}) )," the strongest line in this region of the spectrum is at 2.1885 jim. but we do not detect it.," the strongest line in this region of the spectrum is at 2.1885 $\mu$ m, but we do not detect it." An absorption feature clearly detected near 1.6918 ym in our spectrum could be attributed to the corresponding line., An absorption feature clearly detected near 1.6918 $\mu$ m in our spectrum could be attributed to the corresponding line. However. that this line should be comparable to or weaker than the 2.1885 jum one (Hanson et al. 2005))," However, that this line should be comparable to or weaker than the 2.1885 $\mu$ m one (Hanson et al. \cite{Han05}) )" suggests that it might be an artifact due to subtraction of the sky lines., suggests that it might be an artifact due to subtraction of the sky lines. The lack of lines then implies that Cl is a late O-type or early B-type star., The lack of lines then implies that C1 is a late O-type or early B-type star. Apart from hydrogen and helium lines. we marginally detect other absorption features. which we cannot identify.," Apart from hydrogen and helium lines, we marginally detect other absorption features, which we cannot identify." was found only when data based on all the z<| clusters m their sample were combined (compare with the smaller previous set in their Fig.,was found only when data based on all the $ z < 1 $ clusters in their sample were combined (compare with the smaller previous set in their Fig. 3)., 3). Furthermore. the derived chemical evolution required the use of the formal statistical best fit uncertainty instead of the observed dispersions (e.g. their Fig.," Furthermore, the derived chemical evolution required the use of the formal statistical best fit uncertainty instead of the observed dispersions (e.g. their Fig." 14)., 14). In contrast. for a similar redshift range (below about 0.9). the results of ? are consistent with no evolution.," In contrast, for a similar redshift range (below about 0.9), the results of \citeauthor{Maughan2008} are consistent with no evolution." From the theoretical point of view as described in ?.. ?.. and references therein. the chemical evolution of the ICM is a complex combination of effects due to cluster merging. infall of enriched material. galactic ram pressure stripping. galactic winds. and other possible causes.," From the theoretical point of view as described in \cite{Kapferer}, \cite{Sarazin}, and references therein, the chemical evolution of the ICM is a complex combination of effects due to cluster merging, infall of enriched material, galactic ram pressure stripping, galactic winds, and other possible causes." For the relaxed clusters considered in this paper ? predicted no observable chemical evolution from redshift 0.15 to 0.9., For the relaxed clusters considered in this paper \cite{Kapferer} predicted no observable chemical evolution from redshift 0.15 to 0.9. Our paper shows how it is important to compare like clusters and that there is room for further theoretical studies to understand the apparent lack of evolution of the radial dependence of the enriched material of the ICM. and at the same time induce heating via infall of metal rich gas clouds.," Our paper shows how it is important to compare like clusters and that there is room for further theoretical studies to understand the apparent lack of evolution of the radial dependence of the enriched material of the ICM, and at the same time induce heating via infall of metal rich gas clouds." The data presented here are consistent with no evolution in radial profiles of iron abundance and temperature., The data presented here are consistent with no evolution in radial profiles of iron abundance and temperature. The modeling of this should be consistent with the concept of hierarchical formation of structure in. the universe (e.g.?.andreferencestherein)..," The modeling of this should be consistent with the concept of hierarchical formation of structure in the universe \cite[e.g.][and references therein]{Gao2008}." Because the iron abundance does not appear to be strongly correlated to the overall temperature. gravitational infall is the most likely scenario for heating clusters beyond = 6.5 keV. This infall must take place in such a manner as not to change the radial profile of iron abundance or temperatures.," Because the iron abundance does not appear to be strongly correlated to the overall temperature, gravitational infall is the most likely scenario for heating clusters beyond $\simeq $ 6.5 keV. This infall must take place in such a manner as not to change the radial profile of iron abundance or temperatures." For non-cooling clusters this means the clusters somehow have no measurable temperature gradients inside about 500 kpe but maintain their abundance gradients while (presumably) increasing in temperature in a hierarchical growth model., For non-cooling clusters this means the clusters somehow have no measurable temperature gradients inside about 500 kpc but maintain their abundance gradients while (presumably) increasing in temperature in a hierarchical growth model. In order to demonstrate why infall is the preferred major energy input. the process of heating has to be considered in some detail.," In order to demonstrate why infall is the preferred major energy input, the process of heating has to be considered in some detail." An estimate of the amount of near solar abundance material that is added along with the energy to boost the «KT» from 4 keV to 8 keV is made now., An estimate of the amount of near solar abundance material that is added along with the energy to boost the $<\!\!kT\!\!>$ from 4 keV to 8 keV is made now. We assume typical Ly—T (22?) and Ly—M (e.g.??) relations apply to the clusters studied here.," We assume typical $L_{X}-T$ \citep{Ota,Ettori2004a,Stanek2006} and $L_{X}-M$ \citep[e.g.][]{Rykoff2008,Stanek2006} relations apply to the clusters studied here." Under these assumptions. if the temperature increases by a factor of 2 then the luminosity increases by at least a factor of4 and the mass by a factor of 3. the amount of mass added to the clusters being on the order of 3x10!M...," Under these assumptions, if the temperature increases by a factor of 2 then the luminosity increases by at least a factor of 4 and the mass by a factor of 3, the amount of mass added to the clusters being on the order of $3 \times 10^{14} M_{\odot}$." Since galaxies are thought to make up only about 1/5 of the baryonie mass in clusters (see?.andreferencestherein).. it is implausible that this mass and additional gravitational energy is added by normal galaxies.," Since galaxies are thought to make up only about 1/5 of the baryonic mass in clusters \citep[see][and references there in]{Lowenstein2006}, it is implausible that this mass and additional gravitational energy is added by normal galaxies." This mass and gravitational energy must come instead from the infall of atypical galaxies that have gas masses that greatly exceed their stellar masses or gas clouds that never formed into galaxies., This mass and gravitational energy must come instead from the infall of atypical galaxies that have gas masses that greatly exceed their stellar masses or gas clouds that never formed into galaxies. Damped Lyman « absorbers (DLAs) have metallicities that are near solar at z of | or higher (?.andreferencestherein) which makes the ability to add both mass and metals via infalling clouds plausible.," Damped Lyman $\alpha$ absorbers (DLAs) have metallicities that are near solar at $z$ of 1 or higher \citep[][and references therein]{Meiring2007} which makes the ability to add both mass and metals via infalling clouds plausible." It is beyond the scope of this work. though. to carry out detailed calculations of this infall scenario.," It is beyond the scope of this work, though, to carry out detailed calculations of this infall scenario." However. an implication of the estimates made here ts that sight lines on the outskirts of clusters should show the presence of DLAs at the cluster redshift.," However, an implication of the estimates made here is that sight lines on the outskirts of clusters should show the presence of DLAs at the cluster redshift." Furthermore. if mass 1s added with energy as implied by the L—T and L—M relationships used here. this rules out processes which might provide energy and metals but not significant amounts of additional mass. such as SN or AGNs.," Furthermore, if mass is added with energy as implied by the $L-T$ and $L-M$ relationships used here, this rules out processes which might provide energy and metals but not significant amounts of additional mass, such as SN or AGNs." Instead. suppose that the £L—M relationship used here doesn't apply to these high z clusters.," Instead, suppose that the $L-M$ relationship used here doesn't apply to these high $z$ clusters." In this case. supernovae would still not be a plausible explanation.," In this case, supernovae would still not be a plausible explanation." This is because the energy input of approximately 1097 ergs would require an unreasonably high number of SNe when all the available energy is transferred to the ICM (?).., This is because the energy input of approximately $10^{64}$ ergs would require an unreasonably high number of SNe when all the available energy is transferred to the ICM \citep{Conroy2008}. For example. suppose there are 1.000 galaxies per cluster.," For example, suppose there are 1,000 galaxies per cluster." This translates into 10 SNe per galaxy or 10! SNe/year for 10? years., This translates into $10^{10}$ SNe per galaxy or $10^{1}$ SNe/year for $10^9$ years. It is also implausible that a central AGN could provide this much heat (10% ergs). as this heat would require 10?? erg/year deposited for 1 Gy. or 107 erg s! minimum energy generation assuming efhciency in transfering energy to heat.," It is also implausible that a central AGN could provide this much heat $10^{64}$ ergs), as this heat would require $10^{55}$ erg/year deposited for 1 Gy, or $10^{47}$ erg $^{-1}$ minimum energy generation assuming efficiency in transfering energy to heat." Since the magnitude of heating seems beyond what central AGN activity could provide an infall scenario is a more likely explanation., Since the magnitude of heating seems beyond what central AGN activity could provide an infall scenario is a more likely explanation. Since there is no evidence for evolution in every type of cluster considered in this study (as seen in the figures). it will be assumed for the sake of discussion that clusters are not mixing over this range of redshifts.," Since there is no evidence for evolution in every type of cluster considered in this study (as seen in the figures), it will be assumed for the sake of discussion that clusters are not mixing over this range of redshifts." Beginning with the cool core clusters in Fig. ]..," Beginning with the cool core clusters in Fig. \ref{Fig1}," it is seen that they exhibit almost no signs of evolution in their iron abundance profiles from the 0.4-0.9 redshift bin up to the present day. even though there is a very clear gradient at all redshifts.," it is seen that they exhibit almost no signs of evolution in their iron abundance profiles from the 0.4-0.9 redshift bin up to the present day, even though there is a very clear gradient at all redshifts." This suggests two possible scenarios: either enrichment and mixing both exist in such à way that neither is dominant. or neither process occurs.," This suggests two possible scenarios: either enrichment and mixing both exist in such a way that neither is dominant, or neither process occurs." If neither process occurs. the unchanging iron abundance profile can be explained as being due to the average cluster galaxy having lost most of its gas by z 0.8.," If neither process occurs, the unchanging iron abundance profile can be explained as being due to the average cluster galaxy having lost most of its gas by $z \sim 0.8$ ." In this case the galaxies have no gas to stir up and mix the ICM., In this case the galaxies have no gas to stir up and mix the ICM. An absence of gas in cluster galaxies would also manifest itself in à low. non-evolving star formation rate(?)..," An absence of gas in cluster galaxies would also manifest itself in a low, non-evolving star formation \citep{Homeier2005}." A low star formation rate occurs if ram pressure stripping has removed the majority of the gas from most of the cluster galaxies before redshift z20.8 within 500 kpe of the cluster center. well within theregions observed," A low star formation rate occurs if ram pressure stripping has removed the majority of the gas from most of the cluster galaxies before redshift $z = 0.8$ within 500 kpc of the cluster center, well within theregions observed" makes a prediction: spectral steepening to higher X-rav chereies.,makes a prediction: spectral steepening to higher X-ray energies. For SN 1006. this has been coufiriied. by INTEGRAL (Ialo1ucietal.2006).," For SN 1006, this has been confirmed by INTEGRAL \citep{kalemci06}." ". There are now four known Galactic remnants whose soft N-rav spectrum is dominated by svuchrotrou rave: In addition to SN 1006. 011.910.3. (Revnoldsetal.2008b): €2317.3-0.5 (alsoknownasCNJ1713.1-39016Slaneetal. 1999): aud. (2002-12. ""Vela. Jy. (Aschenbach1998:Slanectal.2001)... ("," There are now four known Galactic remnants whose soft X-ray spectrum is dominated by synchrotron X-rays: in addition to SN 1006, G1.9+0.3 \citep{reynolds08b}; ; G347.3-0.5 \citep[also known as GX J1713.7-3946][] {slane99}; and G266.2-1.2, “Vela Jr.” \citep{aschenbach98, slane01}. (" See Reynolds 2008a for à more detailed review of SNR N-ray aud 5- enudssion.),See Reynolds 2008a for a more detailed review of SNR X-ray and $\gamma$ -ray emission.) Figure 2. shows the images of SN 1006 aud C€1.9|0.3.," Figure \ref{g1.9} shows the images of SN 1006 and G1.9+0.3." For both objects. thermal lines have been detected from fainter regions of the roiinant.," For both objects, thermal lines have been detected from fainter regions of the remnant." The low-euergv (central) eiissiou im Fig., The low-energy (central) emission in Fig. 2 is primarily ejecta euission dominated by oxvgeu., \ref{g1.9} is primarily ejecta emission dominated by oxygen. Figure { shows the spectrum from the interior of G1.9|0.3. with clear clnission lines of Si. S. aud Ar.," Figure \ref{g1.9spec} shows the spectrum from the interior of G1.9+0.3, with clear emission lines of Si, S, and Ar." X-ray Synchrotroneiission contributes to the spectrmufhsstme of several more Galactic remmants (reviewed in Reyvuoldsg 2008a)., Synchrotron X-ray emission contributes to the spectrum of several more Galactic remnants (reviewed in Reynolds 2008a). Iu historical (0r quasi-listorical) ταῖς ROW a6 (SN 1857).," In historical (or quasi-historical) remnants RCW 86 (SN 185?)," " Tycho (SN 1572). Kepler (SN LOL. aud Cas A (SN ~ 1680). ""thin rims” of featureless N-rav cussion lie at the edges of the roeninantfs. and are presumed to indicate the outer blast wave."," Tycho (SN 1572), Kepler (SN 1604), and Cas A (SN $\sim 1680$ ), “thin rims” of featureless X-ray emission lie at the edges of the remnants, and are presumed to indicate the outer blast wave." Furthermore. all these remuauts along with SN 1006 have been reported to have hard X-ray continua in integrated spectral (noun-innagiug) observations with the PCA iustruncut on RNTE (Allen.Gotthelf.&Pe-tre 1999).," Furthermore, all these remnants along with SN 1006 have been reported to have hard X-ray continua in integrated spectral (non-imaging) observations with the PCA instrument on RXTE \citep{allen99}." . It appears that svuchrotron X-ray. cussion from the blast wave is a common feature in voung SNRs. less than a few thousand vears old.," It appears that synchrotron X-ray emission from the blast wave is a common feature in young SNRs, less than a few thousand years old." " The miplications are stridiug: electrons are present m these objects with energies E-—T2(hvflπολ(BAOπαH? Tey, Now he electron distributions are not straight power-aves all the wav from radio-enudttius energies (ca."," The implications are striking: electrons are present in these objects with energies $E = 72 (h\nu/1 \ {\rm keV})^{1/2} (B /10\ \mu{\rm G})^{-1/2}$ TeV. Now the electron distributions are not straight power-laws all the way from radio-emitting energies (ca." 10 GeV) rather. in all known cases the observed ravs fall below that extrapolation (Revnolds&Ίνου-mane 1999).. indicating that some lanitation on electron energies is taking place below 100 TeV (perhaps far low. for those older SNRs with no evidence for svuchrotron N-rav ciuission}).," 10 GeV); rather, in all known cases, the observed X-rays fall below that extrapolation \citep{reynolds99}, indicating that some limitation on electron energies is taking place below 100 TeV (perhaps far below, for those older SNRs with no evidence for synchrotron X-ray emission)." As will be simunnuuuized close. shock acceleration may be mated by the finite age Cor size) of the remnant. particle escape above some euerev due to abseuce of scattering waves upstreun. or (affecting electrons only) radiative losses.," As will be summarized below, shock acceleration may be limited by the finite age (or size) of the remnant, particle escape above some energy due to absence of scattering waves upstream, or (affecting electrons only) radiative losses." Iu standard diffusive shock acceleration (amplyre-viewedinBlaudtford&Eichler 1987).. particles scatter from) inagnetie iuhoimoseneities borne bv couvereiug fiuids ou either side of a shock wave. gaining ΟΠΟΥ with cach reflection.," In standard diffusive shock acceleration \citep[amply reviewed in][]{blandford87}, particles scatter from magnetic inhomogeneities borne by converging fluids on either side of a shock wave, gaining energy with each reflection." Most particles disappear dowustreani after cach return. but a decreasing nunboer remains for further cycles. producing a power-law distribution (see Dell 1978 for a kineticctheory. probabilistic argument).," Most particles disappear downstream after each return, but a decreasing number remains for further cycles, producing a power-law distribution (see Bell 1978 for a kinetic-theory probabilistic argument)." A well-kuown result of this process. for euergeticallv inimnportaut test particles. ix a power-law distribution with index dependent only on the shock compression ratio: N(E)xE5 with s=(r|2)(r1) where r=opofpy is the shock compression ratio. equal to | for «ποιο shocks.," A well-known result of this process, for energetically unimportant test particles, is a power-law distribution with index dependent only on the shock compression ratio: $N(E) \propto E^{-s}$ with $s = (r + 2)/(r - 1)$ where $r \equiv \rho_2/\rho_1$ is the shock compression ratio, equal to 4 for strong shocks." This result applies to extreme-relativistic particles CE=pe. p the momentum aud e the speed of helt).," This result applies to extreme-relativistic particles $E \cong pc,$ $p$ the momentum and $c$ the speed of light)." The prediction is thus s=2 which. for electrons. inples a svuchrotrou spectral iudex a=(s1)/2-0.5. in tolerable agreement with spectra observed from Calactic SNRs.," The prediction is thus $s \cong 2$ which, for electrons, implies a synchrotron spectral index $\alpha = (s - 1)/2 = 0.5$ , in tolerable agreement with spectra observed from Galactic SNRs." The maxinuun euergv to which particles can be accelerated depends ou the hlnuüitimg mechanisu., The maximum energy to which particles can be accelerated depends on the limiting mechanism. We ai cdiffision cocficient & which scales with article cucrey., We assume a diffusion coefficient $\kappa$ which scales with particle energy. " This results if the particle mea- ree path is a iuultiple a of its gvroradius Aug,ry=YLfeD for ultrarclativistic particles. since ry=wanesο (ces units)."," This results if the particle mean free path is a multiple $\eta$ of its gyroradius: $\lambda_{\rm mfp} = \eta r_g = \eta E/eB$ for ultrarelativistic particles, since $r_g = \gamma m c^2/eB$ (cgs units)." Then the “Bolum Πιτ in which he mean free path is a gyroradius is 4j=1., Then the “Bohm limit” in which the mean free path is a gyroradius is $\eta = 1$. For weak urbuleuce. oue expects 421. though this may uot ve a hard plivsical lait.," For weak turbulence, one expects $\eta \ge 1$, though this may not be a hard physical limit." " For a remnant of age f with shock speed ay. with surroundings containius MIID scattering waves only up to a wavelength Aas. the Mand cCulereles scale as Iu all cases. for vy,21000 kins 1 and ages above a few hundred years. maxi enereies of 10 100 TeV are casily obtainable."," For a remnant of age $t$ with shock speed $u_{\rm sh}$, with surroundings containing MHD scattering waves only up to a wavelength $\lambda_{\rm max}$ , the maximum energies scale as In all cases, for $u_{\rm sh} \gapprox 1000$ km $^{-1}$ and ages above a few hundred years, maximum energies of 10 – 100 TeV are easily obtainable." The accelerated-particle spectra should show exponeutial cutoffs with these fiducial energies., The accelerated-particle spectra should show exponential cutoffs with these fiducial energies. " For svuchrotrou emission. the depeudeuce of he peak frequency vy, ou electron energy. of jj,xE? ueans that the svuchrotron spectrmu will then drop roughly as rVUEEas tlat is. considerablv slower han exponential. and hardly differing from a power-law in the bandpass of 1u0sf. N-rav observatories (~0.3.1 sev)."," For synchrotron emission, the dependence of the peak frequency $\nu_m$ on electron energy of $\nu_m \propto E^2$ means that the synchrotron spectrum will then drop roughly as $\nu^{-\sqrt{(E/E_{\rm max})}}$, that is, considerably slower than exponential, and hardly differing from a power-law in the bandpass of most X-ray observatories $\sim 0.3 - 10$ keV)." The diffusion cocficient nav be anisotropic: in articular. diffusion aloug and across magnetic-ficlel ines ds Likely to take place at different rates. with effects on the acceleration time 7 tosome energw.," The diffusion coefficient may be anisotropic; in particular, diffusion along and across magnetic-field lines is likely to take place at different rates, with effects on the acceleration time $\tau$ tosome energy." " If he shock velocity makes au angele Op, with the mca- upstream niageuetic field.we can parameterize this effect with Πο.yer)Opn)τν, 0)."," If the shock velocity makes an angle $\theta_{\rm Bn}$ with the mean upstream magnetic field,we can parameterize this effect with $R_J(\theta_{\rm Bn}, \eta, r) \equiv \tau(\theta_{\rm Bn})/\tau(\theta_{\rm Bn} = 0)$ ." We scale. to ypical values for young SNRs: 4x5—aa/3000 kins |: Πο x: Byy=B/LO pC: aud Ape=Aqase/107 ," We scale to typical values for young SNRs: $u_{8.5} \equiv u_{\rm sh}/3000$ km $^{-1}$ ; $t_3 \equiv t/1000$ yr; $B_{10} \equiv B/10 \ \mu{\rm G}$ ; and $\lambda_{17} \equiv \lambda_{\rm max}/10^{17}$ " increasing frequencies and dust contribution (both galactic and extragalactic) becomes dominant.,increasing frequencies and dust contribution (both galactic and extragalactic) becomes dominant. " Therefore in relatively narrow frequency range the CMB is surpassed by dust aemission, and it is in this frequency range where an extrapolation of dust properties (observed at high frequencies) down to lower frequencies (where CMB is dominant) must be carried out."," Therefore in a relatively narrow frequency range the CMB is surpassed by dust emission, and it is in this frequency range where an extrapolation of dust properties (observed at high frequencies) down to lower frequencies (where CMB is dominant) must be carried out." " On the large angular scales of relevance for the ISW it is dust in the Milky Way the main source of contamination, and its accurate subtraction is actual critical for our purposes."," On the large angular scales of relevance for the ISW it is dust in the Milky Way the main source of contamination, and its accurate subtraction is actual critical for our purposes." " An experiment like HFI counts with frequency channels centered at 353, 545 and 857 GHz, which probe the regime where dust emission is well above the CMB contribution."," An experiment like HFI counts with frequency channels centered at 353, 545 and 857 GHz, which probe the regime where dust emission is well above the CMB contribution." We shall use those channels to correct for dust (both galactic and extragalactic) at lower frequencies., We shall use those channels to correct for dust (both galactic and extragalactic) at lower frequencies. " Our approach attempts by no means to be exhaustive nor systematic, but simply tries to display the degree of accuracy required at subtracting dust emission in order to unveil the tSZ — ISW cross correlation in a Planck-like experiment."," Our approach attempts by no means to be exhaustive nor systematic, but simply tries to display the degree of accuracy required at subtracting dust emission in order to unveil the tSZ – ISW cross correlation in a -like experiment." " We first built a mask that covered those regions where the Milky Way emission, in radio and sub-millimeter was stronger."," We first built a mask that covered those regions where the Milky Way emission, in radio and sub-millimeter was stronger." We sorted in intensity (from bigger to smaller values) the templates of free-free and synchrotron in the V band (as produced by the WMAP team) and the SFD dust template at 353 GHz., We sorted in intensity (from bigger to smaller values) the templates of free-free and synchrotron in the V band (as produced by the WMAP team) and the SFD dust template at 353 GHz. " Masking a given level of emission (for instance, the of brightest pixels) in each template yielded two masks that were very similar (particularly in the galactic plane), with differences corresponding mostly to high latitude clouds being bright either in the radio or submillimeter (but not on both)."," Masking a given level of emission (for instance, the of brightest pixels) in each template yielded two masks that were very similar (particularly in the galactic plane), with differences corresponding mostly to high latitude clouds being bright either in the radio or submillimeter (but not on both)." The final mask was the product of the two masks built upon the radio and dust templates., The final mask was the product of the two masks built upon the radio and dust templates. " The fraction of un-covered sky, fy, was then set as a free parameter in the mask construction."," The fraction of un-covered sky, $f_{sky}$, was then set as a free parameter in the mask construction." " According to the SFD dust templates, one has to take into account the spatial variation of the effective spectral index if one is to accurately correct for dust emission in the 100 - 217 GHz frequency range."," According to the SFD dust templates, one has to take into account the spatial variation of the effective spectral index if one is to accurately correct for dust emission in the 100 - 217 GHz frequency range." " In these templates, an effective spectral coefficient in thermodynamic temperature (defined as the ratio of thermodynamic temperatures between two different channels, L.€., 0353,;=ÓTj/ÓTsss Guz) is correlated with the thermodynamic temperature at 353 GHz, as the left panel of Fig."," In these templates, an effective spectral coefficient in thermodynamic temperature (defined as the ratio of thermodynamic temperatures between two different channels, i.e., $\alpha_{353,\;j} \equiv \delta T_j / \delta T_{353\;GHz} $ ) is correlated with the thermodynamic temperature at 353 GHz, as the left panel of Fig." 11 shows., \ref{fig:galaxy1} shows. " The curvature at low temperatures is a consequence of the grey body law describing the dust emission in IR galaxies, and we make use of it when subtracting the dust emission at low frequencies."," The curvature at low temperatures is a consequence of the grey body law describing the dust emission in IR galaxies, and we make use of it when subtracting the dust emission at low frequencies." " In this low temperature regime, the effective spectral coefficients from IR galaxies differ from the that of the Milky Way, and for this reason a more accurate scaling could be obtained by treating the local cirrus component separately from the extra-galactic IR one."," In this low temperature regime, the effective spectral coefficients from IR galaxies differ from the that of the Milky Way, and for this reason a more accurate scaling could be obtained by treating the local cirrus component separately from the extra-galactic IR one." " This can be achieved, in high lattitude regions, using H1 data that traces the galactic cirrus emission, in order to remove their contribution."," This can be achieved, in high lattitude regions, using H1 data that traces the galactic cirrus emission, in order to remove their contribution." " We sorted pixels64 outside the mask according to their intensity in the dust template at 353 GHz, and binned them in groups of length ng,o,)s, in each of which a different estimate of a5;; is estimated in the low frequencychannels?."," We sorted pixels outside the mask according to their intensity in the dust template at 353 GHz, and binned them in groups of length $n_{groups}$, in each of which a different estimate of $\alpha_{353,j}$ is estimated in the low frequency." . At these frequencies the observed signal in pixel fi is modeled as where M??*(fi) is the dust template at 353 GHz (including both, At these frequencies the observed signal in pixel $\vnh$ is modeled as where $M^{353}(\vnh ) $ is the dust template at 353 GHz (including both adopted thin-disc approximation is vertically constant. as a function of height above the midplane. expressed in units of the tidal scale-height.,"adopted thin-disc approximation is vertically constant), as a function of height above the midplane, expressed in units of the tidal scale-height." The right panel shows corresponding ruus for all velocity commponcuts. measured with respect to the Ieplerian velocity cy and normalised by the isothermal sound speed «e.," The right panel shows corresponding runs for all velocity components, measured with respect to the Keplerian velocity $v_{\rm K}$ and normalised by the isothermal sound speed $c_{\rm s}$." This solution illustrates the main features of wincls accelerated ceutrifueallv from strongh-maguetised discs (W893)., This solution illustrates the main features of winds accelerated centrifugally from strongly-magnetised discs (WK93). Three distinct lavers can typically be identified, Three distinct layers can typically be identified. These lavers are presented schematically in Fig. 3..," These layers are presented schematically in Fig. \ref{fig:sim}," aud described below., and described below. Iu the specific solution shown in Fie. 2..," In the specific solution shown in Fig. \ref{fig:illus}," the quasi-hydrostatic laver. which encompasses the section of the disc associated with strong eracieuts in the fluid density and magnetic field compoucuts. extends from z//hiy—0 to z/fhiyzz0.1 (the region shaded in red in the left pancl of the Seguro).," the quasi-hydrostatic layer, which encompasses the section of the disc associated with strong gradients in the fluid density and magnetic field components, extends from $z/h_{\rm T} = 0$ to $z/h_{\rm T} \approx 0.4$ (the region shaded in red in the left panel of the figure)." The transition region lies directly above it. aud. extends up to the height where the azimuthal velocity becomes Iepleriau (up to the vertical red line iu the right panel) so it constitutes the region where OlXi/hySLs.," The transition region lies directly above it, and extends up to the height where the azimuthal velocity becomes Keplerian (up to the vertical red line in the right panel), so it constitutes the region where $0.4 \lesssim z/h_{\rm T} \lesssim 1.8$." Finally. the wind region satisfies tflig>ds.," Finally, the wind region satisfies $z/h_{\rm T} > 1.8$." Note that in the first two lavers (1.0. within the disc) the radial velocity is negative. the azimuthal velocity is sub-I&eplerian aud the vertical velocity is sunall.," Note that in the first two layers (i.e. within the ) the radial velocity is negative, the azimuthal velocity is sub-Keplerian and the vertical velocity is small." Iu thewired laver. ou the other haud. all these velocities [ένeye)/e.| are positive aud increasing with ," In the layer, on the other hand, all these velocities $(\mathbf{v} - v_{\rm K}\hat{\mathbf{\phi}})/c_{\rm s}$ ] are positive and increasing with $z$." Solutions such as the oue shown in Fig., Solutions such as the one shown in Fig. 2 are found or relatively stroug maguctic fields. such that ay=1.," \ref{fig:illus} are found for relatively strong magnetic fields, such that $a_{\rm 0} \lesssim 1$." Under these fluid couditious. the MBI is expected to )o suppressed because the wavelength of the critical AIBI-uustable mode (ongward of which the instability operates: see Balbus&Hawley19913) exceeds the naeneticallyveduced density scale-height f (W893).," Under these fluid conditions, the MRI is expected to be suppressed because the wavelength of the critical MRI-unstable mode (longward of which the instability operates; see \citealt{BH91}) ) exceeds the magnetically-reduced density scale-height $h$ (WK93)." For the particular solution shown iu the figure. the naenetic field is strouglv coupled to matter even at he disce midplane (Ayὃν1). and ambipolar diffusion dominates over the eutire cross-section of the disc.," For the particular solution shown in the figure, the magnetic field is strongly coupled to matter even at the disc midplane $\Lambda_{\rm 0} \gg 1$ ), and ambipolar diffusion dominates over the entire cross-section of the disc." For siauplicitv. the diffusivity components are assumed to scale with heigh oeji such away that the local Elsasser iuuber (A) remains coustant with :.," For simplicity, the diffusivity components are assumed to scale with height in such a way that the local Elsasser number $\Lambda$ ) remains constant with $z$." Under these approxinationus. it is solf-consisteut to find relatively Heh values of the inward velocity of the fluid at the disc uidplaue (of the order of the isothermal sound. speed. such that the parameter e is in the range of 0.3. 1).," Under these approximations, it is self-consistent to find relatively high values of the inward velocity of the fluid at the disc midplane (of the order of the isothermal sound speed, such that the parameter $\epsilon$ is in the range of 0.3 – 1)." A nore realistic treatineut of the fluid conditions would incorporate the vertical stratification of the diffusivity. with different regimues dominating at different vertical ocatious (see section 2.11). aud possibly a maguetically weakly-coupled region in the disc interior.," A more realistic treatment of the fluid conditions would incorporate the vertical stratification of the diffusivity, with different regimes dominating at different vertical locations (see section \ref{subsec:Magdiff}) ), and possibly a magnetically weakly-coupled region in the disc interior." In the latter case. In particular. more moderate values of the ivard How speed at the midplane are expected (Li1996:War-dle1997.seealsoFig.5. below).," In the latter case, in particular, more moderate values of the inward flow speed at the midplane are expected \citep[][see also Fig.~\ref{fig:real_sol} ." The next issuc to consider is that iu order to compute selfconsisteut. coupled dise-wind solutions. it is essential to solve simultaneously for tle complex iuteractious between the ogas aud the magnetic feld within the dise where the launching process occurs as well as to follow the acceleration of the wind past he critical surfaces of the flow.," The next issue to consider is that in order to compute self-consistent, coupled disc-wind solutions, it is essential to solve simultaneously for the complex interactions between the gas and the magnetic field within the disc – where the launching process occurs – as well as to follow the acceleration of the wind past the critical surfaces of the flow." Physical quantities of critical miportance. such as the eas censity aud he ionisation fraction. are expected to vary by many orders of maguitude between the disc midplane aud its surface.," Physical quantities of critical importance, such as the gas density and the ionisation fraction, are expected to vary by many orders of magnitude between the disc midplane and its surface." For example. the eas density typically drops we ~6 orders of magnitude across the half-thickuess of he disc.," For example, the gas density typically drops by $\sim 6$ orders of magnitude across the half-thickness of the disc." As a result. oelobal sinmlatious of these winds wave adopted a iuuboer of simplifications to treat the nuderlving disc.," As a result, global simulations of these winds have adopted a number of simplifications to treat the underlying disc." Iu some Guchiding the pioucering work of BPs2). the disc is treated as a boundary condition. outside of the computational domain.," In some (including the pioneering work of BP82), the disc is treated as a boundary condition, outside of the computational domain." Other authors have attempted to incorporate the disc. either via," Other authors have attempted to incorporate the disc, either via" DM Tau for gain calibration.,DM Tau for gain calibration. The baudpass respouse was calibrated with observations o“Uranus al| the available bright quasars 3C273. 3C[51.3 aud 3C8L.," The bandpass response was calibrated with observations of Uranus and the available bright quasars 3C273, 3C454.3 and 3C84." Observations o“Uranus and Callisto proviclec| the absolute scale for flux densities. via comparison to theoretical 1iodels for their enission. al| the two calibrators ag‘fee within tlie expected uucertaiuties. but all 'eported data we'e calibrelec| with Callisto.," Observations of Uranus and Callisto provided the absolute scale for flux densities, via comparison to theoretical models for their emission, and the two calibrators agree within the expected uncertainties, but all reported data were calibrated with Callisto." The systeimatic uncertainty in the absolte [ux scale is ων..., The systematic uncertainty in the absolute flux scale is $\sim$. The dat:| were ecditec| and calibrated with t1e IDL-based MIR softwaresage., The data were edited and calibrated with the IDL-based MIR software. ".. Contiu,.nun and spectra line iniiges were eenerated aud CLEANed using MIRIAD.", Continuum and spectral line images were generated and CLEANed using MIRIAD. To check that the Ilix calibration is accurate. we compared the continuuu fluxes of 0.22 Jy at 0.87 uun and 0.30 Jy at 0.81 mun with previously published values (Aud‘ews&Williams2005.2007). :1da found that they agree within the reported uncertaluties.," To check that the flux calibration is accurate, we compared the continuum fluxes of 0.22 Jy at 0.87 mm and 0.30 Jy at 0.81 mm with previously published values \citep{Andrews05,Andrews07} and found that they agree within the reported uncertainties." The H'*CO J=3-2 line at 260.255 GHz was observed toward DA Tau on 2011 January 25 with the IRAM 30 meter telescope., The $^{13}$ $^+$ J=3–2 line at 260.255 GHz was observed toward DM Tau on 2011 January 25 with the IRAM 30 meter telescope. " The observatious were carried out with the EMIR 330 GHz receiver. with a beam size «M 9 ""iTEPIS] (FWHM)."," The observations were carried out with the EMIR 330 GHz receiver, with a beam size of $\sim$ 5 (FWHM)." The receiver was coinected to a unit of the autocorrelator with a spectral resolution of 320 kHz and a baudwidth of 210 MHz. equivalent to ai unsimoothed velocity resolution o 0.E kis +.," The receiver was connected to a unit of the autocorrelator with a spectral resolution of 320 kHz and a bandwidth of 240 MHz, equivalent to an unsmoothed velocity resolution of $\sim$ 0.4 km $^{-1}$." " Typical system temperatu'es were 300-[00 Ix. The observations were carried out usiug wobbler swichine wi ha 100"" throw.", Typical system temperatures were 300-400 K. The observations were carried out using wobbler switching with a $100''$ throw. " Pointing was checkec every 2 hours on JO1304-0252 aixd J03164-113. w‘Uh a typical aceuracy of <2"".", Pointing was checked every $\sim$ 2 hours on J0430+052 and J0316+413 with a typical accuracy of $<2''$. " The imain-beaim brightuess temperature was calcuated from the alela teuperatures inpao using reported maii beam aud forward efficiencies (B,p and Far) of and.. respectively."," The main-beam brightness temperature was calculated from the antenna temperatures in using reported main beam and forward efficiencies $_{\rm eff}$ and $_{\rm eff}$ ) of and, respectively." The data were reduce with the CLASS program. part of he GILDAS sofwarecave’.," The data were reduced with the CLASS program, part of the GILDAS software." Linear baselines were determiuec [rom velocity rauges without emission features. axl then sibtracted Grom the spectra.," Linear baselines were determined from velocity ranges without emission features, and then subtracted from the spectra." " We did not detect either the HoD lio—Ly, line or the NoH J=I1-3 line."," We did not detect either the $_2$ $^+$ $1_{1,0}-1_{1,1}$ line or the $_2$ $^+$ J=4–3 line." Figure 2. slOWS lunagineg upper limits for these lines. aloug with moment maps for the CO J—3-2 liue aud th‘eo |ies [rom other molecular ious. J=3B-2. J—3-2 aud NoH J=3-2 (Obergetal.20.LO).," Figure \ref{fig1} shows imaging upper limits for these lines, along with moment maps for the CO J=3–2 line and three lines from other molecular ions, $^+$ J=3–2, $^+$ J=3–2 and $_2$ $^+$ J=3–2 \citep{Oberg10c}." . The velocity gradjent cue to disk rotation appears πα. in all of the moment maps. evel for the weak NoH and emission.," The velocity gradient due to disk rotation appears similar in all of the moment maps, even for the weak $_2$ $^+$ and $^+$ emission." The apparent disk sizes are also similar within the unceralules., The apparent disk sizes are also similar within the uncertainties. To estimate the cisk emission region. we fit au elliptical Gaussian to the CO J—3-2 visibililes.," To estimate the disk emission region, we fit an elliptical Gaussian to the CO J=3–2 visibilities." The resultiug major aud minor FWHM are 3711 aud 2755., The resulting major and minor FWHM are 1 and 5. The ellective disk size is cleined as, The effective disk size is defined as Flexion should dominate over shear on small scales (Baconetal.2006) since flexion effects ave higher-order deformation of the gravitational potential.,Flexion should dominate over shear on small scales \citep{flexion:bacon06} since flexion effects are higher-order deformation of the gravitational potential. Small scale mass distributions should therefore be covered with higher fidelity with flexion., Small scale mass distributions should therefore be covered with higher fidelity with flexion. But what happens when measurement errors are added to the data?, But what happens when measurement errors are added to the data? The intrinsic ellipticity aud the measurement errors on the shear estimation of background ealaxies result in an additive Gaussian noise on each shear component (see equation 6))., The intrinsic ellipticity and the measurement errors on the shear estimation of background galaxies result in an additive Gaussian noise on each shear component (see equation \ref{eq_gamma}) ). The standard dispersion on the shear measurement is o6;0.3 (Brainerdeal.1996)., The standard dispersion on the shear measurement is $\sigma^{\gamma}_\epsilon \simeq 0.3$ \citep{astro:brainerd96}. ".. The noise on the convergence map &, 1s an additive noiseN: where: The noise NV in ry, is süll white. Gaussian and uncorrelated."," The noise on the convergence map $\kappa_n$ is an additive noise$N^{\gamma}$ : where: The noise $\hat{N}$ in $\hat{\kappa}_n$ is still white, Gaussian and uncorrelated." " The noise is not ampliliec! by the inversion. but #,, can be dominated by noise if Nis large. which happens in practice."," The noise is not amplified by the inversion, but $\hat{\kappa}_n$ can be dominated by noise if $\hat{N}$ is large, which happens in practice." To simulate space observations. a realistic white Gaussian noise has been added (o simulated shear maps.," To simulate space observations, a realistic white Gaussian noise has been added to simulated shear maps." " The reconstructed convergence map is dominated by a while gaussian noise (o,= 0.1831).", The reconstructed convergence map is dominated by a white gaussian noise $\sigma_n=0.181$ ). The middle panel of Fig., The middle panel of Fig. 1. shows the reconstructed convergence map smoothed by a Gaussian kernel of 15°.," \ref{convergence} shows the reconstructed convergence map smoothed by a Gaussian kernel of 15""." The smoothing is used (o enable the detection of sole clusters., The smoothing is used to enable the detection of some clusters. The measurement errors on the flexion estimation of background galaxies result in an additive Gaussian noise on each flexion component J£; (see equation 111)., The measurement errors on the flexion estimation of background galaxies result in an additive Gaussian noise on each flexion component $\mathcal{F}_i$ (see equation \ref{eq:flex6}) ). The dispersion on the flexion measurement (hat comes essentially [rom the flexion measurement errors is chosen to beo?~0.04 +., The dispersion on the flexion measurement that comes essentially from the flexion measurement errors is chosen to be$\sigma^{\mathcal{F}}_\epsilon \simeq 0.04$ $^{-1}$ . " Thenoise appears on the convergence map A, as an additive noise N:", Thenoise appears on the convergence map $\kappa_n$ as an additive noise $N$ : the starburst occurs.,the starburst occurs. Therefore the fraction of metal rich stars becomes large even in cdwarl ellipticals., Therefore the fraction of metal rich stars becomes large even in dwarf ellipticals. When the star formation time-scale is short enough (~2 (αντ). the feedback moclel in the starburst does not allect the CAIR because almost all of the stars are formed in disc where the feedback is always ellective.," When the star formation time-scale is short enough $\sim 2$ Gyr), the feedback model in the starburst does not affect the CMR because almost all of the stars are formed in disc where the feedback is always effective." Such a value of star formation time-scale is often used For describing star formation in early-type disc ealaxies (e.g... Arimoto. Yoshii Takahara 1991).," Such a value of star formation time-scale is often used for describing star formation in early-type disc galaxies (e.g., Arimoto, Yoshii Takahara 1991)." In our model based on the hierarchical clustering scenario. the metals released. to hot. gas return to. cold eas later.," In our model based on the hierarchical clustering scenario, the metals released to hot gas return to cold gas later." We must evaluate whether this metal recycling allects the luminosity-metallicity relation., We must evaluate whether this metal recycling affects the luminosity-metallicity relation. When /z7. the reheated eas mass and. newly formed stellar mass fractions ac When considering small galaxies. which have a strong eedback ellicieney (67> 1). most of cold gas are transformed o hot gas.," When $t\gg\tau_{*}$, the reheated gas mass and newly formed stellar mass fractions are When considering small galaxies, which have a strong feedback efficiency $\beta\gg 1$ ), most of cold gas are transformed to hot gas." So it is dillicult for such small galaxies to form veh metallicity stars., So it is difficult for such small galaxies to form high metallicity stars. Ht means that the amount of metals ormed in the galaxies is small., It means that the amount of metals formed in the galaxies is small. Pherefore the hot gas does not evolve chemically., Therefore the hot gas does not evolve chemically. Thus the ellect of metal recycling fron ιοί eas to cold gas is slight., Thus the effect of metal recycling from hot gas to cold gas is slight. In order to confirm this. we calculate the CMI by using the model in which the metals retος from hot gas to cold gas are removed by hand.," In order to confirm this, we calculate the CMR by using the model in which the metals returned from hot gas to cold gas are removed by hand." We ind that the dillerence between the results of considering such metals and removing metals is small. about 0.2 mag ower in 1A in all range of magnitude. and that. the dillerence. between the slopes is negligible.," We find that the difference between the results of considering such metals and removing metals is small, about 0.2 mag lower in $V-K$ in all range of magnitude, and that the difference between the slopes is negligible." Pherefore. the elfect of the metal recycling is negligible with regard to the slope of the CAI., Therefore the effect of the metal recycling is negligible with regard to the slope of the CMR. In this paper. we show the physical mechanisms forming he CALRs and. discuss the possible effects on the CALs.," In this paper, we show the physical mechanisms forming the CMRs and discuss the possible effects on the CMRs." We find a kind of ‘degeneracy’ among the star formation. he feedback. and the UV background for making the slope of the CARs.," We find a kind of `degeneracy' among the star formation, the feedback, and the UV background for making the slope of the CMRs." This degeneracy will be solved by comparing other statistical properties of galaxies such as. luminosity function ancl colour distribution in future work., This degeneracy will be solved by comparing other statistical properties of galaxies such as luminosity function and colour distribution in future work. Moreover. we should consider the tightness of CALRs.," Moreover, we should consider the tightness of CMRs." The tightness may reflect the dispersion of the mean stellar ages., The tightness may reflect the dispersion of the mean stellar ages. Llowever he colour of each galaxy is not simply estimated through its mean stellar metallicity and age., However the colour of each galaxy is not simply estimated through its mean stellar metallicity and age. “Phis is probably because a recent star formation by merging with small galaxies allects he colour., This is probably because a recent star formation by merging with small galaxies affects the colour. Ες ellect is more emphasized in. U-V. rather han ΧΑ. and the dispersions of the U-V CARs are Larger han those of the V-Ix CALRS especially in the case of 7?=20 Gyr.," This effect is more emphasized in U-V rather than V-K, and the dispersions of the U-V CMRs are larger than those of the V-K CMRs especially in the case of $\tau_{*}^{0}=20$ Gyr." We will investigate the origin of the tightness minutely in future work., We will investigate the origin of the tightness minutely in future work. We wish to thank E. Takahara. Y. Fujita. T. Yano. M. Sasaki. E. Ixodama and N. Arimoto for useful suggestions.," We wish to thank F. Takahara, Y. Fujita, T. Yano, M. Sasaki, T. Kodama and N. Arimoto for useful suggestions." This work was supported in part by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists (No., This work was supported in part by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists (No. 2265). and in part by the Cuant-in-Aicd for Scientific Research (No.," 2265), and in part by the Grant-in-Aid for Scientific Research (No." 10640229) from the Alinistry of Education. Science. Sports and Culture of Japan.," 10640229) from the Ministry of Education, Science, Sports and Culture of Japan." "Let 7CN.1) denote a forest with ;N roots (that is, ;/Nrooted trees) and + non-root vertices.","Let ${\cal T}(N,n)$ denote a forest with $N$ roots (that is, $N$rooted trees) and $n$ non-root vertices." Consider a uniform distribution on the set of such 7(UN.1) forests.," Consider a uniform distribution on the set of such ${\cal T}(N,n)$ forests." Let £;=&nd] .m]...A.- denote the number ol. non-root vertices in the7th tree.," Let $\xi_i=\xi_i^{(n)}$, $i=1,\ldots,N$, denote the number of non-root vertices in the$i$ th tree." " Then (see, e.g., |3].. [0] or[O])), for any ;>0 such that anAyn Note that this distribution is exchangeable and that itis a GAS with jj; in given by We menuion in passing that the distribution of 7; may be identifiedas an Abel distribution discussed in [17]. with Gn their notation) p=1 and 0=InA—A."," Then (see, e.g., \cite{cf}, \cite{p} or \cite{p_bk}) ), for any $k_i\ge 0$ such that $\sum_{i=1}^N\,k_i= n$ Note that this distribution is exchangeable and that it is a GAS with $\eta_i$ in given by We mention in passing that the distribution of $\eta_i$ may be identifiedas an Abel distribution discussed in \cite{lm} with (in their notation) $p=1$ and $\theta=\ln\lambda-\lambda$." " We refer to |17,ExampleD] [or more information onAbel distributions, including further references."," We refer to \cite[Example D]{lm} for more information onAbel distributions, including further references." . ∊∪⊺≳⇂↿↴⋡∖∁∟∣∏⋃⋯↻∁↕⊲∣↝∕∶∩∖↖⇁∁≳∐⊲∁⋯⇂∁↕⊲∁⋝⇂∁∟∣⋯⊔↧∁∏⋃⋯↻∁↕⊲⊳↔⊔∪∣⇂↕⊲∁∁⋝∖↖⇁↥⋔∁≻⋯∁⊔⋝⇁∣↝∏∪∏−↕⊲∪∪⇂∖⇁∁⋯∟⋅∁⋝∶ . ⋅ ⋅ n) . ⋅ ⋅ Since↴⋅ the ⋅ 7th factorial.⋅ moment of S; ≼↝⊏↘∃⋅is of. the form. we have to find the marginal distributions of the random vector (£1.....£x ).," For a fixed number $r\ge 0$ we are interested in the number $S_n^{(r)}$ of trees with exactly $r$ non-root vertices: Since the $i$ th factorial moment of $S_n^{(r)}$ is of the form we have to find the marginal distributions of the random vector $(\xi_1,\ldots,\xi_{N})$ ." " From the identity which is valid [or any natural #7 and s, we easily obtain that, for /;>O such that » μα labelcec 1452"," From the identity which is valid for any natural $m$ and $s$ , we easily obtain that, for $k_j\ge 0$ such that $\sum_{j=1}^{i+1}\,k_j=n$ , Therefore ." " From the identity which is valid [or any natural #7 and s, we easily obtain that, for /;>O such that » μα labelcec 1452)"," From the identity which is valid for any natural $m$ and $s$ , we easily obtain that, for $k_j\ge 0$ such that $\sum_{j=1}^{i+1}\,k_j=n$ , Therefore ." systems with rotation properties uulike anv star iu the control sample or in which the inclination of the transiting planets orbit ἐν aud the inclination of tle host stir spin ἐς are unisaligned.,systems with rotation properties unlike any star in the control sample or in which the inclination of the transiting planet's orbit $i_p$ and the inclination of the host star's spin $i_s$ are misaligned. Since the SPOCS sample is representative of the sample of transiting exoplanet host stars. the former is verv uulikelv.," Since the SPOCS sample is representative of the sample of transiting exoplanet host stars, the former is very unlikely." For that reason. the best explanation of the anomalously slow projected rotation is spin-orbit nuüsalieument aloug the line ofsight.," For that reason, the best explanation of the anomalously slow projected rotation is spin-orbit misalignment along the line of sight." I examine a control sample of stars from the SPOCS catalog of Valenti&Fischer(2005) to quantify the scatter about the simple model, I examine a control sample of stars from the SPOCS catalog of \citet{val05} to quantify the scatter about the simple model. The SPOCS sample selection is described in detail iun Marcyetal.(2001)., The SPOCS sample selection is described in detail in \citet{mar04}. . Tn sununary. the bulk of the sample was initially selected from the DTipparcos catalog such that cach star has BoWV>0.55. is no more than three magnitudes above the main sequence. is not a known spectroscopic binary. and has no stellar companion within two arcsecouds.," In summary, the bulk of the sample was initially selected from the Hipparcos catalog such that each star has $B-V>0.55$, is no more than three magnitudes above the main sequence, is not a known spectroscopic binary, and has no stellar companion within two arcseconds." Subsequent spectroscopic measurements of Call IT aud Ik were then used to dowuselect to those stars with ages τ.2&2 Gyr. though an additional 100 stars with ages between 50 and 500 Myr were later added in.," Subsequent spectroscopic measurements of CaII H and K were then used to downselect to those stars with ages $\tau_{\ast} \gtrsim 2$ Gyr, though an additional 100 stars with ages between 50 and 500 Myr were later added in." As a result. the SPOCS sample has both voung aud evolved stars as indicated in Figure Ll of Valeuti&Fischer(2005).," As a result, the SPOCS sample has both young and evolved stars as indicated in Figure 14 of \citet{val05}." . Iu addition. previously unknown spectroscopic binaries were removed from the SPOCS caudidate list. so there are no spectroscopic binaries in the final catalog.," In addition, previously unknown spectroscopic binaries were removed from the SPOCS candidate list, so there are no spectroscopic binaries in the final catalog." Short-period low-mass binary conipauious or exoplanets would have been readily apparent in the original Califormia-Carneeic plauect search aud would have been announced as such long ago., Short-period low-mass binary companions or exoplanets would have been readily apparent in the original California-Carnegie planet search and would have been announced as such long ago. For those reasons. the rotation properties of stars in SPOCS sample should be unaffected. by close comipanious.," For those reasons, the rotation properties of stars in SPOCS sample should be unaffected by close companions." Moreover. anv overlap between the SPOCS sample and the hosts stars of transiting exoplauets is negligible.," Moreover, any overlap between the SPOCS sample and the hosts stars of transiting exoplanets is negligible." Collectively. all of these selectious and observations sugeest that the SPOCS sample is a für coutrol sample for this analysis.," Collectively, all of these selections and observations suggest that the SPOCS sample is a fair control sample for this analysis." I model the initial mass-periocd relation of a 650 Myr population of Sun-like stars by binning the available ILvades aud Pracsepe data (Bacdicketal.1987:Prosseretal.1995:Scholz&Eisloffel2007) as sumuuarized iu Lewin&Bouvier(2009) in ο AL. bins.," I model the initial mass-period relation of a 650 Myr population of Sun-like stars by binning the available Hyades and Praesepe data \citep{rad87,pro95,sch07} as summarized in \citet{irw09} in 0.1 $M_{\odot}$ bins." The Irwin&Bouvier(2009). data only extends up to about 1.2 AL... so Tsupplement it with average rotation periods for lore massive field stars as preseuted i MeNally(1965).," The \citet{irw09} data only extends up to about 1.2 $M_{\odot}$, so I supplement it with average rotation periods for more massive field stars as presented in \citet{mcn65}." . I use natural cubic spliues to iuterpolate the binned and supplemented data and find that it münnuizes the stun of square residuals relative to high-order polvnomial interpolation., I use natural cubic splines to interpolate the binned and supplemented data and find that it minimizes the sum of square residuals relative to high-order polynomial interpolation. I determine the expected rotation period of a Suu-like star as a function of mass aud age by evolving the initial condition set bv the stellar mass according to the relation (e.g.Weber&Davis1967:Moestel19685:Ixiwaler1988) where ορAle) cau be approximated ax a fifth-order polvnomial i Af. with coefficients in Increasing order I. sunununarize iv echuique in Figure 2..," I determine the expected rotation period of a Sun-like star as a function of mass and age by evolving the initial condition set by the stellar mass according to the relation \citep[e.g.][]{web67,mes68,kaw88} where $P_{\ast,0}(M_{\ast})$ can be approximated as a fifth-order polynomial in $M_{\ast}$ with coefficients in increasing order I summarize my technique in Figure \ref{fig02}." The model described above is likely too simplistic. he relevant iuput parameters (stellar mass. raclius. and age) are all uucertaim. and the output (stellar ooriod) is dificult to observe.," The model described above is likely too simplistic, the relevant input parameters (stellar mass, radius, and age) are all uncertain, and the output (stellar period) is difficult to observe." " For those reasons. I use a Monte Carlo simulation to determine the range of observable esn/;5, expected for a sample of stars given nass. radius. and age as well as the uncertainties iu cach of those quantitics plus the appropriate inclination distribution for that sample."," For those reasons, I use a Monte Carlo simulation to determine the range of observable $v\sin{i}_{sim}$ expected for a sample of stars given mass, radius, and age as well as the uncertainties in each of those quantities plus the appropriate inclination distribution for that sample." " In order to determine the degree of disagreement between the esin/;,, predicted from the simple enipirieal model aud the observed CSDgps that can be expected eiven the observational uncertainties aud the imperfections of the simple enipirical model. I use the control sample of stars from the SPOCS catalog."," In order to determine the degree of disagreement between the $\overline{v\sin{i}}_{sim}$ predicted from the simple empirical model and the observed $v\sin{i}_{obs}$ that can be expected given the observational uncertainties and the imperfections of the simple empirical model, I use the control sample of stars from the SPOCS catalog." For cach stay in the SPOCS catalog. Fuse the estimated stellar mass aud uncertsüntv AL. and 63; (column 9 of Table 9). estimated stellar radius aud unucertaüutv Π. and op (cohunn 8 of Table 9). aud age range Ar (cohunn Ll of Table 9).," For each star in the SPOCS catalog, I use the estimated stellar mass and uncertainty $M_{\ast}$ and $\sigma_{M}$ (column 9 of Table 9), estimated stellar radius and uncertainty $R_{\ast}$ and $\sigma_{R}$ (column 8 of Table 9), and age range $\Delta\tau$ (column 14 of Table 9)." " In the Monte. Carlo. I sample cach stars mass from a uniforii distribution in lass between ALσαι and. AL.|oy,/2. its radius from a uniform distribution 1n radius between 705/2 aud Ro|c0g/2. and its age from a uniform distribution in age between the eiven lower and upper age Buts."," In the Monte Carlo, I sample each star's mass from a uniform distribution in mass between $M_{\ast}-\sigma_{M}/2$ and $M_{\ast}+\sigma_{M}/2$, its radius from a uniform distribution in radius between $R_{\ast}-\sigma_{R}/2$ and $R_{\ast}+\sigma_{R}/2$, and its age from a uniform distribution in age between the given lower and upper age limits." I siuuple the inclinatiou to the line of sight of cach stars rotation axis from the standard random distribution (o9arccos(lC. where CO is drawn unifonuulv from the interval [0.1].," I sample the inclination to the line of sight of each star's rotation axis from the standard random distribution $i \sim \arccos(1-U)$, where $U$ is drawn uniformly from the interval [0,1]." — Using these parameters. I evolve the initial period eiven bv the randomly selected mass aud the initial period-uass relation described iu Figure 2 to the raucomly selected age of the system according to Equation 1..," Using these parameters, I evolve the initial period given by the randomly selected mass and the initial period-mass relation described in Figure \ref{fig02} to the randomly selected age of the system according to Equation \ref{eq1}. ." " 1 then compute esnm/;,, using the randomly eenerated radius of the star and its randomly selected inclination.", I then compute $v\sin{i}_{sim}$ using the randomly generated radius of the star and its randomly selected inclination. " I repeat this process 1000 times aud thereby derive for cach star the distribution of possible esu/,;5 values. dsoiuenn cshnn/g, as well as the width of the distribution 9,;,."," I repeat this process 1000 times and thereby derive for each star the distribution of possible $v\sin{i}_{sim}$ values, its mean $\overline{v\sin{i}}_{sim}$, as well as the width of the distribution $\sigma_{sim}$." " I compare the predicted esn/,5,, with the observed es/,54 relative to the width of the Monte Carlo distribution σε aud the error in the observed CSID/px lucasurement 7,4; through the rotation statistic QO: Note that large positive (negativo) values of Oindicate slower (faster) than expected esin/ values.", I compare the predicted $\overline{v\sin{i}}_{sim}$ with the observed $v\sin{i}_{obs}$ relative to the width of the Monte Carlo distribution $\sigma_{sim}$ and the error in the observed $v\sin{i}_{obs}$ measurement $\sigma_{obs}$ through the rotation statistic $\Theta$: Note that large positive (negative) values of $\Theta$indicate slower (faster) than expected $v\sin{i}$ values. Stars that are well fit by the model will have siuall absolute values of OQ., Stars that are well fit by the model will have small absolute values of $\Theta$. I repeat this calculation on cach of the 866 stars from the SPOCS catalog with M.<1.5AL... assuming the standard isotropic distribution of inclination.," I repeat this calculation on each of the 866 stars from the SPOCS catalog with $M_{\ast} < 1.5~M_{\odot}$, assuming the standard isotropic distribution of inclination." This distribution of O is the null lypothesis that I will use to compare to the distribution of O measured in the transiting exoplauet systems under the assumption of spin-orbit aliguiueut., This distribution of $\Theta$ is the null hypothesis that I will use to compare to the distribution of $\Theta$ measured in the transiting exoplanet systems under the assumption of spin-orbit alignment. I collected. the properties. of the ο transiting exoplaucts systems kuown as of May 2010. of whichthe 75 listed in Table 1 have measured mass. radius. Csin/ pe. aad orbital inclination.," I collected the properties of the 80 transiting exoplanets systems known as of May 2010, of whichthe 75 listed in Table \ref{tbl-1} have measured mass, radius, $v\sin{i}_{obs}$ , and orbital inclination." In this case. the stellar lnasses and radii are more precisely micasured than those," In this case, the stellar masses and radii are more precisely measured than those" sources were iu the ranee 50yIvbbeam +t.,sources were in the range $\mu$ $^{-1}$. Three targets were selected for follow-up with the EVLA. using 2GOIIE of bandwidth to cuhance the seusitivitv.," Three targets were selected for follow-up with the EVLA, using GHz of bandwidth to enhance the sensitivity." We found 36 upper limits of 7.8. 8.3 aud LL2yIvbbeam | for NTE J111s|180. GRO JO122|322 and GRO J1655-10. respectively.," We found $3\sigma$ upper limits of 7.8, 8.3 and $\mu$ $^{-1}$ for XTE J1118+480, GRO J0422+322 and GRO J1655-40, respectively." We find that most quiescent svstenis are bevoud the reach of ¢umeut higli-seusitivitv VEDI arrays. and cannot therefore be used as astrometric targets.," We find that most quiescent systems are beyond the reach of current high-sensitivity VLBI arrays, and cannot therefore be used as astrometric targets." Uucertaiuties in the source distances (Jouker&Nelomanus Εν. in the empirical correlation between radio aud X- cluission. and in the N-rav huninosities at the times of the observations inply that wecannot rule out these sources falling on the radio/N-rav correlation of Galloetal. (2003).," Uncertainties in the source distances \citep{Jon04a}, in the empirical correlation between radio and X-ray emission, and in the X-ray luminosities at the times of the observations imply that wecannot rule out these sources falling on the radio/X-ray correlation of \citet{Gal03}." . Tlowever. while deeper constraints ou the quiescent jet cussion will be possible on completion of the EVLA. the existing upper limits sugeest that it may be difficult to discutanele jet e1uission from stellar radio cnussion at such low radio Iuuinosities.," However, while deeper constraints on the quiescent jet emission will be possible on completion of the EVLA, the existing upper limits suggest that it may be difficult to disentangle jet emission from stellar radio emission at such low radio luminosities." JCANLJ would like to thank Stephane Corbel for making available lis original data on ON339-L., JCAMJ would like to thank Stephane Corbel for making available his original data on GX339-4. The National Badio Astronomy Observatory is a facility of the National Science Foundation operated. under cooperative agreement by Associated Universities. Tne. This research has made use of NASAs Astrophysics Data System. EVLA.. VLA..," The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. This research has made use of NASA's Astrophysics Data System. , ." Thus the differential rotation of the disk makes an appearance in the form of a linear shear.,Thus the differential rotation of the disk makes an appearance in the form of a linear shear. We integrate the above equations using a version of the ZEUS code (Stone 1992)., We integrate the above equations using a version of the ZEUS code \citep{sn92}. . ZEUS is a time-explicil. operator-split scheme on a staggered mesh.," ZEUS is a time-explicit, operator-split scheme on a staggered mesh." It uses artificial viscosity to capture shocks., It uses artificial viscosity to capture shocks. " Our computational domain is a rectangle of size L,x containing V,x grid cells.", Our computational domain is a rectangle of size $L_x \times L_y$ containing $N_x \times N_y$ grid cells. The numerical resolution is therefore Ly/YiVv Ny.," The numerical resolution is therefore $\Delta x \times \Delta y = L_x/N_x \times L_y/N_y$ ." Qur code differs from the standard ZEUS algorithun in two respects., Our code differs from the standard ZEUS algorithm in two respects. First. we have implemented a version of the shearing-box boundary conditions.," First, we have implemented a version of the shearing-box boundary conditions." " The model is then periodic in the y direction: the «2 boundaries are initial joined in a periodic fashion. but thev are allowed to shear with respect to each other. becoming periodic again when /=nL,/(qOQL,). n—1.2....."," The model is then periodic in the $y$ direction; the $x$ boundaries are initial joined in a periodic fashion, but they are allowed to shear with respect to each other, becoming periodic again when $t = n L_y/(q\Omega L_x)$, $n = 1,2,\ldots$." A detailed description of the boundary conditions is given in (1995)., A detailed description of the boundary conditions is given in \cite{hgb95}. second. we (real advection by the mean [low vy=—qQuay separately from advection bv the perturbed flow 9v=v—vy. \l," Second, we treat advection by the mean flow $\bld{v}_0 = -q\Omega x \ey$ separately from advection by the perturbed flow $\delta \bld{v} \equiv \bld{v} - \bld{v}_0$." ean-llow advection can be done by interpolation. using the algorithm described in Gamunie(2001).. which is similar to the FARGO scheme 2000)..," Mean-flow advection can be done by interpolation, using the algorithm described in \cite{gam01}, which is similar to the FARGO scheme \citep{mass00}." This has the advantage that the timestep is not limited by the mean flow velocity (it is [Ov] rather than |v| that enters the Courant condition)., This has the advantage that the timestep is not limited by the mean flow velocity (it is $|\delta \bld{v}|$ rather than $|\bld{v}|$ that enters the Courant condition). " This permits the use of a timestep (hat is larger than (the usual timestep by ~L,/H iL,ΕΕ "," This permits the use of a timestep that is larger than the usual timestep by $\sim L_x/H$ if $L_x \gg H$." The shear-interpolation scheme also makes (he algoritlim more nearly translation-invariant in the c—y plane. thereby more nearly embocdying an important symmetry of the underlving equations.," The shear-interpolation scheme also makes the algorithm more nearly translation-invariant in the $x-y$ plane, thereby more nearly embodying an important symmetry of the underlying equations." Without a specific model for the process that is injecting the vorticity. it is difficult to seltile on a particular set of initial condiüons. or to know how these initial conditions ought to vary when the size of the box is allowed to vary.," Without a specific model for the process that is injecting the vorticity, it is difficult to settle on a particular set of initial conditions, or to know how these initial conditions ought to vary when the size of the box is allowed to vary." Our choice of initial conditions is therefore somewhat arbitrary., Our choice of initial conditions is therefore somewhat arbitrary. We use a set of initial (incompressive) velocity perturbations drawn from a Gaussian random field., We use a set of initial (incompressive) velocity perturbations drawn from a Gaussian random field. The amplitude of the perturbations is cliaracterized by o=(ov/c.|).ον . l," The amplitude of the perturbations is characterized by $\sigma = \<|\delta \bld{v}/c_s|^2\>^{1/2}$ ." "i;The power spectrum is. ου↼⋅↽e&SiniXO. corresponding to the energv spectrum (E,e& 77) of a two-dimensional Kolmogorov inverse turbulent cascade. with ceutolfs at PEEπαολο)/and bye,HC=PEE 325,1..."," The power spectrum is $|\delta \bld{v}|^2 \sim k^{-8/3}$, corresponding to the energy spectrum $E_k \sim k^{-5/3}$ ) of a two-dimensional Kolmogorov inverse turbulent cascade, with cutoffs at $k_{min} = (1/2) (2\pi/H)$and $k_{max} = 32 k_{min}$ ." The surface density is not perturbed., The surface density is not perturbed. bv the NEW (Navarroetal.1997). density. prolile: ∖∖↽∐≼↲↕⋅≼↲∕↗↿⋅∕↘∣⋅∣∶≡∎↽⊰∫⊓⋝⊳∶↕⋝⊋∕∕∣⋖↽∖⋚⊼∪↥⊳∖⊽⊔∐↲≺∢∏∐≺∢≀↧↴↥≺⇂≼↲∐⋝∖⊽∐⋡∖↽∪↓≯⊔∐↲∏∐↕∖↽≼↲↕⋅⊳∖⊽≼↲≀↧↴↥↕⋅≼↲≼⇂⊳∖⇁∐↕∐⊳∶⋅≺↘↼↿⋅∶ ∃∩∩∣↽⇀⋮⋝⋝∕∕∣⊑↽⊰∣∣∣⋜⋝∣↽⇀↕⋝⋅≀↧↴∐≼⇂∣∣∶∣⋮∕∕∕,"by the NFW \citep{NavFreWhi97} density profile: where $\rho_{crit}=3H(z)^2/8\pi G$ is the critical density of the universe at redshift $z$ , $\delta_c = 200c^3/3\textrm{ }m(c)$ , and $u=r/r_s$." ∣⋮⊽∖⋅↴∏∐↲≺∢∐≀↧↴↕⋅≀↧↴≺∢∩↲↕⋅↕⊳∖⇁∐≺∢↕⋅≀↧↴≼∐∏⋝∖⊽∣⋮⊽∖↕⊳∖⇁≼⇂≼↲∐∐≼↲≼⊔∐↥≼↲↕⋅∐↓⊳∖⊽∪↓⋟⊔∐↲≺∢∪∐≺∢≼↲↕∐↕⋅≀↧↴∐∪∐ ↕↽≻≀↧↴↕⋅≀↧↴∐∐↲∩↲↕⋅∪↓⋟⊔∐↲∐≀↧↴↥∪⋅∣↽⇀⋅⊔⋯↴↥↕⊳∖⇁≀↧↴↓⋟∏∐≺∢∐∪∐∪↓≯⊔∐↲∐≀↧↴↥∪∐↓≀↧↪∖⊽⊳∖⇁≀↧↴∐≺⇂⊔∐↲↕⋅≼↲≼⇂," The characteristic radius $r_s$ is defined in terms of the concentration parameter of the halo, $c$, that is a function of the halo mass and the redshift, and the virial radius, $r_{vir}$." ⊳∖⊽∐∐≯↥⋅≀↧↴↕∐⇂⊔∐↲∖↽↕∏≀↧↴↥ ↕⋅≀↧↴≼∐∏⊳∖⊽⋅∣⋮≀⊽∣⋅∕↘⋅↴∏∐↲∖↽↕↕⋅↥≀↧↴↥↕⋅≀↧↴≼∐∏⊳∖⇁↕⊳∖⇁≼⇂≼↲∐∐≼↲≼⊔∐↥≼↲∐∐⊳∖⇁∪↓≯⊔∐↲∐≀↧↴↥∪↕∐≀↧⊔∖⋱∖⊽⋅⇀∪∐⋅∣↽≻∡∖↽⋜⋝⊼∕∕∕⊑↽⊰⇄⋝∣⋮⋮≳⋝⊽⋚∣⋅∕≦⊋⋃∩∕↗↿⋅∕≖∣⋅∕∶ ⇀⋃∐⋅≀↧↴∐≼," The virial radius is defined in terms ofthe halo mass, $M_H$, by $(4\pi /3)r_{vir}^3 200 \rho_{crit}=M_H$ , and the function $m(u) = \textrm{ln}(1+u) - u/(1+u)$." "⇂⊔∐↲↓⋟∏∐≺∢∐∪∐∣∣∣≼⋝∣∣⇄⋝∶↥∐⊔⊹∣∣↕⋟−∣∣∕∕∕⊔⊹∣∣↕⋟⋅⊡≻↕⋅⊔∐↲≺∢∪∐≺∢≼↲↕∐↕⋅≀↧↴∐∪∐↕↽≻≀↧↴↕⋅≀↧↴∐∐↲∥↲↕⋅∖∖⊽≼↲ ⋯⇂∪↕↽≻↥⊔∐↲∐⊔↕∐≸↽↔↴↓⋟∪↕⋅∐∐∐≀↧↴↕↽≻↕⋅∪∖⇁↕≺⇂≼↲≼⇂∣↽≻⋡∖↽∐∪↥≀↧↴≸≟≼↲↥≀↕↴↥⋅⊔∩∩⊥⋝∶∶ based on computations of a ACDM cosmological model with 0,,=0.8. O4=0.7. ο=0.045. and oy=0.9."," For the concentration parameter we adopt the fittingformula provided by \cite{Dol04}:: based on computations of a $\Lambda$ CDM cosmological model with $\Omega_m=0.3$, $\Omega_{\Lambda}=0.7$, $\Omega_b=0.045$, and $\sigma_8 = 0.9$." since (he gravitational potential. o. is determined by the dark matter content of the minihalos. it will be given by: where rod is the radius at which the dark matter density of the halo equals the mean density of the universe.," Since the gravitational potential, $\phi$, is determined by the dark matter content of the minihalos, it will be given by: where $r_sd$ is the radius at which the dark matter density of the halo equals the mean density of the universe." For the gas we used à X=0.76. Y=0.24. and Z=0 composition.," For the gas we used a $X=0.76$, $Y=0.24$, and $Z=0$ composition." " Its density. aud temperature profiles will be determined by assuming 2,=php,/(nyi)ap,. where > is the polvtropie index."," Its density and temperature profiles will be determined by assuming $P_g = \rho_g k_BT_g/(m_p\mu) \textrm{ } \alpha \textrm{ } \rho_g^{\gamma}$, where $\gamma$ is the polytropic index." " Then we can write where p, and 7; are the density and temperature al the center of the halo.", Then we can write where $\rho_c$ and $T_c$ are the density and temperature at the center of the halo. " Since the halos are in hvdrodynamie equilibrium we find. We have three [ree parameters inour gas profile: ος. 7. and 5.The central density will be chosen such that at r=r,;, the ratio between dark and barvonic matter densities is"," Since the halos are in hydrodynamic equilibrium we find, We have three free parameters inour gas profile: $\rho_c$ , $T_c$ , and $\gamma$ .The central density will be chosen such that at $r=r_{vir}$ the ratio between dark and baryonic matter densities is" " CH30H masers are radiatively pumped by IR emission from the warm dust associated exclusively with massive YSOs, while the methanol maser at 44 GHz is collisionally excited in molecular outflows, and particularly at interfaces between outflows and the surrounding ambient cloud (see Cyganowskietal.2009 and references therein).","$_{3}$ OH masers are radiatively pumped by IR emission from the warm dust associated exclusively with massive YSOs, while the methanol maser at 44 GHz is collisionally excited in molecular outflows, and particularly at interfaces between outflows and the surrounding ambient cloud (see \citealt{cyga09} and references therein)." " Considering that EGOg35 is indeed a massive YSO evolving in a dense molecular medium, it is important to understand the physical characteristics of its ambient medium."," Considering that EGOg35 is indeed a massive YSO evolving in a dense molecular medium, it is important to understand the physical characteristics of its ambient medium." We investigated this ambient through several molecular lines obtained with the Atacama Submillimeter Telescope Experiment (ASTE)., We investigated this ambient through several molecular lines obtained with the Atacama Submillimeter Telescope Experiment (ASTE). The results of this investigation are presented in this work., The results of this investigation are presented in this work. " The molecular observations were performed on July 14 and 15, 2010 with the 10 m Atacama Submillimeter Telescope Experiment (ASTE; Ezawaetal. 2004))."," The molecular observations were performed on July 14 and 15, 2010 with the 10 m Atacama Submillimeter Telescope Experiment (ASTE; \citealt{ezawa04}) )." " We used the CATS345 GHz band receiver, which is a two-single band SIS receiver remotely tunable in the LO frequency range of 324-372 GHz."," We used the CATS345 GHz band receiver, which is a two-single band SIS receiver remotely tunable in the LO frequency range of 324-372 GHz." " We simultaneously observed J=3-2 at 345.796 GHz and HCO* J=4-3 at 356.734 GHz, mapping a region of x centered at RA =18554™0.7°,, dec. =--02?011'18.9"","," We simultaneously observed J=3–2 at 345.796 GHz and $^{+}$ J=4–3 at 356.734 GHz, mapping a region of $\times$ centered at RA $=$, dec. $= +$," ", 12000).", J2000). " We also observed J=3-2 at 330.588 GHz and CS J=7-6 at 342.883 GHz towards the same center mapping a region of x50""..", We also observed J=3–2 at 330.588 GHz and CS J=7–6 at 342.883 GHz towards the same center mapping a region of $\times$. The mapping grid spacing was and the integration time was 60 sec per pointing in both cases., The mapping grid spacing was and the integration time was 60 sec per pointing in both cases. All the observations were performed in position switching mode., All the observations were performed in position switching mode. " We verified that the off position (RA =18°53™55.8°,, dec. =+02°077'49.5”,"," We verified that the off position (RA $=$, dec. $= +$," ", J2000) was to be free of emission.", J2000) was to be free of emission. " We used the XF digital spectrometer with a bandwidth and spectral resolution set to 128 MHz and 125 kHz, respectively."," We used the XF digital spectrometer with a bandwidth and spectral resolution set to 128 MHz and 125 kHz, respectively." " The velocity resolution was 0.11 and the half-power beamwidth (HPBW) was22"",, for all observed molecular lines."," The velocity resolution was 0.11 and the half-power beamwidth (HPBW) was, for all observed molecular lines." The system temperature varied from Tsys=150 to 200 K. The main beam efficiency was mp~0.65., The system temperature varied from $_{\rm sys} = 150$ to 200 K. The main beam efficiency was $\eta_{\rm mb} \sim 0.65$. 'The spectra were Hanning smoothed to improve the signal-to-noise ratio and only linear or/and some third order polynomia were used for baseline fitting., The spectra were Hanning smoothed to improve the signal-to-noise ratio and only linear or/and some third order polynomia were used for baseline fitting. The data were reduced with NEWSTAR and the spectra processed using the XSpec software package., The data were reduced with NEWSTAR and the spectra processed using the XSpec software package. " To complement the molecular data we use near- and mid-IR and radio continuum data from public databases and catalogues, which are described in the corresponding sections."," To complement the molecular data we use near- and mid-IR and radio continuum data from public databases and catalogues, which are described in the corresponding sections." The source EGO G35.03+0.35 (EGOg35) is located at the border of an HII region which is delineated mainly by the 8 um emission., The source EGO $+$ 0.35 (EGOg35) is located at the border of an HII region which is delineated mainly by the 8 $\mu$ m emission. Figure 1 (left) shows a composite three-color image of a region towards EGOg35., Figure \ref{present} (left) shows a composite three-color image of a region towards EGOg35. " The image displays three Spitzer-IRAC bands: 3.6 um (in blue),4.5 um (in green) and 8 ym (in red)."," The image displays three -IRAC bands: 3.6 $\mu$ m (in blue),4.5 $\mu$ m (in green) and 8 $\mu$ m (in red)." " EGOg35 is the green structure inside the dashed rectangles, which represent the x and x regions mapped in the molecular lines as described in the previous section."," EGOg35 is the green structure inside the dashed rectangles, which represent the $\times$ and $\times$ regions mapped in the molecular lines as described in the previous section." A zoom in of the surveyed region is shown in Fig., A zoom in of the surveyed region is shown in Fig. 1 (right)., \ref{present} (right). " To study the molecular ambient where EGOg35 is embedded, we analyse the and J=3-2, HCO* J=4-3 and CS J=7-6 transitions, tracers of outflows and dense gas."," To study the molecular ambient where EGOg35 is embedded, we analyse the and J=3–2, $^{+}$ J=4–3 and CS J=7–6 transitions, tracers of outflows and dense gas." Figures 2 and 3 display the molecular lines spectra obtained towards EGOg35., Figures \ref{obs1} and \ref{obs2} display the molecular lines spectra obtained towards EGOg35. " Most of the spectra are far of having a simple Gaussian shape, presenting asymmetries, probable absorption dips, and spectral wings or shoulders, which suggest that the molecular gas is affected by thedynamics of EGOg35."," Most of the spectra are far of having a simple Gaussian shape, presenting asymmetries, probable absorption dips, and spectral wings or shoulders, which suggest that the molecular gas is affected by thedynamics of EGOg35." In what follows we study the gas kinematics., In what follows we study the gas kinematics. " Figure 4 shows the spectra obtained towards the central position of EGOg35, that is the (0,0) offset in Figs."," Figure \ref{spec00} shows the spectra obtained towards the central position of EGOg35, that is the (0,0) offset in Figs." 2 and 3.., \ref{obs1} and \ref{obs2}. " In the case of the HCO* J—4-3 and CS J=7-6 lines, their brightness temperatures were scaled with a factor of x3."," In the case of the $^{+}$ J=4–3 and CS J=7–6 lines, their brightness temperatures were scaled with a factor of $\times3$." " Figure 5 displays a zoom-in of the central and J=3-2 profiles in the intensity range that goes from —0.35 to 2 K, in order to note some weak features."," Figure \ref{spec00zoom} displays a zoom-in of the central and J=3–2 profiles in the intensity range that goes from $-0.35$ to 2 K, in order to note some weak features." In the case of the line can be appreciated a weak component (~5 times above the rms noise) centered at ~41 !., In the case of the line can be appreciated a weak component $\sim5$ times above the rms noise) centered at $\sim41$ . . The parameters determined from Gaussian fitting of these lines are presented in Table 1.., The parameters determined from Gaussian fitting of these lines are presented in Table \ref{lines}. . " Tn» represents the peak brightness temperature, Visr the central velocity referred"," $_{mb}$ represents the peak brightness temperature, $_{LSR}$ the central velocity referred" shock geometries and orientations are able to provide a fit to the data suggesting there is some degeneracy in the solutions.,shock geometries and orientations are able to provide a fit to the data suggesting there is some degeneracy in the solutions. Firstly we tind that X; is a degenerate quantity., Firstly we find that $X_M$ is a degenerate quantity. " The value of X, is determined by the values of my.gy and Ag and therefore ditferent combinations of these values can produce the same latera projected shock extent projected on the plane of the sky."," The value of $X_M$ is determined by the values of $r_M, \varphi_0$ and $\Delta\varphi$ and therefore different combinations of these values can produce the same lateral projected shock extent projected on the plane of the sky." " We have found that .Xy,=5.5A, provides an acceptable fit to the data.", We have found that $X_M=5.5R_p$ provides an acceptable fit to the data. As the temperature of the stellar plasma increases. the wine and static coronal models predict a larger density at the planetary orbital radius.," As the temperature of the stellar plasma increases, the wind and static coronal models predict a larger density at the planetary orbital radius." Therefore the projected area of the shock mus decrease to ensure the transit is not too deep and can still fit the data., Therefore the projected area of the shock must decrease to ensure the transit is not too deep and can still fit the data. This area is determined by the angular extent Ag and the radia extent Ary., This area is determined by the angular extent $\Delta\varphi$ and the radial extent $\Delta r_M$. For the cases where Ag=80 (models LÀ and 2A). a smaller value of Ary; is recuired to fit the data compared to the cases where Ag=40° (models B and 2B).," For the cases where $\Delta\varphi=80^\circ$ (models 1A and 2A), a smaller value of $\Delta r_M$ is required to fit the data compared to the cases where $\Delta\varphi=40^\circ$ (models 1B and 2B)." This is a consequence of the line-of-sight distance through the shock increasing as qo decreases. allowing more starlight to be absorbed at the shock front.," This is a consequence of the line-of-sight distance through the shock increasing as $\varphi_0$ decreases, allowing more starlight to be absorbed at the shock front." In the optical transi the system is completely symmetrical about the mid-transit point. however the addition of a bow shock breaks this symmetry in the near UV transit.," In the optical transit the system is completely symmetrical about the mid-transit point, however the addition of a bow shock breaks this symmetry in the near UV transit." " This can be seen in the simulated lighteurves as they are not centred around phase=| but offset by an amount proportional to X,,.", This can be seen in the simulated lightcurves as they are not centred around $\textrm{phase}=1$ but offset by an amount proportional to $X_M$. Again if better time sumpled observations could be taken. this offset could be used to provide further insight into the stand-off distance between the shock and the planet.," Again if better time sampled observations could be taken, this offset could be used to provide further insight into the stand-off distance between the shock and the planet." Our simulations have shown that it is possible to reproduce the observations of ? by assuming the presence of a bow shock around the planetary magnetosphere., Our simulations have shown that it is possible to reproduce the observations of \citet{Fossati:2010p838} by assuming the presence of a bow shock around the planetary magnetosphere. Using models for the stellar corona and wind (with a solar base density) we have calculated the density of MgII in the shocked material., Using models for the stellar corona and wind (with a solar base density) we have calculated the density of MgII in the shocked material. ? calculated the column density of ΜσΠ around WASP-|2b to be zL4x10%em7., \cite{Lai:2010p808} calculated the column density of MgII around WASP-12b to be $\gtrsim 1.4\times10^{13}\textrm{cm}^{-2}$. " For this calculation they assume an optical depth r=| in the absorption line of MgITL a velocity v=1OOkms and a characteristic length scale S=3A,."," For this calculation they assume an optical depth $\tau=1$ in the absorption line of MgII, a velocity $v\approx 100\textrm{kms}^{-1}$ and a characteristic length scale $S=3R_p$." " From this ?. found the required number density of MgII to be zy,=400cm ‘to reproduce the observed early ingress.", From this \cite{Vidotto:2010p809} found the required number density of MgII to be $n_{\rm MgII}\gtrsim400\textrm{cm}^{-3}$ to reproduce the observed early ingress. " Using these assumed values we have calculated the extinction cross-section of MglI to be: The maximum optical depth Τη can be then be calculated using Equation 6. by setting S to be the maximum path length in the line-of-sight through the shocked material along with the corresponding number density of magnesium. 7,4! (from Table 0) for each of our models."," Using these assumed values we have calculated the extinction cross-section of MgII to be: The maximum optical depth $\tau_{\rm max}$ can be then be calculated using Equation \ref{eqn:tau} by setting $S$ to be the maximum path length in the line-of-sight through the shocked material along with the corresponding number density of magnesium, $n_{\rm MgII}$ (from Table \ref{table:results}) ) for each of our models." These values are shown in the final column of Table I., These values are shown in the final column of Table \ref{table:results}. We have found that it is possible to reproduce the observations with both lower and higher MgII densities and that the resultant shocked material does not need to be optically thick., We have found that it is possible to reproduce the observations with both lower and higher MgII densities and that the resultant shocked material does not need to be optically thick. If similar bow shock structures could be observed in other exoplanetary systems. transit observations could be useful to probe the presence of planetary magnetic fields.," If similar bow shock structures could be observed in other exoplanetary systems, transit observations could be useful to probe the presence of planetary magnetic fields." ?. proposed a list of candidates that could provide signatures of an early-ingress. based on the list of available transiting systems in September 2010.," \cite{Vidotto:2011p803} proposed a list of candidates that could provide signatures of an early-ingress, based on the list of available transiting systems in September 2010." Should UV observations be obtained for these candidates we could apply the model developed here to constrain the allowed geometries and orientations for bow shocks., Should UV observations be obtained for these candidates we could apply the model developed here to constrain the allowed geometries and orientations for bow shocks. J. Llama acknowledges the support of an STFC studentship., J. Llama acknowledges the support of an STFC studentship. Ch., Ch. Helling highlights financial support of the European Community under the FP7 by an ERC starting grant., Helling highlights financial support of the European Community under the FP7 by an ERC starting grant. The wind has a fraction 3/e of total mass aud a fraction 5/u of the total energy., g(r)= f_0 = The wind has a fraction $ 3/\om$ of total mass and a fraction $ 5/\om$ of the total energy. Thus. for w= 9-the fiducial value we will use below - the wiud Las approximately 30%( of mass of the ejecta.," Thus, for $\om=9$ - the fiducial value we will use below - the wind has approximately $30\%$ of mass of the ejecta." Let us cliscuss first the dviauic of a spherical CRB shock propagating through a newly cerated SNR., Let us discuss first the dynamic of a spherical GRB shock propagating through a newly cerated SNR. Iu the Ixompaueets approximation Asstuning that the start of the (RB engine is delayed with respect to the SN explosion by time A/ aud that luminosity Lis is coustaut in time. in the core (where g(r)= 1) the GRB shock propagates according to," In the Kompaneets approximation = = )^2 Assuming that the start of the GRB engine is delayed with respect to the SN explosion by time $\Delta t$ and that luminosity $L_{\rm iso}$ is constant in time, in the core (where $g(r)=1$ ) the GRB shock propagates according to" my=17.77.,$m_r = 17.77$. The Sloan Digital Sky Survey Data Release I. released to tlie astronomical community in 2001 October. covers a photometric area of 6670dee? and a spectroscopic area of L783deg?(Adelinan-MeCarthyetal. (2005): see also Stoughton.etal.(2002).. Abazajianetal.(2003).. Abazajianetal. (2001).. aud. Abazajianetal.(2005))).," The Sloan Digital Sky Survey Data Release 4, released to the astronomical community in 2004 October, covers a photometric area of $6670 {\rm\,deg}^2$ and a spectroscopic area of $4783 {\rm\,deg}^2$\citet{am05}; ; see also \citet{st02}, \citet{ab03}, \citet{ab04}, and \citet{ab05}) )." " The SDSS DRI data processing pipeline provides a morphological star/galaxy separation. with extended objects beiug classified as ""galaxies. aud uuresolved objects being classified as ‘stars’."," The SDSS DR4 data processing pipeline provides a morphological star/galaxy separation, with extended objects being classified as `galaxies' and unresolved objects being classified as `stars'." For each galaxy. in each photometric baud. two models are fitted to the two-cimensional galaxy image.," For each galaxy, in each photometric band, two models are fitted to the two-dimensional galaxy image." The first moclel has a de Vaucouleurs surface profile (deVaucouleurs1918): which is truncated beyond. τὴ to go sioothly to zero at δή., The first model has a de Vaucouleurs surface profile \citep{de48}: which is truncated beyond $7 R_e$ to go smoothly to zero at $8 R_e$. The second. model has au exponential prolile: which is truncated beyoud 32. t0 go smoothly to zero at LR., The second model has an exponential profile: which is truncated beyond $3 R_e$ to go smoothly to zero at $4 R_e$. " For each model. the apparent axis ratio q,4, audthe phase angle ο are assumed to be constant with radius."," For each model, the apparent axis ratio $q_m$ andthe phase angle $\varphi_m$ are assumed to be constant with radius." The parameters dm- ge Re. aud F2 are variedH to giveH the best A7> fitH to the galaxy image.H after+ convolutionH withH a cdouble-Crtaussiau fit to the point spread functiou.," The parameters $q_m$, $\varphi_m$, $R_e$, and $I_e$ are varied to give the best $\chi^2$ fit to the galaxy image, after convolution with a double-Gaussian fit to the point spread function." A [urther fit to each galaxy is made by taking the best de Vaucouleurs model aud the best exponential mocel. aud fiudiug the linear combination of the two that gives a new best fit.," A further fit to each galaxy is made by taking the best de Vaucouleurs model and the best exponential model, and finding the linear combination of the two that gives a new best fit." The fraction of the total flix contributed by the de Vaucouleurs compouent is the parameter lracDeV. which is constrained to lie iu the interval [0. 1].," The fraction of the total flux contributed by the de Vaucouleurs component is the parameter fracDeV, which is constrained to lie in the interval $[0,1]$ ." The fracDeV parameter is functionally equivalent to the Sérsic(1908). index. (0 iu the interval 1x5€f (Vinceut&Ryden2005)., The fracDeV parameter is functionally equivalent to the \citet{se68} index $n$ in the interval $1 \leq n \leq 4$ \citep{vr05}. .. If à galaxy has a Sérrsic uidex wv. then 1= correspouds to fracDeV. = Q. η=| correspouds to [racDeV = 1. aud the depeuclence of LracDeV upon i is mouotouic iu the interval 10.9 (oVZdo) 3.3) are labeled galaxies.," Finally, galaxies with fracDeV $\geq 0.9$ $n \gtrsim 3.3$ ) are labeled galaxies." The SDSS DRI databases provide many different. measures of the apparent. axis ratio q of each galaxy in each of the five photometric bauds., The SDSS DR4 databases provide many different measures of the apparent axis ratio $q$ of each galaxy in each of the five photometric bands. Iu this paper. we use the r baud data. at au effective wavelength of61654: this is the band iu which the star/galaxy classification is made.," In this paper, we use the $r$ band data, at an effective wavelength of; this is the band in which the star/galaxy classification is made." A uxelul measure of the apparent shape in the outer regious of galaxies is tlie axis ratio of the 25 mae 7 isophote., A useful measure of the apparent shape in the outer regions of galaxies is the axis ratio of the 25 mag $^{-2}$ isophote. The SDSS DRI data pipeline finds the best fitting ellipse to the 25 mag 7 isophote in each band: the semimajor axis aud semiiminor axis of this isophotal ellipse are As; aud Bos., The SDSS DR4 data pipeline finds the best fitting ellipse to the 25 mag $^{-2}$ isophote in each band; the semimajor axis and semiminor axis of this isophotal ellipse are $A_{25}$ and $B_{25}$ . " The isophotal axis ratio yo,=Bosof/Aos5 theuprovides a measure of the apparent galaxy. shape at a few times the elective radius.", The isophotal axis ratio $q_{25} \equiv B_{25}/A_{25}$ thenprovides a measure of the apparent galaxy shape at a few times the effective radius. For galaxies in our sample with fracDeV = 1. Ao;~ 3.24: lorealaxies with fracDeV = 0. as~2. 141.," For galaxies in our sample with fracDeV = 1, $A_{25} \sim 3.2 R_e$ ; forgalaxies with fracDeV = 0, $A_{25} \sim 2.4 R_e$ ." E.,E. context of planet formation models in Section 4.,context of planet formation models in Section 4. We present our conclusions in Section 5., We present our conclusions in Section 5. In Gonzalez&Laws(2007) we presented the results of our chemical abundance analyses of 18 clements (including Li) in 31 SWPs., In \citet{gl07} we presented the results of our chemical abundance analyses of 18 elements (including Li) in 31 SWPs. We also calculated: corrections needed. to place our data and the data from other similar studies on Ίο seme abundance seale., We also calculated corrections needed to place our data and the data from other similar studies on the same abundance scale. This procedure. allowed: us to construct larger ancl more accurate SWDP and comparison star samples. which we emploved to compare C. O. Na. Mg. AL Si. Ca. Sc. Ti and Ni abundances.," This procedure allowed us to construct larger and more accurate SWP and comparison star samples, which we employed to compare C, O, Na, Mg, Al, Si, Ca, Sc, Ti and Ni abundances." We concluded. that there is evidence for significant. dillerences between the two samples for some elements., We concluded that there is evidence for significant differences between the two samples for some elements. We adopted a similar procedure for Li., We adopted a similar procedure for Li. We begin with the Li abundance values Listed in Table 1: of Gonzalez&Laws(2007) for 31 SWI's., We begin with the Li abundance values listed in Table 1 of \citet{gl07} for 31 SWPs. To these data we added: Li abundance values (and upper limits) of other SWP's from our previous papers., To these data we added Li abundance values (and upper limits) of other SWPs from our previous papers. We excluded SWIPs with Tt«5000 Ix ancl log g «4.0., We excluded SWPs with $_{\rm eff} < 5000$ K and $\log$ g $< 4.0$. The derived stellar properties tend to be less accurate for cooler stars. and few stars with Tr«5000 Ix have detectable Li.," The derived stellar properties tend to be less accurate for cooler stars, and few stars with $_{\rm eff} < 5000$ K have detectable Li." Phe limit on surface gravity restricts the sample to main sequence stars: a star that has evolved olf the main sequence onto the subeiant or giant branch undergoes dramatic changes in its internal structure that results in changes in the surface Li abundance., The limit on surface gravity restricts the sample to main sequence stars; a star that has evolved off the main sequence onto the subgiant or giant branch undergoes dramatic changes in its internal structure that results in changes in the surface Li abundance. Having applied: these limits. the total number of SWPs with Li abundances (and upper limits) from our studies comes to 52.," Having applied these limits, the total number of SWPs with Li abundances (and upper limits) from our studies comes to 52." Next. we compiled Li abundances (and upper limits) for SWPs with Tar5000 Ix and log & o>4.0 from the following studies (number of SWPs retained from each study is also indicated): Israelianetal.(2004) 83. Luck& 48. ‘Takeda&Ixawanomoto(2005) 27. Takedaetal.(20072) 5.," Next, we compiled Li abundances (and upper limits) for SWPs with $_{\rm eff} > 5000$ K and $\log$ g $> 4.0$ from the following studies (number of SWPs retained from each study is also indicated): \citet{is04} – 83, \citet{luck06} – 48, \citet{tak05} – 27, \citet{tak07} – 5." " Phe same studies include Li abuncances for stars without planets: the totals (after applying the same inits) are: Israelianetal.(2004). 34. Luck&Leiter 112. Takeda&Ixawanomoto(2005) Os. ""Takeda.etal.(20074) We selected these studies for analvsis »ecause they have similar temperature scales. and their data are of comparable equality."," The same studies include Li abundances for stars without planets; the totals (after applying the same limits) are: \citet{is04} – 34, \citet{luck06} – 112, \citet{tak05} – 98, \citet{tak07} – We selected these studies for analysis because they have similar temperature scales, and their data are of comparable quality." One complication that we did not have to consider for the elements examined in Gonzalez&Laws(2007). is he presence of upper limits in the abundance data., One complication that we did not have to consider for the elements examined in \citet{gl07} is the presence of upper limits in the abundance data. The minimum detectable Li abundance varies among the studies we emploved. because their spectra have dillering S/N ratios.," The minimum detectable Li abundance varies among the studies we employed, because their spectra have differing S/N ratios." The Li abundance values [rom our series of studies typically have the lowest upper limits. while those from Luck&Leiter(2006) have the highest (but the upper limits from the other studies are not much lower).," The Li abundance values from our series of studies typically have the lowest upper limits, while those from \citet{luck06} have the highest (but the upper limits from the other studies are not much lower)." We show the stars from Luck&Leiter(2006) that have Li abundance upper limits in Figure 1., We show the stars from \citet{luck06} that have Li abundance upper limits in Figure 1. We also include in the figure a straight line that matches the upper envelope of the upper limits for Tr«6200 Ix: it is described by the equation log Li —3.41|0.00079167 Tou., We also include in the figure a straight line that matches the upper envelope of the upper limits for $_{\rm eff} < 6200$ K; it is described by the equation $\log$ Li $= -3.41 + 0.00079167$ $_{\rm eff}$. We will employ this line as a cutolf for selecting Li abundance values to include in our final sample preparation low., We will employ this line as a cutoff for selecting Li abundance values to include in our final sample preparation below. Next. we selected the Luck&Leiter(2006). study as he reference ancl adjusted the data from the other studies o be consistent with it.," Next, we selected the \citet{luck06} study as the reference and adjusted the data from the other studies to be consistent with it." First. we adjusted the Tr values in each study by applving a simple linear equation calibrated using SWI's in common between it anc Luck.& (2006).," First, we adjusted the $_{\rm eff}$ values in each study by applying a simple linear equation calibrated using SWPs in common between it and \citet{luck06}." . We then adjusted the log ο values using a linear equation including a term with the adjusted Tar values., We then adjusted the $\log$ g values using a linear equation including a term with the adjusted $_{\rm eff}$ values. The adjustments to Fe/11] and. Li are simple constant olfsets: vpical Fe/H] and Li abundance olfsets are about 0.02 and ).05 dex. respectively.," The adjustments to [Fe/H] and Li are simple constant offsets; typical [Fe/H] and Li abundance offsets are about 0.02 and 0.05 dex, respectively." The cutolf line shown in Figure 1 is only valid for Fr Ix. since two of the stars without planets from. LuckLeiter(2006). above this temperature have upper limits much higher than predicted. from the extrapolated eutolf line.," The cutoff line shown in Figure 1 is only valid for $_{\rm eff} < 6200$ K, since two of the stars without planets from \citet{luck06} above this temperature have upper limits much higher than predicted from the extrapolated cutoff line." One possible reason for this discrepancy is the Lact that faster rotation is more common among earlier spectral type ebwarfs. resulting in broader. shallower absorption lines.," One possible reason for this discrepancy is the fact that faster rotation is more common among earlier spectral type dwarfs, resulting in broader, shallower absorption lines." Therefore. in our second eut of the data. we removed stars with Tar>6250 Ix: we also excluded stars with Tr«5550 Ix. given the paucity of SWPs with detected Li in this range.," Therefore, in our second cut of the data, we removed stars with $_{\rm eff} > 6250$ K; we also excluded stars with $_{\rm eff} < 5550$ K, given the paucity of SWPs with detected Li in this range." Our upper Tr limit also excludes stars that might display the Li dip phenomenon (see Balachandran (1995))). which would further complicate our analysis below.," Our upper $_{\rm eff}$ limit also excludes stars that might display the Li dip phenomenon (see \citet{ba95}) ), which would further complicate our analysis below." Finally. we excluded all the stars with log Li values falling below the cutolf line (whether upper limits or detections).," Finally, we excluded all the stars with $\log$ Li values falling below the cutoff line (whether upper limits or detections)." For those stars present in multiple studies. we calculated simple averages of their parameters.," For those stars present in multiple studies, we calculated simple averages of their parameters." We show the resulting Li abundances. plotted: against Er in Figure 2., We show the resulting Li abundances plotted against $_{\rm eff}$ in Figure 2. The final samples include 37 οὃς and 147 stars lacking planets., The final samples include 37 SWPs and 147 stars lacking planets. The corrected individual Tar values cülfer from the Luck values with a typical dispersion of about FE 10 Ix. The corresponding dispersion for log ο is about + 0.13 dex. while for Fe/1] and log Li they are + 0.03 and + ," The corrected individual $_{\rm eff}$ values differ from the \citet{luck06} values with a typical dispersion of about $\pm$ 70 K. The corresponding dispersion for $\log$ g is about $\pm$ 0.13 dex, while for [Fe/H] and $\log$ Li they are $\pm$ 0.03 and $\pm$ " cause (hem to become part of (he sample. or. if negative. to be lost.,"cause them to become part of the sample, or, if negative, to be lost." Since there are generally more objects in the flux distribution below anv given flux than above. the net effect will be that positive errors dominate in the sample.," Since there are generally more objects in the flux distribution below any given flux than above, the net effect will be that positive errors dominate in the sample." The effect on wwill be that for objects with a uniform distribution. the observed value will be larger than 0.5.," The effect on will be that for objects with a uniform distribution, the observed value will be larger than 0.5." We can evaluate the Eddineton ellect on oof our sample through simulations., We can evaluate the Eddington effect on of our sample through simulations. On the average. σ for GUSDAD fluxes of the second brightest illuminated detector is 0.05 ph ? !|.," On the average, $\sigma$ for GUSBAD fluxes of the second brightest illuminated detector is $0.05$ ph $^{-2}$ $^{-1}$." Our adopted limit of 0.5 ph 7s ! (for detector 2) corresponds to ~1.21 ph 7s ! for detectors 14-2. with ¢=0.071 ph 7s +.," Our adopted limit of $0.5$ ph $^{-2}$ $^{-1}$ (for detector $2$ ) corresponds to $\sim1.21$ ph $^{-2}$ $^{-1}$ for detectors $1+2$, with $\sigma = 0.071$ ph $^{-2}$ $^{-1}$." Simulations show that in this case the Eddington excess in iis 0.002. consiclerably less than the mean errors of {for the spectral samples discussed below.," Simulations show that in this case the Eddington excess in is $0.002$, considerably less than the mean errors of for the spectral samples discussed below." " Our goal is to derive (he peak energv of the pF, spectrum.", Our goal is to derive the peak energy of the $\nu F_{\nu}$ spectrum. Given the low spectral resolution. we initially derive [(2;)=E?7NGE;) lor a representative energy ££; in each BATSE channel ;. where N(CE;) is the photon flux density. in ph em7s ! |.," Given the low spectral resolution, we initially derive $I(E_i) = E_i^2 N(E_i)$ for a representative energy $E_i$ in each BATSE channel $i$, where $N(E_i)$ is the photon flux density, in ph $^{-2}$ $^{-1}$ $^{-1}$." We used the peak photon fluxes to derive the Εικ densities NV(7;) al E;= 30. 70. 185 and 420 keV. For channels 13. these energies are close to (he geometric means of the energy band. limits: for channel 4. see below.," We used the peak photon fluxes to derive the flux densities $N(E_i)$ at $E_i = $ 30, 70, 185 and 420 keV. For channels 1–3, these energies are close to the geometric means of the energy band limits; for channel 4, see below." An initial estimate of the peak spectral enerev is provided by the channel with the largest value of ZCE;)., An initial estimate of the peak spectral energy is provided by the channel with the largest value of $I(E_i)$. Table I shows for each of the four BATSE channels the number of GRBs having the peak at £j., Table 1 shows for each of the four BATSE channels the number of GRBs having the peak at $E_i$. We can compare our vvalues with those eiven bv Kanekoetal.(2006) for peak fluxes., We can compare our values with those given by \citet{kan06} for peak fluxes. Their work was based on BATSE LAD data of 350 bright GRBs in the BATSE catalogs., Their work was based on BATSE LAD data of 350 bright GRBs in the BATSE catalogs. They used several LAD data (vpes. and emploved a number of spectral shapes bevond the Band spectrum.," They used several LAD data types, and employed a number of spectral shapes beyond the Band spectrum." The Kaneko list has 219 GRBs that ave in the GUSDAD catalog., The Kaneko list has 219 GRBs that are in the GUSBAD catalog. The last column of Table 1 gives the average Kaneko peak energv lor the GUSDAD sources in the Kaneko list., The last column of Table 1 gives the average Kaneko peak energy for the GUSBAD sources in the Kaneko list. We adopt the Kaneko average lor channel 4. since (here is no well defined upper energy limit to ils energy band.," We adopt the Kaneko average for channel 4, since there is no well defined upper energy limit to its energy band." Only for channel 3 is a meaningful comparison possible: our result differs bv only from the Kaneko average., Only for channel 3 is a meaningful comparison possible: our result differs by only from the Kaneko average. The averages of the Euclidean values of {for peak energies in channels 1-4 are 0.44. 0.45. 0.32. and 0.33. respectively.," The averages of the Euclidean values of for peak energies in channels 1-4 are 0.44, 0.45, 0.32, and 0.33, respectively." It turns oul that the transition from hieh to low values of, It turns out that the transition from high to low values of The phasing of component D. which is also clearly present in the 1986 spectrogram. is Consistent with the motion of an irradiated companion.,"The phasing of component B, which is also clearly present in the 1986 spectrogram, is consistent with the motion of an irradiated companion." Assuming the canonical value of 1.4 M. for the mass of a neutron star primary anc 0.8 M. for the mass of the companion (corresponding to the main sequence turn-olf point for MI5). ancl assuming an inclination of 90° for the system. Ixepler's laws give a velocity for the companion of 198 km . which coincides very Closely with the amplitude of component D. Hf we are indeed seeing recombination from the X-rav-irradiated face of the companion star. it would be the first time that the companion of AC211 has been detected.," Assuming the canonical value of 1.4 ${\rm M}_{\odot}$ for the mass of a neutron star primary and 0.8 ${\rm M}_{\odot}$ for the mass of the companion (corresponding to the main sequence turn-off point for M15), and assuming an inclination of $^{\circ}$ for the system, Kepler's laws give a velocity for the companion of 198 km $^{-1}$, which coincides very closely with the amplitude of component B. If we are indeed seeing recombination from the X-ray-irradiated face of the companion star, it would be the first time that the companion of AC211 has been detected." Component X is substantially broader and stronger than D. and its phasing ancl velocity correspond. to. the motion of the compact object.," Component A is substantially broader and stronger than B, and its phasing and velocity correspond to the motion of the compact object." This component could come from the hot inner regions of the accretion disc. [roni a disc wind. or from the accretion dise corona. which will all have the same phase-dependence as the compact object.," This component could come from the hot inner regions of the accretion disc, from a disc wind, or from the accretion disc corona, which will all have the same phase-dependence as the compact object." This component. may be formed. predominantly. in AC21LIs large aceretion clise corona or disc wind. because the emission is never eclipsed. indicating that the --emitting region is substantially larger than the companion star.," This component may be formed predominantly in AC211's large accretion disc corona or disc wind, because the emission is never eclipsed, indicating that the -emitting region is substantially larger than the companion star." Indeed. work by LIoannou et al. (," Indeed, work by Ioannou et al. (" 2001) on IIST UV spectra. and Torres et al. (,"2001) on HST UV spectra, and Torres et al. (" 2001) on optical spectra. shows that the equivalent width of the lines increases sharply curing eclipse as the continuum flux drops. supporting the idea that the emission is formed in a large corona.,"2001) on optical spectra, shows that the equivalent width of the lines increases sharply during eclipse as the continuum flux drops, supporting the idea that the emission is formed in a large corona." We expect the accretion disc corona of AC211I to be particularly large because of MI5's (and jorefore AC21Is) very low metallicity (Fabian. Guilbert Callanan LOST).," We expect the accretion disc corona of AC211 to be particularly large because of M15's (and therefore AC211's) very low metallicity (Fabian, Guilbert Callanan 1987)." Component €. a third. weaker component in the 1988 spectrogram. appears most strongly between phases 0.1 and 0.3.," Component C, a third, weaker component in the 1988 spectrogram, appears most strongly between phases 0.1 and 0.3." Its phasing suggests that it may come from an accretion stream overllowing the disc., Its phasing suggests that it may come from an accretion stream overflowing the disc. A similar emission component. attributed to an overllowing stream. has been observed in the SW. Sex star V1315. λα (Hellier. 1996).," A similar emission component, attributed to an overflowing stream, has been observed in the SW Sex star V1315 Aql (Hellier 1996)." The velocity amplitude of component C is much lower than what one would expect from a ballistic stream: however a 1 phases at which it is most clearly observed. an overllowing stream would be viewed almost perpendicular. and. therefore its. line-of-sight velocity. would be. low.," The velocity amplitude of component C is much lower than what one would expect from a ballistic stream; however at the phases at which it is most clearly observed, an overflowing stream would be viewed almost perpendicularly, and therefore its line-of-sight velocity would be low." 1n addition. Armitage and Livio (1998) show that an overllowing stream would have a velocity well below [ree-fall.," In addition, Armitage and Livio (1998) show that an overflowing stream would have a velocity well below free-fall." Fig.S shows the trailed spectra and Doppler tomogranis of the line., \ref{fig:doppler} shows the trailed spectra and Doppler tomograms of the line. The signal-to-noise in the lines is poor. but the multiple-component. structure of the line profiles is evident in the 1986 and 1988 data (the LOST dataset is the victim of poor weather: we have not included. it in S)).," The signal-to-noise in the lines is poor, but the multiple-component structure of the line profiles is evident in the 1986 and 1988 data (the 1987 dataset is the victim of poor weather; we have not included it in \ref{fig:doppler}) )." Unlike in Fig.7.. the spectra have been phase-binned.," Unlike in \ref{fig:heII}, the spectra have been phase-binned." " “Phe Roche lobe of the companion and the centres of mass of the companion. neutron star and binary svsten are indicated: we have assumed a mass ratio of Alo/Ad,=OSM./L4~ 0.57."," The Roche lobe of the companion and the centres of mass of the companion, neutron star and binary system are indicated; we have assumed a mass ratio of $M_2/M_1 = 0.8~{\rm M}_{\odot} ~/~ 1.4~{\rm M}_{\odot} \sim 0.57$ ." We have plotted a full orbit «[ the accretion stream. and the ring indicates the position in velocity. space of the outer accretion disc. assumed to be ~0.85IU.," We have plotted a full orbit of the accretion stream, and the ring indicates the position in velocity space of the outer accretion disc, assumed to be $\sim 0.85 R_{\rm L}$." 1n these tomogranms there is no evidence of emission. from the aceretion cise or. bright spot: 16 characteristic rine and the bright-spot. signature in 16 upper-left quadrant typically seen in tomograms of interacting binaries is entirely. absent here., In these tomograms there is no evidence of emission from the accretion disc or bright spot: the characteristic ring and the bright-spot signature in the upper-left quadrant typically seen in tomograms of interacting binaries is entirely absent here. In. this respect jiese tomograms resemble those of the SW. Sex class of ο.Vs., In this respect these tomograms resemble those of the SW Sex class of CVs. SW Sex tomograms. however. tend to be bright in 16 lower-lelt quadrant. (believed to be the signature of an verllowing accretion stream re-impacting the disc). while jese data are bright in the lower-right quadrant. a position in velocity-space which does not coincide with any obvious sites of excess emission within the binary’s geometry.," SW Sex tomograms, however, tend to be bright in the lower-left quadrant (believed to be the signature of an overflowing accretion stream re-impacting the disc), while these data are bright in the lower-right quadrant, a position in velocity-space which does not coincide with any obvious sites of excess emission within the binary's geometry." The very low velocity of this emission indicates that it may be formecl in a bipolar disc wind viewed almost edge-on. or in the ADC. although the olf-set to the right. GL real) is puzzling.," The very low velocity of this emission indicates that it may be formed in a bipolar disc wind viewed almost edge-on, or in the ADC, although the off-set to the right (if real) is puzzling." Our tomograms also show emission in regions associated with the mass donor. which is consistent with the suggestion in the previous subsection that we may have detected the irradiated: companion.," Our tomograms also show emission in regions associated with the mass donor, which is consistent with the suggestion in the previous subsection that we may have detected the irradiated companion." " Component C in Ἐν, possibly a signature of disc overllow. appears as a faint feature to the left of the compact object in the LOSS tomogram. in a region associated with disc overllow in SW Sex stars."," Component C in \ref{fig:heII}, possibly a signature of disc overflow, appears as a faint feature to the left of the compact object in the 1988 tomogram, in a region associated with disc overflow in SW Sex stars." Intriguinglv. there also appears to be a brightening in this area in the 1986 tomogram.," Intriguingly, there also appears to be a brightening in this area in the 1986 tomogram." DBGCG's common envelope model implies that outflow. from Le would result in the Hel lines having à maximum blue shift at phase 0.0., BGG's common envelope model implies that outflow from $_2$ would result in the HeI lines having a maximum blue shift at phase 0.0. A maximum bluc-shift at phase ~0.25. which our reanalysis of the original racial velocity study has revealed. would appear to be incompatible with this model.," A maximum blue-shift at phase $\sim 0.25$, which our reanalysis of the original radial velocity study has revealed, would appear to be incompatible with this model." Llowever. BOGG's modelling involves many simplifications and approximations. and a more extensive development of this option may vield somewhat cillerent results.," However, BGG's modelling involves many simplifications and approximations, and a more extensive development of this option may yield somewhat different results." lfour new results clo rule out an Le-outllow scenario. an alternative explanation for the blue-shifted absorption lines will have to be found.," If our new results do rule out an $_2$ -outflow scenario, an alternative explanation for the blue-shifted absorption lines will have to be found." We consider four possible alternative scenarios:, We consider four possible alternative scenarios: The plate registration is done in the standard way by solving the Εν—1)=124 siniultaneous equations lor the minimization of X7: Note that in these equations. (j.)4(0.0).,"The plate registration is done in the standard way by solving the $4(JK-1)=124$ simultaneous equations for the minimization of $\chi^2$: Note that in these equations, $(j,k)\ne(0,0)$." We use a Newton-Raphson approach to solving the set of equations f;(r;)=0., We use a Newton-Raphson approach to solving the set of equations $f_i(x_j)=0$. " Assume an initial guess ο and make the Tavlor expansion to determine the corrections di;: Solving this svstem gives dry;=—(CAi;)τμ. The new guess becomes ry;=typ+dv. a new Tavlor expansion is made. and a new correction dr,; is estimated and so forth until convergence is achieved."," Assume an initial guess $x_{0j}$ and make the Taylor expansion to determine the corrections $dx_{0j}$: Solving this system gives $dx_{0j}=-(A_{ij})^{-1}f_{0i}.$ The new guess becomes $x_{1j}=x_{0j}+dx_{0j}$, a new Taylor expansion is made, and a new correction $dx_{1j}$ is estimated and so forth until convergence is achieved." Next. (he stellar parameters. their proper motions and distances. are determined [rom the 3/=63 simultaneous equations Now using the non-zero values [or ρενι and IL. the positional errors and. plate registrations are repeated.," Next, the stellar parameters, their proper motions and distances, are determined from the $3I=63$ simultaneous equations Now using the non-zero values for $\mu_{x,i}, \mu_{y,i}$ and $\Pi_i$, the positional errors and plate registrations are repeated." The scheme converges alter about 4 iterations., The scheme converges after about 4 iterations. The target star parameters are established once convergence is achieved by minimizing utilizing (he above expressions for /=NS and solving the equations for / =Ns. where NS is (he index corresponding to the neutron star.," The target star parameters are established once convergence is achieved by minimizing utilizing the above expressions for $i=NS$ and solving the equations for $i=$ NS, where NS is the index corresponding to the neutron star." The transformations are based on between 18 and 21 stars in each visit., The transformations are based on between 18 and 21 stars in each visit. The median residual error in (he translormation (the dillerence between (he modeled stellar positions, The median residual error in the transformation (the difference between the modeled stellar positions the same for all the simulations. and are given in Table lin dimensionless units.,"the same for all the simulations, and are given in Table 1 in dimensionless units." The initial densitv of the clouds is slighth above the tidal shear density at. their. initial locations. so the clouds are mareinally stable to tidal shear byA," The initial density of the clouds is slightly above the tidal shear density at their initial locations, so the clouds are marginally stable to tidal shear by." "Y, In all the tests the initial velocity. of the primary cloud. is kept fixed. anc is of the order of the Keplerian circular velocity for that racius."," In all the tests the initial velocity of the primary cloud is kept fixed, and is of the order of the Keplerian circular velocity for that radius." Orbits in a cusped potential are however not Ixeplerian., Orbits in a cusped potential are however not Keplerian. The initial specific energy. and angular momentum { of a particle can be used to find the pericenter. re. and the apocenter. rs. of the orbit.," The initial specific energy and angular momentum $l$ of a particle can be used to find the pericenter, $r_{\rm pe}$, and the apocenter, $r_{\rm ap}$, of the orbit." The orbits eccentricity e is then defined. via ↓⊔⋯⊔⋅⊳∖⊀↓⊔↓⊔↓⋜∐⊀↓∪⊔⊳∖↓≻⋜⊔⋅↥⋠⊔∙↓∢⋅≱∖⋯∙≼∙⋜↧⊳∖⊲↓∪⊔⋜↧∐∙∖⇁∪∣⋡↿⋜↧⊲↓⊔ ↓↕∙∖⇁↓≻, The orbit's eccentricity $e$ is then defined via In our simulations particles occasionally obtain hyperbolic orbits. ∢⋅↓⋅∣⋡⋖⋟↥↕≼↛∪↓⋅∣⋡⋠⊔≱∖⋡↓⊲↸∪↓⋅⋜⋯⋜↧↓∙∖⇁⊳∖⊀↓⊳∖↿∖↓≻↓∪∏⊀↓⊔⋏∙≟∃↓≻⊔↓⋅↓≻∩≱∖⋖⋅⋡∖∪⊔⇂∙∖," For analysis (plotting) purposes only, the eccentricities are capped at 1." ⇁⋡↥↓↥⋖⋅ ⋖⋅≼∙≼∼⋖⋅↓↕↿↓⋅↕≼⇍↕⇂↕∢⋅≻⋜⊔⋅⋖⊾≼⇍⋜↧↓≻↓≻⋖⋅∠⇂⋜∐↓⊳↓⊔∣⇂↥⋖⊾⊳∖∩⊾∐⋜⊔⋅↓≻∪↿∢⊾⊔↿⊲⋯↓⊔⊳∖⋯⇂ here (equation 2)). the orbit of the primary cloud is slightly eccentric. with pericentre and. apocentre of 25 anc 31.5 respectively. and with eccentricity e=0.12.," In the stellar potential used here (equation \ref{rhocusp}) ), the orbit of the primary cloud is slightly eccentric, with pericentre and apocentre of 25 and 31.5 respectively, and with eccentricity $e = 0.12$." The initial trajectory of the secondary cloud is varied between the tests to cover a small. range of, The initial trajectory of the secondary cloud is varied between the tests to cover a small range of In the rest of this section. we discuss our attempts to understand the reason for the lack of correspondence between the light curves.,"In the rest of this section, we discuss our attempts to understand the reason for the lack of correspondence between the light curves." Apart from the statistical noise (which ts negligible for S4. and small even for Sg). there are three possible sources of variability in the light curves: intrinsic variations of the radio source. unaccounted-for systematic errors in the flux density measurements. and extrinsic variations of the radio source sscintillation).," Apart from the statistical noise (which is negligible for $S_{\rm A}$, and small even for $S_{\rm B}$ ), there are three possible sources of variability in the light curves: intrinsic variations of the radio source, unaccounted-for systematic errors in the flux density measurements, and extrinsic variations of the radio source scintillation)." Below we consider these possibilities in turn., Below we consider these possibilities in turn. It is unlikely that the observed variability in Sp is due entirely (or even mainly) to intrinsic variations of the source—not only because no correlated variability is seen. but also because the fractional variability in Sy is larger than that of $4.," It is unlikely that the observed variability in $S_{\rm B}$ is due entirely (or even mainly) to intrinsic variations of the source—not only because no correlated variability is seen, but also because the fractional variability in $S_{\rm B}$ is larger than that of $S_{\rm A}$." Suppose the quasar is à point source with intrinsic flux density S(r)., Suppose the quasar is a point source with intrinsic flux density $S(t)$ . Then one would expect Sa(7)=fraS(¢—fo) and Sp(t)=frySf—t0—7). where μα and jrg are the image magnifications. fo is the time for image A. and 7 15 the time delay.," Then one would expect $S_{\rm A}(t) = \mu_{\rm A} S(t-t_0)$ and $S_{\rm B}(t) = \mu_{\rm B} S(t-t_0-\tau)$, where $\mu_{\rm A}$ and $\mu_{\rm B}$ are the image magnifications, $t_0$ is the light-travel time for image A, and $\tau$ is the time delay." The fractional variations would be equal. oS;$-OSsDNI. whereas in reality bzs S," The fractional variations would be equal, $\frac{\delta S_{\rm B}}{S_{\rm B}} = \frac{\delta S_{\rm A}}{S_{\rm A}} = \frac{\delta S}{S}$, whereas in reality $\frac{\delta S_{\rm B}}{S_{\rm B}} \approx 2\frac{\delta S_{\rm A}}{S_{\rm A}}$." ince the monitoring duration was 5 times longer than the 2€.expected time delay. the excess variability in image B is unlikely to be a fluke.," Since the monitoring duration was 5 times longer than the expected time delay, the excess variability in image B is unlikely to be a fluke." One way to escape the conclusion that the variability cannot be intrinsic is to suppose that the variable portion of image A is blended with à non-variable component that is not doubly imaged., One way to escape the conclusion that the variability cannot be intrinsic is to suppose that the variable portion of image A is blended with a non-variable component that is not doubly imaged. " For example. image A may have a jet with flux density Sy that has no counterpart in image B. This would decrease the fractional variability in S4, without affecting the fractional variability in Sg."," For example, image A may have a jet with flux density $S_0$ that has no counterpart in image B. This would decrease the fractional variability in $S_{\rm A}$ without affecting the fractional variability in $S_{\rm B}$." The problem is that one would need Syz130 mJy in order to dilute the fractional variability of A by a factor of 2. and although there is evidence for an extended component near image A. it appears to have a smaller flux density.," The problem is that one would need $S_0\approx 130$ mJy in order to dilute the fractional variability of A by a factor of 2, and although there is evidence for an extended component near image A, it appears to have a smaller flux density." Winn et ((2000) found the 5 GHz VLBA flux density of image A to be 55 mJy smaller than the VLA flux density measured 4+ months previously., Winn et (2000) found the 5 GHz VLBA flux density of image A to be 55 mJy smaller than the VLA flux density measured 4 months previously. If not due to souree variability. the discrepancy could be caused by an extended portion of image A that 1s blended with the compact point source at aresecond resolution. but that is nearly invisible at milliarcsecond resolution (due to the lack of short baselines).," If not due to source variability, the discrepancy could be caused by an extended portion of image A that is blended with the compact point source at arcsecond resolution, but that is nearly invisible at milliarcsecond resolution (due to the lack of short baselines)." Since an unknown fraction of this extended component is doubly imaged. and since radio jets tend to have steep radio spectra tthe flux density decreases with increasing frequency). the 9 GHz diluting component should have Sy<55 mJy.," Since an unknown fraction of this extended component is doubly imaged, and since radio jets tend to have steep radio spectra the flux density decreases with increasing frequency), the 9 GHz diluting component should have $S_0 < 55$ mJy." In previous sections we discussed tests for possible systematic errors due to an inaccurate source model. confusing sources. and residual gain-elevation effects.," In previous sections we discussed tests for possible systematic errors due to an inaccurate source model, confusing sources, and residual gain–elevation effects." The excess variability of component B does not seem to be caused by any of these effects., The excess variability of component B does not seem to be caused by any of these effects. The light curves did not change appreciably when the source model was altered to include the diffuse components discovered with the VLA., The light curves did not change appreciably when the source model was altered to include the diffuse components discovered with the VLA. No confusing sources were found. and there are no detectable phase slopes in the visibility data that would indicate a confusing source.," No confusing sources were found, and there are no detectable phase slopes in the visibility data that would indicate a confusing source." There are no significant correlations between the flux densities and the elevation angle. or array configuration.," There are no significant correlations between the flux densities and the elevation angle, or array configuration." In this section we discuss an additional concern: given that the longest ATCA baselines were only just sufficient to resolve the double. there is a potentially large covariance between S4 and Sp.," In this section we discuss an additional concern: given that the longest ATCA baselines were only just sufficient to resolve the double, there is a potentially large covariance between $S_{\rm A}$ and $S_{\rm B}$." For this reason. as mentioned in 2.. we performed simulations prior to the campaign to check the accuracy with which we would be able to separate the flux densities of the components.," For this reason, as mentioned in \ref{sec:design}, we performed simulations prior to the campaign to check the accuracy with which we would be able to separate the flux densities of the components." These simulations suggested we could achieve accuracy in Sy despite the small A-B separation., These simulations suggested we could achieve accuracy in $S_{\rm B}$ despite the small A–B separation. Here we discuss à more detailed simulation based on the actual noise properties of the data. which confirmed our previous estimate of the achievable accuracy.," Here we discuss a more detailed simulation based on the actual noise properties of the data, which confirmed our previous estimate of the achievable accuracy." The light curves are based on the Stokes / (total intensity) data. but the full polarization information was recorded.," The light curves are based on the Stokes $I$ (total intensity) data, but the full polarization information was recorded." Since the fractional circular polarization of PMN 31838-3427 i5 smaller than0.25%.. the Stokes V. visibilities from each epoch were nearly consistent with zero. and they had exactly the same statistical noise level and (4.v) coverage as the 7 data.," Since the fractional circular polarization of PMN J1838–3427 is smaller than, the Stokes $V$ visibilities from each epoch were nearly consistent with zero, and they had exactly the same statistical noise level and $(u,v)$ coverage as the $I$ data." This made the V data useful for testing purposes., This made the $V$ data useful for testing purposes. To the Stokes V. visibilities from each epoch. we added a model visibility function appropriate for PMN J1838-3427. using the MIRIAD task UVMODEL.," To the Stokes $V$ visibilities from each epoch, we added a model visibility function appropriate for PMN J1838–3427, using the MIRIAD task UVMODEL." The relative positions of the 2 point sources in the model were fixed at the values measured with VLBI. and the flux densities were set at 0.252 Jy and 0.019 Jy.," The relative positions of the 2 point sources in the model were fixed at the values measured with VLBI, and the flux densities were set at 0.252 Jy and 0.019 Jy." We then produced light curves from this artificial data set using the same procedure as we had used on the real data., We then produced light curves from this artificial data set using the same procedure as we had used on the real data. The resulting light curves are in Figure 3., The resulting light curves are in Figure 3. The flux density of image A is recovered with precision., The flux density of image A is recovered with precision. There are fluctuations in Sg due to the noise in the visibilities. the model fitting procedure. and varying (4.V)- coverage. but the RMS fractional variation is only2%.," There are fluctuations in $S_{\rm B}$ due to the noise in the visibilities, the model fitting procedure, and varying $(u,v)$ -coverage, but the RMS fractional variation is only." . The variations observed in the actual data must have a different origin., The variations observed in the actual data must have a different origin. Compact radio sources scintillate due to scattering by the ionized interstellar medium (ISM). much as stars twinkle due to scattering by the Earth's atmosphere (see. e.g.. Rickett 1990 or Narayan 1992).," Compact radio sources scintillate due to scattering by the ionized interstellar medium (ISM), much as stars twinkle due to scattering by the Earth's atmosphere (see, e.g., Rickett 1990 or Narayan 1992)." Is seintillation a plausible explanation for the lack of correlation between the light curves. and in particular for the excess variability of image B?," Is scintillation a plausible explanation for the lack of correlation between the light curves, and in particular for the excess variability of image B?" In this section we ask what type and degree of scintillation one might expect to occur along this line of sight through the Galaxy. and whether the amplitude. bandwidth. and time scale of the observed variations are consistent with those expectations.," In this section we ask what type and degree of scintillation one might expect to occur along this line of sight through the Galaxy, and whether the amplitude, bandwidth, and time scale of the observed variations are consistent with those expectations." Walker (1998. 2001) used the Taylor Cordes (1993) model of the ionized ISM to give rough expectations for the scattering. of extragalactic radio sources.," Walker (1998, 2001) used the Taylor Cordes (1993) model of the ionized ISM to give rough expectations for the scattering of extragalactic radio sources." " According to this model. for the line of sight to PMN J1838-3427 (Galactic longitude /j,=074 and latitude 5j,2—1275). the transition frequency between strong (multi-path) and weak scattering Is my~30 GHz. with strong scattering occurring for 7 2kkpc."," Conversely, the enormously successful GHz Parkes multibeam survey \citep[e.g.,][]{mlc+01} search the entire Galactic plane at $260\arcdeg