ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2" 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:"3(kulkarnietal.2010).,\citep{Kul10}.4.. 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 107.5+. 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}."6. 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."7 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."8 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.9 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.10 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."11n Similarlyhighmoleculerichsubmolecular2003.ApJ.592.S19 Lshavealsobeensceninolherinvestigalions(Quast. Heimers&DagagleΗΠΑΡΗΝΟ," Similarly high molecule rich sub-DLAs have also been seen in other investigations \citep{QRB08, Not08a}."12 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."13 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."14 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."15 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."16 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."17 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."18 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."19 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."20 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.21 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.22 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."23 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."24 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.25 VPIx acknowledges partial support from the National Science Foundation grant AS'T-, VPK acknowledges partial support from the National Science Foundation grant AST-0908890.26"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 $m_{\mathrm{gas}}=2.2131 \times 10^5~M_{\sun}$ ."27 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."28 The simulations were evolved using the parallel SPI code (?).., The simulations were evolved using the parallel SPH code \citep{gasoline}.29 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."30 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 $\Lambda_{\mathrm{tot}}(z, \rho, T, Z) = \Lambda_{\mathrm{HI, HeI, HeII}}(z,\rho, T) +31\frac{Z}{Z_{\sun}}\Lambda_{\mathrm{metal},Z_{\sun}}(z, \rho, T)$ ."32The 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}."33 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.34 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."35" 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."36 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}."37 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 $6.32\times 10^4~M_{\sun}$ )."38 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}."39 These masses are correlated to stellar Metinies as described in 7.., These masses are correlated to stellar lifetimes as described in \citet{Raiteri96}.40 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.41 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}.42 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."43 The rest of he supernova energy is radiated away., The rest of the supernova energy is radiated away.44 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}.45 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.46 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.47 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."48 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.49 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 $24334$."50 Ouly stars within the virial radius of the main ealaxy are considered., Only stars within the virial radius of the main galaxy are considered.51 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.52 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 $z=0$."53 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."54 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.55" 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."56" 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."57 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 $3$ ."58 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}. .59 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 $z=3$ ."60 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"61of the same population (σα.οἱal.2002:Grimm.Qillanov.&Sunvaev 2003).,"of the same population \citep{kilgard02,grimm03}."62. 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.63 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}."64 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.65 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.66 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}."67.. 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)."68" 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}. ."69" 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."70" 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."71 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.72 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.73. 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}.74. 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.75 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.76 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."77 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).78 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).79 Al the observations were made on 18 Nov 2003., All the observations were made on 18 Nov 2003.80 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.81 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.82 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.83mass.,mass.84 Close pairs are dominated by galaxies in massive halos., Close pairs are dominated by galaxies in massive halos.85" 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."86" 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."87 This is qualitatively consistent with the findings of Poggiantietal. (2006)., This is qualitatively consistent with the findings of \citet{EDisCS06}.88". However, whereas Poggianti et al."," However, whereas Poggianti et al."89" 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 0.4<z€ 0.8), our method uses the spectra of the local galaxy population to infer the entire cosmic star formation history."," measure instantaneous star formation rates in cluster galaxies identified over a wide range of redshifts (the SDSS at $z\sim 0$, and the ESO Distant Cluster Survey for $0.4\le z\le 0.8$ ), our method uses the spectra of the local galaxy population to infer the entire cosmic star formation history."90" In particular, it does not require classification of the galaxies into ‘cluster’ and ‘field’ populations, nor does it require acquisition of a galaxy sample which spans a wide redshift range."," In particular, it does not require classification of the galaxies into `cluster' and `field' populations, nor does it require acquisition of a galaxy sample which spans a wide redshift range."91 It is remarkable that these two very different methods agree., It is remarkable that these two very different methods agree.92" For similar reasons, the top left panel of Fig."," For similar reasons, the top left panel of Fig."93 3 may be compared with recent studies of the dependence of current star formation on environment2006)., \ref{fig:xiSFF} may be compared with recent studies of the dependence of current star formation on environment.94. We all find smaller star formation rates in dense regions today., We all find smaller star formation rates in dense regions today.95" Note, however, that our analysis is not restricted to the current epoch—it covers 11 Gyrs in lookback time."," Note, however, that our analysis is not restricted to the current epoch—it covers 11 Gyrs in lookback time."96 Halo model interpretations of our measurements will help determine if the environment plays a crucial role in regulating star formation., Halo model interpretations of our measurements will help determine if the environment plays a crucial role in regulating star formation.97 RKS is supported by NASA-ATP NAG-13720 and by the NSF under grant AST-0520647., RKS is supported by NASA-ATP NAG-13720 and by the NSF under grant AST-0520647.98" RJ is supported by NSF grants AST-0408698 and PIRE-0507768, and NASA grant NNG05GGO1G. BDP is supported by the Alexander von Humboldt Foundation, the Federal Ministry of Education and Research, and the Programme for Investment in the Future (ZIP) of the German Government."," RJ is supported by NSF grants AST-0408698 and PIRE-0507768, and NASA grant NNG05GG01G. BDP is supported by the Alexander von Humboldt Foundation, the Federal Ministry of Education and Research, and the Programme for Investment in the Future (ZIP) of the German Government."99" Funding for the SDSS has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, NASA, the Japanese Monbukagakusho, and the Max Planck Society."," Funding for the SDSS has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, NASA, the Japanese Monbukagakusho, and the Max Planck Society."100xpected for theBOLOCAM survey. (,expected for the survey. (101Due to the broad redshift istributions characteristic of the SZ clleet we find that sample variance is typically very small. ie. close to the Poisson limit for the 1 square degree survey which we considered.),"Due to the broad redshift distributions characteristic of the SZ effect we find that sample variance is typically very small, i.e. close to the Poisson limit for the 1 square degree survey which we considered.)"102 Other uncertainties. such as the exact form of PCy) and the density and temperature profiles of cluster eas have slightly smaller effects. but will still dominate over the statistical errors for a full-skv survey.," Other uncertainties, such as the exact form of $P(y)$ and the density and temperature profiles of cluster gas have slightly smaller effects, but will still dominate over the statistical errors for a full-sky survey."103 As such. it will be crucial to further our understanding of cluster gas properties before future SZ surveys can be exploitect fully.," As such, it will be crucial to further our understanding of cluster gas properties before future SZ surveys can be exploited fully."104 Finally. we explored. the constraints that may. be set on cosmological parameters and. also the presence of any non-Gaussianity in the initial conditions or preheating of ICAL eas in the early Universe.," Finally, we explored the constraints that may be set on cosmological parameters and also the presence of any non-Gaussianity in the initial conditions or preheating of ICM gas in the early Universe."105 Itedshift. distributions are potentially very. sensitive to Qo. ax and. the presence of primordial non-Caussianity.," Redshift distributions are potentially very sensitive to $\Omega_0$, $\sigma_8$ and the presence of primordial non-Gaussianity."106 Preheating of clusters has much less cllect on the redshift distributions but can significantly reduce the number of faint SZ clusters and. also. produces a tail to large sizes in the SZ cluster size distribution., Preheating of clusters has much less effect on the redshift distributions but can significantly reduce the number of faint SZ clusters and also produces a tail to large sizes in the SZ cluster size distribution.107 A Fisher-matrix analysis reveals that will provide interesting Constraints on cosmological parameters ancl the degree of non-Gaussianity (modulo uncertainties in. A4) and/or preheating only if redshifts are measured for all the detected clusters (or if prior. probability clistributions are assumed for the cosmological parameters)., A Fisher-matrix analysis reveals that will provide interesting constraints on cosmological parameters and the degree of non-Gaussianity (modulo uncertainties in $K_{34}$ ) and/or preheating only if redshifts are measured for all the detected clusters (or if prior probability distributions are assumed for the cosmological parameters).108 The experiment. due to the large area it will survey. should measure the non-Ciaussianitv or preheating parameters. Cr and A34 respectively. to accuracies of even without redshifts. for any of the clusters.," The experiment, due to the large area it will survey, should measure the non-Gaussianity or preheating parameters, $G$ and $K_{34}$ respectively, to accuracies of even without redshifts for any of the clusters."109 Furthermore. the SZ survey will provide inclependent ancl highly accurate constraints on cosmological parameters that will complement those obtained fron analysis of primordial CALB anisotropies.," Furthermore, the SZ survey will provide independent and highly accurate constraints on cosmological parameters that will complement those obtained from analysis of primordial CMB anisotropies."110 In conclusion. surveys in the SZ ellect will soon provide valuable measurements of various cosmological parameters which will compliment measurements from other techniques.," In conclusion, surveys in the SZ effect will soon provide valuable measurements of various cosmological parameters which will compliment measurements from other techniques."111 Assuming that the theoretical uncertainties highlighted in this paper can be adequately resolved. the SZ clleet also has the potential to constrain the presence of non-Ciaussianity and also to provide strong constraints on the distribution of gas within clusters and the presence or otherwise of any preheating.," Assuming that the theoretical uncertainties highlighted in this paper can be adequately resolved, the SZ effect also has the potential to constrain the presence of non-Gaussianity and also to provide strong constraints on the distribution of gas within clusters and the presence or otherwise of any preheating."112 AJDB acknowledges helpful conversations with Scott hay and Peng Oh., AJB acknowledges helpful conversations with Scott Kay and Peng Oh.113 The Llubble Volume numerical simulations were kindly mace available bv the VIRGO Consortium., The Hubble Volume numerical simulations were kindly made available by the VIRGO Consortium.114 Εις work was supported in part ον NSE AST-0006023. NASA and DolZ DI-ECG03-92-I5140701.," This work was supported in part by NSF AST-0096023, NASA NAG5-8506, and DoE DE-FG03-92-ER40701."115where vg is the number of grains at /=Q0.,where $n_0$ is the number of grains at $t=0$.116 The complete solution. the ιαος of grains in bin kk for |>Q. 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."117 2 along with the results of the numerical simulation., \ref{fig:cna} along with the results of the numerical simulation.118 The numerical results agree exactly with the analytic solution., The numerical results agree exactly with the analytic solution.119 The extra grains in the last bin in the simulation (Figs., The extra grains in the last bin in the simulation (Figs.120 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."121 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."122 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}. ."123 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}.124 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."125 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."126 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)."127" 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."128" The absorption efficiency. Q, is approximated. [or all grain sizes. by"," The absorption efficiency $Q_a$ is approximated, for all grain sizes, by"129lane appears across the granule and roughly along the field lines.,lane appears across the granule and roughly along the field lines.130" 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."131 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.132" 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."133 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.134" 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."135 | is 15 Mx em™., \ref{loop1} is 15 Mx $^{-2}$.136" 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."137" 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."138" From the reconstruction, we find that, around 500 km, R?/R?=0.25."," From the reconstruction, we find that, around 500 km, $R^2/R'^2 \approx 0.25$."139" 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 $^{-3}$."140" 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."141 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."142 The loop of Fig., The loop of Fig.143" | 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."144" 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."145" 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."146" 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"147volume.,volume.148 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.149 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."150 We have no reason to believe that this ts the Case., We have no reason to believe that this is the case.151 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."152 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.153 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."154 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."155 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."156 Recently. Dijkstra et al.," Recently, Dijkstra et al."157 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."158 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.159 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."160 2006(a). see Fig.," 2006(a), see Fig."161 1., 1.162 Further tests are needec to determine how well their model fits., Further tests are needed to determine how well their model fits.163" 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)."164 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).165 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."166 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."167 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).168 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."169 This has to be a rare phenomenon., This has to be a rare phenomenon.170 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.171 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 $\sim17211.5$ (Brocklehurst 1971)."173 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."174 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."175 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.176" 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 $\mathrm{L}_{\mathrm{Ly}\alpha} \sim17710^{43}$ erg $^{-1}$."178 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."179 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."180 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.181 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."182" 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.183 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."184 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 AGN185for 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."186 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.187 For the SBF distance modulus. 3’ equals 11.5 kpc.," For the SBF distance modulus, $\arcm$ equals 11.5 kpc."188 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)."189 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 7814.190 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."191 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."192 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."193" 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."194 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 7814.195 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. ("196Below 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.)197 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 7814.198 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.199 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.200 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}."201. 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)."202 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 $\sim$ $\arcm$."203 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."204 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 $M^T_V$ $=$ $-$ 20.40.205 Combining this with, Combining this with206The 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."207 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.208 Fig., Fig.209 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.210 7 the apparent systemic recession., 7 the apparent systemic recession.211 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).212 As in Fig., As in Fig.213 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."214 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)."215 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."216 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."217 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 $^{-1}$."218 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."219 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.220 5-7., 5-7.221 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)."222 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."223 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.224 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)."225 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 $^{-1}$.226 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.227 | is preferred over the broader., 1 is preferred over the broader.228 As for the He I data. the," As for the He I data, the"229Unlike for many other millisecond pulsars (cf.,Unlike for many other millisecond pulsars (cf.230 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."231 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.232" 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."233" 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."234" 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)."235" 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."236" 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."237 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.238 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.239 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.240" 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}."241" 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."242 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 21.88.243" 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.244 Table 6.7 in Becker 2009)., Table 6.7 in Becker 2009).245 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}. ."24618740097).,18740097).247 TN also has been supported by the same grants 118104003 and 19740094)., TN also has been supported by the same grants 18104003 and 19740094).248 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.249 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},"250 Edward(1983). Philipp(1985)... Alaa ," \citet{edward85} \citet{philipp85}, \ref{fig:sio2}a "251Table 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."252 The values have heen computed. from flux. calibrated near-intrared spectra., The values have been computed from flux calibrated near-infrared spectra.253 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).254 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}.255. 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."256" 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}) )."257 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."258 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."259" 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}.260 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 $1.7 \pm 1.1$.261 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}.262 These values are about m(higher than the raw ratio lor 2M11464-22., These values are about higher than the raw ratio for 2M1146+22.263 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 $2.6 \pm 1.1$."264" 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."265 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 ${\Delta}H \sim 0.35~{\mu}m, {\Delta}S = {\sim}0.15~{\mu}m$ ), ${\sim}2.3$."266Since 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."267 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.268 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."269 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."270 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.271 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."272 We determine a conservative upper limit when the probability. of obtaining, We determine a conservative upper limit when the probability of obtaining273There 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.274 Our method is one specific (and relatively simpler) example., Our method is one specific (and relatively simpler) example.275" 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."276 This paper is organized as follows., This paper is organized as follows.277" 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 $r$."278" 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."279" 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."280" In Section 5,, we presentthe main results of this paper."," In Section \ref{sec:results}, we presentthe main results of this paper."281 We conclude in Section 6.., We conclude in Section \ref{sec:conclusion}.282" 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 $r$."283" 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, $N_l^{BB}$."284" 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 $\sqrt{\Omega_{\rm285pix}}=1$ arcmin."286" 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.287 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.288 Is this sufficient for detecting primordial B modes?, Is this sufficient for detecting primordial $B$ modes?289" 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,290e.g., Appendix A of][]{zaldarriaga/etal:prep, planck:bb}."291".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."292" 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."293" 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)."294 How would this influence our ability to detect r?, How would this influence our ability to detect $r$?295" 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."296" 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.,297Equation~(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."298 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 ${\cal L}(r|\hat{C}^{BB}_l)\propto P(\hat{C}^{BB}_l|r)$ .299" 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 $l_{\rm300max}=2$, 5, 10, and 100."301" 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."302" However, the precision on r does not improve wKbeyond |=5."," However, the precision on $r$ does not improve beyond $l=5$."303 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 $l\ge 5$.304" 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."305" 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 $r=10^{-3}$. ("306"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.)"307" 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."308" Again, this is apparent in Figure 2.."," Again, this is apparent in Figure \ref{fig:clnoise}. ."309" 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."310" 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."311" 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"312dl shows nunerical calculations of the quiesceut radiation conipoueuts of Ser A,1 shows numerical calculations of the quiescent radiation components of Sgr $^*$.313" 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 $\lesssim31410^4\,\rm yr$."315Maguetic 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."316 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."317 But it is also xossible that Bo<By. ia which case a simaller svuchrotron Hux from the pe-scale plerion than shown in Fig.," But it is also possible that $B_2 < B_1$, in which case a smaller synchrotron flux from the $pc$ -scale plerion than shown in Fig."318 l is xedicted., 1 is predicted.319 The inset in 1l shows the nouthermal clectrou distributions., The inset in 1 shows the nonthermal electron distributions.320" Besides svuchrotron aud Compton losses. calculations also include Coulomb and bremsstrabhme osses qnoa mnediun with my,=Lecm? characteristic or central pe regions of Ser A."," Besides synchrotron and Compton losses, calculations also include Coulomb and bremsstrahlung losses in a medium with $n_{gas} = 10^3 \,\rm cm^{-3}$ characteristic for central $pc$ regions of Sgr $^*$."321 Electrons with a power- Ποσο iudex μον=2.2 aud an exponential cutoff above Ling=D5UTeV are injected into 2-sided nebula with total power L.=6.5«10°eres1.," Electrons with a power-law injection index $\alpha_{pler}=2.2$ and an exponential cutoff above $E_{max}=50\,\rm TeV$ are injected into 2-sided nebula with total power $L_{e} = 6.5\times 10^{36}\,\rm erg \, s^{-1}$."322 These electrons raciatively cool downstream of the shock aud. propagate o distances Z7104%cm on the timescale tog.=50 vi. during which most of the injected energy of the iulti-TeV electrous (producing TeV and X-ray fluxes observed) has oen already. lost.," These electrons radiatively cool downstream of the shock and propagate to distances $\geq 10^{17}\,\rm cm$ on the timescale $t_{esc} = 50\,$ yr, during which most of the injected energy of the multi-TeV electrons (producing TeV and X-ray fluxes observed) has been already lost."323 The radio emission is produced at rZ20 iu Dz10€ field bv a relativistic Maxwelliau. electron: distribution xS76CÓ with sg=200 resulting from a balance )etxyceen second-order energy gaius and svuclrotron losses (Schlickeiser1985).," The radio emission is produced at $r\lesssim 20 $ in $B\approx 10\,\rm G$ field by a relativistic Maxwellian electron distribution $\propto \gamma^2 e^{-\gamma/\gamma_0}$ with $\gamma_0 =324200$ resulting from a balance between second-order energy gains and synchrotron losses \citep{sch85}."325. The stochastic acceleration power of radio electrons is therefore about equal to the observed radio Iunünositv Ly., The stochastic acceleration power of radio electrons is therefore about equal to the observed radio luminosity $L_{rad}$.326 The SSC emission componeut of these electrons. shown iu 11 by the dashed curve. falls iu the sub-keV region below the level of the quiesceut. N-vayv flux.," The SSC emission component of these electrons, shown in 1 by the dashed curve, falls in the sub-keV region below the level of the quiescent X-ray flux."327 However. if inaenetic fields X5 CG are assumed. this SSC contribution would rise aud also move to 1 keV. aud could contribute to radiation at that energies.," However, if magnetic fields $\lesssim 5$ G are assumed, this SSC contribution would rise and also move to 1 keV, and could contribute to radiation at that energies."328 It cannot. however. explain the entire quicscent fux extending to 10 keV. The powerful A-vav and NIR fares observed from are explained in our model by the ouset of instabilities of the accretion flow at distances of ouly few Rs.," It cannot, however, explain the entire quiescent flux extending to 10 keV. The powerful X-ray and NIR flares observed from are explained in our model by the onset of instabilities of the accretion flow at distances of only few $R_{S}$."329 They result in strong shocks in the accretion flow and effective. acceleration of particles advected with the flow., They result in strong shocks in the accretion flow and effective acceleration of particles advected with the flow.330 The accelerated particles are then casily taken out of this region iu the wind/jet outflow., The accelerated particles are then easily taken out of this region in the wind/jet outflow.331 Svuchrotron euission of electrons accelerated to >109 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.332" 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."333" 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 $\lesssim 100\,\rm334GHz$ 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."335 Tn 22 we show the flare fluxes expected iu this model., In 2 we show the flare fluxes expected in this model.336 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 $B$."337 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."338 The electron injection time profile is Lyia(f)=Lyf|tftj)?. with ty=720s.," The electron injection time profile is $L_{e.flare}(t)=339L_{0}/ (1+t/t_0)^{2}$, with $t_0 = 720\,\rm s$."340 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 $B=25\,\rm G$."341 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.342 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}."343. 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 $^\ast$."344 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.345 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."346" 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}.347.. 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.348 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.349 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}."350. 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."351 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."352" 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."353 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}."354. 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 $\sim 100 \,\rm355km\, s^{-1}$ could significantly contribute to the radio synchrotron flux of Sgr A West."356 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."357 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."358 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 GLAST359formation 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."360 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."361 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).362" We asstune isotropic turbulent magnetic fields which have broader power spectra Ayia,=LOOxAya, aud caleulate the radiation spectra in the regime of 1<a«5.", We assume isotropic turbulent magnetic fields which have broader power spectra $k_{\mathrm{max}}=100 \times k_{\mathrm{min}}$ and calculate the radiation spectra in the regime of $1<a<\gamma$.363 In 82 we describe caleulation method and numerical results., In 2 we describe calculation method and numerical results.364 In. 83J) we eive a physical interpretation., In 3 we give a physical interpretation.365 Because we focus our attention on caleulating radiation spectrum. we assume (he static [ield with required properties of a. and neglect the back reaction of radiating electrons to the magnetic field.," Because we focus our attention on calculating radiation spectrum, we assume the static field with required properties of $a$, and neglect the back reaction of radiating electrons to the magnetic field."366 We solve the trajectory of electron accurately in each time step and calculate the radiation spectrum., We solve the trajectory of electron accurately in each time step and calculate the radiation spectrum.367 The isotropic turbulent field is generated by using the discrete Fourier transform description as developed in Giacalone Jokipii (1999)., The isotropic turbulent field is generated by using the discrete Fourier transform description as developed in Giacalone Jokipii (1999).368" It is described as a superposition of Fourier modes. each with a random phase. direction and polarization llere. Ἐν.μιΚωand&, ave the amplitude. phase. wave vector and polarization vector for the n-th mode. respectively."," It is described as a superposition of Fourier modes, each with a random phase, direction and polarization Here, $A_n,\beta_n,\bm{k}_n \: \mathrm{and} \: \hat{\xi}_n$ are the amplitude, phase, wave vector and polarization vector for the -th mode, respectively."369" The polarization vector is determined bv a single angle <0,c? where e, and efqd are unit vectors. orthogonal to eZ=ky/h,,."," The polarization vector is determined by a single angle $0<\psi_n<2\pi$ where $\bm{e_x^\prime}$ and $\bm{e_x^\prime}$ are unit vectors, orthogonal to $\bm{e_z^{\prime}} = \bm{k_n}/k_n$."370 The amplitude of each mode is where (he variance σ represents (he amplitude of (he turbulent field., The amplitude of each mode is where the variance $\sigma$ represents the amplitude of the turbulent field.371 We use the following, We use the following372"Scaling to characteristic parameters of a quiesceut dwarf nova disc. this can be written as where {μις is the effective temperature m units of 5000 Is. and the distauce has been expressed in units of the distance from the white dwarf to the £4 poit Ry, as used in the MEAL maps.","Scaling to characteristic parameters of a quiescent dwarf nova disc, this can be written as where $T_{{\rm eff},5}$ is the effective temperature in units of 5000 K, and the distance has been expressed in units of the distance from the white dwarf to the $L_1$ point $R_{L_1}$ as used in the MEM maps."373 It is easy to see that for central temperatures Txd0iK.low values of X<T1irequired by an optically thin model imply am1!," It is easy to see that for central temperatures $T \lta 10^4374K$ , low values of $\Sigma < 1$ required by an optically thin model imply $\alpha\gg 1$!"375 This especially the case of isothermal slab models in which both the lines aud the continuum are ciuitted by the same medimm (Wood et al., This especially the case of isothermal slab models in which both the lines and the continuum are emitted by the same medium (Wood et al.376 1992)., 1992).377 As we see in Section 5. even a more refined model with temperature stratification still requires. in the case of TT Cas. a=1.," As we see in Section 5, even a more refined model with temperature stratification still requires, in the case of HT Cas, $\alpha\gta 1$."378 The SW τος of vertical accretion dise structure assunies that the dise is in a steady state;, The SW model of vertical accretion disc structure assumes that the disc is in a steady state.379 Since quiescent cavarf nova dises are in thermal equilibria one can use the SW model at cach ring of the disc. using the local value of the accretion rate and taking mto account nonsteady disc relations described iu Section 2.2.," Since quiescent dwarf nova discs are in thermal equilibrium one can use the SW model at each ring of the disc, using the local value of the accretion rate and taking into account non–steady disc relations described in Section 2.2."380 First. we verified that SW thermal equilibrium accretion dise solutious lave the same general properties as the dise models used in the DIM.," First, we verified that SW thermal equilibrium accretion disc solutions have the same general properties as the disc models used in the DIM."381 Using the SW model we calculated series of models for several values of the radius aud the viscosity parameter o., Using the SW model we calculated series of models for several values of the radius and the viscosity parameter $\alpha$ .382 We plotted this solutious ou a customary Xτω diaeramuue., We plotted this solutions on a customary $\Sigma - T_{\rm eff}$ diagramme.383 An example is shown on Figure (1))., An example is shown on Figure \ref{scurve}) ).384 We compare the SW models with the ones obtained with the Tameury ct al. (, We compare the SW models with the ones obtained with the Hameury et al. (3851998) code.,1998) code.386 Iu this code two approxinatious can be used: either the transfer is calculated in the diffusion approxinatioun or a (simplified) cerey atmosphere” approach is adopted., In this code two approximations can be used: either the transfer is calculated in the diffusion approximation or a (simplified) `grey atmosphere' approach is adopted.387 Fig. (1)), Fig. \ref{scurve}) )388 show that there is very good agreciment between SW and grev models on the cold brauch of solutions (Xx M44) but there are deviations on the uustable and hot branches.," show that there is very good agreement between SW and `grey' models on the cold branch of solutions $\Sigma389\leq \Sigma_{\rm max}$ ) but there are deviations on the unstable and hot branches."390 The SW and IEuueury ct al. (, The SW and Hameury et al. (3911998) approach eive +he same results oulv for τμ20000 Ix. This differences are most probably duc mainly to differcut opacity tables used in the two codes (Idan et al.,1998) approach give the same results only for $T_{\rm eff} \gta 20 000$ K. This differences are most probably due mainly to different opacity tables used in the two codes (Idan et al.392 L998)., 1998).393 Since in the standard DIM one has to assiuuue a jump iu à (see ce. Tameury ct al., Since in the standard DIM one has to assume a `jump' in $\alpha$ (see e.g. Hameury et al.394 1998) the zinall differences iu the upper branches of solutions are of uo practical iuportauce for the description of a DN outburst., 1998) the small differences in the upper branches of solutions are of no practical importance for the description of a DN outburst.395 The excelleut. agreciment on the lower branch makes it consistent to model cussion from quicscent dwarf nova dises by using in the SW code Tig(r) obtained from the DIN, The excellent agreement on the lower branch makes it consistent to model emission from quiescent dwarf nova discs by using in the SW code $T_{\rm eff}(r)$ obtained from the DIM.396 We used the SW code to study cussion properties of the quiescent accretion disc in WT Cas., We used the SW code to study emission properties of the quiescent accretion disc in HT Cas.397We did not tryto ft the brightuess temperature distribution,We did not tryto fit the brightness temperature distribution398"been deposited ou the surface of a neutron star (6. ον, by accretion from the interstellar iuiediun or from a fallback. disk).","been deposited on the surface of a neutron star (e. g., by accretion from the interstellar medium or from a fallback disk)."399 If the hydrogen laver is not optically thick at all euergies. but only at lower ones. then the atimospherc structure (telpcrature run) js modified. that in tur- should affect the spectra of cinergent radiation.," If the hydrogen layer is not optically thick at all energies, but only at lower ones, then the atmosphere structure (temperature run) is modified, that in turn should affect the spectra of emergent radiation."400 We investigated nonmagnetic atmosphere models wit[um various values of the total column density of πόντους- Voas du the atinosphere., We investigated nonmagnetic atmosphere models with various values of the total column density of hydrogen $_{\rm tot}$ in the atmosphere.401 We assunued the atinosphere to be in the radiative aud hvadrostatie equilibrium. aud that the radiation at the iuuner boundary v—v;; ik given by the diffusion solution (although. the latter condition is not strictly justified sce Discussion).," We assumed the atmosphere to be in the radiative and hydrostatic equilibrium, and that the radiation at the inner boundary $_{\rm tot}$ is given by the diffusion solution (although, the latter condition is not strictly justified — see Discussion)."402 The main result we obtain is rather natural: reducing the total column density lowers the temperature of surface lavers which enüt high-cuerey photons. that in tun leads to the softening of the Wien tail in the model spectra. making hem close to the blackbody oues with the same effective eniperature.," The main result we obtain is rather natural: reducing the total column density lowers the temperature of surface layers which emit high-energy photons, that in turn leads to the softening of the Wien tail in the model spectra, making them close to the blackbody ones with the same effective temperature."403 This imieaus that optical fluxes predicted by hese models applied to X-ray data on INSs are expected o be significantly decreased iu comparison with those even by the standard model. but still larger than values vielded by the dackbody model.," This means that optical fluxes predicted by these models applied to X-ray data on INSs are expected to be significantly decreased in comparison with those given by the standard model, but still larger than values yielded by the blackbody model."404 We computed hydrogen nodels in a eric of effective temperature aud total column lensity(down to ve=10P7 & 7) aud applied these nodels to the UV - optical and Chandra LETGS data ou ttakine iuto accom the nouthermal oower law discovered by Kaplan ct al. (2003))., We computed hydrogen models in a grid of effective temperature and total column density(down to $_{\rm tot}=10^{-3}$ g $^{-2}$ ) and applied these models to the UV - optical and Chandra LETGS data on taking into account the nonthermal power law discovered by Kaplan et al. \cite{kaplan03}) ).405 Α best fittine model is shown in Fig. 5.., A best fitting model is shown in Fig. \ref{rxj0720_spec}.406 The parameters of the uodoel are: otal atmosphere column density Veor=0.16 nο P7. effective temperature Τμ=un TOV. distance to he star D = 201 pc (assuniug the stanard neutron star radius R= LO kun and mass M = 11M). aud iuterstellar absorption Nj=1.1«1079 7.," The parameters of the model are: total atmosphere column density $_{\rm407tot}=0.16$ g $^{-2}$, effective temperature $_{\rm eff}=57$ eV, distance to the star D = 204 pc (assuming the standard neutron star radius R = 10 km and mass M = $\,{\rm M}_\odot$ ), and interstellar absorption $_{\rm H}=1.1\times 10^{20}$ $^{-2}$."408 As secu in Fig. 5.," As seen in Fig. \ref{rxj0720_spec},"409 the nodel niccly fits the LETGS data (4220.91 iu the X-ray domain) and aerees well with the detected optical fiuxes., the model nicely fits the LETGS data $\chi^2_\nu$ =0.94 in the X-ray domain) and agrees well with the detected optical fluxes.410" The total mass of livdrogen obtained iu the fit is | wR? ves = 210% ο, Assuming a stellar age of 109 ve. this translates iuto a lean accretion rate of  ¢e/s. which Is nanny orders of magnitude lower than predicted by the accretion moclel."," The total mass of hydrogen obtained in the fit is 4 $\pi$ $^{2}$ $_{\rm tot}$ = $\times$ $^{12}$ g. Assuming a stellar age of $^{6}$ yr, this translates into a mean accretion rate of $\sim$ g/s, which is many orders of magnitude lower than predicted by the accretion model."411 Despite the fact that the thin atmosphere model provides a good fit to the observational data in the broad enerev range at reasonable neutron star parameters. it serves rather as an illustrative example because of a ΠΡΟ of shorteonmuüugs iu the simplified approach it iis been derived with.," Despite the fact that the thin atmosphere model provides a good fit to the observational data in the broad energy range at reasonable neutron star parameters, it serves rather as an illustrative example because of a number of shortcomings in the simplified approach it has been derived with."412 First of all the assumption on he equilibriun solution at the maximal depth im such an atinosphere may not be justified at higher N-ray chereies where the cuutted radiation could be affected X properties of the stellar surface under the atinosplieric aver.," First of all, the assumption on the equilibrium solution at the maximal depth in such an atmosphere may not be justified at higher X-ray energies where the emitted radiation could be affected by properties of the stellar surface under the atmospheric layer."413 It means that the boundary σολΊο at the iuner ))oundarv V=vaa. taken currently to be the same as in the standard modeling Gvith mach larger values of vi). lav need to be modified.," It means that the boundary condition at the inner boundary $={\rm y}_{\rm tot}$, taken currently to be the same as in the standard modeling (with much larger values of $_{\rm tot}$ ), may need to be modified."414 For iustance. oue could consider such a thin atinosphere on top of a solid neutrou star surface or a thicker laver composed of another chemical clement.," For instance, one could consider such a thin atmosphere on top of a solid neutron star surface or a thicker layer composed of another chemical element."415 Second. the model should be developed with account for the presence of a strong surface magnetic ποια. Bo~105 CL as recentle suggested bv Zaue e al. (2002)).," Second, the model should be developed with account for the presence of a strong surface magnetic field, $B\sim 10^{13}$ G, as recently suggested by Zane et al. \cite{zane02}) )."416" It is safe to assune that in the case of uaenetized models. reducing the atmosphere thickness would also sofen the spectrum of the emcergenu --""aciation."," It is safe to assume that in the case of magnetized models, reducing the atmosphere thickness would also soften the spectrum of the emergent radiation."417 Since du strougC» magneticOo fields the cmereeutOo spectra of he standard models are iutrinsicallv softer than the non-uaenetic ones (Zavlin Pavlov 2002). one may expec hat the magnetized model ueeds a larger atmosphere hickuess in order to describe the broad-band properties of the emission from 1-353125.," Since in strong magnetic fields the emergent spectra of the standard models are intrinsically softer than the non-magnetic ones (Zavlin Pavlov 2002), one may expect that the magnetized model needs a larger atmosphere thickness in order to describe the broad-band properties of the emission from ."418 Another poiut rere is that this model is constructed assunine a uniform neutron star surface. which makes the model cmiussion uupulsed. whereas the observed," Another point here is that this model is constructed assuming a uniform neutron star surface, which makes the model emission unpulsed, whereas the observed"419-22nRQ. Where Ry—vitz37 is the radial distance in the Fourier plane and « and v are the Fourier conjugate variables to (. (e.g.. R.A.) and 0 (e.g.. Dec.) on the sky.,"$\ell = 2 \pi R_{uv}$, where $R_{uv} \equiv \sqrt{u^2+v^2}$ is the radial distance in the Fourier plane and $u$ and $v$ are the Fourier conjugate variables to $\theta_x$ (e.g., R.A.) and $\theta_y$ (e.g., Dec.) on the sky."420 The variance of the Fourier amplitudes at radius Αμ is equal to c;., The variance of the Fourier amplitudes at radius $R_{uv}$ is equal to $c_\ell$.421 Denoting the Fourier transform of the cluster SZ temperature decrement profile as Τ. the angular power spectrum of a galaxy cluster at the center of a field is simply c;277. assuming azimuthal symmetry for the cluster.," Denoting the Fourier transform of the cluster SZ temperature decrement profile as $\tilde{T}$, the angular power spectrum of a galaxy cluster at the center of a field is simply $c_\ell = \tilde{T}^2$, assuming azimuthal symmetry for the cluster."422 Spatial correlations between galaxy clusters are negligible for (=100 (KomatsuandKitayama1999) and in this work we are interested in (21000. so the correlations can be safely neglected.," Spatial correlations between galaxy clusters are negligible for $\ell \ga 100$ \citep{komatsu99a} and in this work we are interested in $\ell \ga 1000$, so the correlations can be safely neglected."423" The angular power spectrum can therefore be thought of as Poisson shot noise. where each ""shot"" has an angular profile."," The angular power spectrum can therefore be thought of as Poisson shot noise, where each “shot” has an angular profile."424 For a Poisson process. at each position in the plane a randomly placed source will have an amplitude T but Fourierwill have a random phase.," For a Poisson process, at each position in the Fourier plane a randomly placed source will have an amplitude $\tilde{T}$ but will have a random phase."425 The collection of sources will thus constitute a random walk of the Fourier amplitude with step size Τ. leading to a final ec;=NT. where N is the number of galaxy clusters.," The collection of sources will thus constitute a random walk of the Fourier amplitude with step size $\tilde{T}$, leading to a final $c_\ell = N \tilde{T}^2$, where N is the number of galaxy clusters."426 As an integral over redshift and cluster mass. this can be eXpressed as where ας) is the angular diameter distance. H(z) is the Hubble constant. and dn/dlnM is the differential comoving number density per log interval in mass.," As an integral over redshift and cluster mass, this can be expressed as where $d_A(z)$ is the angular diameter distance, $H(z)$ is the Hubble constant, and $dn/d\ln{M}$ is the differential comoving number density per log interval in mass."427 A very fast method to obtain Τ for somewhat realistic cluster profiles with azimuthal symmetry is to take advantage of fast Hankel transform routines that exist (Anderson1982)., A very fast method to obtain $\tilde{T}$ for somewhat realistic cluster profiles with azimuthal symmetry is to take advantage of fast Hankel transform routines that exist \citep{anderson82}.428". Note that here. and everywhere below. we work in units where c, has units of iK."," Note that here, and everywhere below, we work in units where $c_\ell$ has units of $\mu K^2$ ."429 The power spectrum calculation exactly follows the procedure of Holder and Carlstrom (2001) , The power spectrum calculation exactly follows the procedure of Holder and Carlstrom (2001) \nocite{holder01}.430"We choose cosmological parameters Q,,=0.3. O42 0.7. og=1. =0.1. Ομ=0.02. n=1. and zero neutrino mass."," We choose cosmological parameters $\Omega_m=0.3$, $\Omega_\Lambda=0.7$ , $\sigma _8=1$, $h=0.7$, $\Omega_{b}h^2 =0.02$, $n=1$, and zero neutrino mass."431 The differential comoving number density 1s adopted from recent fits to large numerical simulations of structure formation (Jenkins. 2001).. and is a function of the variance on mass scale M.," The differential comoving number density is adopted from recent fits to large numerical simulations of structure formation \citep{jenkins01}, and is a function of the variance on mass scale $M$."432 This variance was calculated using the power spectrum for our adopted cosmological model derived from the fitting functions of Eisenstein and Hu (1999) .., This variance was calculated using the power spectrum for our adopted cosmological model derived from the fitting functions of Eisenstein and Hu (1999) \nocite{eisenstein99a}.433" As acluster model. we adopt the simple toy model of Holder and Carlstrom (2001). with a density profile of the form V/Gz4 Rl. with n. a core radius and R, the virial radius. derived from the spherical collapse model (Lahaveta£...1991)."," As a cluster model, we adopt the simple toy model of Holder and Carlstrom (2001), with a density profile of the form $n_e \propto 1/(r_c^2+R_v^2)$ , with $r_c$ a core radius and $R_v$ the virial radius, derived from the spherical collapse model \citep{lahav91}."434. The relation between core radius and virial radius is taken to be a constant value (ten). roughly as would be expected for the case of self-similar evolution of the cluster population.," The relation between core radius and virial radius is taken to be a constant value (ten), roughly as would be expected for the case of self-similar evolution of the cluster population."435 The gas temperature as a function of mass was taken from hydrodynamical simulations (BryanandNorman1998) and the gas was assumed to be isothermal., The gas temperature as a function of mass was taken from hydrodynamical simulations \citep{bryan98} and the gas was assumed to be isothermal.436 For this work. we are interested in the effects of radio point sources on the SZ angular power spectrum. so the details of the power spectrum are not crucial.," For this work, we are interested in the effects of radio point sources on the SZ angular power spectrum, so the details of the power spectrum are not crucial."437 We have verified that the results below are robust to the choice of model for generating the SZ power spectrum., We have verified that the results below are robust to the choice of model for generating the SZ power spectrum.438 The angular power spectrum resulting from our recipe is in broad agreement with results from large cosmological hydrodynamical simulations (Springel.White.andHernquist2000)., The angular power spectrum resulting from our recipe is in broad agreement with results from large cosmological hydrodynamical simulations \citep{springel00}.439. Temperature gradients will affect the details of the shape of the peak of the power spectrum. while shifting the normalization of the mass temperature relation introduces a direct scaling of the amplitude of the angular power spectrum.," Temperature gradients will affect the details of the shape of the peak of the power spectrum, while shifting the normalization of the mass temperature relation introduces a direct scaling of the amplitude of the angular power spectrum."440 For example. using the observed normalization of the mass-temperature relation (Finoguenov.Reiprich.andBóhringer2001) leads to an rms temperature fluctuation that is approximately higher.," For example, using the observed normalization of the mass-temperature relation \citep{finoguenov01} leads to an rms temperature fluctuation that is approximately higher."441 Given the uncertain relation between the observed X-ray temperatures and the (most relevant for our purposes) mean electron temperature. we choose to use the normalization from simulations.," Given the uncertain relation between the observed X-ray temperatures and the (most relevant for our purposes) mean electron temperature, we choose to use the normalization from simulations."442 Putting the pieces together. the integrand of Equation 2. is shown as a function of mass and redshift in Figure |..," Putting the pieces together, the integrand of Equation \ref{eqn:cl} is shown as a function of mass and redshift in Figure \ref{fig:dcl}."443 Self- evolution of the intra-cluster medium was assumed. but the gas evolution history has very little effect on such a plot.," Self-similar evolution of the intra-cluster medium was assumed, but the gas evolution history has very little effect on such a plot."444 At f=1000. most of the signal is coming from somewhat massive. relatively nearby clusters. while the dominant contribution to higher ( is coming from distant low-mass clusters. with a significant tail extending to z=2.," At $\ell=1000$, most of the signal is coming from somewhat massive, relatively nearby clusters, while the dominant contribution to higher $\ell$ is coming from distant low-mass clusters, with a significant tail extending to $z=2$."445 It is easy to see why radio point sources could be a problem., It is easy to see why radio point sources could be a problem.446 At (21000. the signal is coming from nearby clusters. where each point source should be relatively bright. and from fairly massive clusters. which have more cluster members and therefore could be expected to have more point sources.," At $\ell=1000$, the signal is coming from nearby clusters, where each point source should be relatively bright, and from fairly massive clusters, which have more cluster members and therefore could be expected to have more point sources."447" These clusters also have stronger SZ emission and are more extended on the sky. which will somewhat mitigate the point source contamination,"," These clusters also have stronger SZ emission and are more extended on the sky, which will somewhat mitigate the point source contamination."448 At higher (. the clusters have fewer point sources and the ones that they do have are diluted by the lummosity distance.," At higher $\ell$, the clusters have fewer point sources and the ones that they do have are diluted by the luminosity distance."449 However. the cluster signal is weaker. making point sources relatively more important.," However, the cluster signal is weaker, making point sources relatively more important."450 Thus. over the whole range of the peak of the SZ angular spectrum it is expected that radio point source contamination might be important for experiments at low frequencies.," Thus, over the whole range of the peak of the SZ angular spectrum it is expected that radio point source contamination might be important for experiments at low frequencies."451 Radio point sources are well measured and catalogued in terms of their flux distributionand source density at an observing frequency of 1.4 GHz. due to the NVSS (Condon and FIRST (Whiteera£...1997) surveys.," Radio point sources are well measured and catalogued in terms of their flux distributionand source density at an observing frequency of 1.4 GHz, due to the NVSS \citep{condon98} and FIRST \citep{white97} surveys."452 Unfortunately. radio point sources oftenhave non-trivial spectra," Unfortunately, radio point sources oftenhave non-trivial spectra"453whereas the hatched histograms show the distribution for those groups where fi24 aaresec2,"whereas the hatched histograms show the distribution for those groups where $\mu454\le 24$ $^{-2}$."455"? ""he fraction of eroups which contain galaxies at. cliscordant redshifts (that is. chance lince-ol-sight alignments rather than physically dense groups) is expected to be greatly. reduced. for. this latter sample."," The fraction of groups which contain galaxies at discordant redshifts (that is, chance line-of-sight alignments rather than physically dense groups) is expected to be greatly reduced for this latter sample."456 Clearly. the overwhelming majority of groups from both Catalogues A and D have 6 members or less: very few groups in the brighter subsamples have more than 5 members. strongly. suggesting that eroups more numerous than this contain interlopers. at least in part.," Clearly, the overwhelming majority of groups from both Catalogues A and B have 6 members or less; very few groups in the brighter subsamples have more than 5 members, strongly suggesting that groups more numerous than this contain interlopers, at least in part."457 Η groups with more than 6 genuine members exist. they are intrinsicallv VODNV Pare.," If groups with more than 6 genuine members exist, they are intrinsically very rare."458 The left panel of Figure 5. shows the r. band group surface brightness distribution for all eroups identified. in Catalogue A. and the right. panel shows the same for all eroups identified in Catalogue B. More groups are found at lower surface brightness: however. as shown in Paper I. brighter groups are more likely to pe genuine and not contain any interlopers(sce Section3.3.2 for a more detailed investigation of this point).," The left panel of Figure \ref{sbdens} shows the $r-$ band group surface brightness distribution for all groups identified in Catalogue A, and the right panel shows the same for all groups identified in Catalogue B. More groups are found at lower surface brightness; however, as shown in Paper I, brighter groups are more likely to be genuine and not contain any interlopers (see Section 3.3.2 for a more detailed investigation of this point)."459 , 460velocity anisotropy profiles (eqs.,velocity anisotropy profiles (eqs.461 6 aud 7)). along with an NEW profile for Af(r). which adds free parameters esi (the concentration parameter) aud AZ (the virial mass). and derive the parazneters of the three profiles by simultaneously fitting to the galaxy umber density and velocity data. using the Jeans equation.," \ref{beta model} and \ref{beta analytic expression}) ), along with an NFW profile for $M(r)$, which adds free parameters $c_{\rm vir}$ (the concentration parameter) and $M_{\rm vir}$ (the virial mass), and derive the parameters of the three profiles by simultaneously fitting to the galaxy number density and velocity data, using the Jeans equation."462" This method results in relatively weak coustraiuts. as is clear from the rather wide 1-70 contours shown iu figure 10 (black contours) the deduced mass and conceutration are Ma,=1.6!Dl«105 hot and eq>58 (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)."463" 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}."464 We thus expect this coustraiut to be weak., We thus expect this constraint to be weak.465 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:galaxy466number surface density}) ),"467the 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 velocity468dispersion}) )."469 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."470 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."471 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}472 shows that the best-fit NFW mass profile from the Jeans equation is in good agreement with the mass profiles from the other methods."473" 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."474 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)."475 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}476 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)."477" 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 $M_{\rm vir}=(1.3\pm 0.4) \times 47810^{15}$ $^{-1}$ $_{\odot}$ and $c_{\rm vir}>13.4$."479 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 A1689.480 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.481 The fits that we have used in eqs. (1)), The fits that we have used in eqs. \ref{Sigma_tot}) )482 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.483 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.484 For A689 this volt is visible in figure 1.., For A1689 this point is visible in figure \ref{galaxy surface number density}.485 Specifically. the cluster radial edge was estimated to be where ΣΠ>AChe/C and MoafC<AChe/Che ineluding uncertainties in Soal/C he. Vielding a limiting radius of 2.1! |Myc. where the 1-0 uucertaiuties account also for uzthe errors im the various fitting parameters in eq. (1)).," Specifically, the cluster radial edge was estimated to be where $\Sigma_{\rm gal}/C_{\rm bg}>\Delta C_{\rm bg}/C_{\rm bg}$ 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}) )."486 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."487 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)."488 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)."489 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.490" 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."491 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).492 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 virial493Finally. 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}) )."494 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)."495 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, $\propto \sqrt{\dot{E}_{SD}}$."496 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}."497 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.498 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.499 More detailed calculations of the emitted οποιον spectra are needed., More detailed calculations of the emitted energy spectra are needed.500 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."501 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.502 This implies that in this regime acceleration is vighly non-stationary., This implies that in this regime acceleration is highly non-stationary.503 The addition of curvature radiation can. however. establish a steady state.," The addition of curvature radiation can, however, establish a steady state."504 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."505 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.506 Most important is the intrinsically non-isotropic distribution ol soft photons., Most important is the intrinsically non-isotropic distribution of soft photons.507 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."508 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."509 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}."510 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.511 The main argument for this is that, The main argument for this is that512activity 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)."513 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.514 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)."515 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.516 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.517 2003)., 2003).518" Clearly. better theoretical calculations of 7, ure desirable for AZ«0.5M..."," Clearly, better theoretical calculations of $\tau_c$ are desirable for $M<0.5\,M_{\odot}$."519 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.520 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."521 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 $\log N_R \simeq -2.5$.522 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)."523 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."524 There are sufficient M-dwarfs in Fig., There are sufficient M-dwarfs in Fig.525 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."526 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."527 Steppien et al. (, Stȩppień et al. (5282001). 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.529 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."530 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 $\gamma$.531" 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.532" 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)."533 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.534" 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 $\rho_c =5356900$ $^{-3}$ (Siess et al."536 2000)., 2000).537 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."538 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."539 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."540 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."541 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.542 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."543 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).544 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)."545 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."546 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."547 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 $\alpha_c$.548" 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 $M_{\ast}^{1/3} R_{\ast}^{-1}$.549Hence 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 $\alpha_c$.550" 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 $P_{ss}551\propto M^{-1/2} R^{3/2}$, 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."552 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 2.553 To test these ideas Fig., To test these ideas Fig.554" 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."555 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. (5562000) models as described in sections 3 and +.,2000) models as described in sections 3 and 4.557 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."558" 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."559 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.560" 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}."561" 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},"562" 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 $\alpha_c \sim 10$ ."563 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.564 There are only two very low-mass M-dwarfs in our sample, There are only two very low-mass M-dwarfs in our sample565compensation 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."566 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 $\theta$.567 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}) )."568 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."569 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."570 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 $\theta\approx\pm75^{\circ}$."571 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},"572 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},"573 give an overall qualitative agreement with the data (see Fig. 5))., give an overall qualitative agreement with the data (see Fig. \ref{lc_model}) ).574 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.575" 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 $\theta\approx\pm70^{\circ}$ ).576 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."577 4 and 5))., \ref{cool} and \ref{lc_model}) ).578 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}) )."579 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 $r>2\times10^{13}\,\mbox{\rm cm}$."580 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.581 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.582 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.583 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."584 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."585 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."586 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)."587 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.588 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)."589 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."590 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."591 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}) ).592 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.593 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."594 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."595 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."596 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.597"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}."598" 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}."599" 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."600 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.601" 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."602 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.603" 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}."604" 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"")."605 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)."606 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).607" 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."608" 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."609 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.610 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}.611" 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}."612"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$^{\circ}$."613" 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"614high S/Nratio-.. we introduced the same “smearing” in the simulated BFs.,"high S/N, we introduced the same “smearing” in the simulated BFs."615 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."616 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."617 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."618 The primary star has a slightly higher luminosity than the secondary., The primary star has a slightly higher luminosity than the secondary.619 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."620 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."621 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."622 During the eclipses the absolute amount of light changes., During the eclipses the absolute amount of light changes.623 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."624 This has to be incorporated in the calculations of the BFs., This has to be incorporated in the calculations of the BFs.625 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.626 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}.627 The measured BFs and the best fits can be seen in Fig., The measured BFs and the best fits can be seen in Fig.628 8. for the primary eclipse and in Fig., \ref{fig:bf_primary} for the primary eclipse and in Fig.629 9. for the secondary eclipse., \ref{fig:bf_secondary} for the secondary eclipse.630 The uncertainties were calculated using the bootstrap method deseribed in Pressetal.(1992)., The uncertainties were calculated using the bootstrap method described in \cite{Press1992}.631. 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.632 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."633" 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."634 This. i5 also the value stated in Table 2.., This is also the value stated in Table \ref{tab:fit}. .635" 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).636 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 $a \sin i$ ).637 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}) )."638" 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 $M_{s}$ = $\pm$ $M_{\odot}$.639" 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}640 $M_{p}$ = $\pm$ $M_{\odot}$ and $M_{s}$ = $\pm$ $M_{\odot}$, and the values given by \cite{Gimenez1985} $M_{p}$ = $\pm$ $M_{\odot}$ and $M_{s}$ = $\pm$ $M_{\odot}$."641 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.642 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."643 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."644 Looking at Figs., Looking at Figs.645 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."646 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.647 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}) ).648 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.649 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.650" 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 $\beta_{p}$ = $-0.6\pm6511.4^{\circ}$ and $\beta_{s}$ = $-0.3\pm 1.2^{\circ}$ ), we kept $u$ fixed to 0.6 in the final fits."652 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."653 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."654 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."655 The value for the orbital inclination of CCye in the literature is, The value for the orbital inclination of Cyg in the literature is656Tn this paper. we add a collisional chuhamcement due to the atimosphere.,"In this paper, we add a collisional enhancement due to the atmosphere."657" 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}."658. 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."659 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}."660" 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 $\Sigma_{\rm661s}$ for $q = 3/2$."662" 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 $Q_{\rm 0s}=7.0 \times 10^7$ ${\rm erg}\,663{\rm g}^{-1}$, ${\beta_{\rm s}}=-0.45$, $Q_{\rm 0g}=2.1$ ${\rm664cm}^3\,{\rm g}^{-2}$ , ${\beta_{\rm g}} = 1.19$, and $C_{\rm gg} = 9$ \citep{benz99,stewart09}."665".. 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 $\Sigma_{\rm gas} = \Sigma_{\rm666gas,0}\exp(-t/T_{\rm gas,dep})$ , where $T_{\rm gas,dep}$ is the gas depletion timescale, which we set to $T_{\rm gas,dep} = 10^7$ years."667" 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 $t \leq T_{\rm668gas,dep}$."669 Fig., Fig.670 6 shows the at G.LAAU for f=0.01., \ref{fig:comp_growth} shows the at AU for $f=0.01$ .671 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."672 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."673" Nevertheless. emibrvos finally attain asviuptotic Lassen,"," Nevertheless, embryos finally attain asymptotic masses."674 Results for these simulations are ΕΠ in Fie. 3..," Results for these simulations are summarised in Fig. \ref{fig:final_mass_r10},"675" 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.676" 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 $\Sigma_0 =6777.1\,{\rm g\,cm}^{-2}$ ), AU $\Sigma_0 = 21\,{\rm g\,cm}^{-2}$ ), and AU $\Sigma_0 = 71\,{\rm g\,cm}^{-2}$ )."678" However. enibrvos exceed AL, inside AAT for Xy=—.Tlgon2 "," However, embryos exceed $M_{\rm a}$ inside AU for $\Sigma_0 = 71\,{\rm g\,cm}^{-2}$ ."679 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"680"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 $j$."681 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.682 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.683 As explained in Sec., As explained in Sec.684 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."685 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."686 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."687 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.688 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."689 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 $G=1$."690 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 $(GM/R^3)^{-1/2}$."691" 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.692 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.693 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.694 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.695" ""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."696 For a discussion on, For a discussion on697with 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."698 There are more recent observations concerning the putative circumbinary disk., There are more recent observations concerning the putative circumbinary disk.699 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."700 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."701 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)."702 | 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.703 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."704 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)."705 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 +287.706 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)."707 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."708 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."709 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."710 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).711 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 $\alpha$.712 The red side tends to be stronger overall., The red side tends to be stronger overall.713 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)."714 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."715 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."716 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."717 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.718 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.719 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)."720 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.721 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 $^{-1}$."722 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."723" The He I| spectra are noisier than Ha and uncertainties correspondingly larger,", The He I spectra are noisier than $\alpha$ and uncertainties correspondingly larger.724 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.725 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."726 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."727 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)."728 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."729. 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)."730 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.731 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.732 Here | am concerned only with the signal from the narrow components., Here I am concerned only with the signal from the narrow components.733 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."734 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"735us confidence in the reality of the compact objects in the nebula.,us confidence in the reality of the compact objects in the nebula.736" 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."737 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}.738" 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."739" 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}."740" 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."741 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.742 From these observations we confirm the presence of an optical, From these observations we confirm the presence of an optical743Space-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.744 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 $\lambda_{\hat{i}}$.745 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 $L=Q+l^{2}$.746 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.747 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.748 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: with749The 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.750 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."751 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}."752. 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}."753. 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."754 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}."755. 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}."756. 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.757" 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 $R_p$ "758stars.,stars.759" 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."760" 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."761" 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}."762" 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."763 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}.764" 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}) )."765 For an explanation of this we have again used models., For an explanation of this we have again used models.766 From the right panels of Fig., From the right panels of Fig.767 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.768" 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."769 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}) ).770 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.771 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.772 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).773 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 0.05.774 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).775 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 0.03.776 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}) ).777 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.778" 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."779 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.780 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 0.05.781 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}) )782 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}.783 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.784" Therefore, we used a metallicity for NGC 6811 of —0.35 dex."," Therefore, we used a metallicity for NGC 6811 of $-$ 0.35 dex."785 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}.786" 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."787" 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} "788with respect to the first order terms.,with respect to the first order terms.789 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."790 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.791" 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 $\aleph_1 \propto 792\exp (\Im \omega t)$, and the real part to a rotation with constant angular velocity $\Omega_{\mathrm{p}}=\Re \omega/m$."793 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."794" 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 $|k_r| r \gg 1$."795 Paralleling the analysis leading (o equation (84) in Griv et al. (, Paralleling the analysis leading to equation (34) in Griv et al. (796"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, $\omega_*=797\omega-m\Omega$ is the Doppler-shifted (in a rotating reference frame) wavefrequency, $\Omega (r)$ is the angular velocity of differential rotation at the distance $r$ "798magnetic 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."799 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.800 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.801 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).802 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."803 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 23.804 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."805 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."806 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).807 SOIIO is a project of international cooperation between ESA and NASA., SOHO is a project of international cooperation between ESA and NASA.808 SD acknowledges support [rom NSF grant ATM 0348827 and NASA erant NNXIO0AEGOC., SB acknowledges support from NSF grant ATM 0348837 and NASA grant NXX10AE60G.809aapparent column density profiles are shown in Fig 3..,apparent column density profiles are shown in Fig \ref{fig: OVI-AOD}.810" 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."811" 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}."812n-detection]ine in both strong components of the metal-poor cloud., We fit the line in both strong components of the metal-poor cloud.813" ""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."814"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."815". 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."816 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.817" 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"818and 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.819 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."820 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."821 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 $15\,000\,{\rm K}$ )."822 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)."823 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."824 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 HE1356/49-1.825 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."826the 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 $\NH=\expnt{5}{21}\,\percmsq$ )."827 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 $\NH=\expnt{2}{22}\,\percmsq$ )."828 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 $\expnt{3}{32}d_{5.2}^2\,\ergsec$."829" ""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.830 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."831 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."832 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."833 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."834009). 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 )."835 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 $\sim t^{-1/12}$."836.. 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."837 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."838 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; )."839 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.840. 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."841 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."842 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; )."843 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 $\sim 10^{32}\,\ergsec$ ."844They 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."845. 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; )."846 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."847 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."848 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."849 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."850 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."851.. Pherefore ∪⊔↓⋅∐⊔↓⊲↓↿⊳∖≼∼⋜⋯⊔∪↿↓⋅∢⊾⋜↧∐∙∖⇁≼∼∢≱↓↕≻⇂↓⋅⋜↧↕↓↥↿↓↕⋖⋅⋖⋅⇀∖↓≻∢⋅≼∙⊓⋅∠⇂⇂∢⋅∖⇁⋖⋅⇂∪⇂∎ ⊔∪⊔−⇂↓↕∢⊾↓⋅⊔↓⋜↧↓∢⊾↓↥↓↕≻≻↕∢≱↓, Therefore our limits cannot really constrain the expected level of non-thermal emission from these sources.852↕∐⋅∪⊔↓↿↓↕∢⊾⊳∖⋖⋅⊳∖∪⊔↓⋅⊓⋅⋡∖⋡∖∖⊽∢⋅⊔∪↿∢⋅⋡∣⇂↥∪⊔⋏∙≟∐⋡ 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."853. 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."854therein).. 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."855 We would, We would856populations 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)."857 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}.858axyCount 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."859 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."860" 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."861" 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.862 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.863 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.864 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. ("865Quoted errors are variance. as estimated by GalaxyCount.),"Quoted errors are variance, as estimated by .)"866 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)."867 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."868 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}."869 ? 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."870 This 15 largely consistent with the star counts profiles we derive., This is largely consistent with the star counts profiles we derive.871 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."872 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 300.873 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}."874 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."875 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.876 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."877 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.878 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}879 that this approach allows one to reach surface brightnesses $3-4$ mag $^{-2}$ below the limit of surface photometry."880" 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."881 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."882" 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 $F''=1/0.146^2=47$ .883them to previous findines.,them to previous findings.884" Throughout this Letter we asstume IL,250 lain IN and qo=0.5.", Throughout this Letter we assume $_{o}$ =50 km $^{-1}$ $^{-1}$ and $_{o}$ =0.5.885 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.886 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 1999.887 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. (8882000).,2000).889 The MECS (Boclla et al., The MECS (Boella et al.890 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.891 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)."892 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.893 Data preparation and luearization was performed using theSANDAS package under euvironnment., Data preparation and linearization was performed using the package under environment.894 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.895 10.00., 10.00.896 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."897 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.898 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."899 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."900 We remark that we fit spectra individually., We remark that we fit spectra individually.901 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.902 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."903 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.904" 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 $^{\prime}$ $^{\prime}$."905We have also accumulated: a global spectrum from a circle with radius 16’., We have also accumulated a global spectrum from a circle with radius $^{\prime}$.906 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.907 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."908" 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."909 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)."910 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.911 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 $\times 10^{20}$ $^{-2}$."912 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."913 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.914 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).915 As in Molondi et al. (, As in Molendi et al. (916"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."917 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."918 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 $N_{H}$."919 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.920 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.921 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."922" 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.923 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."924 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 $^{\prime}$ $^{\prime}$."925 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.926 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.927 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.928 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.929 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 4.930 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 $^{\prime}$.931 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."932 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.933" 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."934 Iuterestiuglv. a fit to the temperatures of," Interestingly, a fit to the temperatures of"935"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 $\nu$."936 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.:"937 Iu the initial stage /.«/;. the Lorentz factor is constant 5~g.," In the initial stage $t<t_{i}$, the Lorentz factor is constant $\gamma \sim \gamma_{0}$."938 In the interval /;<1<ly. we have 5~54 for thin shells. while >&540//y).U! for thick shells.," In the interval $t_{i}<t<t_{\times}$, we have $\gamma \sim \gamma_{0}$ for thin shells, while $\gamma \sim \gamma_{0} (t/t_{N})^{-1/4}$ for thick shells."939 These evolutions are the same as that of the forward shock., These evolutions are the same as that of the forward shock.940" After the shell crossing /,</. the evolution is approximately given by where 5,=min(sy.p) is the Lorentz [actor al the shell crossing aud ήτο VST,IO yv,is given by 5(7) trom equation CÀT)) (Zhang.IXobavashi. 2000)."," After the shell crossing $t_{\times}<t$, the evolution is approximately given by, where $\gamma_{\times}=\min(\gamma_{0},\gamma_{T})$ is the Lorentz factor at the shell crossing and 100 ,is given by $\gamma(T)$ from equation \ref{eq:gself}) ) \citep{zhang03b,kobayashi00}."941. A reliable calculation alter 4 drops below @! at ly</ requires [ull numerical simulations and is bevond the seope of this paper., A reliable calculation after $\gamma$ drops below $\theta^{-1}$ at $t_{\theta}<t$ requires full numerical simulations and is beyond the scope of this paper.942 Here we use equation. (A25)) till the velocitybecomes non-relativislic 55x5. and use the time dependence of the Sedov solution in equation (À12)) alter that.," Here we use equation \ref{eq:grev}) ) till the velocitybecomes non-relativistic $\gamma \sim \gamma_{NR}$, and use the time dependence of the Sedov solution in equation \ref{eq:sedov}) ) after that."943 Since the evolution in equation (A25)) is the same as that of the sideways expansion in equation (ALO)). this treatment might not be completely wrong.," Since the evolution in equation \ref{eq:grev}) ) is the same as that of the sideways expansion in equation \ref{eq:gth}) ), this treatment might not be completely wrong."944 For simplicity we use the shockradius in equation (A13)) lor all cases.Radiation:, For simplicity we use the shockradius in equation \ref{eq:R}) ) for all cases.:945" At the shell erossing /e /,. the forward and reverse shocks have the same Lorentz [actorαν. energy clensity e. and total energy eV."," At the shell crossing $t \sim t_{\times}$ , the forward and reverse shocks have the same Lorentz factor$\gamma_{\times}$ energy density $e$ , and total energy $e V$ ."946 But these shocks have the different, But these shocks have the different947" (Spite&Spite1982:Ryanetal.2000:Moléndezetal.2007) *Li/Il21.2 «1019. “Li 21 (Spereeletal.2003.2007)— Cocetal.(2001). *Li/TI-CL15 119, “Li 'Liproblem. Pianetal.(2006)."," \citep{spi1982,rya2000,mel2004,asp2006,bon2007,shi2007} $^7$ $=1-2$ $\times 10^{-10}$ $^7$ $2-4$ \citep{spe2003,spe2007} \citet{coc2004} $^7$ $(4.15^{+0.49}_{-0.45})\times 10^{-10}$ $\eta=(6.14\pm 0.25)\times 10^{-10}$ $^7$ $^7$ \citet{pia2006}."948. 2.5x of deuterimm abundance., $2.5\leq$ of deuterium abundance.949 Recent spectroscopic observations of AIPTSs also provide abundances of SLi isotope., Recent spectroscopic observations of MPHSs also provide abundances of $^6$ Li isotope.950" They indicate a likely primordial plateau abundance. simular to the well known “Li plateau. of *Li/II2G <102, which is about 1000 times as large as the BBN prediction."," They indicate a likely primordial plateau abundance, similar to the well known $^7$ Li plateau, of $^6$ $6\times10^{-12}$, which is about 1000 times as large as the BBN prediction."951 Since the standard Galactic cosmic ταν (CR) nucleosvuthesis models predict neelieible amounts of SLI abuudauce with respect tothe observed. plateau level at [Fe/II] <2 (e.g.Praut-zos 2006).. this plateau causes another problem. which iudicates some production process of ?Li.," Since the standard Galactic cosmic ray (CR) nucleosynthesis models predict negligible amounts of $^6$ Li abundance with respect tothe observed plateau level at [Fe/H] $<-2$ \citep[e.g.][]{pra2006}, this plateau causes another problem, which indicates some production process of $^6$ Li."952 Several candidates for carly τα xodnuetiou mechanisius have been suggested., Several candidates for early $^6$ Li production mechanisms have been suggested.953 The non-thermal unclear reactions trigecred by the decay of lone-lived particles is one possibility of the non-standard process (Jedamizik2000.200lad.2006:Kawasakietal.2005:I&usakabeetal.2006:Ciuberbatel 2007)..," The non-thermal nuclear reactions triggered by the decay of long-lived particles is one possibility of the non-standard process \citep{jed2000,jed2004a,jed2004b,jed2006,kawasaki2005,kus2006,cum2007}. ."954" Pospelov(2006) suggested the exotic nuclear reaction of Hey (dX Li to make abundant Τά, where Nis a negatively charged massive particle assuued to decay in the carly universe. and !Hex is the state that has ‘Tle bound to No. Su"," \citet{pos2006} suggested the exotic nuclear reaction of $^4$ $_X$ $d$ $X^-$ $^6$ Li to make abundant $^6$ Li, where $X^-$ is a negatively charged massive particle assumed to decay in the early universe, and $^4$ $_X$ is the state that has $^4$ He bound to $X^-$."955zuki&Iuoue(2002) suggested an a|à fusion reaction with à particles accelerated by lucrarchical structure formation shocks. thought to have been operative at the Galaxy formation epoch.," \citet{suz2002} suggested an $\alpha+\alpha$ fusion reaction with $\alpha$ particles accelerated by hierarchical structure formation shocks, thought to have been operative at the Galaxy formation epoch."956" As a possibility. Rollindectal.(2005) have calculated the ΟΤΑ production by an initial burst of cosmological cosmic ravs (CCRs) to show that this process through o| fusion can for the ""Li plateau without overproduction of ‘Li. οσο"," As a possibility, \citet*{rol2005} have calculated the $^6$ Li production by an initial burst of cosmological cosmic rays (CCRs) to show that this process through $\alpha+\alpha$ fusion can account for the $^6$ Li plateau without overproduction of $^7$ Li."957ι!Rollindeetal.(2006). applied the CCR uncleosvuthesis to a well erounded detailed model., \citet{rol2006} applied the CCR nucleosynthesis to a well grounded detailed model.958 They derived the total CCR energv as a function of redshift from astar formation rates(SFRs)iumodelsof cosmic chemical evolution of Daigneetal. (2006).. which are made to reproduce the observed cosmic SER. SNIL vate. the present fraction of baryous imstructures.thatin stars. the evolution of the metal coutent iu the iuterstellar aedimm (ISM) and ICAL. and carly," They derived the total CCR energy as a function of redshift from astar formation rates(SFRs)inmodelsof cosmic chemical evolution of \citet{dai2006}, , which are made to reproduce the observed cosmic SFR, SNII rate, the present fraction of baryons instructures,thatin stars, the evolution of the metal content in the interstellar medium (ISM) and IGM, and early"959A magnetically confined mountain forms at the magnetic poles of an accreting neutron star during the process of magnetic burial.,A magnetically confined mountain forms at the magnetic poles of an accreting neutron star during the process of magnetic burial.960" The mountain. which is generallv offset [rom the spin axis. generates eravitational waves al /, and 2/,."," The mountain, which is generally offset from the spin axis, generates gravitational waves at $f_*$ and $2 f_*$."961" Sidebands in the eravitational-wave spectrum appear around f, and ο, due to global MILD oscillations of the mountain which may be excited by stochastic variations in accretion rate (e.g. disk instability) or magnetic footpoint motions (e.g. starquake).", Sidebands in the gravitational-wave spectrum appear around $f_*$ and $2f_*$ due to global MHD oscillations of the mountain which may be excited by stochastic variations in accretion rate (e.g. disk instability) or magnetic footpoint motions (e.g. starquake).962" The spectral peaks al f. and 2/, are broadened. with full-widths hall-imaximum Afzs0.2 kIIz."," The spectral peaks at $f_*$ and $2f_*$ are broadened, with full-widths half-maximum $\Delta f \approx 0.2$ kHz."963 We find that the SNR increases as a result of these oscillations by up to 15 per cent due to additional signal from around (he peaks., We find that the SNR increases as a result of these oscillations by up to 15 per cent due to additional signal from around the peaks.964 Our results suggest that sources such as SAN J1308.1—3658 may be detectable by next generation long-baseline interferometers like LIGO II., Our results suggest that sources such as SAX $-$ 3658 may be detectable by next generation long-baseline interferometers like LIGO II.965" Note that. lor à neutron star accreting matter at the rate M,zzLOMALvr! (like SAN JISO0S.4—3658). it takes only 10* vr to reach S/Niτ>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."966 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}.967. 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 $\alpha \neq 0$ ).968 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}."969". 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}. ."970 Equations (4)) and (5)) clisplay this clearly., Equations \ref{eq:hplus}) ) and \ref{eq:hcross}) ) display this clearly.971 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."972 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."973 Moreover. 0(whichreplaces a) in," Moreover, $\theta$(whichreplaces $\alpha$ ) in"974thas providing a tieliter uppor lanit than above.,thus providing a tighter upper limit than above.975 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 $F_\lambda(\mathrm{N})<6.0\xten{-13}\ERG\CM\2\S\1\MIC\1$ )."976 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."977 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."978 244)., \ref{fig:line}d d).979 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.980 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.981 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."982 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},"983 Done et al. 1996))., Done et al. \cite{done96}) ).984 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}) )"985 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}) ):986 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 $\tau\sim 3-5\xten{4}\S$ ."987 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.988 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.989 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};"990 Persic et al. 1998)):, Persic et al. \cite{persic}) );991 whereas the ciission of NGC1915 peaks between 30 andLOOkeV.., whereas the emission of NGC4945 peaks between 30 and.992 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."993 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.994 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.995 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."996" 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.997" 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."998" 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}) )."999 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)."1000 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}) ),"1001 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.1002 Coenze et al (1998)), Genzel et al. \cite{genzel98}) )1003 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."1004 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."1005 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.1006" It is important to recall that Lepy/Lpr- represents the ratio between star formation rates averaged over two differentDr timescales.. ic.. 24qnNLO’ vrs aud <anyLO‘ vrs. respectively,"," It is important to recall that $\LFIR/L_{\BG}$ represents the ratio between star formation rates averaged over two different timescales, i.e. $>10^8$ yrs and $<10^7$ yrs, respectively."1007 Therefore. this ratio strongly depends on the past star formation history.," Therefore, this ratio strongly depends on the past star formation history."1008 For example. objects," For example, objects"1009The 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.1010 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."1011 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."1012 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}) ).1013 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."1014 The values we have found are listed in cols., The values we have found are listed in cols.1015 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.1016 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).1017" 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.1018 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.1019 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."1020 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.1021 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."1022 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 $\beta$.1023 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.1024 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.1025 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.1026 [Ii practice sometimes a correction must be made for unmeasured lines., In practice sometimes a correction must be made for unmeasured lines.1027 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.1028 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.1029 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.1030 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.1031 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.1032 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.1033 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.1034 Preite-Martinez Pottasch calculated three cases., Preite-Martinez Pottasch \cite{pmp} calculated three cases.1035 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.1036 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.1037 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.1038 They find that all three assumptions give similar results., They find that all three assumptions give similar results.1039 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 4.1040 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."1041 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."1042 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.1043 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.1044 The results can be found in Mendez et al. (1988)..," The results can be found in Mendez et al. \cite{mendez},"1045 Kudritzki et al., Kudritzki et al.1046 (1997) and Pauldrach et al. (2004).., \cite{kudritzki} and Pauldrach et al. \cite{pauldrach}.1047 As Pauldrach et al., As Pauldrach et al.1048 (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."1049 Mendez et al., Mendez et al.1050 (1988) Kudritzki et al., \cite{mendez} Kudritzki et al.1051 (1997) base their temperatures on the analysis of hydrogen and helium line profiles while Pauldrach et al.," \cite{kudritzki}1052 base their temperatures on the analysis of hydrogen and helium line profiles while Pauldrach et al."1053 (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.1054 The results are quite similar., The results are quite similar.1055 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."1056 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."1057 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."1058" 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 $_{EB}$.1059" 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)."1060 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.1061 [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.1062 This will presently be discussed in more detail., This will presently be discussed in more detail.1063can be taken care of by recentering the particles.,can be taken care of by recentering the particles.1064 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."1065 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."1066 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."1067 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.1068 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 ${\bf L}$.1069 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.1070 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.1071" 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 $\left|2T/W\right|_0=1/2$.1072 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 $1/2$."1073" 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 $\left|2T/W\right|_0=1.0$."1074 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."1075 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}) )1076 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 $t=120$.1077 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."1078 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 $\rho \sim r^{-2.5}$.1079 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.)1080 We have seen from the previous tests that the code. is, We have seen from the previous tests that the code is1081shown in Fig.8.,shown in Fig.8.1082 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.1083 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."1084 The arrow in Fig.8 shows the duration of the FRED GLE., The arrow in Fig.8 shows the duration of the FRED GLE.1085 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.1086 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.1087 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."1088 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."1089 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).1090 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.1091 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."1092 Every 10 seconds the counting rate and the atmospheric pressure are registered., Every 10 seconds the counting rate and the atmospheric pressure are registered.1093 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."1094 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.1095 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.1096 The arrow in (he upper figure indicates the beeinning of the GLE., The arrow in the upper figure indicates the beginning of the GLE.1097 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.1098 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 $1/f$."1099 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."1100 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."1101 A similar situation has been found for the second GLE., A similar situation has been found for the second GLE.1102 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"1103Let 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."1104" 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."1105 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."1106 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}.1107". 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."1108 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."1109 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.1110 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."1111 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."1112 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.1113 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."1114 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."1115 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.1116 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."1117 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.1118 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 is1119Comparison with previous data.,Comparison with previous data.1120 Upper panels: velocity dispersion. lower panels: rotation curve.," Upper panels: velocity dispersion, lower panels: rotation curve."1121 Different sources are marked with different symbols as explained in the captions., Different sources are marked with different symbols as explained in the captions.1122 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."1123 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.1124 1989 and Stiavelli et al., 1989 and Stiavelli et al.1125 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 $^{\circ}$ 1126"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."1127 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."1128 Tf vou use it. be sure to define it. (," If you use it, be sure to define it. ("1129NJE) (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. ("1130LII) 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."1131 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. ("1132CL) (DW) (BAT) Description: Hilleubraud et al. (,CL) (DW) (BM) Description: Hillenbrand et al. (1133"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."1134 Conuueuts Note that these clefinitions are all quite different from one another., Comments: Note that these definitions are all quite different from one another.1135 If vou use this terii. be sure to define it. (," If you use this term, be sure to define it. ("1136BAD,BM)1137thermal emission aud scattering efficiencies. respectively.,"thermal emission and scattering efficiencies, respectively."1138 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 $^{38}$ $\,$ $^{-1}$."1139P(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 $\theta_{sca}$."1140 g=1l ameans full forward scattering., $g=1$ means full forward scattering.1141 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."1142" 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."1143 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 $^2$, $^3$, $^4$."1144. 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."1145 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."1146" 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)."1147 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."1148 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."1149 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)."1150 The tail of the bow-shock is uuch better described by scattering., The tail of the bow-shock is much better described by scattering.1151 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 $_{*}$ $^2$."1152 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, $R_{0}$."1153" 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."1154 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."1155 These differences cau be better observed iu case of N23., These differences can be better observed in case of X3.1156 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 $R_0$."1157 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."1158 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."1159 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.1160 By changing its value by larger amount. the fit becomes inadequate.," By changing its value by larger amount, the fit becomes inadequate."1161 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."1162 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}) )."1163 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 $^\circ$."1164 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}) ).1165 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}.1166 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}.1167 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.1168 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."1169 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.1170 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 $\theta_0$."1171 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."1172 [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.1173The 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.1174 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 $R_0$."1175 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 $\,$ $\,$ $^\circ$."1176Tn 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."1177 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}.1178 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.1179 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."1180 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."1181" 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}. ."1182The 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).1183 ? 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 $r$ 1184shock aud 2.17<3” for the outer (western) shock.,shock and $''\times3''$ for the outer (western) shock.1185" 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 $''\times13.2''$."1186 These corrections were « in all cases., These corrections were $<$ in all cases.1187 The results aro eiven in Table 2.., The results are given in Table \ref{tab:fluxden}.1188" The resulting spectral indices are Gout = U.6640,03 and a;, 0.06,", The resulting spectral indices are $\alpha_{out}$ = $\pm$ 0.03 and $\alpha_{in}$ = $\pm$ 0.06.1189 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 k25.1190 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.1191 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.1192 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.1193 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}."1194 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."1195 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."1196 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.1197 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)."1198 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.1199 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.1200 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)."

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