ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 2 and 3))., \ref{low_dens_eff} and \ref{high_dens_eff}) ).3" The Monte Carlo simulations are used as a consistency check, and as these simulations are fairly slow, efficiencies are only calculated for a limited number of dust temperatures."," The Monte Carlo simulations are used as a consistency check, and as these simulations are fairly slow, efficiencies are only calculated for a limited number of dust temperatures."4" At dust temperatures Tau,<35—40 K, the Monte Carlo and rate equations method yield the same results, within the uncertainties."," At dust temperatures $T_{\rm dust} < 35-40$ K, the Monte Carlo and rate equations method yield the same results, within the uncertainties."5" At higher dust temperatures, the efficiencies obtained by the two methods start to deviate: the rate equation method systematically obtains larger efficiences than the MC method."," At higher dust temperatures, the efficiencies obtained by the two methods start to deviate: the rate equation method systematically obtains larger efficiences than the MC method."6 This is where the process of OH and H5O formation on dust enters the stochastic regime., This is where the process of OH and $_2$ O formation on dust enters the stochastic regime.7" We fitted analytical expression to the derived results from the rate equations, such that they are easy to implement in any chemistry code."," We fitted analytical expression to the derived results from the rate equations, such that they are easy to implement in any chemistry code."8" We find that: We implemented the analytical expressions for the formation rates in the XDR code, and calculated a model with parameters representative for the inner regions of active galaxies."," We find that: We implemented the analytical expressions for the formation rates in the XDR code, and calculated a model with parameters representative for the inner regions of active galaxies."9 We find that the additional processes enhances the integrated column density of warm water., We find that the additional processes enhances the integrated column density of warm water.10" This increased column helps to explain unusually strong water lines observed for Mrk 231, that has an accreting supermassive black hole with X-ray luminosity Lx~10“ erg/s. This ULIRG shows for example a very high H50 25-11; / CO J=8-7 ratio."," This increased column helps to explain unusually strong water lines observed for Mrk 231, that has an accreting supermassive black hole with X-ray luminosity $L_X \sim1110^{44}$ erg/s. This ULIRG shows for example a very high $_2$ O $2_{02}-1_{11}$ / CO $J=8-7$ ratio."12" These ratios are not observed in typical starforming environments that are mainly exposed to UV only (PDR) environments, such as the one observed in the Orion Bar or M822010),, where this ratio is typically an order of magnitude or more smaller than in Mrk 231, and as such these very bright H2O lines might be typical for regions that are exposed to high X- fluxes, close to the accreting black hole in active galaxies."," These ratios are not observed in typical starforming environments that are mainly exposed to UV only (PDR) environments, such as the one observed in the Orion Bar or M82, where this ratio is typically an order of magnitude or more smaller than in Mrk 231, and as such these very bright $_2$ O lines might be typical for regions that are exposed to high X-ray fluxes, close to the accreting black hole in active galaxies."13capable of star-formation while most other ligh-latitucle cloud are not.,capable of star-formation while most other high-latitude cloud are not.14To produce the probability map using the real data on AISPs we corrected the observed period derivatives for the proper motion effect ancl the relative acceleration in (he Galactic potential using equation (2)),To produce the probability map using the real data on MSPs we corrected the observed period derivatives for the proper motion effect and the relative acceleration in the Galactic potential using equation \ref{pdotprime}) ).15" To this end. we constructed a new dataset consisting of DualPTEpip!—qGd;/e= ay4,;/0. where ji ave the observed proper motions of the MSPs (consistent with zero for 20 out of 48 objects). d; are their distances [rom the sun and ρω ave the accelerations of the pulsars relative to the solar svstem in the Galactic potential projected onto the direction to the pulsars."," To this end, we constructed a new dataset consisting of $\dot{P}_{i,\,new}/P_i'\equiv\dot{P}_i'/P_i'-\mu_i^2 d_i/c-a_{gal, i}/c$ , where $\mu_i$ are the observed proper motions of the MSPs (consistent with zero for 20 out of 48 objects), $d_i$ are their distances from the sun and $a_{gal, i}$ are the accelerations of the pulsars relative to the solar system in the Galactic potential projected onto the direction to the pulsars."16 The (vpical values of the proper motion correction are The correction for the relative Galactic acceleration is perlormecl using the Galactic potential in the form suggested by Paczvuski(1990) (hereafter ‘P90 model) which consists of a disk. a spheroid (bulge) ancl a spherically symmetric halo: the model is normalized to have the rotation velocity of 220 kins | at 8 kpe.," The typical values of the proper motion correction are The correction for the relative Galactic acceleration is performed using the Galactic potential in the form suggested by \citet{pacz90} (hereafter `P90 model') which consists of a disk, a spheroid (bulge) and a spherically symmetric halo; the model is normalized to have the rotation velocity of 220 km $^{-1}$ at 8 kpc."17 This model of the Galactic potential was updated by Dehnen&Binnev(1993)., This model of the Galactic potential was updated by \citet{dehn98}.18. Numerically. (he P90 and the Dehnen models produce similar results (Sun&Lan2004).. but (the P90 potential is easier (o use since ib has an analvüc form.," Numerically, the P90 and the \citet{dehn98} models produce similar results \citep{sun04}, but the P90 potential is easier to use since it has an analytic form."19" The twpical values of this correction are a few times smaller than (he acceleration of the Sun toward the center of the Galaxy. αρο7πρωι/6X(d;/8kpe). where dy./c—6.5x1019I? !,"," The typical values of this correction are a few times smaller than the acceleration of the Sun toward the center of the Galaxy, $a_{gal}/c \sim a_{gal,\odot}/c \times (d_i/8\mbox{ kpc})$, where $a_{gal,\odot}/c=6.5\times 10^{-19}$ $^{-1}$."20 The probability map corrected for proper motions and for relative Galactic accelerations is shown in Figure 3.., The probability map corrected for proper motions and for relative Galactic accelerations is shown in Figure \ref{pic_real}.21 In contrast to the probability map for the simulated. accelerated. dataset. (Figure 2)). the probability map based on the real data (Figure 3)) does not show strong correlations in anv direction and has on average much higher probabilities IT of (he null hypothesis.," In contrast to the probability map for the simulated accelerated dataset (Figure \ref{pic_test_18}) ), the probability map based on the real data (Figure \ref{pic_real}) ) does not show strong correlations in any direction and has on average much higher probabilities $\Pi$ of the null hypothesis."22 The lowest value of IL in anv direction in Figure 3. is 0.213. which is consistent with the null hypothesis.," The lowest value of $\Pi$ in any direction in Figure \ref{pic_real} is 0.213, which is consistent with the null hypothesis."23 Therefore. there is no obvious evidence lor a non-zero acceleration of the solar svstem relative to the MSP population.," Therefore, there is no obvious evidence for a non-zero acceleration of the solar system relative to the MSP population."24" To establish the significance of this null result and to find the maximum acceleration allowed by the data on MSPs. we first created 1000 macde-up datasets bv using (he positions ol the real objects ancl randomly shuffling their /BiaPees/D"" values."," To establish the significance of this null result and to find the maximum acceleration allowed by the data on MSPs, we first created 1000 made-up datasets by using the positions of the real objects and randomly shuffling their $\dot{P}_{new}'/P'$ values."25 For each direction on the skv (0.9). these shullled datasets provide a distribution of rank correlation coellicients of uncorrelated datasets.," For each direction on the sky $\alpha,\delta$ ), these shuffled datasets provide a distribution of rank correlation coefficients of uncorrelated datasets."26" We then correct the dataset /7,,,,/17μα... for a putative acceleration a. directed. toward (0.9) ancl caleulate the rank correlation coefficient. for this corrected dataset."," We then correct the dataset $\dot{P}_{i,new}'/P_i'$ for a putative acceleration $a_{\odot}$ directed toward $\alpha,\delta$ ) and calculate the rank correlation coefficient for this corrected dataset."27 We keep increasing the value of a. until the data start showing (hie presence of a correlation in a statistical sense. i.e.. when (he rank correlation coellicient reaches ils top value as determined from the shuffled datasets (which are presumed uncorrelated with (he position on the skv).," We keep increasing the value of $a_{\odot}$ until the data start showing the presence of a correlation in a statistical sense, i.e., when the rank correlation coefficient reaches its top value as determined from the shuffled datasets (which are presumed uncorrelated with the position on the sky)."28 When such valueof e. is reached. we have overcorrected lor the acceleration. and (his value is ruled out by the data at the level.," When such valueof $a_{\odot}$ is reached, we have overcorrected for the acceleration, and this value is ruled out by the data at the level."29 We calculate these, We calculate these30ead to production of new ele pairs.,lead to production of new $^{+}$ $^{-}$ pairs.31 Jenet Ransom (2001) sugeested that the s-rav beam may coincide with he radio beam of and the energetic οταν photons would rigeer a pair cascade in B's magnetosphere aud lead to he radio fares., Jenet Ransom (2004) suggested that the $\gamma$ -ray beam may coincide with the radio beam of and the energetic $\gamma$ -ray photons would trigger a pair cascade in 's magnetosphere and lead to the radio flares.32 Putting aside the drawhack that the οταν and radio beams are usually misaligned iu kuown 5-rav nulsars (Thompson 2003). we demonstrate below that the physical parameters of this scenario are imiplausible.," Putting aside the drawback that the $\gamma$ -ray and radio beams are usually misaligned in known $\gamma$ -ray pulsars (Thompson 2003), we demonstrate below that the physical parameters of this scenario are implausible."33" To imaxinize its effect. we assume that Avs saw ininositv is close to its highest expected value. L.,4~1075eyes.1 beaming iuto a solid augle AQ.~1."," To maximize its effect, we assume that 's $\gamma$ -ray luminosity is close to its highest expected value, $L_{\gamma,A}34\sim 10^{33} ~{\rm erg~s^{-1}}$ beaming into a solid angle $\Delta35\Omega_\gamma \sim 1$."36" We also assune that the 2-rav spectrum resembles that of known s-rav pulsus. ie. the energv flux vf, is fat between 1 MeV and ~ 30 GeV (Thompson 2003)."," We also assume that the $\gamma$ -ray spectrum resembles that of known $\gamma$ -ray pulsars, i.e. the energy flux $\nu F_\nu$ is flat between 1 MeV and $\sim$ 30 GeV (Thompson 2003)."37 The rauge is bounded from above bv the highest photon cucrey capable of escaping from the polar cap cascade of (see Eq., The range is bounded from above by the highest photon energy capable of escaping from the polar cap cascade of (see Eq.38 29 iu Zhaug Ibudiug 2000)., 29 in Zhang Harding 2000).39 We may then express the injection spectrum asE?N(E)=10?log(3«101)—107ees I.," We may then express the injection spectrum as$E^2 \dot N(E) = 10^{33} / \log (3\times4010^4) \sim 10^{32} ~{\rm erg~s^{-1}}$ ."41" In order to produce a pair in B's magnetosphere, the energv of à 5-1av photon. E.. needs to satisfy CE./2inc?D,By)=xc1/12 (Ruderman Sutherland 1975). where B,=Dsu6,p aud 0 is the anele between the ταν momentum aud the magnetic field B."," In order to produce a pair in 's magnetosphere, the energy of a $\gamma$ -ray photon, $E_\gamma$, needs to satisfy $(E_\gamma / 2 m_e c^2) (B_\perp/B_q)42\geq \chi \sim 1/12$ (Ruderman Sutherland 1975), where $B_\perp43= B \sin \theta_{kB}$ and $\theta_{kB}$ is the angle between the $\gamma$ -ray momentum and the magnetic field ${\vec B}$."44 Again. to maximize the effect we adopt sinη~1.," Again, to maximize the effect we adopt $\sin \theta_{kB} \sim 1$."45" For a pure dipole field. B~B,(Rp)? (chere R is the stellar radius and rds the radius at which pairs are produced). the threshold 5-rav energyv is [τν~1.2MeV(r/Ry."," For a pure dipole field, $B \sim B_p (R/r)^3$ (where $R$ is the stellar radius and $r$ is the radius at which pairs are produced), the threshold $\gamma$ -ray energy is $E_{\gamma,th} \sim 1.2 ~{\rm46MeV} (r/R)^3$."47" Given Le ΓΕ radius for pair production is then ree/Rh=(3101/12)!~ 29, "," Given $E_{\gamma,max}$, the maximum radius for pair production is then $r_{max}/R = (3\times 10^4/1.2)^{1/3} \sim4829$ ."49The external pair cascade process is dominated by the svuchrotrou radiation of the higher generation pairs., The external pair cascade process is dominated by the synchrotron radiation of the higher generation pairs.50 Since the photon energv decreases by a factor 16 in each generation. each primary σαν with euerev FE. can ecucrate 2*5 pairs where ¢=losE-Εν41)flog(16)||1 (c.g. Zhang Marding 2000).," Since the photon energy decreases by a factor 16 in each generation, each primary $\gamma$ -ray with energy $E_\gamma$ can generate $2^{\zeta}$ pairs, where $\zeta = [\log(E_{\gamma} /51E_{\gamma,th}) / {\log (16)}]+1$ (e.g. Zhang Harding 2000)."52" The radius-depeudenut solid angle (includiug both poles) of the open field line region is AQ,nt)=lx?r/eP. and so the pair injection rate iuto B’s open field region due to -ravs from ds where the distance between the two pulsars is dap~9« Gn (Lyne et al."," The radius-dependent solid angle (including both poles) of the open field line region is $\Delta \Omega_{open} (r) = 4\pi^2 r/cP$, and so the pair injection rate into 's open field region due to $\gamma$ -rays from is where the distance between the two pulsars is $d_{AB} \sim 953\times 10^{10}$ cm (Lyne et al."54 2001)., 2004).55 This rate is negligible compared with the intrinsic pair injection rate of itself (Eq. 1))., This rate is negligible compared with the intrinsic pair injection rate of itself (Eq. \ref{NpairB}) ).56" The total pair injection rate iuto Bos magnetosphere (including the closed field line region) is 2&107?s! (calculated by replacing AO,u(r) by la in Eq. 2))."," The total pair injection rate into 's magnetosphere (including the closed field line region) is $2\times5710^{29} ~{\rm s^{-1}}$ (calculated by replacing $\Delta\Omega_{open}(r)$ by $4\pi$ in Eq. \ref{Npair1}) ),"58 but it is believed that pairs iu the closed field line region cau uot contribute to the observed colerent emission from sursl., but it is believed that pairs in the closed field line region can not contribute to the observed coherent emission from .59 A's wind is terminated by the magnetic stress within B's maguetosphere through a bow shock., 's wind is terminated by the magnetic stress within 's magnetosphere through a bow shock.60 The distance of the bow shock from is ευ=(SupeEj)6510?cm (Arons et al.," The distance of the bow shock from is $d_{sB}=({8 \mu_B^2 d_{AB}^2 c}/{\dot61E_A})^{1/6} \sim 5\times 10^9 ~{\rm cm}$ (Arons et al."62 2001). where Hp~3.75«s102? CON is the maguetic moment ofB.," 2004), where $\mu_B \sim 3.75 \times 10^{29}$ cgs is the magnetic moment of."63 The bow shock produces a ~-vay huuiuositv of ~1079eres bat ~20 MeV. (Cranot Mésszárros 2001)., The bow shock produces a $\gamma$ -ray luminosity of $\sim 10^{30}~{\rm erg~s^{-1}}$ at $\sim 20$ MeV (Granot Mésszárros 2004).64 The ratio between the +-rav flux fromaud this conipouent is —(107/1079)4Gp/dag)?3. and so this component does not iucrease significantly the pair abundance iuB's iiiguetosphere.," The ratio between the $\gamma$ -ray flux fromand this component is $\sim (10^{33}/10^{30})\times65(d_{sB}/d_{AB})^2 \sim 3$, and so this component does not increase significantly the pair abundance in's magnetosphere."66" The bow shock also produces ανν, Which may interact with the high energy -ravs from the polar cap to produce pairs (see c.g. Zhane 2001: Ibuxliug et al."," The bow shock also produces X-rays, which may interact with the high energy $\gamma$ -rays from the polar cap to produce pairs (see e.g. Zhang 2001; Harding et al."67 2002)., 2002).68" ITowever. for the estimated X-rav huniuositv 1077eres| (Granot Méssziiros 2001). the nuuber deusitv of X-ray plhotous in the open field line region is only ~10?cmP?(6,/0.1keV)5. leading to an optical depth τος~10 for a sav traveling through the eutire maenetosphere."," However, for the estimated X-ray luminosity $10^{29}~{\rm erg~s^{-1}}$ (Granot Mésszárros 2004), the number density of X-ray photons in the open field line region is only $\sim 10^9 ~{\rm cm^{-3}}~(\epsilon_x / 0.1~{\rm69keV})^{-1}$, leading to an optical depth $\tau_{\gamma\gamma} \sim7010^{-5}$ for a $\gamma$ -ray traveling through the entire magnetosphere."71 The X-rays coming directly from have an effect that is smaller by a factor ~1οπονap/d(gg)?0.03.," The X-rays coming directly from have an effect that is smaller by a factor $\sim (10^{30}/10^{29})\times72(d_{sB}/d_{AB})^2 \sim 0.03$."73 We therefore conclude that the radio flares from are uot due to 5-rav or X-ray precipitatious from either pulsar or from the bow shock around pulsarB., We therefore conclude that the radio flares from are not due to $\gamma$ -ray or X-ray precipitations from either pulsar or from the bow shock around pulsar.74 The huninous wind distorts B's magnetosphere iuto a shape analogous to the Earth maenetosphere as it is combed bv the solar wind., The luminous wind distorts 's magnetosphere into a shape analogous to the Earth magnetosphere as it is combed by the solar wind.75 According to the nuuerical simulation of Arous ct al. (, According to the numerical simulation of Arons et al. (762001). the vertical radius of the niaenetospherie sheath is 7~7.5<10° cm.,"2004), the vertical radius of the magnetospheric sheath is $l \sim 7.5 \times 10^9$ cm."77 Interpreting A's eclipse as svuchrotrou sclbobsorption in the shockedwind requires that the pair iuultiplicitv of be as high as Rac109 (Arons et al, Interpreting 's eclipse as synchrotron self-obsorption in the shockedwind requires that the pair multiplicity of be as high as $\kappa_{A} \sim 10^6$ (Arons et al.78 2001: Lyutikov 2001)., 2004; Lyutikov 2004).79 This multiplicity value is wich larger than in standard cascade theory. <100 (Tibschinan Arous 2001).," This multiplicity value is much larger than in standard cascade theory, $\la80100$ (Hibschman Arons 2001)."81 Horeafter. we normalize wy bv 109. althouel our principal couchisious remain valid at lower values.," Hereafter, we normalize $\kappa_A$ by $10^6$, although our principal conclusions remain valid at lower values."82" The total umber of the pairs deposited to the bow shock region from A's wiud is where AQ, (18 the unknown solid angle of As wind."," The total number of the pairs deposited to the bow shock region from 's wind is where $\Delta\Omega_{w,A}$ is the unknown solid angle of 's wind."83 It has been suggested that spin axis aligus in the direction almost perpendicular to the orbital plane due to the external torque exerted by A's wind (Demorest et al., It has been suggested that spin axis aligns in the direction almost perpendicular to the orbital plane due to the external torque exerted by 's wind (Demorest et al.84 2001: Avons et al., 2004; Arons et al.85 2001)., 2004).86 Since the line of sieht Qvlich sweeps across Bw radio beam) is offset bv 3° from the orbital plane (Lyne et al., Since the line of sight (which sweeps across 's radio beam) is offset by $3^{\circ}$ from the orbital plane (Lyne et al.87 20014: IKaspi et al., 2004; Kaspi et al.88 2001). B's maguetic axis must be oriented at a παπα] angele relative to the orbital plane.," 2004), 's magnetic axis must be oriented at a small angle relative to the orbital plane."89 It is therefore likely that A’s wind would directly stream into at least oue of the open field regions ofB., It is therefore likely that 's wind would directly stream into at least one of the open field regions of.90" The ""leakage"" may be realized hrough resistive effects (see Lyutisov 2001 and refercuces herein).", The “leakage” may be realized through resistive effects (see Lyutikov 2004 and references therein).91 The analogy to the solar wind interaction with he Earth's magnetosphere sugecsts that the pairs gaiu access near B's mmaeuetic pole., The analogy to the solar wind interaction with the Earth's magnetosphere suggests that the pairs gain access near 's magnetic pole.92 When this happens. some raction of the pairs in A's wind can directly slide iuto B's nagnetosphere.," When this happens, some fraction of the pairs in 's wind can directly slide into 's magnetosphere."93 At the same time the open field region in the “daw” side facing isereatlv broadened due to he rani pressure of the wind., At the same time the open field region in the “day” side facing isgreatly broadened due to the ram pressure of the wind.94" Iu principle. the streamyour A’s wind mav cucounter Bos pair stream (""wiud) alongits path."," In principle, the streamfrom 's wind may encounter 's pair stream (“wind”) alongits path."95" The distance frou where the pressures of the twostreams balance. dip. can be found by equating T(AQ,pd?)=Ey(CAOuship dun]. where Δθμxdap is the solid angle of B's wind. and B's"," The distance from where the pressures of the twostreams balance, $d_{bB}$ , can be found by equating $\eta_B \dot E_{B}/(c \Delta \Omega_{w,B} d_{bB}^2) = \dot E_{A} /96[c \Delta \Omega_{w,A} (d_{AB}-d_{dB})^2]$ , where $\Delta97\Omega_{w,B} \propto d_{bB}$ is the solid angle of 's wind, and 's"98To test (he feasibility of searching for planets around the WD remnants of massive stars. we have identified 51 hot. voung WDs in the mass range 0.7M.<Mp1.0... found in (he Palomar-Green (DG) survey.,"To test the feasibility of searching for planets around the WD remnants of massive stars, we have identified 51 hot, young WDs in the mass range $0.7\,M_\odot<M_{\rm WD}<1.0\,M_\odot$, found in the Palomar-Green (PG) survey."99 Liebertetal.(2005) present. a detailed spectroscopic analvsis of these WDs for which they obtained accurate mass and age estimates., \citet{liebert05} present a detailed spectroscopic analysis of these WDs for which they obtained accurate mass and age estimates.100 According to the models of Burrowsetal.(2003).. planet Iuminosityv is heavily suppressed al mi and jan. implying that warm planets will be most easily visible bySpilzer al jum. We therefore further restrict the PG sample to those WDs above 20Jy. at jum. This eliminates just 2 targets. leaving a sample of 49.," According to the models of \citet{burrows03}, planet luminosity is heavily suppressed at $\mu$ m and $\mu$ m, implying that warm planets will be most easily visible by at $\mu$ m. We therefore further restrict the PG sample to those WDs above $20\,\mu$ Jy at $\mu$ m. This eliminates just 2 targets, leaving a sample of 49."101 Figure 8. shows the age distribution of these WDs., Figure \ref{fig:ages} shows the age distribution of these WDs.102 Here “age” is defined as time since main-sequence (and so presumably planet) birth., Here “age” is defined as time since main-sequence (and so presumably planet) birth.103 Note that the sample is peaked at 300 Myr and that the great majority are vounger than 1 Gyr., Note that the sample is peaked at 300 Myr and that the great majority are younger than 1 Gyr.104 Youth is important because it is (he voung planets that provide (he greatest chance of detection., Youth is important because it is the young planets that provide the greatest chance of detection.105 Figure 9 shows planet/WD flux ratio al 4.5 jn as a function of planetmass (verlical axis) and [or various ages and WD temperatures. using Burrowsetal.(2003) models.," Figure \ref{fig:detectability} shows planet/WD flux ratio at 4.5 $\mu$ m as a function of planetmass (vertical axis) and for various ages and WD temperatures, using \citet{burrows03} models."106 A detection requires that the WD IR flux be accurately. predicted based on the temperature and angular radius derived [rom flix measurements al shorter wavelengths. so that the excess flux due to the planet can be inferred [rom theSpitzer measurement.," A detection requires that the WD IR flux be accurately predicted based on the temperature and angular radius derived from flux measurements at shorter wavelengths, so that the excess flux due to the planet can be inferred from the measurement."107 The fundamental limit of the technique is therelore set bv the error in the IRAC absolute flus-calibration (horizontal solid line. Reachetal. 2005)).," The fundamental limit of the technique is therefore set by the error in the IRAC absolute flux-calibration (horizontal solid line, \citealt{reach05}) )."108 Note that there is potentially good sensilivily to [ew-Jupiter mass planets [or the majoritv of the WD ages that are shown in Figure 8.., Note that there is potentially good sensitivity to few-Jupiter mass planets for the majority of the WD ages that are shown in Figure \ref{fig:ages}.109 Such planet masses are not uncommon among the red-giant. targets of RV survevs. which have somewhat lower-mass MS progenitors than these WDs (see refflig:mm)).," Such planet masses are not uncommon among the red-giant targets of RV surveys, which have somewhat lower-mass MS progenitors than these WDs (see \\ref{fig:mm}) )."110 Johnsonοἱal.(2007) [ind that the Jovian-planet [raction increases from for 0.1—0.7.M.. stars to For Sun-like stars. to8.956.. for 1.3—LOAM. stars fora<2.5 AU and m>0.8Mig.," \citet{johnson07} find that the Jovian-planet fraction increases from for $0.1-0.7M_\odot$ stars to for Sun-like stars, to, for $1.3-1.9M_\odot$ stars for $a<2.5\,$ AU and $m>0.8\,M_{\rm jup}$."111 OF course. the analogs of all of these planets around higher mass stars would be swallowed belore they evolved into WDs. and the frequency. of planets around massive stars al wider separations is completely unknown.," Of course, the analogs of all of these planets around higher mass stars would be swallowed before they evolved into WDs, and the frequency of planets around massive stars at wider separations is completely unknown."112" However. if there are comparable nunmbers al wider separations and if the observed trend continues or even flattens at. higher masses. (hen the PG sample would be expected (o contain several detectable planets: roughly 49x8.9%(log(13/2)/log(13/0.3)=2.9.Here we have assumed a detection threshold of in—Αρ and that planet masses are distributed as dN/dincin.| from the threshold to the brown-dwarl limit. 0.8—«m/Mj,< 19. The WDs are quite bright. V.S 16. so obtaining the accurate optical/near-IR. photometry"," However, if there are comparable numbers at wider separations and if the observed trend continues or even flattens at higher masses, then the PG sample would be expected to contain several detectable planets: roughly $49\times 8.9\%\times(\log(13/2)/\log(13/0.8) = 2.9$.Here we have assumed a detection threshold of $m=2\,M_{\rm jup}$ and that planet masses are distributed as $dN/dm\sim m^{-1}$ from the \citet{johnson07}113 threshold to the brown-dwarf limit, $0.8<m/M_{\rm Jup}<13$ The WDs are quite bright, $V\la 16$ , so obtaining the accurate optical/near-IR photometry"114where SM?(A.2) picks out non-linear scales and eyitz) determines the scale at which. the power spectrum approaches the Cit result as a function of redshift.,"where $\Sigma ^2(k,z)$ picks out non-linear scales and $c_{\rm nl}(z)$ determines the scale at which the power spectrum approaches the GR result as a function of redshift."115 In this paper. we use the fitting fomulae for XT(h.i) and ey(z) obtained by perturbation theory (Ixoviuma andconfirmed by N-body simulations (Ovaizuetal.2008:Schmidt 2009).. where fuh.2) is the modified: gravity linear power spectrum.," In this paper, we use the fitting fomulae for $\Sigma ^2(k,z)$ and $c_{\rm nl}(z)$ obtained by perturbation theory \citep{Koyama:2009me} andconfirmed by N-body simulations \citep{Oyaizu:2008tb,Schmidt:2009sg}, where $P_{\rm lin}(k,z)$ is the modified gravity linear power spectrum."116 The non-linear power spectrum for both the Pooncn and Lop is found using the Smithetal.(2003) fitting formula from the linear. power spectrum., The non-linear power spectrum for both the $P_{\rm non-GR}$ and $P_{\rm GR}$ is found using the \cite{Smith:2002dz} fitting formula from the linear power spectrum.117" For DCD. A= 03.0,=I and a»=0.16 and for fi) with fr,=10 we use ο=O.OS. a,=1/3 and a»=1.05 for O<zxT."," For DGP, $A=0.3$, $\alpha_1=1$ and $\alpha_2=0.16$ and for $f(R)$ with $f_{\rm R_0}=10^{-4}$ we use $A=0.08$, $\alpha_1=1/3$ and $\alpha_2=1.05$ for $0\leq z \leq 1$."118" Ht should be noted these values are not. valicl for all 4, ancl e.", It should be noted these values are not valid for all $\Omega_{\rm m}$ and $\sigma_8$.119" However. in DOP. these values depend on Oy, and e very weakly. so within our priors for €, and Ox we can assume the values are constant."," However, in DGP, these values depend on $\Omega_{\rm m}$ and $\sigma_8$ very weakly, so within our priors for $\Omega_{\rm m}$ and $\sigma_8$ we can assume the values are constant."120 We should also emphasise that these fits are confirmed only up to &= Ih/Mpe due to the lack of resolution in N-bodyw simulations. so we are extrapolating the [its ovond this regime.," We should also emphasise that these fits are confirmed only up to $k=1h$ /Mpc due to the lack of resolution in N-body simulations, so we are extrapolating the fits beyond this regime."121 Clearly it is necessary to check the validity of this extrapolation using N-body simulations with ueher resolution (see Schmidtetal.(2008). for a clferent approach using the halo model)., Clearly it is necessary to check the validity of this extrapolation using N-body simulations with higher resolution (see \cite{Schmidt:2008tn} for a different approach using the halo model).122 However. since the mocified eravity power spectrum should approach the Cit non-linear »ower spectrum with the same expansion history. and since he fitting formula (8)) ensures this. our extrapolation is justified.," However, since the modified gravity power spectrum should approach the GR non-linear power spectrum with the same expansion history, and since the fitting formula \ref{eq:husaw}) ) ensures this, our extrapolation is justified."123" In applying this formalism. we found that. although f(P) fits the N-bods results at small &. it failed to converge with . CDM at larger & if o,= 1/3."," In applying this formalism, we found that although $f(R)$ fits the N-body results at small $k$, it failed to converge with $\Lambda$ CDM at larger $k$ if $\alpha_1=1/3$ ."124" This is due to the strong scale dependence of the linear power spectrum. such that Pussycp deviates from Lop strongly on small scales and equation (8)) with a,=1/3 fails to converge with Lor."," This is due to the strong scale dependence of the linear power spectrum, such that $P_{\rm non-GR}$ deviates from $P_{\rm GR}$ strongly on small scales and equation \ref{eq:PPF}) ) with $\alpha_1= 1/3$ fails to converge with $P_{\rm GR}$."125" Thus. we also consider a,=1 and ay=2 cases for f(47) which have more physical behaviour at high &."," Thus, we also consider $\alpha_1=1$ and $\alpha_1=2$ cases for $f(R)$ which have more physical behaviour at high $k$."126 Since we are interested. in how sensitive weak lensing is to dillerent. growth histories with the same expansion history. we will also consider a quintessence cold dark matter (QCDAL) model.," Since we are interested in how sensitive weak lensing is to different growth histories with the same expansion history, we will also consider a quintessence cold dark matter (QCDM) model."127 In this case. the equation of state of the dark energy is altered. to match the expansion history of DGD. while the density perturbation evolution equations are the same as ACDAL.," In this case, the equation of state of the dark energy is altered to match the expansion history of DGP, while the density perturbation evolution equations are the same as $\Lambda$ CDM."128 We show examples of the resulting matter power spectra in Figure L.., We show examples of the resulting matter power spectra in Figure \ref{fig:p_delta}.129 fC?) models show the scale dependent enhancement of the power spectrum in the linear regime compared with ACDAL, $f(R)$ models show the scale dependent enhancement of the power spectrum in the linear regime compared with $\Lambda$ CDM.130" For o,=1/3. which fits N-bocdv results well up to &= Ih/Mpc. the power spectrum fails to converge with ACDAL"," For $\alpha_1=1/3$, which fits N-body results well up to $k=1h$ /Mpc, the power spectrum fails to converge with $\Lambda$ CDM."131" On the other hand. the power spectrum with a,=2 shows clear convergence: this is shown more explicitly in Figure 2.."," On the other hand, the power spectrum with $\alpha_1=2$ shows clear convergence; this is shown more explicitly in Figure \ref{fig:p_delta diff}. ."132 We also show a comparison between DGP anc QCDM power in Figure 3..including our non-linear prescription.," We also show a comparison between DGP and QCDM power in Figure \ref{fig:p_delta_qcdm}, ,including our non-linear prescription."133 In the linear regime the DOP power spectrum receives scaleindependent suppressions. but it converges to the QCDAL power spectrum on non-linear scales due to our inclusion of the GR asymptote.," In the linear regime the DGP power spectrum receives scaleindependent suppressions, but it converges to the QCDM power spectrum on non-linear scales due to our inclusion of the GR asymptote."134colponcuts.,components.135 We lave investigated the radial variation of the ratio between the soft N-ray aud the |O TH] line cluission., We have investigated the radial variation of the ratio between the soft X-ray and the [O III] line emission.136 We represented in Fieure 13 the variation of the brightuess ratio along the axis of the cone (PA= 122°)., We represented in Figure \ref{fig:profX} the variation of the brightness ratio along the axis of the cone $\mathrm{PA}=122^\circ$ ).137 The brightness profiles were extracted using the IRAFpecctor task., The brightness profiles were extracted using the IRAF task.138 Before obtaining the ratio we convolved the [O IH] profile to obtain the resolution of X-ray data., Before obtaining the ratio we convolved the [O III] profile to obtain the resolution of X-ray data.139 As can be seeu from Figure 13. the ratio soft-N/[O III| presents a non-uniform variation showing a niaxininnai at the uucleus: it then drops dramatically at the position of the |O III] ares and returns at roughly half of the nuclear value outside the [O III] ares., As can be seen from Figure \ref{fig:profX} the ratio soft-X/[O III] presents a non-uniform variation showing a maximum at the nucleus; it then drops dramatically at the position of the [O III] arcs and returns at roughly half of the nuclear value outside the [O III] arcs.140 A similar behaviour. namely a small variation of the ratio. has been reported by Bianchietal.(2006) for the case of NGC 3393.," A similar behaviour, namely a small variation of the ratio, has been reported by \citet{Bianchi06} for the case of NGC 3393."141 We have also compared the radial variation with predictions frou photoionization models in Figure 13.., We have also compared the radial variation with predictions from photoionization models in Figure \ref{fig:profX}.142 We lave uxed simple models assume single planeparallel slabs. constant deusitv aud radiation bounded clouds.," We have used simple models assuming single plane--parallel slabs, constant density and radiation bounded clouds."143" The soft N-rav cussion has heen takeu as the stun ofthe predicted values for the most inteuse features identified iu our X-ray spectra,", The soft X-ray emission has been taken as the sum of the predicted values for the most intense features identified in our X-ray spectra.144 We have scaled the model predictions to the observed nuclear values from the model with logU—0.5. which is close to the best fitting value derived above.," We have scaled the model predictions to the observed nuclear values from the model with $\rm{log U = 0.5}$, which is close to the best fitting value derived above."145 The predictions for different values of the ionization parameters are represented im Figure 13.., The predictions for different values of the ionization parameters are represented in Figure \ref{fig:profX}. .146 It can be seen that a variation of ( by one order of magnitude is needed to reproduce the observed variation in the brightuess ratio from the nucleus to the ares. which could be attributed to a combination of radiation dilution plus density cuhancemenuts at the arc positions.," It can be seen that a variation of $U_t$ by one order of magnitude is needed to reproduce the observed variation in the brightness ratio from the nucleus to the arcs, which could be attributed to a combination of radiation dilution plus density enhancements at the arc positions."147 Note. that these variations are qualitatively in agreement with our Cloudy model simulations in which two citferent U values are needed for SE aud NW cones.," Note, that these variations are qualitatively in agreement with our Cloudy model simulations in which two different U values are needed for SE and NW cones."148 A baseline model where the deusity decreases as ο as proposed bv Biauchietal.(2006)... is compatible with our results. except for the regious close to ΟΠΗ arcs.," A baseline model where the density decreases as $r^{-2}$, as proposed by \citet{Bianchi06}, is compatible with our results, except for the regions close to [OIII] arcs."149 It is very Likely that simple photoionization models are not adequate to reproduce the observed ionization variatious. although a more sophisticated treatment nist wait uutil lieher quality N-ray. spectroscopic observations become available.," It is very likely that simple photoionization models are not adequate to reproduce the observed ionization variations, although a more sophisticated treatment must wait until higher quality X-ray spectroscopic observations become available."150 The fact that ionization- auc matter-bouuded clouds are likely constituents of the NLR las not been explored to explain emission lines in the soft-X raugoe., The fact that ionization- and matter-bounded clouds are likely constituents of the NLR has not been explored to explain emission lines in the soft-X range.151 Another important feature of the unified model is the optically thick torus., Another important feature of the unified model is the optically thick torus.152 Uueler this scheme. Tvpe-2 Sevterts like 5573 are obscured due to this material located aloug our liue of sight.," Under this scheme, Type-2 Seyferts like 573 are obscured due to this material located along our line of sight."153 The best way to study and characterize the molecular torus is by modeling the nuclear spectral energy distribution (SED) of the sources., The best way to study and characterize the molecular torus is by modeling the nuclear spectral energy distribution (SED) of the sources.154 The near- aud mid-IR nuclear eimissiou of Sevfert ealaxies is attributed to the reprocessing of the UV/X-rav nuclear radiatiou bv the toroidal dusty structure., The near- and mid-IR nuclear emission of Seyfert galaxies is attributed to the reprocessing of the UV/X-ray nuclear radiation by the toroidal dusty structure.155 For his reason. the infrared range is kev to put coustraiuts on orus modoeling.," For this reason, the infrared range is key to put constraints on torus modeling."156 However. in comparing the predictions of any torus model with observations. the small-scale olus Cluission nmst boe isolated. im order to avoid contanunation from the host ealaxx.," However, in comparing the predictions of any torus model with observations, the small-scale torus emission must be isolated, in order to avoid contamination from the host galaxy."157 For this reason. it is portant to use high aneulay resolution data when ring to model the torus emission.," For this reason, it is important to use high angular resolution data when trying to model the torus emission."158 We have tried here to explain the optical/imfrared imclear SED of Mrk 573 constructed with high spatial resolution data (see Table 1)) using au interpolated version of tle recent models for the chuupy torus scenario o» Nenkovaetal.(200848.b).," We have tried here to explain the optical/infrared nuclear SED of Mrk 573 constructed with high spatial resolution data (see Table \ref{tab:psf}) ) using an interpolated version of the recent models for the clumpy torus scenario by \citet{Nenkova08a,Nenkova08b}."159. We have searched for he bestfitting models using the Bayesian infercuce ool (AseusioRamos&Alincida2009) The results of the fit are shown in Figure LL., We have searched for the bestfitting models using the Bayesian inference tool \citep{Asensio09} The results of the fit are shown in Figure \ref{fig:opirSED}.160 Iudeed. the nuclear SED of Mrk 573 has Όσοι xeviouslv fitted by RamosAlmeidactal.(20091) using lis set of models and tools. although the data poiuts vclow 1 wwere not iucbluded im their analvsis.," Indeed, the nuclear SED of Mrk 573 has been previously fitted by \citet{Ramos09b} using this set of models and tools, although the data points below 1 were not included in their analysis."161 For using the optical photometry derived in this work. the chuupy torus uodel Gt needs an additional extinction factor. which is included as a foreground extinction.," For using the optical photometry derived in this work, the clumpy torus model fit needs an additional extinction factor, which is included as a foreground extinction."162 The derived median value is Ay=7.340.5 mae. which can be translated to a column deusitv of Nj=1.39«1072cu2.," The derived median value is $A_V = 7.3\pm0.5$ mag, which can be translated to a column density of $\rm{N_H = 1.39\times 10^{22}~\mathrm{cm}^{-2}}$."163 This value is nicely consistent with that derived from the optical colour maps (see Sect. ο ))., This value is nicely consistent with that derived from the optical colour–colour maps (see Sect. \ref{sec:morpho}) ).164 The results of the fitting process are the probability distributions for the free paramecters that describe the chuupy models (see RamosAlmeidaetal. 2009b))., The results of the fitting process are the probability distributions for the free parameters that describe the clumpy models (see \citealt{Ramos09b}) ).165 For Abrk 573. the median values of the parameters correspoud to a torus width of 307. Ny=Lc1 clouds in the equatorial direction. optical depth per single cloud GO. and ARDS~300 mae (equivalent to NHScDUEx1075αι 2).," For Mrk 573, the median values of the parameters correspond to a torus width of $^\circ$, $N_0=4\pm1$ clouds in the equatorial direction, optical depth per single cloud $\tau_V \sim 60$ , and $\mathrm{A_V^{LOS}}\sim 300$ mag (equivalent to $\mathrm{N_H^{LOS}}\sim 5.7\times10^{23}~\mathrm{cm}^{-2}$ )."166 These torus parameters are similar to those derived without iucludiug the optical data poiuts bv RamosAliicidaetal.(2009b)., These torus parameters are similar to those derived without including the optical data points by \citet{Ramos09b}.167. We have determined the torus huuiuositv iuteeratiug the corresponding cussion from the torus model corresponding to the median value of the probability distribution of each parameter (dashed line in Figure LU)., We have determined the torus luminosity integrating the corresponding emission from the torus model corresponding to the median value of the probability distribution of each parameter (dashed line in Figure \ref{fig:opirSED}) ).168 The resulting value is Ley=7.1«10%eres5l, The resulting value is $_{bol}^{tor}=7.4 \times 10^{43}~\mathrm{erg s^{-1}}$.169 The chuupy iodel fit vields the bolometric huuuinosity of the intrinsic AGN. L;C=5.2«1075eres+ (the bolometric huninosities are good to a factor of 2).," The clumpy model fit yields the bolometric luminosity of the intrinsic AGN, $_{bol}^{AGN}=5.2 \times 10^{44}~\mathrm{erg s^{-1}}$ (the bolometric luminosities are good to a factor of 2)."170 Combining this value with the torus Inuinosity. we derive the reprocessing efficieucyof the torus. which for Mrk 573 results to be quite low. about ," Combining this value with the torus luminosity, we derive the reprocessing efficiencyof the torus, which for Mrk 573 results to be quite low, about ."171Moreover. we have derived the N-rav Iunuinositv frou the hard N-vav part. assumiue a power lav with photon," Moreover, we have derived the X-ray luminosity from the hard X-ray part, assuming a power law with photon"172gas that are coupled with cach other and invoking mass and energy flux continuity and ensuring that the divergence of the magnetic field explicitly vanishes within the governing equations. we can arrive at a steady-state description of the hybrid clual-luicl wind in the equatorial plane of Betelgeuse (see?)..,"gas that are coupled with each other and invoking mass and energy flux continuity and ensuring that the divergence of the magnetic field explicitly vanishes within the governing equations, we can arrive at a steady-state description of the hybrid dual-fluid wind in the equatorial plane of Betelgeuse \citep[see][]{Thirumalai2010}."173 Phe radial equation for the gas velocity profile is then given by. where. (e=uua ds the gas speed normatisecl using the Alfvénnspeed. and we=rfry. is the radial distance expressed in units of the Alfvénn radius.," The radial equation for the gas velocity profile is then given by, where, $w=u/u_A$ is the gas speed normalised using the Alfvénnspeed and $x=r/r_A$, is the radial distance expressed in units of the Alfvénn radius."174" Hereafter. the subscript ""A refers to values of the different. variables at the Alfvénn radius."," Hereafter, the subscript $A$ ' refers to values of the different variables at the Alfvénn radius."175 Phe quantities IN(i.c) and Deir) are the numerator ancl denominator respectively and are given by. In the above equations.. the parameters Sy;=DR——L. SoS$0000(M= and SoTN= along withον . unicquels. determine rythe locations of thezi critical points. andhence he morphology of the family of solutions of σα. (1)).," The quantities $N(w,x)$ and $D(w,x)$ are the numerator and denominator respectively and are given by, and In the above equations, the parameters $S_T=\frac{2kT_A}{m_p u_A^2}$, $S_G=\frac{GM_*}{r_A u_A^2}$ and $S_\Omega=\frac{\Omega^2176 r_A^2}{u_A^2}$ along with $\gamma$ uniquely determine the locations of the critical points, andhence the morphology of the family of solutions of Eq. \ref{eq:1}) )."177" Here Ta is the eas temperature at the Alfvénn radius. & is the Boltzmann constant ancl my, is the mass of à proton."," Here $T_A$ is the gas temperature at the Alfvénn radius, $k$ is the Boltzmann constant and $m_p$ is the mass of a proton."178 The critical points are. as usual. defined as the locations at which οί the numerator ancl the denominator vanish. thereby keeping the right-hand side of Eq. (1))," The critical points are, as usual, defined as the locations at which both the numerator and the denominator vanish, thereby keeping the right-hand side of Eq. \ref{eq:1}) )"179 finite. these are the sonic point. the racial Alfyénn point and the fast. point (c.g.2)..," finite, these are the sonic point, the radial Alfvénn point and the fast point \citep[e.g.][]{WD67}."180 Phe presence of the Lleaviside function in Eq. (2)), The presence of the Heaviside function in Eq. \ref{eq:2}) )181 represents the formation of dust at the location .=vy. he dust condensation radius in units of the Alfvénn radius.," represents the formation of dust at the location $x=x_d$, the dust condensation radius in units of the Alfvénn radius."182 The eritical wind solution of Iq. (1)), The critical wind solution of Eq. \ref{eq:1}) )183 will vield the gas velocity. profile. thereby. enabling the determination of al other dependent variables. such as the cust velocity. profile (to be discussed below). the Mach. number as a function of distance from the star. the azimuthal velocity of the gas. the azimuthal component of the magnetic field. the temperature profile and the density structure of the eas in the envelope of the Betelgeuse.," will yield the gas velocity profile, thereby enabling the determination of all other dependent variables, such as the dust velocity profile (to be discussed below), the Mach number as a function of distance from the star, the azimuthal velocity of the gas, the azimuthal component of the magnetic field, the temperature profile and the density structure of the gas in the envelope of the Betelgeuse."184 Phe critical solution of Iq. (1)), The critical solution of Eq. \ref{eq:1}) )185 is defined as one that starts olf at the base of the wind sub-sonic. passes through the three critical points in à continuous manner anc emerges super-Alfvénnie at. large distances from the star.," is defined as one that starts off at the base of the wind sub-sonic, passes through the three critical points in a continuous manner and emerges super-Alfvénnic at large distances from the star."186" The dust velocity profile is then given by (see2).. where αν ds the thermal speed given by αν= and pm, is. the mean molecular mass of the 5gas and\ nma is the dust grain number density. which is assumed to be given by. mamafps(0? where (δὲ is the average ratio in the wind (see?).."," The dust velocity profile is then given by \citep187[see][]{Thirumalai2010}, where $a_{th}$ is the thermal speed given by $a_{th}=\sqrt{2kT/\mu m_u}$ and $\mu m_u$ is the mean molecular mass of the gas and $n_d$ is the dust grain number density, which is assumed to be given by, $n_d m_d / \rho \approx \langle\delta\rangle$ where $\langle\delta188\rangle$ is the average ratio in the wind \citep[see][]{Thirumalai2010}."189 Phe dust in the current theory is treated. in a simplistic ancl idealised manner. without rigorously considering the elects of dust radiative properties or including the cHects of scattering and absorption on the radiation pressure mean cllicicney.," The dust in the current theory is treated in a simplistic and idealised manner, without rigorously considering the effects of dust radiative properties or including the effects of scattering and absorption on the radiation pressure mean efficiency."190 While such an analysis would no doubt portray à more complete picture. the current rucimentary treatment. nevertheless captures the salient features of the coupled outldow from the star.," While such an analysis would no doubt portray a more complete picture, the current rudimentary treatment nevertheless captures the salient features of the coupled outflow from the star."191 As our purpose here is to illustrate the feasibility of a hyvbrid-MLIID-dust-driven wind model for DBetelgeuse. the current. simplistic treatment of dust was considered sullicient.," As our purpose here is to illustrate the feasibility of a hybrid-MHD-dust-driven wind model for Betelgeuse, the current simplistic treatment of dust was considered sufficient."192 Ίσα. (1) , Eq. \ref{eq:1}) )193is solved numerically. and the reader is referred to our earlier. work (see?) for complete details on the numerical methodology.," is solved numerically, and the reader is referred to our earlier work \citep[see][]{Thirumalai2010} for complete details on the numerical methodology."194 The pertinent points of the method. are conveved. below. in brief.," The pertinent points of the method are conveyed below, in brief."195 Eq. (1)), Eq. \ref{eq:1}) )196 is solved using the package ΟΡΙΑ employing a finite difference method with chord iteration with the Jacobian supplied (see??)..," is solved using the package ODEPACK employing a finite difference method with chord iteration with the Jacobian supplied \citep[see][]{Hindmarsh1983,Hindmarsh1989}."197 Initial conditions were supplied at the beginning of the integration., Initial conditions were supplied at the beginning of the integration.198 Typical error tolerances for convergence testing that were emploved: were on the order of 10.17 for both the absolute and. relative errors (see?).., Typical error tolerances for convergence testing that were employed were on the order of $10^{-12}$ for both the absolute and relative errors \citep[see][]{Hindmarsh1983}.199 For a typical integration. step sizes of 10° or 10το in units of the Alfvénn radius. were enmploved depending upon the region of integration being near the critical points or sullicienthy away from them.," For a typical integration, step sizes of $10^{-9}$ or $10^{-10}$, in units of the Alfvénn radius, were employed depending upon the region of integration being near the critical points or sufficiently away from them."200" This resulted in typically 107—107"" function evaluations.", This resulted in typically $10^9-10^{10}$ function evaluations.201" ln the current study. in contrast to 2.. we located the radial Alfyvénn point at around 25/2, with an Alfvénnic temperature of àzm720 Ix. ancl Alfvénnie velocity ενz0.15e014 km/s. because we wanted to have a dust formation temperature of ~TOO Ix with dust condensation occurring at  30725."," In the current study, in contrast to \cite{Thirumalai2010}, we located the radial Alfvénn point at around $25R_0$ with an Alfvénnic temperature of $T_A \approx 720$ K, and Alfvénnic velocity $u_A202\approx 0.15 v_\mathrm{esc,0} \approx 14~$ km/s, because we wanted to have a dust formation temperature of $\sim 700$ K with dust condensation occurring at $\sim 30R_0$ ."203 The polvtropic exponent 5. was varied and the locations of the sonic point and the fast point were found. according to the method. described in ?.., The polytropic exponent $\gamma$ was varied and the locations of the sonic point and the fast point were found according to the method described in \cite{Thirumalai2010}. .204 Once a particular value for + is chosen. the bulk radial gas velocity at the photosphere is found using the relation.," Once a particular value for $\gamma$ is chosen, the bulk radial gas velocity at the photosphere is found using the relation,"205"which reads in dimensionless units. We plot the radiative cooling times z(T,.L) calculated with the observed values (7,£L) in Fig.","which reads in dimensionless units, We plot the radiative cooling times $\tau_r(T_p, L)$ calculated with the observed values $(T_p, L)$ in Fig."206 6 (top right panel) as a function of the flare duration zy., 6 (top right panel) as a function of the flare duration $\tau_f$.207 These radiative cooling times based on the REV sealing law are generally longer than the conductive cooling times. and they clearly exceed (he flare durations for most of the flares. up (o an order of magnitude for the short EUV flaves with durations of 7;=10° s. Since the observed flare duration should be an upper limit of the cooling time. either the conductive or radiative cooling time should be equal or shorter.," These radiative cooling times based on the RTV scaling law are generally longer than the conductive cooling times, and they clearly exceed the flare durations for most of the flares, up to an order of magnitude for the short EUV flares with durations of $\tau_f \lapprox 10^3$ s. Since the observed flare duration should be an upper limit of the cooling time, either the conductive or radiative cooling time should be equal or shorter."208 A combined cooling time 7 can be defined [rom the exponential folding lime that would result from the product of the (wo exponential cooling processes. We plot this combined coolingo time 7 as a [function of the flare duration in Fig.," A combined cooling time $\tau$ can be defined from the exponential folding time that would result from the product of the two exponential cooling processes, We plot this combined cooling time $\tau$ as a function of the flare duration in Fig."209o 6 (bot(om left j»anel) usinee the RTV law., 6 (bottom left panel) using the RTV law.210 The so-celinedl combined coolinee (ime 15 almost always shorter than the observed flare duration., The so-defined combined cooling time is almost always shorter than the observed flare duration.211 Including Serios correction factor (Eq., Including Serio's correction factor (Eq.212 25) for the conductive and radiative cooling (ies. vields only small corrections. shown [lor the five solar datasets in Fig.," 25) for the conductive and radiative cooling times, yields only small corrections, shown for the five solar datasets in Fig."213 6., 6.214 The average correction values are <qs«;4>=0.90—0.98 [or the EUV datasets (Aschwanden et al., The average correction values are $<q_{Serio}>=0.90-0.98$ for the EUV datasets (Aschwanden et al.215" 20002: ]|xrucker Benz 2000). and «qs,=0.05—0.95 for Che soft X-ray datasets (Pallavicini et al."," 2000a; Krucker Benz 2000), and $<q_{Serio}>=0.05-0.95$ for the soft X-ray datasets (Pallavicini et al."216 1977: Garcia 1993: Meteall Fisher 1996)., 1977; Garcia 1998; Metcalf Fisher 1996).217 We plot the corrected flare cooling times predicted by Serio’s scaling law in Fie., We plot the corrected flare cooling times predicted by Serio's scaling law in Fig.218 6 (bottom right panel)., 6 (bottom right panel).219 The major effect of Serio's correction is that the cooling times of the larger and hotter soft X-ray emitting flare loops become shorter. limiting essentiallv all flare loop cooling times to 7<10* s. Thus. large flares that last significantly longer (up to 7;Z2x105 s) must consist of multiple subllares.," The major effect of Serio's correction is that the cooling times of the larger and hotter soft X-ray emitting flare loops become shorter, limiting essentially all flare loop cooling times to $\tau \lapprox 10^3$ s. Thus, large flares that last significantly longer (up to $\tau_f \lapprox 2 \times 10^4$ s) must consist of multiple subflares."220"In Fig. 1,,","In Fig. \ref{Fig:selfcorr},"221 we plot the self-correlations., we plot the self-correlations.222" In Fig. 2,,"," In Fig. \ref{Fig:crosscorr},"223" we show the determination of the cross-correlation function for different ranges of magnitude, and the errors computed by using re-sampling errors and field-to-field determinations."," we show the determination of the cross-correlation function for different ranges of magnitude, and the errors computed by using re-sampling errors and field-to-field determinations."224" On the one hand, the errors computed by both the bootstrap and the knife method are of the same order, and on the other hand the three “‘field-to-field” methods yield similar results, which however are much larger than the re-sampling errors."," On the one hand, the errors computed by both the bootstrap and the jack-knife method are of the same order, and on the other hand the three “field-to-field” methods yield similar results, which however are much larger than the re-sampling errors."225" The ""Different fields"" method yields in general a slightly lower r.m.s.", The “Different fields” method yields in general a slightly lower r.m.s.226" than the integral of the self-correlations, possibly because of small positive large-scale correlations, which slightly reduce the dispersion, as mentioned in discussing ""different fields"" in §3.."," than the integral of the self-correlations, possibly because of small positive large-scale correlations, which slightly reduce the dispersion, as mentioned in discussing “different fields” in \ref{.methods}."227" The “Monte Carlo"" method might yield slightly higher values of r.m.s.", The “Monte Carlo” method might yield slightly higher values of r.m.s.228 than the integral of the self-correlations due to the larger amplitude of the low-multipoles in the theoretical power spectrum., than the integral of the self-correlations due to the larger amplitude of the low-multipoles in the theoretical power spectrum.229 The field-to-field fluctuations obtained by using independent determinations of the cross-correlation function are similar to the amplitude of the detected signal or even larger., The field-to-field fluctuations obtained by using independent determinations of the cross-correlation function are similar to the amplitude of the detected signal or even larger.230 Figure 3 illustrates this point by showing that there are, Figure \ref{Fig:crosscorr2} illustrates this point by showing that there are231of stars (~ 1200) with |Z]S2 kpe.,of stars $\sim 1200$ ) with $|Z| \la 2$ kpc.232 Allende Prieto ct ((2006) adopted SDSS photometric distances and radial velocities Gvithout using proper motions). and found a rotational-lag eradicut of 16 lan | |! for stars between {Z|=1 aud 3 kpe.," Allende Prieto et (2006) adopted SDSS photometric distances and radial velocities (without using proper motions), and found a rotational-lag gradient of $-16$ km $^{-1}$ $^{-1}$ for stars between $|Z| = 1$ and 3 kpc."233 In Majewski (1992). the value ds 2lkins | |! based ou deep proper-motion of survey Galaxy out to |Z]~ 6kpe.," In Majewski (1992), the value is $-21$ km $^{-1}$ $^{-1}$ based on deep proper-motion survey of the Galaxy out to $|Z| \sim 6$ kpc."234 Our value of 19 kins tkpethe+ for stars with |Fe/TI]>0.9 and {Z|«15 kpe is quite consistent with previous values witlin the error range., Our value of $-19$ km $^{-1}$ $^{-1}$ for stars with $\feh >-0.9$ and $|Z|< 15 $ kpc is quite consistent with previous values within the error range.235 It has been sugeested that the rotational lag and the velocity dispersious vary with distance from the Galactic aue (Majewski 1991)., It has been suggested that the rotational lag and the velocity dispersions vary with distance from the Galactic plane (Majewski 1994).236 ILowever. our work shows that. x [Fe/H]<—0.9. the (oe? decreases with inereasiug Z| for the region of |Z|«10 kpc. while for |Z|>1 moc. Where the halo donmünates. there is no siguificaut rend.," However, our work shows that, for $\feh < -0.9$, the ${\langle \Vrot \rangle}$ decreases with increasing $|Z|$ for the region of $|Z|< 10 $ kpc, while for $|Z|> 10$ kpc, where the halo dominates, there is no significant trend."237 In Boud et (2010) the halo population with Fe/H]|<Ll does uot show auy trend iu the (ioe) with |Z| over the region of |Z|«5 kpe. which does not agree with our result for |Fe/II]«—0.9 aud |Z]«1 spe.," In Bond et (2010) the halo population with $\feh < -1.1$ does not show any trend in the ${\langle \Vrot \rangle}$ with $|Z|$ over the region of $|Z|< 5 $ kpc, which does not agree with our result for $\feh < -0.9$ and $|Z|< 10 $ kpc."238 This discrepancy may be casily uuderstood if we ο that stars with |Fo/TII|<0.9 in the present worl consist of two halo sub-populations., This discrepancy may be easily understood if we assume that stars with $\feh < -0.9$ in the present work consist of two halo sub-populations.239 Finally. the scatters around these trends in Figure.," Finally, the scatters around these trends in Figure."240 10-12 are rather large. aud further studies with larger samples aud high-quality data are needed.," 10-12 are rather large, and further studies with larger samples and high-quality data are needed."241 As described above. this diagram is a useful way to race the structure of the Calaxy when abundance aud οποιαίσα. data are combined.," As described above, this diagram is a useful way to trace the structure of the Galaxy when abundance and kinematical data are combined."242 Figure 13 shows the üstogranis of Vor (upper paucl) and the |Fe/TI] versus Tha diagrana (lower paucl) for RIID stars., Figure 13 shows the histograms of $\Vrot$ (upper panel) and the $\feh$ versus $\Vrot$ diagram (lower panel) for RHB stars.243 The upper uel shows that the metal-mild component poaks at VnaPrOkmns aud the metal-poor coniponent spans a wide range in Vege without auv sharp peak., The upper panel shows that the metal-mild component peaks at $\Vrot \sim 170 \kmprs$ and the metal-poor component spans a wide range in $\Vrot$ without any sharp peak.244" That is. he Vi, dispersion in the former is smaller than the atter component."," That is, the $\Vrot$ dispersion in the former is smaller than the latter component."245 This is expected im the contest of he Galactic stellar populations with the halo population with [Fe/U]<1.0 having a large velocity dispersion as compared to the thick-disk population. with a metallicity oak at [Fe/T]~— 0.6. and the thin-disk population with a iictallicity peak at |Fe/Il|~ 0.2.," This is expected in the context of the Galactic stellar populations with the halo population with $\feh < -1.0$ having a large velocity dispersion as compared to the thick-disk population, with a metallicity peak at $\feh \sim -0.6$ , and the thin-disk population with a metallicity peak at $\feh \sim -0.2$ ."246 Actually. he distribution in Vor for the metal-poor componcut is rather broad and in this work we separate tle metalpoor coniponeut iuto two groups with Vi;>Ohaus! aud Vie<Olans+ in the lower panel of Figure 13.," Actually, the distribution in $\Vrot$ for the metal-poor component is rather broad and in this work we separate the metal-poor component into two groups with $\Vrot > 0 \kmprs$ and $\Vrot < 0 \kmprs$ in the lower panel of Figure 13."247" The netal-anild population with {PeΠΕ~0.6 has a peak at Viedr0lkans+. which is quite similar to that derived roni the solar ucigliborhood by Soubiran et ((2003). who derive a rotational lag (Stromberg asviunietrical dift) of Vi,~5llans! with respect to the LSR. and is solmewhat lower than the average rotational lag of Έα~SU0lans loy Fulvmann (1998) for a group of 16 thick-disk stars."," The metal-mild population with $\feh \sim -0.6$ has a peak at $\Vrot \sim 170 \kmprs$, which is quite similar to that derived from the solar neighborhood by Soubiran et (2003), who derive a rotational lag (Stromberg asymmetrical drift) of $V_{lag} \sim 51 \kmprs$ with respect to the LSR, and is somewhat lower than the average rotational lag of $V_{lag} \sim 80 \kmprs$ by Fuhrmann (1998) for a group of 16 thick-disk stars."248" For the metal-poor population. we separate them iuto two sub-populations with the division of starswithVL,>Olans! being ""Halo D aud stars"," For the metal-poor population, we separate them into two sub-populations with the division of starswith$\Vrot> 0 \kmprs$ being “Halo I” and stars"249Ay are observation that was recorded on the same night as the M32 data.,Ar arc observation that was recorded on the same night as the M32 data.250 The spectra. were sunuued and (hen divided by the spectrum of a telluric standarcl star. which was observed immediately following the M32 observations.," The wavelength-calibrated spectra were summed and then divided by the spectrum of a telluric standard star, which was observed immediately following the M32 observations."251 There are a number of distinct sources with EWIIM ~0.1 aresec in the two-dimensional NIFS spectra. and these define the locations that are investigated in (he remainder of the paper.," 	There are a number of distinct sources with FWHM $\sim 0.1$ arcsec in the two-dimensional NIFS spectra, and these define the locations that are investigated in the remainder of the paper."252 The locations of these point sources are indicated in Figure 1. where (NX.Y) = (0.0) is the center of M32. while the angular offsets of the sources [rom the center of M32. are listed in Table 1.," The locations of these point sources are indicated in Figure 1, where (X,Y) = (0,0) is the center of M32, while the angular offsets of the sources from the center of M32 are listed in Table 1."253 The detection of objects along the X = 0 axis is hindered by elevated star counts along the major axis of M32. which runs close to X = 0 arcsec. and scattered light from the bright nucleus of M32.," The detection of objects along the X = 0 axis is hindered by elevated star counts along the major axis of M32, which runs close to X = 0 arcsec, and scattered light from the bright nucleus of M32."254 A specirum was extracted of each of the sources in Figure 1., 	A spectrum was extracted of each of the sources in Figure 1.255 The surface brightness in the central arcsec of M32. exceeds 11: mag 7 in A (e.g. Jarrett οἱ al., The surface brightness in the central arcsec of M32 exceeds 11 mag $^{-2}$ in $K$ (e.g. Jarrett et al.256 2003). and thus contributes substantial noise to the extracted spectra.," 2003), and thus contributes substantial noise to the extracted spectra."257 Indeed. (he unresolved stellar background. rather than the ambient ‘skv. is (he dominant source of noise in studies of stars new the centers of most nearby galaxies.," Indeed, the unresolved stellar background, rather than the ambient `sky', is the dominant source of noise in studies of stars near the centers of most nearby galaxies."258 A mean background spectrum was constructed from galaxy light bracketing each source. and the result was subtracted from the extracted spectrum.," A mean background spectrum was constructed from galaxy light bracketing each source, and the result was subtracted from the extracted spectrum."259 The backerounc-sublracted spectra were binned along (he dispersion axis {ο increase (he signal-to-noise ratio. and the final spectral resolution is zz1000.," The background-subtracted spectra were binned along the dispersion axis to increase the signal-to-noise ratio, and the final spectral resolution is $\approx 1000$."260 The continuum was also removed from (he spectra in preparation for the velocity dispersion analvsis., The continuum was also removed from the spectra in preparation for the velocity dispersion analysis.261 With an image quality of EWIIM 20.1 aresec. each angular resolution element near (he center of M32 samples an area wilh an integrated magnitude Mj2—9. which is comparable to that ofa Galactic globular cluster.," 	With an image quality of FWHM $\approx 0.1$ arcsec, each angular resolution element near the center of M32 samples an area with an integrated magnitude $_K \approx -9$, which is comparable to that of a Galactic globular cluster."262 Consequently. all of the sources in Figure 1 are blends. in the sense (hat light [rom more than one star falls within each angular resolution element.," Consequently, all of the sources in Figure 1 are blends, in the sense that light from more than one star falls within each angular resolution element."263 In addition. only objects that have an intrinsic briehtness (hat is comparable (to or greater than (hat in each angular resolution element (i.e. My2—9 in this case) will be resolved.," In addition, only objects that have an intrinsic brightness that is comparable to or greater than that in each angular resolution element (i.e. $_K \approx -9$ in this case) will be resolved."264 The AGD-tip in M32 occurs near IX — 15.5. whieh corresponds to Mgx—9 (Davidge et al.," The AGB-tip in M32 occurs near K = 15.5, which corresponds to $_K \approx -9$ (Davidge et al."265 2000: Davidge Jensen 2007). and so any sources identified here are evolving near the ACGD-tip.," 2000; Davidge Jensen 2007), and so any sources identified here are evolving near the AGB-tip."266 Aye there locations in the NIFS dataset where the light is dominated by a single bright star?, 	Are there locations in the NIFS dataset where the light is dominated by a single bright star?267 Line width measurements are one wav (o determine if such locations are present., Line width measurements are one way to determine if such locations are present.268 If the light in a blend originates from a large number of stars. with no single star contributing more (han a small fraction of the light. then the absorption limes in the composite spectrum," If the light in a blend originates from a large number of stars, with no single star contributing more than a small fraction of the light, then the absorption lines in the composite spectrum"269and redshifts (the lower panel).,and redshifts (the lower panel).270" The objects in the AGN sample and in the SF sample are shown by red crosses and green circles, respectively."," The objects in the AGN sample and in the SF sample are shown by red crosses and green circles, respectively."271" In both panels, starforming galaxies are continually distributed in the diagram."," In both panels, starforming galaxies are continually distributed in the diagram."272" By contrast, the bimodal radial distribution can still be clearly identified for AGNs even when one compares the relative distances between AGNs and starforming galaxies at a given morphological type or redshift."," By contrast, the bimodal radial distribution can still be clearly identified for AGNs even when one compares the relative distances between AGNs and starforming galaxies at a given morphological type or redshift."273" There is an obvious gap at Rgn/Ro5,cor~0.4—0.5 separating the AGNs into two sub-groups."," There is an obvious gap at $R_{\mathrm{SN}}/R_{25,\mathrm{cor}}\sim0.4-0.5$ separating the AGNs into two sub-groups."274" This figure therefore strongly suggests that the bimodal distribution revealed for AGNs is robust, i.e., not correlated to morphological type and luminosity of the supernova host galaxies."," This figure therefore strongly suggests that the bimodal distribution revealed for AGNs is robust, i.e., not correlated to morphological type and luminosity of the supernova host galaxies."275" As an additional test, the bimodal radial distribution of the SNelIII discovered in AGN host galaxies is still significant if we examine the issue more physically."," As an additional test, the bimodal radial distribution of the II discovered in AGN host galaxies is still significant if we examine the issue more physically."276" Figure 4 shows the surface density distribution of the SNeIII as a function of Rsn/Re5,cor for both AGN and SF samples."," Figure 4 shows the surface density distribution of the II as a function of $R_{\mathrm{SN}}/R_{25,\mathrm{cor}}$ for both AGN and SF samples."277" The surface density is calculated as Σον=Ν/Α for each distance bin, where S=2zrAr is the area of a circle with a radius r and a width Ar, and N the number of SNe detected within the circle."," The surface density is calculated as $\Sigma_{\mathrm{SN}}=N/S$ for each distance bin, where $S=2\pi r\Delta r$ is the area of a circle with a radius $r$ and a width $\Delta r$, and $N$ the number of SNe detected within the circle."278" The distributions plotted in Figure 1 are rebinned into a single bin for the outer region Rgn/Ro5,cor>1."," The distributions plotted in Figure 1 are rebinned into a single bin for the outer region $R_{\mathrm{SN}}/R_{25,\mathrm{cor}}>1$."279" In Figure 4, the AGN and SF samples are symbolized by red-triangles and green-open-circles, respectively."," In Figure 4, the AGN and SF samples are symbolized by red-triangles and green-open-circles, respectively."280 The lo Gaussian uncertainty over-plotted in the diagram is calculated according to the error tables given in Gehrels (1986)., The $\sigma$ Gaussian uncertainty over-plotted in the diagram is calculated according to the error tables given in Gehrels (1986).281 'The surface density distribution of the SF sample is weighted through the same method described above., The surface density distribution of the SF sample is weighted through the same method described above.282" 'The surface density of cc-SNe is usually well modelled as an exponential profile as a function of Rsn/Ro5,cor (e.g.; Hakobyan et al."," The surface density of cc-SNe is usually well modelled as an exponential profile as a function of $R_{\mathrm{SN}}/R_{25,\mathrm{cor}}$ (e.g., Hakobyan et al."283 2009; Barunov et al., 2009; Barunov et al.284 1992)., 1992).285" Assuming an exponential model Σον=Xo,swexp(r/h), where r=Rsn/R25,cor and h is the length scale in units of Has,cor, the green long-dashed line in Figure 4 plots the best fitting model for the SF sample."," Assuming an exponential model $\Sigma_{\mathrm{SN}}=\Sigma_{\mathrm{0,SN}}\exp(r/h)$, where $r=R_{\mathrm{SN}}/R_{25,\mathrm{cor}}$ and $h$ is the length scale in units of $R_{25,\mathrm{cor}}$, the green long-dashed line in Figure 4 plots the best fitting model for the SF sample."286" The two points with Εαν/Re25,cor are excluded in the fitting because of the Shaw effect."," The two points with $R_{\mathrm{SN}}/R_{25,\mathrm{cor}}<0.2$ are excluded in the fitting because of the Shaw effect."287" The fitting yields a length scale h=0.2340.03Re5,cor."," The fitting yields a length scale $h=0.23\pm0.03 R_{25,\mathrm{cor}}$."288 Our length scale is slightly less than the value obtained in Hakobyan et al. (, Our length scale is slightly less than the value obtained in Hakobyan et al. (289"2009, and references therein).","2009, and references therein)."290 The slight difference could possibly result from two causes., The slight difference could possibly result from two causes.291" First, it is emphasized that the exponential model is obtained here from SF sample alone, which differs from the previous studies."," First, it is emphasized that the exponential model is obtained here from SF sample alone, which differs from the previous studies."292" In these studies, the authors did not separate their samples into sub-groups according to the central engine of supernova host galaxies."," In these studies, the authors did not separate their samples into sub-groups according to the central engine of supernova host galaxies."293" In fact, our study indicates that the surface density of the SNeIII discovered in AGN host galaxies deviates from an exponential profile significantly."," In fact, our study indicates that the surface density of the II discovered in AGN host galaxies deviates from an exponential profile significantly."294" Secondly, our sample is selected by requiring individual SN to lie within 1 arcminute of the corresponding host galaxy center."," Secondly, our sample is selected by requiring individual SN to lie within 1 arcminute of the corresponding host galaxy center."295 These selection causes the sample to be biased against the SNe discovered at the edge of very nearby host galaxies., These selection causes the sample to be biased against the SNe discovered at the edge of very nearby host galaxies.296 Note that the main conclusion presented in the current paper can not be affected by the bias since both AGN- and starforming sub-samples are selected by the same method., Note that the main conclusion presented in the current paper can not be affected by the bias since both AGN- and starforming sub-samples are selected by the same method.297" To illustrate the deviation from an exponential profile for the AGN sample, we vertically shift the best fitting derived for the SF sample by an amount of -0.31 dex (= log(47/95)) by fixing the exponential index."," To illustrate the deviation from an exponential profile for the AGN sample, we vertically shift the best fitting derived for the SF sample by an amount of -0.31 dex $=\log(47/95)$ ) by fixing the exponential index."298 The shifted exponential model is drawn by a red short-dashed line in Figure 4., The shifted exponential model is drawn by a red short-dashed line in Figure 4.299" The model obviously provides a good match for the points at the two ends (by excluding the two points with Rsgn/Re5,cor«0.2 as well)."," The model obviously provides a good match for the points at the two ends (by excluding the two points with $R_{\mathrm{SN}}/R_{25,\mathrm{cor}}<0.2$ as well)."300" Comparing the model with the calculated surface density allows us to identify an over-density at the region Rsn/Re5,cor~0.6—0.8 and a low density at Rgn/Ro25,cor~0.4, which agrees with the analysis based upon the directly measured number distributions."," Comparing the model with the calculated surface density allows us to identify an over-density at the region $R_{\mathrm{SN}}/R_{25,\mathrm{cor}}\sim0.6-0.8$ and a low density at $R_{\mathrm{SN}}/R_{25,\mathrm{cor}}\sim0.4$, which agrees with the analysis based upon the directly measured number distributions."301" Because SNeIII are generated from the explosion of massive stars (> 8Mo), the SNeIlI radial distribution in their host galaxies reasonably reflects not only the radial distribution of young stellar populations, but also the radial distribution of cold gas, assuming a uniform supernova rate."," Because II are generated from the explosion of massive stars $\geq8M_\odot$ ), the II radial distribution in their host galaxies reasonably reflects not only the radial distribution of young stellar populations, but also the radial distribution of cold gas, assuming a uniform supernova rate."302" By comparing the radial distributions of the SNeIII detected in AGNs and the similar distribution of the III detected in starforming galaxies, we find that the supernova radial distribution in AGN host galaxies deviates greatly from the exponential model that can describe the radial distribution"," By comparing the radial distributions of the II detected in AGNs and the similar distribution of the II detected in starforming galaxies, we find that the supernova radial distribution in AGN host galaxies deviates greatly from the exponential model that can describe the radial distribution"303wissenschaftlichen Forschung under project number P14546-PUY (MD) and the Polish Committee for Scientific Research uncer Grant 5-P03D-012-20CAAP).,wissenschaftlichen Forschung under project number P14546-PHY (MB) and the Polish Committee for Scientific Research under Grant 5-P03D-012-20(AAP).304calculations.,calculations.305 Thus. the structure of the corona. ie.. the temperature and density of the electrons. can be derived. and the spectra of the disc-corona system are available based on the derived disce-corona structure with different magnetic stress tensors given in equation 08).," Thus, the structure of the corona, i.e., the temperature and density of the electrons, can be derived, and the spectra of the disc-corona system are available based on the derived disc-corona structure with different magnetic stress tensors given in equation \ref{viscosity}) )."306 We calculate the disc-corona structure as described in section 2., We calculate the disc-corona structure as described in section 2.307" The black hole mass Aij=107M. is adopted in all our calculations. because the main features of the hard X-ray spectra are almost independent of Adi, for massive black holes in AGN."," The black hole mass $M_{\rm bh}=10^8{\rm M}_\odot$ is adopted in all our calculations, because the main features of the hard X-ray spectra are almost independent of $M_{\rm bh}$ for massive black holes in AGN."308 In Fig. |..," In Fig. \ref{fig1},"309 we plot the ratios of the power radiated in the coronato the total power Lear/Lia as functions of accretion rate mm predicted by the models with different magnetic stress tensors., we plot the ratios of the power radiated in the coronato the total power $L_{\rm cor}/L_{\rm bol}$ as functions of accretion rate $\dot{m}$ predicted by the models with different magnetic stress tensors.310" The model with 7...=api always leads to constant ratios Zi,/Li; independent of accretion rate mm. while the dise-corona model calculations with 7;..-=opas show that LosfLia becomes extremely small for high accretion rates (e.g. hoorLia0.01 form~ 1)."," The model with $\tau_{r\varphi}=\alpha{p}_{\rm tot}$ always leads to constant ratios $L_{\rm cor}/L_{\rm bol}$ independent of accretion rate $\dot{m}$ , while the disc-corona model calculations with $\tau_{r\varphi}=\alpha{p}_{\rm gas}$ show that $L_{\rm cor}/L_{\rm311bol}$ becomes extremely small for high accretion rates (e.g., $L_{\rm cor}/L_{\rm bol}\sim 0.01$ for $\dot{m}\sim 1$ )."312 The model with τι.=aπμ shows that the ratios LossLi090.6 at ip=0.01. while LosgfLiac0.050.1 at i=1. for different values of a.," The model with $\tau_{r\varphi}=\alpha \sqrt{p_{\rm gas}p_{\rm tot}}$ shows that the ratios $L_{\rm cor}/L_{\rm bol}\sim 0.3-0.6$ at $\dot{m}=0.01$, while $L_{\rm cor}/L_{\rm bol}\sim 0.05-0.1$ at $\dot{m}=1$, for different values of $\alpha$."313 The temperature and optical depth for Compton scattering of the hot electrons in the vertical direction of the corona are plotted in Fig. 2.., The temperature and optical depth for Compton scattering of the hot electrons in the vertical direction of the corona are plotted in Fig. \ref{fig2}.314 The electron temperatures are in the range of ~5 K for different valuesof ri., The electron temperatures are in the range of $\sim5\times 10^8-3\times 10^9$ K for different valuesof $\dot{m}$.315 The temperature of the hot electrons in the corona tends to decrease with accretion rate m., The temperature of the hot electrons in the corona tends to decrease with accretion rate $\dot{m}$.316 When the aecretion rate mis as high as ~0.5. the electron temperature of the corona decreases to 5«107 K. In Fig. 3..," When the accretion rate $\dot{m}$ is as high as $\sim0.5$, the electron temperature of the corona decreases to $\sim 5\times10^8$ K. In Fig. \ref{fig3},"317 we plot the spectra of the dise-corona systems calculated with different magnetic stress tensors., we plot the spectra of the disc-corona systems calculated with different magnetic stress tensors.318 The hard X-ray emission indeed exhibits a power-law feature for all the models., The hard X-ray emission indeed exhibits a power-law feature for all the models.319 The photon spectral indices and the ratio of the bolometric luminosity to the X-ray luminosity in 2-10 keV as functions of accretion rate for different magnetic stress models are plotted in Fig.4.. The photon indices P do not change much with accretion rate 7 for the disc-corona models with either τε=opi or Tes=Opus While the hard X-ray spectral index D increases significantly. with accretion rate m for the model with ," The photon spectral indices and the ratio of the bolometric luminosity to the X-ray luminosity in 2–10 keV as functions of accretion rate for different magnetic stress models are plotted in Fig.\ref{fig4}. The photon indices $\Gamma$ do not change much with accretion rate $\dot{m}$ for the disc-corona models with either $\tau_{r\varphi}=\alpha{p}_{\rm tot}$ or $\tau_{r\varphi}=\alpha{p}_{\rm gas}$, while the hard X-ray spectral index $\Gamma$ increases significantly with accretion rate $\dot{m}$ for the model with $\tau_{r\varphi}=\alpha \sqrt{p_{\rm gas}p_{\rm320tot}}$ ."321It is believed that the power generated in the dise is transported vertically with the buoyaney of the magnetic fields in the disc. and the fraction. of the power dissipated in the corona tothe total is mainly regulated by the magnetic fields 2004).," It is believed that the power generated in the disc is transported vertically with the buoyancy of the magnetic fields in the disc, and the fraction of the power dissipated in the corona tothe total is mainly regulated by the magnetic fields ."322 found that the fraction bowLia isabout 0.5 for the sources with low Eddington ratio μηειν 0.01. while it decreases to 0.1 for LigLp~ 1. for a sample of AGN.," found that the fraction $L_{\rm cor}/L_{\rm bol}$ isabout 0.5 for the sources with low Eddington ratio $L_{\rm bol}/L_{\rm Edd}\sim 0.01$ , while it decreases to 0.1 for $L_{\rm bol}/L_{\rm Edd}\sim 1$ , for a sample of AGN."323 From Fig. |.. ," From Fig. \ref{fig1}, ,"324we tind that the model with, we find that the model with325The study of active galactic nuclei (AGN) is an important topic in contemporary astrophysics.,The study of active galactic nuclei (AGN) is an important topic in contemporary astrophysics.326 These objects are interesting in their own right. allowing us to study the extreme physies of accretion in the vicinity of a supermassive black hole.," These objects are interesting in their own right, allowing us to study the extreme physics of accretion in the vicinity of a supermassive black hole."327 Furthermore. numerical simulations suggest that AGN likely have a critical role in the formation and evolution of galaxies. highlighting the need to understand how these objects accrete matter. grow and feedback energy to their surroundings (e.g. 23).," Furthermore, numerical simulations suggest that AGN likely have a critical role in the formation and evolution of galaxies, highlighting the need to understand how these objects accrete matter, grow and feedback energy to their surroundings (e.g. \citealt{croton06}) )."328 Since AGN are bright X-ray sources. they have been popular targets for almost all X-ray observatories.," Since AGN are bright X-ray sources, they have been popular targets for almost all X-ray observatories."329 One of the most interesting results obtained thanks to the high sensitivity of the current generation of X-ray missions (specifically P211. [?]] and. more recently. [?]]) has been the detection of narrow absorption features in the 2 — 10 keV band of several bright AGN (see. e.g. 222722).," One of the most interesting results obtained thanks to the high sensitivity of the current generation of X-ray missions (specifically \citealt{jansen01}] ], \citealt{weisskopf02}] ] and, more recently, \citealt{mitsuda07}] ]) has been the detection of narrow absorption features in the 2 – 10 keV band of several bright AGN (see, e.g. \citealt{pounds03,330reeves04,risaliti05,young05,turner07,braito07}) )."331 Particularly for features in the Fe K region of the spectrum. the observed energies and strengths of these lines suggest identification with very highly ionized species (e.g. Fe and XNXVI) in very fast (up to ~ O.le) outflows.," Particularly for features in the Fe K region of the spectrum, the observed energies and strengths of these lines suggest identification with very highly ionized species (e.g. Fe and ) in very fast (up to $\sim 0.1$ c) outflows."332 Blueshifted absorption lines are well-known from observations of AGN in other wavebands and models explaining such phenomena in terms of winds have been developed (see e.g. ?.. ?.. 25.," Blueshifted absorption lines are well-known from observations of AGN in other wavebands and models explaining such phenomena in terms of winds have been developed (see e.g. \citealt{murray95}, \citealt{elvis00}, \citealt{proga04}) )."333 However. the new X-ray data clearly suggest a component of very highly ionized fast outflowing plasma. the relationship of which to the less ionized material observable in ultraviolet (uv) or softer X-ray wavebands remains unclear.," However, the new X-ray data clearly suggest a component of very highly ionized fast outflowing plasma, the relationship of which to the less ionized material observable in ultraviolet (uv) or softer X-ray wavebands remains unclear."334 In particular. moderately ionized outflows identified in soft X-ray spectra generally have somewhat lower velocity (=1000 km s.1: 2.. 2») while uv spectra can show evidence of either low or high velocity absorption (e.g. 19.," In particular, moderately ionized outflows identified in soft X-ray spectra generally have somewhat lower velocity $\simlt 1000$ km $^{-1}$; \citealt{blustin05}, \citealt{mckernan07}) ) while uv spectra can show evidence of either low or high velocity absorption (e.g. \citealt{elvis00}) )."335 As observational evidence in support of the phenomenon has accumulated. several theoretical studies of the physical properties of highly ionized AGN outflows have been made.," As observational evidence in support of the phenomenon has accumulated, several theoretical studies of the physical properties of highly ionized AGN outflows have been made."336 ? and discussed the blueshifted absorption features in PGI211I4143 in terms of a conical outflow subtending a large solid angle., \citet{pounds03} and \citet{king03} discussed the blueshifted absorption features in PG1211+143 in terms of a conical outflow subtending a large solid angle.337 They suggested that such a flow might be driven by continuum radiation pressure and that emission from such a flow might be responsible for the big blue bump which dominates the bolometric output of PGI2114143., They suggested that such a flow might be driven by continuum radiation pressure and that emission from such a flow might be responsible for the big blue bump which dominates the bolometric output of PG1211+143.338 However. ? considered flows driven by continuum radiation pressure in greater detail and concluded that. while this mechanism could work in principle. the resulting outflows were unlikely to produce spectral signatures as strong as those reported by ?..," However, \citet{everett04} considered flows driven by continuum radiation pressure in greater detail and concluded that, while this mechanism could work in principle, the resulting outflows were unlikely to produce spectral signatures as strong as those reported by \citet{pounds03}."339 ? undertook a two-dimensional (2D) Monte Carlo (MC) radiative transfer study of parameterised conical outflow models and concluded that. for suitable column densities. viewing down such flows could account for the observed blueshifted. narrow absorption lines in PGI2114143.," \citet{sim05b} undertook a two-dimensional (2D) Monte Carlo (MC) radiative transfer study of parameterised conical outflow models and concluded that, for suitable column densities, viewing down such flows could account for the observed blueshifted, narrow absorption lines in PG1211+143."340 However. that study was limited to consideration of only the simplest conical geometry and did not consider theeffect of either rotation oroff-axis lines-of-sight on the spectrum.," However, that study was limited to consideration of only the simplest conical geometry and did not consider theeffect of either rotation oroff-axis lines-of-sight on the spectrum."341 Using a chained version of the ID XSTAR code (2).. 22 have," Using a chained version of the 1D XSTAR code \citep{kallman01}, , \citet{schurch07,schurch08} have"342Belezvuskily.. 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Davies,M.B. 1999a, ApJ, 520,"346 We begin our observational-theoretical comparison with the Simple Model (??) of Galactic chemical evolution.,"	 We begin our observational-theoretical comparison with the Simple Model \citep{Searle1972ApJ,Pagel1975MNRAS} of Galactic chemical evolution."347 It describes the basic form of a closed system which evolves from initially zero-metallicity gas and remains chemically homogeneous at all times., It describes the basic form of a closed system which evolves from initially zero-metallicity gas and remains chemically homogeneous at all times.348 ? extended this model such that star formation ends once the gas is either consumed or removed (essentially relaxing the closure requirement of the system)., \citet{Hartwick1976ApJ} extended this model such that star formation ends once the gas is either consumed or removed (essentially relaxing the closure requirement of the system).349" Here we make use of this model as parameterized by the effective yield, yer, and adopting the same value as in Paper V, logio yeg=—1.7."," Here we make use of this model as parameterized by the effective yield, $y_{\mbox{\scriptsize eff}}$, and adopting the same value as in Paper V, $_{10}$ $y_{\mbox{\scriptsize eff}}=-1.7$."350 The result is shown in Figure 8.., The result is shown in Figure \ref{fig:HES_SM}. .351" As can be seen, the modified Simple Model is able to fit the position —2.0)) but not the height of the peak."," As can be seen, the mass-loss modified Simple Model is able to fit the position ) but not the height of the peak."352" It does, however, well fit the general shape of MDF tail with from -2.7 through —3.6, although it can only predict a smooth drop of the metal-poor tail at—3."," It does, however, well fit the general shape of MDF tail with from $-2.7$ through $-3.6$, although it can only predict a smooth drop of the metal-poor tail at."3536.. This is not entirely unexpected considering the fact that the real Galactic halo(s) could certainly be more complicated than a simple one-zone model assuming the Instantaneous Recycling Approximation (IRA-?).., This is not entirely unexpected considering the fact that the real Galactic halo(s) could certainly be more complicated than a simple one-zone model assuming the Instantaneous Recycling Approximation \citep[IRA -- ][]{Tinsley1980}.354" ? addressed the effect of the IRA in the determination of the MDF of a system such as the Milky Way and suggested a physically motivated modification to the simple outflow model, i.e., a composite model adopting a relaxed IRA, and assuming both early infall and outflow to solve the so-called *G dwarfproblem""."," \citet{Prantzos2003AA} addressed the effect of the IRA in the determination of the MDF of a system such as the Milky Way and suggested a physically motivated modification to the simple outflow model, i.e., a composite model adopting a relaxed IRA, and assuming both early infall and outflow to solve the so-called “G dwarfproblem”."355" Based on this model, and the further accumulation of observational data, ? presented a semi-analytical model in the framework of the hierarchical merging paradigm for structure formation which assumes that the Galactic halo is composed of the stellar debris of several sub-halos following either the Observed properties of dwarf galaxies or a structure formation calculation."," Based on this model, and the further accumulation of observational data, \citet{Prantzos2008AA} presented a semi-analytical model in the framework of the hierarchical merging paradigm for structure formation which assumes that the Galactic halo is composed of the stellar debris of several sub-halos following either the observed properties of dwarf galaxies or a structure formation calculation."356" As shown in Figure 9,, both the composite model with an early phase of gas infall by ? and the hierarchical merging scenario for the formation by ? fit the shape of the observed MDF tail between —2.9 and —3.4 rather well."," As shown in Figure \ref{fig:HES_Pt}, both the composite model with an early phase of gas infall by \citet{Prantzos2003AA} and the hierarchical merging scenario for the formation by \citet{Prantzos2008AA} fit the shape of the observed MDF tail between $-2.9$ and $-3.4$ rather well."357" However, the location of the peak of the MDF is not correctly predicted in either case and neither of them reproduces the sharp drop at—3."," However, the location of the peak of the MDF is not correctly predicted in either case and neither of them reproduces the sharp drop at."358"6.. Rather, they predict a smooth decrease of numbers of EMP stars which extend to—4."," Rather, they predict a smooth decrease of numbers of EMP stars which extend to."359"0.. Besides models based on variations of the chemical evolution scheme of the Simple Model, there are quite a number of other models based on theoretical analyses or simulations."," Besides models based on variations of the chemical evolution scheme of the Simple Model, there are quite a number of other models based on theoretical analyses or simulations."360 Here we compare our observation with two such theoretical predictions., Here we compare our observation with two such theoretical predictions.361" The first considered is the model of ? which focuses on the metal-poor tail with —3.0,, and attempts to explainthe"," The first considered is the model of \citet{Karlsson2006ApJL} which focuses on the metal-poor tail with , and attempts to explainthe"362that the observed IRAS flux can be coutaminated by the neighboring nenmbers of the viplet.,that the observed IRAS flux can be contaminated by the neighboring members of the triplet.363 Even iu the case where we divide the SER and LZrigLp estimates by 3 (roughly). ANE 1931-563 is a galaxy wih very active star formalon.," Even in the case where we divide the SFR and $L_{FIR}/L_B$ estimates by 3 (roughly), AM 1934-563 is a galaxy with very active star formation."364 Fie., Fig.365 5 shows the enuüssiou-line rotation curve of he ealaxy (after correction for the cosinological stretch)., 5 shows the emission-line rotation curve of the galaxy (after correction for the cosmological stretch).366 Thin solid liue iu the bottom panel is a fit by au exponential disk with h(R)=171 01 spe) aud intrinsic axial ratio 0.2 (Monnet Siuicu 1977)., Thin solid line in the bottom panel is a fit by an exponential disk with $h(R)=4\farcs1$ (3.1 kpc) and intrinsic axial ratio 0.2 (Monnet Simien 1977).367" It can be seen that the exponcutial disk approximation gives a σου. description of the observed rotation curve within 12"" (9 kpc) from the nucleus.", It can be seen that the exponential disk approximation gives a good description of the observed rotation curve within $''$ (9 kpc) from the nucleus.368" The maxiumui rotation velocity of the galaxy obtaiue IS V,,4,5195 kimi .", The maximum rotation velocity of the galaxy obtained is $_{max}$ =195 km $^{-1}$.369" The actial V,,4, value can be somewhat arecr due to peculiar appearance of the ealaxy aud uncertain inclination.", The actual $_{max}$ value can be somewhat larger due to peculiar appearance of the galaxy and uncertain inclination.370" The TillyFisher relation xediets that the extinetion-corrected Iunuimositv of a galaxwv with V,,,—195 xli tis MB)x21 (Tully ο al.", The Tully–Fisher relation predicts that the extinction-corrected luminosity of a galaxy with $_{max}$ =195 km $^{-1}$ is $M(B)\approx-21$ (Tully et al.371 1998. Ikaunappan et al.," 1998, Kannappan et al."372 2002)., 2002).373 Therefore. AAT 193-563 equatorial disk lies close to the TullyFisher relation for normal spirals (at least. in the first order approximation).," Therefore, AM 1934-563 equatorial disk lies close to the Tully–Fisher relation for normal spirals (at least, in the first order approximation)."374 Assuming a spherical mass distribution and a flat rotation curve within the optical radius (Rog=19 kpc). we can estimate the AAI 1931-563 mass as L.GS s 105b AL:.," Assuming a spherical mass distribution and a flat rotation curve within the optical radius $_{26}$ =19 kpc), we can estimate the AM 1934-563 mass as 1.68 $\times$ $^{11}$ $_{\sun}$."375 Therefore. the 1iass-to-Iuninositv ratio in the D passband is Lin solar units a rather normal value for a eiaut spiral ealaxy.," Therefore, the mass-to-luminosity ratio in the $B$ passband is 4 in solar units – a rather normal value for a giant spiral galaxy."376 Fie., Fig.377 G presents a deep contour nap of AAT 1931-562., 6 presents a deep contour map of AM 1934-563.378" The most fascinating feature of the eaANV is a elaut (optical diameter reaches G0"" or 15 kx) iucliued S-shaped structure which crosses he nsedn body.", The most fascinating feature of the galaxy is a giant (optical diameter reaches $''$ or 45 kpc) inclined S-shaped structure which crosses the main body.379 Frou the morphological poiut of view. the off-plane structure resenibles the polar rings or disks of the polar-ring galaxies (sce examples in the PRC).," From the morphological point of view, the off-plane structure resembles the polar rings or disks of the polar-ring galaxies (see examples in the PRC)."380 The aypearance of AAT 563 is very siuilar to NCC 660 (see Fie., The appearance of AM 1934-563 is very similar to NGC 660 (see Fig.381 1 iun van Dricl et al., 1 in van Driel et al.382 1995)., 1995).383 But. in contrast to NCC 660 which is a sub-L ealaxy. AM. 1931-563 is a giant spiral galaxy.," But, in contrast to NGC 660 which is a $L^*$ galaxy, AM 1934-563 is a giant spiral galaxy."384 Tje ring is very faint., The ring is very faint.385 Even the brightest iuuer parts show p(B)zz21 (Fig., Even the brightest inner parts show $\mu(B) \approx 24$ (Fig.386 1c)., 4c).387 As the main galaxy. the ring shows a color eracdicut (Fig.," As the main galaxy, the ring shows a color gradient (Fig."388 Id)., 4d).389 T16 polar ring (or polar disk) shows a strong warp., The polar ring (or polar disk) shows a strong warp.390 Its inner part is inclined about 57° with respect to the ANL 1931-563 major axis and the outer one is inclined abou (27., Its inner part is inclined about $^{\rm o}$ with respect to the AM 1934-563 major axis and the outer one is inclined about $^{\rm o}$ .391About a decade ago. pulsations in hot subdwarfs (sdB) were discovered by astronomers at the South. African. Astronomical Observatory series).,"About a decade ago, pulsations in hot subdwarfs (sdB) were discovered by astronomers at the South African Astronomical Observatory ."392 At present. there are two classes of pulsating hot subdwarfs (SdBVs) known: HHya and 11716 stars.," At present, there are two classes of pulsating hot subdwarfs (sdBVs) known: Hya and 1716 stars."393 The former pulsate in p modes which have short periods. typically a few minutes long. the latter. in g modes which have periods an order of magnitude longer.," The former pulsate in p modes which have short periods, typically a few minutes long, the latter, in g modes which have periods an order of magnitude longer."394 Some HHya stars show relatively large amplitudes. reaching or even exceeding 50 mmag in Y. while for 11716 stars only low-amplitude modes are observed.," Some Hya stars show relatively large amplitudes, reaching or even exceeding 50 mmag in $V$, while for 1716 stars only low-amplitude modes are observed."395 The two classes also have slightly different effective temperatures. V361 Hya stars are on average hotter than 11716 stars.," The two classes also have slightly different effective temperatures, V361 Hya stars are on average hotter than 1716 stars."396 Considering the poorly understood evolutionary history of sdB stars. it is very important to obtain information on their internal structure whenever possible.," Considering the poorly understood evolutionary history of sdB stars, it is very important to obtain information on their internal structure whenever possible."397 The discovery of pulsations in sdB stars has opened a new avenue to probe their interiors by means of seismic techniques., The discovery of pulsations in sdB stars has opened a new avenue to probe their interiors by means of seismic techniques.398 However. a prerequisite of a successful application of asteroseismology is detection of at least several modes which are properly identified in terms of their pulsation geometry.," However, a prerequisite of a successful application of asteroseismology is detection of at least several modes which are properly identified in terms of their pulsation geometry."399 The identification can be carried out using different methods that utilize photometric or spectroscopic data or a combination of both., The identification can be carried out using different methods that utilize photometric or spectroscopic data or a combination of both.400 For sdBV stars. spectroscopic methods have an extra layer of difficulty because the currently known objects are fainter than Vom II2 mag. and they all have very short pulsation periods.," For sdBV stars, spectroscopic methods have an extra layer of difficulty because the currently known objects are fainter than $V\,\approx$ 12 mag, and they all have very short pulsation periods."401 Good time-resolved spectroscopic observations can therefore only be obtained using large telescopes., Good time-resolved spectroscopic observations can therefore only be obtained using large telescopes.402 For this reason. there have been many attempts to use only (multicolour) photometric data to identify modes in sdBV stars.," For this reason, there have been many attempts to use only (multicolour) photometric data to identify modes in sdBV stars."403 In particular. methods that compare observed and theoretical behaviours of pulsation amplitude with wavelength have been used to constrain the spherical degree. {.," In particular, methods that compare observed and theoretical behaviours of pulsation amplitude with wavelength have been used to constrain the spherical degree, $\ell$."404 For example. such applications have been presented by for KPD22109—H0I. for 00039-4302 and for. 000144067.," For example, such applications have been presented by for 2109+4401, for 0039+4302 and for 0014+067."405.. Unfortunately. photometric data are limited because the amplitude ratios of modes with different / sometimes have very similar wavelength dependence2004).. and therefore this does not lead to an adequate discrimination of f.," Unfortunately, photometric data are limited because the amplitude ratios of modes with different $\ell$ sometimes have very similar wavelength dependence, and therefore this does not lead to an adequate discrimination of $\ell$."406 In the best case. only some possibilities could be rejected2006).," In the best case, only some possibilities could be rejected."407. Despite the difficulties in. obtaining good-quality. time-resolved spectra for sdBV stars. spectroscopic time-series data have been obtained for some of the brightest objects: for example. 116054072 = 3338 Ser 2003).. KPD221094-H0]. and PB 87832000). PG1627+017 or Balloon 090100001TOO6).," Despite the difficulties in obtaining good-quality, time-resolved spectra for sdBV stars, spectroscopic time-series data have been obtained for some of the brightest objects: for example, 1605+072 = 338 Ser , 2109+4401 and PB 8783, PG1627+017 or Balloon 090100001."408. In this paper we show that the method of can be successfully applied to the extremely interesting pulsating subdwarf BalQ9., In this paper we show that the method of can be successfully applied to the extremely interesting pulsating subdwarf Bal09.409 Bal09 is presently the brightest known sdBV star., Bal09 is presently the brightest known sdBV star.410 Its pulsations were found by from a single night of photometric data., Its pulsations were found by from a single night of photometric data.411 The main mode detected in this star has a, The main mode detected in this star has a412"ddata probe the same regions as the oobservations of |KITO7|, namely the outer parts of star-forming cores, referred to by KTTO7] as theirenvelopes.","data probe the same regions as the observations of \citetalias{hkirk07}, namely the outer parts of star-forming cores, referred to by \citetalias{hkirk07} as their."413" This is probably because of ffreeze-out in the dense, cold interiors of star-forming cores."," This is probably because of freeze-out in the dense, cold interiors of star-forming cores."414 Such regions should see an enhancement in the abundance of say rrelative to, Such regions should see an enhancement in the abundance of say relative to.415C!80.. investigated this possibility for their similar population of candidate cores in Perseus by measuring the variation in the integrated rratio with peak SCUBA flux density (an approximate proxy for central vvolume density)., \citetalias{hkirk07} investigated this possibility for their similar population of candidate cores in Perseus by measuring the variation in the integrated ratio with peak SCUBA flux density (an approximate proxy for central volume density).416" They found high rratios llittle ddepletion) occurred mainly in starless cores, which have the smallest SCUBA fluxes llowest densities), whereas high-flux cores (mainly protostars) have low ratios suggesting high levels of ddepletion."," They found high ratios little depletion) occurred mainly in starless cores, which have the smallest SCUBA fluxes lowest densities), whereas high-flux cores (mainly protostars) have low ratios suggesting high levels of depletion."417" Given that our starless and protostellar C!80 distributions are quite similar, we may also conclude that protostars do not affect their environment significantly."," Given that our starless and protostellar $^{18}$ O distributions are quite similar, we may also conclude (like \citetalias{hkirk07}) ) that protostars do not affect their environment significantly."418" The (like[KTTO7))starless distribution may differ from the true prestellar one as starless clumps with the largest linewidths are likely to beunbound,, and thus the true turbulent fractions will be smaller."," The starless distribution may differ from the true prestellar one as starless clumps with the largest linewidths are likely to be, and thus the true turbulent fractions will be smaller."419" Finally, we also note little correspondence with the simulations of (2005). whose results for a large-scale driven (LSD) gravoturbulent model are also plotted in reffig:fturb.omp;tarl essand"," Finally, we also note little correspondence with the simulations of \citet{klessen05}, whose results for a large-scale driven (LSD) gravoturbulent model are also plotted in \\ref{fig:fturb_comp_starless} and \ref{fig:fturb_comp_proto}. ."420"s| JT O7¢laimt ohaveagood f ittothéK lessendtind. starless population, although the model was designed to match N3H* observations."," \citetalias{hkirk07} claimto have a good fit to the \citeauthor{klessen05} data with their $^{18}$ O starless population, although the model was designed to match $_2$ $^+$ observations."421" If the ddata trace material that will go on to form the final star and not just the ambient gas in which a iis embedded, the core linewidth can inform us about itsstability,, wwhether the cores are gravitationally bound."," If the data trace material that will go on to form the final star and not just the ambient gas in which a is embedded, the core linewidth can inform us about its, whether the cores are gravitationally bound."422" We can then distinguish bound, starless pprestellar cores from unbound ones that will dissipate without forming a star."," We can then distinguish bound, starless prestellar cores from unbound ones that will dissipate without forming a star."423 The virial theorem is often used to examine this stability and we will apply it to our two populations of clumps identified in ddata., The virial theorem is often used to examine this stability and we will apply it to our two populations of clumps identified in data.424" The clump virial mass, Myi;, is used as an estimate of the internal energy of the clump whilst its dust mass atmicron, Mgso, is as an estimate of the potential energy."," The clump virial mass, $M_\mathrm{vir}$, is used as an estimate of the internal energy of the clump whilst its dust mass at, $M_{850}$, is as an estimate of the potential energy."425" If we assume that the linewidths only reflect gravity and we have spherical clumps the virial theorem is where o is the average three-dimensional velocity dispersion, R the clump radiusand a a constant that depends on the form of the density profile (a derivation can be found in citealpbinneytremaine,rohlfswilson))."," If we assume that the linewidths only reflect gravity and we have spherical clumps the virial theorem is where $\sigma$ is the average three-dimensional velocity dispersion, $R$ the clump radiusand $a$ a constant that depends on the form of the density profile (a derivation can be found in \\citealp{binneytremaine,rohlfswilson}) )."426" If we assume a power law density profile, p(r)οςγ΄Ἡ, then citealp*maclaren88)): Provided the ikGENIMAG, traces the bulk of the gas with a Gaussian velocity distribution and the same non-thermallinewidth as H2,, we can estimate"," If we assume a power law density profile, $\rho(r)\propto r^{-n}$, then \\citealp*{maclaren88}) ): Provided the line of , $\Delta427v_\mathrm{C^{18}O}$, traces the bulk of the gas with a Gaussian velocity distribution and the same non-thermallinewidth as , we can estimate"428Our predictions will focus on accreting black holes with masses greater than ~10°M...,Our predictions will focus on accreting black holes with masses greater than $\simeq 10^5 M_\odot$.429" It is of course possible that a more abundant population of black holes with lower masses existed at these early times. left behind as remnants of early generations of massive Pop II stars (2).. acting as “seeds” for the observed z~6 supermassive black hole population (e.g.. ?).. and powering ""miniquasars"" (2).."," It is of course possible that a more abundant population of black holes with lower masses existed at these early times, left behind as remnants of early generations of massive Pop III stars \citep{heger/etal:2003}, acting as “seeds” for the observed $z\sim 6$ supermassive black hole population \citep[e.g.,][]{li/etal:2007}, and powering “miniquasars” \citep{madau/etal:2004}."430 However. radiative feedback from the progenitor stars (2). as well as the accretion radiation itself (2)... would have likely substantially limited their growth and corresponding X-ray emission at early times.," However, radiative feedback from the progenitor stars \citep{johnson/bromm:2007} as well as the accretion radiation itself \citep{alvarez/etal:2009a}, would have likely substantially limited their growth and corresponding X-ray emission at early times."431 An alternative scenario for forming the seeds is gaseous collapse to black holes with masses greater than ~10M. in the first halos with virial temperature greater than ~10 K (e.g..??)..," An alternative scenario for forming the seeds is gaseous collapse to black holes with masses greater than $\simeq 10^4 M_\odot$ in the first halos with virial temperature greater than $\simeq 10^4$ K \citep[e.g.,][]{bromm/loeb:2003,begelman/etal:2006}."432 Formation of black holes by this mechanism may have been quite a rare occurence (e.g..2)..," Formation of black holes by this mechanism may have been quite a rare occurence \citep[e.g.,][]{dijkstra/etal:2008}."433 It is this scenario. in which most accreting black holes in the universe were relatively rare and more massive than ~10°... that is most consistent with the predictions we make here.," It is this scenario, in which most accreting black holes in the universe were relatively rare and more massive than $\simeq 10^5 M_\odot$, that is most consistent with the predictions we make here."434 Because the heating is a time-dependent effect. we will parametrize the total energy radiated during accretion as £j=Ltoso= eMyyc. where we take the radiative efficiency εΞ0.1.," Because the heating is a time-dependent effect, we will parametrize the total energy radiated during accretion as $E_{\rm tot}=Lt_{\rm QSO}=\epsilon M_{\rm BH}c^2$ , where we take the radiative efficiency $\epsilon=0.1$."435 In principle some of the rest mass energy. re. the initial seed mass of the black hole. did not contribute to heating the surroundings. but in general the seed mass is expected to be small compared to the mass of the black hole after it undergoes its first episode of radiatively-efficient aceretion as a quasar. so we neglect it.," In principle some of the rest mass energy, i.e. the initial seed mass of the black hole, did not contribute to heating the surroundings, but in general the seed mass is expected to be small compared to the mass of the black hole after it undergoes its first episode of radiatively-efficient accretion as a quasar, so we neglect it."436" We assume the spectral energy distribution of the quasar 15 given by a broken power-law. S,»1/7? at y«my. and S,p at poog. with fim,=11.8 eV (e.g..2). approximately consistent with the template spectra of ?.."," We assume the spectral energy distribution of the quasar is given by a broken power-law, $S_\nu \propto \nu^{-0.5}$ at $\nu<\nu_{\rm b}$, and $S_\nu \propto \nu^{-1.5}$ at $\nu>\nu_{\rm b}$, with $h\nu_{\rm b}=11.8$ eV \citep[e.g.,][]{bolton/haehnelt:2007b}, approximately consistent with the template spectra of \citet{telfer/etal:2002}."437 If the quasar has a total bolometric luminosity Z. then the spectral energy distribution is(," If the quasar has a total bolometric luminosity $L$, then the spectral energy distribution is."4382) The temperature profile surrounding a quasar can be obtained by considering the fraction of the radiated energy absorbed per atom at comoving distance r and redshift z.Tig — whichgoesintoheat.| — withtherestbeingl XU adis," The temperature profile surrounding a quasar can be obtained by considering the fraction of the radiated energy absorbed per atom at comoving distance $r$ and redshift $z$,, which goes into heat, with the rest being lost to secondary ionizations and excitations."439 ENA oasisow. for all fv>25. eV (?)..," In the limit in which the ionized fraction of the gas is low, $0.1 < \chi_\nu < 0.3$ for all $h\nu>25$ eV \citep{shull/vansteenberg:1985}."440" In what follows we will make the approximation that S,=0.2 for all 7. and assume that the energy radiated is Lr,=eMyyc. with lo short compared to the Hubble time."," In what follows we will make the approximation that $S_\nu = 0.2$ for all $\nu$, and assume that the energy radiated is $Lt_{\rm qso}\equiv441\epsilon M_{\rm BH}c^2$, with $t_{\rm qso}$ short compared to the Hubble time."442" In this case. the relative brightness temperature is given by VIOnz=29mK Lppa where In calculating the optical depth. we assume that the IGM is completely neutral at the mean density. ης). so that Ths)radzrlo,."," In this case, the relative brightness temperature is given by ,r,z)=29 ], where In calculating the optical depth, we assume that the IGM is completely neutral at the mean density, $n_{\rm H}(z)$, so that $\tau_\nu(r,z)=rn_{\rm H}(z)(1+z)^{-1}\sigma_\nu$."443" In reality. the quasar’s own H Il news, NEOPA ALN ΡΕ do Wie are osttosecondarvionizatidRSaconcernedyd with the small amount of heating happening at much larger radii. we neglect the H II region when calculating the optical depth."," In reality, the quasar's own H II region will reduce the opacity at small radii, but given that we are concerned with the small amount of heating happening at much larger radii, we neglect the H II region when calculating the optical depth."444 Shown in Fig., Shown in Fig.445 | are profiles of the observed differential brightness temperature versus comoving distance at three different redshifts., \ref{fig1} are profiles of the observed differential brightness temperature versus comoving distance at three different redshifts.446 The total energy radiated by the quasar. Ltogso in each curve corresponds to [0 per cent of the rest mass. as labeled.," The total energy radiated by the quasar, $Lt_{\rm QSO}$ in each curve corresponds to 10 per cent of the rest mass, as labeled."447" Close to the quasar. the gas is heated above the CMB temperature. and 67),~30-40 mK. Further away. the heating from the quasar declines due to spherical dilution"," Close to the quasar, the gas is heated above the CMB temperature, and $\delta448T_b\simeq 30-40$ mK. Further away, the heating from the quasar declines due to spherical dilution"449origin.,origin.450 Table 2. is the resulting continecucy table., Table \ref{tbl:contingency} is the resulting contingency table.451 Three rows are eiven for SNRs with masers preseut. absent or not surveyed.," Three rows are given for SNRs with masers present, absent or not surveyed."452 Two colmuuus divide SNRs with aud without coimcident x-ray cletections., Two columns divide SNRs with and without coincident $\gamma$ -ray detections.453" Each of the two colunus lists the “Number” of SNRs which meet both classifications. the nunuber ""Expected frou, Counts” assiunuiue the maser aud y-ray properties of remmants are completely independent. aud 7Coutribution to V77 which eives the 47. (observed expected)? /(expected)."," Each of the two columns lists the ""Number"" of SNRs which meet both classifications, the number ""Expected from Counts"" assuming the maser and $\gamma$ -ray properties of remnants are completely independent, and ""Contribution to $\chi^2$ "" which gives the $\chi^2$, (observed – $^2$ /(expected)."454 For this test the total 4 is 31 with— two degrees of freedom., For this test the total $\chi^2$ is 31 with two degrees of freedom.455 This eives a probability of «0.000 that SNR umasers aud -rav counterparts to SNRs are not correlated., This gives a probability of $<$ $\%$ that SNR masers and $\gamma$ -ray counterparts to SNRs are not correlated.456 We note that two of the expected cell frequencies are less than five., We note that two of the expected cell frequencies are less than five.457 To be statistically rigorous we also apply the Fisher Exact Probability Test iu additiou to the \? Test., To be statistically rigorous we also apply the Fisher Exact Probability Test in addition to the $\chi^2$ Test.458 The Fisher test cousiders all possible outcomes of the contingency table in order to determine the probability of finding a correlation at least as strong as ds observed., The Fisher test considers all possible outcomes of the contingency table in order to determine the probability of finding a correlation at least as strong as is observed.459 Here again we find a clear rejection of independence between οταν aud maser detections iu SNRs. with a probability of 0.00254.," Here again we find a clear rejection of independence between $\gamma$ -ray and maser detections in SNRs, with a probability of $\%$."460 The two classes are clearly associated., The two classes are clearly associated.461 A similarcontingency table analysis was used to quantify au association between SNR masers aud uorphologv remumauts. a class of SNRs with shell-ype radio morphologies with prominent thermal N-rav cluission from their interiors (YusefZacdeletal.2003).," A similarcontingency table analysis was used to quantify an association between SNR masers and mixed-morphology remnants, a class of SNRs with shell-type radio morphologies with prominent thermal X-ray emission from their interiors \citep{fyz03mmsnr}."462. Both classes of remnants are thought to result from interaction with dense eas aud are strongly correlated., Both classes of remnants are thought to result from interaction with dense gas and are strongly correlated.463 Of the iceutifed 5-rav SNRs. 9 are classified as both uixedauorphologw and maser-enuütting. 2 are nmüxed-uorphologv without detected masers (SNRs WL9B aud MSIE. 11-61À).. and only SNR 65.7-0.0.— has detected nmiasers but uo N-rav detection.," Of the identified $\gamma$ -ray SNRs, 9 are classified as both mixed-morphology and maser-emitting, 2 are mixed-morphology without detected masers (SNRs W49B and MSH 11-61A), and only SNR G5.7-0.0 has detected masers but no X-ray detection."464 Therefore. either classification produces a nearly ideutically good correlation with 5-rav SNRs.," Therefore, either classification produces a nearly identically good correlation with $\gamma$ -ray SNRs."465 Both N-ravs ancl cosmic ravs are capable of providing the ionization needed to produce SNR. imasers., Both X-rays and cosmic rays are capable of providing the ionization needed to produce SNR masers.466 Detailed discussion is given iu Section ?7.., Detailed discussion is given in Section \ref{sec:ionization}.467 An additional complication arises in that mauv SNRs have associated pulsars with their own wind nebulae that are also capable of accelerating particles to Τον energies., An additional complication arises in that many SNRs have associated pulsars with their own wind nebulae that are also capable of accelerating particles to TeV energies.468 To account for this we separate the οταν SNRs into two categories based on whether a PWN is or is not also detected., To account for this we separate the $\gamma$ -ray SNRs into two categories based on whether a PWN is or is not also detected.469 This reduces the number of sources that fall under cach classification. lowering the probability of independence from the Fisher test to still significant enough to reject the nul hypothesis.," This reduces the number of sources that fall under each classification, lowering the probability of independence from the Fisher test to $\%$, still significant enough to reject the null hypothesis."470 Furthermore. there is evidence that at least four SNRs (see Table 1.. “Group AX) are associatec with 2-rav emission from the SNR-cloud iuteraction. ai uot the PWN.," Furthermore, there is evidence that at least four SNRs (see Table \ref{tbl:list}, ""Group A"") are associated with $\gamma$ -ray emission from the SNR-cloud interaction, and not the PWN."471 Dhuproved spatial resolution is needed. to ciseriuinate between x-ray chussion from the PWN anc SNR. but we note that there are πο markedly ciffereut characteristics between the two groups of SNRs with au without PAWN.," Improved spatial resolution is needed to discriminate between $\gamma$ -ray emission from the PWN and SNR, but we note that there are no markedly different characteristics between the two groups of SNRs with and without PWN."472 For SNRs interacting with dense gas 542a counterparts are likely to be dominated by einissiou from ueutral pion decay originating frou mteractions between hadronic cosmic ravs aud eas uuclei.," For SNRs interacting with dense gas, $\gamma$ -ray counterparts are likely to be dominated by emission from neutral pion decay originating from interactions between hadronic cosmic rays and gas nuclei."473 Iu coutrast to vouug SNRs. older interacting SNRs have little if anv detected Neray svuchnrotroun cussion.," In contrast to young SNRs, older interacting SNRs have little if any detected X-ray synchrotron emission."474 Απ inverse-Comptou scenario requires small magnetic field strengths «1 pC (Yamazakietal.2006) whereas Zeeman splitting of SNR inasers nieasures field streueths of order ~1 iG (Yuset-Zadehctal.1996:Claussenet1997:Broganal. 2000).," An inverse-Compton scenario requires small magnetic field strengths $<$ 1 $\mu$ G \citep{yamazaki06} whereas Zeeman splitting of SNR masers measures field strengths of order $\sim$ 1 mG \citep{fyz96,claussen97,brogan00}."475. Electronic brenmisstrahluus cussion has so been proposed. but the expectation would be for -rav conusson to trace the radio shell morphologv (Bykovetal.2000).," Electronic bremsstrahlung emission has also been proposed, but the expectation would be for $\gamma$ -ray emission to trace the radio shell morphology \citep{bykov00}."476. TeV emission from W28 aud IC 113 shows no correlation with the radio shell. anc an excellent correlation with dense eas (Abaronianetal2008b:Ácciuial. 2009).," TeV emission from W28 and IC 443 shows no correlation with the radio shell, and an excellent correlation with dense gas \citep{hess_w28,veritas_ic443}."477. Forthcoming Fermi observations will have suffiicicut resolution to resolve this question at CieV. enereies., Forthcoming Fermi observations will have sufficient resolution to resolve this question at GeV energies.478 The presence of a laree reservoir of dense eas around the SNR. the expectation that cosmic ravs are accelerated by SNRs. aud the relatively older ages of this subset of interacting SNRs supports a pion decay. origi for *-xav counterparts.," The presence of a large reservoir of dense gas around the SNR, the expectation that cosmic rays are accelerated by SNRs, and the relatively older ages of this subset of interacting SNRs supports a pion decay origin for $\gamma$ -ray counterparts."479 The morphology of 5-xay cussion is seen to be well matched to that of the molecular cloud., The morphology of $\gamma$ -ray emission is seen to be well matched to that of the molecular cloud.480 In Figure 1.. listograms of y-ray Iuuiünosity show jiediaus of «1076 eres 1 and «107 eres + for GeV and TeV detections. respectively.," In Figure \ref{fig:histo}, histograms of $\gamma$ -ray luminosity show medians of $\times$ $^{36}$ ergs $^{-1}$ and $\times$ $^{33}$ ergs $^{-1}$ for GeV and TeV detections, respectively."481 This is consisteut with Iuninositv estimates if a significant fraction of the SN enerev )) is diverted to cosuiic-ravs which are incident on the adjacent molecular cloud (Druryetal. 1991)., This is consistent with luminosity estimates if a significant fraction of the SN energy ) is diverted to cosmic-rays which are incident on the adjacent molecular cloud \citep{drury94}.482. The orders of magnitude differences in the hunuinositv reflect the expected energy spectrum of accelerated particles., The orders of magnitude differences in the luminosity reflect the expected energy spectrum of accelerated particles.483 On average a hardening of the pliotou spectrmm frou GeV to TeV energies is also observed., On average a hardening of the photon spectrum from GeV to TeV energies is also observed.484 The 5-ray spectral index. eiven in colhunus 7 aud 9 of Table L.. steepen at higher energies from a mean of ἄν~ 2.1 to," The $\gamma$ -ray spectral index, given in columns 7 and 9 of Table \ref{tbl:list}, , steepen at higher energies from a mean of $\alpha_{GeV} \sim$ 2.1 to"485"the angular impact parameter between source and lens, in units of Og, is u, then two images are produced on the sky along the lens-source axis at positions relative to the lens of These images are magnified relative to the intrinsic source brightness by factors respectively.","the angular impact parameter between source and lens, in units of $\thetaE$, is $u$, then two images are produced on the sky along the lens-source axis at positions relative to the lens of These images are magnified relative to the intrinsic source brightness by factors respectively."486" The total magnification is the sum of these two terms, In general, the lens and source exhibit finite relative proper motion, meaning that the impact parameter is a function of time."," The total magnification is the sum of these two terms, In general, the lens and source exhibit finite relative proper motion, meaning that the impact parameter is a function of time."487" Usually, the relative motion is well approximated as linear in time, and can be written u(t)=Unin+wt/te, measuring t with respect to the time of smallest impact parameter u,»in."," Usually, the relative motion is well approximated as linear in time, and can be written ${\bm u}(t) = {\bm u}_{\rm min} + {\bm\mu}t/\tE$, measuring $t$ with respect to the time of smallest impact parameter ${\bm488u}_{\rm min}$."489" Here, tg is the event timescale, the time it takes the lens to move one angular Einstein radius relative to the observer-source line of sight, and p is the unit vector on the sky along the relative velocity."," Here, $\tE$ is the event timescale, the time it takes the lens to move one angular Einstein radius relative to the observer-source line of sight, and ${\bm\mu}$ is the unit vector on the sky along the relative velocity."490 Eqns., Eqns.491 2 and 3 then give x;(t) and Αι.)as a function of time.," \ref{x} and \ref{A} then give $x_{1,2}(t)$ and $A_{1,2}(t)$as a function of time."492 An example is shown in Fig. 1.., An example is shown in Fig. \ref{lensgeom}. .493In order to derive an upper limit to the merger rate. we take the observed detections and use the binomial distribution.,"In order to derive an upper limit to the merger rate, we take the observed detections and use the binomial distribution."494" For large samples CN.>100) the error distribution is given by (Burgasseretal. 2003): where e; is the pair fraction. #7 is the number of pairs. .V is the number of objects in the sample. 6 is the upper Lo probability limit to the pair fraction and eb is the lower 1o probability limit to the pair fraction,"," For large samples $N > 100$ ) the error distribution is given by \citep{burgasser03}: : where $\epsilon_b$ is the pair fraction, $n$ is the number of pairs, $N$ is the number of objects in the sample, $\epsilon^U_b$ is the upper $1\sigma$ probability limit to the pair fraction and $\epsilon^L_b$ is the lower $1\sigma$ probability limit to the pair fraction."495 The region between ej and corresponds to the confidence interval for e; for a εξGaussian distribution., The region between $\epsilon^U_b$ and $\epsilon^L_b$ corresponds to the confidence interval for $\epsilon_b$ for a Gaussian distribution.496 In order to obtain aconservative upper limit we decide to use both pairs that we actually find (even though one of these is not within the valid range of separations)., In order to obtain aconservative upper limit we decide to use both pairs that we actually find (even though one of these is not within the valid range of separations).497" For)= 2and NV=7889 this yields N,.=0.09LEO.06654."," For $n=2$ and $N=7889$ this yields $N_c=0.094 \pm 0.066\,\%$."498 The systematic error due to the three possible extra pairs is 0.1Edc0.084., The systematic error due to the three possible extra pairs is $0.14 \pm 0.08\%$.499 We can therefore quote a So upper limit to the pair fraction of 0.11% (random) plus 0.5l4. (systematic). for a total of 1.054.," We can therefore quote a $\sigma$ upper limit to the pair fraction of $0.44\%$ (random) plus $0.54\%$ (systematic), for a total of $1.0\%$."500 As à check. we estimate the pair fraction in each of the separate 28LAQ survey patches: while most regions have no pairs. in one area we find a pair fraction of 0.30%. which is consistent with the upper limit we derived above.," As a check, we estimate the pair fraction in each of the separate 2SLAQ survey patches: while most regions have no pairs, in one area we find a pair fraction of $0.30\%$, which is consistent with the upper limit we derived above."501" Finally. we can also consider pairs with wider separation in both projected distance and velocity: /,,«50%+ kpe and Ae«1000 km +."," Finally, we can also consider pairs with wider separation in both projected distance and velocity: $r_p < 50\, h^{-1}$ kpc and $\Delta v < 1000$ km $^{-1}$."502 This considerably increases the number of contaminants (unphysical pairs). as shown by POO and DeProprisetal. (2007).," This considerably increases the number of contaminants (unphysical pairs), as shown by P00 and \cite{depropris07}."503.. However. this pair fraction may provide a further interesting constraint.," However, this pair fraction may provide a further interesting constraint."504 For the 2SLAQ sample we find 0.1354., For the 2SLAQ sample we find $N_c=0.13\%$ .505" Our upper limit to the pair fraction can be translated into a 5o upper limit to the dry merger rate using the expression: where (2) is the space density of galaxies in our sample. 0.5 is a factor introduced to avoid double counting galaxies (1 pair contains 2 galaxies). ον Is the probability that pairs will merge (assumed to be | here) and is the merger timescale. for which we take the shortest 7,,,possible timescale set by dynamical friction."," Our upper limit to the pair fraction can be translated into a $5\sigma$ upper limit to the dry merger rate using the expression: where $n(z)$ is the space density of galaxies in our sample, 0.5 is a factor introduced to avoid double counting galaxies (1 pair contains 2 galaxies), $p_{merg}$ is the probability that pairs will merge (assumed to be 1 here) and $T_{mg}$ is the merger timescale, for which we take the shortest possible timescale set by dynamical friction."506" We find that a robust 50 upper limit to the merger rate is: <<(0.8«10ο 7 ουν! (including the systematic contribution due to the three extra photometric pairs) for galaxies with 23<M,c21.5 at 0.15«:0.65 (a period of 1.4 Gyrs in the history of the Universe)."," We find that a robust $5\sigma$ upper limit to the merger rate is: $ < 0.8 \times 10^{-5}$ $^{-3}$ $h^{-3}$ $^{-1}$ (including the systematic contribution due to the three extra photometric pairs) for galaxies with $-23 < M_r 507< -21.5$ at $0.45 < z < 0.65$ (a period of 1.4 Gyrs in the history of the Universe)."508 A more realistic merger timescale and merger fraction may decrease this estimate by more than one order of magnitude., A more realistic merger timescale and merger fraction may decrease this estimate by more than one order of magnitude.509 The low dry merger rate we measure here is in good agreement with a number of other estimates: locally. Masjedietal.(2006.2008) obtain an upper limit of <1.7 for the dry merger rate of SDSS LRGs with A/;«—22.75 and 2«0.36. a value which is consistent with ours. albeit for more luminous (massive) galaxies.," The low dry merger rate we measure here is in good agreement with a number of other estimates: locally, \cite{masjedi06,masjedi08} obtain an upper limit of $< 1.7\%$ per Gyr for the dry merger rate of SDSS LRGs with $M_i < -22.75$ and $z < 0.36$, a value which is consistent with ours, albeit for more luminous (massive) galaxies."510" This ts also similar to the dry merger rate of 0.54 measured by Wenetal.(2008). for SDSS LRGs with A,<<21.5 and :< 0.12.", This is also similar to the dry merger rate of $0.8\%$ measured by \cite{wen09} for SDSS LRGs with $M_r < -21.5$ and $z < 0.12$ .511" The integrated dry merger rate for galaxies in the Red Sequence Survey is ~6 since ;=O8 over 25«M,—20. while Bundyetal.(2009) find very low to zero likely dry mergers in GOODS data at :<1.2."," The integrated dry merger rate for galaxies in the Red Sequence Survey is $\sim 6\%$ since $z=0.8$ over $-25 < M_r < -20$, while \cite{bundy09} find very low to zero likely dry mergers in GOODS data at $z < 1.2$."512 Nevertheless there are some discrepant estimates in. the literature., Nevertheless there are some discrepant estimates in the literature.513 Apparently. the most worrying is the value of 2.l4 per Gyr for 0.19<+«0.55 LRGs from 2SLAQ derived by Wakeetal.(2008) using the small scale correlation function.," Apparently, the most worrying is the value of $2.4\%$ per Gyr for $0.19 < z < 0.55$ LRGs from 2SLAQ derived by \cite{wake08} using the small scale correlation function."514 However. Wakeetal.(2008) use LRGs over the entire range of absolute luminosities in the 28LAQ survey. and their sample therefore includes both minor mergers (luminosity ratio greater than 1:4) and less luminous objects.," However, \cite{515wake08} use LRGs over the entire range of absolute luminosities in the 2SLAQ survey, and their sample therefore includes both minor mergers (luminosity ratio greater than 1:4) and less luminous objects."516 As shown by Patton&Atfield(2008) and deRaveletal.(2008).. the merger rate increases significantly for minor mergers and less luminous galaxies.," As shown by \cite{patton08} and \cite{deravel08}, the merger rate increases significantly for minor mergers and less luminous galaxies."517" Therefore the larger value derived by Wakeetal.(2008). is not necessarily in disagreement with ours,", Therefore the larger value derived by \cite{wake08} is not necessarily in disagreement with ours.518 Linetal.(2008) apply the same method as we do (dynamically close pairs) to galaxies in the DEEP? survey and derive an integrated merger rate of 2I4 since »<1.2 for galaxies with 21<Mp19., \cite{lin08} apply the same method as we do (dynamically close pairs) to galaxies in the DEEP2 survey and derive an integrated merger rate of $24\%$ since $z < 1.2$ for galaxies with $-21 < M_B < -19$.519 Assuming a flat evolution of the merger rate (Linetal.2008).. this is equivalent to ~6% per Gyr.," Assuming a flat evolution of the merger rate \citep{520lin08}, this is equivalent to $\sim 6\%$ per Gyr."521 Here. the different luminosity ranges sampled. the bandpass difference.and the fact that dry mergers were selected by morphology. rather than by colors and spectral features as we do. may play a role in explaining the difference.," Here, the different luminosity ranges sampled, the bandpass difference,and the fact that dry mergers were selected by morphology, rather than by colors and spectral features as we do, may play a role in explaining the difference."522 Belletal.(2006a) obtain an integrated dry merger rate of NÜ'X since >=0.8 for galaxies in the Combo-17 survey with Ap< 50.9. while applying the small scale correlation function to the same data. Belletal.(2006b) derive a merger rate of LM per Gyr at 0.1—0.5.," \cite{bell06a} obtain an integrated dry merger rate of $\sim 80\%$ since $z=0.8$ for galaxies in the Combo-17 survey with $M_B < -20.5$ , while applying the small scale correlation function to the same data, \cite{bell06b} derive a merger rate of $4\%$ per Gyr at $0.4 < z < 0.8$."523 As noted by Wakeal.(2008).. the space density of objects in these surveys is 20 times greater than ours. and therefore Belletal.(2006a.b) are sampling considerably less luminous objects than we do.," As noted by \cite{wake08}, , the space density of objects in these surveys is 20 times greater than ours, and therefore \cite{bell06a,524bell06b} are sampling considerably less luminous objects than we do."525 Given the dependence of the merger rate on luminosity (Patton&Atfield2008:deRaveletal.2008) this does not mean that our results are in disagreement.," Given the dependence of the merger rate on luminosity \citep{patton08,deravel08} this does not mean that our results are in disagreement."526 In addition. Khochfar&Silk(2008) show that the above sample includes both wet and dry mergers. unlike ours where we confirm by spectroscopy that the vast majority of the sample has LRG-type spectra (Roseboometal.2006).," In addition, \cite{khochfar08} show that the above sample includes both wet and dry mergers, unlike ours where we confirm by spectroscopy that the vast majority of the sample has LRG-type spectra \citep{527roseboom06}."528 Finally. Whiteetal.(2007) measure an integrated dry merger rate of for LRGs in the NDFWS survey between 0.5<z«0.9.," Finally, \cite{white07} measure an integrated dry merger rate of for LRGs in the NDFWS survey between $0.5 < z < 0.9$."529 Thisis equivalent to a merger rate of per Gyr. but needs to be corrected for the higher mean redshift and different space density than the 2SLAQ sample.," Thisis equivalent to a merger rate of per Gyr, but needs to be corrected for the higher mean redshift and different space density than the 2SLAQ sample."530 Wakeetal.(2008) estimate that this downward revision is about a factor of 10. which places the result by Whiteetal.(2007) in good agreement with ours.," \cite{wake08} estimate that this downward revision is about a factor of 10, which places the result by \cite{white07} in good agreement with ours."531 In addition. there are several estimates of the merger rate for all galaxies using asymmetries for the DEEP? (Lotzetal.2008) and COSMOS surveys (Kampezyketal.2007).. as well as galaxies in the GOODS fields (Lopez-Sanjuan 2009).. and pairs in the COSMOS survey (Kartaltepeetal. 2007)..," In addition, there are several estimates of the merger rate for all galaxies using asymmetries for the DEEP2 \citep{lotz08} and COSMOS surveys \citep{kampczyk07}, as well as galaxies in the GOODS fields \citep{lopez09}, and pairs in the COSMOS survey \citep{kartaltepe07}. ."532 The measured merger rate is approximately 2—1'4 per Gyr for theentire population of £L.>L galaxies. of which dry mergers are only a subset. which is in agreement with our measurement.," The measured merger rate is approximately $2$ $4\%$ per Gyr for theentire population of $L > L^*$ galaxies, of which dry mergers are only a subset, which is in agreement with our measurement."533 Our result is also consistent with the more. indirect merger fraction derived from the evolution of the red galaxy lummosity function., Our result is also consistent with the more indirect merger fraction derived from the evolution of the red galaxy luminosity function.534" Note that.in this case. ""growth"" may take place via the transformation of blue galaxies into quiescentobjects. moving on to the red sequence. but without (necessarily) any major merging."," Note that,in this case, `growth' may take place via the transformation of blue galaxies into quiescentobjects, moving on to the red sequence, but without (necessarily) any major merging."535 Wakeetal.(2006)used the2SLAQ data to show that the LRG luminosity function evolves passively at.< 0.6. a result confirmed by several other studies (Bundyetal.2006:Caputi 2007)..," \cite{wake06} used the2SLAQ data to show that the LRG luminosity function evolves passively at $z < 0.6$ a result confirmed by several other studies \citep{bundy06,caputi06,cimatti06,scarlata07}. ."536 For ~15 LRGs," For $\sim 5374 L^*$ LRGs"538magnetospheric equilibrium based on full NEIID.,magnetospheric equilibrium based on full MHD.539 Instead. of it. the total magnetic Dux of the entire magnetosphere is treated as a free parameter.," Instead of it, the total magnetic flux of the entire magnetosphere is treated as a free parameter."540 This point will be discussed in section 6., This point will be discussed in section 6.541 General relativistic theory of QSO core formation is still an open question., General relativistic theory of QSO core formation is still an open question.542 Hence we do not have statistical properties of the parameters of QSO DBlIs., Hence we do not have statistical properties of the parameters of QSO BHs.543 HE we assume the statistical distributions of the DII mass m (the initial mass function). the Ixerr parameter e (the initial νους parameter function) of seed BIL and the magnetic field. strength. By at. the source region (this should. depend on the BLL mass. the accretion rate and the dynamo theory). we can sum up the contribution of each 1911 over the ensemble. and can suggest the statistical properties of QSOs/AGNs by the Kerr BIL tly-wheel moclel.," If we assume the statistical distributions of the BH mass $m$ (the initial mass function), the Kerr parameter $a$ (the initial Kerr parameter function) of seed BH and the magnetic field strength $B_0$ at the source region (this should depend on the BH mass, the accretion rate and the dynamo theory), we can sum up the contribution of each BH over the ensemble, and can suggest the statistical properties of QSOs/AGNs by the Kerr BH fly-wheel model."544 Lere we will demonstrate a preliminary application of Ixerr DII IHiv-wheel moclel to QSO statistics., Here we will demonstrate a preliminary application of Kerr BH fly-wheel model to QSO statistics.545 Lhe discussion is based on the Press-Schechter formalism. as a probable seed BIL formation scenario., The discussion is based on the Press-Schechter formalism as a probable seed BH formation scenario.546 Sasaki Umeniura (1996) discussed an additional process. the Compton drag scenario. for further angular momentum extractionto form the proto-ealactic cloud to form the seed. DIL. and suggest the initial mass function in figure 1 of their paper.," Sasaki Umemura (1996) discussed an additional process, the Compton drag scenario, for further angular momentum extractionto form the proto-galactic cloud to form the seed BH, and suggest the initial mass function in figure 1 of their paper."547 Unfortunately. the distribution of the νους parameter and the magnetic field streneth at the source region are not mentioned there.," Unfortunately, the distribution of the Kerr parameter and the magnetic field strength at the source region are not mentioned there."548 Hence we should. assume the magnetic field. strength. By at the source region and the initial Kerr parameter em as follows., Hence we should assume the magnetic field strength $B_0$ at the source region and the initial Kerr parameter $a/m$ as follows.549 The magnetic filed at the source region is usually estimated as By~ 1T] for m=10M. in order to explain typical QSO Iuminositv., The magnetic filed at the source region is usually estimated as $B_0 \sim 1$ [T] for $m=10^8 M_\odot$ in order to explain typical QSO luminosity.550 Εις value probably depends on the BIL mass. then we assume We also assume the initial Kerr parameter em~1 (nearly the extreme Werr DII at the initial stage) and the small parameter €—mOp0.1.," This value probably depends on the BH mass, then we assume We also assume the initial Kerr parameter $a/m \sim 1$ (nearly the extreme Kerr BH at the initial stage) and the small parameter $\epsilon \equiv m \Omega_F \sim 0.1$."551 Then the power output Lea is the function of m and /£ (see equation 3))., Then the power output $L_{BH}$ is the function of $m$ and $t$ (see equation \ref{eq:LBH}) ).552 Thus the only we need is the initial mass Function of BIIs., Thus the only we need is the initial mass function of BHs.553 From Sasaki Umemura (1996) we obtain the initial mass function fgg of BlIs based on the standard CDM model as where with AZ is the total (dark matter|barvon) mass of the proto-galactic cloud. po is the present total mass density. Ala=padz(16Mpcy/3.," From Sasaki Umemura (1996) we obtain the initial mass function $f_{BH}$ of BHs based on the standard CDM model as where with $M$ is the total (dark matter+baryon) mass of the proto-galactic cloud, $\rho_0$ is the present total mass density, $M_{c0}=\rho_0 4 \pi (16 \mbox{Mpc})^3/3$."554" AL is related with the DII mass n as where ©, is the fraction of the barvonic mass to the total mass and rey is the ratio of the DII mass to the bakorvonic mass.", $M$ is related with the BH mass $m$ as where $\Omega_b$ is the fraction of the baryonic mass to the total mass and $r_{BH}$ is the ratio of the BH mass to the bakoryonic mass.555" We assume po=6.910)A4. /Mpce?]. 0,=0.05 "," We assume $\rho_0=6.9 \times 10^{10} [M_\odot/\mbox{Mpc}^3]$ , $\Omega_b=0.05$ "556"We perform a separate low-resolution calculation in which we enable ionization when the system has an age of 3.7 Myr (0.64 tg), which is approximately the time when the system begins to give rise to clusters large enough to host O-stars.","We perform a separate low–resolution calculation in which we enable ionization when the system has an age of 3.7 Myr (0.64 $_{\rm ff}$ ), which is approximately the time when the system begins to give rise to clusters large enough to host O–stars."557" At this point in the system's evolution, there are eleven such clusters and these therefore form our ionizing sources."," At this point in the system's evolution, there are eleven such clusters and these therefore form our ionizing sources."558" Figure 4 shows a column-density plot as viewed down the z-axis of the system at this epoch, with white dots representing clusters."," Figure \ref{fig:init_snap} shows a column–density plot as viewed down the $z$ –axis of the system at this epoch, with white dots representing clusters."559" The gas distribution is composed of a network of dense filaments in which most of the star formation is occurring, particularly at their junctions, permeated by a froth of low-density voids."," The gas distribution is composed of a network of dense filaments in which most of the star formation is occurring, particularly at their junctions, permeated by a froth of low–density voids."560" In Figure 5,, plotted to the same linear dimensions, we show the positions of the ionizing sources (obviously as time progresses and clusters accrete, more objects acquire enough mass to become ionizing In Figure 6,, we show at three different epochs column density maps of the cold gas (red in the left and centre panels ) and the HII (blue in the right and centre panels)."," In Figure \ref{fig:sources}, plotted to the same linear dimensions, we show the positions of the ionizing sources (obviously as time progresses and clusters accrete, more objects acquire enough mass to become ionizing In Figure \ref{fig:HII_plots}, we show at three different epochs column density maps of the cold gas (red in the left and centre panels ) and the HII (blue in the right and centre panels)."561" It is clear that the hot, low-density HII fills up cavities in the cold gas, so that the HII bubbles are illuminated from the edge rather than the centre, often by several widely—separated O-stars, and that several small HII regions eventually join to form a single large and irregularly-shaped one."," It is clear that the hot, low–density HII fills up cavities in the cold gas, so that the HII bubbles are illuminated from the edge rather than the centre, often by several widely--separated O–stars, and that several small HII regions eventually join to form a single large and irregularly--shaped one."562" The brightest part of the HII region is not centred on the main concentration of clusters, but instead abuts it."," The brightest part of the HII region is not centred on the main concentration of clusters, but instead abuts it."563" Additionally, as shown in Figure 4,, these cavities existed before the ionizing sources were turned on and were generated by the turbulent velocity field with which the cloud was seeded, so they have not been created by the action of feedback."," Additionally, as shown in Figure \ref{fig:init_snap}, these cavities existed before the ionizing sources were turned on and were generated by the turbulent velocity field with which the cloud was seeded, so they have not been created by the action of feedback."564" We also note that the boundaries of the cavities are delineated by the dense filaments in which star formation is taking place, so that the morphology of the system appears to consist of several overlapping HII-filled bubbles with vigorous star formation activity on their borders."," We also note that the boundaries of the cavities are delineated by the dense filaments in which star formation is taking place, so that the morphology of the system appears to consist of several overlapping HII–filled bubbles with vigorous star formation activity on their borders."565" Several authors (e.g.??) have taken this configuration to be indicative of triggered star formation but in our calculations, this is clearly not so."," Several authors \citep[e.g.][]{2008ApJ...688.1142K,2009A&A...503..107P} have taken this configuration to be indicative of triggered star formation but in our calculations, this is clearly not so."566" The overall HII morphology is irregular, with an approximately round core centred at about (-10,-10) pc and approximately 25 pc across, and several spurs and offshoots, one extending about 50 pc towards the top right in the final frame of the simulation."," The overall HII morphology is irregular, with an approximately round core centred at about (-10,-10) pc and approximately 25 pc across, and several spurs and offshoots, one extending about 50 pc towards the top right in the final frame of the simulation."567 The distribution of HII is also markedly clumpy due to the clumpiness of the gas and the action of, The distribution of HII is also markedly clumpy due to the clumpiness of the gas and the action of568the two images are convolved so that they mateh to à common PSF.,the two images are convolved so that they match to a common PSF.569 The e-band image is used as the reference image for flux measurements in both bands., The $g$ -band image is used as the reference image for flux measurements in both bands.570 This set of photometric measurements is used whenever we consider only optical colours. sizes or colour gradients.," This set of photometric measurements is used whenever we consider only optical colours, sizes or colour gradients."571 We divide each galaxy into an inner and an outer region: the former is enclosed by Rs. the radius enclosing half the total r-band light (determined from the PSF-convolved r band image). and the latter is detined as the region between Asy and 2.5 times the Kron radius (Kron (1980).. also determined from the PSF-convolved r band image).," We divide each galaxy into an inner and an outer region: the former is enclosed by $R_{50}$, the radius enclosing half the total $r$ -band light (determined from the PSF-convolved $r$ band image), and the latter is defined as the region between $R_{50}$ and 2.5 times the Kron radius \citet{Kron80}, , also determined from the PSF-convolved $r$ band image)."572 We measure fluxes in all the bands for both regions., We measure fluxes in all the bands for both regions.573 We define the (NVUV— r) colour ditference ALVUV—ry as eNVUV—Tha;-UVUV—ry (likewise for Ate— 03. so that negative values of A imply that the outer region of the galaxy isblazer than the innerregion?.," We define the $NUV-r$ ) colour difference $\Delta(NUV-r)$ as $(NUV-r)_{out}-(NUV-r)_{in}$ (likewise for $\Delta(g-i)$ ), so that negative values of $\Delta$ imply that the outer region of the galaxy is than the inner."574. To illustrate. Figure 6 shows the HI-detected GASS galaxy G3759.," To illustrate, Figure \ref{fig:3759r} shows the HI-detected GASS galaxy G3759."575 The dashed curve indicates the ellipse enclosing half the r-band light. the dot-dashed curve indicates the 25 mag/aresec? isophote. and the solid curve the ellipse with a semi-major axis equal to 2.5 times the Kron radius.," The dashed curve indicates the ellipse enclosing half the $r$ -band light, the dot-dashed curve indicates the 25 $^2$ isophote, and the solid curve the ellipse with a semi-major axis equal to 2.5 times the Kron radius."576 In Appendix À.. we demonstrate that the 2-zone (NUV— r) color measurement is reliable only when the radius of the inner zone is larger than 6 aresee (about the FWHM of the PSF of a GALEX NUV image) and the error on the total (NUV-r) colour ryyis smaller than 0.1 mag.," In Appendix \ref{sec:testdnuvr}, we demonstrate that the 2-zone $NUV-r$ ) color measurement is reliable only when the radius of the inner zone is larger than 6 arcsec (about the FWHM of the PSF of a GALEX NUV image) and the error on the total $r$ ) colour $\sigma(NUV-r)$ ) is smaller than 0.1 mag."577" If we wereto apply both a size and an error cut. we would be left with ~740° of the galaxies from the HI sample. ~36% of the galaxies from the Cy. sample. ~70% of the galaxies from the Ον,i sample and ~744 of the galaxies from the C.νε.nue sample."," If we wereto apply both a size and an error cut, we would be left with $\sim74\%$ of the galaxies from the HI sample, $\sim36\%$ of the galaxies from the $_{M*}$ sample, $\sim70\%$ of the galaxies from the $_{M*,NUV-r}$ sample and $\sim74\%$ of the galaxies from the $_{M*,NUV-r,\mu*}$ sample."578 If we only apply the cut on size. 78% of the HI sample. 58% of the Cy; sample. 76% of the Οννιi sample and 80% of the Cy;sci4. sample remain.," If we only apply the cut on size, $78\%$ of the HI sample, $58\%$ of the $_{M*}$ sample, $76\%$ of the $_{M*,NUV-r}$ sample and $80\%$ of the $_{M*,NUV-r,\mu*}$ sample remain."579 One problem with making a cut in c&OVUV—r) is that the remaining galaxies are biased toward NUV-bright (i.e. blue) objects. especially in the Cy. sample.," One problem with making a cut in $\sigma(NUV-r)$ is that the remaining galaxies are biased toward NUV-bright (i.e. blue) objects, especially in the $C_{M*}$ sample."580 In order to avoid this problem. we eut the sample only by size. and we stack the images in bins of stellar mass and HI gas fraction in order to boost the S/N of the colour measurements.," In order to avoid this problem, we cut the sample only by size, and we stack the images in bins of stellar mass and HI gas fraction in order to boost the $S/N$ of the colour measurements."581 We then measure average colour and SFR gradients for the stacked images., We then measure average colour and SFR gradients for the stacked images.582 The increased S/N of the stacked images will also improve the quality of the SED fitting (Section 3.39)., The increased $S/N$ of the stacked images will also improve the quality of the SED fitting (Section \ref{subsec:SF_tech}) ).583" We first select galaxies which have Asy larger than 6"". from the HI and “parent” samples."," We first select galaxies which have $R_{50}$ larger than $''$, from the HI and “parent” samples."584" We then make new Ομ. Cyr, and Οννεeye control samples as described in Section 2.3.."," We then make new $_{M*}$, $_{M*,NUV-r}$ and $_{M*,NUV-r,585\mu*}$ control samples as described in Section \ref{subsec:controlsample}."586"> Because the “galaxy pool” from which we draw these control galaxies is now smaller, each galaxy from the HI sample only has one control galaxy matched in stellar mass and one control galaxy matched in stellar mass and (NOUV—r) colour."," Because the “galaxy pool” from which we draw these control galaxies is now smaller, each galaxy from the HI sample only has one control galaxy matched in stellar mass and one control galaxy matched in stellar mass and $(NUV-r)$ colour."587 For simplicity. we will still call these three new samples the HI sample. Cy;. sample. Cij;44i sample and Ci;sije sample.," For simplicity, we will still call these three new samples the HI sample, $_{M*}$ sample, $_{M*,NUV-r}$ sample and $_{M*,NUV-r,588\mu*}$ sample."589 We divide the new HI sample into 4 stellar mass bins with log Μ.Μ rangesof 10-10.25. 10.25-10.5. 10.5-10.75 and 10.75-11.5.," We divide the new HI sample into 4 stellar mass bins with log $M_*/M_{\odot}$ ranges of 10-10.25, 10.25-10.5, 10.5-10.75 and 10.75-11.5."590 Each stellar mass bin includes 80-90 galaxies., Each stellar mass bin includes 80-90 galaxies.591 In each stellar mass bin. we further divide the galaxies into two groups at the median value of ," In each stellar mass bin, we further divide the galaxies into two groups at the median value of $_*$."592In total. the HI sample is divided into 8 groups for stacking. with 40-50 galaxies in each group.," In total, the HI sample is divided into 8 groups for stacking, with 40-50 galaxies in each group."593 We also divide the matched Ci and Οκ; samples into 8 groups for stacking: each group in these control samples will then be matched to the corresponding group from the HI sample.," We also divide the matched $_{M*}$ and $_{M*,NUV-r}$ samples into 8 groups for stacking; each group in these control samples will then be matched to the corresponding group from the HI sample."594 Our stacking procedure consists of the following steps., Our stacking procedure consists of the following steps.595 We rescale the images to the median value of Aso for the galaxies in the group., We rescale the images to the median value of $R_{50}$ for the galaxies in the group.596 We subtract the background. correct for Galactic extinction and any offset in photometric zeropoint. align the centers of all the images. and then add them together.," We subtract the background, correct for Galactic extinction and any offset in photometric zeropoint, align the centers of all the images, and then add them together."597 We create stacked images for the images (convolved to the resolution of the NUV image) for all 7 photometric bands., We create stacked images for the images (convolved to the resolution of the NUV image) for all 7 photometric bands.598 The stacked r-band image is used as the reference image to measure photometrie parameters., The stacked $r$ -band image is used as the reference image to measure photometric parameters.599 We note that the stacked images all have a σονUV—r) less than 0.01., We note that the stacked images all have a $\sigma(NUV-r)$ less than 0.01.600 We have used a spectral energy distribution (SED) fitting technique to derive the average specific star formation rates (SSFR) in the inner and outer regions of our stackedsample of galaxies., We have used a spectral energy distribution (SED) fitting technique to derive the average specific star formation rates (sSFR) in the inner and outer regions of our stackedsample of galaxies.601 We follow the method from Salimetal. (2007). hereafter SO7. with afew key changes that are detailed below.," We follow the method from \citet{Salim07}, , hereafter S07, with a few key changes that are detailed below."602 S07 used the Bruzual population synthesis code to create a library of 100.000 model SEDs in 7 bands (ΕΙΝ. NUV. i.9.7. iz) by generating model galaxies with a range of ages. star formation," S07 used the \citet{BC03} population synthesis code to create a library of 100,000 model SEDs in 7 bands (FUV, NUV, $u, g, r, i, z$ ,) by generating model galaxies with a range of ages, star formation"603"It is thus well established, both observationally and theoretically, that long period Algols develop a permanent or transient accretion disc or disc-like structure during mass transfer.","It is thus well established, both observationally and theoretically, that long period Algols develop a permanent or transient accretion disc or disc-like structure during mass transfer."604 In the next section we examine angular momentum transport and loss mechanisms to explain the asynchronous rotational velocities of detached components in the presence of discs or disc-like structures., In the next section we examine angular momentum transport and loss mechanisms to explain the asynchronous rotational velocities of detached components in the presence of discs or disc-like structures.605" In accretion disc theory, the in-falling matter first forms an accretion ring."," In accretion disc theory, the in-falling matter first forms an accretion ring."606 proposed a model in which the accreting star is driven into differential rotation by the presence of such a ring or disc around it., \citet{stothers1972} proposed a model in which the accreting star is driven into differential rotation by the presence of such a ring or disc around it.607 Viscous forces transfer most of the angular momentum (AM) to the outer edge of the ring while mass falls inwards., Viscous forces transfer most of the angular momentum (AM) to the outer edge of the ring while mass falls inwards.608 The ring spreads out., The ring spreads out.609 Eventually a disc forms and this allows the matter at the inner edge to fall on to the surface of the star., Eventually a disc forms and this allows the matter at the inner edge to fall on to the surface of the star.610" For such a Keplerian disc, the angular velocity Ωι of material at radius R is given by where G is Newton’s gravitational constant and the M is the mass of the accreting star."," For such a Keplerian disc, the angular velocity $\Omega_{\rm k}$ of material at radius $R$ is given by where $G$ is Newton's gravitational constant and the $M$ is the mass of the accreting star."611"where r is the radial distance to the star projected onto an ellipse with the desired geometry, ao is the semi-major axis, Qin>O and dou«0, and R(r) is related to the surface density by o(r)=oo-R(r)-(r/ao).","where $r$ is the radial distance to the star projected onto an ellipse with the desired geometry, $a_0$ is the semi-major axis, $\alpha_\textrm{in} > 0$ and $\alpha_\textrm{out} < 0$, and $R(r)$ is related to the surface density by $\sigma(r) = \sigma_0 \cdot R(r) \cdot \left(r/a_0\right)$."612 We use a Henyey-Greenstein phase function and assume it is the same throughout the disk., We use a Henyey-Greenstein phase function and assume it is the same throughout the disk.613" To compute images, we use the scattering radiative transfer code GRaTeR (Augereausingle-etal.1999) to compute synthetic images."," To compute images, we use the single-scattering radiative transfer code GRaTeR \citep{augereau99} to compute synthetic images."614 EThis approach is valid for an optically thin disk., ÊThis approach is valid for an optically thin disk.615" Given the scope of this model, we do not attempt to fit but merely approximate the real debris disk."," Given the scope of this model, we do not attempt to fit but merely approximate the real debris disk."616" Our working parameters are aj,=35, indicating a very steep inner edge, αοιι=—10, and an asymmetry factor g=0.10, implying a slight preference for forward scattering g=0.16+0.06 in Schneideretal.2009;; g= 0.03--0.06 in Debesetal. 2008))."," Our working parameters are $\alpha_\textrm{in} = 35$, indicating a very steep inner edge, $\alpha_\textrm{out}=-10$, and an asymmetry factor $g = 0.10$, implying a slight preference for forward scattering $g=0.16\pm0.06$ in \citealt{schneider09}; $g=$ 0.03–0.06 in \citealt{deb08}) )."617" Figures 3aa and 3bb show the simulated scattered-light images of the model disk at linear and logarithmic intensity scale, "," Figures \ref{f:model}a a and \ref{f:model}b b show the simulated scattered-light images of the model disk at linear and logarithmic intensity scale, respectively."618"In Figure 3cc, we show the PSF-subtracted image of the respectively.HST/STIS data from Schneideretal.(2009) in logarithmic scale for comparison, revealing an extended halo beyond the bright ring that matches the expected morphology."," In Figure \ref{f:model}c c, we show the PSF-subtracted image of the HST/STIS data from \citet{schneider09} in logarithmic scale for comparison, revealing an extended halo beyond the bright ring that matches the expected morphology."619" Since this dataset is reduced with PSF subtraction rather than ADI, it suffers from virtually no flux loss, but the background is dominated by residual speckle noise."," Since this dataset is reduced with PSF subtraction rather than ADI, it suffers from virtually no flux loss, but the background is dominated by residual speckle noise."620" To investigate the influence of ADI on disk flux, we inject the simulated scattered-light images of the model disk into our raw Subaru/HiCIAO dataset at a position angle offset by with respect to the real disk."," To investigate the influence of ADI on disk flux, we inject the simulated scattered-light images of the model disk into our raw Subaru/HiCIAO dataset at a position angle offset by with respect to the real disk."621 Figures 3dd shows the results of conservative LOCI applied to this modified dataset., Figures \ref{f:model}d d shows the results of conservative LOCI applied to this modified dataset.622" The two disks appear virtually indistinguishable, demonstrating that our simple model adequately explains the observed morphology."," The two disks appear virtually indistinguishable, demonstrating that our simple model adequately explains the observed morphology."623 We explore the viability of using the simple ADI image for the purpose of determining the H-band surface brightness profile of HR 4796 A’s debris disk., We explore the viability of using the simple ADI image for the purpose of determining the $H$ -band surface brightness profile of HR 4796 A's debris disk.624" We extract a strip with a width of 11 pixels centered on the disk’s major axis from the intensity image, and collapse it along the minor axis."," We extract a strip with a width of 11 pixels centered on the disk's major axis from the intensity image, and collapse it along the minor axis."625 We this for the simulated disk , We repeat this for the simulated disk image.626The results are shown in repeat log-log plot in Figure 4.., The results are shown in a log-log plot in Figure \ref{f:slopes}.627 The c image.error bounds are based on athe radial noise profile in empty sky quadrants of the simple ADI image before injecting the model disk., The $\sigma$ error bounds are based on the radial noise profile in empty sky quadrants of the simple ADI image before injecting the model disk.628 Simple ADI the model surface , Simple ADI preserves the model surface brightness profile.629The real disk's preservesobserved profile is consistent with a brightnesssingle profile.power law., The real disk's observed profile is consistent with a single power law.630" We have imaged and characterized the tapered outer boundary of HR 4796 A's debris disk using ground-based differential and find that its H -band surface angularbrightness profile is well imaging,described by a simple power law with a slope around —9.5."," We have imaged and characterized the tapered outer boundary of HR 4796 A's debris disk using ground-based angular differential imaging, and find that its $H$ -band surface brightness profile is well described by a simple power law with a slope around $-9.5$."631" Our observations are consistent with the expected result of a narrow planetesimal ring being ground up in a collisional cascade, yielding dust with a wide range of grain sizes."," Our observations are consistent with the expected result of a narrow planetesimal ring being ground up in a collisional cascade, yielding dust with a wide range of grain sizes."632" Radiation forces leave large grains in the ring and push smaller grains onto elliptical, or even hyperbolic trajectories."," Radiation forces leave large grains in the ring and push smaller grains onto elliptical, or even hyperbolic trajectories."633" Simulations of such this process predict a smoothly tapered outer boundary, consistent with our findings (e.g.,Krivovetal.2006;Strubbe&Chiang 2006)."," Simulations of such this process predict a smoothly tapered outer boundary, consistent with our findings \citep[e.g.,][]{krivov06,strubbe06}."634". have demonstrated that the disk cannot be modeled with a dust size, implying that dust populations of varying singlegrain size grainmust be involved."," have demonstrated that the disk cannot be modeled with a single dust grain size, implying that dust populations of varying grain size must be involved."635 The brightness slope is a result of changing dust densities and grain properties with distance., The brightness slope is a result of changing dust densities and grain properties with distance.636 More detailed modeling is needed to relate the observed slope to the disk’s physical properties., More detailed modeling is needed to relate the observed slope to the disk's physical properties.637" Using our maximum regional merit technique, we have corroborated the evidence for an offset between the debris disk’s inner edge and the star."," Using our maximum regional merit technique, we have corroborated the evidence for an offset between the debris disk's inner edge and the star."638" The dynamical influence of unseen planets within the disk cavity is most commonly invoked to orbitingexplain such offsets (e.g.,Kalasetreferences therein),, and may be the cause of the proposed but unconfirmed intra-ring gap."," The dynamical influence of unseen planets orbiting within the disk cavity is most commonly invoked to explain such offsets \citep[e.g.,]639[and references therein]{kalas05, thalmann09, buenzli10}, , and may be the cause of the proposed but unconfirmed intra-ring gap."640 Our confirmation of the ring offset also speaks against a dynamically cold source planetesimal population as proposed by Thébault&Wu(2008) as an alternative to the planet hypothesis for explaining the morphology of the ring.," Our confirmation of the ring offset also speaks against a dynamically cold source planetesimal population as proposed by \citet{thebault08}641 as an alternative to the planet hypothesis for explaining the morphology of the ring."642 The planets may well be detectable with the upcoming next-generation high-contrast imaging facilities., The planets may well be detectable with the upcoming next-generation high-contrast imaging facilities.643" We thank David Lafreniérre for generously providing us with the source code for his LOCI algorithm, and Jean-Charles Augereau for his GRaTer code."," We thank David Lafrenièrre for generously providing us with the source code for his LOCI algorithm, and Jean-Charles Augereau for his GRaTer code."644" The authors acknowledge partial support from the Swiss National Science Foundation (SNSF), US National Science Foundation grants AST-1009203 and DGE-0646086, and a Japanese MEXT Grant-in-Aid for Specially Promoted Research (No.22000005)."," The authors acknowledge partial support from the Swiss National Science Foundation (SNSF), US National Science Foundation grants AST-1009203 and DGE-0646086, and a Japanese MEXT Grant-in-Aid for Specially Promoted Research (No.22000005)."645The results of the spectral analysis are shown in Figure 7..,The results of the spectral analysis are shown in Figure \ref{fig:alpha}.646 The expected. Lick iudices [or three possible [a /Fe] ratios are shown based on the models of Thomasetal.(2003b)., The expected Lick indices for three possible $\alpha$ /Fe] ratios are shown based on the models of \citet{TMB03}.647. Uulike gian elliptical galaxies. the majority of dwarf elliptical galaxies in Virgo appear to have solar or [a /Fe] ratios.," Unlike giant elliptical galaxies, the majority of dwarf elliptical galaxies in Virgo appear to have solar or sub-solar $\alpha$ /Fe] ratios."648 Similar results are found by Gehaetal.(2003) and Thomasetal.(2003a) for heir samples of Virgo chwarl elliptical galaxies: ini acclition. similar [a /Fe] ratios are seen in stellar abundances of nearby dwarl spheroicdals (e.g..Shetroueetal.2001.2003).," Similar results are found by \citet{GGvM03} and \citet{TBHMG03} for their samples of Virgo dwarf elliptical galaxies; in addition, similar $\alpha$ /Fe] ratios are seen in stellar abundances of nearby dwarf spheroidals \citep[e.g.,][]{SCS01,SVTPHK03}."649. Siuce Type II supernova ooduce the majority of a-rich elements. the obseved [a /Fe ratios trace the timescale of star orumation activity in eacli galaxy (Gilmore&Wyse1991).," Since Type II supernova produce the majority of $\alpha$ –rich elements, the observed $\alpha$ /Fe] ratios trace the timescale of star formation activity in each galaxy \citep{GW91}."650 Iipa ‘ticular. super-solar [a /Fe] indicate:J. ‘apid enricluneut from Type II supernova auc thus implies that the galaxy. has undergone a shor jurst of star formation activity: most elaut elliptica £alaxiesl ave super-solar [a/Fe] 2000).," In particular, super-solar $\alpha$ /Fe] indicates rapid enrichment from Type II supernova and thus implies that the galaxy has undergone a short burst of star formation activity; most giant elliptical galaxies have super-solar $\alpha$ /Fe] \citep[e.g.,][]{TFWG00}."651. In contrast. the solar aud sub-solar abuuclanmcο ratios for dEs iudicate slow chemical eurichuuent. or a more quiescent star formation list«xv.," In contrast, the solar and sub-solar abundance ratios for dEs indicate slow chemical enrichment, or a more quiescent star formation history."652 ΤΙls. he domiuaut stellar populatious iu Vireo dEs may uot be post-burst populations.," Thus, the dominant stellar populations in Virgo dEs may not be post-burst populations."653 Rather. previous star formation activity appears o have occurred on more extended timescales in the low uass galaxies: these ancl similar results (e.g..Gallagher&Wyse1901:Mateo1998) rule out various theoretical models for dE formation. inclucling the possibility that dEs aud dSpls form all stars prior to reionizatiou 1999).," Rather, previous star formation activity appears to have occurred on more extended timescales in the low mass galaxies; these and similar results \citep[e.g.,][]{GW94,M98}654 rule out various theoretical models for dE formation, including the possibility that dEs and dSphs form all stars prior to reionization \citep[e.g.,][]{BL99}."655. The observed [a/Fe] ratios are cousistent with the idea that Virgo dEs are formed hrough the stripping of dis: if star formation activity ceases when the ISM is removed from the OW Lass system. the galaxy. will evolve into a quies'eut. red galaxy with structural aud kinematic j»arameters similar to the progenitor dl. aud with a Chemueal eurichiment history. representative of a more continuous star formation history.," The observed $\alpha$ /Fe] ratios are consistent with the idea that Virgo dEs are formed through the stripping of dIs; if star formation activity ceases when the ISM is removed from the low mass system, the galaxy will evolve into a quiescent, red galaxy with structural and kinematic parameters similar to the progenitor dI, and with a chemical enrichment history representative of a more continuous star formation history."656 Comparison of the Hj aud Mgb indices provides au indication of the age of the domiuaut stellar ;»opulation in the «Es (Figure 7))., Comparison of the $\beta$ and Mgb indices provides an indication of the age of the dominant stellar population in the dEs (Figure \ref{fig:metals}) ).657 Also shown in Figure 7 are the stellar population models of Thomasetal.(2003b) for solar [a /Fe]., Also shown in Figure \ref{fig:metals} are the stellar population models of \citet{TMB03} for solar $\alpha$ /Fe].658 As expected from the optical colors (Section [). the stellar »opulations are both metal-poor aid evolved.," As expected from the optical colors (Section 4), the stellar populations are both metal–poor and evolved."659 Based ou these observations aud stellar population uodels. Virgo dEs have typical ages of 5-7 Gyr and metal abundances between 1/20 aud 1/3fey of solar.," Based on these observations and stellar population models, Virgo dEs have typical ages of 5-7 Gyr and metal abundances between 1/20 and 1/3 of solar."660 Similar results lor Virgo dEs were also obtained by Celiaetal.(2003)., Similar results for Virgo dEs were also obtained by \citet{GGvM03}.661.. The derived age a1 uetallicity estimates for tliese galaxies are also in remarkably good agreement with those obtaine rom the broad band optical images., The derived age and metallicity estimates for these galaxies are also in remarkably good agreement with those obtained from the broad band optical images.662 As found with the optical colors. there is no clear separation ol the kinematic samples in either age or metallicity of the dominant stellar population.," As found with the optical colors, there is no clear separation of the kinematic samples in either age or metallicity of the dominant stellar population."663 Thus. oth stellar population models aud spectral syuthesis indicate that Virgo dEs contain evolved low netallicity stellar populations with typical ages of a several Gyr ancl solar or sub-solar [a /Fe].," Thus, both stellar population models and spectral synthesis indicate that Virgo dEs contain evolved low metallicity stellar populations with typical ages of a several Gyr and solar or sub-solar $\alpha$ /Fe]."664 The derived structural parameters and metal enrichment histories indicate that the Virgo dEs are similar iu nature to field dwarf irregular galaxies with the exception of the age of the dmiuant, The derived structural parameters and metal enrichment histories indicate that the Virgo dEs are similar in nature to field dwarf irregular galaxies with the exception of the age of the dominant665all the other dillerential elements. of the (2.£) plane which are accessible to RDCS.,"all the other differential elements of the $(z,L)$ plane which are accessible to RDCS."666 Assuming Poisson statistics for such probabilities and defining S=——2InZ. tis Ss=25NoeInHpls.Li)]|2|Bκ(ts{diA(z.£). where the sum runs over the occupied. elements. of the (2.L) plane.," Assuming Poisson statistics for such probabilities and defining $S=-2{\mbox{\rm667ln}}{\cal L}$, it is $S=-2\sum_{i=1}^{N_{occ}}{\mbox{\rm668ln}}[\rho(z_i,L_i)]+2\int dz \int dL\,\lambda(z,L)$, where the sum runs over the occupied elements of the $(z,L)$ plane."669 Model predictions are also convolved with statistical errors on measured Fuses. as well as with uncertainties in the luminositymass relation associated to a 2304 scatter in the Los x relation and to a 204 uncertainty in the massemperature conversion.," Model predictions are also convolved with statistical errors on measured fluxes, as well as with uncertainties in the luminosity–mass relation associated to a $\simeq 30\%$ scatter in the $L_{bol}$ $T_X$ relation and to a $20\%$ uncertainty in the mass–temperature conversion."670 Best estimates of the model parameters are obtained by minimizing 5., Best estimates of the model parameters are obtained by minimizing $S$.671" In Figure Lowe show the resulting cemnstraints on the σε O,, plane for cillerent values of the shape parameter E. base on assuming à=3.5 and ol=0 for the Ly dx relation."," In Figure \ref{fi:lz_like_gam} we show the resulting constraints on the $\sigma_8$ $\Omega_m$ plane for different values of the shape parameter $\Gamma$, based on assuming $\alpha=3.5$ and $A=0$ for the $L_{bol}$ $T_X$ relation."672 It is clear that low«ensity models are always preferred. quite independent of E.," It is clear that low–density models are always preferred, quite independent of $\Gamma$."673 We find ο=0.352r ETTLos =0.76ο... and es=0.68. 55) for tat (open) motels. where uncertainties correspond to 37 confidence level for three significant fiting parameter.," We find $\Omega_m=0.35^{+0.35}_{-0.25}$ and $\sigma_8=0.76^{+0.38}_{-0.14}$ $\Omega_m=0.42^{+0.35}_{-0.27}$ and $\sigma_8=0.68^{+0.21}_{-0.12}$ ) for flat (open) models, where uncertainties correspond to $3\sigma$ confidence level for three significant fitting parameter."674 No significant constraints areinstead found for E., No significant constraints areinstead found for $\Gamma$.675 In order to verifv under which circumstances a critical density model may still be viable. we show in Figure 2. the ellect of changing the parameters of the Li.) ἂν relation.," In order to verify under which circumstances a critical density model may still be viable, we show in Figure \ref{fi:lz_like} the effect of changing the parameters of the $L_{bol}$ $T_X$ relation."676" Athough bestfitting values of O,, and ax move somewhat on the parameter space. neither a rather strong evolution nor a quite steep profile for the Law Zx relation can accommocdate a critical density Universe: an O,,=1 Universe is always à 230 event. even allowing for values of the zd and a parameters which are strongly disfavored by. present data."," Although best–fitting values of $\Omega_m$ and $\sigma_8$ move somewhat on the parameter space, neither a rather strong evolution nor a quite steep profile for the $L_{bol}$ $T_X$ relation can accommodate a critical density Universe: an $\Omega_m=1$ Universe is always a $>3\sigma$ event, even allowing for values of the $A$ and $\alpha$ parameters which are strongly disfavored by present data."677 Based on these results. we point out that deep tuxlimited (X. ray. cluster samples. like RDCS. which cover a large. redshift. baseline. (0.15;2% 1.2) and inclucle a fairly large number of clusters ( 100) do indeed place significant constraints on cosmological models.," Based on these results, we point out that deep flux–limited $X$ –ray cluster samples, like RDCS, which cover a large redshift baseline $0.1\mincir z\mincir 1.2$ ) and include a fairly large number of clusters $\magcir 100$ ) do indeed place significant constraints on cosmological models."678 To this aim. some knowledge of the Li.) Zx evolution is needed from a (aot necessarily complete) sample of distant clusters out to zI.," To this aim, some knowledge of the $L_{bol}$ $T_X$ evolution is needed from a (not necessarily complete) sample of distant clusters out to $z\sim 1$ ."679Preprint (French‘&Nicholson:~!2000)U ↴⊳(Showalter∡2008)., \citep{FN00}. \citep{Showalter+08}.680". etal.al2010).Oy.and ↕≯∪↥⋅↥⋅↕∐∶↴∙⊾≼∐∖↑↸∖↸⊳↑↕∪∐≼∐↰⋉∖↕↕≼↧↴∖↴∪↕⋟↑∐↸∖≻↕⋜⋯↸∖↑∎↴∖↴∪↴⋝∐≺∏∏↑⋅↖↽∙ 0.. Barnes&Fortucy(2001). riugs could be detected around transiting extrasolar dauets with a photometric precision of (1.3)«10! and a 15 uunutes time resolution as loug as the ring is an viene MM em ος an long as "" "" us LT j "," \citep{BKB10} $\theta_*$ \citet{BF04} rings could be detected around transiting extrasolar planets with a photometric precision of $(1-3)\times68110^{-4}$ and a 15 minutes time resolution as long as the ring is not viewed close to edge-on (i.e., as long as $\theta_*$ is not $\ll 1$ )."682bugs Is Dae paoromictre aceuraey Toa pu Ixepler spacecraft WPLachieves for Sun-like aud brighter stars (http:offlee/Ieplergo-arc∖nasigov⊾↽∣∢⊀⋅⋅⋠⋅/CalibrationSN.shtiil)., This is within the photometric accuracy that the Kepler spacecraft achieves for Sun-like and brighter stars (http://keplergo.arc.nasa.gov/CalibrationSN.shtml).683Ντα In addition. riugsaround transiting extrasolar planets could als be ∖⋅∖⋅⋅∖idaniidl speetroscopicalls∖ :⋠∖⊀σέ2009j.," In addition, ringsaround transiting extrasolar planets could also be identified spectroscopically \citep{OTS09}."684. alsoOlitaetal.(2009) showed that rings{Ohta withet a.significant obliquities are detectable with currently achievable radial precisa.-OUR :⋅⋅ 1 ∣ways. W.Worens hercasvnouses w-: ithP0: DAlthough1T typical regne ofa radial precision of ol havediscovered less. which is still beyoud velocitythe reach of radial ⋅ SULVCNorsurveys.," \citet{OTS09} showed that rings with significant obliquities are detectable with currently achievable radial velocity precision of 1 m/s, whereas rings with $\theta_* \ll 1$ would typically require a radial velocity precision of 0.1 m/s or less, which is still beyond the reach of radial velocity surveys."685 .due potential obstacle to detecting extrasolar. rings vxoplerTaxes be that most close iu exoplanetsiav could have low obliquities. which would make their rings hard. if not iupossible. to discover.," A potential obstacle to detecting extrasolar rings may be that most close in exoplanets could have low obliquities, which would make their rings hard, if not impossible, to discover."686" The initial obliquities of close iu extrasolar plaucts with masses comparable to and bigecr than Neptune: are ⋅ to be large, since⋅ such planets are thought to have likelyformed at larger senid-niajor axes aud have reaewed current location hy planet scattering. disk. their Or Iyozai with a stellar companion or a migration,combinationby of such oscillationsprocesses (e.g.Lin&Papaloizou1979:etal.1996:RasioWuetal. 2007)."," The initial obliquities of close in extrasolar planets with masses comparable to and bigger than Neptune are likely to be large, since such planets are thought to have formed at larger semi-major axes and have reached their current location by planet-planet scattering, disk migration, or by Kozai oscillations with a stellar companion or a combination of such processes \citep[e.g.][]{LP79,Lin+96,Rasio+96,CF08,Wu+03,Wu+07}."687. Tides raised ou the exoplanet by its host star will. however. lead to dampingof its obliquity.," Tides raised on the exoplanet by its host star will, however, lead to dampingof its obliquity."688 To first. order in.0.. the obliquity25 dampingo timescale. for," To first order in$\theta_*$, the obliquity damping timescale for"689 To first. order in.0.. the obliquity25 dampingo timescale. for.," To first order in$\theta_*$, the obliquity damping timescale for"690redshift.,redshift.691 In moclel SEL. based ou Macau&Pozetti(2000).. the SFR rises rapidly by an order of magnitude between 2=0 and z=1. peaks between z=1 ancl z=2 and declines geutly at higher redshifts.," In model SF1, based on \citet{mad00}, the SFR rises rapidly by an order of magnitude between $z=0$ and $z=1$ , peaks between $z=1$ and $z=2$ and declines gently at higher redshifts."692 In model SF2. based on Stekleletal.(1999)... 1t rises similarly but then remains roughly constant for z>2.," In model SF2, based on \citet{ste99}, it rises similarly but then remains roughly constant for $z>2$."693 Model SF3. reflecting the possibility that extinction has been underestimated (Blaineοἱal. 1999).. has an SFR continuing to rise beyond z=2.," Model SF3, reflecting the possibility that extinction has been underestimated \citep{bla99}, , has an SFR continuing to rise beyond $z=2$ ."694 For the cosinological moclel used in this paper (Hy=65 kins | +. ο=0.3. and Qy=0.7). the star formation rates Lor t=1.3.5 are 9.5. 7.7. 3.1 (SET). 8.3. 12.8. 12.7 (SE2). aud 6.2. 12.8. 16.1 (SF3). respectively.," For the cosmological model used in this paper $H_0 = 65~$ km $^{-1}$ $^{-1}$, $\Omega_M = 0.3$, and $\Omega_{\Lambda} = 0.7$ ), the star formation rates for $z = 1, 3, 5$ are 9.5, 7.7, 3.4 (SF1), 8.3, 12.8, 12.7 (SF2), and 6.2, 12.8, 16.1 (SF3), respectively."695 We use these three models to characterize in the derivation of the luminosity παςτοι., We use these three models to characterize in the derivation of the luminosity function.696 As descibed in the preceding section. we derive the |inosity fuelon al ) for each of ile | spectral classes separately.," As descibed in the preceding section, we derive the luminosity function at $z=0$ for each of the 4 spectral classes separately."697 We set the gaussian dispion of each at σιοι=0.1., We set the gaussian dispersion of each at $\sigma_{\log L} = 0.4$.698" Tie central peak |uuiuosities L, of the spectral classes wer letermiued fron the corrected values of «aaa αμ eiven in Table L..", The central peak luminosities $L_c$ of the spectral classes were determined from the corrected values of $<$ $>$ and given in Table \ref{tbl-1}. .699 The resultiug |inosity. [unctio1s al ) for each of ilὁ four spectral ¢asses for the SF2 model are shown in Fi |.+), The resulting luminosity functions at $z=0$ for each of the four spectral classes for the SF2 model are shown in Figure \ref{fig3}.700 The sum of the spectral luminosity Dunctious constes the overal€ luminosity fuiction., The sum of the spectral luminosity functions constitutes the overall luminosity function.701 Figure { shows tle pesttine luminosity functions for deN distributious SEI. SF2. ali SE3.," Figure \ref{fig4} shows the resulting luminosity functions for density distributions SF1, SF2, and SF3."702" The cent‘al peak luiiuosities logL, ange [roin 50.32—5.20. 50.2T—2l.5T . aud 20.18—51.88. respectively."," The central peak luminosities $\log L_c$ range from $50.32-51.29$, $50.27-51.57$ , and $50.18-51.88$, respectively."703 The DIuminosity [function eenerally appears to be a power law οι ~1050.5 eIOgs 1 to ~10019 erg .. αμα hen to decine more steeply.," The luminosity function generally appears to be a power law from $\sim 10^{50.5}$ erg $^{-1}$ to $\sim 10^{51.5}$ erg $^{-1}$, and then to decline more steeply."704 The total z) CRB densities are Q.15. 0.51. and 0.72  ! for SEL. SF2. aud SE3. respectively.," The total $z=0$ GRB densities are 0.48, 0.51, and 0.72 $^{-3}$ $^{-1}$ for SF1, SF2, and SF3, respectively."705 The luminosities aud clenities quoted ae djsotropic-equivalent’ values, The luminosities and densities quoted are 'isotropic-equivalent' values.706 If all GRBs are beamecd into. say. wdU sleradians. then Iuininosities require ultiplication by wc/1z and densities we πω.," If all GRBs are beamed into, say, $\omega$ steradians, then luminosities require multiplication by $\omega/{4\pi}$ and densities by $4\pi/\omega$."707 If the luni10sity-harduess correlatioi represents the distributio1 of luminosities withi La GRB beau. the situation. would be more complex aud the corrections to luminosity aid density would be a fuuctio1 of luminosity.," If the luminosity-hardness correlation represents the distribution of luminosities within a GRB beam, the situation would be more complex and the corrections to luminosity and density would be a function of luminosity."708 The cumulative distribution of peak fluxes observed iu tie BD2 sample is shown iu Figure 5, The cumulative distribution of peak fluxes observed in the BD2 sample is shown in Figure \ref{fig5}.709 The predicted cistributious are iu excellent to good agreement with tlie observatious., The predicted distributions are in excellent to good agreement with the observations.710 Compared to an aunuil all-sky rate of 691 GRBs based ou the BD2 sample. we expec above 0.1 (0.01) ph cus Laniual rates of 2560 (5090). 2720 (6810). and 2830ve) (8160) [or cases SEL. SF2. aud SE3. respectively.," Compared to an annual all-sky rate of 694 GRBs based on the BD2 sample, we expect above 0.1 (0.01) ph $^{-2}$ $^{-1}$ annual rates of 2560 (5090), 2720 (6810), and 2830 (8460) for cases SF1, SF2, and SF3, respectively."711 In Figuree 6.. we slow histograms of the expected redshift distribuiot iu the BD2 sample.," In Figure \ref{fig6}, we show histograms of the expected redshift distribution in the BD2 sample."712 The fraction of high redslufts Increases [roii SEL to SF2 to SE3: the expec(ου fractions with 5 lare 1. 5. audt.. respectvelv.," The fraction of high redshifts increases from SF1 to SF2 to SF3: the expected fractions with $z>4$ are 1, 5, and, respectively."713 The largest siugle redshift that may be exλοςed iu the BD2 sample of 1391 GRBs ou the basis of these three models is around 6. LU) or 19.respectively.," The largest single redshift that may be expected in the BD2 sample of 1391 GRBs on the basis of these three models is around 6, 13, or 19, respectively."714 These. however. may be overestimates or SF2aud SE3. sinceinthese cases the star Oriation rate remains high at large redshilt. witli 10 provision for the ouset of star formation.," These, however, may be overestimates for SF2and SF3, sinceinthese cases the star formation rate remains high at large redshift, with no provision for the onset of star formation."715Iu the derivation of the luminosity Dunctiou. we assumed thattle W.λοςtrum of the GRBs in,"In the derivation of the luminosity function, we assumed thatthe spectrum of the GRBs in"716is not definitive in terms of their CSA.,is not definitive in terms of their CSM.717 Light echoes might easily provide decisive clues regarding interstellar versus circumstellar inlervening material., Light echoes might easily provide decisive clues regarding interstellar versus circumstellar intervening material.718 We can learn about the 3-D distribution of scattering material by taking an image al (ime / after maximum light. measuring the angular radius r of an echoing cloud ('e.g.. in light-vears). and one can directly infer the clouds foreground distance.," We can learn about the 3-D distribution of scattering material by taking an image at time $t$ after maximum light, measuring the angular radius $r$ of an echoing cloud (e.g., in light-years), and one can directly infer the cloud's foreground distance."719 Only three other SNe Ia have shown the clear evidence of light echoes (SNe 1991T. 1995E and 1993bu).," Only three other SNe Ia have shown the clear evidence of light echoes (SNe 1991T, 1995E and 1998bu)."720 llere we report on the observations that allowed discovery of a fourth. in front of SN 2006X. as well as details of (hose echoes regarding interstellar or cireumstellar origin.," Here we report on the observations that allowed discovery of a fourth, in front of SN 2006X, as well as details of those echoes regarding interstellar or circumstellar origin."721 SAN 2006X is a rare. lortuitous case of à SN in a field imaged extensively by LEST before the Furthermore the extended (ail in the D-band lighteurve of SN 2006X strongly hinted at (he presence of a light echo (Crotts Sugerman 2006).," SN 2006X is a rare, fortuitous case of a SN in a field imaged extensively by $HST$ before the Furthermore the extended tail in the B-band lightcurve of SN 2006X strongly hinted at the presence of a light echo (Crotts Sugerman 2006)."722 We observed SN 2006X on tliree visits with {11 after explosion., We observed SN 2006X on three visits with $HST$ after explosion.723 On UT 2006 May 21 we took a series of rapid exposures (o avoid saturating the SN (then at V= 17.2) to maintain PSF-fitting and image subtraction efficacy Gin total: 1480s F435W. 1080s F555W. ks1080s F775W. in the ACS/IIRC bands closest to those [rom WEDPC? above).," On UT 2006 May 21 we took a series of rapid exposures to avoid saturating the SN (then at $V = 17.2$ ) to maintain PSF-fitting and image subtraction efficacy (in total: 1480s F435W, 1080s F555W, 1080s F775W, in the ACS/HRC bands closest to those from WFPC2 above)."724 We also care to include in each image a bright. unsaturated stellar source lor PSF ," We also took care to include in each image a bright, unsaturated stellar source for PSF comparison."725The same bands were observed on UT 2006 December 24 (920s F435W. 520s F555W. s MEταFri5W).," The same bands were observed on UT 2006 December 24 (920s F435W, 520s F555W, 520s F775W)."726 By the time of our third visit. UT 2008 January 4. ACS was SO We the closest available bands with WFPC2 PC (LO00s F380W. 1000s EF439W. PNdeeOs F555W. 1000s F102W. 100085 FTOIW).," By the time of our third visit, UT 2008 January 4, ACS was unavailable, so we used the closest available bands with WFPC2 PC (1000s F380W, 1000s F439W, 2000s F555W, 1000s F702W, 1000s F791W)."727 Throughout iet we reler (o epochs to V-band maximum on UT2006 Feb 22.8 (Wang et 220084). which for these //ST. visits occur 81. 204 and 630 days post-maximum.," Throughout this paper we refer to epochs relative to $V$ -band maximum on UT 2006 Feb 22.8 (Wang et 2008a), which for these $HST$ visits occur 87, 304 and 680 days post-maximum."728" For our dav304 post-maxinnun epoch. the extension of theimage of SN 20068 bevond the PSF served as a strong clue of a echo. since no such nebulositv was evident at this position in the pre-SN images (Crottsfe""2007)."," For our day 304 post-maximum epoch, the extension of the image of SN 2006X beyond the PSF served as a strong clue of a light echo, since no such nebulosity was evident at this position in the pre-SN images (Crotts 2007)."729 Wang et ((2008b. hereafter W08) show on the basis of these same {11 images presence of extended nebulositv consistent with a light echo. ancl confirm (Bis with IXeck/LBIS aud DEIAIOS spectra of this nebulosity similar to SN 200068 at maximun lieht. as might be expected by a light echo.," Wang et (2008b, hereafter W+08) show on the basis of these same $HST$ images the presence of extended nebulosity consistent with a light echo, and confirm this with Keck/LRIS and DEIMOS spectra of this nebulosity similar to SN 2006X at maximum light, as might be expected by a light echo."730 While a portion of, While a portion of731The Extreme Ultraviolet Explorer. VL)) has also conducted. an extensive all-sky survey at EUM. energies (Bowyer Malina 1991).,The Extreme Ultraviolet Explorer ) has also conducted an extensive all-sky survey at EUV energies (Bowyer Malina 1991).732 Using ssurvey data. Marshall. Pruseione Carone (1995) compiled a list of 13 cxtragalactic sources detected by aat =2.5m. eight of which appear in the current WEC sample.," Using survey data, Marshall, Fruscione Carone (1995) compiled a list of 13 extragalactic sources detected by at $ \ge 2.5 \sigma $, eight of which appear in the current WFC sample."733 However. that study cross-correlated the delata with catalogues of previouslv-known AGN.," However, that study cross-correlated the data with catalogues of previously-known AGN."734 Since [ew NLS1s were known at that time. it is no surprise that this sample contains only three NLSIs (representing of the total. compared to almost in our current sample).," Since few NLS1s were known at that time, it is no surprise that this sample contains only three NLS1s (representing $<$ of the total, compared to almost in our current sample)."735 One can therefore conclude that the ssample is probably incomplete ancl biased against NLS1s., One can therefore conclude that the sample is probably incomplete and biased against NLS1s.736 A low-significance survey by Fruscione (1996) and Craig Fruseione (1997) resulted. in a large number of potential EUV detections of extragalactic sources., A low-significance survey by Fruscione (1996) and Craig Fruscione (1997) resulted in a large number of potential EUV detections of extragalactic sources.737 Llowever. as recognised by the authors. a rather high. Lraction of these EUY sources may be spurious and even the bona fide EUV detections may represent chance coincidences with AGN (in the relatively large eerror circles) or arise cue to the hard leak in the filters.," However, as recognised by the authors, a rather high fraction of these EUV sources may be spurious and even the bona fide EUV detections may represent chance coincidences with AGN (in the relatively large error circles) or arise due to the hard leak in the filters."738 The smaller error circles. the 8S2 discriminant and the sharper filter cutoll are all advantages of the WEC survey compared to that carried out byLEVEL. at least in the narrow context of defining a complete LEUV-selectecl sample of AGN.," The smaller error circles, the S2 discriminant and the sharper filter cutoff are all advantages of the WFC survey compared to that carried out by, at least in the narrow context of defining a complete EUV-selected sample of AGN."739 It must be emphasized that affof the identifications in the current WEC survey are very Likely to be solid. and SeCUre., It must be emphasized that of the identifications in the current WFC survey are very likely to be solid and secure.740 ]t is interesting to compare the properties of our sample of sources selected in EUV band with those ofa sample of ACIN selected at much harder N-ray energies., It is interesting to compare the properties of our sample of sources selected in EUV band with those of a sample of AGN selected at much harder X-ray energies.741 For this purpose. we use the well-stuclicd set of AGN derived from the 210 keV ssurvey (Piecinotti 1982).," For this purpose, we use the well-studied set of AGN derived from the 2–10 keV survey (Piccinotti 1982)."742 Table 4 compares certain properties of the WEC and ssanmiples., Table 4 compares certain properties of the WFC and samples.743 Clearly there is quite a striking dillerence in the make-up of the AGN population as one moves up roughly a factor of 25 in energy., Clearly there is quite a striking difference in the make-up of the AGN population as one moves up roughly a factor of 25 in energy.744 The ssample is dominated by DESIs. and contains four narrow emission-line and Sevfert. 2 galaxies. but NLSIs.," The sample is dominated by BLS1s, and contains four narrow emission-line and Seyfert 2 galaxies, but NLS1s."745 By comparison. almost half of the AGN in the EUV-selected WEC sample are NLSIs. which also contains a significantly higher proportion of BL Lacs. butπο Seyfert 2s.," By comparison, almost half of the AGN in the EUV-selected WFC sample are NLS1s, which also contains a significantly higher proportion of BL Lacs, but Seyfert 2s."746 This is vet another cxample of the relationship between optical emission line width and EUW/X-ray spectral properties., This is yet another example of the relationship between optical emission line width and EUV/X-ray spectral properties.747 The WEC objects are optically fainter and typically are at higher redshift than the ssources., The WFC objects are optically fainter and typically are at higher redshift than the sources.748 Since the ELV sample is selected. from a smaller region of sky (ellectively 731 square degrees: sce 4). it is not unexpected that it is necessary to search to &ereater distances (and fainter magnitudes) in order to find. comparable numbers of sources in the EUW band as contained in the ssaniple.," Since the EUV sample is selected from a smaller region of sky (effectively $\sim$ 31 square degrees; see 4), it is not unexpected that it is necessary to search to greater distances (and fainter magnitudes) in order to find comparable numbers of sources in the EUV band as contained in the sample."749 As noted earlier. the RBSC provides two measures of spectral hardness covering the 0.1.2.0 keV. band. namely the ratios {1H1 and £2.," As noted earlier, the RBSC provides two measures of spectral hardness covering the 0.1–2.0 keV band, namely the ratios $HR1$ and $HR2$."750 Figure 3 shows a plot of £I versus, Figure 3 shows a plot of $HR1$ versus751Iverogen recombination plavs a very important role in many astroplivsical phenomena such as Type HH supernovae. the interstellar medium. ancl cosmic recombination.,"Hydrogen recombination plays a very important role in many astrophysical phenomena such as Type II supernovae, the interstellar medium, and cosmic recombination."752 Time-dependent recombination has been studied for the case of cosmological recombination (?7) and lor supernovae (??7)..," Time-dependent recombination has been studied for the case of cosmological recombination \citep{Zeldovich,Peebles} and for supernovae \citep*{Chugai,dessart08,soma09}."753 In supernovae (his occurs when the hydrogen recombination time-scale becomes comparable to (he age of the supernova., In supernovae this occurs when the hydrogen recombination time-scale becomes comparable to the age of the supernova.754 This effect is found to be dominant in the early epochs of the supernova's evolution (?).., This effect is found to be dominant in the early epochs of the supernova's evolution \citep{soma09}.755 At later times. however. effects due to multi-level atom effects (the importance of having many angular momentum sub-states) become more important than lime-dependent phenomena.," At later times, however, effects due to multi-level atom effects (the importance of having many angular momentum sub-states) become more important than time-dependent phenomena."756 ο discussed how the effective recombination Gimescale can be different based on time-dependent rate equations using different hydrogen atom models.," \citet{soma09}757 discussed how the effective recombination timescale can be different based on time-dependent rate equations using different hydrogen atom models."758 The primary goal of 2? was to determine the epoch in the lifetime of a supernova (during the photospheric phase) where Gime-dependence in (he rate equations is most important.," The primary goal of \citet{soma09}759 was to determine the epoch in the lifetime of a supernova (during the photospheric phase) where time-dependence in the rate equations is most important."760 In doing so we found that at later times model atoms with significantly more energv levels (hat is additional angular-momentiun states) have a strong ellect in determining the effective recombination time-scale., In doing so we found that at later times model atoms with significantly more energy levels (that is additional angular-momentum sub-states) have a strong effect in determining the effective recombination time-scale.761 This issue is also important for applications other than supernovae., This issue is also important for applications other than supernovae.762 Lu fact. considering nore complete atomic models is important to correctly estimate the electron density and recover subtle features in (he spectra.," In fact, considering more complete atomic models is important to correctly estimate the electron density and recover subtle features in the spectra."763 Here. we study multi-level atomic svstenms or hvdrogen alone using a non-LTE treatment which could alter the hydrogen ionization fraction aud therefore produce a dillerent temperature structure.," Here, we study multi-level atomic systems for hydrogen alone using a non-LTE treatment which could alter the hydrogen ionization fraction and therefore produce a different temperature structure."764 Cosmological recombination codes such as RECFAST (???)| and RICO (7) that deal with cosmological recombination and solve for the free electron [raction as a function of redshilt do an excellent job.," Cosmological recombination codes such as RECFAST \citep{SSS99,SSS00,WMS08} and RICO \citep{FCRW09}765 that deal with cosmological recombination and solve for the free electron fraction as a function of redshift do an excellent job."766 Nevertheless (here are assumptions, Nevertheless there are assumptions767matching criterion 15 based only on the positional coincidence of the long time-scale ML events with the X-ray sources of the 2XMM and CSC catalogs.,matching criterion is based only on the positional coincidence of the long time-scale ML events with the X-ray sources of the 2XMM and CSC catalogs.768 Our cross-correlation software computes the projected distance between the selected ML events and the entries of both the 2XMM and CSC catalogs., Our cross-correlation software computes the projected distance between the selected ML events and the entries of both the 2XMM and CSC catalogs.769 A positive match ts found when a ML event lies with the 3c error circle of an X-ray source., A positive match is found when a ML event lies with the $3\sigma$ error circle of an X-ray source.770 Positional errors of single sources are taken from the respective catalogs., Positional errors of single sources are taken from the respective catalogs.771 The positional error of 2XMM sources (POSERR column) already accounts for systematic errors., The positional error of 2XMM sources $POSERR$ column) already accounts for systematic errors.772 The total lo uncertainty is calculated as the squared root of the sum of statistical and systematic errors For CSC sources. to take into account the systematic error (0.16 arc-seconds) we use the equation suggested by the CSC team Typically. the statistical error for on-axis CSC sources ts ~0.2 are-seconds. while for off-axis sources at 14 are-minutes the statistical error is ~3.5 are-seconds.," The total $1\sigma$ uncertainty is calculated as the squared root of the sum of statistical and systematic errors For CSC sources, to take into account the systematic error (0.16 arc-seconds) we use the equation suggested by the CSC team Typically, the statistical error for on-axis CSC sources is $\sim\,0.2$ arc-seconds, while for off-axis sources at 14 arc-minutes the statistical error is $\sim\,3.5$ arc-seconds."773 We assume that positional errors of ML events are of ca;~1.5 are-seconds for all the events.," We assume that positional errors of ML events are of $\sigma_{ML}\,\sim 1.5$ arc-seconds for all the events."774 Thus. the resulting radius of the error circle is assumed to be the root mean square of the X-ray source and ML event positional uncertainties The cross-correlation analysis returned a single positive match in the 2XMM catalog.," Thus, the resulting radius of the error circle is assumed to be the root mean square of the X-ray source and ML event positional uncertainties The cross-correlation analysis returned a single positive match in the 2XMM catalog."775 The associated lensing event was observed in 2004 by both the OGLE and MOA surveys and is identified as OGLE 2004-BLG-81 and MOA 2004-BLG-3. respectively.," The associated lensing event was observed in 2004 by both the OGLE and MOA surveys and is identified as OGLE 2004-BLG-81 and MOA 2004-BLG-3, respectively."776 The duration of the event reported by the OGLE team is ~103.63 days., The duration of the event reported by the OGLE team is $\sim 103.63$ days.777 However. the light curve is poorly fitted by standard lensing models (Fig. 2)).," However, the light curve is poorly fitted by standard lensing models (Fig. \ref{fig-lcurve}) )."778 found that the baseline of the source star. Le. the magnitude outside the ML event (I ~ 17). has a suspected periodicity of ~4 days. thus pointing to an eclipsing binary.," found that the baseline of the source star, i.e. the magnitude outside the ML event (I $\sim\,17$ ), has a suspected periodicity of $\sim 4$ days, thus pointing to an eclipsing binary."779 In particular. the shape of the folded light curve points to a contact binary system.," In particular, the shape of the folded light curve points to a contact binary system."780 To add more confusion. the MOA team reports a baseline I~ 8(sic!).," To add more confusion, the MOA team reports a baseline $I\,\sim\,8$ (sic!),"781 a duration of ~6.73 days and amplification very close to unity. A~1.002.," a duration of $\sim 6.73$ days and amplification very close to unity, $A\,\sim\,1.002$."782 However. a visual inspection of the stellar field does not confirm the presence of such a bright star. whose image would have been affected by diffraction.," However, a visual inspection of the stellar field does not confirm the presence of such a bright star, whose image would have been affected by diffraction."783 Thus we rely exclusively on the OGLE data to characterize the event., Thus we rely exclusively on the OGLE data to characterize the event.784 The X-ray source associated to the ML event. 2XMM J180540.5-273427 (31805 hereafter). has been serendipitously observed during à pointing of MACHO-96-BLG-5. another BH candidate detected through microlensing2006).," The X-ray source associated to the ML event, 2XMM J180540.5-273427 (J1805 hereafter), has been serendipitously observed during a pointing of MACHO-96-BLG-5, another BH candidate detected through microlensing."785 The X-ray properties of the source have been retrieved. with the XCat-DB web interface2009)., The X-ray properties of the source have been retrieved with the XCat-DB web interface.786". The total number of counts is 312.744+ (0.2 12 keV band) corresponding to a flux. of (3.39£0.78)x107%eres!em"", which implies a luminosity. neglecting the photoelectric absorption of the ISM. of ~3x10(41/1kpeyergs7!."," The total number of counts is $312.744 \pm 0.001$ (0.2 - 12 keV band) corresponding to a flux of $(3.39\, \pm 0.78)\, \times 10^{-14}\, \rm erg\,s^{-1}\,cm^{-2}$, which implies a luminosity, neglecting the photoelectric absorption of the ISM, of $\sim 3\, \times 10^{30}\, (d / 1\, \rm kpc)^2\, \rm erg\,s^{-1}$ ."787 If 31085 is the responsible for the magnification of a bulge star (¢~Skpe). then it should be placed at an intermediate distance and its X-ray luminosity should be lower than ~10ergs7!.," If J1085 is the responsible for the magnification of a bulge star $(d \sim 8\, \rm kpc)$, then it should be placed at an intermediate distance and its X-ray luminosity should be lower than $\sim 10^{32}\, \rm erg\,s^{-1}$."788 The positional uncertainty of the source is ~2 arc-seconds and it Hes at ~0.5 are-seconds from the position of the ML event., The positional uncertainty of the source is $\sim 2$ arc-seconds and it lies at $\sim 0.5$ arc-seconds from the position of the ML event.789 We report the fluxes on the different EPIC bands and the relative hardness ratios as given in the XCat database in Table ].., We report the fluxes on the different EPIC bands and the relative hardness ratios as given in the XCat database in Table \ref{tab-xray}.790 The small angular separation (~0.5 are-seconds) between the position of the ML event OGLE 2004-BLG-81 and J1805 is Well below the lo positional uncertainty of the X-ray source and makes the association highly likely., The small angular separation $\sim 0.5$ arc-seconds) between the position of the ML event OGLE 2004-BLG-81 and J1805 is well below the $1\sigma$ positional uncertainty of the X-ray source and makes the association highly likely.791 Thus. if J1805 is actually a BH. it would prove that ML surveys can detect isolated compact objects.," Thus, if J1805 is actually a BH, it would prove that ML surveys can detect isolated compact objects."792 However. there are a number of uncertainties that need to be addressed in order to not discard the claim.," However, there are a number of uncertainties that need to be addressed in order to not discard the claim."793 First. the nature of the event reported by the OGLE and MOA surveys is unclear.," First, the nature of the event reported by the OGLE and MOA surveys is unclear."794 As already pointed out. the shape of the light curve would rule out a ML event. even accounting for secondary effects like parallax or blending.," As already pointed out, the shape of the light curve would rule out a ML event, even accounting for secondary effects like parallax or blending."795 The fact that the source star is possibly a contact binary would indicate a cataclysmic variable (CV). re. an accreting white dwarf.," The fact that the source star is possibly a contact binary would indicate a cataclysmic variable (CV), i.e. an accreting white dwarf."796 This would imply that the event was in reality an outburst episode rather than a genuine gravitational lens., This would imply that the event was in reality an outburst episode rather than a genuine gravitational lens.797 An acereting white dwarf would easily explain the detected X-ray radioation as coming from the matter accreted by the degenerate star., An accreting white dwarf would easily explain the detected X-ray radioation as coming from the matter accreted by the degenerate star.798 However. the duration of the putative outburst and its lighteurve are unusual for this kind of sources2003).. thus challenging the CV hypothesis.," However, the duration of the putative outburst and its lightcurve are unusual for this kind of sources, thus challenging the CV hypothesis."799 In alternative. it has been suggested that the lensed star is a chromospherically active variable2009). possibly of the RS Canum Venaticorum (RS CVn) type.," In alternative, it has been suggested that the lensed star is a chromospherically active variable, possibly of the RS Canum Venaticorum (RS CVn) type."800 This class of variables is known to show periodic variations which are thought to be related to the active regions on the surface of the star or ellipticity of the star itself., This class of variables is known to show periodic variations which are thought to be related to the active regions on the surface of the star or ellipticity of the star itself.801 These effects can mimic the lightcurve of an eclipsing binary and explain the observed modulation of the baseline., These effects can mimic the lightcurve of an eclipsing binary and explain the observed modulation of the baseline.802 Furthermore. RS CVn stars are known X-ray emitters. with luminosities of - 10*!eres7!. and they also show flaring activity at both optical and X-ray wavelengths.," Furthermore, RS CVn stars are known X-ray emitters, with luminosities of $\sim 10^{31} \rm erg\,s^{-1}$, and they also show flaring activity at both optical and X-ray wavelengths."803 Yet. also in this case the amplitude. shape and duration of the optical event are unusual for RS CVn stars (S.N. Shore. private communication).," Yet, also in this case the amplitude, shape and duration of the optical event are unusual for RS CVn stars (S.N. Shore, private communication)."804observed in active latetype stars: (3) XN.rav Iuninosities cluster around the same value of <logLy>=29.2 for A a carly Εtype stars.,observed in active late–type stars; (3) X–ray luminosities cluster around the same value of $<\log L_{X}> = 29.2$ for A– and early F–type stars.805 Iu Fig., In Fig.806 2 we compare the X.ray Iuninosity distribution “sample to that of two sample of latetype stars., 2 we compare the X–ray luminosity distribution of our sample to that of two sample of late–type stars.807 jj shows the Nray luminosity distribution of all known IK aud AL dwarfs in the nuuedciate solar vicinity with distance less than 7 pc (Sclunitt et al., Panel b) shows the X–ray luminosity distribution of all known K and M dwarfs in the immediate solar vicinity with distance less than 7 pc (Schmitt et al.808 1995)., 1995).809 Tu this study he Xrav detection rate for Ik aud AL dwarfs is οSTO., In this study the X–ray detection rate for K and M dwarfs is 87.810 Thus. this sample should be reasonably complete. except possibly for the very faüintest stars. and if is nof biased toward the intrinsically Duuinous ciitters like the Xrav selected. samples of coronal Xrav sources.," Thus, this sample should be reasonably complete, except possibly for the very faintest stars, and it is not biased toward the intrinsically luminous emitters like the X–ray selected samples of coronal X–ray sources."811 luspection of panel b) shows hat the luminosity ranges from Ly&aDQV ore t to Ly~Nm1077 ere +1 clustering: in the rane Ly=13νaqu1075 erg Lo, Inspection of panel b) shows that the luminosity ranges from $L_{X} \simeq 10^{26}$ erg $^{-1}$ to $L_{X} \simeq 10^{29}$ erg $^{-1}$ clustering in the range $L_{X} = 1-3 \times 10^{27}$ erg $^{-1}$.812" Panel c) shows the huuinositv distribution for the sample of the supposedlv single late-tvpe stars (GIs,M spectral type stars) studied by Panarella e al.", Panel c) shows the luminosity distribution for the sample of the supposedly single late-type stars (G–K–M spectral type stars) studied by Panarella et al.813 1996., 1996.814 As this is fux lamited Xrav selected sample. it consists of the most active CGI&M stars.," As this is flux limited X–ray selected sample, it consists of the most active G–K–M stars."815 Their limunesitv is spread in the range Ly~LOPS—107 eyes d., Their luminosity is spread in the range $L_{X} \simeq 10^{28} - 10^{30}$ erg $^{-1}$.816 The comparison of panucls a). b) aud ο) shows that our Iuninositv distribution is similar to that of the X.rav selected sample of latetype stars. but not to that of latetype optically selected stars.," The comparison of panels a), b) and c) shows that our luminosity distribution is similar to that of the X–ray selected sample of late–type stars, but not to that of late--type optically selected stars."817 We tried to characterize the Xταν cluission ofour À aud carly Fotype stars searching for correlations between Ly aud the D.V color. Vsiu/ aud the bolometric huninosity. finding noue.," We tried to characterize the X–ray emission of our A– and early F–type stars searching for correlations between $L_{X}$ and the B–V color, $V \sin{i}$ and the bolometric luminosity, finding none."818 On the coutrary a positive correlation is found between logLy aud the spectral hardness ratio., On the contrary a positive correlation is found between $\log{L_{X}}$ and the spectral hardness ratio.819 A linear reeression analysis vields a correlation cocficient kr=0.6. the probability of a spurious correlation being less than 1019.," A linear regression analysis yields a correlation coefficient $r = 0.6$, the probability of a spurious correlation being less than $10^{-10}$."820 A similar trend was found for samples of latetype stars (see Sclunitt et al., A similar trend was found for samples of late–type stars (see Schmitt et al.821 1995: σοι 1997: Panarella et al., 1995; Schmitt 1997; Panarella et al.822 1996)., 1996).823 The detection of a very stringent upper limit for the X.rav cuuission of the prototvpical Àstar Veea (logLy«25.55: Sehuutt et al., The detection of a very stringent upper limit for the X–ray emission of the prototypical A–star Vega $\log{L_{X}} < 25.55$; Schmitt et al.824 1997). which is well below our values. raises doubts about the existence of corouae in carly type stars.," 1997), which is well below our values, raises doubts about the existence of coronae in early A--type stars."825 In a work sinülu to our. Simon et al. (," In a work similar to our, Simon et al. ("8261995) used ROSAT PSPC observations to study a sample of TLAtype stars detecting Nray emission in 10 carly Atype stars.,1995) used ROSAT PSPC observations to study a sample of 74 A–type stars detecting X–ray emission in 10 early A--type stars.827 Of these five are known to be binaries. while more optical observations are necessary to deteriine the physical nature of the remaining five (four of them are also in our sample: WD20sss. IID30178.. IIDISGIS and IID116160).," Of these five are known to be binaries, while more optical observations are necessary to determine the physical nature of the remaining five (four of them are also in our sample: HD20888, HD30478, HD45618 and HD116160)."828 In the past X.rav cussion was reported for, In the past X–ray emission was reported for829Taking the logarithm and substituting in lor 1 rom equation 51.. gives where we used the approximation /n(l—p)=Pose Lor p.K1 in obtaining the expression to the right of the final equals sign.,"Taking the logarithm and substituting in for l from equation \ref{El}, gives where we used the approximation $ln{(1-p_{esc})} = -p_{esc}$ for $p_{esc} \ll 1$ in obtaining the expression to the right of the final equals sign."830 Differentiating with respect to £. results in where P(E)dE is the unnormalized probability of a post-acceleration electron having ihe energv £.," Differentiating with respect to $E$ , results in where $P(E)dE$ is the unnormalized probability of a post-acceleration electron having the energy $E$."831" In the limit. where p,.. is extremely small. the relativistic STFA spectrum has power law index 1."," In the limit, where $p_{esc}$ is extremely small, the relativistic STFA spectrum has power law index $\sim 1$."832 In a plasma where pz.~A. the power law index can grow larger. ancl (he index is very sensitive to p...," In a plasma where $p_{esc} \sim A$, the power law index can grow larger, and the index is very sensitive to $p_{esc}$."833" In the third regime. where p.>Y. electrons stream out of the turbulent volume quickly, do not experience much acceleration. aud have a very steep power law energv distribution wilh virtually no very high energy electrons (I5£i)."," In the third regime, where $p_{esc} \gg A$, electrons stream out of the turbulent volume quickly, do not experience much acceleration, and have a very steep power law energy distribution with virtually no very high energy electrons $(E \gg E_0)$."834 In section 3.1 we derived the steady acceelration rate for electrons in a low 3 turbulent magnetic plasma., In section 3.1 we derived the steady acceelration rate for electrons in a low $\beta$ turbulent magnetic plasma.835 This derivation was contingent on the assumption that Ff=FF. which is not strictly valid.," This derivation was contingent on the assumption that $F_+ = F_- = F$, which is not strictly valid."836 Dlackman.(1999) ealeulates F [or Fermi acceleration., \citet{Blackman3} calculates $F$ for Fermi acceleration.837" By resetting the limits of the integral in his eq (12). and renormalizing for the smaller phase space. one arrives al where cosó,, is (he minimum pitch angle al which an electron willreflect. and ου is the ratio of the Allvénn speed to the electron speed."," By resetting the limits of the integral in his eq (12), and renormalizing for the smaller phase space, one arrives at where $\cos{\phi_m}$ is the minimum pitch angle at which an electron willreflect and $v_A/v$ is the ratio of the Alfvénn speed to the electron speed."838 We rename these quantities A and D vespectively: both are small quantities., We rename these quantities $A$ and $B$ respectively; both are small quantities.839 By taking a series expansionof eq (54)) and truncating il at second order in D. it can be simplified to," By taking a series expansionof eq \ref{fpm}) ) and truncating it at second order in $B$ , it can be simplified to"840The distributions of errors on a] the velocities iu the catalogue are displaved in Figs.,The distributions of errors on all the velocities in the catalogue are displayed in Figs.841 2 aud 3 for absorption and cussion line measurenieuts respectively., \ref{errorvabs} and \ref{errorvem} for absorption and emission line measurements respectively.842 For the 220 ealaxies with absorption lines taken from our observations. the histogram of the Tourv Davis sienal to noise parameter BR. eiven by the cross-correlatiou nieasure is displaved in Fig.," For the 220 galaxies with absorption lines taken from our observations, the histogram of the Tonry Davis signal to noise parameter R given by the cross-correlation measure is displayed in Fig."843 d (this quautitv is nof eiveu in previously published catalogues)., \ref{Rparam} (this quantity is not given in previously published catalogues).844 The correspondiusg correlation between the Toury Davis Ro parameter aud the error on the velocity is shown in Fie. 5.., The corresponding correlation between the Tonry Davis R parameter and the error on the velocity is shown in Fig. \ref{RTDerr}.845 Iu order to check the quality of our redshifts. we also reobserved 2 ealaxies from Quintana rez (1990) aud 18 from Mahmuth et al. (," In order to check the quality of our redshifts, we also reobserved 2 galaxies from Quintana rez (1990) and 18 from Malumuth et al. ("8461992).,1992).847 The results are shown in Tae l.., The results are shown in Table \ref{doubles}.848 For galaxies observed twice. we ctose to give in our fiwl catalogue the redshift with the smallest error (usuallv our data).," For galaxies observed twice, we chose to give in our final catalogue the redshift with the smallest error (usually our data)."849 The menu absolute differeice. betwee our measurements aud those of Maluuu he al. (, The mean absolute difference between our measurements and those of Malumuth et al. (85018 galaxies) is 117. with a dispersion of 137lo. nuplving that the general agreement is good.,"18 galaxies) is 117, with a dispersion of 137, implying that the general agreement is good."851 NcXe fiat the difference between our velocities axd tlOsC ο| the literature does not tend to be larger for fainter iiagnuitudes., Note that the difference between our velocities and those of the literature does not tend to be larger for fainter magnitudes.852 The agreement with the two ealaxies iu coniLOM Wjth ¢Quiutana rez (1990) ]8 SaifaTorv but cannot be tested, The agreement with the two galaxies in common with Quintana rez (1990) is satisfactory but cannot be tested853"the complex selection effects involved, redshift uncertainty values can also be used (e.g. using a Monte Carlo method) to calculate more robust statistics about the whole population of galaxies.","the complex selection effects involved, redshift uncertainty values can also be used (e.g. using a Monte Carlo method) to calculate more robust statistics about the whole population of galaxies."854" The advantages of GPs demonstrated in this paper suggest that such improved GP algorithms should be pursued, and we are exploring both Monte Carlo and analytic options for improving their treatment of errors."," The advantages of GPs demonstrated in this paper suggest that such improved GP algorithms should be pursued, and we are exploring both Monte Carlo and analytic options for improving their treatment of errors."855the transition point from Geneva to Palla Stahler isochrones as both sets of tracks predict the same NIR magnitudes for stars of this mass in the age range considered.,the transition point from Geneva to Palla Stahler isochrones as both sets of tracks predict the same NIR magnitudes for stars of this mass in the age range considered.856 The values for extinction. distance modulus and age of the cluster. which we present in the following. were derived in an iterative process by fitting isochrones to the Sofl and NACO near-infrared data.," The values for extinction, distance modulus and age of the cluster, which we present in the following, were derived in an iterative process by fitting isochrones to the SofI and NACO near-infrared data."857 As the intrinsic J-Ks colours of main sequence stars with masses in the range 6 to 30MM. just vary between --θ.| and —0.2mmag. the foreground extinction. can be derived by simply fitting a zero-age main-sequence (ZAMS) to the main-sequence population of land assuming a standard Rieke Lebofsky (1985)) extinetion law.," As the intrinsic J–Ks colours of main sequence stars with masses in the range 6 to $_\odot$ just vary between $-0.1$ and $-0.2$ mag, the foreground extinction can be derived by simply fitting a zero-age main-sequence (ZAMS) to the main-sequence population of 1and assuming a standard Rieke Lebofsky \cite{rieke85}) ) extinction law."858" In refemd,ppermsonlystarsintheS o", In \\ref{cmd_upperms} only stars in the SofI data set with DAOPHOT fitting errors less equal mag are shown.859f IdatasetwithDAOPHOT fittingerrors Ks., The artificial star tests carried out as part of the incompleteness simulation indicate that the DAOPHOT fitting errors underestimate the true photometric errors.860thoughl," Interestingly, the recovered magnitudes are on average brighter than the input magnitudes of the artificial stars."861esspronounced.," This asymmetry in the photometric errors around zero is also present in the colour estimate J-Ks, though less pronounced."862T hephotometricerrorsexplainparto f the, The photometric errors explain part of the observed scatter in the colour of the main sequence stars.863obse = ].," By comparing CMDs for different regions in our field of view, we also see evidence for differential extinction."8641320.," In general, the regions to the west and south of the cluster centre suffer slightly lower foreground extinction than the regions to the east and north of the cluster centre."86503 mmag.," As a best fit, we get $_{\rm Ks}$ = $\pm$ mag."866 Since all our measurements are in the near-infrared. and the theoretical isochrones used have been transformed to JHK-magnitudes and colours. the results are relatively insensitive to any deviation from a standard extinction law.," Since all our measurements are in the near-infrared, and the theoretical isochrones used have been transformed to JHK-magnitudes and colours, the results are relatively insensitive to any deviation from a standard extinction law."867 In their analysis of the NIR colours of 18. W-R. stars in Il Crowther et ((2006)) derived Ακ.=0.96+0.143 mmag. which within the quoted uncertainties overlaps with the Ks-band extinction derived by us.," In their analysis of the NIR colours of 18 W-R stars in 1 Crowther et \cite{crowther06}) ) derived $_{\rm Ks} = 0.96 \pm 0.14$ mag, which within the quoted uncertainties overlaps with the Ks-band extinction derived by us."868 We note. however. that for the two W-R stars in overlap with our sample (see," We note, however, that for the two W-R stars in overlap with our sample (see"869"searched within 4 pixels (4.8"". Le. 0.8x FWHM of the MIPS PSF) radit of each source and 25 counterparts were found.","searched within 4 pixels $4.8''$, i.e. $0.8 \, \times$ FWHM of the MIPS PSF) radii of each source and 25 counterparts were found."870 Of these. 16 are also X-ray detected. and are considered to be AGN based on their R band-to-X-ray flux ratios.," Of these, 16 are also X-ray detected, and are considered to be AGN based on their R band-to-X-ray flux ratios."871 The fluxes of the galaxies in the 8/24 jm bands are found in Table 1.., The fluxes of the galaxies in the 8/24 $\mu$ m bands are found in Table \ref{tab:IR}.872 At >=2.25. the MIPS 24ym band corresponds to restframe 5.9—8.8 um. Correspondingly. the 84m [RAC band covers 4—88 um for the z03 emitters.," At $z = 2.25$, the MIPS $24\mu$ m band corresponds to restframe $5.9 - 8.8$ $\mu$ m. Correspondingly, the $8\mu$ m IRAC band covers $4 - 8.8$ $\mu$ m for the z03 emitters."873 To convert this. mid-infrared luminosity to the total infrared luminosity. we use the conversion of Chary Elbaz (2001): The values derived can be found in Table ].. and a histogram of the total infrared luminosities is shown in Fig. Τ..," To convert this mid-infrared luminosity to the total infrared luminosity, we use the conversion of Chary Elbaz (2001): The values derived can be found in Table \ref{tab:IR}, and a histogram of the total infrared luminosities is shown in Fig. \ref{fig:IRnum}."874 At each redshift. the infrared. luminosities for the full samples (25 and 24. respectively). as well as the subsamples with certain identifications. are shown.," At each redshift, the infrared luminosities for the full samples (25 and 24, respectively), as well as the subsamples with certain identifications, are shown."875 It is seen that the flux limits at the two redshifts cause the overlap between the high and z03 sample to be very small., It is seen that the flux limits at the two redshifts cause the overlap between the high and z03 sample to be very small.876" All of the z23 sources are consistent with ULIRG luminosities (Lp>10' Ls). including the ""normal"" LAEs."," All of the z23 sources are consistent with ULIRG luminosities $L_{IR} > 10^{12} L_{\odot}$ ), including the “normal” LAEs."877 The luminosities are also in the same range as high redshift sub-mm galaxies (Chapman et al., The luminosities are also in the same range as high redshift sub-mm galaxies (Chapman et al.878 2005)., 2005).879 At z=0.3. roughly half of the galaxies lie in the range of normal star forming galaxies. seven have LIRG luminosities (40!cLip< OVE»). and two have ULIRG luminosities.," At $z = 0.3$, roughly half of the galaxies lie in the range of normal star forming galaxies, seven have LIRG luminosities $10^{11} < L_{IR} < 10^{12} L_{\odot}$ ), and two have ULIRG luminosities."880" Note that at z=2.3. detected sources are automatically ULIRGs. as the detection limit in the deep survey in the 24m band corresponds to logLjg=12.4L«.. and in the shallow survey to logLj,=12.91..."," Note that at $z = 2.3$, detected sources are automatically ULIRGs, as the detection limit in the deep survey in the $24\mu$ m band corresponds to $\log L_{IR} = 12.4 \, L_{\odot}$, and in the shallow survey to $\log L_{IR} = 12.9 \, L_{\odot}$."881 In Fig., In Fig.882 2. the Lye luminosities are shown as a function of the infrared luminosities of the galaxies., \ref{fig:IRbol} the $\alpha$ luminosities are shown as a function of the infrared luminosities of the galaxies.883 Here and in the following analysis. we have chosen to be conservative and have excluded all AGN from the samples.," Here and in the following analysis, we have chosen to be conservative and have excluded all AGN from the samples."884 In Sect., In Sect.885 2? we return to the question of AGN and test how robust the results are against AGN inclusion., \ref{sec:ulirgcolour} we return to the question of AGN and test how robust the results are against AGN inclusion.886 In Fig., In Fig.887 2. the z23 LAE candidates with MIPS detections seem to follow à given trend between the two flux measurements., \ref{fig:IRbol} the z23 LAE candidates with MIPS detections seem to follow a given trend between the two flux measurements.888 The best-fit ratio between Ένα and infrared lummosity is ~0.02%., The best-fit ratio between $\alpha$ and infrared luminosity is $\sim 0.02$.889. In the z03 sample. the Lyc luminosity interestingly stays constant as a function of infrared luminosity.," In the z03 sample, the $\alpha$ luminosity interestingly stays constant as a function of infrared luminosity."890 This indicates that the physical processes governing the [να and the IR luminosities are not related at low Lya and/or IR lummosities. although the relation seen at bright luminosities is based on small number statistics.," This indicates that the physical processes governing the $\alpha$ and the IR luminosities are not related at low $\alpha$ and/or IR luminosities, although the relation seen at bright luminosities is based on small number statistics."891 As the blue points in this case (sources with no previous identification as either galaxy or AGN) are mixed in the population of galaxy LAEs based on Lye luminosity. these are hereafter considered as normal LAE candidates.," As the blue points in this case (sources with no previous identification as either galaxy or AGN) are mixed in the population of galaxy LAEs based on $\alpha$ luminosity, these are hereafter considered as normal LAE candidates."892 The bolometric luminosity can be calculated from the infrared and ultraviolet lummosity according to where This can further be converted to a dust unobscured star formation rate. assuming that the bolometric luminosity includes all the re-processed light from star forming regions (Kennicutt 1998): The star formation rates found from the bolometric luminosity are in the range 500—5000 M.. yr! for the non-AGN z23 LAEs and 2—3300 M. yr! for the non-AGN z03 LAEs.," The bolometric luminosity can be calculated from the infrared and ultraviolet luminosity according to where This can further be converted to a dust unobscured star formation rate, assuming that the bolometric luminosity includes all the re-processed light from star forming regions (Kennicutt 1998): The star formation rates found from the bolometric luminosity are in the range $500 - 5000$ $_{\odot}$ $^{-1}$ for the non-AGN z23 LAEs and $2 - 3300$ $_{\odot}$ $^{-1}$ for the non-AGN z03 LAEs."893 Comparing the star formation rates found from the Lyc line and from the bolometric luminosity. we find a median ratio of 0.0043+0.0025 and 0.034+0.18 for the high and z03 non- LAEs. where the error bars indicate the spread in the values.," Comparing the star formation rates found from the $\alpha$ line and from the bolometric luminosity, we find a median ratio of $0.0043 \pm 0.0025$ and $0.034 \pm 0.18$ for the high and z03 non-AGN LAEs, where the error bars indicate the spread in the values."894 As the SFR found from the bolometric luminosity 15 the total SER of the galaxy. tracing the same population of star," As the SFR found from the bolometric luminosity is the total SFR of the galaxy, tracing the same population of star"895"In the models that follow, Racc is substituted with Rform.","In the models that follow, $R_{acc}$ is substituted with $R_{form}$."896" for all reaction pairs ij that form species A, where Κι; is the reaction rate, and fj; is defined in Section 4.1."," for all reaction pairs $ij$ that form species $A$, where $k_{ij}$ is the reaction rate, and $f_{ij}$ is defined in Section 4.1."897" As the deterministic part of the production rate in equation (14) is unaffected by the stochastic part, there is no need to iterate the calculations."," As the deterministic part of the production rate in equation (14) is unaffected by the stochastic part, there is no need to iterate the calculations."898" For consistency, equation (17) should include, in the denominator, terms for the reaction of particles A and B with other species, such as CO, that can build up significant abundances on the grains."," For consistency, equation (17) should include, in the denominator, terms for the reaction of particles $A$ and $B$ with other species, such as CO, that can build up significant abundances on the grains."899" If CO, or any other species, has (N(i))>>1 then there is a vanishing probability of finding such a reactant on the grains when two other particles are also present."," If CO, or any other species, has $\langle N(i) \rangle >> 1$ then there is a vanishing probability of finding such a reactant on the grains when two other particles are also present."900" Reactions with that species must be allowed to compete with the reaction between A and B, if such reactions exist."," Reactions with that species must be allowed to compete with the reaction between $A$ and $B$, if such reactions exist."901" In this model, (N(i))] is used as the stochastic-deterministic threshold."," In this model, $\langle N(i) \rangle =1$ is used as the stochastic--deterministic threshold."902 If «Ν(Ὀ)>1 then terms of the form (ki3°KN@)- should be inserted into equation (17) for the reactions of any 1)species j with which species i may react., If $\langle N(i) \rangle > 1$ then terms of the form $\left( k_{ij} \cdot \left[ \langle N(i) \rangle -1 \right] \right)$ should be inserted into equation (17) for the reactions of any species $j$ with which species $i$ may react.903 This means that only the deterministic part of the reaction rate is involved in the competition., This means that only the deterministic part of the reaction rate is involved in the competition.904 This treatment is in keeping with the formalism of equations (14) and (15) and Section 4.1., This treatment is in keeping with the formalism of equations (14) and (15) and Section 4.1.905" In fact, this final precaution actually has no significant effect on the systems modelled in this paper; the activation energy barriers used later, in Section 6, are too high to make reaction with CO or H2CO sufficiently competitive to affect the reactions of atomic hydrogen or oxygen."," In fact, this final precaution actually has no significant effect on the systems modelled in this paper; the activation energy barriers used later, in Section 6, are too high to make reaction with CO or $_2$ CO sufficiently competitive to affect the reactions of atomic hydrogen or oxygen."906" However, for adoption in a generalised system, this eventuality is easily treated."," However, for adoption in a generalised system, this eventuality is easily treated."907Iu order to obtain dust column deusitics along lines of sieht. we consider three different wavs that dust may trace interealactic hvdroseu gas: As our simulation makes no direct prediction for the metallicity of eas. we adopt a heuristic prescription (c.f. Con&Ostriker 1999)).,"In order to obtain dust column densities along lines of sight, we consider three different ways that dust may trace intergalactic hydrogen gas: As our simulation makes no direct prediction for the metallicity of gas, we adopt a heuristic prescription (c.f. \cite{cen99}) ),"908 in the second case above., in the second case above.909 We assunie that the iietallicity is 10? solar if the gas overdeusity is less that 10. solar if the overdcusity is ereater than 1000. aud log-linear in between.," We assume that the metallicity is $10^{-2}$ solar if the gas overdensity is less that 10, solar if the overdensity is greater than 1000, and log-linear in between."910Lin To extract dust extinction values from the simulations. we asstune that the eas associated with cach particle is spread over its SPIT smoothing volume (see c.g... Horuquist&Ivatz 1989)).," To extract dust extinction values from the simulations, we assume that the gas associated with each particle is spread over its SPH smoothing volume (see e.g., \cite{her89}) )."911 We perform a nunierical iutegration of eas column density along 5000 ravs cast through these voluues. at the same tine applying one of the three transformations eiven above to relate gas to dust deusities.," We perform a numerical integration of gas column density along 5000 rays cast through these volumes, at the same time applying one of the three transformations given above to relate gas to dust densities."912 To reach the required path lengths out to :~(0.5. we follow ravs through 26 simüulation volumes. cach ταν entering through a random point on a raudon face.," To reach the required path lengths out to $z\sim 0.5$, we follow rays through 26 simulation volumes, each ray entering through a random point on a random face."913 This vields the column density of dust to 2=0.5 alone each line of sieht., This yields the column density of dust to $z=0.5$ along each line of sight.914 Iu Fieure 1 we show extinction maps of 2.27 patches of sky. for (a) paarMPeas ou (b) Pansκf ," In Figure 1 we show extinction maps of $2.2^\circ\times 2.2^\circ$ patches of sky, for (a) $\rho_{\rm dust}\propto \rho_{\rm gas}$ and (b) $\rho_{\rm dust}\propto \rho^2_{\rm gas}$."915The median extinction to 2=0.5 was set to be equal (to O.L mae} for cases (a) and (b)., The median extinction to $z=0.5$ was set to be equal (to $0.4$ mag) for cases (a) and (b).916 Iu Figure 2. we show how the mean dust extinction and its dispersion varies with redshift.," In Figure 2, we show how the mean dust extinction and its dispersion varies with redshift."917 Tere. the dispersion in all three paucls was set to be the sanie small value. equal to the difference in quadrature of the dispersion i SNe magnitudes at high (σ.95= OST) aud low (o.yys= 0.151) redshifts observed by P99.. nunuclv 0.03 mae.," Here, the dispersion in all three panels was set to be the same small value, equal to the difference in quadrature of the dispersion in SNe magnitudes at high $\sigma_{z=0.5}=0.157$ ) and low $\sigma_{z=0.05}=0.154$ ) redshifts observed by \cite{per99}, namely 0.03 mag."918 Fies., Figs.919 1 and 2 show that the mean extinction is wich greater when the dust is 1nore snioothlv distributed., 1 and 2 show that the mean extinction is much greater when the dust is more smoothly distributed.920 We will now quanutitativelv explore the constraints that can be put on the dust extinction bv using the observed distribution of SNe magnitudes., We will now quantitatively explore the constraints that can be put on the dust extinction by using the observed distribution of SNe magnitudes.9213.00 We nake use of two characteristics of the observed SN data in our comparison. the change with redshift of the dispersion in SNe magnitudes. aud the shape of he histogram of SNe maguitudes.," We make use of two characteristics of the observed SN data in our comparison, the change with redshift of the dispersion in SNe magnitudes, and the shape of the histogram of SNe magnitudes."922 As mentioned above. D99 found little difference iu the dispersions of two suuples with 2~0.05 aud 2~0.5.," As mentioned above, \cite{per99} found little difference in the dispersions of two samples with $\bar{z}\sim0.05$ and $\bar{z}\sim0.5$."923 As they stated. lis leaves little room for dispersion due to dust. as his dispersion is expected to increase for longer path cheths (sec Fie.," As they stated, this leaves little room for dispersion due to dust, as this dispersion is expected to increase for longer path lengths (see Fig."924 2)., 2).925 In order to quantity this. and the effect of the distribution shape. we eeucrate simulated SNe uaenitudes. and compare themto the P99 data using a uaximunna likelihood approach.," In order to quantify this, and the effect of the distribution shape, we generate simulated SNe magnitudes, and compare themto the \cite{per99} data using a maximum likelihood approach."926 The observational datasets we use are both taken from P99 (their Tables 1 aud 2). beiug the hielh-: SNe of the SupernovaCosmology Project. and the low-: sample of Caláuu-Tololo SNe survey (Πανπινetal. 1996)).," The observational datasets we use are both taken from \cite{per99}927 (their Tables 1 and 2), being the $z$ SNe of the SupernovaCosmology Project, and the $z$ sample of Calánn-Tololo SNe survey \cite{ham96}) )."928 We use LO (nou-recddened SNe} of the former SNe. between +=0.172 and 2=0h83 (2~ 0.5). ancl 16 of the latter SNe which lie between 2=0.02 and :—0101 (2 0.05).," We use 40 (non-reddened SNe) of the former SNe, between $z=0.172$ and $z=0.83$ $\bar{z}\sim 0.5$ ), and 16 of the latter SNe which lie between $z=0.02$ and $z=0.101$ $\bar{z}\sim 0.05$ )."929 We generate simulated datasets for cach dust model described in 2., We generate simulated datasets for each dust model described in 2.930" For each dust model. we vary two paralcters: first.Ave. a cosmological magnitude shift applied. to all simulated SNe at a given z. normalized so that Me:= Oat i=0.5 corresponds to the best fitting cosmologv found by P99 (with O,,=0.28 aud O4= 0.72): and second. . Tes the media: αςl inaguitudeOo of dust extinction ou to.— (0.51."," For each dust model, we vary two parameters; first,$M_{C}$, a cosmological magnitude shift applied to all simulated SNe at a given $z$, normalized so that $M_{C}=0$ at $z=0.5$ corresponds to the best fitting cosmology found by \cite{per99} (with $\Omega_{m}=0.28$ and $\Omega_{\Lambda}=0.72$ ); and second, $A_{V}$ , the median V-band magnitude of dust extinction out to $z=0.5$ ."931" Mem1.2 then corresponds to au open model with ,,— 0.3. aud Me:zm0.1 to an"," $M_{C}\approx -0.2$ then corresponds to an open model with $\Omega_{m}\sim0.3$ , and $M_{C}\approx -0.4$ to an"932bb) Transform the model atmosphere in a format readable by MOOG (subroutine kurucz2moog).,b) Transform the model atmosphere in a format readable by MOOG (subroutine kurucz2moog).933 The format of the model atmosphere used by MOOG is not exactly the Kurucz model and should be rewritten accordingly., The format of the model atmosphere used by MOOG is not exactly the Kurucz model and should be rewritten accordingly.934 ce) Call the MOOG program., c) Call the MOOG program.935 In this point. the program takes the file containing the equivalent widths of Fel and Fell lines of the star and the model atmosphere as input for the MOOG program.," In this point, the program takes the file containing the equivalent widths of FeI and FeII lines of the star and the model atmosphere as input for the MOOG program."936" The MOOG program is executed using a driver called ""abfind"" which is selected for the abundance determination.", The MOOG program is executed using a driver called ”abfind” which is selected for the abundance determination.937 dd) Read the new metallicity values calculated by MOOG (subroutine rmr. read-moog-results) and finally. ee) Determine the value of the y function.," d) Read the new metallicity values calculated by MOOG (subroutine rmr, read-moog-results) and finally, e) Determine the value of the $\chi^2$ function."938 This step will be explained below., This step will be explained below.939 We take into account the conditions mentioned in. the introduction in a variable called y., We take into account the conditions mentioned in the introduction in a variable called $\chi^2$.940" We adopt for y the eXpression where are considered weight factors (w; >=0). Waez.e, and e» are the slopes in the plots of [Fe/H] vs. (logarithm of the reduced equivalent width) and [Fe/H] vs. excitation potential.=|Fel/H]-|Fell/H]. and οἱ is the difference between the input ATLAS metallicity (step a) and the resulting metallicity using equivalent widths (step d)."," We adopt for $\chi^2$ the expression where are considered weight factors $_{i}>=$ 0), $_{1}$ and $_{2}$ are the slopes in the plots of [Fe/H] vs. (logarithm of the reduced equivalent width) and [Fe/H] vs. excitation potential, and $_{4}$ is the difference between the input ATLAS metallicity (step a) and the resulting metallicity using equivalent widths (step d)."941 We added explicity the fourth condition: the input metallicity of the model atmosphere should be similar to the output metallicity derived with equivalent widths ie. the term with cy., We added explicity the fourth condition: the input metallicity of the model atmosphere should be similar to the output metallicity derived with equivalent widths i.e. the term with $_{4}$.942 Then. the 4 conditions are quantified in the y function: the solution correspond to the minimum value of y.," Then, the 4 conditions are quantified in the $\chi^2$ function: the solution correspond to the minimum value of $\chi^2$."943 The user is free to modify the values of the weights under their own criteria., The user is free to modify the values of the weights under their own criteria.944 However we show a brief example estimating aproximately the values of the weights., However we show a brief example estimating aproximately the values of the weights.945 Adopting y -1 as the limit. case of a solution. each condition contribute. for example. with 0.25 to the sum0.," Adopting $\chi^2=$ 1 as the limit case of a solution, each condition contribute, for example, with 0.25 to the sum."94625. In this case the 4 conditions are taken equally important within y. which is not always true.," In this case the 4 conditions are taken equally important within $\chi^2$, which is not always true."947 In the plot of abundance vs. eXcitation potential. we accept a maximum slope. for instance. ofdex/eV. taking a difference of in abundance for a total range of -4 eV in the excitation. potential of Fe lines.," In the plot of abundance vs. excitation potential, we accept a maximum slope, for instance, of, taking a difference of in abundance for a total range of $\sim$ 4 eV in the excitation potential of Fe lines."948 Then in the limit case. and thuseV7/dex?.," Then in the limit case, and thus."949 The units of areo forced to obtain the product without units., The units of are forced to obtain the product without units.950 In the plot of abundance vs. (where W and 2 are the equivalent width and wavelength inA. respectively). we accept a maximum slope (for example) of0.015/1.5. taking a difference of 0.015 dex in abundance for a range of ~ 1.5 in the logo (W/2) of Fe lines.," In the plot of abundance vs. (where W and $\lambda$ are the equivalent width and wavelength in, respectively), we accept a maximum slope (for example) of, taking a difference of 0.015 dex in abundance for a range of $\sim$ 1.5 in the ${_{10}}$ $\lambda$ ) of Fe lines."951 Then. and thus2500.," Then, and thus."952 For the third condition. and we adopt a maximum difference of 0.015 dex.," For the third condition, and we adopt a maximum difference of 0.015 dex."953 Then. and thusdex7.," Then, and thus."954 Similarly. for wy resultdex7.," Similarly, for $w_{4}$ result."955" In this estimation the weights resulted 18000 dex"". 2500. 1100 dex and 1100 dex. respectively. for a solution in which the 4 conditions contribute equally with 0.25 to the v function in the limit case of y=1."," In this estimation the weights resulted 18000 $^2$ $^2$, 2500, 1100 $^{-2}$ and 1100 $^{-2}$ , respectively, for a solution in which the 4 conditions contribute equally with 0.25 to the $\chi^2$ function in the limit case of $\chi^2=$ 1."956 In this example those solutions with y»1 do not verify the four conditions., In this example those solutions with $\chi^2>$ 1 do not verify the four conditions.957 It is probably that the user have their own criteria adopting the values ofwj.....w4. instead of the example explained the previous paragraph.," It is probably that the user have their own criteria adopting the values of, instead of the example explained the previous paragraph."958 The user is free to modify the values of (file fundpar.par) and this could result in. more (or less) restrictive conditions., The user is free to modify the values of (file fundpar.par) and this could result in more (or less) restrictive conditions.959 The code use this values to define v and then search the minimum of the function., The code use this values to define $\chi^2$ and then search the minimum of the function.960 Then. the user should read the values of the slopes and metallicities in the output files to verify if the 4 conditions are satisfied.," Then, the user should read the values of the slopes and metallicities in the output files to verify if the 4 conditions are satisfied."961 The values of previously showed seems to verify in practice the requeriments of minimization and verification. of the 4 conditions., The values of previously showed seems to verify in practice the requeriments of minimization and verification of the 4 conditions.962 In the Table | we show a sample of the file fundpar.par where the weights could be modified., In the Table \ref{fundpar.par} we show a sample of the file fundpar.par where the weights could be modified.963 Other parameters will be explained in the next sections., Other parameters will be explained in the next sections.964 Following the definition. y could be considered as a function. that depends of the fundamental parametersogs|Fe/H|.," Following the definition, $\chi^2$ could be considered as a function that depends of the fundamental parameters."965£).. If. y is not ninimum. the algorithm should determine the next set of 4 possible values.," If $\chi^2$ is not minimum, the algorithm should determine the next set of 4 possible values."966 These new variables are used in another iteration step (following the steps a to e) to derive a new model atmosphere. metallicity and finally a new value of y.," These new variables are used in another iteration step (following the steps a to e) to derive a new model atmosphere, metallicity and finally a new value of $\chi^2$."967 The algorithm that determine the next group of 4 parameters is the downhill method. explained in the next section.," The algorithm that determine the next group of 4 parameters is the downhill method, explained in the next section."968 In the Table 2 we show a list of the input and output files used by FUNDPAR., In the Table \ref{input.output} we show a list of the input and output files used by FUNDPAR.969 The format of the input/output files 1s detailed in the file install.txt., The format of the input/output files is detailed in the file install.txt.970 There are two main directories (datain and dataout) containing the input and output files of the stars., There are two main directories (datain and dataout) containing the input and output files of the stars.971 The equivalent widths should be stored in separate files (one file by star). and the names of these files should be listed within another file called filenames.txt.," The equivalent widths should be stored in separate files (one file by star), and the names of these files should be listed within another file called filenames.txt."972 The files atlas.par. bateh.par and fundpar.par determine the value of some parameters used in the model calculation and abundance determination and will be explained in the next sections.," The files atlas.par, batch.par and fundpar.par determine the value of some parameters used in the model calculation and abundance determination and will be explained in the next sections."973 After the execution of FUNDPAR. there are three output files by star: the ATLAS model atmosphere of the solution and two output files directly from the MOOG abundance determination.," After the execution of FUNDPAR, there are three output files by star: the ATLAS model atmosphere of the solution and two output files directly from the MOOG abundance determination."974" The file outputl.screen contain information. similar to. the screen and output2.results list the final parameters and their uncertainties,", The file output1.screen contain information similar to the screen and output2.results list the final parameters and their uncertainties.975 In this section we briefly review the minimization procedure of στ? as a function of4 independent variables. using a Numerical Recipe's routine called (Press.1992).," In this section we briefly review the minimization procedure of $\chi^2$ as a function of 4 independent variables, using a Numerical Recipe's routine called \citep{press92}."976. The downhill simplex method ts due to Nelder&Mead(1965) and requires only function evaluations. not derivatives.," The downhill simplex method is due to \citet{nelder-mead65}977 and requires only function evaluations, not derivatives."978 A simplex could be considered as a geometrical figure of N+1 vertices in a N-dimensional space (in our case. N=4).," A simplex could be considered as a geometrical figure of N+1 vertices in a N-dimensional space (in our case, N=4)."979 Taking any vertice as the origin. then the 4 other points define possible vector directions in the 4-dimensional volume.," Taking any vertice as the origin, then the 4 other points define possible vector directions in the 4-dimensional volume."980 The downhill simplex method start with a group of NI Le. 5 vertices rather than a single pointor vertice., The downhill simplex method start with a group of N+1 i.e. 5 vertices rather than a single pointor vertice.981 These verticesare desplaced in a characteristic lengthscale of the problem., These verticesare desplaced in a characteristic lengthscale of the problem.982 In our case. y is initially calculated adopting displacements," In our case, $\chi^2$ is initially calculated adopting displacements"983that the exponential cutoff of the largeanass tail can be obtained exactly from a saddle-point approach.,that the exponential cutoff of the large-mass tail can be obtained exactly from a saddle-point approach.984 This is equivalent to the saddle-poiut computation of Matarrese et al. (, This is equivalent to the saddle-point computation of Matarrese et al. (9852000). that is often used to model the nou-Catssian halo mass function.,"2000), that is often used to model the non-Gaussian halo mass function."986 Towever. using a different treatuieut. we simmltancously derive the linear density profile of this saddle-poiut. which allows us to check that the latter almost. insensitive to.⋅⋅ primordial mou-Caussianity.⋅ so⋅⋅with that shell-crossiug is not amplified aud exact results cau be obtained provided one uses the correct linear density threshold. rather than the usual one.," However, using a different treatment, we simultaneously derive the linear density profile of this saddle-point, which allows us to check that the latter is almost insensitive to primordial non-Gaussianity, so that shell-crossing is not amplified and exact results can be obtained provided one uses the correct linear density threshold, rather than the usual one."987 We also propose a snnple recipe to match the dependence on xp of the larec-lass tail while keeping the mass fiction normalized to unity., We also propose a simple recipe to match the dependence on $\fNL$ of the large-mass tail while keeping the mass function normalized to unity.988 Then. iu section |. we consider the two-point correlation of dark matter halos in real space. following the spirit of Kaiser (1981).," Then, in section \ref{Bias-of-halos} we consider the two-point correlation of dark matter halos in real space, following the spirit of Kaiser (1984)."989 Next. taking a Fourier traustorm we obtain the halo bias in Fourier space.," Next, taking a Fourier transform we obtain the halo bias in Fourier space."990 Here. our aim is. to show that one does uot need to introduce. free. paralcters to match the results of ummerical siuulatious.," Here, our aim is to show that one does not need to introduce free parameters to match the results of numerical simulations."991 Moreover. the nonlinear real-space expression is of iuterest by itself aud it also allows one to check whether the “linearized” bias is valid on the range of iuterest.," Moreover, the nonlinear real-space expression is of interest by itself and it also allows one to check whether the “linearized” bias is valid on the range of interest."992 Finally. we couclude ii section 5..," Finally, we conclude in section \ref{Conclusion}."993 We focus in this paper ou uou-Caussiauitics of the local type. where Dardecu's potential ® is of the form (1). with o a Gaussian random field.," We focus in this paper on non-Gaussianities of the local type, where Bardeen's potential $\Phi$ is of the form \ref{fNLdef}) ), with $\phi$ a Gaussian random field."994 On scales smaller than the IIubble radius. ® equals iuuus the Newtonian eravitational potential aud the Poisson equation gives du. Fourier space (Slosar et al.," On scales smaller than the Hubble radius, $\Phi$ equals minus the Newtonian gravitational potential and the Poisson equation gives in Fourier space (Slosar et al."995 2008) Po). ah) =sya. where à; is the Hnear matter density contrast. T(k) is the transfer. function. and ος.) is. the linear. erowth factor.. normalized. as Οι)»(11:)» Lat lüehH redshift.," 2008) ,z) = (k,z) ) (k,z) =, where $\delta_L$ is the linear matter density contrast, $T(k)$ is the transfer function and $D(z)$ is the linear growth factor, normalized as $D(z) \rightarrow (1+z)^{-1}$ at high redshift."996aE Unless- stated otherwise. we nonualize the Fourier trausfori as xii cil (KN.," Unless stated otherwise, we normalize the Fourier transform as ) = )."997" Note that we define xp by applying Eq.(1)) at carly fines (Lio. := cox)which is sometimes called the “CAB convention”. whereas some authors first linemrlv extrapolate ® at 2=0 (""LESS convention”)."," Note that we define $\fNL$ by applying \ref{fNLdef}) ) at early times (i.e. $z=\infty$ ),which is sometimes called the “CMB convention”, whereas some authors first linearly extrapolate $\Phi$ at $z=0$ (“LSS convention”)."998 Thus. both conventions are related hy iia=Diofa (Pillepich et al.," Thus, both conventions are related by $\fNL^{\rm CMB} = D(0) \fNL^{\rm LSS}$ (Pillepich et al."999 2009)., 2009).1000" Then. cefinine the time-dependent Ciaussiau field x bx (ντο), we can write the near ceusity field at redshift : as οκ) τικ bk,.. ο--- is a,uUTéatkibatka. This reads m veal space as Chix) where the kernel f$4(x:x4.x2) only depends on the fWo vectors [xjXX»—XJ. as long as the system remains statistically homogeneous. as for the local model (1))."," Then, defining the time-dependent Gaussian field $\chi$ by ,z) = (k,z) ), we can write the linear density field at redshift $z$ as ) = ) + _2 ) _2) _1) _2), with _2)=. This reads in real space as ) = ) + _2 _2) _1) _2), where the kernel $\fNLd(\bx;\bx_1,\bx_2)$ only depends on the two vectors $\{\bx_1-\bx,\bx_2-\bx\}$, _2) = ), as long as the system remains statistically homogeneous, as for the local model \ref{fNLdef}) )."1001 The real-space and Fourier-space kerucls are related by (note the clifferent normalization from CL) ] , The real-space and Fourier-space kernels are related by (note the different normalization from \ref{Fourier_norm}) )) _2) = _2).1002The relationships (8)) and (10)) describe aux homogencous model where the Bardeen potential can be expressed as the sum of linear and quadratic terius over some Caussian feld., The relationships \ref{deltak_chik}) ) and \ref{fNLd_def}) ) describe any homogeneous model where the Bardeen potential can be expressed as the sum of linear and quadratic terms over some Gaussian field.1003" Thus. our analytical results also apply to other ""fxp-tvpe models than the “local” one M ⊟≻↥⋅∙↗↳≓∖↽∟∶"," Thus, our analytical results also apply to other $\fNL$ -type” models than the “local” one \ref{fNLdef}) )."1004"∩↖↖↽↸∖↥⋅↸∖↸⊳∪↖↽↸∖↥⋅≼∣⋜⋯↴∖↴↴∖↴↕⋜⋯∐∐⊓⋜↧↕↸⊳∪∐≼∐↑↕∪∐↴∖↴∙ο ος . ∙∙∙ ∙∙ p~=\. with. a linear. density. power spectrum 2-8 EEyup and a two-point linear density correlation cie ⊻↓⊳⊃⊂∙≖≓∖ Livin, = dk i2 PL)e"," For $\fNL=0$ we recover Gaussian initial conditions, $\delta_L=\chi$, with a linear density power spectrum = _2)P_L(k_1), and a two-point linear density correlation _2) = _1) _2) = k k^2 P_L(k)."1005b As usual. it is convenient to introduce the smoothed linear density coutrast. \(x). within the sphere of radius q and volume V. around position x. with a top-hat window that reads in Fourier space as Wk) ENli o3D .," As usual, it is convenient to introduce the smoothed linear density contrast, $\chi_q(\bx)$, within the sphere of radius $q$ and volume $V$ around position $\bx$ ) = _V ) = ) (k q) , with a top-hat window that reads in Fourier space as (k q) = _V = 3 ."1006because the non-zero DPs and non-zero/non-z CPs shown in Fig.,because the non-zero DPs and $\pi$ CPs shown in Fig.1007 1 indicate that the inhomogeneity is spatially resolved with the current spatial resolution., \ref{obsres} indicate that the inhomogeneity is spatially resolved with the current spatial resolution.1008 We examined time variation using the AMBER data taken at nearly the same uv points., We examined time variation using the AMBER data taken at nearly the same $uv$ points.1009 The shortest and middle baselines of the data sets taken on 2009 Feb 28 and 2009 Apr 15 are almost the same (the | m difference in the longest baseline is too significant to study time variations)., The shortest and middle baselines of the data sets taken on 2009 Feb 28 and 2009 Apr 15 are almost the same (the 1 m difference in the longest baseline is too significant to study time variations).1010 A comparison between these two data sets is shown in Fig. 3.., A comparison between these two data sets is shown in Fig. \ref{tempvar}.1011 The sampled wavelengths are slightly different for the two nights because of the difference in the correction to convert the observed wavelength scale to the heliocentric scale., The sampled wavelengths are slightly different for the two nights because of the difference in the correction to convert the observed wavelength scale to the heliocentric scale.1012" Figures 3aa and 3cc show that the observed spectra and the visibilities on the 32 m baseline measured on the two nights form continuous curves, suggesting no time variation."," Figures \ref{tempvar}a a and \ref{tempvar}c c show that the observed spectra and the visibilities on the 32 m baseline measured on the two nights form continuous curves, suggesting no time variation."1013 This is also the case for the 16 m visibility shown in Fig., This is also the case for the 16 m visibility shown in Fig.1014" 3bb except for the CO band head at 2.2936um,, where the visibility measured on Apr 15 is lower than that measured on Feb 28."," \ref{tempvar}b b except for the CO band head at 2.2936, where the visibility measured on Apr 15 is lower than that measured on Feb 28."1015 This suggests possible time variation on a spatial scale of 30 mas (3 X stellar diameter)., This suggests possible time variation on a spatial scale of 30 mas (3 $\times$ stellar diameter).1016 The decrease in the visibility corresponds to an increase in the uniform-disk diameter by (from 16 to 19.5 mas) or an increase in the Gaussian FWHM by (from 10.5 to 12 mas) between Feb 28 and Apr 15., The decrease in the visibility corresponds to an increase in the uniform-disk diameter by (from 16 to 19.5 mas) or an increase in the Gaussian FWHM by (from 10.5 to 12 mas) between Feb 28 and Apr 15.1017" However, the difference is within 3-σ of the data from Feb 28."," However, the difference is within $\sigma$ of the data from Feb 28."1018" Therefore, more observations are needed to definitively confirm time variations in the visibility."," Therefore, more observations are needed to definitively confirm time variations in the visibility."1019" To interpret the AMBER observations, we use the MARCS models."," To interpret the AMBER observations, we use the MARCS models."1020" As mentioned in Sect. 2,,"," As mentioned in Sect. \ref{sect_obs},"1021 these models assume spherical symmetry., these models assume spherical symmetry.1022" Whereas the asymmetry in the CO-line-forming region is detected, we use these spherical models as the first approximation."," Whereas the asymmetry in the CO-line-forming region is detected, we use these spherical models as the first approximation."1023" To select a MARCS model appropriate for BK Vir, we determined its stellar parameters(Tefr,, 9,Umicro»s M,, and chemical composition) as follows."," To select a MARCS model appropriate for BK Vir, we determined its stellar parameters, $\varg$, $M_{\star}$ , and chemical composition) as follows."1024" We estimated the effective temperature from the observed angular diameter and the bolometric flux obtained by integrating the photometric data available in the literature (Two-Micron Sky Survey, Neugebauer Leighton 1969;; NOMAD Catalog, Zacharias et al. 2004;;"," We estimated the effective temperature from the observed angular diameter and the bolometric flux obtained by integrating the photometric data available in the literature (Two-Micron Sky Survey, Neugebauer Leighton \cite{neugebauer69}; ; NOMAD Catalog, Zacharias et al. \cite{zacharias04};"1025" 2MASS, Skrutskie et al. 2006;;"," 2MASS, Skrutskie et al. \cite{skrutskie06};"1026 Fouque et al. 1992;;, Fouque et al. \cite{fouque92}; ;1027 Kerschbaum Hron 1994;; IRAS Point Source Catalog)., Kerschbaum Hron \cite{kerschbaum94}; IRAS Point Source Catalog).1028 The photometric data were corrected for the interstellar extinction using E(B—V) = 0.023 (Schlegel et al. 1998)), The photometric data were corrected for the interstellar extinction using $E(B-V)$ = 0.023 (Schlegel et al. \cite{schlegel98}) )1029 and assuming Ay=3.1E(B-V)., and assuming $A_{V} = 3.1 E(B-V)$ .1030 Combining the angular diameter of 10.73 mas adopted in Sect., Combining the angular diameter of $10.73$ mas adopted in Sect.1031" 2 and a derived bolometric flux of 2.80x10? results in an effective temperature of 2920 K. While this agrees with the effective temperature of 3074€141 K derived by Dyck et al. (1998)),"," \ref{sect_obs} and a derived bolometric flux of $2.80 \times 10^{-9}$ results in an effective temperature of $2920$ K. While this agrees with the effective temperature of $3074 \pm 141$ K derived by Dyck et al. \cite{dyck98}) ),"1032 they obtained a higher bolometric flux of 3.9x107? Wm.., they obtained a higher bolometric flux of $3.9 \times 10^{-9}$ .1033" If we adopt, as the uncertainty in the bolometric flux, a half of the difference between the values from Dyck et al. (1998))"," If we adopt, as the uncertainty in the bolometric flux, a half of the difference between the values from Dyck et al. \cite{dyck98}) )"1034" and from the present work, the total error (i.e., error resulting from the uncertainties in the angular diameter and in the bolometric flux) in our effective temperature is +150 K. Using the distance of 180 pc based on the Hipparcos parallax of 5.53+0.68 mas (van Leeuwen 2007)) and the above bolometric flux of 2.80x10?Wm?,, we derived a luminosity of 2700 == —3.8)."," and from the present work, the total error (i.e., error resulting from the uncertainties in the angular diameter and in the bolometric flux) in our effective temperature is $\pm 150$ K. Using the distance of 180 pc based on the Hipparcos parallax of $5.53 \pm 0.68$ mas (van Leeuwen \cite{vanleeuwen07}) ) and the above bolometric flux of $2.80 \times 10^{-9}$, we derived a luminosity of 2700 = $-3.8$ )."1035" With the error in the parallax and the above error in the bolometric flux, the total uncertainty in the luminosity is +850Lo."," With the error in the parallax and the above error in the bolometric flux, the total uncertainty in the luminosity is $\pm 850$."1036". To estimate the stellar mass, we compared the position of BK Vir on the H-R diagram with theoretical evolutionary tracks."," To estimate the stellar mass, we compared the position of BK Vir on the H-R diagram with theoretical evolutionary tracks."1037" Figure 4 shows evolutionary tracks for 1 and 2 sstars (Herwig 2005 and Bertelli et al. 2008,,"," Figure \ref{hr_diagram} shows evolutionary tracks for 1 and 2 stars (Herwig \cite{herwig05} and Bertelli et al. \cite{bertelli08},"1038" respectively), together with the observationally derived position of BK Vir."," respectively), together with the observationally derived position of BK Vir."1039 The figure suggests that the mass of BK Vir is close to 1Me., The figure suggests that the mass of BK Vir is close to 1.1040. The adoption of a stellar mass of 1 ttranslates into a surface gravity of logg=—0.17 with a stellar radius of 201 ((0.94 AU)., The adoption of a stellar mass of 1 translates into a surface gravity of $\log \varg = -0.17$ with a stellar radius of 201 (0.94 AU).1041" Whereas BK Vir is classified as an AGB star in most of the literature, Fig."," Whereas BK Vir is classified as an AGB star in most of the literature, Fig."1042 4 shows that the luminosity of BK Vir is just at the tip of the RGB., \ref{hr_diagram} shows that the luminosity of BK Vir is just at the tip of the RGB.1043" Moreover, Lebzelter Hron (1999)) report negative detection ο” Τε, which would be strong evidence of the third dredge-up inthe AGB."," Moreover, Lebzelter Hron \cite{lebzelter99}) ) report negative detection of $^{99}$ Tc, which would be strong evidence of the third dredge-up inthe AGB."1044" Therefore, wecannot conclude whether BK Vir is an RGB star or an early-AGB star that has not yet experienced the third dredge-up."," Therefore, wecannot conclude whether BK Vir is an RGB star or an early-AGB star that has not yet experienced the third dredge-up."1045"In either case, however, the surface chemical composition is expected to be","In either case, however, the surface chemical composition is expected to be"1046Chromospheres are the outer region of stars characterized by a positive temperature gradient and a departure from radiative equilibrium.,Chromospheres are the outer region of stars characterized by a positive temperature gradient and a departure from radiative equilibrium.1047 These properties are caused by a heating mechanism in the low density part of stellar atmospheres. which results 1n temperatures ranging between the minimum of the temperature profile and ~20.000 K. The sources of this heating have not been tightly constrained but surface convection and magnetic fields seem to be the main mechanisms responsible for heating the upper atmospheres of giant stars hotter than K2.," These properties are caused by a heating mechanism in the low density part of stellar atmospheres, which results in temperatures ranging between the minimum of the temperature profile and $\sim 20,000$ K. The sources of this heating have not been tightly constrained but surface convection and magnetic fields seem to be the main mechanisms responsible for heating the upper atmospheres of giant stars hotter than K2."1048 For cooler giants (V—R> 0.8). these chromospheres look more extended relative to the stellar radius than for hot giants (V—R« 0.8) and might be associated with stellar winds and pulsation mechanisms. e.g. mass loss driven by accoustic waves.," For cooler giants $V-R > 0.8$ ), these chromospheres look more extended relative to the stellar radius than for hot giants $V-R < 0.8$ ) and might be associated with stellar winds and pulsation mechanisms, e.g. mass loss driven by accoustic waves."1049 These two groups of giant stars were proposed for the first time by ? from an analysis of ultraviolet spectra., These two groups of giant stars were proposed for the first time by \cite{linsky79} from an analysis of ultraviolet spectra.1050 The group of coronal stars (giant stars hotter than K2) display emission lines that must origninate in chromospheres. transition regions. and by implication coronae.," The group of coronal stars (giant stars hotter than K2) display emission lines that must origninate in chromospheres, transition regions, and by implication coronae."1051 The group of non-coronal stars (giant stars cooler than K2) display emission lines formed at temperatures cooler than 20.000 K. which can originate only in chromospheres.," The group of non-coronal stars (giant stars cooler than K2) display emission lines formed at temperatures cooler than $20,000$ K, which can originate only in chromospheres."1052 The Linsky-Hatsch dividing line separates the groups of coronal and non-coronal stars in the Herzsprung-Russell (HR) diagram and was extensively studied in the 80°s (????)..," The Linsky-Haisch dividing line separates the groups of coronal and non-coronal stars in the Herzsprung-Russell (HR) diagram and was extensively studied in the 80's \citep{simon82,haisch87, brown84,carpenter85}."1053 Even if this division of giant stars into two groups seemed too simplistic. hybrid giant stars with mixed coronae and significant wind activity have been revealed (?.. ?.. and ?)).," Even if this division of giant stars into two groups seemed too simplistic, hybrid giant stars with mixed coronae and significant wind activity have been revealed \citealt{reimers82}, \citealt{hall2008}, and \citealt{ayres2010}) )."1054 For example. the K3IIL giant star. ó And. shows an unexpected presence of C IV in emission. which implies that it contains hot material (about 100.000 K). and evidence of a strong. high-velocity wind (?)..," For example, the K3III giant star, $\delta$ And, shows an unexpected presence of C IV in emission, which implies that it contains hot material (about 100,000 K), and evidence of a strong, high-velocity wind \citep{judge1987}."1055 This hybrid state appears to represent the transition between coronal and non-coronal Whatever the classification into either coronal. non-coronal. or hybrid groups. no real agreement has been reached about the geometrical extent of the chromosphere of cool giant stars.," This hybrid state appears to represent the transition between coronal and non-coronal Whatever the classification into either coronal, non-coronal, or hybrid groups, no real agreement has been reached about the geometrical extent of the chromosphere of cool giant stars."1056 Finally. ? argued the chromosphere extents do not change dramatically às a star crosses the Linsky-Haisch dividing line.," Finally, \cite{judge87} argued the chromosphere extents do not change dramatically as a star crosses the Linsky-Haisch dividing line."1057 This result is also supported by model atmospheres developed by ??.. which predict their extent to be between 5% and 50% of the stellar radius (see Table 3 of ?)).," This result is also supported by model atmospheres developed by \citet{cuntz90A,cuntz90B}, , which predict their extent to be between $\%$ and $\%$ of the stellar radius (see Table 3 of \citealt{cuntz90A}) )."1058 These model atmospheres are constructed using spectroscopic observations ofCi.Meu. and llines in the UV and IR wavelength ranges. forcing the radiative transfer of these lines to fit their cores formed in the chromosphere. transition. or coronae It is apparent that the extents of the chromosphere and its physical conditions are still not fully understood for cool giant stars.," These model atmospheres are constructed using spectroscopic observations of, and lines in the UV and IR wavelength ranges, forcing the radiative transfer of these lines to fit their cores formed in the chromosphere, transition, or coronae It is apparent that the extents of the chromosphere and its physical conditions are still not fully understood for cool giant stars."1059 The geometrical constraints on observed chromospheres are non-existant except for eclipsing binaries for which the radius can be measured in a spectral line as for example for the Z Aur system (?).., The geometrical constraints on observed chromospheres are non-existant except for eclipsing binaries for which the radius can be measured in a spectral line as for example for the $\zeta$ Aur system \citep{eaton93}.1060 It is therefore worthwhile to do interferometric observations of red giant stars in the cores of lines formed in chromospheres and to compare the resulting measured radii with those obtained from the continuum during the same run of observations., It is therefore worthwhile to do interferometric observations of red giant stars in the cores of lines formed in chromospheres and to compare the resulting measured radii with those obtained from the continuum during the same run of observations.1061" For this purpose we need an interferometer working in the visible or near-IR such as CHARA/VEGA (?) allowing us to observe the H, line. the ttriplet lines (849. 855 and 860 nm). and the nearby continuum."," For this purpose we need an interferometer working in the visible or near-IR such as CHARA/VEGA \citep{mourard09} allowing us to observe the $_{{\rm \alpha}}$ line, the triplet lines (849, 855 and 860 nm), and the nearby continuum."1062 This work compares the measured radit in different spectral lines and the continuum for seven K giant stars. one of these stars being classified as a coronal star (6B Cet).," This work compares the measured radii in different spectral lines and the continuum for seven K giant stars, one of these stars being classified as a coronal star $\beta$ Cet)."1063 The observations and data processing are described in Sect., The observations and data processing are described in Sect.1064 2., 2.1065 In Sect., In Sect.1066 3. we present our estimates of the fundamental parameters of the program stars. followed inSect.," 3, we present our estimates of the fundamental parameters of the program stars, followed inSect."1067 4 by our study of, 4 by our study of10680.3-10 keV spectra with 5-s time resolution in the rising phase and 10-s resolution during decay.,0.3–10 keV spectra with 5-s time resolution in the rising phase and 10-s resolution during decay.1069" We chose a s section of data prior to the bursts which we used as our ""background"" for spectral fits to the individual spectra of the bursts.", We chose a 2000-s section of data prior to the bursts which we used as our “background” for spectral fits to the individual spectra of the bursts.1070 The response matrices were created with SAS together with the latest calibration products., The response matrices were created with SAS together with the latest calibration products.1071 The net burst-background emission was well fitted with a simple blackbody model., The net burst–background emission was well fitted with a simple blackbody model.1072 The burst and temperature profiles are plotted in Figure 2., The burst and temperature profiles are plotted in Figure 2.1073 We used the EPIC-pn light curve as a guide to extract the first-order RGS spectra for each burst., We used the EPIC-pn light curve as a guide to extract the first-order RGS spectra for each burst.1074 Since the spectral properties are changing during the bursts (see Fig., Since the spectral properties are changing during the bursts (see Fig.1075 2). we studied the RGS spectra separately according to the blackbody temperatures as derived from the EPIC-pn data.," 2), we studied the RGS spectra separately according to the blackbody temperatures as derived from the EPIC-pn data."1076 In Figure 3. we show the correlation between the blackbody temperatures and count rates of all bursts.," In Figure 3, we show the correlation between the blackbody temperatures and count rates of all bursts."1077 A strong positive correlation is found between the two quantities indicating that the properties are very similar for all bursts., A strong positive correlation is found between the two quantities indicating that the properties are very similar for all bursts.1078 Using this correlation as a reference. we divided the bursts into three phases: KT«1.5 keV. LS keV <KT<2 keV. and ΚΤ>2 keV. We note that the division we used here is different from that in the study of 00748-676 (Cottam et al.," Using this correlation as a reference, we divided the bursts into three phases: $kT <1.5$ keV, 1.5 keV $< kT< 2$ keV, and $kT > 2$ keV. We note that the division we used here is different from that in the study of 0748–676 (Cottam et al."1079" 2002) in which the bursts were divided into ""early"" and ""late"" phases.", 2002) in which the bursts were divided into “early” and “late” phases.1080 For each observation. and for each RGS camera. we extracted three separate first-order spectra of the bursts according to their blackbody temperature as determined by the EPIC-pn count rate (Fig.," For each observation, and for each RGS camera, we extracted three separate first-order spectra of the bursts according to their blackbody temperature as determined by the EPIC-pn count rate (Fig."1081 3)., 3).1082 For each RGS camera we used the same response matrix for each observation., For each RGS camera we used the same response matrix for each observation.1083 Finally. we created background spectra using spatially offset regions.," Finally, we created background spectra using spatially offset regions."1084 We then used the task in the SAS software to combine the three RGS spectra of the two observations separately for each RGS camera., We then used the task in the SAS software to combine the three RGS spectra of the two observations separately for each RGS camera.1085 We ended up with 6 spectra in total. one for each interval of the blackbody temperature of the bursts in each of the two RGS cameras.," We ended up with 6 spectra in total, one for each interval of the blackbody temperature of the bursts in each of the two RGS cameras."1086 Since all bursts are statistically indistinguishable. for each temperature interval we combined the spectra of both RGS cameras using the SAS commandresfluxer.," Since all bursts are statistically indistinguishable, for each temperature interval we combined the spectra of both RGS cameras using the SAS command."1087 In Figure 4 we plot the background-subtracted spectra for the three phases of the average burst., In Figure 4 we plot the background-subtracted spectra for the three phases of the average burst.1088 Above 27 the flux drops significantly due to the effect of the interstellar absorption., Above 27 the flux drops significantly due to the effect of the interstellar absorption.1089 We rebinned the spectra with at least 20 counts per spectral bin. and used X statistics to find the best-fitting parameters.," We rebinned the spectra with at least 20 counts per spectral bin, and used $\chi^2$ statistics to find the best-fitting parameters."1090 All three spectra can be adequately fitted with an absorbed blackbody model with a reduced X of —I., All three spectra can be adequately fitted with an absorbed blackbody model with a reduced $\chi^2$ of $\sim 1$.1091 There is no evidence for absorption edges apart from those due to the ISM (oxygen and neon are the most prominent)., There is no evidence for absorption edges apart from those due to the ISM (oxygen and neon are the most prominent).1092 Any real absorption line must be seen in both RGS spectra where there is simultaneous wavelength coverage., Any real absorption line must be seen in both RGS spectra where there is simultaneous wavelength coverage.1093 The only possible line significant at the 3o level of confidence or higher is Ne X Ly-a (theoretical wavelength: 12.1339À)). though it falls in à range covered by only one RGS spectrum.," The only possible line significant at the $3\sigma$ level of confidence or higher is Ne X $\alpha$ (theoretical wavelength: ), though it falls in a range covered by only one RGS spectrum."1094 Fits with, Fits with1095we also restrict our analysis to local perturbations for which |k|/?>>1.,we also restrict our analysis to local perturbations for which $|{\bf k}|R \gg 1$.1096" Writing p=py+op. B=Bo+ 0B. p.=poop. and py=po+opy. V=oOR+ov (with Weplerian rotation OCR)). ancl working in evlindrical coordinates. the linearized versions of equations (1))-(6)) become (QDILD: py-ov..(9) Dp dup. sss pass CECB6B.Bop.) gogap,. . ο... Path — ο... ik. — |. th.| 208p -luyVPav.Ceib:BSBsinPPL gatas: p.J. LOB,= —b.D.vg. = —h212 Bode,NA EOUHx Bik:ὃν... «OD.=hy B dep. (10)ποιο 57=407+dO?/dln Ris the epicevelic [requency."," Writing $\rho=\rho_0+1097\delta \rho$ ${\bf B}={\bf B_0} + \delta {\bf B}$ , $p_{\Perp}=p_0+\delta p_{\Perp}$, and $p_{\Par}= p_0+\delta p_{\Par}$, ${\bf V} = \hat{\phi} \Omega R + \delta {\bf v}$ (with Keplerian rotation $\Omega(R)$ ), and working in cylindrical coordinates, the linearized versions of equations \ref{eq:MHD1}) \ref{eq:MHD3}) ) become (QDH): _0 , -i _0 v_R - _0 (B_z - i k_R -i _0 + _0 v_R = - i k_z - ], -i _0 v_z= - - i k_z[ ^2 } + ^2 ], B_R= - k_z B_z v_R, = - k_z B_z - v_R +, B_z=k_R B_z v_R, where $\kappa^2=4\Omega^2 + d\Omega^2/d \ln R$ is the epicyclic frequency."1098 To complete our svstem of equations aud derive (he dispersion relation for linear perturbations. we need expressions [or dp_ and op).," To complete our system of equations and derive the dispersion relation for linear perturbations, we need expressions for $\delta p_{\Perp}$ and $\delta p_{\Par}$."1099 These can be obtained by taking moments of the linearized and Fourier (ranslormect cdruüft-kimetic equation Chat includes a linearized. DGIx collision operator., These can be obtained by taking moments of the linearized and Fourier transformed drift-kinetic equation that includes a linearized BGK collision operator.1100 The drift-kinetic MIID model is describedby Ixulsrud. (1983) based on earlier work by Kruskal & Oberman (1953) ancl Rosenbluth&Ros, The drift-kinetic MHD model is describedby Kulsrud (1983) based on earlier work by Kruskal $\&$ Oberman (1958) and \citet{Rosenbluth59}.1101toker(1959).. The equation for the distribution function including the effects of gravity is | .|YE LE M leq OFΟἱ where vp=c(ExB) /D7.ui=(v.—vp/2Dis the magnetic moment (conserved in our approximalions in the absence of collisions). Fy)=GMun- b/R?. and," The drift-kinetic equation for the distribution function including the effects of gravity is + f + B + + ) ), where ${\bf v}_E=c\left({\bf E} \times {\bf B}\right)/B^2$ ,$\mu=({\bf v}_{\Perp}-{\bf v}_E)^2/2B$is the magnetic moment (conserved in our approximations in the absence of collisions), $F_{g \Par}=GM_0m 1102\hat{R} \cdot \hat{\bf b}/R^2$ , and"1103assunuue perfect field-uuatter coupling G.c. negligible diffusivity) or through the prescription of a simplified finite resistivity term (c.e. see the review by Puditzetal.2007 and also Ferreira&Pelletier1995:Li1996:Casse&Ferreira2000:Zaunietal. 20073).,"assuming perfect field-matter coupling (i.e. negligible diffusivity) or through the prescription of a simplified finite resistivity term (e.g. see the review by \citealt{POFB07} and also \citealt{FP95, L96, CF00, Zanni07a}) )."1104 This approach is appropriate to follow the propagation of the outflow to large distances for an essentially wind nss flux. but it can not be used to deteriuine. selt-cousistentlv. whether the wind is iu the first place.," This approach is appropriate to follow the propagation of the outflow to large distances for an essentially wind mass flux, but it can not be used to determine, self-consistently, whether the wind is in the first place."1105 A complementary approach. first developed by ↖↖⊽↕↘⊽∩∶≩↕≯∪↥⋅⋜↧↕⋜↕⋯↴⋝↕⋯⋜∐⋅⊣∐↕−↥⋅∏↴∖↴↕∪∐⊣∪∐∐∐⋜↧↑↸∖≼↧≼∐∖↴↸⊳∙↕↴∖↴↑∪ resolve explicitlv the ↖⇁↸∖↥⋅↑↕↸⊳⋜↧↕↴∖↴⊓⋅⋜↧↑↕∐↸⊳⋜↧↑↕∪∐∪↕⋟↑↕∐∖⇡↿↕≼↧ variables. ionisation fraction aud naenetic diffusivity. as well as the resulπιο fieldanatter coupling. for a racially-localised region of he disc.," A complementary approach, first developed by WK93 for an ambipolar-diffusion-dominated disc, is to resolve explicitly the vertical stratification of the fluid variables, ionisation fraction and magnetic diffusivity, as well as the resulting field-matter coupling, for a radially-localised region of the disc."1106 This formulation systematically reduces the nonlinear governing equa101118 that control the evolution of the fluid into a set o ordinary differential equations (ODE) in :., This formulation systematically reduces the nonlinear governing equations that control the evolution of the fluid into a set of ordinary differential equations (ODE) in $z$.1107 This svsteuni describes. for a particular radial location. the vertica structure of the disc — and the base of the outflow roni the müdpluie up to the critical (sonic) surface of tie flow (see also KSWIO for a ecneralisation of this procedure to a tensor diffusvitv).," This system describes, for a particular radial location, the vertical structure of the disc – and the base of the outflow -- from the midplane up to the critical (sonic) surface of the flow (see also KSW10 for a generalisation of this procedure to a tensor diffusivity)."1108 The svstem of ODE is umunevically integrated by applviug boundary conditions at the midplane and at the sonic poiu (see WIX93 and SKWII for details of the numerica procedure]., The system of ODE is numerically integrated by applying boundary conditions at the midplane and at the sonic point (see WK93 and SKW11 for details of the numerical procedure).1109 The ionisation balance is calculated by evaluating the action of ionisation processes (driven bv cosnüc rave. X-rays cuutted by the central object and radioactive decav] aud recombinations occurriug. in general. both in the eas phase aud on erain surfaces (see Section 2.1)).," The ionisation balance is calculated by evaluating the action of ionisation processes (driven by cosmic rays, X-rays emitted by the central object and radioactive decay) and recombinations occurring, in general, both in the gas phase and on grain surfaces (see Section \ref{subsec:Magdiff}) )."1110" The N-ray jouisation rate is taken your the Monte Carlo calculations of Igea&Classeold (1999).. whereas that of cosmic ravs is calculated * atteuuatiue the standard (""cauouical) rate in the iuterstellar miediun as the cosmic rays netrate the disc [the canonical rate is taken to be 105 1) oer hwdrogen atom: see eg. Umoebavashi&Nakano 1981]."," The X-ray ionisation rate is taken from the Monte Carlo calculations of \citet{IG99}, whereas that of cosmic rays is calculated by attenuating the standard (“canonical"") rate in the interstellar medium as the cosmic rays penetrate the disc [the canonical rate is taken to be $10^{17}$ $^{-1}$ ) per hydrogen atom; see e.g. \citealt{UN81}] ]."1111 The field-inatter diffusivity is reated as a eusor. incorporating the all. Olunic and Am)bipolar CYlus (Section 2.1)).," The field-matter diffusivity is treated as a tensor, incorporating the Hall, Ohmic and Ambipolar terms (Section \ref{subsec:Magdiff}) )."1112 This approach eliminates the reed to. keep separate equatious of motion for cach guid component aud ercatly simplifies the caleulatious. σαΠοπαγ. when dust grains are preseut.," This approach eliminates the need to keep separate equations of motion for each fluid component and greatly simplifies the calculations, particularly when dust grains are present."1113 The methodology just described is appropriate to nodel the launch of the wind. but it cannot be used o follow the xopagation of the outflow far from the source. where the thiu-disc approximation breaks down.," The methodology just described is appropriate to model the launch of the wind, but it cannot be used to follow the propagation of the outflow far from the source, where the thin-disc approximation breaks down."1114 It is. however. clearly liCcossarv to eusure tiat the obtained dise solution! coutinucs to accelerate past the souic point.," It is, however, clearly necessary to ensure that the obtained `disc solution' continues to accelerate past the sonic point."1115 To eusure that this is the case. we evaluate the parsuneters of the outflow at the disc surface and match this local solution to a global wind model (ve use for this purpose the BPs? self-similar wind solutions).," To ensure that this is the case, we evaluate the parameters of the outflow at the disc surface and match this local solution to a global wind model (we use for this purpose the BP82 self-similar wind solutions)."1116 Tn order to facilitate the matching. we constructed a library of these selfsimuilar wind solutions’ for a wide range of their model parameters. which are: the uormatlised mass-toauagnetie flux ratio (A). the normalised total specific angular momentum carried away by the wind (A. which incorporates contributions from the matter aud from the magnetic field). aud the inclination of the field) nes at the dise surface (=Ba/DL).," In order to facilitate the matching, we constructed a library of these self-similar `wind solutions' for a wide range of their model parameters, which are: the normalised mass-to-magnetic flux ratio $\kappa$ ), the normalised total specific angular momentum carried away by the wind $\lambda$, which incorporates contributions from the matter and from the magnetic field), and the inclination of the field lines at the disc surface $\xi_{\rm b}' = B_{\rm rb}/B_z$ )."1117 The combinations of these parameters corresponding to viable global wind solutions are shown eraplically in Fig. L., The combinations of these parameters corresponding to viable global wind solutions are shown graphically in Fig. \ref{fig:windres}.1118 The complete set of these results is also available in the electronic version of SIRWII., The complete set of these results is also available in the electronic version of SKW11.1119 The «escribed overall methodologySsoO is useful to explore the viability of these winds as a function of radius frou. the ceutral object. as well as to obtain a realistic estimate of the wind mass loss rate. which could be used to constrain theoretical models against observational resultpA," The described overall methodology is useful to explore the viability of these winds as a function of radius from the central object, as well as to obtain a realistic estimate of the wind mass loss rate, which could be used to constrain theoretical models against observational results."1120 A represcutative ocal solution. matched to the DP82 elobal. selt-sinilar models. is shown iu Fig.," A representative local solution, matched to the BP82 global, self-similar models, is shown in Fig."1121 5 for r=1 AU in a disc siuroundius a solu-m]Óass protostar., \ref{fig:real_sol} for $r = 1$ AU in a disc surrounding a solar-mass protostar.1122 The surface deusitv Is Y—600 ο ? aud the remaining free model parameters are: αρ=0.75. οκο=10. €=0.1 and ep=0.," The surface density is $\Sigma = 600$ g $^{-2}$ and the remaining free model parameters are: $a_{\rm 0} = 0.75$ , $v_{\rm K}/c_{\rm s} = 10$, $\epsilon = 0.1$ and $\epsilon_{\rm B} = 0$."1123 The maeneic diffusivity componcuts and field-anatter coupling (A) are calculated selt-consistently bv evaluating the iouisation balance of the fluid (see Section 2.1))., The magnetic diffusivity components and field-matter coupling $\Lambda$ ) are calculated self-consistently by evaluating the ionisation balance of the fluid (see Section \ref{subsec:Magdiff}) ).1124 On the left-hand side of the figure. the top panel shows he ionisatiou rates contributed by cosmic ravs (curve labelled bw the subscript cor). N-rvavs Car) aud radioactive decay παςὃς aud the bottoni panel displavs the resulting diffusivity terms.," On the left-hand side of the figure, the top panel shows the ionisation rates contributed by cosmic rays (curve labelled by the subscript `cr'), X-rays (`xr') and radioactive decay (`rad'); and the bottom panel displays the resulting diffusivity terms."1125 Ou the right-hand side. the normalised density and magnetic field components in the plane of the disc are shown in the top panel.," On the right-hand side, the normalised density and magnetic field components in the plane of the disc are shown in the top panel."1126 The normalised velocity colmpoucuts are displaved in the bottom panel., The normalised velocity components are displayed in the bottom panel.1127" The elobal wind model parameters ave: &=2.6«10.©, A=LEO. and £52Bu,/B.=1.6."," The global wind model parameters are: $\kappa = 2.6 \times 10^{-6}$, $\lambda = 4.4 \times 10^{3}$, and $\xi'_{\rm b} \equiv B_{r{\rm b}}/B_z = 1.6$."1128 The local mass accretion rate for this model is ~7&109AL.wro|. which is consistent wit ithe interred values for the early (Class 0/Class D) protostellar accretion phase (e.g.IEu-{σαιetal. 1995).," The local mass accretion rate for this model is $\sim 7 \times 10^{-6} \ M_\odot \ {\rm yr}^{-1}$, which is consistent with the inferred values for the early (Class 0/Class I) protostellar accretion phase \citep[e.g.][]{HEG95}."1129. We have also constrained the parameter space occupied by plivsicallv-iable wind-driving disc solutions (sce W893 for the original derivations i tle ambipolar diffusion limit: as well as IRSWIO for the generalisation to a tensor diffusivity and application to the Wall aud Olun reeimes)., We have also constrained the parameter space occupied by physically-viable wind-driving disc solutions (see WK93 for the original derivations in the ambipolar diffusion limit; as well as KSW10 for the generalisation to a tensor diffusivity and application to the Hall and Ohm regimes).1130 Usiug the hwdrostatie approximation (c.g. neelecting the vertical velocity component of thefluid). we are able to show that the solutious are required to satisfv the following constraints.," Using the hydrostatic approximation (e.g. neglecting the vertical velocity component of thefluid), we are able to show that the solutions are required to satisfy the following constraints."1131We emploved a kind of Artificial Neural Networks. called Probabilistie Neural Network (PNNs Specht L988. 1990) which is suitable for classification.,"We employed a kind of Artificial Neural Networks, called Probabilistic Neural Network (PNNs Specht 1988, 1990) which is suitable for classification."1132 A classification problem is defined with a set of inputs { and targets T., A classification problem is defined with a set of inputs $P$ and targets $T$.1133 PNN is a kind of supervised network., PNN is a kind of supervised network.1134 It means (hat the learning process of the network takes place with an iniGally specified set of inputs and targets. called. (rained samples.," It means that the learning process of the network takes place with an initially specified set of inputs and targets, called trained samples."1135 If we assume that the input vectors contain k different. classes. then every target vector would contains & elements.," If we assume that the input vectors contain $k$ different classes, then every target vector would contains $k$ elements."1136 One of them is 1. which corresponds to its own class and the others ave zero.," One of them is 1, which corresponds to its own class and the others are zero."1137 Tle PNN has (wo lavers( Figure 6))., The PNN has two layers( Figure \ref{fig6}) ).1138 When an input vector is fed to the network. the first laver calculates the distance," When an input vector is fed to the network, the first layer calculates the distance"1139respectively for these two systems). with the seven. [lat-spectrum sources presented in Figs 1 and 4.,respectively for these two systems) with the seven flat-spectrum sources presented in Figs 1 and 4.1140 Outburst dates. distance estimates and associated references are given in table 3: for NTE 1748-288 we assume a distance of 8.5 kpe given its proximity to the galactie centre.," Outburst dates, distance estimates and associated references are given in table 3; for XTE J1748-288 we assume a distance of 8.5 kpc given its proximity to the galactic centre."1141 While this is not a completely comprehensive sample of data for optically thin events. it is probably representative of the range of luminosities observed in optically thin events (Cve N-3 being the brightest radio source associated. with an X-ray binary see e.g. Fender Ixuulkers 2001).," While this is not a completely comprehensive sample of data for optically thin events, it is probably representative of the range of luminosities observed in optically thin events (Cyg X-3 being the brightest radio source associated with an X-ray binary – see e.g. Fender Kuulkers 2001)."1142 Two things are immediately apparent Lt has been shown that. as well as the persistent. svstenis Cve N-1 and GX 339-4. ancl also probably 15 1740.7-2042 and GRS 1758-258. X-ray transient. black hole candidates also show a low-level. [atinverted spectral component. at radio wavelengths when in the Lowανά X-ray state for any length of time.," Two things are immediately apparent: It has been shown that, as well as the persistent systems Cyg X-1 and GX 339-4, and also probably 1E 1740.7-2942 and GRS 1758-258, X-ray transient black hole candidates also show a low-level, flat/inverted spectral component at radio wavelengths when in the Low/Hard X-ray state for any length of time."1143 In this section we discuss the spectral form and extent. polarisation properties and degree of variability of the Hat/inverted spectral components.," In this section we discuss the spectral form and extent, polarisation properties and degree of variability of the flat/inverted spectral components."1144 As discussed in Fender ct al. (, As discussed in Fender et al. (11452000) for the case of Cve N-1. as vet no-one has found either high- or low-freeuencey cutolls to the Dat spectral component ancl as a result the energy associated with it is essentially unconstrained.,"2000) for the case of Cyg X-1, as yet no-one has found either high- or low-frequency cutoffs to the flat spectral component and as a result the energy associated with it is essentially unconstrained."1146 However in Cvg X-1: the flat. spectral component. is overwhelmed bv thermal emission. from. the OB-tywpe companion. star at wavelengths A 3050 (Fender et al., However in Cyg X-1 the flat spectral component is overwhelmed by thermal emission from the OB-type companion star at wavelengths $\lambda \leq 30\mu$ m (Fender et al.1147 2000)., 2000).1148 In. the case of GRS 19151105 (Fender Pooley 1998.2000. and references therein). anc possibly Cvg X-3 (Fender et al.," In the case of GRS 1915+105 (Fender Pooley 1998,2000 and references therein), and possibly Cyg X-3 (Fender et al."1149" 1996) and GX 339-4 (Corbel Fender 2000) there is strong evidence that the at spectral component extends to the near-infrared (X-band. 2.250). and hence has a much larger racliative Luminosity (>107"" org + for GRS 1915|105) than could. be anticipated from radio observations. only."," 1996) and GX 339-4 (Corbel Fender 2000) there is strong evidence that the flat spectral component extends to the near-infrared (K-band, $2.2 \mu$ m), and hence has a much larger radiative luminosity $\geq 10^{36}$ erg $^{-1}$ for GRS 1915+105) than could be anticipated from radio observations only."1150 llowever. only one of these systems (ον 339-4) is in the canonical “Lowατα X-ray state (the X-ray states of (νο X-3 and GRS 1915|105 evade simple classification. although GRS 1915|105 may spend much of its time in something like the Very. High State 3elloni 1998).," However, only one of these systems (GX 339-4) is in the canonical `Low/Hard' X-ray state (the X-ray states of Cyg X-3 and GRS 1915+105 evade simple classification, although GRS 1915+105 may spend much of its time in something like the Very High State – Belloni 1998)."1151 Do the lat spectral components associated with the transients in the Lowση state also extend to the near-infrared or bevond?, Do the flat spectral components associated with the transients in the Low/Hard state also extend to the near-infrared or beyond?1152 Han Ljellming (1992) report a very clear correlation between X-ray. optical anc radio fluxes [rom Cis 2023|38 during the decay following the outburst.," Han Hjellming (1992) report a very clear correlation between X-ray, optical and radio fluxes from GS 2023+38 during the decay following the outburst."1153 Phe spectral evolution from radiooptical is illustrated. in Fie 5., The spectral evolution from radio–optical is illustrated in Fig 5.1154 We asstune an extinction. in the optical R-band of 2.3 magnitudes (based on ely=3 mag Shahbaz et al., We assume an extinction in the optical R-band of 2.3 magnitudes (based on $A_{\rm V}=3$ mag – Shahbaz et al.1155 1994: lüeke Lebolsky 1985)., 1994; Rieke Lebofsky 1985).1156 Phe radiooptical spectrum can be fitted by a single powerlaw shortly after the emergence of the fat spectral component around ALJD 47685., The radio–optical spectrum can be fitted by a single power–law shortly after the emergence of the flat spectral component around MJD 47685.1157 After that the radio spectrum inverts while the highest frequency. (usually 14.9 CGllz) radio [lux densities closely track the ereddened optical Mux., After that the radio spectrum inverts while the highest frequency (usually 14.9 GHz) radio flux densities closely track the dereddened optical flux.1158 Such a strong correlation implies common emission mechanism. and we suggest that in this case the optical Hux during this phase of the decay was dominated by high-frequeney. svnchrotron emission.," Such a strong correlation implies a common emission mechanism, and we suggest that in this case the optical flux during this phase of the decay was dominated by high-frequency synchrotron emission."1159 Why the radio spectrum. should. invert. without allecting the optical Εαν. if it is also svnchrotron. may be ue to free-frece absorption [rom debris local to the system Following the outburst (Zvcki. Done Smith 1999a.b do report a large and variable absorption component present in X-ray spectra following the outburst).," Why the radio spectrum should invert, without affecting the optical flux, if it is also synchrotron, may be due to free-free absorption from debris local to the system following the outburst (Zycki, Done Smith 1999a,b do report a large and variable absorption component present in X-ray spectra following the outburst)."1160 In Appendix A it is shown that a simple model in which the intrinsic jet emission sullers foreground. [rec-free absorption can be used to fit the data. but this is certainly an oversimplification of the true. picture.," In Appendix A it is shown that a simple model in which the intrinsic jet emission suffers foreground free-free absorption can be used to fit the data, but this is certainly an oversimplification of the true picture."1161 Importantly. we cannot rule out varving internal svnchrotron self-absorption. but evaluation of its significance would require modelling of the jet. which is beyond the scope of this work.," Importantly, we cannot rule out varying internal synchrotron self-absorption, but evaluation of its significance would require modelling of the jet, which is beyond the scope of this work."1162 The radio spectra of GRO J0422|32 and GS 1354-64 are also observed to invert as the outburst declines. (Fig 3). in à manner consistent with increasing low-frequency absorption.," The radio spectra of GRO J0422+32 and GS 1354-64 are also observed to invert as the outburst declines (Fig 3), in a manner consistent with increasing low-frequency absorption."1163 There is also evidence in both cases for an extension of the Lat spectral component to the optical bands., There is also evidence in both cases for an extension of the flat spectral component to the optical bands.1164 Van Paradijs et al. (, Van Paradijs et al. (11651994) discuss a Lat spectral component [rom θα through to the optical band. from GRO J0422|32. which they attribute to free-free emission. most probably from. a. disc-wind.,"1994) discuss a flat spectral component from $10 \mu$ m through to the optical band from GRO J0422+32, which they attribute to free-free emission, most probably from a disc-wind."1166 Shrader et al. (, Shrader et al. (11671994) also note that the dereddened: optical continuum of GRO J0422|32 rapidly evolves to a Lat spectrum (a~ 0) during the decay phase of the outburst.,1994) also note that the dereddened optical continuum of GRO J0422+32 rapidly evolves to a flat spectrum $\alpha \sim 0$ ) during the decay phase of the outburst.1168 Finally. Brocksopp et al. (," Finally, Brocksopp et al. ("11692001) also report evidence for correlated radio: optical emission from GS 1354-64.,2001) also report evidence for correlated radio: optical emission from GS 1354-64.1170 In all three sources the spectrum from the highest radio, In all three sources the spectrum from the highest radio1171as the flow of particles coming out of the ram-oessure douunated PWN.,as the flow of particles coming out of the ram-pressure dominated PWN.1172 In this scenario. the N-rav cussion from lis originated from the svuchrotrou radiation from he wind particles accelerated at the teriuinatiou shock.," In this scenario, the X-ray emission from is originated from the synchrotron radiation from the wind particles accelerated at the termination shock."1173 This is consistent with the uupulsed nou-hermal cnussion iuferred from this observation., This is consistent with the unpulsed non-thermal emission inferred from this observation.1174" For the svuchrotron cutting leptons of Loreutz ‘factor 5 distribute as /N(5)xw 5"". the observed yhotou iudex of P.—2.2 from the pulsar location is consistent with he value expected from the fast-cooling scenario. D—(p|2)/2. for he electrou index lies within a typical range of p—2.3 (Cheng. Taam. Wang 2006)."," For the synchrotron emitting leptons of Lorentz factor $\gamma$ distribute as $N\left(\gamma\right)\propto\gamma^{-p}$ , the observed photon index of $\Gamma\sim2.2$ from the pulsar location is consistent with the value expected from the fast-cooling scenario, $\Gamma=\left(p+2\right)/2$, for the electron index lies within a typical range of $p\sim2-3$ (Cheng, Taam, Wang 2006)."1175" This putative feature. which has an extent of ~s"" in EPIC images. should be resolve by Chaudra."," This putative feature, which has an extent of $\sim8''$ in EPIC images, should be resolved by Chandra."1176 Nevertheless. ia reexainuiniug the archival Chandra data. its extent caunot confir.," Nevertheless, in reexamining the archival Chandra data, its extent cannot confirm."1177 On the other hand. the photon distribution of in the iierged Chandra image is slightly deviatec froin a point source with the deformation also toward the direction behind the pulsar proper motion.," On the other hand, the photon distribution of in the merged Chandra image is slightly deviated from a point source with the deformation also toward the direction behind the pulsar proper motion."1178 Although the evidence for je extende source cannot be conclusive with the existing data. the conrpact feature suggested v the Chaudra data can possibly be the portion of the highes surface brightuess.," Although the evidence for the extended source cannot be conclusive with the existing data, the compact feature suggested by the Chandra data can possibly be the portion of the highest surface brightness."1179 Complex. structures of bow-shock PWNe have been observed iu other systems., Complex structures of bow-shock PWNe have been observed in other systems.1180 For example. NMNL-Newtou observation of a nearby pulsar PSR B1929LO has revealed a long N-rav tail of several arc-uuiuutes (Becker et al.," For example, XMM-Newton observation of a nearby pulsar PSR B1929+10 has revealed a long X-ray tail of several arc-minutes (Becker et al."1181 2006)., 2006).1182 Apart from coufirmine he detection of this long trail. a follow-up Clhaudra observation has further resolved a brighter but more compact feature with an extent of ~10” around the pulsar (Thu Becker 2008).," Apart from confirming the detection of this long trail, a follow-up Chandra observation has further resolved a brighter but more compact feature with an extent of $\sim10''$ around the pulsar (Hui Becker 2008)."1183 For a further investigation of65.. a dedicated deep Chandra observation. Which simultaneously provides a sub-arcsecond spatial resolution aud a photon statistic conrparable with this NMM-Newtonu observation. is the only way to confirm or refute this sugeested feature.," For a further investigation of, a dedicated deep Chandra observation, which simultaneously provides a sub-arcsecond spatial resolution and a photon statistic comparable with this XMM-Newton observation, is the only way to confirm or refute this suggested feature."1184 Wile this compact feature is still questionable. the evidence for the ~2’ long jet is nuambignons.," While this compact feature is still questionable, the evidence for the $\sim2'$ long jet is unambiguous."1185 Although all the N-vay studies suggest its non-thermal nature. its plivsical origin remains to be obscure.," Although all the X-ray studies suggest its non-thermal nature, its physical origin remains to be obscure."1186 Very recentlv. a collimated ~9% longs N-rav feature has been discovered from a radio-quiet > rav pulsar PSR JO35713205 (De Luca et al.," Very recently, a collimated $\sim9'$ long X-ray feature has been discovered from a radio-quiet $\gamma-$ ray pulsar PSR J0357+3205 (De Luca et al."1187 2011) which is very similu to the jet ofD2221165., 2011) which is very similar to the jet of.1188. It is interesting to compare the observed properties between these two svsteuis., It is interesting to compare the observed properties between these two systems.1189 The spin-down ποσατν of PSR JO357|3205. E6107 cress. is ~6 times higher than that ofB2221165.. but it is the lowes a1nong i] known noncecveled 5 rav pulsars.," The spin-down luminosity of PSR J0357+3205, $\dot{E}\sim6\times10^{33}$ erg/s, is $\sim6$ times higher than that of, but it is the lowest among all known non-recycled $\gamma-$ ray pulsars."1190 The low cohunn absorption suggests it is à nearby pulsar with a distance of onlv a few hundred parsec., The low column absorption suggests it is a nearby pulsar with a distance of only a few hundred parsec.1191 Asstuning there is no inclination with respect to the skv plane. this sueeests the plysical exteut of the trail associated with PSR J0357|3205 at the order of ~l1 pe which is similar to the case of D2221165.," Assuming there is no inclination with respect to the sky plane, this suggests the physical extent of the trail associated with PSR J0357+3205 at the order of $\sim1$ pc which is similar to the case of ."1192. In both cases. there is no evidence of spectral variation along the feature.," In both cases, there is no evidence of spectral variation along the feature."1193" For a distance of 500 pc. the N-rav. conversion efücienev L,E of its trail du 0.510 keV is ~107."," For a distance of 500 pc, the X-ray conversion efficiency $L_{x}/\dot{E}$ of its trail in $0.5-10$ keV is $\sim10^{-3}$."1194" Adopting a distance of 1 kpc forD22?21|65.. L,/E of its jet iu the same enerey band is found to be ~107 which is au order larger than that for PSR J0357|3205."," Adopting a distance of 1 kpc for, $L_{x}/\dot{E}$ of its jet in the same energy band is found to be $\sim10^{-2}$ which is an order larger than that for PSR J0357+3205."1195 This might be why the jet of ccau still be detected in spite of its larger distance., This might be why the jet of can still be detected in spite of its larger distance.1196 Following De Luca et al. (, Following De Luca et al. (11972011). we estimate the highest achievable energv of svuchrotrou-radiating particles injected bv65.,"2011), we estimate the highest achievable energy of synchrotron-radiating particles injected by."1198. First. we assunme the highest energy of the clectrous/positrous cau be gained is comparable witli maxima potential drop im the maeguetosphere. which is AP=E2e) for an aligned usar (Goldreich Julian 1969).," First, we assume the highest energy of the electrons/positrons can be gained is comparable with maximum potential drop in the magnetosphere, which is $\Delta\Phi=\left(3\dot{E}/2c\right)^{1/2}$ for an aligned pulsar (Goldreich Julian 1969)."1199 Sinular to he case of PSR JO357|3205. this results in a nuaxinuu Lorentz factor of 5444~1075.," Similar to the case of PSR J0357+3205, this results in a maximum Lorentz factor of $\gamma_{\rm max}\sim10^{8}$."1200 In the oesence of a magnetic field. these particles will radiate svuchrotron enuüssion with characteristic Yequenev of vy=οωμο. where Bye is he local magnetic field streugth in the cussion reeion in units of microgauss.," In the presence of a magnetic field, these particles will radiate synchrotron emission with characteristic frequency of $\nu_x=\gamma^2eB/m_ec$, where $B_{\mu G}$ is the local magnetic field strength in the emission region in units of microgauss."

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