ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 We find no significant correlation (ie..," We find no significant correlation (ie.,"3 (r)=0.08 and (P)= 0.08). while only in 16 out of the 40000 cases do we lind a similar e—z correlation having the observed. or higher significance level.," $\langle r\rangle=0.08$ and $\langle{\cal4P}\rangle=0.08$ ), while only in 16 out of the 40000 cases do we find a similar $\epsilon-z$ correlation having the observed, or higher significance level."5 This number drops io 3 if we use a random. instead of a clustered. background in the mock cluster construction.," This number drops to 3 if we use a random, instead of a clustered, background in the mock cluster construction."6 Since we have used (he extreme case where all the background is assiuned to be clustered at the distance of each APM cluster. we should consider the derived significance as an upper limit.," Since we have used the extreme case where all the background is assumed to be clustered at the distance of each APM cluster, we should consider the derived significance as an upper limit."7 Therefore the true significance of the observed €—2 correlation. taking into account the possible redshift dependent svstematic effects. is verifving that our ellipticity determination method. coupled with shot-noise ancl the projection of a clustered background cannot create the observed €—2 trend.," Therefore the true significance of the observed $\epsilon-z$ correlation, taking into account the possible redshift dependent systematic effects, is verifying that our ellipticity determination method, coupled with shot-noise and the projection of a clustered background cannot create the observed $\epsilon-z$ trend."8 Regarding the 1—z relation. we have found (hat there is indeed a correlation. especially apparent in the hieh-L subsample. which spans a larger range in z (see Figure 32 and Table 1)," Regarding the $kT -z$ relation, we have found that there is indeed a correlation, especially apparent in the $L$ subsample, which spans a larger range in $z$ (see Figure 3 and Table 1)."9 The correlation coefficient. for the combined XDAC-DCS high-L subsample (were for ihe common clusters we have used only the more accurate BCS values) is r20.47 with probability of chance correlation being P~3xLO+., The correlation coefficient for the combined XBAC-BCS $L$ subsample (were for the common clusters we have used only the more accurate BCS values) is $r\simeq 0.47$ with probability of chance correlation being ${\cal P}\simeq 3 \times 10^{-4}$.10 This correlation is also apparent in each individual cluster sample as well. alühough with a slightly lower significance.," This correlation is also apparent in each individual cluster sample as well, although with a slightly lower significance."11 A similar but weaker AT—z correlation is found in the low-L sample., A similar but weaker $kT -z$ correlation is found in the $L$ sample.12" Note. however. that many of the used temperatures are based on the L,—£T relation of Whiteetal.(1997) and thus this correlation could be a manifestation of an underlying {τς relation."," Note, however, that many of the used temperatures are based on the $L_x-kT$ relation of \citet{WhiteF} and thus this correlation could be a manifestation of an underlying $L_x-z$ relation."13 In order to investigate this possibility we restrict our analvsis only to those clusters with measured temperatures. reducing our samples considerably (bv more than 50%)). but the correlation of T wilh z persists (see Table 1).," In order to investigate this possibility we restrict our analysis only to those clusters with measured temperatures, reducing our samples considerably (by more than ), but the correlation of $kT$ with $z$ persists (see Table 1)."14" Especially for the low-L, sample the", Especially for the $L_x$ sample the15ended with a much brighter star the detection elliciency or such an event will be very small.,blended with a much brighter star the detection efficiency for such an event will be very small.16 Also the time-scale of an event is alfected by. blending ancl appears shorter with ending (see e.g.. Wozniak&Paczviiski 1997:: Smithetal. Y07)).," Also the time-scale of an event is affected by blending and appears shorter with blending (see e.g., \citealt{Wozniakblending}; ; \citealt{Smith2007blending}) )."17 Ht is eriticallv important to understand the blending and its effects on the optical depth estimator., It is critically important to understand the blending and its effects on the optical depth estimator.18 The amount of blending can be estimated by comparing the eround-based images with much more detailed archivalHUST images and then grouping fields according to their stellar density and applying a fixed correction to the number of monitored stars for cach density level., The amount of blending can be estimated by comparing the ground-based images with much more detailed archival images and then grouping fields according to their stellar density and applying a fixed correction to the number of monitored stars for each density level.19 Such a method was applied. in Paper | and Paper HE lor the OGLE-IL data., Such a method was applied in Paper I and Paper II for the OGLE-II data.20 Llowever. the area covered. in a singleS7 image is tiny. hence such comparison results in very low number statistics of cross-matched stars.," However, the area covered in a single image is tiny, hence such comparison results in very low number statistics of cross-matched stars."21 Moreover. OGLELL fields cover à very wide spectrum of stellar. densities. which is dillieult to cover with enough. number of archival LST images.," Moreover, OGLE–III fields cover a very wide spectrum of stellar densities, which is difficult to cover with enough number of archival HST images."22 “Vherefore to address the issue of blending here. we performed simulations of the OGLE-LL images based on combined stellar luminosity functions derived from the451 and OGLE images.," Therefore to address the issue of blending here, we performed simulations of the OGLE-III images based on combined stellar luminosity functions derived from the and OGLE images."23 Dased on known properties of the OGLE-LU images. such as the point spread. functions (PSE) size ancl shape as well as the shape of the underlsing stellar. luminosity function. we are able to simulate OGLE-LL images with cilferent stellar densities ancl luminosity functions.," Based on known properties of the OGLE-III images, such as the point spread function's (PSF) size and shape as well as the shape of the underlying stellar luminosity function, we are able to simulate OGLE-III images with different stellar densities and luminosity functions."24 We used the LMC photometry from.Photomery (Lloltzmanetal.2006)., We used the LMC photometry from \citep{Holtzman2006}.25. Three selectec LUST fields.U4BLIS.u6500s. and. u65007. were each observed in E555V (ESIAW) filter with the WEDPC?2 for 2000 sec (2000 sec). 2560 sec (2460 sec). ane 1560 sec (1560 sec) seconds.," Three selected HST fields, and , were each observed in F555V (F814W) filter with the WFPC2 for 2000 sec (2000 sec), 2560 sec (2460 sec), and 1560 sec (1560 sec) seconds."26 These fields were calibratec to the standard Z-band filter ancl were located in OGLIZs [lields LAIC162.6 (dense). LMCTI9.2 (medium density). ane LMCT136.1. (sparse).," These fields were calibrated to the standard $I$ -band filter and were located in OGLE's fields LMC162.6 (dense), LMC119.2 (medium density), and LMC136.1 (sparse)."27 Then. the OGLE and457 luminosity functions were combined with a stitching point arounc the red clump Z-band magnitude. ic.fe18.2 mag.," Then, the OGLE and luminosity functions were combined with a stitching point around the red clump $I$ -band magnitude, $I\approx18.2$ mag."28 Due to low number statistics lor stars with £<14d mag we approximated the luminosity function with logCN)x0.4./., Due to low number statistics for stars with $I<14$ mag we approximated the luminosity function with $\log(N)\propto 0.4\times I$.29 Each of the luminosity functions had a slightly: cillerent shape shown in Fig. 7..," Each of the luminosity functions had a slightly different shape shown in Fig. \ref{fig:LF},"30 but. as show Later. this allects the correction [actor for the number of monitored stars by [ess han 5 per cent (Fig. 12)).," but, as show later, this affects the correction factor for the number of monitored stars by less than 5 per cent (Fig. \ref{fig:CF2}) )."31 3elore each simulation the basic parameters of. the OCGLIZ-HLIE template image were measured., Before each simulation the basic parameters of the OGLE-III template image were measured.32" This included the ""SE shapes anc sizes. and the background level."," This included the PSF shapes and sizes, and the background level."33 First. we created a mock image (900:500 pixels) with the background ight and Poisson noise that matched the original OGLE images.," First, we created a mock image $800\times800$ pixels) with the background light and Poisson noise that matched the original OGLE images."34 Next. we chose anLEST stellar density as 2007772 staus/arenmin?. where / is the simulation number. and /=1 o 15.," Next, we chose an stellar density as $200\times i^{3/2}$ $^2$, where $i$ is the simulation number, and $i=1$ to 15."35 Then. we injected stars that were drawn from the combined luminosity Function (top panel in Fig. 7))," Then, we injected stars that were drawn from the combined luminosity function (top panel in Fig. \ref{fig:LF}) )"36 and were xighter than 7z24-8 mag., and were brighter than $I \la 24.8$ mag.37 The faint end (7>23.4 mag) of the luminosity function had a minimal impact on our study (see Fig. 12)), The faint end $I > 23.4$ mag) of the luminosity function had a minimal impact on our study (see Fig. \ref{fig:CF2}) )38 as our limiting search for microlensing events is £=20.4|3.023.4 mag: the faint end. simply serves as à background. here., as our limiting search for microlensing events is $I=20.4+3.0=23.4$ mag; the faint end simply serves as a background here.39 Here. £=20.4 mag is the magnitude threshold for stars(blends) we allow in our search [or microlensing events. hence stars fainter by," Here, $I=20.4$ mag is the magnitude threshold for stars(blends) we allow in our search for microlensing events, hence stars fainter by"40 Here. £=20.4 mag is the magnitude threshold for stars(blends) we allow in our search [or microlensing events. hence stars fainter by," Here, $I=20.4$ mag is the magnitude threshold for stars(blends) we allow in our search for microlensing events, hence stars fainter by$"41 Here. £=20.4 mag is the magnitude threshold for stars(blends) we allow in our search [or microlensing events. hence stars fainter by," Here, $I=20.4$ mag is the magnitude threshold for stars(blends) we allow in our search for microlensing events, hence stars fainter by$\"42 Here. £=20.4 mag is the magnitude threshold for stars(blends) we allow in our search [or microlensing events. hence stars fainter by," Here, $I=20.4$ mag is the magnitude threshold for stars(blends) we allow in our search for microlensing events, hence stars fainter by$\D"43 Here. £=20.4 mag is the magnitude threshold for stars(blends) we allow in our search [or microlensing events. hence stars fainter by," Here, $I=20.4$ mag is the magnitude threshold for stars(blends) we allow in our search for microlensing events, hence stars fainter by$\De"44 Here. £=20.4 mag is the magnitude threshold for stars(blends) we allow in our search [or microlensing events. hence stars fainter by," Here, $I=20.4$ mag is the magnitude threshold for stars(blends) we allow in our search for microlensing events, hence stars fainter by$\Del"45 Here. £=20.4 mag is the magnitude threshold for stars(blends) we allow in our search [or microlensing events. hence stars fainter by," Here, $I=20.4$ mag is the magnitude threshold for stars(blends) we allow in our search for microlensing events, hence stars fainter by$\Delt"46 Here. £=20.4 mag is the magnitude threshold for stars(blends) we allow in our search [or microlensing events. hence stars fainter by," Here, $I=20.4$ mag is the magnitude threshold for stars(blends) we allow in our search for microlensing events, hence stars fainter by$\Delta"47 Here. £=20.4 mag is the magnitude threshold for stars(blends) we allow in our search [or microlensing events. hence stars fainter byA," Here, $I=20.4$ mag is the magnitude threshold for stars(blends) we allow in our search for microlensing events, hence stars fainter by$\Delta "48 Here. £=20.4 mag is the magnitude threshold for stars(blends) we allow in our search [or microlensing events. hence stars fainter byAm," Here, $I=20.4$ mag is the magnitude threshold for stars(blends) we allow in our search for microlensing events, hence stars fainter by$\Delta m"49 Here. £=20.4 mag is the magnitude threshold for stars(blends) we allow in our search [or microlensing events. hence stars fainter byAm=," Here, $I=20.4$ mag is the magnitude threshold for stars(blends) we allow in our search for microlensing events, hence stars fainter by$\Delta m="50 Here. £=20.4 mag is the magnitude threshold for stars(blends) we allow in our search [or microlensing events. hence stars fainter byAm=3," Here, $I=20.4$ mag is the magnitude threshold for stars(blends) we allow in our search for microlensing events, hence stars fainter by$\Delta m=3"51 Here. £=20.4 mag is the magnitude threshold for stars(blends) we allow in our search [or microlensing events. hence stars fainter byAm=3.," Here, $I=20.4$ mag is the magnitude threshold for stars(blends) we allow in our search for microlensing events, hence stars fainter by$\Delta m=3."52 Here. £=20.4 mag is the magnitude threshold for stars(blends) we allow in our search [or microlensing events. hence stars fainter byAm=3.0," Here, $I=20.4$ mag is the magnitude threshold for stars(blends) we allow in our search for microlensing events, hence stars fainter by$\Delta m=3.0"53 Here. £=20.4 mag is the magnitude threshold for stars(blends) we allow in our search [or microlensing events. hence stars fainter byAm=3.0," Here, $I=20.4$ mag is the magnitude threshold for stars(blends) we allow in our search for microlensing events, hence stars fainter by$\Delta m=3.0$"54toward measuring the masses of supermassive black holes (e.g. IXormendy Richstone 1995: Magorrian οἱ al.,toward measuring the masses of supermassive black holes (e.g. Kormendy Richstone 1995; Magorrian et al.55 1998: Ferrarese Merritt 2000: Gebhardt et al., 1998; Ferrarese Merritt 2000; Gebhardt et al.56 2000: Ferrarese Ford 2005). though measuring the spin has been more challenging.," 2000; Ferrarese Ford 2005), though measuring the spin has been more challenging."57 General theoretical studies suggest that the merger ancl accretion history of a supermassive black hole is encoded in the spin of the hole., General theoretical studies suggest that the merger and accretion history of a supermassive black hole is encoded in the spin of the hole.58 For example. successive mergers are likely to produce black holes that are spinning al a moderate rate (j~0.7). while powerful accretion events are likely to produce rapidly rotating black holes (Berti Volonteri 2008).," For example, successive mergers are likely to produce black holes that are spinning at a moderate rate $j \sim 0.7$ ), while powerful accretion events are likely to produce rapidly rotating black holes (Berti Volonteri 2008)."59" Alternatively, most black holes may grow due to many short-lived. uncorrelated. accretion episodes. which would lead to lower spin values (Nine Pringle 2006. 2007)."," Alternatively, most black holes may grow due to many short-lived, uncorrelated accretion episodes, which would lead to lower spin values (King Pringle 2006, 2007)."60 Numerous uncorrelated accretion episodes tend to cause the spin of the hole to decrease over Gime with substantial fluctuations in spin caused bv each episode (xine. Pringle. Hofmann 2008).," Numerous uncorrelated accretion episodes tend to cause the spin of the hole to decrease over time with substantial fluctuations in spin caused by each episode (King, Pringle, Hofmann 2008)."61 At present. only a few observations allow black hole spins to be studied directly.," At present, only a few observations allow black hole spins to be studied directly."62 Observations of Sevfert galaxies suggest rapidly rotating black holes in these svstems (Wilms et al., Observations of Seyfert galaxies suggest rapidly rotating black holes in these systems (Wilms et al.63 2001: Fabian et al., 2001; Fabian et al.64 2002)., 2002).65 A large spin is indicated by observations of the Galactie center black hole (Genzel et al., A large spin is indicated by observations of the Galactic center black hole (Genzel et al.66 2003: Aschenbach οἱ al., 2003; Aschenbach et al.67 2004)., 2004).68 And. X-ray observations of active galaxies suggest rapidly rotating black holes in these svstems (Crumuny οἱ al.," And, X-ray observations of active galaxies suggest rapidly rotating black holes in these systems (Crummy et al."69 2006)., 2006).70 Outflows from AGN that produce extended radio sources allow a lower bound to be placed on the spin of the black hole that powers the outllow., Outflows from AGN that produce extended radio sources allow a lower bound to be placed on the spin of the black hole that powers the outflow.71 Assuming only that the outflow is powered by the spin enerev of the black hole. Daly (2009) showed that the outflow energy and the black hole mass may be combined to obtain a lower limit on the spin of the black hole.," Assuming only that the outflow is powered by the spin energy of the black hole, Daly (2009) showed that the outflow energy and the black hole mass may be combined to obtain a lower limit on the spin of the black hole."72 For a sample of 19 verv powerful classical double sources. the lower bound was about the same for each source in the sample. and indicated. μμ590.12d0.01.," For a sample of 19 very powerful classical double sources, the lower bound was about the same for each source in the sample, and indicated $j_{min} \approx 0.12 \pm 0.01$."73 llere. beam powers ancl black hole masses of radio sources are combined (to study black hole spins in (he contexts of the models of Blandford Znajek (1977). Meier (1999). and models with similar fanctional forms.," Here, beam powers and black hole masses of radio sources are combined to study black hole spins in the contexts of the models of Blandford Znajek (1977), Meier (1999), and models with similar functional forms."74 IH is shown that the spin ancl magnetic field strength of a supermassive black hole can be rather tightly constrained in the contexts of these moclels., It is shown that the spin and magnetic field strength of a supermassive black hole can be rather tightly constrained in the contexts of these models.75 The method is described in section 2., The method is described in section 2.76 It is applied to two samples of sources. and the results are presented in section 3. diseussed in section 4. and summarized in section 5.," It is applied to two samples of sources, and the results are presented in section 3, discussed in section 4, and summarized in section 5."77" A standard cosmological model with ff)=10 km/s/Mpe. Q,,=D0.3. Q4=0.7. and zero space curvature is assumed. throughout."," A standard cosmological model with $H_0 = 70$ km/s/Mpc, $\Omega_m = 0.3$, $\Omega_{\Lambda}=0.7$, and zero space curvature is assumed throughout."78 The well-known model of Blandford Znajek (1917). relerred to as the “BZ model. and other models to power highly collimated! outflows rom ACN are considered here.," The well-known model of Blandford Znajek (1977), referred to as the 'BZ' model, and other models to power highly collimated outflows from AGN are considered here."79 In the, In the80absolute sizes of the binary members.,absolute sizes of the binary members.81" Second, these systems are observed proportional to the total time they spend in each state of their evolution."," Second, these systems are observed proportional to the total time they spend in each state of their evolution."82 Binary asteroid systems comprise a significant fraction (15+4%) of the NEA population et Pravecal.|2006)..," Binary asteroid systems comprise a significant fraction $15 \pm 4\%$ ) of the NEA population \citep{Margot2002, Pravec2006}. ."83" Both |Cuk and McMahon determined that if the BYORP effect dominates the evolution, then synchronous binaries can disrupt in much less than a million years, requiring frequent binary creation to maintain the observed population."," Both \citet{Cuk2007} and \citet{McMahon2010b} determined that if the BYORP effect dominates the evolution, then synchronous binaries can disrupt in much less than a million years, requiring frequent binary creation to maintain the observed population."84" If binaries are trapped in a long-term stable equilibrium, then binary creation could be infrequent."," If binaries are trapped in a long-term stable equilibrium, then binary creation could be infrequent."85" This conclusion is corroborated by evidence that the binary formation process from rotational fission is inefficient, requiring many rotational fission events per asteroid (taking many YORP timescales), in order to create a stable binary system that does not immediately disrupt (Jacobson&Scheeres|/2011)."," This conclusion is corroborated by evidence that the binary formation process from rotational fission is inefficient, requiring many rotational fission events per asteroid (taking many YORP timescales), in order to create a stable binary system that does not immediately disrupt \citep{Jacobson2011}."86. The observed synchronous binary population may be residing in this equilibrium., The observed synchronous binary population may be residing in this equilibrium.87" After the formation of a stable binary asteroid system via rotational fission (or some other mechanism), tides immediately begin to dissipate energy from the system through the mechanical stressing of each body."," After the formation of a stable binary asteroid system via rotational fission (or some other mechanism), tides immediately begin to dissipate energy from the system through the mechanical stressing of each body."88 The fastest process is the synchronization of the secondary which occurs because of tides raised on the secondary by the primary (Goldreich[1963;(Goldreich&Sari|2009)..," The fastest process is the synchronization of the secondary which occurs because of tides raised on the secondary by the primary \citep{Goldreich1963, Goldreich2009}."89 This process is often referred to as tidal locking of the satellite., This process is often referred to as tidal locking of the satellite.90" After the secondary has been synchronized, the system will evolve due to both tides and the BYORP effect, which requires a synchronous secondary."," After the secondary has been synchronized, the system will evolve due to both tides and the BYORP effect, which requires a synchronous secondary."91 Relative motion between components in a binary system leads to tidal dissipation of energy and the transfer of angular momentum between spin and orbit states., Relative motion between components in a binary system leads to tidal dissipation of energy and the transfer of angular momentum between spin and orbit states.92" Assuming spherical, homogenous bodies with identical compositions and a mutualorbit with low eccentricity,"," Assuming spherical, homogenous bodies with identical compositions and a mutualorbit with low eccentricity,"93determine the location of the minimum.,determine the location of the minimum.94 This is equivalent to the linear passage of gas through sinusoidal spiral arms., This is equivalent to the linear passage of gas through sinusoidal spiral arms.95" “Phe dimensionless velocity acquired by gas falling from the peak to the base of the potential is Vu,=v2.2h.", The dimensionless velocity acquired by gas falling from the peak to the base of the potential is $V_{pot}=\sqrt{2\times A}$.96 We tried many different potentials. varving zl and A. and only applying the potential once the gas has passed a minimum.," We tried many different potentials, varying $A$ and $k$, and only applying the potential once the gas has passed a minimum."97 However we Found that the results presented here are largely independen of the exact. nature of the potential., However we found that the results presented here are largely independent of the exact nature of the potential.98 The structure of the shock is similar for cillerent potentials for a given initia distribution., The structure of the shock is similar for different potentials for a given initial distribution.99 The relative strength of the shock determines the magnitude of the velocity. dispersion. whilst the initia clistribution determines the velocity size scaling law.," The relative strength of the shock determines the magnitude of the velocity dispersion, whilst the initial distribution determines the velocity size scaling law."100 For the simulations presented here. we took &=z/4. el=100 ane B=? to produce a minimum at 2 and maxmima at -2 anc 6.," For the simulations presented here, we took $k=\pi/4$, $A=100$ and $B=2$ to produce a minimum at 2 and maxmima at -2 and 6."101" We allocate particles a velocity of 50 ce, in the uw direction and zero velocity in the jy and 2 directions. which for the simulations described here. Ieads to a shock of Mach number z30."," We allocate particles a velocity of 50 $ c_s$ in the $x$ direction and zero velocity in the $y$ and $z$ directions, which for the simulations described here, leads to a shock of Mach number $\approx 30$."102 We set up a distribution of spherical clumps in pressure equilibrium in the same wav as described for the shock tube tests., We set up a distribution of spherical clumps in pressure equilibrium in the same way as described for the shock tube tests.103 Where a hot diffuse phase is used to supply an external pressure. the hot phase is distributed with the same number of particles 10°). but 1/10 of the mass of the cold phase.," Where a hot diffuse phase is used to supply an external pressure, the hot phase is distributed with the same number of particles $ \times 10^5$ ), but 1/10 of the mass of the cold phase."104 We also test a distribution with eblumps of dillerent size-scales and. densities. giving structure on a range of scales.," We also test a distribution with clumps of different size-scales and densities, giving structure on a range of scales."105 The clumps have initial diameters of 0.4. 0.1 and 0.04. with clumps of smaller. diameter placed. inside larger clumps.," The clumps have initial diameters of 0.4, 0.1 and 0.04, with clumps of smaller diameter placed inside larger clumps."106 For the uniform. and. clumpy distributions. particles are positioned. within a cuboicl of dimensions 1.5<r<L5. l]l«ycland 1--," For the uniform and clumpy distributions, particles are positioned within a cuboid of dimensions $-1.5<x<1.5$, $-1<y<1$ and $-1<z<1$."107 We also investigate shocks with an initial fractal distribution. following the method described in 2. to generate fractals.," We also investigate shocks with an initial fractal distribution, following the method described in \citet{Elmegreen1997} to generate fractals."108 The algorithm includes 3 parameters. an intrinsic length. scale. £L. the number of hierarchical levels. ££. aid the number of points in each level. N.," The algorithm includes 3 parameters, an intrinsic length scale $L$, the number of hierarchical levels, $H$, and the number of points in each level, $N$ ."109 The dimension of the fractal is DD=fogN/logL and the number of points is ANE., The dimension of the fractal is $D=logN/logL$ and the number of points is $N^H$.110 We generate a 2.2 D fractal. with L —2.].N—5 and lf—9 requiring zz2 million points. and a 2.5 D fractal. with £L=2.5. N=12 and //=6 requiring zz3 million points.," We generate a 2.2 D fractal, with $L=2.1$, $N=5$ and $H=9$ requiring $\approx 2$ million points, and a 2.7 D fractal, with $L=2.5$, $N=12$ and $H=6$ requiring $\approx 3$ million points."111 We then scale the ηjy.2. coordinates (equally) of cach fractal to fit inside a cube of dimensions LicrcLS LScyecLo and 15<2l5.," We then scale the $x,y,z$ coordinates (equally) of each fractal to fit inside a cube of dimensions $-1.5<x<1.5$, $-1.5<y<1.5$ and $-1.5<z<1.5$."112 Observations estimate the interstellar fractal dimension as D22.3 (7)., Observations estimate the interstellar fractal dimension as D=2.3 \citep{Elmegreen1996}.113 Since for the distributions with fractals or dillerent size clumps the gas exhibits dillerent. densities ancl pressures. constant. pressure boundaries. or an intervening cilfuse phase. are no longer appropriate.," Since for the distributions with fractals or different size clumps the gas exhibits different densities and pressures, constant pressure boundaries, or an intervening diffuse phase, are no longer appropriate."114 Instead. we apply a pressure switch in order that onlv gas in the shocked region is subject to pressure forces., Instead we apply a pressure switch in order that only gas in the shocked region is subject to pressure forces.115 The gas experiences pressure only when die(v)x0 Le. compression of the eas is occurring., The gas experiences pressure only when $div(v)\le0$ i.e. compression of the gas is occurring.116 This enables structure on all scales to be maintained in the gas distribution before gas reaches the shock., This enables structure on all scales to be maintained in the gas distribution before gas reaches the shock.117 Tests for the uniform. density clumps showed. this method produced similar results compared to when constant pressure boundaries were applied., Tests for the uniform density clumps showed this method produced similar results compared to when constant pressure boundaries were applied.118 Column density plots for dillerent. simulations are shown in EF, Column density plots for different simulations are shown in Fig.119 1.2.3 (all for the sinusoidal potential tests).," 1,2,3 (all for the sinusoidal potential tests)."120 The uniform shock in Fig., The uniform shock in Fig.121 1 shows a smooth shocked. region of approximately constant density and width., 1 shows a smooth shocked region of approximately constant density and width.122 By contrast the clumpy shock (Fig., By contrast the clumpy shock (Fig.123 1. middle) shows a much broacer shocked. region of non-uniform clensity.," 1, middle) shows a much broader shocked region of non-uniform density."124 Lhe shock contains more structure and appears more similar to simulations of turbulence., The shock contains more structure and appears more similar to simulations of turbulence.125 In. Fig., In Fig.126 1 (middle). an external pressure field is applied to maintain the clumps in. pressure equilibrium.," 1 (middle), an external pressure field is applied to maintain the clumps in pressure equilibrium."127 Fig., Fig.128 E (lower) shows a shock for similar size clumps. where the clumps are instead. surrounded by hotter gas.," 1 (lower) shows a shock for similar size clumps, where the clumps are instead surrounded by hotter gas."129 In this case. the hot gas takes the same numbers of particles as the Cold gas. but 1/10 of the mass.," In this case, the hot gas takes the same numbers of particles as the cold gas, but 1/10 of the mass."130 The ratio of the densities of cold to hot gas is 30. which is similar to the ratio of densities of the cold and warm neutral components of the ISM C2)...," The ratio of the densities of cold to hot gas is $\sim 30$, which is similar to the ratio of densities of the cold and warm neutral components of the ISM \citep{Cox2005}."131 Ehe structure of the cold gas in the shock is very similar whether the clumps are in equilibrium from external pressure boundaries. or hot eas. indicating that the hot gas has little effect on the gas dynamics.," The structure of the cold gas in the shock is very similar whether the clumps are in equilibrium from external pressure boundaries, or hot gas, indicating that the hot gas has little effect on the gas dynamics."132 The distribution of dillerent size clumps shows similar morphology. although more smaller scale. structure is apparent in the shocked. eas (Eig.," The distribution of different size clumps shows similar morphology, although more smaller scale structure is apparent in the shocked gas (Fig."133 2)., 2).134 The shocked. gas of the fractal distribution. (Fig., The shocked gas of the fractal distribution (Fig.135 3j) shows more filamentarvy structure compared to the clumps. distributions., 3) shows more filamentary structure compared to the clumpy distributions.136 We now calculate the 1D velocity clispersion of the post-shock gas., We now calculate the 1D velocity dispersion of the post-shock gas.137" We only consider the ο, velocities. which corresponds to the direction of motion of the initial gas. since the velocity dispersion in the jy ancl z directions are always subsonic."," We only consider the $v_x$ velocities, which corresponds to the direction of motion of the initial gas, since the velocity dispersion in the $y$ and $z$ directions are always subsonic."138 For a given size. we average the velocity dispersion over numerous regions of that size scale.," For a given size, we average the velocity dispersion over numerous regions of that size scale."139 The regions are 3 D and chosen to centre on the densest particles in the shock., The regions are 3 D and chosen to centre on the densest particles in the shock.140 Only particles with densities greater than the maximum pre-shock density ave considered. for calculating the velocity dispersion. thus ensuring we only include eas in the shock. (," Only particles with densities greater than the maximum pre-shock density are considered for calculating the velocity dispersion, thus ensuring we only include gas in the shock. ("141We find that even for a uniform shock. including the pre and/or post shock eas will produce a Larson tvpe velocity dispersion size-scale relation. theoretically and from. numerical results.),"We find that even for a uniform shock, including the pre and/or post shock gas will produce a Larson type velocity dispersion size-scale relation, theoretically and from numerical results.)"142 We repeat this process for regions of different size-seale to. determine the dependence. of the induced. velocity dispersion on the size-scale., We repeat this process for regions of different size-scale to determine the dependence of the induced velocity dispersion on the size-scale.143 For the shock tube tests. we initially found that. the velocity. dispersion was supersonic. even for the uniform shock.," For the shock tube tests, we initially found that the velocity dispersion was supersonic, even for the uniform shock."144 This is due to the inherently clumpy nature of UuPil which introduces error when calculating the velocity ispersion., This is due to the inherently clumpy nature of SPH which introduces error when calculating the velocity dispersion.145 We therefore increased the viscosity parameters toa—2 and 7—4., We therefore increased the viscosity parameters to $\alpha=2$ and $\beta=4$.146 This lowered the values of the velocity ispersion for both the uniform. Mach. 10 ancl Mach. 20 gajiocks. although the velocity dispersion is still supersonic for the Mach 20 shock.," This lowered the values of the velocity dispersion for both the uniform Mach 10 and Mach 20 shocks, although the velocity dispersion is still supersonic for the Mach 20 shock."147 The results presented for the shock tube tests use the higher viscosity parameters. whilst. for the sinusoidal potential tests. there is less noise ancl the standard. parameters à.=1 and 3=2 are used.," The results presented for the shock tube tests use the higher viscosity parameters, whilst for the sinusoidal potential tests, there is less noise and the standard parameters $\alpha=1$ and $\beta=2$ are used."148 In all cases the higher viscosity parameters had little ellect on the velocity clispersions for the clumpyshocks., In all cases the higher viscosity parameters had little effect on the velocity dispersions for the clumpyshocks.149 Alternatively. the velocity dispersion can be determined. from the SPL smoothed velocities: Since these velocities are smoothed over the neighbouring particles. the velocity dispersion produces less," Alternatively, the velocity dispersion can be determined from the SPH smoothed velocities: Since these velocities are smoothed over the neighbouring particles, the velocity dispersion produces less"150models are reasonable fits to what is thought to be known within (he ambiguities proposed in Section ??..,models are reasonable fits to what is thought to be known within the ambiguities proposed in Section \ref{sec:32}.151 Model 3 has a reasonablysmall A? but three questionable features., Model 3 has a reasonablysmall $\chi^2$ but three questionable features.152 First. it puts LMC near (he edge of the optical image. al d=6.4 kpc.," First, it puts LMC near the edge of the optical image, at $d_\perp =6.4$ kpc."153 Second. MW is more massive (han M3I. which seems unlikely though perhaps not impossible.," Second, MW is more massive than M31, which seems unlikely though perhaps not impossible."154 Third. (the redshift of NGC3109 is 100 kins | below the catalog value. which again seems unlikely.," Third, the redshift of NGC3109 is 100 km $^{-1}$ below the catalog value, which again seems unlikely."155 To be checked is whether a more complete mass model would allow the Type II pattern of motion to better fit arguably reasonable constraints., To be checked is whether a more complete mass model would allow the Type II pattern of motion to better fit arguably reasonable constraints.156 Models 4 and 5. without the large external mass. have acceptable proper motions of LMC and proper motions of M33 (hat are arguably not unreasonable.," Models 4 and 5, without the large external mass, have acceptable proper motions of LMC and proper motions of M33 that are arguably not unreasonable."157 The proper motion of ICIO is off by nearly four standard deviations. but this is may be acceptable for the purpose ol modeling the motion of LMC. because at its greater distance ICIO may have been affected by more distant objects not in this mass model.," The proper motion of IC10 is off by nearly four standard deviations, but this is may be acceptable for the purpose of modeling the motion of LMC, because at its greater distance IC10 may have been affected by more distant objects not in this mass model."158 Perhaps the greatest objection to Models 4 and 5 is that thev replace the external mass wilh a large mass of M33. at roughly. half the mass of (he MW. which seems unlikely.," Perhaps the greatest objection to Models 4 and 5 is that they replace the external mass with a large mass of M33, at roughly half the mass of the MW, which seems unlikely."159 But the important issue for the present study is how {his rearrangement of (he more distant mass affects the orbit of LAIC relative to MW., But the important issue for the present study is how this rearrangement of the more distant mass affects the orbit of LMC relative to MW.160 Figure 3. shows the history of angular positions of LMC and M31 lor an observer fixed in (he MW at the present position of the Sun in the galaxy., Figure \ref{Fig:3} shows the history of angular positions of LMC and M31 for an observer fixed in the MW at the present position of the Sun in the galaxy.161 The present angular position of LMC is near the bottom of the figure., The present angular position of LMC is near the bottom of the figure.162 Model 3. with its questionable value of d... is most different. [rom the other orbits.," Model 3, with its questionable value of $d_\perp$, is most different from the other orbits."163 The considerable scatter among the others includes a clear difference between the orbits of the (wo most plausible Models 1 and 2 (plotted in black)., The considerable scatter among the others includes a clear difference between the orbits of the two most plausible Models 1 and 2 (plotted in black).164 The orbits share some distinctive features. however.," The orbits share some distinctive features, however."165All except Model 3 passed within ~20° of the South galactic pole. in the general direction of the Magellanic strezan. (Mathewson Ford 1934).,"All except Model 3 passed within $\sim 20^\circ$ of the South galactic pole, in the general direction of the Magellanic stream (Mathewson Ford 1984)."166 Within the scatter these models agree with the Besla et al. (, Within the scatter these models agree with the Besla et al. (1672007. Fig.,"2007, Fig."168 5) model for the motion of LMC past the pole., 8) model for the motion of LMC past the pole.169 At redshift near unity all five orbits pass a stationary point in latitude near b— 0., At redshift near unity all five orbits pass a stationary point in latitude near $b=0$ .170 At this point the longitude is near /=90° and decreasing., At this point the longitude is near $l=90^\circ$ and decreasing.171 This behavior is seen also in the more schematic mass model with cosmological initial conditions in P9., This behavior is seen also in the more schematic mass model with cosmological initial conditions in P9.172 The present position of M31 is toward the left sile of Figure 3.., The present position of M31 is toward the left side of Figure \ref{Fig:3}.173 Iu all models M31 is noving to increasing galactic longitude. in the opposite direction to the motion of LMC.," In all models M31 is moving to increasing galactic longitude, in the opposite direction to the motion of LMC."174 The net displacement of M31 is smallest in Models 4 and 5 (and the blue curve is so short il is difficult to see in the figure). as night be expected [rom the absence of torquing by a arge external mass.," The net displacement of M31 is smallest in Models 4 and 5 (and the blue curve is so short it is difficult to see in the figure), as might be expected from the absence of torquing by a large external mass."175" The heliocentric velocity of M31 is e,=234 kan |. vs=—65 kin in Model 1 and ο=223 km 1 toes—8 kms ! in Model 2."," The heliocentric velocity of M31 is $v_\alpha=234$ km $^{-1}$, $v_\delta=-65$ km $^{-1}$ in Model 1 and $v_\alpha=223$ km $^{-1}$, $v_\delta=8$ km $^{-1}$ in Model 2."176" van der Marel Guhathakurta (2008) argue for e,—78dΕ km |. e;=—38434 km I. which differsbv nearly [our limes the stated error."," van der Marel Guhathakurta (2008) argue for $v_\alpha=78\pm 41$ km $^{-1}$ , $v_\delta=-38\pm 34$ km $^{-1}$ , which differsby nearly four times the stated error."177 Understanding this discrepancy requires Iurther discussion of both, Understanding this discrepancy requires further discussion of both178Observatory constitutes the largest database of optical atmospheric turbulence profiles so far.,Observatory constitutes the largest database of optical atmospheric turbulence profiles so far.179 'This paper is based on observations obtained at the Jacobus Kapteyn Telescope operated by the Isaac Newton Group at the Observatorio de Roque de los Muchachos of the Instituto de Astrofíssica de Canarias., This paper is based on observations obtained at the Jacobus Kapteyn Telescope operated by the Isaac Newton Group at the Observatorio de Roque de los Muchachos of the Instituto de sica de Canarias.180 The authors thank all the staff at the observatory for their kind support., The authors thank all the staff at the observatory for their kind support.181" Thanks are also due to all the observers that have recorded generalized SCIDAR data at this site (J. Castro-Almazánn, S. Chueca, J.M. Delgado, E. Sanroma, C. Hoegemann, M.A.C. RodrA-guez-HernAjndez, and H. Vázzquez-Ramió))."," Thanks are also due to all the observers that have recorded generalized SCIDAR data at this site (J. Castro-Almazánn, S. Chueca, J.M. Delgado, E. Sanroma, C. Hoegemann, M.A.C. Rodríguez-Hernández, and H. Vázzquez-Ramió))."182 We also thank A. Eff-Darwich for help and useful discussions., We also thank A. Eff-Darwich for help and useful discussions.183" We are grateful to the referee, Remy Avila, whose comments helped to improve this paper."," We are grateful to the referee, Remy Avila, whose comments helped to improve this paper."184 This work was partially funded by the Instituto de Astrofíssica de Canarias and by the Spanish Ministerio de Educaciónn y Ciencia (AYA2006-13682 and AYA2009-12903)., This work was partially funded by the Instituto de sica de Canarias and by the Spanish Ministerio de Educaciónn y Ciencia (AYA2006-13682 and AYA2009-12903).185 B. Garcíaa-Lorenzo thanks the support from the Ramónn y Cajal program by the Spanish Ministerio de Ciencia e innovaciónn., B. a-Lorenzo thanks the support from the Ramónn y Cajal program by the Spanish Ministerio de Ciencia e innovaciónn.186are all <400 millionths of a hemisphere.,are all $<400$ millionths of a hemisphere.187 Initially the region had a simple bipolar magnetic configuration and hence was given (he Mount Wilson classification 3., Initially the region had a simple bipolar magnetic configuration and hence was given the Mount Wilson classification $\beta$.188 It developed into a  region (a more complex bipolar conliguration such (that a single line cannot be drawn to separate the polariües) flor the period 26 to 29 Oct. and then returned (ο a 75 configuration on 30 Oct. The photospherie magnetic field of AR. 11029 had the polarity orientation associated with the solar cvele 24. being a northern region with a leading negative polarity. although it appeared at an intermediate latitude (around. 15 deg).," It developed into a $\beta$ $\gamma$ region (a more complex bipolar configuration such that a single line cannot be drawn to separate the polarities) for the period 26 to 29 Oct, and then returned to a $\beta$ configuration on 30 Oct. The photospheric magnetic field of AR 11029 had the polarity orientation associated with the solar cycle 24, being a northern region with a leading negative polarity, although it appeared at an intermediate latitude (around 15 deg)."189 At the time of writing (late 2009) there have been relatively [ew new cvele regions. and the interval of minimum since the peak of the last evele. around 2001. has been longer ancl quieter (han anticipated. wilh 2008 and 2009 featuring long stretches of davs without sunspots LLivingston Penn 2009: Salabert οἱ 22009).," At the time of writing (late 2009) there have been relatively few new cycle regions, and the interval of minimum since the peak of the last cycle, around 2001, has been longer and quieter than anticipated, with 2008 and 2009 featuring long stretches of days without sunspots Livingston Penn 2009; Salabert et 2009)."190 Although small. AR 11029 was highly flare productive.," Although small, AR 11029 was highly flare productive."191 The GOES soft X-ray event lists compiled bx the US SWPC (discussed in section 1) list 73 small flares for the interval 24 Oct to 1 Nov. In the SWPC lists. not all these events are attributed to AR. 11029.," The GOES soft X-ray event lists compiled by the US SWPC (discussed in section 1) list 73 small flares for the interval 24 Oct to 1 Nov. In the SWPC lists, not all these events are attributed to AR 11029."192 However. the active region identilication in the GOES event lists is «quite incomplete: many events lack an associated location and active region number. (," However, the active region identification in the GOES event lists is quite incomplete: many events lack an associated location and active region number. ("193The identification is dependent on eround-based optical observations. aud presumably locations are missing when (here are no available optical observations.),"The identification is dependent on ground-based optical observations, and presumably locations are missing when there are no available optical observations.)"194 Inspection of the SolarSolt Latest Events archive produced by ihe Lockheed Martin Solar Astroplivsies Laboratory. which includes Solar and Heliospherie Observatory Extreme Ultraviolet Imaging Telescope (SOILO/EIT) image sequences lor each event. confirms that all 73 events originate in AR The flares are all small (one event. GO B-elass events. and 11 C-class events). with the largest being C2.2.," Inspection of the SolarSoft Latest Events archive produced by the Lockheed Martin Solar Astrophysics Laboratory, which includes Solar and Heliospheric Observatory Extreme Ultraviolet Imaging Telescope (SOHO/EIT) image sequences for each event, confirms that all 73 events originate in AR The flares are all small (one A-class event, 60 B-class events, and 11 C-class events), with the largest being C2.2."195 Table 1 sumunarises the daily behavior of the active region. ancl lists the numbers of flares observed per day.," Table 1 summarises the daily behavior of the active region, and lists the numbers of flares observed per day."196 The region was particularly flare productive on 26 Oct and 27 Oct. the first two davs of assignment of the magnetic classification jJ 5.," The region was particularly flare productive on 26 Oct and 27 Oct, the first two days of assignment of the magnetic classification $\beta$ $\gamma$."197 Figure 2 illustrates the activity observed in AR 11029., Figure 2 illustrates the activity observed in AR 11029.198 The upper panel shows the one-minute GOES 1 SA flux values versus lime from 23 Oct to 3 Nov. in a log-linear representation.," The upper panel shows the one-minute GOES $1$ $8\,\mbox{\AA}$ flux values versus time from 23 Oct to 3 Nov, in a log-linear representation."199 Prior to the emergence of AR 11029 the X-ray flix was at the base level for the detector. ancl it returned to this value when the region rotated. off the disk.," Prior to the emergence of AR 11029 the X-ray flux was at the base level for the detector, and it returned to this value when the region rotated off the disk."200 This suggests that all 1 8A emission from the Sun in this interval originates from AR 11029. providing observation conditions which are close to ideal for identification of X-ray events from this region.," This suggests that all $1$ $8\,\mbox{\AA}$ emission from the Sun in this interval originates from AR 11029, providing observation conditions which are close to ideal for identification of X-ray events from this region."201 The top panel of Figure 2 may be regarded as a soft N-ray. light-curve for Ah 11029., The top panel of Figure 2 may be regarded as a soft X-ray light-curve for AR 11029.202 The lower panel of Figure 2 illustrates the GOES events identified bv the US, The lower panel of Figure 2 illustrates the GOES events identified by the US203"where a=—0.2+0.3, which shows no significant evolution with redshift.","where $\alpha=-0.2\pm0.3$, which shows no significant evolution with redshift."204 This determination is consistent with ? who find a modest evolution of dust content with redshift (a=—1x 0.4)., This determination is consistent with \citet{2008MNRAS.385.1053M} who find a modest evolution of dust content with redshift $\alpha=-1.1\pm0.4$ ).205 While this analysis of the bias-corrected median points has deliberately been confined to absorbers with E(B—V)suc «0.15 it is also possible to test whether the entire observed absorber sample is consistent with no evolution as a function of zaps., While this analysis of the bias-corrected median points has deliberately been confined to absorbers with $E(B-V)_{\mathrm{SMC}}$$<$ 0.15 it is also possible to test whether the entire observed absorber sample is consistent with no evolution as a function of $z_{\mathrm{abs}}$.206" Taking the bias corrected E(B—V)swc distribution of absorbers in the low-redshift (Zaps)=0.77 slice we calculate the observed E(B—V)smc distribution, by applying the inverse of the bias corrections to the (Zaps)= intrinsic distribution, centred on the higher redshift slices (Zabs)=1.25 and (zaps)=1.68 respectively (Fig. 10))."," Taking the bias corrected $E(B-V)_{\mathrm{SMC}}$ distribution of absorbers in the low-redshift $\langle z_{\mathrm{abs}} \rangle =0.77$ slice we calculate the observed $E(B-V)_{\mathrm{SMC}}$ distribution, by applying the inverse of the bias corrections to the $\langle z_{\mathrm{abs}} \rangle=0.77$ intrinsic distribution, centred on the higher redshift slices $\langle207z_{\mathrm{abs}} \rangle=1.25$ and $\langle z_{\mathrm{abs}}208\rangle=1.68$ respectively (Fig. \ref{cap:fullebvz}) )."209" The resulting distributions for the higher redshift slices are consistent with the observed histograms, confirming the lack of evidence for significant evolution in the distribution of E(B—V)swc with redshift."," The resulting distributions for the higher redshift slices are consistent with the observed histograms, confirming the lack of evidence for significant evolution in the distribution of $E(B-V)_{\mathrm{SMC}}$ with redshift."210 Determining the nature of dust in aabsorption line systems is important as it provides a way to constrain the chemical evolution of galaxies over a range of cosmic time., Determining the nature of dust in absorption line systems is important as it provides a way to constrain the chemical evolution of galaxies over a range of cosmic time.211 Of particular interest is whether the strong ~2175 feature observed in the spectrum of the MW is present in our aabsorber sample., Of particular interest is whether the strong $\sim2175$ feature observed in the spectrum of the MW is present in our absorber sample.212" In general, the SMC extinction curve, rather than that of the MW, is found to best describe the average reddening properties of aabsorbers (??7) with low E(B— V)."," In general, the SMC extinction curve, rather than that of the MW, is found to best describe the average reddening properties of absorbers \citep{2005pgqa.conf...86M, 2006MNRAS.367..945Y, 2008MNRAS.385.1053M}213 with low $E(B-V)$ ."214" Taking advantage of the large sample of absorbers, and specifically the availability of a number of absorbers with significant E(B—V), we investigated the form of the extinction curve via construction of a composite spectrum and consideration of the properties of the absorbers with the very highest estimates of E(B—V)."," Taking advantage of the large sample of absorbers, and specifically the availability of a number of absorbers with significant $E(B-V)$, we investigated the form of the extinction curve via construction of a composite spectrum and consideration of the properties of the absorbers with the very highest estimates of $E(B-V)$."215" Despite claims of being able to see evidence for the 2175 bump in single systems (?),, individual extinction curvesÀ have a low S/N. Using the much larger sample of absorbers presented here, we can combine a large number of extinction curves statistically, using an approach similar to ?,, to improve the S/N and increase the sensitivity to the presence of any features."," Despite claims of being able to see evidence for the $2175$ bump in single systems \citep{2008MNRAS.391L..69S}, individual extinction curves have a low S/N. Using the much larger sample of absorbers presented here, we can combine a large number of extinction curves statistically, using an approach similar to \citet{2005MNRAS.361L..30W}, to improve the S/N and increase the sensitivity to the presence of any features."216 An important consideration is the choice of which systems to combine., An important consideration is the choice of which systems to combine.217" The optimum number of spectra to co-add is a trade-offbetween the number of spectra (in principle the more the better), and the median E(B—V) "," The optimum number of spectra to co-add is a trade-offbetween the number of spectra (in principle the more the better), and the median $E(B-V)$ "218by minimizing a X based on the positiois of the core aud jet ceuter until a curve in inage D is obtaiuce that best reproduces the qualitative features of the VLBI map.,by minimizing a $\chi^2$ based on the positions of the core and jet center until a curve in image B is obtained that best reproduces the qualitative features of the VLBI map.219 This method does not use the observec iaenification ratio of the cores as a constrailif so any possible contamination from microleusing by stars is entirely avoided., This method does not use the observed magnification ratio of the cores as a constraint so any possible contamination from microlensing by stars is entirely avoided.220 Figure 3.H shows the results of this fitting., Figure \ref{fig:map_jets} shows the results of this fitting.221 The resulting lens model is not uuique in any quantitative scusc. but there are clear thiies that can be learned frou this fitting process about the kind of substructure that is capable of producing the bend.," The resulting lens model is not unique in any quantitative sense, but there are clear things that can be learned from this fitting process about the kind of substructure that is capable of producing the bend."222 When a point mass is used as a subsructure the shape of iage D is comparatively easy. to reproduce., When a point mass is used as a substructure the shape of image B is comparatively easy to reproduce.223 A point mass can be considered an approximation to anv substructure that is verv compact relative to its own Einstein radius such as a tidally trameated dark matter halo., A point mass can be considered an approximation to any substructure that is very compact relative to its own Einstein radius such as a tidally truncated dark matter halo.224 Such a substructure can cause a strong deflection near its center while having a linit¢d rauge of influeuce., Such a substructure can cause a strong deflection near its center while having a limited range of influence.225 This euables the poiut mass substructure in figure 23? to displace the lower eud of the je while leaving the position ofthe core cud of the jet relatively nuchaneed., This enables the point mass substructure in figure \ref{fig:map_jets} to displace the lower end of the jet while leaving the position of the core end of the jet relatively unchanged.226 Note that the sustructure has tli! effect of attracting the image rather than repelling it as would normally be the case., Note that the substructure has the effect of attracting the image rather than repelling it as would normally be the case.227 This atraction happens in only oue dimension aud is a result of one of the eigenvalues of the magnification matrix¢lexived from the ost lens being negative (image D is reflected iu one dinoenusiou with respect to image A)., This attraction happens in only one dimension and is a result of one of the eigenvalues of the magnification matrix derived from the host lens being negative (image B is reflected in one dimension with respect to image A).228" T10 lass dó:s lost niaturally calculated iu units of the mass of the host lens within its Eiustein radius which in this case is We=(0/0)1X4:‘)1516«10,1(0/217aus19!M."," The mass is most naturally calculated in units of the mass of the host lens within its Einstein radius which in this case is $M_E = (\sigma/c)^4 G^{-1}\Sigma_c(z_s,z_l)^{-1} =2291.6\times 10^{11} h_{65}^{-1} (\sigma/247\kms)^4 \msun$."230" The favored model has a substructure lass o 5)—2,5410""Mg.", The favored model has a substructure mass of $m=2.5\times 10^{-5} M_E$.231 Other model parameters are sunmnuarized in table L.., Other model parameters are summarized in table \ref{table}.232 A point mass wiD inass much more than LO!AZg teuds to displace the leus without creating a bend and aiass of Z10ΑΙ caunot produce a bend ona large enough augulur scale., A point mass with mass much more than $10^{-4} M_E$ tends to displace the lens without creating a bend and a mass of $\simlt 10^{-6} M_E$ cannot produce a bend on a large enough angular scale.233 When a SIS model is used for the substructure it is dificult to reproduce the jet shape., When a SIS model is used for the substructure it is difficult to reproduce the jet shape.234 The tendency is that when the SIS is massive euouchl to displace the lower cud of the jet sufficicutly it also displaces the core cud of the jet so that a significant bend is not created ie. the SIS model is not compact enough., The tendency is that when the SIS is massive enough to displace the lower end of the jet sufficiently it also displaces the core end of the jet so that a significant bend is not created – i.e. the SIS model is not compact enough.235 We, We236In recent years. new radio surveys such as the National Radio Astronomy Observatory (NRAO) Very Large Array (VLA) Sky Survey (NVSS: Condon and the Faint Images of the Radio Sky at Twenty centimetres (FIRST) survey (2). have covered substantial fractions of the sky down to milli-Jansky flux densities. at vastly higher angular resolution than their predecessors.,"In recent years, new radio surveys such as the National Radio Astronomy Observatory (NRAO) Very Large Array (VLA) Sky Survey (NVSS; Condon \nocite{con98} and the Faint Images of the Radio Sky at Twenty centimetres (FIRST) survey \cite{bec95} have covered substantial fractions of the sky down to milli-Jansky flux densities, at vastly higher angular resolution than their predecessors."237 Such radio surveys are dramatically advancing our understanding of extragalactic radio sources. by permitting detailed statistical studies to be carried out.," Such radio surveys are dramatically advancing our understanding of extragalactic radio sources, by permitting detailed statistical studies to be carried out."238 In order to reap the full benefit of these surveys. it is necessary to optically identify the radio sources. so as to obtain spectroscopic redshifts and determine the properties of their host galaxies.," In order to reap the full benefit of these surveys, it is necessary to optically identify the radio sources, so as to obtain spectroscopic redshifts and determine the properties of their host galaxies."239 The availability of new large galaxy redshift surveys. especially the degree Field Galaxy Redshift Survey (2dFGRS: Colless and the Sloan Digital Sky Survey (SDSS: York 22000: Stoughton 220021. means that optical identifications and redshifts are available for large samples of nearby radio sources and allows comprehensive statistical analyses of their host galaxy properties to be carried out.," The availability of new large galaxy redshift surveys, especially the 2-degree Field Galaxy Redshift Survey (2dFGRS; Colless \nocite{col01} and the Sloan Digital Sky Survey (SDSS; York 2000; Stoughton \nocite{yor00,sto02}, means that optical identifications and redshifts are available for large samples of nearby radio sources and allows comprehensive statistical analyses of their host galaxy properties to be carried out."240" Automated. cross—correlation of surveys across different wavelength regimes has a long history in astronomy,", Automated cross–correlation of surveys across different wavelength regimes has a long history in astronomy.241 It is important that this process should maximize both the completeness and the reliability «f he resulting sample. so considerable care needs to be taken in choosing the parameters that determine whether objects in different catalogues are indeed associated.," It is important that this process should maximize both the completeness and the reliability of the resulting sample, so considerable care needs to be taken in choosing the parameters that determine whether objects in different catalogues are indeed associated."242 In the case of optical idenification of radio sources. the choice of radio survey is importan," In the case of optical identification of radio sources, the choice of radio survey is important."243 T1s is because many radio sources are extended. with sizes from a feW üresee up to tens of aremins. and in high angular resolution surveys different components of the same source may be resolved inO0 istinct sources.," This is because many radio sources are extended, with sizes from a few arcsec up to tens of arcmins, and in high angular resolution surveys different components of the same source may be resolved into distinct sources."244 Surveys at lower angular resolution detect mos SC»urees as single components. and also have good," Surveys at lower angular resolution detect most sources as single components, and also have good"245cluster (Jeuseu.Toury.&Luppino1998).,cluster \citep*{jtl1998}.246. We take the distance modulus to be 31.7 mae. a distance of 22 Mpc. so that Pas cmIO0 pc.," We take the distance modulus to be 31.7 mag, a distance of 22 Mpc, so that is $\approx$ 100 pc."247" The effective radius rp. isΌτι, or &5.7 kpe (Bursteinetal.1987)."," The effective radius $r_e$ is, or $\approx$ 5.7 kpc \citep{bur1987}."248. Iu this Letter. we preseut the first complete maps of the kinematics aud stellar populations of 11365. taken with the wide-field inteeral-tield spectroerapli citepbac2001..," In this Letter, we present the first complete maps of the kinematics and stellar populations of 4365, taken with the wide-field integral-field spectrograph \\citep{bac2001}."249 Tn 822. we briefly describe the observations.," In 2, we briefly describe the observations."250 The Sunematics aud line-streugth iudex maps are presenteck in 833. where we consider age-iuctallicity diagnostics. the Me-o diaeranm. and the spatial distribution of non-solar abundance ratios.," The kinematics and line-strength index maps are presented in 3, where we consider age-metallicity diagnostics, the $\sigma$ diagram, and the spatial distribution of non-solar abundance ratios."251 We discuss the tuplications of these results for formation scenarios in ll. aud suunuuize our conclusions iu 855.," We discuss the implications of these results for formation scenarios in 4, and summarize our conclusions in 5."252 We observed 11365 with nunounted ou the δι Willian Herschel Telescope on La Pahna. ou the nights of 29 30 Marchi 2000.," We observed 4365 with mounted on the 4.2m William Herschel Telescope on La Palma, on the nights of 29 30 March 2000."253 hhas a field-of-view of 337°.117.. delivering simultaneously 1131 spectra at a spectral resolution of 3.6 (EWIIND. 0795ς spatial sampling. and sky coverage (Baconetal.2001).," has a field-of-view of $\times$, delivering simultaneously 1431 spectra at a spectral resolution of 3.6 (FWHM), $0\farcs95\times0\farcs95$ spatial sampling, and sky coverage \citep{bac2001}."254. Another 116 spectra are taken 1/9 away from the main field. to allow accurate sky subtraction.," Another 146 spectra are taken $1\farcm9$ away from the main field, to allow accurate sky subtraction."255 The waveleugth range of the current setup is &LSLO5350Α., The wavelength range of the current setup is $\approx$ 4810–5350.256". We observed two fields overlapping by 20"" ou the nuclear region of 11365. cach field. having four separate exposures of 1800 s (dithered by z1.. one leunslet)."," We observed two fields overlapping by $\approx$ on the nuclear region of 4365, each field having four separate exposures of 1800 s (dithered by $\approx$, one lenslet)."257 The combined datacubes cover a total region of « ou the «kv., The combined datacubes cover a total region of $\times$ on the sky.258 The μια offsets between the four 1800 s inteerations at each position enable us to re-unuple the final datacubes onto 078& pixels (drizzling teclinique]., The small offsets between the four 1800 s integrations at each position enable us to re-sample the final datacubes onto $0\farcs8\times0\farcs8$ pixels (drizzling technique).259 The secing of the merged datacube was measured ou three point-like objects iu the reconstructed image., The seeing of the merged datacube was measured on three point-like objects in the reconstructed image.260 It is homogeneous over the field with a value of 176+οὐ] (FWIIM)., It is homogeneous over the field with a value of $1\farcs6 \pm 0\farcs1$ (FWHM).261 We took arc-Inuup spectra before aud after cach individual exposure for accurate waveleugth calibration., We took arc-lamp spectra before and after each individual exposure for accurate wavelength calibration.262 We reduced the raw eexposures by ineans of the algorithims described i- Bacouetal.(2001)., We reduced the raw exposures by means of the algorithms described in \citet{bac2001}.263.. We used the incdividually-extracted. waveleugth-calibrated aud continmum-corrected spectra to derive the stellar kinematics aud line-streugth indices as a function of (two-dimensional) position in 11365.," We used the individually-extracted, wavelength-calibrated and continuum-corrected spectra to derive the stellar kinematics and line-strength indices as a function of (two-dimensional) position in 4365."264 We measured the mean velocity V. aud the velocitydispersion σ with the Fourier Correlation Quotieut method (Beucder1990).. aud obtained the Lne-streneth iudicesIT... ‘and Fe5270 in the Lick/IDS svsteii (Worthey1991).. taking iuto account the iuterual velocity broadeniug aud differences in the instrumental resolution.," We measured the mean velocity $V$ and the velocitydispersion $\sigma$ with the Fourier Correlation Quotient method \citep{ben1990}, and obtained the line-strength indices, and Fe5270 in the Lick/IDS system \citep{wor1994}, taking into account the internal velocity broadening and differences in the instrumental resolution."265 Figure le shows the surface brightness distribution of 11365. as reconstructed from our The reconstructed inteusity map agrees well with the IIST inaege after seciug convolution aud binning to the ‘spatial samplue.," Figure \ref{fig:color}{ shows the surface brightness distribution of 4365, as reconstructed from our The reconstructed intensity map agrees well with the HST image after seeing convolution and binning to the spatial sampling."266 Figue 1b shows the spectacular kinematically decoupled core of 11365 in detail., Figure \ref{fig:color}{ shows the spectacular kinematically decoupled core of 4365 in detail.267 The core extends cU a and rotates about the nünor axis, The core extends $\approx$ $\times$ and rotates about the minor axis.268 The mnaxiuuu observed core rotation speed is SO s, The maximum observed core rotation speed is 80 at a radius of 2.269lowly about au axis iisaligued by 8+2° with the major axis., The main body of the galaxy rotates slowly about an axis misaligned by $8\pm2^{\circ}$ with the major axis.270" The rotation velocity rises to 15 Pater=1"". and remains constant at larecr radii."," The rotation velocity rises to 45 at $r = 7$, and remains constant at larger radii."271 The velocity field of the main body is not svuuuetrie about the nüuor axis and the loci of zero velocity (shown as bold line in Figure 1b) and maxiuu velocity. are not perpendicular.," The velocity field of the main body is not symmetric about the minor axis and the loci of zero velocity (shown as bold line in Figure 1b) and maximum velocity, are not perpendicular."272 We will explore the cousequeuces of this in a later paper preseutiug clvnamical models., We will explore the consequences of this in a later paper presenting dynamical models.273 The velocity dispersion falls off noothlv frou its central masta of 275Ll. and the contours of coustaut dispersion follow the isophotes (Fiewe Le).," The velocity dispersion falls off smoothly from its central maximum of 275, and the contours of constant dispersion follow the isophotes (Figure \ref{fig:color}{ )."274 A detailed comparison shows exccllent agreement with the SB long-slit dataetal. 2001)., A detailed comparison shows excellent agreement with the SB long-slit data\citep{zee2001}.275. Figure ld shows that the distribution of has a ceutral peak. whereas the value is roughly constant across the galaxy. (Figure 1ο.," Figure \ref{fig:color}{ shows that the distribution of has a central peak, whereas the value is roughly constant across the galaxy (Figure \ref{fig:color}{ )."276 Our average value for the ceutral ‘absorption streneth is 1.6150.01 ©. iu good agreement with the Lick/IDS measurement of 1.66E0.21 (Trageretal. 1998)..," Our average value for the central absorption strength is $1.61\pm0.04$ , in good agreement with the Lick/IDS measurement of $1.66\pm0.21$ \citep{tra1998}. ."277 Furthermore. we find no indication for either," Furthermore, we find no indication for either"278of AGN. the black hole masses of AGN can be easily estimated from their optical luminosity and width of broad emission line.,"of AGN, the black hole masses of AGN can be easily estimated from their optical luminosity and width of broad emission line."279 The Eddington ratios for thousands of AGN were estimated with the analyses of the Sloan Digital Sky Survey (SDSS) by (2004). which indicate that the mean Eddington ratio μηπιωο0.1 at z~0.2 to 20.4 at z~2.," The Eddington ratios for thousands of AGN were estimated with the analyses of the Sloan Digital Sky Survey (SDSS) by , which indicate that the mean Eddington ratio $L_{\rm bol}/L_{\rm Edd}\simeq 0.1$ at $z\sim 0.2$ to $\simeq0.4$ at $z\sim 2$."280" also derived the Eddington ratio distribution for a sample of ~ É ""m with redshifts 0Éddineton.", also derived the Eddington ratio distribution for a sample of $\sim$ 500 AGN with redshifts $0\la z\la 5$.281" AS pointed by(2006).. both these derived ratios are heavily -- towards high-luminosity B"" due to the limited sensitivity of SDSS."," As pointed by, both these derived Eddington ratios are heavily weighted towards high-luminosity objects due to the limited sensitivity of SDSS."282 estimated the Eddington ratios of AGN discovered in the AGN and Galaxy Evolution Survey (AGES). which is more sensitive than the SDSS2004).," estimated the Eddington ratios of AGN discovered in the AGN and Galaxy Evolution Survey (AGES), which is more sensitive than the SDSS."283. The derived Eddington ratio distribution at is well described by a single lognormal distribution peaked at ~0.25 independent of redshift and luminositydetails)., The derived Eddington ratio distribution at is well described by a single lognormal distribution peaked at $\sim 0.25$ independent of redshift and luminosity.284 In this work. the Eddington ratio distribution at.luminosity given by is converted to that at by using an AGN LF.," In this work, the Eddington ratio distribution at given by is converted to that at by using an AGN LF."285 We integrate he continuity equation for black hole number density adopting he derived Eddington ratio distributions of AGN to calculate the BHMF of AGN relics at different redshifts z. which is different Tom a free parameter A adopted in most previous works.," We integrate the continuity equation for black hole number density adopting the derived Eddington ratio distributions of AGN to calculate the BHMF of AGN relics at different redshifts $z$ , which is different from a free parameter $\lambda$ adopted in most previous works."286 The resultant BHMF of AGN relies is constrained by those estimated rom the galaxy LFs2, The resultant BHMF of AGN relics is constrained by those estimated from the galaxy LFs.287"006).. n conventional parameters (234;=0.8. Oy,work.=07. and ff,=τί0cosmologicalkms+Mpe have been adopted in his "," The conventional cosmological parameters $\Omega_{\rm M}=0.3$, $\Omega_{\Lambda}=0.7$, and $H_0=70~ {\rm288km~s^{-1}~Mpc^{-1}}$ have been adopted in this work."289The Eddington ratio distribution of AGN for given bolometricluminosity can be approximated as a log-normal distribution: where/=log A.A=LiaLada. Ὁlog0.25 anda= details).," The Eddington ratio distribution of AGN for given bolometricluminosity can be approximated as a log-normal distribution: where ${l}=\log\lambda$, $\lambda=L_{\rm bol}/L_{\rm Edd}$, $\mu\simeq \log 0.25$ and $\sigma\simeq 0.3$ ."290 We can derive the BHMF of AGN from the bolometric LF (2.Li): where logLi)=/|logLpa. Lew=L2514454eres 1 and NI is in units of solar mass.," We can derive the BHMF of AGN from the bolometric LF $\Phi(z,L_{\rm bol})$: where $\log L_{\rm bol}={ l}+\log L_{\rm Edd}$, $L_{\rm291Edd}=1.251\times10^{38} M_{\rm bh}{\rm ~erg~s}^{-1}$ , and $M_{\rm292bh}$ is in units of solar mass."293" Using the bolometric LF @(hole2.£1...) of Aba,AGN. the Eddington ratio distribution for given black mass can be calculated with where Li,P=]ULpg,. and the BHMF of AGN. EddingtonNacun(s.Mua) of available with Equation (25."," Using the bolometric LF $\Phi(z,L_{\rm bol})$ of AGN, the Eddington ratio distribution for given black hole mass $M_{\rm bh}$ can be calculated with where $L_{\rm bol}=10^l L_{\rm Edd}$, and the BHMF of AGN, $N_{\rm294AGN}(z,M_{\rm bh})$, is available with Equation \ref{nagn}) )."295" The mean ratio AGN with AZ, at z is In this work. we adopt the luminosity-dependent density evolution (LDDE) bolometric LF calculated from the rest-frame optical. soft and hard X-ray. and near- and mid-IR bands in the redshift interval 2=06 by200711: with and All the parameters LF are as follows:logo,=Alpe * logL.(ergsofthe+)=45.99d:0.10. 5,=0.933 (.045. »=2.2040.14. logsLe(ergs=46.72:0.05. 1.552 40.025. à=0.274+0.025.""m Landplas=5.95+0.23. plasL654 0.21. 3,=0.294 d=o0.02+O172007)."," The mean Eddington ratio of AGN with $M_{\rm bh}$ at $z$ is In this work, we adopt the luminosity-dependent density evolution (LDDE) bolometric LF calculated from the rest-frame optical, soft and hard X-ray, and near- and mid-IR bands in the redshift interval $z=0-6$ by: The density function $e_{\rm d}$ is given by with and All the parameters of the LF are as follows: $\log\phi_*=-6.20\pm0.15~{\rm Mpc^{-3}}$ , $\log L_{*}({\rm296ergs~s^{-1}})=45.99\pm0.10$, $\gamma_1=0.933\pm0.045$ , $\gamma_2=2.20\pm0.14$, $\log L_{\rm c} ({\rm297ergs~s^{-1}})=46.72\pm0.05$, $z_{\rm c,0}=1.852\pm0.025$ , $\alpha=0.274\pm0.025$, $p1_{46}=5.95\pm0.23$, $p2_{46}=-1.65\pm0.21$ , $\beta_1=0.29\pm0.34$, and $\beta_2=-0.62\pm0.17$."298 In Fig. l|.," In Fig. \ref{fig1},"299 we plot the Eddington ratio distributions m-Mig.1) for fixed black hole mass derived from that for given by (2006).," we plot the Eddington ratio distributions $\chi(z,M_{\rm bh},{ l})$ for fixed black hole mass derived from that for given by ."300. We find that the derived Eddington ratio distributions are close to the lognormal distribution. while their peaks vary with black hole mass and redshift.," We find that the derived Eddington ratio distributions are close to the lognormal distribution, while their peaks vary with black hole mass and redshift."301 We plot the mean Eddington ratios as functions ofblack hole mass in Fig. 2., We plot the mean Eddington ratios as functions ofblack hole mass in Fig. \ref{fig2}.302".It isfound that the mean Eddington ratios A(z.Mia) are in the range of0.10.3 as functions of blackhole mass Adi, and redshift z."," .It isfound that the mean Eddington ratios $\bar{\lambda}(z,M_{\rm bh})$ are in the range of $\sim3030.1-0.3$ as functions of blackhole mass $M_{\rm bh}$ and redshift $z$ ."304 The evolution of massive black hole number density is described by, The evolution of massive black hole number density is described by305obtained only by breaking the conformal invariance of clectromagnetism (already at the time of bubble nucleation) or by introducing some other kind of new physics.,obtained only by breaking the conformal invariance of electromagnetism (already at the time of bubble nucleation) or by introducing some other kind of new physics.306 We thank Misao Sasali for interesting comments., We thank Misao Sasaki for interesting comments.307 JA wants to thank the University of Geneva for hospitality. ancl the German Research Foundation (DEG) for financial support through the Research “Training Group 1147. 7Fheoretical Astrophysics and. Particle Physies.”, JA wants to thank the University of Geneva for hospitality and the German Research Foundation (DFG) for financial support through the Research Training Group 1147 “Theoretical Astrophysics and Particle Physics.”308 Cdlt anc RD are supported by the Swiss National Science Foundation., CdR and RD are supported by the Swiss National Science Foundation.309 We present here the explicit. computation of the moce spectrum in the Milne model. which is one of the simplest open FL geometries.," We present here the explicit computation of the mode spectrum in the Milne model, which is one of the simplest open FL geometries."310 Lt is obtained by rewriting the line clement of Minkowski space as While X»«4FEx and OO:Ro«x are the coordinates of a standard. (spatially flat) spherical coordinate system which covers the full Minkowski spacetime. using 0«/o and 0xr«oc one obtains a metric of the open FL tvpe with e=f. eeq. (1)).," It is obtained by rewriting the line element of Minkowski space as While $-\infty < T < \infty$ and $0 \leq R < \infty$ are the coordinates of a standard (spatially flat) spherical coordinate system which covers the full Minkowski spacetime, using $0 < t < \infty$ and $0 \leq r < \infty$ one obtains a metric of the open FL type with $a = t$, eq. \ref{eq:metric}) )."311 This new coordinate svstem. with 7=/coshr and 2= fsinhr. covers the interior of the future lighteone of 7=f?—0.," This new coordinate system, with $T=t\cosh r$ and $R=t\sinh r$ , covers the interior of the future lightcone of $T = R = 0$."312 Within this very simple setting which vet has all the desired features. we want now to exemplify the reasoning of section 3..," Within this very simple setting which yet has all the desired features, we want now to exemplify the reasoning of section \ref{sec:nosupercurv}. ."313 As a first step. for the mode expansion of eq. (12))," As a first step, for the mode expansion of eq. \ref{eq:openmodes}) )"314 we can immediately solve the mode equation., we can immediately solve the mode equation.315 The solutions to eq. (669) , The solutions to eq. \ref{eq:eom}) )316take the form where νο is a normalization to be determined., take the form where $N_{p\pm}$ is a normalization to be determined.317 To this end. we want to evaluate the IxIein-Cordon inner product on a Cauchy surface.," To this end, we want to evaluate the Klein-Gordon inner product on a Cauchy surface."318 The whole point is that the open spatial hypersurfaces {f=const.) do not represent. proper Cauchy surfaces and one should therefore make a better choice., The whole point is that the open spatial hypersurfaces $\lbrace t = \mathrm{const.}\rbrace$ do not represent proper Cauchy surfaces and one should therefore make a better choice.319 We choose the surface {2=0} which is a proper global section of Minkowski space., We choose the surface $\lbrace T = 0\rbrace$ which is a proper global section of Minkowski space.320 This hypersurface lies entirely outside the coordinate pateh covered. by. for. however. by making appropriate analytic continuations. we can complete the chart to include [77=Of.," This hypersurface lies entirely outside the coordinate patch covered by $t, r$, however, by making appropriate analytic continuations, we can complete the chart to include $\lbrace T = 0\rbrace$."321 More. precisely. by. taking [or dp.rTO ὑπὸ. the region outside the lishtcone is covered bv xeorooo and O«p«co.," More precisely, by taking $t \rightarrow i \rho$, $r \rightarrow \tau - i \pi / 2$ , the region outside the lightcone is covered by $-\infty < \tau < \infty$ and $0 < \rho < \infty$."322 Furthermore. the hypersurface (£7=0j coincides with the one defined by {7=O}.," Furthermore, the hypersurface $\lbrace T = 0\rbrace$ coincides with the one defined by $\lbrace \tau = 0\rbrace$."323 The line clement is given as lt is noteworthy that the role of time and racial distance have been interchanged by the analytic continuation. just as it was done bv ? for the case of de Sitter.," The line element is given as It is noteworthy that the role of time and radial distance have been interchanged by the analytic continuation, just as it was done by \citet{Sasaki:1994yt} for the case of de Sitter."324 The Wlhein-Corcdon inner product is finally given by ὃν makinga change of variables to Inp. one can see that the p. integral is a representation of the delta function δν.p) for p.p! real.," The Klein-Gordon inner product is finally given by By makinga change of variables to $\ln \rho$, one can see that the $\rho-$ integral is a representation of the delta function $\delta(p - p')$ for $p, p'$ real."325 For any imaginary p or p. the integral is badly divergent. whieh implies that the modes with imaginary p have zero norm.," For any imaginary $p$ or $p'$, the integral is badly divergent, which implies that the modes with imaginary $p$ have zero norm."326 In other words. there are no supercurvature modes ofthe Debye potentials in the Milne model.," In other words, there are no supercurvature modes ofthe Debye potentials in the Milne model."327 For the regular modeswith real values of p. the term printed in thelast line of eq. CX4))," For the regular modeswith real values of $p$ , the term printed in thelast line of eq. \ref{eq:KGproduct})"328resolvable by our numerical code (and similar to the seed field in strength and structure) during the galactic evolution.,resolvable by our numerical code (and similar to the seed field in strength and structure) during the galactic evolution.329 Then we link the dynamo and star-formation history to simulate the cosmological evolutioi of the magnetic structure., Then we link the dynamo and star-formation history to simulate the cosmological evolution of the magnetic structure.330 Our model is based on a 2D set of dynamo equations which yields a 2D magnetic field configuration at the equatorial plane of a galaxy., Our model is based on a 2D set of dynamo equations which yields a 2D magnetic field configuration at the equatorial plane of a galaxy.331 Then we restore the vertical magnetic field component at this plane from the divergence-free condition and extrapolate the components from the equatorial plane to the whole disc., Then we restore the vertical magnetic field component at this plane from the divergence-free condition and extrapolate the components from the equatorial plane to the whole disc.332 As a result we get a 3D model after explicit solutior of 2D equations. which is computationally efficient.," As a result we get a 3D model after explicit solution of 2D equations, which is computationally efficient."333 Finally. from the magnetic field structures we simulate the expected total and polarized emission. and Faraday rotatior measures (RMs) in these disc galaxies.," Finally, from the magnetic field structures we simulate the expected total and polarized emission, and Faraday rotation measures (RMs) in these disc galaxies."334 The main message obtained from the model can be summarized as follows., The main message obtained from the model can be summarized as follows.335 We recognize two phases of the evolution of galactic magnetic fields., We recognize two phases of the evolution of galactic magnetic fields.336 Firstly. a large-scale magnetic field configuration develops from the random seed field.," Firstly, a large-scale magnetic field configuration develops from the random seed field."337 This stage is quite short and takes GGyr., This stage is quite short and takes Gyr.338 Secondly. the magnetic field becomes quite regular and close to an axisymmetric spiral structure. but affected by fluctuations.," Secondly, the magnetic field becomes quite regular and close to an axisymmetric spiral structure, but affected by fluctuations."339 The main issue is that we obtain two different types of large-scale magnetic field configuration: (1) axisymmetric structures that have the same field direction over the whole galactic disc. (2) axisymmetric spiral fields that are restricted to two or even three separate intervals in radius (rings) with the field reversing direction between neighbouring rings.," The main issue is that we obtain two different types of large-scale magnetic field configuration: (1) axisymmetric structures that have the same field direction over the whole galactic disc, (2) axisymmetric spiral fields that are restricted to two or even three separate intervals in radius (rings) with the field reversing direction between neighbouring rings."340 A three-phase model for the evolution of magnetic fields in isolated (without merger) disc galaxies 1n the context of the hierarchical structure formation cosmology was developed by Arshakian et al. (, A three-phase model for the evolution of magnetic fields in isolated (without merger) disc galaxies in the context of the hierarchical structure formation cosmology was developed by Arshakian et al. (3412009).,2009).342 According to this model. in the first phase weak fields of order ~107 GG were generated by the Biermann battery mechanism and/or the Weibel instability in the first dark matter halos.," According to this model, in the first phase weak fields of order $\sim 10^{-18}$ G were generated by the Biermann battery mechanism and/or the Weibel instability in the first dark matter halos."343 The second phase was manifested by merging of halos and thermal virialization of protogalaxies., The second phase was manifested by merging of halos and thermal virialization of protogalaxies.344 During this epoch the small-scale dynamo was able to amplify effectively the turbulent magnetic field up to the energy level of equilibrium with turbulent kinetic energy (~107 GG) in a relatively short timescale of a few hundreds of million years., During this epoch the small-scale dynamo was able to amplify effectively the turbulent magnetic field up to the energy level of equilibrium with turbulent kinetic energy $\sim 10^{-5}$ G) in a relatively short timescale of a few hundreds of million years.345 The third phase started at the epoch of dise formation (at a redshift of about 10) that occurred by dissipation of the protogalactic halo., The third phase started at the epoch of disc formation (at a redshift of about 10) that occurred by dissipation of the protogalactic halo.346 The magnetic field preserved in the protogalactic halo served as a seed field in the disc (~1077 GG). which was further amplified by the mean-field dynamo to the equipartition level (~107? GG) in few Gyrs and ordered on scales of up to galactic scale in about GGyr. this stage lasting until the present epoch.," The magnetic field preserved in the protogalactic halo served as a seed field in the disc $\sim 10^{-7}$ G), which was further amplified by the mean-field dynamo to the equipartition level $\sim 10^{-5}$ G) in few Gyrs and ordered on scales of up to galactic scale in about Gyr, this stage lasting until the present epoch."347 In semi-analytical models of the evolution of regular magnetic fields Arshakian et al. (, In semi-analytical models of the evolution of regular magnetic fields Arshakian et al. (3482011) proposed that the configuration of the initial regular field in the third phase was “spotty” over the galactic disc.,2011) proposed that the configuration of the initial regular field in the third phase was “spotty” over the galactic disc.349" The differential rotation initially stretches the magnetic spots m the azimuthal direction as they appear. and field reversals can be formed in few Gyrs by the effects of the large-scale dynamo action. and eventually an axisymmetric field similar to that of many present-day galaxies,"," The differential rotation initially stretches the magnetic spots in the azimuthal direction as they appear, and field reversals can be formed in few Gyrs by the effects of the large-scale dynamo action, and eventually an axisymmetric field similar to that of many present-day galaxies."350 In this section. we adopt some of the ideas of the semi-analytical model of Arshakian et al. (," In this section, we adopt some of the ideas of the semi-analytical model of Arshakian et al. ("3512009. 2011) and develop an evolutionary model of a dise galaxy (phase 3). based on explicit solutions of the dynamo equations coupled to the star formation rate.,"2009, 2011) and develop an evolutionary model of a disc galaxy (phase 3), based on explicit solutions of the dynamo equations coupled to the star formation rate."352 The variations of the star-formation. rate (SFR) and the physical/geometrical parameters of the disc drive the evolution of regular magnetic fields in galaxies (Arshakian et al., The variations of the star-formation rate (SFR) and the physical/geometrical parameters of the disc drive the evolution of regular magnetic fields in galaxies (Arshakian et al.353 2011)., 2011).354 Star formation can be triggered by different processes including. for example. gravitational instability. and the interaction of clouds and tidal forees in isolated and merging galaxies (Kennicutt et al.," Star formation can be triggered by different processes including, for example, gravitational instability, and the interaction of clouds and tidal forces in isolated and merging galaxies (Kennicutt et al."355 1987; Combes 2005)., 1987; Combes 2005).356 The rate of SN explosions is proportional to the SFR., The rate of SN explosions is proportional to the SFR.357 Supernova remnants (SNRs) drive the turbulence of the interstellar medium (ISM) and determine the characteristic velocity dispersion of the gas. characterized by the turbulent velocity v.," Supernova remnants (SNRs) drive the turbulence of the interstellar medium (ISM) and determine the characteristic velocity dispersion of the gas, characterized by the turbulent velocity $v$."358 The latter 1s known to be correlated with SFR for nearby galaxies (Dib et al., The latter is known to be correlated with SFR for nearby galaxies (Dib et al.359 1996); it is almost constant for low SFRs (up to SFR values typical of the Milky Way) with 5IO kkm s' and grows exponentially at higher SFRs as typical for starburst galaxies., 1996); it is almost constant for low SFRs (up to SFR values typical of the Milky Way) with $v\approx 10$ km $^{-1}$ and grows exponentially at higher SFRs as typical for starburst galaxies.360 Star formation in isolated. young galaxies is more efficient because more gas Is available at high redshifts (redshift ~1.3. Ryan et al.," Star formation in isolated, young galaxies is more efficient because more gas is available at high redshifts (redshift $\sim 1.3$, Ryan et al."361 2007)., 2007).362 SFR is proportional to the gas mass density (the Kennicutt-Schmidt law) and. hence. the SFR history of dise galaxies ts different for galaxies with different Hubble types.," SFR is proportional to the gas mass density (the Kennicutt-Schmidt law) and, hence, the SFR history of disc galaxies is different for galaxies with different Hubble types."363 Modelling of SFR indicates that a constant SFR is appropriate for late-type spirals (Sd) while the SFR decreases with galaxy age for earlier types (Sc. Sb. and Sa: Sandage 1986. Kotulla et al.," Modelling of SFR indicates that a constant SFR is appropriate for late-type spirals (Sd) while the SFR decreases with galaxy age for earlier types (Sc, Sb, and Sa; Sandage 1986, Kotulla et al."364 2009)., 2009).365 For simplicity. we consider an evolving Milky Way-type galaxy with constant SFR of 1 Moyr! and constant turbulent velocity. v2 IOkkm s! throughout its evolution.," For simplicity, we consider an evolving Milky Way-type galaxy with constant SFR of 1 $M_{\sun}\,{\mathrm{yr}^{-1}}$ and constant turbulent velocity, $v=10$ km $^{-1}$ throughout its evolution."366 Star formation generates supernova explosions which are the main source of turbulence in the galaxy disc and in turn inject small-scale magnetic fields., Star formation generates supernova explosions which are the main source of turbulence in the galaxy disc and in turn inject small-scale magnetic fields.367 In our model the field injection occurs at regular time intervals simultaneously at à number of random locations with a volume filling factor of about[, In our model the field injection occurs at regular time intervals simultaneously at a number of random locations with a volume filling factor of about.368"σοι We use a thin dise galaxy code with the ""no-z formulation (e.g. Subramanian Mestel 1993; Moss 1995 and subsequent papers). taking the aw approximation."," We use a thin disc galaxy code with the $z$ "" formulation (e.g. Subramanian Mestel 1993; Moss 1995 and subsequent papers), taking the $\alpha\omega$ approximation."369 This code solves explicitly for the field components parallel to the disc plane with the implicit understanding that the component perpendicular to this plane (re. in the —direction) is given by the condition V-B.=©. and that the field has eve1 (quadrupole-like) parity with respect to the disc plane.," This code solves explicitly for the field components parallel to the disc plane with the implicit understanding that the component perpendicular to this plane (i.e. in the $z$ -direction) is given by the condition $\nabla\cdot {\bf B}=0$, and that the field has even (quadrupole-like) parity with respect to the disc plane."370 The field components parallel to the plane can be considered as values. or as a form of vertical average through the disc (see. e.g.. Moss 1995).," The field components parallel to the plane can be considered as mid-plane values, or as a form of vertical average through the disc (see, e.g., Moss 1995)."371 The key parameters are the aspect ratio, The key parameters are the aspect ratio372Magnetized rotating neutron stars can be categorized into different categories based on their emission properties. like AXPs. SGRs. radio pulsars. RRATSerc.,"Magnetized rotating neutron stars can be categorized into different categories based on their emission properties, like AXPs, SGRs, radio pulsars, RRATS."373 Although almost every day some new interesting discoveries relating these objects are being made using the advanced technologies. it is unfortunate that the true description of the dense matter constituting these objects is still not well understood.," Although almost every day some new interesting discoveries relating these objects are being made using the advanced technologies, it is unfortunate that the true description of the dense matter constituting these objects is still not well understood."374 A number of Equations of State (EsoS) are available in the literature trying to describe the state of the matter in such extreme condition as inside neutron stars. see Lattimer Prakash (2007) for a few examples of the EsoS. Better knowledge about the dense matter EsoS will in the long run help us to understand observational features of neutron stars in a better extent.," A number of Equations of State (EsoS) are available in the literature trying to describe the state of the matter in such extreme condition as inside neutron stars, see Lattimer Prakash (2007) for a few examples of the EsoS. Better knowledge about the dense matter EsoS will in the long run help us to understand observational features of neutron stars in a better extent."375 Presently there are a number of approaches trying to constrain the dense matter EsoS through astronomical observations of compact stars., Presently there are a number of approaches trying to constrain the dense matter EsoS through astronomical observations of compact stars.376" The usual approach is to determine the mass and the radius of the stars with the help of various observational features like gravitational redshifts (2) from spectral lines. cooling characteristics. KHz quasi-periodic oscillations (ΟΡΟ) (Lattimer Prakash 2007. Liefe. 1999, Ozzel 2006. Zhang οἱed. 2007)."," The usual approach is to determine the mass and the radius of the stars with the help of various observational features like gravitational redshifts $z$ ) from spectral lines, cooling characteristics, kHz quasi-periodic oscillations (QPO) (Lattimer Prakash 2007, Li $et~al.$ 1999, Özzel 2006, Zhang $et~al.$ 2007)."377 But these methods are not foolproof. e.g. the value of > used in Ozzel’s analysis of EXO 676 can not be reproduced as mentioned by Klahn efe£. (2006).," But these methods are not foolproof, $e.g.$ the value of $z$ used in Özzel's analysis of EXO $-$ 676 can not be reproduced as mentioned by Klahn $et~al.$ (2006)."378 Moreover. to constrain EsoS from ΟΡΟ) observations. one need to believe in some specific model of QPO which is again a subject of debate.," Moreover, to constrain EsoS from QPO observations, one need to believe in some specific model of QPO which is again a subject of debate."379 Another alternative method might be the measurement of the moment of inertia from the faster component (A) of the double pulsar system PSR J0737-3039A/B (Lattimer Schutz 2005. Bagchi efe. 2009).," Another alternative method might be the measurement of the moment of inertia from the faster component (A) of the double pulsar system PSR J0737-3039A/B (Lattimer Schutz 2005, Bagchi $et~al.$ 2009)."380 As some high mass stars like PSR 7190340327. EXO 676 cle. prefer neutron star models and some other stars like 4U 1728-34 (Li e!af. 1999). prefer strange star models. it is possible that both family coexist in nature.," As some high mass stars like PSR J1903+0327, EXO $-$ 676 $etc.$ prefer neutron star models and some other stars like 4U 1728-34 (Li $et~al.$ 1999), prefer strange star models, it is possible that both family coexist in nature."381 But even then. we need some constrains as there are a number of EsoS for neutron stars and also for strange stars.," But even then, we need some constrains as there are a number of EsoS for neutron stars and also for strange stars."382 Because of the lack of any strong constrains on the dense matter EsoS till date. it is interesting to study the effect different choice of EsoS on the stellar properties.," Because of the lack of any strong constrains on the dense matter EsoS till date, it is interesting to study the effect different choice of EsoS on the stellar properties."383 This is our motivation of studying the effect of EsoS in the determination of the values of the pulsar magnetic field and consequent results., This is our motivation of studying the effect of EsoS in the determination of the values of the pulsar magnetic field and consequent results.384 Here we have chosen five EsoS. three for the neutron matter and two for the strange quark matter.," Here we have chosen five EsoS, three for the neutron matter and two for the strange quark matter."385 We discuss the model of the pulsar magnetic field in section 2 dn short and then display our results in section RE43.., We discuss the model of the pulsar magnetic field in section \ref{sec:mag_field} in short and then display our results in section \ref{sec:results}.386 Discussions and conclusions are given in section + and section 5. respectively., Discussions and conclusions are given in section \ref{sec:disc} and section \ref{sec:concl} respectively.387 For a radio pulsar. the value of the surface magnetic field (401) is estimated by equating the spin down luminosity with the dipole radiation power and one gets the following expression :," For a radio pulsar, the value of the surface magnetic field $B_s$ ) is estimated by equating the spin down luminosity with the dipole radiation power and one gets the following expression :"388Universe can be approximated: as homogeneous. bevond that). ancl accurately represents the distribution of matter on small distance scales.,"Universe can be approximated as homogeneous beyond that), and accurately represents the distribution of matter on small distance scales."389 For any single volume-limited subsaniple. these requirements work in opposite directions: the first. calls for a laree volume. while the second calls for a small volume.," For any single volume-limited subsample, these requirements work in opposite directions: the first calls for a large volume, while the second calls for a small volume."390 To resolve this conllict one could consider combining two volume-limitecl samples. à sparse one to cover large distances and a dense one to cover the nearby. region in more detail.," To resolve this conflict one could consider combining two volume-limited samples, a sparse one to cover large distances and a dense one to cover the nearby region in more detail."391" In this paper we discuss a technique ermed. ""sliding-box technique which generalizes this idea bv combining many volume-limited samples.", In this paper we discuss a technique – termed “sliding-box” technique – which generalizes this idea by combining many volume-limited samples.392 Up to a specified. limiting distance the whole Ilux-Iimited catalog is used in this process. so that close-by structures are mapped out with maximum detail by the dim objects in the original catalog.," Up to a specified limiting distance the whole flux-limited catalog is used in this process, so that close-by structures are mapped out with maximum detail by the dim objects in the original catalog."393 Phe crux of the Construction is in an appropriate weighting scheme: We weigh galaxies in the {lux-limitecl sample in a cistance-dependent way so that the progressive incompleteness at arge distances is compensated. by the increasing weight of cach galaxy., The crux of the construction is in an appropriate weighting scheme: We weigh galaxies in the flux-limited sample in a distance-dependent way so that the progressive incompleteness at large distances is compensated by the increasing weight of each galaxy.394 These weights. essentially representing the uminositv per galaxy. can be naturally incorporated. in lux computation algorithms which inherently use some sort of weights to account for the fact that remote sources ooduce less (ux than nearby ones.," These weights, essentially representing the luminosity per galaxy, can be naturally incorporated in flux computation algorithms which inherently use some sort of weights to account for the fact that remote sources produce less flux than nearby ones."395 The sliding-box technique is essentially. a method o deal with the [act that galaxy catalogs clo not contain an infinite number of galaxies., The sliding-box technique is essentially a method to deal with the fact that galaxy catalogs do not contain an infinite number of galaxies.396 Phe finiteness of a galaxy catalog unavoidably leads to [Lactuations in lux oedietions., The finiteness of a galaxy catalog unavoidably leads to fluctuations in flux predictions.397 The sliding-box technique strongly reduces hese fluctuations by ellicient. use of the available cata., The sliding-box technique strongly reduces these fluctuations by efficient use of the available data.398 evertheless. the remaining Dluctuations may still be large enough to spoil the accuracy of Dux maps modeled from a ealaxy catalog.," Nevertheless, the remaining fluctuations may still be large enough to spoil the accuracy of flux maps modeled from a galaxy catalog."399 We will address this problem in detail and oesent a criterion for the applicability of the sliding-box niethod., We will address this problem in detail and present a criterion for the applicability of the sliding-box method.400 An an illustration we will apply the. sliding-box echnique to a subset of the 2 Micron. All-Sky Hecshift Survey (2AIRS) (2?) a Llux-limitec sample of galaxics with observed. A-magnitude m.11.25 that contains measured redshifts for all but a Low We would like to stress. however. that the technique is completely general ancl can be applied to any Dux-limited galaxy sample.," An an illustration we will apply the sliding-box technique to a subset of the 2 Micron All-Sky Redshift Survey (2MRS) \citep{2MRS}, a flux-limited sample of galaxies with observed $K_s$ -magnitude $m \leq 11.25$ that contains measured redshifts for all but a few We would like to stress, however, that the technique is completely general and can be applied to any flux-limited galaxy sample."401 lt is worth noting that the issue addressed. in this paper is related to the well-known astronomical problem ol reconstructing the luminosity function from a quasar or galaxy sample that is limited in apparent magnitude (sec. e.g.. ?? [or a comparison between cdillerent methods and references).," It is worth noting that the issue addressed in this paper is related to the well-known astronomical problem of reconstructing the luminosity function from a quasar or galaxy sample that is limited in apparent magnitude (see, e.g., \citet{1977AJ.....82..861F, 1997AJ....114..898W}402 for a comparison between different methods and references)."403 The sliding-box scheme discussed in this work is an application of the €C' -method that was proposed by 7.. and further developed. by 2?7.. to reconstruct the quasar luminosity function.," The sliding-box scheme discussed in this work is an application of the $C^{-}$ -method that was proposed by \citet{1971MNRAS.155...95L}, and further developed by \citet{1974MNRAS.166..281J,4041987MNRAS.226..273C,1988MNRAS.232..431E}, to reconstruct the quasar luminosity function."405 Our formulation of the scheme is tailored for flux calculations. in. keeping with the aim of the present studs.," Our formulation of the scheme is tailored for flux calculations, in keeping with the aim of the present study."406 The rest of this paper is organized as follows., The rest of this paper is organized as follows.407 Ln section 2 we discuss the sliding-box technique and present an cllicient implementation. scheme., In section \ref{sec:slid-box-weight} we discuss the sliding-box technique and present an efficient implementation scheme.408 We also. discuss the connection between the weights associated with the algorithm on one hand and the luminosity anc selection functions on the other., We also discuss the connection between the weights associated with the algorithm on one hand and the luminosity and selection functions on the other.409 Section 3. is concerned. with the elect. o£ Huctuations on model fluxes due to the finite size of a galaxy sample., Section \ref{sec:fluctuations} is concerned with the effect of fluctuations on model fluxes due to the finite size of a galaxy sample.410 In section. 4.. as an example. we apply the slicing-box method. to model the Εαν of ULIECTIU protons with energies above GO ο) from the PAIRS sample.," In section \ref{section:2MRS}, as an example, we apply the sliding-box method to model the flux of UHECR protons with energies above 60 EeV from the 2MRS sample."411 We summarize our work in section 5.., We summarize our work in section \ref{sec:summary}.412 ‘Lo illustrate the general idea of the sliding-box technique. consider a [ux-limited sample that is complete to a given apparent magnitude mv.," To illustrate the general idea of the sliding-box technique, consider a flux-limited sample that is complete to a given apparent magnitude $m_0$."413 On the ALD plane. where Al is the absolute magnitude and 2 is the distance. this sample occupies the populated. region in Fig. l..," On the $M-D$ plane, where $M$ is the absolute magnitude and $D$ is the distance, this sample occupies the populated region in Fig. \ref{fig:cutting-samples}. ."414 The apparent magnitude m of a source is a function of its absolute magnitude and distance. im=mW.D).," The apparent magnitude $m$ of a source is a function of its absolute magnitude and distance, $m=m(M,D)$."415 For a &iven absolute magnitude. m increases with distance and reaches the limiting value my at a distance J satisfving m(AL2)=my.," For a given absolute magnitude, $m$ increases with distance and reaches the limiting value $m_0$ at a distance $D$ satisfying $m(M,D)=m_0$."416 This determines the line M(D). the boundary of the populated region in Fig. 1..," This determines the line $M_*(D)$, the boundary of the populated region in Fig. \ref{fig:cutting-samples}."417 Beyond this line the objects are too dim and the completeness of the sample cannot be guaranteed., Beyond this line the objects are too dim and the completeness of the sample cannot be guaranteed.418" At a given distance Dy. only objects with absolute magnitude AZ<AA,=ALD) are sullicientlv. bright o be included in the Dux-limited catalog."," At a given distance $D_0$, only objects with absolute magnitude $M<M_0419= M_*(D_0)$ are sufficiently bright to be included in the flux-limited catalog."420 Galaxies that are closer than My and brighter than Ao form a volume-imited sample., Galaxies that are closer than $D_0$ and brighter than $M_0$ form a volume-limited sample.421" These are objects in regions marked with 5, and 5» in Fig. I..", These are objects in regions marked with $S_1$ and $S_2$ in Fig. \ref{fig:cutting-samples}.422 Phe completeness of this subsample ollows from the completeness of the original [DLux-Iimited catalog., The completeness of this subsample follows from the completeness of the original flux-limited catalog.423 lt is clear from fisure 1. that at small distances he volume-linmitecl saniple οιSo contains only a raction of available galaxies which may be insullicient ο. represent accurately the details of the matter distribution., It is clear from figure \ref{fig:cutting-samples} that at small distances the volume-limited sample $S_1+S_2$ contains only a fraction of available galaxies which may be insufficient to represent accurately the details of the matter distribution.424" Fo improve the situation. one may construct a denser volume-limited. sample corresponding to a smaller distance D, (the sample 5»[$3 on Fig. 1))."," To improve the situation, one may construct a denser volume-limited sample corresponding to a smaller distance $D_1$ (the sample $S_2+S_3$ on Fig. \ref{fig:cutting-samples}) )."425" When calculating the llux one may use galaxies from 5»|S5 at distances D«D, and galaxies [rom S, at D,«DDy.", When calculating the flux one may use galaxies from $S_2+S_3$ at distances $D<D_1$ and galaxies from $S_1$ at $D_1<D<D_0$.426" The luminosity of a given. volume is determined by the number of galaxies in the sample 5,|5» contained in that volume.", The luminosity of a given volume is determined by the number of galaxies in the sample $S_1+S_2$ contained in that volume.427 At distances 2<Dj. the same luminosity may be represented. in a greater detail by galaxies from. So|55 providedthey are assigned smaller “weight”. that is. luminosity per galaxy.," At distances $D<D_1$, the same luminosity may be represented in a greater detail by galaxies from $S_2+S_3$ providedthey are assigned smaller “weight”, that is, luminosity per galaxy."428 I the galaxies in the sparse sample have a weight «y each. the galaxies in the dense sample 5S»|55 should be weighted with llere and below we use the same letter to denote," If the galaxies in the sparse sample have a weight $w_0$ each, the galaxies in the dense sample $S_2+S_3$ should be weighted with Here and below we use the same letter to denote"429During the past 39 vears. many varied estimates have been made of (he mass AM of the black hole in Cygnus X-1.,"During the past 39 years, many varied estimates have been made of the mass $M $ of the black hole in Cygnus X-1."430 At one extreme. acting as a devil's advocate against black hole models. Trimbleetal.(1973). proposed a model based on a distance Dον1 kpe which gave a low mass of M.X1M... suggestive of a neutron star or white dwarf. not a black hole.," At one extreme, acting as a devil's advocate against black hole models, \cite{tri+1973} proposed a model based on a distance $D\sim1$ kpc which gave a low mass of $M \lesssim 1\,M_{\odot}$, suggestive of a neutron star or white dwarf, not a black hole."431 several other low-mass models are summarized. considered. ancl found. wanting bv. (1975).," Several other low-mass models are summarized, considered, and found wanting by \cite{bol+1975}."432. By contrast. all conventional binary models Chat assume (he secondary. companion is a massive O-(vpe supergiant fid a Lugebul uncertainmass for (he compact object that significantly exceeds the maximum stable mass for à neutron star of 223.44. 1996).. hence requiring a black hole.," By contrast, all conventional binary models that assume the secondary companion is a massive O-type supergiant find a large—but uncertain—mass for the compact object that significantly exceeds the maximum stable mass for a neutron star of $\approx 3\,M_{\odot}$ \citep{kal+1996}, hence requiring a black hole."433 For example. using geometrical arguments. Paczviski(1974). computed the minimum mass lor the compact object as a function of the distance and found A3.6A. [or D1.4 kpe.," For example, using geometrical arguments, \citet{pac+1974} computed the minimum mass for the compact object as a function of the distance and found $M>3.6\,M_{\odot}$ for $D>1.4$ kpc."434 Based on dvnanmical modeling (1986) [ound M>7AL. and a probable mass of Mj;=16M. for the companion star. and. Ninkovetal.(1987). found M=10zx1AL. (by assuming Mog=2042. ).," Based on dynamical modeling \cite{gie+1986}435 found $M>7\,M_{\odot}$ and a probable mass of $M_{\rm opt}=16\,M_{\odot}$ for the companion star, and \cite{nin+1987} found $M =10\pm1~\,M_{\odot}$ (by assuming $M_{\rm opt}=20\,M_{\odot}$ )."436 llowever. these mass estimates. and all such estimates that have been made to date. are very uncertain because thev are based on unsatisfactory estimates of the distance to Cyenus X-1 (Reidetal.2011).," However, these mass estimates, and all such estimates that have been made to date, are very uncertain because they are based on unsatisfactory estimates of the distance to Cygnus X-1 \citep{rei+2010}."437. The strong ellect of distanceon the model parameters is obvious from an inspection of Table 4 in Caballero-Nievesetal.(2009) (audalsoTable1ofPaczviski 1974)., The strong effect of distanceon the model parameters is obvious from an inspection of Table 4 in \cite{cab+2009} \cite[and also Table 1 of][]{pac+1974}.438. For the dvnamical model favored by Caballero-Nievesοἱal.(2009).. ancl over the wide range of distances they consider. 1.12.5 kpe. (he radius of the companion star and (he mass of the black hole are seen to vary by factors of 2.3 and 11.7. respectively.," For the dynamical model favored by \citet{cab+2009}, and over the wide range of distances they consider, 1.1–2.5 kpc, the radius of the companion star and the mass of the black hole are seen to vary by factors of 2.3 and 11.7, respectively."439 Thus. in order (o obtain useful constraints on (he svsten parameters. it is essential (o have an accurate value of the source distance. as we have demonstrated [or two extragalactic black hole svstems (hat contain O-(vpe supereiants. M33. X-7 (Oroszοἱal.2007) and Ελ X-1 (Oroszetal.2009).. whose distances are known to several percent accuracy via the cosmic distance ladder.," Thus, in order to obtain useful constraints on the system parameters, it is essential to have an accurate value of the source distance, as we have demonstrated for two extragalactic black hole systems that contain O-type supergiants, M33 X-7 \citep{oro+2007} and LMC X-1 \citep{oro+2009}, whose distances are known to several percent accuracy via the cosmic distance ladder."440 In (his paper. weuse a distance from a trigonomeltric parallax measurement for Cyenus X-1 (Reidetal. 2011).. which is aceurate to £6%.. and previouslv-published optical data to," In this paper, weuse a distance from a trigonometric parallax measurement for Cygnus X-1 \citep{rei+2010}, , which is accurate to $\pm6$ , and previously-published optical data to"441absorplion to the Galactic value.,absorption to the Galactic value.442 First. we fitted data wilh a broken power-law ancl neutral absorption model.," First, we fitted data with a broken power-law and neutral absorption model."443 The fit eives a break energy of 1.45250.04 keV ancl a photon-index below the break energy of 3.1140.03., The fit gives a break energy of $\pm$ 0.04 keV and a photon-index below the break energy of $\pm$ 0.03.444 The reduced 4? value is 1.40 for 359 d.o.L., The reduced $\chi^2$ value is 1.40 for 359 d.o.f.445 Next we tried to fit with a two power-law model., Next we tried to fit with a two power-law model.446 This fit gives worse \7 value of 1.69 for the same number of cow, This fit gives worse $\chi^2_\nu$ value of 1.69 for the same number of d.o.f.447 The crossing point of the two power-laws is 1.39 keV. Finally we fitted the κο excess component with a black body model., The crossing point of the two power-laws is 1.39 keV. Finally we fitted the soft excess component with a black body model.448 The fit gives the blackbody temperature of 0.12440.003 keV in the source rest frame and a better AZ. value of 1.34 with the same nunmber of d.o.F., The fit gives the blackbody temperature of $\pm$ 0.003 keV in the source rest frame and a better $\chi^2_\nu$ value of 1.34 with the same number of d.o.f.449 The fits are still not acceptable., The fits are still not acceptable.450 This could be due in part to the edge-like feature around 0.7 keV (hat can be seen in Fig. 3.., This could be due in part to the edge-like feature around 0.7 keV that can be seen in Fig. \ref{fig:pl}.451 Although statistically limited. HETGS data is useful to investigate narrow iron lines.," Although statistically limited, HETGS data is useful to investigate narrow iron K-emission lines."452 We created HIEG c1 and MEG +1 spectra binned at the detector resolution (FWIIM)., We created HEG $\pm$ 1 and MEG $\pm$ 1 spectra binned at the detector resolution (FWHM).453 The spectra have 213 photons per energy bin around the iron Ix-energv. baa., The spectra have 2–13 photons per energy bin around the iron K-energy band.454 since (he data are in (he Poisson regime. we performed (he spectral fitting ancl error analysis using the C statistic.," Since the data are in the Poisson regime, we performed the spectral fitting and error analysis using the $C$ statistic."455 We fitted the data in the 6.07.0 keV energv band with a power-law plus three Gaussian lines assuming all the lines are narrow and at the svstemic velocity., We fitted the data in the 6.0–7.0 keV energy band with a power-law plus three Gaussian lines assuming all the lines are narrow and at the systemic velocity.456 Due to poor statistics. we performed fits fixing the power-law index al several values.," Due to poor statistics, we performed fits fixing the power-law index at several values."457 With the photon-index of 2.56 (the best-fit value from the 2/5 keV band fit in )). the fit gives upper-Imits of the EWs of 45 eV. 53 eV ancl 78 eV [or the neutral. ]le-like and I-like lines. respectively.," With the photon-index of 2.56 (the best-fit value from the 2–5 keV band fit in \\ref{sec:cont}) ), the fit gives upper-limits of the EWs of 45 eV, 53 eV and 78 eV for the neutral, He-like and H-like lines, respectively."458 The upper-limits are weakly subject to the assumed continuum slope. but the difference is as small as 5 eV even in a wide range of photon-index ol 2.03.0.," The upper-limits are weakly subject to the assumed continuum slope, but the difference is as small as 5 eV even in a wide range of photon-index of 2.0–3.0."459 Thus. we can conclude that no strong narrow iron Ix-emission lines are detecte: hence. the diskline feature with huge EW (653485 eV for Ίνα) reported by is not significantly contaminated by narrow lines.," Thus, we can conclude that no strong narrow iron K-emission lines are detected; hence, the diskline feature with huge EW $\pm$ 85 eV for $\alpha$ ) reported by \citet {tur01}460 is not significantly contaminated by narrow lines."461 We investigatecl narrow leatures in the soft X-ray region using the ΡΙΚΟ high resolution spectra., We investigated narrow features in the soft X-ray region using the HETGS high resolution spectra.462 We binned the WETGCS first order spectra according to the following criteria: the energv bin widths are at least as large as (he detector οποιον resolution. and each energy bin contains at least 25 photons.," We binned the HETGS first order spectra according to the following criteria: the energy bin widths are at least as large as the detector energy resolution, and each energy bin contains at least 25 photons."463 The latter criterion allows us to use V? fitting., The latter criterion allows us to use $\chi^2$ fitting.464 First we looked at the edge-like feature around 0.7 keV. If we add an edge to the model. the fit is improved significantly bv F-test).," First we looked at the edge-like feature around 0.7 keV. If we add an edge to the model, the fit is improved significantly by F-test)."465 The edge energy is 0.711d keV in the, The edge energy is $0.711^{+0.004}_{-0.002}$ keV in the466to different stages of T Tauri stars so that higher M corresponds to earlier stage.,to different stages of T Tauri stars so that higher $\dot M$ corresponds to earlier stage.467The conditions in different Groups are listed as follows: We perform 31 runs with the same disk model except varying fi from 0.001 to 1 in each Group.,The conditions in different Groups are listed as follows: We perform 31 runs with the same disk model except varying $f_1$ from 0.001 to 1 in each Group.468 The results are presented as follows., The results are presented as follows.469 One of the most important factors that affects the formation of planets in habitable zone is the speed of type I migration reduced by fi., One of the most important factors that affects the formation of planets in habitable zone is the speed of type I migration reduced by $f_1$.470" If the speed is very slow, the embryos will not migrate too much."," If the speed is very slow, the embryos will not migrate too much."471 Fig.3 shows a typical run of Group 1 with very low migration speed (fi— 0.004)., Fig.3 shows a typical run of Group 1 with very low migration speed $f_1=0.004$ ).472 Planetary mergers mainly occur due to scattering effect of embryo inside two giant plants at t~5 Myr (WZZ09)., Planetary mergers mainly occur due to scattering effect of embryo inside two giant plants at $t \sim 5 $ Myr (WZZ09).473" As we know from the density profile in Figure 1, when M=5x107?Myr, the location of density maximum is at 0.3 AU."," As we know from the density profile in Figure 1, when $\rm \dot {M} = 5\times 10^{-8}\rm~ M_{\odot}/yr$, the location of density maximum is at 0.3 AU."474" At this density maximum, the type I migration of embryos can be stalled due to the negative f in equations (6))."," At this density maximum, the type I migration of embryos can be stalled due to the negative $\beta$ in equations \ref{tauI}) )."475" The inward migration of a second planet may trap the stalled planet into its mean motion resonance, which might increase the eccentricities of both planets."," The inward migration of a second planet may trap the stalled planet into its mean motion resonance, which might increase the eccentricities of both planets."476" As we can see, most of the planets survived at t=10 Myr with a«1 AU are trapped into first order resonance (mainly 4:3)."," As we can see, most of the planets survived at $t=10$ Myr with $a<1$ AU are trapped into first order resonance (mainly 4:3)."477" Among them, one is in the HZ and two of them are at the edge of the HZ in this case."," Among them, one is in the HZ and two of them are at the edge of the HZ in this case."478" With the increase of the type I migration speed, less and less embryos are survived or trapped in HZ before the gas disk was almost depleted."," With the increase of the type I migration speed, less and less embryos are survived or trapped in HZ before the gas disk was almost depleted."479" For example, Figure 4 shows a typical run with migration reduced factor fi=0.08."," For example, Figure 4 shows a typical run with migration reduced factor $f_1=0.08$ ."480 Only two terrestrial planets survived at the inner region (a«1 AU)., Only two terrestrial planets survived at the inner region $a< 1$ AU).481" Interestingly, they are in 2:1 MMR."," Interestingly, they are in 2:1 MMR."482 The inner planet with mass (7.5 Mg) is in the HZ., The inner planet with mass (7.5 $M_\oplus$ ) is in the HZ.483" As the migration speed increases again, fi=0.25, only one planet survived in the HZ (Figure 5a)."," As the migration speed increases again, $f_1=0.25$, only one planet survived in the HZ (Figure 5a)."484 It is stalled under type I migration at the inner edge of MRI dead zone (Figure 5b)., It is stalled under type I migration at the inner edge of MRI dead zone (Figure 5b).485" According to Figure 3b, many planet pairs may be trapped in MMRs under migration."," According to Figure 3b, many planet pairs may be trapped in MMRs under migration."486 Table 1 shows the statistics of the final configurations for the simulations in the four Groups., Table 1 shows the statistics of the final configurations for the simulations in the four Groups.487" We classify the system being in either MMRs, aligned apsidal resonance or anti-aligned apsidal resonance (anti-AARs) if(AARs) there is at least one couple of planets trapped into MMRs, AARs or anti-AARs."," We classify the system being in either MMRs, aligned apsidal resonance (AARs) or anti-aligned apsidal resonance (anti-AARs) if there is at least one couple of planets trapped into MMRs, AARs or anti-AARs."488" Table 1 records the probability of a planet system that is in MMRs, AARs or anti-AARs in the 31 runs of each group (24 runs in Group 3)."," Table 1 records the probability of a planet system that is in MMRs, AARs or anti-AARs in the 31 runs of each group (24 runs in Group 3)."489" As we can see, more than a quarter of the systems contain at least a planet pair that is in MMRs, AARs or anti-AARs."," As we can see, more than a quarter of the systems contain at least a planet pair that is in MMRs, AARs or anti-AARs."490" For systems with only one terrestrial planet, we can get the stable time from the results in WZZ09."," For systems with only one terrestrial planet, we can get the stable time from the results in WZZ09."491 Because the distance of the single terrestrial planet to the central star is closer than 0.56 AU in our results., Because the distance of the single terrestrial planet to the central star is closer than 0.56 AU in our results.492 All the single terrestrial planets systems are stable in more than 108 years., All the single terrestrial planets systems are stable in more than $10^8$ years.493 Based on Zhou et al. (, Based on Zhou et al. (494"2007) about the crossing time of planet system, we estimate the stable time of multiple terrestrial planet system at the end of the simulations.","2007) about the crossing time of planet system, we estimate the stable time of multiple terrestrial planet system at the end of the simulations."495" We test each couple of the planets in the systems and use the average eccentricity, average mass and relative Hill radius for the two planets next to each other in the estimation."," We test each couple of the planets in the systems and use the average eccentricity, average mass and relative Hill radius for the two planets next to each other in the estimation."496 Results are showed in table 2., Results are showed in table 2.497 More than couples of the planets in the system will survive in more than 105 years., More than couples of the planets in the system will survive in more than $10^8$ years.498" According to the results of the stable time of the planets, we get the stable time of the planetary system."," According to the results of the stable time of the planets, we get the stable time of the planetary system."499 We define the shortest time of the planet couples surviving in the system as the stable time of the system., We define the shortest time of the planet couples surviving in the system as the stable time of the system.500 The results are also showed in the last column of table 2., The results are also showed in the last column of table 2.501 More than system will be stable in more than 105 years., More than system will be stable in more than $10^8$ years.502" For terrestrial planets in habitable zone, one important parameter is the water content inside the rock."," For terrestrial planets in habitable zone, one important parameter is the water content inside the rock."503" To model the distribution of water contents within embryos, we"," To model the distribution of water contents within embryos, we"504difference between the specific AM content of old and new stars that is comparable with that of one merger of mass ratio 1:5.,difference between the specific AM content of old and new stars that is comparable with that of one merger of mass ratio 1:5.505" In other words, more massive satellites can have a larger impact on slowing down the stellar disk and produce a larger rotational lag between the old and new stellar populations than less massive satellites (?).."," In other words, more massive satellites can have a larger impact on slowing down the stellar disk and produce a larger rotational lag between the old and new stellar populations than less massive satellites \citep{quDM210a}."506" The substantial difference between the specific AM content of the thin and thick disk stellar populations cannot be due to secular evolution processes alone, which produce a considerably smaller variation in both / and v; in 3 Gyr of evolution (Fig. 11))."," The substantial difference between the specific AM content of the thin and thick disk stellar populations cannot be due to secular evolution processes alone, which produce a considerably smaller variation in both $l$ and $v_t$ in 3 Gyr of evolution (Fig. \ref{histo-iso}) )."507" Note also that secular evolution produces a narrower distribution of /, v, and ν,, thus suggesting that also mixing and radial migration due to secular processes may be less effective than in minor mergers."," Note also that secular evolution produces a narrower distribution of $l$, $v_r$ and $v_t$, thus suggesting that also mixing and radial migration due to secular processes may be less effective than in minor mergers."508" Whereas scattering of stars by massive clumps can induce a rotational lag (in old thin and thick disk stars), the overall impact of scattering by mass concentrations is (moderately) lower than that produced by a direct 1:10 merger on a galaxy with an initial gas fraction of 20%."," Whereas scattering of stars by massive clumps can induce a rotational lag (in old thin and thick disk stars), the overall impact of scattering by mass concentrations is (moderately) lower than that produced by a direct 1:10 merger on a galaxy with an initial gas fraction of $\%$."509" In the previous section we saw that old stars in the thin and thick disk of a minor merger remnant lag with respect to the new stars, and that this lag is higher for stars further from the galaxy midplane (|z |21 kpc)."," In the previous section we saw that old stars in the thin and thick disk of a minor merger remnant lag with respect to the new stars, and that this lag is higher for stars further from the galaxy midplane $\mid z\mid\ge$ 1 kpc)."510" But what is this rotational lag due to — is it mostly associated to stars originally in the satellite or in the primary disk, and how does it depend on the orbital parameters?"," But what is this rotational lag due to – is it mostly associated to stars originally in the satellite or in the primary disk, and how does it depend on the orbital parameters?"511" To answer these questions, we analyzed the tangential velocity v, of old stars at radii between 2 and 3A; in four different regions above the disk midplane: |z|€1 kpc, z |€3 kpc, 3<|z |x5 kpc and 5<|z|x10 kpc."," To answer these questions, we analyzed the tangential velocity $v_t$ of old stars at radii between 2 and $R_d$ in four different regions above the disk midplane: $\mid z\mid\le$ 1 kpc, $<\mid512z\mid\le$ 3 kpc, $<\mid z\mid\le$ 5 kpc and $<\mid z\mid\le$ 10 kpc."513" Results from some representative mergers are shown in Fig. 12,,"," Results from some representative mergers are shown in Fig. \ref{transvel},"514 where for each encounter we distinguished the primary stars from those originally in the satellite., where for each encounter we distinguished the primary stars from those originally in the satellite.515 This figure shows some interesting trends., This figure shows some interesting trends.516" First of all, there is a clear difference between direct and retrograde mergers."," First of all, there is a clear difference between direct and retrograde mergers."517" While in both cases the average v; of old stars is lower than that of new stars (Table 3)), the behavior of v; as a function of height z is significantly different."," While in both cases the average $v_t$ of old stars is lower than that of new stars (Table \ref{lagtable}) ), the behavior of $v_t$ as a function of height z is significantly different."518" Direct mergers produce disks with a tangential velocity v; which decreases with height, meaning that the rotational lag increases with z, whereas in retrograde mergers v, is constant with height up to z~5 kpc, and decreases only at greater heights."," Direct mergers produce disks with a tangential velocity $v_t$ which decreases with height, meaning that the rotational lag increases with z, whereas in retrograde mergers $v_t$ is constant with height up to $\sim$ 5 kpc, and decreases only at greater heights."519" The satellite stars, which in each region constitute only a small percentage of the total stellar content, do not contribute significantly to the lag."," The satellite stars, which in each region constitute only a small percentage of the total stellar content, do not contribute significantly to the lag."520" Moreover, if one compares the tangential velocities of satellite and primary stars for direct orbits, one can find a variety of behaviors in the regions analyzed: in some cases the tangential velocities of satellite stars are always smaller than those of stars from the primary (e.g. for orbit *gSO0dSO01dir33""), while in other cases the values are comparable, and satellite stars show even higher velocities than primary stars in the outer regions (e.g. orbit ""gSadSa01dir33"")."," Moreover, if one compares the tangential velocities of satellite and primary stars for direct orbits, one can find a variety of behaviors in the regions analyzed: in some cases the tangential velocities of satellite stars are always smaller than those of stars from the primary (e.g. for orbit “gS0dS001dir33”), while in other cases the values are comparable, and satellite stars show even higher velocities than primary stars in the outer regions (e.g. orbit “gSadSa01dir33”)."521" In all the cases, however, the strongest variations in v; as a function of z are associated with stars originally in the primary rather than from the satellite."," In all the cases, however, the strongest variations in $v_t$ as a function of z are associated with stars originally in the primary rather than from the satellite."522" For retrograde orbits, the tangential velocities of satellite stars show only small variations with increasing z, as is the case for primary stars."," For retrograde orbits, the tangential velocities of satellite stars show only small variations with increasing z, as is the case for primary stars."523" We note also that a stellar thick disk formed in an unstable clumpy galaxy is characterized by tangential velocities whose variation with z is very similar to that produced in a direct encounter with fas=0.2 (compare, e.g. Fig."," We note also that a stellar thick disk formed in an unstable clumpy galaxy is characterized by tangential velocities whose variation with z is very similar to that produced in a direct encounter with $f_{\rm gas}=0.2$ (compare, e.g. Fig."524 13 with orbit “gSbdSb01dir33” in Fig. 12))., \ref{transvel_clumpy} with orbit “gSbdSb01dir33” in Fig. \ref{transvel}) ).525distance to the nearest counterpart.,distance to the nearest counterpart.526 In conjunction with the space density of Sun-like hosts. which for mid-EF to late-Ix clwarls is 0.01 7. the nearest analogue system should lic within 13 pc.," In conjunction with the space density of Sun-like hosts, which for mid-F to late-K dwarfs is 0.01 $^{-3}$, the nearest analogue system should lie within 13 pc."527 The nearestpresently known analogue candidate (in the sense of planet and comet content) is the GS star LID 154345 at 15 pe distance. which has no obvious Spitzer 10 pum excess and hosts a Jupiter-like planet ab 4 AU.," The nearest known analogue candidate (in the sense of planet and comet content) is the G8 star HD 154345 at 18 pc distance, which has no obvious Spitzer 70 $\umu$ m excess and hosts a Jupiter-like planet at 4 AU."528 However. if only about one-third. of the systems with eas giants bevond 3 AU have so lar been discovered. a completeness correction suggests that a nearer analogue could lie within about 12 pc. or slightly. closer given that not all nearby. Sun-analogues as vet have published debris clata.," However, if only about one-third of the systems with gas giants beyond 3 AU have so far been discovered, a completeness correction suggests that a nearer analogue could lie within about 12 pc, or slightly closer given that not all nearby Sun-analogues as yet have published debris data."529 Systems roughly analogous to our own. hosting a mioclest comet population ancl gas giants at a lew AU or bevond. are inferred to be rather uncommon.," Systems roughly analogous to our own, hosting a modest comet population and gas giants at a few AU or beyond, are inferred to be rather uncommon."530 If Sun-like stars ofn host terrestrial planets in the habitable zone. only a few per cent of these are likely to have a similar debris environment.," If Sun-like stars often host terrestrial planets in the habitable zone, only a few per cent of these are likely to have a similar debris environment."531 A few systems may have catastrophic bombardmoent. even at mid-main sequence age. if gas giants perturh some of their numerous comets into the inner svstem.," A few systems may have catastrophic bombardment, even at mid-main sequence age, if gas giants perturb some of their numerous comets into the inner system."532 At the other extreme. the majority population should be stars without giant planets but with many comets. for which furthq modelling is needed to assess the rate of planetary impacts.," At the other extreme, the majority population should be stars without giant planets but with many comets, for which further modelling is needed to assess the rate of planetary impacts."533 The closest presently-known system that is roughly like our own lies at 18 pc. but another probably exists with around 10 pc given the completeness of debris ancl giant planet surveys so Far.," The closest presently-known system that is roughly like our own lies at 18 pc, but another probably exists with around 10 pc given the completeness of debris and giant planet surveys so far."534 This result is encouraging for Future facilities aiming to study habitable exo-IEarths. such as DARAVIN. TPE and ELT.," This result is encouraging for future facilities aiming to study habitable exo-Earths, such as DARWIN, TPF and ELT."535 We thank the referee for comments that helped to clarify several lines of argument., We thank the referee for comments that helped to clarify several lines of argument.536 JSC thanks STEC and SUPA for support of this work., JSG thanks STFC and SUPA for support of this work.537The data CObsID 93027) were reduced using v.6.8 and the CALDB.,The data (ObsID 93027) were reduced using v.6.8 and the CALDB.538 We used data taken both by RXTE//PCA (3-25 keV) and HEXTE (25-100 keV)., We used data taken both by /PCA (3–25 keV) and HEXTE (25–100 keV).539 In cases where ΠΕΝΤΕ. exposures were short. we ignored the noisy channels above ~60 keV. Standard 0.5 per cent systematic was applied to the PCAspectra Jahodaetal.20063.," In cases where HEXTE exposures were short, we ignored the noisy channels above $\sim 60$ keV. Standard 0.5 per cent systematic was applied to the PCAspectra \citep{JMR06}."540.. To Keep the calibration uniform. we used data from PCU 2 only Call layers).," To keep the calibration uniform, we used data from PCU 2 only (all layers)."541 The ΣΕΤ data (0.6— keV) were reduced using the v.0.12.3 in v.6.8., The /XRT data (0.6--7 keV) were reduced using the v.0.12.3 in v.6.8.542 The observations were performed in window-timing mode., The observations were performed in window-timing mode.543 We used standard filtering and screening criteria for the event selection., We used standard filtering and screening criteria for the event selection.544 Exposure maps were generated with the task and the ancillary response files with to account for different extraction regions (we used circular regions of 20 pixel radius). vignetting and psf corrections.," Exposure maps were generated with the task and the ancillary response files with to account for different extraction regions (we used circular regions of 20 pixel radius), vignetting and psf corrections."545 The redistribution matrices (v.01D) were taken from the CALDB., The redistribution matrices (v.011) were taken from the CALDB.546 The XRT spectra were then grouped using to have at least 20 counts in each bin., The XRT spectra were then grouped using to have at least 20 counts in each bin.547 We used the Swif//XRT data to model the time averaged spectra together with the quasi-simultaneous ppointings., We used the /XRT data to model the time averaged spectra together with the quasi-simultaneous pointings.548 There were a few cases where we could not use all the XRT data., There were a few cases where we could not use all the XRT data.549 The first XRT observation (observation 2. see Table 1») was triggered by an X-ray burst.," The first XRT observation (observation 2, see Table \ref{tab:obslog}) ) was triggered by an X-ray burst."550 We found that the XRT spectrum differed from the PCA spectrum taken before the X-ray burst and also from the XRT spectrum taken only 3 hours after the X-ray burst (observation 3)., We found that the XRT spectrum differed from the PCA spectrum taken before the X-ray burst and also from the XRT spectrum taken only 3 hours after the X-ray burst (observation 3).551 The spectra of observations | and 3 matched well indicating that the first XRT spectra was affected by the X-ray burst and it was therefore excluded from the analysis., The spectra of observations 1 and 3 matched well indicating that the first XRT spectra was affected by the X-ray burst and it was therefore excluded from the analysis.552 Also. we did not use the observation 18. because the source was right on top of the bad columns.," Also, we did not use the observation 18, because the source was right on top of the bad columns."553 In two occasions. where XRT observations were split into two snapshots (1+ and 24). we used the data from the longer snapshot.," In two occasions, where XRT observations were split into two snapshots (14 and 24), we used the data from the longer snapshot."554 During the slow decay stage of the 2008 outburst — on September 27 (MID 54736) — the pulse amplitude dropped and the pulse profile changed significantly (seeHartmanetal.2009.fig.13., During the slow decay stage of the 2008 outburst – on September 27 (MJD 54736) – the pulse amplitude dropped and the pulse profile changed significantly \citep[see][fig. 1]{HPC09}.555. The origin of these type of timing changes is not well understood. but they must be caused by some changes in the accretion geometry.," The origin of these type of timing changes is not well understood, but they must be caused by some changes in the accretion geometry."556 In order to analyse this timing transition. we construct pulse profiles at various energies and different time intervals using ephemeris from Hartmanetal.(2009)..," In order to analyse this timing transition, we construct pulse profiles at various energies and different time intervals using ephemeris from \citet{HPC09}."557" The observed pulse profiles are then fitted by a sum of two harmonics: Fco) FII) σος. F'isthemoeeanf'ircandaj. a». Oy, and ó» are the amplitudes and phases of the fundamental and the first overtone. respectively."," The observed pulse profiles are then fitted by a sum of two harmonics: ) = 1 + a_1 is the mean flux and $a_1$, $a_2$, $\phi_1$ and $\phi_2$ are the amplitudes and phases of the fundamental and the first overtone, respectively."558 The best-fitting amplitudes and phases are presented in Fig., The best-fitting amplitudes and phases are presented in Fig.559 |. for the soft (3.7—55.7 keV) and hard (9.8— keV) energy bands., \ref{fig:ampl_phases} for the soft (3.7–5.7 keV) and hard (9.8--23.2 keV) energy bands.560 We selected these two bands because in the hard band we have emission only from the Comptonized component. whereas in the soft band there is a contribution from the blackbody component (e.g. Ibragimov&Poutanen 2009)).," We selected these two bands because in the hard band we have emission only from the Comptonized component, whereas in the soft band there is a contribution from the blackbody component (e.g. \citealt{IP09}) )."561 We see a drop in the fundamental amplitude and a change in the pulse profile on September 27 (MJD 54736). but we do not detect significant jumps in the pulse phases during the transition.," We see a drop in the fundamental amplitude and a change in the pulse profile on September 27 (MJD 54736), but we do not detect significant jumps in the pulse phases during the transition."562 However. we find that the timing transition was accompanied with a simultaneous softening of the energy spectrum below ~5 keV. This can be seen by taking a ratio of the observed spectra before and after the timing transition (from XRT observations | and [4 and PCA observations 160 and 12).," However, we find that the timing transition was accompanied with a simultaneous softening of the energy spectrum below $\sim5$ keV. This can be seen by taking a ratio of the observed spectra before and after the timing transition (from XRT observations 11 and 14 and PCA observations 10 and 12)."563 The ratio spectra are shown in Fig., The ratio spectra are shown in Fig.564 2. and the softening is clearly seen in the aus well as in the AXVE/PCA data., \ref{fig:ratio_spectra} and the softening is clearly seen in the as well as in the /PCA data.565 The fact that the timing- and spectral transition occur simultaneously suggests a common physical origin. so a detailed broad band spectral analysis and pulse profile modelling of this transition 1s warranted.," The fact that the timing- and spectral transition occur simultaneously suggests a common physical origin, so a detailed broad band spectral analysis and pulse profile modelling of this transition is warranted."566 We modelled the spectra using (Arnaud1996)., We modelled the spectra using \citep{Arn96}.567.. Errors are quoted at the confidence level and the errors in the fluxes were computed with the model in XSPEC., Errors are quoted at the confidence level and the errors in the fluxes were computed with the model in .568 The reported luminosities are bolometric (calculated in the range of 0.01—500 keV from the best-fitting model) assuming a distance of D=3.5 kpe (Galloway&Cumming2006)., The reported luminosities are bolometric (calculated in the range of 0.01–500 keV from the best-fitting model) assuming a distance of $D=3.5$ kpc \citep{GC06}.569. Our spectral model consist. ofCOMPPS)., Our spectral model consist of.570 The spectral model is rather complex and has a large number of parameters., The spectral model is rather complex and has a large number of parameters.571 The model component accounts for the different instrument normalizations between Swif//XRT. RXTE//PCA and HEXTE.," The model component accounts for the different instrument normalizations between /XRT, /PCA and HEXTE."572 We fixed the normalization of PCA and allowed XRT and HEXTE normalizationsto vary., We fixed the normalization of PCA and allowed XRT and HEXTE normalizationsto vary.573 For XRT. the normalizations varied in a tight range around 0.9 between the different exposures. whereas HEXTE normalizations variedin the range of 0.52 0.62.," For XRT, the normalizations varied in a tight range around $0.9$ between the different exposures, whereas HEXTE normalizations variedin the range of $0.52 - 0.62$ ."574 The effect of interstellar absorptionwas taken into account using the model (Morrison&MeCammon 1983).. which," The effect of interstellar absorptionwas taken into account using the model \citep{MM83}, , which"575"19) the ALFALFA WF is very well described ly a imnocdified Schechter function of the The least squares are 04,=(0.011+ ""dex |. logi=255+ a=O85£010 and §=2.7+0.5 (uncertainties are statistical lo errors due to Poisson errors on the madiidual bin values).",") the ALFALFA WF is very well described by a modified Schechter function of the The least squares are $\phi_\ast = 0.011 \, \pm \, 0.002 \;\; h_{70}^3 \; $ $^{-3}$ $^{-1}$, $\log w_\ast = 2.58 \, \pm \, 0.03$ , $\alpha = -0.85 \, \pm \, 0.10$ and $\beta = 2.7 \, \pm \, 0.3$ (uncertainties are statistical $1\sigma$ errors due to Poisson errors on the individual bin values)."576 Note. however. that the final saluple contaius 163 sources that lack a coufidentlv identified optical counterpart.," Note, however, that the final sample contains 163 sources that lack a confidently identified optical counterpart."577 Some of these sources correspoud to tidal debris from ucarby interacting ealaxies and may not be hosted by individual DM iilos., Some of these sources correspond to tidal debris from nearby interacting galaxies and may not be hosted by individual DM halos.578 Excluding these galaxies from the WE calculation cads to a somewhat shallower narrow-cucd slope of a=O.68+ 0.11.," Excluding these galaxies from the WF calculation leads to a somewhat shallower narrow-end slope of $\alpha = -0.68 \, \pm \, 0.11$ ."579" ALFALFA finds significantly more high-width ealaxics han HIPASS (a factor of ~3 at dwπε100|l. erowing to a factor of ~10 at ez500 J). which is also evident from the marked difference i the value of he position of the “nec” of the WE for the two surveys οσο,=2.58+0.03 for ALFALFA versus logaw.=2.21+0.10 forHIDPASS?.. in disagreeineut at tlie 22360 evel)."," ALFALFA finds significantly more high-width galaxies than HIPASS (a factor of $\sim 3$ at $w \approx 400$, growing to a factor of $\sim 10$ at $w \approx 800$ ), which is also evident from the marked difference in the value of the position of the “knee” of the WF for the two surveys $\log w_\ast = 2.58 \, \pm \, 0.03$ for ALFALFA versus $\log w_\ast = 2.21 \, \pm \, 0.10$ for, in disagreement at the $> 3\sigma$ level)."580 Despite the fact that the nominal IIIPASS volue isa factor of ~5 leger than the 6.10 voluue. ALFALFA is able to find more hieh-width ealaxies thinks to its etter scusitivity (see Figure 5)).," Despite the fact that the nominal HIPASS volume is a factor of $\sim 5$ larger than the $\alpha$ .40 volume, ALFALFA is able to find more high-width galaxies thanks to its better sensitivity (see Figure \ref{fig:spanhauer}) )."581 The same effect can be seen in the IIIMEs published by the two surveys. with ALFALFA fuxliug a factor of a few more of the vehest IHLEauass galaxies compared to ΠΙΑος(?).," The same effect can be seen in the HIMFs published by the two surveys, with ALFALFA finding a factor of a few more of the highest HI-mass galaxies compared to HIPASS."582. On the low-width cud. ALFALFA finds a rising slope (a <0) which is. however. bv uo nieaus steep enough o match the CDM prediction (sec Sec. 5)).," On the low-width end, ALFALFA finds a rising slope $\alpha < 0$ ) which is, however, by no means steep enough to match the CDM prediction (see Sec. \ref{sec:theory}) )."583 Despite the vastly different value for the narrow-cud slope reported v the two survers (a=0.10+0.39 for IHIPASS versus a=o(k85+0.10 for ALFALFA) the IIIPASS aud ALFALFA datapoints are cousisteut in the width range Γον XoaeX2001aus+.," Despite the vastly different value for the narrow-end slope reported by the two surveys $\alpha = 0.10 \, \pm \, 0.39$ for HIPASS versus $\alpha = -0.85 \, \pm \, 0.10$ for ALFALFA) the HIPASS and ALFALFA datapoints are consistent in the width range $40$ $ \lesssim w \lesssim 200$."584 The HIPASS 6 parameter is not well constrained. as their WF does not extend to low enough widths and suffers from considerable counting error in the low-widtl bius.," The HIPASS $\alpha$ parameter is not well constrained, as their WF does not extend to low enough widths and suffers from considerable counting error in the low-width bins."585 Measurement errors on (59 can shift ealaxies among width bins. altering the bin counts and therefore the inferred space density.," Measurement errors on $w_{50}$ can shift galaxies among width bins, altering the bin counts and therefore the inferred space density."586 The wsy value for ALFALFA sources is subject to two separate sources of error: one is statistical i nature and preseut for all sources. while the other is svsteinatic and concerns only a fraction of the a.lO sample.," The $w_{50}$ value for ALFALFA sources is subject to two separate sources of error: one is statistical in nature and present for all sources, while the other is systematic and concerns only a fraction of the $\alpha$ .40 sample."587 The former is due to the distortion of the signal profile shape by noise: the latter results from the fact that the measurement of the spectral widtl of a signal relics on the accurate visual ideutification of its spectral boundaries. which is non-trivial for a uunuber of sources (especially those found im the vicinity of REI).," The former is due to the distortion of the signal profile shape by noise; the latter results from the fact that the measurement of the spectral width of a signal relies on the accurate visual identification of its spectral boundaries, which is non-trivial for a number of sources (especially those found in the vicinity of RFI)."588 The final width error reported in the ALFALFA catalogs. Atsy. is the stan in quadrature of the random and systematic error terms described above.," The final width error reported in the ALFALFA catalogs, $\Delta w_{50}$, is the sum in quadrature of the random and systematic error terms described above."589 Owing to the fact that all a. lO galaxies are detected with high signal to noise and have a clean spectral profile in the vast majoritv of cases. the typical a. lO width error is relatively siuall and its distribution well behaved.," Owing to the fact that all $\alpha$ .40 galaxies are detected with high signal to noise and have a clean spectral profile in the vast majority of cases, the typical $\alpha$ .40 width error is relatively small and its distribution well behaved."590 The median error is AuspmedienS aaud ~TO% of the sources have a fractional eror of αποt9x10..," The median error is $\Delta w_{50,median} \approx 8$ and $\sim$ of the sources have a fractional error of $\Delta w_{50} / w_{50} \leqslant 10$."591" Tn order to assess the effect of Awsy on the WE. we create 50 iiock galaxy samples bv re-assigniug randoms widths to everv galaxy / in the primary ALFALFA dataset according to their mdividual measured width (ορ) and error (CA«cs9,;)."," In order to assess the effect of $\Delta w_{50}$ on the WF, we create 50 mock galaxy samples by re-assigning random widths to every galaxy $i$ in the primary ALFALFA dataset according to their individual measured width $w_{50,i}$ ) and error $\Delta w_{50,i}$ )."592" Each mock sample is subject to the same cuts as the a. LO sample aud a new realization of the WE is caleulated €""Ix set).", Each mock sample is subject to the same cuts as the $\alpha$ .40 sample and a new realization of the WF is calculated (“1x” set).593 In order to illustrate the systematic trends introduced. we also perform au additional set of WE realizations with artificially inflated width errors (twice the reported ALFALFA width errors. “2x7 set).," In order to illustrate the systematic trends introduced, we also perform an additional set of WF realizations with artificially inflated width errors (twice the reported ALFALFA width errors, “2x” set)."594 The results are shown in Figure 6G: overplotted to the original ALFALFA WF (datapoints auc solid black hue) are a modified Schechter fit to the mean WF corresponding to the Ix (red solid liue) aud 2x (dashed red lino) realizations., The results are shown in Figure \ref{fig:widtherrors}: overplotted to the original ALFALFA WF (datapoints and solid black line) are a modified Schechter fit to the mean WF corresponding to the 1x (red solid line) and 2x (dashed red line) realizations.595 Width errors at the ALFALFA error levels ποσα to onlv sliehtlv affect the ποσπατι end of the WE., Width errors at the ALFALFA error levels seem to only slightly affect the high-width end of the WF.596" As evideuced by the 2x run. width errors eenerallv lead to a rise of the high-width end. due to a uet ""diffusion of galaxies frou iuterimediate-widthn bius with large nuuber counts to high-width bius with lower uunber counts."," As evidenced by the 2x run, width errors generally lead to a rise of the high-width end, due to a net “diffusion” of galaxies from intermediate-width bins with large number counts to high-width bins with lower number counts."597 Since velocity width is a distance-ineependcut quantity. galaxy couuts m width bins are uot altered by distance errors.," Since velocity width is a distance-independent quantity, galaxy counts in width bins are not altered by distance errors."598 Dowever. the weights νε) that each ealaxy contributes to its bin depend on W-ass (see Equ.," However, the weights $1/V_{eff,i}$ ) that each galaxy contributes to its bin depend on HI-mass (see Eqn."599 l aud discussion iu refsubscc:aawt)). aud therefore ou the assumed distance.," \ref{eqn:veff} and discussion in \\ref{subsec:aawf}) ), and therefore on the assumed distance."600 have shown that ignoring the local peculiar velocity feld can lead to biased estimates of galaxy statistical distributions. especially for surveys drawing a lugo fraction of their sample from the Vireo direction (VdR).," have shown that ignoring the local peculiar velocity field can lead to biased estimates of galaxy statistical distributions, especially for surveys drawing a large fraction of their sample from the Virgo direction (VdR)."601 To avoid this bias ALFALFA uses redshift distances only for distant (e:=6000 1)) galaxies aud assigns distances to nearby galaxies hrough a parametric flow inodel developed bw?., To avoid this bias ALFALFA uses redshift distances only for distant $cz > 6000$ ) galaxies and assigns distances to nearby galaxies through a parametric flow model developed by.602. The model inclides two attractors (Virgo Cluster Creat Attractor}. a dipole component (Local Croup oeculiar velocity). a quadrupole component (Local Group asviunetrie expansion) and a random thermal residual of σι%160iL.," The model includes two attractors (Virgo Cluster Great Attractor), a dipole component (Local Group peculiar velocity), a quadrupole component (Local Group asymmetric expansion) and a random thermal residual of $\sigma_{local} \approx 160$."603 Tere we assume hat most of the cohereut motion of nearby galaxies is correctly described by the flow model. aud no significant yas resultsfrom this systematic component of galaxy )eculiar velocities.," Here we assume that most of the coherent motion of nearby galaxies is correctly described by the flow model, and no significant bias resultsfrom this systematic component of galaxy peculiar velocities."604" Contrary to intuition however. even he random component 67,4; Cal induce a systematic jas through the ""Eddiusetou effect” (see for example Figure 6 in ?2))."," Contrary to intuition however, even the random component $\sigma_{local}$ can induce a systematic bias through the “Eddington effect” (see for example Figure 6 in )."605" Tn order to asses the effect of 6;,,; ou the WE. we"," In order to asses the effect of $\sigma_{local}$ on the WF, we"606time.,time.607 The scatter is somehow intrinsic to the merger history. thus calling for further modification of the baryons behaviour with respect to the CDM.," The scatter is somehow intrinsic to the merger history, thus calling for further modification of the baryons behaviour with respect to the CDM."608 In other words we envisage a lack of a self-regulating mechanisms which acts on a galactic scale and counterbalances to some extent the random nature of the merger trees., In other words we envisage a lack of a self-regulating mechanisms which acts on a galactic scale and counterbalances to some extent the random nature of the merger trees.609 As expected from chemical evolution studies. is the shape of the SFH which sets the final [a/Fe]: a galaxy with a shorter duration of the SFH (summed over all the progenitors) will have a higher [@/Fe] than a galaxy with a longer one. even if the latter had less mergers.," As expected from chemical evolution studies, is the shape of the SFH which sets the final $\alpha$ /Fe]: a galaxy with a shorter duration of the SFH (summed over all the progenitors) will have a higher $\alpha$ /Fe] than a galaxy with a longer one, even if the latter had less mergers."610 Moreover the [o/Fe] achieved by the galaxies are in general 0.1-0.3 higher than what expected by feeding the integral SFH in à pure chemical evolution model., Moreover the $\alpha$ /Fe] achieved by the galaxies are in general 0.1-0.3 higher than what expected by feeding the integral SFH in a pure chemical evolution model.611 This happens because in GallCS galaxies do not evolve as closed boxes., This happens because in GalICS galaxies do not evolve as closed boxes.612 They instead exchange metals with the surrounding hot halo. undergo dry-mergers. as well as stars can be created in dises and the moved to bulges because of mergers or instabilities.," They instead exchange metals with the surrounding hot halo, undergo dry-mergers, as well as stars can be created in discs and the moved to bulges because of mergers or instabilities."613 In order to understand such a difference and to find viable solutions we tested the effect of several model parameters., In order to understand such a difference and to find viable solutions we tested the effect of several model parameters.614 Among those. we emphasise that an increase in the star formation efficiency and Fe-enhanced winds driven by the SNla activity might play a role in removing galaxies with too a low [a/Fe] ratio.," Among those, we emphasise that an increase in the star formation efficiency and Fe-enhanced winds driven by the SNIa activity might play a role in removing galaxies with too a low $\alpha$ /Fe] ratio."615 However. given the way they act on the galaxy evolution. the cannot be effective in either making the slope of the predicted a/Fe-mass relation steeper or in reducing its scatter.," However, given the way they act on the galaxy evolution, the cannot be effective in either making the slope of the predicted $\alpha/Fe$ -mass relation steeper or in reducing its scatter."616 In particular. it seems hard to remove the low-mass galaxy too a-enhanced.," In particular, it seems hard to remove the low-mass galaxy too $\alpha$ -enhanced."617 AP acknowledges useful discussions with A. Cattaneo., AP acknowledges useful discussions with A. Cattaneo.618Gravitational microlensing as one of the applications of general relativity is proposed by Paezyfisski (1986) for detecting the dark compact halo objects so-called MACHOs in the Galactic halo.,Gravitational microlensing as one of the applications of general relativity is proposed by Paczyńsski (1986) for detecting the dark compact halo objects so-called MACHOs in the Galactic halo.619 While not enough MACHOSs have been detected in the halo (Milsztajn&Lasserre2001).. however the microlensing technic 148 been used as an astrophysical tool for studying the atmosphere of the stars and exploring the exo-planets.," While not enough MACHOs have been detected in the halo \cite{mil}, however the microlensing technic has been used as an astrophysical tool for studying the atmosphere of the stars and exploring the exo-planets."620 In the standard method or exploring. planets with the mierolensing. a star with the companion planets can play the role of lens and produce caustic ines where crossing the caustics by the source star produces a ugh magnification on the light curve (Mao&Paezynski19911.," In the standard method for exploring planets with the microlensing, a star with the companion planets can play the role of lens and produce caustic lines where crossing the caustics by the source star produces a high magnification on the light curve \cite{pac91}."621 In this case in addition to the standard microlensing light curve we can detect a short duration spark due to the caustic crossing. ormed by the planet.," In this case in addition to the standard microlensing light curve we can detect a short duration spark due to the caustic crossing, formed by the planet."622 A precise photometry of the event is essential to find out this short duration signature of the planet., A precise photometry of the event is essential to find out this short duration signature of the planet.623 The advantage of this technie compare to the other methods of he exo-planet detection is that it is sensitive to the observation of earth mass planets (Beaulieuetal.2006). and. also those planets ocated beyond the snow line (Gouldetal.2010)., The advantage of this technic compare to the other methods of the exo-planet detection is that it is sensitive to the observation of earth mass planets \cite{bal05} and also those planets located beyond the snow line \cite{gould01}.624.. There is also other methods in gravitational microlensing such as. planetary microlensing signals from the orbital motion of the source star around the common barycenter of source star-planet. system (Rahvar&Dominik2009)., There is also other methods in gravitational microlensing such as planetary microlensing signals from the orbital motion of the source star around the common barycenter of source star–planet system \cite{rahvar}.625 In addition to the mentioned methods. Graff Gaudi (2000) proposed caustic crossing of a close-in Jupiter size planet. produced by a binary lens.," In addition to the mentioned methods, Graff Gaudi (2000) proposed caustic crossing of a close-in Jupiter size planet, produced by a binary lens."626 In this case the planet's light is magnified so much that it can be detected by a [O-m class telescope., In this case the planet's light is magnified so much that it can be detected by a 10-m class telescope.627 Here we extend this work looking to the details of the light curves and study the most favorite pass band for this observation., Here we extend this work looking to the details of the light curves and study the most favorite pass band for this observation.628 Since in a close-in Jupiter. the thermal emission due to the high temperature of the planet is more significant than the reflected light from the parent star. the observations in the Infra-red pass band is more favorable than the visual pass band.," Since in a close-in Jupiter, the thermal emission due to the high temperature of the planet is more significant than the reflected light from the parent star, the observations in the Infra-red pass band is more favorable than the visual pass band."629 We also do a Monte-Carlo simulation with a given observational strategy to obtain the number of observable events in terms of the parameters of the planet and the parent star., We also do a Monte-Carlo simulation with a given observational strategy to obtain the number of observable events in terms of the parameters of the planet and the parent star.630 We emphasize that while the observations of the hot Jupiters is simpler in nearby stars via the eclipsing and doppler methods. the microlensing method can detect distant systems and enable us to compare the statistics of the hot Jupiters with the nearby observations.," We emphasize that while the observations of the hot Jupiters is simpler in nearby stars via the eclipsing and doppler methods, the microlensing method can detect distant systems and enable us to compare the statistics of the hot Jupiters with the nearby observations."631 One of the interesting features of the ligh curve for the planet caustic crossing is that the planet can cross the caustic more than that of parent star. us it traces effectively a longer path due to the revolving motion around the parent star.," One of the interesting features of the light curve for the planet caustic crossing is that the planet can cross the caustic more than that of parent star, as it traces effectively a longer path due to the revolving motion around the parent star."632 The paper is organized as follows., The paper is organized as follows.633 In Section 2. we will introduce the caustic crossing of the parent star and planet system and generate light curve wit1 inverse ray shooting technic. introducing a new development in tree-code algorithm.," In Section \ref{lightcurve} we will introduce the caustic crossing of the parent star and planet system and generate light curve with inverse ray shooting technic, introducing a new development in tree-code algorithm."634 In section 3 we study the characteristics oftye light curve in terms of the orbital parameters of the planet and he parent star., In section \ref{char} we study the characteristics of the light curve in terms of the orbital parameters of the planet and the parent star.635 In section + we explain our Monte-Carlo simulation for estimating the probability of illuminating Hot Jupiters with this method., In section \ref{mc} we explain our Monte-Carlo simulation for estimating the probability of illuminating Hot Jupiters with this method.636 In section S we give the conclusions.," In section \ref{conc}637 we give the conclusions."638 A binary system deflects the light ray with more complicated way than a single lens., A binary system deflects the light ray with more complicated way than a single lens.639" Let us represents£ as the position of the image in the lens plane and 7 the position of the source in the source plane. the geometrical relation between these parameters is given by the lens equation as follows (Schneider&Wiess1986): where underline represents the vector. a is the overall deflection angle due to a double lens and {2.. D; and Dj, are the distance of the source and lens from the observer and distance"," Let us represents $\xi$ as the position of the image in the lens plane and $\eta$ the position of the source in the source plane, the geometrical relation between these parameters is given by the lens equation as follows \cite{sw86}: where underline represents the vector, $\underline{\alpha}$ is the overall deflection angle due to a double lens and $D_{s}$, $D_{l}$ and $D_{ls}$ are the distance of the source and lens from the observer and distance"640how this sample divides into AGN and Galactic stellar populations.,how this sample divides into AGN and Galactic stellar sub-populations.641 Next we consider the properties of the EUV-bright ACN including a comparison with a hard X-ray selected ACN sample., Next we consider the properties of the EUV-bright AGN including a comparison with a hard X-ray selected AGN sample.642 In 4 we derive an approximate luminosity function for EWUV-selected AGN ancl calculate the local volume emissivity of such sources., In 4 we derive an approximate luminosity function for EUV-selected AGN and calculate the local volume emissivity of such sources.643 Finally. in 5. we briefly sumnmiarise our results and consider possible future extensions of this work.," Finally, in 5, we briefly summarise our results and consider possible future extensions of this work."644 The selection criteria we have used in order to include a source in our preliminary source List is as follows: (1) A WEC all-skv. survey SI band (90210 eV: A)) detection at c2.50: (2) An S2 band (GO110 eV: 110.210 A9)ull detection: (3) X coincident strong RBSC X-ray detection (0.1.2.4 keV count rate 20.3 ct/sec) within ool the SL position: (4) A value of the foreground Galactic column density in the direction of the source of Nyx2.5«107 em.7 (Dickey Lockman 1990)., The selection criteria we have used in order to include a source in our preliminary source list is as follows: (1) A WFC all-sky survey S1 band (90–210 eV; 60--140 ) detection at $ \ge 2.5 \sigma $; (2) An S2 band (60–110 eV; 110–210 ) detection; (3) A coincident strong RBSC X-ray detection (0.1–2.4 keV count rate $\ge$ 0.3 ct/sec) within of the S1 position; (4) A value of the foreground Galactic column density in the direction of the source of $ N_H \le 2.5 \times 10^{20} $ $^{-2}$ (Dickey Lockman 1990).645 Criterion (3) allows the current survey to &o more than a [actor of 2 below the 5.5¢ WEC 2HI survey limit (Pye 1995). since the requirement for an S1 ancl soft X-ray detection limits the number chance coincidences in the sample to much less than one.," Criterion (3) allows the current survey to go more than a factor of 2 below the $\sigma$ WFC 2RE survey limit (Pye 1995), since the requirement for an S1 and soft X-ray detection limits the number chance coincidences in the sample to much less than one."646 Criteria. (2) and. (4) select against Galactic sources. since there is no reasonable expectation of extragalactic sources being detectable in the S2 band anywhere in the sky or in the S1 band if the Galactic column is too high.," Criteria (2) and (4) select against Galactic sources, since there is no reasonable expectation of extragalactic sources being detectable in the S2 band anywhere in the sky or in the S1 band if the Galactic column is too high."647 For example. in the 8S2 band. even for the lowest-column source in the sample. (which has Ng!=6.⋅LOM⋅⋅ em⊳↘ 7). του=⋅n3.7. corresponding. to à fractional transmission of only2.," For example, in the S2 band, even for the lowest-column source in the sample (which has $ N_H = 6 \times 10^{19} $ $^{-2}$ ), $ \tau_{S2} = 3.7 $, corresponding to a fractional transmission of only."64864.. For comparison the transmission inthe SI band is for this same source., For comparison the transmission inthe S1 band is for this same source.649 Llowever. at the survey limit of Ng=2.5.107em7. even the SL transmission has declined to0.," However, at the survey limit of $ N_H = 2.5 \times 10^{20} \rm~cm^{-2}$, even the S1 transmission has declined to."6506%.. Clearly only the brightest extragalactic sources would be able to be detected in the presence of such strong attenuation., Clearly only the brightest extragalactic sources would be able to be detected in the presence of such strong attenuation.651 A total of 34 WEC sources were found. to satisly the above criteria., A total of 34 WFC sources were found to satisfy the above criteria.652 For this preliminary sample of EUV sources. SIMIBAD and other catalogues were searched for potential optical counterparts.," For this preliminary sample of EUV sources, SIMBAD and other catalogues were searched for potential optical counterparts."653 This process proved efficient. in that all but one of the sources (AX 043747: sce 2.2.), This process proved efficient in that all but one of the sources (RX J0437–47; see 2.2.)654 were identified in this fashion., were identified in this fashion.655 Phe sample is now fully identified and comprises 19 cxtragalactic and 15 Galactic sources., The sample is now fully identified and comprises 19 extragalactic and 15 Galactic sources.656 Details of these sources are presented below., Details of these sources are presented below.657" ‘Table 1 contains a compilation of the deata for the extragalactic sample as detailed in the table footnote,", Table 1 contains a compilation of the data for the extragalactic sample as detailed in the table footnote.658 Note that the two hardness ratios 4/1 and 1/02 apply to the full. PSPC band and the hard. PSPC bane respectively (he. HI=(Mοί|€ and where C is the 0.1:0.41 keV. count rate. 41 the 0.52 keV count rate. {11 the 0.50.9 keV count rate. and £72 the 0.92 keV count rate).," Note that the two hardness ratios $HR1$ and $HR2$ apply to the full PSPC band and the hard PSPC band respectively (i.e., $ HR1 = (H-C)/(H+C)$ and where $C$ is the 0.1–0.4 keV count rate, $H$ the 0.5–2 keV count rate, $H1$ the 0.5–0.9 keV count rate, and $H2$ the 0.9–2 keV count rate)."659 Also we quote the RBSC positions in preference to the WEC positions since the former are more accurate (the X-ray telescope has better spatial resolution and tvpically records at least. 10. times more counts than the WEC)., Also we quote the RBSC positions in preference to the WFC positions since the former are more accurate (the X-ray telescope has better spatial resolution and typically records at least 10 times more counts than the WFC).660 Information from other wavebancs ids. presented: in ‘Table 2: column 3 gives the Galactic value of Ny derived from the survey of Dickey Lockman (1990). columns +6 eive the V-banc optical magnitude. redshift’ and. 11:7 line width. as reported. in the optical observations referenced in column 9.," Information from other wavebands is presented in Table 2: column 3 gives the Galactic value of $N_H$ derived from the survey of Dickey Lockman (1990), columns 4–6 give the V-band optical magnitude, redshift and $\beta$ line width, as reported in the optical observations referenced in column 9."661 Columns 7 and 8 give the monochromatic luminosity at 200 eV (Leo) and optical/IEUV spectral slope. Oo. as derived in aand 3.3..," Columns 7 and 8 give the monochromatic luminosity at 200 eV $L_{200}$ ) and optical/EUV spectral slope, $\alpha_{OE}$, as derived in and 3.3.,"662. respectively., respectively.663 Since the EUV and soft. X-ray data in Table. 1 were eathered from a single mission at the same time. correlations and colours measured from. them. are reliable.," Since the EUV and soft X-ray data in Table 1 were gathered from a single mission at the same time, correlations and colours measured from them are reliable."664 However. many of the data in Table 2 were taken from à variety of non-simultaneous measurements. and thus any ratios involving these quantities (e.g. aoe) max be inlluenced by any temporal variability of the source.," However, many of the data in Table 2 were taken from a variety of non-simultaneous measurements, and thus any ratios involving these quantities (e.g., $\alpha_{OE}$ ) may be influenced by any temporal variability of the source."665 With Uhl=0.97. this NLSI is the softest AGN in the sample.," With $ HR1 = -0.97 $, this NLS1 is the softest AGN in the sample."666 Phere are almost no counts in. bauds Hil and 19. so the hardness ratio /4/22 is not well-determined.," There are almost no counts in bands $H1$ and $H2$, so the hardness ratio $HR2$ is not well-determined."667 The. foreground LIE column is comparatively high at 2.5107 7 and. after correcting for the Galactic transmission. this is the brightest. Sevfert. galaxy in the sample (in terms of its incident. lux).," The foreground HI column is comparatively high at $ 2.5 \times 10^{20} 668$ $^{-2}$ and, after correcting for the Galactic transmission, this is the brightest Seyfert galaxy in the sample (in terms of its incident flux)."669 WPVS 7 appears to be à transient source. as subsequent. pointed. oobservations show that its X-ray. [lux dropped by a factor of ~400 with respect to the survey. measurement. the largest such variation seen for any Sevíert |. galaxy (Cirupe 1995).," WPVS 7 appears to be a transient source, as subsequent pointed observations show that its X-ray flux dropped by a factor of $\sim$ 400 with respect to the survey measurement, the largest such variation seen for any Seyfert 1 galaxy (Grupe 1995)."670 The WEC 2RE catalogue reports the detection of an πΧ source identified. with the Seyfert 1 galaxy LB 1727 (LLL 0419S77) but at a position over oollset from the optical counterpart ancl a corresponding RBSC detection., The WFC 2RE catalogue reports the detection of an EUV source identified with the Seyfert 1 galaxy LB 1727 (1H 0419–577) but at a position over offset from the optical counterpart and a corresponding RBSC detection.671 A close examination of the WEC data for this field. reveals that the 2RIE source is a fact a blend of two sources of roughly equal brightness in the S1 band., A close examination of the WFC data for this field reveals that the 2RE source is a fact a blend of two sources of roughly equal brightness in the S1 band.672" ‘These two sources are clearly resolved in pointed LEUVIS and LR observations and have been identified: respectively with the Sevfert galaxy LB 1727 (CGuainazzi 1998: ""Turner 1999) and an AM Her star EUVE 0425.65714 (Halpern 1998).", These two sources are clearly resolved in pointed EUVE and HRI observations and have been identified respectively with the Seyfert galaxy LB 1727 (Guainazzi 1998; Turner 1999) and an AM Her star EUVE J0425.6--5714 (Halpern 1998).673 When the ellects of the source confusion are taken into account. the WEC source associated with LB 1727 meets all the criteria defined in 82 and hence we include it in our sample.," When the effects of the source confusion are taken into account, the WFC source associated with LB 1727 meets all the criteria defined in 2 and hence we include it in our sample."674 lhis was the only source in the sample without a published optical spectrum., This was the only source in the sample without a published optical spectrum.675 Low-resolution optical spectra were therefore acquired. from the 3.9m Anelo-Australian Telescope. using theRCO anc FORS, Low-resolution optical spectra were therefore acquired from the 3.9m Anglo-Australian Telescope using theRGO and FORS676Equation (41)) is analoguis to (24)) except the last term in brackets.,Equation \ref{mu2}) ) is analoguis to \ref{mu}) ) except the last term in brackets.677" For a given vr, equations (36)). (87)) are solved nunerically to determine p. and cy."," For a given $x_c$ , equations \ref{meq1PW}) ), \ref{meq2PW}) ) are solved numerically to determine $p_c$ and $a_1$."678 Then (35)) is integrated numerically as described in the text., Then \ref{PW1}) ) is integrated numerically as described in the text.679 Comparative results of the numerical solution of (35)) are depicted ofFigure 4., Comparative results of the numerical solution of \ref{PW1}) ) are depicted ofFigure 4.680We asste a single instarancous burst occurring at the ceuter of a eas-rich cava SULTonaded by a dard matter halo.,We assume a single instantaneous burst occurring at the center of a gas-rich dwarf surrounded by a dark matter halo.681 The mass of stars formed is SM... the gas mass is Moas=d10ML aa the mass of the «ark halo is Masse=6.5.105AZ...," The mass of stars formed is $M_{*}=6 \cdot 10^{5} M_{\odot}$ , the gas mass is $M_{gas}=1.7 \cdot 10^{7} M_{\odot}$ and the mass of the dark halo is $M_{dark}=6.5 \cdot 10^{8} M_{\odot}$."682 TLOS8C paraletcrs are chosen to reproduce. fex what JOSS]dle. the characteristics of IZwls (unevolved οσα]. galaxy).," These parameters are chosen to reproduce, for what possible, the characteristics of IZw18 (unevolved local galaxy)."683 The ealactic regio1 extends for 700 pe in the vertical (z) directiou aud for Uspe in fje radial càrection (Ry., The galactic region extends for 700 pc in the vertical (z) direction and for 1kpc in the radial direction (R).684 In order to s1dv. the chemo-dyvuamical evolution couseTucut to he burst. we adopt a 2-D wdrocode coupled wih detailed eheimical vields roni typ| TT SNe. type Ia SNe and low aud inermediate lass sars (see Reece uct al.," In order to study the chemo-dynamical evolution consequent to the burst, we adopt a 2-D hydrocode coupled with detailed chemical yields from: type II SNe, type Ia SNe and low and intermediate mass stars (see Recchi et al."685 2001 OY noreetails about this model)., 2001 for more details about this model).686 We follow the evolutiou of the abuudauces of II. Ue. C. δν O. Me. Si. Fe in the eas.," We follow the evolution of the abundances of H, He, C, N, O, Mg, Si, Fe in the gas."687 The evolution is ollowed. {κy 35svr suce the burst., The evolution is followed for 375 Myr since the burst.688 We also consider a case with a second o»urst occtiriug after 300 Vvr from the first oue The mass in stars formed duriic the fust burst is M.=1PAL... whereas the mass in stars formed iu he seco burst is A.—58SOIM...," We also consider a case with a second burst occurring after 300 Myr from the first one The mass in stars formed during the first burst is $M_{*}=10^{5}M_{\odot}$, whereas the mass in stars formed in the second burst is $M_{*}=5.8 \cdot 10^{5}M_{\odot}$."689 The initial eas mass aud dark mater ino are f1ο salue as in the one-murst case., The initial gas mass and dark matter halo are the same as in the one-burst case.690 The simulation lasts £50 Myr iu ota since the firs burst., The simulation lasts 450 Myr in total since the first burst.691 The SN efficiencics of cnerey transter iuto the ISAL Yoni SNe is the same iu both cases. in particular: for type II SNe we assune hat the eificiency is y=0.03 anc for type Ia SNe 4j21.," The SN efficiencies of energy transfer into the ISM from SNe is the same in both cases, in particular: for type II SNe we assume that the efficiency is $\eta=0.03$ and for type Ia SNe $\eta=1$."692 This choice is due to nests from Draciunaute et al. (, This choice is due to results from Bradamante et al. (6931998) for type ID SNe indicating that the first SNe to explode lose a large fracion of their initial enerev by radiation «πο o the cold aud deuse ISM in thei,"1998) for type II SNe indicating that the first SNe to explode lose a large fraction of their initial energy by radiation due to the cold and dense ISM in their surroundings, whereas for type Ia SNe the efficiency is maximum due to the fact that they explode into an ISM already hot and rarefied (see Recchi et al."694r s," 2001, for details)."695urroundings. w," We find that the starburst triggers indeed a galactic wind and the metals leave the galaxy more easily than the unprocessed gas confirming previous results (e.g. McLow and Ferrara, 1999)."696hereas for ty, We find that SNe Ia eject their metals more efficiently than SNe II since they inject all of their initial energy into the ISM.697pe Ia SNe t, This is a new result relative to previous studies since it is the first time that type Ia SNe are taken into account.698he efficienev i," At variance with previous studies (see e.g. Tenorio-Tagle 1996) we find that most of the metals are already in the cold gas phase after 8-10 Myr from the beginning of the burst, due to the fact that the superbubble created by the SNe does not break immediately and thermal conduction can act efficiently."699s 1i," We find that one single instantaneous burst, occurring in a primordial gas (no metallicity), at an age of $\sim 31$ Myr can reasonably reproduce the abundances measured in IZw18 (see figure 1)."700axiuuin d," From this one would conclude that perhaps this galaxy is experiencing its first burst of SF, although one cannot exclude a previous burst which enriched the gas no more than 1/50 $_{\odot}$."701ue to the fact that ," However, as evident in figure 1, the correct N/O ratio would last only for a very short time since for $t > 31$ Myr the N/O ratio will start to increase outside the permitted observational range."702t," In addition, Color Magnitude Diagram studies (e.g. Aloisi et al."703hey explo," 1999) indicate the presence of an old underlying stellar population in IZw18, thus suggesting that the two-burst case is more realistic."704de iuto an ISAL al," An interesting result is that the $\alpha$ /Fe] ratios in the gas outside the galaxy (i.e. in the galactic wind) are lower than inside, due to the larger ejection efficiency by type Ia SNe (more iron is lost than $\alpha$ -elements)."705ready, This creates an interesting dichotomy706"where nmi4 is the total particle number density. D is (he dust-to-gas ratio ancl Dig is its value in the local ISM,","where $n_{\rm tot}$ is the total particle number density, ${\cal D}$ is the dust-to-gas ratio and ${\cal D_{\rm MW}}$ is its value in the local ISM."707" Combining these equations. we can easily solve for the dust-to-gas ratio at which Jy.ως and ys dust. Which I denote as D: In the common case that. Ryvy29A,qq; - Unis equation reduces to where rz, and f44 are given by equations Ll and lt respectively."," Combining these equations, we can easily solve for the dust-to-gas ratio at which $R_{\mHt, {\rm gas}}$ and $ R_{\mHt, {\rm dust}}$ , which I denote as ${\cal D}_{\rm cr}$ : In the common case that $R_{\mHt, \Hm} \gg R_{\mHt, \mHtp}$ , this equation reduces to where $x_{\rm cr}$ and $f_{\rm rad}$ are given by equations \ref{xcr} and \ref{frad} respectively."708" A similar equation can be written in the much less common case that Z2,4429Rina "," A similar equation can be written in the much less common case that $R_{\mHt, \mHtp} \gg R_{\mHt, \Hm}$."709"In order to help illustrate the behaviour of these equations. I plot in figures 1 to 4 the value of ους as a [function of temperature for gas illuminated by the Mathise£a£.(1983) radiation field in four different scenarios: low ionization. low densitv gas (6=  fiewre D). low ionization. hieh densitv 55eas (0=10lo»,110em: figure 2)). ∐↕↖≺↽↔↴∐↕∪∐↕∠≀↧↴∐∪∐⋅↥⋯∖⇁≺⇂≼↲∐⋟∖⊽∐⋡∖⇁≸≟≀↧⊔∖⊽⋖⋡⋅≀⋮∶↓∩⋅−⋟⋅∣∣⊔∶↓≺∢∐↕⋮⋡⋝∶⇂∎↓↖≺↽↔↴∏↕⋅≼↲⊑↽⊰↕⋝↕⋝≀↧↴∐≺⊔∏≸↽↔↴∐↕∪∐↕∠≀↧↴∐∪∐⋅ hieh∙ density∙ gas Cr=10>7.njLO’a3em3: figuretl 4))."," In order to help illustrate the behaviour of these equations, I plot in figures \ref{fig1} to \ref{fig4} the value of ${\cal D}_{\rm cr}$ as a function of temperature for gas illuminated by the \citet{mathis} radiation field in four different scenarios: low ionization, low density gas $x = 10^{-4}, n_{\mH} = 1 \: \rm{cm}^{-3}$ ; figure \ref{fig1}) ), low ionization, high density gas $x = 10^{-4}, n_{\mH} = 10^{3} \: \rm{cm}^{-3}$; figure \ref{fig2}) ), high ionization, low density gas $x = 10^{-2}, 710n_{\mH} = 1 \: 711\rm{cm}^{-3}$; figure \ref{fig3}) ) and high ionization, high density gas $x = 10^{-2}, n_{\mH} = 10^{3} \: \rm{cm}^{-3}$; figure \ref{fig4}) )."712"MN In each case. I adopt. a fixed. grain. temperature 7;,,=20lv. although small changes in {νι have little effect on the results provided (hat it remains less than T7."," In each case, I adopt a fixed grain temperature $T_{\rm gr} =20 \: \rm{K}$, although small changes in $T_{\rm gr}$ have little effect on the results provided that it remains less than $T_{\rm cr}$."713 A striking feature of these plots is the strong temperature dependence of Di., A striking feature of these plots is the strong temperature dependence of ${\cal D}_{\rm cr}$.714 At low temperatures. grain-catalvzed Ils formation is relatively efficient and very little cust is needed before grain catalvsis dominates.," At low temperatures, grain-catalyzed $\mHt$ formation is relatively efficient and very little dust is needed before grain catalysis dominates."715 Above a few hundred Ix. however. the efficienev of grain calalvsis decreases signilicantlv. while the efficiency. of gas-phase Hà formation continues {ο erow.," Above a few hundred K, however, the efficiency of grain catalysis decreases significantly, while the efficiency of gas-phase $\mHt$ formation continues to grow."716 As a result. the required dust abundance rises sharply with increasing temperature.," As a result, the required dust abundance rises sharply with increasing temperature."717 From the behaviour outlined in figures 1- 4.. it is clear that. gas-phase IH» formation is ab ils most effective in warm. dense gas with a high lractional ionization.," From the behaviour outlined in figures \ref{fig1}- \ref{fig4}, it is clear that gas-phase $\mHt$ formation is at its most effective in warm, dense gas with a high fractional ionization."718 HLowever. most ol the molecular gas that we observe in our galaxy is in (he form of molecular clouds with low temperatures (T.~20 IX) and very low fractional ionizations Gr~LO *) and in these conditions grain catalyzed formation dominates by manyordersof magnitude.," However, most of the molecular gas that we observe in our galaxy is in the form of molecular clouds with low temperatures $T \sim 20 \: \rm{K}$ ) and very low fractional ionizations $x \sim 10^{-7}$ ) and in these conditions grain catalyzed formation dominates by manyordersof magnitude."719A more promising place to look for gas-phase Hs formation is in the so-called warm neutral medium (WNM).,A more promising place to look for gas-phase $\mHt$ formation is in the so-called warm neutral medium (WNM).720 In models of themultiphase ISM that assume thermal pressure, In models of themultiphase ISM that assume thermal pressure721he on aud the off beams at a rate of —0.1IIz.,the on and the off beams at a rate of $\sim$ 0.1Hz.722" The poiut- sensitivity of SUARC at yan is ~1v/VTIEz and he beam size is ~9"" FWIIN"," The point-source sensitivity of SHARC at $\,\mu$ m is $\rm \sim 1 \,723Jy/\sqrt{Hz}$ and the beam size is $\sim9''$ FWHM."724"L All nieasurenients were nade at 350¢an with the exception of M1113|117 which was also observed at 1504. Pointing was checked regularly on nearby strong galactic sources Which also served as secondary calibrators. anc was found to be stable with a typical accuracy of <3”,"," All measurements were made at $350\mu$ m with the exception of $\,$ 1413+117 which was also observed at $450\mu$ m. Pointing was checked regularly on nearby strong galactic sources which also served as secondary calibrators, and was found to be stable with a typical accuracy of $ \lesssim 3^{\prime\prime}$."725 The planets Mars. Saturn aud Uranus served as primary flux calibrators.," The planets Mars, Saturn and Uranus served as primary flux calibrators."726 The absolute calibration was found to be accurate to within, The absolute calibration was found to be accurate to within.727 Repeated observations of Wills|117 and 10211|1721 confirmed a relative fiux accuracv of ~ 20%.," Repeated observations of $\,1413+117$ and $\,10214+4724$ confirmed a relative flux accuracy of $\sim20\%$ ."728 The data were reduced using the CSO DADRS software package., The data were reduced using the CSO BADRS software package.729 Typical seusitivities (10) of —20 muJv were achieved. after ~ 25008 of ousource iuteeratiou time.," Typical sensitivities $\rm 1 \sigma$ ) of $\sim20$ mJy were achieved, after $\sim 2500\,$ s of on–source integration time."730 Nine sources were detected at levels of La aud above. as outlined am Table 1..," Nine sources were detected at levels of $4\,\sigma$ and above, as outlined in Table \ref{detections}."731 Iuchuded are the DocLl quasars DR1202 0725. DRI1355 0117 and TALO000 263.," Included are the $z\,>\,4$ quasars $\,$ $-$ 0725, $\,$ $-$ 0417 and $\,$ $-$ 263."732 Except for the Cloverleaf 11123|117: Barvainis.Autonucci.&Coleman 1992)). the preseut measurements are the first reported detections for high redshift quasars at 350422. Mau of the sources were measured three or more times providing both consistency checks aud improvements in the accuracy of the fis densities.," Except for the Cloverleaf $\,$ 1413+117; \cite{Barvainis92}) ), the present measurements are the first reported detections for high redshift quasars at $\,\mu$ m. Many of the sources were measured three or more times providing both consistency checks and improvements in the accuracy of the flux densities."733 The two strougest sources. IDL113|)117 aud TRAS F102111L721. were often measured before starting the long (~2-3 hours) iuteerations on the weaker sources.," The two strongest sources, $\,$ 1413+117 and IRAS F10214+4724, were often measured before starting the long $\sim$ 2-3 hours) integrations on the weaker sources."734 As an illustration of the data quality. Figure 1 shows the 3504440. CSOSTARC measurement towards DR1202 0725 at :=1.69.," As an illustration of the data quality, Figure 1 shows the $\,\mu$ m CSO–SHARC measurement towards $\,$ $-$ 0725 at $z\,=\,4.69$."735 This ineasureiment corresponds to a total of L hours integration ou source., This measurement corresponds to a total of 4 hours integration on source.736 The source is ceutered at offset zero., The source is centered at offset zero.737 The other chiauncls provide a measure of the neigliboriug blauk sky. eniission and a reference for the quality of the detection., The other channels provide a measure of the neighboring blank sky emission and a reference for the quality of the detection.738 LL sources with redshifts between 1.8 aud {ο were not detected at ja. with flax deusity upper Μες at the 30 levelof 30-125 1iJv.," 11 sources with redshifts between 1.8 and 4.5 were not detected at $\,\mu$ m, with flux density upper limits at the $\,\sigma$ levelof $\,$ $\,125\,$ mJy."739 Table 2 lists their names. redshifts. pau flux deusity measurciuents with cle crrors. aud a 30 upper luit to their Iuniuosities (see below).," Table 2 lists their names, redshifts, $\,\mu$ m flux density measurements with $\pm1\,\sigma$ errors, and a $\,\sigma$ upper limit to their luminosities (see below)."740 sampling., sampling.741models to ensure that the global 4 PEEis near the iiums of the trough in Fie.,models to ensure that the global $\chi^2$ is near the minimum of the trough in Fig.742 l. however the distribution of mass between the elliptical rich aud spiral rich groups is modified between models.," 1, however the distribution of mass between the elliptical rich and spiral rich groups is modified between models."743 Tere. tg=13 €vr.," Here, $t_0=13$ Gyr."744 In the case of the curve with the smallest swing. all components are eiven the same M/L=200M./L..," In the case of the curve with the smallest swing, all components are given the same $M/L=200 M_{\odot}/L_{\odot}$."745 The intermediate curve is generated with the elliptical-dominated eroups Gucluding the Vireo Cluster) eiven M/Lpg=500 aud the spiral-dominated eroups given ης=171., The intermediate curve is generated with the elliptical-dominated groups (including the Virgo Cluster) given $M/L_E=500$ and the spiral-dominated groups given $M/L_S=174$.746 The curve with the largest swing refiects M/Lp=500 and AMiLs=llis., The curve with the largest swing reflects $M/L_E=800$ and $M/L_S=148$.747 In the model illustrated by the muddle curve in Fie., In the model illustrated by the middle curve in Fig.748 2. the cluster is given the uecessary aud just sufficient mass of 9<101A...," 2, the cluster is given the necessary and just sufficient mass of $9 \times 10^{14} M_{\odot}$."749 The 11Ὁ group aud a couple of others provide the ercatest demands on the mass of the chluster and are inferred to lic uear a tip along a triple-value curve., The 11–3 group and a couple of others provide the greatest demands on the mass of the cluster and are inferred to lie near a tip along a triple-value curve.750 Au adequate description of the amplitude of their iufall velocities requires an assiguinent of AL/£=500A.EL. to the Vireo Cluster if ty=13 Cyr., An adequate description of the amplitude of their infall velocities requires an assignment of $M/L=500 M_{\odot}/L_{\odot}$ to the Virgo Cluster if $t_0=13$ Gyr.751" As with the overall Supercluster modeling. less cluster mass is required if eiven more time (Tully&Shava1981):e.g. 8«LOMAS, suffices if ty=Ll Gyr."," As with the overall Supercluster modeling, less cluster mass is required if given more time \citep{tul84}:, $8 \times 10^{14} M_{\odot}$ suffices if $t_0=14$ Gyr."752 In both these 13 and Ll Cor cases. as the mass assigned to the cluster is augmented. the models require a reduction of mass assigned to the field to remain at the minima ofthe 4? trough of Fie.," In both these 13 and 14 Gyr cases, as the mass assigned to the cluster is augmented, the models require a reduction of mass assigned to the field to remain at the minimum of the $\chi^2$ trough of Fig."753 1., 1.754 The ratio of cluster. C. to field. F. mass to light values is CU/L)e(ML)ep=~3 with the mass assiguuents required to explain the infall motious.," The ratio of cluster, $C$, to field, $F$, mass to light values is $(M/L)_C/(M/L)_F \simeq 3$ with the mass assignments required to explain the infall motions."755 This factor 3 probably uuderestiuates the ML differcuce between Virgo and bound groups in the Ποια because some of the mass contributing to the field ratio lies outside the eroups., This factor 3 probably underestimates the $M/L$ difference between Virgo and bound groups in the field because some of the mass contributing to the field ratio lies outside the groups.756 Studies of the dvuamics of nearby eroups (Tully2005) sueeest that bound groups of spiral galaxies in the field have ML~90., Studies of the dynamics of nearby groups \citep{tul05b} suggest that bound groups of spiral galaxies in the field have $M/L \sim 90$.757 The mass to light ratio of the Virgo Cluster is 56 times larger., The mass to light ratio of the Virgo Cluster is 5–6 times larger.758 Qur first result on the mean deusitv of the Universe coluplements the and imeasurenieuts of the density parameter because the error ellipses in the domain Οι{μυ ave steeply inclined to each other.," Our first result on the mean density of the Universe complements the and measurements of the density parameter because the error ellipses in the domain $\Omega_m, H_0$ are steeply inclined to each other."759" A harrow range of parauecter space around ty=13.5 Cor. O,,=0.22£0.02 is permitted bv the combined experinoents."," A narrow range of parameter space around $t_0=13.5$ Gyr, $\Omega_m=0.22\pm0.02$ is permitted by the combined experiments."760 Our second result concerus the local fluctuations around this mean deusitv., Our second result concerns the local fluctuations around this mean density.761 Although most of the blue itin the local Universe is associated with the spiral field. there is close to parity iu the partition of mass between the spiral Ποια aud the Virgo Cluster.," Although most of the blue light in the local Universe is associated with the spiral field, there is close to parity in the partition of mass between the spiral field and the Virgo Cluster."762 The AL value associated with the E/SO dominated Virgo Cluster is significautly higher than that associated with the spiral dominated field., The $M/L$ value associated with the E/S0 dominated Virgo Cluster is significantly higher than that associated with the spiral dominated field.763 The complex problem of MEL variatious with cnviromment shall be discussed in a future paper. STScll, The complex problem of $M/L$ variations with environment shall be discussed in a future more-detailed paper.764 ancl NSE awards., I and NSF awards.765haloes from DarkMatter only simulations.,haloes from Dark–Matter only simulations.766 This current work merely introduces the algorithm. along with some systematic tests.," This current work merely introduces the algorithm, along with some systematic tests."767 In a future study. we plan to apply the methods outlined here redshift)space data from mock galaxy catalogues and actual observed galaxy surveys.," In a future study, we plan to apply the methods outlined here redshift–space data from mock galaxy catalogues and actual observed galaxy surveys."768 The Millennium Run simulation used in this paper was carried out by the Virgo Consortium. (httpz//www.virgo.dur.ac.uk) at the Computing Center of the AlaxPlanckGesellschaft. in. Garching. Germany.," The Millennium Run simulation used in this paper was carried out by the Virgo Consortium (http://www.virgo.dur.ac.uk) at the Computing Center of the Max–Planck–Gesellschaft in Garching, Germany."769 We thank Rupert Croft. Carlos Frenk. Tiziana di Matteo. Cameron AleBride. Volker Springel. and Naoki Yoshicla for helpful cliseussions and comments on earlier. drafts of this work. and the anonvmous referee for very helpful suggestions for improvements.," We thank Rupert Croft, Carlos Frenk, Tiziana di Matteo, Cameron McBride, Volker Springel, and Naoki Yoshida for helpful discussions and comments on earlier drafts of this work, and the anonymous referee for very helpful suggestions for improvements."770 Thanks are also due to Esther Jesurum for advice concerning advanced. C| techniques and to Rien van de Weveaert for providing his code used in to prepare an earlier version of the structure.finding code., Thanks are also due to Esther Jesurum for advice concerning advanced C++ techniques and to Rien van de Weygaert for providing his code used in to prepare an earlier version of the structure–finding code.771 1n a nutshell. structure elements of the AIST are found. by erouping its individual elements into [arger units.," In a nutshell, structure elements of the MST are found by grouping its individual elements into larger units."772 These larger units are constructed on the basis of how the elements of the AIST are interconnected., These larger units are constructed on the basis of how the elements of the MST are interconnected.773 Before discussing the algorithm in detail. it is important that the notation used in the folowing is clear.," Before discussing the algorithm in detail, it is important that the notation used in the folowing is clear."774 Our starting configuration is à AIST. constructed from cells on a grid.," Our starting configuration is a MST, constructed from cells on a grid."775 X is simply such a cell. that is an individual member of the MST.," A is simply such a cell, that is an individual member of the MST."776 Xn is a connection between two nodes., An is a connection between two nodes.777 Each node is connected to at least one other node. and we will call the set of nodes that any given node is connected to itsnode(s}.," Each node is connected to at least one other node, and we will call the set of nodes that any given node is connected to its."778 As alreacly mentioned. the algorithm groups nodes into larger units.," As already mentioned, the algorithm groups nodes into larger units."779 Any such unit we will call abranch. and it might contain a collection of connected nodes and other branches.," Any such unit we will call a, and it might contain a collection of connected nodes and other branches."780 Each branch contain at least one node., Each branch contain at least one node.781 If à branch contains other branches then the longest of those branches will be called. thebranch. with the remaining one(s) beingsubbranches.," If a branch contains other branches then the longest of those branches will be called the, with the remaining one(s) being."782 A branch is represented by the last node aclelecl to it., A branch is represented by the last node added to it.783 Lt is probably easiest to understant. the classification algorithm by referring to Figure Al... which schematically depicts the application of the algorithm to a very. simple case.," It is probably easiest to understant the classification algorithm by referring to Figure \ref{tree_finding}, which schematically depicts the application of the algorithm to a very simple case."784 Figure A1 shows the same MST at six dillerent steps of the algorithm.," Figure \ref{tree_finding}785 shows the same MST at six different steps of the algorithm."786 As the individual nodes are being grouped into units. the cdilferent. branches are shown as erey boxes around the nodes and edges they consist. of.," As the individual nodes are being grouped into units, the different branches are shown as grey boxes around the nodes and edges they consist of."787 The algorithm constructs branches from the MST's nodes and edges using a simple set of rules., The algorithm constructs branches from the MST's nodes and edges using a simple set of rules.788 The rules are applied sequentially until cach node is contained in at least one branch., The rules are applied sequentially until each node is contained in at least one branch.789 The initial set of branches is constructed from all nodes that are connected to only one other node — the loose ends of the structure., The initial set of branches is constructed from all nodes that are connected to only one other node – the loose ends of the structure.790 In Figure Al.. these are nodes A to E. In order not to make Figure Al too cluttered. there are no ervey boxes drawn around these initial branches.," In Figure \ref{tree_finding}, these are nodes A to F. In order not to make Figure \ref{tree_finding} too cluttered, there are no grey boxes drawn around these initial branches."791 Using the set of initial branches. the full classification of the MST is done by applying the following rules:," Using the set of initial branches, the full classification of the MST is done by applying the following rules:"792reaction (o mass-loss aud other processes that mieht influence the planets evolution. ancl in 866 we discuss the planets overall survival.,"reaction to mass-loss and other processes that might influence the planet's evolution, and in 6 we discuss the planet's overall survival."793 Our conclusions follow., Our conclusions follow.794 single white dwail progenitors are expected to have main sequence masses in the range rom | to about 8 mass (the upper mass limit is not well established)., Single white dwarf progenitors are expected to have main sequence masses in the range from 1 to about 8 mass (the upper mass limit is not well established).795 As these stars eave (he main sequence they evolve into the RGB. Horizontal Draneh. AGB. and PN phases in (he IIertzsprung-Itussell (11A) diagram. before descending the white dwarl cooling track.," As these stars leave the main sequence they evolve into the RGB, Horizontal Branch, AGB, and PN phases in the Hertzsprung-Russell (HR) diagram, before descending the white dwarf cooling track."796 The major structural changes in the post-main sequence evolution of low- ancl stars occur during the RGB and AGB phases., The major structural changes in the post-main sequence evolution of low- and intermediate-mass stars occur during the RGB and AGB phases.797 During the RGB and AGB the stellar effeclive temperature is always lower (han its main sequence value and therelore it has no influence on the planets survival., During the RGB and AGB the stellar effective temperature is always lower than its main sequence value and therefore it has no influence on the planet's survival.798 Ilowever. it is curving the late AGB evolution. the so-called ihermal-pulsing AGB phase. that à planets orbit will be most inlluenced. since during this phase the star loses most of its initial mass ancl reaches ils maximun radius.," However, it is during the late AGB evolution, the so-called thermal-pulsing AGB phase, that a planet's orbit will be most influenced, since during this phase the star loses most of its initial mass and reaches its maximum radius."799 The planet will spiral-in aud evaporate totally (or in rare cases will accrete mass and become a close. low-mass companion to the star) if the planets orbital distance is within the reach of the stars radius during the AGB phase (Livio&Soker1934).," The planet will spiral-in and evaporate totally (or in rare cases will accrete mass and become a close, low-mass companion to the star) if the planet's orbital distance is within the reach of the star's radius during the AGB phase \citep{Ls:84}."800. An estimate ol the maximum planet mass that can be evaporated inside an AGB envelope can be obtained by equating the location of the evaporation region (where the local sound speed in the stellar envelope matches (the escape velocity from (he planets surface) to the energy required to expel the envelope (Soker1996.1998:Nelemans&Tauris1993).," An estimate of the maximum planet mass that can be evaporated inside an AGB envelope can be obtained by equating the location of the evaporation region (where the local sound speed in the stellar envelope matches the escape velocity from the planet's surface) to the energy required to expel the envelope \citep{Sok:96,Sok:98,Nt:98}."801. The value of this ANIM Mass is verv uncertain because it depends on several factors. such as (lie efficiency of envelope ejection (PortegiesZwart&Yungelson1993).. which are largely unknown.," The value of this maximum mass is very uncertain because it depends on several factors, such as the efficiency of envelope ejection \citep{Pzy:98}, which are largely unknown."802 Using (he simplified formalism of Nelemans&Tauris(1998) we find that planets wil masses less than 0.014 or 15 (where is the Jupiter mass) will evaporate inside (ie envelope ol an AGB star with main sequence mass of |M., Using the simplified formalism of \cite{Nt:98} we find that planets with masses less than 0.014 or 15 (where is the Jupiter mass) will evaporate inside the envelope of an AGB star with main sequence mass of 1.803.. This mass limit is much higher. ~ 120 (O.11. M.) well into the stellar regime. if the planet (or brown clwarl) is engulled inside ihe AGB envelope of à 5 star.," This mass limit is much higher, $\sim$ 120 (0.11 ) well into the stellar regime, if the planet (or brown dwarf) is engulfed inside the AGB envelope of a 5 star."804 We can therefore safely assume that planets less massive than 15 (hat are engulfed. will be dissipated. because this limit corresponds to the temperature (and therefore planets escape velocity) reached inside the AGB envelope for the lowest mass stars (in the range examined here).," We can therefore safely assume that planets less massive than 15 that are engulfed, will be dissipated, because this limit corresponds to the temperature (and therefore planet's escape velocity) reached inside the AGB envelope for the lowest mass stars (in the range examined here)."805" Note (hat this planet mass limit is well below the mass of the brown cw (52 Nj)) recently discovered bv Maxtedetal.(2006) orbiting an under-massive white dwarl,", Note that this planet mass limit is well below the mass of the brown dwarf (52 ) recently discovered by \cite{Max:06} orbiting an under-massive white dwarf.806 On the other hand. the case of total planet evaporation (lor a planet in a close orbit around a solar-like star) has been proposed to explain the formation of single under-massive white," On the other hand, the case of total planet evaporation (for a planet in a close orbit around a solar-like star) has been proposed to explain the formation of single under-massive white"807the ambient ICAL. we assume that dissipation occurs ouly in the regions sumroundiug the buovaut eas.,"the ambient ICM, we assume that dissipation occurs only in the regions surrounding the buoyant gas."808 To this eud we impose a condition that switches on viscous effects provided that the fraction of the injected σας in a given cell is much simaller than unity., To this end we impose a condition that switches on viscous effects provided that the fraction of the injected gas in a given cell is much smaller than unity.809" We poiut out that the value of viscosity iu the ICAL just as any other transport paralucters such as. ee thermal conduction. is highlv ""uncertain. and especially the role of maeuetic fields is We inupleineuted a fully compressible version of the viscous velocity diffusion equation iu the FLASII code."," We point out that the value of viscosity in the ICM, just as any other transport parameters such as, e.g., thermal conduction, is highly uncertain, and especially the role of magnetic fields is We implemented a fully compressible version of the viscous velocity diffusion equation in the FLASH code."810 Velocity diffusion was simulated by solving the moments equation where and where all other saubols have their usual 1icaniug., Velocity diffusion was simulated by solving the momentum equation where and where all other symbols have their usual meaning.811 We switched off radiative cooling because tle initial cooling tine iu the center is longer than the overall duration of the simulation., We switched off radiative cooling because the initial cooling time in the center is longer than the overall duration of the simulation.812 Towever. we calculate the radiative cooling rates in order to compare them with the viscous lieating rates.," However, we calculate the radiative cooling rates in order to compare them with the viscous heating rates."813" For this purpose we use the fit to the cooling function by Tozzi&Norman(2001).. which is based on detailed caleulatious by Sutherlaud&Dopita(1993) where s; is the lou uunber deusitv aud the uuits for Apt are keV. For an average metallicity Z=0.52... the constants in equation (8) area=LT. 3=O. Cp=SG«10 7, Co—58<102 and Cs=102 and we can approximate vj,=CX|0.530X.6.10.25YMpmuy"," For this purpose we use the fit to the cooling function by \citet{to01}, which is based on detailed calculations by \citet{sd93}814 where $n_{i}$ is the ion number density and the units for $k_{B}T$ are keV. For an average metallicity $Z=0.3 Z_{\odot}$, the constants in equation (8) are $\alpha =-1.7$, $\beta =0.5$, $C_{1}=8.6\times 10^{-3}$ , $C_{2}=5.8\times 10^{-2}$ and $C_{3}=6.4\times 10^{-2}$ and we can approximate $n_{i}n_{e}=(X+0.5Y)(X+0.25Y)(\rho/m_{p})^{2}$."815 The: units: of+ A are +LO2272 ere eni?3 sf., The units of $\Lambda$ are $10^{-22}$ erg $^{3}$ $s^{-1}$.816 The top paiels in Figure 1 show a time sequence of density nia», The top panels in Figure 1 show a time sequence of density maps.817" One can observe that the eas rises subsonicallv iu the cluster atinosphere and spreads out laterally,", One can observe that the gas rises subsonically in the cluster atmosphere and spreads out laterally.818 No strong shocks are present iu this simulation. which imuplies hat heating is gentle in aerecmeut withChandra observatious.," No strong shocks are present in this simulation, which implies that heating is gentle in agreement with observations."819 Deusity waves have inaxiuuni wuplitudes of up to about 20 to 30 per cent close to the cluster ceucr (~ 20 kpce) and decrease as the waves propagate The bottom panels in Figure 1 preseut the evolution of the viscous dissipation rate., Density waves have maximum amplitudes of up to about 20 to 30 per cent close to the cluster center $\sim$ 20 kpc) and decrease as the waves propagate The bottom panels in Figure 1 present the evolution of the viscous dissipation rate.820 Heating waves generated by subsequent ACN activations are clearly visible aud tle energv dissipated in these waves is spatially distributed in a relatively sviuinetric manner., Heating waves generated by subsequent AGN activations are clearly visible and the energy dissipated in these waves is spatially distributed in a relatively symmetric manner.821 The timescale for the wave pattern to reach a particular region is shorter than the local cooling time., The timescale for the wave pattern to reach a particular region is shorter than the local cooling time.822 Thus. this heating mechamisi meets at least one of the basic requirements for this model to be able to reach a quasi-steady state.," Thus, this heating mechanism meets at least one of the basic requirements for this model to be able to reach a quasi-steady state."823 We note that the wave frouts propagate at slightly above the sound speed (Mach uunuber ~1.25: faster than the buovautly risiug bubbles) as can be seen from Figure 2 by dividing the radius of au azunulus by the time it takes for the wave reach it., We note that the wave fronts propagate at slightly above the sound speed (Mach number $\sim 1.25$; faster than the buoyantly rising bubbles) as can be seen from Figure 2 by dividing the radius of an annulus by the time it takes for the wave reach it.824 It is quite likely that more than one ripple is generated ver episode of AGN activity., It is quite likely that more than one ripple is generated per episode of AGN activity.825 That is. subsequeut outbursts nay occur when the bubble has not vet settled down roni the previous outburst and it still overpressured. eadiug to complex time-depeucdence.," That is, subsequent outbursts may occur when the bubble has not yet settled down from the previous outburst and it still overpressured, leading to complex time-dependence."826 We assumed that heo radio source is intermittent on a time scale of 1.5«10* vrs., We assumed that the radio source is intermittent on a time scale of $1.5\times 10^7$ yrs.827 This simplified assuuptiou on the behavior of the source reproduces two phenomena: (4) the inflation of wo well-defined cavities frou: the cumulative effects. of uultiple outbursts and Gi) the production of a nuuber of ripples or deusitvavaves that propagate racially outward at the speed of sound. as the pressure pulse from cach outburst inflates the expanding cavity slehtly (sec Fig.," This simplified assumption on the behavior of the source reproduces two phenomena: (i) the inflation of two well-defined cavities from the cumulative effects of multiple outbursts and (ii) the production of a number of ripples or density-waves that propagate radially outward at the speed of sound, as the pressure pulse from each outburst inflates the expanding cavity slightly (see Fig."828 1), 1).829 The fragmentary. scalloped appearance of the cavities and sound waves is probably overemphasized because the siuulation is two-dimensional.," The fragmentary, scalloped appearance of the cavities and sound waves is probably overemphasized because the simulation is two-dimensional."830 The simall-scale structure would prestunably be suppressed in a three-«dinieusional model viewed in projection onto the plaue of the sky., The small-scale structure would presumably be suppressed in a three-dimensional model viewed in projection onto the plane of the sky.831 Note that the waves disperse as they propagate away from the center., Note that the waves disperse as they propagate away from the center.832 This dispersion is almost cutirely due to explicit velocity diffusion. as tests without this effect have demonstrated.," This dispersion is almost entirely due to explicit velocity diffusion, as tests without this effect have demonstrated."833 We stress that our use of the Spitzer viscosity is iueaut to be illustrative and lay not accurately represent inonientun transport in the magnetized intracluster medium., We stress that our use of the Spitzer viscosity is meant to be illustrative and may not accurately represent momentum transport in the magnetized intracluster medium.834 For onc thing. maguetic shear stress is likelv to dominate over molecular viscosity in the transport of bulk momentum.," For one thing, magnetic shear stress is likely to dominate over molecular viscosity in the transport of bulk momentum."835 This could either enhance or suppress the dissipation of sound wave. aud will almost certainly make the dependence of stress ou the velocity field iore complicated.," This could either enhance or suppress the dissipation of sound wave, and will almost certainly make the dependence of stress on the velocity field more complicated."836" For another. in this macroscopic formu, of momentum transport the rate of dissipation (due to reconnection) is nonlocallv related to the stress tensor."," For another, in this macroscopic form of momentum transport the rate of dissipation (due to reconnection) is nonlocally related to the stress tensor."837 Ποιοι of these effects will require high-resolution imaenuetolvdrodvuaimical siuulations., Treatment of these effects will require high-resolution magnetohydrodynamical simulations.838 Moreover. magnetic fields could introduce effects simular to bulk viscosity. as a result of plasia nucroistabilitiss.," Moreover, magnetic fields could introduce effects similar to bulk viscosity, as a result of plasma microinstabilities."839 In our simulations we neglected bulk viscosity. since it vanishes for au ideal gas.," In our simulations we neglected bulk viscosity, since it vanishes for an ideal gas."840 We note that bulk viscosity. 1 present. could dissipate waves even iore effiicicutly.," We note that bulk viscosity, if present, could dissipate waves even more efficiently."841 FinaIv. we have ucelected the effects of thermal conduction. Which (assunune Spitzer couductivity) could damp the sou waves more quickly than Spitzer viscosity (since the couductive dissipation exceeds viscous one by a factor ~10 uider simplified asstuuption that waves are plane aud Lucar aud that the eas has constant density and pressure and eravity can be neglected (Laudau&Litshitz 1975)))," Finally, we have neglected the effects of thermal conduction, which (assuming Spitzer conductivity) could damp the sound waves more quickly than Spitzer viscosity (since the conductive dissipation exceeds viscous one by a factor $\sim 10$ under simplified assumption that waves are plane and linear and that the gas has constant density and pressure and gravity can be neglected \citep{landau}) )."842 Since couductivitv is expected to be suppressed by magnetic fields. a realistic assessment of whether conduction cuhances the damping rate of sounds waves is beyond the scope of this Recognizing these caveats. in Fieure 2 we compute the ratio of the viscous heating rate to the raciative cooling rate as afunction of time. averaged over a series of concentric annuli around the cluster ceuter.," Since conductivity is expected to be suppressed by magnetic fields, a realistic assessment of whether conduction enhances the damping rate of sounds waves is beyond the scope of this Recognizing these caveats, in Figure 2 we compute the ratio of the viscous heating rate to the radiative cooling rate as afunction of time, averaged over a series of concentric annuli around the cluster center."843Using eq. (,Using eq. (8441) for the optical depth of free-free emission under the Altenhoff approximation. an optical depth of unity at 1.3 cm and 6.9 mm correspond to emission measures of 2.1x10? and 8.4x10° pe em? respectively.,"1) for the optical depth of free-free emission under the Altenhoff approximation, an optical depth of unity at 1.3 cm and 6.9 mm correspond to emission measures of $2.1 \times 10^9$ and $8.4 \times 10^9$ pc $^{-6}$ respectively."845 Hence. as mentioned in refindi.. the two sources that have continuum emission that 1s optically thick between 1.3 cm and 6.9 mm (40.28-0.22 and 40.62-0.14) can be classified as hypercompact regions.," Hence, as mentioned in \\ref{indi}, the two sources that have continuum emission that is optically thick between 1.3 cm and 6.9 mm (40.28–0.22 and 40.62–0.14) can be classified as hypercompact regions."846 Three sources. 38.66+0.08. 39.39-0.14 and 42.43-0.26. are ultracompact regions. while the source 42.70-0.15 is potentially a hypercompact region.," Three sources, 38.66+0.08, 39.39–0.14 and 42.43–0.26, are ultracompact regions, while the source 42.70–0.15 is potentially a hypercompact region."847 The lack of centimeter wave counterparts for the majority of the sample is consistent with the results from previous work., The lack of centimeter wave counterparts for the majority of the sample is consistent with the results from previous work.848 This could arise from two scenarios: the methanol masers could be associated with very early phases of massive star formation that had their regions quenched by rapid accretion., This could arise from two scenarios: the methanol masers could be associated with very early phases of massive star formation that had their regions quenched by rapid accretion.849 Alternatively. the masers could arise around intermediate mass stars whose tonizing flux is too weak to result in detectable regions.," Alternatively, the masers could arise around intermediate mass stars whose ionizing flux is too weak to result in detectable regions."850 To try to distinguish between the two scenarios. we adopt two approaches.," To try to distinguish between the two scenarios, we adopt two approaches."851 First. we use the centimeter wave data to obtain upper limits on the sizes of any undetected regions and the ionizing radiation of the central star.," First, we use the centimeter wave data to obtain upper limits on the sizes of any undetected regions and the ionizing radiation of the central star."852" Assuming that any undetected region is optically thick at frequency. v. and that the electron temperature in the region is 7,=107K. the solid angle of the source. O, is related to the flux density. S, by where B,(T) is the black body function."," Assuming that any undetected region is optically thick at frequency, $\nu$, and that the electron temperature in the region is $T_e = 10^4$K, the solid angle of the source, $\Omega_s$ is related to the flux density, $S_\nu$ by where $B_\nu(T)$ is the black body function."853 Using the 3c flux density limits at 1.3 em (v=22.46 GHz). we calculate the limits on the source size. which are tabulated in Table 4..," Using the $3\sigma$ flux density limits at 1.3 cm $\nu = 22.46$ GHz), we calculate the limits on the source size, which are tabulated in Table \ref{table4}."854" Further. we have a constraint or the emission measure. which to first order can be taken to be /7/ where 7, is the electron density and / is the size of the source."," Further, we have a constraint on the emission measure, which to first order can be taken to be $n_e^2 l$ where $n_e$ is the electron density and $l$ is the size of the source."855 We then use ionization equilibrium to calculate limits on the ionizing flux of the central star. the results being tabulated in Table 4..," We then use ionization equilibrium to calculate limits on the ionizing flux of the central star, the results being tabulated in Table \ref{table4}."856" The limits on the ionizing flux from the central object are not inconsistent with the presence of massive stars since the optical depth of free-free emission at 1.3 em (7,3 1n Table 4)) is unknown.", The limits on the ionizing flux from the central object are not inconsistent with the presence of massive stars since the optical depth of free-free emission at 1.3 cm $\tau_{1.3}$ in Table \ref{table4}) ) is unknown.857 However. the limits or the source size show that any ionized region nust be confined to a volume that is comparable to that of the solar system (up to the Kuiper belt).," However, the limits on the source size show that any ionized region must be confined to a volume that is comparable to that of the solar system (up to the Kuiper belt)."858 As mentioned previously. these results could also be explained by the central objects being intermediate mass stars.," As mentioned previously, these results could also be explained by the central objects being intermediate mass stars."859 It is worth pointing out that the HC regions associated with CRL 2136. W33 A. NGC 2391. NGC 7538 IRS9 (??).. which all have bona fide associated class II CH;OH masers. would not or only marginally have been detected at the flux density limits. of our VLA observations.," It is worth pointing out that the HC regions associated with CRL 2136, W33 A, NGC 2591, NGC 7538 IRS9 \citep{ment04, van05}, which all have bona fide associated class II $_3$ OH masers, would not or only marginally have been detected at the flux density limits of our VLA observations."860 Consequently. the sizes that these authors determine for the above sources (80. 150. 20. and 50 AU. respectively) are all at or lower than the upper limits on sizes we present in Table 4..," Consequently, the sizes that these authors determine for the above sources (80, 150, 20, and 50 AU, respectively) are all at or lower than the upper limits on sizes we present in Table \ref{table4}."861 An alternate approach to the problem is to fit the infrared flux densities using models of young stellar objects which provides constraints on the physical parameters of the sources., An alternate approach to the problem is to fit the infrared flux densities using models of young stellar objects which provides constraints on the physical parameters of the sources.862 We used the SED fitter of ?.. which uses a grid of 200.000 precomputed model SEDs spanning a wide range of evolutionary stages for different stellar masses (assuming that stars form by accretion through a disk and envelope).," We used the SED fitter of \citet{robi07}, which uses a grid of 200,000 precomputed model SEDs spanning a wide range of evolutionary stages for different stellar masses (assuming that stars form by accretion through a disk and envelope)."863 The fittingprocedure involves interpolation of the model fluxes to the apertures used to perform the photometry. scaling them to a number of distances between dj; and diay (Calculated from the uncertainties in the distance determination). followed by fitting to the data with the visual extinction. Αν. being a free parameter (allowed to vary between 0 and 100 magnitudes in our fitting).," The fittingprocedure involves interpolation of the model fluxes to the apertures used to perform the photometry, scaling them to a number of distances between $d_{\mathrm{min}}$ and $d_{\mathrm{max}}$ (calculated from the uncertainties in the distance determination), followed by fitting to the data with the visual extinction, $A_V$, being a free parameter (allowed to vary between 0 and 100 magnitudes in our fitting)."864 The extinction model used by ? is the method of ? modified for the mid-infrared extinction properties derived by 9, The extinction model used by \citet{robi07} is the method of \citet{kim94} modified for the mid-infrared extinction properties derived by \citet{inde05}.865 To account for possible calibration errors between different data sets. we set the minimum uncertainty in the flux densities to be10%.," To account for possible calibration errors between different data sets, we set the minimum uncertainty in the flux densities to be."866". For the millimeter and submillimeter data. the aperture sizes were set to the source sizes measured by ""JMFEIT""."," For the millimeter and submillimeter data, the aperture sizes were set to the source sizes measured by “JMFIT”."867" The measured source sizes for the 1.2 mm data typically ranged from 10 to 40"". while for the 870 jam data. the sizes were 20 to 40""."," The measured source sizes for the 1.2 mm data typically ranged from 10 to $''$, while for the 870 $\mu$ m data, the sizes were 20 to $''$."868 The visual extinetion. was set to vary between 0 and 100 magnitudes., The visual extinction was set to vary between 0 and 100 magnitudes.869 The SED fitter provides the parameters of the models that fit the data in order of increasing y- goodness of fit, The SED fitter provides the parameters of the models that fit the data in order of increasing $\chi^2$ goodness of fit.870 We calculate the mean and standard deviatio1 of the stellar mass (M.). temperature (T..). radius (R.). envelope accretion rate (M). age. total luminosity ο). visual extiction (Ay). and inclination to the line of sight (/) from the mocels using weighting in accordance with the v probability distribution.," We calculate the mean and standard deviation of the stellar mass $M_*$ ), temperature $T_*$ ), radius $R_*$ ), envelope accretion rate $\dot{M}$ ), age, total luminosity $L_{tot}$ ), visual extinction $A_V$ ), and inclination to the line of sight $i$ ) from the models using weighting in accordance with the $\chi^2$ probability distribution."871 The standard deviation is typically asymmetric about the mean. anc in some cases unrealistically small when few models fit the data and the difference in y between successive models ts large.," The standard deviation is typically asymmetric about the mean, and in some cases unrealistically small when few models fit the data and the difference in $\chi^2$ between successive models is large."872 The results of this study are summarized in Table 5.. and the model fits are shown in Figure 3..," The results of this study are summarized in Table \ref{table5}, , and the model fits are shown in Figure \ref{sedfits}. ."873 We do not show any disk parameters since the models are dominated by the envelope and the disk mass is small compared to the mass of the central star., We do not show any disk parameters since the models are dominated by the envelope and the disk mass is small compared to the mass of the central star.874y.ars and las a shallower radial profile.,stars and has a shallower radial profile.875 So the ratios iu +1e tables above are definite upper Buts., So the ratios in the tables above are definite upper limits.876" In order to take ooito account the effect that i1 late-type systems the gas 'outributes significantly to the eravitatioual force we have ""added"" for types Scd aud Sd a similar amount of gas as oeji stars aud half of hat for Sc's.", In order to take into account the effect that in late-type systems the gas contributes significantly to the gravitational force we have “added” for types Scd and Sd a similar amount of gas as in stars and half of that for Sc's.877" The distribution of IL, iu spiral galaxies ix a lore conrplex matter: it is often centrally peaked. although sole Sb galaxies exhibit central holes (for a recent review. see Ivenney 1997)."," The distribution of $_2$ in spiral galaxies is a more complex matter; it is often centrally peaked, although some Sb galaxies exhibit central holes (for a recent review, see Kenney 1997)."878 The molecular fraction of the eas appears to be lower iu low-mass aud late-type galaxies. assuming that the conversion factor from CO to molecular livdrogen isuniversal’.," The molecular fraction of the gas appears to be lower in low-mass and late-type galaxies, assuming that the conversion factor from CO to molecular hydrogen is."879.. Siuee our sample salaxies are eenerallv low-mass. later-type svstems. we believe that the corrections for molecular gas are small. and therefore contribute little to the correction for the preseuce of gas.," Since our sample galaxies are generally low-mass, later-type systems, we believe that the corrections for molecular gas are small, and therefore contribute little to the correction for the presence of gas."880 We added (a) the galaxies from vau der να Searle (1982) to the sample. (b) our Galaxy using the Lewis Freeuiai (1989) velocity dispersion and the structural parameters m van der Ίνα (1990). aud (ο) the observational results for NGC[88 from Cerssen et al. (," We added (a) the galaxies from van der Kruit Searle (1982) to the sample, (b) our Galaxy using the Lewis Freeman (1989) velocity dispersion and the structural parameters in van der Kruit (1990), and (c) the observational results for NGC488 from Gerssen et al. ("8811997).,1997).882 We leave the few carly type (SO aud Sa) galaxies out of the discussion. because the componcut seperation in the surface brightuess distributions is troublesome aud sole of our asstunptions (iu particular the selt-exavitatiug nature of the disks) are probably seriously svrong.," We leave the few early type (S0 and Sa) galaxies out of the discussion, because the component seperation in the surface brightness distributions is troublesome and some of our assumptions (in particular the self-gravitating nature of the disks) are probably seriously wrong."883 Iu order to be able to trace the origin of our results. we first show iu Fie.," In order to be able to trace the origin of our results, we first show in Fig."884 1 the radial aud vertical scale leneths of the sample as a function of the rotation velocity., 1 the radial and vertical scale lengths of the sample as a function of the rotation velocity.885 Both increase with Vor. which would be expected intuitively.," Both increase with $V_{\rm rot}$, which would be expected intuitively."886 The main result is preseuted in Figs., The main result is presented in Figs.887 2 aud 3., 2 and 3.888 From Fig., From Fig.889 2 we see that the vertical velocity dispersions. that have been derived frou lvdrostatic equilibrimm. increase with the rotation speed (the radial velocity dispersions do the sale automatically as a result of the use of the Bottcma relations).," 2 we see that the vertical velocity dispersions, that have been derived from hydrostatic equilibrium, increase with the rotation speed (the radial velocity dispersions do the same automatically as a result of the use of the Bottema relations)."890 For the slowest rotation speeds tje. predicted vertical velocity dispersion is on the order of 10-20 kin 1 which is close to that observed in the neutral hydrogen iu face-on galaxies (van der Kamit Shostak 1981).," For the slowest rotation speeds the predicted vertical velocity dispersion is on the order of 10-20 km $^{-1}$, which is close to that observed in the neutral hydrogen in face-on galaxies (van der Kruit Shostak 1984)."891 The distribution of the axis ratio of the velocity clipsoid with morphological type is as follows: Not much of a trend is seen here., The distribution of the axis ratio of the velocity ellipsoid with morphological type is as follows: Not much of a trend is seen here.892 It is in order to coment here briefly on the effects of our corrections for the eas to obtain vertical velocity dispersious., It is in order to comment here briefly on the effects of our corrections for the gas to obtain vertical velocity dispersions.893 Frou. our discussion above we conclude that there would be ιο systematic effect introduced. as ai function of rotation velocity., From our discussion above we conclude that there would be no systematic effect introduced as a function of rotation velocity.894 Furthermore. taking away our correction altogethero reduces the values for the average axis ratio in the table just eiven to about 0.55 for Scd aud Sed," Furthermore, taking away our correction altogether reduces the values for the average axis ratio in the table just given to about 0.55 for Scd and Sd"895Stopping our calculations after [ Cir is justified. which can be seen frou Fig. 5..,"Stopping our calculations after 4 Gyr is justified, which can be seen from Fig. \ref{age},"896" where the mass distribution at 0.02 AU for different ages of the system is shown for a Jupiter anda Neptunemass planet. respectively,"," where the mass distribution at 0.02 AU for different ages of the system is shown for a Jupiter– and a Neptune–mass planet, respectively."897 One can see that the main loss takes place in the first Cir after the system's origin when high energy stellar cussion is higher., One can see that the main loss takes place in the first Gyr after the system's origin when high energy stellar emission is higher.898 At later stages. the mass loss is negligible compared with the loss during carly stages.," At later stages, the mass loss is negligible compared with the loss during early stages."899the observations. although it is ecnerally realized that extra euecrgyv mst be furnished to eet photous out iu the GRB. by saving that there is an efficiency. often taken to be ~LOY.,"the observations, although it is generally realized that extra energy must be furnished to get photons out in the GRB, by saying that there is an efficiency, often taken to be $\sim 10\%$."900 We wish to poiut out that there is observational support for our choice of the LAIC as a site for the loug bursts., We wish to point out that there is observational support for our choice of the LMC as a site for the long gamma-ray bursts.901 Larssonetal.(2007) provide a new coustraiut for σαλάτα burst progenitor mass., \citet{Lar07} provide a new constraint for gamma-ray burst progenitor mass.902 They show that long-duration gamma-ray bursts (L-CRBs} are much more concentrated on their host galaxy light than core collapse supernova explosions., They show that long-duration gamma-ray bursts (L-GRBs) are much more concentrated on their host galaxy light than core collapse supernova explosions.903 From this they wavhale.” As a template aud close by natural analogue of starburst galaxies they use NGC 1038/39., From this they way As a template and close by natural analogue of starburst galaxies they use NGC 4038/39.904 Γον sav. however. the honinosity function and surface density of clusters an NCC 4038/39 is comparable to that seen in other local star-forming yalacies of varying morphology in which they include the LAUC.," They say, however, the luminosity function and surface density of clusters on NGC 4038/39 is comparable to that seen in other local star-forming galaxies of varying morphology in which they include the LMC."905The line-ofsieht velocities. aud. thus the separation of the peaks in the phase-averaged line proliles. are also affected by the actual size of the neutrou star. for a given stellar compactuess.,"The line-of-sight velocities, and thus the separation of the peaks in the phase-averaged line profiles, are also affected by the actual size of the neutron star, for a given stellar compactness."906 In Figure 3. we show the line profiles measured at παν that originate from two neutron stars of the same compactuess. 2/AL—2.1/6. but of different radii.," In Figure 3, we show the line profiles measured at infinity that originate from two neutron stars of the same compactness, $R/M = 2.41 G/c^2$, but of different radii."907 Clearly. the larger peak separation corresponds to the larger ueutron-star radius.," Clearly, the larger peak separation corresponds to the larger neutron-star radius."908 This effect allows in principle au tudepenclent determiuatiou ol the mass aud radius (1uodulo euission geometry) of a neutron star of kuowu spin frequency. given the shape aud overall redshift of atomic spectral lines.," This effect allows in principle an independent determination of the mass and radius (modulo emission geometry) of a neutron star of known spin frequency, given the shape and overall redshift of atomic spectral lines."909 We studied spectral line profiles from rotating neutron stars taking into account the effects of relativistic Doppler boosts aud stroug gravitational lensiug., We studied spectral line profiles from rotating neutron stars taking into account the effects of relativistic Doppler boosts and strong gravitational lensing.910 We showed that the liue profiles are broad. as expected. and also siguilicautly asyiumetric.," We showed that the line profiles are broad, as expected, and also significantly asymmetric."911 The asyuunetry becomes more prominent wheu the surface emission is nou-uniform., The asymmetry becomes more prominent when the surface emission is non-uniform.912 Our results have a number of plications for the current searches lor gravitationally redshliifted line features iu the spectra of neutron stars., Our results have a number of implications for the current searches for gravitationally redshifted line features in the spectra of neutron stars.913In the original paper. Aharonianetal.(2008) presented a general cleseription of the scenario with calculations of model SEDs. but the obtained spectra were not compared wilh available data.,"In the original paper, \citet{aharonian08} presented a general description of the scenario with calculations of model SEDs, but the obtained spectra were not compared with available data."914 In the present paper. we discuss the multiwavelength properties of the radiation in the internal absorption scenario. and apply the model to the data of two distant AGN. namely LES 0229-200 (2=0.1396) and ος GGA (estimated al z=0.444). detected in TeV band (Aharonianetal.2007:Alin2009:Acciai 2009).," In the present paper, we discuss the multiwavelength properties of the radiation in the internal absorption scenario, and apply the model to the data of two distant AGN, namely 1ES 0229+200 $z=0.1396$ ) and 3C 66A (estimated at $z=0.444$ ), detected in TeV band \citep{aharonian07,aliu09,acciari09*c,reyes09}."915. Here we adopt the proton svnchrotron radiation as the source of primary 5-ravs. and consider (he absorption due to 5-5 pair production both in the οταν production region and in (he surroundings.," Here we adopt the proton synchrotron radiation as the source of primary $\gamma$ -rays, and consider the absorption due to $\gamma$ $\gamma$ pair production both in the $\gamma$ -ray production region and in the surroundings."916 The svnchirotron radiation of secondary pairs gives rise to an additional lower enerev non-thermal component., The synchrotron radiation of secondary pairs gives rise to an additional lower energy non-thermal component.917 The lattercan be calculated sell-consistentlv. aud depends on the primary 5-ray spectrum. (he tuget photon field and the relativistic motion of the 5-rav. production region.," The lattercan be calculated self-consistently and depends on the primary $\gamma$ -ray spectrum, the target photon field and the relativistic motion of the $\gamma$ -ray production region."918 A sketch of the model adopted in this paper is shown in Fig. l..," A sketch of the model adopted in this paper is shown in Fig. \ref{fig:model},"919 and the main ingredients of the model] are described in the figure caption., and the main ingredients of the model are described in the figure caption.920 The primary 5-ravs are produced through svnelirotron radiation of protons., The primary $\gamma$ -rays are produced through synchrotron radiation of protons.921 Generally. in such a scenario (he energy is stored in (he magnetic field and episodically can be transferred (o protons of extremely high energies forming a non-thermal population of particles (seelordetailsAharonian 2000)..," Generally, in such a scenario the energy is stored in the magnetic field and episodically can be transferred to protons of extremely high energies forming a non-thermal population of particles \citep[see for details][]{aharonian00}. ."922 The energy released in non-thermal protons can, The energy released in non-thermal protons can923In this Letter. we combine dvnamies and chemistry in order to study the evolution of molecular Lue profiles toward a dense core forming within a large turbulent cloud.,"In this Letter, we combine dynamics and chemistry in order to study the evolution of molecular line profiles toward a dense core forming within a large turbulent cloud."924 We show that the velocity structure at the outer part of the core can sienilicantlv affect. molecular line proliles., We show that the velocity structure at the outer part of the core can significantly affect molecular line profiles.925 Indeed. simulated line profiles exhibit a mixture of infall and outflow signatures as a [function of time.," Indeed, simulated line profiles exhibit a mixture of infall and outflow signatures as a function of time."926 Thus a snap shot of core conditions of a single object cannot provide a [ull accounting of core formation and evolution toward collapse., Thus a snap shot of core conditions of a single object cannot provide a full accounting of core formation and evolution toward collapse.927 This Letter is organized as follow., This Letter is organized as follow.928 The dvnanmical and chemical models of a core are. presented in 32. results. and summary and discussion are given in §3 and 84. respectively.," The dynamical and chemical models of a core are presented in 2, results, and summary and discussion are given in 3 and 4, respectively."929 What we are interested in Chis study is to follow up the evolution of molecular line profiles of a core forming in a turbulent molecular cloud., What we are interested in this study is to follow up the evolution of molecular line profiles of a core forming in a turbulent molecular cloud.930 For this purpose. we perform a couple of (hree-climensional numerical experiments oLa sell-gravitating. isothermal. turbulent. magnetized molecular cloud.," For this purpose, we perform a couple of three-dimensional numerical experiments of a self-gravitating, isothermal, turbulent, magnetized molecular cloud."931 In fact. we integrate. as a function of time. the isothermal MIID and Poisson equations.," In fact, we integrate, as a function of time, the isothermal MHD and Poisson equations."932 The number of cells used in the experiments is 512%., The number of cells used in the experiments is $512^3$.933 A typical core is covered with more than 32? cells., A typical core is covered with more than $32^3$ cells.934 There are (wo parameters in (he numerical experiments: one is (he plasma 2. which is the ratio of gas pressure to magnetic pressure. and the other is (he Jeans number J. which is the ratio of the one dimensional size of a computational box L. to the Jeans length Ly.," There are two parameters in the numerical experiments: one is the plasma $\beta$, which is the ratio of gas pressure to magnetic pressure, and the other is the Jeans number $J$, which is the ratio of the one dimensional size of a computational box $L$ , to the Jeans length $L_J$."935 A nass-tLo-fIux ratio normalized with its eritical value ye. can be svritten in terms of these two parameters ji—zxJ νο. where we use the critical mass-to-[hux ratio (V/O).-- in Nagano Nagamura (1978).," A mass-to-flux ratio normalized with its critical value $\mu$, can be written in terms of these two parameters $\mu=\pi J\sqrt{\beta/2}$ , where we use the critical mass-to-flux ratio $(M/\phi)_{\rm cr} = (4\pi^2G)^{-1/2}$ in Nagano Nagamura (1978)."936 Initially a uniform molecular cloud is threaded with a uniform nagnelic field., Initially a uniform molecular cloud is threaded with a uniform magnetic field.937 In order to generate a turbulent. flow ancl keep the level of the turbulence inside the molecular cloud. we add velocity perturbations generated in the Fourier space with wavelengths (hat span from half to full size of the box.," In order to generate a turbulent flow and keep the level of the turbulence inside the molecular cloud, we add velocity perturbations generated in the Fourier space with wavelengths that span from half to full size of the box."938" We adjust the input rate of the kinetic enerev so (hat the root-mean-square sonic Mach number AZ, of a turbulent flow becomes 10 (Mac Low 1999: Stone et al.", We adjust the input rate of the kinetic energy so that the root-mean-square sonic Mach number $M_s$ of a turbulent flow becomes 10 (Mac Low 1999; Stone et al.939 1993)., 1998).940 Once a fully saturated turbulent [low is generated. we (turn on (he sell-gravitv of eas and follow up the evolution of a densest core formed in the cloud.," Once a fully saturated turbulent flow is generated, we turn on the self-gravity of gas and follow up the evolution of a densest core formed in the cloud."941 If ¢=0.1 and J=4. then the ji value is 2.8.," If $\beta=0.1$ and $J=4$, then the $\mu$ value is 2.8."942" So the initial molecular cloud is in a highlv supersonic (M,>> 1). Jeans unstable (J> 1). and magnetically super-ceritical (ye> 1) state."," So the initial molecular cloud is in a highly supersonic $M_s>>1$ ), Jeans unstable $J>1$ ), and magnetically super-critical $\mu>1$ ) state."943 since (he combined isothermal MIID and Poisson equations can be written in dimensionless form with the (wo parameters. we canselect anv unitsof. for example. length. (nme. and mass," Since the combined isothermal MHD and Poisson equations can be written in dimensionless form with the two parameters, we canselect any unitsof, for example, length, time, and mass"944"that essentially all of these galaxies (GN~ 6.700) were located in a peak at e~ 0.7 andr, £z2"". ie. 3-5 pixels.","that essentially all of these galaxies $N \sim$ 6,700) were located in a peak at $e \sim$ 0.7 and $r_e \lesssim$, i.e., 3-5 pixels."945" A combination of low 05 and high e values is expected when the fitting algorithni fries to make the bulee profile as flat aud as elongated as possible to trv to fit a bar or iuclude off-ceuter components (poiu sources, very close iuergers. ete)."," A combination of low $n_b$ and high $e$ values is expected when the fitting algorithm tries to make the bulge profile as flat and as elongated as possible to try to fit a bar or include off-center components (point sources, very close mergers, etc.)."946 We visually inspectcc a subsanrple of galaxies iut= this peak using the SDSS SkvServer Object to confirm this expectation., We visually inspected a subsample of galaxies in this peak using the SDSS SkyServer Object to confirm this expectation.947" Second. the my, distribution has a broad bump aroun a,=5.5.6.0."," Second, the $n_b$ distribution has a broad bump around $n_b = 5.5-6.0$."948 The de Vaucouleurs value of 04=Lis not preferred for this subsample., The de Vaucouleurs value of $n_b = 4$ is not preferred for this subsample.949 However. choosing ο= for the cutive sample is still a reasonable choice for the following reason.," However, choosing $n_b=4$ for the entire sample is still a reasonable choice for the following reason."950 When the bulge Séórrsic iudex camo be constrained due to spatial resolution and/or sigual-to-noise limitations. its posterior probability distribution Q@vhich is fully mapped by GIM2D) will be uuiforiily flat between the minimum and maxiuimui allowed values.," When the bulge Sérrsic index cannot be constrained due to spatial resolution and/or signal-to-noise limitations, its posterior probability distribution (which is fully mapped by GIM2D) will be uniformly flat between the minimum and maximum allowed values."951 Our allowed range of values was 0.5-8 based ou previous studies of the Sérrsic index of spheroids., Our allowed range of values was 0.5-8 based on previous studies of the Sérrsic index of spheroids.952 The median value of a flat posterior probability distribution (which we take to be the best-fit value) will therefore be around 1., The median value of a flat posterior probability distribution (which we take to be the best-fit value) will therefore be around 4.953 Tudeecd. if we re-plot Figure 15. for the entire sample with no F-test selection. we see a very stroue peal. at Dp=d. but this peak reflects a lack of constraint on bulee profile rather than its actual shape.," Indeed, if we re-plot Figure \ref{bulge_freen_dist} for the entire sample with no $F$ -test selection, we see a very strong peak at $n_b=4$, but this peak reflects a lack of constraint on bulge profile rather than its actual shape."954 Third. there is an upturm in the ο distribution at »&2 7.5.," Third, there is an upturn in the $n_b$ distribution at $n_b \gtrsim$ 7.5."955" We again examined a plot of r. versus e for these galaxies and found peaks at ο~0 aud ο~0.7 with a uniform distribution in sizes over the range +,SU.", We again examined a plot of $r_e$ versus $e$ for these galaxies and found peaks at $e \sim 0$ and $e \sim 0.7$ with a uniform distribution in sizes over the range $r_e < 3$.956 Visual inspection of galaxies at e0 aud e  0.71 with smaller sizes (rsm LL) showed them to lave nuclear.center sources;," Visual inspection of galaxies at $e \sim 0$ and e $\sim$ 0.7 with smaller sizes $r_e \lesssim $ 4) showed them to have nuclear, sources."957 Galaxies at ο0 aud. larger sizes (ri~ )) did not exhibit any distinguishing characteristic as n group. and ealaxies at c~0.7 and larecr sizes (re~ 37)) had a bar]point source coufiguration.," Galaxies at $e \sim 0$ and larger sizes $r_e \sim $ $-$ ) did not exhibit any distinguishing characteristic as a group, and galaxies at $e \sim 0.7$ and larger sizes $r_e \sim$ $-$ ) had a bar+point source configuration."958" Galaxies with low and high ο values in Figure 15 also have low and high 5,4 values in Figure 1L.", Galaxies with low and high $n_b$ values in Figure \ref{bulge_freen_dist} also have low and high $n_g$ values in Figure \ref{dr7_fn_n4_pS_cmp_struct}.959 All of these different sub-classes of objects highlight the power of conrpariug differeut fitting models to identity different types of galaxy substructures., All of these different sub-classes of objects highlight the power of comparing different fitting models to identify different types of galaxy substructures.960" Galaxy halflight radii fom 55,=Ll aud free n, decompositions ρε aud 7j,5, respectivelv) are quite consistent over the full rauge of allowed ny, values (Figure 16))"," Galaxy half-light radii from $n_b = 4$ and free $n_b$ decompositions $r_{hl,n4}$ and $r_{hl,fn}$ respectively) are quite consistent over the full range of allowed $n_b$ values (Figure \ref{dr7_fn_n4_pS_cmp_radii}) )."961" Not surprisingly. galaxy laltlight radii differ between pure Sersic (0755,55) aud bulge|disk fits at p,> Lwith being 50% larger at vy,= 8."," Not surprisingly, galaxy half-light radii differ between pure Sersic $r_{hl,pS}$ ) and bulge+disk fits at $n_g > 4$ with $r_{hl,pS}$ being $\%$ larger at $n_g = 8$ ."962 This is cutircly due to rgusthe fact that the halflisht radii are calculated by iutegratiug best-fit models with different profiles in their outer wines., This is entirely due to the fact that the half-light radii are calculated by integrating best-fit models with different profiles in their outer wings.963" The bulge radii exhibit the expected shape from the well-known and strong covariance between my, and r,.. and the choice of ο will obviously have a significant impact ou the iieasurements of r.."," The bulge radii exhibit the expected shape from the well-known and strong covariance between $n_b$ and $r_e$ , and the choice of $n_b$ will obviously have a significant impact on the measurements of $r_e$ ."964 Ou the other liaud. it is very important to note that the disk scale length doesnot appear to be affected by the Sérrsic iudex of the bulee for the majority (500) of the galaxies in our sample. aud that the scatter in the disk huninositv-size relation (Figure 7)) therefore does not depend ou the choice of bulge Sérrsic index.," On the other hand, it is very important to note that the disk scale length does appear to be affected by the Sérrsic index of the bulge for the majority $\%$ ) of the galaxies in our sample, and that the scatter in the disk luminosity-size relation (Figure \ref{disk-lumsize}) ) therefore does not depend on the choice of bulge Sérrsic index."965" This apparent lack of dependence of ry on ny, Imav be due to the lack of coustraimt on bulee profile shape discussed earlier. but it mayalso be due to bulges being usually more compact than their disks."," This apparent lack of dependence of $r_d$ on $n_b$ may be due to the lack of constraint on bulge profile shape discussed earlier, but it mayalso be due to bulges being usually more compact than their disks."966 The covariance between measured bulec aud disk parameters will be weaker in galaxies where the two conpouenuts are more spatially distinct., The covariance between measured bulge and disk parameters will be weaker in galaxies where the two components are more spatially distinct.967 More details on the disk hunuinositv-size distribution are given in Simard 2011. in preparation.," More details on the disk luminosity-size distribution are given in Simard 2011, in preparation."968 The New York University Valie-Added Galaxy Catalog (Blantonctal.2005a) provides Sérrsic model structural parameters for galaxies in the SDSS spectroscopic sample., The New York University Value-Added Galaxy Catalog \citep{blanton05a} provides Sérrsic model structural parameters for galaxies in the SDSS spectroscopic sample.969 The details aud tests of the NYU ράσο measurements iucludiug artificial galaxy siauulations are described in the appeudix of Blautouetal.(2005b)., The details and tests of the NYU Sérrsic measurements including artificial galaxy simulations are described in the appendix of \citet{blanton05b}.970. We matched objects in our pure Sérrsic structural catalog with objects in the NYT catalog using MJD. PLATEID and FIBERID for cross-ideutifications. and a match was found for 666.7LO objects.," We matched objects in our pure Sérrsic structural catalog with objects in the NYU catalog using MJD, PLATEID and FIBERID for cross-identifications, and a match was found for 666,740 objects."971 Figure 17 shows the comparison between NYU and GIM2D ealaxy Sérrsic haltlieht radi and indices., Figure \ref{nyu-g2d_cmp} shows the comparison between NYU and GIM2D galaxy Sérrsic half-light radii and indices.972" The trend iu laltlieht radius shown iu the left-laud paucl is filly cousisteut with the NYU simulations if iy.géezd aNd ο ave taken to be equivalent to the put (""true) values used for the NYU simulations η aud yin xespectivolv)."," The trend in half-light radius shown in the left-hand panel is fully consistent with the NYU simulations if $n_{g,gim2d}$ and $r_{hl,gim2d}$ are taken to be equivalent to the input (“true"") values used for the NYU simulations $n_{in}$ and $r_{50,in}$ respectively)."973 The ealaxy half-light radii from the NYT fits are ziialler by about 20% than both their input simulation values and the GIM2D values for objects witli ny25., The galaxy half-light radii from the NYU fits are smaller by about $\%$ than both their input simulation values and the GIM2D values for objects with $n_g \geq 5$.974" There is an offset An ~ 03-0.1 between GIM2D and NYU Sévrsic indices at ay, = 1.", There is an offset $\Delta n$ $\sim$ 0.3-0.4 between GIM2D and NYU Sérrsic indices at $n_g$ = 1.975 This offset depeuds ou galaxy ellipticity: it increases from 0.2 at low ο (< 0.1) to 0.5 at higher ο (2 0.1)., This offset depends on galaxy ellipticity: it increases from 0.2 at low $e$ $<$ 0.1) to 0.5 at higher $e$ $>$ 0.4).976 This dependence on ellipticitv comes from the fact that the NYU profile fits were done ou one-dimensional profiles extracted from two-dimensional iiages usinecireidaer aul., This dependence on ellipticity comes from the fact that the NYU profile fits were done on one-dimensional profiles extracted from two-dimensional images using annuli.977 The offset Aoes not completely disappear even at low ο possibly as a Καμας'esult of the fact that the NYU fits were done our baud nages only whereas our fits were done simultaneously ou g and band images. aud a redder baud will be more meaoninated bv the redder. spheroidal (1.c.. higher Sévrsic idex) compoucut of a galaxy.," The offset does not completely disappear even at low $e$ possibly as a result of the fact that the NYU fits were done on $r-$ band images only whereas our fits were done simultaneously on $g-$ and $r-$ band images, and a redder band will be more dominated by the redder, spheroidal (i.e., higher Sérrsic index) component of a galaxy."978 The comparison between the NYU and GIM2D Sérrsic paralucters therefore shows good agreecnieut elven the ifferences iu how the two sets of parameters were measured., The comparison between the NYU and GIM2D Sérrsic parameters therefore shows good agreement given the differences in how the two sets of parameters were measured.979" The data quality metrics used iu Section ?? show that the CIARD ""SIM|SENTDEDLCARDBIC dataset gives the most robust photometric results."," The data quality metrics used in Section \ref{QAmetrics} show that the GIM2D “SIM+SEXTDEBL+GM2DBKG"" dataset gives the most robust photometric results."980" The photometric data for this dataset are given in Tables 1.. 2 and 3. for the my,= bulee | disk. the pp bulee | disk and the pure Sérrsic decommpositious respectively."," The photometric data for this dataset are given in Tables \ref{sdss_data_table_bd_n4}, \ref{sdss_data_table_bd_fn} and \ref{sdss_data_table_pS} for the $n_b=4$ bulge + disk, the $n_b$ bulge + disk and the pure Sérrsic decompositions respectively."981 Two sets of galaxy. half-light radii are giveu in these tables., Two sets of galaxy half-light radii are given in these tables.982" The semi-major halflight radius 7225, of a galaxy was calculated by individually collapsing the bulge aud disk components outo their respective major axes. adding these two one-dimensionalprofiles intoa elobal galaxy profile and computing the half heht radius of this sununed one-dimensional profile."," The semi-major half-light radius $R_{hl}$ of a galaxy was calculated by individually collapsing the bulge and disk components onto their respective major axes, adding these two one-dimensionalprofiles intoa global galaxy profile and computing the half light radius of this summed one-dimensional profile."983 The circular half helt radius 2.5; was computed by performing curve-of- plotometryin circular apertures on the (i.c.. notli PSF convolved) GIM2D best-fit model image," The circular half light radius $R_{chl}$ was computed by performing curve-of-growth photometryin circular apertures on the (i.e., not PSF convolved) GIM2D best-fit model image"984star formation time-scale.,star formation time-scale.985 Pherefore. when the major merger occurs. the number of stars formed through the starburst is small.," Therefore, when the major merger occurs, the number of stars formed through the starburst is small."986 Note that when stars are formed. with the feedback. the stellar metallicity becomes lower than that in the case of the starburst without the feedback. 7=f0 (see Section 77)).," Note that when stars are formed with the feedback, the stellar metallicity becomes lower than that in the case of the starburst without the feedback, $\beta=f=0$ (see Section \ref{sec:feedback}) )."987 Thus the metallicity becomes small compared to that in the model €. in which most of stars are formed. during the starburst without the supernova feedback.," Thus the metallicity becomes small compared to that in the model C, in which most of stars are formed during the starburst without the supernova feedback."988 Besides the difference between the feedback models during the starburst does not allect the metallicity because of the small number of stars formed during the starburst., Besides the difference between the feedback models during the starburst does not affect the metallicity because of the small number of stars formed during the starburst.989 Thus the metallicities of ellipticals in the model I2 are higher than those in the model A and lower than those in the model €. and the results do not depend on the feedback moclel.," Thus the metallicities of ellipticals in the model E are higher than those in the model A and lower than those in the model C, and the results do not depend on the feedback model."990 Next we investigate the evolution of metallicities of some sample galaxies in order to show the time-scale of the metallicity increase and that most of stars are formed. in disc in the mocels I2 and FE. We explicitly show the evolution of the mean metallicity of four ellipticals in 10..., Next we investigate the evolution of metallicities of some sample galaxies in order to show the time-scale of the metallicity increase and that most of stars are formed in disc in the models E and F. We explicitly show the evolution of the mean metallicity of four ellipticals in \ref{fig:idef}.991 Phe magnitudes and colours of the picked out Luminous cllipticals are Ady=22:00L6LVA —321and A4;=220.0VSHlLi7V3.34 in the mocdels I2 and E. respectively.," The magnitudes and colours of the picked out luminous ellipticals are $M_{V}=-22.0, U-V=1.61, V-K=3.21$ and $M_{V}=-22.0, U-V=1.77, V-K=3.34$ in the models E and F, respectively."992 Those of the faint ellipticals are Ady=18.5.0Vaαμτν-3.07 and Ady=19.0.0.V—L60.V—A3.24. respectively.," Those of the faint ellipticals are $M_{V}=-18.5,993U-V=1.44, V-K=3.07$ and $M_{V}=-19.0, U-V=1.60, V-K=3.24$, respectively."994 This ligure resembles Fie.6 of the models A and B with the starburst model sb. rather than Fig.7. of the mocdels C and D with the starburst model shB. Note that. the starburst model in the models E and. E is the same as that of the models € and D. In the models A and D. there are many cases that the starburst occurs in the middle of the metallicity increase. while in the end of the metallicity increase in the models IE and E. Vhis shows that the star formation time-scale is short enough and that most of stars are formed in disc. where the supernova feedback is effective.," This figure resembles \ref{fig:idab} of the models A and B with the starburst model sbA rather than \ref{fig:idcd}995 of the models C and D with the starburst model sbB. Note that the starburst model in the models E and F is the same as that of the models C and D. In the models A and B, there are many cases that the starburst occurs in the middle of the metallicity increase, while in the end of the metallicity increase in the models E and F. This shows that the star formation time-scale is short enough and that most of stars are formed in disc, where the supernova feedback is effective."996 In the models € and D. many stars are formed during the starburst without the feedback. so tha i0 mean stellar metallicity becomes very high. (see Section. 72?7)).," In the models C and D, many stars are formed during the starburst without the feedback, so that the mean stellar metallicity becomes very high (see Section \ref{sec:feedback}) )."997 On the other hand. in the models A and D. the feedback is ellective even during the starburst.," On the other hand, in the models A and B, the feedback is effective even during the starburst."998 So the resulting CMlis of the models E and E resemble those of the models A and D. while the mean metallicities of the models LE and E are higher than that of the models A and B because of the short star formation time-scale.," So the resulting CMRs of the models E and F resemble those of the models A and B, while the mean metallicities of the models E and F are higher than that of the models A and B because of the short star formation time-scale."999" ""hus most of stars are formed in disc and the dillerence between the CMS with the starburst mocdoels sb. and shB is negligible when the star formation time-scale is short enough.", Thus most of stars are formed in disc and the difference between the CMRs with the starburst models sbA and sbB is negligible when the star formation time-scale is short enough.1000 1n this subsection we investigate how the CALR depends on the parameter an., In this subsection we investigate how the CMR depends on the parameter $\alpha_{hot}$.1001 We adopt ayo=5.5 in the models C and LH. Εις value of ay. hasbeen adopted by Durham eroup (e.g.. Cole et al.," We adopt $\alpha_{hot}=5.5$ in the models G and H. This value of $\alpha_{hot}$ hasbeen adopted by Durham group (e.g., Cole et al."1002 1994)., 1994).1003" In the model G. V5,=240 km ὃν "," In the model G, $V_{hot}=240$ km $^{-1}$ ."1004In this case. the feedback strength d has the same," In this case, the feedback strength $\beta$ has the same"1005The NEW svstem (mocilied bx the DII erowth) is similar in some respects to the svstem wilh ὁ=2: both share the same density. aud radial velocity profiles at small radii.,The NFW system (modified by the BH growth) is similar in some respects to the self-similar system with $\delta = 2$; both share the same density and radial velocity profiles at small radii.1006 Indeed. the timescale calculation for the NEW svstem vields results similar to the 0=2 case. with the only difference being a smaller value for constant. at &=115 ArSPs ! ," Indeed, the timescale calculation for the NFW system yields results similar to the $\delta = 2$ case, with the only difference being a smaller value for constant, at $\kappa = 115$ $M_\odot ^{2/3}$ $^{-1}$."1007This smaller constant gives a timescale of just over 10.000 vears for the DII to grow ten times larger (han its initial mass of 105 M...," This smaller constant gives a timescale of just over 10,000 years for the BH to grow ten times larger than its initial mass of $10^8$ $M_\odot$."1008" This may be accounted for by the more pronounced anisotropy of the NEW DF at larger τας],", This may be accounted for by the more pronounced anisotropy of the NFW DF at larger radii.1009 It should be noted that changing the initial constants (rj. py. and the initial DII mass Aly) can vary these numbers by a [ew orders of magnitude in both directions.," It should be noted that changing the initial constants $r_0$, $\rho_0$, and the initial BH mass $M_0$ ) can vary these numbers by a few orders of magnitude in both directions."1010 From the work of vanderMarel(1999)... which fits an isothermal sphere to a varietv. of galaxies. il seenis that the core radius can be as small as a few (ens of parsecs Lor “power-law galaxies ancl as large as a lew kiloparsecs lor vcore” galaxies.," From the work of \citet{mar99}, which fits an isothermal sphere to a variety of galaxies, it seems that the core radius can be as small as a few tens of parsecs for “power-law” galaxies and as large as a few kiloparsecs for “core” galaxies."1011 Assuming the same scaling laws uses. the density pj will depend onthe value we take for the core radius.," Assuming the same scaling laws \citet{mar99} uses, the density $\rho_0$ will depend onthe value we take for the core radius."1012 According to these scaing laws. a radius of ry=20 pe. for example. corresponds to a denist. of py=8360 AL. . while at ry=2000 pe the density will be py=3 AL. .," According to these scaing laws, a radius of $r_0 = 20$ pc, for example, corresponds to a denisty of $\rho_0 = 8360$ $M_\odot$ $^{-3}$, while at $r_0 = 2000$ pc the density will be $\rho_0 = 3$ $M_\odot$ $^{-3}$."1013 Using these (wo sets of values. and assuming that the initial seed DII mass can vary between 10? M. and 10° ΛΙ. we see that the isothermal sphere can grow by a factor of ten anywhere between a million vears and 10H. years.," Using these two sets of values, and assuming that the initial seed BH mass can vary between $10^5$ $M_\odot$ and $10^9$ $M_\odot$, we see that the isothermal sphere can grow by a factor of ten anywhere between a million years and $10^{14}$ years."1014 For the self-similar svstem with o<1. changing the constants has essenGally no effect. since the timescale is too short: [or ὁ291. however. the timescale can approach a lew billion vears.," For the self-similar system with $\delta < 1$, changing the constants has essentially no effect, since the timescale is too short; for $\delta \gg 1$, however, the timescale can approach a few billion years."1015 The Gimescale for the NEW svstem will not go bevond a lew hundred million vears., The timescale for the NFW system will not go beyond a few hundred million years.1016 It seems. then. that only the isothermal or Gaussian DF ean vield a black hole mass age relation of the (vpe detected by Alerrifieldlefa£.(2000) by acliabalic growth from a collisionless DF.," It seems, then, that only the isothermal or Gaussian DF can yield a black hole mass age relation of the type detected by \citet{mer00} by adiabatic growth from a collisionless DF."1017 The other svstenmis studied here grow more quickly than (he isothermal sphere. mainly because of their stronger central density. cusp.," The other systems studied here grow more quickly than the isothermal sphere, mainly because of their stronger central density cusp."1018 Recent observations (Ferrarese&Merritt.2000:Gebhardt.efaf2000). have [found a strong correlation between the mass of the central DII aid (he line-ol-sight velocity dispersion in the bulge of its host galaxy.," Recent observations \citep{fer00, geb00} have found a strong correlation between the mass of the central BH and the line-of-sight velocity dispersion in the bulge of its host galaxy."1019" Although various theories have been suggested to explain this relationship (e.g.. Haehnelt&INauffimann (200001: Adamsefal. (2001))). none have vet to be proven conclusively,"," Although various theories have been suggested to explain this relationship (e.g., \citet{hae00}; ; \citet{ada01}) ), none have yet to be proven conclusively."1020 This relationship has been shown to follow where a is somewhere between 3.5 and 5., This relationship has been shown to follow where $\alpha$ is somewhere between 3.5 and 5.1021the scleuce target star.,the science target star.1022 ? has show: hat the RAS deviation is as low as alter using a model (Stellar spect‘tun. teuric absorption and Atimonia absorption) to fit an observed NIB spectruu.," \citet{Bean2010} has shown that the RMS deviation is as low as after using a 3-component model (Stellar spectrum, telluric absorption and Ammonia absorption) to fit an observed NIR spectrum."1023 Iu both cases. aLa value of better than 0.01 las been demonstrated showing great potential of precision Doppler measurement in the NIR baud.," In both cases, an $\alpha$ value of better than 0.01 has been demonstrated showing great potential of precision Doppler measurement in the NIR band."1024 Fig., Fig.1025 7 showst he percentage contrition of RV ucertality introduced by telluric coutamination at different a valtes., \ref{fig:Frac_Wav} shows the percentage contribution of RV uncertainty introduced by telluric contamination at different $\alpha$ values.1026 Π no telluric liie removal is performed. the RV uncertainty in te NIR is domiuated by hose caused by eric contamination. Le.. the percentage coutributious are iore 11an in Y. J. A and ty uid.," If no telluric line removal is performed, the RV uncertainty in the NIR is dominated by those caused by telluric contamination, i.e., the percentage contributions are more than in $Y$, $J$, $H$ and $K$ band."1027 Iu. comparison. the percentage contribution of ellric contamination iudicec RV uncertaiuy is2.9%... and in B. Y aud & baud respectively.," In comparison, the percentage contribution of telluric contamination induced RV uncertainty is, and in $B$, $Y$ and $R$ band respectively."1028 As à decreases. Le.. more streneth of telluric lines is 'eiuoved. less RW uucertainty is coutribLect 10 the fina RV μιςertainty budget.," As $\alpha$ decreases, i.e., more strength of telluric lines is removed, less RV uncertainty is contributed to the final RV uncertainty budget."1029 However. there is still asignificant fraction (more than Jol RV uncertalLuly ¢‘Onl‘ibuted by telluric contamination in J. A and dy band even alter of elluriric line strenetl is 'emoved.," However, there is still asignificant fraction (more than ) of RV uncertainty contributed by telluric contamination in $J$, $H$ and $K$ band even after of telluric line strength is removed."1030 The percentage contribution drops below throughout corside'ed observaional baulpasses when more than st'eugthi is removed., The percentage contribution drops below throughout considered observational bandpasses when more than strength is removed.1031 To sum up the discussion. DW uncertaily is dominated by telluric contaminaion iu the NIR baud.," To sum up the discussion, RV uncertainty is dominated by telluric contamination in the NIR band."1032 Therefore. tellric line removal in tve NIB. is a necessary step to reduce the (δις coutziminatiou aud extract nore of Doppler info‘haion iutrinsically carried by a stellar spectrum.," Therefore, telluric line removal in the NIR is a necessary step to reduce the telluric contamination and extract more of Doppler information intrinsically carried by a stellar spectrum."1033 There are works that have been previously done in attempts to uuderstaud the fundamental j»Xhotou-limited RV uucertaiuties based ou high resolution svuthetic stellar spectra., There are works that have been previously done in attempts to understand the fundamental photon-limited RV uncertainties based on high resolution synthetic stellar spectra.1034 ? calculated Q actors [or a se ol syutlieticstellar spectra for solar type dwarl stars., \citet{Bouchy2001} calculated Q factors for a set of syntheticstellar spectra for solar type dwarf stars.1035 We restrict tle coniparisou [9] spectra with he same turbulence velocity (Vj)., We restrict the comparison to spectra with the same turbulence velocity $V_t$ ).1036 Since the spectra for solar type stars in ourdy have a V; «X 1.0 kines1. We OILy compare the results [rom spectra with Vj «of 1.0 kines ?..," Since the spectra for solar type stars in ourstudy have a $V_t$ of 1.0 $\rm{km}\cdot\rm{s}^{-1}$, we only compare the results from spectra with $V_t$ of 1.0 $\rm{km}\cdot\rm{s}^{-1}$ in \citet{Bouchy2001}."1037 Table 5. sΠασος a conparisou of our results to those from 2.., Table \ref{tab:Comp_Bouchy} summarizes a comparison of our results to those from \citet{Bouchy2001}.1038 The Q [actors [rou ourstldy are generally10-15% lower if i ellar rotation is cousidered. i.e.. V sinz-0 km:sLg," The Q factors from ourstudy are generally$-$ lower if no stellar rotation is considered, i.e., $V\sin i$ =0 $\rm{km}\cdot\rm{s}^{-1}$."1039 uay be due a clierent sampling rate in the svuthetic spectra. Q.005 Ain ? aud0.02 A in our λαyer.," It may be due a different sampling rate in the synthetic spectra, 0.005 $\AA$ in \citet{Bouchy2001} and0.02 $\AA$ in our paper."1040 More fiue eatures are seeu iu a spectrum with higher sampling rate aud thus more Doppler iufOrmation is coritained., More fine features are seen in a spectrum with higher sampling rate and thus more Doppler information is contained.1041 At low stellar rotation rate (V sinl and 8 km-s !). our results agree wih theirs witliu656.. which is improved compared to non-rotatiug case because the fiue features are smoothed ouU by stellar rotation.," At low stellar rotation rate $V\sin i$ =4 and 8 $\rm{km}\cdot\rm{s}^{-1}$ ), our results agree with theirs within, which is improved compared to non-rotating case because the fine features are smoothed out by stellar rotation."1042 For fast rotators. ie. V sin—12 kms.|. difference is seen iu the worst case. or which a different limb-darkeniug value might be respousible.," For fast rotators, i.e., $V\sin i$ =12 $\rm{km}\cdot\rm{s}^{-1}$, difference is seen in the worst case, for which a different limb-darkening value might be responsible."1043 ? invest]gated tle precision that can be reached in RV neasureiments fc stellar objects COCjer than solar type sars in the NIB., \citet{Reiners2010} investigated the precision that can be reached in RV measurements for stellar objects cooler than solar type stars in the NIR.1044 The treatineut of tellric lines in their calcilatious wastoblock the regiors where the telluric absorption is over and 30 kinesJ| in the vicinity., The treatment of telluric lines in their calculations wastoblock the regions where the telluric absorption is over and 30 $\rm{km}\cdot\rm{s}^{-1}$ in the vicinity.1045 Following the method described iitheir paper. we calculated the fraction ofthe wavelength rauge alfected by telluric Contamination i 1V.Y. and A band. the results are 2.1%... c... and 50.," Following the method described intheir paper, we calculated the fraction of the wavelength range affected by telluric contamination in $V$ , $Y$ , $J$ and $H$ band, the results are , , and ."1046"656... In comparison. the results are C. Τους, aud for V. Y. J and A band in their paper."," In comparison, the results are , , and for $V$ , $Y$ , $J$ and $H$ band in their paper."1047 The, The1048distance of about 300 pe (Cernis1993:Lulimanetal.1998:Herbst2007). and uuclergoes an eclipse thatlasts ~3.5 vears (Cohen.Herbst&Williams2003). (herealter Paper I).,"distance of about 300 pc \citep{c93, lrll, h07} and undergoes an eclipse thatlasts $\sim 3.5$ years \citep{chw03} (hereafter Paper I)."1049 Like KI 15D it was discovered αἱ Weslevan Universitys Van Vleck Observatory (VVO) as part ol a CCD photometric monitoring program of voung clusters that has been going; on for 15 vears and covers about a thousand stars in several different clusters., Like KH 15D it was discovered at Wesleyan University's Van Vleck Observatory (VVO) as part of a CCD photometric monitoring program of young clusters that has been going on for 15 years and covers about a thousand stars in several different clusters.1050 Tt was not clear [rom Paper I. which covered only live vears of monitoring. whether this lenethv eclipse event would recur aud. if so. on what time scale.," It was not clear from Paper I, which covered only five years of monitoring, whether this lengthy eclipse event would recur and, if so, on what time scale."1051 Now that three additional vears have passed. we have obtained enough data to answer these questions rather clelinitively.," Now that three additional years have passed, we have obtained enough data to answer these questions rather definitively."1052 We have also obtained new color data that help to constrain models of the system., We have also obtained new color data that help to constrain models of the system.1053 It is now clear (ο us that IIENIWI5 is an object worthy of intensive study over the coming vears and we hope that the new evidence for periodic recurrence of (he eclipse will stimulate additional work on it by other investigators., It is now clear to us that HMW15 is an object worthy of intensive study over the coming years and we hope that the new evidence for periodic recurrence of the eclipse will stimulate additional work on it by other investigators.1054 Observations of IC 348 at Weslevan have been obtainedsince 1993: Herbst.Malev& and Cohen.Herbst&Williams(2004) have reported results for Che first five vears. while the findings of the most recent study were documented in (2006).," Observations of IC 348 at Wesleyan have been obtainedsince 1998; \citet{hmw00} and \citet{chw04} have reported results for the first five years, while the findings of the most recent study were documented in \citet{n06}."1055. The interested reader is referred to those papers lor a detailed description of the data accquisition and reduction methods used al VVO., The interested reader is referred to those papers for a detailed description of the data acquisition and reduction methods used at VVO.1056 Six comparison stars (IINIW 3. T. 8. 10. 13. and 17) were emploved in computing differential magnitudes and these displaved standard deviations of less than 0.01 mag in each season.," Six comparison stars (HMW 3, 7, 8, 10, 13, and 17) were employed in computing differential magnitudes and these displayed standard deviations of less than 0.01 mag in each season."1057 Instrumental differential magnitudes (£)) were computed for each star on each night relative to (he average magnitude of comparison stars., Instrumental differential magnitudes ) were computed for each star on each night relative to the average magnitude of comparison stars.1058 These values were transformed (o standard magnitude (7)) using the adopted offset of 11.23 mae. which provides an excellent match to the calibrated European system described below.," These values were transformed to standard magnitude ) using the adopted offset of 11.23 mag, which provides an excellent match to the calibrated European system described below."1059 Differential magnitudes for ILNIW. 15 were given in earlier papers in (his series and an updated file is available upon request to the second author (W. IL)., Differential magnitudes for HMW 15 were given in earlier papers in this series and an updated file is available upon request to the second author (W. H.).1060 Data were also obtained for the last (wo seasons with three European telescopes: the 2-11 Tütchev-Chreten-Coude (RCC) and the 50/70 cm Schmidt (Sem) telescopes of the National Astronomical Observatory Rozhen (Bulearia) and the 1.3-m Ritchev-Cretien telescope of the Skinakas of the Institute of Astronomy. Universitv of Crete (Greece).," Data were also obtained for the last two seasons with three European telescopes: the 2-m Ritchey-Chretien-Coude (RCC) and the 50/70 cm Schmidt (Scm) telescopes of the National Astronomical Observatory Rozhen (Bulgaria) and the 1.3-m Ritchey-Cretien telescope of the Skinakas of the Institute of Astronomy, University of Crete (Greece)."1061" These telescopes are equipped with the following makes of CCD. pixel sizes and scales. in respective order: VersArry (VÀ: 19 yam: 0.25"" /pix). Photometries (Phot: 24 jan: 0.5"" /pix). and SBIG"," These telescopes are equipped with the following makes of CCD, pixel sizes and scales, in respective order: VersArry (VA; 19 $\micron$ ; $\arcsec$ /pix), Photometrics (Phot; 24 $\micron$ ; $\arcsec$ /pix), and SBIG"1062in Fig.,in Fig.1063 2)., 2).1064 Iu kIIz QPO NS systems. these components are the lower frequency ΚΠΣ QPOs. 14. and the low frequency. BO or IIBO-like QPOs. vypo.," In kHz QPO NS systems, these components are the lower frequency kHz QPOs, $\nu_1$, and the low frequency, HBO or HBO-like QPOs, $\nu_{HBO}$."1065 For BIC svstems and lower luminosity NS LAINRBs the correlation involves either two QPOs. or a QPO and a peaked noise component.," For BHC systems and lower luminosity NS LMXRBs the correlation involves either two QPOs, or a QPO and a peaked noise component."1066 Ii all cases the frequency separation is about a decade and an approximate linear relationship (vype~wp) holds., In all cases the frequency separation is about a decade and an approximate linear relationship $\nu_{HBO} \sim \nu_1^{0.95}$ ) holds.1067 The QPO frequencies from the peculiar NS system Cir XN-1 varies over nearly a decade while closely following the PBV correlation and bridging its low aud lieh frequeney euds., The QPO frequencies from the peculiar NS system Cir X-1 varies over nearly a decade while closely following the PBV correlation and bridging its low and high frequency ends.1068 Psaltis. Belloni vau der Whs (1999) noted also that the m vs. Éj relations of different Atoll aud Z-sources line-up with good accuracy.," Psaltis, Belloni van der Klis (1999) noted also that the $\nu_2$ vs. $\nu_1$ relations of different Atoll and Z-sources line-up with good accuracy."1069 The RPM matches precisely the PBV correlation. without resorting to inv additional assumption (see Stella. Vietri Morsiuk 1999).," The RPM matches precisely the PBV correlation, without resorting to any additional assumption (see Stella, Vietri Morsink 1999)."1070" We assume that in al QPO sources. iucludiug DIICSs. 7g;poz275,5; as in IULT28-31 (see Sect.3)."," We assume that in all QPO sources, including BHCs, $\nu_{HBO} \simeq 2\nu_{nod}$ as in 4U1728-34 (see Sect.3)."1071 Fig., Fig.1072" 2A shows 274, aud 14, obtained frou Eqs.", 2A shows $2\nu_{nod}$ and $\nu_\phi$ obtained from Eqs.1073 1-2 as à fiction of μον for corotating orbits and selected values of M and a/AL., 1-3 as a function of $\nu_{per}$ for corotating orbits and selected values of $M$ and $a/M$.1074 The high frequency end of cach line is dictate by the orbital radius reaching the mareinally stable orbit., The high frequency end of each line is dictated by the orbital radius reaching the marginally stable orbit.1075 The separation of the lines in Fie., The separation of the lines in Fig.1076" 2A testifies that while 7, depends weakly outhe mass and more strongly on αν the opposite is true for v,,."," 2A testifies that while $\nu_{nod}$ depends weakly onthe mass and more strongly on $a/M$, the opposite is true for $\nu_\phi$."1077 By taking the weak field (AL/r< 1) aud slow rotation (6/8.« 1) limit of Eqs., By taking the weak field $M/r \ll 1$ ) and slow rotation $a/M \ll 1$ ) limit of Eqs.1078 1-3 the relevaut first order dependence is made explicit. For the case of rotating NSs wo adopt the numerical approach outlined in Sect.," 1-3 the relevant first order dependence is made explicit, For the case of rotating NSs we adopt the numerical approach outlined in Sect."1079 2., 3.1080 Results ave shown in Fie., Results are shown in Fig.1081 2B for à NS mass of 1.95 M... EOS AU and i4= 300. 600. 900 and 1200 Iz (correspouding to a/Af= 0.11. 0.22. 0.31 aud 0.17. respectively).," 2B for a NS mass of 1.95 $_{\odot}$, EOS AU and $\nu_{s} = $ 300, 600, 900 and 1200 Hz (corresponding to $a/M =$ 0.11, 0.22, 0.34 and 0.47, respectively)."1082 Note that the approximate scaliuegs in Eqs., Note that the approximate scalings in Eqs.1083 6-7 remain valid over a wide range of frequencies., 6-7 remain valid over a wide range of frequencies.1084 Ouly for the largest values of vy. ad i. μυ departs substantially from the ~V2 dependenuce.," Only for the largest values of $\nu_{per}$ and $\nu_{s}$, $\nu_{nod}$ departs substantially from the $\sim \nu_{per}^{6/5}$ dependence."1085 The measured QPO and peaked noise frequencies eiviug rise to the PDV correlation are also plotted in Fie., The measured QPO and peaked noise frequencies giving rise to the PBV correlation are also plotted in Fig.1086 2D. Higher kIIz QPO frequencies from NS systems (72) are included (for the sake of clarity NBOs and FBOs were excluded)., 2B. Higher kHz QPO frequencies from NS systems $\nu_2$ ) are included (for the sake of clarity NBOs and FBOs were excluded).1087 The aerecment over the range of frequeucies spauued by cach kz QPO NS svsteii should not be surprising: together with the accurate matching of the correspondiug 7pο relationship in Z-sources. this is indeed part of the evidence ou which the RPM model was proposed.," The agreement over the range of frequencies spanned by each kHz QPO NS system should not be surprising: together with the accurate matching of the corresponding $\nu_1-\nu_2$ relationship in Z-sources, this is indeed part of the evidence on which the RPM model was proposed."1088 However the fact that the dependence of oq 01 Όροι matches the observed vypeo14 correlation to a good accuracy over 73 decades in frequency (down to r4 of a few Iz). euconipassiug both NS aud BITC svstenis. provides additional independent evidence in favor of the RPM.," However the fact that the dependence of $\nu_{nod}$ on $\nu_{per}$ matches the observed $\nu_{HBO} - \nu_{1}$ correlation to a good accuracy over $\sim 3$ decades in frequency (down to $\nu_1$ of a few Hz), encompassing both NS and BHC systems, provides additional independent evidence in favor of the RPM."1089 The observed variation of Vipo 14d 2774 i individual sources (Cir X-1 is the most striking example. see Fie.," The observed variation of $\nu_{HBO}$ and $\nu_1$ in individual sources (Cir X-1 is the most striking example, see Fig."1090 2B) further supports the scaling predicted by the RPM., 2B) further supports the scaling predicted by the RPM.1091" The matching of the observed 0 vs. νι relation in terms of 14, VS. Όρων is also quite accurate.", The matching of the observed $\nu_{2}$ vs. $\nu_{1}$ relation in terms of $\nu_{\phi}$ vs. $\nu_{per}$ is also quite accurate.1092 For EOS AU aud i»= 1.95. the ipo vs. 14 values of most NS LAINRBs are best matched for v. in the ~600 to 900 ITz range.," For EOS AU and $m=1.95$ , the $\nu_{HBO}$ vs. $\nu_{1}$ values of most NS LMXRBs are best matched for $\nu_{s}$ in the $\sim 600$ to 900 Hz range."1093 It is apparent from Fie., It is apparent from Fig.1094 2B, 2B1095The new observations clearly ilentifv a turuover in the SED of JJ2135 at ~350;nn (Fig. 1)).,The new observations clearly identify a turnover in the SED of J2135 at $\sim$ $\mu$ m (Fig. \ref{fig:SED}) ).1096 We use the far-IR photometry (Table 1. and. 2)) to calculate its rest-frame 1000-712 huninosity directly. which is due largely to dust-reprocessed UV lieht aud provides a measure of its iustantaneous SER.," We use the far-IR photometry (Table \ref{tab:Phot} and \citealt{swinbank10a}) ) to calculate its rest-frame $\mu$ m luminosity directly, which is due largely to dust-reprocessed UV light and provides a measure of its instantaneous SFR."1097 Correcting for lensing amplification. wo fud Ly.)=(2.30.2)«101? LL... indicating a SER of ~ MAL. Le?)," Correcting for lensing amplification, we find $L_{\rm bol}=(2.3\pm 0.2)\times 10^{12}$ $_{\odot}$, indicating a SFR of $\sim$ $_{\odot}$ $^{-1}$ \citep{kennicutt98a}."1098 Lay is thus conrparable to that of 2220 and rather higher than that quoted by ? who integrated the best modified blackbody fit to the 350-. 131- and μαι Cinission. missing ΠΙΟ of the energy at rest-frame eS pun. If we parineterise the far-IR SED of JJ21235 using a modified blackbody spectra. a single component," $L_{\rm1099bol}$ is thus comparable to that of 220 and rather higher than that quoted by \citet{swinbank10a} who integrated the best modified blackbody fit to the 350-, 434- and $\mu$ m emission, missing much of the energy at rest-frame $\sim$ $\mu$ m. If we parameterise the far-IR SED of J2135 using a modified blackbody spectrum, a single component"1100"-Ipt cumuiblü £102 σι10 scaled12001 clevenmib=""177 Preprint 15uuau The optically thin. advection-douniiated accretion flows (ADAFs) have been studied. by a πο of authors durimg past several vears (0.8. Naravan & Yi 1991. 1995a. Lh: Abramowicz et 11995: Nidaguuura ct 11997. Abuuuoto. Mineshiee Iusunose 1997: Noiravan ct 11995).","-4pt cmmib10 2 cmmib10 1 '177 ics}} }} 15mm The optically thin, advection-dominated accretion flows (ADAFs) have been studied by a number of authors during past several years (e.g. Narayan $\&$ Yi 1994, 1995a, b; Abramowicz et 1995; Nakamura et 1997, Manmoto, Mineshige Kusunose 1997; Narayan et 1998)."1101 These models are very successful iu describing both spectra and dviauies of accreting black hole svstcms such as those in binaries aud oin low-huuinosity active ealactic απο (AGNs)., These models are very successful in describing both spectra and dynamics of accreting black hole systems such as those in binaries and in low-luminosity active galactic nuclei (AGNs).1102 The observed spectra can be explained as follows., The observed spectra can be explained as follows.1103 The radio cussion is due to the svuchrotron chussion iu turbulent magnetic fields im the accretion flow., The radio emission is due to the synchrotron emission in turbulent magnetic fields in the accretion flow.1104 These synchrotron pliotous serve as seed photons for the inverse Compton process by lot electrons., These synchrotron photons serve as seed photons for the inverse Compton process by hot electrons.1105 Ouce-scattered Compton photons are mainly distributed in the optical baud and twice-scattered Compton plotous. in soft) X-ray band.," Once-scattered Compton photons are mainly distributed in the optical band and twice-scattered Compton photons, in soft X-ray band."1106 Drenisstrahluns due το clectron-electron and clectrou-proton collisions gives rise to the observed hard X-ray spectra., Bremsstrahlung due to electron-electron and electron-proton collisions gives rise to the observed hard X-ray spectra.1107 Thus. these ADAF iodels provide a good framework for nuderstancding the observed spectra.," Thus, these ADAF models provide a good framework for understanding the observed spectra."1108 In these models. both aneulay momentum trausfer aud cucrev dissipation in the accretion flow is asstuned to be undertaken by the turbulent viscosity whose size is specified by so-called à paralcter.," In these models, both angular momentum transfer and energy dissipation in the accretion flow is assumed to be undertaken by the turbulent viscosity whose size is specified by so-called $\alpha$ parameter."1109 For this reason. hereafter we call this type of models the “viscous” ADAF model in this paper.," For this reason, hereafter we call this type of models the “viscous” ADAF model in this paper."1110 The magnetic fields are regarded as of turbulence origin aud are described by another parameter ο) which specifies the ratio of the magnetic pressure to the σας pressure., The magnetic fields are regarded as of turbulence origin and are described by another parameter $\beta$ which specifies the ratio of the magnetic pressure to the gas pressure.1111 However there is no reason to believe that the turbulent viscosity is the only caudidate that coutrols the accretion processes., However there is no reason to believe that the turbulent viscosity is the only candidate that controls the accretion processes.1112 Rather. it is quite natural to think that some types of global magnetic fields mav play an csscutial role.," Rather, it is quite natural to think that some types of global magnetic fields may play an essential role."1113" Indeed. there are some evidences for the presence of such an ordered maguetic ficld in the central region of our Calaxy (οιοι, YusefZadeh. Morris Chance 1981)."," Indeed, there are some evidences for the presence of such an ordered magnetic field in the central region of our Galaxy (e.g., Yusef-Zadeh, Morris Chance 1984)."1114 As Kato. Fukue Mineshige (1998) has pointed out the hvdromagnetie turbulence in accretion disks iav also generate elobal magnetic fields by dynamo processes due to the presence of helical motions.," As Kato, Fukue Mineshige (1998) has pointed out the hydromagnetic turbulence in accretion disks may also generate global magnetic fields by dynamo processes due to the presence of helical motions."1115 In view of such Circluustances. another type of ADAF model las been proposed by one of the present. authors (IKaburaki 1999. 2000: hereafter referred to as [99 and KOO).," In view of such circumstances, another type of ADAF model has been proposed by one of the present authors (Kaburaki 1999, 2000; hereafter referred to as K99 and K00)."1116 In order to distinguish it from the above viscous ADAF models. hereafter we call it the ‘resistive’ ADAF models since energv dissipation in the accretion flow is due to the electric resistivity and aneular momentum transfer is supported not by the viscosity but by the maenetic stress of a large scale 1nagnoetic field.," In order to distinguish it from the above viscous ADAF models, hereafter we call it the “resistive” ADAF models since energy dissipation in the accretion flow is due to the electric resistivity and angular momentum transfer is supported not by the viscosity but by the magnetic stress of a large scale magnetic field."1117 The purpose of the present study is to calculate the expected radiation spectra from ADAFs in a global maenetic field based on the resistive ADAF model. in order to compare its precdictious with those of the viscous ADAF models.," The purpose of the present study is to calculate the expected radiation spectra from ADAFs in a global magnetic field based on the resistive ADAF model, in order to compare its predictions with those of the viscous ADAF models."1118 As a inmost suitable candidate for such a coluparison. Ser is taken up here because it has been observed in niv wave lengths as the nearest galactic micleus aud its spectu has been reproduced many ties x the successively advancing viscous ADAF iuidclels.," As a most suitable candidate for such a comparison, Sgr $^*$ is taken up here because it has been observed in many wave lengths as the nearest galactic nucleus and its spectrum has been reproduced many times by the successively advancing viscous ADAF models."1119 Tn 8?7.. we introduce the set of analytic solutions for resistive ADAFs ina suitably scaled form aud cliscuss their asic Characteristics.," In \ref{scaled}, we introduce the set of analytic solutions for resistive ADAFs in a suitably scaled form and discuss their basic characteristics."1120 The relevaut radiation mechaisis and the methods of calculation of thefluxes are described iu 877.., The relevant radiation mechanisms and the methods of calculation of thefluxes are described in \ref{cal}.1121 These schemes ave applied to Ser in 877. and he results are discussed in comparison with those of the viscous ADAF models., These schemes are applied to Sgr $^*$ in \ref{result} and the results are discussed in comparison with those of the viscous ADAF models.1122 Finally in 877... we sunuucrize the nain results aud discuss some related issues;," Finally in \ref{sum}, , we summerize the main results and discuss some related issues."1123"spectra, with identical settings to those before.","spectra, with identical settings to those before."1124 The aim was to investigate whether an LTE inversion can still capture the propagation of waves and shocks in the lower atmospheric layers., The aim was to investigate whether an LTE inversion can still capture the propagation of waves and shocks in the lower atmospheric layers.1125 Appendix AppendixB: shows some examples of the observed and best-fit profiles of this inversion setup., Appendix \ref{appb} shows some examples of the observed and best-fit profiles of this inversion setup.1126" From the satisfactory reproduction of the observed spectra — excluding the actual Ca line core and maybe the [W1 band — we conclude that the continuum bands defined should be accessible by an LTE inversion (cf.?,fortheCaIIKwing)..", From the satisfactory reproduction of the observed spectra – excluding the actual Ca line core and maybe the IW1 band – we conclude that the continuum bands defined should be accessible by an LTE inversion \citep[cf.][for the Ca II K wing]{owocki+etal1980}.1127" However, we refrain from using these inversion results at present before a rigid investigation of their reliability."," However, we refrain from using these inversion results at present before a rigid investigation of their reliability."1128 The line-core velocities of the Fe I lines at nm and nm were determined as additional measurements of the photospheric velocity field., The line-core velocities of the Fe I lines at nm and nm were determined as additional measurements of the photospheric velocity field.1129" The velocity dispersion of the red channel of 0.7 kms! per pixel is about two times smaller than in the blue channel, giving a better velocity resolution."," The velocity dispersion of the red channel of 0.7 $^{-1}$ per pixel is about two times smaller than in the blue channel, giving a better velocity resolution."1130 Figure 4 shows the temporal evolution of the intensity along the slit in the wavelength bands of Table 1.., Figure \ref{fig5} shows the temporal evolution of the intensity along the slit in the wavelength bands of Table \ref{tab1}.1131" Passing from continuum wavelengths to the Ca line core, the structures visible change drastically."," Passing from continuum wavelengths to the Ca line core, the structures visible change drastically."1132" The tempo-spatial maps from continuum to MW1 are dominated by the structure and the temporal evolution of the granulation, leading to a mainly horizontally («temporal axis) oriented pattern of bright and dark stripes."," The tempo-spatial maps from continuum to MW1 are dominated by the structure and the temporal evolution of the granulation, leading to a mainly horizontally $\equiv$ temporal axis) oriented pattern of bright and dark stripes."1133" For all other maps, the granulation signature is completely lost and exchanged by a vertically (sspatial axis) oriented pattern of isolated (repeated) brightenings."," For all other maps, the granulation signature is completely lost and exchanged by a vertically $\equiv$ spatial axis) oriented pattern of isolated (repeated) brightenings."1134" The brightenings in Hoy or core last only shortly (20-60 sec) and extend over 2"" to 3"" along the slit.", The brightenings in $_{\rm 2V}$ or core last only shortly (20-60 sec) and extend over $^{\prime\prime}$ to $^{\prime\prime}$ along the slit.1135 Many of the brightenings on locations without strong magnetic fields are repetitive with periods of 150 sec to 250 sec., Many of the brightenings on locations without strong magnetic fields are repetitive with periods of 150 sec to 250 sec.1136" Four magnetic elements were intersected by the slit 12"", 15"", 20"", 50""), which are seen all throughout the time series at approximately the same locations."," Four magnetic elements were intersected by the slit $\sim 12^{\prime\prime}$ , $^{\prime\prime}$, $^{\prime\prime}$, $^{\prime\prime}$ ), which are seen all throughout the time series at approximately the same locations."1137" Almost all locations that were inverted with a magnetic atmosphere belong to these four patches; they outline network fields (B.~1.3 kG, Fig. B1))."," Almost all locations that were inverted with a magnetic atmosphere belong to these four patches; they outline network fields $B \sim 1.3$ kG, Fig. \ref{fig6}) )."1138 Other locations only show transient weak polarization signals., Other locations only show transient weak polarization signals.1139 Comparing the map of polarization signal (bottom right of Fig. 4)), Comparing the map of polarization signal (bottom right of Fig. \ref{fig5}) )1140" and that of, e.g, Hoy (bottom left), one can discriminate between three different types of locations in the FOV."," and that of, e.g., $_{\rm 2V}$ (bottom left), one can discriminate between three different types of locations in the FOV."1141" Cospatial to strong photospheric fields, one finds a quasi-static intensity increase with less signatures of oscillations, and a small halo with higher intensity on the neighboring pixels."," Cospatial to strong photospheric fields, one finds a quasi-static intensity increase with less signatures of oscillations, and a small halo with higher intensity on the neighboring pixels."1142" Contrary to the field-free locations, the oscillations on the field concentrations only modulate the emission, but do not lead to its disappearance, especially in the Hog map."," Contrary to the field-free locations, the oscillations on the field concentrations only modulate the emission, but do not lead to its disappearance, especially in the $_{\rm 2R}$ map."1143" Close to fields (y22"" to 27"" and ~37"" to 42""), the periodic structure of the brightenings is most prominent tracks"")."," Close to fields $\sim 22^{\prime\prime}$ to $27^{\prime\prime}$ and $\sim 37^{\prime\prime}$ to $42^{\prime\prime}$ ), the periodic structure of the brightenings is most prominent ”)."1144" In very quiet locations (27"" to 37”), fewer and often non-repetitive brightenings can be found (t~20 min, y 32”)."," In very quiet locations $\sim 27^{\prime\prime}$ to $37^{\prime\prime}$ ), fewer and often non-repetitive brightenings can be found $\sim 20$ min, $\sim 32^{\prime\prime}$ )."1145" To quantify the properties of the intensity and velocity oscillations, we took the Fourier transform of the tempo-spatial maps."," To quantify the properties of the intensity and velocity oscillations, we took the Fourier transform of the tempo-spatial maps."1146" We try to isolate the general properties of the oscillations in the full FOV, and later investigate differences between locations with or without field, or in the very quiet area, by using spatially resolved information."," We try to isolate the general properties of the oscillations in the full FOV, and later investigate differences between locations with or without field, or in the very quiet area, by using spatially resolved information."1147bv strong absorption.,by strong absorption.1148 Finally. the A-vayv luminosity iu the 0.56 keV hand (1.521 keV in the QSO rest frame) is estimated to be 3.1&10/5 erg/s asstuning Ly=50 kan/s/AIpe and gy=0.5. where we corrected ouly for the ealactic absorption.," Finally, the X-ray luminosity in the 0.5–6 keV band (1.8–21 keV in the QSO rest frame) is estimated to be $3.4 \times 10^{45}$ erg/s assuming $H_0=$ 50 km/s/Mpc and $q_0 =0.5$, where we corrected only for the galactic absorption."1149 The huinositv is 5.0«10% ore/s if we also correct for the intrinsic absorption of the continua., The luminosity is $5.0 \times 10^{45}$ erg/s if we also correct for the intrinsic absorption of the continuum.1150 Since the maenification of the lens 1s estimated to be —10 (Chartas2000).. the true luminosity of the QSO is a factor of 10 lower than the above values.," Since the magnification of the lens is estimated to be $\sim$ 10 \citep{Chartas_2000}, the true luminosity of the QSO is a factor of 10 lower than the above values."1151" The observed EW of the cinission line. 960!TA eV iu the QSO vest frame. is an order of magnitude larecr than those of typical Sevfert 1 galaxies (οιο, Mushliotzky. Done. Pounds 1993)."," The observed EW of the emission line, $960^{+1400}_{-480}$ eV in the QSO rest frame, is an order of magnitude larger than those of typical Seyfert 1 galaxies (e.g. Mushotzky, Done, Pounds 1993)."1152 The large EW suggests that a considerable part of direct bean of the ionizing X-ravs is blocked by some intervening material. while the reprocessed enission is not significantly absorbed.," The large EW suggests that a considerable part of direct beam of the ionizing X-rays is blocked by some intervening material, while the reprocessed emission is not significantly absorbed."1153 Thus we reed some low-ionization material which partly covers the central engine and serves as an efficient. N-ray reprocessor., Thus we need some low-ionization material which partly covers the central engine and serves as an efficient X-ray reprocessor.1154 A candidate for such beam blockers and/or reprocessors is he BAL flow., A candidate for such beam blockers and/or reprocessors is the BAL flow.1155 The BAL flow is believed to be a 1iass flow with velocities of 6 «10! Iau/s alone the line of sieht., The BAL flow is believed to be a mass flow with velocities of 1 – 6 $\times 10^4$ km/s along the line of sight.1156 If he flow is neither aligued with the accretiou-disk plane nor he disk axis. aud if the syste is axially svuumetric. the How nmst have a conical structure. as proposed by Elvis (2000).," If the flow is neither aligned with the accretion-disk plane nor the disk axis, and if the system is axially symmetric, the flow must have a conical structure, as proposed by \cite{Elvis_2000}."1157. The BAL flow is believed to cover about LO50% of the solid angele around the ceutral cueine (sxrolik Voit 1998: Coodrich 1997)., The BAL flow is believed to cover about 10–50 of the solid angle around the central engine (Krolik Voit 1998; Goodrich 1997).1158 Then the BAL flow may be a conical thin sheet irradiated from the apex of the cone., Then the BAL flow may be a conical thin sheet irradiated from the apex of the cone.1159 According to Elvis(2000).. the conical BAL flow is optically-thick in the direction of X-ray inadiation while it is optically thin in other directions for photons above 26 keV (sec reffie:schematic)).," According to \cite{Elvis_2000}, the conical BAL flow is optically-thick in the direction of X-ray irradiation while it is optically thin in other directions for photons above $^{>}_{\sim}$ 6 keV (see \\ref{fig:schematic}) )."1160 Then almost all N-rav photons from the central source that enter the BAL flow are cither absorbed or scattered. while the most of re-cinitted aud scattered phnotous escape frou the flow (Elvis—2000).," Then almost all X-ray photons from the central source that enter the BAL flow are either absorbed or scattered, while the most of re-emitted and scattered photons escape from the flow \citep{Elvis_2000}."1161. Thus in spite of the small covering solid augle. the conical BAL flow can be a more effective N-ray reprocessor than a molecular torus or an accretion disk. for which the reprocessing efficiency is limited by self-absorption.," Thus in spite of the small covering solid angle, the conical BAL flow can be a more effective X-ray reprocessor than a molecular torus or an accretion disk, for which the reprocessing efficiency is limited by self-absorption."1162 Although a conical BAL flow is not the only possibility. it is worth studyiug iu more detail," Although a conical BAL flow is not the only possibility, it is worth studying in more detail."1163 Assuming the above econetry. the total intensities of the won I& euissiou aud the Thomson scattered photons are estimated as. andl where FGE) is the photon cussion spectrum from the central X-ray. source inteerated over Li solid angle aud is proportional to E.F; and Ey. 644. eaCE). Opa. wk. and fray are respectively. the edge euergv. the electron-scattering cross section. the absorption cross section. the solid augle of the BAL flow. the iron IN fluorescence vield. and the fraction of mon I absorption over the cutire absorption for the photous above the I edge cnerey.," Assuming the above geometry, the total intensities of the iron K emission and the Thomson scattered photons are estimated as, and where $F(E)$ is the photon emission spectrum from the central X-ray source integrated over $4\pi$ solid angle and is proportional to $E^{-\Gamma}$, and $E_{\rm K}$, $\sigma_{\rm sca}$, $\sigma_{\rm1164abs}(E)$, $\Omega_{\rm BAL}$, $\omega_{\rm K}$, and $f_{\rm FeK}$ are respectively, the edge energy, the electron-scattering cross section, the absorption cross section, the solid angle of the BAL flow, the iron K fluorescence yield, and the fraction of iron K absorption over the entire absorption for the photons above the K edge energy."1165" The factor. 4. is defined as jg=Te(tantE)(Toon|TiUSDFUEWEE?fe FUEWEE, and is 0.30 for T.—Ls. assuming the BAL flow to be neutral and of solar abundance."," The factor, $\eta$, is defined as $\eta = \int_{E_{\rm1166K}}^{\infty}(\sigma_{\rm abs}(E)/(\sigma_{\rm sca} + \sigma_{\rm1167abs}(E)) F(E) dE/\int_{E_{\rm K}}^{\infty} F(E) dE$ , and is 0.30 for $\Gamma=1.8$, assuming the BAL flow to be neutral and of solar abundance."1168 The highest EW. expected when the direct N-ray plioton beam from the central source is totally blocked. is where Eu is the line cuerev.," The highest EW, expected when the direct X-ray photon beam from the central source is totally blocked, is where $E_{\rm e}$ is the line energy."1169 Ou the other hand. when the central engine is directly visible. the EW is the lowest: The factor 1/2 is included because oue of the two BAL cones may be behind the accretiou disk aud not be visible to the observer.," On the other hand, when the central engine is directly visible, the EW is the lowest; The factor $1/2$ is included because one of the two BAL cones may be behind the accretion disk and not be visible to the observer."1170 Thus the laree observed EW cau be explained if most of the direct beam is blocked by the BAL flow. which is generally. believed. to be the case for BAL QSOs.," Thus the large observed EW can be explained if most of the direct beam is blocked by the BAL flow, which is generally believed to be the case for BAL QSOs."1171" Then the observed continu spectrum is dominated by the scattered photons as described by refeqisca,pec.", Then the observed continuum spectrum is dominated by the scattered photons as described by \\ref{eq:sca_spec}.1172 Lhisspeetrumisbetterapprowinatedbyapartialabsor) , This spectrum is better approximated by a partial absorption model (G2001) than a single absorption model.1173," However in the present observation, we do not have enough statistics to distinguish between these two."1174Depending on the inclination angle to the line of sight and the cone angle of the BAL flow. 0. the iron ciission line originating from a certain portion of the BAL cone is either blue or red shifted.," Depending on the inclination angle to the line of sight and the cone angle of the BAL flow, $\theta$, the iron emission line originating from a certain portion of the BAL cone is either blue or red shifted."1175 For BAL QSOs. our liue of sieht is aligned with the BAL flow of a certain azimuthal auele.," For BAL QSOs, our line of sight is aligned with the BAL flow of a certain azimuthal angle."1176 Then most of iron emission we observe is frou the far side of the cone. aud is redshifted with cucrey shifts rauging from 0 to eparfes[cost20)| if 015 deg.," Then most of iron emission we observe is from the far side of the cone, and is redshifted with energy shifts ranging from 0 to $v_{BAL}/c \times | \cos(2\theta) |$ if $\theta>45$ deg."1177 Thus the center of the cussion line is redshitted aud the line is broad., Thus the center of the emission line is redshifted and the line is broad.1178 For T1113)117. the velocity of the BAL fow is ~0.0le=12000 ins (IIlazirdetal.1981) which uuplies a maxiuun enerev shift of ~200 eV if 0~70 dee.," For H1413+117, the velocity of the BAL flow is $\sim 0.04c1179= 12000$ km/s \citep{Hazard_etal_1984} which implies a maximum energy shift of $\sim$ 200 eV if $\theta \sim$ 70 deg."1180 Thus the enerev shift aud the broadness of the line suggested οι the preseut observation are roughly consistent with these estimations., Thus the energy shift and the broadness of the line suggested from the present observation are roughly consistent with these estimations.1181" Although the siguificauce of the line itself is at the confidence level the hue paramcters are not well coustrained because of the linited statistics. possible calibration uncertainties, and also possible uncertainties of the contimmiuu spectrum."," Although the significance of the line itself is at the confidence level, the line parameters are not well constrained because of the limited statistics, possible calibration uncertainties, and also possible uncertainties of the continuum spectrum."1182 Since the ceutroid energy aud the line broadening are kev signatures of the reprocessing in the BAL flow. further observations with better statistics and/or better energy resolutions will be indispensable.," Since the centroid energy and the line broadening are key signatures of the reprocessing in the BAL flow, further observations with better statistics and/or better energy resolutions will be indispensable."1183 Finally we would like to poiut out that if the line of sight was inside the BAL cone. we should observe a blueshifted cluission liue. or both blueshifted aud redshitted lines depending ou the inclination anele.," Finally we would like to point out that if the line of sight was inside the BAL cone, we should observe a blueshifted emission line, or both blueshifted and redshifted lines depending on the inclination angle."1184 Since the direct beam would be visible iu this case. the EW of the line would v0 60 eV. These line features look similar to the broad ine features observed iu some Sevfert galaxies which are often described with disk-line models.," Since the direct beam would be visible in this case, the EW of the line would be $\sim$ 60 eV. These line features look similar to the broad line features observed in some Seyfert galaxies which are often described with disk-line models."1185 Thus reprocessing in the BAL flow nav at least partly account for those xoad lines., Thus reprocessing in the BAL flow may at least partly account for those broad lines.1186 Receutly the detection of a redshifted broad strong 600 eV) line feature i the N-rav spectrum of a Sevtert 2 ealaxy at z ~1 ds reported (6. ITainger 2001. xivate communication).," Recently the detection of a redshifted broad strong $\sim$ 600 eV) line feature in the X-ray spectrum of a Seyfert 2 galaxy at $z \sim$ 1 is reported (G. Hasinger 2001, private communication)."1187 We conjecture that this may have sole connection to the euission line of ITE113|117., We conjecture that this may have some connection to the emission line of H1413+117.1188 We thank P. Edwards for reviewing the manuscipt., We thank P. Edwards for reviewing the manuscript.1189 I.M. is grateful to W. Drimkauaun for valuable discussions., K.M. is grateful to W. Brinkmann for valuable discussions.1190 NO. and δι. ave supported bv the JSPS Research Fellowship for Youug Scicutists., N.O. and N.I. are supported by the JSPS Research Fellowship for Young Scientists.1191 JPER acknowledecs support from CNRS., JPK acknowledges support from CNRS.1192be readily identified iu the rain plots for any of the candidates presented here excep IXOI 191.,be readily identified in the rain plots for any of the candidates presented here except KOI 191.1193 This is reflected in the Motion statistics reported iu Table 2.., This is reflected in the Motion statistics reported in Table \ref{FPtab}.1194" NOT 191 has a correlation with a sjenificauce {aking the conmpkBITE of the value reporte 11 Table 2))COMP.able to a ο,Ίσα detectlon.", KOI 191 has a correlation with a significance (taking the complement of the value reported in Table \ref{FPtab}) )—comparable to a 2.3-sigma detection.1195 A correlation docSs nof necessarily rule out ti6 planetary interpreation rather it should be iuterpreted as a warning that the photometric aperure is crowded.," A correlation does not necessarily rule out the planetary interpretation, rather it should be interpreted as a warning that the photometric aperture is crowded."1196 Addilonal analysis or observational ollow-up is required to determine the location ai magnitude of eac star in the νιτν and. 1]timatelv. the origin «X the ransit-like features.," Additional analysis or observational follow-up is required to determine the location and magnitude of each star in the vicinity and, ultimately, the origin of the transit-like features."1197 None of the DV binary discrimination staistics repor ediu Table 2. are significant at the 3-si¢na evel or higher (correspondiug to a significaice of ).997 or larger)., None of the DV binary discrimination statistics reported in Table \ref{FPtab} are significant at the 3-sigma level or higher (corresponding to a significance of 0.997 or larger).1198 However. DV statistics for NOI 152axd 209 are not available due to the fac that he dominant transit feature in the Quarter 1 ieht Curve aypears only once.," However, DV statistics for KOI 152 and 209 are not available due to the fact that the dominant transit feature in the Quarter 1 light curve appears only once."1199 A planet transit uode Calo be fitted to a light curve with a sinele transit with DV., A planet transit model cannot be fitted to a light curve with a single transit with DV.1200 Consequeutlv. it does iot eet filtered and passed back to TPS for the detection of t1e shallower. shorter-period transits.," Consequently, it does not get filtered and passed back to TPS for the detection of the shallower, shorter-period transits."

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