ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2obtained by van Leeuwen (2007)) shows a good agreement of the two measurements. within 1.20.,"obtained by van Leeuwen \cite{vanleeuwen07}) ) shows a good agreement of the two measurements, within $1.2\,\sigma$."3 This confirmation of the true accuracy of these independent measurements. at the level. shows that the measurement was not disturbed by the binary nature of ó VVel A. This somewhat surprising result is due to the similar brightness ratio Laa/Lap=1.3 and mass ratio Ma4/Mayx1.1 of theo VVel A pair.," This confirmation of the true accuracy of these independent measurements, at the level, shows that the measurement was not disturbed by the binary nature of $\delta$ Vel A. This somewhat surprising result is due to the similar brightness ratio $L_\mathrm{Aa}/L_\mathrm{Ab}4\approx 1.3$ and mass ratio $M_\mathrm{Aa}/M_\mathrm{Ab} \approx 1.1$ of the $\delta$ Vel A pair."5 This results in a very small apparent displacement of the center of light of the Aab system during the orbit. with respect to the center of gravity of the two stars.," This results in a very small apparent displacement of the center of light of the Aab system during the orbit, with respect to the center of gravity of the two stars."6 Using our model of the eclipsing system. we computed the expected photocenter displacement during an full orbit.," Using our model of the eclipsing system, we computed the expected photocenter displacement during an full orbit."7 We find that the peak-to-peak photocenter displacement ts of the order of one milliaresecond. which ts much smaller than the apparent astrometric shift due to the parallax.," We find that the peak-to-peak photocenter displacement is of the order of one milliarcsecond, which is much smaller than the apparent astrometric shift due to the parallax."8 The binarity of the system therefore did not bias significantly the parallax measurement. neither did the low brightness of the B component.," The binarity of the system therefore did not bias significantly the parallax measurement, neither did the low brightness of the B component."9 The observations of the photocenter displacement through high-precision differential astrometry with the VLT/NACO instrument will be the subject of a future article., The observations of the photocenter displacement through high-precision differential astrometry with the VLT/NACO instrument will be the subject of a future article.10 The binarity of 6 VVel was discovered by S. I. Bailey in 1894 from Arequipa. Peru (and independently by Innes 1895)).," The binarity of $\delta$ Vel was discovered by S. I. Bailey in 1894 from Arequipa, Peru (and independently by Innes \cite{innes1895}) )."11 Over more than one century. the separation between 0 Vel A and B has been decreasing at a rate which nicely matches the progression of the angular resolution of the successive generations of imaging instruments (visual observations. photography. electronic devices).," Over more than one century, the separation between $\delta$ Vel A and B has been decreasing at a rate which nicely matches the progression of the angular resolution of the successive generations of imaging instruments (visual observations, photography, electronic devices)."12 This progression allowed a relatively regular tracing of the visual orbit of the pair. down to the sub-arcsecond separations that occur around the periastron passage.," This progression allowed a relatively regular tracing of the visual orbit of the pair, down to the sub-arcsecond separations that occur around the periastron passage."13 With the advent of speckle interferometry (Tango et al. 1979)), With the advent of speckle interferometry (Tango et al. \cite{tango79}) )14 and the satellite (ESA 1997)) the accuracy of the measured relative positions improved significantly., and the satellite (ESA \cite{esa97}) ) the accuracy of the measured relative positions improved significantly.15 In Paper 1. we present in details the new data we obtained with theTelescope.. using both the K-band adaptive optic system VLT/NACO (Rousset et al. 2003::," In Paper I, we present in details the new data we obtained with the, using both the K-band adaptive optic system VLT/NACO (Rousset et al. \cite{rousset03};"16 Lenzen et al. 1998)), Lenzen et al. \cite{lenzen98}) )17 and the N-band camera VLT/VISIR (Lagage et al. 2004))., and the N-band camera VLT/VISIR (Lagage et al. \cite{lagage04}) ).18 Thanks to the large aperture of the telescopes and the diffraction-limited angular resolution. these observations provide us with new high-precision astrometry of the A-B pair.," Thanks to the large aperture of the telescopes and the diffraction-limited angular resolution, these observations provide us with new high-precision astrometry of the A-B pair."19 The resulting separations of 6 Vel B relatively to A are presented in. Table 5.., The resulting separations of $\delta$ Vel B relatively to A are presented in Table \ref{tab:diffastrom-table}.20 For the conversion of the separation measured in pixels to angular separations. we adopted the pixel scale of 13.26+0.03 mmas/pixel (Masciadri et al. 2003) ," For the conversion of the separation measured in pixels to angular separations, we adopted the pixel scale of $13.26 \pm 0.03$ mas/pixel (Masciadri et al. \cite{masciadri03}) )"21for NACO and 75+| mmas/pixel for VISIR., for NACO and $75 \pm 1$ mas/pixel for VISIR.22 The assumed NACO plate scale is in good agreement with the calibration by Neuhiiuuser et al. (2008)).," The assumed NACO plate scale is in good agreement with the calibration by Neuhäuuser et al. \cite{neuhauser08}) ),"23 who demonstrated that this figure ts stable over a period of at least 3 years., who demonstrated that this figure is stable over a period of at least 3 years.24 The VISIR plate scale uncertainty is set arbitrarily to =1%. although it ts probably better in reality.," The VISIR plate scale uncertainty is set arbitrarily to $\approx 1\%$, although it is probably better in reality."25 The angular separation was only =0.6” for the epoch of our observations., The angular separation was only $\approx 0.6\arcsec$ for the epoch of our observations.26 In addition to these new astrometric measurements. we also take advantage of the historical astrometric positions assembled by Argyle et al. (2002))," In addition to these new astrometric measurements, we also take advantage of the historical astrometric positions assembled by Argyle et al. \cite{argyle02}) )"27 in his Table 5. that includes 17epochs between 1895 and 1999.," in his Table 5, that includes 17epochs between 1895 and 1999."28 It is to be noted that these authors used the two speckle interferometry epochs from Tango et al. (1979)), It is to be noted that these authors used the two speckle interferometry epochs from Tango et al. \cite{tango79}) )29 with a different definition for the projection angle. leading to an apparent inconsistency with the other measurements.," with a different definition for the projection angle, leading to an apparent inconsistency with the other measurements."30 Transforming the Tango et al., Transforming the Tango et al.31 projection angle PA using PA—(180PA). these two data points become much more consistent with the other epochs and observing techniques.," projection angle $PA$ using $PA\rightarrow(180-PA)$, these two data points become much more consistent with the other epochs and observing techniques."32 We adjusted the orbital parameters of the 6 Vel A-B pair to the whole sample of astrometric data. and the result is presented graphically in Fig. 8..," We adjusted the orbital parameters of the $\delta$ Vel A-B pair to the whole sample of astrometric data, and the result is presented graphically in Fig. \ref{fig:AB_orbit}."33 The corresponding orbital elements are listed in Table 6.., The corresponding orbital elements are listed in Table \ref{tab:AB_orbit}.34 It should be noted that thanks to a semi-major axis twice more precise. and a period ten time more precise. the total mass value derived from based Kepler's third law ts significantly improved. which becomes limited by our parallax estimation ofx=39.8+ 0.4.," It should be noted that thanks to a semi-major axis twice more precise, and a period ten time more precise, the total mass value derived from based Kepler's third law is significantly improved, which becomes limited by our parallax estimation of $\pi = 39.8 \pm 0.4$ ."35"defined as the difference between the mean d,, of disc-bearing low mass and solar-type stars.",defined as the difference between the mean $d_{av}$ of disc-bearing low mass and solar-type stars.36" The solar-type star discs are assumed to disperse after 2 Myr and we vary the lifetime of the low mass star discs, Τιμ, between 2 and 10 Myr in steps of 1 Myr."," The solar-type star discs are assumed to disperse after 2 Myr and we vary the lifetime of the low mass star discs, $\tau_{lm}$, between 2 and 10 Myr in steps of 1 Myr."37 We assign the direction of motion of each star stochastically with a velocity module equal to the literature value of the velocity dispersion measured for the given region (Table 1)., We assign the direction of motion of each star stochastically with a velocity module equal to the literature value of the velocity dispersion measured for the given region (Table 1).38" For each simulation we measure Ad,,, after stochastically culling the synthetic clusters to the same number of sources available in the observed clusters (see Table 2)."," For each simulation we measure $\Delta39d_{av}$, after stochastically culling the synthetic clusters to the same number of sources available in the observed clusters (see Table 2)."40" We summarise the results of our Monte Carlo simulations in Figure 1, where each region-specific simulation is plotted in individual panels."," We summarise the results of our Monte Carlo simulations in Figure 1, where each region-specific simulation is plotted in individual panels."41" The black, red, green, blue, magenta and cyan asterisks represent models with low-mass star disc lifetimes of 2, 3, 4, 5, 6 and 7 Myr, respectively, while the black, red and green triangles represent models with low-mass star discs dispersal timescales of 8, 9 and 10 Myr."," The black, red, green, blue, magenta and cyan asterisks represent models with low-mass star disc lifetimes of 2, 3, 4, 5, 6 and 7 Myr, respectively, while the black, red and green triangles represent models with low-mass star discs dispersal timescales of 8, 9 and 10 Myr."42 The solar type disc dispersal timescales are kept fixed at 2 Myr., The solar type disc dispersal timescales are kept fixed at 2 Myr.43" We note that in our very simplified model, what"," We note that in our very simplified model, what"44 ," \citep[see e.g.][]{SandersMirabel, BarnesHernquist, Genzel, DiMatteo, Hopkins06}."45"102Lo. extinguished, and eventually a “red and dead”» elliptical galaxy is produced with a more massive black hole at its core."," $10^{12} L_{\sun}$ extinguished, and eventually a “red and dead"" elliptical galaxy is produced with a more massive black hole at its core."46" NGC 6240 (z=0.0243, d=98 Mpc for Ho=75 km s! Mpc-!, 1” = 470 pc), with Lrg~10!5L sits on the boundary between LIRGs and ULIRGs."," NGC 6240 $z=0.0243$ , $d=98$ Mpc for $H_0 = 75$ km $^{-1}$ $^{-1}$, 1"" = 470 pc), with $L_{IR} \sim 10^{11.8} L_{\sun}$ sits on the boundary between LIRGs and ULIRGs."47" Because of its close proximity and spectacular tidal tails and loops, it has become the prototypical example of a gas-rich system in the phase where the two nuclei are close to merging into one."," Because of its close proximity and spectacular tidal tails and loops, it has become the prototypical example of a gas-rich system in the phase where the two nuclei are close to merging into one."48 It has been studied in great detail and in almost every wavelength regime (e.g. x-ray - Komossa et al., It has been studied in great detail and in almost every wavelength regime (e.g. x-ray - Komossa et al.49 2003; optical - Gerssen et al., 2003; optical - Gerssen et al.50 2004; near-IR - Max et al., 2004; near-IR - Max et al.51" 2005, 2007; Scoville et al."," 2005, 2007; Scoville et al."52 2000; Tecza et al., 2000; Tecza et al.53 2000; Engel et al., 2000; Engel et al.54 2010; mid-IR - Armus et al., 2010; mid-IR - Armus et al.55 2006; mm - Tacconi et al., 2006; mm - Tacconi et al.56" 1999; radio - Gallimore Beswick 2004, Hagiwara et al."," 1999; radio - Gallimore Beswick 2004, Hagiwara et al."57 2011)., 2011).58" Near the core of NGC 6240, the nuclei of the two progenitors are visible 1.2-1.5 arcsec apart, depending on wavelength."," Near the core of NGC 6240, the nuclei of the two progenitors are visible 1.2-1.5 arcsec apart, depending on wavelength."59 Each of these nuclei holds an AGN; the two sources are resolved in hard rays by the Chandra X-Ray Observatory (Komossaetal., Each of these nuclei holds an AGN; the two sources are resolved in hard x-rays by the Chandra X-Ray Observatory \citep{Komossa}.60" 2003). The AGNs are deeply obscured at optical wavelengths, however, due to large quantities of dust also present in this region."," The AGNs are deeply obscured at optical wavelengths, however, due to large quantities of dust also present in this region."61" By looking into the near-infrared, Pollacketal.(2007) have seen young star clusters through some of the dust, products of the most recent close passage of the nuclei visible in Figure "," By looking into the near-infrared, \citet{Lindsay} have seen young star clusters through some of the dust, products of the most recent close passage of the nuclei (also visible in Figure \ref{image}) )."62"Supermassive black hole (alsomasses are knownto 1)).scale with certain hostgalaxy properties, such as bulge light and mass (e.g.Kormendy&Richstone1995;Kor- and"," Supermassive black hole masses are knownto scale with certain hostgalaxy properties, such as bulge light and mass \citep[e.g.][]{KormARAA, KormGeb, Magorrian} and"63"power spectrum estimates are expected to be underevolved by roughly <A5.3 and O.1 per cent for Mii,=0.95.0.475 and O.beV. respectively. for &zmO2hAlpetats =0.","power spectrum estimates are expected to be underevolved by roughly $\!\ltwid\!5,3$ and $0.1$ per cent for $\Sigma m_\nu=0.95, 0.475$ and $0.1\,{\rm eV}$ , respectively, for $k\!\gtwid\!0.2\,h\textrm{Mpc}^{-1}$ at $z=0$."64 Fig., Fig.65" Lin ? shows that the power is further suppressed. by 5 per cent for “im,<12eVa ke02.O3hApe! when the neutrino non-lincaritics are neglected."," 1 in \cite{BraHan09} shows that the power is further suppressed by $\!\twid\!5$ per cent for $\Sigma m_\nu\leq1.2\,{\rm eV}$ at $k\approx0.2-0.3\,h\textrm{Mpc}^{-1}$ when the neutrino non-linearities are neglected."66" Overall. we estimate our N-body spectrum errors to be <10.4 and 0.1. per cent for Xi,=0.95.0.475 and 0.1ολ), respectively. for k2O02hAlpe 5atz-0."," Overall, we estimate our $\it{N}$ -body spectrum errors to be $\!\ltwid\!10,4$ and $0.1$ per cent for $\Sigma m_\nu=0.95, 0.475$ and $0.1\,{\rm eV}$ , respectively, for $k\!\gtwid\!0.2\,h\textrm{Mpc}^{-1}$ at $z=0$."67 In this paper we simulated. the matter power spectrum αι z=O in order to study how massive neutrinos impact structure formation., In this paper we simulated the matter power spectrum at $z=0$ in order to study how massive neutrinos impact structure formation.68 The most important factors in obtaining an accurate power spectrum are (i) the Nvquist wavenumboer. which depends on the simulation box size aud the number of particles ancl (ii) the force resolution. which depends on the size of the root. grid.," The most important factors in obtaining an accurate power spectrum are (i) the Nyquist wavenumber, which depends on the simulation box size and the number of particles and (ii) the force resolution, which depends on the size of the root grid."69 Above the Nyquist wavenumber.the power spectrum is dominated: by shot noise.," Above the Nyquist wavenumber,the power spectrum is dominated by shot noise."70" For the semi-non-linear modes (0.1:Az:0.6Alpe+). we found that Noga,22565 in a 2005‘Alpe box is enough o keep the sampling errors under 0.5 per cent."," For the semi-non-linear modes $(0.1\!\ltwid\!k\!\ltwid\!0.6\, h \textrm{Mpc}^{-1})$, we found that $N_{\rm cdm}\!=\!256^3$ in a $200\,h^{-1}\textrm{Mpc}$ box is enough to keep the sampling errors under $0.5$ per cent."71 We used a root grid of Nan.=512°. which is twice as fine as IN. o accurately calculate the gravitational forces down to the scale of the meaninterparticle spacing.," We used a root grid of $N_{\rm gas}\!=\!512^3$, which is twice as fine as $N_{\rm cdm}$, to accurately calculate the gravitational forces down to the scale of the meaninterparticle spacing."72" We also found that he non-linear evolution of perturbations are accurate to withinnu 1 per cent level only for⋅ the scales &z,EAMpcn when using. .2000n“Alpe box."," We also found that the non-linear evolution of perturbations are accurate to within $1$ per cent level only for the scales $k\!\ltwid\!1\,h\textrm{Mpc}^{-1}$ when using $200\,h^{-1}\textrm{Mpc}$ box."73 Probing. smaller scales. with. igher precision requires a smaller simulation box or a finer root grid., Probing smaller scales with higher precision requires a smaller simulation box or a finer root grid.74" We have presented a suite. of /N-body simulations showing the effect of massive neutrinos in the range (2,= (Xin,=0.05 1.9eV) on the distribution of matter."," We have presented a suite of $\it{N}$ -body simulations showing the effect of massive neutrinos in the range $\Omega_\nu=0.001-0.04$ $\Sigma m_\nu=0.05-1.9\,{\rm eV}$ ) on the distribution of matter."75 Massive neutrinos smooth the neutrino density field on sub-frec-streaming scales., Massive neutrinos smooth the neutrino density field on sub-free-streaming scales.76 This makes the gravitational potential wells shallower than their counterparts in a pure AC'DAL universe. leading to a suppressed growth of structure formation.," This makes the gravitational potential wells shallower than their counterparts in a pure $\Lambda CDM$ universe, leading to a suppressed growth of structure formation."77" Phe power is suppressed by as much as 3.590 per cent at &~O.6Alpe! for Vi,=0.051.9eV. respectively."," The power is suppressed by as much as $3.5-90$ per cent at $k\!\twid\!0.6\,h\textrm{Mpc}^{-1}$ for $\Sigma m_\nu=0.05-1.9\,{\rm eV}$ respectively."78 In. our simulations. we include neutrinos asneutrino-weighted CDAL and. barvon transfer. functions at the starting redshift. z;=20.," In our simulations, we include neutrinos asneutrino-weighted CDM and baryon transfer functions at the starting redshift, $z_{\rm i}=20$."79" We have neglected the non-linear neutrino corrections to the matter power spectrum which max be as high as 1.25 per cent for Nin,=0.6eV and 5 per cent for Nin,=12eV as measured by 2..."," We have neglected the non-linear neutrino corrections to the matter power spectrum which may be as high as $1.25$ per cent for $\Sigma m_\nu=0.6\,{\rm eV}$ and $5$ per cent for $\Sigma m_\nu=1.2\,{\rm eV}$ as measured by \cite{BraHan09}."80" Although direct. comparison of our A-body. results with those from 2 owas not possible since we ran our simulations with a slightly. different set. of cosmological parameters and. “an... nevertheless. we expect our N-body power spectra to be in error by zz10.4 and 0.1 per cent for Xm,=0.95.0.475 and 0.10V. respectively. for &2O2hMpe| at z—0."," Although direct comparison of our $\it{N}$ -body results with those from \cite{BraHan09} was not possible since we ran our simulations with a slightly different set of cosmological parameters and $\Sigma m_\nu$ , nevertheless, we expect our $\it{N}$ -body power spectra to be in error by $\!\ltwid\!10,4$ and $0.1$ per cent for $\Sigma m_\nu=0.95, 0.475$ and $0.1\,{\rm eV}$, respectively, for $k\!\gtwid\!0.2\,h\textrm{Mpc}^{-1}$ at $z=0$."81" We found an overall suppression of power from our simulations at 2—0 t0 be APP10f. For Xm,x0.5eV. which is slightly higher than the results o£ ? and ? who reported AP/Pofs and AP/P~9.5f, respectively for Nm,<00ον."," We found an overall suppression of power from our simulations at $z=0$ to be $\Delta P/P\!\twid\!-10f_\nu$ for $\Sigma m_\nu\leq0.5\,{\rm eV}$ which is slightly higher than the results of \cite{BraHan08} and \cite{VieHaeSpr10} who reported $\Delta P/P\!\twid\!-9.8f_\nu$ and $\Delta P/P\!\twid\!-9.5f_\nu$ respectively for $\Sigma m_\nu\leq0.6\,{\rm eV}$."82" As part of the Sloan Digital Sky Survey-LLL. the Barvon Oscillation Spectroscopic Survey (BOSS: ?7)) is expected to measure the power spectrum with precisions at.which OQ,~QO.0l(Xm,O4750NV) could. be ruled. out."," As part of the Sloan Digital Sky Survey-III, the Baryon Oscillation Spectroscopic Survey (BOSS; \citealt{BOSS}) ) is expected to measure the power spectrum with precisions atwhich $\Omega_\nu\!\twid\!0.01\,(\Sigma m_\nu\twid\!0.475\,{\rm eV})$ could be ruled out."83" This would significantly. improve thecurrent T-vr WAZAP data alone constraint of Xm,«1.3eV."," This would significantly improve thecurrent 7-yr data alone constraint of $\Sigma m_\nu<1.3\,{\rm eV}$ ."84" IW Xm, constraints [rom cosmology eet as low as ΟΕ—0.2eV. it will open up a possibility to resolve the normal and. inverted: mass hierarchies. though the matter power spectrum would need to be determined. withprecision levels well below 0.5 "," If $\Sigma m_\nu$ constraints from cosmology get as low as $0.1-0.2\,{\rm eV}$ , it will open up a possibility to resolve the normal and inverted mass hierarchies, though the matter power spectrum would need to be determined withprecision levels well below $0.5$ "85For the radio structure part of a shell. we can compare its contour level with that of a shell model convolved with the same beam.,"For the radio structure part of a shell, we can compare its contour level with that of a shell model convolved with the same beam."86 For a shell model with a fractional shell width of 0.3. which ts the shell width found for 11993J by Marcaide et al. (2009)).," For a shell model with a fractional shell width of 0.3, which is the shell width found for 1993J by Marcaide et al. \cite{Marcaide2009}) ),"87 the outer radius of SN22008ax would be 1.15z0.15 mmas (hereafter. all the uncertainties given are equal to the square root of the corresponding diagonal element of the covariance natrix. with the errors having been first uniformly scaled so that the reduced y is equal to 1).," the outer radius of 2008ax would be $\pm$ mas (hereafter, all the uncertainties given are equal to the square root of the corresponding diagonal element of the covariance matrix, with the errors having been first uniformly scaled so that the reduced $\chi^2$ is equal to 1)."88 This size translates into an average expansion velocity of (4.8+0.8)*10? ! which ts superluminal.," This size translates into an average expansion velocity of $(4.8 \pm 0.8) \times 10^5$ $^{-1}$, which is superluminal."89 Indeed. we still obtain superluminal expansion velocities 1 we change the fractional shell width to different. unrealistic. values such as 0.1 (a narrower shell width translates into a smaller fitted shell size).," Indeed, we still obtain superluminal expansion velocities if we change the fractional shell width to different, unrealistic, values such as 0.1 (a narrower shell width translates into a smaller fitted shell size)."90 Hence. it is unlikely that the radio structure is part of an expanding shell.," Hence, it is unlikely that the radio structure is part of an expanding shell."91 If we instead fit the visibilities to two point sources. one to model the brightness peak (at the North) and the other one to model the source extension. towards the South. we find components of 0.4020.11 and 0.24250.11 mmJy. separated by 0.9320.10 mmas.," If we instead fit the visibilities to two point sources, one to model the brightness peak (at the North) and the other one to model the source extension towards the South, we find components of $\pm$ 0.11 and $\pm$ mJy, separated by $\pm$ mas."92 This result translates into an average relative velocity between components of (3.90+0.62)x10° !. which is superluminal.," This result translates into an average relative velocity between components of $(3.90 \pm 0.62) \times 10^5$ $^{-1}$, which is superluminal."93 If the two components were moving in Opposite directions with respect to the explosion center. the average expansion velocity of the radiostructure would be (1.90+0.31)x10° kkmss7!. a factor ~7.3 higher than the maximum ejecta velocity estimated from the optical-line emission of this supernova (~2.6x10? kkmss7!. Blondin 2008)).," If the two components were moving in opposite directions with respect to the explosion center, the average expansion velocity of the radiostructure would be $(1.90 \pm 0.31) \times 10^5$ $^{-1}$, a factor $\sim$ 7.3 higher than the maximum ejecta velocity estimated from the optical-line emission of this supernova $\sim 2.6 \times 10^4$ $^{-1}$, Blondin \cite{Blondin2008}) )."94 This velocity is also much higher than the typical expansion velocities of the radiostructures of other supernovae (~1-2I0 ss7' )., This velocity is also much higher than the typical expansion velocities of the radiostructures of other supernovae $\sim 1-2 \times 10^4$ $^{-1}$ ).95 Hence. the two-point source model is also unlikely.," Hence, the two-point source model is also unlikely."96 Perhaps. then. we could consider that the structure shown in the map is due to a chance (near) superposition of a marginally detected radio source and a noise peak.," Perhaps, then, we could consider that the structure shown in the map is due to a chance (near) superposition of a marginally detected radio source and a noise peak."97 In this case. the radio emission. would not be resolved and its detection would be even more marginal.," In this case, the radio emission would not be resolved and its detection would be even more marginal."98 Fitting a shell model (with a fractional width of 0.3) to the northern flux density peak results in a source outer diameter of 0.25€0.05 mmas and a flux density of 0.48+0.12 mmJy., Fitting a shell model (with a fractional width of 0.3) to the northern flux density peak results in a source outer diameter of $0.25\pm0.05$ mas and a flux density of $0.48\pm0.12$ mJy.99 We notice that this flux density is consistent with the flux densities registered by Stockdale et al., We notice that this flux density is consistent with the flux densities registered by Stockdale et al.100 2008b at the same radio frequency and at epochs enclosing that of our VLBI observations., \cite{Stockdale2008b} at the same radio frequency and at epochs enclosing that of our VLBI observations.101 The resulting average expansion velocity is (5.2+1.3)xIO! kkmss7!. a factor of 2 larger than the velocity inferred from. optical-line emissio.," The resulting average expansion velocity is $(5.2 \pm 1.3) \times 10^4$ $^{-1}$, a factor of 2 larger than the velocity inferred from optical-line emission."102 This velocity is also ~3 times larger than the expansion velocities of the other radio supernovae that were observed with VLBI (<2.0xIO? kkmss7! ). and would imply (if we assume a non-decelerated expansion at least until the epoch of our," This velocity is also $\sim$ 3 times larger than the expansion velocities of the other radio supernovae that were observed with VLBI $<2.0\times10^4$ $^{-1}$ ), and would imply (if we assume a non-decelerated expansion at least until the epoch of our"103HD 177830 is a V — 7.177 magnitude star of spectral class KOIV.,HD 177830 is a V = 7.177 magnitude star of spectral class K0IV.104" Relative to the Sun, HD 177830 is quite metal-rich ([Fe/H] — 0.55)."," Relative to the Sun, HD 177830 is quite metal-rich ([Fe/H] = 0.55)."105" We show the 88 Keck radial velocity measurements in Table 5,, spanning approximately 15 years of RV monitoring."," We show the 88 Keck radial velocity measurements in Table \ref{tab:rvdata_HD177830}, spanning approximately 15 years of RV monitoring."106" The median internal uncertainty for our observations is 1.05ms~1,, and the peak-to-peak velocity variation is 87.15!."," The median internal uncertainty for our observations is 1.05, and the peak-to-peak velocity variation is 87.15."107. The velocity scatter around the average RV in our observations is 24.68!., The velocity scatter around the average RV in our observations is 24.68.108. The individual RV observations for HDs 177830 are shown in the top panel of Figure 5.., The individual RV observations for HD 177830 are shown in the top panel of Figure \ref{fig:data_HD177830}.109 The middle panel shows the error-weighted Lomb-Scargle (LS) periodogram of the full RV dataset., The middle panel shows the error-weighted Lomb-Scargle (LS) periodogram of the full RV dataset.110" Finally, the lower panel of Figure 5 shows the spectral window."," Finally, the lower panel of Figure \ref{fig:data_HD177830} shows the spectral window."111" The strongest peak in the periodogram is well-fit with a Keplerian model with period 407.31 days, semi-amplitude K=31.17 and estimated FAP <3x 1079."," The strongest peak in the periodogram is well-fit with a Keplerian model with period 407.31 days, semi-amplitude $K = 31.17$ and estimated FAP $ < 3\times 10^{-6}$ ."112" Together with the assumed stellar mass of 1.48 Mo, this amplitude corresponds to a minimum mass of Msini=1.48M;."," Together with the assumed stellar mass of 1.48 $\msun$ , this amplitude corresponds to a minimum mass of $\mass \sin i = 1.48 \mjup$."113 The best-fit orbit for the planet is essentially circular., The best-fit orbit for the planet is essentially circular.114" This 1-planet fit achieves a reduced x?=27.53, with an RMS of 5.24s-!."," This 1-planet fit achieves a reduced $\chi^2 = 27.53$, with an RMS of 5.24."115. The top panel of Figure 6 shows the phased Keplerian fit for the 407-d planet., The top panel of Figure \ref{fig:1pfit_HD177830} shows the phased Keplerian fit for the 407-d planet.116 'The bottom panel of Figure 6 shows the periodogram of the residuals to the single-planet fit and the corresponding FAPs., The bottom panel of Figure \ref{fig:1pfit_HD177830} shows the periodogram of the residuals to the single-planet fit and the corresponding FAPs.117 The dominant peak at P — 110.98 with a FAP =5x1075 indicates the rather secure presence of an additionalplanet., The dominant peak at P = 110.98 with a FAP $\approx 5 \times 10^{-5}$ indicates the rather secure presence of an additionalplanet.118" Our best combined 2- fit indicates a new planet with P—110.91 days,"," Our best combined 2-planet fit indicates a new planet with $P = 110.91$ days,"119Extragalactic novae are potentially important as tracers of close binary. stus in other ealaxies.,Extragalactic novae are potentially important as tracers of close binary stars in other galaxies.120 Current. estimates of the bulk nova rates in galaxies such as M31. of 37 | imply that in a few vears the number of observed novae could be quite large for such a system., Current estimates of the bulk nova rates in galaxies such as M31 \citep{sha01} of $\sim$ 37 $^{-1}$ imply that in a few years the number of observed novae could be quite large for such a system.121 Novae represent an important complement to the increasing data on extragalactic X-ray binaries afforded by ancNAM., Novae represent an important complement to the increasing data on extragalactic X-ray binaries afforded by and.122 The brightness of the nova oulburst (Al; of —6 to —10 at maximum) betrays (their presence to bevond the Virgo cluster with current telescopes., The brightness of the nova outburst $_V$ of $-6$ to $-10$ at maximum) betrays their presence to beyond the Virgo cluster with current telescopes.123 By observing extragalactic novae il is possible to trace the frequency ancl distribution of the close binaries (hat produce them in many extragalactic environments. thus allowing an exploration of close binary populations and the factors (hat influence their formation.," By observing extragalactic novae it is possible to trace the frequency and distribution of the close binaries that produce them in many extragalactic environments, thus allowing an exploration of close binary populations and the factors that influence their formation."124 One of the most basic investigations into these [actors is to plot the normalized nova rate versus the luminosity of the host galaxy and see if any. trend can be detected., One of the most basic investigations into these factors is to plot the normalized nova rate versus the luminosity of the host galaxy and see if any trend can be detected.125 Various versions of this plot have been produced over the vears (dellaValleetal.1994:Ciardullo.&Pritehet2000:Ferrarese.Coté.Jordin 2003).. but svstematic effects continue to dominate the published nova rates.," Various versions of this plot have been produced over the years \citep{del94,sha00,fer03}, but systematic effects continue to dominate the published nova rates."126 We have found that nova rates are subject to biases that tend to underestimate (he bulk rate for a given galaxy. (Neill&Shara2004)., We have found that nova rates are subject to biases that tend to underestimate the bulk rate for a given galaxy \citep{nei04}.127. Most severe of these biases is (he one imposed by telescope scheduling. which. until recently.," Most severe of these biases is the one imposed by telescope scheduling, which, until recently,"128portion of the centroid position is dominated by a small fraction of the integrated. πας. vielding again a small observable change in (he centroid position.,"portion of the centroid position is dominated by a small fraction of the integrated flux, yielding again a small observable change in the centroid position."129" However, we mav also show this explicitly by considering the asvimptolic expansions ol eq. (7))."," However, we may also show this explicitly by considering the asymptotic expansions of eq. \ref{eq:dr1D}) )."130" For small £2 (large period P). the sinc-term is roughly unity and In contrast. for large Q. |AXenaxs|(7AT) is strongly oscillatory,"," For small $\Omega$ (large period $P$ ), the $\sinc$ -term is roughly unity and In contrast, for large $\Omega$, $\left| \Delta \bmath{X}_{C,\rm max} \right| (T,\Delta T)$ is strongly oscillatory."131 Nevertheless. it is bounded from above by Che sine term. ancl thus selüng these limiting expressions equal to each other gives (he desired condition that a maximun observed displacement occurs near O2//PAT.," Nevertheless, it is bounded from above by the $\sinc$ term, and thus Setting these limiting expressions equal to each other gives the desired condition that a maximum observed displacement occurs near $\Omega \simeq 2/\sqrt{T\Delta T}$."132 Note that this is (true for the envelope obtained by varving LT and AT in the prescribed ranges as well ancl serves as a simple estimate of the sensitivity of these (vpes of measurements.," Note that this is true for the envelope obtained by varying $T$ and $\Delta T$ in the prescribed ranges as well, and serves as a simple estimate of the sensitivity of these types of measurements."133 We now consider a more realistic model in which a hot spot is embedded in an accretion disk. including the relativistic beaming. Doppler boosting. strong eravitational lensine ancl the opacity of the disk and hot spot.," We now consider a more realistic model in which a hot spot is embedded in an accretion disk, including the relativistic beaming, Doppler boosting, strong gravitational lensing and the opacity of the disk and hot spot."134 This is necessarily a more complicated model. and thus we acldress it numerically via the rav-(racing. racliative-transler code described in Loeb(2006) (to which we direct the reader for more information. the model only being sumniarized below).," This is necessarily a more complicated model, and thus we address it numerically via the ray-tracing, radiative-transfer code described in \citet{Brod-Loeb:2006} (to which we direct the reader for more information, the model only being summarized below)."135 Due to its ability to shield the hot spot [rom view. the structure of the backeround disk is of particular importance.," Due to its ability to shield the hot spot from view, the structure of the background disk is of particular importance."136 In the absence of an unambiguous prediction [rom existing acerelion flow (theory. we have modeled it as a self-similar Radiativelv Ineflicient Accretion Flow (RIAF) following Yuanetal.(2003).," In the absence of an unambiguous prediction from existing accretion flow theory, we have modeled it as a self-similar Radiatively Inefficient Accretion Flow (RIAF) following \citet{Yuan-Quat-Nara:2003}."137. Specifically. the accretion How is characterized bv a Weplerian velocity distribution. a population of thermal electrons with density and (emperatiure respectively. a population of non-(hermal electrons," Specifically, the accretion flow is characterized by a Keplerian velocity distribution, a population of thermal electrons with density and temperature respectively, a population of non-thermal electrons"138rotating with the critical angular velocity. can be written Dividing this by the square of the mass. eq. (79)).,"rotating with the critical angular velocity, can be written Dividing this by the square of the mass, eq. \ref{LE_mass}) ),"139 then vields the couditiou Iu the bottom panel of Figure 6 we show the right haud side of this equation for a ο=3 polvtrope aud for CR/Mei=150., then yields the condition In the bottom panel of Figure 6 we show the right hand side of this equation for a $n=3$ polytrope and for $(R/M)_{\rm crit} = 450$.140 The dotted. horizontal line is the critical value of unity.," The dotted, horizontal line is the critical value of unity."141 A region inside a radius © can form a Kerr black hole ouly if (5)/i(£)? is less than unity., A region inside a radius $\xi$ can form a Kerr black hole only if $J(\xi)/m(\xi)^2$ is less than unity.142 This condition is satisfied evervwhere except for the mnermnost regions ©<Gun~θέ. ," This condition is satisfied everywhere except for the innermost regions $\xi < \xi_{\rm min} \sim1430.1 \,\xi_1$."144At the surface. $=£4. we recover the value (€AD=(L876 found in eq. (33)).," At the surface, $\xi = \xi_1$, we recover the value $(J/M)^2_{\rm crit} = 0.876$ found in eq. \ref{crit_values}) )."145 Note that for any polytrope. i is proportional to ο) for stuall radios aud oJ is proportional to mG)Qr~Qu.," Note that for any polytrope, $m$ is proportional to $r^3$ for small radii $r$ and $J$ is proportional to $m(r) \Omega r^2 \sim146\Omega r^5$."147 Therefore. Ji? scales like Qr close to the center. which prevents the formation of arbitrarily simall black holes from rotating polvtropes.," Therefore, $J/m^2$ scales like $\Omega/r$ close to the center, which prevents the formation of arbitrarily small black holes from rotating polytropes."148 In our case. the region inside Gun~θέ. containins about of the total mass. defines the mimi mass which can collapse to form: au initial black hole.," In our case, the region inside $\xi_{\rm min} \sim 0.1\,149\xi_1$, containing about of the total mass, defines the minimum mass which can collapse to form an initial black hole."150 Since 0(£)/0'(£4) exceeds the threshold for ©Guin. such a “ininimal” seed black hole could accrete mfurther material from the star.," Since $\theta'(\xi)/\theta'(\xi_1)$ exceeds the threshold for $\xi \gtrsim151\xi_{\rm min}$, such a “minimal” seed black hole could accrete further material from the star."152 Finally. we note that a bar instability may form duiug the collapse of the star.," Finally, we note that a bar instability may form during the collapse of the star."153 The criterion for the formation of a bar on a dynamical timescale is (see. e... Chandrasekhar 1969: Shapiro Teukolsky 1983).," The criterion for the formation of a bar on a dynamical timescale is (see, e.g., Chandrasekhar 1969; Shapiro Teukolsky 1983)."154 Since M. aud J are approximately conserved duriug the collapse. ΤΠ scales with Rot. so a bar will start to form when The value of R/AL at bar formation is then Ee. (85))," Since $M$ and $J$ are approximately conserved during the collapse, $T/|W|$ scales with $R^{-1}$, so a bar will start to form when The value of $R/M$ at bar formation is then Eg. \ref{R_bar}) )"155 suggests that the collapsing star may form a nonaxisviunetrie bar before it forms a black hole., suggests that the collapsing star may form a nonaxisymmetric bar before it forms a black hole.156 This Is an portant result. since such a bar may result in a quasiperiodic Cluission of eravitational waves (cf.," This is an important result, since such a bar may result in a quasiperiodic emission of gravitational waves (cf."157 ΤΗ. Houser Coutrella 1996).," Smith, Houser Centrella 1996)."158 The frequency of these waves can be estimated from the expected bar rotation rate For a SMS of LO°AL.. this vields a frequency of 5«10.! Uz. which is iu the range in which LISA is expected to be most sensitive (sec. e.g. Thorne 1995).," The frequency of these waves can be estimated from the expected bar rotation rate For a SMS of $10^6 M_{\odot}$ this yields a frequency of $5 \times15910^{-4}$ Hz, which is in the range in which LISA is expected to be most sensitive (see, e.g., Thorne 1995)."160" The frequency increases at later stages of the collapse. when AR, becomes luger."," The frequency increases at later stages of the collapse, when $M/R_{\rm bar}$ becomes larger."161 The streneth of the gravitational wave signal can be crudely estimated to be where Q is the stars quadrupole moment. aud d is the distance. which we scale to 1 pc (the IIubble distance is 3 Cpe).," The strength of the gravitational wave signal can be crudely estimated to be where $Q$ is the star's quadrupole moment, and $d$ is the distance, which we scale to 1 Gpc (the Hubble distance is $\sim 3$ Gpc)."162" The signal streneth increases with AMRi, at late stages of the collapse.", The signal strength increases with $M/R_{\rm bar}$ at late stages of the collapse.163 Apart from anv bar. the inplosion itself will be wonspherical. due to rotation. aud will result iu a gravitational wave burst.," Apart from any bar, the implosion itself will be nonspherical, due to rotation, and will result in a gravitational wave burst."164 The collapse of a superlassive star may therefore be a very promising candidate for detection by space based eravitational wave detectors (LISA Pre-Phase A report 1995)., The collapse of a supermassive star may therefore be a very promising candidate for detection by space based gravitational wave detectors (LISA Pre-Phase A report 1995).165 Obvioush. the arguineuts presented in this section are very crude and do not replace a fully sel£-consisteut relativistic lyvdrodvnamical calculation.," Obviously, the arguments presented in this section are very crude and do not replace a fully self-consistent relativistic hydrodynamical calculation."166 Our arguinenuts nevertheless sugeest that. upon reaching the onset of instability. supermassive stars may forni a superniassive black hole. countainiug a large part of tle mass. aud leaving ouly a few percent of the initial mass outside of the black hole. mmost likely in the form of a disk.," Our arguments nevertheless suggest that, upon reaching the onset of instability, supermassive stars may form a supermassive black hole, containing a large part of the mass, and leaving only a few percent of the initial mass outside of the black hole, most likely in the form of a disk."167" We furthermore anticipate that a bar max form during the collapse. which iav lead to the cussion of quasiperiodic gravitational waves,"," We furthermore anticipate that a bar may form during the collapse, which may lead to the emission of quasiperiodic gravitational waves."168 We have launched a fully relativistic study of the formation of SMDIIs via the collapse of SMSs., We have launched a fully relativistic study of the formation of SMBHs via the collapse of SMSs.169 Iu this paper we study the quasistationary. secular evolution of SMSs up to the critical configuration at which racia iustabilitv sets in ancl focus on the effects of rotation aux eecneral relativity.," In this paper we study the quasistationary, secular evolution of SMSs up to the critical configuration at which radial instability sets in and focus on the effects of rotation and general relativity."170 We identify the critical configuration and its characteristic parameters PM. —T/lV] ane J/AM?.," We identify the critical configuration and its characteristic parameters $R/M$, $T/|W|$ and $J/M^2$."171 These paraucters are independent of the uss of the SMS. and are therefore universal constants.," These parameters are independent of the mass of the SMS, and are therefore universal constants."172 The subsequent iniplosion. starting from this universal critica configuration. is therefore also uniquely determined iux should produce a unique eravitational waveform.," The subsequent implosion, starting from this universal critical configuration, is therefore also uniquely determined and should produce a unique gravitational waveform."173 We conrpare results from an analytic. approximate treatiuent aud a fully relativistic. numerical calculation. aud fine eood agreement.," We compare results from an analytic, approximate treatment and a fully relativistic, numerical calculation, and find good agreement."174 We furthermore solve analytically for the time evolution of these parameters up to the onset of instability., We furthermore solve analytically for the time evolution of these parameters up to the onset of instability.175 Ideutiftving the critical configuration at the onset of instability is interesting for its own sake., Identifying the critical configuration at the onset of instability is interesting for its own sake.176 More iuportautlv. however. this configuration will be adopted as initial data for future numerical sinulatious of SMS collapse (Bamuearte. Shapiro Shibata 1999).," More importantly, however, this configuration will be adopted as initial data for future numerical simulations of SMS collapse (Baumgarte, Shapiro Shibata 1999)."177 Iu this paper we assemble qualitative arguments to anticipate the outcome of the collapse aud find that the formation of a SMB containing an appreciable fraction of the mass is not ruled out., In this paper we assemble qualitative arguments to anticipate the outcome of the collapse and find that the formation of a SMBH containing an appreciable fraction of the mass is not ruled out.178 Our aremments suggest that a trausicut phase asa SMS may be an efficient way for primordial eas, Our arguments suggest that a transient phase as a SMS may be an efficient way for primordial gas179conversion of the jet οποίον (o thermal energy suggests that 0>AY1.,conversion of the jet energy to thermal energy suggests that $0 \ge M \ge 1$.180 Constraints 1-3 reduce to GV+1)//N=0.360.03., Constraints 1-3 reduce to $(M+1)/N=0.36 \pm 0.03$.181 Constraints 4 and 5 give NV=3.14£0.34.," Constraints 4 and 5 give $N=3.14 \pm1820.34$."183 These two results then implv that Af=0.18+0.15. which is consistent with constraint. 6.," These two results then imply that $M=0.13 \pm 0.15$, which is consistent with constraint 6."184 In round numbers. N=3 and M=0.," In round numbers, $N=3$ and $M=0$."185 What should verv high red shift (2~10) GRBs look like?, What should very high red shift $z \sim 10$ ) GRBs look like?186 A first guess might be that the cosmological red shift will transform (hem (o appear more like x-ray bursts with [ρω~20 keV. The analvsis in this paper shows that this first guess is wrong since (he z~10 bursts must have a very. high. luminosity and hence a very. high D which will blue shift the Ej; back to gamma-ray energies.," A first guess \citep[e.g.,][]{blo01} might be that the cosmological red shift will transform them to appear more like x-ray bursts with $E_{peak} \sim 20$ keV. The analysis in this paper shows that this first guess is wrong since the $z \sim 10$ bursts must have a very high luminosity and hence a very high $\Gamma$ which will blue shift the $E_{peak}$ back to gamma-ray energies."187" In. particular. [rom either equation 5 or Figure 1. we see that the highest red shift bursts will all have the same E, as the nearby events of the same 555."," In particular, from either equation 5 or Figure 1, we see that the highest red shift bursts will all have the same $E_{peak}$ as the nearby events of the same $P_{256}$."188 Thus. any z>5 bursts that ave in the BATSE catalog will have Bragον ΟΘΟΝΕΣ”. K," Thus, any $z>5$ bursts that are in the BATSE catalog will have $E_{peak} \sim 200 keV$ ."189ippenetal.(2001) have used BATSE real-time data to look at [ast x-ray. transients discovered by the BeppoSAX satellite (Ileiseetal...2001)., \citet{kip01} have used BATSE real-time data to look at fast x-ray transients discovered by the BeppoSAX satellite \citep{hei01}.190. They find that these events have similar light curves and clurations as GRBs. which is suggestive that the events are normal bursts.," They find that these events have similar light curves and durations as GRBs, which is suggestive that the events are normal bursts."191" Their peak ας is up to 3 times lower than the DATSE trigger threshold while their median £,,; value is 10 keV. The natural suggestion was made that very [aint and very soft bursts might be at very. hieh red shift.", Their peak flux is up to 3 times lower than the BATSE trigger threshold while their median $E_{peak}$ value is 70 keV. The natural suggestion was made that very faint and very soft bursts might be at very high red shift.192 However. the model presented in this paper shows thatall bursts below the BATSE threshold will on average have a low Γέρος. wilh no necessity of hieh red shift. (," However, the model presented in this paper shows that bursts below the BATSE threshold will on average have a low $E_{peak}$, with no necessity of high red shift. ("193This is also realized [rom a simple extrapolation of the data from Mallozzi et al.,This is also realized from a simple extrapolation of the data from Mallozzi et al.194 as shown in Figure 2.), as shown in Figure 2.)195 That is. a low {οσο is due to some combination of low luminosity (hence a low blue shift [rom the jet) and large distance (hence a large cosmological red shilt) which will produce systematically low ρω values.," That is, a low $P_{256}$ is due to some combination of low luminosity (hence a low blue shift from the jet) and large distance (hence a large cosmological red shift) which will produce systematically low $E_{peak}$ values."196 While some of the fast x-ray. transients might be at high z. the steepness of the GRB huminosity function implies that almost all are ad moclerate red shift.," While some of the fast x-ray transients might be at high $z$ , the steepness of the GRB luminosity function implies that almost all are at moderate red shift."197" It is disappointing that lines of constant. E, are closely parallel to lines of constant D»; in the L versus z plot.", It is disappointing that lines of constant $E_{peak}$ are closely parallel to lines of constant $P_{256}$ in the $L$ versus $z$ plot.198" If this had not been true. then a simple measurement of E, and 555 would define the bursts. position in the plot and we would hence know the burst luminosity and red shift."," If this had not been true, then a simple measurement of $E_{peak}$ and $P_{256}$ would define the bursts' position in the plot and we would hence know the burst luminosity and red shift."199" The value of Zi, is approximately constant for all bursts.", The value of $E_0$ is approximately constant for all bursts.200 This constancey is similar (o recent results Chat bursts are standard candles [rom the Iag/Iuminosity and variability/Iuminosity relations as well as that the total enerevof bursts is nearly a constant., This constancy is similar to recent results that bursts are 'standard candles' from the lag/luminosity and variability/luminosity relations as well as that the total energyof bursts is nearly a constant.201 Thus itnow seems, Thus itnow seems202the GC candidate list. but some coutaminatioun still remains.,"the GC candidate list, but some contamination still remains."203 Section 3.6 describes how we quantify the contamination level.," Section \ref{section:contamination}204 describes how we quantify the contamination level."205 A series of completeness tests was carried out to establish the point source detection limit in the WIYN images., A series of completeness tests was carried out to establish the point source detection limit in the WIYN images.206 Fifty artificial point. sources with magnitudes within Q.1 maguitude of a eiven brightness were added to each image. the same detection steps used ou the original image were performed. and the fraction of artificial sources detected was recorded.," Fifty artificial point sources with magnitudes within 0.1 magnitude of a given brightness were added to each image, the same detection steps used on the original image were performed, and the fraction of artificial sources detected was recorded."207 Fifty to sixty such tests were executed on each image so that the completeness was calculated over a range of 5 to 6 iuagnitudes per filter., Fifty to sixty such tests were executed on each image so that the completeness was calculated over a range of 5 to 6 magnitudes per filter.208 The data are complete at B= 25.3. V 21.5. and 2 — 23.9.," The data are complete at $B$ $=$ 25.3, $V$ $=$ 24.8, and $R$ $=$ 23.9."209 HST resolves iuauy Faint backgrouud objects that can appear as poiut sources in eround-basec images. so to estimate the galaxy coutaimiuation in the selected CC sample. we analyzed the archiva HST data described iu Section 2..," HST resolves many faint background objects that can appear as point sources in ground-based images, so to estimate the galaxy contamination in the selected GC sample, we analyzed the archival HST data described in Section \ref{section:obs and redux}."210 Sixteen of the 12 WIYN GC candidates were located in at least oue of the two HST poiutiugs., Sixteen of the 42 WIYN GC candidates were located in at least one of the two HST pointings.211 We followed tlie method of Ixunduetal.(1999) to determine whicl ol these were true poiut sources., We followed the method of \cite{kundu99} to determine which of these were true point sources.212 Photometry was performed with aperture radii of 0.5 pixels aux 3 pixels and a sky annulus [rom 5 {ο 8 pixels., Photometry was performed with aperture radii of 0.5 pixels and 3 pixels and a sky annulus from 5 to 8 pixels.213" Objects in the PC1 chip with countsap;,/couutsqspis < 13 and those in the WE chips with countsa;,/countsosp;, « 10 were point sources and thus rea GC candidates.", Objects in the PC chip with $_{3pix}$ $_{0.5pix}$ $<$ 13 and those in the WF chips with $_{3pix}$ $_{0.5pix}$ $<$ 10 were point sources and thus real GC candidates.214 Usiug these criteria (aud confirming the results with visual inspection). we [oui that two of the 16 objects were actually galaxies.," Using these criteria (and confirming the results with visual inspection), we found that two of the 16 objects were actually galaxies."215 To calculate the surface deusity of background galaxies iu the CC sample. we first scaled the HST images to the same pixel scale as the WIYN images. aligned them to the WIYN poiuting. aud computed the total area covered by HST.," To calculate the surface density of background galaxies in the GC sample, we first scaled the HST images to the same pixel scale as the WIYN images, aligned them to the WIYN pointing, and computed the total area covered by HST."216 The HST frames covered {.[1 square are minutes around NGC Y8LL vielding a deusity of 0.15 galaxies per square arc miuute.," The HST frames covered 4.41 square arc minutes around NGC 7814, yielding a density of 0.45 galaxies per square arc minute."217 We used the latest version of the Galactic structure code from Mendez aud van Altena (1996) auc Mendez et ((2000) to estimate the zunount of stellar contamination in the CC sample., We used the latest version of the Galactic structure code from Mendez and van Altena (1996) and Mendez et (2000) to estimate the amount of stellar contamination in the GC sample.218 The moclel allows the user to choose such parameters as the contribution to star counts from the Galaxy disk. thick disk. and halo. aud the galactocentric distance aud z-height of the Sun.," The model allows the user to choose such parameters as the contribution to star counts from the Galaxy disk, thick disk, and halo, and the galactocentric distance and z-height of the Sun."219 Output includes the surface clensity of stars expected within a given magnitude and color range iu a given direction on the sky., Output includes the surface density of stars expected within a given magnitude and color range in a given direction on the sky.220 A selection in two colors was not easily implemented so we used only a B—V cut., A selection in two colors was not easily implemented so we used only a $B-V$ cut.221 The, The222for overdense regions to condcuse out.,for overdense regions to condense out.223 When ting&fo. however (as in Doudi's spherical accretion solution). mass drop out is neglieible since the gas accretes before cooling.," When $\ti \ll \tc$, however (as in Bondi's spherical accretion solution), mass drop out is negligible since the gas accretes before cooling."224 The parameter 4 iu equation (2)) normalizes the efficiency of mass drop out: we expect q1., The parameter $q$ in equation \ref{mdot}) ) normalizes the efficiency of mass drop out; we expect $q \sim 1$.225" We take the Dexavitational potential to be Deiven by -u ↴∖↴⋯∪∪↑∐⊓⋅⋜⋯↴∖↴↕↑↕∪∐∙ : uSeay outer .forrrotkpepe<et”radiusrp,οι (5)r. taken- here- terii. in. equations (1)) audrate (5))at is the the eravitational potential due to a black bole of mass AL aud Selivarzschild radius e,=26M.es the ηra) nuüuuces the effects of General Relativity (Paczvisski Wiita 1980).", We take the gravitational potential to be given by = + r > r_b and = - ^2 } r < r_b The left most term in equations \ref{fg1}) ) and \ref{fg2}) ) is the gravitational potential due to a black hole of mass $M$ and Schwarzschild radius $r_g = 2GM/c^2$; the $1/(r-r_g)$ mimics the effects of General Relativity (Paczyńsski Wiita 1980).226HST observatious of the ceuters of elliptical. galaxies indicate that those which harbor massive black holes have ceutral surface brightuess “cores.”, observations of the centers of elliptical galaxies indicate that those which harbor massive black holes have central surface brightness “cores.”227 The surface bielituess rises steeply with decreasing radius at laree radi. but flattens out iu the inner portions of the ealaxy (e.g... Lauer et al.," The surface brightness rises steeply with decreasing radius at large radii, but flattens out in the inner portions of the galaxy (e.g., Lauer et al."228 1995: Faber et al, 1995; Faber et al.229" 1995: Iwormendy Richstone Our mass model for the galaxy in equations (1)) aud (53) is intended to reflect these observatious,", 1995; Kormendy Richstone Our mass model for the galaxy in equations \ref{fg1}) ) and \ref{fg2}) ) is intended to reflect these observations.230 Outside a break radius rj. the ealaxy has a constaut velocity dispersion (0) while inside that radius we assume that ight traces mass (aside from the black hole) aud so the enclosed iiass profile flattens (0< 1) iu accord with the Hattening surface brightness.," Outside a break radius $r_b$, the galaxy has a constant velocity dispersion $\sigma$ ) while inside that radius we assume that light traces mass (aside from the black hole) and so the enclosed mass profile flattens $\beta < 1$ ) in accord with the flattening surface brightness."231 Typical observed values of οὐ and à are zz0.25 aud z1 spc. respectively (Faber et al.," Typical observed values of $\beta$ and $r_b$ are $\approx 0.25$ and $\approx 1$ kpc, respectively (Faber et al."232 1995): we use such values in our nuuerical results of 8333.1., 1995); we use such values in our numerical results of 3.1.233 For analytical estimates. iowever. we take rj>0. Lie. we model the galaxy as waving a constant velocity dispersion everywhere.," For analytical estimates, however, we take $r_b \rightarrow 0$, i.e., we model the galaxy as having a constant velocity dispersion everywhere."234 The eravitational poteutial is predominantly that of the ealaxv for r2rg While it is predominautly that of the dack hole for rS oru. where the trausition radius is (for ry >) 0.05 )7.," The gravitational potential is predominantly that of the galaxy for $r235\gsim \rt$ while it is predominantly that of the black hole for $r236\lsim \rt$ , where the transition radius is (for $r_b \rightarrow 0$ ) 0.05 )."237 For a galaxy with oz300 kins| in the Virgo cluster. a distance =20 Mpe away. rg corresponds to =0.5 aresec.," For a galaxy with $\sigma238\approx 300$ km $^{-1}$ in the Virgo cluster, a distance $\approx 20$ Mpc away, $\rt$ corresponds to $\approx 0.5$ arcsec."239 This is comparable to the angular resolution of the(CXOJ. indicating that the presence of a ceutral black hole in nearby ellipticals may have observable effects on the cooling flow N-ray euidssion (sce SILET).," This is comparable to the angular resolution of the, indicating that the presence of a central black hole in nearby ellipticals may have observable effects on the cooling flow X-ray emission (see 4.1)."240 We- are interested. in. solutions+ to our model problem which undergo a subsonic to supersonic trausition at a sonic radius r;., We are interested in solutions to our model problem which undergo a subsonic to supersonic transition at a sonic radius $r_s$.241 Rewriting equations (2))-(2]) vields Ü —L. where V= aud ," Rewriting equations \ref{mdot}) \ref{energy}) ) yields v =, where N = and D = 1 -."242"Siuce. D—0at the sonic. point.. woe must have /N.—0 for. a (1) p,⋅⋅ ↖↖↸∖⋜↧↨↘↽↸∖"," Since $D = 0$at the sonic point, we must have $N = 0$ for a smooth transition."243"≺∏∐⋅∪∏↑↸∖↥⋅↴⋝≺∏⋯≺↧⋜∐⋅⋅↖↽↸⊳∪∐≼∐↑↕∪∐↴∖↴↑∪↴⋝↸∖↴∖↴⋉∖↸⊳↕∏↸∖≼⇂ values audc,. the deusityv aud souud speed. at au aud |."," We take our outer boundary conditions to be specified valuesof $\rho_o$ and $c_o$, the density and sound speed, atan outer radius $\ro$."244" Equations (2))-(2))⋅ have twoGAL eigenvalues.ae — = ney be the sonic radius. ry. audO= theFoo accretion 4 . .0 sonic radius. εκ),"," Equations \ref{mdot}) \ref{energy}) ) have two eigenvalues, taken here to be the sonic radius, $r_s$ , and the accretion rate at the sonic radius, $\dot M(r_s)$."245 We- find⋅ our solutions↴ bv. The left. most shooting out from ry. aud adjusting Mire) aud rs to satisty the outer boundary coucitionus., We find our solutions by shooting out from $r_s$ and adjusting $\dot M (r_s)$ and $r_s$ to satisfy the outer boundary conditions.246" For inost of this paper we scale our models to observations of MBST: οz100 kpe. p,z10ean i)? στ00 kms toe, so (οι, Stewart et al."," For most of this paper we scale our models to observations of M87: $\ro \approx 100$ kpc, $\rho_o \approx 10^{-27}$ g $^{-3}$, $\sigma247\approx 300$ km $^{-1}$, $c_o \approx \sigma$ (e.g., Stewart et al."248 1981) aud AFzm3<10?AZ. (Ianus et al., 1984) and $M \approx 3 \times 10^9 M_\odot$ (Harms et al.249 1991: Ford et al., 1994; Ford et al.250 199L: AMacchoetto ct al., 1994; Macchetto et al.251 1997)., 1997).252 In. MS8T. AL ds inferred to decrease from 10M.srtats TU kpe to <LAL.vr tata few Kilo-parsees (Stewart et al.," In M87, $\dot M$ is inferred to decrease from $\approx \, 10 \, \mpy$ at $\approx 70$ kpc to $\lsim \,2531 \, \mpy$ at a few kilo-parsecs (Stewart et al."254 108D)., 1984).255" As shown below, this is reasonably well captured by ay =0.6 model."," As shown below, this is reasonably well captured by a $q = 0.6$ model."256" Although strictly an eigenvalue of our problem. au excellent estimate of the value of M at the outer boundary. Mí(r,)=M, can be made by imposing the requireimeut that the gas be a cooling Sow αἲ τον"," Although strictly an eigenvalue of our problem, an excellent estimate of the value of $\dot M$ at the outer boundary, $\dot M(\ro) \equiv257\md$, can be made by imposing the requirement that the gas be a cooling flow at $\ro$."258" This requires that the inflow tine of the gas be comparable to the local radiative cooling time which iu turn requires e(r,)=Προ, aud therefore (cf Fabian Nulseu 1977) The primary. question. is. what happens to matter accreting at this rate at simaller τας,", This requires that the inflow time of the gas be comparable to the local radiative cooling time which in turn requires $v(\ro) \equiv v_o \approx - B \rho_o r_o/c_o$ and therefore (cf Fabian Nulsen 1977) The primary question is what happens to matter accreting at this rate at smaller radii.259" Iu the abseuce of a ceutral point mass a cooling flow with AL, given by equation (10)) would have the following structure: C. 0L. AL 2) pex 2"," In the absence of a central point mass a cooling flow with $\md$ given by equation \ref{md})) would have the following structure: c_s , M , v ."260" ceqhisiscreadilgeerif icdbisubstitutionintocquations(2)) (2))undertheassumptionthatthegasissubsonicandthatthepotential (Ur,» 0)"," This isreadily verified by substitution into equations \ref{mdot}) \ref{energy}) ) under the assumption that the gas is subsonic and that the potential is logarithmic $M = 0$ , $r_b261 \rightarrow 0$ )."262 Note. however. that if 4.L1 the above," Note, however, that if $q < 1$ the above"263although both reeions also contain clusters spanning the entire age range observed for the NGC 3310 star cluster syslem.,although both regions also contain clusters spanning the entire age range observed for the NGC 3310 star cluster system.264 The CLE is the result of a complex interplay of 10 intrinsic cluster mass distribution. age spread. and ‘Luster disruption processes.," The CLF is the result of a complex interplay of the intrinsic cluster mass distribution, age spread and cluster disruption processes."265 We therefore determined. the --=iciviclual cluster masses by scaling our model SEDs for the rest-Lit age. extinction values and metallicity estimates to 10 observed SEDs.," We therefore determined the individual cluster masses by scaling our model SEDs for the best-fit age, extinction values and metallicity estimates to the observed SEDs."266 We estimate the cluster svstem to have v median mass of σηfll.>~5.2540.1. not including systematic uncertainties introduced by the uncertainties in 16 low-mass IME slope.," We estimate the cluster system to have a median mass of $\langle \log( m/M_\odot ) \rangle \sim 5.25 \pm 0.1$, not including systematic uncertainties introduced by the uncertainties in the low-mass IMF slope."267 Our metallicity determinations are strongly dominated ον (signilicantlv) subsolar metallicities. which is consistent with independent. metallicity measurements.," Our metallicity determinations are strongly dominated by (significantly) subsolar metallicities, which is consistent with independent metallicity measurements."268 Fhere is some evidence that the most actively star [forming regions. in xwticular the Jumbo region and the northern spiral arm. are »edominantIys: composed. of lower-abundance star clusters.," There is some evidence that the most actively star forming regions, in particular the Jumbo region and the northern spiral arm, are predominantly composed of lower-abundance star clusters."269 The V-band CLE slope in the range LO!<Lyoosw10° for the NGC 3310 star cluster system ds opsusw7vl.S+ 0.4. which is consistent with the power-law slopes of other voung CLEs.," The -band CLF slope in the range $10^6 \le L_{\rm F606W}/L_\odot \le27010^7$ for the NGC 3310 star cluster system is $\alpha_{\rm F606W} \sim271-1.8 \pm 0.4$ , which is consistent with the power-law slopes of other young CLFs."272 Finally. we point out. that our. estimates for the ages. masses. metallicities anc extinction. values of. the YSCs in NGC 3310 closely match previous. independent determinations of these parameters. where available (e.g... Grotheus Scehmidt-Ixaler 1991. P93. Meurer ct al.," Finally, we point out that our estimates for the ages, masses, metallicities and extinction values of the YSCs in NGC 3310 closely match previous, independent determinations of these parameters, where available (e.g., Grotheus Schmidt-Kaler 1991, P93, Meurer et al."273 1995. D00. 02).," 1995, D00, E02)."274" ""This implies. to first order. that this type of analysis is reasonably robust."," This implies, to first order, that this type of analysis is reasonably robust."275 This paper is based on new ancl archival observations with he NASA/ESATelescope. obtained at the Space Telescope Science Enstitute (οἱ). which is operated wv the Association of Universities for Itesearch in Astronomy (AURA). Inc.. under NASA contract NAS 5-26555.," This paper is based on new and archival observations with the NASA/ESA, obtained at the Space Telescope Science Institute (STScI), which is operated by the Association of Universities for Research in Astronomy (AURA), Inc., under NASA contract NAS 5-26555."276" ‘This xiper is also partially based. on ASTROVIRTEL research support. a project funded. by the European Commission under SEP Contract HEPIU-C""E-1999-00081."," This paper is also partially based on ASTROVIRTEL research support, a project funded by the European Commission under 5FP Contract HPRI-CT-1999-00081."277. his. research iw made use of NASA's Astrophysics Data System Abstract Service., This research has made use of NASA's Astrophysics Data System Abstract Service.278 PA is partially supported by DEC: erant Fr 916/11-1: PA also acknowledges partial funding from he Maric Curie. Fellowship programme EARASTARGAL “The Evolution of Stars anc Galaxies”. funded. by he European Commission. under ΡΕ contract IPMT-C'[-2000-00132.," PA is partially supported by DFG grant Fr 916/11-1; PA also acknowledges partial funding from the Marie Curie Fellowship programme EARASTARGAL “The Evolution of Stars and Galaxies”, funded by the European Commission under 5FP contract HPMT-CT-2000-00132."279 VAP and RAW acknowledge support rom NASA erants GO-8645.*.," VAT and RAW acknowledge support from NASA grants GO-8645.*,"280. awarded. by S'TScL. RelG acknowledecs preliminary analysis of the Cycle 9HST UV. data by Nsitaaz Chacdee as part of the 2001 PARC/Cambricec International. Uneleregracduate Summer School., awarded by STScI. RdG acknowledges preliminary analysis of the Cycle 9 UV data by Xsitaaz Chadee as part of the 2001 PPARC/Cambridge International Undergraduate Summer School.281For the current study we selected more than tweuty VV galaxies looking like iultiple svstems or singular nreeulu svstenis iu he POSS/DSS images. for which such indicators of interaction as well defined tidal tails or bridges are absent.,"For the current study we selected more than twenty VV galaxies looking like multiple systems or singular irregular systems in the POSS/DSS images, for which such indicators of interaction as well defined tidal tails or bridges are absent."282 The man objectives of our investigation are: o clarify the distances. total luminosities aud masses of those systems. systemic velocities of which are not known or badly kuowu: to carry out high S/N ratio spectrophotometry iu order to address problems of chemical abundances aud evolutional status of these objects. to analyse the iuner gas kinematics aud structural xoperties of the objects.," The main objectives of our investigation are: – to clarify the distances, total luminosities and masses of those systems, systemic velocities of which are not known or badly known; – to carry out high S/N ratio spectrophotometry in order to address problems of chemical abundances and evolutional status of these objects, – to analyse the inner gas kinematics and structural properties of the objects."283 Since many of VV ealaxies in question are dwarts with recent or current SEburst. if is also nuportaut to check xossible companious Which could exert stroug chough tidal action.," Since many of VV galaxies in question are dwarfs with recent or current SF burst, it is also important to check possible companions which could exert strong enough tidal action."284 Tn this paper. the first iu the SCLICS. we present he results of recent loue-slit spectroscopy for three VV objects: VV. 132. VV 513 aud VV TIT aud the observation in III-line of VV 717.," In this paper, the first in the series, we present the results of recent long-slit spectroscopy for three VV objects: VV 432, VV 543 and VV 747 and the observation in HI-line of VV 747."285 lusection 2. we describe observations. data reduction. abundances determunation and the leasurelents of velocity distribution of ionized eas alone the slit.," In section \ref{observations} we describe observations, data reduction, abundances determination and the measurements of velocity distribution of ionized gas along the slit."286 Observations of VV 717 in the MW1-line 21 cui and their results are presented iu section 3.., Observations of VV 747 in the HI-line 21 cm and their results are presented in section \ref{HI_observations}.287 In section b we consider the individual properties of studied galaxies., In section \ref{Individual_prop} we consider the individual properties of studied galaxies.288 Discussions and preliminary conclusions are preseuted in section .5.., Discussions and preliminary conclusions are presented in section \ref{Conclusions}.289 Wo adopt throughout the oper Hg 275 an L, We adopt throughout the paper $_0 =$ 75 km $^{-1}$.290 The spectroscopic data were obtained with the Guu telescope of the Special Astroplivsical Observatorv of Russian Academy of Scicuce(SAO RAS) during two runs in February aud April 1999., The spectroscopic data were obtained with the m telescope of the Special Astrophysical Observatory of Russian Academy of Science (SAO RAS) during two runs in February and April 1999.291 The Lone-Slit spectroerap[um (LSSin Table 13)(Afanasiey et al. 1995)), The Long-Slit spectrograph (LSS in Table \ref{Tab1}) ) (Afanasiev et al. \cite{Afanasiev95}) )292 at the telescop« prime focus was equipped with a Photometrics CCD-detector PMIO21 (8th 21 212 pixel size) (PMCCD in Table 1)) iustalled at Schinidt-Casscerain camera F/1.5., at the telescope prime focus was equipped with a Photometrics CCD-detector PM1024 (with $24\times24\mu$ m pixel size) (PMCCD in Table \ref{Tab1}) ) installed at Schmidt-Cassegrain camera F/1.5.293" Most of the ong-xlit spectra (1.27.« 180) were obtained with the erating of:325 evooves/nuu. eiviug a disporsio- of L6 ""pixel."," Most of the long-slit spectra $1.2\arcsec\times180\arcsec$ ) were obtained with the grating of 325 grooves/mm, giving a dispersion of 4.6 /pixel."294 Additional data were obtained with the erating of 1302 erooves/iuin and dispersion 1.2 pixel., Additional data were obtained with the grating of 1302 grooves/mm and dispersion 1.2 /pixel.295" For the latter set-up the slit of 27&180"" was used.", For the latter set-up the slit of $2\arcsec\times180\arcsec$ was used.296" The scale along the slit was 0.39"" /pixel.", The scale along the slit was $\arcsec$ /pixel.297 The resulting resolution(PWIIMO was about 1115 for the first set-up. aud about3.7 for the second set-up.," The resulting resolution (FWHM) was about $14-15$ for the first set-up, and about 3.7 for the second set-up."298 Reference spectra of an ArNeIIo lamp were recorded before or after each observatiou to provide waveleneth calibration., Reference spectra of an Ar--Ne--He lamp were recorded before or after each observation to provide wavelength calibration.299 Spectroplotometric standard stars from Massey ot al. (1988)), Spectrophotometric standard stars from Massey et al. \cite{Massey88}) )300 were observed for flux calibration at least twice a nieht., were observed for flux calibration at least twice a night.301 Observations and data processing in this set-up have been conducted mainly under the software package in MIDAS. described by Kuiazev Sherein (1995)).," Observations and data processing in this set-up have been conducted mainly under the software package in MIDAS, described by Kniazev Shergin \cite{Kniazev95}) )."302 The data reduction was performed in SAO RAS. using various packages of MIDAS (see IKuiazev et al. (2000))," The data reduction was performed in SAO RAS, using various packages of MIDAS (see Kniazev et al. \cite{Kniazev2000}) )"303 for cletails)., for details).304 In Table 2. we stuumarize the main observational parameters of the discussed three VW “nests”., In Table \ref{Tab2} we summarize the main observational parameters of the discussed three VV “nests”.305" They include the names of the objects. their coordinates for the epoch J200¢"". the apparent blue magnitudes aud the correspouding rerOnces. the radial heliocentric velocities. measured iu this work. with thei raus"," They include the names of the objects, their coordinates for the epoch J2000, the apparent blue magnitudes and the corresponding references, the radial heliocentric velocities, measured in this work with their r.m.s."306 uncertainties. maximal angular sizes. absolute blue maguitucdes aud the oxveen abundances (12|log(O/IT)).," uncertainties, maximal angular sizes, absolute blue magnitudes and the oxygen abundances (12+log(O/H))."307 Direct mages of studied. ealaxies. extracted from the DSS aud the »oxitiou of lone slit. indicated dy bar are preseuted in Fig.," Direct images of studied galaxies, extracted from the DSS and the position of long slit, indicated by bar are presented in Fig."308 laa. 2aa. Baa. Correspondingo 2-D spectra are shown in Fie.," \ref{VV432_fig}a a, \ref{VV543_fig}a a, \ref{VV747_fig}a a. Corresponding 2-D spectra are shown in Fig."309" Loe. 2ec. ος, The brightness profiles of Ilo line along the slit. and corresponding velocity ονο are illustrated in Fig."," \ref{VV432_fig}c c, \ref{VV543_fig}c c, \ref{VV747_fig}c c. The brightness profiles of $\alpha$ line along the slit, and corresponding velocity curves are illustrated in Fig."310 Lob. 2bb. 3bb. In Fig.," \ref{VV432_fig}b b, \ref{VV543_fig}b b, \ref{VV747_fig}b b. In Fig."311 1dd. 2dd. auk 3dd we present 1-D spectra. extracted from 2-D spectra. which were used for the measurements of line intensities. determination of plysical conditious aud abundances of Ilr-egious.," \ref{VV432_fig}d d, \ref{VV543_fig}d d, and \ref{VV747_fig}d d we present 1-D spectra, extracted from 2-D spectra, which were used for the measurements of line intensities, determination of physical conditions and abundances of -regions."312 The resulting observed emissiou liue intensities F(A) of various lous relative to ILA both uncorrected aie corrected for iuterstellar extinction aud underlvius stellar absorption Z/(À) (following the procedure deseribed bx Izotov et al. 19973) ," The resulting observed emission line intensities $F(\lambda)$ of various ions relative to $\beta$ , both uncorrected and corrected for interstellar extinction and underlying stellar absorption $I(\lambda)$ (following the procedure described by Izotov et al. \cite{Izotov97}) )"313for the 1xiehtest warts of the galaxies aro presented im Tables 3. along with the extinction cocficicnt 2). the equivalent width of ibsorptiou Daher lbydrogen lines EW(abs). the equivalent width of IL? line EW(IL) aud the observed II.) fu.," for the brightest parts of the galaxies are presented in Tables \ref{Tab3}314 along with the extinction coefficient $\beta$ ), the equivalent width of absorption Balmer hydrogen lines EW(abs), the equivalent width of $\beta$ line $\beta$ ) and the observed $\beta$ flux."315 For the abuudances determination we usec the scelienace. described iu detail bw Izotov et al. (1991.. 1997)).," For the abundances determination we used the scheme, described in detail by Izotov et al. \cite{Izotov94}, \cite{Izotov97}) )."316 The electron temperatures aud deusities iu Iraegious of the observe VV-ealaxies aud their abundances of O. N and Ne are sunnarzed in Table ," The electron temperatures and densities in -regions of the observed VV-galaxies and their abundances of O, N and Ne are summarized in Table \ref{Tab6}."317For VV 513 the [Orn]-line 1363 ls not detected., For VV 543 the ]-line 4363 is not detected.318 Therefore to estimate its metallicity we eniploy the empirical mcthod (see e.g. Pagel et al. (1979)).," Therefore to estimate its metallicity we employ the empirical method (see e.g. Pagel et al. \cite{Pagel79}) ),"319 MeGaneh (1991)) and Olofssou (1997)))., McGaugh \cite{McGaugh91}) ) and Olofsson \cite{Olofsson97}) )).320 Its uucertaiuty for 12| log(O/II) canbe as large as 0.20.3 dex., Its uncertainty for 12+log(O/H) can be as large as 0.2–0.3 dex.321 We also applied this empirical method to allfour iudividual knots of VV 132., We also applied this empirical method to allfour individual knots of VV 432.322" The ratio Nu] of extinction corrected iuteusities of the A 11959.5007 and A665 Meemes""[8.658| eena one avoid well known ambiguity of the eimipirical method (Alloin ot al. 1979))."," The ratio ] of extinction corrected intensities of the lines $\lambda$ 4959,5007 and $\lambda$ 6548,6584 enable one to avoid well known ambiguity of the empirical method (Alloin et al. \cite{Alloin79}) )."323 Taking mto account these, Taking into account these324we should note that the level of hardening of the VUE 5-rav spectrum depends. in fact. only on the temperature of the photon fiekl and the optical depth.,"we should note that the level of hardening of the VHE $\gamma$ -ray spectrum depends, in fact, only on the temperature of the photon field and the optical depth."325 On the other hand. while the fhix ratio of the VIIE 5- and X-ray components depends mainly on (he size of the production area. the location of the secondary svuchrotvon peak is sensitive to the strength of (he magnetic field. to the photon temperature and the bulk Lorentz factor.," On the other hand, while the flux ratio of the VHE $\gamma$ - and X-ray components depends mainly on the size of the production area, the location of the secondary synchrotron peak is sensitive to the strength of the magnetic field, to the photon temperature and the bulk Lorentz factor."326 Finally. we note (hat certain radiation features of (he scenario do not depend on the model parameters ab all.," Finally, we note that certain radiation features of the scenario do not depend on the model parameters at all."327 This concerns. in particular. the slope of the 5-rav specüirum al GeV. energies. and the shape of the X-ray. spectrum.," This concerns, in particular, the slope of the $\gamma$ -ray spectrum at GeV energies, and the shape of the X-ray spectrum."328 The dependence of the results of radiation properties on several parameters limits. lo a certain extent. the predictive power of the suggested model.," The dependence of the results of radiation properties on several parameters limits, to a certain extent, the predictive power of the suggested model."329 This is à consequence of complex environment in blazars where several radiation and absorption processes can proceed simultaneously., This is a consequence of complex environment in blazars where several radiation and absorption processes can proceed simultaneously.330 In (his regard. the often used one-zone models wilh consideration of only svnchrotron aud IC radiation components produced in (he same region. are cuite useful for understanding the basic aspects of the problem. but can hardly properly describe the complex scenarios (hat take place in blazars.," In this regard, the often used one-zone models with consideration of only synchrotron and IC radiation components produced in the same region, are quite useful for understanding the basic aspects of the problem, but can hardly properly describe the complex scenarios that take place in blazars."331 In. particular. the results of (his paper demonstrate that the internal absorption not only cannot bepriory excluded from the consideration. but. in fact. in some cases can be invoked [or better explanation of observations of TeV 5-rav blazars.," In particular, the results of this paper demonstrate that the internal absorption not only cannot be excluded from the consideration, but, in fact, in some cases can be invoked for better explanation of observations of TeV $\gamma$ -ray blazars."332been used for £ in üme-scale comparisons. Smith(1998) has demonstrated (hat LeLf is nol appropriate and that the mixing length L is some fraction of // that depends upon the thermal ancl eddy: profiles of the substellar object. aud upon the abundance prolile of the atmospheric constituent. (e.g.. CO) under consideration.,"been used for $L$ in time-scale comparisons, \citet{smith1998} has demonstrated that $L\approx H$ is not appropriate and that the mixing length $L$ is some fraction of $H$ that depends upon the thermal and eddy profiles of the substellar object, and upon the abundance profile of the atmospheric constituent (e.g., CO) under consideration."333 Using the procedure outlined in Smith(1998).. Dézardetal.(2002) and Visscheretal.(2010) have confirmed that L~0.1H lor CO quenching kinetics in Jupiters (roposphlere. ancl we find that {ο0.1L to 0.341 is appropriate for CO quenching kinetics on Gliese 229D. A summary of results [rom our lime-scale approach is given in Table 1.. which lists L/1/ ratios for CO quenching for different. values of A...," Using the procedure outlined in \citet{smith1998}, \citet{bezard2002} and \citet{visscher2010icarus} have confirmed that $L\sim 0.1H$ for CO quenching kinetics in Jupiter's troposphere, and we find that $L\sim0.1H$ to $0.3H$ is appropriate for CO quenching kinetics on Gliese 229B. A summary of results from our time-scale approach is given in Table \ref{tab: CO quench}, which lists $L/H$ ratios for CO quenching for different values of $K_{zz}$."334 The use of £Lzz{ in chemical models involving CO=CIL; quenching kinetics (along with the use of incorrectly caleulated reverse rate coefficients: see relss;Hteverse Reactions)) mav have serious implications for vertical mixing estimates on brown clwarls such as Gliese 229D. for which CO quench chenistrv has been used to estimate the value of νι. (Griffith&Yelle1999).," The use of $L\approx H$ in chemical models involving $\textrm{CO}\rightleftarrows\textrm{CH}_{4}$ quenching kinetics (along with the use of incorrectly calculated reverse rate coefficients; see \\ref{ss:Reverse Reactions}) ) may have serious implications for vertical mixing estimates on brown dwarfs such as Gliese 229B, for which CO quench chemistry has been used to estimate the value of $K_{zz}$ \citep[][]{griffith1999}."335. For example. earlier investigators have constrained Kk... on Gliese 229B tobe in the range of ~107210 eni? ! based upon previous suggestions of the rate-Imiting step and assuming Leff (e.g..Griffith&Yelle1999:Saumonetal. 2007).," For example, earlier investigators have constrained $K_{zz}$ on Gliese 229B tobe in the range of $\sim10^{2}-10^{4}$ $^{2}$ $^{-1}$ based upon previous suggestions of the rate-limiting step and assuming $L\approx H$ \citep[e.g.,][]{griffith1999,saumon2000,leggett2007,mainzer2007}."336. One explanation [or relatively low A.. values is Chal the CO quench level could be in the radiative zone where convection no longer dominates. such that. A. could approach the slugeish values tvpically found in planetary lower stratospheres (e.g..Griffith&Yelle1999:Sammonetal.2000.2003)..," One explanation for relatively low $K_{zz}$ values is that the CO quench level could be in the radiative zone where convection no longer dominates, such that $K_{zz}$ could approach the sluggish values typically found in planetary lower stratospheres \citep[e.g.,][]{griffith1999,saumon2000,saumon2003iau}."337 ILowever. the predicted negative temperature gradient. (Sammonοἱal.2000) at the CO quench point of a [few tens of bars on Gliese 229D is larger (han is (wpically found in stagnant. low-mixine regions in planetary alinospheres (in fact. temperature gradients are twpically positive in such stagnant regions where A.. is inferred to be in the ~10? 101| en? ! range in planetary almospheres: see Yung&DeMore 1999)).," However, the predicted negative temperature gradient \citep{saumon2000} at the CO quench point of a few tens of bars on Gliese 229B is larger than is typically found in stagnant, low-mixing regions in planetary atmospheres (in fact, temperature gradients are typically positive in such stagnant regions where $K_{zz}$ is inferred to be in the $\sim$ $^{2}$ $10^{4}$ $^{2}$ $^{-1}$ range in planetary atmospheres; see \citealt{yung1999}) )."338 The low derived A.. values in the ~10 100-bar region of Gliese 229B and other brown clwarls are therelore surprising., The low derived $K_{zz}$ values in the $\sim$ 10–100-bar region of Gliese 229B and other brown dwarfs are therefore surprising.339 However. in contrast lo previous investigations. our thermochemical kinetics and transport model and model-data comparisons shown in Figure 2. suggest that the atmosphere of Gliese 229D is unlikely (o be stagnant at the CO quench point.," However, in contrast to previous investigations, our thermochemical kinetics and transport model and model-data comparisons shown in Figure \ref{figure:monoxide} suggest that the atmosphere of Gliese 229B is unlikely to be stagnant at the CO quench point."340 We find (hat A. values greater than i Cli2 1 are. needed (o explain (he observed CO mole fraction of GQGOO ppm for assumed metalliticites that range from [Fe/Il] = -0.5 to -0.1 (Sammonetal.2000.. from an analysis of the 4.7 jou data of Nolletal.L997 and Oppenheimeretal. 1998)). or Ae. values greater 107 cni ! are needed [or the observed. lower limit on the CO mole fraction of 20 ppm. for an asstuned metallicity of [Fe/IH] = -0.6 (Griffith&Yelle 1999)..," We find that $K_{zz}$ values greater than $^7$ $^2$ $^{-1}$ are needed to explain the observed CO mole fraction of 60–600 ppm for assumed metalliticites that range from $[\textrm{Fe/H}]$ = -0.5 to -0.1 \citealt{saumon2000}, from an analysis of the 4.7 $\mu$ m data of \citealt{noll1997} and \citealt{oppenheimer1998}) ), or $K_{zz}$ values greater $^4$ $^2$ $^{-1}$ are needed for the observed lower limit on the CO mole fraction of 20 ppm, for an assumed metallicity of $[\textrm{Fe/H}]$ = -0.6 \citep{griffith1999}. ."341" In comparison. free-convection and mixine-length theories (Stone1976). predict a A. values of 105 to 10"" cm? ! in the convection region of Gliese 229D. Our results therefore do not preclude strong convective mixing at the CO quench point on brown dwarls like Gliese 229D."," In comparison, free-convection and mixing-length theories \citep{stone1976} predict a $K_{zz}$ values of $^8$ to $^9$ $^2$ $^{-1}$ in the convection region of Gliese 229B. Our results therefore do not preclude strong convective mixing at the CO quench point on brown dwarfs like Gliese 229B."342The main observational challenge is obtaining high signal-to-noise measurements ancl then extracting both the circular velocity. [field and the vertical velocity dispersion.,The main observational challenge is obtaining high signal-to-noise measurements and then extracting both the circular velocity field and the vertical velocity dispersion.343 This is a (ractable problem., This is a tractable problem.344 The projected circular velocity produces a Doppler-shilted centroid of a spectral feature., The projected circular velocity produces a Doppler-shifted centroid of a spectral feature.345 The velocity dispersion can be determined from either the broadening of spectral lines. or by the width of the velocity distribution of a set of individual resolved objects.," The velocity dispersion can be determined from either the broadening of spectral lines, or by the width of the velocity distribution of a set of individual resolved objects."346 We emphasize (he fact that as long as the disk scale height. zi is independent of kr. ancl the selfl-supporting stellar disk dominates p(r.2). only velocity data are needed to test. [or variation in CP(r).," We emphasize the fact that as long as the disk scale height $z_0$ is independent of $r$, and the self-supporting stellar disk dominates $\rho(r,z)$, only velocity data are needed to test for variation in $CP(r)$."347 By selecting nearly lace-on galaxies [or (his test. we lose the ability to measure their vertical scale height and must instead appeal to a statistical argument that invokes measurements of edge-on analogous svstems.," By selecting nearly face-on galaxies for this test, we lose the ability to measure their vertical scale height and must instead appeal to a statistical argument that invokes measurements of edge-on analogous systems."348" Measurements of the light distribution of edge-on galaxies in {he near infrared. using images [rom the 2Mass survev (Dizvaev&Mitronova.2002) indicate (hat for (vpical galaxies the vertical scale heieht2s independent of galactic radius. with typical values of zo/f, varving between 0.1 and 0.4."," Measurements of the light distribution of edge-on galaxies in the near infrared, using images from the 2Mass survey \citep{Bizyaev02} indicate that for typical galaxies the vertical scale height independent of galactic radius, with typical values of $z_0/R_0$ varying between 0.1 and 0.4."349 We will therefore adopt the working hypothesis that το in equation (3) is independent of r., We will therefore adopt the working hypothesis that $z_0$ in equation (3) is independent of $r$.350 There are a few instances where a galaxy disks vertical velocity dispersion has been measured (e.g. Bottema (1993)))., 	 	 There are a few instances where a galaxy disk's vertical velocity 	 dispersion has been measured (e.g. \citet{Bottema93}) ).351 A recent data set on the kinematies of M33 (Ciardullo provides an interesting test case., A recent data set on the 	 kinematics of M33 \citep{Ciardullo04} provides an interesting test case.352 These authors obtained line-ol-sight velocity data on 140 planetary nebulae in M32., These 	 authors obtained line-of-sight velocity data on 140 planetary 	 nebulae in M33.353 This archival data set provides an opportunity [or aconcrele example of the C'P-xiolation test outlined. above., This archival data set provides an opportunity for a concrete 	 example of the $CP$ -violation test outlined above.354 This local group galaxy is inclined al 56 degrees to the plane of the sky., 	 	 This local group galaxy is inclined at 56 degrees to the plane of the sky.355 Various determinations (using multiple techniques) vield a distance modulus of 24.8 4 0.1mag., 	 Various determinations (using multiple techniques) yield a distance modulus of 	 24.8 $\pm$ 0.1.356 The radial scale lengths for light ave -- 2.5 kpe and RO= 1.56 kpe in the V and Ix bands. respectively.," The radial scale lengths for light are 	 $R_0^V=$ 2.5 kpc and $R_0^K=$ 1.56 kpc in the V and K bands, respectively."357 This implies (taking the 2\lass-derived (vpical values for. /5/z5) a, 	 This implies 	 (taking the 2Mass-derived typical values for $R_0/z_0$ ) a358internal pressure (n~3 LOW *j and leniperature (~ LOWS) of molecular gas cooled by CO line emission the characteristic stellar mass is around a solar mass.,internal pressure $nT \sim 3 \times 10^5$ K $^{-3}$ ) and temperature $\sim 10$ K) of molecular gas cooled by CO line emission the characteristic stellar mass is around a solar mass.359 In order to extend this argument so as to predict the characteristic mass scale for star formation at other epochs. and in dillerent environments. it is evidently. necessary to consider the factors determining both the gas temperature and the mean pressure within star forming complexes.," In order to extend this argument so as to predict the characteristic mass scale for star formation at other epochs, and in different environments, it is evidently necessary to consider the factors determining both the gas temperature and the mean pressure within star forming complexes."360 The former issue has been considered by numerous authors with he well known result that higher mass stars are to be expected at high redshift. both due to inellicient. cooling of primordial eas and also to the raising of the floor set » the temperature of the cosmic microwave background (c.g. Schwarzschild Spitzer 1953: Larson 150. 1998b).," The former issue has been considered by numerous authors with the well known result that higher mass stars are to be expected at high redshift, both due to inefficient cooling of primordial gas and also to the raising of the floor set by the temperature of the cosmic microwave background (e.g. Schwarzschild Spitzer 1953; Larson 1986, 1998b)."361 The vole of pressure variations has received. less attention. xuwtlv because of the much weaker (inverse. square root) dependence of the Jeans mass on pressure compared: with hat on temperature.," The role of pressure variations has received less attention, partly because of the much weaker (inverse square root) dependence of the Jeans mass on pressure compared with that on temperature."362 In nearby molecular clouds. two factors appear to be relevant in setting the pressure.," In nearby molecular clouds, two factors appear to be relevant in setting the pressure."363 First. it is evident that he attainment of the low temperatures needed: for star ormation requires that molecular coolants are selt-shielded against photodissociation bv the ambient. UV field (c.g. van Dishoeck Black LOSS)," First, it is evident that the attainment of the low temperatures needed for star formation requires that molecular coolants are self-shielded against photodissociation by the ambient UV field (e.g. van Dishoeck Black 1988)."364 ‘This imposes a minimum column density or molecular clouds. of around. 310-4 em7.," This imposes a minimum column density for molecular clouds of around $ 3 \times36510^{21}$ $^{-2}$."366 In a sel-eravitating svstem in which the Low velocities are comparable to their free-fall values. the pressure depends on the column density. according to 2CN? and thus he self-shielding requirement translates into a minimum viable pressure of around. 2. LOK em.7.," In a self-gravitating system in which the flow velocities are comparable to their free-fall values, the pressure depends on the column density according to $P \sim G \Sigma^2$ and thus the self-shielding requirement translates into a minimum viable pressure of around $2 \times 10^4$ K $^{-3}$."367 On the other iand. it is also apparent that the ambient pressure of he interstellar medium. (LSAL) plays a role in setting a ower limit to the mean internal pressure.," On the other hand, it is also apparent that the ambient pressure of the interstellar medium (ISM) plays a role in setting a lower limit to the mean internal pressure."368 Local giant molecular clouds (GAICS) are somewhat. self-gravitating and the internal pressure of molecular clouds thus exceeds he ambient pressure by around an order of magnitude., Local giant molecular clouds (GMCs) are somewhat self-gravitating and the internal pressure of molecular clouds thus exceeds the ambient pressure by around an order of magnitude.369 The pressure within GALCS (or. equivalentlv. their column densities) does however appear to scale with the ambient interstellar pressure. in that the pressures within CMCS in the Galactic centre are significantly higher than those in local clouds (Sanders. Scoville Solomon 1985).," The pressure within GMCs (or, equivalently, their column densities) does however appear to scale with the ambient interstellar pressure, in that the pressures within GMCs in the Galactic centre are significantly higher than those in local clouds (Sanders, Scoville Solomon 1985)."370 In the Following. we hypothesise that the pressure in star forming environments mocdestly exceeds that of the ambient. ISM.," In the following, we hypothesise that the pressure in star forming environments modestly exceeds that of the ambient ISM."371 Whereas we here focus on possible variations in the stellar EE. we co not actelress the history of the cosmic star ormation rate (SER).," Whereas we here focus on possible variations in the stellar IMF, we do not address the history of the cosmic star formation rate (SFR)."372 This problem has been investigate » many authors. both analytically anc numerically (e.g. orman Spaans 1997: Barkana Loch 2000: Springe Lernquist 2003).," This problem has been investigated by many authors, both analytically and numerically (e.g. Norman Spaans 1997; Barkana Loeb 2000; Springel Hernquist 2003)."373 A physical understanding of the cosmic SER crucially depends on the nature of the feedback exertec ov stàr formation on its surroundings., A physical understanding of the cosmic SFR crucially depends on the nature of the feedback exerted by star formation on its surroundings.374 The character of his feedback is in turn determined by the ünderlving EME., The character of this feedback is in turn determined by the underlying IMF.375 The results from our studs therefore provide an importan ingredient to the overall cllort to elucidate the star formation ustory of the universe., The results from our study therefore provide an important ingredient to the overall effort to elucidate the star formation history of the universe.376 In this paper. we estimate the characteristic stellar miss associated with bursts of star formation accompanving the formation of galaxies.," In this paper, we estimate the characteristic stellar mass associated with bursts of star formation accompanying the formation of galaxies."377 To this end. we consider the tvpical gas pressure and temperature in protogalaxies as they collapse and virialise.," To this end, we consider the typical gas pressure and temperature in protogalaxies as they collapse and virialise."378 In the context of a hierarchica model of cosmic structure formation. we evaluate how the characteristic stellar mass varies as a function of collapse redshift’ and halo mass.," In the context of a hierarchical model of cosmic structure formation, we evaluate how the characteristic stellar mass varies as a function of collapse redshift and halo mass."379" Specifically. we assume a ACDA cosmology with density parameters in matter O,,= and in barvons 5=0.045. a Hubble constan of b=io108 km ! |=0.7. and a scale-invarian power spectrum of density. Huctuations with an amplitude ax—0.9 on a scale of Sh + Alpe."," Specifically, we assume a $\Lambda$ CDM cosmology with density parameters in matter $\Omega_{m}=1-\Omega_{\Lambda}=0.3$ , and in baryons $\Omega_{\rmn B}=0.045$, a Hubble constant of $h=H_{0}/100$ km $^{-1}$ $^{-1}=0.7$, and a scale-invariant power spectrum of density fluctuations with an amplitude $\sigma_{8}=0.9$ on a scale of 8 $h^{-1}$ Mpc."380 In what follows. we adopt the view that the internal pressure in star forming svstems at cliferent cosmological epochs is approximately determined. by the ambient pressure in the JISM.," In what follows, we adopt the view that the internal pressure in star forming systems at different cosmological epochs is approximately determined by the ambient pressure in the ISM."381 In. particular. we will of focusing on the bursts of star formation that accompany the first collapse of gas into dark haloes during the assembly of galaxies.," In particular, we will be focusing on the bursts of star formation that accompany the first collapse of gas into dark haloes during the assembly of galaxies."382 We use insights rom recent numerical simulations into the thermodynamic xhaviour of gas in dark haloes virialising at high. recdshifts (Dromm. Coppi Larson 1999. 2002: Abel. Brvan Soran 2002).," We use insights from recent numerical simulations into the thermodynamic behaviour of gas in dark haloes virialising at high redshifts (Bromm, Coppi Larson 1999, 2002; Abel, Bryan Norman 2002)."383 As overdensities in the dark mater distribution turn around from the mean cosmic expansion ancl collapse. he barvons they contain are initially heated. by adiabatic compression.," As overdensities in the dark mater distribution turn around from the mean cosmic expansion and collapse, the baryons they contain are initially heated by adiabatic compression."384 For a halo virialising at redshilt z. the clark matter density at the point of virialisation is: where is the density of the background. Universe.," For a halo virialising at redshift $z$, the dark matter density at the point of virialisation is: where is the density of the background Universe."385" Assuming a cosmic ratio of barvons to clark matter of 0.15. the barvonic density at this point is: At this stage the temperature attained through acliabatic compression. 7500Ix. is considerably less than the virial temperature of the halo (see Barkana Loeb 2001) where Al,=AL/LO""AL.."," Assuming a cosmic ratio of baryons to dark matter of $0.15$, the baryonic density at this point is: At this stage the temperature attained through adiabatic compression, $T\sim386500{\rm \,K}$, is considerably less than the virial temperature of the halo (see Barkana Loeb 2001) where $M_{x}=M/10^{x}M_{\odot}$."387 The barvons. not being pressure supported in such a well. thus contract and continue to heat up.," The baryons, not being pressure supported in such a well, thus contract and continue to heat up."388 The further evolution depends on the mass of the halo., The further evolution depends on the mass of the halo.389" In the case of low mass haloes. the gas can attain a temperatureof i, by adiabatic compression alone."," In the case of low mass haloes, the gas can attain a temperatureof $\sim T_{\rmn vir}$ by adiabatic compression alone."390 The corresponding density can readily be estimated by extrapolating the adiabat from the thermodynamic state ats=100 (n=O.1em ον To 200K) to Lei:," The corresponding density can readily be estimated by extrapolating the adiabat from the thermodynamic state at $z=100$ $n \simeq 0.1 {\rm cm}^{-3}$ , $T\simeq 200 {\rm K}$ ) to $T_{\rmn vir}$ :"391by the five extremely metal poor stars (i.e. stars having [Fe/H]<—3.3) recently published by Norris.Ivan&Beers(2001).,by the five extremely metal poor stars (i.e. stars having $\rm [Fe/H]<-3.3$ ) recently published by \cite{NRB01}.392. The outline of the paper is as follows: the observational database will be discussed in section 2 while the theoretical vields will be presented in section 3., The outline of the paper is as follows: the observational database will be discussed in section 2 while the theoretical yields will be presented in section 3.393 Section 4 is devoted to the comparison between the observational ancl theoretical data., Section 4 is devoted to the comparison between the observational and theoretical data.394 A final discussion and conclusion follows., A final discussion and conclusion follows.395 The most recent and homogeneous database of surface abundances of extremely metal poor stus available up to now is the one published by Norris.Ryan&Beers(2001) and consists of five stars of metallicity lower than |Fe/I1I]—-3.3., The most recent and homogeneous database of surface abundances of extremely metal poor stars available up to now is the one published by \cite{NRB01} and consists of five stars of metallicity lower than [Fe/H]=-3.3.396 Three out of these five stars. Le. CD—38°245 (|[Fe/1I]—-3.98). CS 22172-002 ([Fe/II]—-3.61) and CS 22885-096 ([Fe/II]—-3.66) show a remarkably similar pattern (panel a in Figure 1)) with the exception of [C/Fe] which shows significative differences between CS 22172- 002 and CS 22385-096 (πο C abundance is available for CD— 387245).," Three out of these five stars, i.e. $\rm CD-38^{\rm o}245$ ([Fe/H]=-3.98), CS 22172-002 ([Fe/H]=-3.61) and CS 22885-096 ([Fe/H]=-3.66) show a remarkably similar pattern (panel a in Figure \ref{fig01}) ) with the exception of [C/Fe] which shows significative differences between CS 22172- 002 and CS 22885-096 (no C abundance is available for $\rm CD-38^{\rm o}245$ )."397 Given the close similarity among these three stars it is meaningful to define an “average” (hereinafter AVG) star which represents all three of them.," Given the close similarity among these three stars it is meaningful to define an ""average"" (hereinafter AVG) star which represents all three of them."398 The chemical pattern of this AVG star is shown in panel b) of the same ligure., The chemical pattern of this AVG star is shown in panel b) of the same figure.399 The comparison between the AVG star and CD—24717504 ([Fe/I1I1]—-3.37) is shown in panel c)., The comparison between the AVG star and $\rm CD-24^{\rm o}17504$ ([Fe/H]=-3.37) is shown in panel c).400 Also this star shows a chemical pattern which closely matehes that of the other three stars with the exception of the elements Cr and Mn which are significantly more abundant. (by a [actor three (to four) in CD—24°17504 than in the other three stars.," Also this star shows a chemical pattern which closely matches that of the other three stars with the exception of the elements Cr and Mn which are significantly more abundant (by a factor three to four) in $\rm CD-24^{\rm 401o}17504$ than in the other three stars."402 No C abundance determination is available for (his star., No C abundance determination is available for this star.403 Panel d) in the same figure shows the comparison between the AVG star and CS 22949-037 ([Fe/II]—- 3.79)., Panel d) in the same figure shows the comparison between the AVG star and CS 22949-037 ([Fe/H]=- 3.79).404 While there is a clear agreement between this and the AVG star for the elements from Ca to Ni. the lighter ones appear to be. in this star. much more abundant (bv a factor of five on the mean) (than in the AVG star.," While there is a clear agreement between this and the AVG star for the elements from Ca to Ni, the lighter ones appear to be, in this star, much more abundant (by a factor of five on the mean) than in the AVG star."405 This is clearly shown in panel e) where all the abundances of CS 22949-037 have been shifted downwarel bv 0.7 dex: all the elements between C and Si now follow a pattern similar to the one shown by the AVG star., This is clearly shown in panel e) where all the abundances of CS 22949-037 have been shifted downward by 0.7 dex: all the elements between C and Si now follow a pattern similar to the one shown by the AVG star.406" This star shows also an extremely high [N/Fe] ( 2.7 dex). value which is much larger than the factor of live required to fit the bulk of the elements up to Si,"," This star shows also an extremely high [N/Fe] $\simeq$ 2.7 dex), value which is much larger than the factor of five required to fit the bulk of the elements up to Si."407" Leaving apart this last star which certainly shows sienificative diflerences respect (o the other ones. we feel confident to sav that the other four stars are similar enough to be well represented bv the AVG star: therefore in the following we will consider (his ""template"" star as the ""observable"" worth to be compared with the theoretical expectations."," Leaving apart this last star which certainly shows significative differences respect to the other ones, we feel confident to say that the other four stars are similar enough to be well represented by the AVG star: therefore in the following we will consider this ""template"" star as the ""observable"" worth to be compared with the theoretical expectations."408the PDS are well described by a power law with iudex ~ cl. but the emission spectra for NS aud BIT XDs are very different.,"the PDS are well described by a power law with index $\gamma$ $\sim$ 1, but the emission spectra for NS and BH XBs are very different."409 For a disc-accretiug NB with a NS primary. the emission corresponding to the power law PDS is nou-thermal. while disc-acercting DII NBs exhibiting the same PDS have a thermal X-ray ciission spectra (7)..," For a disc-accreting XB with a NS primary, the emission corresponding to the power law PDS is non-thermal, while disc-accreting BH XBs exhibiting the same PDS have a thermal X-ray emission spectrum \citep{vdk94}."410 Indeed. ? oexiuunmed ~ 1 Thyte of RNTE archival data ou Galactic NBs. and found a region iu colom-colour space that is mniquely associated with BIT NBs in this ligh. soft state.," Indeed, \citet{don04} examined $\sim$ 1 Tbyte of RXTE archival data on Galactic XBs, and found a region in colour-colour space that is uniquely associated with BH XBs in this high, soft state."411 Hence. we mav lear a ercat deal about disc-accretiug binaries from their X-ray variability aud emission spectra.," Hence, we may learn a great deal about disc-accreting binaries from their X-ray variability and emission spectra."412 NGC300 X-1 and ICIO N-1 both have orbital periods ~30 hr and N-rav luminosities 107 Cres Lboprem.," NGC300 X-1 and IC10 X-1 both have orbital periods $\sim$ 30 hr and X-ray luminosities $\sim$ $^{38}$ erg $^{-1}$ \citep{carp07a,prest07,sf08}."413 We examined all existing NMM-Newton observations of NGC300 N-1 and ICLO A-1. in order to compare their properties.," We examined all existing XMM-Newton observations of NGC300 X-1 and IC10 X-1, in order to compare their properties."414 In particular. we examined the PDS from the N-rav lightcurves of these svstenüus for the first time.," In particular, we examined the PDS from the X-ray lightcurves of these systems for the first time."415 Iu Sect., In Sect.416 2 we describe the observations aud data analysis. then provide the results youn NGC 300 N-1 and ICIO liu turn in Sect. 3..," \ref{obs} we describe the observations and data analysis, then provide the results from NGC 300 X-1 and IC10 X-1 in turn in Sect. \ref{res}."417 We discuss our findings in Sect. 1.," We discuss our findings in Sect. \ref{discuss},"418 and consider four scenarios for NCC300 X-1 aud IC10 X-1l: wind accretion outo a neutron star. disc accretion outo a neutron star. wind accretion onto a black hole aud disc accretion outo a black hole.," and consider four scenarios for NGC300 X-1 and IC10 X-1: wind accretion onto a neutron star, disc accretion onto a neutron star, wind accretion onto a black hole and disc accretion onto a black hole."419 Finally we cdaaw our conclusions in Sect. 5.., Finally we draw our conclusions in Sect. \ref{conc}.420 Four NADENewton observations have been made of NGC 300 X-1. aud one of ICLO X-1: à journal of observations is provided iu Table 1..," Four XMM-Newton observations have been made of NGC 300 X-1, and one of IC10 X-1; a journal of observations is provided in Table \ref{journal}."421 For our analysis we used the NMME- SAS version 7.0. aud the FTOOLS suite. version 5.3.1.," For our analysis we used the XMM-Newton SAS version 7.0, and the FTOOLS suite, version 5.3.1."422 For each observation. we filtered out intervals of high backeround (faving). using the criteria reconuuended by the SAS team.," For each observation, we filtered out intervals of high background (flaring), using the criteria recommended by the SAS team."423 We note that 10 flaring occiued dunug the 2001. January or 2005. November observations of NCC300 λος," We note that no flaring occurred during the 2001, January or 2005, November observations of NGC300 X-1."424 We then extracted pu auc AIOS 0.3.10 keV Lehtcurves and spectra from a circular region centred on the source. along with corresponding response files.," We then extracted pn and MOS 0.3–10 keV lightcurves and spectra from a circular region centred on the source, along with corresponding response files."425 Background PC@IOUS were then chosen. aux hehtcurves aud spectra were obtained from these regions or pu aud MOS also.," Background regions were then chosen, and lightcurves and spectra were obtained from these regions for pn and MOS also."426 The pu ane MOS source aud background Lelitcurves ποσο co-acdced. after careful svuchromsatio: XMM ightcurves are non-svuchronised bv default. leaciug o artificial variability if uo treated properly (?)..," The pn and MOS source and background lightcurves were co-added, after careful synchronisation; XMM lightcurves are non-synchronised by default, leading to artificial variability if not treated properly \citep{bs07}."427 Backeround-subtracted lightcurves were analysed for variability. and PDS were made from the combined EPIC source lightcurves (hackgromc vot subtracted).," Background-subtracted lightcurves were analysed for variability, and PDS were made from the combined EPIC source lightcurves (background not subtracted)."428 These ightcurves were averaged over several intervals of 1021 nus. with 5.2 s linnine and ecoletric eroupile: the sanuple frequency range was U.10020.1 IIz.," These lightcurves were averaged over several intervals of 1024 bins, with 5.2 s binning and geometric grouping; the sampled frequency range was $\sim$ 0.0002–0.1 Hz."429 The source and background cussion spectra frou he two MOS cameras were combined with the FTOOL nathpha to give MOSI|MOS2 source and backerouud spectra. and the correspondiugo response inatrices and ancillary response files were combined also. with adcdriuf and addarf.," The source and background emission spectra from the two MOS cameras were combined with the FTOOL mathpha to give MOS1+MOS2 source and background spectra, and the corresponding response matrices and ancillary response files were combined also, with addrmf and addarf."430 We modeled the pu and combined MOS spectra simultaneously using NSPEC 11.3. with a coustaut of normalisation to account for differences in the pu aud MOS responses.," We modeled the pn and combined MOS spectra simultaneously using XSPEC 11.3, with a constant of normalisation to account for differences in the pn and MOS responses."431 We discuss our analysis of the variability aud N-rav spectra from δις000 ΔΝ and 1010 X-1 in the following sections., We discuss our analysis of the variability and X-ray spectra from NGC300 X-1 and IC10 X-1 in the following sections.432 The lightcurves frou the four NMM-Neswtou observatious of NO C300.N-1 are well described by ? aud will not be discussed. further here., The lightcurves from the four XMM-Newton observations of NGC300 X-1 are well described by \citet{carp07a} and will not be discussed further here.433 Each observation, Each observation434In this section. we discuss the potential of extracting information from. measurements of the combination frequencies.,"In this section, we discuss the potential of extracting information from measurements of the combination frequencies."435 We first. describe what information may be available. and then compare the observations of two variable white cwarls (a DA and à DB) with our analytical results.," We first describe what information may be available, and then compare the observations of two variable white dwarfs (a DA and a DB) with our analytical results."436 A major dilliculty of white dwarf asteroseimologv lies in our inability to securely identify the spherical degree (6) for the pulsation modes., A major difficulty of white dwarf asteroseimology lies in our inability to securely identify the spherical degree $\ell$ ) for the pulsation modes.437 In the cases where combination frequencies are detected. one could. use the observed. values of £2. (eq. 20] ," In the cases where combination frequencies are detected, one could use the observed values of $R_c$ (eq. \ref{eq:theory-Rc}] ])"438to determine the ( value for the principal modes., to determine the $\ell$ value for the principal modes.439 To illustrate this possibility. we consider the harmonic of a m=0 principal mode.," To illustrate this possibility, we consider the harmonic of a $m = 0$ principal mode."440 Phe ratio 67ές} (and. consequently the value of 42.) is significantly higher for (=2 than for (=]. except when Oy approaches 90° (sce Fig.," The ratio $G_{\ell \ell}^{04410}/(g_{\ell}^0 g_{\ell}^0)$ (and consequently the value of $R_c$ ) is significantly higher for $\ell= 2$ than for $\ell=1$, except when $\Theta_0 $ approaches $90^{\circ}$ (see Fig."442 2. and eq. 7]., \ref{fig:LtCv-Gfunctions} and eq. \ref{eq:Gvalueforl}] ]).443 This arises as the apparent amplitudes of higher é mocles suller stronger cancellation when integrated: over the stellar. cise while the harmonies of these modes. do not., This arises as the apparent amplitudes of higher $\ell$ modes suffer stronger cancellation when integrated over the stellar disc while the harmonics of these modes do not.444 Note that this is purely a geometric argument and a similar method. of £ identification would work not only for the sum or cdilference. combinations of two principal moces in white ναιΕς. but also for other variable stars that exhibit combination frequencies ancl where the amplitude of a combination frequency satisfies γεκατα; (as in eq. A4]])," Note that this is purely a geometric argument and a similar method of $\ell$ identification would work not only for the sum or difference combinations of two principal modes in white dwarfs, but also for other variable stars that exhibit combination frequencies and where the amplitude of a combination frequency satisfies $a_{i\pm j} \propto a_i a_j$ (as in eq. \ref{eq:general_combin}] ])"445 for every point on the stellar surface., for every point on the stellar surface.446 Inside the pulsational instability strip. the thermal time constant of the convection zone (τι) varies monotonically and sensitively with the stellar effective temperature.," Inside the pulsational instability strip, the thermal time constant of the convection zone $\tau_{c_0}$ ) varies monotonically and sensitively with the stellar effective temperature."447" The value of nz, discloses the relative location of a variable in the strip.", The value of $\tau_{c_0}$ discloses the relative location of a variable in the strip.448" In. addition. we can study convection under the white dwarf environment if we can empirically determine the TorTe, relation."," In addition, we can study convection under the white dwarf environment if we can empirically determine the $T_{\rm449eff}$ $\tau_{c_0}$ relation."450 Vime-resolyved spectroscopy. provides one wav to measure τρ (vanIxerkwij]ketal.1999)., Time-resolved spectroscopy provides one way to measure $\tau_{c_0}$ \cite{ltcv-marten98}.451.. Llowever. this technique requires. large telescopes ancl works only for relatively bright white chwarls.," However, this technique requires large telescopes and works only for relatively bright white dwarfs."452 What about using the combination frequencies?, What about using the combination frequencies?453" The relative phase between a combination. frequency and its principal modes (65,tja(oy,cU,) vields 7 straightforwardly (eq. 15].", The relative phase between a combination frequency and its principal modes $\psi_{i_0 \pm j_0} - (\psi_{i_0} \pm \psi_{j_0})$ ) yields $\tau_{c_0}$ straightforwardly (eq. \ref{eq:general-phase}] ]).454 This phase depends on τι more sensitively at. low frequency., This phase depends on $\tau_{c_0}$ more sensitively at low frequency.455 However. care needs to be taken to avoid svstematic ellects that allect phase measurcments adversely. such as the presence. of small neighbouring periodicities that are not accounted for.," However, care needs to be taken to avoid systematic effects that affect phase measurements adversely, such as the presence of small neighbouring periodicities that are not accounted for."456 Another way to measure τι is to take the ratio between the amplitudes of the sum ancl the dillerence combinations from the same pair of principal modes. (eq. 14] ," Another way to measure $\tau_{c_0}$ is to take the ratio between the amplitudes of the sum and the difference combinations from the same pair of principal modes, (eq. \ref{eq:general_combin}] ])"457the geometric factor cancels when one or both of mi. m; is 0.," the geometric factor cancels when one or both of $m_i$, $m_j$ is $0$."458 Note that amplitudes measured in the lower frequency region are generally [ess accurate due to higher noise levels., Note that amplitudes measured in the lower frequency region are generally less accurate due to higher noise levels.459 The two dimensionless numbers. 7 and 5. quantify the deepening of the convection zone when a white dwarf cools.," The two dimensionless numbers, $\beta$ and $\gamma$, quantify the deepening of the convection zone when a white dwarf cools."460 lt is therefore related: to the width of the white dwarf instability strip., It is therefore related to the width of the white dwarf instability strip.461" Let us associate the blue edge of the ZZ Ceti instability strip (Zi&12.000K) with τι=20s (when the lowest order (=1 eravity-mode miocle satisfies wt,=1. see Paper BD). and the red edge of the strip with τιν=1300s (when the 10005 period mode beconies invisible at the surface. wr,=10>l. see Paper 1)."," Let us associate the blue edge of the ZZ Ceti instability strip $T_{\rm eff} \approx 12,000 \K$ ) with $\tau_{c_0} = 20 \s$ (when the lowest order $\ell = 1$ gravity-mode mode satisfies $\omega \tau_{c_0}462= 1$, see Paper I), and the red edge of the strip with $\tau_{c_0} =4631300 \s$ (when the $1000 \s$ period mode becomes invisible at the surface, $\omega \tau_{c_0} = 10 \gg 1$, see Paper I)."464 We find the width of the instability strip to be ~1000Ix when we adopt 9|14 as in E2.1.., We find the width of the instability strip to be $\sim 1000 \K$ when we adopt $\beta + \gamma \sim -14$ as in \ref{sec:LtCv-origin}.465 A larger value of [72|5| would correspond. to a narrower instability strip., A larger value of $|\beta + \gamma|$ would correspond to a narrower instability strip.466 These numbers can be obtained from combination frequency measurements together with other unknown quantities., These numbers can be obtained from combination frequency measurements together with other unknown quantities.467 A number of practical cdilliculties may arise. in the actual analysis., A number of practical difficulties may arise in the actual analysis.468 For instance. dillerent 7 components of a eravitv-mocde are closely. spaced in frequency and. may not be resolved by observations of short duration. whereas in observations of sulliciently long duration temporal changes in the amplitudes of pulsation may occur.," For instance, different $m$ components of a gravity-mode are closely spaced in frequency and may not be resolved by observations of short duration, whereas in observations of sufficiently long duration temporal changes in the amplitudes of pulsation may occur."469 In the following sections. we apply our results ignoring these dilliculties.," In the following sections, we apply our results ignoring these difficulties."470 Lor our analysis of the DB variable GDS358. we use the Whole Earth Telescope (WET) data," For our analysis of the DB variable GD358, we use the Whole Earth Telescope (WET) data"471strongly suggests that these are noise artifacts.,strongly suggests that these are noise artifacts.472" Each of them, however, does show emission at some point along the ballistic stream."," Each of them, however, does show emission at some point along the ballistic stream."473 The Hell lline produces good results despite being far from the strongest line., The HeII line produces good results despite being far from the strongest line.474 The emission is spread out in a ring consistent with emission from a disk., The emission is spread out in a ring consistent with emission from a disk.475 Emission appears to extend along the stream in a similar way to the optical He line maps., Emission appears to extend along the stream in a similar way to the optical He line maps.476" Here, however, this emission region is significantly extended around the rim of the disk."," Here, however, this emission region is significantly extended around the rim of the disk."477 All of the ultraviolet maps from the ddataset also show a ring of emission consistent with a disk., All of the ultraviolet maps from the dataset also show a ring of emission consistent with a disk.478 A possible exception is OV wwhich appears to lack emission in the orbital phase range $= 0.1-0.5., A possible exception is OV which appears to lack emission in the orbital phase range $\phi=0.1$ –0.5.479 This may just be a relative deficit compared to the strong emission region., This may just be a relative deficit compared to the strong emission region.480 The NV line suffers from the interference of the Lya adjacent absorption which is difficult. to remove with great confidence., The NV line suffers from the interference of the $\alpha$ adjacent absorption which is difficult to remove with great confidence.481" The more isolated CIV wwould seem a better bet for a good result but, unfortunately, the line consists of two components separated by the equivalent ~500kms."," The more isolated CIV would seem a better bet for a good result but, unfortunately, the line consists of two components separated by the equivalent $\sim500~\mbox{km s}^{-1}$."482 Convolved with the double peaked disk profile this leaves a difficult dataset to disentangle and gives rise to the filling in of emission at low velocity., Convolved with the double peaked disk profile this leaves a difficult dataset to disentangle and gives rise to the filling in of emission at low velocity.483" The CIIIAA,, OV aand SiIV lines are all weaker, with the latter also sharing the complication of being a doublet."," The CIII, OV and SiIV lines are all weaker, with the latter also sharing the complication of being a doublet."484 While the reconstruction routine does allow such doublet lines to be specified with their relative strengths there is inevitably a loss of information in such an entangled case., While the reconstruction routine does allow such doublet lines to be specified with their relative strengths there is inevitably a loss of information in such an entangled case.485 The high points of emission in the CIII mmap all occur along the projected ballistic stream deep into the disk., The high points of emission in the CIII map all occur along the projected ballistic stream deep into the disk.486" The line is extremely weak and so potentially unreliable, however."," The line is extremely weak and so potentially unreliable, however."487" 'The high excitation line SiIVAA,, CIVAA,, NV aand OV ttomograms all show emission in the phase range $~ 0.65-0.75."," The high excitation line SiIV, CIV, NV and OV tomograms all show emission in the phase range $\phi\sim0.65$ –0.75."488" The latter two lines, with higher, but almost equal, ionization potentials, appear to come from further into the disk."," The latter two lines, with higher, but almost equal, ionization potentials, appear to come from further into the disk."489 None of this emission lies along the continuation of the ballistic stream or the Keplerian velocity corresponding to the stream position as envisioned by the overflowing stream model., None of this emission lies along the continuation of the ballistic stream or the Keplerian velocity corresponding to the stream position as envisioned by the overflowing stream model.490" However, it is consistent with the region downstream of the hot spot impact and/or the early part of a stream overflow."," However, it is consistent with the region downstream of the hot spot impact and/or the early part of a stream overflow."491 The SiIV, The SiIV492unWw,\ref{Choice}.493 We carried out observations for the MALT90 pilot survey in the austral winter of 2009 from June 19-91., We carried out observations for the MALT90 pilot survey in the austral winter of 2009 from June 15-24.494 The On-The-Fly (OTF) mapping mode of Mopra. was used., The On-The-Fly (OTF) mapping mode of Mopra was used.495 Maps were made with the beam center zuunius ou aJ. Ex ο Lerid., Maps were made with the beam center running on a .4 x .4 grid.496 At typical distances to ligl-mass star-ornüue regions (several kpc) this map size is suffiicicut o cover the expected spaial extent of a few parsces for our dense molecular cliys., At typical distances to high-mass star-forming regions (several kpc) this map size is sufficient to cover the expected spatial extent of a few parsecs for our dense molecular clumps.497 The scan rate was yper secoud., The scan rate was per second.498 The map is nade with sspacing between the rows. giviug 17 rows por map.," The map is made with spacing between the rows, giving 17 rows per map."499" Since he Mopra beam at 90 €Wz is36"". this row spacius xovides redundiauev iun he map."," Since the Mopra beam at 90 GHz is, this row spacing provides redundancy in the map."500 OFF positions were chosen at + 1 degree in Calactic latitude away from he plane (positive offset for sources at positive Galactic atitude aud vice-versa). aud though the OFF positions were not explicitly checked for line ciission. no map showed evidence of contamination from signal iu the OFF.," OFF positions were chosen at $\pm$ 1 degree in Galactic latitude away from the plane (positive offset for sources at positive Galactic latitude and vice-versa), and though the OFF positions were not explicitly checked for line emission, no map showed evidence of contamination from signal in the OFF."501 A single OFF position was observed for every two scan rows., A single OFF position was observed for every two scan rows.502 In general. maps were made scanning in strips of coustant Calactic longitude. although for two sources naps were also taken by scamming in strips of coustant Galactic latitucle.," In general, maps were made scanning in strips of constant Galactic longitude, although for two sources maps were also taken by scanning in strips of constant Galactic latitude."503" Pointing ou SiO imasers was performed every 1-10 hour. meiutainius pointing precision to better than about 10""."," Pointing on SiO masers was performed every 1-1.5 hour, maintaining pointing precision to better than about ."504". Typical system temperatures (T,,,) were 150 - 250 Iv aud were measured by paddle scans every 15 nüuutes.", Typical system temperatures $_{sys}$ ) were 150 - 250 K and were measured by paddle scans every 15 minutes.505 Weather conditions were variable., Weather conditions were variable.506 Sources observed uuder poor svsteiu temperatures (Ti; 2 500 19) or rapidly varvine conditions were re-observed πάσα nore clement conditions., Sources observed under poor system temperatures $_{sys}$ $>$ 500 K) or rapidly varying conditions were re-observed under more clement conditions.507" For cach source. ouly tle map taken with the lowest Ty,,. is preseuted here."," For each source, only the map taken with the lowest $_{sys}$ is presented here."508 The full 58 Giz bandwidth of MOPS was split into 16 zoom bands of 138 MIIZ each providing a velocity resolution of ~ (.11 kin 5 in cach baud. easily sufficient to resolve line cussion in a highauass star-forming region.," The full 8 GHz bandwidth of MOPS was split into 16 zoom bands of 138 MHz each providing a velocity resolution of $\sim$ 0.11 km $^{-1}$ in each band, easily sufficient to resolve line emission in a high-mass star-forming region."509 The ceutral frequencies are shown iu Table 2.. along with the line targeted at that frequency and what information that line primarily provides.," The central frequencies are shown in Table \ref{lines}, along with the line targeted at that frequency and what information that line primarily provides."510 The strougest lines were (1-0). UNC(1-0). (1-0). and TCN(1-0).," The strongest lines were (1-0), (1-0), (1-0), and (1-0)."511 These lines are all good tracers of dense gas. but provide slightly different information.," These lines are all good tracers of dense gas, but provide slightly different information."512 lis nore resistant to freeze-out on eraius than the bearing species (?).., is more resistant to freeze-out on grains than the carbon-bearing species \citep[][]{Bergin:2001}.513 iis particularly prevaleut in cold gas (2).., is particularly prevalent in cold gas \citep[][]{Hirota:1998}.514 ootten shows iufall signatures aud outflow wines (6.8. ?7)..," often shows infall signatures and outflow wings \citep[e.g.,][]{Rawlings:2004, Fuller:2005}."515 These stroug lines cau all be optically thick., These strong lines can all be optically thick.516 Two ixotopolosues. ((1-0) and ((1-0) were also observed and provide optical depth aud line profile information. (," Two isotopologues, (1-0) and (1-0) were also observed and provide optical depth and line profile information. ("517(2-1) is another optically thin colin density tracer by virtue of its low abundance.,2-1) is another optically thin column density tracer by virtue of its low abundance.518 We also iuclude ((2-1) but this molecule is too rare to be detected., We also include (2-1) but this molecule is too rare to be detected.519" A uunber of lines were chosen as tracers of hot core chenustry: (y=Sy Rh). (0-10. 9). (F=10%F=9 s8SLIINCO (Thy,Ny,—lo.1 29,3). GCav,=lig 31.2) C)."," A number of lines were chosen as tracers of hot core chemistry: $J_K = 5_1 - 4_1$ ), $J = 10 - 9 $ ), $J = 10 - 9, F = 9 - 8$ ), $J_{K_a,K_b}=4_{0,4}-3_{0,3}$ ), $J_{K_a,K_b}=4_{1,3}-3_{1,2}$ ) \citep[][]{Brown:1988}."520 These earbou-beariug species are typically oulv secu iu the hot cores around biglianuass protostars once molecules have been liberated off dust eraius by radiation or shocks., These carbon-bearing species are typically only seen in the hot cores around high-mass protostars once molecules have been liberated off dust grains by radiation or shocks.521 Three more lines trace particular euvironments: the recombination line ttraces ionized gas (2): ((2-1) is seen when lis formed from shocked dust erams. typically iu outflows ο lis produced in photocissociation regions (c.g..??).. the N=ο.=3/22.F=21 transition is the strongest of several limes in this spectral window.," Three more lines trace particular environments: the recombination line traces ionized gas \citep{Shukla:2004}; (2-1) is seen when is formed from shocked dust grains, typically in outflows \citep{Schilke:1997}; is produced in photodissociation regions \citep[e.g.,][]{Lo:2009, Gerin:2011}, the $N = 1 - 0, J = 3/2 - 1/2, F = 2 - 1 $ transition is the strongest of several lines in this spectral window."522 Henceforth we will refer to these line transitions by the molecule name where this usage is unanibieuous (i.c. iinstead of (1-0))., Henceforth we will refer to these line transitions by the molecule name where this usage is unambiguous (i.e. instead of (1-0)).523 The maps were reduced using the andpackages!?., The maps were reduced using the and.524. performs bandpass calibration using refercuce OFF scaus aud fits a 2ud order polvuoiial to the baseline., performs bandpass calibration using reference OFF scans and fits a 2nd order polynomial to the baseline.525 uses lis output to construct a uniformly eridded cube., uses this output to construct a uniformly gridded cube.526 Both polavizations were averaged together., Both polarizations were averaged together.527 A top-hat siuoothing kernel with radius of wwas used to determine which spectra coutribute signal o à pixel in the output map. aud spectra were weighted x the system tempcratire.," A top-hat smoothing kernel with radius of was used to determine which spectra contribute signal to a pixel in the output map, and spectra were weighted by the system temperature."528" This choice of parameters xoduces an effective heain size of FWIIM =72"".", This choice of parameters produces an effective beam size of FWHM =.529. The final cube is oversample in spatial frequency ypixels) aud is l'.6 x νο with the edees having sienificautly lower coverage. Le. iutegration time.," The final cube is over-sampled in spatial frequency pixels) and is .6 x .6 with the edges having significantly lower coverage, i.e. integration time."530 The data are presented on fjio antenna temperature scale , The data are presented on the antenna temperature scale$_{A}^{*}$ ).531"The bean efficieucv of Mopra is between 0.19 at 86 (Τὸ).GIIz aud 0.12 at 115€Wz (2). for converting T, iuto main-beam brightucss teuperature CE,,4)..", The beam efficiency of Mopra is between 0.49 at 86 GHz and 0.42 at 115 GHz \citep{Ladd:2005} for converting $_{A}^{*}$ into main-beam brightness temperature $_{mb}$ ).532 All the data, All the data533objects.,objects.534 Hubble Space Telescope imaging would likely reveal if this object is indeed gravitationally lensed., Hubble Space Telescope imaging would likely reveal if this object is indeed gravitationally lensed.535 'There are two sub-DLAs in the spectrum of this QSO., There are two sub-DLAs in the spectrum of this QSO.536" One system has an absorption redshift of za5;=00.8426 with a low metallicity ([Zn/H]« —0.98 and [Fe/H]=—1.28 and a kinematical width of Avgg=336 (2007)) and log =220.20+0.06 (Rao,Turnshek&Nestor 2006), and a second system at 245,,—00.8866 has a high metallicity ([Zn/H]=+0.25+0.06 and [Fe/H]=—0.58 with Avgo=994 Meiringetal. (2007))) and log =119.48 (Rao,Turnshek&Nestor2006)."," One system has an absorption redshift of 0.8426 with a low metallicity $<-$ 0.98 and $-1.28$ and a kinematical width of 36 \citet{Mei07}) ) and log $\pm$ 0.06 \citep{Rao06}, and a second system at 0.8866 has a high metallicity $\pm$ 0.06 and $-0.58$ with 94 \citet{Mei07}) ) and log 19.48 \citep{Rao06}."537. This field was observed in the griz filters., This field was observed in the $griz$ filters.538 Exposure times are given in Table 1.., Exposure times are given in Table \ref{Tab:Obs}. .539" The final combined frames are shown in the second row of Figure 1,, and the colour combined image composed of the gri frames is shown in Figure 2.."," The final combined frames are shown in the second row of Figure \ref{Fig:Fig1}, , and the colour combined image composed of the $gri$ frames is shown in Figure \ref{Fig:RGB}."540" The seeing in the final combined frames was ~0.9, 0.8, 1.1, and 1.1 arcsec in the g,r,i, and z filters respectively."," The seeing in the final combined frames was $\sim$ 0.9, 0.8, 1.1, and 1.1 arcsec in the $g,r,i,$ and $z$ filters respectively."541" Limiting magnitudes of ~26,25.5,25, and 23.5 were reached in the g,,i,z filters."," Limiting magnitudes of $\sim26,25.5,25,$ and 23.5 were reached in the $g,r,i,z$ filters."542" One object is detected in the imageswithin 10 arcsec of the QSO, 4.6 arcsec to the west of the QSO (corresponding to a comoving impact parameter of ~35 kpc at z=0.8426 or 36 kpc at z=0.8866)."," One object is detected in the imageswithin 10 arcsec of the QSO, 4.6 arcsec to the west of the QSO (corresponding to a comoving impact parameter of $\sim$ 35 kpc at z=0.8426 or $\sim$ 36 kpc at z=0.8866)."543 This object has been confirmed to be at z—0.8866 via integral field unit (IFU) observations (Pérouxetal. 2010).., This object has been confirmed to be at $z=0.8866$ via integral field unit (IFU) observations \citep{Per10}. .544 The software package was usedtodetermine a photometric redshift of zpno¢=0.79+ 0.08., The software package was usedtodetermine a photometric redshift of $z_{phot}=0.79\pm0.08$ .545have often been rejected as unfeasible for the most massive black holes A10M...,"have often been rejected as unfeasible for the most massive black holes $M > 10^9546\Msun$."547 This is because. if aceretion is assumed. to proceed at. or close to. the IEddington limit. extreme black hole masses AlLOMAL. will then. be produced in only 1LO” vr. and as discussed in Section 3 we find no evidence for any significant population of suc extreme-mass black holes within the SDSS quasar sample.," This is because, if accretion is assumed to proceed at, or close to, the Eddington limit, extreme black hole masses $M > 10^{10} \Msun$ will then be produced in only $1 \times 10^8$ yr, and as discussed in Section 3.2 we find no evidence for any significant population of such extreme-mass black holes within the SDSS quasar sample."548 Llowever. the lack of such extreme objects can be reconciled with our inferred Lower limit on quasar lifetime £o2.107 ve by revisiting the results shown in Fig 3..," However, the lack of such extreme objects can be reconciled with our inferred lower limit on quasar lifetime $t_Q > 2549\times 10^8$ yr by revisiting the results shown in Fig \ref{fig3}."550 Here it can be seen that. continued. Eddington-limited exponential erowth owards AZ~LO!AL. requires mass accretion rates which rapidly approach 100ML.vr.|.," Here it can be seen that continued Eddington-limited exponential growth towards $M \simeq 10^{10}551\Msun$ requires mass accretion rates which rapidly approach $100552{\rm M_{\odot} yr^{-1}}$."553 In contrast. allowing for the known scatter in the caleulation of bolometric luminosities (elvis et al.," In contrast, allowing for the known scatter in the calculation of bolometric luminosities (Elvis et al."554 1994). Fig 3. provides σου evidence that the most massive black holes are not acereting matter at a rate significantly.I in. excess of⋅ I0M.vr.nc.," 1994), Fig \ref{fig3}555 provides good evidence that the most massive black holes are not accreting matter at a rate significantly in excess of $10 {\rm M_{\odot} yr^{-1}}$."556 ‘Clearly. a 1079M. black role can continue to acerete niatter at Chis rate. and produce right quasar light fora substantial fraction ofa Civr withou ooducing a final black-hole mass in excess of a few times Lo’M...," Clearly, a $10^9 \Msun$ black hole can continue to accrete matter at this rate, and produce bright quasar light for a substantial fraction of a Gyr without producing a final black-hole mass in excess of a few times $10^9 \Msun$."557" In conclusion. our results imply that the majority of he most massive black-holes are in place by z2 and tha he most massive black holes accrete the bulk of their fina mass (Le.. as they grow fron⋅ c1077↽∣M. to 21070,7 M.) as optically luminous quasars. at à growth rate limitedsof » the Eedeington limit but by some other physical limi on fuel supply which prevents aceretion rates significantly in excess of LOAL.ver"," In conclusion, our results imply that the majority of the most massive black-holes are in place by $z \simeq 2$ and that the most massive black holes accrete the bulk of their final mass (i.e. as they grow from $\simeq 10^{8.5} \Msun$ to $\simeq 10^{9.5} \Msun$ ) as optically luminous quasars, at a growth rate limited by the Eddington limit but by some other physical limit on fuel supply which prevents accretion rates significantly in excess of $10 {\rm M_{\odot} yr^{-1}}$."558 Such a physical limit on. black-1ole Fuel supply might be imposed by accretion disc physics (ος. the calculations of Burkert Silk (2001) indicate that accretion disc viscosity can be expected to [limit the mass consumption rate of a supermassive black-hole at the centre ofa forming spheroid to 22.20M.vr. 4+) or by the physics of galaxy formation (e.g. Archibald et al.," Such a physical limit on black-hole fuel supply might be imposed by accretion disc physics (e.g. the calculations of Burkert Silk (2001) indicate that accretion disc viscosity can be expected to limit the mass consumption rate of a supermassive black-hole at the centre of a forming spheroid to $\simeq5592 - 20 {\rm M_{\odot} yr^{-1}}$ ) or by the physics of galaxy formation (e.g. Archibald et al."560 2002: Cuanato ct al., 2002; Granato et al.561 2001. 2003).," 2001, 2003)."562 In addition. one might speculate that the apparent lack of a substantial population of highly obsceured supermassive black holes may be a consequence of this sub-Edcineton accretion. as compared to the Lcledington-limited. accretion more Likely to be experienced. by. lower mass objects (Fabian 2003).," In addition, one might speculate that the apparent lack of a substantial population of highly obscured supermassive black holes may be a consequence of this sub-Eddington accretion, as compared to the Eddington-limited accretion more likely to be experienced by lower mass objects (Fabian 2003)."563 Virial black-hole mass estimates have been calculated for sample of 126908 quasars in the redshift interval 0.1<2o2 drawn from the SDSS Quasar Catalogue 11 (Schneider ct al., Virial black-hole mass estimates have been calculated for a sample of 12698 quasars in the redshift interval $0.1<z<2.1$ drawn from the SDSS Quasar Catalogue II (Schneider et al.564 2003)., 2003).565 The distribution of the quasar black-hole masses as a function of redshift has been presented and compared with the masses of dormant black-holes observed in the local Universe., The distribution of the quasar black-hole masses as a function of redshift has been presented and compared with the masses of dormant black-holes observed in the local Universe.566 In. addition. the quasar host-ealaxy properties implied. from an application of the locally observed: relationship between. black-hole and bulge mass have been compared with the known properties of local early-type galaxies.," In addition, the quasar host-galaxy properties implied from an application of the locally observed relationship between black-hole and bulge mass have been compared with the known properties of local early-type galaxies."567 By combining the black-hole mass estimates with the quasar bolometric uminosities the distribution of quasar accretion rates have oen investigated., By combining the black-hole mass estimates with the quasar bolometric luminosities the distribution of quasar accretion rates have been investigated.568 Furthermore. in combination with the optical quasar luminosity function. the new SDSS black-ole mass estimates have been used to estimate the number density of black-holes at z2 as a function of mass.," Furthermore, in combination with the optical quasar luminosity function, the new SDSS black-hole mass estimates have been used to estimate the number density of black-holes at $z\simeq 2$ as a function of mass."569 Finally. the activation fraction of black holes at 2.2 ws been estimated. by comparing the estimated. number density of active black holes with the local dormant black- mass function.," Finally, the activation fraction of black holes at $z\simeq 2$ has been estimated by comparing the estimated number density of active black holes with the local dormant black-hole mass function."570 The main conclusions of this study can » summarized as follows:, The main conclusions of this study can be summarized as follows:571G-band images used to derive the characteristic time scale of penumbral intensity variations.,G-band images used to derive the characteristic time scale of penumbral intensity variations.572 | used a simple inversion setup with field. properties constant with optical depth. corresponding to a horizontal separation of the field components.," I used a simple inversion setup with field properties constant with optical depth, corresponding to a horizontal separation of the field components."573 A more sophisticated setup. taking into account the variations along the line-of-sight. is planned to be discussed in a forthcoming paper.," A more sophisticated setup, taking into account the variations along the line-of-sight, is planned to be discussed in a forthcoming paper."574 For this work. two observations of the sunspot NOAA 10425 were analyzed.," For this work, two observations of the sunspot NOAA 10425 were analyzed."575 They were taken on the 7th and 9th of August 2003 with the two vector spectropolarimeters of the German Vacuum Tower Telescope (VTT) on Tenerife: the Polarimetric Littrow Spectrograph (POLIS:?) and the Tenerife Infrared Polarimeter (TIP:?).., They were taken on the 7th and 9th of August 2003 with the two vector spectropolarimeters of the German Vacuum Tower Telescope (VTT) on Tenerife: the Polarimetric Littrow Spectrograph \citep[POLIS;][]{beck+etal2005b} and the Tenerife Infrared Polarimeter \citep[TIP;][]{martinez+etal1999}.576 The two instruments. were used simultaneously using an achromatic 50-50-beamsplitter., The two instruments were used simultaneously using an achromatic 50-50-beamsplitter.577 During the observations. POLIS was remote-controlled by TIP to ensure strictly simultaneous exposures.," During the observations, POLIS was remote-controlled by TIP to ensure strictly simultaneous exposures."578 The image motion was reduced using the Correlation Tracker System (??)..," The image motion was reduced using the Correlation Tracker System \citep{schmidt+kentischer1995,ballesteros+etal1996}."579 The Stokes vector in the visible and infrared spectral lines listed in Table | was retrieved., The Stokes vector in the visible and infrared spectral lines listed in Table \ref{tablines} was retrieved.580 An integration time of around 3.5 see was used for each slit position., An integration time of around 3.5 sec was used for each slit position.581 The slit width was 07336 for TIP and 0755 for POLIS., The slit width was 36 for TIP and 5 for POLIS.582 The scanning step width was 0336., The scanning step width was 36.583 Spatial sampling along the slit was 07337 for TIP and 071145 for POLIS., Spatial sampling along the slit was 37 for TIP and 145 for POLIS.584 The POLIS data were interpolated later to have the same spatial sampling along the slit as TIP., The POLIS data were interpolated later to have the same spatial sampling along the slit as TIP.585 Figure 3. displays maps of the continuum intensity in the infrared., Figure \ref{spotim} displays maps of the continuum intensity in the infrared.586 The 2-D intensity. maps were constructed from the intensity along the slit for each scan step. the scanning direction is left to right.," The 2-D intensity maps were constructed from the intensity along the slit for each scan step, the scanning direction is left to right."587 The heliocentric angle of the spot on the August 7th and 9th was 7° and 30°. respectively.," The heliocentric angle of the spot on the August 7th and 9th was $^\circ$ and $^\circ$, respectively."588 The spatial resolution. was estimated. from the spatial Fourier power spectrum to be around I., The spatial resolution was estimated from the spatial Fourier power spectrum to be around $^{\prime\prime}$.589 The data from TIP and POLIS were treated with the flatfielding procedures and polarimetric corrections for instrumental effects (seeforexample??)..," The data from TIP and POLIS were treated with the flatfielding procedures and polarimetric corrections for instrumental effects \citep[see590for example][]{beck+etal2005b,beck+etal2005a}."591 Residual crosstalk between the different Stokes parameters was estimated to be on the order of 1077.., Residual crosstalk between the different Stokes parameters was estimated to be on the order of $10^{-3} I_{\rm c}$.592 The remaining rms noise in the profiles in continuum windows was 4x10777. for the IR spectra and 071. for the visible spectra., The remaining rms noise in the profiles in continuum windows was $4 \times 10^{-4} I_{\rm c}$ for the IR spectra and $10^{-3} I_{\rm c}$ for the visible spectra.593 The data alignment was done in the same way as described in detail in 2. or the Appendix of ?.., The data alignment was done in the same way as described in detail in \citet{beckthesis2006} or the Appendix of \citet{beck+etal2006d}.594 The wavelength scale was also set up like in the latter. with the blue-shift values predicted by the quiet Sun (QS) model of ὁ as a reference.," The wavelength scale was also set up like in the latter, with the blue-shift values predicted by the quiet Sun (QS) model of \citet{borrero+bellot2002} as a reference."595 The Stokes profiles of each spectral range were normalized to the continuum intensity of the quiet Sun at disk center in a two-step procedure., The Stokes profiles of each spectral range were normalized to the continuum intensity of the quiet Sun at disk center in a two-step procedure.596 An average QS profile for each wavelength range was calculated from pixels located outside the sunspot., An average QS profile for each wavelength range was calculated from pixels located outside the sunspot.597 This profile was normalized to unity with its respective average continuum intensity., This profile was normalized to unity with its respective average continuum intensity.598 The off-center position was taken into account by a multiplication of the QS profile and all other profiles with the appropriate limb-darkening coefficient., The off-center position was taken into account by a multiplication of the QS profile and all other profiles with the appropriate limb-darkening coefficient.599 The four visible and the three infrared lines have been inverted together using the SIR code (StokesInversionbasedonRe-sponsefunctions: ??)..," The four visible and the three infrared lines have been inverted together using the SIR code \citep[Stokes Inversion600based on Response functions;][]{cobo+toroiniesta1992,cobo1998}."601 To facilitate a good choice for the inversion setup and the initial model components to be used. | created masks of the inversion type.," To facilitate a good choice for the inversion setup and the initial model components to be used, I created masks of the inversion type."602 I used the intensity maps in infrared to define the boundaries between umbra and penumbra. and penumbra and surrounding granulation. respectively.," I used the intensity maps in infrared to define the boundaries between umbra and penumbra, and penumbra and surrounding granulation, respectively."603 Outside the sunspot. [ used a threshold 1 polarization degree to distinguish between field-free pixels and those with a polarization signal sufficiently large to derive the magnetic field.," Outside the sunspot, I used a threshold in polarization degree to distinguish between field-free pixels and those with a polarization signal sufficiently large to derive the magnetic field."604 The threshold was set to 0.4 for the infrared spectral lines (1564.8. nm) and 0.75 for the visible spectral lines (630.15. 630.25nm).," The threshold was set to 0.4 for the infrared spectral lines (1564.8, nm) and 0.75 for the visible spectral lines (630.15, nm)."605 If any one of the lines exceeded its respective threshold. a magnetic field was assumec to be present.," If any one of the lines exceeded its respective threshold, a magnetic field was assumed to be present."606 All model atmospheres were prescribed as a functior of continuum optical depth. r. in the range from logr=| to —4.," All model atmospheres were prescribed as a function of continuum optical depth, $\tau$ , in the range from $\log \tau = 1$ to $-4$."607 For the initial temperature stratification. 1 always adopted the HSRA model (?)..," For the initial temperature stratification, I always adopted the HSRA model \citep{gingerich+etal1971}."608 Temperature was allowed to be varied with two nodes. re. perturbations of the initial model atmosphere with a straight line of arbitrary slope were possible.," Temperature was allowed to be varied with two nodes, i.e. perturbations of the initial model atmosphere with a straight line of arbitrary slope were possible."609 A contribution of stray light to the observed profiles was also always allowed for: as proxy of the stray light profile the average QS profile was used., A contribution of stray light to the observed profiles was also always allowed for; as proxy of the stray light profile the average QS profile was used.610 | employed a two-component inversion with one magnetic and one field-free component forpixels outside the sunspot, I employed a two-component inversion with one magnetic and one field-free component forpixels outside the sunspot611objects are ejected at relatively high velocity before they are able to accrete enough material to become stars. thereby producing brown dwarfs.,"objects are ejected at relatively high velocity before they are able to accrete enough material to become stars, thereby producing brown dwarfs."612 We agree with the hypothesis of Reipurth Clarke (2001) and Bate et al. (, We agree with the hypothesis of Reipurth Clarke (2001) and Bate et al. (6132002a) that an effective mechanism for the formation of brown dwarves is the ejection of protostellar embryos from their natal cores.,2002a) that an effective mechanism for the formation of brown dwarves is the ejection of protostellar embryos from their natal cores.614 Such a mechanism also explains the low binarity of brown dwarfs., Such a mechanism also explains the low binarity of brown dwarfs.615 In our simulations. only one brown dwarf is present in a multiple system.," In our simulations, only one brown dwarf is present in a multiple system."616 The average ejection velocity of low mass objects is. - 2kms!. but brown dwarves have a slightly larger average ejection velocity than low-mass stars.," The average ejection velocity of low mass objects is $\sim 2\,{\rm km}\,{\rm s}^{-1}$ , but brown dwarves have a slightly larger average ejection velocity than low-mass stars."617 Also. no binary systems are ejected from cores.," Also, no binary systems are ejected from cores."618 Thus. dynamical ejections lead to a population of low-mass objects with low binarity.," Thus, dynamical ejections lead to a population of low-mass objects with low binarity."619 The higher velocity dispersion of this population should result in mass segregation in. young clusters on a relatively short timescale., The higher velocity dispersion of this population should result in mass segregation in young clusters on a relatively short timescale.620 Indeed. the average ejection velocity of brown dwarts (~2 kms ') exceeds the escape velocity from many small clusters.," Indeed, the average ejection velocity of brown dwarfs $\sim 2$ km $^{-1}$ ) exceeds the escape velocity from many small clusters."621 Thus. m small clusters of only a few Myrs. we would expect the spatial distribution of brown dwarves to be significantly larger than that of stars: and in older clusters the brown dwarf populatior may be significantly depleted by dispersion.," Thus, in small clusters of only a few Myrs, we would expect the spatial distribution of brown dwarves to be significantly larger than that of stars; and in older clusters the brown dwarf population may be significantly depleted by dispersion."622 The companion star frequency (CSF) over our ensemble is ~0.5., The companion star frequency (CSF) over our ensemble is $\sim 0.5$.623 This is far higher than in the field (e.g. Duquennoy Mayor 1991). but in good agreement with the high CSF observed for young clusters and T Tauri stars of 0.3 to 0.4 (Patience et al.," This is far higher than in the field (e.g. Duquennoy Mayor 1991), but in good agreement with the high CSF observed for young clusters and T Tauri stars of 0.3 to 0.4 (Patience et al."624 2002). especially given that we do not have the selection effects which may have reduced the observed CSFs.," 2002), especially given that we do not have the selection effects which may have reduced the observed CSFs."625 Presumably. over time the CSF of a young stellar population is altered by the disruption of multiple systems. reducing high initial CSFs to the field value (e.g. Kroupa 1995a. b).," Presumably, over time the CSF of a young stellar population is altered by the disruption of multiple systems, reducing high initial CSFs to the field value (e.g. Kroupa 1995a, b)."626 The CSF is very dependent upon mass. with low mass objects (< 0.5M..) having a CSF of only ~0.1. while more massive stars have a CSF of ~0.9.," The CSF is very dependent upon mass, with low mass objects $< 0.5 M_{\odot}$ ) having a CSF of only $\sim 0.1$, while more massive stars have a CSF of $\sim 0.9\,$."627 The huge difference between these two CSFs is due to the divide between low-mass systems which. almost by definition. are ejected from the natal core at an early stage in their growth. and high-mass systems which stick around in the centre of the natal core (interacting with the gas reservoir and with other stars) for a long time.," The huge difference between these two CSFs is due to the divide between low-mass systems which, almost by definition, are ejected from the natal core at an early stage in their growth, and high-mass systems which stick around in the centre of the natal core (interacting with the gas reservoir and with other stars) for a long time."628 This dependence of the CSF on mass ts in the same sense as the observed decline of CSF with decreasing mass (Patience et al., This dependence of the CSF on mass is in the same sense as the observed decline of CSF with decreasing mass (Patience et al.629 2002: Sterzik Durisen 2003 and references therein)., 2002; Sterzik Durisen 2003 and references therein).630 The binary and higher multiple systems m our simulations have properties consistent with observations of pre-Main Sequence and Main Sequence binaries., The binary and higher multiple systems in our simulations have properties consistent with observations of pre-Main Sequence and Main Sequence binaries.631 The distribution of orbital separations is wide. between 4 and 1.000au. with a median semi-major axis of ~30au.," The distribution of orbital separations is wide, between 4 and $1,000\,{\rm au}\,$, with a median semi-major axis of $\sim 30\,{\rm au}$."632 The distribution is consistent with a Gaussian fit to Duquennoy Mayor's (1991) sample of Main Sequence G-dwarves., The distribution is consistent with a Gaussian fit to Duquennoy Mayor's (1991) sample of Main Sequence G-dwarves.633 Close binaries are formed mainly by dynamical hardening of wider binaries., Close binaries are formed mainly by dynamical hardening of wider binaries.634 The distribution of orbital separations is then further modified by accretion. which can both harden or soften existing binaries (Whitworth et al.," The distribution of orbital separations is then further modified by accretion, which can both harden or soften existing binaries (Whitworth et al."635 1995: Bate Bonnell 1997)., 1995; Bate Bonnell 1997).636" The distribution of eccentricities is also consistent with the observations of Duquennoy Mayor (1991),", The distribution of eccentricities is also consistent with the observations of Duquennoy Mayor (1991).637 Mass ratios are the one binary property that evolves significantly in all of the simulations after 0.2Myr.," Mass ratios are the one binary property that evolves significantly in all of the simulations after $0.2\,{\rm Myr}\,$."638 At 0.2Myr. the mass ratios show a wide distribution with a peak in the range from q=0.5 to q=0.7.As close binaries evolve. their mass ratios tend towards higher values as (a) the lower-mass companion is more able to acerete material due to its higher angular momentum and location in the disc. and (b) even with similar accretion rates. the proportional increase in the mass of the secondary is larger (Whitworth et al.," At $0.2\,{\rm Myr}\,$, the mass ratios show a wide distribution with a peak in the range from $q = 0.5$ to $q = 0.7$.As close binaries evolve, their mass ratios tend towards higher values as (a) the lower-mass companion is more able to accrete material due to its higher angular momentum and location in the disc, and (b) even with similar accretion rates, the proportional increase in the mass of the secondary is larger (Whitworth et al."639 1995; Bate Bonnell 1997)., 1995; Bate Bonnell 1997).640 By 0.3Myr. the distribution of mass ratios shows a roughly linear rise with q. consistent with the observations of local G-dwarfs (Duquennoy Mayor 1991: Mahez et al.," By $0.3\,{\rm Myr}\,$, the distribution of mass ratios shows a roughly linear rise with $q$, consistent with the observations of local G-dwarfs (Duquennoy Mayor 1991; Mahez et al."641 1992)., 1992).642 Close binaries have higher mass ratios than wide binaries: viz., Close binaries have higher mass ratios than wide binaries; viz.643 all binaries with e<20au have gy>0.4 by 0.3Myr. whereas all but one of the binaries with ¢>20au have g<0.5.," all binaries with $a < 20\,{\rm au}$ have $q > 0.4$ by $0.3\,{\rm Myr}\,$, whereas all but one of the binaries with $a > 20\,{\rm au}$ have $q < 0.5\,$."644 The ensemble of simulations presented in. this paper represents only a single point in an extended parameter space., The ensemble of simulations presented in this paper represents only a single point in an extended parameter space.645 In future papers in this series we will examine the effect of different levels of turbulence on cores. as well as the effects of the power spectrum of the turbulence and the shape and structure of cores on star formation.," In future papers in this series we will examine the effect of different levels of turbulence on cores, as well as the effects of the power spectrum of the turbulence and the shape and structure of cores on star formation."646 We will also examine cores with different masses., We will also examine cores with different masses.647 We have presented an ensemble of simulations of star formation in turbulent dense cores. using initial. conditions based on observation.," We have presented an ensemble of simulations of star formation in turbulent dense cores, using initial conditions based on observation."648 The cores have an initial density profile with a flat 5.000au central region (the kernel) and an =1/77 fall-off beyond this out to 50.000au (the envelope).," The cores have an initial density profile with a flat $5,000\,{\rm au}$ central region (the kernel) and an $\approx 1/r^4$ fall-off beyond this out to $50,000\,{\rm au}$ (the envelope)."649 The central density is 3x1075eem. and the total core mass is 5.4M..," The central density is $3 \times 10^{-18}\,{\rm g}\,{\rm cm}^{-3}$, and the total core mass is $5.4 M_{\odot}$."650 The initial ratio of thermal to gravitational energy is cina= 0.45., The initial ratio of thermal to gravitational energy is $\alpha_{\rm therm} = 0.45$ .651 Without turbulence. a single. central star forms. as would be expected from analytical studies (e.g. Whitworth Ward- 2001).," Without turbulence, a single, central star forms, as would be expected from analytical studies (e.g. Whitworth Ward-Thompson 2001)."652" We then add low levels of turbulence with a low ratio of turbulent to gravitational energy of o4,= 0.05. The results can be summarised as follows.", We then add low levels of turbulence with a low ratio of turbulent to gravitational energy of $\alpha_{\rm turb} = 0.05$ The results can be summarised as follows.653"planetaries must have a deficit of objects between 2 ind ~4 mag below JA"". due to the rapid [ling of central stars whose nuclear reactions have recently stopped.","planetaries must have a deficit of objects between $\sim 2$ and $\sim 4$ mag below $M^*$, due to the rapid fading of central stars whose nuclear reactions have recently stopped."654 Indeed. ihe PNLFs of the 9MC and M33 show just this elfect: in these star-forming galaxies. the number of intermediate brightness planetaries drops significantly Ciardulloetal. 2004)...," Indeed, the PNLFs of the SMC and M33 show just this effect: in these star-forming galaxies, the number of intermediate brightness planetaries drops significantly \citep{jd02, m33}."655 No such deficit is present in the old stellar population of M31's bulge (Ciardulloetal.2004)., No such deficit is present in the old stellar population of M31's bulge \citep{m33}.656. In this svstem. it is likelv that most of the PNs do not participate in ihe PNLF cutolf. and join the luminosity [unction at fainter magnitudes.," In this system, it is likely that most of the PNs do not participate in the PNLF cutoff, and join the luminosity function at fainter magnitudes."657 These lower mass objects fill in the deficit produced by the high core-mass. binarv-evolved PNs. ancl cause the PNLF to appear strictly monotonic.," These lower mass objects fill in the deficit produced by the high core-mass, binary-evolved PNs, and cause the PNLF to appear strictly monotonic."658 Another implication of our blue strageler theory involves the stellar populations of elliptical galaxies., Another implication of our blue straggler theory involves the stellar populations of elliptical galaxies.659 Under our conservative mass transfer binary coalescence model. (he PNLE of early-(wpe systems is defined by binaries whose combined mass on the main sequence is erealer ~211...," Under our conservative mass transfer binary coalescence model, the PNLF of early-type systems is defined by binaries whose combined mass on the main sequence is greater $\sim 2 M_{\odot}$."660" As a population ages. fewer ancl fewer binaries will satisfy. this condition: consequently the number of such svstems. as reflected by Che 09,5. should decrease with time."," As a population ages, fewer and fewer binaries will satisfy this condition; consequently the number of such systems, as reflected by the $\alpha_{0.5}$, should decrease with time."661 The parameter therefore has the potential to probe a populations turnolE mass. even when that (πο is too faint [or cireet observation.," The parameter therefore has the potential to probe a population's turnoff mass, even when that turnoff is too faint for direct observation."662" Moreover. unlike the results of integrated light spectroscopy. the information provided by 04,5 will not be luminosity weighted."," Moreover, unlike the results of integrated light spectroscopy, the information provided by $\alpha_{0.5}$ will not be luminosity weighted."663 It may therefore be an effective complement to the traditional approach of studying elliptical galaxy populations via absorption-line indices., It may therefore be an effective complement to the traditional approach of studying elliptical galaxy populations via absorption-line indices.664 Of course. if à population is old enough. no binary svstem will have enough mass to evolve into an M* planetary. and (he PNLF will cease {ο be a reliable distance indicator.," Of course, if a population is old enough, no binary system will have enough mass to evolve into an $M^*$ planetary, and the PNLF will cease to be a reliable distance indicator."665 Fortunately. judging from the PNLF measurements to date (ie.Jacobyetal.1992:Ciardlullo2003).. and the presence of a high core-amass planetary in the Galactic globular cluster M15 (Alves.Dond.&Livio2000).. this time has not vel occurred.," Fortunately, judging from the PNLF measurements to date \citep[\ie][]{mudville, chile}, and the presence of a high core-mass planetary in the Galactic globular cluster M15 \citep{alves}, this time has not yet occurred."666 Finally. the contribution of binarv-evolved PNs to the PNLE has important implications for the use of planetary nebulae as (racers of a system's star-formation history aud chemical evolution.," Finally, the contribution of binary-evolved PNs to the PNLF has important implications for the use of planetary nebulae as tracers of a system's star-formation history and chemical evolution."667" For example. bv analvzing the line ratios and line fluxes of a set of PNs at a known distance. Dopitaetal.(L997) has shown (hat it is not only possible to measure the objects"" chemistry. but also the masses of the PNs’ central stars."," For example, by analyzing the line ratios and line fluxes of a set of PNs at a known distance, \citet{dopita} has shown that it is not only possible to measure the objects' chemistry, but also the masses of the PNs' central stars."668 Consequently. with the aid of an inilial-mass final-mass relation (e.g..Weidemann2000).. it is theoretically possible lo use planetaries (to (race a galaxys star formation and chemical enrichment history. back 10! vy.," Consequently, with the aid of an initial-mass final-mass relation \citep[\eg][]{weidemann}, it is theoretically possible to use planetaries to trace a galaxy's star formation and chemical enrichment history back $\sim 10^{10}$ yr."669 Unfortunately. the method only works if there is a unique relation between the mass of a PN's core and (he main-sequence mass of its progenitor star.," Unfortunately, the method only works if there is a unique relation between the mass of a PN's core and the main-sequence mass of its progenitor star."670 Our observations suggest that this is not the case. at least for the brightest. PNs in a galaxy.," Our observations suggest that this is not the case, at least for the brightest PNs in a galaxy."671 Because a substantial fraction of these objects evolve from binary stars. the use of bright planetaries for chemical evolution studies is problematic.," Because a substantial fraction of these objects evolve from binary stars, the use of bright planetaries for chemical evolution studies is problematic."672 (Westetal.2008).. Schiuuidtetal.2010b)..,"\citep[e.g.][]{boo10} \citep{west08}. \citep{H02, west04, west05,673 bootem, schmidt_sam}, \citep{west04,west08, kowalski09,674 kruse10,hilton10},"675 ancl tjo loxv-nuüass 1Utial mass ancl nuimositv fuucloli (Coveyetal.20080:Dochauskicta.2010).," and the low-mass initial mass and luminosity functions \citep{covey08,boo10}."676. AD chwarts have all sequeice. Lifetimes that are Cymusiclerably longer han the age of the Universe anc cal be used to trace the evolution o: both stellar propeities ixl the Milky Wax disks., M dwarfs have main sequence lifetimes that are considerably longer than the age of the Universe and can be used to trace the evolution of both stellar properties and the Milky Way disks.677 Westetal.(2006.20) Erowed that maceic activity {as traced by Πα} iiu M cawarts decreases wihn age aud tiat AL dwarts appe:w to have finite activity lifetinies from ~1-2 Cr for early-ype chwarts (MO-M3) ο 7 T-N Cv or later type stars (AI5-," \citet{west06,678 west08} showed that magnetic activity (as traced by $\alpha$ ) in M dwarfs decreases with age and that M dwarfs appear to have finite activity lifetimes from $\sim$ 1-2 Gyr for early-type M dwarfs (M0-M3) to $\sim$ 7-8 Gyr for later type stars (M5-M7)."679 These results are important for the habitability of extrasolar planets orbiting \ dwarfs (c.g.CharOli-neanctal. 2009).. as active stars may diuXt planeary amospheres (Seguraetal.2010).," These results are important for the habitability of extrasolar planets orbiting M dwarfs \citep[e.g.][]{mearth09}, as active stars may disrupt planetary atmospheres \citep{segura10}."680. The Ta enission does uot have sufficient energy to significautlv attect planeary nenis but has heen fouud to be correlate with X-ray euission (Reidetal.1995b:Covey20δα}. wuch can interact with extrasolar planet atinosphleres.," The $\alpha$ emission does not have sufficient energy to significantly affect planetary systems but has been found to be correlate with X-ray emission \citep{reid95,champ}, which can interact with extrasolar planet atmospheres."681 While Wa is the most commonly stucied emission line in M dwarts. the hieher-energy hydrogen Dalur al Ca II transitions are also present in the ootical spectra of active stars.," While $\alpha$ is the most commonly studied emission line in M dwarfs, the higher-energy hydrogen Balmer and Ca II transitions are also present in the optical spectra of active stars."682 The higher energy emission lines appear to trace different teniperature regions in the chromiospiere aud can be used to characonze the upper atinospl10105 of active M. dafs (Walkowiez&Hawley2009.audreferences therein)..., The higher energy emission lines appear to trace different temperature regions in the chromosphere and can be used to characterize the upper atmospheres of active M dwarfs \citep[and references therein]{walkowicz09}.683 However. lacking large suues of QW-lass stars with spectroscojc coverage across the eutire optical bandpass. it is sti] uot clear how hne various activity iudicators trace each other m active CM chwarts (Rauscher&Marcy.2006:WalkosviezTaw," However, lacking large samples of low-mass stars with spectroscopic coverage across the entire optical bandpass, it is still not clear how the various activity indicators trace each other in active M dwarfs \citep{rm06,walkowicz09}."684ev2009).. Westotal.(2008.hereaTerWS) also showed that the ratio of Call/TiO moleculay indices (aqiantitvthatislikelyrelatedtometallicity:Gizis1997) decreased with height in the Calactic disk (a proxy for age).," \citet[hereafter W08]{west08} also showed that the ratio of CaH/TiO molecular indices \citep[a quantity that is likely related to metallicity;][]{gizis97}685 decreased with height in the Galactic disk (a proxy for age)."686 This tantalizing result sugeests that AL dwarfs cau be used to reconstruct the chemical evolution of the local, This tantalizing result suggests that M dwarfs can be used to reconstruct the chemical evolution of the local687increasing fraction of (he cloud mass starts to expand.,increasing fraction of the cloud mass starts to expand.688 Such expansion costs energy., Such expansion costs energy.689 Thus. configurations of verv high . are not physically accessible. as we shall see.," Thus, configurations of very high $\beta$ are not physically accessible, as we shall see."690 The lower dashed. horizontal line in Figure 1 corresponds to a o-value of 14.1.," The lower dashed, horizontal line in Figure 1 corresponds to a $\beta$ -value of 14.1."691 This is ihe Donnor-Ebert density contrast., This is the Bonnor-Ebert density contrast.692 In the standard. analysis. clouds of higher contrast are denamically unstable (Ebert1955:Bonnor1956).," In the standard analysis, clouds of higher contrast are dynamically unstable \citep{e55,b56}."693. We recall. however. (hat this instability arises [rom perturbations of a cloudFemperature.," We recall, however, that this instability arises from perturbations of a cloud."694 In. contrast. our sequence has varving effective sound speed.," In contrast, our sequence has varying effective sound speed."695 The DBonner-Ebert contrast no longer marks a stability transition., The Bonner-Ebert contrast no longer marks a stability transition.696 Nevertheless. (his value. which we denote as μμ. is still of interest.," Nevertheless, this value, which we denote as $\beta_{\rm min}$, is still of interest."697 It signifies. al least in an approximate wav. (he point where sell-eravily starts to overwhelm external pressure as (he main compressive force.," It signifies, at least in an approximate way, the point where self-gravity starts to overwhelm external pressure as the main compressive force."698 Our description of cloud evolution will hencelorth focus on such gravitv-dominated configurations. i... those lor whichyin.," Our description of cloud evolution will henceforth focus on such gravity-dominated configurations, i.e., those for which."699 To analvze stability in (he present sequence. we first need to invoke thermodyvnanmics.," To analyze stability in the present sequence, we first need to invoke thermodynamics."700 We showed in Paper I that energy dissipation in an isothermal cloud results in a decrease of the total enthalpy., We showed in Paper I that energy dissipation in an isothermal cloud results in a decrease of the total enthalpy.701 Returning to dimensional notation. equation (ALO) stated where L is the luminosity.," Returning to dimensional notation, equation (A10) stated where $L$ is the luminosity."702 The enthalpy Jf is the generalization. to a sell-gravitating gas. of the classic definition: where Zia and £44 ave the thermal and gravitational potential energies. respectively. and V is the eloud volume.," The enthalpy $H$ is the generalization, to a self-gravitating gas, of the classic definition: where $E_{\rm therm}$ and $E_{\rm grav}$ are the thermal and gravitational potential energies, respectively, and $V$ is the cloud volume."703 To evaluate [μμ we employ the general expression for a nonrelativistic gas. (3/2)fPdV," To evaluate $E_{\rm therm}$ , we employ the general expression for a nonrelativistic gas, $(3/2)\int\!P\,dV$."704 Using equation (3) for P. this integral becomes (3/2).«5.," Using equation (3) for $P$, this integral becomes $(3/2) M_\circ\,a_T^2$."705 Instead of evaluating. E directly. we invoke the virial theorem. in the form After expressing the eloud volume in terms of theradius. the enthalpy is," Instead of evaluating $E_{\rm grav}$ directly, we invoke the virial theorem, in the form After expressing the cloud volume in terms of theradius, the enthalpy is"706A reanalysis is made for the helium. abundance determination for the Izotov-Thuan (2004) spectroscopic sample of extragalactic IL IL regions.,A reanalysis is made for the helium abundance determination for the Izotov-Thuan (2004) spectroscopic sample of extragalactic H II regions.707" We find that the effect of underlving stellar absorption of the He I lines. which is more important for metal poor svstems. affects signilicantlv the inferred. primordial helium abundance Y, obtained in the zero metallicity liit and the slope of linear extrapolation. dY/dZ."," We find that the effect of underlying stellar absorption of the He I lines, which is more important for metal poor systems, affects significantly the inferred primordial helium abundance $Y_p$ obtained in the zero metallicity limit and the slope of linear extrapolation, $dY/dZ$."708" This brings Y, from 0.234+0.004 to 0.25040.004 and dY/dZ=4.741.0 0 L.12c1.4.", This brings $Y_p$ from $0.234\pm0.004$ to $0.250\pm 0.004$ and $dY/dZ=4.7\pm 1.0$ to $1.1\pm 1.4$.709" Conservativelv. (is indicates (he importance of the proper understanding of wnderlving stellar absorption for accurate determinations of the primordial helium abundance to the error of 03,70.002—0.004."," Conservatively, this indicates the importance of the proper understanding of underlying stellar absorption for accurate determinations of the primordial helium abundance to the error of $\delta Y_p\simeq 0.002-0.004$."710" lzotov and Thuan (2004: hereinafter FT04) presented the primordial helium abundance Y,=0.242+0.002. consistently with their earlier publications (Izotov and Thuan 1993. and references therein). from. helium recombination lines in metal poor extragalactic HII regions."," Izotov and Thuan (2004; hereinafter IT04) presented the primordial helium abundance $Y_p=0.242\pm0.002$, consistently with their earlier publications (Izotov and Thuan 1998, and references therein), from helium recombination lines in metal poor extragalactic HII regions."711 This is significantly higher than the earlier values given by a number of authors (Pagel et al., This is significantly higher than the earlier values given by a number of authors (Pagel et al.712 1992: Olive et al., 1992; Olive et al.713 1997: Peimbert et al., 1997; Peimbert et al.714 2000). vet is significantly lower bv three standard deviations (han the expectation from the barvon abundance constrained from CMD temperature anisotroples (Spereel et al.," 2000), yet is significantly lower by three standard deviations than the expectation from the baryon abundance constrained from CMB temperature anisotropies (Spergel et al."715 2003)» with the aid of Dig-Dang nucleosvuthesis, 2003) with the aid of Big-Bang nucleosynthesis.716 Particularly intriguing is the small errors which are common (o nearly all analyses., Particularly intriguing is the small errors which are common to nearly all analyses.717 We suspect that (his mieht not represent properly the error including svstematics., We suspect that this might not represent properly the error including systematics.718 IT04 provided high quality spectroscopic data for 33 HIT regions detailed enough for us to repeat (he analvsis., IT04 provided high quality spectroscopic data for 33 HII regions detailed enough for us to repeat the analysis.719 In (his paper we are particularly concerned with the effect induced by, In this paper we are particularly concerned with the effect induced by720Puzia (2006) (see also Sharina Davoust. 2009) allowed us to estimate age. |Z/1l]. and alpha-element ratio for each individual GC simultaneously.,"Puzia (2006) (see also Sharina Davoust, 2009) allowed us to estimate age, [Z/H], and alpha-element ratio for each individual GC simultaneously."721 It minimizes the summed difference over all Lick indices between the observational ancl (theoretical index values. weighed bv the errors of index measurements.," It minimizes the summed difference over all Lick indices between the observational and theoretical index values, weighed by the errors of index measurements."722 The theoretical Lick indices were obtained using linear interpolation on the grids of Simple Stellar Population models of Thomas et al. (, The theoretical Lick indices were obtained using linear interpolation on the grids of Simple Stellar Population models of Thomas et al. (7232003. 2004).,"2003, 2004)."724 The errors on the evolutionary parameters depend on (he errors of Lick indices and on the accuracy of the radial velocities., The errors on the evolutionary parameters depend on the errors of Lick indices and on the accuracy of the radial velocities.725 The random errors of Lick index measurement in mnmdividual spectra depend primarily on the S/N ratio in the spectra., The random errors of Lick index measurement in individual spectra depend primarily on the S/N ratio in the spectra.726 The twpical source of systematic errors of Lick indices is quality of calibrations of an instrumental svstem into the Lick standard one (Worthey et al., The typical source of systematic errors of Lick indices is quality of calibrations of an instrumental system into the Lick standard one (Worthey et al.727 1994)., 1994).728 The comparison of our new metallicity determinations for the entire data set of GCs from Beasley et al. (, The comparison of our new metallicity determinations for the entire data set of GCs from Beasley et al. (7292008). based on their published Lick indices. with metallicities from Beaslev οἱ al.,"2008), based on their published Lick indices, with metallicities from Beasley et al."730 show a very good correlation (r  0.9: Fig., show a very good correlation (r $\simeq$ 0.9; Fig.731 1)., 1).732 The photometric metallicities are available for all the GCs of our In PCA our goal is to reduce the large number of parameters in a data set to a minimum number while retaining a maximum variation among the objects (here GCs) under consideration., The photometric metallicities are available for all the GCs of our In PCA our goal is to reduce the large number of parameters in a data set to a minimum number while retaining a maximum variation among the objects (here GCs) under consideration.733 The techuique therefore helps to sort out the optimum set of parameters that causes the maximum overall variation in the nature of GC's in NGC 5128., The technique therefore helps to sort out the optimum set of parameters that causes the maximum overall variation in the nature of GCs in NGC 5128.734" We initiallv excluded the observations corresponding to C117 because the values of Riga, and <p.2 for this GC are significantlv. higher than those of all other GCs.", We initially excluded the observations corresponding to C177 because the values of $R_{tid}$ $r_{h}$ and $<\mu_v>_h$ for this GC are significantly higher than those of all other GCs.735 We started with the, We started with the736The goal of iupaiuntiug is to restore missing or damaged regions of an iuase. in such a wav that the restored nap las the same statistical properties as the underlying tunasked map (2).,"The goal of inpainting is to restore missing or damaged regions of an image, in such a way that the restored map has the same statistical properties as the underlying unmasked map ."737. Sparse Iupaiutiug has been proposed or filling the gaps in CMD maps and for weak lensing bass nap reconstruction (27)., Sparse Inpainting has been proposed for filling the gaps in CMB maps and for weak lensing mass map reconstruction .738. Iu. ?).. it has been shown hat he sparse inpaintineC» method does not destrov the CNID weals leusing signal. aud is therefore an elegaur way o handle the mask problem.," In , it has been shown that the sparse inpainting method does not destroy the CMB weak lensing signal, and is therefore an elegant way to handle the mask problem."739 The inpainting problem can be defined as follows., The inpainting problem can be defined as follows.740 Let X be the ideal complete inage. Y the observed incomplete nuage (nuages can be fields ou the sphere) aud £ the binary mask (ic. Z|h.7]= lif we have information at pixel (hk.T). L|h.1|=0) otherwise).," Let $X$ be the ideal complete image, $Y$ the observed incomplete image (images can be fields on the sphere) and $L$ the binary mask (i.e. $L[k,l] = 1$ if we have information at pixel $(k,l)$, $L[k,l] = 0$ otherwise)."741 In short. we have: Y= LX.," In short, we have: $Y = L X$ ."742 lupaiutiug cousists in recovering VY kuowine Y aud £L., Inpainting consists in recovering $X$ knowing $Y$ and $L$.743 The masking effect can be thought of as a loss of sparsity in the spherical harmonic domain since the information required to defiue the map has been spread across the spherical Larinonic basis., The masking effect can be thought of as a loss of sparsity in the spherical harmonic domain since the information required to define the map has been spread across the spherical harmonic basis.744 Sparsity means that most of the information is concentrated in a few cocficieuts. which wheu sorted from the largest to the smallest. follow an expouential decay.," Sparsity means that most of the information is concentrated in a few coefficients, which when sorted from the largest to the smallest, follow an exponential decay."745 More details can be found in(?)., More details can be found in.746. In this paper. the choscu ‘dictionary’ is the spherical harmonic domain.," In this paper, the chosen `dictionary' is the spherical harmonic domain."747" Denoting the spherical harmonic basis as ® (so OF is the spherical harmonic transform. ic. the projector outo the spherical harmonic space). |y the fy pseudo-horn. i.c. the uuiuber of non-zero eutries in + aud | theclassical fy norm (i.e. |23,(cn }2). we thus want to"," Denoting the spherical harmonic basis as $\Phi$ (so $\Phi^T$ is the spherical harmonic transform, i.e. the projector onto the spherical harmonic space), $|| z ||_0$ the $l_0$ pseudo-norm, i.e. the number of non-zero entries in $z$ and $|| z ||$ theclassical $l_2$ norm (i.e. $ || z ||^2 = \sum_k (z_k)2 $ ), we thus want to"748The determination of the correct distance scale for metal-20ος objects has a large impact on a wide range of astrophysical problems. including the derivation of ages of globular clusters (a stringent lower limit to the age of he Universe). of the extragalactic distance scale (allecting he determination of the Llubble constant). as well as important test on stellar evolution models.,"The determination of the correct distance scale for metal-poor objects has a large impact on a wide range of astrophysical problems, including the derivation of ages of globular clusters (a stringent lower limit to the age of the Universe), of the extragalactic distance scale (affecting the determination of the Hubble constant), as well as important test on stellar evolution models."749 A long-stancing ively debate divides the astronomical community amongst supporters ofa short” and a” lone” distance scale: adoption of either of these two scales would have a deep inlluence on models for the universe. or for the formation of our own Galaxy (see e.g. Sandage 1993).," A long-standing lively debate divides the astronomical community amongst supporters of a ""short"" and a ""long"" distance scale: adoption of either of these two scales would have a deep influence on models for the universe, or for the formation of our own Galaxy (see e.g. Sandage 1993)."750 The recent distribution of the catalogue of calibrated trigonometric parallaxes. measured. by the LLPPARCOS satellite (Perryman et al., The recent distribution of the catalogue of calibrated trigonometric parallaxes measured by the HIPPARCOS satellite (Perryman et al.751 1997). has provided new opportunities for accurate estimates of this distance scale., 1997) has provided new opportunities for accurate estimates of this distance scale.752 Various authors (Reid 1997: Gratton et al., Various authors (Reid 1997; Gratton et al.753 19975: Pont et al., 1997b; Pont et al.754 1997) have used. parallaxes of nearby. subcwarls to calibrate the distances to globular clusters., 1997) have used parallaxes of nearby subdwarfs to calibrate the distances to globular clusters.755 Results obtained bv these three papers are significantly: different: this is because clillerent reddening anc metal abundance. scales were adopted for subedwarfs. anc dillerent corrections were applied to the original values in order to take into account [or the presence of undetected binaries.," Results obtained by these three papers are significantly different: this is because different reddening and metal abundance scales were adopted for subdwarfs, and different corrections were applied to the original values in order to take into account for the presence of undetected binaries."756 Undirect estimates of the distances to metal-poor objects have been obtained by considering the LMC distances based. on Cepheids. on turn calibrated against nearby objects (Feast. Catchpole 1991).," Undirect estimates of the distances to metal-poor objects have been obtained by considering the LMC distances based on Cepheids, on turn calibrated against nearby objects (Feast Catchpole 1997)."757 An alternative way to use ΕΙΟΛΗο parallaxes is to consider horizontal branch (LIB) stars. a traclitional distance Ladder for metal-poor population.," An alternative way to use HIPPARCOS parallaxes is to consider horizontal branch (HB) stars, a traditional distance ladder for metal-poor population."758 Fernley ct al. (, Fernley et al. (7591997) tried to measure cirectIv the distances to RR Lyrae variables: however only the prototvpe of this important class of pulsating stars is within 300 pe from the Sun. so that its parallax can be measured. with some reliability.,"1997) tried to measure directly the distances to RR Lyrae variables: however only the prototype of this important class of pulsating stars is within 300 pc from the Sun, so that its parallax can be measured with some reliability."760 In this paper we will use LUIPPARCOS parallaxes for three RR Lyracs. for a sample of nine red LED stars. selected on the basis of Strommeren photometry colours. and for ten field blue LIB branch stars.," In this paper we will use HIPPARCOS parallaxes for three RR Lyraes, for a sample of nine red HB stars, selected on the basis of Strömmgren photometry colours, and for ten field blue HB branch stars."761 Consideration of these other stars substantially enlarge the sample of nearby. metal-poor Η stars., Consideration of these other stars substantially enlarge the sample of nearby metal-poor HB stars.762 The sample is presented in Section 2: in Section 3 we discuss the derivation of the absolute magnitudes: finally the impact of the present results is briefly. discussed in Section 1., The sample is presented in Section 2; in Section 3 we discuss the derivation of the absolute magnitudes; finally the impact of the present results is briefly discussed in Section 4.763the on-axis case is constant with à=I. while in the OA case the flux could actually still be risine at the time of first detection.,"the on-axis case is constant with $\alpha = 1$, while in the OA case the flux could actually still be rising at the time of first detection."764 Iu adclition. the flux decay around τρως Is much shallower tha- a=L. which explains the larger fraction of second detections in OA case.," In addition, the flux decay around $M_{\rm max}$ is much shallower than $\alpha = 1$, which explains the larger fraction of second detections in OA case."765" To check the seusibility of OA simulation results. we look at the correlation hetween redshift cand jet halbopeniug augle 6;. shown iu Figure 7 (left),"," To check the sensibility of OA simulation results, we look at the correlation between redshift $z$ and jet half-opening angle $\theta_{\rm j}$, shown in Figure \ref{fig7} (left)."766 As expected. most 05 values are concentrated around the peak of 65 distribution (section 3.2.3}).," As expected, most $\theta_{\rm j}$ values are concentrated around the peak of $\theta_{\rm j}$ distribution (section \ref{sss3}) )."767 Most points have values of :<2., Most points have values of $z < 2$.768 This can be understood. since ligher redshift value results in a lower observed fux.," This can be understood, since higher redshift value results in a lower observed flux."769 Iu addition. the GRB redshift distribution (section 3.2.2)) peaks at :=1 and starts to decline at higher +.," In addition, the GRB redshift distribution (section \ref{sss2}) ) peaks at $z = 1$ and starts to decline at higher $z$."770 Nevertheless. a few OAs with high redshift are detected in the simulation.," Nevertheless, a few OAs with high redshift are detected in the simulation."771" Since all of these OAs have relatively low 6;. which uentralizes the ucgative redshift effect on the flux value. their detection is understandable,"," Since all of these OAs have relatively low $\theta_{\rm j}$, which neutralizes the negative redshift effect on the flux value, their detection is understandable."772 The majority of second detections have low redshift values aud uo preferable (64., The majority of second detections have low redshift values and no preferable $\theta_{\rm j}$.773 This is mostly because the majority of detections with the first telescope have low redshift values., This is mostly because the majority of detections with the first telescope have low redshift values.774 Because of the relatively fat Πο curve around the peakvalue (Figure 3)). once the OA lias becu detected with the first telescope. redshitt aud 6] are uot the crucial parameters for the second detection.," Because of the relatively flat light curve around the peakvalue (Figure \ref{fig3}) ), once the OA has been detected with the first telescope, redshift and $\theta_{\rm j}$ are not the crucial parameters for the second detection."775 In order to detect OA with the second clescope. the time tfy of the first detection. 1.6.. vefore or after the peak fw value. is inportaut.," In order to detect OA with the second telescope, the time $t-t_0$ of the first detection, i.e., before or after the peak flux value, is important."776" Figue 7T (right) also shows the correlation yetween redshift z aud observing auele 0, (vhich or the OAs has to be larger than 0; of a particular πα).", Figure \ref{fig7} (right) also shows the correlation between redshift $z$ and observing angle $\theta_{\rm obs}$ (which for the OAs has to be larger than $\theta_{\rm j}$ of a particular burst).777" If à burst has a low redshift. 0,4, can be quite large. as is evident in the long tail."," If a burst has a low redshift, $\theta_{\rm obs}$ can be quite large, as is evident in the long tail."778" On the other hand. a verv low obscrving angele helps iu he detection of an OA from a distant object. since the difference between 0; aud Goi, i5 nal and the burst is “almost? on-axis."," On the other hand, a very low observing angle helps in the detection of an OA from a distant object, since the difference between $\theta_{\rm j}$ and $\theta_{\rm obs}$ is small and the burst is 'almost' on-axis."779 Detectious with he second telescope do not appear to have a xeferable position iu the eraph., Detections with the second telescope do not appear to have a preferable position in the graph.780 Our-axis afterelows are initially rapidly facing aud they will be observed for lL. ls by each of nine transiting CCD detectors., On-axis afterglows are initially rapidly fading and they will be observed for 4.4 s by each of nine transiting CCD detectors.781 Iu principle. the change of magnitude iu that time. Le. iu observations bv two successive CCDs or CCD fieldl transit. could be observable.," In principle, the change of magnitude in that time, i.e., in observations by two successive CCDs or CCD field transit, could be observable."782 Therefore. we calculated the change of magnitude im Ll s for all detected on-axis atterglows and also for observations lastingas long as a particular afterglow is in the telescopes field of view.," Therefore, we calculated the change of magnitude in 4.4 s for all detected on-axis afterglows and also for observations lastingas long as a particular afterglow is in the telescope's field of view."783 The distribution of the chauge of maguitude for both cases is shown in Figure 8 (left)., The distribution of the change of magnitude for both cases is shown in Figure \ref{fig8} (left).784 We calculated the changes only for the first afterglow detection. since the probability of detection with the secoud telescope is siuall.," We calculated the changes only for the first afterglow detection, since the probability of detection with the second telescope is small."785 Iu practice. the change of magnitude could be detected only if it was larger than the photometric error.," In practice, the change of magnitude could be detected only if it was larger than the photometric error."786" The expected photometric errors. averaged across the sky. iu the case of Afi,=20 mae will ο 10 ummae at best (though it will be smaller or brighter events} (Perrvinanetal.2001)."," The expected photometric errors, averaged across the sky, in the case of $M_{\rm lim} = 20$ mag will be 10 mmag at best (though it will be smaller for brighter events) \citep{perryman}."787. The chances of observing the change in magnitudes will hus be Imited., The chances of observing the change in magnitudes will thus be limited.788" The change in magnitude of OAs will be even harder to detect. since the flux rises and decays unore slowly,"," The change in magnitude of OAs will be even harder to detect, since the flux rises and decays more slowly."789 Also. OA could actually (conie brighter through the observation if the detection happened prior to the peak lisht-curve value (Figure 8.. right).," Also, OA could actually become brighter through the observation if the detection happened prior to the peak light-curve value (Figure \ref{fig8}, right)."790 Looking at the time of detection relative to the initial CRB (Fieure 9)). most of on-axis afterelows are expected to be detected at ~0.1 dav after he GRD.," Looking at the time of detection relative to the initial GRB (Figure \ref{fig9}) ), most of on-axis afterglows are expected to be detected at $\sim 0.1$ day after the GRB."791 The time of detection is considerably arecr for OAs., The time of detection is considerably larger for OAs.792 Since they are still bright a few davs after a CRB. in addition to a considerable xobabilitv of prepeak detection. they could. also ο observed with Gere's second telescope and. if identified quickly. with erounud-based telescopes.," Since they are still bright a few days after a GRB, in addition to a considerable probability of prepeak detection, they could also be observed with $\textit{Gaia}$ 's second telescope and, if identified quickly, with ground-based telescopes."793 Since the chanee in afterglow magnitude while ρολο scanned by Gia dis not expected to be laree chougho to enable reliable wav of identification of a transient source as a CRB optical afterglow. we consider other possibilities for CRB afterelow identification from one short detection.," Since the change in afterglow magnitude while being scanned by $\textit{Gaia}$ is not expected to be large enough to enable reliable way of identification of a transient source as a GRB optical afterglow, we consider other possibilities for GRB afterglow identification from one short detection."794 Since Cia will have a photometric instruueut onboard. there is the possibility to ideutifv afterelow frou its spectral cnerey distribution (SED).," Since $\textit{Gaia}$ will have a photometric instrument onboard, there is the possibility to identify afterglow from its spectral energy distribution (SED)."795 It has been observed that the SED of afterelows follows a power-law (FLx Ü) modulated by extinction (Schadyetal.2010:Cremer2011).," It has been observed that the SED of afterglows follows a power-law $F_\nu \propto \nu^{-\beta}$ ) modulated by extinction \citep{schady, greiner}."796. We show the expected SED shape in UV-to-NIR. frequency range in Figure 10.. where an average spectral iudex value 9=0.6 has been assumed (Creeret 2011).," We show the expected SED shape in UV-to-NIR frequency range in Figure \ref{fig10}, where an average spectral index value $\beta = 0.6$ has been assumed \citep{greiner}. ."797. As shown in may statistical analyses. in the majority of cases the extinction iu CRB host ealaxies is best described with a so-called SAIC extinction profile (Pei 1991)..," As shown in many statistical analyses, in the majority of cases the extinction in GRB host galaxies is best described with a so-called SMC extinction profile \citep{pei}. ."798 Thus. we added," Thus, we added"799garect. degeneracy’ can be broken bw postulating that 1ο surface mass density of a reasonable galaxy cluster gaiould have dropped. to insignificant values αἲ the roundaries of a large field of view. or bw exploiting =nagnilication effects. either through the lensing elfects on 1 number counts of background galaxies. (Broadhurst. lTavlor Peacock 1995) or the size-magnitude relation (Dartelmann suavan 1995). which are not invariant under the transformation (11)).,"sheet degeneracy' can be broken by postulating that the surface mass density of a reasonable galaxy cluster should have dropped to insignificant values at the boundaries of a large field of view, or by exploiting magnification effects, either through the lensing effects on the number counts of background galaxies (Broadhurst, Taylor Peacock 1995) or the size-magnitude relation (Bartelmann Narayan 1995), which are not invariant under the transformation \ref{mass-sheet}) )."800 Another technical dilliculty is the following: In addition o the reconstructed surface mass density. the likelihood method to be described in Section ?? also requires a map of the shear which corresponds to this mass distribution.," Another technical difficulty is the following: In addition to the reconstructed surface mass density, the likelihood method to be described in Section \ref{ml-meth} also requires a map of the shear which corresponds to this mass distribution."801 However. calculating the shear from the surface mass density involves an integration extending bevond. the limited. data. region.," However, calculating the shear from the surface mass density involves an integration extending beyond the limited data region."802 Again. there will be no practical problems. if the surface mass density attains negligible values at the boundary. of the feld of view. provided. that there are no huge mass clumps lurking just outside of it.," Again, there will be no practical problems, if the surface mass density attains negligible values at the boundary of the field of view, provided that there are no huge mass clumps lurking just outside of it."803 ]xaiser (1995) showed that the dillerence. of the average surface mass densities within a circular aperture (με). and an annulus around that aperture &(Grj..c) can be calculated from the shear within the annulus: The variable  represents à radial coordinate measured from the centre of the aperture. and ry and we denote the inner and the outer radius of the annulus. respectively.," Kaiser (1995) showed that the difference of the average surface mass densities within a circular aperture $\overline{\kappa}(x_1)$ and an annulus around that aperture $\overline{\kappa}(x_1,x_2)$ can be calculated from the shear within the annulus: The variable $x$ represents a radial coordinate measured from the centre of the aperture, and $x_1$ and $x_2$ denote the inner and the outer radius of the annulus, respectively."804  is the tangential component of the shear and £(54)Gr) is its circularly averaged value as a function of the racial distance., $\gamma_{\rm t}$ is the tangential component of the shear and $\langle\gamma_{\rm t}\rangle(x)$ is its circularly averaged value as a function of the radial distance.805 This equation was first applied by Fablman et al. (, This equation was first applied by Fahlman et al. (8061994) in order to determine a rigorous lower limit on the mass of the ealaxy cluster MS1224. without the need to worry about non-linear lensing properties or the confusion of background and cluster galaxies in the cluster centre.,"1994) in order to determine a rigorous lower limit on the mass of the galaxy cluster MS1224, without the need to worry about non-linear lensing properties or the confusion of background and cluster galaxies in the cluster centre."807 In. this section we investigate the possibilities ollered by this method. for obtaining information on the mass distribution of cluster ealaxies., In this section we investigate the possibilities offered by this method for obtaining information on the mass distribution of cluster galaxies.808 Phis can be achieved by analysing the distortion of background galaxy images in annuli centred. on individual cluster galaxies and adding the cllects of a large number of them in order to got a significant signal., This can be achieved by analysing the distortion of background galaxy images in annuli centred on individual cluster galaxies and adding the effects of a large number of them in order to get a significant signal.809 A nice feature of this application of relation (12)) is that the reference to the surface mass density in the annulus automatically takes into account an underlying cluster mass distribution and directly. measures the galaxy masses. provided the surface mass density of the eluster can be reasonably. approximated locally as a linear function.," A nice feature of this application of relation \ref{zeta-def}) ) is that the reference to the surface mass density in the annulus automatically takes into account an underlying cluster mass distribution and directly measures the galaxy masses, provided the surface mass density of the cluster can be reasonably approximated locally as a linear function."810 Ht is easy to see that a linear trend in the cluster mass profile does not allect sr.) and so only higher order variations of the cluster mass distribution on scales comparable to the size of the annulus could bias the mass measurement.," It is easy to see that a linear trend in the cluster mass profile does not affect $\overline{\kappa}(x_1,x_2)$ and so only higher order variations of the cluster mass distribution on scales comparable to the size of the annulus could bias the mass measurement."811" The right-hand-side of equation (12)) can be written as a two-dimensional integral and. therefore. be approximated by à sum over the discrete data points which are provided bv the imagesὃν of background> ogalaxies: With our definition for the ellipticity parameter ο, the expectation value for observed. image cllipticitics is equal to the reduced shear: (οὖν=g (Schramm νάνου 1995. Seitz Sehneicder 1997)."," The right-hand-side of equation \ref{zeta-def}) ) can be written as a two-dimensional integral and, therefore, be approximated by a sum over the discrete data points which are provided by the images of background galaxies: With our definition for the ellipticity parameter $\epsilon$, the expectation value for observed image ellipticities is equal to the reduced shear: $\exep=g$ (Schramm Kayser 1995, Seitz Schneider 1997)."812 Therefore. cach observed image ellipticity e; is an unbiased ποσα very noisy estimate for the reduced shear g;=*;/(1αν) at the image »osition. and σε; can be replaced by e;(1.8;) in the above equation. (," Therefore, each observed image ellipticity $\epsilon_i$ is an unbiased – though very noisy – estimate for the reduced shear $g_i=\gamma_i/(1-\kappa_i)$ at the image position, and $\gamma_{{\rm t}i}$ can be replaced by $\epsilon_{{\rm t}i}\,(1-\kappa_i)$ in the above equation. ("813Llere we restricted. the treatment to the even- region: in the odd-parity case (οὖν=1/g'.),Here we restricted the treatment to the even-parity region; in the odd-parity case $\exep=1/g^{\ast}$ .)814 In the imit &«1 the shear can be directly estimated. from the image ellipticities (£e).&5) and no further information about the cluster mass distribution is required for applying he ¢-statistic., In the limit $\kappa\ll 1$ the shear can be directly estimated from the image ellipticities $\exep\approx\gamma$ ) and no further information about the cluster mass distribution is required for applying the $\zeta$ -statistic.815 When leaving the linear regime. however. he corrective factor (1B) becomes important.," When leaving the linear regime, however, the corrective factor $1-\kappa$ ) becomes important."816 In this case. the surface mass density 58; at the image positions can be taken from a reconstruction of the cluster mass Performing a mass sheet transformation of the reconstructed mass distribution according to equation (11)) mocifies ¢ and all galaxy mass estimates derived from it by a factor (1B.).," In this case, the surface mass density $\kappa_i$ at the image positions can be taken from a reconstruction of the cluster mass [Performing a mass sheet transformation of the reconstructed mass distribution according to equation \ref{mass-sheet}) ) modifies $\zeta$ and all galaxy mass estimates derived from it by a factor $(1-\kappa_{\rm s})$."817 This can easily. be seen by replacing 5; with (1win;|ας dn equation (13)).]," This can easily be seen by replacing $\kappa_i$ with $(1-\kappa_{\rm s})\,\kappa_i+\kappa_{\rm s}$ in equation \ref{zeta-sum}) ).]"818 The calculation of ¢ according to equation (13)) can be regarded as a kind. of noisy Monte-Carlo. integration., The calculation of $\zeta$ according to equation \ref{zeta-sum}) ) can be regarded as a kind of noisy Monte-Carlo integration.819 Both of the two approximate-equality signs only hold. for a rather large number NV of background images and become equalities for UVx., Both of the two approximate-equality signs only hold for a rather large number $N$ of background images and become equalities for $N\rightarrow\infty$.820 They express two dillerent. kinds of uncertainties: the first one those which are arising [rom sparse sampling of the integration area. and the second one those from the noisy data points.," They express two different kinds of uncertainties; the first one those which are arising from sparse sampling of the integration area, and the second one those from the noisy data points."821 The errors in ς due to the latter may be expressed in terms of the intrinsic ellipticity dispersion σι as which is not quite exact. because lensing changes the dispersion of the probability cüstribution for the observed image cllipticities (see Section ??)).," The errors in $\zeta$ due to the latter may be expressed in terms of the intrinsic ellipticity dispersion $\sigma_{\epss}$ as which is not quite exact, because lensing changes the dispersion of the probability distribution for the observed image ellipticities (see Section \ref{probability}) )."822 Due to the rather inhomogeneous shear pattern which is induced by the eluster ealaxies (see, Due to the rather inhomogeneous shear pattern which is induced by the cluster galaxies (see823a dnareinal detection of a period of 2.11 hr (11.1 c/d). period is found to dominate Ql (seo andFigue this 13)).,"a marginal detection of a period of 2.11 hr (11.4 c/d), and this period is found to dominate the Q4 data (see Figure \ref{fig: q4dft}) )."824" The average pulse shape hefor this datasignal averaged over davs ,200-275 eeeis shown in: Figure: ,1.", The average pulse shape for this signal averaged over days 200-275 is shown in Figure \ref{fig: avelcporb}.825 We- can now safelv ideutify this 2.11 hr (11.1 c/d) signal as the svstem orbital period. which then indicates that the 2.062. hir (1.7. e/d) signalSIG is; a negative5 «ΠΟΜΠΗ. ↴∖," We can now safely identify this 2.11 hr (11.4 c/d) signal as the system orbital period, which then indicates that the 2.06 hr (11.7 c/d) signal is a negative superhump."826⋅⋅⋪ M ↴∙∩ ∖∖ ∪↕≯∐∪∐≓∐∐↸∖⋜∐⋅↕↸∖⋜↧↴∖↴↑↴∖↴≺∣∏⋜∐⋅↸∖↴∖↴∐↑↑↕∐∶↴⋁⋜↧↕≯∏∐↸⊳↑↕∪∐∪↕≯↑∐↸∖↕≯∪↥⋅⋯⋜⋯∏≻∐↑⋯∐∖↴∖↴∪↕↑∐↸∖↻∪↴∖↴↕⊓↖↽↸∖⋜⋯≼↧∐↸∖∶↴∙⊾⋜↧↑↕↖⇁↸∖↴∖↴↿∏⋉∖↥⋅↕∐∐⊔↻↴∖↴∐↕ the results of the fit are superhunipiug Note. that the anMitude. is. only roughly or25 ning an order of maguitude or more smaller than the peak ⋅ . - ∐∪↥⋝↕↑≺↧↻↸⊔∪≺↖⋯↴∖∩↑↸↥∐∐∐⊓↿↴∖↕∐↴↑∐∐∐↑⋯≼ : . BU sten.. . .- ∙∙ ., The orbital period was determined using the method of non-linear least squares fitting a function of the form The results of the fit are Note that the amplitude is only roughly 25 mmag – an order of magnitude or more smaller than the peak amplitudes of the positive and negative superhumps in the system.827↽∕∏↓⋜↧↑⋜⋯∪↥⋅↴⋝↕↑⋜↧↕↴∖↴↕∩⊾∐⋜↧↕↸∖↘↕↴∖↴↑↴∖↴↕∐≺∐↸⊳⋜↧↑↸∖↴∖↴↑∐⋜↧↑↑∐↸∖↴∖↴↖↽↴∖↴↑↸∖⋯ not face-on., That an orbital signal exists indicates that the system is not face-on.828 The source of the orbital signal of a uou- TheCV can be either the variable dus along the line of site from a bright spot⋅ that is periodically (," The source of the orbital signal of a non-superhumping CV can be either the variable flux along the line of site from a bright spot that is periodically shadowed as it sweeps around the back rim of the disk, or"829"NGC 4151 is one of the nearest (13.2 Mpe. Il,=75 km ! 1!) and best studied aclive galactic nuclei (AGN).","NGC 4151 is one of the nearest (13.2 Mpc, $_{o}=75$ km $^{-1}$ $^{-1}$ ) and best studied active galactic nuclei (AGN)."830 The nucleus hosts a highly variable continuum and line emission source., The nucleus hosts a highly variable continuum and line emission source.831 Conünuunm variability. first reported by Fitch et al. (," Continuum variability, first reported by Fitch et al. ("8321967). has been observed. αἱ several wavelengths including X-ray (Papadakis et al.,"1967), has been observed at several wavelengths including X-ray (Papadakis et al."833 1995). UV. (Clavel et al.," 1995), UV (Clavel et al."834 1990). and optical (Lyutyi 1972).," 1990), and optical (Lyutyi 1972)."835 Classilied as a Sevlert 1.5 by Osterbrock Noski (19716). 44151 displaved cliaracteristies of a Sevlert 2 (Penston Pérez 1984) during a low Iuminosityv state in 1984. and at a later date eharacteristies of a Sevfert 1: (Avani Maehara 1991).," Classified as a Seyfert 1.5 by Osterbrock Koski (1976), 4151 displayed characteristics of a Seyfert 2 (Penston rez 1984) during a low luminosity state in 1984, and at a later date characteristics of a Seyfert 1 (Ayani Maehara 1991)."836 The mid-inlrared emission from 44151 has been suggested (o arise [rom either thermal emission from dust. grains or svnchrotron emission., The mid-infrared emission from 4151 has been suggested to arise from either thermal emission from dust grains or synchrotron emission.837 Discussions of the thermal vs. nonthermal origin of (he infrared emission in NGC! 4151 can be found in Rieke Lebolsky (1981). Edelson Alalkan (1986). Carelton et al. (," Discussions of the thermal vs. nonthermal origin of the infrared emission in NGC 4151 can be found in Rieke Lebofsky (1981), Edelson Malkan (1986), Carelton et al. ("8381987). Edelson et al. (,"1987), Edelson et al. ("8391987). and ce ]xool Begelman (1989).,"1987), and de Kool Begelman (1989)."840 A direct method to investigate the origin of the mid-IR emission mechanism. as proposed by Neugebauer et al. (," A direct method to investigate the origin of the mid-IR emission mechanism, as proposed by Neugebauer et al. ("8411990) (herealter N90). is a measurement of the size of the emitting region.,"1990) (hereafter N90), is a measurement of the size of the emitting region."842 Thev suggest Chat à nonthermal sell-absorbed svichrotron source would be < Imas. and hence unresolvable.," They suggest that a nonthermal self-absorbed synchrotron source would be $<1$ mas, and hence unresolvable."843" ILowever. if the mid-IR emission is due to heated dust egrains. the size of the regionex would be >0.1""."," However, if the mid-IR emission is due to heated dust grains, the size of the region would be $>0.1\arcsec$."844 Observations show that the mil-IK emission in NGC 4151 is compact., Observations show that the mid-IR emission in NGC 4151 is compact.845" Comparison between 60” resolution IIRAS 12 jun flux density measurements and 6"" resolution 10.6 jai measurements agree to within e6% (Edelson et al.", Comparison between $\arcsec$ resolution IRAS 12 $\micron$ flux density measurements and $\arcsec$ resolution ground-based 10.6 $\micron$ measurements agree to within $\thicksim 6\%$ (Edelson et al.846 1987)., 1987).847 Mid-IIt observations bv Rieke Low 1972: Rieke Lebofskv 1981: Ward et al., Mid-IR observations by Rieke Low 1972; Rieke Lebofsky 1981; Ward et al.848" 1987. also did. not detect. any extended emission with resolutions =6"".", 1987 also did not detect any extended emission with resolutions $\gtrsim 6\arcsec$.849 Observations by ISO (Infrared Space Observatory: Rodviquez-Espinosa οἱ al., Observations by ISO (Infrared Space Observatory; Rodriquez-Espinosa et al.850 1996 - herealter RE96) show a strong warm dust component in 44151 and suggest a thermal origin from a eeometrically and optically thick dusty torus and/or a dustv narrow line region (NLR)., 1996 - hereafter RE96) show a strong warm dust component in 4151 and suggest a thermal origin from a geometrically and optically thick dusty torus and/or a dusty narrow line region (NLR).851" These observations however were at a resolution of 180"".", These observations however were at a resolution of $180\arcsec$.852 Using a technique of near-simmultaneous north-south scans at 2.2 jm and 11.2 pam. N90 was able to resolve the 11.2 sam emitting region to be 071162:07004.," Using a technique of near-simultaneous north-south scans at 2.2 $\micron$ and 11.2 $\micron$, N90 was able to resolve the 11.2 $\micron$ emitting region to be $\pm 0$ 04."853 However this technique measured (he size in only one spatial direction and was insufficient (o. explore the morphology of the cireumnuclear region., However this technique measured the size in only one spatial direction and was insufficient to explore the mid-IR morphology of the circumnuclear region.854 I addition. these north-south scans could not investigate (he NLR of NGC 4151 which is primarily orientated in an east-west direction.," In addition, these north-south scans could not investigate the NLR of NGC 4151 which is primarily orientated in an east-west direction."855 In (his paper we present high resolution mic-IR imagine which. to the best of our knowledge. resolves the inner oof NGC 4151 for the first Gime at 10 n and 18 jan.," In this paper we present high resolution mid-IR imaging which, to the best of our knowledge, resolves the inner of NGC 4151 for the first time at 10 $%856\micro n and 18 $\micron$ ."857The secondary cluster has a virial radius of 0.79 pe so the mean density is (he same for both primary and secondary clusters.,The secondary cluster has a virial radius of 0.79 pc so the mean density is the same for both primary and secondary clusters.858 The behavior of the orbital separation is similar to that found in the previous section but the soft ionization process is slightly slower (see Figure 4))., The behavior of the orbital separation is similar to that found in the previous section but the soft ionization process is slightly slower (see Figure \ref{evolhalfsd}) ).859" The merging timescale is also alfected: mergers lor models with e,> 0.5 take longer now but those for less eccentric pairs are faster.", The merging timescale is also affected: mergers for models with $e_o >$ 0.5 take longer now but those for less eccentric pairs are faster.860 Merging is only observed Lor models with an initial apoclustron distance of 10.0 pc., Merging is only observed for models with an initial apoclustron distance of 10.0 pc.861 Cores of merger remnants are more extended than (hose observed in (he previous case., Cores of merger remnants are more extended than those observed in the previous case.862 The secondary cluster has a virial radius of 0.5 pe with a mean density of 1956 M. ., The secondary cluster has a virial radius of 0.5 pc with a mean density of 1956 $M_{\odot}$ $^{-3}$.863 The behavior of the orbital separation is similar to that found in (he previous section (see Figure 6))., The behavior of the orbital separation is similar to that found in the previous section (see Figure \ref{evolhalfdd}) ).864 This is to be expected: a study by Sensui et al. (, This is to be expected: a study by Sensui et al. (8652000) showed that the internal structure ol galaxies does not plav a role in (he merging time-scales (inside a galaxy cluster) | only the distribution of galaxies inside (he cluster matters.,2000) showed that the internal structure of galaxies does not play a role in the merging time-scales (inside a galaxy cluster) – only the distribution of galaxies inside the cluster matters.866 This argument should also hold for star clusters in à star cluster complex (Fellhaner et al., This argument should also hold for star clusters in a star cluster complex (Fellhauer et al.867 2002. 2009).," 2002, 2009)."868" The single main dilference appears for highlv eccentric models in which merging is observed in two cases (as in Ny = No): 5, = 10.0 aud 20.0 pe.", The single main difference appears for highly eccentric models in which merging is observed in two cases (as in $N_1$ = $N_2$ ): $S_o$ = 10.0 and 20.0 pc.869 This set of simulations is designed to study. (he impact of enhanced (tidal forces on the secondary cluster., This set of simulations is designed to study the impact of enhanced tidal forces on the secondary cluster.870 With a virial radius of 0.63 pce. it still has the same reference mean density used throughout this study.," With a virial radius of 0.63 pc, it still has the same reference mean density used throughout this study."871 The dynamical behavior of the pair is now substantially different (see Figure 7))., The dynamical behavior of the pair is now substantially different (see Figure \ref{evolfourth}) ).872 The tidal disruption timescale is much shorter (han that for merging., The tidal disruption timescale is much shorter than that for merging.873 Eventual destruction of the less massive cluster is observed in all cases. including close pairs.," Eventual destruction of the less massive cluster is observed in all cases, including close pairs."874 In some cases. (he secondary cluster appears extremely distorted. ancl elongated. with no Clearly identifiable core (see Figure 3)): in other words. (he secondary cluster gets torn apart in a relatively short Uimescale.," In some cases, the secondary cluster appears extremely distorted and elongated with no clearly identifiable core (see Figure \ref{spaghetti}) ): in other words, the secondary cluster gets torn apart in a relatively short timescale."875 Technically speaking. shredded: clusters are different. from ivpical open cluster remnants. (μον look more like stellar streams and they may be rather voung.," Technically speaking, shredded clusters are different from typical open cluster remnants, they look more like stellar streams and they may be rather young."876 Remnants of shredded clusters may show up in kinematic studies even if (hev cannot be detected. as stellar overdensities., Remnants of shredded clusters may show up in kinematic studies even if they cannot be detected as stellar overdensities.877 Tidal shreclding is à form of shearing bv differential rotation., Tidal shredding is a form of shearing by differential rotation.878 The secondary cluster in proximity (o (he most massive primary becomes stretched oul by (dal forces., The secondary cluster in proximity to the most massive primary becomes stretched out by tidal forces.879 The secondary distends ancl flattens in the direction of the primary evolving as to minimize ils gravitational potential energv becoming an ovoid stretched along, The secondary distends and flattens in the direction of the primary evolving as to minimize its gravitational potential energy becoming an ovoid stretched along880ionizing influence of the QSOs.,ionizing influence of the QSOs.881" In contrast, ordinary star forming galaxies have modest proximity zones of size 0.157! physical Mpc etal.2003),, thereby enabling the study of H(Adelberger I and its structure in the vicinity of deep potential wells where the gas is not ionized."," In contrast, ordinary star forming galaxies have modest proximity zones of size $ 0.1 h^{-1}$ physical Mpc \citep{Adelberger:03}, thereby enabling the study of H I and its structure in the vicinity of deep potential wells where the gas is not ionized."882" Despite the advantage of a small proximity zone, galaxies suffer from being much fainter in the ultraviolet."," Despite the advantage of a small proximity zone, galaxies suffer from being much fainter in the ultraviolet."883" Unlike the vast majority of star-forming galaxies, our target is bright because it is strongly-lensed, thereby yielding a spectrum suitable for measuring the transmitted flux T' in the Lya forest in the proximity of agalaxy. We calculate the Gunn-Peterson (GP) optical depth (Gunn&Peterson1965), τος= where T is the ratio of the average observed —In(T),flux to the average unabsorbed continuum flux, T=<fy/feont>, and feont is determined by stellar synthesis models fit to the photometric data."," Unlike the vast majority of star-forming galaxies, our target is bright because it is strongly-lensed, thereby yielding a spectrum suitable for measuring the transmitted flux $T$ in the $\alpha$ forest in the proximity of a. We calculate the Gunn-Peterson (GP) optical depth \citep{Gunn:65}, $\tau_{GP}^{eff} = -ln (T)$ , where $T$ is the ratio of the average observed flux to the average unabsorbed continuum flux, $T = <f_{\lambda}/f_{cont}>$, and $f_{cont}$ is determined by stellar synthesis models fit to the photometric data."884 We compute refs in several redshift bins extending from a wavelength clear of the red wing of Ly up to the blue edge of our model fit to the H I in the source (blue dashed line in Figure 2 inset delimits the extent of the highest redshift , We compute $\tau_{GP}^{eff}$ in several redshift bins extending from a wavelength clear of the red wing of $\beta$ up to the blue edge of our model fit to the H I in the source (blue dashed line in Figure 2 inset delimits the extent of the highest redshift bin).885"Uncertainties in refs are dominated by the intrinsic bin).scatter of the continuum flux levels due tothe stochastic nature of the absorption in the IGM, or sample variance (Tepper-García&Fritze but also include continuum placement errors and shot 2008),,noise."," Uncertainties in $\tau_{GP}^{eff}$ are dominated by the intrinsic scatter of the continuum flux levels due tothe stochastic nature of the absorption in the IGM, or sample variance \citep{Tepper-Garcia:08}, but also include continuum placement errors and shot noise."886 Figure 3 shows the results measured from the 7.1 spectrum and compares our values for refs to those 41689.observed toward a large sample of QSOs (Fan et al., Figure 3 shows the results measured from the $A1689\_7.1$ spectrum and compares our values for $\tau_{GP}^{eff}$ to those observed toward a large sample of QSOs (Fan et al.887 2006; Songaila 2004)., 2006; Songaila 2004).888" We emphasize that the values for τρeff are measured in the same way towards both the QSOs and the galaxy, and after first excluding the proximity zone, thereby yielding information only on the pervasive IGM; that is the IGM immediatelyoutside the photoionizing influence of the source."," We emphasize that the values for $\tau^{eff}_{GP}$ are measured in the same way towards both the QSOs and the galaxy, and after first excluding the proximity zone, thereby yielding information only on the pervasive IGM; that is the IGM immediately the photoionizing influence of the source."889" Assuming to be the same in the standard IGM towardsany τόbackgroundis object, we would expect to rise steadily towards A1689_7.1 with absorption refsredshift following the bulk of the QSO points."," Assuming $\tau^{eff}_{GP}$ to be the same in the standard IGM towards background object, we would expect $\tau^{eff}_{GP}$ to rise steadily towards $A1689\_7.1$ with absorption redshift following the bulk of the QSO points."890 Compared to the predictions of a power-law model based on the density distribution (Fan et al., Compared to the predictions of a power-law model based on the density distribution (Fan et al.891 2006) and a lognormal optical depth distribution (Becker et al., 2006) and a lognormal optical depth distribution (Becker et al.892" refs measurements toward A1689_7.1 are in good 2007),agreement at z«4.5; at z> 4.5, however, we see a significant excess in ."," 2007), $\tau_{GP}^{eff}$ measurements toward $A1689\_7.1$ are in good agreement at $z < 4.5$; at $z>4.5$ , however, we see a significant excess in $\tau_{GP}^{eff}$."893" If the underlying mass distribution were unaltered by refsthe presence of the galaxy, then this highest-redshift point, the one in closest physical proximity of the galaxy, should have also followed the behavior of the other points."," If the underlying mass distribution were unaltered by the presence of the galaxy, then this highest-redshift point, the one in closest physical proximity of the galaxy, should have also followed the behavior of the other points."894" The highest redshift point is the most deviant; it corresponds to a physical radius ~14 (physical) Mpc, and this result suggests that there is more H I gas close to the galaxy compared to the standard IGM."," The highest redshift point is the most deviant; it corresponds to a physical radius $\sim14$ (physical) Mpc, and this result suggests that there is more H I gas close to the galaxy compared to the standard IGM."895" A1689_7.1 is imaged in several bands, as follows: i775=23.10+0.01 (HST ACS), Jiro=23.10+0.02 (HST Η=23.45+0.38 and K,=23.45+0.35 (Son of Isaac NICMOS),Instrument on ESO New Technology Telescope), and Ρος=23.3+0.02, and Py.5=23.34+0.03 (IRAC on Spitzer Space Telecope)."," $A1689\_7.1$ is imaged in several bands, as follows: $i_{775} = 23.10 \pm 0.01$ (HST ACS), $J_{110}=23.10 \pm 0.02$ (HST NICMOS), $H = 23.45 \pm 0.38$ and $K_s = 23.45 \pm 0.35$ (Son of Isaac Instrument on ESO New Technology Telescope), and $P_{3.6}=23.3 \pm 0.02$, and $P_{4.5} = 23.34 \pm 0.03$ (IRAC on Spitzer Space Telecope)."896 The observing details for these data are discussed elsewhere (Frye et al., The observing details for these data are discussed elsewhere (Frye et al.897 2007)., 2007).898 From these data we set initial constraints on the galaxy age and dust extinction., From these data we set initial constraints on the galaxy age and dust extinction.899" Our high quality Jj19, P3 and P4, points indicate only a modest H I Balmer series continuum break at rest-frame ~4000 and thus a young underlying stellar population dominated by O stars with a minimum age of t210 Myr (Figure 4)."," Our high quality $J_{110}$, $P_{3.6}$ and $P_{4.5}$ points indicate only a modest H I Balmer series continuum break at rest-frame $\sim$ 4000 and thus a young underlying stellar population dominated by O stars with a minimum age of $t\apg10$ Myr (Figure 4)."900 'The age of the universe for our adopted cosmology sets the upper limit on the galaxy age of 1.2 Gyr., The age of the universe for our adopted cosmology sets the upper limit on the galaxy age of 1.2 Gyr.901" The dust extinction, as parameterized by the color excess E(B—V), is fit with a broad range spectral energy distribution templates."," The dust extinction, as parameterized by the color excess $E(B-V)$, is fit with a broad range spectral energy distribution templates."902" From these fits it is found that any model with E(B—V)>0.1 provides a poor fit to the slope of data, as the continuum becomes significantly flatter in the blue with the addition of even moderate amounts of dust."," From these fits it is found that any model with $E(B-V)>0.1$ provides a poor fit to the slope of data, as the continuum becomes significantly flatter in the blue with the addition of even moderate amounts of dust."903 Thus we restrict our parameterspace to E(B—V)€0.1., Thus we restrict our parameterspace to $E(B-V) \leq 0.1$.904 Model spectral energy distributions are generated using the stellar synthesis code of Bruzual&Char-lot (2003)., Model spectral energy distributions are generated using the stellar synthesis code of \citet{Bruzual:03}.905". We select a Chabrier initial mass function (Padova 1994), stellar evolution tracks, and solar metallicity."," We select a Chabrier initial mass function (Padova 1994), stellar evolution tracks, and solar metallicity."906" We choose a single starburst model with a range of decay rates r and a star formation rate (SFR) that depends exponentially on 7 as follows: SF'R(t)ος with τς 0.1, 0.2, 0.3, 0.5, 1, and 1.2 Gyr."," We choose a single starburst model with a range of decay rates $\tau$ and a star formation rate (SFR) that depends exponentially on $\tau$ as follows: $SFR(t) \propto exp(t/\tau)$ with $\tau =$ 0.1, 0.2, 0.3, 0.5, 1, and 1.2 Gyr."907" Continuous star-formation models are also considered, as approximated by selecting 7 to be the age of the universe at z= 5, and we do not consider more complicated starformation histories."," Continuous star-formation models are also considered, as approximated by selecting $\tau$ to be the age of the universe at $z=5$ , and we do not consider more complicated starformation histories."908" For each 7, three parameters remain"," For each $\tau$ , three parameters remain"909"The other observed star,2165.. does not xovide any definite detection of ""Li.","The other observed star, does not provide any definite detection of $^6$ Li."910 The S/N ratio reached is even lower. and does not enable amy firm constraint.," The S/N ratio reached is even lower, and does not enable any firm constraint."911" The observation of TD 81937 has esseutial consequeuces. first on the depletion of ?Li (and iudirectlv that of of ""Li) in Pop EH stars. and on the cosmological status of Li/Il observed i old mietabpoor stars. and also on ""Li (and De aud D) production."," The observation of HD 84937 has essential consequences, first on the depletion of $^6$ Li (and indirectly that of of $^7$ Li) in Pop II stars, and on the cosmological status of Li/H observed in old metal-poor stars, and also on $^6$ Li (and Be and B) production."912" The ""Li isotope is a pure spallation product (see Reeves 1991. for a review).", The $^6$ Li isotope is a pure spallation product (see Reeves \cite{Reev94} for a review).913 This fracile nucleus is burut at low tenperature (about 2.109 IC) and cannot be svuthesized inside stars., This fragile nucleus is burnt at low temperature (about $ 2. 10 ^6$ K) and cannot be synthesized inside stars.914 Spallation ageuts are (i) galactic cosmic raves (CCR). specifically acting in the ealactic disk through p. 6. | Tle.CNO » PLLi and (0) iu the halo phase (|Fe‘TI x 1) low energv aC and O nuclei ejected and accelerated by. superiovac. interacting with II and Πο in the Τον (Cassé et al. 1995..," Spallation agents are (i) galactic cosmic rays (GCR), specifically acting in the galactic disk through p, $\alpha$ + He,CNO $\rightarrow$ $^6$ $^7$ Li and (ii) in the halo phase ([Fe/H] $\leq -1$ ), low energy $\alpha $ ,C and O nuclei ejected and accelerated by supernovae, interacting with H and He in the ISM (Cassé et al. \cite{Cas95},"915 Ramaty et al. 1996))., Ramaty et al. \cite{Rama96}) ).916 This low cuerey componcut (LEC) is likely to be responsible for the linear relationship between Be. D and [Fe/T] discovered recently (Duncan ct al. 1997..," This low energy component (LEC) is likely to be responsible for the linear relationship between Be, B and [Fe/H] discovered recently (Duncan et al. \cite{DPR97},"917 Molaro et al. 1997..," Molaro et al. \cite{MBCP97},"918 Thorburn Tobbs 1996..Wc Pruuas 1906 Carctaa Lóppez et al. 1998))," Thorburn Hobbs \cite{TH96}, Primas \cite{Pri96}919 a Lóppez et al. \cite{Gar98}) )"920 as shown by Vaugioni-Fluu et al. (199 1))., as shown by Vangioni-Flam et al. \cite{VLC94}) ).921 This luear relationship. specifically in the carly Galaxy. is due to the fact that freshly svuthesized a. C aud ο from: SNe are accelerated at imoderate energv aud fragment ou the IT. Ue nuclei iu the ISML.," This linear relationship, specifically in the early Galaxy, is due to the fact that freshly synthesized $\alpha $, C and O from SNe are accelerated at moderate energy and fragment on the H, He nuclei in the ISM."922" Thus. the production rate is independeut of the ISM inetallicity. (Ισ means that Be aud D are ""opriuuuwv)"," Thus, the production rate is independent of the ISM metallicity (which means that Be and B are “ primary”)."923" The Τα isotope itself is also produced by primary processes, through the two spallative processes GCR aud LEC."," The $^6$ Li isotope itself is also produced by primary processes, through the two spallative processes GCR and LEC."924 Consequeutly. its slope in the (loe(Li ID. |Fe/TI]) plane is unity.," Consequently, its slope in the $\log $ $^6$ Li /H), [Fe/H]) plane is unity."925 The 9Li abundance observed iu the atmosphere of ID SLO37 ix a lower limit to that of the interstellar medina out of which this star has formed since this, The $^6$ Li abundance observed in the atmosphere of HD 84937 is a lower limit to that of the interstellar medium out of which this star has formed since this926 tateau “Pvpe Lb supernovae (SNeLIIP) are. believed to come from the explosion of massive supergiant stars whose envelopes are rich in hvdrogen.," Plateau Type II supernovae $\,$ IIP) are believed to come from the explosion of massive supergiant stars whose envelopes are rich in hydrogen."927 Their light curves are easy o identify by a lone plateau. (sometimes up to 120150 d) which is the result of the propagation of a cooling-and-recombination wave (CRW) through the supernova envelope hat is in à state of free inertial expansion (η=rjl)., Their light curves are easy to identify by a long plateau (sometimes up to 120–150 d) which is the result of the propagation of a cooling-and-recombination wave (CRW) through the supernova envelope that is in a state of free inertial expansion $(u=r/t)$.928 The CRW. physies 1s discussed in detail by. Imshennik Nadvozhin (1964). Cirassberg. lmshennik Nacdvozhin (1971). and Grassberg Nadyvozhin (1976).," The CRW physics is discussed in detail by Imshennik Nadyozhin (1964), Grassberg, Imshennik Nadyozhin (1971), and Grassberg Nadyozhin (1976)."929 Vhe CRAY propagates supersonically downward through the expanding supernova envelope and separates almost recombined outer avers from still strongly. ionized inner ones., The CRW propagates supersonically downward through the expanding supernova envelope and separates almost recombined outer layers from still strongly ionized inner ones.930 During the rlateau phase. the photosphere sits on the upper edge of he CRAY front.," During the plateau phase, the photosphere sits on the upper edge of the CRW front."931 Since the CRW downward speed turns out o be close to the velocity of the outward. expansion. the »hotospheric radius changes only slowly. during the plateau yhase.," Since the CRW downward speed turns out to be close to the velocity of the outward expansion, the photospheric radius changes only slowly during the plateau phase."932 I£ one takes into account that also the effective emperature does not change appreciably (it approximately equals the recombination. temperature 7000 IN). the approximate constancy of the luminosity becomes obvious.," If one takes into account that also the effective temperature does not change appreciably (it approximately equals the recombination temperature $\,$ K), the approximate constancy of the luminosity becomes obvious."933 The supernova outburst properties are. determined mainlv by three physical parameters: the explosion energy fe. the mass Mo of the envelope expelled. ancl the initial radius A? of the star just before the explosion (presupernova).," The supernova outburst properties are determined mainly by three physical parameters: the explosion energy $E$, the mass ${\cal M}$ of the envelope expelled, and the initial radius $R$ of the star just before the explosion (presupernova)."934 Litvinova Nadvozhin (1983. 1985) have undertaken an attempt to derive these parameters from a comparison of the hyvdrodynamical supernova models with observations.," Litvinova Nadyozhin (1983, 1985) have undertaken an attempt to derive these parameters from a comparison of the hydrodynamical supernova models with observations."935 They constructed simple approximation formulae which allow to estimate ££. M. and. /2 from the observations of individual SNelLIP.," They constructed simple approximation formulae which allow to estimate $E$, ${\cal M}$, and $R$ from the observations of individual $\,$ IIP."936 Their results were confirmed. by an independent semi-analvtical study (Popov 1993)., Their results were confirmed by an independent semi-analytical study (Popov 1993).937 At that time. only one or (wo supernovae were sullicientIv observed to apply these formulae.," At that time, only one or two supernovae were sufficiently observed to apply these formulae."938 At present. there exist detailed observationaldata [or 14 such supernovae. including in 12 cases expanding photosphere (IPM) distances. which we use in section 2 to estimate ££. VE. and 2 by means of these formulae.," At present, there exist detailed observational data for 14 such supernovae, including in 12 cases expanding photosphere (EPM) distances, which we use in section 2 to estimate $E$, ${\cal M}$, and $R$ by means of these formulae."939 In section 3. we propose a new method of distance determination and employ it to 9 individual LLP which are well-observed. both at. the plateau and," In section 3, we propose a new method of distance determination and employ it to 9 individual $\,$ IIP which are well-observed both at the plateau and"940 In section 3. we propose a new method of distance determination and employ it to 9 individual LLP which are well-observed. both at. the plateau and.," In section 3, we propose a new method of distance determination and employ it to 9 individual $\,$ IIP which are well-observed both at the plateau and"941Both of the two classes of models are currently viable candidates to explain the observed cosnic acceleration.,Both of the two classes of models are currently viable candidates to explain the observed cosmic acceleration.942 Unless stated otherwise. throughout the paper we calculate the best fit values found. ancl vary (he parameters within (heir 2e uncertainties for either class of moclel.," Unless stated otherwise, throughout the paper we calculate the best fit values found, and vary the parameters within their $\sigma$ uncertainties for either class of model."943 Next. we shall outline the basic equations describing the evolution of (he cosmic expansion in both dark energy models and calculate the best-fit parameters.," Next, we shall outline the basic equations describing the evolution of the cosmic expansion in both dark energy models and calculate the best-fit parameters."944 In the simplest scenario. the dark energy is simply a cosmological constant. A. aa component with constant equation of state w=p/p——1.," In the simplest scenario, the dark energy is simply a cosmological constant, $\Lambda$, a component with constant equation of state $w=p/\rho=-1$."945" If flatness of the FRW metric is assumed. the IIubble parameter according to the Friedinann equation is: where Q,,, and O4 parameterize the density of matter aud cosmological constant. respectively."," If flatness of the FRW metric is assumed, the Hubble parameter according to the Friedmann equation is: where $\Omega_m$ and $\Omega_\Lambda$ parameterize the density of matter and cosmological constant, respectively."946" Moreover. in (he zero-curvature case (Q=Q,,FO, 1). this model has only one independent parameter: 0=4."," Moreover, in the zero-curvature case $\Omega=\Omega_m+\Omega_\Lambda=1$ ), this model has only one independent parameter: ${\theta}=\Omega_{\Lambda}$."947 We plot the likelihood distribution function for tliis model in Fig. 1.., We plot the likelihood distribution function for this model in Fig. \ref{1}. .948 The best-fit value of the parameter is: Q4=0.85(rl., The best-fit value of the parameter is: $\Omega_\Lambda=0.85^{+0.11}_{-0.18}$.949 It is obvious that the lens redshift data only give a relatively. weak constraint on the model parameter O4. though the universally recognized value of Q4=0.75 is still included at CL (lo).," It is obvious that the lens redshift data only give a relatively weak constraint on the model parameter $\Omega_\Lambda$, though the universally recognized value of $\Omega_\Lambda=0.75$ is still included at CL $\sigma$ )."950 To make a comparison. it is necessary to refer to the previous results: the current. best fit value from cosmological observations is: O4=0.73£0.04 in the flat case (Davisetal.2007).. which is in relatively stringent accordance with our result.," To make a comparison, it is necessary to refer to the previous results: the current best fit value from cosmological observations is: $\Omega_\Lambda=0.73\pm 0.04$ in the flat case \citep{Davis07}, which is in relatively stringent accordance with our result."951" Moreover. Komatsuetal.(2009) gave the best-fit. parameter: Q,,=0.274 for the flat A CDM model from the WMADP 5-vear results with the BAO and SN Union data."," Moreover, \citet{Komatsu09} gave the best-fit parameter: $\Omega_{m}=0.274$ for the flat $\Lambda$ CDM model from the WMAP 5-year results with the BAO and SN Union data."952 We find that the constraint result [rom the lens redshift data is marginally consistent with the previous works above., We find that the constraint result from the lens redshift data is marginally consistent with the previous works above.953 For the BAO data. the parameter Ais used. which. for a flat universe can be expressed," For the BAO data, the parameter $\mathcal{A}$is used, which, for a flat universe can be expressed"954the phase-averaged flux.,the phase-averaged flux.955 Thus. the relative increase in the phase-averaged flux is actually much lager than the increase in pulsed [lux seen in the AXTE//PCAÀ light curve (the phase-averaged flix time history may have exhibited a stronger peak).," Thus, the relative increase in the phase-averaged flux is actually much larger than the increase in pulsed flux seen in the /PCA light curve the phase-averaged flux time history may have exhibited a stronger peak)."956 We have discovered the longest. most luminous aud most energetic burst from (thus far.," We have discovered the longest, most luminous and most energetic burst from thus far."957 The short-term pulsed flux enhancement al the Gime of the burst establishes that iis definitely the burst source aud in all likelihood was the source of the 2001 bursts as well., The short-term pulsed flux enhancement at the time of the burst establishes that is definitely the burst source and in all likelihood was the source of the 2001 bursts as well.958 An interesting property of all three bursts from iis that they occur prelerentially at pulse maximum., An interesting property of all three bursts from is that they occur preferentially at pulse maximum.959 A similar trend was found for the iransient ANP for which four bursts occurred near pulse maximum (Woodsοἱal.2005)., A similar trend was found for the transient AXP for which four bursts occurred near pulse maximum \citep{wkg+05}.960. Furthermore. in a major outburst from ANP involving 980 bursts. Gavriiletal.(2004) found (hat bursts occurred prelerentially al pulse phases lor which the pulsed emission was high (notethatthepulseprofileofLE22594-5386191.seeGaviil&Ixaspi 2002)..," Furthermore, in a major outburst from AXP involving $\sim$ 80 bursts, \citet{gkw04} found that bursts occurred preferentially at pulse phases for which the pulsed emission was high \citep[note that the pulse profile of \tfn\ is double-peaked961as opposed to the quasi-sinusoidal profiles of \tfe\ and \ett,962see][]{gk02}."963 SGR bursts on the other hand show no correlation with pulse phase., SGR bursts on the other hand show no correlation with pulse phase.964 Palmer(2002) found that hundreds of bursts [rom SGR. 19004714. were distributed unilormlvin phase., \citet{pal02} found that hundreds of bursts from SGR $+$ 14 were distributed uniformlyin phase.965 However as discussed by Gavriiletal.(2004).. Woodsetal.(2005). and below. this is not the only difference between SGR and AXP bursts.," However as discussed by \citet{gkw04}, \citet{wkg+05} and below, this is not the only difference between SGR and AXP bursts."966 If AXP bursts do oecur at specifie pulse phases then they must be associated with parlicularly active regions of the star., If AXP bursts do occur at specific pulse phases then they must be associated with particularly active regions of the star.967 This would imply that AXPs burst. much. more yequently than is observed. but the bursts go unseen because they are beamed away [rom us.," This would imply that AXPs burst much more frequently than is observed, but the bursts go unseen because they are beamed away from us."968 Llowever. even if à burst is missed. it may still leave two characteristic signatures.," However, even if a burst is missed, it may still leave two characteristic signatures."969 One is a verv long tail: those observed in aand lasted. several pulse evcles., One is a very long tail: those observed in and lasted several pulse cycles.970 Second. short-term increases in pulsed {lux like those observed in this paper would be an indication of a burst whose onset went unobserved.," Second, short-term increases in pulsed flux like those observed in this paper would be an indication of a burst whose onset went unobserved."971" A search [or ""naked tails” or short time scale pulsed flux enhancements could in principle demonstrate (he existence of missed bursts.", A search for “naked tails” or short time scale pulsed flux enhancements could in principle demonstrate the existence of missed bursts.972 The verv long tail (2699 s) of the burst reported here makes it very. similar to one burst observed [rom5937.. some of the bursts seen in ANP 2259--586.. and to," The very long tail $>699$ s) of the burst reported here makes it very similar to one burst observed from, some of the bursts seen in AXP , and to"973coellicient is assumed to be Dohm-like ancl the magnetic field close to the shock is (1). one obtains: The magnetic fiekl in the shock vicinity is amplified by streaming imstabilitv. induced by (he accelerated particles both resonanüly ancl non-resonantly.,"coefficient is assumed to be Bohm-like and the magnetic field close to the shock is $\delta B(t)$, one obtains: The magnetic field in the shock vicinity is amplified by streaming instability, induced by the accelerated particles both resonantly and non-resonantly."974 Let us introduce (he acceleration efficiency as a [function of time: £40)=—DP)/C(GpgVu))., Let us introduce the acceleration efficiency as a function of time: $\xi_c(t)=P_c(t)/(\rho_0 V_{sh}(t)^2)$.975" In terms of £2 the strength of the resonantly amplified magnetic fiekl al Che saturation level can be estimated. as: OB?—SapV8./M4 (AL, is the Allvénn Mach number). which leads to: In a similar wav. the strength of the field in the case of non-resonant aniplilication can be estimated [rom 0B?=2x(Vu(e/g) and leads to: In general the two channels of magnetic field amplification work together but the channel dominates at earlier times and leads (ο stronger magnetic field amplification."," In terms of $\xi_c$, the strength of the resonantly amplified magnetic field at the saturation level can be estimated as: $\delta B^2= 8\pi\rho_0 V^2 \xi_c/M_A$ $M_A$ is the Alfvénn Mach number), which leads to: In a similar way, the strength of the field in the case of non-resonant amplification can be estimated from $\delta B^2=2\pi \rho_0 (V_{sh}(t)^3/c) \xi_c(t)$ and leads to: In general the two channels of magnetic field amplification work together but the non-resonant channel dominates at earlier times and leads to stronger magnetic field amplification."976 The maximum momentum in the two cases is as follows: in the resonant case. and in the non-resonant regime.," The maximum momentum in the two cases is as follows: in the resonant case, and in the non-resonant regime."977 In (he naive assumption that the acceleration efficiency is constant in time. we see (hat ων) scales with time as /1/710 a earlier times and as /IF? at later times. when resonant scattering dominates.," In the naive assumption that the acceleration efficiency is constant in time, we see that $E_{max}(t)$ scales with time as $t^{-11/10}$ at earlier times and as $t^{-1/2}$ at later times, when resonant scattering dominates."978 In actuality the scalings will be more complex because of the non-linear effects (especially the formation of a precursor upstream) induced by accelerated particles. which also lead to a tme dependence of €.(/).," In actuality the scalings will be more complex because of the non-linear effects (especially the formation of a precursor upstream) induced by accelerated particles, which also lead to a time dependence of $\xi_c(t)$."979 As discussed in the previous sections. it is not clear how to describe the non-resonant waves in (he context of the conservation equations.," As discussed in the previous sections, it is not clear how to describe the non-resonant waves in the context of the conservation equations."980 A calculation of the dynamical effect of these modes on the shock is therefore not reliable at the present time., A calculation of the dynamical effect of these modes on the shock is therefore not reliable at the present time.981 For (his reason. here we confine ourselves to the investigation of the effects of resonant waves. for which there is no ambiguity.," For this reason, here we confine ourselves to the investigation of the effects of resonant waves, for which there is no ambiguity."982 It is however worth keeping in mind (hat the introduction of the non-resonant, It is however worth keeping in mind that the introduction of the non-resonant983In this subsection we present the proof of several lemuuas leading to the proof of Theorem1.1..,In this subsection we present the proof of several lemmas leading to the proof of Theorem\ref{theorem1}.984 We start with the following lenuma coucerning mean estimates of functious ou parabolic cubes., We start with the following lemma concerning mean estimates of functions on parabolic cubes.985" Call QoCE"".tj >0. any arbitrary parabolie cube of radius 2/ (see (2.3)) for the definition of parabolic cubes)."," Call $Q_{2^{j}}\subset \R^{n+1}$, $j\geq 0$, any arbitrary parabolic cube of radius $2^{j}$ (see \ref{haAnas}) ) for the definition of parabolic cubes)."986 For the sake of simplicity. we deuote Our next leruma reads: We easily remark that: We compute: imimeciately gives (2.21)). and couseqtuently (2.22)).," For the sake of simplicity, we denote Our next lemma reads: We easily remark that: We compute: which immediately gives \ref{meanest_eq1}) ), and consequently \ref{EfS_eq1}) )."987 α The following two lemmas are of notable importance for the prool of the logaritlimic Sobolev inequality (1.3))., $\hfill{\blacksquare}$ The following two lemmas are of notable importance for the proof of the logarithmic Sobolev inequality \ref{cara_eq2}) ).988 In the first lemma we bound the terms ©;x for j> 1. while. in the second lemma. we give a bound on opxu.," In the first lemma we bound the terms $\phi_{j}*u$ for $j\geq 1$ , while, in the second lemma, we give a bound on $\phi_{0}*u$."989 We will show that, We will show that990All the works cited above consider only apsidal alignment and neglect nodal alignment.,All the works cited above consider only apsidal alignment and neglect nodal alignment.991 Nodal alignment. but not apsidal alignment. is studied by Dorderies. Goldreich. Tremaine (19823a). who consider ring sellgravitv and planetary gravitv. but. neglect. collisions.," Nodal alignment, but not apsidal alignment, is studied by Borderies, Goldreich, Tremaine (1983a), who consider ring self-gravity and planetary gravity, but neglect collisions."992 Ring eccentricilies are sel (o zero in their analvsis., Ring eccentricities are set to zero in their analysis.993 The rings (rue surface density. profile must be simultaneously reconciliable with both the alignment of apsides and the alignment of nodes: the horizontal structure of a narrow rine is entwined wilh its vertical structure., The ring's true surface density profile must be simultaneously reconciliable with both the alignment of apsides and the alignment of nodes; the horizontal structure of a narrow ring is entwined with its vertical structure.994 This paper seeks (to simultaneously. (reat. apsidal and nodal alignment while accounting for the full panoply of forces due (ο the planetary quadrupole field. ring sell-gravitv. and interparticle collisions.," This paper seeks to simultaneously treat apsidal and nodal alignment while accounting for the full panoply of forces due to the planetary quadrupole field, ring self-gravity, and interparticle collisions."995 In relecuilibrium.. we derive equilibrium ring surface densities and vertical geometries (hat lock (he apsides ancl nodes of a given ring.," In \\ref{equilibrium}, we derive equilibrium ring surface densities and vertical geometries that lock the apsides and nodes of a given ring."996 We apply our solutions to the a and 2 vines of Uranus. and the Maxwell and Colombo ringlets of Saturn.," We apply our solutions to the $\alpha$ and $\beta$ rings of Uranus, and the Maxwell and Colombo ringlets of Saturn."997 In relstabilitv.. we present a proof that circular. nodally locked. rings are linearly stable to perturbations to their inclinations and nodes.," In \\ref{stability}, we present a proof that circular, nodally locked rings are linearly stable to perturbations to their inclinations and nodes."998 The beeinnings of such a proof can be found in Borderies. Goldreich. Tremaine (1933b): here. we state the arguments more completely and explicitly.," The beginnings of such a proof can be found in Borderies, Goldreich, Tremaine (1983b); here, we state the arguments more completely and explicitly."999 In reldiscussion.. we discuss our results. highlighting the future impact of the Cassini spacecralt on studies of narrow rings and unresolved theoretical issues.," In \\ref{discussion}, we discuss our results, highlighting the future impact of the Cassini spacecraft on studies of narrow rings and unresolved theoretical issues."1000 Our procedure for deriving the mass and 3-dimensional structure of a narrow ring is summarized as follows., Our procedure for deriving the mass and 3-dimensional structure of a narrow ring is summarized as follows.1001 The range of semi-major axes spanned by the ring. (hie eccentricity profile [e(a)]. and the mean inclination (1) are assumed to be given.," The range of semi-major axes spanned by the ring, the eccentricity profile $e(a)$ ], and the mean inclination $\bar{I}$ ) are assumed to be given."1002 From e(a). we compute the surface densitv profile. δα). bv enforcing apsidal alienment across the ring and bv accounting for planetary oblateness. ring sell-gravitv. and interparticle This computation is described in detail in refsurf..," From $e(a)$, we compute the surface density profile, $\Sigma(a)$, by enforcing apsidal alignment across the ring and by accounting for planetary oblateness, ring self-gravity, and interparticle This computation is described in detail in \\ref{surf}."1003 Next. [rom X(a) and J. we compute the inclination profile. Z(«). by enforcing nodal alignment across (he ring and by accounting for planetary oblateness and ring sell-gravity but not interparticle collisions.," Next, from $\Sigma(a)$ and $\bar{I}$, we compute the inclination profile, $I(a)$, by enforcing nodal alignment across the ring and by accounting for planetary oblateness and ring self-gravity but not interparticle collisions."1004 The computation of Z(«) is described in relinca.., The computation of $I(a)$ is described in \\ref{inca}. .1005 Finally. in," Finally, in"1006seen all right at a first glance.,seem all right at a first glance.1007 Bul. what would be the significance of the line that is parallel to E(d) ancl passes trough w?," But, what would be the significance of the line that is parallel to $E_-(\omega_c)$ and passes through $\omega$?"1008 We do not know., We do not know.1009 However. we know that (he corresponding equallon de=constant (given bx the value of the £ component of the particular source position) can not be derived from the quadratic lens equation (17)).," However, we know that the corresponding equation $\delta\omega_+ = constant$ (given by the value of the $E_+$ component of the particular source position) can not be derived from the quadratic lens equation \ref{eqxy}) )."1010 Given the irrelevance. we can discard the case [rom the list of potentially confusing interpretations.," Given the irrelevance, we can discard the case from the list of potentially confusing interpretations."1011 What else can one imagine for δω=Q0)?, What else can one imagine for $\delta\omega (J=0)$?1012 Currently. we lack imagination for other possibilities of confusion.," Currently, we lack imagination for other possibilities of confusion."1013 We take it as a good enough reason (to pardon our notation and close the case., We take it as a good enough reason to pardon our notation and close the case.1014 That is. of course. until someone brings a brilliant confusion candidate to our attention.," That is, of course, until someone brings a brilliant confusion candidate to our attention."1015both the angular diameter of the inner boundary and the stellar contribution to the 2.11jan flux only moderately increase with Τμ.,"both the angular diameter of the inner boundary and the stellar contribution to the $2.11\,{\rm\mu m}$ flux only moderately increase with $T_{\rm eff}$."1016 Correspondingly. the visibility approaches a slightly higher constant value at a slightly smaller spatial frequency resulting in the minor differences for V541 at spatial frequencies q<13.5aresec. +.," Correspondingly, the visibility approaches a slightly higher constant value at a slightly smaller spatial frequency resulting in the minor differences for $V_{2.11}$ at spatial frequencies $q<13.5\,{\rm arcsec^{-1}}$ ."1017 Thus. changing the 774 within a reasonable range cannot produce a model. which matches the observed visibility.," Thus, changing the $T_{\rm eff}$ within a reasonable range cannot produce a model, which matches the observed visibility."1018 The effects of different grain radii on the caleulated SED and the 2.11ju visibility are displayed in refsed-Ow92-a0..," The effects of different grain radii on the calculated SED and the $2.11\,{\rm\mu m}$ visibility are displayed in \\ref{sed-Ow92-a0}. ."1019 The grain radius is varied between a.= and ay=O12yan.The derived properties of the corresponding models are given in Table 5..," The grain radius is varied between $a_{\rm gr}=0.04\,{\rm\mu m}$ and $a_{\rm gr}=0.12\,{\rm\mu m}$.The derived properties of the corresponding models are given in Table \ref{tab-Ow92-a0}. ."1020" Figure 12 shows the extinction coefficient per unit volume of the grains Wot/Vu, Obtained from the optical data for “warm” silicates from Ossenkopf et ((1992)).", Figure \ref{sed-Ow92-a0-qext} shows the extinction coefficient per unit volume of the grains $\kappa_{\rm ext}/V_{\rm gr}$ obtained from the optical data for `warm' silicates from Ossenkopf et \cite{OHM92}) ).1021" The choice of the grain radiusonly affects the short wavelength tail of the SED below A=3μια, because at these wavelengths 544των still depeds on «4. but it becomes ndependent of «4 at longer wavelengths (see efsed-Ow92-a0-qext))."," The choice of the grain radiusonly affects the short wavelength tail of the SED below $\lambda \la 3\,{\rm\mu m}$, because at these wavelengths $\kappa_{\rm ext} / V_{\rm gr}$ still depends on $a_{\rm1022 gr}$, but it becomes independent of $a_{\rm gr}$ at longer wavelengths (see \\ref{sed-Ow92-a0-qext}) )."1023 This behaviour is caused by two Factors: the contribution of scatteriο to extinction and the οependence of the absorption efficiency on the grain size., This behaviour is caused by two factors: the contribution of scattering to extinction and the dependence of the absorption efficiency on the grain size.1024" The nrcattering efficieney per unit volume of the grains. which is x(5. steeply declines with increasing wavelength and can be eglected above a certain wavelength depending on «,,."," The scattering efficiency per unit volume of the grains, which is $\propto a_{\rm gr}^3$, steeply declines with increasing wavelength and can be neglected above a certain wavelength depending on $a_{\rm gr}$."1025 The absorption efficiency depends on the grain size only at short wavelengths and becomes independent of a. once the grains are sufficiently small compared to the wavelength., The absorption efficiency depends on the grain size only at short wavelengths and becomes independent of $a_{\rm gr}$ once the grains are sufficiently small compared to the wavelength.1026 Therefore. the grain radius is constrained by the observed fluxes at the shortest wavelengths À<μια.," Therefore, the grain radius is constrained by the observed fluxes at the shortest wavelengths $\lambda \la 2\,{\rm\mu m}$."1027 In our case the photometry at A1.65jon excludes grain radi ai.<0.12pam and (oyὃςO.06p and the photometry at A=1.25pu restricts the grain radii to values close to ων=0.1gan.," In our case the photometry at $\lambda=1.65\,{\rm\mu m}$ excludes grain radii $a_{\rm1028 gr} \ga 0.12\,{\rm\mu m}$ and $a_{\rm gr} \la 0.06\,{\rm\mu m}$ and the photometry at $\lambda=1.25\,{\rm\mu m}$ restricts the grain radii to values close to $a_{\rm gr} = 0.1\,{\rm\mu m}$."1029 However. the values of the absorption and scattering efficiency depend on the adopted optical data.," However, the values of the absorption and scattering efficiency depend on the adopted optical data."1030 A different data set can result in vastly different grain radii (see Appendix A)., A different data set can result in vastly different grain radii (see Appendix A).1031 The variation of the grain radius has two effects on the 2.]lnun visibility.," The variation of the grain radius has two effects on the $2.11\,{\rm1032 \mu m}$ visibility."1033 First. the slope of 1544 steepens with increasing values of μι. because models with larger grain radius require a higher optical depth at 2.11jiu in order to match the observed SED for Ao>2jan.," First, the slope of $V_{2.11}$ steepens with increasing values of $a_{\rm gr}$, because models with larger grain radius require a higher optical depth at $2.11\,{\rm\mu m}$ in order to match the observed SED for $\lambda>2\,{\rm\mu m}$."1034 With increasing optical depth the intensity distribution becomes broader and the stellar contribution to the monochromatic flux at 2.11ju decreases.," With increasing optical depth the intensity distribution becomes broader and the stellar contribution to the monochromatic flux at $2.11\,{\rm1035\mu m}$ decreases."1036 Correspondingly. the decline of visibility with spatial frequency becomes steeper (see Ivezié Elitzur 1996)).," Correspondingly, the decline of visibility with spatial frequency becomes steeper (see Ivezić Elitzur \cite{IE96}) )."1037 The second effect is the change of the curvature of V5 44. which is noticable at low spatial frequencies.," The second effect is the change of the curvature of $V_{2.11}$ , which is noticable at low spatial frequencies."1038 The curvature changes its sign at about ανν—«0.1gn.," The curvature changes its sign at about $a_{\rm gr}<0.1\,{\rm\mu m}$."1039 This behaviour reflects the changes of the spatial intensity. distribution., This behaviour reflects the changes of the spatial intensity distribution.1040 At large radial offsets > from the star the intensitydecreases approximatelyasIb)xb. 7. because the optical depth along the line of sight at b becomes small (see Jura Jacoby 1976)).," At large radial offsets $b$ from the star the intensitydecreases approximatelyas$I(b) \propto b^{-3}$ , because the optical depth along the line of sight at b becomes small (see Jura Jacoby \cite{JuJa76}) )."1041 For smaller offsets 5. however. the decline of the intensity steepens and the slope," For smaller offsets$b$ , however, the decline of the intensity steepens and the slope"1042PAH emission exists around NGC 5529.,PAH emission exists around NGC 5529.1043 The Inset to Fig., The Inset to Fig.1044 6bb shows the same averaged data from the main figure. but over the north-east side of the disk only. to avoid contamination by the small galaxy (likely a background object with το=0.123) on the south-west side.," \ref{slices_fig}b b shows the same averaged data from the main figure, but over the north-east side of the disk only, to avoid contamination by the small galaxy (likely a background object with $z_{ph}\,=\,0.123$ ) on the south-west side."1045" To the 3c limit of the averaged minor axis slice (shown by the short horizontal bar). emission ts seen out to 5x60"" (5x12.8 kpc)."," To the $\sigma$ limit of the averaged minor axis slice (shown by the short horizontal bar), emission is seen out to $z\,\approx\,60^{\prime\prime}$ $z\,\approx\,12.8$ kpc)."1046" After subtracting the modeled Gaussian of the prominent disk emission. the wing emission can be fit with an exponential οὓς, =17.5"" (3.7 kpe)."," After subtracting the modeled Gaussian of the prominent disk emission, the wing emission can be fit with an exponential of $z_e\,\approx\,17.5^{\prime\prime}$ (3.7 kpc)."1047" Miller Veilleux (2003) found an exponential fit of z;,=4.5 kpe for the high latitude wings of the Ha emission. i.e. the scale height of the high latitude Πα emission is =1.2x larger than that of the PAH emission."," Miller Veilleux (2003) found an exponential fit of $z_e\,=\,4.5$ kpc for the high latitude wings of the $\alpha$ emission, i.e. the scale height of the high latitude $\alpha$ emission is $\approx\,1.2\,\times$ larger than that of the PAH emission."1048 Could the extended οἱ6.7 um emission be explained in some other way than a PAH halo?," Could the extended $\lambda\,6.7~\mu$ m emission be explained in some other way than a PAH halo?"1049 As indicated in Sect. 4.1..," As indicated in Sect. \ref{band_contributions},"1050 the global contribution of stellar emission is within the absolute calibration error of the 6.7 gam band emission. if standard extrapolations are reliable.," the global contribution of stellar emission is within the absolute calibration error of the $\lambda\,6.7~\mu$ m band emission, if standard extrapolations are reliable."1051" To further compare the halo stellar emission with that of the ,16.7 jm band. we repeat the same averaging technique to the Ks band image of Fig."," To further compare the halo stellar emission with that of the $\lambda\,6.7~\mu$ m band, we repeat the same averaging technique to the Ks band image of Fig."1052 6. (Inset) and we show the resulting stellar emission profile in Fig., \ref{iso_optical} (Inset) and we show the resulting stellar emission profile in Fig.1053 6bb (Inset. grey curve).," \ref{slices_fig}b b (Inset, grey curve)."1054" No emission above the 3c level of this plot is seen beyond z«20” (short horizontal grey line) in contrast ίος=60"" seen at 26.7 um. Similar results are obtained when the SDSS 1 and z-band images are examined in the same way (slices not shown)."," No emission above the $\sigma$ level of this plot is seen beyond $z\,\approx\,20^{\prime\prime}$ (short horizontal grey line) in contrast to $z\,\approx\,60^{\prime\prime}$ seen at $\lambda\,6.7~\mu$ m. Similar results are obtained when the SDSS i and z-band images are examined in the same way (slices not shown)."1055 Even if we allow the Ks band emission to contribute to the wings at approximately a Io level over the entire wing extent. stellar emissio1 could not account for the 46.7 um halo.," Even if we allow the Ks band emission to contribute to the wings at approximately a $1\sigma$ level over the entire wing extent, stellar emission could not account for the $\lambda\,6.7~\mu$ m halo."1056" However. taking this conservative approach. the maximum extent of the halo then adjusts to z=50"" (z=10.6 kpe)."," However, taking this conservative approach, the maximum extent of the halo then adjusts to $z\,\approx\,50^{\prime\prime}$ $z\,\approx\,10.6$ kpc)."1057 Finally. we note that the PSF is known to be Gaussian to high accuracy (see Galliano 2004 and Irwin Madden 2006) in this ISO band and the extended PAH emission cannot be explained by PSF emission wings.," Finally, we note that the PSF is known to be Gaussian to high accuracy (see Galliano 2004 and Irwin Madden 2006) in this ISO band and the extended PAH emission cannot be explained by PSF emission wings."1058 In summary. a significant halo of PAH emission is seen around NGC 5529 and shows considerable substructure with some features that are vertical or are-like with respect to the disk.," In summary, a significant halo of PAH emission is seen around NGC 5529 and shows considerable substructure with some features that are vertical or arc-like with respect to the disk."1059" The bulk of the emission in the vertical z direction can be fit by a gaussian with dispersion. 7;=3.4"" (726 pe) and. after subtracting this main emission. faint PAH wings are seen with an exponential vertical scale height of z;=17.5"" (3.7 kpe)."," The bulk of the emission in the vertical $z$ direction can be fit by a gaussian with dispersion, $\sigma_G\,=\,3.4^{\prime\prime}$ (726 pc) and, after subtracting this main emission, faint PAH wings are seen with an exponential vertical scale height of $z_e\,=\,17.5^{\prime\prime}$ (3.7 kpc)."1060" To the 3c limit of the data and allowing for a small contribution from stars. emission is seen as far out as z=50"" (10.6 kpe)."," To the $3\sigma$ limit of the data and allowing for a small contribution from stars, emission is seen as far out as $z\,=\,50^{\prime\prime}$ (10.6 kpc)."1061 This is an exceptional distance from the plane. exceeding that of z=6.5 kpe found for NGC 5907 (Irwin Madden 2006).," This is an exceptional distance from the plane, exceeding that of $z\,\approx\,6.5$ kpc found for NGC 5907 (Irwin Madden 2006)."1062 As indicated in Sect. 2..," As indicated in Sect. \ref{ngc5529},"1063 the only previously-observed gaseous halo in NGC 5529 was detected by Miller Veilleux (2003) in He emission. and we have shown in Sect.," the only previously-observed gaseous halo in NGC 5529 was detected by Miller Veilleux (2003) in $\,\alpha$ emission, and we have shown in Sect."1064 4.3. that the vertical distributions in both these bands can be fit with two vertical components. a narrower Gaussian containing most of the emission. and fainter exponential wings that extend much farther.," \ref{halo_emission} that the vertical distributions in both these bands can be fit with two vertical components, a narrower Gaussian containing most of the emission, and fainter exponential wings that extend much farther."1065 The He scale heights are. on average. =1.4 times larger than those of the PAHs when global halo emission ts considered.," The $\alpha$ scale heights are, on average, $\approx\,1.4$ times larger than those of the PAHs when global halo emission is considered."1066 In this section. we wish to investigate a possible spatial correlation between the Ha and PAH band emission.," In this section, we wish to investigate a possible spatial correlation between the $\alpha$ and PAH band emission."1067 This is shown in the two overlays of Fig. 7.., This is shown in the two overlays of Fig. \ref{iso_halpha}.1068 In Fig., In Fig.1069 7aa. the Ha emisstor is shown in greyscale with in-disk emission emphasized in order to discern whether the high-latitude PAH emission may be related to underlying in-disk emission.," \ref{iso_halpha}a a, the $\,\alpha$ emission is shown in greyscale with in-disk emission emphasized in order to discern whether the high-latitude PAH emission may be related to underlying in-disk emission."1070 The comparison is not straight-forward since th(0 observed halo structure results from an integration of emissio> along lines-of-sight that vary with radius. the Ha emission in the disk suffers from extinction. and the spatial resolutions are different.," The comparison is not straight-forward since the observed halo structure results from an integration of emission along lines-of-sight that vary with radius, the $\,\alpha$ emission in the disk suffers from extinction, and the spatial resolutions are different."1071 The are (see Sect. 4.3)), The arc (see Sect. \ref{halo_emission}) )1072 that. in projection. 1s located above the nucleus is possibly related to enhanced SF activity in the nuclear vicinity. but since the extended halo emission Is so pervasive. one-to-one correlations with in-disk activity cannot be pinpointed with certainty from these observations.," that, in projection, is located above the nucleus is possibly related to enhanced SF activity in the nuclear vicinity, but since the extended halo emission is so pervasive, one-to-one correlations with in-disk activity cannot be pinpointed with certainty from these observations."1073 Fig., Fig.1074 7bb shows the « emission in contours. smoothed to the same resolution as the [SO data. over the ISO emission in greyscale.," \ref{iso_halpha}b b shows the $\,\alpha$ emission in contours, smoothed to the same resolution as the ISO data, over the ISO emission in greyscale."1075 With the Ha emission smoothed. the Ha halo ts very conspicuous and the ‘filamentary eDIG' on the northeast side of the galaxy noted by Miller Veilleux (2003) Is now seen with prominent structure that bears a remarkable resemblance to that of the PAH emission.," With the $\,\alpha$ emission smoothed, the $\,\alpha$ halo is very conspicuous and the 'filamentary eDIG' on the northeast side of the galaxy noted by Miller Veilleux (2003) is now seen with prominent structure that bears a remarkable resemblance to that of the PAH emission."1076" The two PAH halo ares are also seen in He as is an above-disk feature located at RA = 14? 15"" 32, DEC = 36° 14 40""."," The two PAH halo arcs are also seen in $\,\alpha$ as is an above-disk feature located at RA $\approx$ $^{\rm h}$ $^{\rm m}$ $^{\rm s}$, DEC $\approx$ $^\circ$ $^\prime$ $^{\prime\prime}$."1077 Similarities on the south-west side of the disk are also apparent., Similarities on the south-west side of the disk are also apparent.1078 Thus. although the vertical scale heights of the Ha emission exceed those of the PAHs (Sect. 4.3)).," Thus, although the vertical scale heights of the $\alpha$ emission exceed those of the PAHs (Sect. \ref{halo_emission}) ),"1079 there appears to be a spatial correlation between the PAH halo structure and that of the e-emitting eDIG in NGC 5529.," there appears to be a spatial correlation between the PAH halo structure and that of the $\,\alpha$ -emitting eDIG in NGC 5529."1080 To properly quantify such a correlation requires a three-dimensional model of the two components and the low S/N of the data in the halo region does not support such an approach., To properly quantify such a correlation requires a three-dimensional model of the two components and the low S/N of the data in the halo region does not support such an approach.1081 However. to “zeroth order’. we have investigated whether the two maps are correlated in the region of the the north-east halo.," However, to `zeroth order', we have investigated whether the two maps are correlated in the region of the the north-east halo."1082 After applying a 2 cutoff to both maps. the resulting halo emission spans a projected area of 0.79 square areminutes.," After applying a $2\,\sigma$ cutoff to both maps, the resulting halo emission spans a projected area of 0.79 square arcminutes."1083 For this region. we computed cross-correlation. coefficients between the two maps. finding a best value of for zero shift in position.," For this region, we computed cross-correlation coefficients between the two maps, finding a best value of for zero shift in position."1084 This confirms that there is à correlation between the PAH and Ha halo emission in NGC 5529., This confirms that there is a correlation between the PAH and $\alpha$ halo emission in NGC 5529.1085 The presence of a large-scale. structured PAH halo about NGC 5529 ts a significant result of these observations.," The presence of a large-scale, structured PAH halo about NGC 5529 is a significant result of these observations."1086 Few statistics exist on the presence of PAHs in galaxy halos., Few statistics exist on the presence of PAHs in galaxy halos.1087 Of normal star forming galaxies or those of low SFR. NGC 5529 and NGC 5907 appear to be the only known examples. thus far (see Table 5)).," Of normal star forming galaxies or those of low SFR, NGC 5529 and NGC 5907 appear to be the only known examples, thus far (see Table \ref{basic_parameters}) )."1088 Tacconi-Garman et al. (, Tacconi-Garman et al. (10892005) have found à 43.3 zm PAH feature in the superwind of the starburst galaxy. NGC 253. with z extent <120 pc. and there is now a clear PAH signature in the halo and superwind of M $82 to a distance of 6 kpe from the plane of that galaxy (Engelbracht et al.,"2005) have found a $\lambda\,3.3~\mu$ m PAH feature in the superwind of the starburst galaxy, NGC 253, with $z$ extent $< 120$ pc, and there is now a clear PAH signature in the halo and superwind of M 82 to a distance of 6 kpc from the plane of that galaxy (Engelbracht et al."1090 2006)., 2006).1091 Its 8 jm emission. which has a strong PAH component. resembles the Ha emission of the superwind in M 82. indicating that PAHs can survive in such," Its 8 $\mu$ m emission, which has a strong PAH component, resembles the $\alpha$ emission of the superwind in M 82, indicating that PAHs can survive in such"1092Fig 9..,Fig \ref{SFH_p2}.1093 shows that P-mode generates potential vorticity with a positive sign., shows that P-mode generates potential vorticity with a positive sign.1094" However, the sign of the generated potential vorticity depends on the initial phase of the P-mode."," However, the sign of the generated potential vorticity depends on the initial phase of the P-mode."1095" Hence, our numerical results show generation of the W-mode with both positive and negative signs."," Hence, our numerical results show generation of the W-mode with both positive and negative signs."1096 It is interesting also to look at the P-mode dynamics in flows stable to baroclinic perturbations (see Fig. 9))., It is interesting also to look at the P-mode dynamics in flows stable to baroclinic perturbations (see Fig. \ref{SFH_p2}) ).1097" The initially imposed P-mode is able to generate the S-mode and consequently the W-mode, that gives a growth of the potential vorticity with time."," The initially imposed P-mode is able to generate the S-mode and consequently the W-mode, that gives a growth of the potential vorticity with time."1098" Apart from the intrinsic limitations (the dependence of the sign of the generated potential vorticity on the initial phase of the P-mode and the low efficiency of the W-mode generation), this process demonstrates the fact that potential vorticity can be actually generated in flows with positive radial buoyancy (7<0) and Richardson number."," Apart from the intrinsic limitations (the dependence of the sign of the generated potential vorticity on the initial phase of the P-mode and the low efficiency of the W-mode generation), this process demonstrates the fact that potential vorticity can be actually generated in flows with positive radial buoyancy $\eta<0$ ) and Richardson number."1099 Fig., Fig.1100 10 shows the dependence of the S and W-mode generation on the pressure and entropy stratification scales., \ref{surf_p} shows the dependence of the S and W-mode generation on the pressure and entropy stratification scales.1101" In good agreement with qualitative estimates, the S-mode excitation depends strongly on the entropy stratification scale ks, while the generation of the potential vorticity generally grows with η."," In good agreement with qualitative estimates, the S-mode excitation depends strongly on the entropy stratification scale $k_S$, while the generation of the potential vorticity generally grows with $\eta$."1102" We have studied the dynamics of linear perturbations in a 2D, radially stratified, compressible, differentially rotating flow with different radial density, pressure and entropy gradients."," We have studied the dynamics of linear perturbations in a 2D, radially stratified, compressible, differentially rotating flow with different radial density, pressure and entropy gradients."1103 We employed global radial scaling of linear perturbations and removed the algebraic modulation due to the background stratification., We employed global radial scaling of linear perturbations and removed the algebraic modulation due to the background stratification.1104 We derived a local dispersion equation for nonaxisymmetric perturbations and the corresponding eigenfunctions in the zero shear limit., We derived a local dispersion equation for nonaxisymmetric perturbations and the corresponding eigenfunctions in the zero shear limit.1105 We show that the local stability of baroclinic perturbations in the barotropic equilibrium state is defined by the Schwarzschild-Ledoux criterion., We show that the local stability of baroclinic perturbations in the barotropic equilibrium state is defined by the Schwarzschild-Ledoux criterion.1106 We study the shear flow induced linear coupling and the related possibility of the energy transfer between the different modes of perturbations using qualitative and a more detailed numerical analysis., We study the shear flow induced linear coupling and the related possibility of the energy transfer between the different modes of perturbations using qualitative and a more detailed numerical analysis.1107 We employ a three-mode formalism and describe the behavior of S W and P-modes under the action of the baroclinic and velocity shear forces in local approximation., We employ a three-mode formalism and describe the behavior of S W and P-modes under the action of the baroclinic and velocity shear forces in local approximation.1108 We find that the system exhibits an asymmetric coupling pattern with five energy exchange channels between three different, We find that the system exhibits an asymmetric coupling pattern with five energy exchange channels between three different11094765-f01-1504 (Carrascoetal.2006).,4765-f01-1504 \citep{camein2006}.1110. This source has negligible emission above 2 keV. We describe the multi-wavelength observations of the source and the data reduction in Section 2.., This source has negligible emission above 2 keV. We describe the multi-wavelength observations of the source and the data reduction in Section \ref{sec:reduction}.1111" In Section 3,, we first give the multi-wavelength detections of the source, followed by presentations of its detailed X-ray spectral and timing properties."," In Section \ref{sec:results}, we first give the multi-wavelength detections of the source, followed by presentations of its detailed X-ray spectral and timing properties."1112 We discuss its possible nature in Section 4 and draw our conclusions in Section 5.., We discuss its possible nature in Section \ref{sec:discussion} and draw our conclusions in Section \ref{sec:conclusion}. .1113" was observed twice by ((Table 1)), on 2006 September 7 and 2007 April 16."," was observed twice by (Table \ref{tbl:obslog}) ), on 2006 September 7 and 2007 April 16."1114" These two observations of this source will be referred to hereafter as XMM1 and XMM2, respectively."," These two observations of this source will be referred to hereafter as XMM1 and XMM2, respectively."1115" The source was detected in all the three European Photon Imaging Cameras in the imaging mode, i.e., pn, MOSI, and MOS2 (Jansenetal.2001;StriiderTurneretal. 2001),, in both observations."," The source was detected in all the three European Photon Imaging Cameras in the imaging mode, i.e., pn, MOS1, and MOS2 \citep{jalual2001,stbrde2001,tuabar2001}, in both observations."1116" The source was also detected by the Optical Monitor (OM;Masonetal.2001) in XMM1, but it was not in the FOV of the OM in XMM2."," The source was also detected by the Optical Monitor \citep[OM;][]{mabrmu2001} in XMM1, but it was not in the FOV of the OM in XMM2."1117" In XMM1, the two UV filters UVW1 and UVM2 were used, and we obtained the source detection information directly from the pipeline products."," In XMM1, the two UV filters UVW1 and UVM2 were used, and we obtained the source detection information directly from the pipeline products."1118 We used SAS 10.0.0 and the calibration files of 2010 November for reprocessing the X-ray event files and follow-up analysis., We used SAS 10.0.0 and the calibration files of 2010 November for reprocessing the X-ray event files and follow-up analysis.1119" The data in strong background flare intervals, mostly at the end of the XMM2 observation in the pn camera, are excluded following the SAS thread for the filtering against high backgrounds."," The data in strong background flare intervals, mostly at the end of the XMM2 observation in the pn camera, are excluded following the SAS thread for the filtering against high backgrounds."1120 The final exposures used are given in Table 1.., The final exposures used are given in Table \ref{tbl:obslog}.1121" We extracted the source spectra of the pn, MOS1, and MOS2 cameras from a circular region centered on the source using 15” and 35"" radii for XMM1 and ΧΜΜΡ, respectively."," We extracted the source spectra of the pn, MOS1, and MOS2 cameras from a circular region centered on the source using $''$ and $''$ radii for XMM1 and XMM2, respectively."1122 A smaller radius was used for XMM1 because the source was fainter and near the CCD gap., A smaller radius was used for XMM1 because the source was fainter and near the CCD gap.1123" The background spectrum was extracted from a large circular region with a radius of 100"" near the source in each camera.", The background spectrum was extracted from a large circular region with a radius of $''$ near the source in each camera.1124 The event selection criteria followed the default values in the pipeline (see Table 5 in Watsonetal. (2009)))., The event selection criteria followed the default values in the pipeline (see Table 5 in \citet{wascfy2009}) ).1125 We rebinned the spectra to have at least 20 counts in each bin so as to adopt the x? statistic for the spectral fits., We rebinned the spectra to have at least 20 counts in each bin so as to adopt the $\chi^2$ statistic for the spectral fits.1126" We also extracted light curves from the pn camera, which has a larger effective area and a higher timing resolution than the MOS cameras, using the same apertures as those for spectral extraction."," We also extracted light curves from the pn camera, which has a larger effective area and a higher timing resolution than the MOS cameras, using the same apertures as those for spectral extraction."1127" We first extracted background-subtracted light curves with a bin size of 250 s, using the SAS taskepiclccorr to apply relative corrections."," We first extracted background-subtracted light curves with a bin size of 250 s, using the SAS task to apply relative corrections."1128" To create the power density spectra (PDS), we also extracted light curves from the source region using the frame time as the bin size, which is 199.1 ms for XMM1 the extended-full-frame mode) and 73.4 ms for (usingXMM2 (using the full-frame mode)."," To create the power density spectra (PDS), we also extracted light curves from the source region using the frame time as the bin size, which is 199.1 ms for XMM1 (using the extended-full-frame mode) and 73.4 ms for XMM2 (using the full-frame mode)."1129" Considering that the source is very soft and the background dominates above 2 keV, all light curves were extracted in the energy range 0.2-2.0 keV. We calculated the PDS using a similar procedure as, e.g., Goadetal. (2006)."," Considering that the source is very soft and the background dominates above 2 keV, all light curves were extracted in the energy range 0.2–2.0 keV. We calculated the PDS using a similar procedure as, e.g., \citet{gorore2006}."1130". The XMM1 199.1 ms and XMM2 73.4 ms pn light curves were split into segments each with 32768 and 65536 data bins, respectively, resulting in four segments for XMMI and five for XMM2."," The XMM1 199.1 ms and XMM2 73.4 ms pn light curves were split into segments each with 32768 and 65536 data bins, respectively, resulting in four segments for XMM1 and five for XMM2."1131" The PDS was calculated for each segment, and all PDS for each light curve were merged and averaged by binning in frequency using a logarithmic factor of 1.1, under the condition that each bin contains at least 20 individual PDS measurements."," The PDS was calculated for each segment, and all PDS for each light curve were merged and averaged by binning in frequency using a logarithmic factor of 1.1, under the condition that each bin contains at least 20 individual PDS measurements."1132 The errors were calculated from the sample standard deviation of PDS measurements in each bin., The errors were calculated from the sample standard deviation of PDS measurements in each bin.1133" Our source was not detected in theROSAT All-Sky Survey in 1990, which had a detection limit of 0.1—2.4 keV flux 5x10-P? erg s! cm? (Vogesetal.1999)."," Our source was not detected in the All-Sky Survey in 1990, which had a detection limit of 0.1–2.4 keV flux $\times$ $^{-13}$ erg $^{-1}$ $^{-2}$ \citep{voasbo1999}."1134". Our source was in the FOV of oneROSAT PSPC pointed observation (the sequence number 800256, 1992 October, ~11 ks), at an off-axis angle of ~2.6’."," Our source was in the FOV of one PSPC pointed observation (the sequence number 800256, 1992 October, $\sim$ 11 ks), at an off-axis angle of $\sim$ $'$."1135 It was not detected either and was (thus) not listed in the WGA catalog of the ROSAT point sources (Whiteetal.1994)., It was not detected either and was (thus) not listed in the WGA catalog of the point sources \citep{whgian1994}.1136 We calculated the confidence interval of the source detection using Bayesian statistics as described in Kraftetal.(1991)., We calculated the confidence interval of the source detection using Bayesian statistics as described in \citet{krbuno1991}.1137". Circular source and background regions with radii of 40"" and 2' respectively were used.", Circular source and background regions with radii of $\arcsec$ and $\arcmin$ respectively were used.1138 The corresponding (ancillary plus photon redistribution) response matrix was generated and used to convert the count rates to the fluxes., The corresponding (ancillary plus photon redistribution) response matrix was generated and used to convert the count rates to the fluxes.1139" At our request, theSwift Gamma Ray Burst Explorer mission (Gehrelsetal.2004) observed the field of on 2011 February 23 for a total of 5 ks (observation ID 00031930001)."," At our request, the Gamma Ray Burst Explorer mission \citep{gechgi2004} observed the field of on 2011 February 23 for a total of 5 ks (observation ID 00031930001)."1140 The X-ray telescope Burrowsetal. was operated in Photon (XRT;Counting mode (Hill2005)etal.2004)., The X-ray telescope \citep[XRT;][]{buhino2005} was operated in Photon Counting mode \citep{hibuno2004}.1141. X-ray data were reduced with the taskzrtpipeline version 0.12.1., X-ray data were reduced with the task version 0.12.1.1142" We found an enhanced count rate at the position of our source, but it is very weak."," We found an enhanced count rate at the position of our source, but it is very weak."1143 We also calculated the confidence interval of the detection., We also calculated the confidence interval of the detection.1144" Radii of 23/55 and 235"" were used for the circular source and background regions, respectively."," Radii of 5 and $\arcsec$ were used for the circular source and background regions, respectively."1145 The corresponding response matrix was generated using the calibration files of 2011 February., The corresponding response matrix was generated using the calibration files of 2011 February.1146 The UV-Optical Telescope (UVOT;Romingetal.2005) was operated using the UVW1 filter for 5 ks., The UV-Optical Telescope \citep[UVOT;][]{rokema2005} was operated using the UVW1 filter for 5 ks.1147 The magnitude and flux were measured with the task version 3 based on the most recent UVOT calibration as described in Pooleetal.(2008) and Breeveldetal.(2010)., The magnitude and flux were measured with the task version 3 based on the most recent UVOT calibration as described in \citet{pobrpa2008} and \citet{becuho2010}.1148". Circular source and background regions with radii of 5"" and 20"", respectively, were used."," Circular source and background regions with radii of $\arcsec$ and $\arcsec$, respectively, were used."1149 Our source is in the direction of the center of the galaxy IC 4765-f01-1504 (Carrascoetal., Our source is in the direction of the center of the galaxy IC 4765-f01-1504 \citep{camein2006}.1150" This galaxy is located in the background of the rich2006).. group of galaxies IC 4765 (also known as Abell S0805, z=0.01497)."," This galaxy is located in the background of the rich group of galaxies IC 4765 (also known as Abell S0805, $z$ =0.01497)."1151 It was imaged with the 1.3 m Warsaw telescope at Las Campanas Observatory in Chile through the standard Johnson V and Cousins I filters in 1998., It was imaged with the 1.3 m Warsaw telescope at Las Campanas Observatory in Chile through the standard Johnson V and Cousins I filters in 1998.1152 We used the V- and I-filter images from Carrascoetal.(2006) to derive the main photometric parameters of the galaxy with a Sérrsic model in GALFIT (Pengetal.2010)., We used the V- and I-filter images from \citet{camein2006} to derive the main photometric parameters of the galaxy with a Sérrsic model in GALFIT \citep{pehoim2010}.1153. The images have a FWHM of the PSF of about 122., The images have a FWHM of the PSF of about 2.1154" Carrascoetal.(2006) also obtained an optical spectrum of the galaxy on 1999 June 19 with the Wide Field CCD camera mounted on the 2.5 m Du Pont Telescope at the Las Campanas Observatory in Chile, but it has poor quality."," \citet{camein2006} also obtained an optical spectrum of the galaxy on 1999 June 19 with the Wide Field CCD camera mounted on the 2.5 m Du Pont Telescope at the Las Campanas Observatory in Chile, but it has poor quality."1155" Weobtained a new longslit spectrum of this galaxy with theGemini Multi-Object Spectrograph (GMOS,Hooketal.2004) at the Gemini South Telescope in the queue mode."," Weobtained a new longslit spectrum of this galaxy with theGemini Multi-Object Spectrograph \citep[GMOS,][]{hojoal2004} at the Gemini South Telescope in the queue mode."1156 The observation was made on the night of 2011 March 19 (UT) during bright, The observation was made on the night of 2011 March 19 (UT) during bright1157sullicienthy short time scale to have an appreciable inlluence on the cillusion of the highest energy cosmic rays.,sufficiently short time scale to have an appreciable influence on the diffusion of the highest energy cosmic rays.1158 From the expression for the growth rate given in equation (35)). it can be seen that the filamentation instability operates most ellectively in strongly. amplified small scale turbulence. anc when the cosmic-rays driving the instability have lower minimum energv.," From the expression for the growth rate given in equation \ref{filgrowth}) ), it can be seen that the filamentation instability operates most effectively in strongly amplified small scale turbulence, and when the cosmic-rays driving the instability have lower minimum energy."1159 However. if the energy. of the cosmic-rayvs driving the filamentation instability is too small. the particles will be trapped.," However, if the energy of the cosmic-rays driving the filamentation instability is too small, the particles will be trapped."1160 This condition. as derived in section 20 is peὃνομις.," This condition, as derived in section \ref{anal_sect}1161 is $pc\gg eA_\|u_{\rm sh}$."1162 Using the fiducial values from Bell(2004) (Equation (21)) 2. JU. the filunentation operates provided qochusip ( )(," Using the fiducial values from \citet{bell04} (Equation (21)) $k_{\rm max}^{-1}\approx2\times 10^{13} {\rm m}$ , the filamentation operates provided e ( )."1163260) TeV s-ray za)!observations of most historical supernova remnants provide conclusive evidence for the presence of cosmic ravs. either protons or electrons. that satisfy this condition.," TeV $\gamma$ -ray observations of most historical supernova remnants provide conclusive evidence for the presence of cosmic rays, either protons or electrons, that satisfy this condition."1164 To investigate which mechanism determines the transport properties of the highest energy cosmic rays in the precursor. we compare the erowth rate of the filamentation instability to that of the streaming instability given in (2004).. which has a growth rate.," To investigate which mechanism determines the transport properties of the highest energy cosmic rays in the precursor, we compare the growth rate of the filamentation instability to that of the streaming instability given in \citet{bell04}, which has a growth rate,."11653T) This enexpression is equivalent to equation. (26)) on replacing Dor by Ay (cL.Bell2005)., This expression is equivalent to equation \ref{nrgrowth}) ) on replacing $B_{\theta}/r$ by $kB_0$ \citep[cf.][]{bell05}.1166". Por &+ ion-cvclotron resonance takes over and the growth rate <r,steepens xb.", For $k<r_{\rm g}^{-1}$ ion-cyclotron resonance takes over and the growth rate steepens $\propto k$.1167 Hence the growth rate Puy can be considered an upper imit for all &., Hence the growth rate $\Gamma_{\rm nr}$ can be considered an upper limit for all $k$.1168 Since the magnetic field amplified by the non-resonant instability is on too small a scale to cllectively scatter the lighest cnergy cosmic ravs driving the growth. i.e. those with £XLinas. these particles will continue to gvrate about he mean Geld Bo.," Since the magnetic field amplified by the non-resonant instability is on too small a scale to effectively scatter the highest energy cosmic rays driving the growth, i.e. those with $E\lesssim E_{\rm max}$, these particles will continue to gyrate about the mean field $B_0$."1169 On the scale of the evroraclius of these xuticles &2ουEus. the ratio of the growth rate of the ilamentation instability. equation (35)). to the non-resonant instability is where £j; is the corresponding energy dominating the cosmic-ray current.," On the scale of the gyroradius of these particles $k=eB_0c/E_{\rm max}$, the ratio of the growth rate of the filamentation instability, equation \ref{filgrowth}) ), to the non-resonant instability is, where $E_{\rm min}$ is the corresponding energy dominating the cosmic-ray current."1170 We note here that the small scale fields are amplified over a distance much less than the scale-height of the precursor at the outer extremity of the precursor zBIS) πο. suggesting that Linas/Iii should not greatly exceed. unity.," We note here that the small scale fields are amplified over a distance much less than the scale-height of the precursor at the outer extremity of the precursor $\approx \kappa(E_{\rm max})/u_{\rm sh}$ , suggesting that ${E_{\rm max}}/{E_{\rm min}}$ should not greatly exceed unity."1171 Thus. provided the small scale fields can be driven to non-linear values. the filamentation instability will play the dominant role in generating the fields. recquirect to scatter. the highest energy. cosmic ravs in supernova remnants.," Thus, provided the small scale fields can be driven to non-linear values, the filamentation instability will play the dominant role in generating the fields required to scatter the highest energy cosmic rays in supernova remnants."1172 The two growth rates are equal when where ry=fininfeBoe., The two growth rates are equal when where $r_g=E_{\rm min}/eB_0c$.1173 This indicates. to order of magnitude. the length scale above which the filamentation dominates over the non-resonant mode.," This indicates, to order of magnitude, the length scale above which the filamentation dominates over the non-resonant mode."1174 Substitution of the parameters used in the simulations suggests the transition occurs at &L/25x10. in agreement with what was found.," Substitution of the parameters used in the simulations suggests the transition occurs at $kL/2\pi\sim 10$, in agreement with what was found."1175 In acidition. comparing the terms in equation (27)). it is readily seen that (40)) corresponds to the scale on which the first term becomes comparable with the other terms.," In addition, comparing the terms in equation \ref{MHDj}) ), it is readily seen that \ref{rcond}) ) corresponds to the scale on which the first term becomes comparable with the other terms."1176 To demonstrate. the important role. plavec by the lilaumentation instability. we calculate the growth rate using typical parameters for voung supernova remnants.," To demonstrate the important role played by the filamentation instability, we calculate the growth rate using typical parameters for young supernova remnants."1177 Assuming the magnetic field is amplified initially on small length scales to a level comparable with those inferred from observations. the typical time-scale for growth of magnetic field on long wavelengths by the filamentation instability can be as short D[(—mDES )us(4l)bhe value of μμ driving (Ge)!the erowth is the largest. uncertainty.," Assuming the magnetic field is amplified initially on small length scales to a level comparable with those inferred from observations, the typical time-scale for growth of magnetic field on long wavelengths by the filamentation instability can be as short as ) The value of $E_{\rm min}$ driving the growth is the largest uncertainty."1178 At the onset of the filamentation. provided the lower energy. cosmic rays salisfv the condition. (36)). the growth can be extremely rapid.," At the onset of the filamentation, provided the lower energy cosmic rays satisfy the condition \ref{Econd}) ), the growth can be extremely rapid."1179 As the magnetic fields. evolve. the scale. of. the filaments becomes comparable to the evroracdius of the lower energy. particles. such that fin should remain large.," As the magnetic fields evolve, the scale of the filaments becomes comparable to the gyroradius of the lower energy particles, such that $E_{\rm min}$ should remain large."1180 Saturation mav occur when the high energy particles become trapped on the self-ecneratecl large scale. fields., Saturation may occur when the high energy particles become trapped on the self-generated large scale fields.1181 This will almost certainly allect the diffusion of cosmic rays and may even alter the transport. properties of particles at clilferent energies. which can inlluence the shape of the spectrum (Ixirkctal.1996).," This will almost certainly affect the diffusion of cosmic rays and may even alter the transport properties of particles at different energies, which can influence the shape of the spectrum \citep{kirketal96}."1182.. Future simulations in three dimensions will help to elucidate this process further., Future simulations in three dimensions will help to elucidate this process further.1183 While the lamentation of photon or high energy. electron beams in laboratory laser plasma experiments is a well studied phenomenon (e.g.Craxton&AleCrory1984)... its analogv with cosmic ravs has been largely overlooked.," While the filamentation of photon or high energy electron beams in laboratory laser plasma experiments is a well studied phenomenon \cite[e.g.][]{craxtonmccrory84}, its analogy with cosmic rays has been largely overlooked."1184 1n this paper. it has been demonstrated: both analytically and. confirmed. with numerical simulations. that the Gilamentation of cosmic rays is an important process that can occur in the precursors of supernova remnants shocks where dilfusive shock acceleration is taking place.," In this paper, it has been demonstrated both analytically and confirmed with numerical simulations, that the filamentation of cosmic rays is an important process that can occur in the precursors of supernova remnants shocks where diffusive shock acceleration is taking place."1185 In widition. we have identified. a mechanism for amplifving magnetic field. on large length scales as a result of the filamentation.," In addition, we have identified a mechanism for amplifying magnetic field on large length scales as a result of the filamentation."1186 The process provides a natural mechanism to couple the rapid growth of magnetic field on small scales. as driven bv the non-resonant instability (Bell 2004).. to length. scales comparable to. or larger than. the evroradius of the particles driving this instability. avoiding the need for an inverse-cascade.," The process provides a natural mechanism to couple the rapid growth of magnetic field on small scales, as driven by the non-resonant instability \citep{bell04}, to length scales comparable to, or larger than, the gyroradius of the particles driving this instability, avoiding the need for an inverse-cascade."1187 The erowth-time for this instability can operate on time scales as short as a fewvears. provided the small scale fields are aniplifiecd to a sullicient level.," The growth-time for this instability can operate on time scales as short as a fewyears, provided the small scale fields are amplified to a sufficient level."1188 Phe reason for the short growth time as compared with previous calculations of linear. cüspersion relations. is that the instability develops in non-linear small," The reason for the short growth time as compared with previous calculations of linear dispersion relations, is that the instability develops in non-linear small"1189an interesting possibility is that the kinematic perturbation has been triggered by interaction with the radio structures.,an interesting possibility is that the kinematic perturbation has been triggered by interaction with the radio structures.1190 In this interpretation the observed. kinematies reflect material being driven out by the jet., In this interpretation the observed kinematics reflect material being driven out by the jet.1191 Phe impact of such an outllow on the surrounding. medium. stirs. up the gas. presumably by the vortices trailing the jet. shock-front. leading to large (random) gas motions.," The impact of such an outflow on the surrounding medium stirs up the gas, presumably by the vortices trailing the jet shock-front, leading to large (random) gas motions."1192 A caveat here is that the observed. kinematies could. also be attributed to eas falling into the nucleus (possibly as the result. of the interact:ion with the companion galaxy)., A caveat here is that the observed kinematics could also be attributed to gas falling into the nucleus (possibly as the result of the interaction with the companion galaxy).1193 However. in that scenari. rit is dillicult to explain the high velocity dispersion of the gas.," However, in that scenario it is difficult to explain the high velocity dispersion of the gas."1194that [or e»=0. this system has a comparison principle.,"that for $c_2=0$, this system has a comparison principle."1195" More precisely. if p=t and p="" are two solutions of svstem (2.14)) with e»=0 such that holes at time /=0. then this is true for all time />0."," More precisely, if $\rho^{\pm,1}$ and $\rho^{\pm,2}$ are two solutions of system \ref{eq::7}) ) with $c_2=0$ such that holds at time $t=0$, then this is true for all time $t>0$."1196 Aloreover for svstem (2.14)). it is possible to write an upwind scheme and (o prove a Crandall-Lions tvpe discrete-continuous error estimate for (his scheme. as it is done in ΕΙ Hajj. Forcadel 10].," Moreover for system \ref{eq::7}) ), it is possible to write an upwind scheme and to prove a Crandall-Lions type discrete-continuous error estimate for this scheme, as it is done in El Hajj, Forcadel \cite{EF}."1197 Let us mention that an existence ancl uniqueness result [or svstem (2.14)) has also been obtained by El Hajj [0| in the framework of ΠΑΕ} initial data with solutions in Hj(RR.x[0.2x).," Let us mention that an existence and uniqueness result for system \ref{eq::7}) ) has also been obtained by El Hajj \cite{E} in the framework of $H^1_{loc}(\R)$ initial data with solutions in $H^1_{loc}(\R\times [0,+\infty))$."1198 This svstem has also been studied in the case of periodic external applied stress., This system has also been studied in the case of periodic external applied stress.1199 In the svstem (2.14)). this corresponds (ο add a (me-periodic term to the «quantity (p—p).," In the system \ref{eq::7}) ), this corresponds to add a time-periodic term to the quantity $(\rho^+-\rho^-)$."1200 Then lor this non-local svstem. it is shown formally in Briani. Cardaliaguet. Monneau [1] (see also Souganidis. Monneau |0|. for a local 8vstem in the stationary ergodic setting) that the long time behaviour of the svstem is an equivalent quasilinear diffusion equation.," Then for this non-local system, it is shown formally in Briani, Cardaliaguet, Monneau \cite{BCM} (see also Souganidis, Monneau \cite{SM} for a local system in the stationary ergodic setting) that the long time behaviour of the system is an equivalent quasilinear diffusion equation."

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